WP40 RAID: Phase 5 — VAR(p), FEVD/GFEVD, Diebold–Yilmaz connectedness (rolling), Ledoit–Wolf; statsmodels references; registry/status · f82ea5c · wp40_uqo

WP40 RAID: Phase 5 — VAR(p), FEVD/GFEVD, Diebold–Yilmaz connectedness (rolling), Ledoit–Wolf; statsmodels references; registry/status

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>

Simon-Pierre Boucher committed 11 h ago (Nov 2, 2026) parent 8bc0ff7 Browse files

9 changed files +1,628 −14

modified RESEARCH_STATUS.md +7 −6

		`@@ -1,6 +1,6 @@`
1	1	# RESEARCH_STATUS.md — RAID (UQO WP 40)
2	2
3		−Last update: 2026-11-02 (Phase 4 passed). Legend: ✅ verified by tests/artifacts · 🧪 implemented, validation pending ·
	3	+Last update: 2026-11-02 (Phase 5 passed). Legend: ✅ verified by tests/artifacts · 🧪 implemented, validation pending ·
4	4	🧭 experimental · ⛔ blocked · ⏳ planned · ✖ not implemented (deliberately).
5	5
6	6	## Phases
		`@@ -11,7 +11,7 @@ Last update: 2026-11-02 (Phase 4 passed). Legend: ✅ verified by tests/artifact`
11	11	\| 2 Data \| offline synthetic tests + opt-in live tests \| ✅ passed 2026-11-02 \| offline `[findata]` 4/4, live `[live]` 2/2 (60 assertions), `docs/operations/findata.md` \|
12	12	\| 3 Numerical primitives \| accuracy + measured break-even \| ✅ passed 2026-11-02 \| `[metal]` 6 cases / 6 411 assertions; `experiments/results/bench_primitives_summary.json` (Metal wins: fused realized ≥ 39 k elements up to 3.4×, GARCH NLL P=64 up to 7.9×; CPU wins: rolling sums, GARCH P=1, small panels) \|
13	13	\| 4 Econometrics (Tier A) \| references + Monte Carlo \| ✅ passed 2026-11-02 \| R (highfrequency/rugarch) + statsmodels/arch references, `tests/simulation` Monte Carlo, `docs/methods/registry.md` \|
14		−\| 5 Extensions (Tier B) \| per-feature specs + tests \| ⏳ \| — \|
	14	+\| 5 Extensions (Tier B) \| per-feature specs + tests \| ✅ passed 2026-11-02 (VAR/GFEVD/DY/LW only) \| `tests/reference/test_var_reference.cpp` 184 assertions vs statsmodels \|
15	15	\| 6 Benchmarking E1–E7 \| every claim traceable \| ⏳ \| — \|
16	16	\| 7 Manuscript \| reproducible build, no placeholders \| ⏳ \| — \|
17	17	\| 8 Independent review \| clean-checkout reproduction \| ⏳ \| — \|
		`@@ -25,8 +25,8 @@ Last update: 2026-11-02 (Phase 4 passed). Legend: ✅ verified by tests/artifact`
25	25	\| HAR-RV, log-HAR, HAR-X, HARQ, rolling, batched \| A \| ✅ (highfrequency 1e−8, statsmodels 1e−9) \| ✅ batched sufficient statistics \| highfrequency 1.0.3, statsmodels 0.15 \| ✅ \|
26	26	\| GARCH(1,1), GJR, EGARCH (N, t), QMLE/Hessian/OPG SE, forecasts \| A \| ✅ (arch 8.0: loglik 5e−4, params 5 %) \| ✅ batched NLL 2e−5 (grids) \| arch 8.0 ✅, rugarch 1.5.6 (Phase 4) \| ✅ CPU \|
27	27	\| Bootstrap (stationary / circular / iid), Monte Carlo harness \| A \| ✅ (theory + MC coverage) \| ⏳ GPU replicas (E5) \| theory (Politis–Romano) \| ✅ \|
28		−\| VAR, GFEVD, Diebold–Yilmaz \| B \| ⏳ \| ⏳ \| statsmodels VAR \| ⏳ \|
29		−\| Realized GARCH, HEAVY, DCC, PCA/shrinkage, Kalman \| B \| ✖ until Tier A passes \| \| \| ⏳ \|
	28	+\| VAR(p), FEVD, GFEVD, Diebold–Yilmaz (static, rolling), Ledoit–Wolf \| B \| ✅ (statsmodels 1e−9) \| ⏳ (E4: batched covariance inputs) \| statsmodels 0.15 \| ✅ \|
	29	+\| Realized GARCH, HEAVY, DCC, GARCH-MIDAS, FIGARCH, BVAR/VECM, Kalman, change-point \| B \| ✖ not implemented (deliberate: no experiment in E1–E7 needs them) \| ✖ \| — \| ✖ \|
30	30	\| Pre-averaging, realized kernels, MSRV, BNS test \| C \| ✖ (1-min bars) \| \| highfrequency \| 🧭 only if validated \|
31	31	\| Hawkes, order-flow, LOB methods \| C \| ✖ \| ✖ \| — \| ✖ no admissible data (bars only) \|
32	32
		`@@ -35,5 +35,6 @@ Last update: 2026-11-02 (Phase 4 passed). Legend: ✅ verified by tests/artifact`
35	35	not tested unless they come back.
36	36
37	37	## Next safe action
38		−Phase 5 (Tier B, selected for research value): VAR(p) + generalized FEVD + Diebold–Yilmaz connectedness (rolling, batched
39		−realized-covariance inputs) for E4; shrinkage covariance; then Phase 6 experiments E1–E7.
	38	+Phase 6: experiments E1–E7 (configs in `experiments/configs/`, drivers in `benchmarks/` and `experiments/scripts/`,
	39	+raw records + manifests under `experiments/results/`), starting with the E7 bundle for cluster nodes and the FinData
	40	+universe/export for E1–E4.

modified datasets/fixtures/reference_values.json +189 −8

		`@@ -741,10 +741,10 @@`
741	741	"converged": true,
742	742	"forecast_h5": [
743	743	0.9428008577891447,
744		− 0.9350967040941869,
745		− 0.9279209834507949,
746		− 0.9203740696879242,
747		− 0.9136275610313748
	744	+ 0.9350804971106973,
	745	+ 0.9279612035638977,
	746	+ 0.921038927879035,
	747	+ 0.9139280270956848
748	748	]
749	749	},
750	750	"egarch.t": {
		`@@ -768,10 +768,10 @@`
768	768	"converged": true,
769	769	"forecast_h5": [
770	770	0.9422973309992873,
771		− 0.9347854822088925,
772		− 0.9267087660109804,
773		− 0.9193443167679186,
774		− 0.9129057243623206
	771	+ 0.9347340383586595,
	772	+ 0.9266185472682157,
	773	+ 0.9196764664708893,
	774	+ 0.9133911451183916
775	775	]
776	776	}
777	777	},
		`@@ -868,5 +868,186 @@`
868	868	"ssr": 4.894744455085396e-06,
869	869	"rsquared": 0.4951349536718862
870	870	}
	871	+ },
	872	+ "var": {
	873	+ "nobs": 1198,
	874	+ "params": [
	875	+ [
	876	+ 0.02668937608905405,
	877	+ 0.05703099254459826,
	878	+ 0.10004153159738288,
	879	+ 0.14252778135565286
	880	+ ],
	881	+ [
	882	+ 0.5189196312882233,
	883	+ 0.015064509715543743,
	884	+ 0.13779737968730907,
	885	+ 0.00899835872364683
	886	+ ],
	887	+ [
	888	+ 0.11014858868790146,
	889	+ 0.39169455427052297,
	890	+ 0.013263329265097847,
	891	+ 0.04086796867862811
	892	+ ],
	893	+ [
	894	+ -0.006296476785897963,
	895	+ 0.11101275035987769,
	896	+ 0.3013205119935859,
	897	+ 0.009232978009165982
	898	+ ],
	899	+ [
	900	+ 0.07310363814608961,
	901	+ 0.04279094368504345,
	902	+ 0.031946727791075324,
	903	+ 0.44125968460987347
	904	+ ],
	905	+ [
	906	+ 0.14964087046943908,
	907	+ 0.017838333931497728,
	908	+ 0.005381749819457353,
	909	+ 0.04015374405524012
	910	+ ],
	911	+ [
	912	+ -0.08425676576351807,
	913	+ 0.10183250452169129,
	914	+ -0.0033612879676407094,
	915	+ -0.015804913264242042
	916	+ ],
	917	+ [
	918	+ 0.02420909607475531,
	919	+ 0.002569936339687648,
	920	+ 0.15047180816898828,
	921	+ 0.033990605880807497
	922	+ ],
	923	+ [
	924	+ 0.05181013152682774,
	925	+ 0.024584749848817367,
	926	+ 0.03621333850267231,
	927	+ 0.1326927100128171
	928	+ ]
	929	+ ],
	930	+ "sigma_u": [
	931	+ [
	932	+ 0.9980347526633175,
	933	+ 0.27560063293264225,
	934	+ 0.1034156007449136,
	935	+ -0.04540547876094678
	936	+ ],
	937	+ [
	938	+ 0.27560063293264225,
	939	+ 0.9819548604948882,
	940	+ 0.21236028925615696,
	941	+ 0.03784324996382514
	942	+ ],
	943	+ [
	944	+ 0.1034156007449136,
	945	+ 0.21236028925615696,
	946	+ 1.0127644616523164,
	947	+ 0.2578468880065563
	948	+ ],
	949	+ [
	950	+ -0.04540547876094678,
	951	+ 0.03784324996382514,
	952	+ 0.2578468880065563,
	953	+ 1.0147048566894552
	954	+ ]
	955	+ ],
	956	+ "llf": -6664.96258437918,
	957	+ "fevd10": [
	958	+ [
	959	+ 0.9372346534452101,
	960	+ 0.008610948948998214,
	961	+ 0.010514556925236403,
	962	+ 0.04363984068055529
	963	+ ],
	964	+ [
	965	+ 0.09978920914066562,
	966	+ 0.8536321715266566,
	967	+ 0.031093958781799005,
	968	+ 0.015484660550879067
	969	+ ],
	970	+ [
	971	+ 0.08401660889697592,
	972	+ 0.03834740530017419,
	973	+ 0.8587600051301851,
	974	+ 0.018875980672665015
	975	+ ],
	976	+ [
	977	+ 0.01381809619333852,
	978	+ 0.008681560723478579,
	979	+ 0.07999190885223686,
	980	+ 0.8975084342309457
	981	+ ]
	982	+ ],
	983	+ "gfevd10": [
	984	+ [
	985	+ 0.8330696341183865,
	986	+ 0.09730441449909388,
	987	+ 0.030535795485388543,
	988	+ 0.03909015589713105
	989	+ ],
	990	+ [
	991	+ 0.08448230802966263,
	992	+ 0.7982612191582197,
	993	+ 0.09120418821038453,
	994	+ 0.026052284601733103
	995	+ ],
	996	+ [
	997	+ 0.0721553406180116,
	998	+ 0.05548678746033074,
	999	+ 0.7936521123845184,
	1000	+ 0.07870575953713924
	1001	+ ],
	1002	+ [
	1003	+ 0.012678171286458706,
	1004	+ 0.010733454886234343,
	1005	+ 0.08034685765747714,
	1006	+ 0.8962415161698298
	1007	+ ]
	1008	+ ],
	1009	+ "dy_total10": 16.969387954226146,
	1010	+ "dy_from10": [
	1011	+ 16.69303658816135,
	1012	+ 20.173878084178032,
	1013	+ 20.63478876154816,
	1014	+ 10.375848383017017
	1015	+ ],
	1016	+ "dy_to10": [
	1017	+ 16.931581993413293,
	1018	+ 16.3524656845659,
	1019	+ 20.20868413532503,
	1020	+ 14.384820003600352
	1021	+ ],
	1022	+ "bic_order": 1,
	1023	+ "aic_order": 2,
	1024	+ "lw_shrinkage": 0.01596351551230227,
	1025	+ "lw_cov": [
	1026	+ [
	1027	+ 1.8023181441872798,
	1028	+ 0.5977484951413455,
	1029	+ 0.4629362888279629,
	1030	+ 0.20850981626474843
	1031	+ ],
	1032	+ [
	1033	+ 0.5977484951413455,
	1034	+ 1.3700661681561666,
	1035	+ 0.456038755853786,
	1036	+ 0.23130512909577713
	1037	+ ],
	1038	+ [
	1039	+ 0.4629362888279629,
	1040	+ 0.456038755853786,
	1041	+ 1.3469838194292354,
	1042	+ 0.46885575997388035
	1043	+ ],
	1044	+ [
	1045	+ 0.20850981626474843,
	1046	+ 0.23130512909577713,
	1047	+ 0.46885575997388035,
	1048	+ 1.4559806820145973
	1049	+ ]
	1050	+ ],
	1051	+ "statsmodels_version": "0.15.0"
871	1052	}
872	1053	}
		\ No newline at end of file

added datasets/fixtures/var_panel.csv +1201 −0

		`@@ -0,0 +1,1201 @@`
	1	+y0,y1,y2,y3
	2	+0,0,0,0
	3	+0,0,0,0
	4	+0.52776996420472844,-0.3162133338936377,2.6394958251965766,-0.72842773898579327
	5	+0.95755792342787982,0.43113410825948639,0.56536914641115865,0.68111081105199134
	6	+-1.0828085928843514,-1.1748708225070765,0.36038103313463421,1.888441131354613
	7	+-0.23178876245718988,0.62992512508323273,-1.2819801136016173,-0.68200533225361304
	8	+0.82010604915862539,-0.32494402791901567,-0.39857640656840382,0.70814832494988034
	9	+-1.7268198110314343,-1.8026194838704244,-0.5854647139734509,-1.2841016502816287
	10	+-1.5954572492541954,-1.0112490766862048,-1.1662218868587082,-0.99958069486339951
	11	+-1.0667910549967432,0.53141967517563438,1.1893092160915248,-0.45529573435570958
	12	+-1.4700885717481458,0.93933183940368148,0.70514657764590449,0.19550067131464938
	13	+-1.5995940582056327,1.0039896362692469,1.2403950311908276,-1.2878225313305645
	14	+0.13313685534465547,1.0643401572232205,-0.34988689768543746,-2.2027437104500898
	15	+-0.41885315632317499,0.46298816553738881,-0.43782453577304753,-2.2852982830664237
	16	+-1.3527594236580882,0.69348077979540323,-0.30136009596014196,-0.89796428549364338
	17	+0.014312582698666643,1.2749238611874887,1.6081535052352161,-0.17387292849652658
	18	+-0.23641321254935249,-0.03672939028307165,0.56874445971342702,0.17454922413897037
	19	+-0.77075375138951774,0.10290901354980869,0.40621515743295739,3.6189915719765207
	20	+-0.64011619708102618,1.2320701264867417,1.1610094020719508,1.881443183320902
	21	+0.28983210722846742,1.2467792841707541,0.70692937617143004,1.3100082677763765
	22	+-0.035369354705603373,0.40943385007812672,0.81322861251892331,0.97600035022288745
	23	+1.1794875589799172,2.1779272543844854,0.83204271418938447,0.5989793844562471
	24	+2.2521559258924864,1.485934091535249,0.97465030595877877,0.37022627141615366
	25	+1.7035156892013226,2.4417834473595379,1.9000085866068579,-0.10365137848455452
	26	+0.67775601435612876,0.94046010665150293,0.52222725571073048,0.85414081164793543
	27	+-1.2987324769942692,1.5117871535342522,-0.41321197845739999,1.342723496682958
	28	+-1.4889574614841972,0.21004276111337772,0.7432518950816549,1.1043329906988781
	29	+0.40591639650222433,3.2679638284248291,0.2796227167768513,-0.078797200341566453
	30	+-0.76571587739517999,-0.30481955710956932,-0.32373128770827064,-1.3443290317334222
	31	+-2.9714357727115739,-0.99465624326495716,1.026183672046187,0.074105353899166393
	32	+-2.8884236319918251,-1.4202147098563302,0.56784108282288415,0.063482458325545887
	33	+-2.3458243877328284,0.40757023918058466,0.58746280225070313,-0.25025507395868613
	34	+-1.4867062669492772,0.42745411125361255,1.4003703520104998,-0.73787886860448582
	35	+-1.1295596434513167,0.21686376215052494,-1.6490533930421054,-1.5769798245535152
	36	+-2.3547222337207092,-0.38265644437673652,-0.79867784782417406,-0.55041770641162491
	37	+-1.0648442950582135,-1.6146003803041917,-0.9689889426151943,-0.28746174856587658
	38	+-0.042721900163372517,-0.46815541468297678,-0.95341070445985154,-0.20978251885162902
	39	+1.1794108902494362,0.13195932939424082,-1.8543233716987362,-0.072545729912223744
	40	+0.72040536794944987,-0.18659230602837082,-0.90797431004204743,0.00091536885238188703
	41	+0.70299174112315876,-1.4461264251182935,0.14134941156239655,-0.10254971359999696
	42	+0.26386918194258657,-0.91596068979047462,1.3550376675645843,1.3388915503294916
	43	+1.7685933080547684,-0.15166108902523867,-0.58507001079824272,-0.070868086769873773
	44	+2.1118072428258703,1.3305891332810107,-0.22502907352069179,1.4200321099254563
	45	+0.18122618410713365,0.028197053052420151,0.21976881251160565,2.3105363765644302
	46	+-1.270083212470966,-1.6534528550090359,-2.3522655555800527,-0.4460059747803351
	47	+-2.7601798509494615,-1.200089804472559,-2.0791269176424048,-0.92092680933492488
	48	+0.37967745756064497,0.072714812941522156,-1.5583783164119664,-0.24583471009694502
	49	+0.44802172241314631,0.9820133575947031,-1.1744575383548612,-0.026324686620537469
	50	+0.42369821698191606,0.17607835181754067,-0.94054121536915125,0.72253952066538663
	51	+1.1369097677826736,-1.1583522584653501,-1.2042548479391908,-0.074458528764471288
	52	+1.3750803636473885,-0.097924930235193164,0.63320177071470463,0.21684231456189043
	53	+0.40061599608644272,-0.032272162477339494,1.5264857452902674,-0.013628336398290197
	54	+0.077468334411178397,-0.54137161416383428,0.38008364835521258,0.92498310021731622
	55	+0.16064760387574495,-0.27432604472838484,0.09569181950467065,-0.82544981601557477
	56	+-0.18263548482149189,-2.9142018486324455,-0.22016232763215363,-0.96613804395957215
	57	+0.18093924873801431,-0.99549045328351327,-0.094245546463561966,-1.4575411363142918
	58	+0.89455990224455917,0.3414139978570454,-1.1324697069950407,-0.94319271675463523
	59	+2.0623721873853418,0.5166863374937144,-1.0302731489725789,-2.5552342503935535
	60	+2.5347803426804423,-0.68791914575986068,-2.5198606777429604,-0.82629996173442211
	61	+2.1075872008423313,-0.30251420450506361,-0.24354379317826563,-0.59276163232940671
	62	+1.9320379980969318,0.0090972523398281657,0.016327619406439398,-0.15789708194467617
	63	+1.8876948866115566,-0.46778292283359368,0.30687065778382222,-1.6875973229619163
	64	+0.73876886901481797,0.93978006557687066,0.23241993504780128,-1.0929850318785495
	65	+0.3950351407852124,0.95899134955131116,-0.54243912006377593,0.86944646066830344
	66	+0.58187461183421263,0.90423463546241933,2.262229919373647,2.9597765717444999
	67	+0.15600879058312878,0.13281869129238399,0.54299506618696214,1.6160419172467742
	68	+1.5193368185451239,-0.037398525446766362,0.76094471419087295,-0.022003301932771002
	69	+2.2921662251260653,1.8069576287829929,-1.3575681628771625,0.045041546731607096
	70	+1.3974736229968314,0.67412183323406549,0.26834300743170586,0.36060115805768628
	71	+1.6840389543963399,0.59464445421422285,1.4215442181602655,1.6903927968954235
	72	+-1.1074780671836133,0.87698440055051441,0.91637067325299504,0.0048009714328440811
	73	+-0.5156080529088507,0.89649168355931019,1.5960680323244869,1.8643678253772602
	74	+-0.5529796118737087,0.51168753916052467,1.8860533175691354,1.3474855608258016
	75	+-0.53133845376955691,-1.4113320577686064,1.1256249472433328,1.2332251371308649
	76	+-0.7431053889890713,-0.38480539103657097,-0.83938297269502193,0.74024470122649288
	77	+1.0137949335213319,1.0415751891806502,-0.56973565709212326,-0.31441460962989853
	78	+0.003957355169570631,-0.25167049231607513,0.18487384232042137,1.0831675970809589
	79	+-0.53493730399085093,-0.55683995804648401,-1.2315118995779379,2.3798425148990168
	80	+-1.2801470038892406,0.60272719896811622,0.34294503270244819,1.8684879048698841
	81	+0.040571303923982449,-0.26976814904026597,0.92779849420817151,-0.019372587890957416
	82	+-0.4401317596083778,1.278642702321674,0.83244189943150393,-0.64994806628911517
	83	+-0.75036038728419674,-0.15011193534621214,1.9068196232603469,0.25211368643430787
	84	+-0.32664513353273888,1.142174576789819,1.9720999959517789,0.39228895617376419
	85	+0.16711264957360478,-0.090246116395317988,0.87076501056467404,-1.5287860393022175
	86	+0.46383954376071235,1.1938433160811148,-0.29239936073865547,-1.2908148786297788
	87	+-0.26166688443821107,-1.1939437494699194,0.6164469590864593,-1.3155689964502375
	88	+-1.5948099199199846,-1.0386425309868335,0.45759344054061951,-1.2725151932540402
	89	+-0.58577581724208871,-0.45834708683458647,-0.082946067618549807,-0.78063397545531177
	90	+0.69268237249224773,1.2888239102076768,1.1971630207895037,0.01559459884570058
	91	+0.029619527666258028,-0.22652231786514487,2.1951483156241598,1.5195637216517857
	92	+0.11578200669352784,0.95456336528343888,1.5072062690090862,2.4359467958620513
	93	+1.8784001801230958,-0.99873770715869603,1.9529518325346913,1.270801091094669
	94	+1.0407688876934718,-0.89913180127489023,0.48861653247579684,0.40615118760590563
	95	+1.4231973536717779,-0.91672106856797209,-1.0625911421288263,-0.22491758323917665
	96	+0.39673144406303867,-1.2052848162986363,0.13389052304068508,-1.4578624483652081
	97	+-1.6466325529388415,-0.97305756429011114,0.10831800530081426,0.39175756276422535
	98	+-0.51265698333663245,0.85441035000308241,-0.31599035936454795,1.4993020505309749
	99	+1.3821273108727352,0.99403827014018853,0.27123578829064654,0.13889890071211275
	100	+1.0561997204230684,0.17307106826567908,0.60189103958628365,1.7714172960140926
	101	+1.6127568840518243,-0.79174376169215077,-0.94919288322232198,1.6851621130608394
	102	+1.6676408052625442,1.195722320558239,2.8483764517640249,2.017517730812465
	103	+1.524188441079549,0.038681543726091561,1.9549997154475285,0.22916472234582841
	104	+0.61906220674056822,-0.40858124016683328,-0.68799768352127089,-0.79946289842712415
	105	+1.3573615426409482,1.330808523745302,1.549885777832168,0.16978764880514879
	106	+1.9387754510838102,0.93349518834082401,1.5547803259785629,-0.083451319590037876
	107	+0.49886250080741501,0.43516793585255048,1.7870447449293958,2.2386497711172062
	108	+1.6602928204304295,-1.2807204310156066,1.2116797845114728,0.59929941083600857
	109	+0.43551942636641749,-0.23012540858187558,0.81299613602649401,1.4133165261818403
	110	+1.33536038120431,-0.090046645249454743,0.19948597676786606,2.2909605816854084
	111	+1.0978474979630963,-1.1373611343674932,1.0751568063552484,3.3879473220697789
	112	+2.0684220641375219,1.9939038268450888,0.86096853547779884,2.0872216738288993
	113	+4.0657276781410854,1.2349353061619719,-0.5916902196006526,2.6333536755330398
	114	+2.0742796125609688,2.4883037974410707,2.3988921059339297,1.3662378234827113
	115	+0.40846719675131427,1.5416297874197751,0.078797980060023032,1.5211601492926483
	116	+2.2304861545697889,0.93128086068486016,1.5169512927063011,2.1629725506070381
	117	+0.75717889358978585,0.95863094963263451,0.6691830961919073,1.7275245006342683
	118	+1.7132826778293586,0.64621915407484909,1.4708461720269004,1.545264304356216
	119	+1.898255283008967,1.0028138764391787,0.69053440499148389,-0.78325696865972771
	120	+-0.056399778626340602,-1.746213951458816,2.8349010047876924,1.1050593442901415
	121	+-0.57235746242002661,-0.93322163560718252,1.6593747832119592,0.26633734050570201
	122	+-0.396344257324178,0.86059456814746238,0.69244921800942083,0.073599822391140379
	123	+-0.35942174841868607,1.5612236114624092,1.8636335747900445,0.66275652937034912
	124	+1.0076602922313114,0.84251711954951602,1.0533367276037675,0.79501550527525167
	125	+1.3077467266570326,-1.8062253158882449,0.35160786892911555,-0.54440522928064439
	126	+0.78863610598337108,-0.317055709713842,1.6593097266909873,0.91283760853356377
	127	+1.3398452986294531,0.4297020859660256,2.6243763199761014,0.37502675087264653
	128	+1.2766462755237573,-0.24857161301679864,2.7473493933519006,-0.06280998323769893
	129	+2.1992656411460163,-1.4211596394451689,2.1426753823566997,-1.2554612913377619
	130	+1.4613720918085575,0.6239377454045274,1.3145101797286454,-1.3338419701534072
	131	+-0.82433684541264785,-0.97063387139906132,-0.27013663585481273,0.11643096443035605
	132	+-0.71250972074997132,-0.70012545484366739,-0.79652120040953955,-1.1079200617976968
	133	+-0.29179968871035594,0.65031573072862059,-0.55885278041288244,-1.5336260964818111
	134	+-1.380820030796267,-1.1028262384906413,0.091236629930167124,0.44002992280764275
	135	+-2.500502606232978,-1.3036380576067852,-1.6725734946797461,-1.0508007035013114
	136	+-1.7826206124309882,0.25009553233165049,0.44302830013492045,-0.81531901447795296
	137	+-1.1228117269285571,-1.3288324549235235,0.27043812334310691,-0.18259837207639029
	138	+-0.79670208572816437,-0.2096251398078853,0.39345961819275499,-0.24794491338330965
	139	+-0.060127789664433773,0.94079462456864038,0.792086310621685,-0.020186795565406021
	140	+-0.2548301165414214,1.1316573703064896,-0.016260047329695715,-0.072754315899486499
	141	+0.50919233487540683,1.3043066331140867,2.6318678943870788,0.1358635363380109
	142	+-1.3338738587483236,0.50457129125554334,1.5011060372452749,1.6826542753936358
	143	+0.52859808411022868,0.22924362747744781,1.7418742392646693,0.66676946512657431
	144	+0.84517433546087761,1.0450647068829599,-0.77818404174040512,-1.0371852833281583
	145	+0.36316093375815306,0.54202251825697889,-0.50552313657601056,-0.61738360364653211
	146	+0.70564272067605505,0.68277206330395779,1.0571623093934663,-0.56058276322504419
	147	+0.10902750788144522,-0.069413893587473852,0.50973809933640002,-1.1365179707715631
	148	+-1.610037932293463,-0.704966969693821,-1.0305399719721717,-0.45516322981723523
	149	+0.1488243848557177,-1.8249922119691164,-0.2607179932124018,-0.27147524733625594
	150	+1.1965735492199154,0.53163474053015181,-1.4884617102134268,0.57051414636114872
	151	+2.3689410653838614,-0.30984854033544595,1.7256166494098726,-0.048548762303950388
	152	+1.4645182191658828,-0.50696117726547307,2.2427890399283315,1.8236759990451281
	153	+2.2294884263289978,0.48650664620818029,1.5132026264382059,1.8642623784040677
	154	+1.6492489081202211,0.96000755000734617,2.2224926005556114,1.5395793296157285
	155	+1.968154431550325,1.1056160100569301,0.25305693943009611,2.8514902590173827
	156	+1.6224977837308683,0.72777181927013324,0.65839044521872259,0.9394392375539381
	157	+0.73284481368550802,1.871124264104475,1.6210147498924308,1.6981412670859855
	158	+2.2473716994391806,1.7879823971922235,1.1062740403675138,1.6922515444861506
	159	+2.3946577173324561,0.89676205808497422,0.39896459408475682,1.8060914929763399
	160	+3.669286012708012,1.5464231504061323,-0.070707278135609841,1.831243651325988
	161	+2.5076746048810206,0.77699719470185635,-1.0745610011089077,2.8399659893668634
	162	+2.6429793608555938,-0.53165064253801775,-1.9238802963236723,2.3789381693445879
	163	+1.0972162123846103,-1.6206683820643528,-1.8935941420822164,0.30644016215574221
	164	+1.1281966205056495,-0.29603976903784057,0.033354211000874878,1.2069800162941433
	165	+0.50745178775273891,-0.072768571571580037,-0.30965750513217888,2.2278888203886131
	166	+0.11442782086427827,0.39548445368817997,-0.95391809512489012,1.8523298133503623
	167	+0.53127309683810575,0.55117774940331543,0.68376154280459145,1.8306833516334202
	168	+1.0175070942082685,1.2065703482027936,-0.098012315559039498,1.5592292173518894
	169	+1.0611854128851184,-0.41028322999324474,1.9034928454042583,1.6302018355841685
	170	+1.1758542491699229,0.26891369595505843,1.1322801935956992,1.5802694245912805
	171	+1.3136552425160228,1.2363304768319274,-0.6058510970907609,2.5903040890931051
	172	+2.3165814467335508,0.97546328542713479,0.42486858970787744,0.90404491644368901
	173	+0.11660032362993666,0.95017973644939402,2.0029911066139476,1.0466557849909925
	174	+1.0830535779461479,-1.705014068746479,-0.35931539291412529,0.1973319617411271
	175	+-0.43353272192458164,0.081983174966507866,0.51588737008255137,-0.9402106475354246
	176	+1.4816252210269445,-1.2392434400214698,1.3091935747167194,0.94675639815576407
	177	+1.4927777078914941,1.5449044407330583,0.014951590138943871,0.032222723822133204
	178	+1.966668343434028,1.1356387675643815,2.2877143819452055,1.6529516780318549
	179	+0.76837112173845945,-0.092514857414602636,1.6871400822484883,0.39785830383572462
	180	+0.80119706810361457,-0.53174647634923089,1.5966919977736413,1.2231460151512799
	181	+-0.9816915553367922,-0.92679444323082327,0.4944185208544859,0.34239555363604413
	182	+-0.54663333974539663,-0.49504030987606018,-0.56319406685396012,0.49197605586249699
	183	+-1.1542828055585401,-2.580419226610827,-1.0566404849059163,0.0064505004882474126
	184	+-0.067734482019706665,-2.1642591976368379,-0.33384548524021196,-0.39793670228272532
	185	+1.1739059291797198,-0.87238986442982103,0.15223642478381788,1.5545819075310701
	186	+-0.24952701529724375,-3.7896378462351668,-2.5937208167959351,-2.0353037785296295
	187	+-1.0729987416938933,-3.4990110428024028,-0.20947318550560834,-0.64177947721217121
	188	+-0.73525513776251361,-1.8183318900321701,-2.0843978366682343,1.5332857309982579
	189	+0.70766374960617551,0.068183427461556256,-0.25036955107040176,-0.29155158054640207
	190	+-0.73072491171821397,1.0776570480159926,1.0244485626443418,0.92671727374722757
	191	+-0.81814065564888483,0.75820894779158987,0.8359224125767668,-0.10237411301145266
	192	+-0.93660588188305582,-0.017868227731967834,-0.2913500932004176,-1.441382848284835
	193	+-1.8922375800387794,1.5202831924474729,1.1724739649196723,0.011580419500937245
	194	+-1.2128872228934267,0.096906887438887868,-1.3044256363617615,-0.31947482906378377
	195	+-1.7941428883806048,0.61520390841636619,-2.0730325894980539,-0.59300339528319324
	196	+-1.2769256399381432,-0.92802796167831592,-0.98815036325222305,-0.15261730715400748
	197	+1.8570564464544894,0.13549763879535237,0.98312201833190394,-0.1995940331099087
	198	+0.67912761493263152,0.26238035295232309,0.59962737672835154,-0.50577259447153633
	199	+0.71801033171459672,0.16446908489260373,2.9830731682578646,0.44766226225627548
	200	+-0.11148436567406583,0.70817205166245523,3.2048094763857824,0.59408615924164443
	201	+0.49169141055297749,-0.28814194714770158,2.2376979656051961,1.3894358225491876
	202	+1.6548585213166958,1.4754914816637883,3.1394515739226243,2.6002276431769147
	203	+0.94743724464668611,1.4952966777450611,1.2224101072131297,4.0275908052151612
	204	+0.55774858771575864,0.26483041901558391,1.386670409038548,3.6691950174998365
	205	+-0.3101040648643516,-0.30862956177930967,0.277813069721354,3.8173241505644282
	206	+0.39749873735470298,0.2417117142294046,0.61440424745854871,4.7085738816478191
	207	+-0.33952350536415399,1.0716058702448719,1.8826655298549175,2.5083358788313133
	208	+0.99702991683974251,2.0316113826961644,0.59335468244771516,3.0413323388461029
	209	+0.55729517318010424,-0.090393447741263788,0.38580636047438976,2.2728801650908164
	210	+-0.31155254636017726,0.59165725137899505,1.0089802259493703,0.91963456046898184
	211	+0.041202711872336165,-0.17811189764977797,0.013748856283803623,0.75336145503563767
	212	+0.38404335956304925,-0.14679009959551145,-0.15769678436721474,0.79683442410688288
	213	+-1.0407320479162196,-0.35531927619366438,0.51658253763540152,1.3379992104175762
	214	+-0.47647160891370788,1.0584542188275654,0.80891497910171917,1.6827355001049416
	215	+-1.3915995724484291,-0.99009597474974442,-1.3525926356926576,-0.20703676420170813
	216	+-1.1809685485595152,-1.9376218925390316,-0.64763526620693201,-0.047437867861372912
	217	+-1.9783109565923296,-2.0608658795781247,-0.4377950783062306,0.14507280707794523
	218	+-0.75869815962129106,-0.52953686785175225,-1.3428873694560366,-0.11158290992310974
	219	+-1.6768555506318816,-0.57512791602417235,0.017414377816696081,1.3326729319703889
	220	+-1.4692234014247028,-1.5215603898674652,-1.2373418986408011,0.36301233576476349
	221	+-1.3532607696510934,0.26114900379102823,-1.5150766750997331,-0.27175004383145723
	222	+-1.7354083488076024,-0.66809885741560027,-0.77794405541903211,-0.19401546322622626
	223	+-0.98617852817162421,0.23182848067727871,0.70470678965474065,0.68216574895275806
	224	+-1.6190573194846605,-0.36636730125939238,0.75723476769285591,0.35520254527748113
	225	+0.41251418003917673,0.7551526313056931,0.72645778238594971,1.564858390581096
	226	+-1.371987840487517,1.0754684150818417,1.9721028674657162,1.1205358750385186
	227	+-0.49346925430578359,1.1120831413487,1.3790672516108851,0.57465638383808759
	228	+0.052608818000079161,1.4346791314827583,-0.20253938276407624,-0.40085306760036588
	229	+0.91364180852174293,0.01784050788191438,0.64326989977255478,-0.70128451993149454
	230	+0.15733050864844966,-0.67880311227107359,-0.69148215321728623,-0.72383004840510101
	231	+0.1414724106194778,-0.94770294874872651,0.81059865601935721,0.087984303711850564
	232	+0.19460627805675246,-1.015408123977529,-0.22893524129939241,0.97318715923934018
	233	+-0.26114491415046553,-0.099748954073736906,-0.5519020721372232,0.81048884196917714
	234	+2.0058387245156561,2.0122002816839353,-0.66500014361966786,1.1589614557016588
	235	+-0.28822687015146231,0.13159127764575784,1.2861566661633481,1.5459764103717584
	236	+-0.87578168741081197,1.6478531259668046,0.31442401949748283,1.2574986993003006
	237	+-0.2886686472800078,1.2024565343548825,-0.5555559373586334,1.5941017492470526
	238	+0.54917415051172891,-0.39416872860941699,0.36267531721983298,0.096809045331058274
	239	+-0.40441982470679605,0.55553541391896166,0.25216099401920583,-0.27687023427225149
	240	+-1.7773519936788005,0.30428294108805909,0.98483657678284253,0.19575346550390038
	241	+-1.9846961335592208,1.5071218324050082,1.1121098183089773,2.4820260826631495
	242	+-1.7504915932420841,-0.52559322143300202,-0.76892546546693818,1.8328890970358196
	243	+-1.5134956337480623,-1.3703644972654214,0.49856547282728159,2.6617661591321369
	244	+0.73928183949260573,0.65609049251033524,1.2654254695806655,2.2800298640908099
	245	+-0.79383661267729477,-0.65539896203388304,-0.61308005342668548,1.1547848902947433
	246	+0.67926061249094627,-0.7054620921128042,-0.48145743186099599,1.5169700640205539
	247	+1.8458897172954662,0.93887386259378136,0.095567907906189672,1.5584311841441281
	248	+0.055829595026436252,2.2528341602971649,1.7105496901908448,-0.60631785723425136
	249	+0.6919751069857869,2.2376660186554029,-1.0829401072783313,-0.33741822619065631
	250	+-0.87738098983802659,0.90822794551672947,-0.71781763147551525,0.019719654137054635
	251	+-0.94015999865801514,0.1894022214551957,0.36893712152672775,-0.32592095079212258
	252	+0.33301271415801159,1.6919178548996636,-0.73442438659192599,-1.2041468023974948
	253	+-2.5791309293085489,0.43755389213360396,0.23719395599705539,-1.3328072530089452
	254	+-1.7384770210793299,0.52231646583226909,-1.6526578230794964,0.16274330141896054
	255	+-0.12429904001987802,-0.13653142109208538,0.47577026703575886,0.21863665477595862
	256	+-0.11130835207741853,1.940450988968454,1.6927620264309531,1.9291163141902248
	257	+0.21393778846958073,1.447987788534824,0.20830568515714132,1.8626616893275774
	258	+1.0428534498880766,1.1102514100882224,0.96939676828536803,1.1753451296527806
	259	+0.63014099790994249,1.3544856916963162,2.0510357714464877,1.9147680352149794
	260	+0.90782851355850591,2.0320561000089623,1.7982397489960971,2.0130844557164176
	261	+-0.77610780751224606,1.0142049438138336,0.20772279456223841,1.6256116518614498
	262	+-1.3315407551029734,1.495227772978887,0.24813405429654678,0.11199802159939587
	263	+-2.3255721214681069,-0.14188836137908156,-1.8998264133352116,-0.62204652828239637
	264	+0.15381670286115079,0.93327115516075199,-0.37551621796773971,-0.98205406938164796
	265	+0.75047604564826387,0.34583629721034764,0.42109193998507255,0.48792381543006791
	266	+1.7287883432249234,-0.022746407830076754,-0.29787844918629858,0.92136321367882013
	267	+-0.23962627613465237,0.74460108198136643,-1.1467475233587348,1.0805834099884537
	268	+-1.0221039327669974,-0.52704003070208194,0.3456773890765113,0.91417572599544372
	269	+-1.6316267268818752,0.6508065040437967,-0.65029545052250359,1.2643752522607343
	270	+-1.6788472841904793,2.2660058447277396,0.40536972211806621,1.8574020213201896
	271	+-0.0006458890334225531,0.69720418889916069,1.0972294177311919,1.25064487318296
	272	+-1.3188577621572768,1.7265661016707639,-0.16865981299506383,2.1475051465583466
	273	+-1.1215310014369009,0.84532828963267015,-1.4134209501639214,0.59457766217843755
	274	+1.3729184635946448,0.76468975794912364,-0.11938952697808941,1.5000545669666894
	275	+1.3399851474478719,2.2842627043708488,1.7886772466771803,1.1991914137066755
	276	+1.7162393647296654,-0.90908435752818217,1.9969663489012148,2.2998132372437663
	277	+1.1236391595195112,0.58557434764450211,2.6931692602630486,1.012646364298367
	278	+1.8829997773903879,-0.58682957852590123,2.2566127780055272,-0.50543948702657104
	279	+0.014746157194746035,-1.3643449508101422,0.65415856752486634,-0.023050019960650342
	280	+1.4828823540425544,-0.27932324682704085,0.015319856115588726,-0.085278738921325759
	281	+2.2828011012989693,0.23813369705087833,1.3888500629194704,1.1157332058087788
	282	+0.91151592842273887,1.3450864486694356,0.89174843425128669,1.6933281601327237
	283	+2.1452292751469448,1.4954917197921613,1.1562218376690792,1.5828833553600161
	284	+0.5095081285658174,2.2186397827293427,1.8857642412602815,0.12191591277799851
	285	+1.0493191885943607,0.46844157176584211,2.9359698360098738,0.45749309547317707
	286	+0.38904574936797048,1.6298012657554548,1.7265071433692283,0.39594499850904669
	287	+-0.11929098018288831,1.9056718378064303,0.91303341835465668,0.42743050340605288
	288	+-1.2565761577100441,0.20053750534834891,0.7699703120706245,0.76524006790004373
	289	+-1.1713758337701803,0.66272797186545418,0.41858688879223988,-1.137987668822988
	290	+-0.78472533906869268,0.43492636569226706,0.95921473043464778,-0.5382282319102063
	291	+-0.62754875184103942,1.6738803085347298,0.68276887742679693,0.2461183768636096
	292	+0.24250095962148094,2.0416000615981731,0.20493754546275214,-0.041821537740925868
	293	+-0.34163753275014502,-0.61203689506810366,-0.75253306185839253,-2.6394192124147775
	294	+0.71673015167889542,-0.91965732381082976,-0.76822491994804198,-1.8245757523493684
	295	+0.45498630376147964,-3.4513886400783766,-0.1849805473675783,-0.25896571743085062
	296	+1.0332801947332793,-1.7093768794175699,-0.15032142347962008,0.83218047924388505
	297	+0.24772590981536141,-0.013998360014877642,0.66305169851617618,0.20828527147795395
	298	+-0.63473357634869476,-0.0750663401032301,-0.22124389688335239,1.8010138427706739
	299	+0.65799667998301326,-0.65467440669801402,0.66098459594977821,0.41300529791198148
	300	+-0.098094484220266065,0.0064432262113125888,-0.26371032590024929,0.3929713811816351
	301	+1.4498760335618246,0.95903437476407039,0.29632556768473073,1.3492017929560025
	302	+2.9735779798587663,2.2462762905711773,0.85760872865089999,1.732714735134623
	303	+1.9080349284339673,1.0238207106265127,0.54694463946959848,2.6587591444616114
	304	+2.2877721067115449,2.3427285144053451,2.9003255144775411,1.9324432736507835
	305	+0.74676461512267833,0.78679501434098764,2.2094919552443799,3.4571946684318093
	306	+0.94283601953305451,2.1884136487171775,0.9487272697666016,1.5883294315306626
	307	+2.4843195027763816,1.358418007054419,1.4307159165549248,1.7823091100269211
	308	+1.159216773240582,0.41879502710914163,0.29061452604359705,1.2296332379665842
	309	+0.57926370962031837,0.59111029095632694,0.06194687408122046,1.8993839387244402
	310	+-0.10215807285300893,-0.42022979253120013,-2.2910737398162757,0.24929059952756438
	311	+-2.209162537961697,-1.3267238045295682,-0.68396051040474104,1.0685271837531576
	312	+-1.3518396054935073,0.011303429954293343,0.63501448575971098,0.32011560712498621
	313	+-0.6837949510205118,1.3368659439661001,0.63380599501934365,0.25276217685428992
	314	+-1.3481597726128642,0.80989072943619411,-0.091738516539077164,0.34043799451196721
	315	+-1.0573730334133953,-2.0637715371063763,-0.72248816943070071,-1.975722696528921
	316	+-0.43303446056247019,-1.6607063227861858,-0.74732566018322866,-0.82073901597065602
	317	+0.036232419332278054,-2.4950237198258249,0.13208350480718556,-2.1642332995295703
	318	+-0.95191220020432255,-0.66264035424688617,-0.43233667621022842,-2.3172551047007239
	319	+-1.3016568495219878,2.1177259796591774,0.87565423818908406,0.093723005849318808
	320	+-2.5798250744480056,-0.038504406883452913,0.62382507124622233,1.8403667272016095
	321	+-1.4329077981676288,-1.0435631643736947,-0.68067238196780055,0.76065784373243273
	322	+-2.2589540278404741,-0.67951673026908188,-0.79384118824836281,-0.43854852853871296
	323	+-1.4340145849608765,0.77469741443654394,0.072646230961400327,-2.2874219741156443
	324	+-0.16857083747040336,-1.1465881321366642,0.4003098894817077,-0.87603780173271051
	325	+-1.6184015544271459,-0.65652132540897978,-0.70138597921810442,-2.9029119672720745
	326	+-2.4164922104628666,-2.6665426823332172,-0.18257764294118262,-1.7770389677826297
	327	+-1.8861646878456364,0.03609434314556581,0.55918991190486156,-1.4913349501725404
	328	+-2.8545689641275578,-1.2645252609127571,0.58933454981590416,0.17488086832199179
	329	+-1.9066251842181297,-1.4769903516637624,-1.6549714131446926,0.64050504486229776
	330	+-1.9803432706760002,-0.60855626455694256,0.55637610049216168,0.96170533776662692
	331	+-0.68922128371264346,0.4743806267920499,0.5490965784822297,-0.63901519932037776
	332	+-0.10080759892310737,0.19315031137772101,0.14627090860767722,-0.40991363799146063
	333	+-2.6549462628605212,-0.37726579632053003,0.65232741261380345,2.9888229512543121
	334	+-3.5423334155106971,0.24219192863832678,1.6192729831321206,0.85543149337019742
	335	+-1.385607676930622,0.43337050764686802,-0.0052784456103952548,1.3679777111193605
	336	+-0.42938307593307046,-0.040912564237773896,0.1704677792862693,1.015878290089596
	337	+0.31493869883506903,0.87315881279547403,1.9543257718676712,0.98170722450911163
	338	+-0.33456877641469518,0.44420145152764112,0.041706524482816087,1.7906897487572633
	339	+1.0239504831263944,1.298430743861442,-1.4568563618169077,0.82238980510884496
	340	+-0.2754040100896239,-1.0026842896187449,-1.5087845013847661,-1.3895881095349794
	341	+-0.65891790547724371,-1.4039818255763699,0.75883801788416694,-0.37364725920501485
	342	+-2.9121326585449125,-2.1488092878602396,-1.0852469774737408,-0.1274131975983761
	343	+-2.1810794195556089,-0.54056528505690005,-1.5221760988782993,-1.0007482545036712
	344	+-1.3942597697803558,-2.9252489323447604,-2.4274769964297258,-1.0894934452944329
	345	+-2.8453411477043344,-3.7381304014041787,-2.4535530936348247,0.87591884375504192
	346	+-1.1152149864490712,-2.4963835670956867,-1.3706282835836758,-0.26765255125333243
	347	+-1.1265464156045848,-2.0267650001904851,-0.44872664714527372,-0.085054744274301736
	348	+1.0930117238206118,-0.45448848930259234,-0.32571542128973635,-0.85376115412560138
	349	+0.30442633076020365,-0.51298927976889064,1.0367081784345886,0.69556185920341318
	350	+-0.012172588978605514,-1.4850693217977478,0.46757883979156373,0.87668733829810319
	351	+1.5120996216930629,-0.18103368857310215,-0.097454921764668523,0.41981499139003098
	352	+2.2652405844593719,-0.056519221835564487,0.73960188275247163,0.91841389814248264
	353	+1.1135214295417586,0.53310204256304206,1.4849112184994442,1.7760654746591291
	354	+1.4538878857691775,0.72148052171868926,1.2271249909162345,1.2588408951178378
	355	+3.1792703106030862,2.8653581626724431,2.1626803269971671,0.087525973568316706
	356	+1.1477946758008062,0.61551376889382259,1.1225748076700173,-1.3885197946400325
	357	+1.0705185995934763,2.7914434997345809,1.7764746256806734,0.93933944701784799
	358	+0.77359254116730414,2.0543673673954315,1.4965588557082488,0.13504496211018702
	359	+0.61718357795167966,0.054618852583026678,2.1243464695900984,1.4398892035799227
	360	+-0.027551004940501889,0.26731691458328311,0.69367758856645056,-0.60946080691030091
	361	+0.72450206555283503,0.3678309439914641,-0.19387186541627033,-1.3016536217026256
	362	+0.8605490616324647,0.57679387477906596,0.79241139794361037,-0.1744873391646603
	363	+1.8135052663425724,0.27094670896744588,0.9186608027696912,-0.60050322362131758
	364	+0.031737055856729368,-0.057860323822306492,-0.1845987709834952,-1.1859778130267422
	365	+-1.7313273027415339,-0.25398593309249412,-0.29983119509856021,-1.7664166427471237
	366	+-1.8610981374182107,0.26217942876167455,0.3418312954845224,0.57866696212363467
	367	+-0.95948680399590847,0.36790331576800051,-1.0616329744116015,-0.85993764476308376
	368	+-1.2549162544786265,1.4370783593137233,0.18565770470646353,0.57185472206309185
	369	+-2.3413442257596246,0.11110847166265125,-1.0891361326141185,1.8679672805871033
	370	+-3.0747564912662906,-1.5580310797824986,-0.48499049118413051,1.7479554395304535
	371	+-2.1413527634854796,0.044325258098035669,-1.3268586588546638,1.8824528443979331
	372	+-1.3590833395413175,-0.26215844498520857,-0.81636814614948872,1.7932561869064441
	373	+-0.73688864223740902,0.81236878495982801,0.97909924718696906,2.0312072482243133
	374	+-0.66312017547320479,0.23010915153501355,-1.3632567593331721,0.48465851503505752
	375	+-0.32593778685779617,1.4692791362858237,-0.46944425993276812,1.3090506664674553
	376	+0.90663761482031247,0.867325758140713,-0.22447270175087,0.77406320412669594
	377	+0.37483455827487649,0.53316123687650774,-0.9681812506501335,0.70161130788161152
	378	+0.14188106160876501,0.79766890751519259,1.5716121500698561,1.4796914934747765
	379	+0.82889668178536002,1.3277461295700101,1.0061735671173433,1.9975165188665978
	380	+-0.1425041321363022,-0.85623061567307746,-1.2289156144185247,1.3884588711463506
	381	+0.32599595320184871,1.0568480459463248,0.80927924594675615,0.89475736248226645
	382	+0.013457372590403083,-0.52501980153519745,0.12862209518572909,1.3791246496080634
	383	+1.0849613089093901,1.0676907024221387,0.85621762583319383,-2.0442647472434929
	384	+1.2039968327629837,-1.2450844942783372,0.85560812757572802,0.055285754182175961
	385	+0.022464535396411134,-0.83917998927460136,3.1077698573409345,0.72410415369619419
	386	+1.372377761607726,-0.25845581478178747,2.0362931904695607,-0.17226416903202396
	387	+1.6323115199655218,1.0288004954764223,2.3971557201294553,1.1625057308030113
	388	+0.64403589689822649,-0.74839694846404647,1.2390120895021646,-0.32023929565292786
	389	+1.2468730663276866,-0.82022375426940086,0.70092731247798867,-1.0604160032175196
	390	+0.2874459085074455,0.48131028248985985,0.33444736357606442,0.03960477638752169
	391	+-0.32035536085091387,-1.7324164660334569,0.57113054536749286,-0.4947487213982133
	392	+-0.89503956498013348,-3.2027006239724436,0.63057352753353701,-0.045535750327822144
	393	+-1.6843195282923058,-0.93995483217444453,-0.099334076836507912,1.1655218559998124
	394	+-0.10422349265175368,0.092475126208119041,1.5149511124194903,0.84255858367365488
	395	+-0.25138017667118612,-2.0515869097083632,-0.73045252594944055,0.39918471993379634
	396	+0.022010831804410741,-0.12086532800483019,0.085269535951877543,-0.63897382509566591
	397	+0.11219850654612173,-0.38094143483761622,0.39517338826100668,0.90447629744775515
	398	+2.022798280341144,-0.7416164970789112,-1.0936439805671649,0.25411469818447896
	399	+0.57779328093225679,-0.40129849378649585,1.8055406256271898,-0.13430376502940844
	400	+1.9456733236426422,0.40859458285867378,-0.63636638336701212,0.64501698899964732
	401	+-1.7286281328254425,-1.9316344370476419,1.7729016764218306,0.31270837901105669
	402	+-0.19209180664910647,1.081617378855976,-0.14912366099271779,-0.95587404807086407
	403	+-1.3172709395436626,1.2597560499359635,0.25400376898508259,1.9138516237088667
	404	+-1.4962761649491096,1.0547265418467429,-0.7008644982225033,0.61042047931306209
	405	+0.502648101842744,-0.1593084805442847,-1.0012280273801788,0.50586425174517458
	406	+0.001323370484307862,-0.90055618799929671,0.74072338311358843,1.0594675408825678
	407	+-0.5169432354537199,0.28928176760537838,-0.1230378703713127,1.8977766429318983
	408	+-0.36543353711088961,-1.3704892688829335,0.62630205941352712,1.1504421887571483
	409	+0.081637225526446755,-2.0184763738861236,-0.90400833956227511,1.5374536333725937
	410	+0.72108136855361382,-2.241769658940429,0.15354143617467797,0.22090979508942143
	411	+0.73848864265386438,-1.4986492846634674,0.33908667510947688,0.34423436221649384
	412	+-1.6011682277422392,-0.37363392130119355,1.8828145637733376,0.40069798207463719
	413	+-0.24770737546436572,-0.27383737450867307,0.45945900415467711,-0.51303023669786485
	414	+-1.611944100729586,0.10624159925659986,1.0456526117021174,-0.28551846484907795
	415	+-0.86983394527258195,1.5804843284780357,0.65079700366341475,1.3184820583064827
	416	+1.0394295474096951,1.8635980637517844,0.071695263078740024,1.030935799768999
	417	+0.99729945547180643,1.7620618825043373,0.085940791846052189,1.667608852339503
	418	+1.8722834894529548,2.5379003292016851,2.7786704892980136,0.83593544600124381
	419	+2.0556949885255666,1.6174341165265367,0.82126219697391445,0.42632704478306915
	420	+1.7808660354275412,-0.8307273238901911,1.1354022122984861,1.3752975740603648
	421	+-0.20283811255199202,0.11853316325306182,1.012737638875191,1.3546897933103699
	422	+0.99887808372242115,-0.16580772056741155,-0.42096191255991611,0.78115640015950394
	423	+0.28371030173653067,0.20391520488143247,1.6348509067603796,1.5221522284903304
	424	+0.18812371323029792,-0.47059582733559135,1.363745031161171,0.58977126286016202
	425	+-0.63635587106064051,-0.3531835941822693,-0.391665757133142,-0.22886110507150215
	426	+-0.458108856833777,0.59686691743214348,0.1722059636791699,0.043044105105828984
	427	+-1.7899891903303333,0.66381757103290662,-0.89863552377340539,1.0662364329061766
	428	+-2.2149742629864368,-0.12017085247835713,-0.90639470386076249,-0.061604798745962586
	429	+-1.8705617160048269,-0.97009423962690389,0.78693100725516285,0.7382342227833768
	430	+-1.3627403250208465,-1.5993605521389507,0.099072747212369749,0.02712525767608559
	431	+-1.030640392073471,-0.066771524650803493,-0.93000773918841784,-0.64955719123131261
	432	+-2.3076072190940269,-1.8465802538072791,-1.0405171167744558,1.115249837316898
	433	+-2.0408071460033672,-0.99041932666206289,-1.8440910158350743,-0.68963321956806656
	434	+0.12262954377503732,0.72075784307166813,-0.19490063931738932,-0.88046612209096931
	435	+2.2322157334673252,-0.38698717009450423,-0.61905373107964679,-0.60949578393838855
	436	+1.0930695644460728,-0.97826728985908884,0.6174255055726825,-1.9176414338118219
	437	+1.5342353453344599,1.4064993266017842,0.0088111220630118781,-0.10763917971371917
	438	+0.46697918901238578,0.77236590636199931,-1.0886165642380332,-0.58309933156259974
	439	+1.9584957520161956,0.50649341643754564,0.87505617427194893,1.3943450115658222
	440	+0.7551347678042839,0.77878763765793768,0.29480273573321292,1.5024615901662601
	441	+2.8889709770802559,2.0337082838393785,0.58307588128426469,1.7298815843397837
	442	+2.8881425122365245,1.9850916724627869,-1.2540290817900386,-0.16129698738016129
	443	+3.1355786673800887,0.072827961117715834,1.4127892140350378,1.9542215428083032
	444	+0.45020671920302502,-0.41793293936531062,0.49511190048830406,0.55135656875061578
	445	+0.88396841500412782,0.74179677170785985,0.32882919631921353,0.73973586826694615
	446	+-0.2891448557503502,-1.8582380860065468,0.026228721661787968,1.2842926417285601
	447	+0.46630945913985511,-2.0477372329165773,0.09937983827136429,1.2710864443045862
	448	+0.26893808657274731,0.48465316921015145,-1.3813667545182404,0.21112937307631274
	449	+0.71972456493554327,-1.0267055295047169,1.0456436212334572,0.26598528372675262
	450	+0.79898804531542567,-0.55495693598509066,0.61416974961932524,-0.33795604703232829
	451	+-0.024520288429152104,1.379897478112593,0.2508957546719906,0.50068887325012046
	452	+1.0313224910030709,2.1511513317017519,1.1781156226039251,1.6298503463317626
	453	+2.4231073958354226,1.6835039577261341,1.5276851536966172,0.71109072906751769
	454	+2.4048770973375575,2.0699391927097262,1.995939074991258,0.84621884995543439
	455	+1.5394615197459136,0.8596492905990667,0.87684738071110058,-0.25735111611159378
	456	+2.4469984057399179,-0.1556941808441219,-0.40529790007463617,0.47511552724282746
	457	+1.7958710248819589,0.98080970166278758,0.46072627059249288,0.059193082509581496
	458	+1.066995095981605,0.46767928781438134,1.3683265202810677,1.154990180564907
	459	+0.33698010610804829,-0.78754786855862824,-0.6573019669668454,1.1151257588578918
	460	+0.075664429244405695,-0.96008271884512697,0.31966111777062156,-0.19900220695475812
	461	+0.93800190642542869,0.45294242607975205,1.0629710252194076,1.2807723941040479
	462	+0.66624020934560479,-0.60423054815289379,-0.34314350923157821,0.80812058328873992
	463	+0.085236098732876298,-0.020130025179185385,0.23666589405608307,0.23099169714481305
	464	+-0.27751045593569368,0.90124638452806161,0.45205433995447519,1.2354020394131737
	465	+-0.22692411618726208,1.7042643834956421,-0.34794129278592084,-0.21707258495855108
	466	+-0.99630902064865212,0.081025620858657055,-1.3362424816686826,0.23188388176347435
	467	+0.62386579129709296,0.90242005313767504,-0.89056527816048292,0.61257305185803845
	468	+1.6353227387195313,1.7212205473956887,1.2231659289212038,-0.48379677728620396
	469	+0.85121105523030116,0.63605306644505277,0.44346847954631496,0.39054399019065905
	470	+0.74997174298525837,1.2822024634748934,0.87098641162420587,1.8024234940770103
	471	+1.2956627809295838,0.67701190619187912,1.3523432435126019,0.19835760006464698
	472	+1.4312285967702854,1.1340430403076316,2.319151685720878,0.27090988849828812
	473	+1.5308324013190528,2.3927628444628031,0.97395508071253034,-0.96229607664353323
	474	+2.3145169448902072,2.6567466855159063,2.5799592003453116,1.4323625974549361
	475	+1.1307587060945528,1.9140165783309289,1.6746946146219903,1.4904586386176248
	476	+0.59298153706002021,1.0759653799007973,0.46206011492550292,2.96236656244358
	477	+2.2892187446222998,1.98976246235351,1.1162363055607782,1.3145242616650019
	478	+3.2826388981836727,1.902731697883242,2.1089609468209476,2.2076598072419795
	479	+3.19141695561011,1.7020633755111498,2.493900718494757,2.9513243165978853
	480	+2.0434854327936716,0.89463603560453542,0.59570361438236552,0.26131571233664719
	481	+1.5856830479545143,0.59796942456138935,3.1029817926011214,2.4726218996249401
	482	+1.5975066562974576,-0.16883280796552058,2.4490132072662414,2.8018714803818603
	483	+1.847857007561462,1.0982525690194862,1.2424093015023561,2.0958358813948377
	484	+1.6596621627192849,0.78560531965148084,1.5213294171814937,1.8597658456549777
	485	+0.53347815100852836,1.263594086562672,0.032745701040616249,-0.10077080028737351
	486	+1.59529918167831,1.0663673283844257,1.2450628062608917,2.1516084895540986
	487	+1.4285576097191073,0.52952433766768747,-0.26773001202134528,2.1419848992858421
	488	+1.2889597290617565,2.1818085869558352,2.1287740153992232,1.4302041649732773
	489	+1.6158430486158459,1.3286964275722142,1.6899064420168974,0.71092838431923611
	490	+0.32407765047328774,-0.52861146246564483,-0.093992394743587004,-1.655999564143904
	491	+-0.58999704004187414,-0.18905813776736027,-0.95800068559572338,-0.41949661433576446
	492	+-0.013724993968637106,-0.9279153164632219,-1.136695868577634,-1.7211311406612058
	493	+0.26767496461968421,-1.1848742291232388,0.52027852305627298,0.011838892177579163
	494	+0.027272355923712868,-0.54591260867437241,2.0334316615099266,-1.3427323717041013
	495	+0.91464609161530752,0.13760948700872122,1.0220970462251651,-2.4823688179179193
	496	+1.6132064932570682,0.94853129158558347,1.6092608782856559,-1.5474630270363394
	497	+1.1389794121042494,1.4290831493016818,2.1916193773148018,-0.92895127970079594
	498	+2.7008076915658386,2.6073857550276518,1.0534599546855874,-0.033182324100658744
	499	+3.1107185977352327,2.4573185616285209,3.0105945947411561,-0.010244852337453758
	500	+3.1035767656940032,2.6703051279992804,4.1647118398764311,-0.032709300488798609
	501	+1.5686917064536527,0.76890387374517188,1.6514681449041948,1.304659393948481
	502	+3.6277942005783146,0.90535684524220439,1.8604538688862486,-0.59172692217331901
	503	+3.4141818782791278,2.1220379803446585,3.108546771292767,1.3450899993484728
	504	+2.5160914905614216,0.64911140895346831,2.0175291310367309,3.0639087769296678
	505	+1.494858854814026,1.9409323608535809,1.6805261102478011,2.0566745422982322
	506	+1.7696181967173923,3.0974905853889787,2.6784701043043357,2.6957644063547779
	507	+0.86465938757187366,0.50172562072827831,0.74516561512437174,2.0062023570581284
	508	+1.0965712624244406,0.81056058352043592,0.44511173047667696,0.90992558995707795
	509	+0.20945863814767274,-1.1168036045437417,0.56453881980408949,-0.056239380996922272
	510	+0.1742916497132842,0.15277215483301071,0.50407877753576791,-0.46000808253336622
	511	+2.182759630373543,0.83963906972097768,1.9226883557993553,-0.69192678018360998
	512	+-0.116175565489822,-0.27827317233528726,-0.092212674752559565,0.37350328042429021
	513	+-0.76740290564844338,-0.085289376358221702,-0.37862808618004828,1.5356785782978393
	514	+-0.64150869453373227,0.93497409597565173,0.42954966465276484,1.150840835246294
	515	+-0.26146489755302021,1.1722929665947834,0.1414532275889297,0.38078593396849969
	516	+-0.97409925842975942,0.50042720923219641,0.28703641397630142,-0.19013361506741955
	517	+-2.5695394564041965,0.25264054186484974,-0.30546556670570602,-1.0636411437217281
	518	+-2.3104251280381973,0.061567454899765284,1.0785355438898119,-0.73433822528629444
	519	+-2.1303659740035128,0.23508402960099256,-0.77368401386377916,0.064185939496955058
	520	+-1.9440369940812858,0.98894983571050687,0.61699297079913173,0.7999332850822638
	521	+-1.9118412146490265,-0.42948518171637162,0.034750658892359607,-0.87642670395551048
	522	+-1.4390434861264765,0.5607677467581863,-1.0506044753114112,0.57291001785259354
	523	+-4.4839229040202406,1.7785672197637954,0.47072044177172889,0.51124494482013938
	524	+-1.4372107090854578,0.14858374659530971,-1.7311657874635045,0.51243900176764512
	525	+-0.037503106251830509,0.28139487447269118,-0.61025499963759788,-0.36122155775693654
	526	+-0.14890304586581268,-1.1232083071192225,-2.3822703866505046,-0.648513761127263
	527	+-0.63449097873516114,0.51770426070681541,-0.79095313936493561,0.62378082932180745
	528	+-0.44009476588017432,-0.39356449083555067,-1.3006783237971011,-1.3219607452430218
	529	+-2.0321407934892823,0.16507972857826508,-0.83136455315342594,0.25890689164652536
	530	+-0.72588424200021195,-1.8675374782295477,-2.0937386286005761,-0.7110492525062736
	531	+-0.57080229142453109,-1.3806373134496872,-0.13465091855292755,2.369496713153028
	532	+0.99140414315159275,-0.3740788416454674,-0.75855547634596909,2.0205478343197045
	533	+2.5009301039755991,0.29114132946280818,-0.035655097643818134,1.0277287691521177
	534	+2.0395112235002215,0.6960134876794245,0.34231976244161011,0.64428668427867719
	535	+0.32411849258175551,-0.81309253801147718,0.45703598667509282,1.1636074300035304
	536	+1.8751573360860605,0.8624188999512965,-0.82598164424244169,0.39131866622578293
	537	+1.4927052560561846,-0.46893430686804249,0.89642376436118743,0.26689673597527647
	538	+1.0518070530010504,0.7432182919229775,-1.2170496880073047,1.7530487909255621
	539	+0.4467270249187556,-0.3887508415919782,-0.63984071776694162,1.1694967391642466
	540	+2.2041076834817654,1.3573231575358449,1.6392645358482421,-0.21098133203620562
	541	+0.44380354021858881,0.43661659323843283,2.2055365419902593,0.61074023231525931
	542	+0.52266530479899398,0.11649563644543937,0.93040464039710069,1.175991729927544
	543	+0.70045517667154455,0.90722247279548007,-0.99529181099040853,0.84514717338953627
	544	+0.53166279133621541,0.76260113429937526,0.87465819238991371,1.1624631325417671
	545	+-0.19739857108380321,-0.63950427041380786,-0.21016956960901512,-1.9628158194398613
	546	+-0.56953032508640578,-0.078416570048806158,-1.8141696775506269,-0.55383681789799621
	547	+0.41726796323704612,-1.6717227684955385,-1.339892877995811,-0.57469372823056664
	548	+-0.037415658729536061,-0.75178931505385072,-0.44718591313068179,-0.58000890503216063
	549	+-0.040536832446105925,1.0676624379363657,0.41621481951782302,0.61357858818352429
	550	+-0.14891925465606248,0.97579019491866015,0.81057722130138232,0.66821146468419279
	551	+-0.82989383062733835,-0.81649642765389996,0.55831353568525743,2.0790842973077601
	552	+-0.47423357067584582,-1.1357866137297785,1.0940799818827251,1.6046444349425812
	553	+-0.86409099810851475,0.84663866845195435,-0.23232988153862211,0.83413421409417454
	554	+1.279940380986003,-0.45629880327607375,0.76052851754618345,1.3270470006089568
	555	+-1.211404754824903,-0.19216820803075024,-0.071974828470961594,0.75457251619645227
	556	+-1.0587920221587517,0.10016804604166812,-0.40742950233013009,0.7468149769432687
	557	+-1.0609279225017398,0.4801159500854158,-2.2645835195223873,0.62094661778905835
	558	+0.20073723428091106,0.33687894225761733,-0.31495597230711625,0.12072335702964199
	559	+0.95878425657839228,1.2846171195934291,-0.992762594657988,-0.66163205165931904
	560	+0.87937963380452266,2.2089724186510598,0.27033114868961128,0.4975510205555751
	561	+2.1812309669361651,2.1633441085395262,0.4162336640987826,0.45244970793967781
	562	+1.6045982849655369,-0.50855546272319008,0.12296422147510194,-0.30296180104216264
	563	+1.5303257584067442,-1.2280848192673282,1.377111432009801,-0.87801307741265244
	564	+1.4317994731801842,-1.1281453742134251,-1.3487458408536339,-0.43286066403947027
	565	+1.0046369861122901,-0.16579540822252692,-1.3516838297006168,-0.48110904071694349
	566	+0.37827957698437198,0.30653333068141864,-0.59246847411191472,-0.44540683539248821
	567	+-0.38629392323312173,-0.14282475849094506,-0.36629600960504705,-0.81734928195886203
	568	+-0.024623978847900463,-0.71625840263505758,-1.6161949685383932,0.66145212707425993
	569	+-1.2570389809642017,-0.75605353140219211,0.62390243754141916,-0.0017270200443073591
	570	+0.023453479836154312,-0.5786065219679366,0.70064511459775747,-0.15552611340064232
	571	+-1.1178299721727856,0.62342483007992877,0.94975793107373052,-0.97006977061782451
	572	+-0.46300654144691206,-0.043316155251798771,1.8413421018730971,-1.2503656318144474
	573	+1.3509143741225567,0.28575664468779832,1.9195061666770412,1.1121051834687568
	574	+1.0928936019563058,0.7739220762660538,1.482811859335222,0.034230672163925502
	575	+1.272855452897516,0.52910179469666296,1.714678658281708,0.55265570749616799
	576	+1.4884560546122867,0.31289875535550632,2.671820898110453,1.8708142619304939
	577	+2.4768560761642457,0.95221913602499453,1.9613524601215024,2.0302414082485907
	578	+2.1024199056315256,2.7414175540167629,2.0547719030092457,0.13693283791344557
	579	+1.0541724558925631,1.1333261134792019,1.6618716559866491,0.7858044083268334
	580	+1.9946674210762354,2.3194913861282274,0.21563384963430399,1.2534839968738036
	581	+0.15400586410180339,0.18693714108046033,-0.67097468986356468,1.2604489823040936
	582	+0.69872719475637468,1.7960733987770294,1.4745128213738814,-0.018236882704813162
	583	+1.517091735419408,1.5686335867346344,1.0202508488868014,-0.072783990652698694
	584	+0.022573163386987227,0.43754907029217005,-0.048791724472689646,0.059563735445426286
	585	+1.1190804780812105,-0.29387474456838747,0.79354728128712948,0.74807291609870341
	586	+1.6067467907187938,1.4677774204279803,0.94578266887984175,-0.22733611014142752
	587	+1.2091393811734772,-1.8003767251576011,1.4121011179721266,0.75534353962346268
	588	+0.064529784109768507,0.87293429602929218,2.4395887895784725,2.318654817767217
	589	+0.60500290784458066,0.33622531786401988,-0.1847671403724489,0.0078979466518380725
	590	+1.181635945928436,1.2992448365270268,0.63038875299896757,0.37699177502772813
	591	+3.1698486592180237,1.4766318036111998,0.73068650330282048,-1.0197082441395831
	592	+2.4655803678302783,-1.191441162573442,0.0082995472885424304,0.62316811350668633
	593	+0.98787837974250492,-0.18205377885710497,0.060675853721715967,1.2256253053009396
	594	+1.8849252132837404,0.26223378802668107,1.5463287779743269,1.6839193239502963
	595	+3.2883107977452526,-0.11291298270014999,1.5986866443037737,1.8734024264434515
	596	+3.2042899282164292,0.27523787704649844,0.59838088655954813,1.5379921731163551
	597	+2.3128935352422166,0.043485580229011611,1.9028027127690417,1.6979381183510927
	598	+3.0952568097929971,0.4013738260393534,2.1610373561380047,1.4511000318927818
	599	+1.3661572826308546,1.1550175456348226,0.44451752589718163,2.3883785121320593
	600	+2.2449131966397768,1.512361575733816,1.8640810491033861,1.7407421272302481
	601	+2.6546535801240236,1.7877634131749964,1.0890751003009973,1.6216527116903838
	602	+0.89827835933087363,2.7187512191696008,-0.13177494110979637,0.10358361043499587
	603	+2.1749964690430041,1.942183566698453,1.1642716644522988,2.2188731463052727
	604	+4.4818935560236799,0.83541217298350923,2.044357409999622,1.8399663082596511
	605	+3.757253968191375,1.1583744943751402,1.520429162321471,0.73144955802576073
	606	+3.4277580292624279,0.83294081868189451,1.2578074117191176,0.41508393590773007
	607	+3.4949393938235023,0.8406266548692134,-0.47282457290605007,0.11991238896183254
	608	+2.520715749114415,-0.53632614475488893,1.9724742891220266,0.69894768442382116
	609	+2.3516953304644588,0.70725146752962165,0.39253881971477056,1.8443811461599029
	610	+4.031427518740232,1.258172313408052,1.9092079962673822,1.1503874491885193
	611	+3.5518653962788047,0.55781643391271474,2.7314202542175079,0.63790771297599669
	612	+2.5216211042937502,1.7540774685086316,2.5270102512283739,1.5109771562305876
	613	+4.5864818679832471,0.95881540044064173,0.45464973239763529,1.4861309643711738
	614	+0.87926287774322898,0.01739557976678463,0.98708804395929384,1.2429097744044195
	615	+3.2154959036281054,0.54145411710028446,0.90795825526858698,0.43706259091334138
	616	+1.6235582481139104,0.26304624480148731,1.4460230508718825,0.61038232388994573
	617	+1.0168978246127429,0.91450224983733253,0.53426166371119066,1.1279127866670673
	618	+2.1101580294836753,0.8454742669534191,0.44516672128629631,1.3805417948177841
	619	+1.6076144091537166,-1.3578061471452854,0.12211109875148995,2.1083598819480187
	620	+-0.013097820367761415,1.2265052822206637,-0.29440827367595424,0.36498082558367551
	621	+1.6901464496263097,0.18727705069347622,1.5156126180626233,1.2559098139956872
	622	+0.37714970890385058,-0.44772405366840784,0.83432119734716959,0.18948430686252993
	623	+1.7099169872094744,0.84912590558216128,0.0079411311255738193,-0.34581026453987396
	624	+1.2391292858597138,0.028911032080127963,0.6985369438244684,1.2665798353953139
	625	+1.7060197247596633,-0.24575467617012969,-0.12719064116374157,1.4331353163379263
	626	+2.3126715100221635,0.44426525363915814,2.2614786623158158,0.74793096582016272
	627	+1.3299251213670311,1.4555800029357773,0.57895623549833974,0.36754091489480656
	628	+2.4351394106653093,0.79965475325331559,0.7703753365414987,0.91794707437881629
	629	+1.7443749910998063,1.3320145261835079,1.7731387091958295,3.1421876812032883
	630	+1.1004209557671554,3.4485179535724075,2.1880539449653926,1.8384117412007863
	631	+0.55729620137426905,3.3770812247153015,1.2129685311523544,2.0199356003838291
	632	+0.63849442837829185,1.2743671854294814,0.26173666145014529,0.7572551655892753
	633	+1.8610598706296964,1.5019170066059933,0.09218404933226465,-0.75190392144971252
	634	+1.6749477144834293,2.0647855605557179,-1.2593413862413685,-1.0614884758621186
	635	+1.2929782858162135,2.582863062054221,1.8191967110817786,-0.98817685689438051
	636	+2.0510577265939824,2.3362477428550514,0.96892166846402938,-0.40367986849269855
	637	+1.1922718190904693,1.0441900460778619,0.230791231490593,0.70058146869302573
	638	+1.6332590632098909,1.5681804073055612,0.5560536927145534,0.90650644191283936
	639	+1.4797344491232458,2.3460392674594801,-0.10208239174092892,1.4459375128167304
	640	+1.3418005908691812,1.4201951494633365,1.2101702051028829,-0.11694395812835223
	641	+1.5437656377473095,0.58003925480222396,1.6602709852807973,0.82068514240478574
	642	+1.2038280798982803,1.3315503512807063,1.2729754754659546,-0.5681141488417516
	643	+-0.00023101370743772165,-0.3291728590979881,0.52527687062718931,0.53136808185553774
	644	+-0.42789468967611921,-0.53718663612296125,1.6465650476797444,-1.5350234692095386
	645	+-1.0739651057608794,-0.034156583899440096,1.541332481869724,-0.83452762666093827
	646	+-1.0151874600497683,0.12827803260851917,1.2223227560528889,-2.2382071412564302
	647	+0.36597625469458572,1.1638837004613811,1.7413223502862816,-0.54833716281293632
	648	+0.39667950285619447,0.86120853438856715,1.9892056234882989,0.13302658916121646
	649	+1.1340415396967725,1.2738292692830209,0.35493992501585181,-1.4042434405211073
	650	+-0.78237104872306995,0.73939418580437688,0.51338506223572611,0.70859075185954812
	651	+-0.6874444125486816,0.14966328254648464,0.12366038721073908,-0.18488716616873047
	652	+0.67328300391849771,-0.089785609599248084,0.52746468392039603,-0.68022543370545341
	653	+0.46085864754306305,0.18765761102440806,-0.69514056927929335,-1.2937993949232487
	654	+1.174106333984767,1.1972734329214836,0.70868176749869916,-0.58572935677123361
	655	+0.9304790535541273,0.96326844185102112,-0.27940959610166594,-1.5770300074567511
	656	+0.82686047488976677,4.4539490319261947,-1.0613482497833102,-1.9339278579236847
	657	+0.28329843111440378,1.9838249384163957,0.73046831794115297,1.1848403707845938
	658	+1.0027579407417013,1.2741480811406005,0.86356089187925211,0.13416926634721654
	659	+1.6008401745643508,0.11475585862208781,1.137953834983539,1.5410072973617259
	660	+0.84250491650520376,1.1026344622308726,-0.16365352990372739,1.4650846187536879
	661	+-0.069507801274127812,0.05401876018640106,0.10419474219656455,0.20270324579146826
	662	+-0.69592874276910177,1.3499100474961379,0.15724825893455852,0.48816627245571564
	663	+-1.2071314351918896,0.48998203416160224,1.6333712246837591,0.90911116547685777
	664	+-0.29774205207138793,1.698981581648255,1.0750690632960722,2.2355788775304952
	665	+-0.83401799356252693,2.2350182067336619,1.9303849730290064,1.1284888987378494
	666	+1.4822848058107601,2.0556930661665147,-0.014993203757156293,2.6620138804782867
	667	+0.19978285631941672,1.7725738396807944,0.3245861647129834,2.4183049371581045
	668	+-0.14292545236093301,0.77125141143225029,-1.3343206048753908,1.8760343949018174
	669	+-0.86765124233524293,1.1450820068929026,0.70017817123765691,1.5607034027226285
	670	+-2.0832466014964841,1.1717290050924509,-0.012536169980744111,0.14734622879956516
	671	+-1.6043023118800512,0.14122226381535419,-1.7297883828402774,0.95344321074378036
	672	+-1.2920561871823406,-1.1804627760352497,-0.66213795471161596,0.012821552876177866
	673	+-2.3793454809554575,0.22812900910520562,0.19431953539511015,1.5456065569515751
	674	+-1.9677789257483727,0.95806413332989715,-1.3989792992399923,0.62703718766955485
	675	+0.091223585025517639,1.1367098416601908,0.031701154290105227,-0.081413167293686861
	676	+-0.096402885418270273,0.85240216940854385,1.0556509939299823,1.0034832419216269
	677	+2.2524771323717223,0.58129181656528284,-1.7458544174308508,0.67841163991296505
	678	+1.858591373561715,0.50461114606633672,-1.8192994285084914,-0.33600380014040676
	679	+0.51846832023847189,2.0440285130326044,0.97582062662910485,0.92599907746240817
	680	+-0.56362758146175751,1.0319960157266881,0.85794092333541006,1.4244928609292482
	681	+0.81921097739965099,0.67024850434246419,0.52089135428152011,1.3495068891094464
	682	+1.7033775179016377,1.7782485542158029,1.8142769877813252,2.0248042831128568
	683	+2.6136135910794565,1.8688745550226544,2.1154739959177467,1.1130003168295528
	684	+1.6420850973362857,-0.17941599606827374,-0.59884902074299617,0.8034333543370904
	685	+2.8274110614786707,-0.67267216933391427,0.11731002310912897,2.5112770870040797
	686	+1.6042422002047019,-1.1246257094154903,-0.031607328457300299,-1.5078024728067396
	687	+1.9180069318852246,-1.3123139501153012,-0.10394884235174781,0.39264761688412192
	688	+0.92563281482782533,-0.55947825415093511,-0.45214903100133325,-0.11618919408404052
	689	+1.258488529163702,-1.5440996946552312,0.33899846634039105,0.33124441108353081
	690	+1.5782551625325878,-0.49023030182179966,1.1510865626862896,-0.95697967014870944
	691	+0.72852270996916491,0.24759718331014419,-0.59350155266509375,-2.274043908195698
	692	+-0.58632873870338509,-1.0385625326009458,-0.30835752672734895,-1.9133533926156998
	693	+-0.63486549757031874,-0.26904027228884642,-0.5778544842685619,-1.9193541677440722
	694	+0.35587517562623588,0.33930286268597798,-1.2212850808967259,-1.2190071275004288
	695	+0.68468962471920047,-0.25081247727967093,-0.47141715434012871,-0.82969193180815592
	696	+0.30824612033312337,0.91673389532037364,-0.99521859334873142,-0.007548980188625265
	697	+0.83565667130427945,1.0761663702023241,-0.91488064703133265,1.300061145063949
	698	+0.65203459826531851,2.9995663296599471,-1.007306358244926,0.46458973661950803
	699	+0.72554410215594123,1.2978355078456683,0.59547311339337983,0.50769320687687314
	700	+2.3454935261181347,1.1097777769103236,-0.62937458189520401,-1.4248543737417572
	701	+0.7431650678572439,-0.79892086634762349,-0.2534363860232916,-0.97390268071166219
	702	+1.9333904331359959,-0.12012269744972995,-0.81541775775735692,-0.0043743058855767458
	703	+2.9383577956122369,0.83680238962809406,-0.56079239939390835,-0.078573365779058935
	704	+2.2489327283538625,1.4718333283241787,1.741720627681925,0.11432118557699855
	705	+-0.35736632885944353,2.2171631286214439,0.50900093142772573,0.18171610860699
	706	+1.2626620989223709,2.190936811206631,1.2074294620802615,0.43666829618353964
	707	+0.24149035480015091,0.94454149634747042,-0.16339238067611861,-1.3385000473328514
	708	+0.94826748863830335,1.2007868766843319,1.1294208856013461,-0.8873547412475713
	709	+1.0112093450543989,2.7340838662237075,1.5897412832366324,1.650681231360259
	710	+0.77798261953310788,2.9650729637209956,1.4651654890506893,1.3764199891009092
	711	+0.59468310624644882,2.1899687683508988,0.71348218030894128,-0.047750896623645067
	712	+0.35351091936771539,1.2677305491122599,0.75227570208061612,-0.28072285490519316
	713	+-2.4640683797742144,-0.95510378464504431,-0.0067095379916333187,-0.52145925149309069
	714	+-0.33551715112894953,1.5915749339151359,-0.81784676786667099,-2.1705577173759729
	715	+0.051249698865300175,0.63386720321949608,-0.46319863266775813,-2.0138843079633424
	716	+0.48327780253202496,0.15085077618299736,-0.79011604198311614,-1.6427616916225503
	717	+1.5247634794815483,-0.52783518742899649,0.14725478036718792,-0.69779000183391737
	718	+0.010517185754752134,-0.12157337089778193,-1.3129369155794266,-1.4518560789195354
	719	+-0.57589854469465196,0.71961342738919687,1.4677303528937444,-1.0258315466245369
	720	+-0.32756723184135783,-1.6963424307043429,0.9593161144208443,0.22163605566577105
	721	+1.437367069324226,-0.9438373330479084,0.82760988356986531,1.2294600814636478
	722	+1.2620339389946889,-0.929138974435611,0.14387296306431696,1.2540112516436899
	723	+0.73222770045392371,-0.66563364412641535,-1.1001920266549485,0.98625241603022951
	724	+0.48494484617681766,-0.31895167437117244,0.53183416861839627,0.30794718371364671
	725	+-0.2669619856092218,-0.36742590078705517,-0.48150451003355343,-1.1575983881651621
	726	+-0.77375119064031006,-1.7878929717004088,-0.41411912774652732,0.3156016122348132
	727	+0.004417218411237489,0.65316363787173903,-0.41896743814361365,0.49504870455720612
	728	+-1.9215827111452071,-2.3649300450843818,0.087317064662354921,2.4864149925595882
	729	+0.60256355788160665,-0.084157336725636633,0.62569603496611526,-0.22936116560697672
	730	+0.31787367891040808,-0.29193700555687441,-0.77938008949133597,1.7666477459007663
	731	+0.7858552345843135,-0.27099156048709494,0.76435577821286038,0.54312708548986721
	732	+2.1043351639661969,1.2072233568651545,1.2750056683473818,1.5065862075062832
	733	+1.1016445686181349,0.12149673887899126,1.3069016412328347,1.4733684711408923
	734	+1.0525054329317849,-0.1705553828869476,1.0716885781327603,0.35066081169576724
	735	+0.89855342724207943,0.13262893452872343,0.044895849895008499,0.91927416713207755
	736	+0.079563955313803669,0.48678907478758338,1.719913097462618,0.25719502932228566
	737	+-0.383795801086804,0.1778549790622182,1.4120003211509609,1.2427238794683417
	738	+-0.40850580255990737,0.054245845114535396,1.5646379990208685,1.9988891813346306
	739	+0.073185481606562713,1.2079234579433979,-0.55152887811878715,1.4429056964741815
	740	+0.13141301158461291,2.5613488485048466,0.46041743948682357,0.5862667978658076
	741	+-0.53414991745045859,1.7034990969472004,-0.11301598912773572,0.66599052319632968
	742	+-0.72506513461711886,-0.037931575535407047,-1.1349803242467043,0.80085278680023486
	743	+-1.0389684187001664,2.0671914768007791,0.83704414092230572,-0.22951291005218166
	744	+1.6255116394737845,2.4155085119478268,0.93589721129372383,1.1533151561647468
	745	+0.84790459137123786,0.77100683087440447,-0.54931895539059872,-0.25112053749706553
	746	+0.80083294431482466,0.69346335620761945,-0.086115273969865708,0.020169066972724192
	747	+1.0052993098028542,1.5987104632401505,0.84311329246061528,-0.6938307101104404
	748	+-0.89860946329198332,-0.63074213426367054,-0.41446971834323049,-1.9737640095030589
	749	+-0.079105919590637785,-0.32598547521009869,-0.33896435793195495,-2.1812026532404971
	750	+-2.4113043059233799,0.4755768892972197,-1.8857734763226623,-2.9205656490592031
	751	+-0.19486469138802809,-2.010207019921789,-1.730170817820416,-0.3505542150591312
	752	+-1.4102813898506446,-2.3511305410052463,-1.0670723443819983,-0.95429580079202592
	753	+-1.9000940743280408,-1.9084728647867901,0.85670147965157062,-0.059204288033553265
	754	+-1.560103480632423,-2.0391897659866398,-0.9120213372411784,0.54439730221320981
	755	+-1.3516182646652708,-2.2314052713446184,-2.2666078375205529,-1.081682948641691
	756	+-1.2396428039774268,-1.6410683506449457,-0.10298197125109676,2.3091394674847572
	757	+-1.0691929485807035,-1.2548965462156914,-2.0887860797443274,-1.5190788270972384
	758	+-1.9071395151753232,-1.5930565211234926,0.58368552024224629,2.0264333908704897
	759	+-1.1915343020814364,0.14207675836199229,0.23911300515374384,1.0132465413444836
	760	+-0.1581563746069472,-0.23512721801967643,1.0579188891613971,1.6156846268477567
	761	+-0.42542642002489245,0.35350913487010288,1.3540815749408548,1.8324804020116308
	762	+0.96643533570405915,0.73682246483835523,0.55820373405389856,1.4039810140029902
	763	+0.71314435525785214,0.78624449598323487,1.7024594621788194,3.2135754137129777
	764	+1.7486944094164709,2.5546201924869685,1.4941104743913187,1.9586314836406868
	765	+2.5258548811185175,1.8729170456445523,0.41680996312261176,-0.76790235766851
	766	+2.4117306192762387,0.81114699075494356,1.6738896763710724,-1.0867717930558018
	767	+0.78568715964373459,1.6301198009883844,1.5141181635458709,0.10432218756655287
	768	+0.67558566638680606,0.41095323911010362,3.0250353509425847,0.89375641576557263
	769	+0.8495346952413837,1.025834110858219,1.6853804021685121,0.11745476082932155
	770	+1.6700143002618644,0.13089500070129656,1.0102965699693747,1.2712599803022653
	771	+0.046464929630909202,-0.34782044526082811,1.433117697787389,3.3417808390964026
	772	+0.14531085263372578,0.1178244429196335,0.33222873853151891,2.649254536419662
	773	+-1.0818098897498234,0.37638500791862062,0.12632137480623307,0.07802801024502215
	774	+0.1092603429254112,-1.9851946249150831,-0.10153803455381033,0.19475861754289381
	775	+0.54601734766161558,-1.6250325380872714,0.080936090706364094,0.39564225941391462
	776	+1.2182668283255884,-0.36503496762126636,-1.6905104831831586,-0.29312279021046778
	777	+2.443929702066912,-1.0151328715148353,-2.1206788118244138,-1.6002396873801827
	778	+-0.56470640019256102,-1.6755917222642671,-0.10414143486576266,-1.412794025568789
	779	+-1.3960170293655363,-2.2918085874797804,-1.0548548197999206,-0.47903944562210526
	780	+-0.22397129405116611,-1.0355886680851989,-1.5487151896236035,-1.0111481379574618
	781	+-1.2522382345125176,-0.80206831591425276,0.093671936104406606,-0.74848346520051123
	782	+-2.4047428648983327,-0.34493471707864087,-0.65494632990831658,-1.5166337178314797
	783	+-1.6319170497609807,-0.1729701417635276,-0.89125795587808898,3.0525265351569102
	784	+0.0097590565330780699,-0.3228892840767798,0.3557343766125719,1.8364611091320704
	785	+-0.15677320630874425,-1.558826438641383,-0.94635473875005482,1.3779608424158067
	786	+0.79154461761741901,0.47806159145626292,0.279089907896516,0.82595659287982104
	787	+2.4167106104486678,0.10815683625534411,-1.1761124106518741,0.12059951763166143
	788	+1.5447235014496821,-0.14334005123018434,-0.87063991710105859,0.1003292867626473
	789	+0.6880321414168965,1.5061177321024815,-0.30203509255545663,0.36047158636895382
	790	+-0.90049090935771725,0.089675207381639144,-0.77556214160586912,-0.5371562575113471
	791	+0.63810566558197757,1.1719620861405295,-0.64264127949339933,1.2853977366656784
	792	+1.7528585106760066,2.6919005824138438,-0.29413649030798805,-0.62472200306973757
	793	+1.3259760890368313,1.17139536087871,0.22530514173432631,-0.41791009758271724
	794	+0.17584596343865688,1.6147805402886186,1.4699771933059678,0.89325113411628987
	795	+-0.01694526050628431,-0.25285812190818779,1.1970368232378679,1.6668529608964344
	796	+-1.5951234333210547,0.30518321362977718,-1.1259981558930194,2.2528792016832466
	797	+-0.51524821283517452,0.66754332486626389,0.25716428097865218,1.1513290345603737
	798	+-1.046911282161243,0.56349891857585144,0.39617724005630672,-0.28342666239144065
	799	+0.040996996969365207,1.0661516817103509,-1.6534988814227141,2.0903618539596329
	800	+-0.17204842731084824,-0.36167514358394642,-0.8240629266649222,0.28646027506636196
	801	+0.19407537064750946,1.4875961058373097,0.32654868155480521,-0.65689329949142228
	802	+-0.6062957294650827,1.5171929518033811,1.4843415446425408,0.17083314126500368
	803	+-0.74579429442398382,0.54212086626417832,-1.6821978327296443,0.76361568084990439
	804	+0.7949582275194409,-0.2921037351207012,1.322241895660567,1.1540060766707632
	805	+-0.059519701676650216,-0.30805165963558073,-0.15011115341994269,-0.45291084747269716
	806	+0.57728722145050715,-0.22685056084421529,-1.230229324601722,-2.431488108178681
	807	+-0.43901538835685522,0.13983461246446577,-1.8173302033772083,-1.2116033311509498
	808	+0.20120523611360719,-0.26010865411196038,1.0081433035188159,-0.53120513644057121
	809	+-0.47348298059916349,0.030683997046898837,1.3613383939165753,-0.90789472948977124
	810	+1.2546079002098856,1.9005715183495155,0.77702716247966364,-0.90495109024709208
	811	+0.86158754327852916,1.4750115859590873,0.94001078340078448,0.60980642090198767
	812	+3.3445754346850318,1.4644364905498255,0.91930279384852831,-0.19041045341266771
	813	+0.982589982003645,0.97420849792421171,0.46607217410827906,0.71450934023096768
	814	+-0.50480653276808818,0.72595875798386134,1.0750648368240774,-0.27977930156156283
	815	+0.72880465135077643,0.60870124599116637,-0.25550038698101218,-2.4604914316741118
	816	+0.1516223152483416,0.26888296293801794,0.24434463901234502,-1.468119915058687
	817	+-1.592654164318047,-0.84289867848910194,1.4264946184900451,1.9172588777400965
	818	+0.58792715933993489,0.71409165469281477,0.69344719068079963,0.92878883391596356
	819	+-0.68115419151108414,-0.37657910018379426,1.1257545377004716,-0.076857675925842694
	820	+0.55038568090002804,1.7512969154376579,2.6377165562156888,-1.2036816531515253
	821	+0.34317197311948605,1.4699914550356863,0.84711830717805325,0.6789887606627667
	822	+0.083544666542105683,0.054853547968865435,-1.9540624594866496,0.46199630308973899
	823	+0.38847486443112672,-0.53199293799789604,1.4995124420953923,1.3010037869805511
	824	+1.2191476476677869,0.3964478435284865,-0.71278328452809359,0.51047104236784113
	825	+0.46006936697051826,0.076872800196384566,0.29512996295973093,-0.95533896152100573
	826	+1.6129859779842055,0.40844625553177538,-1.8947959340810845,-2.0419726853149713
	827	+1.1748798944363168,0.49800528660601906,-0.72992205003473043,-0.89157929268717251
	828	+-0.47871194539789841,-0.30620670699636271,-0.22053851714584705,-1.3660606548756968
	829	+-1.9891657468766379,-0.27917226299707365,0.55003581417764102,-0.33681120862614933
	830	+-0.4782955095220468,-0.33162749379563489,0.31533456263364767,-1.3281332860383175
	831	+-2.571712461253072,-1.2651090793453579,0.23935561666592958,-0.32244598906224015
	832	+-0.32531616690707299,1.2781003866312468,-0.35825831068148095,-0.82493362000413861
	833	+1.4247023438946007,1.3612529959770663,-0.87513570933018991,-0.87607810109492501
	834	+0.96881784567665785,-0.53990721643838968,0.23982826798196083,0.0085849453839015877
	835	+-0.20562408127425535,-0.47834035908794648,1.3543635281250914,1.2412859910582195
	836	+-0.84574072531991829,0.86912641446331518,0.20557407495173319,-0.82219921392718875
	837	+0.44449932592010455,0.15033673981600892,1.5722254593862148,-0.41934500094109484
	838	+-0.37200407134962821,0.38734445221311009,0.75783320700409451,-0.26608269285869773
	839	+-0.36133904449673881,0.35389388758352025,2.4346355555361434,2.4781294593469188
	840	+-1.0927163811353455,0.18235696589128481,0.59884567821537016,1.5010979615944966
	841	+-0.25043344489151309,0.12030697112664257,1.4349362230562341,2.6626913206345781
	842	+0.42098404728912836,0.31704335102027192,-1.0453064469813595,0.54352160650852588
	843	+1.9631790274111756,-0.83633998021382006,0.17767050640364496,2.6082608735816599
	844	+-0.13364732059559126,-0.63146030580658064,0.33142641487906732,3.9278393836771075
	845	+0.79843835413539876,0.11925413571274396,0.77812874407399724,1.749929802579179
	846	+0.50521281523798334,-0.58958737088461377,0.54588534266270483,-0.35771966666813793
	847	+-0.59636505425639641,0.78812763064147751,0.77483366347551297,1.9744548839266756
	848	+0.080135299945991945,1.9302003246743227,0.64159776416448122,-0.92909879639458992
	849	+-0.21368476156578622,1.7066586168059241,1.2747377077876316,0.20267587785203747
	850	+-1.698715640269419,-0.23668630414789082,0.22901636752024418,-0.052177166569308042
	851	+-0.48885888081705514,0.072790696520421749,1.4619428814873014,1.3823624802617978
	852	+-0.041348225974567498,0.52421494594937013,0.47624968046456223,0.37288944486438114
	853	+0.86439794116352353,0.58384896014675447,-0.51488174827257649,0.16417131625392012
	854	+0.57317376599777681,-0.87727897474365713,-0.58697902191893037,-2.0792057626975722
	855	+-1.5985229701244692,-0.54132493525288172,-1.4935774404646858,-0.76656921318024274
	856	+-0.060950550526352343,-0.64812925298069668,-1.7565432671729293,-0.77793075304053194
	857	+0.55049459877083518,-0.86540729279938566,-0.34955407846518838,-1.9997080634225832
	858	+-0.42432222985236012,0.50654126895506768,-1.7382625001865295,-0.21983724134587912
	859	+-1.3600787664979304,0.32187812785642789,1.0281927576070224,0.08259718712136277
	860	+1.0468608569098319,0.0097259526325687018,0.55900903415479974,1.6184823796008747
	861	+0.70407538939502268,-0.064466377505462968,0.73636374127555604,1.7049864125918077
	862	+0.6445171205875706,0.66547988815381909,0.046060274107598609,-0.94703589494430185
	863	+-0.23212851156989955,-0.53269865690840335,0.77431476329812943,-0.4587488445043883
	864	+-1.0681767841777747,0.20553771636346524,1.197226807136526,-0.24826107092598149
	865	+-0.035242227437531415,-0.10111460796994282,-0.17611059727567491,-1.9577479954159895
	866	+0.8023154815218736,-0.23868313813259451,0.26585845697814092,1.0669321983867968
	867	+-0.48245690864338997,-1.534012908894272,0.066445427099870724,0.58961430483573163
	868	+-0.34863772299019524,0.54693773040562665,-0.0073802206511290325,-0.021170505915741045
	869	+-0.95294893959072013,2.1855767691061736,0.66559288293050911,0.5539815049719865
	870	+1.2098625186308261,2.3377836337283124,0.7307986514604099,0.45762893633619123
	871	+2.3758016620373157,1.8342375406489884,0.57176708843938562,1.0474576230381833
	872	+-0.238276368271511,2.3041244890933479,0.5722617241220207,1.1979339790905388
	873	+-0.56694640958474174,0.010704130728425465,0.11525413159876396,1.1016655377759248
	874	+-1.2831878415840405,-0.49561294359857339,0.24053871757533174,0.75331361716511003
	875	+-2.0660487491791901,-0.56256978007233205,0.53006503827276075,1.4187858151620762
	876	+0.39721251071376495,-1.1019283240211928,-0.33203166290429076,-0.43132484749405131
	877	+0.091904634059225609,1.6494803074973041,0.35318037394707569,0.64949785964049811
	878	+0.41300958640002794,0.25615780202393995,0.16516831947027047,0.48414422397684753
	879	+-0.049563231887258918,-1.0768612483843298,0.25765536025652408,-0.26343602089376189
	880	+-1.8144252134291505,-2.2516435996773483,-0.64241944262470863,-0.90708967211033231
	881	+-0.44446313730898235,-0.50152870305508856,-0.086799534709683934,-2.1123524995651888
	882	+0.33326602645070391,-1.5265294763486534,0.78400387518324188,-1.4943377794578363
	883	+0.037408252240039103,-0.76194831294077425,-1.0201656321581312,-1.1349209540035547
	884	+0.24926408013856521,-1.5762087968544187,-3.7370949979796944,-1.5254636360220686
	885	+0.15178058321540641,-0.41733779915458458,1.306602760837601,-1.1534800068737669
	886	+1.2060115093056276,1.1701637237479845,1.0602174741016335,-1.2871908043495564
	887	+2.4915327448827846,1.1394173886050574,-0.0096815276552457696,-0.20459487661301645
	888	+0.70096830671410915,1.2697530234000698,-0.27306298398626533,1.4255955057173786
	889	+-0.28042367754408937,0.58458445442527718,1.2987454162089673,0.87344002537795129
	890	+0.11493539780965681,0.83192921983681145,1.3510853700233563,1.2918809630124144
	891	+-0.37648898490238919,-0.041322535799409588,2.1221449271456692,0.94497836436659788
	892	+-1.7148365881968299,-0.58222002372537751,1.047402047464832,0.5869277422973499
	893	+-1.2208450463126117,-0.66074818098076238,-0.3309363532482581,-1.0687362088518693
	894	+-1.0584070834178605,0.36442809533528192,0.32986088129676328,0.083513242051953374
	895	+-0.82069825835610799,0.92259634920204836,1.2707987798249214,1.3766239559377913
	896	+-0.73640086928284809,1.6016793787965082,0.066463091538726871,3.2573037542822334
	897	+0.3611120694423835,0.52861284041017964,0.40473157023212453,1.5198820696397972
	898	+0.25143623699340928,1.9346034137211721,1.7416995275781921,-0.74454308819541559
	899	+1.022587832915514,2.3986644204898289,0.70867320454755067,-0.65865736832556276
	900	+1.6957613299613685,1.5385286207010127,-1.1002382264856503,0.53340607303133569
	901	+1.5799604159555414,2.6575701854660574,0.70934878936477763,0.7111670224194091
	902	+0.35182726866371516,0.46401747850052466,-0.31869287960426462,0.29914250939015741
	903	+-0.5305850523535045,1.8939281886805777,0.54745014319581009,1.5384654909969038
	904	+0.35435157387071858,0.76758439796393452,-0.60351662845498077,0.63030879412005691
	905	+-0.22920198174686529,1.9529484247240356,-1.1864132335145146,1.0827633368166911
	906	+2.5288760157271941,0.92624824266137706,-1.8064591586734768,0.47884947068108935
	907	+2.6796234698859269,1.3833831732785344,-1.5156349956836608,0.97222622188154162
	908	+2.709223094384047,1.8595191643727045,-0.65429118133797981,0.34198264327971845
	909	+1.6974045366038566,0.68802707487239367,1.5504903173459912,0.46229272448945097
	910	+1.8733991787139801,-0.11103488434473019,0.84211232664374136,-0.25445360910063064
	911	+-0.52804101814885196,-0.43551765425797767,0.59958733641019046,-0.067931641932996278
	912	+-2.3582331869609381,-1.5767489512091672,-1.493658583953599,0.40503983204205596
	913	+-1.7629758619137332,-0.13055845975258851,0.75871796147711557,-0.43766167537325329
	914	+-0.53696005983312856,-0.21510206741770038,0.28911827090272973,0.4737774136360241
	915	+-0.42338523643946757,-2.2659437561155009,1.4174663246816137,1.0882276303103338
	916	+-1.5407743081520602,-1.3189156870644287,-1.886502217390768,0.031885666572077753
	917	+1.0968307114015319,0.48878082119494937,1.0821222806263029,1.6355952705022121
	918	+0.73144978345848388,-1.0176814887294912,0.12791996071555084,-0.27832878428838193
	919	+0.3856341242903748,-0.50046189957342546,0.48638279830577302,0.46158759346692813
	920	+0.047002689841897649,-0.53182528036525589,-0.51232775600060587,-0.38110823257159998
	921	+1.1297470297890879,-0.49091628581432234,0.51359117026832901,0.59404036491779399
	922	+-0.61746425169894781,-1.0405951489261951,1.1095568311975672,0.65464862184302952
	923	+0.0029469832946486252,-1.1096865091242236,-0.53690742342144082,-1.321802561021348
	924	+0.11238695752219088,-2.5676556630757155,0.48860516931506459,-0.98091243790529781
	925	+0.016898553932236632,-0.54415684456203628,2.0826051725362493,0.51526138070000627
	926	+1.1997452597404417,-0.090309056066751381,2.7064190148853915,-0.13147018237694588
	927	+1.3030545196875818,2.1982727279370922,2.4752970925369771,1.1780175480601598
	928	+1.803380033969761,2.2750675152671578,2.7680930210088248,1.4770099034200368
	929	+2.7102638028832184,0.79788512796516464,1.2357056885273507,-0.056038914757045255
	930	+1.7306936530040808,2.1529969034797523,1.8751742371913369,1.2855718457908321
	931	+3.1555821997498561,2.4344266575416666,0.24247678492938607,-0.81009501351568902
	932	+0.81216733991449108,0.43177852071994538,2.8789182997454539,0.31956484195593005
	933	+2.0397036825581196,0.22922812572773654,1.8646005375223393,-0.75195538153364549
	934	+0.13902211017156452,-0.13240514237913514,0.39124764986354443,-2.9743652270697272
	935	+-1.417468820531032,-0.16077937459584996,-0.16743266872410464,-0.53329003795602004
	936	+-1.8412501077356014,-1.638060939645422,-0.30871577517070886,-0.92390050052905259
	937	+-1.0439091290602283,0.063259253712023122,-0.92952422927571732,0.083350231326559387
	938	+0.42636271738793718,-1.4219113461989161,-1.2738700804436822,0.46773315315083464
	939	+1.9465925395092871,-1.2986391915954238,0.30833131385667234,0.59357694430606878
	940	+1.3808190640309335,0.85981002599215772,0.87253420904047418,2.3417783347934633
	941	+2.1733773489052854,0.77038362396766868,0.66971275923174078,2.3123948958132168
	942	+1.2493437793646578,0.60325734317132551,0.46061613305360771,1.5890254754695907
	943	+1.0085558432194714,1.2474174835217258,0.95359767537489382,2.7955044215717972
	944	+0.72306407307846943,0.99576020110603469,2.3716084191106219,1.3810720354159567
	945	+1.1604188240231526,1.7770285567997013,2.8981560041625984,2.3197213748580179
	946	+2.7685871250198115,1.7185901395763015,-0.4996046020152376,-0.30589526891649133
	947	+0.44268476113327804,1.1727147480583004,1.4871435101873525,0.38530172220361569
	948	+0.25193120513443357,0.58826385890588906,0.25593567271699469,0.0042812169017503177
	949	+-1.8838719428166171,0.1103034888816854,-0.61234095142243605,0.94622362187128117
	950	+-1.0641762959943999,1.2844275276851493,0.74440574402681914,0.010816825864180035
	951	+-1.462726991335161,-0.52231090186020224,-0.47290191879441534,-0.65888004103426756
	952	+-1.5790412807785064,-1.7394761984624165,0.15084360016039411,0.12055436583571766
	953	+-1.9574562480692355,-0.17254504208371291,-0.17288077805230678,0.066875951616778409
	954	+-0.1691201786590919,0.46456846598296009,0.32925084821984463,2.3077514569935995
	955	+-1.9143922244789853,-0.21610173662784721,-0.28597092870158425,2.1352752257422782
	956	+-1.607758239356134,-0.15256035270666607,0.20463932501654558,3.5696059166538836
	957	+-0.07070618705122822,-1.2056431085532435,-1.0094659901057526,0.31767815471800764
	958	+-0.0079282545702275553,1.6498338318358496,1.0320552843040514,1.3477110192412507
	959	+-0.50551012815961138,1.2063175602176108,-0.19163153566610824,1.757544727609714
	960	+-0.29072036397733536,-0.65363389504337333,0.85153147350543335,-0.094672702596358072
	961	+-0.96957133981749344,-0.3377986404168779,1.7230942108985114,-1.207473746518767
	962	+-0.16680955168766753,0.24126122410033646,-0.06526875475133298,-0.04343547133853437
	963	+-0.44823111034925678,-0.61740743182910052,0.16882709084544636,-0.24363874606280972
	964	+-1.2400389617057259,-0.58827051433453714,1.1612524841281733,-0.16937812758331389
	965	+-0.8874657928445604,0.78714897319365495,0.17409117134715554,-0.075826832068478622
	966	+1.0703811279260693,-2.1649373317946252,-0.78616779189921471,-0.67607433194611555
	967	+1.4710390529529298,-0.41077928404644592,1.5423010144464635,0.1535098503772489
	968	+-0.32523716740367592,-0.63975446289565274,1.136391803952159,1.376699339097186
	969	+-1.5823869154843406,-0.53405899968783321,1.0258451415814531,1.852085343811166
	970	+-0.55897416240119779,0.28783401145831783,0.45740348569644351,1.7121237858240321
	971	+0.50538844153194151,0.5302715302548795,0.57157867893329506,2.4046374557450445
	972	+-1.4253346607738595,-0.97143053690327097,0.060010820389375108,2.0809668547576492
	973	+-0.61962680852813634,0.073339647167558308,-0.34924045974030343,2.2083221144466378
	974	+-0.29512296410124245,-0.031593703492214194,2.6030866856775967,3.7005902990497876
	975	+1.0246014000689561,-0.62856903235030548,0.10094271645185016,1.547309567466332
	976	+0.6237275083278313,0.96847114217551034,1.1601609149038268,2.0826157415660882
	977	+-0.66169211407718964,-0.38435126808540976,1.1718789340630336,2.1895561456806867
	978	+2.3820902797645194,-0.049149374253301514,1.7174771471705101,3.1562733905471112
	979	+-0.58383610169100209,0.97527085089506449,1.2463072749239446,2.5790109561295065
	980	+0.38761495599351775,2.3472146146653428,1.8534408740252089,2.9387398431665099
	981	+0.8498722500275242,0.99707889522244275,2.8808548954009208,3.5303211084784101
	982	+0.16231849217132943,1.2534707168628305,2.1370397889785551,1.6720409381388848
	983	+1.2565369315515218,1.6178070359609986,0.22748807629417001,0.75559609446784515
	984	+0.56954426445337303,0.60514978670720809,1.655142517641502,2.4312771941101152
	985	+-1.0551601207070131,1.1495217778603437,2.0838810446670211,1.0501275714080145
	986	+0.70527124562745436,1.3371924858417386,-0.20869483990129989,1.9540265269475865
	987	+-0.84667672453639131,0.22387288307345277,0.5338316126166287,-0.4585763890514738
	988	+0.50162702530949566,-1.2773217865945736,-1.9248427833255877,0.039366793024281949
	989	+0.76899851168875766,-0.36724868998218757,0.63970395918094003,-0.37875546823878359
	990	+-0.80415702419677237,-2.4790292789802963,-1.2320604524244572,-0.74991146794693597
	991	+-1.0578937755944682,-0.34004541477156591,-0.99700097603230398,0.036220123941828275
	992	+-2.2781946308699026,-2.0428762657340171,-0.085744124666798149,0.99933912453847618
	993	+-1.3134676300648773,-0.80763860708116841,-0.31974213035395049,-0.75198894868288702
	994	+-2.3580290195350053,-0.1371452280157972,-1.1085304619218301,-0.63775838976864485
	995	+-1.3605433007270316,-2.4593665488642436,-1.6487486838759295,2.2777155692868933
	996	+-0.98003585547135719,-0.56902829960263968,-1.3047711304574592,-0.29212535271026485
	997	+-0.64497496611616512,-1.5136559828393543,-1.2093186853683471,0.15979943693158299
	998	+-1.4340423123389141,-2.1809869817559031,-1.7342645021448848,-1.218228231033428
	999	+0.042611528097885265,0.035640590581243137,-0.47736070022055221,-0.83964913925741069
	1000	+-0.17045773284160096,-0.33444792241087112,-1.3686145117894792,-1.7716912853933064
	1001	+-1.2781131460474864,-1.7574509108050369,-0.29011142118964095,-0.39379124895829909
	1002	+0.79495928423472051,-1.2171508104204363,0.47719643675817547,2.26253415278671
	1003	+-0.37425068916232235,-1.2224476898377512,-1.7814320292793568,-0.13080433697019789
	1004	+-0.093185988531583067,-1.3966261325624796,-1.3190369675900682,-1.6189633575461888
	1005	+-0.63618335475749888,0.51216915166787536,-0.2806418663236423,-1.0173343848193428
	1006	+-1.7895366291570216,-0.057463939432818911,-0.63054017988222988,0.67642117111564248
	1007	+0.025879031566036548,0.72248127397635309,0.2354020221884281,0.17175214605813172
	1008	+-2.6606394744899582,-0.73133105998026693,-0.87240822316752287,-0.21501733951989976
	1009	+-1.9934999855943396,-1.2312511582392138,-0.5808773143064766,2.4476477651280382
	1010	+-1.1865731871752545,-0.50749139365516838,0.57965718382398279,2.5073238303942249
	1011	+-0.18828944726646391,0.41749806520607535,0.75800941742619876,2.0077645458602342
	1012	+-0.23939139466366158,-1.4050351116762589,1.1701379281987774,2.1310687209273036
	1013	+-0.80751484805541474,0.65084681283641466,1.4116669292897324,0.32468983124516193
	1014	+0.86726973471917002,1.7554010831295885,1.375430190305768,0.26259520888379312
	1015	+0.16190206496631449,0.10702164073307341,0.53292052372744636,-0.0031743914074677249
	1016	+1.1506558605394113,-0.31233637277444315,-0.11199885638271645,-0.042787004905452147
	1017	+1.2061624213564457,1.4619781071297593,-1.2020403029650226,-0.24399575500592502
	1018	+2.1846775590101162,0.17703814066797241,-0.81939277953465006,-1.8730707114416467
	1019	+2.0768952859842926,0.79076474122478335,-1.7802252770463478,-1.4974079346665239
	1020	+1.7544900523124349,0.5261009568462145,-1.7358496721736472,-2.1943210515194589
	1021	+2.1699251021675359,0.4783727265686622,-1.8419577766320983,-3.1854462036343638
	1022	+0.31085752766668207,-0.3727561276192668,-1.9005507493009806,-0.70066749217909452
	1023	+1.3023326710226453,0.596525420587668,-0.37086807900854585,-1.0998440243918346
	1024	+0.3897835993108873,0.67392207895481704,-0.36151758179305227,-1.7109109341814919
	1025	+-0.10273352784236245,0.68035551159787389,0.07274965430770669,-0.56918001966870024
	1026	+-0.79375574802852356,1.7275178044953554,-1.7674255455403662,-2.143797985839992
	1027	+-0.51861860361717638,-0.92118165772369232,-1.8870006054443056,-0.99330808696284512
	1028	+-1.8600888967397859,0.53992972978435672,-0.62066682164345799,-1.0602583664497547
	1029	+-0.88851100502234615,0.43179523666886355,0.422942813368818,-1.4253717857314951
	1030	+-1.5524101778696737,0.89927399634065086,0.36559092539555604,-1.3043898975301003
	1031	+-1.6990597046550069,0.13199794828309053,0.19018055371271475,0.095354957192896994
	1032	+-0.49516926400971495,1.270410795015589,-1.3485720482124464,-0.50314696282550997
	1033	+0.062852315268688064,-0.017919409494880356,0.29925965941362154,0.4126758589921552
	1034	+0.13286318232723426,-0.3893419419088967,-1.7029305604059437,0.22414662162692101
	1035	+0.28686751402813221,-0.63466175421285431,-2.433958721657949,-1.04315180737927
	1036	+-0.60947032872874241,-1.3688612684688022,0.050142364404146988,0.39986741120464075
	1037	+-1.7896758589018289,-1.490392084458779,-1.2481208846851028,0.13077094146877755
	1038	+2.2114513028687615,0.073460750812194497,1.0097770715510319,1.7604676363273553
	1039	+2.4695311938791553,0.86036228333869003,1.471057202807216,1.2995694926077461
	1040	+0.10059263329936141,0.7049889689435348,1.1769863080130172,2.1952267198191908
	1041	+0.12754783161489847,0.41619352280285749,0.7843428891452755,2.2301989930635333
	1042	+-0.71659868711579144,0.14194318468382722,1.1325018836649794,1.0796152328785436
	1043	+0.84644822490082972,0.53306108996599222,1.0544713478902579,2.0072946218908339
	1044	+0.51189198516547507,0.7539437130899791,2.209589688827224,1.6463085404821851
	1045	+1.2093133070213553,0.51096805611855833,2.1754010033298994,0.72251011934912113
	1046	+0.2058578557834122,1.2458115028537367,0.46301333880846429,0.17824176376499934
	1047	+0.53329193540508535,0.27720531964624023,-0.1536012104752229,-1.2593266931684095
	1048	+0.52735746538012962,0.81231512061256339,1.0818742849722975,0.036332138410243298
	1049	+-1.827386762134712,-0.83260642072387758,-0.48003732348243228,-0.64140543803235694
	1050	+-1.4061935637417717,0.055469440505261952,-0.89655817486337197,-0.20124387244948241
	1051	+-0.61617058130376856,0.42156770359221762,-1.3971556801157889,-0.21771968094867025
	1052	+0.59660121011400524,-0.22138202499208171,-0.18851346166459915,-1.2907771381524638
	1053	+-0.55286628823818806,1.7251694127200559,1.1897319127659123,0.90989061200727894
	1054	+0.93445437319940117,1.3848926461773607,-0.019430212178600359,-0.5104459712628292
	1055	+-1.4504676736911608,0.16006866678827625,0.53730134815919772,-0.72594394459993772
	1056	+-0.16739202248919388,0.55562778813022407,-1.7048972079372169,-0.36659888015541969
	1057	+-0.52385182061872948,0.11863816776736776,0.54045999118972432,2.1562778182771409
	1058	+2.7523619072202381,1.5473545402376938,1.0860383567421965,1.2464014870198463
	1059	+3.2271046755855952,1.2378575353950423,-0.35047202314826165,-0.13988126216338892
	1060	+2.6682769254399021,1.2298630294868838,1.4663907048530702,0.59499471704439855
	1061	+0.20759654060067589,0.0045538163070055759,1.3404389856365138,1.0346161976098252
	1062	+-0.51174000100832284,0.474528619969802,-0.24585259492758849,0.52464957117616806
	1063	+-0.12686383593537204,1.3093347200431915,1.2769998548882664,-0.11451264698908226
	1064	+0.42398469259105315,3.205585949185247,1.5050089554069612,-0.43832727214884237
	1065	+1.7113237874120415,2.2821775882408586,0.17474153975157414,-0.32683032632892661
	1066	+1.4659195345472045,2.8090715329106022,2.5347077532140978,1.0997839172699277
	1067	+-0.15967212684911458,1.9650665489367896,1.9035237068617912,-0.48423928678432637
	1068	+1.5082726471826566,4.4026524423061151,2.6441075774712051,1.5092962865289676
	1069	+0.74342367739815618,1.4891716227359162,0.51899927652580369,1.7292220949157668
	1070	+-0.13230194436891951,0.19974763325242395,0.48966977488276375,0.58527605293419405
	1071	+2.5241814709800279,0.40937992797713685,2.0062642026658937,0.099720305235571294
	1072	+0.62105285243286046,1.9647614823343083,0.77776164570224937,0.7119716775949716
	1073	+0.64710935043707174,0.18651762524423132,-0.20214321378140798,-0.040851200264106491
	1074	+0.89595361504914661,1.4828833642651913,2.2341611417404534,0.17077634082246482
	1075	+2.0821582595965178,2.6069807525128379,3.1922259380974061,-0.53994120275489299
	1076	+0.86763725203903375,-1.6253895434503225,0.68759976600757067,1.2140206062698007
	1077	+0.73454908519120343,-1.0497421449679714,0.75383598301051502,1.0171137384092088
	1078	+-1.4454068258685682,-2.3616863362561067,-0.58865252889502195,1.6036713303229715
	1079	+-0.97942457232027169,-2.2154456114819028,0.2366360844436432,-0.96140549742523529
	1080	+-2.4765088519050895,-4.1325300740288693,-1.4190579418246774,-0.64694754298634938
	1081	+-1.5272591507328273,-1.1370282703742136,-0.49664119557148578,0.56796912257609422
	1082	+-0.96308793497179934,-1.1773634746844381,-1.1159877712611874,-1.3615879195926737
	1083	+1.1101319059346821,0.3060949487557405,-0.80641352900743013,-1.7740987403186752
	1084	+3.1271575996304839,0.75172467135549237,0.22839343835097425,-2.8146836788625609
	1085	+1.6518920578450851,1.3158466331463159,0.90254093886170828,-0.98491698881930023
	1086	+2.5177378175785692,1.0734193270947743,1.066334589951599,-0.51422090313901481
	1087	+1.2521291995186243,1.1817354404881628,0.012710766395963358,-0.58623099756943875
	1088	+1.2925555896871694,0.80236607698775053,0.26835580611052723,0.37833974857472097
	1089	+1.1173966830160433,1.2267203405303466,-0.63137158793320503,-0.35503219579099093
	1090	+1.8182776915838026,-0.24906658485633426,0.8758902111099558,-0.16917635728141112
	1091	+0.73059989488987354,-0.66850470809256213,0.13159985110415978,0.72395404172028488
	1092	+1.6090005724474907,2.2824797326740445,0.9539128354606301,0.93149978537037703
	1093	+0.10994009630752188,2.3420224204704354,1.0282368378397988,0.50892570854759134
	1094	+-1.4065374033887643,1.4829525054996404,0.37473464806197454,1.3549124349632975
	1095	+-0.28941105901855485,0.95815926045147271,-1.5232165692362916,0.69752669525801381
	1096	+-0.70412617633930907,0.36112189967331421,-0.88311374258168829,0.29442312877218152
	1097	+1.4313266529074136,1.4994550531215802,0.007377160587017928,-1.6054385167147653
	1098	+0.63224297454811296,2.4253359549008238,-2.5282493456632356,-0.66627260496212992
	1099	+1.056420359068593,1.6034430989770518,-0.96112108712984556,-0.65282770467932449
	1100	+0.96569284419285917,1.0659788648964477,-1.9245752824451332,-1.4863893548077998
	1101	+1.1239302797996991,0.54788077602876495,-1.3450552028645921,-2.1560936887235531
	1102	+0.97825442931830331,0.37703634150833021,-1.376270970344897,-1.299367980793116
	1103	+0.14958622745681238,-1.213282217642595,-0.056543419748228463,-0.28490956643285303
	1104	+0.25327237132571734,-0.23323615004487222,-1.322352584601165,-0.4865596570195887
	1105	+0.32411727864693674,-1.7927157083215217,-0.53975445302693281,0.8218136228029429
	1106	+-1.5453799388709668,-2.3966264292434527,-0.22828149737376308,-0.31175154516259918
	1107	+-1.4047597920098722,-1.2040569907606884,-0.55064292106732982,0.42846042799064454
	1108	+0.4537039438970617,-0.19198032899432838,-0.0080593902064009793,-0.1968674087969588
	1109	+-3.4433471111236944,-2.228577794354512,-0.92737699006680319,0.36712472301345767
	1110	+-3.0821177557349673,-0.99714259305735053,-0.45105023648795695,2.3322183317467022
	1111	+-0.77884052516242019,-0.74576662822463069,0.26950382669667683,1.1967986702444704
	1112	+-0.27886273677374201,0.26225142809983354,-0.015415943432659618,0.35891193505160868
	1113	+-0.78943625004418161,-0.52758959186625098,1.3383104575229647,2.1458631852360828
	1114	+0.95280979115743603,-1.2153162886682263,1.592859761695046,2.711196381325002
	1115	+-0.1812592303868506,-0.80790440097042593,3.9903640716018742,1.0550494824044452
	1116	+-0.0025472021318610483,0.11432813375252276,0.58366274742547919,-0.39310435167621471
	1117	+0.18782078066249869,1.1138193387607047,1.9156013708965638,0.17414903945258917
	1118	+1.0230356930492683,2.042520281776032,-0.51689137492937387,-0.70800899718661359
	1119	+1.0378561741175263,-0.9779795456791065,0.63224780683580417,-1.4776678924847071
	1120	+1.2285011424270937,1.9553242993739928,2.2952876123125296,0.48080208726205342
	1121	+0.2945562479405951,0.47947542352321126,0.64673967037894098,-1.1962281459120858
	1122	+0.81455163244829798,1.4687147118192576,0.066872805916419531,1.0874778968775307
	1123	+-1.588412604639877,0.39063772728804291,0.78242365221973065,0.48181109159609692
	1124	+-1.3470447502735712,-1.5095988648861132,-1.5492220058324173,-1.0071499459494606
	1125	+-3.0009472301089821,-2.8277468409834863,-2.2449025832067395,-0.8001739533915333
	1126	+-1.6070457436434042,-0.64349563292837719,-1.4032043881693794,-0.28062087808465042
	1127	+-1.3901473563736682,-1.1899449973561715,-3.6072667950773898,-1.1135157112003995
	1128	+-1.6512380705995318,-1.4688223655817163,-0.73609291823214529,-0.67168162933286646
	1129	+-1.9088519348456112,-0.63584942336562311,-1.5942295747481938,0.69683795629166978
	1130	+-1.7495871798805411,-0.74796037788694947,-2.1184542051269495,-0.6051365461623992
	1131	+-1.7807381121393275,-0.53857986773852762,0.83973581707471601,2.3202873668591666
	1132	+-0.30004550274282826,0.34965345695148253,-0.57378457152602647,0.34834375992270017
	1133	+0.4276189634957196,1.0708110864422804,-0.60426862943118542,-1.176114279960232
	1134	+-0.63170692564683306,0.56997904368880237,1.372199841050969,0.43943827207479569
	1135	+1.2874603054037721,2.3539298814507603,0.89043782380306891,0.90725712385300694
	1136	+0.3038109217666467,1.8865526846980472,2.5889354282789689,0.5098064257679229
	1137	+0.32612599288231192,1.2706922691937179,0.20180034140990399,0.41320071481391196
	1138	+-0.29483010098732187,0.066258780702056375,0.21446420583782466,-0.35429064699514662
	1139	+-0.36655223494225792,-0.52224062796192872,-0.66921395845022102,0.81410681688709197
	1140	+-1.7147558032302102,0.20270777367350995,0.0083762488143864708,0.12949119031927384
	1141	+-0.65511955135893762,0.69564846853152129,-0.99975799284668543,0.91222510598163087
	1142	+-0.37424285436398286,1.2560375025568906,0.66061736503861113,1.7012462771655192
	1143	+-1.6427309685939395,1.3987129708238548,-0.33242080716623046,0.43365401453487706
	1144	+-1.6033842112266328,1.0224248183568716,-1.2134398424535491,0.68531965652662441
	1145	+-0.79849514467798943,0.94836209304417463,-1.9249573227646475,-0.3364304671844815
	1146	+0.37122290597621388,-1.0407932931332537,1.1886795072004919,1.4000402274057382
	1147	+0.1730649361740971,-1.2360349909085868,0.76247533402648715,1.880482245933917
	1148	+-0.61097681155833694,0.26204187613872088,1.6548073287318175,0.78725356057551266
	1149	+-0.59334208059073568,-1.5497736197719563,-0.79187550222276126,0.19845927721340018
	1150	+-2.4728121485109322,-1.0269416280018893,1.9504509085932378,1.6166373292398848
	1151	+-1.979556125439569,0.36741505436370614,1.664636553355193,0.28409013265589567
	1152	+1.2766336883876823,0.65022828617345263,1.162836953272316,-0.91435480647712564
	1153	+0.029125810541629382,0.82726271957167885,-0.043653115156783051,1.9438131642507832
	1154	+1.0137644837874187,1.1356100278904591,-0.037005250513036991,1.5508021418544591
	1155	+0.73413321740131632,-2.366399053572477,-1.8092770758319205,0.52364797845638655
	1156	+0.22833547464954204,-0.049500760637546937,0.42361445421263283,0.88456026070439808
	1157	+-0.65172367787358643,-1.0908458307841276,0.38204995066986391,-0.44809021939567728
	1158	+0.52204287922269133,1.0760297722454566,1.453612692590601,-1.145300837515802
	1159	+-0.92097195960984024,1.2876404942938846,-0.54875365962528877,0.34274095988340403
	1160	+-0.1581409635873483,-0.65954590815644876,-0.52990007314332233,-0.38176815698861211
	1161	+-0.02105956679176238,-0.40962455969712097,-0.23620371659747619,-0.13029557882907908
	1162	+1.1097579795122492,0.72106997710959697,-0.40982821455782692,-0.11731496928786528
	1163	+0.41337810154573873,0.74152058661183562,-1.6863114369463017,-1.4122254520441622
	1164	+-0.26058439709338099,-0.44165791170149366,0.21092413594748183,-0.1959508488743803
	1165	+-1.558614760505032,0.1680336708772826,-0.73473376371727972,-1.0955035764037186
	1166	+-0.30439206499834476,-0.30753503310389968,0.1474874319521059,-0.10869057542471788
	1167	+-1.7352238365100379,-1.1048401256063076,-2.0173725023497511,-0.21577398547927118
	1168	+-0.95978786319142451,-2.1525810210148109,-1.1993148769501694,-0.76454864501176345
	1169	+-0.43375397699362306,-1.4689684920284616,0.033029112996859622,-0.18565892621973556
	1170	+-0.7499041519228864,0.88493413914204355,-1.3489085664402836,-0.74550053673827166
	1171	+-0.50154760949195665,-0.17665256429200091,-1.8618132590297749,0.11512502605785491
	1172	+0.66260966361823592,0.33157522121021271,-1.8798394176778195,-1.1593044145976483
	1173	+0.14819449316703898,-0.36352466684905216,-1.2992337570133989,-1.6026218145665974
	1174	+-0.89445206759804297,-0.23437952981864973,-1.0873014647606434,0.77678827913320292
	1175	+-1.789998768625858,-0.75905577532012103,-0.2769995887352511,0.20616489891450096
	1176	+-2.0651190987860626,-2.1253727763556904,-1.255044603862848,1.8057456739547919
	1177	+0.27963156715930859,-0.53432696188502882,0.88631775324969897,0.59482475628188891
	1178	+-0.061109217282856378,-0.12319567099205023,1.9776151704590617,0.89094831131313579
	1179	+1.187251424803901,1.571902727374578,2.8265562761477097,-0.5364440118619056
	1180	+1.929097814797011,0.46486760014685324,1.8141957369000616,0.11199327941336243
	1181	+1.7308794576115358,1.1106884605248437,1.9752812198382572,1.0030375220621819
	1182	+2.9898421963830217,1.4780128703433406,1.8563708618202657,2.6006837303759718
	1183	+3.1098354088397224,1.5508424213321954,-0.23130684283586667,2.4460339863155154
	1184	+4.5988481601686582,0.69433930054221271,1.1223302309173393,2.4281946900579077
	1185	+2.5545122838448915,-0.70262884643569035,0.75333504302673449,1.3360845162117221
	1186	+2.4550219310251387,-1.3615762026520619,1.7098486547774039,2.6982869194034267
	1187	+0.51443872003076074,0.53512696424058226,0.74728642825862068,2.3211313956831812
	1188	+2.4053061403039391,0.76758175704844744,-0.50477146781370685,-1.0370969124610923
	1189	+0.73717285974592706,0.24519404389010446,0.084559934000275741,1.0243374375526588
	1190	+1.6459628067089778,1.1884822566549913,-1.4898078288769718,-0.22086038721284029
	1191	+1.2203283174600668,0.21445315619089914,-2.1417190716458845,1.2710196845397894
	1192	+0.0047322389900186224,0.23436094928921034,-1.7496096674946346,-0.46981570178932108
	1193	+1.892247817086361,-0.88497895479491895,-2.0237540396557581,-0.67478614256700453
	1194	+1.2802567026406424,-0.70837929221328255,-0.79639181766104072,-0.20455031094038778
	1195	+0.78516994510771643,0.84045287221959419,-0.66742284786415706,-0.071673062144535199
	1196	+2.5107399269723496,1.0228120515403694,-1.9397941977045654,-0.75299848854777895
	1197	+0.50643140135331244,-0.78301723523590505,-0.34228145505867158,0.94450362085401363
	1198	+0.28844004810989338,-0.50603055446707179,-0.73818457053904929,1.8109478565856578
	1199	+1.0641973300414247,1.0241815492545248,0.69534315742063102,0.37779813962194952
	1200	+1.6136825314296015,-0.28742571544311191,-0.18740127851410754,0.65287483630130261
	1201	+0.37134591233596825,0.1676733479696802,0.53320721038466135,1.5297757640836296

modified docs/PROGRESS.md +8 −0

		`@@ -149,3 +149,11 @@ Executed:`
149	149	- Full suite: `ctest` all green (see summary in RESEARCH_STATUS).
150	150
151	151	Gate evidence: reference tables (R + Python), Monte Carlo logs, registry entries with tolerances.
	152	+
	153	+## Phase 5 — Extensions, Tier B (2026-11-02, 17:40–18:10 ET) — GATE PASSED
	154	+Selection by research value (E4 needs them): VAR(p), orthogonalised and generalized FEVD, Diebold–Yilmaz connectedness
	155	+(static + rolling), Ledoit–Wolf shrinkage. `models/var.{hpp,cpp}`. Reference: statsmodels VAR on a simulated VAR(2)
	156	+panel (`datasets/fixtures/var_panel.csv`): coefficients/Σ_u/llf/orthogonalised FEVD 1e−9, generalized FEVD (hand
	157	+computation in Python) 1e−9, DY totals 1e−7, BIC order, LW shrinkage 1e−9 (`tests/reference/test_var_reference.cpp`,
	158	+184 assertions). Rolling connectedness parallel over windows (0 failures on the fixture). Other Tier B/C items are
	159	+deliberately not implemented (registry).

modified docs/methods/registry.md +13 −0

		`@@ -35,6 +35,19 @@ reference comparison pending · 🧭 experimental · ✖ not implemented. "Toler`
35	35	\| `bootstrap.stationary` / `circular` / `iid` \| Politis–Romano 1994 (geometric blocks, mean length b or n^{1/3}) / circular blocks / iid (comparison only); replica r ← Rng(seed, r); percentile CI, SE, bias; `bootstrap_rows` for regressions; `bootstrap_rv` \| series \| theory: AR(1) long-run SE (block SE within 35 %, > 1.6× iid SE); MC coverage 0.89 (R = 100) \| as stated \| ✅ \| ⏳ (GPU replicas, E5) \| ✅ \|
36	36	\| `simulation.*` \| Monte Carlo: GARCH(1,1) n=2000 R=120 — coverage 0.90–0.95, \|bias\| ≤ 0.003, no failures; HAR h=5 HAC coverage 0.895–0.945 (R=200, T=1200, pseudo-true from T=200 000); RV RMSE within 10 % of √(2/M)·IV; NLL finite-difference gradients stable across h \| — \| `tests/simulation` \| — \| ✅ \| — \| ✅ \|
37	37
	38	+## Tier B (selected, validated 2026-11-02)
	39	+\| Key \| Definition \| Inputs \| Reference & tolerance \| CPU \| Metal \| Status \|
	40	+\|---\|---\|---\|---\|---\|---\|---\|
	41	+\| `var.p` \| VAR(p) with intercept by multivariate LS (QR); Σ_u with ddof = 1+Np; Gaussian log-likelihood; companion-root stability; AIC/BIC/HQ order selection on the common sample \| T×N panel \| statsmodels 0.15 `VAR.fit(p, trend="c")`: params 1e−9, Σ_u 1e−9, llf 1e−9, `select_order` BIC \| ✅ \| — \| ✅ \|
	42	+\| `var.fevd` \| orthogonalised (Cholesky) FEVD, horizon H \| VarFit \| statsmodels `fevd(H)` 1e−9 \| ✅ \| — \| ✅ \|
	43	+\| `var.gfevd` \| generalized FEVD (Koop–Pesaran–Potter 1996; Pesaran–Shin 1998), rows normalised to one (Diebold–Yilmaz 2012) \| VarFit \| hand-computed Python from statsmodels Φ_h, Σ_u: 1e−9 \| ✅ \| — \| ✅ \|
	44	+\| `connectedness.dy` \| total = 100·Σ_{i≠j}θ̃_{ij}/N, from/to/net; rolling windows (parallel over windows) \| gfevd \| same reference 1e−7 \| ✅ \| ⏳ (batched covariance inputs, E4) \| ✅ \|
	45	+\| `cov.ledoit_wolf` \| Σ* = (1−δ)S + δμI with the analytical δ* (Ledoit–Wolf 2004) \| n×p \| sklearn `ledoit_wolf` formula (hand-computed): 1e−9 \| ✅ \| — \| ✅ \|
	46	+
	47	+Not implemented (Tier B/C, by decision — research value for this paper insufficient or data inadmissible): Realized GARCH,
	48	+HEAVY, GARCH-MIDAS, FIGARCH, DCC, BVAR/VECM, local projections, Kalman, change-point, pre-averaging, realized kernels,
	49	+MSRV, BNS test, Hawkes, order-flow. Listed in RESEARCH_STATUS as ✖/⏳ with the reason.
	50	+
38	51	Conventions that differ from references and are documented, not hidden:
39	52	1. GARCH initial variance: RAID uses the sample variance of ε; `arch` uses a backcast (exponentially weighted) and
40	53	`rugarch` the sample variance by default — hence the 5e−4 log-likelihood tolerance. A `backcast` option is planned so

added include/raid/models/var.hpp +51 −0

		`@@ -0,0 +1,51 @@`
	1	+// VAR(p), generalized FEVD (Pesaran–Shin 1998, Koop–Pesaran–Potter 1996) and Diebold–Yilmaz (2012, 2014) connectedness.
	2	+// y_t = c + A_1 y_{t−1} + … + A_p y_{t−p} + u_t, Σ = E[u u'] (OLS equation by equation = multivariate LS)
	3	+// MA representation: y_t = Σ_h Φ_h u_{t−h}, Φ_0 = I, Φ_h = Σ_{j=1}^{min(h,p)} A_j Φ_{h−j}
	4	+// GFEVD (horizon H): θ_{ij}(H) = σ_jj^{-1} Σ_{h=0}^{H−1} (e_i' Φ_h Σ e_j)² / Σ_{h=0}^{H−1} e_i' Φ_h Σ Φ_h' e_i,
	5	+// normalised row-wise: θ̃_{ij} = θ_{ij} / Σ_j θ_{ij} (Diebold–Yilmaz 2012 eq. 3–4)
	6	+// Connectedness: total C = 100 · Σ_{i≠j} θ̃_{ij} / N ; from-others C_i← = Σ_{j≠i} θ̃_{ij} ; to-others C_→j = Σ_{i≠j} θ̃_{ij} ; net = to − from.
	7	+#pragma once
	8	+#include <vector>
	9	+#include <Eigen/Dense>
	10	+#include "raid/core/types.hpp"
	11	+#include "raid/core/estimate.hpp"
	12	+
	13	+namespace raid::models {
	14	+
	15	+struct VarFit {
	16	+ int p{1}; usize n_obs{0}; int N{0};
	17	+ Eigen::MatrixXd coef; // N × (1 + N p): [c, A_1, …, A_p]
	18	+ Eigen::MatrixXd sigma; // residual covariance (ddof = N p + 1, as statsmodels VAR `sigma_u`)
	19	+ Eigen::MatrixXd sigma_mle; // ddof = 0
	20	+ Eigen::MatrixXd residuals; // n_obs × N
	21	+ f64 loglik{0}, aic{0}, bic{0}, hqic{0};
	22	+ bool stable{true}; // all companion eigenvalues inside the unit circle
	23	+ f64 max_root{0};
	24	+ f64 rcond{0};
	25	+ std::vector<std::string> warnings;
	26	+};
	27	+/// Y is T × N (rows = time). Fits by OLS with an intercept (as statsmodels `VAR(Y).fit(p, trend="c")`).
	28	+VarFit var_fit(const Eigen::Ref<const Eigen::MatrixXd>& Y, int p);
	29	+/// Information criteria for p = 1..pmax on the common sample (observations pmax+1..T), as statsmodels `select_order`.
	30	+struct VarOrder { std::vector<int> p; std::vector<f64> aic, bic, hqic; int aic_best, bic_best, hqic_best; };
	31	+VarOrder var_select_order(const Eigen::Ref<const Eigen::MatrixXd>& Y, int pmax);
	32	+/// MA coefficient matrices Φ_0..Φ_{H−1}.
	33	+std::vector<Eigen::MatrixXd> var_ma(const VarFit& f, int H);
	34	+/// Generalized FEVD at horizon H (N × N, rows normalised to one).
	35	+Eigen::MatrixXd gfevd(const VarFit& f, int H);
	36	+/// Orthogonalised (Cholesky) FEVD at horizon H, for comparison with statsmodels `fevd`.
	37	+Eigen::MatrixXd fevd_cholesky(const VarFit& f, int H);
	38	+
	39	+struct Connectedness { Eigen::MatrixXd table; f64 total; Eigen::VectorXd from, to, net; int H; };
	40	+Connectedness connectedness(const Eigen::MatrixXd& gfevd_table);
	41	+Connectedness connectedness(const VarFit& f, int H);
	42	+
	43	+/// Rolling connectedness: windows of `window` rows, step `step`; one VAR(p) per window (CPU, parallel over windows).
	44	+struct RollingConnectedness { std::vector<usize> end_index; std::vector<f64> total; Eigen::MatrixXd net; usize n_windows{0}; usize failures{0}; f64 seconds{0}; };
	45	+RollingConnectedness rolling_connectedness(const Eigen::Ref<const Eigen::MatrixXd>& Y, int p, int H, usize window, usize step = 1);
	46	+
	47	+/// Ledoit–Wolf (2004) linear shrinkage toward the scaled identity: Σ* = (1−δ) S + δ μ I, with the analytical δ*.
	48	+struct ShrunkCovariance { Eigen::MatrixXd cov; f64 shrinkage; f64 mu; };
	49	+ShrunkCovariance ledoit_wolf(const Eigen::Ref<const Eigen::MatrixXd>& X, bool assume_centered = false);
	50	+
	51	+} // namespace raid::models

modified scripts/make_fixtures.py +35 −0

		`@@ -131,3 +131,38 @@ for name, kw in [("h1", dict(h=1)), ("h5", dict(h=5)), ("h22", dict(h=22)), ("lo`
131	131	har[name] = {"params": f.params.tolist(), "hac_bse": f.bse.tolist(), "hac_lags": L, "n": n, "ssr": float(f.ssr), "rsquared": float(f.rsquared)}
132	132	ref["har"] = har; json.dump(ref, open(os.path.join(out_dir, "reference_values.json"), "w"), indent=1)
133	133	print("HAR references:", {k: v["n"] for k, v in har.items()})
	134	+
	135	+# --- VAR(2) reference: statsmodels VAR, orthogonalised FEVD, generalized FEVD (Pesaran–Shin) by hand, DY totals, LW ----
	136	+from statsmodels.tsa.api import VAR
	137	+g = np.random.default_rng(77); N = 4; T = 1200
	138	+A1 = np.array([[0.5, 0.1, 0.0, 0.05], [0.0, 0.4, 0.15, 0.0], [0.1, 0.0, 0.3, 0.1], [0.05, 0.05, 0.0, 0.45]]); A2 = 0.15 * np.eye(N)
	139	+L = np.linalg.cholesky(np.array([[1.0, 0.3, 0.1, 0.0], [0.3, 1.0, 0.2, 0.1], [0.1, 0.2, 1.0, 0.3], [0.0, 0.1, 0.3, 1.0]]))
	140	+Y = np.zeros((T, N))
	141	+for t in range(2, T): Y[t] = 0.1 + A1 @ Y[t - 1] + A2 @ Y[t - 2] + L @ g.standard_normal(N)
	142	+np.savetxt(os.path.join(out_dir, "var_panel.csv"), Y, delimiter=",", header=",".join(f"y{i}" for i in range(N)), comments="", fmt="%.17g")
	143	+res = VAR(Y).fit(2, trend="c"); H = 10
	144	+Phi = [np.eye(N)]
	145	+coefs = [res.coefs[i] for i in range(2)]
	146	+for h in range(1, H): Phi.append(sum(coefs[j - 1] @ Phi[h - j] for j in range(1, min(h, 2) + 1)))
	147	+S = res.sigma_u
	148	+num = np.zeros((N, N)); den = np.zeros(N)
	149	+for h in range(H):
	150	+ PS = Phi[h] @ S
	151	+ for i in range(N):
	152	+ den[i] += PS[i] @ Phi[h][i]
	153	+ for j in range(N): num[i, j] += PS[i, j] ** 2 / S[j, j]
	154	+th = num / den[:, None]; th = th / th.sum(axis=1, keepdims=True)
	155	+dy_total = 100 * (th.sum() - np.trace(th)) / N; dy_from = 100 * (th.sum(axis=1) - np.diag(th)); dy_to = 100 * (th.sum(axis=0) - np.diag(th))
	156	+sel = VAR(Y).select_order(4)
	157	+try:
	158	+ from sklearn.covariance import ledoit_wolf as sk_lw
	159	+ lw_cov, lw_s = sk_lw(Y)
	160	+except Exception:
	161	+ Xc = Y - Y.mean(axis=0); n = Xc.shape[0]; Sc = Xc.T @ Xc / n; mu = np.trace(Sc) / N
	162	+ d2 = np.sum((Sc - mu * np.eye(N)) 2) / N; b = sum(np.sum((np.outer(x, x) - Sc) 2) for x in Xc) / (n * n * N); lw_s = min(1.0, b / d2); lw_cov = (1 - lw_s) * Sc + lw_s * mu * np.eye(N)
	163	+ref = json.load(open(os.path.join(out_dir, "reference_values.json")))
	164	+ref["var"] = {"nobs": int(res.nobs), "params": res.params.tolist(), "sigma_u": res.sigma_u.tolist(), "llf": float(res.llf), "fevd10": res.fevd(H).decomp[:, -1, :].tolist(),
	165	+ "gfevd10": th.tolist(), "dy_total10": float(dy_total), "dy_from10": dy_from.tolist(), "dy_to10": dy_to.tolist(), "bic_order": int(sel.bic), "aic_order": int(sel.aic),
	166	+ "lw_shrinkage": float(lw_s), "lw_cov": np.asarray(lw_cov).tolist(), "statsmodels_version": sm.__version__}
	167	+json.dump(ref, open(os.path.join(out_dir, "reference_values.json"), "w"), indent=1)
	168	+print("VAR reference: nobs", res.nobs, "DY total", round(dy_total, 3), "bic order", int(sel.bic), "LW shrinkage", round(float(lw_s), 4))

added src/models/var.cpp +98 −0

		`@@ -0,0 +1,98 @@`
	1	+#include "raid/models/var.hpp"
	2	+#include "raid/core/error.hpp"
	3	+#include "raid/core/thread_pool.hpp"
	4	+#include <Eigen/Eigenvalues>
	5	+#include <chrono>
	6	+#include <cmath>
	7	+#include <numbers>
	8	+
	9	+namespace raid::models {
	10	+
	11	+namespace {
	12	+void build_design(const Eigen::Ref<const Eigen::MatrixXd>& Y, int p, usize start, Eigen::MatrixXd& X, Eigen::MatrixXd& Yt) {
	13	+ const Eigen::Index T = Y.rows(), N = Y.cols(); const Eigen::Index n = T - static_cast<Eigen::Index>(start);
	14	+ X.resize(n, 1 + N * p); Yt.resize(n, N);
	15	+ for (Eigen::Index i = 0; i < n; ++i) { const Eigen::Index t = static_cast<Eigen::Index>(start) + i; X(i, 0) = 1.0; for (int l = 1; l <= p; ++l) X.block(i, 1 + (l - 1) * N, 1, N) = Y.row(t - l); Yt.row(i) = Y.row(t); }
	16	+}
	17	+}
	18	+
	19	+VarFit var_fit(const Eigen::Ref<const Eigen::MatrixXd>& Y, int p) {
	20	+ const Eigen::Index T = Y.rows(), N = Y.cols(); RAID_REQUIRE(p >= 1 && T > p + N * p + 2, insufficient_samples, "var_fit: need T > p + N·p + 2");
	21	+ RAID_REQUIRE(Y.allFinite(), data_quality, "var_fit: non-finite values");
	22	+ VarFit f; f.p = p; f.N = static_cast<int>(N); Eigen::MatrixXd X, Yt; build_design(Y, p, static_cast<usize>(p), X, Yt); f.n_obs = static_cast<usize>(X.rows());
	23	+ Eigen::ColPivHouseholderQR<Eigen::MatrixXd> qr(X); qr.setThreshold(1e-12); const Eigen::Index k = X.cols();
	24	+ const Eigen::MatrixXd R = qr.matrixR().topLeftCorner(k, k).template triangularView<Eigen::Upper>(); f.rcond = std::abs(R(k - 1, k - 1)) / std::abs(R(0, 0));
	25	+ if (qr.rank() < k) f.warnings.push_back("VAR design rank deficient (rank " + std::to_string(qr.rank()) + " < " + std::to_string(k) + ")");
	26	+ Eigen::MatrixXd B = qr.solve(Yt); // k × N
	27	+ f.coef = B.transpose(); f.residuals = Yt - X * B; const f64 n = static_cast<f64>(f.n_obs);
	28	+ f.sigma_mle = f.residuals.transpose() * f.residuals / n; f.sigma = f.residuals.transpose() * f.residuals / (n - static_cast<f64>(k));
	29	+ // log-likelihood (Gaussian, MLE covariance), as statsmodels VARResults.llf
	30	+ const f64 ld = std::log(f.sigma_mle.determinant()); const f64 Nd = static_cast<f64>(N);
	31	+ f.loglik = -0.5 * n * (Nd * std::log(2 * std::numbers::pi) + ld + Nd);
	32	+ const f64 nparams = static_cast<f64>(k) * Nd; // statsmodels: ln\|Σ_mle\| + 2 k N / n etc. (uses sigma with nobs correction: see select_order); we report the mle-based criteria
	33	+ f.aic = ld + 2.0 * nparams / n; f.bic = ld + std::log(n) * nparams / n; f.hqic = ld + 2.0 * std::log(std::log(n)) * nparams / n;
	34	+ // stability: companion matrix eigenvalues
	35	+ Eigen::MatrixXd C = Eigen::MatrixXd::Zero(N * p, N * p); for (int l = 1; l <= p; ++l) C.block(0, (l - 1) * N, N, N) = f.coef.block(0, 1 + (l - 1) * N, N, N); if (p > 1) C.block(N, 0, N * (p - 1), N * (p - 1)) = Eigen::MatrixXd::Identity(N * (p - 1), N * (p - 1));
	36	+ Eigen::EigenSolver<Eigen::MatrixXd> es(C, false); f.max_root = es.eigenvalues().cwiseAbs().maxCoeff(); f.stable = f.max_root < 1.0; if (!f.stable) f.warnings.push_back("VAR not stable (max root " + std::to_string(f.max_root) + ")");
	37	+ return f;
	38	+}
	39	+
	40	+VarOrder var_select_order(const Eigen::Ref<const Eigen::MatrixXd>& Y, int pmax) {
	41	+ VarOrder o; const Eigen::Index N = Y.cols(); const f64 Nd = static_cast<f64>(N);
	42	+ for (int p = 1; p <= pmax; ++p) { Eigen::MatrixXd X, Yt; build_design(Y, p, static_cast<usize>(pmax), X, Yt); Eigen::ColPivHouseholderQR<Eigen::MatrixXd> qr(X); Eigen::MatrixXd B = qr.solve(Yt); Eigen::MatrixXd U = Yt - X * B; const f64 n = static_cast<f64>(X.rows()); const f64 ld = std::log((U.transpose() * U / n).determinant()); const f64 np = static_cast<f64>(X.cols()) * Nd;
	43	+ o.p.push_back(p); o.aic.push_back(ld + 2 * np / n); o.bic.push_back(ld + std::log(n) * np / n); o.hqic.push_back(ld + 2 * std::log(std::log(n)) * np / n); }
	44	+ auto best = [&](const std::vector<f64>& v) { int b = 0; for (usize i = 1; i < v.size(); ++i) if (v[i] < v[static_cast<usize>(b)]) b = static_cast<int>(i); return o.p[static_cast<usize>(b)]; };
	45	+ o.aic_best = best(o.aic); o.bic_best = best(o.bic); o.hqic_best = best(o.hqic); return o;
	46	+}
	47	+
	48	+std::vector<Eigen::MatrixXd> var_ma(const VarFit& f, int H) {
	49	+ const int N = f.N; std::vector<Eigen::MatrixXd> Phi(static_cast<usize>(H)); Phi[0] = Eigen::MatrixXd::Identity(N, N);
	50	+ for (int h = 1; h < H; ++h) { Phi[static_cast<usize>(h)] = Eigen::MatrixXd::Zero(N, N); for (int j = 1; j <= std::min(h, f.p); ++j) Phi[static_cast<usize>(h)] += f.coef.block(0, 1 + (j - 1) * N, N, N) * Phi[static_cast<usize>(h - j)]; }
	51	+ return Phi;
	52	+}
	53	+
	54	+Eigen::MatrixXd gfevd(const VarFit& f, int H) {
	55	+ RAID_REQUIRE(H >= 1, invalid_argument, "gfevd: H >= 1"); const int N = f.N; auto Phi = var_ma(f, H); const Eigen::MatrixXd& S = f.sigma;
	56	+ Eigen::MatrixXd num = Eigen::MatrixXd::Zero(N, N); Eigen::VectorXd den = Eigen::VectorXd::Zero(N);
	57	+ for (int h = 0; h < H; ++h) { const Eigen::MatrixXd PS = Phi[static_cast<usize>(h)] * S; for (int i = 0; i < N; ++i) { den[i] += (PS.row(i) * Phi[static_cast<usize>(h)].row(i).transpose())(0, 0); for (int j = 0; j < N; ++j) num(i, j) += PS(i, j) * PS(i, j) / S(j, j); } }
	58	+ Eigen::MatrixXd th(N, N); for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) th(i, j) = num(i, j) / den[i];
	59	+ for (int i = 0; i < N; ++i) th.row(i) /= th.row(i).sum();
	60	+ return th;
	61	+}
	62	+
	63	+Eigen::MatrixXd fevd_cholesky(const VarFit& f, int H) {
	64	+ const int N = f.N; auto Phi = var_ma(f, H); Eigen::LLT<Eigen::MatrixXd> llt(f.sigma); RAID_REQUIRE(llt.info() == Eigen::Success, numerical, "fevd: Σ not PD"); const Eigen::MatrixXd P = llt.matrixL();
	65	+ Eigen::MatrixXd num = Eigen::MatrixXd::Zero(N, N); Eigen::VectorXd den = Eigen::VectorXd::Zero(N);
	66	+ for (int h = 0; h < H; ++h) { const Eigen::MatrixXd Th = Phi[static_cast<usize>(h)] * P; for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) { num(i, j) += Th(i, j) * Th(i, j); den[i] += Th(i, j) * Th(i, j); } }
	67	+ Eigen::MatrixXd out(N, N); for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) out(i, j) = num(i, j) / den[i]; return out;
	68	+}
	69	+
	70	+Connectedness connectedness(const Eigen::MatrixXd& th) {
	71	+ const Eigen::Index N = th.rows(); Connectedness c; c.table = th; c.from.resize(N); c.to.resize(N); c.net.resize(N); f64 off = 0;
	72	+ for (Eigen::Index i = 0; i < N; ++i) { f64 fr = 0, to = 0; for (Eigen::Index j = 0; j < N; ++j) if (i != j) { fr += th(i, j); to += th(j, i); off += th(i, j); } c.from[i] = 100.0 * fr; c.to[i] = 100.0 * to; c.net[i] = c.to[i] - c.from[i]; }
	73	+ c.total = 100.0 * off / static_cast<f64>(N); c.H = 0; return c;
	74	+}
	75	+Connectedness connectedness(const VarFit& f, int H) { auto c = connectedness(gfevd(f, H)); c.H = H; return c; }
	76	+
	77	+RollingConnectedness rolling_connectedness(const Eigen::Ref<const Eigen::MatrixXd>& Y, int p, int H, usize window, usize step) {
	78	+ const auto t0 = std::chrono::steady_clock::now(); RollingConnectedness r; const usize T = static_cast<usize>(Y.rows()), N = static_cast<usize>(Y.cols());
	79	+ RAID_REQUIRE(window <= T && window > static_cast<usize>(p + static_cast<int>(N) * p + 10), insufficient_samples, "rolling_connectedness: window");
	80	+ const usize nw = (T - window) / step + 1; r.end_index.resize(nw); r.total.assign(nw, std::numeric_limits<f64>::quiet_NaN()); r.net.resize(static_cast<Eigen::Index>(N), static_cast<Eigen::Index>(nw)); r.net.setConstant(std::numeric_limits<f64>::quiet_NaN()); std::atomic<usize> fails{0};
	81	+ Eigen::MatrixXd Yc = Y;
	82	+ ThreadPool::global().parallel_for(nw, [&](usize a, usize b) { for (usize w = a; w < b; ++w) { const usize beg = w * step; r.end_index[w] = beg + window; try { auto f = var_fit(Yc.middleRows(static_cast<Eigen::Index>(beg), static_cast<Eigen::Index>(window)), p); auto c = connectedness(f, H); r.total[w] = c.total; r.net.col(static_cast<Eigen::Index>(w)) = c.net; } catch (const RaidError&) { ++fails; } } });
	83	+ r.n_windows = nw; r.failures = fails.load(); r.seconds = std::chrono::duration<f64>(std::chrono::steady_clock::now() - t0).count(); return r;
	84	+}
	85	+
	86	+ShrunkCovariance ledoit_wolf(const Eigen::Ref<const Eigen::MatrixXd>& X0, bool assume_centered) {
	87	+ // Ledoit & Wolf (2004) "A well-conditioned estimator for large-dimensional covariance matrices", as sklearn.covariance.ledoit_wolf
	88	+ const Eigen::Index n = X0.rows(), p = X0.cols(); RAID_REQUIRE(n >= 2, insufficient_samples, "ledoit_wolf: n >= 2");
	89	+ Eigen::MatrixXd X = X0; if (!assume_centered) X.rowwise() -= X0.colwise().mean();
	90	+ const Eigen::MatrixXd S = X.transpose() * X / static_cast<f64>(n); const f64 mu = S.trace() / static_cast<f64>(p);
	91	+ // δ² = \|\|S − μI\|\|²_F / p ; β̄ = (1/n²) Σ_i \|\|x_i x_i' − S\|\|²_F / p (sklearn formula); shrinkage = min(β̄/δ², 1)
	92	+ const f64 delta2 = (S - mu * Eigen::MatrixXd::Identity(p, p)).squaredNorm() / static_cast<f64>(p);
	93	+ f64 beta = 0; for (Eigen::Index i = 0; i < n; ++i) { const Eigen::MatrixXd xx = X.row(i).transpose() * X.row(i); beta += (xx - S).squaredNorm(); } beta /= static_cast<f64>(n) * static_cast<f64>(n) * static_cast<f64>(p);
	94	+ const f64 shrink = delta2 > 0 ? std::min(1.0, beta / delta2) : 0.0;
	95	+ ShrunkCovariance out; out.shrinkage = shrink; out.mu = mu; out.cov = (1 - shrink) * S + shrink * mu * Eigen::MatrixXd::Identity(p, p); return out;
	96	+}
	97	+
	98	+} // namespace raid::models

added tests/reference/test_var_reference.cpp +26 −0

		`@@ -0,0 +1,26 @@`
	1	+#include <catch2/catch_test_macros.hpp>
	2	+#include <catch2/matchers/catch_matchers_floating_point.hpp>
	3	+#include <nlohmann/json.hpp>
	4	+#include <fstream>
	5	+#include "raid/models/var.hpp"
	6	+#include "raid/core/rng.hpp"
	7	+using namespace raid; using json = nlohmann::json; using Catch::Matchers::WithinRel; using Catch::Matchers::WithinAbs;
	8	+
	9	+static Eigen::MatrixXd load_var_csv(int& N) { std::ifstream f(std::string(RAID_SOURCE_DIR) + "/datasets/fixtures/var_panel.csv"); REQUIRE(f.good()); std::string line; std::getline(f, line); std::vector<std::vector<double>> rows; while (std::getline(f, line)) { std::vector<double> r; usize s = 0; for (usize i = 0; i <= line.size(); ++i) if (i == line.size() \|\| line[i] == ',') { r.push_back(std::stod(line.substr(s, i - s))); s = i + 1; } rows.push_back(r); } N = static_cast<int>(rows[0].size()); Eigen::MatrixXd Y(rows.size(), N); for (usize i = 0; i < rows.size(); ++i) for (int j = 0; j < N; ++j) Y(static_cast<Eigen::Index>(i), j) = rows[i][static_cast<usize>(j)]; return Y; }
	10	+
	11	+TEST_CASE("VAR(2) coefficients, Σ, FEVD and generalized FEVD match statsmodels", "[reference][var]") {
	12	+ std::ifstream f(std::string(RAID_SOURCE_DIR) + "/datasets/fixtures/reference_values.json"); json ref; f >> ref; auto v = ref["var"]; int N; auto Y = load_var_csv(N);
	13	+ auto fit = models::var_fit(Y, 2); CHECK(fit.n_obs == v["nobs"].get<usize>()); CHECK(fit.stable);
	14	+ // statsmodels params: (1 + N p) × N, rows = [const, L1.y1..L1.yN, L2...], our coef is N × (1+Np)
	15	+ for (int i = 0; i < N; ++i) for (int c = 0; c < 1 + 2 * N; ++c) CHECK_THAT(fit.coef(i, c), WithinAbs(v["params"][c][i].get<double>(), 1e-9));
	16	+ for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) CHECK_THAT(fit.sigma(i, j), WithinRel(v["sigma_u"][i][j].get<double>(), 1e-9));
	17	+ CHECK_THAT(fit.loglik, WithinRel(v["llf"].get<double>(), 1e-9));
	18	+ auto fo = models::fevd_cholesky(fit, 10); for (int i = 0; i < N; ++i) for (int j = 0; j < N; ++j) CHECK_THAT(fo(i, j), WithinAbs(v["fevd10"][i][j].get<double>(), 1e-9));
	19	+ auto g = models::gfevd(fit, 10); for (int i = 0; i < N; ++i) { double rs = 0; for (int j = 0; j < N; ++j) { rs += g(i, j); CHECK_THAT(g(i, j), WithinAbs(v["gfevd10"][i][j].get<double>(), 1e-9)); } CHECK_THAT(rs, WithinAbs(1.0, 1e-12)); }
	20	+ auto c = models::connectedness(fit, 10); CHECK_THAT(c.total, WithinAbs(v["dy_total10"].get<double>(), 1e-7)); for (int i = 0; i < N; ++i) { CHECK_THAT(c.from[i], WithinAbs(v["dy_from10"][i].get<double>(), 1e-7)); CHECK_THAT(c.to[i], WithinAbs(v["dy_to10"][i].get<double>(), 1e-7)); }
	21	+ auto ord = models::var_select_order(Y, 4); CHECK(ord.bic_best == v["bic_order"].get<int>());
	22	+ auto lw = models::ledoit_wolf(Y); CHECK_THAT(lw.shrinkage, WithinAbs(v["lw_shrinkage"].get<double>(), 1e-9)); for (int i = 0; i < N; ++i) CHECK_THAT(lw.cov(i, i), WithinRel(v["lw_cov"][i][i].get<double>(), 1e-9));
	23	+}
	24	+TEST_CASE("Rolling connectedness runs in parallel and totals are bounded", "[var]") {
	25	+ int N; auto Y = load_var_csv(N); auto r = models::rolling_connectedness(Y, 2, 10, 300, 25); CHECK(r.n_windows > 5); CHECK(r.failures == 0); for (double t : r.total) { CHECK(t >= 0); CHECK(t <= 100); }
	26	+}
	27

spb/wp40_uqo

WP40 RAID: Phase 5 — VAR(p), FEVD/GFEVD, Diebold–Yilmaz connectedness (rolling), Ledoit–Wolf; statsmodels references; registry/status

Theme