LMFDB - Embedded newform 287.3.d.a.286.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,3,Mod(286,287)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("287.286");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	287.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$7.82018358714$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	7.7.19468476636329.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 14x^{5} + 56x^{3} - 56x - 15 $ x^7 - 14x^5 + 56x^3 - 56*x - 15
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{2}]$

Embedding invariants

Embedding label			286.6
Root			$-2.67770$ of defining polynomial
Character	$\chi$	$=$	287.286

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3.17010 q^{2} +5.18274 q^{3} +6.04955 q^{4} +16.4298 q^{6} -7.00000 q^{7} +6.49729 q^{8} +17.8608 q^{9} +O(q^{10})$	$q+3.17010 q^{2} +5.18274 q^{3} +6.04955 q^{4} +16.4298 q^{6} -7.00000 q^{7} +6.49729 q^{8} +17.8608 q^{9} +31.3533 q^{12} -19.8559 q^{13} -22.1907 q^{14} -3.60112 q^{16} -33.9825 q^{17} +56.6206 q^{18} +30.2825 q^{19} -36.2792 q^{21} +30.2483 q^{23} +33.6738 q^{24} +25.0000 q^{25} -62.9452 q^{26} +45.9234 q^{27} -42.3469 q^{28} -37.4051 q^{32} -107.728 q^{34} +108.050 q^{36} -70.5775 q^{37} +95.9985 q^{38} -102.908 q^{39} +41.0000 q^{41} -115.009 q^{42} +45.0824 q^{43} +95.8901 q^{46} +56.2266 q^{47} -18.6637 q^{48} +49.0000 q^{49} +79.2526 q^{50} -176.122 q^{51} -120.119 q^{52} +145.582 q^{54} -45.4810 q^{56} +156.946 q^{57} -125.026 q^{63} -104.174 q^{64} -205.579 q^{68} +156.769 q^{69} +116.047 q^{72} -223.738 q^{74} +129.569 q^{75} +183.195 q^{76} -326.229 q^{78} +77.2616 q^{81} +129.974 q^{82} -219.473 q^{84} +142.916 q^{86} +113.630 q^{89} +138.991 q^{91} +182.988 q^{92} +178.244 q^{94} -193.861 q^{96} -185.731 q^{97} +155.335 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 28 q^{4} - 49 q^{7} + 63 q^{9}+O(q^{10}) $ 7 * q + 28 * q^4 - 49 * q^7 + 63 * q^9	$ 7 q + 28 q^{4} - 49 q^{7} + 63 q^{9} + 119 q^{12} + 112 q^{16} + 175 q^{25} - 77 q^{26} - 196 q^{28} + 252 q^{36} + 287 q^{41} + 476 q^{48} + 343 q^{49} - 469 q^{54} - 441 q^{63} + 448 q^{64} + 182 q^{69} - 1001 q^{72} - 973 q^{74} - 917 q^{78} + 567 q^{81} - 833 q^{84} - 721 q^{92} + 1267 q^{94} - 1057 q^{96}+O(q^{100}) $ 7 * q + 28 * q^4 - 49 * q^7 + 63 * q^9 + 119 * q^12 + 112 * q^16 + 175 * q^25 - 77 * q^26 - 196 * q^28 + 252 * q^36 + 287 * q^41 + 476 * q^48 + 343 * q^49 - 469 * q^54 - 441 * q^63 + 448 * q^64 + 182 * q^69 - 1001 * q^72 - 973 * q^74 - 917 * q^78 + 567 * q^81 - 833 * q^84 - 721 * q^92 + 1267 * q^94 - 1057 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$-1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	3.17010	1.58505	0.792526	−	0.609838i	$-0.208766\pi$
$2$	3.17010	1.58505	0.792526	+	0.609838i	$0.208766\pi$
$3$	5.18274	1.72758	0.863790	−	0.503851i	$-0.168084\pi$
$3$	5.18274	1.72758	0.863790	+	0.503851i	$0.168084\pi$
$4$	6.04955	1.51239
$5$	0	0	1.00000			$0$
$5$	0	0	−1.00000			$\pi$
$6$	16.4298	2.73830
$7$	−7.00000	−1.00000
$7$	−7.00000	−1.00000
$8$	6.49729	0.812162
$9$	17.8608	1.98454
$10$	0	0
$11$	0	0	1.00000			$0$
$11$	0	0	−1.00000			$\pi$
$12$	31.3533	2.61277
$13$	−19.8559	−1.52737	−0.763687	−	0.645586i	$-0.776613\pi$
$13$	−19.8559	−1.52737	−0.763687	+	0.645586i	$0.776613\pi$
$14$	−22.1907	−1.58505
$15$	0	0
$16$	−3.60112	−0.225070
$17$	−33.9825	−1.99897	−0.999484	−	0.0321234i	$-0.989773\pi$
$17$	−33.9825	−1.99897	−0.999484	+	0.0321234i	$0.989773\pi$
$18$	56.6206	3.14559
$19$	30.2825	1.59381	0.796907	−	0.604102i	$-0.206468\pi$
$19$	30.2825	1.59381	0.796907	+	0.604102i	$0.206468\pi$
$20$	0	0
$21$	−36.2792	−1.72758
$22$	0	0
$23$	30.2483	1.31514	0.657571	−	0.753393i	$-0.271584\pi$
$23$	30.2483	1.31514	0.657571	+	0.753393i	$0.271584\pi$
$24$	33.6738	1.40307
$25$	25.0000	1.00000
$26$	−62.9452	−2.42097
$27$	45.9234	1.70087
$28$	−42.3469	−1.51239
$29$	0	0	1.00000			$0$
$29$	0	0	−1.00000			$\pi$
$30$	0	0
$31$	0	0	1.00000			$0$
$31$	0	0	−1.00000			$\pi$
$32$	−37.4051	−1.16891
$33$	0	0
$34$	−107.728	−3.16847
$35$	0	0
$36$	108.050	3.00139
$37$	−70.5775	−1.90750	−0.953750	−	0.300600i	$-0.902813\pi$
$37$	−70.5775	−1.90750	−0.953750	+	0.300600i	$0.902813\pi$
$38$	95.9985	2.52628
$39$	−102.908	−2.63866
$40$	0	0
$41$	41.0000	1.00000
$41$	41.0000	1.00000
$42$	−115.009	−2.73830
$43$	45.0824	1.04843	0.524214	−	0.851586i	$-0.324359\pi$
$43$	45.0824	1.04843	0.524214	+	0.851586i	$0.324359\pi$
$44$	0	0
$45$	0	0
$46$	95.8901	2.08457
$47$	56.2266	1.19631	0.598155	−	0.801380i	$-0.295901\pi$
$47$	56.2266	1.19631	0.598155	+	0.801380i	$0.295901\pi$
$48$	−18.6637	−0.388827
$49$	49.0000	1.00000
$50$	79.2526	1.58505
$51$	−176.122	−3.45338
$52$	−120.119	−2.30998
$53$	0	0	1.00000			$0$
$53$	0	0	−1.00000			$\pi$
$54$	145.582	2.69596
$55$	0	0
$56$	−45.4810	−0.812162
$57$	156.946	2.75344
$58$	0	0
$59$	0	0	1.00000			$0$
$59$	0	0	−1.00000			$\pi$
$60$	0	0
$61$	0	0	1.00000			$0$
$61$	0	0	−1.00000			$\pi$
$62$	0	0
$63$	−125.026	−1.98454
$64$	−104.174	−1.62771
$65$	0	0
$66$	0	0
$67$	0	0	1.00000			$0$
$67$	0	0	−1.00000			$\pi$
$68$	−205.579	−3.02322
$69$	156.769	2.27201
$70$	0	0
$71$	0	0	1.00000			$0$
$71$	0	0	−1.00000			$\pi$
$72$	116.047	1.61176
$73$	0	0	1.00000			$0$
$73$	0	0	−1.00000			$\pi$
$74$	−223.738	−3.02349
$75$	129.569	1.72758
$76$	183.195	2.41047
$77$	0	0
$78$	−326.229	−4.18242
$79$	0	0	1.00000			$0$
$79$	0	0	−1.00000			$\pi$
$80$	0	0
$81$	77.2616	0.953847
$82$	129.974	1.58505
$83$	0	0	1.00000			$0$
$83$	0	0	−1.00000			$\pi$
$84$	−219.473	−2.61277
$85$	0	0
$86$	142.916	1.66181
$87$	0	0
$88$	0	0
$89$	113.630	1.27674	0.638372	−	0.769728i	$-0.279608\pi$
$89$	113.630	1.27674	0.638372	+	0.769728i	$0.279608\pi$
$90$	0	0
$91$	138.991	1.52737
$92$	182.988	1.98901
$93$	0	0
$94$	178.244	1.89621
$95$	0	0
$96$	−193.861	−2.01939
$97$	−185.731	−1.91475	−0.957374	−	0.288851i	$-0.906727\pi$
$97$	−185.731	−1.91475	−0.957374	+	0.288851i	$0.906727\pi$
$98$	155.335	1.58505
$99$	0	0
$100$	151.239	1.51239
$101$	−110.534	−1.09440	−0.547198	−	0.837003i	$-0.684306\pi$
$101$	−110.534	−1.09440	−0.547198	+	0.837003i	$0.684306\pi$
$102$	−558.326	−5.47378
$103$	0	0	1.00000			$0$
$103$	0	0	−1.00000			$\pi$
$104$	−129.009	−1.24048
$105$	0	0
$106$	0	0
$107$	−127.847	−1.19483	−0.597417	−	0.801931i	$-0.703806\pi$
$107$	−127.847	−1.19483	−0.597417	+	0.801931i	$0.703806\pi$
$108$	277.816	2.57237
$109$	0	0	1.00000			$0$
$109$	0	0	−1.00000			$\pi$
$110$	0	0
$111$	−365.785	−3.29536
$112$	25.2079	0.225070
$113$	−120.145	−1.06323	−0.531614	−	0.846986i	$-0.678414\pi$
$113$	−120.145	−1.06323	−0.531614	+	0.846986i	$0.678414\pi$
$114$	497.536	4.36435
$115$	0	0
$116$	0	0
$117$	−354.642	−3.03113
$118$	0	0
$119$	237.877	1.99897
$120$	0	0
$121$	121.000	1.00000
$122$	0	0
$123$	212.492	1.72758
$124$	0	0
$125$	0	0
$126$	−396.345	−3.14559
$127$	−51.8987	−0.408651	−0.204326	−	0.978903i	$-0.565500\pi$
$127$	−51.8987	−0.408651	−0.204326	+	0.978903i	$0.565500\pi$
$128$	−180.620	−1.41110
$129$	233.651	1.81125
$130$	0	0
$131$	0	0	1.00000			$0$
$131$	0	0	−1.00000			$\pi$
$132$	0	0
$133$	−211.977	−1.59381
$134$	0	0
$135$	0	0
$136$	−220.794	−1.62348
$137$	0	0	1.00000			$0$
$137$	0	0	−1.00000			$\pi$
$138$	496.974	3.60126
$139$	0	0	1.00000			$0$
$139$	0	0	−1.00000			$\pi$
$140$	0	0
$141$	291.408	2.06672
$142$	0	0
$143$	0	0
$144$	−64.3190	−0.446660
$145$	0	0
$146$	0	0
$147$	253.954	1.72758
$148$	−426.962	−2.88488
$149$	0	0	1.00000			$0$
$149$	0	0	−1.00000			$\pi$
$150$	410.746	2.73830
$151$	0	0	1.00000			$0$
$151$	0	0	−1.00000			$\pi$
$152$	196.754	1.29443
$153$	−606.955	−3.96702
$154$	0	0
$155$	0	0
$156$	−622.547	−3.99068
$157$	−53.8475	−0.342978	−0.171489	−	0.985186i	$-0.554858\pi$
$157$	−53.8475	−0.342978	−0.171489	+	0.985186i	$0.554858\pi$
$158$	0	0
$159$	0	0
$160$	0	0
$161$	−211.738	−1.31514
$162$	244.927	1.51190
$163$	−143.327	−0.879306	−0.439653	−	0.898168i	$-0.644899\pi$
$163$	−143.327	−0.879306	−0.439653	+	0.898168i	$0.644899\pi$
$164$	248.032	1.51239
$165$	0	0
$166$	0	0
$167$	267.477	1.60166	0.800830	−	0.598892i	$-0.204392\pi$
$167$	267.477	1.60166	0.800830	+	0.598892i	$0.204392\pi$
$168$	−235.717	−1.40307
$169$	225.256	1.33287
$170$	0	0
$171$	540.870	3.16298
$172$	272.729	1.58563
$173$	0	0	1.00000			$0$
$173$	0	0	−1.00000			$\pi$
$174$	0	0
$175$	−175.000	−1.00000
$176$	0	0
$177$	0	0
$178$	360.220	2.02371
$179$	0	0	1.00000			$0$
$179$	0	0	−1.00000			$\pi$
$180$	0	0
$181$	164.245	0.907431	0.453715	−	0.891147i	$-0.350098\pi$
$181$	164.245	0.907431	0.453715	+	0.891147i	$0.350098\pi$
$182$	440.616	2.42097
$183$	0	0
$184$	196.532	1.06811
$185$	0	0
$186$	0	0
$187$	0	0
$188$	340.146	1.80929
$189$	−321.464	−1.70087
$190$	0	0
$191$	0	0	1.00000			$0$
$191$	0	0	−1.00000			$\pi$
$192$	−539.905	−2.81200
$193$	0	0	1.00000			$0$
$193$	0	0	−1.00000			$\pi$
$194$	−588.785	−3.03497
$195$	0	0
$196$	296.428	1.51239
$197$	−384.907	−1.95384	−0.976921	−	0.213600i	$-0.931481\pi$
$197$	−384.907	−1.95384	−0.976921	+	0.213600i	$0.931481\pi$
$198$	0	0
$199$	323.199	1.62411	0.812057	−	0.583577i	$-0.198348\pi$
$199$	323.199	1.62411	0.812057	+	0.583577i	$0.198348\pi$
$200$	162.432	0.812162
$201$	0	0
$202$	−350.404	−1.73467
$203$	0	0
$204$	−1065.46	−5.22285
$205$	0	0
$206$	0	0
$207$	540.259	2.60995
$208$	71.5034	0.343767
$209$	0	0
$210$	0	0
$211$	0	0	1.00000			$0$
$211$	0	0	−1.00000			$\pi$
$212$	0	0
$213$	0	0
$214$	−405.289	−1.89387
$215$	0	0
$216$	298.378	1.38138
$217$	0	0
$218$	0	0
$219$	0	0
$220$	0	0
$221$	674.751	3.05317
$222$	−1159.58	−5.22332
$223$	0	0	1.00000			$0$
$223$	0	0	−1.00000			$\pi$
$224$	261.836	1.16891
$225$	446.521	1.98454
$226$	−380.872	−1.68527
$227$	202.000	0.889868	0.444934	−	0.895563i	$-0.353227\pi$
$227$	202.000	0.889868	0.444934	+	0.895563i	$0.353227\pi$
$228$	949.454	4.16427
$229$	−162.549	−0.709819	−0.354910	−	0.934901i	$-0.615488\pi$
$229$	−162.549	−0.709819	−0.354910	+	0.934901i	$0.615488\pi$
$230$	0	0
$231$	0	0
$232$	0	0
$233$	0	0	1.00000			$0$
$233$	0	0	−1.00000			$\pi$
$234$	−1124.25	−4.80450
$235$	0	0
$236$	0	0
$237$	0	0
$238$	754.095	3.16847
$239$	0	0	1.00000			$0$
$239$	0	0	−1.00000			$\pi$
$240$	0	0
$241$	0	0	1.00000			$0$
$241$	0	0	−1.00000			$\pi$
$242$	383.582	1.58505
$243$	−12.8833	−0.0530176
$244$	0	0
$245$	0	0
$246$	673.623	2.73830
$247$	−601.285	−2.43435
$248$	0	0
$249$	0	0
$250$	0	0
$251$	0	0	1.00000			$0$
$251$	0	0	−1.00000			$\pi$
$252$	−756.350	−3.00139
$253$	0	0
$254$	−164.524	−0.647733
$255$	0	0
$256$	−155.891	−0.608950
$257$	363.827	1.41567	0.707835	−	0.706377i	$-0.249672\pi$
$257$	363.827	1.41567	0.707835	+	0.706377i	$0.249672\pi$
$258$	740.697	2.87092
$259$	494.043	1.90750
$260$	0	0
$261$	0	0
$262$	0	0
$263$	0	0	1.00000			$0$
$263$	0	0	−1.00000			$\pi$
$264$	0	0
$265$	0	0
$266$	−671.990	−2.52628
$267$	588.916	2.20568
$268$	0	0
$269$	0	0	1.00000			$0$
$269$	0	0	−1.00000			$\pi$
$270$	0	0
$271$	0	0	1.00000			$0$
$271$	0	0	−1.00000			$\pi$
$272$	122.375	0.449908
$273$	720.355	2.63866
$274$	0	0
$275$	0	0
$276$	948.382	3.43617
$277$	504.610	1.82170	0.910848	−	0.412743i	$-0.135429\pi$
$277$	504.610	1.82170	0.910848	+	0.412743i	$0.135429\pi$
$278$	0	0
$279$	0	0
$280$	0	0
$281$	0	0	1.00000			$0$
$281$	0	0	−1.00000			$\pi$
$282$	923.793	3.27586
$283$	0	0	1.00000			$0$
$283$	0	0	−1.00000			$\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−287.000	−1.00000
$288$	−668.086	−2.31974
$289$	865.807	2.99587
$290$	0	0
$291$	−962.594	−3.30788
$292$	0	0
$293$	−422.000	−1.44027	−0.720137	−	0.693832i	$-0.755921\pi$
$293$	−422.000	−1.44027	−0.720137	+	0.693832i	$0.755921\pi$
$294$	805.062	2.73830
$295$	0	0
$296$	−458.563	−1.54920
$297$	0	0
$298$	0	0
$299$	−600.606	−2.00871
$300$	783.832	2.61277
$301$	−315.577	−1.04843
$302$	0	0
$303$	−572.869	−1.89066
$304$	−109.051	−0.358720
$305$	0	0
$306$	−1924.11	−6.28794
$307$	0	0	1.00000			$0$
$307$	0	0	−1.00000			$\pi$
$308$	0	0
$309$	0	0
$310$	0	0
$311$	5.74760	0.0184810	0.00924051	−	0.999957i	$-0.497059\pi$
$311$	5.74760	0.0184810	0.00924051	+	0.999957i	$0.497059\pi$
$312$	−668.623	−2.14302
$313$	440.407	1.40705	0.703525	−	0.710670i	$-0.251608\pi$
$313$	440.407	1.40705	0.703525	+	0.710670i	$0.251608\pi$
$314$	−170.702	−0.543637
$315$	0	0
$316$	0	0
$317$	0	0	1.00000			$0$
$317$	0	0	−1.00000			$\pi$
$318$	0	0
$319$	0	0
$320$	0	0
$321$	−662.600	−2.06417
$322$	−671.231	−2.08457
$323$	−1029.07	−3.18598
$324$	467.398	1.44259
$325$	−496.397	−1.52737
$326$	−454.361	−1.39374
$327$	0	0
$328$	266.389	0.812162
$329$	−393.586	−1.19631
$330$	0	0
$331$	0	0	1.00000			$0$
$331$	0	0	−1.00000			$\pi$
$332$	0	0
$333$	−1260.57	−3.78550
$334$	847.930	2.53871
$335$	0	0
$336$	130.646	0.388827
$337$	−643.695	−1.91008	−0.955038	−	0.296484i	$-0.904186\pi$
$337$	−643.695	−1.91008	−0.955038	+	0.296484i	$0.904186\pi$
$338$	714.083	2.11267
$339$	−622.680	−1.83681
$340$	0	0
$341$	0	0
$342$	1714.61	5.01349
$343$	−343.000	−1.00000
$344$	292.914	0.851493
$345$	0	0
$346$	0	0
$347$	0	0	1.00000			$0$
$347$	0	0	−1.00000			$\pi$
$348$	0	0
$349$	0	0	1.00000			$0$
$349$	0	0	−1.00000			$\pi$
$350$	−554.768	−1.58505
$351$	−911.848	−2.59786
$352$	0	0
$353$	0	0	1.00000			$0$
$353$	0	0	−1.00000			$\pi$
$354$	0	0
$355$	0	0
$356$	687.412	1.93093
$357$	1232.86	3.45338
$358$	0	0
$359$	−717.962	−1.99989	−0.999947	−	0.0102692i	$-0.996731\pi$
$359$	−717.962	−1.99989	−0.999947	+	0.0102692i	$0.996731\pi$
$360$	0	0
$361$	556.028	1.54024
$362$	520.673	1.43832
$363$	627.112	1.72758
$364$	840.834	2.30998
$365$	0	0
$366$	0	0
$367$	0	0	1.00000			$0$
$367$	0	0	−1.00000			$\pi$
$368$	−108.928	−0.295999
$369$	732.294	1.98454
$370$	0	0
$371$	0	0
$372$	0	0
$373$	732.131	1.96282	0.981409	−	0.191926i	$-0.0614732\pi$
$373$	732.131	1.96282	0.981409	+	0.191926i	$0.0614732\pi$
$374$	0	0
$375$	0	0
$376$	365.321	0.971598
$377$	0	0
$378$	−1019.07	−2.69596
$379$	753.381	1.98781	0.993907	−	0.110225i	$-0.0351570\pi$
$379$	753.381	1.98781	0.993907	+	0.110225i	$0.0351570\pi$
$380$	0	0
$381$	−268.978	−0.705978
$382$	0	0
$383$	−683.274	−1.78400	−0.892002	−	0.452031i	$-0.850700\pi$
$383$	−683.274	−1.78400	−0.892002	+	0.452031i	$0.850700\pi$
$384$	−936.109	−2.43778
$385$	0	0
$386$	0	0
$387$	805.209	2.08064
$388$	−1123.59	−2.89584
$389$	−50.5315	−0.129901	−0.0649505	−	0.997888i	$-0.520689\pi$
$389$	−50.5315	−0.129901	−0.0649505	+	0.997888i	$0.520689\pi$
$390$	0	0
$391$	−1027.91	−2.62893
$392$	318.367	0.812162
$393$	0	0
$394$	−1220.19	−3.09694
$395$	0	0
$396$	0	0
$397$	682.000	1.71788	0.858942	−	0.512073i	$-0.171122\pi$
$397$	682.000	1.71788	0.858942	+	0.512073i	$0.171122\pi$
$398$	1024.57	2.57431
$399$	−1098.62	−2.75344
$400$	−90.0281	−0.225070
$401$	−775.366	−1.93358	−0.966790	−	0.255571i	$-0.917737\pi$
$401$	−775.366	−1.93358	−0.966790	+	0.255571i	$0.917737\pi$
$402$	0	0
$403$	0	0
$404$	−668.681	−1.65515
$405$	0	0
$406$	0	0
$407$	0	0
$408$	−1144.32	−2.80470
$409$	0	0	1.00000			$0$
$409$	0	0	−1.00000			$\pi$
$410$	0	0
$411$	0	0
$412$	0	0
$413$	0	0
$414$	1712.68	4.13690
$415$	0	0
$416$	742.711	1.78536
$417$	0	0
$418$	0	0
$419$	0	0	1.00000			$0$
$419$	0	0	−1.00000			$\pi$
$420$	0	0
$421$	0	0	1.00000			$0$
$421$	0	0	−1.00000			$\pi$
$422$	0	0
$423$	1004.25	2.37412
$424$	0	0
$425$	−849.561	−1.99897
$426$	0	0
$427$	0	0
$428$	−773.419	−1.80705
$429$	0	0
$430$	0	0
$431$	−286.000	−0.663573	−0.331787	−	0.943354i	$-0.607651\pi$
$431$	−286.000	−0.663573	−0.331787	+	0.943354i	$0.607651\pi$
$432$	−165.376	−0.382814
$433$	0	0	1.00000			$0$
$433$	0	0	−1.00000			$\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	915.992	2.09609
$438$	0	0
$439$	−859.674	−1.95826	−0.979128	−	0.203245i	$-0.934851\pi$
$439$	−859.674	−1.95826	−0.979128	+	0.203245i	$0.934851\pi$
$440$	0	0
$441$	875.180	1.98454
$442$	2139.03	4.83944
$443$	159.037	0.359000	0.179500	−	0.983758i	$-0.442552\pi$
$443$	159.037	0.359000	0.179500	+	0.983758i	$0.442552\pi$
$444$	−2212.84	−4.98387
$445$	0	0
$446$	0	0
$447$	0	0
$448$	729.215	1.62771
$449$	−290.895	−0.647872	−0.323936	−	0.946079i	$-0.605006\pi$
$449$	−290.895	−0.647872	−0.323936	+	0.946079i	$0.605006\pi$
$450$	1415.52	3.14559
$451$	0	0
$452$	−726.823	−1.60801
$453$	0	0
$454$	640.361	1.41049
$455$	0	0
$456$	1019.73	2.23624
$457$	0	0	1.00000			$0$
$457$	0	0	−1.00000			$\pi$
$458$	−515.296	−1.12510
$459$	−1560.59	−3.39998
$460$	0	0
$461$	0	0	1.00000			$0$
$461$	0	0	−1.00000			$\pi$
$462$	0	0
$463$	0	0	1.00000			$0$
$463$	0	0	−1.00000			$\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	0	0	1.00000			$0$
$467$	0	0	−1.00000			$\pi$
$468$	−2145.43	−4.58424
$469$	0	0
$470$	0	0
$471$	−279.078	−0.592522
$472$	0	0
$473$	0	0
$474$	0	0
$475$	757.062	1.59381
$476$	1439.05	3.02322
$477$	0	0
$478$	0	0
$479$	−107.709	−0.224861	−0.112431	−	0.993660i	$-0.535864\pi$
$479$	−107.709	−0.224861	−0.112431	+	0.993660i	$0.535864\pi$
$480$	0	0
$481$	1401.38	2.91347
$482$	0	0
$483$	−1097.38	−2.27201
$484$	731.996	1.51239
$485$	0	0
$486$	−40.8413	−0.0840356
$487$	836.126	1.71689	0.858446	−	0.512904i	$-0.171430\pi$
$487$	836.126	1.71689	0.858446	+	0.512904i	$0.171430\pi$
$488$	0	0
$489$	−742.826	−1.51907
$490$	0	0
$491$	−122.970	−0.250448	−0.125224	−	0.992128i	$-0.539965\pi$
$491$	−122.970	−0.250448	−0.125224	+	0.992128i	$0.539965\pi$
$492$	1285.48	2.61277
$493$	0	0
$494$	−1906.13	−3.85857
$495$	0	0
$496$	0	0
$497$	0	0
$498$	0	0
$499$	0	0	1.00000			$0$
$499$	0	0	−1.00000			$\pi$
$500$	0	0
$501$	1386.27	2.76700
$502$	0	0
$503$	−885.682	−1.76080	−0.880399	−	0.474233i	$-0.842725\pi$
$503$	−885.682	−1.76080	−0.880399	+	0.474233i	$0.842725\pi$
$504$	−812.329	−1.61176
$505$	0	0
$506$	0	0
$507$	1167.44	2.30265
$508$	−313.964	−0.618039
$509$	−304.140	−0.597524	−0.298762	−	0.954328i	$-0.596574\pi$
$509$	−304.140	−0.597524	−0.298762	+	0.954328i	$0.596574\pi$
$510$	0	0
$511$	0	0
$512$	228.291	0.445880
$513$	1390.67	2.71086
$514$	1153.37	2.24391
$515$	0	0
$516$	1413.48	2.73931
$517$	0	0
$518$	1566.17	3.02349
$519$	0	0
$520$	0	0
$521$	−21.2231	−0.0407354	−0.0203677	−	0.999793i	$-0.506484\pi$
$521$	−21.2231	−0.0407354	−0.0203677	+	0.999793i	$0.506484\pi$
$522$	0	0
$523$	0	0	1.00000			$0$
$523$	0	0	−1.00000			$\pi$
$524$	0	0
$525$	−906.980	−1.72758
$526$	0	0
$527$	0	0
$528$	0	0
$529$	385.958	0.729598
$530$	0	0
$531$	0	0
$532$	−1282.37	−2.41047
$533$	−814.091	−1.52737
$534$	1866.93	3.49612
$535$	0	0
$536$	0	0
$537$	0	0
$538$	0	0
$539$	0	0
$540$	0	0
$541$	−518.107	−0.957683	−0.478842	−	0.877901i	$-0.658943\pi$
$541$	−518.107	−0.957683	−0.478842	+	0.877901i	$0.658943\pi$
$542$	0	0
$543$	851.239	1.56766
$544$	1271.12	2.33661
$545$	0	0
$546$	2283.60	4.18242
$547$	0	0	1.00000			$0$
$547$	0	0	−1.00000			$\pi$
$548$	0	0
$549$	0	0
$550$	0	0
$551$	0	0
$552$	1018.57	1.84524
$553$	0	0
$554$	1599.66	2.88748
$555$	0	0
$556$	0	0
$557$	0	0	1.00000			$0$
$557$	0	0	−1.00000			$\pi$
$558$	0	0
$559$	−895.151	−1.60134
$560$	0	0
$561$	0	0
$562$	0	0
$563$	1027.99	1.82591	0.912955	−	0.408061i	$-0.133795\pi$
$563$	1027.99	1.82591	0.912955	+	0.408061i	$0.133795\pi$
$564$	1762.89	3.12569
$565$	0	0
$566$	0	0
$567$	−540.831	−0.953847
$568$	0	0
$569$	−1047.42	−1.84081	−0.920405	−	0.390966i	$-0.872141\pi$
$569$	−1047.42	−1.84081	−0.920405	+	0.390966i	$0.872141\pi$
$570$	0	0
$571$	0	0	1.00000			$0$
$571$	0	0	−1.00000			$\pi$
$572$	0	0
$573$	0	0
$574$	−909.820	−1.58505
$575$	756.207	1.31514
$576$	−1860.63	−3.23025
$577$	233.791	0.405183	0.202592	−	0.979263i	$-0.435064\pi$
$577$	233.791	0.405183	0.202592	+	0.979263i	$0.435064\pi$
$578$	2744.70	4.74861
$579$	0	0
$580$	0	0
$581$	0	0
$582$	−3051.52	−5.24316
$583$	0	0
$584$	0	0
$585$	0	0
$586$	−1337.78	−2.28291
$587$	−532.907	−0.907848	−0.453924	−	0.891040i	$-0.649976\pi$
$587$	−532.907	−0.907848	−0.453924	+	0.891040i	$0.649976\pi$
$588$	1536.31	2.61277
$589$	0	0
$590$	0	0
$591$	−1994.87	−3.37542
$592$	254.158	0.429322
$593$	−1181.14	−1.99180	−0.995901	−	0.0904463i	$-0.971171\pi$
$593$	−1181.14	−1.99180	−0.995901	+	0.0904463i	$0.971171\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	1675.06	2.80579
$598$	−1903.98	−3.18392
$599$	654.257	1.09225	0.546124	−	0.837704i	$-0.316103\pi$
$599$	654.257	1.09225	0.546124	+	0.837704i	$0.316103\pi$
$600$	841.845	1.40307
$601$	−83.0522	−0.138190	−0.0690950	−	0.997610i	$-0.522011\pi$
$601$	−83.0522	−0.138190	−0.0690950	+	0.997610i	$0.522011\pi$
$602$	−1000.41	−1.66181
$603$	0	0
$604$	0	0
$605$	0	0
$606$	−1816.05	−2.99679
$607$	0	0	1.00000			$0$
$607$	0	0	−1.00000			$\pi$
$608$	−1132.72	−1.86302
$609$	0	0
$610$	0	0
$611$	−1116.43	−1.82721
$612$	−3671.80	−5.99968
$613$	−895.292	−1.46051	−0.730255	−	0.683175i	$-0.760599\pi$
$613$	−895.292	−1.46051	−0.730255	+	0.683175i	$0.760599\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	415.477	0.673382	0.336691	−	0.941615i	$-0.390692\pi$
$617$	415.477	0.673382	0.336691	+	0.941615i	$0.390692\pi$
$618$	0	0
$619$	0	0	1.00000			$0$
$619$	0	0	−1.00000			$\pi$
$620$	0	0
$621$	1389.10	2.23688
$622$	18.2205	0.0292934
$623$	−795.412	−1.27674
$624$	370.584	0.593885
$625$	625.000	1.00000
$626$	1396.13	2.23025
$627$	0	0
$628$	−325.753	−0.518715
$629$	2398.40	3.81303
$630$	0	0
$631$	1242.87	1.96968	0.984842	−	0.173454i	$-0.0554928\pi$
$631$	1242.87	1.96968	0.984842	+	0.173454i	$0.0554928\pi$
$632$	0	0
$633$	0	0
$634$	0	0
$635$	0	0
$636$	0	0
$637$	−972.938	−1.52737
$638$	0	0
$639$	0	0
$640$	0	0
$641$	0	0	1.00000			$0$
$641$	0	0	−1.00000			$\pi$
$642$	−2100.51	−3.27182
$643$	−1142.41	−1.77669	−0.888347	−	0.459173i	$-0.848146\pi$
$643$	−1142.41	−1.77669	−0.888347	+	0.459173i	$0.848146\pi$
$644$	−1280.92	−1.98901
$645$	0	0
$646$	−3262.27	−5.04995
$647$	0	0	1.00000			$0$
$647$	0	0	−1.00000			$\pi$
$648$	501.991	0.774678
$649$	0	0
$650$	−1573.63	−2.42097
$651$	0	0
$652$	−867.063	−1.32985
$653$	0	0	1.00000			$0$
$653$	0	0	−1.00000			$\pi$
$654$	0	0
$655$	0	0
$656$	−147.646	−0.225070
$657$	0	0
$658$	−1247.71	−1.89621
$659$	0	0	1.00000			$0$
$659$	0	0	−1.00000			$\pi$
$660$	0	0
$661$	0	0	1.00000			$0$
$661$	0	0	−1.00000			$\pi$
$662$	0	0
$663$	3497.06	5.27460
$664$	0	0
$665$	0	0
$666$	−3996.14	−6.00022
$667$	0	0
$668$	1618.12	2.42233
$669$	0	0
$670$	0	0
$671$	0	0
$672$	1357.03	2.01939
$673$	0	0	1.00000			$0$
$673$	0	0	−1.00000			$\pi$
$674$	−2040.58	−3.02757
$675$	1148.08	1.70087
$676$	1362.70	2.01582
$677$	0	0	1.00000			$0$
$677$	0	0	−1.00000			$\pi$
$678$	−1973.96	−2.91144
$679$	1300.11	1.91475
$680$	0	0
$681$	1046.91	1.53732
$682$	0	0
$683$	0	0	1.00000			$0$
$683$	0	0	−1.00000			$\pi$
$684$	3272.02	4.78365
$685$	0	0
$686$	−1087.35	−1.58505
$687$	−842.448	−1.22627
$688$	−162.347	−0.235970
$689$	0	0
$690$	0	0
$691$	359.189	0.519811	0.259905	−	0.965634i	$-0.416309\pi$
$691$	359.189	0.519811	0.259905	+	0.965634i	$0.416309\pi$
$692$	0	0
$693$	0	0
$694$	0	0
$695$	0	0
$696$	0	0
$697$	−1393.28	−1.99897
$698$	0	0
$699$	0	0
$700$	−1058.67	−1.51239
$701$	939.908	1.34081	0.670405	−	0.741995i	$-0.266120\pi$
$701$	939.908	1.34081	0.670405	+	0.741995i	$0.266120\pi$
$702$	−2890.65	−4.11774
$703$	−2137.26	−3.04020
$704$	0	0
$705$	0	0
$706$	0	0
$707$	773.738	1.09440
$708$	0	0
$709$	0	0	1.00000			$0$
$709$	0	0	−1.00000			$\pi$
$710$	0	0
$711$	0	0
$712$	738.289	1.03692
$713$	0	0
$714$	3908.28	5.47378
$715$	0	0
$716$	0	0
$717$	0	0
$718$	−2276.01	−3.16994
$719$	1186.00	1.64951	0.824757	−	0.565488i	$-0.191312\pi$
$719$	1186.00	1.64951	0.824757	+	0.565488i	$0.191312\pi$
$720$	0	0
$721$	0	0
$722$	1762.66	2.44136
$723$	0	0
$724$	993.609	1.37239
$725$	0	0
$726$	1988.01	2.73830
$727$	188.017	0.258620	0.129310	−	0.991604i	$-0.458724\pi$
$727$	188.017	0.258620	0.129310	+	0.991604i	$0.458724\pi$
$728$	903.066	1.24048
$729$	−762.125	−1.04544
$730$	0	0
$731$	−1532.01	−2.09577
$732$	0	0
$733$	0	0	1.00000			$0$
$733$	0	0	−1.00000			$\pi$
$734$	0	0
$735$	0	0
$736$	−1131.44	−1.53728
$737$	0	0
$738$	2321.45	3.14559
$739$	670.201	0.906903	0.453451	−	0.891281i	$-0.350193\pi$
$739$	670.201	0.906903	0.453451	+	0.891281i	$0.350193\pi$
$740$	0	0
$741$	−3116.30	−4.20554
$742$	0	0
$743$	144.408	0.194357	0.0971787	−	0.995267i	$-0.469018\pi$
$743$	144.408	0.194357	0.0971787	+	0.995267i	$0.469018\pi$
$744$	0	0
$745$	0	0
$746$	2320.93	3.11117
$747$	0	0
$748$	0	0
$749$	894.931	1.19483
$750$	0	0
$751$	0	0	1.00000			$0$
$751$	0	0	−1.00000			$\pi$
$752$	−202.479	−0.269254
$753$	0	0
$754$	0	0
$755$	0	0
$756$	−1944.71	−2.57237
$757$	0	0	1.00000			$0$
$757$	0	0	−1.00000			$\pi$
$758$	2388.30	3.15079
$759$	0	0
$760$	0	0
$761$	0	0	1.00000			$0$
$761$	0	0	−1.00000			$\pi$
$762$	−852.687	−1.11901
$763$	0	0
$764$	0	0
$765$	0	0
$766$	−2166.05	−2.82774
$767$	0	0
$768$	−807.944	−1.05201
$769$	0	0	1.00000			$0$
$769$	0	0	−1.00000			$\pi$
$770$	0	0
$771$	1885.62	2.44569
$772$	0	0
$773$	925.321	1.19705	0.598526	−	0.801103i	$-0.295753\pi$
$773$	925.321	1.19705	0.598526	+	0.801103i	$0.295753\pi$
$774$	2552.60	3.29793
$775$	0	0
$776$	−1206.75	−1.55508
$777$	2560.50	3.29536
$778$	−160.190	−0.205900
$779$	1241.58	1.59381
$780$	0	0
$781$	0	0
$782$	−3258.58	−4.16698
$783$	0	0
$784$	−176.455	−0.225070
$785$	0	0
$786$	0	0
$787$	0	0	1.00000			$0$
$787$	0	0	−1.00000			$\pi$
$788$	−2328.51	−2.95497
$789$	0	0
$790$	0	0
$791$	841.014	1.06323
$792$	0	0
$793$	0	0
$794$	2162.01	2.72293
$795$	0	0
$796$	1955.21	2.45629
$797$	0	0	1.00000			$0$
$797$	0	0	−1.00000			$\pi$
$798$	−3482.75	−4.36435
$799$	−1910.72	−2.39139
$800$	−935.128	−1.16891
$801$	2029.53	2.53375
$802$	−2457.99	−3.06482
$803$	0	0
$804$	0	0
$805$	0	0
$806$	0	0
$807$	0	0
$808$	−718.172	−0.888826
$809$	0	0	1.00000			$0$
$809$	0	0	−1.00000			$\pi$
$810$	0	0
$811$	0	0	1.00000			$0$
$811$	0	0	−1.00000			$\pi$
$812$	0	0
$813$	0	0
$814$	0	0
$815$	0	0
$816$	634.238	0.777253
$817$	1365.21	1.67100
$818$	0	0
$819$	2482.50	3.03113
$820$	0	0
$821$	−478.377	−0.582675	−0.291338	−	0.956620i	$-0.594100\pi$
$821$	−478.377	−0.582675	−0.291338	+	0.956620i	$0.594100\pi$
$822$	0	0
$823$	0	0	1.00000			$0$
$823$	0	0	−1.00000			$\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	0	0	1.00000			$0$
$827$	0	0	−1.00000			$\pi$
$828$	3268.32	3.94725
$829$	0	0	1.00000			$0$
$829$	0	0	−1.00000			$\pi$
$830$	0	0
$831$	2615.26	3.14713
$832$	2068.46	2.48613
$833$	−1665.14	−1.99897
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0	0
$838$	0	0
$839$	−714.932	−0.852124	−0.426062	−	0.904694i	$-0.640099\pi$
$839$	−714.932	−0.852124	−0.426062	+	0.904694i	$0.640099\pi$
$840$	0	0
$841$	841.000	1.00000
$842$	0	0
$843$	0	0
$844$	0	0
$845$	0	0
$846$	3183.59	3.76310
$847$	−847.000	−1.00000
$848$	0	0
$849$	0	0
$850$	−2693.20	−3.16847
$851$	−2134.85	−2.50863
$852$	0	0
$853$	0	0	1.00000			$0$
$853$	0	0	−1.00000			$\pi$
$854$	0	0
$855$	0	0
$856$	−830.661	−0.970399
$857$	0	0	1.00000			$0$
$857$	0	0	−1.00000			$\pi$
$858$	0	0
$859$	0	0	1.00000			$0$
$859$	0	0	−1.00000			$\pi$
$860$	0	0
$861$	−1487.45	−1.72758
$862$	−906.649	−1.05180
$863$	578.000	0.669757	0.334878	−	0.942261i	$-0.391305\pi$
$863$	578.000	0.669757	0.334878	+	0.942261i	$0.391305\pi$
$864$	−1717.77	−1.98816
$865$	0	0
$866$	0	0
$867$	4487.26	5.17561
$868$	0	0
$869$	0	0
$870$	0	0
$871$	0	0
$872$	0	0
$873$	−3317.30	−3.79989
$874$	2903.79	3.32241
$875$	0	0
$876$	0	0
$877$	1598.07	1.82221	0.911103	−	0.412179i	$-0.135232\pi$
$877$	1598.07	1.82221	0.911103	+	0.412179i	$0.135232\pi$
$878$	−2725.26	−3.10394
$879$	−2187.12	−2.48819
$880$	0	0
$881$	0	0	1.00000			$0$
$881$	0	0	−1.00000			$\pi$
$882$	2774.41	3.14559
$883$	0	0	1.00000			$0$
$883$	0	0	−1.00000			$\pi$
$884$	4081.94	4.61758
$885$	0	0
$886$	504.164	0.569034
$887$	−779.313	−0.878595	−0.439297	−	0.898342i	$-0.644773\pi$
$887$	−779.313	−0.878595	−0.439297	+	0.898342i	$0.644773\pi$
$888$	−2376.61	−2.67637
$889$	363.291	0.408651
$890$	0	0
$891$	0	0
$892$	0	0
$893$	1702.68	1.90670
$894$	0	0
$895$	0	0
$896$	1264.34	1.41110
$897$	−3112.78	−3.47022
$898$	−922.166	−1.02691
$899$	0	0
$900$	2701.25	3.00139
$901$	0	0
$902$	0	0
$903$	−1635.55	−1.81125
$904$	−780.616	−0.863514
$905$	0	0
$906$	0	0
$907$	−1173.09	−1.29337	−0.646687	−	0.762756i	$-0.723846\pi$
$907$	−1173.09	−1.29337	−0.646687	+	0.762756i	$0.723846\pi$
$908$	1222.01	1.34583
$909$	−1974.23	−2.17187
$910$	0	0
$911$	375.747	0.412455	0.206228	−	0.978504i	$-0.433881\pi$
$911$	375.747	0.412455	0.206228	+	0.978504i	$0.433881\pi$
$912$	−565.183	−0.619718
$913$	0	0
$914$	0	0
$915$	0	0
$916$	−983.346	−1.07352
$917$	0	0
$918$	−4947.23	−5.38914
$919$	0	0	1.00000			$0$
$919$	0	0	−1.00000			$\pi$
$920$	0	0
$921$	0	0
$922$	0	0
$923$	0	0
$924$	0	0
$925$	−1764.44	−1.90750
$926$	0	0
$927$	0	0
$928$	0	0
$929$	705.327	0.759232	0.379616	−	0.925144i	$-0.376056\pi$
$929$	705.327	0.759232	0.379616	+	0.925144i	$0.376056\pi$
$930$	0	0
$931$	1483.84	1.59381
$932$	0	0
$933$	29.7883	0.0319274
$934$	0	0
$935$	0	0
$936$	−2304.21	−2.46177
$937$	1864.89	1.99028	0.995141	−	0.0984596i	$-0.0313915\pi$
$937$	1864.89	1.99028	0.995141	+	0.0984596i	$0.0313915\pi$
$938$	0	0
$939$	2282.52	2.43079
$940$	0	0
$941$	0	0	1.00000			$0$
$941$	0	0	−1.00000			$\pi$
$942$	−884.705	−0.939177
$943$	1240.18	1.31514
$944$	0	0
$945$	0	0
$946$	0	0
$947$	−1361.18	−1.43736	−0.718679	−	0.695342i	$-0.755253\pi$
$947$	−1361.18	−1.43736	−0.718679	+	0.695342i	$0.755253\pi$
$948$	0	0
$949$	0	0
$950$	2399.96	2.52628
$951$	0	0
$952$	1545.56	1.62348
$953$	1587.29	1.66557	0.832787	−	0.553593i	$-0.186744\pi$
$953$	1587.29	1.66557	0.832787	+	0.553593i	$0.186744\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	0	0
$958$	−341.447	−0.356417
$959$	0	0
$960$	0	0
$961$	961.000	1.00000
$962$	4442.51	4.61800
$963$	−2283.46	−2.37119
$964$	0	0
$965$	0	0
$966$	−3478.82	−3.60126
$967$	0	0	1.00000			$0$
$967$	0	0	−1.00000			$\pi$
$968$	786.172	0.812162
$969$	−5333.42	−5.50404
$970$	0	0
$971$	−1378.88	−1.42006	−0.710029	−	0.704173i	$-0.751318\pi$
$971$	−1378.88	−1.42006	−0.710029	+	0.704173i	$0.751318\pi$
$972$	−77.9381	−0.0801832
$973$	0	0
$974$	2650.61	2.72136
$975$	−2572.70	−2.63866
$976$	0	0
$977$	0	0	1.00000			$0$
$977$	0	0	−1.00000			$\pi$
$978$	−2354.84	−2.40781
$979$	0	0
$980$	0	0
$981$	0	0
$982$	−389.828	−0.396974
$983$	0	0	1.00000			$0$
$983$	0	0	−1.00000			$\pi$
$984$	1380.63	1.40307
$985$	0	0
$986$	0	0
$987$	−2039.86	−2.06672
$988$	−3637.50	−3.68168
$989$	1363.67	1.37883
$990$	0	0
$991$	0	0	1.00000			$0$
$991$	0	0	−1.00000			$\pi$
$992$	0	0
$993$	0	0
$994$	0	0
$995$	0	0
$996$	0	0
$997$	1983.67	1.98964	0.994819	−	0.101665i	$-0.0324170\pi$
$997$	1983.67	1.98964	0.994819	+	0.101665i	$0.0324170\pi$
$998$	0	0
$999$	−3241.16	−3.24440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.3.d.a.286.6	✓	7
7.6	odd	2		287.3.d.b.286.6	yes	7
41.40	even	2		287.3.d.b.286.6	yes	7
287.286	odd	2	CM	287.3.d.a.286.6	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.3.d.a.286.6	✓	7	1.1	even	1	trivial
287.3.d.a.286.6	✓	7	287.286	odd	2	CM
287.3.d.b.286.6	yes	7	7.6	odd	2
287.3.d.b.286.6	yes	7	41.40	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	287.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.17010 q^{2} +5.18274 q^{3} +6.04955 q^{4} +16.4298 q^{6} -7.00000 q^{7} +6.49729 q^{8} +17.8608 q^{9} +O(q^{10})\)	\(q+3.17010 q^{2} +5.18274 q^{3} +6.04955 q^{4} +16.4298 q^{6} -7.00000 q^{7} +6.49729 q^{8} +17.8608 q^{9} +31.3533 q^{12} -19.8559 q^{13} -22.1907 q^{14} -3.60112 q^{16} -33.9825 q^{17} +56.6206 q^{18} +30.2825 q^{19} -36.2792 q^{21} +30.2483 q^{23} +33.6738 q^{24} +25.0000 q^{25} -62.9452 q^{26} +45.9234 q^{27} -42.3469 q^{28} -37.4051 q^{32} -107.728 q^{34} +108.050 q^{36} -70.5775 q^{37} +95.9985 q^{38} -102.908 q^{39} +41.0000 q^{41} -115.009 q^{42} +45.0824 q^{43} +95.8901 q^{46} +56.2266 q^{47} -18.6637 q^{48} +49.0000 q^{49} +79.2526 q^{50} -176.122 q^{51} -120.119 q^{52} +145.582 q^{54} -45.4810 q^{56} +156.946 q^{57} -125.026 q^{63} -104.174 q^{64} -205.579 q^{68} +156.769 q^{69} +116.047 q^{72} -223.738 q^{74} +129.569 q^{75} +183.195 q^{76} -326.229 q^{78} +77.2616 q^{81} +129.974 q^{82} -219.473 q^{84} +142.916 q^{86} +113.630 q^{89} +138.991 q^{91} +182.988 q^{92} +178.244 q^{94} -193.861 q^{96} -185.731 q^{97} +155.335 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 28 q^{4} - 49 q^{7} + 63 q^{9}+O(q^{10}) \) 7 * q + 28 * q^4 - 49 * q^7 + 63 * q^9	\( 7 q + 28 q^{4} - 49 q^{7} + 63 q^{9} + 119 q^{12} + 112 q^{16} + 175 q^{25} - 77 q^{26} - 196 q^{28} + 252 q^{36} + 287 q^{41} + 476 q^{48} + 343 q^{49} - 469 q^{54} - 441 q^{63} + 448 q^{64} + 182 q^{69} - 1001 q^{72} - 973 q^{74} - 917 q^{78} + 567 q^{81} - 833 q^{84} - 721 q^{92} + 1267 q^{94} - 1057 q^{96}+O(q^{100}) \) 7 * q + 28 * q^4 - 49 * q^7 + 63 * q^9 + 119 * q^12 + 112 * q^16 + 175 * q^25 - 77 * q^26 - 196 * q^28 + 252 * q^36 + 287 * q^41 + 476 * q^48 + 343 * q^49 - 469 * q^54 - 441 * q^63 + 448 * q^64 + 182 * q^69 - 1001 * q^72 - 973 * q^74 - 917 * q^78 + 567 * q^81 - 833 * q^84 - 721 * q^92 + 1267 * q^94 - 1057 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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