LMFDB - Embedded newform 2.36.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,36,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2, base_ring=CyclotomicField(1))

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

N = Newforms(chi, 36, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 36);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 36 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

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:	$15.5190261267$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-131072. q^{2} +3.64947e7 q^{3} +1.71799e10 q^{4} +3.89071e11 q^{5} -4.78344e12 q^{6} -1.29689e14 q^{7} -2.25180e15 q^{8} -4.86997e16 q^{9} +O(q^{10})$

\(q-131072. q^{2} +3.64947e7 q^{3} +1.71799e10 q^{4} +3.89071e11 q^{5} -4.78344e12 q^{6} -1.29689e14 q^{7} -2.25180e15 q^{8} -4.86997e16 q^{9} -5.09963e16 q^{10} +4.69639e17 q^{11} +6.26975e17 q^{12} +2.85415e19 q^{13} +1.69986e19 q^{14} +1.41990e19 q^{15} +2.95148e20 q^{16} +5.39030e21 q^{17} +6.38316e21 q^{18} +3.41889e22 q^{19} +6.68419e21 q^{20} -4.73298e21 q^{21} -6.15565e22 q^{22} -1.70205e23 q^{23} -8.21789e22 q^{24} -2.75901e24 q^{25} -3.74100e24 q^{26} -3.60317e24 q^{27} -2.22805e24 q^{28} +4.54556e25 q^{29} -1.86110e24 q^{30} +1.93288e26 q^{31} -3.86856e25 q^{32} +1.71393e25 q^{33} -7.06517e26 q^{34} -5.04584e25 q^{35} -8.36654e26 q^{36} +1.49985e27 q^{37} -4.48120e27 q^{38} +1.04162e27 q^{39} -8.76110e26 q^{40} +1.51218e28 q^{41} +6.20361e26 q^{42} +3.75644e28 q^{43} +8.06833e27 q^{44} -1.89476e28 q^{45} +2.23091e28 q^{46} -3.10292e29 q^{47} +1.07713e28 q^{48} -3.61999e29 q^{49} +3.61629e29 q^{50} +1.96718e29 q^{51} +4.90340e29 q^{52} +6.52810e29 q^{53} +4.72275e29 q^{54} +1.82723e29 q^{55} +2.92034e29 q^{56} +1.24771e30 q^{57} -5.95795e30 q^{58} -1.25702e30 q^{59} +2.43938e29 q^{60} +1.66767e29 q^{61} -2.53347e31 q^{62} +6.31583e30 q^{63} +5.07060e30 q^{64} +1.11047e31 q^{65} -2.24649e30 q^{66} +1.12725e32 q^{67} +9.26046e31 q^{68} -6.21160e30 q^{69} +6.61368e30 q^{70} -3.97712e32 q^{71} +1.09662e32 q^{72} -3.33895e32 q^{73} -1.96588e32 q^{74} -1.00689e32 q^{75} +5.87360e32 q^{76} -6.09071e31 q^{77} -1.36527e32 q^{78} +1.38290e33 q^{79} +1.14833e32 q^{80} +2.30502e33 q^{81} -1.98205e33 q^{82} -8.28639e32 q^{83} -8.13120e31 q^{84} +2.09721e33 q^{85} -4.92364e33 q^{86} +1.65889e33 q^{87} -1.05753e33 q^{88} -1.38639e34 q^{89} +2.48350e33 q^{90} -3.70154e33 q^{91} -2.92410e33 q^{92} +7.05400e33 q^{93} +4.06705e34 q^{94} +1.33019e34 q^{95} -1.41182e33 q^{96} +1.22546e34 q^{97} +4.74480e34 q^{98} -2.28712e34 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 $

$2$	−131072.	−0.707107
$2$	−131072.	−0.707107
$3$	3.64947e7	0.163158	0.0815790	−	0.996667i	$-0.474004\pi$
$3$	3.64947e7	0.163158	0.0815790	+	0.996667i	$0.474004\pi$
$4$	1.71799e10	0.500000
$5$	3.89071e11	0.228062	0.114031	−	0.993477i	$-0.463624\pi$
$5$	3.89071e11	0.228062	0.114031	+	0.993477i	$0.463624\pi$
$6$	−4.78344e12	−0.115370
$7$	−1.29689e14	−0.210712	−0.105356	−	0.994435i	$-0.533598\pi$
$7$	−1.29689e14	−0.210712	−0.105356	+	0.994435i	$0.533598\pi$
$8$	−2.25180e15	−0.353553
$9$	−4.86997e16	−0.973379
$10$	−5.09963e16	−0.161264
$11$	4.69639e17	0.280151	0.140075	−	0.990141i	$-0.455266\pi$
$11$	4.69639e17	0.280151	0.140075	+	0.990141i	$0.455266\pi$
$12$	6.26975e17	0.0815790
$13$	2.85415e19	0.915101	0.457550	−	0.889184i	$-0.348727\pi$
$13$	2.85415e19	0.915101	0.457550	+	0.889184i	$0.348727\pi$
$14$	1.69986e19	0.148996
$15$	1.41990e19	0.0372102
$16$	2.95148e20	0.250000
$17$	5.39030e21	1.58036	0.790181	−	0.612873i	$-0.209986\pi$
$17$	5.39030e21	1.58036	0.790181	+	0.612873i	$0.209986\pi$
$18$	6.38316e21	0.688283
$19$	3.41889e22	1.43119	0.715594	−	0.698517i	$-0.246156\pi$
$19$	3.41889e22	1.43119	0.715594	+	0.698517i	$0.246156\pi$
$20$	6.68419e21	0.114031
$21$	−4.73298e21	−0.0343793
$22$	−6.15565e22	−0.198096
$23$	−1.70205e23	−0.251615	−0.125807	−	0.992055i	$-0.540152\pi$
$23$	−1.70205e23	−0.251615	−0.125807	+	0.992055i	$0.540152\pi$
$24$	−8.21789e22	−0.0576851
$25$	−2.75901e24	−0.947988
$26$	−3.74100e24	−0.647074
$27$	−3.60317e24	−0.321973
$28$	−2.22805e24	−0.105356
$29$	4.54556e25	1.16311	0.581557	−	0.813506i	$-0.302444\pi$
$29$	4.54556e25	1.16311	0.581557	+	0.813506i	$0.302444\pi$
$30$	−1.86110e24	−0.0263116
$31$	1.93288e26	1.53949	0.769743	−	0.638354i	$-0.220384\pi$
$31$	1.93288e26	1.53949	0.769743	+	0.638354i	$0.220384\pi$
$32$	−3.86856e25	−0.176777
$33$	1.71393e25	0.0457088
$34$	−7.06517e26	−1.11749
$35$	−5.04584e25	−0.0480554
$36$	−8.36654e26	−0.486690
$37$	1.49985e27	0.540153	0.270076	−	0.962839i	$-0.412951\pi$
$37$	1.49985e27	0.540153	0.270076	+	0.962839i	$0.412951\pi$
$38$	−4.48120e27	−1.01200
$39$	1.04162e27	0.149306
$40$	−8.76110e26	−0.0806322
$41$	1.51218e28	0.903414	0.451707	−	0.892166i	$-0.350815\pi$
$41$	1.51218e28	0.903414	0.451707	+	0.892166i	$0.350815\pi$
$42$	6.20361e26	0.0243098
$43$	3.75644e28	0.975165	0.487582	−	0.873077i	$-0.337879\pi$
$43$	3.75644e28	0.975165	0.487582	+	0.873077i	$0.337879\pi$
$44$	8.06833e27	0.140075
$45$	−1.89476e28	−0.221991
$46$	2.23091e28	0.177918
$47$	−3.10292e29	−1.69847	−0.849234	−	0.528016i	$-0.822936\pi$
$47$	−3.10292e29	−1.69847	−0.849234	+	0.528016i	$0.822936\pi$
$48$	1.07713e28	0.0407895
$49$	−3.61999e29	−0.955601
$50$	3.61629e29	0.670328
$51$	1.96718e29	0.257849
$52$	4.90340e29	0.457550
$53$	6.52810e29	0.436475	0.218237	−	0.975896i	$-0.429969\pi$
$53$	6.52810e29	0.436475	0.218237	+	0.975896i	$0.429969\pi$
$54$	4.72275e29	0.227669
$55$	1.82723e29	0.0638918
$56$	2.92034e29	0.0744978
$57$	1.24771e30	0.233510
$58$	−5.95795e30	−0.822446
$59$	−1.25702e30	−0.128657	−0.0643285	−	0.997929i	$-0.520491\pi$
$59$	−1.25702e30	−0.128657	−0.0643285	+	0.997929i	$0.520491\pi$
$60$	2.43938e29	0.0186051
$61$	1.66767e29	0.00952442	0.00476221	−	0.999989i	$-0.498484\pi$
$61$	1.66767e29	0.00952442	0.00476221	+	0.999989i	$0.498484\pi$
$62$	−2.53347e31	−1.08858
$63$	6.31583e30	0.205102
$64$	5.07060e30	0.125000
$65$	1.11047e31	0.208700
$66$	−2.24649e30	−0.0323210
$67$	1.12725e32	1.24656	0.623278	−	0.782000i	$-0.285801\pi$
$67$	1.12725e32	1.24656	0.623278	+	0.782000i	$0.285801\pi$
$68$	9.26046e31	0.790181
$69$	−6.21160e30	−0.0410529
$70$	6.61368e30	0.0339803
$71$	−3.97712e32	−1.59422	−0.797109	−	0.603836i	$-0.793638\pi$
$71$	−3.97712e32	−1.59422	−0.797109	+	0.603836i	$0.793638\pi$
$72$	1.09662e32	0.344142
$73$	−3.33895e32	−0.823115	−0.411557	−	0.911384i	$-0.635015\pi$
$73$	−3.33895e32	−0.823115	−0.411557	+	0.911384i	$0.635015\pi$
$74$	−1.96588e32	−0.381946
$75$	−1.00689e32	−0.154672
$76$	5.87360e32	0.715594
$77$	−6.09071e31	−0.0590310
$78$	−1.36527e32	−0.105575
$79$	1.38290e33	0.855693	0.427847	−	0.903851i	$-0.359272\pi$
$79$	1.38290e33	0.855693	0.427847	+	0.903851i	$0.359272\pi$
$80$	1.14833e32	0.0570156
$81$	2.30502e33	0.920847
$82$	−1.98205e33	−0.638810
$83$	−8.28639e32	−0.216022	−0.108011	−	0.994150i	$-0.534448\pi$
$83$	−8.28639e32	−0.216022	−0.108011	+	0.994150i	$0.534448\pi$
$84$	−8.13120e31	−0.0171897
$85$	2.09721e33	0.360421
$86$	−4.92364e33	−0.689546
$87$	1.65889e33	0.189771
$88$	−1.05753e33	−0.0990482
$89$	−1.38639e34	−1.06552	−0.532759	−	0.846267i	$-0.678845\pi$
$89$	−1.38639e34	−1.06552	−0.532759	+	0.846267i	$0.678845\pi$
$90$	2.48350e33	0.156972
$91$	−3.70154e33	−0.192822
$92$	−2.92410e33	−0.125807
$93$	7.05400e33	0.251179
$94$	4.06705e34	1.20100
$95$	1.33019e34	0.326400
$96$	−1.41182e33	−0.0288425
$97$	1.22546e34	0.208831	0.104416	−	0.994534i	$-0.466703\pi$
$97$	1.22546e34	0.208831	0.104416	+	0.994534i	$0.466703\pi$
$98$	4.74480e34	0.675712
$99$	−2.28712e34	−0.272693
$100$	−4.73994e34	−0.473994
$101$	−1.10671e35	−0.929845	−0.464922	−	0.885351i	$-0.653918\pi$
$101$	−1.10671e35	−0.929845	−0.464922	+	0.885351i	$0.653918\pi$
$102$	−2.57842e34	−0.182327
$103$	−9.30401e34	−0.554649	−0.277325	−	0.960776i	$-0.589448\pi$
$103$	−9.30401e34	−0.554649	−0.277325	+	0.960776i	$0.589448\pi$
$104$	−6.42699e34	−0.323537
$105$	−1.84146e33	−0.00784063
$106$	−8.55651e34	−0.308634
$107$	5.37362e35	1.64456	0.822282	−	0.569081i	$-0.192701\pi$
$107$	5.37362e35	1.64456	0.822282	+	0.569081i	$0.192701\pi$
$108$	−6.19020e34	−0.160986
$109$	2.76195e35	0.611298	0.305649	−	0.952144i	$-0.401127\pi$
$109$	2.76195e35	0.611298	0.305649	+	0.952144i	$0.401127\pi$
$110$	−2.39498e34	−0.0451784
$111$	5.47365e34	0.0881303
$112$	−3.82775e34	−0.0526779
$113$	1.52159e34	0.0179236	0.00896180	−	0.999960i	$-0.497147\pi$
$113$	1.52159e34	0.0179236	0.00896180	+	0.999960i	$0.497147\pi$
$114$	−1.63540e35	−0.165116
$115$	−6.62219e34	−0.0573838
$116$	7.80921e35	0.581557
$117$	−1.38996e36	−0.890740
$118$	1.64761e35	0.0909743
$119$	−6.99064e35	−0.333001
$120$	−3.19734e34	−0.0131558
$121$	−2.58968e36	−0.921516
$122$	−2.18585e34	−0.00673478
$123$	5.51867e35	0.147399
$124$	3.32067e36	0.769743
$125$	−2.20579e36	−0.444263
$126$	−8.27829e35	−0.145029
$127$	1.12446e37	1.71546	0.857729	−	0.514102i	$-0.171875\pi$
$127$	1.12446e37	1.71546	0.857729	+	0.514102i	$0.171875\pi$
$128$	−6.64614e35	−0.0883883
$129$	1.37090e36	0.159106
$130$	−1.45551e36	−0.147573
$131$	4.75712e36	0.421791	0.210895	−	0.977509i	$-0.432362\pi$
$131$	4.75712e36	0.421791	0.210895	+	0.977509i	$0.432362\pi$
$132$	2.94452e35	0.0228544
$133$	−4.43393e36	−0.301568
$134$	−1.47751e37	−0.881448
$135$	−1.40189e36	−0.0734299
$136$	−1.21379e37	−0.558743
$137$	−3.70115e37	−1.49874	−0.749371	−	0.662150i	$-0.769644\pi$
$137$	−3.70115e37	−1.49874	−0.749371	+	0.662150i	$0.769644\pi$
$138$	8.14166e35	0.0290288
$139$	4.67337e37	1.46849	0.734245	−	0.678884i	$-0.237536\pi$
$139$	4.67337e37	1.46849	0.734245	+	0.678884i	$0.237536\pi$
$140$	−8.66868e35	−0.0240277
$141$	−1.13240e37	−0.277119
$142$	5.21289e37	1.12728
$143$	1.34042e37	0.256366
$144$	−1.43736e37	−0.243345
$145$	1.76854e37	0.265263
$146$	4.37643e37	0.582030
$147$	−1.32111e37	−0.155914
$148$	2.57672e37	0.270076
$149$	−1.58885e38	−1.48021	−0.740104	−	0.672493i	$-0.765224\pi$
$149$	−1.58885e38	−1.48021	−0.740104	+	0.672493i	$0.765224\pi$
$150$	1.31975e37	0.109369
$151$	1.69139e38	1.24781	0.623903	−	0.781502i	$-0.285546\pi$
$151$	1.69139e38	1.24781	0.623903	+	0.781502i	$0.285546\pi$
$152$	−7.69864e37	−0.506001
$153$	−2.62506e38	−1.53829
$154$	7.98322e36	0.0417412
$155$	7.52028e37	0.351099
$156$	1.78948e37	0.0746530
$157$	9.79838e37	0.365519	0.182760	−	0.983158i	$-0.441497\pi$
$157$	9.79838e37	0.365519	0.182760	+	0.983158i	$0.441497\pi$
$158$	−1.81260e38	−0.605066
$159$	2.38241e37	0.0712144
$160$	−1.50514e37	−0.0403161
$161$	2.20738e37	0.0530181
$162$	−3.02124e38	−0.651137
$163$	8.36903e38	1.61954	0.809770	−	0.586747i	$-0.199592\pi$
$163$	8.36903e38	1.61954	0.809770	+	0.586747i	$0.199592\pi$
$164$	2.59791e38	0.451707
$165$	6.66842e36	0.0104245
$166$	1.08611e38	0.152751
$167$	3.70702e38	0.469339	0.234670	−	0.972075i	$-0.424599\pi$
$167$	3.70702e38	0.469339	0.234670	+	0.972075i	$0.424599\pi$
$168$	1.06577e37	0.0121549
$169$	−1.58166e38	−0.162591
$170$	−2.74885e38	−0.254856
$171$	−1.66499e39	−1.39309
$172$	6.45351e38	0.487582
$173$	−2.06410e39	−1.40905	−0.704523	−	0.709682i	$-0.748839\pi$
$173$	−2.06410e39	−1.40905	−0.704523	+	0.709682i	$0.748839\pi$
$174$	−2.17434e38	−0.134189
$175$	3.57814e38	0.199752
$176$	1.38613e38	0.0700377
$177$	−4.58748e37	−0.0209914
$178$	1.81717e39	0.753435
$179$	−1.17678e39	−0.442350	−0.221175	−	0.975234i	$-0.570989\pi$
$179$	−1.17678e39	−0.442350	−0.221175	+	0.975234i	$0.570989\pi$
$180$	−3.25518e38	−0.110996
$181$	5.48011e39	1.69595	0.847977	−	0.530034i	$-0.177821\pi$
$181$	5.48011e39	1.69595	0.847977	+	0.530034i	$0.177821\pi$
$182$	4.85168e38	0.136346
$183$	6.08612e36	0.00155398
$184$	3.83268e38	0.0889592
$185$	5.83547e38	0.123189
$186$	−9.24583e38	−0.177611
$187$	2.53149e39	0.442740
$188$	−5.33077e39	−0.849234
$189$	4.67293e38	0.0678434
$190$	−1.74350e39	−0.230800
$191$	−1.01617e40	−1.22711	−0.613554	−	0.789653i	$-0.710261\pi$
$191$	−1.01617e40	−1.22711	−0.613554	+	0.789653i	$0.710261\pi$
$192$	1.85050e38	0.0203948
$193$	4.09679e39	0.412279	0.206139	−	0.978523i	$-0.433910\pi$
$193$	4.09679e39	0.412279	0.206139	+	0.978523i	$0.433910\pi$
$194$	−1.60624e39	−0.147666
$195$	4.05263e38	0.0340511
$196$	−6.21910e39	−0.477800
$197$	1.31502e40	0.924215	0.462108	−	0.886824i	$-0.347093\pi$
$197$	1.31502e40	0.924215	0.462108	+	0.886824i	$0.347093\pi$
$198$	2.99778e39	0.192823
$199$	−1.72061e40	−1.01333	−0.506667	−	0.862142i	$-0.669123\pi$
$199$	−1.72061e40	−1.01333	−0.506667	+	0.862142i	$0.669123\pi$
$200$	6.21273e39	0.335164
$201$	4.11388e39	0.203386
$202$	1.45059e40	0.657500
$203$	−5.89511e39	−0.245082
$204$	3.37958e39	0.128924
$205$	5.88346e39	0.206035
$206$	1.21949e40	0.392196
$207$	8.28894e39	0.244916
$208$	8.42398e39	0.228775
$209$	1.60564e40	0.400948
$210$	2.41364e38	0.00554416
$211$	−7.02875e40	−1.48571	−0.742857	−	0.669450i	$-0.766530\pi$
$211$	−7.02875e40	−1.48571	−0.742857	+	0.669450i	$0.766530\pi$
$212$	1.12152e40	0.218237
$213$	−1.45144e40	−0.260109
$214$	−7.04331e40	−1.16288
$215$	1.46152e40	0.222398
$216$	8.11362e39	0.113835
$217$	−2.50674e40	−0.324388
$218$	−3.62015e40	−0.432253
$219$	−1.21854e40	−0.134298
$220$	3.13915e39	0.0319459
$221$	1.53847e41	1.44619
$222$	−7.17443e39	−0.0623175
$223$	2.49570e40	0.200381	0.100191	−	0.994968i	$-0.468055\pi$
$223$	2.49570e40	0.200381	0.100191	+	0.994968i	$0.468055\pi$
$224$	5.01711e39	0.0372489
$225$	1.34363e41	0.922752
$226$	−1.99438e39	−0.0126739
$227$	2.44076e41	1.43573	0.717865	−	0.696182i	$-0.245119\pi$
$227$	2.44076e41	1.43573	0.717865	+	0.696182i	$0.245119\pi$
$228$	2.14356e40	0.116755
$229$	−3.57853e41	−1.80544	−0.902722	−	0.430225i	$-0.858434\pi$
$229$	−3.57853e41	−1.80544	−0.902722	+	0.430225i	$0.858434\pi$
$230$	8.67984e39	0.0405765
$231$	−2.22279e39	−0.00963139
$232$	−1.02357e41	−0.411223
$233$	−3.46702e41	−1.29190	−0.645948	−	0.763382i	$-0.723538\pi$
$233$	−3.46702e41	−1.29190	−0.645948	+	0.763382i	$0.723538\pi$
$234$	1.82185e41	0.629848
$235$	−1.20725e41	−0.387357
$236$	−2.15955e40	−0.0643285
$237$	5.04688e40	0.139613
$238$	9.16278e40	0.235467
$239$	−8.71138e40	−0.208029	−0.104014	−	0.994576i	$-0.533169\pi$
$239$	−8.71138e40	−0.208029	−0.104014	+	0.994576i	$0.533169\pi$
$240$	4.19082e39	0.00930255
$241$	−2.68663e41	−0.554511	−0.277256	−	0.960796i	$-0.589425\pi$
$241$	−2.68663e41	−0.554511	−0.277256	+	0.960796i	$0.589425\pi$
$242$	3.39435e41	0.651610
$243$	2.64393e41	0.472216
$244$	2.86504e39	0.00476221
$245$	−1.40843e41	−0.217937
$246$	−7.23343e40	−0.104227
$247$	9.75803e41	1.30968
$248$	−4.35246e41	−0.544290
$249$	−3.02410e40	−0.0352458
$250$	2.89118e41	0.314141
$251$	5.90425e41	0.598239	0.299120	−	0.954216i	$-0.403307\pi$
$251$	5.90425e41	0.598239	0.299120	+	0.954216i	$0.403307\pi$
$252$	1.08505e41	0.102551
$253$	−7.99349e40	−0.0704900
$254$	−1.47386e42	−1.21301
$255$	7.65371e40	0.0588056
$256$	8.71123e40	0.0625000
$257$	1.90235e41	0.127485	0.0637426	−	0.997966i	$-0.479696\pi$
$257$	1.90235e41	0.127485	0.0637426	+	0.997966i	$0.479696\pi$
$258$	−1.79687e41	−0.112505
$259$	−1.94514e41	−0.113817
$260$	1.90777e41	0.104350
$261$	−2.21367e42	−1.13215
$262$	−6.23526e41	−0.298251
$263$	−3.27029e41	−0.146339	−0.0731695	−	0.997320i	$-0.523311\pi$
$263$	−3.27029e41	−0.146339	−0.0731695	+	0.997320i	$0.523311\pi$
$264$	−3.85944e40	−0.0161605
$265$	2.53989e41	0.0995435
$266$	5.81164e41	0.213241
$267$	−5.05960e41	−0.173848
$268$	1.93660e42	0.623278
$269$	2.52040e42	0.759983	0.379992	−	0.924990i	$-0.375927\pi$
$269$	2.52040e42	0.759983	0.379992	+	0.924990i	$0.375927\pi$
$270$	1.83748e41	0.0519227
$271$	1.90773e42	0.505305	0.252653	−	0.967557i	$-0.418697\pi$
$271$	1.90773e42	0.505305	0.252653	+	0.967557i	$0.418697\pi$
$272$	1.59094e42	0.395091
$273$	−1.35087e41	−0.0314605
$274$	4.85117e42	1.05977
$275$	−1.29574e42	−0.265579
$276$	−1.06714e41	−0.0205265
$277$	3.33230e41	0.0601656	0.0300828	−	0.999547i	$-0.490423\pi$
$277$	3.33230e41	0.0601656	0.0300828	+	0.999547i	$0.490423\pi$
$278$	−6.12548e42	−1.03838
$279$	−9.41307e42	−1.49850
$280$	1.13622e41	0.0169902
$281$	2.30223e40	0.00323436	0.00161718	−	0.999999i	$-0.499485\pi$
$281$	2.30223e40	0.00323436	0.00161718	+	0.999999i	$0.499485\pi$
$282$	1.48426e42	0.195953
$283$	−1.17268e41	−0.0145519	−0.00727593	−	0.999974i	$-0.502316\pi$
$283$	−1.17268e41	−0.0145519	−0.00727593	+	0.999974i	$0.502316\pi$
$284$	−6.83264e42	−0.797109
$285$	4.85449e41	0.0532548
$286$	−1.75692e42	−0.181278
$287$	−1.96114e42	−0.190360
$288$	1.88398e42	0.172071
$289$	1.74218e43	1.49755
$290$	−2.31807e42	−0.187569
$291$	4.47230e41	0.0340725
$292$	−5.73628e42	−0.411557
$293$	1.44939e43	0.979497	0.489749	−	0.871864i	$-0.337089\pi$
$293$	1.44939e43	0.979497	0.489749	+	0.871864i	$0.337089\pi$
$294$	1.73160e42	0.110248
$295$	−4.89072e41	−0.0293418
$296$	−3.37735e42	−0.190973
$297$	−1.69219e42	−0.0902009
$298$	2.08253e43	1.04666
$299$	−4.85792e42	−0.230253
$300$	−1.72983e42	−0.0773359
$301$	−4.87170e42	−0.205479
$302$	−2.21694e43	−0.882332
$303$	−4.03892e42	−0.151712
$304$	1.00908e43	0.357797
$305$	6.48842e40	0.00217216
$306$	3.44072e43	1.08774
$307$	−5.23753e43	−1.56388	−0.781942	−	0.623351i	$-0.785771\pi$
$307$	−5.23753e43	−1.56388	−0.781942	+	0.623351i	$0.785771\pi$
$308$	−1.04638e42	−0.0295155
$309$	−3.39547e42	−0.0904955
$310$	−9.85698e42	−0.248264
$311$	1.45176e43	0.345611	0.172805	−	0.984956i	$-0.444717\pi$
$311$	1.45176e43	0.345611	0.172805	+	0.984956i	$0.444717\pi$
$312$	−2.34551e42	−0.0527876
$313$	−4.55361e43	−0.969014	−0.484507	−	0.874787i	$-0.661001\pi$
$313$	−4.55361e43	−0.969014	−0.484507	+	0.874787i	$0.661001\pi$
$314$	−1.28429e43	−0.258461
$315$	2.45731e42	0.0467762
$316$	2.37581e43	0.427847
$317$	3.87117e43	0.659638	0.329819	−	0.944044i	$-0.393012\pi$
$317$	3.87117e43	0.659638	0.329819	+	0.944044i	$0.393012\pi$
$318$	−3.12268e42	−0.0503562
$319$	2.13477e43	0.325847
$320$	1.97282e42	0.0285078
$321$	1.96109e43	0.268324
$322$	−2.89326e42	−0.0374895
$323$	1.84288e44	2.26179
$324$	3.96000e43	0.460424
$325$	−7.87463e43	−0.867504
$326$	−1.09695e44	−1.14519
$327$	1.00797e43	0.0997381
$328$	−3.40513e43	−0.319405
$329$	4.02415e43	0.357887
$330$	−8.74043e41	−0.00737121
$331$	−1.00563e44	−0.804358	−0.402179	−	0.915561i	$-0.631747\pi$
$331$	−1.00563e44	−0.804358	−0.402179	+	0.915561i	$0.631747\pi$
$332$	−1.42359e43	−0.108011
$333$	−7.30420e43	−0.525774
$334$	−4.85887e43	−0.331873
$335$	4.38581e43	0.284292
$336$	−1.39693e42	−0.00859483
$337$	−2.38319e44	−1.39199	−0.695994	−	0.718048i	$-0.745036\pi$
$337$	−2.38319e44	−1.39199	−0.695994	+	0.718048i	$0.745036\pi$
$338$	2.07312e43	0.114969
$339$	5.55301e41	0.00292438
$340$	3.60298e43	0.180211
$341$	9.07756e43	0.431288
$342$	2.18233e44	0.985062
$343$	9.60762e43	0.412068
$344$	−8.45874e43	−0.344773
$345$	−2.41675e42	−0.00936263
$346$	2.70546e44	0.996345
$347$	3.03431e44	1.06241	0.531207	−	0.847242i	$-0.321739\pi$
$347$	3.03431e44	1.06241	0.531207	+	0.847242i	$0.321739\pi$
$348$	2.84995e43	0.0948857
$349$	−2.02034e44	−0.639706	−0.319853	−	0.947467i	$-0.603633\pi$
$349$	−2.02034e44	−0.639706	−0.319853	+	0.947467i	$0.603633\pi$
$350$	−4.68994e43	−0.141246
$351$	−1.02840e44	−0.294637
$352$	−1.81683e43	−0.0495241
$353$	−7.85788e43	−0.203821	−0.101910	−	0.994794i	$-0.532495\pi$
$353$	−7.85788e43	−0.203821	−0.101910	+	0.994794i	$0.532495\pi$
$354$	6.01290e42	0.0148432
$355$	−1.54738e44	−0.363581
$356$	−2.38180e44	−0.532759
$357$	−2.55122e43	−0.0543318
$358$	1.54242e44	0.312789
$359$	−2.44272e44	−0.471759	−0.235880	−	0.971782i	$-0.575797\pi$
$359$	−2.44272e44	−0.471759	−0.235880	+	0.971782i	$0.575797\pi$
$360$	4.26663e43	0.0784858
$361$	5.98219e44	1.04830
$362$	−7.18288e44	−1.19922
$363$	−9.45098e43	−0.150353
$364$	−6.35919e43	−0.0964112
$365$	−1.29909e44	−0.187721
$366$	−7.97721e41	−0.00109883
$367$	6.83597e44	0.897726	0.448863	−	0.893601i	$-0.351829\pi$
$367$	6.83597e44	0.897726	0.448863	+	0.893601i	$0.351829\pi$
$368$	−5.02357e43	−0.0629036
$369$	−7.36428e44	−0.879364
$370$	−7.64866e43	−0.0871074
$371$	−8.46625e43	−0.0919704
$372$	1.21187e44	0.125590
$373$	1.51817e45	1.50112	0.750559	−	0.660804i	$-0.229784\pi$
$373$	1.51817e45	1.50112	0.750559	+	0.660804i	$0.229784\pi$
$374$	−3.31808e44	−0.313064
$375$	−8.04999e43	−0.0724850
$376$	6.98715e44	0.600499
$377$	1.29737e45	1.06437
$378$	−6.12490e43	−0.0479725
$379$	−1.52556e45	−1.14089	−0.570446	−	0.821335i	$-0.693230\pi$
$379$	−1.52556e45	−1.14089	−0.570446	+	0.821335i	$0.693230\pi$
$380$	2.28525e44	0.163200
$381$	4.10370e44	0.279891
$382$	1.33192e45	0.867697
$383$	−1.07362e45	−0.668149	−0.334074	−	0.942547i	$-0.608424\pi$
$383$	−1.07362e45	−0.668149	−0.334074	+	0.942547i	$0.608424\pi$
$384$	−2.42549e43	−0.0144213
$385$	−2.36972e43	−0.0134628
$386$	−5.36975e44	−0.291525
$387$	−1.82937e45	−0.949206
$388$	2.10533e44	0.104416
$389$	−2.34347e45	−1.11107	−0.555534	−	0.831494i	$-0.687486\pi$
$389$	−2.34347e45	−1.11107	−0.555534	+	0.831494i	$0.687486\pi$
$390$	−5.31186e43	−0.0240777
$391$	−9.17457e44	−0.397642
$392$	8.15150e44	0.337856
$393$	1.73610e44	0.0688185
$394$	−1.72362e45	−0.653519
$395$	5.38048e44	0.195151
$396$	−3.92925e44	−0.136346
$397$	1.46972e45	0.487978	0.243989	−	0.969778i	$-0.421544\pi$
$397$	1.46972e45	0.487978	0.243989	+	0.969778i	$0.421544\pi$
$398$	2.25523e45	0.716536
$399$	−1.61815e44	−0.0492032
$400$	−8.14315e44	−0.236997
$401$	4.92536e45	1.37218	0.686091	−	0.727516i	$-0.259325\pi$
$401$	4.92536e45	1.37218	0.686091	+	0.727516i	$0.259325\pi$
$402$	−5.39214e44	−0.143815
$403$	5.51674e45	1.40878
$404$	−1.90132e45	−0.464922
$405$	8.96817e44	0.210011
$406$	7.72683e44	0.173299
$407$	7.04386e44	0.151324
$408$	−4.42969e44	−0.0911633
$409$	−5.37711e45	−1.06021	−0.530104	−	0.847933i	$-0.677847\pi$
$409$	−5.37711e45	−1.06021	−0.530104	+	0.847933i	$0.677847\pi$
$410$	−7.71157e44	−0.145689
$411$	−1.35073e45	−0.244532
$412$	−1.59842e45	−0.277325
$413$	1.63023e44	0.0271095
$414$	−1.08645e45	−0.173182
$415$	−3.22399e44	−0.0492666
$416$	−1.10415e45	−0.161768
$417$	1.70553e45	0.239596
$418$	−2.10454e45	−0.283513
$419$	−8.82956e45	−1.14076	−0.570379	−	0.821382i	$-0.693204\pi$
$419$	−8.82956e45	−1.14076	−0.570379	+	0.821382i	$0.693204\pi$
$420$	−3.16361e43	−0.00392031
$421$	−6.31832e45	−0.751043	−0.375521	−	0.926814i	$-0.622536\pi$
$421$	−6.31832e45	−0.751043	−0.375521	+	0.926814i	$0.622536\pi$
$422$	9.21272e45	1.05056
$423$	1.51111e46	1.65325
$424$	−1.47000e45	−0.154317
$425$	−1.48719e46	−1.49816
$426$	1.90243e45	0.183925
$427$	−2.16279e43	−0.00200691
$428$	9.23180e45	0.822282
$429$	4.89183e44	0.0418282
$430$	−1.91564e45	−0.157259
$431$	1.20041e46	0.946190	0.473095	−	0.881011i	$-0.343137\pi$
$431$	1.20041e46	0.946190	0.473095	+	0.881011i	$0.343137\pi$
$432$	−1.06347e45	−0.0804932
$433$	−5.57649e44	−0.0405343	−0.0202672	−	0.999795i	$-0.506452\pi$
$433$	−5.57649e44	−0.0405343	−0.0202672	+	0.999795i	$0.506452\pi$
$434$	3.28564e45	0.229377
$435$	6.45426e44	0.0432797
$436$	4.74500e45	0.305649
$437$	−5.81912e45	−0.360108
$438$	1.59717e45	0.0949629
$439$	−1.21977e46	−0.696866	−0.348433	−	0.937334i	$-0.613286\pi$
$439$	−1.21977e46	−0.696866	−0.348433	+	0.937334i	$0.613286\pi$
$440$	−4.11455e44	−0.0225892
$441$	1.76293e46	0.930162
$442$	−2.01651e46	−1.02261
$443$	2.18740e46	1.06626	0.533130	−	0.846033i	$-0.321016\pi$
$443$	2.18740e46	1.06626	0.533130	+	0.846033i	$0.321016\pi$
$444$	9.40366e44	0.0440651
$445$	−5.39405e45	−0.243005
$446$	−3.27116e45	−0.141691
$447$	−5.79846e45	−0.241508
$448$	−6.57603e44	−0.0263390
$449$	−3.45043e46	−1.32911	−0.664557	−	0.747237i	$-0.731380\pi$
$449$	−3.45043e46	−1.32911	−0.664557	+	0.747237i	$0.731380\pi$
$450$	−1.76112e46	−0.652484
$451$	7.10179e45	0.253092
$452$	2.61407e44	0.00896180
$453$	6.17268e45	0.203589
$454$	−3.19916e46	−1.01522
$455$	−1.44016e45	−0.0439755
$456$	−2.80960e45	−0.0825581
$457$	1.89882e46	0.536969	0.268485	−	0.963284i	$-0.413477\pi$
$457$	1.89882e46	0.536969	0.268485	+	0.963284i	$0.413477\pi$
$458$	4.69045e46	1.27664
$459$	−1.94222e46	−0.508834
$460$	−1.13768e45	−0.0286919
$461$	3.72909e46	0.905392	0.452696	−	0.891665i	$-0.350462\pi$
$461$	3.72909e46	0.905392	0.452696	+	0.891665i	$0.350462\pi$
$462$	2.91346e44	0.00681042
$463$	7.00793e46	1.57733	0.788665	−	0.614823i	$-0.210773\pi$
$463$	7.00793e46	1.57733	0.788665	+	0.614823i	$0.210773\pi$
$464$	1.34161e46	0.290778
$465$	2.74451e45	0.0572846
$466$	4.54429e46	0.913508
$467$	−7.74190e46	−1.49900	−0.749501	−	0.662004i	$-0.769706\pi$
$467$	−7.74190e46	−1.49900	−0.749501	+	0.662004i	$0.769706\pi$
$468$	−2.38794e46	−0.445370
$469$	−1.46193e46	−0.262664
$470$	1.58237e46	0.273903
$471$	3.57590e45	0.0596374
$472$	2.83057e45	0.0454871
$473$	1.76417e46	0.273193
$474$	−6.61504e45	−0.0987214
$475$	−9.43273e46	−1.35675
$476$	−1.20098e46	−0.166500
$477$	−3.17916e46	−0.424856
$478$	1.14182e46	0.147099
$479$	−1.00348e47	−1.24634	−0.623169	−	0.782087i	$-0.714155\pi$
$479$	−1.00348e47	−1.24634	−0.623169	+	0.782087i	$0.714155\pi$
$480$	−5.49299e44	−0.00657790
$481$	4.28079e46	0.494294
$482$	3.52143e46	0.392099
$483$	8.05578e44	0.00865033
$484$	−4.44904e46	−0.460758
$485$	4.76792e45	0.0476265
$486$	−3.46546e46	−0.333907
$487$	1.58667e47	1.47478	0.737392	−	0.675465i	$-0.236057\pi$
$487$	1.58667e47	1.47478	0.737392	+	0.675465i	$0.236057\pi$
$488$	−3.75526e44	−0.00336739
$489$	3.05426e46	0.264241
$490$	1.84606e46	0.154104
$491$	−6.77122e46	−0.545433	−0.272716	−	0.962095i	$-0.587922\pi$
$491$	−6.77122e46	−0.545433	−0.272716	+	0.962095i	$0.587922\pi$
$492$	9.48101e45	0.0736996
$493$	2.45019e47	1.83814
$494$	−1.27900e47	−0.926084
$495$	−8.89854e45	−0.0621910
$496$	5.70486e46	0.384872
$497$	5.15790e46	0.335920
$498$	3.96375e45	0.0249225
$499$	−9.74905e46	−0.591838	−0.295919	−	0.955213i	$-0.595626\pi$
$499$	−9.74905e46	−0.591838	−0.295919	+	0.955213i	$0.595626\pi$
$500$	−3.78953e46	−0.222131
$501$	1.35287e46	0.0765765
$502$	−7.73882e46	−0.423019
$503$	9.21536e46	0.486488	0.243244	−	0.969965i	$-0.421788\pi$
$503$	9.21536e46	0.486488	0.243244	+	0.969965i	$0.421788\pi$
$504$	−1.42220e46	−0.0725147
$505$	−4.30589e46	−0.212063
$506$	1.04772e46	0.0498440
$507$	−5.77223e45	−0.0265280
$508$	1.93181e47	0.857729
$509$	−3.64921e47	−1.56544	−0.782721	−	0.622372i	$-0.786169\pi$
$509$	−3.64921e47	−1.56544	−0.782721	+	0.622372i	$0.786169\pi$
$510$	−1.00319e46	−0.0415818
$511$	4.33027e46	0.173440
$512$	−1.14180e46	−0.0441942
$513$	−1.23188e47	−0.460803
$514$	−2.49344e46	−0.0901457
$515$	−3.61992e46	−0.126495
$516$	2.35519e46	0.0795530
$517$	−1.45725e47	−0.475827
$518$	2.54954e46	0.0804804
$519$	−7.53290e46	−0.229897
$520$	−2.50055e46	−0.0737866
$521$	1.41456e47	0.403610	0.201805	−	0.979426i	$-0.435319\pi$
$521$	1.41456e47	0.403610	0.201805	+	0.979426i	$0.435319\pi$
$522$	2.90150e47	0.800552
$523$	−2.44011e47	−0.651073	−0.325537	−	0.945529i	$-0.605545\pi$
$523$	−2.44011e47	−0.651073	−0.325537	+	0.945529i	$0.605545\pi$
$524$	8.17268e46	0.210895
$525$	1.30583e46	0.0325912
$526$	4.28643e46	0.103477
$527$	1.04188e48	2.43295
$528$	5.05864e45	0.0114272
$529$	−4.28618e47	−0.936690
$530$	−3.32909e46	−0.0703879
$531$	6.12167e46	0.125232
$532$	−7.61743e46	−0.150784
$533$	4.31600e47	0.826715
$534$	6.63172e46	0.122929
$535$	2.09072e47	0.375063
$536$	−2.53834e47	−0.440724
$537$	−4.29462e46	−0.0721729
$538$	−3.30353e47	−0.537389
$539$	−1.70009e47	−0.267712
$540$	−2.40843e46	−0.0367149
$541$	−8.47356e47	−1.25059	−0.625293	−	0.780390i	$-0.715021\pi$
$541$	−8.47356e47	−1.25059	−0.625293	+	0.780390i	$0.715021\pi$
$542$	−2.50050e47	−0.357305
$543$	1.99995e47	0.276708
$544$	−2.08527e47	−0.279371
$545$	1.07460e47	0.139414
$546$	1.77061e46	0.0222459
$547$	−9.95905e47	−1.21182	−0.605912	−	0.795531i	$-0.707192\pi$
$547$	−9.95905e47	−1.21182	−0.605912	+	0.795531i	$0.707192\pi$
$548$	−6.35853e47	−0.749371
$549$	−8.12151e45	−0.00927087
$550$	1.69835e47	0.187793
$551$	1.55407e48	1.66463
$552$	1.39873e46	0.0145144
$553$	−1.79348e47	−0.180305
$554$	−4.36771e46	−0.0425435
$555$	2.12964e46	0.0200992
$556$	8.02879e47	0.734245
$557$	4.00710e47	0.355111	0.177556	−	0.984111i	$-0.443181\pi$
$557$	4.00710e47	0.355111	0.177556	+	0.984111i	$0.443181\pi$
$558$	1.23379e48	1.05960
$559$	1.07215e48	0.892374
$560$	−1.48927e46	−0.0120139
$561$	9.23862e46	0.0722365
$562$	−3.01758e45	−0.00228704
$563$	−1.98871e48	−1.46108	−0.730539	−	0.682871i	$-0.760731\pi$
$563$	−1.98871e48	−1.46108	−0.730539	+	0.682871i	$0.760731\pi$
$564$	−1.94545e47	−0.138559
$565$	5.92007e45	0.00408770
$566$	1.53706e46	0.0102897
$567$	−2.98937e47	−0.194033
$568$	8.95568e47	0.563641
$569$	3.08338e47	0.188175	0.0940877	−	0.995564i	$-0.470007\pi$
$569$	3.08338e47	0.188175	0.0940877	+	0.995564i	$0.470007\pi$
$570$	−6.36288e46	−0.0376568
$571$	−2.00159e48	−1.14880	−0.574398	−	0.818576i	$-0.694764\pi$
$571$	−2.00159e48	−1.14880	−0.574398	+	0.818576i	$0.694764\pi$
$572$	2.30283e47	0.128183
$573$	−3.70849e47	−0.200213
$574$	2.57051e47	0.134605
$575$	4.69597e47	0.238527
$576$	−2.46937e47	−0.121672
$577$	1.16907e47	0.0558810	0.0279405	−	0.999610i	$-0.491105\pi$
$577$	1.16907e47	0.0558810	0.0279405	+	0.999610i	$0.491105\pi$
$578$	−2.28351e48	−1.05892
$579$	1.49511e47	0.0672666
$580$	3.03834e47	0.132631
$581$	1.07466e47	0.0455185
$582$	−5.86193e46	−0.0240929
$583$	3.06585e47	0.122279
$584$	7.51866e47	0.291015
$585$	−5.40795e47	−0.203144
$586$	−1.89975e48	−0.692609
$587$	−3.36306e48	−1.19006	−0.595029	−	0.803704i	$-0.702859\pi$
$587$	−3.36306e48	−1.19006	−0.595029	+	0.803704i	$0.702859\pi$
$588$	−2.26965e47	−0.0779569
$589$	6.60830e48	2.20329
$590$	6.41036e46	0.0207478
$591$	4.79913e47	0.150793
$592$	4.42677e47	0.135038
$593$	2.54339e48	0.753280	0.376640	−	0.926360i	$-0.377079\pi$
$593$	2.54339e48	0.753280	0.376640	+	0.926360i	$0.377079\pi$
$594$	2.21798e47	0.0637817
$595$	−2.71986e47	−0.0759450
$596$	−2.72962e48	−0.740104
$597$	−6.27931e47	−0.165334
$598$	6.36737e47	0.162813
$599$	4.57696e48	1.13660	0.568299	−	0.822822i	$-0.307602\pi$
$599$	4.57696e48	1.13660	0.568299	+	0.822822i	$0.307602\pi$
$600$	2.26732e47	0.0546847
$601$	1.31304e48	0.307591	0.153795	−	0.988103i	$-0.450850\pi$
$601$	1.31304e48	0.307591	0.153795	+	0.988103i	$0.450850\pi$
$602$	6.38543e47	0.145295
$603$	−5.48968e48	−1.21337
$604$	2.90578e48	0.623903
$605$	−1.00757e48	−0.210163
$606$	5.29389e47	0.107276
$607$	4.08519e48	0.804286	0.402143	−	0.915577i	$-0.368266\pi$
$607$	4.08519e48	0.804286	0.402143	+	0.915577i	$0.368266\pi$
$608$	−1.32262e48	−0.253001
$609$	−2.15140e47	−0.0399871
$610$	−8.50451e45	−0.00153595
$611$	−8.85620e48	−1.55427
$612$	−4.50982e48	−0.769146
$613$	−8.49710e48	−1.40836	−0.704178	−	0.710023i	$-0.748684\pi$
$613$	−8.49710e48	−1.40836	−0.704178	+	0.710023i	$0.748684\pi$
$614$	6.86493e48	1.10583
$615$	2.14715e47	0.0336162
$616$	1.37151e47	0.0208706
$617$	−5.42788e48	−0.802860	−0.401430	−	0.915890i	$-0.631487\pi$
$617$	−5.42788e48	−0.802860	−0.401430	+	0.915890i	$0.631487\pi$
$618$	4.45052e47	0.0639900
$619$	−8.30474e46	−0.0116075	−0.00580377	−	0.999983i	$-0.501847\pi$
$619$	−8.30474e46	−0.0116075	−0.00580377	+	0.999983i	$0.501847\pi$
$620$	1.29197e48	0.175549
$621$	6.13279e47	0.0810130
$622$	−1.90285e48	−0.244384
$623$	1.79800e48	0.224517
$624$	3.07431e47	0.0373265
$625$	7.17156e48	0.846668
$626$	5.96851e48	0.685196
$627$	5.85974e47	0.0654179
$628$	1.68335e48	0.182760
$629$	8.08462e48	0.853637
$630$	−3.22084e47	−0.0330757
$631$	1.13286e49	1.13152	0.565762	−	0.824568i	$-0.308582\pi$
$631$	1.13286e49	1.13152	0.565762	+	0.824568i	$0.308582\pi$
$632$	−3.11402e48	−0.302533
$633$	−2.56512e48	−0.242406
$634$	−5.07402e48	−0.466434
$635$	4.37496e48	0.391231
$636$	4.09296e47	0.0356072
$637$	−1.03320e49	−0.874471
$638$	−2.79809e48	−0.230409
$639$	1.93684e49	1.55178
$640$	−2.58582e47	−0.0201581
$641$	−1.52221e49	−1.15467	−0.577337	−	0.816506i	$-0.695908\pi$
$641$	−1.52221e49	−1.15467	−0.577337	+	0.816506i	$0.695908\pi$
$642$	−2.57044e48	−0.189733
$643$	−9.60787e48	−0.690136	−0.345068	−	0.938578i	$-0.612144\pi$
$643$	−9.60787e48	−0.690136	−0.345068	+	0.938578i	$0.612144\pi$
$644$	3.79225e47	0.0265091
$645$	5.33378e47	0.0362861
$646$	−2.41550e49	−1.59933
$647$	5.64865e48	0.364016	0.182008	−	0.983297i	$-0.441740\pi$
$647$	5.64865e48	0.364016	0.182008	+	0.983297i	$0.441740\pi$
$648$	−5.19045e48	−0.325569
$649$	−5.90347e47	−0.0360434
$650$	1.03214e49	0.613418
$651$	−9.14829e47	−0.0529265
$652$	1.43779e49	0.809770
$653$	−2.00154e49	−1.09744	−0.548722	−	0.836005i	$-0.684886\pi$
$653$	−2.00154e49	−1.09744	−0.548722	+	0.836005i	$0.684886\pi$
$654$	−1.32116e48	−0.0705255
$655$	1.85086e48	0.0961946
$656$	4.46317e48	0.225853
$657$	1.62606e49	0.801203
$658$	−5.27454e48	−0.253065
$659$	−8.34030e48	−0.389661	−0.194830	−	0.980837i	$-0.562416\pi$
$659$	−8.34030e48	−0.389661	−0.194830	+	0.980837i	$0.562416\pi$
$660$	1.14563e47	0.00521223
$661$	1.02289e49	0.453214	0.226607	−	0.973986i	$-0.427237\pi$
$661$	1.02289e49	0.453214	0.226607	+	0.973986i	$0.427237\pi$
$662$	1.31810e49	0.568767
$663$	5.61462e48	0.235958
$664$	1.86593e48	0.0763755
$665$	−1.72511e48	−0.0687763
$666$	9.57377e48	0.371778
$667$	−7.73678e48	−0.292656
$668$	6.36862e48	0.234670
$669$	9.10799e47	0.0326938
$670$	−5.74856e48	−0.201025
$671$	7.83203e46	0.00266827
$672$	1.83098e47	0.00607746
$673$	−3.25489e49	−1.05262	−0.526311	−	0.850292i	$-0.676425\pi$
$673$	−3.25489e49	−1.05262	−0.526311	+	0.850292i	$0.676425\pi$
$674$	3.12369e49	0.984284
$675$	9.94117e48	0.305226
$676$	−2.71727e48	−0.0812954
$677$	2.34682e49	0.684192	0.342096	−	0.939665i	$-0.388863\pi$
$677$	2.34682e49	0.684192	0.342096	+	0.939665i	$0.388863\pi$
$678$	−7.27844e46	−0.00206785
$679$	−1.58930e48	−0.0440031
$680$	−4.72249e48	−0.127428
$681$	8.90750e48	0.234251
$682$	−1.18981e49	−0.304967
$683$	−2.36004e49	−0.589600	−0.294800	−	0.955559i	$-0.595253\pi$
$683$	−2.36004e49	−0.589600	−0.294800	+	0.955559i	$0.595253\pi$
$684$	−2.86042e49	−0.696544
$685$	−1.44001e49	−0.341807
$686$	−1.25929e49	−0.291376
$687$	−1.30598e49	−0.294573
$688$	1.10870e49	0.243791
$689$	1.86322e49	0.399418
$690$	3.16768e47	0.00662038
$691$	−4.39789e49	−0.896146	−0.448073	−	0.893997i	$-0.647889\pi$
$691$	−4.39789e49	−0.896146	−0.448073	+	0.893997i	$0.647889\pi$
$692$	−3.54610e49	−0.704523
$693$	2.96616e48	0.0574596
$694$	−3.97713e49	−0.751240
$695$	1.81827e49	0.334907
$696$	−3.73549e48	−0.0670943
$697$	8.15112e49	1.42772
$698$	2.64810e49	0.452340
$699$	−1.26528e49	−0.210783
$700$	6.14720e48	0.0998760
$701$	4.60473e49	0.729691	0.364846	−	0.931068i	$-0.381122\pi$
$701$	4.60473e49	0.729691	0.364846	+	0.931068i	$0.381122\pi$
$702$	1.34795e49	0.208340
$703$	5.12780e49	0.773060
$704$	2.38135e48	0.0350188
$705$	−4.40584e48	−0.0632004
$706$	1.02995e49	0.144123
$707$	1.43529e49	0.195929
$708$	−7.88123e47	−0.0104957
$709$	3.64987e49	0.474207	0.237104	−	0.971484i	$-0.423802\pi$
$709$	3.64987e49	0.474207	0.237104	+	0.971484i	$0.423802\pi$
$710$	2.02818e49	0.257091
$711$	−6.73470e49	−0.832914
$712$	3.12188e49	0.376718
$713$	−3.28987e49	−0.387357
$714$	3.34393e48	0.0384184
$715$	5.21519e48	0.0584675
$716$	−2.02169e49	−0.221175
$717$	−3.17920e48	−0.0339416
$718$	3.20172e49	0.333584
$719$	−1.67716e50	−1.70538	−0.852688	−	0.522420i	$-0.825029\pi$
$719$	−1.67716e50	−1.70538	−0.852688	+	0.522420i	$0.825029\pi$
$720$	−5.59235e48	−0.0554978
$721$	1.20663e49	0.116871
$722$	−7.84098e49	−0.741258
$723$	−9.80481e48	−0.0904730
$724$	9.41475e49	0.847977
$725$	−1.25412e50	−1.10262
$726$	1.23876e49	0.106315
$727$	−1.07655e50	−0.901949	−0.450974	−	0.892537i	$-0.648923\pi$
$727$	−1.07655e50	−0.901949	−0.450974	+	0.892537i	$0.648923\pi$
$728$	8.33512e48	0.0681730
$729$	−1.05675e50	−0.843801
$730$	1.70274e49	0.132739
$731$	2.02483e50	1.54111
$732$	1.04559e47	0.000776992 0
$733$	1.62649e50	1.18013	0.590067	−	0.807355i	$-0.299101\pi$
$733$	1.62649e50	1.18013	0.590067	+	0.807355i	$0.299101\pi$
$734$	−8.96004e49	−0.634788
$735$	−5.14004e48	−0.0355581
$736$	6.58450e48	0.0444796
$737$	5.29401e49	0.349223
$738$	9.65251e49	0.621805
$739$	1.08002e50	0.679444	0.339722	−	0.940526i	$-0.389667\pi$
$739$	1.08002e50	0.679444	0.339722	+	0.940526i	$0.389667\pi$
$740$	1.00253e49	0.0615943
$741$	3.56117e49	0.213685
$742$	1.10969e49	0.0650329
$743$	4.06689e49	0.232787	0.116393	−	0.993203i	$-0.462867\pi$
$743$	4.06689e49	0.232787	0.116393	+	0.993203i	$0.462867\pi$
$744$	−1.58842e49	−0.0888054
$745$	−6.18174e49	−0.337580
$746$	−1.98989e50	−1.06145
$747$	4.03545e49	0.210272
$748$	4.34907e49	0.221370
$749$	−6.96901e49	−0.346529
$750$	1.05513e49	0.0512546
$751$	2.86918e50	1.36163	0.680814	−	0.732456i	$-0.261626\pi$
$751$	2.86918e50	1.36163	0.680814	+	0.732456i	$0.261626\pi$
$752$	−9.15819e49	−0.424617
$753$	2.15474e49	0.0976075
$754$	−1.70049e50	−0.752621
$755$	6.58070e49	0.284577
$756$	8.02803e48	0.0339217
$757$	−3.87152e50	−1.59847	−0.799234	−	0.601021i	$-0.794761\pi$
$757$	−3.87152e50	−1.59847	−0.799234	+	0.601021i	$0.794761\pi$
$758$	1.99959e50	0.806732
$759$	−2.91721e48	−0.0115010
$760$	−2.99532e49	−0.115400
$761$	1.34112e50	0.504937	0.252468	−	0.967605i	$-0.418758\pi$
$761$	1.34112e50	0.504937	0.252468	+	0.967605i	$0.418758\pi$
$762$	−5.37880e49	−0.197913
$763$	−3.58196e49	−0.128808
$764$	−1.74577e50	−0.613554
$765$	−1.02133e50	−0.350827
$766$	1.40722e50	0.472452
$767$	−3.58774e49	−0.117734
$768$	3.17914e48	0.0101974
$769$	−4.33833e50	−1.36023	−0.680113	−	0.733107i	$-0.738069\pi$
$769$	−4.33833e50	−1.36023	−0.680113	+	0.733107i	$0.738069\pi$
$770$	3.10604e48	0.00951961
$771$	6.94256e48	0.0208002
$772$	7.03823e49	0.206139
$773$	3.68317e50	1.05458	0.527291	−	0.849685i	$-0.323208\pi$
$773$	3.68317e50	1.05458	0.527291	+	0.849685i	$0.323208\pi$
$774$	2.39780e50	0.671190
$775$	−5.33284e50	−1.45941
$776$	−2.75950e49	−0.0738329
$777$	−7.09874e48	−0.0185701
$778$	3.07163e50	0.785644
$779$	5.16998e50	1.29295
$780$	6.96236e48	0.0170255
$781$	−1.86781e50	−0.446621
$782$	1.20253e50	0.281175
$783$	−1.63784e50	−0.374491
$784$	−1.06843e50	−0.238900
$785$	3.81227e49	0.0833612
$786$	−2.27554e49	−0.0486620
$787$	8.76823e50	1.83381	0.916905	−	0.399106i	$-0.130679\pi$
$787$	8.76823e50	1.83381	0.916905	+	0.399106i	$0.130679\pi$
$788$	2.25919e50	0.462108
$789$	−1.19348e49	−0.0238764
$790$	−7.05230e49	−0.137993
$791$	−1.97334e48	−0.00377671
$792$	5.15015e49	0.0964115
$793$	4.75979e48	0.00871580
$794$	−1.92639e50	−0.345053
$795$	9.26928e48	0.0162413
$796$	−2.95598e50	−0.506667
$797$	2.83941e49	0.0476110	0.0238055	−	0.999717i	$-0.492422\pi$
$797$	2.83941e49	0.0476110	0.0238055	+	0.999717i	$0.492422\pi$
$798$	2.12094e49	0.0347919
$799$	−1.67256e51	−2.68420
$800$	1.06734e50	0.167582
$801$	6.75168e50	1.03715
$802$	−6.45577e50	−0.970279
$803$	−1.56810e50	−0.230596
$804$	7.06758e49	0.101693
$805$	8.58827e48	0.0120914
$806$	−7.23091e50	−0.996161
$807$	9.19813e49	0.123997
$808$	2.49209e50	0.328750
$809$	−2.31085e50	−0.298314	−0.149157	−	0.988814i	$-0.547656\pi$
$809$	−2.31085e50	−0.298314	−0.149157	+	0.988814i	$0.547656\pi$
$810$	−1.17548e50	−0.148500
$811$	5.77595e50	0.714099	0.357049	−	0.934085i	$-0.383783\pi$
$811$	5.77595e50	0.714099	0.357049	+	0.934085i	$0.383783\pi$
$812$	−1.01277e50	−0.122541
$813$	6.96221e49	0.0824446
$814$	−9.23253e49	−0.107002
$815$	3.25614e50	0.369356
$816$	5.80608e49	0.0644622
$817$	1.28428e51	1.39564
$818$	7.04788e50	0.749680
$819$	1.80264e50	0.187689
$820$	1.01077e50	0.103017
$821$	4.94379e50	0.493236	0.246618	−	0.969113i	$-0.420681\pi$
$821$	4.94379e50	0.493236	0.246618	+	0.969113i	$0.420681\pi$
$822$	1.77042e50	0.172910
$823$	−9.94681e50	−0.951014	−0.475507	−	0.879712i	$-0.657735\pi$
$823$	−9.94681e50	−0.951014	−0.475507	+	0.879712i	$0.657735\pi$
$824$	2.09508e50	0.196098
$825$	−4.72876e49	−0.0433314
$826$	−2.13677e49	−0.0191693
$827$	−6.49390e50	−0.570373	−0.285187	−	0.958472i	$-0.592056\pi$
$827$	−6.49390e50	−0.570373	−0.285187	+	0.958472i	$0.592056\pi$
$828$	1.42403e50	0.122458
$829$	1.22822e51	1.03412	0.517062	−	0.855948i	$-0.327026\pi$
$829$	1.22822e51	1.03412	0.517062	+	0.855948i	$0.327026\pi$
$830$	4.22575e49	0.0348367
$831$	1.21611e49	0.00981650
$832$	1.44723e50	0.114388
$833$	−1.95128e51	−1.51020
$834$	−2.23548e50	−0.169420
$835$	1.44229e50	0.107039
$836$	2.75847e50	0.200474
$837$	−6.96451e50	−0.495672
$838$	1.15731e51	0.806638
$839$	−2.20156e51	−1.50278	−0.751391	−	0.659858i	$-0.770617\pi$
$839$	−2.20156e51	−1.50278	−0.751391	+	0.659858i	$0.770617\pi$
$840$	4.14661e48	0.00277208
$841$	5.38891e50	0.352834
$842$	8.28154e50	0.531068
$843$	8.40194e47	0.000527712 0
$844$	−1.20753e51	−0.742857
$845$	−6.15378e49	−0.0370809
$846$	−1.98064e51	−1.16903
$847$	3.35854e50	0.194174
$848$	1.92676e50	0.109119
$849$	−4.27968e48	−0.00237425
$850$	1.94929e51	1.05936
$851$	−2.55282e50	−0.135910
$852$	−2.49355e50	−0.130055
$853$	−3.83582e50	−0.195997	−0.0979986	−	0.995187i	$-0.531244\pi$
$853$	−3.83582e50	−0.195997	−0.0979986	+	0.995187i	$0.531244\pi$
$854$	2.83482e48	0.00141910
$855$	−6.47798e50	−0.317711
$856$	−1.21003e51	−0.581441
$857$	1.72305e51	0.811213	0.405606	−	0.914048i	$-0.367060\pi$
$857$	1.72305e51	0.811213	0.405606	+	0.914048i	$0.367060\pi$
$858$	−6.41182e49	−0.0295770
$859$	4.35017e51	1.96619	0.983096	−	0.183089i	$-0.0586097\pi$
$859$	4.35017e51	1.96619	0.983096	+	0.183089i	$0.0586097\pi$
$860$	2.51087e50	0.111199
$861$	−7.15713e49	−0.0310587
$862$	−1.57341e51	−0.669058
$863$	−2.21379e50	−0.0922459	−0.0461229	−	0.998936i	$-0.514687\pi$
$863$	−2.21379e50	−0.0922459	−0.0461229	+	0.998936i	$0.514687\pi$
$864$	1.39391e50	0.0569173
$865$	−8.03083e50	−0.321350
$866$	7.30922e49	0.0286621
$867$	6.35803e50	0.244337
$868$	−4.30655e50	−0.162194
$869$	6.49465e50	0.239723
$870$	−8.45972e49	−0.0306034
$871$	3.21735e51	1.14072
$872$	−6.21937e50	−0.216126
$873$	−5.96797e50	−0.203272
$874$	7.62724e50	0.254634
$875$	2.86068e50	0.0936113
$876$	−2.09344e50	−0.0671489
$877$	1.81379e50	0.0570287	0.0285144	−	0.999593i	$-0.490922\pi$
$877$	1.81379e50	0.0570287	0.0285144	+	0.999593i	$0.490922\pi$
$878$	1.59878e51	0.492759
$879$	5.28953e50	0.159813
$880$	5.39302e49	0.0159730
$881$	−3.30626e51	−0.959973	−0.479987	−	0.877276i	$-0.659358\pi$
$881$	−3.30626e51	−0.959973	−0.479987	+	0.877276i	$0.659358\pi$
$882$	−2.31070e51	−0.657724
$883$	−4.96554e51	−1.38565	−0.692826	−	0.721105i	$-0.743634\pi$
$883$	−4.96554e51	−1.38565	−0.692826	+	0.721105i	$0.743634\pi$
$884$	2.64308e51	0.723095
$885$	−1.78485e49	−0.00478735
$886$	−2.86707e51	−0.753960
$887$	4.50120e50	0.116055	0.0580277	−	0.998315i	$-0.481519\pi$
$887$	4.50120e50	0.116055	0.0580277	+	0.998315i	$0.481519\pi$
$888$	−1.23256e50	−0.0311588
$889$	−1.45831e51	−0.361467
$890$	7.07008e50	0.171830
$891$	1.08253e51	0.257976
$892$	4.28758e50	0.100191
$893$	−1.06085e52	−2.43083
$894$	7.60016e50	0.170772
$895$	−4.57850e50	−0.100883
$896$	8.61934e49	0.0186245
$897$	−1.77289e50	−0.0375676
$898$	4.52255e51	0.939826
$899$	8.78603e51	1.79060
$900$	2.30833e51	0.461376
$901$	3.51884e51	0.689788
$902$	−9.30846e50	−0.178963
$903$	−1.77791e50	−0.0335255
$904$	−3.42632e49	−0.00633695
$905$	2.13215e51	0.386783
$906$	−8.09066e50	−0.143959
$907$	−3.19477e51	−0.557586	−0.278793	−	0.960351i	$-0.589934\pi$
$907$	−3.19477e51	−0.557586	−0.278793	+	0.960351i	$0.589934\pi$
$908$	4.19320e51	0.717865
$909$	5.38965e51	0.905092
$910$	1.88765e50	0.0310954
$911$	9.93121e50	0.160484	0.0802418	−	0.996775i	$-0.474431\pi$
$911$	9.93121e50	0.160484	0.0802418	+	0.996775i	$0.474431\pi$
$912$	3.68260e50	0.0583774
$913$	−3.89161e50	−0.0605188
$914$	−2.48882e51	−0.379695
$915$	2.36793e48	0.000354405 0
$916$	−6.14787e51	−0.902722
$917$	−6.16949e50	−0.0888762
$918$	2.54570e51	0.359800
$919$	5.56026e51	0.771034	0.385517	−	0.922701i	$-0.374023\pi$
$919$	5.56026e51	0.771034	0.385517	+	0.922701i	$0.374023\pi$
$920$	1.49118e50	0.0202882
$921$	−1.91142e51	−0.255160
$922$	−4.88779e51	−0.640209
$923$	−1.13513e52	−1.45887
$924$	−3.81872e49	−0.00481569
$925$	−4.13809e51	−0.512058
$926$	−9.18544e51	−1.11534
$927$	4.53102e51	0.539884
$928$	−1.75848e51	−0.205611
$929$	1.36142e52	1.56213	0.781067	−	0.624448i	$-0.214676\pi$
$929$	1.36142e52	1.56213	0.781067	+	0.624448i	$0.214676\pi$
$930$	−3.59728e50	−0.0405063
$931$	−1.23763e52	−1.36764
$932$	−5.95629e51	−0.645948
$933$	5.29815e50	0.0563891
$934$	1.01475e52	1.05995
$935$	9.84930e50	0.100972
$936$	3.12992e51	0.314924
$937$	−4.51029e51	−0.445412	−0.222706	−	0.974886i	$-0.571489\pi$
$937$	−4.51029e51	−0.445412	−0.222706	+	0.974886i	$0.571489\pi$
$938$	1.91617e51	0.185731
$939$	−1.66183e51	−0.158102
$940$	−2.07405e51	−0.193678
$941$	2.11924e52	1.94250	0.971251	−	0.238060i	$-0.0765114\pi$
$941$	2.11924e52	1.94250	0.971251	+	0.238060i	$0.0765114\pi$
$942$	−4.68700e50	−0.0421700
$943$	−2.57381e51	−0.227312
$944$	−3.71008e50	−0.0321643
$945$	1.81810e50	0.0154725
$946$	−2.31233e51	−0.193177
$947$	5.49721e51	0.450835	0.225417	−	0.974262i	$-0.427625\pi$
$947$	5.49721e51	0.450835	0.225417	+	0.974262i	$0.427625\pi$
$948$	8.67047e50	0.0698066
$949$	−9.52989e51	−0.753233
$950$	1.23637e52	0.959366
$951$	1.41278e51	0.107625
$952$	1.57415e51	0.117734
$953$	−1.23050e52	−0.903558	−0.451779	−	0.892130i	$-0.649210\pi$
$953$	−1.23050e52	−0.903558	−0.451779	+	0.892130i	$0.649210\pi$
$954$	4.16699e51	0.300418
$955$	−3.95363e51	−0.279857
$956$	−1.49660e51	−0.104014
$957$	7.79079e50	0.0531646
$958$	1.31528e52	0.881295
$959$	4.80000e51	0.315803
$960$	7.19977e49	0.00465128
$961$	2.15966e52	1.37002
$962$	−5.61092e51	−0.349519
$963$	−2.61693e52	−1.60078
$964$	−4.61560e51	−0.277256
$965$	1.59394e51	0.0940253
$966$	−1.05589e50	−0.00611671
$967$	−9.18452e51	−0.522508	−0.261254	−	0.965270i	$-0.584136\pi$
$967$	−9.18452e51	−0.522508	−0.261254	+	0.965270i	$0.584136\pi$
$968$	5.83145e51	0.325805
$969$	6.72555e51	0.369030
$970$	−6.24941e50	−0.0336770
$971$	−9.34425e51	−0.494547	−0.247274	−	0.968946i	$-0.579535\pi$
$971$	−9.34425e51	−0.494547	−0.247274	+	0.968946i	$0.579535\pi$
$972$	4.54225e51	0.236108
$973$	−6.06086e51	−0.309428
$974$	−2.07967e52	−1.04283
$975$	−2.87383e51	−0.141540
$976$	4.92210e49	0.00238110
$977$	−5.62348e51	−0.267209	−0.133604	−	0.991035i	$-0.542655\pi$
$977$	−5.62348e51	−0.267209	−0.133604	+	0.991035i	$0.542655\pi$
$978$	−4.00327e51	−0.186847
$979$	−6.51103e51	−0.298506
$980$	−2.41967e51	−0.108968
$981$	−1.34506e52	−0.595024
$982$	8.87518e51	0.385679
$983$	3.83628e52	1.63766	0.818831	−	0.574035i	$-0.194623\pi$
$983$	3.83628e52	1.63766	0.818831	+	0.574035i	$0.194623\pi$
$984$	−1.24269e51	−0.0521135
$985$	5.11636e51	0.210779
$986$	−3.21152e52	−1.29976
$987$	1.46860e51	0.0583922
$988$	1.67642e52	0.654840
$989$	−6.39365e51	−0.245366
$990$	1.16635e51	0.0439757
$991$	4.91576e52	1.82096	0.910482	−	0.413549i	$-0.135711\pi$
$991$	4.91576e52	1.82096	0.910482	+	0.413549i	$0.135711\pi$
$992$	−7.47748e51	−0.272145
$993$	−3.67003e51	−0.131237
$994$	−6.76057e51	−0.237532
$995$	−6.69438e51	−0.231104
$996$	−5.19536e50	−0.0176229
$997$	5.37392e52	1.79112	0.895562	−	0.444936i	$-0.146774\pi$
$997$	5.37392e52	1.79112	0.895562	+	0.444936i	$0.146774\pi$
$998$	1.27783e52	0.418493
$999$	−5.40420e51	−0.173914

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.36.a.a.1.1	✓	1
3.2	odd	2		18.36.a.c.1.1		1
4.3	odd	2		16.36.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.36.a.a.1.1	✓	1	1.1	even	1	trivial
16.36.a.b.1.1		1	4.3	odd	2
18.36.a.c.1.1		1	3.2	odd	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:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 36 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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