LMFDB - Embedded newform 6.22.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,22,Mod(1,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("6.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	6.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:	$16.7686406572$
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	$\chi$	$=$	6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1024.00 q^{2} -59049.0 q^{3} +1.04858e6 q^{4} +1.29542e7 q^{5} -6.04662e7 q^{6} -4.79513e8 q^{7} +1.07374e9 q^{8} +3.48678e9 q^{9} +O(q^{10})$

\(q+1024.00 q^{2} -59049.0 q^{3} +1.04858e6 q^{4} +1.29542e7 q^{5} -6.04662e7 q^{6} -4.79513e8 q^{7} +1.07374e9 q^{8} +3.48678e9 q^{9} +1.32651e10 q^{10} +1.15658e11 q^{11} -6.19174e10 q^{12} +2.95658e11 q^{13} -4.91021e11 q^{14} -7.64931e11 q^{15} +1.09951e12 q^{16} +6.62698e12 q^{17} +3.57047e12 q^{18} +2.85762e13 q^{19} +1.35834e13 q^{20} +2.83148e13 q^{21} +1.18434e14 q^{22} +3.35385e14 q^{23} -6.34034e13 q^{24} -3.09027e14 q^{25} +3.02754e14 q^{26} -2.05891e14 q^{27} -5.02806e14 q^{28} -6.99224e14 q^{29} -7.83289e14 q^{30} -3.48496e15 q^{31} +1.12590e15 q^{32} -6.82948e15 q^{33} +6.78603e15 q^{34} -6.21170e15 q^{35} +3.65616e15 q^{36} -3.51815e16 q^{37} +2.92620e16 q^{38} -1.74583e16 q^{39} +1.39094e16 q^{40} +6.13206e15 q^{41} +2.89943e16 q^{42} +2.33261e17 q^{43} +1.21276e17 q^{44} +4.51684e16 q^{45} +3.43434e17 q^{46} -5.80206e17 q^{47} -6.49251e16 q^{48} -3.28613e17 q^{49} -3.16443e17 q^{50} -3.91317e17 q^{51} +3.10020e17 q^{52} -1.39447e18 q^{53} -2.10833e17 q^{54} +1.49825e18 q^{55} -5.14873e17 q^{56} -1.68740e18 q^{57} -7.16006e17 q^{58} +2.35248e18 q^{59} -8.02088e17 q^{60} +9.92063e18 q^{61} -3.56860e18 q^{62} -1.67196e18 q^{63} +1.15292e18 q^{64} +3.83001e18 q^{65} -6.99338e18 q^{66} +2.60690e19 q^{67} +6.94890e18 q^{68} -1.98042e19 q^{69} -6.36078e18 q^{70} -1.33370e19 q^{71} +3.74391e18 q^{72} +9.03753e18 q^{73} -3.60259e19 q^{74} +1.82477e19 q^{75} +2.99643e19 q^{76} -5.54594e19 q^{77} -1.78773e19 q^{78} -7.72839e19 q^{79} +1.42433e19 q^{80} +1.21577e19 q^{81} +6.27923e18 q^{82} -1.55698e20 q^{83} +2.96902e19 q^{84} +8.58471e19 q^{85} +2.38859e20 q^{86} +4.12885e19 q^{87} +1.24187e20 q^{88} +2.53837e20 q^{89} +4.62525e19 q^{90} -1.41772e20 q^{91} +3.51677e20 q^{92} +2.05783e20 q^{93} -5.94131e20 q^{94} +3.70181e20 q^{95} -6.64833e19 q^{96} -1.03072e21 q^{97} -3.36500e20 q^{98} +4.03274e20 q^{99} +O(q^{100})\)

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 $

$2$	1024.00	0.707107
$2$	1024.00	0.707107
$3$	−59049.0	−0.577350
$3$	−59049.0	−0.577350
$4$	1.04858e6	0.500000
$5$	1.29542e7	0.593232	0.296616	−	0.954997i	$-0.404142\pi$
$5$	1.29542e7	0.593232	0.296616	+	0.954997i	$0.404142\pi$
$6$	−6.04662e7	−0.408248
$7$	−4.79513e8	−0.641610	−0.320805	−	0.947145i	$-0.603953\pi$
$7$	−4.79513e8	−0.641610	−0.320805	+	0.947145i	$0.603953\pi$
$8$	1.07374e9	0.353553
$9$	3.48678e9	0.333333
$10$	1.32651e10	0.419478
$11$	1.15658e11	1.34447	0.672236	−	0.740337i	$-0.265334\pi$
$11$	1.15658e11	1.34447	0.672236	+	0.740337i	$0.265334\pi$
$12$	−6.19174e10	−0.288675
$13$	2.95658e11	0.594819	0.297409	−	0.954750i	$-0.403877\pi$
$13$	2.95658e11	0.594819	0.297409	+	0.954750i	$0.403877\pi$
$14$	−4.91021e11	−0.453687
$15$	−7.64931e11	−0.342503
$16$	1.09951e12	0.250000
$17$	6.62698e12	0.797264	0.398632	−	0.917111i	$-0.369485\pi$
$17$	6.62698e12	0.797264	0.398632	+	0.917111i	$0.369485\pi$
$18$	3.57047e12	0.235702
$19$	2.85762e13	1.06928	0.534640	−	0.845080i	$-0.320447\pi$
$19$	2.85762e13	1.06928	0.534640	+	0.845080i	$0.320447\pi$
$20$	1.35834e13	0.296616
$21$	2.83148e13	0.370434
$22$	1.18434e14	0.950685
$23$	3.35385e14	1.68811	0.844057	−	0.536254i	$-0.180161\pi$
$23$	3.35385e14	1.68811	0.844057	+	0.536254i	$0.180161\pi$
$24$	−6.34034e13	−0.204124
$25$	−3.09027e14	−0.648076
$26$	3.02754e14	0.420601
$27$	−2.05891e14	−0.192450
$28$	−5.02806e14	−0.320805
$29$	−6.99224e14	−0.308630	−0.154315	−	0.988022i	$-0.549317\pi$
$29$	−6.99224e14	−0.308630	−0.154315	+	0.988022i	$0.549317\pi$
$30$	−7.83289e14	−0.242186
$31$	−3.48496e15	−0.763659	−0.381830	−	0.924233i	$-0.624706\pi$
$31$	−3.48496e15	−0.763659	−0.381830	+	0.924233i	$0.624706\pi$
$32$	1.12590e15	0.176777
$33$	−6.82948e15	−0.776231
$34$	6.78603e15	0.563751
$35$	−6.21170e15	−0.380624
$36$	3.65616e15	0.166667
$37$	−3.51815e16	−1.20281	−0.601404	−	0.798945i	$-0.705392\pi$
$37$	−3.51815e16	−1.20281	−0.601404	+	0.798945i	$0.705392\pi$
$38$	2.92620e16	0.756095
$39$	−1.74583e16	−0.343419
$40$	1.39094e16	0.209739
$41$	6.13206e15	0.0713470	0.0356735	−	0.999363i	$-0.488642\pi$
$41$	6.13206e15	0.0713470	0.0356735	+	0.999363i	$0.488642\pi$
$42$	2.89943e16	0.261936
$43$	2.33261e17	1.64597	0.822987	−	0.568060i	$-0.192306\pi$
$43$	2.33261e17	1.64597	0.822987	+	0.568060i	$0.192306\pi$
$44$	1.21276e17	0.672236
$45$	4.51684e16	0.197744
$46$	3.43434e17	1.19368
$47$	−5.80206e17	−1.60899	−0.804497	−	0.593957i	$-0.797565\pi$
$47$	−5.80206e17	−1.60899	−0.804497	+	0.593957i	$0.797565\pi$
$48$	−6.49251e16	−0.144338
$49$	−3.28613e17	−0.588337
$50$	−3.16443e17	−0.458259
$51$	−3.91317e17	−0.460301
$52$	3.10020e17	0.297409
$53$	−1.39447e18	−1.09525	−0.547625	−	0.836724i	$-0.684468\pi$
$53$	−1.39447e18	−1.09525	−0.547625	+	0.836724i	$0.684468\pi$
$54$	−2.10833e17	−0.136083
$55$	1.49825e18	0.797584
$56$	−5.14873e17	−0.226843
$57$	−1.68740e18	−0.617349
$58$	−7.16006e17	−0.218234
$59$	2.35248e18	0.599210	0.299605	−	0.954063i	$-0.403145\pi$
$59$	2.35248e18	0.599210	0.299605	+	0.954063i	$0.403145\pi$
$60$	−8.02088e17	−0.171251
$61$	9.92063e18	1.78064	0.890320	−	0.455336i	$-0.150481\pi$
$61$	9.92063e18	1.78064	0.890320	+	0.455336i	$0.150481\pi$
$62$	−3.56860e18	−0.539989
$63$	−1.67196e18	−0.213870
$64$	1.15292e18	0.125000
$65$	3.83001e18	0.352866
$66$	−6.99338e18	−0.548878
$67$	2.60690e19	1.74718	0.873592	−	0.486659i	$-0.161785\pi$
$67$	2.60690e19	1.74718	0.873592	+	0.486659i	$0.161785\pi$
$68$	6.94890e18	0.398632
$69$	−1.98042e19	−0.974633
$70$	−6.36078e18	−0.269142
$71$	−1.33370e19	−0.486233	−0.243116	−	0.969997i	$-0.578170\pi$
$71$	−1.33370e19	−0.486233	−0.243116	+	0.969997i	$0.578170\pi$
$72$	3.74391e18	0.117851
$73$	9.03753e18	0.246127	0.123064	−	0.992399i	$-0.460728\pi$
$73$	9.03753e18	0.246127	0.123064	+	0.992399i	$0.460728\pi$
$74$	−3.60259e19	−0.850514
$75$	1.82477e19	0.374167
$76$	2.99643e19	0.534640
$77$	−5.54594e19	−0.862626
$78$	−1.78773e19	−0.242834
$79$	−7.72839e19	−0.918342	−0.459171	−	0.888348i	$-0.651853\pi$
$79$	−7.72839e19	−0.918342	−0.459171	+	0.888348i	$0.651853\pi$
$80$	1.42433e19	0.148308
$81$	1.21577e19	0.111111
$82$	6.27923e18	0.0504499
$83$	−1.55698e20	−1.10145	−0.550724	−	0.834687i	$-0.685648\pi$
$83$	−1.55698e20	−1.10145	−0.550724	+	0.834687i	$0.685648\pi$
$84$	2.96902e19	0.185217
$85$	8.58471e19	0.472963
$86$	2.38859e20	1.16388
$87$	4.12885e19	0.178187
$88$	1.24187e20	0.475343
$89$	2.53837e20	0.862900	0.431450	−	0.902137i	$-0.358002\pi$
$89$	2.53837e20	0.862900	0.431450	+	0.902137i	$0.358002\pi$
$90$	4.62525e19	0.139826
$91$	−1.41772e20	−0.381642
$92$	3.51677e20	0.844057
$93$	2.05783e20	0.440899
$94$	−5.94131e20	−1.13773
$95$	3.70181e20	0.634331
$96$	−6.64833e19	−0.102062
$97$	−1.03072e21	−1.41918	−0.709591	−	0.704613i	$-0.751120\pi$
$97$	−1.03072e21	−1.41918	−0.709591	+	0.704613i	$0.751120\pi$
$98$	−3.36500e20	−0.416017
$99$	4.03274e20	0.448157
$100$	−3.24038e20	−0.324038
$101$	−7.65513e20	−0.689570	−0.344785	−	0.938682i	$-0.612048\pi$
$101$	−7.65513e20	−0.689570	−0.344785	+	0.938682i	$0.612048\pi$
$102$	−4.00708e20	−0.325482
$103$	−8.97524e20	−0.658044	−0.329022	−	0.944322i	$-0.606719\pi$
$103$	−8.97524e20	−0.658044	−0.329022	+	0.944322i	$0.606719\pi$
$104$	3.17461e20	0.210300
$105$	3.66794e20	0.219753
$106$	−1.42794e21	−0.774458
$107$	1.71774e21	0.844166	0.422083	−	0.906557i	$-0.361299\pi$
$107$	1.71774e21	0.844166	0.422083	+	0.906557i	$0.361299\pi$
$108$	−2.15892e20	−0.0962250
$109$	2.99848e21	1.21317	0.606586	−	0.795018i	$-0.292539\pi$
$109$	2.99848e21	1.21317	0.606586	+	0.795018i	$0.292539\pi$
$110$	1.53421e21	0.563977
$111$	2.07743e21	0.694442
$112$	−5.27230e20	−0.160402
$113$	−5.11711e21	−1.41808	−0.709041	−	0.705168i	$-0.750872\pi$
$113$	−5.11711e21	−1.41808	−0.709041	+	0.705168i	$0.750872\pi$
$114$	−1.72789e21	−0.436532
$115$	4.34464e21	1.00144
$116$	−7.33190e20	−0.154315
$117$	1.03090e21	0.198273
$118$	2.40894e21	0.423706
$119$	−3.17773e21	−0.511533
$120$	−8.21338e20	−0.121093
$121$	5.97647e21	0.807604
$122$	1.01587e22	1.25910
$123$	−3.62092e20	−0.0411922
$124$	−3.65424e21	−0.381830
$125$	−1.01802e22	−0.977691
$126$	−1.71209e21	−0.151229
$127$	4.05103e21	0.329326	0.164663	−	0.986350i	$-0.447346\pi$
$127$	4.05103e21	0.329326	0.164663	+	0.986350i	$0.447346\pi$
$128$	1.18059e21	0.0883883
$129$	−1.37738e22	−0.950304
$130$	3.92193e21	0.249514
$131$	−1.92867e22	−1.13217	−0.566083	−	0.824348i	$-0.691542\pi$
$131$	−1.92867e22	−1.13217	−0.566083	+	0.824348i	$0.691542\pi$
$132$	−7.16122e21	−0.388116
$133$	−1.37027e22	−0.686061
$134$	2.66946e22	1.23545
$135$	−2.66715e21	−0.114168
$136$	7.11567e21	0.281875
$137$	−2.93536e22	−1.07670	−0.538351	−	0.842721i	$-0.680953\pi$
$137$	−2.93536e22	−1.07670	−0.538351	+	0.842721i	$0.680953\pi$
$138$	−2.02795e22	−0.689169
$139$	4.24068e22	1.33592	0.667959	−	0.744198i	$-0.267168\pi$
$139$	4.24068e22	1.33592	0.667959	+	0.744198i	$0.267168\pi$
$140$	−6.51344e21	−0.190312
$141$	3.42606e22	0.928953
$142$	−1.36570e22	−0.343818
$143$	3.41952e22	0.799717
$144$	3.83376e21	0.0833333
$145$	−9.05787e21	−0.183089
$146$	9.25443e21	0.174038
$147$	1.94043e22	0.339676
$148$	−3.68905e22	−0.601404
$149$	5.04492e22	0.766299	0.383150	−	0.923686i	$-0.374839\pi$
$149$	5.04492e22	0.766299	0.383150	+	0.923686i	$0.374839\pi$
$150$	1.86857e22	0.264576
$151$	8.30789e22	1.09707	0.548533	−	0.836129i	$-0.315186\pi$
$151$	8.30789e22	1.09707	0.548533	+	0.836129i	$0.315186\pi$
$152$	3.06834e22	0.378048
$153$	2.31069e22	0.265755
$154$	−5.67904e22	−0.609969
$155$	−4.51447e22	−0.453027
$156$	−1.83064e22	−0.171709
$157$	−1.66285e23	−1.45850	−0.729250	−	0.684247i	$-0.760131\pi$
$157$	−1.66285e23	−1.45850	−0.729250	+	0.684247i	$0.760131\pi$
$158$	−7.91387e22	−0.649366
$159$	8.23422e22	0.632343
$160$	1.45851e22	0.104870
$161$	−1.60822e23	−1.08311
$162$	1.24494e22	0.0785674
$163$	−1.13921e23	−0.673958	−0.336979	−	0.941512i	$-0.609405\pi$
$163$	−1.13921e23	−0.673958	−0.336979	+	0.941512i	$0.609405\pi$
$164$	6.42993e21	0.0356735
$165$	−8.84702e22	−0.460485
$166$	−1.59435e23	−0.778842
$167$	3.52378e23	1.61617	0.808084	−	0.589068i	$-0.200505\pi$
$167$	3.52378e23	1.61617	0.808084	+	0.589068i	$0.200505\pi$
$168$	3.04028e22	0.130968
$169$	−1.59651e23	−0.646190
$170$	8.79074e22	0.334435
$171$	9.96390e22	0.356427
$172$	2.44592e23	0.822987
$173$	−5.43709e22	−0.172140	−0.0860702	−	0.996289i	$-0.527431\pi$
$173$	−5.43709e22	−0.172140	−0.0860702	+	0.996289i	$0.527431\pi$
$174$	4.22794e22	0.125997
$175$	1.48182e23	0.415812
$176$	1.27167e23	0.336118
$177$	−1.38911e23	−0.345954
$178$	2.59929e23	0.610162
$179$	5.57843e23	1.23468	0.617341	−	0.786695i	$-0.288210\pi$
$179$	5.57843e23	1.23468	0.617341	+	0.786695i	$0.288210\pi$
$180$	4.73625e22	0.0988720
$181$	−5.29021e23	−1.04195	−0.520976	−	0.853571i	$-0.674432\pi$
$181$	−5.29021e23	−1.04195	−0.520976	+	0.853571i	$0.674432\pi$
$182$	−1.45175e23	−0.269861
$183$	−5.85803e23	−1.02805
$184$	3.60117e23	0.596838
$185$	−4.55748e23	−0.713545
$186$	2.10722e23	0.311763
$187$	7.66462e23	1.07190
$188$	−6.08390e23	−0.804497
$189$	9.87275e22	0.123478
$190$	3.79065e23	0.448540
$191$	−8.19262e22	−0.0917429	−0.0458715	−	0.998947i	$-0.514606\pi$
$191$	−8.19262e22	−0.0917429	−0.0458715	+	0.998947i	$0.514606\pi$
$192$	−6.80789e22	−0.0721688
$193$	6.60174e23	0.662684	0.331342	−	0.943511i	$-0.392499\pi$
$193$	6.60174e23	0.662684	0.331342	+	0.943511i	$0.392499\pi$
$194$	−1.05546e24	−1.00351
$195$	−2.26158e23	−0.203727
$196$	−3.44576e23	−0.294168
$197$	−8.79420e23	−0.711707	−0.355853	−	0.934542i	$-0.615810\pi$
$197$	−8.79420e23	−0.711707	−0.355853	+	0.934542i	$0.615810\pi$
$198$	4.12952e23	0.316895
$199$	8.82376e23	0.642239	0.321119	−	0.947039i	$-0.395941\pi$
$199$	8.82376e23	0.642239	0.321119	+	0.947039i	$0.395941\pi$
$200$	−3.31815e23	−0.229129
$201$	−1.53935e24	−1.00874
$202$	−7.83885e23	−0.487599
$203$	3.35287e23	0.198020
$204$	−4.10325e23	−0.230150
$205$	7.94357e22	0.0423253
$206$	−9.19064e23	−0.465308
$207$	1.16942e24	0.562704
$208$	3.25080e23	0.148705
$209$	3.30506e24	1.43762
$210$	3.75598e23	0.155389
$211$	−2.86260e24	−1.12667	−0.563333	−	0.826230i	$-0.690481\pi$
$211$	−2.86260e24	−1.12667	−0.563333	+	0.826230i	$0.690481\pi$
$212$	−1.46221e24	−0.547625
$213$	7.87534e23	0.280727
$214$	1.75897e24	0.596915
$215$	3.02170e24	0.976445
$216$	−2.21074e23	−0.0680414
$217$	1.67108e24	0.489971
$218$	3.07044e24	0.857842
$219$	−5.33657e23	−0.142102
$220$	1.57103e24	0.398792
$221$	1.95932e24	0.474228
$222$	2.12729e24	0.491045
$223$	−1.04892e24	−0.230963	−0.115481	−	0.993310i	$-0.536841\pi$
$223$	−1.04892e24	−0.230963	−0.115481	+	0.993310i	$0.536841\pi$
$224$	−5.39884e23	−0.113422
$225$	−1.07751e24	−0.216025
$226$	−5.23992e24	−1.00273
$227$	−4.22561e24	−0.772002	−0.386001	−	0.922498i	$-0.626144\pi$
$227$	−4.22561e24	−0.772002	−0.386001	+	0.922498i	$0.626144\pi$
$228$	−1.76936e24	−0.308675
$229$	−9.40000e24	−1.56623	−0.783115	−	0.621877i	$-0.786370\pi$
$229$	−9.40000e24	−1.56623	−0.783115	+	0.621877i	$0.786370\pi$
$230$	4.44891e24	0.708127
$231$	3.27482e24	0.498038
$232$	−7.50786e23	−0.109117
$233$	−5.59528e24	−0.777293	−0.388646	−	0.921387i	$-0.627057\pi$
$233$	−5.59528e24	−0.777293	−0.388646	+	0.921387i	$0.627057\pi$
$234$	1.05564e24	0.140200
$235$	−7.51609e24	−0.954507
$236$	2.46675e24	0.299605
$237$	4.56353e24	0.530205
$238$	−3.25399e24	−0.361708
$239$	−4.79661e24	−0.510219	−0.255109	−	0.966912i	$-0.582111\pi$
$239$	−4.79661e24	−0.510219	−0.255109	+	0.966912i	$0.582111\pi$
$240$	−8.41051e23	−0.0856257
$241$	1.30240e24	0.126930	0.0634649	−	0.997984i	$-0.479785\pi$
$241$	1.30240e24	0.126930	0.0634649	+	0.997984i	$0.479785\pi$
$242$	6.11991e24	0.571062
$243$	−7.17898e23	−0.0641500
$244$	1.04025e25	0.890320
$245$	−4.25691e24	−0.349020
$246$	−3.70782e23	−0.0291273
$247$	8.44878e24	0.636028
$248$	−3.74194e24	−0.269994
$249$	9.19384e24	0.635922
$250$	−1.04245e25	−0.691332
$251$	−1.25489e25	−0.798055	−0.399027	−	0.916939i	$-0.630652\pi$
$251$	−1.25489e25	−0.798055	−0.399027	+	0.916939i	$0.630652\pi$
$252$	−1.75318e24	−0.106935
$253$	3.87899e25	2.26962
$254$	4.14825e24	0.232869
$255$	−5.06919e24	−0.273065
$256$	1.20893e24	0.0625000
$257$	3.12478e25	1.55068	0.775339	−	0.631546i	$-0.217579\pi$
$257$	3.12478e25	1.55068	0.775339	+	0.631546i	$0.217579\pi$
$258$	−1.41044e25	−0.671966
$259$	1.68700e25	0.771734
$260$	4.01605e24	0.176433
$261$	−2.43804e24	−0.102877
$262$	−1.97496e25	−0.800562
$263$	−2.04345e25	−0.795845	−0.397923	−	0.917419i	$-0.630269\pi$
$263$	−2.04345e25	−0.795845	−0.397923	+	0.917419i	$0.630269\pi$
$264$	−7.33309e24	−0.274439
$265$	−1.80642e25	−0.649737
$266$	−1.40315e25	−0.485118
$267$	−1.49888e25	−0.498195
$268$	2.73353e25	0.873592
$269$	−6.02651e24	−0.185211	−0.0926055	−	0.995703i	$-0.529520\pi$
$269$	−6.02651e24	−0.185211	−0.0926055	+	0.995703i	$0.529520\pi$
$270$	−2.73116e24	−0.0807287
$271$	−1.13011e25	−0.321324	−0.160662	−	0.987009i	$-0.551363\pi$
$271$	−1.13011e25	−0.321324	−0.160662	+	0.987009i	$0.551363\pi$
$272$	7.28645e24	0.199316
$273$	8.37150e24	0.220341
$274$	−3.00581e25	−0.761343
$275$	−3.57413e25	−0.871319
$276$	−2.07662e25	−0.487316
$277$	7.51731e25	1.69834	0.849170	−	0.528119i	$-0.177103\pi$
$277$	7.51731e25	1.69834	0.849170	+	0.528119i	$0.177103\pi$
$278$	4.34245e25	0.944637
$279$	−1.21513e25	−0.254553
$280$	−6.66976e24	−0.134571
$281$	−2.24659e25	−0.436623	−0.218312	−	0.975879i	$-0.570055\pi$
$281$	−2.24659e25	−0.436623	−0.218312	+	0.975879i	$0.570055\pi$
$282$	3.50828e25	0.656869
$283$	−6.02460e25	−1.08685	−0.543426	−	0.839457i	$-0.682873\pi$
$283$	−6.02460e25	−1.08685	−0.543426	+	0.839457i	$0.682873\pi$
$284$	−1.39848e25	−0.243116
$285$	−2.18588e25	−0.366231
$286$	3.50159e25	0.565485
$287$	−2.94040e24	−0.0457769
$288$	3.92577e24	0.0589256
$289$	−2.51750e25	−0.364370
$290$	−9.27526e24	−0.129463
$291$	6.08631e25	0.819366
$292$	9.47654e24	0.123064
$293$	4.65033e24	0.0582604	0.0291302	−	0.999576i	$-0.490726\pi$
$293$	4.65033e24	0.0582604	0.0291302	+	0.999576i	$0.490726\pi$
$294$	1.98700e25	0.240187
$295$	3.04744e25	0.355471
$296$	−3.77759e25	−0.425257
$297$	−2.38129e25	−0.258744
$298$	5.16600e25	0.541855
$299$	9.91594e25	1.00412
$300$	1.91341e25	0.187083
$301$	−1.11852e26	−1.05607
$302$	8.50728e25	0.775743
$303$	4.52028e25	0.398123
$304$	3.14198e25	0.267320
$305$	1.28514e26	1.05633
$306$	2.36614e25	0.187917
$307$	−6.89098e25	−0.528844	−0.264422	−	0.964407i	$-0.585181\pi$
$307$	−6.89098e25	−0.528844	−0.264422	+	0.964407i	$0.585181\pi$
$308$	−5.81534e25	−0.431313
$309$	5.29979e25	0.379922
$310$	−4.62282e25	−0.320339
$311$	−2.75254e25	−0.184395	−0.0921976	−	0.995741i	$-0.529389\pi$
$311$	−2.75254e25	−0.184395	−0.0921976	+	0.995741i	$0.529389\pi$
$312$	−1.87457e25	−0.121417
$313$	−1.51255e26	−0.947316	−0.473658	−	0.880709i	$-0.657067\pi$
$313$	−1.51255e26	−0.947316	−0.473658	+	0.880709i	$0.657067\pi$
$314$	−1.70276e26	−1.03132
$315$	−2.16588e25	−0.126875
$316$	−8.10380e25	−0.459171
$317$	−5.45958e25	−0.299252	−0.149626	−	0.988743i	$-0.547807\pi$
$317$	−5.45958e25	−0.299252	−0.149626	+	0.988743i	$0.547807\pi$
$318$	8.43184e25	0.447134
$319$	−8.08707e25	−0.414944
$320$	1.49351e25	0.0741540
$321$	−1.01431e26	−0.487379
$322$	−1.64681e26	−0.765875
$323$	1.89374e26	0.852499
$324$	1.27482e25	0.0555556
$325$	−9.13662e25	−0.385488
$326$	−1.16655e26	−0.476561
$327$	−1.77057e26	−0.700425
$328$	6.58425e24	0.0252250
$329$	2.78216e26	1.03235
$330$	−9.05935e25	−0.325612
$331$	4.57958e26	1.59453	0.797263	−	0.603632i	$-0.206280\pi$
$331$	4.57958e26	1.59453	0.797263	+	0.603632i	$0.206280\pi$
$332$	−1.63262e26	−0.550724
$333$	−1.22670e26	−0.400936
$334$	3.60836e26	1.14280
$335$	3.37702e26	1.03649
$336$	3.11324e25	0.0926084
$337$	1.77477e26	0.511714	0.255857	−	0.966715i	$-0.417642\pi$
$337$	1.77477e26	0.511714	0.255857	+	0.966715i	$0.417642\pi$
$338$	−1.63482e26	−0.456926
$339$	3.02160e26	0.818730
$340$	9.00172e25	0.236481
$341$	−4.03062e26	−1.02672
$342$	1.02030e26	0.252032
$343$	4.25404e26	1.01909
$344$	2.50462e26	0.581940
$345$	−2.56547e26	−0.578183
$346$	−5.56758e25	−0.121722
$347$	−3.31317e26	−0.702724	−0.351362	−	0.936240i	$-0.614281\pi$
$347$	−3.31317e26	−0.702724	−0.351362	+	0.936240i	$0.614281\pi$
$348$	4.32941e25	0.0890937
$349$	−1.82866e26	−0.365146	−0.182573	−	0.983192i	$-0.558443\pi$
$349$	−1.82866e26	−0.365146	−0.182573	+	0.983192i	$0.558443\pi$
$350$	1.51739e26	0.294023
$351$	−6.08734e25	−0.114473
$352$	1.30219e26	0.237671
$353$	−5.58761e26	−0.989900	−0.494950	−	0.868921i	$-0.664814\pi$
$353$	−5.58761e26	−0.989900	−0.494950	+	0.868921i	$0.664814\pi$
$354$	−1.42245e26	−0.244627
$355$	−1.72769e26	−0.288449
$356$	2.66168e26	0.431450
$357$	1.87642e26	0.295333
$358$	5.71232e26	0.873053
$359$	−8.65986e26	−1.28534	−0.642671	−	0.766142i	$-0.722174\pi$
$359$	−8.65986e26	−1.28534	−0.642671	+	0.766142i	$0.722174\pi$
$360$	4.84992e25	0.0699131
$361$	1.02389e26	0.143360
$362$	−5.41717e26	−0.736771
$363$	−3.52905e26	−0.466270
$364$	−1.48659e26	−0.190821
$365$	1.17074e26	0.146011
$366$	−5.99862e26	−0.726943
$367$	−1.31813e26	−0.155227	−0.0776133	−	0.996984i	$-0.524730\pi$
$367$	−1.31813e26	−0.155227	−0.0776133	+	0.996984i	$0.524730\pi$
$368$	3.68760e26	0.422028
$369$	2.13812e25	0.0237823
$370$	−4.66686e26	−0.504552
$371$	6.68667e26	0.702723
$372$	2.15779e26	0.220449
$373$	−4.80048e26	−0.476806	−0.238403	−	0.971166i	$-0.576624\pi$
$373$	−4.80048e26	−0.476806	−0.238403	+	0.971166i	$0.576624\pi$
$374$	7.84857e26	0.757947
$375$	6.01132e26	0.564470
$376$	−6.22991e26	−0.568865
$377$	−2.06731e26	−0.183579
$378$	1.01097e26	0.0873120
$379$	3.61041e26	0.303281	0.151640	−	0.988436i	$-0.451544\pi$
$379$	3.61041e26	0.303281	0.151640	+	0.988436i	$0.451544\pi$
$380$	3.88163e26	0.317166
$381$	−2.39209e26	−0.190136
$382$	−8.38924e25	−0.0648720
$383$	−4.45743e26	−0.335349	−0.167675	−	0.985842i	$-0.553626\pi$
$383$	−4.45743e26	−0.335349	−0.167675	+	0.985842i	$0.553626\pi$
$384$	−6.97128e25	−0.0510310
$385$	−7.18431e26	−0.511738
$386$	6.76018e26	0.468588
$387$	8.13330e26	0.548658
$388$	−1.08079e27	−0.709591
$389$	2.63616e27	1.68461	0.842307	−	0.538998i	$-0.181197\pi$
$389$	2.63616e27	1.68461	0.842307	+	0.538998i	$0.181197\pi$
$390$	−2.31586e26	−0.144057
$391$	2.22259e27	1.34587
$392$	−3.52846e26	−0.208008
$393$	1.13886e27	0.653657
$394$	−9.00526e26	−0.503253
$395$	−1.00115e27	−0.544790
$396$	4.22863e26	0.224079
$397$	−1.91276e27	−0.987100	−0.493550	−	0.869717i	$-0.664301\pi$
$397$	−1.91276e27	−0.987100	−0.493550	+	0.869717i	$0.664301\pi$
$398$	9.03553e26	0.454131
$399$	8.09128e26	0.396097
$400$	−3.39778e26	−0.162019
$401$	2.31621e27	1.07588	0.537939	−	0.842984i	$-0.319203\pi$
$401$	2.31621e27	1.07588	0.537939	+	0.842984i	$0.319203\pi$
$402$	−1.57629e27	−0.713285
$403$	−1.03036e27	−0.454239
$404$	−8.02698e26	−0.344785
$405$	1.57493e26	0.0659147
$406$	3.43334e26	0.140021
$407$	−4.06902e27	−1.61714
$408$	−4.20173e26	−0.162741
$409$	1.77500e27	0.670045	0.335022	−	0.942210i	$-0.391256\pi$
$409$	1.77500e27	0.670045	0.335022	+	0.942210i	$0.391256\pi$
$410$	8.13422e25	0.0299285
$411$	1.73330e27	0.621634
$412$	−9.41122e26	−0.329022
$413$	−1.12804e27	−0.384459
$414$	1.19748e27	0.397892
$415$	−2.01694e27	−0.653415
$416$	3.32882e26	0.105150
$417$	−2.50408e27	−0.771293
$418$	3.38438e27	1.01655
$419$	−2.22580e27	−0.651988	−0.325994	−	0.945372i	$-0.605699\pi$
$419$	−2.22580e27	−0.651988	−0.325994	+	0.945372i	$0.605699\pi$
$420$	3.84612e26	0.109877
$421$	2.26274e27	0.630482	0.315241	−	0.949012i	$-0.397915\pi$
$421$	2.26274e27	0.630482	0.315241	+	0.949012i	$0.397915\pi$
$422$	−2.93131e27	−0.796674
$423$	−2.02305e27	−0.536331
$424$	−1.49730e27	−0.387229
$425$	−2.04791e27	−0.516687
$426$	8.06435e26	0.198504
$427$	−4.75707e27	−1.14248
$428$	1.80118e27	0.422083
$429$	−2.01919e27	−0.461717
$430$	3.09422e27	0.690451
$431$	−1.80751e27	−0.393612	−0.196806	−	0.980442i	$-0.563057\pi$
$431$	−1.80751e27	−0.393612	−0.196806	+	0.980442i	$0.563057\pi$
$432$	−2.26380e26	−0.0481125
$433$	7.12467e27	1.47789	0.738945	−	0.673766i	$-0.235324\pi$
$433$	7.12467e27	1.47789	0.738945	+	0.673766i	$0.235324\pi$
$434$	1.71119e27	0.346462
$435$	5.34858e26	0.105706
$436$	3.14413e27	0.606586
$437$	9.58403e27	1.80507
$438$	−5.46465e26	−0.100481
$439$	1.58875e27	0.285218	0.142609	−	0.989779i	$-0.454451\pi$
$439$	1.58875e27	0.285218	0.142609	+	0.989779i	$0.454451\pi$
$440$	1.60873e27	0.281988
$441$	−1.14580e27	−0.196112
$442$	2.00635e27	0.335330
$443$	3.52672e26	0.0575614	0.0287807	−	0.999586i	$-0.490838\pi$
$443$	3.52672e26	0.0575614	0.0287807	+	0.999586i	$0.490838\pi$
$444$	2.17835e27	0.347221
$445$	3.28825e27	0.511900
$446$	−1.07410e27	−0.163315
$447$	−2.97897e27	−0.442423
$448$	−5.52841e26	−0.0802012
$449$	7.74724e27	1.09789	0.548947	−	0.835857i	$-0.315029\pi$
$449$	7.74724e27	1.09789	0.548947	+	0.835857i	$0.315029\pi$
$450$	−1.10337e27	−0.152753
$451$	7.09220e26	0.0959240
$452$	−5.36568e27	−0.709041
$453$	−4.90573e27	−0.633391
$454$	−4.32703e27	−0.545888
$455$	−1.83654e27	−0.226402
$456$	−1.81183e27	−0.218266
$457$	−1.41977e28	−1.67147	−0.835735	−	0.549132i	$-0.814958\pi$
$457$	−1.41977e28	−1.67147	−0.835735	+	0.549132i	$0.814958\pi$
$458$	−9.62560e27	−1.10749
$459$	−1.36444e27	−0.153434
$460$	4.55568e27	0.500722
$461$	−2.10321e27	−0.225956	−0.112978	−	0.993598i	$-0.536039\pi$
$461$	−2.10321e27	−0.225956	−0.112978	+	0.993598i	$0.536039\pi$
$462$	3.35342e27	0.352166
$463$	1.66348e28	1.70772	0.853860	−	0.520503i	$-0.174256\pi$
$463$	1.66348e28	1.70772	0.853860	+	0.520503i	$0.174256\pi$
$464$	−7.68805e26	−0.0771574
$465$	2.66575e27	0.261555
$466$	−5.72957e27	−0.549629
$467$	−1.92552e28	−1.80601	−0.903006	−	0.429629i	$-0.858644\pi$
$467$	−1.92552e28	−1.80601	−0.903006	+	0.429629i	$0.858644\pi$
$468$	1.08097e27	0.0991365
$469$	−1.25004e28	−1.12101
$470$	−7.69647e27	−0.674938
$471$	9.81896e27	0.842065
$472$	2.52595e27	0.211853
$473$	2.69784e28	2.21297
$474$	4.67306e27	0.374911
$475$	−8.83080e27	−0.692974
$476$	−3.33209e27	−0.255766
$477$	−4.86222e27	−0.365083
$478$	−4.91173e27	−0.360779
$479$	1.98417e28	1.42579	0.712894	−	0.701272i	$-0.247384\pi$
$479$	1.98417e28	1.42579	0.712894	+	0.701272i	$0.247384\pi$
$480$	−8.61236e26	−0.0605465
$481$	−1.04017e28	−0.715454
$482$	1.33365e27	0.0897530
$483$	9.49635e27	0.625334
$484$	6.26679e27	0.403802
$485$	−1.33522e28	−0.841905
$486$	−7.35128e26	−0.0453609
$487$	−1.91036e26	−0.0115361	−0.00576807	−	0.999983i	$-0.501836\pi$
$487$	−1.91036e26	−0.0115361	−0.00576807	+	0.999983i	$0.501836\pi$
$488$	1.06522e28	0.629551
$489$	6.72691e27	0.389110
$490$	−4.35908e27	−0.246795
$491$	8.06003e27	0.446664	0.223332	−	0.974742i	$-0.428307\pi$
$491$	8.06003e27	0.446664	0.223332	+	0.974742i	$0.428307\pi$
$492$	−3.79681e26	−0.0205961
$493$	−4.63375e27	−0.246059
$494$	8.65156e27	0.449740
$495$	5.22408e27	0.265861
$496$	−3.83175e27	−0.190915
$497$	6.39525e27	0.311972
$498$	9.41449e27	0.449665
$499$	3.12631e28	1.46210	0.731048	−	0.682326i	$-0.239032\pi$
$499$	3.12631e28	1.46210	0.731048	+	0.682326i	$0.239032\pi$
$500$	−1.06747e28	−0.488846
$501$	−2.08076e28	−0.933095
$502$	−1.28501e28	−0.564310
$503$	−4.14717e28	−1.78356	−0.891782	−	0.452466i	$-0.850544\pi$
$503$	−4.14717e28	−1.78356	−0.891782	+	0.452466i	$0.850544\pi$
$504$	−1.79525e27	−0.0756145
$505$	−9.91659e27	−0.409075
$506$	3.97209e28	1.60486
$507$	9.42722e27	0.373078
$508$	4.24781e27	0.164663
$509$	2.54263e28	0.965488	0.482744	−	0.875762i	$-0.339640\pi$
$509$	2.54263e28	0.965488	0.482744	+	0.875762i	$0.339640\pi$
$510$	−5.19085e27	−0.193086
$511$	−4.33361e27	−0.157918
$512$	1.23794e27	0.0441942
$513$	−5.88358e27	−0.205783
$514$	3.19977e28	1.09649
$515$	−1.16267e28	−0.390373
$516$	−1.44429e28	−0.475152
$517$	−6.71053e28	−2.16325
$518$	1.72749e28	0.545698
$519$	3.21055e27	0.0993853
$520$	4.11244e27	0.124757
$521$	−3.24742e28	−0.965479	−0.482739	−	0.875764i	$-0.660358\pi$
$521$	−3.24742e28	−0.965479	−0.482739	+	0.875764i	$0.660358\pi$
$522$	−2.49656e27	−0.0727447
$523$	1.45605e28	0.415822	0.207911	−	0.978148i	$-0.433334\pi$
$523$	1.45605e28	0.415822	0.207911	+	0.978148i	$0.433334\pi$
$524$	−2.02236e28	−0.566083
$525$	−8.75002e27	−0.240069
$526$	−2.09249e28	−0.562748
$527$	−2.30948e28	−0.608838
$528$	−7.50909e27	−0.194058
$529$	7.30116e28	1.84973
$530$	−1.84978e28	−0.459434
$531$	8.20258e27	0.199737
$532$	−1.43683e28	−0.343030
$533$	1.81299e27	0.0424385
$534$	−1.53486e28	−0.352277
$535$	2.22519e28	0.500786
$536$	2.79914e28	0.617723
$537$	−3.29401e28	−0.712844
$538$	−6.17114e27	−0.130964
$539$	−3.80067e28	−0.791002
$540$	−2.79671e27	−0.0570838
$541$	1.59820e28	0.319933	0.159967	−	0.987122i	$-0.448861\pi$
$541$	1.59820e28	0.319933	0.159967	+	0.987122i	$0.448861\pi$
$542$	−1.15723e28	−0.227210
$543$	3.12381e28	0.601571
$544$	7.46132e27	0.140938
$545$	3.88428e28	0.719692
$546$	8.57241e27	0.155805
$547$	1.03425e29	1.84399	0.921994	−	0.387203i	$-0.126559\pi$
$547$	1.03425e29	1.84399	0.921994	+	0.387203i	$0.126559\pi$
$548$	−3.07795e28	−0.538351
$549$	3.45911e28	0.593546
$550$	−3.65991e28	−0.616116
$551$	−1.99812e28	−0.330011
$552$	−2.12646e28	−0.344585
$553$	3.70586e28	0.589217
$554$	7.69772e28	1.20091
$555$	2.69114e28	0.411965
$556$	4.44667e28	0.667959
$557$	−9.81350e28	−1.44659	−0.723293	−	0.690541i	$-0.757372\pi$
$557$	−9.81350e28	−1.44659	−0.723293	+	0.690541i	$0.757372\pi$
$558$	−1.24429e28	−0.179996
$559$	6.89655e28	0.979057
$560$	−6.82983e27	−0.0951559
$561$	−4.52588e28	−0.618861
$562$	−2.30051e28	−0.308739
$563$	7.10142e28	0.935421	0.467711	−	0.883882i	$-0.345079\pi$
$563$	7.10142e28	0.935421	0.467711	+	0.883882i	$0.345079\pi$
$564$	3.59248e28	0.464477
$565$	−6.62879e28	−0.841251
$566$	−6.16919e28	−0.768521
$567$	−5.82976e27	−0.0712900
$568$	−1.43204e28	−0.171909
$569$	1.47837e29	1.74222	0.871110	−	0.491087i	$-0.163400\pi$
$569$	1.47837e29	1.74222	0.871110	+	0.491087i	$0.163400\pi$
$570$	−2.23834e28	−0.258965
$571$	−1.30988e29	−1.48783	−0.743914	−	0.668275i	$-0.767033\pi$
$571$	−1.30988e29	−1.48783	−0.743914	+	0.668275i	$0.767033\pi$
$572$	3.58562e28	0.399859
$573$	4.83766e27	0.0529678
$574$	−3.01097e27	−0.0323692
$575$	−1.03643e29	−1.09403
$576$	4.01999e27	0.0416667
$577$	−1.13007e29	−1.15017	−0.575083	−	0.818095i	$-0.695030\pi$
$577$	−1.13007e29	−1.15017	−0.575083	+	0.818095i	$0.695030\pi$
$578$	−2.57792e28	−0.257648
$579$	−3.89826e28	−0.382601
$580$	−9.49787e27	−0.0915445
$581$	7.46594e28	0.706700
$582$	6.23238e28	0.579379
$583$	−1.61281e29	−1.47253
$584$	9.70397e27	0.0870191
$585$	1.33544e28	0.117622
$586$	4.76194e27	0.0411963
$587$	−1.05612e29	−0.897455	−0.448728	−	0.893669i	$-0.648123\pi$
$587$	−1.05612e29	−0.897455	−0.448728	+	0.893669i	$0.648123\pi$
$588$	2.03469e28	0.169838
$589$	−9.95868e28	−0.816566
$590$	3.12058e28	0.251356
$591$	5.19289e28	0.410904
$592$	−3.86825e28	−0.300702
$593$	1.22381e29	0.934630	0.467315	−	0.884091i	$-0.345221\pi$
$593$	1.22381e29	0.934630	0.467315	+	0.884091i	$0.345221\pi$
$594$	−2.43844e28	−0.182959
$595$	−4.11648e28	−0.303458
$596$	5.28998e28	0.383150
$597$	−5.21034e28	−0.370797
$598$	1.01539e29	0.710021
$599$	1.37213e29	0.942789	0.471394	−	0.881922i	$-0.343751\pi$
$599$	1.37213e29	0.942789	0.471394	+	0.881922i	$0.343751\pi$
$600$	1.95933e28	0.132288
$601$	1.89598e29	1.25792	0.628958	−	0.777439i	$-0.283482\pi$
$601$	1.89598e29	1.25792	0.628958	+	0.777439i	$0.283482\pi$
$602$	−1.14536e29	−0.746757
$603$	9.08969e28	0.582395
$604$	8.71146e28	0.548533
$605$	7.74203e28	0.479097
$606$	4.62876e28	0.281516
$607$	−1.07832e29	−0.644563	−0.322281	−	0.946644i	$-0.604450\pi$
$607$	−1.07832e29	−0.644563	−0.322281	+	0.946644i	$0.604450\pi$
$608$	3.21739e28	0.189024
$609$	−1.97984e28	−0.114327
$610$	1.31598e29	0.746940
$611$	−1.71543e29	−0.957060
$612$	2.42293e28	0.132877
$613$	4.49900e28	0.242538	0.121269	−	0.992620i	$-0.461304\pi$
$613$	4.49900e28	0.242538	0.121269	+	0.992620i	$0.461304\pi$
$614$	−7.05636e28	−0.373949
$615$	−4.69060e27	−0.0244365
$616$	−5.95491e28	−0.304984
$617$	2.83973e29	1.42982	0.714911	−	0.699215i	$-0.246467\pi$
$617$	2.83973e29	1.42982	0.714911	+	0.699215i	$0.246467\pi$
$618$	5.42698e28	0.268645
$619$	1.17452e29	0.571624	0.285812	−	0.958286i	$-0.407737\pi$
$619$	1.17452e29	0.571624	0.285812	+	0.958286i	$0.407737\pi$
$620$	−4.73377e28	−0.226514
$621$	−6.90528e28	−0.324878
$622$	−2.81860e28	−0.130387
$623$	−1.21718e29	−0.553645
$624$	−1.91956e28	−0.0858547
$625$	1.54791e28	0.0680776
$626$	−1.54885e29	−0.669854
$627$	−1.95160e29	−0.830008
$628$	−1.74362e29	−0.729250
$629$	−2.33147e29	−0.958956
$630$	−2.21787e28	−0.0897138
$631$	1.11858e29	0.444999	0.222500	−	0.974933i	$-0.428578\pi$
$631$	1.11858e29	0.444999	0.222500	+	0.974933i	$0.428578\pi$
$632$	−8.29829e28	−0.324683
$633$	1.69034e29	0.650481
$634$	−5.59061e28	−0.211603
$635$	5.24777e28	0.195367
$636$	8.63420e28	0.316171
$637$	−9.71572e28	−0.349954
$638$	−8.28116e28	−0.293409
$639$	−4.65031e28	−0.162078
$640$	1.52936e28	0.0524348
$641$	5.02292e29	1.69413	0.847066	−	0.531488i	$-0.178367\pi$
$641$	5.02292e29	1.69413	0.847066	+	0.531488i	$0.178367\pi$
$642$	−1.03865e29	−0.344629
$643$	4.27106e29	1.39419	0.697093	−	0.716980i	$-0.254476\pi$
$643$	4.27106e29	1.39419	0.697093	+	0.716980i	$0.254476\pi$
$644$	−1.68634e29	−0.541555
$645$	−1.78428e29	−0.563751
$646$	1.93919e29	0.602807
$647$	−4.32869e29	−1.32392	−0.661960	−	0.749539i	$-0.730275\pi$
$647$	−4.32869e29	−1.32392	−0.661960	+	0.749539i	$0.730275\pi$
$648$	1.30542e28	0.0392837
$649$	2.72082e29	0.805621
$650$	−9.35590e28	−0.272581
$651$	−9.86758e28	−0.282885
$652$	−1.19455e29	−0.336979
$653$	−2.73969e29	−0.760525	−0.380263	−	0.924879i	$-0.624166\pi$
$653$	−2.73969e29	−0.760525	−0.380263	+	0.924879i	$0.624166\pi$
$654$	−1.81306e29	−0.495275
$655$	−2.49844e29	−0.671637
$656$	6.74227e27	0.0178367
$657$	3.15119e28	0.0820424
$658$	2.84893e29	0.729979
$659$	3.07743e28	0.0776053	0.0388026	−	0.999247i	$-0.487646\pi$
$659$	3.07743e28	0.0776053	0.0388026	+	0.999247i	$0.487646\pi$
$660$	−9.27678e28	−0.230243
$661$	−3.06325e29	−0.748286	−0.374143	−	0.927371i	$-0.622063\pi$
$661$	−3.06325e29	−0.748286	−0.374143	+	0.927371i	$0.622063\pi$
$662$	4.68949e29	1.12750
$663$	−1.15696e29	−0.273796
$664$	−1.67180e29	−0.389421
$665$	−1.77507e29	−0.406993
$666$	−1.25615e29	−0.283505
$667$	−2.34509e29	−0.521002
$668$	3.69496e29	0.808084
$669$	6.19378e28	0.133346
$670$	3.45807e29	0.732906
$671$	1.14740e30	2.39402
$672$	3.18796e28	0.0654840
$673$	5.09843e29	1.03105	0.515523	−	0.856876i	$-0.327598\pi$
$673$	5.09843e29	1.03105	0.515523	+	0.856876i	$0.327598\pi$
$674$	1.81736e29	0.361836
$675$	6.36258e28	0.124722
$676$	−1.67406e29	−0.323095
$677$	−7.38047e29	−1.40250	−0.701250	−	0.712915i	$-0.747374\pi$
$677$	−7.38047e29	−1.40250	−0.701250	+	0.712915i	$0.747374\pi$
$678$	3.09412e29	0.578929
$679$	4.94245e29	0.910562
$680$	9.21776e28	0.167218
$681$	2.49518e29	0.445716
$682$	−4.12736e29	−0.726000
$683$	−4.68059e29	−0.810743	−0.405372	−	0.914152i	$-0.632858\pi$
$683$	−4.68059e29	−0.810743	−0.405372	+	0.914152i	$0.632858\pi$
$684$	1.04479e29	0.178213
$685$	−3.80252e29	−0.638734
$686$	4.35614e29	0.720607
$687$	5.55061e29	0.904263
$688$	2.56473e29	0.411494
$689$	−4.12287e29	−0.651475
$690$	−2.62704e29	−0.408837
$691$	−4.77475e29	−0.731865	−0.365932	−	0.930641i	$-0.619250\pi$
$691$	−4.77475e29	−0.731865	−0.365932	+	0.930641i	$0.619250\pi$
$692$	−5.70120e28	−0.0860702
$693$	−1.93375e29	−0.287542
$694$	−3.39269e29	−0.496901
$695$	5.49345e29	0.792510
$696$	4.43332e28	0.0629987
$697$	4.06370e28	0.0568824
$698$	−1.87255e29	−0.258197
$699$	3.30396e29	0.448770
$700$	1.55380e29	0.207906
$701$	−9.76926e29	−1.28772	−0.643862	−	0.765142i	$-0.722669\pi$
$701$	−9.76926e29	−1.28772	−0.643862	+	0.765142i	$0.722669\pi$
$702$	−6.23344e28	−0.0809446
$703$	−1.00535e30	−1.28614
$704$	1.33344e29	0.168059
$705$	4.43817e29	0.551085
$706$	−5.72171e29	−0.699965
$707$	3.67073e29	0.442435
$708$	−1.45659e29	−0.172977
$709$	−8.06956e29	−0.944201	−0.472101	−	0.881545i	$-0.656504\pi$
$709$	−8.06956e29	−0.944201	−0.472101	+	0.881545i	$0.656504\pi$
$710$	−1.76916e29	−0.203964
$711$	−2.69472e29	−0.306114
$712$	2.72556e29	0.305081
$713$	−1.16880e30	−1.28914
$714$	1.92145e29	0.208832
$715$	4.42970e29	0.474418
$716$	5.84941e29	0.617341
$717$	2.83235e29	0.294575
$718$	−8.86769e29	−0.908875
$719$	2.20303e29	0.222519	0.111259	−	0.993791i	$-0.464512\pi$
$719$	2.20303e29	0.222519	0.111259	+	0.993791i	$0.464512\pi$
$720$	4.96632e28	0.0494360
$721$	4.30374e29	0.422208
$722$	1.04846e29	0.101371
$723$	−7.69051e28	−0.0732830
$724$	−5.54718e29	−0.520976
$725$	2.16079e29	0.200015
$726$	−3.61374e29	−0.329703
$727$	1.52128e30	1.36804	0.684020	−	0.729463i	$-0.260230\pi$
$727$	1.52128e30	1.36804	0.684020	+	0.729463i	$0.260230\pi$
$728$	−1.52227e29	−0.134931
$729$	4.23912e28	0.0370370
$730$	1.19884e29	0.103245
$731$	1.54582e30	1.31228
$732$	−6.14259e29	−0.514026
$733$	3.36651e29	0.277708	0.138854	−	0.990313i	$-0.455658\pi$
$733$	3.36651e29	0.277708	0.138854	+	0.990313i	$0.455658\pi$
$734$	−1.34977e29	−0.109762
$735$	2.51366e29	0.201507
$736$	3.77610e29	0.298419
$737$	3.01508e30	2.34904
$738$	2.18943e28	0.0168166
$739$	−2.59622e29	−0.196596	−0.0982982	−	0.995157i	$-0.531340\pi$
$739$	−2.59622e29	−0.196596	−0.0982982	+	0.995157i	$0.531340\pi$
$740$	−4.77886e29	−0.356772
$741$	−4.98892e29	−0.367211
$742$	6.84715e29	0.496900
$743$	−1.31717e30	−0.942455	−0.471227	−	0.882012i	$-0.656189\pi$
$743$	−1.31717e30	−0.942455	−0.471227	+	0.882012i	$0.656189\pi$
$744$	2.20958e29	0.155881
$745$	6.53528e29	0.454593
$746$	−4.91569e29	−0.337153
$747$	−5.42887e29	−0.367150
$748$	8.03694e29	0.535950
$749$	−8.23679e29	−0.541625
$750$	6.15559e29	0.399141
$751$	1.46730e29	0.0938209	0.0469104	−	0.998899i	$-0.485062\pi$
$751$	1.46730e29	0.0938209	0.0469104	+	0.998899i	$0.485062\pi$
$752$	−6.37943e29	−0.402249
$753$	7.41002e29	0.460757
$754$	−2.11693e29	−0.129810
$755$	1.07622e30	0.650815
$756$	1.03523e29	0.0617389
$757$	−3.16010e29	−0.185864	−0.0929318	−	0.995672i	$-0.529624\pi$
$757$	−3.16010e29	−0.185864	−0.0929318	+	0.995672i	$0.529624\pi$
$758$	3.69706e29	0.214452
$759$	−2.29051e30	−1.31037
$760$	3.97479e29	0.224270
$761$	−2.02639e30	−1.12767	−0.563837	−	0.825886i	$-0.690676\pi$
$761$	−2.02639e30	−1.12767	−0.563837	+	0.825886i	$0.690676\pi$
$762$	−2.44950e29	−0.134447
$763$	−1.43781e30	−0.778383
$764$	−8.59059e28	−0.0458715
$765$	2.99330e29	0.157654
$766$	−4.56441e29	−0.237128
$767$	6.95529e29	0.356422
$768$	−7.13859e28	−0.0360844
$769$	1.55510e30	0.775410	0.387705	−	0.921783i	$-0.373268\pi$
$769$	1.55510e30	0.775410	0.387705	+	0.921783i	$0.373268\pi$
$770$	−7.35673e29	−0.361853
$771$	−1.84515e30	−0.895284
$772$	6.92242e29	0.331342
$773$	−3.90527e30	−1.84402	−0.922012	−	0.387161i	$-0.873456\pi$
$773$	−3.90527e30	−1.84402	−0.922012	+	0.387161i	$0.873456\pi$
$774$	8.32850e29	0.387960
$775$	1.07694e30	0.494909
$776$	−1.10673e30	−0.501757
$777$	−9.96157e29	−0.445561
$778$	2.69943e30	1.19120
$779$	1.75231e29	0.0762899
$780$	−2.37144e29	−0.101864
$781$	−1.54252e30	−0.653726
$782$	2.27593e30	0.951675
$783$	1.43964e29	0.0593958
$784$	−3.61314e29	−0.147084
$785$	−2.15408e30	−0.865229
$786$	1.16620e30	0.462205
$787$	−6.91303e29	−0.270355	−0.135177	−	0.990821i	$-0.543160\pi$
$787$	−6.91303e29	−0.270355	−0.135177	+	0.990821i	$0.543160\pi$
$788$	−9.22139e29	−0.355853
$789$	1.20664e30	0.459481
$790$	−1.02518e30	−0.385225
$791$	2.45372e30	0.909855
$792$	4.33012e29	0.158448
$793$	2.93312e30	1.05916
$794$	−1.95867e30	−0.697985
$795$	1.06667e30	0.375126
$796$	9.25238e29	0.321119
$797$	3.05715e30	1.04714	0.523569	−	0.851983i	$-0.324600\pi$
$797$	3.05715e30	1.04714	0.523569	+	0.851983i	$0.324600\pi$
$798$	8.28547e29	0.280083
$799$	−3.84501e30	−1.28279
$800$	−3.47933e29	−0.114565
$801$	8.85076e29	0.287633
$802$	2.37180e30	0.760760
$803$	1.04526e30	0.330911
$804$	−1.61412e30	−0.504369
$805$	−2.08331e30	−0.642536
$806$	−1.05508e30	−0.321196
$807$	3.55859e29	0.106932
$808$	−8.21963e29	−0.243800
$809$	5.62302e30	1.64630	0.823152	−	0.567821i	$-0.192213\pi$
$809$	5.62302e30	1.64630	0.823152	+	0.567821i	$0.192213\pi$
$810$	1.61272e29	0.0466087
$811$	−3.35752e30	−0.957854	−0.478927	−	0.877855i	$-0.658974\pi$
$811$	−3.35752e30	−0.957854	−0.478927	+	0.877855i	$0.658974\pi$
$812$	3.51574e29	0.0990099
$813$	6.67319e29	0.185517
$814$	−4.16667e30	−1.14349
$815$	−1.47575e30	−0.399814
$816$	−4.30257e29	−0.115075
$817$	6.66571e30	1.76001
$818$	1.81760e30	0.473793
$819$	−4.94328e29	−0.127214
$820$	8.32944e28	0.0211627
$821$	1.66494e30	0.417634	0.208817	−	0.977955i	$-0.433039\pi$
$821$	1.66494e30	0.417634	0.208817	+	0.977955i	$0.433039\pi$
$822$	1.77490e30	0.439562
$823$	−4.79393e30	−1.17218	−0.586088	−	0.810247i	$-0.699333\pi$
$823$	−4.79393e30	−1.17218	−0.586088	+	0.810247i	$0.699333\pi$
$824$	−9.63709e29	−0.232654
$825$	2.11049e30	0.503056
$826$	−1.15512e30	−0.271854
$827$	6.92737e30	1.60976	0.804879	−	0.593439i	$-0.202230\pi$
$827$	6.92737e30	1.60976	0.804879	+	0.593439i	$0.202230\pi$
$828$	1.22622e30	0.281352
$829$	−2.55745e30	−0.579408	−0.289704	−	0.957116i	$-0.593557\pi$
$829$	−2.55745e30	−0.579408	−0.289704	+	0.957116i	$0.593557\pi$
$830$	−2.06535e30	−0.462034
$831$	−4.43890e30	−0.980537
$832$	3.40871e29	0.0743524
$833$	−2.17771e30	−0.469060
$834$	−2.56418e30	−0.545386
$835$	4.56477e30	0.958763
$836$	3.46560e30	0.718808
$837$	7.17522e29	0.146966
$838$	−2.27922e30	−0.461025
$839$	−4.16860e29	−0.0832702	−0.0416351	−	0.999133i	$-0.513257\pi$
$839$	−4.16860e29	−0.0832702	−0.0416351	+	0.999133i	$0.513257\pi$
$840$	3.93843e29	0.0776945
$841$	−4.64393e30	−0.904748
$842$	2.31704e30	0.445818
$843$	1.32659e30	0.252085
$844$	−3.00166e30	−0.563333
$845$	−2.06814e30	−0.383341
$846$	−2.07161e30	−0.379244
$847$	−2.86580e30	−0.518167
$848$	−1.53324e30	−0.273812
$849$	3.55747e30	0.627495
$850$	−2.09706e30	−0.365353
$851$	−1.17994e31	−2.03048
$852$	8.25789e29	0.140363
$853$	7.40771e30	1.24371	0.621855	−	0.783132i	$-0.286379\pi$
$853$	7.40771e30	1.24371	0.621855	+	0.783132i	$0.286379\pi$
$854$	−4.87124e30	−0.807852
$855$	1.29074e30	0.211444
$856$	1.84441e30	0.298458
$857$	−3.64448e30	−0.582555	−0.291277	−	0.956639i	$-0.594080\pi$
$857$	−3.64448e30	−0.582555	−0.291277	+	0.956639i	$0.594080\pi$
$858$	−2.06765e30	−0.326483
$859$	−3.70416e30	−0.577778	−0.288889	−	0.957363i	$-0.593286\pi$
$859$	−3.70416e30	−0.577778	−0.288889	+	0.957363i	$0.593286\pi$
$860$	3.16848e30	0.488222
$861$	1.73628e29	0.0264293
$862$	−1.85089e30	−0.278326
$863$	6.86612e29	0.101999	0.0509997	−	0.998699i	$-0.483759\pi$
$863$	6.86612e29	0.101999	0.0509997	+	0.998699i	$0.483759\pi$
$864$	−2.31813e29	−0.0340207
$865$	−7.04330e29	−0.102119
$866$	7.29567e30	1.04503
$867$	1.48656e30	0.210369
$868$	1.75226e30	0.244986
$869$	−8.93848e30	−1.23468
$870$	5.47695e29	0.0747458
$871$	7.70751e30	1.03926
$872$	3.21959e30	0.428921
$873$	−3.59391e30	−0.473061
$874$	9.81405e30	1.27637
$875$	4.88155e30	0.627297
$876$	−5.59580e29	−0.0710508
$877$	1.41886e31	1.78010	0.890049	−	0.455865i	$-0.150670\pi$
$877$	1.41886e31	1.78010	0.890049	+	0.455865i	$0.150670\pi$
$878$	1.62688e30	0.201680
$879$	−2.74597e29	−0.0336367
$880$	1.64734e30	0.199396
$881$	9.83090e30	1.17583	0.587917	−	0.808921i	$-0.299948\pi$
$881$	9.83090e30	1.17583	0.587917	+	0.808921i	$0.299948\pi$
$882$	−1.17330e30	−0.138672
$883$	1.06031e30	0.123835	0.0619176	−	0.998081i	$-0.480278\pi$
$883$	1.06031e30	0.123835	0.0619176	+	0.998081i	$0.480278\pi$
$884$	2.05450e30	0.237114
$885$	−1.79948e30	−0.205231
$886$	3.61136e29	0.0407021
$887$	−8.96894e30	−0.998949	−0.499474	−	0.866329i	$-0.666473\pi$
$887$	−8.96894e30	−0.998949	−0.499474	+	0.866329i	$0.666473\pi$
$888$	2.23063e30	0.245522
$889$	−1.94252e30	−0.211299
$890$	3.36717e30	0.361968
$891$	1.40613e30	0.149386
$892$	−1.09987e30	−0.115481
$893$	−1.65801e31	−1.72047
$894$	−3.05047e30	−0.312840
$895$	7.22640e30	0.732453
$896$	−5.66109e29	−0.0567108
$897$	−5.85526e30	−0.579730
$898$	7.93318e30	0.776329
$899$	2.43677e30	0.235688
$900$	−1.12985e30	−0.108013
$901$	−9.24114e30	−0.873203
$902$	7.26241e29	0.0678285
$903$	6.60473e30	0.609724
$904$	−5.49445e30	−0.501367
$905$	−6.85303e30	−0.618119
$906$	−5.02346e30	−0.447875
$907$	3.04599e30	0.268443	0.134221	−	0.990951i	$-0.457147\pi$
$907$	3.04599e30	0.268443	0.134221	+	0.990951i	$0.457147\pi$
$908$	−4.43088e30	−0.386001
$909$	−2.66918e30	−0.229857
$910$	−1.88062e30	−0.160090
$911$	9.54796e30	0.803466	0.401733	−	0.915757i	$-0.368408\pi$
$911$	9.54796e30	0.803466	0.401733	+	0.915757i	$0.368408\pi$
$912$	−1.85531e30	−0.154337
$913$	−1.80077e31	−1.48087
$914$	−1.45385e31	−1.18191
$915$	−7.58860e30	−0.609874
$916$	−9.85661e30	−0.783115
$917$	9.24824e30	0.726409
$918$	−1.39718e30	−0.108494
$919$	1.56370e31	1.20044	0.600219	−	0.799835i	$-0.295080\pi$
$919$	1.56370e31	1.20044	0.600219	+	0.799835i	$0.295080\pi$
$920$	4.66502e30	0.354064
$921$	4.06905e30	0.305328
$922$	−2.15369e30	−0.159775
$923$	−3.94318e30	−0.289220
$924$	3.43390e30	0.249019
$925$	1.08720e31	0.779511
$926$	1.70340e31	1.20754
$927$	−3.12947e30	−0.219348
$928$	−7.87256e29	−0.0545585
$929$	−4.04044e30	−0.276862	−0.138431	−	0.990372i	$-0.544206\pi$
$929$	−4.04044e30	−0.276862	−0.138431	+	0.990372i	$0.544206\pi$
$930$	2.72973e30	0.184948
$931$	−9.39051e30	−0.629097
$932$	−5.86708e30	−0.388646
$933$	1.62535e30	0.106461
$934$	−1.97173e31	−1.27704
$935$	9.92888e30	0.635885
$936$	1.10692e30	0.0701001
$937$	−2.09838e31	−1.31407	−0.657035	−	0.753860i	$-0.728190\pi$
$937$	−2.09838e31	−1.31407	−0.657035	+	0.753860i	$0.728190\pi$
$938$	−1.28004e31	−0.792674
$939$	8.93147e30	0.546933
$940$	−7.88119e30	−0.477254
$941$	2.17744e31	1.30393	0.651967	−	0.758247i	$-0.273944\pi$
$941$	2.17744e31	1.30393	0.651967	+	0.758247i	$0.273944\pi$
$942$	1.00546e31	0.595430
$943$	2.05660e30	0.120442
$944$	2.58658e30	0.149803
$945$	1.27893e30	0.0732511
$946$	2.76259e31	1.56480
$947$	1.21468e31	0.680435	0.340218	−	0.940347i	$-0.389499\pi$
$947$	1.21468e31	0.680435	0.340218	+	0.940347i	$0.389499\pi$
$948$	4.78521e30	0.265102
$949$	2.67202e30	0.146401
$950$	−9.04274e30	−0.490007
$951$	3.22383e30	0.172773
$952$	−3.41206e30	−0.180854
$953$	6.95212e30	0.364453	0.182227	−	0.983257i	$-0.441670\pi$
$953$	6.95212e30	0.364453	0.182227	+	0.983257i	$0.441670\pi$
$954$	−4.97892e30	−0.258153
$955$	−1.06129e30	−0.0544248
$956$	−5.02961e30	−0.255109
$957$	4.77534e30	0.239568
$958$	2.03179e31	1.00818
$959$	1.40754e31	0.690823
$960$	−8.81905e29	−0.0428128
$961$	−8.68058e30	−0.416824
$962$	−1.06514e31	−0.505902
$963$	5.98939e30	0.281389
$964$	1.36566e30	0.0634649
$965$	8.55201e30	0.393126
$966$	9.72427e30	0.442178
$967$	−8.85795e30	−0.398433	−0.199216	−	0.979956i	$-0.563840\pi$
$967$	−8.85795e30	−0.398433	−0.199216	+	0.979956i	$0.563840\pi$
$968$	6.41719e30	0.285531
$969$	−1.11823e31	−0.492190
$970$	−1.36726e31	−0.595317
$971$	−3.05382e31	−1.31535	−0.657676	−	0.753301i	$-0.728460\pi$
$971$	−3.05382e31	−1.31535	−0.657676	+	0.753301i	$0.728460\pi$
$972$	−7.52771e29	−0.0320750
$973$	−2.03346e31	−0.857138
$974$	−1.95621e29	−0.00815728
$975$	5.39509e30	0.222561
$976$	1.09078e31	0.445160
$977$	−2.38019e31	−0.960989	−0.480495	−	0.876998i	$-0.659543\pi$
$977$	−2.38019e31	−0.960989	−0.480495	+	0.876998i	$0.659543\pi$
$978$	6.88835e30	0.275142
$979$	2.93583e31	1.16014
$980$	−4.46369e30	−0.174510
$981$	1.04550e31	0.404391
$982$	8.25347e30	0.315839
$983$	−3.40761e31	−1.29014	−0.645072	−	0.764122i	$-0.723173\pi$
$983$	−3.40761e31	−1.29014	−0.645072	+	0.764122i	$0.723173\pi$
$984$	−3.88793e29	−0.0145636
$985$	−1.13922e31	−0.422207
$986$	−4.74496e30	−0.173990
$987$	−1.64284e31	−0.596026
$988$	8.85919e30	0.318014
$989$	7.82322e31	2.77859
$990$	5.34946e30	0.187992
$991$	−3.53546e31	−1.22934	−0.614671	−	0.788784i	$-0.710711\pi$
$991$	−3.53546e31	−1.22934	−0.614671	+	0.788784i	$0.710711\pi$
$992$	−3.92371e30	−0.134997
$993$	−2.70420e31	−0.920600
$994$	6.54873e30	0.220597
$995$	1.14305e31	0.380997
$996$	9.64044e30	0.317961
$997$	−4.23577e31	−1.38240	−0.691199	−	0.722664i	$-0.742917\pi$
$997$	−4.23577e31	−1.38240	−0.691199	+	0.722664i	$0.742917\pi$
$998$	3.20134e31	1.03386
$999$	7.24357e30	0.231481

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.22.a.b.1.1	✓	1
3.2	odd	2		18.22.a.a.1.1		1
4.3	odd	2		48.22.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.22.a.b.1.1	✓	1	1.1	even	1	trivial
18.22.a.a.1.1		1	3.2	odd	2
48.22.a.f.1.1		1	4.3	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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	6.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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