LMFDB - Embedded newform 3.22.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3,22,Mod(1,3)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3, 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("3.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 3 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	3.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:	$8.38432032861$
Analytic rank:	$1$
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	$\chi$	$=$	3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+1728.00 q^{2} -59049.0 q^{3} +888832. q^{4} -4.15128e7 q^{5} -1.02037e8 q^{6} +5.38430e8 q^{7} -2.08798e9 q^{8} +3.48678e9 q^{9} +O(q^{10})$

\(q+1728.00 q^{2} -59049.0 q^{3} +888832. q^{4} -4.15128e7 q^{5} -1.02037e8 q^{6} +5.38430e8 q^{7} -2.08798e9 q^{8} +3.48678e9 q^{9} -7.17341e10 q^{10} -6.41130e10 q^{11} -5.24846e10 q^{12} -1.30980e11 q^{13} +9.30407e11 q^{14} +2.45129e12 q^{15} -5.47204e12 q^{16} +8.24203e12 q^{17} +6.02516e12 q^{18} +1.34921e13 q^{19} -3.68979e13 q^{20} -3.17937e13 q^{21} -1.10787e14 q^{22} -2.33185e14 q^{23} +1.23293e14 q^{24} +1.24647e15 q^{25} -2.26334e14 q^{26} -2.05891e14 q^{27} +4.78574e14 q^{28} -2.02456e15 q^{29} +4.23582e15 q^{30} -6.86919e15 q^{31} -5.07688e15 q^{32} +3.78581e15 q^{33} +1.42422e16 q^{34} -2.23517e16 q^{35} +3.09917e15 q^{36} +3.44400e15 q^{37} +2.33144e16 q^{38} +7.73424e15 q^{39} +8.66777e16 q^{40} -2.18424e16 q^{41} -5.49396e16 q^{42} -7.17928e16 q^{43} -5.69857e16 q^{44} -1.44746e17 q^{45} -4.02943e17 q^{46} +2.83545e17 q^{47} +3.23118e17 q^{48} -2.68639e17 q^{49} +2.15391e18 q^{50} -4.86684e17 q^{51} -1.16419e17 q^{52} -2.17229e18 q^{53} -3.55780e17 q^{54} +2.66151e18 q^{55} -1.12423e18 q^{56} -7.96695e17 q^{57} -3.49844e18 q^{58} +1.53483e18 q^{59} +2.17878e18 q^{60} +4.31159e18 q^{61} -1.18700e19 q^{62} +1.87739e18 q^{63} +2.70285e18 q^{64} +5.43735e18 q^{65} +6.54188e18 q^{66} +9.24391e18 q^{67} +7.32578e18 q^{68} +1.37693e19 q^{69} -3.86238e19 q^{70} -2.03874e19 q^{71} -7.28033e18 q^{72} +1.66178e19 q^{73} +5.95123e18 q^{74} -7.36030e19 q^{75} +1.19922e19 q^{76} -3.45204e19 q^{77} +1.33648e19 q^{78} +6.79403e19 q^{79} +2.27160e20 q^{80} +1.21577e19 q^{81} -3.77437e19 q^{82} +3.95037e19 q^{83} -2.82593e19 q^{84} -3.42149e20 q^{85} -1.24058e20 q^{86} +1.19548e20 q^{87} +1.33867e20 q^{88} +4.16117e19 q^{89} -2.50121e20 q^{90} -7.05236e19 q^{91} -2.07262e20 q^{92} +4.05619e20 q^{93} +4.89965e20 q^{94} -5.60095e20 q^{95} +2.99785e20 q^{96} +5.71815e19 q^{97} -4.64209e20 q^{98} -2.23548e20 q^{99} +O(q^{100})\)

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 $

$2$	1728.00	1.19324	0.596621	−	0.802523i	$-0.296509\pi$
$2$	1728.00	1.19324	0.596621	+	0.802523i	$0.296509\pi$
$3$	−59049.0	−0.577350
$3$	−59049.0	−0.577350
$4$	888832.	0.423828
$5$	−4.15128e7	−1.90106	−0.950532	−	0.310627i	$-0.899461\pi$
$5$	−4.15128e7	−1.90106	−0.950532	+	0.310627i	$0.899461\pi$
$6$	−1.02037e8	−0.688919
$7$	5.38430e8	0.720443	0.360222	−	0.932867i	$-0.382701\pi$
$7$	5.38430e8	0.720443	0.360222	+	0.932867i	$0.382701\pi$
$8$	−2.08798e9	−0.687513
$9$	3.48678e9	0.333333
$10$	−7.17341e10	−2.26843
$11$	−6.41130e10	−0.745286	−0.372643	−	0.927975i	$-0.621548\pi$
$11$	−6.41130e10	−0.745286	−0.372643	+	0.927975i	$0.621548\pi$
$12$	−5.24846e10	−0.244697
$13$	−1.30980e11	−0.263512	−0.131756	−	0.991282i	$-0.542062\pi$
$13$	−1.30980e11	−0.263512	−0.131756	+	0.991282i	$0.542062\pi$
$14$	9.30407e11	0.859663
$15$	2.45129e12	1.09758
$16$	−5.47204e12	−1.24420
$17$	8.24203e12	0.991563	0.495782	−	0.868447i	$-0.334882\pi$
$17$	8.24203e12	0.991563	0.495782	+	0.868447i	$0.334882\pi$
$18$	6.02516e12	0.397748
$19$	1.34921e13	0.504855	0.252428	−	0.967616i	$-0.418771\pi$
$19$	1.34921e13	0.504855	0.252428	+	0.967616i	$0.418771\pi$
$20$	−3.68979e13	−0.805724
$21$	−3.17937e13	−0.415948
$22$	−1.10787e14	−0.889308
$23$	−2.33185e14	−1.17370	−0.586851	−	0.809695i	$-0.699633\pi$
$23$	−2.33185e14	−1.17370	−0.586851	+	0.809695i	$0.699633\pi$
$24$	1.23293e14	0.396936
$25$	1.24647e15	2.61404
$26$	−2.26334e14	−0.314434
$27$	−2.05891e14	−0.192450
$28$	4.78574e14	0.305344
$29$	−2.02456e15	−0.893618	−0.446809	−	0.894629i	$-0.647440\pi$
$29$	−2.02456e15	−0.893618	−0.446809	+	0.894629i	$0.647440\pi$
$30$	4.23582e15	1.30968
$31$	−6.86919e15	−1.50525	−0.752624	−	0.658451i	$-0.771212\pi$
$31$	−6.86919e15	−1.50525	−0.752624	+	0.658451i	$0.771212\pi$
$32$	−5.07688e15	−0.797117
$33$	3.78581e15	0.430291
$34$	1.42422e16	1.18318
$35$	−2.23517e16	−1.36961
$36$	3.09917e15	0.141276
$37$	3.44400e15	0.117746	0.0588728	−	0.998265i	$-0.481249\pi$
$37$	3.44400e15	0.117746	0.0588728	+	0.998265i	$0.481249\pi$
$38$	2.33144e16	0.602415
$39$	7.73424e15	0.152139
$40$	8.66777e16	1.30701
$41$	−2.18424e16	−0.254138	−0.127069	−	0.991894i	$-0.540557\pi$
$41$	−2.18424e16	−0.254138	−0.127069	+	0.991894i	$0.540557\pi$
$42$	−5.49396e16	−0.496327
$43$	−7.17928e16	−0.506597	−0.253298	−	0.967388i	$-0.581515\pi$
$43$	−7.17928e16	−0.506597	−0.253298	+	0.967388i	$0.581515\pi$
$44$	−5.69857e16	−0.315873
$45$	−1.44746e17	−0.633688
$46$	−4.02943e17	−1.40051
$47$	2.83545e17	0.786310	0.393155	−	0.919472i	$-0.371383\pi$
$47$	2.83545e17	0.786310	0.393155	+	0.919472i	$0.371383\pi$
$48$	3.23118e17	0.718338
$49$	−2.68639e17	−0.480962
$50$	2.15391e18	3.11919
$51$	−4.86684e17	−0.572479
$52$	−1.16419e17	−0.111684
$53$	−2.17229e18	−1.70616	−0.853081	−	0.521779i	$-0.825269\pi$
$53$	−2.17229e18	−1.70616	−0.853081	+	0.521779i	$0.825269\pi$
$54$	−3.55780e17	−0.229640
$55$	2.66151e18	1.41684
$56$	−1.12423e18	−0.495314
$57$	−7.96695e17	−0.291478
$58$	−3.49844e18	−1.06630
$59$	1.53483e18	0.390944	0.195472	−	0.980709i	$-0.437376\pi$
$59$	1.53483e18	0.390944	0.195472	+	0.980709i	$0.437376\pi$
$60$	2.17878e18	0.465185
$61$	4.31159e18	0.773881	0.386940	−	0.922105i	$-0.373532\pi$
$61$	4.31159e18	0.773881	0.386940	+	0.922105i	$0.373532\pi$
$62$	−1.18700e19	−1.79613
$63$	1.87739e18	0.240148
$64$	2.70285e18	0.293044
$65$	5.43735e18	0.500953
$66$	6.54188e18	0.513442
$67$	9.24391e18	0.619541	0.309771	−	0.950811i	$-0.399748\pi$
$67$	9.24391e18	0.619541	0.309771	+	0.950811i	$0.399748\pi$
$68$	7.32578e18	0.420252
$69$	1.37693e19	0.677637
$70$	−3.86238e19	−1.63427
$71$	−2.03874e19	−0.743273	−0.371636	−	0.928378i	$-0.621203\pi$
$71$	−2.03874e19	−0.743273	−0.371636	+	0.928378i	$0.621203\pi$
$72$	−7.28033e18	−0.229171
$73$	1.66178e19	0.452566	0.226283	−	0.974062i	$-0.427343\pi$
$73$	1.66178e19	0.452566	0.226283	+	0.974062i	$0.427343\pi$
$74$	5.95123e18	0.140499
$75$	−7.36030e19	−1.50922
$76$	1.19922e19	0.213972
$77$	−3.45204e19	−0.536936
$78$	1.33648e19	0.181538
$79$	6.79403e19	0.807315	0.403658	−	0.914910i	$-0.367739\pi$
$79$	6.79403e19	0.807315	0.403658	+	0.914910i	$0.367739\pi$
$80$	2.27160e20	2.36530
$81$	1.21577e19	0.111111
$82$	−3.77437e19	−0.303249
$83$	3.95037e19	0.279459	0.139730	−	0.990190i	$-0.455377\pi$
$83$	3.95037e19	0.279459	0.139730	+	0.990190i	$0.455377\pi$
$84$	−2.82593e19	−0.176290
$85$	−3.42149e20	−1.88503
$86$	−1.24058e20	−0.604493
$87$	1.19548e20	0.515931
$88$	1.33867e20	0.512394
$89$	4.16117e19	0.141456	0.0707278	−	0.997496i	$-0.477468\pi$
$89$	4.16117e19	0.141456	0.0707278	+	0.997496i	$0.477468\pi$
$90$	−2.50121e20	−0.756143
$91$	−7.05236e19	−0.189845
$92$	−2.07262e20	−0.497448
$93$	4.05619e20	0.869055
$94$	4.89965e20	0.938259
$95$	−5.60095e20	−0.959762
$96$	2.99785e20	0.460216
$97$	5.71815e19	0.0787322	0.0393661	−	0.999225i	$-0.487466\pi$
$97$	5.71815e19	0.0787322	0.0393661	+	0.999225i	$0.487466\pi$
$98$	−4.64209e20	−0.573904
$99$	−2.23548e20	−0.248429
$100$	1.10791e21	1.10791
$101$	4.32417e20	0.389518	0.194759	−	0.980851i	$-0.437607\pi$
$101$	4.32417e20	0.389518	0.194759	+	0.980851i	$0.437607\pi$
$102$	−8.40989e20	−0.683107
$103$	1.84123e21	1.34995	0.674974	−	0.737841i	$-0.264155\pi$
$103$	1.84123e21	1.34995	0.674974	+	0.737841i	$0.264155\pi$
$104$	2.73483e20	0.181168
$105$	1.31985e21	0.790744
$106$	−3.75371e21	−2.03587
$107$	−2.43805e21	−1.19815	−0.599077	−	0.800691i	$-0.704466\pi$
$107$	−2.43805e21	−1.19815	−0.599077	+	0.800691i	$0.704466\pi$
$108$	−1.83003e20	−0.0815658
$109$	−4.13676e21	−1.67372	−0.836859	−	0.547418i	$-0.815611\pi$
$109$	−4.13676e21	−1.67372	−0.836859	+	0.547418i	$0.815611\pi$
$110$	4.59909e21	1.69063
$111$	−2.03365e20	−0.0679805
$112$	−2.94631e21	−0.896374
$113$	3.47910e21	0.964146	0.482073	−	0.876131i	$-0.339884\pi$
$113$	3.47910e21	0.964146	0.482073	+	0.876131i	$0.339884\pi$
$114$	−1.37669e21	−0.347804
$115$	9.68015e21	2.23128
$116$	−1.79950e21	−0.378741
$117$	−4.56699e20	−0.0878373
$118$	2.65219e21	0.466491
$119$	4.43775e21	0.714365
$120$	−5.11823e21	−0.754600
$121$	−3.28977e21	−0.444548
$122$	7.45043e21	0.923428
$123$	1.28977e21	0.146727
$124$	−6.10556e21	−0.637966
$125$	−3.19497e22	−3.06840
$126$	3.24413e21	0.286554
$127$	1.37141e21	0.111488	0.0557438	−	0.998445i	$-0.482247\pi$
$127$	1.37141e21	0.111488	0.0557438	+	0.998445i	$0.482247\pi$
$128$	1.53175e22	1.14679
$129$	4.23929e21	0.292484
$130$	9.39574e21	0.597758
$131$	−2.45276e22	−1.43981	−0.719907	−	0.694071i	$-0.755815\pi$
$131$	−2.45276e22	−1.43981	−0.719907	+	0.694071i	$0.755815\pi$
$132$	3.36495e21	0.182370
$133$	7.26455e21	0.363719
$134$	1.59735e22	0.739263
$135$	8.54711e21	0.365860
$136$	−1.72092e22	−0.681713
$137$	1.02835e22	0.377204	0.188602	−	0.982054i	$-0.439604\pi$
$137$	1.02835e22	0.377204	0.188602	+	0.982054i	$0.439604\pi$
$138$	2.37934e22	0.808586
$139$	8.70692e21	0.274289	0.137145	−	0.990551i	$-0.456207\pi$
$139$	8.70692e21	0.274289	0.137145	+	0.990551i	$0.456207\pi$
$140$	−1.98669e22	−0.580478
$141$	−1.67430e22	−0.453977
$142$	−3.52294e22	−0.886905
$143$	8.39753e21	0.196392
$144$	−1.90798e22	−0.414733
$145$	8.40452e22	1.69883
$146$	2.87155e22	0.540022
$147$	1.58629e22	0.277683
$148$	3.06114e21	0.0499039
$149$	−9.03997e22	−1.37313	−0.686564	−	0.727069i	$-0.740882\pi$
$149$	−9.03997e22	−1.37313	−0.686564	+	0.727069i	$0.740882\pi$
$150$	−1.27186e23	−1.80086
$151$	−4.75206e22	−0.627514	−0.313757	−	0.949503i	$-0.601588\pi$
$151$	−4.75206e22	−0.627514	−0.313757	+	0.949503i	$0.601588\pi$
$152$	−2.81712e22	−0.347094
$153$	2.87382e22	0.330521
$154$	−5.96512e22	−0.640695
$155$	2.85159e23	2.86157
$156$	6.87444e21	0.0644806
$157$	−1.50901e23	−1.32356	−0.661781	−	0.749697i	$-0.730199\pi$
$157$	−1.50901e23	−1.32356	−0.661781	+	0.749697i	$0.730199\pi$
$158$	1.17401e23	0.963323
$159$	1.28271e23	0.985053
$160$	2.10755e23	1.51537
$161$	−1.25554e23	−0.845586
$162$	2.10084e22	0.132583
$163$	−4.83503e22	−0.286042	−0.143021	−	0.989720i	$-0.545682\pi$
$163$	−4.83503e22	−0.286042	−0.143021	+	0.989720i	$0.545682\pi$
$164$	−1.94142e22	−0.107711
$165$	−1.57159e23	−0.818011
$166$	6.82624e22	0.333462
$167$	4.78731e20	0.00219568	0.00109784	−	0.999999i	$-0.499651\pi$
$167$	4.78731e20	0.00219568	0.00109784	+	0.999999i	$0.499651\pi$
$168$	6.63846e22	0.285970
$169$	−2.29909e23	−0.930562
$170$	−5.91234e23	−2.24929
$171$	4.70440e22	0.168285
$172$	−6.38118e22	−0.214710
$173$	−1.61804e23	−0.512277	−0.256139	−	0.966640i	$-0.582450\pi$
$173$	−1.61804e23	−0.512277	−0.256139	+	0.966640i	$0.582450\pi$
$174$	2.06580e23	0.615631
$175$	6.71138e23	1.88327
$176$	3.50829e23	0.927284
$177$	−9.06303e22	−0.225712
$178$	7.19050e22	0.168791
$179$	−8.76377e22	−0.193970	−0.0969849	−	0.995286i	$-0.530920\pi$
$179$	−8.76377e22	−0.193970	−0.0969849	+	0.995286i	$0.530920\pi$
$180$	−1.28655e23	−0.268575
$181$	9.36624e22	0.184476	0.0922381	−	0.995737i	$-0.470598\pi$
$181$	9.36624e22	0.184476	0.0922381	+	0.995737i	$0.470598\pi$
$182$	−1.21865e23	−0.226532
$183$	−2.54595e23	−0.446800
$184$	4.86885e23	0.806936
$185$	−1.42970e23	−0.223842
$186$	7.00910e23	1.03699
$187$	−5.28422e23	−0.738999
$188$	2.52024e23	0.333260
$189$	−1.10858e23	−0.138649
$190$	−9.67843e23	−1.14523
$191$	1.20858e24	1.35340	0.676699	−	0.736260i	$-0.263410\pi$
$191$	1.20858e24	1.35340	0.676699	+	0.736260i	$0.263410\pi$
$192$	−1.59601e23	−0.169189
$193$	−1.78822e24	−1.79502	−0.897509	−	0.440997i	$-0.854625\pi$
$193$	−1.78822e24	−1.79502	−0.897509	+	0.440997i	$0.854625\pi$
$194$	9.88096e22	0.0939466
$195$	−3.21070e23	−0.289225
$196$	−2.38775e23	−0.203845
$197$	1.90963e24	1.54545	0.772723	−	0.634743i	$-0.218894\pi$
$197$	1.90963e24	1.54545	0.772723	+	0.634743i	$0.218894\pi$
$198$	−3.86292e23	−0.296436
$199$	1.44254e24	1.04995	0.524977	−	0.851116i	$-0.324074\pi$
$199$	1.44254e24	1.04995	0.524977	+	0.851116i	$0.324074\pi$
$200$	−2.60261e24	−1.79719
$201$	−5.45844e23	−0.357692
$202$	7.47216e23	0.464790
$203$	−1.09008e24	−0.643801
$204$	−4.32580e23	−0.242633
$205$	9.06739e23	0.483133
$206$	3.18165e24	1.61082
$207$	−8.13065e23	−0.391234
$208$	7.16728e23	0.327861
$209$	−8.65020e23	−0.376262
$210$	2.28069e24	0.943549
$211$	3.98848e24	1.56979	0.784895	−	0.619629i	$-0.212717\pi$
$211$	3.98848e24	1.56979	0.784895	+	0.619629i	$0.212717\pi$
$212$	−1.93080e24	−0.723119
$213$	1.20385e24	0.429129
$214$	−4.21295e24	−1.42969
$215$	2.98032e24	0.963072
$216$	4.29896e23	0.132312
$217$	−3.69858e24	−1.08445
$218$	−7.14833e24	−1.99715
$219$	−9.81262e23	−0.261289
$220$	2.36564e24	0.600495
$221$	−1.07954e24	−0.261289
$222$	−3.51414e23	−0.0811172
$223$	−4.62963e24	−1.01940	−0.509700	−	0.860352i	$-0.670244\pi$
$223$	−4.62963e24	−1.01940	−0.509700	+	0.860352i	$0.670244\pi$
$224$	−2.73354e24	−0.574278
$225$	4.34618e24	0.871348
$226$	6.01188e24	1.15046
$227$	−3.43010e24	−0.626664	−0.313332	−	0.949644i	$-0.601445\pi$
$227$	−3.43010e24	−0.626664	−0.313332	+	0.949644i	$0.601445\pi$
$228$	−7.08128e23	−0.123537
$229$	8.11792e23	0.135261	0.0676304	−	0.997710i	$-0.478456\pi$
$229$	8.11792e23	0.135261	0.0676304	+	0.997710i	$0.478456\pi$
$230$	1.67273e25	2.66246
$231$	2.03839e24	0.310000
$232$	4.22724e24	0.614374
$233$	8.22188e23	0.114218	0.0571089	−	0.998368i	$-0.481812\pi$
$233$	8.22188e23	0.114218	0.0571089	+	0.998368i	$0.481812\pi$
$234$	−7.89177e23	−0.104811
$235$	−1.17707e25	−1.49483
$236$	1.36421e24	0.165693
$237$	−4.01181e24	−0.466104
$238$	7.66844e24	0.852411
$239$	−8.85525e24	−0.941940	−0.470970	−	0.882149i	$-0.656096\pi$
$239$	−8.85525e24	−0.941940	−0.470970	+	0.882149i	$0.656096\pi$
$240$	−1.34135e25	−1.36561
$241$	7.46934e24	0.727953	0.363977	−	0.931408i	$-0.381419\pi$
$241$	7.46934e24	0.727953	0.363977	+	0.931408i	$0.381419\pi$
$242$	−5.68472e24	−0.530454
$243$	−7.17898e23	−0.0641500
$244$	3.83228e24	0.327992
$245$	1.11520e25	0.914339
$246$	2.22873e24	0.175081
$247$	−1.76720e24	−0.133035
$248$	1.43427e25	1.03488
$249$	−2.33266e24	−0.161346
$250$	−5.52091e25	−3.66134
$251$	9.46474e23	0.0601914	0.0300957	−	0.999547i	$-0.490419\pi$
$251$	9.46474e23	0.0601914	0.0300957	+	0.999547i	$0.490419\pi$
$252$	1.66868e24	0.101781
$253$	1.49502e25	0.874744
$254$	2.36979e24	0.133032
$255$	2.02036e25	1.08832
$256$	2.08004e25	1.07535
$257$	−1.91825e25	−0.951936	−0.475968	−	0.879463i	$-0.657902\pi$
$257$	−1.91825e25	−0.951936	−0.475968	+	0.879463i	$0.657902\pi$
$258$	7.32550e24	0.349004
$259$	1.85435e24	0.0848290
$260$	4.83289e24	0.212318
$261$	−7.05921e24	−0.297873
$262$	−4.23837e25	−1.71805
$263$	8.88429e23	0.0346009	0.0173004	−	0.999850i	$-0.494493\pi$
$263$	8.88429e23	0.0346009	0.0173004	+	0.999850i	$0.494493\pi$
$264$	−7.90469e24	−0.295831
$265$	9.01776e25	3.24352
$266$	1.25531e25	0.434006
$267$	−2.45713e24	−0.0816694
$268$	8.21628e24	0.262579
$269$	−2.13847e25	−0.657211	−0.328605	−	0.944467i	$-0.606579\pi$
$269$	−2.13847e25	−0.657211	−0.328605	+	0.944467i	$0.606579\pi$
$270$	1.47694e25	0.436560
$271$	−1.56435e25	−0.444791	−0.222395	−	0.974957i	$-0.571388\pi$
$271$	−1.56435e25	−0.444791	−0.222395	+	0.974957i	$0.571388\pi$
$272$	−4.51007e25	−1.23370
$273$	4.16435e24	0.109607
$274$	1.77699e25	0.450095
$275$	−7.99152e25	−1.94821
$276$	1.22386e25	0.287202
$277$	−8.04973e25	−1.81863	−0.909313	−	0.416112i	$-0.863392\pi$
$277$	−8.04973e25	−1.81863	−0.909313	+	0.416112i	$0.863392\pi$
$278$	1.50456e25	0.327294
$279$	−2.39514e25	−0.501749
$280$	4.66699e25	0.941623
$281$	8.33171e25	1.61926	0.809632	−	0.586938i	$-0.199667\pi$
$281$	8.33171e25	1.61926	0.809632	+	0.586938i	$0.199667\pi$
$282$	−2.89320e25	−0.541704
$283$	−4.46130e24	−0.0804829	−0.0402415	−	0.999190i	$-0.512813\pi$
$283$	−4.46130e24	−0.0804829	−0.0402415	+	0.999190i	$0.512813\pi$
$284$	−1.81209e25	−0.315020
$285$	3.30730e25	0.554119
$286$	1.45109e25	0.234343
$287$	−1.17606e25	−0.183092
$288$	−1.77020e25	−0.265706
$289$	−1.16088e24	−0.0168020
$290$	1.45230e26	2.02711
$291$	−3.37651e24	−0.0454560
$292$	1.47704e25	0.191810
$293$	9.67128e25	1.21164	0.605820	−	0.795602i	$-0.292845\pi$
$293$	9.67128e25	1.21164	0.605820	+	0.795602i	$0.292845\pi$
$294$	2.74111e25	0.331344
$295$	−6.37151e25	−0.743209
$296$	−7.19099e24	−0.0809516
$297$	1.32003e25	0.143430
$298$	−1.56211e26	−1.63848
$299$	3.05426e25	0.309284
$300$	−6.54207e25	−0.639649
$301$	−3.86554e25	−0.364974
$302$	−8.21155e25	−0.748777
$303$	−2.55338e25	−0.224889
$304$	−7.38293e25	−0.628140
$305$	−1.78986e26	−1.47120
$306$	4.96596e25	0.394392
$307$	1.68163e26	1.29056	0.645278	−	0.763948i	$-0.276742\pi$
$307$	1.68163e26	1.29056	0.645278	+	0.763948i	$0.276742\pi$
$308$	−3.06828e25	−0.227569
$309$	−1.08723e26	−0.779393
$310$	4.92755e26	3.41455
$311$	2.30370e26	1.54327	0.771636	−	0.636065i	$-0.219439\pi$
$311$	2.30370e26	1.54327	0.771636	+	0.636065i	$0.219439\pi$
$312$	−1.61489e25	−0.104597
$313$	−2.79658e26	−1.75151	−0.875753	−	0.482759i	$-0.839635\pi$
$313$	−2.79658e26	−1.75151	−0.875753	+	0.482759i	$0.839635\pi$
$314$	−2.60756e26	−1.57933
$315$	−7.79356e25	−0.456536
$316$	6.03875e25	0.342163
$317$	2.98501e25	0.163615	0.0818075	−	0.996648i	$-0.473931\pi$
$317$	2.98501e25	0.163615	0.0818075	+	0.996648i	$0.473931\pi$
$318$	2.21653e26	1.17541
$319$	1.29801e26	0.666002
$320$	−1.12203e26	−0.557095
$321$	1.43964e26	0.691755
$322$	−2.16957e26	−1.00899
$323$	1.11202e26	0.500596
$324$	1.08061e25	0.0470920
$325$	−1.63263e26	−0.688831
$326$	−8.35494e25	−0.341317
$327$	2.44272e26	0.966322
$328$	4.56064e25	0.174723
$329$	1.52669e26	0.566492
$330$	−2.71572e26	−0.976086
$331$	2.55594e26	0.889933	0.444967	−	0.895547i	$-0.353216\pi$
$331$	2.55594e26	0.889933	0.444967	+	0.895547i	$0.353216\pi$
$332$	3.51122e25	0.118443
$333$	1.20085e25	0.0392485
$334$	8.27248e23	0.00261998
$335$	−3.83740e26	−1.17779
$336$	1.73977e26	0.517522
$337$	−4.91931e25	−0.141837	−0.0709187	−	0.997482i	$-0.522593\pi$
$337$	−4.91931e25	−0.141837	−0.0709187	+	0.997482i	$0.522593\pi$
$338$	−3.97282e26	−1.11039
$339$	−2.05437e26	−0.556650
$340$	−3.04113e26	−0.798927
$341$	4.40405e26	1.12184
$342$	8.12921e25	0.200805
$343$	−4.45381e26	−1.06695
$344$	1.49902e26	0.348292
$345$	−5.71603e26	−1.28823
$346$	−2.79597e26	−0.611271
$347$	2.98136e26	0.632345	0.316173	−	0.948702i	$-0.397602\pi$
$347$	2.98136e26	0.632345	0.316173	+	0.948702i	$0.397602\pi$
$348$	1.06258e26	0.218666
$349$	7.72834e26	1.54319	0.771595	−	0.636115i	$-0.219459\pi$
$349$	7.72834e26	1.54319	0.771595	+	0.636115i	$0.219459\pi$
$350$	1.15973e27	2.24720
$351$	2.69676e25	0.0507129
$352$	3.25494e26	0.594081
$353$	−7.30755e26	−1.29461	−0.647303	−	0.762233i	$-0.724103\pi$
$353$	−7.30755e26	−1.29461	−0.647303	+	0.762233i	$0.724103\pi$
$354$	−1.56609e26	−0.269329
$355$	8.46336e26	1.41301
$356$	3.69858e25	0.0599529
$357$	−2.62045e26	−0.412439
$358$	−1.51438e26	−0.231453
$359$	−1.58936e25	−0.0235901	−0.0117951	−	0.999930i	$-0.503755\pi$
$359$	−1.58936e25	−0.0235901	−0.0117951	+	0.999930i	$0.503755\pi$
$360$	3.02226e26	0.435669
$361$	−5.32173e26	−0.745121
$362$	1.61849e26	0.220125
$363$	1.94258e26	0.256660
$364$	−6.26836e25	−0.0804618
$365$	−6.89849e26	−0.860358
$366$	−4.39940e26	−0.533141
$367$	−1.40734e27	−1.65732	−0.828660	−	0.559752i	$-0.810896\pi$
$367$	−1.40734e27	−1.65732	−0.828660	+	0.559752i	$0.810896\pi$
$368$	1.27600e27	1.46032
$369$	−7.61598e25	−0.0847127
$370$	−2.47052e26	−0.267098
$371$	−1.16962e27	−1.22919
$372$	3.60527e26	0.368330
$373$	−9.30077e26	−0.923797	−0.461898	−	0.886933i	$-0.652831\pi$
$373$	−9.30077e26	−0.923797	−0.461898	+	0.886933i	$0.652831\pi$
$374$	−9.13112e26	−0.881805
$375$	1.88660e27	1.77154
$376$	−5.92035e26	−0.540599
$377$	2.65177e26	0.235479
$378$	−1.91562e26	−0.165442
$379$	2.18541e27	1.83578	0.917892	−	0.396830i	$-0.129890\pi$
$379$	2.18541e27	1.83578	0.917892	+	0.396830i	$0.129890\pi$
$380$	−4.97830e26	−0.406774
$381$	−8.09801e25	−0.0643674
$382$	2.08843e27	1.61493
$383$	2.10347e27	1.58252	0.791258	−	0.611482i	$-0.209426\pi$
$383$	2.10347e27	1.58252	0.791258	+	0.611482i	$0.209426\pi$
$384$	−9.04484e26	−0.662099
$385$	1.43304e27	1.02075
$386$	−3.09004e27	−2.14189
$387$	−2.50326e26	−0.168866
$388$	5.08247e25	0.0333689
$389$	−2.97815e26	−0.190316	−0.0951582	−	0.995462i	$-0.530336\pi$
$389$	−2.97815e26	−0.190316	−0.0951582	+	0.995462i	$0.530336\pi$
$390$	−5.54809e26	−0.345116
$391$	−1.92192e27	−1.16380
$392$	5.60912e26	0.330667
$393$	1.44833e27	0.831277
$394$	3.29984e27	1.84409
$395$	−2.82039e27	−1.53476
$396$	−1.98697e26	−0.105291
$397$	6.36504e26	0.328474	0.164237	−	0.986421i	$-0.447484\pi$
$397$	6.36504e26	0.328474	0.164237	+	0.986421i	$0.447484\pi$
$398$	2.49271e27	1.25285
$399$	−4.28964e26	−0.209993
$400$	−6.82075e27	−3.25239
$401$	2.43888e27	1.13286	0.566428	−	0.824111i	$-0.308325\pi$
$401$	2.43888e27	1.13286	0.566428	+	0.824111i	$0.308325\pi$
$402$	−9.43218e26	−0.426814
$403$	8.99728e26	0.396651
$404$	3.84346e26	0.165089
$405$	−5.04698e26	−0.211229
$406$	−1.88367e27	−0.768211
$407$	−2.20805e26	−0.0877542
$408$	1.01618e27	0.393587
$409$	5.48032e26	0.206876	0.103438	−	0.994636i	$-0.467016\pi$
$409$	5.48032e26	0.206876	0.103438	+	0.994636i	$0.467016\pi$
$410$	1.56684e27	0.576495
$411$	−6.07232e26	−0.217779
$412$	1.63654e27	0.572146
$413$	8.26399e26	0.281653
$414$	−1.40498e27	−0.466837
$415$	−1.63991e27	−0.531269
$416$	6.64970e26	0.210050
$417$	−5.14135e26	−0.158361
$418$	−1.49475e27	−0.448971
$419$	−6.08246e27	−1.78169	−0.890844	−	0.454309i	$-0.849886\pi$
$419$	−6.08246e27	−1.78169	−0.890844	+	0.454309i	$0.849886\pi$
$420$	1.17312e27	0.335139
$421$	−4.05990e27	−1.13124	−0.565618	−	0.824667i	$-0.691362\pi$
$421$	−4.05990e27	−1.13124	−0.565618	+	0.824667i	$0.691362\pi$
$422$	6.89209e27	1.87314
$423$	9.88659e26	0.262103
$424$	4.53568e27	1.17301
$425$	1.02735e28	2.59199
$426$	2.08026e27	0.512055
$427$	2.32149e27	0.557537
$428$	−2.16702e27	−0.507811
$429$	−4.95866e26	−0.113387
$430$	5.14999e27	1.14918
$431$	−7.87214e27	−1.71428	−0.857140	−	0.515084i	$-0.827761\pi$
$431$	−7.87214e27	−1.71428	−0.857140	+	0.515084i	$0.827761\pi$
$432$	1.12664e27	0.239446
$433$	−1.73785e27	−0.360486	−0.180243	−	0.983622i	$-0.557688\pi$
$433$	−1.73785e27	−0.360486	−0.180243	+	0.983622i	$0.557688\pi$
$434$	−6.39115e27	−1.29401
$435$	−4.96278e27	−0.980817
$436$	−3.67689e27	−0.709369
$437$	−3.14615e27	−0.592550
$438$	−1.69562e27	−0.311782
$439$	8.37416e27	1.50336	0.751681	−	0.659526i	$-0.229243\pi$
$439$	8.37416e27	1.50336	0.751681	+	0.659526i	$0.229243\pi$
$440$	−5.55717e27	−0.974094
$441$	−9.36687e26	−0.160321
$442$	−1.86545e27	−0.311781
$443$	−3.30286e25	−0.00539077	−0.00269539	−	0.999996i	$-0.500858\pi$
$443$	−3.30286e25	−0.00539077	−0.00269539	+	0.999996i	$0.500858\pi$
$444$	−1.80757e26	−0.0288120
$445$	−1.72742e27	−0.268916
$446$	−7.99999e27	−1.21639
$447$	5.33801e27	0.792776
$448$	1.45530e27	0.211121
$449$	5.21713e27	0.739341	0.369670	−	0.929163i	$-0.379471\pi$
$449$	5.21713e27	0.739341	0.369670	+	0.929163i	$0.379471\pi$
$450$	7.51020e27	1.03973
$451$	1.40038e27	0.189406
$452$	3.09233e27	0.408632
$453$	2.80604e27	0.362296
$454$	−5.92721e27	−0.747763
$455$	2.92763e27	0.360908
$456$	1.66348e27	0.200395
$457$	2.15211e26	0.0253363	0.0126682	−	0.999920i	$-0.495967\pi$
$457$	2.15211e26	0.0253363	0.0126682	+	0.999920i	$0.495967\pi$
$458$	1.40278e27	0.161399
$459$	−1.69696e27	−0.190826
$460$	8.60403e27	0.945681
$461$	1.68699e28	1.81239	0.906197	−	0.422855i	$-0.138972\pi$
$461$	1.68699e28	1.81239	0.906197	+	0.422855i	$0.138972\pi$
$462$	3.52234e27	0.369906
$463$	−1.90352e28	−1.95415	−0.977074	−	0.212898i	$-0.931710\pi$
$463$	−1.90352e28	−1.95415	−0.977074	+	0.212898i	$0.931710\pi$
$464$	1.10785e28	1.11184
$465$	−1.68384e28	−1.65213
$466$	1.42074e27	0.136290
$467$	−1.21027e28	−1.13515	−0.567576	−	0.823321i	$-0.692119\pi$
$467$	−1.21027e28	−1.13515	−0.567576	+	0.823321i	$0.692119\pi$
$468$	−4.05929e26	−0.0372279
$469$	4.97720e27	0.446344
$470$	−2.03398e28	−1.78369
$471$	8.91053e27	0.764159
$472$	−3.20469e27	−0.268779
$473$	4.60286e27	0.377559
$474$	−6.93240e27	−0.556175
$475$	1.68175e28	1.31971
$476$	3.94442e27	0.302768
$477$	−7.57429e27	−0.568721
$478$	−1.53019e28	−1.12396
$479$	6.95253e27	0.499597	0.249798	−	0.968298i	$-0.419636\pi$
$479$	6.95253e27	0.499597	0.249798	+	0.968298i	$0.419636\pi$
$480$	−1.24449e28	−0.874900
$481$	−4.51095e26	−0.0310274
$482$	1.29070e28	0.868625
$483$	7.41382e27	0.488199
$484$	−2.92405e27	−0.188412
$485$	−2.37376e27	−0.149675
$486$	−1.24053e27	−0.0765466
$487$	−1.06412e28	−0.642596	−0.321298	−	0.946978i	$-0.604119\pi$
$487$	−1.06412e28	−0.642596	−0.321298	+	0.946978i	$0.604119\pi$
$488$	−9.00250e27	−0.532053
$489$	2.85504e27	0.165146
$490$	1.92706e28	1.09103
$491$	1.68064e28	0.931361	0.465681	−	0.884953i	$-0.345810\pi$
$491$	1.68064e28	0.931361	0.465681	+	0.884953i	$0.345810\pi$
$492$	1.14639e27	0.0621869
$493$	−1.66865e28	−0.886079
$494$	−3.05372e27	−0.158743
$495$	9.28011e27	0.472279
$496$	3.75885e28	1.87283
$497$	−1.09772e28	−0.535486
$498$	−4.03083e27	−0.192525
$499$	−5.12285e27	−0.239583	−0.119792	−	0.992799i	$-0.538223\pi$
$499$	−5.12285e27	−0.239583	−0.119792	+	0.992799i	$0.538223\pi$
$500$	−2.83979e28	−1.30047
$501$	−2.82686e25	−0.00126768
$502$	1.63551e27	0.0718229
$503$	1.99606e28	0.858442	0.429221	−	0.903200i	$-0.358788\pi$
$503$	1.99606e28	0.858442	0.429221	+	0.903200i	$0.358788\pi$
$504$	−3.91994e27	−0.165105
$505$	−1.79508e28	−0.740499
$506$	2.58339e28	1.04378
$507$	1.35759e28	0.537260
$508$	1.21895e27	0.0472516
$509$	−2.57966e27	−0.0979550	−0.0489775	−	0.998800i	$-0.515596\pi$
$509$	−2.57966e27	−0.0979550	−0.0489775	+	0.998800i	$0.515596\pi$
$510$	3.49118e28	1.29863
$511$	8.94749e27	0.326048
$512$	3.81989e27	0.136369
$513$	−2.77790e27	−0.0971594
$514$	−3.31474e28	−1.13589
$515$	−7.64346e28	−2.56634
$516$	3.76802e27	0.123963
$517$	−1.81789e28	−0.586026
$518$	3.20432e27	0.101222
$519$	9.55436e27	0.295763
$520$	−1.13531e28	−0.344412
$521$	−2.61230e28	−0.776652	−0.388326	−	0.921522i	$-0.626947\pi$
$521$	−2.61230e28	−0.776652	−0.388326	+	0.921522i	$0.626947\pi$
$522$	−1.21983e28	−0.355435
$523$	6.70750e28	1.91555	0.957774	−	0.287523i	$-0.0928317\pi$
$523$	6.70750e28	1.91555	0.957774	+	0.287523i	$0.0928317\pi$
$524$	−2.18009e28	−0.610233
$525$	−3.96300e28	−1.08731
$526$	1.53520e27	0.0412873
$527$	−5.66161e28	−1.49255
$528$	−2.07161e28	−0.535367
$529$	1.49036e28	0.377577
$530$	1.55827e29	3.87031
$531$	5.35163e27	0.130315
$532$	6.45696e27	0.154155
$533$	2.86092e27	0.0669684
$534$	−4.24592e27	−0.0974514
$535$	1.01210e29	2.27777
$536$	−1.93011e28	−0.425943
$537$	5.17492e27	0.111988
$538$	−3.69528e28	−0.784212
$539$	1.72233e28	0.358454
$540$	7.59695e27	0.155062
$541$	−2.15196e28	−0.430787	−0.215394	−	0.976527i	$-0.569103\pi$
$541$	−2.15196e28	−0.430787	−0.215394	+	0.976527i	$0.569103\pi$
$542$	−2.70319e28	−0.530743
$543$	−5.53067e27	−0.106507
$544$	−4.18438e28	−0.790392
$545$	1.71728e29	3.18185
$546$	7.19599e27	0.130788
$547$	−7.46789e28	−1.33147	−0.665734	−	0.746189i	$-0.731882\pi$
$547$	−7.46789e28	−1.33147	−0.665734	+	0.746189i	$0.731882\pi$
$548$	9.14032e27	0.159870
$549$	1.50336e28	0.257960
$550$	−1.38093e29	−2.32469
$551$	−2.73156e28	−0.451148
$552$	−2.87500e28	−0.465884
$553$	3.65811e28	0.581625
$554$	−1.39099e29	−2.17006
$555$	8.44223e27	0.129235
$556$	7.73899e27	0.116252
$557$	−7.95166e28	−1.17214	−0.586068	−	0.810262i	$-0.699325\pi$
$557$	−7.95166e28	−1.17214	−0.586068	+	0.810262i	$0.699325\pi$
$558$	−4.13880e28	−0.598709
$559$	9.40343e27	0.133494
$560$	1.22309e29	1.70406
$561$	3.12028e28	0.426661
$562$	1.43972e29	1.93217
$563$	5.46305e28	0.719609	0.359805	−	0.933028i	$-0.382843\pi$
$563$	5.46305e28	0.719609	0.359805	+	0.933028i	$0.382843\pi$
$564$	−1.48817e28	−0.192408
$565$	−1.44427e29	−1.83290
$566$	−7.70912e27	−0.0960356
$567$	6.54605e27	0.0800492
$568$	4.25683e28	0.511010
$569$	9.43478e28	1.11187	0.555933	−	0.831227i	$-0.312361\pi$
$569$	9.43478e28	1.11187	0.555933	+	0.831227i	$0.312361\pi$
$570$	5.71502e28	0.661198
$571$	8.05027e28	0.914390	0.457195	−	0.889367i	$-0.348854\pi$
$571$	8.05027e28	0.914390	0.457195	+	0.889367i	$0.348854\pi$
$572$	7.46400e27	0.0832364
$573$	−7.13655e28	−0.781384
$574$	−2.03223e28	−0.218473
$575$	−2.90659e29	−3.06811
$576$	9.42426e27	0.0976812
$577$	−1.67132e28	−0.170104	−0.0850519	−	0.996377i	$-0.527106\pi$
$577$	−1.67132e28	−0.170104	−0.0850519	+	0.996377i	$0.527106\pi$
$578$	−2.00600e27	−0.0200488
$579$	1.05592e29	1.03635
$580$	7.47020e28	0.720010
$581$	2.12700e28	0.201334
$582$	−5.83461e27	−0.0542401
$583$	1.39272e29	1.27158
$584$	−3.46975e28	−0.311145
$585$	1.89589e28	0.166984
$586$	1.67120e29	1.44578
$587$	3.15730e28	0.268297	0.134149	−	0.990961i	$-0.457170\pi$
$587$	3.15730e28	0.268297	0.134149	+	0.990961i	$0.457170\pi$
$588$	1.40994e28	0.117690
$589$	−9.26799e28	−0.759932
$590$	−1.10100e29	−0.886829
$591$	−1.12762e29	−0.892264
$592$	−1.88457e28	−0.146499
$593$	−5.48493e27	−0.0418887	−0.0209443	−	0.999781i	$-0.506667\pi$
$593$	−5.48493e27	−0.0418887	−0.0209443	+	0.999781i	$0.506667\pi$
$594$	2.28101e28	0.171147
$595$	−1.84223e29	−1.35805
$596$	−8.03502e28	−0.581971
$597$	−8.51805e28	−0.606191
$598$	5.27776e28	0.369051
$599$	1.25621e29	0.863136	0.431568	−	0.902080i	$-0.357960\pi$
$599$	1.25621e29	0.863136	0.431568	+	0.902080i	$0.357960\pi$
$600$	1.53681e29	1.03761
$601$	3.99325e28	0.264938	0.132469	−	0.991187i	$-0.457709\pi$
$601$	3.99325e28	0.264938	0.132469	+	0.991187i	$0.457709\pi$
$602$	−6.67965e28	−0.435503
$603$	3.22315e28	0.206514
$604$	−4.22378e28	−0.265958
$605$	1.36567e29	0.845115
$606$	−4.41223e28	−0.268347
$607$	−2.46990e29	−1.47638	−0.738189	−	0.674594i	$-0.764319\pi$
$607$	−2.46990e29	−1.47638	−0.738189	+	0.674594i	$0.764319\pi$
$608$	−6.84978e28	−0.402429
$609$	6.43684e28	0.371699
$610$	−3.09288e29	−1.75549
$611$	−3.71387e28	−0.207202
$612$	2.55434e28	0.140084
$613$	2.63911e28	0.142273	0.0711364	−	0.997467i	$-0.477337\pi$
$613$	2.63911e28	0.142273	0.0711364	+	0.997467i	$0.477337\pi$
$614$	2.90585e29	1.53995
$615$	−5.35420e28	−0.278937
$616$	7.20777e28	0.369151
$617$	3.09820e29	1.55997	0.779984	−	0.625800i	$-0.215227\pi$
$617$	3.09820e29	1.55997	0.779984	+	0.625800i	$0.215227\pi$
$618$	−1.87873e29	−0.930005
$619$	−2.50758e29	−1.22040	−0.610202	−	0.792246i	$-0.708912\pi$
$619$	−2.50758e29	−1.22040	−0.610202	+	0.792246i	$0.708912\pi$
$620$	2.53459e29	1.21281
$621$	4.80107e28	0.225879
$622$	3.98080e29	1.84150
$623$	2.24050e28	0.101911
$624$	−4.23221e28	−0.189291
$625$	7.31956e29	3.21918
$626$	−4.83249e29	−2.08997
$627$	5.10785e28	0.217235
$628$	−1.34125e29	−0.560963
$629$	2.83855e28	0.116752
$630$	−1.34673e29	−0.544758
$631$	−4.32770e28	−0.172167	−0.0860833	−	0.996288i	$-0.527435\pi$
$631$	−4.32770e28	−0.172167	−0.0860833	+	0.996288i	$0.527435\pi$
$632$	−1.41858e29	−0.555039
$633$	−2.35516e29	−0.906318
$634$	5.15809e28	0.195232
$635$	−5.69309e28	−0.211945
$636$	1.14012e29	0.417493
$637$	3.51864e28	0.126739
$638$	2.24296e29	0.794702
$639$	−7.10863e28	−0.247758
$640$	−6.35872e29	−2.18012
$641$	−8.73381e28	−0.294574	−0.147287	−	0.989094i	$-0.547054\pi$
$641$	−8.73381e28	−0.294574	−0.147287	+	0.989094i	$0.547054\pi$
$642$	2.48770e29	0.825431
$643$	−4.72013e29	−1.54077	−0.770386	−	0.637578i	$-0.779937\pi$
$643$	−4.72013e29	−1.54077	−0.770386	+	0.637578i	$0.779937\pi$
$644$	−1.11596e29	−0.358383
$645$	−1.75985e29	−0.556030
$646$	1.92158e29	0.597332
$647$	1.26799e28	0.0387812	0.0193906	−	0.999812i	$-0.493827\pi$
$647$	1.26799e28	0.0387812	0.0193906	+	0.999812i	$0.493827\pi$
$648$	−2.53849e28	−0.0763903
$649$	−9.84027e28	−0.291365
$650$	−2.82119e29	−0.821943
$651$	2.18397e29	0.626105
$652$	−4.29753e28	−0.121233
$653$	−2.76226e29	−0.766790	−0.383395	−	0.923584i	$-0.625245\pi$
$653$	−2.76226e29	−0.766790	−0.383395	+	0.923584i	$0.625245\pi$
$654$	4.22102e29	1.15306
$655$	1.01821e30	2.73718
$656$	1.19523e29	0.316198
$657$	5.79425e28	0.150855
$658$	2.63812e29	0.675962
$659$	6.46511e28	0.163034	0.0815172	−	0.996672i	$-0.474023\pi$
$659$	6.46511e28	0.163034	0.0815172	+	0.996672i	$0.474023\pi$
$660$	−1.39688e29	−0.346696
$661$	−2.27730e29	−0.556295	−0.278147	−	0.960538i	$-0.589720\pi$
$661$	−2.27730e29	−0.556295	−0.278147	+	0.960538i	$0.589720\pi$
$662$	4.41667e29	1.06191
$663$	6.37459e28	0.150855
$664$	−8.24829e28	−0.192132
$665$	−3.01572e29	−0.691454
$666$	2.07507e28	0.0468330
$667$	4.72097e29	1.04884
$668$	4.25512e26	0.000930591 0
$669$	2.73375e29	0.588551
$670$	−6.63103e29	−1.40539
$671$	−2.76429e29	−0.576763
$672$	1.61413e29	0.331559
$673$	−3.79243e29	−0.766936	−0.383468	−	0.923554i	$-0.625270\pi$
$673$	−3.79243e29	−0.766936	−0.383468	+	0.923554i	$0.625270\pi$
$674$	−8.50057e28	−0.169246
$675$	−2.56638e29	−0.503073
$676$	−2.04350e29	−0.394398
$677$	−3.39717e29	−0.645559	−0.322780	−	0.946474i	$-0.604617\pi$
$677$	−3.39717e29	−0.645559	−0.322780	+	0.946474i	$0.604617\pi$
$678$	−3.54995e29	−0.664218
$679$	3.07882e28	0.0567220
$680$	7.14400e29	1.29598
$681$	2.02544e29	0.361805
$682$	7.61020e29	1.33863
$683$	4.54742e29	0.787677	0.393838	−	0.919180i	$-0.371147\pi$
$683$	4.54742e29	0.787677	0.393838	+	0.919180i	$0.371147\pi$
$684$	4.18143e28	0.0713239
$685$	−4.26897e29	−0.717088
$686$	−7.69619e29	−1.27313
$687$	−4.79355e28	−0.0780929
$688$	3.92853e29	0.630306
$689$	2.84526e29	0.449594
$690$	−9.87730e29	−1.53717
$691$	−3.71838e29	−0.569947	−0.284974	−	0.958535i	$-0.591985\pi$
$691$	−3.71838e29	−0.569947	−0.284974	+	0.958535i	$0.591985\pi$
$692$	−1.43817e29	−0.217118
$693$	−1.20365e29	−0.178979
$694$	5.15178e29	0.754542
$695$	−3.61448e29	−0.521442
$696$	−2.49614e29	−0.354709
$697$	−1.80026e29	−0.251994
$698$	1.33546e30	1.84140
$699$	−4.85494e28	−0.0659437
$700$	5.96529e29	0.798183
$701$	−9.37969e29	−1.23637	−0.618186	−	0.786032i	$-0.712132\pi$
$701$	−9.37969e29	−1.23637	−0.618186	+	0.786032i	$0.712132\pi$
$702$	4.66001e28	0.0605128
$703$	4.64668e28	0.0594445
$704$	−1.73288e29	−0.218401
$705$	6.95050e29	0.863038
$706$	−1.26275e30	−1.54478
$707$	2.32826e29	0.280626
$708$	−8.05551e28	−0.0956629
$709$	−7.54578e29	−0.882914	−0.441457	−	0.897282i	$-0.645538\pi$
$709$	−7.54578e29	−0.882914	−0.441457	+	0.897282i	$0.645538\pi$
$710$	1.46247e30	1.68606
$711$	2.36893e29	0.269105
$712$	−8.68842e28	−0.0972525
$713$	1.60179e30	1.76671
$714$	−4.52814e29	−0.492140
$715$	−3.48605e29	−0.373353
$716$	−7.78952e28	−0.0822098
$717$	5.22894e29	0.543829
$718$	−2.74641e28	−0.0281488
$719$	1.22754e30	1.23989	0.619944	−	0.784646i	$-0.287155\pi$
$719$	1.22754e30	1.23989	0.619944	+	0.784646i	$0.287155\pi$
$720$	7.92056e29	0.788433
$721$	9.91374e29	0.972561
$722$	−9.19594e29	−0.889111
$723$	−4.41057e29	−0.420284
$724$	8.32502e28	0.0781862
$725$	−2.52356e30	−2.33596
$726$	3.35677e29	0.306258
$727$	9.04407e29	0.813303	0.406652	−	0.913583i	$-0.366696\pi$
$727$	9.04407e29	0.813303	0.406652	+	0.913583i	$0.366696\pi$
$728$	1.47252e29	0.130521
$729$	4.23912e28	0.0370370
$730$	−1.19206e30	−1.02662
$731$	−5.91719e29	−0.502323
$732$	−2.26292e29	−0.189367
$733$	−1.38874e30	−1.14559	−0.572795	−	0.819699i	$-0.694141\pi$
$733$	−1.38874e30	−1.14559	−0.572795	+	0.819699i	$0.694141\pi$
$734$	−2.43189e30	−1.97759
$735$	−6.58512e29	−0.527894
$736$	1.18385e30	0.935578
$737$	−5.92655e29	−0.461736
$738$	−1.31604e29	−0.101083
$739$	2.11506e30	1.60161	0.800804	−	0.598927i	$-0.204406\pi$
$739$	2.11506e30	1.60161	0.800804	+	0.598927i	$0.204406\pi$
$740$	−1.27076e29	−0.0948705
$741$	1.04351e29	0.0768080
$742$	−2.02111e30	−1.46673
$743$	2.26805e30	1.62282	0.811411	−	0.584476i	$-0.198700\pi$
$743$	2.26805e30	1.62282	0.811411	+	0.584476i	$0.198700\pi$
$744$	−8.46923e29	−0.597487
$745$	3.75274e30	2.61040
$746$	−1.60717e30	−1.10231
$747$	1.37741e29	0.0931530
$748$	−4.69678e29	−0.313208
$749$	−1.31272e30	−0.863202
$750$	3.26004e30	2.11388
$751$	−6.98349e29	−0.446533	−0.223266	−	0.974757i	$-0.571672\pi$
$751$	−6.98349e29	−0.446533	−0.223266	+	0.974757i	$0.571672\pi$
$752$	−1.55157e30	−0.978326
$753$	−5.58883e28	−0.0347515
$754$	4.58226e29	0.280984
$755$	1.97271e30	1.19294
$756$	−9.85341e28	−0.0587635
$757$	−3.79778e29	−0.223369	−0.111685	−	0.993744i	$-0.535625\pi$
$757$	−3.79778e29	−0.223369	−0.111685	+	0.993744i	$0.535625\pi$
$758$	3.77639e30	2.19054
$759$	−8.82794e29	−0.505034
$760$	1.16946e30	0.659849
$761$	−7.50371e29	−0.417577	−0.208789	−	0.977961i	$-0.566952\pi$
$761$	−7.50371e29	−0.417577	−0.208789	+	0.977961i	$0.566952\pi$
$762$	−1.39934e29	−0.0768060
$763$	−2.22736e30	−1.20582
$764$	1.07423e30	0.573608
$765$	−1.19300e30	−0.628342
$766$	3.63479e30	1.88833
$767$	−2.01032e29	−0.103018
$768$	−1.22824e30	−0.620856
$769$	2.16884e29	0.108144	0.0540719	−	0.998537i	$-0.482780\pi$
$769$	2.16884e29	0.108144	0.0540719	+	0.998537i	$0.482780\pi$
$770$	2.47629e30	1.21800
$771$	1.13271e30	0.549600
$772$	−1.58943e30	−0.760779
$773$	−3.08128e30	−1.45495	−0.727473	−	0.686136i	$-0.759305\pi$
$773$	−3.08128e30	−1.45495	−0.727473	+	0.686136i	$0.759305\pi$
$774$	−4.32563e29	−0.201498
$775$	−8.56227e30	−3.93478
$776$	−1.19394e29	−0.0541294
$777$	−1.09498e29	−0.0489761
$778$	−5.14625e29	−0.227094
$779$	−2.94700e29	−0.128303
$780$	−2.85377e29	−0.122582
$781$	1.30710e30	0.553951
$782$	−3.32107e30	−1.38870
$783$	4.16839e29	0.171977
$784$	1.47000e30	0.598412
$785$	6.26430e30	2.51618
$786$	2.50271e30	0.991915
$787$	1.46460e30	0.572775	0.286387	−	0.958114i	$-0.407546\pi$
$787$	1.46460e30	0.572775	0.286387	+	0.958114i	$0.407546\pi$
$788$	1.69734e30	0.655004
$789$	−5.24608e28	−0.0199768
$790$	−4.87363e30	−1.83134
$791$	1.87325e30	0.694612
$792$	4.66764e29	0.170798
$793$	−5.64732e29	−0.203927
$794$	1.09988e30	0.391949
$795$	−5.32490e30	−1.87265
$796$	1.28217e30	0.445000
$797$	1.27731e30	0.437505	0.218752	−	0.975780i	$-0.429801\pi$
$797$	1.27731e30	0.437505	0.218752	+	0.975780i	$0.429801\pi$
$798$	−7.41250e29	−0.250573
$799$	2.33698e30	0.779677
$800$	−6.32819e30	−2.08370
$801$	1.45091e29	0.0471519
$802$	4.21439e30	1.35177
$803$	−1.06541e30	−0.337292
$804$	−4.85163e29	−0.151600
$805$	5.21208e30	1.60751
$806$	1.55473e30	0.473301
$807$	1.26275e30	0.379441
$808$	−9.02876e29	−0.267799
$809$	−4.24975e30	−1.24424	−0.622120	−	0.782922i	$-0.713728\pi$
$809$	−4.24975e30	−1.24424	−0.622120	+	0.782922i	$0.713728\pi$
$810$	−8.72119e29	−0.252048
$811$	2.05863e30	0.587298	0.293649	−	0.955913i	$-0.405130\pi$
$811$	2.05863e30	0.587298	0.293649	+	0.955913i	$0.405130\pi$
$812$	−9.68902e29	−0.272861
$813$	9.23732e29	0.256800
$814$	−3.81551e29	−0.104712
$815$	2.00716e30	0.543784
$816$	2.66315e30	0.712278
$817$	−9.68636e29	−0.255758
$818$	9.46999e29	0.246854
$819$	−2.45901e29	−0.0632818
$820$	8.05938e29	0.204765
$821$	−1.80717e29	−0.0453309	−0.0226655	−	0.999743i	$-0.507215\pi$
$821$	−1.80717e29	−0.0453309	−0.0226655	+	0.999743i	$0.507215\pi$
$822$	−1.04930e30	−0.259863
$823$	−6.23532e30	−1.52462	−0.762308	−	0.647214i	$-0.775934\pi$
$823$	−6.23532e30	−1.52462	−0.762308	+	0.647214i	$0.775934\pi$
$824$	−3.84445e30	−0.928107
$825$	4.71891e30	1.12480
$826$	1.42802e30	0.336080
$827$	3.37179e30	0.783524	0.391762	−	0.920067i	$-0.371866\pi$
$827$	3.37179e30	0.783524	0.391762	+	0.920067i	$0.371866\pi$
$828$	−7.22678e29	−0.165816
$829$	−2.70711e29	−0.0613315	−0.0306658	−	0.999530i	$-0.509763\pi$
$829$	−2.70711e29	−0.0613315	−0.0306658	+	0.999530i	$0.509763\pi$
$830$	−2.83376e30	−0.633933
$831$	4.75328e30	1.04998
$832$	−3.54020e29	−0.0772205
$833$	−2.21413e30	−0.476904
$834$	−8.88425e29	−0.188963
$835$	−1.98735e28	−0.00417413
$836$	−7.68857e29	−0.159470
$837$	1.41431e30	0.289685
$838$	−1.05105e31	−2.12599
$839$	−7.45457e30	−1.48909	−0.744547	−	0.667570i	$-0.767334\pi$
$839$	−7.45457e30	−1.48909	−0.744547	+	0.667570i	$0.767334\pi$
$840$	−2.75581e30	−0.543646
$841$	−1.03399e30	−0.201446
$842$	−7.01551e30	−1.34984
$843$	−4.91979e30	−0.934882
$844$	3.54509e30	0.665321
$845$	9.54415e30	1.76906
$846$	1.70840e30	0.312753
$847$	−1.77131e30	−0.320272
$848$	1.18868e31	2.12280
$849$	2.63435e29	0.0464668
$850$	1.77526e31	3.09287
$851$	−8.03088e29	−0.138198
$852$	1.07002e30	0.181877
$853$	−6.10653e30	−1.02525	−0.512625	−	0.858613i	$-0.671327\pi$
$853$	−6.10653e30	−1.02525	−0.512625	+	0.858613i	$0.671327\pi$
$854$	4.01153e30	0.665277
$855$	−1.95293e30	−0.319921
$856$	5.09059e30	0.823746
$857$	−4.08307e30	−0.652662	−0.326331	−	0.945256i	$-0.605812\pi$
$857$	−4.08307e30	−0.652662	−0.326331	+	0.945256i	$0.605812\pi$
$858$	−8.56856e29	−0.135298
$859$	5.27189e30	0.822316	0.411158	−	0.911564i	$-0.365125\pi$
$859$	5.27189e30	0.822316	0.411158	+	0.911564i	$0.365125\pi$
$860$	2.64900e30	0.408177
$861$	6.94452e29	0.105708
$862$	−1.36031e31	−2.04555
$863$	1.05537e31	1.56780	0.783902	−	0.620884i	$-0.213226\pi$
$863$	1.05537e31	1.56780	0.783902	+	0.620884i	$0.213226\pi$
$864$	1.04528e30	0.153405
$865$	6.71693e30	0.973872
$866$	−3.00300e30	−0.430147
$867$	6.85488e28	0.00970062
$868$	−3.28742e30	−0.459619
$869$	−4.35586e30	−0.601681
$870$	−8.57569e30	−1.17035
$871$	−1.21077e30	−0.163256
$872$	8.63747e30	1.15070
$873$	1.99379e29	0.0262441
$874$	−5.43655e30	−0.707056
$875$	−1.72027e31	−2.21061
$876$	−8.72177e29	−0.110742
$877$	7.16069e30	0.898378	0.449189	−	0.893437i	$-0.351713\pi$
$877$	7.16069e30	0.898378	0.449189	+	0.893437i	$0.351713\pi$
$878$	1.44706e31	1.79388
$879$	−5.71079e30	−0.699541
$880$	−1.45639e31	−1.76283
$881$	−1.05943e31	−1.26714	−0.633568	−	0.773687i	$-0.718410\pi$
$881$	−1.05943e31	−1.26714	−0.633568	+	0.773687i	$0.718410\pi$
$882$	−1.61860e30	−0.191301
$883$	6.60744e30	0.771695	0.385848	−	0.922562i	$-0.373909\pi$
$883$	6.60744e30	0.771695	0.385848	+	0.922562i	$0.373909\pi$
$884$	−9.59531e29	−0.110742
$885$	3.76231e30	0.429092
$886$	−5.70734e28	−0.00643250
$887$	−2.74467e30	−0.305698	−0.152849	−	0.988250i	$-0.548845\pi$
$887$	−2.74467e30	−0.305698	−0.152849	+	0.988250i	$0.548845\pi$
$888$	4.24621e29	0.0467374
$889$	7.38406e29	0.0803205
$890$	−2.98497e30	−0.320882
$891$	−7.79465e29	−0.0828096
$892$	−4.11496e30	−0.432051
$893$	3.82561e30	0.396973
$894$	9.22409e30	0.945974
$895$	3.63808e30	0.368749
$896$	8.24741e30	0.826196
$897$	−1.80351e30	−0.178565
$898$	9.01519e30	0.882213
$899$	1.39071e31	1.34512
$900$	3.86303e30	0.369302
$901$	−1.79040e31	−1.69177
$902$	2.41986e30	0.226007
$903$	2.28256e30	0.210718
$904$	−7.26427e30	−0.662863
$905$	−3.88819e30	−0.350701
$906$	4.84884e30	0.432307
$907$	5.45568e30	0.480809	0.240404	−	0.970673i	$-0.422720\pi$
$907$	5.45568e30	0.480809	0.240404	+	0.970673i	$0.422720\pi$
$908$	−3.04878e30	−0.265598
$909$	1.50774e30	0.129839
$910$	5.05894e30	0.430651
$911$	−8.75739e30	−0.736940	−0.368470	−	0.929640i	$-0.620118\pi$
$911$	−8.75739e30	−0.736940	−0.368470	+	0.929640i	$0.620118\pi$
$912$	4.35955e30	0.362657
$913$	−2.53270e30	−0.208277
$914$	3.71884e29	0.0302324
$915$	1.05689e31	0.849396
$916$	7.21547e29	0.0573274
$917$	−1.32064e31	−1.03730
$918$	−2.93235e30	−0.227702
$919$	1.24295e31	0.954206	0.477103	−	0.878847i	$-0.341687\pi$
$919$	1.24295e31	0.954206	0.477103	+	0.878847i	$0.341687\pi$
$920$	−2.02119e31	−1.53404
$921$	−9.92984e30	−0.745102
$922$	2.91512e31	2.16263
$923$	2.67034e30	0.195861
$924$	1.81179e30	0.131387
$925$	4.29285e30	0.307792
$926$	−3.28929e31	−2.33177
$927$	6.41997e30	0.449983
$928$	1.02785e31	0.712319
$929$	2.24310e31	1.53703	0.768517	−	0.639829i	$-0.220995\pi$
$929$	2.24310e31	1.53703	0.768517	+	0.639829i	$0.220995\pi$
$930$	−2.90967e31	−1.97139
$931$	−3.62451e30	−0.242816
$932$	7.30787e29	0.0484087
$933$	−1.36031e31	−0.891008
$934$	−2.09134e31	−1.35451
$935$	2.19362e31	1.40488
$936$	9.53578e29	0.0603893
$937$	−1.10052e31	−0.689176	−0.344588	−	0.938754i	$-0.611981\pi$
$937$	−1.10052e31	−0.689176	−0.344588	+	0.938754i	$0.611981\pi$
$938$	8.60060e30	0.532597
$939$	1.65135e31	1.01123
$940$	−1.04622e31	−0.633549
$941$	−2.38036e31	−1.42545	−0.712725	−	0.701444i	$-0.752539\pi$
$941$	−2.38036e31	−1.42545	−0.712725	+	0.701444i	$0.752539\pi$
$942$	1.53974e31	0.911828
$943$	5.09332e30	0.298283
$944$	−8.39866e30	−0.486412
$945$	4.60202e30	0.263581
$946$	7.95373e30	0.450520
$947$	8.09762e30	0.453610	0.226805	−	0.973940i	$-0.427172\pi$
$947$	8.09762e30	0.453610	0.226805	+	0.973940i	$0.427172\pi$
$948$	−3.56582e30	−0.197548
$949$	−2.17660e30	−0.119257
$950$	2.90607e31	1.57474
$951$	−1.76262e30	−0.0944631
$952$	−9.26593e30	−0.491135
$953$	−3.42232e30	−0.179410	−0.0897048	−	0.995968i	$-0.528592\pi$
$953$	−3.42232e30	−0.179410	−0.0897048	+	0.995968i	$0.528592\pi$
$954$	−1.30884e31	−0.678622
$955$	−5.01715e31	−2.57290
$956$	−7.87083e30	−0.399220
$957$	−7.66461e30	−0.384516
$958$	1.20140e31	0.596140
$959$	5.53695e30	0.271754
$960$	6.62546e30	0.321639
$961$	2.63603e31	1.26577
$962$	−7.79493e29	−0.0370232
$963$	−8.50095e30	−0.399385
$964$	6.63899e30	0.308527
$965$	7.42339e31	3.41244
$966$	1.28111e31	0.582540
$967$	1.33121e31	0.598780	0.299390	−	0.954131i	$-0.403217\pi$
$967$	1.33121e31	0.598780	0.299390	+	0.954131i	$0.403217\pi$
$968$	6.86896e30	0.305633
$969$	−6.56638e30	−0.289019
$970$	−4.10186e30	−0.178598
$971$	9.71774e30	0.418565	0.209283	−	0.977855i	$-0.432887\pi$
$971$	9.71774e30	0.418565	0.209283	+	0.977855i	$0.432887\pi$
$972$	−6.38091e29	−0.0271886
$973$	4.68806e30	0.197610
$974$	−1.83881e31	−0.766773
$975$	9.64053e30	0.397697
$976$	−2.35932e31	−0.962861
$977$	−1.40637e31	−0.567816	−0.283908	−	0.958851i	$-0.591631\pi$
$977$	−1.40637e31	−0.567816	−0.283908	+	0.958851i	$0.591631\pi$
$978$	4.93351e30	0.197060
$979$	−2.66785e30	−0.105425
$980$	9.91222e30	0.387523
$981$	−1.44240e31	−0.557906
$982$	2.90414e31	1.11134
$983$	−4.87291e31	−1.84492	−0.922458	−	0.386098i	$-0.873823\pi$
$983$	−4.87291e31	−1.84492	−0.922458	+	0.386098i	$0.873823\pi$
$984$	−2.69301e30	−0.100877
$985$	−7.92741e31	−2.93799
$986$	−2.88343e31	−1.05731
$987$	−9.01495e30	−0.327064
$988$	−1.57074e30	−0.0563841
$989$	1.67410e31	0.594594
$990$	1.60360e31	0.563543
$991$	1.17847e30	0.0409773	0.0204887	−	0.999790i	$-0.493478\pi$
$991$	1.17847e30	0.0409773	0.0204887	+	0.999790i	$0.493478\pi$
$992$	3.48741e31	1.19986
$993$	−1.50926e31	−0.513803
$994$	−1.89685e31	−0.638965
$995$	−5.98838e31	−1.99603
$996$	−2.07334e30	−0.0683829
$997$	5.05438e31	1.64956	0.824781	−	0.565453i	$-0.191299\pi$
$997$	5.05438e31	1.64956	0.824781	+	0.565453i	$0.191299\pi$
$998$	−8.85229e30	−0.285881
$999$	−7.09089e29	−0.0226602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3.22.a.b.1.1	✓	1
3.2	odd	2		9.22.a.a.1.1		1
4.3	odd	2		48.22.a.d.1.1		1
5.2	odd	4		75.22.b.b.49.2		2
5.3	odd	4		75.22.b.b.49.1		2
5.4	even	2		75.22.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.22.a.b.1.1	✓	1	1.1	even	1	trivial
9.22.a.a.1.1		1	3.2	odd	2
48.22.a.d.1.1		1	4.3	odd	2
75.22.a.a.1.1		1	5.4	even	2
75.22.b.b.49.1		2	5.3	odd	4
75.22.b.b.49.2		2	5.2	odd	4

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:	\( N \)	\(=\)	\( 3 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	3.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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