LMFDB - Embedded newform 2.30.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2,30,Mod(1,2)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 30, names="a")

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

chi := DirichletCharacter("2.1");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 2 $
Weight:	$ k $	$=$	$ 30 $
Character orbit:	$[\chi]$	$=$	2.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$10.6556084766$
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	$\chi$	$=$	2.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-16384.0 q^{2} -2.79256e6 q^{3} +2.68435e8 q^{4} +6.65186e9 q^{5} +4.57532e10 q^{6} +1.43252e12 q^{7} -4.39805e12 q^{8} -6.08320e13 q^{9} +O(q^{10})$

\(q-16384.0 q^{2} -2.79256e6 q^{3} +2.68435e8 q^{4} +6.65186e9 q^{5} +4.57532e10 q^{6} +1.43252e12 q^{7} -4.39805e12 q^{8} -6.08320e13 q^{9} -1.08984e14 q^{10} -7.77023e14 q^{11} -7.49621e14 q^{12} -2.70958e16 q^{13} -2.34704e16 q^{14} -1.85757e16 q^{15} +7.20576e16 q^{16} +6.23720e17 q^{17} +9.96672e17 q^{18} +2.33976e16 q^{19} +1.78559e18 q^{20} -4.00039e18 q^{21} +1.27307e19 q^{22} -1.01962e20 q^{23} +1.22818e19 q^{24} -1.42017e20 q^{25} +4.43937e20 q^{26} +3.61531e20 q^{27} +3.84539e20 q^{28} -1.93843e20 q^{29} +3.04344e20 q^{30} -4.41169e21 q^{31} -1.18059e21 q^{32} +2.16988e21 q^{33} -1.02190e22 q^{34} +9.52891e21 q^{35} -1.63295e22 q^{36} +6.84647e22 q^{37} -3.83346e20 q^{38} +7.56664e22 q^{39} -2.92552e22 q^{40} -1.30597e23 q^{41} +6.55424e22 q^{42} -6.55176e23 q^{43} -2.08580e23 q^{44} -4.04646e23 q^{45} +1.67054e24 q^{46} +1.88349e24 q^{47} -2.01225e23 q^{48} -1.16780e24 q^{49} +2.32681e24 q^{50} -1.74177e24 q^{51} -7.27346e24 q^{52} +6.52990e24 q^{53} -5.92332e24 q^{54} -5.16864e24 q^{55} -6.30028e24 q^{56} -6.53390e22 q^{57} +3.17592e24 q^{58} +4.48941e25 q^{59} -4.98637e24 q^{60} +3.53091e25 q^{61} +7.22812e25 q^{62} -8.71430e25 q^{63} +1.93428e25 q^{64} -1.80237e26 q^{65} -3.55513e25 q^{66} -3.83658e26 q^{67} +1.67429e26 q^{68} +2.84733e26 q^{69} -1.56122e26 q^{70} +7.28985e26 q^{71} +2.67542e26 q^{72} +7.24287e26 q^{73} -1.12173e27 q^{74} +3.96591e26 q^{75} +6.28073e24 q^{76} -1.11310e27 q^{77} -1.23972e27 q^{78} -2.01341e27 q^{79} +4.79317e26 q^{80} +3.16533e27 q^{81} +2.13971e27 q^{82} -7.23674e27 q^{83} -1.07385e27 q^{84} +4.14890e27 q^{85} +1.07344e28 q^{86} +5.41317e26 q^{87} +3.41738e27 q^{88} +1.35782e28 q^{89} +6.62972e27 q^{90} -3.88152e28 q^{91} -2.73701e28 q^{92} +1.23199e28 q^{93} -3.08591e28 q^{94} +1.55637e26 q^{95} +3.29687e27 q^{96} +2.25184e28 q^{97} +1.91332e28 q^{98} +4.72678e28 q^{99} +O(q^{100})\)

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 $

$2$	−16384.0	−0.707107
$2$	−16384.0	−0.707107
$3$	−2.79256e6	−0.337088	−0.168544	−	0.985694i	$-0.553907\pi$
$3$	−2.79256e6	−0.337088	−0.168544	+	0.985694i	$0.553907\pi$
$4$	2.68435e8	0.500000
$5$	6.65186e9	0.487391	0.243696	−	0.969852i	$-0.421640\pi$
$5$	6.65186e9	0.487391	0.243696	+	0.969852i	$0.421640\pi$
$6$	4.57532e10	0.238357
$7$	1.43252e12	0.798323	0.399162	−	0.916881i	$-0.369301\pi$
$7$	1.43252e12	0.798323	0.399162	+	0.916881i	$0.369301\pi$
$8$	−4.39805e12	−0.353553
$9$	−6.08320e13	−0.886371
$10$	−1.08984e14	−0.344638
$11$	−7.77023e14	−0.616935	−0.308468	−	0.951235i	$-0.599816\pi$
$11$	−7.77023e14	−0.616935	−0.308468	+	0.951235i	$0.599816\pi$
$12$	−7.49621e14	−0.168544
$13$	−2.70958e16	−1.90863	−0.954317	−	0.298797i	$-0.903415\pi$
$13$	−2.70958e16	−1.90863	−0.954317	+	0.298797i	$0.903415\pi$
$14$	−2.34704e16	−0.564500
$15$	−1.85757e16	−0.164294
$16$	7.20576e16	0.250000
$17$	6.23720e17	0.898422	0.449211	−	0.893426i	$-0.351705\pi$
$17$	6.23720e17	0.898422	0.449211	+	0.893426i	$0.351705\pi$
$18$	9.96672e17	0.626759
$19$	2.33976e16	0.00671805	0.00335903	−	0.999994i	$-0.498931\pi$
$19$	2.33976e16	0.00671805	0.00335903	+	0.999994i	$0.498931\pi$
$20$	1.78559e18	0.243696
$21$	−4.00039e18	−0.269105
$22$	1.27307e19	0.436239
$23$	−1.01962e20	−1.83393	−0.916965	−	0.398968i	$-0.869368\pi$
$23$	−1.01962e20	−1.83393	−0.916965	+	0.398968i	$0.869368\pi$
$24$	1.22818e19	0.119179
$25$	−1.42017e20	−0.762450
$26$	4.43937e20	1.34961
$27$	3.61531e20	0.635874
$28$	3.84539e20	0.399162
$29$	−1.93843e20	−0.120970	−0.0604851	−	0.998169i	$-0.519265\pi$
$29$	−1.93843e20	−0.120970	−0.0604851	+	0.998169i	$0.519265\pi$
$30$	3.04344e20	0.116173
$31$	−4.41169e21	−1.04679	−0.523396	−	0.852089i	$-0.675335\pi$
$31$	−4.41169e21	−1.04679	−0.523396	+	0.852089i	$0.675335\pi$
$32$	−1.18059e21	−0.176777
$33$	2.16988e21	0.207962
$34$	−1.02190e22	−0.635281
$35$	9.52891e21	0.389096
$36$	−1.63295e22	−0.443186
$37$	6.84647e22	1.24894	0.624470	−	0.781049i	$-0.285315\pi$
$37$	6.84647e22	1.24894	0.624470	+	0.781049i	$0.285315\pi$
$38$	−3.83346e20	−0.00475038
$39$	7.56664e22	0.643378
$40$	−2.92552e22	−0.172319
$41$	−1.30597e23	−0.537735	−0.268868	−	0.963177i	$-0.586649\pi$
$41$	−1.30597e23	−0.537735	−0.268868	+	0.963177i	$0.586649\pi$
$42$	6.55424e22	0.190286
$43$	−6.55176e23	−1.35228	−0.676138	−	0.736775i	$-0.736348\pi$
$43$	−6.55176e23	−1.35228	−0.676138	+	0.736775i	$0.736348\pi$
$44$	−2.08580e23	−0.308468
$45$	−4.04646e23	−0.432010
$46$	1.67054e24	1.29678
$47$	1.88349e24	1.07039	0.535197	−	0.844727i	$-0.320237\pi$
$47$	1.88349e24	1.07039	0.535197	+	0.844727i	$0.320237\pi$
$48$	−2.01225e23	−0.0842721
$49$	−1.16780e24	−0.362680
$50$	2.32681e24	0.539133
$51$	−1.74177e24	−0.302848
$52$	−7.27346e24	−0.954317
$53$	6.52990e24	0.649990	0.324995	−	0.945716i	$-0.394637\pi$
$53$	6.52990e24	0.649990	0.324995	+	0.945716i	$0.394637\pi$
$54$	−5.92332e24	−0.449631
$55$	−5.16864e24	−0.300689
$56$	−6.30028e24	−0.282250
$57$	−6.53390e22	−0.00226458
$58$	3.17592e24	0.0855389
$59$	4.48941e25	0.943702	0.471851	−	0.881678i	$-0.343586\pi$
$59$	4.48941e25	0.943702	0.471851	+	0.881678i	$0.343586\pi$
$60$	−4.98637e24	−0.0821470
$61$	3.53091e25	0.457725	0.228862	−	0.973459i	$-0.426499\pi$
$61$	3.53091e25	0.457725	0.228862	+	0.973459i	$0.426499\pi$
$62$	7.22812e25	0.740194
$63$	−8.71430e25	−0.707611
$64$	1.93428e25	0.125000
$65$	−1.80237e26	−0.930252
$66$	−3.55513e25	−0.147051
$67$	−3.83658e26	−1.27603	−0.638014	−	0.770025i	$-0.720244\pi$
$67$	−3.83658e26	−1.27603	−0.638014	+	0.770025i	$0.720244\pi$
$68$	1.67429e26	0.449211
$69$	2.84733e26	0.618196
$70$	−1.56122e26	−0.275132
$71$	7.28985e26	1.04586	0.522929	−	0.852376i	$-0.324839\pi$
$71$	7.28985e26	1.04586	0.522929	+	0.852376i	$0.324839\pi$
$72$	2.67542e26	0.313380
$73$	7.24287e26	0.694591	0.347295	−	0.937756i	$-0.387100\pi$
$73$	7.24287e26	0.694591	0.347295	+	0.937756i	$0.387100\pi$
$74$	−1.12173e27	−0.883134
$75$	3.96591e26	0.257013
$76$	6.28073e24	0.00335903
$77$	−1.11310e27	−0.492514
$78$	−1.23972e27	−0.454937
$79$	−2.01341e27	−0.614242	−0.307121	−	0.951670i	$-0.599366\pi$
$79$	−2.01341e27	−0.614242	−0.307121	+	0.951670i	$0.599366\pi$
$80$	4.79317e26	0.121848
$81$	3.16533e27	0.672026
$82$	2.13971e27	0.380236
$83$	−7.23674e27	−1.07872	−0.539362	−	0.842074i	$-0.681335\pi$
$83$	−7.23674e27	−1.07872	−0.539362	+	0.842074i	$0.681335\pi$
$84$	−1.07385e27	−0.134553
$85$	4.14890e27	0.437883
$86$	1.07344e28	0.956204
$87$	5.41317e26	0.0407777
$88$	3.41738e27	0.218120
$89$	1.35782e28	0.735674	0.367837	−	0.929890i	$-0.380098\pi$
$89$	1.35782e28	0.735674	0.367837	+	0.929890i	$0.380098\pi$
$90$	6.62972e27	0.305477
$91$	−3.88152e28	−1.52371
$92$	−2.73701e28	−0.916965
$93$	1.23199e28	0.352862
$94$	−3.08591e28	−0.756883
$95$	1.55637e26	0.00327432
$96$	3.29687e27	0.0595894
$97$	2.25184e28	0.350225	0.175112	−	0.984548i	$-0.443971\pi$
$97$	2.25184e28	0.350225	0.175112	+	0.984548i	$0.443971\pi$
$98$	1.91332e28	0.256454
$99$	4.72678e28	0.546834
$100$	−3.81225e28	−0.381225
$101$	2.22681e29	1.92762	0.963812	−	0.266583i	$-0.0858945\pi$
$101$	2.22681e29	1.92762	0.963812	+	0.266583i	$0.0858945\pi$
$102$	2.85372e28	0.214146
$103$	−2.93841e29	−1.91413	−0.957067	−	0.289865i	$-0.906389\pi$
$103$	−2.93841e29	−1.91413	−0.957067	+	0.289865i	$0.906389\pi$
$104$	1.19168e29	0.674804
$105$	−2.66100e28	−0.131160
$106$	−1.06986e29	−0.459612
$107$	−1.80718e29	−0.677544	−0.338772	−	0.940868i	$-0.610012\pi$
$107$	−1.80718e29	−0.677544	−0.338772	+	0.940868i	$0.610012\pi$
$108$	9.70477e28	0.317937
$109$	−1.59004e29	−0.455747	−0.227874	−	0.973691i	$-0.573177\pi$
$109$	−1.59004e29	−0.455747	−0.227874	+	0.973691i	$0.573177\pi$
$110$	8.46830e28	0.212619
$111$	−1.91192e29	−0.421003
$112$	1.03224e29	0.199581
$113$	6.49105e29	1.10326	0.551630	−	0.834089i	$-0.314006\pi$
$113$	6.49105e29	1.10326	0.551630	+	0.834089i	$0.314006\pi$
$114$	1.07051e27	0.00160130
$115$	−6.78233e29	−0.893841
$116$	−5.20343e28	−0.0604851
$117$	1.64829e30	1.69176
$118$	−7.35545e29	−0.667298
$119$	8.93491e29	0.717231
$120$	8.16967e28	0.0580867
$121$	−9.82545e29	−0.619391
$122$	−5.78505e29	−0.323660
$123$	3.64701e29	0.181264
$124$	−1.18425e30	−0.523396
$125$	−2.18368e30	−0.859003
$126$	1.42775e30	0.500356
$127$	−3.49190e30	−1.09121	−0.545604	−	0.838043i	$-0.683700\pi$
$127$	−3.49190e30	−1.09121	−0.545604	+	0.838043i	$0.683700\pi$
$128$	−3.16913e29	−0.0883883
$129$	1.82962e30	0.455837
$130$	2.95300e30	0.657787
$131$	5.19973e30	1.03645	0.518223	−	0.855245i	$-0.326594\pi$
$131$	5.19973e30	1.03645	0.518223	+	0.855245i	$0.326594\pi$
$132$	5.82473e29	0.103981
$133$	3.35174e28	0.00536318
$134$	6.28586e30	0.902288
$135$	2.40485e30	0.309919
$136$	−2.74315e30	−0.317640
$137$	−1.42627e31	−1.48510	−0.742549	−	0.669792i	$-0.766383\pi$
$137$	−1.42627e31	−1.48510	−0.742549	+	0.669792i	$0.766383\pi$
$138$	−4.66507e30	−0.437131
$139$	8.85960e28	0.00747652	0.00373826	−	0.999993i	$-0.498810\pi$
$139$	8.85960e28	0.00747652	0.00373826	+	0.999993i	$0.498810\pi$
$140$	2.55790e30	0.194548
$141$	−5.25974e30	−0.360817
$142$	−1.19437e31	−0.739533
$143$	2.10540e31	1.17750
$144$	−4.38341e30	−0.221593
$145$	−1.28941e30	−0.0589599
$146$	−1.18667e31	−0.491150
$147$	3.26114e30	0.122255
$148$	1.83784e31	0.624470
$149$	1.66266e31	0.512391	0.256195	−	0.966625i	$-0.417531\pi$
$149$	1.66266e31	0.512391	0.256195	+	0.966625i	$0.417531\pi$
$150$	−6.49775e30	−0.181736
$151$	3.87352e31	0.983874	0.491937	−	0.870631i	$-0.336289\pi$
$151$	3.87352e31	0.983874	0.491937	+	0.870631i	$0.336289\pi$
$152$	−1.02904e29	−0.00237519
$153$	−3.79422e31	−0.796336
$154$	1.82370e31	0.348260
$155$	−2.93459e31	−0.510198
$156$	2.03115e31	0.321689
$157$	−3.42328e31	−0.494194	−0.247097	−	0.968991i	$-0.579477\pi$
$157$	−3.42328e31	−0.494194	−0.247097	+	0.968991i	$0.579477\pi$
$158$	3.29877e31	0.434335
$159$	−1.82351e31	−0.219104
$160$	−7.85313e30	−0.0861594
$161$	−1.46062e32	−1.46407
$162$	−5.18607e31	−0.475194
$163$	1.22833e32	1.02942	0.514712	−	0.857363i	$-0.327899\pi$
$163$	1.22833e32	1.02942	0.514712	+	0.857363i	$0.327899\pi$
$164$	−3.50570e31	−0.268868
$165$	1.44337e31	0.101359
$166$	1.18567e32	0.762773
$167$	−1.08585e32	−0.640299	−0.320149	−	0.947367i	$-0.603733\pi$
$167$	−1.08585e32	−0.640299	−0.320149	+	0.947367i	$0.603733\pi$
$168$	1.75939e31	0.0951431
$169$	5.32642e32	2.64288
$170$	−6.79756e31	−0.309630
$171$	−1.42332e30	−0.00595469
$172$	−1.75873e32	−0.676138
$173$	−8.13504e30	−0.0287535	−0.0143768	−	0.999897i	$-0.504576\pi$
$173$	−8.13504e30	−0.0287535	−0.0143768	+	0.999897i	$0.504576\pi$
$174$	−8.86894e30	−0.0288342
$175$	−2.03442e32	−0.608681
$176$	−5.59904e31	−0.154234
$177$	−1.25369e32	−0.318111
$178$	−2.22464e32	−0.520200
$179$	−3.91205e32	−0.843403	−0.421702	−	0.906735i	$-0.638567\pi$
$179$	−3.91205e32	−0.843403	−0.421702	+	0.906735i	$0.638567\pi$
$180$	−1.08621e32	−0.216005
$181$	1.26477e32	0.232099	0.116049	−	0.993243i	$-0.462977\pi$
$181$	1.26477e32	0.232099	0.116049	+	0.993243i	$0.462977\pi$
$182$	6.35948e32	1.07742
$183$	−9.86027e31	−0.154294
$184$	4.48431e32	0.648392
$185$	4.55417e32	0.608723
$186$	−2.01849e32	−0.249511
$187$	−4.84645e32	−0.554269
$188$	5.05595e32	0.535197
$189$	5.17900e32	0.507633
$190$	−2.54996e30	−0.00231529
$191$	−2.30536e32	−0.193979	−0.0969896	−	0.995285i	$-0.530921\pi$
$191$	−2.30536e32	−0.193979	−0.0969896	+	0.995285i	$0.530921\pi$
$192$	−5.40159e31	−0.0421360
$193$	−4.30456e32	−0.311421	−0.155711	−	0.987803i	$-0.549767\pi$
$193$	−4.30456e32	−0.311421	−0.155711	+	0.987803i	$0.549767\pi$
$194$	−3.68941e32	−0.247646
$195$	5.03322e32	0.313577
$196$	−3.13478e32	−0.181340
$197$	2.20727e32	0.118603	0.0593013	−	0.998240i	$-0.481113\pi$
$197$	2.20727e32	0.118603	0.0593013	+	0.998240i	$0.481113\pi$
$198$	−7.74436e32	−0.386670
$199$	−1.28486e33	−0.596331	−0.298165	−	0.954514i	$-0.596375\pi$
$199$	−1.28486e33	−0.596331	−0.298165	+	0.954514i	$0.596375\pi$
$200$	6.24599e32	0.269567
$201$	1.07139e33	0.430134
$202$	−3.64840e33	−1.36304
$203$	−2.77683e32	−0.0965734
$204$	−4.67554e32	−0.151424
$205$	−8.68715e32	−0.262088
$206$	4.81429e33	1.35350
$207$	6.20252e33	1.62554
$208$	−1.95245e33	−0.477158
$209$	−1.81804e31	−0.00414460
$210$	4.35978e32	0.0927439
$211$	9.42940e32	0.187236	0.0936178	−	0.995608i	$-0.470157\pi$
$211$	9.42940e32	0.187236	0.0936178	+	0.995608i	$0.470157\pi$
$212$	1.75286e33	0.324995
$213$	−2.03573e33	−0.352547
$214$	2.96089e33	0.479096
$215$	−4.35814e33	−0.659088
$216$	−1.59003e33	−0.224815
$217$	−6.31983e33	−0.835679
$218$	2.60512e33	0.322262
$219$	−2.02261e33	−0.234138
$220$	−1.38745e33	−0.150344
$221$	−1.69002e34	−1.71476
$222$	3.13248e33	0.297694
$223$	7.89801e33	0.703229	0.351615	−	0.936145i	$-0.385633\pi$
$223$	7.89801e33	0.703229	0.351615	+	0.936145i	$0.385633\pi$
$224$	−1.69122e33	−0.141125
$225$	8.63920e33	0.675814
$226$	−1.06349e34	−0.780122
$227$	1.89655e34	1.30493	0.652467	−	0.757817i	$-0.273734\pi$
$227$	1.89655e34	1.30493	0.652467	+	0.757817i	$0.273734\pi$
$228$	−1.75393e31	−0.00113229
$229$	1.80669e34	1.09463	0.547316	−	0.836926i	$-0.315650\pi$
$229$	1.80669e34	1.09463	0.547316	+	0.836926i	$0.315650\pi$
$230$	1.11122e34	0.632041
$231$	3.10839e33	0.166021
$232$	8.52530e32	0.0427695
$233$	−2.63861e34	−1.24370	−0.621849	−	0.783137i	$-0.713618\pi$
$233$	−2.63861e34	−1.24370	−0.621849	+	0.783137i	$0.713618\pi$
$234$	−2.70056e34	−1.19625
$235$	1.25287e34	0.521701
$236$	1.20512e34	0.471851
$237$	5.62256e33	0.207054
$238$	−1.46390e34	−0.507159
$239$	−1.60955e34	−0.524728	−0.262364	−	0.964969i	$-0.584502\pi$
$239$	−1.60955e34	−0.524728	−0.262364	+	0.964969i	$0.584502\pi$
$240$	−1.33852e33	−0.0410735
$241$	−5.02213e31	−0.00145091	−0.000725456	−	1.00000i	$-0.500231\pi$
$241$	−5.02213e31	−0.00145091	−0.000725456		1.00000i	$0.500231\pi$
$242$	1.60980e34	0.437975
$243$	−3.36514e34	−0.862406
$244$	9.47822e33	0.228862
$245$	−7.76802e33	−0.176767
$246$	−5.97525e33	−0.128173
$247$	−6.33974e32	−0.0128223
$248$	1.94028e34	0.370097
$249$	2.02090e34	0.363625
$250$	3.57775e34	0.607407
$251$	−5.87216e34	−0.940869	−0.470434	−	0.882435i	$-0.655903\pi$
$251$	−5.87216e34	−0.940869	−0.470434	+	0.882435i	$0.655903\pi$
$252$	−2.33923e34	−0.353805
$253$	7.92264e34	1.13142
$254$	5.72113e34	0.771601
$255$	−1.15860e34	−0.147605
$256$	5.19230e33	0.0625000
$257$	1.32349e34	0.150553	0.0752767	−	0.997163i	$-0.476016\pi$
$257$	1.32349e34	0.150553	0.0752767	+	0.997163i	$0.476016\pi$
$258$	−2.99764e34	−0.322325
$259$	9.80770e34	0.997058
$260$	−4.83820e34	−0.465126
$261$	1.17918e34	0.107225
$262$	−8.51924e34	−0.732878
$263$	−2.27613e35	−1.85284	−0.926422	−	0.376486i	$-0.877132\pi$
$263$	−2.27613e35	−1.85284	−0.926422	+	0.376486i	$0.877132\pi$
$264$	−9.54323e33	−0.0735256
$265$	4.34360e34	0.316799
$266$	−5.49150e32	−0.00379234
$267$	−3.79178e34	−0.247987
$268$	−1.02988e35	−0.638014
$269$	8.55442e34	0.502091	0.251046	−	0.967975i	$-0.419226\pi$
$269$	8.55442e34	0.502091	0.251046	+	0.967975i	$0.419226\pi$
$270$	−3.94011e34	−0.219146
$271$	1.12405e35	0.592556	0.296278	−	0.955102i	$-0.404254\pi$
$271$	1.12405e35	0.592556	0.296278	+	0.955102i	$0.404254\pi$
$272$	4.49438e34	0.224606
$273$	1.08394e35	0.513624
$274$	2.33681e35	1.05012
$275$	1.10351e35	0.470382
$276$	7.64325e34	0.309098
$277$	−2.97851e35	−1.14299	−0.571495	−	0.820605i	$-0.693636\pi$
$277$	−2.97851e35	−1.14299	−0.571495	+	0.820605i	$0.693636\pi$
$278$	−1.45156e33	−0.00528670
$279$	2.68372e35	0.927847
$280$	−4.19086e34	−0.137566
$281$	−3.63080e34	−0.113178	−0.0565889	−	0.998398i	$-0.518022\pi$
$281$	−3.63080e34	−0.113178	−0.0565889	+	0.998398i	$0.518022\pi$
$282$	8.61756e34	0.255136
$283$	−5.66565e35	−1.59348	−0.796739	−	0.604324i	$-0.793443\pi$
$283$	−5.66565e35	−1.59348	−0.796739	+	0.604324i	$0.793443\pi$
$284$	1.95686e35	0.522929
$285$	−4.34626e32	−0.00110374
$286$	−3.44949e35	−0.832621
$287$	−1.87083e35	−0.429286
$288$	7.18178e34	0.156690
$289$	−9.29415e34	−0.192837
$290$	2.11258e34	0.0416909
$291$	−6.28838e34	−0.118057
$292$	1.94424e35	0.347295
$293$	5.56965e34	0.0946777	0.0473389	−	0.998879i	$-0.484926\pi$
$293$	5.56965e34	0.0946777	0.0473389	+	0.998879i	$0.484926\pi$
$294$	−5.34305e34	−0.0864476
$295$	2.98629e35	0.459952
$296$	−3.01111e35	−0.441567
$297$	−2.80918e35	−0.392293
$298$	−2.72409e35	−0.362315
$299$	2.76272e36	3.50030
$300$	1.06459e35	0.128506
$301$	−9.38552e35	−1.07955
$302$	−6.34637e35	−0.695704
$303$	−6.21848e35	−0.649780
$304$	1.68597e33	0.00167951
$305$	2.34871e35	0.223091
$306$	6.21644e35	0.563095
$307$	2.86613e35	0.247622	0.123811	−	0.992306i	$-0.460488\pi$
$307$	2.86613e35	0.247622	0.123811	+	0.992306i	$0.460488\pi$
$308$	−2.98795e35	−0.246257
$309$	8.20567e35	0.645232
$310$	4.80804e35	0.360764
$311$	−1.26179e36	−0.903569	−0.451785	−	0.892127i	$-0.649212\pi$
$311$	−1.26179e36	−0.903569	−0.451785	+	0.892127i	$0.649212\pi$
$312$	−3.32784e35	−0.227469
$313$	−1.73714e36	−1.13355	−0.566777	−	0.823871i	$-0.691810\pi$
$313$	−1.73714e36	−1.13355	−0.566777	+	0.823871i	$0.691810\pi$
$314$	5.60870e35	0.349448
$315$	−5.79663e35	−0.344883
$316$	−5.40471e35	−0.307121
$317$	−1.70738e36	−0.926767	−0.463383	−	0.886158i	$-0.653365\pi$
$317$	−1.70738e36	−0.926767	−0.463383	+	0.886158i	$0.653365\pi$
$318$	2.98764e35	0.154930
$319$	1.50620e35	0.0746309
$320$	1.28666e35	0.0609239
$321$	5.04666e35	0.228392
$322$	2.39308e36	1.03525
$323$	1.45935e34	0.00603565
$324$	8.49686e35	0.336013
$325$	3.84807e36	1.45524
$326$	−2.01249e36	−0.727913
$327$	4.44028e35	0.153627
$328$	5.74373e35	0.190118
$329$	2.69813e36	0.854520
$330$	−2.36482e35	−0.0716715
$331$	4.49483e34	0.0130379	0.00651894	−	0.999979i	$-0.497925\pi$
$331$	4.49483e34	0.0130379	0.00651894	+	0.999979i	$0.497925\pi$
$332$	−1.94260e36	−0.539362
$333$	−4.16485e36	−1.10703
$334$	1.77906e36	0.452759
$335$	−2.55204e36	−0.621925
$336$	−2.88258e35	−0.0672763
$337$	2.90611e36	0.649648	0.324824	−	0.945775i	$-0.394695\pi$
$337$	2.90611e36	0.649648	0.324824	+	0.945775i	$0.394695\pi$
$338$	−8.72680e36	−1.86880
$339$	−1.81266e36	−0.371896
$340$	1.11371e36	0.218942
$341$	3.42799e36	0.645804
$342$	2.33197e34	0.00421060
$343$	−6.28546e36	−1.08786
$344$	2.88150e36	0.478102
$345$	1.89400e36	0.301303
$346$	1.33284e35	0.0203318
$347$	6.84729e36	1.00171	0.500854	−	0.865532i	$-0.333019\pi$
$347$	6.84729e36	1.00171	0.500854	+	0.865532i	$0.333019\pi$
$348$	1.45309e35	0.0203888
$349$	8.63782e36	1.16261	0.581307	−	0.813685i	$-0.302542\pi$
$349$	8.63782e36	1.16261	0.581307	+	0.813685i	$0.302542\pi$
$350$	3.33320e36	0.430403
$351$	−9.79595e36	−1.21365
$352$	9.17346e35	0.109060
$353$	−6.18156e36	−0.705285	−0.352642	−	0.935758i	$-0.614717\pi$
$353$	−6.18156e36	−0.705285	−0.352642	+	0.935758i	$0.614717\pi$
$354$	2.05405e36	0.224938
$355$	4.84911e36	0.509742
$356$	3.64486e36	0.367837
$357$	−2.49512e36	−0.241770
$358$	6.40950e36	0.596376
$359$	−6.34728e35	−0.0567176	−0.0283588	−	0.999598i	$-0.509028\pi$
$359$	−6.34728e35	−0.0567176	−0.0283588	+	0.999598i	$0.509028\pi$
$360$	1.77965e36	0.152739
$361$	−1.21293e37	−0.999955
$362$	−2.07220e36	−0.164118
$363$	2.74381e36	0.208789
$364$	−1.04194e37	−0.761853
$365$	4.81785e36	0.338538
$366$	1.61551e36	0.109102
$367$	−1.26942e37	−0.824041	−0.412020	−	0.911175i	$-0.635177\pi$
$367$	−1.26942e37	−0.824041	−0.412020	+	0.911175i	$0.635177\pi$
$368$	−7.34710e36	−0.458482
$369$	7.94450e36	0.476633
$370$	−7.46156e36	−0.430432
$371$	9.35421e36	0.518902
$372$	3.30710e36	0.176431
$373$	−1.44149e37	−0.739663	−0.369831	−	0.929099i	$-0.620585\pi$
$373$	−1.44149e37	−0.739663	−0.369831	+	0.929099i	$0.620585\pi$
$374$	7.94042e36	0.391927
$375$	6.09806e36	0.289560
$376$	−8.28366e36	−0.378441
$377$	5.25232e36	0.230888
$378$	−8.48527e36	−0.358951
$379$	4.26310e37	1.73563	0.867815	−	0.496887i	$-0.165524\pi$
$379$	4.26310e37	1.73563	0.867815	+	0.496887i	$0.165524\pi$
$380$	4.17785e34	0.00163716
$381$	9.75133e36	0.367834
$382$	3.77710e36	0.137164
$383$	−6.28792e36	−0.219849	−0.109925	−	0.993940i	$-0.535061\pi$
$383$	−6.28792e36	−0.219849	−0.109925	+	0.993940i	$0.535061\pi$
$384$	8.84996e35	0.0297947
$385$	−7.40418e36	−0.240047
$386$	7.05260e36	0.220208
$387$	3.98557e37	1.19862
$388$	6.04473e36	0.175112
$389$	−3.51582e37	−0.981200	−0.490600	−	0.871385i	$-0.663222\pi$
$389$	−3.51582e37	−0.981200	−0.490600	+	0.871385i	$0.663222\pi$
$390$	−8.24643e36	−0.221732
$391$	−6.35955e37	−1.64764
$392$	5.13602e36	0.128227
$393$	−1.45205e37	−0.349374
$394$	−3.61638e36	−0.0838647
$395$	−1.33929e37	−0.299376
$396$	1.26884e37	0.273417
$397$	−6.72150e37	−1.39638	−0.698190	−	0.715913i	$-0.746011\pi$
$397$	−6.72150e37	−1.39638	−0.698190	+	0.715913i	$0.746011\pi$
$398$	2.10512e37	0.421669
$399$	−9.35993e34	−0.00180786
$400$	−1.02334e37	−0.190612
$401$	1.74160e37	0.312863	0.156432	−	0.987689i	$-0.450001\pi$
$401$	1.74160e37	0.312863	0.156432	+	0.987689i	$0.450001\pi$
$402$	−1.75536e37	−0.304151
$403$	1.19538e38	1.99794
$404$	5.97754e37	0.963812
$405$	2.10553e37	0.327540
$406$	4.54957e36	0.0682877
$407$	−5.31986e37	−0.770516
$408$	7.66040e36	0.107073
$409$	2.48596e37	0.335355	0.167678	−	0.985842i	$-0.446373\pi$
$409$	2.48596e37	0.335355	0.167678	+	0.985842i	$0.446373\pi$
$410$	1.42330e37	0.185324
$411$	3.98295e37	0.500609
$412$	−7.88773e37	−0.957067
$413$	6.43116e37	0.753379
$414$	−1.01622e38	−1.14943
$415$	−4.81377e37	−0.525761
$416$	3.19890e37	0.337402
$417$	−2.47409e35	−0.00252025
$418$	2.97868e35	0.00293068
$419$	−5.65207e37	−0.537161	−0.268580	−	0.963257i	$-0.586555\pi$
$419$	−5.65207e37	−0.537161	−0.268580	+	0.963257i	$0.586555\pi$
$420$	−7.14307e36	−0.0655798
$421$	1.35712e38	1.20373	0.601865	−	0.798598i	$-0.294425\pi$
$421$	1.35712e38	1.20373	0.601865	+	0.798598i	$0.294425\pi$
$422$	−1.54491e37	−0.132396
$423$	−1.14576e38	−0.948767
$424$	−2.87188e37	−0.229806
$425$	−8.85791e37	−0.685002
$426$	3.33534e37	0.249288
$427$	5.05810e37	0.365412
$428$	−4.85112e37	−0.338772
$429$	−5.87945e37	−0.396923
$430$	7.14037e37	0.466045
$431$	−1.25590e38	−0.792562	−0.396281	−	0.918129i	$-0.629699\pi$
$431$	−1.25590e38	−0.792562	−0.396281	+	0.918129i	$0.629699\pi$
$432$	2.60511e37	0.158968
$433$	2.60317e38	1.53613	0.768065	−	0.640371i	$-0.221220\pi$
$433$	2.60317e38	1.53613	0.768065	+	0.640371i	$0.221220\pi$
$434$	1.03544e38	0.590914
$435$	3.60076e36	0.0198747
$436$	−4.26823e37	−0.227874
$437$	−2.38565e36	−0.0123204
$438$	3.31385e37	0.165561
$439$	−2.54018e38	−1.22780	−0.613901	−	0.789383i	$-0.710401\pi$
$439$	−2.54018e38	−1.22780	−0.613901	+	0.789383i	$0.710401\pi$
$440$	2.27319e37	0.106310
$441$	7.10394e37	0.321470
$442$	2.76892e38	1.21252
$443$	2.42259e38	1.02666	0.513329	−	0.858192i	$-0.328412\pi$
$443$	2.42259e38	1.02666	0.513329	+	0.858192i	$0.328412\pi$
$444$	−5.13226e37	−0.210502
$445$	9.03199e37	0.358561
$446$	−1.29401e38	−0.497258
$447$	−4.64306e37	−0.172721
$448$	2.77089e37	0.0997904
$449$	−4.91992e38	−1.71548	−0.857740	−	0.514083i	$-0.828132\pi$
$449$	−4.91992e38	−1.71548	−0.857740	+	0.514083i	$0.828132\pi$
$450$	−1.41545e38	−0.477872
$451$	1.01477e38	0.331748
$452$	1.74243e38	0.551630
$453$	−1.08170e38	−0.331652
$454$	−3.10730e38	−0.922728
$455$	−2.58193e38	−0.742641
$456$	2.87364e35	0.000800649 0
$457$	2.07288e38	0.559487	0.279743	−	0.960075i	$-0.409751\pi$
$457$	2.07288e38	0.559487	0.279743	+	0.960075i	$0.409751\pi$
$458$	−2.96007e38	−0.774021
$459$	2.25494e38	0.571283
$460$	−1.82062e38	−0.446921
$461$	3.62984e38	0.863425	0.431712	−	0.902011i	$-0.357910\pi$
$461$	3.62984e38	0.863425	0.431712	+	0.902011i	$0.357910\pi$
$462$	−5.09279e37	−0.117394
$463$	1.35939e38	0.303682	0.151841	−	0.988405i	$-0.451480\pi$
$463$	1.35939e38	0.303682	0.151841	+	0.988405i	$0.451480\pi$
$464$	−1.39678e37	−0.0302426
$465$	8.19502e37	0.171982
$466$	4.32310e38	0.879427
$467$	5.71729e38	1.12744	0.563722	−	0.825964i	$-0.309369\pi$
$467$	5.71729e38	1.12744	0.563722	+	0.825964i	$0.309369\pi$
$468$	4.42459e38	0.845879
$469$	−5.49598e38	−1.01868
$470$	−2.05270e38	−0.368898
$471$	9.55970e37	0.166587
$472$	−1.97446e38	−0.333649
$473$	5.09087e38	0.834267
$474$	−9.21201e37	−0.146409
$475$	−3.32286e36	−0.00512218
$476$	2.39845e38	0.358616
$477$	−3.97227e38	−0.576132
$478$	2.63708e38	0.371039
$479$	−6.60236e38	−0.901227	−0.450614	−	0.892719i	$-0.648795\pi$
$479$	−6.60236e38	−0.901227	−0.450614	+	0.892719i	$0.648795\pi$
$480$	2.19303e37	0.0290433
$481$	−1.85510e39	−2.38377
$482$	8.22826e35	0.00102595
$483$	4.07886e38	0.493520
$484$	−2.63750e38	−0.309695
$485$	1.49789e38	0.170697
$486$	5.51344e38	0.609813
$487$	−2.40331e38	−0.258012	−0.129006	−	0.991644i	$-0.541179\pi$
$487$	−2.40331e38	−0.258012	−0.129006	+	0.991644i	$0.541179\pi$
$488$	−1.55291e38	−0.161830
$489$	−3.43018e38	−0.347007
$490$	1.27271e38	0.124993
$491$	1.56227e39	1.48962	0.744809	−	0.667278i	$-0.232541\pi$
$491$	1.56227e39	1.48962	0.744809	+	0.667278i	$0.232541\pi$
$492$	9.78985e37	0.0906321
$493$	−1.20904e38	−0.108682
$494$	1.03870e37	0.00906674
$495$	3.14419e38	0.266522
$496$	−3.17896e38	−0.261698
$497$	1.04429e39	0.834933
$498$	−3.31104e38	−0.257122
$499$	−1.40587e39	−1.06044	−0.530222	−	0.847859i	$-0.677891\pi$
$499$	−1.40587e39	−1.06044	−0.530222	+	0.847859i	$0.677891\pi$
$500$	−5.86178e38	−0.429501
$501$	3.03231e38	0.215837
$502$	9.62095e38	0.665295
$503$	1.47502e39	0.990976	0.495488	−	0.868615i	$-0.334989\pi$
$503$	1.47502e39	0.990976	0.495488	+	0.868615i	$0.334989\pi$
$504$	3.83259e38	0.250178
$505$	1.48124e39	0.939507
$506$	−1.29805e39	−0.800032
$507$	−1.48743e39	−0.890885
$508$	−9.37350e38	−0.545604
$509$	7.11334e38	0.402407	0.201204	−	0.979549i	$-0.435515\pi$
$509$	7.11334e38	0.402407	0.201204	+	0.979549i	$0.435515\pi$
$510$	1.89826e38	0.104373
$511$	1.03755e39	0.554508
$512$	−8.50706e37	−0.0441942
$513$	8.45894e36	0.00427183
$514$	−2.16841e38	−0.106457
$515$	−1.95459e39	−0.932933
$516$	4.91134e38	0.227918
$517$	−1.46351e39	−0.660364
$518$	−1.60689e39	−0.705026
$519$	2.27175e37	0.00969248
$520$	7.92691e38	0.328894
$521$	−3.51484e39	−1.41827	−0.709134	−	0.705073i	$-0.750914\pi$
$521$	−3.51484e39	−1.41827	−0.709134	+	0.705073i	$0.750914\pi$
$522$	−1.93198e38	−0.0758193
$523$	1.29307e38	0.0493568	0.0246784	−	0.999695i	$-0.492144\pi$
$523$	1.29307e38	0.0493568	0.0246784	+	0.999695i	$0.492144\pi$
$524$	1.39579e39	0.518223
$525$	5.68124e38	0.205179
$526$	3.72921e39	1.31016
$527$	−2.75166e39	−0.940462
$528$	1.56356e38	0.0519904
$529$	7.30509e39	2.36330
$530$	−7.11655e38	−0.224011
$531$	−2.73100e39	−0.836471
$532$	8.99727e36	0.00268159
$533$	3.53863e39	1.02634
$534$	6.21245e38	0.175353
$535$	−1.20211e39	−0.330229
$536$	1.68735e39	0.451144
$537$	1.09246e39	0.284301
$538$	−1.40156e39	−0.355032
$539$	9.07404e38	0.223750
$540$	6.45548e38	0.154960
$541$	−2.95510e39	−0.690577	−0.345288	−	0.938497i	$-0.612219\pi$
$541$	−2.95510e39	−0.690577	−0.345288	+	0.938497i	$0.612219\pi$
$542$	−1.84164e39	−0.419001
$543$	−3.53194e38	−0.0782377
$544$	−7.36359e38	−0.158820
$545$	−1.05767e39	−0.222127
$546$	−1.77592e39	−0.363187
$547$	5.64187e38	0.112359	0.0561793	−	0.998421i	$-0.482108\pi$
$547$	5.64187e38	0.112359	0.0561793	+	0.998421i	$0.482108\pi$
$548$	−3.82863e39	−0.742549
$549$	−2.14793e39	−0.405714
$550$	−1.80799e39	−0.332610
$551$	−4.53545e36	−0.000812685 0
$552$	−1.25227e39	−0.218565
$553$	−2.88425e39	−0.490364
$554$	4.87999e39	0.808216
$555$	−1.27178e39	−0.205193
$556$	2.37823e37	0.00373826
$557$	2.40790e39	0.368755	0.184378	−	0.982855i	$-0.440973\pi$
$557$	2.40790e39	0.368755	0.184378	+	0.982855i	$0.440973\pi$
$558$	−4.39701e39	−0.656087
$559$	1.77525e40	2.58100
$560$	6.86630e38	0.0972739
$561$	1.35340e39	0.186837
$562$	5.94871e38	0.0800287
$563$	−8.33804e39	−1.09318	−0.546591	−	0.837400i	$-0.684075\pi$
$563$	−8.33804e39	−1.09318	−0.546591	+	0.837400i	$0.684075\pi$
$564$	−1.41190e39	−0.180409
$565$	4.31776e39	0.537719
$566$	9.28259e39	1.12676
$567$	4.53439e39	0.536494
$568$	−3.20611e39	−0.369767
$569$	−7.78796e39	−0.875580	−0.437790	−	0.899077i	$-0.644239\pi$
$569$	−7.78796e39	−0.875580	−0.437790	+	0.899077i	$0.644239\pi$
$570$	7.12091e36	0.000780459 0
$571$	−1.07384e40	−1.14740	−0.573700	−	0.819066i	$-0.694492\pi$
$571$	−1.07384e40	−1.14740	−0.573700	+	0.819066i	$0.694492\pi$
$572$	5.65164e39	0.588752
$573$	6.43785e38	0.0653881
$574$	3.06517e39	0.303551
$575$	1.44803e40	1.39828
$576$	−1.17666e39	−0.110796
$577$	−1.98468e40	−1.82239	−0.911193	−	0.411979i	$-0.864838\pi$
$577$	−1.98468e40	−1.82239	−0.911193	+	0.411979i	$0.864838\pi$
$578$	1.52275e39	0.136356
$579$	1.20207e39	0.104976
$580$	−3.46125e38	−0.0294799
$581$	−1.03668e40	−0.861170
$582$	1.03029e39	0.0834787
$583$	−5.07388e39	−0.401002
$584$	−3.18545e39	−0.245575
$585$	1.09642e40	0.824548
$586$	−9.12532e38	−0.0669473
$587$	−5.81533e39	−0.416219	−0.208110	−	0.978106i	$-0.566731\pi$
$587$	−5.81533e39	−0.416219	−0.208110	+	0.978106i	$0.566731\pi$
$588$	8.75405e38	0.0611277
$589$	−1.03223e38	−0.00703241
$590$	−4.89274e39	−0.325235
$591$	−6.16391e38	−0.0399796
$592$	4.93340e39	0.312235
$593$	2.08055e39	0.128495	0.0642474	−	0.997934i	$-0.479535\pi$
$593$	2.08055e39	0.128495	0.0642474	+	0.997934i	$0.479535\pi$
$594$	4.60256e39	0.277393
$595$	5.94337e39	0.349572
$596$	4.46316e39	0.256195
$597$	3.58805e39	0.201016
$598$	−4.52645e40	−2.47509
$599$	2.19282e40	1.17035	0.585173	−	0.810908i	$-0.301027\pi$
$599$	2.19282e40	1.17035	0.585173	+	0.810908i	$0.301027\pi$
$600$	−1.74423e39	−0.0908678
$601$	1.16438e40	0.592129	0.296065	−	0.955168i	$-0.404326\pi$
$601$	1.16438e40	0.592129	0.296065	+	0.955168i	$0.404326\pi$
$602$	1.53772e40	0.763360
$603$	2.33387e40	1.13103
$604$	1.03979e40	0.491937
$605$	−6.53575e39	−0.301886
$606$	1.01884e40	0.459464
$607$	9.01948e39	0.397142	0.198571	−	0.980087i	$-0.436370\pi$
$607$	9.01948e39	0.397142	0.198571	+	0.980087i	$0.436370\pi$
$608$	−2.76230e37	−0.00118760
$609$	7.75446e38	0.0325538
$610$	−3.84813e39	−0.157749
$611$	−5.10345e40	−2.04299
$612$	−1.01850e40	−0.398168
$613$	7.07487e39	0.270110	0.135055	−	0.990838i	$-0.456879\pi$
$613$	7.07487e39	0.270110	0.135055	+	0.990838i	$0.456879\pi$
$614$	−4.69587e39	−0.175095
$615$	2.42594e39	0.0883466
$616$	4.89546e39	0.174130
$617$	2.47470e39	0.0859782	0.0429891	−	0.999076i	$-0.486312\pi$
$617$	2.47470e39	0.0859782	0.0429891	+	0.999076i	$0.486312\pi$
$618$	−1.34442e40	−0.456248
$619$	−5.55735e40	−1.84227	−0.921135	−	0.389243i	$-0.872737\pi$
$619$	−5.55735e40	−1.84227	−0.921135	+	0.389243i	$0.872737\pi$
$620$	−7.87749e39	−0.255099
$621$	−3.68622e40	−1.16615
$622$	2.06732e40	0.638920
$623$	1.94510e40	0.587306
$624$	5.45234e39	0.160845
$625$	1.19272e40	0.343779
$626$	2.84613e40	0.801544
$627$	5.07699e37	0.00139710
$628$	−9.18929e39	−0.247097
$629$	4.27028e40	1.12208
$630$	9.49719e39	0.243869
$631$	6.80135e39	0.170675	0.0853374	−	0.996352i	$-0.472803\pi$
$631$	6.80135e39	0.170675	0.0853374	+	0.996352i	$0.472803\pi$
$632$	8.85508e39	0.217167
$633$	−2.63321e39	−0.0631149
$634$	2.79737e40	0.655323
$635$	−2.32276e40	−0.531846
$636$	−4.89495e39	−0.109552
$637$	3.16423e40	0.692224
$638$	−2.46776e39	−0.0527720
$639$	−4.43456e40	−0.927019
$640$	−2.10806e39	−0.0430797
$641$	5.50508e40	1.09982	0.549911	−	0.835223i	$-0.314662\pi$
$641$	5.50508e40	1.09982	0.549911	+	0.835223i	$0.314662\pi$
$642$	−8.26845e39	−0.161498
$643$	4.13272e40	0.789181	0.394591	−	0.918857i	$-0.370886\pi$
$643$	4.13272e40	0.789181	0.394591	+	0.918857i	$0.370886\pi$
$644$	−3.92081e40	−0.732034
$645$	1.21703e40	0.222171
$646$	−2.39100e38	−0.00426785
$647$	−7.12949e40	−1.24436	−0.622180	−	0.782874i	$-0.713753\pi$
$647$	−7.12949e40	−1.24436	−0.622180	+	0.782874i	$0.713753\pi$
$648$	−1.39213e40	−0.237597
$649$	−3.48837e40	−0.582203
$650$	−6.30467e40	−1.02901
$651$	1.76485e40	0.281698
$652$	3.29727e40	0.514712
$653$	2.55638e40	0.390287	0.195144	−	0.980775i	$-0.437483\pi$
$653$	2.55638e40	0.390287	0.195144	+	0.980775i	$0.437483\pi$
$654$	−7.27495e39	−0.108631
$655$	3.45878e40	0.505155
$656$	−9.41053e39	−0.134434
$657$	−4.40598e40	−0.615665
$658$	−4.42062e40	−0.604237
$659$	2.31450e40	0.309470	0.154735	−	0.987956i	$-0.450548\pi$
$659$	2.31450e40	0.309470	0.154735	+	0.987956i	$0.450548\pi$
$660$	3.87452e39	0.0506794
$661$	−4.73448e40	−0.605830	−0.302915	−	0.953018i	$-0.597960\pi$
$661$	−4.73448e40	−0.605830	−0.302915	+	0.953018i	$0.597960\pi$
$662$	−7.36433e38	−0.00921918
$663$	4.71947e40	0.578025
$664$	3.18275e40	0.381387
$665$	2.22953e38	0.00261397
$666$	6.82368e40	0.782785
$667$	1.97645e40	0.221851
$668$	−2.91482e40	−0.320149
$669$	−2.20556e40	−0.237050
$670$	4.18126e40	0.439767
$671$	−2.74360e40	−0.282387
$672$	4.72282e39	0.0475716
$673$	1.15677e41	1.14033	0.570164	−	0.821531i	$-0.306880\pi$
$673$	1.15677e41	1.14033	0.570164	+	0.821531i	$0.306880\pi$
$674$	−4.76136e40	−0.459370
$675$	−5.13437e40	−0.484822
$676$	1.42980e41	1.32144
$677$	−1.15938e41	−1.04879	−0.524397	−	0.851474i	$-0.675709\pi$
$677$	−1.15938e41	−1.04879	−0.524397	+	0.851474i	$0.675709\pi$
$678$	2.96987e40	0.262970
$679$	3.22580e40	0.279593
$680$	−1.82470e40	−0.154815
$681$	−5.29621e40	−0.439878
$682$	−5.61641e40	−0.456652
$683$	2.27986e41	1.81471	0.907355	−	0.420365i	$-0.138098\pi$
$683$	2.27986e41	1.81471	0.907355	+	0.420365i	$0.138098\pi$
$684$	−3.82070e38	−0.00297734
$685$	−9.48737e40	−0.723824
$686$	1.02981e41	0.769233
$687$	−5.04527e40	−0.368988
$688$	−4.72104e40	−0.338069
$689$	−1.76933e41	−1.24059
$690$	−3.10314e40	−0.213054
$691$	−1.28263e41	−0.862319	−0.431160	−	0.902276i	$-0.641895\pi$
$691$	−1.28263e41	−0.862319	−0.431160	+	0.902276i	$0.641895\pi$
$692$	−2.18373e39	−0.0143768
$693$	6.77121e40	0.436550
$694$	−1.12186e41	−0.708315
$695$	5.89328e38	0.00364399
$696$	−2.38074e39	−0.0144171
$697$	−8.14562e40	−0.483113
$698$	−1.41522e41	−0.822092
$699$	7.36847e40	0.419236
$700$	−5.46112e40	−0.304341
$701$	2.62615e41	1.43354	0.716769	−	0.697311i	$-0.245620\pi$
$701$	2.62615e41	1.43354	0.716769	+	0.697311i	$0.245620\pi$
$702$	1.60497e41	0.858180
$703$	1.60191e39	0.00839045
$704$	−1.50298e40	−0.0771169
$705$	−3.49871e40	−0.175859
$706$	1.01279e41	0.498712
$707$	3.18994e41	1.53887
$708$	−3.36536e40	−0.159056
$709$	−1.98212e41	−0.917824	−0.458912	−	0.888482i	$-0.651761\pi$
$709$	−1.98212e41	−0.917824	−0.458912	+	0.888482i	$0.651761\pi$
$710$	−7.94478e40	−0.360442
$711$	1.22480e41	0.544447
$712$	−5.97174e40	−0.260100
$713$	4.49823e41	1.91974
$714$	4.08801e40	0.170957
$715$	1.40048e41	0.573905
$716$	−1.05013e41	−0.421702
$717$	4.49475e40	0.176880
$718$	1.03994e40	0.0401054
$719$	−4.90474e41	−1.85373	−0.926867	−	0.375390i	$-0.877509\pi$
$719$	−4.90474e41	−1.85373	−0.926867	+	0.375390i	$0.877509\pi$
$720$	−2.91578e40	−0.108002
$721$	−4.20933e41	−1.52810
$722$	1.98726e41	0.707075
$723$	1.40246e38	0.000489086 0
$724$	3.39509e40	0.116049
$725$	2.75290e40	0.0922338
$726$	−4.49546e40	−0.147636
$727$	−4.24029e41	−1.36504	−0.682522	−	0.730865i	$-0.739117\pi$
$727$	−4.24029e41	−1.36504	−0.682522	+	0.730865i	$0.739117\pi$
$728$	1.70711e41	0.538711
$729$	−1.23264e41	−0.381319
$730$	−7.89357e40	−0.239382
$731$	−4.08647e41	−1.21492
$732$	−2.64685e40	−0.0771469
$733$	2.92123e41	0.834754	0.417377	−	0.908733i	$-0.362949\pi$
$733$	2.92123e41	0.834754	0.417377	+	0.908733i	$0.362949\pi$
$734$	2.07982e41	0.582685
$735$	2.16926e40	0.0595862
$736$	1.20375e41	0.324196
$737$	2.98111e41	0.787227
$738$	−1.30163e41	−0.337031
$739$	4.81596e41	1.22275	0.611376	−	0.791340i	$-0.290616\pi$
$739$	4.81596e41	1.22275	0.611376	+	0.791340i	$0.290616\pi$
$740$	1.22250e41	0.304361
$741$	1.77041e39	0.00432225
$742$	−1.53259e41	−0.366919
$743$	−5.86417e41	−1.37679	−0.688397	−	0.725334i	$-0.741685\pi$
$743$	−5.86417e41	−1.37679	−0.688397	+	0.725334i	$0.741685\pi$
$744$	−5.41835e40	−0.124755
$745$	1.10597e41	0.249735
$746$	2.36174e41	0.523021
$747$	4.40225e41	0.956150
$748$	−1.30096e41	−0.277134
$749$	−2.58883e41	−0.540899
$750$	−9.99106e40	−0.204750
$751$	1.83133e41	0.368118	0.184059	−	0.982915i	$-0.441076\pi$
$751$	1.83133e41	0.368118	0.184059	+	0.982915i	$0.441076\pi$
$752$	1.35720e41	0.267599
$753$	1.63983e41	0.317156
$754$	−8.60540e40	−0.163262
$755$	2.57661e41	0.479532
$756$	1.39023e41	0.253816
$757$	6.08700e41	1.09022	0.545109	−	0.838365i	$-0.316488\pi$
$757$	6.08700e41	1.09022	0.545109	+	0.838365i	$0.316488\pi$
$758$	−6.98467e41	−1.22728
$759$	−2.21244e41	−0.381387
$760$	−6.84500e38	−0.00115765
$761$	1.50858e41	0.250317	0.125159	−	0.992137i	$-0.460056\pi$
$761$	1.50858e41	0.250317	0.125159	+	0.992137i	$0.460056\pi$
$762$	−1.59766e41	−0.260098
$763$	−2.27776e41	−0.363833
$764$	−6.18841e40	−0.0969896
$765$	−2.52386e41	−0.388127
$766$	1.03021e41	0.155457
$767$	−1.21644e42	−1.80118
$768$	−1.44998e40	−0.0210680
$769$	7.27607e41	1.03745	0.518723	−	0.854943i	$-0.326408\pi$
$769$	7.27607e41	1.03745	0.518723	+	0.854943i	$0.326408\pi$
$770$	1.21310e41	0.169739
$771$	−3.69592e40	−0.0507498
$772$	−1.15550e41	−0.155711
$773$	−3.92968e41	−0.519702	−0.259851	−	0.965649i	$-0.583673\pi$
$773$	−3.92968e41	−0.519702	−0.259851	+	0.965649i	$0.583673\pi$
$774$	−6.52995e41	−0.847552
$775$	6.26537e41	0.798127
$776$	−9.90369e40	−0.123823
$777$	−2.73885e41	−0.336097
$778$	5.76032e41	0.693813
$779$	−3.05566e39	−0.00361253
$780$	1.35109e41	0.156788
$781$	−5.66438e41	−0.645227
$782$	1.04195e42	1.16506
$783$	−7.00802e40	−0.0769218
$784$	−8.41486e40	−0.0906701
$785$	−2.27712e41	−0.240866
$786$	2.37904e41	0.247045
$787$	8.52629e41	0.869214	0.434607	−	0.900620i	$-0.356887\pi$
$787$	8.52629e41	0.869214	0.434607	+	0.900620i	$0.356887\pi$
$788$	5.92509e40	0.0593013
$789$	6.35622e41	0.624572
$790$	2.19430e41	0.211691
$791$	9.29855e41	0.880758
$792$	−2.07886e41	−0.193335
$793$	−9.56728e41	−0.873629
$794$	1.10125e42	0.987390
$795$	−1.21297e41	−0.106789
$796$	−3.44903e41	−0.298165
$797$	−9.95077e41	−0.844716	−0.422358	−	0.906429i	$-0.638798\pi$
$797$	−9.95077e41	−0.844716	−0.422358	+	0.906429i	$0.638798\pi$
$798$	1.53353e39	0.00127835
$799$	1.17477e42	0.961666
$800$	1.67664e41	0.134783
$801$	−8.25986e41	−0.652081
$802$	−2.85343e41	−0.221228
$803$	−5.62787e41	−0.428518
$804$	2.87598e41	0.215067
$805$	−9.71582e41	−0.713574
$806$	−1.95851e42	−1.41276
$807$	−2.38887e41	−0.169249
$808$	−9.79359e41	−0.681518
$809$	7.25598e41	0.495955	0.247978	−	0.968766i	$-0.420234\pi$
$809$	7.25598e41	0.495955	0.247978	+	0.968766i	$0.420234\pi$
$810$	−3.44970e41	−0.231605
$811$	−5.73901e41	−0.378473	−0.189236	−	0.981932i	$-0.560601\pi$
$811$	−5.73901e41	−0.378473	−0.189236	+	0.981932i	$0.560601\pi$
$812$	−7.45401e40	−0.0482867
$813$	−3.13896e41	−0.199744
$814$	8.71606e41	0.544837
$815$	8.17067e41	0.501732
$816$	−1.25508e41	−0.0757119
$817$	−1.53295e40	−0.00908466
$818$	−4.07299e41	−0.237132
$819$	2.36120e42	1.35057
$820$	−2.33194e41	−0.131044
$821$	2.73841e42	1.51190	0.755950	−	0.654629i	$-0.227175\pi$
$821$	2.73841e42	1.51190	0.755950	+	0.654629i	$0.227175\pi$
$822$	−6.52567e41	−0.353984
$823$	−5.81100e41	−0.309709	−0.154854	−	0.987937i	$-0.549491\pi$
$823$	−5.81100e41	−0.309709	−0.154854	+	0.987937i	$0.549491\pi$
$824$	1.29233e42	0.676749
$825$	−3.08160e41	−0.158560
$826$	−1.05368e42	−0.532720
$827$	−3.47953e41	−0.172858	−0.0864292	−	0.996258i	$-0.527546\pi$
$827$	−3.47953e41	−0.172858	−0.0864292	+	0.996258i	$0.527546\pi$
$828$	1.66498e42	0.812771
$829$	5.41233e41	0.259623	0.129812	−	0.991539i	$-0.458563\pi$
$829$	5.41233e41	0.259623	0.129812	+	0.991539i	$0.458563\pi$
$830$	7.88688e41	0.371769
$831$	8.31766e41	0.385289
$832$	−5.24108e41	−0.238579
$833$	−7.28379e41	−0.325840
$834$	4.05355e39	0.00178208
$835$	−7.22294e41	−0.312076
$836$	−4.88027e39	−0.00207230
$837$	−1.59496e42	−0.665628
$838$	9.26036e41	0.379830
$839$	−6.31678e41	−0.254652	−0.127326	−	0.991861i	$-0.540639\pi$
$839$	−6.31678e41	−0.254652	−0.127326	+	0.991861i	$0.540639\pi$
$840$	1.17032e41	0.0463719
$841$	−2.53011e42	−0.985366
$842$	−2.22351e42	−0.851166
$843$	1.01392e41	0.0381509
$844$	2.53118e41	0.0936178
$845$	3.54306e42	1.28812
$846$	1.87722e42	0.670879
$847$	−1.40751e42	−0.494474
$848$	4.70529e41	0.162497
$849$	1.58216e42	0.537143
$850$	1.45128e42	0.484369
$851$	−6.98076e42	−2.29047
$852$	−5.46463e41	−0.176273
$853$	−3.80532e42	−1.20679	−0.603393	−	0.797444i	$-0.706185\pi$
$853$	−3.80532e42	−1.20679	−0.603393	+	0.797444i	$0.706185\pi$
$854$	−8.28719e41	−0.258386
$855$	−9.46772e39	−0.00290226
$856$	7.94808e41	0.239548
$857$	5.43316e42	1.61002	0.805009	−	0.593262i	$-0.202160\pi$
$857$	5.43316e42	1.61002	0.805009	+	0.593262i	$0.202160\pi$
$858$	9.63289e41	0.280667
$859$	−1.23039e42	−0.352486	−0.176243	−	0.984347i	$-0.556395\pi$
$859$	−1.23039e42	−0.352486	−0.176243	+	0.984347i	$0.556395\pi$
$860$	−1.16988e42	−0.329544
$861$	5.22440e41	0.144707
$862$	2.05766e42	0.560426
$863$	1.94970e42	0.522168	0.261084	−	0.965316i	$-0.415920\pi$
$863$	1.94970e42	0.522168	0.261084	+	0.965316i	$0.415920\pi$
$864$	−4.26820e41	−0.112408
$865$	−5.41131e40	−0.0140142
$866$	−4.26504e42	−1.08621
$867$	2.59544e41	0.0650032
$868$	−1.69647e42	−0.417839
$869$	1.56447e42	0.378948
$870$	−5.89949e40	−0.0140535
$871$	1.03955e43	2.43547
$872$	6.99307e41	0.161131
$873$	−1.36984e42	−0.310429
$874$	3.90865e40	0.00871186
$875$	−3.12817e42	−0.685762
$876$	−5.42941e41	−0.117069
$877$	2.90946e42	0.617047	0.308524	−	0.951217i	$-0.400165\pi$
$877$	2.90946e42	0.617047	0.308524	+	0.951217i	$0.400165\pi$
$878$	4.16182e42	0.868187
$879$	−1.55536e41	−0.0319148
$880$	−3.72440e41	−0.0751722
$881$	7.45482e42	1.48008	0.740042	−	0.672561i	$-0.234806\pi$
$881$	7.45482e42	1.48008	0.740042	+	0.672561i	$0.234806\pi$
$882$	−1.16391e42	−0.227313
$883$	−6.98315e42	−1.34159	−0.670797	−	0.741641i	$-0.734048\pi$
$883$	−6.98315e42	−1.34159	−0.670797	+	0.741641i	$0.734048\pi$
$884$	−4.53661e42	−0.857380
$885$	−8.33938e41	−0.155045
$886$	−3.96917e42	−0.725957
$887$	−3.03500e42	−0.546093	−0.273046	−	0.962001i	$-0.588031\pi$
$887$	−3.03500e42	−0.546093	−0.273046	+	0.962001i	$0.588031\pi$
$888$	8.40869e41	0.148847
$889$	−5.00221e42	−0.871137
$890$	−1.47980e42	−0.253541
$891$	−2.45953e42	−0.414597
$892$	2.12010e42	0.351615
$893$	4.40690e40	0.00719096
$894$	7.60719e41	0.122132
$895$	−2.60224e42	−0.411067
$896$	−4.53983e41	−0.0705625
$897$	−7.71506e42	−1.17991
$898$	8.06079e42	1.21303
$899$	8.55175e41	0.126631
$900$	2.31907e42	0.337907
$901$	4.07283e42	0.583965
$902$	−1.66260e42	−0.234581
$903$	2.62096e42	0.363905
$904$	−2.85480e42	−0.390061
$905$	8.41307e41	0.113123
$906$	1.77226e42	0.234514
$907$	1.17002e43	1.52366	0.761828	−	0.647780i	$-0.224302\pi$
$907$	1.17002e43	1.52366	0.761828	+	0.647780i	$0.224302\pi$
$908$	5.09100e42	0.652467
$909$	−1.35461e43	−1.70859
$910$	4.23023e42	0.525127
$911$	1.40568e42	0.171739	0.0858696	−	0.996306i	$-0.472633\pi$
$911$	1.40568e42	0.171739	0.0858696	+	0.996306i	$0.472633\pi$
$912$	−4.70817e39	−0.000566144 0
$913$	5.62311e42	0.665503
$914$	−3.39621e42	−0.395617
$915$	−6.55891e41	−0.0752014
$916$	4.84978e42	0.547316
$917$	7.44871e42	0.827419
$918$	−3.69450e42	−0.403958
$919$	9.41015e42	1.01280	0.506398	−	0.862300i	$-0.330977\pi$
$919$	9.41015e42	1.01280	0.506398	+	0.862300i	$0.330977\pi$
$920$	2.98290e42	0.316021
$921$	−8.00384e41	−0.0834706
$922$	−5.94714e42	−0.610533
$923$	−1.97524e43	−1.99616
$924$	8.34403e41	0.0830103
$925$	−9.72317e42	−0.952254
$926$	−2.22722e42	−0.214736
$927$	1.78749e43	1.69663
$928$	2.28849e41	0.0213847
$929$	−1.48051e43	−1.36202	−0.681012	−	0.732272i	$-0.738460\pi$
$929$	−1.48051e43	−1.36202	−0.681012	+	0.732272i	$0.738460\pi$
$930$	−1.34267e42	−0.121609
$931$	−2.73236e40	−0.00243651
$932$	−7.08297e42	−0.621849
$933$	3.52362e42	0.304583
$934$	−9.36720e42	−0.797224
$935$	−3.22379e42	−0.270146
$936$	−7.24925e42	−0.598127
$937$	1.18857e42	0.0965606	0.0482803	−	0.998834i	$-0.484626\pi$
$937$	1.18857e42	0.0965606	0.0482803	+	0.998834i	$0.484626\pi$
$938$	9.00461e42	0.720317
$939$	4.85106e42	0.382108
$940$	3.36314e42	0.260850
$941$	4.56958e42	0.349001	0.174500	−	0.984657i	$-0.444169\pi$
$941$	4.56958e42	0.349001	0.174500	+	0.984657i	$0.444169\pi$
$942$	−1.56626e42	−0.117795
$943$	1.33159e43	0.986169
$944$	3.23496e42	0.235926
$945$	3.44500e42	0.247416
$946$	−8.34088e42	−0.589916
$947$	3.71116e42	0.258485	0.129242	−	0.991613i	$-0.458746\pi$
$947$	3.71116e42	0.258485	0.129242	+	0.991613i	$0.458746\pi$
$948$	1.50930e42	0.103527
$949$	−1.96251e43	−1.32572
$950$	5.44417e40	0.00362193
$951$	4.76795e42	0.312402
$952$	−3.92961e42	−0.253580
$953$	1.84294e43	1.17129	0.585646	−	0.810567i	$-0.300841\pi$
$953$	1.84294e43	1.17129	0.585646	+	0.810567i	$0.300841\pi$
$954$	6.50817e42	0.407387
$955$	−1.53349e42	−0.0945438
$956$	−4.32060e42	−0.262364
$957$	−4.20615e41	−0.0251572
$958$	1.08173e43	0.637264
$959$	−2.04316e43	−1.18559
$960$	−3.59306e41	−0.0205367
$961$	1.70115e42	0.0957752
$962$	3.03940e43	1.68558
$963$	1.09935e43	0.600556
$964$	−1.34812e40	−0.000725456 0
$965$	−2.86333e42	−0.151784
$966$	−6.68280e42	−0.348971
$967$	−2.84485e43	−1.46344	−0.731722	−	0.681604i	$-0.761283\pi$
$967$	−2.84485e43	−1.46344	−0.731722	+	0.681604i	$0.761283\pi$
$968$	4.32128e42	0.218988
$969$	−4.07533e40	−0.00203455
$970$	−2.45414e42	−0.120701
$971$	2.17992e43	1.05624	0.528119	−	0.849171i	$-0.322898\pi$
$971$	2.17992e43	1.05624	0.528119	+	0.849171i	$0.322898\pi$
$972$	−9.03322e42	−0.431203
$973$	1.26915e41	0.00596868
$974$	3.93758e42	0.182442
$975$	−1.07459e43	−0.490543
$976$	2.54429e42	0.114431
$977$	−2.24726e43	−0.995822	−0.497911	−	0.867228i	$-0.665899\pi$
$977$	−2.24726e43	−0.995822	−0.497911	+	0.867228i	$0.665899\pi$
$978$	5.62000e42	0.245371
$979$	−1.05505e43	−0.453864
$980$	−2.08521e42	−0.0883836
$981$	9.67253e42	0.403961
$982$	−2.55963e43	−1.05332
$983$	−3.71193e43	−1.50513	−0.752565	−	0.658518i	$-0.771184\pi$
$983$	−3.71193e43	−1.50513	−0.752565	+	0.658518i	$0.771184\pi$
$984$	−1.60397e42	−0.0640866
$985$	1.46824e42	0.0578059
$986$	1.98089e42	0.0768501
$987$	−7.53468e42	−0.288049
$988$	−1.70181e41	−0.00641115
$989$	6.68027e43	2.47998
$990$	−5.15144e42	−0.188460
$991$	3.41473e42	0.123108	0.0615542	−	0.998104i	$-0.480394\pi$
$991$	3.41473e42	0.123108	0.0615542	+	0.998104i	$0.480394\pi$
$992$	5.20841e42	0.185049
$993$	−1.25521e41	−0.00439492
$994$	−1.71096e43	−0.590386
$995$	−8.54672e42	−0.290646
$996$	5.42481e42	0.181813
$997$	1.03265e43	0.341092	0.170546	−	0.985350i	$-0.445447\pi$
$997$	1.03265e43	0.341092	0.170546	+	0.985350i	$0.445447\pi$
$998$	2.30338e43	0.749847
$999$	2.47521e43	0.794168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2.30.a.a.1.1	✓	1
3.2	odd	2		18.30.a.c.1.1		1
4.3	odd	2		16.30.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2.30.a.a.1.1	✓	1	1.1	even	1	trivial
16.30.a.b.1.1		1	4.3	odd	2
18.30.a.c.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2 \)
Weight:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	2.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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