LMFDB - Embedded newform 10.20.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,20,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 20, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 20 $
Character orbit:	$[\chi]$	$=$	10.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:	$22.8816696556$
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	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+512.000 q^{2} +24642.0 q^{3} +262144. q^{4} -1.95312e6 q^{5} +1.26167e7 q^{6} -1.71901e8 q^{7} +1.34218e8 q^{8} -5.55033e8 q^{9} +O(q^{10})$

\(q+512.000 q^{2} +24642.0 q^{3} +262144. q^{4} -1.95312e6 q^{5} +1.26167e7 q^{6} -1.71901e8 q^{7} +1.34218e8 q^{8} -5.55033e8 q^{9} -1.00000e9 q^{10} -1.18738e10 q^{11} +6.45975e9 q^{12} +3.59720e10 q^{13} -8.80134e10 q^{14} -4.81289e10 q^{15} +6.87195e10 q^{16} -7.46262e11 q^{17} -2.84177e11 q^{18} +2.68219e12 q^{19} -5.12000e11 q^{20} -4.23599e12 q^{21} -6.07940e12 q^{22} +1.59244e10 q^{23} +3.30739e12 q^{24} +3.81470e12 q^{25} +1.84176e13 q^{26} -4.23176e13 q^{27} -4.50628e13 q^{28} -1.06191e14 q^{29} -2.46420e13 q^{30} -1.58223e14 q^{31} +3.51844e13 q^{32} -2.92595e14 q^{33} -3.82086e14 q^{34} +3.35744e14 q^{35} -1.45499e14 q^{36} -8.02461e13 q^{37} +1.37328e15 q^{38} +8.86421e14 q^{39} -2.62144e14 q^{40} +1.89594e15 q^{41} -2.16883e15 q^{42} +3.27866e15 q^{43} -3.11265e15 q^{44} +1.08405e15 q^{45} +8.15330e12 q^{46} +1.29665e15 q^{47} +1.69339e15 q^{48} +1.81511e16 q^{49} +1.95312e15 q^{50} -1.83894e16 q^{51} +9.42984e15 q^{52} +1.24837e16 q^{53} -2.16666e16 q^{54} +2.31911e16 q^{55} -2.30722e16 q^{56} +6.60944e16 q^{57} -5.43697e16 q^{58} -1.10747e17 q^{59} -1.26167e16 q^{60} -1.78925e16 q^{61} -8.10103e16 q^{62} +9.54108e16 q^{63} +1.80144e16 q^{64} -7.02577e16 q^{65} -1.49809e17 q^{66} +5.32957e16 q^{67} -1.95628e17 q^{68} +3.92409e14 q^{69} +1.71901e17 q^{70} +4.06846e17 q^{71} -7.44953e16 q^{72} -5.99276e17 q^{73} -4.10860e16 q^{74} +9.40018e16 q^{75} +7.03119e17 q^{76} +2.04113e18 q^{77} +4.53848e17 q^{78} -1.83795e17 q^{79} -1.34218e17 q^{80} -3.97696e17 q^{81} +9.70720e17 q^{82} -8.97307e17 q^{83} -1.11044e18 q^{84} +1.45754e18 q^{85} +1.67868e18 q^{86} -2.61675e18 q^{87} -1.59368e18 q^{88} +4.98699e17 q^{89} +5.55033e17 q^{90} -6.18362e18 q^{91} +4.17449e15 q^{92} -3.89894e18 q^{93} +6.63887e17 q^{94} -5.23864e18 q^{95} +8.67013e17 q^{96} -1.08835e18 q^{97} +9.29336e18 q^{98} +6.59037e18 q^{99} +O(q^{100})\)

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 $

$2$	512.000	0.707107
$2$	512.000	0.707107
$3$	24642.0	0.722810	0.361405	−	0.932409i	$-0.382297\pi$
$3$	24642.0	0.722810	0.361405	+	0.932409i	$0.382297\pi$
$4$	262144.	0.500000
$5$	−1.95312e6	−0.447214
$5$	−1.95312e6	−0.447214
$6$	1.26167e7	0.511104
$7$	−1.71901e8	−1.61008	−0.805040	−	0.593221i	$-0.797856\pi$
$7$	−1.71901e8	−1.61008	−0.805040	+	0.593221i	$0.797856\pi$
$8$	1.34218e8	0.353553
$9$	−5.55033e8	−0.477546
$10$	−1.00000e9	−0.316228
$11$	−1.18738e10	−1.51831	−0.759155	−	0.650910i	$-0.774388\pi$
$11$	−1.18738e10	−1.51831	−0.759155	+	0.650910i	$0.774388\pi$
$12$	6.45975e9	0.361405
$13$	3.59720e10	0.940811	0.470405	−	0.882450i	$-0.344108\pi$
$13$	3.59720e10	0.940811	0.470405	+	0.882450i	$0.344108\pi$
$14$	−8.80134e10	−1.13850
$15$	−4.81289e10	−0.323250
$16$	6.87195e10	0.250000
$17$	−7.46262e11	−1.52625	−0.763127	−	0.646249i	$-0.776337\pi$
$17$	−7.46262e11	−1.52625	−0.763127	+	0.646249i	$0.776337\pi$
$18$	−2.84177e11	−0.337676
$19$	2.68219e12	1.90691	0.953454	−	0.301539i	$-0.0975003\pi$
$19$	2.68219e12	1.90691	0.953454	+	0.301539i	$0.0975003\pi$
$20$	−5.12000e11	−0.223607
$21$	−4.23599e12	−1.16378
$22$	−6.07940e12	−1.07361
$23$	1.59244e10	0.00184352	0.000921762	−	1.00000i	$-0.499707\pi$
$23$	1.59244e10	0.00184352	0.000921762		1.00000i	$0.499707\pi$
$24$	3.30739e12	0.255552
$25$	3.81470e12	0.200000
$26$	1.84176e13	0.665254
$27$	−4.23176e13	−1.06798
$28$	−4.50628e13	−0.805040
$29$	−1.06191e14	−1.35927	−0.679635	−	0.733550i	$-0.737862\pi$
$29$	−1.06191e14	−1.35927	−0.679635	+	0.733550i	$0.737862\pi$
$30$	−2.46420e13	−0.228573
$31$	−1.58223e14	−1.07482	−0.537408	−	0.843322i	$-0.680597\pi$
$31$	−1.58223e14	−1.07482	−0.537408	+	0.843322i	$0.680597\pi$
$32$	3.51844e13	0.176777
$33$	−2.92595e14	−1.09745
$34$	−3.82086e14	−1.07922
$35$	3.35744e14	0.720049
$36$	−1.45499e14	−0.238773
$37$	−8.02461e13	−0.101510	−0.0507548	−	0.998711i	$-0.516163\pi$
$37$	−8.02461e13	−0.101510	−0.0507548	+	0.998711i	$0.516163\pi$
$38$	1.37328e15	1.34839
$39$	8.86421e14	0.680027
$40$	−2.62144e14	−0.158114
$41$	1.89594e15	0.904435	0.452217	−	0.891908i	$-0.350633\pi$
$41$	1.89594e15	0.904435	0.452217	+	0.891908i	$0.350633\pi$
$42$	−2.16883e15	−0.822918
$43$	3.27866e15	0.994825	0.497412	−	0.867514i	$-0.334284\pi$
$43$	3.27866e15	0.994825	0.497412	+	0.867514i	$0.334284\pi$
$44$	−3.11265e15	−0.759155
$45$	1.08405e15	0.213565
$46$	8.15330e12	0.00130357
$47$	1.29665e15	0.169003	0.0845015	−	0.996423i	$-0.473070\pi$
$47$	1.29665e15	0.169003	0.0845015	+	0.996423i	$0.473070\pi$
$48$	1.69339e15	0.180702
$49$	1.81511e16	1.59236
$50$	1.95312e15	0.141421
$51$	−1.83894e16	−1.10319
$52$	9.42984e15	0.470405
$53$	1.24837e16	0.519664	0.259832	−	0.965654i	$-0.416333\pi$
$53$	1.24837e16	0.519664	0.259832	+	0.965654i	$0.416333\pi$
$54$	−2.16666e16	−0.755179
$55$	2.31911e16	0.679009
$56$	−2.30722e16	−0.569249
$57$	6.60944e16	1.37833
$58$	−5.43697e16	−0.961149
$59$	−1.10747e17	−1.66432	−0.832160	−	0.554536i	$-0.812896\pi$
$59$	−1.10747e17	−1.66432	−0.832160	+	0.554536i	$0.812896\pi$
$60$	−1.26167e16	−0.161625
$61$	−1.78925e16	−0.195901	−0.0979506	−	0.995191i	$-0.531229\pi$
$61$	−1.78925e16	−0.195901	−0.0979506	+	0.995191i	$0.531229\pi$
$62$	−8.10103e16	−0.760010
$63$	9.54108e16	0.768887
$64$	1.80144e16	0.125000
$65$	−7.02577e16	−0.420743
$66$	−1.49809e17	−0.776014
$67$	5.32957e16	0.239322	0.119661	−	0.992815i	$-0.461819\pi$
$67$	5.32957e16	0.239322	0.119661	+	0.992815i	$0.461819\pi$
$68$	−1.95628e17	−0.763127
$69$	3.92409e14	0.00133252
$70$	1.71901e17	0.509152
$71$	4.06846e17	1.05312	0.526558	−	0.850139i	$-0.323482\pi$
$71$	4.06846e17	1.05312	0.526558	+	0.850139i	$0.323482\pi$
$72$	−7.44953e16	−0.168838
$73$	−5.99276e17	−1.19141	−0.595703	−	0.803205i	$-0.703126\pi$
$73$	−5.99276e17	−1.19141	−0.595703	+	0.803205i	$0.703126\pi$
$74$	−4.10860e16	−0.0717782
$75$	9.40018e16	0.144562
$76$	7.03119e17	0.953454
$77$	2.04113e18	2.44460
$78$	4.53848e17	0.480852
$79$	−1.83795e17	−0.172535	−0.0862673	−	0.996272i	$-0.527494\pi$
$79$	−1.83795e17	−0.172535	−0.0862673	+	0.996272i	$0.527494\pi$
$80$	−1.34218e17	−0.111803
$81$	−3.97696e17	−0.294404
$82$	9.70720e17	0.639532
$83$	−8.97307e17	−0.526865	−0.263432	−	0.964678i	$-0.584855\pi$
$83$	−8.97307e17	−0.526865	−0.263432	+	0.964678i	$0.584855\pi$
$84$	−1.11044e18	−0.581891
$85$	1.45754e18	0.682561
$86$	1.67868e18	0.703447
$87$	−2.61675e18	−0.982494
$88$	−1.59368e18	−0.536804
$89$	4.98699e17	0.150881	0.0754403	−	0.997150i	$-0.475964\pi$
$89$	4.98699e17	0.150881	0.0754403	+	0.997150i	$0.475964\pi$
$90$	5.55033e17	0.151013
$91$	−6.18362e18	−1.51478
$92$	4.17449e15	0.000921762 0
$93$	−3.89894e18	−0.776888
$94$	6.63887e17	0.119503
$95$	−5.23864e18	−0.852795
$96$	8.67013e17	0.127776
$97$	−1.08835e18	−0.145357	−0.0726785	−	0.997355i	$-0.523155\pi$
$97$	−1.08835e18	−0.145357	−0.0726785	+	0.997355i	$0.523155\pi$
$98$	9.29336e18	1.12597
$99$	6.59037e18	0.725063
$100$	1.00000e18	0.100000
$101$	−1.24783e19	−1.13528	−0.567640	−	0.823277i	$-0.692144\pi$
$101$	−1.24783e19	−1.13528	−0.567640	+	0.823277i	$0.692144\pi$
$102$	−9.41537e18	−0.780074
$103$	4.36765e18	0.329833	0.164917	−	0.986308i	$-0.447265\pi$
$103$	4.36765e18	0.329833	0.164917	+	0.986308i	$0.447265\pi$
$104$	4.82808e18	0.332627
$105$	8.27341e18	0.520459
$106$	6.39166e18	0.367458
$107$	8.27714e18	0.435246	0.217623	−	0.976033i	$-0.430170\pi$
$107$	8.27714e18	0.435246	0.217623	+	0.976033i	$0.430170\pi$
$108$	−1.10933e19	−0.533992
$109$	3.32702e18	0.146725	0.0733624	−	0.997305i	$-0.476627\pi$
$109$	3.32702e18	0.146725	0.0733624	+	0.997305i	$0.476627\pi$
$110$	1.18738e19	0.480132
$111$	−1.97742e18	−0.0733722
$112$	−1.18130e19	−0.402520
$113$	−2.24605e18	−0.0703354	−0.0351677	−	0.999381i	$-0.511197\pi$
$113$	−2.24605e18	−0.0703354	−0.0351677	+	0.999381i	$0.511197\pi$
$114$	3.38403e19	0.974628
$115$	−3.11024e16	−0.000824449 0
$116$	−2.78373e19	−0.679635
$117$	−1.99656e19	−0.449280
$118$	−5.67023e19	−1.17685
$119$	1.28283e20	2.45739
$120$	−6.45975e18	−0.114286
$121$	7.98288e19	1.30527
$122$	−9.16095e18	−0.138523
$123$	4.67197e19	0.653734
$124$	−4.14773e19	−0.537408
$125$	−7.45058e18	−0.0894427
$126$	4.88504e19	0.543685
$127$	−7.77016e19	−0.802222	−0.401111	−	0.916029i	$-0.631376\pi$
$127$	−7.77016e19	−0.802222	−0.401111	+	0.916029i	$0.631376\pi$
$128$	9.22337e18	0.0883883
$129$	8.07928e19	0.719069
$130$	−3.59720e19	−0.297511
$131$	−1.95142e20	−1.50063	−0.750317	−	0.661079i	$-0.770099\pi$
$131$	−1.95142e20	−1.50063	−0.750317	+	0.661079i	$0.770099\pi$
$132$	−7.67020e19	−0.548725
$133$	−4.61071e20	−3.07027
$134$	2.72874e19	0.169226
$135$	8.26515e19	0.477617
$136$	−1.00162e20	−0.539612
$137$	5.77740e19	0.290327	0.145163	−	0.989408i	$-0.453629\pi$
$137$	5.77740e19	0.290327	0.145163	+	0.989408i	$0.453629\pi$
$138$	2.00914e17	0.000942232 0
$139$	2.78267e20	1.21849	0.609243	−	0.792983i	$-0.291473\pi$
$139$	2.78267e20	1.21849	0.609243	+	0.792983i	$0.291473\pi$
$140$	8.80134e19	0.360025
$141$	3.19521e19	0.122157
$142$	2.08305e20	0.744666
$143$	−4.27125e20	−1.42844
$144$	−3.81416e19	−0.119386
$145$	2.07404e20	0.607884
$146$	−3.06829e20	−0.842451
$147$	4.47279e20	1.15097
$148$	−2.10360e19	−0.0507548
$149$	9.93945e19	0.224953	0.112477	−	0.993654i	$-0.464122\pi$
$149$	9.93945e19	0.224953	0.112477	+	0.993654i	$0.464122\pi$
$150$	4.81289e19	0.102221
$151$	−2.29016e20	−0.456651	−0.228326	−	0.973585i	$-0.573325\pi$
$151$	−2.29016e20	−0.456651	−0.228326	+	0.973585i	$0.573325\pi$
$152$	3.59997e20	0.674194
$153$	4.14200e20	0.728856
$154$	1.04506e21	1.72859
$155$	3.09030e20	0.480672
$156$	2.32370e20	0.340014
$157$	−1.18724e21	−1.63491	−0.817454	−	0.575994i	$-0.804615\pi$
$157$	−1.18724e21	−1.63491	−0.817454	+	0.575994i	$0.804615\pi$
$158$	−9.41031e19	−0.122000
$159$	3.07623e20	0.375618
$160$	−6.87195e19	−0.0790569
$161$	−2.73742e18	−0.00296822
$162$	−2.03620e20	−0.208175
$163$	−1.01852e21	−0.982175	−0.491088	−	0.871110i	$-0.663401\pi$
$163$	−1.01852e21	−0.982175	−0.491088	+	0.871110i	$0.663401\pi$
$164$	4.97008e20	0.452217
$165$	5.71475e20	0.490794
$166$	−4.59421e20	−0.372549
$167$	6.57822e20	0.503851	0.251925	−	0.967747i	$-0.418936\pi$
$167$	6.57822e20	0.503851	0.251925	+	0.967747i	$0.418936\pi$
$168$	−5.68545e20	−0.411459
$169$	−1.67938e20	−0.114875
$170$	7.46262e20	0.482644
$171$	−1.48870e21	−0.910636
$172$	8.59482e20	0.497412
$173$	−1.66694e21	−0.913022	−0.456511	−	0.889718i	$-0.650901\pi$
$173$	−1.66694e21	−0.913022	−0.456511	+	0.889718i	$0.650901\pi$
$174$	−1.33978e21	−0.694728
$175$	−6.55751e20	−0.322016
$176$	−8.15964e20	−0.379577
$177$	−2.72902e21	−1.20299
$178$	2.55334e20	0.106689
$179$	7.15712e20	0.283553	0.141776	−	0.989899i	$-0.454719\pi$
$179$	7.15712e20	0.283553	0.141776	+	0.989899i	$0.454719\pi$
$180$	2.84177e20	0.106783
$181$	3.50745e21	1.25039	0.625195	−	0.780469i	$-0.285019\pi$
$181$	3.50745e21	1.25039	0.625195	+	0.780469i	$0.285019\pi$
$182$	−3.16601e21	−1.07111
$183$	−4.40907e20	−0.141599
$184$	2.13734e18	0.000651784 0
$185$	1.56731e20	0.0453965
$186$	−1.99626e21	−0.549343
$187$	8.86099e21	2.31733
$188$	3.39910e20	0.0845015
$189$	7.27444e21	1.71954
$190$	−2.68219e21	−0.603017
$191$	−1.13805e21	−0.243413	−0.121706	−	0.992566i	$-0.538837\pi$
$191$	−1.13805e21	−0.243413	−0.121706	+	0.992566i	$0.538837\pi$
$192$	4.43911e20	0.0903512
$193$	−6.61368e21	−1.28129	−0.640647	−	0.767835i	$-0.721334\pi$
$193$	−6.61368e21	−1.28129	−0.640647	+	0.767835i	$0.721334\pi$
$194$	−5.57234e20	−0.102783
$195$	−1.73129e21	−0.304117
$196$	4.75820e21	0.796178
$197$	−9.19488e21	−1.46594	−0.732971	−	0.680260i	$-0.761867\pi$
$197$	−9.19488e21	−1.46594	−0.732971	+	0.680260i	$0.761867\pi$
$198$	3.37427e21	0.512697
$199$	1.12293e22	1.62648	0.813241	−	0.581927i	$-0.197701\pi$
$199$	1.12293e22	1.62648	0.813241	+	0.581927i	$0.197701\pi$
$200$	5.12000e20	0.0707107
$201$	1.31331e21	0.172984
$202$	−6.38890e21	−0.802765
$203$	1.82543e22	2.18853
$204$	−4.82067e21	−0.551596
$205$	−3.70300e21	−0.404476
$206$	2.23624e21	0.233227
$207$	−8.83858e18	−0.000880368 0
$208$	2.47197e21	0.235203
$209$	−3.18478e22	−2.89528
$210$	4.23599e21	0.368020
$211$	1.17508e22	0.975856	0.487928	−	0.872884i	$-0.337753\pi$
$211$	1.17508e22	0.975856	0.487928	+	0.872884i	$0.337753\pi$
$212$	3.27253e21	0.259832
$213$	1.00255e22	0.761203
$214$	4.23790e21	0.307765
$215$	−6.40364e21	−0.444899
$216$	−5.67977e21	−0.377590
$217$	2.71988e22	1.73054
$218$	1.70343e21	0.103750
$219$	−1.47674e22	−0.861160
$220$	6.07940e21	0.339504
$221$	−2.68445e22	−1.43592
$222$	−1.01244e21	−0.0518820
$223$	−1.69880e22	−0.834153	−0.417076	−	0.908871i	$-0.636945\pi$
$223$	−1.69880e22	−0.834153	−0.417076	+	0.908871i	$0.636945\pi$
$224$	−6.04823e21	−0.284625
$225$	−2.11728e21	−0.0955092
$226$	−1.14998e21	−0.0497347
$227$	−2.97376e22	−1.23328	−0.616639	−	0.787246i	$-0.711506\pi$
$227$	−2.97376e22	−1.23328	−0.616639	+	0.787246i	$0.711506\pi$
$228$	1.73263e22	0.689166
$229$	−4.09030e22	−1.56070	−0.780348	−	0.625345i	$-0.784958\pi$
$229$	−4.09030e22	−1.56070	−0.780348	+	0.625345i	$0.784958\pi$
$230$	−1.59244e19	−0.000582974 0
$231$	5.02974e22	1.76698
$232$	−1.42527e22	−0.480575
$233$	−1.43967e22	−0.465995	−0.232998	−	0.972477i	$-0.574853\pi$
$233$	−1.43967e22	−0.465995	−0.232998	+	0.972477i	$0.574853\pi$
$234$	−1.02224e22	−0.317689
$235$	−2.53253e21	−0.0755804
$236$	−2.90316e22	−0.832160
$237$	−4.52908e21	−0.124710
$238$	6.56810e22	1.73764
$239$	−1.33869e21	−0.0340331	−0.0170165	−	0.999855i	$-0.505417\pi$
$239$	−1.33869e21	−0.0340331	−0.0170165	+	0.999855i	$0.505417\pi$
$240$	−3.30739e21	−0.0808126
$241$	4.45807e20	0.0104709	0.00523546	−	0.999986i	$-0.498333\pi$
$241$	4.45807e20	0.0104709	0.00523546	+	0.999986i	$0.498333\pi$
$242$	4.08724e22	0.922962
$243$	3.93841e22	0.855187
$244$	−4.69041e21	−0.0979506
$245$	−3.54514e22	−0.712123
$246$	2.39205e22	0.462260
$247$	9.64835e22	1.79404
$248$	−2.12364e22	−0.380005
$249$	−2.21114e22	−0.380823
$250$	−3.81470e21	−0.0632456
$251$	6.49626e22	1.03696	0.518481	−	0.855089i	$-0.326498\pi$
$251$	6.49626e22	1.03696	0.518481	+	0.855089i	$0.326498\pi$
$252$	2.50114e22	0.384443
$253$	−1.89084e20	−0.00279904
$254$	−3.97832e22	−0.567257
$255$	3.59168e22	0.493362
$256$	4.72237e21	0.0625000
$257$	5.50451e22	0.702027	0.351014	−	0.936370i	$-0.385837\pi$
$257$	5.50451e22	0.702027	0.351014	+	0.936370i	$0.385837\pi$
$258$	4.13659e22	0.508459
$259$	1.37944e22	0.163439
$260$	−1.84176e22	−0.210372
$261$	5.89394e22	0.649114
$262$	−9.99129e22	−1.06111
$263$	−1.50721e23	−1.54381	−0.771905	−	0.635739i	$-0.780696\pi$
$263$	−1.50721e23	−1.54381	−0.771905	+	0.635739i	$0.780696\pi$
$264$	−3.92714e22	−0.388007
$265$	−2.43822e22	−0.232401
$266$	−2.36068e23	−2.17101
$267$	1.22889e22	0.109058
$268$	1.39712e22	0.119661
$269$	2.46567e22	0.203840	0.101920	−	0.994793i	$-0.467501\pi$
$269$	2.46567e22	0.203840	0.101920	+	0.994793i	$0.467501\pi$
$270$	4.23176e22	0.337726
$271$	1.19461e23	0.920486	0.460243	−	0.887793i	$-0.347762\pi$
$271$	1.19461e23	0.920486	0.460243	+	0.887793i	$0.347762\pi$
$272$	−5.12827e22	−0.381563
$273$	−1.52377e23	−1.09490
$274$	2.95803e22	0.205292
$275$	−4.52951e22	−0.303662
$276$	1.02868e20	0.000666259 0
$277$	−2.64149e23	−1.65307	−0.826534	−	0.562887i	$-0.809691\pi$
$277$	−2.64149e23	−1.65307	−0.826534	+	0.562887i	$0.809691\pi$
$278$	1.42473e23	0.861600
$279$	8.78192e22	0.513274
$280$	4.50628e22	0.254576
$281$	1.29520e23	0.707336	0.353668	−	0.935371i	$-0.384934\pi$
$281$	1.29520e23	0.707336	0.353668	+	0.935371i	$0.384934\pi$
$282$	1.63595e22	0.0863781
$283$	1.58389e23	0.808637	0.404319	−	0.914618i	$-0.367509\pi$
$283$	1.58389e23	0.808637	0.404319	+	0.914618i	$0.367509\pi$
$284$	1.06652e23	0.526558
$285$	−1.29091e23	−0.616409
$286$	−2.18688e23	−1.01006
$287$	−3.25914e23	−1.45621
$288$	−1.95285e22	−0.0844190
$289$	3.17835e23	1.32945
$290$	1.06191e23	0.429839
$291$	−2.68190e22	−0.105065
$292$	−1.57097e23	−0.595703
$293$	−2.31547e23	−0.849956	−0.424978	−	0.905204i	$-0.639718\pi$
$293$	−2.31547e23	−0.849956	−0.424978	+	0.905204i	$0.639718\pi$
$294$	2.29007e23	0.813859
$295$	2.16302e23	0.744306
$296$	−1.07704e22	−0.0358891
$297$	5.02472e23	1.62153
$298$	5.08900e22	0.159066
$299$	5.72832e20	0.00173441
$300$	2.46420e22	0.0722810
$301$	−5.63606e23	−1.60175
$302$	−1.17256e23	−0.322901
$303$	−3.07491e23	−0.820592
$304$	1.84318e23	0.476727
$305$	3.49463e22	0.0876097
$306$	2.12071e23	0.515379
$307$	6.27409e23	1.47821	0.739105	−	0.673590i	$-0.235249\pi$
$307$	6.27409e23	1.47821	0.739105	+	0.673590i	$0.235249\pi$
$308$	5.35069e23	1.22230
$309$	1.07628e23	0.238407
$310$	1.58223e23	0.339887
$311$	1.94001e23	0.404185	0.202092	−	0.979366i	$-0.435226\pi$
$311$	1.94001e23	0.404185	0.202092	+	0.979366i	$0.435226\pi$
$312$	1.18973e23	0.240426
$313$	−5.32021e23	−1.04294	−0.521468	−	0.853271i	$-0.674615\pi$
$313$	−5.32021e23	−1.04294	−0.521468	+	0.853271i	$0.674615\pi$
$314$	−6.07869e23	−1.15605
$315$	−1.86349e23	−0.343857
$316$	−4.81808e22	−0.0862673
$317$	−3.53503e23	−0.614229	−0.307115	−	0.951673i	$-0.599364\pi$
$317$	−3.53503e23	−0.614229	−0.307115	+	0.951673i	$0.599364\pi$
$318$	1.57503e23	0.265602
$319$	1.26089e24	2.06379
$320$	−3.51844e22	−0.0559017
$321$	2.03965e23	0.314600
$322$	−1.40156e21	−0.00209885
$323$	−2.00161e24	−2.91042
$324$	−1.04254e23	−0.147202
$325$	1.37222e23	0.188162
$326$	−5.21484e23	−0.694503
$327$	8.19844e22	0.106054
$328$	2.54468e23	0.319766
$329$	−2.22896e23	−0.272108
$330$	2.92595e23	0.347044
$331$	−4.17532e23	−0.481198	−0.240599	−	0.970625i	$-0.577344\pi$
$331$	−4.17532e23	−0.481198	−0.240599	+	0.970625i	$0.577344\pi$
$332$	−2.35224e23	−0.263432
$333$	4.45392e22	0.0484755
$334$	3.36805e23	0.356276
$335$	−1.04093e23	−0.107028
$336$	−2.91095e23	−0.290945
$337$	2.40223e23	0.233416	0.116708	−	0.993166i	$-0.462766\pi$
$337$	2.40223e23	0.233416	0.116708	+	0.993166i	$0.462766\pi$
$338$	−8.59842e22	−0.0812288
$339$	−5.53472e22	−0.0508391
$340$	3.82086e23	0.341281
$341$	1.87872e24	1.63190
$342$	−7.62216e23	−0.643917
$343$	−1.16071e24	−0.953740
$344$	4.40055e23	0.351724
$345$	−7.66424e20	−0.000595920 0
$346$	−8.53472e23	−0.645604
$347$	3.89549e23	0.286703	0.143352	−	0.989672i	$-0.454212\pi$
$347$	3.89549e23	0.286703	0.143352	+	0.989672i	$0.454212\pi$
$348$	−6.85966e23	−0.491247
$349$	−1.58467e24	−1.10432	−0.552162	−	0.833737i	$-0.686197\pi$
$349$	−1.58467e24	−1.10432	−0.552162	+	0.833737i	$0.686197\pi$
$350$	−3.35744e23	−0.227700
$351$	−1.52225e24	−1.00477
$352$	−4.17773e23	−0.268402
$353$	2.44509e24	1.52910	0.764549	−	0.644566i	$-0.222962\pi$
$353$	2.44509e24	1.52910	0.764549	+	0.644566i	$0.222962\pi$
$354$	−1.39726e24	−0.850640
$355$	−7.94622e23	−0.470968
$356$	1.30731e23	0.0754403
$357$	3.16116e24	1.77623
$358$	3.66444e23	0.200502
$359$	−5.89119e23	−0.313911	−0.156955	−	0.987606i	$-0.550168\pi$
$359$	−5.89119e23	−0.313911	−0.156955	+	0.987606i	$0.550168\pi$
$360$	1.45499e23	0.0755067
$361$	5.21570e24	2.63630
$362$	1.79582e24	0.884159
$363$	1.96714e24	0.943458
$364$	−1.62100e24	−0.757390
$365$	1.17046e24	0.532813
$366$	−2.25744e23	−0.100126
$367$	−2.11054e24	−0.912151	−0.456076	−	0.889941i	$-0.650745\pi$
$367$	−2.11054e24	−0.912151	−0.456076	+	0.889941i	$0.650745\pi$
$368$	1.09432e21	0.000460881 0
$369$	−1.05231e24	−0.431909
$370$	8.02461e22	0.0321002
$371$	−2.14596e24	−0.836700
$372$	−1.02208e24	−0.388444
$373$	3.05511e24	1.13186	0.565930	−	0.824453i	$-0.308517\pi$
$373$	3.05511e24	1.13186	0.565930	+	0.824453i	$0.308517\pi$
$374$	4.53683e24	1.63860
$375$	−1.83597e23	−0.0646501
$376$	1.74034e23	0.0597516
$377$	−3.81989e24	−1.27882
$378$	3.72451e24	1.21590
$379$	3.60276e24	1.14700	0.573499	−	0.819206i	$-0.305586\pi$
$379$	3.60276e24	1.14700	0.573499	+	0.819206i	$0.305586\pi$
$380$	−1.37328e24	−0.426398
$381$	−1.91472e24	−0.579854
$382$	−5.82680e23	−0.172119
$383$	1.73444e24	0.499771	0.249886	−	0.968275i	$-0.419607\pi$
$383$	1.73444e24	0.499771	0.249886	+	0.968275i	$0.419607\pi$
$384$	2.27282e23	0.0638880
$385$	−3.98657e24	−1.09326
$386$	−3.38621e24	−0.906012
$387$	−1.81977e24	−0.475075
$388$	−2.85304e23	−0.0726785
$389$	−4.06649e24	−1.01088	−0.505439	−	0.862862i	$-0.668669\pi$
$389$	−4.06649e24	−1.01088	−0.505439	+	0.862862i	$0.668669\pi$
$390$	−8.86421e23	−0.215044
$391$	−1.18838e22	−0.00281369
$392$	2.43620e24	0.562983
$393$	−4.80870e24	−1.08467
$394$	−4.70778e24	−1.03658
$395$	3.58975e23	0.0771599
$396$	1.72763e24	0.362531
$397$	−3.09096e24	−0.633262	−0.316631	−	0.948549i	$-0.602552\pi$
$397$	−3.09096e24	−0.633262	−0.316631	+	0.948549i	$0.602552\pi$
$398$	5.74941e24	1.15010
$399$	−1.13617e25	−2.21922
$400$	2.62144e23	0.0500000
$401$	3.67661e24	0.684819	0.342410	−	0.939551i	$-0.388757\pi$
$401$	3.67661e24	0.684819	0.342410	+	0.939551i	$0.388757\pi$
$402$	6.72416e23	0.122318
$403$	−5.69160e24	−1.01120
$404$	−3.27112e24	−0.567640
$405$	7.76750e23	0.131661
$406$	9.34621e24	1.54753
$407$	9.52828e23	0.154123
$408$	−2.46818e24	−0.390037
$409$	6.36544e24	0.982781	0.491391	−	0.870939i	$-0.336489\pi$
$409$	6.36544e24	0.982781	0.491391	+	0.870939i	$0.336489\pi$
$410$	−1.89594e24	−0.286007
$411$	1.42367e24	0.209851
$412$	1.14495e24	0.164917
$413$	1.90375e25	2.67969
$414$	−4.52535e21	−0.000622514 0
$415$	1.75255e24	0.235621
$416$	1.26565e24	0.166313
$417$	6.85705e24	0.880734
$418$	−1.63061e25	−2.04727
$419$	6.35539e23	0.0780026	0.0390013	−	0.999239i	$-0.487582\pi$
$419$	6.35539e23	0.0780026	0.0390013	+	0.999239i	$0.487582\pi$
$420$	2.16883e24	0.260229
$421$	−1.08840e25	−1.27676	−0.638379	−	0.769722i	$-0.720395\pi$
$421$	−1.08840e25	−1.27676	−0.638379	+	0.769722i	$0.720395\pi$
$422$	6.01643e24	0.690035
$423$	−7.19686e23	−0.0807067
$424$	1.67553e24	0.183729
$425$	−2.84676e24	−0.305251
$426$	5.13306e24	0.538252
$427$	3.07574e24	0.315417
$428$	2.16980e24	0.217623
$429$	−1.05252e25	−1.03249
$430$	−3.27866e24	−0.314591
$431$	1.35649e25	1.27316	0.636581	−	0.771210i	$-0.280348\pi$
$431$	1.35649e25	1.27316	0.636581	+	0.771210i	$0.280348\pi$
$432$	−2.90804e24	−0.266996
$433$	3.29653e24	0.296089	0.148045	−	0.988981i	$-0.452702\pi$
$433$	3.29653e24	0.296089	0.148045	+	0.988981i	$0.452702\pi$
$434$	1.39258e25	1.22368
$435$	5.11085e24	0.439385
$436$	8.72158e23	0.0733624
$437$	4.27122e22	0.00351543
$438$	−7.56089e24	−0.608932
$439$	−9.64911e23	−0.0760456	−0.0380228	−	0.999277i	$-0.512106\pi$
$439$	−9.64911e23	−0.0760456	−0.0380228	+	0.999277i	$0.512106\pi$
$440$	3.11265e24	0.240066
$441$	−1.00745e25	−0.760423
$442$	−1.37444e25	−1.01535
$443$	8.91796e24	0.644808	0.322404	−	0.946602i	$-0.395509\pi$
$443$	8.91796e24	0.644808	0.322404	+	0.946602i	$0.395509\pi$
$444$	−5.18370e23	−0.0366861
$445$	−9.74022e23	−0.0674759
$446$	−8.69784e24	−0.589835
$447$	2.44928e24	0.162599
$448$	−3.09670e24	−0.201260
$449$	1.16852e25	0.743527	0.371763	−	0.928328i	$-0.378753\pi$
$449$	1.16852e25	0.743527	0.371763	+	0.928328i	$0.378753\pi$
$450$	−1.08405e24	−0.0675352
$451$	−2.25120e25	−1.37321
$452$	−5.88789e23	−0.0351677
$453$	−5.64341e24	−0.330072
$454$	−1.52257e25	−0.872059
$455$	1.20774e25	0.677430
$456$	8.87104e24	0.487314
$457$	1.98632e25	1.06868	0.534338	−	0.845271i	$-0.320561\pi$
$457$	1.98632e25	1.06868	0.534338	+	0.845271i	$0.320561\pi$
$458$	−2.09424e25	−1.10358
$459$	3.15800e25	1.63002
$460$	−8.15330e21	−0.000412225 0
$461$	−1.83474e25	−0.908689	−0.454344	−	0.890826i	$-0.650126\pi$
$461$	−1.83474e25	−0.908689	−0.454344	+	0.890826i	$0.650126\pi$
$462$	2.57523e25	1.24944
$463$	5.05460e24	0.240252	0.120126	−	0.992759i	$-0.461670\pi$
$463$	5.05460e24	0.240252	0.120126	+	0.992759i	$0.461670\pi$
$464$	−7.29737e24	−0.339818
$465$	7.61511e24	0.347435
$466$	−7.37111e24	−0.329508
$467$	−3.18740e25	−1.39613	−0.698066	−	0.716034i	$-0.745956\pi$
$467$	−3.18740e25	−1.39613	−0.698066	+	0.716034i	$0.745956\pi$
$468$	−5.23387e24	−0.224640
$469$	−9.16160e24	−0.385327
$470$	−1.29665e24	−0.0534434
$471$	−2.92561e25	−1.18173
$472$	−1.48642e25	−0.588426
$473$	−3.89303e25	−1.51045
$474$	−2.31889e24	−0.0881831
$475$	1.02317e25	0.381382
$476$	3.36287e25	1.22869
$477$	−6.92887e24	−0.248164
$478$	−6.85411e23	−0.0240650
$479$	3.50098e25	1.20504	0.602522	−	0.798102i	$-0.294163\pi$
$479$	3.50098e25	1.20504	0.602522	+	0.798102i	$0.294163\pi$
$480$	−1.69339e24	−0.0571431
$481$	−2.88661e24	−0.0955014
$482$	2.28253e23	0.00740406
$483$	−6.74556e22	−0.00214546
$484$	2.09266e25	0.652633
$485$	2.12568e24	0.0650056
$486$	2.01646e25	0.604708
$487$	−1.57498e25	−0.463180	−0.231590	−	0.972813i	$-0.574393\pi$
$487$	−1.57498e25	−0.463180	−0.231590	+	0.972813i	$0.574393\pi$
$488$	−2.40149e24	−0.0692616
$489$	−2.50985e25	−0.709926
$490$	−1.81511e25	−0.503547
$491$	−3.70143e24	−0.100715	−0.0503576	−	0.998731i	$-0.516036\pi$
$491$	−3.70143e24	−0.100715	−0.0503576	+	0.998731i	$0.516036\pi$
$492$	1.22473e25	0.326867
$493$	7.92462e25	2.07459
$494$	4.93996e25	1.26858
$495$	−1.28718e25	−0.324258
$496$	−1.08730e25	−0.268704
$497$	−6.99374e25	−1.69560
$498$	−1.13211e25	−0.269282
$499$	6.92981e25	1.61721	0.808605	−	0.588352i	$-0.200223\pi$
$499$	6.92981e25	1.61721	0.808605	+	0.588352i	$0.200223\pi$
$500$	−1.95313e24	−0.0447214
$501$	1.62100e25	0.364188
$502$	3.32608e25	0.733243
$503$	−2.62932e25	−0.568784	−0.284392	−	0.958708i	$-0.591792\pi$
$503$	−2.62932e25	−0.568784	−0.284392	+	0.958708i	$0.591792\pi$
$504$	1.28058e25	0.271843
$505$	2.43717e25	0.507713
$506$	−9.68109e22	−0.00197922
$507$	−4.13832e24	−0.0830326
$508$	−2.03690e25	−0.401111
$509$	2.76861e25	0.535110	0.267555	−	0.963543i	$-0.413784\pi$
$509$	2.76861e25	0.535110	0.267555	+	0.963543i	$0.413784\pi$
$510$	1.83894e25	0.348860
$511$	1.03016e26	1.91826
$512$	2.41785e24	0.0441942
$513$	−1.13504e26	−2.03655
$514$	2.81831e25	0.496408
$515$	−8.53057e24	−0.147506
$516$	2.11794e25	0.359535
$517$	−1.53963e25	−0.256599
$518$	7.06273e24	0.115569
$519$	−4.10767e25	−0.659941
$520$	−9.42984e24	−0.148755
$521$	−1.13503e26	−1.75812	−0.879062	−	0.476707i	$-0.841830\pi$
$521$	−1.13503e26	−1.75812	−0.879062	+	0.476707i	$0.841830\pi$
$522$	3.01770e25	0.458993
$523$	3.81599e25	0.569956	0.284978	−	0.958534i	$-0.408014\pi$
$523$	3.81599e25	0.569956	0.284978	+	0.958534i	$0.408014\pi$
$524$	−5.11554e25	−0.750317
$525$	−1.61590e25	−0.232756
$526$	−7.71690e25	−1.09164
$527$	1.18076e26	1.64044
$528$	−2.01070e25	−0.274362
$529$	−7.46152e25	−0.999997
$530$	−1.24837e25	−0.164332
$531$	6.14681e25	0.794789
$532$	−1.20867e26	−1.53514
$533$	6.82006e25	0.850902
$534$	6.29194e24	0.0771157
$535$	−1.61663e25	−0.194648
$536$	7.15323e24	0.0846129
$537$	1.76366e25	0.204955
$538$	1.26242e25	0.144136
$539$	−2.15523e26	−2.41769
$540$	2.16666e25	0.238809
$541$	5.74865e25	0.622575	0.311288	−	0.950316i	$-0.399240\pi$
$541$	5.74865e25	0.622575	0.311288	+	0.950316i	$0.399240\pi$
$542$	6.11639e25	0.650882
$543$	8.64307e25	0.903794
$544$	−2.62568e25	−0.269806
$545$	−6.49808e24	−0.0656173
$546$	−7.80169e25	−0.774210
$547$	5.65466e25	0.551477	0.275738	−	0.961233i	$-0.411078\pi$
$547$	5.65466e25	0.551477	0.275738	+	0.961233i	$0.411078\pi$
$548$	1.51451e25	0.145163
$549$	9.93093e24	0.0935519
$550$	−2.31911e25	−0.214721
$551$	−2.84823e26	−2.59200
$552$	5.26683e22	0.000471116 0
$553$	3.15946e25	0.277795
$554$	−1.35244e26	−1.16890
$555$	3.86216e24	0.0328130
$556$	7.29460e25	0.609243
$557$	−1.64938e26	−1.35424	−0.677122	−	0.735871i	$-0.736773\pi$
$557$	−1.64938e26	−1.35424	−0.677122	+	0.735871i	$0.736773\pi$
$558$	4.49634e25	0.362940
$559$	1.17940e26	0.935942
$560$	2.30722e25	0.180012
$561$	2.18353e26	1.67499
$562$	6.63141e25	0.500162
$563$	1.25674e26	0.931998	0.465999	−	0.884785i	$-0.345695\pi$
$563$	1.25674e26	0.931998	0.465999	+	0.884785i	$0.345695\pi$
$564$	8.37606e24	0.0610785
$565$	4.38682e24	0.0314550
$566$	8.10951e25	0.571793
$567$	6.83644e25	0.474014
$568$	5.46060e25	0.372333
$569$	1.89079e26	1.26787	0.633937	−	0.773384i	$-0.281438\pi$
$569$	1.89079e26	1.26787	0.633937	+	0.773384i	$0.281438\pi$
$570$	−6.60944e25	−0.435867
$571$	2.20726e26	1.43156	0.715782	−	0.698324i	$-0.246070\pi$
$571$	2.20726e26	1.43156	0.715782	+	0.698324i	$0.246070\pi$
$572$	−1.11968e26	−0.714221
$573$	−2.80438e25	−0.175941
$574$	−1.66868e26	−1.02970
$575$	6.07468e22	0.000368705 0
$576$	−9.99859e24	−0.0596932
$577$	2.17793e26	1.27901	0.639504	−	0.768788i	$-0.279140\pi$
$577$	2.17793e26	1.27901	0.639504	+	0.768788i	$0.279140\pi$
$578$	1.62731e26	0.940063
$579$	−1.62974e26	−0.926132
$580$	5.43697e25	0.303942
$581$	1.54248e26	0.848294
$582$	−1.37314e25	−0.0742925
$583$	−1.48229e26	−0.789011
$584$	−8.04335e25	−0.421226
$585$	3.89954e25	0.200924
$586$	−1.18552e26	−0.601010
$587$	1.18966e26	0.593418	0.296709	−	0.954968i	$-0.404111\pi$
$587$	1.18966e26	0.593418	0.296709	+	0.954968i	$0.404111\pi$
$588$	1.17252e26	0.575485
$589$	−4.24384e26	−2.04958
$590$	1.10747e26	0.526304
$591$	−2.26580e26	−1.05960
$592$	−5.51447e24	−0.0253774
$593$	−1.59827e26	−0.723819	−0.361909	−	0.932213i	$-0.617875\pi$
$593$	−1.59827e26	−0.723819	−0.361909	+	0.932213i	$0.617875\pi$
$594$	2.57266e26	1.14660
$595$	−2.50553e26	−1.09898
$596$	2.60557e25	0.112477
$597$	2.76713e26	1.17564
$598$	2.93290e23	0.00122641
$599$	−3.43041e26	−1.41186	−0.705929	−	0.708283i	$-0.749470\pi$
$599$	−3.43041e26	−1.41186	−0.705929	+	0.708283i	$0.749470\pi$
$600$	1.26167e25	0.0511104
$601$	8.43100e25	0.336180	0.168090	−	0.985772i	$-0.446240\pi$
$601$	8.43100e25	0.336180	0.168090	+	0.985772i	$0.446240\pi$
$602$	−2.88566e26	−1.13261
$603$	−2.95809e25	−0.114287
$604$	−6.00352e25	−0.228326
$605$	−1.55916e26	−0.583732
$606$	−1.57435e26	−0.580246
$607$	−2.96322e26	−1.07515	−0.537577	−	0.843215i	$-0.680660\pi$
$607$	−2.96322e26	−1.07515	−0.537577	+	0.843215i	$0.680660\pi$
$608$	9.43710e25	0.337097
$609$	4.49823e26	1.58189
$610$	1.78925e25	0.0619494
$611$	4.66432e25	0.159000
$612$	1.08580e26	0.364428
$613$	−2.49098e26	−0.823182	−0.411591	−	0.911369i	$-0.635027\pi$
$613$	−2.49098e26	−0.823182	−0.411591	+	0.911369i	$0.635027\pi$
$614$	3.21234e26	1.04525
$615$	−9.12494e25	−0.292359
$616$	2.73955e26	0.864296
$617$	−2.81111e26	−0.873311	−0.436655	−	0.899629i	$-0.643837\pi$
$617$	−2.81111e26	−0.873311	−0.436655	+	0.899629i	$0.643837\pi$
$618$	5.51054e25	0.168579
$619$	3.54941e26	1.06929	0.534644	−	0.845077i	$-0.320446\pi$
$619$	3.54941e26	1.06929	0.534644	+	0.845077i	$0.320446\pi$
$620$	8.10103e25	0.240336
$621$	−6.73882e23	−0.00196886
$622$	9.93284e25	0.285802
$623$	−8.57269e25	−0.242930
$624$	6.09144e25	0.170007
$625$	1.45519e25	0.0400000
$626$	−2.72395e26	−0.737467
$627$	−7.84794e26	−2.09273
$628$	−3.11229e26	−0.817454
$629$	5.98846e25	0.154929
$630$	−9.54108e25	−0.243143
$631$	4.45381e26	1.11803	0.559014	−	0.829158i	$-0.311180\pi$
$631$	4.45381e26	1.11803	0.559014	+	0.829158i	$0.311180\pi$
$632$	−2.46686e25	−0.0610002
$633$	2.89564e26	0.705359
$634$	−1.80994e26	−0.434326
$635$	1.51761e26	0.358765
$636$	8.06416e25	0.187809
$637$	6.52931e26	1.49811
$638$	6.45576e26	1.45932
$639$	−2.25813e26	−0.502911
$640$	−1.80144e25	−0.0395285
$641$	−7.95345e26	−1.71951	−0.859755	−	0.510707i	$-0.829384\pi$
$641$	−7.95345e26	−1.71951	−0.859755	+	0.510707i	$0.829384\pi$
$642$	1.04430e26	0.222456
$643$	−5.79551e26	−1.21643	−0.608215	−	0.793772i	$-0.708114\pi$
$643$	−5.79551e26	−1.21643	−0.608215	+	0.793772i	$0.708114\pi$
$644$	−7.17599e23	−0.00148411
$645$	−1.57799e26	−0.321577
$646$	−1.02483e27	−2.05798
$647$	1.30894e26	0.259017	0.129508	−	0.991578i	$-0.458660\pi$
$647$	1.30894e26	0.259017	0.129508	+	0.991578i	$0.458660\pi$
$648$	−5.33778e25	−0.104087
$649$	1.31499e27	2.52695
$650$	7.02577e25	0.133051
$651$	6.70232e26	1.25085
$652$	−2.67000e26	−0.491088
$653$	4.41638e25	0.0800555	0.0400278	−	0.999199i	$-0.487255\pi$
$653$	4.41638e25	0.0800555	0.0400278	+	0.999199i	$0.487255\pi$
$654$	4.19760e25	0.0749916
$655$	3.81138e26	0.671103
$656$	1.30288e26	0.226109
$657$	3.32618e26	0.568951
$658$	−1.14123e26	−0.192410
$659$	4.31537e26	0.717145	0.358572	−	0.933502i	$-0.383264\pi$
$659$	4.31537e26	0.717145	0.358572	+	0.933502i	$0.383264\pi$
$660$	1.49809e26	0.245397
$661$	2.81428e26	0.454416	0.227208	−	0.973846i	$-0.427040\pi$
$661$	2.81428e26	0.454416	0.227208	+	0.973846i	$0.427040\pi$
$662$	−2.13776e26	−0.340258
$663$	−6.61503e26	−1.03789
$664$	−1.20434e26	−0.186275
$665$	9.00529e26	1.37307
$666$	2.28041e25	0.0342774
$667$	−1.69103e24	−0.00250585
$668$	1.72444e26	0.251925
$669$	−4.18618e26	−0.602934
$670$	−5.32957e25	−0.0756801
$671$	2.12452e26	0.297439
$672$	−1.49041e26	−0.205729
$673$	−1.08863e27	−1.48162	−0.740808	−	0.671717i	$-0.765557\pi$
$673$	−1.08863e27	−1.48162	−0.740808	+	0.671717i	$0.765557\pi$
$674$	1.22994e26	0.165050
$675$	−1.61429e26	−0.213597
$676$	−4.40239e25	−0.0574374
$677$	6.72261e26	0.864859	0.432430	−	0.901668i	$-0.357656\pi$
$677$	6.72261e26	0.864859	0.432430	+	0.901668i	$0.357656\pi$
$678$	−2.83377e25	−0.0359487
$679$	1.87088e26	0.234036
$680$	1.95628e26	0.241322
$681$	−7.32795e26	−0.891425
$682$	9.61903e26	1.15393
$683$	1.31935e27	1.56085	0.780426	−	0.625248i	$-0.215002\pi$
$683$	1.31935e27	1.56085	0.780426	+	0.625248i	$0.215002\pi$
$684$	−3.90254e26	−0.455318
$685$	−1.12840e26	−0.129838
$686$	−5.94284e26	−0.674396
$687$	−1.00793e27	−1.12809
$688$	2.25308e26	0.248706
$689$	4.49063e26	0.488906
$690$	−3.92409e23	−0.000421379 0
$691$	−5.30733e26	−0.562127	−0.281063	−	0.959689i	$-0.590687\pi$
$691$	−5.30733e26	−0.562127	−0.281063	+	0.959689i	$0.590687\pi$
$692$	−4.36978e26	−0.456511
$693$	−1.13289e27	−1.16741
$694$	1.99449e26	0.202730
$695$	−5.43490e26	−0.544924
$696$	−3.51215e26	−0.347364
$697$	−1.41487e27	−1.38040
$698$	−8.11349e26	−0.780875
$699$	−3.54763e26	−0.336826
$700$	−1.71901e26	−0.161008
$701$	7.21166e26	0.666368	0.333184	−	0.942862i	$-0.391877\pi$
$701$	7.21166e26	0.666368	0.333184	+	0.942862i	$0.391877\pi$
$702$	−7.79390e26	−0.710481
$703$	−2.15235e26	−0.193570
$704$	−2.13900e26	−0.189789
$705$	−6.24065e25	−0.0546303
$706$	1.25189e27	1.08124
$707$	2.14504e27	1.82789
$708$	−7.15396e26	−0.601493
$709$	−1.98688e27	−1.64829	−0.824144	−	0.566380i	$-0.808344\pi$
$709$	−1.98688e27	−1.64829	−0.824144	+	0.566380i	$0.808344\pi$
$710$	−4.06846e26	−0.333025
$711$	1.02012e26	0.0823932
$712$	6.69343e25	0.0533444
$713$	−2.51961e24	−0.00198145
$714$	1.61851e27	1.25598
$715$	8.34229e26	0.638819
$716$	1.87619e26	0.141776
$717$	−3.29881e25	−0.0245994
$718$	−3.01629e26	−0.221968
$719$	−6.59753e26	−0.479134	−0.239567	−	0.970880i	$-0.577005\pi$
$719$	−6.59753e26	−0.479134	−0.239567	+	0.970880i	$0.577005\pi$
$720$	7.44953e25	0.0533913
$721$	−7.50804e26	−0.531058
$722$	2.67044e27	1.86414
$723$	1.09856e25	0.00756848
$724$	9.19458e26	0.625195
$725$	−4.05086e26	−0.271854
$726$	1.00718e27	0.667126
$727$	9.21607e26	0.602517	0.301258	−	0.953543i	$-0.402593\pi$
$727$	9.21607e26	0.602517	0.301258	+	0.953543i	$0.402593\pi$
$728$	−8.29952e26	−0.535556
$729$	1.43273e27	0.912541
$730$	5.99276e26	0.376756
$731$	−2.44674e27	−1.51835
$732$	−1.15581e26	−0.0707997
$733$	2.55317e27	1.54380	0.771902	−	0.635741i	$-0.219305\pi$
$733$	2.55317e27	1.54380	0.771902	+	0.635741i	$0.219305\pi$
$734$	−1.08060e27	−0.644988
$735$	−8.73592e26	−0.514730
$736$	5.60290e23	0.000325892 0
$737$	−6.32825e26	−0.363364
$738$	−5.38782e26	−0.305406
$739$	8.61254e26	0.481958	0.240979	−	0.970530i	$-0.422532\pi$
$739$	8.61254e26	0.481958	0.240979	+	0.970530i	$0.422532\pi$
$740$	4.10860e25	0.0226983
$741$	2.37755e27	1.29675
$742$	−1.09873e27	−0.591637
$743$	1.77819e27	0.945332	0.472666	−	0.881242i	$-0.343292\pi$
$743$	1.77819e27	0.945332	0.472666	+	0.881242i	$0.343292\pi$
$744$	−5.23306e26	−0.274671
$745$	−1.94130e26	−0.100602
$746$	1.56422e27	0.800346
$747$	4.98035e26	0.251602
$748$	2.32286e27	1.15866
$749$	−1.42285e27	−0.700780
$750$	−9.40018e25	−0.0457145
$751$	−7.84064e26	−0.376506	−0.188253	−	0.982121i	$-0.560283\pi$
$751$	−7.84064e26	−0.376506	−0.188253	+	0.982121i	$0.560283\pi$
$752$	8.91054e25	0.0422507
$753$	1.60081e27	0.749526
$754$	−1.95578e27	−0.904260
$755$	4.47297e26	0.204221
$756$	1.90695e27	0.859770
$757$	−2.37844e27	−1.05896	−0.529482	−	0.848321i	$-0.677614\pi$
$757$	−2.37844e27	−1.05896	−0.529482	+	0.848321i	$0.677614\pi$
$758$	1.84461e27	0.811050
$759$	−4.65940e24	−0.00202317
$760$	−7.03119e26	−0.301509
$761$	−2.10930e26	−0.0893274	−0.0446637	−	0.999002i	$-0.514222\pi$
$761$	−2.10930e26	−0.0893274	−0.0446637	+	0.999002i	$0.514222\pi$
$762$	−9.80338e26	−0.410019
$763$	−5.71918e26	−0.236239
$764$	−2.98332e26	−0.121706
$765$	−8.08985e26	−0.325954
$766$	8.88034e26	0.353392
$767$	−3.98378e27	−1.56581
$768$	1.16369e26	0.0451756
$769$	−4.28007e27	−1.64116	−0.820580	−	0.571531i	$-0.806350\pi$
$769$	−4.28007e27	−1.64116	−0.820580	+	0.571531i	$0.806350\pi$
$770$	−2.04113e27	−0.773050
$771$	1.35642e27	0.507432
$772$	−1.73374e27	−0.640647
$773$	2.45388e27	0.895672	0.447836	−	0.894116i	$-0.352195\pi$
$773$	2.45388e27	0.895672	0.447836	+	0.894116i	$0.352195\pi$
$774$	−9.31721e26	−0.335928
$775$	−6.03574e26	−0.214963
$776$	−1.46075e26	−0.0513915
$777$	3.39921e26	0.118135
$778$	−2.08204e27	−0.714798
$779$	5.08526e27	1.72467
$780$	−4.53848e26	−0.152059
$781$	−4.83083e27	−1.59896
$782$	−6.08450e24	−0.00198958
$783$	4.49374e27	1.45168
$784$	1.24733e27	0.398089
$785$	2.31884e27	0.731153
$786$	−2.46205e27	−0.766979
$787$	2.50919e27	0.772277	0.386139	−	0.922441i	$-0.373809\pi$
$787$	2.50919e27	0.772277	0.386139	+	0.922441i	$0.373809\pi$
$788$	−2.41038e27	−0.732971
$789$	−3.71406e27	−1.11588
$790$	1.83795e26	0.0545603
$791$	3.86098e26	0.113246
$792$	8.84545e26	0.256348
$793$	−6.43628e26	−0.184306
$794$	−1.58257e27	−0.447784
$795$	−6.00827e26	−0.167982
$796$	2.94370e27	0.813241
$797$	−1.61921e27	−0.442027	−0.221014	−	0.975271i	$-0.570937\pi$
$797$	−1.61921e27	−0.442027	−0.221014	+	0.975271i	$0.570937\pi$
$798$	−5.81719e27	−1.56923
$799$	−9.67644e26	−0.257941
$800$	1.34218e26	0.0353553
$801$	−2.76795e26	−0.0720524
$802$	1.88242e27	0.484240
$803$	7.11570e27	1.80892
$804$	3.44277e26	0.0864920
$805$	5.34653e24	0.00132743
$806$	−2.91410e27	−0.715026
$807$	6.07591e26	0.147337
$808$	−1.67481e27	−0.401382
$809$	−7.94590e27	−1.88205	−0.941027	−	0.338331i	$-0.890138\pi$
$809$	−7.94590e27	−1.88205	−0.941027	+	0.338331i	$0.890138\pi$
$810$	3.97696e26	0.0930987
$811$	2.91673e27	0.674836	0.337418	−	0.941355i	$-0.390446\pi$
$811$	2.91673e27	0.674836	0.337418	+	0.941355i	$0.390446\pi$
$812$	4.78526e27	1.09427
$813$	2.94375e27	0.665336
$814$	4.87848e26	0.108982
$815$	1.98930e27	0.439242
$816$	−1.26371e27	−0.275798
$817$	8.79399e27	1.89704
$818$	3.25910e27	0.694931
$819$	3.43212e27	0.723377
$820$	−9.70720e26	−0.202238
$821$	4.62333e27	0.952127	0.476064	−	0.879411i	$-0.342063\pi$
$821$	4.62333e27	0.952127	0.476064	+	0.879411i	$0.342063\pi$
$822$	7.28918e26	0.148387
$823$	−6.19239e27	−1.24612	−0.623060	−	0.782174i	$-0.714111\pi$
$823$	−6.19239e27	−1.24612	−0.623060	+	0.782174i	$0.714111\pi$
$824$	5.86216e26	0.116614
$825$	−1.11616e27	−0.219490
$826$	9.74719e27	1.89482
$827$	−4.54495e27	−0.873427	−0.436714	−	0.899601i	$-0.643858\pi$
$827$	−4.54495e27	−0.873427	−0.436714	+	0.899601i	$0.643858\pi$
$828$	−2.31698e24	−0.000440184 0
$829$	1.99146e27	0.374028	0.187014	−	0.982357i	$-0.440119\pi$
$829$	1.99146e27	0.374028	0.187014	+	0.982357i	$0.440119\pi$
$830$	8.97307e26	0.166609
$831$	−6.50915e27	−1.19485
$832$	6.48013e26	0.117601
$833$	−1.35455e28	−2.43034
$834$	3.51081e27	0.622773
$835$	−1.28481e27	−0.225329
$836$	−8.34872e27	−1.44764
$837$	6.69562e27	1.14789
$838$	3.25396e26	0.0551562
$839$	3.76828e27	0.631546	0.315773	−	0.948835i	$-0.397736\pi$
$839$	3.76828e27	0.631546	0.315773	+	0.948835i	$0.397736\pi$
$840$	1.11044e27	0.184010
$841$	5.17322e27	0.847615
$842$	−5.57261e27	−0.902805
$843$	3.19163e27	0.511270
$844$	3.08041e27	0.487928
$845$	3.28004e26	0.0513736
$846$	−3.68479e26	−0.0570683
$847$	−1.37227e28	−2.10158
$848$	8.57874e26	0.129916
$849$	3.90302e27	0.584491
$850$	−1.45754e27	−0.215845
$851$	−1.27787e24	−0.000187136 0
$852$	2.62813e27	0.380601
$853$	4.42489e27	0.633704	0.316852	−	0.948475i	$-0.397374\pi$
$853$	4.42489e27	0.633704	0.316852	+	0.948475i	$0.397374\pi$
$854$	1.57478e27	0.223033
$855$	2.90762e27	0.407249
$856$	1.11094e27	0.153883
$857$	2.76062e26	0.0378171	0.0189086	−	0.999821i	$-0.493981\pi$
$857$	2.76062e26	0.0378171	0.0189086	+	0.999821i	$0.493981\pi$
$858$	−5.38891e27	−0.730082
$859$	−3.05008e27	−0.408673	−0.204337	−	0.978901i	$-0.565504\pi$
$859$	−3.05008e27	−0.408673	−0.204337	+	0.978901i	$0.565504\pi$
$860$	−1.67868e27	−0.222450
$861$	−8.03116e27	−1.05256
$862$	6.94525e27	0.900262
$863$	−1.22346e28	−1.56851	−0.784255	−	0.620439i	$-0.786955\pi$
$863$	−1.22346e28	−1.56851	−0.784255	+	0.620439i	$0.786955\pi$
$864$	−1.48892e27	−0.188795
$865$	3.25574e27	0.408316
$866$	1.68782e27	0.209367
$867$	7.83209e27	0.960939
$868$	7.12999e27	0.865270
$869$	2.18235e27	0.261961
$870$	2.61675e27	0.310692
$871$	1.91715e27	0.225156
$872$	4.46545e26	0.0518750
$873$	6.04069e26	0.0694146
$874$	2.18687e25	0.00248578
$875$	1.28076e27	0.144010
$876$	−3.87118e27	−0.430580
$877$	−7.55805e27	−0.831599	−0.415799	−	0.909456i	$-0.636498\pi$
$877$	−7.55805e27	−0.831599	−0.415799	+	0.909456i	$0.636498\pi$
$878$	−4.94034e26	−0.0537724
$879$	−5.70578e27	−0.614357
$880$	1.59368e27	0.169752
$881$	−9.37300e27	−0.987661	−0.493830	−	0.869558i	$-0.664404\pi$
$881$	−9.37300e27	−0.987661	−0.493830	+	0.869558i	$0.664404\pi$
$882$	−5.15813e27	−0.537700
$883$	−1.36374e28	−1.40639	−0.703196	−	0.710996i	$-0.748244\pi$
$883$	−1.36374e28	−1.40639	−0.703196	+	0.710996i	$0.748244\pi$
$884$	−7.03713e27	−0.717958
$885$	5.33012e27	0.537992
$886$	4.56600e27	0.455948
$887$	−1.16121e28	−1.14720	−0.573598	−	0.819137i	$-0.694453\pi$
$887$	−1.16121e28	−1.14720	−0.573598	+	0.819137i	$0.694453\pi$
$888$	−2.65405e26	−0.0259410
$889$	1.33570e28	1.29164
$890$	−4.98699e26	−0.0477127
$891$	4.72218e27	0.446996
$892$	−4.45330e27	−0.417076
$893$	3.47787e27	0.322273
$894$	1.25403e27	0.114975
$895$	−1.39787e27	−0.126809
$896$	−1.58551e27	−0.142312
$897$	1.41157e25	0.00125365
$898$	5.98283e27	0.525753
$899$	1.68018e28	1.46097
$900$	−5.55033e26	−0.0477546
$901$	−9.31612e27	−0.793139
$902$	−1.15262e28	−0.971008
$903$	−1.38884e28	−1.15776
$904$	−3.01460e26	−0.0248673
$905$	−6.85050e27	−0.559191
$906$	−2.88943e27	−0.233396
$907$	−1.97468e27	−0.157844	−0.0789220	−	0.996881i	$-0.525148\pi$
$907$	−1.97468e27	−0.157844	−0.0789220	+	0.996881i	$0.525148\pi$
$908$	−7.79555e27	−0.616639
$909$	6.92589e27	0.542149
$910$	6.18362e27	0.479016
$911$	−2.08882e28	−1.60131	−0.800657	−	0.599123i	$-0.795516\pi$
$911$	−2.08882e28	−1.60131	−0.800657	+	0.599123i	$0.795516\pi$
$912$	4.54197e27	0.344583
$913$	1.06545e28	0.799944
$914$	1.01700e28	0.755667
$915$	8.61146e26	0.0633252
$916$	−1.07225e28	−0.780348
$917$	3.35452e28	2.41614
$918$	1.61690e28	1.15259
$919$	1.79207e28	1.26432	0.632161	−	0.774837i	$-0.282168\pi$
$919$	1.79207e28	1.26432	0.632161	+	0.774837i	$0.282168\pi$
$920$	−4.17449e24	−0.000291487 0
$921$	1.54606e28	1.06847
$922$	−9.39385e27	−0.642540
$923$	1.46351e28	0.990783
$924$	1.31852e28	0.883490
$925$	−3.06114e26	−0.0203019
$926$	2.58796e27	0.169884
$927$	−2.42419e27	−0.157511
$928$	−3.73626e27	−0.240287
$929$	5.15951e27	0.328442	0.164221	−	0.986424i	$-0.447489\pi$
$929$	5.15951e27	0.328442	0.164221	+	0.986424i	$0.447489\pi$
$930$	3.89894e27	0.245673
$931$	4.86846e28	3.03648
$932$	−3.77401e27	−0.232998
$933$	4.78057e27	0.292149
$934$	−1.63195e28	−0.987214
$935$	−1.73066e28	−1.03634
$936$	−2.67974e27	−0.158845
$937$	−6.09796e27	−0.357815	−0.178907	−	0.983866i	$-0.557256\pi$
$937$	−6.09796e27	−0.357815	−0.178907	+	0.983866i	$0.557256\pi$
$938$	−4.69074e27	−0.272467
$939$	−1.31101e28	−0.753844
$940$	−6.63887e26	−0.0377902
$941$	1.85597e28	1.04585	0.522926	−	0.852378i	$-0.324840\pi$
$941$	1.85597e28	1.04585	0.522926	+	0.852378i	$0.324840\pi$
$942$	−1.49791e28	−0.835607
$943$	3.01917e25	0.00166735
$944$	−7.61045e27	−0.416080
$945$	−1.42079e28	−0.769002
$946$	−1.99323e28	−1.06805
$947$	−6.33527e27	−0.336078	−0.168039	−	0.985780i	$-0.553743\pi$
$947$	−6.33527e27	−0.336078	−0.168039	+	0.985780i	$0.553743\pi$
$948$	−1.18727e27	−0.0623549
$949$	−2.15571e28	−1.12089
$950$	5.23864e27	0.269677
$951$	−8.71103e27	−0.443971
$952$	1.72179e28	0.868818
$953$	−1.79400e28	−0.896270	−0.448135	−	0.893966i	$-0.647912\pi$
$953$	−1.79400e28	−0.896270	−0.448135	+	0.893966i	$0.647912\pi$
$954$	−3.54758e27	−0.175478
$955$	2.22275e27	0.108857
$956$	−3.50930e26	−0.0170165
$957$	3.10709e28	1.49173
$958$	1.79250e28	0.852094
$959$	−9.93142e27	−0.467449
$960$	−8.67013e26	−0.0404063
$961$	3.36393e27	0.155230
$962$	−1.47794e27	−0.0675297
$963$	−4.59409e27	−0.207850
$964$	1.16866e26	0.00523546
$965$	1.29173e28	0.573012
$966$	−3.45373e25	−0.00151707
$967$	−1.97692e28	−0.859878	−0.429939	−	0.902858i	$-0.641465\pi$
$967$	−1.97692e28	−0.859878	−0.429939	+	0.902858i	$0.641465\pi$
$968$	1.07144e28	0.461481
$969$	−4.93238e28	−2.10368
$970$	1.08835e27	0.0459659
$971$	−2.38503e28	−0.997497	−0.498749	−	0.866747i	$-0.666207\pi$
$971$	−2.38503e28	−0.997497	−0.498749	+	0.866747i	$0.666207\pi$
$972$	1.03243e28	0.427593
$973$	−4.78344e28	−1.96186
$974$	−8.06389e27	−0.327518
$975$	3.38143e27	0.136005
$976$	−1.22956e27	−0.0489753
$977$	3.35823e28	1.32468	0.662342	−	0.749202i	$-0.269563\pi$
$977$	3.35823e28	1.32468	0.662342	+	0.749202i	$0.269563\pi$
$978$	−1.28504e28	−0.501994
$979$	−5.92147e27	−0.229084
$980$	−9.29336e27	−0.356062
$981$	−1.84661e27	−0.0700678
$982$	−1.89513e27	−0.0712164
$983$	6.16542e27	0.229458	0.114729	−	0.993397i	$-0.463400\pi$
$983$	6.16542e27	0.229458	0.114729	+	0.993397i	$0.463400\pi$
$984$	6.27061e27	0.231130
$985$	1.79588e28	0.655589
$986$	4.05740e28	1.46696
$987$	−5.49261e27	−0.196683
$988$	2.52926e28	0.897020
$989$	5.22108e25	0.00183398
$990$	−6.59037e27	−0.229285
$991$	−8.76452e27	−0.302015	−0.151007	−	0.988533i	$-0.548252\pi$
$991$	−8.76452e27	−0.302015	−0.151007	+	0.988533i	$0.548252\pi$
$992$	−5.56699e27	−0.190002
$993$	−1.02888e28	−0.347814
$994$	−3.58079e28	−1.19897
$995$	−2.19323e28	−0.727385
$996$	−5.79638e27	−0.190411
$997$	−5.05411e28	−1.64453	−0.822263	−	0.569107i	$-0.807289\pi$
$997$	−5.05411e28	−1.64453	−0.822263	+	0.569107i	$0.807289\pi$
$998$	3.54806e28	1.14354
$999$	3.39582e27	0.108411

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.20.a.c.1.1	✓	1
3.2	odd	2		90.20.a.b.1.1		1
4.3	odd	2		80.20.a.b.1.1		1
5.2	odd	4		50.20.b.d.49.2		2
5.3	odd	4		50.20.b.d.49.1		2
5.4	even	2		50.20.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.20.a.c.1.1	✓	1	1.1	even	1	trivial
50.20.a.a.1.1		1	5.4	even	2
50.20.b.d.49.1		2	5.3	odd	4
50.20.b.d.49.2		2	5.2	odd	4
80.20.a.b.1.1		1	4.3	odd	2
90.20.a.b.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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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