LMFDB - Embedded newform 10.16.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,16,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, 16, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 16 $
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:	$14.2693505100$
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)

$f(q)$

$=$

$q-128.000 q^{2} -5568.00 q^{3} +16384.0 q^{4} +78125.0 q^{5} +712704. q^{6} +2.56500e6 q^{7} -2.09715e6 q^{8} +1.66537e7 q^{9} +O(q^{10})$

\(q-128.000 q^{2} -5568.00 q^{3} +16384.0 q^{4} +78125.0 q^{5} +712704. q^{6} +2.56500e6 q^{7} -2.09715e6 q^{8} +1.66537e7 q^{9} -1.00000e7 q^{10} -8.10677e7 q^{11} -9.12261e7 q^{12} +3.51412e8 q^{13} -3.28319e8 q^{14} -4.35000e8 q^{15} +2.68435e8 q^{16} -2.15783e9 q^{17} -2.13168e9 q^{18} -5.10746e9 q^{19} +1.28000e9 q^{20} -1.42819e10 q^{21} +1.03767e10 q^{22} +1.17843e10 q^{23} +1.16769e10 q^{24} +6.10352e9 q^{25} -4.49807e10 q^{26} -1.28332e10 q^{27} +4.20249e10 q^{28} -2.04006e10 q^{29} +5.56800e10 q^{30} -1.23614e11 q^{31} -3.43597e10 q^{32} +4.51385e11 q^{33} +2.76202e11 q^{34} +2.00390e11 q^{35} +2.72854e11 q^{36} -2.24996e10 q^{37} +6.53755e11 q^{38} -1.95666e12 q^{39} -1.63840e11 q^{40} -1.04406e12 q^{41} +1.82808e12 q^{42} -2.98423e12 q^{43} -1.32821e12 q^{44} +1.30107e12 q^{45} -1.50840e12 q^{46} -2.26736e12 q^{47} -1.49465e12 q^{48} +1.83164e12 q^{49} -7.81250e11 q^{50} +1.20148e13 q^{51} +5.75753e12 q^{52} -8.65580e12 q^{53} +1.64265e12 q^{54} -6.33341e12 q^{55} -5.37919e12 q^{56} +2.84383e13 q^{57} +2.61127e12 q^{58} -2.59530e13 q^{59} -7.12704e12 q^{60} +2.98097e13 q^{61} +1.58226e13 q^{62} +4.27167e13 q^{63} +4.39805e12 q^{64} +2.74541e13 q^{65} -5.77773e13 q^{66} -7.81037e13 q^{67} -3.53538e13 q^{68} -6.56152e13 q^{69} -2.56500e13 q^{70} +6.77469e13 q^{71} -3.49254e13 q^{72} +1.34520e14 q^{73} +2.87995e12 q^{74} -3.39844e13 q^{75} -8.36806e13 q^{76} -2.07938e14 q^{77} +2.50453e14 q^{78} +1.67235e13 q^{79} +2.09715e13 q^{80} -1.67507e14 q^{81} +1.33640e14 q^{82} +8.08836e13 q^{83} -2.33995e14 q^{84} -1.68580e14 q^{85} +3.81982e14 q^{86} +1.13590e14 q^{87} +1.70011e14 q^{88} -5.23835e14 q^{89} -1.66537e14 q^{90} +9.01370e14 q^{91} +1.93075e14 q^{92} +6.88282e14 q^{93} +2.90222e14 q^{94} -3.99020e14 q^{95} +1.91315e14 q^{96} +1.18664e15 q^{97} -2.34450e14 q^{98} -1.35008e15 q^{99} +O(q^{100})\)

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 $

$2$	−128.000	−0.707107
$2$	−128.000	−0.707107
$3$	−5568.00	−1.46991	−0.734953	−	0.678118i	$-0.762796\pi$
$3$	−5568.00	−1.46991	−0.734953	+	0.678118i	$0.762796\pi$
$4$	16384.0	0.500000
$5$	78125.0	0.447214
$5$	78125.0	0.447214
$6$	712704.	1.03938
$7$	2.56500e6	1.17720	0.588602	−	0.808423i	$-0.299679\pi$
$7$	2.56500e6	1.17720	0.588602	+	0.808423i	$0.299679\pi$
$8$	−2.09715e6	−0.353553
$9$	1.66537e7	1.16063
$10$	−1.00000e7	−0.316228
$11$	−8.10677e7	−1.25430	−0.627152	−	0.778897i	$-0.715779\pi$
$11$	−8.10677e7	−1.25430	−0.627152	+	0.778897i	$0.715779\pi$
$12$	−9.12261e7	−0.734953
$13$	3.51412e8	1.55325	0.776625	−	0.629963i	$-0.216930\pi$
$13$	3.51412e8	1.55325	0.776625	+	0.629963i	$0.216930\pi$
$14$	−3.28319e8	−0.832408
$15$	−4.35000e8	−0.657362
$16$	2.68435e8	0.250000
$17$	−2.15783e9	−1.27541	−0.637704	−	0.770281i	$-0.720116\pi$
$17$	−2.15783e9	−1.27541	−0.637704	+	0.770281i	$0.720116\pi$
$18$	−2.13168e9	−0.820687
$19$	−5.10746e9	−1.31085	−0.655425	−	0.755261i	$-0.727510\pi$
$19$	−5.10746e9	−1.31085	−0.655425	+	0.755261i	$0.727510\pi$
$20$	1.28000e9	0.223607
$21$	−1.42819e10	−1.73038
$22$	1.03767e10	0.886926
$23$	1.17843e10	0.721683	0.360842	−	0.932627i	$-0.382490\pi$
$23$	1.17843e10	0.721683	0.360842	+	0.932627i	$0.382490\pi$
$24$	1.16769e10	0.519691
$25$	6.10352e9	0.200000
$26$	−4.49807e10	−1.09831
$27$	−1.28332e10	−0.236106
$28$	4.20249e10	0.588602
$29$	−2.04006e10	−0.219613	−0.109806	−	0.993953i	$-0.535023\pi$
$29$	−2.04006e10	−0.219613	−0.109806	+	0.993953i	$0.535023\pi$
$30$	5.56800e10	0.464825
$31$	−1.23614e11	−0.806964	−0.403482	−	0.914988i	$-0.632200\pi$
$31$	−1.23614e11	−0.806964	−0.403482	+	0.914988i	$0.632200\pi$
$32$	−3.43597e10	−0.176777
$33$	4.51385e11	1.84371
$34$	2.76202e11	0.901850
$35$	2.00390e11	0.526461
$36$	2.72854e11	0.580313
$37$	−2.24996e10	−0.0389639	−0.0194819	−	0.999810i	$-0.506202\pi$
$37$	−2.24996e10	−0.0389639	−0.0194819	+	0.999810i	$0.506202\pi$
$38$	6.53755e11	0.926911
$39$	−1.95666e12	−2.28313
$40$	−1.63840e11	−0.158114
$41$	−1.04406e12	−0.837233	−0.418617	−	0.908163i	$-0.637485\pi$
$41$	−1.04406e12	−0.837233	−0.418617	+	0.908163i	$0.637485\pi$
$42$	1.82808e12	1.22356
$43$	−2.98423e12	−1.67425	−0.837123	−	0.547014i	$-0.815764\pi$
$43$	−2.98423e12	−1.67425	−0.837123	+	0.547014i	$0.815764\pi$
$44$	−1.32821e12	−0.627152
$45$	1.30107e12	0.519048
$46$	−1.50840e12	−0.510307
$47$	−2.26736e12	−0.652810	−0.326405	−	0.945230i	$-0.605837\pi$
$47$	−2.26736e12	−0.652810	−0.326405	+	0.945230i	$0.605837\pi$
$48$	−1.49465e12	−0.367477
$49$	1.83164e12	0.385807
$50$	−7.81250e11	−0.141421
$51$	1.20148e13	1.87473
$52$	5.75753e12	0.776625
$53$	−8.65580e12	−1.01213	−0.506067	−	0.862494i	$-0.668901\pi$
$53$	−8.65580e12	−1.01213	−0.506067	+	0.862494i	$0.668901\pi$
$54$	1.64265e12	0.166952
$55$	−6.33341e12	−0.560941
$56$	−5.37919e12	−0.416204
$57$	2.84383e13	1.92683
$58$	2.61127e12	0.155290
$59$	−2.59530e13	−1.35768	−0.678840	−	0.734286i	$-0.737517\pi$
$59$	−2.59530e13	−1.35768	−0.678840	+	0.734286i	$0.737517\pi$
$60$	−7.12704e12	−0.328681
$61$	2.98097e13	1.21446	0.607231	−	0.794525i	$-0.292280\pi$
$61$	2.98097e13	1.21446	0.607231	+	0.794525i	$0.292280\pi$
$62$	1.58226e13	0.570610
$63$	4.27167e13	1.36629
$64$	4.39805e12	0.125000
$65$	2.74541e13	0.694635
$66$	−5.77773e13	−1.30370
$67$	−7.81037e13	−1.57438	−0.787191	−	0.616709i	$-0.788466\pi$
$67$	−7.81037e13	−1.57438	−0.787191	+	0.616709i	$0.788466\pi$
$68$	−3.53538e13	−0.637704
$69$	−6.56152e13	−1.06081
$70$	−2.56500e13	−0.372264
$71$	6.77469e13	0.883999	0.442000	−	0.897015i	$-0.354269\pi$
$71$	6.77469e13	0.883999	0.442000	+	0.897015i	$0.354269\pi$
$72$	−3.49254e13	−0.410343
$73$	1.34520e14	1.42517	0.712584	−	0.701587i	$-0.247525\pi$
$73$	1.34520e14	1.42517	0.712584	+	0.701587i	$0.247525\pi$
$74$	2.87995e12	0.0275516
$75$	−3.39844e13	−0.293981
$76$	−8.36806e13	−0.655425
$77$	−2.07938e14	−1.47657
$78$	2.50453e14	1.61442
$79$	1.67235e13	0.0979768	0.0489884	−	0.998799i	$-0.484400\pi$
$79$	1.67235e13	0.0979768	0.0489884	+	0.998799i	$0.484400\pi$
$80$	2.09715e13	0.111803
$81$	−1.67507e14	−0.813573
$82$	1.33640e14	0.592013
$83$	8.08836e13	0.327171	0.163586	−	0.986529i	$-0.447694\pi$
$83$	8.08836e13	0.327171	0.163586	+	0.986529i	$0.447694\pi$
$84$	−2.33995e14	−0.865189
$85$	−1.68580e14	−0.570380
$86$	3.81982e14	1.18387
$87$	1.13590e14	0.322810
$88$	1.70011e14	0.443463
$89$	−5.23835e14	−1.25536	−0.627682	−	0.778470i	$-0.715996\pi$
$89$	−5.23835e14	−1.25536	−0.627682	+	0.778470i	$0.715996\pi$
$90$	−1.66537e14	−0.367022
$91$	9.01370e14	1.82849
$92$	1.93075e14	0.360842
$93$	6.88282e14	1.18616
$94$	2.90222e14	0.461607
$95$	−3.99020e14	−0.586230
$96$	1.91315e14	0.259845
$97$	1.18664e15	1.49119	0.745593	−	0.666402i	$-0.232166\pi$
$97$	1.18664e15	1.49119	0.745593	+	0.666402i	$0.232166\pi$
$98$	−2.34450e14	−0.272807
$99$	−1.35008e15	−1.45578
$100$	1.00000e14	0.100000
$101$	−7.80125e14	−0.724025	−0.362013	−	0.932173i	$-0.617910\pi$
$101$	−7.80125e14	−0.724025	−0.362013	+	0.932173i	$0.617910\pi$
$102$	−1.53789e15	−1.32564
$103$	−1.57939e15	−1.26535	−0.632673	−	0.774419i	$-0.718042\pi$
$103$	−1.57939e15	−1.26535	−0.632673	+	0.774419i	$0.718042\pi$
$104$	−7.36964e14	−0.549157
$105$	−1.11577e15	−0.773849
$106$	1.10794e15	0.715687
$107$	−1.27492e14	−0.0767543	−0.0383772	−	0.999263i	$-0.512219\pi$
$107$	−1.27492e14	−0.0767543	−0.0383772	+	0.999263i	$0.512219\pi$
$108$	−2.10259e14	−0.118053
$109$	−8.47400e14	−0.444007	−0.222003	−	0.975046i	$-0.571260\pi$
$109$	−8.47400e14	−0.444007	−0.222003	+	0.975046i	$0.571260\pi$
$110$	8.10677e14	0.396646
$111$	1.25278e14	0.0572733
$112$	6.88536e14	0.294301
$113$	4.77135e15	1.90789	0.953945	−	0.299982i	$-0.0969808\pi$
$113$	4.77135e15	1.90789	0.953945	+	0.299982i	$0.0969808\pi$
$114$	−3.64011e15	−1.36247
$115$	9.20652e14	0.322746
$116$	−3.34243e14	−0.109806
$117$	5.85232e15	1.80274
$118$	3.32198e15	0.960025
$119$	−5.53481e15	−1.50141
$120$	9.12261e14	0.232413
$121$	2.39472e15	0.573277
$122$	−3.81564e15	−0.858754
$123$	5.81333e15	1.23066
$124$	−2.02529e15	−0.403482
$125$	4.76837e14	0.0894427
$126$	−5.46774e15	−0.966115
$127$	−3.83186e15	−0.638090	−0.319045	−	0.947740i	$-0.603362\pi$
$127$	−3.83186e15	−0.638090	−0.319045	+	0.947740i	$0.603362\pi$
$128$	−5.62950e14	−0.0883883
$129$	1.66162e16	2.46099
$130$	−3.51412e15	−0.491181
$131$	−7.50300e15	−0.990148	−0.495074	−	0.868851i	$-0.664859\pi$
$131$	−7.50300e15	−0.990148	−0.495074	+	0.868851i	$0.664859\pi$
$132$	7.39549e15	0.921854
$133$	−1.31006e16	−1.54314
$134$	9.99727e15	1.11326
$135$	−1.00259e15	−0.105590
$136$	4.52529e15	0.450925
$137$	−8.01818e15	−0.756261	−0.378130	−	0.925752i	$-0.623433\pi$
$137$	−8.01818e15	−0.756261	−0.378130	+	0.925752i	$0.623433\pi$
$138$	8.39875e15	0.750104
$139$	−9.76022e15	−0.825750	−0.412875	−	0.910788i	$-0.635475\pi$
$139$	−9.76022e15	−0.825750	−0.412875	+	0.910788i	$0.635475\pi$
$140$	3.28319e15	0.263231
$141$	1.26247e16	0.959570
$142$	−8.67161e15	−0.625082
$143$	−2.84882e16	−1.94825
$144$	4.47045e15	0.290157
$145$	−1.59379e15	−0.0982138
$146$	−1.72186e16	−1.00775
$147$	−1.01986e16	−0.567101
$148$	−3.68634e14	−0.0194819
$149$	3.61042e15	0.181410	0.0907049	−	0.995878i	$-0.471088\pi$
$149$	3.61042e15	0.181410	0.0907049	+	0.995878i	$0.471088\pi$
$150$	4.35000e15	0.207876
$151$	3.37586e16	1.53482	0.767411	−	0.641156i	$-0.221545\pi$
$151$	3.37586e16	1.53482	0.767411	+	0.641156i	$0.221545\pi$
$152$	1.07111e16	0.463455
$153$	−3.59358e16	−1.48027
$154$	2.66161e16	1.04409
$155$	−9.65733e15	−0.360885
$156$	−3.20580e16	−1.14157
$157$	3.41436e15	0.115894	0.0579472	−	0.998320i	$-0.481544\pi$
$157$	3.41436e15	0.115894	0.0579472	+	0.998320i	$0.481544\pi$
$158$	−2.14060e15	−0.0692800
$159$	4.81955e16	1.48774
$160$	−2.68435e15	−0.0790569
$161$	3.02268e16	0.849568
$162$	2.14410e16	0.575283
$163$	1.15872e16	0.296875	0.148437	−	0.988922i	$-0.452576\pi$
$163$	1.15872e16	0.296875	0.148437	+	0.988922i	$0.452576\pi$
$164$	−1.71059e16	−0.418617
$165$	3.52644e16	0.824532
$166$	−1.03531e16	−0.231345
$167$	−4.69359e16	−1.00261	−0.501305	−	0.865271i	$-0.667146\pi$
$167$	−4.69359e16	−1.00261	−0.501305	+	0.865271i	$0.667146\pi$
$168$	2.99513e16	0.611781
$169$	7.23045e16	1.41259
$170$	2.15783e16	0.403320
$171$	−8.50582e16	−1.52141
$172$	−4.88937e16	−0.837123
$173$	−3.26239e16	−0.534798	−0.267399	−	0.963586i	$-0.586164\pi$
$173$	−3.26239e16	−0.534798	−0.267399	+	0.963586i	$0.586164\pi$
$174$	−1.45396e16	−0.228261
$175$	1.56555e16	0.235441
$176$	−2.17614e16	−0.313576
$177$	1.44506e17	1.99566
$178$	6.70509e16	0.887677
$179$	−2.12170e16	−0.269331	−0.134666	−	0.990891i	$-0.542996\pi$
$179$	−2.12170e16	−0.269331	−0.134666	+	0.990891i	$0.542996\pi$
$180$	2.13168e16	0.259524
$181$	−3.93436e16	−0.459500	−0.229750	−	0.973250i	$-0.573791\pi$
$181$	−3.93436e16	−0.459500	−0.229750	+	0.973250i	$0.573791\pi$
$182$	−1.15375e17	−1.29294
$183$	−1.65980e17	−1.78515
$184$	−2.47136e16	−0.255154
$185$	−1.75778e15	−0.0174252
$186$	−8.81000e16	−0.838743
$187$	1.74930e17	1.59975
$188$	−3.71485e16	−0.326405
$189$	−3.29171e16	−0.277944
$190$	5.10746e16	0.414527
$191$	−1.72512e16	−0.134607	−0.0673037	−	0.997733i	$-0.521440\pi$
$191$	−1.72512e16	−0.134607	−0.0673037	+	0.997733i	$0.521440\pi$
$192$	−2.44883e16	−0.183738
$193$	5.85196e16	0.422301	0.211150	−	0.977454i	$-0.432279\pi$
$193$	5.85196e16	0.422301	0.211150	+	0.977454i	$0.432279\pi$
$194$	−1.51890e17	−1.05443
$195$	−1.52864e17	−1.02105
$196$	3.00096e16	0.192904
$197$	−1.53782e17	−0.951502	−0.475751	−	0.879580i	$-0.657824\pi$
$197$	−1.53782e17	−0.951502	−0.475751	+	0.879580i	$0.657824\pi$
$198$	1.72810e17	1.02939
$199$	−1.96784e17	−1.12874	−0.564368	−	0.825523i	$-0.690880\pi$
$199$	−1.96784e17	−1.12874	−0.564368	+	0.825523i	$0.690880\pi$
$200$	−1.28000e16	−0.0707107
$201$	4.34881e17	2.31420
$202$	9.98559e16	0.511963
$203$	−5.23274e16	−0.258529
$204$	1.96850e17	0.937366
$205$	−8.15672e16	−0.374422
$206$	2.02162e17	0.894735
$207$	1.96253e17	0.837604
$208$	9.43314e16	0.388313
$209$	4.14050e17	1.64420
$210$	1.42819e17	0.547194
$211$	3.07033e17	1.13519	0.567593	−	0.823309i	$-0.307875\pi$
$211$	3.07033e17	1.13519	0.567593	+	0.823309i	$0.307875\pi$
$212$	−1.41817e17	−0.506067
$213$	−3.77215e17	−1.29940
$214$	1.63189e16	0.0542735
$215$	−2.33143e17	−0.748746
$216$	2.69131e16	0.0834759
$217$	−3.17069e17	−0.949961
$218$	1.08467e17	0.313960
$219$	−7.49008e17	−2.09486
$220$	−1.03767e17	−0.280471
$221$	−7.58286e17	−1.98103
$222$	−1.60356e16	−0.0404983
$223$	7.70244e17	1.88080	0.940399	−	0.340074i	$-0.110452\pi$
$223$	7.70244e17	1.88080	0.940399	+	0.340074i	$0.110452\pi$
$224$	−8.81326e16	−0.208102
$225$	1.01646e17	0.232125
$226$	−6.10733e17	−1.34908
$227$	3.12002e17	0.666751	0.333376	−	0.942794i	$-0.391812\pi$
$227$	3.12002e17	0.666751	0.333376	+	0.942794i	$0.391812\pi$
$228$	4.65934e17	0.963413
$229$	−1.22581e17	−0.245278	−0.122639	−	0.992451i	$-0.539136\pi$
$229$	−1.22581e17	−0.245278	−0.122639	+	0.992451i	$0.539136\pi$
$230$	−1.17843e17	−0.228216
$231$	1.15780e18	2.17042
$232$	4.27831e16	0.0776448
$233$	−3.59894e17	−0.632419	−0.316209	−	0.948689i	$-0.602410\pi$
$233$	−3.59894e17	−0.632419	−0.316209	+	0.948689i	$0.602410\pi$
$234$	−7.49096e17	−1.27473
$235$	−1.77138e17	−0.291946
$236$	−4.25214e17	−0.678840
$237$	−9.31162e16	−0.144017
$238$	7.08456e17	1.06166
$239$	−1.04275e17	−0.151424	−0.0757120	−	0.997130i	$-0.524123\pi$
$239$	−1.04275e17	−0.151424	−0.0757120	+	0.997130i	$0.524123\pi$
$240$	−1.16769e17	−0.164341
$241$	−3.25986e16	−0.0444705	−0.0222352	−	0.999753i	$-0.507078\pi$
$241$	−3.25986e16	−0.0444705	−0.0222352	+	0.999753i	$0.507078\pi$
$242$	−3.06524e17	−0.405368
$243$	1.11682e18	1.43198
$244$	4.88402e17	0.607231
$245$	1.43097e17	0.172538
$246$	−7.44106e17	−0.870205
$247$	−1.79482e18	−2.03608
$248$	2.59237e17	0.285305
$249$	−4.50360e17	−0.480911
$250$	−6.10352e16	−0.0632456
$251$	6.36624e17	0.640222	0.320111	−	0.947380i	$-0.396280\pi$
$251$	6.36624e17	0.640222	0.320111	+	0.947380i	$0.396280\pi$
$252$	6.99871e17	0.683146
$253$	−9.55329e17	−0.905209
$254$	4.90478e17	0.451197
$255$	9.38654e17	0.838406
$256$	7.20576e16	0.0625000
$257$	1.86448e18	1.57057	0.785287	−	0.619132i	$-0.212515\pi$
$257$	1.86448e18	1.57057	0.785287	+	0.619132i	$0.212515\pi$
$258$	−2.12688e18	−1.74018
$259$	−5.77114e16	−0.0458684
$260$	4.49807e17	0.347317
$261$	−3.39745e17	−0.254888
$262$	9.60384e17	0.700140
$263$	1.83256e18	1.29835	0.649174	−	0.760640i	$-0.275115\pi$
$263$	1.83256e18	1.29835	0.649174	+	0.760640i	$0.275115\pi$
$264$	−9.46622e17	−0.651850
$265$	−6.76235e17	−0.452640
$266$	1.67688e18	1.09116
$267$	2.91672e18	1.84527
$268$	−1.27965e18	−0.787191
$269$	2.38508e18	1.42679	0.713397	−	0.700760i	$-0.247155\pi$
$269$	2.38508e18	1.42679	0.713397	+	0.700760i	$0.247155\pi$
$270$	1.28332e17	0.0746631
$271$	1.03754e18	0.587134	0.293567	−	0.955939i	$-0.405158\pi$
$271$	1.03754e18	0.587134	0.293567	+	0.955939i	$0.405158\pi$
$272$	−5.79237e17	−0.318852
$273$	−5.01883e18	−2.68771
$274$	1.02633e18	0.534757
$275$	−4.94798e17	−0.250861
$276$	−1.07504e18	−0.530403
$277$	−2.21708e18	−1.06459	−0.532297	−	0.846558i	$-0.678671\pi$
$277$	−2.21708e18	−1.06459	−0.532297	+	0.846558i	$0.678671\pi$
$278$	1.24931e18	0.583894
$279$	−2.05863e18	−0.936584
$280$	−4.20249e17	−0.186132
$281$	−1.42584e18	−0.614854	−0.307427	−	0.951572i	$-0.599468\pi$
$281$	−1.42584e18	−0.614854	−0.307427	+	0.951572i	$0.599468\pi$
$282$	−1.61596e18	−0.678519
$283$	−3.57390e18	−1.46132	−0.730658	−	0.682744i	$-0.760787\pi$
$283$	−3.57390e18	−1.46132	−0.730658	+	0.682744i	$0.760787\pi$
$284$	1.10997e18	0.442000
$285$	2.22174e18	0.861703
$286$	3.64648e18	1.37762
$287$	−2.67801e18	−0.985594
$288$	−5.72217e17	−0.205172
$289$	1.79379e18	0.626667
$290$	2.04006e17	0.0694476
$291$	−6.60722e18	−2.19190
$292$	2.20398e18	0.712584
$293$	4.06061e18	1.27963	0.639815	−	0.768529i	$-0.279011\pi$
$293$	4.06061e18	1.27963	0.639815	+	0.768529i	$0.279011\pi$
$294$	1.30542e18	0.401001
$295$	−2.02758e18	−0.607173
$296$	4.71851e16	0.0137758
$297$	1.04036e18	0.296148
$298$	−4.62134e17	−0.128276
$299$	4.14116e18	1.12095
$300$	−5.56800e17	−0.146991
$301$	−7.65455e18	−1.97093
$302$	−4.32110e18	−1.08528
$303$	4.34373e18	1.06425
$304$	−1.37102e18	−0.327712
$305$	2.32888e18	0.543124
$306$	4.59978e18	1.04671
$307$	7.80974e17	0.173420	0.0867100	−	0.996234i	$-0.472365\pi$
$307$	7.80974e17	0.173420	0.0867100	+	0.996234i	$0.472365\pi$
$308$	−3.40686e18	−0.738285
$309$	8.79403e18	1.85994
$310$	1.23614e18	0.255184
$311$	1.24314e18	0.250505	0.125253	−	0.992125i	$-0.460026\pi$
$311$	1.24314e18	0.250505	0.125253	+	0.992125i	$0.460026\pi$
$312$	4.10342e18	0.807210
$313$	1.83929e18	0.353237	0.176619	−	0.984279i	$-0.443484\pi$
$313$	1.83929e18	0.353237	0.176619	+	0.984279i	$0.443484\pi$
$314$	−4.37039e17	−0.0819497
$315$	3.33724e18	0.611025
$316$	2.73997e17	0.0489884
$317$	−7.29992e18	−1.27460	−0.637299	−	0.770616i	$-0.719949\pi$
$317$	−7.29992e18	−1.27460	−0.637299	+	0.770616i	$0.719949\pi$
$318$	−6.16903e18	−1.05199
$319$	1.65383e18	0.275461
$320$	3.43597e17	0.0559017
$321$	7.09873e17	0.112822
$322$	−3.86903e18	−0.600735
$323$	1.10210e19	1.67187
$324$	−2.74444e18	−0.406787
$325$	2.14485e18	0.310650
$326$	−1.48317e18	−0.209922
$327$	4.71832e18	0.652649
$328$	2.18955e18	0.296007
$329$	−5.81578e18	−0.768490
$330$	−4.51385e18	−0.583032
$331$	5.92377e18	0.747977	0.373989	−	0.927433i	$-0.377990\pi$
$331$	5.92377e18	0.747977	0.373989	+	0.927433i	$0.377990\pi$
$332$	1.32520e18	0.163586
$333$	−3.74702e17	−0.0452225
$334$	6.00780e18	0.708952
$335$	−6.10185e18	−0.704085
$336$	−3.83377e18	−0.432595
$337$	−1.01555e19	−1.12067	−0.560335	−	0.828266i	$-0.689328\pi$
$337$	−1.01555e19	−1.12067	−0.560335	+	0.828266i	$0.689328\pi$
$338$	−9.25498e18	−0.998850
$339$	−2.65669e19	−2.80442
$340$	−2.76202e18	−0.285190
$341$	1.00211e19	1.01218
$342$	1.08874e19	1.07580
$343$	−7.47932e18	−0.723030
$344$	6.25839e18	0.591936
$345$	−5.12619e18	−0.474407
$346$	4.17586e18	0.378160
$347$	8.01797e15	0.000710548 0	0.000355274	−	1.00000i	$-0.499887\pi$
$347$	8.01797e15	0.000710548 0	0.000355274		1.00000i	$0.499887\pi$
$348$	1.86107e18	0.161405
$349$	−4.38113e18	−0.371874	−0.185937	−	0.982562i	$-0.559532\pi$
$349$	−4.38113e18	−0.371874	−0.185937	+	0.982562i	$0.559532\pi$
$350$	−2.00390e18	−0.166482
$351$	−4.50973e18	−0.366731
$352$	2.78546e18	0.221732
$353$	9.15164e18	0.713163	0.356582	−	0.934264i	$-0.383942\pi$
$353$	9.15164e18	0.713163	0.356582	+	0.934264i	$0.383942\pi$
$354$	−1.84968e19	−1.41115
$355$	5.29273e18	0.395337
$356$	−8.58252e18	−0.627682
$357$	3.08178e19	2.20694
$358$	2.71578e18	0.190446
$359$	6.27104e18	0.430657	0.215328	−	0.976542i	$-0.430918\pi$
$359$	6.27104e18	0.430657	0.215328	+	0.976542i	$0.430918\pi$
$360$	−2.72854e18	−0.183511
$361$	1.09050e19	0.718326
$362$	5.03599e18	0.324915
$363$	−1.33338e19	−0.842663
$364$	1.47681e19	0.914246
$365$	1.05094e19	0.637354
$366$	2.12455e19	1.26229
$367$	−1.13310e19	−0.659590	−0.329795	−	0.944053i	$-0.606980\pi$
$367$	−1.13310e19	−0.659590	−0.329795	+	0.944053i	$0.606980\pi$
$368$	3.16333e18	0.180421
$369$	−1.73875e19	−0.971715
$370$	2.24996e17	0.0123215
$371$	−2.22021e19	−1.19149
$372$	1.12768e19	0.593081
$373$	2.25401e19	1.16182	0.580911	−	0.813967i	$-0.302696\pi$
$373$	2.25401e19	1.16182	0.580911	+	0.813967i	$0.302696\pi$
$374$	−2.23910e19	−1.13119
$375$	−2.65503e18	−0.131472
$376$	4.75500e18	0.230803
$377$	−7.16901e18	−0.341113
$378$	4.21338e18	0.196536
$379$	−5.85604e18	−0.267800	−0.133900	−	0.990995i	$-0.542750\pi$
$379$	−5.85604e18	−0.267800	−0.133900	+	0.990995i	$0.542750\pi$
$380$	−6.53755e18	−0.293115
$381$	2.13358e19	0.937932
$382$	2.20815e18	0.0951818
$383$	2.68309e19	1.13408	0.567041	−	0.823689i	$-0.308088\pi$
$383$	2.68309e19	1.13408	0.567041	+	0.823689i	$0.308088\pi$
$384$	3.13451e18	0.129923
$385$	−1.62452e19	−0.660342
$386$	−7.49052e18	−0.298612
$387$	−4.96986e19	−1.94317
$388$	1.94419e19	0.745593
$389$	−2.97703e19	−1.11985	−0.559927	−	0.828542i	$-0.689171\pi$
$389$	−2.97703e19	−1.11985	−0.559927	+	0.828542i	$0.689171\pi$
$390$	1.95666e19	0.721990
$391$	−2.54285e19	−0.920441
$392$	−3.84123e18	−0.136403
$393$	4.17767e19	1.45543
$394$	1.96841e19	0.672813
$395$	1.30652e18	0.0438165
$396$	−2.21197e19	−0.727889
$397$	2.97881e19	0.961865	0.480932	−	0.876758i	$-0.340298\pi$
$397$	2.97881e19	0.961865	0.480932	+	0.876758i	$0.340298\pi$
$398$	2.51884e19	0.798137
$399$	7.29442e19	2.26827
$400$	1.63840e18	0.0500000
$401$	−8.21635e18	−0.246091	−0.123046	−	0.992401i	$-0.539266\pi$
$401$	−8.21635e18	−0.246091	−0.123046	+	0.992401i	$0.539266\pi$
$402$	−5.56648e19	−1.63638
$403$	−4.34394e19	−1.25342
$404$	−1.27816e19	−0.362013
$405$	−1.30865e19	−0.363841
$406$	6.69791e18	0.182807
$407$	1.82399e18	0.0488725
$408$	−2.51968e19	−0.662818
$409$	−3.79171e19	−0.979287	−0.489643	−	0.871923i	$-0.662873\pi$
$409$	−3.79171e19	−0.979287	−0.489643	+	0.871923i	$0.662873\pi$
$410$	1.04406e19	0.264756
$411$	4.46452e19	1.11163
$412$	−2.58767e19	−0.632673
$413$	−6.65693e19	−1.59827
$414$	−2.51204e19	−0.592276
$415$	6.31903e18	0.146315
$416$	−1.20744e19	−0.274578
$417$	5.43449e19	1.21378
$418$	−5.29984e19	−1.16263
$419$	1.24561e19	0.268397	0.134199	−	0.990954i	$-0.457154\pi$
$419$	1.24561e19	0.268397	0.134199	+	0.990954i	$0.457154\pi$
$420$	−1.82808e19	−0.386924
$421$	−4.77554e19	−0.992902	−0.496451	−	0.868065i	$-0.665364\pi$
$421$	−4.77554e19	−0.992902	−0.496451	+	0.868065i	$0.665364\pi$
$422$	−3.93003e19	−0.802698
$423$	−3.77600e19	−0.757669
$424$	1.81525e19	0.357844
$425$	−1.31703e19	−0.255082
$426$	4.82835e19	0.918812
$427$	7.64618e19	1.42967
$428$	−2.08882e18	−0.0383772
$429$	1.58622e20	2.86374
$430$	2.98423e19	0.529443
$431$	2.14947e19	0.374759	0.187380	−	0.982288i	$-0.440001\pi$
$431$	2.14947e19	0.374759	0.187380	+	0.982288i	$0.440001\pi$
$432$	−3.44488e18	−0.0590264
$433$	−1.90251e19	−0.320381	−0.160191	−	0.987086i	$-0.551211\pi$
$433$	−1.90251e19	−0.320381	−0.160191	+	0.987086i	$0.551211\pi$
$434$	4.05848e19	0.671724
$435$	8.87425e18	0.144365
$436$	−1.38838e19	−0.222003
$437$	−6.01880e19	−0.946018
$438$	9.58730e19	1.48129
$439$	9.50249e19	1.44329	0.721645	−	0.692264i	$-0.243386\pi$
$439$	9.50249e19	1.44329	0.721645	+	0.692264i	$0.243386\pi$
$440$	1.32821e19	0.198323
$441$	3.05037e19	0.447778
$442$	9.70606e19	1.40080
$443$	−3.48596e19	−0.494646	−0.247323	−	0.968933i	$-0.579551\pi$
$443$	−3.48596e19	−0.494646	−0.247323	+	0.968933i	$0.579551\pi$
$444$	2.05255e18	0.0286366
$445$	−4.09246e19	−0.561416
$446$	−9.85913e19	−1.32992
$447$	−2.01028e19	−0.266656
$448$	1.12810e19	0.147150
$449$	−1.02318e20	−1.31252	−0.656261	−	0.754534i	$-0.727863\pi$
$449$	−1.02318e20	−1.31252	−0.656261	+	0.754534i	$0.727863\pi$
$450$	−1.30107e19	−0.164137
$451$	8.46395e19	1.05014
$452$	7.81738e19	0.953945
$453$	−1.87968e20	−2.25604
$454$	−3.99363e19	−0.471464
$455$	7.04196e19	0.817726
$456$	−5.96395e19	−0.681236
$457$	−9.66189e18	−0.108565	−0.0542826	−	0.998526i	$-0.517287\pi$
$457$	−9.66189e18	−0.108565	−0.0542826	+	0.998526i	$0.517287\pi$
$458$	1.56904e19	0.173438
$459$	2.76918e19	0.301131
$460$	1.50840e19	0.161373
$461$	−3.81342e19	−0.401382	−0.200691	−	0.979655i	$-0.564319\pi$
$461$	−3.81342e19	−0.401382	−0.200691	+	0.979655i	$0.564319\pi$
$462$	−1.48198e20	−1.53472
$463$	−9.28999e19	−0.946581	−0.473291	−	0.880906i	$-0.656934\pi$
$463$	−9.28999e19	−0.946581	−0.473291	+	0.880906i	$0.656934\pi$
$464$	−5.47624e18	−0.0549032
$465$	5.37720e19	0.530468
$466$	4.60664e19	0.447188
$467$	4.33170e18	0.0413792	0.0206896	−	0.999786i	$-0.493414\pi$
$467$	4.33170e18	0.0413792	0.0206896	+	0.999786i	$0.493414\pi$
$468$	9.58844e19	0.901372
$469$	−2.00336e20	−1.85337
$470$	2.26736e19	0.206437
$471$	−1.90112e19	−0.170354
$472$	5.44274e19	0.480012
$473$	2.41925e20	2.10001
$474$	1.19189e19	0.101835
$475$	−3.11735e19	−0.262170
$476$	−9.06824e19	−0.750707
$477$	−1.44151e20	−1.17471
$478$	1.33472e19	0.107073
$479$	1.40047e19	0.110601	0.0553005	−	0.998470i	$-0.482388\pi$
$479$	1.40047e19	0.110601	0.0553005	+	0.998470i	$0.482388\pi$
$480$	1.49465e19	0.116206
$481$	−7.90664e18	−0.0605207
$482$	4.17263e18	0.0314454
$483$	−1.68303e20	−1.24879
$484$	3.92351e19	0.286638
$485$	9.27064e19	0.666879
$486$	−1.42953e20	−1.01256
$487$	1.25475e20	0.875167	0.437584	−	0.899178i	$-0.355834\pi$
$487$	1.25475e20	0.875167	0.437584	+	0.899178i	$0.355834\pi$
$488$	−6.25155e19	−0.429377
$489$	−6.45178e19	−0.436378
$490$	−1.83164e19	−0.122003
$491$	−1.58514e20	−1.03982	−0.519909	−	0.854222i	$-0.674034\pi$
$491$	−1.58514e20	−1.03982	−0.519909	+	0.854222i	$0.674034\pi$
$492$	9.52455e19	0.615328
$493$	4.40209e19	0.280096
$494$	2.29737e20	1.43972
$495$	−1.05475e20	−0.651043
$496$	−3.31823e19	−0.201741
$497$	1.73771e20	1.04065
$498$	5.76461e19	0.340055
$499$	1.58200e20	0.919292	0.459646	−	0.888102i	$-0.347976\pi$
$499$	1.58200e20	0.919292	0.459646	+	0.888102i	$0.347976\pi$
$500$	7.81250e18	0.0447214
$501$	2.61339e20	1.47374
$502$	−8.14879e19	−0.452705
$503$	3.18873e20	1.74525	0.872625	−	0.488391i	$-0.162416\pi$
$503$	3.18873e20	1.74525	0.872625	+	0.488391i	$0.162416\pi$
$504$	−8.95834e19	−0.483057
$505$	−6.09472e19	−0.323794
$506$	1.22282e20	0.640080
$507$	−4.02592e20	−2.07637
$508$	−6.27812e19	−0.319045
$509$	−2.07260e20	−1.03784	−0.518922	−	0.854822i	$-0.673667\pi$
$509$	−2.07260e20	−1.03784	−0.518922	+	0.854822i	$0.673667\pi$
$510$	−1.20148e20	−0.592842
$511$	3.45044e20	1.67771
$512$	−9.22337e18	−0.0441942
$513$	6.55449e19	0.309499
$514$	−2.38653e20	−1.11056
$515$	−1.23390e20	−0.565880
$516$	2.72240e20	1.23049
$517$	1.83810e20	0.818822
$518$	7.38707e18	0.0324339
$519$	1.81650e20	0.786104
$520$	−5.75753e19	−0.245590
$521$	2.54307e20	1.06924	0.534620	−	0.845092i	$-0.320455\pi$
$521$	2.54307e20	1.06924	0.534620	+	0.845092i	$0.320455\pi$
$522$	4.34874e19	0.180233
$523$	1.74715e20	0.713786	0.356893	−	0.934145i	$-0.383836\pi$
$523$	1.74715e20	0.713786	0.356893	+	0.934145i	$0.383836\pi$
$524$	−1.22929e20	−0.495074
$525$	−8.71698e19	−0.346076
$526$	−2.34568e20	−0.918071
$527$	2.66737e20	1.02921
$528$	1.21168e20	0.460927
$529$	−1.27765e20	−0.479174
$530$	8.65580e19	0.320065
$531$	−4.32214e20	−1.57576
$532$	−2.14640e20	−0.771568
$533$	−3.66895e20	−1.30043
$534$	−3.73340e20	−1.30480
$535$	−9.96027e18	−0.0343256
$536$	1.63795e20	0.556628
$537$	1.18136e20	0.395892
$538$	−3.05291e20	−1.00890
$539$	−1.48487e20	−0.483919
$540$	−1.64265e19	−0.0527948
$541$	−2.55653e20	−0.810346	−0.405173	−	0.914240i	$-0.632789\pi$
$541$	−2.55653e20	−0.810346	−0.405173	+	0.914240i	$0.632789\pi$
$542$	−1.32806e20	−0.415166
$543$	2.19065e20	0.675422
$544$	7.41423e19	0.225463
$545$	−6.62031e19	−0.198566
$546$	6.42410e20	1.90050
$547$	−2.42491e20	−0.707606	−0.353803	−	0.935320i	$-0.615112\pi$
$547$	−2.42491e20	−0.707606	−0.353803	+	0.935320i	$0.615112\pi$
$548$	−1.31370e20	−0.378130
$549$	4.96442e20	1.40954
$550$	6.33341e19	0.177385
$551$	1.04195e20	0.287879
$552$	1.37605e20	0.375052
$553$	4.28956e19	0.115339
$554$	2.83787e20	0.752782
$555$	9.78734e18	0.0256134
$556$	−1.59911e20	−0.412875
$557$	−1.50696e20	−0.383873	−0.191936	−	0.981407i	$-0.561477\pi$
$557$	−1.50696e20	−0.383873	−0.191936	+	0.981407i	$0.561477\pi$
$558$	2.63505e20	0.662265
$559$	−1.04870e21	−2.60052
$560$	5.37919e19	0.131615
$561$	−9.74009e20	−2.35148
$562$	1.82507e20	0.434768
$563$	8.35266e20	1.96341	0.981706	−	0.190401i	$-0.0609789\pi$
$563$	8.35266e20	1.96341	0.981706	+	0.190401i	$0.0609789\pi$
$564$	2.06843e20	0.479785
$565$	3.72762e20	0.853234
$566$	4.57459e20	1.03331
$567$	−4.29656e20	−0.957741
$568$	−1.42076e20	−0.312541
$569$	−4.49857e18	−0.00976637	−0.00488318	−	0.999988i	$-0.501554\pi$
$569$	−4.49857e18	−0.00976637	−0.00488318	+	0.999988i	$0.501554\pi$
$570$	−2.84383e20	−0.609316
$571$	−5.05145e20	−1.06818	−0.534091	−	0.845427i	$-0.679346\pi$
$571$	−5.05145e20	−1.06818	−0.534091	+	0.845427i	$0.679346\pi$
$572$	−4.66750e20	−0.974123
$573$	9.60547e19	0.197860
$574$	3.42785e20	0.696920
$575$	7.19259e19	0.144337
$576$	7.32438e19	0.145078
$577$	5.09389e20	0.995934	0.497967	−	0.867196i	$-0.334080\pi$
$577$	5.09389e20	0.995934	0.497967	+	0.867196i	$0.334080\pi$
$578$	−2.29605e20	−0.443120
$579$	−3.25837e20	−0.620743
$580$	−2.61127e19	−0.0491069
$581$	2.07466e20	0.385147
$582$	8.45725e20	1.54991
$583$	7.01706e20	1.26952
$584$	−2.82109e20	−0.503873
$585$	4.57212e20	0.806211
$586$	−5.19758e20	−0.904835
$587$	−2.72381e20	−0.468156	−0.234078	−	0.972218i	$-0.575207\pi$
$587$	−2.72381e20	−0.468156	−0.234078	+	0.972218i	$0.575207\pi$
$588$	−1.67094e20	−0.283550
$589$	6.31352e20	1.05781
$590$	2.59530e20	0.429336
$591$	8.56260e20	1.39862
$592$	−6.03970e18	−0.00974097
$593$	−6.69109e20	−1.06558	−0.532791	−	0.846247i	$-0.678857\pi$
$593$	−6.69109e20	−1.06558	−0.532791	+	0.846247i	$0.678857\pi$
$594$	−1.33166e20	−0.209408
$595$	−4.32407e20	−0.671453
$596$	5.91531e19	0.0907049
$597$	1.09570e21	1.65914
$598$	−5.30068e20	−0.792635
$599$	4.70329e20	0.694546	0.347273	−	0.937764i	$-0.387108\pi$
$599$	4.70329e20	0.694546	0.347273	+	0.937764i	$0.387108\pi$
$600$	7.12704e19	0.103938
$601$	−2.04342e20	−0.294305	−0.147153	−	0.989114i	$-0.547011\pi$
$601$	−2.04342e20	−0.294305	−0.147153	+	0.989114i	$0.547011\pi$
$602$	9.79782e20	1.39366
$603$	−1.30072e21	−1.82727
$604$	5.53101e20	0.767411
$605$	1.87087e20	0.256377
$606$	−5.55998e20	−0.752538
$607$	2.59341e19	0.0346702	0.0173351	−	0.999850i	$-0.494482\pi$
$607$	2.59341e19	0.0346702	0.0173351	+	0.999850i	$0.494482\pi$
$608$	1.75491e20	0.231728
$609$	2.91359e20	0.380013
$610$	−2.98097e20	−0.384047
$611$	−7.96778e20	−1.01398
$612$	−5.88772e20	−0.740136
$613$	8.09739e20	1.00552	0.502761	−	0.864425i	$-0.332318\pi$
$613$	8.09739e20	1.00552	0.502761	+	0.864425i	$0.332318\pi$
$614$	−9.99647e19	−0.122626
$615$	4.54166e20	0.550366
$616$	4.36078e20	0.522046
$617$	−1.40064e21	−1.65649	−0.828246	−	0.560365i	$-0.810661\pi$
$617$	−1.40064e21	−1.65649	−0.828246	+	0.560365i	$0.810661\pi$
$618$	−1.12564e21	−1.31518
$619$	6.75237e20	0.779429	0.389715	−	0.920936i	$-0.372574\pi$
$619$	6.75237e20	0.779429	0.389715	+	0.920936i	$0.372574\pi$
$620$	−1.58226e20	−0.180443
$621$	−1.51231e20	−0.170393
$622$	−1.59122e20	−0.177134
$623$	−1.34364e21	−1.47782
$624$	−5.25237e20	−0.570783
$625$	3.72529e19	0.0400000
$626$	−2.35429e20	−0.249777
$627$	−2.30543e21	−2.41682
$628$	5.59410e19	0.0579472
$629$	4.85503e19	0.0496949
$630$	−4.27167e20	−0.432060
$631$	9.67329e20	0.966838	0.483419	−	0.875389i	$-0.339395\pi$
$631$	9.67329e20	0.966838	0.483419	+	0.875389i	$0.339395\pi$
$632$	−3.50716e19	−0.0346400
$633$	−1.70956e21	−1.66862
$634$	9.34389e20	0.901277
$635$	−2.99364e20	−0.285362
$636$	7.89635e20	0.743872
$637$	6.43661e20	0.599255
$638$	−2.11690e20	−0.194780
$639$	1.12824e21	1.02599
$640$	−4.39805e19	−0.0395285
$641$	1.02605e21	0.911455	0.455728	−	0.890119i	$-0.349379\pi$
$641$	1.02605e21	0.911455	0.455728	+	0.890119i	$0.349379\pi$
$642$	−9.08637e19	−0.0797770
$643$	1.95616e20	0.169755	0.0848774	−	0.996391i	$-0.472950\pi$
$643$	1.95616e20	0.169755	0.0848774	+	0.996391i	$0.472950\pi$
$644$	4.95236e20	0.424784
$645$	1.29814e21	1.10059
$646$	−1.41069e21	−1.18219
$647$	1.68777e20	0.139808	0.0699040	−	0.997554i	$-0.477731\pi$
$647$	1.68777e20	0.139808	0.0699040	+	0.997554i	$0.477731\pi$
$648$	3.51289e20	0.287642
$649$	2.10395e21	1.70294
$650$	−2.74541e20	−0.219663
$651$	1.76544e21	1.39635
$652$	1.89845e20	0.148437
$653$	1.29425e21	1.00039	0.500195	−	0.865913i	$-0.333262\pi$
$653$	1.29425e21	1.00039	0.500195	+	0.865913i	$0.333262\pi$
$654$	−6.03945e20	−0.461492
$655$	−5.86172e20	−0.442808
$656$	−2.80263e20	−0.209308
$657$	2.24026e21	1.65409
$658$	7.44419e20	0.543405
$659$	−1.57433e21	−1.13620	−0.568101	−	0.822959i	$-0.692322\pi$
$659$	−1.57433e21	−1.13620	−0.568101	+	0.822959i	$0.692322\pi$
$660$	5.77773e20	0.412266
$661$	−2.17948e21	−1.53760	−0.768799	−	0.639491i	$-0.779145\pi$
$661$	−2.17948e21	−1.53760	−0.768799	+	0.639491i	$0.779145\pi$
$662$	−7.58243e20	−0.528900
$663$	4.22213e21	2.91193
$664$	−1.69625e20	−0.115672
$665$	−1.02349e21	−0.690111
$666$	4.79619e19	0.0319771
$667$	−2.40407e20	−0.158491
$668$	−7.68998e20	−0.501305
$669$	−4.28872e21	−2.76460
$670$	7.81037e20	0.497864
$671$	−2.41660e21	−1.52330
$672$	4.90722e20	0.305891
$673$	−7.55056e20	−0.465443	−0.232721	−	0.972543i	$-0.574763\pi$
$673$	−7.55056e20	−0.465443	−0.232721	+	0.972543i	$0.574763\pi$
$674$	1.29991e21	0.792434
$675$	−7.83275e19	−0.0472211
$676$	1.18464e21	0.706293
$677$	−1.24803e21	−0.735886	−0.367943	−	0.929848i	$-0.619938\pi$
$677$	−1.24803e21	−0.735886	−0.367943	+	0.929848i	$0.619938\pi$
$678$	3.40056e21	1.98302
$679$	3.04373e21	1.75543
$680$	3.53538e20	0.201660
$681$	−1.73723e21	−0.980062
$682$	−1.28270e21	−0.715718
$683$	1.47929e20	0.0816391	0.0408195	−	0.999167i	$-0.487003\pi$
$683$	1.47929e20	0.0816391	0.0408195	+	0.999167i	$0.487003\pi$
$684$	−1.39359e21	−0.760703
$685$	−6.26420e20	−0.338210
$686$	9.57353e20	0.511259
$687$	6.82533e20	0.360536
$688$	−8.01074e20	−0.418562
$689$	−3.04175e21	−1.57210
$690$	6.56152e20	0.335457
$691$	2.57228e20	0.130087	0.0650434	−	0.997882i	$-0.479281\pi$
$691$	2.57228e20	0.130087	0.0650434	+	0.997882i	$0.479281\pi$
$692$	−5.34510e20	−0.267399
$693$	−3.46294e21	−1.71375
$694$	−1.02630e18	−0.000502434 0
$695$	−7.62517e20	−0.369287
$696$	−2.38216e20	−0.114131
$697$	2.25290e21	1.06781
$698$	5.60785e20	0.262955
$699$	2.00389e21	0.929597
$700$	2.56500e20	0.117720
$701$	4.10568e21	1.86423	0.932116	−	0.362159i	$-0.117960\pi$
$701$	4.10568e21	1.86423	0.932116	+	0.362159i	$0.117960\pi$
$702$	5.77246e20	0.259318
$703$	1.14916e20	0.0510758
$704$	−3.56539e20	−0.156788
$705$	9.86303e20	0.429133
$706$	−1.17141e21	−0.504282
$707$	−2.00102e21	−0.852325
$708$	2.36759e21	0.997832
$709$	−4.15264e21	−1.73172	−0.865859	−	0.500288i	$-0.833228\pi$
$709$	−4.15264e21	−1.73172	−0.865859	+	0.500288i	$0.833228\pi$
$710$	−6.77469e20	−0.279545
$711$	2.78508e20	0.113714
$712$	1.09856e21	0.443838
$713$	−1.45671e21	−0.582372
$714$	−3.94468e21	−1.56054
$715$	−2.22564e21	−0.871283
$716$	−3.47620e20	−0.134666
$717$	5.80602e20	0.222579
$718$	−8.02693e20	−0.304520
$719$	3.11903e21	1.17099	0.585494	−	0.810677i	$-0.300900\pi$
$719$	3.11903e21	1.17099	0.585494	+	0.810677i	$0.300900\pi$
$720$	3.49254e20	0.129762
$721$	−4.05112e21	−1.48957
$722$	−1.39584e21	−0.507933
$723$	1.81509e20	0.0653674
$724$	−6.44606e20	−0.229750
$725$	−1.24515e20	−0.0439225
$726$	1.70673e21	0.595853
$727$	3.88354e21	1.34190	0.670949	−	0.741503i	$-0.265887\pi$
$727$	3.88354e21	1.34190	0.670949	+	0.741503i	$0.265887\pi$
$728$	−1.89031e21	−0.646469
$729$	−3.81493e21	−1.29131
$730$	−1.34520e21	−0.450677
$731$	6.43945e21	2.13535
$732$	−2.71942e21	−0.892573
$733$	1.94990e21	0.633481	0.316740	−	0.948512i	$-0.397412\pi$
$733$	1.94990e21	0.633481	0.316740	+	0.948512i	$0.397412\pi$
$734$	1.45037e21	0.466401
$735$	−7.96765e20	−0.253615
$736$	−4.04907e20	−0.127577
$737$	6.33168e21	1.97475
$738$	2.22560e21	0.687106
$739$	−4.59729e21	−1.40498	−0.702488	−	0.711696i	$-0.747927\pi$
$739$	−4.59729e21	−1.40498	−0.702488	+	0.711696i	$0.747927\pi$
$740$	−2.87995e19	−0.00871259
$741$	9.99357e21	2.99284
$742$	2.84187e21	0.842509
$743$	−5.65680e20	−0.166018	−0.0830089	−	0.996549i	$-0.526453\pi$
$743$	−5.65680e20	−0.166018	−0.0830089	+	0.996549i	$0.526453\pi$
$744$	−1.44343e21	−0.419372
$745$	2.82064e20	0.0811289
$746$	−2.88513e21	−0.821532
$747$	1.34701e21	0.379723
$748$	2.86605e21	0.799875
$749$	−3.27015e20	−0.0903555
$750$	3.39844e20	0.0929651
$751$	−2.82202e21	−0.764294	−0.382147	−	0.924101i	$-0.624815\pi$
$751$	−2.82202e21	−0.764294	−0.382147	+	0.924101i	$0.624815\pi$
$752$	−6.08640e20	−0.163203
$753$	−3.54472e21	−0.941066
$754$	9.17633e20	0.241204
$755$	2.63739e21	0.686393
$756$	−5.39313e20	−0.138972
$757$	−4.04173e21	−1.03121	−0.515607	−	0.856825i	$-0.672433\pi$
$757$	−4.04173e21	−1.03121	−0.515607	+	0.856825i	$0.672433\pi$
$758$	7.49573e20	0.189363
$759$	5.31927e21	1.33057
$760$	8.36806e20	0.207263
$761$	5.59515e21	1.37223	0.686115	−	0.727493i	$-0.259315\pi$
$761$	5.59515e21	1.37223	0.686115	+	0.727493i	$0.259315\pi$
$762$	−2.73098e21	−0.663218
$763$	−2.17358e21	−0.522686
$764$	−2.82644e20	−0.0673037
$765$	−2.80748e21	−0.661998
$766$	−3.43436e21	−0.801918
$767$	−9.12020e21	−2.10882
$768$	−4.01217e20	−0.0918692
$769$	7.64084e21	1.73258	0.866291	−	0.499540i	$-0.166498\pi$
$769$	7.64084e21	1.73258	0.866291	+	0.499540i	$0.166498\pi$
$770$	2.07938e21	0.466932
$771$	−1.03814e22	−2.30860
$772$	9.58786e20	0.211150
$773$	4.07185e21	0.888067	0.444033	−	0.896010i	$-0.353547\pi$
$773$	4.07185e21	0.888067	0.444033	+	0.896010i	$0.353547\pi$
$774$	6.36142e21	1.37403
$775$	−7.54479e20	−0.161393
$776$	−2.48857e21	−0.527214
$777$	3.21337e20	0.0674223
$778$	3.81060e21	0.791857
$779$	5.33249e21	1.09749
$780$	−2.50453e21	−0.510524
$781$	−5.49208e21	−1.10880
$782$	3.25485e21	0.650850
$783$	2.61804e20	0.0518518
$784$	4.91678e20	0.0964518
$785$	2.66747e20	0.0518296
$786$	−5.34742e21	−1.02914
$787$	−8.43219e21	−1.60742	−0.803710	−	0.595021i	$-0.797144\pi$
$787$	−8.43219e21	−1.60742	−0.803710	+	0.595021i	$0.797144\pi$
$788$	−2.51957e21	−0.475751
$789$	−1.02037e22	−1.90845
$790$	−1.67235e20	−0.0309830
$791$	1.22385e22	2.24597
$792$	2.83132e21	0.514695
$793$	1.04755e22	1.88636
$794$	−3.81288e21	−0.680141
$795$	3.76527e21	0.665339
$796$	−3.22412e21	−0.564368
$797$	2.90783e21	0.504234	0.252117	−	0.967697i	$-0.418873\pi$
$797$	2.90783e21	0.504234	0.252117	+	0.967697i	$0.418873\pi$
$798$	−9.33686e21	−1.60391
$799$	4.89257e21	0.832600
$800$	−2.09715e20	−0.0353553
$801$	−8.72381e21	−1.45701
$802$	1.05169e21	0.174013
$803$	−1.09052e22	−1.78759
$804$	7.12509e21	1.15710
$805$	2.36147e21	0.379938
$806$	5.56024e21	0.886300
$807$	−1.32801e22	−2.09726
$808$	1.63604e21	0.255982
$809$	−9.45931e21	−1.46638	−0.733189	−	0.680025i	$-0.761969\pi$
$809$	−9.45931e21	−1.46638	−0.733189	+	0.680025i	$0.761969\pi$
$810$	1.67507e21	0.257274
$811$	−8.85935e21	−1.34817	−0.674087	−	0.738652i	$-0.735463\pi$
$811$	−8.85935e21	−1.34817	−0.674087	+	0.738652i	$0.735463\pi$
$812$	−8.57332e20	−0.129264
$813$	−5.77705e21	−0.863032
$814$	−2.33471e20	−0.0345581
$815$	9.05253e20	0.132766
$816$	3.22519e21	0.468683
$817$	1.52419e22	2.19469
$818$	4.85338e21	0.692460
$819$	1.50112e22	2.12219
$820$	−1.33640e21	−0.187211
$821$	−3.07426e21	−0.426744	−0.213372	−	0.976971i	$-0.568445\pi$
$821$	−3.07426e21	−0.426744	−0.213372	+	0.976971i	$0.568445\pi$
$822$	−5.71459e21	−0.786043
$823$	−6.26136e21	−0.853434	−0.426717	−	0.904385i	$-0.640330\pi$
$823$	−6.26136e21	−0.853434	−0.426717	+	0.904385i	$0.640330\pi$
$824$	3.31222e21	0.447368
$825$	2.75503e21	0.368742
$826$	8.52088e21	1.13014
$827$	1.07936e21	0.141865	0.0709325	−	0.997481i	$-0.477402\pi$
$827$	1.07936e21	0.141865	0.0709325	+	0.997481i	$0.477402\pi$
$828$	3.21541e21	0.418802
$829$	−7.93238e21	−1.02387	−0.511934	−	0.859025i	$-0.671071\pi$
$829$	−7.93238e21	−1.02387	−0.511934	+	0.859025i	$0.671071\pi$
$830$	−8.08836e20	−0.103461
$831$	1.23447e22	1.56485
$832$	1.54553e21	0.194156
$833$	−3.95237e21	−0.492062
$834$	−6.95615e21	−0.858269
$835$	−3.66687e21	−0.448381
$836$	6.78379e21	0.822101
$837$	1.58636e21	0.190529
$838$	−1.59438e21	−0.189785
$839$	1.00607e22	1.18690	0.593449	−	0.804871i	$-0.297766\pi$
$839$	1.00607e22	1.18690	0.593449	+	0.804871i	$0.297766\pi$
$840$	2.33995e21	0.273597
$841$	−8.21301e21	−0.951770
$842$	6.11269e21	0.702088
$843$	7.93905e21	0.903778
$844$	5.03044e21	0.567593
$845$	5.64879e21	0.631728
$846$	4.83328e21	0.535753
$847$	6.14244e21	0.674863
$848$	−2.32352e21	−0.253034
$849$	1.98995e22	2.14800
$850$	1.68580e21	0.180370
$851$	−2.65143e20	−0.0281196
$852$	−6.18029e21	−0.649698
$853$	−1.37013e22	−1.42772	−0.713862	−	0.700286i	$-0.753056\pi$
$853$	−1.37013e22	−1.42772	−0.713862	+	0.700286i	$0.753056\pi$
$854$	−9.78711e21	−1.01093
$855$	−6.64517e21	−0.680394
$856$	2.67369e20	0.0271368
$857$	1.36805e22	1.37640	0.688202	−	0.725519i	$-0.258400\pi$
$857$	1.36805e22	1.37640	0.688202	+	0.725519i	$0.258400\pi$
$858$	−2.03036e22	−2.02497
$859$	−6.43980e21	−0.636684	−0.318342	−	0.947976i	$-0.603126\pi$
$859$	−6.43980e21	−0.636684	−0.318342	+	0.947976i	$0.603126\pi$
$860$	−3.81982e21	−0.374373
$861$	1.49112e22	1.44873
$862$	−2.75132e21	−0.264995
$863$	−2.66511e21	−0.254468	−0.127234	−	0.991873i	$-0.540610\pi$
$863$	−2.66511e21	−0.254468	−0.127234	+	0.991873i	$0.540610\pi$
$864$	4.40945e20	0.0417380
$865$	−2.54874e21	−0.239169
$866$	2.43521e21	0.226544
$867$	−9.98780e21	−0.921142
$868$	−5.19486e21	−0.474980
$869$	−1.35573e21	−0.122893
$870$	−1.13590e21	−0.102082
$871$	−2.74466e22	−2.44541
$872$	1.77713e21	0.156980
$873$	1.97620e22	1.73071
$874$	7.70407e21	0.668936
$875$	1.22309e21	0.105292
$876$	−1.22717e22	−1.04743
$877$	1.81272e22	1.53403	0.767014	−	0.641630i	$-0.221742\pi$
$877$	1.81272e22	1.53403	0.767014	+	0.641630i	$0.221742\pi$
$878$	−1.21632e22	−1.02056
$879$	−2.26095e22	−1.88094
$880$	−1.70011e21	−0.140235
$881$	−2.37009e22	−1.93841	−0.969204	−	0.246258i	$-0.920799\pi$
$881$	−2.37009e22	−1.93841	−0.969204	+	0.246258i	$0.920799\pi$
$882$	−3.90447e21	−0.316627
$883$	9.97113e21	0.801750	0.400875	−	0.916133i	$-0.368706\pi$
$883$	9.97113e21	0.801750	0.400875	+	0.916133i	$0.368706\pi$
$884$	−1.24238e22	−0.990514
$885$	1.12896e22	0.892488
$886$	4.46203e21	0.349768
$887$	−1.73838e22	−1.35119	−0.675596	−	0.737272i	$-0.736114\pi$
$887$	−1.73838e22	−1.35119	−0.675596	+	0.737272i	$0.736114\pi$
$888$	−2.62727e20	−0.0202492
$889$	−9.82870e21	−0.751161
$890$	5.23835e21	0.396981
$891$	1.35794e22	1.02047
$892$	1.26197e22	0.940399
$893$	1.15805e22	0.855736
$894$	2.57316e21	0.188554
$895$	−1.65758e21	−0.120449
$896$	−1.44396e21	−0.104051
$897$	−2.30580e22	−1.64770
$898$	1.30968e22	0.928093
$899$	2.52179e21	0.177220
$900$	1.66537e21	0.116063
$901$	1.86777e22	1.29089
$902$	−1.08339e22	−0.742564
$903$	4.26205e22	2.89708
$904$	−1.00063e22	−0.674541
$905$	−3.07372e21	−0.205495
$906$	2.40599e22	1.59526
$907$	2.88475e22	1.89694	0.948468	−	0.316872i	$-0.102632\pi$
$907$	2.88475e22	1.89694	0.948468	+	0.316872i	$0.102632\pi$
$908$	5.11184e21	0.333376
$909$	−1.29920e22	−0.840323
$910$	−9.01370e21	−0.578220
$911$	−2.05475e22	−1.30729	−0.653645	−	0.756802i	$-0.726761\pi$
$911$	−2.05475e22	−1.30729	−0.653645	+	0.756802i	$0.726761\pi$
$912$	7.63386e21	0.481707
$913$	−6.55705e21	−0.410372
$914$	1.23672e21	0.0767672
$915$	−1.29672e22	−0.798342
$916$	−2.00837e21	−0.122639
$917$	−1.92452e22	−1.16561
$918$	−3.54455e21	−0.212932
$919$	−4.61696e21	−0.275099	−0.137550	−	0.990495i	$-0.543923\pi$
$919$	−4.61696e21	−0.275099	−0.137550	+	0.990495i	$0.543923\pi$
$920$	−1.93075e21	−0.114108
$921$	−4.34847e21	−0.254911
$922$	4.88118e21	0.283820
$923$	2.38071e22	1.37307
$924$	1.89694e22	1.08521
$925$	−1.37327e20	−0.00779278
$926$	1.18912e22	0.669334
$927$	−2.63027e22	−1.46859
$928$	7.00958e20	0.0388224
$929$	−2.98584e21	−0.164039	−0.0820197	−	0.996631i	$-0.526137\pi$
$929$	−2.98584e21	−0.164039	−0.0820197	+	0.996631i	$0.526137\pi$
$930$	−6.88282e21	−0.375097
$931$	−9.35504e21	−0.505735
$932$	−5.89650e21	−0.316209
$933$	−6.92180e21	−0.368219
$934$	−5.54458e20	−0.0292595
$935$	1.36664e22	0.715430
$936$	−1.22732e22	−0.637366
$937$	1.72383e22	0.888070	0.444035	−	0.896009i	$-0.353547\pi$
$937$	1.72383e22	0.888070	0.444035	+	0.896009i	$0.353547\pi$
$938$	2.56430e22	1.31053
$939$	−1.02411e22	−0.519226
$940$	−2.90222e21	−0.145973
$941$	3.70481e22	1.84860	0.924301	−	0.381664i	$-0.124649\pi$
$941$	3.70481e22	1.84860	0.924301	+	0.381664i	$0.124649\pi$
$942$	2.43343e21	0.120458
$943$	−1.23036e22	−0.604217
$944$	−6.96671e21	−0.339420
$945$	−2.57165e21	−0.124300
$946$	−3.09664e22	−1.48493
$947$	−1.92960e22	−0.918001	−0.459001	−	0.888436i	$-0.651792\pi$
$947$	−1.92960e22	−0.918001	−0.459001	+	0.888436i	$0.651792\pi$
$948$	−1.52562e21	−0.0720083
$949$	4.72720e22	2.21364
$950$	3.99020e21	0.185382
$951$	4.06459e22	1.87354
$952$	1.16073e22	0.530830
$953$	−1.82891e22	−0.829841	−0.414920	−	0.909858i	$-0.636191\pi$
$953$	−1.82891e22	−0.829841	−0.414920	+	0.909858i	$0.636191\pi$
$954$	1.84514e22	0.830646
$955$	−1.34775e21	−0.0601983
$956$	−1.70844e21	−0.0757120
$957$	−9.20851e21	−0.404902
$958$	−1.79261e21	−0.0782067
$959$	−2.05666e22	−0.890272
$960$	−1.91315e21	−0.0821703
$961$	−8.18489e21	−0.348809
$962$	1.01205e21	0.0427946
$963$	−2.12321e21	−0.0890831
$964$	−5.34096e20	−0.0222352
$965$	4.57185e21	0.188859
$966$	2.15428e22	0.883024
$967$	1.27240e21	0.0517519	0.0258760	−	0.999665i	$-0.491763\pi$
$967$	1.27240e21	0.0517519	0.0258760	+	0.999665i	$0.491763\pi$
$968$	−5.02209e21	−0.202684
$969$	−6.13649e22	−2.45749
$970$	−1.18664e22	−0.471554
$971$	2.66767e22	1.05193	0.525967	−	0.850505i	$-0.323704\pi$
$971$	2.66767e22	1.05193	0.525967	+	0.850505i	$0.323704\pi$
$972$	1.82980e22	0.715991
$973$	−2.50349e22	−0.972076
$974$	−1.60608e22	−0.618837
$975$	−1.19425e22	−0.456627
$976$	8.00198e21	0.303616
$977$	4.90709e21	0.184763	0.0923815	−	0.995724i	$-0.470552\pi$
$977$	4.90709e21	0.184763	0.0923815	+	0.995724i	$0.470552\pi$
$978$	8.25827e21	0.308566
$979$	4.24661e22	1.57461
$980$	2.34450e21	0.0862691
$981$	−1.41124e22	−0.515326
$982$	2.02898e22	0.735262
$983$	−9.02729e21	−0.324643	−0.162321	−	0.986738i	$-0.551898\pi$
$983$	−9.02729e21	−0.324643	−0.162321	+	0.986738i	$0.551898\pi$
$984$	−1.21914e22	−0.435102
$985$	−1.20142e22	−0.425524
$986$	−5.63467e21	−0.198058
$987$	3.23822e22	1.12961
$988$	−2.94064e22	−1.01804
$989$	−3.51672e22	−1.20828
$990$	1.35008e22	0.460357
$991$	−1.62672e22	−0.550505	−0.275253	−	0.961372i	$-0.588761\pi$
$991$	−1.62672e22	−0.550505	−0.275253	+	0.961372i	$0.588761\pi$
$992$	4.24734e21	0.142652
$993$	−3.29836e22	−1.09946
$994$	−2.22426e22	−0.735848
$995$	−1.53738e22	−0.504786
$996$	−7.37870e21	−0.240456
$997$	−3.95160e22	−1.27808	−0.639042	−	0.769172i	$-0.720669\pi$
$997$	−3.95160e22	−1.27808	−0.639042	+	0.769172i	$0.720669\pi$
$998$	−2.02497e22	−0.650038
$999$	2.88742e20	0.00919959

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.16.a.a.1.1	✓	1
3.2	odd	2		90.16.a.f.1.1		1
4.3	odd	2		80.16.a.c.1.1		1
5.2	odd	4		50.16.b.d.49.1		2
5.3	odd	4		50.16.b.d.49.2		2
5.4	even	2		50.16.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.16.a.a.1.1	✓	1	1.1	even	1	trivial
50.16.a.d.1.1		1	5.4	even	2
50.16.b.d.49.1		2	5.2	odd	4
50.16.b.d.49.2		2	5.3	odd	4
80.16.a.c.1.1		1	4.3	odd	2
90.16.a.f.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:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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