LMFDB - Embedded newform 6.16.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,16,Mod(1,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 16, names="a")

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

chi := DirichletCharacter("6.1");

S:= CuspForms(chi, 16);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 16 $
Character orbit:	$[\chi]$	$=$	6.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$8.56161030600$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-128.000 q^{2} -2187.00 q^{3} +16384.0 q^{4} -314490. q^{5} +279936. q^{6} +2.02506e6 q^{7} -2.09715e6 q^{8} +4.78297e6 q^{9} +O(q^{10})$

\(q-128.000 q^{2} -2187.00 q^{3} +16384.0 q^{4} -314490. q^{5} +279936. q^{6} +2.02506e6 q^{7} -2.09715e6 q^{8} +4.78297e6 q^{9} +4.02547e7 q^{10} +1.10255e8 q^{11} -3.58318e7 q^{12} +5.60479e7 q^{13} -2.59207e8 q^{14} +6.87790e8 q^{15} +2.68435e8 q^{16} -1.93010e9 q^{17} -6.12220e8 q^{18} +2.16319e9 q^{19} -5.15260e9 q^{20} -4.42880e9 q^{21} -1.41126e10 q^{22} +6.22897e9 q^{23} +4.58647e9 q^{24} +6.83864e10 q^{25} -7.17413e9 q^{26} -1.04604e10 q^{27} +3.31785e10 q^{28} +6.47437e10 q^{29} -8.80371e10 q^{30} -2.02376e10 q^{31} -3.43597e10 q^{32} -2.41128e11 q^{33} +2.47053e11 q^{34} -6.36860e11 q^{35} +7.83642e10 q^{36} +4.88968e11 q^{37} -2.76888e11 q^{38} -1.22577e11 q^{39} +6.59533e11 q^{40} -7.72359e11 q^{41} +5.66886e11 q^{42} +1.30677e12 q^{43} +1.80642e12 q^{44} -1.50420e12 q^{45} -7.97309e11 q^{46} +3.35182e12 q^{47} -5.87068e11 q^{48} -6.46710e11 q^{49} -8.75346e12 q^{50} +4.22114e12 q^{51} +9.18288e11 q^{52} +9.38781e12 q^{53} +1.33893e12 q^{54} -3.46741e13 q^{55} -4.24685e12 q^{56} -4.73089e12 q^{57} -8.28720e12 q^{58} +2.89304e13 q^{59} +1.12687e13 q^{60} +4.23931e13 q^{61} +2.59041e12 q^{62} +9.68578e12 q^{63} +4.39805e12 q^{64} -1.76265e13 q^{65} +3.08644e13 q^{66} -5.22472e13 q^{67} -3.16228e13 q^{68} -1.36228e13 q^{69} +8.15181e13 q^{70} -2.71945e13 q^{71} -1.00306e13 q^{72} -9.16042e13 q^{73} -6.25879e13 q^{74} -1.49561e14 q^{75} +3.54417e13 q^{76} +2.23273e14 q^{77} +1.56898e13 q^{78} +6.28821e13 q^{79} -8.44203e13 q^{80} +2.28768e13 q^{81} +9.88620e13 q^{82} -2.23567e14 q^{83} -7.25614e13 q^{84} +6.06999e14 q^{85} -1.67266e14 q^{86} -1.41595e14 q^{87} -2.31222e14 q^{88} +5.54199e14 q^{89} +1.92537e14 q^{90} +1.13500e14 q^{91} +1.02056e14 q^{92} +4.42597e13 q^{93} -4.29033e14 q^{94} -6.80301e14 q^{95} +7.51447e13 q^{96} -1.38887e15 q^{97} +8.27788e13 q^{98} +5.27346e14 q^{99} +O(q^{100})\)

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
$3$	−2187.00	−0.577350
$3$	−2187.00	−0.577350
$4$	16384.0	0.500000
$5$	−314490.	−1.80025	−0.900123	−	0.435636i	$-0.856523\pi$
$5$	−314490.	−1.80025	−0.900123	+	0.435636i	$0.856523\pi$
$6$	279936.	0.408248
$7$	2.02506e6	0.929398	0.464699	−	0.885469i	$-0.346163\pi$
$7$	2.02506e6	0.929398	0.464699	+	0.885469i	$0.346163\pi$
$8$	−2.09715e6	−0.353553
$9$	4.78297e6	0.333333
$10$	4.02547e7	1.27297
$11$	1.10255e8	1.70590	0.852950	−	0.521993i	$-0.174811\pi$
$11$	1.10255e8	1.70590	0.852950	+	0.521993i	$0.174811\pi$
$12$	−3.58318e7	−0.288675
$13$	5.60479e7	0.247733	0.123867	−	0.992299i	$-0.460471\pi$
$13$	5.60479e7	0.247733	0.123867	+	0.992299i	$0.460471\pi$
$14$	−2.59207e8	−0.657184
$15$	6.87790e8	1.03937
$16$	2.68435e8	0.250000
$17$	−1.93010e9	−1.14081	−0.570406	−	0.821363i	$-0.693214\pi$
$17$	−1.93010e9	−1.14081	−0.570406	+	0.821363i	$0.693214\pi$
$18$	−6.12220e8	−0.235702
$19$	2.16319e9	0.555191	0.277595	−	0.960698i	$-0.410463\pi$
$19$	2.16319e9	0.555191	0.277595	+	0.960698i	$0.410463\pi$
$20$	−5.15260e9	−0.900123
$21$	−4.42880e9	−0.536588
$22$	−1.41126e10	−1.20625
$23$	6.22897e9	0.381468	0.190734	−	0.981642i	$-0.438913\pi$
$23$	6.22897e9	0.381468	0.190734	+	0.981642i	$0.438913\pi$
$24$	4.58647e9	0.204124
$25$	6.83864e10	2.24088
$26$	−7.17413e9	−0.175174
$27$	−1.04604e10	−0.192450
$28$	3.31785e10	0.464699
$29$	6.47437e10	0.696968	0.348484	−	0.937315i	$-0.386697\pi$
$29$	6.47437e10	0.696968	0.348484	+	0.937315i	$0.386697\pi$
$30$	−8.80371e10	−0.734947
$31$	−2.02376e10	−0.132113	−0.0660567	−	0.997816i	$-0.521042\pi$
$31$	−2.02376e10	−0.132113	−0.0660567	+	0.997816i	$0.521042\pi$
$32$	−3.43597e10	−0.176777
$33$	−2.41128e11	−0.984901
$34$	2.47053e11	0.806676
$35$	−6.36860e11	−1.67314
$36$	7.83642e10	0.166667
$37$	4.88968e11	0.846773	0.423387	−	0.905949i	$-0.360841\pi$
$37$	4.88968e11	0.846773	0.423387	+	0.905949i	$0.360841\pi$
$38$	−2.76888e11	−0.392579
$39$	−1.22577e11	−0.143029
$40$	6.59533e11	0.636483
$41$	−7.72359e11	−0.619356	−0.309678	−	0.950841i	$-0.600221\pi$
$41$	−7.72359e11	−0.619356	−0.309678	+	0.950841i	$0.600221\pi$
$42$	5.66886e11	0.379425
$43$	1.30677e12	0.733136	0.366568	−	0.930391i	$-0.380533\pi$
$43$	1.30677e12	0.733136	0.366568	+	0.930391i	$0.380533\pi$
$44$	1.80642e12	0.852950
$45$	−1.50420e12	−0.600082
$46$	−7.97309e11	−0.269738
$47$	3.35182e12	0.965044	0.482522	−	0.875884i	$-0.339721\pi$
$47$	3.35182e12	0.965044	0.482522	+	0.875884i	$0.339721\pi$
$48$	−5.87068e11	−0.144338
$49$	−6.46710e11	−0.136219
$50$	−8.75346e12	−1.58454
$51$	4.22114e12	0.658648
$52$	9.18288e11	0.123867
$53$	9.38781e12	1.09773	0.548865	−	0.835911i	$-0.315060\pi$
$53$	9.38781e12	1.09773	0.548865	+	0.835911i	$0.315060\pi$
$54$	1.33893e12	0.136083
$55$	−3.46741e13	−3.07104
$56$	−4.24685e12	−0.328592
$57$	−4.73089e12	−0.320540
$58$	−8.28720e12	−0.492831
$59$	2.89304e13	1.51343	0.756717	−	0.653742i	$-0.226802\pi$
$59$	2.89304e13	1.51343	0.756717	+	0.653742i	$0.226802\pi$
$60$	1.12687e13	0.519686
$61$	4.23931e13	1.72711	0.863557	−	0.504251i	$-0.168231\pi$
$61$	4.23931e13	1.72711	0.863557	+	0.504251i	$0.168231\pi$
$62$	2.59041e12	0.0934182
$63$	9.68578e12	0.309799
$64$	4.39805e12	0.125000
$65$	−1.76265e13	−0.445980
$66$	3.08644e13	0.696430
$67$	−5.22472e13	−1.05318	−0.526590	−	0.850120i	$-0.676530\pi$
$67$	−5.22472e13	−1.05318	−0.526590	+	0.850120i	$0.676530\pi$
$68$	−3.16228e13	−0.570406
$69$	−1.36228e13	−0.220240
$70$	8.15181e13	1.18309
$71$	−2.71945e13	−0.354849	−0.177425	−	0.984134i	$-0.556777\pi$
$71$	−2.71945e13	−0.354849	−0.177425	+	0.984134i	$0.556777\pi$
$72$	−1.00306e13	−0.117851
$73$	−9.16042e13	−0.970496	−0.485248	−	0.874376i	$-0.661271\pi$
$73$	−9.16042e13	−0.970496	−0.485248	+	0.874376i	$0.661271\pi$
$74$	−6.25879e13	−0.598759
$75$	−1.49561e14	−1.29378
$76$	3.54417e13	0.277595
$77$	2.23273e14	1.58546
$78$	1.56898e13	0.101137
$79$	6.28821e13	0.368404	0.184202	−	0.982888i	$-0.441030\pi$
$79$	6.28821e13	0.368404	0.184202	+	0.982888i	$0.441030\pi$
$80$	−8.44203e13	−0.450061
$81$	2.28768e13	0.111111
$82$	9.88620e13	0.437951
$83$	−2.23567e14	−0.904321	−0.452161	−	0.891937i	$-0.649347\pi$
$83$	−2.23567e14	−0.904321	−0.452161	+	0.891937i	$0.649347\pi$
$84$	−7.25614e13	−0.268294
$85$	6.06999e14	2.05374
$86$	−1.67266e14	−0.518405
$87$	−1.41595e14	−0.402394
$88$	−2.31222e14	−0.603126
$89$	5.54199e14	1.32813	0.664065	−	0.747675i	$-0.268830\pi$
$89$	5.54199e14	1.32813	0.664065	+	0.747675i	$0.268830\pi$
$90$	1.92537e14	0.424322
$91$	1.13500e14	0.230243
$92$	1.02056e14	0.190734
$93$	4.42597e13	0.0762756
$94$	−4.29033e14	−0.682389
$95$	−6.80301e14	−0.999480
$96$	7.51447e13	0.102062
$97$	−1.38887e15	−1.74531	−0.872657	−	0.488333i	$-0.837605\pi$
$97$	−1.38887e15	−1.74531	−0.872657	+	0.488333i	$0.837605\pi$
$98$	8.27788e13	0.0963216
$99$	5.27346e14	0.568633
$100$	1.12044e15	1.12044
$101$	−4.19546e14	−0.389376	−0.194688	−	0.980865i	$-0.562369\pi$
$101$	−4.19546e14	−0.389376	−0.194688	+	0.980865i	$0.562369\pi$
$102$	−5.40306e14	−0.465734
$103$	−9.82508e14	−0.787149	−0.393575	−	0.919293i	$-0.628762\pi$
$103$	−9.82508e14	−0.787149	−0.393575	+	0.919293i	$0.628762\pi$
$104$	−1.17541e14	−0.0875869
$105$	1.39281e15	0.965991
$106$	−1.20164e15	−0.776212
$107$	−2.46544e14	−0.148428	−0.0742141	−	0.997242i	$-0.523645\pi$
$107$	−2.46544e14	−0.148428	−0.0742141	+	0.997242i	$0.523645\pi$
$108$	−1.71382e14	−0.0962250
$109$	8.45123e14	0.442814	0.221407	−	0.975182i	$-0.428935\pi$
$109$	8.45123e14	0.442814	0.221407	+	0.975182i	$0.428935\pi$
$110$	4.43829e15	2.17155
$111$	−1.06937e15	−0.488885
$112$	5.43597e14	0.232350
$113$	3.00170e15	1.20027	0.600135	−	0.799899i	$-0.295113\pi$
$113$	3.00170e15	1.20027	0.600135	+	0.799899i	$0.295113\pi$
$114$	6.05554e14	0.226656
$115$	−1.95895e15	−0.686736
$116$	1.06076e15	0.348484
$117$	2.68075e14	0.0825777
$118$	−3.70309e15	−1.07016
$119$	−3.90857e15	−1.06027
$120$	−1.44240e15	−0.367474
$121$	7.97893e15	1.91009
$122$	−5.42631e15	−1.22125
$123$	1.68915e15	0.357585
$124$	−3.31573e14	−0.0660567
$125$	−1.19094e16	−2.23390
$126$	−1.23978e15	−0.219061
$127$	1.75446e15	0.292157	0.146078	−	0.989273i	$-0.453335\pi$
$127$	1.75446e15	0.292157	0.146078	+	0.989273i	$0.453335\pi$
$128$	−5.62950e14	−0.0883883
$129$	−2.85790e15	−0.423276
$130$	2.25619e15	0.315356
$131$	1.07149e16	1.41402	0.707009	−	0.707205i	$-0.250044\pi$
$131$	1.07149e16	1.41402	0.707009	+	0.707205i	$0.250044\pi$
$132$	−3.95064e15	−0.492451
$133$	4.38058e15	0.515993
$134$	6.68765e15	0.744710
$135$	3.28968e15	0.346457
$136$	4.04772e15	0.403338
$137$	−4.07675e15	−0.384512	−0.192256	−	0.981345i	$-0.561580\pi$
$137$	−4.07675e15	−0.384512	−0.192256	+	0.981345i	$0.561580\pi$
$138$	1.74371e15	0.155734
$139$	6.18797e15	0.523524	0.261762	−	0.965132i	$-0.415696\pi$
$139$	6.18797e15	0.523524	0.261762	+	0.965132i	$0.415696\pi$
$140$	−1.04343e16	−0.836572
$141$	−7.33043e15	−0.557168
$142$	3.48090e15	0.250916
$143$	6.17956e15	0.422608
$144$	1.28392e15	0.0833333
$145$	−2.03613e16	−1.25471
$146$	1.17253e16	0.686245
$147$	1.41435e15	0.0786463
$148$	8.01125e15	0.423387
$149$	4.10483e15	0.206252	0.103126	−	0.994668i	$-0.467116\pi$
$149$	4.10483e15	0.206252	0.103126	+	0.994668i	$0.467116\pi$
$150$	1.91438e16	0.914837
$151$	−4.30971e15	−0.195939	−0.0979696	−	0.995189i	$-0.531235\pi$
$151$	−4.30971e15	−0.195939	−0.0979696	+	0.995189i	$0.531235\pi$
$152$	−4.53653e15	−0.196290
$153$	−9.23163e15	−0.380271
$154$	−2.85789e16	−1.12109
$155$	6.36453e15	0.237836
$156$	−2.00830e15	−0.0715144
$157$	−4.10493e16	−1.39334	−0.696672	−	0.717390i	$-0.745337\pi$
$157$	−4.10493e16	−1.39334	−0.696672	+	0.717390i	$0.745337\pi$
$158$	−8.04891e15	−0.260501
$159$	−2.05311e16	−0.633775
$160$	1.08058e16	0.318242
$161$	1.26140e16	0.354535
$162$	−2.92823e15	−0.0785674
$163$	−3.67161e15	−0.0940698	−0.0470349	−	0.998893i	$-0.514977\pi$
$163$	−3.67161e15	−0.0940698	−0.0470349	+	0.998893i	$0.514977\pi$
$164$	−1.26543e16	−0.309678
$165$	7.58323e16	1.77306
$166$	2.86166e16	0.639452
$167$	3.97703e16	0.849544	0.424772	−	0.905300i	$-0.360354\pi$
$167$	3.97703e16	0.849544	0.424772	+	0.905300i	$0.360354\pi$
$168$	9.28786e15	0.189713
$169$	−4.80445e16	−0.938628
$170$	−7.76958e16	−1.45221
$171$	1.03465e16	0.185064
$172$	2.14101e16	0.366568
$173$	3.10617e16	0.509189	0.254595	−	0.967048i	$-0.418058\pi$
$173$	3.10617e16	0.509189	0.254595	+	0.967048i	$0.418058\pi$
$174$	1.81241e16	0.284536
$175$	1.38486e17	2.08267
$176$	2.95964e16	0.426475
$177$	−6.32707e16	−0.873782
$178$	−7.09374e16	−0.939130
$179$	5.31753e16	0.675013	0.337507	−	0.941323i	$-0.390416\pi$
$179$	5.31753e16	0.675013	0.337507	+	0.941323i	$0.390416\pi$
$180$	−2.46447e16	−0.300041
$181$	7.28364e16	0.850666	0.425333	−	0.905037i	$-0.360157\pi$
$181$	7.28364e16	0.850666	0.425333	+	0.905037i	$0.360157\pi$
$182$	−1.45280e16	−0.162806
$183$	−9.27137e16	−0.997150
$184$	−1.30631e16	−0.134869
$185$	−1.53775e17	−1.52440
$186$	−5.66524e15	−0.0539350
$187$	−2.12804e17	−1.94611
$188$	5.49162e16	0.482522
$189$	−2.11828e16	−0.178863
$190$	8.70785e16	0.706739
$191$	−9.39928e16	−0.733406	−0.366703	−	0.930338i	$-0.619513\pi$
$191$	−9.39928e16	−0.733406	−0.366703	+	0.930338i	$0.619513\pi$
$192$	−9.61853e15	−0.0721688
$193$	1.88578e17	1.36085	0.680426	−	0.732816i	$-0.261795\pi$
$193$	1.88578e17	1.36085	0.680426	+	0.732816i	$0.261795\pi$
$194$	1.77775e17	1.23412
$195$	3.85491e16	0.257487
$196$	−1.05957e16	−0.0681097
$197$	−1.86952e17	−1.15673	−0.578366	−	0.815778i	$-0.696309\pi$
$197$	−1.86952e17	−1.15673	−0.578366	+	0.815778i	$0.696309\pi$
$198$	−6.75004e16	−0.402084
$199$	3.33410e16	0.191241	0.0956204	−	0.995418i	$-0.469517\pi$
$199$	3.33410e16	0.191241	0.0956204	+	0.995418i	$0.469517\pi$
$200$	−1.43417e17	−0.792272
$201$	1.14265e17	0.608053
$202$	5.37019e16	0.275331
$203$	1.31110e17	0.647760
$204$	6.91591e16	0.329324
$205$	2.42899e17	1.11499
$206$	1.25761e17	0.556599
$207$	2.97930e16	0.127156
$208$	1.50452e16	0.0619333
$209$	2.38502e17	0.947100
$210$	−1.78280e17	−0.683059
$211$	−4.60034e17	−1.70087	−0.850436	−	0.526079i	$-0.823662\pi$
$211$	−4.60034e17	−1.70087	−0.850436	+	0.526079i	$0.823662\pi$
$212$	1.53810e17	0.548865
$213$	5.94744e16	0.204872
$214$	3.15577e16	0.104955
$215$	−4.10965e17	−1.31982
$216$	2.19370e16	0.0680414
$217$	−4.09823e16	−0.122786
$218$	−1.08176e17	−0.313117
$219$	2.00338e17	0.560316
$220$	−5.68101e17	−1.53552
$221$	−1.08178e17	−0.282617
$222$	1.36880e17	0.345694
$223$	2.73469e17	0.667762	0.333881	−	0.942615i	$-0.391642\pi$
$223$	2.73469e17	0.667762	0.333881	+	0.942615i	$0.391642\pi$
$224$	−6.95804e16	−0.164296
$225$	3.27090e17	0.746962
$226$	−3.84218e17	−0.848719
$227$	4.06444e17	0.868573	0.434287	−	0.900775i	$-0.357000\pi$
$227$	4.06444e17	0.868573	0.434287	+	0.900775i	$0.357000\pi$
$228$	−7.75109e16	−0.160270
$229$	1.30379e17	0.260880	0.130440	−	0.991456i	$-0.458361\pi$
$229$	1.30379e17	0.260880	0.130440	+	0.991456i	$0.458361\pi$
$230$	2.50746e17	0.485595
$231$	−4.88297e17	−0.915365
$232$	−1.35777e17	−0.246415
$233$	−2.73060e17	−0.479832	−0.239916	−	0.970794i	$-0.577120\pi$
$233$	−2.73060e17	−0.479832	−0.239916	+	0.970794i	$0.577120\pi$
$234$	−3.43136e16	−0.0583912
$235$	−1.05411e18	−1.73732
$236$	4.73995e17	0.756717
$237$	−1.37523e17	−0.212698
$238$	5.00297e17	0.749723
$239$	1.21033e18	1.75760	0.878802	−	0.477186i	$-0.158343\pi$
$239$	1.21033e18	1.75760	0.878802	+	0.477186i	$0.158343\pi$
$240$	1.84627e17	0.259843
$241$	3.86893e17	0.527793	0.263896	−	0.964551i	$-0.414992\pi$
$241$	3.86893e17	0.527793	0.263896	+	0.964551i	$0.414992\pi$
$242$	−1.02130e18	−1.35064
$243$	−5.00315e16	−0.0641500
$244$	6.94568e17	0.863557
$245$	2.03384e17	0.245228
$246$	−2.16211e17	−0.252851
$247$	1.21242e17	0.137539
$248$	4.24413e16	0.0467091
$249$	4.88942e17	0.522110
$250$	1.52440e18	1.57960
$251$	−9.15208e17	−0.920379	−0.460190	−	0.887821i	$-0.652219\pi$
$251$	−9.15208e17	−0.920379	−0.460190	+	0.887821i	$0.652219\pi$
$252$	1.58692e17	0.154900
$253$	6.86776e17	0.650745
$254$	−2.24571e17	−0.206586
$255$	−1.32751e18	−1.18573
$256$	7.20576e16	0.0625000
$257$	−2.15995e18	−1.81947	−0.909734	−	0.415191i	$-0.863715\pi$
$257$	−2.15995e18	−1.81947	−0.909734	+	0.415191i	$0.863715\pi$
$258$	3.65811e17	0.299302
$259$	9.90187e17	0.786989
$260$	−2.88792e17	−0.222990
$261$	3.09667e17	0.232323
$262$	−1.37151e18	−0.999861
$263$	5.35139e17	0.379139	0.189570	−	0.981867i	$-0.439291\pi$
$263$	5.35139e17	0.379139	0.189570	+	0.981867i	$0.439291\pi$
$264$	5.05682e17	0.348215
$265$	−2.95237e18	−1.97618
$266$	−5.60714e17	−0.364862
$267$	−1.21203e18	−0.766796
$268$	−8.56019e17	−0.526590
$269$	−5.06061e17	−0.302734	−0.151367	−	0.988478i	$-0.548368\pi$
$269$	−5.06061e17	−0.302734	−0.151367	+	0.988478i	$0.548368\pi$
$270$	−4.21079e17	−0.244982
$271$	2.92815e18	1.65700	0.828501	−	0.559987i	$-0.189194\pi$
$271$	2.92815e18	1.65700	0.828501	+	0.559987i	$0.189194\pi$
$272$	−5.18108e17	−0.285203
$273$	−2.48225e17	−0.132931
$274$	5.21824e17	0.271891
$275$	7.53994e18	3.82272
$276$	−2.23195e17	−0.110120
$277$	3.77192e17	0.181119	0.0905596	−	0.995891i	$-0.471134\pi$
$277$	3.77192e17	0.181119	0.0905596	+	0.995891i	$0.471134\pi$
$278$	−7.92060e17	−0.370188
$279$	−9.67959e16	−0.0440378
$280$	1.33559e18	0.591546
$281$	−2.76493e18	−1.19231	−0.596153	−	0.802871i	$-0.703305\pi$
$281$	−2.76493e18	−1.19231	−0.596153	+	0.802871i	$0.703305\pi$
$282$	9.38296e17	0.393977
$283$	−1.13987e18	−0.466075	−0.233038	−	0.972468i	$-0.574867\pi$
$283$	−1.13987e18	−0.466075	−0.233038	+	0.972468i	$0.574867\pi$
$284$	−4.45555e17	−0.177425
$285$	1.48782e18	0.577050
$286$	−7.90984e17	−0.298829
$287$	−1.56407e18	−0.575628
$288$	−1.64342e17	−0.0589256
$289$	8.62880e17	0.301451
$290$	2.60624e18	0.887216
$291$	3.03746e18	1.00766
$292$	−1.50084e18	−0.485248
$293$	5.84207e18	1.84102	0.920512	−	0.390714i	$-0.127772\pi$
$293$	5.84207e18	1.84102	0.920512	+	0.390714i	$0.127772\pi$
$294$	−1.81037e17	−0.0556113
$295$	−9.09831e18	−2.72455
$296$	−1.02544e18	−0.299380
$297$	−1.15331e18	−0.328300
$298$	−5.25418e17	−0.145842
$299$	3.49121e17	0.0945022
$300$	−2.45041e18	−0.646888
$301$	2.64627e18	0.681375
$302$	5.51643e17	0.138550
$303$	9.17548e17	0.224807
$304$	5.80676e17	0.138798
$305$	−1.33322e19	−3.10923
$306$	1.18165e18	0.268892
$307$	−3.59204e18	−0.797633	−0.398816	−	0.917031i	$-0.630579\pi$
$307$	−3.59204e18	−0.797633	−0.398816	+	0.917031i	$0.630579\pi$
$308$	3.65810e18	0.792730
$309$	2.14875e18	0.454461
$310$	−8.14659e17	−0.168176
$311$	2.18535e18	0.440371	0.220185	−	0.975458i	$-0.429334\pi$
$311$	2.18535e18	0.440371	0.220185	+	0.975458i	$0.429334\pi$
$312$	2.57062e17	0.0505683
$313$	5.59874e18	1.07525	0.537623	−	0.843185i	$-0.319322\pi$
$313$	5.59874e18	1.07525	0.537623	+	0.843185i	$0.319322\pi$
$314$	5.25431e18	0.985242
$315$	−3.04608e18	−0.557715
$316$	1.03026e18	0.184202
$317$	−7.36219e18	−1.28547	−0.642736	−	0.766088i	$-0.722201\pi$
$317$	−7.36219e18	−1.28547	−0.642736	+	0.766088i	$0.722201\pi$
$318$	2.62799e18	0.448146
$319$	7.13832e18	1.18896
$320$	−1.38314e18	−0.225031
$321$	5.39192e17	0.0856951
$322$	−1.61459e18	−0.250694
$323$	−4.17518e18	−0.633368
$324$	3.74813e17	0.0555556
$325$	3.83291e18	0.555141
$326$	4.69967e17	0.0665174
$327$	−1.84828e18	−0.255659
$328$	1.61975e18	0.218975
$329$	6.78763e18	0.896910
$330$	−9.70653e18	−1.25375
$331$	7.52026e18	0.949562	0.474781	−	0.880104i	$-0.342527\pi$
$331$	7.52026e18	0.949562	0.474781	+	0.880104i	$0.342527\pi$
$332$	−3.66293e18	−0.452161
$333$	2.33872e18	0.282258
$334$	−5.09060e18	−0.600718
$335$	1.64312e19	1.89598
$336$	−1.18885e18	−0.134147
$337$	−4.01228e18	−0.442759	−0.221380	−	0.975188i	$-0.571056\pi$
$337$	−4.01228e18	−0.442759	−0.221380	+	0.975188i	$0.571056\pi$
$338$	6.14970e18	0.663710
$339$	−6.56472e18	−0.692976
$340$	9.94506e18	1.02687
$341$	−2.23130e18	−0.225372
$342$	−1.32435e18	−0.130860
$343$	−1.09237e19	−1.05600
$344$	−2.74049e18	−0.259203
$345$	4.28422e18	0.396487
$346$	−3.97590e18	−0.360051
$347$	−1.92570e19	−1.70654	−0.853271	−	0.521467i	$-0.825385\pi$
$347$	−1.92570e19	−1.70654	−0.853271	+	0.521467i	$0.825385\pi$
$348$	−2.31988e18	−0.201197
$349$	1.07863e19	0.915550	0.457775	−	0.889068i	$-0.348646\pi$
$349$	1.07863e19	0.915550	0.457775	+	0.889068i	$0.348646\pi$
$350$	−1.77262e19	−1.47267
$351$	−5.86280e17	−0.0476762
$352$	−3.78833e18	−0.301563
$353$	3.62430e18	0.282432	0.141216	−	0.989979i	$-0.454899\pi$
$353$	3.62430e18	0.282432	0.141216	+	0.989979i	$0.454899\pi$
$354$	8.09865e18	0.617857
$355$	8.55241e18	0.638816
$356$	9.07999e18	0.664065
$357$	8.54804e18	0.612146
$358$	−6.80644e18	−0.477306
$359$	−1.75871e19	−1.20778	−0.603889	−	0.797069i	$-0.706383\pi$
$359$	−1.75871e19	−1.20778	−0.603889	+	0.797069i	$0.706383\pi$
$360$	3.15453e18	0.212161
$361$	−1.05017e19	−0.691763
$362$	−9.32306e18	−0.601512
$363$	−1.74499e19	−1.10279
$364$	1.85958e18	0.115121
$365$	2.88086e19	1.74713
$366$	1.18673e19	0.705092
$367$	−2.74539e19	−1.59812	−0.799059	−	0.601253i	$-0.794668\pi$
$367$	−2.74539e19	−1.59812	−0.799059	+	0.601253i	$0.794668\pi$
$368$	1.67208e18	0.0953669
$369$	−3.69417e18	−0.206452
$370$	1.96833e19	1.07791
$371$	1.90108e19	1.02023
$372$	7.25150e17	0.0381378
$373$	1.44712e19	0.745914	0.372957	−	0.927849i	$-0.378344\pi$
$373$	1.44712e19	0.745914	0.372957	+	0.927849i	$0.378344\pi$
$374$	2.72389e19	1.37611
$375$	2.60458e19	1.28974
$376$	−7.02928e18	−0.341194
$377$	3.62875e18	0.172662
$378$	2.71140e18	0.126475
$379$	6.83690e18	0.312655	0.156328	−	0.987705i	$-0.450034\pi$
$379$	6.83690e18	0.312655	0.156328	+	0.987705i	$0.450034\pi$
$380$	−1.11461e19	−0.499740
$381$	−3.83701e18	−0.168677
$382$	1.20311e19	0.518596
$383$	1.45278e19	0.614058	0.307029	−	0.951700i	$-0.400665\pi$
$383$	1.45278e19	0.614058	0.307029	+	0.951700i	$0.400665\pi$
$384$	1.23117e18	0.0510310
$385$	−7.02170e19	−2.85422
$386$	−2.41380e19	−0.962268
$387$	6.25022e18	0.244379
$388$	−2.27553e19	−0.872657
$389$	−8.73653e18	−0.328638	−0.164319	−	0.986407i	$-0.552543\pi$
$389$	−8.73653e18	−0.328638	−0.164319	+	0.986407i	$0.552543\pi$
$390$	−4.93429e18	−0.182071
$391$	−1.20226e19	−0.435183
$392$	1.35625e18	0.0481608
$393$	−2.34336e19	−0.816383
$394$	2.39298e19	0.817933
$395$	−1.97758e19	−0.663217
$396$	8.64004e18	0.284317
$397$	4.36058e19	1.40804	0.704021	−	0.710179i	$-0.251386\pi$
$397$	4.36058e19	1.40804	0.704021	+	0.710179i	$0.251386\pi$
$398$	−4.26765e18	−0.135228
$399$	−9.58032e18	−0.297909
$400$	1.83573e19	0.560221
$401$	−1.31498e19	−0.393854	−0.196927	−	0.980418i	$-0.563096\pi$
$401$	−1.31498e19	−0.393854	−0.196927	+	0.980418i	$0.563096\pi$
$402$	−1.46259e19	−0.429959
$403$	−1.13427e18	−0.0327288
$404$	−6.87385e18	−0.194688
$405$	−7.19452e18	−0.200027
$406$	−1.67820e19	−0.458036
$407$	5.39111e19	1.44451
$408$	−8.85237e18	−0.232867
$409$	−1.26643e19	−0.327082	−0.163541	−	0.986537i	$-0.552292\pi$
$409$	−1.26643e19	−0.327082	−0.163541	+	0.986537i	$0.552292\pi$
$410$	−3.10911e19	−0.788419
$411$	8.91585e18	0.221998
$412$	−1.60974e19	−0.393575
$413$	5.85856e19	1.40658
$414$	−3.81350e18	−0.0899128
$415$	7.03097e19	1.62800
$416$	−1.92579e18	−0.0437934
$417$	−1.35331e19	−0.302257
$418$	−3.05283e19	−0.669701
$419$	−4.10992e19	−0.885581	−0.442790	−	0.896625i	$-0.646011\pi$
$419$	−4.10992e19	−0.885581	−0.442790	+	0.896625i	$0.646011\pi$
$420$	2.28198e19	0.482995
$421$	7.41791e19	1.54229	0.771145	−	0.636660i	$-0.219684\pi$
$421$	7.41791e19	1.54229	0.771145	+	0.636660i	$0.219684\pi$
$422$	5.88844e19	1.20270
$423$	1.60317e19	0.321681
$424$	−1.96877e19	−0.388106
$425$	−1.31993e20	−2.55643
$426$	−7.61273e18	−0.144867
$427$	8.58484e19	1.60518
$428$	−4.03938e18	−0.0742141
$429$	−1.35147e19	−0.243993
$430$	5.26035e19	0.933257
$431$	−7.56855e19	−1.31957	−0.659786	−	0.751454i	$-0.729353\pi$
$431$	−7.56855e19	−1.31957	−0.659786	+	0.751454i	$0.729353\pi$
$432$	−2.80793e18	−0.0481125
$433$	−1.11039e19	−0.186990	−0.0934949	−	0.995620i	$-0.529804\pi$
$433$	−1.11039e19	−0.186990	−0.0934949	+	0.995620i	$0.529804\pi$
$434$	5.24573e18	0.0868227
$435$	4.45301e19	0.724409
$436$	1.38465e19	0.221407
$437$	1.34744e19	0.211787
$438$	−2.56433e19	−0.396203
$439$	−5.15079e19	−0.782330	−0.391165	−	0.920321i	$-0.627928\pi$
$439$	−5.15079e19	−0.782330	−0.391165	+	0.920321i	$0.627928\pi$
$440$	7.27169e19	1.08578
$441$	−3.09319e18	−0.0454064
$442$	1.38468e19	0.199840
$443$	4.77898e19	0.678122	0.339061	−	0.940764i	$-0.389891\pi$
$443$	4.77898e19	0.678122	0.339061	+	0.940764i	$0.389891\pi$
$444$	−1.75206e19	−0.244442
$445$	−1.74290e20	−2.39096
$446$	−3.50041e19	−0.472179
$447$	−8.97726e18	−0.119080
$448$	8.90629e18	0.116175
$449$	5.91210e19	0.758393	0.379196	−	0.925316i	$-0.376201\pi$
$449$	5.91210e19	0.758393	0.379196	+	0.925316i	$0.376201\pi$
$450$	−4.18675e19	−0.528182
$451$	−8.51565e19	−1.05656
$452$	4.91799e19	0.600135
$453$	9.42534e18	0.113125
$454$	−5.20248e19	−0.614174
$455$	−3.56946e19	−0.414493
$456$	9.92140e18	0.113328
$457$	3.59497e19	0.403947	0.201973	−	0.979391i	$-0.435265\pi$
$457$	3.59497e19	0.403947	0.201973	+	0.979391i	$0.435265\pi$
$458$	−1.66885e19	−0.184470
$459$	2.01896e19	0.219549
$460$	−3.20954e19	−0.343368
$461$	7.56833e18	0.0796605	0.0398303	−	0.999206i	$-0.487318\pi$
$461$	7.56833e18	0.0796605	0.0398303	+	0.999206i	$0.487318\pi$
$462$	6.25021e19	0.647261
$463$	4.36170e19	0.444425	0.222213	−	0.974998i	$-0.428672\pi$
$463$	4.36170e19	0.444425	0.222213	+	0.974998i	$0.428672\pi$
$464$	1.73795e19	0.174242
$465$	−1.39192e19	−0.137315
$466$	3.49517e19	0.339293
$467$	−5.47599e19	−0.523102	−0.261551	−	0.965190i	$-0.584234\pi$
$467$	−5.47599e19	−0.523102	−0.261551	+	0.965190i	$0.584234\pi$
$468$	4.39214e18	0.0412888
$469$	−1.05804e20	−0.978823
$470$	1.34927e20	1.22847
$471$	8.97748e19	0.804447
$472$	−6.06714e19	−0.535080
$473$	1.44078e20	1.25066
$474$	1.76030e19	0.150400
$475$	1.47933e20	1.24412
$476$	−6.40380e19	−0.530134
$477$	4.49016e19	0.365910
$478$	−1.54923e20	−1.24281
$479$	−2.20355e20	−1.74023	−0.870113	−	0.492852i	$-0.835954\pi$
$479$	−2.20355e20	−1.74023	−0.870113	+	0.492852i	$0.835954\pi$
$480$	−2.36323e19	−0.183737
$481$	2.74056e19	0.209774
$482$	−4.95223e19	−0.373206
$483$	−2.75869e19	−0.204691
$484$	1.30727e20	0.955046
$485$	4.36786e20	3.14200
$486$	6.40404e18	0.0453609
$487$	2.46263e20	1.71764	0.858819	−	0.512279i	$-0.171198\pi$
$487$	2.46263e20	1.71764	0.858819	+	0.512279i	$0.171198\pi$
$488$	−8.89047e19	−0.610627
$489$	8.02982e18	0.0543112
$490$	−2.60331e19	−0.173403
$491$	−1.45290e20	−0.953069	−0.476534	−	0.879156i	$-0.658107\pi$
$491$	−1.45290e20	−0.953069	−0.476534	+	0.879156i	$0.658107\pi$
$492$	2.76750e19	0.178793
$493$	−1.24962e20	−0.795109
$494$	−1.55190e19	−0.0972548
$495$	−1.65845e20	−1.02368
$496$	−5.43249e18	−0.0330283
$497$	−5.50704e19	−0.329796
$498$	−6.25845e19	−0.369188
$499$	−2.71400e20	−1.57709	−0.788544	−	0.614978i	$-0.789165\pi$
$499$	−2.71400e20	−1.57709	−0.788544	+	0.614978i	$0.789165\pi$
$500$	−1.95123e20	−1.11695
$501$	−8.69777e19	−0.490484
$502$	1.17147e20	0.650806
$503$	−5.02955e19	−0.275276	−0.137638	−	0.990483i	$-0.543951\pi$
$503$	−5.02955e19	−0.275276	−0.137638	+	0.990483i	$0.543951\pi$
$504$	−2.03126e19	−0.109531
$505$	1.31943e20	0.700973
$506$	−8.79073e19	−0.460147
$507$	1.05073e20	0.541917
$508$	2.87451e19	0.146078
$509$	−3.41886e20	−1.71198	−0.855989	−	0.516995i	$-0.827051\pi$
$509$	−3.41886e20	−1.71198	−0.855989	+	0.516995i	$0.827051\pi$
$510$	1.69921e20	0.838436
$511$	−1.85504e20	−0.901977
$512$	−9.22337e18	−0.0441942
$513$	−2.26277e19	−0.106847
$514$	2.76473e20	1.28656
$515$	3.08989e20	1.41706
$516$	−4.68238e19	−0.211638
$517$	3.69555e20	1.64627
$518$	−1.26744e20	−0.556486
$519$	−6.79319e19	−0.293981
$520$	3.69654e19	0.157678
$521$	3.04623e20	1.28080	0.640398	−	0.768043i	$-0.278769\pi$
$521$	3.04623e20	1.28080	0.640398	+	0.768043i	$0.278769\pi$
$522$	−3.96374e19	−0.164277
$523$	−6.22853e19	−0.254462	−0.127231	−	0.991873i	$-0.540609\pi$
$523$	−6.22853e19	−0.254462	−0.127231	+	0.991873i	$0.540609\pi$
$524$	1.75553e20	0.707009
$525$	−3.02869e20	−1.20243
$526$	−6.84978e19	−0.268092
$527$	3.90607e19	0.150716
$528$	−6.47273e19	−0.246225
$529$	−2.27835e20	−0.854482
$530$	3.77904e20	1.39737
$531$	1.38373e20	0.504478
$532$	7.17714e19	0.257997
$533$	−4.32891e19	−0.153435
$534$	1.55140e20	0.542207
$535$	7.75357e19	0.267207
$536$	1.09570e20	0.372355
$537$	−1.16294e20	−0.389719
$538$	6.47758e19	0.214065
$539$	−7.13030e19	−0.232376
$540$	5.38981e19	0.173229
$541$	5.09061e20	1.61358	0.806790	−	0.590839i	$-0.201203\pi$
$541$	5.09061e20	1.61358	0.806790	+	0.590839i	$0.201203\pi$
$542$	−3.74803e20	−1.17168
$543$	−1.59293e20	−0.491132
$544$	6.63179e19	0.201669
$545$	−2.65783e20	−0.797174
$546$	3.17728e19	0.0939961
$547$	−5.58818e20	−1.63067	−0.815333	−	0.578992i	$-0.803446\pi$
$547$	−5.58818e20	−1.63067	−0.815333	+	0.578992i	$0.803446\pi$
$548$	−6.67935e19	−0.192256
$549$	2.02765e20	0.575705
$550$	−9.65113e20	−2.70307
$551$	1.40053e20	0.386950
$552$	2.85690e19	0.0778668
$553$	1.27340e20	0.342394
$554$	−4.82806e19	−0.128071
$555$	3.36307e20	0.880113
$556$	1.01384e20	0.261762
$557$	1.40176e20	0.357076	0.178538	−	0.983933i	$-0.442863\pi$
$557$	1.40176e20	0.357076	0.178538	+	0.983933i	$0.442863\pi$
$558$	1.23899e19	0.0311394
$559$	7.32415e19	0.181622
$560$	−1.70956e20	−0.418286
$561$	4.65402e20	1.12359
$562$	3.53912e20	0.843087
$563$	−3.17601e20	−0.746567	−0.373284	−	0.927717i	$-0.621768\pi$
$563$	−3.17601e20	−0.746567	−0.373284	+	0.927717i	$0.621768\pi$
$564$	−1.20102e20	−0.278584
$565$	−9.44005e20	−2.16078
$566$	1.45903e20	0.329565
$567$	4.63268e19	0.103266
$568$	5.70311e19	0.125458
$569$	1.25453e20	0.272357	0.136178	−	0.990684i	$-0.456518\pi$
$569$	1.25453e20	0.272357	0.136178	+	0.990684i	$0.456518\pi$
$570$	−1.90441e20	−0.408036
$571$	−4.47156e19	−0.0945557	−0.0472779	−	0.998882i	$-0.515055\pi$
$571$	−4.47156e19	−0.0945557	−0.0472779	+	0.998882i	$0.515055\pi$
$572$	1.01246e20	0.211304
$573$	2.05562e20	0.423432
$574$	2.00201e20	0.407031
$575$	4.25977e20	0.854825
$576$	2.10357e19	0.0416667
$577$	−2.39371e20	−0.468008	−0.234004	−	0.972236i	$-0.575183\pi$
$577$	−2.39371e20	−0.468008	−0.234004	+	0.972236i	$0.575183\pi$
$578$	−1.10449e20	−0.213158
$579$	−4.12420e20	−0.785689
$580$	−3.33599e20	−0.627357
$581$	−4.52736e20	−0.840474
$582$	−3.88795e20	−0.712522
$583$	1.03505e21	1.87262
$584$	1.92108e20	0.343122
$585$	−8.43070e19	−0.148660
$586$	−7.47785e20	−1.30180
$587$	2.93609e20	0.504642	0.252321	−	0.967644i	$-0.418806\pi$
$587$	2.93609e20	0.504642	0.252321	+	0.967644i	$0.418806\pi$
$588$	2.31728e19	0.0393231
$589$	−4.37778e19	−0.0733481
$590$	1.16458e21	1.92655
$591$	4.08863e20	0.667839
$592$	1.31256e20	0.211693
$593$	5.11155e20	0.814033	0.407017	−	0.913421i	$-0.366569\pi$
$593$	5.11155e20	0.814033	0.407017	+	0.913421i	$0.366569\pi$
$594$	1.47623e20	0.232143
$595$	1.22921e21	1.90874
$596$	6.72535e19	0.103126
$597$	−7.29167e19	−0.110413
$598$	−4.46874e19	−0.0668231
$599$	−2.14049e20	−0.316091	−0.158045	−	0.987432i	$-0.550519\pi$
$599$	−2.14049e20	−0.316091	−0.158045	+	0.987432i	$0.550519\pi$
$600$	3.13652e20	0.457419
$601$	−4.24612e19	−0.0611553	−0.0305777	−	0.999532i	$-0.509735\pi$
$601$	−4.24612e19	−0.0611553	−0.0305777	+	0.999532i	$0.509735\pi$
$602$	−3.38723e20	−0.481805
$603$	−2.49897e20	−0.351060
$604$	−7.06103e19	−0.0979696
$605$	−2.50929e21	−3.43864
$606$	−1.17446e20	−0.158962
$607$	−1.75100e20	−0.234084	−0.117042	−	0.993127i	$-0.537341\pi$
$607$	−1.75100e20	−0.234084	−0.117042	+	0.993127i	$0.537341\pi$
$608$	−7.43266e19	−0.0981448
$609$	−2.86737e20	−0.373985
$610$	1.70652e21	2.19856
$611$	1.87862e20	0.239073
$612$	−1.51251e20	−0.190135
$613$	−6.98870e20	−0.867846	−0.433923	−	0.900950i	$-0.642871\pi$
$613$	−6.98870e20	−0.867846	−0.433923	+	0.900950i	$0.642871\pi$
$614$	4.59781e20	0.564012
$615$	−5.31221e20	−0.643742
$616$	−4.68237e20	−0.560545
$617$	−1.22078e20	−0.144378	−0.0721888	−	0.997391i	$-0.522998\pi$
$617$	−1.22078e20	−0.144378	−0.0721888	+	0.997391i	$0.522998\pi$
$618$	−2.75039e20	−0.321352
$619$	−5.30802e20	−0.612707	−0.306354	−	0.951918i	$-0.599109\pi$
$619$	−5.30802e20	−0.612707	−0.306354	+	0.951918i	$0.599109\pi$
$620$	1.04276e20	0.118918
$621$	−6.51573e19	−0.0734135
$622$	−2.79725e20	−0.311389
$623$	1.12228e21	1.23436
$624$	−3.29039e19	−0.0357572
$625$	1.65839e21	1.78068
$626$	−7.16639e20	−0.760314
$627$	−5.21605e20	−0.546808
$628$	−6.72551e20	−0.696672
$629$	−9.43759e20	−0.966009
$630$	3.89898e20	0.394364
$631$	−1.55994e21	−1.55915	−0.779573	−	0.626311i	$-0.784564\pi$
$631$	−1.55994e21	−1.55915	−0.779573	+	0.626311i	$0.784564\pi$
$632$	−1.31873e20	−0.130250
$633$	1.00609e21	0.981999
$634$	9.42360e20	0.908965
$635$	−5.51760e20	−0.525954
$636$	−3.36382e20	−0.316887
$637$	−3.62467e19	−0.0337460
$638$	−9.13705e20	−0.840719
$639$	−1.30071e20	−0.118283
$640$	1.77042e20	0.159121
$641$	1.38155e21	1.22725	0.613624	−	0.789598i	$-0.289711\pi$
$641$	1.38155e21	1.22725	0.613624	+	0.789598i	$0.289711\pi$
$642$	−6.90166e19	−0.0605956
$643$	1.66386e21	1.44389	0.721947	−	0.691949i	$-0.243248\pi$
$643$	1.66386e21	1.44389	0.721947	+	0.691949i	$0.243248\pi$
$644$	2.06668e20	0.177268
$645$	8.98780e20	0.762001
$646$	5.34423e20	0.447859
$647$	−4.89973e20	−0.405873	−0.202937	−	0.979192i	$-0.565049\pi$
$647$	−4.89973e20	−0.405873	−0.202937	+	0.979192i	$0.565049\pi$
$648$	−4.79761e19	−0.0392837
$649$	3.18972e21	2.58177
$650$	−4.90613e20	−0.392544
$651$	8.96283e19	0.0708904
$652$	−6.01557e19	−0.0470349
$653$	1.85767e21	1.43588	0.717942	−	0.696103i	$-0.245084\pi$
$653$	1.85767e21	1.43588	0.717942	+	0.696103i	$0.245084\pi$
$654$	2.36580e20	0.180778
$655$	−3.36974e21	−2.54558
$656$	−2.07329e20	−0.154839
$657$	−4.38140e20	−0.323499
$658$	−8.68816e20	−0.634211
$659$	1.98175e21	1.43024	0.715120	−	0.699002i	$-0.246372\pi$
$659$	1.98175e21	1.43024	0.715120	+	0.699002i	$0.246372\pi$
$660$	1.24244e21	0.886532
$661$	−1.98920e21	−1.40335	−0.701677	−	0.712495i	$-0.747565\pi$
$661$	−1.98920e21	−1.40335	−0.701677	+	0.712495i	$0.747565\pi$
$662$	−9.62594e20	−0.671441
$663$	2.36586e20	0.163169
$664$	4.68855e20	0.319726
$665$	−1.37765e21	−0.928915
$666$	−2.99356e20	−0.199586
$667$	4.03287e20	0.265871
$668$	6.51597e20	0.424772
$669$	−5.98077e20	−0.385533
$670$	−2.10320e21	−1.34066
$671$	4.67405e21	2.94628
$672$	1.52172e20	0.0948563
$673$	−1.59503e21	−0.983232	−0.491616	−	0.870812i	$-0.663594\pi$
$673$	−1.59503e21	−0.983232	−0.491616	+	0.870812i	$0.663594\pi$
$674$	5.13572e20	0.313078
$675$	−7.15346e20	−0.431259
$676$	−7.87162e20	−0.469314
$677$	−1.18527e21	−0.698878	−0.349439	−	0.936959i	$-0.613628\pi$
$677$	−1.18527e21	−0.698878	−0.349439	+	0.936959i	$0.613628\pi$
$678$	8.40284e20	0.490008
$679$	−2.81254e21	−1.62209
$680$	−1.27297e21	−0.726107
$681$	−8.88893e20	−0.501471
$682$	2.85606e20	0.159362
$683$	−2.44489e21	−1.34929	−0.674644	−	0.738144i	$-0.735703\pi$
$683$	−2.44489e21	−1.34929	−0.674644	+	0.738144i	$0.735703\pi$
$684$	1.69516e20	0.0925318
$685$	1.28210e21	0.692216
$686$	1.39823e21	0.746705
$687$	−2.85139e20	−0.150619
$688$	3.50782e20	0.183284
$689$	5.26167e20	0.271944
$690$	−5.48381e20	−0.280359
$691$	−1.13986e21	−0.576454	−0.288227	−	0.957562i	$-0.593066\pi$
$691$	−1.13986e21	−0.576454	−0.288227	+	0.957562i	$0.593066\pi$
$692$	5.08915e20	0.254595
$693$	1.06791e21	0.528486
$694$	2.46489e21	1.20671
$695$	−1.94605e21	−0.942472
$696$	2.96945e20	0.142268
$697$	1.49073e21	0.706568
$698$	−1.38065e21	−0.647392
$699$	5.97183e20	0.277031
$700$	2.26896e21	1.04134
$701$	3.11199e19	0.0141303	0.00706517	−	0.999975i	$-0.497751\pi$
$701$	3.11199e19	0.0141303	0.00706517	+	0.999975i	$0.497751\pi$
$702$	7.50439e19	0.0337122
$703$	1.05773e21	0.470121
$704$	4.84907e20	0.213237
$705$	2.30535e21	1.00304
$706$	−4.63911e20	−0.199710
$707$	−8.49605e20	−0.361886
$708$	−1.03663e21	−0.436891
$709$	2.13474e21	0.890220	0.445110	−	0.895476i	$-0.353165\pi$
$709$	2.13474e21	0.890220	0.445110	+	0.895476i	$0.353165\pi$
$710$	−1.09471e21	−0.451711
$711$	3.00763e20	0.122801
$712$	−1.16224e21	−0.469565
$713$	−1.26060e20	−0.0503970
$714$	−1.09415e21	−0.432853
$715$	−1.94341e21	−0.760797
$716$	8.71224e20	0.337507
$717$	−2.64700e21	−1.01475
$718$	2.25115e21	0.854027
$719$	−8.33849e20	−0.313055	−0.156528	−	0.987674i	$-0.550030\pi$
$719$	−8.33849e20	−0.313055	−0.156528	+	0.987674i	$0.550030\pi$
$720$	−4.03780e20	−0.150020
$721$	−1.98963e21	−0.731575
$722$	1.34422e21	0.489150
$723$	−8.46136e20	−0.304721
$724$	1.19335e21	0.425333
$725$	4.42759e21	1.56182
$726$	2.23359e21	0.779792
$727$	4.62186e21	1.59702	0.798508	−	0.601985i	$-0.205623\pi$
$727$	4.62186e21	1.59702	0.798508	+	0.601985i	$0.205623\pi$
$728$	−2.38027e20	−0.0814030
$729$	1.09419e20	0.0370370
$730$	−3.68750e21	−1.23541
$731$	−2.52220e21	−0.836370
$732$	−1.51902e21	−0.498575
$733$	3.02391e21	0.982403	0.491201	−	0.871046i	$-0.336558\pi$
$733$	3.02391e21	0.982403	0.491201	+	0.871046i	$0.336558\pi$
$734$	3.51410e21	1.13004
$735$	−4.44800e20	−0.141583
$736$	−2.14026e20	−0.0674346
$737$	−5.76052e21	−1.79662
$738$	4.72854e20	0.145984
$739$	5.97168e21	1.82500	0.912501	−	0.409075i	$-0.134148\pi$
$739$	5.97168e21	1.82500	0.912501	+	0.409075i	$0.134148\pi$
$740$	−2.51946e21	−0.762200
$741$	−2.65156e20	−0.0794082
$742$	−2.43339e21	−0.721410
$743$	−2.73039e20	−0.0801324	−0.0400662	−	0.999197i	$-0.512757\pi$
$743$	−2.73039e20	−0.0801324	−0.0400662	+	0.999197i	$0.512757\pi$
$744$	−9.28192e19	−0.0269675
$745$	−1.29093e21	−0.371304
$746$	−1.85232e21	−0.527441
$747$	−1.06932e21	−0.301440
$748$	−3.48658e21	−0.973055
$749$	−4.99266e20	−0.137949
$750$	−3.33386e21	−0.911985
$751$	1.84036e20	0.0498429	0.0249215	−	0.999689i	$-0.492066\pi$
$751$	1.84036e20	0.0498429	0.0249215	+	0.999689i	$0.492066\pi$
$752$	8.99748e20	0.241261
$753$	2.00156e21	0.531381
$754$	−4.64480e20	−0.122090
$755$	1.35536e21	0.352739
$756$	−3.47059e20	−0.0894314
$757$	−2.94398e21	−0.751131	−0.375565	−	0.926796i	$-0.622551\pi$
$757$	−2.94398e21	−0.751131	−0.375565	+	0.926796i	$0.622551\pi$
$758$	−8.75124e20	−0.221080
$759$	−1.50198e21	−0.375708
$760$	1.42669e21	0.353370
$761$	−1.39071e20	−0.0341077	−0.0170539	−	0.999855i	$-0.505429\pi$
$761$	−1.39071e20	−0.0341077	−0.0170539	+	0.999855i	$0.505429\pi$
$762$	4.91137e20	0.119272
$763$	1.71142e21	0.411550
$764$	−1.53998e21	−0.366703
$765$	2.90326e21	0.684580
$766$	−1.85956e21	−0.434204
$767$	1.62148e21	0.374928
$768$	−1.57590e20	−0.0360844
$769$	−7.43550e21	−1.68602	−0.843010	−	0.537898i	$-0.819218\pi$
$769$	−7.43550e21	−1.68602	−0.843010	+	0.537898i	$0.819218\pi$
$770$	8.98778e21	2.01824
$771$	4.72380e21	1.05047
$772$	3.08966e21	0.680426
$773$	−2.24172e21	−0.488917	−0.244459	−	0.969660i	$-0.578610\pi$
$773$	−2.24172e21	−0.488917	−0.244459	+	0.969660i	$0.578610\pi$
$774$	−8.00029e20	−0.172802
$775$	−1.38398e21	−0.296051
$776$	2.91267e21	0.617062
$777$	−2.16554e21	−0.454369
$778$	1.11828e21	0.232382
$779$	−1.67076e21	−0.343861
$780$	6.31589e20	0.128743
$781$	−2.99833e21	−0.605337
$782$	1.53889e21	0.307721
$783$	−6.77242e20	−0.134131
$784$	−1.73600e20	−0.0340548
$785$	1.29096e22	2.50836
$786$	2.99950e21	0.577270
$787$	3.80561e21	0.725460	0.362730	−	0.931894i	$-0.381845\pi$
$787$	3.80561e21	0.725460	0.362730	+	0.931894i	$0.381845\pi$
$788$	−3.06302e21	−0.578366
$789$	−1.17035e21	−0.218896
$790$	2.53130e21	0.468965
$791$	6.07861e21	1.11553
$792$	−1.10593e21	−0.201042
$793$	2.37604e21	0.427863
$794$	−5.58155e21	−0.995636
$795$	6.45684e21	1.14095
$796$	5.46259e20	0.0956204
$797$	−7.33682e21	−1.27224	−0.636122	−	0.771589i	$-0.719462\pi$
$797$	−7.33682e21	−1.27224	−0.636122	+	0.771589i	$0.719462\pi$
$798$	1.22628e21	0.210653
$799$	−6.46937e21	−1.10093
$800$	−2.34974e21	−0.396136
$801$	2.65072e21	0.442710
$802$	1.68317e21	0.278497
$803$	−1.00998e22	−1.65557
$804$	1.87211e21	0.304027
$805$	−3.96698e21	−0.638251
$806$	1.45187e20	0.0231428
$807$	1.10676e21	0.174783
$808$	8.79852e20	0.137665
$809$	−1.11403e22	−1.72696	−0.863481	−	0.504381i	$-0.831721\pi$
$809$	−1.11403e22	−1.72696	−0.863481	+	0.504381i	$0.831721\pi$
$810$	9.20899e20	0.141441
$811$	−9.59033e21	−1.45941	−0.729704	−	0.683763i	$-0.760342\pi$
$811$	−9.59033e21	−1.45941	−0.729704	+	0.683763i	$0.760342\pi$
$812$	2.14810e21	0.323880
$813$	−6.40386e21	−0.956671
$814$	−6.90063e21	−1.02142
$815$	1.15469e21	0.169349
$816$	1.13310e21	0.164662
$817$	2.82678e21	0.407030
$818$	1.62103e21	0.231282
$819$	5.42867e20	0.0767475
$820$	3.97966e21	0.557497
$821$	1.24329e22	1.72583	0.862914	−	0.505352i	$-0.168637\pi$
$821$	1.24329e22	1.72583	0.862914	+	0.505352i	$0.168637\pi$
$822$	−1.14123e21	−0.156976
$823$	1.29492e22	1.76500	0.882501	−	0.470310i	$-0.155858\pi$
$823$	1.29492e22	1.76500	0.882501	+	0.470310i	$0.155858\pi$
$824$	2.06047e21	0.278299
$825$	−1.64899e22	−2.20705
$826$	−7.49896e21	−0.994605
$827$	5.99673e21	0.788175	0.394088	−	0.919073i	$-0.371061\pi$
$827$	5.99673e21	0.788175	0.394088	+	0.919073i	$0.371061\pi$
$828$	4.88128e20	0.0635780
$829$	1.19803e22	1.54635	0.773174	−	0.634195i	$-0.218668\pi$
$829$	1.19803e22	1.54635	0.773174	+	0.634195i	$0.218668\pi$
$830$	−8.99964e21	−1.15117
$831$	−8.24920e20	−0.104569
$832$	2.46501e20	0.0309666
$833$	1.24822e21	0.155401
$834$	1.73223e21	0.213728
$835$	−1.25074e22	−1.52939
$836$	3.90762e21	0.473550
$837$	2.11693e20	0.0254252
$838$	5.26070e21	0.626200
$839$	−1.44455e21	−0.170419	−0.0852096	−	0.996363i	$-0.527156\pi$
$839$	−1.44455e21	−0.170419	−0.0852096	+	0.996363i	$0.527156\pi$
$840$	−2.92094e21	−0.341529
$841$	−4.43744e21	−0.514236
$842$	−9.49493e21	−1.09056
$843$	6.04691e21	0.688378
$844$	−7.53720e21	−0.850436
$845$	1.51095e22	1.68976
$846$	−2.05205e21	−0.227463
$847$	1.61578e22	1.77524
$848$	2.52002e21	0.274432
$849$	2.49289e21	0.269089
$850$	1.68951e22	1.80767
$851$	3.04577e21	0.323017
$852$	9.74429e20	0.102436
$853$	−5.94981e21	−0.619991	−0.309996	−	0.950738i	$-0.600328\pi$
$853$	−5.94981e21	−0.619991	−0.309996	+	0.950738i	$0.600328\pi$
$854$	−1.09886e22	−1.13503
$855$	−3.25386e21	−0.333160
$856$	5.17041e20	0.0524773
$857$	5.36930e21	0.540209	0.270104	−	0.962831i	$-0.412942\pi$
$857$	5.36930e21	0.540209	0.270104	+	0.962831i	$0.412942\pi$
$858$	1.72988e21	0.172529
$859$	1.42295e22	1.40683	0.703415	−	0.710779i	$-0.251657\pi$
$859$	1.42295e22	1.40683	0.703415	+	0.710779i	$0.251657\pi$
$860$	−6.73325e21	−0.659912
$861$	3.42062e21	0.332339
$862$	9.68774e21	0.933078
$863$	−1.26362e22	−1.20652	−0.603261	−	0.797543i	$-0.706132\pi$
$863$	−1.26362e22	−1.20652	−0.603261	+	0.797543i	$0.706132\pi$
$864$	3.59415e20	0.0340207
$865$	−9.76859e21	−0.916666
$866$	1.42130e21	0.132222
$867$	−1.88712e21	−0.174043
$868$	−6.71454e20	−0.0613929
$869$	6.93307e21	0.628459
$870$	−5.69985e21	−0.512235
$871$	−2.92835e21	−0.260907
$872$	−1.77235e21	−0.156558
$873$	−6.64292e21	−0.581772
$874$	−1.72473e21	−0.149756
$875$	−2.41171e22	−2.07618
$876$	3.28234e21	0.280158
$877$	1.94622e22	1.64700	0.823502	−	0.567313i	$-0.192017\pi$
$877$	1.94622e22	1.64700	0.823502	+	0.567313i	$0.192017\pi$
$878$	6.59301e21	0.553191
$879$	−1.27766e22	−1.06292
$880$	−9.30776e21	−0.767759
$881$	−4.01382e20	−0.0328275	−0.0164138	−	0.999865i	$-0.505225\pi$
$881$	−4.01382e20	−0.0328275	−0.0164138	+	0.999865i	$0.505225\pi$
$882$	3.95929e20	0.0321072
$883$	−1.87591e22	−1.50837	−0.754183	−	0.656664i	$-0.771967\pi$
$883$	−1.87591e22	−1.50837	−0.754183	+	0.656664i	$0.771967\pi$
$884$	−1.77239e21	−0.141308
$885$	1.98980e22	1.57302
$886$	−6.11710e21	−0.479504
$887$	−3.48285e21	−0.270712	−0.135356	−	0.990797i	$-0.543218\pi$
$887$	−3.48285e21	−0.270712	−0.135356	+	0.990797i	$0.543218\pi$
$888$	2.24264e21	0.172847
$889$	3.55288e21	0.271530
$890$	2.23091e22	1.69066
$891$	2.52228e21	0.189544
$892$	4.48052e21	0.333881
$893$	7.25062e21	0.535783
$894$	1.14909e21	0.0842020
$895$	−1.67231e22	−1.21519
$896$	−1.14001e21	−0.0821480
$897$	−7.63527e20	−0.0545608
$898$	−7.56749e21	−0.536265
$899$	−1.31026e21	−0.0920787
$900$	5.35904e21	0.373481
$901$	−1.81195e22	−1.25230
$902$	1.09000e22	0.747100
$903$	−5.78740e21	−0.393392
$904$	−6.29502e21	−0.424360
$905$	−2.29063e22	−1.53141
$906$	−1.20644e21	−0.0799918
$907$	2.79349e22	1.83693	0.918464	−	0.395505i	$-0.129430\pi$
$907$	2.79349e22	1.83693	0.918464	+	0.395505i	$0.129430\pi$
$908$	6.65918e21	0.434287
$909$	−2.00668e21	−0.129792
$910$	4.56891e21	0.293091
$911$	−1.46026e22	−0.929059	−0.464530	−	0.885558i	$-0.653777\pi$
$911$	−1.46026e22	−0.929059	−0.464530	+	0.885558i	$0.653777\pi$
$912$	−1.26994e21	−0.0801349
$913$	−2.46494e22	−1.54268
$914$	−4.60156e21	−0.285633
$915$	2.91575e22	1.79512
$916$	2.13613e21	0.130440
$917$	2.16983e22	1.31419
$918$	−2.58427e21	−0.155245
$919$	−1.53275e22	−0.913281	−0.456640	−	0.889651i	$-0.650947\pi$
$919$	−1.53275e22	−0.913281	−0.456640	+	0.889651i	$0.650947\pi$
$920$	4.10822e21	0.242798
$921$	7.85579e21	0.460514
$922$	−9.68746e20	−0.0563285
$923$	−1.52420e21	−0.0879079
$924$	−8.00026e21	−0.457683
$925$	3.34387e22	1.89752
$926$	−5.58298e21	−0.314256
$927$	−4.69931e21	−0.262383
$928$	−2.22458e21	−0.123208
$929$	1.72599e22	0.948243	0.474121	−	0.880459i	$-0.342766\pi$
$929$	1.72599e22	0.948243	0.474121	+	0.880459i	$0.342766\pi$
$930$	1.78166e21	0.0970963
$931$	−1.39895e21	−0.0756277
$932$	−4.47382e21	−0.239916
$933$	−4.77936e21	−0.254248
$934$	7.00927e21	0.369889
$935$	6.69247e22	3.50348
$936$	−5.62194e20	−0.0291956
$937$	2.57190e21	0.132497	0.0662486	−	0.997803i	$-0.478897\pi$
$937$	2.57190e21	0.132497	0.0662486	+	0.997803i	$0.478897\pi$
$938$	1.35429e22	0.692132
$939$	−1.22444e22	−0.620793
$940$	−1.72706e22	−0.868658
$941$	−1.86347e22	−0.929823	−0.464911	−	0.885357i	$-0.653914\pi$
$941$	−1.86347e22	−0.929823	−0.464911	+	0.885357i	$0.653914\pi$
$942$	−1.14912e22	−0.568830
$943$	−4.81101e21	−0.236264
$944$	7.76593e21	0.378359
$945$	6.66178e21	0.321997
$946$	−1.84419e22	−0.884347
$947$	−2.87836e22	−1.36937	−0.684684	−	0.728840i	$-0.740060\pi$
$947$	−2.87836e22	−1.36937	−0.684684	+	0.728840i	$0.740060\pi$
$948$	−2.25318e21	−0.106349
$949$	−5.13422e21	−0.240424
$950$	−1.89354e22	−0.879725
$951$	1.61011e22	0.742167
$952$	8.19686e21	0.374861
$953$	−5.82222e21	−0.264175	−0.132088	−	0.991238i	$-0.542168\pi$
$953$	−5.82222e21	−0.264175	−0.132088	+	0.991238i	$0.542168\pi$
$954$	−5.74741e21	−0.258737
$955$	2.95598e22	1.32031
$956$	1.98301e22	0.878802
$957$	−1.56115e22	−0.686444
$958$	2.82054e22	1.23053
$959$	−8.25565e21	−0.357365
$960$	3.02493e21	0.129922
$961$	−2.30557e22	−0.982546
$962$	−3.50792e21	−0.148332
$963$	−1.17921e21	−0.0494761
$964$	6.33886e21	0.263896
$965$	−5.93059e22	−2.44987
$966$	3.53112e21	0.144738
$967$	−1.36325e22	−0.554470	−0.277235	−	0.960802i	$-0.589418\pi$
$967$	−1.36325e22	−0.554470	−0.277235	+	0.960802i	$0.589418\pi$
$968$	−1.67330e22	−0.675320
$969$	9.13112e21	0.365675
$970$	−5.59086e22	−2.22173
$971$	−2.33092e22	−0.919144	−0.459572	−	0.888141i	$-0.651997\pi$
$971$	−2.33092e22	−0.919144	−0.459572	+	0.888141i	$0.651997\pi$
$972$	−8.19717e20	−0.0320750
$973$	1.25310e22	0.486562
$974$	−3.15217e22	−1.21455
$975$	−8.38258e21	−0.320511
$976$	1.13798e22	0.431779
$977$	−3.08656e21	−0.116216	−0.0581080	−	0.998310i	$-0.518507\pi$
$977$	−3.08656e21	−0.116216	−0.0581080	+	0.998310i	$0.518507\pi$
$978$	−1.02782e21	−0.0384038
$979$	6.11032e22	2.26566
$980$	3.33224e21	0.122614
$981$	4.04220e21	0.147605
$982$	1.85971e22	0.673921
$983$	4.05804e22	1.45937	0.729684	−	0.683784i	$-0.239667\pi$
$983$	4.05804e22	1.45937	0.729684	+	0.683784i	$0.239667\pi$
$984$	−3.54240e21	−0.126426
$985$	5.87944e22	2.08240
$986$	1.59952e22	0.562227
$987$	−1.48445e22	−0.517831
$988$	1.98643e21	0.0687696
$989$	8.13981e21	0.279668
$990$	2.12282e22	0.723851
$991$	−2.37255e22	−0.802903	−0.401451	−	0.915880i	$-0.631494\pi$
$991$	−2.37255e22	−0.802903	−0.401451	+	0.915880i	$0.631494\pi$
$992$	6.95359e20	0.0233546
$993$	−1.64468e22	−0.548230
$994$	7.04902e21	0.233201
$995$	−1.04854e22	−0.344280
$996$	8.01082e21	0.261055
$997$	2.95460e21	0.0955620	0.0477810	−	0.998858i	$-0.484785\pi$
$997$	2.95460e21	0.0955620	0.0477810	+	0.998858i	$0.484785\pi$
$998$	3.47392e22	1.11517
$999$	−5.11477e21	−0.162962

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.16.a.a.1.1	✓	1
3.2	odd	2		18.16.a.f.1.1		1
4.3	odd	2		48.16.a.c.1.1		1
5.2	odd	4		150.16.c.i.49.1		2
5.3	odd	4		150.16.c.i.49.2		2
5.4	even	2		150.16.a.h.1.1		1
12.11	even	2		144.16.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.16.a.a.1.1	✓	1	1.1	even	1	trivial
18.16.a.f.1.1		1	3.2	odd	2
48.16.a.c.1.1		1	4.3	odd	2
144.16.a.o.1.1		1	12.11	even	2
150.16.a.h.1.1		1	5.4	even	2
150.16.c.i.49.1		2	5.2	odd	4
150.16.c.i.49.2		2	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 16 \)
Character orbit:	\([\chi]\)	\(=\)	6.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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