LMFDB - Embedded newform 10.18.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,18,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, 18, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 18 $
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:	$18.3222087345$
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)

$f(q)$

$=$

$q+256.000 q^{2} -14976.0 q^{3} +65536.0 q^{4} +390625. q^{5} -3.83386e6 q^{6} +1.48087e7 q^{7} +1.67772e7 q^{8} +9.51404e7 q^{9} +O(q^{10})$

\(q+256.000 q^{2} -14976.0 q^{3} +65536.0 q^{4} +390625. q^{5} -3.83386e6 q^{6} +1.48087e7 q^{7} +1.67772e7 q^{8} +9.51404e7 q^{9} +1.00000e8 q^{10} -1.08503e9 q^{11} -9.81467e8 q^{12} -4.59530e9 q^{13} +3.79102e9 q^{14} -5.85000e9 q^{15} +4.29497e9 q^{16} -1.61047e10 q^{17} +2.43559e10 q^{18} +4.80931e10 q^{19} +2.56000e10 q^{20} -2.21775e11 q^{21} -2.77769e11 q^{22} -5.71023e11 q^{23} -2.51256e11 q^{24} +1.52588e11 q^{25} -1.17640e12 q^{26} +5.09180e11 q^{27} +9.70501e11 q^{28} -1.72642e12 q^{29} -1.49760e12 q^{30} -5.62372e12 q^{31} +1.09951e12 q^{32} +1.62495e13 q^{33} -4.12280e12 q^{34} +5.78464e12 q^{35} +6.23512e12 q^{36} -1.00131e13 q^{37} +1.23118e13 q^{38} +6.88193e13 q^{39} +6.55360e12 q^{40} -3.75051e13 q^{41} -5.67743e13 q^{42} +1.36226e14 q^{43} -7.11088e13 q^{44} +3.71642e13 q^{45} -1.46182e14 q^{46} -3.76813e13 q^{47} -6.43214e13 q^{48} -1.33339e13 q^{49} +3.90625e13 q^{50} +2.41184e14 q^{51} -3.01158e14 q^{52} -2.25437e13 q^{53} +1.30350e14 q^{54} -4.23842e14 q^{55} +2.48448e14 q^{56} -7.20243e14 q^{57} -4.41965e14 q^{58} +2.21364e14 q^{59} -3.83386e14 q^{60} -2.76238e14 q^{61} -1.43967e15 q^{62} +1.40890e15 q^{63} +2.81475e14 q^{64} -1.79504e15 q^{65} +4.15987e15 q^{66} +6.16540e15 q^{67} -1.05544e15 q^{68} +8.55164e15 q^{69} +1.48087e15 q^{70} -1.29446e14 q^{71} +1.59619e15 q^{72} -9.75122e15 q^{73} -2.56336e15 q^{74} -2.28516e15 q^{75} +3.15183e15 q^{76} -1.60679e16 q^{77} +1.76177e16 q^{78} -2.55383e16 q^{79} +1.67772e15 q^{80} -1.99119e16 q^{81} -9.60131e15 q^{82} +2.99301e16 q^{83} -1.45342e16 q^{84} -6.29090e15 q^{85} +3.48739e16 q^{86} +2.58549e16 q^{87} -1.82039e16 q^{88} -2.42584e16 q^{89} +9.51404e15 q^{90} -6.80503e16 q^{91} -3.74226e16 q^{92} +8.42209e16 q^{93} -9.64642e15 q^{94} +1.87864e16 q^{95} -1.64663e16 q^{96} +1.23350e17 q^{97} -3.41347e15 q^{98} -1.03231e17 q^{99} +O(q^{100})\)

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 $

$2$	256.000	0.707107
$2$	256.000	0.707107
$3$	−14976.0	−1.31785	−0.658924	−	0.752210i	$-0.728988\pi$
$3$	−14976.0	−1.31785	−0.658924	+	0.752210i	$0.728988\pi$
$4$	65536.0	0.500000
$5$	390625.	0.447214
$5$	390625.	0.447214
$6$	−3.83386e6	−0.931859
$7$	1.48087e7	0.970918	0.485459	−	0.874259i	$-0.338652\pi$
$7$	1.48087e7	0.970918	0.485459	+	0.874259i	$0.338652\pi$
$8$	1.67772e7	0.353553
$9$	9.51404e7	0.736722
$10$	1.00000e8	0.316228
$11$	−1.08503e9	−1.52618	−0.763090	−	0.646292i	$-0.776319\pi$
$11$	−1.08503e9	−1.52618	−0.763090	+	0.646292i	$0.776319\pi$
$12$	−9.81467e8	−0.658924
$13$	−4.59530e9	−1.56241	−0.781206	−	0.624273i	$-0.785395\pi$
$13$	−4.59530e9	−1.56241	−0.781206	+	0.624273i	$0.785395\pi$
$14$	3.79102e9	0.686543
$15$	−5.85000e9	−0.589359
$16$	4.29497e9	0.250000
$17$	−1.61047e10	−0.559934	−0.279967	−	0.960010i	$-0.590324\pi$
$17$	−1.61047e10	−0.559934	−0.279967	+	0.960010i	$0.590324\pi$
$18$	2.43559e10	0.520941
$19$	4.80931e10	0.649647	0.324823	−	0.945775i	$-0.394695\pi$
$19$	4.80931e10	0.649647	0.324823	+	0.945775i	$0.394695\pi$
$20$	2.56000e10	0.223607
$21$	−2.21775e11	−1.27952
$22$	−2.77769e11	−1.07917
$23$	−5.71023e11	−1.52043	−0.760216	−	0.649670i	$-0.774907\pi$
$23$	−5.71023e11	−1.52043	−0.760216	+	0.649670i	$0.774907\pi$
$24$	−2.51256e11	−0.465929
$25$	1.52588e11	0.200000
$26$	−1.17640e12	−1.10479
$27$	5.09180e11	0.346960
$28$	9.70501e11	0.485459
$29$	−1.72642e12	−0.640862	−0.320431	−	0.947272i	$-0.603828\pi$
$29$	−1.72642e12	−0.640862	−0.320431	+	0.947272i	$0.603828\pi$
$30$	−1.49760e12	−0.416740
$31$	−5.62372e12	−1.18427	−0.592133	−	0.805840i	$-0.701714\pi$
$31$	−5.62372e12	−1.18427	−0.592133	+	0.805840i	$0.701714\pi$
$32$	1.09951e12	0.176777
$33$	1.62495e13	2.01127
$34$	−4.12280e12	−0.395933
$35$	5.78464e12	0.434208
$36$	6.23512e12	0.368361
$37$	−1.00131e13	−0.468657	−0.234329	−	0.972157i	$-0.575289\pi$
$37$	−1.00131e13	−0.468657	−0.234329	+	0.972157i	$0.575289\pi$
$38$	1.23118e13	0.459370
$39$	6.88193e13	2.05902
$40$	6.55360e12	0.158114
$41$	−3.75051e13	−0.733547	−0.366773	−	0.930310i	$-0.619538\pi$
$41$	−3.75051e13	−0.733547	−0.366773	+	0.930310i	$0.619538\pi$
$42$	−5.67743e13	−0.904759
$43$	1.36226e14	1.77737	0.888687	−	0.458515i	$-0.151618\pi$
$43$	1.36226e14	1.77737	0.888687	+	0.458515i	$0.151618\pi$
$44$	−7.11088e13	−0.763090
$45$	3.71642e13	0.329472
$46$	−1.46182e14	−1.07511
$47$	−3.76813e13	−0.230831	−0.115416	−	0.993317i	$-0.536820\pi$
$47$	−3.76813e13	−0.230831	−0.115416	+	0.993317i	$0.536820\pi$
$48$	−6.43214e13	−0.329462
$49$	−1.33339e13	−0.0573178
$50$	3.90625e13	0.141421
$51$	2.41184e14	0.737908
$52$	−3.01158e14	−0.781206
$53$	−2.25437e13	−0.0497372	−0.0248686	−	0.999691i	$-0.507917\pi$
$53$	−2.25437e13	−0.0497372	−0.0248686	+	0.999691i	$0.507917\pi$
$54$	1.30350e14	0.245338
$55$	−4.23842e14	−0.682528
$56$	2.48448e14	0.343271
$57$	−7.20243e14	−0.856135
$58$	−4.41965e14	−0.453158
$59$	2.21364e14	0.196275	0.0981373	−	0.995173i	$-0.468712\pi$
$59$	2.21364e14	0.196275	0.0981373	+	0.995173i	$0.468712\pi$
$60$	−3.83386e14	−0.294680
$61$	−2.76238e14	−0.184493	−0.0922465	−	0.995736i	$-0.529405\pi$
$61$	−2.76238e14	−0.184493	−0.0922465	+	0.995736i	$0.529405\pi$
$62$	−1.43967e15	−0.837403
$63$	1.40890e15	0.715297
$64$	2.81475e14	0.125000
$65$	−1.79504e15	−0.698732
$66$	4.15987e15	1.42218
$67$	6.16540e15	1.85492	0.927461	−	0.373921i	$-0.121987\pi$
$67$	6.16540e15	1.85492	0.927461	+	0.373921i	$0.121987\pi$
$68$	−1.05544e15	−0.279967
$69$	8.55164e15	2.00370
$70$	1.48087e15	0.307031
$71$	−1.29446e14	−0.0237898	−0.0118949	−	0.999929i	$-0.503786\pi$
$71$	−1.29446e14	−0.0237898	−0.0118949	+	0.999929i	$0.503786\pi$
$72$	1.59619e15	0.260471
$73$	−9.75122e15	−1.41519	−0.707595	−	0.706619i	$-0.750220\pi$
$73$	−9.75122e15	−1.41519	−0.707595	+	0.706619i	$0.750220\pi$
$74$	−2.56336e15	−0.331391
$75$	−2.28516e15	−0.263570
$76$	3.15183e15	0.324823
$77$	−1.60679e16	−1.48180
$78$	1.76177e16	1.45595
$79$	−2.55383e16	−1.89392	−0.946959	−	0.321355i	$-0.895862\pi$
$79$	−2.55383e16	−1.89392	−0.946959	+	0.321355i	$0.895862\pi$
$80$	1.67772e15	0.111803
$81$	−1.99119e16	−1.19396
$82$	−9.60131e15	−0.518696
$83$	2.99301e16	1.45863	0.729314	−	0.684179i	$-0.239839\pi$
$83$	2.99301e16	1.45863	0.729314	+	0.684179i	$0.239839\pi$
$84$	−1.45342e16	−0.639761
$85$	−6.29090e15	−0.250410
$86$	3.48739e16	1.25679
$87$	2.58549e16	0.844559
$88$	−1.82039e16	−0.539586
$89$	−2.42584e16	−0.653200	−0.326600	−	0.945163i	$-0.605903\pi$
$89$	−2.42584e16	−0.653200	−0.326600	+	0.945163i	$0.605903\pi$
$90$	9.51404e15	0.232972
$91$	−6.80503e16	−1.51697
$92$	−3.74226e16	−0.760216
$93$	8.42209e16	1.56068
$94$	−9.64642e15	−0.163222
$95$	1.87864e16	0.290531
$96$	−1.64663e16	−0.232965
$97$	1.23350e17	1.59801	0.799006	−	0.601323i	$-0.205360\pi$
$97$	1.23350e17	1.59801	0.799006	+	0.601323i	$0.205360\pi$
$98$	−3.41347e15	−0.0405298
$99$	−1.03231e17	−1.12437
$100$	1.00000e16	0.100000
$101$	1.97890e17	1.81841	0.909205	−	0.416350i	$-0.136691\pi$
$101$	1.97890e17	1.81841	0.909205	+	0.416350i	$0.136691\pi$
$102$	6.17431e16	0.521779
$103$	2.07946e16	0.161747	0.0808733	−	0.996724i	$-0.474229\pi$
$103$	2.07946e16	0.161747	0.0808733	+	0.996724i	$0.474229\pi$
$104$	−7.70964e16	−0.552396
$105$	−8.66307e16	−0.572220
$106$	−5.77120e15	−0.0351695
$107$	1.55264e17	0.873593	0.436796	−	0.899560i	$-0.356113\pi$
$107$	1.55264e17	0.873593	0.436796	+	0.899560i	$0.356113\pi$
$108$	3.33696e16	0.173480
$109$	−1.74006e17	−0.836446	−0.418223	−	0.908344i	$-0.637347\pi$
$109$	−1.74006e17	−0.836446	−0.418223	+	0.908344i	$0.637347\pi$
$110$	−1.08503e17	−0.482620
$111$	1.49957e17	0.617619
$112$	6.36027e16	0.242730
$113$	6.79597e16	0.240483	0.120242	−	0.992745i	$-0.461633\pi$
$113$	6.79597e16	0.240483	0.120242	+	0.992745i	$0.461633\pi$
$114$	−1.84382e17	−0.605379
$115$	−2.23056e17	−0.679958
$116$	−1.13143e17	−0.320431
$117$	−4.37199e17	−1.15106
$118$	5.66691e16	0.138787
$119$	−2.38489e17	−0.543650
$120$	−9.81467e16	−0.208370
$121$	6.71853e17	1.32923
$122$	−7.07169e16	−0.130456
$123$	5.61677e17	0.966703
$124$	−3.68556e17	−0.592133
$125$	5.96046e16	0.0894427
$126$	3.60679e17	0.505791
$127$	−4.32909e17	−0.567629	−0.283815	−	0.958879i	$-0.591600\pi$
$127$	−4.32909e17	−0.567629	−0.283815	+	0.958879i	$0.591600\pi$
$128$	7.20576e16	0.0883883
$129$	−2.04012e18	−2.34231
$130$	−4.59530e17	−0.494078
$131$	−3.30165e17	−0.332602	−0.166301	−	0.986075i	$-0.553182\pi$
$131$	−3.30165e17	−0.332602	−0.166301	+	0.986075i	$0.553182\pi$
$132$	1.06493e18	1.00564
$133$	7.12195e17	0.630754
$134$	1.57834e18	1.31163
$135$	1.98899e17	0.155165
$136$	−2.70192e17	−0.197967
$137$	−1.77040e18	−1.21884	−0.609420	−	0.792847i	$-0.708598\pi$
$137$	−1.77040e18	−1.21884	−0.609420	+	0.792847i	$0.708598\pi$
$138$	2.18922e18	1.41683
$139$	1.49548e18	0.910236	0.455118	−	0.890431i	$-0.349597\pi$
$139$	1.49548e18	0.910236	0.455118	+	0.890431i	$0.349597\pi$
$140$	3.79102e17	0.217104
$141$	5.64315e17	0.304200
$142$	−3.31381e16	−0.0168220
$143$	4.98606e18	2.38452
$144$	4.08625e17	0.184181
$145$	−6.74385e17	−0.286602
$146$	−2.49631e18	−1.00069
$147$	1.99688e17	0.0755361
$148$	−6.56220e17	−0.234329
$149$	−4.77351e18	−1.60973	−0.804867	−	0.593455i	$-0.797764\pi$
$149$	−4.77351e18	−1.60973	−0.804867	+	0.593455i	$0.797764\pi$
$150$	−5.85000e17	−0.186372
$151$	1.01526e18	0.305684	0.152842	−	0.988251i	$-0.451157\pi$
$151$	1.01526e18	0.305684	0.152842	+	0.988251i	$0.451157\pi$
$152$	8.06869e17	0.229685
$153$	−1.53221e18	−0.412516
$154$	−4.11339e18	−1.04779
$155$	−2.19677e18	−0.529620
$156$	4.51014e18	1.02951
$157$	2.03854e18	0.440729	0.220365	−	0.975418i	$-0.429275\pi$
$157$	2.03854e18	0.440729	0.220365	+	0.975418i	$0.429275\pi$
$158$	−6.53779e18	−1.33920
$159$	3.37615e17	0.0655460
$160$	4.29497e17	0.0790569
$161$	−8.45609e18	−1.47622
$162$	−5.09745e18	−0.844259
$163$	−5.84386e18	−0.918555	−0.459278	−	0.888293i	$-0.651892\pi$
$163$	−5.84386e18	−0.918555	−0.459278	+	0.888293i	$0.651892\pi$
$164$	−2.45794e18	−0.366773
$165$	6.34745e18	0.899468
$166$	7.66211e18	1.03141
$167$	1.10139e19	1.40881	0.704405	−	0.709798i	$-0.251214\pi$
$167$	1.10139e19	1.40881	0.704405	+	0.709798i	$0.251214\pi$
$168$	−3.72076e18	−0.452379
$169$	1.24664e19	1.44113
$170$	−1.61047e18	−0.177067
$171$	4.57560e18	0.478609
$172$	8.92772e18	0.888687
$173$	−8.93637e18	−0.846778	−0.423389	−	0.905948i	$-0.639160\pi$
$173$	−8.93637e18	−0.846778	−0.423389	+	0.905948i	$0.639160\pi$
$174$	6.61886e18	0.597193
$175$	2.25962e18	0.194184
$176$	−4.66019e18	−0.381545
$177$	−3.31514e18	−0.258660
$178$	−6.21014e18	−0.461882
$179$	7.63124e18	0.541183	0.270591	−	0.962694i	$-0.412781\pi$
$179$	7.63124e18	0.541183	0.270591	+	0.962694i	$0.412781\pi$
$180$	2.43559e18	0.164736
$181$	−2.78815e18	−0.179907	−0.0899534	−	0.995946i	$-0.528672\pi$
$181$	−2.78815e18	−0.179907	−0.0899534	+	0.995946i	$0.528672\pi$
$182$	−1.74209e19	−1.07266
$183$	4.13694e18	0.243134
$184$	−9.58018e18	−0.537554
$185$	−3.91138e18	−0.209590
$186$	2.15605e19	1.10357
$187$	1.74742e19	0.854560
$188$	−2.46948e18	−0.115416
$189$	7.54028e18	0.336870
$190$	4.80931e18	0.205436
$191$	−3.85345e19	−1.57422	−0.787111	−	0.616812i	$-0.788424\pi$
$191$	−3.85345e19	−1.57422	−0.787111	+	0.616812i	$0.788424\pi$
$192$	−4.21537e18	−0.164731
$193$	3.02774e19	1.13209	0.566046	−	0.824374i	$-0.308473\pi$
$193$	3.02774e19	1.13209	0.566046	+	0.824374i	$0.308473\pi$
$194$	3.15776e19	1.12997
$195$	2.68825e19	0.920822
$196$	−8.73848e17	−0.0286589
$197$	−5.29954e19	−1.66447	−0.832234	−	0.554424i	$-0.812939\pi$
$197$	−5.29954e19	−1.66447	−0.832234	+	0.554424i	$0.812939\pi$
$198$	−2.64270e19	−0.795050
$199$	4.25776e19	1.22724	0.613620	−	0.789601i	$-0.289713\pi$
$199$	4.25776e19	1.22724	0.613620	+	0.789601i	$0.289713\pi$
$200$	2.56000e18	0.0707107
$201$	−9.23330e19	−2.44450
$202$	5.06598e19	1.28581
$203$	−2.55661e19	−0.622225
$204$	1.58062e19	0.368954
$205$	−1.46504e19	−0.328052
$206$	5.32343e18	0.114372
$207$	−5.43274e19	−1.12014
$208$	−1.97367e19	−0.390603
$209$	−5.21827e19	−0.991478
$210$	−2.21775e19	−0.404620
$211$	5.71907e18	0.100213	0.0501066	−	0.998744i	$-0.484044\pi$
$211$	5.71907e18	0.100213	0.0501066	+	0.998744i	$0.484044\pi$
$212$	−1.47743e18	−0.0248686
$213$	1.93858e18	0.0313514
$214$	3.97476e19	0.617724
$215$	5.32134e19	0.794866
$216$	8.54263e18	0.122669
$217$	−8.32798e19	−1.14983
$218$	−4.45454e19	−0.591457
$219$	1.46034e20	1.86500
$220$	−2.77769e19	−0.341264
$221$	7.40060e19	0.874848
$222$	3.83889e19	0.436722
$223$	9.56843e19	1.04773	0.523865	−	0.851801i	$-0.324490\pi$
$223$	9.56843e19	1.04773	0.523865	+	0.851801i	$0.324490\pi$
$224$	1.62823e19	0.171636
$225$	1.45173e19	0.147344
$226$	1.73977e19	0.170047
$227$	−2.16165e19	−0.203500	−0.101750	−	0.994810i	$-0.532444\pi$
$227$	−2.16165e19	−0.203500	−0.101750	+	0.994810i	$0.532444\pi$
$228$	−4.72018e19	−0.428068
$229$	−3.84000e19	−0.335529	−0.167764	−	0.985827i	$-0.553655\pi$
$229$	−3.84000e19	−0.335529	−0.167764	+	0.985827i	$0.553655\pi$
$230$	−5.71023e19	−0.480803
$231$	2.40633e20	1.95278
$232$	−2.89646e19	−0.226579
$233$	−1.29997e20	−0.980407	−0.490204	−	0.871608i	$-0.663078\pi$
$233$	−1.29997e20	−0.980407	−0.490204	+	0.871608i	$0.663078\pi$
$234$	−1.11923e20	−0.813925
$235$	−1.47193e19	−0.103231
$236$	1.45073e19	0.0981373
$237$	3.82461e20	2.49589
$238$	−6.10532e19	−0.384419
$239$	−1.37009e20	−0.832466	−0.416233	−	0.909258i	$-0.636650\pi$
$239$	−1.37009e20	−0.832466	−0.416233	+	0.909258i	$0.636650\pi$
$240$	−2.51256e19	−0.147340
$241$	−1.30006e20	−0.735901	−0.367950	−	0.929845i	$-0.619940\pi$
$241$	−1.30006e20	−0.735901	−0.367950	+	0.929845i	$0.619940\pi$
$242$	1.71994e20	0.939904
$243$	2.32445e20	1.22650
$244$	−1.81035e19	−0.0922465
$245$	−5.20854e18	−0.0256333
$246$	1.43789e20	0.683562
$247$	−2.21002e20	−1.01502
$248$	−9.43504e19	−0.418701
$249$	−4.48233e20	−1.92225
$250$	1.52588e19	0.0632456
$251$	−4.52136e20	−1.81152	−0.905759	−	0.423793i	$-0.860698\pi$
$251$	−4.52136e20	−1.81152	−0.905759	+	0.423793i	$0.860698\pi$
$252$	9.23339e19	0.357648
$253$	6.19580e20	2.32045
$254$	−1.10825e20	−0.401375
$255$	9.42125e19	0.330002
$256$	1.84467e19	0.0625000
$257$	−4.08755e20	−1.33977	−0.669887	−	0.742463i	$-0.733658\pi$
$257$	−4.08755e20	−1.33977	−0.669887	+	0.742463i	$0.733658\pi$
$258$	−5.22272e20	−1.65626
$259$	−1.48281e20	−0.455028
$260$	−1.17640e20	−0.349366
$261$	−1.64253e20	−0.472137
$262$	−8.45222e19	−0.235185
$263$	9.77636e19	0.263362	0.131681	−	0.991292i	$-0.457963\pi$
$263$	9.77636e19	0.263362	0.131681	+	0.991292i	$0.457963\pi$
$264$	2.72621e20	0.711092
$265$	−8.80615e18	−0.0222431
$266$	1.82322e20	0.446010
$267$	3.63293e20	0.860819
$268$	4.04056e20	0.927461
$269$	−6.44075e19	−0.143233	−0.0716163	−	0.997432i	$-0.522816\pi$
$269$	−6.44075e19	−0.143233	−0.0716163	+	0.997432i	$0.522816\pi$
$270$	5.09180e19	0.109718
$271$	−2.38017e20	−0.497014	−0.248507	−	0.968630i	$-0.579940\pi$
$271$	−2.38017e20	−0.497014	−0.248507	+	0.968630i	$0.579940\pi$
$272$	−6.91692e19	−0.139983
$273$	1.01912e21	1.99914
$274$	−4.53223e20	−0.861851
$275$	−1.65563e20	−0.305236
$276$	5.60440e20	1.00185
$277$	5.75763e20	0.998081	0.499040	−	0.866579i	$-0.333686\pi$
$277$	5.75763e20	0.998081	0.499040	+	0.866579i	$0.333686\pi$
$278$	3.82842e20	0.643634
$279$	−5.35043e20	−0.872475
$280$	9.70501e19	0.153516
$281$	5.02358e20	0.770921	0.385460	−	0.922724i	$-0.374043\pi$
$281$	5.02358e20	0.770921	0.385460	+	0.922724i	$0.374043\pi$
$282$	1.44465e20	0.215102
$283$	−1.31863e20	−0.190520	−0.0952598	−	0.995452i	$-0.530368\pi$
$283$	−1.31863e20	−0.190520	−0.0952598	+	0.995452i	$0.530368\pi$
$284$	−8.48335e18	−0.0118949
$285$	−2.81345e20	−0.382875
$286$	1.27643e21	1.68611
$287$	−5.55401e20	−0.712214
$288$	1.04608e20	0.130235
$289$	−5.67879e20	−0.686474
$290$	−1.72642e20	−0.202658
$291$	−1.84729e21	−2.10594
$292$	−6.39056e20	−0.707595
$293$	3.98158e20	0.428234	0.214117	−	0.976808i	$-0.431313\pi$
$293$	3.98158e20	0.428234	0.214117	+	0.976808i	$0.431313\pi$
$294$	5.11201e19	0.0534121
$295$	8.64702e19	0.0877767
$296$	−1.67992e20	−0.165695
$297$	−5.52478e20	−0.529524
$298$	−1.22202e21	−1.13825
$299$	2.62402e21	2.37554
$300$	−1.49760e20	−0.131785
$301$	2.01733e21	1.72568
$302$	2.59906e20	0.216151
$303$	−2.96360e21	−2.39639
$304$	2.06558e20	0.162412
$305$	−1.07905e20	−0.0825078
$306$	−3.92245e20	−0.291693
$307$	−1.94368e20	−0.140588	−0.0702942	−	0.997526i	$-0.522394\pi$
$307$	−1.94368e20	−0.140588	−0.0702942	+	0.997526i	$0.522394\pi$
$308$	−1.05303e21	−0.740898
$309$	−3.11421e20	−0.213157
$310$	−5.62372e20	−0.374498
$311$	1.01768e21	0.659400	0.329700	−	0.944086i	$-0.393052\pi$
$311$	1.01768e21	0.659400	0.329700	+	0.944086i	$0.393052\pi$
$312$	1.15460e21	0.727974
$313$	2.32833e21	1.42862	0.714312	−	0.699828i	$-0.246740\pi$
$313$	2.32833e21	1.42862	0.714312	+	0.699828i	$0.246740\pi$
$314$	5.21866e20	0.311643
$315$	5.50353e20	0.319891
$316$	−1.67368e21	−0.946959
$317$	−1.47717e21	−0.813627	−0.406814	−	0.913511i	$-0.633360\pi$
$317$	−1.47717e21	−0.813627	−0.406814	+	0.913511i	$0.633360\pi$
$318$	8.64294e19	0.0463480
$319$	1.87323e21	0.978071
$320$	1.09951e20	0.0559017
$321$	−2.32524e21	−1.15126
$322$	−2.16476e21	−1.04384
$323$	−7.74525e20	−0.363759
$324$	−1.30495e21	−0.596981
$325$	−7.01188e20	−0.312483
$326$	−1.49603e21	−0.649516
$327$	2.60591e21	1.10231
$328$	−6.29231e20	−0.259348
$329$	−5.58010e20	−0.224118
$330$	1.62495e21	0.636020
$331$	−1.13218e21	−0.431893	−0.215947	−	0.976405i	$-0.569284\pi$
$331$	−1.13218e21	−0.431893	−0.215947	+	0.976405i	$0.569284\pi$
$332$	1.96150e21	0.729314
$333$	−9.52653e20	−0.345270
$334$	2.81957e21	0.996179
$335$	2.40836e21	0.829546
$336$	−9.52515e20	−0.319881
$337$	1.92667e21	0.630890	0.315445	−	0.948944i	$-0.397846\pi$
$337$	1.92667e21	0.630890	0.315445	+	0.948944i	$0.397846\pi$
$338$	3.19140e21	1.01903
$339$	−1.01777e21	−0.316920
$340$	−4.12280e20	−0.125205
$341$	6.10193e21	1.80740
$342$	1.17135e21	0.338428
$343$	−3.64240e21	−1.02657
$344$	2.28550e21	0.628396
$345$	3.34048e21	0.896081
$346$	−2.28771e21	−0.598762
$347$	−4.65616e21	−1.18912	−0.594562	−	0.804050i	$-0.702675\pi$
$347$	−4.65616e21	−1.18912	−0.594562	+	0.804050i	$0.702675\pi$
$348$	1.69443e21	0.422279
$349$	1.19163e21	0.289819	0.144909	−	0.989445i	$-0.453711\pi$
$349$	1.19163e21	0.289819	0.144909	+	0.989445i	$0.453711\pi$
$350$	5.78464e20	0.137309
$351$	−2.33984e21	−0.542095
$352$	−1.19301e21	−0.269793
$353$	5.22179e20	0.115275	0.0576375	−	0.998338i	$-0.481643\pi$
$353$	5.22179e20	0.115275	0.0576375	+	0.998338i	$0.481643\pi$
$354$	−8.48676e20	−0.182900
$355$	−5.05647e19	−0.0106391
$356$	−1.58980e21	−0.326600
$357$	3.57161e21	0.716448
$358$	1.95360e21	0.382674
$359$	5.07950e21	0.971668	0.485834	−	0.874051i	$-0.338516\pi$
$359$	5.07950e21	0.971668	0.485834	+	0.874051i	$0.338516\pi$
$360$	6.23512e20	0.116486
$361$	−3.16744e21	−0.577959
$362$	−7.13765e20	−0.127213
$363$	−1.00617e22	−1.75172
$364$	−4.45975e21	−0.758487
$365$	−3.80907e21	−0.632892
$366$	1.05906e21	0.171921
$367$	−9.77977e21	−1.55120	−0.775599	−	0.631226i	$-0.782552\pi$
$367$	−9.77977e21	−1.55120	−0.775599	+	0.631226i	$0.782552\pi$
$368$	−2.45253e21	−0.380108
$369$	−3.56825e21	−0.540420
$370$	−1.00131e21	−0.148202
$371$	−3.33843e20	−0.0482907
$372$	5.51950e21	0.780341
$373$	−1.20930e22	−1.67112	−0.835560	−	0.549400i	$-0.814856\pi$
$373$	−1.20930e22	−1.67112	−0.835560	+	0.549400i	$0.814856\pi$
$374$	4.47338e21	0.604265
$375$	−8.92639e20	−0.117872
$376$	−6.32188e20	−0.0816111
$377$	7.93345e21	1.00129
$378$	1.93031e21	0.238203
$379$	8.55957e21	1.03281	0.516403	−	0.856346i	$-0.327271\pi$
$379$	8.55957e21	1.03281	0.516403	+	0.856346i	$0.327271\pi$
$380$	1.23118e21	0.145265
$381$	6.48324e21	0.748049
$382$	−9.86482e21	−1.11314
$383$	1.65383e21	0.182516	0.0912581	−	0.995827i	$-0.470911\pi$
$383$	1.65383e21	0.182516	0.0912581	+	0.995827i	$0.470911\pi$
$384$	−1.07913e21	−0.116482
$385$	−6.27653e21	−0.662679
$386$	7.75102e21	0.800510
$387$	1.29606e22	1.30943
$388$	8.08388e21	0.799006
$389$	−9.80968e21	−0.948600	−0.474300	−	0.880363i	$-0.657299\pi$
$389$	−9.80968e21	−0.948600	−0.474300	+	0.880363i	$0.657299\pi$
$390$	6.88193e21	0.651120
$391$	9.19615e21	0.851342
$392$	−2.23705e20	−0.0202649
$393$	4.94455e21	0.438319
$394$	−1.35668e22	−1.17696
$395$	−9.97588e21	−0.846986
$396$	−6.76532e21	−0.562185
$397$	5.46313e21	0.444347	0.222174	−	0.975007i	$-0.428685\pi$
$397$	5.46313e21	0.444347	0.222174	+	0.975007i	$0.428685\pi$
$398$	1.08999e22	0.867790
$399$	−1.06658e22	−0.831238
$400$	6.55360e20	0.0500000
$401$	1.23774e21	0.0924487	0.0462243	−	0.998931i	$-0.485281\pi$
$401$	1.23774e21	0.0924487	0.0462243	+	0.998931i	$0.485281\pi$
$402$	−2.36373e22	−1.72852
$403$	2.58427e22	1.85031
$404$	1.29689e22	0.909205
$405$	−7.77810e21	−0.533956
$406$	−6.54491e21	−0.439979
$407$	1.08646e22	0.715255
$408$	4.04640e21	0.260890
$409$	2.21977e22	1.40171	0.700857	−	0.713302i	$-0.252801\pi$
$409$	2.21977e22	1.40171	0.700857	+	0.713302i	$0.252801\pi$
$410$	−3.75051e21	−0.231968
$411$	2.65135e22	1.60625
$412$	1.36280e21	0.0808733
$413$	3.27810e21	0.190567
$414$	−1.39078e22	−0.792056
$415$	1.16914e22	0.652318
$416$	−5.05259e21	−0.276198
$417$	−2.23963e22	−1.19955
$418$	−1.33588e22	−0.701081
$419$	9.91389e21	0.509829	0.254915	−	0.966964i	$-0.417953\pi$
$419$	9.91389e21	0.509829	0.254915	+	0.966964i	$0.417953\pi$
$420$	−5.67743e21	−0.286110
$421$	−2.28757e22	−1.12974	−0.564868	−	0.825181i	$-0.691073\pi$
$421$	−2.28757e22	−1.12974	−0.564868	+	0.825181i	$0.691073\pi$
$422$	1.46408e21	0.0708614
$423$	−3.58502e21	−0.170058
$424$	−3.78221e20	−0.0175847
$425$	−2.45738e21	−0.111987
$426$	4.96276e20	0.0221688
$427$	−4.09072e21	−0.179128
$428$	1.01754e22	0.436796
$429$	−7.46713e22	−3.14244
$430$	1.36226e22	0.562055
$431$	−1.37799e22	−0.557427	−0.278713	−	0.960374i	$-0.589908\pi$
$431$	−1.37799e22	−0.557427	−0.278713	+	0.960374i	$0.589908\pi$
$432$	2.18691e21	0.0867400
$433$	3.44028e22	1.33797	0.668985	−	0.743276i	$-0.266729\pi$
$433$	3.44028e22	1.33797	0.668985	+	0.743276i	$0.266729\pi$
$434$	−2.13196e22	−0.813050
$435$	1.00996e22	0.377698
$436$	−1.14036e22	−0.418223
$437$	−2.74623e22	−0.987744
$438$	3.73848e22	1.31876
$439$	−1.64984e22	−0.570812	−0.285406	−	0.958407i	$-0.592128\pi$
$439$	−1.64984e22	−0.570812	−0.285406	+	0.958407i	$0.592128\pi$
$440$	−7.11088e21	−0.241310
$441$	−1.26859e21	−0.0422273
$442$	1.89455e22	0.618611
$443$	−4.67106e22	−1.49618	−0.748090	−	0.663597i	$-0.769029\pi$
$443$	−4.67106e22	−1.49618	−0.748090	+	0.663597i	$0.769029\pi$
$444$	9.82756e21	0.308809
$445$	−9.47592e21	−0.292120
$446$	2.44952e22	0.740857
$447$	7.14880e22	2.12138
$448$	4.16827e21	0.121365
$449$	1.01211e21	0.0289158	0.0144579	−	0.999895i	$-0.495398\pi$
$449$	1.01211e21	0.0289158	0.0144579	+	0.999895i	$0.495398\pi$
$450$	3.71642e21	0.104188
$451$	4.06943e22	1.11952
$452$	4.45381e21	0.120242
$453$	−1.52045e22	−0.402845
$454$	−5.53382e21	−0.143896
$455$	−2.65822e22	−0.678412
$456$	−1.20837e22	−0.302690
$457$	−3.22679e21	−0.0793384	−0.0396692	−	0.999213i	$-0.512630\pi$
$457$	−3.22679e21	−0.0793384	−0.0396692	+	0.999213i	$0.512630\pi$
$458$	−9.83041e21	−0.237255
$459$	−8.20019e21	−0.194275
$460$	−1.46182e22	−0.339979
$461$	3.79274e22	0.865955	0.432977	−	0.901405i	$-0.357463\pi$
$461$	3.79274e22	0.865955	0.432977	+	0.901405i	$0.357463\pi$
$462$	6.16021e22	1.38082
$463$	1.54030e22	0.338975	0.169488	−	0.985532i	$-0.445789\pi$
$463$	1.54030e22	0.338975	0.169488	+	0.985532i	$0.445789\pi$
$464$	−7.41494e21	−0.160216
$465$	3.28988e22	0.697959
$466$	−3.32791e22	−0.693252
$467$	−3.68344e22	−0.753461	−0.376730	−	0.926323i	$-0.622952\pi$
$467$	−3.68344e22	−0.753461	−0.376730	+	0.926323i	$0.622952\pi$
$468$	−2.86523e22	−0.575532
$469$	9.13014e22	1.80098
$470$	−3.76813e21	−0.0729952
$471$	−3.05291e22	−0.580814
$472$	3.71386e21	0.0693935
$473$	−1.47810e23	−2.71259
$474$	9.79100e22	1.76486
$475$	7.33843e21	0.129929
$476$	−1.56296e22	−0.271825
$477$	−2.14482e21	−0.0366425
$478$	−3.50743e22	−0.588642
$479$	−6.20162e22	−1.02248	−0.511238	−	0.859439i	$-0.670813\pi$
$479$	−6.20162e22	−1.02248	−0.511238	+	0.859439i	$0.670813\pi$
$480$	−6.43214e21	−0.104185
$481$	4.60134e22	0.732236
$482$	−3.32816e22	−0.520360
$483$	1.26638e23	1.94543
$484$	4.40306e22	0.664613
$485$	4.81837e22	0.714653
$486$	5.95060e22	0.867267
$487$	−9.00040e21	−0.128904	−0.0644519	−	0.997921i	$-0.520530\pi$
$487$	−9.00040e21	−0.128904	−0.0644519	+	0.997921i	$0.520530\pi$
$488$	−4.63450e21	−0.0652281
$489$	8.75177e22	1.21052
$490$	−1.33339e21	−0.0181255
$491$	−2.64468e22	−0.353330	−0.176665	−	0.984271i	$-0.556531\pi$
$491$	−2.64468e22	−0.353330	−0.176665	+	0.984271i	$0.556531\pi$
$492$	3.68100e22	0.483351
$493$	2.78036e22	0.358840
$494$	−5.65766e22	−0.717725
$495$	−4.03245e22	−0.502834
$496$	−2.41537e22	−0.296067
$497$	−1.91692e21	−0.0230980
$498$	−1.14748e23	−1.35924
$499$	−1.99387e22	−0.232189	−0.116095	−	0.993238i	$-0.537038\pi$
$499$	−1.99387e22	−0.232189	−0.116095	+	0.993238i	$0.537038\pi$
$500$	3.90625e21	0.0447214
$501$	−1.64945e23	−1.85660
$502$	−1.15747e23	−1.28094
$503$	−2.06706e22	−0.224919	−0.112459	−	0.993656i	$-0.535873\pi$
$503$	−2.06706e22	−0.224919	−0.112459	+	0.993656i	$0.535873\pi$
$504$	2.36375e22	0.252896
$505$	7.73007e22	0.813217
$506$	1.58612e23	1.64081
$507$	−1.86697e23	−1.89919
$508$	−2.83711e22	−0.283815
$509$	9.16337e22	0.901476	0.450738	−	0.892656i	$-0.351161\pi$
$509$	9.16337e22	0.901476	0.450738	+	0.892656i	$0.351161\pi$
$510$	2.41184e22	0.233347
$511$	−1.44403e23	−1.37403
$512$	4.72237e21	0.0441942
$513$	2.44881e22	0.225402
$514$	−1.04641e23	−0.947363
$515$	8.12291e21	0.0723353
$516$	−1.33702e23	−1.17115
$517$	4.08855e22	0.352290
$518$	−3.79600e22	−0.321753
$519$	1.33831e23	1.11592
$520$	−3.01158e22	−0.247039
$521$	−7.60700e22	−0.613893	−0.306947	−	0.951727i	$-0.599307\pi$
$521$	−7.60700e22	−0.613893	−0.306947	+	0.951727i	$0.599307\pi$
$522$	−4.20487e22	−0.333852
$523$	9.53312e22	0.744681	0.372341	−	0.928096i	$-0.378555\pi$
$523$	9.53312e22	0.744681	0.372341	+	0.928096i	$0.378555\pi$
$524$	−2.16377e22	−0.166301
$525$	−3.38401e22	−0.255904
$526$	2.50275e22	0.186225
$527$	9.05683e22	0.663111
$528$	6.97910e22	0.502818
$529$	1.85017e23	1.31171
$530$	−2.25437e21	−0.0157283
$531$	2.10606e22	0.144600
$532$	4.66744e22	0.315377
$533$	1.72347e23	1.14610
$534$	9.30031e22	0.608691
$535$	6.06501e22	0.390683
$536$	1.03438e23	0.655814
$537$	−1.14285e23	−0.713197
$538$	−1.64883e22	−0.101281
$539$	1.44677e22	0.0874773
$540$	1.30350e22	0.0775826
$541$	7.55066e22	0.442393	0.221196	−	0.975229i	$-0.429004\pi$
$541$	7.55066e22	0.442393	0.221196	+	0.975229i	$0.429004\pi$
$542$	−6.09324e22	−0.351442
$543$	4.17553e22	0.237090
$544$	−1.77073e22	−0.0989833
$545$	−6.79709e22	−0.374070
$546$	2.60895e23	1.41361
$547$	2.23192e23	1.19066	0.595328	−	0.803483i	$-0.297022\pi$
$547$	2.23192e23	1.19066	0.595328	+	0.803483i	$0.297022\pi$
$548$	−1.16025e23	−0.609420
$549$	−2.62814e22	−0.135920
$550$	−4.23842e22	−0.215834
$551$	−8.30292e22	−0.416334
$552$	1.43473e23	0.708414
$553$	−3.78188e23	−1.83884
$554$	1.47395e23	0.705750
$555$	5.85768e22	0.276207
$556$	9.80076e22	0.455118
$557$	1.63717e23	0.748728	0.374364	−	0.927282i	$-0.377861\pi$
$557$	1.63717e23	0.748728	0.374364	+	0.927282i	$0.377861\pi$
$558$	−1.36971e23	−0.616933
$559$	−6.26001e23	−2.77699
$560$	2.48448e22	0.108552
$561$	−2.61693e23	−1.12618
$562$	1.28604e23	0.545123
$563$	−1.58801e23	−0.663026	−0.331513	−	0.943451i	$-0.607559\pi$
$563$	−1.58801e23	−0.663026	−0.331513	+	0.943451i	$0.607559\pi$
$564$	3.69830e22	0.152100
$565$	2.65468e22	0.107547
$566$	−3.37570e22	−0.134718
$567$	−2.94869e23	−1.15924
$568$	−2.17174e21	−0.00841098
$569$	−3.66491e21	−0.0139833	−0.00699163	−	0.999976i	$-0.502226\pi$
$569$	−3.66491e21	−0.0139833	−0.00699163	+	0.999976i	$0.502226\pi$
$570$	−7.20243e22	−0.270734
$571$	−1.16824e23	−0.432638	−0.216319	−	0.976323i	$-0.569405\pi$
$571$	−1.16824e23	−0.432638	−0.216319	+	0.976323i	$0.569405\pi$
$572$	3.26767e23	1.19226
$573$	5.77092e23	2.07458
$574$	−1.42183e23	−0.503611
$575$	−8.71312e22	−0.304086
$576$	2.67796e22	0.0920903
$577$	1.52165e23	0.515608	0.257804	−	0.966197i	$-0.417001\pi$
$577$	1.52165e23	0.515608	0.257804	+	0.966197i	$0.417001\pi$
$578$	−1.45377e23	−0.485410
$579$	−4.53434e23	−1.49192
$580$	−4.41965e22	−0.143301
$581$	4.43225e23	1.41621
$582$	−4.72907e23	−1.48912
$583$	2.44607e22	0.0759079
$584$	−1.63598e23	−0.500345
$585$	−1.70781e23	−0.514771
$586$	1.01928e23	0.302807
$587$	3.37707e23	0.988819	0.494409	−	0.869229i	$-0.335384\pi$
$587$	3.37707e23	0.988819	0.494409	+	0.869229i	$0.335384\pi$
$588$	1.30868e22	0.0377681
$589$	−2.70462e23	−0.769355
$590$	2.21364e22	0.0620675
$591$	7.93660e23	2.19352
$592$	−4.30061e22	−0.117164
$593$	−1.67609e23	−0.450125	−0.225063	−	0.974344i	$-0.572259\pi$
$593$	−1.67609e23	−0.450125	−0.225063	+	0.974344i	$0.572259\pi$
$594$	−1.41434e23	−0.374430
$595$	−9.31598e22	−0.243128
$596$	−3.12837e23	−0.804867
$597$	−6.37642e23	−1.61732
$598$	6.71750e23	1.67976
$599$	−1.98640e23	−0.489711	−0.244855	−	0.969560i	$-0.578740\pi$
$599$	−1.98640e23	−0.489711	−0.244855	+	0.969560i	$0.578740\pi$
$600$	−3.83386e22	−0.0931859
$601$	−5.77827e22	−0.138473	−0.0692365	−	0.997600i	$-0.522056\pi$
$601$	−5.77827e22	−0.138473	−0.0692365	+	0.997600i	$0.522056\pi$
$602$	5.16436e23	1.22024
$603$	5.86579e23	1.36656
$604$	6.65359e22	0.152842
$605$	2.62443e23	0.594448
$606$	−7.58681e23	−1.69450
$607$	−5.63223e23	−1.24044	−0.620221	−	0.784427i	$-0.712957\pi$
$607$	−5.63223e23	−1.24044	−0.620221	+	0.784427i	$0.712957\pi$
$608$	5.28789e22	0.114842
$609$	3.82877e23	0.819997
$610$	−2.76238e22	−0.0583418
$611$	1.73157e23	0.360653
$612$	−1.00415e23	−0.206258
$613$	7.82482e23	1.58511	0.792556	−	0.609799i	$-0.208750\pi$
$613$	7.82482e23	1.58511	0.792556	+	0.609799i	$0.208750\pi$
$614$	−4.97583e22	−0.0994110
$615$	2.19405e23	0.432323
$616$	−2.69575e23	−0.523894
$617$	1.52050e23	0.291448	0.145724	−	0.989325i	$-0.453449\pi$
$617$	1.52050e23	0.291448	0.145724	+	0.989325i	$0.453449\pi$
$618$	−7.97237e22	−0.150725
$619$	4.11398e23	0.767169	0.383585	−	0.923506i	$-0.374689\pi$
$619$	4.11398e23	0.767169	0.383585	+	0.923506i	$0.374689\pi$
$620$	−1.43967e23	−0.264810
$621$	−2.90754e23	−0.527529
$622$	2.60527e23	0.466266
$623$	−3.59234e23	−0.634204
$624$	2.95577e23	0.514755
$625$	2.32831e22	0.0400000
$626$	5.96053e23	1.01019
$627$	7.81488e23	1.30662
$628$	1.33598e23	0.220365
$629$	1.61258e23	0.262417
$630$	1.40890e23	0.226197
$631$	−1.06612e24	−1.68872	−0.844359	−	0.535778i	$-0.820018\pi$
$631$	−1.06612e24	−1.68872	−0.844359	+	0.535778i	$0.820018\pi$
$632$	−4.28461e23	−0.669601
$633$	−8.56488e22	−0.132066
$634$	−3.78154e23	−0.575321
$635$	−1.69105e23	−0.253852
$636$	2.21259e22	0.0327730
$637$	6.12732e22	0.0895540
$638$	4.79547e23	0.691601
$639$	−1.23155e22	−0.0175265
$640$	2.81475e22	0.0395285
$641$	1.06676e24	1.47834	0.739171	−	0.673518i	$-0.235218\pi$
$641$	1.06676e24	1.47834	0.739171	+	0.673518i	$0.235218\pi$
$642$	−5.95260e23	−0.814065
$643$	−9.84055e22	−0.132809	−0.0664043	−	0.997793i	$-0.521153\pi$
$643$	−9.84055e22	−0.132809	−0.0664043	+	0.997793i	$0.521153\pi$
$644$	−5.54178e23	−0.738108
$645$	−7.96923e23	−1.04751
$646$	−1.98278e23	−0.257217
$647$	9.33277e21	0.0119488	0.00597440	−	0.999982i	$-0.498098\pi$
$647$	9.33277e21	0.0119488	0.00597440	+	0.999982i	$0.498098\pi$
$648$	−3.34067e23	−0.422130
$649$	−2.40187e23	−0.299550
$650$	−1.79504e23	−0.220959
$651$	1.24720e24	1.51530
$652$	−3.82983e23	−0.459278
$653$	−8.57642e23	−1.01518	−0.507591	−	0.861598i	$-0.669464\pi$
$653$	−8.57642e23	−1.01518	−0.507591	+	0.861598i	$0.669464\pi$
$654$	6.67112e23	0.779450
$655$	−1.28971e23	−0.148744
$656$	−1.61083e23	−0.183387
$657$	−9.27735e23	−1.04260
$658$	−1.42851e23	−0.158475
$659$	1.05319e24	1.15340	0.576702	−	0.816954i	$-0.304339\pi$
$659$	1.05319e24	1.15340	0.576702	+	0.816954i	$0.304339\pi$
$660$	4.15987e23	0.449734
$661$	−1.10171e24	−1.17586	−0.587928	−	0.808913i	$-0.700056\pi$
$661$	−1.10171e24	−1.17586	−0.587928	+	0.808913i	$0.700056\pi$
$662$	−2.89838e23	−0.305395
$663$	−1.10831e24	−1.15292
$664$	5.02144e23	0.515703
$665$	2.78201e23	0.282082
$666$	−2.43879e23	−0.244143
$667$	9.85828e23	0.974388
$668$	7.21809e23	0.704405
$669$	−1.43297e24	−1.38075
$670$	6.16540e23	0.586578
$671$	2.99728e23	0.281569
$672$	−2.43844e23	−0.226190
$673$	−1.42572e24	−1.30588	−0.652942	−	0.757408i	$-0.726466\pi$
$673$	−1.42572e24	−1.30588	−0.652942	+	0.757408i	$0.726466\pi$
$674$	4.93228e23	0.446107
$675$	7.76947e22	0.0693920
$676$	8.16998e23	0.720567
$677$	−5.15613e23	−0.449076	−0.224538	−	0.974465i	$-0.572087\pi$
$677$	−5.15613e23	−0.449076	−0.224538	+	0.974465i	$0.572087\pi$
$678$	−2.60548e23	−0.224097
$679$	1.82665e24	1.55154
$680$	−1.05544e23	−0.0885333
$681$	3.23728e23	0.268182
$682$	1.56209e24	1.27803
$683$	−1.88105e24	−1.51994	−0.759968	−	0.649961i	$-0.774785\pi$
$683$	−1.88105e24	−1.51994	−0.759968	+	0.649961i	$0.774785\pi$
$684$	2.99866e23	0.239305
$685$	−6.91563e23	−0.545082
$686$	−9.32456e23	−0.725894
$687$	5.75079e23	0.442176
$688$	5.85087e23	0.444343
$689$	1.03595e23	0.0777100
$690$	8.55164e23	0.633625
$691$	−8.16767e23	−0.597771	−0.298885	−	0.954289i	$-0.596615\pi$
$691$	−8.16767e23	−0.597771	−0.298885	+	0.954289i	$0.596615\pi$
$692$	−5.85654e23	−0.423389
$693$	−1.52871e24	−1.09167
$694$	−1.19198e24	−0.840838
$695$	5.84171e23	0.407070
$696$	4.33774e23	0.298597
$697$	6.04009e23	0.410738
$698$	3.05058e23	0.204933
$699$	1.94683e24	1.29203
$700$	1.48087e23	0.0970918
$701$	5.71079e23	0.369907	0.184954	−	0.982747i	$-0.440787\pi$
$701$	5.71079e23	0.369907	0.184954	+	0.982747i	$0.440787\pi$
$702$	−5.98999e23	−0.383319
$703$	−4.81563e23	−0.304462
$704$	−3.05410e23	−0.190773
$705$	2.20436e23	0.136042
$706$	1.33678e23	0.0815117
$707$	2.93048e24	1.76553
$708$	−2.17261e23	−0.129330
$709$	2.98369e23	0.175493	0.0877465	−	0.996143i	$-0.472033\pi$
$709$	2.98369e23	0.175493	0.0877465	+	0.996143i	$0.472033\pi$
$710$	−1.29446e22	−0.00752301
$711$	−2.42972e24	−1.39529
$712$	−4.06988e23	−0.230941
$713$	3.21127e24	1.80060
$714$	9.14333e23	0.506605
$715$	1.94768e24	1.06639
$716$	5.00121e23	0.270591
$717$	2.05184e24	1.09706
$718$	1.30035e24	0.687073
$719$	6.44700e23	0.336637	0.168319	−	0.985733i	$-0.446166\pi$
$719$	6.44700e23	0.336637	0.168319	+	0.985733i	$0.446166\pi$
$720$	1.59619e23	0.0823680
$721$	3.07941e23	0.157043
$722$	−8.10864e23	−0.408679
$723$	1.94697e24	0.969805
$724$	−1.82724e23	−0.0899534
$725$	−2.63432e23	−0.128172
$726$	−2.57579e24	−1.23865
$727$	−2.42742e24	−1.15372	−0.576862	−	0.816841i	$-0.695723\pi$
$727$	−2.42742e24	−1.15372	−0.576862	+	0.816841i	$0.695723\pi$
$728$	−1.14170e24	−0.536332
$729$	−9.09673e23	−0.422378
$730$	−9.75122e23	−0.447522
$731$	−2.19388e24	−0.995212
$732$	2.71119e23	0.121567
$733$	−1.25242e24	−0.555092	−0.277546	−	0.960712i	$-0.589521\pi$
$733$	−1.25242e24	−0.555092	−0.277546	+	0.960712i	$0.589521\pi$
$734$	−2.50362e24	−1.09686
$735$	7.80031e22	0.0337808
$736$	−6.27847e23	−0.268777
$737$	−6.68967e24	−2.83094
$738$	−9.13473e23	−0.382135
$739$	−1.14714e24	−0.474395	−0.237198	−	0.971461i	$-0.576229\pi$
$739$	−1.14714e24	−0.474395	−0.237198	+	0.971461i	$0.576229\pi$
$740$	−2.56336e23	−0.104795
$741$	3.30973e24	1.33764
$742$	−8.54637e22	−0.0341467
$743$	−4.70913e24	−1.86010	−0.930050	−	0.367433i	$-0.880237\pi$
$743$	−4.70913e24	−1.86010	−0.930050	+	0.367433i	$0.880237\pi$
$744$	1.41299e24	0.551785
$745$	−1.86465e24	−0.719895
$746$	−3.09580e24	−1.18166
$747$	2.84756e24	1.07460
$748$	1.14519e24	0.427280
$749$	2.29926e24	0.848187
$750$	−2.28516e23	−0.0833480
$751$	1.63995e24	0.591412	0.295706	−	0.955279i	$-0.404445\pi$
$751$	1.63995e24	0.591412	0.295706	+	0.955279i	$0.404445\pi$
$752$	−1.61840e23	−0.0577078
$753$	6.77119e24	2.38730
$754$	2.03096e24	0.708020
$755$	3.96585e23	0.136706
$756$	4.94160e23	0.168435
$757$	−6.13170e23	−0.206665	−0.103332	−	0.994647i	$-0.532951\pi$
$757$	−6.13170e23	−0.206665	−0.103332	+	0.994647i	$0.532951\pi$
$758$	2.19125e24	0.730304
$759$	−9.27883e24	−3.05800
$760$	3.15183e23	0.102718
$761$	1.32760e24	0.427856	0.213928	−	0.976849i	$-0.431374\pi$
$761$	1.32760e24	0.427856	0.213928	+	0.976849i	$0.431374\pi$
$762$	1.65971e24	0.528951
$763$	−2.57679e24	−0.812121
$764$	−2.52539e24	−0.787111
$765$	−5.98519e23	−0.184483
$766$	4.23381e23	0.129059
$767$	−1.01723e24	−0.306662
$768$	−2.76258e23	−0.0823655
$769$	6.31829e24	1.86306	0.931528	−	0.363670i	$-0.118476\pi$
$769$	6.31829e24	1.86306	0.931528	+	0.363670i	$0.118476\pi$
$770$	−1.60679e24	−0.468585
$771$	6.12152e24	1.76562
$772$	1.98426e24	0.566046
$773$	1.94584e24	0.549012	0.274506	−	0.961585i	$-0.411486\pi$
$773$	1.94584e24	0.549012	0.274506	+	0.961585i	$0.411486\pi$
$774$	3.31792e24	0.925907
$775$	−8.58112e23	−0.236853
$776$	2.06947e24	0.564983
$777$	2.22066e24	0.599657
$778$	−2.51128e24	−0.670762
$779$	−1.80374e24	−0.476546
$780$	1.76177e24	0.460411
$781$	1.40453e23	0.0363076
$782$	2.35422e24	0.601989
$783$	−8.79061e23	−0.222354
$784$	−5.72685e22	−0.0143294
$785$	7.96304e23	0.197100
$786$	1.26580e24	0.309938
$787$	−2.09496e24	−0.507447	−0.253723	−	0.967277i	$-0.581655\pi$
$787$	−2.09496e24	−0.507447	−0.253723	+	0.967277i	$0.581655\pi$
$788$	−3.47311e24	−0.832234
$789$	−1.46411e24	−0.347071
$790$	−2.55383e24	−0.598909
$791$	1.00639e24	0.233490
$792$	−1.73192e24	−0.397525
$793$	1.26940e24	0.288254
$794$	1.39856e24	0.314201
$795$	1.31881e23	0.0293131
$796$	2.79036e24	0.613620
$797$	−5.41022e24	−1.17712	−0.588558	−	0.808455i	$-0.700304\pi$
$797$	−5.41022e24	−1.17712	−0.588558	+	0.808455i	$0.700304\pi$
$798$	−2.73045e24	−0.587774
$799$	6.06846e23	0.129250
$800$	1.67772e23	0.0353553
$801$	−2.30795e24	−0.481227
$802$	3.16860e23	0.0653711
$803$	1.05804e25	2.15983
$804$	−6.05114e24	−1.22225
$805$	−3.30316e24	−0.660184
$806$	6.61573e24	1.30837
$807$	9.64566e23	0.188759
$808$	3.32004e24	0.642905
$809$	−7.69852e24	−1.47518	−0.737590	−	0.675249i	$-0.764036\pi$
$809$	−7.69852e24	−1.47518	−0.737590	+	0.675249i	$0.764036\pi$
$810$	−1.99119e24	−0.377564
$811$	−3.00129e24	−0.563159	−0.281580	−	0.959538i	$-0.590858\pi$
$811$	−3.00129e24	−0.563159	−0.281580	+	0.959538i	$0.590858\pi$
$812$	−1.67550e24	−0.311112
$813$	3.56454e24	0.654989
$814$	2.78134e24	0.505762
$815$	−2.28276e24	−0.410790
$816$	1.03588e24	0.184477
$817$	6.55154e24	1.15467
$818$	5.68260e24	0.991161
$819$	−6.47434e24	−1.11759
$820$	−9.60131e23	−0.164026
$821$	−1.09571e25	−1.85259	−0.926294	−	0.376801i	$-0.877024\pi$
$821$	−1.09571e25	−1.85259	−0.926294	+	0.376801i	$0.877024\pi$
$822$	6.78747e24	1.13579
$823$	2.99882e24	0.496651	0.248326	−	0.968677i	$-0.420120\pi$
$823$	2.99882e24	0.496651	0.248326	+	0.968677i	$0.420120\pi$
$824$	3.48876e23	0.0571860
$825$	2.47947e24	0.402255
$826$	8.39194e23	0.134751
$827$	−1.44396e24	−0.229487	−0.114743	−	0.993395i	$-0.536605\pi$
$827$	−1.44396e24	−0.229487	−0.114743	+	0.993395i	$0.536605\pi$
$828$	−3.56040e24	−0.560068
$829$	5.53769e24	0.862213	0.431107	−	0.902301i	$-0.358123\pi$
$829$	5.53769e24	0.862213	0.431107	+	0.902301i	$0.358123\pi$
$830$	2.99301e24	0.461259
$831$	−8.62262e24	−1.31532
$832$	−1.29346e24	−0.195302
$833$	2.14738e23	0.0320942
$834$	−5.73344e24	−0.848211
$835$	4.30232e24	0.630039
$836$	−3.41985e24	−0.495739
$837$	−2.86349e24	−0.410893
$838$	2.53795e24	0.360504
$839$	−9.12755e24	−1.28345	−0.641723	−	0.766936i	$-0.721780\pi$
$839$	−9.12755e24	−1.28345	−0.641723	+	0.766936i	$0.721780\pi$
$840$	−1.45342e24	−0.202310
$841$	−4.27661e24	−0.589296
$842$	−5.85619e24	−0.798844
$843$	−7.52331e24	−1.01596
$844$	3.74805e23	0.0501066
$845$	4.86969e24	0.644494
$846$	−9.17764e23	−0.120249
$847$	9.94925e24	1.29057
$848$	−9.68246e22	−0.0124343
$849$	1.97479e24	0.251076
$850$	−6.29090e23	−0.0791866
$851$	5.71773e24	0.712561
$852$	1.27047e23	0.0156757
$853$	−1.07821e24	−0.131716	−0.0658579	−	0.997829i	$-0.520978\pi$
$853$	−1.07821e24	−0.131716	−0.0658579	+	0.997829i	$0.520978\pi$
$854$	−1.04722e24	−0.126662
$855$	1.78734e24	0.214041
$856$	2.60490e24	0.308862
$857$	−5.20779e24	−0.611388	−0.305694	−	0.952130i	$-0.598888\pi$
$857$	−5.20779e24	−0.611388	−0.305694	+	0.952130i	$0.598888\pi$
$858$	−1.91158e25	−2.22204
$859$	4.22981e24	0.486832	0.243416	−	0.969922i	$-0.421732\pi$
$859$	4.22981e24	0.486832	0.243416	+	0.969922i	$0.421732\pi$
$860$	3.48739e24	0.397433
$861$	8.31768e24	0.938589
$862$	−3.52764e24	−0.394160
$863$	4.42295e24	0.489351	0.244675	−	0.969605i	$-0.421319\pi$
$863$	4.42295e24	0.489351	0.244675	+	0.969605i	$0.421319\pi$
$864$	5.59850e23	0.0613345
$865$	−3.49077e24	−0.378690
$866$	8.80711e24	0.946088
$867$	8.50456e24	0.904668
$868$	−5.45783e24	−0.574913
$869$	2.77099e25	2.89046
$870$	2.58549e24	0.267073
$871$	−2.83319e25	−2.89815
$872$	−2.91933e24	−0.295728
$873$	1.17356e25	1.17729
$874$	−7.03034e24	−0.698440
$875$	8.82665e23	0.0868416
$876$	9.57050e24	0.932502
$877$	4.80029e24	0.463202	0.231601	−	0.972811i	$-0.425604\pi$
$877$	4.80029e24	0.463202	0.231601	+	0.972811i	$0.425604\pi$
$878$	−4.22359e24	−0.403625
$879$	−5.96282e24	−0.564347
$880$	−1.82039e24	−0.170632
$881$	9.96018e24	0.924639	0.462319	−	0.886714i	$-0.347017\pi$
$881$	9.96018e24	0.924639	0.462319	+	0.886714i	$0.347017\pi$
$882$	−3.24759e23	−0.0298592
$883$	9.80350e24	0.892720	0.446360	−	0.894853i	$-0.352720\pi$
$883$	9.80350e24	0.892720	0.446360	+	0.894853i	$0.352720\pi$
$884$	4.85006e24	0.437424
$885$	−1.29498e24	−0.115676
$886$	−1.19579e25	−1.05796
$887$	5.97993e24	0.524017	0.262008	−	0.965066i	$-0.415615\pi$
$887$	5.97993e24	0.524017	0.262008	+	0.965066i	$0.415615\pi$
$888$	2.51585e24	0.218361
$889$	−6.41081e24	−0.551122
$890$	−2.42584e24	−0.206560
$891$	2.16051e25	1.82220
$892$	6.27076e24	0.523865
$893$	−1.81221e24	−0.149959
$894$	1.83009e25	1.50005
$895$	2.98095e24	0.242024
$896$	1.06708e24	0.0858179
$897$	−3.92974e25	−3.13060
$898$	2.59101e23	0.0204466
$899$	9.70893e24	0.758952
$900$	9.51404e23	0.0736722
$901$	3.63060e23	0.0278495
$902$	1.04178e25	0.791623
$903$	−3.02115e25	−2.27419
$904$	1.14018e24	0.0850237
$905$	−1.08912e24	−0.0804568
$906$	−3.89235e24	−0.284854
$907$	1.20569e25	0.874126	0.437063	−	0.899431i	$-0.356019\pi$
$907$	1.20569e25	0.874126	0.437063	+	0.899431i	$0.356019\pi$
$908$	−1.41666e24	−0.101750
$909$	1.88273e25	1.33966
$910$	−6.80503e24	−0.479710
$911$	−4.95471e24	−0.346029	−0.173014	−	0.984919i	$-0.555351\pi$
$911$	−4.95471e24	−0.346029	−0.173014	+	0.984919i	$0.555351\pi$
$912$	−3.09342e24	−0.214034
$913$	−3.24752e25	−2.22613
$914$	−8.26059e23	−0.0561007
$915$	1.61599e24	0.108733
$916$	−2.51658e24	−0.167764
$917$	−4.88930e24	−0.322929
$918$	−2.09925e24	−0.137373
$919$	−1.62235e25	−1.05187	−0.525935	−	0.850525i	$-0.676284\pi$
$919$	−1.62235e25	−1.05187	−0.525935	+	0.850525i	$0.676284\pi$
$920$	−3.74226e24	−0.240401
$921$	2.91086e24	0.185274
$922$	9.70942e24	0.612323
$923$	5.94842e23	0.0371695
$924$	1.57701e25	0.976391
$925$	−1.52788e24	−0.0937314
$926$	3.94318e24	0.239692
$927$	1.97841e24	0.119162
$928$	−1.89822e24	−0.113290
$929$	2.22798e25	1.31758	0.658791	−	0.752326i	$-0.271068\pi$
$929$	2.22798e25	1.31758	0.658791	+	0.752326i	$0.271068\pi$
$930$	8.42209e24	0.493531
$931$	−6.41267e23	−0.0372363
$932$	−8.51945e24	−0.490204
$933$	−1.52408e25	−0.868989
$934$	−9.42962e24	−0.532777
$935$	6.82584e24	0.382171
$936$	−7.33498e24	−0.406963
$937$	−2.86250e25	−1.57383	−0.786916	−	0.617060i	$-0.788324\pi$
$937$	−2.86250e25	−1.57383	−0.786916	+	0.617060i	$0.788324\pi$
$938$	2.33731e25	1.27348
$939$	−3.48691e25	−1.88271
$940$	−9.64642e23	−0.0516154
$941$	−3.17215e25	−1.68206	−0.841031	−	0.540986i	$-0.818051\pi$
$941$	−3.17215e25	−1.68206	−0.841031	+	0.540986i	$0.818051\pi$
$942$	−7.81546e24	−0.410697
$943$	2.14163e25	1.11531
$944$	9.50749e23	0.0490686
$945$	2.94542e24	0.150653
$946$	−3.78394e25	−1.91809
$947$	1.76219e25	0.885275	0.442638	−	0.896701i	$-0.354043\pi$
$947$	1.76219e25	0.885275	0.442638	+	0.896701i	$0.354043\pi$
$948$	2.50650e25	1.24795
$949$	4.48098e25	2.21111
$950$	1.87864e24	0.0918739
$951$	2.21220e25	1.07224
$952$	−4.00118e24	−0.192209
$953$	−1.43143e25	−0.681521	−0.340760	−	0.940150i	$-0.610684\pi$
$953$	−1.43143e25	−0.681521	−0.340760	+	0.940150i	$0.610684\pi$
$954$	−5.49074e23	−0.0259101
$955$	−1.50525e25	−0.704013
$956$	−8.97901e24	−0.416233
$957$	−2.80535e25	−1.28895
$958$	−1.58761e25	−0.723000
$959$	−2.62173e25	−1.18339
$960$	−1.64663e24	−0.0736699
$961$	9.07613e24	0.402487
$962$	1.17794e25	0.517769
$963$	1.47719e25	0.643595
$964$	−8.52009e24	−0.367950
$965$	1.18271e25	0.506287
$966$	3.24194e25	1.37562
$967$	3.08004e25	1.29548	0.647741	−	0.761860i	$-0.275714\pi$
$967$	3.08004e25	1.29548	0.647741	+	0.761860i	$0.275714\pi$
$968$	1.12718e25	0.469952
$969$	1.15993e25	0.479379
$970$	1.23350e25	0.505336
$971$	−7.76760e23	−0.0315445	−0.0157722	−	0.999876i	$-0.505021\pi$
$971$	−7.76760e23	−0.0315445	−0.0157722	+	0.999876i	$0.505021\pi$
$972$	1.52335e25	0.613250
$973$	2.21460e25	0.883764
$974$	−2.30410e24	−0.0911487
$975$	1.05010e25	0.411804
$976$	−1.18643e24	−0.0461232
$977$	−8.75653e24	−0.337465	−0.168732	−	0.985662i	$-0.553967\pi$
$977$	−8.75653e24	−0.337465	−0.168732	+	0.985662i	$0.553967\pi$
$978$	2.24045e25	0.855964
$979$	2.63212e25	0.996901
$980$	−3.41347e23	−0.0128166
$981$	−1.65550e25	−0.616228
$982$	−6.77038e24	−0.249842
$983$	1.82331e25	0.667045	0.333523	−	0.942742i	$-0.391763\pi$
$983$	1.82331e25	0.667045	0.333523	+	0.942742i	$0.391763\pi$
$984$	9.42337e24	0.341781
$985$	−2.07013e25	−0.744373
$986$	7.11771e24	0.253739
$987$	8.35676e24	0.295354
$988$	−1.44836e25	−0.507508
$989$	−7.77883e25	−2.70238
$990$	−1.03231e25	−0.355557
$991$	4.83827e25	1.65221	0.826103	−	0.563520i	$-0.190553\pi$
$991$	4.83827e25	1.65221	0.826103	+	0.563520i	$0.190553\pi$
$992$	−6.18335e24	−0.209351
$993$	1.69555e25	0.569170
$994$	−4.90731e23	−0.0163327
$995$	1.66319e25	0.548839
$996$	−2.93754e25	−0.961125
$997$	4.09224e25	1.32756	0.663778	−	0.747930i	$-0.268952\pi$
$997$	4.09224e25	1.32756	0.663778	+	0.747930i	$0.268952\pi$
$998$	−5.10430e24	−0.164182
$999$	−5.09849e24	−0.162605

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.18.a.a.1.1	✓	1
3.2	odd	2		90.18.a.b.1.1		1
4.3	odd	2		80.18.a.a.1.1		1
5.2	odd	4		50.18.b.a.49.2		2
5.3	odd	4		50.18.b.a.49.1		2
5.4	even	2		50.18.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.18.a.a.1.1	✓	1	1.1	even	1	trivial
50.18.a.b.1.1		1	5.4	even	2
50.18.b.a.49.1		2	5.3	odd	4
50.18.b.a.49.2		2	5.2	odd	4
80.18.a.a.1.1		1	4.3	odd	2
90.18.a.b.1.1		1	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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