LMFDB - Embedded newform 10.12.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,12,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, 12, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
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:	$7.68343180560$
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)

$f(q)$

$=$

$q+32.0000 q^{2} -318.000 q^{3} +1024.00 q^{4} -3125.00 q^{5} -10176.0 q^{6} -70714.0 q^{7} +32768.0 q^{8} -76023.0 q^{9} +O(q^{10})$

\(q+32.0000 q^{2} -318.000 q^{3} +1024.00 q^{4} -3125.00 q^{5} -10176.0 q^{6} -70714.0 q^{7} +32768.0 q^{8} -76023.0 q^{9} -100000. q^{10} +238272. q^{11} -325632. q^{12} -2.09748e6 q^{13} -2.26285e6 q^{14} +993750. q^{15} +1.04858e6 q^{16} +5.95555e6 q^{17} -2.43274e6 q^{18} +1.02108e7 q^{19} -3.20000e6 q^{20} +2.24871e7 q^{21} +7.62470e6 q^{22} -3.53576e6 q^{23} -1.04202e7 q^{24} +9.76562e6 q^{25} -6.71193e7 q^{26} +8.05081e7 q^{27} -7.24111e7 q^{28} -1.39305e8 q^{29} +3.18000e7 q^{30} -1.01002e8 q^{31} +3.35544e7 q^{32} -7.57705e7 q^{33} +1.90577e8 q^{34} +2.20981e8 q^{35} -7.78476e7 q^{36} -5.24914e8 q^{37} +3.26746e8 q^{38} +6.66998e8 q^{39} -1.02400e8 q^{40} +2.84590e8 q^{41} +7.19586e8 q^{42} -1.25364e9 q^{43} +2.43991e8 q^{44} +2.37572e8 q^{45} -1.13144e8 q^{46} -2.16106e8 q^{47} -3.33447e8 q^{48} +3.02314e9 q^{49} +3.12500e8 q^{50} -1.89386e9 q^{51} -2.14782e9 q^{52} -4.88128e9 q^{53} +2.57626e9 q^{54} -7.44600e8 q^{55} -2.31716e9 q^{56} -3.24704e9 q^{57} -4.45776e9 q^{58} +8.69247e9 q^{59} +1.01760e9 q^{60} +3.29649e9 q^{61} -3.23208e9 q^{62} +5.37589e9 q^{63} +1.07374e9 q^{64} +6.55462e9 q^{65} -2.42466e9 q^{66} +1.82750e10 q^{67} +6.09848e9 q^{68} +1.12437e9 q^{69} +7.07140e9 q^{70} -1.32874e10 q^{71} -2.49112e9 q^{72} -3.25053e10 q^{73} -1.67972e10 q^{74} -3.10547e9 q^{75} +1.04559e10 q^{76} -1.68492e10 q^{77} +2.13439e10 q^{78} +9.29746e9 q^{79} -3.27680e9 q^{80} -1.21343e10 q^{81} +9.10689e9 q^{82} -2.27415e10 q^{83} +2.30267e10 q^{84} -1.86111e10 q^{85} -4.01163e10 q^{86} +4.42989e10 q^{87} +7.80770e9 q^{88} -9.33789e10 q^{89} +7.60230e9 q^{90} +1.48321e11 q^{91} -3.62062e9 q^{92} +3.21187e10 q^{93} -6.91541e9 q^{94} -3.19088e10 q^{95} -1.06703e10 q^{96} -5.81113e9 q^{97} +9.67406e10 q^{98} -1.81142e10 q^{99} +O(q^{100})\)

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 $

$2$	32.0000	0.707107
$2$	32.0000	0.707107
$3$	−318.000	−0.755545	−0.377772	−	0.925898i	$-0.623310\pi$
$3$	−318.000	−0.755545	−0.377772	+	0.925898i	$0.623310\pi$
$4$	1024.00	0.500000
$5$	−3125.00	−0.447214
$5$	−3125.00	−0.447214
$6$	−10176.0	−0.534251
$7$	−70714.0	−1.59025	−0.795126	−	0.606444i	$-0.792596\pi$
$7$	−70714.0	−1.59025	−0.795126	+	0.606444i	$0.792596\pi$
$8$	32768.0	0.353553
$9$	−76023.0	−0.429152
$10$	−100000.	−0.316228
$11$	238272.	0.446081	0.223040	−	0.974809i	$-0.428402\pi$
$11$	238272.	0.446081	0.223040	+	0.974809i	$0.428402\pi$
$12$	−325632.	−0.377772
$13$	−2.09748e6	−1.56678	−0.783392	−	0.621528i	$-0.786512\pi$
$13$	−2.09748e6	−1.56678	−0.783392	+	0.621528i	$0.786512\pi$
$14$	−2.26285e6	−1.12448
$15$	993750.	0.337890
$16$	1.04858e6	0.250000
$17$	5.95555e6	1.01731	0.508654	−	0.860971i	$-0.330143\pi$
$17$	5.95555e6	1.01731	0.508654	+	0.860971i	$0.330143\pi$
$18$	−2.43274e6	−0.303456
$19$	1.02108e7	0.946054	0.473027	−	0.881048i	$-0.343161\pi$
$19$	1.02108e7	0.946054	0.473027	+	0.881048i	$0.343161\pi$
$20$	−3.20000e6	−0.223607
$21$	2.24871e7	1.20151
$22$	7.62470e6	0.315427
$23$	−3.53576e6	−0.114546	−0.0572729	−	0.998359i	$-0.518241\pi$
$23$	−3.53576e6	−0.114546	−0.0572729	+	0.998359i	$0.518241\pi$
$24$	−1.04202e7	−0.267125
$25$	9.76562e6	0.200000
$26$	−6.71193e7	−1.10788
$27$	8.05081e7	1.07979
$28$	−7.24111e7	−0.795126
$29$	−1.39305e8	−1.26118	−0.630590	−	0.776116i	$-0.717187\pi$
$29$	−1.39305e8	−1.26118	−0.630590	+	0.776116i	$0.717187\pi$
$30$	3.18000e7	0.238924
$31$	−1.01002e8	−0.633639	−0.316820	−	0.948486i	$-0.602615\pi$
$31$	−1.01002e8	−0.633639	−0.316820	+	0.948486i	$0.602615\pi$
$32$	3.35544e7	0.176777
$33$	−7.57705e7	−0.337034
$34$	1.90577e8	0.719345
$35$	2.20981e8	0.711183
$36$	−7.78476e7	−0.214576
$37$	−5.24914e8	−1.24445	−0.622227	−	0.782837i	$-0.713772\pi$
$37$	−5.24914e8	−1.24445	−0.622227	+	0.782837i	$0.713772\pi$
$38$	3.26746e8	0.668961
$39$	6.66998e8	1.18378
$40$	−1.02400e8	−0.158114
$41$	2.84590e8	0.383627	0.191813	−	0.981431i	$-0.438563\pi$
$41$	2.84590e8	0.383627	0.191813	+	0.981431i	$0.438563\pi$
$42$	7.19586e8	0.849594
$43$	−1.25364e9	−1.30045	−0.650226	−	0.759740i	$-0.725326\pi$
$43$	−1.25364e9	−1.30045	−0.650226	+	0.759740i	$0.725326\pi$
$44$	2.43991e8	0.223040
$45$	2.37572e8	0.191923
$46$	−1.13144e8	−0.0809962
$47$	−2.16106e8	−0.137445	−0.0687226	−	0.997636i	$-0.521892\pi$
$47$	−2.16106e8	−0.137445	−0.0687226	+	0.997636i	$0.521892\pi$
$48$	−3.33447e8	−0.188886
$49$	3.02314e9	1.52890
$50$	3.12500e8	0.141421
$51$	−1.89386e9	−0.768622
$52$	−2.14782e9	−0.783392
$53$	−4.88128e9	−1.60330	−0.801652	−	0.597791i	$-0.796045\pi$
$53$	−4.88128e9	−1.60330	−0.801652	+	0.597791i	$0.796045\pi$
$54$	2.57626e9	0.763526
$55$	−7.44600e8	−0.199493
$56$	−2.31716e9	−0.562239
$57$	−3.24704e9	−0.714786
$58$	−4.45776e9	−0.891789
$59$	8.69247e9	1.58291	0.791457	−	0.611225i	$-0.209323\pi$
$59$	8.69247e9	1.58291	0.791457	+	0.611225i	$0.209323\pi$
$60$	1.01760e9	0.168945
$61$	3.29649e9	0.499733	0.249866	−	0.968280i	$-0.419613\pi$
$61$	3.29649e9	0.499733	0.249866	+	0.968280i	$0.419613\pi$
$62$	−3.23208e9	−0.448051
$63$	5.37589e9	0.682460
$64$	1.07374e9	0.125000
$65$	6.55462e9	0.700687
$66$	−2.42466e9	−0.238319
$67$	1.82750e10	1.65366	0.826831	−	0.562451i	$-0.190141\pi$
$67$	1.82750e10	1.65366	0.826831	+	0.562451i	$0.190141\pi$
$68$	6.09848e9	0.508654
$69$	1.12437e9	0.0865445
$70$	7.07140e9	0.502882
$71$	−1.32874e10	−0.874019	−0.437009	−	0.899457i	$-0.643962\pi$
$71$	−1.32874e10	−0.874019	−0.437009	+	0.899457i	$0.643962\pi$
$72$	−2.49112e9	−0.151728
$73$	−3.25053e10	−1.83518	−0.917588	−	0.397532i	$-0.869867\pi$
$73$	−3.25053e10	−1.83518	−0.917588	+	0.397532i	$0.869867\pi$
$74$	−1.67972e10	−0.879961
$75$	−3.10547e9	−0.151109
$76$	1.04559e10	0.473027
$77$	−1.68492e10	−0.709381
$78$	2.13439e10	0.837055
$79$	9.29746e9	0.339950	0.169975	−	0.985448i	$-0.445631\pi$
$79$	9.29746e9	0.339950	0.169975	+	0.985448i	$0.445631\pi$
$80$	−3.27680e9	−0.111803
$81$	−1.21343e10	−0.386676
$82$	9.10689e9	0.271265
$83$	−2.27415e10	−0.633708	−0.316854	−	0.948474i	$-0.602627\pi$
$83$	−2.27415e10	−0.633708	−0.316854	+	0.948474i	$0.602627\pi$
$84$	2.30267e10	0.600754
$85$	−1.86111e10	−0.454954
$86$	−4.01163e10	−0.919559
$87$	4.42989e10	0.952878
$88$	7.80770e9	0.157713
$89$	−9.33789e10	−1.77257	−0.886285	−	0.463139i	$-0.846723\pi$
$89$	−9.33789e10	−1.77257	−0.886285	+	0.463139i	$0.846723\pi$
$90$	7.60230e9	0.135710
$91$	1.48321e11	2.49158
$92$	−3.62062e9	−0.0572729
$93$	3.21187e10	0.478743
$94$	−6.91541e9	−0.0971884
$95$	−3.19088e10	−0.423088
$96$	−1.06703e10	−0.133563
$97$	−5.81113e9	−0.0687094	−0.0343547	−	0.999410i	$-0.510938\pi$
$97$	−5.81113e9	−0.0687094	−0.0343547	+	0.999410i	$0.510938\pi$
$98$	9.67406e10	1.08110
$99$	−1.81142e10	−0.191436
$100$	1.00000e10	0.100000
$101$	6.29368e10	0.595850	0.297925	−	0.954589i	$-0.403705\pi$
$101$	6.29368e10	0.595850	0.297925	+	0.954589i	$0.403705\pi$
$102$	−6.06036e10	−0.543498
$103$	1.34667e11	1.14461	0.572303	−	0.820042i	$-0.306050\pi$
$103$	1.34667e11	1.14461	0.572303	+	0.820042i	$0.306050\pi$
$104$	−6.87302e10	−0.553942
$105$	−7.02720e10	−0.537330
$106$	−1.56201e11	−1.13371
$107$	−1.36264e11	−0.939228	−0.469614	−	0.882872i	$-0.655607\pi$
$107$	−1.36264e11	−0.939228	−0.469614	+	0.882872i	$0.655607\pi$
$108$	8.24403e10	0.539894
$109$	1.03466e11	0.644097	0.322049	−	0.946723i	$-0.395629\pi$
$109$	1.03466e11	0.644097	0.322049	+	0.946723i	$0.395629\pi$
$110$	−2.38272e10	−0.141063
$111$	1.66923e11	0.940240
$112$	−7.41490e10	−0.397563
$113$	−1.85470e11	−0.946985	−0.473492	−	0.880798i	$-0.657007\pi$
$113$	−1.85470e11	−0.946985	−0.473492	+	0.880798i	$0.657007\pi$
$114$	−1.03905e11	−0.505430
$115$	1.10492e10	0.0512265
$116$	−1.42648e11	−0.630590
$117$	1.59457e11	0.672388
$118$	2.78159e11	1.11929
$119$	−4.21140e11	−1.61778
$120$	3.25632e10	0.119462
$121$	−2.28538e11	−0.801012
$122$	1.05488e11	0.353364
$123$	−9.04998e10	−0.289847
$124$	−1.03426e11	−0.316820
$125$	−3.05176e10	−0.0894427
$126$	1.72028e11	0.482572
$127$	5.00128e11	1.34326	0.671631	−	0.740886i	$-0.265594\pi$
$127$	5.00128e11	1.34326	0.671631	+	0.740886i	$0.265594\pi$
$128$	3.43597e10	0.0883883
$129$	3.98656e11	0.982550
$130$	2.09748e11	0.495460
$131$	3.97121e11	0.899355	0.449678	−	0.893191i	$-0.351539\pi$
$131$	3.97121e11	0.899355	0.449678	+	0.893191i	$0.351539\pi$
$132$	−7.75890e10	−0.168517
$133$	−7.22048e11	−1.50446
$134$	5.84801e11	1.16932
$135$	−2.51588e11	−0.482896
$136$	1.95151e11	0.359673
$137$	1.67638e11	0.296762	0.148381	−	0.988930i	$-0.452594\pi$
$137$	1.67638e11	0.296762	0.148381	+	0.988930i	$0.452594\pi$
$138$	3.59799e10	0.0611962
$139$	5.52425e10	0.0903009	0.0451504	−	0.998980i	$-0.485623\pi$
$139$	5.52425e10	0.0903009	0.0451504	+	0.998980i	$0.485623\pi$
$140$	2.26285e11	0.355591
$141$	6.87218e10	0.103846
$142$	−4.25198e11	−0.618024
$143$	−4.99770e11	−0.698912
$144$	−7.97159e10	−0.107288
$145$	4.35328e11	0.564017
$146$	−1.04017e12	−1.29767
$147$	−9.61359e11	−1.15516
$148$	−5.37512e11	−0.622227
$149$	6.27642e11	0.700145	0.350072	−	0.936723i	$-0.386157\pi$
$149$	6.27642e11	0.700145	0.350072	+	0.936723i	$0.386157\pi$
$150$	−9.93750e10	−0.106850
$151$	−1.20573e12	−1.24991	−0.624953	−	0.780662i	$-0.714882\pi$
$151$	−1.20573e12	−1.24991	−0.624953	+	0.780662i	$0.714882\pi$
$152$	3.34588e11	0.334481
$153$	−4.52758e11	−0.436580
$154$	−5.39173e11	−0.501608
$155$	3.15632e11	0.283372
$156$	6.83006e11	0.591888
$157$	5.86707e11	0.490877	0.245439	−	0.969412i	$-0.421068\pi$
$157$	5.86707e11	0.490877	0.245439	+	0.969412i	$0.421068\pi$
$158$	2.97519e11	0.240381
$159$	1.55225e12	1.21137
$160$	−1.04858e11	−0.0790569
$161$	2.50028e11	0.182157
$162$	−3.88298e11	−0.273422
$163$	4.33241e11	0.294916	0.147458	−	0.989068i	$-0.452891\pi$
$163$	4.33241e11	0.294916	0.147458	+	0.989068i	$0.452891\pi$
$164$	2.91421e11	0.191813
$165$	2.36783e11	0.150726
$166$	−7.27728e11	−0.448099
$167$	−3.58129e11	−0.213353	−0.106677	−	0.994294i	$-0.534021\pi$
$167$	−3.58129e11	−0.213353	−0.106677	+	0.994294i	$0.534021\pi$
$168$	7.36856e11	0.424797
$169$	2.60725e12	1.45481
$170$	−5.95555e11	−0.321701
$171$	−7.76257e11	−0.406001
$172$	−1.28372e12	−0.650226
$173$	2.34626e12	1.15112	0.575562	−	0.817758i	$-0.304783\pi$
$173$	2.34626e12	1.15112	0.575562	+	0.817758i	$0.304783\pi$
$174$	1.41757e12	0.673787
$175$	−6.90566e11	−0.318051
$176$	2.49846e11	0.111520
$177$	−2.76421e12	−1.19596
$178$	−2.98812e12	−1.25340
$179$	−3.33505e12	−1.35647	−0.678235	−	0.734845i	$-0.737255\pi$
$179$	−3.33505e12	−1.35647	−0.678235	+	0.734845i	$0.737255\pi$
$180$	2.43274e11	0.0959613
$181$	3.81920e12	1.46130	0.730652	−	0.682750i	$-0.239216\pi$
$181$	3.81920e12	1.46130	0.730652	+	0.682750i	$0.239216\pi$
$182$	4.74627e12	1.76181
$183$	−1.04828e12	−0.377571
$184$	−1.15860e11	−0.0404981
$185$	1.64036e12	0.556536
$186$	1.02780e12	0.338522
$187$	1.41904e12	0.453801
$188$	−2.21293e11	−0.0687226
$189$	−5.69305e12	−1.71714
$190$	−1.02108e12	−0.299168
$191$	−2.56250e12	−0.729426	−0.364713	−	0.931120i	$-0.618833\pi$
$191$	−2.56250e12	−0.729426	−0.364713	+	0.931120i	$0.618833\pi$
$192$	−3.41450e11	−0.0944431
$193$	−1.93905e11	−0.0521222	−0.0260611	−	0.999660i	$-0.508296\pi$
$193$	−1.93905e11	−0.0521222	−0.0260611	+	0.999660i	$0.508296\pi$
$194$	−1.85956e11	−0.0485849
$195$	−2.08437e12	−0.529400
$196$	3.09570e12	0.764452
$197$	3.68562e11	0.0885006	0.0442503	−	0.999020i	$-0.485910\pi$
$197$	3.68562e11	0.0885006	0.0442503	+	0.999020i	$0.485910\pi$
$198$	−5.79653e11	−0.135366
$199$	−7.19856e12	−1.63514	−0.817568	−	0.575832i	$-0.804678\pi$
$199$	−7.19856e12	−1.63514	−0.817568	+	0.575832i	$0.804678\pi$
$200$	3.20000e11	0.0707107
$201$	−5.81146e12	−1.24942
$202$	2.01398e12	0.421329
$203$	9.85080e12	2.00560
$204$	−1.93932e12	−0.384311
$205$	−8.89345e11	−0.171563
$206$	4.30934e12	0.809359
$207$	2.68799e11	0.0491576
$208$	−2.19937e12	−0.391696
$209$	2.43295e12	0.422016
$210$	−2.24871e12	−0.379950
$211$	5.67398e12	0.933974	0.466987	−	0.884264i	$-0.345340\pi$
$211$	5.67398e12	0.933974	0.466987	+	0.884264i	$0.345340\pi$
$212$	−4.99843e12	−0.801652
$213$	4.22541e12	0.660360
$214$	−4.36045e12	−0.664134
$215$	3.91761e12	0.581580
$216$	2.63809e12	0.381763
$217$	7.14228e12	1.00765
$218$	3.31091e12	0.455446
$219$	1.03367e13	1.38656
$220$	−7.62470e11	−0.0997466
$221$	−1.24916e13	−1.59390
$222$	5.34152e12	0.664850
$223$	7.99247e12	0.970519	0.485259	−	0.874370i	$-0.338725\pi$
$223$	7.99247e12	0.970519	0.485259	+	0.874370i	$0.338725\pi$
$224$	−2.37277e12	−0.281120
$225$	−7.42412e11	−0.0858304
$226$	−5.93505e12	−0.669619
$227$	−5.39300e12	−0.593866	−0.296933	−	0.954898i	$-0.595964\pi$
$227$	−5.39300e12	−0.593866	−0.296933	+	0.954898i	$0.595964\pi$
$228$	−3.32497e12	−0.357393
$229$	−1.22239e13	−1.28267	−0.641333	−	0.767263i	$-0.721618\pi$
$229$	−1.22239e13	−1.28267	−0.641333	+	0.767263i	$0.721618\pi$
$230$	3.53576e11	0.0362226
$231$	5.35803e12	0.535969
$232$	−4.56474e12	−0.445895
$233$	−7.84141e11	−0.0748060	−0.0374030	−	0.999300i	$-0.511909\pi$
$233$	−7.84141e11	−0.0748060	−0.0374030	+	0.999300i	$0.511909\pi$
$234$	5.10261e12	0.475450
$235$	6.75333e11	0.0614673
$236$	8.90109e12	0.791457
$237$	−2.95659e12	−0.256848
$238$	−1.34765e13	−1.14394
$239$	4.35218e12	0.361010	0.180505	−	0.983574i	$-0.442227\pi$
$239$	4.35218e12	0.361010	0.180505	+	0.983574i	$0.442227\pi$
$240$	1.04202e12	0.0844725
$241$	4.45936e12	0.353329	0.176664	−	0.984271i	$-0.443469\pi$
$241$	4.45936e12	0.353329	0.176664	+	0.984271i	$0.443469\pi$
$242$	−7.31322e12	−0.566401
$243$	−1.04030e13	−0.787637
$244$	3.37561e12	0.249866
$245$	−9.44732e12	−0.683747
$246$	−2.89599e12	−0.204953
$247$	−2.14170e13	−1.48226
$248$	−3.30964e12	−0.224025
$249$	7.23179e12	0.478795
$250$	−9.76562e11	−0.0632456
$251$	−8.61852e12	−0.546043	−0.273022	−	0.962008i	$-0.588023\pi$
$251$	−8.61852e12	−0.546043	−0.273022	+	0.962008i	$0.588023\pi$
$252$	5.50491e12	0.341230
$253$	−8.42472e11	−0.0510967
$254$	1.60041e13	0.949830
$255$	5.91832e12	0.343738
$256$	1.09951e12	0.0625000
$257$	4.59520e12	0.255665	0.127833	−	0.991796i	$-0.459198\pi$
$257$	4.59520e12	0.255665	0.127833	+	0.991796i	$0.459198\pi$
$258$	1.27570e13	0.694768
$259$	3.71188e13	1.97900
$260$	6.71193e12	0.350343
$261$	1.05904e13	0.541238
$262$	1.27079e13	0.635940
$263$	−2.66039e13	−1.30373	−0.651866	−	0.758334i	$-0.726014\pi$
$263$	−2.66039e13	−1.30373	−0.651866	+	0.758334i	$0.726014\pi$
$264$	−2.48285e12	−0.119159
$265$	1.52540e13	0.717020
$266$	−2.31055e13	−1.06382
$267$	2.96945e13	1.33926
$268$	1.87136e13	0.826831
$269$	−2.12378e13	−0.919333	−0.459666	−	0.888092i	$-0.652031\pi$
$269$	−2.12378e13	−0.919333	−0.459666	+	0.888092i	$0.652031\pi$
$270$	−8.05081e12	−0.341459
$271$	4.43969e12	0.184511	0.0922554	−	0.995735i	$-0.470592\pi$
$271$	4.43969e12	0.184511	0.0922554	+	0.995735i	$0.470592\pi$
$272$	6.24484e12	0.254327
$273$	−4.71661e13	−1.88250
$274$	5.36441e12	0.209843
$275$	2.32688e12	0.0892161
$276$	1.15136e12	0.0432723
$277$	−2.63525e12	−0.0970921	−0.0485460	−	0.998821i	$-0.515459\pi$
$277$	−2.63525e12	−0.0970921	−0.0485460	+	0.998821i	$0.515459\pi$
$278$	1.76776e12	0.0638524
$279$	7.67850e12	0.271928
$280$	7.24111e12	0.251441
$281$	−2.99856e13	−1.02100	−0.510502	−	0.859877i	$-0.670540\pi$
$281$	−2.99856e13	−1.02100	−0.510502	+	0.859877i	$0.670540\pi$
$282$	2.19910e12	0.0734302
$283$	5.05205e11	0.0165441	0.00827203	−	0.999966i	$-0.497367\pi$
$283$	5.05205e11	0.0165441	0.00827203	+	0.999966i	$0.497367\pi$
$284$	−1.36063e13	−0.437009
$285$	1.01470e13	0.319662
$286$	−1.59926e13	−0.494205
$287$	−2.01245e13	−0.610064
$288$	−2.55091e12	−0.0758641
$289$	1.19663e12	0.0349158
$290$	1.39305e13	0.398820
$291$	1.84794e12	0.0519131
$292$	−3.32854e13	−0.917588
$293$	4.95629e13	1.34086	0.670432	−	0.741971i	$-0.266109\pi$
$293$	4.95629e13	1.34086	0.670432	+	0.741971i	$0.266109\pi$
$294$	−3.07635e13	−0.816818
$295$	−2.71640e13	−0.707901
$296$	−1.72004e13	−0.439981
$297$	1.91828e13	0.481673
$298$	2.00846e13	0.495077
$299$	7.41617e12	0.179469
$300$	−3.18000e12	−0.0755545
$301$	8.86496e13	2.06805
$302$	−3.85834e13	−0.883818
$303$	−2.00139e13	−0.450191
$304$	1.07068e13	0.236513
$305$	−1.03015e13	−0.223487
$306$	−1.44883e13	−0.308709
$307$	1.16245e13	0.243283	0.121642	−	0.992574i	$-0.461184\pi$
$307$	1.16245e13	0.243283	0.121642	+	0.992574i	$0.461184\pi$
$308$	−1.72535e13	−0.354690
$309$	−4.28241e13	−0.864801
$310$	1.01002e13	0.200374
$311$	−1.03105e13	−0.200955	−0.100478	−	0.994939i	$-0.532037\pi$
$311$	−1.03105e13	−0.200955	−0.100478	+	0.994939i	$0.532037\pi$
$312$	2.18562e13	0.418528
$313$	−4.04998e13	−0.762006	−0.381003	−	0.924574i	$-0.624421\pi$
$313$	−4.04998e13	−0.762006	−0.381003	+	0.924574i	$0.624421\pi$
$314$	1.87746e13	0.347103
$315$	−1.67997e13	−0.305206
$316$	9.52059e12	0.169975
$317$	7.38617e13	1.29597	0.647983	−	0.761655i	$-0.275613\pi$
$317$	7.38617e13	1.29597	0.647983	+	0.761655i	$0.275613\pi$
$318$	4.96719e13	0.856567
$319$	−3.31924e13	−0.562588
$320$	−3.35544e12	−0.0559017
$321$	4.33320e13	0.709629
$322$	8.00088e12	0.128804
$323$	6.08110e13	0.962428
$324$	−1.24255e13	−0.193338
$325$	−2.04832e13	−0.313357
$326$	1.38637e13	0.208537
$327$	−3.29022e13	−0.486644
$328$	9.32546e12	0.135633
$329$	1.52818e13	0.218573
$330$	7.57705e12	0.106579
$331$	2.51206e13	0.347516	0.173758	−	0.984788i	$-0.444409\pi$
$331$	2.51206e13	0.347516	0.173758	+	0.984788i	$0.444409\pi$
$332$	−2.32873e13	−0.316854
$333$	3.99055e13	0.534060
$334$	−1.14601e13	−0.150863
$335$	−5.71095e13	−0.739540
$336$	2.35794e13	0.300377
$337$	−1.54631e13	−0.193791	−0.0968954	−	0.995295i	$-0.530891\pi$
$337$	−1.54631e13	−0.193791	−0.0968954	+	0.995295i	$0.530891\pi$
$338$	8.34321e13	1.02871
$339$	5.89796e13	0.715490
$340$	−1.90577e13	−0.227477
$341$	−2.40660e13	−0.282654
$342$	−2.48402e13	−0.287086
$343$	−7.39539e13	−0.841091
$344$	−4.10791e13	−0.459780
$345$	−3.51366e12	−0.0387039
$346$	7.50802e13	0.813967
$347$	−1.31168e14	−1.39964	−0.699819	−	0.714320i	$-0.746736\pi$
$347$	−1.31168e14	−1.39964	−0.699819	+	0.714320i	$0.746736\pi$
$348$	4.53621e13	0.476439
$349$	−1.50978e14	−1.56089	−0.780446	−	0.625223i	$-0.785008\pi$
$349$	−1.50978e14	−1.56089	−0.780446	+	0.625223i	$0.785008\pi$
$350$	−2.20981e13	−0.224896
$351$	−1.68864e14	−1.69179
$352$	7.99508e12	0.0788566
$353$	6.04914e13	0.587399	0.293699	−	0.955898i	$-0.405114\pi$
$353$	6.04914e13	0.587399	0.293699	+	0.955898i	$0.405114\pi$
$354$	−8.84546e13	−0.845673
$355$	4.15233e13	0.390873
$356$	−9.56200e13	−0.886285
$357$	1.33923e14	1.22230
$358$	−1.06722e14	−0.959170
$359$	−3.30947e13	−0.292913	−0.146456	−	0.989217i	$-0.546787\pi$
$359$	−3.30947e13	−0.292913	−0.146456	+	0.989217i	$0.546787\pi$
$360$	7.78476e12	0.0678549
$361$	−1.22294e13	−0.104982
$362$	1.22215e14	1.03330
$363$	7.26751e13	0.605201
$364$	1.51881e14	1.24579
$365$	1.01579e14	0.820716
$366$	−3.35451e13	−0.266983
$367$	−2.09978e14	−1.64630	−0.823152	−	0.567821i	$-0.807787\pi$
$367$	−2.09978e14	−1.64630	−0.823152	+	0.567821i	$0.807787\pi$
$368$	−3.70751e12	−0.0286365
$369$	−2.16354e13	−0.164634
$370$	5.24914e13	0.393531
$371$	3.45175e14	2.54966
$372$	3.28896e13	0.239371
$373$	−1.12373e14	−0.805864	−0.402932	−	0.915230i	$-0.632009\pi$
$373$	−1.12373e14	−0.805864	−0.402932	+	0.915230i	$0.632009\pi$
$374$	4.54093e13	0.320886
$375$	9.70459e12	0.0675780
$376$	−7.08138e12	−0.0485942
$377$	2.92189e14	1.97600
$378$	−1.82178e14	−1.21420
$379$	1.71420e12	0.0112602	0.00563008	−	0.999984i	$-0.498208\pi$
$379$	1.71420e12	0.0112602	0.00563008	+	0.999984i	$0.498208\pi$
$380$	−3.26746e13	−0.211544
$381$	−1.59041e14	−1.01490
$382$	−8.20001e13	−0.515782
$383$	1.53137e14	0.949481	0.474740	−	0.880126i	$-0.342542\pi$
$383$	1.53137e14	0.949481	0.474740	+	0.880126i	$0.342542\pi$
$384$	−1.09264e13	−0.0667814
$385$	5.26536e13	0.317245
$386$	−6.20495e12	−0.0368560
$387$	9.53051e13	0.558092
$388$	−5.95060e12	−0.0343547
$389$	2.61488e14	1.48843	0.744215	−	0.667940i	$-0.232824\pi$
$389$	2.61488e14	1.48843	0.744215	+	0.667940i	$0.232824\pi$
$390$	−6.66998e13	−0.374343
$391$	−2.10574e13	−0.116528
$392$	9.90624e13	0.540549
$393$	−1.26285e14	−0.679503
$394$	1.17940e13	0.0625794
$395$	−2.90545e13	−0.152030
$396$	−1.85489e13	−0.0957182
$397$	−2.29528e14	−1.16812	−0.584060	−	0.811711i	$-0.698537\pi$
$397$	−2.29528e14	−1.16812	−0.584060	+	0.811711i	$0.698537\pi$
$398$	−2.30354e14	−1.15622
$399$	2.29611e14	1.13669
$400$	1.02400e13	0.0500000
$401$	−3.54324e14	−1.70650	−0.853251	−	0.521500i	$-0.825373\pi$
$401$	−3.54324e14	−1.70650	−0.853251	+	0.521500i	$0.825373\pi$
$402$	−1.85967e14	−0.883470
$403$	2.11850e14	0.992776
$404$	6.44472e13	0.297925
$405$	3.79197e13	0.172927
$406$	3.15226e14	1.41817
$407$	−1.25072e14	−0.555126
$408$	−6.20581e13	−0.271749
$409$	−1.38195e14	−0.597053	−0.298526	−	0.954401i	$-0.596495\pi$
$409$	−1.38195e14	−0.597053	−0.298526	+	0.954401i	$0.596495\pi$
$410$	−2.84590e13	−0.121313
$411$	−5.33088e13	−0.224217
$412$	1.37899e14	0.572303
$413$	−6.14680e14	−2.51723
$414$	8.60157e12	0.0347597
$415$	7.10671e13	0.283403
$416$	−7.03797e13	−0.276971
$417$	−1.75671e13	−0.0682264
$418$	7.78545e13	0.298410
$419$	1.43461e14	0.542695	0.271348	−	0.962481i	$-0.412531\pi$
$419$	1.43461e14	0.542695	0.271348	+	0.962481i	$0.412531\pi$
$420$	−7.19586e13	−0.268665
$421$	−3.62390e13	−0.133544	−0.0667721	−	0.997768i	$-0.521270\pi$
$421$	−3.62390e13	−0.133544	−0.0667721	+	0.997768i	$0.521270\pi$
$422$	1.81567e14	0.660419
$423$	1.64291e13	0.0589849
$424$	−1.59950e14	−0.566854
$425$	5.81596e13	0.203462
$426$	1.35213e14	0.466945
$427$	−2.33108e14	−0.794702
$428$	−1.39535e14	−0.469614
$429$	1.58927e14	0.528059
$430$	1.25364e14	0.411239
$431$	−1.42358e14	−0.461061	−0.230530	−	0.973065i	$-0.574046\pi$
$431$	−1.42358e14	−0.461061	−0.230530	+	0.973065i	$0.574046\pi$
$432$	8.44188e13	0.269947
$433$	4.82775e14	1.52427	0.762134	−	0.647419i	$-0.224152\pi$
$433$	4.82775e14	1.52427	0.762134	+	0.647419i	$0.224152\pi$
$434$	2.28553e14	0.712514
$435$	−1.38434e14	−0.426140
$436$	1.05949e14	0.322049
$437$	−3.61030e13	−0.108367
$438$	3.30773e14	0.980444
$439$	2.04060e14	0.597313	0.298657	−	0.954361i	$-0.403461\pi$
$439$	2.04060e14	0.597313	0.298657	+	0.954361i	$0.403461\pi$
$440$	−2.43991e13	−0.0705315
$441$	−2.29828e14	−0.656132
$442$	−3.99732e14	−1.12706
$443$	3.33038e14	0.927413	0.463707	−	0.885989i	$-0.346519\pi$
$443$	3.33038e14	0.927413	0.463707	+	0.885989i	$0.346519\pi$
$444$	1.70929e14	0.470120
$445$	2.91809e14	0.792718
$446$	2.55759e14	0.686261
$447$	−1.99590e14	−0.528991
$448$	−7.59286e13	−0.198782
$449$	−7.24364e14	−1.87328	−0.936639	−	0.350297i	$-0.886081\pi$
$449$	−7.24364e14	−1.87328	−0.936639	+	0.350297i	$0.886081\pi$
$450$	−2.37572e13	−0.0606913
$451$	6.78099e13	0.171128
$452$	−1.89922e14	−0.473492
$453$	3.83423e14	0.944361
$454$	−1.72576e14	−0.419927
$455$	−4.63503e14	−1.11427
$456$	−1.06399e14	−0.252715
$457$	4.30781e14	1.01092	0.505460	−	0.862850i	$-0.331323\pi$
$457$	4.30781e14	1.01092	0.505460	+	0.862850i	$0.331323\pi$
$458$	−3.91164e14	−0.906981
$459$	4.79469e14	1.09848
$460$	1.13144e13	0.0256132
$461$	4.15819e14	0.930142	0.465071	−	0.885273i	$-0.346029\pi$
$461$	4.15819e14	0.930142	0.465071	+	0.885273i	$0.346029\pi$
$462$	1.71457e14	0.378987
$463$	2.00146e14	0.437171	0.218586	−	0.975818i	$-0.429856\pi$
$463$	2.00146e14	0.437171	0.218586	+	0.975818i	$0.429856\pi$
$464$	−1.46072e14	−0.315295
$465$	−1.00371e14	−0.214100
$466$	−2.50925e13	−0.0528959
$467$	4.75882e14	0.991417	0.495709	−	0.868489i	$-0.334908\pi$
$467$	4.75882e14	0.991417	0.495709	+	0.868489i	$0.334908\pi$
$468$	1.63284e14	0.336194
$469$	−1.29230e15	−2.62974
$470$	2.16106e13	0.0434640
$471$	−1.86573e14	−0.370880
$472$	2.84835e14	0.559645
$473$	−2.98706e14	−0.580107
$474$	−9.46109e13	−0.181619
$475$	9.97150e13	0.189211
$476$	−4.31248e14	−0.808889
$477$	3.71089e14	0.688061
$478$	1.39270e14	0.255272
$479$	−4.70642e14	−0.852797	−0.426399	−	0.904535i	$-0.640218\pi$
$479$	−4.70642e14	−0.852797	−0.426399	+	0.904535i	$0.640218\pi$
$480$	3.33447e13	0.0597311
$481$	1.10100e15	1.94979
$482$	1.42700e14	0.249841
$483$	−7.95088e13	−0.137628
$484$	−2.34023e14	−0.400506
$485$	1.81598e13	0.0307278
$486$	−3.32898e14	−0.556943
$487$	−6.02090e14	−0.995983	−0.497991	−	0.867182i	$-0.665929\pi$
$487$	−6.02090e14	−0.995983	−0.497991	+	0.867182i	$0.665929\pi$
$488$	1.08019e14	0.176682
$489$	−1.37771e14	−0.222822
$490$	−3.02314e14	−0.483482
$491$	−5.53669e14	−0.875593	−0.437797	−	0.899074i	$-0.644241\pi$
$491$	−5.53669e14	−0.875593	−0.437797	+	0.899074i	$0.644241\pi$
$492$	−9.26717e13	−0.144924
$493$	−8.29636e14	−1.28301
$494$	−6.85343e14	−1.04812
$495$	5.66067e13	0.0856129
$496$	−1.05909e14	−0.158410
$497$	9.39609e14	1.38991
$498$	2.31417e14	0.338559
$499$	5.68166e14	0.822095	0.411048	−	0.911614i	$-0.365163\pi$
$499$	5.68166e14	0.822095	0.411048	+	0.911614i	$0.365163\pi$
$500$	−3.12500e13	−0.0447214
$501$	1.13885e14	0.161198
$502$	−2.75792e14	−0.386111
$503$	−1.23359e14	−0.170824	−0.0854118	−	0.996346i	$-0.527221\pi$
$503$	−1.23359e14	−0.170824	−0.0854118	+	0.996346i	$0.527221\pi$
$504$	1.76157e14	0.241286
$505$	−1.96677e14	−0.266472
$506$	−2.69591e13	−0.0361308
$507$	−8.29107e14	−1.09917
$508$	5.12131e14	0.671631
$509$	1.27570e15	1.65501	0.827505	−	0.561459i	$-0.189760\pi$
$509$	1.27570e15	1.65501	0.827505	+	0.561459i	$0.189760\pi$
$510$	1.89386e14	0.243060
$511$	2.29858e15	2.91839
$512$	3.51844e13	0.0441942
$513$	8.22053e14	1.02154
$514$	1.47046e14	0.180783
$515$	−4.20834e14	−0.511883
$516$	4.08224e14	0.491275
$517$	−5.14921e13	−0.0613116
$518$	1.18780e15	1.39936
$519$	−7.46109e14	−0.869725
$520$	2.14782e14	0.247730
$521$	−1.15596e15	−1.31928	−0.659638	−	0.751583i	$-0.729291\pi$
$521$	−1.15596e15	−1.31928	−0.659638	+	0.751583i	$0.729291\pi$
$522$	3.38892e14	0.382713
$523$	−6.30879e13	−0.0704996	−0.0352498	−	0.999379i	$-0.511223\pi$
$523$	−6.30879e13	−0.0704996	−0.0352498	+	0.999379i	$0.511223\pi$
$524$	4.06652e14	0.449678
$525$	2.19600e14	0.240301
$526$	−8.51324e14	−0.921878
$527$	−6.01524e14	−0.644606
$528$	−7.94511e13	−0.0842585
$529$	−9.40308e14	−0.986879
$530$	4.88128e14	0.507009
$531$	−6.60828e14	−0.679311
$532$	−7.39377e14	−0.752232
$533$	−5.96922e14	−0.601060
$534$	9.50224e14	0.946998
$535$	4.25826e14	0.420036
$536$	5.98836e14	0.584658
$537$	1.06055e15	1.02487
$538$	−6.79611e14	−0.650066
$539$	7.20330e14	0.682014
$540$	−2.57626e14	−0.241448
$541$	3.17732e14	0.294765	0.147383	−	0.989080i	$-0.452915\pi$
$541$	3.17732e14	0.294765	0.147383	+	0.989080i	$0.452915\pi$
$542$	1.42070e14	0.130469
$543$	−1.21451e15	−1.10408
$544$	1.99835e14	0.179836
$545$	−3.23331e14	−0.288049
$546$	−1.50932e15	−1.33113
$547$	−1.80976e15	−1.58012	−0.790061	−	0.613028i	$-0.789951\pi$
$547$	−1.80976e15	−1.58012	−0.790061	+	0.613028i	$0.789951\pi$
$548$	1.71661e14	0.148381
$549$	−2.50609e14	−0.214461
$550$	7.44600e13	0.0630853
$551$	−1.42242e15	−1.19314
$552$	3.68434e13	0.0305981
$553$	−6.57460e14	−0.540607
$554$	−8.43281e13	−0.0686545
$555$	−5.21633e14	−0.420488
$556$	5.65683e13	0.0451504
$557$	4.07238e14	0.321844	0.160922	−	0.986967i	$-0.448553\pi$
$557$	4.07238e14	0.321844	0.160922	+	0.986967i	$0.448553\pi$
$558$	2.45712e14	0.192282
$559$	2.62947e15	2.03753
$560$	2.31716e14	0.177796
$561$	−4.51255e14	−0.342867
$562$	−9.59538e14	−0.721959
$563$	−1.07535e15	−0.801221	−0.400610	−	0.916249i	$-0.631202\pi$
$563$	−1.07535e15	−0.801221	−0.400610	+	0.916249i	$0.631202\pi$
$564$	7.03712e13	0.0519230
$565$	5.79595e14	0.423505
$566$	1.61665e13	0.0116984
$567$	8.58066e14	0.614913
$568$	−4.35403e14	−0.309012
$569$	2.23965e15	1.57421	0.787103	−	0.616821i	$-0.211580\pi$
$569$	2.23965e15	1.57421	0.787103	+	0.616821i	$0.211580\pi$
$570$	3.24704e14	0.226035
$571$	7.97473e14	0.549816	0.274908	−	0.961471i	$-0.411353\pi$
$571$	7.97473e14	0.549816	0.274908	+	0.961471i	$0.411353\pi$
$572$	−5.11765e14	−0.349456
$573$	8.14876e14	0.551114
$574$	−6.43985e14	−0.431380
$575$	−3.45289e13	−0.0229092
$576$	−8.16291e13	−0.0536440
$577$	6.90255e14	0.449307	0.224653	−	0.974439i	$-0.427875\pi$
$577$	6.90255e14	0.449307	0.224653	+	0.974439i	$0.427875\pi$
$578$	3.82922e13	0.0246892
$579$	6.16617e13	0.0393807
$580$	4.45776e14	0.282009
$581$	1.60814e15	1.00776
$582$	5.91341e13	0.0367081
$583$	−1.16307e15	−0.715203
$584$	−1.06513e15	−0.648833
$585$	−4.98302e14	−0.300701
$586$	1.58601e15	0.948134
$587$	4.08705e14	0.242047	0.121024	−	0.992650i	$-0.461382\pi$
$587$	4.08705e14	0.242047	0.121024	+	0.992650i	$0.461382\pi$
$588$	−9.84432e14	−0.577578
$589$	−1.03132e15	−0.599457
$590$	−8.69247e14	−0.500561
$591$	−1.17203e14	−0.0668662
$592$	−5.50412e14	−0.311113
$593$	−2.80245e14	−0.156941	−0.0784705	−	0.996916i	$-0.525004\pi$
$593$	−2.80245e14	−0.156941	−0.0784705	+	0.996916i	$0.525004\pi$
$594$	6.13850e14	0.340594
$595$	1.31606e15	0.723492
$596$	6.42706e14	0.350072
$597$	2.28914e15	1.23542
$598$	2.37318e14	0.126903
$599$	1.58122e15	0.837806	0.418903	−	0.908031i	$-0.362415\pi$
$599$	1.58122e15	0.837806	0.418903	+	0.908031i	$0.362415\pi$
$600$	−1.01760e14	−0.0534251
$601$	−1.67984e15	−0.873895	−0.436947	−	0.899487i	$-0.643940\pi$
$601$	−1.67984e15	−0.873895	−0.436947	+	0.899487i	$0.643940\pi$
$602$	2.83679e15	1.46233
$603$	−1.38932e15	−0.709672
$604$	−1.23467e15	−0.624953
$605$	7.14182e14	0.358224
$606$	−6.40444e14	−0.318333
$607$	6.83439e14	0.336637	0.168319	−	0.985733i	$-0.446166\pi$
$607$	6.83439e14	0.336637	0.168319	+	0.985733i	$0.446166\pi$
$608$	3.42618e14	0.167240
$609$	−3.13256e15	−1.51532
$610$	−3.29649e14	−0.158029
$611$	4.53278e14	0.215347
$612$	−4.63625e14	−0.218290
$613$	9.43749e14	0.440376	0.220188	−	0.975457i	$-0.429333\pi$
$613$	9.43749e14	0.440376	0.220188	+	0.975457i	$0.429333\pi$
$614$	3.71983e14	0.172027
$615$	2.82812e14	0.129624
$616$	−5.52113e14	−0.250804
$617$	−2.65031e15	−1.19324	−0.596621	−	0.802523i	$-0.703490\pi$
$617$	−2.65031e15	−1.19324	−0.596621	+	0.802523i	$0.703490\pi$
$618$	−1.37037e15	−0.611507
$619$	−2.47875e15	−1.09631	−0.548156	−	0.836376i	$-0.684670\pi$
$619$	−2.47875e15	−1.09631	−0.548156	+	0.836376i	$0.684670\pi$
$620$	3.23208e14	0.141686
$621$	−2.84657e14	−0.123685
$622$	−3.29938e14	−0.142097
$623$	6.60319e15	2.81884
$624$	6.99398e14	0.295944
$625$	9.53674e13	0.0400000
$626$	−1.29599e15	−0.538820
$627$	−7.73679e14	−0.318852
$628$	6.00788e14	0.245439
$629$	−3.12615e15	−1.26599
$630$	−5.37589e14	−0.215813
$631$	−7.69636e13	−0.0306284	−0.0153142	−	0.999883i	$-0.504875\pi$
$631$	−7.69636e13	−0.0306284	−0.0153142	+	0.999883i	$0.504875\pi$
$632$	3.04659e14	0.120190
$633$	−1.80433e15	−0.705659
$634$	2.36358e15	0.916386
$635$	−1.56290e15	−0.600725
$636$	1.58950e15	0.605684
$637$	−6.34098e15	−2.39546
$638$	−1.06216e15	−0.397810
$639$	1.01015e15	0.375087
$640$	−1.07374e14	−0.0395285
$641$	−1.72264e15	−0.628747	−0.314373	−	0.949299i	$-0.601794\pi$
$641$	−1.72264e15	−0.628747	−0.314373	+	0.949299i	$0.601794\pi$
$642$	1.38662e15	0.501783
$643$	2.90666e15	1.04288	0.521440	−	0.853288i	$-0.325395\pi$
$643$	2.90666e15	1.04288	0.521440	+	0.853288i	$0.325395\pi$
$644$	2.56028e14	0.0910784
$645$	−1.24580e15	−0.439410
$646$	1.94595e15	0.680539
$647$	1.87910e15	0.651593	0.325796	−	0.945440i	$-0.394368\pi$
$647$	1.87910e15	0.651593	0.325796	+	0.945440i	$0.394368\pi$
$648$	−3.97617e14	−0.136711
$649$	2.07117e15	0.706107
$650$	−6.55462e14	−0.221577
$651$	−2.27125e15	−0.761322
$652$	4.43639e14	0.147458
$653$	2.33782e15	0.770529	0.385264	−	0.922806i	$-0.374110\pi$
$653$	2.33782e15	0.770529	0.385264	+	0.922806i	$0.374110\pi$
$654$	−1.05287e15	−0.344110
$655$	−1.24100e15	−0.402204
$656$	2.98415e14	0.0959067
$657$	2.47115e15	0.787570
$658$	4.89016e14	0.154554
$659$	−5.00431e15	−1.56846	−0.784232	−	0.620468i	$-0.786943\pi$
$659$	−5.00431e15	−1.56846	−0.784232	+	0.620468i	$0.786943\pi$
$660$	2.42466e14	0.0753630
$661$	3.07383e15	0.947485	0.473742	−	0.880663i	$-0.342903\pi$
$661$	3.07383e15	0.947485	0.473742	+	0.880663i	$0.342903\pi$
$662$	8.03858e14	0.245731
$663$	3.97234e15	1.20426
$664$	−7.45193e14	−0.224050
$665$	2.25640e15	0.672817
$666$	1.27698e15	0.377637
$667$	4.92548e14	0.144463
$668$	−3.66724e14	−0.106677
$669$	−2.54160e15	−0.733271
$670$	−1.82750e15	−0.522934
$671$	7.85462e14	0.222921
$672$	7.54540e14	0.212398
$673$	−9.90717e14	−0.276609	−0.138305	−	0.990390i	$-0.544165\pi$
$673$	−9.90717e14	−0.276609	−0.138305	+	0.990390i	$0.544165\pi$
$674$	−4.94820e14	−0.137031
$675$	7.86212e14	0.215958
$676$	2.66983e15	0.727405
$677$	−4.76307e15	−1.28721	−0.643605	−	0.765358i	$-0.722562\pi$
$677$	−4.76307e15	−1.28721	−0.643605	+	0.765358i	$0.722562\pi$
$678$	1.88735e15	0.505927
$679$	4.10929e14	0.109265
$680$	−6.09848e14	−0.160851
$681$	1.71498e15	0.448692
$682$	−7.70113e14	−0.199867
$683$	3.86750e14	0.0995673	0.0497837	−	0.998760i	$-0.484147\pi$
$683$	3.86750e14	0.0995673	0.0497837	+	0.998760i	$0.484147\pi$
$684$	−7.94887e14	−0.203000
$685$	−5.23868e14	−0.132716
$686$	−2.36652e15	−0.594741
$687$	3.88719e15	0.969111
$688$	−1.31453e15	−0.325113
$689$	1.02384e16	2.51203
$690$	−1.12437e14	−0.0273678
$691$	2.55033e15	0.615839	0.307920	−	0.951412i	$-0.400367\pi$
$691$	2.55033e15	0.615839	0.307920	+	0.951412i	$0.400367\pi$
$692$	2.40257e15	0.575562
$693$	1.28092e15	0.304432
$694$	−4.19738e15	−0.989694
$695$	−1.72633e14	−0.0403838
$696$	1.45159e15	0.336893
$697$	1.69489e15	0.390267
$698$	−4.83128e15	−1.10372
$699$	2.49357e14	0.0565193
$700$	−7.07140e14	−0.159025
$701$	−2.63967e15	−0.588980	−0.294490	−	0.955655i	$-0.595150\pi$
$701$	−2.63967e15	−0.588980	−0.294490	+	0.955655i	$0.595150\pi$
$702$	−5.40364e15	−1.19628
$703$	−5.35980e15	−1.17732
$704$	2.55843e14	0.0557601
$705$	−2.14756e14	−0.0464413
$706$	1.93573e15	0.415354
$707$	−4.45051e15	−0.947552
$708$	−2.83055e15	−0.597981
$709$	−2.45062e15	−0.513714	−0.256857	−	0.966449i	$-0.582687\pi$
$709$	−2.45062e15	−0.513714	−0.256857	+	0.966449i	$0.582687\pi$
$710$	1.32874e15	0.276389
$711$	−7.06820e14	−0.145890
$712$	−3.05984e15	−0.626698
$713$	3.57120e14	0.0725808
$714$	4.28553e15	0.864299
$715$	1.56178e15	0.312563
$716$	−3.41509e15	−0.678235
$717$	−1.38399e15	−0.272759
$718$	−1.05903e15	−0.207121
$719$	−6.03237e15	−1.17079	−0.585395	−	0.810748i	$-0.699061\pi$
$719$	−6.03237e15	−1.17079	−0.585395	+	0.810748i	$0.699061\pi$
$720$	2.49112e14	0.0479807
$721$	−9.52283e15	−1.82021
$722$	−3.91341e14	−0.0742337
$723$	−1.41808e15	−0.266956
$724$	3.91087e15	0.730652
$725$	−1.36040e15	−0.252236
$726$	2.32560e15	0.427941
$727$	9.09102e15	1.66025	0.830125	−	0.557577i	$-0.188269\pi$
$727$	9.09102e15	1.66025	0.830125	+	0.557577i	$0.188269\pi$
$728$	4.86018e15	0.880907
$729$	5.45773e15	0.981772
$730$	3.25053e15	0.580334
$731$	−7.46608e15	−1.32296
$732$	−1.07344e15	−0.188785
$733$	−7.47227e14	−0.130431	−0.0652155	−	0.997871i	$-0.520773\pi$
$733$	−7.47227e14	−0.130431	−0.0652155	+	0.997871i	$0.520773\pi$
$734$	−6.71929e15	−1.16411
$735$	3.00425e15	0.516601
$736$	−1.18640e14	−0.0202490
$737$	4.35443e15	0.737666
$738$	−6.92333e14	−0.116414
$739$	−3.44053e15	−0.574223	−0.287111	−	0.957897i	$-0.592695\pi$
$739$	−3.44053e15	−0.574223	−0.287111	+	0.957897i	$0.592695\pi$
$740$	1.67972e15	0.278268
$741$	6.81060e15	1.11991
$742$	1.10456e16	1.80288
$743$	−3.26654e15	−0.529236	−0.264618	−	0.964353i	$-0.585246\pi$
$743$	−3.26654e15	−0.529236	−0.264618	+	0.964353i	$0.585246\pi$
$744$	1.05247e15	0.169261
$745$	−1.96138e15	−0.313114
$746$	−3.59592e15	−0.569832
$747$	1.72888e15	0.271957
$748$	1.45310e15	0.226901
$749$	9.63579e15	1.49361
$750$	3.10547e14	0.0477848
$751$	5.58103e15	0.852501	0.426251	−	0.904605i	$-0.359834\pi$
$751$	5.58103e15	0.852501	0.426251	+	0.904605i	$0.359834\pi$
$752$	−2.26604e14	−0.0343613
$753$	2.74069e15	0.412560
$754$	9.35004e15	1.39724
$755$	3.76791e15	0.558975
$756$	−5.82968e15	−0.858568
$757$	4.34704e15	0.635574	0.317787	−	0.948162i	$-0.397060\pi$
$757$	4.34704e15	0.635574	0.317787	+	0.948162i	$0.397060\pi$
$758$	5.48543e13	0.00796214
$759$	2.67906e14	0.0386058
$760$	−1.04559e15	−0.149584
$761$	−7.77253e14	−0.110394	−0.0551971	−	0.998475i	$-0.517579\pi$
$761$	−7.77253e14	−0.110394	−0.0551971	+	0.998475i	$0.517579\pi$
$762$	−5.08931e15	−0.717639
$763$	−7.31649e15	−1.02428
$764$	−2.62400e15	−0.364713
$765$	1.41487e15	0.195244
$766$	4.90038e15	0.671384
$767$	−1.82323e16	−2.48008
$768$	−3.49645e14	−0.0472215
$769$	1.55329e15	0.208284	0.104142	−	0.994562i	$-0.466790\pi$
$769$	1.55329e15	0.208284	0.104142	+	0.994562i	$0.466790\pi$
$770$	1.68492e15	0.224326
$771$	−1.46127e15	−0.193167
$772$	−1.98558e14	−0.0260611
$773$	−2.19749e15	−0.286378	−0.143189	−	0.989695i	$-0.545736\pi$
$773$	−2.19749e15	−0.286378	−0.143189	+	0.989695i	$0.545736\pi$
$774$	3.04976e15	0.394631
$775$	−9.86351e14	−0.126728
$776$	−1.90419e14	−0.0242925
$777$	−1.18038e16	−1.49522
$778$	8.36761e15	1.05248
$779$	2.90590e15	0.362932
$780$	−2.13439e15	−0.264700
$781$	−3.16603e15	−0.389883
$782$	−6.73836e14	−0.0823981
$783$	−1.12152e16	−1.36181
$784$	3.17000e15	0.382226
$785$	−1.83346e15	−0.219527
$786$	−4.04111e15	−0.480481
$787$	9.74230e15	1.15027	0.575136	−	0.818058i	$-0.304949\pi$
$787$	9.74230e15	1.15027	0.575136	+	0.818058i	$0.304949\pi$
$788$	3.77407e14	0.0442503
$789$	8.46003e15	0.985028
$790$	−9.29746e14	−0.107502
$791$	1.31154e16	1.50595
$792$	−5.93565e14	−0.0676830
$793$	−6.91432e15	−0.782973
$794$	−7.34488e15	−0.825985
$795$	−4.85077e15	−0.541740
$796$	−7.37133e15	−0.817568
$797$	2.19908e15	0.242226	0.121113	−	0.992639i	$-0.461354\pi$
$797$	2.19908e15	0.242226	0.121113	+	0.992639i	$0.461354\pi$
$798$	7.34756e15	0.803762
$799$	−1.28703e15	−0.139824
$800$	3.27680e14	0.0353553
$801$	7.09894e15	0.760702
$802$	−1.13384e16	−1.20668
$803$	−7.74509e15	−0.818636
$804$	−5.95093e15	−0.624708
$805$	−7.81336e14	−0.0814630
$806$	6.77921e15	0.701998
$807$	6.75363e15	0.694597
$808$	2.06231e15	0.210665
$809$	1.54202e15	0.156450	0.0782248	−	0.996936i	$-0.475075\pi$
$809$	1.54202e15	0.156450	0.0782248	+	0.996936i	$0.475075\pi$
$810$	1.21343e15	0.122278
$811$	−5.24351e15	−0.524816	−0.262408	−	0.964957i	$-0.584517\pi$
$811$	−5.24351e15	−0.524816	−0.262408	+	0.964957i	$0.584517\pi$
$812$	1.00872e16	1.00280
$813$	−1.41182e15	−0.139406
$814$	−4.00231e15	−0.392534
$815$	−1.35388e15	−0.131890
$816$	−1.98586e15	−0.192155
$817$	−1.28006e16	−1.23030
$818$	−4.42222e15	−0.422180
$819$	−1.12758e16	−1.06927
$820$	−9.10689e14	−0.0857816
$821$	1.48875e16	1.39295	0.696475	−	0.717581i	$-0.254751\pi$
$821$	1.48875e16	1.39295	0.696475	+	0.717581i	$0.254751\pi$
$822$	−1.70588e15	−0.158546
$823$	1.77963e16	1.64298	0.821488	−	0.570226i	$-0.193144\pi$
$823$	1.77963e16	1.64298	0.821488	+	0.570226i	$0.193144\pi$
$824$	4.41276e15	0.404679
$825$	−7.39946e14	−0.0674068
$826$	−1.96697e16	−1.77995
$827$	1.67076e16	1.50187	0.750937	−	0.660374i	$-0.229602\pi$
$827$	1.67076e16	1.50187	0.750937	+	0.660374i	$0.229602\pi$
$828$	2.75250e14	0.0245788
$829$	−8.53952e15	−0.757501	−0.378751	−	0.925499i	$-0.623646\pi$
$829$	−8.53952e15	−0.757501	−0.378751	+	0.925499i	$0.623646\pi$
$830$	2.27415e15	0.200396
$831$	8.38011e14	0.0733574
$832$	−2.25215e15	−0.195848
$833$	1.80045e16	1.55537
$834$	−5.62148e14	−0.0482433
$835$	1.11915e15	0.0954144
$836$	2.49134e15	0.211008
$837$	−8.13150e15	−0.684196
$838$	4.59074e15	0.383743
$839$	−1.05768e16	−0.878344	−0.439172	−	0.898403i	$-0.644728\pi$
$839$	−1.05768e16	−0.878344	−0.439172	+	0.898403i	$0.644728\pi$
$840$	−2.30267e15	−0.189975
$841$	7.20533e15	0.590576
$842$	−1.15965e15	−0.0944300
$843$	9.53541e15	0.771414
$844$	5.81016e15	0.466987
$845$	−8.14767e15	−0.650611
$846$	5.25730e14	0.0417086
$847$	1.61608e16	1.27381
$848$	−5.11839e15	−0.400826
$849$	−1.60655e14	−0.0124998
$850$	1.86111e15	0.143869
$851$	1.85597e15	0.142547
$852$	4.32682e15	0.330180
$853$	8.27601e15	0.627482	0.313741	−	0.949509i	$-0.398418\pi$
$853$	8.27601e15	0.627482	0.313741	+	0.949509i	$0.398418\pi$
$854$	−7.45946e15	−0.561939
$855$	2.42580e15	0.181569
$856$	−4.46511e15	−0.332067
$857$	1.70584e15	0.126050	0.0630250	−	0.998012i	$-0.479925\pi$
$857$	1.70584e15	0.126050	0.0630250	+	0.998012i	$0.479925\pi$
$858$	5.08566e15	0.373394
$859$	3.03339e15	0.221292	0.110646	−	0.993860i	$-0.464708\pi$
$859$	3.03339e15	0.221292	0.110646	+	0.993860i	$0.464708\pi$
$860$	4.01163e15	0.290790
$861$	6.39960e15	0.460931
$862$	−4.55547e15	−0.326019
$863$	−1.24917e16	−0.888305	−0.444153	−	0.895951i	$-0.646495\pi$
$863$	−1.24917e16	−0.888305	−0.444153	+	0.895951i	$0.646495\pi$
$864$	2.70140e15	0.190881
$865$	−7.33205e15	−0.514798
$866$	1.54488e16	1.07782
$867$	−3.80529e14	−0.0263805
$868$	7.31369e15	0.503823
$869$	2.21532e15	0.151645
$870$	−4.42989e15	−0.301327
$871$	−3.83315e16	−2.59093
$872$	3.39037e15	0.227723
$873$	4.41780e14	0.0294868
$874$	−1.15530e15	−0.0766267
$875$	2.15802e15	0.142237
$876$	1.05847e16	0.693279
$877$	−7.83589e15	−0.510024	−0.255012	−	0.966938i	$-0.582079\pi$
$877$	−7.83589e15	−0.510024	−0.255012	+	0.966938i	$0.582079\pi$
$878$	6.52991e15	0.422364
$879$	−1.57610e16	−1.01308
$880$	−7.80770e14	−0.0498733
$881$	7.14642e15	0.453650	0.226825	−	0.973936i	$-0.427165\pi$
$881$	7.14642e15	0.453650	0.226825	+	0.973936i	$0.427165\pi$
$882$	−7.35451e15	−0.463956
$883$	1.25932e15	0.0789503	0.0394751	−	0.999221i	$-0.487431\pi$
$883$	1.25932e15	0.0789503	0.0394751	+	0.999221i	$0.487431\pi$
$884$	−1.27914e16	−0.796951
$885$	8.63815e15	0.534851
$886$	1.06572e16	0.655780
$887$	3.31404e15	0.202664	0.101332	−	0.994853i	$-0.467690\pi$
$887$	3.31404e15	0.202664	0.101332	+	0.994853i	$0.467690\pi$
$888$	5.46972e15	0.332425
$889$	−3.53661e16	−2.13613
$890$	9.33789e15	0.560536
$891$	−2.89127e15	−0.172489
$892$	8.18428e15	0.485259
$893$	−2.20662e15	−0.130031
$894$	−6.38689e15	−0.374053
$895$	1.04220e16	0.606632
$896$	−2.42971e15	−0.140560
$897$	−2.35834e15	−0.135597
$898$	−2.31797e16	−1.32461
$899$	1.40701e16	0.799134
$900$	−7.60230e14	−0.0429152
$901$	−2.90707e16	−1.63105
$902$	2.16992e15	0.121006
$903$	−2.81906e16	−1.56250
$904$	−6.07749e15	−0.334810
$905$	−1.19350e16	−0.653515
$906$	1.22695e16	0.667764
$907$	2.57375e16	1.39228	0.696140	−	0.717906i	$-0.254899\pi$
$907$	2.57375e16	1.39228	0.696140	+	0.717906i	$0.254899\pi$
$908$	−5.52244e15	−0.296933
$909$	−4.78464e15	−0.255710
$910$	−1.48321e16	−0.787907
$911$	2.65757e16	1.40324	0.701622	−	0.712549i	$-0.252460\pi$
$911$	2.65757e16	1.40324	0.701622	+	0.712549i	$0.252460\pi$
$912$	−3.40477e15	−0.178696
$913$	−5.41866e15	−0.282685
$914$	1.37850e16	0.714829
$915$	3.27589e15	0.168855
$916$	−1.25172e16	−0.641333
$917$	−2.80820e16	−1.43020
$918$	1.53430e16	0.776741
$919$	3.69577e16	1.85981	0.929906	−	0.367796i	$-0.119888\pi$
$919$	3.69577e16	1.85981	0.929906	+	0.367796i	$0.119888\pi$
$920$	3.62062e14	0.0181113
$921$	−3.69658e15	−0.183811
$922$	1.33062e16	0.657710
$923$	2.78701e16	1.36940
$924$	5.48663e15	0.267984
$925$	−5.12611e15	−0.248891
$926$	6.40467e15	0.309127
$927$	−1.02378e16	−0.491210
$928$	−4.67430e15	−0.222947
$929$	8.61835e15	0.408637	0.204319	−	0.978904i	$-0.434502\pi$
$929$	8.61835e15	0.408637	0.204319	+	0.978904i	$0.434502\pi$
$930$	−3.21187e15	−0.151392
$931$	3.08688e16	1.44643
$932$	−8.02960e14	−0.0374030
$933$	3.27875e15	0.151831
$934$	1.52282e16	0.701038
$935$	−4.43450e15	−0.202946
$936$	5.22507e15	0.237725
$937$	1.13163e16	0.511841	0.255921	−	0.966698i	$-0.417621\pi$
$937$	1.13163e16	0.511841	0.255921	+	0.966698i	$0.417621\pi$
$938$	−4.13536e16	−1.85951
$939$	1.28789e16	0.575730
$940$	6.91541e14	0.0307337
$941$	−2.08626e16	−0.921778	−0.460889	−	0.887458i	$-0.652469\pi$
$941$	−2.08626e16	−0.921778	−0.460889	+	0.887458i	$0.652469\pi$
$942$	−5.97033e15	−0.262252
$943$	−1.00624e15	−0.0439429
$944$	9.11472e15	0.395728
$945$	1.77908e16	0.767927
$946$	−9.55860e15	−0.410197
$947$	−3.85751e16	−1.64582	−0.822909	−	0.568174i	$-0.807650\pi$
$947$	−3.85751e16	−1.64582	−0.822909	+	0.568174i	$0.807650\pi$
$948$	−3.02755e15	−0.128424
$949$	6.81790e16	2.87532
$950$	3.19088e15	0.133792
$951$	−2.34880e16	−0.979160
$952$	−1.37999e16	−0.571971
$953$	2.79679e16	1.15252	0.576260	−	0.817266i	$-0.304511\pi$
$953$	2.79679e16	1.15252	0.576260	+	0.817266i	$0.304511\pi$
$954$	1.18749e16	0.486533
$955$	8.00783e15	0.326209
$956$	4.45664e15	0.180505
$957$	1.05552e16	0.425060
$958$	−1.50606e16	−0.603019
$959$	−1.18543e16	−0.471927
$960$	1.06703e15	0.0422362
$961$	−1.52070e16	−0.598501
$962$	3.52318e16	1.37871
$963$	1.03592e16	0.403072
$964$	4.56639e15	0.176664
$965$	6.05952e14	0.0233098
$966$	−2.54428e15	−0.0973175
$967$	2.43876e16	0.927519	0.463760	−	0.885961i	$-0.346500\pi$
$967$	2.43876e16	0.927519	0.463760	+	0.885961i	$0.346500\pi$
$968$	−7.48874e15	−0.283201
$969$	−1.93379e16	−0.727158
$970$	5.81113e14	0.0217278
$971$	−7.42571e15	−0.276078	−0.138039	−	0.990427i	$-0.544080\pi$
$971$	−7.42571e15	−0.276078	−0.138039	+	0.990427i	$0.544080\pi$
$972$	−1.06527e16	−0.393819
$973$	−3.90642e15	−0.143601
$974$	−1.92669e16	−0.704266
$975$	6.51365e15	0.236755
$976$	3.45662e15	0.124933
$977$	−4.78553e16	−1.71993	−0.859963	−	0.510357i	$-0.829513\pi$
$977$	−4.78553e16	−1.71993	−0.859963	+	0.510357i	$0.829513\pi$
$978$	−4.40866e15	−0.157559
$979$	−2.22496e16	−0.790709
$980$	−9.67406e15	−0.341873
$981$	−7.86579e15	−0.276416
$982$	−1.77174e16	−0.619138
$983$	−4.10261e16	−1.42566	−0.712830	−	0.701337i	$-0.752587\pi$
$983$	−4.10261e16	−1.42566	−0.712830	+	0.701337i	$0.752587\pi$
$984$	−2.96550e15	−0.102477
$985$	−1.15176e15	−0.0395787
$986$	−2.65484e16	−0.907224
$987$	−4.85960e15	−0.165141
$988$	−2.19310e16	−0.741131
$989$	4.43255e15	0.148962
$990$	1.81142e15	0.0605375
$991$	−7.80629e15	−0.259442	−0.129721	−	0.991551i	$-0.541408\pi$
$991$	−7.80629e15	−0.259442	−0.129721	+	0.991551i	$0.541408\pi$
$992$	−3.38908e15	−0.112013
$993$	−7.98834e15	−0.262564
$994$	3.00675e16	0.982815
$995$	2.24955e16	0.731255
$996$	7.40536e15	0.239397
$997$	3.93275e16	1.26437	0.632183	−	0.774819i	$-0.282159\pi$
$997$	3.93275e16	1.26437	0.632183	+	0.774819i	$0.282159\pi$
$998$	1.81813e16	0.581309
$999$	−4.22598e16	−1.34375

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.12.a.c.1.1	✓	1
3.2	odd	2		90.12.a.b.1.1		1
4.3	odd	2		80.12.a.e.1.1		1
5.2	odd	4		50.12.b.b.49.2		2
5.3	odd	4		50.12.b.b.49.1		2
5.4	even	2		50.12.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.12.a.c.1.1	✓	1	1.1	even	1	trivial
50.12.a.b.1.1		1	5.4	even	2
50.12.b.b.49.1		2	5.3	odd	4
50.12.b.b.49.2		2	5.2	odd	4
80.12.a.e.1.1		1	4.3	odd	2
90.12.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:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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