LMFDB - Embedded newform 30.12.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [30,12,Mod(1,30)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(30, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("30.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 30 = 2 \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	30.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:	$23.0502954168$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	30.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

\(q-32.0000 q^{2} -243.000 q^{3} +1024.00 q^{4} -3125.00 q^{5} +7776.00 q^{6} -22876.0 q^{7} -32768.0 q^{8} +59049.0 q^{9} +100000. q^{10} -259128. q^{11} -248832. q^{12} -2.32346e6 q^{13} +732032. q^{14} +759375. q^{15} +1.04858e6 q^{16} -1.91827e6 q^{17} -1.88957e6 q^{18} -1.61374e6 q^{19} -3.20000e6 q^{20} +5.55887e6 q^{21} +8.29210e6 q^{22} +3.28492e7 q^{23} +7.96262e6 q^{24} +9.76562e6 q^{25} +7.43508e7 q^{26} -1.43489e7 q^{27} -2.34250e7 q^{28} +1.52590e8 q^{29} -2.43000e7 q^{30} +5.68101e7 q^{31} -3.35544e7 q^{32} +6.29681e7 q^{33} +6.13845e7 q^{34} +7.14875e7 q^{35} +6.04662e7 q^{36} +5.71517e8 q^{37} +5.16397e7 q^{38} +5.64601e8 q^{39} +1.02400e8 q^{40} +7.34063e8 q^{41} -1.77884e8 q^{42} -5.80697e8 q^{43} -2.65347e8 q^{44} -1.84528e8 q^{45} -1.05117e9 q^{46} +4.78847e8 q^{47} -2.54804e8 q^{48} -1.45402e9 q^{49} -3.12500e8 q^{50} +4.66139e8 q^{51} -2.37923e9 q^{52} -2.55379e9 q^{53} +4.59165e8 q^{54} +8.09775e8 q^{55} +7.49601e8 q^{56} +3.92139e8 q^{57} -4.88289e9 q^{58} +6.31792e9 q^{59} +7.77600e8 q^{60} -7.86138e8 q^{61} -1.81792e9 q^{62} -1.35080e9 q^{63} +1.07374e9 q^{64} +7.26082e9 q^{65} -2.01498e9 q^{66} -2.12877e10 q^{67} -1.96430e9 q^{68} -7.98236e9 q^{69} -2.28760e9 q^{70} +1.17195e10 q^{71} -1.93492e9 q^{72} +2.31756e10 q^{73} -1.82886e10 q^{74} -2.37305e9 q^{75} -1.65247e9 q^{76} +5.92781e9 q^{77} -1.80672e10 q^{78} +2.69897e9 q^{79} -3.27680e9 q^{80} +3.48678e9 q^{81} -2.34900e10 q^{82} +3.26587e10 q^{83} +5.69228e9 q^{84} +5.99458e9 q^{85} +1.85823e10 q^{86} -3.70794e10 q^{87} +8.49111e9 q^{88} +7.45563e10 q^{89} +5.90490e9 q^{90} +5.31515e10 q^{91} +3.36376e10 q^{92} -1.38048e10 q^{93} -1.53231e10 q^{94} +5.04294e9 q^{95} +8.15373e9 q^{96} +4.14349e10 q^{97} +4.65285e10 q^{98} -1.53012e10 q^{99} +O(q^{100})\)

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
$3$	−243.000	−0.577350
$3$	−243.000	−0.577350
$4$	1024.00	0.500000
$5$	−3125.00	−0.447214
$5$	−3125.00	−0.447214
$6$	7776.00	0.408248
$7$	−22876.0	−0.514447	−0.257224	−	0.966352i	$-0.582808\pi$
$7$	−22876.0	−0.514447	−0.257224	+	0.966352i	$0.582808\pi$
$8$	−32768.0	−0.353553
$9$	59049.0	0.333333
$10$	100000.	0.316228
$11$	−259128.	−0.485126	−0.242563	−	0.970136i	$-0.577988\pi$
$11$	−259128.	−0.485126	−0.242563	+	0.970136i	$0.577988\pi$
$12$	−248832.	−0.288675
$13$	−2.32346e6	−1.73559	−0.867795	−	0.496922i	$-0.834463\pi$
$13$	−2.32346e6	−1.73559	−0.867795	+	0.496922i	$0.834463\pi$
$14$	732032.	0.363769
$15$	759375.	0.258199
$16$	1.04858e6	0.250000
$17$	−1.91827e6	−0.327672	−0.163836	−	0.986488i	$-0.552387\pi$
$17$	−1.91827e6	−0.327672	−0.163836	+	0.986488i	$0.552387\pi$
$18$	−1.88957e6	−0.235702
$19$	−1.61374e6	−0.149516	−0.0747582	−	0.997202i	$-0.523818\pi$
$19$	−1.61374e6	−0.149516	−0.0747582	+	0.997202i	$0.523818\pi$
$20$	−3.20000e6	−0.223607
$21$	5.55887e6	0.297016
$22$	8.29210e6	0.343036
$23$	3.28492e7	1.06420	0.532098	−	0.846683i	$-0.321404\pi$
$23$	3.28492e7	1.06420	0.532098	+	0.846683i	$0.321404\pi$
$24$	7.96262e6	0.204124
$25$	9.76562e6	0.200000
$26$	7.43508e7	1.22725
$27$	−1.43489e7	−0.192450
$28$	−2.34250e7	−0.257224
$29$	1.52590e8	1.38146	0.690729	−	0.723113i	$-0.257290\pi$
$29$	1.52590e8	1.38146	0.690729	+	0.723113i	$0.257290\pi$
$30$	−2.43000e7	−0.182574
$31$	5.68101e7	0.356399	0.178199	−	0.983994i	$-0.442973\pi$
$31$	5.68101e7	0.356399	0.178199	+	0.983994i	$0.442973\pi$
$32$	−3.35544e7	−0.176777
$33$	6.29681e7	0.280088
$34$	6.13845e7	0.231699
$35$	7.14875e7	0.230068
$36$	6.04662e7	0.166667
$37$	5.71517e8	1.35494	0.677470	−	0.735551i	$-0.263076\pi$
$37$	5.71517e8	1.35494	0.677470	+	0.735551i	$0.263076\pi$
$38$	5.16397e7	0.105724
$39$	5.64601e8	1.00204
$40$	1.02400e8	0.158114
$41$	7.34063e8	0.989515	0.494757	−	0.869031i	$-0.335257\pi$
$41$	7.34063e8	0.989515	0.494757	+	0.869031i	$0.335257\pi$
$42$	−1.77884e8	−0.210022
$43$	−5.80697e8	−0.602383	−0.301192	−	0.953564i	$-0.597384\pi$
$43$	−5.80697e8	−0.602383	−0.301192	+	0.953564i	$0.597384\pi$
$44$	−2.65347e8	−0.242563
$45$	−1.84528e8	−0.149071
$46$	−1.05117e9	−0.752501
$47$	4.78847e8	0.304550	0.152275	−	0.988338i	$-0.451340\pi$
$47$	4.78847e8	0.304550	0.152275	+	0.988338i	$0.451340\pi$
$48$	−2.54804e8	−0.144338
$49$	−1.45402e9	−0.735344
$50$	−3.12500e8	−0.141421
$51$	4.66139e8	0.189182
$52$	−2.37923e9	−0.867795
$53$	−2.55379e9	−0.838818	−0.419409	−	0.907797i	$-0.637763\pi$
$53$	−2.55379e9	−0.838818	−0.419409	+	0.907797i	$0.637763\pi$
$54$	4.59165e8	0.136083
$55$	8.09775e8	0.216955
$56$	7.49601e8	0.181885
$57$	3.92139e8	0.0863233
$58$	−4.88289e9	−0.976839
$59$	6.31792e9	1.15050	0.575252	−	0.817976i	$-0.304904\pi$
$59$	6.31792e9	1.15050	0.575252	+	0.817976i	$0.304904\pi$
$60$	7.77600e8	0.129099
$61$	−7.86138e8	−0.119175	−0.0595874	−	0.998223i	$-0.518979\pi$
$61$	−7.86138e8	−0.119175	−0.0595874	+	0.998223i	$0.518979\pi$
$62$	−1.81792e9	−0.252012
$63$	−1.35080e9	−0.171482
$64$	1.07374e9	0.125000
$65$	7.26082e9	0.776179
$66$	−2.01498e9	−0.198052
$67$	−2.12877e10	−1.92627	−0.963135	−	0.269020i	$-0.913300\pi$
$67$	−2.12877e10	−1.92627	−0.963135	+	0.269020i	$0.913300\pi$
$68$	−1.96430e9	−0.163836
$69$	−7.98236e9	−0.614414
$70$	−2.28760e9	−0.162683
$71$	1.17195e10	0.770881	0.385441	−	0.922733i	$-0.374049\pi$
$71$	1.17195e10	0.770881	0.385441	+	0.922733i	$0.374049\pi$
$72$	−1.93492e9	−0.117851
$73$	2.31756e10	1.30845	0.654223	−	0.756302i	$-0.272996\pi$
$73$	2.31756e10	1.30845	0.654223	+	0.756302i	$0.272996\pi$
$74$	−1.82886e10	−0.958087
$75$	−2.37305e9	−0.115470
$76$	−1.65247e9	−0.0747582
$77$	5.92781e9	0.249572
$78$	−1.80672e10	−0.708552
$79$	2.69897e9	0.0986845	0.0493423	−	0.998782i	$-0.484287\pi$
$79$	2.69897e9	0.0986845	0.0493423	+	0.998782i	$0.484287\pi$
$80$	−3.27680e9	−0.111803
$81$	3.48678e9	0.111111
$82$	−2.34900e10	−0.699692
$83$	3.26587e10	0.910059	0.455029	−	0.890476i	$-0.349629\pi$
$83$	3.26587e10	0.910059	0.455029	+	0.890476i	$0.349629\pi$
$84$	5.69228e9	0.148508
$85$	5.99458e9	0.146540
$86$	1.85823e10	0.425949
$87$	−3.70794e10	−0.797586
$88$	8.49111e9	0.171518
$89$	7.45563e10	1.41527	0.707635	−	0.706578i	$-0.249762\pi$
$89$	7.45563e10	1.41527	0.707635	+	0.706578i	$0.249762\pi$
$90$	5.90490e9	0.105409
$91$	5.31515e10	0.892870
$92$	3.36376e10	0.532098
$93$	−1.38048e10	−0.205767
$94$	−1.53231e10	−0.215349
$95$	5.04294e9	0.0668658
$96$	8.15373e9	0.102062
$97$	4.14349e10	0.489916	0.244958	−	0.969534i	$-0.421226\pi$
$97$	4.14349e10	0.489916	0.244958	+	0.969534i	$0.421226\pi$
$98$	4.65285e10	0.519967
$99$	−1.53012e10	−0.161709
$100$	1.00000e10	0.100000
$101$	1.16600e11	1.10391	0.551954	−	0.833875i	$-0.313882\pi$
$101$	1.16600e11	1.10391	0.551954	+	0.833875i	$0.313882\pi$
$102$	−1.49164e10	−0.133772
$103$	4.30231e10	0.365676	0.182838	−	0.983143i	$-0.441472\pi$
$103$	4.30231e10	0.365676	0.182838	+	0.983143i	$0.441472\pi$
$104$	7.61352e10	0.613624
$105$	−1.73715e10	−0.132830
$106$	8.17212e10	0.593134
$107$	−2.15323e11	−1.48416	−0.742078	−	0.670313i	$-0.766160\pi$
$107$	−2.15323e11	−1.48416	−0.742078	+	0.670313i	$0.766160\pi$
$108$	−1.46933e10	−0.0962250
$109$	−2.56069e11	−1.59409	−0.797044	−	0.603922i	$-0.793604\pi$
$109$	−2.56069e11	−1.59409	−0.797044	+	0.603922i	$0.793604\pi$
$110$	−2.59128e10	−0.153410
$111$	−1.38879e11	−0.782275
$112$	−2.39872e10	−0.128612
$113$	1.32713e11	0.677613	0.338807	−	0.940856i	$-0.389977\pi$
$113$	1.32713e11	0.677613	0.338807	+	0.940856i	$0.389977\pi$
$114$	−1.25484e10	−0.0610398
$115$	−1.02654e11	−0.475923
$116$	1.56252e11	0.690729
$117$	−1.37198e11	−0.578530
$118$	−2.02173e11	−0.813529
$119$	4.38823e10	0.168570
$120$	−2.48832e10	−0.0912871
$121$	−2.18164e11	−0.764653
$122$	2.51564e10	0.0842694
$123$	−1.78377e11	−0.571296
$124$	5.81735e10	0.178199
$125$	−3.05176e10	−0.0894427
$126$	4.32258e10	0.121256
$127$	−5.99930e11	−1.61132	−0.805658	−	0.592382i	$-0.798188\pi$
$127$	−5.99930e11	−1.61132	−0.805658	+	0.592382i	$0.798188\pi$
$128$	−3.43597e10	−0.0883883
$129$	1.41109e11	0.347786
$130$	−2.32346e11	−0.548842
$131$	−2.86450e11	−0.648719	−0.324360	−	0.945934i	$-0.605149\pi$
$131$	−2.86450e11	−0.648719	−0.324360	+	0.945934i	$0.605149\pi$
$132$	6.44793e10	0.140044
$133$	3.69159e10	0.0769183
$134$	6.81206e11	1.36208
$135$	4.48403e10	0.0860663
$136$	6.28577e10	0.115850
$137$	−2.68219e11	−0.474817	−0.237408	−	0.971410i	$-0.576298\pi$
$137$	−2.68219e11	−0.474817	−0.237408	+	0.971410i	$0.576298\pi$
$138$	2.55435e11	0.434456
$139$	1.00413e12	1.64138	0.820692	−	0.571371i	$-0.193588\pi$
$139$	1.00413e12	1.64138	0.820692	+	0.571371i	$0.193588\pi$
$140$	7.32032e10	0.115034
$141$	−1.16360e11	−0.175832
$142$	−3.75023e11	−0.545095
$143$	6.02074e11	0.841980
$144$	6.19174e10	0.0833333
$145$	−4.76845e11	−0.617807
$146$	−7.41620e11	−0.925211
$147$	3.53326e11	0.424551
$148$	5.85234e11	0.677470
$149$	6.60408e11	0.736695	0.368348	−	0.929688i	$-0.379924\pi$
$149$	6.60408e11	0.736695	0.368348	+	0.929688i	$0.379924\pi$
$150$	7.59375e10	0.0816497
$151$	1.86615e11	0.193453	0.0967263	−	0.995311i	$-0.469163\pi$
$151$	1.86615e11	0.193453	0.0967263	+	0.995311i	$0.469163\pi$
$152$	5.28790e10	0.0528620
$153$	−1.13272e11	−0.109224
$154$	−1.89690e11	−0.176474
$155$	−1.77531e11	−0.159386
$156$	5.78152e11	0.501022
$157$	4.52456e11	0.378554	0.189277	−	0.981924i	$-0.439386\pi$
$157$	4.52456e11	0.378554	0.189277	+	0.981924i	$0.439386\pi$
$158$	−8.63670e10	−0.0697805
$159$	6.20570e11	0.484292
$160$	1.04858e11	0.0790569
$161$	−7.51458e11	−0.547473
$162$	−1.11577e11	−0.0785674
$163$	1.51667e12	1.03243	0.516213	−	0.856460i	$-0.327341\pi$
$163$	1.51667e12	1.03243	0.516213	+	0.856460i	$0.327341\pi$
$164$	7.51681e11	0.494757
$165$	−1.96775e11	−0.125259
$166$	−1.04508e12	−0.643509
$167$	−2.35061e12	−1.40036	−0.700181	−	0.713965i	$-0.746897\pi$
$167$	−2.35061e12	−1.40036	−0.700181	+	0.713965i	$0.746897\pi$
$168$	−1.82153e11	−0.105011
$169$	3.60632e12	2.01227
$170$	−1.91827e11	−0.103619
$171$	−9.52897e10	−0.0498388
$172$	−5.94633e11	−0.301192
$173$	9.01111e11	0.442104	0.221052	−	0.975262i	$-0.429051\pi$
$173$	9.01111e11	0.442104	0.221052	+	0.975262i	$0.429051\pi$
$174$	1.18654e12	0.563978
$175$	−2.23398e11	−0.102889
$176$	−2.71715e11	−0.121282
$177$	−1.53525e12	−0.664244
$178$	−2.38580e12	−1.00075
$179$	−9.77006e11	−0.397379	−0.198690	−	0.980062i	$-0.563669\pi$
$179$	−9.77006e11	−0.397379	−0.198690	+	0.980062i	$0.563669\pi$
$180$	−1.88957e11	−0.0745356
$181$	3.83020e12	1.46551	0.732756	−	0.680491i	$-0.238234\pi$
$181$	3.83020e12	1.46551	0.732756	+	0.680491i	$0.238234\pi$
$182$	−1.70085e12	−0.631354
$183$	1.91032e11	0.0688057
$184$	−1.07640e12	−0.376250
$185$	−1.78599e12	−0.605947
$186$	4.41755e11	0.145499
$187$	4.97076e11	0.158962
$188$	4.90339e11	0.152275
$189$	3.28246e11	0.0990054
$190$	−1.61374e11	−0.0472812
$191$	−2.49694e12	−0.710764	−0.355382	−	0.934721i	$-0.615649\pi$
$191$	−2.49694e12	−0.710764	−0.355382	+	0.934721i	$0.615649\pi$
$192$	−2.60919e11	−0.0721688
$193$	5.19794e12	1.39722	0.698612	−	0.715500i	$-0.253801\pi$
$193$	5.19794e12	1.39722	0.698612	+	0.715500i	$0.253801\pi$
$194$	−1.32592e12	−0.346423
$195$	−1.76438e12	−0.448127
$196$	−1.48891e12	−0.367672
$197$	−5.70399e12	−1.36967	−0.684833	−	0.728700i	$-0.740125\pi$
$197$	−5.70399e12	−1.36967	−0.684833	+	0.728700i	$0.740125\pi$
$198$	4.89640e11	0.114345
$199$	−6.39817e11	−0.145333	−0.0726664	−	0.997356i	$-0.523151\pi$
$199$	−6.39817e11	−0.145333	−0.0726664	+	0.997356i	$0.523151\pi$
$200$	−3.20000e11	−0.0707107
$201$	5.17291e12	1.11213
$202$	−3.73122e12	−0.780581
$203$	−3.49066e12	−0.710688
$204$	4.77326e11	0.0945909
$205$	−2.29395e12	−0.442524
$206$	−1.37674e12	−0.258572
$207$	1.93971e12	0.354732
$208$	−2.43633e12	−0.433897
$209$	4.18165e11	0.0725343
$210$	5.55887e11	0.0939248
$211$	2.47025e12	0.406618	0.203309	−	0.979115i	$-0.434830\pi$
$211$	2.47025e12	0.406618	0.203309	+	0.979115i	$0.434830\pi$
$212$	−2.61508e12	−0.419409
$213$	−2.84783e12	−0.445068
$214$	6.89034e12	1.04946
$215$	1.81468e12	0.269394
$216$	4.70185e11	0.0680414
$217$	−1.29959e12	−0.183348
$218$	8.19422e12	1.12719
$219$	−5.63168e12	−0.755432
$220$	8.29210e11	0.108477
$221$	4.45702e12	0.568705
$222$	4.44412e12	0.553152
$223$	−5.26711e12	−0.639581	−0.319790	−	0.947488i	$-0.603613\pi$
$223$	−5.26711e12	−0.639581	−0.319790	+	0.947488i	$0.603613\pi$
$224$	7.67591e11	0.0909423
$225$	5.76650e11	0.0666667
$226$	−4.24682e12	−0.479145
$227$	−1.14447e13	−1.26027	−0.630133	−	0.776488i	$-0.716999\pi$
$227$	−1.14447e13	−1.26027	−0.630133	+	0.776488i	$0.716999\pi$
$228$	4.01550e11	0.0431617
$229$	3.62497e12	0.380372	0.190186	−	0.981748i	$-0.439091\pi$
$229$	3.62497e12	0.380372	0.190186	+	0.981748i	$0.439091\pi$
$230$	3.28492e12	0.336528
$231$	−1.44046e12	−0.144090
$232$	−5.00008e12	−0.488419
$233$	1.44062e13	1.37433	0.687165	−	0.726501i	$-0.258855\pi$
$233$	1.44062e13	1.37433	0.687165	+	0.726501i	$0.258855\pi$
$234$	4.39034e12	0.409082
$235$	−1.49640e12	−0.136199
$236$	6.46955e12	0.575252
$237$	−6.55850e11	−0.0569755
$238$	−1.40423e12	−0.119197
$239$	−1.33198e13	−1.10487	−0.552433	−	0.833557i	$-0.686301\pi$
$239$	−1.33198e13	−1.10487	−0.552433	+	0.833557i	$0.686301\pi$
$240$	7.96262e11	0.0645497
$241$	1.13769e13	0.901428	0.450714	−	0.892668i	$-0.351169\pi$
$241$	1.13769e13	0.901428	0.450714	+	0.892668i	$0.351169\pi$
$242$	6.98126e12	0.540691
$243$	−8.47289e11	−0.0641500
$244$	−8.05005e11	−0.0595874
$245$	4.54380e12	0.328856
$246$	5.70807e12	0.403968
$247$	3.74946e12	0.259499
$248$	−1.86155e12	−0.126006
$249$	−7.93607e12	−0.525423
$250$	9.76562e11	0.0632456
$251$	−2.83662e12	−0.179719	−0.0898597	−	0.995954i	$-0.528642\pi$
$251$	−2.83662e12	−0.179719	−0.0898597	+	0.995954i	$0.528642\pi$
$252$	−1.38322e12	−0.0857412
$253$	−8.51215e12	−0.516269
$254$	1.91978e13	1.13937
$255$	−1.45668e12	−0.0846046
$256$	1.09951e12	0.0625000
$257$	3.01443e13	1.67715	0.838576	−	0.544784i	$-0.183388\pi$
$257$	3.01443e13	1.67715	0.838576	+	0.544784i	$0.183388\pi$
$258$	−4.51550e12	−0.245922
$259$	−1.30740e13	−0.697045
$260$	7.43508e12	0.388090
$261$	9.01030e12	0.460486
$262$	9.16641e12	0.458714
$263$	3.80917e13	1.86670	0.933349	−	0.358971i	$-0.116872\pi$
$263$	3.80917e13	1.86670	0.933349	+	0.358971i	$0.116872\pi$
$264$	−2.06334e12	−0.0990259
$265$	7.98059e12	0.375131
$266$	−1.18131e12	−0.0543894
$267$	−1.81172e13	−0.817107
$268$	−2.17986e13	−0.963135
$269$	2.00988e12	0.0870026	0.0435013	−	0.999053i	$-0.486149\pi$
$269$	2.00988e12	0.0870026	0.0435013	+	0.999053i	$0.486149\pi$
$270$	−1.43489e12	−0.0608581
$271$	−3.06081e13	−1.27205	−0.636027	−	0.771667i	$-0.719423\pi$
$271$	−3.06081e13	−1.27205	−0.636027	+	0.771667i	$0.719423\pi$
$272$	−2.01145e12	−0.0819181
$273$	−1.29158e13	−0.515498
$274$	8.58300e12	0.335746
$275$	−2.53055e12	−0.0970252
$276$	−8.17393e12	−0.307207
$277$	2.77790e13	1.02348	0.511738	−	0.859142i	$-0.329002\pi$
$277$	2.77790e13	1.02348	0.511738	+	0.859142i	$0.329002\pi$
$278$	−3.21323e13	−1.16063
$279$	3.35458e12	0.118800
$280$	−2.34250e12	−0.0813413
$281$	−3.95175e13	−1.34557	−0.672783	−	0.739840i	$-0.734901\pi$
$281$	−3.95175e13	−1.34557	−0.672783	+	0.739840i	$0.734901\pi$
$282$	3.72351e12	0.124332
$283$	−3.57563e13	−1.17092	−0.585460	−	0.810701i	$-0.699086\pi$
$283$	−3.57563e13	−1.17092	−0.585460	+	0.810701i	$0.699086\pi$
$284$	1.20007e13	0.385441
$285$	−1.22543e12	−0.0386050
$286$	−1.92664e13	−0.595370
$287$	−1.67924e13	−0.509053
$288$	−1.98136e12	−0.0589256
$289$	−3.05922e13	−0.892631
$290$	1.52590e13	0.436856
$291$	−1.00687e13	−0.282853
$292$	2.37318e13	0.654223
$293$	1.16731e13	0.315801	0.157901	−	0.987455i	$-0.449527\pi$
$293$	1.16731e13	0.315801	0.157901	+	0.987455i	$0.449527\pi$
$294$	−1.13064e13	−0.300203
$295$	−1.97435e13	−0.514521
$296$	−1.87275e13	−0.479043
$297$	3.71820e12	0.0933625
$298$	−2.11331e13	−0.520922
$299$	−7.63239e13	−1.84701
$300$	−2.43000e12	−0.0577350
$301$	1.32840e13	0.309894
$302$	−5.97169e12	−0.136792
$303$	−2.83339e13	−0.637342
$304$	−1.69213e12	−0.0373791
$305$	2.45668e12	0.0532966
$306$	3.62469e12	0.0772331
$307$	8.98114e13	1.87962	0.939811	−	0.341695i	$-0.111001\pi$
$307$	8.98114e13	1.87962	0.939811	+	0.341695i	$0.111001\pi$
$308$	6.07008e12	0.124786
$309$	−1.04546e13	−0.211123
$310$	5.68101e12	0.112703
$311$	6.75879e13	1.31731	0.658653	−	0.752446i	$-0.271126\pi$
$311$	6.75879e13	1.31731	0.658653	+	0.752446i	$0.271126\pi$
$312$	−1.85009e13	−0.354276
$313$	9.87171e13	1.85737	0.928685	−	0.370869i	$-0.120940\pi$
$313$	9.87171e13	1.85737	0.928685	+	0.370869i	$0.120940\pi$
$314$	−1.44786e13	−0.267678
$315$	4.22127e12	0.0766893
$316$	2.76374e12	0.0493423
$317$	1.10523e14	1.93921	0.969605	−	0.244674i	$-0.0786811\pi$
$317$	1.10523e14	1.93921	0.969605	+	0.244674i	$0.0786811\pi$
$318$	−1.98583e13	−0.342446
$319$	−3.95404e13	−0.670182
$320$	−3.35544e12	−0.0559017
$321$	5.23235e13	0.856878
$322$	2.40467e13	0.387122
$323$	3.09558e12	0.0489924
$324$	3.57047e12	0.0555556
$325$	−2.26901e13	−0.347118
$326$	−4.85334e13	−0.730036
$327$	6.22249e13	0.920347
$328$	−2.40538e13	−0.349846
$329$	−1.09541e13	−0.156675
$330$	6.29681e12	0.0885715
$331$	−5.00155e13	−0.691912	−0.345956	−	0.938251i	$-0.612445\pi$
$331$	−5.00155e13	−0.691912	−0.345956	+	0.938251i	$0.612445\pi$
$332$	3.34425e13	0.455029
$333$	3.37475e13	0.451647
$334$	7.52196e13	0.990205
$335$	6.65240e13	0.861454
$336$	5.82890e12	0.0742541
$337$	−3.62478e12	−0.0454274	−0.0227137	−	0.999742i	$-0.507231\pi$
$337$	−3.62478e12	−0.0454274	−0.0227137	+	0.999742i	$0.507231\pi$
$338$	−1.15402e14	−1.42289
$339$	−3.22493e13	−0.391220
$340$	6.13845e12	0.0732698
$341$	−1.47211e13	−0.172898
$342$	3.04927e12	0.0352413
$343$	7.84954e13	0.892743
$344$	1.90283e13	0.212975
$345$	2.49449e13	0.274774
$346$	−2.88355e13	−0.312615
$347$	6.56058e12	0.0700051	0.0350026	−	0.999387i	$-0.488856\pi$
$347$	6.56058e12	0.0700051	0.0350026	+	0.999387i	$0.488856\pi$
$348$	−3.79693e13	−0.398793
$349$	−8.14353e13	−0.841924	−0.420962	−	0.907078i	$-0.638307\pi$
$349$	−8.14353e13	−0.841924	−0.420962	+	0.907078i	$0.638307\pi$
$350$	7.14875e12	0.0727538
$351$	3.33391e13	0.334014
$352$	8.69489e12	0.0857590
$353$	1.03792e14	1.00787	0.503934	−	0.863742i	$-0.331885\pi$
$353$	1.03792e14	1.00787	0.503934	+	0.863742i	$0.331885\pi$
$354$	4.91281e13	0.469691
$355$	−3.66234e13	−0.344749
$356$	7.63457e13	0.707635
$357$	−1.06634e13	−0.0973240
$358$	3.12642e13	0.280990
$359$	−1.38258e14	−1.22369	−0.611845	−	0.790978i	$-0.709572\pi$
$359$	−1.38258e14	−1.22369	−0.611845	+	0.790978i	$0.709572\pi$
$360$	6.04662e12	0.0527046
$361$	−1.13886e14	−0.977645
$362$	−1.22566e14	−1.03627
$363$	5.30139e13	0.441472
$364$	5.44272e13	0.446435
$365$	−7.24239e13	−0.585155
$366$	−6.11301e12	−0.0486529
$367$	1.16357e14	0.912282	0.456141	−	0.889908i	$-0.349231\pi$
$367$	1.16357e14	0.912282	0.456141	+	0.889908i	$0.349231\pi$
$368$	3.44449e13	0.266049
$369$	4.33457e13	0.329838
$370$	5.71517e13	0.428470
$371$	5.84205e13	0.431527
$372$	−1.41362e13	−0.102883
$373$	−6.72186e13	−0.482049	−0.241024	−	0.970519i	$-0.577483\pi$
$373$	−6.72186e13	−0.482049	−0.241024	+	0.970519i	$0.577483\pi$
$374$	−1.59064e13	−0.112403
$375$	7.41577e12	0.0516398
$376$	−1.56908e13	−0.107675
$377$	−3.54538e14	−2.39765
$378$	−1.05039e13	−0.0700074
$379$	−1.32840e14	−0.872598	−0.436299	−	0.899802i	$-0.643711\pi$
$379$	−1.32840e14	−0.872598	−0.436299	+	0.899802i	$0.643711\pi$
$380$	5.16397e12	0.0334329
$381$	1.45783e14	0.930293
$382$	7.99022e13	0.502586
$383$	−2.69810e14	−1.67288	−0.836439	−	0.548060i	$-0.815367\pi$
$383$	−2.69810e14	−1.67288	−0.836439	+	0.548060i	$0.815367\pi$
$384$	8.34942e12	0.0510310
$385$	−1.85244e13	−0.111612
$386$	−1.66334e14	−0.987987
$387$	−3.42896e13	−0.200794
$388$	4.24293e13	0.244958
$389$	9.81084e13	0.558449	0.279224	−	0.960226i	$-0.409923\pi$
$389$	9.81084e13	0.558449	0.279224	+	0.960226i	$0.409923\pi$
$390$	5.64601e13	0.316874
$391$	−6.30135e13	−0.348708
$392$	4.76452e13	0.259983
$393$	6.96074e13	0.374538
$394$	1.82528e14	0.968500
$395$	−8.43428e12	−0.0441331
$396$	−1.56685e13	−0.0808543
$397$	−6.44136e13	−0.327816	−0.163908	−	0.986476i	$-0.552410\pi$
$397$	−6.44136e13	−0.327816	−0.163908	+	0.986476i	$0.552410\pi$
$398$	2.04741e13	0.102766
$399$	−8.97057e12	−0.0444088
$400$	1.02400e13	0.0500000
$401$	2.05799e14	0.991172	0.495586	−	0.868559i	$-0.334953\pi$
$401$	2.05799e14	0.991172	0.495586	+	0.868559i	$0.334953\pi$
$402$	−1.65533e14	−0.786396
$403$	−1.31996e14	−0.618562
$404$	1.19399e14	0.551954
$405$	−1.08962e13	−0.0496904
$406$	1.11701e14	0.502532
$407$	−1.48096e14	−0.657316
$408$	−1.52744e13	−0.0668858
$409$	5.95615e13	0.257328	0.128664	−	0.991688i	$-0.458931\pi$
$409$	5.95615e13	0.257328	0.128664	+	0.991688i	$0.458931\pi$
$410$	7.34063e13	0.312912
$411$	6.51772e13	0.274136
$412$	4.40556e13	0.182838
$413$	−1.44529e14	−0.591874
$414$	−6.20708e13	−0.250834
$415$	−1.02058e14	−0.406991
$416$	7.79624e13	0.306812
$417$	−2.44004e14	−0.947653
$418$	−1.33813e13	−0.0512895
$419$	−8.26291e13	−0.312576	−0.156288	−	0.987712i	$-0.549953\pi$
$419$	−8.26291e13	−0.312576	−0.156288	+	0.987712i	$0.549953\pi$
$420$	−1.77884e13	−0.0664149
$421$	−1.55708e14	−0.573800	−0.286900	−	0.957961i	$-0.592625\pi$
$421$	−1.55708e14	−0.573800	−0.286900	+	0.957961i	$0.592625\pi$
$422$	−7.90479e13	−0.287523
$423$	2.82754e13	0.101517
$424$	8.36825e13	0.296567
$425$	−1.87331e13	−0.0655345
$426$	9.11307e13	0.314711
$427$	1.79837e13	0.0613092
$428$	−2.20491e14	−0.742078
$429$	−1.46304e14	−0.486117
$430$	−5.80697e13	−0.190490
$431$	4.40261e14	1.42589	0.712944	−	0.701221i	$-0.247361\pi$
$431$	4.40261e14	1.42589	0.712944	+	0.701221i	$0.247361\pi$
$432$	−1.50459e13	−0.0481125
$433$	3.21850e14	1.01618	0.508089	−	0.861304i	$-0.330352\pi$
$433$	3.21850e14	1.01618	0.508089	+	0.861304i	$0.330352\pi$
$434$	4.15868e13	0.129647
$435$	1.15873e14	0.356691
$436$	−2.62215e14	−0.797044
$437$	−5.30101e13	−0.159115
$438$	1.80214e14	0.534171
$439$	6.53476e14	1.91282	0.956411	−	0.292025i	$-0.0943289\pi$
$439$	6.53476e14	1.91282	0.956411	+	0.292025i	$0.0943289\pi$
$440$	−2.65347e13	−0.0767052
$441$	−8.58582e13	−0.245115
$442$	−1.42625e14	−0.402135
$443$	5.50129e14	1.53195	0.765974	−	0.642872i	$-0.222257\pi$
$443$	5.50129e14	1.53195	0.765974	+	0.642872i	$0.222257\pi$
$444$	−1.42212e14	−0.391137
$445$	−2.32989e14	−0.632928
$446$	1.68547e14	0.452252
$447$	−1.60479e14	−0.425331
$448$	−2.45629e13	−0.0643059
$449$	2.56147e13	0.0662421	0.0331210	−	0.999451i	$-0.489455\pi$
$449$	2.56147e13	0.0662421	0.0331210	+	0.999451i	$0.489455\pi$
$450$	−1.84528e13	−0.0471405
$451$	−1.90216e14	−0.480039
$452$	1.35898e14	0.338807
$453$	−4.53476e13	−0.111690
$454$	3.66230e14	0.891142
$455$	−1.66098e14	−0.399303
$456$	−1.28496e13	−0.0305199
$457$	1.73882e13	0.0408052	0.0204026	−	0.999792i	$-0.493505\pi$
$457$	1.73882e13	0.0408052	0.0204026	+	0.999792i	$0.493505\pi$
$458$	−1.15999e14	−0.268964
$459$	2.75250e13	0.0630606
$460$	−1.05117e14	−0.237962
$461$	7.61820e14	1.70411	0.852055	−	0.523453i	$-0.175356\pi$
$461$	7.61820e14	1.70411	0.852055	+	0.523453i	$0.175356\pi$
$462$	4.60947e13	0.101887
$463$	3.88545e14	0.848684	0.424342	−	0.905502i	$-0.360505\pi$
$463$	3.88545e14	0.848684	0.424342	+	0.905502i	$0.360505\pi$
$464$	1.60003e14	0.345365
$465$	4.31401e13	0.0920217
$466$	−4.60998e14	−0.971799
$467$	1.22217e14	0.254618	0.127309	−	0.991863i	$-0.459366\pi$
$467$	1.22217e14	0.254618	0.127309	+	0.991863i	$0.459366\pi$
$468$	−1.40491e14	−0.289265
$469$	4.86977e14	0.990964
$470$	4.78847e13	0.0963071
$471$	−1.09947e14	−0.218558
$472$	−2.07026e14	−0.406765
$473$	1.50475e14	0.292232
$474$	2.09872e13	0.0402878
$475$	−1.57592e13	−0.0299033
$476$	4.49354e13	0.0842851
$477$	−1.50799e14	−0.279606
$478$	4.26234e14	0.781259
$479$	4.35912e14	0.789866	0.394933	−	0.918710i	$-0.370768\pi$
$479$	4.35912e14	0.789866	0.394933	+	0.918710i	$0.370768\pi$
$480$	−2.54804e13	−0.0456435
$481$	−1.32790e15	−2.35162
$482$	−3.64061e14	−0.637406
$483$	1.82604e14	0.316084
$484$	−2.23400e14	−0.382326
$485$	−1.29484e14	−0.219097
$486$	2.71132e13	0.0453609
$487$	6.66191e14	1.10202	0.551010	−	0.834499i	$-0.314243\pi$
$487$	6.66191e14	1.10202	0.551010	+	0.834499i	$0.314243\pi$
$488$	2.57602e13	0.0421347
$489$	−3.68551e14	−0.596072
$490$	−1.45402e14	−0.232536
$491$	2.23817e13	0.0353953	0.0176976	−	0.999843i	$-0.494366\pi$
$491$	2.23817e13	0.0353953	0.0176976	+	0.999843i	$0.494366\pi$
$492$	−1.82658e14	−0.285648
$493$	−2.92709e14	−0.452666
$494$	−1.19983e14	−0.183494
$495$	4.78164e13	0.0723183
$496$	5.95697e13	0.0890997
$497$	−2.68095e14	−0.396578
$498$	2.53954e14	0.371530
$499$	−4.87506e13	−0.0705386	−0.0352693	−	0.999378i	$-0.511229\pi$
$499$	−4.87506e13	−0.0705386	−0.0352693	+	0.999378i	$0.511229\pi$
$500$	−3.12500e13	−0.0447214
$501$	5.71199e14	0.808499
$502$	9.07717e13	0.127081
$503$	2.64333e14	0.366039	0.183019	−	0.983109i	$-0.441413\pi$
$503$	2.64333e14	0.366039	0.183019	+	0.983109i	$0.441413\pi$
$504$	4.42632e13	0.0606282
$505$	−3.64377e14	−0.493683
$506$	2.72389e14	0.365058
$507$	−8.76335e14	−1.16179
$508$	−6.14329e14	−0.805658
$509$	8.09106e13	0.104968	0.0524841	−	0.998622i	$-0.483286\pi$
$509$	8.09106e13	0.104968	0.0524841	+	0.998622i	$0.483286\pi$
$510$	4.66139e13	0.0598245
$511$	−5.30166e14	−0.673127
$512$	−3.51844e13	−0.0441942
$513$	2.31554e13	0.0287744
$514$	−9.64617e14	−1.18593
$515$	−1.34447e14	−0.163535
$516$	1.44496e14	0.173893
$517$	−1.24083e14	−0.147745
$518$	4.18369e14	0.492885
$519$	−2.18970e14	−0.255249
$520$	−2.37923e14	−0.274421
$521$	−1.10833e14	−0.126491	−0.0632456	−	0.997998i	$-0.520145\pi$
$521$	−1.10833e14	−0.126491	−0.0632456	+	0.997998i	$0.520145\pi$
$522$	−2.88330e14	−0.325613
$523$	6.91114e14	0.772308	0.386154	−	0.922434i	$-0.373803\pi$
$523$	6.91114e14	0.772308	0.386154	+	0.922434i	$0.373803\pi$
$524$	−2.93325e14	−0.324360
$525$	5.42858e13	0.0594033
$526$	−1.21894e15	−1.31995
$527$	−1.08977e14	−0.116782
$528$	6.60268e13	0.0700219
$529$	1.26261e14	0.132514
$530$	−2.55379e14	−0.265257
$531$	3.73067e14	0.383501
$532$	3.78019e13	0.0384591
$533$	−1.70557e15	−1.71739
$534$	5.79750e14	0.577782
$535$	6.72884e14	0.663735
$536$	6.97555e14	0.681039
$537$	2.37412e14	0.229427
$538$	−6.43161e13	−0.0615201
$539$	3.76776e14	0.356735
$540$	4.59165e13	0.0430331
$541$	−2.02808e15	−1.88148	−0.940741	−	0.339125i	$-0.889869\pi$
$541$	−2.02808e15	−1.88148	−0.940741	+	0.339125i	$0.889869\pi$
$542$	9.79460e14	0.899478
$543$	−9.30739e14	−0.846114
$544$	6.43663e13	0.0579248
$545$	8.00217e14	0.712897
$546$	4.13306e14	0.364512
$547$	2.06348e15	1.80165	0.900826	−	0.434180i	$-0.142962\pi$
$547$	2.06348e15	1.80165	0.900826	+	0.434180i	$0.142962\pi$
$548$	−2.74656e14	−0.237408
$549$	−4.64207e13	−0.0397250
$550$	8.09775e13	0.0686072
$551$	−2.46241e14	−0.206551
$552$	2.61566e14	0.217228
$553$	−6.17416e13	−0.0507680
$554$	−8.88927e14	−0.723707
$555$	4.33996e14	0.349844
$556$	1.02823e15	0.820692
$557$	−2.11828e15	−1.67409	−0.837047	−	0.547130i	$-0.815720\pi$
$557$	−2.11828e15	−1.67409	−0.837047	+	0.547130i	$0.815720\pi$
$558$	−1.07346e14	−0.0840040
$559$	1.34923e15	1.04549
$560$	7.49601e13	0.0575170
$561$	−1.20790e14	−0.0917770
$562$	1.26456e15	0.951458
$563$	−1.16211e15	−0.865870	−0.432935	−	0.901425i	$-0.642522\pi$
$563$	−1.16211e15	−0.865870	−0.432935	+	0.901425i	$0.642522\pi$
$564$	−1.19152e14	−0.0879159
$565$	−4.14728e14	−0.303038
$566$	1.14420e15	0.827965
$567$	−7.97637e13	−0.0571608
$568$	−3.84024e14	−0.272548
$569$	1.19782e15	0.841927	0.420964	−	0.907077i	$-0.361692\pi$
$569$	1.19782e15	0.841927	0.420964	+	0.907077i	$0.361692\pi$
$570$	3.92139e13	0.0272978
$571$	1.46355e15	1.00904	0.504522	−	0.863399i	$-0.331669\pi$
$571$	1.46355e15	1.00904	0.504522	+	0.863399i	$0.331669\pi$
$572$	6.16524e14	0.420990
$573$	6.06757e14	0.410360
$574$	5.37358e14	0.359955
$575$	3.20793e14	0.212839
$576$	6.34034e13	0.0416667
$577$	1.97111e15	1.28305	0.641526	−	0.767101i	$-0.278302\pi$
$577$	1.97111e15	1.28305	0.641526	+	0.767101i	$0.278302\pi$
$578$	9.78949e14	0.631185
$579$	−1.26310e15	−0.806688
$580$	−4.88289e14	−0.308904
$581$	−7.47101e14	−0.468177
$582$	3.22198e14	0.200007
$583$	6.61758e14	0.406932
$584$	−7.59419e14	−0.462606
$585$	4.28744e14	0.258726
$586$	−3.73539e14	−0.223305
$587$	3.58593e14	0.212369	0.106185	−	0.994346i	$-0.466137\pi$
$587$	3.58593e14	0.212369	0.106185	+	0.994346i	$0.466137\pi$
$588$	3.61806e14	0.212276
$589$	−9.16767e13	−0.0532874
$590$	6.31792e14	0.363821
$591$	1.38607e15	0.790777
$592$	5.99279e14	0.338735
$593$	−1.43925e15	−0.806003	−0.403001	−	0.915199i	$-0.632033\pi$
$593$	−1.43925e15	−0.806003	−0.403001	+	0.915199i	$0.632033\pi$
$594$	−1.18983e14	−0.0660173
$595$	−1.37132e14	−0.0753869
$596$	6.76258e14	0.368348
$597$	1.55475e14	0.0839079
$598$	2.44236e15	1.30603
$599$	−3.41497e15	−1.80942	−0.904710	−	0.426028i	$-0.859912\pi$
$599$	−3.41497e15	−1.80942	−0.904710	+	0.426028i	$0.859912\pi$
$600$	7.77600e13	0.0408248
$601$	2.49987e15	1.30049	0.650245	−	0.759725i	$-0.274666\pi$
$601$	2.49987e15	1.30049	0.650245	+	0.759725i	$0.274666\pi$
$602$	−4.25089e14	−0.219128
$603$	−1.25702e15	−0.642090
$604$	1.91094e14	0.0967263
$605$	6.81764e14	0.341963
$606$	9.06685e14	0.450669
$607$	−2.34097e13	−0.0115308	−0.00576538	−	0.999983i	$-0.501835\pi$
$607$	−2.34097e13	−0.0115308	−0.00576538	+	0.999983i	$0.501835\pi$
$608$	5.41481e13	0.0264310
$609$	8.48229e14	0.410316
$610$	−7.86138e13	−0.0376864
$611$	−1.11258e15	−0.528573
$612$	−1.15990e14	−0.0546121
$613$	−1.82595e15	−0.852032	−0.426016	−	0.904716i	$-0.640083\pi$
$613$	−1.82595e15	−0.852032	−0.426016	+	0.904716i	$0.640083\pi$
$614$	−2.87397e15	−1.32909
$615$	5.57429e14	0.255492
$616$	−1.94243e14	−0.0882369
$617$	−9.58777e14	−0.431667	−0.215834	−	0.976430i	$-0.569247\pi$
$617$	−9.58777e14	−0.431667	−0.215834	+	0.976430i	$0.569247\pi$
$618$	3.34548e14	0.149287
$619$	−6.16431e13	−0.0272638	−0.0136319	−	0.999907i	$-0.504339\pi$
$619$	−6.16431e13	−0.0272638	−0.0136319	+	0.999907i	$0.504339\pi$
$620$	−1.81792e14	−0.0796932
$621$	−4.71350e14	−0.204805
$622$	−2.16281e15	−0.931477
$623$	−1.70555e15	−0.728082
$624$	5.92027e14	0.250511
$625$	9.53674e13	0.0400000
$626$	−3.15895e15	−1.31336
$627$	−1.01614e14	−0.0418777
$628$	4.63315e14	0.189277
$629$	−1.09632e15	−0.443976
$630$	−1.35080e14	−0.0542275
$631$	−3.38937e15	−1.34883	−0.674416	−	0.738352i	$-0.735604\pi$
$631$	−3.38937e15	−1.34883	−0.674416	+	0.738352i	$0.735604\pi$
$632$	−8.84398e13	−0.0348902
$633$	−6.00270e14	−0.234761
$634$	−3.53672e15	−1.37123
$635$	1.87478e15	0.720602
$636$	6.35464e14	0.242146
$637$	3.37835e15	1.27626
$638$	1.26529e15	0.473890
$639$	6.92024e14	0.256960
$640$	1.07374e14	0.0395285
$641$	2.53363e15	0.924749	0.462375	−	0.886685i	$-0.346998\pi$
$641$	2.53363e15	0.924749	0.462375	+	0.886685i	$0.346998\pi$
$642$	−1.67435e15	−0.605904
$643$	−4.33651e15	−1.55589	−0.777946	−	0.628331i	$-0.783739\pi$
$643$	−4.33651e15	−1.55589	−0.777946	+	0.628331i	$0.783739\pi$
$644$	−7.69493e14	−0.273736
$645$	−4.40966e14	−0.155535
$646$	−9.90586e13	−0.0346428
$647$	−1.86323e15	−0.646090	−0.323045	−	0.946384i	$-0.604706\pi$
$647$	−1.86323e15	−0.646090	−0.323045	+	0.946384i	$0.604706\pi$
$648$	−1.14255e14	−0.0392837
$649$	−1.63715e15	−0.558139
$650$	7.26082e14	0.245449
$651$	3.15800e14	0.105856
$652$	1.55307e15	0.516213
$653$	5.87157e15	1.93523	0.967613	−	0.252440i	$-0.0812329\pi$
$653$	5.87157e15	1.93523	0.967613	+	0.252440i	$0.0812329\pi$
$654$	−1.99120e15	−0.650783
$655$	8.95157e14	0.290116
$656$	7.69721e14	0.247379
$657$	1.36850e15	0.436149
$658$	3.50531e14	0.110786
$659$	−1.57270e14	−0.0492920	−0.0246460	−	0.999696i	$-0.507846\pi$
$659$	−1.57270e14	−0.0492920	−0.0246460	+	0.999696i	$0.507846\pi$
$660$	−2.01498e14	−0.0626295
$661$	−4.86756e15	−1.50039	−0.750193	−	0.661219i	$-0.770039\pi$
$661$	−4.86756e15	−1.50039	−0.750193	+	0.661219i	$0.770039\pi$
$662$	1.60050e15	0.489256
$663$	−1.08306e15	−0.328342
$664$	−1.07016e15	−0.321754
$665$	−1.15362e14	−0.0343989
$666$	−1.07992e15	−0.319362
$667$	5.01247e15	1.47014
$668$	−2.40703e15	−0.700181
$669$	1.27991e15	0.369262
$670$	−2.12877e15	−0.609140
$671$	2.03710e14	0.0578148
$672$	−1.86525e14	−0.0525056
$673$	−5.94031e14	−0.165854	−0.0829270	−	0.996556i	$-0.526427\pi$
$673$	−5.94031e14	−0.165854	−0.0829270	+	0.996556i	$0.526427\pi$
$674$	1.15993e14	0.0321220
$675$	−1.40126e14	−0.0384900
$676$	3.69287e15	1.00614
$677$	3.03615e15	0.820513	0.410257	−	0.911970i	$-0.365439\pi$
$677$	3.03615e15	0.820513	0.410257	+	0.911970i	$0.365439\pi$
$678$	1.03198e15	0.276635
$679$	−9.47864e14	−0.252036
$680$	−1.96430e14	−0.0518095
$681$	2.78106e15	0.727615
$682$	4.71075e14	0.122258
$683$	2.38176e15	0.613174	0.306587	−	0.951843i	$-0.400813\pi$
$683$	2.38176e15	0.613174	0.306587	+	0.951843i	$0.400813\pi$
$684$	−9.75767e13	−0.0249194
$685$	8.38184e14	0.212345
$686$	−2.51185e15	−0.631265
$687$	−8.80867e14	−0.219608
$688$	−6.08905e14	−0.150596
$689$	5.93363e15	1.45584
$690$	−7.98236e14	−0.194295
$691$	1.02015e15	0.246339	0.123170	−	0.992386i	$-0.460694\pi$
$691$	1.02015e15	0.246339	0.123170	+	0.992386i	$0.460694\pi$
$692$	9.22737e14	0.221052
$693$	3.50031e14	0.0831906
$694$	−2.09938e14	−0.0495011
$695$	−3.13792e15	−0.734049
$696$	1.21502e15	0.281989
$697$	−1.40813e15	−0.324237
$698$	2.60593e15	0.595330
$699$	−3.50070e15	−0.793470
$700$	−2.28760e14	−0.0514447
$701$	−9.47724e14	−0.211462	−0.105731	−	0.994395i	$-0.533718\pi$
$701$	−9.47724e14	−0.211462	−0.105731	+	0.994395i	$0.533718\pi$
$702$	−1.06685e15	−0.236184
$703$	−9.22280e14	−0.202586
$704$	−2.78237e14	−0.0606408
$705$	3.63624e14	0.0786344
$706$	−3.32135e15	−0.712671
$707$	−2.66735e15	−0.567902
$708$	−1.57210e15	−0.332122
$709$	1.41385e15	0.296380	0.148190	−	0.988959i	$-0.452655\pi$
$709$	1.41385e15	0.296380	0.148190	+	0.988959i	$0.452655\pi$
$710$	1.17195e15	0.243774
$711$	1.59371e14	0.0328948
$712$	−2.44306e15	−0.500374
$713$	1.86617e15	0.379278
$714$	3.41228e14	0.0688185
$715$	−1.88148e15	−0.376545
$716$	−1.00045e15	−0.198690
$717$	3.23672e15	0.637895
$718$	4.42426e15	0.865280
$719$	7.85082e15	1.52372	0.761862	−	0.647739i	$-0.224285\pi$
$719$	7.85082e15	1.52372	0.761862	+	0.647739i	$0.224285\pi$
$720$	−1.93492e14	−0.0372678
$721$	−9.84196e14	−0.188121
$722$	3.64436e15	0.691299
$723$	−2.76459e15	−0.520440
$724$	3.92213e15	0.732756
$725$	1.49014e15	0.276292
$726$	−1.69645e15	−0.312168
$727$	−6.17476e15	−1.12767	−0.563833	−	0.825889i	$-0.690674\pi$
$727$	−6.17476e15	−1.12767	−0.563833	+	0.825889i	$0.690674\pi$
$728$	−1.74167e15	−0.315677
$729$	2.05891e14	0.0370370
$730$	2.31756e15	0.413767
$731$	1.11393e15	0.197384
$732$	1.95616e14	0.0344028
$733$	−7.25819e15	−1.26694	−0.633471	−	0.773767i	$-0.718370\pi$
$733$	−7.25819e15	−1.26694	−0.633471	+	0.773767i	$0.718370\pi$
$734$	−3.72342e15	−0.645081
$735$	−1.10414e15	−0.189865
$736$	−1.10224e15	−0.188125
$737$	5.51623e15	0.934483
$738$	−1.38706e15	−0.233231
$739$	1.04737e16	1.74806	0.874030	−	0.485872i	$-0.161498\pi$
$739$	1.04737e16	1.74806	0.874030	+	0.485872i	$0.161498\pi$
$740$	−1.82886e15	−0.302974
$741$	−9.11120e14	−0.149822
$742$	−1.86945e15	−0.305136
$743$	2.62290e15	0.424956	0.212478	−	0.977166i	$-0.431847\pi$
$743$	2.62290e15	0.424956	0.212478	+	0.977166i	$0.431847\pi$
$744$	4.52357e14	0.0727496
$745$	−2.06377e15	−0.329460
$746$	2.15099e15	0.340860
$747$	1.92846e15	0.303353
$748$	5.09006e14	0.0794812
$749$	4.92573e15	0.763520
$750$	−2.37305e14	−0.0365148
$751$	3.09275e15	0.472417	0.236208	−	0.971702i	$-0.424095\pi$
$751$	3.09275e15	0.472417	0.236208	+	0.971702i	$0.424095\pi$
$752$	5.02107e14	0.0761374
$753$	6.89298e14	0.103761
$754$	1.13452e16	1.69539
$755$	−5.83173e14	−0.0865146
$756$	3.36123e14	0.0495027
$757$	−5.54759e15	−0.811105	−0.405553	−	0.914072i	$-0.632921\pi$
$757$	−5.54759e15	−0.811105	−0.405553	+	0.914072i	$0.632921\pi$
$758$	4.25089e15	0.617020
$759$	2.06845e15	0.298068
$760$	−1.65247e14	−0.0236406
$761$	1.79365e13	0.00254754	0.00127377	−	0.999999i	$-0.499595\pi$
$761$	1.79365e13	0.00254754	0.00127377	+	0.999999i	$0.499595\pi$
$762$	−4.66506e15	−0.657817
$763$	5.85784e15	0.820074
$764$	−2.55687e15	−0.355382
$765$	3.53974e14	0.0488465
$766$	8.63391e15	1.18290
$767$	−1.46794e16	−1.99680
$768$	−2.67181e14	−0.0360844
$769$	−1.07234e16	−1.43794	−0.718968	−	0.695043i	$-0.755385\pi$
$769$	−1.07234e16	−1.43794	−0.718968	+	0.695043i	$0.755385\pi$
$770$	5.92781e14	0.0789215
$771$	−7.32506e15	−0.968305
$772$	5.32269e15	0.698612
$773$	6.56995e15	0.856199	0.428100	−	0.903732i	$-0.359183\pi$
$773$	6.56995e15	0.856199	0.428100	+	0.903732i	$0.359183\pi$
$774$	1.09727e15	0.141983
$775$	5.54786e14	0.0712797
$776$	−1.35774e15	−0.173211
$777$	3.17699e15	0.402439
$778$	−3.13947e15	−0.394883
$779$	−1.18459e15	−0.147949
$780$	−1.80672e15	−0.224064
$781$	−3.03685e15	−0.373975
$782$	2.01643e15	0.246574
$783$	−2.18950e15	−0.265862
$784$	−1.52465e15	−0.183836
$785$	−1.41392e15	−0.169295
$786$	−2.22744e15	−0.264839
$787$	−1.38290e16	−1.63279	−0.816394	−	0.577495i	$-0.804030\pi$
$787$	−1.38290e16	−1.63279	−0.816394	+	0.577495i	$0.804030\pi$
$788$	−5.84088e15	−0.684833
$789$	−9.25629e15	−1.07774
$790$	2.69897e14	0.0312068
$791$	−3.03594e15	−0.348596
$792$	5.01391e14	0.0571727
$793$	1.82656e15	0.206839
$794$	2.06124e15	0.231801
$795$	−1.93928e15	−0.216582
$796$	−6.55172e14	−0.0726664
$797$	−5.66909e15	−0.624442	−0.312221	−	0.950009i	$-0.601073\pi$
$797$	−5.66909e15	−0.624442	−0.312221	+	0.950009i	$0.601073\pi$
$798$	2.87058e14	0.0314018
$799$	−9.18555e14	−0.0997925
$800$	−3.27680e14	−0.0353553
$801$	4.40248e15	0.471757
$802$	−6.58557e15	−0.700865
$803$	−6.00546e15	−0.634761
$804$	5.29706e15	0.556066
$805$	2.34831e15	0.244837
$806$	4.22387e15	0.437389
$807$	−4.88400e14	−0.0502310
$808$	−3.82077e15	−0.390290
$809$	1.22726e16	1.24514	0.622572	−	0.782563i	$-0.286088\pi$
$809$	1.22726e16	1.24514	0.622572	+	0.782563i	$0.286088\pi$
$810$	3.48678e14	0.0351364
$811$	2.48630e15	0.248851	0.124426	−	0.992229i	$-0.460291\pi$
$811$	2.48630e15	0.248851	0.124426	+	0.992229i	$0.460291\pi$
$812$	−3.57443e15	−0.355344
$813$	7.43777e15	0.734420
$814$	4.73908e15	0.464793
$815$	−4.73959e15	−0.461715
$816$	4.88782e14	0.0472954
$817$	9.37093e14	0.0900661
$818$	−1.90597e15	−0.181959
$819$	3.13854e15	0.297623
$820$	−2.34900e15	−0.221262
$821$	−1.90122e16	−1.77887	−0.889435	−	0.457062i	$-0.848902\pi$
$821$	−1.90122e16	−1.77887	−0.889435	+	0.457062i	$0.848902\pi$
$822$	−2.08567e15	−0.193843
$823$	2.42079e15	0.223490	0.111745	−	0.993737i	$-0.464356\pi$
$823$	2.42079e15	0.223490	0.111745	+	0.993737i	$0.464356\pi$
$824$	−1.40978e15	−0.129286
$825$	6.14923e14	0.0560175
$826$	4.62492e15	0.418518
$827$	−1.83310e16	−1.64781	−0.823903	−	0.566731i	$-0.808208\pi$
$827$	−1.83310e16	−1.64781	−0.823903	+	0.566731i	$0.808208\pi$
$828$	1.98627e15	0.177366
$829$	−7.71702e15	−0.684541	−0.342271	−	0.939601i	$-0.611196\pi$
$829$	−7.71702e15	−0.684541	−0.342271	+	0.939601i	$0.611196\pi$
$830$	3.26587e15	0.287786
$831$	−6.75029e15	−0.590904
$832$	−2.49480e15	−0.216949
$833$	2.78919e15	0.240952
$834$	7.80814e15	0.670092
$835$	7.34566e15	0.626261
$836$	4.28201e14	0.0362671
$837$	−8.15162e14	−0.0685889
$838$	2.64413e15	0.221025
$839$	−1.33884e16	−1.11183	−0.555914	−	0.831240i	$-0.687632\pi$
$839$	−1.33884e16	−1.11183	−0.555914	+	0.831240i	$0.687632\pi$
$840$	5.69228e14	0.0469624
$841$	1.10833e16	0.908428
$842$	4.98267e15	0.405738
$843$	9.60275e15	0.776862
$844$	2.52953e15	0.203309
$845$	−1.12697e16	−0.899916
$846$	−9.04813e14	−0.0717831
$847$	4.99073e15	0.393374
$848$	−2.67784e15	−0.209704
$849$	8.68878e15	0.676031
$850$	5.99458e14	0.0463399
$851$	1.87739e16	1.44192
$852$	−2.91618e15	−0.222534
$853$	3.99518e15	0.302912	0.151456	−	0.988464i	$-0.451604\pi$
$853$	3.99518e15	0.302912	0.151456	+	0.988464i	$0.451604\pi$
$854$	−5.75478e14	−0.0433522
$855$	2.97780e14	0.0222886
$856$	7.05570e15	0.524728
$857$	1.50656e16	1.11324	0.556622	−	0.830766i	$-0.312097\pi$
$857$	1.50656e16	1.11324	0.556622	+	0.830766i	$0.312097\pi$
$858$	4.68173e15	0.343737
$859$	−2.66635e16	−1.94516	−0.972579	−	0.232572i	$-0.925286\pi$
$859$	−2.66635e16	−1.94516	−0.972579	+	0.232572i	$0.925286\pi$
$860$	1.85823e15	0.134697
$861$	4.08056e15	0.293902
$862$	−1.40884e16	−1.00826
$863$	1.36614e16	0.971486	0.485743	−	0.874102i	$-0.338549\pi$
$863$	1.36614e16	0.971486	0.485743	+	0.874102i	$0.338549\pi$
$864$	4.81469e14	0.0340207
$865$	−2.81597e15	−0.197715
$866$	−1.02992e16	−0.718547
$867$	7.43389e15	0.515361
$868$	−1.33078e15	−0.0916742
$869$	−6.99379e14	−0.0478744
$870$	−3.70794e15	−0.252219
$871$	4.94611e16	3.34321
$872$	8.39088e15	0.563595
$873$	2.44669e15	0.163305
$874$	1.69632e15	0.112511
$875$	6.98120e14	0.0460136
$876$	−5.76684e15	−0.377716
$877$	−2.44903e16	−1.59403	−0.797016	−	0.603958i	$-0.793590\pi$
$877$	−2.44903e16	−1.59403	−0.797016	+	0.603958i	$0.793590\pi$
$878$	−2.09112e16	−1.35257
$879$	−2.83656e15	−0.182328
$880$	8.49111e14	0.0542387
$881$	9.28368e15	0.589322	0.294661	−	0.955602i	$-0.404793\pi$
$881$	9.28368e15	0.589322	0.294661	+	0.955602i	$0.404793\pi$
$882$	2.74746e15	0.173322
$883$	1.88185e16	1.17978	0.589890	−	0.807484i	$-0.299171\pi$
$883$	1.88185e16	1.17978	0.589890	+	0.807484i	$0.299171\pi$
$884$	4.56399e15	0.284352
$885$	4.79767e15	0.297059
$886$	−1.76041e16	−1.08325
$887$	−6.50887e14	−0.0398039	−0.0199020	−	0.999802i	$-0.506335\pi$
$887$	−6.50887e14	−0.0398039	−0.0199020	+	0.999802i	$0.506335\pi$
$888$	4.55078e15	0.276576
$889$	1.37240e16	0.828937
$890$	7.45563e15	0.447548
$891$	−9.03523e14	−0.0539029
$892$	−5.39352e15	−0.319790
$893$	−7.72734e14	−0.0455352
$894$	5.13533e15	0.300755
$895$	3.05314e15	0.177713
$896$	7.86013e14	0.0454711
$897$	1.85467e16	1.06637
$898$	−8.19670e14	−0.0468402
$899$	8.66867e15	0.492350
$900$	5.90490e14	0.0333333
$901$	4.89884e15	0.274857
$902$	6.08692e15	0.339439
$903$	−3.22802e15	−0.178918
$904$	−4.34874e15	−0.239573
$905$	−1.19694e16	−0.655397
$906$	1.45112e15	0.0789767
$907$	2.01411e16	1.08954	0.544770	−	0.838585i	$-0.316617\pi$
$907$	2.01411e16	1.08954	0.544770	+	0.838585i	$0.316617\pi$
$908$	−1.17194e16	−0.630133
$909$	6.88514e15	0.367969
$910$	5.31515e15	0.282350
$911$	−4.85179e15	−0.256184	−0.128092	−	0.991762i	$-0.540885\pi$
$911$	−4.85179e15	−0.256184	−0.128092	+	0.991762i	$0.540885\pi$
$912$	4.11187e14	0.0215808
$913$	−8.46279e15	−0.441493
$914$	−5.56422e14	−0.0288536
$915$	−5.96974e14	−0.0307708
$916$	3.71197e15	0.190186
$917$	6.55283e15	0.333732
$918$	−8.80801e14	−0.0445906
$919$	7.50130e15	0.377486	0.188743	−	0.982026i	$-0.439559\pi$
$919$	7.50130e15	0.377486	0.188743	+	0.982026i	$0.439559\pi$
$920$	3.36376e15	0.168264
$921$	−2.18242e16	−1.08520
$922$	−2.43782e16	−1.20499
$923$	−2.72298e16	−1.33793
$924$	−1.47503e15	−0.0720452
$925$	5.58122e15	0.270988
$926$	−1.24335e16	−0.600111
$927$	2.54047e15	0.121892
$928$	−5.12008e15	−0.244210
$929$	−6.04589e15	−0.286664	−0.143332	−	0.989675i	$-0.545782\pi$
$929$	−6.04589e15	−0.286664	−0.143332	+	0.989675i	$0.545782\pi$
$930$	−1.38048e15	−0.0650692
$931$	2.34640e15	0.109946
$932$	1.47519e16	0.687165
$933$	−1.64239e16	−0.760547
$934$	−3.91094e15	−0.180042
$935$	−1.55336e15	−0.0710901
$936$	4.49571e15	0.204541
$937$	1.17484e16	0.531389	0.265694	−	0.964057i	$-0.414399\pi$
$937$	1.17484e16	0.531389	0.265694	+	0.964057i	$0.414399\pi$
$938$	−1.55833e16	−0.700717
$939$	−2.39883e16	−1.07235
$940$	−1.53231e15	−0.0680994
$941$	−5.89103e15	−0.260284	−0.130142	−	0.991495i	$-0.541543\pi$
$941$	−5.89103e15	−0.260284	−0.130142	+	0.991495i	$0.541543\pi$
$942$	3.51830e15	0.154544
$943$	2.41134e16	1.05304
$944$	6.62482e15	0.287626
$945$	−1.02577e15	−0.0442766
$946$	−4.81519e15	−0.206639
$947$	2.96672e15	0.126576	0.0632881	−	0.997995i	$-0.479841\pi$
$947$	2.96672e15	0.126576	0.0632881	+	0.997995i	$0.479841\pi$
$948$	−6.71590e14	−0.0284878
$949$	−5.38477e16	−2.27093
$950$	5.04294e14	0.0211448
$951$	−2.68570e16	−1.11960
$952$	−1.43793e15	−0.0595985
$953$	1.10371e15	0.0454826	0.0227413	−	0.999741i	$-0.492761\pi$
$953$	1.10371e15	0.0454826	0.0227413	+	0.999741i	$0.492761\pi$
$954$	4.82556e15	0.197711
$955$	7.80295e15	0.317863
$956$	−1.36395e16	−0.552433
$957$	9.60832e15	0.386930
$958$	−1.39492e16	−0.558520
$959$	6.13577e15	0.244268
$960$	8.15373e14	0.0322749
$961$	−2.21811e16	−0.872980
$962$	4.24928e16	1.66285
$963$	−1.27146e16	−0.494719
$964$	1.16500e16	0.450714
$965$	−1.62436e16	−0.624858
$966$	−5.84334e15	−0.223505
$967$	−1.84533e15	−0.0701826	−0.0350913	−	0.999384i	$-0.511172\pi$
$967$	−1.84533e15	−0.0701826	−0.0350913	+	0.999384i	$0.511172\pi$
$968$	7.14881e15	0.270346
$969$	−7.52227e14	−0.0282858
$970$	4.14349e15	0.154925
$971$	−1.46125e16	−0.543273	−0.271636	−	0.962400i	$-0.587565\pi$
$971$	−1.46125e16	−0.543273	−0.271636	+	0.962400i	$0.587565\pi$
$972$	−8.67624e14	−0.0320750
$973$	−2.29706e16	−0.844405
$974$	−2.13181e16	−0.779245
$975$	5.51368e15	0.200409
$976$	−8.24326e14	−0.0297937
$977$	1.87225e16	0.672891	0.336445	−	0.941703i	$-0.390775\pi$
$977$	1.87225e16	0.672891	0.336445	+	0.941703i	$0.390775\pi$
$978$	1.17936e16	0.421486
$979$	−1.93196e16	−0.686585
$980$	4.65285e15	0.164428
$981$	−1.51206e16	−0.531362
$982$	−7.16215e14	−0.0250282
$983$	2.79209e16	0.970253	0.485126	−	0.874444i	$-0.338774\pi$
$983$	2.79209e16	0.970253	0.485126	+	0.874444i	$0.338774\pi$
$984$	5.84507e15	0.201984
$985$	1.78250e16	0.612533
$986$	9.36668e15	0.320083
$987$	2.66184e15	0.0904562
$988$	3.83945e15	0.129750
$989$	−1.90754e16	−0.641054
$990$	−1.53012e15	−0.0511368
$991$	2.46391e16	0.818878	0.409439	−	0.912337i	$-0.365724\pi$
$991$	2.46391e16	0.818878	0.409439	+	0.912337i	$0.365724\pi$
$992$	−1.90623e15	−0.0630030
$993$	1.21538e16	0.399475
$994$	8.57903e15	0.280423
$995$	1.99943e15	0.0649948
$996$	−8.12653e15	−0.262711
$997$	4.80148e16	1.54366	0.771831	−	0.635828i	$-0.219341\pi$
$997$	4.80148e16	1.54366	0.771831	+	0.635828i	$0.219341\pi$
$998$	1.56002e15	0.0498783
$999$	−8.20065e15	−0.260758

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	30.12.a.a.1.1	✓	1
3.2	odd	2		90.12.a.j.1.1		1
4.3	odd	2		240.12.a.d.1.1		1
5.2	odd	4		150.12.c.g.49.1		2
5.3	odd	4		150.12.c.g.49.2		2
5.4	even	2		150.12.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.12.a.a.1.1	✓	1	1.1	even	1	trivial
90.12.a.j.1.1		1	3.2	odd	2
150.12.a.h.1.1		1	5.4	even	2
150.12.c.g.49.1		2	5.2	odd	4
150.12.c.g.49.2		2	5.3	odd	4
240.12.a.d.1.1		1	4.3	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:	\( N \)	\(=\)	\( 30 = 2 \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	30.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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