LMFDB - Embedded newform 6.18.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6,18,Mod(1,6)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 18, names="a")

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

chi := DirichletCharacter("6.1");

S:= CuspForms(chi, 18);

N := Newforms(S);

Level:	$ N $	$=$	$ 6 = 2 \cdot 3 $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	6.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$10.9933252407$
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	$\chi$	$=$	6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-256.000 q^{2} -6561.00 q^{3} +65536.0 q^{4} +645150. q^{5} +1.67962e6 q^{6} +3.97443e6 q^{7} -1.67772e7 q^{8} +4.30467e7 q^{9} +O(q^{10})$

\(q-256.000 q^{2} -6561.00 q^{3} +65536.0 q^{4} +645150. q^{5} +1.67962e6 q^{6} +3.97443e6 q^{7} -1.67772e7 q^{8} +4.30467e7 q^{9} -1.65158e8 q^{10} -5.00069e8 q^{11} -4.29982e8 q^{12} -5.42566e9 q^{13} -1.01745e9 q^{14} -4.23283e9 q^{15} +4.29497e9 q^{16} -5.46699e9 q^{17} -1.10200e10 q^{18} -5.38899e10 q^{19} +4.22806e10 q^{20} -2.60762e10 q^{21} +1.28018e11 q^{22} +5.78907e11 q^{23} +1.10075e11 q^{24} -3.46721e11 q^{25} +1.38897e12 q^{26} -2.82430e11 q^{27} +2.60468e11 q^{28} -4.61958e12 q^{29} +1.08360e12 q^{30} -6.80282e12 q^{31} -1.09951e12 q^{32} +3.28095e12 q^{33} +1.39955e12 q^{34} +2.56410e12 q^{35} +2.82111e12 q^{36} -1.95719e13 q^{37} +1.37958e13 q^{38} +3.55978e13 q^{39} -1.08238e13 q^{40} +5.72136e13 q^{41} +6.67552e12 q^{42} -2.45013e13 q^{43} -3.27725e13 q^{44} +2.77716e13 q^{45} -1.48200e14 q^{46} +1.84284e14 q^{47} -2.81793e13 q^{48} -2.16834e14 q^{49} +8.87606e13 q^{50} +3.58689e13 q^{51} -3.55576e14 q^{52} -2.06543e14 q^{53} +7.23020e13 q^{54} -3.22619e14 q^{55} -6.66799e13 q^{56} +3.53571e14 q^{57} +1.18261e15 q^{58} -4.18648e14 q^{59} -2.77403e14 q^{60} +2.50129e15 q^{61} +1.74152e15 q^{62} +1.71086e14 q^{63} +2.81475e14 q^{64} -3.50037e15 q^{65} -8.39923e14 q^{66} -1.45693e14 q^{67} -3.58285e14 q^{68} -3.79821e15 q^{69} -6.56411e14 q^{70} -5.36431e15 q^{71} -7.22204e14 q^{72} +3.30206e15 q^{73} +5.01041e15 q^{74} +2.27484e15 q^{75} -3.53173e15 q^{76} -1.98749e15 q^{77} -9.11303e15 q^{78} +2.20675e16 q^{79} +2.77090e15 q^{80} +1.85302e15 q^{81} -1.46467e16 q^{82} +2.04384e16 q^{83} -1.70893e15 q^{84} -3.52703e15 q^{85} +6.27232e15 q^{86} +3.03091e16 q^{87} +8.38976e15 q^{88} -5.60638e16 q^{89} -7.10953e15 q^{90} -2.15639e16 q^{91} +3.79392e16 q^{92} +4.46333e16 q^{93} -4.71767e16 q^{94} -3.47671e16 q^{95} +7.21390e15 q^{96} -1.18254e17 q^{97} +5.55096e16 q^{98} -2.15263e16 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−256.000	−0.707107
$2$	−256.000	−0.707107
$3$	−6561.00	−0.577350
$3$	−6561.00	−0.577350
$4$	65536.0	0.500000
$5$	645150.	0.738611	0.369305	−	0.929308i	$-0.379596\pi$
$5$	645150.	0.738611	0.369305	+	0.929308i	$0.379596\pi$
$6$	1.67962e6	0.408248
$7$	3.97443e6	0.260580	0.130290	−	0.991476i	$-0.458409\pi$
$7$	3.97443e6	0.260580	0.130290	+	0.991476i	$0.458409\pi$
$8$	−1.67772e7	−0.353553
$9$	4.30467e7	0.333333
$10$	−1.65158e8	−0.522277
$11$	−5.00069e8	−0.703383	−0.351691	−	0.936116i	$-0.614393\pi$
$11$	−5.00069e8	−0.703383	−0.351691	+	0.936116i	$0.614393\pi$
$12$	−4.29982e8	−0.288675
$13$	−5.42566e9	−1.84474	−0.922368	−	0.386313i	$-0.873749\pi$
$13$	−5.42566e9	−1.84474	−0.922368	+	0.386313i	$0.873749\pi$
$14$	−1.01745e9	−0.184258
$15$	−4.23283e9	−0.426437
$16$	4.29497e9	0.250000
$17$	−5.46699e9	−0.190078	−0.0950392	−	0.995474i	$-0.530298\pi$
$17$	−5.46699e9	−0.190078	−0.0950392	+	0.995474i	$0.530298\pi$
$18$	−1.10200e10	−0.235702
$19$	−5.38899e10	−0.727950	−0.363975	−	0.931409i	$-0.618581\pi$
$19$	−5.38899e10	−0.727950	−0.363975	+	0.931409i	$0.618581\pi$
$20$	4.22806e10	0.369305
$21$	−2.60762e10	−0.150446
$22$	1.28018e11	0.497367
$23$	5.78907e11	1.54142	0.770712	−	0.637184i	$-0.219901\pi$
$23$	5.78907e11	1.54142	0.770712	+	0.637184i	$0.219901\pi$
$24$	1.10075e11	0.204124
$25$	−3.46721e11	−0.454454
$26$	1.38897e12	1.30443
$27$	−2.82430e11	−0.192450
$28$	2.60468e11	0.130290
$29$	−4.61958e12	−1.71483	−0.857413	−	0.514630i	$-0.827929\pi$
$29$	−4.61958e12	−1.71483	−0.857413	+	0.514630i	$0.827929\pi$
$30$	1.08360e12	0.301537
$31$	−6.80282e12	−1.43256	−0.716282	−	0.697810i	$-0.754158\pi$
$31$	−6.80282e12	−1.43256	−0.716282	+	0.697810i	$0.754158\pi$
$32$	−1.09951e12	−0.176777
$33$	3.28095e12	0.406098
$34$	1.39955e12	0.134406
$35$	2.56410e12	0.192467
$36$	2.82111e12	0.166667
$37$	−1.95719e13	−0.916049	−0.458024	−	0.888940i	$-0.651443\pi$
$37$	−1.95719e13	−0.916049	−0.458024	+	0.888940i	$0.651443\pi$
$38$	1.37958e13	0.514738
$39$	3.55978e13	1.06506
$40$	−1.08238e13	−0.261138
$41$	5.72136e13	1.11902	0.559508	−	0.828825i	$-0.310990\pi$
$41$	5.72136e13	1.11902	0.559508	+	0.828825i	$0.310990\pi$
$42$	6.67552e12	0.106381
$43$	−2.45013e13	−0.319673	−0.159837	−	0.987143i	$-0.551097\pi$
$43$	−2.45013e13	−0.319673	−0.159837	+	0.987143i	$0.551097\pi$
$44$	−3.27725e13	−0.351691
$45$	2.77716e13	0.246204
$46$	−1.48200e14	−1.08995
$47$	1.84284e14	1.12890	0.564450	−	0.825467i	$-0.309088\pi$
$47$	1.84284e14	1.12890	0.564450	+	0.825467i	$0.309088\pi$
$48$	−2.81793e13	−0.144338
$49$	−2.16834e14	−0.932098
$50$	8.87606e13	0.321348
$51$	3.58689e13	0.109742
$52$	−3.55576e14	−0.922368
$53$	−2.06543e14	−0.455685	−0.227842	−	0.973698i	$-0.573167\pi$
$53$	−2.06543e14	−0.455685	−0.227842	+	0.973698i	$0.573167\pi$
$54$	7.23020e13	0.136083
$55$	−3.22619e14	−0.519526
$56$	−6.66799e13	−0.0921291
$57$	3.53571e14	0.420282
$58$	1.18261e15	1.21256
$59$	−4.18648e14	−0.371199	−0.185600	−	0.982625i	$-0.559423\pi$
$59$	−4.18648e14	−0.371199	−0.185600	+	0.982625i	$0.559423\pi$
$60$	−2.77403e14	−0.213219
$61$	2.50129e15	1.67055	0.835276	−	0.549831i	$-0.185308\pi$
$61$	2.50129e15	1.67055	0.835276	+	0.549831i	$0.185308\pi$
$62$	1.74152e15	1.01298
$63$	1.71086e14	0.0868601
$64$	2.81475e14	0.125000
$65$	−3.50037e15	−1.36254
$66$	−8.39923e14	−0.287155
$67$	−1.45693e14	−0.0438331	−0.0219166	−	0.999760i	$-0.506977\pi$
$67$	−1.45693e14	−0.0438331	−0.0219166	+	0.999760i	$0.506977\pi$
$68$	−3.58285e14	−0.0950392
$69$	−3.79821e15	−0.889941
$70$	−6.56411e14	−0.136095
$71$	−5.36431e15	−0.985867	−0.492933	−	0.870067i	$-0.664075\pi$
$71$	−5.36431e15	−0.985867	−0.492933	+	0.870067i	$0.664075\pi$
$72$	−7.22204e14	−0.117851
$73$	3.30206e15	0.479226	0.239613	−	0.970868i	$-0.422979\pi$
$73$	3.30206e15	0.479226	0.239613	+	0.970868i	$0.422979\pi$
$74$	5.01041e15	0.647744
$75$	2.27484e15	0.262379
$76$	−3.53173e15	−0.363975
$77$	−1.98749e15	−0.183288
$78$	−9.11303e15	−0.753110
$79$	2.20675e16	1.63652	0.818262	−	0.574846i	$-0.194938\pi$
$79$	2.20675e16	1.63652	0.818262	+	0.574846i	$0.194938\pi$
$80$	2.77090e15	0.184653
$81$	1.85302e15	0.111111
$82$	−1.46467e16	−0.791264
$83$	2.04384e16	0.996053	0.498027	−	0.867162i	$-0.334058\pi$
$83$	2.04384e16	0.996053	0.498027	+	0.867162i	$0.334058\pi$
$84$	−1.70893e15	−0.0752231
$85$	−3.52703e15	−0.140394
$86$	6.27232e15	0.226043
$87$	3.03091e16	0.990055
$88$	8.38976e15	0.248683
$89$	−5.60638e16	−1.50962	−0.754810	−	0.655944i	$-0.772271\pi$
$89$	−5.60638e16	−1.50962	−0.754810	+	0.655944i	$0.772271\pi$
$90$	−7.10953e15	−0.174092
$91$	−2.15639e16	−0.480702
$92$	3.79392e16	0.770712
$93$	4.46333e16	0.827092
$94$	−4.71767e16	−0.798254
$95$	−3.47671e16	−0.537672
$96$	7.21390e15	0.102062
$97$	−1.18254e17	−1.53200	−0.765998	−	0.642843i	$-0.777755\pi$
$97$	−1.18254e17	−1.53200	−0.765998	+	0.642843i	$0.777755\pi$
$98$	5.55096e16	0.659093
$99$	−2.15263e16	−0.234461
$100$	−2.27227e16	−0.227227
$101$	−4.40843e16	−0.405091	−0.202546	−	0.979273i	$-0.564921\pi$
$101$	−4.40843e16	−0.405091	−0.202546	+	0.979273i	$0.564921\pi$
$102$	−9.18245e15	−0.0775992
$103$	7.90408e16	0.614802	0.307401	−	0.951580i	$-0.400541\pi$
$103$	7.90408e16	0.614802	0.307401	+	0.951580i	$0.400541\pi$
$104$	9.10275e16	0.652213
$105$	−1.68231e16	−0.111121
$106$	5.28749e16	0.322218
$107$	1.51196e17	0.850702	0.425351	−	0.905028i	$-0.360151\pi$
$107$	1.51196e17	0.850702	0.425351	+	0.905028i	$0.360151\pi$
$108$	−1.85093e16	−0.0962250
$109$	−1.47830e16	−0.0710619	−0.0355310	−	0.999369i	$-0.511312\pi$
$109$	−1.47830e16	−0.0710619	−0.0355310	+	0.999369i	$0.511312\pi$
$110$	8.25905e16	0.367361
$111$	1.28411e17	0.528881
$112$	1.70701e16	0.0651451
$113$	−3.39020e16	−0.119966	−0.0599831	−	0.998199i	$-0.519105\pi$
$113$	−3.39020e16	−0.119966	−0.0599831	+	0.998199i	$0.519105\pi$
$114$	−9.05143e16	−0.297184
$115$	3.73482e17	1.13851
$116$	−3.02749e17	−0.857413
$117$	−2.33557e17	−0.614912
$118$	1.07174e17	0.262477
$119$	−2.17282e16	−0.0495307
$120$	7.10151e16	0.150768
$121$	−2.55378e17	−0.505252
$122$	−6.40330e17	−1.18126
$123$	−3.75379e17	−0.646065
$124$	−4.45829e17	−0.716282
$125$	−7.15897e17	−1.07428
$126$	−4.37981e16	−0.0614194
$127$	1.36055e18	1.78395	0.891976	−	0.452082i	$-0.149319\pi$
$127$	1.36055e18	1.78395	0.891976	+	0.452082i	$0.149319\pi$
$128$	−7.20576e16	−0.0883883
$129$	1.60753e17	0.184563
$130$	8.96094e17	0.963463
$131$	9.90913e17	0.998228	0.499114	−	0.866536i	$-0.333659\pi$
$131$	9.90913e17	0.998228	0.499114	+	0.866536i	$0.333659\pi$
$132$	2.15020e17	0.203049
$133$	−2.14182e17	−0.189690
$134$	3.72974e16	0.0309947
$135$	−1.82209e17	−0.142146
$136$	9.17209e16	0.0672028
$137$	4.57633e17	0.315059	0.157530	−	0.987514i	$-0.449647\pi$
$137$	4.57633e17	0.315059	0.157530	+	0.987514i	$0.449647\pi$
$138$	9.72341e17	0.629284
$139$	−2.32367e18	−1.41432	−0.707161	−	0.707053i	$-0.750024\pi$
$139$	−2.32367e18	−1.41432	−0.707161	+	0.707053i	$0.750024\pi$
$140$	1.68041e17	0.0962337
$141$	−1.20909e18	−0.651771
$142$	1.37326e18	0.697113
$143$	2.71320e18	1.29756
$144$	1.84884e17	0.0833333
$145$	−2.98032e18	−1.26659
$146$	−8.45327e17	−0.338864
$147$	1.42265e18	0.538147
$148$	−1.28266e18	−0.458024
$149$	1.54007e18	0.519348	0.259674	−	0.965696i	$-0.416385\pi$
$149$	1.54007e18	0.519348	0.259674	+	0.965696i	$0.416385\pi$
$150$	−5.82358e17	−0.185530
$151$	−2.48650e18	−0.748659	−0.374329	−	0.927296i	$-0.622127\pi$
$151$	−2.48650e18	−0.748659	−0.374329	+	0.927296i	$0.622127\pi$
$152$	9.04122e17	0.257369
$153$	−2.35336e17	−0.0633595
$154$	5.08797e17	0.129604
$155$	−4.38884e18	−1.05811
$156$	2.33294e18	0.532529
$157$	−5.18657e17	−0.112133	−0.0560665	−	0.998427i	$-0.517856\pi$
$157$	−5.18657e17	−0.112133	−0.0560665	+	0.998427i	$0.517856\pi$
$158$	−5.64927e18	−1.15720
$159$	1.35513e18	0.263090
$160$	−7.09350e17	−0.130569
$161$	2.30083e18	0.401665
$162$	−4.74373e17	−0.0785674
$163$	4.05852e17	0.0637930	0.0318965	−	0.999491i	$-0.489845\pi$
$163$	4.05852e17	0.0637930	0.0318965	+	0.999491i	$0.489845\pi$
$164$	3.74955e18	0.559508
$165$	2.11671e18	0.299949
$166$	−5.23222e18	−0.704316
$167$	4.48847e18	0.574127	0.287064	−	0.957912i	$-0.407321\pi$
$167$	4.48847e18	0.574127	0.287064	+	0.957912i	$0.407321\pi$
$168$	4.37487e17	0.0531907
$169$	2.07874e19	2.40305
$170$	9.02920e17	0.0992735
$171$	−2.31978e18	−0.242650
$172$	−1.60571e18	−0.159837
$173$	1.69540e18	0.160650	0.0803250	−	0.996769i	$-0.474404\pi$
$173$	1.69540e18	0.160650	0.0803250	+	0.996769i	$0.474404\pi$
$174$	−7.75913e18	−0.700074
$175$	−1.37802e18	−0.118422
$176$	−2.14778e18	−0.175846
$177$	2.74675e18	0.214312
$178$	1.43523e19	1.06746
$179$	−1.95772e19	−1.38835	−0.694176	−	0.719806i	$-0.744231\pi$
$179$	−1.95772e19	−1.38835	−0.694176	+	0.719806i	$0.744231\pi$
$180$	1.82004e18	0.123102
$181$	−2.38897e18	−0.154150	−0.0770748	−	0.997025i	$-0.524558\pi$
$181$	−2.38897e18	−0.154150	−0.0770748	+	0.997025i	$0.524558\pi$
$182$	5.52036e18	0.339908
$183$	−1.64109e19	−0.964494
$184$	−9.71245e18	−0.544976
$185$	−1.26268e19	−0.676603
$186$	−1.14261e19	−0.584842
$187$	2.73387e18	0.133698
$188$	1.20772e19	0.564450
$189$	−1.12250e18	−0.0501487
$190$	8.90037e18	0.380191
$191$	−2.99357e19	−1.22294	−0.611470	−	0.791267i	$-0.709422\pi$
$191$	−2.99357e19	−1.22294	−0.611470	+	0.791267i	$0.709422\pi$
$192$	−1.84676e18	−0.0721688
$193$	−1.76590e19	−0.660279	−0.330140	−	0.943932i	$-0.607096\pi$
$193$	−1.76590e19	−0.660279	−0.330140	+	0.943932i	$0.607096\pi$
$194$	3.02731e19	1.08328
$195$	2.29659e19	0.786664
$196$	−1.42105e19	−0.466049
$197$	2.79982e19	0.879360	0.439680	−	0.898154i	$-0.355092\pi$
$197$	2.79982e19	0.879360	0.439680	+	0.898154i	$0.355092\pi$
$198$	5.51074e18	0.165789
$199$	3.33860e19	0.962305	0.481152	−	0.876637i	$-0.340218\pi$
$199$	3.33860e19	0.962305	0.481152	+	0.876637i	$0.340218\pi$
$200$	5.81701e18	0.160674
$201$	9.55891e17	0.0253071
$202$	1.12856e19	0.286443
$203$	−1.83602e19	−0.446850
$204$	2.35071e18	0.0548709
$205$	3.69114e19	0.826518
$206$	−2.02345e19	−0.434731
$207$	2.49200e19	0.513808
$208$	−2.33030e19	−0.461184
$209$	2.69486e19	0.512028
$210$	4.30671e18	0.0785745
$211$	−7.35415e19	−1.28864	−0.644320	−	0.764756i	$-0.722859\pi$
$211$	−7.35415e19	−1.28864	−0.644320	+	0.764756i	$0.722859\pi$
$212$	−1.35360e19	−0.227842
$213$	3.51953e19	0.569190
$214$	−3.87061e19	−0.601537
$215$	−1.58070e19	−0.236114
$216$	4.73838e18	0.0680414
$217$	−2.70373e19	−0.373298
$218$	3.78445e18	0.0502484
$219$	−2.16648e19	−0.276681
$220$	−2.11432e19	−0.259763
$221$	2.96621e19	0.350644
$222$	−3.28733e19	−0.373975
$223$	−5.42250e19	−0.593756	−0.296878	−	0.954915i	$-0.595946\pi$
$223$	−5.42250e19	−0.593756	−0.296878	+	0.954915i	$0.595946\pi$
$224$	−4.36993e18	−0.0460645
$225$	−1.49252e19	−0.151485
$226$	8.67892e18	0.0848289
$227$	1.65578e20	1.55877	0.779386	−	0.626544i	$-0.215531\pi$
$227$	1.65578e20	1.55877	0.779386	+	0.626544i	$0.215531\pi$
$228$	2.31717e19	0.210141
$229$	−1.06929e20	−0.934319	−0.467159	−	0.884173i	$-0.654723\pi$
$229$	−1.06929e20	−0.934319	−0.467159	+	0.884173i	$0.654723\pi$
$230$	−9.56113e19	−0.805050
$231$	1.30399e19	0.105821
$232$	7.75038e19	0.606282
$233$	4.42287e19	0.333564	0.166782	−	0.985994i	$-0.446662\pi$
$233$	4.42287e19	0.333564	0.166782	+	0.985994i	$0.446662\pi$
$234$	5.97906e19	0.434808
$235$	1.18891e20	0.833818
$236$	−2.74365e19	−0.185600
$237$	−1.44785e20	−0.944847
$238$	5.56242e18	0.0350235
$239$	−1.28343e20	−0.779815	−0.389907	−	0.920854i	$-0.627493\pi$
$239$	−1.28343e20	−0.779815	−0.389907	+	0.920854i	$0.627493\pi$
$240$	−1.81799e19	−0.106609
$241$	1.09128e20	0.617718	0.308859	−	0.951108i	$-0.400053\pi$
$241$	1.09128e20	0.617718	0.308859	+	0.951108i	$0.400053\pi$
$242$	6.53769e19	0.357267
$243$	−1.21577e19	−0.0641500
$244$	1.63924e20	0.835276
$245$	−1.39891e20	−0.688458
$246$	9.60969e19	0.456837
$247$	2.92388e20	1.34288
$248$	1.14132e20	0.506488
$249$	−1.34096e20	−0.575072
$250$	1.83270e20	0.759627
$251$	1.61577e20	0.647369	0.323685	−	0.946165i	$-0.395078\pi$
$251$	1.61577e20	0.647369	0.323685	+	0.946165i	$0.395078\pi$
$252$	1.12123e19	0.0434301
$253$	−2.89493e20	−1.08421
$254$	−3.48301e20	−1.26145
$255$	2.31408e19	0.0810565
$256$	1.84467e19	0.0625000
$257$	−1.85421e20	−0.607755	−0.303878	−	0.952711i	$-0.598281\pi$
$257$	−1.85421e20	−0.607755	−0.303878	+	0.952711i	$0.598281\pi$
$258$	−4.11527e19	−0.130506
$259$	−7.77872e19	−0.238704
$260$	−2.29400e20	−0.681271
$261$	−1.98858e20	−0.571608
$262$	−2.53674e20	−0.705854
$263$	−2.27751e20	−0.613531	−0.306765	−	0.951785i	$-0.599247\pi$
$263$	−2.27751e20	−0.613531	−0.306765	+	0.951785i	$0.599247\pi$
$264$	−5.50452e19	−0.143577
$265$	−1.33251e20	−0.336574
$266$	5.48305e19	0.134131
$267$	3.67835e20	0.871579
$268$	−9.54813e18	−0.0219166
$269$	4.50866e20	1.00266	0.501329	−	0.865257i	$-0.332845\pi$
$269$	4.50866e20	1.00266	0.501329	+	0.865257i	$0.332845\pi$
$270$	4.66456e19	0.100512
$271$	3.27632e20	0.684143	0.342071	−	0.939674i	$-0.388872\pi$
$271$	3.27632e20	0.684143	0.342071	+	0.939674i	$0.388872\pi$
$272$	−2.34806e19	−0.0475196
$273$	1.41481e20	0.277533
$274$	−1.17154e20	−0.222781
$275$	1.73384e20	0.319655
$276$	−2.48919e20	−0.444971
$277$	−2.30896e19	−0.0400256	−0.0200128	−	0.999800i	$-0.506371\pi$
$277$	−2.30896e19	−0.0400256	−0.0200128	+	0.999800i	$0.506371\pi$
$278$	5.94859e20	1.00008
$279$	−2.92839e20	−0.477522
$280$	−4.30185e19	−0.0680475
$281$	1.04319e21	1.60089	0.800443	−	0.599408i	$-0.204597\pi$
$281$	1.04319e21	1.60089	0.800443	+	0.599408i	$0.204597\pi$
$282$	3.09526e20	0.460872
$283$	6.50286e19	0.0939550	0.0469775	−	0.998896i	$-0.485041\pi$
$283$	6.50286e19	0.0939550	0.0469775	+	0.998896i	$0.485041\pi$
$284$	−3.51556e20	−0.492933
$285$	2.28107e20	0.310425
$286$	−6.94580e20	−0.917510
$287$	2.27392e20	0.291594
$288$	−4.73304e19	−0.0589256
$289$	−7.97352e20	−0.963870
$290$	7.62963e20	0.895613
$291$	7.75867e20	0.884498
$292$	2.16404e20	0.239613
$293$	−1.13177e21	−1.21726	−0.608631	−	0.793454i	$-0.708281\pi$
$293$	−1.13177e21	−1.21726	−0.608631	+	0.793454i	$0.708281\pi$
$294$	−3.64199e20	−0.380527
$295$	−2.70091e20	−0.274172
$296$	3.28362e20	0.323872
$297$	1.41234e20	0.135366
$298$	−3.94259e20	−0.367234
$299$	−3.14095e21	−2.84352
$300$	1.49084e20	0.131190
$301$	−9.73786e19	−0.0833006
$302$	6.36543e20	0.529382
$303$	2.89237e20	0.233879
$304$	−2.31455e20	−0.181988
$305$	1.61371e21	1.23389
$306$	6.02460e19	0.0448019
$307$	3.02065e20	0.218486	0.109243	−	0.994015i	$-0.465157\pi$
$307$	3.02065e20	0.218486	0.109243	+	0.994015i	$0.465157\pi$
$308$	−1.30252e20	−0.0916439
$309$	−5.18587e20	−0.354956
$310$	1.12354e21	0.748195
$311$	−2.52790e21	−1.63793	−0.818967	−	0.573840i	$-0.805453\pi$
$311$	−2.52790e21	−1.63793	−0.818967	+	0.573840i	$0.805453\pi$
$312$	−5.97231e20	−0.376555
$313$	−2.83982e19	−0.0174246	−0.00871232	−	0.999962i	$-0.502773\pi$
$313$	−2.83982e19	−0.0174246	−0.00871232	+	0.999962i	$0.502773\pi$
$314$	1.32776e20	0.0792900
$315$	1.10376e20	0.0641558
$316$	1.44621e21	0.818262
$317$	1.55787e21	0.858081	0.429040	−	0.903285i	$-0.358852\pi$
$317$	1.55787e21	0.858081	0.429040	+	0.903285i	$0.358852\pi$
$318$	−3.46912e20	−0.186033
$319$	2.31011e21	1.20618
$320$	1.81594e20	0.0923264
$321$	−9.91995e20	−0.491153
$322$	−5.89011e20	−0.284020
$323$	2.94616e20	0.138368
$324$	1.21440e20	0.0555556
$325$	1.88119e21	0.838348
$326$	−1.03898e20	−0.0451085
$327$	9.69912e19	0.0410276
$328$	−9.59885e20	−0.395632
$329$	7.32424e20	0.294169
$330$	−5.41877e20	−0.212096
$331$	−1.24132e21	−0.473529	−0.236765	−	0.971567i	$-0.576087\pi$
$331$	−1.24132e21	−0.473529	−0.236765	+	0.971567i	$0.576087\pi$
$332$	1.33945e21	0.498027
$333$	−8.42507e20	−0.305350
$334$	−1.14905e21	−0.405969
$335$	−9.39938e19	−0.0323756
$336$	−1.11997e20	−0.0376115
$337$	5.68981e21	1.86313	0.931566	−	0.363572i	$-0.118443\pi$
$337$	5.68981e21	1.86313	0.931566	+	0.363572i	$0.118443\pi$
$338$	−5.32157e21	−1.69921
$339$	2.22431e20	0.0692625
$340$	−2.31147e20	−0.0701970
$341$	3.40187e21	1.00764
$342$	5.93864e20	0.171579
$343$	−1.78637e21	−0.503467
$344$	4.11063e20	0.113022
$345$	−2.45041e21	−0.657320
$346$	−4.34023e20	−0.113597
$347$	−2.68242e21	−0.685056	−0.342528	−	0.939508i	$-0.611283\pi$
$347$	−2.68242e21	−0.685056	−0.342528	+	0.939508i	$0.611283\pi$
$348$	1.98634e21	0.495027
$349$	−7.74946e21	−1.88476	−0.942378	−	0.334549i	$-0.891416\pi$
$349$	−7.74946e21	−1.88476	−0.942378	+	0.334549i	$0.891416\pi$
$350$	3.52773e20	0.0837369
$351$	1.53237e21	0.355020
$352$	5.49831e20	0.124342
$353$	1.49092e21	0.329132	0.164566	−	0.986366i	$-0.447378\pi$
$353$	1.49092e21	0.329132	0.164566	+	0.986366i	$0.447378\pi$
$354$	−7.03168e20	−0.151541
$355$	−3.46079e21	−0.728172
$356$	−3.67420e21	−0.754810
$357$	1.42559e20	0.0285966
$358$	5.01176e21	0.981713
$359$	−4.46649e20	−0.0854404	−0.0427202	−	0.999087i	$-0.513602\pi$
$359$	−4.46649e20	−0.0854404	−0.0427202	+	0.999087i	$0.513602\pi$
$360$	−4.65930e20	−0.0870461
$361$	−2.57627e21	−0.470089
$362$	6.11576e20	0.109000
$363$	1.67554e21	0.291708
$364$	−1.41321e21	−0.240351
$365$	2.13032e21	0.353962
$366$	4.20120e21	0.682000
$367$	7.86235e21	1.24707	0.623535	−	0.781795i	$-0.285696\pi$
$367$	7.86235e21	1.24707	0.623535	+	0.781795i	$0.285696\pi$
$368$	2.48639e21	0.385356
$369$	2.46286e21	0.373006
$370$	3.23247e21	0.478431
$371$	−8.20889e20	−0.118743
$372$	2.92509e21	0.413546
$373$	−1.21059e22	−1.67290	−0.836451	−	0.548042i	$-0.815373\pi$
$373$	−1.21059e22	−1.67290	−0.836451	+	0.548042i	$0.815373\pi$
$374$	−6.99871e20	−0.0945387
$375$	4.69700e21	0.620233
$376$	−3.09177e21	−0.399127
$377$	2.50643e22	3.16340
$378$	2.87359e20	0.0354605
$379$	−1.37665e21	−0.166108	−0.0830538	−	0.996545i	$-0.526467\pi$
$379$	−1.37665e21	−0.166108	−0.0830538	+	0.996545i	$0.526467\pi$
$380$	−2.27849e21	−0.268836
$381$	−8.92658e21	−1.02997
$382$	7.66353e21	0.864750
$383$	−1.46554e22	−1.61736	−0.808680	−	0.588249i	$-0.799818\pi$
$383$	−1.46554e22	−1.61736	−0.808680	+	0.588249i	$0.799818\pi$
$384$	4.72770e20	0.0510310
$385$	−1.28223e21	−0.135378
$386$	4.52069e21	0.466888
$387$	−1.05470e21	−0.106558
$388$	−7.74992e21	−0.765998
$389$	−1.63718e22	−1.58316	−0.791578	−	0.611069i	$-0.790740\pi$
$389$	−1.63718e22	−1.58316	−0.791578	+	0.611069i	$0.790740\pi$
$390$	−5.87927e21	−0.556255
$391$	−3.16488e21	−0.292991
$392$	3.63788e21	0.329546
$393$	−6.50138e21	−0.576327
$394$	−7.16753e21	−0.621802
$395$	1.42368e22	1.20875
$396$	−1.41075e21	−0.117230
$397$	−2.81337e21	−0.228827	−0.114414	−	0.993433i	$-0.536499\pi$
$397$	−2.81337e21	−0.228827	−0.114414	+	0.993433i	$0.536499\pi$
$398$	−8.54680e21	−0.680452
$399$	1.40525e21	0.109517
$400$	−1.48916e21	−0.113614
$401$	−1.25446e22	−0.936976	−0.468488	−	0.883470i	$-0.655201\pi$
$401$	−1.25446e22	−0.936976	−0.468488	+	0.883470i	$0.655201\pi$
$402$	−2.44708e20	−0.0178948
$403$	3.69098e22	2.64270
$404$	−2.88911e21	−0.202546
$405$	1.19548e21	0.0820679
$406$	4.70022e21	0.315971
$407$	9.78730e21	0.644333
$408$	−6.01781e20	−0.0387996
$409$	5.26567e21	0.332511	0.166255	−	0.986083i	$-0.446832\pi$
$409$	5.26567e21	0.332511	0.166255	+	0.986083i	$0.446832\pi$
$410$	−9.44931e21	−0.584436
$411$	−3.00253e21	−0.181900
$412$	5.18002e21	0.307401
$413$	−1.66389e21	−0.0967272
$414$	−6.37953e21	−0.363317
$415$	1.31858e22	0.735696
$416$	5.96558e21	0.326106
$417$	1.52456e22	0.816559
$418$	−6.89885e21	−0.362058
$419$	−2.69138e22	−1.38406	−0.692031	−	0.721867i	$-0.743284\pi$
$419$	−2.69138e22	−1.38406	−0.692031	+	0.721867i	$0.743284\pi$
$420$	−1.10252e21	−0.0555606
$421$	−6.21080e21	−0.306725	−0.153363	−	0.988170i	$-0.549010\pi$
$421$	−6.21080e21	−0.306725	−0.153363	+	0.988170i	$0.549010\pi$
$422$	1.88266e22	0.911206
$423$	7.93282e21	0.376300
$424$	3.46521e21	0.161109
$425$	1.89552e21	0.0863819
$426$	−9.00999e21	−0.402478
$427$	9.94120e21	0.435313
$428$	9.90876e21	0.425351
$429$	−1.78013e22	−0.749144
$430$	4.04659e21	0.166958
$431$	4.58123e21	0.185321	0.0926606	−	0.995698i	$-0.470463\pi$
$431$	4.58123e21	0.185321	0.0926606	+	0.995698i	$0.470463\pi$
$432$	−1.21303e21	−0.0481125
$433$	1.55342e22	0.604144	0.302072	−	0.953285i	$-0.402322\pi$
$433$	1.55342e22	0.604144	0.302072	+	0.953285i	$0.402322\pi$
$434$	6.92156e21	0.263962
$435$	1.95539e22	0.731265
$436$	−9.68818e20	−0.0355310
$437$	−3.11972e22	−1.12208
$438$	5.54619e21	0.195643
$439$	−3.24405e22	−1.12238	−0.561188	−	0.827688i	$-0.689656\pi$
$439$	−3.24405e22	−1.12238	−0.561188	+	0.827688i	$0.689656\pi$
$440$	5.41265e21	0.183680
$441$	−9.33401e21	−0.310699
$442$	−7.59349e21	−0.247943
$443$	−4.22765e22	−1.35415	−0.677077	−	0.735912i	$-0.736753\pi$
$443$	−4.22765e22	−1.35415	−0.677077	+	0.735912i	$0.736753\pi$
$444$	8.41556e21	0.264440
$445$	−3.61696e22	−1.11502
$446$	1.38816e22	0.419849
$447$	−1.01044e22	−0.299846
$448$	1.11870e21	0.0325725
$449$	6.16238e22	1.76058	0.880288	−	0.474440i	$-0.157349\pi$
$449$	6.16238e22	1.76058	0.880288	+	0.474440i	$0.157349\pi$
$450$	3.82085e21	0.107116
$451$	−2.86107e22	−0.787097
$452$	−2.22180e21	−0.0599831
$453$	1.63139e22	0.432238
$454$	−4.23880e22	−1.10222
$455$	−1.39120e22	−0.355052
$456$	−5.93195e21	−0.148592
$457$	1.87584e22	0.461219	0.230610	−	0.973046i	$-0.425928\pi$
$457$	1.87584e22	0.461219	0.230610	+	0.973046i	$0.425928\pi$
$458$	2.73739e22	0.660663
$459$	1.54404e21	0.0365806
$460$	2.44765e22	0.569256
$461$	2.71382e22	0.619617	0.309808	−	0.950799i	$-0.399735\pi$
$461$	2.71382e22	0.619617	0.309808	+	0.950799i	$0.399735\pi$
$462$	−3.33822e21	−0.0748269
$463$	−5.35664e22	−1.17884	−0.589419	−	0.807827i	$-0.700643\pi$
$463$	−5.35664e22	−1.17884	−0.589419	+	0.807827i	$0.700643\pi$
$464$	−1.98410e22	−0.428706
$465$	2.87952e22	0.610899
$466$	−1.13225e22	−0.235865
$467$	5.39478e22	1.10352	0.551760	−	0.834003i	$-0.313956\pi$
$467$	5.39478e22	1.10352	0.551760	+	0.834003i	$0.313956\pi$
$468$	−1.53064e22	−0.307456
$469$	−5.79046e20	−0.0114221
$470$	−3.04361e22	−0.589599
$471$	3.40291e21	0.0647400
$472$	7.02375e21	0.131239
$473$	1.22523e22	0.224853
$474$	3.70649e22	0.668108
$475$	1.86847e22	0.330820
$476$	−1.42398e21	−0.0247653
$477$	−8.89098e21	−0.151895
$478$	3.28559e22	0.551412
$479$	7.35402e22	1.21248	0.606238	−	0.795284i	$-0.292678\pi$
$479$	7.35402e22	1.21248	0.606238	+	0.795284i	$0.292678\pi$
$480$	4.65404e21	0.0753842
$481$	1.06191e23	1.68987
$482$	−2.79367e22	−0.436793
$483$	−1.50957e22	−0.231901
$484$	−1.67365e22	−0.252626
$485$	−7.62918e22	−1.13155
$486$	3.11236e21	0.0453609
$487$	−1.75596e22	−0.251489	−0.125745	−	0.992063i	$-0.540132\pi$
$487$	−1.75596e22	−0.251489	−0.125745	+	0.992063i	$0.540132\pi$
$488$	−4.19646e22	−0.590629
$489$	−2.66280e21	−0.0368309
$490$	3.58120e22	0.486813
$491$	−2.28182e22	−0.304851	−0.152426	−	0.988315i	$-0.548708\pi$
$491$	−2.28182e22	−0.304851	−0.152426	+	0.988315i	$0.548708\pi$
$492$	−2.46008e22	−0.323032
$493$	2.52552e22	0.325951
$494$	−7.48514e22	−0.949556
$495$	−1.38877e22	−0.173175
$496$	−2.92179e22	−0.358141
$497$	−2.13201e22	−0.256898
$498$	3.43286e22	0.406637
$499$	−8.12217e21	−0.0945839	−0.0472920	−	0.998881i	$-0.515059\pi$
$499$	−8.12217e21	−0.0945839	−0.0472920	+	0.998881i	$0.515059\pi$
$500$	−4.69171e22	−0.537138
$501$	−2.94488e22	−0.331472
$502$	−4.13636e22	−0.457759
$503$	−8.07772e22	−0.878944	−0.439472	−	0.898256i	$-0.644834\pi$
$503$	−8.07772e22	−0.878944	−0.439472	+	0.898256i	$0.644834\pi$
$504$	−2.87035e21	−0.0307097
$505$	−2.84410e22	−0.299205
$506$	7.41103e22	0.766653
$507$	−1.36386e23	−1.38740
$508$	8.91651e22	0.891976
$509$	4.89899e22	0.481954	0.240977	−	0.970531i	$-0.422532\pi$
$509$	4.89899e22	0.481954	0.240977	+	0.970531i	$0.422532\pi$
$510$	−5.92406e21	−0.0573156
$511$	1.31238e22	0.124877
$512$	−4.72237e21	−0.0441942
$513$	1.52201e22	0.140094
$514$	4.74679e22	0.429748
$515$	5.09932e22	0.454099
$516$	1.05351e22	0.0922817
$517$	−9.21547e22	−0.794050
$518$	1.99135e22	0.168789
$519$	−1.11235e22	−0.0927513
$520$	5.87264e22	0.481731
$521$	1.57587e23	1.27174	0.635872	−	0.771794i	$-0.280641\pi$
$521$	1.57587e23	1.27174	0.635872	+	0.771794i	$0.280641\pi$
$522$	5.09076e22	0.404188
$523$	−1.04092e22	−0.0813116	−0.0406558	−	0.999173i	$-0.512945\pi$
$523$	−1.04092e22	−0.0813116	−0.0406558	+	0.999173i	$0.512945\pi$
$524$	6.49405e22	0.499114
$525$	9.04118e21	0.0683709
$526$	5.83042e22	0.433832
$527$	3.71909e22	0.272300
$528$	1.40916e22	0.101525
$529$	1.94083e23	1.37599
$530$	3.41122e22	0.237994
$531$	−1.80214e22	−0.123733
$532$	−1.40366e22	−0.0948448
$533$	−3.10422e23	−2.06429
$534$	−9.41657e22	−0.616300
$535$	9.75439e22	0.628338
$536$	2.44432e21	0.0154974
$537$	1.28446e23	0.801565
$538$	−1.15422e23	−0.708986
$539$	1.08432e23	0.655622
$540$	−1.19413e22	−0.0710729
$541$	−2.15031e23	−1.25987	−0.629934	−	0.776649i	$-0.716918\pi$
$541$	−2.15031e23	−1.25987	−0.629934	+	0.776649i	$0.716918\pi$
$542$	−8.38737e22	−0.483762
$543$	1.56740e22	0.0889983
$544$	6.01102e21	0.0336014
$545$	−9.53725e21	−0.0524871
$546$	−3.62191e22	−0.196246
$547$	−3.59066e23	−1.91550	−0.957750	−	0.287604i	$-0.907141\pi$
$547$	−3.59066e23	−1.91550	−0.957750	+	0.287604i	$0.907141\pi$
$548$	2.99914e22	0.157530
$549$	1.07672e23	0.556851
$550$	−4.43864e22	−0.226030
$551$	2.48949e23	1.24831
$552$	6.37234e22	0.314642
$553$	8.77056e22	0.426446
$554$	5.91093e21	0.0283024
$555$	8.28445e22	0.390637
$556$	−1.52284e23	−0.707161
$557$	−3.74661e23	−1.71344	−0.856720	−	0.515782i	$-0.827502\pi$
$557$	−3.74661e23	−1.71344	−0.856720	+	0.515782i	$0.827502\pi$
$558$	7.49668e22	0.337659
$559$	1.32935e23	0.589713
$560$	1.10127e22	0.0481169
$561$	−1.79369e22	−0.0771905
$562$	−2.67057e23	−1.13200
$563$	2.42245e23	1.01143	0.505713	−	0.862702i	$-0.331230\pi$
$563$	2.42245e23	1.01143	0.505713	+	0.862702i	$0.331230\pi$
$564$	−7.92387e22	−0.325886
$565$	−2.18719e22	−0.0886083
$566$	−1.66473e22	−0.0664362
$567$	7.36470e21	0.0289534
$568$	8.99982e22	0.348556
$569$	−2.55956e23	−0.976586	−0.488293	−	0.872680i	$-0.662380\pi$
$569$	−2.55956e23	−0.976586	−0.488293	+	0.872680i	$0.662380\pi$
$570$	−5.83953e22	−0.219504
$571$	1.28710e23	0.476655	0.238328	−	0.971185i	$-0.423401\pi$
$571$	1.28710e23	0.476655	0.238328	+	0.971185i	$0.423401\pi$
$572$	1.77812e23	0.648778
$573$	1.96408e23	0.706065
$574$	−5.82123e22	−0.206188
$575$	−2.00719e23	−0.700506
$576$	1.21166e22	0.0416667
$577$	−1.67941e22	−0.0569064	−0.0284532	−	0.999595i	$-0.509058\pi$
$577$	−1.67941e22	−0.0569064	−0.0284532	+	0.999595i	$0.509058\pi$
$578$	2.04122e23	0.681559
$579$	1.15860e23	0.381213
$580$	−1.95319e23	−0.633294
$581$	8.12309e22	0.259552
$582$	−1.98622e23	−0.625435
$583$	1.03285e23	0.320521
$584$	−5.53994e22	−0.169432
$585$	−1.50679e23	−0.454181
$586$	2.89733e23	0.860734
$587$	2.74559e23	0.803919	0.401960	−	0.915657i	$-0.368329\pi$
$587$	2.74559e23	0.803919	0.401960	+	0.915657i	$0.368329\pi$
$588$	9.32348e22	0.269073
$589$	3.66603e23	1.04284
$590$	6.91432e22	0.193869
$591$	−1.83696e23	−0.507699
$592$	−8.40607e22	−0.229012
$593$	−2.80613e23	−0.753604	−0.376802	−	0.926294i	$-0.622976\pi$
$593$	−2.80613e23	−0.753604	−0.376802	+	0.926294i	$0.622976\pi$
$594$	−3.61559e22	−0.0957183
$595$	−1.40179e22	−0.0365839
$596$	1.00930e23	0.259674
$597$	−2.19045e23	−0.555587
$598$	8.04084e23	2.01067
$599$	6.35662e23	1.56710	0.783552	−	0.621326i	$-0.213406\pi$
$599$	6.35662e23	1.56710	0.783552	+	0.621326i	$0.213406\pi$
$600$	−3.81654e22	−0.0927650
$601$	−1.18232e23	−0.283335	−0.141668	−	0.989914i	$-0.545246\pi$
$601$	−1.18232e23	−0.283335	−0.141668	+	0.989914i	$0.545246\pi$
$602$	2.49289e22	0.0589024
$603$	−6.27160e21	−0.0146110
$604$	−1.62955e23	−0.374329
$605$	−1.64757e23	−0.373185
$606$	−7.40448e22	−0.165378
$607$	−3.65228e23	−0.804379	−0.402189	−	0.915556i	$-0.631751\pi$
$607$	−3.65228e23	−0.804379	−0.402189	+	0.915556i	$0.631751\pi$
$608$	5.92525e22	0.128685
$609$	1.20461e23	0.257989
$610$	−4.13109e23	−0.872491
$611$	−9.99863e23	−2.08252
$612$	−1.54230e22	−0.0316797
$613$	−6.19597e22	−0.125515	−0.0627575	−	0.998029i	$-0.519989\pi$
$613$	−6.19597e22	−0.125515	−0.0627575	+	0.998029i	$0.519989\pi$
$614$	−7.73287e22	−0.154493
$615$	−2.42175e23	−0.477190
$616$	3.33445e22	0.0648020
$617$	−5.04348e23	−0.966733	−0.483367	−	0.875418i	$-0.660586\pi$
$617$	−5.04348e23	−0.966733	−0.483367	+	0.875418i	$0.660586\pi$
$618$	1.32758e23	0.250992
$619$	6.84062e23	1.27563	0.637815	−	0.770190i	$-0.279838\pi$
$619$	6.84062e23	1.27563	0.637815	+	0.770190i	$0.279838\pi$
$620$	−2.87627e23	−0.529054
$621$	−1.63500e23	−0.296647
$622$	6.47142e23	1.15819
$623$	−2.22822e23	−0.393377
$624$	1.52891e23	0.266265
$625$	−1.97334e23	−0.339017
$626$	7.26994e21	0.0123211
$627$	−1.76810e23	−0.295619
$628$	−3.39907e22	−0.0560665
$629$	1.06999e23	0.174121
$630$	−2.82563e22	−0.0453650
$631$	−4.64193e23	−0.735273	−0.367637	−	0.929969i	$-0.619833\pi$
$631$	−4.64193e23	−0.735273	−0.367637	+	0.929969i	$0.619833\pi$
$632$	−3.70231e23	−0.578598
$633$	4.82506e23	0.743996
$634$	−3.98815e23	−0.606755
$635$	8.77760e23	1.31765
$636$	8.88095e22	0.131545
$637$	1.17647e24	1.71947
$638$	−5.91388e23	−0.852897
$639$	−2.30916e23	−0.328622
$640$	−4.64880e22	−0.0652846
$641$	1.07950e24	1.49599	0.747995	−	0.663705i	$-0.231017\pi$
$641$	1.07950e24	1.49599	0.747995	+	0.663705i	$0.231017\pi$
$642$	2.53951e23	0.347298
$643$	−5.46104e23	−0.737025	−0.368512	−	0.929623i	$-0.620133\pi$
$643$	−5.46104e23	−0.737025	−0.368512	+	0.929623i	$0.620133\pi$
$644$	1.50787e23	0.200832
$645$	1.03710e23	0.136321
$646$	−7.54216e22	−0.0978406
$647$	−5.00118e22	−0.0640304	−0.0320152	−	0.999487i	$-0.510192\pi$
$647$	−5.00118e22	−0.0640304	−0.0320152	+	0.999487i	$0.510192\pi$
$648$	−3.10885e22	−0.0392837
$649$	2.09353e23	0.261095
$650$	−4.81585e23	−0.592801
$651$	1.77392e23	0.215524
$652$	2.65979e22	0.0318965
$653$	1.01552e24	1.20206	0.601028	−	0.799228i	$-0.294758\pi$
$653$	1.01552e24	1.20206	0.601028	+	0.799228i	$0.294758\pi$
$654$	−2.48297e22	−0.0290109
$655$	6.39288e23	0.737302
$656$	2.45731e23	0.279754
$657$	1.42143e23	0.159742
$658$	−1.87501e23	−0.208009
$659$	1.22908e24	1.34603	0.673015	−	0.739629i	$-0.264999\pi$
$659$	1.22908e24	1.34603	0.673015	+	0.739629i	$0.264999\pi$
$660$	1.38720e23	0.149974
$661$	−1.07432e24	−1.14662	−0.573312	−	0.819337i	$-0.694342\pi$
$661$	−1.07432e24	−1.14662	−0.573312	+	0.819337i	$0.694342\pi$
$662$	3.17779e23	0.334836
$663$	−1.94613e23	−0.202445
$664$	−3.42899e23	−0.352158
$665$	−1.38179e23	−0.140107
$666$	2.15682e23	0.215915
$667$	−2.67431e24	−2.64327
$668$	2.94156e23	0.287064
$669$	3.55770e23	0.342805
$670$	2.40624e22	0.0228930
$671$	−1.25082e24	−1.17504
$672$	2.86711e22	0.0265954
$673$	−9.62651e23	−0.881741	−0.440870	−	0.897571i	$-0.645330\pi$
$673$	−9.62651e23	−0.881741	−0.440870	+	0.897571i	$0.645330\pi$
$674$	−1.45659e24	−1.31743
$675$	9.79242e22	0.0874597
$676$	1.36232e24	1.20153
$677$	1.15477e24	1.00575	0.502877	−	0.864358i	$-0.332275\pi$
$677$	1.15477e24	1.00575	0.502877	+	0.864358i	$0.332275\pi$
$678$	−5.69424e22	−0.0489760
$679$	−4.69994e23	−0.399208
$680$	5.91738e22	0.0496368
$681$	−1.08636e24	−0.899958
$682$	−8.70880e23	−0.712510
$683$	−1.58385e24	−1.27979	−0.639894	−	0.768463i	$-0.721022\pi$
$683$	−1.58385e24	−1.27979	−0.639894	+	0.768463i	$0.721022\pi$
$684$	−1.52029e23	−0.121325
$685$	2.95242e23	0.232706
$686$	4.57310e23	0.356005
$687$	7.01563e23	0.539429
$688$	−1.05232e23	−0.0799183
$689$	1.12063e24	0.840618
$690$	6.27306e23	0.464796
$691$	2.26307e24	1.65629	0.828143	−	0.560516i	$-0.189397\pi$
$691$	2.26307e24	1.65629	0.828143	+	0.560516i	$0.189397\pi$
$692$	1.11110e23	0.0803250
$693$	−8.55549e22	−0.0610959
$694$	6.86699e23	0.484408
$695$	−1.49911e24	−1.04463
$696$	−5.08502e23	−0.350037
$697$	−3.12786e23	−0.212701
$698$	1.98386e24	1.33272
$699$	−2.90184e23	−0.192583
$700$	−9.03098e22	−0.0592109
$701$	−2.20609e23	−0.142896	−0.0714479	−	0.997444i	$-0.522762\pi$
$701$	−2.20609e23	−0.142896	−0.0714479	+	0.997444i	$0.522762\pi$
$702$	−3.92286e23	−0.251037
$703$	1.05473e24	0.666838
$704$	−1.40757e23	−0.0879229
$705$	−7.80043e23	−0.481405
$706$	−3.81676e23	−0.232732
$707$	−1.75210e23	−0.105559
$708$	1.80011e23	0.107156
$709$	1.08401e24	0.637588	0.318794	−	0.947824i	$-0.396722\pi$
$709$	1.08401e24	0.637588	0.318794	+	0.947824i	$0.396722\pi$
$710$	8.85961e23	0.514895
$711$	9.49932e23	0.545508
$712$	9.40595e23	0.533731
$713$	−3.93820e24	−2.20819
$714$	−3.64950e22	−0.0202208
$715$	1.75042e24	0.958389
$716$	−1.28301e24	−0.694176
$717$	8.42061e23	0.450226
$718$	1.14342e23	0.0604155
$719$	2.90074e23	0.151465	0.0757327	−	0.997128i	$-0.475870\pi$
$719$	2.90074e23	0.151465	0.0757327	+	0.997128i	$0.475870\pi$
$720$	1.19278e23	0.0615509
$721$	3.14142e23	0.160205
$722$	6.59525e23	0.332403
$723$	−7.15987e23	−0.356640
$724$	−1.56563e23	−0.0770748
$725$	1.60171e24	0.779309
$726$	−4.28938e23	−0.206268
$727$	9.54750e23	0.453782	0.226891	−	0.973920i	$-0.427144\pi$
$727$	9.54750e23	0.453782	0.226891	+	0.973920i	$0.427144\pi$
$728$	3.61783e23	0.169954
$729$	7.97664e22	0.0370370
$730$	−5.45363e23	−0.250289
$731$	1.33948e23	0.0607630
$732$	−1.07551e24	−0.482247
$733$	6.99257e23	0.309922	0.154961	−	0.987921i	$-0.450475\pi$
$733$	6.99257e23	0.309922	0.154961	+	0.987921i	$0.450475\pi$
$734$	−2.01276e24	−0.881812
$735$	9.17823e23	0.397481
$736$	−6.36515e23	−0.272488
$737$	7.28564e22	0.0308315
$738$	−6.30492e23	−0.263755
$739$	−7.60786e23	−0.314619	−0.157309	−	0.987549i	$-0.550282\pi$
$739$	−7.60786e23	−0.314619	−0.157309	+	0.987549i	$0.550282\pi$
$740$	−8.27511e23	−0.338302
$741$	−1.91836e24	−0.775310
$742$	2.10148e23	0.0839637
$743$	−6.46819e23	−0.255492	−0.127746	−	0.991807i	$-0.540774\pi$
$743$	−6.46819e23	−0.255492	−0.127746	+	0.991807i	$0.540774\pi$
$744$	−7.48822e23	−0.292421
$745$	9.93579e23	0.383596
$746$	3.09910e24	1.18292
$747$	8.79805e23	0.332018
$748$	1.79167e23	0.0668489
$749$	6.00917e23	0.221676
$750$	−1.20243e24	−0.438571
$751$	−6.84480e23	−0.246843	−0.123422	−	0.992354i	$-0.539387\pi$
$751$	−6.84480e23	−0.246843	−0.123422	+	0.992354i	$0.539387\pi$
$752$	7.91494e23	0.282225
$753$	−1.06010e24	−0.373759
$754$	−6.41646e24	−2.23686
$755$	−1.60416e24	−0.552967
$756$	−7.35640e22	−0.0250744
$757$	−1.83496e24	−0.618461	−0.309230	−	0.950987i	$-0.600071\pi$
$757$	−1.83496e24	−0.618461	−0.309230	+	0.950987i	$0.600071\pi$
$758$	3.52422e23	0.117456
$759$	1.89936e24	0.625970
$760$	5.83294e23	0.190096
$761$	−1.40753e24	−0.453614	−0.226807	−	0.973940i	$-0.572829\pi$
$761$	−1.40753e24	−0.453614	−0.226807	+	0.973940i	$0.572829\pi$
$762$	2.28520e24	0.728296
$763$	−5.87540e22	−0.0185174
$764$	−1.96186e24	−0.611470
$765$	−1.51827e23	−0.0467980
$766$	3.75177e24	1.14365
$767$	2.27144e24	0.684764
$768$	−1.21029e23	−0.0360844
$769$	−5.57939e24	−1.64518	−0.822589	−	0.568637i	$-0.807471\pi$
$769$	−5.57939e24	−1.64518	−0.822589	+	0.568637i	$0.807471\pi$
$770$	3.28250e23	0.0957269
$771$	1.21655e24	0.350888
$772$	−1.15730e24	−0.330140
$773$	5.98699e24	1.68921	0.844604	−	0.535391i	$-0.179836\pi$
$773$	5.98699e24	1.68921	0.844604	+	0.535391i	$0.179836\pi$
$774$	2.70003e23	0.0753477
$775$	2.35868e24	0.651035
$776$	1.98398e24	0.541642
$777$	5.10362e23	0.137816
$778$	4.19117e24	1.11946
$779$	−3.08323e24	−0.814588
$780$	1.50509e24	0.393332
$781$	2.68252e24	0.693442
$782$	8.10209e23	0.207176
$783$	1.30471e24	0.330018
$784$	−9.31297e23	−0.233024
$785$	−3.34612e23	−0.0828226
$786$	1.66435e24	0.407525
$787$	4.19082e24	1.01511	0.507556	−	0.861619i	$-0.330549\pi$
$787$	4.19082e24	1.01511	0.507556	+	0.861619i	$0.330549\pi$
$788$	1.83489e24	0.439680
$789$	1.49427e24	0.354222
$790$	−3.64463e24	−0.854718
$791$	−1.34741e23	−0.0312608
$792$	3.61152e23	0.0828945
$793$	−1.35711e25	−3.08173
$794$	7.20223e23	0.161805
$795$	8.74259e23	0.194321
$796$	2.18798e24	0.481152
$797$	5.25660e22	0.0114369	0.00571847	−	0.999984i	$-0.498180\pi$
$797$	5.25660e22	0.0114369	0.00571847	+	0.999984i	$0.498180\pi$
$798$	−3.59743e23	−0.0774404
$799$	−1.00748e24	−0.214580
$800$	3.81224e23	0.0803369
$801$	−2.41336e24	−0.503207
$802$	3.21141e24	0.662542
$803$	−1.65126e24	−0.337079
$804$	6.26453e22	0.0126535
$805$	1.48438e24	0.296674
$806$	−9.44890e24	−1.86867
$807$	−2.95813e24	−0.578885
$808$	7.39613e23	0.143221
$809$	1.66505e24	0.319055	0.159527	−	0.987194i	$-0.449003\pi$
$809$	1.66505e24	0.319055	0.159527	+	0.987194i	$0.449003\pi$
$810$	−3.06042e23	−0.0580307
$811$	−1.37435e23	−0.0257881	−0.0128941	−	0.999917i	$-0.504104\pi$
$811$	−1.37435e23	−0.0257881	−0.0128941	+	0.999917i	$0.504104\pi$
$812$	−1.20326e24	−0.223425
$813$	−2.14959e24	−0.394990
$814$	−2.50555e24	−0.455612
$815$	2.61835e23	0.0471182
$816$	1.54056e23	0.0274354
$817$	1.32037e24	0.232706
$818$	−1.34801e24	−0.235120
$819$	−9.28256e23	−0.160234
$820$	2.41902e24	0.413259
$821$	−2.33660e24	−0.395064	−0.197532	−	0.980296i	$-0.563293\pi$
$821$	−2.33660e24	−0.395064	−0.197532	+	0.980296i	$0.563293\pi$
$822$	7.68647e23	0.128622
$823$	−2.24612e24	−0.371993	−0.185997	−	0.982550i	$-0.559551\pi$
$823$	−2.24612e24	−0.371993	−0.185997	+	0.982550i	$0.559551\pi$
$824$	−1.32609e24	−0.217365
$825$	−1.13757e24	−0.184553
$826$	4.25955e23	0.0683965
$827$	7.40795e24	1.17734	0.588669	−	0.808374i	$-0.299652\pi$
$827$	7.40795e24	1.17734	0.588669	+	0.808374i	$0.299652\pi$
$828$	1.63316e24	0.256904
$829$	−1.76259e21	−0.000274434 0	−0.000137217	−	1.00000i	$-0.500044\pi$
$829$	−1.76259e21	−0.000274434 0	−0.000137217		1.00000i	$0.500044\pi$
$830$	−3.37557e24	−0.520216
$831$	1.51491e23	0.0231088
$832$	−1.52719e24	−0.230592
$833$	1.18543e24	0.177172
$834$	−3.90287e24	−0.577394
$835$	2.89573e24	0.424056
$836$	1.76611e24	0.256014
$837$	1.92132e24	0.275697
$838$	6.88993e24	0.978680
$839$	−1.89777e24	−0.266850	−0.133425	−	0.991059i	$-0.542598\pi$
$839$	−1.89777e24	−0.266850	−0.133425	+	0.991059i	$0.542598\pi$
$840$	2.82245e23	0.0392873
$841$	1.40834e25	1.94063
$842$	1.58996e24	0.216888
$843$	−6.84438e24	−0.924272
$844$	−4.81961e24	−0.644320
$845$	1.34110e25	1.77492
$846$	−2.03080e24	−0.266085
$847$	−1.01498e24	−0.131659
$848$	−8.87094e23	−0.113921
$849$	−4.26653e23	−0.0542449
$850$	−4.85253e23	−0.0610812
$851$	−1.13303e25	−1.41202
$852$	2.30656e24	0.284595
$853$	6.86031e24	0.838064	0.419032	−	0.907971i	$-0.362370\pi$
$853$	6.86031e24	0.838064	0.419032	+	0.907971i	$0.362370\pi$
$854$	−2.54495e24	−0.307813
$855$	−1.49661e24	−0.179224
$856$	−2.53664e24	−0.300769
$857$	1.37062e25	1.60909	0.804544	−	0.593893i	$-0.202410\pi$
$857$	1.37062e25	1.60909	0.804544	+	0.593893i	$0.202410\pi$
$858$	4.55714e24	0.529725
$859$	1.44877e24	0.166747	0.0833734	−	0.996518i	$-0.473431\pi$
$859$	1.44877e24	0.166747	0.0833734	+	0.996518i	$0.473431\pi$
$860$	−1.03593e24	−0.118057
$861$	−1.49192e24	−0.168352
$862$	−1.17279e24	−0.131042
$863$	−2.36595e24	−0.261767	−0.130883	−	0.991398i	$-0.541781\pi$
$863$	−2.36595e24	−0.261767	−0.130883	+	0.991398i	$0.541781\pi$
$864$	3.10535e23	0.0340207
$865$	1.09379e24	0.118658
$866$	−3.97674e24	−0.427194
$867$	5.23143e24	0.556491
$868$	−1.77192e24	−0.186649
$869$	−1.10352e25	−1.15110
$870$	−5.00580e24	−0.517083
$871$	7.90480e23	0.0808605
$872$	2.48017e23	0.0251242
$873$	−5.09046e24	−0.510665
$874$	7.98649e24	0.793430
$875$	−2.84529e24	−0.279935
$876$	−1.41982e24	−0.138341
$877$	−6.05312e24	−0.584094	−0.292047	−	0.956404i	$-0.594336\pi$
$877$	−6.05312e24	−0.584094	−0.292047	+	0.956404i	$0.594336\pi$
$878$	8.30476e24	0.793640
$879$	7.42555e24	0.702786
$880$	−1.38564e24	−0.129882
$881$	−1.33966e25	−1.24365	−0.621824	−	0.783157i	$-0.713608\pi$
$881$	−1.33966e25	−1.24365	−0.621824	+	0.783157i	$0.713608\pi$
$882$	2.38951e24	0.219698
$883$	−1.86489e25	−1.69820	−0.849098	−	0.528236i	$-0.822854\pi$
$883$	−1.86489e25	−1.69820	−0.849098	+	0.528236i	$0.822854\pi$
$884$	1.94393e24	0.175322
$885$	1.77207e24	0.158293
$886$	1.08228e25	0.957531
$887$	−1.74962e25	−1.53318	−0.766591	−	0.642135i	$-0.778049\pi$
$887$	−1.74962e25	−1.53318	−0.766591	+	0.642135i	$0.778049\pi$
$888$	−2.15438e24	−0.186988
$889$	5.40742e24	0.464863
$890$	9.25941e24	0.788439
$891$	−9.26637e23	−0.0781537
$892$	−3.55369e24	−0.296878
$893$	−9.93104e24	−0.821784
$894$	2.58673e24	0.212023
$895$	−1.26302e25	−1.02545
$896$	−2.86388e23	−0.0230323
$897$	2.06078e25	1.64171
$898$	−1.57757e25	−1.24492
$899$	3.14262e25	2.45660
$900$	−9.78138e23	−0.0757423
$901$	1.12917e24	0.0866158
$902$	7.32435e24	0.556562
$903$	6.38901e23	0.0480936
$904$	5.68782e23	0.0424145
$905$	−1.54124e24	−0.113857
$906$	−4.17636e24	−0.305639
$907$	−1.20500e25	−0.873622	−0.436811	−	0.899553i	$-0.643892\pi$
$907$	−1.20500e25	−0.873622	−0.436811	+	0.899553i	$0.643892\pi$
$908$	1.08513e25	0.779386
$909$	−1.89769e24	−0.135030
$910$	3.56146e24	0.251059
$911$	−8.00930e24	−0.559356	−0.279678	−	0.960094i	$-0.590228\pi$
$911$	−8.00930e24	−0.559356	−0.279678	+	0.960094i	$0.590228\pi$
$912$	1.51858e24	0.105071
$913$	−1.02206e25	−0.700607
$914$	−4.80214e24	−0.326131
$915$	−1.05875e25	−0.712386
$916$	−7.00772e24	−0.467159
$917$	3.93832e24	0.260119
$918$	−3.95274e23	−0.0258664
$919$	1.26791e25	0.822068	0.411034	−	0.911620i	$-0.365168\pi$
$919$	1.26791e25	0.822068	0.411034	+	0.911620i	$0.365168\pi$
$920$	−6.26598e24	−0.402525
$921$	−1.98185e24	−0.126143
$922$	−6.94738e24	−0.438135
$923$	2.91049e25	1.81866
$924$	8.54584e23	0.0529106
$925$	6.78599e24	0.416302
$926$	1.37130e25	0.833565
$927$	3.40245e24	0.204934
$928$	5.07929e24	0.303141
$929$	3.48248e24	0.205947	0.102973	−	0.994684i	$-0.467164\pi$
$929$	3.48248e24	0.205947	0.102973	+	0.994684i	$0.467164\pi$
$930$	−7.37156e24	−0.431971
$931$	1.16852e25	0.678521
$932$	2.89857e24	0.166782
$933$	1.65856e25	0.945662
$934$	−1.38106e25	−0.780307
$935$	1.76376e24	0.0987507
$936$	3.91844e24	0.217404
$937$	1.26255e25	0.694166	0.347083	−	0.937834i	$-0.387172\pi$
$937$	1.26255e25	0.694166	0.347083	+	0.937834i	$0.387172\pi$
$938$	1.48236e23	0.00807661
$939$	1.86321e23	0.0100601
$940$	7.79163e24	0.416909
$941$	−2.57702e25	−1.36649	−0.683245	−	0.730189i	$-0.739432\pi$
$941$	−2.57702e25	−1.36649	−0.683245	+	0.730189i	$0.739432\pi$
$942$	−8.71145e23	−0.0457781
$943$	3.31214e25	1.72488
$944$	−1.79808e24	−0.0927998
$945$	−7.24179e23	−0.0370404
$946$	−3.13659e24	−0.158995
$947$	−6.66193e24	−0.334676	−0.167338	−	0.985900i	$-0.553517\pi$
$947$	−6.66193e24	−0.334676	−0.167338	+	0.985900i	$0.553517\pi$
$948$	−9.48861e24	−0.472424
$949$	−1.79159e25	−0.884046
$950$	−4.78330e24	−0.233925
$951$	−1.02212e25	−0.495413
$952$	3.64539e23	0.0175117
$953$	−1.09771e25	−0.522633	−0.261316	−	0.965253i	$-0.584157\pi$
$953$	−1.09771e25	−0.522633	−0.261316	+	0.965253i	$0.584157\pi$
$954$	2.27609e24	0.107406
$955$	−1.93130e25	−0.903277
$956$	−8.41111e24	−0.389907
$957$	−1.51566e25	−0.696388
$958$	−1.88263e25	−0.857349
$959$	1.81883e24	0.0820983
$960$	−1.19144e24	−0.0533046
$961$	2.37282e25	1.05224
$962$	−2.71848e25	−1.19492
$963$	6.50848e24	0.283567
$964$	7.15180e24	0.308859
$965$	−1.13927e25	−0.487690
$966$	3.86450e24	0.163979
$967$	−2.49499e25	−1.04941	−0.524704	−	0.851285i	$-0.675824\pi$
$967$	−2.49499e25	−1.04941	−0.524704	+	0.851285i	$0.675824\pi$
$968$	4.28454e24	0.178634
$969$	−1.93297e24	−0.0798865
$970$	1.95307e25	0.800126
$971$	−3.22129e24	−0.130818	−0.0654088	−	0.997859i	$-0.520835\pi$
$971$	−3.22129e24	−0.130818	−0.0654088	+	0.997859i	$0.520835\pi$
$972$	−7.96765e23	−0.0320750
$973$	−9.23526e24	−0.368544
$974$	4.49527e24	0.177830
$975$	−1.23425e25	−0.484020
$976$	1.07429e25	0.417638
$977$	−1.34578e25	−0.518643	−0.259322	−	0.965791i	$-0.583499\pi$
$977$	−1.34578e25	−0.518643	−0.259322	+	0.965791i	$0.583499\pi$
$978$	6.81676e23	0.0260434
$979$	2.80358e25	1.06184
$980$	−9.16788e24	−0.344229
$981$	−6.36359e23	−0.0236873
$982$	5.84145e24	0.215562
$983$	2.69957e25	0.987620	0.493810	−	0.869570i	$-0.335604\pi$
$983$	2.69957e25	0.987620	0.493810	+	0.869570i	$0.335604\pi$
$984$	6.29781e24	0.228418
$985$	1.80630e25	0.649505
$986$	−6.46534e24	−0.230482
$987$	−4.80544e24	−0.169839
$988$	1.91620e25	0.671438
$989$	−1.41839e25	−0.492752
$990$	3.55525e24	0.122454
$991$	3.87841e25	1.32443	0.662213	−	0.749316i	$-0.269617\pi$
$991$	3.87841e25	1.32443	0.662213	+	0.749316i	$0.269617\pi$
$992$	7.47977e24	0.253244
$993$	8.14432e24	0.273392
$994$	5.45795e24	0.181654
$995$	2.15389e25	0.710769
$996$	−8.78813e24	−0.287536
$997$	−5.15811e25	−1.67333	−0.836665	−	0.547715i	$-0.815498\pi$
$997$	−5.15811e25	−1.67333	−0.836665	+	0.547715i	$0.815498\pi$
$998$	2.07927e24	0.0668809
$999$	5.52769e24	0.176294

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6.18.a.a.1.1	✓	1
3.2	odd	2		18.18.a.c.1.1		1
4.3	odd	2		48.18.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.18.a.a.1.1	✓	1	1.1	even	1	trivial
18.18.a.c.1.1		1	3.2	odd	2
48.18.a.f.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:	\( N \)	\(=\)	\( 6 = 2 \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	6.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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