LMFDB - Embedded newform 6.18.a.b.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:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q-256.000 q^{2} +6561.00 q^{3} +65536.0 q^{4} -72186.0 q^{5} -1.67962e6 q^{6} -8.64018e6 q^{7} -1.67772e7 q^{8} +4.30467e7 q^{9} +O(q^{10})$

\(q-256.000 q^{2} +6561.00 q^{3} +65536.0 q^{4} -72186.0 q^{5} -1.67962e6 q^{6} -8.64018e6 q^{7} -1.67772e7 q^{8} +4.30467e7 q^{9} +1.84796e7 q^{10} +1.15930e9 q^{11} +4.29982e8 q^{12} +2.80106e9 q^{13} +2.21189e9 q^{14} -4.73612e8 q^{15} +4.29497e9 q^{16} +3.29797e10 q^{17} -1.10200e10 q^{18} +5.77850e9 q^{19} -4.73078e9 q^{20} -5.66882e10 q^{21} -2.96782e11 q^{22} +1.69117e11 q^{23} -1.10075e11 q^{24} -7.57729e11 q^{25} -7.17072e11 q^{26} +2.82430e11 q^{27} -5.66243e11 q^{28} +3.63174e12 q^{29} +1.21245e11 q^{30} +6.88098e12 q^{31} -1.09951e12 q^{32} +7.60620e12 q^{33} -8.44279e12 q^{34} +6.23700e11 q^{35} +2.82111e12 q^{36} -3.54645e13 q^{37} -1.47930e12 q^{38} +1.83778e13 q^{39} +1.21108e12 q^{40} -8.92377e12 q^{41} +1.45122e13 q^{42} -1.29966e14 q^{43} +7.59762e13 q^{44} -3.10737e12 q^{45} -4.32940e13 q^{46} +1.29500e14 q^{47} +2.81793e13 q^{48} -1.57978e14 q^{49} +1.93979e14 q^{50} +2.16380e14 q^{51} +1.83570e14 q^{52} +2.18262e14 q^{53} -7.23020e13 q^{54} -8.36856e13 q^{55} +1.44958e14 q^{56} +3.79127e13 q^{57} -9.29724e14 q^{58} -1.78340e15 q^{59} -3.10387e13 q^{60} +1.46915e15 q^{61} -1.76153e15 q^{62} -3.71932e14 q^{63} +2.81475e14 q^{64} -2.02198e14 q^{65} -1.94719e15 q^{66} +5.05156e15 q^{67} +2.16136e15 q^{68} +1.10958e15 q^{69} -1.59667e14 q^{70} -7.93481e14 q^{71} -7.22204e14 q^{72} +6.34350e15 q^{73} +9.07891e15 q^{74} -4.97146e15 q^{75} +3.78700e14 q^{76} -1.00166e16 q^{77} -4.70471e15 q^{78} -8.29288e15 q^{79} -3.10037e14 q^{80} +1.85302e15 q^{81} +2.28448e15 q^{82} -2.40315e16 q^{83} -3.71512e15 q^{84} -2.38067e15 q^{85} +3.32714e16 q^{86} +2.38278e16 q^{87} -1.94499e16 q^{88} -1.54665e16 q^{89} +7.95487e14 q^{90} -2.42017e16 q^{91} +1.10833e16 q^{92} +4.51461e16 q^{93} -3.31519e16 q^{94} -4.17127e14 q^{95} -7.21390e15 q^{96} +7.97460e16 q^{97} +4.04423e16 q^{98} +4.99043e16 q^{99} +O(q^{100})\)

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
$5$	−72186.0	−0.0826434	−0.0413217	−	0.999146i	$-0.513157\pi$
$5$	−72186.0	−0.0826434	−0.0413217	+	0.999146i	$0.513157\pi$
$6$	−1.67962e6	−0.408248
$7$	−8.64018e6	−0.566487	−0.283243	−	0.959048i	$-0.591410\pi$
$7$	−8.64018e6	−0.566487	−0.283243	+	0.959048i	$0.591410\pi$
$8$	−1.67772e7	−0.353553
$9$	4.30467e7	0.333333
$10$	1.84796e7	0.0584377
$11$	1.15930e9	1.63065	0.815323	−	0.579006i	$-0.196559\pi$
$11$	1.15930e9	1.63065	0.815323	+	0.579006i	$0.196559\pi$
$12$	4.29982e8	0.288675
$13$	2.80106e9	0.952367	0.476184	−	0.879346i	$-0.342020\pi$
$13$	2.80106e9	0.952367	0.476184	+	0.879346i	$0.342020\pi$
$14$	2.21189e9	0.400567
$15$	−4.73612e8	−0.0477142
$16$	4.29497e9	0.250000
$17$	3.29797e10	1.14665	0.573324	−	0.819329i	$-0.305654\pi$
$17$	3.29797e10	1.14665	0.573324	+	0.819329i	$0.305654\pi$
$18$	−1.10200e10	−0.235702
$19$	5.77850e9	0.0780566	0.0390283	−	0.999238i	$-0.487574\pi$
$19$	5.77850e9	0.0780566	0.0390283	+	0.999238i	$0.487574\pi$
$20$	−4.73078e9	−0.0413217
$21$	−5.66882e10	−0.327061
$22$	−2.96782e11	−1.15304
$23$	1.69117e11	0.450299	0.225149	−	0.974324i	$-0.427713\pi$
$23$	1.69117e11	0.450299	0.225149	+	0.974324i	$0.427713\pi$
$24$	−1.10075e11	−0.204124
$25$	−7.57729e11	−0.993170
$26$	−7.17072e11	−0.673425
$27$	2.82430e11	0.192450
$28$	−5.66243e11	−0.283243
$29$	3.63174e12	1.34813	0.674064	−	0.738673i	$-0.264547\pi$
$29$	3.63174e12	1.34813	0.674064	+	0.738673i	$0.264547\pi$
$30$	1.21245e11	0.0337390
$31$	6.88098e12	1.44902	0.724512	−	0.689262i	$-0.242065\pi$
$31$	6.88098e12	1.44902	0.724512	+	0.689262i	$0.242065\pi$
$32$	−1.09951e12	−0.176777
$33$	7.60620e12	0.941454
$34$	−8.44279e12	−0.810803
$35$	6.23700e11	0.0468164
$36$	2.82111e12	0.166667
$37$	−3.54645e13	−1.65989	−0.829945	−	0.557846i	$-0.811628\pi$
$37$	−3.54645e13	−1.65989	−0.829945	+	0.557846i	$0.811628\pi$
$38$	−1.47930e12	−0.0551943
$39$	1.83778e13	0.549849
$40$	1.21108e12	0.0292188
$41$	−8.92377e12	−0.174536	−0.0872681	−	0.996185i	$-0.527814\pi$
$41$	−8.92377e12	−0.174536	−0.0872681	+	0.996185i	$0.527814\pi$
$42$	1.45122e13	0.231267
$43$	−1.29966e14	−1.69570	−0.847851	−	0.530235i	$-0.822104\pi$
$43$	−1.29966e14	−1.69570	−0.847851	+	0.530235i	$0.822104\pi$
$44$	7.59762e13	0.815323
$45$	−3.10737e12	−0.0275478
$46$	−4.32940e13	−0.318409
$47$	1.29500e14	0.793300	0.396650	−	0.917970i	$-0.370173\pi$
$47$	1.29500e14	0.793300	0.396650	+	0.917970i	$0.370173\pi$
$48$	2.81793e13	0.144338
$49$	−1.57978e14	−0.679093
$50$	1.93979e14	0.702277
$51$	2.16380e14	0.662018
$52$	1.83570e14	0.476184
$53$	2.18262e14	0.481541	0.240771	−	0.970582i	$-0.422600\pi$
$53$	2.18262e14	0.481541	0.240771	+	0.970582i	$0.422600\pi$
$54$	−7.23020e13	−0.136083
$55$	−8.36856e13	−0.134762
$56$	1.44958e14	0.200283
$57$	3.79127e13	0.0450660
$58$	−9.29724e14	−0.953271
$59$	−1.78340e15	−1.58127	−0.790637	−	0.612286i	$-0.790250\pi$
$59$	−1.78340e15	−1.58127	−0.790637	+	0.612286i	$0.790250\pi$
$60$	−3.10387e13	−0.0238571
$61$	1.46915e15	0.981209	0.490604	−	0.871382i	$-0.336776\pi$
$61$	1.46915e15	0.981209	0.490604	+	0.871382i	$0.336776\pi$
$62$	−1.76153e15	−1.02462
$63$	−3.71932e14	−0.188829
$64$	2.81475e14	0.125000
$65$	−2.02198e14	−0.0787068
$66$	−1.94719e15	−0.665708
$67$	5.05156e15	1.51981	0.759906	−	0.650033i	$-0.225245\pi$
$67$	5.05156e15	1.51981	0.759906	+	0.650033i	$0.225245\pi$
$68$	2.16136e15	0.573324
$69$	1.10958e15	0.259980
$70$	−1.59667e14	−0.0331042
$71$	−7.93481e14	−0.145828	−0.0729139	−	0.997338i	$-0.523230\pi$
$71$	−7.93481e14	−0.145828	−0.0729139	+	0.997338i	$0.523230\pi$
$72$	−7.22204e14	−0.117851
$73$	6.34350e15	0.920629	0.460315	−	0.887756i	$-0.347737\pi$
$73$	6.34350e15	0.920629	0.460315	+	0.887756i	$0.347737\pi$
$74$	9.07891e15	1.17372
$75$	−4.97146e15	−0.573407
$76$	3.78700e14	0.0390283
$77$	−1.00166e16	−0.923739
$78$	−4.70471e15	−0.388802
$79$	−8.29288e15	−0.615000	−0.307500	−	0.951548i	$-0.599492\pi$
$79$	−8.29288e15	−0.615000	−0.307500	+	0.951548i	$0.599492\pi$
$80$	−3.10037e14	−0.0206608
$81$	1.85302e15	0.111111
$82$	2.28448e15	0.123416
$83$	−2.40315e16	−1.17116	−0.585581	−	0.810614i	$-0.699134\pi$
$83$	−2.40315e16	−1.17116	−0.585581	+	0.810614i	$0.699134\pi$
$84$	−3.71512e15	−0.163531
$85$	−2.38067e15	−0.0947629
$86$	3.32714e16	1.19904
$87$	2.38278e16	0.778342
$88$	−1.94499e16	−0.576520
$89$	−1.54665e16	−0.416463	−0.208231	−	0.978080i	$-0.566771\pi$
$89$	−1.54665e16	−0.416463	−0.208231	+	0.978080i	$0.566771\pi$
$90$	7.95487e14	0.0194792
$91$	−2.42017e16	−0.539503
$92$	1.10833e16	0.225149
$93$	4.51461e16	0.836595
$94$	−3.31519e16	−0.560948
$95$	−4.17127e14	−0.00645086
$96$	−7.21390e15	−0.102062
$97$	7.97460e16	1.03312	0.516558	−	0.856252i	$-0.327213\pi$
$97$	7.97460e16	1.03312	0.516558	+	0.856252i	$0.327213\pi$
$98$	4.04423e16	0.480191
$99$	4.99043e16	0.543549
$100$	−4.96585e16	−0.496585
$101$	1.75678e17	1.61430	0.807152	−	0.590344i	$-0.201008\pi$
$101$	1.75678e17	1.61430	0.807152	+	0.590344i	$0.201008\pi$
$102$	−5.53932e16	−0.468117
$103$	−1.00292e17	−0.780098	−0.390049	−	0.920794i	$-0.627542\pi$
$103$	−1.00292e17	−0.780098	−0.390049	+	0.920794i	$0.627542\pi$
$104$	−4.69940e16	−0.336713
$105$	4.09210e15	0.0270294
$106$	−5.58751e16	−0.340501
$107$	−2.65519e17	−1.49394	−0.746969	−	0.664859i	$-0.768492\pi$
$107$	−2.65519e17	−1.49394	−0.746969	+	0.664859i	$0.768492\pi$
$108$	1.85093e16	0.0962250
$109$	−2.27850e16	−0.109528	−0.0547639	−	0.998499i	$-0.517441\pi$
$109$	−2.27850e16	−0.109528	−0.0547639	+	0.998499i	$0.517441\pi$
$110$	2.14235e16	0.0952912
$111$	−2.32683e17	−0.958338
$112$	−3.71093e16	−0.141622
$113$	5.66220e16	0.200363	0.100182	−	0.994969i	$-0.468058\pi$
$113$	5.66220e16	0.200363	0.100182	+	0.994969i	$0.468058\pi$
$114$	−9.70566e15	−0.0318665
$115$	−1.22079e16	−0.0372142
$116$	2.38009e17	0.674064
$117$	1.20577e17	0.317456
$118$	4.56551e17	1.11813
$119$	−2.84950e17	−0.649561
$120$	7.94590e15	0.0168695
$121$	8.38540e17	1.65901
$122$	−3.76101e17	−0.693819
$123$	−5.85488e16	−0.100769
$124$	4.50952e17	0.724512
$125$	1.09771e17	0.164722
$126$	9.52145e16	0.133522
$127$	−8.70466e16	−0.114135	−0.0570677	−	0.998370i	$-0.518175\pi$
$127$	−8.70466e16	−0.114135	−0.0570677	+	0.998370i	$0.518175\pi$
$128$	−7.20576e16	−0.0883883
$129$	−8.52710e17	−0.979014
$130$	5.17626e16	0.0556541
$131$	−2.91550e17	−0.293702	−0.146851	−	0.989159i	$-0.546914\pi$
$131$	−2.91550e17	−0.293702	−0.146851	+	0.989159i	$0.546914\pi$
$132$	4.98480e17	0.470727
$133$	−4.99273e16	−0.0442180
$134$	−1.29320e18	−1.07467
$135$	−2.03875e16	−0.0159047
$136$	−5.53307e17	−0.405402
$137$	1.04611e18	0.720201	0.360100	−	0.932914i	$-0.382742\pi$
$137$	1.04611e18	0.720201	0.360100	+	0.932914i	$0.382742\pi$
$138$	−2.84052e17	−0.183834
$139$	−2.65852e18	−1.61813	−0.809067	−	0.587717i	$-0.800027\pi$
$139$	−2.65852e18	−1.61813	−0.809067	+	0.587717i	$0.800027\pi$
$140$	4.08748e16	0.0234082
$141$	8.49648e17	0.458012
$142$	2.03131e17	0.103116
$143$	3.24728e18	1.55297
$144$	1.84884e17	0.0833333
$145$	−2.62160e17	−0.111414
$146$	−1.62394e18	−0.650983
$147$	−1.03649e18	−0.392074
$148$	−2.32420e18	−0.829945
$149$	3.05941e18	1.03170	0.515851	−	0.856678i	$-0.327476\pi$
$149$	3.05941e18	1.03170	0.515851	+	0.856678i	$0.327476\pi$
$150$	1.27269e18	0.405460
$151$	2.17598e18	0.655167	0.327583	−	0.944822i	$-0.393766\pi$
$151$	2.17598e18	0.655167	0.327583	+	0.944822i	$0.393766\pi$
$152$	−9.69471e16	−0.0275972
$153$	1.41967e18	0.382216
$154$	2.56425e18	0.653182
$155$	−4.96710e17	−0.119752
$156$	1.20441e18	0.274925
$157$	−5.88541e18	−1.27242	−0.636209	−	0.771517i	$-0.719498\pi$
$157$	−5.88541e18	−1.27242	−0.636209	+	0.771517i	$0.719498\pi$
$158$	2.12298e18	0.434871
$159$	1.43202e18	0.278018
$160$	7.93693e16	0.0146094
$161$	−1.46120e18	−0.255088
$162$	−4.74373e17	−0.0785674
$163$	−1.48688e18	−0.233712	−0.116856	−	0.993149i	$-0.537282\pi$
$163$	−1.48688e18	−0.233712	−0.116856	+	0.993149i	$0.537282\pi$
$164$	−5.84828e17	−0.0872681
$165$	−5.49061e17	−0.0778049
$166$	6.15206e18	0.828137
$167$	−8.41252e18	−1.07606	−0.538030	−	0.842926i	$-0.680831\pi$
$167$	−8.41252e18	−1.07606	−0.538030	+	0.842926i	$0.680831\pi$
$168$	9.51071e17	0.115634
$169$	−8.04463e17	−0.0929970
$170$	6.09451e17	0.0670075
$171$	2.48745e17	0.0260189
$172$	−8.51748e18	−0.847851
$173$	−1.34369e19	−1.27323	−0.636617	−	0.771180i	$-0.719667\pi$
$173$	−1.34369e19	−1.27323	−0.636617	+	0.771180i	$0.719667\pi$
$174$	−6.09992e18	−0.550371
$175$	6.54691e18	0.562618
$176$	4.97917e18	0.407661
$177$	−1.17009e19	−0.912949
$178$	3.95941e18	0.294483
$179$	7.86864e18	0.558019	0.279009	−	0.960288i	$-0.409994\pi$
$179$	7.86864e18	0.558019	0.279009	+	0.960288i	$0.409994\pi$
$180$	−2.03645e17	−0.0137739
$181$	2.09609e19	1.35251	0.676256	−	0.736666i	$-0.263601\pi$
$181$	2.09609e19	1.35251	0.676256	+	0.736666i	$0.263601\pi$
$182$	6.19563e18	0.381486
$183$	9.63907e18	0.566501
$184$	−2.83731e18	−0.159205
$185$	2.56004e18	0.137179
$186$	−1.15574e19	−0.591562
$187$	3.82335e19	1.86978
$188$	8.48690e18	0.396650
$189$	−2.44024e18	−0.109020
$190$	1.06784e17	0.00456144
$191$	1.88595e19	0.770454	0.385227	−	0.922822i	$-0.374123\pi$
$191$	1.88595e19	0.770454	0.385227	+	0.922822i	$0.374123\pi$
$192$	1.84676e18	0.0721688
$193$	−3.86285e19	−1.44435	−0.722173	−	0.691712i	$-0.756857\pi$
$193$	−3.86285e19	−1.44435	−0.722173	+	0.691712i	$0.756857\pi$
$194$	−2.04150e19	−0.730523
$195$	−1.32662e18	−0.0454414
$196$	−1.03532e19	−0.339546
$197$	−4.60526e19	−1.44641	−0.723205	−	0.690633i	$-0.757332\pi$
$197$	−4.60526e19	−1.44641	−0.723205	+	0.690633i	$0.757332\pi$
$198$	−1.27755e19	−0.384347
$199$	8.82274e18	0.254304	0.127152	−	0.991883i	$-0.459416\pi$
$199$	8.82274e18	0.254304	0.127152	+	0.991883i	$0.459416\pi$
$200$	1.27126e19	0.351139
$201$	3.31433e19	0.877464
$202$	−4.49735e19	−1.14148
$203$	−3.13789e19	−0.763697
$204$	1.41807e19	0.331009
$205$	6.44171e17	0.0144243
$206$	2.56747e19	0.551613
$207$	7.27993e18	0.150100
$208$	1.20305e19	0.238092
$209$	6.69904e18	0.127283
$210$	−1.04758e18	−0.0191127
$211$	−5.23642e19	−0.917558	−0.458779	−	0.888550i	$-0.651713\pi$
$211$	−5.23642e19	−0.917558	−0.458779	+	0.888550i	$0.651713\pi$
$212$	1.43040e19	0.240771
$213$	−5.20603e18	−0.0841937
$214$	6.79727e19	1.05637
$215$	9.38176e18	0.140138
$216$	−4.73838e18	−0.0680414
$217$	−5.94529e19	−0.820853
$218$	5.83297e18	0.0774479
$219$	4.16197e19	0.531525
$220$	−5.48442e18	−0.0673810
$221$	9.23781e19	1.09203
$222$	5.95667e19	0.677647
$223$	−2.94838e19	−0.322844	−0.161422	−	0.986885i	$-0.551608\pi$
$223$	−2.94838e19	−0.322844	−0.161422	+	0.986885i	$0.551608\pi$
$224$	9.49998e18	0.100142
$225$	−3.26177e19	−0.331057
$226$	−1.44952e19	−0.141678
$227$	1.66853e19	0.157078	0.0785390	−	0.996911i	$-0.474974\pi$
$227$	1.66853e19	0.157078	0.0785390	+	0.996911i	$0.474974\pi$
$228$	2.48465e18	0.0225330
$229$	1.67860e19	0.146671	0.0733356	−	0.997307i	$-0.476636\pi$
$229$	1.67860e19	0.146671	0.0733356	+	0.997307i	$0.476636\pi$
$230$	3.12522e18	0.0263144
$231$	−6.57189e19	−0.533321
$232$	−6.09304e19	−0.476635
$233$	1.66093e20	1.25264	0.626319	−	0.779567i	$-0.284561\pi$
$233$	1.66093e20	1.25264	0.626319	+	0.779567i	$0.284561\pi$
$234$	−3.08676e19	−0.224475
$235$	−9.34807e18	−0.0655609
$236$	−1.16877e20	−0.790637
$237$	−5.44096e19	−0.355071
$238$	7.29473e19	0.459309
$239$	−1.97774e20	−1.20167	−0.600836	−	0.799372i	$-0.705166\pi$
$239$	−1.97774e20	−1.20167	−0.600836	+	0.799372i	$0.705166\pi$
$240$	−2.03415e18	−0.0119285
$241$	1.20674e20	0.683074	0.341537	−	0.939868i	$-0.389053\pi$
$241$	1.20674e20	0.683074	0.341537	+	0.939868i	$0.389053\pi$
$242$	−2.14666e20	−1.17309
$243$	1.21577e19	0.0641500
$244$	9.62819e19	0.490604
$245$	1.14038e19	0.0561225
$246$	1.49885e19	0.0712541
$247$	1.61859e19	0.0743385
$248$	−1.15444e20	−0.512308
$249$	−1.57671e20	−0.676171
$250$	−2.81014e19	−0.116476
$251$	9.47695e18	0.0379701	0.0189851	−	0.999820i	$-0.493957\pi$
$251$	9.47695e18	0.0379701	0.0189851	+	0.999820i	$0.493957\pi$
$252$	−2.43749e19	−0.0944144
$253$	1.96058e20	0.734278
$254$	2.22839e19	0.0807059
$255$	−1.56196e19	−0.0547114
$256$	1.84467e19	0.0625000
$257$	1.44668e20	0.474177	0.237088	−	0.971488i	$-0.423807\pi$
$257$	1.44668e20	0.474177	0.237088	+	0.971488i	$0.423807\pi$
$258$	2.18294e20	0.692267
$259$	3.06420e20	0.940305
$260$	−1.32512e19	−0.0393534
$261$	1.56334e20	0.449376
$262$	7.46367e19	0.207678
$263$	−1.65480e20	−0.445781	−0.222890	−	0.974844i	$-0.571549\pi$
$263$	−1.65480e20	−0.445781	−0.222890	+	0.974844i	$0.571549\pi$
$264$	−1.27611e20	−0.332854
$265$	−1.57555e19	−0.0397962
$266$	1.27814e19	0.0312668
$267$	−1.01475e20	−0.240445
$268$	3.31059e20	0.759906
$269$	7.65963e20	1.70339	0.851694	−	0.524039i	$-0.175576\pi$
$269$	7.65963e20	1.70339	0.851694	+	0.524039i	$0.175576\pi$
$270$	5.21919e18	0.0112463
$271$	−5.20543e20	−1.08697	−0.543485	−	0.839419i	$-0.682895\pi$
$271$	−5.20543e20	−1.08697	−0.543485	+	0.839419i	$0.682895\pi$
$272$	1.41647e20	0.286662
$273$	−1.58787e20	−0.311482
$274$	−2.67805e20	−0.509259
$275$	−8.78438e20	−1.61951
$276$	7.27172e19	0.129990
$277$	−1.09322e21	−1.89508	−0.947541	−	0.319634i	$-0.896440\pi$
$277$	−1.09322e21	−1.89508	−0.947541	+	0.319634i	$0.896440\pi$
$278$	6.80581e20	1.14419
$279$	2.96204e20	0.483008
$280$	−1.04640e19	−0.0165521
$281$	−4.24848e20	−0.651973	−0.325987	−	0.945374i	$-0.605696\pi$
$281$	−4.24848e20	−0.651973	−0.325987	+	0.945374i	$0.605696\pi$
$282$	−2.17510e20	−0.323863
$283$	−1.22464e20	−0.176939	−0.0884693	−	0.996079i	$-0.528198\pi$
$283$	−1.22464e20	−0.176939	−0.0884693	+	0.996079i	$0.528198\pi$
$284$	−5.20016e19	−0.0729139
$285$	−2.73677e18	−0.00372440
$286$	−8.31305e20	−1.09812
$287$	7.71030e19	0.0988724
$288$	−4.73304e19	−0.0589256
$289$	2.60418e20	0.314803
$290$	6.71131e19	0.0787815
$291$	5.23213e20	0.596470
$292$	4.15728e20	0.460315
$293$	7.27955e20	0.782942	0.391471	−	0.920190i	$-0.371966\pi$
$293$	7.27955e20	0.782942	0.391471	+	0.920190i	$0.371966\pi$
$294$	2.65342e20	0.277239
$295$	1.28737e20	0.130682
$296$	5.94996e20	0.586860
$297$	3.27422e20	0.313818
$298$	−7.83209e20	−0.729524
$299$	4.73707e20	0.428850
$300$	−3.25809e20	−0.286704
$301$	1.12293e21	0.960592
$302$	−5.57052e20	−0.463273
$303$	1.15262e21	0.932018
$304$	2.48185e19	0.0195141
$305$	−1.06052e20	−0.0810904
$306$	−3.63435e20	−0.270268
$307$	1.00525e21	0.727108	0.363554	−	0.931573i	$-0.381563\pi$
$307$	1.00525e21	0.727108	0.363554	+	0.931573i	$0.381563\pi$
$308$	−6.56448e20	−0.461870
$309$	−6.58015e20	−0.450390
$310$	1.27158e20	0.0846776
$311$	−2.32350e21	−1.50549	−0.752746	−	0.658311i	$-0.771271\pi$
$311$	−2.32350e21	−1.50549	−0.752746	+	0.658311i	$0.771271\pi$
$312$	−3.08328e20	−0.194401
$313$	−9.16081e20	−0.562092	−0.281046	−	0.959694i	$-0.590681\pi$
$313$	−9.16081e20	−0.562092	−0.281046	+	0.959694i	$0.590681\pi$
$314$	1.50667e21	0.899735
$315$	2.68483e19	0.0156055
$316$	−5.43482e20	−0.307500
$317$	−1.09459e21	−0.602903	−0.301451	−	0.953482i	$-0.597471\pi$
$317$	−1.09459e21	−0.602903	−0.301451	+	0.953482i	$0.597471\pi$
$318$	−3.66597e20	−0.196588
$319$	4.21029e21	2.19832
$320$	−2.03186e19	−0.0103304
$321$	−1.74207e21	−0.862526
$322$	3.74068e20	0.180375
$323$	1.90573e20	0.0895035
$324$	1.21440e20	0.0555556
$325$	−2.12245e21	−0.945862
$326$	3.80641e20	0.165259
$327$	−1.49493e20	−0.0632359
$328$	1.49716e20	0.0617079
$329$	−1.11890e21	−0.449394
$330$	1.40560e20	0.0550164
$331$	9.06412e19	0.0345770	0.0172885	−	0.999851i	$-0.494497\pi$
$331$	9.06412e19	0.0345770	0.0172885	+	0.999851i	$0.494497\pi$
$332$	−1.57493e21	−0.585581
$333$	−1.52663e21	−0.553297
$334$	2.15361e21	0.760889
$335$	−3.64652e20	−0.125602
$336$	−2.43474e20	−0.0817653
$337$	−5.80404e21	−1.90054	−0.950268	−	0.311434i	$-0.899191\pi$
$337$	−5.80404e21	−1.90054	−0.950268	+	0.311434i	$0.899191\pi$
$338$	2.05942e20	0.0657588
$339$	3.71497e20	0.115680
$340$	−1.56020e20	−0.0473814
$341$	7.97715e21	2.36285
$342$	−6.36788e19	−0.0183981
$343$	3.37493e21	0.951184
$344$	2.18048e21	0.599521
$345$	−8.00959e19	−0.0214856
$346$	3.43985e21	0.900312
$347$	−6.71227e21	−1.71423	−0.857115	−	0.515126i	$-0.827745\pi$
$347$	−6.71227e21	−1.71423	−0.857115	+	0.515126i	$0.827745\pi$
$348$	1.56158e21	0.389171
$349$	3.89119e21	0.946383	0.473191	−	0.880960i	$-0.343102\pi$
$349$	3.89119e21	0.946383	0.473191	+	0.880960i	$0.343102\pi$
$350$	−1.67601e21	−0.397831
$351$	7.91103e20	0.183283
$352$	−1.27467e21	−0.288260
$353$	1.49617e21	0.330289	0.165145	−	0.986269i	$-0.447191\pi$
$353$	1.49617e21	0.330289	0.165145	+	0.986269i	$0.447191\pi$
$354$	2.99543e21	0.645552
$355$	5.72782e19	0.0120517
$356$	−1.01361e21	−0.208231
$357$	−1.86956e21	−0.375024
$358$	−2.01437e21	−0.394579
$359$	7.57807e21	1.44962	0.724812	−	0.688946i	$-0.241926\pi$
$359$	7.57807e21	1.44962	0.724812	+	0.688946i	$0.241926\pi$
$360$	5.21330e19	0.00973961
$361$	−5.44700e21	−0.993907
$362$	−5.36598e21	−0.956371
$363$	5.50166e21	0.957828
$364$	−1.58608e21	−0.269752
$365$	−4.57912e20	−0.0760839
$366$	−2.46760e21	−0.400577
$367$	−1.15447e22	−1.83114	−0.915570	−	0.402160i	$-0.868260\pi$
$367$	−1.15447e22	−1.83114	−0.915570	+	0.402160i	$0.868260\pi$
$368$	7.26352e20	0.112575
$369$	−3.84139e20	−0.0581787
$370$	−6.55370e20	−0.0970001
$371$	−1.88582e21	−0.272787
$372$	2.95869e21	0.418297
$373$	2.92117e21	0.403676	0.201838	−	0.979419i	$-0.435309\pi$
$373$	2.92117e21	0.403676	0.201838	+	0.979419i	$0.435309\pi$
$374$	−9.78777e21	−1.32213
$375$	7.20207e20	0.0951024
$376$	−2.17265e21	−0.280474
$377$	1.01727e22	1.28391
$378$	6.24702e20	0.0770891
$379$	−2.67087e21	−0.322270	−0.161135	−	0.986932i	$-0.551515\pi$
$379$	−2.67087e21	−0.322270	−0.161135	+	0.986932i	$0.551515\pi$
$380$	−2.73368e19	−0.00322543
$381$	−5.71113e20	−0.0658961
$382$	−4.82803e21	−0.544793
$383$	−7.54502e21	−0.832665	−0.416333	−	0.909212i	$-0.636685\pi$
$383$	−7.54502e21	−0.832665	−0.416333	+	0.909212i	$0.636685\pi$
$384$	−4.72770e20	−0.0510310
$385$	7.23059e20	0.0763409
$386$	9.88891e21	1.02131
$387$	−5.59463e21	−0.565234
$388$	5.22623e21	0.516558
$389$	1.70961e22	1.65320	0.826600	−	0.562790i	$-0.190272\pi$
$389$	1.70961e22	1.65320	0.826600	+	0.562790i	$0.190272\pi$
$390$	3.39614e20	0.0321319
$391$	5.57742e21	0.516334
$392$	2.65043e21	0.240096
$393$	−1.91286e21	−0.169569
$394$	1.17895e22	1.02277
$395$	5.98630e20	0.0508257
$396$	3.27053e21	0.271774
$397$	3.54092e21	0.288003	0.144002	−	0.989577i	$-0.454003\pi$
$397$	3.54092e21	0.288003	0.144002	+	0.989577i	$0.454003\pi$
$398$	−2.25862e21	−0.179820
$399$	−3.27573e20	−0.0255293
$400$	−3.25442e21	−0.248293
$401$	−9.13632e21	−0.682408	−0.341204	−	0.939989i	$-0.610835\pi$
$401$	−9.13632e21	−0.682408	−0.341204	+	0.939989i	$0.610835\pi$
$402$	−8.48468e21	−0.620461
$403$	1.92741e22	1.38000
$404$	1.15132e22	0.807152
$405$	−1.33762e20	−0.00918260
$406$	8.03299e21	0.540015
$407$	−4.11142e22	−2.70669
$408$	−3.63025e21	−0.234059
$409$	−1.66232e22	−1.04971	−0.524853	−	0.851193i	$-0.675880\pi$
$409$	−1.66232e22	−1.04971	−0.524853	+	0.851193i	$0.675880\pi$
$410$	−1.64908e20	−0.0101995
$411$	6.86354e21	0.415808
$412$	−6.57273e21	−0.390049
$413$	1.54089e22	0.895770
$414$	−1.86366e21	−0.106136
$415$	1.73474e21	0.0967888
$416$	−3.07980e21	−0.168356
$417$	−1.74426e22	−0.934230
$418$	−1.71495e21	−0.0900024
$419$	−2.57530e22	−1.32437	−0.662185	−	0.749341i	$-0.730371\pi$
$419$	−2.57530e22	−1.32437	−0.662185	+	0.749341i	$0.730371\pi$
$420$	2.68180e20	0.0135147
$421$	2.69352e22	1.33022	0.665108	−	0.746747i	$-0.268386\pi$
$421$	2.69352e22	1.33022	0.665108	+	0.746747i	$0.268386\pi$
$422$	1.34052e22	0.648812
$423$	5.57454e21	0.264433
$424$	−3.66183e21	−0.170251
$425$	−2.49896e22	−1.13882
$426$	1.33274e21	0.0595340
$427$	−1.26937e22	−0.555842
$428$	−1.74010e22	−0.746969
$429$	2.13054e22	0.896610
$430$	−2.40173e21	−0.0990929
$431$	2.28986e22	0.926300	0.463150	−	0.886280i	$-0.346719\pi$
$431$	2.28986e22	0.926300	0.463150	+	0.886280i	$0.346719\pi$
$432$	1.21303e21	0.0481125
$433$	1.48345e22	0.576933	0.288467	−	0.957490i	$-0.406855\pi$
$433$	1.48345e22	0.576933	0.288467	+	0.957490i	$0.406855\pi$
$434$	1.52199e22	0.580431
$435$	−1.72003e21	−0.0643248
$436$	−1.49324e21	−0.0547639
$437$	9.77242e20	0.0351488
$438$	−1.06546e22	−0.375845
$439$	5.89808e21	0.204062	0.102031	−	0.994781i	$-0.467466\pi$
$439$	5.89808e21	0.204062	0.102031	+	0.994781i	$0.467466\pi$
$440$	1.40401e21	0.0476456
$441$	−6.80042e21	−0.226364
$442$	−2.36488e22	−0.772182
$443$	2.13673e22	0.684412	0.342206	−	0.939625i	$-0.388826\pi$
$443$	2.13673e22	0.684412	0.342206	+	0.939625i	$0.388826\pi$
$444$	−1.52491e22	−0.479169
$445$	1.11646e21	0.0344179
$446$	7.54787e21	0.228285
$447$	2.00728e22	0.595654
$448$	−2.43200e21	−0.0708108
$449$	3.05976e22	0.874165	0.437082	−	0.899422i	$-0.356012\pi$
$449$	3.05976e22	0.874165	0.437082	+	0.899422i	$0.356012\pi$
$450$	8.35014e21	0.234092
$451$	−1.03454e22	−0.284607
$452$	3.71078e21	0.100182
$453$	1.42766e22	0.378261
$454$	−4.27145e21	−0.111071
$455$	1.74702e21	0.0445864
$456$	−6.36070e20	−0.0159332
$457$	−3.38931e22	−0.833343	−0.416672	−	0.909057i	$-0.636804\pi$
$457$	−3.38931e22	−0.833343	−0.416672	+	0.909057i	$0.636804\pi$
$458$	−4.29721e21	−0.103712
$459$	9.31443e21	0.220673
$460$	−8.00056e20	−0.0186071
$461$	4.27786e22	0.976717	0.488359	−	0.872643i	$-0.337596\pi$
$461$	4.27786e22	0.976717	0.488359	+	0.872643i	$0.337596\pi$
$462$	1.68240e22	0.377115
$463$	−1.59893e22	−0.351876	−0.175938	−	0.984401i	$-0.556296\pi$
$463$	−1.59893e22	−0.351876	−0.175938	+	0.984401i	$0.556296\pi$
$464$	1.55982e22	0.337032
$465$	−3.25892e21	−0.0691390
$466$	−4.25198e22	−0.885749
$467$	3.28047e22	0.671031	0.335516	−	0.942035i	$-0.391089\pi$
$467$	3.28047e22	0.671031	0.335516	+	0.942035i	$0.391089\pi$
$468$	7.90211e21	0.158728
$469$	−4.36464e22	−0.860953
$470$	2.39311e21	0.0463586
$471$	−3.86142e22	−0.734631
$472$	2.99205e22	0.559065
$473$	−1.50671e23	−2.76509
$474$	1.39289e22	0.251073
$475$	−4.37853e21	−0.0775234
$476$	−1.86745e22	−0.324781
$477$	9.39547e21	0.160514
$478$	5.06300e22	0.849711
$479$	−7.31303e21	−0.120572	−0.0602859	−	0.998181i	$-0.519201\pi$
$479$	−7.31303e21	−0.120572	−0.0602859	+	0.998181i	$0.519201\pi$
$480$	5.20742e20	0.00843475
$481$	−9.93383e22	−1.58082
$482$	−3.08925e22	−0.483006
$483$	−9.58695e21	−0.147275
$484$	5.49545e22	0.829503
$485$	−5.75654e21	−0.0853801
$486$	−3.11236e21	−0.0453609
$487$	6.48093e22	0.928199	0.464100	−	0.885783i	$-0.346378\pi$
$487$	6.48093e22	0.928199	0.464100	+	0.885783i	$0.346378\pi$
$488$	−2.46482e22	−0.346910
$489$	−9.75540e21	−0.134934
$490$	−2.91937e21	−0.0396846
$491$	8.70141e22	1.16251	0.581255	−	0.813721i	$-0.302562\pi$
$491$	8.70141e22	1.16251	0.581255	+	0.813721i	$0.302562\pi$
$492$	−3.83706e21	−0.0503843
$493$	1.19773e23	1.54583
$494$	−4.14360e21	−0.0525653
$495$	−3.60239e21	−0.0449207
$496$	2.95536e22	0.362256
$497$	6.85582e21	0.0826095
$498$	4.03637e22	0.478125
$499$	1.03056e23	1.20010	0.600051	−	0.799962i	$-0.295147\pi$
$499$	1.03056e23	1.20010	0.600051	+	0.799962i	$0.295147\pi$
$500$	7.19395e21	0.0823611
$501$	−5.51946e22	−0.621263
$502$	−2.42610e21	−0.0268489
$503$	5.57442e22	0.606557	0.303279	−	0.952902i	$-0.401919\pi$
$503$	5.57442e22	0.606557	0.303279	+	0.952902i	$0.401919\pi$
$504$	6.23998e21	0.0667611
$505$	−1.26815e22	−0.133411
$506$	−5.01909e22	−0.519213
$507$	−5.27808e21	−0.0536918
$508$	−5.70469e21	−0.0570677
$509$	2.40566e20	0.00236665	0.00118332	−	0.999999i	$-0.499623\pi$
$509$	2.40566e20	0.00236665	0.00118332	+	0.999999i	$0.499623\pi$
$510$	3.99861e21	0.0386868
$511$	−5.48090e22	−0.521524
$512$	−4.72237e21	−0.0441942
$513$	1.63202e21	0.0150220
$514$	−3.70350e22	−0.335294
$515$	7.23967e21	0.0644700
$516$	−5.58832e22	−0.489507
$517$	1.50130e23	1.29359
$518$	−7.84435e22	−0.664896
$519$	−8.81597e22	−0.735102
$520$	3.39231e21	0.0278271
$521$	−8.31701e22	−0.671192	−0.335596	−	0.942006i	$-0.608938\pi$
$521$	−8.31701e22	−0.671192	−0.335596	+	0.942006i	$0.608938\pi$
$522$	−4.00216e22	−0.317757
$523$	−1.83386e23	−1.43252	−0.716260	−	0.697834i	$-0.754148\pi$
$523$	−1.83386e23	−1.43252	−0.716260	+	0.697834i	$0.754148\pi$
$524$	−1.91070e22	−0.146851
$525$	4.29543e22	0.324827
$526$	4.23628e22	0.315215
$527$	2.26932e23	1.66152
$528$	3.26684e22	0.235363
$529$	−1.12449e23	−0.797231
$530$	4.03340e21	0.0281401
$531$	−7.67696e22	−0.527091
$532$	−3.27204e21	−0.0221090
$533$	−2.49960e22	−0.166222
$534$	2.59777e22	0.170020
$535$	1.91667e22	0.123464
$536$	−8.47511e22	−0.537335
$537$	5.16261e22	0.322172
$538$	−1.96087e23	−1.20448
$539$	−1.83144e23	−1.10736
$540$	−1.33611e21	−0.00795236
$541$	1.44978e23	0.849424	0.424712	−	0.905329i	$-0.360375\pi$
$541$	1.44978e23	0.849424	0.424712	+	0.905329i	$0.360375\pi$
$542$	1.33259e23	0.768603
$543$	1.37524e23	0.780874
$544$	−3.62615e22	−0.202701
$545$	1.64476e21	0.00905175
$546$	4.06496e22	0.220251
$547$	−3.26687e22	−0.174277	−0.0871384	−	0.996196i	$-0.527772\pi$
$547$	−3.26687e22	−0.174277	−0.0871384	+	0.996196i	$0.527772\pi$
$548$	6.85580e22	0.360100
$549$	6.32419e22	0.327070
$550$	2.24880e23	1.14517
$551$	2.09860e22	0.105230
$552$	−1.86156e22	−0.0919168
$553$	7.16520e22	0.348389
$554$	2.79863e23	1.34003
$555$	1.67964e22	0.0792002
$556$	−1.74229e23	−0.809067
$557$	5.89565e22	0.269627	0.134813	−	0.990871i	$-0.456957\pi$
$557$	5.89565e22	0.269627	0.134813	+	0.990871i	$0.456957\pi$
$558$	−7.58281e22	−0.341538
$559$	−3.64044e23	−1.61493
$560$	2.67877e21	0.0117041
$561$	2.50850e23	1.07952
$562$	1.08761e23	0.461015
$563$	−1.04477e23	−0.436213	−0.218106	−	0.975925i	$-0.569988\pi$
$563$	−1.04477e23	−0.436213	−0.218106	+	0.975925i	$0.569988\pi$
$564$	5.56825e22	0.229006
$565$	−4.08731e21	−0.0165587
$566$	3.13507e22	0.125115
$567$	−1.60104e22	−0.0629430
$568$	1.33124e22	0.0515579
$569$	−3.22207e23	−1.22937	−0.614683	−	0.788774i	$-0.710716\pi$
$569$	−3.22207e23	−1.22937	−0.614683	+	0.788774i	$0.710716\pi$
$570$	7.00613e20	0.00263355
$571$	−1.25038e23	−0.463056	−0.231528	−	0.972828i	$-0.574373\pi$
$571$	−1.25038e23	−0.463056	−0.231528	+	0.972828i	$0.574373\pi$
$572$	2.12814e23	0.776487
$573$	1.23737e23	0.444822
$574$	−1.97384e22	−0.0699133
$575$	−1.28145e23	−0.447223
$576$	1.21166e22	0.0416667
$577$	2.74545e22	0.0930293	0.0465146	−	0.998918i	$-0.485189\pi$
$577$	2.74545e22	0.0930293	0.0465146	+	0.998918i	$0.485189\pi$
$578$	−6.66670e22	−0.222599
$579$	−2.53442e23	−0.833894
$580$	−1.71809e22	−0.0557069
$581$	2.07637e23	0.663448
$582$	−1.33943e23	−0.421768
$583$	2.53032e23	0.785223
$584$	−1.06426e23	−0.325492
$585$	−8.70394e21	−0.0262356
$586$	−1.86356e23	−0.553624
$587$	4.31074e23	1.26220	0.631100	−	0.775701i	$-0.282604\pi$
$587$	4.31074e23	1.26220	0.631100	+	0.775701i	$0.282604\pi$
$588$	−6.79275e22	−0.196037
$589$	3.97617e22	0.113106
$590$	−3.29566e22	−0.0924059
$591$	−3.02151e23	−0.835086
$592$	−1.52319e23	−0.414972
$593$	−6.47624e23	−1.73923	−0.869617	−	0.493727i	$-0.835634\pi$
$593$	−6.47624e23	−1.73923	−0.869617	+	0.493727i	$0.835634\pi$
$594$	−8.38200e22	−0.221903
$595$	2.05694e22	0.0536819
$596$	2.00502e23	0.515851
$597$	5.78860e22	0.146822
$598$	−1.21269e23	−0.303242
$599$	−1.19466e23	−0.294521	−0.147261	−	0.989098i	$-0.547046\pi$
$599$	−1.19466e23	−0.294521	−0.147261	+	0.989098i	$0.547046\pi$
$600$	8.34072e22	0.202730
$601$	6.14541e23	1.47271	0.736357	−	0.676594i	$-0.236545\pi$
$601$	6.14541e23	1.47271	0.736357	+	0.676594i	$0.236545\pi$
$602$	−2.87471e23	−0.679241
$603$	2.17453e23	0.506604
$604$	1.42605e23	0.327583
$605$	−6.05308e22	−0.137106
$606$	−2.95071e23	−0.659037
$607$	−5.22882e22	−0.115159	−0.0575797	−	0.998341i	$-0.518338\pi$
$607$	−5.22882e22	−0.115159	−0.0575797	+	0.998341i	$0.518338\pi$
$608$	−6.35353e21	−0.0137986
$609$	−2.05877e23	−0.440920
$610$	2.71493e22	0.0573395
$611$	3.62737e23	0.755512
$612$	9.30393e22	0.191108
$613$	1.88812e23	0.382486	0.191243	−	0.981543i	$-0.438748\pi$
$613$	1.88812e23	0.382486	0.191243	+	0.981543i	$0.438748\pi$
$614$	−2.57345e23	−0.514143
$615$	4.22641e21	0.00832785
$616$	1.68051e23	0.326591
$617$	7.79201e23	1.49357	0.746785	−	0.665066i	$-0.231596\pi$
$617$	7.79201e23	1.49357	0.746785	+	0.665066i	$0.231596\pi$
$618$	1.68452e23	0.318474
$619$	9.13434e22	0.170336	0.0851680	−	0.996367i	$-0.472857\pi$
$619$	9.13434e22	0.170336	0.0851680	+	0.996367i	$0.472857\pi$
$620$	−3.25524e22	−0.0598761
$621$	4.77636e22	0.0866600
$622$	5.94815e23	1.06454
$623$	1.33633e23	0.235920
$624$	7.89319e22	0.137462
$625$	5.70177e23	0.979557
$626$	2.34517e23	0.397459
$627$	4.39524e22	0.0734867
$628$	−3.85706e23	−0.636209
$629$	−1.16961e24	−1.90331
$630$	−6.87315e21	−0.0110347
$631$	1.27853e23	0.202517	0.101259	−	0.994860i	$-0.467713\pi$
$631$	1.27853e23	0.202517	0.101259	+	0.994860i	$0.467713\pi$
$632$	1.39131e23	0.217435
$633$	−3.43561e23	−0.529752
$634$	2.80215e23	0.426317
$635$	6.28355e21	0.00943253
$636$	9.38487e22	0.139009
$637$	−4.42506e23	−0.646746
$638$	−1.07783e24	−1.55445
$639$	−3.41567e22	−0.0486093
$640$	5.20155e21	0.00730471
$641$	1.46205e23	0.202613	0.101307	−	0.994855i	$-0.467698\pi$
$641$	1.46205e23	0.202613	0.101307	+	0.994855i	$0.467698\pi$
$642$	4.45969e23	0.609898
$643$	−5.18714e23	−0.700059	−0.350029	−	0.936739i	$-0.613828\pi$
$643$	−5.18714e23	−0.700059	−0.350029	+	0.936739i	$0.613828\pi$
$644$	−9.57613e22	−0.127544
$645$	6.15537e22	0.0809090
$646$	−4.87867e22	−0.0632885
$647$	−7.16386e23	−0.917192	−0.458596	−	0.888645i	$-0.651648\pi$
$647$	−7.16386e23	−0.917192	−0.458596	+	0.888645i	$0.651648\pi$
$648$	−3.10885e22	−0.0392837
$649$	−2.06751e24	−2.57850
$650$	5.43346e23	0.668826
$651$	−3.90071e23	−0.473920
$652$	−9.74440e22	−0.116856
$653$	1.12266e24	1.32888	0.664441	−	0.747341i	$-0.268670\pi$
$653$	1.12266e24	1.32888	0.664441	+	0.747341i	$0.268670\pi$
$654$	3.82701e22	0.0447146
$655$	2.10458e22	0.0242725
$656$	−3.83273e22	−0.0436340
$657$	2.73067e23	0.306876
$658$	2.86439e23	0.317769
$659$	8.07222e23	0.884030	0.442015	−	0.897008i	$-0.354264\pi$
$659$	8.07222e23	0.884030	0.442015	+	0.897008i	$0.354264\pi$
$660$	−3.59833e22	−0.0389025
$661$	−1.82166e24	−1.94426	−0.972130	−	0.234444i	$-0.924673\pi$
$661$	−1.82166e24	−1.94426	−0.972130	+	0.234444i	$0.924673\pi$
$662$	−2.32041e22	−0.0244496
$663$	6.06093e23	0.630484
$664$	4.03182e23	0.414068
$665$	3.60405e21	0.00365432
$666$	3.90817e23	0.391240
$667$	6.14188e23	0.607060
$668$	−5.51323e23	−0.538030
$669$	−1.93444e23	−0.186394
$670$	9.33509e22	0.0888143
$671$	1.70319e24	1.60000
$672$	6.23294e22	0.0578168
$673$	1.67636e24	1.53546	0.767732	−	0.640771i	$-0.221385\pi$
$673$	1.67636e24	1.53546	0.767732	+	0.640771i	$0.221385\pi$
$674$	1.48583e24	1.34388
$675$	−2.14005e23	−0.191136
$676$	−5.27213e22	−0.0464985
$677$	−2.99561e23	−0.260905	−0.130452	−	0.991455i	$-0.541643\pi$
$677$	−2.99561e23	−0.260905	−0.130452	+	0.991455i	$0.541643\pi$
$678$	−9.51032e22	−0.0817980
$679$	−6.89020e23	−0.585246
$680$	3.99410e22	0.0335037
$681$	1.09473e23	0.0906890
$682$	−2.04215e24	−1.67078
$683$	1.62280e23	0.131126	0.0655629	−	0.997848i	$-0.479116\pi$
$683$	1.62280e23	0.131126	0.0655629	+	0.997848i	$0.479116\pi$
$684$	1.63018e22	0.0130094
$685$	−7.55147e22	−0.0595198
$686$	−8.63981e23	−0.672588
$687$	1.10133e23	0.0846807
$688$	−5.58202e23	−0.423925
$689$	6.11366e23	0.458604
$690$	2.05045e22	0.0151926
$691$	2.06149e24	1.50875	0.754375	−	0.656444i	$-0.227940\pi$
$691$	2.06149e24	1.50875	0.754375	+	0.656444i	$0.227940\pi$
$692$	−8.80603e23	−0.636617
$693$	−4.31182e23	−0.307913
$694$	1.71834e24	1.21214
$695$	1.91908e23	0.133728
$696$	−3.99764e23	−0.275186
$697$	−2.94303e23	−0.200132
$698$	−9.96146e23	−0.669194
$699$	1.08974e24	0.723211
$700$	4.29059e23	0.281309
$701$	−2.13838e24	−1.38510	−0.692551	−	0.721369i	$-0.743513\pi$
$701$	−2.13838e24	−1.38510	−0.692551	+	0.721369i	$0.743513\pi$
$702$	−2.02522e23	−0.129601
$703$	−2.04932e23	−0.129565
$704$	3.26315e23	0.203831
$705$	−6.13327e22	−0.0378516
$706$	−3.83018e23	−0.233550
$707$	−1.51789e24	−0.914481
$708$	−7.66830e23	−0.456474
$709$	1.18597e24	0.697559	0.348780	−	0.937205i	$-0.386596\pi$
$709$	1.18597e24	0.697559	0.348780	+	0.937205i	$0.386596\pi$
$710$	−1.46632e22	−0.00852184
$711$	−3.56981e23	−0.205000
$712$	2.59484e23	0.147242
$713$	1.16369e24	0.652494
$714$	4.78607e23	0.265182
$715$	−2.34408e23	−0.128343
$716$	5.15679e23	0.279009
$717$	−1.29759e24	−0.693786
$718$	−1.93999e24	−1.02504
$719$	−2.44086e24	−1.27452	−0.637262	−	0.770648i	$-0.719933\pi$
$719$	−2.44086e24	−1.27452	−0.637262	+	0.770648i	$0.719933\pi$
$720$	−1.33461e22	−0.00688695
$721$	8.66540e23	0.441915
$722$	1.39443e24	0.702799
$723$	7.91740e23	0.394373
$724$	1.37369e24	0.676256
$725$	−2.75187e24	−1.33892
$726$	−1.40842e24	−0.677286
$727$	1.82776e24	0.868712	0.434356	−	0.900741i	$-0.356976\pi$
$727$	1.82776e24	0.868712	0.434356	+	0.900741i	$0.356976\pi$
$728$	4.06037e23	0.190743
$729$	7.97664e22	0.0370370
$730$	1.17225e23	0.0537994
$731$	−4.28625e24	−1.94437
$732$	6.31706e23	0.283251
$733$	1.10371e24	0.489181	0.244591	−	0.969626i	$-0.421346\pi$
$733$	1.10371e24	0.489181	0.244591	+	0.969626i	$0.421346\pi$
$734$	2.95544e24	1.29481
$735$	7.48202e22	0.0324024
$736$	−1.85946e23	−0.0796023
$737$	5.85630e24	2.47827
$738$	9.83396e22	0.0411386
$739$	−2.28247e24	−0.943905	−0.471952	−	0.881624i	$-0.656451\pi$
$739$	−2.28247e24	−0.943905	−0.471952	+	0.881624i	$0.656451\pi$
$740$	1.67775e23	0.0685894
$741$	1.06196e23	0.0429194
$742$	4.82771e23	0.192889
$743$	−5.66594e23	−0.223804	−0.111902	−	0.993719i	$-0.535694\pi$
$743$	−5.66594e23	−0.223804	−0.111902	+	0.993719i	$0.535694\pi$
$744$	−7.57426e23	−0.295781
$745$	−2.20847e23	−0.0852634
$746$	−7.47821e23	−0.285442
$747$	−1.03448e24	−0.390387
$748$	2.50567e24	0.934889
$749$	2.29413e24	0.846296
$750$	−1.84373e23	−0.0672476
$751$	3.95873e24	1.42763	0.713817	−	0.700333i	$-0.246965\pi$
$751$	3.95873e24	1.42763	0.713817	+	0.700333i	$0.246965\pi$
$752$	5.56197e23	0.198325
$753$	6.21783e22	0.0219221
$754$	−2.60422e24	−0.907864
$755$	−1.57076e23	−0.0541452
$756$	−1.59924e23	−0.0545102
$757$	−4.71860e24	−1.59037	−0.795185	−	0.606367i	$-0.792626\pi$
$757$	−4.71860e24	−1.59037	−0.795185	+	0.606367i	$0.792626\pi$
$758$	6.83743e23	0.227879
$759$	1.28634e24	0.423935
$760$	6.99823e21	0.00228072
$761$	1.21212e24	0.390641	0.195320	−	0.980739i	$-0.437425\pi$
$761$	1.21212e24	0.390641	0.195320	+	0.980739i	$0.437425\pi$
$762$	1.46205e23	0.0465956
$763$	1.96867e23	0.0620461
$764$	1.23598e24	0.385227
$765$	−1.02480e23	−0.0315876
$766$	1.93152e24	0.588783
$767$	−4.99542e24	−1.50595
$768$	1.21029e23	0.0360844
$769$	8.50447e23	0.250769	0.125384	−	0.992108i	$-0.459984\pi$
$769$	8.50447e23	0.250769	0.125384	+	0.992108i	$0.459984\pi$
$770$	−1.85103e23	−0.0539812
$771$	9.49166e23	0.273766
$772$	−2.53156e24	−0.722173
$773$	3.88022e24	1.09479	0.547395	−	0.836874i	$-0.315620\pi$
$773$	3.88022e24	1.09479	0.547395	+	0.836874i	$0.315620\pi$
$774$	1.43223e24	0.399681
$775$	−5.21391e24	−1.43913
$776$	−1.33792e24	−0.365262
$777$	2.01042e24	0.542885
$778$	−4.37660e24	−1.16899
$779$	−5.15660e22	−0.0136237
$780$	−8.69412e22	−0.0227207
$781$	−9.19886e23	−0.237794
$782$	−1.42782e24	−0.365104
$783$	1.02571e24	0.259447
$784$	−6.78509e23	−0.169773
$785$	4.24844e23	0.105157
$786$	4.89691e23	0.119903
$787$	−6.88745e24	−1.66830	−0.834148	−	0.551540i	$-0.814040\pi$
$787$	−6.88745e24	−1.66830	−0.834148	+	0.551540i	$0.814040\pi$
$788$	−3.01811e24	−0.723205
$789$	−1.08571e24	−0.257372
$790$	−1.53249e23	−0.0359392
$791$	−4.89224e23	−0.113503
$792$	−8.37254e23	−0.192173
$793$	4.11517e24	0.934471
$794$	−9.06477e23	−0.203649
$795$	−1.03372e23	−0.0229763
$796$	5.78207e23	0.127152
$797$	−2.01952e24	−0.439391	−0.219696	−	0.975568i	$-0.570506\pi$
$797$	−2.01952e24	−0.439391	−0.219696	+	0.975568i	$0.570506\pi$
$798$	8.38587e22	0.0180519
$799$	4.27086e24	0.909636
$800$	8.33131e23	0.175569
$801$	−6.65781e23	−0.138821
$802$	2.33890e24	0.482535
$803$	7.35405e24	1.50122
$804$	2.17208e24	0.438732
$805$	1.05478e23	0.0210813
$806$	−4.93416e24	−0.975810
$807$	5.02549e24	0.983452
$808$	−2.94738e24	−0.570742
$809$	3.68395e24	0.705913	0.352957	−	0.935640i	$-0.385176\pi$
$809$	3.68395e24	0.705913	0.352957	+	0.935640i	$0.385176\pi$
$810$	3.42431e22	0.00649308
$811$	6.75357e24	1.26723	0.633616	−	0.773648i	$-0.281570\pi$
$811$	6.75357e24	1.26723	0.633616	+	0.773648i	$0.281570\pi$
$812$	−2.05645e24	−0.381848
$813$	−3.41528e24	−0.627562
$814$	1.05252e25	1.91392
$815$	1.07332e23	0.0193147
$816$	9.29343e23	0.165504
$817$	−7.51011e23	−0.132361
$818$	4.25555e24	0.742254
$819$	−1.04180e24	−0.179834
$820$	4.22164e22	0.00721213
$821$	4.18654e24	0.707846	0.353923	−	0.935275i	$-0.384847\pi$
$821$	4.18654e24	0.707846	0.353923	+	0.935275i	$0.384847\pi$
$822$	−1.75707e24	−0.294021
$823$	1.80939e24	0.299664	0.149832	−	0.988711i	$-0.452127\pi$
$823$	1.80939e24	0.299664	0.149832	+	0.988711i	$0.452127\pi$
$824$	1.68262e24	0.275806
$825$	−5.76343e24	−0.935024
$826$	−3.94468e24	−0.633405
$827$	−9.98751e22	−0.0158731	−0.00793653	−	0.999969i	$-0.502526\pi$
$827$	−9.98751e22	−0.0158731	−0.00793653	+	0.999969i	$0.502526\pi$
$828$	4.77098e23	0.0750498
$829$	−1.20364e25	−1.87405	−0.937027	−	0.349258i	$-0.886434\pi$
$829$	−1.20364e25	−1.87405	−0.937027	+	0.349258i	$0.886434\pi$
$830$	−4.44093e23	−0.0684400
$831$	−7.17259e24	−1.09413
$832$	7.88429e23	0.119046
$833$	−5.21005e24	−0.778681
$834$	4.46529e24	0.660600
$835$	6.07267e23	0.0889292
$836$	4.39028e23	0.0636413
$837$	1.94339e24	0.278865
$838$	6.59277e24	0.936470
$839$	−4.29513e24	−0.603947	−0.301974	−	0.953316i	$-0.597645\pi$
$839$	−4.29513e24	−0.603947	−0.301974	+	0.953316i	$0.597645\pi$
$840$	−6.86540e22	−0.00955635
$841$	5.93235e24	0.817450
$842$	−6.89540e24	−0.940604
$843$	−2.78743e24	−0.376417
$844$	−3.43174e24	−0.458779
$845$	5.80709e22	0.00768558
$846$	−1.42708e24	−0.186983
$847$	−7.24514e24	−0.939805
$848$	9.37429e23	0.120385
$849$	−8.03485e23	−0.102156
$850$	6.39735e24	0.805265
$851$	−5.99765e24	−0.747446
$852$	−3.41182e23	−0.0420969
$853$	−2.88159e23	−0.0352018	−0.0176009	−	0.999845i	$-0.505603\pi$
$853$	−2.88159e23	−0.0352018	−0.0176009	+	0.999845i	$0.505603\pi$
$854$	3.24958e24	0.393039
$855$	−1.79559e22	−0.00215029
$856$	4.45466e24	0.528187
$857$	−3.73825e24	−0.438866	−0.219433	−	0.975628i	$-0.570421\pi$
$857$	−3.73825e24	−0.438866	−0.219433	+	0.975628i	$0.570421\pi$
$858$	−5.45419e24	−0.633999
$859$	5.44580e24	0.626786	0.313393	−	0.949623i	$-0.398534\pi$
$859$	5.44580e24	0.626786	0.313393	+	0.949623i	$0.398534\pi$
$860$	6.14843e23	0.0700692
$861$	5.05873e23	0.0570840
$862$	−5.86203e24	−0.654993
$863$	1.35864e25	1.50319	0.751595	−	0.659625i	$-0.229285\pi$
$863$	1.35864e25	1.50319	0.751595	+	0.659625i	$0.229285\pi$
$864$	−3.10535e23	−0.0340207
$865$	9.69958e23	0.105224
$866$	−3.79763e24	−0.407953
$867$	1.70860e24	0.181752
$868$	−3.89631e24	−0.410427
$869$	−9.61398e24	−1.00285
$870$	4.40329e23	0.0454845
$871$	1.41497e25	1.44742
$872$	3.82270e23	0.0387239
$873$	3.43280e24	0.344372
$874$	−2.50174e23	−0.0248539
$875$	−9.48441e23	−0.0933130
$876$	2.72759e24	0.265763
$877$	−4.39361e24	−0.423960	−0.211980	−	0.977274i	$-0.567991\pi$
$877$	−4.39361e24	−0.423960	−0.211980	+	0.977274i	$0.567991\pi$
$878$	−1.50991e24	−0.144294
$879$	4.77611e24	0.452032
$880$	−3.59427e23	−0.0336905
$881$	1.21131e24	0.112450	0.0562250	−	0.998418i	$-0.482094\pi$
$881$	1.21131e24	0.112450	0.0562250	+	0.998418i	$0.482094\pi$
$882$	1.74091e24	0.160064
$883$	5.44602e23	0.0495922	0.0247961	−	0.999693i	$-0.492106\pi$
$883$	5.44602e23	0.0495922	0.0247961	+	0.999693i	$0.492106\pi$
$884$	6.05409e24	0.546015
$885$	8.44641e23	0.0754491
$886$	−5.47002e24	−0.483952
$887$	−3.39596e24	−0.297586	−0.148793	−	0.988868i	$-0.547539\pi$
$887$	−3.39596e24	−0.297586	−0.148793	+	0.988868i	$0.547539\pi$
$888$	3.90377e24	0.338824
$889$	7.52099e23	0.0646562
$890$	−2.85814e23	−0.0243371
$891$	2.14821e24	0.181183
$892$	−1.93225e24	−0.161422
$893$	7.48314e23	0.0619222
$894$	−5.13864e24	−0.421191
$895$	−5.68005e23	−0.0461165
$896$	6.22591e23	0.0500708
$897$	3.10799e24	0.247596
$898$	−7.83298e24	−0.618128
$899$	2.49899e25	1.95347
$900$	−2.13764e24	−0.165528
$901$	7.19821e24	0.552159
$902$	2.64841e24	0.201247
$903$	7.36757e24	0.554598
$904$	−9.49959e23	−0.0708391
$905$	−1.51308e24	−0.111776
$906$	−3.65482e24	−0.267471
$907$	−5.67139e24	−0.411176	−0.205588	−	0.978639i	$-0.565911\pi$
$907$	−5.67139e24	−0.411176	−0.205588	+	0.978639i	$0.565911\pi$
$908$	1.09349e24	0.0785390
$909$	7.56235e24	0.538101
$910$	−4.47238e23	−0.0315273
$911$	−1.16111e25	−0.810898	−0.405449	−	0.914118i	$-0.632885\pi$
$911$	−1.16111e25	−0.810898	−0.405449	+	0.914118i	$0.632885\pi$
$912$	1.62834e23	0.0112665
$913$	−2.78598e25	−1.90975
$914$	8.67664e24	0.589263
$915$	−6.95806e23	−0.0468175
$916$	1.10009e24	0.0733356
$917$	2.51904e24	0.166378
$918$	−2.38449e24	−0.156039
$919$	−2.16732e25	−1.40521	−0.702605	−	0.711580i	$-0.747980\pi$
$919$	−2.16732e25	−1.40521	−0.702605	+	0.711580i	$0.747980\pi$
$920$	2.04814e23	0.0131572
$921$	6.59546e24	0.419796
$922$	−1.09513e25	−0.690643
$923$	−2.22259e24	−0.138882
$924$	−4.30696e24	−0.266661
$925$	2.68725e25	1.64855
$926$	4.09325e24	0.248814
$927$	−4.31724e24	−0.260033
$928$	−3.99314e24	−0.238318
$929$	−2.56575e25	−1.51733	−0.758667	−	0.651479i	$-0.774149\pi$
$929$	−2.56575e25	−1.51733	−0.758667	+	0.651479i	$0.774149\pi$
$930$	8.34283e23	0.0488887
$931$	−9.12874e23	−0.0530077
$932$	1.08851e25	0.626319
$933$	−1.52445e25	−0.869197
$934$	−8.39801e24	−0.474491
$935$	−2.75992e24	−0.154525
$936$	−2.02294e24	−0.112238
$937$	−9.78997e24	−0.538264	−0.269132	−	0.963103i	$-0.586737\pi$
$937$	−9.78997e24	−0.538264	−0.269132	+	0.963103i	$0.586737\pi$
$938$	1.11735e25	0.608786
$939$	−6.01041e24	−0.324524
$940$	−6.12635e23	−0.0327805
$941$	−9.97402e24	−0.528882	−0.264441	−	0.964402i	$-0.585187\pi$
$941$	−9.97402e24	−0.528882	−0.264441	+	0.964402i	$0.585187\pi$
$942$	9.88523e24	0.519462
$943$	−1.50916e24	−0.0785934
$944$	−7.65965e24	−0.395318
$945$	1.76151e23	0.00900981
$946$	3.85717e25	1.95521
$947$	2.05305e25	1.03139	0.515697	−	0.856771i	$-0.327533\pi$
$947$	2.05305e25	1.03139	0.515697	+	0.856771i	$0.327533\pi$
$948$	−3.56579e24	−0.177535
$949$	1.77685e25	0.876777
$950$	1.12090e24	0.0548174
$951$	−7.18160e24	−0.348086
$952$	4.78067e24	0.229655
$953$	−5.55090e24	−0.264286	−0.132143	−	0.991231i	$-0.542186\pi$
$953$	−5.55090e24	−0.264286	−0.132143	+	0.991231i	$0.542186\pi$
$954$	−2.40524e24	−0.113500
$955$	−1.36139e24	−0.0636729
$956$	−1.29613e25	−0.600836
$957$	2.76237e25	1.26920
$958$	1.87214e24	0.0852571
$959$	−9.03861e24	−0.407984
$960$	−1.33310e23	−0.00596427
$961$	2.47977e25	1.09967
$962$	2.54306e25	1.11781
$963$	−1.14297e25	−0.497980
$964$	7.90847e24	0.341537
$965$	2.78844e24	0.119366
$966$	2.45426e24	0.104139
$967$	7.03876e24	0.296054	0.148027	−	0.988983i	$-0.452708\pi$
$967$	7.03876e24	0.296054	0.148027	+	0.988983i	$0.452708\pi$
$968$	−1.40684e25	−0.586547
$969$	1.25035e24	0.0516748
$970$	1.47367e24	0.0603729
$971$	−1.32921e25	−0.539797	−0.269898	−	0.962889i	$-0.586990\pi$
$971$	−1.32921e25	−0.539797	−0.269898	+	0.962889i	$0.586990\pi$
$972$	7.96765e23	0.0320750
$973$	2.29701e25	0.916651
$974$	−1.65912e25	−0.656336
$975$	−1.39254e25	−0.546094
$976$	6.30993e24	0.245302
$977$	2.38151e25	0.917801	0.458901	−	0.888488i	$-0.348243\pi$
$977$	2.38151e25	0.917801	0.458901	+	0.888488i	$0.348243\pi$
$978$	2.49738e24	0.0954124
$979$	−1.79303e25	−0.679103
$980$	7.47358e23	0.0280613
$981$	−9.80821e23	−0.0365093
$982$	−2.22756e25	−0.822019
$983$	1.40706e25	0.514765	0.257382	−	0.966310i	$-0.417140\pi$
$983$	1.40706e25	0.514765	0.257382	+	0.966310i	$0.417140\pi$
$984$	9.82286e23	0.0356270
$985$	3.32436e24	0.119536
$986$	−3.06620e25	−1.09307
$987$	−7.34112e24	−0.259458
$988$	1.06076e24	0.0371692
$989$	−2.19795e25	−0.763572
$990$	9.22211e23	0.0317637
$991$	2.35370e25	0.803758	0.401879	−	0.915693i	$-0.368357\pi$
$991$	2.35370e25	0.803758	0.401879	+	0.915693i	$0.368357\pi$
$992$	−7.56572e24	−0.256154
$993$	5.94697e23	0.0199631
$994$	−1.75509e24	−0.0584137
$995$	−6.36879e23	−0.0210165
$996$	−1.03331e25	−0.338085
$997$	2.92213e25	0.947961	0.473980	−	0.880535i	$-0.342817\pi$
$997$	2.92213e25	0.947961	0.473980	+	0.880535i	$0.342817\pi$
$998$	−2.63823e25	−0.848601
$999$	−1.00162e25	−0.319446

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6.18.a.b.1.1	✓	1	1.1	even	1	trivial
18.18.a.d.1.1		1	3.2	odd	2
48.18.a.a.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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