LMFDB - Embedded newform 16.26.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,26,Mod(1,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("16.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	16.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:	$63.3594847924$
Analytic rank:	$0$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+195804. q^{3} -7.41990e8 q^{5} -3.90806e10 q^{7} -8.08949e11 q^{9} +O(q^{10})$

$q+195804. q^{3} -7.41990e8 q^{5} -3.90806e10 q^{7} -8.08949e11 q^{9} -8.41952e12 q^{11} -8.16510e13 q^{13} -1.45285e14 q^{15} -2.51990e15 q^{17} +6.08206e15 q^{19} -7.65214e15 q^{21} +9.49953e16 q^{23} +2.52526e17 q^{25} -3.24298e17 q^{27} -2.71247e17 q^{29} -4.29167e18 q^{31} -1.64857e18 q^{33} +2.89974e19 q^{35} +2.03015e19 q^{37} -1.59876e19 q^{39} -1.83744e20 q^{41} -3.00902e20 q^{43} +6.00232e20 q^{45} +9.24361e20 q^{47} +1.86224e20 q^{49} -4.93407e20 q^{51} -9.90292e20 q^{53} +6.24719e21 q^{55} +1.19089e21 q^{57} -1.30526e22 q^{59} +9.01545e21 q^{61} +3.16142e22 q^{63} +6.05842e22 q^{65} +2.66891e22 q^{67} +1.86005e22 q^{69} +1.92391e23 q^{71} +4.24046e22 q^{73} +4.94455e22 q^{75} +3.29040e23 q^{77} +2.71681e23 q^{79} +6.21915e23 q^{81} +9.31454e23 q^{83} +1.86974e24 q^{85} -5.31112e22 q^{87} -1.76364e24 q^{89} +3.19097e24 q^{91} -8.40325e23 q^{93} -4.51282e24 q^{95} +2.82924e24 q^{97} +6.81096e24 q^{99} +O(q^{100})$

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 $

$2$	0	0
$2$	0	0
$3$	195804.	0.212719	0.106359	−	0.994328i	$-0.466081\pi$
$3$	195804.	0.212719	0.106359	+	0.994328i	$0.466081\pi$
$4$	0	0
$5$	−7.41990e8	−1.35917	−0.679584	−	0.733598i	$-0.737840\pi$
$5$	−7.41990e8	−1.35917	−0.679584	+	0.733598i	$0.737840\pi$
$6$	0	0
$7$	−3.90806e10	−1.06718	−0.533588	−	0.845745i	$-0.679157\pi$
$7$	−3.90806e10	−1.06718	−0.533588	+	0.845745i	$0.679157\pi$
$8$	0	0
$9$	−8.08949e11	−0.954751
$10$	0	0
$11$	−8.41952e12	−0.808870	−0.404435	−	0.914567i	$-0.632532\pi$
$11$	−8.41952e12	−0.808870	−0.404435	+	0.914567i	$0.632532\pi$
$12$	0	0
$13$	−8.16510e13	−0.972008	−0.486004	−	0.873957i	$-0.661546\pi$
$13$	−8.16510e13	−0.972008	−0.486004	+	0.873957i	$0.661546\pi$
$14$	0	0
$15$	−1.45285e14	−0.289120
$16$	0	0
$17$	−2.51990e15	−1.04899	−0.524496	−	0.851413i	$-0.675746\pi$
$17$	−2.51990e15	−1.04899	−0.524496	+	0.851413i	$0.675746\pi$
$18$	0	0
$19$	6.08206e15	0.630421	0.315210	−	0.949022i	$-0.397925\pi$
$19$	6.08206e15	0.630421	0.315210	+	0.949022i	$0.397925\pi$
$20$	0	0
$21$	−7.65214e15	−0.227008
$22$	0	0
$23$	9.49953e16	0.903866	0.451933	−	0.892052i	$-0.350735\pi$
$23$	9.49953e16	0.903866	0.451933	+	0.892052i	$0.350735\pi$
$24$	0	0
$25$	2.52526e17	0.847336
$26$	0	0
$27$	−3.24298e17	−0.415812
$28$	0	0
$29$	−2.71247e17	−0.142361	−0.0711803	−	0.997463i	$-0.522677\pi$
$29$	−2.71247e17	−0.142361	−0.0711803	+	0.997463i	$0.522677\pi$
$30$	0	0
$31$	−4.29167e18	−0.978599	−0.489299	−	0.872116i	$-0.662747\pi$
$31$	−4.29167e18	−0.978599	−0.489299	+	0.872116i	$0.662747\pi$
$32$	0	0
$33$	−1.64857e18	−0.172062
$34$	0	0
$35$	2.89974e19	1.45047
$36$	0	0
$37$	2.03015e19	0.506998	0.253499	−	0.967336i	$-0.418419\pi$
$37$	2.03015e19	0.506998	0.253499	+	0.967336i	$0.418419\pi$
$38$	0	0
$39$	−1.59876e19	−0.206764
$40$	0	0
$41$	−1.83744e20	−1.27179	−0.635895	−	0.771775i	$-0.719369\pi$
$41$	−1.83744e20	−1.27179	−0.635895	+	0.771775i	$0.719369\pi$
$42$	0	0
$43$	−3.00902e20	−1.14834	−0.574168	−	0.818737i	$-0.694674\pi$
$43$	−3.00902e20	−1.14834	−0.574168	+	0.818737i	$0.694674\pi$
$44$	0	0
$45$	6.00232e20	1.29767
$46$	0	0
$47$	9.24361e20	1.16043	0.580214	−	0.814464i	$-0.302969\pi$
$47$	9.24361e20	1.16043	0.580214	+	0.814464i	$0.302969\pi$
$48$	0	0
$49$	1.86224e20	0.138863
$50$	0	0
$51$	−4.93407e20	−0.223140
$52$	0	0
$53$	−9.90292e20	−0.276895	−0.138447	−	0.990370i	$-0.544211\pi$
$53$	−9.90292e20	−0.276895	−0.138447	+	0.990370i	$0.544211\pi$
$54$	0	0
$55$	6.24719e21	1.09939
$56$	0	0
$57$	1.19089e21	0.134102
$58$	0	0
$59$	−1.30526e22	−0.955093	−0.477547	−	0.878606i	$-0.658474\pi$
$59$	−1.30526e22	−0.955093	−0.477547	+	0.878606i	$0.658474\pi$
$60$	0	0
$61$	9.01545e21	0.434875	0.217438	−	0.976074i	$-0.430230\pi$
$61$	9.01545e21	0.434875	0.217438	+	0.976074i	$0.430230\pi$
$62$	0	0
$63$	3.16142e22	1.01889
$64$	0	0
$65$	6.05842e22	1.32112
$66$	0	0
$67$	2.66891e22	0.398473	0.199236	−	0.979951i	$-0.436154\pi$
$67$	2.66891e22	0.398473	0.199236	+	0.979951i	$0.436154\pi$
$68$	0	0
$69$	1.86005e22	0.192269
$70$	0	0
$71$	1.92391e23	1.39141	0.695704	−	0.718329i	$-0.255093\pi$
$71$	1.92391e23	1.39141	0.695704	+	0.718329i	$0.255093\pi$
$72$	0	0
$73$	4.24046e22	0.216709	0.108355	−	0.994112i	$-0.465442\pi$
$73$	4.24046e22	0.216709	0.108355	+	0.994112i	$0.465442\pi$
$74$	0	0
$75$	4.94455e22	0.180244
$76$	0	0
$77$	3.29040e23	0.863206
$78$	0	0
$79$	2.71681e23	0.517274	0.258637	−	0.965975i	$-0.416727\pi$
$79$	2.71681e23	0.517274	0.258637	+	0.965975i	$0.416727\pi$
$80$	0	0
$81$	6.21915e23	0.866300
$82$	0	0
$83$	9.31454e23	0.956501	0.478251	−	0.878223i	$-0.341271\pi$
$83$	9.31454e23	0.956501	0.478251	+	0.878223i	$0.341271\pi$
$84$	0	0
$85$	1.86974e24	1.42575
$86$	0	0
$87$	−5.31112e22	−0.0302828
$88$	0	0
$89$	−1.76364e24	−0.756892	−0.378446	−	0.925623i	$-0.623541\pi$
$89$	−1.76364e24	−0.756892	−0.378446	+	0.925623i	$0.623541\pi$
$90$	0	0
$91$	3.19097e24	1.03730
$92$	0	0
$93$	−8.40325e23	−0.208166
$94$	0	0
$95$	−4.51282e24	−0.856847
$96$	0	0
$97$	2.82924e24	0.414022	0.207011	−	0.978339i	$-0.433626\pi$
$97$	2.82924e24	0.414022	0.207011	+	0.978339i	$0.433626\pi$
$98$	0	0
$99$	6.81096e24	0.772269
$100$	0	0
$101$	1.86342e24	0.164549	0.0822744	−	0.996610i	$-0.473782\pi$
$101$	1.86342e24	0.164549	0.0822744	+	0.996610i	$0.473782\pi$
$102$	0	0
$103$	−4.85812e24	−0.335740	−0.167870	−	0.985809i	$-0.553689\pi$
$103$	−4.85812e24	−0.335740	−0.167870	+	0.985809i	$0.553689\pi$
$104$	0	0
$105$	5.67781e24	0.308542
$106$	0	0
$107$	−3.58304e25	−1.53799	−0.768997	−	0.639252i	$-0.779244\pi$
$107$	−3.58304e25	−1.53799	−0.768997	+	0.639252i	$0.779244\pi$
$108$	0	0
$109$	−4.77795e25	−1.62709	−0.813543	−	0.581505i	$-0.802464\pi$
$109$	−4.77795e25	−1.62709	−0.813543	+	0.581505i	$0.802464\pi$
$110$	0	0
$111$	3.97511e24	0.107848
$112$	0	0
$113$	−7.46476e25	−1.62008	−0.810038	−	0.586378i	$-0.800553\pi$
$113$	−7.46476e25	−1.62008	−0.810038	+	0.586378i	$0.800553\pi$
$114$	0	0
$115$	−7.04855e25	−1.22851
$116$	0	0
$117$	6.60516e25	0.928025
$118$	0	0
$119$	9.84792e25	1.11946
$120$	0	0
$121$	−3.74588e25	−0.345730
$122$	0	0
$123$	−3.59779e25	−0.270534
$124$	0	0
$125$	3.37587e25	0.207496
$126$	0	0
$127$	−3.35905e26	−1.69305	−0.846524	−	0.532350i	$-0.821309\pi$
$127$	−3.35905e26	−1.69305	−0.846524	+	0.532350i	$0.821309\pi$
$128$	0	0
$129$	−5.89178e25	−0.244273
$130$	0	0
$131$	1.74971e26	0.598513	0.299257	−	0.954173i	$-0.403261\pi$
$131$	1.74971e26	0.598513	0.299257	+	0.954173i	$0.403261\pi$
$132$	0	0
$133$	−2.37690e26	−0.672769
$134$	0	0
$135$	2.40626e26	0.565158
$136$	0	0
$137$	6.18313e26	1.20837	0.604187	−	0.796843i	$-0.293498\pi$
$137$	6.18313e26	1.20837	0.604187	+	0.796843i	$0.293498\pi$
$138$	0	0
$139$	4.84462e26	0.789905	0.394952	−	0.918702i	$-0.370761\pi$
$139$	4.84462e26	0.789905	0.394952	+	0.918702i	$0.370761\pi$
$140$	0	0
$141$	1.80994e26	0.246845
$142$	0	0
$143$	6.87462e26	0.786228
$144$	0	0
$145$	2.01262e26	0.193492
$146$	0	0
$147$	3.64635e25	0.0295387
$148$	0	0
$149$	9.05569e26	0.619574	0.309787	−	0.950806i	$-0.399742\pi$
$149$	9.05569e26	0.619574	0.309787	+	0.950806i	$0.399742\pi$
$150$	0	0
$151$	−1.16190e27	−0.672907	−0.336454	−	0.941700i	$-0.609228\pi$
$151$	−1.16190e27	−0.672907	−0.336454	+	0.941700i	$0.609228\pi$
$152$	0	0
$153$	2.03847e27	1.00152
$154$	0	0
$155$	3.18437e27	1.33008
$156$	0	0
$157$	−3.41505e26	−0.121521	−0.0607605	−	0.998152i	$-0.519353\pi$
$157$	−3.41505e26	−0.121521	−0.0607605	+	0.998152i	$0.519353\pi$
$158$	0	0
$159$	−1.93903e26	−0.0589008
$160$	0	0
$161$	−3.71247e27	−0.964583
$162$	0	0
$163$	−4.63202e27	−1.03140	−0.515698	−	0.856771i	$-0.672467\pi$
$163$	−4.63202e27	−1.03140	−0.515698	+	0.856771i	$0.672467\pi$
$164$	0	0
$165$	1.22323e27	0.233861
$166$	0	0
$167$	8.26470e27	1.35916	0.679581	−	0.733600i	$-0.262162\pi$
$167$	8.26470e27	1.35916	0.679581	+	0.733600i	$0.262162\pi$
$168$	0	0
$169$	−3.89517e26	−0.0552004
$170$	0	0
$171$	−4.92008e27	−0.601895
$172$	0	0
$173$	−6.02602e27	−0.637462	−0.318731	−	0.947845i	$-0.603257\pi$
$173$	−6.02602e27	−0.637462	−0.318731	+	0.947845i	$0.603257\pi$
$174$	0	0
$175$	−9.86886e27	−0.904256
$176$	0	0
$177$	−2.55575e27	−0.203166
$178$	0	0
$179$	−2.41023e28	−1.66493	−0.832463	−	0.554081i	$-0.813070\pi$
$179$	−2.41023e28	−1.66493	−0.832463	+	0.554081i	$0.813070\pi$
$180$	0	0
$181$	−8.19193e27	−0.492498	−0.246249	−	0.969207i	$-0.579198\pi$
$181$	−8.19193e27	−0.492498	−0.246249	+	0.969207i	$0.579198\pi$
$182$	0	0
$183$	1.76526e27	0.0925061
$184$	0	0
$185$	−1.50635e28	−0.689095
$186$	0	0
$187$	2.12163e28	0.848497
$188$	0	0
$189$	1.26738e28	0.443744
$190$	0	0
$191$	−5.50602e27	−0.169013	−0.0845066	−	0.996423i	$-0.526931\pi$
$191$	−5.50602e27	−0.169013	−0.0845066	+	0.996423i	$0.526931\pi$
$192$	0	0
$193$	2.08716e28	0.562457	0.281228	−	0.959641i	$-0.409258\pi$
$193$	2.08716e28	0.562457	0.281228	+	0.959641i	$0.409258\pi$
$194$	0	0
$195$	1.18626e28	0.281027
$196$	0	0
$197$	−5.99370e28	−1.24988	−0.624938	−	0.780674i	$-0.714876\pi$
$197$	−5.99370e28	−1.24988	−0.624938	+	0.780674i	$0.714876\pi$
$198$	0	0
$199$	−2.24042e27	−0.0411782	−0.0205891	−	0.999788i	$-0.506554\pi$
$199$	−2.24042e27	−0.0411782	−0.0205891	+	0.999788i	$0.506554\pi$
$200$	0	0
$201$	5.22583e27	0.0847626
$202$	0	0
$203$	1.06005e28	0.151924
$204$	0	0
$205$	1.36336e29	1.72858
$206$	0	0
$207$	−7.68464e28	−0.862967
$208$	0	0
$209$	−5.12080e28	−0.509928
$210$	0	0
$211$	7.52475e28	0.665214	0.332607	−	0.943066i	$-0.392072\pi$
$211$	7.52475e28	0.665214	0.332607	+	0.943066i	$0.392072\pi$
$212$	0	0
$213$	3.76708e28	0.295979
$214$	0	0
$215$	2.23266e29	1.56078
$216$	0	0
$217$	1.67721e29	1.04434
$218$	0	0
$219$	8.30299e27	0.0460981
$220$	0	0
$221$	2.05752e29	1.01963
$222$	0	0
$223$	3.16696e29	1.40227	0.701135	−	0.713029i	$-0.252677\pi$
$223$	3.16696e29	1.40227	0.701135	+	0.713029i	$0.252677\pi$
$224$	0	0
$225$	−2.04281e29	−0.808994
$226$	0	0
$227$	−3.85094e29	−1.36535	−0.682674	−	0.730723i	$-0.739183\pi$
$227$	−3.85094e29	−1.36535	−0.682674	+	0.730723i	$0.739183\pi$
$228$	0	0
$229$	−5.68261e29	−1.80553	−0.902765	−	0.430134i	$-0.858466\pi$
$229$	−5.68261e29	−1.80553	−0.902765	+	0.430134i	$0.858466\pi$
$230$	0	0
$231$	6.44273e28	0.183620
$232$	0	0
$233$	4.95586e29	1.26815	0.634075	−	0.773272i	$-0.281381\pi$
$233$	4.95586e29	1.26815	0.634075	+	0.773272i	$0.281381\pi$
$234$	0	0
$235$	−6.85867e29	−1.57722
$236$	0	0
$237$	5.31962e28	0.110034
$238$	0	0
$239$	1.44023e29	0.268200	0.134100	−	0.990968i	$-0.457186\pi$
$239$	1.44023e29	0.268200	0.134100	+	0.990968i	$0.457186\pi$
$240$	0	0
$241$	−3.19456e29	−0.536041	−0.268020	−	0.963413i	$-0.586369\pi$
$241$	−3.19456e29	−0.536041	−0.268020	+	0.963413i	$0.586369\pi$
$242$	0	0
$243$	3.96547e29	0.600090
$244$	0	0
$245$	−1.38177e29	−0.188738
$246$	0	0
$247$	−4.96606e29	−0.612774
$248$	0	0
$249$	1.82383e29	0.203466
$250$	0	0
$251$	−6.21677e29	−0.627543	−0.313771	−	0.949499i	$-0.601593\pi$
$251$	−6.21677e29	−0.627543	−0.313771	+	0.949499i	$0.601593\pi$
$252$	0	0
$253$	−7.99814e29	−0.731110
$254$	0	0
$255$	3.66103e29	0.303285
$256$	0	0
$257$	−2.29446e30	−1.72392	−0.861960	−	0.506977i	$-0.830763\pi$
$257$	−2.29446e30	−1.72392	−0.861960	+	0.506977i	$0.830763\pi$
$258$	0	0
$259$	−7.93394e29	−0.541056
$260$	0	0
$261$	2.19425e29	0.135919
$262$	0	0
$263$	−7.73316e29	−0.435422	−0.217711	−	0.976013i	$-0.569859\pi$
$263$	−7.73316e29	−0.435422	−0.217711	+	0.976013i	$0.569859\pi$
$264$	0	0
$265$	7.34787e29	0.376347
$266$	0	0
$267$	−3.45327e29	−0.161005
$268$	0	0
$269$	3.62259e30	1.53856	0.769282	−	0.638910i	$-0.220614\pi$
$269$	3.62259e30	1.53856	0.769282	+	0.638910i	$0.220614\pi$
$270$	0	0
$271$	3.62767e30	1.40447	0.702234	−	0.711946i	$-0.252186\pi$
$271$	3.62767e30	1.40447	0.702234	+	0.711946i	$0.252186\pi$
$272$	0	0
$273$	6.24805e29	0.220654
$274$	0	0
$275$	−2.12614e30	−0.685384
$276$	0	0
$277$	−2.54808e30	−0.750266	−0.375133	−	0.926971i	$-0.622403\pi$
$277$	−2.54808e30	−0.750266	−0.375133	+	0.926971i	$0.622403\pi$
$278$	0	0
$279$	3.47174e30	0.934318
$280$	0	0
$281$	3.59817e30	0.885631	0.442816	−	0.896613i	$-0.353980\pi$
$281$	3.59817e30	0.885631	0.442816	+	0.896613i	$0.353980\pi$
$282$	0	0
$283$	−3.82265e30	−0.861061	−0.430530	−	0.902576i	$-0.641673\pi$
$283$	−3.82265e30	−0.861061	−0.430530	+	0.902576i	$0.641673\pi$
$284$	0	0
$285$	−8.83629e29	−0.182267
$286$	0	0
$287$	7.18084e30	1.35722
$288$	0	0
$289$	5.79269e29	0.100382
$290$	0	0
$291$	5.53977e29	0.0880702
$292$	0	0
$293$	1.30007e29	0.0189723	0.00948615	−	0.999955i	$-0.496980\pi$
$293$	1.30007e29	0.0189723	0.00948615	+	0.999955i	$0.496980\pi$
$294$	0	0
$295$	9.68487e30	1.29813
$296$	0	0
$297$	2.73043e30	0.336338
$298$	0	0
$299$	−7.75646e30	−0.878565
$300$	0	0
$301$	1.17594e31	1.22548
$302$	0	0
$303$	3.64866e29	0.0350026
$304$	0	0
$305$	−6.68937e30	−0.591068
$306$	0	0
$307$	−1.43602e31	−1.16931	−0.584657	−	0.811281i	$-0.698771\pi$
$307$	−1.43602e31	−1.16931	−0.584657	+	0.811281i	$0.698771\pi$
$308$	0	0
$309$	−9.51239e29	−0.0714182
$310$	0	0
$311$	2.24630e31	1.55584	0.777918	−	0.628366i	$-0.216276\pi$
$311$	2.24630e31	1.55584	0.777918	+	0.628366i	$0.216276\pi$
$312$	0	0
$313$	−1.37956e30	−0.0881934	−0.0440967	−	0.999027i	$-0.514041\pi$
$313$	−1.37956e30	−0.0881934	−0.0440967	+	0.999027i	$0.514041\pi$
$314$	0	0
$315$	−2.34574e31	−1.38484
$316$	0	0
$317$	−1.02787e31	−0.560655	−0.280327	−	0.959904i	$-0.590443\pi$
$317$	−1.02787e31	−0.560655	−0.280327	+	0.959904i	$0.590443\pi$
$318$	0	0
$319$	2.28377e30	0.115151
$320$	0	0
$321$	−7.01574e30	−0.327160
$322$	0	0
$323$	−1.53262e31	−0.661306
$324$	0	0
$325$	−2.06190e31	−0.823617
$326$	0	0
$327$	−9.35542e30	−0.346112
$328$	0	0
$329$	−3.61246e31	−1.23838
$330$	0	0
$331$	5.75356e30	0.182847	0.0914233	−	0.995812i	$-0.470858\pi$
$331$	5.75356e30	0.182847	0.0914233	+	0.995812i	$0.470858\pi$
$332$	0	0
$333$	−1.64229e31	−0.484057
$334$	0	0
$335$	−1.98030e31	−0.541591
$336$	0	0
$337$	6.69268e31	1.69913	0.849564	−	0.527485i	$-0.176865\pi$
$337$	6.69268e31	1.69913	0.849564	+	0.527485i	$0.176865\pi$
$338$	0	0
$339$	−1.46163e31	−0.344621
$340$	0	0
$341$	3.61337e31	0.791559
$342$	0	0
$343$	4.51320e31	0.918984
$344$	0	0
$345$	−1.38013e31	−0.261326
$346$	0	0
$347$	−9.41781e29	−0.0165894	−0.00829472	−	0.999966i	$-0.502640\pi$
$347$	−9.41781e29	−0.0165894	−0.00829472	+	0.999966i	$0.502640\pi$
$348$	0	0
$349$	−3.39081e31	−0.555886	−0.277943	−	0.960598i	$-0.589653\pi$
$349$	−3.39081e31	−0.555886	−0.277943	+	0.960598i	$0.589653\pi$
$350$	0	0
$351$	2.64793e31	0.404173
$352$	0	0
$353$	1.30313e31	0.185269	0.0926346	−	0.995700i	$-0.470471\pi$
$353$	1.30313e31	0.185269	0.0926346	+	0.995700i	$0.470471\pi$
$354$	0	0
$355$	−1.42752e32	−1.89116
$356$	0	0
$357$	1.92826e31	0.238130
$358$	0	0
$359$	1.30336e32	1.50101	0.750506	−	0.660864i	$-0.229810\pi$
$359$	1.30336e32	1.50101	0.750506	+	0.660864i	$0.229810\pi$
$360$	0	0
$361$	−5.60851e31	−0.602570
$362$	0	0
$363$	−7.33459e30	−0.0735433
$364$	0	0
$365$	−3.14638e31	−0.294544
$366$	0	0
$367$	2.06294e32	1.80369	0.901844	−	0.432061i	$-0.142214\pi$
$367$	2.06294e32	1.80369	0.901844	+	0.432061i	$0.142214\pi$
$368$	0	0
$369$	1.48640e32	1.21424
$370$	0	0
$371$	3.87012e31	0.295495
$372$	0	0
$373$	2.46051e32	1.75657	0.878283	−	0.478142i	$-0.158689\pi$
$373$	2.46051e32	1.75657	0.878283	+	0.478142i	$0.158689\pi$
$374$	0	0
$375$	6.61009e30	0.0441384
$376$	0	0
$377$	2.21476e31	0.138376
$378$	0	0
$379$	−7.12743e31	−0.416815	−0.208407	−	0.978042i	$-0.566828\pi$
$379$	−7.12743e31	−0.416815	−0.208407	+	0.978042i	$0.566828\pi$
$380$	0	0
$381$	−6.57715e31	−0.360143
$382$	0	0
$383$	−1.33051e32	−0.682393	−0.341196	−	0.939992i	$-0.610832\pi$
$383$	−1.33051e32	−0.682393	−0.341196	+	0.939992i	$0.610832\pi$
$384$	0	0
$385$	−2.44144e32	−1.17324
$386$	0	0
$387$	2.43414e32	1.09637
$388$	0	0
$389$	2.40509e32	1.01569	0.507844	−	0.861449i	$-0.330443\pi$
$389$	2.40509e32	1.01569	0.507844	+	0.861449i	$0.330443\pi$
$390$	0	0
$391$	−2.39379e32	−0.948147
$392$	0	0
$393$	3.42599e31	0.127315
$394$	0	0
$395$	−2.01585e32	−0.703062
$396$	0	0
$397$	−4.12137e32	−1.34946	−0.674730	−	0.738065i	$-0.735740\pi$
$397$	−4.12137e32	−1.34946	−0.674730	+	0.738065i	$0.735740\pi$
$398$	0	0
$399$	−4.65407e31	−0.143111
$400$	0	0
$401$	−7.16647e31	−0.207014	−0.103507	−	0.994629i	$-0.533006\pi$
$401$	−7.16647e31	−0.207014	−0.103507	+	0.994629i	$0.533006\pi$
$402$	0	0
$403$	3.50419e32	0.951206
$404$	0	0
$405$	−4.61454e32	−1.17745
$406$	0	0
$407$	−1.70929e32	−0.410095
$408$	0	0
$409$	1.34430e32	0.303358	0.151679	−	0.988430i	$-0.451532\pi$
$409$	1.34430e32	0.303358	0.151679	+	0.988430i	$0.451532\pi$
$410$	0	0
$411$	1.21068e32	0.257044
$412$	0	0
$413$	5.10102e32	1.01925
$414$	0	0
$415$	−6.91130e32	−1.30004
$416$	0	0
$417$	9.48596e31	0.168028
$418$	0	0
$419$	1.71876e32	0.286774	0.143387	−	0.989667i	$-0.454201\pi$
$419$	1.71876e32	0.286774	0.143387	+	0.989667i	$0.454201\pi$
$420$	0	0
$421$	−8.27664e32	−1.30115	−0.650576	−	0.759441i	$-0.725472\pi$
$421$	−8.27664e32	−1.30115	−0.650576	+	0.759441i	$0.725472\pi$
$422$	0	0
$423$	−7.47761e32	−1.10792
$424$	0	0
$425$	−6.36340e32	−0.888848
$426$	0	0
$427$	−3.52329e32	−0.464088
$428$	0	0
$429$	1.34608e32	0.167245
$430$	0	0
$431$	7.83836e31	0.0918881	0.0459441	−	0.998944i	$-0.485370\pi$
$431$	7.83836e31	0.0918881	0.0459441	+	0.998944i	$0.485370\pi$
$432$	0	0
$433$	6.33273e32	0.700635	0.350318	−	0.936631i	$-0.386074\pi$
$433$	6.33273e32	0.700635	0.350318	+	0.936631i	$0.386074\pi$
$434$	0	0
$435$	3.94080e31	0.0411594
$436$	0	0
$437$	5.77767e32	0.569816
$438$	0	0
$439$	1.48299e33	1.38144	0.690718	−	0.723124i	$-0.257295\pi$
$439$	1.48299e33	1.38144	0.690718	+	0.723124i	$0.257295\pi$
$440$	0	0
$441$	−1.50646e32	−0.132579
$442$	0	0
$443$	1.20901e33	1.00551	0.502753	−	0.864430i	$-0.332321\pi$
$443$	1.20901e33	1.00551	0.502753	+	0.864430i	$0.332321\pi$
$444$	0	0
$445$	1.30860e33	1.02874
$446$	0	0
$447$	1.77314e32	0.131795
$448$	0	0
$449$	−9.48861e32	−0.666996	−0.333498	−	0.942751i	$-0.608229\pi$
$449$	−9.48861e32	−0.666996	−0.333498	+	0.942751i	$0.608229\pi$
$450$	0	0
$451$	1.54704e33	1.02871
$452$	0	0
$453$	−2.27504e32	−0.143140
$454$	0	0
$455$	−2.36767e33	−1.40987
$456$	0	0
$457$	1.90644e33	1.07466	0.537329	−	0.843373i	$-0.319433\pi$
$457$	1.90644e33	1.07466	0.537329	+	0.843373i	$0.319433\pi$
$458$	0	0
$459$	8.17199e32	0.436183
$460$	0	0
$461$	−4.56270e31	−0.0230653	−0.0115327	−	0.999933i	$-0.503671\pi$
$461$	−4.56270e31	−0.0230653	−0.0115327	+	0.999933i	$0.503671\pi$
$462$	0	0
$463$	−2.13521e33	−1.02254	−0.511269	−	0.859421i	$-0.670824\pi$
$463$	−2.13521e33	−1.02254	−0.511269	+	0.859421i	$0.670824\pi$
$464$	0	0
$465$	6.23513e32	0.282933
$466$	0	0
$467$	2.67225e33	1.14926	0.574628	−	0.818415i	$-0.305147\pi$
$467$	2.67225e33	1.14926	0.574628	+	0.818415i	$0.305147\pi$
$468$	0	0
$469$	−1.04302e33	−0.425240
$470$	0	0
$471$	−6.68680e31	−0.0258498
$472$	0	0
$473$	2.53345e33	0.928854
$474$	0	0
$475$	1.53588e33	0.534178
$476$	0	0
$477$	8.01096e32	0.264366
$478$	0	0
$479$	−1.97240e33	−0.617733	−0.308867	−	0.951105i	$-0.599950\pi$
$479$	−1.97240e33	−0.617733	−0.308867	+	0.951105i	$0.599950\pi$
$480$	0	0
$481$	−1.65764e33	−0.492806
$482$	0	0
$483$	−7.26917e32	−0.205185
$484$	0	0
$485$	−2.09927e33	−0.562725
$486$	0	0
$487$	3.96366e32	0.100922	0.0504608	−	0.998726i	$-0.483931\pi$
$487$	3.96366e32	0.100922	0.0504608	+	0.998726i	$0.483931\pi$
$488$	0	0
$489$	−9.06968e32	−0.219397
$490$	0	0
$491$	7.22626e33	1.66110	0.830548	−	0.556947i	$-0.188027\pi$
$491$	7.22626e33	1.66110	0.830548	+	0.556947i	$0.188027\pi$
$492$	0	0
$493$	6.83515e32	0.149335
$494$	0	0
$495$	−5.05366e33	−1.04964
$496$	0	0
$497$	−7.51874e33	−1.48488
$498$	0	0
$499$	−8.19830e33	−1.53981	−0.769905	−	0.638159i	$-0.779696\pi$
$499$	−8.19830e33	−1.53981	−0.769905	+	0.638159i	$0.779696\pi$
$500$	0	0
$501$	1.61826e33	0.289119
$502$	0	0
$503$	−4.72562e33	−0.803265	−0.401633	−	0.915801i	$-0.631557\pi$
$503$	−4.72562e33	−0.803265	−0.401633	+	0.915801i	$0.631557\pi$
$504$	0	0
$505$	−1.38264e33	−0.223649
$506$	0	0
$507$	−7.62689e31	−0.0117422
$508$	0	0
$509$	1.96955e33	0.288665	0.144332	−	0.989529i	$-0.453897\pi$
$509$	1.96955e33	0.288665	0.144332	+	0.989529i	$0.453897\pi$
$510$	0	0
$511$	−1.65720e33	−0.231267
$512$	0	0
$513$	−1.97240e33	−0.262137
$514$	0	0
$515$	3.60468e33	0.456327
$516$	0	0
$517$	−7.78267e33	−0.938635
$518$	0	0
$519$	−1.17992e33	−0.135600
$520$	0	0
$521$	7.39782e33	0.810274	0.405137	−	0.914256i	$-0.367224\pi$
$521$	7.39782e33	0.810274	0.405137	+	0.914256i	$0.367224\pi$
$522$	0	0
$523$	−1.70332e34	−1.77838	−0.889191	−	0.457535i	$-0.848732\pi$
$523$	−1.70332e34	−1.77838	−0.889191	+	0.457535i	$0.848732\pi$
$524$	0	0
$525$	−1.93236e33	−0.192352
$526$	0	0
$527$	1.08146e34	1.02654
$528$	0	0
$529$	−2.02166e33	−0.183026
$530$	0	0
$531$	1.05589e34	0.911876
$532$	0	0
$533$	1.50029e34	1.23619
$534$	0	0
$535$	2.65858e34	2.09039
$536$	0	0
$537$	−4.71932e33	−0.354161
$538$	0	0
$539$	−1.56792e33	−0.112322
$540$	0	0
$541$	−1.28681e34	−0.880134	−0.440067	−	0.897965i	$-0.645045\pi$
$541$	−1.28681e34	−0.880134	−0.440067	+	0.897965i	$0.645045\pi$
$542$	0	0
$543$	−1.60401e33	−0.104764
$544$	0	0
$545$	3.54519e34	2.21148
$546$	0	0
$547$	−2.06624e34	−1.23123	−0.615616	−	0.788046i	$-0.711093\pi$
$547$	−2.06624e34	−1.23123	−0.615616	+	0.788046i	$0.711093\pi$
$548$	0	0
$549$	−7.29304e33	−0.415197
$550$	0	0
$551$	−1.64974e33	−0.0897471
$552$	0	0
$553$	−1.06175e34	−0.552022
$554$	0	0
$555$	−2.94949e33	−0.146583
$556$	0	0
$557$	−3.28751e33	−0.156198	−0.0780992	−	0.996946i	$-0.524885\pi$
$557$	−3.28751e33	−0.156198	−0.0780992	+	0.996946i	$0.524885\pi$
$558$	0	0
$559$	2.45689e34	1.11619
$560$	0	0
$561$	4.15424e33	0.180491
$562$	0	0
$563$	1.80804e34	0.751371	0.375685	−	0.926747i	$-0.377407\pi$
$563$	1.80804e34	0.751371	0.375685	+	0.926747i	$0.377407\pi$
$564$	0	0
$565$	5.53878e34	2.20195
$566$	0	0
$567$	−2.43048e34	−0.924493
$568$	0	0
$569$	−3.05967e33	−0.111371	−0.0556854	−	0.998448i	$-0.517734\pi$
$569$	−3.05967e33	−0.111371	−0.0556854	+	0.998448i	$0.517734\pi$
$570$	0	0
$571$	1.29884e34	0.452486	0.226243	−	0.974071i	$-0.427356\pi$
$571$	1.29884e34	0.452486	0.226243	+	0.974071i	$0.427356\pi$
$572$	0	0
$573$	−1.07810e33	−0.0359523
$574$	0	0
$575$	2.39888e34	0.765878
$576$	0	0
$577$	−7.31490e31	−0.00223620	−0.00111810	−	0.999999i	$-0.500356\pi$
$577$	−7.31490e31	−0.00223620	−0.00111810	+	0.999999i	$0.500356\pi$
$578$	0	0
$579$	4.08674e33	0.119645
$580$	0	0
$581$	−3.64018e34	−1.02075
$582$	0	0
$583$	8.33778e33	0.223972
$584$	0	0
$585$	−4.90096e34	−1.26134
$586$	0	0
$587$	−5.16226e34	−1.27310	−0.636551	−	0.771234i	$-0.719640\pi$
$587$	−5.16226e34	−1.27310	−0.636551	+	0.771234i	$0.719640\pi$
$588$	0	0
$589$	−2.61022e34	−0.616929
$590$	0	0
$591$	−1.17359e34	−0.265872
$592$	0	0
$593$	2.40705e34	0.522758	0.261379	−	0.965236i	$-0.415823\pi$
$593$	2.40705e34	0.522758	0.261379	+	0.965236i	$0.415823\pi$
$594$	0	0
$595$	−7.30706e34	−1.52153
$596$	0	0
$597$	−4.38684e32	−0.00875937
$598$	0	0
$599$	8.30672e33	0.159072	0.0795361	−	0.996832i	$-0.474656\pi$
$599$	8.30672e33	0.159072	0.0795361	+	0.996832i	$0.474656\pi$
$600$	0	0
$601$	−3.00405e34	−0.551792	−0.275896	−	0.961187i	$-0.588975\pi$
$601$	−3.00405e34	−0.551792	−0.275896	+	0.961187i	$0.588975\pi$
$602$	0	0
$603$	−2.15901e34	−0.380442
$604$	0	0
$605$	2.77941e34	0.469905
$606$	0	0
$607$	1.00963e35	1.63796	0.818978	−	0.573825i	$-0.194541\pi$
$607$	1.00963e35	1.63796	0.818978	+	0.573825i	$0.194541\pi$
$608$	0	0
$609$	2.07562e33	0.0323170
$610$	0	0
$611$	−7.54750e34	−1.12795
$612$	0	0
$613$	−1.02453e33	−0.0146983	−0.00734915	−	0.999973i	$-0.502339\pi$
$613$	−1.02453e33	−0.0146983	−0.00734915	+	0.999973i	$0.502339\pi$
$614$	0	0
$615$	2.66952e34	0.367701
$616$	0	0
$617$	4.53271e34	0.599505	0.299753	−	0.954017i	$-0.403096\pi$
$617$	4.53271e34	0.599505	0.299753	+	0.954017i	$0.403096\pi$
$618$	0	0
$619$	−1.24784e35	−1.58499	−0.792496	−	0.609878i	$-0.791219\pi$
$619$	−1.24784e35	−1.58499	−0.792496	+	0.609878i	$0.791219\pi$
$620$	0	0
$621$	−3.08068e34	−0.375839
$622$	0	0
$623$	6.89239e34	0.807736
$624$	0	0
$625$	−1.00307e35	−1.12936
$626$	0	0
$627$	−1.00267e34	−0.108471
$628$	0	0
$629$	−5.11577e34	−0.531836
$630$	0	0
$631$	−4.83338e34	−0.482930	−0.241465	−	0.970410i	$-0.577628\pi$
$631$	−4.83338e34	−0.482930	−0.241465	+	0.970410i	$0.577628\pi$
$632$	0	0
$633$	1.47338e34	0.141503
$634$	0	0
$635$	2.49238e35	2.30114
$636$	0	0
$637$	−1.52054e34	−0.134976
$638$	0	0
$639$	−1.55634e35	−1.32845
$640$	0	0
$641$	8.30494e34	0.681728	0.340864	−	0.940113i	$-0.389280\pi$
$641$	8.30494e34	0.681728	0.340864	+	0.940113i	$0.389280\pi$
$642$	0	0
$643$	−5.25724e34	−0.415069	−0.207535	−	0.978228i	$-0.566544\pi$
$643$	−5.25724e34	−0.415069	−0.207535	+	0.978228i	$0.566544\pi$
$644$	0	0
$645$	4.37164e34	0.332008
$646$	0	0
$647$	2.03021e35	1.48333	0.741665	−	0.670770i	$-0.234036\pi$
$647$	2.03021e35	1.48333	0.741665	+	0.670770i	$0.234036\pi$
$648$	0	0
$649$	1.09896e35	0.772546
$650$	0	0
$651$	3.28404e34	0.222150
$652$	0	0
$653$	1.67657e35	1.09146	0.545728	−	0.837962i	$-0.316253\pi$
$653$	1.67657e35	1.09146	0.545728	+	0.837962i	$0.316253\pi$
$654$	0	0
$655$	−1.29826e35	−0.813479
$656$	0	0
$657$	−3.43032e34	−0.206903
$658$	0	0
$659$	2.92521e35	1.69859	0.849296	−	0.527917i	$-0.177027\pi$
$659$	2.92521e35	1.69859	0.849296	+	0.527917i	$0.177027\pi$
$660$	0	0
$661$	8.30227e34	0.464172	0.232086	−	0.972695i	$-0.425445\pi$
$661$	8.30227e34	0.464172	0.232086	+	0.972695i	$0.425445\pi$
$662$	0	0
$663$	4.02872e34	0.216894
$664$	0	0
$665$	1.76364e35	0.914406
$666$	0	0
$667$	−2.57672e34	−0.128675
$668$	0	0
$669$	6.20103e34	0.298289
$670$	0	0
$671$	−7.59057e34	−0.351757
$672$	0	0
$673$	−3.23598e35	−1.44483	−0.722417	−	0.691458i	$-0.756969\pi$
$673$	−3.23598e35	−1.44483	−0.722417	+	0.691458i	$0.756969\pi$
$674$	0	0
$675$	−8.18936e34	−0.352333
$676$	0	0
$677$	7.76333e34	0.321877	0.160938	−	0.986964i	$-0.448548\pi$
$677$	7.76333e34	0.321877	0.160938	+	0.986964i	$0.448548\pi$
$678$	0	0
$679$	−1.10568e35	−0.441834
$680$	0	0
$681$	−7.54029e34	−0.290435
$682$	0	0
$683$	2.49909e35	0.927945	0.463973	−	0.885850i	$-0.346424\pi$
$683$	2.49909e35	0.927945	0.463973	+	0.885850i	$0.346424\pi$
$684$	0	0
$685$	−4.58782e35	−1.64238
$686$	0	0
$687$	−1.11268e35	−0.384070
$688$	0	0
$689$	8.08584e34	0.269144
$690$	0	0
$691$	8.56964e34	0.275098	0.137549	−	0.990495i	$-0.456078\pi$
$691$	8.56964e34	0.275098	0.137549	+	0.990495i	$0.456078\pi$
$692$	0	0
$693$	−2.66176e35	−0.824146
$694$	0	0
$695$	−3.59466e35	−1.07361
$696$	0	0
$697$	4.63017e35	1.33410
$698$	0	0
$699$	9.70378e34	0.269759
$700$	0	0
$701$	4.53464e35	1.21637	0.608187	−	0.793793i	$-0.291897\pi$
$701$	4.53464e35	1.21637	0.608187	+	0.793793i	$0.291897\pi$
$702$	0	0
$703$	1.23475e35	0.319622
$704$	0	0
$705$	−1.34295e35	−0.335504
$706$	0	0
$707$	−7.28238e34	−0.175602
$708$	0	0
$709$	−4.93254e35	−1.14813	−0.574067	−	0.818808i	$-0.694635\pi$
$709$	−4.93254e35	−1.14813	−0.574067	+	0.818808i	$0.694635\pi$
$710$	0	0
$711$	−2.19776e35	−0.493868
$712$	0	0
$713$	−4.07688e35	−0.884522
$714$	0	0
$715$	−5.10090e35	−1.06862
$716$	0	0
$717$	2.82004e34	0.0570513
$718$	0	0
$719$	−2.13499e35	−0.417142	−0.208571	−	0.978007i	$-0.566881\pi$
$719$	−2.13499e35	−0.417142	−0.208571	+	0.978007i	$0.566881\pi$
$720$	0	0
$721$	1.89858e35	0.358293
$722$	0	0
$723$	−6.25508e34	−0.114026
$724$	0	0
$725$	−6.84968e34	−0.120627
$726$	0	0
$727$	−5.12190e35	−0.871467	−0.435734	−	0.900076i	$-0.643511\pi$
$727$	−5.12190e35	−0.871467	−0.435734	+	0.900076i	$0.643511\pi$
$728$	0	0
$729$	−4.49296e35	−0.738649
$730$	0	0
$731$	7.58243e35	1.20459
$732$	0	0
$733$	1.77366e35	0.272315	0.136157	−	0.990687i	$-0.456525\pi$
$733$	1.77366e35	0.272315	0.136157	+	0.990687i	$0.456525\pi$
$734$	0	0
$735$	−2.70555e34	−0.0401481
$736$	0	0
$737$	−2.24709e35	−0.322312
$738$	0	0
$739$	1.13535e36	1.57425	0.787124	−	0.616794i	$-0.211569\pi$
$739$	1.13535e36	1.57425	0.787124	+	0.616794i	$0.211569\pi$
$740$	0	0
$741$	−9.72375e34	−0.130349
$742$	0	0
$743$	−4.03749e34	−0.0523301	−0.0261651	−	0.999658i	$-0.508330\pi$
$743$	−4.03749e34	−0.0523301	−0.0261651	+	0.999658i	$0.508330\pi$
$744$	0	0
$745$	−6.71923e35	−0.842104
$746$	0	0
$747$	−7.53500e35	−0.913220
$748$	0	0
$749$	1.40027e36	1.64131
$750$	0	0
$751$	−7.72405e35	−0.875681	−0.437840	−	0.899053i	$-0.644256\pi$
$751$	−7.72405e35	−0.875681	−0.437840	+	0.899053i	$0.644256\pi$
$752$	0	0
$753$	−1.21727e35	−0.133490
$754$	0	0
$755$	8.62115e35	0.914594
$756$	0	0
$757$	3.31585e35	0.340327	0.170163	−	0.985416i	$-0.445570\pi$
$757$	3.31585e35	0.340327	0.170163	+	0.985416i	$0.445570\pi$
$758$	0	0
$759$	−1.56607e35	−0.155521
$760$	0	0
$761$	2.02230e36	1.94329	0.971646	−	0.236440i	$-0.0759807\pi$
$761$	2.02230e36	1.94329	0.971646	+	0.236440i	$0.0759807\pi$
$762$	0	0
$763$	1.86725e36	1.73639
$764$	0	0
$765$	−1.51253e36	−1.36124
$766$	0	0
$767$	1.06576e36	0.928358
$768$	0	0
$769$	7.71193e35	0.650255	0.325128	−	0.945670i	$-0.394593\pi$
$769$	7.71193e35	0.650255	0.325128	+	0.945670i	$0.394593\pi$
$770$	0	0
$771$	−4.49265e35	−0.366710
$772$	0	0
$773$	1.96060e36	1.54934	0.774668	−	0.632368i	$-0.217917\pi$
$773$	1.96060e36	1.54934	0.774668	+	0.632368i	$0.217917\pi$
$774$	0	0
$775$	−1.08376e36	−0.829202
$776$	0	0
$777$	−1.55350e35	−0.115093
$778$	0	0
$779$	−1.11754e36	−0.801763
$780$	0	0
$781$	−1.61983e36	−1.12547
$782$	0	0
$783$	8.79649e34	0.0591953
$784$	0	0
$785$	2.53393e35	0.165167
$786$	0	0
$787$	8.92654e35	0.563637	0.281818	−	0.959468i	$-0.409062\pi$
$787$	8.92654e35	0.563637	0.281818	+	0.959468i	$0.409062\pi$
$788$	0	0
$789$	−1.51418e35	−0.0926224
$790$	0	0
$791$	2.91727e36	1.72890
$792$	0	0
$793$	−7.36121e35	−0.422702
$794$	0	0
$795$	1.43874e35	0.0800560
$796$	0	0
$797$	−2.35494e36	−1.26984	−0.634921	−	0.772577i	$-0.718968\pi$
$797$	−2.35494e36	−1.26984	−0.634921	+	0.772577i	$0.718968\pi$
$798$	0	0
$799$	−2.32930e36	−1.21728
$800$	0	0
$801$	1.42669e36	0.722643
$802$	0	0
$803$	−3.57026e35	−0.175289
$804$	0	0
$805$	2.75462e36	1.31103
$806$	0	0
$807$	7.09317e35	0.327281
$808$	0	0
$809$	−1.29617e36	−0.579834	−0.289917	−	0.957052i	$-0.593628\pi$
$809$	−1.29617e36	−0.579834	−0.289917	+	0.957052i	$0.593628\pi$
$810$	0	0
$811$	−2.63606e36	−1.14339	−0.571695	−	0.820467i	$-0.693714\pi$
$811$	−2.63606e36	−1.14339	−0.571695	+	0.820467i	$0.693714\pi$
$812$	0	0
$813$	7.10313e35	0.298757
$814$	0	0
$815$	3.43691e36	1.40184
$816$	0	0
$817$	−1.83010e36	−0.723935
$818$	0	0
$819$	−2.58133e36	−0.990366
$820$	0	0
$821$	−5.92271e35	−0.220410	−0.110205	−	0.993909i	$-0.535151\pi$
$821$	−5.92271e35	−0.220410	−0.110205	+	0.993909i	$0.535151\pi$
$822$	0	0
$823$	−4.76928e35	−0.172169	−0.0860845	−	0.996288i	$-0.527436\pi$
$823$	−4.76928e35	−0.172169	−0.0860845	+	0.996288i	$0.527436\pi$
$824$	0	0
$825$	−4.16308e35	−0.145794
$826$	0	0
$827$	−4.17794e36	−1.41953	−0.709763	−	0.704440i	$-0.751198\pi$
$827$	−4.17794e36	−1.41953	−0.709763	+	0.704440i	$0.751198\pi$
$828$	0	0
$829$	−3.18023e36	−1.04840	−0.524199	−	0.851596i	$-0.675635\pi$
$829$	−3.18023e36	−1.04840	−0.524199	+	0.851596i	$0.675635\pi$
$830$	0	0
$831$	−4.98924e35	−0.159596
$832$	0	0
$833$	−4.69267e35	−0.145666
$834$	0	0
$835$	−6.13232e36	−1.84733
$836$	0	0
$837$	1.39178e36	0.406913
$838$	0	0
$839$	3.57270e36	1.01384	0.506922	−	0.861992i	$-0.330783\pi$
$839$	3.57270e36	1.01384	0.506922	+	0.861992i	$0.330783\pi$
$840$	0	0
$841$	−3.55679e36	−0.979733
$842$	0	0
$843$	7.04537e35	0.188390
$844$	0	0
$845$	2.89018e35	0.0750266
$846$	0	0
$847$	1.46391e36	0.368954
$848$	0	0
$849$	−7.48489e35	−0.183164
$850$	0	0
$851$	1.92855e36	0.458258
$852$	0	0
$853$	−1.75466e36	−0.404884	−0.202442	−	0.979294i	$-0.564888\pi$
$853$	−1.75466e36	−0.404884	−0.202442	+	0.979294i	$0.564888\pi$
$854$	0	0
$855$	3.65065e36	0.818075
$856$	0	0
$857$	7.10324e36	1.54595	0.772976	−	0.634435i	$-0.218767\pi$
$857$	7.10324e36	1.54595	0.772976	+	0.634435i	$0.218767\pi$
$858$	0	0
$859$	7.56695e36	1.59958	0.799791	−	0.600279i	$-0.204944\pi$
$859$	7.56695e36	1.59958	0.799791	+	0.600279i	$0.204944\pi$
$860$	0	0
$861$	1.40604e36	0.288707
$862$	0	0
$863$	−5.72195e36	−1.14132	−0.570662	−	0.821185i	$-0.693313\pi$
$863$	−5.72195e36	−1.14132	−0.570662	+	0.821185i	$0.693313\pi$
$864$	0	0
$865$	4.47125e36	0.866418
$866$	0	0
$867$	1.13423e35	0.0213532
$868$	0	0
$869$	−2.28742e36	−0.418407
$870$	0	0
$871$	−2.17919e36	−0.387318
$872$	0	0
$873$	−2.28871e36	−0.395288
$874$	0	0
$875$	−1.31931e36	−0.221435
$876$	0	0
$877$	3.21926e36	0.525123	0.262561	−	0.964915i	$-0.415433\pi$
$877$	3.21926e36	0.525123	0.262561	+	0.964915i	$0.415433\pi$
$878$	0	0
$879$	2.54558e34	0.00403576
$880$	0	0
$881$	−1.04633e37	−1.61238	−0.806191	−	0.591655i	$-0.798475\pi$
$881$	−1.04633e37	−1.61238	−0.806191	+	0.591655i	$0.798475\pi$
$882$	0	0
$883$	−4.11745e36	−0.616765	−0.308382	−	0.951263i	$-0.599788\pi$
$883$	−4.11745e36	−0.616765	−0.308382	+	0.951263i	$0.599788\pi$
$884$	0	0
$885$	1.89634e36	0.276137
$886$	0	0
$887$	2.52904e36	0.358022	0.179011	−	0.983847i	$-0.442710\pi$
$887$	2.52904e36	0.358022	0.179011	+	0.983847i	$0.442710\pi$
$888$	0	0
$889$	1.31273e37	1.80678
$890$	0	0
$891$	−5.23622e36	−0.700723
$892$	0	0
$893$	5.62202e36	0.731558
$894$	0	0
$895$	1.78836e37	2.26291
$896$	0	0
$897$	−1.51875e36	−0.186887
$898$	0	0
$899$	1.16410e36	0.139314
$900$	0	0
$901$	2.49544e36	0.290460
$902$	0	0
$903$	2.30254e36	0.260682
$904$	0	0
$905$	6.07833e36	0.669387
$906$	0	0
$907$	4.93129e36	0.528286	0.264143	−	0.964484i	$-0.414911\pi$
$907$	4.93129e36	0.528286	0.264143	+	0.964484i	$0.414911\pi$
$908$	0	0
$909$	−1.50742e36	−0.157103
$910$	0	0
$911$	7.10548e36	0.720466	0.360233	−	0.932862i	$-0.382697\pi$
$911$	7.10548e36	0.720466	0.360233	+	0.932862i	$0.382697\pi$
$912$	0	0
$913$	−7.84240e36	−0.773685
$914$	0	0
$915$	−1.30981e36	−0.125731
$916$	0	0
$917$	−6.83795e36	−0.638718
$918$	0	0
$919$	−2.64155e36	−0.240112	−0.120056	−	0.992767i	$-0.538307\pi$
$919$	−2.64155e36	−0.240112	−0.120056	+	0.992767i	$0.538307\pi$
$920$	0	0
$921$	−2.81179e36	−0.248735
$922$	0	0
$923$	−1.57089e37	−1.35246
$924$	0	0
$925$	5.12665e36	0.429597
$926$	0	0
$927$	3.92997e36	0.320548
$928$	0	0
$929$	5.01934e36	0.398520	0.199260	−	0.979947i	$-0.436146\pi$
$929$	5.01934e36	0.398520	0.199260	+	0.979947i	$0.436146\pi$
$930$	0	0
$931$	1.13263e36	0.0875419
$932$	0	0
$933$	4.39835e36	0.330955
$934$	0	0
$935$	−1.57423e37	−1.15325
$936$	0	0
$937$	−1.70189e37	−1.21391	−0.606956	−	0.794735i	$-0.707610\pi$
$937$	−1.70189e37	−1.21391	−0.606956	+	0.794735i	$0.707610\pi$
$938$	0	0
$939$	−2.70123e35	−0.0187604
$940$	0	0
$941$	−1.51254e37	−1.02291	−0.511455	−	0.859310i	$-0.670893\pi$
$941$	−1.51254e37	−1.02291	−0.511455	+	0.859310i	$0.670893\pi$
$942$	0	0
$943$	−1.74548e37	−1.14953
$944$	0	0
$945$	−9.40380e36	−0.603123
$946$	0	0
$947$	−1.65329e36	−0.103270	−0.0516351	−	0.998666i	$-0.516443\pi$
$947$	−1.65329e36	−0.103270	−0.0516351	+	0.998666i	$0.516443\pi$
$948$	0	0
$949$	−3.46238e36	−0.210643
$950$	0	0
$951$	−2.01260e36	−0.119262
$952$	0	0
$953$	2.77784e37	1.60341	0.801706	−	0.597718i	$-0.203926\pi$
$953$	2.77784e37	1.60341	0.801706	+	0.597718i	$0.203926\pi$
$954$	0	0
$955$	4.08541e36	0.229717
$956$	0	0
$957$	4.47171e35	0.0244948
$958$	0	0
$959$	−2.41640e37	−1.28955
$960$	0	0
$961$	−8.14395e35	−0.0423441
$962$	0	0
$963$	2.89850e37	1.46840
$964$	0	0
$965$	−1.54865e37	−0.764473
$966$	0	0
$967$	−3.82441e36	−0.183965	−0.0919823	−	0.995761i	$-0.529320\pi$
$967$	−3.82441e36	−0.183965	−0.0919823	+	0.995761i	$0.529320\pi$
$968$	0	0
$969$	−3.00093e36	−0.140672
$970$	0	0
$971$	1.67087e37	0.763311	0.381655	−	0.924305i	$-0.375354\pi$
$971$	1.67087e37	0.763311	0.381655	+	0.924305i	$0.375354\pi$
$972$	0	0
$973$	−1.89331e37	−0.842967
$974$	0	0
$975$	−4.03728e36	−0.175199
$976$	0	0
$977$	−3.54376e37	−1.49893	−0.749466	−	0.662043i	$-0.769690\pi$
$977$	−3.54376e37	−1.49893	−0.749466	+	0.662043i	$0.769690\pi$
$978$	0	0
$979$	1.48490e37	0.612227
$980$	0	0
$981$	3.86512e37	1.55346
$982$	0	0
$983$	−2.26759e37	−0.888476	−0.444238	−	0.895909i	$-0.646525\pi$
$983$	−2.26759e37	−0.888476	−0.444238	+	0.895909i	$0.646525\pi$
$984$	0	0
$985$	4.44726e37	1.69879
$986$	0	0
$987$	−7.07334e36	−0.263427
$988$	0	0
$989$	−2.85843e37	−1.03794
$990$	0	0
$991$	1.82706e36	0.0646891	0.0323445	−	0.999477i	$-0.489703\pi$
$991$	1.82706e36	0.0646891	0.0323445	+	0.999477i	$0.489703\pi$
$992$	0	0
$993$	1.12657e36	0.0388949
$994$	0	0
$995$	1.66237e36	0.0559680
$996$	0	0
$997$	2.34599e37	0.770260	0.385130	−	0.922862i	$-0.374157\pi$
$997$	2.34599e37	0.770260	0.385130	+	0.922862i	$0.374157\pi$
$998$	0	0
$999$	−6.58373e36	−0.210816

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.26.a.b.1.1		1
4.3	odd	2		1.26.a.a.1.1	✓	1
12.11	even	2		9.26.a.a.1.1		1
20.3	even	4		25.26.b.a.24.2		2
20.7	even	4		25.26.b.a.24.1		2
20.19	odd	2		25.26.a.a.1.1		1
28.27	even	2		49.26.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.26.a.a.1.1	✓	1	4.3	odd	2
9.26.a.a.1.1		1	12.11	even	2
16.26.a.b.1.1		1	1.1	even	1	trivial
25.26.a.a.1.1		1	20.19	odd	2
25.26.b.a.24.1		2	20.7	even	4
25.26.b.a.24.2		2	20.3	even	4
49.26.a.a.1.1		1	28.27	even	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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	16.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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