LMFDB - Embedded newform 98.14.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,14,Mod(1,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 14, names="a")

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

chi := DirichletCharacter("98.1");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	98.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:	$105.086310373$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	98.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+64.0000 q^{2} +1026.00 q^{3} +4096.00 q^{4} -4320.00 q^{5} +65664.0 q^{6} +262144. q^{8} -541647. q^{9} +O(q^{10})$

\(q+64.0000 q^{2} +1026.00 q^{3} +4096.00 q^{4} -4320.00 q^{5} +65664.0 q^{6} +262144. q^{8} -541647. q^{9} -276480. q^{10} -8.78731e6 q^{11} +4.20250e6 q^{12} +2.04209e7 q^{13} -4.43232e6 q^{15} +1.67772e7 q^{16} -1.71946e6 q^{17} -3.46654e7 q^{18} +1.09703e8 q^{19} -1.76947e7 q^{20} -5.62388e8 q^{22} -6.46760e8 q^{23} +2.68960e8 q^{24} -1.20204e9 q^{25} +1.30694e9 q^{26} -2.19151e9 q^{27} +7.28867e8 q^{29} -2.83668e8 q^{30} -1.02805e9 q^{31} +1.07374e9 q^{32} -9.01578e9 q^{33} -1.10046e8 q^{34} -2.21859e9 q^{36} +1.42294e10 q^{37} +7.02099e9 q^{38} +2.09519e10 q^{39} -1.13246e9 q^{40} -4.45445e10 q^{41} -5.46898e10 q^{43} -3.59928e10 q^{44} +2.33992e9 q^{45} -4.13927e10 q^{46} -4.78683e10 q^{47} +1.72134e10 q^{48} -7.69306e10 q^{50} -1.76417e9 q^{51} +8.36441e10 q^{52} -1.69987e11 q^{53} -1.40256e11 q^{54} +3.79612e10 q^{55} +1.12555e11 q^{57} +4.66475e10 q^{58} +3.00766e11 q^{59} -1.81548e10 q^{60} -3.69996e11 q^{61} -6.57951e10 q^{62} +6.87195e10 q^{64} -8.82184e10 q^{65} -5.77010e11 q^{66} -7.87011e11 q^{67} -7.04292e9 q^{68} -6.63576e11 q^{69} +5.59441e11 q^{71} -1.41990e11 q^{72} -1.21138e11 q^{73} +9.10681e11 q^{74} -1.23329e12 q^{75} +4.49343e11 q^{76} +1.34092e12 q^{78} +2.90427e11 q^{79} -7.24776e10 q^{80} -1.38492e12 q^{81} -2.85085e12 q^{82} +3.96511e12 q^{83} +7.42808e9 q^{85} -3.50015e12 q^{86} +7.47818e11 q^{87} -2.30354e12 q^{88} +6.02592e12 q^{89} +1.49755e11 q^{90} -2.64913e12 q^{92} -1.05478e12 q^{93} -3.06357e12 q^{94} -4.73917e11 q^{95} +1.10166e12 q^{96} -1.13028e13 q^{97} +4.75962e12 q^{99} +O(q^{100})\)

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 $

$2$	64.0000	0.707107
$2$	64.0000	0.707107
$3$	1026.00	0.812567	0.406284	−	0.913747i	$-0.366825\pi$
$3$	1026.00	0.812567	0.406284	+	0.913747i	$0.366825\pi$
$4$	4096.00	0.500000
$5$	−4320.00	−0.123646	−0.0618228	−	0.998087i	$-0.519691\pi$
$5$	−4320.00	−0.123646	−0.0618228	+	0.998087i	$0.519691\pi$
$6$	65664.0	0.574572
$7$	0	0
$7$	0	0
$8$	262144.	0.353553
$9$	−541647.	−0.339735
$10$	−276480.	−0.0874307
$11$	−8.78731e6	−1.49556	−0.747780	−	0.663947i	$-0.768880\pi$
$11$	−8.78731e6	−1.49556	−0.747780	+	0.663947i	$0.768880\pi$
$12$	4.20250e6	0.406284
$13$	2.04209e7	1.17339	0.586697	−	0.809807i	$-0.300428\pi$
$13$	2.04209e7	1.17339	0.586697	+	0.809807i	$0.300428\pi$
$14$	0	0
$15$	−4.43232e6	−0.100470
$16$	1.67772e7	0.250000
$17$	−1.71946e6	−0.0172772	−0.00863862	−	0.999963i	$-0.502750\pi$
$17$	−1.71946e6	−0.0172772	−0.00863862	+	0.999963i	$0.502750\pi$
$18$	−3.46654e7	−0.240229
$19$	1.09703e8	0.534958	0.267479	−	0.963564i	$-0.413809\pi$
$19$	1.09703e8	0.534958	0.267479	+	0.963564i	$0.413809\pi$
$20$	−1.76947e7	−0.0618228
$21$	0	0
$22$	−5.62388e8	−1.05752
$23$	−6.46760e8	−0.910987	−0.455494	−	0.890239i	$-0.650537\pi$
$23$	−6.46760e8	−0.910987	−0.455494	+	0.890239i	$0.650537\pi$
$24$	2.68960e8	0.287286
$25$	−1.20204e9	−0.984712
$26$	1.30694e9	0.829715
$27$	−2.19151e9	−1.08862
$28$	0	0
$29$	7.28867e8	0.227542	0.113771	−	0.993507i	$-0.463707\pi$
$29$	7.28867e8	0.227542	0.113771	+	0.993507i	$0.463707\pi$
$30$	−2.83668e8	−0.0710433
$31$	−1.02805e9	−0.208048	−0.104024	−	0.994575i	$-0.533172\pi$
$31$	−1.02805e9	−0.208048	−0.104024	+	0.994575i	$0.533172\pi$
$32$	1.07374e9	0.176777
$33$	−9.01578e9	−1.21524
$34$	−1.10046e8	−0.0122169
$35$	0	0
$36$	−2.21859e9	−0.169867
$37$	1.42294e10	0.911749	0.455874	−	0.890044i	$-0.349327\pi$
$37$	1.42294e10	0.911749	0.455874	+	0.890044i	$0.349327\pi$
$38$	7.02099e9	0.378273
$39$	2.09519e10	0.953461
$40$	−1.13246e9	−0.0437153
$41$	−4.45445e10	−1.46453	−0.732266	−	0.681019i	$-0.761537\pi$
$41$	−4.45445e10	−1.46453	−0.732266	+	0.681019i	$0.761537\pi$
$42$	0	0
$43$	−5.46898e10	−1.31935	−0.659677	−	0.751549i	$-0.729307\pi$
$43$	−5.46898e10	−1.31935	−0.659677	+	0.751549i	$0.729307\pi$
$44$	−3.59928e10	−0.747780
$45$	2.33992e9	0.0420067
$46$	−4.13927e10	−0.644165
$47$	−4.78683e10	−0.647757	−0.323879	−	0.946099i	$-0.604987\pi$
$47$	−4.78683e10	−0.647757	−0.323879	+	0.946099i	$0.604987\pi$
$48$	1.72134e10	0.203142
$49$	0	0
$50$	−7.69306e10	−0.696296
$51$	−1.76417e9	−0.0140389
$52$	8.36441e10	0.586697
$53$	−1.69987e11	−1.05347	−0.526735	−	0.850029i	$-0.676584\pi$
$53$	−1.69987e11	−1.05347	−0.526735	+	0.850029i	$0.676584\pi$
$54$	−1.40256e11	−0.769774
$55$	3.79612e10	0.184919
$56$	0	0
$57$	1.12555e11	0.434689
$58$	4.66475e10	0.160896
$59$	3.00766e11	0.928304	0.464152	−	0.885756i	$-0.346359\pi$
$59$	3.00766e11	0.928304	0.464152	+	0.885756i	$0.346359\pi$
$60$	−1.81548e10	−0.0502352
$61$	−3.69996e11	−0.919504	−0.459752	−	0.888047i	$-0.652062\pi$
$61$	−3.69996e11	−0.919504	−0.459752	+	0.888047i	$0.652062\pi$
$62$	−6.57951e10	−0.147112
$63$	0	0
$64$	6.87195e10	0.125000
$65$	−8.82184e10	−0.145085
$66$	−5.77010e11	−0.859306
$67$	−7.87011e11	−1.06291	−0.531453	−	0.847088i	$-0.678354\pi$
$67$	−7.87011e11	−1.06291	−0.531453	+	0.847088i	$0.678354\pi$
$68$	−7.04292e9	−0.00863862
$69$	−6.63576e11	−0.740238
$70$	0	0
$71$	5.59441e11	0.518293	0.259147	−	0.965838i	$-0.416559\pi$
$71$	5.59441e11	0.518293	0.259147	+	0.965838i	$0.416559\pi$
$72$	−1.41990e11	−0.120114
$73$	−1.21138e11	−0.0936872	−0.0468436	−	0.998902i	$-0.514916\pi$
$73$	−1.21138e11	−0.0936872	−0.0468436	+	0.998902i	$0.514916\pi$
$74$	9.10681e11	0.644704
$75$	−1.23329e12	−0.800144
$76$	4.49343e11	0.267479
$77$	0	0
$78$	1.34092e12	0.674199
$79$	2.90427e11	0.134419	0.0672095	−	0.997739i	$-0.478590\pi$
$79$	2.90427e11	0.134419	0.0672095	+	0.997739i	$0.478590\pi$
$80$	−7.24776e10	−0.0309114
$81$	−1.38492e12	−0.544845
$82$	−2.85085e12	−1.03558
$83$	3.96511e12	1.33121	0.665606	−	0.746303i	$-0.268173\pi$
$83$	3.96511e12	1.33121	0.665606	+	0.746303i	$0.268173\pi$
$84$	0	0
$85$	7.42808e9	0.00213626
$86$	−3.50015e12	−0.932925
$87$	7.47818e11	0.184893
$88$	−2.30354e12	−0.528760
$89$	6.02592e12	1.28525	0.642626	−	0.766180i	$-0.277845\pi$
$89$	6.02592e12	1.28525	0.642626	+	0.766180i	$0.277845\pi$
$90$	1.49755e11	0.0297032
$91$	0	0
$92$	−2.64913e12	−0.455494
$93$	−1.05478e12	−0.169053
$94$	−3.06357e12	−0.458033
$95$	−4.73917e11	−0.0661452
$96$	1.10166e12	0.143643
$97$	−1.13028e13	−1.37775	−0.688875	−	0.724880i	$-0.741895\pi$
$97$	−1.13028e13	−1.37775	−0.688875	+	0.724880i	$0.741895\pi$
$98$	0	0
$99$	4.75962e12	0.508093
$100$	−4.92356e12	−0.492356
$101$	−1.71411e13	−1.60675	−0.803377	−	0.595471i	$-0.796966\pi$
$101$	−1.71411e13	−1.60675	−0.803377	+	0.595471i	$0.796966\pi$
$102$	−1.12907e11	−0.00992702
$103$	−1.14509e13	−0.944926	−0.472463	−	0.881351i	$-0.656635\pi$
$103$	−1.14509e13	−0.944926	−0.472463	+	0.881351i	$0.656635\pi$
$104$	5.35322e12	0.414857
$105$	0	0
$106$	−1.08792e13	−0.744916
$107$	2.87875e13	1.85443	0.927213	−	0.374533i	$-0.122197\pi$
$107$	2.87875e13	1.85443	0.927213	+	0.374533i	$0.122197\pi$
$108$	−8.97641e12	−0.544312
$109$	−6.83588e12	−0.390411	−0.195205	−	0.980762i	$-0.562537\pi$
$109$	−6.83588e12	−0.390411	−0.195205	+	0.980762i	$0.562537\pi$
$110$	2.42952e12	0.130758
$111$	1.45994e13	0.740857
$112$	0	0
$113$	−2.32309e13	−1.04968	−0.524840	−	0.851201i	$-0.675875\pi$
$113$	−2.32309e13	−1.04968	−0.524840	+	0.851201i	$0.675875\pi$
$114$	7.20353e12	0.307372
$115$	2.79400e12	0.112640
$116$	2.98544e12	0.113771
$117$	−1.10609e13	−0.398643
$118$	1.92490e13	0.656410
$119$	0	0
$120$	−1.16191e12	−0.0355216
$121$	4.26941e13	1.23670
$122$	−2.36798e13	−0.650187
$123$	−4.57026e13	−1.19003
$124$	−4.21089e12	−0.104024
$125$	1.04663e13	0.245401
$126$	0	0
$127$	−9.33280e13	−1.97373	−0.986865	−	0.161546i	$-0.948352\pi$
$127$	−9.33280e13	−1.97373	−0.986865	+	0.161546i	$0.948352\pi$
$128$	4.39805e12	0.0883883
$129$	−5.61118e13	−1.07206
$130$	−5.64598e12	−0.102591
$131$	6.61126e13	1.14293	0.571467	−	0.820625i	$-0.306375\pi$
$131$	6.61126e13	1.14293	0.571467	+	0.820625i	$0.306375\pi$
$132$	−3.69286e13	−0.607621
$133$	0	0
$134$	−5.03687e13	−0.751587
$135$	9.46730e12	0.134604
$136$	−4.50747e11	−0.00610843
$137$	4.80824e13	0.621301	0.310651	−	0.950524i	$-0.399453\pi$
$137$	4.80824e13	0.621301	0.310651	+	0.950524i	$0.399453\pi$
$138$	−4.24689e13	−0.523427
$139$	1.29911e14	1.52774	0.763871	−	0.645369i	$-0.223296\pi$
$139$	1.29911e14	1.52774	0.763871	+	0.645369i	$0.223296\pi$
$140$	0	0
$141$	−4.91129e13	−0.526346
$142$	3.58043e13	0.366489
$143$	−1.79445e14	−1.75488
$144$	−9.08733e12	−0.0849337
$145$	−3.14871e12	−0.0281346
$146$	−7.75281e12	−0.0662469
$147$	0	0
$148$	5.82836e13	0.455874
$149$	1.26590e14	0.947740	0.473870	−	0.880595i	$-0.342857\pi$
$149$	1.26590e14	0.947740	0.473870	+	0.880595i	$0.342857\pi$
$150$	−7.89308e13	−0.565787
$151$	−2.38306e14	−1.63601	−0.818003	−	0.575214i	$-0.804919\pi$
$151$	−2.38306e14	−1.63601	−0.818003	+	0.575214i	$0.804919\pi$
$152$	2.87580e13	0.189136
$153$	9.31341e11	0.00586968
$154$	0	0
$155$	4.44117e12	0.0257242
$156$	8.58189e13	0.476731
$157$	−3.31263e14	−1.76533	−0.882665	−	0.470003i	$-0.844253\pi$
$157$	−3.31263e14	−1.76533	−0.882665	+	0.470003i	$0.844253\pi$
$158$	1.85873e13	0.0950486
$159$	−1.74407e14	−0.856015
$160$	−4.63856e12	−0.0218577
$161$	0	0
$162$	−8.86351e13	−0.385264
$163$	−3.09482e14	−1.29246	−0.646228	−	0.763144i	$-0.723655\pi$
$163$	−3.09482e14	−1.29246	−0.646228	+	0.763144i	$0.723655\pi$
$164$	−1.82454e14	−0.732266
$165$	3.89482e13	0.150259
$166$	2.53767e14	0.941309
$167$	−1.89624e13	−0.0676452	−0.0338226	−	0.999428i	$-0.510768\pi$
$167$	−1.89624e13	−0.0676452	−0.0338226	+	0.999428i	$0.510768\pi$
$168$	0	0
$169$	1.14139e14	0.376853
$170$	4.75397e11	0.00151056
$171$	−5.94203e13	−0.181744
$172$	−2.24010e14	−0.659677
$173$	−5.14033e14	−1.45778	−0.728889	−	0.684632i	$-0.759963\pi$
$173$	−5.14033e14	−1.45778	−0.728889	+	0.684632i	$0.759963\pi$
$174$	4.78603e13	0.130739
$175$	0	0
$176$	−1.47427e14	−0.373890
$177$	3.08585e14	0.754309
$178$	3.85659e14	0.908810
$179$	−1.38537e14	−0.314791	−0.157395	−	0.987536i	$-0.550310\pi$
$179$	−1.38537e14	−0.314791	−0.157395	+	0.987536i	$0.550310\pi$
$180$	9.58429e12	0.0210034
$181$	8.79858e14	1.85995	0.929976	−	0.367619i	$-0.119827\pi$
$181$	8.79858e14	1.85995	0.929976	+	0.367619i	$0.119827\pi$
$182$	0	0
$183$	−3.79616e14	−0.747158
$184$	−1.69544e14	−0.322083
$185$	−6.14710e13	−0.112734
$186$	−6.75058e13	−0.119538
$187$	1.51094e13	0.0258391
$188$	−1.96069e14	−0.323879
$189$	0	0
$190$	−3.03307e13	−0.0467717
$191$	2.19513e14	0.327147	0.163574	−	0.986531i	$-0.447698\pi$
$191$	2.19513e14	0.327147	0.163574	+	0.986531i	$0.447698\pi$
$192$	7.05062e13	0.101571
$193$	−7.98168e14	−1.11166	−0.555830	−	0.831296i	$-0.687599\pi$
$193$	−7.98168e14	−1.11166	−0.555830	+	0.831296i	$0.687599\pi$
$194$	−7.23380e14	−0.974216
$195$	−9.05121e13	−0.117891
$196$	0	0
$197$	7.97364e14	0.971911	0.485955	−	0.873984i	$-0.338472\pi$
$197$	7.97364e14	0.971911	0.485955	+	0.873984i	$0.338472\pi$
$198$	3.04616e14	0.359276
$199$	−1.73404e13	−0.0197932	−0.00989658	−	0.999951i	$-0.503150\pi$
$199$	−1.73404e13	−0.0197932	−0.00989658	+	0.999951i	$0.503150\pi$
$200$	−3.15108e14	−0.348148
$201$	−8.07473e14	−0.863682
$202$	−1.09703e15	−1.13615
$203$	0	0
$204$	−7.22603e12	−0.00701946
$205$	1.92432e14	0.181083
$206$	−7.32858e14	−0.668163
$207$	3.50316e14	0.309494
$208$	3.42606e14	0.293348
$209$	−9.63994e14	−0.800062
$210$	0	0
$211$	−1.27735e15	−0.996490	−0.498245	−	0.867036i	$-0.666022\pi$
$211$	−1.27735e15	−0.996490	−0.498245	+	0.867036i	$0.666022\pi$
$212$	−6.96266e14	−0.526735
$213$	5.73987e14	0.421148
$214$	1.84240e15	1.31128
$215$	2.36260e14	0.163132
$216$	−5.74490e14	−0.384887
$217$	0	0
$218$	−4.37496e14	−0.276062
$219$	−1.24287e14	−0.0761271
$220$	1.55489e14	0.0924597
$221$	−3.51130e13	−0.0202730
$222$	9.34359e14	0.523865
$223$	1.51063e15	0.822578	0.411289	−	0.911505i	$-0.365079\pi$
$223$	1.51063e15	0.822578	0.411289	+	0.911505i	$0.365079\pi$
$224$	0	0
$225$	6.51082e14	0.334541
$226$	−1.48678e15	−0.742235
$227$	3.78583e15	1.83651	0.918254	−	0.395992i	$-0.129599\pi$
$227$	3.78583e15	1.83651	0.918254	+	0.395992i	$0.129599\pi$
$228$	4.61026e14	0.217345
$229$	2.20481e15	1.01028	0.505139	−	0.863038i	$-0.331441\pi$
$229$	2.20481e15	1.01028	0.505139	+	0.863038i	$0.331441\pi$
$230$	1.78816e14	0.0796482
$231$	0	0
$232$	1.91068e14	0.0804482
$233$	2.58262e14	0.105742	0.0528709	−	0.998601i	$-0.483163\pi$
$233$	2.58262e14	0.105742	0.0528709	+	0.998601i	$0.483163\pi$
$234$	−7.07900e14	−0.281883
$235$	2.06791e14	0.0800923
$236$	1.23194e15	0.464152
$237$	2.97978e14	0.109224
$238$	0	0
$239$	4.42554e15	1.53596	0.767980	−	0.640474i	$-0.221262\pi$
$239$	4.42554e15	1.53596	0.767980	+	0.640474i	$0.221262\pi$
$240$	−7.43620e13	−0.0251176
$241$	2.49149e15	0.819121	0.409561	−	0.912283i	$-0.365682\pi$
$241$	2.49149e15	0.819121	0.409561	+	0.912283i	$0.365682\pi$
$242$	2.73242e15	0.874477
$243$	2.07304e15	0.645901
$244$	−1.51550e15	−0.459752
$245$	0	0
$246$	−2.92497e15	−0.841478
$247$	2.24024e15	0.627717
$248$	−2.69497e14	−0.0735560
$249$	4.06820e15	1.08170
$250$	6.69840e14	0.173525
$251$	2.25448e15	0.569071	0.284535	−	0.958666i	$-0.408161\pi$
$251$	2.25448e15	0.569071	0.284535	+	0.958666i	$0.408161\pi$
$252$	0	0
$253$	5.68328e15	1.36244
$254$	−5.97299e15	−1.39564
$255$	7.62121e12	0.00173585
$256$	2.81475e14	0.0625000
$257$	5.44108e15	1.17793	0.588965	−	0.808159i	$-0.299536\pi$
$257$	5.44108e15	1.17793	0.588965	+	0.808159i	$0.299536\pi$
$258$	−3.59115e15	−0.758064
$259$	0	0
$260$	−3.61343e14	−0.0725425
$261$	−3.94789e14	−0.0773039
$262$	4.23121e15	0.808176
$263$	4.12754e15	0.769093	0.384546	−	0.923106i	$-0.374358\pi$
$263$	4.12754e15	0.769093	0.384546	+	0.923106i	$0.374358\pi$
$264$	−2.36343e15	−0.429653
$265$	7.34343e14	0.130257
$266$	0	0
$267$	6.18259e15	1.04435
$268$	−3.22360e15	−0.531453
$269$	2.72580e15	0.438636	0.219318	−	0.975653i	$-0.429617\pi$
$269$	2.72580e15	0.438636	0.219318	+	0.975653i	$0.429617\pi$
$270$	6.05907e14	0.0951791
$271$	−8.99073e15	−1.37878	−0.689389	−	0.724391i	$-0.742121\pi$
$271$	−8.99073e15	−1.37878	−0.689389	+	0.724391i	$0.742121\pi$
$272$	−2.88478e13	−0.00431931
$273$	0	0
$274$	3.07727e15	0.439326
$275$	1.05627e16	1.47269
$276$	−2.71801e15	−0.370119
$277$	−6.66188e15	−0.886091	−0.443046	−	0.896499i	$-0.646102\pi$
$277$	−6.66188e15	−0.886091	−0.443046	+	0.896499i	$0.646102\pi$
$278$	8.31431e15	1.08028
$279$	5.56840e14	0.0706810
$280$	0	0
$281$	2.11519e15	0.256306	0.128153	−	0.991754i	$-0.459095\pi$
$281$	2.11519e15	0.256306	0.128153	+	0.991754i	$0.459095\pi$
$282$	−3.14323e15	−0.372183
$283$	8.15579e15	0.943744	0.471872	−	0.881667i	$-0.343578\pi$
$283$	8.15579e15	0.943744	0.471872	+	0.881667i	$0.343578\pi$
$284$	2.29147e15	0.259147
$285$	−4.86239e14	−0.0537474
$286$	−1.14845e16	−1.24089
$287$	0	0
$288$	−5.81589e14	−0.0600572
$289$	−9.90162e15	−0.999701
$290$	−2.01517e14	−0.0198941
$291$	−1.15967e16	−1.11951
$292$	−4.96180e14	−0.0468436
$293$	1.31022e16	1.20977	0.604886	−	0.796312i	$-0.293219\pi$
$293$	1.31022e16	1.20977	0.604886	+	0.796312i	$0.293219\pi$
$294$	0	0
$295$	−1.29931e15	−0.114781
$296$	3.73015e15	0.322352
$297$	1.92574e16	1.62810
$298$	8.10177e15	0.670153
$299$	−1.32074e16	−1.06895
$300$	−5.05157e15	−0.400072
$301$	0	0
$302$	−1.52516e16	−1.15683
$303$	−1.75868e16	−1.30560
$304$	1.84051e15	0.133740
$305$	1.59838e15	0.113693
$306$	5.96059e13	0.00415049
$307$	−9.48454e15	−0.646572	−0.323286	−	0.946301i	$-0.604788\pi$
$307$	−9.48454e15	−0.646572	−0.323286	+	0.946301i	$0.604788\pi$
$308$	0	0
$309$	−1.17486e16	−0.767815
$310$	2.84235e14	0.0181897
$311$	−6.03028e15	−0.377916	−0.188958	−	0.981985i	$-0.560511\pi$
$311$	−6.03028e15	−0.377916	−0.188958	+	0.981985i	$0.560511\pi$
$312$	5.49241e15	0.337099
$313$	−1.56485e16	−0.940662	−0.470331	−	0.882490i	$-0.655865\pi$
$313$	−1.56485e16	−0.940662	−0.470331	+	0.882490i	$0.655865\pi$
$314$	−2.12009e16	−1.24828
$315$	0	0
$316$	1.18959e15	0.0672095
$317$	1.05035e16	0.581367	0.290683	−	0.956819i	$-0.406117\pi$
$317$	1.05035e16	0.581367	0.290683	+	0.956819i	$0.406117\pi$
$318$	−1.11620e16	−0.605294
$319$	−6.40478e15	−0.340302
$320$	−2.96868e14	−0.0154557
$321$	2.95360e16	1.50685
$322$	0	0
$323$	−1.88630e14	−0.00924261
$324$	−5.67265e15	−0.272423
$325$	−2.45468e16	−1.15545
$326$	−1.98069e16	−0.913905
$327$	−7.01361e15	−0.317235
$328$	−1.16771e16	−0.517790
$329$	0	0
$330$	2.49268e15	0.106249
$331$	3.49129e16	1.45916	0.729582	−	0.683893i	$-0.239715\pi$
$331$	3.49129e16	1.45916	0.729582	+	0.683893i	$0.239715\pi$
$332$	1.62411e16	0.665606
$333$	−7.70731e15	−0.309753
$334$	−1.21360e15	−0.0478324
$335$	3.39989e15	0.131424
$336$	0	0
$337$	4.41702e16	1.64261	0.821306	−	0.570488i	$-0.193246\pi$
$337$	4.41702e16	1.64261	0.821306	+	0.570488i	$0.193246\pi$
$338$	7.30492e15	0.266475
$339$	−2.38349e16	−0.852935
$340$	3.04254e13	0.00106813
$341$	9.03379e15	0.311148
$342$	−3.80290e15	−0.128512
$343$	0	0
$344$	−1.43366e16	−0.466462
$345$	2.86665e15	0.0915272
$346$	−3.28981e16	−1.03080
$347$	−1.06243e16	−0.326707	−0.163354	−	0.986568i	$-0.552231\pi$
$347$	−1.06243e16	−0.326707	−0.163354	+	0.986568i	$0.552231\pi$
$348$	3.06306e15	0.0924465
$349$	3.45748e16	1.02422	0.512112	−	0.858919i	$-0.328863\pi$
$349$	3.45748e16	1.02422	0.512112	+	0.858919i	$0.328863\pi$
$350$	0	0
$351$	−4.47526e16	−1.27738
$352$	−9.43530e15	−0.264380
$353$	−5.07700e16	−1.39660	−0.698299	−	0.715807i	$-0.746059\pi$
$353$	−5.07700e16	−1.39660	−0.698299	+	0.715807i	$0.746059\pi$
$354$	1.97495e16	0.533377
$355$	−2.41679e15	−0.0640847
$356$	2.46822e16	0.642626
$357$	0	0
$358$	−8.86638e15	−0.222591
$359$	7.66771e15	0.189039	0.0945196	−	0.995523i	$-0.469868\pi$
$359$	7.66771e15	0.189039	0.0945196	+	0.995523i	$0.469868\pi$
$360$	6.13395e14	0.0148516
$361$	−3.00182e16	−0.713820
$362$	5.63109e16	1.31519
$363$	4.38042e16	1.00490
$364$	0	0
$365$	5.23314e14	0.0115840
$366$	−2.42954e16	−0.528321
$367$	1.57288e16	0.336020	0.168010	−	0.985785i	$-0.446266\pi$
$367$	1.57288e16	0.336020	0.168010	+	0.985785i	$0.446266\pi$
$368$	−1.08508e16	−0.227747
$369$	2.41274e16	0.497552
$370$	−3.93414e15	−0.0797148
$371$	0	0
$372$	−4.32037e15	−0.0845263
$373$	5.18943e16	0.997729	0.498864	−	0.866680i	$-0.333751\pi$
$373$	5.18943e16	0.997729	0.498864	+	0.866680i	$0.333751\pi$
$374$	9.67005e14	0.0182710
$375$	1.07384e16	0.199405
$376$	−1.25484e16	−0.229017
$377$	1.48841e16	0.266996
$378$	0	0
$379$	−4.38471e16	−0.759951	−0.379976	−	0.924997i	$-0.624068\pi$
$379$	−4.38471e16	−0.759951	−0.379976	+	0.924997i	$0.624068\pi$
$380$	−1.94116e15	−0.0330726
$381$	−9.57545e16	−1.60379
$382$	1.40488e16	0.231328
$383$	−3.97036e16	−0.642744	−0.321372	−	0.946953i	$-0.604144\pi$
$383$	−3.97036e16	−0.642744	−0.321372	+	0.946953i	$0.604144\pi$
$384$	4.51240e15	0.0718215
$385$	0	0
$386$	−5.10828e16	−0.786062
$387$	2.96226e16	0.448231
$388$	−4.62963e16	−0.688875
$389$	−3.41982e16	−0.500415	−0.250208	−	0.968192i	$-0.580499\pi$
$389$	−3.41982e16	−0.500415	−0.250208	+	0.968192i	$0.580499\pi$
$390$	−5.79277e15	−0.0833617
$391$	1.11208e15	0.0157394
$392$	0	0
$393$	6.78315e16	0.928710
$394$	5.10313e16	0.687245
$395$	−1.25464e15	−0.0166203
$396$	1.94954e16	0.254047
$397$	3.06428e16	0.392817	0.196408	−	0.980522i	$-0.437072\pi$
$397$	3.06428e16	0.392817	0.196408	+	0.980522i	$0.437072\pi$
$398$	−1.10979e15	−0.0139959
$399$	0	0
$400$	−2.01669e16	−0.246178
$401$	6.95213e16	0.834987	0.417493	−	0.908680i	$-0.362909\pi$
$401$	6.95213e16	0.834987	0.417493	+	0.908680i	$0.362909\pi$
$402$	−5.16783e16	−0.610715
$403$	−2.09937e16	−0.244122
$404$	−7.02099e16	−0.803377
$405$	5.98287e15	0.0673678
$406$	0	0
$407$	−1.25038e17	−1.36357
$408$	−4.62466e14	−0.00496351
$409$	1.16046e17	1.22582	0.612912	−	0.790151i	$-0.289998\pi$
$409$	1.16046e17	1.22582	0.612912	+	0.790151i	$0.289998\pi$
$410$	1.23157e16	0.128045
$411$	4.93325e16	0.504849
$412$	−4.69029e16	−0.472463
$413$	0	0
$414$	2.24202e16	0.218845
$415$	−1.71293e16	−0.164599
$416$	2.19268e16	0.207429
$417$	1.33289e17	1.24139
$418$	−6.16956e16	−0.565729
$419$	−1.40052e17	−1.26444	−0.632220	−	0.774789i	$-0.717856\pi$
$419$	−1.40052e17	−1.26444	−0.632220	+	0.774789i	$0.717856\pi$
$420$	0	0
$421$	−9.65022e16	−0.844702	−0.422351	−	0.906432i	$-0.638795\pi$
$421$	−9.65022e16	−0.844702	−0.422351	+	0.906432i	$0.638795\pi$
$422$	−8.17502e16	−0.704625
$423$	2.59277e16	0.220066
$424$	−4.45610e16	−0.372458
$425$	2.06686e15	0.0170131
$426$	3.67352e16	0.297797
$427$	0	0
$428$	1.17914e17	0.927213
$429$	−1.84111e17	−1.42596
$430$	1.51206e16	0.115352
$431$	−1.51333e17	−1.13719	−0.568595	−	0.822618i	$-0.692513\pi$
$431$	−1.51333e17	−1.13719	−0.568595	+	0.822618i	$0.692513\pi$
$432$	−3.67674e16	−0.272156
$433$	−1.97235e17	−1.43818	−0.719090	−	0.694917i	$-0.755441\pi$
$433$	−1.97235e17	−1.43818	−0.719090	+	0.694917i	$0.755441\pi$
$434$	0	0
$435$	−3.23057e15	−0.0228612
$436$	−2.79998e16	−0.195205
$437$	−7.09515e16	−0.487340
$438$	−7.95438e15	−0.0538300
$439$	5.38282e16	0.358914	0.179457	−	0.983766i	$-0.442566\pi$
$439$	5.38282e16	0.358914	0.179457	+	0.983766i	$0.442566\pi$
$440$	9.95130e15	0.0653789
$441$	0	0
$442$	−2.24723e15	−0.0143352
$443$	1.55429e17	0.977029	0.488514	−	0.872556i	$-0.337539\pi$
$443$	1.55429e17	0.977029	0.488514	+	0.872556i	$0.337539\pi$
$444$	5.97990e16	0.370428
$445$	−2.60320e16	−0.158916
$446$	9.66805e16	0.581651
$447$	1.29881e17	0.770102
$448$	0	0
$449$	2.52502e17	1.45433	0.727166	−	0.686462i	$-0.240837\pi$
$449$	2.52502e17	1.45433	0.727166	+	0.686462i	$0.240837\pi$
$450$	4.16692e16	0.236556
$451$	3.91426e17	2.19029
$452$	−9.51539e16	−0.524840
$453$	−2.44502e17	−1.32936
$454$	2.42293e17	1.29861
$455$	0	0
$456$	2.95057e16	0.153686
$457$	−2.55752e17	−1.31330	−0.656650	−	0.754196i	$-0.728027\pi$
$457$	−2.55752e17	−1.31330	−0.656650	+	0.754196i	$0.728027\pi$
$458$	1.41108e17	0.714375
$459$	3.76821e15	0.0188084
$460$	1.14442e16	0.0563198
$461$	8.90986e15	0.0432329	0.0216165	−	0.999766i	$-0.493119\pi$
$461$	8.90986e15	0.0432329	0.0216165	+	0.999766i	$0.493119\pi$
$462$	0	0
$463$	2.01347e17	0.949878	0.474939	−	0.880019i	$-0.342470\pi$
$463$	2.01347e17	0.949878	0.474939	+	0.880019i	$0.342470\pi$
$464$	1.22284e16	0.0568855
$465$	4.55664e15	0.0209026
$466$	1.65288e16	0.0747708
$467$	−1.01467e17	−0.452651	−0.226325	−	0.974052i	$-0.572671\pi$
$467$	−1.01467e17	−0.452651	−0.226325	+	0.974052i	$0.572671\pi$
$468$	−4.53056e16	−0.199321
$469$	0	0
$470$	1.32346e16	0.0566338
$471$	−3.39876e17	−1.43445
$472$	7.88439e16	0.328205
$473$	4.80577e17	1.97317
$474$	1.90706e16	0.0772333
$475$	−1.31867e17	−0.526780
$476$	0	0
$477$	9.20729e16	0.357900
$478$	2.83234e17	1.08609
$479$	−1.44101e17	−0.545112	−0.272556	−	0.962140i	$-0.587869\pi$
$479$	−1.44101e17	−0.545112	−0.272556	+	0.962140i	$0.587869\pi$
$480$	−4.75917e15	−0.0177608
$481$	2.90577e17	1.06984
$482$	1.59455e17	0.579206
$483$	0	0
$484$	1.74875e17	0.618349
$485$	4.88282e16	0.170353
$486$	1.32674e17	0.456721
$487$	3.33007e17	1.13114	0.565568	−	0.824701i	$-0.308657\pi$
$487$	3.33007e17	1.13114	0.565568	+	0.824701i	$0.308657\pi$
$488$	−9.69923e16	−0.325094
$489$	−3.17529e17	−1.05021
$490$	0	0
$491$	1.41803e17	0.456726	0.228363	−	0.973576i	$-0.426663\pi$
$491$	1.41803e17	0.456726	0.228363	+	0.973576i	$0.426663\pi$
$492$	−1.87198e17	−0.595015
$493$	−1.25326e15	−0.00393130
$494$	1.43375e17	0.443863
$495$	−2.05616e16	−0.0628235
$496$	−1.72478e16	−0.0520119
$497$	0	0
$498$	2.60365e17	0.764877
$499$	−3.84703e17	−1.11551	−0.557753	−	0.830007i	$-0.688336\pi$
$499$	−3.84703e17	−1.11551	−0.557753	+	0.830007i	$0.688336\pi$
$500$	4.28698e16	0.122700
$501$	−1.94554e16	−0.0549662
$502$	1.44286e17	0.402394
$503$	−5.67445e17	−1.56218	−0.781091	−	0.624417i	$-0.785337\pi$
$503$	−5.67445e17	−1.56218	−0.781091	+	0.624417i	$0.785337\pi$
$504$	0	0
$505$	7.40495e16	0.198668
$506$	3.63730e17	0.963387
$507$	1.17107e17	0.306218
$508$	−3.82272e17	−0.986865
$509$	6.29561e17	1.60462	0.802310	−	0.596907i	$-0.203604\pi$
$509$	6.29561e17	1.60462	0.802310	+	0.596907i	$0.203604\pi$
$510$	4.87757e14	0.00122743
$511$	0	0
$512$	1.80144e16	0.0441942
$513$	−2.40415e17	−0.582369
$514$	3.48229e17	0.832922
$515$	4.94679e16	0.116836
$516$	−2.29834e17	−0.536032
$517$	4.20634e17	0.968759
$518$	0	0
$519$	−5.27398e17	−1.18454
$520$	−2.31259e16	−0.0512953
$521$	3.60435e17	0.789553	0.394777	−	0.918777i	$-0.370822\pi$
$521$	3.60435e17	0.789553	0.394777	+	0.918777i	$0.370822\pi$
$522$	−2.52665e16	−0.0546621
$523$	2.47279e17	0.528355	0.264178	−	0.964474i	$-0.414900\pi$
$523$	2.47279e17	0.528355	0.264178	+	0.964474i	$0.414900\pi$
$524$	2.70797e17	0.571467
$525$	0	0
$526$	2.64162e17	0.543831
$527$	1.76769e15	0.00359449
$528$	−1.51260e17	−0.303811
$529$	−8.57377e16	−0.170102
$530$	4.69980e16	0.0921056
$531$	−1.62909e17	−0.315377
$532$	0	0
$533$	−9.09639e17	−1.71847
$534$	3.95686e17	0.738469
$535$	−1.24362e17	−0.229292
$536$	−2.06310e17	−0.375794
$537$	−1.42139e17	−0.255788
$538$	1.74451e17	0.310163
$539$	0	0
$540$	3.87781e16	0.0673018
$541$	1.38955e15	0.00238282	0.00119141	−	0.999999i	$-0.499621\pi$
$541$	1.38955e15	0.00238282	0.00119141	+	0.999999i	$0.499621\pi$
$542$	−5.75406e17	−0.974943
$543$	9.02735e17	1.51134
$544$	−1.84626e15	−0.00305421
$545$	2.95310e16	0.0482726
$546$	0	0
$547$	−4.75094e17	−0.758336	−0.379168	−	0.925328i	$-0.623790\pi$
$547$	−4.75094e17	−0.758336	−0.379168	+	0.925328i	$0.623790\pi$
$548$	1.96945e17	0.310651
$549$	2.00407e17	0.312387
$550$	6.76013e17	1.04135
$551$	7.99589e16	0.121725
$552$	−1.73952e17	−0.261714
$553$	0	0
$554$	−4.26360e17	−0.626561
$555$	−6.30692e16	−0.0916037
$556$	5.32116e17	0.763871
$557$	−1.09328e18	−1.55122	−0.775610	−	0.631212i	$-0.782558\pi$
$557$	−1.09328e18	−1.55122	−0.775610	+	0.631212i	$0.782558\pi$
$558$	3.56377e16	0.0499790
$559$	−1.11682e18	−1.54812
$560$	0	0
$561$	1.55023e16	0.0209960
$562$	1.35372e17	0.181236
$563$	−1.02565e18	−1.35736	−0.678680	−	0.734435i	$-0.737447\pi$
$563$	−1.02565e18	−1.35736	−0.678680	+	0.734435i	$0.737447\pi$
$564$	−2.01166e17	−0.263173
$565$	1.00358e17	0.129788
$566$	5.21971e17	0.667328
$567$	0	0
$568$	1.46654e17	0.183244
$569$	4.34267e17	0.536447	0.268223	−	0.963357i	$-0.413563\pi$
$569$	4.34267e17	0.536447	0.268223	+	0.963357i	$0.413563\pi$
$570$	−3.11193e16	−0.0380052
$571$	5.55274e17	0.670460	0.335230	−	0.942136i	$-0.391186\pi$
$571$	5.55274e17	0.670460	0.335230	+	0.942136i	$0.391186\pi$
$572$	−7.35007e17	−0.877440
$573$	2.25220e17	0.265829
$574$	0	0
$575$	7.77432e17	0.897060
$576$	−3.72217e16	−0.0424668
$577$	−1.23043e18	−1.38808	−0.694038	−	0.719939i	$-0.744170\pi$
$577$	−1.23043e18	−1.38808	−0.694038	+	0.719939i	$0.744170\pi$
$578$	−6.33704e17	−0.706896
$579$	−8.18921e17	−0.903298
$580$	−1.28971e16	−0.0140673
$581$	0	0
$582$	−7.42188e17	−0.791616
$583$	1.49373e18	1.57553
$584$	−3.17555e16	−0.0331234
$585$	4.77832e16	0.0492904
$586$	8.38538e17	0.855438
$587$	1.56262e18	1.57654	0.788271	−	0.615328i	$-0.210976\pi$
$587$	1.56262e18	1.57654	0.788271	+	0.615328i	$0.210976\pi$
$588$	0	0
$589$	−1.12780e17	−0.111297
$590$	−8.31557e16	−0.0811622
$591$	8.18096e17	0.789743
$592$	2.38730e17	0.227937
$593$	−1.09533e18	−1.03440	−0.517201	−	0.855864i	$-0.673026\pi$
$593$	−1.09533e18	−1.03440	−0.517201	+	0.855864i	$0.673026\pi$
$594$	1.23248e18	1.15124
$595$	0	0
$596$	5.18513e17	0.473870
$597$	−1.77913e16	−0.0160833
$598$	−8.45276e17	−0.755860
$599$	−1.47045e18	−1.30070	−0.650348	−	0.759636i	$-0.725377\pi$
$599$	−1.47045e18	−1.30070	−0.650348	+	0.759636i	$0.725377\pi$
$600$	−3.23301e17	−0.282894
$601$	−7.31235e17	−0.632955	−0.316477	−	0.948600i	$-0.602500\pi$
$601$	−7.31235e17	−0.632955	−0.316477	+	0.948600i	$0.602500\pi$
$602$	0	0
$603$	4.26282e17	0.361106
$604$	−9.76101e17	−0.818003
$605$	−1.84439e17	−0.152912
$606$	−1.12555e18	−0.923195
$607$	5.47904e17	0.444608	0.222304	−	0.974977i	$-0.428642\pi$
$607$	5.47904e17	0.444608	0.222304	+	0.974977i	$0.428642\pi$
$608$	1.17793e17	0.0945681
$609$	0	0
$610$	1.02297e17	0.0803928
$611$	−9.77516e17	−0.760074
$612$	3.81477e15	0.00293484
$613$	−3.76450e17	−0.286559	−0.143280	−	0.989682i	$-0.545765\pi$
$613$	−3.76450e17	−0.286559	−0.143280	+	0.989682i	$0.545765\pi$
$614$	−6.07010e17	−0.457195
$615$	1.97435e17	0.147142
$616$	0	0
$617$	−1.60929e18	−1.17431	−0.587153	−	0.809476i	$-0.699751\pi$
$617$	−1.60929e18	−1.17431	−0.587153	+	0.809476i	$0.699751\pi$
$618$	−7.51912e17	−0.542927
$619$	−1.57696e18	−1.12676	−0.563379	−	0.826199i	$-0.690499\pi$
$619$	−1.57696e18	−1.12676	−0.563379	+	0.826199i	$0.690499\pi$
$620$	1.81910e16	0.0128621
$621$	1.41738e18	0.991723
$622$	−3.85938e17	−0.267227
$623$	0	0
$624$	3.51514e17	0.238365
$625$	1.42212e18	0.954369
$626$	−1.00150e18	−0.665148
$627$	−9.89058e17	−0.650104
$628$	−1.35686e18	−0.882665
$629$	−2.44669e16	−0.0157525
$630$	0	0
$631$	3.96768e17	0.250234	0.125117	−	0.992142i	$-0.460069\pi$
$631$	3.96768e17	0.250234	0.125117	+	0.992142i	$0.460069\pi$
$632$	7.61336e16	0.0475243
$633$	−1.31056e18	−0.809715
$634$	6.72226e17	0.411088
$635$	4.03177e17	0.244043
$636$	−7.14369e17	−0.428008
$637$	0	0
$638$	−4.09906e17	−0.240630
$639$	−3.03020e17	−0.176082
$640$	−1.89996e16	−0.0109288
$641$	−1.05830e18	−0.602605	−0.301303	−	0.953529i	$-0.597421\pi$
$641$	−1.05830e18	−0.602605	−0.301303	+	0.953529i	$0.597421\pi$
$642$	1.89030e18	1.06550
$643$	4.45532e17	0.248604	0.124302	−	0.992244i	$-0.460331\pi$
$643$	4.45532e17	0.248604	0.124302	+	0.992244i	$0.460331\pi$
$644$	0	0
$645$	2.42403e17	0.132556
$646$	−1.20723e16	−0.00653551
$647$	−5.21651e17	−0.279578	−0.139789	−	0.990181i	$-0.544642\pi$
$647$	−5.21651e17	−0.279578	−0.139789	+	0.990181i	$0.544642\pi$
$648$	−3.63050e17	−0.192632
$649$	−2.64292e18	−1.38833
$650$	−1.57099e18	−0.817030
$651$	0	0
$652$	−1.26764e18	−0.646228
$653$	−7.10700e17	−0.358716	−0.179358	−	0.983784i	$-0.557402\pi$
$653$	−7.10700e17	−0.358716	−0.179358	+	0.983784i	$0.557402\pi$
$654$	−4.48871e17	−0.224319
$655$	−2.85606e17	−0.141319
$656$	−7.47332e17	−0.366133
$657$	6.56138e16	0.0318288
$658$	0	0
$659$	6.78922e17	0.322897	0.161449	−	0.986881i	$-0.448383\pi$
$659$	6.78922e17	0.322897	0.161449	+	0.986881i	$0.448383\pi$
$660$	1.59532e17	0.0751297
$661$	2.18063e18	1.01689	0.508443	−	0.861096i	$-0.330221\pi$
$661$	2.18063e18	1.01689	0.508443	+	0.861096i	$0.330221\pi$
$662$	2.23443e18	1.03178
$663$	−3.60260e16	−0.0164732
$664$	1.03943e18	0.470654
$665$	0	0
$666$	−4.93268e17	−0.219028
$667$	−4.71402e17	−0.207288
$668$	−7.76701e16	−0.0338226
$669$	1.54991e18	0.668400
$670$	2.17593e17	0.0929305
$671$	3.25127e18	1.37517
$672$	0	0
$673$	−1.35118e17	−0.0560551	−0.0280275	−	0.999607i	$-0.508923\pi$
$673$	−1.35118e17	−0.0560551	−0.0280275	+	0.999607i	$0.508923\pi$
$674$	2.82689e18	1.16150
$675$	2.63428e18	1.07198
$676$	4.67515e17	0.188426
$677$	−3.21927e18	−1.28508	−0.642541	−	0.766251i	$-0.722120\pi$
$677$	−3.21927e18	−1.28508	−0.642541	+	0.766251i	$0.722120\pi$
$678$	−1.52544e18	−0.603116
$679$	0	0
$680$	1.94723e15	0.000755281 0
$681$	3.88426e18	1.49229
$682$	5.78162e17	0.220015
$683$	−8.09936e17	−0.305292	−0.152646	−	0.988281i	$-0.548779\pi$
$683$	−8.09936e17	−0.305292	−0.152646	+	0.988281i	$0.548779\pi$
$684$	−2.43385e17	−0.0908720
$685$	−2.07716e17	−0.0768212
$686$	0	0
$687$	2.26214e18	0.820919
$688$	−9.17543e17	−0.329839
$689$	−3.47129e18	−1.23614
$690$	1.83465e17	0.0647195
$691$	1.11845e18	0.390851	0.195425	−	0.980719i	$-0.437391\pi$
$691$	1.11845e18	0.390851	0.195425	+	0.980719i	$0.437391\pi$
$692$	−2.10548e18	−0.728889
$693$	0	0
$694$	−6.79955e17	−0.231017
$695$	−5.61216e17	−0.188899
$696$	1.96036e17	0.0653696
$697$	7.65925e16	0.0253031
$698$	2.21279e18	0.724235
$699$	2.64977e17	0.0859223
$700$	0	0
$701$	−5.96521e18	−1.89871	−0.949354	−	0.314208i	$-0.898261\pi$
$701$	−5.96521e18	−1.89871	−0.949354	+	0.314208i	$0.898261\pi$
$702$	−2.86417e18	−0.903248
$703$	1.56101e18	0.487747
$704$	−6.03859e17	−0.186945
$705$	2.12168e17	0.0650804
$706$	−3.24928e18	−0.987543
$707$	0	0
$708$	1.26397e18	0.377154
$709$	−4.10758e18	−1.21447	−0.607234	−	0.794523i	$-0.707721\pi$
$709$	−4.10758e18	−1.21447	−0.607234	+	0.794523i	$0.707721\pi$
$710$	−1.54674e17	−0.0453147
$711$	−1.57309e17	−0.0456668
$712$	1.57966e18	0.454405
$713$	6.64901e17	0.189529
$714$	0	0
$715$	7.75203e17	0.216983
$716$	−5.67448e17	−0.157395
$717$	4.54060e18	1.24807
$718$	4.90734e17	0.133671
$719$	4.67199e18	1.26114	0.630572	−	0.776131i	$-0.282821\pi$
$719$	4.67199e18	1.26114	0.630572	+	0.776131i	$0.282821\pi$
$720$	3.92573e16	0.0105017
$721$	0	0
$722$	−1.92117e18	−0.504747
$723$	2.55627e18	0.665591
$724$	3.60390e18	0.929976
$725$	−8.76128e17	−0.224063
$726$	2.80347e18	0.710571
$727$	1.83347e18	0.460574	0.230287	−	0.973123i	$-0.426033\pi$
$727$	1.83347e18	0.460574	0.230287	+	0.973123i	$0.426033\pi$
$728$	0	0
$729$	4.33495e18	1.06968
$730$	3.34921e16	0.00819113
$731$	9.40371e16	0.0227948
$732$	−1.55491e18	−0.373579
$733$	1.91535e18	0.456113	0.228056	−	0.973648i	$-0.426763\pi$
$733$	1.91535e18	0.456113	0.228056	+	0.973648i	$0.426763\pi$
$734$	1.00664e18	0.237602
$735$	0	0
$736$	−6.94453e17	−0.161041
$737$	6.91571e18	1.58964
$738$	1.54415e18	0.351823
$739$	6.47297e18	1.46189	0.730946	−	0.682436i	$-0.239079\pi$
$739$	6.47297e18	1.46189	0.730946	+	0.682436i	$0.239079\pi$
$740$	−2.51785e17	−0.0563669
$741$	2.29848e18	0.510062
$742$	0	0
$743$	2.82487e18	0.615986	0.307993	−	0.951389i	$-0.400343\pi$
$743$	2.82487e18	0.615986	0.307993	+	0.951389i	$0.400343\pi$
$744$	−2.76504e17	−0.0597691
$745$	−5.46869e17	−0.117184
$746$	3.32124e18	0.705501
$747$	−2.14769e18	−0.452259
$748$	6.18883e16	0.0129196
$749$	0	0
$750$	6.87256e17	0.141000
$751$	−6.08896e18	−1.23846	−0.619232	−	0.785208i	$-0.712556\pi$
$751$	−6.08896e18	−1.23846	−0.619232	+	0.785208i	$0.712556\pi$
$752$	−8.03097e17	−0.161939
$753$	2.31309e18	0.462408
$754$	9.52586e17	0.188795
$755$	1.02948e18	0.202285
$756$	0	0
$757$	8.68895e18	1.67820	0.839101	−	0.543975i	$-0.183082\pi$
$757$	8.68895e18	1.67820	0.839101	+	0.543975i	$0.183082\pi$
$758$	−2.80621e18	−0.537367
$759$	5.83105e18	1.10707
$760$	−1.24234e17	−0.0233859
$761$	−3.79700e18	−0.708664	−0.354332	−	0.935120i	$-0.615292\pi$
$761$	−3.79700e18	−0.708664	−0.354332	+	0.935120i	$0.615292\pi$
$762$	−6.12829e18	−1.13405
$763$	0	0
$764$	8.99125e17	0.163574
$765$	−4.02339e15	−0.000725761 0
$766$	−2.54103e18	−0.454488
$767$	6.14191e18	1.08927
$768$	2.88793e17	0.0507854
$769$	−4.02466e18	−0.701792	−0.350896	−	0.936415i	$-0.614123\pi$
$769$	−4.02466e18	−0.701792	−0.350896	+	0.936415i	$0.614123\pi$
$770$	0	0
$771$	5.58254e18	0.957147
$772$	−3.26930e18	−0.555830
$773$	−1.21905e18	−0.205521	−0.102760	−	0.994706i	$-0.532767\pi$
$773$	−1.21905e18	−0.205521	−0.102760	+	0.994706i	$0.532767\pi$
$774$	1.89585e18	0.316947
$775$	1.23576e18	0.204867
$776$	−2.96297e18	−0.487108
$777$	0	0
$778$	−2.18868e18	−0.353847
$779$	−4.88666e18	−0.783463
$780$	−3.70738e17	−0.0589456
$781$	−4.91599e18	−0.775138
$782$	7.11731e16	0.0111294
$783$	−1.59732e18	−0.247708
$784$	0	0
$785$	1.43106e18	0.218275
$786$	4.34122e18	0.656697
$787$	1.01206e19	1.51835	0.759173	−	0.650889i	$-0.225604\pi$
$787$	1.01206e19	1.51835	0.759173	+	0.650889i	$0.225604\pi$
$788$	3.26600e18	0.485955
$789$	4.23486e18	0.624940
$790$	−8.02972e16	−0.0117523
$791$	0	0
$792$	1.24771e18	0.179638
$793$	−7.55567e18	−1.07894
$794$	1.96114e18	0.277763
$795$	7.53436e17	0.105843
$796$	−7.10264e16	−0.00989658
$797$	6.89153e18	0.952437	0.476219	−	0.879327i	$-0.342007\pi$
$797$	6.89153e18	0.952437	0.476219	+	0.879327i	$0.342007\pi$
$798$	0	0
$799$	8.23078e16	0.0111915
$800$	−1.29068e18	−0.174074
$801$	−3.26392e18	−0.436645
$802$	4.44937e18	0.590425
$803$	1.06447e18	0.140115
$804$	−3.30741e18	−0.431841
$805$	0	0
$806$	−1.34360e18	−0.172620
$807$	2.79667e18	0.356421
$808$	−4.49343e18	−0.568073
$809$	−1.11644e19	−1.40014	−0.700070	−	0.714075i	$-0.746848\pi$
$809$	−1.11644e19	−1.40014	−0.700070	+	0.714075i	$0.746848\pi$
$810$	3.82904e17	0.0476362
$811$	−8.00768e18	−0.988260	−0.494130	−	0.869388i	$-0.664513\pi$
$811$	−8.00768e18	−0.988260	−0.494130	+	0.869388i	$0.664513\pi$
$812$	0	0
$813$	−9.22448e18	−1.12035
$814$	−8.00244e18	−0.964192
$815$	1.33696e18	0.159807
$816$	−2.95978e16	−0.00350973
$817$	−5.99964e18	−0.705800
$818$	7.42694e18	0.866789
$819$	0	0
$820$	7.88202e17	0.0905414
$821$	8.20324e18	0.934878	0.467439	−	0.884025i	$-0.345177\pi$
$821$	8.20324e18	0.934878	0.467439	+	0.884025i	$0.345177\pi$
$822$	3.15728e18	0.356982
$823$	−8.64677e18	−0.969963	−0.484982	−	0.874524i	$-0.661174\pi$
$823$	−8.64677e18	−0.969963	−0.484982	+	0.874524i	$0.661174\pi$
$824$	−3.00178e18	−0.334082
$825$	1.08373e19	1.19666
$826$	0	0
$827$	6.18723e18	0.672528	0.336264	−	0.941768i	$-0.390837\pi$
$827$	6.18723e18	0.672528	0.336264	+	0.941768i	$0.390837\pi$
$828$	1.43489e18	0.154747
$829$	9.34155e18	0.999573	0.499787	−	0.866148i	$-0.333412\pi$
$829$	9.34155e18	0.999573	0.499787	+	0.866148i	$0.333412\pi$
$830$	−1.09627e18	−0.116389
$831$	−6.83509e18	−0.720008
$832$	1.40332e18	0.146674
$833$	0	0
$834$	8.53049e18	0.877798
$835$	8.19177e16	0.00836403
$836$	−3.94852e18	−0.400031
$837$	2.25298e18	0.226486
$838$	−8.96334e18	−0.894095
$839$	−5.15941e18	−0.510678	−0.255339	−	0.966852i	$-0.582187\pi$
$839$	−5.15941e18	−0.510678	−0.255339	+	0.966852i	$0.582187\pi$
$840$	0	0
$841$	−9.72938e18	−0.948225
$842$	−6.17614e18	−0.597295
$843$	2.17019e18	0.208266
$844$	−5.23202e18	−0.498245
$845$	−4.93082e17	−0.0465962
$846$	1.65938e18	0.155610
$847$	0	0
$848$	−2.85191e18	−0.263368
$849$	8.36784e18	0.766855
$850$	1.32279e17	0.0120301
$851$	−9.20300e18	−0.830591
$852$	2.35105e18	0.210574
$853$	−6.65105e17	−0.0591182	−0.0295591	−	0.999563i	$-0.509410\pi$
$853$	−6.65105e17	−0.0591182	−0.0295591	+	0.999563i	$0.509410\pi$
$854$	0	0
$855$	2.56696e17	0.0224718
$856$	7.54648e18	0.655639
$857$	−1.61551e19	−1.39295	−0.696475	−	0.717581i	$-0.745249\pi$
$857$	−1.61551e19	−1.39295	−0.696475	+	0.717581i	$0.745249\pi$
$858$	−1.17831e19	−1.00830
$859$	4.54541e18	0.386027	0.193014	−	0.981196i	$-0.438174\pi$
$859$	4.54541e18	0.386027	0.193014	+	0.981196i	$0.438174\pi$
$860$	9.67721e17	0.0815662
$861$	0	0
$862$	−9.68534e18	−0.804114
$863$	6.02609e18	0.496553	0.248276	−	0.968689i	$-0.420136\pi$
$863$	6.02609e18	0.496553	0.248276	+	0.968689i	$0.420136\pi$
$864$	−2.35311e18	−0.192443
$865$	2.22062e18	0.180248
$866$	−1.26231e19	−1.01695
$867$	−1.01591e19	−0.812324
$868$	0	0
$869$	−2.55207e18	−0.201032
$870$	−2.06757e17	−0.0161653
$871$	−1.60715e19	−1.24721
$872$	−1.79198e18	−0.138031
$873$	6.12214e18	0.468070
$874$	−4.54090e18	−0.344602
$875$	0	0
$876$	−5.09080e17	−0.0380636
$877$	−2.94276e18	−0.218402	−0.109201	−	0.994020i	$-0.534829\pi$
$877$	−2.94276e18	−0.218402	−0.109201	+	0.994020i	$0.534829\pi$
$878$	3.44501e18	0.253791
$879$	1.34428e19	0.983021
$880$	6.36883e17	0.0462298
$881$	−7.22714e18	−0.520743	−0.260371	−	0.965509i	$-0.583845\pi$
$881$	−7.22714e18	−0.520743	−0.260371	+	0.965509i	$0.583845\pi$
$882$	0	0
$883$	−8.75073e18	−0.621297	−0.310649	−	0.950525i	$-0.600546\pi$
$883$	−8.75073e18	−0.621297	−0.310649	+	0.950525i	$0.600546\pi$
$884$	−1.43823e17	−0.0101365
$885$	−1.33309e18	−0.0932670
$886$	9.94744e18	0.690864
$887$	−1.86545e19	−1.28611	−0.643057	−	0.765818i	$-0.722334\pi$
$887$	−1.86545e19	−1.28611	−0.643057	+	0.765818i	$0.722334\pi$
$888$	3.82713e18	0.261932
$889$	0	0
$890$	−1.66605e18	−0.112370
$891$	1.21698e19	0.814849
$892$	6.18755e18	0.411289
$893$	−5.25130e18	−0.346523
$894$	8.31241e18	0.544544
$895$	5.98481e17	0.0389225
$896$	0	0
$897$	−1.35508e19	−0.868591
$898$	1.61601e19	1.02837
$899$	−7.49311e17	−0.0473396
$900$	2.66683e18	0.167270
$901$	2.92286e17	0.0182011
$902$	2.50513e19	1.54877
$903$	0	0
$904$	−6.08985e18	−0.371118
$905$	−3.80099e18	−0.229975
$906$	−1.56481e19	−0.940002
$907$	1.66306e19	0.991885	0.495942	−	0.868355i	$-0.334823\pi$
$907$	1.66306e19	0.991885	0.495942	+	0.868355i	$0.334823\pi$
$908$	1.55068e19	0.918254
$909$	9.28442e18	0.545870
$910$	0	0
$911$	6.96284e18	0.403568	0.201784	−	0.979430i	$-0.435326\pi$
$911$	6.96284e18	0.403568	0.201784	+	0.979430i	$0.435326\pi$
$912$	1.88836e18	0.108672
$913$	−3.48426e19	−1.99091
$914$	−1.63681e19	−0.928643
$915$	1.63994e18	0.0923828
$916$	9.03091e18	0.505139
$917$	0	0
$918$	2.41165e17	0.0132996
$919$	−6.18631e18	−0.338751	−0.169376	−	0.985552i	$-0.554175\pi$
$919$	−6.18631e18	−0.338751	−0.169376	+	0.985552i	$0.554175\pi$
$920$	7.32431e17	0.0398241
$921$	−9.73113e18	−0.525383
$922$	5.70231e17	0.0305703
$923$	1.14243e19	0.608162
$924$	0	0
$925$	−1.71043e19	−0.897810
$926$	1.28862e19	0.671665
$927$	6.20235e18	0.321024
$928$	7.82615e17	0.0402241
$929$	1.96781e19	1.00434	0.502169	−	0.864769i	$-0.332535\pi$
$929$	1.96781e19	1.00434	0.502169	+	0.864769i	$0.332535\pi$
$930$	2.91625e17	0.0147804
$931$	0	0
$932$	1.05784e18	0.0528709
$933$	−6.18707e18	−0.307082
$934$	−6.49386e18	−0.320072
$935$	−6.52728e16	−0.00319490
$936$	−2.89956e18	−0.140941
$937$	−1.33696e19	−0.645371	−0.322686	−	0.946506i	$-0.604586\pi$
$937$	−1.33696e19	−0.645371	−0.322686	+	0.946506i	$0.604586\pi$
$938$	0	0
$939$	−1.60553e19	−0.764351
$940$	8.47017e17	0.0400462
$941$	−3.85086e19	−1.80811	−0.904056	−	0.427414i	$-0.859425\pi$
$941$	−3.85086e19	−1.80811	−0.904056	+	0.427414i	$0.859425\pi$
$942$	−2.17521e19	−1.01431
$943$	2.88096e19	1.33417
$944$	5.04601e18	0.232076
$945$	0	0
$946$	3.07569e19	1.39524
$947$	−7.96055e18	−0.358648	−0.179324	−	0.983790i	$-0.557391\pi$
$947$	−7.96055e18	−0.358648	−0.179324	+	0.983790i	$0.557391\pi$
$948$	1.22052e18	0.0546122
$949$	−2.47374e18	−0.109932
$950$	−8.43951e18	−0.372489
$951$	1.07766e19	0.472399
$952$	0	0
$953$	−3.64992e18	−0.157826	−0.0789131	−	0.996882i	$-0.525145\pi$
$953$	−3.64992e18	−0.157826	−0.0789131	+	0.996882i	$0.525145\pi$
$954$	5.89266e18	0.253074
$955$	−9.48296e17	−0.0404503
$956$	1.81270e19	0.767980
$957$	−6.57131e18	−0.276519
$958$	−9.22245e18	−0.385452
$959$	0	0
$960$	−3.04587e17	−0.0125588
$961$	−2.33607e19	−0.956716
$962$	1.85970e19	0.756491
$963$	−1.55927e19	−0.630013
$964$	1.02051e19	0.409561
$965$	3.44809e18	0.137452
$966$	0	0
$967$	−1.55216e19	−0.610470	−0.305235	−	0.952277i	$-0.598735\pi$
$967$	−1.55216e19	−0.610470	−0.305235	+	0.952277i	$0.598735\pi$
$968$	1.11920e19	0.437238
$969$	−1.93534e17	−0.00751024
$970$	3.12500e18	0.120458
$971$	1.62625e19	0.622677	0.311339	−	0.950299i	$-0.399223\pi$
$971$	1.62625e19	0.622677	0.311339	+	0.950299i	$0.399223\pi$
$972$	8.49115e18	0.322950
$973$	0	0
$974$	2.13125e19	0.799835
$975$	−2.51850e19	−0.938884
$976$	−6.20751e18	−0.229876
$977$	3.04754e19	1.12107	0.560537	−	0.828129i	$-0.310595\pi$
$977$	3.04754e19	1.12107	0.560537	+	0.828129i	$0.310595\pi$
$978$	−2.03218e19	−0.742609
$979$	−5.29516e19	−1.92217
$980$	0	0
$981$	3.70263e18	0.132636
$982$	9.07539e18	0.322954
$983$	3.77304e19	1.33381	0.666904	−	0.745144i	$-0.267619\pi$
$983$	3.77304e19	1.33381	0.666904	+	0.745144i	$0.267619\pi$
$984$	−1.19807e19	−0.420739
$985$	−3.44461e18	−0.120172
$986$	−8.02086e16	−0.00277985
$987$	0	0
$988$	9.17601e18	0.313858
$989$	3.53712e19	1.20192
$990$	−1.31594e18	−0.0444229
$991$	2.73247e19	0.916383	0.458191	−	0.888854i	$-0.348497\pi$
$991$	2.73247e19	0.916383	0.458191	+	0.888854i	$0.348497\pi$
$992$	−1.10386e18	−0.0367780
$993$	3.58207e19	1.18567
$994$	0	0
$995$	7.49107e16	0.00244734
$996$	1.66633e19	0.540849
$997$	−6.04420e19	−1.94904	−0.974518	−	0.224308i	$-0.927988\pi$
$997$	−6.04420e19	−1.94904	−0.974518	+	0.224308i	$0.927988\pi$
$998$	−2.46210e19	−0.788782
$999$	−3.11838e19	−0.992552

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.14.a.d.1.1		1
7.2	even	3		98.14.c.b.67.1		2
7.3	odd	6		98.14.c.c.79.1		2
7.4	even	3		98.14.c.b.79.1		2
7.5	odd	6		98.14.c.c.67.1		2
7.6	odd	2		14.14.a.b.1.1	✓	1
21.20	even	2		126.14.a.a.1.1		1
28.27	even	2		112.14.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.14.a.b.1.1	✓	1	7.6	odd	2
98.14.a.d.1.1		1	1.1	even	1	trivial
98.14.c.b.67.1		2	7.2	even	3
98.14.c.b.79.1		2	7.4	even	3
98.14.c.c.67.1		2	7.5	odd	6
98.14.c.c.79.1		2	7.3	odd	6
112.14.a.b.1.1		1	28.27	even	2
126.14.a.a.1.1		1	21.20	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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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