LMFDB - Embedded newform 98.10.a.a.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,10,Mod(1,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	98.a (trivial)

Newform invariants

comment:select newform

sage:traces = [1,-16,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$50.4735119441$
Analytic rank:	$0$
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)

$f(q)$

$=$

\(q-16.0000 q^{2} +6.00000 q^{3} +256.000 q^{4} -560.000 q^{5} -96.0000 q^{6} -4096.00 q^{8} -19647.0 q^{9} +8960.00 q^{10} -54152.0 q^{11} +1536.00 q^{12} +113172. q^{13} -3360.00 q^{15} +65536.0 q^{16} -6262.00 q^{17} +314352. q^{18} -257078. q^{19} -143360. q^{20} +866432. q^{22} -266000. q^{23} -24576.0 q^{24} -1.63952e6 q^{25} -1.81075e6 q^{26} -235980. q^{27} +1.57471e6 q^{29} +53760.0 q^{30} +4.63748e6 q^{31} -1.04858e6 q^{32} -324912. q^{33} +100192. q^{34} -5.02963e6 q^{36} -1.19462e7 q^{37} +4.11325e6 q^{38} +679032. q^{39} +2.29376e6 q^{40} -2.19091e7 q^{41} +2.75206e7 q^{43} -1.38629e7 q^{44} +1.10023e7 q^{45} +4.25600e6 q^{46} -5.29278e7 q^{47} +393216. q^{48} +2.62324e7 q^{50} -37572.0 q^{51} +2.89720e7 q^{52} +1.62212e7 q^{53} +3.77568e6 q^{54} +3.03251e7 q^{55} -1.54247e6 q^{57} -2.51954e7 q^{58} +1.40510e8 q^{59} -860160. q^{60} +2.02964e8 q^{61} -7.41997e7 q^{62} +1.67772e7 q^{64} -6.33763e7 q^{65} +5.19859e6 q^{66} +1.53735e8 q^{67} -1.60307e6 q^{68} -1.59600e6 q^{69} +2.79656e8 q^{71} +8.04741e7 q^{72} +4.04023e8 q^{73} +1.91140e8 q^{74} -9.83715e6 q^{75} -6.58120e7 q^{76} -1.08645e7 q^{78} -1.30690e8 q^{79} -3.67002e7 q^{80} +3.85296e8 q^{81} +3.50546e8 q^{82} -4.20134e8 q^{83} +3.50672e6 q^{85} -4.40329e8 q^{86} +9.44828e6 q^{87} +2.21807e8 q^{88} +4.69542e8 q^{89} -1.76037e8 q^{90} -6.80960e7 q^{92} +2.78249e7 q^{93} +8.46845e8 q^{94} +1.43964e8 q^{95} -6.29146e6 q^{96} +8.72502e8 q^{97} +1.06392e9 q^{99} +O(q^{100})\)

Coefficient data

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

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

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

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	6.00000	0.0427667	0.0213833	−	0.999771i	$-0.493193\pi$
$3$	6.00000	0.0427667	0.0213833	+	0.999771i	$0.493193\pi$
$4$	256.000	0.500000
$5$	−560.000	−0.400703	−0.200352	−	0.979724i	$-0.564208\pi$
$5$	−560.000	−0.400703	−0.200352	+	0.979724i	$0.564208\pi$
$6$	−96.0000	−0.0302406
$7$	0	0
$7$	0	0
$8$	−4096.00	−0.353553
$9$	−19647.0	−0.998171
$10$	8960.00	0.283340
$11$	−54152.0	−1.11519	−0.557593	−	0.830114i	$-0.688275\pi$
$11$	−54152.0	−1.11519	−0.557593	+	0.830114i	$0.688275\pi$
$12$	1536.00	0.0213833
$13$	113172.	1.09899	0.549495	−	0.835497i	$-0.314820\pi$
$13$	113172.	1.09899	0.549495	+	0.835497i	$0.314820\pi$
$14$	0	0
$15$	−3360.00	−0.0171368
$16$	65536.0	0.250000
$17$	−6262.00	−0.0181841	−0.00909207	−	0.999959i	$-0.502894\pi$
$17$	−6262.00	−0.0181841	−0.00909207	+	0.999959i	$0.502894\pi$
$18$	314352.	0.705813
$19$	−257078.	−0.452557	−0.226279	−	0.974063i	$-0.572656\pi$
$19$	−257078.	−0.452557	−0.226279	+	0.974063i	$0.572656\pi$
$20$	−143360.	−0.200352
$21$	0	0
$22$	866432.	0.788556
$23$	−266000.	−0.198201	−0.0991006	−	0.995077i	$-0.531597\pi$
$23$	−266000.	−0.198201	−0.0991006	+	0.995077i	$0.531597\pi$
$24$	−24576.0	−0.0151203
$25$	−1.63952e6	−0.839437
$26$	−1.81075e6	−0.777104
$27$	−235980.	−0.0854552
$28$	0	0
$29$	1.57471e6	0.413438	0.206719	−	0.978400i	$-0.433721\pi$
$29$	1.57471e6	0.413438	0.206719	+	0.978400i	$0.433721\pi$
$30$	53760.0	0.0121175
$31$	4.63748e6	0.901893	0.450946	−	0.892551i	$-0.351087\pi$
$31$	4.63748e6	0.901893	0.450946	+	0.892551i	$0.351087\pi$
$32$	−1.04858e6	−0.176777
$33$	−324912.	−0.0476928
$34$	100192.	0.0128581
$35$	0	0
$36$	−5.02963e6	−0.499086
$37$	−1.19462e7	−1.04791	−0.523954	−	0.851746i	$-0.675544\pi$
$37$	−1.19462e7	−1.04791	−0.523954	+	0.851746i	$0.675544\pi$
$38$	4.11325e6	0.320006
$39$	679032.	0.0470002
$40$	2.29376e6	0.141670
$41$	−2.19091e7	−1.21087	−0.605435	−	0.795895i	$-0.707001\pi$
$41$	−2.19091e7	−1.21087	−0.605435	+	0.795895i	$0.707001\pi$
$42$	0	0
$43$	2.75206e7	1.22758	0.613790	−	0.789469i	$-0.289644\pi$
$43$	2.75206e7	1.22758	0.613790	+	0.789469i	$0.289644\pi$
$44$	−1.38629e7	−0.557593
$45$	1.10023e7	0.399970
$46$	4.25600e6	0.140149
$47$	−5.29278e7	−1.58214	−0.791068	−	0.611728i	$-0.790475\pi$
$47$	−5.29278e7	−1.58214	−0.791068	+	0.611728i	$0.790475\pi$
$48$	393216.	0.0106917
$49$	0	0
$50$	2.62324e7	0.593571
$51$	−37572.0	−0.000777676 0
$52$	2.89720e7	0.549495
$53$	1.62212e7	0.282385	0.141193	−	0.989982i	$-0.454906\pi$
$53$	1.62212e7	0.282385	0.141193	+	0.989982i	$0.454906\pi$
$54$	3.77568e6	0.0604259
$55$	3.03251e7	0.446859
$56$	0	0
$57$	−1.54247e6	−0.0193544
$58$	−2.51954e7	−0.292345
$59$	1.40510e8	1.50964	0.754818	−	0.655935i	$-0.227725\pi$
$59$	1.40510e8	1.50964	0.754818	+	0.655935i	$0.227725\pi$
$60$	−860160.	−0.00856838
$61$	2.02964e8	1.87687	0.938434	−	0.345458i	$-0.112276\pi$
$61$	2.02964e8	1.87687	0.938434	+	0.345458i	$0.112276\pi$
$62$	−7.41997e7	−0.637734
$63$	0	0
$64$	1.67772e7	0.125000
$65$	−6.33763e7	−0.440369
$66$	5.19859e6	0.0337239
$67$	1.53735e8	0.932041	0.466020	−	0.884774i	$-0.345687\pi$
$67$	1.53735e8	0.932041	0.466020	+	0.884774i	$0.345687\pi$
$68$	−1.60307e6	−0.00909207
$69$	−1.59600e6	−0.00847641
$70$	0	0
$71$	2.79656e8	1.30606	0.653028	−	0.757334i	$-0.273499\pi$
$71$	2.79656e8	1.30606	0.653028	+	0.757334i	$0.273499\pi$
$72$	8.04741e7	0.352907
$73$	4.04023e8	1.66515	0.832574	−	0.553913i	$-0.186866\pi$
$73$	4.04023e8	1.66515	0.832574	+	0.553913i	$0.186866\pi$
$74$	1.91140e8	0.740983
$75$	−9.83715e6	−0.0358999
$76$	−6.58120e7	−0.226279
$77$	0	0
$78$	−1.08645e7	−0.0332341
$79$	−1.30690e8	−0.377503	−0.188751	−	0.982025i	$-0.560444\pi$
$79$	−1.30690e8	−0.377503	−0.188751	+	0.982025i	$0.560444\pi$
$80$	−3.67002e7	−0.100176
$81$	3.85296e8	0.994516
$82$	3.50546e8	0.856215
$83$	−4.20134e8	−0.971709	−0.485855	−	0.874040i	$-0.661492\pi$
$83$	−4.20134e8	−0.971709	−0.485855	+	0.874040i	$0.661492\pi$
$84$	0	0
$85$	3.50672e6	0.00728645
$86$	−4.40329e8	−0.868030
$87$	9.44828e6	0.0176814
$88$	2.21807e8	0.394278
$89$	4.69542e8	0.793268	0.396634	−	0.917977i	$-0.370178\pi$
$89$	4.69542e8	0.793268	0.396634	+	0.917977i	$0.370178\pi$
$90$	−1.76037e8	−0.282822
$91$	0	0
$92$	−6.80960e7	−0.0991006
$93$	2.78249e7	0.0385710
$94$	8.46845e8	1.11874
$95$	1.43964e8	0.181341
$96$	−6.29146e6	−0.00756015
$97$	8.72502e8	1.00068	0.500338	−	0.865830i	$-0.333209\pi$
$97$	8.72502e8	1.00068	0.500338	+	0.865830i	$0.333209\pi$
$98$	0	0
$99$	1.06392e9	1.11315
$100$	−4.19718e8	−0.419718
$101$	1.20901e9	1.15607	0.578037	−	0.816011i	$-0.303819\pi$
$101$	1.20901e9	1.15607	0.578037	+	0.816011i	$0.303819\pi$
$102$	601152.	0.000549900 0
$103$	−6.90563e8	−0.604555	−0.302277	−	0.953220i	$-0.597747\pi$
$103$	−6.90563e8	−0.604555	−0.302277	+	0.953220i	$0.597747\pi$
$104$	−4.63553e8	−0.388552
$105$	0	0
$106$	−2.59540e8	−0.199677
$107$	1.79499e8	0.132384	0.0661921	−	0.997807i	$-0.478915\pi$
$107$	1.79499e8	0.132384	0.0661921	+	0.997807i	$0.478915\pi$
$108$	−6.04109e7	−0.0427276
$109$	−1.60361e9	−1.08813	−0.544063	−	0.839044i	$-0.683115\pi$
$109$	−1.60361e9	−1.08813	−0.544063	+	0.839044i	$0.683115\pi$
$110$	−4.85202e8	−0.315977
$111$	−7.16774e7	−0.0448156
$112$	0	0
$113$	1.42785e9	0.823815	0.411908	−	0.911226i	$-0.364863\pi$
$113$	1.42785e9	0.823815	0.411908	+	0.911226i	$0.364863\pi$
$114$	2.46795e7	0.0136856
$115$	1.48960e8	0.0794199
$116$	4.03127e8	0.206719
$117$	−2.22349e9	−1.09698
$118$	−2.24815e9	−1.06747
$119$	0	0
$120$	1.37626e7	0.00605876
$121$	5.74491e8	0.243640
$122$	−3.24742e9	−1.32715
$123$	−1.31455e8	−0.0517849
$124$	1.18720e9	0.450946
$125$	2.01188e9	0.737069
$126$	0	0
$127$	−2.35873e9	−0.804565	−0.402282	−	0.915516i	$-0.631783\pi$
$127$	−2.35873e9	−0.804565	−0.402282	+	0.915516i	$0.631783\pi$
$128$	−2.68435e8	−0.0883883
$129$	1.65124e8	0.0524995
$130$	1.01402e9	0.311388
$131$	−6.01665e8	−0.178498	−0.0892492	−	0.996009i	$-0.528447\pi$
$131$	−6.01665e8	−0.178498	−0.0892492	+	0.996009i	$0.528447\pi$
$132$	−8.31775e7	−0.0238464
$133$	0	0
$134$	−2.45975e9	−0.659052
$135$	1.32149e8	0.0342422
$136$	2.56492e7	0.00642907
$137$	−5.16009e9	−1.25145	−0.625726	−	0.780043i	$-0.715197\pi$
$137$	−5.16009e9	−1.25145	−0.625726	+	0.780043i	$0.715197\pi$
$138$	2.55360e7	0.00599373
$139$	7.14356e9	1.62311	0.811556	−	0.584275i	$-0.198621\pi$
$139$	7.14356e9	1.62311	0.811556	+	0.584275i	$0.198621\pi$
$140$	0	0
$141$	−3.17567e8	−0.0676627
$142$	−4.47449e9	−0.923520
$143$	−6.12849e9	−1.22558
$144$	−1.28759e9	−0.249543
$145$	−8.81840e8	−0.165666
$146$	−6.46437e9	−1.17744
$147$	0	0
$148$	−3.05824e9	−0.523954
$149$	9.10424e9	1.51323	0.756616	−	0.653859i	$-0.226851\pi$
$149$	9.10424e9	1.51323	0.756616	+	0.653859i	$0.226851\pi$
$150$	1.57394e8	0.0253851
$151$	−2.89432e8	−0.0453054	−0.0226527	−	0.999743i	$-0.507211\pi$
$151$	−2.89432e8	−0.0453054	−0.0226527	+	0.999743i	$0.507211\pi$
$152$	1.05299e9	0.160003
$153$	1.23030e8	0.0181509
$154$	0	0
$155$	−2.59699e9	−0.361391
$156$	1.73832e8	0.0235001
$157$	−1.39068e10	−1.82675	−0.913373	−	0.407124i	$-0.866532\pi$
$157$	−1.39068e10	−1.82675	−0.913373	+	0.407124i	$0.866532\pi$
$158$	2.09104e9	0.266935
$159$	9.73273e7	0.0120767
$160$	5.87203e8	0.0708350
$161$	0	0
$162$	−6.16474e9	−0.703229
$163$	1.66232e10	1.84447	0.922235	−	0.386629i	$-0.126361\pi$
$163$	1.66232e10	1.84447	0.922235	+	0.386629i	$0.126361\pi$
$164$	−5.60874e9	−0.605435
$165$	1.81951e8	0.0191107
$166$	6.72214e9	0.687102
$167$	1.58019e10	1.57212	0.786061	−	0.618149i	$-0.212117\pi$
$167$	1.58019e10	1.57212	0.786061	+	0.618149i	$0.212117\pi$
$168$	0	0
$169$	2.20340e9	0.207780
$170$	−5.61075e7	−0.00515230
$171$	5.05081e9	0.451730
$172$	7.04527e9	0.613790
$173$	−3.23125e9	−0.274260	−0.137130	−	0.990553i	$-0.543788\pi$
$173$	−3.23125e9	−0.274260	−0.137130	+	0.990553i	$0.543788\pi$
$174$	−1.51173e8	−0.0125026
$175$	0	0
$176$	−3.54891e9	−0.278797
$177$	8.43058e8	0.0645621
$178$	−7.51268e9	−0.560925
$179$	−2.41408e10	−1.75757	−0.878785	−	0.477218i	$-0.841645\pi$
$179$	−2.41408e10	−1.75757	−0.878785	+	0.477218i	$0.841645\pi$
$180$	2.81659e9	0.199985
$181$	3.89332e9	0.269629	0.134814	−	0.990871i	$-0.456956\pi$
$181$	3.89332e9	0.269629	0.134814	+	0.990871i	$0.456956\pi$
$182$	0	0
$183$	1.21778e9	0.0802674
$184$	1.08954e9	0.0700747
$185$	6.68989e9	0.419901
$186$	−4.45198e8	−0.0272738
$187$	3.39100e8	0.0202787
$188$	−1.35495e10	−0.791068
$189$	0	0
$190$	−2.30342e9	−0.128228
$191$	−2.58988e10	−1.40809	−0.704043	−	0.710157i	$-0.748624\pi$
$191$	−2.58988e10	−1.40809	−0.704043	+	0.710157i	$0.748624\pi$
$192$	1.00663e8	0.00534584
$193$	1.59367e10	0.826783	0.413391	−	0.910553i	$-0.364344\pi$
$193$	1.59367e10	0.826783	0.413391	+	0.910553i	$0.364344\pi$
$194$	−1.39600e10	−0.707585
$195$	−3.80258e8	−0.0188331
$196$	0	0
$197$	−3.34685e9	−0.158321	−0.0791604	−	0.996862i	$-0.525224\pi$
$197$	−3.34685e9	−0.158321	−0.0791604	+	0.996862i	$0.525224\pi$
$198$	−1.70228e10	−0.787114
$199$	1.34261e10	0.606891	0.303445	−	0.952849i	$-0.401863\pi$
$199$	1.34261e10	0.606891	0.303445	+	0.952849i	$0.401863\pi$
$200$	6.71549e9	0.296786
$201$	9.22407e8	0.0398603
$202$	−1.93442e10	−0.817467
$203$	0	0
$204$	−9.61843e6	−0.000388838 0
$205$	1.22691e10	0.485200
$206$	1.10490e10	0.427485
$207$	5.22610e9	0.197839
$208$	7.41684e9	0.274748
$209$	1.39213e10	0.504686
$210$	0	0
$211$	3.01702e10	1.04787	0.523935	−	0.851759i	$-0.324464\pi$
$211$	3.01702e10	1.04787	0.523935	+	0.851759i	$0.324464\pi$
$212$	4.15263e9	0.141193
$213$	1.67794e9	0.0558556
$214$	−2.87199e9	−0.0936097
$215$	−1.54115e10	−0.491895
$216$	9.66574e8	0.0302130
$217$	0	0
$218$	2.56577e10	0.769421
$219$	2.42414e9	0.0712129
$220$	7.76323e9	0.223429
$221$	−7.08683e8	−0.0199842
$222$	1.14684e9	0.0316894
$223$	−5.35030e10	−1.44879	−0.724396	−	0.689384i	$-0.757881\pi$
$223$	−5.35030e10	−1.44879	−0.724396	+	0.689384i	$0.757881\pi$
$224$	0	0
$225$	3.22117e10	0.837901
$226$	−2.28456e10	−0.582525
$227$	4.02704e10	1.00663	0.503315	−	0.864103i	$-0.332114\pi$
$227$	4.02704e10	1.00663	0.503315	+	0.864103i	$0.332114\pi$
$228$	−3.94872e8	−0.00967719
$229$	−1.90247e10	−0.457150	−0.228575	−	0.973526i	$-0.573407\pi$
$229$	−1.90247e10	−0.457150	−0.228575	+	0.973526i	$0.573407\pi$
$230$	−2.38336e9	−0.0561584
$231$	0	0
$232$	−6.45003e9	−0.146173
$233$	−3.67748e10	−0.817426	−0.408713	−	0.912663i	$-0.634022\pi$
$233$	−3.67748e10	−0.817426	−0.408713	+	0.912663i	$0.634022\pi$
$234$	3.55758e10	0.775682
$235$	2.96396e10	0.633967
$236$	3.59705e10	0.754818
$237$	−7.84139e8	−0.0161445
$238$	0	0
$239$	6.56110e9	0.130073	0.0650363	−	0.997883i	$-0.479284\pi$
$239$	6.56110e9	0.130073	0.0650363	+	0.997883i	$0.479284\pi$
$240$	−2.20201e8	−0.00428419
$241$	8.96818e10	1.71249	0.856244	−	0.516572i	$-0.172792\pi$
$241$	8.96818e10	1.71249	0.856244	+	0.516572i	$0.172792\pi$
$242$	−9.19186e9	−0.172280
$243$	6.95657e9	0.127987
$244$	5.19587e10	0.938434
$245$	0	0
$246$	2.10328e9	0.0366175
$247$	−2.90940e10	−0.497356
$248$	−1.89951e10	−0.318867
$249$	−2.52080e9	−0.0415568
$250$	−3.21901e10	−0.521186
$251$	−5.33703e9	−0.0848727	−0.0424363	−	0.999099i	$-0.513512\pi$
$251$	−5.33703e9	−0.0848727	−0.0424363	+	0.999099i	$0.513512\pi$
$252$	0	0
$253$	1.44044e10	0.221031
$254$	3.77396e10	0.568913
$255$	2.10403e7	0.000311617 0
$256$	4.29497e9	0.0625000
$257$	8.35575e10	1.19478	0.597388	−	0.801952i	$-0.296205\pi$
$257$	8.35575e10	1.19478	0.597388	+	0.801952i	$0.296205\pi$
$258$	−2.64198e9	−0.0371228
$259$	0	0
$260$	−1.62243e10	−0.220185
$261$	−3.09384e10	−0.412682
$262$	9.62665e9	0.126217
$263$	1.08635e11	1.40013	0.700065	−	0.714079i	$-0.253154\pi$
$263$	1.08635e11	1.40013	0.700065	+	0.714079i	$0.253154\pi$
$264$	1.33084e9	0.0168620
$265$	−9.08388e9	−0.113153
$266$	0	0
$267$	2.81725e9	0.0339254
$268$	3.93561e10	0.466020
$269$	−1.41401e11	−1.64652	−0.823258	−	0.567668i	$-0.807846\pi$
$269$	−1.41401e11	−1.64652	−0.823258	+	0.567668i	$0.807846\pi$
$270$	−2.11438e9	−0.0242129
$271$	9.08353e10	1.02304	0.511520	−	0.859271i	$-0.329083\pi$
$271$	9.08353e10	1.02304	0.511520	+	0.859271i	$0.329083\pi$
$272$	−4.10386e8	−0.00454604
$273$	0	0
$274$	8.25614e10	0.884911
$275$	8.87836e10	0.936128
$276$	−4.08576e8	−0.00423821
$277$	−2.65075e10	−0.270527	−0.135263	−	0.990810i	$-0.543188\pi$
$277$	−2.65075e10	−0.270527	−0.135263	+	0.990810i	$0.543188\pi$
$278$	−1.14297e11	−1.14771
$279$	−9.11126e10	−0.900243
$280$	0	0
$281$	−1.86968e11	−1.78891	−0.894455	−	0.447158i	$-0.852436\pi$
$281$	−1.86968e11	−1.78891	−0.894455	+	0.447158i	$0.852436\pi$
$282$	5.08107e9	0.0478448
$283$	5.33413e9	0.0494338	0.0247169	−	0.999694i	$-0.492132\pi$
$283$	5.33413e9	0.0494338	0.0247169	+	0.999694i	$0.492132\pi$
$284$	7.15919e10	0.653028
$285$	8.63782e8	0.00775537
$286$	9.80558e10	0.866615
$287$	0	0
$288$	2.06014e10	0.176453
$289$	−1.18549e11	−0.999669
$290$	1.41094e10	0.117144
$291$	5.23501e9	0.0427956
$292$	1.03430e11	0.832574
$293$	−7.65433e10	−0.606741	−0.303370	−	0.952873i	$-0.598112\pi$
$293$	−7.65433e10	−0.606741	−0.303370	+	0.952873i	$0.598112\pi$
$294$	0	0
$295$	−7.86854e10	−0.604916
$296$	4.89318e10	0.370492
$297$	1.27788e10	0.0952984
$298$	−1.45668e11	−1.07002
$299$	−3.01038e10	−0.217821
$300$	−2.51831e9	−0.0179500
$301$	0	0
$302$	4.63091e9	0.0320358
$303$	7.25409e9	0.0494414
$304$	−1.68479e10	−0.113139
$305$	−1.13660e11	−0.752068
$306$	−1.96847e9	−0.0128346
$307$	7.51944e10	0.483128	0.241564	−	0.970385i	$-0.422340\pi$
$307$	7.51944e10	0.483128	0.241564	+	0.970385i	$0.422340\pi$
$308$	0	0
$309$	−4.14338e9	−0.0258548
$310$	4.15519e10	0.255542
$311$	−2.15134e11	−1.30403	−0.652014	−	0.758207i	$-0.726076\pi$
$311$	−2.15134e11	−1.30403	−0.652014	+	0.758207i	$0.726076\pi$
$312$	−2.78132e9	−0.0166171
$313$	−9.59075e10	−0.564811	−0.282405	−	0.959295i	$-0.591132\pi$
$313$	−9.59075e10	−0.564811	−0.282405	+	0.959295i	$0.591132\pi$
$314$	2.22508e11	1.29170
$315$	0	0
$316$	−3.34566e10	−0.188751
$317$	1.70586e11	0.948807	0.474403	−	0.880308i	$-0.342664\pi$
$317$	1.70586e11	0.948807	0.474403	+	0.880308i	$0.342664\pi$
$318$	−1.55724e9	−0.00853951
$319$	−8.52739e10	−0.461061
$320$	−9.39524e9	−0.0500879
$321$	1.07700e9	0.00566163
$322$	0	0
$323$	1.60982e9	0.00822937
$324$	9.86358e10	0.497258
$325$	−1.85548e11	−0.922533
$326$	−2.65972e11	−1.30424
$327$	−9.62165e9	−0.0465355
$328$	8.97398e10	0.428107
$329$	0	0
$330$	−2.91121e9	−0.0135133
$331$	−1.23992e11	−0.567762	−0.283881	−	0.958859i	$-0.591622\pi$
$331$	−1.23992e11	−0.567762	−0.283881	+	0.958859i	$0.591622\pi$
$332$	−1.07554e11	−0.485855
$333$	2.34708e11	1.04599
$334$	−2.52831e11	−1.11166
$335$	−8.60914e10	−0.373472
$336$	0	0
$337$	−7.29335e10	−0.308030	−0.154015	−	0.988069i	$-0.549220\pi$
$337$	−7.29335e10	−0.308030	−0.154015	+	0.988069i	$0.549220\pi$
$338$	−3.52544e10	−0.146923
$339$	8.56710e9	0.0352318
$340$	8.97720e8	0.00364322
$341$	−2.51129e11	−1.00578
$342$	−8.08130e10	−0.319421
$343$	0	0
$344$	−1.12724e11	−0.434015
$345$	8.93760e8	0.00339653
$346$	5.17000e10	0.193931
$347$	−1.55720e11	−0.576584	−0.288292	−	0.957542i	$-0.593087\pi$
$347$	−1.55720e11	−0.576584	−0.288292	+	0.957542i	$0.593087\pi$
$348$	2.41876e9	0.00884069
$349$	−1.08728e11	−0.392310	−0.196155	−	0.980573i	$-0.562846\pi$
$349$	−1.08728e11	−0.392310	−0.196155	+	0.980573i	$0.562846\pi$
$350$	0	0
$351$	−2.67063e10	−0.0939144
$352$	5.67825e10	0.197139
$353$	−3.25585e11	−1.11604	−0.558018	−	0.829829i	$-0.688438\pi$
$353$	−3.25585e11	−1.11604	−0.558018	+	0.829829i	$0.688438\pi$
$354$	−1.34889e10	−0.0456523
$355$	−1.56607e11	−0.523341
$356$	1.20203e11	0.396634
$357$	0	0
$358$	3.86252e11	1.24279
$359$	−2.27550e11	−0.723022	−0.361511	−	0.932368i	$-0.617739\pi$
$359$	−2.27550e11	−0.723022	−0.361511	+	0.932368i	$0.617739\pi$
$360$	−4.50655e10	−0.141411
$361$	−2.56599e11	−0.795192
$362$	−6.22931e10	−0.190656
$363$	3.44695e9	0.0104197
$364$	0	0
$365$	−2.26253e11	−0.667231
$366$	−1.94845e10	−0.0567577
$367$	4.21993e11	1.21425	0.607125	−	0.794607i	$-0.292323\pi$
$367$	4.21993e11	1.21425	0.607125	+	0.794607i	$0.292323\pi$
$368$	−1.74326e10	−0.0495503
$369$	4.30449e11	1.20866
$370$	−1.07038e11	−0.296915
$371$	0	0
$372$	7.12318e9	0.0192855
$373$	3.83283e11	1.02525	0.512625	−	0.858613i	$-0.328673\pi$
$373$	3.83283e11	1.02525	0.512625	+	0.858613i	$0.328673\pi$
$374$	−5.42560e9	−0.0143392
$375$	1.20713e10	0.0315220
$376$	2.16792e11	0.559370
$377$	1.78214e11	0.454365
$378$	0	0
$379$	−1.21462e11	−0.302386	−0.151193	−	0.988504i	$-0.548312\pi$
$379$	−1.21462e11	−0.302386	−0.151193	+	0.988504i	$0.548312\pi$
$380$	3.68547e10	0.0906706
$381$	−1.41524e10	−0.0344086
$382$	4.14381e11	0.995667
$383$	3.97721e11	0.944461	0.472230	−	0.881475i	$-0.343449\pi$
$383$	3.97721e11	0.944461	0.472230	+	0.881475i	$0.343449\pi$
$384$	−1.61061e9	−0.00378008
$385$	0	0
$386$	−2.54988e11	−0.584624
$387$	−5.40697e11	−1.22533
$388$	2.23360e11	0.500338
$389$	6.75462e10	0.149564	0.0747821	−	0.997200i	$-0.476174\pi$
$389$	6.75462e10	0.149564	0.0747821	+	0.997200i	$0.476174\pi$
$390$	6.08413e9	0.0133170
$391$	1.66569e9	0.00360412
$392$	0	0
$393$	−3.60999e9	−0.00763378
$394$	5.35495e10	0.111950
$395$	7.31863e10	0.151267
$396$	2.72365e11	0.556573
$397$	−1.24656e11	−0.251857	−0.125929	−	0.992039i	$-0.540191\pi$
$397$	−1.24656e11	−0.251857	−0.125929	+	0.992039i	$0.540191\pi$
$398$	−2.14817e11	−0.429136
$399$	0	0
$400$	−1.07448e11	−0.209859
$401$	3.51196e11	0.678265	0.339133	−	0.940739i	$-0.389866\pi$
$401$	3.51196e11	0.678265	0.339133	+	0.940739i	$0.389866\pi$
$402$	−1.47585e10	−0.0281855
$403$	5.24833e11	0.991171
$404$	3.09508e11	0.578037
$405$	−2.15766e11	−0.398506
$406$	0	0
$407$	6.46913e11	1.16861
$408$	1.53895e8	0.000274950 0
$409$	3.81956e10	0.0674930	0.0337465	−	0.999430i	$-0.489256\pi$
$409$	3.81956e10	0.0674930	0.0337465	+	0.999430i	$0.489256\pi$
$410$	−1.96306e11	−0.343088
$411$	−3.09605e10	−0.0535205
$412$	−1.76784e11	−0.302277
$413$	0	0
$414$	−8.36176e10	−0.139893
$415$	2.35275e11	0.389367
$416$	−1.18669e11	−0.194276
$417$	4.28614e10	0.0694151
$418$	−2.22741e11	−0.356867
$419$	−2.15268e11	−0.341205	−0.170603	−	0.985340i	$-0.554571\pi$
$419$	−2.15268e11	−0.341205	−0.170603	+	0.985340i	$0.554571\pi$
$420$	0	0
$421$	1.19933e12	1.86066	0.930332	−	0.366718i	$-0.119519\pi$
$421$	1.19933e12	1.86066	0.930332	+	0.366718i	$0.119519\pi$
$422$	−4.82723e11	−0.740955
$423$	1.03987e12	1.57924
$424$	−6.64421e10	−0.0998383
$425$	1.02667e10	0.0152644
$426$	−2.68470e10	−0.0394959
$427$	0	0
$428$	4.59518e10	0.0661921
$429$	−3.67709e10	−0.0524140
$430$	2.46585e11	0.347823
$431$	7.91117e11	1.10432	0.552158	−	0.833740i	$-0.313805\pi$
$431$	7.91117e11	1.10432	0.552158	+	0.833740i	$0.313805\pi$
$432$	−1.54652e10	−0.0213638
$433$	1.15451e12	1.57834	0.789170	−	0.614174i	$-0.210511\pi$
$433$	1.15451e12	1.57834	0.789170	+	0.614174i	$0.210511\pi$
$434$	0	0
$435$	−5.29104e9	−0.00708499
$436$	−4.10524e11	−0.544063
$437$	6.83827e10	0.0896974
$438$	−3.87862e10	−0.0503551
$439$	2.12728e11	0.273360	0.136680	−	0.990615i	$-0.456357\pi$
$439$	2.12728e11	0.273360	0.136680	+	0.990615i	$0.456357\pi$
$440$	−1.24212e11	−0.157988
$441$	0	0
$442$	1.13389e10	0.0141310
$443$	−6.48300e10	−0.0799759	−0.0399880	−	0.999200i	$-0.512732\pi$
$443$	−6.48300e10	−0.0799759	−0.0399880	+	0.999200i	$0.512732\pi$
$444$	−1.83494e10	−0.0224078
$445$	−2.62944e11	−0.317865
$446$	8.56047e11	1.02445
$447$	5.46255e10	0.0647159
$448$	0	0
$449$	−1.08031e12	−1.25441	−0.627207	−	0.778853i	$-0.715802\pi$
$449$	−1.08031e12	−1.25441	−0.627207	+	0.778853i	$0.715802\pi$
$450$	−5.15388e11	−0.592486
$451$	1.18642e12	1.35035
$452$	3.65530e11	0.411908
$453$	−1.73659e9	−0.00193756
$454$	−6.44326e11	−0.711794
$455$	0	0
$456$	6.31795e9	0.00684281
$457$	−6.46725e10	−0.0693581	−0.0346790	−	0.999399i	$-0.511041\pi$
$457$	−6.46725e10	−0.0693581	−0.0346790	+	0.999399i	$0.511041\pi$
$458$	3.04395e11	0.323254
$459$	1.47771e9	0.00155393
$460$	3.81338e10	0.0397100
$461$	−4.29254e11	−0.442649	−0.221325	−	0.975200i	$-0.571038\pi$
$461$	−4.29254e11	−0.442649	−0.221325	+	0.975200i	$0.571038\pi$
$462$	0	0
$463$	1.61883e12	1.63715	0.818574	−	0.574401i	$-0.194765\pi$
$463$	1.61883e12	1.63715	0.818574	+	0.574401i	$0.194765\pi$
$464$	1.03200e11	0.103360
$465$	−1.55819e10	−0.0154555
$466$	5.88396e11	0.578007
$467$	−3.27321e11	−0.318455	−0.159228	−	0.987242i	$-0.550900\pi$
$467$	−3.27321e11	−0.318455	−0.159228	+	0.987242i	$0.550900\pi$
$468$	−5.69214e11	−0.548490
$469$	0	0
$470$	−4.74233e11	−0.448283
$471$	−8.34407e10	−0.0781239
$472$	−5.75527e11	−0.533737
$473$	−1.49030e12	−1.36898
$474$	1.25462e10	0.0114159
$475$	4.21486e11	0.379893
$476$	0	0
$477$	−3.18698e11	−0.281869
$478$	−1.04978e11	−0.0919752
$479$	−2.84811e11	−0.247199	−0.123600	−	0.992332i	$-0.539444\pi$
$479$	−2.84811e11	−0.247199	−0.123600	+	0.992332i	$0.539444\pi$
$480$	3.52322e9	0.00302938
$481$	−1.35198e12	−1.15164
$482$	−1.43491e12	−1.21091
$483$	0	0
$484$	1.47070e11	0.121820
$485$	−4.88601e11	−0.400974
$486$	−1.11305e11	−0.0905007
$487$	−7.14776e11	−0.575824	−0.287912	−	0.957657i	$-0.592961\pi$
$487$	−7.14776e11	−0.575824	−0.287912	+	0.957657i	$0.592961\pi$
$488$	−8.31339e11	−0.663573
$489$	9.97395e10	0.0788819
$490$	0	0
$491$	1.01506e12	0.788176	0.394088	−	0.919073i	$-0.371061\pi$
$491$	1.01506e12	0.788176	0.394088	+	0.919073i	$0.371061\pi$
$492$	−3.36524e10	−0.0258925
$493$	−9.86086e9	−0.00751802
$494$	4.65505e11	0.351684
$495$	−5.95798e11	−0.446042
$496$	3.03922e11	0.225473
$497$	0	0
$498$	4.03329e10	0.0293851
$499$	1.33412e12	0.963260	0.481630	−	0.876375i	$-0.340045\pi$
$499$	1.33412e12	0.963260	0.481630	+	0.876375i	$0.340045\pi$
$500$	5.15042e11	0.368534
$501$	9.48116e10	0.0672345
$502$	8.53925e10	0.0600140
$503$	5.68445e11	0.395943	0.197971	−	0.980208i	$-0.436565\pi$
$503$	5.68445e11	0.395943	0.197971	+	0.980208i	$0.436565\pi$
$504$	0	0
$505$	−6.77048e11	−0.463243
$506$	−2.30471e11	−0.156293
$507$	1.32204e10	0.00888606
$508$	−6.03834e11	−0.402282
$509$	−3.57173e11	−0.235857	−0.117928	−	0.993022i	$-0.537625\pi$
$509$	−3.57173e11	−0.235857	−0.117928	+	0.993022i	$0.537625\pi$
$510$	−3.36645e8	−0.000220347 0
$511$	0	0
$512$	−6.87195e10	−0.0441942
$513$	6.06653e10	0.0386734
$514$	−1.33692e12	−0.844834
$515$	3.86715e11	0.242247
$516$	4.22716e10	0.0262498
$517$	2.86615e12	1.76438
$518$	0	0
$519$	−1.93875e10	−0.0117292
$520$	2.59589e11	0.155694
$521$	−2.17972e12	−1.29608	−0.648040	−	0.761606i	$-0.724411\pi$
$521$	−2.17972e12	−1.29608	−0.648040	+	0.761606i	$0.724411\pi$
$522$	4.95014e11	0.291810
$523$	1.57081e12	0.918048	0.459024	−	0.888424i	$-0.348199\pi$
$523$	1.57081e12	0.918048	0.459024	+	0.888424i	$0.348199\pi$
$524$	−1.54026e11	−0.0892492
$525$	0	0
$526$	−1.73816e12	−0.990042
$527$	−2.90399e10	−0.0164001
$528$	−2.12934e10	−0.0119232
$529$	−1.73040e12	−0.960716
$530$	1.45342e11	0.0800111
$531$	−2.76059e12	−1.50687
$532$	0	0
$533$	−2.47950e12	−1.33074
$534$	−4.50761e10	−0.0239889
$535$	−1.00520e11	−0.0530468
$536$	−6.29697e11	−0.329526
$537$	−1.44845e11	−0.0751655
$538$	2.26241e12	1.16426
$539$	0	0
$540$	3.38301e10	0.0171211
$541$	2.24544e12	1.12697	0.563486	−	0.826126i	$-0.309460\pi$
$541$	2.24544e12	1.12697	0.563486	+	0.826126i	$0.309460\pi$
$542$	−1.45336e12	−0.723399
$543$	2.33599e10	0.0115311
$544$	6.56618e9	0.00321453
$545$	8.98021e11	0.436016
$546$	0	0
$547$	−3.86062e11	−0.184380	−0.0921899	−	0.995741i	$-0.529387\pi$
$547$	−3.86062e11	−0.184380	−0.0921899	+	0.995741i	$0.529387\pi$
$548$	−1.32098e12	−0.625726
$549$	−3.98763e12	−1.87344
$550$	−1.42054e12	−0.661943
$551$	−4.04824e11	−0.187105
$552$	6.53722e9	0.00299686
$553$	0	0
$554$	4.24120e11	0.191291
$555$	4.01394e10	0.0179578
$556$	1.82875e12	0.811556
$557$	−7.95102e11	−0.350005	−0.175003	−	0.984568i	$-0.555993\pi$
$557$	−7.95102e11	−0.350005	−0.175003	+	0.984568i	$0.555993\pi$
$558$	1.45780e12	0.636568
$559$	3.11456e12	1.34910
$560$	0	0
$561$	2.03460e9	0.000867253 0
$562$	2.99149e12	1.26495
$563$	2.13667e12	0.896292	0.448146	−	0.893960i	$-0.352084\pi$
$563$	2.13667e12	0.896292	0.448146	+	0.893960i	$0.352084\pi$
$564$	−8.12972e10	−0.0338314
$565$	−7.99596e11	−0.330105
$566$	−8.53460e10	−0.0349550
$567$	0	0
$568$	−1.14547e12	−0.461760
$569$	2.17461e12	0.869714	0.434857	−	0.900500i	$-0.356799\pi$
$569$	2.17461e12	0.869714	0.434857	+	0.900500i	$0.356799\pi$
$570$	−1.38205e10	−0.00548387
$571$	9.95075e11	0.391736	0.195868	−	0.980630i	$-0.437248\pi$
$571$	9.95075e11	0.391736	0.195868	+	0.980630i	$0.437248\pi$
$572$	−1.56889e12	−0.612790
$573$	−1.55393e11	−0.0602192
$574$	0	0
$575$	4.36114e11	0.166377
$576$	−3.29622e11	−0.124771
$577$	−4.30588e12	−1.61723	−0.808614	−	0.588340i	$-0.799782\pi$
$577$	−4.30588e12	−1.61723	−0.808614	+	0.588340i	$0.799782\pi$
$578$	1.89678e12	0.706873
$579$	9.56204e10	0.0353588
$580$	−2.25751e11	−0.0828331
$581$	0	0
$582$	−8.37602e10	−0.0302611
$583$	−8.78412e11	−0.314912
$584$	−1.65488e12	−0.588719
$585$	1.24515e12	0.439564
$586$	1.22469e12	0.429030
$587$	−5.05762e12	−1.75822	−0.879112	−	0.476615i	$-0.841864\pi$
$587$	−5.05762e12	−1.75822	−0.879112	+	0.476615i	$0.841864\pi$
$588$	0	0
$589$	−1.19220e12	−0.408158
$590$	1.25897e12	0.427740
$591$	−2.00811e10	−0.00677085
$592$	−7.82909e11	−0.261977
$593$	2.80300e12	0.930844	0.465422	−	0.885089i	$-0.345903\pi$
$593$	2.80300e12	0.930844	0.465422	+	0.885089i	$0.345903\pi$
$594$	−2.04461e11	−0.0673862
$595$	0	0
$596$	2.33069e12	0.756616
$597$	8.05565e10	0.0259547
$598$	4.81660e11	0.154023
$599$	3.20907e12	1.01849	0.509247	−	0.860620i	$-0.329924\pi$
$599$	3.20907e12	1.01849	0.509247	+	0.860620i	$0.329924\pi$
$600$	4.02930e10	0.0126925
$601$	−7.49502e11	−0.234335	−0.117168	−	0.993112i	$-0.537381\pi$
$601$	−7.49502e11	−0.234335	−0.117168	+	0.993112i	$0.537381\pi$
$602$	0	0
$603$	−3.02042e12	−0.930336
$604$	−7.40946e10	−0.0226527
$605$	−3.21715e11	−0.0976275
$606$	−1.16065e11	−0.0349604
$607$	1.74097e12	0.520526	0.260263	−	0.965538i	$-0.416191\pi$
$607$	1.74097e12	0.520526	0.260263	+	0.965538i	$0.416191\pi$
$608$	2.69566e11	0.0800016
$609$	0	0
$610$	1.81855e12	0.531792
$611$	−5.98995e12	−1.73875
$612$	3.14956e10	0.00907544
$613$	−4.03977e12	−1.15554	−0.577770	−	0.816200i	$-0.696077\pi$
$613$	−4.03977e12	−1.15554	−0.577770	+	0.816200i	$0.696077\pi$
$614$	−1.20311e12	−0.341623
$615$	7.36147e10	0.0207504
$616$	0	0
$617$	−2.93367e12	−0.814945	−0.407472	−	0.913218i	$-0.633590\pi$
$617$	−2.93367e12	−0.814945	−0.407472	+	0.913218i	$0.633590\pi$
$618$	6.62940e10	0.0182821
$619$	5.77691e12	1.58157	0.790784	−	0.612095i	$-0.209673\pi$
$619$	5.77691e12	1.58157	0.790784	+	0.612095i	$0.209673\pi$
$620$	−6.64830e11	−0.180696
$621$	6.27707e10	0.0169373
$622$	3.44214e12	0.922088
$623$	0	0
$624$	4.45010e10	0.0117500
$625$	2.07554e12	0.544091
$626$	1.53452e12	0.399381
$627$	8.35277e10	0.0215837
$628$	−3.56014e12	−0.913373
$629$	7.48073e10	0.0190553
$630$	0	0
$631$	3.99985e12	1.00441	0.502206	−	0.864748i	$-0.332522\pi$
$631$	3.99985e12	1.00441	0.502206	+	0.864748i	$0.332522\pi$
$632$	5.35305e11	0.133467
$633$	1.81021e11	0.0448139
$634$	−2.72938e12	−0.670908
$635$	1.32089e12	0.322392
$636$	2.49158e10	0.00603834
$637$	0	0
$638$	1.36438e12	0.326019
$639$	−5.49440e12	−1.30367
$640$	1.50324e11	0.0354175
$641$	4.68328e12	1.09569	0.547846	−	0.836579i	$-0.315448\pi$
$641$	4.68328e12	1.09569	0.547846	+	0.836579i	$0.315448\pi$
$642$	−1.72319e10	−0.00400338
$643$	1.54877e12	0.357304	0.178652	−	0.983912i	$-0.442826\pi$
$643$	1.54877e12	0.357304	0.178652	+	0.983912i	$0.442826\pi$
$644$	0	0
$645$	−9.24692e10	−0.0210367
$646$	−2.57572e10	−0.00581904
$647$	8.14493e12	1.82733	0.913667	−	0.406463i	$-0.133238\pi$
$647$	8.14493e12	1.82733	0.913667	+	0.406463i	$0.133238\pi$
$648$	−1.57817e12	−0.351615
$649$	−7.60888e12	−1.68352
$650$	2.96877e12	0.652329
$651$	0	0
$652$	4.25555e12	0.922235
$653$	−2.88925e12	−0.621836	−0.310918	−	0.950437i	$-0.600636\pi$
$653$	−2.88925e12	−0.621836	−0.310918	+	0.950437i	$0.600636\pi$
$654$	1.53946e11	0.0329056
$655$	3.36933e11	0.0715249
$656$	−1.43584e12	−0.302718
$657$	−7.93784e12	−1.66210
$658$	0	0
$659$	5.20255e12	1.07456	0.537281	−	0.843403i	$-0.319451\pi$
$659$	5.20255e12	1.07456	0.537281	+	0.843403i	$0.319451\pi$
$660$	4.65794e10	0.00955534
$661$	−2.88973e12	−0.588777	−0.294388	−	0.955686i	$-0.595116\pi$
$661$	−2.88973e12	−0.588777	−0.294388	+	0.955686i	$0.595116\pi$
$662$	1.98387e12	0.401469
$663$	−4.25210e9	−0.000854658 0
$664$	1.72087e12	0.343551
$665$	0	0
$666$	−3.75532e12	−0.739628
$667$	−4.18874e11	−0.0819440
$668$	4.04530e12	0.786061
$669$	−3.21018e11	−0.0619600
$670$	1.37746e12	0.264085
$671$	−1.09909e13	−2.09306
$672$	0	0
$673$	9.46362e12	1.77824	0.889119	−	0.457677i	$-0.151318\pi$
$673$	9.46362e12	1.77824	0.889119	+	0.457677i	$0.151318\pi$
$674$	1.16694e12	0.217810
$675$	3.86895e11	0.0717342
$676$	5.64071e11	0.103890
$677$	6.52268e12	1.19338	0.596688	−	0.802474i	$-0.296483\pi$
$677$	6.52268e12	1.19338	0.596688	+	0.802474i	$0.296483\pi$
$678$	−1.37074e11	−0.0249127
$679$	0	0
$680$	−1.43635e10	−0.00257615
$681$	2.41622e11	0.0430502
$682$	4.01806e12	0.711193
$683$	5.37240e12	0.944660	0.472330	−	0.881422i	$-0.343413\pi$
$683$	5.37240e12	0.944660	0.472330	+	0.881422i	$0.343413\pi$
$684$	1.29301e12	0.225865
$685$	2.88965e12	0.501461
$686$	0	0
$687$	−1.14148e11	−0.0195508
$688$	1.80359e12	0.306895
$689$	1.83579e12	0.310339
$690$	−1.43002e10	−0.00240171
$691$	−2.01563e12	−0.336325	−0.168163	−	0.985759i	$-0.553783\pi$
$691$	−2.01563e12	−0.336325	−0.168163	+	0.985759i	$0.553783\pi$
$692$	−8.27200e11	−0.137130
$693$	0	0
$694$	2.49153e12	0.407707
$695$	−4.00040e12	−0.650386
$696$	−3.87002e10	−0.00625131
$697$	1.37195e11	0.0220186
$698$	1.73966e12	0.277405
$699$	−2.20649e11	−0.0349586
$700$	0	0
$701$	−1.06523e13	−1.66614	−0.833068	−	0.553171i	$-0.813418\pi$
$701$	−1.06523e13	−1.66614	−0.833068	+	0.553171i	$0.813418\pi$
$702$	4.27301e11	0.0664075
$703$	3.07111e12	0.474239
$704$	−9.08520e11	−0.139398
$705$	1.77838e11	0.0271127
$706$	5.20936e12	0.789157
$707$	0	0
$708$	2.15823e11	0.0322810
$709$	3.46187e12	0.514520	0.257260	−	0.966342i	$-0.417180\pi$
$709$	3.46187e12	0.514520	0.257260	+	0.966342i	$0.417180\pi$
$710$	2.50572e12	0.370058
$711$	2.56766e12	0.376812
$712$	−1.92325e12	−0.280462
$713$	−1.23357e12	−0.178756
$714$	0	0
$715$	3.43195e12	0.491094
$716$	−6.18004e12	−0.878785
$717$	3.93666e10	0.00556277
$718$	3.64080e12	0.511253
$719$	9.62025e12	1.34248	0.671238	−	0.741242i	$-0.265763\pi$
$719$	9.62025e12	1.34248	0.671238	+	0.741242i	$0.265763\pi$
$720$	7.21048e11	0.0999926
$721$	0	0
$722$	4.10558e12	0.562285
$723$	5.38091e11	0.0732374
$724$	9.96689e11	0.134814
$725$	−2.58178e12	−0.347055
$726$	−5.51512e10	−0.00736784
$727$	3.13479e12	0.416202	0.208101	−	0.978107i	$-0.433272\pi$
$727$	3.13479e12	0.416202	0.208101	+	0.978107i	$0.433272\pi$
$728$	0	0
$729$	−7.54204e12	−0.989043
$730$	3.62004e12	0.471803
$731$	−1.72334e11	−0.0223225
$732$	3.11752e11	0.0401337
$733$	−6.47775e12	−0.828812	−0.414406	−	0.910092i	$-0.636011\pi$
$733$	−6.47775e12	−0.828812	−0.414406	+	0.910092i	$0.636011\pi$
$734$	−6.75189e12	−0.858604
$735$	0	0
$736$	2.78921e11	0.0350374
$737$	−8.32503e12	−1.03940
$738$	−6.88718e12	−0.854649
$739$	−1.12510e12	−0.138769	−0.0693843	−	0.997590i	$-0.522103\pi$
$739$	−1.12510e12	−0.138769	−0.0693843	+	0.997590i	$0.522103\pi$
$740$	1.71261e12	0.209950
$741$	−1.74564e11	−0.0212703
$742$	0	0
$743$	1.65266e12	0.198945	0.0994725	−	0.995040i	$-0.468284\pi$
$743$	1.65266e12	0.198945	0.0994725	+	0.995040i	$0.468284\pi$
$744$	−1.13971e11	−0.0136369
$745$	−5.09838e12	−0.606357
$746$	−6.13253e12	−0.724961
$747$	8.25437e12	0.969932
$748$	8.68096e10	0.0101394
$749$	0	0
$750$	−1.93141e11	−0.0222894
$751$	6.03299e12	0.692074	0.346037	−	0.938221i	$-0.387527\pi$
$751$	6.03299e12	0.692074	0.346037	+	0.938221i	$0.387527\pi$
$752$	−3.46868e12	−0.395534
$753$	−3.20222e10	−0.00362972
$754$	−2.85142e12	−0.321284
$755$	1.62082e11	0.0181540
$756$	0	0
$757$	−8.02798e12	−0.888535	−0.444268	−	0.895894i	$-0.646536\pi$
$757$	−8.02798e12	−0.888535	−0.444268	+	0.895894i	$0.646536\pi$
$758$	1.94338e12	0.213820
$759$	8.64266e10	0.00945278
$760$	−5.89675e11	−0.0641138
$761$	6.51923e12	0.704637	0.352318	−	0.935880i	$-0.385393\pi$
$761$	6.51923e12	0.704637	0.352318	+	0.935880i	$0.385393\pi$
$762$	2.26438e11	0.0243305
$763$	0	0
$764$	−6.63009e12	−0.704043
$765$	−6.88965e10	−0.00727312
$766$	−6.36354e12	−0.667835
$767$	1.59018e13	1.65907
$768$	2.57698e10	0.00267292
$769$	1.34250e13	1.38435	0.692175	−	0.721730i	$-0.256653\pi$
$769$	1.34250e13	1.38435	0.692175	+	0.721730i	$0.256653\pi$
$770$	0	0
$771$	5.01345e11	0.0510966
$772$	4.07980e12	0.413391
$773$	−7.85934e12	−0.791733	−0.395866	−	0.918308i	$-0.629556\pi$
$773$	−7.85934e12	−0.791733	−0.395866	+	0.918308i	$0.629556\pi$
$774$	8.65115e12	0.866442
$775$	−7.60327e12	−0.757082
$776$	−3.57377e12	−0.353792
$777$	0	0
$778$	−1.08074e12	−0.105758
$779$	5.63235e12	0.547988
$780$	−9.73460e10	−0.00941657
$781$	−1.51439e13	−1.45649
$782$	−2.66511e10	−0.00254850
$783$	−3.71601e11	−0.0353304
$784$	0	0
$785$	7.78780e12	0.731983
$786$	5.77599e10	0.00539790
$787$	1.47720e12	0.137263	0.0686316	−	0.997642i	$-0.478137\pi$
$787$	1.47720e12	0.137263	0.0686316	+	0.997642i	$0.478137\pi$
$788$	−8.56793e11	−0.0791604
$789$	6.51809e11	0.0598789
$790$	−1.17098e12	−0.106962
$791$	0	0
$792$	−4.35783e12	−0.393557
$793$	2.29698e13	2.06266
$794$	1.99449e12	0.178090
$795$	−5.45033e10	−0.00483917
$796$	3.43708e12	0.303445
$797$	6.47327e12	0.568278	0.284139	−	0.958783i	$-0.408292\pi$
$797$	6.47327e12	0.568278	0.284139	+	0.958783i	$0.408292\pi$
$798$	0	0
$799$	3.31434e11	0.0287698
$800$	1.71917e12	0.148393
$801$	−9.22510e12	−0.791817
$802$	−5.61913e12	−0.479606
$803$	−2.18786e13	−1.85695
$804$	2.36136e11	0.0199301
$805$	0	0
$806$	−8.39733e12	−0.700864
$807$	−8.48403e11	−0.0704160
$808$	−4.95212e12	−0.408734
$809$	−1.53631e13	−1.26099	−0.630493	−	0.776195i	$-0.717147\pi$
$809$	−1.53631e13	−1.26099	−0.630493	+	0.776195i	$0.717147\pi$
$810$	3.45225e12	0.281786
$811$	1.29056e13	1.04757	0.523787	−	0.851849i	$-0.324519\pi$
$811$	1.29056e13	1.04757	0.523787	+	0.851849i	$0.324519\pi$
$812$	0	0
$813$	5.45012e11	0.0437520
$814$	−1.03506e13	−0.826334
$815$	−9.30902e12	−0.739085
$816$	−2.46232e9	−0.000194419 0
$817$	−7.07494e12	−0.555550
$818$	−6.11130e11	−0.0477247
$819$	0	0
$820$	3.14089e12	0.242600
$821$	8.93771e11	0.0686566	0.0343283	−	0.999411i	$-0.489071\pi$
$821$	8.93771e11	0.0686566	0.0343283	+	0.999411i	$0.489071\pi$
$822$	4.95368e11	0.0378447
$823$	−2.29844e13	−1.74636	−0.873182	−	0.487394i	$-0.837947\pi$
$823$	−2.29844e13	−1.74636	−0.873182	+	0.487394i	$0.837947\pi$
$824$	2.82854e12	0.213742
$825$	5.32701e11	0.0400351
$826$	0	0
$827$	−2.75618e12	−0.204896	−0.102448	−	0.994738i	$-0.532667\pi$
$827$	−2.75618e12	−0.204896	−0.102448	+	0.994738i	$0.532667\pi$
$828$	1.33788e12	0.0989194
$829$	3.15925e12	0.232321	0.116160	−	0.993230i	$-0.462941\pi$
$829$	3.15925e12	0.232321	0.116160	+	0.993230i	$0.462941\pi$
$830$	−3.76440e12	−0.275324
$831$	−1.59045e11	−0.0115695
$832$	1.89871e12	0.137374
$833$	0	0
$834$	−6.85782e11	−0.0490839
$835$	−8.84909e12	−0.629955
$836$	3.56385e12	0.252343
$837$	−1.09435e12	−0.0770714
$838$	3.44428e12	0.241269
$839$	−1.92403e13	−1.34055	−0.670277	−	0.742111i	$-0.733825\pi$
$839$	−1.92403e13	−1.34055	−0.670277	+	0.742111i	$0.733825\pi$
$840$	0	0
$841$	−1.20274e13	−0.829069
$842$	−1.91892e13	−1.31569
$843$	−1.12181e12	−0.0765058
$844$	7.72357e12	0.523935
$845$	−1.23391e12	−0.0832581
$846$	−1.66380e13	−1.11669
$847$	0	0
$848$	1.06307e12	0.0705963
$849$	3.20048e10	0.00211412
$850$	−1.64267e11	−0.0107936
$851$	3.17770e12	0.207697
$852$	4.29552e11	0.0279278
$853$	2.60804e13	1.68672	0.843362	−	0.537345i	$-0.180573\pi$
$853$	2.60804e13	1.68672	0.843362	+	0.537345i	$0.180573\pi$
$854$	0	0
$855$	−2.82845e12	−0.181010
$856$	−7.35229e11	−0.0468049
$857$	−2.19177e13	−1.38797	−0.693986	−	0.719988i	$-0.744147\pi$
$857$	−2.19177e13	−1.38797	−0.693986	+	0.719988i	$0.744147\pi$
$858$	5.88335e11	0.0370623
$859$	3.55588e12	0.222832	0.111416	−	0.993774i	$-0.464461\pi$
$859$	3.55588e12	0.222832	0.111416	+	0.993774i	$0.464461\pi$
$860$	−3.94535e12	−0.245948
$861$	0	0
$862$	−1.26579e13	−0.780869
$863$	2.22084e13	1.36292	0.681458	−	0.731858i	$-0.261346\pi$
$863$	2.22084e13	1.36292	0.681458	+	0.731858i	$0.261346\pi$
$864$	2.47443e11	0.0151065
$865$	1.80950e12	0.109897
$866$	−1.84721e13	−1.11606
$867$	−7.11292e11	−0.0427525
$868$	0	0
$869$	7.07711e12	0.420986
$870$	8.46566e10	0.00500985
$871$	1.73984e13	1.02430
$872$	6.56838e12	0.384711
$873$	−1.71420e13	−0.998846
$874$	−1.09412e12	−0.0634257
$875$	0	0
$876$	6.20579e11	0.0356064
$877$	3.38004e12	0.192941	0.0964703	−	0.995336i	$-0.469245\pi$
$877$	3.38004e12	0.192941	0.0964703	+	0.995336i	$0.469245\pi$
$878$	−3.40365e12	−0.193295
$879$	−4.59260e11	−0.0259483
$880$	1.98739e12	0.111715
$881$	−5.25103e11	−0.0293665	−0.0146833	−	0.999892i	$-0.504674\pi$
$881$	−5.25103e11	−0.0293665	−0.0146833	+	0.999892i	$0.504674\pi$
$882$	0	0
$883$	3.33972e13	1.84879	0.924393	−	0.381441i	$-0.124572\pi$
$883$	3.33972e13	1.84879	0.924393	+	0.381441i	$0.124572\pi$
$884$	−1.81423e11	−0.00999210
$885$	−4.72112e11	−0.0258702
$886$	1.03728e12	0.0565515
$887$	9.61964e12	0.521798	0.260899	−	0.965366i	$-0.415981\pi$
$887$	9.61964e12	0.521798	0.260899	+	0.965366i	$0.415981\pi$
$888$	2.93591e11	0.0158447
$889$	0	0
$890$	4.20710e12	0.224765
$891$	−2.08646e13	−1.10907
$892$	−1.36968e13	−0.724396
$893$	1.36066e13	0.716007
$894$	−8.74007e11	−0.0457611
$895$	1.35188e13	0.704264
$896$	0	0
$897$	−1.80623e11	−0.00931549
$898$	1.72850e13	0.887004
$899$	7.30271e12	0.372877
$900$	8.24621e12	0.418951
$901$	−1.01577e11	−0.00513494
$902$	−1.89828e13	−0.954839
$903$	0	0
$904$	−5.84848e12	−0.291263
$905$	−2.18026e12	−0.108041
$906$	2.77855e10	0.00137006
$907$	−2.08341e13	−1.02221	−0.511107	−	0.859517i	$-0.670764\pi$
$907$	−2.08341e13	−1.02221	−0.511107	+	0.859517i	$0.670764\pi$
$908$	1.03092e13	0.503315
$909$	−2.37535e13	−1.15396
$910$	0	0
$911$	−1.33789e13	−0.643560	−0.321780	−	0.946814i	$-0.604281\pi$
$911$	−1.33789e13	−0.643560	−0.321780	+	0.946814i	$0.604281\pi$
$912$	−1.01087e11	−0.00483860
$913$	2.27511e13	1.08364
$914$	1.03476e12	0.0490436
$915$	−6.81958e11	−0.0321634
$916$	−4.87033e12	−0.228575
$917$	0	0
$918$	−2.36433e10	−0.00109879
$919$	−1.38352e13	−0.639830	−0.319915	−	0.947446i	$-0.603654\pi$
$919$	−1.38352e13	−0.639830	−0.319915	+	0.947446i	$0.603654\pi$
$920$	−6.10140e11	−0.0280792
$921$	4.51166e11	0.0206618
$922$	6.86806e12	0.313000
$923$	3.16492e13	1.43534
$924$	0	0
$925$	1.95862e13	0.879653
$926$	−2.59013e13	−1.15764
$927$	1.35675e13	0.603449
$928$	−1.65121e12	−0.0730863
$929$	1.74073e13	0.766761	0.383380	−	0.923591i	$-0.374760\pi$
$929$	1.74073e13	0.766761	0.383380	+	0.923591i	$0.374760\pi$
$930$	2.49311e11	0.0109287
$931$	0	0
$932$	−9.41434e12	−0.408713
$933$	−1.29080e12	−0.0557690
$934$	5.23714e12	0.225182
$935$	−1.89896e11	−0.00812575
$936$	9.10742e12	0.387841
$937$	−1.98361e12	−0.0840676	−0.0420338	−	0.999116i	$-0.513384\pi$
$937$	−1.98361e12	−0.0840676	−0.0420338	+	0.999116i	$0.513384\pi$
$938$	0	0
$939$	−5.75445e11	−0.0241551
$940$	7.58773e12	0.316984
$941$	2.33533e13	0.970946	0.485473	−	0.874252i	$-0.338647\pi$
$941$	2.33533e13	0.970946	0.485473	+	0.874252i	$0.338647\pi$
$942$	1.33505e12	0.0552419
$943$	5.82783e12	0.239996
$944$	9.20844e12	0.377409
$945$	0	0
$946$	2.38447e13	0.968015
$947$	3.59882e13	1.45407	0.727035	−	0.686600i	$-0.240898\pi$
$947$	3.59882e13	1.45407	0.727035	+	0.686600i	$0.240898\pi$
$948$	−2.00740e11	−0.00807227
$949$	4.57241e13	1.82998
$950$	−6.74377e12	−0.268625
$951$	1.02352e12	0.0405773
$952$	0	0
$953$	−1.37662e13	−0.540624	−0.270312	−	0.962773i	$-0.587127\pi$
$953$	−1.37662e13	−0.540624	−0.270312	+	0.962773i	$0.587127\pi$
$954$	5.09917e12	0.199311
$955$	1.45033e13	0.564225
$956$	1.67964e12	0.0650363
$957$	−5.11643e11	−0.0197180
$958$	4.55698e12	0.174796
$959$	0	0
$960$	−5.63714e10	−0.00214209
$961$	−4.93336e12	−0.186590
$962$	2.16317e13	0.814334
$963$	−3.52662e12	−0.132142
$964$	2.29585e13	0.856244
$965$	−8.92457e12	−0.331295
$966$	0	0
$967$	−3.02718e12	−0.111332	−0.0556659	−	0.998449i	$-0.517728\pi$
$967$	−3.02718e12	−0.111332	−0.0556659	+	0.998449i	$0.517728\pi$
$968$	−2.35312e12	−0.0861399
$969$	9.65893e9	0.000351943 0
$970$	7.81762e12	0.283532
$971$	2.53183e13	0.914003	0.457002	−	0.889466i	$-0.348923\pi$
$971$	2.53183e13	0.914003	0.457002	+	0.889466i	$0.348923\pi$
$972$	1.78088e12	0.0639937
$973$	0	0
$974$	1.14364e13	0.407169
$975$	−1.11329e12	−0.0394537
$976$	1.33014e13	0.469217
$977$	9.90729e12	0.347880	0.173940	−	0.984756i	$-0.444350\pi$
$977$	9.90729e12	0.347880	0.173940	+	0.984756i	$0.444350\pi$
$978$	−1.59583e12	−0.0557779
$979$	−2.54267e13	−0.884641
$980$	0	0
$981$	3.15061e13	1.08614
$982$	−1.62409e13	−0.557325
$983$	−2.40523e13	−0.821610	−0.410805	−	0.911723i	$-0.634752\pi$
$983$	−2.40523e13	−0.821610	−0.410805	+	0.911723i	$0.634752\pi$
$984$	5.38439e11	0.0183087
$985$	1.87423e12	0.0634397
$986$	1.57774e11	0.00531604
$987$	0	0
$988$	−7.44807e12	−0.248678
$989$	−7.32048e12	−0.243308
$990$	9.53276e12	0.315399
$991$	3.15782e13	1.04005	0.520027	−	0.854150i	$-0.325922\pi$
$991$	3.15782e13	1.04005	0.520027	+	0.854150i	$0.325922\pi$
$992$	−4.86275e12	−0.159434
$993$	−7.43950e11	−0.0242813
$994$	0	0
$995$	−7.51860e12	−0.243183
$996$	−6.45326e11	−0.0207784
$997$	−9.32241e12	−0.298813	−0.149407	−	0.988776i	$-0.547736\pi$
$997$	−9.32241e12	−0.298813	−0.149407	+	0.988776i	$0.547736\pi$
$998$	−2.13460e13	−0.681128
$999$	2.81907e12	0.0895492

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.a.a.1.1		1
7.2	even	3		98.10.c.e.67.1		2
7.3	odd	6		98.10.c.f.79.1		2
7.4	even	3		98.10.c.e.79.1		2
7.5	odd	6		98.10.c.f.67.1		2
7.6	odd	2		14.10.a.a.1.1	✓	1
21.20	even	2		126.10.a.e.1.1		1
28.27	even	2		112.10.a.b.1.1		1
35.13	even	4		350.10.c.b.99.2		2
35.27	even	4		350.10.c.b.99.1		2
35.34	odd	2		350.10.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.a.a.1.1	✓	1	7.6	odd	2
98.10.a.a.1.1		1	1.1	even	1	trivial
98.10.c.e.67.1		2	7.2	even	3
98.10.c.e.79.1		2	7.4	even	3
98.10.c.f.67.1		2	7.5	odd	6
98.10.c.f.79.1		2	7.3	odd	6
112.10.a.b.1.1		1	28.27	even	2
126.10.a.e.1.1		1	21.20	even	2
350.10.a.c.1.1		1	35.34	odd	2
350.10.c.b.99.1		2	35.27	even	4
350.10.c.b.99.2		2	35.13	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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