LMFDB - Embedded newform 350.10.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,10,Mod(1,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("350.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	350.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:	$180.262542657$
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	$\chi$	$=$	350.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+16.0000 q^{2} +6.00000 q^{3} +256.000 q^{4} +96.0000 q^{6} +2401.00 q^{7} +4096.00 q^{8} -19647.0 q^{9} +O(q^{10})$

\(q+16.0000 q^{2} +6.00000 q^{3} +256.000 q^{4} +96.0000 q^{6} +2401.00 q^{7} +4096.00 q^{8} -19647.0 q^{9} -54152.0 q^{11} +1536.00 q^{12} +113172. q^{13} +38416.0 q^{14} +65536.0 q^{16} -6262.00 q^{17} -314352. q^{18} +257078. q^{19} +14406.0 q^{21} -866432. q^{22} +266000. q^{23} +24576.0 q^{24} +1.81075e6 q^{26} -235980. q^{27} +614656. q^{28} +1.57471e6 q^{29} -4.63748e6 q^{31} +1.04858e6 q^{32} -324912. q^{33} -100192. q^{34} -5.02963e6 q^{36} +1.19462e7 q^{37} +4.11325e6 q^{38} +679032. q^{39} +2.19091e7 q^{41} +230496. q^{42} -2.75206e7 q^{43} -1.38629e7 q^{44} +4.25600e6 q^{46} -5.29278e7 q^{47} +393216. q^{48} +5.76480e6 q^{49} -37572.0 q^{51} +2.89720e7 q^{52} -1.62212e7 q^{53} -3.77568e6 q^{54} +9.83450e6 q^{56} +1.54247e6 q^{57} +2.51954e7 q^{58} -1.40510e8 q^{59} -2.02964e8 q^{61} -7.41997e7 q^{62} -4.71724e7 q^{63} +1.67772e7 q^{64} -5.19859e6 q^{66} -1.53735e8 q^{67} -1.60307e6 q^{68} +1.59600e6 q^{69} +2.79656e8 q^{71} -8.04741e7 q^{72} +4.04023e8 q^{73} +1.91140e8 q^{74} +6.58120e7 q^{76} -1.30019e8 q^{77} +1.08645e7 q^{78} -1.30690e8 q^{79} +3.85296e8 q^{81} +3.50546e8 q^{82} -4.20134e8 q^{83} +3.68794e6 q^{84} -4.40329e8 q^{86} +9.44828e6 q^{87} -2.21807e8 q^{88} -4.69542e8 q^{89} +2.71726e8 q^{91} +6.80960e7 q^{92} -2.78249e7 q^{93} -8.46845e8 q^{94} +6.29146e6 q^{96} +8.72502e8 q^{97} +9.22368e7 q^{98} +1.06392e9 q^{99} +O(q^{100})\)

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 $

$2$	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
$5$	0	0
$5$	0	0
$6$	96.0000	0.0302406
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	4096.00	0.353553
$9$	−19647.0	−0.998171
$10$	0	0
$11$	−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	$0.314820\pi$
$14$	38416.0	0.267261
$15$	0	0
$16$	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	$-0.427344\pi$
$19$	257078.	0.452557	0.226279	+	0.974063i	$0.427344\pi$
$20$	0	0
$21$	14406.0	0.0161643
$22$	−866432.	−0.788556
$23$	266000.	0.198201	0.0991006	−	0.995077i	$-0.468403\pi$
$23$	266000.	0.198201	0.0991006	+	0.995077i	$0.468403\pi$
$24$	24576.0	0.0151203
$25$	0	0
$26$	1.81075e6	0.777104
$27$	−235980.	−0.0854552
$28$	614656.	0.188982
$29$	1.57471e6	0.413438	0.206719	−	0.978400i	$-0.433721\pi$
$29$	1.57471e6	0.413438	0.206719	+	0.978400i	$0.433721\pi$
$30$	0	0
$31$	−4.63748e6	−0.901893	−0.450946	−	0.892551i	$-0.648913\pi$
$31$	−4.63748e6	−0.901893	−0.450946	+	0.892551i	$0.648913\pi$
$32$	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	$-0.324456\pi$
$37$	1.19462e7	1.04791	0.523954	+	0.851746i	$0.324456\pi$
$38$	4.11325e6	0.320006
$39$	679032.	0.0470002
$40$	0	0
$41$	2.19091e7	1.21087	0.605435	−	0.795895i	$-0.292999\pi$
$41$	2.19091e7	1.21087	0.605435	+	0.795895i	$0.292999\pi$
$42$	230496.	0.0114299
$43$	−2.75206e7	−1.22758	−0.613790	−	0.789469i	$-0.710356\pi$
$43$	−2.75206e7	−1.22758	−0.613790	+	0.789469i	$0.710356\pi$
$44$	−1.38629e7	−0.557593
$45$	0	0
$46$	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
$49$	5.76480e6	0.142857
$50$	0	0
$51$	−37572.0	−0.000777676 0
$52$	2.89720e7	0.549495
$53$	−1.62212e7	−0.282385	−0.141193	−	0.989982i	$-0.545094\pi$
$53$	−1.62212e7	−0.282385	−0.141193	+	0.989982i	$0.545094\pi$
$54$	−3.77568e6	−0.0604259
$55$	0	0
$56$	9.83450e6	0.133631
$57$	1.54247e6	0.0193544
$58$	2.51954e7	0.292345
$59$	−1.40510e8	−1.50964	−0.754818	−	0.655935i	$-0.772275\pi$
$59$	−1.40510e8	−1.50964	−0.754818	+	0.655935i	$0.772275\pi$
$60$	0	0
$61$	−2.02964e8	−1.87687	−0.938434	−	0.345458i	$-0.887724\pi$
$61$	−2.02964e8	−1.87687	−0.938434	+	0.345458i	$0.887724\pi$
$62$	−7.41997e7	−0.637734
$63$	−4.71724e7	−0.377273
$64$	1.67772e7	0.125000
$65$	0	0
$66$	−5.19859e6	−0.0337239
$67$	−1.53735e8	−0.932041	−0.466020	−	0.884774i	$-0.654313\pi$
$67$	−1.53735e8	−0.932041	−0.466020	+	0.884774i	$0.654313\pi$
$68$	−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
$75$	0	0
$76$	6.58120e7	0.226279
$77$	−1.30019e8	−0.421501
$78$	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	$0.560444\pi$
$80$	0	0
$81$	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	$0.661492\pi$
$84$	3.68794e6	0.00808214
$85$	0	0
$86$	−4.40329e8	−0.868030
$87$	9.44828e6	0.0176814
$88$	−2.21807e8	−0.394278
$89$	−4.69542e8	−0.793268	−0.396634	−	0.917977i	$-0.629822\pi$
$89$	−4.69542e8	−0.793268	−0.396634	+	0.917977i	$0.629822\pi$
$90$	0	0
$91$	2.71726e8	0.415379
$92$	6.80960e7	0.0991006
$93$	−2.78249e7	−0.0385710
$94$	−8.46845e8	−1.11874
$95$	0	0
$96$	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	$0.333209\pi$
$98$	9.22368e7	0.101015
$99$	1.06392e9	1.11315
$100$	0	0
$101$	−1.20901e9	−1.15607	−0.578037	−	0.816011i	$-0.696181\pi$
$101$	−1.20901e9	−1.15607	−0.578037	+	0.816011i	$0.696181\pi$
$102$	−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	$-0.521085\pi$
$107$	−1.79499e8	−0.132384	−0.0661921	+	0.997807i	$0.521085\pi$
$108$	−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	$0.683115\pi$
$110$	0	0
$111$	7.16774e7	0.0448156
$112$	1.57352e8	0.0944911
$113$	−1.42785e9	−0.823815	−0.411908	−	0.911226i	$-0.635137\pi$
$113$	−1.42785e9	−0.823815	−0.411908	+	0.911226i	$0.635137\pi$
$114$	2.46795e7	0.0136856
$115$	0	0
$116$	4.03127e8	0.206719
$117$	−2.22349e9	−1.09698
$118$	−2.24815e9	−1.06747
$119$	−1.50351e7	−0.00687296
$120$	0	0
$121$	5.74491e8	0.243640
$122$	−3.24742e9	−1.32715
$123$	1.31455e8	0.0517849
$124$	−1.18720e9	−0.450946
$125$	0	0
$126$	−7.54759e8	−0.266772
$127$	2.35873e9	0.804565	0.402282	−	0.915516i	$-0.368217\pi$
$127$	2.35873e9	0.804565	0.402282	+	0.915516i	$0.368217\pi$
$128$	2.68435e8	0.0883883
$129$	−1.65124e8	−0.0524995
$130$	0	0
$131$	6.01665e8	0.178498	0.0892492	−	0.996009i	$-0.471553\pi$
$131$	6.01665e8	0.178498	0.0892492	+	0.996009i	$0.471553\pi$
$132$	−8.31775e7	−0.0238464
$133$	6.17244e8	0.171051
$134$	−2.45975e9	−0.659052
$135$	0	0
$136$	−2.56492e7	−0.00642907
$137$	5.16009e9	1.25145	0.625726	−	0.780043i	$-0.284803\pi$
$137$	5.16009e9	1.25145	0.625726	+	0.780043i	$0.284803\pi$
$138$	2.55360e7	0.00599373
$139$	−7.14356e9	−1.62311	−0.811556	−	0.584275i	$-0.801379\pi$
$139$	−7.14356e9	−1.62311	−0.811556	+	0.584275i	$0.801379\pi$
$140$	0	0
$141$	−3.17567e8	−0.0676627
$142$	4.47449e9	0.923520
$143$	−6.12849e9	−1.22558
$144$	−1.28759e9	−0.249543
$145$	0	0
$146$	6.46437e9	1.17744
$147$	3.45888e7	0.00610953
$148$	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	$0.226851\pi$
$150$	0	0
$151$	−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
$154$	−2.08030e9	−0.298046
$155$	0	0
$156$	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
$160$	0	0
$161$	6.38666e8	0.0749130
$162$	6.16474e9	0.703229
$163$	−1.66232e10	−1.84447	−0.922235	−	0.386629i	$-0.873639\pi$
$163$	−1.66232e10	−1.84447	−0.922235	+	0.386629i	$0.873639\pi$
$164$	5.60874e9	0.605435
$165$	0	0
$166$	−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	$0.212117\pi$
$168$	5.90070e7	0.00571494
$169$	2.20340e9	0.207780
$170$	0	0
$171$	−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	$0.841645\pi$
$180$	0	0
$181$	−3.89332e9	−0.269629	−0.134814	−	0.990871i	$-0.543044\pi$
$181$	−3.89332e9	−0.269629	−0.134814	+	0.990871i	$0.543044\pi$
$182$	4.34762e9	0.293718
$183$	−1.21778e9	−0.0802674
$184$	1.08954e9	0.0700747
$185$	0	0
$186$	−4.45198e8	−0.0272738
$187$	3.39100e8	0.0202787
$188$	−1.35495e10	−0.791068
$189$	−5.66588e8	−0.0322990
$190$	0	0
$191$	−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	$-0.635656\pi$
$193$	−1.59367e10	−0.826783	−0.413391	+	0.910553i	$0.635656\pi$
$194$	1.39600e10	0.707585
$195$	0	0
$196$	1.47579e9	0.0714286
$197$	3.34685e9	0.158321	0.0791604	−	0.996862i	$-0.474776\pi$
$197$	3.34685e9	0.158321	0.0791604	+	0.996862i	$0.474776\pi$
$198$	1.70228e10	0.787114
$199$	−1.34261e10	−0.606891	−0.303445	−	0.952849i	$-0.598137\pi$
$199$	−1.34261e10	−0.606891	−0.303445	+	0.952849i	$0.598137\pi$
$200$	0	0
$201$	−9.22407e8	−0.0398603
$202$	−1.93442e10	−0.817467
$203$	3.78089e9	0.156265
$204$	−9.61843e6	−0.000388838 0
$205$	0	0
$206$	−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
$215$	0	0
$216$	−9.66574e8	−0.0302130
$217$	−1.11346e10	−0.340883
$218$	−2.56577e10	−0.769421
$219$	2.42414e9	0.0712129
$220$	0	0
$221$	−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	$0.757881\pi$
$224$	2.51763e9	0.0668153
$225$	0	0
$226$	−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	$-0.426593\pi$
$229$	1.90247e10	0.457150	0.228575	+	0.973526i	$0.426593\pi$
$230$	0	0
$231$	−7.80114e8	−0.0180262
$232$	6.45003e9	0.146173
$233$	3.67748e10	0.817426	0.408713	−	0.912663i	$-0.365978\pi$
$233$	3.67748e10	0.817426	0.408713	+	0.912663i	$0.365978\pi$
$234$	−3.55758e10	−0.775682
$235$	0	0
$236$	−3.59705e10	−0.754818
$237$	−7.84139e8	−0.0161445
$238$	−2.40561e8	−0.00485992
$239$	6.56110e9	0.130073	0.0650363	−	0.997883i	$-0.479284\pi$
$239$	6.56110e9	0.130073	0.0650363	+	0.997883i	$0.479284\pi$
$240$	0	0
$241$	−8.96818e10	−1.71249	−0.856244	−	0.516572i	$-0.827208\pi$
$241$	−8.96818e10	−1.71249	−0.856244	+	0.516572i	$0.827208\pi$
$242$	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
$250$	0	0
$251$	5.33703e9	0.0848727	0.0424363	−	0.999099i	$-0.486488\pi$
$251$	5.33703e9	0.0848727	0.0424363	+	0.999099i	$0.486488\pi$
$252$	−1.20761e10	−0.188637
$253$	−1.44044e10	−0.221031
$254$	3.77396e10	0.568913
$255$	0	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
$259$	2.86829e10	0.396072
$260$	0	0
$261$	−3.09384e10	−0.412682
$262$	9.62665e9	0.126217
$263$	−1.08635e11	−1.40013	−0.700065	−	0.714079i	$-0.746846\pi$
$263$	−1.08635e11	−1.40013	−0.700065	+	0.714079i	$0.746846\pi$
$264$	−1.33084e9	−0.0168620
$265$	0	0
$266$	9.87591e9	0.120951
$267$	−2.81725e9	−0.0339254
$268$	−3.93561e10	−0.466020
$269$	1.41401e11	1.64652	0.823258	−	0.567668i	$-0.192154\pi$
$269$	1.41401e11	1.64652	0.823258	+	0.567668i	$0.192154\pi$
$270$	0	0
$271$	−9.08353e10	−1.02304	−0.511520	−	0.859271i	$-0.670917\pi$
$271$	−9.08353e10	−1.02304	−0.511520	+	0.859271i	$0.670917\pi$
$272$	−4.10386e8	−0.00454604
$273$	1.63036e9	0.0177644
$274$	8.25614e10	0.884911
$275$	0	0
$276$	4.08576e8	0.00423821
$277$	2.65075e10	0.270527	0.135263	−	0.990810i	$-0.456812\pi$
$277$	2.65075e10	0.270527	0.135263	+	0.990810i	$0.456812\pi$
$278$	−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
$285$	0	0
$286$	−9.80558e10	−0.866615
$287$	5.26038e10	0.457666
$288$	−2.06014e10	−0.176453
$289$	−1.18549e11	−0.999669
$290$	0	0
$291$	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	$0.598112\pi$
$294$	5.53421e8	0.00432009
$295$	0	0
$296$	4.89318e10	0.370492
$297$	1.27788e10	0.0952984
$298$	1.45668e11	1.07002
$299$	3.01038e10	0.217821
$300$	0	0
$301$	−6.60769e10	−0.463982
$302$	−4.63091e9	−0.0320358
$303$	−7.25409e9	−0.0494414
$304$	1.68479e10	0.113139
$305$	0	0
$306$	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	$0.422340\pi$
$308$	−3.32849e10	−0.210750
$309$	−4.14338e9	−0.0258548
$310$	0	0
$311$	2.15134e11	1.30403	0.652014	−	0.758207i	$-0.273924\pi$
$311$	2.15134e11	1.30403	0.652014	+	0.758207i	$0.273924\pi$
$312$	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	$-0.657336\pi$
$317$	−1.70586e11	−0.948807	−0.474403	+	0.880308i	$0.657336\pi$
$318$	−1.55724e9	−0.00853951
$319$	−8.52739e10	−0.461061
$320$	0	0
$321$	−1.07700e9	−0.00566163
$322$	1.02187e10	0.0529715
$323$	−1.60982e9	−0.00822937
$324$	9.86358e10	0.497258
$325$	0	0
$326$	−2.65972e11	−1.30424
$327$	−9.62165e9	−0.0465355
$328$	8.97398e10	0.428107
$329$	−1.27080e11	−0.597991
$330$	0	0
$331$	−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
$335$	0	0
$336$	9.44112e8	0.00404107
$337$	7.29335e10	0.308030	0.154015	−	0.988069i	$-0.450780\pi$
$337$	7.29335e10	0.308030	0.154015	+	0.988069i	$0.450780\pi$
$338$	3.52544e10	0.146923
$339$	−8.56710e9	−0.0352318
$340$	0	0
$341$	2.51129e11	1.00578
$342$	−8.08130e10	−0.319421
$343$	1.38413e10	0.0539949
$344$	−1.12724e11	−0.434015
$345$	0	0
$346$	−5.17000e10	−0.193931
$347$	1.55720e11	0.576584	0.288292	−	0.957542i	$-0.406913\pi$
$347$	1.55720e11	0.576584	0.288292	+	0.957542i	$0.406913\pi$
$348$	2.41876e9	0.00884069
$349$	1.08728e11	0.392310	0.196155	−	0.980573i	$-0.437154\pi$
$349$	1.08728e11	0.392310	0.196155	+	0.980573i	$0.437154\pi$
$350$	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
$355$	0	0
$356$	−1.20203e11	−0.396634
$357$	−9.02104e7	−0.000293934 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	$0.617739\pi$
$360$	0	0
$361$	−2.56599e11	−0.795192
$362$	−6.22931e10	−0.190656
$363$	3.44695e9	0.0104197
$364$	6.95618e10	0.207690
$365$	0	0
$366$	−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
$370$	0	0
$371$	−3.89472e10	−0.106732
$372$	−7.12318e9	−0.0192855
$373$	−3.83283e11	−1.02525	−0.512625	−	0.858613i	$-0.671327\pi$
$373$	−3.83283e11	−1.02525	−0.512625	+	0.858613i	$0.671327\pi$
$374$	5.42560e9	0.0143392
$375$	0	0
$376$	−2.16792e11	−0.559370
$377$	1.78214e11	0.454365
$378$	−9.06541e9	−0.0228389
$379$	−1.21462e11	−0.302386	−0.151193	−	0.988504i	$-0.548312\pi$
$379$	−1.21462e11	−0.302386	−0.151193	+	0.988504i	$0.548312\pi$
$380$	0	0
$381$	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	$0.476174\pi$
$390$	0	0
$391$	−1.66569e9	−0.00360412
$392$	2.36126e10	0.0505076
$393$	3.60999e9	0.00763378
$394$	5.35495e10	0.111950
$395$	0	0
$396$	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
$399$	3.70347e9	0.00731527
$400$	0	0
$401$	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
$405$	0	0
$406$	6.04942e10	0.110496
$407$	−6.46913e11	−1.16861
$408$	−1.53895e8	−0.000274950 0
$409$	−3.81956e10	−0.0674930	−0.0337465	−	0.999430i	$-0.510744\pi$
$409$	−3.81956e10	−0.0674930	−0.0337465	+	0.999430i	$0.510744\pi$
$410$	0	0
$411$	3.09605e10	0.0535205
$412$	−1.76784e11	−0.302277
$413$	−3.37364e11	−0.570588
$414$	−8.36176e10	−0.139893
$415$	0	0
$416$	1.18669e11	0.194276
$417$	−4.28614e10	−0.0694151
$418$	−2.22741e11	−0.356867
$419$	2.15268e11	0.341205	0.170603	−	0.985340i	$-0.445429\pi$
$419$	2.15268e11	0.341205	0.170603	+	0.985340i	$0.445429\pi$
$420$	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
$425$	0	0
$426$	2.68470e10	0.0394959
$427$	−4.87316e11	−0.709390
$428$	−4.59518e10	−0.0661921
$429$	−3.67709e10	−0.0524140
$430$	0	0
$431$	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	$0.210511\pi$
$434$	−1.78154e11	−0.241041
$435$	0	0
$436$	−4.10524e11	−0.544063
$437$	6.83827e10	0.0896974
$438$	3.87862e10	0.0503551
$439$	−2.12728e11	−0.273360	−0.136680	−	0.990615i	$-0.543643\pi$
$439$	−2.12728e11	−0.273360	−0.136680	+	0.990615i	$0.543643\pi$
$440$	0	0
$441$	−1.13261e11	−0.142596
$442$	−1.13389e10	−0.0141310
$443$	6.48300e10	0.0799759	0.0399880	−	0.999200i	$-0.487268\pi$
$443$	6.48300e10	0.0799759	0.0399880	+	0.999200i	$0.487268\pi$
$444$	1.83494e10	0.0224078
$445$	0	0
$446$	−8.56047e11	−1.02445
$447$	5.46255e10	0.0647159
$448$	4.02821e10	0.0472456
$449$	−1.08031e12	−1.25441	−0.627207	−	0.778853i	$-0.715802\pi$
$449$	−1.08031e12	−1.25441	−0.627207	+	0.778853i	$0.715802\pi$
$450$	0	0
$451$	−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	$-0.488959\pi$
$457$	6.46725e10	0.0693581	0.0346790	+	0.999399i	$0.488959\pi$
$458$	3.04395e11	0.323254
$459$	1.47771e9	0.00155393
$460$	0	0
$461$	4.29254e11	0.442649	0.221325	−	0.975200i	$-0.428962\pi$
$461$	4.29254e11	0.442649	0.221325	+	0.975200i	$0.428962\pi$
$462$	−1.24818e10	−0.0127464
$463$	−1.61883e12	−1.63715	−0.818574	−	0.574401i	$-0.805235\pi$
$463$	−1.61883e12	−1.63715	−0.818574	+	0.574401i	$0.805235\pi$
$464$	1.03200e11	0.103360
$465$	0	0
$466$	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
$469$	−3.69117e11	−0.352278
$470$	0	0
$471$	−8.34407e10	−0.0781239
$472$	−5.75527e11	−0.533737
$473$	1.49030e12	1.36898
$474$	−1.25462e10	−0.0114159
$475$	0	0
$476$	−3.84898e9	−0.00343648
$477$	3.18698e11	0.281869
$478$	1.04978e11	0.0919752
$479$	2.84811e11	0.247199	0.123600	−	0.992332i	$-0.460556\pi$
$479$	2.84811e11	0.247199	0.123600	+	0.992332i	$0.460556\pi$
$480$	0	0
$481$	1.35198e12	1.15164
$482$	−1.43491e12	−1.21091
$483$	3.83200e9	0.00320378
$484$	1.47070e11	0.121820
$485$	0	0
$486$	1.11305e11	0.0905007
$487$	7.14776e11	0.575824	0.287912	−	0.957657i	$-0.407039\pi$
$487$	7.14776e11	0.575824	0.287912	+	0.957657i	$0.407039\pi$
$488$	−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
$495$	0	0
$496$	−3.03922e11	−0.225473
$497$	6.71454e11	0.493642
$498$	−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	$0.340045\pi$
$500$	0	0
$501$	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	$0.436565\pi$
$504$	−1.93218e11	−0.133386
$505$	0	0
$506$	−2.30471e11	−0.156293
$507$	1.32204e10	0.00888606
$508$	6.03834e11	0.402282
$509$	3.57173e11	0.235857	0.117928	−	0.993022i	$-0.462375\pi$
$509$	3.57173e11	0.235857	0.117928	+	0.993022i	$0.462375\pi$
$510$	0	0
$511$	9.70059e11	0.629367
$512$	6.87195e10	0.0441942
$513$	−6.06653e10	−0.0386734
$514$	1.33692e12	0.844834
$515$	0	0
$516$	−4.22716e10	−0.0262498
$517$	2.86615e12	1.76438
$518$	4.58927e11	0.280065
$519$	−1.93875e10	−0.0117292
$520$	0	0
$521$	2.17972e12	1.29608	0.648040	−	0.761606i	$-0.275589\pi$
$521$	2.17972e12	1.29608	0.648040	+	0.761606i	$0.275589\pi$
$522$	−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
$530$	0	0
$531$	2.76059e12	1.50687
$532$	1.58015e11	0.0855253
$533$	2.47950e12	1.33074
$534$	−4.50761e10	−0.0239889
$535$	0	0
$536$	−6.29697e11	−0.329526
$537$	−1.44845e11	−0.0751655
$538$	2.26241e12	1.16426
$539$	−3.12176e11	−0.159312
$540$	0	0
$541$	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
$545$	0	0
$546$	2.60857e10	0.0125613
$547$	3.86062e11	0.184380	0.0921899	−	0.995741i	$-0.470613\pi$
$547$	3.86062e11	0.184380	0.0921899	+	0.995741i	$0.470613\pi$
$548$	1.32098e12	0.625726
$549$	3.98763e12	1.87344
$550$	0	0
$551$	4.04824e11	0.187105
$552$	6.53722e9	0.00299686
$553$	−3.13786e11	−0.142683
$554$	4.24120e11	0.191291
$555$	0	0
$556$	−1.82875e12	−0.811556
$557$	7.95102e11	0.350005	0.175003	−	0.984568i	$-0.444007\pi$
$557$	7.95102e11	0.350005	0.175003	+	0.984568i	$0.444007\pi$
$558$	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
$565$	0	0
$566$	8.53460e10	0.0349550
$567$	9.25096e11	0.375892
$568$	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	$0.356799\pi$
$570$	0	0
$571$	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
$574$	8.41661e11	0.323619
$575$	0	0
$576$	−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
$580$	0	0
$581$	−1.00874e12	−0.367272
$582$	8.37602e10	0.0302611
$583$	8.78412e11	0.314912
$584$	1.65488e12	0.588719
$585$	0	0
$586$	−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	$0.841864\pi$
$588$	8.85473e9	0.00305476
$589$	−1.19220e12	−0.408158
$590$	0	0
$591$	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	$0.329924\pi$
$600$	0	0
$601$	7.49502e11	0.234335	0.117168	−	0.993112i	$-0.462619\pi$
$601$	7.49502e11	0.234335	0.117168	+	0.993112i	$0.462619\pi$
$602$	−1.05723e12	−0.328084
$603$	3.02042e12	0.930336
$604$	−7.40946e10	−0.0226527
$605$	0	0
$606$	−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
$609$	2.26853e10	0.00668294
$610$	0	0
$611$	−5.98995e12	−1.73875
$612$	3.14956e10	0.00907544
$613$	4.03977e12	1.15554	0.577770	−	0.816200i	$-0.303923\pi$
$613$	4.03977e12	1.15554	0.577770	+	0.816200i	$0.303923\pi$
$614$	1.20311e12	0.341623
$615$	0	0
$616$	−5.32558e11	−0.149023
$617$	2.93367e12	0.814945	0.407472	−	0.913218i	$-0.366410\pi$
$617$	2.93367e12	0.814945	0.407472	+	0.913218i	$0.366410\pi$
$618$	−6.62940e10	−0.0182821
$619$	−5.77691e12	−1.58157	−0.790784	−	0.612095i	$-0.790327\pi$
$619$	−5.77691e12	−1.58157	−0.790784	+	0.612095i	$0.790327\pi$
$620$	0	0
$621$	−6.27707e10	−0.0169373
$622$	3.44214e12	0.922088
$623$	−1.12737e12	−0.299827
$624$	4.45010e10	0.0117500
$625$	0	0
$626$	−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
$635$	0	0
$636$	−2.49158e10	−0.00603834
$637$	6.52414e11	0.156999
$638$	−1.36438e12	−0.326019
$639$	−5.49440e12	−1.30367
$640$	0	0
$641$	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	$0.442826\pi$
$644$	1.63498e11	0.0374565
$645$	0	0
$646$	−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
$650$	0	0
$651$	−6.68076e10	−0.0145785
$652$	−4.25555e12	−0.922235
$653$	2.88925e12	0.621836	0.310918	−	0.950437i	$-0.399364\pi$
$653$	2.88925e12	0.621836	0.310918	+	0.950437i	$0.399364\pi$
$654$	−1.53946e11	−0.0329056
$655$	0	0
$656$	1.43584e12	0.302718
$657$	−7.93784e12	−1.66210
$658$	−2.03328e12	−0.422844
$659$	5.20255e12	1.07456	0.537281	−	0.843403i	$-0.319451\pi$
$659$	5.20255e12	1.07456	0.537281	+	0.843403i	$0.319451\pi$
$660$	0	0
$661$	2.88973e12	0.588777	0.294388	−	0.955686i	$-0.404884\pi$
$661$	2.88973e12	0.588777	0.294388	+	0.955686i	$0.404884\pi$
$662$	−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
$670$	0	0
$671$	1.09909e13	2.09306
$672$	1.51058e10	0.00285747
$673$	−9.46362e12	−1.77824	−0.889119	−	0.457677i	$-0.848682\pi$
$673$	−9.46362e12	−1.77824	−0.889119	+	0.457677i	$0.848682\pi$
$674$	1.16694e12	0.217810
$675$	0	0
$676$	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
$679$	2.09488e12	0.378220
$680$	0	0
$681$	2.41622e11	0.0430502
$682$	4.01806e12	0.711193
$683$	−5.37240e12	−0.944660	−0.472330	−	0.881422i	$-0.656587\pi$
$683$	−5.37240e12	−0.944660	−0.472330	+	0.881422i	$0.656587\pi$
$684$	−1.29301e12	−0.225865
$685$	0	0
$686$	2.21461e11	0.0381802
$687$	1.14148e11	0.0195508
$688$	−1.80359e12	−0.306895
$689$	−1.83579e12	−0.310339
$690$	0	0
$691$	2.01563e12	0.336325	0.168163	−	0.985759i	$-0.446217\pi$
$691$	2.01563e12	0.336325	0.168163	+	0.985759i	$0.446217\pi$
$692$	−8.27200e11	−0.137130
$693$	2.55448e12	0.420730
$694$	2.49153e12	0.407707
$695$	0	0
$696$	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
$705$	0	0
$706$	−5.20936e12	−0.789157
$707$	−2.90284e12	−0.436955
$708$	−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	$0.417180\pi$
$710$	0	0
$711$	2.56766e12	0.376812
$712$	−1.92325e12	−0.280462
$713$	−1.23357e12	−0.178756
$714$	−1.44337e9	−0.000207843 0
$715$	0	0
$716$	−6.18004e12	−0.878785
$717$	3.93666e10	0.00556277
$718$	−3.64080e12	−0.511253
$719$	−9.62025e12	−1.34248	−0.671238	−	0.741242i	$-0.734237\pi$
$719$	−9.62025e12	−1.34248	−0.671238	+	0.741242i	$0.734237\pi$
$720$	0	0
$721$	−1.65804e12	−0.228500
$722$	−4.10558e12	−0.562285
$723$	−5.38091e11	−0.0732374
$724$	−9.96689e11	−0.134814
$725$	0	0
$726$	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	$0.433272\pi$
$728$	1.11299e12	0.146859
$729$	−7.54204e12	−0.989043
$730$	0	0
$731$	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	$0.522103\pi$
$740$	0	0
$741$	1.74564e11	0.0212703
$742$	−6.23154e11	−0.0754707
$743$	−1.65266e12	−0.198945	−0.0994725	−	0.995040i	$-0.531716\pi$
$743$	−1.65266e12	−0.198945	−0.0994725	+	0.995040i	$0.531716\pi$
$744$	−1.13971e11	−0.0136369
$745$	0	0
$746$	−6.13253e12	−0.724961
$747$	8.25437e12	0.969932
$748$	8.68096e10	0.0101394
$749$	−4.30978e11	−0.0500365
$750$	0	0
$751$	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
$755$	0	0
$756$	−1.45047e11	−0.0161495
$757$	8.02798e12	0.888535	0.444268	−	0.895894i	$-0.353464\pi$
$757$	8.02798e12	0.888535	0.444268	+	0.895894i	$0.353464\pi$
$758$	−1.94338e12	−0.213820
$759$	−8.64266e10	−0.00945278
$760$	0	0
$761$	−6.51923e12	−0.704637	−0.352318	−	0.935880i	$-0.614607\pi$
$761$	−6.51923e12	−0.704637	−0.352318	+	0.935880i	$0.614607\pi$
$762$	2.26438e11	0.0243305
$763$	−3.85026e12	−0.411273
$764$	−6.63009e12	−0.704043
$765$	0	0
$766$	6.36354e12	0.667835
$767$	−1.59018e13	−1.65907
$768$	2.57698e10	0.00267292
$769$	−1.34250e13	−1.38435	−0.692175	−	0.721730i	$-0.743347\pi$
$769$	−1.34250e13	−1.38435	−0.692175	+	0.721730i	$0.743347\pi$
$770$	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
$775$	0	0
$776$	3.57377e12	0.353792
$777$	1.72098e11	0.0169387
$778$	1.08074e12	0.105758
$779$	5.63235e12	0.547988
$780$	0	0
$781$	−1.51439e13	−1.45649
$782$	−2.66511e10	−0.00254850
$783$	−3.71601e11	−0.0353304
$784$	3.77802e11	0.0357143
$785$	0	0
$786$	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
$790$	0	0
$791$	−3.42827e12	−0.311373
$792$	4.35783e12	0.393557
$793$	−2.29698e13	−2.06266
$794$	−1.99449e12	−0.178090
$795$	0	0
$796$	−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	$0.408292\pi$
$798$	5.92555e10	0.00517268
$799$	3.31434e11	0.0287698
$800$	0	0
$801$	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	$0.717147\pi$
$810$	0	0
$811$	−1.29056e13	−1.04757	−0.523787	−	0.851849i	$-0.675481\pi$
$811$	−1.29056e13	−1.04757	−0.523787	+	0.851849i	$0.675481\pi$
$812$	9.67907e11	0.0781325
$813$	−5.45012e11	−0.0437520
$814$	−1.03506e13	−0.826334
$815$	0	0
$816$	−2.46232e9	−0.000194419 0
$817$	−7.07494e12	−0.555550
$818$	−6.11130e11	−0.0477247
$819$	−5.33860e12	−0.414620
$820$	0	0
$821$	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	$-0.162053\pi$
$823$	2.29844e13	1.74636	0.873182	+	0.487394i	$0.162053\pi$
$824$	−2.82854e12	−0.213742
$825$	0	0
$826$	−5.39782e12	−0.403467
$827$	2.75618e12	0.204896	0.102448	−	0.994738i	$-0.467333\pi$
$827$	2.75618e12	0.204896	0.102448	+	0.994738i	$0.467333\pi$
$828$	−1.33788e12	−0.0989194
$829$	−3.15925e12	−0.232321	−0.116160	−	0.993230i	$-0.537059\pi$
$829$	−3.15925e12	−0.232321	−0.116160	+	0.993230i	$0.537059\pi$
$830$	0	0
$831$	1.59045e11	0.0115695
$832$	1.89871e12	0.137374
$833$	−3.60992e10	−0.00259774
$834$	−6.85782e11	−0.0490839
$835$	0	0
$836$	−3.56385e12	−0.252343
$837$	1.09435e12	0.0770714
$838$	3.44428e12	0.241269
$839$	1.92403e13	1.34055	0.670277	−	0.742111i	$-0.266175\pi$
$839$	1.92403e13	1.34055	0.670277	+	0.742111i	$0.266175\pi$
$840$	0	0
$841$	−1.20274e13	−0.829069
$842$	1.91892e13	1.31569
$843$	−1.12181e12	−0.0765058
$844$	7.72357e12	0.523935
$845$	0	0
$846$	1.66380e13	1.11669
$847$	1.37935e12	0.0920874
$848$	−1.06307e12	−0.0705963
$849$	3.20048e10	0.00211412
$850$	0	0
$851$	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	$0.180573\pi$
$854$	−7.79705e12	−0.501614
$855$	0	0
$856$	−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	$-0.535539\pi$
$859$	−3.55588e12	−0.222832	−0.111416	+	0.993774i	$0.535539\pi$
$860$	0	0
$861$	3.15623e11	0.0195729
$862$	1.26579e13	0.780869
$863$	−2.22084e13	−1.36292	−0.681458	−	0.731858i	$-0.738654\pi$
$863$	−2.22084e13	−1.36292	−0.681458	+	0.731858i	$0.738654\pi$
$864$	−2.47443e11	−0.0151065
$865$	0	0
$866$	1.84721e13	1.11606
$867$	−7.11292e11	−0.0427525
$868$	−2.85046e12	−0.170442
$869$	7.07711e12	0.420986
$870$	0	0
$871$	−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	$-0.530755\pi$
$877$	−3.38004e12	−0.192941	−0.0964703	+	0.995336i	$0.530755\pi$
$878$	−3.40365e12	−0.193295
$879$	−4.59260e11	−0.0259483
$880$	0	0
$881$	5.25103e11	0.0293665	0.0146833	−	0.999892i	$-0.495326\pi$
$881$	5.25103e11	0.0293665	0.0146833	+	0.999892i	$0.495326\pi$
$882$	−1.81218e12	−0.100830
$883$	−3.33972e13	−1.84879	−0.924393	−	0.381441i	$-0.875428\pi$
$883$	−3.33972e13	−1.84879	−0.924393	+	0.381441i	$0.875428\pi$
$884$	−1.81423e11	−0.00999210
$885$	0	0
$886$	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
$889$	5.66331e12	0.304097
$890$	0	0
$891$	−2.08646e13	−1.10907
$892$	−1.36968e13	−0.724396
$893$	−1.36066e13	−0.716007
$894$	8.74007e11	0.0457611
$895$	0	0
$896$	6.44514e11	0.0334077
$897$	1.80623e11	0.00931549
$898$	−1.72850e13	−0.887004
$899$	−7.30271e12	−0.372877
$900$	0	0
$901$	1.01577e11	0.00513494
$902$	−1.89828e13	−0.954839
$903$	−3.96462e11	−0.0198430
$904$	−5.84848e12	−0.291263
$905$	0	0
$906$	−2.77855e10	−0.00137006
$907$	2.08341e13	1.02221	0.511107	−	0.859517i	$-0.329236\pi$
$907$	2.08341e13	1.02221	0.511107	+	0.859517i	$0.329236\pi$
$908$	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
$915$	0	0
$916$	4.87033e12	0.228575
$917$	1.44460e12	0.0674660
$918$	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	$0.603654\pi$
$920$	0	0
$921$	4.51166e11	0.0206618
$922$	6.86806e12	0.313000
$923$	3.16492e13	1.43534
$924$	−1.99709e11	−0.00901310
$925$	0	0
$926$	−2.59013e13	−1.15764
$927$	1.35675e13	0.603449
$928$	1.65121e12	0.0730863
$929$	−1.74073e13	−0.766761	−0.383380	−	0.923591i	$-0.625240\pi$
$929$	−1.74073e13	−0.766761	−0.383380	+	0.923591i	$0.625240\pi$
$930$	0	0
$931$	1.48200e12	0.0646511
$932$	9.41434e12	0.408713
$933$	1.29080e12	0.0557690
$934$	−5.23714e12	−0.225182
$935$	0	0
$936$	−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	$0.513384\pi$
$938$	−5.90587e12	−0.249098
$939$	−5.75445e11	−0.0241551
$940$	0	0
$941$	−2.33533e13	−0.970946	−0.485473	−	0.874252i	$-0.661353\pi$
$941$	−2.33533e13	−0.970946	−0.485473	+	0.874252i	$0.661353\pi$
$942$	−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	$-0.759102\pi$
$947$	−3.59882e13	−1.45407	−0.727035	+	0.686600i	$0.759102\pi$
$948$	−2.00740e11	−0.00807227
$949$	4.57241e13	1.82998
$950$	0	0
$951$	−1.02352e12	−0.0405773
$952$	−6.15836e10	−0.00242996
$953$	1.37662e13	0.540624	0.270312	−	0.962773i	$-0.412873\pi$
$953$	1.37662e13	0.540624	0.270312	+	0.962773i	$0.412873\pi$
$954$	5.09917e12	0.199311
$955$	0	0
$956$	1.67964e12	0.0650363
$957$	−5.11643e11	−0.0197180
$958$	4.55698e12	0.174796
$959$	1.23894e13	0.473005
$960$	0	0
$961$	−4.93336e12	−0.186590
$962$	2.16317e13	0.814334
$963$	3.52662e12	0.132142
$964$	−2.29585e13	−0.856244
$965$	0	0
$966$	6.13119e10	0.00226542
$967$	3.02718e12	0.111332	0.0556659	−	0.998449i	$-0.482272\pi$
$967$	3.02718e12	0.111332	0.0556659	+	0.998449i	$0.482272\pi$
$968$	2.35312e12	0.0861399
$969$	−9.65893e9	−0.000351943 0
$970$	0	0
$971$	−2.53183e13	−0.914003	−0.457002	−	0.889466i	$-0.651077\pi$
$971$	−2.53183e13	−0.914003	−0.457002	+	0.889466i	$0.651077\pi$
$972$	1.78088e12	0.0639937
$973$	−1.71517e13	−0.613478
$974$	1.14364e13	0.407169
$975$	0	0
$976$	−1.33014e13	−0.469217
$977$	−9.90729e12	−0.347880	−0.173940	−	0.984756i	$-0.555650\pi$
$977$	−9.90729e12	−0.347880	−0.173940	+	0.984756i	$0.555650\pi$
$978$	−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
$985$	0	0
$986$	−1.57774e11	−0.00531604
$987$	−7.62478e11	−0.0255741
$988$	7.44807e12	0.248678
$989$	−7.32048e12	−0.243308
$990$	0	0
$991$	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
$994$	1.07433e13	0.349058
$995$	0	0
$996$	−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	350.10.a.c.1.1		1
5.2	odd	4		350.10.c.b.99.2		2
5.3	odd	4		350.10.c.b.99.1		2
5.4	even	2		14.10.a.a.1.1	✓	1
15.14	odd	2		126.10.a.e.1.1		1
20.19	odd	2		112.10.a.b.1.1		1
35.4	even	6		98.10.c.f.79.1		2
35.9	even	6		98.10.c.f.67.1		2
35.19	odd	6		98.10.c.e.67.1		2
35.24	odd	6		98.10.c.e.79.1		2
35.34	odd	2		98.10.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.a.a.1.1	✓	1	5.4	even	2
98.10.a.a.1.1		1	35.34	odd	2
98.10.c.e.67.1		2	35.19	odd	6
98.10.c.e.79.1		2	35.24	odd	6
98.10.c.f.67.1		2	35.9	even	6
98.10.c.f.79.1		2	35.4	even	6
112.10.a.b.1.1		1	20.19	odd	2
126.10.a.e.1.1		1	15.14	odd	2
350.10.a.c.1.1		1	1.1	even	1	trivial
350.10.c.b.99.1		2	5.3	odd	4
350.10.c.b.99.2		2	5.2	odd	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	350.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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