LMFDB - Embedded newform 177.14.a.c.1.13

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	177.a (trivial)

Newform invariants

Self dual:	yes
Analytic conductor:	$189.798744245$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-50.5493 q^{2} +729.000 q^{3} -5636.77 q^{4} +37474.1 q^{5} -36850.4 q^{6} +131476. q^{7} +699034. q^{8} +531441. q^{9} +O(q^{10})$	\(q-50.5493 q^{2} +729.000 q^{3} -5636.77 q^{4} +37474.1 q^{5} -36850.4 q^{6} +131476. q^{7} +699034. q^{8} +531441. q^{9} -1.89429e6 q^{10} +4.83579e6 q^{11} -4.10921e6 q^{12} +7.84739e6 q^{13} -6.64603e6 q^{14} +2.73186e7 q^{15} +1.08408e7 q^{16} +1.27632e8 q^{17} -2.68639e7 q^{18} +1.07870e8 q^{19} -2.11233e8 q^{20} +9.58462e7 q^{21} -2.44446e8 q^{22} +4.53568e8 q^{23} +5.09596e8 q^{24} +1.83602e8 q^{25} -3.96680e8 q^{26} +3.87420e8 q^{27} -7.41102e8 q^{28} +2.96893e9 q^{29} -1.38093e9 q^{30} +5.30309e9 q^{31} -6.27448e9 q^{32} +3.52529e9 q^{33} -6.45171e9 q^{34} +4.92695e9 q^{35} -2.99561e9 q^{36} +1.26704e10 q^{37} -5.45275e9 q^{38} +5.72075e9 q^{39} +2.61956e10 q^{40} +4.56042e10 q^{41} -4.84495e9 q^{42} +2.06237e10 q^{43} -2.72582e10 q^{44} +1.99153e10 q^{45} -2.29275e10 q^{46} -3.67643e10 q^{47} +7.90293e9 q^{48} -7.96030e10 q^{49} -9.28094e9 q^{50} +9.30439e10 q^{51} -4.42340e10 q^{52} -1.16034e11 q^{53} -1.95838e10 q^{54} +1.81217e11 q^{55} +9.19064e10 q^{56} +7.86372e10 q^{57} -1.50077e11 q^{58} -4.21805e10 q^{59} -1.53989e11 q^{60} -2.48903e11 q^{61} -2.68067e11 q^{62} +6.98719e10 q^{63} +2.28363e11 q^{64} +2.94074e11 q^{65} -1.78201e11 q^{66} +7.76631e11 q^{67} -7.19434e11 q^{68} +3.30651e11 q^{69} -2.49054e11 q^{70} +6.93339e9 q^{71} +3.71495e11 q^{72} +1.40771e12 q^{73} -6.40479e11 q^{74} +1.33846e11 q^{75} -6.08038e11 q^{76} +6.35791e11 q^{77} -2.89180e11 q^{78} -1.00584e12 q^{79} +4.06248e11 q^{80} +2.82430e11 q^{81} -2.30526e12 q^{82} -3.96993e12 q^{83} -5.40263e11 q^{84} +4.78290e12 q^{85} -1.04251e12 q^{86} +2.16435e12 q^{87} +3.38038e12 q^{88} -3.15383e12 q^{89} -1.00670e12 q^{90} +1.03175e12 q^{91} -2.55666e12 q^{92} +3.86595e12 q^{93} +1.85841e12 q^{94} +4.04232e12 q^{95} -4.57410e12 q^{96} -3.57023e12 q^{97} +4.02387e12 q^{98} +2.56994e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) $	\( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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 $

$2$	−50.5493	−0.558496	−0.279248	−	0.960219i	$-0.590085\pi$
$2$	−50.5493	−0.558496	−0.279248	+	0.960219i	$0.590085\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−5636.77	−0.688083
$5$	37474.1	1.07257	0.536285	−	0.844037i	$-0.319827\pi$
$5$	37474.1	1.07257	0.536285	+	0.844037i	$0.319827\pi$
$6$	−36850.4	−0.322448
$7$	131476.	0.422386	0.211193	−	0.977444i	$-0.432265\pi$
$7$	131476.	0.422386	0.211193	+	0.977444i	$0.432265\pi$
$8$	699034.	0.942787
$9$	531441.	0.333333
$10$	−1.89429e6	−0.599026
$11$	4.83579e6	0.823028	0.411514	−	0.911403i	$-0.365000\pi$
$11$	4.83579e6	0.823028	0.411514	+	0.911403i	$0.365000\pi$
$12$	−4.10921e6	−0.397265
$13$	7.84739e6	0.450914	0.225457	−	0.974253i	$-0.427613\pi$
$13$	7.84739e6	0.450914	0.225457	+	0.974253i	$0.427613\pi$
$14$	−6.64603e6	−0.235901
$15$	2.73186e7	0.619249
$16$	1.08408e7	0.161540
$17$	1.27632e8	1.28246	0.641228	−	0.767351i	$-0.278425\pi$
$17$	1.27632e8	1.28246	0.641228	+	0.767351i	$0.278425\pi$
$18$	−2.68639e7	−0.186165
$19$	1.07870e8	0.526020	0.263010	−	0.964793i	$-0.415285\pi$
$19$	1.07870e8	0.526020	0.263010	+	0.964793i	$0.415285\pi$
$20$	−2.11233e8	−0.738017
$21$	9.58462e7	0.243865
$22$	−2.44446e8	−0.459658
$23$	4.53568e8	0.638869	0.319435	−	0.947608i	$-0.396507\pi$
$23$	4.53568e8	0.638869	0.319435	+	0.947608i	$0.396507\pi$
$24$	5.09596e8	0.544318
$25$	1.83602e8	0.150407
$26$	−3.96680e8	−0.251833
$27$	3.87420e8	0.192450
$28$	−7.41102e8	−0.290637
$29$	2.96893e9	0.926858	0.463429	−	0.886134i	$-0.346619\pi$
$29$	2.96893e9	0.926858	0.463429	+	0.886134i	$0.346619\pi$
$30$	−1.38093e9	−0.345848
$31$	5.30309e9	1.07319	0.536596	−	0.843839i	$-0.319710\pi$
$31$	5.30309e9	1.07319	0.536596	+	0.843839i	$0.319710\pi$
$32$	−6.27448e9	−1.03301
$33$	3.52529e9	0.475176
$34$	−6.45171e9	−0.716246
$35$	4.92695e9	0.453039
$36$	−2.99561e9	−0.229361
$37$	1.26704e10	0.811856	0.405928	−	0.913905i	$-0.366948\pi$
$37$	1.26704e10	0.811856	0.405928	+	0.913905i	$0.366948\pi$
$38$	−5.45275e9	−0.293780
$39$	5.72075e9	0.260335
$40$	2.61956e10	1.01120
$41$	4.56042e10	1.49937	0.749687	−	0.661792i	$-0.230204\pi$
$41$	4.56042e10	1.49937	0.749687	+	0.661792i	$0.230204\pi$
$42$	−4.84495e9	−0.136198
$43$	2.06237e10	0.497533	0.248766	−	0.968564i	$-0.419975\pi$
$43$	2.06237e10	0.497533	0.248766	+	0.968564i	$0.419975\pi$
$44$	−2.72582e10	−0.566312
$45$	1.99153e10	0.357523
$46$	−2.29275e10	−0.356806
$47$	−3.67643e10	−0.497496	−0.248748	−	0.968568i	$-0.580019\pi$
$47$	−3.67643e10	−0.497496	−0.248748	+	0.968568i	$0.580019\pi$
$48$	7.90293e9	0.0932653
$49$	−7.96030e10	−0.821590
$50$	−9.28094e9	−0.0840015
$51$	9.30439e10	0.740426
$52$	−4.42340e10	−0.310266
$53$	−1.16034e11	−0.719105	−0.359552	−	0.933125i	$-0.617071\pi$
$53$	−1.16034e11	−0.719105	−0.359552	+	0.933125i	$0.617071\pi$
$54$	−1.95838e10	−0.107483
$55$	1.81217e11	0.882756
$56$	9.19064e10	0.398220
$57$	7.86372e10	0.303698
$58$	−1.50077e11	−0.517646
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−1.53989e11	−0.426094
$61$	−2.48903e11	−0.618565	−0.309283	−	0.950970i	$-0.600089\pi$
$61$	−2.48903e11	−0.618565	−0.309283	+	0.950970i	$0.600089\pi$
$62$	−2.68067e11	−0.599373
$63$	6.98719e10	0.140795
$64$	2.28363e11	0.415389
$65$	2.94074e11	0.483637
$66$	−1.78201e11	−0.265384
$67$	7.76631e11	1.04889	0.524443	−	0.851445i	$-0.324274\pi$
$67$	7.76631e11	1.04889	0.524443	+	0.851445i	$0.324274\pi$
$68$	−7.19434e11	−0.882435
$69$	3.30651e11	0.368851
$70$	−2.49054e11	−0.253020
$71$	6.93339e9	0.00642342	0.00321171	−	0.999995i	$-0.498978\pi$
$71$	6.93339e9	0.00642342	0.00321171	+	0.999995i	$0.498978\pi$
$72$	3.71495e11	0.314262
$73$	1.40771e12	1.08871	0.544357	−	0.838853i	$-0.316774\pi$
$73$	1.40771e12	1.08871	0.544357	+	0.838853i	$0.316774\pi$
$74$	−6.40479e11	−0.453418
$75$	1.33846e11	0.0868373
$76$	−6.08038e11	−0.361945
$77$	6.35791e11	0.347636
$78$	−2.89180e11	−0.145396
$79$	−1.00584e12	−0.465535	−0.232767	−	0.972532i	$-0.574778\pi$
$79$	−1.00584e12	−0.465535	−0.232767	+	0.972532i	$0.574778\pi$
$80$	4.06248e11	0.173263
$81$	2.82430e11	0.111111
$82$	−2.30526e12	−0.837394
$83$	−3.96993e12	−1.33283	−0.666416	−	0.745580i	$-0.732172\pi$
$83$	−3.96993e12	−1.33283	−0.666416	+	0.745580i	$0.732172\pi$
$84$	−5.40263e11	−0.167799
$85$	4.78290e12	1.37552
$86$	−1.04251e12	−0.277870
$87$	2.16435e12	0.535122
$88$	3.38038e12	0.775940
$89$	−3.15383e12	−0.672671	−0.336335	−	0.941742i	$-0.609188\pi$
$89$	−3.15383e12	−0.672671	−0.336335	+	0.941742i	$0.609188\pi$
$90$	−1.00670e12	−0.199675
$91$	1.03175e12	0.190460
$92$	−2.55666e12	−0.439595
$93$	3.86595e12	0.619608
$94$	1.85841e12	0.277850
$95$	4.04232e12	0.564193
$96$	−4.57410e12	−0.596406
$97$	−3.57023e12	−0.435191	−0.217595	−	0.976039i	$-0.569821\pi$
$97$	−3.57023e12	−0.435191	−0.217595	+	0.976039i	$0.569821\pi$
$98$	4.02387e12	0.458854
$99$	2.56994e12	0.274343
$100$	−1.03492e12	−0.103492
$101$	5.34316e12	0.500852	0.250426	−	0.968136i	$-0.419429\pi$
$101$	5.34316e12	0.500852	0.250426	+	0.968136i	$0.419429\pi$
$102$	−4.70330e12	−0.413525
$103$	−9.32875e11	−0.0769807	−0.0384903	−	0.999259i	$-0.512255\pi$
$103$	−9.32875e11	−0.0769807	−0.0384903	+	0.999259i	$0.512255\pi$
$104$	5.48559e12	0.425116
$105$	3.59175e12	0.261562
$106$	5.86543e12	0.401617
$107$	−2.96981e13	−1.91309	−0.956543	−	0.291591i	$-0.905815\pi$
$107$	−2.96981e13	−1.91309	−0.956543	+	0.291591i	$0.905815\pi$
$108$	−2.18380e12	−0.132422
$109$	−1.10515e13	−0.631175	−0.315587	−	0.948897i	$-0.602202\pi$
$109$	−1.10515e13	−0.631175	−0.315587	+	0.948897i	$0.602202\pi$
$110$	−9.16037e12	−0.493015
$111$	9.23672e12	0.468725
$112$	1.42531e12	0.0682324
$113$	−2.10986e13	−0.953332	−0.476666	−	0.879085i	$-0.658155\pi$
$113$	−2.10986e13	−0.953332	−0.476666	+	0.879085i	$0.658155\pi$
$114$	−3.97505e12	−0.169614
$115$	1.69970e13	0.685232
$116$	−1.67352e13	−0.637755
$117$	4.17042e12	0.150305
$118$	2.13219e12	0.0727099
$119$	1.67806e13	0.541692
$120$	1.90966e13	0.583819
$121$	−1.11379e13	−0.322624
$122$	1.25818e13	0.345466
$123$	3.32455e13	0.865664
$124$	−2.98923e13	−0.738445
$125$	−3.88644e13	−0.911248
$126$	−3.53197e12	−0.0786337
$127$	2.42799e13	0.513480	0.256740	−	0.966481i	$-0.417352\pi$
$127$	2.42799e13	0.513480	0.256740	+	0.966481i	$0.417352\pi$
$128$	3.98570e13	0.801013
$129$	1.50347e13	0.287251
$130$	−1.48652e13	−0.270109
$131$	3.33833e13	0.577119	0.288560	−	0.957462i	$-0.406824\pi$
$131$	3.33833e13	0.577119	0.288560	+	0.957462i	$0.406824\pi$
$132$	−1.98713e13	−0.326960
$133$	1.41823e13	0.222184
$134$	−3.92581e13	−0.585798
$135$	1.45182e13	0.206416
$136$	8.92193e13	1.20908
$137$	3.87450e13	0.500647	0.250324	−	0.968162i	$-0.419463\pi$
$137$	3.87450e13	0.500647	0.250324	+	0.968162i	$0.419463\pi$
$138$	−1.67142e13	−0.206002
$139$	1.49591e12	0.0175918	0.00879588	−	0.999961i	$-0.497200\pi$
$139$	1.49591e12	0.0175918	0.00879588	+	0.999961i	$0.497200\pi$
$140$	−2.77721e13	−0.311728
$141$	−2.68012e13	−0.287230
$142$	−3.50477e11	−0.00358745
$143$	3.79483e13	0.371115
$144$	5.76124e12	0.0538467
$145$	1.11258e14	0.994120
$146$	−7.11586e13	−0.608042
$147$	−5.80306e13	−0.474345
$148$	−7.14202e13	−0.558624
$149$	−2.11317e14	−1.58206	−0.791031	−	0.611776i	$-0.790456\pi$
$149$	−2.11317e14	−1.58206	−0.791031	+	0.611776i	$0.790456\pi$
$150$	−6.76581e12	−0.0484983
$151$	−1.29104e14	−0.886318	−0.443159	−	0.896443i	$-0.646142\pi$
$151$	−1.29104e14	−0.886318	−0.443159	+	0.896443i	$0.646142\pi$
$152$	7.54048e13	0.495924
$153$	6.78290e13	0.427485
$154$	−3.21388e13	−0.194153
$155$	1.98728e14	1.15107
$156$	−3.22466e13	−0.179132
$157$	1.12893e14	0.601618	0.300809	−	0.953684i	$-0.402743\pi$
$157$	1.12893e14	0.601618	0.300809	+	0.953684i	$0.402743\pi$
$158$	5.08444e13	0.259999
$159$	−8.45888e13	−0.415175
$160$	−2.35130e14	−1.10797
$161$	5.96335e13	0.269850
$162$	−1.42766e13	−0.0620551
$163$	−1.72378e14	−0.719883	−0.359942	−	0.932975i	$-0.617203\pi$
$163$	−1.72378e14	−0.719883	−0.359942	+	0.932975i	$0.617203\pi$
$164$	−2.57061e14	−1.03169
$165$	1.32107e14	0.509659
$166$	2.00677e14	0.744380
$167$	−1.24963e14	−0.445784	−0.222892	−	0.974843i	$-0.571550\pi$
$167$	−1.24963e14	−0.445784	−0.222892	+	0.974843i	$0.571550\pi$
$168$	6.69998e13	0.229913
$169$	−2.41294e14	−0.796677
$170$	−2.41772e14	−0.768224
$171$	5.73265e13	0.175340
$172$	−1.16251e14	−0.342344
$173$	−5.39672e14	−1.53049	−0.765245	−	0.643739i	$-0.777382\pi$
$173$	−5.39672e14	−1.53049	−0.765245	+	0.643739i	$0.777382\pi$
$174$	−1.09406e14	−0.298863
$175$	2.41393e13	0.0635298
$176$	5.24237e13	0.132952
$177$	−3.07496e13	−0.0751646
$178$	1.59424e14	0.375684
$179$	−3.85664e14	−0.876324	−0.438162	−	0.898896i	$-0.644370\pi$
$179$	−3.85664e14	−0.876324	−0.438162	+	0.898896i	$0.644370\pi$
$180$	−1.12258e14	−0.246006
$181$	3.33508e14	0.705011	0.352505	−	0.935810i	$-0.385330\pi$
$181$	3.33508e14	0.705011	0.352505	+	0.935810i	$0.385330\pi$
$182$	−5.21540e13	−0.106371
$183$	−1.81450e14	−0.357129
$184$	3.17060e14	0.602317
$185$	4.74811e14	0.870773
$186$	−1.95421e14	−0.346048
$187$	6.17202e14	1.05550
$188$	2.07232e14	0.342319
$189$	5.09366e13	0.0812883
$190$	−2.04337e14	−0.315099
$191$	−7.47095e14	−1.11342	−0.556710	−	0.830707i	$-0.687936\pi$
$191$	−7.47095e14	−1.11342	−0.556710	+	0.830707i	$0.687936\pi$
$192$	1.66476e14	0.239825
$193$	8.67669e14	1.20846	0.604229	−	0.796811i	$-0.293481\pi$
$193$	8.67669e14	1.20846	0.604229	+	0.796811i	$0.293481\pi$
$194$	1.80472e14	0.243052
$195$	2.14380e14	0.279228
$196$	4.48704e14	0.565322
$197$	1.35605e14	0.165289	0.0826447	−	0.996579i	$-0.473663\pi$
$197$	1.35605e14	0.165289	0.0826447	+	0.996579i	$0.473663\pi$
$198$	−1.29908e14	−0.153219
$199$	6.88092e14	0.785419	0.392709	−	0.919663i	$-0.371538\pi$
$199$	6.88092e14	0.785419	0.392709	+	0.919663i	$0.371538\pi$
$200$	1.28344e14	0.141801
$201$	5.66164e14	0.605575
$202$	−2.70093e14	−0.279724
$203$	3.90344e14	0.391492
$204$	−5.24467e14	−0.509474
$205$	1.70898e15	1.60818
$206$	4.71562e13	0.0429934
$207$	2.41045e14	0.212956
$208$	8.50718e13	0.0728407
$209$	5.21636e14	0.432929
$210$	−1.81560e14	−0.146081
$211$	1.75853e15	1.37187	0.685936	−	0.727662i	$-0.259393\pi$
$211$	1.75853e15	1.37187	0.685936	+	0.727662i	$0.259393\pi$
$212$	6.54058e14	0.494804
$213$	5.05444e12	0.00370856
$214$	1.50122e15	1.06845
$215$	7.72854e14	0.533639
$216$	2.70820e14	0.181439
$217$	6.97230e14	0.453302
$218$	5.58646e14	0.352508
$219$	1.02622e15	0.628570
$220$	−1.02148e15	−0.607409
$221$	1.00158e15	0.578277
$222$	−4.66909e14	−0.261781
$223$	4.86298e14	0.264802	0.132401	−	0.991196i	$-0.457731\pi$
$223$	4.86298e14	0.264802	0.132401	+	0.991196i	$0.457731\pi$
$224$	−8.24945e14	−0.436328
$225$	9.75736e13	0.0501356
$226$	1.06652e15	0.532432
$227$	3.06890e15	1.48873	0.744363	−	0.667775i	$-0.232753\pi$
$227$	3.06890e15	1.48873	0.744363	+	0.667775i	$0.232753\pi$
$228$	−4.43260e14	−0.208969
$229$	3.73527e15	1.71156	0.855779	−	0.517341i	$-0.173078\pi$
$229$	3.73527e15	1.71156	0.855779	+	0.517341i	$0.173078\pi$
$230$	−8.59188e14	−0.382699
$231$	4.63492e14	0.200708
$232$	2.07538e15	0.873830
$233$	2.87430e15	1.17684	0.588421	−	0.808555i	$-0.299750\pi$
$233$	2.87430e15	1.17684	0.588421	+	0.808555i	$0.299750\pi$
$234$	−2.10812e14	−0.0839445
$235$	−1.37771e15	−0.533600
$236$	2.37762e14	0.0895807
$237$	−7.33256e14	−0.268777
$238$	−8.48247e14	−0.302533
$239$	4.07439e15	1.41409	0.707043	−	0.707170i	$-0.250029\pi$
$239$	4.07439e15	1.41409	0.707043	+	0.707170i	$0.250029\pi$
$240$	2.96155e14	0.100034
$241$	−3.84825e15	−1.26518	−0.632591	−	0.774486i	$-0.718008\pi$
$241$	−3.84825e15	−1.26518	−0.632591	+	0.774486i	$0.718008\pi$
$242$	5.63011e14	0.180184
$243$	2.05891e14	0.0641500
$244$	1.40301e15	0.425624
$245$	−2.98305e15	−0.881213
$246$	−1.68053e15	−0.483470
$247$	8.46498e14	0.237190
$248$	3.70704e15	1.01179
$249$	−2.89408e15	−0.769510
$250$	1.96457e15	0.508928
$251$	1.83859e15	0.464094	0.232047	−	0.972705i	$-0.425458\pi$
$251$	1.83859e15	0.464094	0.232047	+	0.972705i	$0.425458\pi$
$252$	−3.93852e14	−0.0968789
$253$	2.19336e15	0.525807
$254$	−1.22733e15	−0.286776
$255$	3.48673e15	0.794159
$256$	−3.88549e15	−0.862752
$257$	5.98665e15	1.29604	0.648020	−	0.761623i	$-0.275597\pi$
$257$	5.98665e15	1.29604	0.648020	+	0.761623i	$0.275597\pi$
$258$	−7.59992e14	−0.160428
$259$	1.66586e15	0.342917
$260$	−1.65763e15	−0.332782
$261$	1.57781e15	0.308953
$262$	−1.68750e15	−0.322319
$263$	8.06577e15	1.50291	0.751456	−	0.659783i	$-0.229352\pi$
$263$	8.06577e15	1.50291	0.751456	+	0.659783i	$0.229352\pi$
$264$	2.46430e15	0.447989
$265$	−4.34827e15	−0.771290
$266$	−7.16906e14	−0.124089
$267$	−2.29914e15	−0.388367
$268$	−4.37769e15	−0.721720
$269$	−4.03220e15	−0.648862	−0.324431	−	0.945909i	$-0.605173\pi$
$269$	−4.03220e15	−0.648862	−0.324431	+	0.945909i	$0.605173\pi$
$270$	−7.33885e14	−0.115283
$271$	−3.67388e15	−0.563410	−0.281705	−	0.959501i	$-0.590900\pi$
$271$	−3.67388e15	−0.563410	−0.281705	+	0.959501i	$0.590900\pi$
$272$	1.38363e15	0.207168
$273$	7.52142e14	0.109962
$274$	−1.95853e15	−0.279609
$275$	8.87860e14	0.123789
$276$	−1.86381e15	−0.253800
$277$	1.16773e16	1.55319	0.776596	−	0.629999i	$-0.216945\pi$
$277$	1.16773e16	1.55319	0.776596	+	0.629999i	$0.216945\pi$
$278$	−7.56172e13	−0.00982493
$279$	2.81828e15	0.357731
$280$	3.44411e15	0.427119
$281$	2.58808e15	0.313608	0.156804	−	0.987630i	$-0.449881\pi$
$281$	2.58808e15	0.313608	0.156804	+	0.987630i	$0.449881\pi$
$282$	1.35478e15	0.160416
$283$	−1.06904e16	−1.23704	−0.618520	−	0.785769i	$-0.712267\pi$
$283$	−1.06904e16	−1.23704	−0.618520	+	0.785769i	$0.712267\pi$
$284$	−3.90819e13	−0.00441984
$285$	2.94685e15	0.325737
$286$	−1.91826e15	−0.207266
$287$	5.99587e15	0.633316
$288$	−3.33452e15	−0.344335
$289$	6.38541e15	0.644693
$290$	−5.62401e15	−0.555212
$291$	−2.60269e15	−0.251257
$292$	−7.93493e15	−0.749126
$293$	−1.26671e16	−1.16960	−0.584802	−	0.811176i	$-0.698828\pi$
$293$	−1.26671e16	−1.16960	−0.584802	+	0.811176i	$0.698828\pi$
$294$	2.93340e15	0.264920
$295$	−1.58068e15	−0.139637
$296$	8.85704e15	0.765407
$297$	1.87348e15	0.158392
$298$	1.06819e16	0.883575
$299$	3.55933e15	0.288075
$300$	−7.54458e14	−0.0597513
$301$	2.71153e15	0.210151
$302$	6.52611e15	0.495005
$303$	3.89516e15	0.289167
$304$	1.16939e15	0.0849734
$305$	−9.32739e15	−0.663455
$306$	−3.42871e15	−0.238749
$307$	−2.07449e16	−1.41420	−0.707102	−	0.707112i	$-0.749998\pi$
$307$	−2.07449e16	−1.41420	−0.707102	+	0.707112i	$0.749998\pi$
$308$	−3.58381e15	−0.239202
$309$	−6.80066e14	−0.0444448
$310$	−1.00456e16	−0.642870
$311$	−2.62817e15	−0.164707	−0.0823533	−	0.996603i	$-0.526244\pi$
$311$	−2.62817e15	−0.164707	−0.0823533	+	0.996603i	$0.526244\pi$
$312$	3.99900e15	0.245441
$313$	1.92988e15	0.116009	0.0580046	−	0.998316i	$-0.481526\pi$
$313$	1.92988e15	0.116009	0.0580046	+	0.998316i	$0.481526\pi$
$314$	−5.70668e15	−0.336001
$315$	2.61838e15	0.151013
$316$	5.66968e15	0.320326
$317$	2.88022e16	1.59419	0.797095	−	0.603854i	$-0.206369\pi$
$317$	2.88022e16	1.59419	0.797095	+	0.603854i	$0.206369\pi$
$318$	4.27590e15	0.231874
$319$	1.43571e16	0.762830
$320$	8.55768e15	0.445534
$321$	−2.16499e16	−1.10452
$322$	−3.01443e15	−0.150710
$323$	1.37677e16	0.674597
$324$	−1.59199e15	−0.0764536
$325$	1.44080e15	0.0678204
$326$	8.71357e15	0.402052
$327$	−8.05656e15	−0.364409
$328$	3.18789e16	1.41359
$329$	−4.83363e15	−0.210136
$330$	−6.67791e15	−0.284642
$331$	2.39044e16	0.999069	0.499534	−	0.866294i	$-0.333504\pi$
$331$	2.39044e16	0.999069	0.499534	+	0.866294i	$0.333504\pi$
$332$	2.23776e16	0.917098
$333$	6.73357e15	0.270619
$334$	6.31678e15	0.248968
$335$	2.91035e16	1.12500
$336$	1.03905e15	0.0393940
$337$	−3.42727e15	−0.127454	−0.0637271	−	0.997967i	$-0.520299\pi$
$337$	−3.42727e15	−0.127454	−0.0637271	+	0.997967i	$0.520299\pi$
$338$	1.21972e16	0.444941
$339$	−1.53809e16	−0.550406
$340$	−2.69601e16	−0.946474
$341$	2.56446e16	0.883268
$342$	−2.89781e15	−0.0979266
$343$	−2.32045e16	−0.769415
$344$	1.44167e16	0.469067
$345$	1.23908e16	0.395619
$346$	2.72800e16	0.854772
$347$	−2.56153e16	−0.787696	−0.393848	−	0.919176i	$-0.628856\pi$
$347$	−2.56153e16	−0.787696	−0.393848	+	0.919176i	$0.628856\pi$
$348$	−1.22000e16	−0.368208
$349$	−2.32184e16	−0.687808	−0.343904	−	0.939005i	$-0.611749\pi$
$349$	−2.32184e16	−0.687808	−0.343904	+	0.939005i	$0.611749\pi$
$350$	−1.22022e15	−0.0354811
$351$	3.04024e15	0.0867784
$352$	−3.03421e16	−0.850194
$353$	2.19899e16	0.604906	0.302453	−	0.953164i	$-0.402195\pi$
$353$	2.19899e16	0.604906	0.302453	+	0.953164i	$0.402195\pi$
$354$	1.55437e15	0.0419791
$355$	2.59822e14	0.00688956
$356$	1.77774e16	0.462853
$357$	1.22331e16	0.312746
$358$	1.94950e16	0.489423
$359$	5.31112e16	1.30940	0.654700	−	0.755889i	$-0.272795\pi$
$359$	5.31112e16	1.30940	0.654700	+	0.755889i	$0.272795\pi$
$360$	1.39214e16	0.337068
$361$	−3.04171e16	−0.723303
$362$	−1.68586e16	−0.393745
$363$	−8.11950e15	−0.186267
$364$	−5.81571e15	−0.131052
$365$	5.27525e16	1.16772
$366$	9.17217e15	0.199455
$367$	−2.82440e16	−0.603389	−0.301694	−	0.953405i	$-0.597552\pi$
$367$	−2.82440e16	−0.603389	−0.301694	+	0.953405i	$0.597552\pi$
$368$	4.91704e15	0.103203
$369$	2.42360e16	0.499792
$370$	−2.40014e16	−0.486323
$371$	−1.52557e16	−0.303740
$372$	−2.17915e16	−0.426341
$373$	−7.71493e16	−1.48329	−0.741643	−	0.670795i	$-0.765953\pi$
$373$	−7.71493e16	−1.48329	−0.741643	+	0.670795i	$0.765953\pi$
$374$	−3.11991e16	−0.589491
$375$	−2.83321e16	−0.526110
$376$	−2.56995e16	−0.469033
$377$	2.32984e16	0.417933
$378$	−2.57481e15	−0.0453992
$379$	−2.09459e16	−0.363031	−0.181515	−	0.983388i	$-0.558100\pi$
$379$	−2.09459e16	−0.363031	−0.181515	+	0.983388i	$0.558100\pi$
$380$	−2.27857e16	−0.388211
$381$	1.77001e16	0.296458
$382$	3.77651e16	0.621840
$383$	−8.59456e16	−1.39133	−0.695667	−	0.718364i	$-0.744891\pi$
$383$	−8.59456e16	−1.39133	−0.695667	+	0.718364i	$0.744891\pi$
$384$	2.90557e16	0.462465
$385$	2.38257e16	0.372864
$386$	−4.38600e16	−0.674918
$387$	1.09603e16	0.165844
$388$	2.01246e16	0.299447
$389$	−6.66476e16	−0.975241	−0.487621	−	0.873056i	$-0.662135\pi$
$389$	−6.66476e16	−0.975241	−0.487621	+	0.873056i	$0.662135\pi$
$390$	−1.08367e16	−0.155947
$391$	5.78899e16	0.819321
$392$	−5.56452e16	−0.774584
$393$	2.43364e16	0.333200
$394$	−6.85473e15	−0.0923134
$395$	−3.76928e16	−0.499319
$396$	−1.44861e16	−0.188771
$397$	−3.52260e16	−0.451570	−0.225785	−	0.974177i	$-0.572495\pi$
$397$	−3.52260e16	−0.451570	−0.225785	+	0.974177i	$0.572495\pi$
$398$	−3.47825e16	−0.438653
$399$	1.03389e16	0.128278
$400$	1.99039e15	0.0242967
$401$	−7.75262e16	−0.931129	−0.465564	−	0.885014i	$-0.654149\pi$
$401$	−7.75262e16	−0.931129	−0.465564	+	0.885014i	$0.654149\pi$
$402$	−2.86192e16	−0.338211
$403$	4.16154e16	0.483917
$404$	−3.01182e16	−0.344628
$405$	1.05838e16	0.119174
$406$	−1.97316e16	−0.218647
$407$	6.12714e16	0.668181
$408$	6.50409e16	0.698064
$409$	1.31106e17	1.38491	0.692455	−	0.721461i	$-0.256529\pi$
$409$	1.31106e17	1.38491	0.692455	+	0.721461i	$0.256529\pi$
$410$	−8.63875e16	−0.898164
$411$	2.82451e16	0.289049
$412$	5.25841e15	0.0529691
$413$	−5.54574e15	−0.0549900
$414$	−1.21846e16	−0.118935
$415$	−1.48769e17	−1.42956
$416$	−4.92383e16	−0.465797
$417$	1.09052e15	0.0101566
$418$	−2.63683e16	−0.241789
$419$	1.72833e16	0.156040	0.0780198	−	0.996952i	$-0.475140\pi$
$419$	1.72833e16	0.156040	0.0780198	+	0.996952i	$0.475140\pi$
$420$	−2.02459e16	−0.179976
$421$	1.22446e17	1.07179	0.535896	−	0.844284i	$-0.319974\pi$
$421$	1.22446e17	1.07179	0.535896	+	0.844284i	$0.319974\pi$
$422$	−8.88924e16	−0.766185
$423$	−1.95380e16	−0.165832
$424$	−8.11118e16	−0.677963
$425$	2.34335e16	0.192890
$426$	−2.55498e14	−0.00207122
$427$	−3.27248e16	−0.261274
$428$	1.67402e17	1.31636
$429$	2.76643e16	0.214263
$430$	−3.90672e16	−0.298035
$431$	7.09734e16	0.533327	0.266663	−	0.963790i	$-0.414079\pi$
$431$	7.09734e16	0.533327	0.266663	+	0.963790i	$0.414079\pi$
$432$	4.19994e15	0.0310884
$433$	−1.40125e17	−1.02175	−0.510875	−	0.859655i	$-0.670679\pi$
$433$	−1.40125e17	−1.02175	−0.510875	+	0.859655i	$0.670679\pi$
$434$	−3.52444e16	−0.253167
$435$	8.11070e16	0.573956
$436$	6.22949e16	0.434300
$437$	4.89264e16	0.336058
$438$	−5.18746e16	−0.351053
$439$	−2.30870e16	−0.153939	−0.0769694	−	0.997033i	$-0.524524\pi$
$439$	−2.30870e16	−0.153939	−0.0769694	+	0.997033i	$0.524524\pi$
$440$	1.26677e17	0.832250
$441$	−4.23043e16	−0.273863
$442$	−5.06291e16	−0.322965
$443$	2.20068e17	1.38335	0.691676	−	0.722208i	$-0.256873\pi$
$443$	2.20068e17	1.38335	0.691676	+	0.722208i	$0.256873\pi$
$444$	−5.20653e16	−0.322522
$445$	−1.18187e17	−0.721487
$446$	−2.45820e16	−0.147891
$447$	−1.54050e17	−0.913404
$448$	3.00243e16	0.175455
$449$	6.32643e16	0.364382	0.182191	−	0.983263i	$-0.441681\pi$
$449$	6.32643e16	0.364382	0.182191	+	0.983263i	$0.441681\pi$
$450$	−4.93227e15	−0.0280005
$451$	2.20532e17	1.23403
$452$	1.18928e17	0.655971
$453$	−9.41169e16	−0.511716
$454$	−1.55131e17	−0.831447
$455$	3.86637e16	0.204282
$456$	5.49701e16	0.286322
$457$	−1.15038e17	−0.590728	−0.295364	−	0.955385i	$-0.595441\pi$
$457$	−1.15038e17	−0.590728	−0.295364	+	0.955385i	$0.595441\pi$
$458$	−1.88815e17	−0.955898
$459$	4.94473e16	0.246809
$460$	−9.58085e16	−0.471496
$461$	−2.24004e17	−1.08693	−0.543464	−	0.839433i	$-0.682887\pi$
$461$	−2.24004e17	−1.08693	−0.543464	+	0.839433i	$0.682887\pi$
$462$	−2.34292e16	−0.112094
$463$	−1.51465e17	−0.714556	−0.357278	−	0.933998i	$-0.616295\pi$
$463$	−1.51465e17	−0.714556	−0.357278	+	0.933998i	$0.616295\pi$
$464$	3.21855e16	0.149725
$465$	1.44873e17	0.664573
$466$	−1.45294e17	−0.657261
$467$	−1.19765e17	−0.534281	−0.267141	−	0.963658i	$-0.586079\pi$
$467$	−1.19765e17	−0.534281	−0.267141	+	0.963658i	$0.586079\pi$
$468$	−2.35077e16	−0.103422
$469$	1.02109e17	0.443035
$470$	6.96420e16	0.298013
$471$	8.22993e16	0.347344
$472$	−2.94856e16	−0.122740
$473$	9.97319e16	0.409484
$474$	3.70656e16	0.150111
$475$	1.98051e16	0.0791169
$476$	−9.45885e16	−0.372729
$477$	−6.16652e16	−0.239702
$478$	−2.05957e17	−0.789761
$479$	−1.49450e17	−0.565348	−0.282674	−	0.959216i	$-0.591222\pi$
$479$	−1.49450e17	−0.565348	−0.282674	+	0.959216i	$0.591222\pi$
$480$	−1.71410e17	−0.639688
$481$	9.94296e16	0.366077
$482$	1.94526e17	0.706598
$483$	4.34728e16	0.155798
$484$	6.27816e16	0.221992
$485$	−1.33791e17	−0.466772
$486$	−1.04076e16	−0.0358275
$487$	−2.25150e17	−0.764774	−0.382387	−	0.924002i	$-0.624898\pi$
$487$	−2.25150e17	−0.764774	−0.382387	+	0.924002i	$0.624898\pi$
$488$	−1.73991e17	−0.583175
$489$	−1.25663e17	−0.415625
$490$	1.50791e17	0.492153
$491$	−3.25842e17	−1.04949	−0.524744	−	0.851260i	$-0.675839\pi$
$491$	−3.25842e17	−1.04949	−0.524744	+	0.851260i	$0.675839\pi$
$492$	−1.87397e17	−0.595649
$493$	3.78931e17	1.18865
$494$	−4.27898e16	−0.132469
$495$	9.63059e16	0.294252
$496$	5.74896e16	0.173364
$497$	9.11575e14	0.00271316
$498$	1.46294e17	0.429768
$499$	−3.24801e17	−0.941811	−0.470906	−	0.882184i	$-0.656073\pi$
$499$	−3.24801e17	−0.941811	−0.470906	+	0.882184i	$0.656073\pi$
$500$	2.19070e17	0.627014
$501$	−9.10980e16	−0.257373
$502$	−9.29395e16	−0.259195
$503$	1.20825e17	0.332633	0.166316	−	0.986072i	$-0.446813\pi$
$503$	1.20825e17	0.332633	0.166316	+	0.986072i	$0.446813\pi$
$504$	4.88428e16	0.132740
$505$	2.00230e17	0.537199
$506$	−1.10873e17	−0.293661
$507$	−1.75903e17	−0.459962
$508$	−1.36860e17	−0.353316
$509$	4.57191e17	1.16528	0.582642	−	0.812729i	$-0.302019\pi$
$509$	4.57191e17	1.16528	0.582642	+	0.812729i	$0.302019\pi$
$510$	−1.76252e17	−0.443534
$511$	1.85080e17	0.459858
$512$	−1.30100e17	−0.319170
$513$	4.17910e16	0.101233
$514$	−3.02621e17	−0.723833
$515$	−3.49586e16	−0.0825672
$516$	−8.47471e16	−0.197652
$517$	−1.77784e17	−0.409454
$518$	−8.42078e16	−0.191518
$519$	−3.93421e17	−0.883629
$520$	2.05567e17	0.455966
$521$	5.22701e17	1.14501	0.572503	−	0.819902i	$-0.305972\pi$
$521$	5.22701e17	1.14501	0.572503	+	0.819902i	$0.305972\pi$
$522$	−7.97572e16	−0.172549
$523$	−2.81260e17	−0.600961	−0.300481	−	0.953788i	$-0.597147\pi$
$523$	−2.81260e17	−0.600961	−0.300481	+	0.953788i	$0.597147\pi$
$524$	−1.88174e17	−0.397106
$525$	1.75975e16	0.0366789
$526$	−4.07719e17	−0.839370
$527$	6.76845e17	1.37632
$528$	3.82169e16	0.0767600
$529$	−2.98312e17	−0.591846
$530$	2.19802e17	0.430762
$531$	−2.24165e16	−0.0433963
$532$	−7.99426e16	−0.152881
$533$	3.57874e17	0.676089
$534$	1.16220e17	0.216901
$535$	−1.11291e18	−2.05192
$536$	5.42892e17	0.988876
$537$	−2.81149e17	−0.505946
$538$	2.03825e17	0.362386
$539$	−3.84943e17	−0.676192
$540$	−8.18359e16	−0.142031
$541$	−2.86138e17	−0.490674	−0.245337	−	0.969438i	$-0.578899\pi$
$541$	−2.86138e17	−0.490674	−0.245337	+	0.969438i	$0.578899\pi$
$542$	1.85712e17	0.314662
$543$	2.43127e17	0.407038
$544$	−8.00826e17	−1.32478
$545$	−4.14145e17	−0.676979
$546$	−3.80202e16	−0.0614133
$547$	1.02844e18	1.64157	0.820786	−	0.571236i	$-0.193536\pi$
$547$	1.02844e18	1.64157	0.820786	+	0.571236i	$0.193536\pi$
$548$	−2.18397e17	−0.344487
$549$	−1.32277e17	−0.206188
$550$	−4.48807e16	−0.0691356
$551$	3.20258e17	0.487546
$552$	2.31137e17	0.347748
$553$	−1.32244e17	−0.196636
$554$	−5.90280e17	−0.867451
$555$	3.46137e17	0.502741
$556$	−8.43211e15	−0.0121046
$557$	1.07069e17	0.151916	0.0759580	−	0.997111i	$-0.475799\pi$
$557$	1.07069e17	0.151916	0.0759580	+	0.997111i	$0.475799\pi$
$558$	−1.42462e17	−0.199791
$559$	1.61842e17	0.224344
$560$	5.34120e16	0.0731840
$561$	4.49941e17	0.609392
$562$	−1.30826e17	−0.175149
$563$	2.92192e17	0.386691	0.193346	−	0.981131i	$-0.438066\pi$
$563$	2.92192e17	0.386691	0.193346	+	0.981131i	$0.438066\pi$
$564$	1.51072e17	0.197638
$565$	−7.90651e17	−1.02252
$566$	5.40393e17	0.690881
$567$	3.71328e16	0.0469318
$568$	4.84667e15	0.00605591
$569$	−1.23283e18	−1.52290	−0.761452	−	0.648222i	$-0.775513\pi$
$569$	−1.23283e18	−1.52290	−0.761452	+	0.648222i	$0.775513\pi$
$570$	−1.48961e17	−0.181923
$571$	−3.24861e17	−0.392250	−0.196125	−	0.980579i	$-0.562836\pi$
$571$	−3.24861e17	−0.392250	−0.196125	+	0.980579i	$0.562836\pi$
$572$	−2.13906e17	−0.255358
$573$	−5.44632e17	−0.642833
$574$	−3.03087e17	−0.353704
$575$	8.32760e16	0.0960902
$576$	1.21361e17	0.138463
$577$	9.43612e17	1.06451	0.532256	−	0.846583i	$-0.321344\pi$
$577$	9.43612e17	1.06451	0.532256	+	0.846583i	$0.321344\pi$
$578$	−3.22778e17	−0.360058
$579$	6.32530e17	0.697703
$580$	−6.27136e17	−0.684037
$581$	−5.21951e17	−0.562970
$582$	1.31564e17	0.140326
$583$	−5.61116e17	−0.591844
$584$	9.84036e17	1.02643
$585$	1.56283e17	0.161212
$586$	6.40314e17	0.653219
$587$	−2.58102e17	−0.260401	−0.130201	−	0.991488i	$-0.541562\pi$
$587$	−2.58102e17	−0.260401	−0.130201	+	0.991488i	$0.541562\pi$
$588$	3.27105e17	0.326389
$589$	5.72043e17	0.564520
$590$	7.99020e16	0.0779865
$591$	9.88560e16	0.0954298
$592$	1.37357e17	0.131147
$593$	3.35694e16	0.0317021	0.0158511	−	0.999874i	$-0.494954\pi$
$593$	3.35694e16	0.0317021	0.0158511	+	0.999874i	$0.494954\pi$
$594$	−9.47032e16	−0.0884612
$595$	6.28837e17	0.581003
$596$	1.19115e18	1.08859
$597$	5.01619e17	0.453462
$598$	−1.79921e17	−0.160889
$599$	1.41440e18	1.25112	0.625559	−	0.780177i	$-0.284871\pi$
$599$	1.41440e18	1.25112	0.625559	+	0.780177i	$0.284871\pi$
$600$	9.35628e16	0.0818691
$601$	1.01261e18	0.876512	0.438256	−	0.898850i	$-0.355596\pi$
$601$	1.01261e18	0.876512	0.438256	+	0.898850i	$0.355596\pi$
$602$	−1.37066e17	−0.117368
$603$	4.12733e17	0.349629
$604$	7.27730e17	0.609860
$605$	−4.17381e17	−0.346037
$606$	−1.96898e17	−0.161499
$607$	8.06416e17	0.654384	0.327192	−	0.944958i	$-0.393898\pi$
$607$	8.06416e17	0.654384	0.327192	+	0.944958i	$0.393898\pi$
$608$	−6.76828e17	−0.543382
$609$	2.84561e17	0.226028
$610$	4.71493e17	0.370537
$611$	−2.88504e17	−0.224328
$612$	−3.82337e17	−0.294145
$613$	−8.03049e17	−0.611293	−0.305646	−	0.952145i	$-0.598873\pi$
$613$	−8.03049e17	−0.611293	−0.305646	+	0.952145i	$0.598873\pi$
$614$	1.04864e18	0.789827
$615$	1.24584e18	0.928486
$616$	4.44440e17	0.327747
$617$	1.06814e18	0.779424	0.389712	−	0.920937i	$-0.372575\pi$
$617$	1.06814e18	0.779424	0.389712	+	0.920937i	$0.372575\pi$
$618$	3.43768e16	0.0248222
$619$	1.16855e18	0.834945	0.417473	−	0.908689i	$-0.362916\pi$
$619$	1.16855e18	0.834945	0.417473	+	0.908689i	$0.362916\pi$
$620$	−1.12019e18	−0.792034
$621$	1.75722e17	0.122950
$622$	1.32852e17	0.0919879
$623$	−4.14653e17	−0.284127
$624$	6.20174e16	0.0420546
$625$	−1.68053e18	−1.12778
$626$	−9.75540e16	−0.0647906
$627$	3.80273e17	0.249952
$628$	−6.36355e17	−0.413963
$629$	1.61715e18	1.04117
$630$	−1.32357e17	−0.0843401
$631$	1.21646e17	0.0767198	0.0383599	−	0.999264i	$-0.487787\pi$
$631$	1.21646e17	0.0767198	0.0383599	+	0.999264i	$0.487787\pi$
$632$	−7.03115e17	−0.438900
$633$	1.28197e18	0.792051
$634$	−1.45593e18	−0.890348
$635$	9.09867e17	0.550743
$636$	4.76808e17	0.285675
$637$	−6.24676e17	−0.370466
$638$	−7.25742e17	−0.426038
$639$	3.68469e15	0.00214114
$640$	1.49360e18	0.859143
$641$	−2.14933e18	−1.22384	−0.611921	−	0.790919i	$-0.709603\pi$
$641$	−2.14933e18	−1.22384	−0.611921	+	0.790919i	$0.709603\pi$
$642$	1.09439e18	0.616870
$643$	−1.31472e18	−0.733602	−0.366801	−	0.930299i	$-0.619547\pi$
$643$	−1.31472e18	−0.733602	−0.366801	+	0.930299i	$0.619547\pi$
$644$	−3.36140e17	−0.185679
$645$	5.63410e17	0.308097
$646$	−6.95946e17	−0.376760
$647$	1.16316e18	0.623393	0.311696	−	0.950182i	$-0.399103\pi$
$647$	1.16316e18	0.623393	0.311696	+	0.950182i	$0.399103\pi$
$648$	1.97428e17	0.104754
$649$	−2.03976e17	−0.107149
$650$	−7.28312e16	−0.0378774
$651$	5.08280e17	0.261714
$652$	9.71655e17	0.495339
$653$	−7.99999e16	−0.0403788	−0.0201894	−	0.999796i	$-0.506427\pi$
$653$	−7.99999e16	−0.0403788	−0.0201894	+	0.999796i	$0.506427\pi$
$654$	4.07253e17	0.203521
$655$	1.25101e18	0.619001
$656$	4.94386e17	0.242209
$657$	7.48114e17	0.362905
$658$	2.44336e17	0.117360
$659$	−4.14903e18	−1.97329	−0.986646	−	0.162880i	$-0.947922\pi$
$659$	−4.14903e18	−1.97329	−0.986646	+	0.162880i	$0.947922\pi$
$660$	−7.44657e17	−0.350688
$661$	−1.23438e18	−0.575624	−0.287812	−	0.957687i	$-0.592928\pi$
$661$	−1.23438e18	−0.575624	−0.287812	+	0.957687i	$0.592928\pi$
$662$	−1.20835e18	−0.557976
$663$	7.30152e17	0.333868
$664$	−2.77512e18	−1.25658
$665$	5.31470e17	0.238308
$666$	−3.40377e17	−0.151139
$667$	1.34661e18	0.592141
$668$	7.04388e17	0.306736
$669$	3.54511e17	0.152883
$670$	−1.47116e18	−0.628310
$671$	−1.20364e18	−0.509097
$672$	−6.01385e17	−0.251914
$673$	−1.37752e18	−0.571478	−0.285739	−	0.958307i	$-0.592239\pi$
$673$	−1.37752e18	−0.571478	−0.285739	+	0.958307i	$0.592239\pi$
$674$	1.73246e17	0.0711826
$675$	7.11311e16	0.0289458
$676$	1.36012e18	0.548179
$677$	−2.42610e18	−0.968462	−0.484231	−	0.874940i	$-0.660901\pi$
$677$	−2.42610e18	−0.968462	−0.484231	+	0.874940i	$0.660901\pi$
$678$	7.77493e17	0.307400
$679$	−4.69400e17	−0.183819
$680$	3.34341e18	1.29683
$681$	2.23723e18	0.859517
$682$	−1.29632e18	−0.493301
$683$	4.97289e18	1.87445	0.937226	−	0.348723i	$-0.113384\pi$
$683$	4.97289e18	1.87445	0.937226	+	0.348723i	$0.113384\pi$
$684$	−3.23137e17	−0.120648
$685$	1.45193e18	0.536979
$686$	1.17297e18	0.429715
$687$	2.72301e18	0.988169
$688$	2.23577e17	0.0803716
$689$	−9.10564e17	−0.324254
$690$	−6.26348e17	−0.220951
$691$	1.17508e18	0.410638	0.205319	−	0.978695i	$-0.434177\pi$
$691$	1.17508e18	0.410638	0.205319	+	0.978695i	$0.434177\pi$
$692$	3.04201e18	1.05310
$693$	3.37886e17	0.115879
$694$	1.29484e18	0.439925
$695$	5.60578e16	0.0188684
$696$	1.51296e18	0.504506
$697$	5.82057e18	1.92288
$698$	1.17367e18	0.384138
$699$	2.09536e18	0.679450
$700$	−1.36068e17	−0.0437137
$701$	−1.07940e18	−0.343571	−0.171785	−	0.985134i	$-0.554954\pi$
$701$	−1.07940e18	−0.343571	−0.171785	+	0.985134i	$0.554954\pi$
$702$	−1.53682e17	−0.0484654
$703$	1.36676e18	0.427052
$704$	1.10431e18	0.341877
$705$	−1.00435e18	−0.308074
$706$	−1.11157e18	−0.337837
$707$	7.02499e17	0.211553
$708$	1.73329e17	0.0517195
$709$	1.40723e18	0.416069	0.208035	−	0.978121i	$-0.433293\pi$
$709$	1.40723e18	0.416069	0.208035	+	0.978121i	$0.433293\pi$
$710$	−1.31338e16	−0.00384779
$711$	−5.34544e17	−0.155178
$712$	−2.20463e18	−0.634185
$713$	2.40531e18	0.685629
$714$	−6.18372e17	−0.174667
$715$	1.42208e18	0.398047
$716$	2.17390e18	0.602983
$717$	2.97023e18	0.816423
$718$	−2.68473e18	−0.731294
$719$	5.79677e18	1.56476	0.782381	−	0.622801i	$-0.214005\pi$
$719$	5.79677e18	1.56476	0.782381	+	0.622801i	$0.214005\pi$
$720$	2.15897e17	0.0577544
$721$	−1.22651e17	−0.0325156
$722$	1.53756e18	0.403962
$723$	−2.80538e18	−0.730453
$724$	−1.87991e18	−0.485106
$725$	5.45102e17	0.139406
$726$	4.10435e17	0.104029
$727$	−2.50807e18	−0.630037	−0.315019	−	0.949085i	$-0.602011\pi$
$727$	−2.50807e18	−0.630037	−0.315019	+	0.949085i	$0.602011\pi$
$728$	7.21225e17	0.179563
$729$	1.50095e17	0.0370370
$730$	−2.66660e18	−0.652168
$731$	2.63225e18	0.638064
$732$	1.02279e18	0.245734
$733$	−2.09009e18	−0.497726	−0.248863	−	0.968539i	$-0.580057\pi$
$733$	−2.09009e18	−0.497726	−0.248863	+	0.968539i	$0.580057\pi$
$734$	1.42772e18	0.336990
$735$	−2.17464e18	−0.508768
$736$	−2.84591e18	−0.659956
$737$	3.75562e18	0.863263
$738$	−1.22511e18	−0.279131
$739$	−6.12341e18	−1.38294	−0.691471	−	0.722404i	$-0.743037\pi$
$739$	−6.12341e18	−1.38294	−0.691471	+	0.722404i	$0.743037\pi$
$740$	−2.67640e18	−0.599164
$741$	6.17097e17	0.136941
$742$	7.71165e17	0.169638
$743$	−2.69022e18	−0.586626	−0.293313	−	0.956016i	$-0.594758\pi$
$743$	−2.69022e18	−0.586626	−0.293313	+	0.956016i	$0.594758\pi$
$744$	2.70243e18	0.584158
$745$	−7.91891e18	−1.69687
$746$	3.89984e18	0.828408
$747$	−2.10978e18	−0.444277
$748$	−3.47903e18	−0.726269
$749$	−3.90460e18	−0.808062
$750$	1.43217e18	0.293830
$751$	3.80510e18	0.773938	0.386969	−	0.922093i	$-0.373522\pi$
$751$	3.80510e18	0.773938	0.386969	+	0.922093i	$0.373522\pi$
$752$	−3.98553e17	−0.0803657
$753$	1.34033e18	0.267945
$754$	−1.17772e18	−0.233414
$755$	−4.83805e18	−0.950639
$756$	−2.87118e17	−0.0559331
$757$	−2.06600e18	−0.399032	−0.199516	−	0.979895i	$-0.563937\pi$
$757$	−2.06600e18	−0.399032	−0.199516	+	0.979895i	$0.563937\pi$
$758$	1.05880e18	0.202751
$759$	1.59896e18	0.303575
$760$	2.82572e18	0.531914
$761$	−3.14582e18	−0.587130	−0.293565	−	0.955939i	$-0.594842\pi$
$761$	−3.14582e18	−0.587130	−0.293565	+	0.955939i	$0.594842\pi$
$762$	−8.94725e17	−0.165570
$763$	−1.45301e18	−0.266600
$764$	4.21120e18	0.766125
$765$	2.54183e18	0.458508
$766$	4.34448e18	0.777054
$767$	−3.31007e17	−0.0587040
$768$	−2.83252e18	−0.498110
$769$	1.51535e18	0.264236	0.132118	−	0.991234i	$-0.457822\pi$
$769$	1.51535e18	0.264236	0.132118	+	0.991234i	$0.457822\pi$
$770$	−1.20437e18	−0.208243
$771$	4.36427e18	0.748269
$772$	−4.89085e18	−0.831519
$773$	−6.82449e18	−1.15055	−0.575273	−	0.817962i	$-0.695104\pi$
$773$	−6.82449e18	−1.15055	−0.575273	+	0.817962i	$0.695104\pi$
$774$	−5.54034e17	−0.0926233
$775$	9.73657e17	0.161415
$776$	−2.49571e18	−0.410292
$777$	1.21441e18	0.197983
$778$	3.36899e18	0.544668
$779$	4.91933e18	0.788701
$780$	−1.20841e18	−0.192132
$781$	3.35284e16	0.00528665
$782$	−2.92629e18	−0.457587
$783$	1.15022e18	0.178374
$784$	−8.62959e17	−0.132720
$785$	4.23057e18	0.645278
$786$	−1.23019e18	−0.186091
$787$	−1.16429e18	−0.174673	−0.0873367	−	0.996179i	$-0.527836\pi$
$787$	−1.16429e18	−0.174673	−0.0873367	+	0.996179i	$0.527836\pi$
$788$	−7.64374e17	−0.113733
$789$	5.87995e18	0.867706
$790$	1.90535e18	0.278867
$791$	−2.77397e18	−0.402674
$792$	1.79647e18	0.258647
$793$	−1.95324e18	−0.278920
$794$	1.78065e18	0.252200
$795$	−3.16989e18	−0.445305
$796$	−3.87862e18	−0.540433
$797$	2.02210e17	0.0279462	0.0139731	−	0.999902i	$-0.495552\pi$
$797$	2.02210e17	0.0279462	0.0139731	+	0.999902i	$0.495552\pi$
$798$	−5.22625e17	−0.0716426
$799$	−4.69231e18	−0.638017
$800$	−1.15201e18	−0.155371
$801$	−1.67607e18	−0.224224
$802$	3.91889e18	0.520031
$803$	6.80738e18	0.896043
$804$	−3.19134e18	−0.416685
$805$	2.23471e18	0.289433
$806$	−2.10363e18	−0.270266
$807$	−2.93947e18	−0.374620
$808$	3.73505e18	0.472197
$809$	5.98015e18	0.749975	0.374987	−	0.927030i	$-0.377647\pi$
$809$	5.98015e18	0.749975	0.374987	+	0.927030i	$0.377647\pi$
$810$	−5.35002e17	−0.0665584
$811$	1.53057e18	0.188894	0.0944471	−	0.995530i	$-0.469892\pi$
$811$	1.53057e18	0.188894	0.0944471	+	0.995530i	$0.469892\pi$
$812$	−2.20028e18	−0.269379
$813$	−2.67826e18	−0.325285
$814$	−3.09722e18	−0.373176
$815$	−6.45970e18	−0.772125
$816$	1.00867e18	0.119609
$817$	2.22468e18	0.261712
$818$	−6.62732e18	−0.773467
$819$	5.48312e17	0.0634866
$820$	−9.63311e18	−1.10656
$821$	−2.74455e18	−0.312782	−0.156391	−	0.987695i	$-0.549986\pi$
$821$	−2.74455e18	−0.312782	−0.156391	+	0.987695i	$0.549986\pi$
$822$	−1.42777e18	−0.161433
$823$	−8.61227e18	−0.966092	−0.483046	−	0.875595i	$-0.660470\pi$
$823$	−8.61227e18	−0.966092	−0.483046	+	0.875595i	$0.660470\pi$
$824$	−6.52112e17	−0.0725764
$825$	6.47250e17	0.0714696
$826$	2.80333e17	0.0307117
$827$	−6.85627e18	−0.745250	−0.372625	−	0.927982i	$-0.621542\pi$
$827$	−6.85627e18	−0.745250	−0.372625	+	0.927982i	$0.621542\pi$
$828$	−1.35872e18	−0.146532
$829$	−1.12805e19	−1.20705	−0.603525	−	0.797344i	$-0.706238\pi$
$829$	−1.12805e19	−1.20705	−0.603525	+	0.797344i	$0.706238\pi$
$830$	7.52018e18	0.798400
$831$	8.51277e18	0.896735
$832$	1.79205e18	0.187305
$833$	−1.01599e19	−1.05365
$834$	−5.51249e16	−0.00567242
$835$	−4.68287e18	−0.478134
$836$	−2.94034e18	−0.297891
$837$	2.05452e18	0.206536
$838$	−8.73656e17	−0.0871474
$839$	1.13544e19	1.12386	0.561930	−	0.827185i	$-0.310059\pi$
$839$	1.13544e19	1.12386	0.561930	+	0.827185i	$0.310059\pi$
$840$	2.51075e18	0.246597
$841$	−1.44607e18	−0.140934
$842$	−6.18954e18	−0.598591
$843$	1.88671e18	0.181061
$844$	−9.91243e18	−0.943961
$845$	−9.04225e18	−0.854492
$846$	9.87633e17	0.0926165
$847$	−1.46436e18	−0.136272
$848$	−1.25790e18	−0.116164
$849$	−7.79333e18	−0.714205
$850$	−1.18455e18	−0.107728
$851$	5.74689e18	0.518670
$852$	−2.84907e16	−0.00255180
$853$	1.96407e19	1.74577	0.872887	−	0.487922i	$-0.162245\pi$
$853$	1.96407e19	1.74577	0.872887	+	0.487922i	$0.162245\pi$
$854$	1.65421e18	0.145920
$855$	2.14826e18	0.188064
$856$	−2.07600e19	−1.80363
$857$	1.13444e19	0.978149	0.489074	−	0.872242i	$-0.337335\pi$
$857$	1.13444e19	0.978149	0.489074	+	0.872242i	$0.337335\pi$
$858$	−1.39841e18	−0.119665
$859$	2.24083e18	0.190306	0.0951532	−	0.995463i	$-0.469666\pi$
$859$	2.24083e18	0.190306	0.0951532	+	0.995463i	$0.469666\pi$
$860$	−4.35640e18	−0.367188
$861$	4.37099e18	0.365645
$862$	−3.58765e18	−0.297861
$863$	−9.16519e17	−0.0755216	−0.0377608	−	0.999287i	$-0.512023\pi$
$863$	−9.16519e17	−0.0755216	−0.0377608	+	0.999287i	$0.512023\pi$
$864$	−2.43086e18	−0.198802
$865$	−2.02237e19	−1.64156
$866$	7.08322e18	0.570643
$867$	4.65496e18	0.372213
$868$	−3.93013e18	−0.311909
$869$	−4.86402e18	−0.383148
$870$	−4.09990e18	−0.320552
$871$	6.09453e18	0.472957
$872$	−7.72539e18	−0.595063
$873$	−1.89736e18	−0.145064
$874$	−2.47319e18	−0.187687
$875$	−5.10974e18	−0.384899
$876$	−5.78457e18	−0.432508
$877$	6.09511e17	0.0452360	0.0226180	−	0.999744i	$-0.492800\pi$
$877$	6.09511e17	0.0452360	0.0226180	+	0.999744i	$0.492800\pi$
$878$	1.16703e18	0.0859742
$879$	−9.23434e18	−0.675271
$880$	1.96453e18	0.142601
$881$	1.39303e19	1.00373	0.501864	−	0.864946i	$-0.332648\pi$
$881$	1.39303e19	1.00373	0.501864	+	0.864946i	$0.332648\pi$
$882$	2.13845e18	0.152951
$883$	1.02586e18	0.0728353	0.0364176	−	0.999337i	$-0.488405\pi$
$883$	1.02586e18	0.0728353	0.0364176	+	0.999337i	$0.488405\pi$
$884$	−5.64568e18	−0.397902
$885$	−1.15231e18	−0.0806193
$886$	−1.11243e19	−0.772596
$887$	−1.27239e19	−0.877240	−0.438620	−	0.898673i	$-0.644533\pi$
$887$	−1.27239e19	−0.877240	−0.438620	+	0.898673i	$0.644533\pi$
$888$	6.45678e18	0.441908
$889$	3.19223e18	0.216887
$890$	5.97425e18	0.402947
$891$	1.36577e18	0.0914476
$892$	−2.74115e18	−0.182206
$893$	−3.96576e18	−0.261693
$894$	7.78712e18	0.510132
$895$	−1.44524e19	−0.939919
$896$	5.24025e18	0.338337
$897$	2.59475e18	0.166320
$898$	−3.19796e18	−0.203506
$899$	1.57445e19	0.994697
$900$	−5.50000e17	−0.0344974
$901$	−1.48097e19	−0.922220
$902$	−1.11478e19	−0.689199
$903$	1.97670e18	0.121331
$904$	−1.47487e19	−0.898789
$905$	1.24979e19	0.756173
$906$	4.75754e18	0.285791
$907$	5.55451e18	0.331282	0.165641	−	0.986186i	$-0.447031\pi$
$907$	5.55451e18	0.331282	0.165641	+	0.986186i	$0.447031\pi$
$908$	−1.72987e19	−1.02437
$909$	2.83958e18	0.166951
$910$	−1.95442e18	−0.114090
$911$	−1.15177e19	−0.667567	−0.333784	−	0.942650i	$-0.608326\pi$
$911$	−1.15177e19	−0.667567	−0.333784	+	0.942650i	$0.608326\pi$
$912$	8.52489e17	0.0490594
$913$	−1.91977e19	−1.09696
$914$	5.81510e18	0.329919
$915$	−6.79967e18	−0.383046
$916$	−2.10549e19	−1.17769
$917$	4.38911e18	0.243767
$918$	−2.49953e18	−0.137842
$919$	2.72242e19	1.49075	0.745374	−	0.666647i	$-0.232271\pi$
$919$	2.72242e19	1.49075	0.745374	+	0.666647i	$0.232271\pi$
$920$	1.18815e19	0.646028
$921$	−1.51230e19	−0.816491
$922$	1.13233e19	0.607044
$923$	5.44090e16	0.00289641
$924$	−2.61260e18	−0.138104
$925$	2.32631e18	0.122109
$926$	7.65645e18	0.399076
$927$	−4.95768e17	−0.0256602
$928$	−1.86285e19	−0.957450
$929$	−1.58452e19	−0.808714	−0.404357	−	0.914601i	$-0.632505\pi$
$929$	−1.58452e19	−0.808714	−0.404357	+	0.914601i	$0.632505\pi$
$930$	−7.32321e18	−0.371161
$931$	−8.58677e18	−0.432172
$932$	−1.62018e19	−0.809764
$933$	−1.91594e18	−0.0950934
$934$	6.05403e18	0.298394
$935$	2.31291e19	1.13210
$936$	2.91527e18	0.141705
$937$	−2.19948e19	−1.06172	−0.530862	−	0.847458i	$-0.678132\pi$
$937$	−2.19948e19	−1.06172	−0.530862	+	0.847458i	$0.678132\pi$
$938$	−5.16151e18	−0.247433
$939$	1.40688e18	0.0669779
$940$	7.76582e18	0.367161
$941$	3.77332e19	1.77170	0.885852	−	0.463968i	$-0.153575\pi$
$941$	3.77332e19	1.77170	0.885852	+	0.463968i	$0.153575\pi$
$942$	−4.16017e18	−0.193990
$943$	2.06846e19	0.957904
$944$	−4.57270e17	−0.0210307
$945$	1.90880e18	0.0871874
$946$	−5.04137e18	−0.228695
$947$	6.17356e17	0.0278138	0.0139069	−	0.999903i	$-0.495573\pi$
$947$	6.17356e17	0.0278138	0.0139069	+	0.999903i	$0.495573\pi$
$948$	4.13320e18	0.184941
$949$	1.10468e19	0.490916
$950$	−1.00113e18	−0.0441864
$951$	2.09968e19	0.920406
$952$	1.17302e19	0.510700
$953$	7.22414e18	0.312379	0.156190	−	0.987727i	$-0.450079\pi$
$953$	7.22414e18	0.312379	0.156190	+	0.987727i	$0.450079\pi$
$954$	3.11713e18	0.133872
$955$	−2.79967e19	−1.19422
$956$	−2.29664e19	−0.973008
$957$	1.04663e19	0.440420
$958$	7.55460e18	0.315745
$959$	5.09405e18	0.211467
$960$	6.23855e18	0.257229
$961$	3.70516e18	0.151742
$962$	−5.02609e18	−0.204452
$963$	−1.57828e19	−0.637695
$964$	2.16917e19	0.870549
$965$	3.25151e19	1.29616
$966$	−2.19752e18	−0.0870124
$967$	4.16904e17	0.0163970	0.00819849	−	0.999966i	$-0.497390\pi$
$967$	4.16904e17	0.0163970	0.00819849	+	0.999966i	$0.497390\pi$
$968$	−7.78575e18	−0.304166
$969$	1.00366e19	0.389479
$970$	6.76303e18	0.260690
$971$	1.84255e19	0.705496	0.352748	−	0.935718i	$-0.385247\pi$
$971$	1.84255e19	0.705496	0.352748	+	0.935718i	$0.385247\pi$
$972$	−1.16056e18	−0.0441405
$973$	1.96677e17	0.00743052
$974$	1.13811e19	0.427123
$975$	1.05034e18	0.0391562
$976$	−2.69830e18	−0.0999232
$977$	1.95997e19	0.720997	0.360499	−	0.932760i	$-0.382607\pi$
$977$	1.95997e19	0.720997	0.360499	+	0.932760i	$0.382607\pi$
$978$	6.35220e18	0.232125
$979$	−1.52512e19	−0.553627
$980$	1.68148e19	0.606347
$981$	−5.87323e18	−0.210392
$982$	1.64711e19	0.586135
$983$	4.19418e19	1.48269	0.741343	−	0.671126i	$-0.234189\pi$
$983$	4.19418e19	1.48269	0.741343	+	0.671126i	$0.234189\pi$
$984$	2.32397e19	0.816137
$985$	5.08167e18	0.177284
$986$	−1.91547e19	−0.663858
$987$	−3.52371e18	−0.121322
$988$	−4.77151e18	−0.163206
$989$	9.35426e18	0.317858
$990$	−4.86819e18	−0.164338
$991$	−1.17649e19	−0.394558	−0.197279	−	0.980347i	$-0.563211\pi$
$991$	−1.17649e19	−0.394558	−0.197279	+	0.980347i	$0.563211\pi$
$992$	−3.32741e19	−1.10861
$993$	1.74263e19	0.576813
$994$	−4.60795e16	−0.00151529
$995$	2.57856e19	0.842417
$996$	1.63133e19	0.529487
$997$	−3.12611e19	−1.00806	−0.504028	−	0.863687i	$-0.668149\pi$
$997$	−3.12611e19	−1.00806	−0.504028	+	0.863687i	$0.668149\pi$
$998$	1.64184e19	0.525997
$999$	4.90877e18	0.156242

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.13	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.13	✓	31	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-50.5493 q^{2} +729.000 q^{3} -5636.77 q^{4} +37474.1 q^{5} -36850.4 q^{6} +131476. q^{7} +699034. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-50.5493 q^{2} +729.000 q^{3} -5636.77 q^{4} +37474.1 q^{5} -36850.4 q^{6} +131476. q^{7} +699034. q^{8} +531441. q^{9} -1.89429e6 q^{10} +4.83579e6 q^{11} -4.10921e6 q^{12} +7.84739e6 q^{13} -6.64603e6 q^{14} +2.73186e7 q^{15} +1.08408e7 q^{16} +1.27632e8 q^{17} -2.68639e7 q^{18} +1.07870e8 q^{19} -2.11233e8 q^{20} +9.58462e7 q^{21} -2.44446e8 q^{22} +4.53568e8 q^{23} +5.09596e8 q^{24} +1.83602e8 q^{25} -3.96680e8 q^{26} +3.87420e8 q^{27} -7.41102e8 q^{28} +2.96893e9 q^{29} -1.38093e9 q^{30} +5.30309e9 q^{31} -6.27448e9 q^{32} +3.52529e9 q^{33} -6.45171e9 q^{34} +4.92695e9 q^{35} -2.99561e9 q^{36} +1.26704e10 q^{37} -5.45275e9 q^{38} +5.72075e9 q^{39} +2.61956e10 q^{40} +4.56042e10 q^{41} -4.84495e9 q^{42} +2.06237e10 q^{43} -2.72582e10 q^{44} +1.99153e10 q^{45} -2.29275e10 q^{46} -3.67643e10 q^{47} +7.90293e9 q^{48} -7.96030e10 q^{49} -9.28094e9 q^{50} +9.30439e10 q^{51} -4.42340e10 q^{52} -1.16034e11 q^{53} -1.95838e10 q^{54} +1.81217e11 q^{55} +9.19064e10 q^{56} +7.86372e10 q^{57} -1.50077e11 q^{58} -4.21805e10 q^{59} -1.53989e11 q^{60} -2.48903e11 q^{61} -2.68067e11 q^{62} +6.98719e10 q^{63} +2.28363e11 q^{64} +2.94074e11 q^{65} -1.78201e11 q^{66} +7.76631e11 q^{67} -7.19434e11 q^{68} +3.30651e11 q^{69} -2.49054e11 q^{70} +6.93339e9 q^{71} +3.71495e11 q^{72} +1.40771e12 q^{73} -6.40479e11 q^{74} +1.33846e11 q^{75} -6.08038e11 q^{76} +6.35791e11 q^{77} -2.89180e11 q^{78} -1.00584e12 q^{79} +4.06248e11 q^{80} +2.82430e11 q^{81} -2.30526e12 q^{82} -3.96993e12 q^{83} -5.40263e11 q^{84} +4.78290e12 q^{85} -1.04251e12 q^{86} +2.16435e12 q^{87} +3.38038e12 q^{88} -3.15383e12 q^{89} -1.00670e12 q^{90} +1.03175e12 q^{91} -2.55666e12 q^{92} +3.86595e12 q^{93} +1.85841e12 q^{94} +4.04232e12 q^{95} -4.57410e12 q^{96} -3.57023e12 q^{97} +4.02387e12 q^{98} +2.56994e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \)	\( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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