LMFDB - Embedded newform 177.14.a.c.1.5

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			1.5
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-121.100 q^{2} +729.000 q^{3} +6473.28 q^{4} -61050.1 q^{5} -88282.1 q^{6} +274195. q^{7} +208137. q^{8} +531441. q^{9} +O(q^{10})$	\(q-121.100 q^{2} +729.000 q^{3} +6473.28 q^{4} -61050.1 q^{5} -88282.1 q^{6} +274195. q^{7} +208137. q^{8} +531441. q^{9} +7.39319e6 q^{10} -3.07589e6 q^{11} +4.71902e6 q^{12} -2.44374e7 q^{13} -3.32051e7 q^{14} -4.45056e7 q^{15} -7.82346e7 q^{16} +3.05792e7 q^{17} -6.43577e7 q^{18} -2.42138e8 q^{19} -3.95195e8 q^{20} +1.99888e8 q^{21} +3.72491e8 q^{22} +1.25066e8 q^{23} +1.51732e8 q^{24} +2.50642e9 q^{25} +2.95938e9 q^{26} +3.87420e8 q^{27} +1.77494e9 q^{28} -1.37616e9 q^{29} +5.38964e9 q^{30} -3.28072e9 q^{31} +7.76917e9 q^{32} -2.24232e9 q^{33} -3.70315e9 q^{34} -1.67397e10 q^{35} +3.44017e9 q^{36} +9.54723e8 q^{37} +2.93229e10 q^{38} -1.78149e10 q^{39} -1.27068e10 q^{40} -2.77688e9 q^{41} -2.42065e10 q^{42} -1.07940e10 q^{43} -1.99111e10 q^{44} -3.24445e10 q^{45} -1.51456e10 q^{46} +4.60463e10 q^{47} -5.70330e10 q^{48} -2.17060e10 q^{49} -3.03528e11 q^{50} +2.22922e10 q^{51} -1.58190e11 q^{52} -8.57839e10 q^{53} -4.69167e10 q^{54} +1.87784e11 q^{55} +5.70702e10 q^{56} -1.76518e11 q^{57} +1.66653e11 q^{58} -4.21805e10 q^{59} -2.88097e11 q^{60} -8.82203e10 q^{61} +3.97296e11 q^{62} +1.45719e11 q^{63} -2.99952e11 q^{64} +1.49191e12 q^{65} +2.71546e11 q^{66} -3.21100e11 q^{67} +1.97948e11 q^{68} +9.11734e10 q^{69} +2.02718e12 q^{70} -3.12169e11 q^{71} +1.10613e11 q^{72} -1.78284e12 q^{73} -1.15617e11 q^{74} +1.82718e12 q^{75} -1.56743e12 q^{76} -8.43394e11 q^{77} +2.15739e12 q^{78} -3.29175e12 q^{79} +4.77623e12 q^{80} +2.82430e11 q^{81} +3.36281e11 q^{82} -2.11978e12 q^{83} +1.29393e12 q^{84} -1.86686e12 q^{85} +1.30716e12 q^{86} -1.00322e12 q^{87} -6.40207e11 q^{88} +5.49190e12 q^{89} +3.92904e12 q^{90} -6.70062e12 q^{91} +8.09590e11 q^{92} -2.39164e12 q^{93} -5.57622e12 q^{94} +1.47825e13 q^{95} +5.66373e12 q^{96} -1.88598e12 q^{97} +2.62860e12 q^{98} -1.63465e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−121.100	−1.33798	−0.668991	−	0.743271i	$-0.733274\pi$
$2$	−121.100	−1.33798	−0.668991	+	0.743271i	$0.733274\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	6473.28	0.790196
$5$	−61050.1	−1.74736	−0.873678	−	0.486504i	$-0.838272\pi$
$5$	−61050.1	−1.74736	−0.873678	+	0.486504i	$0.838272\pi$
$6$	−88282.1	−0.772484
$7$	274195.	0.880892	0.440446	−	0.897779i	$-0.354820\pi$
$7$	274195.	0.880892	0.440446	+	0.897779i	$0.354820\pi$
$8$	208137.	0.280714
$9$	531441.	0.333333
$10$	7.39319e6	2.33793
$11$	−3.07589e6	−0.523502	−0.261751	−	0.965135i	$-0.584300\pi$
$11$	−3.07589e6	−0.523502	−0.261751	+	0.965135i	$0.584300\pi$
$12$	4.71902e6	0.456220
$13$	−2.44374e7	−1.40418	−0.702091	−	0.712087i	$-0.747750\pi$
$13$	−2.44374e7	−1.40418	−0.702091	+	0.712087i	$0.747750\pi$
$14$	−3.32051e7	−1.17862
$15$	−4.45056e7	−1.00884
$16$	−7.82346e7	−1.16579
$17$	3.05792e7	0.307261	0.153631	−	0.988128i	$-0.450903\pi$
$17$	3.05792e7	0.307261	0.153631	+	0.988128i	$0.450903\pi$
$18$	−6.43577e7	−0.445994
$19$	−2.42138e8	−1.18077	−0.590383	−	0.807123i	$-0.701023\pi$
$19$	−2.42138e8	−1.18077	−0.590383	+	0.807123i	$0.701023\pi$
$20$	−3.95195e8	−1.38075
$21$	1.99888e8	0.508583
$22$	3.72491e8	0.700436
$23$	1.25066e8	0.176161	0.0880805	−	0.996113i	$-0.471927\pi$
$23$	1.25066e8	0.176161	0.0880805	+	0.996113i	$0.471927\pi$
$24$	1.51732e8	0.162071
$25$	2.50642e9	2.05326
$26$	2.95938e9	1.87877
$27$	3.87420e8	0.192450
$28$	1.77494e9	0.696077
$29$	−1.37616e9	−0.429616	−0.214808	−	0.976656i	$-0.568913\pi$
$29$	−1.37616e9	−0.429616	−0.214808	+	0.976656i	$0.568913\pi$
$30$	5.38964e9	1.34981
$31$	−3.28072e9	−0.663924	−0.331962	−	0.943293i	$-0.607710\pi$
$31$	−3.28072e9	−0.663924	−0.331962	+	0.943293i	$0.607710\pi$
$32$	7.76917e9	1.27909
$33$	−2.24232e9	−0.302244
$34$	−3.70315e9	−0.411110
$35$	−1.67397e10	−1.53923
$36$	3.44017e9	0.263399
$37$	9.54723e8	0.0611739	0.0305870	−	0.999532i	$-0.490262\pi$
$37$	9.54723e8	0.0611739	0.0305870	+	0.999532i	$0.490262\pi$
$38$	2.93229e10	1.57984
$39$	−1.78149e10	−0.810705
$40$	−1.27068e10	−0.490508
$41$	−2.77688e9	−0.0912981	−0.0456491	−	0.998958i	$-0.514536\pi$
$41$	−2.77688e9	−0.0912981	−0.0456491	+	0.998958i	$0.514536\pi$
$42$	−2.42065e10	−0.680475
$43$	−1.07940e10	−0.260398	−0.130199	−	0.991488i	$-0.541562\pi$
$43$	−1.07940e10	−0.260398	−0.130199	+	0.991488i	$0.541562\pi$
$44$	−1.99111e10	−0.413669
$45$	−3.24445e10	−0.582452
$46$	−1.51456e10	−0.235700
$47$	4.60463e10	0.623102	0.311551	−	0.950230i	$-0.399152\pi$
$47$	4.60463e10	0.623102	0.311551	+	0.950230i	$0.399152\pi$
$48$	−5.70330e10	−0.673067
$49$	−2.17060e10	−0.224029
$50$	−3.03528e11	−2.74722
$51$	2.22922e10	0.177397
$52$	−1.58190e11	−1.10958
$53$	−8.57839e10	−0.531634	−0.265817	−	0.964024i	$-0.585642\pi$
$53$	−8.57839e10	−0.531634	−0.265817	+	0.964024i	$0.585642\pi$
$54$	−4.69167e10	−0.257495
$55$	1.87784e11	0.914745
$56$	5.70702e10	0.247279
$57$	−1.76518e11	−0.681715
$58$	1.66653e11	0.574819
$59$	−4.21805e10	−0.130189
$59$	−4.21805e10	−0.130189
$60$	−2.88097e11	−0.797179
$61$	−8.82203e10	−0.219243	−0.109621	−	0.993973i	$-0.534964\pi$
$61$	−8.82203e10	−0.219243	−0.109621	+	0.993973i	$0.534964\pi$
$62$	3.97296e11	0.888318
$63$	1.45719e11	0.293631
$64$	−2.99952e11	−0.545609
$65$	1.49191e12	2.45361
$66$	2.71546e11	0.404397
$67$	−3.21100e11	−0.433664	−0.216832	−	0.976209i	$-0.569572\pi$
$67$	−3.21100e11	−0.433664	−0.216832	+	0.976209i	$0.569572\pi$
$68$	1.97948e11	0.242797
$69$	9.11734e10	0.101707
$70$	2.02718e12	2.05947
$71$	−3.12169e11	−0.289208	−0.144604	−	0.989490i	$-0.546191\pi$
$71$	−3.12169e11	−0.289208	−0.144604	+	0.989490i	$0.546191\pi$
$72$	1.10613e11	0.0935715
$73$	−1.78284e12	−1.37884	−0.689419	−	0.724363i	$-0.742134\pi$
$73$	−1.78284e12	−1.37884	−0.689419	+	0.724363i	$0.742134\pi$
$74$	−1.15617e11	−0.0818496
$75$	1.82718e12	1.18545
$76$	−1.56743e12	−0.933036
$77$	−8.43394e11	−0.461149
$78$	2.15739e12	1.08471
$79$	−3.29175e12	−1.52353	−0.761765	−	0.647853i	$-0.775667\pi$
$79$	−3.29175e12	−1.52353	−0.761765	+	0.647853i	$0.775667\pi$
$80$	4.77623e12	2.03705
$81$	2.82430e11	0.111111
$82$	3.36281e11	0.122155
$83$	−2.11978e12	−0.711677	−0.355839	−	0.934547i	$-0.615805\pi$
$83$	−2.11978e12	−0.711677	−0.355839	+	0.934547i	$0.615805\pi$
$84$	1.29393e12	0.401880
$85$	−1.86686e12	−0.536895
$86$	1.30716e12	0.348407
$87$	−1.00322e12	−0.248039
$88$	−6.40207e11	−0.146955
$89$	5.49190e12	1.17135	0.585676	−	0.810545i	$-0.300829\pi$
$89$	5.49190e12	1.17135	0.585676	+	0.810545i	$0.300829\pi$
$90$	3.92904e12	0.779311
$91$	−6.70062e12	−1.23693
$92$	8.09590e11	0.139202
$93$	−2.39164e12	−0.383316
$94$	−5.57622e12	−0.833699
$95$	1.47825e13	2.06322
$96$	5.66373e12	0.738481
$97$	−1.88598e12	−0.229890	−0.114945	−	0.993372i	$-0.536669\pi$
$97$	−1.88598e12	−0.229890	−0.114945	+	0.993372i	$0.536669\pi$
$98$	2.62860e12	0.299747
$99$	−1.63465e12	−0.174501
$100$	1.62247e13	1.62247
$101$	9.71006e12	0.910192	0.455096	−	0.890442i	$-0.349605\pi$
$101$	9.71006e12	0.910192	0.455096	+	0.890442i	$0.349605\pi$
$102$	−2.69960e12	−0.237355
$103$	−8.58384e12	−0.708336	−0.354168	−	0.935182i	$-0.615236\pi$
$103$	−8.58384e12	−0.708336	−0.354168	+	0.935182i	$0.615236\pi$
$104$	−5.08633e12	−0.394174
$105$	−1.22032e13	−0.888676
$106$	1.03885e13	0.711316
$107$	−1.17403e13	−0.756282	−0.378141	−	0.925748i	$-0.623437\pi$
$107$	−1.17403e13	−0.756282	−0.378141	+	0.925748i	$0.623437\pi$
$108$	2.50788e12	0.152073
$109$	−2.63894e13	−1.50715	−0.753577	−	0.657359i	$-0.771673\pi$
$109$	−2.63894e13	−1.50715	−0.753577	+	0.657359i	$0.771673\pi$
$110$	−2.27406e13	−1.22391
$111$	6.95993e11	0.0353188
$112$	−2.14516e13	−1.02693
$113$	−1.85358e13	−0.837530	−0.418765	−	0.908095i	$-0.637537\pi$
$113$	−1.85358e13	−0.837530	−0.418765	+	0.908095i	$0.637537\pi$
$114$	2.13764e13	0.912123
$115$	−7.63532e12	−0.307816
$116$	−8.90824e12	−0.339481
$117$	−1.29870e13	−0.468061
$118$	5.10808e12	0.174190
$119$	8.38467e12	0.270664
$120$	−9.26326e12	−0.283195
$121$	−2.50616e13	−0.725946
$122$	1.06835e13	0.293343
$123$	−2.02434e12	−0.0527110
$124$	−2.12370e13	−0.524629
$125$	−7.84930e13	−1.84041
$126$	−1.76466e13	−0.392873
$127$	4.43860e13	0.938689	0.469345	−	0.883015i	$-0.344490\pi$
$127$	4.43860e13	0.938689	0.469345	+	0.883015i	$0.344490\pi$
$128$	−2.73209e13	−0.549072
$129$	−7.86882e12	−0.150341
$130$	−1.80670e14	−3.28288
$131$	−9.98618e11	−0.0172638	−0.00863189	−	0.999963i	$-0.502748\pi$
$131$	−9.98618e11	−0.0172638	−0.00863189	+	0.999963i	$0.502748\pi$
$132$	−1.45152e13	−0.238832
$133$	−6.63930e13	−1.04013
$134$	3.88853e13	0.580235
$135$	−2.36521e13	−0.336279
$136$	6.36467e12	0.0862527
$137$	−3.21919e13	−0.415971	−0.207985	−	0.978132i	$-0.566691\pi$
$137$	−3.21919e13	−0.415971	−0.207985	+	0.978132i	$0.566691\pi$
$138$	−1.10411e13	−0.136082
$139$	−4.94997e13	−0.582111	−0.291056	−	0.956706i	$-0.594006\pi$
$139$	−4.94997e13	−0.582111	−0.291056	+	0.956706i	$0.594006\pi$
$140$	−1.08361e14	−1.21630
$141$	3.35678e13	0.359748
$142$	3.78038e13	0.386956
$143$	7.51668e13	0.735092
$144$	−4.15771e13	−0.388595
$145$	8.40145e13	0.750693
$146$	2.15902e14	1.84486
$147$	−1.58237e13	−0.129343
$148$	6.18019e12	0.0483394
$149$	−1.37835e14	−1.03193	−0.515964	−	0.856611i	$-0.672566\pi$
$149$	−1.37835e14	−1.03193	−0.515964	+	0.856611i	$0.672566\pi$
$150$	−2.21272e14	−1.58611
$151$	4.68429e13	0.321583	0.160792	−	0.986988i	$-0.448595\pi$
$151$	4.68429e13	0.321583	0.160792	+	0.986988i	$0.448595\pi$
$152$	−5.03978e13	−0.331458
$153$	1.62510e13	0.102420
$154$	1.02135e14	0.617009
$155$	2.00288e14	1.16011
$156$	−1.15321e14	−0.640616
$157$	−3.32582e14	−1.77236	−0.886179	−	0.463343i	$-0.846650\pi$
$157$	−3.32582e14	−1.77236	−0.886179	+	0.463343i	$0.846650\pi$
$158$	3.98632e14	2.03846
$159$	−6.25364e13	−0.306939
$160$	−4.74309e14	−2.23502
$161$	3.42926e13	0.155179
$162$	−3.42023e13	−0.148665
$163$	1.44110e14	0.601829	0.300915	−	0.953651i	$-0.402708\pi$
$163$	1.44110e14	0.601829	0.300915	+	0.953651i	$0.402708\pi$
$164$	−1.79755e13	−0.0721434
$165$	1.36894e14	0.528128
$166$	2.56706e14	0.952211
$167$	4.87703e14	1.73980	0.869898	−	0.493231i	$-0.164184\pi$
$167$	4.87703e14	1.73980	0.869898	+	0.493231i	$0.164184\pi$
$168$	4.16042e13	0.142767
$169$	2.94312e14	0.971729
$170$	2.26078e14	0.718356
$171$	−1.28682e14	−0.393589
$172$	−6.98726e13	−0.205765
$173$	−1.07018e14	−0.303499	−0.151750	−	0.988419i	$-0.548491\pi$
$173$	−1.07018e14	−0.303499	−0.151750	+	0.988419i	$0.548491\pi$
$174$	1.21490e14	0.331872
$175$	6.87247e14	1.80870
$176$	2.40641e14	0.610292
$177$	−3.07496e13	−0.0751646
$178$	−6.65071e14	−1.56725
$179$	5.73790e13	0.130379	0.0651896	−	0.997873i	$-0.479235\pi$
$179$	5.73790e13	0.130379	0.0651896	+	0.997873i	$0.479235\pi$
$180$	−2.10023e14	−0.460251
$181$	7.11425e14	1.50390	0.751949	−	0.659222i	$-0.229114\pi$
$181$	7.11425e14	1.50390	0.751949	+	0.659222i	$0.229114\pi$
$182$	8.11448e14	1.65499
$183$	−6.43126e13	−0.126580
$184$	2.60310e13	0.0494509
$185$	−5.82860e13	−0.106893
$186$	2.89629e14	0.512870
$187$	−9.40582e13	−0.160852
$188$	2.98071e14	0.492372
$189$	1.06229e14	0.169528
$190$	−1.79017e15	−2.76055
$191$	−8.97598e13	−0.133772	−0.0668860	−	0.997761i	$-0.521306\pi$
$191$	−8.97598e13	−0.133772	−0.0668860	+	0.997761i	$0.521306\pi$
$192$	−2.18665e14	−0.315007
$193$	−7.79025e14	−1.08500	−0.542499	−	0.840056i	$-0.682522\pi$
$193$	−7.79025e14	−1.08500	−0.542499	+	0.840056i	$0.682522\pi$
$194$	2.28392e14	0.307588
$195$	1.08760e15	1.41659
$196$	−1.40509e14	−0.177027
$197$	−6.92027e14	−0.843514	−0.421757	−	0.906709i	$-0.638586\pi$
$197$	−6.92027e14	−0.843514	−0.421757	+	0.906709i	$0.638586\pi$
$198$	1.97957e14	0.233479
$199$	−1.38580e15	−1.58181	−0.790906	−	0.611937i	$-0.790391\pi$
$199$	−1.38580e15	−1.58181	−0.790906	+	0.611937i	$0.790391\pi$
$200$	5.21678e14	0.576379
$201$	−2.34082e14	−0.250376
$202$	−1.17589e15	−1.21782
$203$	−3.77335e14	−0.378445
$204$	1.44304e14	0.140179
$205$	1.69529e14	0.159530
$206$	1.03951e15	0.947741
$207$	6.64654e13	0.0587203
$208$	1.91185e15	1.63698
$209$	7.44789e14	0.618133
$210$	1.47781e15	1.18903
$211$	1.57225e15	1.22655	0.613276	−	0.789869i	$-0.289851\pi$
$211$	1.57225e15	1.22655	0.613276	+	0.789869i	$0.289851\pi$
$212$	−5.55303e14	−0.420095
$213$	−2.27571e14	−0.166975
$214$	1.42175e15	1.01189
$215$	6.58975e14	0.455008
$216$	8.06366e13	0.0540235
$217$	−8.99558e14	−0.584845
$218$	3.19577e15	2.01655
$219$	−1.29969e15	−0.796073
$220$	1.21558e15	0.722827
$221$	−7.47277e14	−0.431451
$222$	−8.42850e13	−0.0472559
$223$	−6.96136e14	−0.379064	−0.189532	−	0.981875i	$-0.560697\pi$
$223$	−6.96136e14	−0.379064	−0.189532	+	0.981875i	$0.560697\pi$
$224$	2.13027e15	1.12674
$225$	1.33201e15	0.684419
$226$	2.24469e15	1.12060
$227$	−8.89211e14	−0.431357	−0.215678	−	0.976464i	$-0.569196\pi$
$227$	−8.89211e14	−0.431357	−0.215678	+	0.976464i	$0.569196\pi$
$228$	−1.14265e15	−0.538689
$229$	3.28787e15	1.50655	0.753275	−	0.657705i	$-0.228473\pi$
$229$	3.28787e15	1.50655	0.753275	+	0.657705i	$0.228473\pi$
$230$	9.24640e14	0.411852
$231$	−6.14834e14	−0.266244
$232$	−2.86429e14	−0.120599
$233$	2.67543e15	1.09542	0.547710	−	0.836668i	$-0.315500\pi$
$233$	2.67543e15	1.09542	0.547710	+	0.836668i	$0.315500\pi$
$234$	1.57274e15	0.626257
$235$	−2.81113e15	−1.08878
$236$	−2.73047e14	−0.102875
$237$	−2.39969e15	−0.879611
$238$	−1.01539e15	−0.362144
$239$	3.21727e15	1.11661	0.558304	−	0.829637i	$-0.311452\pi$
$239$	3.21727e15	1.11661	0.558304	+	0.829637i	$0.311452\pi$
$240$	3.48187e15	1.17609
$241$	−1.52954e15	−0.502864	−0.251432	−	0.967875i	$-0.580902\pi$
$241$	−1.52954e15	−0.502864	−0.251432	+	0.967875i	$0.580902\pi$
$242$	3.03497e15	0.971302
$243$	2.05891e14	0.0641500
$244$	−5.71075e14	−0.173244
$245$	1.32515e15	0.391459
$246$	2.45149e14	0.0705264
$247$	5.91722e15	1.65801
$248$	−6.82840e14	−0.186373
$249$	−1.54532e15	−0.410887
$250$	9.50552e15	2.46244
$251$	2.68892e15	0.678734	0.339367	−	0.940654i	$-0.389787\pi$
$251$	2.68892e15	0.678734	0.339367	+	0.940654i	$0.389787\pi$
$252$	9.43278e14	0.232026
$253$	−3.84690e14	−0.0922206
$254$	−5.37516e15	−1.25595
$255$	−1.36094e15	−0.309977
$256$	5.76577e15	1.28026
$257$	−7.56048e15	−1.63676	−0.818378	−	0.574681i	$-0.805126\pi$
$257$	−7.56048e15	−1.63676	−0.818378	+	0.574681i	$0.805126\pi$
$258$	9.52917e14	0.201153
$259$	2.61781e14	0.0538876
$260$	9.65754e15	1.93883
$261$	−7.31345e14	−0.143205
$262$	1.20933e14	0.0230986
$263$	2.02110e15	0.376596	0.188298	−	0.982112i	$-0.439703\pi$
$263$	2.02110e15	0.376596	0.188298	+	0.982112i	$0.439703\pi$
$264$	−4.66711e14	−0.0848442
$265$	5.23712e15	0.928954
$266$	8.04021e15	1.39167
$267$	4.00359e15	0.676280
$268$	−2.07857e15	−0.342680
$269$	−1.16386e16	−1.87288	−0.936440	−	0.350827i	$-0.885901\pi$
$269$	−1.16386e16	−1.87288	−0.936440	+	0.350827i	$0.885901\pi$
$270$	2.86427e15	0.449935
$271$	5.92073e15	0.907977	0.453989	−	0.891007i	$-0.350001\pi$
$271$	5.92073e15	0.907977	0.453989	+	0.891007i	$0.350001\pi$
$272$	−2.39235e15	−0.358201
$273$	−4.88475e15	−0.714144
$274$	3.89845e15	0.556561
$275$	−7.70946e15	−1.07488
$276$	5.90191e14	0.0803681
$277$	5.31697e15	0.707206	0.353603	−	0.935396i	$-0.384956\pi$
$277$	5.31697e15	0.707206	0.353603	+	0.935396i	$0.384956\pi$
$278$	5.99442e15	0.778854
$279$	−1.74351e15	−0.221308
$280$	−3.48414e15	−0.432085
$281$	9.06497e15	1.09844	0.549219	−	0.835679i	$-0.314925\pi$
$281$	9.06497e15	1.09844	0.549219	+	0.835679i	$0.314925\pi$
$282$	−4.06507e15	−0.481336
$283$	9.24656e15	1.06996	0.534981	−	0.844864i	$-0.320319\pi$
$283$	9.24656e15	1.06996	0.534981	+	0.844864i	$0.320319\pi$
$284$	−2.02076e15	−0.228531
$285$	1.07765e16	1.19120
$286$	−9.10272e15	−0.983540
$287$	−7.61407e14	−0.0804238
$288$	4.12886e15	0.426362
$289$	−8.96949e15	−0.905590
$290$	−1.01742e16	−1.00441
$291$	−1.37488e15	−0.132727
$292$	−1.15408e16	−1.08955
$293$	4.36941e14	0.0403444	0.0201722	−	0.999797i	$-0.493579\pi$
$293$	4.36941e14	0.0403444	0.0201722	+	0.999797i	$0.493579\pi$
$294$	1.91625e15	0.173059
$295$	2.57513e15	0.227487
$296$	1.98713e14	0.0171724
$297$	−1.19166e15	−0.100748
$298$	1.66919e16	1.38070
$299$	−3.05630e15	−0.247362
$300$	1.18278e16	0.936736
$301$	−2.95966e15	−0.229382
$302$	−5.67269e15	−0.430273
$303$	7.07863e15	0.525499
$304$	1.89435e16	1.37652
$305$	5.38586e15	0.383095
$306$	−1.96801e15	−0.137037
$307$	−7.47865e15	−0.509828	−0.254914	−	0.966964i	$-0.582047\pi$
$307$	−7.47865e15	−0.509828	−0.254914	+	0.966964i	$0.582047\pi$
$308$	−5.45953e15	−0.364398
$309$	−6.25762e15	−0.408958
$310$	−2.42550e16	−1.55221
$311$	1.12353e16	0.704110	0.352055	−	0.935979i	$-0.385483\pi$
$311$	1.12353e16	0.704110	0.352055	+	0.935979i	$0.385483\pi$
$312$	−3.70794e15	−0.227577
$313$	2.80446e16	1.68582	0.842911	−	0.538053i	$-0.180840\pi$
$313$	2.80446e16	1.68582	0.842911	+	0.538053i	$0.180840\pi$
$314$	4.02758e16	2.37138
$315$	−8.89614e15	−0.513078
$316$	−2.13085e16	−1.20389
$317$	2.90786e16	1.60949	0.804744	−	0.593622i	$-0.202302\pi$
$317$	2.90786e16	1.60949	0.804744	+	0.593622i	$0.202302\pi$
$318$	7.57318e15	0.410679
$319$	4.23290e15	0.224905
$320$	1.83121e16	0.953373
$321$	−8.55866e15	−0.436639
$322$	−4.15284e15	−0.207626
$323$	−7.40437e15	−0.362804
$324$	1.82825e15	0.0877995
$325$	−6.12504e16	−2.88315
$326$	−1.74517e16	−0.805237
$327$	−1.92379e16	−0.870156
$328$	−5.77972e14	−0.0256287
$329$	1.26257e16	0.548885
$330$	−1.65779e16	−0.706626
$331$	−1.33097e16	−0.556271	−0.278136	−	0.960542i	$-0.589717\pi$
$331$	−1.33097e16	−0.556271	−0.278136	+	0.960542i	$0.589717\pi$
$332$	−1.37219e16	−0.562364
$333$	5.07379e14	0.0203913
$334$	−5.90610e16	−2.32782
$335$	1.96032e16	0.757766
$336$	−1.56382e16	−0.592899
$337$	−1.66329e16	−0.618547	−0.309274	−	0.950973i	$-0.600086\pi$
$337$	−1.66329e16	−0.618547	−0.309274	+	0.950973i	$0.600086\pi$
$338$	−3.56413e16	−1.30016
$339$	−1.35126e16	−0.483548
$340$	−1.20847e16	−0.424252
$341$	1.00911e16	0.347565
$342$	1.55834e16	0.526614
$343$	−3.25182e16	−1.07824
$344$	−2.24663e15	−0.0730974
$345$	−5.56615e15	−0.177718
$346$	1.29599e16	0.406076
$347$	1.41261e16	0.434391	0.217195	−	0.976128i	$-0.430309\pi$
$347$	1.41261e16	0.434391	0.217195	+	0.976128i	$0.430309\pi$
$348$	−6.49411e15	−0.195999
$349$	4.64435e16	1.37581	0.687907	−	0.725799i	$-0.258530\pi$
$349$	4.64435e16	1.37581	0.687907	+	0.725799i	$0.258530\pi$
$350$	−8.32259e16	−2.42000
$351$	−9.46756e15	−0.270235
$352$	−2.38971e16	−0.669605
$353$	6.70363e16	1.84406	0.922029	−	0.387121i	$-0.126530\pi$
$353$	6.70363e16	1.84406	0.922029	+	0.387121i	$0.126530\pi$
$354$	3.72379e15	0.100569
$355$	1.90580e16	0.505350
$356$	3.55506e16	0.925597
$357$	6.11242e15	0.156268
$358$	−6.94862e15	−0.174445
$359$	−8.02458e15	−0.197837	−0.0989187	−	0.995096i	$-0.531538\pi$
$359$	−8.02458e15	−0.197837	−0.0989187	+	0.995096i	$0.531538\pi$
$360$	−6.75292e15	−0.163503
$361$	1.65776e16	0.394208
$362$	−8.61537e16	−2.01219
$363$	−1.82699e16	−0.419125
$364$	−4.33750e16	−0.977419
$365$	1.08843e17	2.40932
$366$	7.78828e15	0.169361
$367$	7.02076e16	1.49987	0.749937	−	0.661509i	$-0.230084\pi$
$367$	7.02076e16	1.49987	0.749937	+	0.661509i	$0.230084\pi$
$368$	−9.78452e15	−0.205366
$369$	−1.47575e15	−0.0304327
$370$	7.05845e15	0.143020
$371$	−2.35215e16	−0.468312
$372$	−1.54818e16	−0.302895
$373$	3.05940e16	0.588205	0.294102	−	0.955774i	$-0.404979\pi$
$373$	3.05940e16	0.588205	0.294102	+	0.955774i	$0.404979\pi$
$374$	1.13905e16	0.215217
$375$	−5.72214e16	−1.06256
$376$	9.58395e15	0.174914
$377$	3.36297e16	0.603259
$378$	−1.28643e16	−0.226825
$379$	4.13153e16	0.716070	0.358035	−	0.933708i	$-0.383447\pi$
$379$	4.13153e16	0.716070	0.358035	+	0.933708i	$0.383447\pi$
$380$	9.56915e16	1.63035
$381$	3.23574e16	0.541952
$382$	1.08699e16	0.178984
$383$	−1.92088e16	−0.310962	−0.155481	−	0.987839i	$-0.549693\pi$
$383$	−1.92088e16	−0.310962	−0.155481	+	0.987839i	$0.549693\pi$
$384$	−1.99169e16	−0.317007
$385$	5.14893e16	0.805791
$386$	9.43402e16	1.45171
$387$	−5.73637e15	−0.0867992
$388$	−1.22085e16	−0.181658
$389$	−5.74473e16	−0.840614	−0.420307	−	0.907382i	$-0.638078\pi$
$389$	−5.74473e16	−0.840614	−0.420307	+	0.907382i	$0.638078\pi$
$390$	−1.31709e17	−1.89537
$391$	3.82443e15	0.0541275
$392$	−4.51782e15	−0.0628883
$393$	−7.27993e14	−0.00996725
$394$	8.38046e16	1.12861
$395$	2.00962e17	2.66215
$396$	−1.05816e16	−0.137890
$397$	−8.63214e16	−1.10657	−0.553287	−	0.832991i	$-0.686627\pi$
$397$	−8.63214e16	−1.10657	−0.553287	+	0.832991i	$0.686627\pi$
$398$	1.67821e17	2.11644
$399$	−4.84005e16	−0.600518
$400$	−1.96089e17	−2.39366
$401$	5.95325e16	0.715016	0.357508	−	0.933910i	$-0.383627\pi$
$401$	5.95325e16	0.715016	0.357508	+	0.933910i	$0.383627\pi$
$402$	2.83474e16	0.334999
$403$	8.01723e16	0.932270
$404$	6.28559e16	0.719229
$405$	−1.72424e16	−0.194151
$406$	4.56954e16	0.506353
$407$	−2.93662e15	−0.0320247
$408$	4.63984e15	0.0497980
$409$	1.70471e17	1.80073	0.900367	−	0.435131i	$-0.143298\pi$
$409$	1.70471e17	1.80073	0.900367	+	0.435131i	$0.143298\pi$
$410$	−2.05300e16	−0.213449
$411$	−2.34679e16	−0.240161
$412$	−5.55656e16	−0.559724
$413$	−1.15657e16	−0.114682
$414$	−8.04898e15	−0.0785667
$415$	1.29413e17	1.24355
$416$	−1.89859e17	−1.79607
$417$	−3.60852e16	−0.336082
$418$	−9.01941e16	−0.827051
$419$	−7.73612e16	−0.698444	−0.349222	−	0.937040i	$-0.613554\pi$
$419$	−7.73612e16	−0.698444	−0.349222	+	0.937040i	$0.613554\pi$
$420$	−7.89948e16	−0.702228
$421$	−4.89260e16	−0.428259	−0.214129	−	0.976805i	$-0.568691\pi$
$421$	−4.89260e16	−0.428259	−0.214129	+	0.976805i	$0.568691\pi$
$422$	−1.90400e17	−1.64111
$423$	2.44709e16	0.207701
$424$	−1.78548e16	−0.149237
$425$	7.66442e16	0.630887
$426$	2.75590e16	0.223409
$427$	−2.41896e16	−0.193129
$428$	−7.59981e16	−0.597611
$429$	5.47966e16	0.424406
$430$	−7.98020e16	−0.608792
$431$	1.40520e17	1.05593	0.527967	−	0.849265i	$-0.322954\pi$
$431$	1.40520e17	1.05593	0.527967	+	0.849265i	$0.322954\pi$
$432$	−3.03097e16	−0.224356
$433$	−1.11981e16	−0.0816533	−0.0408266	−	0.999166i	$-0.512999\pi$
$433$	−1.11981e16	−0.0816533	−0.0408266	+	0.999166i	$0.512999\pi$
$434$	1.08937e17	0.782512
$435$	6.12466e16	0.433413
$436$	−1.70826e17	−1.19095
$437$	−3.02833e16	−0.208005
$438$	1.57393e17	1.06513
$439$	−5.98073e16	−0.398781	−0.199391	−	0.979920i	$-0.563896\pi$
$439$	−5.98073e16	−0.398781	−0.199391	+	0.979920i	$0.563896\pi$
$440$	3.90847e16	0.256782
$441$	−1.15354e16	−0.0746765
$442$	9.04954e16	0.577274
$443$	−1.04301e17	−0.655635	−0.327818	−	0.944741i	$-0.606313\pi$
$443$	−1.04301e17	−0.655635	−0.327818	+	0.944741i	$0.606313\pi$
$444$	4.50536e15	0.0279087
$445$	−3.35281e17	−2.04677
$446$	8.43023e16	0.507181
$447$	−1.00482e17	−0.595783
$448$	−8.22453e16	−0.480622
$449$	1.84771e17	1.06422	0.532112	−	0.846674i	$-0.321399\pi$
$449$	1.84771e17	1.06422	0.532112	+	0.846674i	$0.321399\pi$
$450$	−1.61307e17	−0.915740
$451$	8.54137e15	0.0477947
$452$	−1.19987e17	−0.661813
$453$	3.41485e16	0.185666
$454$	1.07684e17	0.577148
$455$	4.09074e17	2.16136
$456$	−3.67400e16	−0.191367
$457$	−1.40580e17	−0.721887	−0.360944	−	0.932588i	$-0.617545\pi$
$457$	−1.40580e17	−0.721887	−0.360944	+	0.932588i	$0.617545\pi$
$458$	−3.98162e17	−2.01574
$459$	1.18470e16	0.0591325
$460$	−4.94256e16	−0.243235
$461$	3.62232e17	1.75764	0.878821	−	0.477152i	$-0.158331\pi$
$461$	3.62232e17	1.75764	0.878821	+	0.477152i	$0.158331\pi$
$462$	7.44566e16	0.356230
$463$	−8.62407e16	−0.406851	−0.203426	−	0.979090i	$-0.565208\pi$
$463$	−8.62407e16	−0.406851	−0.203426	+	0.979090i	$0.565208\pi$
$464$	1.07663e17	0.500841
$465$	1.46010e17	0.669791
$466$	−3.23996e17	−1.46565
$467$	8.73900e16	0.389854	0.194927	−	0.980818i	$-0.437553\pi$
$467$	8.73900e16	0.389854	0.194927	+	0.980818i	$0.437553\pi$
$468$	−8.40688e16	−0.369860
$469$	−8.80440e16	−0.382011
$470$	3.40429e17	1.45677
$471$	−2.42453e17	−1.02327
$472$	−8.77934e15	−0.0365459
$473$	3.32011e16	0.136319
$474$	2.90603e17	1.17690
$475$	−6.06898e17	−2.42442
$476$	5.42763e16	0.213878
$477$	−4.55891e16	−0.177211
$478$	−3.89612e17	−1.49400
$479$	4.14866e17	1.56937	0.784687	−	0.619892i	$-0.212824\pi$
$479$	4.14866e17	1.56937	0.784687	+	0.619892i	$0.212824\pi$
$480$	−3.45771e17	−1.29039
$481$	−2.33310e16	−0.0858993
$482$	1.85228e17	0.672823
$483$	2.49993e16	0.0895925
$484$	−1.62231e17	−0.573639
$485$	1.15139e17	0.401700
$486$	−2.49335e16	−0.0858316
$487$	−3.38059e17	−1.14830	−0.574149	−	0.818751i	$-0.694667\pi$
$487$	−3.38059e17	−1.14830	−0.574149	+	0.818751i	$0.694667\pi$
$488$	−1.83619e16	−0.0615445
$489$	1.05056e17	0.347466
$490$	−1.60476e17	−0.523765
$491$	−4.52509e17	−1.45746	−0.728731	−	0.684800i	$-0.759890\pi$
$491$	−4.52509e17	−1.45746	−0.728731	+	0.684800i	$0.759890\pi$
$492$	−1.31042e16	−0.0416520
$493$	−4.20817e16	−0.132004
$494$	−7.16577e17	−2.21839
$495$	9.97959e16	0.304915
$496$	2.56666e17	0.773993
$497$	−8.55953e16	−0.254761
$498$	1.87139e17	0.549759
$499$	−3.07360e17	−0.891237	−0.445619	−	0.895223i	$-0.647016\pi$
$499$	−3.07360e17	−0.891237	−0.445619	+	0.895223i	$0.647016\pi$
$500$	−5.08107e17	−1.45429
$501$	3.55536e17	1.00447
$502$	−3.25629e17	−0.908133
$503$	−1.76801e17	−0.486734	−0.243367	−	0.969934i	$-0.578252\pi$
$503$	−1.76801e17	−0.486734	−0.243367	+	0.969934i	$0.578252\pi$
$504$	3.03295e16	0.0824263
$505$	−5.92800e17	−1.59043
$506$	4.65861e16	0.123390
$507$	2.14554e17	0.561028
$508$	2.87323e17	0.741748
$509$	6.95952e16	0.177384	0.0886919	−	0.996059i	$-0.471731\pi$
$509$	6.95952e16	0.177384	0.0886919	+	0.996059i	$0.471731\pi$
$510$	1.64811e17	0.414743
$511$	−4.88846e17	−1.21461
$512$	−4.74424e17	−1.16389
$513$	−9.38091e16	−0.227238
$514$	9.15576e17	2.18995
$515$	5.24044e17	1.23772
$516$	−5.09371e16	−0.118799
$517$	−1.41633e17	−0.326195
$518$	−3.17017e16	−0.0721006
$519$	−7.80162e16	−0.175225
$520$	3.10521e17	0.688763
$521$	−5.04741e17	−1.10566	−0.552832	−	0.833293i	$-0.686453\pi$
$521$	−5.04741e17	−1.10566	−0.552832	+	0.833293i	$0.686453\pi$
$522$	8.85662e16	0.191606
$523$	−4.26871e16	−0.0912086	−0.0456043	−	0.998960i	$-0.514521\pi$
$523$	−4.26871e16	−0.0912086	−0.0456043	+	0.998960i	$0.514521\pi$
$524$	−6.46434e15	−0.0136418
$525$	5.01003e17	1.04425
$526$	−2.44756e17	−0.503878
$527$	−1.00322e17	−0.203998
$528$	1.75427e17	0.352352
$529$	−4.88395e17	−0.968967
$530$	−6.34216e17	−1.24292
$531$	−2.24165e16	−0.0433963
$532$	−4.29780e17	−0.821904
$533$	6.78598e16	0.128199
$534$	−4.84836e17	−0.904851
$535$	7.16745e17	1.32149
$536$	−6.68327e16	−0.121736
$537$	4.18293e16	0.0752745
$538$	1.40944e18	2.50588
$539$	6.67652e16	0.117280
$540$	−1.53107e17	−0.265726
$541$	7.38366e16	0.126616	0.0633081	−	0.997994i	$-0.479835\pi$
$541$	7.38366e16	0.126616	0.0633081	+	0.997994i	$0.479835\pi$
$542$	−7.17003e17	−1.21486
$543$	5.18628e17	0.868275
$544$	2.37575e17	0.393014
$545$	1.61108e18	2.63354
$546$	5.91545e17	0.955511
$547$	1.17777e18	1.87993	0.939966	−	0.341269i	$-0.110857\pi$
$547$	1.17777e18	1.87993	0.939966	+	0.341269i	$0.110857\pi$
$548$	−2.08387e17	−0.328698
$549$	−4.68839e16	−0.0730808
$550$	9.33618e17	1.43818
$551$	3.33219e17	0.507276
$552$	1.89766e16	0.0285505
$553$	−9.02583e17	−1.34207
$554$	−6.43887e17	−0.946229
$555$	−4.24905e16	−0.0617145
$556$	−3.20425e17	−0.459982
$557$	−3.89846e17	−0.553139	−0.276569	−	0.960994i	$-0.589198\pi$
$557$	−3.89846e17	−0.553139	−0.276569	+	0.960994i	$0.589198\pi$
$558$	2.11139e17	0.296106
$559$	2.63777e17	0.365646
$560$	1.30962e18	1.79442
$561$	−6.85685e16	−0.0928679
$562$	−1.09777e18	−1.46969
$563$	−1.00758e18	−1.33344	−0.666719	−	0.745309i	$-0.732302\pi$
$563$	−1.00758e18	−1.33344	−0.666719	+	0.745309i	$0.732302\pi$
$564$	2.17294e17	0.284271
$565$	1.13161e18	1.46346
$566$	−1.11976e18	−1.43159
$567$	7.74408e16	0.0978769
$568$	−6.49740e16	−0.0811849
$569$	1.46828e18	1.81376	0.906880	−	0.421389i	$-0.138457\pi$
$569$	1.46828e18	1.81376	0.906880	+	0.421389i	$0.138457\pi$
$570$	−1.30503e18	−1.59380
$571$	−4.20427e17	−0.507640	−0.253820	−	0.967252i	$-0.581687\pi$
$571$	−4.20427e17	−0.507640	−0.253820	+	0.967252i	$0.581687\pi$
$572$	4.86576e17	0.580867
$573$	−6.54349e16	−0.0772333
$574$	9.22066e16	0.107606
$575$	3.13468e17	0.361704
$576$	−1.59407e17	−0.181870
$577$	−1.50538e18	−1.69826	−0.849131	−	0.528183i	$-0.822874\pi$
$577$	−1.50538e18	−1.69826	−0.849131	+	0.528183i	$0.822874\pi$
$578$	1.08621e18	1.21166
$579$	−5.67909e17	−0.626424
$580$	5.43850e17	0.593194
$581$	−5.81233e17	−0.626911
$582$	1.66498e17	0.177586
$583$	2.63862e17	0.278311
$584$	−3.71075e17	−0.387060
$585$	7.92861e17	0.817869
$586$	−5.29136e16	−0.0539800
$587$	−5.11404e16	−0.0515960	−0.0257980	−	0.999667i	$-0.508213\pi$
$587$	−5.11404e16	−0.0515960	−0.0257980	+	0.999667i	$0.508213\pi$
$588$	−1.02431e17	−0.102207
$589$	7.94385e17	0.783938
$590$	−3.11849e17	−0.304373
$591$	−5.04487e17	−0.487003
$592$	−7.46924e16	−0.0713157
$593$	−1.67701e18	−1.58373	−0.791863	−	0.610699i	$-0.790889\pi$
$593$	−1.67701e18	−1.58373	−0.791863	+	0.610699i	$0.790889\pi$
$594$	1.44311e17	0.134799
$595$	−5.11885e17	−0.472947
$596$	−8.92245e17	−0.815424
$597$	−1.01025e18	−0.913260
$598$	3.70119e17	0.330966
$599$	−2.13441e18	−1.88801	−0.944004	−	0.329933i	$-0.892974\pi$
$599$	−2.13441e18	−1.88801	−0.944004	+	0.329933i	$0.892974\pi$
$600$	3.80304e17	0.332772
$601$	3.06273e17	0.265109	0.132555	−	0.991176i	$-0.457682\pi$
$601$	3.06273e17	0.265109	0.132555	+	0.991176i	$0.457682\pi$
$602$	3.58416e17	0.306909
$603$	−1.70645e17	−0.144555
$604$	3.03227e17	0.254114
$605$	1.53002e18	1.26849
$606$	−8.57224e17	−0.703109
$607$	−1.44125e18	−1.16953	−0.584765	−	0.811203i	$-0.698813\pi$
$607$	−1.44125e18	−1.16953	−0.584765	+	0.811203i	$0.698813\pi$
$608$	−1.88121e18	−1.51030
$609$	−2.75077e17	−0.218496
$610$	−6.52230e17	−0.512574
$611$	−1.12525e18	−0.874948
$612$	1.05198e17	0.0809322
$613$	−4.13566e17	−0.314812	−0.157406	−	0.987534i	$-0.550313\pi$
$613$	−4.13566e17	−0.314812	−0.157406	+	0.987534i	$0.550313\pi$
$614$	9.05667e17	0.682141
$615$	1.23587e17	0.0921049
$616$	−1.75542e17	−0.129451
$617$	1.32421e18	0.966282	0.483141	−	0.875543i	$-0.339496\pi$
$617$	1.32421e18	0.966282	0.483141	+	0.875543i	$0.339496\pi$
$618$	7.57799e17	0.547179
$619$	7.43808e17	0.531461	0.265731	−	0.964047i	$-0.414387\pi$
$619$	7.43808e17	0.531461	0.265731	+	0.964047i	$0.414387\pi$
$620$	1.29652e18	0.916715
$621$	4.84533e16	0.0339022
$622$	−1.36059e18	−0.942086
$623$	1.50585e18	1.03183
$624$	1.39374e18	0.945109
$625$	1.73242e18	1.16261
$626$	−3.39621e18	−2.25560
$627$	5.42951e17	0.356879
$628$	−2.15290e18	−1.40051
$629$	2.91947e16	0.0187964
$630$	1.07733e18	0.686489
$631$	1.03057e18	0.649960	0.324980	−	0.945721i	$-0.394642\pi$
$631$	1.03057e18	0.649960	0.324980	+	0.945721i	$0.394642\pi$
$632$	−6.85136e17	−0.427677
$633$	1.14617e18	0.708150
$634$	−3.52142e18	−2.15347
$635$	−2.70977e18	−1.64023
$636$	−4.04816e17	−0.242542
$637$	5.30438e17	0.314578
$638$	−5.12606e17	−0.300919
$639$	−1.65900e17	−0.0964028
$640$	1.66794e18	0.959425
$641$	1.80067e18	1.02531	0.512657	−	0.858594i	$-0.328661\pi$
$641$	1.80067e18	1.02531	0.512657	+	0.858594i	$0.328661\pi$
$642$	1.03646e18	0.584216
$643$	1.03269e18	0.576232	0.288116	−	0.957595i	$-0.406971\pi$
$643$	1.03269e18	0.576232	0.288116	+	0.957595i	$0.406971\pi$
$644$	2.21986e17	0.122622
$645$	4.80393e17	0.262699
$646$	8.96672e17	0.485425
$647$	2.70114e18	1.44767	0.723833	−	0.689975i	$-0.242378\pi$
$647$	2.70114e18	1.44767	0.723833	+	0.689975i	$0.242378\pi$
$648$	5.87841e16	0.0311905
$649$	1.29743e17	0.0681542
$650$	7.41744e18	3.85760
$651$	−6.55777e17	−0.337660
$652$	9.32862e17	0.475563
$653$	2.27483e18	1.14819	0.574095	−	0.818789i	$-0.305354\pi$
$653$	2.27483e18	1.14819	0.574095	+	0.818789i	$0.305354\pi$
$654$	2.32971e18	1.16425
$655$	6.09658e16	0.0301660
$656$	2.17248e17	0.106434
$657$	−9.47473e17	−0.459613
$658$	−1.52897e18	−0.734398
$659$	−2.42135e18	−1.15160	−0.575802	−	0.817589i	$-0.695310\pi$
$659$	−2.42135e18	−1.15160	−0.575802	+	0.817589i	$0.695310\pi$
$660$	8.86155e17	0.417325
$661$	2.49936e18	1.16552	0.582759	−	0.812645i	$-0.301973\pi$
$661$	2.49936e18	1.16552	0.582759	+	0.812645i	$0.301973\pi$
$662$	1.61181e18	0.744281
$663$	−5.44765e17	−0.249098
$664$	−4.41205e17	−0.199778
$665$	4.05330e18	1.81747
$666$	−6.14437e16	−0.0272832
$667$	−1.72111e17	−0.0756816
$668$	3.15704e18	1.37478
$669$	−5.07483e17	−0.218853
$670$	−2.37395e18	−1.01388
$671$	2.71356e17	0.114774
$672$	1.55297e18	0.650522
$673$	1.86948e18	0.775574	0.387787	−	0.921749i	$-0.373240\pi$
$673$	1.86948e18	0.775574	0.387787	+	0.921749i	$0.373240\pi$
$674$	2.01425e18	0.827605
$675$	9.71037e17	0.395149
$676$	1.90517e18	0.767856
$677$	−2.48844e18	−0.993347	−0.496673	−	0.867938i	$-0.665445\pi$
$677$	−2.48844e18	−0.993347	−0.496673	+	0.867938i	$0.665445\pi$
$678$	1.63638e18	0.646979
$679$	−5.17125e17	−0.202508
$680$	−3.88564e17	−0.150714
$681$	−6.48235e17	−0.249044
$682$	−1.22204e18	−0.465036
$683$	−3.32409e17	−0.125296	−0.0626482	−	0.998036i	$-0.519955\pi$
$683$	−3.32409e17	−0.125296	−0.0626482	+	0.998036i	$0.519955\pi$
$684$	−8.32994e17	−0.311012
$685$	1.96532e18	0.726849
$686$	3.93796e18	1.44266
$687$	2.39686e18	0.869808
$688$	8.44464e17	0.303568
$689$	2.09634e18	0.746511
$690$	6.74062e17	0.237783
$691$	2.91763e18	1.01958	0.509791	−	0.860298i	$-0.329723\pi$
$691$	2.91763e18	1.01958	0.509791	+	0.860298i	$0.329723\pi$
$692$	−6.92758e17	−0.239824
$693$	−4.48214e17	−0.153716
$694$	−1.71067e18	−0.581207
$695$	3.02196e18	1.01716
$696$	−2.08807e17	−0.0696281
$697$	−8.49147e16	−0.0280524
$698$	−5.62432e18	−1.84081
$699$	1.95039e18	0.632441
$700$	4.44875e18	1.42922
$701$	5.23262e18	1.66553	0.832764	−	0.553629i	$-0.186757\pi$
$701$	5.23262e18	1.66553	0.832764	+	0.553629i	$0.186757\pi$
$702$	1.14652e18	0.361570
$703$	−2.31174e17	−0.0722321
$704$	9.22618e17	0.285627
$705$	−2.04932e18	−0.628608
$706$	−8.11812e18	−2.46732
$707$	2.66245e18	0.801780
$708$	−1.99051e17	−0.0593947
$709$	2.70447e18	0.799617	0.399809	−	0.916599i	$-0.369077\pi$
$709$	2.70447e18	0.799617	0.399809	+	0.916599i	$0.369077\pi$
$710$	−2.30793e18	−0.676149
$711$	−1.74937e18	−0.507844
$712$	1.14307e18	0.328815
$713$	−4.10308e17	−0.116957
$714$	−7.40216e17	−0.209084
$715$	−4.58894e18	−1.28447
$716$	3.71431e17	0.103025
$717$	2.34539e18	0.644674
$718$	9.71779e17	0.264703
$719$	−1.14317e18	−0.308585	−0.154292	−	0.988025i	$-0.549310\pi$
$719$	−1.14317e18	−0.308585	−0.154292	+	0.988025i	$0.549310\pi$
$720$	2.53829e18	0.679015
$721$	−2.35365e18	−0.623968
$722$	−2.00755e18	−0.527443
$723$	−1.11504e18	−0.290329
$724$	4.60525e18	1.18837
$725$	−3.44922e18	−0.882112
$726$	2.21249e18	0.560782
$727$	4.45771e18	1.11979	0.559897	−	0.828562i	$-0.310841\pi$
$727$	4.45771e18	1.11979	0.559897	+	0.828562i	$0.310841\pi$
$728$	−1.39465e18	−0.347225
$729$	1.50095e17	0.0370370
$730$	−1.31809e19	−3.22363
$731$	−3.30072e17	−0.0800102
$732$	−4.16314e17	−0.100023
$733$	−2.25620e18	−0.537280	−0.268640	−	0.963241i	$-0.586574\pi$
$733$	−2.25620e18	−0.537280	−0.268640	+	0.963241i	$0.586574\pi$
$734$	−8.50216e18	−2.00680
$735$	9.66037e17	0.226009
$736$	9.71663e17	0.225325
$737$	9.87667e17	0.227024
$738$	1.78713e17	0.0407184
$739$	1.89825e18	0.428710	0.214355	−	0.976756i	$-0.431235\pi$
$739$	1.89825e18	0.428710	0.214355	+	0.976756i	$0.431235\pi$
$740$	−3.77302e17	−0.0844661
$741$	4.31365e18	0.957253
$742$	2.84846e18	0.626593
$743$	5.77525e18	1.25934	0.629671	−	0.776862i	$-0.283190\pi$
$743$	5.77525e18	1.25934	0.629671	+	0.776862i	$0.283190\pi$
$744$	−4.97790e17	−0.107602
$745$	8.41485e18	1.80315
$746$	−3.70494e18	−0.787007
$747$	−1.12654e18	−0.237226
$748$	−6.08866e17	−0.127105
$749$	−3.21913e18	−0.666202
$750$	6.92953e18	1.42169
$751$	4.34729e18	0.884217	0.442109	−	0.896962i	$-0.354231\pi$
$751$	4.34729e18	0.884217	0.442109	+	0.896962i	$0.354231\pi$
$752$	−3.60242e18	−0.726403
$753$	1.96023e18	0.391867
$754$	−4.07257e18	−0.807150
$755$	−2.85977e18	−0.561921
$756$	6.87649e17	0.133960
$757$	1.27677e18	0.246598	0.123299	−	0.992370i	$-0.460653\pi$
$757$	1.27677e18	0.246598	0.123299	+	0.992370i	$0.460653\pi$
$758$	−5.00329e18	−0.958089
$759$	−2.80439e17	−0.0532436
$760$	3.07679e18	0.579175
$761$	2.52588e18	0.471425	0.235713	−	0.971823i	$-0.424258\pi$
$761$	2.52588e18	0.471425	0.235713	+	0.971823i	$0.424258\pi$
$762$	−3.91849e18	−0.725123
$763$	−7.23586e18	−1.32764
$764$	−5.81041e17	−0.105706
$765$	−9.92128e17	−0.178965
$766$	2.32619e18	0.416062
$767$	1.03078e18	0.182809
$768$	4.20324e18	0.739157
$769$	4.70991e18	0.821280	0.410640	−	0.911797i	$-0.365305\pi$
$769$	4.70991e18	0.821280	0.410640	+	0.911797i	$0.365305\pi$
$770$	−6.23538e18	−1.07813
$771$	−5.51159e18	−0.944981
$772$	−5.04285e18	−0.857361
$773$	−1.03352e19	−1.74242	−0.871209	−	0.490912i	$-0.836664\pi$
$773$	−1.03352e19	−1.74242	−0.871209	+	0.490912i	$0.836664\pi$
$774$	6.94676e17	0.116136
$775$	−8.22285e18	−1.36321
$776$	−3.92542e17	−0.0645334
$777$	1.90838e17	0.0311120
$778$	6.95688e18	1.12473
$779$	6.72387e17	0.107802
$780$	7.04035e18	1.11938
$781$	9.60198e17	0.151401
$782$	−4.63140e17	−0.0724216
$783$	−5.33151e17	−0.0826797
$784$	1.69816e18	0.261170
$785$	2.03042e19	3.09694
$786$	8.81601e16	0.0133360
$787$	−7.83829e18	−1.17594	−0.587971	−	0.808882i	$-0.700073\pi$
$787$	−7.83829e18	−1.17594	−0.587971	+	0.808882i	$0.700073\pi$
$788$	−4.47968e18	−0.666541
$789$	1.47338e18	0.217428
$790$	−2.43366e19	−3.56191
$791$	−5.08242e18	−0.737774
$792$	−3.40232e17	−0.0489848
$793$	2.15588e18	0.307857
$794$	1.04536e19	1.48058
$795$	3.81786e18	0.536332
$796$	−8.97067e18	−1.24994
$797$	9.69196e18	1.33947	0.669734	−	0.742601i	$-0.266408\pi$
$797$	9.69196e18	1.33947	0.669734	+	0.742601i	$0.266408\pi$
$798$	5.86131e18	0.803482
$799$	1.40806e18	0.191455
$800$	1.94728e19	2.62629
$801$	2.91862e18	0.390451
$802$	−7.20940e18	−0.956678
$803$	5.48381e18	0.721825
$804$	−1.51528e18	−0.197846
$805$	−2.09357e18	−0.271153
$806$	−9.70889e18	−1.24736
$807$	−8.48452e18	−1.08131
$808$	2.02102e18	0.255504
$809$	−1.39322e18	−0.174725	−0.0873625	−	0.996177i	$-0.527844\pi$
$809$	−1.39322e18	−0.174725	−0.0873625	+	0.996177i	$0.527844\pi$
$810$	2.08806e18	0.259770
$811$	−1.14333e19	−1.41102	−0.705512	−	0.708698i	$-0.749283\pi$
$811$	−1.14333e19	−1.41102	−0.705512	+	0.708698i	$0.749283\pi$
$812$	−2.44260e18	−0.299046
$813$	4.31621e18	0.524221
$814$	3.55626e17	0.0428484
$815$	−8.79791e18	−1.05161
$816$	−1.74402e18	−0.206808
$817$	2.61363e18	0.307469
$818$	−2.06441e19	−2.40935
$819$	−3.56099e18	−0.412311
$820$	1.09741e18	0.126060
$821$	−9.33974e18	−1.06440	−0.532200	−	0.846619i	$-0.678634\pi$
$821$	−9.33974e18	−1.06440	−0.532200	+	0.846619i	$0.678634\pi$
$822$	2.84197e18	0.321331
$823$	−1.64755e19	−1.84816	−0.924082	−	0.382195i	$-0.875168\pi$
$823$	−1.64755e19	−1.84816	−0.924082	+	0.382195i	$0.875168\pi$
$824$	−1.78662e18	−0.198840
$825$	−5.62020e18	−0.620584
$826$	1.40061e18	0.153443
$827$	−2.37125e18	−0.257746	−0.128873	−	0.991661i	$-0.541136\pi$
$827$	−2.37125e18	−0.257746	−0.128873	+	0.991661i	$0.541136\pi$
$828$	4.30249e17	0.0464005
$829$	1.47626e19	1.57964	0.789821	−	0.613338i	$-0.210174\pi$
$829$	1.47626e19	1.57964	0.789821	+	0.613338i	$0.210174\pi$
$830$	−1.56719e19	−1.66385
$831$	3.87607e18	0.408305
$832$	7.33004e18	0.766134
$833$	−6.63752e17	−0.0688356
$834$	4.36993e18	0.449672
$835$	−2.97743e19	−3.04005
$836$	4.82123e18	0.488446
$837$	−1.27102e18	−0.127772
$838$	9.36846e18	0.934506
$839$	−1.80444e19	−1.78603	−0.893016	−	0.450025i	$-0.851415\pi$
$839$	−1.80444e19	−1.78603	−0.893016	+	0.450025i	$0.851415\pi$
$840$	−2.53994e18	−0.249464
$841$	−8.36682e18	−0.815430
$842$	5.92496e18	0.573003
$843$	6.60836e18	0.634183
$844$	1.01776e19	0.969216
$845$	−1.79678e19	−1.69796
$846$	−2.96343e18	−0.277900
$847$	−6.87177e18	−0.639480
$848$	6.71127e18	0.619771
$849$	6.74075e18	0.617743
$850$	−9.28164e18	−0.844115
$851$	1.19404e17	0.0107765
$852$	−1.47313e18	−0.131943
$853$	−2.51116e18	−0.223206	−0.111603	−	0.993753i	$-0.535599\pi$
$853$	−2.51116e18	−0.223206	−0.111603	+	0.993753i	$0.535599\pi$
$854$	2.92937e18	0.258403
$855$	7.85604e18	0.687740
$856$	−2.44359e18	−0.212299
$857$	4.39477e18	0.378932	0.189466	−	0.981887i	$-0.439324\pi$
$857$	4.39477e18	0.378932	0.189466	+	0.981887i	$0.439324\pi$
$858$	−6.63589e18	−0.567847
$859$	−7.28347e17	−0.0618561	−0.0309280	−	0.999522i	$-0.509846\pi$
$859$	−7.28347e17	−0.0618561	−0.0309280	+	0.999522i	$0.509846\pi$
$860$	4.26573e18	0.359545
$861$	−5.55066e17	−0.0464327
$862$	−1.70171e19	−1.41282
$863$	1.16775e19	0.962232	0.481116	−	0.876657i	$-0.340232\pi$
$863$	1.16775e19	0.962232	0.481116	+	0.876657i	$0.340232\pi$
$864$	3.00994e18	0.246160
$865$	6.53347e18	0.530321
$866$	1.35610e18	0.109251
$867$	−6.53876e18	−0.522843
$868$	−5.82309e18	−0.462142
$869$	1.01251e19	0.797571
$870$	−7.41698e18	−0.579898
$871$	7.84685e18	0.608944
$872$	−5.49262e18	−0.423080
$873$	−1.00228e18	−0.0766299
$874$	3.66731e18	0.278307
$875$	−2.15224e19	−1.62121
$876$	−8.41325e18	−0.629053
$877$	1.82012e19	1.35084	0.675420	−	0.737434i	$-0.263962\pi$
$877$	1.82012e19	1.35084	0.675420	+	0.737434i	$0.263962\pi$
$878$	7.24268e18	0.533562
$879$	3.18530e17	0.0232928
$880$	−1.46912e19	−1.06640
$881$	2.45990e18	0.177245	0.0886225	−	0.996065i	$-0.471754\pi$
$881$	2.45990e18	0.177245	0.0886225	+	0.996065i	$0.471754\pi$
$882$	1.39695e18	0.0999158
$883$	−6.44851e18	−0.457841	−0.228921	−	0.973445i	$-0.573520\pi$
$883$	−6.44851e18	−0.457841	−0.228921	+	0.973445i	$0.573520\pi$
$884$	−4.83733e18	−0.340931
$885$	1.87727e18	0.131339
$886$	1.26308e19	0.877228
$887$	5.94950e18	0.410183	0.205091	−	0.978743i	$-0.434251\pi$
$887$	5.94950e18	0.410183	0.205091	+	0.978743i	$0.434251\pi$
$888$	1.44862e17	0.00991449
$889$	1.21704e19	0.826884
$890$	4.06027e19	2.73854
$891$	−8.68722e17	−0.0581669
$892$	−4.50629e18	−0.299535
$893$	−1.11495e19	−0.735737
$894$	1.21684e19	0.797147
$895$	−3.50300e18	−0.227819
$896$	−7.49125e18	−0.483673
$897$	−2.22804e18	−0.142815
$898$	−2.23758e19	−1.42391
$899$	4.51478e18	0.285232
$900$	8.62249e18	0.540825
$901$	−2.62320e18	−0.163351
$902$	−1.03436e18	−0.0639485
$903$	−2.15759e18	−0.132434
$904$	−3.85798e18	−0.235107
$905$	−4.34326e19	−2.62785
$906$	−4.13539e18	−0.248418
$907$	−2.82484e19	−1.68479	−0.842396	−	0.538859i	$-0.818856\pi$
$907$	−2.82484e19	−1.68479	−0.842396	+	0.538859i	$0.818856\pi$
$908$	−5.75611e18	−0.340856
$909$	5.16032e18	0.303397
$910$	−4.95390e19	−2.89187
$911$	1.04031e19	0.602970	0.301485	−	0.953471i	$-0.402518\pi$
$911$	1.04031e19	0.602970	0.301485	+	0.953471i	$0.402518\pi$
$912$	1.38098e19	0.794735
$913$	6.52021e18	0.372564
$914$	1.70243e19	0.965872
$915$	3.92629e18	0.221180
$916$	2.12833e19	1.19047
$917$	−2.73816e17	−0.0152075
$918$	−1.43468e18	−0.0791182
$919$	1.98217e18	0.108540	0.0542699	−	0.998526i	$-0.482717\pi$
$919$	1.98217e18	0.108540	0.0542699	+	0.998526i	$0.482717\pi$
$920$	−1.58919e18	−0.0864084
$921$	−5.45193e18	−0.294349
$922$	−4.38664e19	−2.35169
$923$	7.62861e18	0.406101
$924$	−3.98000e18	−0.210385
$925$	2.39293e18	0.125606
$926$	1.04438e19	0.544360
$927$	−4.56180e18	−0.236112
$928$	−1.06916e19	−0.549516
$929$	−2.39212e19	−1.22090	−0.610450	−	0.792055i	$-0.709011\pi$
$929$	−2.39212e19	−1.22090	−0.610450	+	0.792055i	$0.709011\pi$
$930$	−1.76819e19	−0.896168
$931$	5.25583e18	0.264526
$932$	1.73188e19	0.865596
$933$	8.19050e18	0.406518
$934$	−1.05830e19	−0.521618
$935$	5.74227e18	0.281066
$936$	−2.70309e18	−0.131391
$937$	−2.64946e19	−1.27894	−0.639470	−	0.768816i	$-0.720846\pi$
$937$	−2.64946e19	−1.27894	−0.639470	+	0.768816i	$0.720846\pi$
$938$	1.06622e19	0.511124
$939$	2.04445e19	0.973309
$940$	−1.81973e19	−0.860350
$941$	1.00832e19	0.473440	0.236720	−	0.971578i	$-0.423928\pi$
$941$	1.00832e19	0.473440	0.236720	+	0.971578i	$0.423928\pi$
$942$	2.93611e19	1.36912
$943$	−3.47294e17	−0.0160832
$944$	3.29998e18	0.151772
$945$	−6.48529e18	−0.296225
$946$	−4.02067e18	−0.182392
$947$	−3.84959e18	−0.173436	−0.0867181	−	0.996233i	$-0.527638\pi$
$947$	−3.84959e18	−0.173436	−0.0867181	+	0.996233i	$0.527638\pi$
$948$	−1.55339e19	−0.695065
$949$	4.35680e19	1.93614
$950$	7.34955e19	3.24382
$951$	2.11983e19	0.929239
$952$	1.74516e18	0.0759793
$953$	2.19742e19	0.950187	0.475093	−	0.879935i	$-0.342414\pi$
$953$	2.19742e19	0.950187	0.475093	+	0.879935i	$0.342414\pi$
$954$	5.52085e18	0.237105
$955$	5.47985e18	0.233747
$956$	2.08263e19	0.882339
$957$	3.08579e18	0.129849
$958$	−5.02403e19	−2.09979
$959$	−8.82686e18	−0.366425
$960$	1.33495e19	0.550430
$961$	−1.36544e19	−0.559206
$962$	2.82539e18	0.114932
$963$	−6.23926e18	−0.252094
$964$	−9.90116e18	−0.397361
$965$	4.75596e19	1.89588
$966$	−3.02742e18	−0.119873
$967$	−2.51950e19	−0.990928	−0.495464	−	0.868628i	$-0.665002\pi$
$967$	−2.51950e19	−0.990928	−0.495464	+	0.868628i	$0.665002\pi$
$968$	−5.21625e18	−0.203783
$969$	−5.39779e18	−0.209465
$970$	−1.39434e19	−0.537467
$971$	−1.58447e19	−0.606680	−0.303340	−	0.952882i	$-0.598102\pi$
$971$	−1.58447e19	−0.606680	−0.303340	+	0.952882i	$0.598102\pi$
$972$	1.33279e18	0.0506911
$973$	−1.35726e19	−0.512777
$974$	4.09391e19	1.53640
$975$	−4.46515e19	−1.66459
$976$	6.90188e18	0.255590
$977$	3.10880e19	1.14361	0.571805	−	0.820389i	$-0.306243\pi$
$977$	3.10880e19	1.14361	0.571805	+	0.820389i	$0.306243\pi$
$978$	−1.27223e19	−0.464904
$979$	−1.68925e19	−0.613205
$980$	8.57809e18	0.309329
$981$	−1.40244e19	−0.502385
$982$	5.47989e19	1.95006
$983$	1.32946e19	0.469979	0.234989	−	0.971998i	$-0.424494\pi$
$983$	1.32946e19	0.469979	0.234989	+	0.971998i	$0.424494\pi$
$984$	−4.21341e17	−0.0147967
$985$	4.22483e19	1.47392
$986$	5.09611e18	0.176620
$987$	9.20412e18	0.316899
$988$	3.83038e19	1.31015
$989$	−1.34997e18	−0.0458719
$990$	−1.20853e19	−0.407971
$991$	−3.07838e19	−1.03239	−0.516194	−	0.856472i	$-0.672652\pi$
$991$	−3.07838e19	−1.03239	−0.516194	+	0.856472i	$0.672652\pi$
$992$	−2.54885e19	−0.849216
$993$	−9.70278e18	−0.321163
$994$	1.03656e19	0.340866
$995$	8.46032e19	2.76399
$996$	−1.00033e19	−0.324681
$997$	1.34236e19	0.432863	0.216431	−	0.976298i	$-0.430558\pi$
$997$	1.34236e19	0.432863	0.216431	+	0.976298i	$0.430558\pi$
$998$	3.72214e19	1.19246
$999$	3.69879e17	0.0117729

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.c.1.5	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.c.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-121.100 q^{2} +729.000 q^{3} +6473.28 q^{4} -61050.1 q^{5} -88282.1 q^{6} +274195. q^{7} +208137. q^{8} +531441. q^{9} +O(q^{10})\)	\(q-121.100 q^{2} +729.000 q^{3} +6473.28 q^{4} -61050.1 q^{5} -88282.1 q^{6} +274195. q^{7} +208137. q^{8} +531441. q^{9} +7.39319e6 q^{10} -3.07589e6 q^{11} +4.71902e6 q^{12} -2.44374e7 q^{13} -3.32051e7 q^{14} -4.45056e7 q^{15} -7.82346e7 q^{16} +3.05792e7 q^{17} -6.43577e7 q^{18} -2.42138e8 q^{19} -3.95195e8 q^{20} +1.99888e8 q^{21} +3.72491e8 q^{22} +1.25066e8 q^{23} +1.51732e8 q^{24} +2.50642e9 q^{25} +2.95938e9 q^{26} +3.87420e8 q^{27} +1.77494e9 q^{28} -1.37616e9 q^{29} +5.38964e9 q^{30} -3.28072e9 q^{31} +7.76917e9 q^{32} -2.24232e9 q^{33} -3.70315e9 q^{34} -1.67397e10 q^{35} +3.44017e9 q^{36} +9.54723e8 q^{37} +2.93229e10 q^{38} -1.78149e10 q^{39} -1.27068e10 q^{40} -2.77688e9 q^{41} -2.42065e10 q^{42} -1.07940e10 q^{43} -1.99111e10 q^{44} -3.24445e10 q^{45} -1.51456e10 q^{46} +4.60463e10 q^{47} -5.70330e10 q^{48} -2.17060e10 q^{49} -3.03528e11 q^{50} +2.22922e10 q^{51} -1.58190e11 q^{52} -8.57839e10 q^{53} -4.69167e10 q^{54} +1.87784e11 q^{55} +5.70702e10 q^{56} -1.76518e11 q^{57} +1.66653e11 q^{58} -4.21805e10 q^{59} -2.88097e11 q^{60} -8.82203e10 q^{61} +3.97296e11 q^{62} +1.45719e11 q^{63} -2.99952e11 q^{64} +1.49191e12 q^{65} +2.71546e11 q^{66} -3.21100e11 q^{67} +1.97948e11 q^{68} +9.11734e10 q^{69} +2.02718e12 q^{70} -3.12169e11 q^{71} +1.10613e11 q^{72} -1.78284e12 q^{73} -1.15617e11 q^{74} +1.82718e12 q^{75} -1.56743e12 q^{76} -8.43394e11 q^{77} +2.15739e12 q^{78} -3.29175e12 q^{79} +4.77623e12 q^{80} +2.82430e11 q^{81} +3.36281e11 q^{82} -2.11978e12 q^{83} +1.29393e12 q^{84} -1.86686e12 q^{85} +1.30716e12 q^{86} -1.00322e12 q^{87} -6.40207e11 q^{88} +5.49190e12 q^{89} +3.92904e12 q^{90} -6.70062e12 q^{91} +8.09590e11 q^{92} -2.39164e12 q^{93} -5.57622e12 q^{94} +1.47825e13 q^{95} +5.66373e12 q^{96} -1.88598e12 q^{97} +2.62860e12 q^{98} -1.63465e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + O(q^{10}) \)	\( 31q + 310q^{2} + 22599q^{3} + 126886q^{4} + 81008q^{5} + 225990q^{6} + 1002941q^{7} + 4632723q^{8} + 16474671q^{9} + 4647481q^{10} + 17937316q^{11} + 92499894q^{12} + 40664720q^{13} + 139193613q^{14} + 59054832q^{15} + 370110498q^{16} + 213442823q^{17} + 164746710q^{18} - 62592329q^{19} + 1637085153q^{20} + 731143989q^{21} + 4142028314q^{22} + 1873486387q^{23} + 3377255067q^{24} + 8307272395q^{25} - 534777728q^{26} + 12010035159q^{27} + 766416778q^{28} + 13765513563q^{29} + 3388013649q^{30} + 14274077235q^{31} + 30574460156q^{32} + 13076303364q^{33} - 677551028q^{34} + 36023610185q^{35} + 67432422726q^{36} - 18278838391q^{37} - 23650502933q^{38} + 29644580880q^{39} + 10045447572q^{40} + 34748006725q^{41} + 101472143877q^{42} + 40350158146q^{43} + 163101196592q^{44} + 43050972528q^{45} + 296118466353q^{46} + 233954631099q^{47} + 269810553042q^{48} + 324065402790q^{49} - 102960745787q^{50} + 155599817967q^{51} + 668297695096q^{52} + 500927963876q^{53} + 120100351590q^{54} + 884972340924q^{55} + 1392234478810q^{56} - 45629807841q^{57} + 689262776200q^{58} - 1307596542871q^{59} + 1193435076537q^{60} + 1716832157925q^{61} + 1816094290366q^{62} + 533003967981q^{63} + 4381780009133q^{64} + 1457007885906q^{65} + 3019538640906q^{66} + 1212131702006q^{67} + 6552992665503q^{68} + 1365771576123q^{69} + 8806714081634q^{70} + 6074000239936q^{71} + 2462018943843q^{72} + 3756145185973q^{73} + 8066450143602q^{74} + 6056001575955q^{75} + 7913230001992q^{76} + 6031241575915q^{77} - 389852963712q^{78} + 11377744190862q^{79} + 16473302366969q^{80} + 8755315630911q^{81} + 10413363680159q^{82} + 19915461517429q^{83} + 558717831162q^{84} + 15280981141573q^{85} + 7573325358452q^{86} + 10035059387427q^{87} + 19271409121081q^{88} + 14115863121241q^{89} + 2469861950121q^{90} + 18296287784699q^{91} + 15158951168774q^{92} + 10405802304315q^{93} - 18637923572412q^{94} - 2294034679397q^{95} + 22288781453724q^{96} + 38558536599054q^{97} - 1998410212380q^{98} + 9532625152356q^{99} + O(q^{100}) \)

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