LMFDB - Embedded newform 177.14.a.a.1.3

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:	$1$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	177.1

$q$-expansion

$f(q)$	$=$	$q-153.212 q^{2} +729.000 q^{3} +15282.0 q^{4} +58431.3 q^{5} -111692. q^{6} +57012.1 q^{7} -1.08627e6 q^{8} +531441. q^{9} +O(q^{10})$	\(q-153.212 q^{2} +729.000 q^{3} +15282.0 q^{4} +58431.3 q^{5} -111692. q^{6} +57012.1 q^{7} -1.08627e6 q^{8} +531441. q^{9} -8.95239e6 q^{10} -8.87077e6 q^{11} +1.11405e7 q^{12} -4.66223e6 q^{13} -8.73495e6 q^{14} +4.25964e7 q^{15} +4.12395e7 q^{16} -9.15066e7 q^{17} -8.14232e7 q^{18} -1.77197e8 q^{19} +8.92945e8 q^{20} +4.15618e7 q^{21} +1.35911e9 q^{22} +7.81026e8 q^{23} -7.91889e8 q^{24} +2.19352e9 q^{25} +7.14310e8 q^{26} +3.87420e8 q^{27} +8.71257e8 q^{28} -3.99585e9 q^{29} -6.52629e9 q^{30} +5.30502e9 q^{31} +2.58031e9 q^{32} -6.46679e9 q^{33} +1.40199e10 q^{34} +3.33129e9 q^{35} +8.12146e9 q^{36} +1.42793e10 q^{37} +2.71487e10 q^{38} -3.39876e9 q^{39} -6.34720e10 q^{40} +3.50267e10 q^{41} -6.36778e9 q^{42} -2.93576e10 q^{43} -1.35563e11 q^{44} +3.10528e10 q^{45} -1.19663e11 q^{46} -4.10994e10 q^{47} +3.00636e10 q^{48} -9.36386e10 q^{49} -3.36073e11 q^{50} -6.67083e10 q^{51} -7.12480e10 q^{52} +2.99702e11 q^{53} -5.93575e10 q^{54} -5.18331e11 q^{55} -6.19304e10 q^{56} -1.29176e11 q^{57} +6.12212e11 q^{58} +4.21805e10 q^{59} +6.50957e11 q^{60} -6.54690e11 q^{61} -8.12793e11 q^{62} +3.02986e10 q^{63} -7.33168e11 q^{64} -2.72420e11 q^{65} +9.90791e11 q^{66} +1.22057e12 q^{67} -1.39840e12 q^{68} +5.69368e11 q^{69} -5.10395e11 q^{70} -1.52971e12 q^{71} -5.77287e11 q^{72} +1.65969e12 q^{73} -2.18776e12 q^{74} +1.59907e12 q^{75} -2.70791e12 q^{76} -5.05742e11 q^{77} +5.20732e11 q^{78} -2.59604e12 q^{79} +2.40968e12 q^{80} +2.82430e11 q^{81} -5.36651e12 q^{82} -2.52953e12 q^{83} +6.35146e11 q^{84} -5.34685e12 q^{85} +4.49794e12 q^{86} -2.91297e12 q^{87} +9.63603e12 q^{88} +6.85235e12 q^{89} -4.75766e12 q^{90} -2.65804e11 q^{91} +1.19356e13 q^{92} +3.86736e12 q^{93} +6.29692e12 q^{94} -1.03538e13 q^{95} +1.88104e12 q^{96} -5.66680e12 q^{97} +1.43466e13 q^{98} -4.71429e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) $	\( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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 $

$2$	−153.212	−1.69277	−0.846385	−	0.532571i	$-0.821226\pi$
$2$	−153.212	−1.69277	−0.846385	+	0.532571i	$0.821226\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	15282.0	1.86547
$5$	58431.3	1.67240	0.836201	−	0.548423i	$-0.184772\pi$
$5$	58431.3	1.67240	0.836201	+	0.548423i	$0.184772\pi$
$6$	−111692.	−0.977322
$7$	57012.1	0.183160	0.0915799	−	0.995798i	$-0.470808\pi$
$7$	57012.1	0.183160	0.0915799	+	0.995798i	$0.470808\pi$
$8$	−1.08627e6	−1.46505
$9$	531441.	0.333333
$10$	−8.95239e6	−2.83099
$11$	−8.87077e6	−1.50976	−0.754882	−	0.655861i	$-0.772306\pi$
$11$	−8.87077e6	−1.50976	−0.754882	+	0.655861i	$0.772306\pi$
$12$	1.11405e7	1.07703
$13$	−4.66223e6	−0.267893	−0.133947	−	0.990989i	$-0.542765\pi$
$13$	−4.66223e6	−0.267893	−0.133947	+	0.990989i	$0.542765\pi$
$14$	−8.73495e6	−0.310047
$15$	4.25964e7	0.965562
$16$	4.12395e7	0.614516
$17$	−9.15066e7	−0.919464	−0.459732	−	0.888058i	$-0.652054\pi$
$17$	−9.15066e7	−0.919464	−0.459732	+	0.888058i	$0.652054\pi$
$18$	−8.14232e7	−0.564257
$19$	−1.77197e8	−0.864087	−0.432043	−	0.901853i	$-0.642207\pi$
$19$	−1.77197e8	−0.864087	−0.432043	+	0.901853i	$0.642207\pi$
$20$	8.92945e8	3.11982
$21$	4.15618e7	0.105747
$22$	1.35911e9	2.55568
$23$	7.81026e8	1.10011	0.550053	−	0.835130i	$-0.314608\pi$
$23$	7.81026e8	1.10011	0.550053	+	0.835130i	$0.314608\pi$
$24$	−7.91889e8	−0.845845
$25$	2.19352e9	1.79693
$26$	7.14310e8	0.453482
$27$	3.87420e8	0.192450
$28$	8.71257e8	0.341680
$29$	−3.99585e9	−1.24745	−0.623723	−	0.781645i	$-0.714381\pi$
$29$	−3.99585e9	−1.24745	−0.623723	+	0.781645i	$0.714381\pi$
$30$	−6.52629e9	−1.63447
$31$	5.30502e9	1.07358	0.536792	−	0.843715i	$-0.319636\pi$
$31$	5.30502e9	1.07358	0.536792	+	0.843715i	$0.319636\pi$
$32$	2.58031e9	0.424812
$33$	−6.46679e9	−0.871663
$34$	1.40199e10	1.55644
$35$	3.33129e9	0.306317
$36$	8.12146e9	0.621824
$37$	1.42793e10	0.914945	0.457473	−	0.889224i	$-0.348755\pi$
$37$	1.42793e10	0.914945	0.457473	+	0.889224i	$0.348755\pi$
$38$	2.71487e10	1.46270
$39$	−3.39876e9	−0.154668
$40$	−6.34720e10	−2.45015
$41$	3.50267e10	1.15161	0.575803	−	0.817588i	$-0.304689\pi$
$41$	3.50267e10	1.15161	0.575803	+	0.817588i	$0.304689\pi$
$42$	−6.36778e9	−0.179006
$43$	−2.93576e10	−0.708232	−0.354116	−	0.935202i	$-0.615218\pi$
$43$	−2.93576e10	−0.708232	−0.354116	+	0.935202i	$0.615218\pi$
$44$	−1.35563e11	−2.81642
$45$	3.10528e10	0.557467
$46$	−1.19663e11	−1.86223
$47$	−4.10994e10	−0.556159	−0.278080	−	0.960558i	$-0.589698\pi$
$47$	−4.10994e10	−0.556159	−0.278080	+	0.960558i	$0.589698\pi$
$48$	3.00636e10	0.354791
$49$	−9.36386e10	−0.966453
$50$	−3.36073e11	−3.04179
$51$	−6.67083e10	−0.530853
$52$	−7.12480e10	−0.499748
$53$	2.99702e11	1.85736	0.928679	−	0.370883i	$-0.120945\pi$
$53$	2.99702e11	1.85736	0.928679	+	0.370883i	$0.120945\pi$
$54$	−5.93575e10	−0.325774
$55$	−5.18331e11	−2.52493
$56$	−6.19304e10	−0.268338
$57$	−1.29176e11	−0.498881
$58$	6.12212e11	2.11164
$59$	4.21805e10	0.130189
$59$	4.21805e10	0.130189
$60$	6.50957e11	1.80123
$61$	−6.54690e11	−1.62702	−0.813508	−	0.581553i	$-0.802445\pi$
$61$	−6.54690e11	−1.62702	−0.813508	+	0.581553i	$0.802445\pi$
$62$	−8.12793e11	−1.81733
$63$	3.02986e10	0.0610532
$64$	−7.33168e11	−1.33363
$65$	−2.72420e11	−0.448025
$66$	9.90791e11	1.47553
$67$	1.22057e12	1.64846	0.824228	−	0.566257i	$-0.191609\pi$
$67$	1.22057e12	1.64846	0.824228	+	0.566257i	$0.191609\pi$
$68$	−1.39840e12	−1.71523
$69$	5.69368e11	0.635146
$70$	−5.10395e11	−0.518524
$71$	−1.52971e12	−1.41720	−0.708598	−	0.705612i	$-0.750672\pi$
$71$	−1.52971e12	−1.41720	−0.708598	+	0.705612i	$0.750672\pi$
$72$	−5.77287e11	−0.488349
$73$	1.65969e12	1.28359	0.641797	−	0.766874i	$-0.278189\pi$
$73$	1.65969e12	1.28359	0.641797	+	0.766874i	$0.278189\pi$
$74$	−2.18776e12	−1.54879
$75$	1.59907e12	1.03746
$76$	−2.70791e12	−1.61193
$77$	−5.05742e11	−0.276528
$78$	5.20732e11	0.261818
$79$	−2.59604e12	−1.20153	−0.600766	−	0.799425i	$-0.705138\pi$
$79$	−2.59604e12	−1.20153	−0.600766	+	0.799425i	$0.705138\pi$
$80$	2.40968e12	1.02772
$81$	2.82430e11	0.111111
$82$	−5.36651e12	−1.94941
$83$	−2.52953e12	−0.849243	−0.424622	−	0.905371i	$-0.639593\pi$
$83$	−2.52953e12	−0.849243	−0.424622	+	0.905371i	$0.639593\pi$
$84$	6.35146e11	0.197269
$85$	−5.34685e12	−1.53771
$86$	4.49794e12	1.19887
$87$	−2.91297e12	−0.720213
$88$	9.63603e12	2.21188
$89$	6.85235e12	1.46152	0.730759	−	0.682635i	$-0.239166\pi$
$89$	6.85235e12	1.46152	0.730759	+	0.682635i	$0.239166\pi$
$90$	−4.75766e12	−0.943664
$91$	−2.65804e11	−0.0490673
$92$	1.19356e13	2.05222
$93$	3.86736e12	0.619833
$94$	6.29692e12	0.941450
$95$	−1.03538e13	−1.44510
$96$	1.88104e12	0.245265
$97$	−5.66680e12	−0.690752	−0.345376	−	0.938464i	$-0.612249\pi$
$97$	−5.66680e12	−0.690752	−0.345376	+	0.938464i	$0.612249\pi$
$98$	1.43466e13	1.63598
$99$	−4.71429e12	−0.503255
$100$	3.35212e13	3.35212
$101$	−8.69804e12	−0.815328	−0.407664	−	0.913132i	$-0.633657\pi$
$101$	−8.69804e12	−0.815328	−0.407664	+	0.913132i	$0.633657\pi$
$102$	1.02205e13	0.898612
$103$	1.24127e13	1.02429	0.512147	−	0.858898i	$-0.328850\pi$
$103$	1.24127e13	1.02429	0.512147	+	0.858898i	$0.328850\pi$
$104$	5.06442e12	0.392476
$105$	2.42851e12	0.176852
$106$	−4.59179e13	−3.14408
$107$	−4.89900e12	−0.315582	−0.157791	−	0.987472i	$-0.550437\pi$
$107$	−4.89900e12	−0.315582	−0.157791	+	0.987472i	$0.550437\pi$
$108$	5.92054e12	0.359010
$109$	1.80653e13	1.03175	0.515875	−	0.856664i	$-0.327467\pi$
$109$	1.80653e13	1.03175	0.515875	+	0.856664i	$0.327467\pi$
$110$	7.94146e13	4.27413
$111$	1.04096e13	0.528244
$112$	2.35115e12	0.112555
$113$	−3.11508e13	−1.40754	−0.703768	−	0.710430i	$-0.748501\pi$
$113$	−3.11508e13	−1.40754	−0.703768	+	0.710430i	$0.748501\pi$
$114$	1.97914e13	0.844491
$115$	4.56364e13	1.83982
$116$	−6.10643e13	−2.32708
$117$	−2.47770e12	−0.0892977
$118$	−6.46257e12	−0.220380
$119$	−5.21699e12	−0.168409
$120$	−4.62711e13	−1.41459
$121$	4.41679e13	1.27939
$122$	1.00306e14	2.75417
$123$	2.55345e13	0.664880
$124$	8.10710e13	2.00274
$125$	5.68427e13	1.33278
$126$	−4.64211e12	−0.103349
$127$	−3.45890e13	−0.731500	−0.365750	−	0.930713i	$-0.619187\pi$
$127$	−3.45890e13	−0.731500	−0.365750	+	0.930713i	$0.619187\pi$
$128$	9.11924e13	1.83271
$129$	−2.14017e13	−0.408898
$130$	4.17381e13	0.758404
$131$	−9.05081e13	−1.56467	−0.782337	−	0.622855i	$-0.785973\pi$
$131$	−9.05081e13	−1.56467	−0.782337	+	0.622855i	$0.785973\pi$
$132$	−9.88253e13	−1.62606
$133$	−1.01024e13	−0.158266
$134$	−1.87007e14	−2.79046
$135$	2.26375e13	0.321854
$136$	9.94006e13	1.34706
$137$	6.91594e13	0.893650	0.446825	−	0.894621i	$-0.352555\pi$
$137$	6.91594e13	0.893650	0.446825	+	0.894621i	$0.352555\pi$
$138$	−8.72341e13	−1.07516
$139$	−4.61403e13	−0.542605	−0.271303	−	0.962494i	$-0.587454\pi$
$139$	−4.61403e13	−0.542605	−0.271303	+	0.962494i	$0.587454\pi$
$140$	5.09087e13	0.571425
$141$	−2.99614e13	−0.321099
$142$	2.34370e14	2.39899
$143$	4.13576e13	0.404456
$144$	2.19164e13	0.204839
$145$	−2.33483e14	−2.08623
$146$	−2.54284e14	−2.17283
$147$	−6.82626e13	−0.557982
$148$	2.18215e14	1.70681
$149$	−1.48180e14	−1.10938	−0.554688	−	0.832059i	$-0.687162\pi$
$149$	−1.48180e14	−1.10938	−0.554688	+	0.832059i	$0.687162\pi$
$150$	−2.44997e14	−1.75618
$151$	1.72056e14	1.18119	0.590596	−	0.806967i	$-0.298893\pi$
$151$	1.72056e14	1.18119	0.590596	+	0.806967i	$0.298893\pi$
$152$	1.92483e14	1.26593
$153$	−4.86304e13	−0.306488
$154$	7.74858e13	0.468099
$155$	3.09979e14	1.79546
$156$	−5.19398e13	−0.288529
$157$	−1.31345e14	−0.699950	−0.349975	−	0.936759i	$-0.613810\pi$
$157$	−1.31345e14	−0.699950	−0.349975	+	0.936759i	$0.613810\pi$
$158$	3.97745e14	2.03392
$159$	2.18482e14	1.07235
$160$	1.50771e14	0.710456
$161$	4.45280e13	0.201495
$162$	−4.32716e13	−0.188086
$163$	−4.51031e13	−0.188359	−0.0941797	−	0.995555i	$-0.530023\pi$
$163$	−4.51031e13	−0.188359	−0.0941797	+	0.995555i	$0.530023\pi$
$164$	5.35276e14	2.14829
$165$	−3.77863e14	−1.45777
$166$	3.87555e14	1.43757
$167$	−9.10640e13	−0.324855	−0.162427	−	0.986720i	$-0.551932\pi$
$167$	−9.10640e13	−0.324855	−0.162427	+	0.986720i	$0.551932\pi$
$168$	−4.51473e13	−0.154925
$169$	−2.81139e14	−0.928233
$170$	8.19203e14	2.60299
$171$	−9.41696e13	−0.288029
$172$	−4.48641e14	−1.32119
$173$	−4.89378e14	−1.38786	−0.693929	−	0.720044i	$-0.744122\pi$
$173$	−4.89378e14	−1.38786	−0.693929	+	0.720044i	$0.744122\pi$
$174$	4.46303e14	1.21916
$175$	1.25057e14	0.329125
$176$	−3.65826e14	−0.927775
$177$	3.07496e13	0.0751646
$178$	−1.04986e15	−2.47402
$179$	−4.93063e14	−1.12036	−0.560180	−	0.828371i	$-0.689268\pi$
$179$	−4.93063e14	−1.12036	−0.560180	+	0.828371i	$0.689268\pi$
$180$	4.74547e14	1.03994
$181$	−6.09433e14	−1.28830	−0.644148	−	0.764901i	$-0.722788\pi$
$181$	−6.09433e14	−1.28830	−0.644148	+	0.764901i	$0.722788\pi$
$182$	4.07243e13	0.0830596
$183$	−4.77269e14	−0.939358
$184$	−8.48403e14	−1.61171
$185$	8.34357e14	1.53016
$186$	−5.92526e14	−1.04924
$187$	8.11735e14	1.38817
$188$	−6.28079e14	−1.03750
$189$	2.20877e13	0.0352491
$190$	1.58633e15	2.44622
$191$	−8.52949e14	−1.27118	−0.635589	−	0.772028i	$-0.719243\pi$
$191$	−8.52949e14	−1.27118	−0.635589	+	0.772028i	$0.719243\pi$
$192$	−5.34480e14	−0.769969
$193$	4.00836e14	0.558270	0.279135	−	0.960252i	$-0.409952\pi$
$193$	4.00836e14	0.558270	0.279135	+	0.960252i	$0.409952\pi$
$194$	8.68223e14	1.16928
$195$	−1.98594e14	−0.258667
$196$	−1.43098e15	−1.80289
$197$	−1.18643e15	−1.44615	−0.723074	−	0.690770i	$-0.757272\pi$
$197$	−1.18643e15	−1.44615	−0.723074	+	0.690770i	$0.757272\pi$
$198$	7.22287e14	0.851895
$199$	−6.72887e14	−0.768064	−0.384032	−	0.923320i	$-0.625465\pi$
$199$	−6.72887e14	−0.768064	−0.384032	+	0.923320i	$0.625465\pi$
$200$	−2.38274e15	−2.63258
$201$	8.89798e14	0.951737
$202$	1.33264e15	1.38016
$203$	−2.27812e14	−0.228482
$204$	−1.01943e15	−0.990291
$205$	2.04666e15	1.92595
$206$	−1.90178e15	−1.73389
$207$	4.15069e14	0.366702
$208$	−1.92268e14	−0.164625
$209$	1.57187e15	1.30457
$210$	−3.72078e14	−0.299370
$211$	−4.17827e13	−0.0325958	−0.0162979	−	0.999867i	$-0.505188\pi$
$211$	−4.17827e13	−0.0325958	−0.0162979	+	0.999867i	$0.505188\pi$
$212$	4.58003e15	3.46485
$213$	−1.11516e15	−0.818218
$214$	7.50586e14	0.534209
$215$	−1.71540e15	−1.18445
$216$	−4.20842e14	−0.281948
$217$	3.02450e14	0.196637
$218$	−2.76783e15	−1.74651
$219$	1.20991e15	0.741084
$220$	−7.92111e15	−4.71019
$221$	4.26625e14	0.246318
$222$	−1.59488e15	−0.894196
$223$	−2.33490e14	−0.127141	−0.0635706	−	0.997977i	$-0.520249\pi$
$223$	−2.33490e14	−0.127141	−0.0635706	+	0.997977i	$0.520249\pi$
$224$	1.47109e14	0.0778084
$225$	1.16572e15	0.598976
$226$	4.77268e15	2.38264
$227$	−1.06554e15	−0.516893	−0.258447	−	0.966026i	$-0.583211\pi$
$227$	−1.06554e15	−0.516893	−0.258447	+	0.966026i	$0.583211\pi$
$228$	−1.97407e15	−0.930649
$229$	−3.34037e14	−0.153061	−0.0765303	−	0.997067i	$-0.524384\pi$
$229$	−3.34037e14	−0.153061	−0.0765303	+	0.997067i	$0.524384\pi$
$230$	−6.99205e15	−3.11439
$231$	−3.68686e14	−0.159654
$232$	4.34056e15	1.82757
$233$	−3.54779e15	−1.45259	−0.726296	−	0.687382i	$-0.758760\pi$
$233$	−3.54779e15	−1.45259	−0.726296	+	0.687382i	$0.758760\pi$
$234$	3.79614e14	0.151161
$235$	−2.40149e15	−0.930122
$236$	6.44601e14	0.242864
$237$	−1.89251e15	−0.693705
$238$	7.99306e14	0.285077
$239$	−1.34856e15	−0.468039	−0.234020	−	0.972232i	$-0.575188\pi$
$239$	−1.34856e15	−0.468039	−0.234020	+	0.972232i	$0.575188\pi$
$240$	1.75666e15	0.593353
$241$	3.35663e15	1.10355	0.551777	−	0.833992i	$-0.313950\pi$
$241$	3.35663e15	1.10355	0.551777	+	0.833992i	$0.313950\pi$
$242$	−6.76706e15	−2.16571
$243$	2.05891e14	0.0641500
$244$	−1.00049e16	−3.03516
$245$	−5.47143e15	−1.61630
$246$	−3.91219e15	−1.12549
$247$	8.26132e14	0.231483
$248$	−5.76266e15	−1.57285
$249$	−1.84403e15	−0.490311
$250$	−8.70899e15	−2.25610
$251$	−1.90252e13	−0.00480231	−0.00240115	−	0.999997i	$-0.500764\pi$
$251$	−1.90252e13	−0.00480231	−0.00240115	+	0.999997i	$0.500764\pi$
$252$	4.63022e14	0.113893
$253$	−6.92831e15	−1.66090
$254$	5.29946e15	1.23826
$255$	−3.89785e15	−0.887799
$256$	−7.96567e15	−1.76873
$257$	−3.82535e15	−0.828143	−0.414072	−	0.910244i	$-0.635894\pi$
$257$	−3.82535e15	−0.828143	−0.414072	+	0.910244i	$0.635894\pi$
$258$	3.27900e15	0.692170
$259$	8.14092e14	0.167581
$260$	−4.16311e15	−0.835779
$261$	−2.12356e15	−0.415815
$262$	1.38669e16	2.64863
$263$	−5.52965e15	−1.03035	−0.515176	−	0.857084i	$-0.672273\pi$
$263$	−5.52965e15	−1.03035	−0.515176	+	0.857084i	$0.672273\pi$
$264$	7.02467e15	1.27703
$265$	1.75120e16	3.10625
$266$	1.54780e15	0.267908
$267$	4.99536e15	0.843808
$268$	1.86527e16	3.07515
$269$	1.66099e15	0.267287	0.133644	−	0.991029i	$-0.457332\pi$
$269$	1.66099e15	0.267287	0.133644	+	0.991029i	$0.457332\pi$
$270$	−3.46834e15	−0.544825
$271$	−5.59072e14	−0.0857368	−0.0428684	−	0.999081i	$-0.513650\pi$
$271$	−5.59072e14	−0.0857368	−0.0428684	+	0.999081i	$0.513650\pi$
$272$	−3.77369e15	−0.565025
$273$	−1.93771e14	−0.0283290
$274$	−1.05961e16	−1.51275
$275$	−1.94582e16	−2.71294
$276$	8.70105e15	1.18485
$277$	−3.38679e15	−0.450475	−0.225237	−	0.974304i	$-0.572316\pi$
$277$	−3.38679e15	−0.450475	−0.225237	+	0.974304i	$0.572316\pi$
$278$	7.06925e15	0.918507
$279$	2.81930e15	0.357861
$280$	−3.61867e15	−0.448768
$281$	−4.65875e15	−0.564519	−0.282259	−	0.959338i	$-0.591084\pi$
$281$	−4.65875e15	−0.564519	−0.282259	+	0.959338i	$0.591084\pi$
$282$	4.59046e15	0.543547
$283$	1.19560e16	1.38349	0.691743	−	0.722144i	$-0.256843\pi$
$283$	1.19560e16	1.38349	0.691743	+	0.722144i	$0.256843\pi$
$284$	−2.33770e16	−2.64374
$285$	−7.54795e15	−0.834329
$286$	−6.33648e15	−0.684651
$287$	1.99695e15	0.210928
$288$	1.37128e15	0.141604
$289$	−1.53112e15	−0.154587
$290$	3.57724e16	3.53151
$291$	−4.13110e15	−0.398806
$292$	2.53633e16	2.39451
$293$	−9.27759e14	−0.0856635	−0.0428318	−	0.999082i	$-0.513638\pi$
$293$	−9.27759e14	−0.0856635	−0.0428318	+	0.999082i	$0.513638\pi$
$294$	1.04587e16	0.944535
$295$	2.46466e15	0.217728
$296$	−1.55111e16	−1.34044
$297$	−3.43672e15	−0.290554
$298$	2.27030e16	1.87792
$299$	−3.64132e15	−0.294711
$300$	2.44370e16	1.93535
$301$	−1.67374e15	−0.129720
$302$	−2.63611e16	−1.99949
$303$	−6.34087e15	−0.470730
$304$	−7.30751e15	−0.530996
$305$	−3.82544e16	−2.72103
$306$	7.45076e15	0.518814
$307$	6.32361e15	0.431088	0.215544	−	0.976494i	$-0.430848\pi$
$307$	6.32361e15	0.431088	0.215544	+	0.976494i	$0.430848\pi$
$308$	−7.72872e15	−0.515855
$309$	9.04886e15	0.591376
$310$	−4.74925e16	−3.03931
$311$	1.71650e15	0.107573	0.0537864	−	0.998552i	$-0.482871\pi$
$311$	1.71650e15	0.107573	0.0537864	+	0.998552i	$0.482871\pi$
$312$	3.69197e15	0.226596
$313$	1.38424e16	0.832096	0.416048	−	0.909343i	$-0.363415\pi$
$313$	1.38424e16	0.832096	0.416048	+	0.909343i	$0.363415\pi$
$314$	2.01237e16	1.18486
$315$	1.77039e15	0.102106
$316$	−3.96726e16	−2.24143
$317$	2.59932e16	1.43871	0.719357	−	0.694641i	$-0.244437\pi$
$317$	2.59932e16	1.43871	0.719357	+	0.694641i	$0.244437\pi$
$318$	−3.34742e16	−1.81524
$319$	3.54463e16	1.88335
$320$	−4.28400e16	−2.23036
$321$	−3.57137e15	−0.182202
$322$	−6.82222e15	−0.341085
$323$	1.62147e16	0.794496
$324$	4.31608e15	0.207275
$325$	−1.02267e16	−0.481385
$326$	6.91035e15	0.318849
$327$	1.31696e16	0.595681
$328$	−3.80483e16	−1.68716
$329$	−2.34316e15	−0.101866
$330$	5.78932e16	2.46767
$331$	−3.81986e16	−1.59649	−0.798243	−	0.602336i	$-0.794237\pi$
$331$	−3.81986e16	−1.59649	−0.798243	+	0.602336i	$0.794237\pi$
$332$	−3.86561e16	−1.58424
$333$	7.58859e15	0.304982
$334$	1.39521e16	0.549905
$335$	7.13197e16	2.75688
$336$	1.71399e15	0.0649835
$337$	3.04057e16	1.13073	0.565367	−	0.824839i	$-0.308735\pi$
$337$	3.04057e16	1.13073	0.565367	+	0.824839i	$0.308735\pi$
$338$	4.30739e16	1.57129
$339$	−2.27089e16	−0.812641
$340$	−8.17103e16	−2.86856
$341$	−4.70596e16	−1.62086
$342$	1.44279e16	0.487567
$343$	−1.08624e16	−0.360175
$344$	3.18902e16	1.03759
$345$	3.32689e16	1.06222
$346$	7.49786e16	2.34932
$347$	−6.75832e15	−0.207825	−0.103912	−	0.994586i	$-0.533136\pi$
$347$	−6.75832e15	−0.207825	−0.103912	+	0.994586i	$0.533136\pi$
$348$	−4.45159e16	−1.34354
$349$	−2.88294e16	−0.854025	−0.427013	−	0.904246i	$-0.640434\pi$
$349$	−2.88294e16	−0.854025	−0.427013	+	0.904246i	$0.640434\pi$
$350$	−1.91602e16	−0.557133
$351$	−1.80624e15	−0.0515561
$352$	−2.28893e16	−0.641366
$353$	5.73974e16	1.57891	0.789454	−	0.613810i	$-0.210364\pi$
$353$	5.73974e16	1.57891	0.789454	+	0.613810i	$0.210364\pi$
$354$	−4.71121e15	−0.127236
$355$	−8.93830e16	−2.37012
$356$	1.04717e17	2.72642
$357$	−3.80318e15	−0.0972308
$358$	7.55432e16	1.89651
$359$	−2.48176e15	−0.0611852	−0.0305926	−	0.999532i	$-0.509739\pi$
$359$	−2.48176e15	−0.0611852	−0.0305926	+	0.999532i	$0.509739\pi$
$360$	−3.37316e16	−0.816716
$361$	−1.06543e16	−0.253354
$362$	9.33726e16	2.18079
$363$	3.21984e16	0.738655
$364$	−4.06200e15	−0.0915336
$365$	9.69778e16	2.14669
$366$	7.31234e16	1.59012
$367$	6.29557e16	1.34495	0.672474	−	0.740121i	$-0.265232\pi$
$367$	6.29557e16	1.34495	0.672474	+	0.740121i	$0.265232\pi$
$368$	3.22091e16	0.676033
$369$	1.86146e16	0.383869
$370$	−1.27834e17	−2.59020
$371$	1.70866e16	0.340193
$372$	5.91008e16	1.15628
$373$	4.61935e16	0.888124	0.444062	−	0.895996i	$-0.353537\pi$
$373$	4.61935e16	0.888124	0.444062	+	0.895996i	$0.353537\pi$
$374$	−1.24368e17	−2.34986
$375$	4.14383e16	0.769483
$376$	4.46449e16	0.814800
$377$	1.86295e16	0.334182
$378$	−3.38410e15	−0.0596687
$379$	6.73317e16	1.16698	0.583492	−	0.812119i	$-0.301686\pi$
$379$	6.73317e16	1.16698	0.583492	+	0.812119i	$0.301686\pi$
$380$	−1.58227e17	−2.69580
$381$	−2.52154e16	−0.422332
$382$	1.30682e17	2.15181
$383$	−3.33882e16	−0.540506	−0.270253	−	0.962789i	$-0.587107\pi$
$383$	−3.33882e16	−0.540506	−0.270253	+	0.962789i	$0.587107\pi$
$384$	6.64793e16	1.05812
$385$	−2.95512e16	−0.462466
$386$	−6.14130e16	−0.945023
$387$	−1.56018e16	−0.236077
$388$	−8.65998e16	−1.28858
$389$	−1.12862e17	−1.65149	−0.825744	−	0.564045i	$-0.809245\pi$
$389$	−1.12862e17	−1.65149	−0.825744	+	0.564045i	$0.809245\pi$
$390$	3.04270e16	0.437865
$391$	−7.14690e16	−1.01151
$392$	1.01717e17	1.41590
$393$	−6.59804e16	−0.903365
$394$	1.81776e17	2.44800
$395$	−1.51690e17	−2.00945
$396$	−7.20436e16	−0.938808
$397$	1.19950e17	1.53767	0.768833	−	0.639450i	$-0.220838\pi$
$397$	1.19950e17	1.53767	0.768833	+	0.639450i	$0.220838\pi$
$398$	1.03094e17	1.30016
$399$	−7.36462e15	−0.0913749
$400$	9.04595e16	1.10424
$401$	−1.05944e17	−1.27244	−0.636218	−	0.771509i	$-0.719502\pi$
$401$	−1.05944e17	−1.27244	−0.636218	+	0.771509i	$0.719502\pi$
$402$	−1.36328e17	−1.61107
$403$	−2.47332e16	−0.287606
$404$	−1.32923e17	−1.52097
$405$	1.65027e16	0.185822
$406$	3.49035e16	0.386768
$407$	−1.26668e17	−1.38135
$408$	7.24631e16	0.777724
$409$	8.17113e16	0.863139	0.431569	−	0.902080i	$-0.357960\pi$
$409$	8.17113e16	0.863139	0.431569	+	0.902080i	$0.357960\pi$
$410$	−3.13572e17	−3.26019
$411$	5.04172e16	0.515949
$412$	1.89690e17	1.91079
$413$	2.40480e15	0.0238454
$414$	−6.35936e16	−0.620742
$415$	−1.47804e17	−1.42028
$416$	−1.20300e16	−0.113804
$417$	−3.36363e16	−0.313273
$418$	−2.40830e17	−2.20833
$419$	1.49815e17	1.35259	0.676294	−	0.736632i	$-0.263585\pi$
$419$	1.49815e17	1.35259	0.676294	+	0.736632i	$0.263585\pi$
$420$	3.71124e16	0.329913
$421$	1.82154e16	0.159443	0.0797216	−	0.996817i	$-0.474597\pi$
$421$	1.82154e16	0.159443	0.0797216	+	0.996817i	$0.474597\pi$
$422$	6.40162e15	0.0551771
$423$	−2.18419e16	−0.185386
$424$	−3.25556e17	−2.72112
$425$	−2.00721e17	−1.65221
$426$	1.70856e17	1.38506
$427$	−3.73253e16	−0.298004
$428$	−7.48663e16	−0.588711
$429$	3.01497e16	0.233513
$430$	2.62820e17	2.00500
$431$	−4.17536e16	−0.313756	−0.156878	−	0.987618i	$-0.550143\pi$
$431$	−4.17536e16	−0.313756	−0.156878	+	0.987618i	$0.550143\pi$
$432$	1.59770e16	0.118264
$433$	−2.04882e17	−1.49394	−0.746968	−	0.664860i	$-0.768491\pi$
$433$	−2.04882e17	−1.49394	−0.746968	+	0.664860i	$0.768491\pi$
$434$	−4.63390e16	−0.332862
$435$	−1.70209e17	−1.20449
$436$	2.76074e17	1.92470
$437$	−1.38395e17	−0.950587
$438$	−1.85373e17	−1.25449
$439$	−5.00437e16	−0.333680	−0.166840	−	0.985984i	$-0.553356\pi$
$439$	−5.00437e16	−0.333680	−0.166840	+	0.985984i	$0.553356\pi$
$440$	5.63046e17	3.69915
$441$	−4.97634e16	−0.322151
$442$	−6.53641e16	−0.416960
$443$	−1.52884e17	−0.961029	−0.480515	−	0.876987i	$-0.659550\pi$
$443$	−1.52884e17	−0.961029	−0.480515	+	0.876987i	$0.659550\pi$
$444$	1.59079e17	0.985425
$445$	4.00392e17	2.44425
$446$	3.57735e16	0.215221
$447$	−1.08023e17	−0.640498
$448$	−4.17995e16	−0.244267
$449$	−1.34269e17	−0.773347	−0.386674	−	0.922217i	$-0.626376\pi$
$449$	−1.34269e17	−0.773347	−0.386674	+	0.922217i	$0.626376\pi$
$450$	−1.78603e17	−1.01393
$451$	−3.10714e17	−1.73865
$452$	−4.76045e17	−2.62572
$453$	1.25429e17	0.681962
$454$	1.63253e17	0.874982
$455$	−1.55312e16	−0.0820602
$456$	1.40320e17	0.730884
$457$	5.54766e16	0.284875	0.142438	−	0.989804i	$-0.454506\pi$
$457$	5.54766e16	0.284875	0.142438	+	0.989804i	$0.454506\pi$
$458$	5.11785e16	0.259097
$459$	−3.54515e16	−0.176951
$460$	6.97413e17	3.43213
$461$	6.60499e16	0.320491	0.160246	−	0.987077i	$-0.448771\pi$
$461$	6.60499e16	0.320491	0.160246	+	0.987077i	$0.448771\pi$
$462$	5.64871e16	0.270257
$463$	−2.51121e17	−1.18469	−0.592346	−	0.805683i	$-0.701798\pi$
$463$	−2.51121e17	−1.18469	−0.592346	+	0.805683i	$0.701798\pi$
$464$	−1.64787e17	−0.766576
$465$	2.25975e17	1.03661
$466$	5.43564e17	2.45891
$467$	−3.50096e17	−1.56181	−0.780903	−	0.624652i	$-0.785241\pi$
$467$	−3.50096e17	−1.56181	−0.780903	+	0.624652i	$0.785241\pi$
$468$	−3.78641e16	−0.166583
$469$	6.95875e16	0.301931
$470$	3.67938e17	1.57448
$471$	−9.57508e16	−0.404116
$472$	−4.58193e16	−0.190733
$473$	2.60425e17	1.06926
$474$	2.89956e17	1.17428
$475$	−3.88684e17	−1.55270
$476$	−7.97258e16	−0.314162
$477$	1.59274e17	0.619120
$478$	2.06615e17	0.792283
$479$	1.07914e16	0.0408224	0.0204112	−	0.999792i	$-0.493502\pi$
$479$	1.07914e16	0.0408224	0.0204112	+	0.999792i	$0.493502\pi$
$480$	1.09912e17	0.410182
$481$	−6.65733e16	−0.245108
$482$	−5.14277e17	−1.86806
$483$	3.24609e16	0.116333
$484$	6.74972e17	2.38666
$485$	−3.31119e17	−1.15521
$486$	−3.15450e16	−0.108591
$487$	−7.52372e16	−0.255561	−0.127781	−	0.991802i	$-0.540785\pi$
$487$	−7.52372e16	−0.255561	−0.127781	+	0.991802i	$0.540785\pi$
$488$	7.11168e17	2.38366
$489$	−3.28802e16	−0.108749
$490$	8.38289e17	2.73602
$491$	4.39043e17	1.41409	0.707046	−	0.707168i	$-0.250027\pi$
$491$	4.39043e17	1.41409	0.707046	+	0.707168i	$0.250027\pi$
$492$	3.90216e17	1.24032
$493$	3.65646e17	1.14698
$494$	−1.26573e17	−0.391848
$495$	−2.75462e17	−0.841644
$496$	2.18776e17	0.659734
$497$	−8.72120e16	−0.259573
$498$	2.82527e17	0.829984
$499$	−4.51983e17	−1.31059	−0.655297	−	0.755371i	$-0.727456\pi$
$499$	−4.51983e17	−1.31059	−0.655297	+	0.755371i	$0.727456\pi$
$500$	8.68667e17	2.48627
$501$	−6.63856e16	−0.187555
$502$	2.91489e15	0.00812921
$503$	−5.56259e17	−1.53139	−0.765694	−	0.643205i	$-0.777604\pi$
$503$	−5.56259e17	−1.53139	−0.765694	+	0.643205i	$0.777604\pi$
$504$	−3.29124e16	−0.0894459
$505$	−5.08238e17	−1.36356
$506$	1.06150e18	2.81152
$507$	−2.04950e17	−0.535916
$508$	−5.28588e17	−1.36459
$509$	−5.22554e16	−0.133188	−0.0665941	−	0.997780i	$-0.521213\pi$
$509$	−5.22554e16	−0.133188	−0.0665941	+	0.997780i	$0.521213\pi$
$510$	5.97199e17	1.50284
$511$	9.46224e16	0.235103
$512$	4.73388e17	1.16135
$513$	−6.86497e16	−0.166294
$514$	5.86089e17	1.40186
$515$	7.25291e17	1.71303
$516$	−3.27059e17	−0.762788
$517$	3.64583e17	0.839669
$518$	−1.24729e17	−0.283676
$519$	−3.56757e17	−0.801280
$520$	2.95921e17	0.656378
$521$	−4.20569e17	−0.921281	−0.460641	−	0.887587i	$-0.652380\pi$
$521$	−4.20569e17	−0.921281	−0.460641	+	0.887587i	$0.652380\pi$
$522$	3.25355e17	0.703880
$523$	1.62460e17	0.347126	0.173563	−	0.984823i	$-0.444472\pi$
$523$	1.62460e17	0.347126	0.173563	+	0.984823i	$0.444472\pi$
$524$	−1.38314e18	−2.91886
$525$	9.11665e16	0.190020
$526$	8.47210e17	1.74415
$527$	−4.85444e17	−0.987120
$528$	−2.66687e17	−0.535651
$529$	1.05965e17	0.210233
$530$	−2.68304e18	−5.25817
$531$	2.24165e16	0.0433963
$532$	−1.54384e17	−0.295241
$533$	−1.63302e17	−0.308508
$534$	−7.65350e17	−1.42837
$535$	−2.86255e17	−0.527781
$536$	−1.32587e18	−2.41507
$537$	−3.59443e17	−0.646840
$538$	−2.54484e17	−0.452456
$539$	8.30647e17	1.45912
$540$	3.45945e17	0.600410
$541$	1.04629e18	1.79420	0.897099	−	0.441829i	$-0.145670\pi$
$541$	1.04629e18	1.79420	0.897099	+	0.441829i	$0.145670\pi$
$542$	8.56566e16	0.145133
$543$	−4.44277e17	−0.743798
$544$	−2.36115e17	−0.390599
$545$	1.05558e18	1.72550
$546$	2.96880e16	0.0479545
$547$	2.72176e17	0.434442	0.217221	−	0.976122i	$-0.430301\pi$
$547$	2.72176e17	0.434442	0.217221	+	0.976122i	$0.430301\pi$
$548$	1.05689e18	1.66708
$549$	−3.47929e17	−0.542339
$550$	2.98123e18	4.59238
$551$	7.08051e17	1.07790
$552$	−6.18486e17	−0.930520
$553$	−1.48006e17	−0.220072
$554$	5.18898e17	0.762550
$555$	6.08246e17	0.883436
$556$	−7.05114e17	−1.01222
$557$	1.89819e17	0.269328	0.134664	−	0.990891i	$-0.457004\pi$
$557$	1.89819e17	0.269328	0.134664	+	0.990891i	$0.457004\pi$
$558$	−4.31951e17	−0.605777
$559$	1.36872e17	0.189730
$560$	1.37381e17	0.188237
$561$	5.91755e17	0.801462
$562$	7.13777e17	0.955601
$563$	1.25172e18	1.65654	0.828269	−	0.560331i	$-0.189326\pi$
$563$	1.25172e18	1.65654	0.828269	+	0.560331i	$0.189326\pi$
$564$	−4.57870e17	−0.599001
$565$	−1.82018e18	−2.35397
$566$	−1.83181e18	−2.34192
$567$	1.61019e16	0.0203511
$568$	1.66167e18	2.07626
$569$	−9.61875e17	−1.18820	−0.594099	−	0.804392i	$-0.702491\pi$
$569$	−9.61875e17	−1.18820	−0.594099	+	0.804392i	$0.702491\pi$
$570$	1.15644e18	1.41233
$571$	9.77698e17	1.18051	0.590256	−	0.807216i	$-0.299027\pi$
$571$	9.77698e17	1.18051	0.590256	+	0.807216i	$0.299027\pi$
$572$	6.32025e17	0.754501
$573$	−6.21800e17	−0.733915
$574$	−3.05956e17	−0.357053
$575$	1.71319e18	1.97681
$576$	−3.89636e17	−0.444542
$577$	−8.76615e17	−0.988931	−0.494466	−	0.869197i	$-0.664636\pi$
$577$	−8.76615e17	−0.988931	−0.494466	+	0.869197i	$0.664636\pi$
$578$	2.34586e17	0.261680
$579$	2.92210e17	0.322317
$580$	−3.56807e18	−3.89181
$581$	−1.44214e17	−0.155547
$582$	6.32935e17	0.675086
$583$	−2.65858e18	−2.80417
$584$	−1.80286e18	−1.88053
$585$	−1.44775e17	−0.149342
$586$	1.42144e17	0.145009
$587$	−9.80311e17	−0.989045	−0.494523	−	0.869165i	$-0.664657\pi$
$587$	−9.80311e17	−0.989045	−0.494523	+	0.869165i	$0.664657\pi$
$588$	−1.04319e18	−1.04090
$589$	−9.40032e17	−0.927669
$590$	−3.77616e17	−0.368564
$591$	−8.64910e17	−0.834934
$592$	5.88870e17	0.562249
$593$	6.09093e17	0.575212	0.287606	−	0.957749i	$-0.407141\pi$
$593$	6.09093e17	0.575212	0.287606	+	0.957749i	$0.407141\pi$
$594$	5.26547e17	0.491842
$595$	−3.04835e17	−0.281647
$596$	−2.26448e18	−2.06951
$597$	−4.90535e17	−0.443442
$598$	5.57895e17	0.498878
$599$	−1.10894e18	−0.980920	−0.490460	−	0.871464i	$-0.663171\pi$
$599$	−1.10894e18	−0.980920	−0.490460	+	0.871464i	$0.663171\pi$
$600$	−1.73702e18	−1.51992
$601$	−9.40985e17	−0.814514	−0.407257	−	0.913314i	$-0.633515\pi$
$601$	−9.40985e17	−0.814514	−0.407257	+	0.913314i	$0.633515\pi$
$602$	2.56437e17	0.219585
$603$	6.48663e17	0.549486
$604$	2.62936e18	2.20348
$605$	2.58079e18	2.13965
$606$	9.71498e17	0.796838
$607$	1.11409e18	0.904054	0.452027	−	0.892004i	$-0.350701\pi$
$607$	1.11409e18	0.904054	0.452027	+	0.892004i	$0.350701\pi$
$608$	−4.57222e17	−0.367074
$609$	−1.66075e17	−0.131914
$610$	5.86104e18	4.60607
$611$	1.91615e17	0.148991
$612$	−7.43167e17	−0.571745
$613$	−8.90339e17	−0.677739	−0.338870	−	0.940833i	$-0.610045\pi$
$613$	−8.90339e17	−0.677739	−0.338870	+	0.940833i	$0.610045\pi$
$614$	−9.68854e17	−0.729733
$615$	1.49201e18	1.11195
$616$	5.49371e17	0.405127
$617$	−1.68253e18	−1.22775	−0.613876	−	0.789403i	$-0.710390\pi$
$617$	−1.68253e18	−1.22775	−0.613876	+	0.789403i	$0.710390\pi$
$618$	−1.38640e18	−1.00106
$619$	−2.41905e18	−1.72844	−0.864222	−	0.503110i	$-0.832189\pi$
$619$	−2.41905e18	−1.72844	−0.864222	+	0.503110i	$0.832189\pi$
$620$	4.73709e18	3.34939
$621$	3.02585e17	0.211715
$622$	−2.62989e17	−0.182096
$623$	3.90667e17	0.267691
$624$	−1.40163e17	−0.0950462
$625$	6.43762e17	0.432021
$626$	−2.12082e18	−1.40855
$627$	1.14590e18	0.753192
$628$	−2.00721e18	−1.30574
$629$	−1.30665e18	−0.841259
$630$	−2.71245e17	−0.172841
$631$	6.67951e16	0.0421263	0.0210632	−	0.999778i	$-0.493295\pi$
$631$	6.67951e16	0.0421263	0.0210632	+	0.999778i	$0.493295\pi$
$632$	2.81999e18	1.76030
$633$	−3.04596e16	−0.0188192
$634$	−3.98247e18	−2.43541
$635$	−2.02108e18	−1.22336
$636$	3.33884e18	2.00043
$637$	4.36565e17	0.258906
$638$	−5.43080e18	−3.18808
$639$	−8.12951e17	−0.472399
$640$	5.32849e18	3.06503
$641$	1.37427e18	0.782520	0.391260	−	0.920280i	$-0.372039\pi$
$641$	1.37427e18	0.782520	0.391260	+	0.920280i	$0.372039\pi$
$642$	5.47177e17	0.308426
$643$	−1.38564e18	−0.773177	−0.386589	−	0.922252i	$-0.626347\pi$
$643$	−1.38564e18	−0.773177	−0.386589	+	0.922252i	$0.626347\pi$
$644$	6.80474e17	0.375884
$645$	−1.25053e18	−0.683841
$646$	−2.48429e18	−1.34490
$647$	−1.84558e18	−0.989133	−0.494567	−	0.869140i	$-0.664673\pi$
$647$	−1.84558e18	−0.989133	−0.494567	+	0.869140i	$0.664673\pi$
$648$	−3.06794e17	−0.162783
$649$	−3.74174e17	−0.196555
$650$	1.56685e18	0.814874
$651$	2.20486e17	0.113529
$652$	−6.89264e17	−0.351379
$653$	1.84638e18	0.931934	0.465967	−	0.884802i	$-0.345707\pi$
$653$	1.84638e18	0.931934	0.465967	+	0.884802i	$0.345707\pi$
$654$	−2.01775e18	−1.00835
$655$	−5.28851e18	−2.61676
$656$	1.44448e18	0.707681
$657$	8.82027e17	0.427865
$658$	3.59001e17	0.172436
$659$	2.20948e18	1.05084	0.525418	−	0.850844i	$-0.323909\pi$
$659$	2.20948e18	1.05084	0.525418	+	0.850844i	$0.323909\pi$
$660$	−5.77449e18	−2.71943
$661$	1.56589e18	0.730218	0.365109	−	0.930965i	$-0.381032\pi$
$661$	1.56589e18	0.730218	0.365109	+	0.930965i	$0.381032\pi$
$662$	5.85248e18	2.70248
$663$	3.11009e17	0.142212
$664$	2.74774e18	1.24418
$665$	−5.90294e17	−0.264684
$666$	−1.16266e18	−0.516264
$667$	−3.12086e18	−1.37232
$668$	−1.39164e18	−0.606008
$669$	−1.70214e17	−0.0734050
$670$	−1.09270e19	−4.66677
$671$	5.80761e18	2.45641
$672$	1.07242e17	0.0449227
$673$	5.89216e17	0.244442	0.122221	−	0.992503i	$-0.460998\pi$
$673$	5.89216e17	0.244442	0.122221	+	0.992503i	$0.460998\pi$
$674$	−4.65852e18	−1.91407
$675$	8.49813e17	0.345819
$676$	−4.29635e18	−1.73159
$677$	3.48655e18	1.39178	0.695889	−	0.718150i	$-0.255011\pi$
$677$	3.48655e18	1.39178	0.695889	+	0.718150i	$0.255011\pi$
$678$	3.47929e18	1.37562
$679$	−3.23077e17	−0.126518
$680$	5.80811e18	2.25282
$681$	−7.76777e17	−0.298428
$682$	7.21010e18	2.74374
$683$	1.72730e18	0.651077	0.325539	−	0.945529i	$-0.394454\pi$
$683$	1.72730e18	0.651077	0.325539	+	0.945529i	$0.394454\pi$
$684$	−1.43910e18	−0.537310
$685$	4.04108e18	1.49454
$686$	1.66425e18	0.609694
$687$	−2.43513e17	−0.0883696
$688$	−1.21069e18	−0.435220
$689$	−1.39728e18	−0.497574
$690$	−5.09720e18	−1.79810
$691$	−2.01516e18	−0.704210	−0.352105	−	0.935960i	$-0.614534\pi$
$691$	−2.01516e18	−0.704210	−0.352105	+	0.935960i	$0.614534\pi$
$692$	−7.47865e18	−2.58901
$693$	−2.68772e17	−0.0921760
$694$	1.03546e18	0.351799
$695$	−2.69604e18	−0.907454
$696$	3.16427e18	1.05515
$697$	−3.20517e18	−1.05886
$698$	4.41702e18	1.44567
$699$	−2.58634e18	−0.838655
$700$	1.91111e18	0.613973
$701$	9.53155e17	0.303387	0.151693	−	0.988428i	$-0.451527\pi$
$701$	9.53155e17	0.303387	0.151693	+	0.988428i	$0.451527\pi$
$702$	2.76738e17	0.0872726
$703$	−2.53024e18	−0.790592
$704$	6.50377e18	2.01346
$705$	−1.75069e18	−0.537006
$706$	−8.79398e18	−2.67273
$707$	−4.95894e17	−0.149335
$708$	4.69914e17	0.140218
$709$	3.49354e18	1.03292	0.516458	−	0.856312i	$-0.327250\pi$
$709$	3.49354e18	1.03292	0.516458	+	0.856312i	$0.327250\pi$
$710$	1.36946e19	4.01207
$711$	−1.37964e18	−0.400511
$712$	−7.44348e18	−2.14119
$713$	4.14335e18	1.18106
$714$	5.82694e17	0.164589
$715$	2.41658e18	0.676412
$716$	−7.53496e18	−2.09000
$717$	−9.83097e17	−0.270223
$718$	3.80236e17	0.103572
$719$	−3.75865e18	−1.01460	−0.507299	−	0.861770i	$-0.669356\pi$
$719$	−3.75865e18	−1.01460	−0.507299	+	0.861770i	$0.669356\pi$
$720$	1.28060e18	0.342573
$721$	7.07675e17	0.187609
$722$	1.63237e18	0.428870
$723$	2.44699e18	0.637137
$724$	−9.31333e18	−2.40328
$725$	−8.76495e18	−2.24157
$726$	−4.93319e18	−1.25037
$727$	5.59357e18	1.40513	0.702563	−	0.711621i	$-0.252039\pi$
$727$	5.59357e18	1.40513	0.702563	+	0.711621i	$0.252039\pi$
$728$	2.88734e17	0.0718858
$729$	1.50095e17	0.0370370
$730$	−1.48582e19	−3.63385
$731$	2.68641e18	0.651193
$732$	−7.29361e18	−1.75235
$733$	−3.88978e18	−0.926295	−0.463148	−	0.886281i	$-0.653280\pi$
$733$	−3.88978e18	−0.926295	−0.463148	+	0.886281i	$0.653280\pi$
$734$	−9.64558e18	−2.27669
$735$	−3.98867e18	−0.933169
$736$	2.01529e18	0.467338
$737$	−1.08274e19	−2.48878
$738$	−2.85199e18	−0.649802
$739$	−3.40683e18	−0.769417	−0.384708	−	0.923038i	$-0.625698\pi$
$739$	−3.40683e18	−0.769417	−0.384708	+	0.923038i	$0.625698\pi$
$740$	1.27506e19	2.85446
$741$	6.02250e17	0.133647
$742$	−2.61788e18	−0.575869
$743$	−3.77410e17	−0.0822973	−0.0411486	−	0.999153i	$-0.513102\pi$
$743$	−3.77410e17	−0.0822973	−0.0411486	+	0.999153i	$0.513102\pi$
$744$	−4.20098e18	−0.908085
$745$	−8.65834e18	−1.85532
$746$	−7.07740e18	−1.50339
$747$	−1.34430e18	−0.283081
$748$	1.24049e19	2.58960
$749$	−2.79302e17	−0.0578020
$750$	−6.34885e18	−1.30256
$751$	3.65610e18	0.743633	0.371817	−	0.928306i	$-0.378735\pi$
$751$	3.65610e18	0.743633	0.371817	+	0.928306i	$0.378735\pi$
$752$	−1.69492e18	−0.341769
$753$	−1.38694e16	−0.00277261
$754$	−2.85427e18	−0.565694
$755$	1.00535e19	1.97543
$756$	3.37543e17	0.0657563
$757$	1.20802e18	0.233320	0.116660	−	0.993172i	$-0.462781\pi$
$757$	1.20802e18	0.233320	0.116660	+	0.993172i	$0.462781\pi$
$758$	−1.03160e19	−1.97544
$759$	−5.05073e18	−0.958921
$760$	1.12470e19	2.11714
$761$	4.06658e18	0.758978	0.379489	−	0.925196i	$-0.376100\pi$
$761$	4.06658e18	0.758978	0.379489	+	0.925196i	$0.376100\pi$
$762$	3.86331e18	0.714911
$763$	1.02994e18	0.188975
$764$	−1.30347e19	−2.37135
$765$	−2.84154e18	−0.512571
$766$	5.11547e18	0.914953
$767$	−1.96655e17	−0.0348767
$768$	−5.80697e18	−1.02118
$769$	−3.10739e18	−0.541844	−0.270922	−	0.962601i	$-0.587328\pi$
$769$	−3.10739e18	−0.541844	−0.270922	+	0.962601i	$0.587328\pi$
$770$	4.52760e18	0.782849
$771$	−2.78868e18	−0.478129
$772$	6.12556e18	1.04144
$773$	−3.80298e17	−0.0641146	−0.0320573	−	0.999486i	$-0.510206\pi$
$773$	−3.80298e17	−0.0641146	−0.0320573	+	0.999486i	$0.510206\pi$
$774$	2.39039e18	0.399625
$775$	1.16366e19	1.92915
$776$	6.15566e18	1.01198
$777$	5.93473e17	0.0967530
$778$	1.72918e19	2.79559
$779$	−6.20662e18	−0.995088
$780$	−3.03491e18	−0.482537
$781$	1.35697e19	2.13963
$782$	1.09499e19	1.71225
$783$	−1.54807e18	−0.240071
$784$	−3.86161e18	−0.593901
$785$	−7.67468e18	−1.17060
$786$	1.01090e19	1.52919
$787$	6.37155e18	0.955893	0.477947	−	0.878389i	$-0.341381\pi$
$787$	6.37155e18	0.955893	0.477947	+	0.878389i	$0.341381\pi$
$788$	−1.81310e19	−2.69775
$789$	−4.03112e18	−0.594874
$790$	2.32408e19	3.40153
$791$	−1.77597e18	−0.257804
$792$	5.12098e18	0.737292
$793$	3.05232e18	0.435867
$794$	−1.83778e19	−2.60291
$795$	1.27662e19	1.79339
$796$	−1.02830e19	−1.43280
$797$	1.12213e19	1.55083	0.775416	−	0.631450i	$-0.217540\pi$
$797$	1.12213e19	1.55083	0.775416	+	0.631450i	$0.217540\pi$
$798$	1.12835e18	0.154677
$799$	3.76087e18	0.511368
$800$	5.65994e18	0.763356
$801$	3.64162e18	0.487173
$802$	1.62318e19	2.15394
$803$	−1.47227e19	−1.93793
$804$	1.35978e19	1.77544
$805$	2.60183e18	0.336981
$806$	3.78942e18	0.486850
$807$	1.21086e18	0.154318
$808$	9.44839e18	1.19449
$809$	7.22737e18	0.906390	0.453195	−	0.891412i	$-0.350284\pi$
$809$	7.22737e18	0.906390	0.453195	+	0.891412i	$0.350284\pi$
$810$	−2.52842e18	−0.314555
$811$	1.17677e19	1.45230	0.726148	−	0.687538i	$-0.241309\pi$
$811$	1.17677e19	1.45230	0.726148	+	0.687538i	$0.241309\pi$
$812$	−3.48141e18	−0.426227
$813$	−4.07563e17	−0.0495001
$814$	1.94071e19	2.33831
$815$	−2.63544e18	−0.315013
$816$	−2.75102e18	−0.326218
$817$	5.20207e18	0.611974
$818$	−1.25192e19	−1.46110
$819$	−1.41259e17	−0.0163558
$820$	3.12769e19	3.59281
$821$	1.60658e19	1.83093	0.915466	−	0.402396i	$-0.131823\pi$
$821$	1.60658e19	1.83093	0.915466	+	0.402396i	$0.131823\pi$
$822$	−7.72453e18	−0.873384
$823$	2.19199e18	0.245889	0.122945	−	0.992414i	$-0.460766\pi$
$823$	2.19199e18	0.245889	0.122945	+	0.992414i	$0.460766\pi$
$824$	−1.34835e19	−1.50064
$825$	−1.41850e19	−1.56631
$826$	−3.68445e17	−0.0403647
$827$	−1.59480e19	−1.73349	−0.866744	−	0.498754i	$-0.833791\pi$
$827$	−1.59480e19	−1.73349	−0.866744	+	0.498754i	$0.833791\pi$
$828$	6.34307e18	0.684073
$829$	2.38520e18	0.255223	0.127611	−	0.991824i	$-0.459269\pi$
$829$	2.38520e18	0.255223	0.127611	+	0.991824i	$0.459269\pi$
$830$	2.26453e19	2.40420
$831$	−2.46897e18	−0.260082
$832$	3.41820e18	0.357269
$833$	8.56855e18	0.888618
$834$	5.15349e18	0.530300
$835$	−5.32099e18	−0.543288
$836$	2.40213e19	2.43364
$837$	2.05527e18	0.206611
$838$	−2.29535e19	−2.28962
$839$	9.60090e18	0.950296	0.475148	−	0.879906i	$-0.342394\pi$
$839$	9.60090e18	0.950296	0.475148	+	0.879906i	$0.342394\pi$
$840$	−2.63801e18	−0.259097
$841$	5.70616e18	0.556122
$842$	−2.79083e18	−0.269901
$843$	−3.39623e18	−0.325925
$844$	−6.38522e17	−0.0608065
$845$	−1.64273e19	−1.55238
$846$	3.34644e18	0.313817
$847$	2.51811e18	0.234332
$848$	1.23595e19	1.14138
$849$	8.71594e18	0.798756
$850$	3.07529e19	2.79681
$851$	1.11525e19	1.00654
$852$	−1.70418e19	−1.52636
$853$	4.86237e18	0.432195	0.216097	−	0.976372i	$-0.430667\pi$
$853$	4.86237e18	0.432195	0.216097	+	0.976372i	$0.430667\pi$
$854$	5.71869e18	0.504452
$855$	−5.50246e18	−0.481700
$856$	5.32162e18	0.462343
$857$	1.56370e19	1.34827	0.674137	−	0.738606i	$-0.264516\pi$
$857$	1.56370e19	1.34827	0.674137	+	0.738606i	$0.264516\pi$
$858$	−4.61930e18	−0.395283
$859$	−5.94500e18	−0.504890	−0.252445	−	0.967611i	$-0.581235\pi$
$859$	−5.94500e18	−0.504890	−0.252445	+	0.967611i	$0.581235\pi$
$860$	−2.62147e19	−2.20956
$861$	1.45577e18	0.121779
$862$	6.39716e18	0.531117
$863$	−1.26892e19	−1.04560	−0.522798	−	0.852456i	$-0.675112\pi$
$863$	−1.26892e19	−1.04560	−0.522798	+	0.852456i	$0.675112\pi$
$864$	9.99664e17	0.0817551
$865$	−2.85950e19	−2.32105
$866$	3.13904e19	2.52889
$867$	−1.11618e18	−0.0892507
$868$	4.62203e18	0.366821
$869$	2.30289e19	1.81403
$870$	2.60780e19	2.03892
$871$	−5.69059e18	−0.441610
$872$	−1.96238e19	−1.51156
$873$	−3.01157e18	−0.230251
$874$	2.12038e19	1.60913
$875$	3.24072e18	0.244112
$876$	1.84898e19	1.38247
$877$	1.49793e19	1.11171	0.555857	−	0.831278i	$-0.312390\pi$
$877$	1.49793e19	1.11171	0.555857	+	0.831278i	$0.312390\pi$
$878$	7.66730e18	0.564843
$879$	−6.76337e17	−0.0494578
$880$	−2.13757e19	−1.55161
$881$	1.25429e19	0.903761	0.451881	−	0.892078i	$-0.350753\pi$
$881$	1.25429e19	0.903761	0.451881	+	0.892078i	$0.350753\pi$
$882$	7.62436e18	0.545328
$883$	−1.17294e19	−0.832782	−0.416391	−	0.909186i	$-0.636705\pi$
$883$	−1.17294e19	−0.832782	−0.416391	+	0.909186i	$0.636705\pi$
$884$	6.51966e18	0.459500
$885$	1.79674e18	0.125705
$886$	2.34236e19	1.62680
$887$	−1.51666e19	−1.04565	−0.522824	−	0.852440i	$-0.675122\pi$
$887$	−1.51666e19	−1.04565	−0.522824	+	0.852440i	$0.675122\pi$
$888$	−1.13076e19	−0.773902
$889$	−1.97199e18	−0.133981
$890$	−6.13448e19	−4.13755
$891$	−2.50537e18	−0.167752
$892$	−3.56818e18	−0.237179
$893$	7.28268e18	0.480570
$894$	1.65505e19	1.08422
$895$	−2.88103e19	−1.87369
$896$	5.19907e18	0.335679
$897$	−2.65452e18	−0.170151
$898$	2.05716e19	1.30910
$899$	−2.11980e19	−1.33924
$900$	1.78145e19	1.11737
$901$	−2.74247e19	−1.70777
$902$	4.76051e19	2.94314
$903$	−1.22016e18	−0.0748936
$904$	3.38381e19	2.06211
$905$	−3.56100e19	−2.15455
$906$	−1.92173e19	−1.15440
$907$	7.67289e18	0.457627	0.228814	−	0.973470i	$-0.426515\pi$
$907$	7.67289e18	0.457627	0.228814	+	0.973470i	$0.426515\pi$
$908$	−1.62835e19	−0.964250
$909$	−4.62249e18	−0.271776
$910$	2.37958e18	0.138909
$911$	−2.63661e19	−1.52818	−0.764092	−	0.645107i	$-0.776813\pi$
$911$	−2.63661e19	−1.52818	−0.764092	+	0.645107i	$0.776813\pi$
$912$	−5.32717e18	−0.306570
$913$	2.24389e19	1.28216
$914$	−8.49969e18	−0.482229
$915$	−2.78875e19	−1.57098
$916$	−5.10473e18	−0.285531
$917$	−5.16006e18	−0.286585
$918$	5.43161e18	0.299537
$919$	−2.84367e19	−1.55714	−0.778572	−	0.627555i	$-0.784056\pi$
$919$	−2.84367e19	−1.55714	−0.778572	+	0.627555i	$0.784056\pi$
$920$	−4.95733e19	−2.69542
$921$	4.60991e18	0.248889
$922$	−1.01196e19	−0.542518
$923$	7.13186e18	0.379657
$924$	−5.63424e18	−0.297829
$925$	3.13218e19	1.64409
$926$	3.84747e19	2.00541
$927$	6.59662e18	0.341431
$928$	−1.03105e19	−0.529930
$929$	9.80405e18	0.500384	0.250192	−	0.968196i	$-0.419506\pi$
$929$	9.80405e18	0.500384	0.250192	+	0.968196i	$0.419506\pi$
$930$	−3.46221e19	−1.75474
$931$	1.65925e19	0.835099
$932$	−5.42171e19	−2.70977
$933$	1.25133e18	0.0621072
$934$	5.36389e19	2.64378
$935$	4.74307e19	2.32158
$936$	2.69144e18	0.130825
$937$	−3.24278e19	−1.56535	−0.782673	−	0.622433i	$-0.786144\pi$
$937$	−3.24278e19	−1.56535	−0.782673	+	0.622433i	$0.786144\pi$
$938$	−1.06616e19	−0.511100
$939$	1.00911e19	0.480411
$940$	−3.66995e19	−1.73512
$941$	−2.62189e19	−1.23107	−0.615533	−	0.788111i	$-0.711059\pi$
$941$	−2.62189e19	−1.23107	−0.615533	+	0.788111i	$0.711059\pi$
$942$	1.46702e19	0.684076
$943$	2.73568e19	1.26689
$944$	1.73950e18	0.0800032
$945$	1.29061e18	0.0589507
$946$	−3.99002e19	−1.81002
$947$	−1.67473e19	−0.754517	−0.377258	−	0.926108i	$-0.623133\pi$
$947$	−1.67473e19	−0.754517	−0.377258	+	0.926108i	$0.623133\pi$
$948$	−2.89213e19	−1.29409
$949$	−7.73785e18	−0.343866
$950$	5.95511e19	2.62837
$951$	1.89490e19	0.830641
$952$	5.66704e18	0.246727
$953$	2.46685e19	1.06669	0.533346	−	0.845897i	$-0.320935\pi$
$953$	2.46685e19	1.06669	0.533346	+	0.845897i	$0.320935\pi$
$954$	−2.44027e19	−1.04803
$955$	−4.98389e19	−2.12592
$956$	−2.06086e19	−0.873115
$957$	2.58403e19	1.08735
$958$	−1.65338e18	−0.0691029
$959$	3.94293e18	0.163681
$960$	−3.12304e19	−1.28770
$961$	3.72564e18	0.152581
$962$	1.01998e19	0.414911
$963$	−2.60353e18	−0.105194
$964$	5.12959e19	2.05865
$965$	2.34214e19	0.933652
$966$	−4.97340e18	−0.196926
$967$	7.19705e18	0.283062	0.141531	−	0.989934i	$-0.454797\pi$
$967$	7.19705e18	0.283062	0.141531	+	0.989934i	$0.454797\pi$
$968$	−4.79782e19	−1.87436
$969$	1.18205e19	0.458703
$970$	5.07314e19	1.95551
$971$	−2.33356e19	−0.893497	−0.446749	−	0.894660i	$-0.647418\pi$
$971$	−2.33356e19	−0.893497	−0.446749	+	0.894660i	$0.647418\pi$
$972$	3.14642e18	0.119670
$973$	−2.63056e18	−0.0993835
$974$	1.15273e19	0.432606
$975$	−7.45524e18	−0.277928
$976$	−2.69991e19	−0.999828
$977$	6.22648e18	0.229049	0.114524	−	0.993420i	$-0.463466\pi$
$977$	6.22648e18	0.229049	0.114524	+	0.993420i	$0.463466\pi$
$978$	5.03764e18	0.184088
$979$	−6.07856e19	−2.20655
$980$	−8.36141e19	−3.01516
$981$	9.60067e18	0.343916
$982$	−6.72667e19	−2.39373
$983$	−3.70282e19	−1.30898	−0.654492	−	0.756069i	$-0.727118\pi$
$983$	−3.70282e19	−1.30898	−0.654492	+	0.756069i	$0.727118\pi$
$984$	−2.77372e19	−0.974081
$985$	−6.93249e19	−2.41854
$986$	−5.60215e19	−1.94158
$987$	−1.70817e18	−0.0588124
$988$	1.26249e19	0.431825
$989$	−2.29290e19	−0.779130
$990$	4.22042e19	1.42471
$991$	4.09604e19	1.37368	0.686840	−	0.726809i	$-0.258997\pi$
$991$	4.09604e19	1.37368	0.686840	+	0.726809i	$0.258997\pi$
$992$	1.36886e19	0.456071
$993$	−2.78468e19	−0.921732
$994$	1.33619e19	0.439398
$995$	−3.93177e19	−1.28451
$996$	−2.81803e19	−0.914662
$997$	6.89215e18	0.222247	0.111124	−	0.993807i	$-0.464555\pi$
$997$	6.89215e18	0.222247	0.111124	+	0.993807i	$0.464555\pi$
$998$	6.92492e19	2.21853
$999$	5.53209e18	0.176081

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.14.a.a.1.3	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.14.a.a.1.3	✓	30	1.1	even	1	trivial

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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)

\(f(q)\)	\(=\)	\(q-153.212 q^{2} +729.000 q^{3} +15282.0 q^{4} +58431.3 q^{5} -111692. q^{6} +57012.1 q^{7} -1.08627e6 q^{8} +531441. q^{9} +O(q^{10})\)	\(q-153.212 q^{2} +729.000 q^{3} +15282.0 q^{4} +58431.3 q^{5} -111692. q^{6} +57012.1 q^{7} -1.08627e6 q^{8} +531441. q^{9} -8.95239e6 q^{10} -8.87077e6 q^{11} +1.11405e7 q^{12} -4.66223e6 q^{13} -8.73495e6 q^{14} +4.25964e7 q^{15} +4.12395e7 q^{16} -9.15066e7 q^{17} -8.14232e7 q^{18} -1.77197e8 q^{19} +8.92945e8 q^{20} +4.15618e7 q^{21} +1.35911e9 q^{22} +7.81026e8 q^{23} -7.91889e8 q^{24} +2.19352e9 q^{25} +7.14310e8 q^{26} +3.87420e8 q^{27} +8.71257e8 q^{28} -3.99585e9 q^{29} -6.52629e9 q^{30} +5.30502e9 q^{31} +2.58031e9 q^{32} -6.46679e9 q^{33} +1.40199e10 q^{34} +3.33129e9 q^{35} +8.12146e9 q^{36} +1.42793e10 q^{37} +2.71487e10 q^{38} -3.39876e9 q^{39} -6.34720e10 q^{40} +3.50267e10 q^{41} -6.36778e9 q^{42} -2.93576e10 q^{43} -1.35563e11 q^{44} +3.10528e10 q^{45} -1.19663e11 q^{46} -4.10994e10 q^{47} +3.00636e10 q^{48} -9.36386e10 q^{49} -3.36073e11 q^{50} -6.67083e10 q^{51} -7.12480e10 q^{52} +2.99702e11 q^{53} -5.93575e10 q^{54} -5.18331e11 q^{55} -6.19304e10 q^{56} -1.29176e11 q^{57} +6.12212e11 q^{58} +4.21805e10 q^{59} +6.50957e11 q^{60} -6.54690e11 q^{61} -8.12793e11 q^{62} +3.02986e10 q^{63} -7.33168e11 q^{64} -2.72420e11 q^{65} +9.90791e11 q^{66} +1.22057e12 q^{67} -1.39840e12 q^{68} +5.69368e11 q^{69} -5.10395e11 q^{70} -1.52971e12 q^{71} -5.77287e11 q^{72} +1.65969e12 q^{73} -2.18776e12 q^{74} +1.59907e12 q^{75} -2.70791e12 q^{76} -5.05742e11 q^{77} +5.20732e11 q^{78} -2.59604e12 q^{79} +2.40968e12 q^{80} +2.82430e11 q^{81} -5.36651e12 q^{82} -2.52953e12 q^{83} +6.35146e11 q^{84} -5.34685e12 q^{85} +4.49794e12 q^{86} -2.91297e12 q^{87} +9.63603e12 q^{88} +6.85235e12 q^{89} -4.75766e12 q^{90} -2.65804e11 q^{91} +1.19356e13 q^{92} +3.86736e12 q^{93} +6.29692e12 q^{94} -1.03538e13 q^{95} +1.88104e12 q^{96} -5.66680e12 q^{97} +1.43466e13 q^{98} -4.71429e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} + O(q^{10}) \)	\( 30q - 138q^{2} + 21870q^{3} + 114598q^{4} - 137742q^{5} - 100602q^{6} - 879443q^{7} - 872301q^{8} + 15943230q^{9} - 5352519q^{10} - 13950782q^{11} + 83541942q^{12} - 17256988q^{13} + 33780109q^{14} - 100413918q^{15} + 499996762q^{16} - 317583695q^{17} - 73338858q^{18} - 863401469q^{19} - 1841280623q^{20} - 641113947q^{21} - 2723764842q^{22} - 3142075981q^{23} - 635907429q^{24} + 5435751692q^{25} - 6441414040q^{26} + 11622614670q^{27} - 7538400046q^{28} - 4604589283q^{29} - 3901986351q^{30} + 4308675373q^{31} + 6094556360q^{32} - 10170120078q^{33} + 38097713432q^{34} - 15447827315q^{35} + 60902075718q^{36} - 19633376949q^{37} - 18152222923q^{38} - 12580344252q^{39} + 14680384170q^{40} - 103644439493q^{41} + 24625699461q^{42} - 64494894924q^{43} - 199714496208q^{44} - 73201746222q^{45} - 265425792847q^{46} - 293365585139q^{47} + 364497639498q^{48} + 414396765797q^{49} - 126058522207q^{50} - 231518513655q^{51} + 156029960316q^{52} - 76747013118q^{53} - 53464027482q^{54} - 433465885754q^{55} - 502955241518q^{56} - 629419670901q^{57} - 1755031845830q^{58} + 1265416009230q^{59} - 1342293574167q^{60} - 2022612531219q^{61} - 3816005187046q^{62} - 467372067363q^{63} - 3570205594131q^{64} - 3889749040576q^{65} - 1985624569818q^{66} - 502618987776q^{67} - 8953998390517q^{68} - 2290573390149q^{69} - 6805178272420q^{70} - 1599540605456q^{71} - 463576515741q^{72} - 3826795087235q^{73} - 7573387813210q^{74} + 3962662983468q^{75} - 19498723328388q^{76} - 9088623115219q^{77} - 4695790835160q^{78} - 8595482172338q^{79} - 17452527463963q^{80} + 8472886094430q^{81} - 11181116792901q^{82} - 13548556984389q^{83} - 5495493633534q^{84} - 12851795888367q^{85} + 8539949468848q^{86} - 3356745587307q^{87} - 25134826741387q^{88} - 21826401667403q^{89} - 2844548049879q^{90} - 26577050621355q^{91} - 34908210763168q^{92} + 3141024346917q^{93} - 26426808959500q^{94} - 29105233533993q^{95} + 4442931586440q^{96} + 417815797414q^{97} + 29159956938360q^{98} - 7414017536862q^{99} + O(q^{100}) \)

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