LMFDB - Embedded newform 260.2.p.d.103.14

Newspace parameters

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.p (of order $4$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			103.14
Character	$\chi$	$=$	260.103
Dual form			260.2.p.d.207.14

$q$-expansion

$f(q)$	$=$	$q+(-0.417327 + 1.35124i) q^{2} +(-0.561614 + 0.561614i) q^{3} +(-1.65168 - 1.12781i) q^{4} +(2.09189 - 0.789927i) q^{5} +(-0.524497 - 0.993250i) q^{6} +(1.48711 - 1.48711i) q^{7} +(2.21323 - 1.76114i) q^{8} +2.36918i q^{9} +O(q^{10})$	\(q+(-0.417327 + 1.35124i) q^{2} +(-0.561614 + 0.561614i) q^{3} +(-1.65168 - 1.12781i) q^{4} +(2.09189 - 0.789927i) q^{5} +(-0.524497 - 0.993250i) q^{6} +(1.48711 - 1.48711i) q^{7} +(2.21323 - 1.76114i) q^{8} +2.36918i q^{9} +(0.194375 + 3.15630i) q^{10} +5.21705 q^{11} +(1.56100 - 0.294209i) q^{12} +(-3.24368 + 1.57435i) q^{13} +(1.38883 + 2.63005i) q^{14} +(-0.731203 + 1.61847i) q^{15} +(1.45607 + 3.72557i) q^{16} +(0.793724 - 0.793724i) q^{17} +(-3.20132 - 0.988721i) q^{18} -0.101632i q^{19} +(-4.34602 - 1.05456i) q^{20} +1.67036i q^{21} +(-2.17721 + 7.04946i) q^{22} +(-2.99025 + 2.99025i) q^{23} +(-0.253901 + 2.23206i) q^{24} +(3.75203 - 3.30488i) q^{25} +(-0.773642 - 5.03999i) q^{26} +(-3.01541 - 3.01541i) q^{27} +(-4.13341 + 0.779042i) q^{28} +3.15871i q^{29} +(-1.88179 - 1.66346i) q^{30} +5.55833 q^{31} +(-5.64178 + 0.412721i) q^{32} +(-2.92997 + 2.92997i) q^{33} +(0.741267 + 1.40375i) q^{34} +(1.93617 - 4.28558i) q^{35} +(2.67199 - 3.91312i) q^{36} +(3.25224 + 3.25224i) q^{37} +(0.137329 + 0.0424138i) q^{38} +(0.937519 - 2.70587i) q^{39} +(3.23867 - 5.43240i) q^{40} -6.47910i q^{41} +(-2.25706 - 0.697087i) q^{42} +(2.45533 - 2.45533i) q^{43} +(-8.61688 - 5.88386i) q^{44} +(1.87148 + 4.95607i) q^{45} +(-2.79263 - 5.28845i) q^{46} +(-3.39043 + 3.39043i) q^{47} +(-2.91008 - 1.27458i) q^{48} +2.57701i q^{49} +(2.89986 + 6.44910i) q^{50} +0.891534i q^{51} +(7.13307 + 1.05795i) q^{52} +(-6.94382 - 6.94382i) q^{53} +(5.33294 - 2.81612i) q^{54} +(10.9135 - 4.12109i) q^{55} +(0.672311 - 5.91032i) q^{56} +(0.0570780 + 0.0570780i) q^{57} +(-4.26816 - 1.31821i) q^{58} -10.5517i q^{59} +(3.03304 - 1.84853i) q^{60} -1.49686 q^{61} +(-2.31964 + 7.51061i) q^{62} +(3.52323 + 3.52323i) q^{63} +(1.79678 - 7.79561i) q^{64} +(-5.54180 + 5.85563i) q^{65} +(-2.73632 - 5.18183i) q^{66} +(-6.37568 + 6.37568i) q^{67} +(-2.20615 + 0.415803i) q^{68} -3.35874i q^{69} +(4.98282 + 4.40470i) q^{70} -1.73544 q^{71} +(4.17245 + 5.24354i) q^{72} +(5.87285 - 5.87285i) q^{73} +(-5.75179 + 3.03730i) q^{74} +(-0.251124 + 3.96327i) q^{75} +(-0.114622 + 0.167863i) q^{76} +(7.75832 - 7.75832i) q^{77} +(3.26502 + 2.39604i) q^{78} -1.43236 q^{79} +(5.98888 + 6.64330i) q^{80} -3.72054 q^{81} +(8.75480 + 2.70390i) q^{82} +(-10.2973 - 10.2973i) q^{83} +(1.88386 - 2.75890i) q^{84} +(1.03340 - 2.28737i) q^{85} +(2.29306 + 4.34241i) q^{86} +(-1.77398 - 1.77398i) q^{87} +(11.5465 - 9.18794i) q^{88} +6.49614 q^{89} +(-7.47783 + 0.460509i) q^{90} +(-2.48247 + 7.16493i) q^{91} +(8.31138 - 1.56649i) q^{92} +(-3.12164 + 3.12164i) q^{93} +(-3.16635 - 5.99618i) q^{94} +(-0.0802819 - 0.212603i) q^{95} +(2.93671 - 3.40029i) q^{96} +(-6.63009 - 6.63009i) q^{97} +(-3.48215 - 1.07545i) q^{98} +12.3601i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 24 q^{12} - 4 q^{16} - 40 q^{17} - 36 q^{22} + 44 q^{26} + 24 q^{30} + 28 q^{36} + 16 q^{38} - 44 q^{40} + 8 q^{42} - 44 q^{48} + 56 q^{52} - 48 q^{53} - 64 q^{56} + 80 q^{61} + 20 q^{62} - 72 q^{65} - 24 q^{66} - 76 q^{68} - 112 q^{77} - 20 q^{78} + 80 q^{81} + 52 q^{82} - 152 q^{88} - 64 q^{90} + 56 q^{92}+O(q^{100}) $ 64 * q - 24 * q^12 - 4 * q^16 - 40 * q^17 - 36 * q^22 + 44 * q^26 + 24 * q^30 + 28 * q^36 + 16 * q^38 - 44 * q^40 + 8 * q^42 - 44 * q^48 + 56 * q^52 - 48 * q^53 - 64 * q^56 + 80 * q^61 + 20 * q^62 - 72 * q^65 - 24 * q^66 - 76 * q^68 - 112 * q^77 - 20 * q^78 + 80 * q^81 + 52 * q^82 - 152 * q^88 - 64 * q^90 + 56 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.417327	+	1.35124i	−0.295094	+	0.955468i
$2$	−0.417327	+	1.35124i	−0.295094	+	0.955468i
$3$	−0.561614	+	0.561614i	−0.324248	+	0.324248i	−0.850394	−	0.526146i	$-0.823637\pi$
$3$	−0.561614	+	0.561614i	−0.324248	+	0.324248i	0.526146	+	0.850394i	$0.323637\pi$
$4$	−1.65168	−	1.12781i	−0.825838	−	0.563907i
$5$	2.09189	−	0.789927i	0.935523	−	0.353266i
$5$	2.09189	−	0.789927i	0.935523	−	0.353266i
$6$	−0.524497	−	0.993250i	−0.214125	−	0.405493i
$7$	1.48711	−	1.48711i	0.562075	−	0.562075i	−0.367822	−	0.929896i	$-0.619896\pi$
$7$	1.48711	−	1.48711i	0.562075	−	0.562075i	0.929896	+	0.367822i	$0.119896\pi$
$8$	2.21323	−	1.76114i	0.782495	−	0.622657i
$9$			2.36918i			0.789726i
$10$	0.194375	+	3.15630i	0.0614668	+	0.998109i
$11$	5.21705			1.57300			0.786499	−	0.617591i	$-0.211891\pi$
$11$	5.21705			1.57300			0.786499	+	0.617591i	$0.211891\pi$
$12$	1.56100	−	0.294209i	0.450622	−	0.0849309i
$13$	−3.24368	+	1.57435i	−0.899634	+	0.436645i
$13$	−3.24368	+	1.57435i	−0.899634	+	0.436645i
$14$	1.38883	+	2.63005i	0.371179	+	0.702909i
$15$	−0.731203	+	1.61847i	−0.188796	+	0.417887i
$16$	1.45607	+	3.72557i	0.364018	+	0.931392i
$17$	0.793724	−	0.793724i	0.192506	−	0.192506i	−0.604272	−	0.796778i	$-0.706536\pi$
$17$	0.793724	−	0.793724i	0.192506	−	0.192506i	0.796778	+	0.604272i	$0.206536\pi$
$18$	−3.20132	−	0.988721i	−0.754558	−	0.233044i
$19$		−	0.101632i		−	0.0233160i	−0.999932	−	0.0116580i	$-0.996289\pi$
$19$		−	0.101632i		−	0.0233160i	0.999932	−	0.0116580i	$-0.00371094\pi$
$20$	−4.34602	−	1.05456i	−0.971800	−	0.235807i
$21$			1.67036i			0.364503i
$22$	−2.17721	+	7.04946i	−0.464183	+	1.50295i
$23$	−2.99025	+	2.99025i	−0.623511	+	0.623511i	−0.946428	−	0.322916i	$-0.895337\pi$
$23$	−2.99025	+	2.99025i	−0.623511	+	0.623511i	0.322916	+	0.946428i	$0.395337\pi$
$24$	−0.253901	+	2.23206i	−0.0518274	+	0.455618i
$25$	3.75203	−	3.30488i	0.750406	−	0.660977i
$26$	−0.773642	−	5.03999i	−0.151724	−	0.988423i
$27$	−3.01541	−	3.01541i	−0.580315	−	0.580315i
$28$	−4.13341	+	0.779042i	−0.781141	+	0.147225i
$29$			3.15871i			0.586558i	0.956027	+	0.293279i	$0.0947465\pi$
$29$			3.15871i			0.586558i	−0.956027	+	0.293279i	$0.905254\pi$
$30$	−1.88179	−	1.66346i	−0.343566	−	0.303705i
$31$	5.55833			0.998305			0.499152	−	0.866514i	$-0.333645\pi$
$31$	5.55833			0.998305			0.499152	+	0.866514i	$0.333645\pi$
$32$	−5.64178	+	0.412721i	−0.997335	+	0.0729594i
$33$	−2.92997	+	2.92997i	−0.510042	+	0.510042i
$34$	0.741267	+	1.40375i	0.127126	+	0.240741i
$35$	1.93617	−	4.28558i	0.327272	−	0.724396i
$36$	2.67199	−	3.91312i	0.445332	−	0.652186i
$37$	3.25224	+	3.25224i	0.534665	+	0.534665i	0.921957	−	0.387292i	$-0.126589\pi$
$37$	3.25224	+	3.25224i	0.534665	+	0.534665i	−0.387292	+	0.921957i	$0.626589\pi$
$38$	0.137329	+	0.0424138i	0.0222777	+	0.00688042i
$39$	0.937519	−	2.70587i	0.150123	−	0.433286i
$40$	3.23867	−	5.43240i	0.512079	−	0.858938i
$41$		−	6.47910i		−	1.01187i	−0.862573	−	0.505933i	$-0.831148\pi$
$41$		−	6.47910i		−	1.01187i	0.862573	−	0.505933i	$-0.168852\pi$
$42$	−2.25706	−	0.697087i	−0.348271	−	0.107563i
$43$	2.45533	−	2.45533i	0.374435	−	0.374435i	−0.494655	−	0.869090i	$-0.664705\pi$
$43$	2.45533	−	2.45533i	0.374435	−	0.374435i	0.869090	+	0.494655i	$0.164705\pi$
$44$	−8.61688	−	5.88386i	−1.29904	−	0.887025i
$45$	1.87148	+	4.95607i	0.278983	+	0.738807i
$46$	−2.79263	−	5.28845i	−0.411750	−	0.779740i
$47$	−3.39043	+	3.39043i	−0.494545	+	0.494545i	−0.909735	−	0.415190i	$-0.863715\pi$
$47$	−3.39043	+	3.39043i	−0.494545	+	0.494545i	0.415190	+	0.909735i	$0.363715\pi$
$48$	−2.91008	−	1.27458i	−0.420034	−	0.183970i
$49$			2.57701i			0.368144i
$50$	2.89986	+	6.44910i	0.410102	+	0.912040i
$51$			0.891534i			0.124840i
$52$	7.13307	+	1.05795i	0.989179	+	0.146711i
$53$	−6.94382	−	6.94382i	−0.953807	−	0.953807i	0.0451723	−	0.998979i	$-0.485616\pi$
$53$	−6.94382	−	6.94382i	−0.953807	−	0.953807i	−0.998979	+	0.0451723i	$0.985616\pi$
$54$	5.33294	−	2.81612i	0.725721	−	0.383225i
$55$	10.9135	−	4.12109i	1.47158	−	0.555687i
$56$	0.672311	−	5.91032i	0.0898413	−	0.789800i
$57$	0.0570780	+	0.0570780i	0.00756017	+	0.00756017i
$58$	−4.26816	−	1.31821i	−0.560437	−	0.173090i
$59$		−	10.5517i		−	1.37372i	−0.726789	−	0.686860i	$-0.758988\pi$
$59$		−	10.5517i		−	1.37372i	0.726789	−	0.686860i	$-0.241012\pi$
$60$	3.03304	−	1.84853i	0.391564	−	0.238644i
$61$	−1.49686			−0.191653			−0.0958264	−	0.995398i	$-0.530549\pi$
$61$	−1.49686			−0.191653			−0.0958264	+	0.995398i	$0.530549\pi$
$62$	−2.31964	+	7.51061i	−0.294594	+	0.953848i
$63$	3.52323	+	3.52323i	0.443885	+	0.443885i
$64$	1.79678	−	7.79561i	0.224598	−	0.974452i
$65$	−5.54180	+	5.85563i	−0.687376	+	0.726302i
$66$	−2.73632	−	5.18183i	−0.336818	−	0.637840i
$67$	−6.37568	+	6.37568i	−0.778914	+	0.778914i	−0.979646	−	0.200732i	$-0.935668\pi$
$67$	−6.37568	+	6.37568i	−0.778914	+	0.778914i	0.200732	+	0.979646i	$0.435668\pi$
$68$	−2.20615	+	0.415803i	−0.267535	+	0.0504236i
$69$		−	3.35874i		−	0.404345i
$70$	4.98282	+	4.40470i	0.595561	+	0.526463i
$71$	−1.73544			−0.205959			−0.102979	−	0.994683i	$-0.532838\pi$
$71$	−1.73544			−0.205959			−0.102979	+	0.994683i	$0.532838\pi$
$72$	4.17245	+	5.24354i	0.491728	+	0.617957i
$73$	5.87285	−	5.87285i	0.687366	−	0.687366i	−0.274283	−	0.961649i	$-0.588441\pi$
$73$	5.87285	−	5.87285i	0.687366	−	0.687366i	0.961649	+	0.274283i	$0.0884406\pi$
$74$	−5.75179	+	3.03730i	−0.668632	+	0.353079i
$75$	−0.251124	+	3.96327i	−0.0289973	+	0.457638i
$76$	−0.114622	+	0.167863i	−0.0131480	+	0.0192552i
$77$	7.75832	−	7.75832i	0.884143	−	0.884143i
$78$	3.26502	+	2.39604i	0.369690	+	0.271298i
$79$	−1.43236			−0.161153			−0.0805767	−	0.996748i	$-0.525676\pi$
$79$	−1.43236			−0.161153			−0.0805767	+	0.996748i	$0.525676\pi$
$80$	5.98888	+	6.64330i	0.669577	+	0.742743i
$81$	−3.72054			−0.413394
$82$	8.75480	+	2.70390i	0.966806	+	0.298596i
$83$	−10.2973	−	10.2973i	−1.13028	−	1.13028i	−0.990131	−	0.140144i	$-0.955243\pi$
$83$	−10.2973	−	10.2973i	−1.13028	−	1.13028i	−0.140144	−	0.990131i	$-0.544757\pi$
$84$	1.88386	−	2.75890i	0.205546	−	0.301021i
$85$	1.03340	−	2.28737i	0.112088	−	0.248100i
$86$	2.29306	+	4.34241i	0.247267	+	0.468254i
$87$	−1.77398	−	1.77398i	−0.190190	−	0.190190i
$88$	11.5465	−	9.18794i	1.23086	−	0.979438i
$89$	6.49614			0.688589			0.344295	−	0.938862i	$-0.388118\pi$
$89$	6.49614			0.688589			0.344295	+	0.938862i	$0.388118\pi$
$90$	−7.47783	+	0.460509i	−0.788233	+	0.0485419i
$91$	−2.48247	+	7.16493i	−0.260234	+	0.751089i
$92$	8.31138	−	1.56649i	0.866522	−	0.163317i
$93$	−3.12164	+	3.12164i	−0.323699	+	0.323699i
$94$	−3.16635	−	5.99618i	−0.326584	−	0.618459i
$95$	−0.0802819	−	0.212603i	−0.00823675	−	0.0218126i
$96$	2.93671	−	3.40029i	0.299727	−	0.347041i
$97$	−6.63009	−	6.63009i	−0.673184	−	0.673184i	0.285265	−	0.958449i	$-0.407918\pi$
$97$	−6.63009	−	6.63009i	−0.673184	−	0.673184i	−0.958449	+	0.285265i	$0.907918\pi$
$98$	−3.48215	−	1.07545i	−0.351750	−	0.108637i
$99$			12.3601i			1.24224i
$100$	−9.92444	+	1.22701i	−0.992444	+	0.122701i
$101$	−18.8956			−1.88018			−0.940092	−	0.340920i	$-0.889262\pi$
$101$	−18.8956			−1.88018			−0.940092	+	0.340920i	$0.889262\pi$
$102$	−1.20467	−	0.372061i	−0.119280	−	0.0368395i
$103$	−7.95014	+	7.95014i	−0.783351	+	0.783351i	−0.980395	−	0.197044i	$-0.936866\pi$
$103$	−7.95014	+	7.95014i	−0.783351	+	0.783351i	0.197044	+	0.980395i	$0.436866\pi$
$104$	−4.40636	+	9.19696i	−0.432079	+	0.901836i
$105$	1.31947	+	3.49422i	0.128767	+	0.341001i
$106$	12.2806	−	6.48490i	1.19280	−	0.629869i
$107$	−13.3326	−	13.3326i	−1.28891	−	1.28891i	−0.935448	−	0.353463i	$-0.885004\pi$
$107$	−13.3326	−	13.3326i	−1.28891	−	1.28891i	−0.353463	−	0.935448i	$-0.614996\pi$
$108$	1.57966	+	8.38130i	0.152003	+	0.806491i
$109$	−17.2986			−1.65690			−0.828451	−	0.560062i	$-0.810777\pi$
$109$	−17.2986			−1.65690			−0.828451	+	0.560062i	$0.810777\pi$
$110$	1.01406	+	16.4666i	0.0966872	+	1.57002i
$111$	−3.65301			−0.346728
$112$	7.70567	+	3.37499i	0.728117	+	0.318906i
$113$	11.9985	+	11.9985i	1.12872	+	1.12872i	0.990386	+	0.138334i	$0.0441746\pi$
$113$	11.9985	+	11.9985i	1.12872	+	1.12872i	0.138334	+	0.990386i	$0.455825\pi$
$114$	−0.100946	+	0.0533057i	−0.00945446	+	0.00499254i
$115$	−3.89321	+	8.61737i	−0.363044	+	0.803574i
$116$	3.56244	−	5.21717i	0.330764	−	0.484402i
$117$	−3.72991	−	7.68485i	−0.344830	−	0.710464i
$118$	14.2579	+	4.40353i	1.31255	+	0.405377i
$119$		−	2.36071i		−	0.216406i
$120$	1.23203	+	4.86980i	0.112469	+	0.444550i
$121$	16.2176			1.47433
$122$	0.624678	−	2.02261i	0.0565557	−	0.183118i
$123$	3.63876	+	3.63876i	0.328096	+	0.328096i
$124$	−9.18056	−	6.26875i	−0.824439	−	0.562951i
$125$	5.23823	−	9.87729i	0.468521	−	0.883452i
$126$	−6.23105	+	3.29038i	−0.555106	+	0.293130i
$127$	4.63191	+	4.63191i	0.411016	+	0.411016i	0.882092	−	0.471077i	$-0.156134\pi$
$127$	4.63191	+	4.63191i	0.411016	+	0.411016i	−0.471077	+	0.882092i	$0.656134\pi$
$128$	9.78387	+	5.68119i	0.864780	+	0.502151i
$129$			2.75790i			0.242820i
$130$	−5.59960	−	9.93199i	−0.491117	−	0.871093i
$131$			20.8492i			1.82161i	0.412840	+	0.910804i	$0.364537\pi$
$131$			20.8492i			1.82161i	−0.412840	+	0.910804i	$0.635463\pi$
$132$	8.14382	−	1.53490i	0.708829	−	0.133596i
$133$	−0.151138	−	0.151138i	−0.0131053	−	0.0131053i
$134$	−5.95431	−	11.2758i	−0.514374	−	0.974080i
$135$	−8.68986	−	3.92596i	−0.747904	−	0.337893i
$136$	0.358837	−	3.15455i	0.0307700	−	0.270501i
$137$	−0.119502	−	0.119502i	−0.0102097	−	0.0102097i	0.701983	−	0.712193i	$-0.252298\pi$
$137$	−0.119502	−	0.119502i	−0.0102097	−	0.0102097i	−0.712193	+	0.701983i	$0.752298\pi$
$138$	4.53845	+	1.40169i	0.386338	+	0.119320i
$139$	20.1901			1.71250			0.856252	−	0.516559i	$-0.172787\pi$
$139$	20.1901			1.71250			0.856252	+	0.516559i	$0.172787\pi$
$140$	−8.03126	+	4.89476i	−0.678765	+	0.413683i
$141$		−	3.80823i		−	0.320710i
$142$	0.724245	−	2.34499i	0.0607773	−	0.196787i
$143$	−16.9224	+	8.21344i	−1.41512	+	0.686843i
$144$	−8.82653	+	3.44970i	−0.735544	+	0.287475i
$145$	2.49515	+	6.60769i	0.207211	+	0.548738i
$146$	5.48471	+	10.3865i	0.453918	+	0.859594i
$147$	−1.44729	−	1.44729i	−0.119370	−	0.119370i
$148$	−1.70373	−	9.03957i	−0.140046	−	0.743048i
$149$	9.51723			0.779682			0.389841	−	0.920882i	$-0.372530\pi$
$149$	9.51723			0.779682			0.389841	+	0.920882i	$0.372530\pi$
$150$	−5.25051	−	1.99330i	−0.428702	−	0.162753i
$151$	3.70969			0.301890			0.150945	−	0.988542i	$-0.451768\pi$
$151$	3.70969			0.301890			0.150945	+	0.988542i	$0.451768\pi$
$152$	−0.178988	−	0.224935i	−0.0145179	−	0.0182447i
$153$	1.88048	+	1.88048i	0.152027	+	0.152027i
$154$	7.24557	+	13.7211i	0.583865	+	1.10568i
$155$	11.6274	−	4.39067i	0.933937	−	0.352667i
$156$	−4.60020	+	3.41188i	−0.368310	+	0.273169i
$157$	−2.55204	+	2.55204i	−0.203675	+	0.203675i	−0.801573	−	0.597898i	$-0.796003\pi$
$157$	−2.55204	+	2.55204i	−0.203675	+	0.203675i	0.597898	+	0.801573i	$0.296003\pi$
$158$	0.597763	−	1.93546i	0.0475555	−	0.153977i
$159$	7.79950			0.618540
$160$	−11.4760	+	5.31996i	−0.907256	+	0.420580i
$161$			8.89367i			0.700920i
$162$	1.55268	−	5.02733i	0.121990	−	0.394985i
$163$	3.79158	+	3.79158i	0.296979	+	0.296979i	0.839830	−	0.542850i	$-0.182655\pi$
$163$	3.79158	+	3.79158i	0.296979	+	0.296979i	−0.542850	+	0.839830i	$0.682655\pi$
$164$	−7.30722	+	10.7014i	−0.570598	+	0.835638i
$165$	−3.81472	+	8.44364i	−0.296975	+	0.657337i
$166$	18.2114	−	9.61674i	1.41348	−	0.746404i
$167$	−8.86404	+	8.86404i	−0.685920	+	0.685920i	−0.961328	−	0.275408i	$-0.911187\pi$
$167$	−8.86404	+	8.86404i	−0.685920	+	0.685920i	0.275408	+	0.961328i	$0.411187\pi$
$168$	2.94174	+	3.69690i	0.226960	+	0.285222i
$169$	8.04286	−	10.2133i	0.618682	−	0.785642i
$170$	2.65951	+	2.35095i	0.203975	+	0.180310i
$171$	0.240784			0.0184132
$172$	−6.82458	+	1.28626i	−0.520369	+	0.0980764i
$173$	−8.52255	−	8.52255i	−0.647958	−	0.647958i	0.304541	−	0.952499i	$-0.401497\pi$
$173$	−8.52255	−	8.52255i	−0.647958	−	0.647958i	−0.952499	+	0.304541i	$0.901497\pi$
$174$	3.13739	−	1.65673i	0.237845	−	0.125597i
$175$	0.664955	−	10.4944i	0.0502659	−	0.793303i
$176$	7.59640	+	19.4365i	0.572601	+	1.46508i
$177$	5.92601	+	5.92601i	0.445426	+	0.445426i
$178$	−2.71101	+	8.77782i	−0.203199	+	0.657925i
$179$	−19.5455			−1.46090			−0.730449	−	0.682967i	$-0.760689\pi$
$179$	−19.5455			−1.46090			−0.730449	+	0.682967i	$0.760689\pi$
$180$	2.49844	−	10.2965i	0.186223	−	0.767456i
$181$	−11.2087			−0.833132			−0.416566	−	0.909105i	$-0.636767\pi$
$181$	−11.2087			−0.833132			−0.416566	+	0.909105i	$0.636767\pi$
$182$	−8.64551	−	6.34452i	−0.640847	−	0.470287i
$183$	0.840656	−	0.840656i	0.0621431	−	0.0621431i
$184$	−1.35187	+	11.8844i	−0.0996612	+	0.876128i
$185$	9.37237	+	4.23431i	0.689070	+	0.311312i
$186$	−2.91532	−	5.52081i	−0.213762	−	0.404805i
$187$	4.14090	−	4.14090i	0.302812	−	0.302812i
$188$	9.42366	−	1.77612i	0.687291	−	0.129537i
$189$	−8.96848			−0.652361
$190$	0.320781	−	0.0197547i	0.0232719	−	0.00143316i
$191$		−	14.4302i		−	1.04414i	−0.852904	−	0.522068i	$-0.825161\pi$
$191$		−	14.4302i		−	1.04414i	0.852904	−	0.522068i	$-0.174839\pi$
$192$	3.36903	+	5.38723i	0.243139	+	0.388790i
$193$	7.31079	−	7.31079i	0.526242	−	0.526242i	−0.393207	−	0.919450i	$-0.628635\pi$
$193$	7.31079	−	7.31079i	0.526242	−	0.526242i	0.919450	+	0.393207i	$0.128635\pi$
$194$	11.7257	−	6.19190i	0.841858	−	0.444553i
$195$	−0.176251	−	6.40096i	−0.0126216	−	0.458382i
$196$	2.90639	−	4.25639i	0.207599	−	0.304028i
$197$	4.58324	+	4.58324i	0.326542	+	0.326542i	0.851270	−	0.524728i	$-0.175833\pi$
$197$	4.58324	+	4.58324i	0.326542	+	0.326542i	−0.524728	+	0.851270i	$0.675833\pi$
$198$	−16.7014	−	5.15821i	−1.18692	−	0.366578i
$199$	1.85757			0.131680			0.0658398	−	0.997830i	$-0.479027\pi$
$199$	1.85757			0.131680			0.0658398	+	0.997830i	$0.479027\pi$
$200$	2.48375	−	13.9223i	0.175628	−	0.984457i
$201$		−	7.16135i		−	0.505123i
$202$	7.88565	−	25.5324i	0.554832	−	1.79646i
$203$	4.69735	+	4.69735i	0.329689	+	0.329689i
$204$	1.00548	−	1.47253i	0.0703980	−	0.103097i
$205$	−5.11802	−	13.5536i	−0.357458	−	0.946624i
$206$	−7.42471	−	14.0603i	−0.517304	−	0.979629i
$207$	−7.08445	−	7.08445i	−0.492403	−	0.492403i
$208$	−10.5884	−	9.79217i	−0.734171	−	0.678965i
$209$		−	0.530219i		−	0.0366760i
$210$	−5.27217	+	0.324677i	−0.363814	+	0.0224048i
$211$		−	4.26614i		−	0.293694i	−0.989159	−	0.146847i	$-0.953088\pi$
$211$		−	4.26614i		−	0.293694i	0.989159	−	0.146847i	$-0.0469124\pi$
$212$	3.63761	+	19.3003i	0.249832	+	1.32555i
$213$	0.974647	−	0.974647i	0.0667817	−	0.0667817i
$214$	23.5795	−	12.4514i	1.61186	−	0.851163i
$215$	3.19676	−	7.07583i	0.218017	−	0.482568i
$216$	−11.9843	−	1.36324i	−0.815431	−	0.0927569i
$217$	8.26584	−	8.26584i	0.561122	−	0.561122i
$218$	7.21915	−	23.3744i	0.488943	−	1.58312i
$219$			6.59656i			0.445754i
$220$	−22.6734	−	5.50169i	−1.52864	−	0.370924i
$221$	−1.32499	+	3.82418i	−0.0891283	+	0.257242i
$222$	1.52450	−	4.93608i	0.102318	−	0.331288i
$223$	12.0709	+	12.0709i	0.808329	+	0.808329i	0.984381	−	0.176052i	$-0.0563328\pi$
$223$	12.0709	+	12.0709i	0.808329	+	0.808329i	−0.176052	+	0.984381i	$0.556333\pi$
$224$	−7.77618	+	9.00370i	−0.519568	+	0.601585i
$225$	7.82986	+	8.88923i	0.521991	+	0.592615i
$226$	−21.2200	+	11.2055i	−1.41153	+	0.745376i
$227$	9.70954	−	9.70954i	0.644445	−	0.644445i	−0.307200	−	0.951645i	$-0.599392\pi$
$227$	9.70954	−	9.70954i	0.644445	−	0.644445i	0.951645	+	0.307200i	$0.0993920\pi$
$228$	−0.0299011	−	0.158648i	−0.00198025	−	0.0105067i
$229$	−9.74332			−0.643856			−0.321928	−	0.946764i	$-0.604331\pi$
$229$	−9.74332			−0.643856			−0.321928	+	0.946764i	$0.604331\pi$
$230$	−10.0194	−	8.85690i	−0.660657	−	0.584007i
$231$			8.71437i			0.573363i
$232$	5.56293	+	6.99096i	0.365224	+	0.458979i
$233$	2.40053	+	2.40053i	0.157264	+	0.157264i	0.781353	−	0.624089i	$-0.214530\pi$
$233$	2.40053	+	2.40053i	0.157264	+	0.157264i	−0.624089	+	0.781353i	$0.714530\pi$
$234$	11.9406	−	1.83290i	0.780584	−	0.119820i
$235$	−4.41422	+	9.77060i	−0.287952	+	0.637364i
$236$	−11.9004	+	17.4281i	−0.774650	+	1.13447i
$237$	0.804435	−	0.804435i	0.0522537	−	0.0522537i
$238$	3.18988	+	0.985187i	0.206769	+	0.0638602i
$239$		−	14.8314i		−	0.959363i	−0.877443	−	0.479682i	$-0.840752\pi$
$239$		−	14.8314i		−	0.959363i	0.877443	−	0.479682i	$-0.159248\pi$
$240$	−7.09441	−	0.367532i	−0.457942	−	0.0237241i
$241$			9.39857i			0.605415i	0.953083	+	0.302708i	$0.0978906\pi$
$241$			9.39857i			0.605415i	−0.953083	+	0.302708i	$0.902109\pi$
$242$	−6.76803	+	21.9138i	−0.435065	+	1.40867i
$243$	11.1357	−	11.1357i	0.714358	−	0.714358i
$244$	2.47232	+	1.68817i	0.158274	+	0.108074i
$245$	2.03565	+	5.39083i	0.130053	+	0.344407i
$246$	−6.43537	+	3.39827i	−0.410304	+	0.216666i
$247$	0.160004	+	0.329661i	0.0101808	+	0.0209759i
$248$	12.3019	−	9.78898i	0.781169	−	0.621601i
$249$	11.5662			0.732979
$250$	11.1605	+	11.2001i	0.705852	+	0.708359i
$251$		−	12.8154i		−	0.808900i	−0.914560	−	0.404450i	$-0.867463\pi$
$251$		−	12.8154i		−	0.808900i	0.914560	−	0.404450i	$-0.132537\pi$
$252$	−1.84569	−	9.79278i	−0.116268	−	0.616887i
$253$	−15.6003	+	15.6003i	−0.980782	+	0.980782i
$254$	−8.19182	+	4.32578i	−0.514001	+	0.271424i
$255$	0.704247	+	1.86499i	0.0441016	+	0.116790i
$256$	−11.7597	+	10.8494i	−0.734981	+	0.678087i
$257$	4.63552	−	4.63552i	0.289156	−	0.289156i	−0.547591	−	0.836746i	$-0.684455\pi$
$257$	4.63552	−	4.63552i	0.289156	−	0.289156i	0.836746	+	0.547591i	$0.184455\pi$
$258$	−3.72658	−	1.15095i	−0.232006	−	0.0716548i
$259$	9.67288			0.601043
$260$	15.7573	−	3.42149i	0.977228	−	0.212192i
$261$	−7.48355			−0.463220
$262$	−28.1723	−	8.70095i	−1.74049	−	0.537546i
$263$	21.0322	−	21.0322i	1.29690	−	1.29690i	0.366472	−	0.930429i	$-0.380565\pi$
$263$	21.0322	−	21.0322i	1.29690	−	1.29690i	0.930429	−	0.366472i	$-0.119435\pi$
$264$	−1.32462	+	11.6448i	−0.0815245	+	0.716687i
$265$	−20.0108	−	9.04062i	−1.22926	−	0.555361i
$266$	0.267297	−	0.141149i	0.0163890	−	0.00865441i
$267$	−3.64833	+	3.64833i	−0.223274	+	0.223274i
$268$	17.7212	−	3.33999i	1.08249	−	0.204022i
$269$		−	11.3028i		−	0.689143i	−0.938760	−	0.344572i	$-0.888024\pi$
$269$		−	11.3028i		−	0.689143i	0.938760	−	0.344572i	$-0.111976\pi$
$270$	8.93141	−	10.1036i	0.543548	−	0.614888i
$271$	0.932858			0.0566671			0.0283335	−	0.999599i	$-0.490980\pi$
$271$	0.932858			0.0566671			0.0283335	+	0.999599i	$0.490980\pi$
$272$	4.11279	+	1.80135i	0.249375	+	0.109223i
$273$	−2.62973	−	5.41812i	−0.159159	−	0.327920i
$274$	0.211346	−	0.111604i	0.0127679	−	0.00674223i
$275$	19.5745	−	17.2417i	1.18039	−	1.03972i
$276$	−3.78803	+	5.54755i	−0.228013	+	0.333923i
$277$	−15.7265	+	15.7265i	−0.944912	+	0.944912i	−0.998560	−	0.0536481i	$-0.982915\pi$
$277$	−15.7265	+	15.7265i	−0.944912	+	0.944912i	0.0536481	+	0.998560i	$0.482915\pi$
$278$	−8.42587	+	27.2816i	−0.505350	+	1.63624i
$279$			13.1687i			0.788387i
$280$	−3.26232	−	12.8948i	−0.194961	−	0.770614i
$281$			30.0274i			1.79128i	0.444775	+	0.895642i	$0.353284\pi$
$281$			30.0274i			1.79128i	−0.444775	+	0.895642i	$0.646716\pi$
$282$	5.14581	+	1.58927i	0.306429	+	0.0946399i
$283$	−14.6116	+	14.6116i	−0.868570	+	0.868570i	−0.992314	−	0.123744i	$-0.960510\pi$
$283$	−14.6116	+	14.6116i	−0.868570	+	0.868570i	0.123744	+	0.992314i	$0.460510\pi$
$284$	2.86638	+	1.95725i	0.170089	+	0.116142i
$285$	0.164489	+	0.0743136i	0.00974346	+	0.00440196i
$286$	−4.03613	−	26.2939i	−0.238661	−	1.55479i
$287$	−9.63514	−	9.63514i	−0.568744	−	0.568744i
$288$	−0.977809	−	13.3664i	−0.0576179	−	0.787622i
$289$			15.7400i			0.925883i
$290$	−9.96983	+	0.613975i	−0.585449	+	0.0360538i
$291$	7.44711			0.436557
$292$	−16.3235	+	3.07657i	−0.955263	+	0.180043i
$293$	8.55742	−	8.55742i	0.499930	−	0.499930i	−0.411486	−	0.911416i	$-0.634990\pi$
$293$	8.55742	−	8.55742i	0.499930	−	0.499930i	0.911416	+	0.411486i	$0.134990\pi$
$294$	2.55962	−	1.35163i	0.149280	−	0.0788289i
$295$	−8.33511	−	22.0731i	−0.485289	−	1.28515i
$296$	12.9256	+	1.47031i	0.751286	+	0.0854602i
$297$	−15.7315	−	15.7315i	−0.912836	−	0.912836i
$298$	−3.97179	+	12.8600i	−0.230080	+	0.744961i
$299$	4.99172	−	14.4071i	0.288678	−	0.833185i
$300$	4.88460	−	6.26281i	0.282012	−	0.361584i
$301$		−	7.30270i		−	0.420921i
$302$	−1.54815	+	5.01267i	−0.0890861	+	0.288446i
$303$	10.6121	−	10.6121i	0.609647	−	0.609647i
$304$	0.378637	−	0.147984i	0.0217163	−	0.00848745i
$305$	−3.13126	+	1.18241i	−0.179296	+	0.0677044i
$306$	−3.32574	+	1.75619i	−0.190120	+	0.100395i
$307$	13.3065	−	13.3065i	0.759441	−	0.759441i	−0.216779	−	0.976221i	$-0.569555\pi$
$307$	13.3065	−	13.3065i	0.759441	−	0.759441i	0.976221	+	0.216779i	$0.0695552\pi$
$308$	−21.5642	+	4.06430i	−1.22873	+	0.231585i
$309$		−	8.92983i		−	0.508000i
$310$	1.08040	+	17.5437i	0.0613626	+	0.996417i
$311$			12.3858i			0.702336i	0.936313	+	0.351168i	$0.114215\pi$
$311$			12.3858i			0.702336i	−0.936313	+	0.351168i	$0.885785\pi$
$312$	−2.69047	−	7.63982i	−0.152318	−	0.432519i
$313$	−9.10805	−	9.10805i	−0.514817	−	0.514817i	0.401181	−	0.915999i	$-0.368600\pi$
$313$	−9.10805	−	9.10805i	−0.514817	−	0.514817i	−0.915999	+	0.401181i	$0.868600\pi$
$314$	−2.38337	−	4.51344i	−0.134502	−	0.254708i
$315$	10.1533	+	4.58712i	0.572074	+	0.258455i
$316$	2.36580	+	1.61544i	0.133087	+	0.0908755i
$317$	9.85317	+	9.85317i	0.553409	+	0.553409i	0.927423	−	0.374014i	$-0.122019\pi$
$317$	9.85317	+	9.85317i	0.553409	+	0.553409i	−0.374014	+	0.927423i	$0.622019\pi$
$318$	−3.25494	+	10.5390i	−0.182528	+	0.590996i
$319$			16.4791i			0.922655i
$320$	−2.39929	−	17.7269i	−0.134124	−	0.990965i
$321$	14.9756			0.835855
$322$	−12.0174	−	3.71157i	−0.669706	−	0.206838i
$323$	−0.0806678	−	0.0806678i	−0.00448848	−	0.00448848i
$324$	6.14514	+	4.19608i	0.341396	+	0.233116i
$325$	−6.96734	+	16.6270i	−0.386478	+	0.922299i
$326$	−6.70564	+	3.54099i	−0.371391	+	0.196117i
$327$	9.71512	−	9.71512i	0.537247	−	0.537247i
$328$	−11.4106	−	14.3398i	−0.630045	−	0.791780i
$329$			10.0839i			0.555942i
$330$	−9.81737	−	8.67834i	−0.540428	−	0.477727i
$331$	−26.8753			−1.47720			−0.738599	−	0.674145i	$-0.764512\pi$
$331$	−26.8753			−1.47720			−0.738599	+	0.674145i	$0.764512\pi$
$332$	5.39438	+	28.6212i	0.296055	+	1.57079i
$333$	−7.70514	+	7.70514i	−0.422239	+	0.422239i
$334$	−8.27821	−	15.6766i	−0.452963	−	0.857786i
$335$	−8.30092	+	18.3736i	−0.453528	+	1.00386i
$336$	−6.22305	+	2.43217i	−0.339495	+	0.132686i
$337$	−11.8914	+	11.8914i	−0.647768	+	0.647768i	−0.952453	−	0.304685i	$-0.901449\pi$
$337$	−11.8914	+	11.8914i	−0.647768	+	0.647768i	0.304685	+	0.952453i	$0.401449\pi$
$338$	10.4441	+	15.1301i	0.568086	+	0.822969i
$339$	−13.4770			−0.731970
$340$	−4.28657	+	2.61251i	−0.232472	+	0.141683i
$341$	28.9980			1.57033
$342$	−0.100486	+	0.325357i	−0.00543365	+	0.0175933i
$343$	14.2421	+	14.2421i	0.768999	+	0.768999i
$344$	1.11004	−	9.75841i	0.0598492	−	0.526138i
$345$	−2.65316	−	7.02612i	−0.142841	−	0.378274i
$346$	15.0727	−	7.95929i	0.810312	−	0.427894i
$347$	7.80289	+	7.80289i	0.418881	+	0.418881i	0.884818	−	0.465937i	$-0.154283\pi$
$347$	7.80289	+	7.80289i	0.418881	+	0.418881i	−0.465937	+	0.884818i	$0.654283\pi$
$348$	0.929322	+	4.93075i	0.0498169	+	0.264316i
$349$	23.0829			1.23560			0.617799	−	0.786336i	$-0.288025\pi$
$349$	23.0829			1.23560			0.617799	+	0.786336i	$0.288025\pi$
$350$	13.9029	+	5.27811i	0.743142	+	0.282127i
$351$	14.5283	+	5.03371i	0.775463	+	0.268679i
$352$	−29.4334	+	2.15318i	−1.56881	+	0.114765i
$353$	12.4513	−	12.4513i	0.662717	−	0.662717i	−0.293303	−	0.956020i	$-0.594754\pi$
$353$	12.4513	−	12.4513i	0.662717	−	0.662717i	0.956020	+	0.293303i	$0.0947544\pi$
$354$	−10.4805	+	5.53436i	−0.557034	+	0.294148i
$355$	−3.63035	+	1.37087i	−0.192679	+	0.0727582i
$356$	−10.7295	−	7.32643i	−0.568664	−	0.388300i
$357$	1.32581	+	1.32581i	0.0701692	+	0.0701692i
$358$	8.15685	−	26.4106i	0.431103	−	1.39584i
$359$		−	1.28531i		−	0.0678361i	−0.999425	−	0.0339181i	$-0.989201\pi$
$359$		−	1.28531i		−	0.0678361i	0.999425	−	0.0339181i	$-0.0107985\pi$
$360$	12.8703	+	7.67299i	0.678326	+	0.404402i
$361$	18.9897			0.999456
$362$	4.67767	−	15.1455i	0.245853	−	0.796031i
$363$	−9.10803	+	9.10803i	−0.478047	+	0.478047i
$364$	12.1809	−	9.03438i	0.638455	−	0.473530i
$365$	7.64626	−	16.9245i	0.400223	−	0.885869i
$366$	0.785096	+	1.48675i	0.0410376	+	0.0777138i
$367$	3.03025	+	3.03025i	0.158178	+	0.158178i	0.781759	−	0.623581i	$-0.214323\pi$
$367$	3.03025	+	3.03025i	0.158178	+	0.158178i	−0.623581	+	0.781759i	$0.714323\pi$
$368$	−15.4944	−	6.78636i	−0.807703	−	0.353764i
$369$	15.3502			0.799097
$370$	−9.63289	+	10.8972i	−0.500790	+	0.566518i
$371$	−20.6524			−1.07222
$372$	8.67656	−	1.63531i	0.449858	−	0.0847869i
$373$	12.5458	+	12.5458i	0.649597	+	0.649597i	0.952896	−	0.303299i	$-0.0980879\pi$
$373$	12.5458	+	12.5458i	0.649597	+	0.649597i	−0.303299	+	0.952896i	$0.598088\pi$
$374$	3.86722	+	7.32344i	0.199969	+	0.378686i
$375$	2.60537	+	8.48910i	0.134541	+	0.438375i
$376$	−1.53279	+	13.4748i	−0.0790474	+	0.694910i
$377$	−4.97291	−	10.2458i	−0.256118	−	0.527687i
$378$	3.74279	−	12.1185i	0.192508	−	0.623310i
$379$			19.8910i			1.02173i	0.859660	+	0.510866i	$0.170675\pi$
$379$			19.8910i			1.02173i	−0.859660	+	0.510866i	$0.829325\pi$
$380$	−0.107177	+	0.441695i	−0.00549807	+	0.0226585i
$381$	−5.20269			−0.266542
$382$	19.4987	+	6.02212i	0.997638	+	0.308119i
$383$	1.94725	+	1.94725i	0.0994996	+	0.0994996i	0.755104	−	0.655605i	$-0.227586\pi$
$383$	1.94725	+	1.94725i	0.0994996	+	0.0994996i	−0.655605	+	0.755104i	$0.727586\pi$
$384$	−8.68540	+	2.30412i	−0.443225	+	0.117582i
$385$	10.1011	−	22.3581i	0.514798	−	1.13947i
$386$	6.82762	+	12.9296i	0.347517	+	0.658099i
$387$	5.81713	+	5.81713i	0.295701	+	0.295701i
$388$	3.47326	+	18.4283i	0.176328	+	0.935554i
$389$			15.2218i			0.771778i	0.922545	+	0.385889i	$0.126105\pi$
$389$			15.2218i			0.771778i	−0.922545	+	0.385889i	$0.873895\pi$
$390$	8.72276	+	2.43314i	0.441694	+	0.123207i
$391$			4.74688i			0.240060i
$392$	4.53847	+	5.70352i	0.229227	+	0.288071i
$393$	−11.7092	−	11.7092i	−0.590653	−	0.590653i
$394$	−8.10574	+	4.28033i	−0.408361	+	0.215640i
$395$	−2.99635	+	1.13146i	−0.150763	+	0.0569300i
$396$	13.9399	−	20.4149i	0.700507	−	1.02589i
$397$	6.29063	+	6.29063i	0.315718	+	0.315718i	0.847120	−	0.531402i	$-0.178335\pi$
$397$	6.29063	+	6.29063i	0.315718	+	0.315718i	−0.531402	+	0.847120i	$0.678335\pi$
$398$	−0.775213	+	2.51001i	−0.0388579	+	0.125816i
$399$	0.169763			0.00849876
$400$	17.7758	+	9.16629i	0.888790	+	0.458314i
$401$			9.05500i			0.452185i	0.974106	+	0.226093i	$0.0725952\pi$
$401$			9.05500i			0.452185i	−0.974106	+	0.226093i	$0.927405\pi$
$402$	9.67667	+	2.98862i	0.482629	+	0.149059i
$403$	−18.0294	+	8.75073i	−0.898109	+	0.435905i
$404$	31.2095	+	21.3107i	1.55273	+	1.06025i
$405$	−7.78298	+	2.93896i	−0.386739	+	0.146038i
$406$	−8.30756	+	4.38690i	−0.412297	+	0.217718i
$407$	16.9671	+	16.9671i	0.841028	+	0.841028i
$408$	1.57012	+	1.97317i	0.0777323	+	0.0976865i
$409$	9.54287			0.471865			0.235932	−	0.971769i	$-0.424186\pi$
$409$	9.54287			0.471865			0.235932	+	0.971769i	$0.424186\pi$
$410$	20.4500	−	1.25938i	1.00995	−	0.0621961i
$411$	0.134228			0.00662097
$412$	22.0973	−	4.16479i	1.08866	−	0.205184i
$413$	−15.6916	−	15.6916i	−0.772133	−	0.772133i
$414$	12.5293	−	6.61623i	0.615781	−	0.325170i
$415$	−29.6750	−	13.4067i	−1.45669	−	0.658110i
$416$	17.6503	−	10.2208i	0.865379	−	0.501118i
$417$	−11.3391	+	11.3391i	−0.555276	+	0.555276i
$418$	0.716451	+	0.221275i	0.0350428	+	0.0108229i
$419$	−17.1056			−0.835662			−0.417831	−	0.908525i	$-0.637210\pi$
$419$	−17.1056			−0.835662			−0.417831	+	0.908525i	$0.637210\pi$
$420$	1.76150	−	7.25944i	0.0859524	−	0.354224i
$421$		−	7.59120i		−	0.369972i	−0.982741	−	0.184986i	$-0.940776\pi$
$421$		−	7.59120i		−	0.369972i	0.982741	−	0.184986i	$-0.0592240\pi$
$422$	5.76457	+	1.78038i	0.280615	+	0.0866673i
$423$	−8.03253	−	8.03253i	−0.390555	−	0.390555i
$424$	−27.5973	−	3.13925i	−1.34024	−	0.152455i
$425$	0.354911	−	5.60125i	0.0172157	−	0.271700i
$426$	0.910232	+	1.72372i	0.0441009	+	0.0835147i
$427$	−2.22599	+	2.22599i	−0.107723	+	0.107723i
$428$	6.98447	+	37.0578i	0.337607	+	1.79126i
$429$	4.89108	−	14.1167i	0.236144	−	0.681559i
$430$	8.22702	+	7.27251i	0.396742	+	0.350712i
$431$	−28.3057			−1.36344			−0.681718	−	0.731615i	$-0.738767\pi$
$431$	−28.3057			−1.36344			−0.681718	+	0.731615i	$0.738767\pi$
$432$	6.84345	−	15.6248i	0.329256	−	0.751747i
$433$	12.4675	+	12.4675i	0.599151	+	0.599151i	0.940087	−	0.340936i	$-0.110744\pi$
$433$	12.4675	+	12.4675i	0.599151	+	0.599151i	−0.340936	+	0.940087i	$0.610744\pi$
$434$	7.71954	+	14.6187i	0.370550	+	0.701718i
$435$	−5.11228	−	2.30966i	−0.245115	−	0.110740i
$436$	28.5716	+	19.5096i	1.36833	+	0.934338i
$437$	0.303906	+	0.303906i	0.0145378	+	0.0145378i
$438$	−8.91351	−	2.75292i	−0.425904	−	0.131540i
$439$	−0.183524			−0.00875913			−0.00437956	−	0.999990i	$-0.501394\pi$
$439$	−0.183524			−0.00875913			−0.00437956	+	0.999990i	$0.501394\pi$
$440$	16.8963	−	28.3411i	0.805499	−	1.35111i
$441$	−6.10540			−0.290733
$442$	−4.61442	−	3.38630i	−0.219486	−	0.161070i
$443$	5.69369	−	5.69369i	0.270516	−	0.270516i	−0.558792	−	0.829308i	$-0.688735\pi$
$443$	5.69369	−	5.69369i	0.270516	−	0.270516i	0.829308	+	0.558792i	$0.188735\pi$
$444$	6.03359	+	4.11991i	0.286342	+	0.195522i
$445$	13.5892	−	5.13148i	0.644191	−	0.243255i
$446$	−21.3482	+	11.2731i	−1.01087	+	0.533799i
$447$	−5.34501	+	5.34501i	−0.252810	+	0.252810i
$448$	−8.92092	−	14.2649i	−0.421474	−	0.673955i
$449$	−33.2458			−1.56896			−0.784482	−	0.620151i	$-0.787071\pi$
$449$	−33.2458			−1.56896			−0.784482	+	0.620151i	$0.787071\pi$
$450$	−15.2791	+	6.87028i	−0.720262	+	0.323868i
$451$		−	33.8018i		−	1.59166i
$452$	−6.28555	−	33.3496i	−0.295647	−	1.56863i
$453$	−2.08341	+	2.08341i	−0.0978874	+	0.0978874i
$454$	9.06783	+	17.1719i	0.425575	+	0.805919i
$455$	0.466699	+	16.9492i	0.0218792	+	0.794592i
$456$	0.226849	+	0.0258045i	0.0106232	+	0.00120841i
$457$	4.43340	+	4.43340i	0.207386	+	0.207386i	0.803155	−	0.595770i	$-0.203153\pi$
$457$	4.43340	+	4.43340i	0.207386	+	0.207386i	−0.595770	+	0.803155i	$0.703153\pi$
$458$	4.06615	−	13.1655i	0.189998	−	0.615184i
$459$	−4.78681			−0.223429
$460$	16.1491	−	9.84230i	0.752956	−	0.458900i
$461$		−	32.9895i		−	1.53648i	−0.640165	−	0.768238i	$-0.721134\pi$
$461$		−	32.9895i		−	1.53648i	0.640165	−	0.768238i	$-0.278866\pi$
$462$	−11.7752	−	3.63674i	−0.547830	−	0.169196i
$463$	−14.2854	−	14.2854i	−0.663897	−	0.663897i	0.292399	−	0.956296i	$-0.405546\pi$
$463$	−14.2854	−	14.2854i	−0.663897	−	0.663897i	−0.956296	+	0.292399i	$0.905546\pi$
$464$	−11.7680	+	4.59932i	−0.546315	+	0.213518i
$465$	−4.06426	+	8.99599i	−0.188476	+	0.417179i
$466$	−4.24548	+	2.24187i	−0.196668	+	0.103853i
$467$	21.2595	+	21.2595i	0.983774	+	0.983774i	0.999870	−	0.0160967i	$-0.00512396\pi$
$467$	21.2595	+	21.2595i	0.983774	+	0.983774i	−0.0160967	+	0.999870i	$0.505124\pi$
$468$	−2.50647	+	16.8995i	−0.115862	+	0.781181i
$469$			18.9627i			0.875615i
$470$	−11.3602	−	10.0422i	−0.524008	−	0.463212i
$471$		−	2.86652i		−	0.132082i
$472$	−18.5831	−	23.3535i	−0.855356	−	1.07493i
$473$	12.8096	−	12.8096i	0.588986	−	0.588986i
$474$	0.751270	+	1.42269i	0.0345070	+	0.0653465i
$475$	−0.335882	−	0.381327i	−0.0154113	−	0.0174965i
$476$	−2.66244	+	3.89913i	−0.122033	+	0.178716i
$477$	16.4511	−	16.4511i	0.753246	−	0.753246i
$478$	20.0407	+	6.18953i	0.916641	+	0.283103i
$479$		−	28.2046i		−	1.28870i	−0.764730	−	0.644351i	$-0.777128\pi$
$479$		−	28.2046i		−	1.28870i	0.764730	−	0.644351i	$-0.222872\pi$
$480$	3.45731	−	9.43284i	0.157804	−	0.430548i
$481$	−15.6694	−	5.42906i	−0.714462	−	0.247544i
$482$	−12.6997	−	3.92227i	−0.578455	−	0.178655i
$483$	−4.99481	−	4.99481i	−0.227272	−	0.227272i
$484$	−26.7862	−	18.2904i	−1.21755	−	0.831382i
$485$	−19.1067	−	8.63215i	−0.867592	−	0.391966i
$486$	10.3998	+	19.6942i	0.471743	+	0.893349i
$487$	−5.60275	+	5.60275i	−0.253885	+	0.253885i	−0.822561	−	0.568676i	$-0.807456\pi$
$487$	−5.60275	+	5.60275i	−0.253885	+	0.253885i	0.568676	+	0.822561i	$0.307456\pi$
$488$	−3.31289	+	2.63617i	−0.149967	+	0.119334i
$489$	−4.25881			−0.192590
$490$	−8.13381	+	0.500906i	−0.367448	+	0.0226286i
$491$			19.7932i			0.893253i	0.894720	+	0.446627i	$0.147375\pi$
$491$			19.7932i			0.893253i	−0.894720	+	0.446627i	$0.852625\pi$
$492$	−1.90621	−	10.1139i	−0.0859387	−	0.455969i
$493$	2.50715	+	2.50715i	0.112916	+	0.112916i
$494$	−0.512224	+	0.0786268i	−0.0230461	+	0.00353759i
$495$	9.76359	+	25.8560i	0.438841	+	1.16214i
$496$	8.09333	+	20.7079i	0.363401	+	0.929813i
$497$	−2.58079	+	2.58079i	−0.115764	+	0.115764i
$498$	−4.82689	+	15.6287i	−0.216298	+	0.700338i
$499$			15.1230i			0.677000i	0.940966	+	0.338500i	$0.109920\pi$
$499$			15.1230i			0.677000i	−0.940966	+	0.338500i	$0.890080\pi$
$500$	−19.7916	+	10.4064i	−0.885108	+	0.465386i
$501$		−	9.95634i		−	0.444817i
$502$	17.3166	+	5.34821i	0.772879	+	0.238702i
$503$	7.15930	−	7.15930i	0.319218	−	0.319218i	−0.529249	−	0.848467i	$-0.677526\pi$
$503$	7.15930	−	7.15930i	0.319218	−	0.319218i	0.848467	+	0.529249i	$0.177526\pi$
$504$	14.0026	+	1.59282i	0.623726	+	0.0709500i
$505$	−39.5276	+	14.9262i	−1.75896	+	0.664205i
$506$	−14.5693	−	27.5901i	−0.647683	−	1.22653i
$507$	1.21897	+	10.2529i	0.0541365	+	0.455349i
$508$	−2.42649	−	12.8744i	−0.107658	−	0.571207i
$509$	−42.1615			−1.86877			−0.934387	−	0.356259i	$-0.884052\pi$
$509$	−42.1615			−1.86877			−0.934387	+	0.356259i	$0.884052\pi$
$510$	−2.81395	+	0.173292i	−0.124604	+	0.00767350i
$511$		−	17.4672i		−	0.772701i
$512$	−9.75246	−	20.4179i	−0.431002	−	0.902351i
$513$	−0.306462	+	0.306462i	−0.0135306	+	0.0135306i
$514$	4.32915	+	8.19821i	0.190951	+	0.361607i
$515$	−10.3508	+	22.9109i	−0.456111	+	1.00957i
$516$	3.11040	−	4.55516i	0.136928	−	0.200530i
$517$	−17.6880	+	17.6880i	−0.777918	+	0.777918i
$518$	−4.03675	+	13.0703i	−0.177365	+	0.574278i
$519$	9.57278			0.420198
$520$	−1.95271	+	22.7197i	−0.0856319	+	0.996327i
$521$	7.84375			0.343641			0.171821	−	0.985128i	$-0.445035\pi$
$521$	7.84375			0.343641			0.171821	+	0.985128i	$0.445035\pi$
$522$	3.12309	−	10.1120i	0.136694	−	0.442592i
$523$	23.4710	−	23.4710i	1.02631	−	1.02631i	0.0266693	−	0.999644i	$-0.491510\pi$
$523$	23.4710	−	23.4710i	1.02631	−	1.02631i	0.999644	−	0.0266693i	$-0.00849009\pi$
$524$	23.5141	−	34.4362i	1.02722	−	1.50435i
$525$	5.52036	+	6.26726i	0.240928	+	0.273526i
$526$	19.6422	+	37.1968i	0.856439	+	1.62186i
$527$	4.41178	−	4.41178i	0.192180	−	0.192180i
$528$	−15.1820	−	6.64954i	−0.660714	−	0.289384i
$529$			5.11676i			0.222468i
$530$	20.5671	−	23.2665i	0.893376	−	1.01063i
$531$	24.9990			1.08486
$532$	0.0791757	+	0.420087i	0.00343270	+	0.0182131i
$533$	10.2004	+	21.0161i	0.441826	+	0.910309i
$534$	−3.40720	−	6.45229i	−0.147444	−	0.279218i
$535$	−38.4222	−	17.3586i	−1.66114	−	0.750478i
$536$	−2.88240	+	25.3393i	−0.124501	+	1.09449i
$537$	10.9770	−	10.9770i	0.473694	−	0.473694i
$538$	15.2727	+	4.71695i	0.658454	+	0.203362i
$539$			13.4444i			0.579091i
$540$	9.92510	+	16.2850i	0.427108	+	0.700793i
$541$		−	23.2720i		−	1.00054i	−0.865869	−	0.500271i	$-0.833234\pi$
$541$		−	23.2720i		−	1.00054i	0.865869	−	0.500271i	$-0.166766\pi$
$542$	−0.389306	+	1.26051i	−0.0167221	+	0.0541436i
$543$	6.29494	−	6.29494i	0.270142	−	0.270142i
$544$	−4.15043	+	4.80560i	−0.177948	+	0.206039i
$545$	−36.1867	+	13.6646i	−1.55007	+	0.585327i
$546$	8.41862	−	1.29226i	0.360283	−	0.0553038i
$547$	11.5816	+	11.5816i	0.495195	+	0.495195i	0.909938	−	0.414743i	$-0.136129\pi$
$547$	11.5816	+	11.5816i	0.495195	+	0.495195i	−0.414743	+	0.909938i	$0.636129\pi$
$548$	0.0626026	+	0.332154i	0.00267425	+	0.0141889i
$549$		−	3.54632i		−	0.151353i
$550$	15.1287	+	33.6452i	0.645089	+	1.43464i
$551$	0.321026			0.0136762
$552$	−5.91521	−	7.43367i	−0.251768	−	0.316398i
$553$	−2.13008	+	2.13008i	−0.0905802	+	0.0905802i
$554$	−14.6871	−	27.8132i	−0.623995	−	1.18167i
$555$	−7.64170	+	2.88561i	−0.324372	+	0.122487i
$556$	−33.3476	−	22.7707i	−1.41425	−	0.965692i
$557$	1.38433	+	1.38433i	0.0586558	+	0.0586558i	0.735826	−	0.677170i	$-0.236794\pi$
$557$	1.38433	+	1.38433i	0.0586558	+	0.0586558i	−0.677170	+	0.735826i	$0.736794\pi$
$558$	−17.7940	−	5.49564i	−0.753279	−	0.232649i
$559$	−4.09876	+	11.8299i	−0.173359	+	0.500350i
$560$	18.7854	+	0.973194i	0.793829	+	0.0411250i
$561$			4.65118i			0.196373i
$562$	−40.5741	−	12.5312i	−1.71152	−	0.528598i
$563$	−1.09528	+	1.09528i	−0.0461608	+	0.0461608i	−0.729810	−	0.683650i	$-0.760392\pi$
$563$	−1.09528	+	1.09528i	−0.0461608	+	0.0461608i	0.683650	+	0.729810i	$0.260392\pi$
$564$	−4.29497	+	6.28996i	−0.180851	+	0.264855i
$565$	34.5774	+	15.6216i	1.45468	+	0.657205i
$566$	−13.6459	−	25.8415i	−0.573581	−	1.08620i
$567$	−5.53286	+	5.53286i	−0.232358	+	0.232358i
$568$	−3.84093	+	3.05635i	−0.161162	+	0.128242i
$569$		−	26.0963i		−	1.09401i	−0.837129	−	0.547006i	$-0.815767\pi$
$569$		−	26.0963i		−	1.09401i	0.837129	−	0.547006i	$-0.184233\pi$
$570$	−0.169061	+	0.191250i	−0.00708117	+	0.00801057i
$571$		−	38.4087i		−	1.60735i	−0.595066	−	0.803677i	$-0.702874\pi$
$571$		−	38.4087i		−	1.60735i	0.595066	−	0.803677i	$-0.297126\pi$
$572$	37.2136	+	5.51937i	1.55598	+	0.230776i
$573$	8.10423	+	8.10423i	0.338559	+	0.338559i
$574$	17.0403	−	8.99834i	0.711250	−	0.375584i
$575$	−1.33708	+	21.1020i	−0.0557601	+	0.880013i
$576$	18.4692	+	4.25690i	0.769550	+	0.177371i
$577$	7.40764	+	7.40764i	0.308384	+	0.308384i	0.844282	−	0.535898i	$-0.180027\pi$
$577$	7.40764	+	7.40764i	0.308384	+	0.308384i	−0.535898	+	0.844282i	$0.680027\pi$
$578$	−21.2685	−	6.56872i	−0.884651	−	0.273223i
$579$			8.21169i			0.341266i
$580$	3.33105	−	13.7278i	0.138314	−	0.570017i
$581$	−30.6264			−1.27060
$582$	−3.10788	+	10.0628i	−0.128826	+	0.417117i
$583$	−36.2262	−	36.2262i	−1.50034	−	1.50034i
$584$	2.65507	−	23.3409i	0.109868	−	0.965853i
$585$	−13.8730	−	13.1295i	−0.573580	−	0.542839i
$586$	7.99186	+	15.1343i	0.330141	+	0.625194i
$587$	2.55282	−	2.55282i	0.105366	−	0.105366i	−0.652458	−	0.757825i	$-0.726262\pi$
$587$	2.55282	−	2.55282i	0.105366	−	0.105366i	0.757825	+	0.652458i	$0.226262\pi$
$588$	0.758180	+	4.02272i	0.0312668	+	0.165894i
$589$		−	0.564904i		−	0.0232765i
$590$	33.3045	−	2.05100i	1.37112	−	0.0844382i
$591$	−5.14802			−0.211761
$592$	−7.38094	+	16.8519i	−0.303355	+	0.692611i
$593$	11.4211	−	11.4211i	0.469008	−	0.469008i	−0.432585	−	0.901593i	$-0.642398\pi$
$593$	11.4211	−	11.4211i	0.469008	−	0.469008i	0.901593	+	0.432585i	$0.142398\pi$
$594$	27.8222	−	14.6918i	1.14156	−	0.602813i
$595$	−1.86479	−	4.93835i	−0.0764489	−	0.202453i
$596$	−15.7194	−	10.7337i	−0.643891	−	0.439668i
$597$	−1.04324	+	1.04324i	−0.0426969	+	0.0426969i
$598$	17.3842	+	12.7575i	0.710894	+	0.521691i
$599$	−32.8264			−1.34125			−0.670625	−	0.741796i	$-0.733974\pi$
$599$	−32.8264			−1.34125			−0.670625	+	0.741796i	$0.733974\pi$
$600$	6.42406	+	9.21388i	0.262261	+	0.376155i
$601$	4.74265			0.193457			0.0967284	−	0.995311i	$-0.469162\pi$
$601$	4.74265			0.193457			0.0967284	+	0.995311i	$0.469162\pi$
$602$	9.86767	+	3.04761i	0.402176	+	0.124211i
$603$	−15.1051	−	15.1051i	−0.615129	−	0.615129i
$604$	−6.12721	−	4.18384i	−0.249313	−	0.170238i
$605$	33.9254	−	12.8107i	1.37927	−	0.520829i
$606$	9.91070	+	18.7681i	0.402594	+	0.762401i
$607$	12.6061	+	12.6061i	0.511664	+	0.511664i	0.915036	−	0.403372i	$-0.132162\pi$
$607$	12.6061	+	12.6061i	0.511664	+	0.511664i	−0.403372	+	0.915036i	$0.632162\pi$
$608$	0.0419456	+	0.573385i	0.00170112	+	0.0232539i
$609$	−5.27620			−0.213802
$610$	−0.290951	−	4.72452i	−0.0117803	−	0.191290i
$611$	5.65974	−	16.3352i	0.228968	−	0.660850i
$612$	−0.985112	−	5.22676i	−0.0398208	−	0.211279i
$613$	−18.6468	+	18.6468i	−0.753135	+	0.753135i	−0.975063	−	0.221928i	$-0.928765\pi$
$613$	−18.6468	+	18.6468i	−0.753135	+	0.753135i	0.221928	+	0.975063i	$0.428765\pi$
$614$	12.4270	+	23.5334i	0.501515	+	0.949729i
$615$	10.4862	+	4.73754i	0.422846	+	0.191036i
$616$	3.50748	−	30.8344i	0.141320	−	1.24235i
$617$	−9.07508	−	9.07508i	−0.365349	−	0.365349i	0.500429	−	0.865778i	$-0.333176\pi$
$617$	−9.07508	−	9.07508i	−0.365349	−	0.365349i	−0.865778	+	0.500429i	$0.833176\pi$
$618$	12.0663	+	3.72666i	0.485378	+	0.149908i
$619$		−	38.4906i		−	1.54707i	−0.633754	−	0.773535i	$-0.718487\pi$
$619$		−	38.4906i		−	1.54707i	0.633754	−	0.773535i	$-0.281513\pi$
$620$	−24.1566	−	5.86159i	−0.970153	−	0.235407i
$621$	18.0337			0.723666
$622$	−16.7362	−	5.16893i	−0.671059	−	0.207255i
$623$	9.66047	−	9.66047i	0.387039	−	0.387039i
$624$	11.4460	−	0.447157i	0.458207	−	0.0179006i
$625$	3.15547	−	24.8001i	0.126219	−	0.992002i
$626$	16.1082	−	8.50609i	0.643811	−	0.339972i
$627$	0.297779	+	0.297779i	0.0118921	+	0.0118921i
$628$	7.09337	−	1.33692i	0.283056	−	0.0533489i
$629$	5.16277			0.205853
$630$	−10.4355	+	11.8052i	−0.415762	+	0.470330i
$631$	36.4065			1.44932			0.724660	−	0.689107i	$-0.241997\pi$
$631$	36.4065			1.44932			0.724660	+	0.689107i	$0.241997\pi$
$632$	−3.17015	+	2.52259i	−0.126102	+	0.100343i
$633$	2.39593	+	2.39593i	0.0952296	+	0.0952296i
$634$	−17.4260	+	9.20197i	−0.692073	+	0.365457i
$635$	13.3483	+	6.03059i	0.529712	+	0.239317i
$636$	−12.8822	−	8.79638i	−0.510814	−	0.348799i
$637$	−4.05711	−	8.35898i	−0.160748	−	0.331195i
$638$	−22.2672	−	6.87719i	−0.881567	−	0.272270i
$639$		−	4.11156i		−	0.162651i
$640$	24.9545	+	4.15591i	0.986414	+	0.164277i
$641$	−13.3606			−0.527712			−0.263856	−	0.964562i	$-0.584994\pi$
$641$	−13.3606			−0.527712			−0.263856	+	0.964562i	$0.584994\pi$
$642$	−6.24970	+	20.2355i	−0.246656	+	0.798632i
$643$	16.9126	+	16.9126i	0.666968	+	0.666968i	0.957013	−	0.290045i	$-0.0936702\pi$
$643$	16.9126	+	16.9126i	0.666968	+	0.666968i	−0.290045	+	0.957013i	$0.593670\pi$
$644$	10.0304	−	14.6895i	0.395253	−	0.578846i
$645$	2.17854	+	5.76923i	0.0857800	+	0.227163i
$646$	0.142666	−	0.0753364i	0.00561312	−	0.00296407i
$647$	−20.3051	−	20.3051i	−0.798274	−	0.798274i	0.184549	−	0.982823i	$-0.440918\pi$
$647$	−20.3051	−	20.3051i	−0.798274	−	0.798274i	−0.982823	+	0.184549i	$0.940918\pi$
$648$	−8.23442	+	6.55239i	−0.323479	+	0.257402i
$649$		−	55.0490i		−	2.16086i
$650$	−19.5593	−	16.3534i	−0.767179	−	0.641433i
$651$			9.28443i			0.363885i
$652$	−1.98627	−	10.5387i	−0.0777883	−	0.412725i
$653$	21.8481	+	21.8481i	0.854982	+	0.854982i	0.990742	−	0.135760i	$-0.0433475\pi$
$653$	21.8481	+	21.8481i	0.854982	+	0.854982i	−0.135760	+	0.990742i	$0.543348\pi$
$654$	9.07304	+	17.1818i	0.354784	+	0.671861i
$655$	16.4694	+	43.6144i	0.643512	+	1.70416i
$656$	24.1383	−	9.43405i	0.942444	−	0.368338i
$657$	13.9138	+	13.9138i	0.542831	+	0.542831i
$658$	−13.6257	−	4.20827i	−0.531185	−	0.164055i
$659$	19.3163			0.752456			0.376228	−	0.926527i	$-0.377221\pi$
$659$	19.3163			0.752456			0.376228	+	0.926527i	$0.377221\pi$
$660$	15.8235	−	9.64388i	0.615930	−	0.375387i
$661$		−	5.24920i		−	0.204170i	−0.994776	−	0.102085i	$-0.967449\pi$
$661$		−	5.24920i		−	0.204170i	0.994776	−	0.102085i	$-0.0325514\pi$
$662$	11.2158	−	36.3148i	0.435913	−	1.41142i
$663$	−1.40358	−	2.89185i	−0.0545107	−	0.112310i
$664$	−40.9253	−	4.65533i	−1.58821	−	0.180662i
$665$	−0.435552	−	0.196777i	−0.0168900	−	0.00763067i
$666$	−7.19590	−	13.6270i	−0.278835	−	0.528036i
$667$	−9.44535	−	9.44535i	−0.365725	−	0.365725i
$668$	24.6375	−	4.64355i	0.953254	−	0.179664i
$669$	−13.5584			−0.524198
$670$	−21.3628	−	18.8843i	−0.825318	−	0.729564i
$671$	−7.80917			−0.301470
$672$	−0.689394	−	9.42382i	−0.0265939	−	0.363532i
$673$	−9.09875	−	9.09875i	−0.350731	−	0.350731i	0.509650	−	0.860382i	$-0.329775\pi$
$673$	−9.09875	−	9.09875i	−0.350731	−	0.350731i	−0.860382	+	0.509650i	$0.829775\pi$
$674$	−11.1055	−	21.0307i	−0.427769	−	0.810074i
$675$	−21.2795	−	1.34833i	−0.819048	−	0.0518972i
$676$	−24.8030	+	7.79829i	−0.953960	+	0.299934i
$677$	11.0809	−	11.0809i	0.425873	−	0.425873i	−0.461347	−	0.887220i	$-0.652634\pi$
$677$	11.0809	−	11.0809i	0.425873	−	0.425873i	0.887220	+	0.461347i	$0.152634\pi$
$678$	5.62431	−	18.2106i	0.216000	−	0.699374i
$679$	−19.7193			−0.756759
$680$	−1.74122	−	6.88244i	−0.0667727	−	0.263930i
$681$			10.9060i			0.417920i
$682$	−12.1017	+	39.1832i	−0.463396	+	1.50040i
$683$	10.4003	+	10.4003i	0.397957	+	0.397957i	0.877512	−	0.479555i	$-0.159202\pi$
$683$	10.4003	+	10.4003i	0.397957	+	0.397957i	−0.479555	+	0.877512i	$0.659202\pi$
$684$	−0.397698	−	0.271560i	−0.0152064	−	0.0103834i
$685$	−0.344382	−	0.155587i	−0.0131582	−	0.00594468i
$686$	−25.1880	+	13.3008i	−0.961682	+	0.507827i
$687$	5.47199	−	5.47199i	0.208769	−	0.208769i
$688$	12.7227	+	5.57236i	0.485047	+	0.212444i
$689$	33.4555	+	11.5915i	1.27455	+	0.441602i
$690$	10.6012	−	0.652855i	0.403580	−	0.0248538i
$691$	−7.44985			−0.283406			−0.141703	−	0.989909i	$-0.545258\pi$
$691$	−7.44985			−0.283406			−0.141703	+	0.989909i	$0.545258\pi$
$692$	4.46466	+	23.6884i	0.169721	+	0.900496i
$693$	18.3808	+	18.3808i	0.698231	+	0.698231i
$694$	−13.7999	+	7.28719i	−0.523837	+	0.276618i
$695$	42.2356	−	15.9487i	1.60209	−	0.604969i
$696$	−7.05044	−	0.802001i	−0.267246	−	0.0303998i
$697$	−5.14262	−	5.14262i	−0.194791	−	0.194791i
$698$	−9.63310	+	31.1904i	−0.364618	+	1.18057i
$699$	−2.69634			−0.101985
$700$	−12.9340	+	16.5834i	−0.488860	+	0.626795i
$701$	26.0315			0.983196			0.491598	−	0.870822i	$-0.336413\pi$
$701$	26.0315			0.983196			0.491598	+	0.870822i	$0.336413\pi$
$702$	−12.8648	+	17.5305i	−0.485550	+	0.661645i
$703$	0.330532	−	0.330532i	0.0124662	−	0.0124662i
$704$	9.37389	−	40.6701i	0.353292	−	1.53281i
$705$	−3.00822	−	7.96640i	−0.113296	−	0.300032i
$706$	11.6284	+	22.0209i	0.437641	+	0.828769i
$707$	−28.0999	+	28.0999i	−1.05680	+	1.05680i
$708$	−3.10442	−	16.4713i	−0.116671	−	0.619029i
$709$	29.8029			1.11927			0.559636	−	0.828738i	$-0.310941\pi$
$709$	29.8029			1.11927			0.559636	+	0.828738i	$0.310941\pi$
$710$	−0.337326	−	5.47756i	−0.0126596	−	0.205569i
$711$		−	3.39352i		−	0.127267i
$712$	14.3775	−	11.4406i	0.538818	−	0.428755i
$713$	−16.6208	+	16.6208i	−0.622454	+	0.622454i
$714$	−2.34478	+	1.23819i	−0.0877510	+	0.0463379i
$715$	−28.9118	+	30.5491i	−1.08124	+	1.14247i
$716$	32.2828	+	22.0437i	1.20647	+	0.823810i
$717$	8.32952	+	8.32952i	0.311072	+	0.311072i
$718$	1.73676	+	0.536394i	0.0648152	+	0.0200181i
$719$	−3.67225			−0.136952			−0.0684760	−	0.997653i	$-0.521814\pi$
$719$	−3.67225			−0.136952			−0.0684760	+	0.997653i	$0.521814\pi$
$720$	−15.7392	+	14.1887i	−0.586564	+	0.528782i
$721$			23.6455i			0.880603i
$722$	−7.92490	+	25.6595i	−0.294934	+	0.954949i
$723$	−5.27837	−	5.27837i	−0.196305	−	0.196305i
$724$	18.5131	+	12.6413i	0.688033	+	0.469809i
$725$	10.4392	+	11.8516i	0.387701	+	0.440157i
$726$	−8.50607	−	16.1081i	−0.315690	−	0.597828i
$727$	20.5737	+	20.5737i	0.763037	+	0.763037i	0.976870	−	0.213833i	$-0.0685950\pi$
$727$	20.5737	+	20.5737i	0.763037	+	0.763037i	−0.213833	+	0.976870i	$0.568595\pi$
$728$	7.12414	+	20.2296i	0.264038	+	0.749760i
$729$			1.34635i			0.0498646i
$730$	19.6780	+	17.3949i	0.728316	+	0.643816i
$731$		−	3.89772i		−	0.144162i
$732$	−2.33659	+	0.440389i	−0.0863630	+	0.0162772i
$733$	12.1861	−	12.1861i	0.450105	−	0.450105i	−0.445284	−	0.895389i	$-0.646897\pi$
$733$	12.1861	−	12.1861i	0.450105	−	0.450105i	0.895389	+	0.445284i	$0.146897\pi$
$734$	−5.35918	+	2.82998i	−0.197811	+	0.104456i
$735$	−4.17082	−	1.88432i	−0.153843	−	0.0695041i
$736$	15.6362	−	18.1045i	0.576358	−	0.667340i
$737$	−33.2622	+	33.2622i	−1.22523	+	1.22523i
$738$	−6.40603	+	20.7417i	−0.235809	+	0.763512i
$739$		−	40.3506i		−	1.48432i	−0.670223	−	0.742160i	$-0.733802\pi$
$739$		−	40.3506i		−	1.48432i	0.670223	−	0.742160i	$-0.266198\pi$
$740$	−10.7046	−	17.5640i	−0.393510	−	0.645665i
$741$	−0.275003	−	0.0952820i	−0.0101025	−	0.00350027i
$742$	8.61881	−	27.9063i	0.316407	−	1.02447i
$743$	28.7552	+	28.7552i	1.05493	+	1.05493i	0.998401	+	0.0565244i	$0.0180019\pi$
$743$	28.7552	+	28.7552i	1.05493	+	1.05493i	0.0565244	+	0.998401i	$0.481998\pi$
$744$	−1.41127	+	12.4065i	−0.0517396	+	0.454846i
$745$	19.9090	−	7.51791i	0.729410	−	0.275435i
$746$	−22.1880	+	11.7166i	−0.812362	+	0.428977i
$747$	24.3961	−	24.3961i	0.892608	−	0.892608i
$748$	−11.5096	+	2.16927i	−0.420832	+	0.0793162i
$749$	−39.6541			−1.44893
$750$	−12.5581	−	0.0222617i	−0.458555	−	0.000812882i
$751$			15.9959i			0.583698i	0.956464	+	0.291849i	$0.0942704\pi$
$751$			15.9959i			0.583698i	−0.956464	+	0.291849i	$0.905730\pi$
$752$	−17.5680	−	7.69455i	−0.640638	−	0.280592i
$753$	7.19731	+	7.19731i	0.262285	+	0.262285i
$754$	15.9199	−	2.44371i	0.579767	−	0.0889947i
$755$	7.76027	−	2.93038i	0.282425	−	0.106648i
$756$	14.8130	+	10.1148i	0.538745	+	0.367871i
$757$	−17.8098	+	17.8098i	−0.647308	+	0.647308i	−0.952342	−	0.305033i	$-0.901332\pi$
$757$	−17.8098	+	17.8098i	−0.647308	+	0.647308i	0.305033	+	0.952342i	$0.401332\pi$
$758$	−26.8774	−	8.30104i	−0.976232	−	0.301507i
$759$		−	17.5227i		−	0.636034i
$760$	−0.552106	−	0.329153i	−0.0200270	−	0.0119396i
$761$			17.5187i			0.635053i	0.948249	+	0.317526i	$0.102852\pi$
$761$			17.5187i			0.635053i	−0.948249	+	0.317526i	$0.897148\pi$
$762$	2.17122	−	7.03007i	0.0786551	−	0.254672i
$763$	−25.7249	+	25.7249i	−0.931302	+	0.931302i
$764$	−16.2746	+	23.8341i	−0.588795	+	0.862287i
$765$	5.41919	+	2.44831i	0.195931	+	0.0885190i
$766$	−3.44383	+	1.81855i	−0.124430	+	0.0657069i
$767$	16.6121	+	34.2264i	0.599829	+	1.23585i
$768$	0.511238	−	12.6976i	0.0184477	−	0.458185i
$769$	0.804873			0.0290244			0.0145122	−	0.999895i	$-0.495380\pi$
$769$	0.804873			0.0290244			0.0145122	+	0.999895i	$0.495380\pi$
$770$	25.9956	+	22.9796i	0.936816	+	0.828126i
$771$			5.20675i			0.187516i
$772$	−20.3203	+	3.82986i	−0.731343	+	0.137840i
$773$	−9.62801	+	9.62801i	−0.346296	+	0.346296i	−0.858728	−	0.512432i	$-0.828745\pi$
$773$	−9.62801	+	9.62801i	−0.346296	+	0.346296i	0.512432	+	0.858728i	$0.328745\pi$
$774$	−10.2880	+	5.43267i	−0.369793	+	0.195273i
$775$	20.8550	−	18.3696i	0.749134

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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.417327 + 1.35124i) q^{2} +(-0.561614 + 0.561614i) q^{3} +(-1.65168 - 1.12781i) q^{4} +(2.09189 - 0.789927i) q^{5} +(-0.524497 - 0.993250i) q^{6} +(1.48711 - 1.48711i) q^{7} +(2.21323 - 1.76114i) q^{8} +2.36918i q^{9} +O(q^{10})\)	\(q+(-0.417327 + 1.35124i) q^{2} +(-0.561614 + 0.561614i) q^{3} +(-1.65168 - 1.12781i) q^{4} +(2.09189 - 0.789927i) q^{5} +(-0.524497 - 0.993250i) q^{6} +(1.48711 - 1.48711i) q^{7} +(2.21323 - 1.76114i) q^{8} +2.36918i q^{9} +(0.194375 + 3.15630i) q^{10} +5.21705 q^{11} +(1.56100 - 0.294209i) q^{12} +(-3.24368 + 1.57435i) q^{13} +(1.38883 + 2.63005i) q^{14} +(-0.731203 + 1.61847i) q^{15} +(1.45607 + 3.72557i) q^{16} +(0.793724 - 0.793724i) q^{17} +(-3.20132 - 0.988721i) q^{18} -0.101632i q^{19} +(-4.34602 - 1.05456i) q^{20} +1.67036i q^{21} +(-2.17721 + 7.04946i) q^{22} +(-2.99025 + 2.99025i) q^{23} +(-0.253901 + 2.23206i) q^{24} +(3.75203 - 3.30488i) q^{25} +(-0.773642 - 5.03999i) q^{26} +(-3.01541 - 3.01541i) q^{27} +(-4.13341 + 0.779042i) q^{28} +3.15871i q^{29} +(-1.88179 - 1.66346i) q^{30} +5.55833 q^{31} +(-5.64178 + 0.412721i) q^{32} +(-2.92997 + 2.92997i) q^{33} +(0.741267 + 1.40375i) q^{34} +(1.93617 - 4.28558i) q^{35} +(2.67199 - 3.91312i) q^{36} +(3.25224 + 3.25224i) q^{37} +(0.137329 + 0.0424138i) q^{38} +(0.937519 - 2.70587i) q^{39} +(3.23867 - 5.43240i) q^{40} -6.47910i q^{41} +(-2.25706 - 0.697087i) q^{42} +(2.45533 - 2.45533i) q^{43} +(-8.61688 - 5.88386i) q^{44} +(1.87148 + 4.95607i) q^{45} +(-2.79263 - 5.28845i) q^{46} +(-3.39043 + 3.39043i) q^{47} +(-2.91008 - 1.27458i) q^{48} +2.57701i q^{49} +(2.89986 + 6.44910i) q^{50} +0.891534i q^{51} +(7.13307 + 1.05795i) q^{52} +(-6.94382 - 6.94382i) q^{53} +(5.33294 - 2.81612i) q^{54} +(10.9135 - 4.12109i) q^{55} +(0.672311 - 5.91032i) q^{56} +(0.0570780 + 0.0570780i) q^{57} +(-4.26816 - 1.31821i) q^{58} -10.5517i q^{59} +(3.03304 - 1.84853i) q^{60} -1.49686 q^{61} +(-2.31964 + 7.51061i) q^{62} +(3.52323 + 3.52323i) q^{63} +(1.79678 - 7.79561i) q^{64} +(-5.54180 + 5.85563i) q^{65} +(-2.73632 - 5.18183i) q^{66} +(-6.37568 + 6.37568i) q^{67} +(-2.20615 + 0.415803i) q^{68} -3.35874i q^{69} +(4.98282 + 4.40470i) q^{70} -1.73544 q^{71} +(4.17245 + 5.24354i) q^{72} +(5.87285 - 5.87285i) q^{73} +(-5.75179 + 3.03730i) q^{74} +(-0.251124 + 3.96327i) q^{75} +(-0.114622 + 0.167863i) q^{76} +(7.75832 - 7.75832i) q^{77} +(3.26502 + 2.39604i) q^{78} -1.43236 q^{79} +(5.98888 + 6.64330i) q^{80} -3.72054 q^{81} +(8.75480 + 2.70390i) q^{82} +(-10.2973 - 10.2973i) q^{83} +(1.88386 - 2.75890i) q^{84} +(1.03340 - 2.28737i) q^{85} +(2.29306 + 4.34241i) q^{86} +(-1.77398 - 1.77398i) q^{87} +(11.5465 - 9.18794i) q^{88} +6.49614 q^{89} +(-7.47783 + 0.460509i) q^{90} +(-2.48247 + 7.16493i) q^{91} +(8.31138 - 1.56649i) q^{92} +(-3.12164 + 3.12164i) q^{93} +(-3.16635 - 5.99618i) q^{94} +(-0.0802819 - 0.212603i) q^{95} +(2.93671 - 3.40029i) q^{96} +(-6.63009 - 6.63009i) q^{97} +(-3.48215 - 1.07545i) q^{98} +12.3601i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 24 q^{12} - 4 q^{16} - 40 q^{17} - 36 q^{22} + 44 q^{26} + 24 q^{30} + 28 q^{36} + 16 q^{38} - 44 q^{40} + 8 q^{42} - 44 q^{48} + 56 q^{52} - 48 q^{53} - 64 q^{56} + 80 q^{61} + 20 q^{62} - 72 q^{65} - 24 q^{66} - 76 q^{68} - 112 q^{77} - 20 q^{78} + 80 q^{81} + 52 q^{82} - 152 q^{88} - 64 q^{90} + 56 q^{92}+O(q^{100}) \) 64 * q - 24 * q^12 - 4 * q^16 - 40 * q^17 - 36 * q^22 + 44 * q^26 + 24 * q^30 + 28 * q^36 + 16 * q^38 - 44 * q^40 + 8 * q^42 - 44 * q^48 + 56 * q^52 - 48 * q^53 - 64 * q^56 + 80 * q^61 + 20 * q^62 - 72 * q^65 - 24 * q^66 - 76 * q^68 - 112 * q^77 - 20 * q^78 + 80 * q^81 + 52 * q^82 - 152 * q^88 - 64 * q^90 + 56 * q^92

Introduction

L-functions

Modular forms

Varieties

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