LMFDB - Embedded newform 260.2.p.d.103.4

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			103.4
Character	$\chi$	$=$	260.103
Dual form			260.2.p.d.207.4

$q$-expansion

$f(q)$	$=$	$q+(-1.31170 + 0.528615i) q^{2} +(-0.834468 + 0.834468i) q^{3} +(1.44113 - 1.38677i) q^{4} +(-0.462357 - 2.18774i) q^{5} +(0.653463 - 1.53569i) q^{6} +(-1.21162 + 1.21162i) q^{7} +(-1.15727 + 2.58084i) q^{8} +1.60733i q^{9} +O(q^{10})$	\(q+(-1.31170 + 0.528615i) q^{2} +(-0.834468 + 0.834468i) q^{3} +(1.44113 - 1.38677i) q^{4} +(-0.462357 - 2.18774i) q^{5} +(0.653463 - 1.53569i) q^{6} +(-1.21162 + 1.21162i) q^{7} +(-1.15727 + 2.58084i) q^{8} +1.60733i q^{9} +(1.76295 + 2.62526i) q^{10} +0.135866 q^{11} +(-0.0453632 + 2.35980i) q^{12} +(1.01757 + 3.45898i) q^{13} +(0.948804 - 2.22976i) q^{14} +(2.21142 + 1.43978i) q^{15} +(0.153730 - 3.99704i) q^{16} +(-1.10965 + 1.10965i) q^{17} +(-0.849657 - 2.10834i) q^{18} +6.12150i q^{19} +(-3.70022 - 2.51165i) q^{20} -2.02211i q^{21} +(-0.178217 + 0.0718210i) q^{22} +(-4.72792 + 4.72792i) q^{23} +(-1.18792 - 3.11933i) q^{24} +(-4.57245 + 2.02304i) q^{25} +(-3.16322 - 3.99926i) q^{26} +(-3.84467 - 3.84467i) q^{27} +(-0.0658656 + 3.42634i) q^{28} -4.39615i q^{29} +(-3.66182 - 0.719575i) q^{30} -3.12087 q^{31} +(1.91125 + 5.32420i) q^{32} +(-0.113376 + 0.113376i) q^{33} +(0.868956 - 2.04211i) q^{34} +(3.21091 + 2.09051i) q^{35} +(2.22900 + 2.31637i) q^{36} +(6.39942 + 6.39942i) q^{37} +(-3.23592 - 8.02960i) q^{38} +(-3.73554 - 2.03728i) q^{39} +(6.18129 + 1.33855i) q^{40} +2.92506i q^{41} +(1.06892 + 2.65241i) q^{42} +(-1.51561 + 1.51561i) q^{43} +(0.195802 - 0.188416i) q^{44} +(3.51642 - 0.743158i) q^{45} +(3.70239 - 8.70089i) q^{46} +(8.14297 - 8.14297i) q^{47} +(3.20712 + 3.46369i) q^{48} +4.06397i q^{49} +(4.92830 - 5.07069i) q^{50} -1.85194i q^{51} +(6.26327 + 3.57372i) q^{52} +(-5.39849 - 5.39849i) q^{53} +(7.07541 + 3.01072i) q^{54} +(-0.0628188 - 0.297241i) q^{55} +(-1.72481 - 4.52915i) q^{56} +(-5.10820 - 5.10820i) q^{57} +(2.32387 + 5.76645i) q^{58} +5.47588i q^{59} +(5.18360 - 0.991824i) q^{60} +11.7875 q^{61} +(4.09366 - 1.64974i) q^{62} +(-1.94746 - 1.94746i) q^{63} +(-5.32144 - 5.97346i) q^{64} +(7.09689 - 3.82547i) q^{65} +(0.0887836 - 0.208648i) q^{66} +(7.10562 - 7.10562i) q^{67} +(-0.0603226 + 3.13799i) q^{68} -7.89060i q^{69} +(-5.31683 - 1.04480i) q^{70} -4.49049 q^{71} +(-4.14825 - 1.86011i) q^{72} +(-6.04423 + 6.04423i) q^{73} +(-11.7770 - 5.01132i) q^{74} +(2.12741 - 5.50372i) q^{75} +(8.48913 + 8.82190i) q^{76} +(-0.164618 + 0.164618i) q^{77} +(5.97685 + 0.697647i) q^{78} -0.944179 q^{79} +(-8.81559 + 1.51174i) q^{80} +1.59452 q^{81} +(-1.54623 - 3.83681i) q^{82} +(-4.61273 - 4.61273i) q^{83} +(-2.80420 - 2.91413i) q^{84} +(2.94069 + 1.91458i) q^{85} +(1.18686 - 2.78920i) q^{86} +(3.66845 + 3.66845i) q^{87} +(-0.157234 + 0.350649i) q^{88} -3.22796 q^{89} +(-4.21966 + 2.83364i) q^{90} +(-5.42386 - 2.95805i) q^{91} +(-0.257018 + 13.3701i) q^{92} +(2.60427 - 2.60427i) q^{93} +(-6.37667 + 14.9857i) q^{94} +(13.3923 - 2.83032i) q^{95} +(-6.03775 - 2.84800i) q^{96} +(-2.31733 - 2.31733i) q^{97} +(-2.14827 - 5.33073i) q^{98} +0.218382i 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 $

$2$	−1.31170	+	0.528615i	−0.927515	+	0.373787i
$2$	−1.31170	+	0.528615i	−0.927515	+	0.373787i
$3$	−0.834468	+	0.834468i	−0.481780	+	0.481780i	−0.905700	−	0.423920i	$-0.860654\pi$
$3$	−0.834468	+	0.834468i	−0.481780	+	0.481780i	0.423920	+	0.905700i	$0.360654\pi$
$4$	1.44113	−	1.38677i	0.720567	−	0.693386i
$5$	−0.462357	−	2.18774i	−0.206772	−	0.978389i
$5$	−0.462357	−	2.18774i	−0.206772	−	0.978389i
$6$	0.653463	−	1.53569i	0.266775	−	0.626941i
$7$	−1.21162	+	1.21162i	−0.457948	+	0.457948i	−0.897981	−	0.440033i	$-0.854967\pi$
$7$	−1.21162	+	1.21162i	−0.457948	+	0.457948i	0.440033	+	0.897981i	$0.354967\pi$
$8$	−1.15727	+	2.58084i	−0.409158	+	0.912464i
$9$			1.60733i			0.535776i
$10$	1.76295	+	2.62526i	0.557493	+	0.830181i
$11$	0.135866			0.0409653			0.0204826	−	0.999790i	$-0.493480\pi$
$11$	0.135866			0.0409653			0.0204826	+	0.999790i	$0.493480\pi$
$12$	−0.0453632	+	2.35980i	−0.0130952	+	0.681214i
$13$	1.01757	+	3.45898i	0.282223	+	0.959349i
$13$	1.01757	+	3.45898i	0.282223	+	0.959349i
$14$	0.948804	−	2.22976i	0.253578	−	0.595928i
$15$	2.21142	+	1.43978i	0.570987	+	0.371750i
$16$	0.153730	−	3.99704i	0.0384325	−	0.999261i
$17$	−1.10965	+	1.10965i	−0.269130	+	0.269130i	−0.828750	−	0.559620i	$-0.810947\pi$
$17$	−1.10965	+	1.10965i	−0.269130	+	0.269130i	0.559620	+	0.828750i	$0.310947\pi$
$18$	−0.849657	−	2.10834i	−0.200266	−	0.496940i
$19$			6.12150i			1.40437i	0.711995	+	0.702185i	$0.247792\pi$
$19$			6.12150i			1.40437i	−0.711995	+	0.702185i	$0.752208\pi$
$20$	−3.70022	−	2.51165i	−0.827394	−	0.561622i
$21$		−	2.02211i		−	0.441261i
$22$	−0.178217	+	0.0718210i	−0.0379959	+	0.0153123i
$23$	−4.72792	+	4.72792i	−0.985840	+	0.985840i	−0.999901	−	0.0140607i	$-0.995524\pi$
$23$	−4.72792	+	4.72792i	−0.985840	+	0.985840i	0.0140607	+	0.999901i	$0.495524\pi$
$24$	−1.18792	−	3.11933i	−0.242483	−	0.636731i
$25$	−4.57245	+	2.02304i	−0.914491	+	0.404607i
$26$	−3.16322	−	3.99926i	−0.620358	−	0.784319i
$27$	−3.84467	−	3.84467i	−0.739906	−	0.739906i
$28$	−0.0658656	+	3.42634i	−0.0124474	+	0.647517i
$29$		−	4.39615i		−	0.816345i	−0.912905	−	0.408172i	$-0.866166\pi$
$29$		−	4.39615i		−	0.816345i	0.912905	−	0.408172i	$-0.133834\pi$
$30$	−3.66182	−	0.719575i	−0.668554	−	0.131376i
$31$	−3.12087			−0.560525			−0.280263	−	0.959923i	$-0.590422\pi$
$31$	−3.12087			−0.560525			−0.280263	+	0.959923i	$0.590422\pi$
$32$	1.91125	+	5.32420i	0.337864	+	0.941195i
$33$	−0.113376	+	0.113376i	−0.0197363	+	0.0197363i
$34$	0.868956	−	2.04211i	0.149025	−	0.350219i
$35$	3.21091	+	2.09051i	0.542742	+	0.353360i
$36$	2.22900	+	2.31637i	0.371499	+	0.386062i
$37$	6.39942	+	6.39942i	1.05206	+	1.05206i	0.998568	+	0.0534895i	$0.0170344\pi$
$37$	6.39942	+	6.39942i	1.05206	+	1.05206i	0.0534895	+	0.998568i	$0.482966\pi$
$38$	−3.23592	−	8.02960i	−0.524935	−	1.30257i
$39$	−3.73554	−	2.03728i	−0.598165	−	0.326226i
$40$	6.18129	+	1.33855i	0.977347	+	0.211643i
$41$			2.92506i			0.456817i	0.973565	+	0.228409i	$0.0733522\pi$
$41$			2.92506i			0.456817i	−0.973565	+	0.228409i	$0.926648\pi$
$42$	1.06892	+	2.65241i	0.164937	+	0.409276i
$43$	−1.51561	+	1.51561i	−0.231128	+	0.231128i	−0.813163	−	0.582035i	$-0.802256\pi$
$43$	−1.51561	+	1.51561i	−0.231128	+	0.231128i	0.582035	+	0.813163i	$0.302256\pi$
$44$	0.195802	−	0.188416i	0.0295182	−	0.0284047i
$45$	3.51642	−	0.743158i	0.524197	−	0.110784i
$46$	3.70239	−	8.70089i	0.545887	−	1.28288i
$47$	8.14297	−	8.14297i	1.18777	−	1.18777i	0.210093	−	0.977681i	$-0.432623\pi$
$47$	8.14297	−	8.14297i	1.18777	−	1.18777i	0.977681	−	0.210093i	$-0.0673766\pi$
$48$	3.20712	+	3.46369i	0.462908	+	0.499940i
$49$			4.06397i			0.580567i
$50$	4.92830	−	5.07069i	0.696966	−	0.717104i
$51$		−	1.85194i		−	0.259323i
$52$	6.26327	+	3.57372i	0.868559	+	0.495585i
$53$	−5.39849	−	5.39849i	−0.741540	−	0.741540i	0.231334	−	0.972874i	$-0.425691\pi$
$53$	−5.39849	−	5.39849i	−0.741540	−	0.741540i	−0.972874	+	0.231334i	$0.925691\pi$
$54$	7.07541	+	3.01072i	0.962841	+	0.409707i
$55$	−0.0628188	−	0.297241i	−0.00847048	−	0.0400800i
$56$	−1.72481	−	4.52915i	−0.230488	−	0.605234i
$57$	−5.10820	−	5.10820i	−0.676597	−	0.676597i
$58$	2.32387	+	5.76645i	0.305139	+	0.757172i
$59$			5.47588i			0.712899i	0.934315	+	0.356449i	$0.116013\pi$
$59$			5.47588i			0.712899i	−0.934315	+	0.356449i	$0.883987\pi$
$60$	5.18360	−	0.991824i	0.669200	−	0.128044i
$61$	11.7875			1.50923			0.754616	−	0.656167i	$-0.227823\pi$
$61$	11.7875			1.50923			0.754616	+	0.656167i	$0.227823\pi$
$62$	4.09366	−	1.64974i	0.519895	−	0.209517i
$63$	−1.94746	−	1.94746i	−0.245357	−	0.245357i
$64$	−5.32144	−	5.97346i	−0.665180	−	0.746683i
$65$	7.09689	−	3.82547i	0.880261	−	0.474491i
$66$	0.0887836	−	0.208648i	0.0109285	−	0.0256828i
$67$	7.10562	−	7.10562i	0.868089	−	0.868089i	−0.124172	−	0.992261i	$-0.539627\pi$
$67$	7.10562	−	7.10562i	0.868089	−	0.868089i	0.992261	+	0.124172i	$0.0396273\pi$
$68$	−0.0603226	+	3.13799i	−0.00731519	+	0.380537i
$69$		−	7.89060i		−	0.949917i
$70$	−5.31683	−	1.04480i	−0.635483	−	0.124877i
$71$	−4.49049			−0.532923			−0.266461	−	0.963846i	$-0.585854\pi$
$71$	−4.49049			−0.532923			−0.266461	+	0.963846i	$0.585854\pi$
$72$	−4.14825	−	1.86011i	−0.488876	−	0.219217i
$73$	−6.04423	+	6.04423i	−0.707424	+	0.707424i	−0.965993	−	0.258569i	$-0.916749\pi$
$73$	−6.04423	+	6.04423i	−0.707424	+	0.707424i	0.258569	+	0.965993i	$0.416749\pi$
$74$	−11.7770	−	5.01132i	−1.36904	−	0.582554i
$75$	2.12741	−	5.50372i	0.245652	−	0.635515i
$76$	8.48913	+	8.82190i	0.973769	+	1.01194i
$77$	−0.164618	+	0.164618i	−0.0187600	+	0.0187600i
$78$	5.97685	+	0.697647i	0.676745	+	0.0789930i
$79$	−0.944179			−0.106228			−0.0531142	−	0.998588i	$-0.516915\pi$
$79$	−0.944179			−0.106228			−0.0531142	+	0.998588i	$0.516915\pi$
$80$	−8.81559	+	1.51174i	−0.985613	+	0.169017i
$81$	1.59452			0.177169
$82$	−1.54623	−	3.83681i	−0.170752	−	0.423705i
$83$	−4.61273	−	4.61273i	−0.506313	−	0.506313i	0.407079	−	0.913393i	$-0.366547\pi$
$83$	−4.61273	−	4.61273i	−0.506313	−	0.506313i	−0.913393	+	0.407079i	$0.866547\pi$
$84$	−2.80420	−	2.91413i	−0.305964	−	0.317958i
$85$	2.94069	+	1.91458i	0.318962	+	0.207665i
$86$	1.18686	−	2.78920i	0.127982	−	0.300767i
$87$	3.66845	+	3.66845i	0.393299	+	0.393299i
$88$	−0.157234	+	0.350649i	−0.0167613	+	0.0373793i
$89$	−3.22796			−0.342163			−0.171082	−	0.985257i	$-0.554726\pi$
$89$	−3.22796			−0.342163			−0.171082	+	0.985257i	$0.554726\pi$
$90$	−4.21966	+	2.83364i	−0.444791	+	0.298691i
$91$	−5.42386	−	2.95805i	−0.568575	−	0.310088i
$92$	−0.257018	+	13.3701i	−0.0267960	+	1.39393i
$93$	2.60427	−	2.60427i	0.270050	−	0.270050i
$94$	−6.37667	+	14.9857i	−0.657703	+	1.54565i
$95$	13.3923	−	2.83032i	1.37402	−	0.290384i
$96$	−6.03775	−	2.84800i	−0.616225	−	0.290673i
$97$	−2.31733	−	2.31733i	−0.235289	−	0.235289i	0.579607	−	0.814896i	$-0.303206\pi$
$97$	−2.31733	−	2.31733i	−0.235289	−	0.235289i	−0.814896	+	0.579607i	$0.803206\pi$
$98$	−2.14827	−	5.33073i	−0.217009	−	0.538485i
$99$			0.218382i			0.0219482i
$100$	−3.78402	+	9.25641i	−0.378402	+	0.925641i
$101$	2.63267			0.261960			0.130980	−	0.991385i	$-0.458188\pi$
$101$	2.63267			0.261960			0.130980	+	0.991385i	$0.458188\pi$
$102$	0.978961	+	2.42919i	0.0969316	+	0.240526i
$103$	7.36490	−	7.36490i	0.725685	−	0.725685i	−0.244072	−	0.969757i	$-0.578483\pi$
$103$	7.36490	−	7.36490i	0.725685	−	0.725685i	0.969757	+	0.244072i	$0.0784833\pi$
$104$	−10.1047	−	1.37680i	−0.990845	−	0.135006i
$105$	−4.42386	+	0.934936i	−0.431724	+	0.0912404i
$106$	9.93494	+	4.22750i	0.964967	+	0.410611i
$107$	11.9158	+	11.9158i	1.15194	+	1.15194i	0.986163	+	0.165780i	$0.0530141\pi$
$107$	11.9158	+	11.9158i	1.15194	+	1.15194i	0.165780	+	0.986163i	$0.446986\pi$
$108$	−10.8723	−	0.209003i	−1.04619	−	0.0201113i
$109$	1.57023			0.150401			0.0752004	−	0.997168i	$-0.476040\pi$
$109$	1.57023			0.150401			0.0752004	+	0.997168i	$0.476040\pi$
$110$	0.239526	+	0.356685i	0.0228379	+	0.0340086i
$111$	−10.6802			−1.01372
$112$	4.65662	+	5.02915i	0.440010	+	0.475210i
$113$	0.755135	+	0.755135i	0.0710371	+	0.0710371i	0.741733	−	0.670696i	$-0.234004\pi$
$113$	0.755135	+	0.755135i	0.0710371	+	0.0710371i	−0.670696	+	0.741733i	$0.734004\pi$
$114$	9.40071	+	4.00017i	0.880457	+	0.374651i
$115$	12.5295	+	8.15750i	1.16838	+	0.760691i
$116$	−6.09646	−	6.33544i	−0.566042	−	0.588231i
$117$	−5.55971	+	1.63557i	−0.513996	+	0.151208i
$118$	−2.89463	−	7.18273i	−0.266472	−	0.661224i
$119$		−	2.68894i		−	0.246495i
$120$	−6.27506	+	4.04111i	−0.572832	+	0.368901i
$121$	−10.9815			−0.998322
$122$	−15.4617	+	6.23103i	−1.39983	+	0.564131i
$123$	−2.44087	−	2.44087i	−0.220085	−	0.220085i
$124$	−4.49759	+	4.32794i	−0.403896	+	0.388660i
$125$	6.53999	+	9.06799i	0.584955	+	0.811066i
$126$	3.58395	+	1.52504i	0.319284	+	0.135861i
$127$	−15.1631	−	15.1631i	−1.34551	−	1.34551i	−0.890472	−	0.455037i	$-0.849626\pi$
$127$	−15.1631	−	15.1631i	−1.34551	−	1.34551i	−0.455037	−	0.890472i	$-0.650374\pi$
$128$	10.1378	+	5.02242i	0.896065	+	0.443923i
$129$		−	2.52945i		−	0.222706i
$130$	−7.28682	+	8.76940i	−0.639096	+	0.769127i
$131$			0.235056i			0.0205370i	0.999947	+	0.0102685i	$0.00326862\pi$
$131$			0.235056i			0.0205370i	−0.999947	+	0.0102685i	$0.996731\pi$
$132$	−0.00616333	+	0.320617i	−0.000536449	+	0.0279061i
$133$	−7.41691	−	7.41691i	−0.643128	−	0.643128i
$134$	−5.56433	+	13.0766i	−0.480685	+	1.12965i
$135$	−6.63354	+	10.1888i	−0.570924	+	0.876908i
$136$	−1.57966	−	4.14800i	−0.135455	−	0.355688i
$137$	−12.2710	−	12.2710i	−1.04838	−	1.04838i	−0.998768	−	0.0496147i	$-0.984201\pi$
$137$	−12.2710	−	12.2710i	−1.04838	−	1.04838i	−0.0496147	−	0.998768i	$-0.515799\pi$
$138$	4.17109	+	10.3501i	0.355067	+	0.881062i
$139$	19.6129			1.66354			0.831772	−	0.555117i	$-0.187327\pi$
$139$	19.6129			1.66354			0.831772	+	0.555117i	$0.187327\pi$
$140$	7.52640	−	1.44009i	0.636097	−	0.121710i
$141$			13.5901i			1.14449i
$142$	5.89019	−	2.37374i	0.494294	−	0.199200i
$143$	0.138254	+	0.469960i	0.0115613	+	0.0393000i
$144$	6.42456	+	0.247094i	0.535380	+	0.0205912i
$145$	−9.61766	+	2.03259i	−0.798703	+	0.168797i
$146$	4.73317	−	11.1233i	0.391720	−	0.920572i
$147$	−3.39125	−	3.39125i	−0.279706	−	0.279706i
$148$	18.0969	+	0.347884i	1.48756	+	0.0285959i
$149$	−2.39818			−0.196467			−0.0982333	−	0.995163i	$-0.531319\pi$
$149$	−2.39818			−0.196467			−0.0982333	+	0.995163i	$0.531319\pi$
$150$	0.118822	+	8.34383i	0.00970181	+	0.681271i
$151$	5.63264			0.458378			0.229189	−	0.973382i	$-0.426393\pi$
$151$	5.63264			0.458378			0.229189	+	0.973382i	$0.426393\pi$
$152$	−15.7986	−	7.08424i	−1.28144	−	0.574608i
$153$	−1.78357	−	1.78357i	−0.144193	−	0.144193i
$154$	0.128911	−	0.302950i	0.0103879	−	0.0244124i
$155$	1.44296	+	6.82767i	0.115901	+	0.548412i
$156$	−8.20865	+	2.24435i	−0.657218	+	0.179691i
$157$	−3.62360	+	3.62360i	−0.289195	+	0.289195i	−0.836762	−	0.547567i	$-0.815554\pi$
$157$	−3.62360	+	3.62360i	−0.289195	+	0.289195i	0.547567	+	0.836762i	$0.315554\pi$
$158$	1.23848	−	0.499107i	0.0985284	−	0.0397068i
$159$	9.00974			0.714519
$160$	10.7643	−	6.64300i	0.850994	−	0.525175i
$161$		−	11.4569i		−	0.902927i
$162$	−2.09154	+	0.842886i	−0.164327	+	0.0662233i
$163$	−6.40798	−	6.40798i	−0.501911	−	0.501911i	0.410120	−	0.912032i	$-0.365487\pi$
$163$	−6.40798	−	6.40798i	−0.501911	−	0.501911i	−0.912032	+	0.410120i	$0.865487\pi$
$164$	4.05639	+	4.21540i	0.316751	+	0.329167i
$165$	0.300458	+	0.195618i	0.0233906	+	0.0152288i
$166$	8.48890	+	3.61218i	0.658866	+	0.280360i
$167$	5.94641	−	5.94641i	0.460147	−	0.460147i	−0.438556	−	0.898704i	$-0.644510\pi$
$167$	5.94641	−	5.94641i	0.460147	−	0.460147i	0.898704	+	0.438556i	$0.144510\pi$
$168$	5.21874	+	2.34013i	0.402634	+	0.180545i
$169$	−10.9291	+	7.03951i	−0.840700	+	0.541501i
$170$	−4.86939	−	0.956870i	−0.373465	−	0.0733886i
$171$	−9.83926			−0.752427
$172$	−0.0823911	+	4.28599i	−0.00628226	+	0.326804i
$173$	8.64623	+	8.64623i	0.657361	+	0.657361i	0.954755	−	0.297394i	$-0.0961175\pi$
$173$	8.64623	+	8.64623i	0.657361	+	0.657361i	−0.297394	+	0.954755i	$0.596117\pi$
$174$	−6.75111	−	2.87272i	−0.511800	−	0.217780i
$175$	3.08891	−	7.99120i	0.233500	−	0.604078i
$176$	0.0208867	−	0.543064i	0.00157440	−	0.0409350i
$177$	−4.56944	−	4.56944i	−0.343460	−	0.343460i
$178$	4.23413	−	1.70635i	0.317361	−	0.127896i
$179$	−12.7865			−0.955706			−0.477853	−	0.878440i	$-0.658585\pi$
$179$	−12.7865			−0.955706			−0.477853	+	0.878440i	$0.658585\pi$
$180$	4.03704	−	5.94746i	0.300903	−	0.443298i
$181$	−4.48458			−0.333337			−0.166668	−	0.986013i	$-0.553301\pi$
$181$	−4.48458			−0.333337			−0.166668	+	0.986013i	$0.553301\pi$
$182$	8.67817	+	1.01296i	0.643269	+	0.0750854i
$183$	−9.83627	+	9.83627i	−0.727118	+	0.727118i
$184$	−6.73051	−	17.6735i	−0.496180	−	1.30291i
$185$	11.0415	−	16.9591i	0.811786	−	1.24686i
$186$	−2.03937	+	4.79268i	−0.149534	+	0.351416i
$187$	−0.150764	+	0.150764i	−0.0110250	+	0.0110250i
$188$	0.442666	−	23.0275i	0.0322848	−	1.67946i
$189$	9.31652			0.677677
$190$	−16.0706	+	10.7919i	−1.16588	+	0.782926i
$191$			23.2641i			1.68333i	0.540000	+	0.841665i	$0.318424\pi$
$191$			23.2641i			1.68333i	−0.540000	+	0.841665i	$0.681576\pi$
$192$	9.42523	+	0.544090i	0.680208	+	0.0392663i
$193$	0.896999	−	0.896999i	0.0645674	−	0.0645674i	−0.674086	−	0.738653i	$-0.735462\pi$
$193$	0.896999	−	0.896999i	0.0645674	−	0.0645674i	0.738653	+	0.674086i	$0.235462\pi$
$194$	4.26463	+	1.81468i	0.306182	+	0.130286i
$195$	−2.72990	+	9.11435i	−0.195492	+	0.652692i
$196$	5.63580	+	5.85672i	0.402557	+	0.418337i
$197$	6.48712	+	6.48712i	0.462188	+	0.462188i	0.899372	−	0.437184i	$-0.144024\pi$
$197$	6.48712	+	6.48712i	0.462188	+	0.462188i	−0.437184	+	0.899372i	$0.644024\pi$
$198$	−0.115440	−	0.286452i	−0.00820395	−	0.0203573i
$199$	6.60481			0.468203			0.234101	−	0.972212i	$-0.424785\pi$
$199$	6.60481			0.468203			0.234101	+	0.972212i	$0.424785\pi$
$200$	0.0704444	−	14.1420i	0.00498117	−	0.999988i
$201$			11.8588i			0.836456i
$202$	−3.45328	+	1.39167i	−0.242972	+	0.0979173i
$203$	5.32645	+	5.32645i	0.373843	+	0.373843i
$204$	−2.56821	−	2.66889i	−0.179811	−	0.186859i
$205$	6.39928	−	1.35242i	0.446945	−	0.0944571i
$206$	−5.76737	+	13.5538i	−0.401832	+	0.944335i
$207$	−7.59932	−	7.59932i	−0.528189	−	0.528189i
$208$	13.9821	−	3.53552i	0.969487	−	0.245144i
$209$			0.831707i			0.0575304i
$210$	5.30857	−	3.56488i	0.366326	−	0.246000i
$211$		−	6.75732i		−	0.465193i	−0.972573	−	0.232596i	$-0.925278\pi$
$211$		−	6.75732i		−	0.465193i	0.972573	−	0.232596i	$-0.0747221\pi$
$212$	−15.2664	−	0.293472i	−1.04850	−	0.0201557i
$213$	3.74717	−	3.74717i	0.256752	−	0.256752i
$214$	−21.9288	−	9.33112i	−1.49902	−	0.637862i
$215$	4.01651	+	2.61501i	0.273924	+	0.178342i
$216$	14.3718	−	5.47313i	0.977876	−	0.372399i
$217$	3.78130	−	3.78130i	0.256691	−	0.256691i
$218$	−2.05968	+	0.830047i	−0.139499	+	0.0562179i
$219$		−	10.0874i		−	0.681646i
$220$	−0.502736	−	0.341249i	−0.0338944	−	0.0230070i
$221$	−4.96741	−	2.70912i	−0.334144	−	0.182235i
$222$	14.0093	−	5.64572i	0.940241	−	0.378916i
$223$	4.45155	+	4.45155i	0.298098	+	0.298098i	0.840268	−	0.542171i	$-0.182397\pi$
$223$	4.45155	+	4.45155i	0.298098	+	0.298098i	−0.542171	+	0.840268i	$0.682397\pi$
$224$	−8.76659	−	4.13519i	−0.585742	−	0.276294i
$225$	−3.25168	−	7.34943i	−0.216779	−	0.489962i
$226$	−1.38969	−	0.591338i	−0.0924407	−	0.0393352i
$227$	8.81803	−	8.81803i	0.585273	−	0.585273i	−0.351075	−	0.936348i	$-0.614184\pi$
$227$	8.81803	−	8.81803i	0.585273	−	0.585273i	0.936348	+	0.351075i	$0.114184\pi$
$228$	−14.4455	−	0.277691i	−0.956676	−	0.0183905i
$229$	29.3112			1.93694			0.968470	−	0.249129i	$-0.0801442\pi$
$229$	29.3112			1.93694			0.968470	+	0.249129i	$0.0801442\pi$
$230$	−20.7471	−	4.07696i	−1.36803	−	0.268827i
$231$		−	0.274737i		−	0.0180764i
$232$	11.3458	+	5.08754i	0.744885	+	0.334014i
$233$	17.8139	+	17.8139i	1.16703	+	1.16703i	0.982903	+	0.184122i	$0.0589443\pi$
$233$	17.8139	+	17.8139i	1.16703	+	1.16703i	0.184122	+	0.982903i	$0.441056\pi$
$234$	6.42811	−	5.08433i	0.420219	−	0.332373i
$235$	−21.5797	−	14.0498i	−1.40770	−	0.916507i
$236$	7.59379	+	7.89147i	0.494314	+	0.513691i
$237$	0.787887	−	0.787887i	0.0511787	−	0.0511787i
$238$	1.42141	+	3.52710i	0.0921366	+	0.228628i
$239$			15.2637i			0.987328i	0.869653	+	0.493664i	$0.164343\pi$
$239$			15.2637i			0.987328i	−0.869653	+	0.493664i	$0.835657\pi$
$240$	6.09483	−	8.61782i	0.393420	−	0.556278i
$241$		−	12.6676i		−	0.815990i	−0.912984	−	0.407995i	$-0.866228\pi$
$241$		−	12.6676i		−	0.815990i	0.912984	−	0.407995i	$-0.133772\pi$
$242$	14.4045	−	5.80500i	0.925958	−	0.373160i
$243$	10.2034	−	10.2034i	0.654550	−	0.654550i
$244$	16.9873	−	16.3465i	1.08750	−	1.04648i
$245$	8.89093	−	1.87900i	0.568021	−	0.120045i
$246$	4.49197	+	1.91142i	0.286398	+	0.121867i
$247$	−21.1742	+	6.22906i	−1.34728	+	0.396345i
$248$	3.61170	−	8.05446i	0.229343	−	0.511459i
$249$	7.69836			0.487863
$250$	−13.3720	−	8.43739i	−0.845720	−	0.533627i
$251$			16.0887i			1.01551i	0.861501	+	0.507755i	$0.169525\pi$
$251$			16.0887i			1.01551i	−0.861501	+	0.507755i	$0.830475\pi$
$252$	−5.50724	−	0.105868i	−0.346924	−	0.00666903i
$253$	−0.642366	+	0.642366i	−0.0403852	+	0.0403852i
$254$	27.9050	+	11.8741i	1.75091	+	0.745046i
$255$	−4.05156	+	0.856255i	−0.253719	+	0.0536208i
$256$	−15.9527	−	1.22893i	−0.997046	−	0.0768082i
$257$	−16.0293	+	16.0293i	−0.999880	+	0.999880i	−1.00000		0.000120104i	$-0.999962\pi$
$257$	−16.0293	+	16.0293i	−0.999880	+	0.999880i	0.000120104		1.00000i	$0.499962\pi$
$258$	1.33710	+	3.31789i	0.0832445	+	0.206563i
$259$	−15.5073			−0.963576
$260$	4.92251	−	15.3548i	0.305281	−	0.952262i
$261$	7.06605			0.437378
$262$	−0.124254	−	0.308324i	−0.00767645	−	0.0190483i
$263$	1.00613	−	1.00613i	0.0620408	−	0.0620408i	−0.675406	−	0.737446i	$-0.736031\pi$
$263$	1.00613	−	1.00613i	0.0620408	−	0.0620408i	0.737446	+	0.675406i	$0.236031\pi$
$264$	−0.161398	−	0.423813i	−0.00993338	−	0.0260839i
$265$	−9.31449	+	14.3066i	−0.572185	+	0.878844i
$266$	13.6495	+	5.80810i	0.836903	+	0.356118i
$267$	2.69363	−	2.69363i	0.164848	−	0.164848i
$268$	0.386274	−	20.0940i	0.0235954	−	1.22744i
$269$		−	19.2720i		−	1.17504i	−0.809211	−	0.587519i	$-0.800105\pi$
$269$		−	19.2720i		−	1.17504i	0.809211	−	0.587519i	$-0.199895\pi$
$270$	3.31532	−	16.8712i	0.201764	−	1.02675i
$271$	28.0613			1.70460			0.852301	−	0.523052i	$-0.175207\pi$
$271$	28.0613			1.70460			0.852301	+	0.523052i	$0.175207\pi$
$272$	4.26474	+	4.60591i	0.258588	+	0.279274i
$273$	6.99444	−	2.05764i	0.423323	−	0.124534i
$274$	22.5826	+	9.60929i	1.36426	+	0.580519i
$275$	−0.621243	+	0.274863i	−0.0374624	+	0.0165748i
$276$	−10.9425	−	11.3714i	−0.658659	−	0.684478i
$277$	12.7073	−	12.7073i	0.763505	−	0.763505i	−0.213449	−	0.976954i	$-0.568470\pi$
$277$	12.7073	−	12.7073i	0.763505	−	0.763505i	0.976954	+	0.213449i	$0.0684697\pi$
$278$	−25.7263	+	10.3677i	−1.54296	+	0.621811i
$279$		−	5.01626i		−	0.300316i
$280$	−9.11115	+	5.86754i	−0.544496	+	0.350653i
$281$			17.4196i			1.03917i	0.854420	+	0.519583i	$0.173913\pi$
$281$			17.4196i			1.03917i	−0.854420	+	0.519583i	$0.826087\pi$
$282$	−7.18392	−	17.8262i	−0.427796	−	1.06153i
$283$	−10.9442	+	10.9442i	−0.650568	+	0.650568i	−0.953130	−	0.302562i	$-0.902158\pi$
$283$	−10.9442	+	10.9442i	−0.650568	+	0.650568i	0.302562	+	0.953130i	$0.402158\pi$
$284$	−6.47139	+	6.22728i	−0.384006	+	0.369521i
$285$	−8.81362	+	13.5372i	−0.522074	+	0.801877i
$286$	−0.429775	−	0.543365i	−0.0254131	−	0.0321298i
$287$	−3.54405	−	3.54405i	−0.209199	−	0.209199i
$288$	−8.55773	+	3.07200i	−0.504269	+	0.181019i
$289$			14.5373i			0.855138i
$290$	11.5411	−	7.75019i	0.677714	−	0.455107i
$291$	3.86748			0.226716
$292$	−0.328575	+	17.0925i	−0.0192284	+	1.00026i
$293$	−1.56341	+	1.56341i	−0.0913353	+	0.0913353i	−0.751298	−	0.659963i	$-0.770572\pi$
$293$	−1.56341	+	1.56341i	−0.0913353	+	0.0913353i	0.659963	+	0.751298i	$0.270572\pi$
$294$	6.24099	+	2.65565i	0.363982	+	0.154881i
$295$	11.9798	−	2.53181i	0.697492	−	0.147408i
$296$	−23.9217	+	9.10999i	−1.39042	+	0.529507i
$297$	−0.522361	−	0.522361i	−0.0303105	−	0.0303105i
$298$	3.14570	−	1.26771i	0.182226	−	0.0734366i
$299$	−21.1648	−	11.5428i	−1.22399	−	0.667538i
$300$	−4.56653	−	10.8818i	−0.263649	−	0.628262i
$301$		−	3.67267i		−	0.211689i
$302$	−7.38836	+	2.97750i	−0.425152	+	0.171336i
$303$	−2.19688	+	2.19688i	−0.126207	+	0.126207i
$304$	24.4679	+	0.941058i	1.40333	+	0.0539734i
$305$	−5.45002	−	25.7880i	−0.312067	−	1.47662i
$306$	3.28234	+	1.39670i	0.187639	+	0.0798438i
$307$	−12.1227	+	12.1227i	−0.691877	+	0.691877i	−0.962645	−	0.270768i	$-0.912723\pi$
$307$	−12.1227	+	12.1227i	−0.691877	+	0.691877i	0.270768	+	0.962645i	$0.412723\pi$
$308$	−0.00894893	+	0.465524i	−0.000509913	+	0.0265257i
$309$			12.2915i			0.699241i
$310$	−5.50194	−	8.19312i	−0.312489	−	0.465338i
$311$			18.9025i			1.07186i	0.844261	+	0.535932i	$0.180040\pi$
$311$			18.9025i			1.07186i	−0.844261	+	0.535932i	$0.819960\pi$
$312$	9.58092	−	7.28313i	0.542413	−	0.412326i
$313$	5.87564	+	5.87564i	0.332111	+	0.332111i	0.853388	−	0.521277i	$-0.174544\pi$
$313$	5.87564	+	5.87564i	0.332111	+	0.332111i	−0.521277	+	0.853388i	$0.674544\pi$
$314$	2.83760	−	6.66858i	0.160135	−	0.376330i
$315$	−3.36013	+	5.16098i	−0.189322	+	0.290788i
$316$	−1.36069	+	1.30936i	−0.0765446	+	0.0736572i
$317$	10.2637	+	10.2637i	0.576467	+	0.576467i	0.933928	−	0.357461i	$-0.116357\pi$
$317$	10.2637	+	10.2637i	0.576467	+	0.576467i	−0.357461	+	0.933928i	$0.616357\pi$
$318$	−11.8181	+	4.76268i	−0.662726	+	0.267078i
$319$		−	0.597290i		−	0.0334418i
$320$	−10.6080	+	14.4038i	−0.593006	+	0.805198i
$321$	−19.8867			−1.10997
$322$	6.05626	+	15.0280i	0.337502	+	0.837478i
$323$	−6.79273	−	6.79273i	−0.377958	−	0.377958i
$324$	2.29791	−	2.21123i	0.127662	−	0.122846i
$325$	−11.6504	−	13.7574i	−0.646250	−	0.763126i
$326$	11.7927	+	5.01802i	0.653138	+	0.277922i
$327$	−1.31031	+	1.31031i	−0.0724602	+	0.0724602i
$328$	−7.54910	−	3.38509i	−0.416829	−	0.186910i
$329$			19.7323i			1.08788i
$330$	−0.497519	−	0.0977660i	−0.0273875	−	0.00538184i
$331$	−16.3191			−0.896980			−0.448490	−	0.893788i	$-0.648038\pi$
$331$	−16.3191			−0.896980			−0.448490	+	0.893788i	$0.648038\pi$
$332$	−13.0444	−	0.250756i	−0.715903	−	0.0137620i
$333$	−10.2860	+	10.2860i	−0.563667	+	0.563667i
$334$	−4.65657	+	10.9433i	−0.254796	+	0.598790i
$335$	−18.8306	−	12.2599i	−1.02883	−	0.669832i
$336$	−8.08246	−	0.310859i	−0.440934	−	0.0169587i
$337$	14.5265	−	14.5265i	0.791309	−	0.791309i	−0.190398	−	0.981707i	$-0.560978\pi$
$337$	14.5265	−	14.5265i	0.791309	−	0.791309i	0.981707	+	0.190398i	$0.0609779\pi$
$338$	10.6146	−	15.0110i	0.577356	−	0.816493i
$339$	−1.26027			−0.0684485
$340$	6.89301	−	1.31890i	0.373826	−	0.0715274i
$341$	−0.424022			−0.0229621
$342$	12.9062	−	5.20117i	0.697887	−	0.281247i
$343$	−13.4053	−	13.4053i	−0.723818	−	0.723818i
$344$	−2.15757	−	5.66551i	−0.116328	−	0.305464i
$345$	−17.2626	+	3.64827i	−0.929388	+	0.196416i
$346$	−15.9118	−	6.77077i	−0.855425	−	0.363999i
$347$	7.03773	+	7.03773i	0.377805	+	0.377805i	0.870310	−	0.492505i	$-0.163919\pi$
$347$	7.03773	+	7.03773i	0.377805	+	0.377805i	−0.492505	+	0.870310i	$0.663919\pi$
$348$	10.3740	+	0.199423i	0.556106	+	0.0106902i
$349$	−19.3224			−1.03430			−0.517152	−	0.855894i	$-0.673008\pi$
$349$	−19.3224			−1.03430			−0.517152	+	0.855894i	$0.673008\pi$
$350$	0.172526	+	12.1149i	0.00922189	+	0.647571i
$351$	9.38641	−	17.2108i	0.501010	−	0.918647i
$352$	0.259674	+	0.723380i	0.0138407	+	0.0385563i
$353$	1.78993	−	1.78993i	0.0952685	−	0.0952685i	−0.657866	−	0.753135i	$-0.728541\pi$
$353$	1.78993	−	1.78993i	0.0952685	−	0.0952685i	0.753135	+	0.657866i	$0.228541\pi$
$354$	8.40923	+	3.57828i	0.446946	+	0.190184i
$355$	2.07621	+	9.82404i	0.110194	+	0.521406i
$356$	−4.65192	+	4.47645i	−0.246551	+	0.237251i
$357$	2.24384	+	2.24384i	0.118756	+	0.118756i
$358$	16.7721	−	6.75912i	0.886431	−	0.357230i
$359$			7.57948i			0.400029i	0.979793	+	0.200015i	$0.0640990\pi$
$359$			7.57948i			0.400029i	−0.979793	+	0.200015i	$0.935901\pi$
$360$	−2.15149	+	9.93535i	−0.113393	+	0.523639i
$361$	−18.4728			−0.972252
$362$	5.88245	−	2.37062i	0.309175	−	0.124597i
$363$	9.16374	−	9.16374i	0.480972	−	0.480972i
$364$	−11.9187	+	3.25871i	−0.624707	+	0.170803i
$365$	16.0178	+	10.4286i	0.838411	+	0.545860i
$366$	7.70268	−	18.1019i	0.402625	−	0.946200i
$367$	25.0286	+	25.0286i	1.30648	+	1.30648i	0.923937	+	0.382544i	$0.124952\pi$
$367$	25.0286	+	25.0286i	1.30648	+	1.30648i	0.382544	+	0.923937i	$0.375048\pi$
$368$	18.1709	+	19.6245i	0.947224	+	1.02300i
$369$	−4.70152			−0.244752
$370$	−5.51832	+	28.0820i	−0.286884	+	1.45991i
$371$	13.0818			0.679173
$372$	0.141573	−	7.36462i	0.00734020	−	0.381838i
$373$	−12.9400	−	12.9400i	−0.670007	−	0.670007i	0.287711	−	0.957717i	$-0.407106\pi$
$373$	−12.9400	−	12.9400i	−0.670007	−	0.670007i	−0.957717	+	0.287711i	$0.907106\pi$
$374$	0.118062	−	0.277454i	0.00610484	−	0.0143468i
$375$	−13.0244	−	2.10954i	−0.672575	−	0.108936i
$376$	11.5920	+	30.4393i	0.597814	+	1.56979i
$377$	15.2062	−	4.47339i	0.783159	−	0.230391i
$378$	−12.2205	+	4.92485i	−0.628555	+	0.253307i
$379$			25.4640i			1.30800i	0.756495	+	0.653999i	$0.226910\pi$
$379$			25.4640i			1.30800i	−0.756495	+	0.653999i	$0.773090\pi$
$380$	15.3751	−	22.6509i	0.788724	−	1.16197i
$381$	25.3063			1.29648
$382$	−12.2977	−	30.5156i	−0.629207	−	1.56131i
$383$	23.7178	+	23.7178i	1.21192	+	1.21192i	0.970394	+	0.241528i	$0.0776485\pi$
$383$	23.7178	+	23.7178i	1.21192	+	1.21192i	0.241528	+	0.970394i	$0.422351\pi$
$384$	−12.6507	+	4.26863i	−0.645580	+	0.217833i
$385$	0.436254	+	0.284030i	0.0222336	+	0.0144755i
$386$	−0.702430	+	1.65076i	−0.0357528	+	0.0840217i
$387$	−2.43608	−	2.43608i	−0.123833	−	0.123833i
$388$	−6.55319	−	0.125974i	−0.332688	−	0.00639537i
$389$		−	27.0309i		−	1.37052i	−0.728297	−	0.685262i	$-0.759688\pi$
$389$		−	27.0309i		−	1.37052i	0.728297	−	0.685262i	$-0.240312\pi$
$390$	−1.23716	−	13.3984i	−0.0626463	−	0.678454i
$391$		−	10.4927i		−	0.530638i
$392$	−10.4884	−	4.70312i	−0.529747	−	0.237543i
$393$	−0.196147	−	0.196147i	−0.00989431	−	0.00989431i
$394$	−11.9384	−	5.07999i	−0.601446	−	0.255926i
$395$	0.436547	+	2.06562i	0.0219651	+	0.103933i
$396$	0.302846	+	0.314717i	0.0152186	+	0.0158151i
$397$	9.49107	+	9.49107i	0.476343	+	0.476343i	0.903960	−	0.427617i	$-0.140647\pi$
$397$	9.49107	+	9.49107i	0.476343	+	0.476343i	−0.427617	+	0.903960i	$0.640647\pi$
$398$	−8.66356	+	3.49140i	−0.434265	+	0.175008i
$399$	12.3783			0.619693
$400$	7.38324	+	18.5873i	0.369162	+	0.929365i
$401$		−	16.6170i		−	0.829811i	−0.909864	−	0.414906i	$-0.863815\pi$
$401$		−	16.6170i		−	0.829811i	0.909864	−	0.414906i	$-0.136185\pi$
$402$	−6.26874	−	15.5553i	−0.312656	−	0.775825i
$403$	−3.17571	−	10.7950i	−0.158193	−	0.537739i
$404$	3.79403	−	3.65091i	0.188760	−	0.181640i
$405$	−0.737236	−	3.48840i	−0.0366336	−	0.173340i
$406$	−9.80236	−	4.17108i	−0.486483	−	0.207007i
$407$	0.869466	+	0.869466i	0.0430978	+	0.0430978i
$408$	4.77955	+	2.14319i	0.236623	+	0.106104i
$409$	−9.84810			−0.486957			−0.243479	−	0.969906i	$-0.578289\pi$
$409$	−9.84810			−0.486957			−0.243479	+	0.969906i	$0.578289\pi$
$410$	−7.67905	+	5.15673i	−0.379241	+	0.254673i
$411$	20.4795			1.01018
$412$	0.400369	−	20.8272i	0.0197248	−	1.02608i
$413$	−6.63466	−	6.63466i	−0.326470	−	0.326470i
$414$	13.9852	+	5.95095i	0.687334	+	0.292473i
$415$	−7.95876	+	12.2242i	−0.390680	+	0.600063i
$416$	−16.4715	+	12.0287i	−0.807581	+	0.589756i
$417$	−16.3663	+	16.3663i	−0.801463	+	0.801463i
$418$	−0.439652	−	1.09095i	−0.0215041	−	0.0533603i
$419$	35.8407			1.75093			0.875466	−	0.483279i	$-0.160554\pi$
$419$	35.8407			1.75093			0.875466	+	0.483279i	$0.160554\pi$
$420$	−5.07883	+	7.48225i	−0.247821	+	0.365096i
$421$		−	29.4970i		−	1.43760i	−0.695218	−	0.718799i	$-0.744692\pi$
$421$		−	29.4970i		−	1.43760i	0.695218	−	0.718799i	$-0.255308\pi$
$422$	3.57202	+	8.86360i	0.173883	+	0.431473i
$423$	13.0884	+	13.0884i	0.636381	+	0.636381i
$424$	20.1802	−	7.68511i	0.980035	−	0.373222i
$425$	2.82896	−	7.31869i	0.137225	−	0.355009i
$426$	−2.93437	+	6.89598i	−0.142170	+	0.334111i
$427$	−14.2819	+	14.2819i	−0.691150	+	0.691150i
$428$	33.6967	+	0.647763i	1.62879	+	0.0313108i
$429$	−0.507534	−	0.276798i	−0.0245040	−	0.0133639i
$430$	−6.65081	−	1.30693i	−0.320730	−	0.0630259i
$431$	−19.7901			−0.953253			−0.476627	−	0.879106i	$-0.658141\pi$
$431$	−19.7901			−0.953253			−0.476627	+	0.879106i	$0.658141\pi$
$432$	−15.9583	+	14.7763i	−0.767796	+	0.710923i
$433$	−2.28416	−	2.28416i	−0.109770	−	0.109770i	0.650089	−	0.759858i	$-0.274732\pi$
$433$	−2.28416	−	2.28416i	−0.109770	−	0.109770i	−0.759858	+	0.650089i	$0.774732\pi$
$434$	−2.96110	+	6.95880i	−0.142137	+	0.334033i
$435$	6.32949	−	9.72176i	0.303476	−	0.466122i
$436$	2.26291	−	2.17755i	0.108374	−	0.104286i
$437$	−28.9420	−	28.9420i	−1.38448	−	1.38448i
$438$	5.33237	+	13.2317i	0.254790	+	0.632236i
$439$	6.80513			0.324791			0.162396	−	0.986726i	$-0.448078\pi$
$439$	6.80513			0.324791			0.162396	+	0.986726i	$0.448078\pi$
$440$	0.839829	+	0.181864i	0.0400373	+	0.00867002i
$441$	−6.53213			−0.311054
$442$	7.94785	+	0.927711i	0.378041	+	0.0441267i
$443$	15.2445	−	15.2445i	0.724286	−	0.724286i	−0.245189	−	0.969475i	$-0.578850\pi$
$443$	15.2445	−	15.2445i	0.724286	−	0.724286i	0.969475	+	0.245189i	$0.0788501\pi$
$444$	−15.3916	+	14.8110i	−0.730454	+	0.702900i
$445$	1.49247	+	7.06196i	0.0707499	+	0.334769i
$446$	−8.19227	−	3.48596i	−0.387915	−	0.165065i
$447$	2.00120	−	2.00120i	0.0946537	−	0.0946537i
$448$	13.6851	+	0.789998i	0.646560	+	0.0373239i
$449$	8.62094			0.406847			0.203424	−	0.979091i	$-0.434793\pi$
$449$	8.62094			0.406847			0.203424	+	0.979091i	$0.434793\pi$
$450$	8.15026	+	7.92138i	0.384207	+	0.373418i
$451$			0.397417i			0.0187136i
$452$	2.13545	+	0.0410505i	0.100443	+	0.00193085i
$453$	−4.70026	+	4.70026i	−0.220837	+	0.220837i
$454$	−6.90530	+	16.2280i	−0.324082	+	0.761617i
$455$	−3.96371	+	13.2337i	−0.185822	+	0.620406i
$456$	19.0950	−	7.27185i	0.894205	−	0.340536i
$457$	15.8492	+	15.8492i	0.741395	+	0.741395i	0.972846	−	0.231452i	$-0.0743475\pi$
$457$	15.8492	+	15.8492i	0.741395	+	0.741395i	−0.231452	+	0.972846i	$0.574347\pi$
$458$	−38.4477	+	15.4943i	−1.79654	+	0.724003i
$459$	8.53248			0.398262
$460$	29.3692	−	5.61947i	1.36935	−	0.262009i
$461$			31.2187i			1.45400i	0.686638	+	0.726999i	$0.259086\pi$
$461$			31.2187i			1.45400i	−0.686638	+	0.726999i	$0.740914\pi$
$462$	0.145230	+	0.360373i	0.00675671	+	0.0167661i
$463$	−17.2870	−	17.2870i	−0.803396	−	0.803396i	0.180229	−	0.983625i	$-0.442316\pi$
$463$	−17.2870	−	17.2870i	−0.803396	−	0.803396i	−0.983625	+	0.180229i	$0.942316\pi$
$464$	−17.5716	−	0.675820i	−0.815742	−	0.0313742i
$465$	−6.90157	−	4.49337i	−0.320053	−	0.208375i
$466$	−32.7832	−	13.9499i	−1.51865	−	0.646214i
$467$	3.44862	+	3.44862i	0.159583	+	0.159583i	0.782382	−	0.622799i	$-0.214005\pi$
$467$	3.44862	+	3.44862i	0.159583	+	0.159583i	−0.622799	+	0.782382i	$0.714005\pi$
$468$	−5.74413	+	10.0671i	−0.265523	+	0.465353i
$469$			17.2186i			0.795079i
$470$	35.7331	+	7.02181i	1.64824	+	0.323892i
$471$		−	6.04756i		−	0.278657i
$472$	−14.1324	−	6.33708i	−0.650494	−	0.291688i
$473$	−0.205920	+	0.205920i	−0.00946822	+	0.00946822i
$474$	−0.616985	+	1.44996i	−0.0283391	+	0.0665990i
$475$	−12.3840	−	27.9903i	−0.568218	−	1.28428i
$476$	−3.72895	−	3.87513i	−0.170916	−	0.177616i
$477$	8.67714	−	8.67714i	0.397299	−	0.397299i
$478$	−8.06863	−	20.0215i	−0.369050	−	0.915761i
$479$		−	30.8029i		−	1.40742i	−0.710488	−	0.703710i	$-0.751526\pi$
$479$		−	30.8029i		−	1.40742i	0.710488	−	0.703710i	$-0.248474\pi$
$480$	−3.43910	+	14.5258i	−0.156973	+	0.663011i
$481$	−15.6236	+	28.6473i	−0.712376	+	1.30621i
$482$	6.69626	+	16.6161i	0.305006	+	0.756843i
$483$	9.56038	+	9.56038i	0.435012	+	0.435012i
$484$	−15.8259	+	15.2289i	−0.719357	+	0.692222i
$485$	−3.99830	+	6.14116i	−0.181553	+	0.278856i
$486$	−7.99019	+	18.7775i	−0.362442	+	0.851767i
$487$	−21.5008	+	21.5008i	−0.974296	+	0.974296i	−0.999678	−	0.0253815i	$-0.991920\pi$
$487$	−21.5008	+	21.5008i	−0.974296	+	0.974296i	0.0253815	+	0.999678i	$0.491920\pi$
$488$	−13.6413	+	30.4216i	−0.617514	+	1.37712i
$489$	10.6945			0.483622
$490$	−10.6690	+	7.16457i	−0.481976	+	0.323662i
$491$		−	31.4355i		−	1.41866i	−0.704875	−	0.709332i	$-0.748997\pi$
$491$		−	31.4355i		−	1.41866i	0.704875	−	0.709332i	$-0.251003\pi$
$492$	−6.90254	−	0.132690i	−0.311190	−	0.00598212i
$493$	4.87820	+	4.87820i	0.219703	+	0.219703i
$494$	24.4815	−	19.3636i	1.10147	−	0.871212i
$495$	0.477764	−	0.100970i	0.0214739	−	0.00453828i
$496$	−0.479772	+	12.4743i	−0.0215424	+	0.560111i
$497$	5.44075	−	5.44075i	0.244051	−	0.244051i
$498$	−10.0980	+	4.06946i	−0.452500	+	0.182357i
$499$		−	30.8204i		−	1.37971i	−0.723948	−	0.689855i	$-0.757674\pi$
$499$		−	30.8204i		−	1.37971i	0.723948	−	0.689855i	$-0.242326\pi$
$500$	22.0002	+	3.99872i	0.983880	+	0.178828i
$501$			9.92418i			0.443380i
$502$	−8.50473	−	21.1036i	−0.379585	−	0.941901i
$503$	15.7158	−	15.7158i	0.700733	−	0.700733i	−0.263835	−	0.964568i	$-0.584987\pi$
$503$	15.7158	−	15.7158i	0.700733	−	0.700733i	0.964568	+	0.263835i	$0.0849874\pi$
$504$	7.27983	−	2.77234i	0.324270	−	0.123490i
$505$	−1.21723	−	5.75961i	−0.0541661	−	0.256299i
$506$	0.503030	−	1.18216i	0.0223624	−	0.0525534i
$507$	3.24574	−	14.9942i	0.144148	−	0.665917i
$508$	−42.8799	−	0.824294i	−1.90249	−	0.0365722i
$509$	−38.9696			−1.72730			−0.863649	−	0.504093i	$-0.831827\pi$
$509$	−38.9696			−1.72730			−0.863649	+	0.504093i	$0.831827\pi$
$510$	4.86182	−	3.26487i	0.215285	−	0.144571i
$511$		−	14.6466i		−	0.647927i
$512$	21.5749	−	6.82085i	0.953485	−	0.301442i
$513$	23.5351	−	23.5351i	1.03910	−	1.03910i
$514$	12.5524	−	29.4990i	0.553661	−	1.30115i
$515$	−19.5177	−	12.7073i	−0.860054	−	0.559951i
$516$	−3.50777	−	3.64528i	−0.154421	−	0.160474i
$517$	1.10636	−	1.10636i	0.0486575	−	0.0486575i
$518$	20.3410	−	8.19738i	0.893730	−	0.360172i
$519$	−14.4300			−0.633407
$520$	1.65987	+	22.7430i	0.0727903	+	0.997347i
$521$	6.74679			0.295582			0.147791	−	0.989019i	$-0.452784\pi$
$521$	6.74679			0.295582			0.147791	+	0.989019i	$0.452784\pi$
$522$	−9.26857	+	3.73522i	−0.405674	+	0.163486i
$523$	−17.7325	+	17.7325i	−0.775387	+	0.775387i	−0.979043	−	0.203655i	$-0.934718\pi$
$523$	−17.7325	+	17.7325i	−0.775387	+	0.775387i	0.203655	+	0.979043i	$0.434718\pi$
$524$	0.325970	+	0.338748i	0.0142400	+	0.0147983i
$525$	4.09080	+	9.24600i	0.178537	+	0.403529i
$526$	−0.787892	+	1.85161i	−0.0343537	+	0.0807338i
$527$	3.46308	−	3.46308i	0.150854	−	0.150854i
$528$	0.435740	+	0.470599i	0.0189632	+	0.0204802i
$529$		−	21.7065i		−	0.943763i
$530$	4.65520	−	23.6897i	0.202209	−	1.02902i
$531$	−8.80153			−0.381954
$532$	−20.9743	−	0.403197i	−0.909352	−	0.0174808i
$533$	−10.1177	+	2.97645i	−0.438247	+	0.128924i
$534$	−2.10935	+	4.95714i	−0.0912806	+	0.214516i
$535$	20.5594	−	31.5780i	0.888858	−	1.36524i
$536$	10.1153	+	26.5616i	0.436915	+	1.14729i
$537$	10.6699	−	10.6699i	0.460440	−	0.460440i
$538$	10.1875	+	25.2792i	0.439214	+	1.08986i
$539$			0.552157i			0.0237831i
$540$	4.56966	+	23.8826i	0.196647	+	1.02774i
$541$		−	31.9567i		−	1.37393i	−0.726692	−	0.686963i	$-0.758943\pi$
$541$		−	31.9567i		−	1.37393i	0.726692	−	0.686963i	$-0.241057\pi$
$542$	−36.8081	+	14.8336i	−1.58104	+	0.637158i
$543$	3.74224	−	3.74224i	0.160595	−	0.160595i
$544$	−8.02883	−	3.78719i	−0.344233	−	0.162374i
$545$	−0.726007	−	3.43527i	−0.0310987	−	0.147151i
$546$	−8.08693	+	6.39637i	−0.346089	+	0.273740i
$547$	6.16147	+	6.16147i	0.263445	+	0.263445i	0.826452	−	0.563007i	$-0.190356\pi$
$547$	6.16147	+	6.16147i	0.263445	+	0.263445i	−0.563007	+	0.826452i	$0.690356\pi$
$548$	−34.7012	−	0.667074i	−1.48236	−	0.0284960i
$549$			18.9463i			0.808610i
$550$	0.669590	−	0.688937i	0.0285514	−	0.0293764i
$551$	26.9111			1.14645
$552$	20.3644	+	9.13157i	0.866765	+	0.388666i
$553$	1.14398	−	1.14398i	0.0486471	−	0.0486471i
$554$	−9.95092	+	23.3854i	−0.422774	+	0.993551i
$555$	4.93807	+	23.3656i	0.209609	+	0.991814i
$556$	28.2648	−	27.1986i	1.19869	−	1.15348i
$557$	22.6497	+	22.6497i	0.959697	+	0.959697i	0.999219	−	0.0395221i	$-0.0125835\pi$
$557$	22.6497	+	22.6497i	0.959697	+	0.959697i	−0.0395221	+	0.999219i	$0.512584\pi$
$558$	2.65167	+	6.57985i	0.112254	+	0.278547i
$559$	−6.78469	−	3.70022i	−0.286962	−	0.156503i
$560$	8.84947	−	12.5128i	0.373958	−	0.528761i
$561$		−	0.251616i		−	0.0106232i
$562$	−9.20825	−	22.8493i	−0.388426	−	0.963841i
$563$	6.24205	−	6.24205i	0.263071	−	0.263071i	−0.563229	−	0.826301i	$-0.690441\pi$
$563$	6.24205	−	6.24205i	0.263071	−	0.263071i	0.826301	+	0.563229i	$0.190441\pi$
$564$	18.8464	+	19.5851i	0.793575	+	0.824683i
$565$	1.30290	−	2.00118i	0.0548134	−	0.0841904i
$566$	8.57032	−	20.1409i	0.360237	−	0.846585i
$567$	−1.93194	+	1.93194i	−0.0811340	+	0.0811340i
$568$	5.19672	−	11.5892i	0.218049	−	0.486273i
$569$			10.8680i			0.455611i	0.973707	+	0.227805i	$0.0731550\pi$
$569$			10.8680i			0.455611i	−0.973707	+	0.227805i	$0.926845\pi$
$570$	4.40488	−	22.4159i	0.184500	−	0.938897i
$571$		−	19.4497i		−	0.813943i	−0.913441	−	0.406971i	$-0.866585\pi$
$571$		−	19.4497i		−	0.813943i	0.913441	−	0.406971i	$-0.133415\pi$
$572$	0.850968	+	0.485548i	0.0355808	+	0.0203018i
$573$	−19.4131	−	19.4131i	−0.810995	−	0.810995i
$574$	6.52218	+	2.77530i	0.272230	+	0.115839i
$575$	12.0534	−	31.1830i	0.502664	−	1.30042i
$576$	9.60131	−	8.55330i	0.400055	−	0.356387i
$577$	12.4491	+	12.4491i	0.518263	+	0.518263i	0.917046	−	0.398782i	$-0.130567\pi$
$577$	12.4491	+	12.4491i	0.518263	+	0.518263i	−0.398782	+	0.917046i	$0.630567\pi$
$578$	−7.68465	−	19.0687i	−0.319639	−	0.793153i
$579$			1.49703i			0.0622146i
$580$	−11.0416	+	16.2667i	−0.458477	+	0.675439i
$581$	11.1777			0.463730
$582$	−5.07298	+	2.04440i	−0.210282	+	0.0847433i
$583$	−0.733474	−	0.733474i	−0.0303774	−	0.0303774i
$584$	−8.60436	−	22.5940i	−0.356051	−	0.934947i
$585$	6.14877	+	11.4070i	0.254221	+	0.471622i
$586$	1.22429	−	2.87717i	0.0505749	−	0.118855i
$587$	0.126933	−	0.126933i	0.00523910	−	0.00523910i	−0.704482	−	0.709721i	$-0.748821\pi$
$587$	0.126933	−	0.126933i	0.00523910	−	0.00523910i	0.709721	+	0.704482i	$0.248821\pi$
$588$	−9.59014	−	0.184355i	−0.395491	−	0.00760265i
$589$		−	19.1044i		−	0.787184i
$590$	−14.3756	+	9.65369i	−0.591835	+	0.397436i
$591$	−10.8266			−0.445346
$592$	26.5625	−	24.5950i	1.09171	−	1.01085i
$593$	2.22865	−	2.22865i	0.0915195	−	0.0915195i	−0.659865	−	0.751384i	$-0.729386\pi$
$593$	2.22865	−	2.22865i	0.0915195	−	0.0915195i	0.751384	+	0.659865i	$0.229386\pi$
$594$	0.961311	+	0.409055i	0.0394431	+	0.0167837i
$595$	−5.88272	+	1.24325i	−0.241168	+	0.0509683i
$596$	−3.45610	+	3.32573i	−0.141567	+	0.136227i
$597$	−5.51150	+	5.51150i	−0.225571	+	0.225571i
$598$	33.8636	+	3.95273i	1.38479	+	0.161639i
$599$	−9.98842			−0.408116			−0.204058	−	0.978959i	$-0.565413\pi$
$599$	−9.98842			−0.408116			−0.204058	+	0.978959i	$0.565413\pi$
$600$	11.7422	+	11.8598i	0.479374	+	0.484174i
$601$	26.6091			1.08541			0.542705	−	0.839924i	$-0.317400\pi$
$601$	26.6091			1.08541			0.542705	+	0.839924i	$0.317400\pi$
$602$	1.94143	+	4.81745i	0.0791266	+	0.196345i
$603$	11.4210	+	11.4210i	0.465101	+	0.465101i
$604$	8.11739	−	7.81119i	0.330292	−	0.317833i
$605$	5.07739	+	24.0248i	0.206425	+	0.976747i
$606$	1.72035	−	4.04295i	0.0698845	−	0.164234i
$607$	7.48637	+	7.48637i	0.303863	+	0.303863i	0.842523	−	0.538660i	$-0.181069\pi$
$607$	7.48637	+	7.48637i	0.303863	+	0.303863i	−0.538660	+	0.842523i	$0.681069\pi$
$608$	−32.5921	+	11.6997i	−1.32178	+	0.474486i
$609$	−8.88950			−0.360221
$610$	20.7807	+	30.9452i	0.841387	+	1.25294i
$611$	36.4524	+	19.8803i	1.47471	+	0.804273i
$612$	−5.04377	−	0.0969582i	−0.203882	−	0.00391930i
$613$	25.6786	−	25.6786i	1.03715	−	1.03715i	0.0378679	−	0.999283i	$-0.487943\pi$
$613$	25.6786	−	25.6786i	1.03715	−	1.03715i	0.999283	−	0.0378679i	$-0.0120566\pi$
$614$	9.49313	−	22.3096i	0.383112	−	0.900341i
$615$	−4.21144	+	6.46854i	−0.169822	+	0.260837i
$616$	−0.234344	−	0.615360i	−0.00944201	−	0.0247936i
$617$	3.95103	+	3.95103i	0.159062	+	0.159062i	0.782151	−	0.623089i	$-0.214122\pi$
$617$	3.95103	+	3.95103i	0.159062	+	0.159062i	−0.623089	+	0.782151i	$0.714122\pi$
$618$	−6.49749	−	16.1229i	−0.261367	−	0.648557i
$619$		−	8.51161i		−	0.342111i	−0.985261	−	0.171055i	$-0.945282\pi$
$619$		−	8.51161i		−	0.342111i	0.985261	−	0.171055i	$-0.0547177\pi$
$620$	11.5479	+	7.83854i	0.463775	+	0.314803i
$621$	36.3546			1.45886
$622$	−9.99215	−	24.7945i	−0.400649	−	0.994169i
$623$	3.91105	−	3.91105i	0.156693	−	0.156693i
$624$	−8.71736	+	14.6179i	−0.348974	+	0.585185i
$625$	16.8146	−	18.5005i	0.672586	−	0.740019i
$626$	−10.8130	−	4.60115i	−0.432176	−	0.183899i
$627$	−0.694033	−	0.694033i	−0.0277170	−	0.0277170i
$628$	−0.196986	+	10.2472i	−0.00786058	+	0.408908i
$629$	−14.2022			−0.566281
$630$	1.67933	−	8.54589i	0.0669060	−	0.340476i
$631$	−7.04210			−0.280341			−0.140171	−	0.990127i	$-0.544765\pi$
$631$	−7.04210			−0.280341			−0.140171	+	0.990127i	$0.544765\pi$
$632$	1.09267	−	2.43677i	0.0434641	−	0.0969296i
$633$	5.63876	+	5.63876i	0.224121	+	0.224121i
$634$	−18.8885	−	8.03740i	−0.750158	−	0.319206i
$635$	−26.1623	+	40.1838i	−1.03822	+	1.59465i
$636$	12.9842	−	12.4944i	0.514858	−	0.495437i
$637$	−14.0572	+	4.13537i	−0.556967	+	0.163849i
$638$	0.315736	+	0.783467i	0.0125001	+	0.0310178i
$639$		−	7.21768i		−	0.285527i
$640$	6.30049	−	24.5011i	0.249049	−	0.968491i
$641$	−36.7633			−1.45206			−0.726032	−	0.687661i	$-0.758638\pi$
$641$	−36.7633			−1.45206			−0.726032	+	0.687661i	$0.758638\pi$
$642$	26.0854	−	10.5124i	1.02951	−	0.414891i
$643$	20.9784	+	20.9784i	0.827306	+	0.827306i	0.987143	−	0.159838i	$-0.0510971\pi$
$643$	20.9784	+	20.9784i	0.827306	+	0.827306i	−0.159838	+	0.987143i	$0.551097\pi$
$644$	−15.8880	−	16.5109i	−0.626077	−	0.650619i
$645$	−5.53379	+	1.16951i	−0.217893	+	0.0460494i
$646$	12.5008	+	5.31932i	0.491837	+	0.209286i
$647$	8.79846	+	8.79846i	0.345903	+	0.345903i	0.858581	−	0.512678i	$-0.171346\pi$
$647$	8.79846	+	8.79846i	0.345903	+	0.345903i	−0.512678	+	0.858581i	$0.671346\pi$
$648$	−1.84529	+	4.11519i	−0.0724899	+	0.161660i
$649$			0.743988i			0.0292041i
$650$	22.5543	+	11.8871i	0.884653	+	0.466251i
$651$			6.31075i			0.247338i
$652$	−18.1211	−	0.348349i	−0.709679	−	0.0136424i
$653$	−26.6946	−	26.6946i	−1.04464	−	1.04464i	−0.998956	−	0.0456859i	$-0.985453\pi$
$653$	−26.6946	−	26.6946i	−1.04464	−	1.04464i	−0.0456859	−	0.998956i	$-0.514547\pi$
$654$	1.02609	−	2.41138i	0.0401232	−	0.0942925i
$655$	0.514243	−	0.108680i	0.0200932	−	0.00424648i
$656$	11.6916	+	0.449669i	0.456480	+	0.0175566i
$657$	−9.71506	−	9.71506i	−0.379021	−	0.379021i
$658$	−10.4308	−	25.8829i	−0.406634	−	1.00902i
$659$	−30.2389			−1.17794			−0.588970	−	0.808155i	$-0.700466\pi$
$659$	−30.2389			−1.17794			−0.588970	+	0.808155i	$0.700466\pi$
$660$	0.704278	−	0.134756i	0.0274140	−	0.00524535i
$661$		−	44.3556i		−	1.72523i	−0.505857	−	0.862617i	$-0.668824\pi$
$661$		−	44.3556i		−	1.72523i	0.505857	−	0.862617i	$-0.331176\pi$
$662$	21.4059	−	8.62653i	0.831962	−	0.335279i
$663$	6.40581	−	1.88447i	0.248781	−	0.0731869i
$664$	17.2429	−	6.56653i	0.669154	−	0.254831i
$665$	−12.7971	+	19.6556i	−0.496248	+	0.762210i
$666$	8.05482	−	18.9294i	0.312118	−	0.733501i
$667$	20.7847	+	20.7847i	0.804786	+	0.804786i
$668$	0.323258	−	16.8159i	0.0125072	−	0.650626i
$669$	−7.42935			−0.287235
$670$	31.1810	+	6.12728i	1.20463	+	0.236718i
$671$	1.60152			0.0618261
$672$	10.7661	−	3.86475i	0.415312	−	0.149086i
$673$	8.50808	+	8.50808i	0.327962	+	0.327962i	0.851811	−	0.523849i	$-0.175504\pi$
$673$	8.50808	+	8.50808i	0.327962	+	0.327962i	−0.523849	+	0.851811i	$0.675504\pi$
$674$	−11.3755	+	26.7334i	−0.438169	+	1.02973i
$675$	25.3575	+	9.80165i	0.976009	+	0.377266i
$676$	−5.98810	+	25.3010i	−0.230312	+	0.973117i
$677$	−9.05251	+	9.05251i	−0.347916	+	0.347916i	−0.859333	−	0.511417i	$-0.829121\pi$
$677$	−9.05251	+	9.05251i	−0.347916	+	0.347916i	0.511417	+	0.859333i	$0.329121\pi$
$678$	1.65310	−	0.666198i	0.0634870	−	0.0255852i
$679$	5.61543			0.215501
$680$	−8.34439	+	5.37375i	−0.319993	+	0.206074i
$681$			14.7167i			0.563946i
$682$	0.556191	−	0.224144i	0.0212977	−	0.00858292i
$683$	19.2696	+	19.2696i	0.737331	+	0.737331i	0.972061	−	0.234730i	$-0.0754205\pi$
$683$	19.2696	+	19.2696i	0.737331	+	0.737331i	−0.234730	+	0.972061i	$0.575420\pi$
$684$	−14.1797	+	13.6448i	−0.542174	+	0.521722i
$685$	−21.1723	+	32.5194i	−0.808950	+	1.24250i
$686$	24.6700	+	10.4975i	0.941905	+	0.400798i
$687$	−24.4593	+	24.4593i	−0.933180	+	0.933180i
$688$	5.82496	+	6.29095i	0.222074	+	0.239840i
$689$	13.1799	−	24.1666i	0.502116	−	0.920675i
$690$	20.7149	−	13.9107i	0.788603	−	0.529572i
$691$	−19.1766			−0.729511			−0.364756	−	0.931103i	$-0.618847\pi$
$691$	−19.1766			−0.729511			−0.364756	+	0.931103i	$0.618847\pi$
$692$	24.4507	+	0.470025i	0.929477	+	0.0178677i
$693$	−0.264595	−	0.264595i	−0.0100511	−	0.0100511i
$694$	−12.9517	−	5.51117i	−0.491638	−	0.209201i
$695$	−9.06815	−	42.9080i	−0.343975	−	1.62759i
$696$	−13.7131	+	5.22227i	−0.519792	+	0.197950i
$697$	−3.24579	−	3.24579i	−0.122943	−	0.122943i
$698$	25.3453	−	10.2141i	0.959332	−	0.386609i
$699$	−29.7302			−1.12450
$700$	−6.63043	−	15.8000i	−0.250607	−	0.597184i
$701$	1.64833			0.0622567			0.0311284	−	0.999515i	$-0.490090\pi$
$701$	1.64833			0.0622567			0.0311284	+	0.999515i	$0.490090\pi$
$702$	−3.21429	+	27.5373i	−0.121315	+	1.03933i
$703$	−39.1741	+	39.1741i	−1.47748	+	1.47748i
$704$	−0.723005	−	0.811593i	−0.0272493	−	0.0305881i
$705$	29.7316	−	6.28347i	1.11976	−	0.236649i
$706$	−1.40168	+	3.29405i	−0.0527528	+	0.123973i
$707$	−3.18978	+	3.18978i	−0.119964	+	0.119964i
$708$	−12.9220	−	0.248403i	−0.485637	−	0.00933556i
$709$	19.9349			0.748672			0.374336	−	0.927293i	$-0.377871\pi$
$709$	19.9349			0.748672			0.374336	+	0.927293i	$0.377871\pi$
$710$	−7.91650	−	11.7887i	−0.297101	−	0.442423i
$711$		−	1.51760i		−	0.0569146i
$712$	3.73563	−	8.33085i	0.139999	−	0.312212i
$713$	14.7553	−	14.7553i	0.552588	−	0.552588i
$714$	−4.12937	−	1.75712i	−0.154538	−	0.0657587i
$715$	0.964229	−	0.519752i	0.0360601	−	0.0194376i
$716$	−18.4270	+	17.7319i	−0.688650	+	0.662673i
$717$	−12.7371	−	12.7371i	−0.475675	−	0.475675i
$718$	−4.00662	−	9.94203i	−0.149526	−	0.371033i
$719$	−30.5169			−1.13809			−0.569044	−	0.822307i	$-0.692687\pi$
$719$	−30.5169			−1.13809			−0.569044	+	0.822307i	$0.692687\pi$
$720$	−2.42986	−	14.1695i	−0.0905555	−	0.528068i
$721$			17.8469i			0.664652i
$722$	24.2308	−	9.76499i	0.901778	−	0.363415i
$723$	10.5707	+	10.5707i	0.393128	+	0.393128i
$724$	−6.46288	+	6.21909i	−0.240191	+	0.231131i
$725$	8.89357	+	20.1012i	0.330299	+	0.746540i
$726$	−7.17603	+	16.8642i	−0.266327	+	0.625889i
$727$	−16.6943	−	16.6943i	−0.619157	−	0.619157i	0.326159	−	0.945315i	$-0.394246\pi$
$727$	−16.6943	−	16.6943i	−0.619157	−	0.619157i	−0.945315	+	0.326159i	$0.894246\pi$
$728$	13.9111	−	10.5748i	0.515581	−	0.391929i
$729$			21.8124i			0.807867i
$730$	−26.5234	−	5.21204i	−0.981674	−	0.192906i
$731$		−	3.36359i		−	0.124407i
$732$	−0.534717	+	27.8160i	−0.0197637	+	1.02811i
$733$	−24.1094	+	24.1094i	−0.890499	+	0.890499i	−0.994570	−	0.104071i	$-0.966813\pi$
$733$	−24.1094	+	24.1094i	−0.890499	+	0.890499i	0.104071	+	0.994570i	$0.466813\pi$
$734$	−46.0606	−	19.5996i	−1.70013	−	0.723435i
$735$	−5.85123	+	8.98716i	−0.215826	+	0.331497i
$736$	−34.2087	−	16.1362i	−1.26095	−	0.594788i
$737$	0.965415	−	0.965415i	0.0355615	−	0.0355615i
$738$	6.16701	−	2.48529i	0.227011	−	0.0914849i
$739$			38.8417i			1.42881i	0.699731	+	0.714407i	$0.253303\pi$
$739$			38.8417i			1.42881i	−0.699731	+	0.714407i	$0.746697\pi$
$740$	−7.60616	−	39.7523i	−0.279608	−	1.46133i
$741$	12.4712	−	22.8671i	0.458141	−	0.840044i
$742$	−17.1595	+	6.91523i	−0.629943	+	0.253866i
$743$	1.46488	+	1.46488i	0.0537411	+	0.0537411i	0.733467	−	0.679726i	$-0.237901\pi$
$743$	1.46488	+	1.46488i	0.0537411	+	0.0537411i	−0.679726	+	0.733467i	$0.737901\pi$
$744$	3.70734	+	9.73504i	0.135918	+	0.356904i
$745$	1.10881	+	5.24660i	0.0406238	+	0.192221i
$746$	23.8137	+	10.1332i	0.871881	+	0.371001i
$747$	7.41417	−	7.41417i	0.271270	−	0.271270i
$748$	−0.00819582	+	0.426347i	−0.000299669	+	0.0155888i
$749$	−28.8747			−1.05506
$750$	18.1992	−	4.11778i	0.664542	−	0.150360i
$751$			3.07742i			0.112297i	0.998422	+	0.0561484i	$0.0178820\pi$
$751$			3.07742i			0.112297i	−0.998422	+	0.0561484i	$0.982118\pi$
$752$	−31.2960	−	33.7996i	−1.14125	−	1.23255i
$753$	−13.4255	−	13.4255i	−0.489253	−	0.489253i
$754$	−17.5813	+	13.9060i	−0.640275	+	0.506426i
$755$	−2.60429	−	12.3228i	−0.0947798	−	0.448472i
$756$	13.4263	−	12.9199i	0.488312	−	0.469892i
$757$	−31.9991	+	31.9991i	−1.16303	+	1.16303i	−0.179219	+	0.983809i	$0.557357\pi$
$757$	−31.9991	+	31.9991i	−1.16303	+	1.16303i	−0.983809	+	0.179219i	$0.942643\pi$
$758$	−13.4606	−	33.4012i	−0.488913	−	1.21319i
$759$		−	1.07207i		−	0.0389136i
$760$	−8.19393	+	37.8388i	−0.297225	+	1.37256i
$761$			9.64916i			0.349782i	0.984588	+	0.174891i	$0.0559572\pi$
$761$			9.64916i			0.349782i	−0.984588	+	0.174891i	$0.944043\pi$
$762$	−33.1943	+	13.3773i	−1.20250	+	0.484607i
$763$	−1.90252	+	1.90252i	−0.0688758	+	0.0688758i
$764$	32.2620	+	33.5267i	1.16720	+	1.21295i
$765$	−3.07735	+	4.72665i	−0.111262	+	0.170892i
$766$	−43.6483	−	18.5731i	−1.57708	−	0.671075i
$767$	−18.9410	+	5.57209i	−0.683918	+	0.201196i
$768$	14.3375	−	12.2865i	0.517362	−	0.443352i
$769$	13.2266			0.476963			0.238481	−	0.971147i	$-0.423350\pi$
$769$	13.2266			0.476963			0.238481	+	0.971147i	$0.423350\pi$
$770$	−0.722379	−	0.141953i	−0.0260327	−	0.00511562i
$771$		−	26.7519i		−	0.963445i
$772$	0.0487625	−	2.53663i	0.00175500	−	0.0912952i
$773$	0.434455	−	0.434455i	0.0156263	−	0.0156263i	−0.699250	−	0.714877i	$-0.746483\pi$
$773$	0.434455	−	0.434455i	0.0156263	−	0.0156263i	0.714877	+	0.699250i	$0.246483\pi$
$774$	4.48316	+	1.90767i	0.161144	+	0.0685696i
$775$	14.2700	−

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)

\(f(q)\)	\(=\)	\(q+(-1.31170 + 0.528615i) q^{2} +(-0.834468 + 0.834468i) q^{3} +(1.44113 - 1.38677i) q^{4} +(-0.462357 - 2.18774i) q^{5} +(0.653463 - 1.53569i) q^{6} +(-1.21162 + 1.21162i) q^{7} +(-1.15727 + 2.58084i) q^{8} +1.60733i q^{9} +O(q^{10})\)	\(q+(-1.31170 + 0.528615i) q^{2} +(-0.834468 + 0.834468i) q^{3} +(1.44113 - 1.38677i) q^{4} +(-0.462357 - 2.18774i) q^{5} +(0.653463 - 1.53569i) q^{6} +(-1.21162 + 1.21162i) q^{7} +(-1.15727 + 2.58084i) q^{8} +1.60733i q^{9} +(1.76295 + 2.62526i) q^{10} +0.135866 q^{11} +(-0.0453632 + 2.35980i) q^{12} +(1.01757 + 3.45898i) q^{13} +(0.948804 - 2.22976i) q^{14} +(2.21142 + 1.43978i) q^{15} +(0.153730 - 3.99704i) q^{16} +(-1.10965 + 1.10965i) q^{17} +(-0.849657 - 2.10834i) q^{18} +6.12150i q^{19} +(-3.70022 - 2.51165i) q^{20} -2.02211i q^{21} +(-0.178217 + 0.0718210i) q^{22} +(-4.72792 + 4.72792i) q^{23} +(-1.18792 - 3.11933i) q^{24} +(-4.57245 + 2.02304i) q^{25} +(-3.16322 - 3.99926i) q^{26} +(-3.84467 - 3.84467i) q^{27} +(-0.0658656 + 3.42634i) q^{28} -4.39615i q^{29} +(-3.66182 - 0.719575i) q^{30} -3.12087 q^{31} +(1.91125 + 5.32420i) q^{32} +(-0.113376 + 0.113376i) q^{33} +(0.868956 - 2.04211i) q^{34} +(3.21091 + 2.09051i) q^{35} +(2.22900 + 2.31637i) q^{36} +(6.39942 + 6.39942i) q^{37} +(-3.23592 - 8.02960i) q^{38} +(-3.73554 - 2.03728i) q^{39} +(6.18129 + 1.33855i) q^{40} +2.92506i q^{41} +(1.06892 + 2.65241i) q^{42} +(-1.51561 + 1.51561i) q^{43} +(0.195802 - 0.188416i) q^{44} +(3.51642 - 0.743158i) q^{45} +(3.70239 - 8.70089i) q^{46} +(8.14297 - 8.14297i) q^{47} +(3.20712 + 3.46369i) q^{48} +4.06397i q^{49} +(4.92830 - 5.07069i) q^{50} -1.85194i q^{51} +(6.26327 + 3.57372i) q^{52} +(-5.39849 - 5.39849i) q^{53} +(7.07541 + 3.01072i) q^{54} +(-0.0628188 - 0.297241i) q^{55} +(-1.72481 - 4.52915i) q^{56} +(-5.10820 - 5.10820i) q^{57} +(2.32387 + 5.76645i) q^{58} +5.47588i q^{59} +(5.18360 - 0.991824i) q^{60} +11.7875 q^{61} +(4.09366 - 1.64974i) q^{62} +(-1.94746 - 1.94746i) q^{63} +(-5.32144 - 5.97346i) q^{64} +(7.09689 - 3.82547i) q^{65} +(0.0887836 - 0.208648i) q^{66} +(7.10562 - 7.10562i) q^{67} +(-0.0603226 + 3.13799i) q^{68} -7.89060i q^{69} +(-5.31683 - 1.04480i) q^{70} -4.49049 q^{71} +(-4.14825 - 1.86011i) q^{72} +(-6.04423 + 6.04423i) q^{73} +(-11.7770 - 5.01132i) q^{74} +(2.12741 - 5.50372i) q^{75} +(8.48913 + 8.82190i) q^{76} +(-0.164618 + 0.164618i) q^{77} +(5.97685 + 0.697647i) q^{78} -0.944179 q^{79} +(-8.81559 + 1.51174i) q^{80} +1.59452 q^{81} +(-1.54623 - 3.83681i) q^{82} +(-4.61273 - 4.61273i) q^{83} +(-2.80420 - 2.91413i) q^{84} +(2.94069 + 1.91458i) q^{85} +(1.18686 - 2.78920i) q^{86} +(3.66845 + 3.66845i) q^{87} +(-0.157234 + 0.350649i) q^{88} -3.22796 q^{89} +(-4.21966 + 2.83364i) q^{90} +(-5.42386 - 2.95805i) q^{91} +(-0.257018 + 13.3701i) q^{92} +(2.60427 - 2.60427i) q^{93} +(-6.37667 + 14.9857i) q^{94} +(13.3923 - 2.83032i) q^{95} +(-6.03775 - 2.84800i) q^{96} +(-2.31733 - 2.31733i) q^{97} +(-2.14827 - 5.33073i) q^{98} +0.218382i 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

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