LMFDB - Embedded newform 546.2.u.a.185.4

Newspace parameters

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.u (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.4
Character	$\chi$	$=$	546.185
Dual form			546.2.u.a.425.4

$q$-expansion

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.51699 - 0.835899i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.699535 - 1.21163i) q^{5} +(0.895807 + 1.48241i) q^{6} +(1.97618 + 1.75918i) q^{7} -1.00000i q^{8} +(1.60255 + 2.53611i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.51699 - 0.835899i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.699535 - 1.21163i) q^{5} +(0.895807 + 1.48241i) q^{6} +(1.97618 + 1.75918i) q^{7} -1.00000i q^{8} +(1.60255 + 2.53611i) q^{9} +1.39907i q^{10} -1.26560i q^{11} +(-0.0345880 - 1.73171i) q^{12} +(-3.58555 - 0.379286i) q^{13} +(-0.831830 - 2.51159i) q^{14} +(0.0483911 + 2.42278i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.43402 + 5.94790i) q^{17} +(-0.119792 - 2.99761i) q^{18} +4.61200i q^{19} +(0.699535 - 1.21163i) q^{20} +(-1.52735 - 4.32055i) q^{21} +(-0.632798 + 1.09604i) q^{22} +(2.17983 + 1.25852i) q^{23} +(-0.835899 + 1.51699i) q^{24} +(1.52130 - 2.63497i) q^{25} +(2.91553 + 2.12124i) q^{26} +(-0.311127 - 5.18683i) q^{27} +(-0.535407 + 2.59101i) q^{28} +(4.55247 - 2.62837i) q^{29} +(1.16948 - 2.12238i) q^{30} +(4.41277 + 2.54772i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.05791 + 1.91990i) q^{33} -6.86805i q^{34} +(0.749072 - 3.62501i) q^{35} +(-1.39506 + 2.65590i) q^{36} +(3.45697 - 5.98766i) q^{37} +(2.30600 - 3.99411i) q^{38} +(5.12221 + 3.57253i) q^{39} +(-1.21163 + 0.699535i) q^{40} +(-3.22591 - 5.58745i) q^{41} +(-0.837549 + 4.50539i) q^{42} +(6.08396 - 10.5377i) q^{43} +(1.09604 - 0.632798i) q^{44} +(1.95179 - 3.71579i) q^{45} +(-1.25852 - 2.17983i) q^{46} +(1.58414 + 2.74382i) q^{47} +(1.48241 - 0.895807i) q^{48} +(0.810561 + 6.95291i) q^{49} +(-2.63497 + 1.52130i) q^{50} +(-0.237552 - 11.8934i) q^{51} +(-1.46430 - 3.29482i) q^{52} +(0.444106 + 0.256405i) q^{53} +(-2.32397 + 4.64749i) q^{54} +(-1.53343 + 0.885329i) q^{55} +(1.75918 - 1.97618i) q^{56} +(3.85517 - 6.99639i) q^{57} -5.25674 q^{58} +(7.18719 + 12.4486i) q^{59} +(-2.07399 + 1.25330i) q^{60} +3.07454i q^{61} +(-2.54772 - 4.41277i) q^{62} +(-1.29456 + 7.83097i) q^{63} -1.00000 q^{64} +(2.04866 + 4.60968i) q^{65} +(1.87613 - 1.13373i) q^{66} -0.624480 q^{67} +(-3.43402 + 5.94790i) q^{68} +(-2.25479 - 3.73129i) q^{69} +(-2.46122 + 2.76481i) q^{70} +(3.78894 + 2.18755i) q^{71} +(2.53611 - 1.60255i) q^{72} +(-7.24349 - 4.18203i) q^{73} +(-5.98766 + 3.45697i) q^{74} +(-4.51037 + 2.72558i) q^{75} +(-3.99411 + 2.30600i) q^{76} +(2.22641 - 2.50104i) q^{77} +(-2.64970 - 5.65501i) q^{78} +(7.13902 + 12.3651i) q^{79} +1.39907 q^{80} +(-3.86369 + 8.12846i) q^{81} +6.45183i q^{82} +3.52068 q^{83} +(2.97803 - 3.48301i) q^{84} +(4.80444 - 8.32154i) q^{85} +(-10.5377 + 6.08396i) q^{86} +(-9.10312 + 0.181820i) q^{87} -1.26560 q^{88} +(7.94368 - 13.7588i) q^{89} +(-3.54819 + 2.24208i) q^{90} +(-6.41845 - 7.05716i) q^{91} +2.51705i q^{92} +(-4.56452 - 7.55351i) q^{93} -3.16829i q^{94} +(5.58804 - 3.22626i) q^{95} +(-1.73171 + 0.0345880i) q^{96} +(-2.18746 - 1.26293i) q^{97} +(2.77449 - 6.42668i) q^{98} +(3.20969 - 2.02818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−1.51699	−	0.835899i	−0.875837	−	0.482606i
$3$	−1.51699	−	0.835899i	−0.875837	−	0.482606i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.699535	−	1.21163i	−0.312842	−	0.541858i	0.666135	−	0.745831i	$-0.267948\pi$
$5$	−0.699535	−	1.21163i	−0.312842	−	0.541858i	−0.978976	+	0.203974i	$0.934614\pi$
$6$	0.895807	+	1.48241i	0.365712	+	0.605190i
$7$	1.97618	+	1.75918i	0.746925	+	0.664908i
$7$	1.97618	+	1.75918i	0.746925	+	0.664908i
$8$		−	1.00000i		−	0.353553i
$9$	1.60255	+	2.53611i	0.534182	+	0.845369i
$10$			1.39907i			0.442425i
$11$		−	1.26560i		−	0.381592i	−0.981630	−	0.190796i	$-0.938893\pi$
$11$		−	1.26560i		−	0.381592i	0.981630	−	0.190796i	$-0.0611068\pi$
$12$	−0.0345880	−	1.73171i	−0.00998470	−	0.499900i
$13$	−3.58555	−	0.379286i	−0.994452	−	0.105195i
$13$	−3.58555	−	0.379286i	−0.994452	−	0.105195i
$14$	−0.831830	−	2.51159i	−0.222316	−	0.671249i
$15$	0.0483911	+	2.42278i	0.0124945	+	0.625558i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.43402	+	5.94790i	0.832873	+	1.44258i	0.895750	+	0.444557i	$0.146639\pi$
$17$	3.43402	+	5.94790i	0.832873	+	1.44258i	−0.0628771	+	0.998021i	$0.520028\pi$
$18$	−0.119792	−	2.99761i	−0.0282354	−	0.706543i
$19$			4.61200i			1.05807i	0.848601	+	0.529033i	$0.177445\pi$
$19$			4.61200i			1.05807i	−0.848601	+	0.529033i	$0.822555\pi$
$20$	0.699535	−	1.21163i	0.156421	−	0.270929i
$21$	−1.52735	−	4.32055i	−0.333296	−	0.942822i
$22$	−0.632798	+	1.09604i	−0.134913	+	0.233676i
$23$	2.17983	+	1.25852i	0.454525	+	0.262420i	0.709739	−	0.704464i	$-0.248813\pi$
$23$	2.17983	+	1.25852i	0.454525	+	0.262420i	−0.255214	+	0.966885i	$0.582146\pi$
$24$	−0.835899	+	1.51699i	−0.170627	+	0.309655i
$25$	1.52130	−	2.63497i	0.304260	−	0.526994i
$26$	2.91553	+	2.12124i	0.571783	+	0.416010i
$27$	−0.311127	−	5.18683i	−0.0598763	−	0.998206i
$28$	−0.535407	+	2.59101i	−0.101182	+	0.489655i
$29$	4.55247	−	2.62837i	0.845372	−	0.488076i	−0.0137143	−	0.999906i	$-0.504366\pi$
$29$	4.55247	−	2.62837i	0.845372	−	0.488076i	0.859087	+	0.511830i	$0.171032\pi$
$30$	1.16948	−	2.12238i	0.213517	−	0.387492i
$31$	4.41277	+	2.54772i	0.792558	+	0.457583i	0.840862	−	0.541249i	$-0.182048\pi$
$31$	4.41277	+	2.54772i	0.792558	+	0.457583i	−0.0483045	+	0.998833i	$0.515382\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−1.05791	+	1.91990i	−0.184158	+	0.334212i
$34$		−	6.86805i		−	1.17786i
$35$	0.749072	−	3.62501i	0.126616	−	0.612738i
$36$	−1.39506	+	2.65590i	−0.232510	+	0.442650i
$37$	3.45697	−	5.98766i	0.568323	−	0.984365i	−0.428409	−	0.903585i	$-0.640926\pi$
$37$	3.45697	−	5.98766i	0.568323	−	0.984365i	0.996732	−	0.0807796i	$-0.0257410\pi$
$38$	2.30600	−	3.99411i	0.374083	−	0.647931i
$39$	5.12221	+	3.57253i	0.820210	+	0.572062i
$40$	−1.21163	+	0.699535i	−0.191576	+	0.110606i
$41$	−3.22591	−	5.58745i	−0.503803	−	0.872613i	−0.999990	−	0.00439709i	$-0.998600\pi$
$41$	−3.22591	−	5.58745i	−0.503803	−	0.872613i	0.496187	−	0.868216i	$-0.334733\pi$
$42$	−0.837549	+	4.50539i	−0.129237	+	0.695196i
$43$	6.08396	−	10.5377i	0.927796	−	1.60699i	0.140794	−	0.990039i	$-0.455034\pi$
$43$	6.08396	−	10.5377i	0.927796	−	1.60699i	0.787002	−	0.616951i	$-0.211632\pi$
$44$	1.09604	−	0.632798i	0.165234	−	0.0953979i
$45$	1.95179	−	3.71579i	0.290955	−	0.553917i
$46$	−1.25852	−	2.17983i	−0.185559	−	0.321398i
$47$	1.58414	+	2.74382i	0.231071	+	0.400227i	0.958124	−	0.286355i	$-0.0924437\pi$
$47$	1.58414	+	2.74382i	0.231071	+	0.400227i	−0.727053	+	0.686582i	$0.759110\pi$
$48$	1.48241	−	0.895807i	0.213967	−	0.129299i
$49$	0.810561	+	6.95291i	0.115794	+	0.993273i
$50$	−2.63497	+	1.52130i	−0.372641	+	0.215144i
$51$	−0.237552	−	11.8934i	−0.0332639	−	1.66541i
$52$	−1.46430	−	3.29482i	−0.203062	−	0.456909i
$53$	0.444106	+	0.256405i	0.0610026	+	0.0352199i	0.530191	−	0.847878i	$-0.322120\pi$
$53$	0.444106	+	0.256405i	0.0610026	+	0.0352199i	−0.469188	+	0.883098i	$0.655454\pi$
$54$	−2.32397	+	4.64749i	−0.316252	+	0.632443i
$55$	−1.53343	+	0.885329i	−0.206768	+	0.119378i
$56$	1.75918	−	1.97618i	0.235081	−	0.264078i
$57$	3.85517	−	6.99639i	0.510629	−	0.926694i
$58$	−5.25674			−0.690244
$59$	7.18719	+	12.4486i	0.935693	+	1.62067i	0.773393	+	0.633926i	$0.218558\pi$
$59$	7.18719	+	12.4486i	0.935693	+	1.62067i	0.162300	+	0.986742i	$0.448109\pi$
$60$	−2.07399	+	1.25330i	−0.267751	+	0.161800i
$61$			3.07454i			0.393654i	0.980438	+	0.196827i	$0.0630638\pi$
$61$			3.07454i			0.393654i	−0.980438	+	0.196827i	$0.936936\pi$
$62$	−2.54772	−	4.41277i	−0.323560	−	0.560423i
$63$	−1.29456	+	7.83097i	−0.163099	+	0.986610i
$64$	−1.00000			−0.125000
$65$	2.04866	+	4.60968i	0.254105	+	0.571760i
$66$	1.87613	−	1.13373i	0.230935	−	0.139552i
$67$	−0.624480			−0.0762924			−0.0381462	−	0.999272i	$-0.512145\pi$
$67$	−0.624480			−0.0762924			−0.0381462	+	0.999272i	$0.512145\pi$
$68$	−3.43402	+	5.94790i	−0.416437	+	0.721289i
$69$	−2.25479	−	3.73129i	−0.271444	−	0.449194i
$70$	−2.46122	+	2.76481i	−0.294172	+	0.330458i
$71$	3.78894	+	2.18755i	0.449665	+	0.259614i	0.707689	−	0.706524i	$-0.249738\pi$
$71$	3.78894	+	2.18755i	0.449665	+	0.259614i	−0.258024	+	0.966139i	$0.583071\pi$
$72$	2.53611	−	1.60255i	0.298883	−	0.188862i
$73$	−7.24349	−	4.18203i	−0.847786	−	0.489470i	0.0121171	−	0.999927i	$-0.496143\pi$
$73$	−7.24349	−	4.18203i	−0.847786	−	0.489470i	−0.859903	+	0.510457i	$0.829476\pi$
$74$	−5.98766	+	3.45697i	−0.696051	+	0.401865i
$75$	−4.51037	+	2.72558i	−0.520813	+	0.314723i
$76$	−3.99411	+	2.30600i	−0.458156	+	0.264517i
$77$	2.22641	−	2.50104i	0.253723	−	0.285020i
$78$	−2.64970	−	5.65501i	−0.300020	−	0.640303i
$79$	7.13902	+	12.3651i	0.803203	+	1.39119i	0.917498	+	0.397741i	$0.130206\pi$
$79$	7.13902	+	12.3651i	0.803203	+	1.39119i	−0.114295	+	0.993447i	$0.536461\pi$
$80$	1.39907			0.156421
$81$	−3.86369	+	8.12846i	−0.429298	+	0.903163i
$82$			6.45183i			0.712485i
$83$	3.52068			0.386444			0.193222	−	0.981155i	$-0.438106\pi$
$83$	3.52068			0.386444			0.193222	+	0.981155i	$0.438106\pi$
$84$	2.97803	−	3.48301i	0.324930	−	0.380027i
$85$	4.80444	−	8.32154i	0.521115	−	0.902597i
$86$	−10.5377	+	6.08396i	−1.13631	+	0.656051i
$87$	−9.10312	+	0.181820i	−0.975957	+	0.0194932i
$88$	−1.26560			−0.134913
$89$	7.94368	−	13.7588i	0.842028	−	1.45844i	−0.0461496	−	0.998935i	$-0.514695\pi$
$89$	7.94368	−	13.7588i	0.842028	−	1.45844i	0.888177	−	0.459501i	$-0.151972\pi$
$90$	−3.54819	+	2.24208i	−0.374012	+	0.236336i
$91$	−6.41845	−	7.05716i	−0.672836	−	0.739792i
$92$			2.51705i			0.262420i
$93$	−4.56452	−	7.55351i	−0.473319	−	0.783262i
$94$		−	3.16829i		−	0.326784i
$95$	5.58804	−	3.22626i	0.573321	−	0.331007i
$96$	−1.73171	+	0.0345880i	−0.176741	+	0.00353012i
$97$	−2.18746	−	1.26293i	−0.222102	−	0.128231i	0.384821	−	0.922991i	$-0.374263\pi$
$97$	−2.18746	−	1.26293i	−0.222102	−	0.128231i	−0.606923	+	0.794760i	$0.707597\pi$
$98$	2.77449	−	6.42668i	0.280266	−	0.649193i
$99$	3.20969	−	2.02818i	0.322586	−	0.203839i
$100$	3.04260			0.304260
$101$	8.43460			0.839274			0.419637	−	0.907692i	$-0.362157\pi$
$101$	8.43460			0.839274			0.419637	+	0.907692i	$0.362157\pi$
$102$	−5.74099	+	10.4188i	−0.568443	+	1.03161i
$103$	−10.2521	+	5.91907i	−1.01017	+	0.583224i	−0.911242	−	0.411871i	$-0.864876\pi$
$103$	−10.2521	+	5.91907i	−1.01017	+	0.583224i	−0.0989308	+	0.995094i	$0.531542\pi$
$104$	−0.379286	+	3.58555i	−0.0371920	+	0.351592i
$105$	−4.16648	+	4.87297i	−0.406606	+	0.475553i
$106$	−0.256405	−	0.444106i	−0.0249042	−	0.0431354i
$107$	1.80672	+	1.04311i	0.174663	+	0.100841i	0.584783	−	0.811190i	$-0.301180\pi$
$107$	1.80672	+	1.04311i	0.174663	+	0.100841i	−0.410120	+	0.912032i	$0.634513\pi$
$108$	4.33636	−	2.86286i	0.417267	−	0.275479i
$109$	−7.90043	+	13.6840i	−0.756724	+	1.31068i	0.187788	+	0.982210i	$0.439868\pi$
$109$	−7.90043	+	13.6840i	−0.756724	+	1.31068i	−0.944513	+	0.328475i	$0.893465\pi$
$110$	1.77066			0.168826
$111$	−10.2493	+	6.19356i	−0.972819	+	0.587867i
$112$	−2.51159	+	0.831830i	−0.237322	+	0.0786005i
$113$	−10.6760	−	6.16378i	−1.00431	−	0.579840i	−0.0947910	−	0.995497i	$-0.530218\pi$
$113$	−10.6760	−	6.16378i	−1.00431	−	0.579840i	−0.909521	+	0.415657i	$0.863552\pi$
$114$	−6.83687	+	4.13146i	−0.640331	+	0.386947i
$115$		−	3.52152i		−	0.328384i
$116$	4.55247	+	2.62837i	0.422686	+	0.244038i
$117$	−4.78410	−	9.70116i	−0.442290	−	0.896872i
$118$		−	14.3744i		−	1.32327i
$119$	−3.67720	+	17.7952i	−0.337088	+	1.63128i
$120$	2.42278	−	0.0483911i	0.221168	−	0.00441748i
$121$	9.39827			0.854388
$122$	1.53727	−	2.66263i	0.139178	−	0.241063i
$123$	0.223156	+	11.1727i	0.0201213	+	1.00741i
$124$			5.09543i			0.457583i
$125$	−11.2522			−1.00642
$126$	5.03660	−	6.13454i	0.448696	−	0.546509i
$127$	4.41803	+	7.65224i	0.392036	+	0.679027i	0.992718	−	0.120461i	$-0.0384374\pi$
$127$	4.41803	+	7.65224i	0.392036	+	0.679027i	−0.600682	+	0.799488i	$0.705104\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−18.0378	+	10.9001i	−1.58814	+	0.959701i
$130$	0.530647	−	5.01643i	0.0465408	−	0.439970i
$131$	8.68707	+	15.0464i	0.758993	+	1.31461i	0.943365	+	0.331757i	$0.107642\pi$
$131$	8.68707	+	15.0464i	0.758993	+	1.31461i	−0.184372	+	0.982857i	$0.559025\pi$
$132$	−2.19164	+	0.0437744i	−0.190758	+	0.00381008i
$133$	−8.11335	+	9.11414i	−0.703517	+	0.790296i
$134$	0.540816	+	0.312240i	0.0467194	+	0.0269734i
$135$	−6.06688	+	4.00534i	−0.522154	+	0.344725i
$136$	5.94790	−	3.43402i	0.510029	−	0.294465i
$137$	−6.13476	+	3.54190i	−0.524128	+	0.302605i	−0.738622	−	0.674120i	$-0.764523\pi$
$137$	−6.13476	+	3.54190i	−0.524128	+	0.302605i	0.214494	+	0.976725i	$0.431190\pi$
$138$	0.0870596	+	4.35878i	0.00741101	+	0.371044i
$139$	1.93885	+	1.11939i	0.164451	+	0.0949457i	0.579967	−	0.814640i	$-0.303066\pi$
$139$	1.93885	+	1.11939i	0.164451	+	0.0949457i	−0.415516	+	0.909586i	$0.636399\pi$
$140$	3.51388	−	1.16379i	0.296977	−	0.0983581i
$141$	−0.109585	−	5.48654i	−0.00922870	−	0.462050i
$142$	−2.18755	−	3.78894i	−0.183575	−	0.317961i
$143$	−0.480022	+	4.53785i	−0.0401415	+	0.379474i
$144$	−2.99761	+	0.119792i	−0.249801	+	0.00998271i
$145$	−6.36923	−	3.67727i	−0.528935	−	0.305381i
$146$	4.18203	+	7.24349i	0.346107	+	0.599475i
$147$	4.58231	−	11.2251i	0.377943	−	0.925829i
$148$	6.91395			0.568323
$149$		−	9.99843i		−	0.819103i	−0.912287	−	0.409552i	$-0.865685\pi$
$149$		−	9.99843i		−	0.819103i	0.912287	−	0.409552i	$-0.134315\pi$
$150$	5.26889	−	0.105238i	0.430203	−	0.00859261i
$151$	3.60495	−	6.24397i	0.293367	−	0.508127i	−0.681237	−	0.732063i	$-0.738558\pi$
$151$	3.60495	−	6.24397i	0.293367	−	0.508127i	0.974604	+	0.223937i	$0.0718909\pi$
$152$	4.61200			0.374083
$153$	−9.58134	+	18.2409i	−0.774606	+	1.47469i
$154$	−3.17865	+	1.05276i	−0.256143	+	0.0848339i
$155$		−	7.12887i		−	0.572605i
$156$	−0.532794	+	6.22223i	−0.0426576	+	0.498177i
$157$	−5.32283	−	3.07314i	−0.424808	−	0.245263i	0.272324	−	0.962206i	$-0.412208\pi$
$157$	−5.32283	−	3.07314i	−0.424808	−	0.245263i	−0.697132	+	0.716942i	$0.745541\pi$
$158$		−	14.2780i		−	1.13590i
$159$	−0.459378	−	0.760192i	−0.0364310	−	0.0602871i
$160$	−1.21163	−	0.699535i	−0.0957878	−	0.0553031i
$161$	2.09375	+	6.32178i	0.165011	+	0.498226i
$162$	7.41028	−	5.10761i	0.582207	−	0.401292i
$163$	−13.7896			−1.08009			−0.540044	−	0.841637i	$-0.681593\pi$
$163$	−13.7896			−1.08009			−0.540044	+	0.841637i	$0.681593\pi$
$164$	3.22591	−	5.58745i	0.251902	−	0.436306i
$165$	3.06626	−	0.0612435i	0.238708	−	0.00476780i
$166$	−3.04900	−	1.76034i	−0.236648	−	0.136629i
$167$	−7.46828	−	12.9354i	−0.577913	−	1.00097i	−0.995718	−	0.0924384i	$-0.970534\pi$
$167$	−7.46828	−	12.9354i	−0.577913	−	1.00097i	0.417805	−	0.908537i	$-0.362799\pi$
$168$	−4.32055	+	1.52735i	−0.333338	+	0.117838i
$169$	12.7123	+	2.71989i	0.977868	+	0.209222i
$170$	−8.32154	+	4.80444i	−0.638233	+	0.368484i
$171$	−11.6965	+	7.39095i	−0.894457	+	0.565200i
$172$	12.1679			0.927796
$173$	5.48732			0.417193			0.208597	−	0.978002i	$-0.433110\pi$
$173$	5.48732			0.417193			0.208597	+	0.978002i	$0.433110\pi$
$174$	7.97445	+	4.39410i	0.604541	+	0.333116i
$175$	7.64175	−	2.53093i	0.577662	−	0.191320i
$176$	1.09604	+	0.632798i	0.0826170	+	0.0476989i
$177$	−0.497181	−	24.8922i	−0.0373704	−	1.87101i
$178$	−13.7588	+	7.94368i	−1.03127	+	0.595404i
$179$			6.22348i			0.465164i	0.972577	+	0.232582i	$0.0747175\pi$
$179$			6.22348i			0.465164i	−0.972577	+	0.232582i	$0.925283\pi$
$180$	4.19386	−	0.167598i	0.312592	−	0.0124920i
$181$		−	10.2706i		−	0.763407i	−0.924285	−	0.381704i	$-0.875337\pi$
$181$		−	10.2706i		−	0.763407i	0.924285	−	0.381704i	$-0.124663\pi$
$182$	2.02996	+	9.32091i	0.150470	+	0.690911i
$183$	2.57000	−	4.66406i	0.189980	−	0.344777i
$184$	1.25852	−	2.17983i	0.0927795	−	0.160699i
$185$	−9.67310			−0.711181
$186$	0.176241	+	8.82379i	0.0129226	+	0.646992i
$187$	7.52764	−	4.34609i	0.550476	−	0.317817i
$188$	−1.58414	+	2.74382i	−0.115536	+	0.200113i
$189$	8.50973	−	10.7974i	0.618992	−	0.785397i
$190$	−6.45252			−0.468115
$191$			9.71283i			0.702796i	0.936226	+	0.351398i	$0.114294\pi$
$191$			9.71283i			0.702796i	−0.936226	+	0.351398i	$0.885706\pi$
$192$	1.51699	+	0.835899i	0.109480	+	0.0603258i
$193$	5.46485			0.393368			0.196684	−	0.980467i	$-0.436983\pi$
$193$	5.46485			0.393368			0.196684	+	0.980467i	$0.436983\pi$
$194$	1.26293	+	2.18746i	0.0906729	+	0.157050i
$195$	0.745416	−	8.70534i	0.0533804	−	0.623402i
$196$	−5.61612	+	4.17842i	−0.401151	+	0.298459i
$197$	−22.5837	+	13.0387i	−1.60902	+	0.928971i	−0.619435	+	0.785048i	$0.712638\pi$
$197$	−22.5837	+	13.0387i	−1.60902	+	0.928971i	−0.989589	+	0.143923i	$0.954028\pi$
$198$	−3.79376	+	0.151609i	−0.269611	+	0.0107744i
$199$	11.8705	−	6.85344i	0.841478	−	0.485828i	−0.0162883	−	0.999867i	$-0.505185\pi$
$199$	11.8705	−	6.85344i	0.841478	−	0.485828i	0.857766	+	0.514040i	$0.171852\pi$
$200$	−2.63497	−	1.52130i	−0.186321	−	0.107572i
$201$	0.947333	+	0.522002i	0.0668197	+	0.0368192i
$202$	−7.30458	−	4.21730i	−0.513948	−	0.296728i
$203$	13.6203	+	2.81449i	0.955956	+	0.197539i
$204$	10.1812	−	6.15244i	0.712830	−	0.430757i
$205$	−4.51328	+	7.81723i	−0.315221	+	0.545979i
$206$	11.8381			0.824803
$207$	0.301523	+	7.54512i	0.0209573	+	0.524422i
$208$	2.12124	−	2.91553i	0.147082	−	0.202156i
$209$	5.83693			0.403749
$210$	6.04476	−	2.13688i	0.417128	−	0.147459i
$211$	6.43745	+	11.1500i	0.443172	+	0.767597i	0.997923	−	0.0644199i	$-0.0205197\pi$
$211$	6.43745	+	11.1500i	0.443172	+	0.767597i	−0.554751	+	0.832017i	$0.687186\pi$
$212$			0.512809i			0.0352199i
$213$	−3.91924	−	6.48567i	−0.268542	−	0.444391i
$214$	−1.04311	−	1.80672i	−0.0713057	−	0.123505i
$215$	−17.0238			−1.16101
$216$	−5.18683	+	0.311127i	−0.352919	+	0.0211695i
$217$	4.23853	+	12.7976i	0.287730	+	0.868759i
$218$	13.6840	−	7.90043i	0.926794	−	0.535085i
$219$	7.49258	+	12.3989i	0.506302	+	0.837843i
$220$	−1.53343	−	0.885329i	−0.103384	−	0.0596889i
$221$	−10.0569	−	22.6290i	−0.676500	−	1.52219i
$222$	11.9729	−	0.239140i	0.803570	−	0.0160500i
$223$	17.8707	−	10.3176i	1.19671	−	0.690919i	0.236888	−	0.971537i	$-0.423873\pi$
$223$	17.8707	−	10.3176i	1.19671	−	0.690919i	0.959820	+	0.280618i	$0.0905393\pi$
$224$	2.59101	+	0.535407i	0.173119	+	0.0357734i
$225$	9.12053	−	0.364481i	0.608035	−	0.0242987i
$226$	6.16378	+	10.6760i	0.410009	+	0.710156i
$227$	−9.10254	−	15.7661i	−0.604157	−	1.04643i	−0.992184	−	0.124783i	$-0.960177\pi$
$227$	−9.10254	−	15.7661i	−0.604157	−	1.04643i	0.388027	−	0.921648i	$-0.373157\pi$
$228$	7.98663	−	0.159520i	0.528928	−	0.0105645i
$229$	−16.0335	+	9.25697i	−1.05953	+	0.611717i	−0.925301	−	0.379233i	$-0.876188\pi$
$229$	−16.0335	+	9.25697i	−1.05953	+	0.611717i	−0.134225	+	0.990951i	$0.542854\pi$
$230$	−1.76076	+	3.04973i	−0.116101	+	0.201093i
$231$	−5.46808	+	1.93301i	−0.359773	+	0.127183i
$232$	−2.62837	−	4.55247i	−0.172561	−	0.298884i
$233$	9.27681	−	5.35597i	0.607744	−	0.350881i	−0.164338	−	0.986404i	$-0.552549\pi$
$233$	9.27681	−	5.35597i	0.607744	−	0.350881i	0.772082	+	0.635523i	$0.219215\pi$
$234$	−0.707428	+	10.7935i	−0.0462460	+	0.705593i
$235$	2.21633	−	3.83879i	0.144577	−	0.250415i
$236$	−7.18719	+	12.4486i	−0.467847	+	0.810334i
$237$	−0.493849	−	24.7254i	−0.0320789	−	1.60608i
$238$	12.0821	−	13.5725i	0.783169	−	0.879774i
$239$		−	3.88709i		−	0.251435i	−0.992066	−	0.125718i	$-0.959877\pi$
$239$		−	3.88709i		−	0.251435i	0.992066	−	0.125718i	$-0.0401233\pi$
$240$	−2.12238	−	1.16948i	−0.136999	−	0.0754897i
$241$	−5.35649	+	3.09257i	−0.345042	+	0.199210i	−0.662499	−	0.749063i	$-0.730504\pi$
$241$	−5.35649	+	3.09257i	−0.345042	+	0.199210i	0.317458	+	0.948272i	$0.397171\pi$
$242$	−8.13914	−	4.69913i	−0.523204	−	0.302072i
$243$	12.6558	−	9.10119i	0.811868	−	0.583842i
$244$	−2.66263	+	1.53727i	−0.170457	+	0.0984136i
$245$	7.85734	−	5.84591i	0.501987	−	0.373481i
$246$	5.39307	−	9.78739i	0.343850	−	0.624021i
$247$	1.74927	−	16.5366i	0.111303	−	1.05220i
$248$	2.54772	−	4.41277i	0.161780	−	0.280211i
$249$	−5.34085	−	2.94293i	−0.338463	−	0.186501i
$250$	9.74466	+	5.62608i	0.616307	+	0.355825i
$251$	−0.889061	+	1.53990i	−0.0561171	+	0.0971976i	−0.892719	−	0.450613i	$-0.851205\pi$
$251$	−0.889061	+	1.53990i	−0.0561171	+	0.0971976i	0.836602	+	0.547811i	$0.184539\pi$
$252$	−7.42910	+	2.79437i	−0.467989	+	0.176029i
$253$	1.59278	−	2.75878i	0.100137	−	0.173443i
$254$		−	8.83605i		−	0.554423i
$255$	−14.2443	+	8.60770i	−0.892011	+	0.539035i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.01246	−	10.4139i	0.375047	−	0.649600i	−0.615287	−	0.788303i	$-0.710960\pi$
$257$	6.01246	−	10.4139i	0.375047	−	0.649600i	0.990334	+	0.138703i	$0.0442933\pi$
$258$	21.0713	−	0.420864i	1.31184	−	0.0262019i
$259$	17.3650	−	5.75123i	1.07901	−	0.357364i
$260$	−2.96777	+	4.07903i	−0.184053	+	0.252971i
$261$	13.9614	+	7.33347i	0.864188	+	0.453930i
$262$		−	17.3741i		−	1.07338i
$263$		−	1.89489i		−	0.116844i	−0.998292	−	0.0584219i	$-0.981393\pi$
$263$		−	1.89489i		−	0.116844i	0.998292	−	0.0584219i	$-0.0186069\pi$
$264$	1.91990	+	1.05791i	0.118162	+	0.0651099i
$265$		−	0.717456i		−	0.0440730i
$266$	11.5834	−	3.83640i	0.710226	−	0.235225i
$267$	−23.5515	+	14.2320i	−1.44133	+	0.870984i
$268$	−0.312240	−	0.540816i	−0.0190731	−	0.0330356i
$269$	−12.4864	−	21.6270i	−0.761306	−	1.31862i	−0.942177	−	0.335115i	$-0.891225\pi$
$269$	−12.4864	−	21.6270i	−0.761306	−	1.31862i	0.180871	−	0.983507i	$-0.442108\pi$
$270$	7.25674	−	0.435288i	0.441631	−	0.0264908i
$271$	6.91993	+	3.99522i	0.420356	+	0.242693i	0.695230	−	0.718788i	$-0.255303\pi$
$271$	6.91993	+	3.99522i	0.420356	+	0.242693i	−0.274874	+	0.961480i	$0.588636\pi$
$272$	−6.86805			−0.416437
$273$	3.83768	+	16.0709i	0.232267	+	0.972652i
$274$	7.08381			0.427948
$275$	−3.33481	−	1.92535i	−0.201097	−	0.116103i
$276$	2.10400	−	3.81835i	0.126646	−	0.229837i
$277$	8.28352	+	14.3475i	0.497708	+	0.862056i	0.999997	−	0.00264429i	$-0.000841705\pi$
$277$	8.28352	+	14.3475i	0.497708	+	0.862056i	−0.502288	+	0.864700i	$0.667508\pi$
$278$	−1.11939	−	1.93885i	−0.0671367	−	0.116284i
$279$	0.610395	+	15.2741i	0.0365434	+	0.914437i
$280$	−3.62501	−	0.749072i	−0.216636	−	0.0447656i
$281$		−	1.18198i		−	0.0705110i	−0.999378	−	0.0352555i	$-0.988776\pi$
$281$		−	1.18198i		−	0.0705110i	0.999378	−	0.0352555i	$-0.0112245\pi$
$282$	−2.64837	+	4.80628i	−0.157708	+	0.286210i
$283$			32.8544i			1.95299i	0.215542	+	0.976495i	$0.430848\pi$
$283$			32.8544i			1.95299i	−0.215542	+	0.976495i	$0.569152\pi$
$284$			4.37510i			0.259614i
$285$	−11.1739	+	0.223180i	−0.661882	+	0.0132200i
$286$	2.68464	−	3.68989i	0.158746	−	0.218187i
$287$	3.45435	−	16.7168i	0.203904	−	0.986759i
$288$	2.65590	+	1.39506i	0.156500	+	0.0822047i
$289$	−15.0850	+	26.1281i	−0.887356	+	1.53695i
$290$	3.67727	+	6.36923i	0.215937	+	0.374014i
$291$	2.26268	+	3.74435i	0.132641	+	0.219497i
$292$		−	8.36406i		−	0.489470i
$293$	−2.82022	+	4.88477i	−0.164759	+	0.285371i	−0.936570	−	0.350481i	$-0.886018\pi$
$293$	−2.82022	+	4.88477i	−0.164759	+	0.285371i	0.771811	+	0.635852i	$0.219351\pi$
$294$	−9.58094	+	7.43005i	−0.558772	+	0.433329i
$295$	10.0554	−	17.4164i	0.585447	−	1.01402i
$296$	−5.98766	−	3.45697i	−0.348025	−	0.200933i
$297$	−6.56443	+	0.393761i	−0.380907	+	0.0228483i
$298$	−4.99921	+	8.65889i	−0.289597	+	0.501596i
$299$	−7.33853	−	5.33927i	−0.424398	−	0.308778i
$300$	−4.61561	−	2.54331i	−0.266482	−	0.146838i
$301$	30.5608	−	10.1216i	1.76149	−	0.583402i
$302$	−6.24397	+	3.60495i	−0.359300	+	0.207442i
$303$	−12.7952	−	7.05047i	−0.735068	−	0.405039i
$304$	−3.99411	−	2.30600i	−0.229078	−	0.132258i
$305$	3.72520	−	2.15075i	0.213305	−	0.123151i
$306$	17.4181	−	11.0064i	0.995727	−	0.629192i
$307$		−	25.4559i		−	1.45284i	−0.687249	−	0.726422i	$-0.741182\pi$
$307$		−	25.4559i		−	1.45284i	0.687249	−	0.726422i	$-0.258818\pi$
$308$	3.27917	+	0.677609i	0.186848	+	0.0386103i
$309$	20.5002	−	0.409458i	1.16621	−	0.0232933i
$310$	−3.56443	+	6.17378i	−0.202446	+	0.350647i
$311$	−7.30444	+	12.6517i	−0.414197	+	0.717410i	−0.995344	−	0.0963890i	$-0.969271\pi$
$311$	−7.30444	+	12.6517i	−0.414197	+	0.717410i	0.581147	+	0.813798i	$0.302604\pi$
$312$	3.57253	−	5.12221i	0.202255	−	0.289988i
$313$	−9.58723	+	5.53519i	−0.541902	+	0.312868i	−0.745850	−	0.666114i	$-0.767956\pi$
$313$	−9.58723	+	5.53519i	−0.541902	+	0.312868i	0.203947	+	0.978982i	$0.434623\pi$
$314$	3.07314	+	5.32283i	0.173427	+	0.300385i
$315$	10.3938	−	3.90952i	0.585626	−	0.220276i
$316$	−7.13902	+	12.3651i	−0.401601	+	0.695594i
$317$	13.3841	−	7.72732i	0.751727	−	0.434010i	−0.0745906	−	0.997214i	$-0.523765\pi$
$317$	13.3841	−	7.72732i	0.751727	−	0.434010i	0.826318	+	0.563205i	$0.190432\pi$
$318$	0.0177370	+	0.888034i	0.000994644	+	0.0497985i
$319$	−3.32645	−	5.76159i	−0.186246	−	0.322587i
$320$	0.699535	+	1.21163i	0.0391052	+	0.0677322i
$321$	−1.86885	−	3.09263i	−0.104309	−	0.172614i
$322$	1.34764	−	6.52169i	0.0751012	−	0.363440i
$323$	−27.4318	+	15.8377i	−1.52634	+	0.881235i
$324$	−8.97130	+	0.718182i	−0.498406	+	0.0398990i
$325$	−6.45410	+	8.87080i	−0.358009	+	0.492064i
$326$	11.9422	+	6.89482i	0.661417	+	0.381869i
$327$	23.4233	−	14.1545i	1.29531	−	0.782747i
$328$	−5.58745	+	3.22591i	−0.308515	+	0.178121i
$329$	−1.69632	+	8.20907i	−0.0935213	+	0.452581i
$330$	−2.68608	−	1.48009i	−0.147864	−	0.0814763i
$331$	−0.993316			−0.0545976			−0.0272988	−	0.999627i	$-0.508691\pi$
$331$	−0.993316			−0.0545976			−0.0272988	+	0.999627i	$0.508691\pi$
$332$	1.76034	+	3.04900i	0.0966111	+	0.167335i
$333$	20.7253	−	0.828239i	1.13574	−	0.0453872i
$334$			14.9366i			0.817293i
$335$	0.436846	+	0.756639i	0.0238674	+	0.0413396i
$336$	4.50539	+	0.837549i	0.245789	+	0.0456920i
$337$	16.8178			0.916123			0.458061	−	0.888921i	$-0.348544\pi$
$337$	16.8178			0.916123			0.458061	+	0.888921i	$0.348544\pi$
$338$	−9.64922	−	8.71164i	−0.524848	−	0.473851i
$339$	11.0431	+	18.2745i	0.599780	+	0.992533i
$340$	9.60888			0.521115
$341$	3.22438	−	5.58479i	0.174610	−	0.302433i
$342$	13.8250	−	0.552483i	0.747569	−	0.0298749i
$343$	−10.6296	+	15.1661i	−0.573946	+	0.818893i
$344$	−10.5377	−	6.08396i	−0.568157	−	0.328025i
$345$	−2.94364	+	5.34213i	−0.158480	+	0.287611i
$346$	−4.75216	−	2.74366i	−0.255478	−	0.147500i
$347$	−7.63572	+	4.40848i	−0.409907	+	0.236660i	−0.690750	−	0.723094i	$-0.742719\pi$
$347$	−7.63572	+	4.40848i	−0.409907	+	0.236660i	0.280843	+	0.959754i	$0.409386\pi$
$348$	−4.70902	−	7.79263i	−0.252430	−	0.417729i
$349$	−11.1058	+	6.41193i	−0.594479	+	0.343223i	−0.766866	−	0.641807i	$-0.778185\pi$
$349$	−11.1058	+	6.41193i	−0.594479	+	0.343223i	0.172388	+	0.985029i	$0.444852\pi$
$350$	−7.88342	−	1.62903i	−0.421386	−	0.0870753i
$351$	−0.851731	+	18.7156i	−0.0454620	+	0.998966i
$352$	−0.632798	−	1.09604i	−0.0337282	−	0.0584190i
$353$	34.4686			1.83458			0.917289	−	0.398222i	$-0.130373\pi$
$353$	34.4686			1.83458			0.917289	+	0.398222i	$0.130373\pi$
$354$	−12.0155	+	21.8059i	−0.638618	+	1.15897i
$355$		−	6.12107i		−	0.324872i
$356$	15.8874			0.842028
$357$	20.4533	−	23.9214i	1.08250	−	1.26606i
$358$	3.11174	−	5.38969i	0.164460	−	0.284854i
$359$	−24.1704	+	13.9548i	−1.27567	+	0.736506i	−0.976048	−	0.217554i	$-0.930192\pi$
$359$	−24.1704	+	13.9548i	−1.27567	+	0.736506i	−0.299617	+	0.954060i	$0.596859\pi$
$360$	−3.71579	−	1.95179i	−0.195839	−	0.102868i
$361$	−2.27057			−0.119504
$362$	−5.13530	+	8.89460i	−0.269905	+	0.467490i
$363$	−14.2571	−	7.85600i	−0.748305	−	0.412333i
$364$	2.90246	−	9.08712i	0.152130	−	0.476294i
$365$			11.7019i			0.612506i
$366$	−4.55772	+	2.75419i	−0.238236	+	0.143964i
$367$		−	3.39933i		−	0.177444i	−0.996056	−	0.0887219i	$-0.971722\pi$
$367$		−	3.39933i		−	0.177444i	0.996056	−	0.0887219i	$-0.0282782\pi$
$368$	−2.17983	+	1.25852i	−0.113631	+	0.0656050i
$369$	9.00069	−	17.1354i	0.468557	−	0.892034i
$370$	8.37715	+	4.83655i	0.435507	+	0.251440i
$371$	0.426570	+	1.28796i	0.0221464	+	0.0668677i
$372$	4.25927	−	7.72975i	0.220833	−	0.400769i
$373$	8.44346			0.437186			0.218593	−	0.975816i	$-0.429853\pi$
$373$	8.44346			0.437186			0.218593	+	0.975816i	$0.429853\pi$
$374$	−8.69218			−0.449462
$375$	17.0695	+	9.40567i	0.881464	+	0.485707i
$376$	2.74382	−	1.58414i	0.141502	−	0.0816960i
$377$	−17.3200	+	7.69746i	−0.892025	+	0.396439i
$378$	−12.7684	+	5.09598i	−0.656734	+	0.262109i
$379$	−12.2942	−	21.2942i	−0.631512	−	1.09381i	−0.987243	−	0.159223i	$-0.949101\pi$
$379$	−12.2942	−	21.2942i	−0.631512	−	1.09381i	0.355730	−	0.934589i	$-0.384232\pi$
$380$	5.58804	+	3.22626i	0.286661	+	0.165504i
$381$	−0.305621	−	15.3014i	−0.0156575	−	0.783916i
$382$	4.85641	−	8.41156i	0.248476	−	0.430373i
$383$	−24.6588			−1.26001			−0.630003	−	0.776592i	$-0.716947\pi$
$383$	−24.6588			−1.26001			−0.630003	+	0.776592i	$0.716947\pi$
$384$	−0.895807	−	1.48241i	−0.0457139	−	0.0756488i
$385$	−4.58779	−	0.948022i	−0.233816	−	0.0483157i
$386$	−4.73270	−	2.73242i	−0.240888	−	0.139077i
$387$	36.4747	−	1.45763i	1.85411	−	0.0740953i
$388$		−	2.52586i		−	0.128231i
$389$	3.13636	+	1.81078i	0.159020	+	0.0918101i	0.577398	−	0.816463i	$-0.304068\pi$
$389$	3.13636	+	1.81078i	0.159020	+	0.0918101i	−0.418378	+	0.908273i	$0.637401\pi$
$390$	−4.99822	+	7.16633i	−0.253095	+	0.362881i
$391$			17.2872i			0.874251i
$392$	6.95291	−	0.810561i	0.351175	−	0.0409395i
$393$	−0.600937	−	30.0869i	−0.0303132	−	1.51768i
$394$	26.0774			1.31376
$395$	9.98799	−	17.2997i	0.502550	−	0.870443i
$396$	3.36130	+	1.76558i	0.168912	+	0.0887239i
$397$			14.0275i			0.704018i	0.935997	+	0.352009i	$0.114501\pi$
$397$			14.0275i			0.704018i	−0.935997	+	0.352009i	$0.885499\pi$
$398$	−13.7069			−0.687064
$399$	19.9264	−	7.04417i	0.997568	−	0.352649i
$400$	1.52130	+	2.63497i	0.0760651	+	0.131749i
$401$	−27.6911	−	15.9875i	−1.38283	−	0.798376i	−0.390335	−	0.920673i	$-0.627641\pi$
$401$	−27.6911	−	15.9875i	−1.38283	−	0.798376i	−0.992494	+	0.122296i	$0.960974\pi$
$402$	−0.559414	−	0.925734i	−0.0279010	−	0.0461714i
$403$	−14.8559	−	10.8087i	−0.740025	−	0.538418i
$404$	4.21730	+	7.30458i	0.209819	+	0.363416i
$405$	12.5515	−	1.00479i	0.623688	−	0.0499282i
$406$	−10.3883	−	9.24756i	−0.515560	−	0.458949i
$407$	−7.57795	−	4.37513i	−0.375625	−	0.216867i
$408$	−11.8934	+	0.237552i	−0.588813	+	0.0117606i
$409$	−0.481903	+	0.278227i	−0.0238286	+	0.0137574i	−0.511867	−	0.859065i	$-0.671046\pi$
$409$	−0.481903	+	0.278227i	−0.0238286	+	0.0137574i	0.488038	+	0.872822i	$0.337713\pi$
$410$	7.81723	−	4.51328i	0.386066	−	0.222895i
$411$	12.2671	−	0.245015i	0.605090	−	0.0120857i
$412$	−10.2521	−	5.91907i	−0.505087	−	0.291612i
$413$	−7.69615	+	37.2442i	−0.378703	+	1.83267i
$414$	3.51143	−	6.68502i	0.172577	−	0.328551i
$415$	−2.46284	−	4.26576i	−0.120896	−	0.209398i
$416$	−3.29482	+	1.46430i	−0.161542	+	0.0717933i
$417$	−2.00552	−	3.31879i	−0.0982107	−	0.162522i
$418$	−5.05493	−	2.91847i	−0.247245	−	0.142747i
$419$	−7.69809	−	13.3335i	−0.376076	−	0.651383i	0.614411	−	0.788986i	$-0.289394\pi$
$419$	−7.69809	−	13.3335i	−0.376076	−	0.651383i	−0.990488	+	0.137603i	$0.956060\pi$
$420$	−6.30335	−	1.17179i	−0.307572	−	0.0571775i
$421$	5.44197			0.265225			0.132613	−	0.991168i	$-0.457663\pi$
$421$	5.44197			0.265225			0.132613	+	0.991168i	$0.457663\pi$
$422$		−	12.8749i		−	0.626740i
$423$	−4.41995	+	8.41465i	−0.214905	+	0.409135i
$424$	0.256405	−	0.444106i	0.0124521	−	0.0215677i
$425$	20.8967			1.01364
$426$	0.151326	+	7.57638i	0.00733176	+	0.367077i
$427$	−5.40867	+	6.07584i	−0.261744	+	0.294030i
$428$			2.08622i			0.100841i
$429$	4.52138	−	6.48265i	0.218294	−	0.312985i
$430$	14.7430	+	8.51189i	0.710972	+	0.410480i
$431$		−	22.8528i		−	1.10078i	−0.834907	−	0.550391i	$-0.814479\pi$
$431$		−	22.8528i		−	1.10078i	0.834907	−	0.550391i	$-0.185521\pi$
$432$	4.64749	+	2.32397i	0.223602	+	0.111812i
$433$	−6.71928	−	3.87938i	−0.322908	−	0.186431i	0.329780	−	0.944058i	$-0.393025\pi$
$433$	−6.71928	−	3.87938i	−0.322908	−	0.186431i	−0.652688	+	0.757627i	$0.726359\pi$
$434$	2.72813	−	13.2023i	0.130954	−	0.633732i
$435$	6.58825	+	10.9024i	0.315883	+	0.522732i
$436$	−15.8009			−0.756724
$437$	−5.80431	+	10.0534i	−0.277658	+	0.480918i
$438$	−0.289296	−	14.4841i	−0.0138231	−	0.692077i
$439$	−36.0776	−	20.8294i	−1.72189	−	0.994134i	−0.915025	−	0.403398i	$-0.867829\pi$
$439$	−36.0776	−	20.8294i	−1.72189	−	0.994134i	−0.806865	−	0.590736i	$-0.798838\pi$
$440$	0.885329	+	1.53343i	0.0422064	+	0.0731036i
$441$	−16.3344	+	13.1980i	−0.777827	+	0.628478i
$442$	−2.60495	+	24.6257i	−0.123905	+	1.17133i
$443$	22.4612	−	12.9680i	1.06716	−	0.616127i	0.139758	−	0.990186i	$-0.455368\pi$
$443$	22.4612	−	12.9680i	1.06716	−	0.616127i	0.927405	+	0.374059i	$0.122034\pi$
$444$	−10.4884	−	5.77936i	−0.497759	−	0.274276i
$445$	−22.2275			−1.05369
$446$	−20.6353			−0.977108
$447$	−8.35767	+	15.1676i	−0.395304	+	0.717401i
$448$	−1.97618	−	1.75918i	−0.0933656	−	0.0831135i
$449$	−5.20037	−	3.00244i	−0.245421	−	0.141694i	0.372245	−	0.928135i	$-0.378588\pi$
$449$	−5.20037	−	3.00244i	−0.245421	−	0.141694i	−0.617666	+	0.786441i	$0.711921\pi$
$450$	−8.08085	−	4.24461i	−0.380935	−	0.200093i
$451$	−7.07145	+	4.08270i	−0.332982	+	0.192247i
$452$		−	12.3276i		−	0.579840i
$453$	−10.6880	+	6.45869i	−0.502167	+	0.303456i
$454$			18.2051i			0.854407i
$455$	−4.06074	+	12.7135i	−0.190371	+	0.596019i
$456$	−6.99639	−	3.85517i	−0.327636	−	0.180535i
$457$	14.8245	−	25.6767i	0.693460	−	1.20111i	−0.277237	−	0.960801i	$-0.589419\pi$
$457$	14.8245	−	25.6767i	0.693460	−	1.20111i	0.970697	−	0.240306i	$-0.0772478\pi$
$458$	18.5139			0.865099
$459$	29.7824	−	19.6622i	1.39012	−	0.917755i
$460$	3.04973	−	1.76076i	0.142194	−	0.0820960i
$461$	3.80284	−	6.58672i	0.177116	−	0.306774i	−0.763775	−	0.645482i	$-0.776657\pi$
$461$	3.80284	−	6.58672i	0.177116	−	0.306774i	0.940892	+	0.338708i	$0.109990\pi$
$462$	5.70200	+	1.06000i	0.265281	+	0.0493156i
$463$	−13.7605			−0.639506			−0.319753	−	0.947501i	$-0.603600\pi$
$463$	−13.7605			−0.639506			−0.319753	+	0.947501i	$0.603600\pi$
$464$			5.25674i			0.244038i
$465$	−5.95901	+	10.8145i	−0.276343	+	0.501509i
$466$	−10.7119			−0.496221
$467$	8.10576	+	14.0396i	0.375090	+	0.649675i	0.990341	−	0.138657i	$-0.0442785\pi$
$467$	8.10576	+	14.0396i	0.375090	+	0.649675i	−0.615250	+	0.788332i	$0.710945\pi$
$468$	6.00940	−	8.99373i	0.277785	−	0.415735i
$469$	−1.23408	−	1.09857i	−0.0569847	−	0.0507274i
$470$	−3.83879	+	2.21633i	−0.177070	+	0.102232i
$471$	5.50588	+	9.11128i	0.253697	+	0.419826i
$472$	12.4486	−	7.18719i	0.572993	−	0.330817i
$473$	−13.3365	−	7.69984i	−0.613214	−	0.354039i
$474$	−11.9350	+	21.6597i	−0.548192	+	0.994864i
$475$	12.1525	+	7.01625i	0.557595	+	0.321927i
$476$	−17.2497	+	5.71305i	−0.790638	+	0.261857i
$477$	0.0614307	+	1.53720i	0.00281272	+	0.0703836i
$478$	−1.94355	+	3.36632i	−0.0888958	+	0.153972i
$479$	7.66898			0.350405			0.175202	−	0.984532i	$-0.443942\pi$
$479$	7.66898			0.350405			0.175202	+	0.984532i	$0.443942\pi$
$480$	1.25330	+	2.07399i	0.0572049	+	0.0946643i
$481$	−14.6662	+	20.1578i	−0.668720	+	0.919118i
$482$	6.18514			0.281725
$483$	2.10815	−	11.3403i	0.0959241	−	0.516000i
$484$	4.69913	+	8.13914i	0.213597	+	0.369961i
$485$			3.53385i			0.160464i
$486$	−15.5108	+	1.55398i	−0.703585	+	0.0704899i
$487$	−0.626367	−	1.08490i	−0.0283834	−	0.0491615i	0.851485	−	0.524379i	$-0.175703\pi$
$487$	−0.626367	−	1.08490i	−0.0283834	−	0.0491615i	−0.879868	+	0.475218i	$0.842369\pi$
$488$	3.07454			0.139178
$489$	20.9188	+	11.5267i	0.945982	+	0.521258i
$490$	−9.72761	+	1.13403i	−0.439449	+	0.0512303i
$491$	−1.78584	+	1.03105i	−0.0805938	+	0.0465308i	−0.539755	−	0.841822i	$-0.681483\pi$
$491$	−1.78584	+	1.03105i	−0.0805938	+	0.0465308i	0.459162	+	0.888353i	$0.348150\pi$
$492$	−9.56423	+	5.77959i	−0.431189	+	0.260564i
$493$	31.2666	+	18.0518i	1.40818	+	0.813011i
$494$	−9.78318	+	13.4464i	−0.440166	+	0.604984i
$495$	−4.70269	−	2.47017i	−0.211370	−	0.111026i
$496$	−4.41277	+	2.54772i	−0.198139	+	0.114396i
$497$	3.63933	+	10.9884i	0.163246	+	0.492898i
$498$	3.15385	+	5.21908i	0.141327	+	0.233872i
$499$	−6.12234	−	10.6042i	−0.274074	−	0.474710i	0.695827	−	0.718209i	$-0.255038\pi$
$499$	−6.12234	−	10.6042i	−0.274074	−	0.474710i	−0.969901	+	0.243500i	$0.921705\pi$
$500$	−5.62608	−	9.74466i	−0.251606	−	0.435795i
$501$	0.516626	+	25.8657i	0.0230812	+	1.15560i
$502$	1.53990	−	0.889061i	0.0687291	−	0.0396808i
$503$	−19.8446	+	34.3719i	−0.884828	+	1.53257i	−0.0389171	+	0.999242i	$0.512391\pi$
$503$	−19.8446	+	34.3719i	−0.884828	+	1.53257i	−0.845911	+	0.533324i	$0.820943\pi$
$504$	7.83097	+	1.29456i	0.348819	+	0.0576641i
$505$	−5.90030	−	10.2196i	−0.262560	−	0.454767i
$506$	−2.75878	+	1.59278i	−0.122643	+	0.0708078i
$507$	−17.0109	−	14.7522i	−0.755481	−	0.655170i
$508$	−4.41803	+	7.65224i	−0.196018	+	0.339513i
$509$	−11.4006	+	19.7465i	−0.505325	+	0.875248i	0.494657	+	0.869089i	$0.335294\pi$
$509$	−11.4006	+	19.7465i	−0.505325	+	0.875248i	−0.999981	+	0.00615918i	$0.998039\pi$
$510$	16.6398	−	0.332352i	0.736821	−	0.0147168i
$511$	−6.95747	−	21.0070i	−0.307781	−	0.929297i
$512$			1.00000i			0.0441942i
$513$	23.9217	−	1.43492i	1.05617	−	0.0633531i
$514$	−10.4139	+	6.01246i	−0.459337	+	0.265198i
$515$	14.3435	+	8.28120i	0.632048	+	0.364913i
$516$	−18.4587	−	10.1712i	−0.812598	−	0.447760i
$517$	3.47256	−	2.00489i	0.152723	−	0.0881748i
$518$	−17.9141	−	3.70178i	−0.787101	−	0.162647i
$519$	−8.32424	−	4.58684i	−0.365393	−	0.201340i
$520$	4.60968	−	2.04866i	0.202148	−	0.0898398i
$521$	−1.95101	+	3.37925i	−0.0854752	+	0.148047i	−0.905594	−	0.424146i	$-0.860574\pi$
$521$	−1.95101	+	3.37925i	−0.0854752	+	0.148047i	0.820118	+	0.572194i	$0.193908\pi$
$522$	−8.42417	−	13.3317i	−0.368716	−	0.583511i
$523$	−6.73834	−	3.89038i	−0.294647	−	0.170115i	0.345389	−	0.938460i	$-0.387747\pi$
$523$	−6.73834	−	3.89038i	−0.294647	−	0.170115i	−0.640036	+	0.768345i	$0.721080\pi$
$524$	−8.68707	+	15.0464i	−0.379496	+	0.657307i
$525$	−13.7081	−	2.54833i	−0.598271	−	0.111218i
$526$	−0.947444	+	1.64102i	−0.0413105	+	0.0715520i
$527$			34.9957i			1.52444i
$528$	−1.13373	−	1.87613i	−0.0493392	−	0.0816480i
$529$	−8.33224	−	14.4319i	−0.362271	−	0.627472i
$530$	−0.358728	+	0.621335i	−0.0155821	+	0.0269891i
$531$	−20.0531	+	38.1769i	−0.870232	+	1.65674i
$532$	−11.9498	−	2.46930i	−0.518087	−	0.107058i
$533$	9.44743	+	21.2576i	0.409213	+	0.920769i
$534$	27.5122	−	0.549512i	1.19057	−	0.0237797i
$535$		−	2.91877i		−	0.126190i
$536$			0.624480i			0.0269734i
$537$	5.20219	−	9.44098i	0.224491	−	0.407408i
$538$			24.9727i			1.07665i
$539$	8.79958	−	1.02584i	0.379025	−	0.0441862i
$540$	−6.50216	−	3.25140i	−0.279809	−	0.139918i
$541$	−2.23765	−	3.87573i	−0.0962042	−	0.166631i	0.813906	−	0.580996i	$-0.197337\pi$
$541$	−2.23765	−	3.87573i	−0.0962042	−	0.166631i	−0.910111	+	0.414366i	$0.864004\pi$
$542$	−3.99522	−	6.91993i	−0.171610	−	0.297237i
$543$	−8.58518	+	15.5804i	−0.368425	+	0.668621i
$544$	5.94790	+	3.43402i	0.255014	+	0.147233i
$545$	22.1065			0.946939
$546$	4.71190	−	15.8366i	0.201651	−	0.677744i
$547$	−35.3736			−1.51246			−0.756232	−	0.654304i	$-0.772962\pi$
$547$	−35.3736			−1.51246			−0.756232	+	0.654304i	$0.772962\pi$
$548$	−6.13476	−	3.54190i	−0.262064	−	0.151303i
$549$	−7.79736	+	4.92709i	−0.332783	+	0.210283i
$550$	1.92535	+	3.33481i	0.0820973	+	0.142197i
$551$	12.1221	+	20.9960i	0.516417	+	0.894460i
$552$	−3.73129	+	2.25479i	−0.158814	+	0.0959701i
$553$	−7.64456	+	36.9946i	−0.325080	+	1.57317i
$554$		−	16.5670i		−	0.703866i
$555$	14.6740	+	8.08573i	0.622879	+	0.343220i
$556$			2.23879i			0.0949457i
$557$		−	20.8010i		−	0.881368i	−0.897662	−	0.440684i	$-0.854736\pi$
$557$		−	20.8010i		−	0.881368i	0.897662	−	0.440684i	$-0.145264\pi$
$558$	7.10844	−	13.5330i	0.300924	−	0.572896i
$559$	−25.8111	+	35.4760i	−1.09170	+	1.50047i
$560$	2.76481	+	2.46122i	0.116835	+	0.104005i
$561$	−15.0523	+	0.300645i	−0.635508	+	0.0126932i
$562$	−0.590990	+	1.02362i	−0.0249294	+	0.0431790i
$563$	−12.0960	−	20.9508i	−0.509784	−	0.882972i	−0.999936	−	0.0113351i	$-0.996392\pi$
$563$	−12.0960	−	20.9508i	−0.509784	−	0.882972i	0.490151	−	0.871637i	$-0.336941\pi$
$564$	4.69669	−	2.83817i	0.197766	−	0.119509i
$565$			17.2471i			0.725592i
$566$	16.4272	−	28.4527i	0.690486	−	1.19596i
$567$	−21.9348	+	9.26637i	−0.921174	+	0.389151i
$568$	2.18755	−	3.78894i	0.0917875	−	0.158981i
$569$	30.3762	+	17.5377i	1.27344	+	0.735219i	0.975633	−	0.219408i	$-0.0704125\pi$
$569$	30.3762	+	17.5377i	1.27344	+	0.735219i	0.297804	+	0.954627i	$0.403746\pi$
$570$	9.78843	+	5.39365i	0.409992	+	0.225915i
$571$	10.1633	−	17.6034i	0.425321	−	0.736678i	−0.571129	−	0.820860i	$-0.693494\pi$
$571$	10.1633	−	17.6034i	0.425321	−	0.736678i	0.996450	+	0.0841821i	$0.0268277\pi$
$572$	−4.16991	+	1.85322i	−0.174353	+	0.0774868i
$573$	8.11894	−	14.7343i	0.339174	−	0.615535i
$574$	−11.3499	+	12.7500i	−0.473737	+	0.532173i
$575$	6.63234	−	3.82919i	0.276588	−	0.159688i
$576$	−1.60255	−	2.53611i	−0.0667728	−	0.105671i
$577$	−12.8575	−	7.42329i	−0.535266	−	0.309036i	0.207892	−	0.978152i	$-0.433340\pi$
$577$	−12.8575	−	7.42329i	−0.535266	−	0.309036i	−0.743158	+	0.669116i	$0.766673\pi$
$578$	26.1281	−	15.0850i	1.08678	−	0.627455i
$579$	−8.29015	−	4.56806i	−0.344527	−	0.189842i
$580$		−	7.35455i		−	0.305381i
$581$	6.95748	+	6.19351i	0.288645	+	0.256950i
$582$	−0.0873643	−	4.37404i	−0.00362137	−	0.181310i
$583$	0.324505	−	0.562058i	0.0134396	−	0.0232781i
$584$	−4.18203	+	7.24349i	−0.173054	+	0.299738i
$585$	−8.40757	+	12.5829i	−0.347610	+	0.520237i
$586$	4.88477	−	2.82022i	0.201788	−	0.116502i
$587$	−10.5944	−	18.3500i	−0.437276	−	0.757384i	0.560202	−	0.828356i	$-0.310723\pi$
$587$	−10.5944	−	18.3500i	−0.437276	−	0.757384i	−0.997478	+	0.0709716i	$0.977390\pi$
$588$	12.0124	−	1.64414i	0.495381	−	0.0678032i
$589$	−11.7501	+	20.3517i	−0.484154	+	0.838578i
$590$	−17.4164	+	10.0554i	−0.717024	+	0.413974i
$591$	45.1585	−	0.901967i	1.85757	−	0.0371020i
$592$	3.45697	+	5.98766i	0.142081	+	0.246091i
$593$	−12.5747	−	21.7800i	−0.516381	−	0.894397i	−0.999819	−	0.0190190i	$-0.993946\pi$
$593$	−12.5747	−	21.7800i	−0.516381	−	0.894397i	0.483439	−	0.875378i	$-0.339388\pi$
$594$	5.88184	+	2.94121i	0.241335	+	0.120679i
$595$	24.1335	−	7.99295i	0.989378	−	0.327679i
$596$	8.65889	−	4.99921i	0.354682	−	0.204776i
$597$	−23.7363	+	0.474094i	−0.971461	+	0.0194034i
$598$	3.68572	+	8.29321i	0.150720	+	0.339134i
$599$	−27.8317	−	16.0687i	−1.13717	−	0.656547i	−0.191444	−	0.981503i	$-0.561317\pi$
$599$	−27.8317	−	16.0687i	−1.13717	−	0.656547i	−0.945729	+	0.324956i	$0.894650\pi$
$600$	2.72558	+	4.51037i	0.111271	+	0.184135i
$601$	15.0678	−	8.69938i	0.614627	−	0.354855i	−0.160147	−	0.987093i	$-0.551197\pi$
$601$	15.0678	−	8.69938i	0.614627	−	0.354855i	0.774774	+	0.632238i	$0.217864\pi$
$602$	−31.5272	−	6.51479i	−1.28495	−	0.265523i
$603$	−1.00076	−	1.58375i	−0.0407540	−	0.0644952i
$604$	7.20991			0.293367
$605$	−6.57442	−	11.3872i	−0.267288	−	0.462957i
$606$	7.55577	+	12.5035i	0.306932	+	0.507920i
$607$		−	29.3529i		−	1.19140i	−0.803208	−	0.595698i	$-0.796875\pi$
$607$		−	29.3529i		−	1.19140i	0.803208	−	0.595698i	$-0.203125\pi$
$608$	2.30600	+	3.99411i	0.0935207	+	0.161983i
$609$	−18.3093	−	15.6547i	−0.741928	−	0.634362i
$610$	−4.30150			−0.174162
$611$	−4.63933	−	10.4389i	−0.187687	−	0.422314i
$612$	−20.5877	+	0.822741i	−0.832209	+	0.0332573i
$613$	−34.8285			−1.40671			−0.703355	−	0.710839i	$-0.748316\pi$
$613$	−34.8285			−1.40671			−0.703355	+	0.710839i	$0.748316\pi$
$614$	−12.7279	+	22.0454i	−0.513658	+	0.889682i
$615$	13.3810	−	8.08606i	0.539575	−	0.326061i
$616$	−2.50104	−	2.22641i	−0.100770	−	0.0897047i
$617$	15.1344	+	8.73785i	0.609288	+	0.351773i	0.772687	−	0.634787i	$-0.218912\pi$
$617$	15.1344	+	8.73785i	0.609288	+	0.351773i	−0.163399	+	0.986560i	$0.552246\pi$
$618$	−17.9584	−	9.89549i	−0.722393	−	0.398055i
$619$	−20.5117	−	11.8425i	−0.824436	−	0.475989i	0.0275075	−	0.999622i	$-0.491243\pi$
$619$	−20.5117	−	11.8425i	−0.824436	−	0.475989i	−0.851944	+	0.523633i	$0.824576\pi$
$620$	6.17378	−	3.56443i	0.247945	−	0.143151i
$621$	5.84954	−	11.6979i	0.234734	−	0.469422i
$622$	12.6517	−	7.30444i	0.507285	−	0.292881i
$623$	39.9024	−	13.2156i	1.59866	−	0.529471i
$624$	−5.65501	+	2.64970i	−0.226381	+	0.106073i
$625$	0.264780	+	0.458612i	0.0105912	+	0.0183445i
$626$	11.0704			0.442461
$627$	−8.85460	−	4.87908i	−0.353619	−	0.194852i
$628$		−	6.14628i		−	0.245263i
$629$	47.4853			1.89336
$630$	−10.9561	−	1.81117i	−0.436501	−	0.0721589i
$631$	3.58972	−	6.21757i	0.142904	−	0.247518i	−0.785685	−	0.618627i	$-0.787689\pi$
$631$	3.58972	−	6.21757i	0.142904	−	0.247518i	0.928589	+	0.371109i	$0.121023\pi$
$632$	12.3651	−	7.13902i	0.491859	−	0.283975i
$633$	−0.445317	−	22.2955i	−0.0176998	−	0.886168i
$634$	−15.4546			−0.613782
$635$	6.18113	−	10.7060i	0.245291	−	0.424856i
$636$	0.428656	−	0.777929i	0.0169973	−	0.0308469i
$637$	−0.269164	−	25.2374i	−0.0106647	−	0.999943i
$638$			6.65291i			0.263391i
$639$	0.524104	+	13.1148i	0.0207332	+	0.518814i
$640$		−	1.39907i		−	0.0553031i
$641$	−24.6906	+	14.2551i	−0.975221	+	0.563044i	−0.900824	−	0.434185i	$-0.857036\pi$
$641$	−24.6906	+	14.2551i	−0.975221	+	0.563044i	−0.0743968	+	0.997229i	$0.523703\pi$
$642$	0.0721583	+	3.61273i	0.00284786	+	0.142583i
$643$	39.1207	+	22.5863i	1.54277	+	0.890718i	0.998663	+	0.0517020i	$0.0164646\pi$
$643$	39.1207	+	22.5863i	1.54277	+	0.890718i	0.544106	+	0.839016i	$0.316869\pi$
$644$	−4.42794	+	4.97413i	−0.174485	+	0.196008i
$645$	25.8250	+	14.2302i	1.01686	+	0.560312i
$646$	31.6755			1.24625
$647$	−17.9381			−0.705220			−0.352610	−	0.935770i	$-0.614706\pi$
$647$	−17.9381			−0.705220			−0.352610	+	0.935770i	$0.614706\pi$
$648$	8.12846	+	3.86369i	0.319316	+	0.151780i
$649$	15.7549	−	9.09609i	0.618433	−	0.357053i
$650$	10.0248	−	4.45529i	0.393206	−	0.174751i
$651$	4.26767	−	22.9569i	0.167263	−	0.899752i
$652$	−6.89482	−	11.9422i	−0.270022	−	0.467692i
$653$	−24.5311	−	14.1630i	−0.959977	−	0.554243i	−0.0638110	−	0.997962i	$-0.520325\pi$
$653$	−24.5311	−	14.1630i	−0.959977	−	0.554243i	−0.896166	+	0.443719i	$0.853659\pi$
$654$	−27.3624	+	0.546520i	−1.06996	+	0.0213706i
$655$	12.1538	−	21.0510i	0.474889	−	0.822532i
$656$	6.45183			0.251902
$657$	−1.00195	−	25.0722i	−0.0390899	−	0.978158i
$658$	5.57359	−	6.26110i	0.217281	−	0.244083i
$659$	33.6960	+	19.4544i	1.31261	+	0.757836i	0.982528	−	0.186116i	$-0.0595902\pi$
$659$	33.6960	+	19.4544i	1.31261	+	0.757836i	0.330082	+	0.943952i	$0.392924\pi$
$660$	1.58617	+	2.62484i	0.0617415	+	0.102172i
$661$		−	14.1995i		−	0.552296i	−0.961115	−	0.276148i	$-0.910942\pi$
$661$		−	14.1995i		−	0.552296i	0.961115	−	0.276148i	$-0.0890581\pi$
$662$	0.860237	+	0.496658i	0.0334340	+	0.0193032i
$663$	−3.65925	+	42.7346i	−0.142114	+	1.65967i
$664$		−	3.52068i		−	0.136629i
$665$	16.7185	+	3.45472i	0.648317	+	0.133968i
$666$	−18.3628	−	9.64538i	−0.711543	−	0.373751i
$667$	13.2315			0.512324
$668$	7.46828	−	12.9354i	0.288957	−	0.500487i
$669$	−35.7342	+	0.713732i	−1.38156	+	0.0275945i
$670$		−	0.873692i		−	0.0337537i
$671$	3.89112			0.150215
$672$	−3.48301	−	2.97803i	−0.134360	−	0.114880i
$673$	10.7809	+	18.6731i	0.415574	+	0.719795i	0.995489	−	0.0948822i	$-0.0302475\pi$
$673$	10.7809	+	18.6731i	0.415574	+	0.719795i	−0.579915	+	0.814677i	$0.696914\pi$
$674$	−14.5646	−	8.40889i	−0.561008	−	0.323898i
$675$	−14.1405	−	7.07092i	−0.544267	−	0.272160i
$676$	4.00065	+	12.3691i	0.153871	+	0.475735i
$677$	−20.3440	−	35.2368i	−0.781883	−	1.35426i	−0.930844	−	0.365418i	$-0.880926\pi$
$677$	−20.3440	−	35.2368i	−0.781883	−	1.35426i	0.148960	−	0.988843i	$-0.452407\pi$
$678$	−0.426386	−	21.3477i	−0.0163753	−	0.819854i
$679$	−2.10108	−	6.34390i	−0.0806321	−	0.243457i
$680$	−8.32154	−	4.80444i	−0.319116	−	0.184242i
$681$	0.629678	+	31.5258i	0.0241293	+	1.20807i
$682$	−5.58479	+	3.22438i	−0.213853	+	0.123468i
$683$	31.3548	−	18.1027i	1.19976	−	0.692681i	0.239258	−	0.970956i	$-0.423096\pi$
$683$	31.3548	−	18.1027i	1.19976	−	0.692681i	0.960501	+	0.278275i	$0.0897626\pi$
$684$	−12.2490	−	6.43402i	−0.468353	−	0.246011i
$685$	8.58296	+	4.95537i	0.327938	+	0.189335i
$686$	16.7886	−	7.81943i	0.640991	−	0.298547i
$687$	32.0607	−	0.640360i	1.22319	−	0.0244313i
$688$	6.08396	+	10.5377i	0.231949	+	0.401747i
$689$	−1.49511	−	1.08779i	−0.0569592	−	0.0414416i
$690$	5.22033	−	3.15461i	0.198735	−	0.120094i
$691$	−7.19174	−	4.15215i	−0.273587	−	0.157955i	0.356930	−	0.934131i	$-0.383824\pi$
$691$	−7.19174	−	4.15215i	−0.273587	−	0.157955i	−0.630516	+	0.776176i	$0.717157\pi$
$692$	2.74366	+	4.75216i	0.104298	+	0.180650i
$693$	9.91085	+	1.63838i	0.376482	+	0.0622371i
$694$	8.81697			0.334688
$695$		−	3.13222i		−	0.118812i
$696$	0.181820	+	9.10312i	0.00689187	+	0.345053i
$697$	22.1557	−	38.3749i	0.839208	−	1.45355i
$698$	12.8239			0.485390
$699$	−18.5499	+	0.370505i	−0.701623	+	0.0140138i
$700$	6.01272	+	5.35249i	0.227260	+	0.202305i
$701$			48.0958i			1.81655i	0.418371	+	0.908276i	$0.362601\pi$
$701$			48.0958i			1.81655i	−0.418371	+	0.908276i	$0.637399\pi$
$702$	10.0954	−	15.7823i	0.381028	−	0.595666i
$703$	27.6151	+	15.9436i	1.04152	+	0.601323i
$704$			1.26560i			0.0476989i
$705$	−6.57100	+	3.97080i	−0.247478	+	0.149549i
$706$	−29.8507	−	17.2343i	−1.12345	−	0.648621i
$707$	16.6683	+	14.8380i	0.626875	+	0.558040i
$708$	21.3087	−	12.8767i	0.800830	−	0.483935i
$709$	−31.4206			−1.18003			−0.590013	−	0.807394i	$-0.700877\pi$
$709$	−31.4206			−1.18003			−0.590013	+	0.807394i	$0.700877\pi$
$710$	−3.06053	+	5.30100i	−0.114860	+	0.198943i
$711$	−19.9187	+	37.9211i	−0.747011	+	1.42215i
$712$	−13.7588	−	7.94368i	−0.515635	−	0.297702i
$713$	6.41272	+	11.1072i	0.240158	+	0.415966i
$714$	−29.6738	+	10.4899i	−1.11051	+	0.392576i
$715$	5.83399	−	2.59278i	0.218179	−	0.0969644i
$716$	−5.38969	+	3.11174i	−0.201422	+	0.116291i
$717$	−3.24922	+	5.89670i	−0.121344	+	0.220216i
$718$	27.9096			1.04158
$719$	25.3643			0.945931			0.472965	−	0.881081i	$-0.343184\pi$
$719$	25.3643			0.945931			0.472965	+	0.881081i	$0.343184\pi$
$720$	2.24208	+	3.54819i	0.0835572	+	0.132233i
$721$	−30.6728	−	6.33823i	−1.14231	−	0.236048i
$722$	1.96637	+	1.13529i	0.0731809	+	0.0422510i
$723$	10.7108	−	0.213932i	0.398341	−	0.00795621i
$724$	8.89460	−	5.13530i	0.330565	−	0.190852i
$725$		−	15.9942i		−	0.594009i
$726$	8.41903	+	13.9321i	0.312460	+	0.517067i
$727$			2.55940i			0.0949230i	0.998873	+	0.0474615i	$0.0151132\pi$
$727$			2.55940i			0.0949230i	−0.998873	+	0.0474615i	$0.984887\pi$
$728$	−7.05716	+	6.41845i	−0.261556	+	0.237883i
$729$	−26.8064	+	3.22752i	−0.992830	+	0.119538i
$730$	5.85095	−	10.1341i	0.216554	−	0.375082i
$731$	83.5699			3.09095
$732$	5.32420	−	0.106342i	0.196788	−	0.00393052i
$733$	41.4839	−	23.9507i	1.53224	−	0.884641i	0.532985	−	0.846125i	$-0.321070\pi$
$733$	41.4839	−	23.9507i	1.53224	−	0.884641i	0.999258	−	0.0385160i	$-0.0122631\pi$
$734$	−1.69967	+	2.94391i	−0.0627359	+	0.108662i
$735$	−16.8061	+	2.30027i	−0.619904	+	0.0848466i
$736$	2.51705			0.0927795
$737$			0.790340i			0.0291125i
$738$	−16.3625	+	10.3394i	−0.602313	+	0.380597i
$739$	1.30533			0.0480174			0.0240087	−	0.999712i	$-0.492357\pi$
$739$	1.30533			0.0480174			0.0240087	+	0.999712i	$0.492357\pi$
$740$	−4.83655	−	8.37715i	−0.177795	−	0.307950i
$741$	−16.4765	+	23.6237i	−0.605280	+	0.867837i
$742$	0.274561	−	1.32869i	0.0100795	−	0.0487779i
$743$	−4.26349	+	2.46153i	−0.156412	+	0.0903046i	−0.576163	−	0.817335i	$-0.695451\pi$
$743$	−4.26349	+	2.46153i	−0.156412	+	0.0903046i	0.419751	+	0.907639i	$0.362117\pi$
$744$	−7.55351	+	4.56452i	−0.276925	+	0.167344i
$745$	−12.1144	+	6.99425i	−0.443837	+	0.256250i
$746$	−7.31225	−	4.22173i	−0.267721	−	0.154569i
$747$	5.64205	+	8.92882i	0.206432	+	0.326688i
$748$	7.52764	+	4.34609i	0.275238	+	0.158909i
$749$	1.73538	+	5.23973i	0.0634095	+	0.191456i
$750$	−10.0798	−	16.6803i	−0.368061	−	0.609078i
$751$	23.3939	−	40.5194i	0.853656	−	1.47858i	−0.0242306	−	0.999706i	$-0.507714\pi$
$751$	23.3939	−	40.5194i	0.853656	−	1.47858i	0.877886	−	0.478869i	$-0.158953\pi$
$752$	−3.16829			−0.115536
$753$	2.63590	−	1.59285i	0.0960576	−	0.0580468i
$754$	18.8483	+	1.99381i	0.686414	+	0.0726101i
$755$	−10.0872			−0.367110
$756$	13.6057	+	1.97093i	0.494835	+	0.0716821i
$757$	−2.63180	−	4.55840i	−0.0956542	−	0.165678i	0.814227	−	0.580546i	$-0.197161\pi$
$757$	−2.63180	−	4.55840i	−0.0956542	−	0.165678i	−0.909881	+	0.414868i	$0.863828\pi$
$758$			24.5885i			0.893093i
$759$	−4.72230	+	2.85365i	−0.171409	+	0.103581i
$760$	−3.22626	−	5.58804i	−0.117029	−	0.202700i
$761$	−12.7328			−0.461562			−0.230781	−	0.973006i	$-0.574128\pi$
$761$	−12.7328			−0.461562			−0.230781	+	0.973006i	$0.574128\pi$
$762$	−7.38604	+	13.4042i	−0.267568	+	0.485585i
$763$	−39.6852	+	13.1436i	−1.43670	+	0.475831i
$764$	−8.41156	+	4.85641i	−0.304319	+	0.175699i
$765$	28.8037	−	1.15107i	1.04140	−	0.0416171i
$766$	21.3552	+	12.3294i	0.771593	+	0.445480i
$767$	−21.0485	−	47.3610i	−0.760016	−	1.71011i
$768$	0.0345880	+	1.73171i	0.00124809	+	0.0624875i
$769$	28.1406	−	16.2470i	1.01478	−	0.585881i	0.102189	−	0.994765i	$-0.467415\pi$
$769$	28.1406	−	16.2470i	1.01478	−	0.585881i	0.912586	+	0.408884i	$0.134082\pi$
$770$	3.49914	+	3.11491i	0.126100	+	0.112254i
$771$	−17.8258	+	10.7720i	−0.641981	+	0.387944i
$772$	2.73242	+	4.73270i	0.0983421	+	0.170334i
$773$	−6.15935	−	10.6683i	−0.221537	−	0.383713i	0.733738	−	0.679432i	$-0.237774\pi$
$773$	−6.15935	−	10.6683i	−0.221537	−	0.383713i	−0.955275	+	0.295720i	$0.904441\pi$
$774$	−32.3168	−	16.9750i

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.51699 - 0.835899i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.699535 - 1.21163i) q^{5} +(0.895807 + 1.48241i) q^{6} +(1.97618 + 1.75918i) q^{7} -1.00000i q^{8} +(1.60255 + 2.53611i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.51699 - 0.835899i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.699535 - 1.21163i) q^{5} +(0.895807 + 1.48241i) q^{6} +(1.97618 + 1.75918i) q^{7} -1.00000i q^{8} +(1.60255 + 2.53611i) q^{9} +1.39907i q^{10} -1.26560i q^{11} +(-0.0345880 - 1.73171i) q^{12} +(-3.58555 - 0.379286i) q^{13} +(-0.831830 - 2.51159i) q^{14} +(0.0483911 + 2.42278i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.43402 + 5.94790i) q^{17} +(-0.119792 - 2.99761i) q^{18} +4.61200i q^{19} +(0.699535 - 1.21163i) q^{20} +(-1.52735 - 4.32055i) q^{21} +(-0.632798 + 1.09604i) q^{22} +(2.17983 + 1.25852i) q^{23} +(-0.835899 + 1.51699i) q^{24} +(1.52130 - 2.63497i) q^{25} +(2.91553 + 2.12124i) q^{26} +(-0.311127 - 5.18683i) q^{27} +(-0.535407 + 2.59101i) q^{28} +(4.55247 - 2.62837i) q^{29} +(1.16948 - 2.12238i) q^{30} +(4.41277 + 2.54772i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.05791 + 1.91990i) q^{33} -6.86805i q^{34} +(0.749072 - 3.62501i) q^{35} +(-1.39506 + 2.65590i) q^{36} +(3.45697 - 5.98766i) q^{37} +(2.30600 - 3.99411i) q^{38} +(5.12221 + 3.57253i) q^{39} +(-1.21163 + 0.699535i) q^{40} +(-3.22591 - 5.58745i) q^{41} +(-0.837549 + 4.50539i) q^{42} +(6.08396 - 10.5377i) q^{43} +(1.09604 - 0.632798i) q^{44} +(1.95179 - 3.71579i) q^{45} +(-1.25852 - 2.17983i) q^{46} +(1.58414 + 2.74382i) q^{47} +(1.48241 - 0.895807i) q^{48} +(0.810561 + 6.95291i) q^{49} +(-2.63497 + 1.52130i) q^{50} +(-0.237552 - 11.8934i) q^{51} +(-1.46430 - 3.29482i) q^{52} +(0.444106 + 0.256405i) q^{53} +(-2.32397 + 4.64749i) q^{54} +(-1.53343 + 0.885329i) q^{55} +(1.75918 - 1.97618i) q^{56} +(3.85517 - 6.99639i) q^{57} -5.25674 q^{58} +(7.18719 + 12.4486i) q^{59} +(-2.07399 + 1.25330i) q^{60} +3.07454i q^{61} +(-2.54772 - 4.41277i) q^{62} +(-1.29456 + 7.83097i) q^{63} -1.00000 q^{64} +(2.04866 + 4.60968i) q^{65} +(1.87613 - 1.13373i) q^{66} -0.624480 q^{67} +(-3.43402 + 5.94790i) q^{68} +(-2.25479 - 3.73129i) q^{69} +(-2.46122 + 2.76481i) q^{70} +(3.78894 + 2.18755i) q^{71} +(2.53611 - 1.60255i) q^{72} +(-7.24349 - 4.18203i) q^{73} +(-5.98766 + 3.45697i) q^{74} +(-4.51037 + 2.72558i) q^{75} +(-3.99411 + 2.30600i) q^{76} +(2.22641 - 2.50104i) q^{77} +(-2.64970 - 5.65501i) q^{78} +(7.13902 + 12.3651i) q^{79} +1.39907 q^{80} +(-3.86369 + 8.12846i) q^{81} +6.45183i q^{82} +3.52068 q^{83} +(2.97803 - 3.48301i) q^{84} +(4.80444 - 8.32154i) q^{85} +(-10.5377 + 6.08396i) q^{86} +(-9.10312 + 0.181820i) q^{87} -1.26560 q^{88} +(7.94368 - 13.7588i) q^{89} +(-3.54819 + 2.24208i) q^{90} +(-6.41845 - 7.05716i) q^{91} +2.51705i q^{92} +(-4.56452 - 7.55351i) q^{93} -3.16829i q^{94} +(5.58804 - 3.22626i) q^{95} +(-1.73171 + 0.0345880i) q^{96} +(-2.18746 - 1.26293i) q^{97} +(2.77449 - 6.42668i) q^{98} +(3.20969 - 2.02818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Introduction

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