LMFDB - Embedded newform 114.2.l.b.29.1

Newspace parameters

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.l (of order $18$, degree $6$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
Defining polynomial:	$x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + 162 x^{7} + 270 x^{6} + 2916 x^{5} - 4374 x^{4} - 729 x^{3} + 19683$
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			29.1
Root			$1.47158 + 0.913487i$ of defining polynomial
Character	$\chi$	$=$	114.29
Dual form			114.2.l.b.59.1

$q$-expansion

$f(q)$	$=$	$q+(0.173648 + 0.984808i) q^{2} +(-1.69526 - 0.355087i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.882820 + 2.42553i) q^{5} +(0.0553136 - 1.73117i) q^{6} +(-1.58376 + 2.74316i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.74783 + 1.20393i) q^{9} +O(q^{10})$	\(q+(0.173648 + 0.984808i) q^{2} +(-1.69526 - 0.355087i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.882820 + 2.42553i) q^{5} +(0.0553136 - 1.73117i) q^{6} +(-1.58376 + 2.74316i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.74783 + 1.20393i) q^{9} +(-2.54198 - 0.448219i) q^{10} +(-2.16590 + 1.25049i) q^{11} +(1.71447 - 0.246141i) q^{12} +(2.71907 - 3.24046i) q^{13} +(-2.97650 - 1.08336i) q^{14} +(2.35788 - 3.79843i) q^{15} +(0.766044 - 0.642788i) q^{16} +(1.32278 - 0.233243i) q^{17} +(-0.708487 + 2.91514i) q^{18} +(3.14841 + 3.01455i) q^{19} -2.58119i q^{20} +(3.65896 - 4.08800i) q^{21} +(-1.60759 - 1.91586i) q^{22} +(-1.30503 - 3.58554i) q^{23} +(0.540116 + 1.64568i) q^{24} +(-1.27359 - 1.06867i) q^{25} +(3.66340 + 2.11506i) q^{26} +(-4.23078 - 3.01670i) q^{27} +(0.550036 - 3.11941i) q^{28} +(-1.32242 + 7.49981i) q^{29} +(4.15016 + 1.66247i) q^{30} +(6.89193 + 3.97906i) q^{31} +(0.766044 + 0.642788i) q^{32} +(4.11581 - 1.35082i) q^{33} +(0.459398 + 1.26219i) q^{34} +(-5.25543 - 6.26318i) q^{35} +(-2.99388 - 0.191514i) q^{36} +4.10469i q^{37} +(-2.42204 + 3.62405i) q^{38} +(-5.76019 + 4.52793i) q^{39} +(2.54198 - 0.448219i) q^{40} +(4.95792 - 4.16019i) q^{41} +(4.66127 + 2.89350i) q^{42} +(-11.7465 - 4.27537i) q^{43} +(1.60759 - 1.91586i) q^{44} +(-5.34601 + 5.60207i) q^{45} +(3.30445 - 1.90782i) q^{46} +(6.16940 + 1.08783i) q^{47} +(-1.52689 + 0.817681i) q^{48} +(-1.51662 - 2.62686i) q^{49} +(0.831277 - 1.43981i) q^{50} +(-2.32529 - 0.0742967i) q^{51} +(-1.44679 + 3.97502i) q^{52} +(-3.46508 + 1.26118i) q^{53} +(2.23620 - 4.69035i) q^{54} +(-1.12098 - 6.35742i) q^{55} +3.16753 q^{56} +(-4.26694 - 6.22842i) q^{57} -7.61550 q^{58} +(-1.54335 - 8.75275i) q^{59} +(-0.916549 + 4.37580i) q^{60} +(-0.133301 + 0.0485177i) q^{61} +(-2.72184 + 7.47818i) q^{62} +(-7.65449 + 5.63098i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(5.45938 + 9.45593i) q^{65} +(2.04500 + 3.81871i) q^{66} +(-4.48795 - 0.791347i) q^{67} +(-1.16324 + 0.671595i) q^{68} +(0.939187 + 6.54182i) q^{69} +(5.25543 - 6.26318i) q^{70} +(8.59275 + 3.12750i) q^{71} +(-0.331277 - 2.98165i) q^{72} +(-1.67672 + 1.40694i) q^{73} +(-4.04233 + 0.712771i) q^{74} +(1.77960 + 2.26391i) q^{75} +(-3.98957 - 1.75594i) q^{76} -7.92190i q^{77} +(-5.45938 - 4.88641i) q^{78} +(6.41515 + 7.64528i) q^{79} +(0.882820 + 2.42553i) q^{80} +(6.10110 + 6.61639i) q^{81} +(4.95792 + 4.16019i) q^{82} +(12.3308 + 7.11920i) q^{83} +(-2.04012 + 5.09290i) q^{84} +(-0.602044 + 3.41436i) q^{85} +(2.17066 - 12.3104i) q^{86} +(4.90493 - 12.2446i) q^{87} +(2.16590 + 1.25049i) q^{88} +(-12.7492 - 10.6978i) q^{89} +(-6.44529 - 4.29200i) q^{90} +(4.58274 + 12.5910i) q^{91} +(2.45265 + 2.92296i) q^{92} +(-10.2707 - 9.19278i) q^{93} +6.26457i q^{94} +(-10.0914 + 4.97524i) q^{95} +(-1.07040 - 1.36171i) q^{96} +(0.538573 - 0.0949649i) q^{97} +(2.32360 - 1.94973i) q^{98} +(-7.45703 + 0.828515i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18q + 3q^{3} - 9q^{8} - 3q^{9} + O(q^{10}) $	$ 18q + 3q^{3} - 9q^{8} - 3q^{9} - 12q^{13} - 12q^{14} + 18q^{15} + 6q^{17} - 6q^{19} - 24q^{22} + 3q^{24} - 18q^{25} + 18q^{26} - 6q^{27} + 6q^{28} - 6q^{29} - 24q^{33} - 6q^{34} - 24q^{35} + 3q^{38} + 6q^{39} + 3q^{41} - 6q^{43} + 24q^{44} - 54q^{45} + 18q^{46} + 30q^{47} + 21q^{49} + 3q^{50} + 42q^{51} - 6q^{52} - 60q^{53} + 54q^{54} + 30q^{55} + 12q^{57} + 12q^{58} + 3q^{59} + 24q^{60} + 54q^{61} + 6q^{62} - 18q^{63} - 9q^{64} + 24q^{65} - 27q^{66} - 15q^{67} - 27q^{68} + 30q^{69} + 24q^{70} + 36q^{71} + 6q^{72} - 42q^{73} + 6q^{74} - 24q^{78} - 6q^{79} - 3q^{81} + 3q^{82} + 36q^{83} - 30q^{84} - 6q^{86} - 60q^{89} - 18q^{91} - 66q^{93} + 6q^{95} + 9q^{97} + 12q^{98} - 102q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{17}{18}\right)$

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 $

$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$2$	0.173648	+	0.984808i	0.122788	+	0.696364i
$3$	−1.69526	−	0.355087i	−0.978760	−	0.205010i
$3$	−1.69526	−	0.355087i	−0.978760	−	0.205010i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.882820	+	2.42553i	−0.394809	+	1.08473i	0.569970	+	0.821666i	$0.306955\pi$
$5$	−0.882820	+	2.42553i	−0.394809	+	1.08473i	−0.964779	+	0.263063i	$0.915267\pi$
$6$	0.0553136	−	1.73117i	0.0225817	−	0.706746i
$7$	−1.58376	+	2.74316i	−0.598607	+	1.03682i	0.394420	+	0.918930i	$0.370945\pi$
$7$	−1.58376	+	2.74316i	−0.598607	+	1.03682i	−0.993027	+	0.117887i	$0.962388\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	2.74783	+	1.20393i	0.915942	+	0.401311i
$10$	−2.54198	−	0.448219i	−0.803844	−	0.141739i
$11$	−2.16590	+	1.25049i	−0.653045	+	0.377036i	−0.789622	−	0.613594i	$-0.789723\pi$
$11$	−2.16590	+	1.25049i	−0.653045	+	0.377036i	0.136577	+	0.990629i	$0.456390\pi$
$12$	1.71447	−	0.246141i	0.494925	−	0.0710547i
$13$	2.71907	−	3.24046i	0.754135	−	0.898743i	−0.243327	−	0.969944i	$-0.578239\pi$
$13$	2.71907	−	3.24046i	0.754135	−	0.898743i	0.997462	+	0.0712015i	$0.0226833\pi$
$14$	−2.97650	−	1.08336i	−0.795504	−	0.289540i
$15$	2.35788	−	3.79843i	0.608803	−	0.980749i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	1.32278	−	0.233243i	0.320822	−	0.0565696i	−0.0109180	−	0.999940i	$-0.503475\pi$
$17$	1.32278	−	0.233243i	0.320822	−	0.0565696i	0.331740	+	0.943371i	$0.392364\pi$
$18$	−0.708487	+	2.91514i	−0.166992	+	0.687105i
$19$	3.14841	+	3.01455i	0.722294	+	0.691586i
$19$	3.14841	+	3.01455i	0.722294	+	0.691586i
$20$		−	2.58119i		−	0.577172i
$21$	3.65896	−	4.08800i	0.798450	−	0.892075i
$22$	−1.60759	−	1.91586i	−0.342740	−	0.408462i
$23$	−1.30503	−	3.58554i	−0.272117	−	0.747636i	−0.998197	−	0.0600255i	$-0.980882\pi$
$23$	−1.30503	−	3.58554i	−0.272117	−	0.747636i	0.726080	−	0.687611i	$-0.241340\pi$
$24$	0.540116	+	1.64568i	0.110251	+	0.335924i
$25$	−1.27359	−	1.06867i	−0.254718	−	0.213734i
$26$	3.66340	+	2.11506i	0.718451	+	0.414798i
$27$	−4.23078	−	3.01670i	−0.814215	−	0.580564i
$28$	0.550036	−	3.11941i	0.103947	−	0.589513i
$29$	−1.32242	+	7.49981i	−0.245567	+	1.39268i	0.573606	+	0.819132i	$0.305544\pi$
$29$	−1.32242	+	7.49981i	−0.245567	+	1.39268i	−0.819172	+	0.573547i	$0.805567\pi$
$30$	4.15016	+	1.66247i	0.757712	+	0.303525i
$31$	6.89193	+	3.97906i	1.23783	+	0.714660i	0.968650	−	0.248431i	$-0.0799149\pi$
$31$	6.89193	+	3.97906i	1.23783	+	0.714660i	0.269177	+	0.963091i	$0.413248\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	4.11581	−	1.35082i	0.716470	−	0.235147i
$34$	0.459398	+	1.26219i	0.0787861	+	0.216463i
$35$	−5.25543	−	6.26318i	−0.888330	−	1.05867i
$36$	−2.99388	−	0.191514i	−0.498980	−	0.0319190i
$37$			4.10469i			0.674806i	0.941360	+	0.337403i	$0.109549\pi$
$37$			4.10469i			0.674806i	−0.941360	+	0.337403i	$0.890451\pi$
$38$	−2.42204	+	3.62405i	−0.392907	+	0.587898i
$39$	−5.76019	+	4.52793i	−0.922368	+	0.725048i
$40$	2.54198	−	0.448219i	0.401922	−	0.0708697i
$41$	4.95792	−	4.16019i	0.774297	−	0.649712i	−0.167509	−	0.985871i	$-0.553572\pi$
$41$	4.95792	−	4.16019i	0.774297	−	0.649712i	0.941805	+	0.336158i	$0.109128\pi$
$42$	4.66127	+	2.89350i	0.719249	+	0.446476i
$43$	−11.7465	−	4.27537i	−1.79132	−	0.651987i	−0.999130	−	0.0417144i	$-0.986718\pi$
$43$	−11.7465	−	4.27537i	−1.79132	−	0.651987i	−0.792191	−	0.610273i	$-0.791060\pi$
$44$	1.60759	−	1.91586i	0.242354	−	0.288826i
$45$	−5.34601	+	5.60207i	−0.796935	+	0.835108i
$46$	3.30445	−	1.90782i	0.487214	−	0.281293i
$47$	6.16940	+	1.08783i	0.899899	+	0.158676i	0.604414	−	0.796671i	$-0.293407\pi$
$47$	6.16940	+	1.08783i	0.899899	+	0.158676i	0.295486	+	0.955347i	$0.404519\pi$
$48$	−1.52689	+	0.817681i	−0.220388	+	0.118022i
$49$	−1.51662	−	2.62686i	−0.216660	−	0.375266i
$50$	0.831277	−	1.43981i	0.117560	−	0.203621i
$51$	−2.32529	−	0.0742967i	−0.325605	−	0.0104036i
$52$	−1.44679	+	3.97502i	−0.200633	+	0.551236i
$53$	−3.46508	+	1.26118i	−0.475965	+	0.173237i	−0.568853	−	0.822440i	$-0.692612\pi$
$53$	−3.46508	+	1.26118i	−0.475965	+	0.173237i	0.0928877	+	0.995677i	$0.470390\pi$
$54$	2.23620	−	4.69035i	0.304308	−	0.638276i
$55$	−1.12098	−	6.35742i	−0.151153	−	0.857234i
$56$	3.16753			0.423279
$57$	−4.26694	−	6.22842i	−0.565170	−	0.824974i
$58$	−7.61550			−0.999964
$59$	−1.54335	−	8.75275i	−0.200927	−	1.13951i	−0.903722	−	0.428119i	$-0.859176\pi$
$59$	−1.54335	−	8.75275i	−0.200927	−	1.13951i	0.702796	−	0.711392i	$-0.251935\pi$
$60$	−0.916549	+	4.37580i	−0.118326	+	0.564913i
$61$	−0.133301	+	0.0485177i	−0.0170675	+	0.00621206i	−0.350540	−	0.936548i	$-0.614002\pi$
$61$	−0.133301	+	0.0485177i	−0.0170675	+	0.00621206i	0.333472	+	0.942760i	$0.391780\pi$
$62$	−2.72184	+	7.47818i	−0.345673	+	0.949730i
$63$	−7.65449	+	5.63098i	−0.964375	+	0.709437i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	5.45938	+	9.45593i	0.677153	+	1.17286i
$66$	2.04500	+	3.81871i	0.251722	+	0.470051i
$67$	−4.48795	−	0.791347i	−0.548291	−	0.0966784i	−0.107361	−	0.994220i	$-0.534240\pi$
$67$	−4.48795	−	0.791347i	−0.548291	−	0.0966784i	−0.440930	+	0.897542i	$0.645351\pi$
$68$	−1.16324	+	0.671595i	−0.141063	+	0.0814429i
$69$	0.939187	+	6.54182i	0.113065	+	0.787543i
$70$	5.25543	−	6.26318i	0.628144	−	0.748593i
$71$	8.59275	+	3.12750i	1.01977	+	0.371166i	0.797178	−	0.603745i	$-0.206325\pi$
$71$	8.59275	+	3.12750i	1.01977	+	0.371166i	0.222594	+	0.974911i	$0.428548\pi$
$72$	−0.331277	−	2.98165i	−0.0390414	−	0.351391i
$73$	−1.67672	+	1.40694i	−0.196245	+	0.164670i	−0.735615	−	0.677399i	$-0.763107\pi$
$73$	−1.67672	+	1.40694i	−0.196245	+	0.164670i	0.539370	+	0.842069i	$0.318662\pi$
$74$	−4.04233	+	0.712771i	−0.469911	+	0.0828580i
$75$	1.77960	+	2.26391i	0.205490	+	0.261414i
$76$	−3.98957	−	1.75594i	−0.457635	−	0.201420i
$77$		−	7.92190i		−	0.902784i
$78$	−5.45938	−	4.88641i	−0.618153	−	0.553277i
$79$	6.41515	+	7.64528i	0.721760	+	0.860161i	0.994801	−	0.101842i	$-0.0324736\pi$
$79$	6.41515	+	7.64528i	0.721760	+	0.860161i	−0.273040	+	0.962003i	$0.588029\pi$
$80$	0.882820	+	2.42553i	0.0987023	+	0.271182i
$81$	6.10110	+	6.61639i	0.677900	+	0.735155i
$82$	4.95792	+	4.16019i	0.547511	+	0.459416i
$83$	12.3308	+	7.11920i	1.35348	+	0.781433i	0.988735	−	0.149673i	$-0.0478222\pi$
$83$	12.3308	+	7.11920i	1.35348	+	0.781433i	0.364747	+	0.931107i	$0.381156\pi$
$84$	−2.04012	+	5.09290i	−0.222595	+	0.555681i
$85$	−0.602044	+	3.41436i	−0.0653008	+	0.370339i
$86$	2.17066	−	12.3104i	0.234068	−	1.32747i
$87$	4.90493	−	12.2446i	0.525864	−	1.31275i
$88$	2.16590	+	1.25049i	0.230886	+	0.133302i
$89$	−12.7492	−	10.6978i	−1.35141	−	1.13397i	−0.978533	−	0.206089i	$-0.933926\pi$
$89$	−12.7492	−	10.6978i	−1.35141	−	1.13397i	−0.372879	−	0.927880i	$-0.621629\pi$
$90$	−6.44529	−	4.29200i	−0.679393	−	0.452416i
$91$	4.58274	+	12.5910i	0.480402	+	1.31989i
$92$	2.45265	+	2.92296i	0.255707	+	0.304739i
$93$	−10.2707	−	9.19278i	−1.06502	−	0.953247i
$94$			6.26457i			0.646141i
$95$	−10.0914	+	4.97524i	−1.03535	+	0.510448i
$96$	−1.07040	−	1.36171i	−0.109247	−	0.138979i
$97$	0.538573	−	0.0949649i	0.0546838	−	0.00964223i	−0.146239	−	0.989249i	$-0.546717\pi$
$97$	0.538573	−	0.0949649i	0.0546838	−	0.00964223i	0.200923	+	0.979607i	$0.435606\pi$
$98$	2.32360	−	1.94973i	0.234719	−	0.196952i
$99$	−7.45703	+	0.828515i	−0.749460	+	0.0832689i
$100$	1.56229	+	0.568627i	0.156229	+	0.0568627i
$101$	7.56338	−	9.01368i	0.752584	−	0.896895i	−0.244771	−	0.969581i	$-0.578713\pi$
$101$	7.56338	−	9.01368i	0.752584	−	0.896895i	0.997355	+	0.0726860i	$0.0231571\pi$
$102$	−0.330614	−	2.30286i	−0.0327357	−	0.228017i
$103$	6.77528	−	3.91171i	0.667588	−	0.385432i	−0.127574	−	0.991829i	$-0.540719\pi$
$103$	6.77528	−	3.91171i	0.667588	−	0.385432i	0.795162	+	0.606397i	$0.207386\pi$
$104$	−4.16586	−	0.734553i	−0.408496	−	0.0720289i
$105$	6.68536	+	12.4839i	0.652424	+	1.21830i
$106$	−1.84373	−	3.19343i	−0.179079	−	0.310174i
$107$	2.82951	−	4.90085i	0.273539	−	0.473783i	−0.696227	−	0.717822i	$-0.745139\pi$
$107$	2.82951	−	4.90085i	0.273539	−	0.473783i	0.969765	+	0.244039i	$0.0784725\pi$
$108$	5.00741	+	1.38776i	0.481838	+	0.133537i
$109$	5.64501	−	15.5095i	0.540694	−	1.48554i	−0.305251	−	0.952272i	$-0.598740\pi$
$109$	5.64501	−	15.5095i	0.540694	−	1.48554i	0.845944	−	0.533271i	$-0.179038\pi$
$110$	6.06618	−	2.20791i	0.578387	−	0.210516i
$111$	1.45752	−	6.95852i	0.138342	−	0.660473i
$112$	0.550036	+	3.11941i	0.0519735	+	0.294756i
$113$	5.15697			0.485127			0.242564	−	0.970136i	$-0.422012\pi$
$113$	5.15697			0.485127			0.242564	+	0.970136i	$0.422012\pi$
$114$	5.39285	−	5.28367i	0.505087	−	0.494861i
$115$	9.84893			0.918417
$116$	−1.32242	−	7.49981i	−0.122783	−	0.696339i
$117$	11.3728	−	5.63065i	1.05142	−	0.520554i
$118$	8.35178	−	3.03980i	0.768843	−	0.279836i
$119$	−1.45516	+	3.99801i	−0.133394	+	0.366497i
$120$	−4.46848	−	0.142775i	−0.407914	−	0.0130335i
$121$	−2.37257	+	4.10941i	−0.215688	+	0.373583i
$122$	−0.0709282	−	0.122851i	−0.00642154	−	0.0111224i
$123$	−9.88220	+	5.29211i	−0.891048	+	0.477174i
$124$	−7.83721	−	1.38191i	−0.703802	−	0.124099i
$125$	−7.46045	+	4.30729i	−0.667283	+	0.385256i
$126$	−6.87462	−	6.56039i	−0.612440	−	0.584446i
$127$	5.03745	−	6.00340i	0.447001	−	0.532715i	−0.494746	−	0.869038i	$-0.664739\pi$
$127$	5.03745	−	6.00340i	0.447001	−	0.532715i	0.941747	+	0.336322i	$0.109183\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	18.3952	+	11.4189i	1.61961	+	1.00538i
$130$	−8.36426	+	7.01845i	−0.733594	+	0.615559i
$131$	−4.43285	+	0.781631i	−0.387300	+	0.0682914i	−0.363908	−	0.931435i	$-0.618558\pi$
$131$	−4.43285	+	0.781631i	−0.387300	+	0.0682914i	−0.0233919	+	0.999726i	$0.507447\pi$
$132$	−3.40559	+	2.67704i	−0.296418	+	0.233006i
$133$	−13.2557	+	3.86224i	−1.14942	+	0.334898i
$134$		−	4.55719i		−	0.393681i
$135$	11.0521	−	7.59868i	0.951214	−	0.653990i
$136$	−0.863386	−	1.02894i	−0.0740347	−	0.0882312i
$137$	−2.69063	−	7.39245i	−0.229876	−	0.631580i	0.770104	−	0.637919i	$-0.220204\pi$
$137$	−2.69063	−	7.39245i	−0.229876	−	0.631580i	−0.999980	+	0.00633905i	$0.997982\pi$
$138$	−6.27935	+	2.06089i	−0.534534	+	0.175435i
$139$	−5.76780	−	4.83976i	−0.489219	−	0.410503i	0.364528	−	0.931193i	$-0.381230\pi$
$139$	−5.76780	−	4.83976i	−0.489219	−	0.410503i	−0.853746	+	0.520689i	$0.825675\pi$
$140$	7.08063	+	4.08800i	0.598422	+	0.345499i
$141$	−10.0725	−	4.03483i	−0.848255	−	0.339794i
$142$	−1.58788	+	9.00529i	−0.133252	+	0.755707i
$143$	−1.83710	+	10.4187i	−0.153626	+	0.871255i
$144$	2.87883	−	0.844003i	0.239902	−	0.0703336i
$145$	−17.0235	−	9.82854i	−1.41373	−	0.816216i
$146$	−1.67672	−	1.40694i	−0.138767	−	0.116439i
$147$	1.63830	+	4.99175i	0.135125	+	0.411713i
$148$	−1.40389	−	3.85714i	−0.115399	−	0.317055i
$149$	8.79633	+	10.4831i	0.720624	+	0.858806i	0.994691	−	0.102905i	$-0.0328137\pi$
$149$	8.79633	+	10.4831i	0.720624	+	0.858806i	−0.274068	+	0.961710i	$0.588369\pi$
$150$	−1.92049	+	2.14569i	−0.156808	+	0.175195i
$151$		−	8.63653i		−	0.702831i	−0.936220	−	0.351415i	$-0.885700\pi$
$151$		−	8.63653i		−	0.702831i	0.936220	−	0.351415i	$-0.114300\pi$
$152$	1.03648	−	4.23388i	0.0840695	−	0.343413i
$153$	3.91559	+	0.951632i	0.316557	+	0.0769349i
$154$	7.80155	−	1.37562i	0.628667	−	0.110851i
$155$	−15.7356	+	13.2038i	−1.26392	+	1.06055i
$156$	3.86416	−	6.22496i	0.309381	−	0.498396i
$157$	−3.22785	−	1.17484i	−0.257610	−	0.0937625i	0.209987	−	0.977704i	$-0.432658\pi$
$157$	−3.22785	−	1.17484i	−0.257610	−	0.0937625i	−0.467597	+	0.883942i	$0.654880\pi$
$158$	−6.41515	+	7.64528i	−0.510362	+	0.608225i
$159$	6.32204	−	0.907634i	0.501371	−	0.0719800i
$160$	−2.23538	+	1.29060i	−0.176722	+	0.102031i
$161$	11.9026	+	2.09874i	0.938053	+	0.165404i
$162$	−5.45643	+	7.15733i	−0.428698	+	0.562333i
$163$	3.83308	+	6.63909i	0.300230	+	0.520014i	0.976188	−	0.216926i	$-0.0696032\pi$
$163$	3.83308	+	6.63909i	0.300230	+	0.520014i	−0.675958	+	0.736940i	$0.736270\pi$
$164$	−3.23605	+	5.60501i	−0.252693	+	0.437677i
$165$	−0.357076	+	11.1755i	−0.0277983	+	0.870014i
$166$	−4.86982	+	13.3797i	−0.377971	+	1.03847i
$167$	−2.20429	+	0.802294i	−0.170573	+	0.0620834i	−0.425895	−	0.904773i	$-0.640041\pi$
$167$	−2.20429	+	0.802294i	−0.170573	+	0.0620834i	0.255322	+	0.966856i	$0.417818\pi$
$168$	−5.36979	−	1.12475i	−0.414288	−	0.0867763i
$169$	−0.849826	−	4.81960i	−0.0653712	−	0.370739i
$170$	−3.46703			−0.265909
$171$	5.02195	+	12.0739i	0.384038	+	0.923317i
$172$	12.5003			0.953142
$173$	2.59056	+	14.6918i	0.196956	+	1.11700i	0.909605	+	0.415474i	$0.136384\pi$
$173$	2.59056	+	14.6918i	0.196956	+	1.11700i	−0.712649	+	0.701521i	$0.752505\pi$
$174$	12.9103	+	2.70417i	0.978725	+	0.205002i
$175$	4.94860	−	1.80114i	0.374079	−	0.136154i
$176$	−0.855383	+	2.35014i	−0.0644769	+	0.177149i
$177$	−0.491615	+	15.3862i	−0.0369520	+	1.15650i
$178$	8.32145	−	14.4132i	0.623719	−	1.08031i
$179$	−0.0974666	−	0.168817i	−0.00728500	−	0.0126180i	0.862360	−	0.506296i	$-0.168986\pi$
$179$	−0.0974666	−	0.168817i	−0.00728500	−	0.0126180i	−0.869645	+	0.493678i	$0.835652\pi$
$180$	3.10758	−	7.09267i	0.231625	−	0.528656i
$181$	−7.00507	−	1.23518i	−0.520683	−	0.0918105i	−0.0928709	−	0.995678i	$-0.529604\pi$
$181$	−7.00507	−	1.23518i	−0.520683	−	0.0918105i	−0.427812	+	0.903868i	$0.640715\pi$
$182$	−11.6039	+	6.69952i	−0.860139	+	0.496602i
$183$	0.243209	−	0.0349166i	0.0179785	−	0.00258111i
$184$	−2.45265	+	2.92296i	−0.180812	+	0.215483i
$185$	−9.95603	−	3.62370i	−0.731982	−	0.266420i
$186$	7.26963	−	11.7110i	0.533035	−	0.858691i
$187$	−2.57336	+	2.15930i	−0.188183	+	0.157904i
$188$	−6.16940	+	1.08783i	−0.449950	+	0.0793382i
$189$	14.9759	−	6.82798i	1.08933	−	0.496662i
$190$	−6.65200	−	9.07411i	−0.482587	−	0.658305i
$191$			11.2480i			0.813878i	0.913455	+	0.406939i	$0.133404\pi$
$191$			11.2480i			0.813878i	−0.913455	+	0.406939i	$0.866596\pi$
$192$	1.15515	−	1.29060i	0.0833655	−	0.0931408i
$193$	−10.3664	−	12.3541i	−0.746187	−	0.889271i	0.250704	−	0.968064i	$-0.419338\pi$
$193$	−10.3664	−	12.3541i	−0.746187	−	0.889271i	−0.996891	+	0.0787930i	$0.974893\pi$
$194$	0.187044	+	0.513900i	0.0134290	+	0.0368959i
$195$	−5.89740	−	17.9688i	−0.422322	−	1.28677i
$196$	2.32360	+	1.94973i	0.165971	+	0.139266i
$197$	−19.7987	−	11.4308i	−1.41060	−	0.814411i	−0.415157	−	0.909750i	$-0.636273\pi$
$197$	−19.7987	−	11.4308i	−1.41060	−	0.814411i	−0.995445	+	0.0953383i	$0.969607\pi$
$198$	−2.11083	−	7.19987i	−0.150010	−	0.511673i
$199$	0.0579780	−	0.328809i	0.00410995	−	0.0233087i	−0.982684	−	0.185290i	$-0.940677\pi$
$199$	0.0579780	−	0.328809i	0.00410995	−	0.0233087i	0.986794	+	0.161982i	$0.0517885\pi$
$200$	−0.288700	+	1.63730i	−0.0204141	+	0.115774i
$201$	7.32726	+	2.93516i	0.516825	+	0.207030i
$202$	10.1901	+	5.88326i	0.716974	+	0.413945i
$203$	−18.4788	−	15.5055i	−1.29696	−	1.08827i
$204$	2.21047	−	0.725479i	0.154764	−	0.0507937i
$205$	5.71370	+	15.6983i	0.399062	+	1.09641i
$206$	5.02879	+	5.99308i	0.350373	+	0.417558i
$207$	0.730751	−	11.4236i	0.0507907	−	0.793995i
$208$		−	4.23012i		−	0.293306i
$209$	−10.5888	−	2.59220i	−0.732443	−	0.179306i
$210$	−11.1333	+	8.75159i	−0.768271	+	0.603917i
$211$	2.52603	−	0.445407i	0.173899	−	0.0306631i	−0.0860206	−	0.996293i	$-0.527415\pi$
$211$	2.52603	−	0.445407i	0.173899	−	0.0306631i	0.259919	+	0.965630i	$0.416304\pi$
$212$	2.82476	−	2.37025i	0.194005	−	0.162790i
$213$	−13.4564	−	8.35311i	−0.922019	−	0.572346i
$214$	5.31773	+	1.93550i	0.363513	+	0.132308i
$215$	20.7400	−	24.7170i	1.41446	−	1.68569i
$216$	−0.497145	+	5.17232i	−0.0338265	+	0.351931i
$217$	−21.8304	+	12.6038i	−1.48194	+	0.855600i
$218$	16.2542	+	2.86605i	1.10087	+	0.194113i
$219$	3.34207	−	1.78974i	0.225836	−	0.120940i
$220$	3.22774	+	5.59062i	0.217614	+	0.376919i
$221$	2.84093	−	4.92064i	0.191102	−	0.330998i
$222$	7.10590	+	0.227045i	0.476917	+	0.0152383i
$223$	2.28294	−	6.27232i	0.152877	−	0.420026i	−0.839486	−	0.543382i	$-0.817144\pi$
$223$	2.28294	−	6.27232i	0.152877	−	0.420026i	0.992362	+	0.123356i	$0.0393658\pi$
$224$	−2.97650	+	1.08336i	−0.198876	+	0.0723849i
$225$	−2.21300	−	4.46983i	−0.147533	−	0.297989i
$226$	0.895499	+	5.07863i	0.0595677	+	0.337825i
$227$	20.0547			1.33108			0.665539	−	0.746363i	$-0.268202\pi$
$227$	20.0547			1.33108			0.665539	+	0.746363i	$0.268202\pi$
$228$	6.13986	+	4.39342i	0.406622	+	0.290961i
$229$	16.5068			1.09080			0.545400	−	0.838176i	$-0.316378\pi$
$229$	16.5068			1.09080			0.545400	+	0.838176i	$0.316378\pi$
$230$	1.71025	+	9.69930i	0.112770	+	0.639553i
$231$	−2.81297	+	13.4297i	−0.185080	+	0.883609i
$232$	7.15623	−	2.60466i	0.469830	−	0.171004i
$233$	−2.12137	+	5.82843i	−0.138976	+	0.381833i	−0.989582	−	0.143970i	$-0.954013\pi$
$233$	−2.12137	+	5.82843i	−0.138976	+	0.381833i	0.850606	+	0.525803i	$0.176235\pi$
$234$	7.51998	+	10.2223i	0.491597	+	0.668253i
$235$	−8.08503	+	14.0037i	−0.527409	+	0.913500i
$236$	4.44389	+	7.69704i	0.289272	+	0.501035i
$237$	−8.16062	−	15.2387i	−0.530089	−	0.989859i
$238$	−4.18996	−	0.738802i	−0.271595	−	0.0478895i
$239$	−0.498666	+	0.287905i	−0.0322560	+	0.0186230i	−0.516041	−	0.856564i	$-0.672595\pi$
$239$	−0.498666	+	0.287905i	−0.0322560	+	0.0186230i	0.483785	+	0.875187i	$0.339262\pi$
$240$	−0.635337	−	4.42538i	−0.0410108	−	0.285657i
$241$	−1.09166	+	1.30099i	−0.0703198	+	0.0838039i	−0.800058	−	0.599923i	$-0.795198\pi$
$241$	−1.09166	+	1.30099i	−0.0703198	+	0.0838039i	0.729738	+	0.683727i	$0.239642\pi$
$242$	−4.45897	−	1.62293i	−0.286634	−	0.104326i
$243$	−7.99356	−	13.3829i	−0.512787	−	0.858516i
$244$	0.108668	−	0.0911835i	0.00695677	−	0.00583743i
$245$	7.71043	−	1.35956i	0.492601	−	0.0868589i
$246$	−6.92774	−	8.81310i	−0.441697	−	0.561903i
$247$	18.3293	−	2.00550i	1.16627	−	0.127607i
$248$		−	7.95811i		−	0.505341i
$249$	−18.3760	−	16.4474i	−1.16453	−	1.04231i
$250$	−5.53735	−	6.59916i	−0.350213	−	0.417367i
$251$	2.05161	+	5.63675i	0.129496	+	0.355789i	0.987449	−	0.157941i	$-0.0504856\pi$
$251$	2.05161	+	5.63675i	0.129496	+	0.355789i	−0.857952	+	0.513730i	$0.828263\pi$
$252$	5.26696	−	7.90938i	0.331787	−	0.498244i
$253$	7.31023	+	6.13401i	0.459590	+	0.385642i
$254$	6.78694	+	3.91844i	0.425850	+	0.245865i
$255$	2.23302	−	5.57446i	0.139837	−	0.349086i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	3.23144	−	18.3264i	0.201572	−	1.14317i	−0.701172	−	0.712992i	$-0.747340\pi$
$257$	3.23144	−	18.3264i	0.201572	−	1.14317i	0.902744	−	0.430178i	$-0.141549\pi$
$258$	−8.05112	+	20.0986i	−0.501241	+	1.25129i
$259$	−11.2598	−	6.50086i	−0.699651	−	0.403944i
$260$	−8.36426	−	7.01845i	−0.518729	−	0.435266i
$261$	−12.6630	+	19.0161i	−0.783822	+	1.17706i
$262$	−1.53951	−	4.22977i	−0.0951113	−	0.261316i
$263$	−1.37946	−	1.64398i	−0.0850614	−	0.101372i	0.721835	−	0.692065i	$-0.243299\pi$
$263$	−1.37946	−	1.64398i	−0.0850614	−	0.101372i	−0.806896	+	0.590693i	$0.798854\pi$
$264$	−3.22774	−	2.88899i	−0.198654	−	0.177805i
$265$		−	9.51804i		−	0.584688i
$266$	−6.10540	−	12.3837i	−0.374346	−	0.759293i
$267$	17.8146	+	22.6627i	1.09023	+	1.38694i
$268$	4.48795	−	0.791347i	0.274145	−	0.0483392i
$269$	19.9247	−	16.7188i	1.21483	−	1.01936i	0.215752	−	0.976448i	$-0.430780\pi$
$269$	19.9247	−	16.7188i	1.21483	−	1.01936i	0.999079	−	0.0429154i	$-0.0136646\pi$
$270$	9.40242	+	9.56470i	0.572213	+	0.582089i
$271$	4.62857	+	1.68466i	0.281166	+	0.102336i	0.478754	−	0.877949i	$-0.341089\pi$
$271$	4.62857	+	1.68466i	0.281166	+	0.102336i	−0.197588	+	0.980285i	$0.563311\pi$
$272$	0.863386	−	1.02894i	0.0523505	−	0.0623889i
$273$	−3.29805	−	22.9723i	−0.199607	−	1.39035i
$274$	6.81292	−	3.93344i	0.411583	−	0.237628i
$275$	4.09483	+	0.722029i	0.246928	+	0.0435400i
$276$	−3.11998	−	5.82608i	−0.187801	−	0.350689i
$277$	−0.845901	−	1.46514i	−0.0508252	−	0.0880319i	0.839493	−	0.543370i	$-0.182852\pi$
$277$	−0.845901	−	1.46514i	−0.0508252	−	0.0880319i	−0.890319	+	0.455338i	$0.849518\pi$
$278$	3.76467	−	6.52059i	0.225790	−	0.391079i
$279$	14.1473	+	19.2312i	0.846977	+	1.15134i
$280$	−2.79636	+	7.68293i	−0.167114	+	0.459143i
$281$	−28.0317	+	10.2027i	−1.67223	+	0.608642i	−0.992213	−	0.124555i	$-0.960250\pi$
$281$	−28.0317	+	10.2027i	−1.67223	+	0.608642i	−0.680017	+	0.733196i	$0.738028\pi$
$282$	2.22447	−	10.6201i	0.132465	−	0.632417i
$283$	4.10223	+	23.2649i	0.243852	+	1.38296i	0.823143	+	0.567834i	$0.192219\pi$
$283$	4.10223	+	23.2649i	0.243852	+	1.38296i	−0.579290	+	0.815121i	$0.696670\pi$
$284$	−9.14421			−0.542609
$285$	18.8741	−	4.85101i	1.11801	−	0.287349i
$286$	−10.5794			−0.625574
$287$	3.55989	+	20.1891i	0.210134	+	1.19173i
$288$	1.33108	+	2.68853i	0.0784349	+	0.158423i
$289$	−14.2794	+	5.19728i	−0.839966	+	0.305723i
$290$	6.72312	−	18.4716i	0.394795	−	1.08469i
$291$	−0.946743	−	0.0302500i	−0.0554991	−	0.00177328i
$292$	1.09440	−	1.89556i	0.0640451	−	0.110929i
$293$	4.63502	+	8.02810i	0.270781	+	0.469006i	0.969062	−	0.246817i	$-0.0793847\pi$
$293$	4.63502	+	8.02810i	0.270781	+	0.469006i	−0.698281	+	0.715824i	$0.746051\pi$
$294$	−4.63143	+	2.48022i	−0.270110	+	0.144649i
$295$	22.5925	+	3.98367i	1.31539	+	0.231938i
$296$	3.55476	−	2.05234i	0.206616	−	0.119290i
$297$	12.9358	+	1.24335i	0.750612	+	0.0721463i
$298$	−8.79633	+	10.4831i	−0.509558	+	0.607267i
$299$	−15.1673	−	5.52043i	−0.877146	−	0.319255i
$300$	−2.44658	−	1.51872i	−0.141253	−	0.0876834i
$301$	30.3317	−	25.4513i	1.74829	−	1.46699i
$302$	8.50532	−	1.49972i	0.489426	−	0.0862991i
$303$	−16.0226	+	12.5949i	−0.920472	+	0.723558i
$304$	4.34954	+	0.285527i	0.249463	+	0.0163761i
$305$		−	0.366159i		−	0.0209662i
$306$	−0.257240	+	4.02135i	−0.0147054	+	0.229885i
$307$	1.76414	+	2.10242i	0.100685	+	0.119991i	0.814034	−	0.580818i	$-0.197267\pi$
$307$	1.76414	+	2.10242i	0.100685	+	0.119991i	−0.713349	+	0.700809i	$0.752823\pi$
$308$	2.70945	+	7.44415i	0.154385	+	0.424170i
$309$	−12.8749	+	4.22555i	−0.732425	+	0.240383i
$310$	−15.7356	−	13.2038i	−0.893724	−	0.749924i
$311$	19.8290	+	11.4483i	1.12440	+	0.649172i	0.942520	−	0.334148i	$-0.108449\pi$
$311$	19.8290	+	11.4483i	1.12440	+	0.649172i	0.181879	+	0.983321i	$0.441782\pi$
$312$	6.80139	+	2.72450i	0.385053	+	0.154245i
$313$	−2.33240	+	13.2277i	−0.131835	+	0.747673i	0.845177	+	0.534487i	$0.179495\pi$
$313$	−2.33240	+	13.2277i	−0.131835	+	0.747673i	−0.977012	+	0.213186i	$0.931616\pi$
$314$	0.596482	−	3.38282i	0.0336614	−	0.190903i
$315$	−6.90057	−	23.5373i	−0.388803	−	1.32618i
$316$	−8.64310	−	4.99010i	−0.486213	−	0.280715i
$317$	15.9117	+	13.3515i	0.893689	+	0.749894i	0.968947	−	0.247270i	$-0.0795336\pi$
$317$	15.9117	+	13.3515i	0.893689	+	0.749894i	−0.0752579	+	0.997164i	$0.523978\pi$
$318$	1.99166	+	6.06839i	0.111687	+	0.340298i
$319$	−6.51417	−	17.8975i	−0.364723	−	1.00207i
$320$	−1.65916	−	1.97731i	−0.0927498	−	0.110535i
$321$	−6.53699	+	7.30350i	−0.364859	+	0.407642i
$322$			12.0862i			0.673536i
$323$	4.86778	+	3.25326i	0.270851	+	0.181016i
$324$	−7.99609	−	4.13068i	−0.444227	−	0.229482i
$325$	−6.92597	+	1.22124i	−0.384184	+	0.0677419i
$326$	−5.87262	+	4.92772i	−0.325254	+	0.272921i
$327$	−15.0770	+	24.2882i	−0.833760	+	1.34314i
$328$	−6.08179	−	2.21359i	−0.335811	−	0.122225i
$329$	−12.7550	+	15.2008i	−0.703204	+	0.838046i
$330$	−11.0678	+	1.58896i	−0.609260	+	0.0874693i
$331$	7.79345	−	4.49955i	0.428367	−	0.247318i	−0.270284	−	0.962781i	$-0.587118\pi$
$331$	7.79345	−	4.49955i	0.428367	−	0.247318i	0.698651	+	0.715463i	$0.253784\pi$
$332$	−14.0221	−	2.47247i	−0.769562	−	0.135694i
$333$	−4.94176	+	11.2790i	−0.270807	+	0.618083i
$334$	−1.17288	−	2.03148i	−0.0641769	−	0.111158i
$335$	5.88149	−	10.1870i	0.321340	−	0.556577i
$336$	0.175207	−	5.48352i	0.00955835	−	0.299151i
$337$	4.39017	−	12.0619i	0.239148	−	0.657053i	−0.760819	−	0.648964i	$-0.775203\pi$
$337$	4.39017	−	12.0619i	0.239148	−	0.657053i	0.999967	−	0.00808963i	$-0.00257504\pi$
$338$	4.59881	−	1.67383i	0.250142	−	0.0910444i
$339$	−8.74242	−	1.83117i	−0.474823	−	0.0994558i
$340$	−0.602044	−	3.41436i	−0.0326504	−	0.185170i
$341$	−19.9030			−1.07781
$342$	−11.0185	+	7.04227i	−0.595810	+	0.380803i
$343$	−12.5648			−0.678437
$344$	2.17066	+	12.3104i	0.117034	+	0.663734i
$345$	−16.6965	−	3.49723i	−0.898910	−	0.188284i
$346$	−14.0187	+	5.10240i	−0.753652	+	0.274307i
$347$	4.73541	−	13.0104i	0.254210	−	0.698436i	−0.745288	−	0.666743i	$-0.767688\pi$
$347$	4.73541	−	13.0104i	0.254210	−	0.698436i	0.999498	−	0.0316932i	$-0.0100899\pi$
$348$	−0.421241	+	13.1837i	−0.0225809	+	0.706721i
$349$	−10.3158	+	17.8674i	−0.552190	+	0.956421i	0.445926	+	0.895070i	$0.352874\pi$
$349$	−10.3158	+	17.8674i	−0.552190	+	0.956421i	−0.998116	+	0.0613514i	$0.980459\pi$
$350$	2.63310	+	4.56065i	0.140745	+	0.243777i
$351$	−21.2793	+	5.50708i	−1.13581	+	0.293946i
$352$	−2.46298	−	0.434289i	−0.131277	−	0.0231477i
$353$	19.7460	−	11.4004i	1.05098	−	0.606781i	0.128053	−	0.991767i	$-0.459127\pi$
$353$	19.7460	−	11.4004i	1.05098	−	0.606781i	0.922922	+	0.384987i	$0.125794\pi$
$354$	−15.2378	+	2.18764i	−0.809882	+	0.116272i
$355$	−15.1717	+	18.0809i	−0.805230	+	0.959636i
$356$	15.6392	+	5.69220i	0.828876	+	0.301686i
$357$	3.88651	−	6.26097i	0.205696	−	0.331366i
$358$	0.149328	−	0.125301i	0.00789221	−	0.00662235i
$359$	7.31056	−	1.28905i	0.385837	−	0.0680334i	0.0226346	−	0.999744i	$-0.492795\pi$
$359$	7.31056	−	1.28905i	0.385837	−	0.0680334i	0.363202	+	0.931710i	$0.381683\pi$
$360$	7.52454	+	1.82874i	0.396578	+	0.0963831i
$361$	0.824917	+	18.9821i	0.0434167	+	0.999057i
$362$		−	7.11314i		−	0.373858i
$363$	5.48133	−	6.12406i	0.287695	−	0.321430i
$364$	−8.61274	−	10.2643i	−0.451430	−	0.537993i
$365$	−1.93232	−	5.30901i	−0.101142	−	0.277886i
$366$	0.0766189	+	0.233451i	0.00400494	+	0.0122027i
$367$	−15.2065	−	12.7597i	−0.793771	−	0.666053i	0.152904	−	0.988241i	$-0.451137\pi$
$367$	−15.2065	−	12.7597i	−0.793771	−	0.666053i	−0.946676	+	0.322188i	$0.895582\pi$
$368$	−3.30445	−	1.90782i	−0.172256	−	0.0994522i
$369$	18.6321	−	5.46248i	0.969947	−	0.284365i
$370$	1.83980	−	10.4340i	0.0956467	−	0.542439i
$371$	2.02823	−	11.5027i	0.105301	−	0.597189i
$372$	12.7954	+	5.12560i	0.663412	+	0.265750i
$373$	16.5145	+	9.53467i	0.855090	+	0.493687i	0.862365	−	0.506287i	$-0.168982\pi$
$373$	16.5145	+	9.53467i	0.855090	+	0.493687i	−0.00727484	+	0.999974i	$0.502316\pi$
$374$	−2.57336	−	2.15930i	−0.133065	−	0.111655i
$375$	14.1769	−	4.65288i	0.732091	−	0.240274i
$376$	−2.14261	−	5.88677i	−0.110497	−	0.303587i
$377$	20.7071	+	24.6778i	1.06647	+	1.27097i
$378$	9.32478	+	13.5627i	0.479615	+	0.697588i
$379$		−	30.0894i		−	1.54559i	−0.634656	−	0.772795i	$-0.718858\pi$
$379$		−	30.0894i		−	1.54559i	0.634656	−	0.772795i	$-0.281142\pi$
$380$	7.78115	−	8.12664i	0.399164	−	0.416888i
$381$	−10.6715	+	8.38860i	−0.546719	+	0.429761i
$382$	−11.0771	+	1.95320i	−0.566755	+	0.0999342i
$383$	−4.60213	+	3.86165i	−0.235158	+	0.197321i	−0.752750	−	0.658307i	$-0.771273\pi$
$383$	−4.60213	+	3.86165i	−0.235158	+	0.197321i	0.517592	+	0.855628i	$0.326829\pi$
$384$	1.47158	+	0.913487i	0.0750962	+	0.0466162i
$385$	19.2148	+	6.99361i	0.979276	+	0.356427i
$386$	10.3664	−	12.3541i	0.527634	−	0.628809i
$387$	−27.1300	−	25.8899i	−1.37910	−	1.31606i
$388$	−0.473613	+	0.273441i	−0.0240441	+	0.0138818i
$389$	−20.4701	−	3.60942i	−1.03787	−	0.183005i	−0.371353	−	0.928492i	$-0.621106\pi$
$389$	−20.4701	−	3.60942i	−1.03787	−	0.183005i	−0.666520	+	0.745487i	$0.732217\pi$
$390$	16.6718	−	8.92806i	0.844208	−	0.452090i
$391$	−2.56257	−	4.43850i	−0.129595	−	0.224465i
$392$	−1.51662	+	2.62686i	−0.0766009	+	0.132677i
$393$	7.79238	+	0.248979i	0.393074	+	0.0125593i
$394$	7.81913	−	21.4829i	0.393922	−	1.08229i
$395$	−24.2072	+	8.81072i	−1.21800	+	0.443315i
$396$	6.72395	−	3.32900i	0.337891	−	0.167289i
$397$	1.82838	+	10.3692i	0.0917636	+	0.520417i	0.995691	+	0.0927316i	$0.0295599\pi$
$397$	1.82838	+	10.3692i	0.0917636	+	0.520417i	−0.903928	+	0.427686i	$0.859329\pi$
$398$	0.333882			0.0167360
$399$	23.8434	−	1.84056i	1.19366	−	0.0921432i
$400$	−1.66255			−0.0831277
$401$	1.59795	+	9.06241i	0.0797977	+	0.452555i	0.998358	+	0.0572753i	$0.0182413\pi$
$401$	1.59795	+	9.06241i	0.0797977	+	0.452555i	−0.918561	+	0.395280i	$0.870648\pi$
$402$	−1.61820	+	7.72562i	−0.0807084	+	0.385319i
$403$	31.6336	−	11.5137i	1.57578	−	0.573538i
$404$	−4.02439	+	11.0569i	−0.200221	+	0.550102i
$405$	−21.4344	+	8.95729i	−1.06508	+	0.445092i
$406$	12.0612	−	20.8905i	0.598585	−	1.03678i
$407$	−5.13285	−	8.89036i	−0.254426	−	0.440679i
$408$	1.09830	+	2.05091i	0.0543740	+	0.101535i
$409$	23.2080	+	4.09220i	1.14756	+	0.202346i	0.714911	−	0.699215i	$-0.246467\pi$
$409$	23.2080	+	4.09220i	1.14756	+	0.202346i	0.432651	+	0.901561i	$0.357578\pi$
$410$	−14.4676	+	8.35287i	−0.714504	+	0.412519i
$411$	1.93636	+	13.4875i	0.0955136	+	0.665292i
$412$	−5.02879	+	5.99308i	−0.247751	+	0.295258i
$413$	26.4545	+	9.62865i	1.30174	+	0.473795i
$414$	11.3769	−	1.26404i	0.559146	−	0.0621241i
$415$	−28.1537	+	23.6238i	−1.38201	+	1.15964i
$416$	4.16586	−	0.734553i	0.204248	−	0.0360144i
$417$	8.05940	+	10.2527i	0.394670	+	0.502079i
$418$	0.714095	−	10.8781i	0.0349275	−	0.532064i
$419$		−	20.4238i		−	0.997766i	−0.866669	−	0.498883i	$-0.833744\pi$
$419$		−	20.4238i		−	0.997766i	0.866669	−	0.498883i	$-0.166256\pi$
$420$	−10.5519	−	9.44447i	−0.514881	−	0.460843i
$421$	−0.259039	−	0.308710i	−0.0126248	−	0.0150456i	0.759695	−	0.650279i	$-0.225348\pi$
$421$	−0.259039	−	0.308710i	−0.0126248	−	0.0150456i	−0.772320	+	0.635234i	$0.780904\pi$
$422$	0.877280	+	2.41031i	0.0427053	+	0.117332i
$423$	15.6428	+	10.4167i	0.760577	+	0.506478i
$424$	2.82476	+	2.37025i	0.137182	+	0.115110i
$425$	−1.93394	−	1.11656i	−0.0938101	−	0.0541613i
$426$	5.88953	−	14.7025i	0.285349	−	0.712338i
$427$	0.0780261	−	0.442508i	0.00377595	−	0.0214144i
$428$	−0.982678	+	5.57304i	−0.0474995	+	0.269383i
$429$	6.81391	−	17.0101i	0.328979	−	0.821255i
$430$	27.9430	+	16.1329i	1.34753	+	0.777997i
$431$	−7.15165	−	6.00095i	−0.344483	−	0.289055i	0.454087	−	0.890957i	$-0.349965\pi$
$431$	−7.15165	−	6.00095i	−0.344483	−	0.289055i	−0.798570	+	0.601902i	$0.794410\pi$
$432$	−5.18006	+	0.408571i	−0.249226	+	0.0196574i
$433$	−7.03421	−	19.3263i	−0.338043	−	0.928765i	−0.985949	−	0.167045i	$-0.946577\pi$
$433$	−7.03421	−	19.3263i	−0.338043	−	0.928765i	0.647907	−	0.761720i	$-0.275645\pi$
$434$	−16.2031	−	19.3101i	−0.777774	−	0.926915i
$435$	25.3694	+	22.7068i	1.21637	+	1.08871i
$436$			16.5049i			0.790441i
$437$	6.70004	−	15.2228i	0.320506	−	0.728206i
$438$	2.34290	+	2.98051i	0.111948	+	0.142414i
$439$	−25.2438	+	4.45116i	−1.20482	+	0.212442i	−0.739781	−	0.672847i	$-0.765071\pi$
$439$	−25.2438	+	4.45116i	−1.20482	+	0.212442i	−0.465040	+	0.885290i	$0.653960\pi$
$440$	−4.94519	+	4.14951i	−0.235753	+	0.197820i
$441$	−1.00484	−	9.04407i	−0.0478497	−	0.430670i
$442$	5.33920	+	1.94331i	0.253960	+	0.0924339i
$443$	17.0745	−	20.3486i	0.811235	−	0.966792i	−0.188649	−	0.982045i	$-0.560411\pi$
$443$	17.0745	−	20.3486i	0.811235	−	0.966792i	0.999884	+	0.0152527i	$0.00485526\pi$
$444$	1.01033	+	7.03737i	0.0479482	+	0.333979i
$445$	37.2032	−	21.4793i	1.76360	−	1.01821i
$446$	6.57346	+	1.15908i	0.311262	+	0.0548839i
$447$	−11.1897	−	20.8950i	−0.529254	−	0.988300i
$448$	−1.58376	−	2.74316i	−0.0748258	−	0.129602i
$449$	−5.66925	+	9.81944i	−0.267549	+	0.463408i	−0.968228	−	0.250068i	$-0.919547\pi$
$449$	−5.66925	+	9.81944i	−0.267549	+	0.463408i	0.700680	+	0.713476i	$0.252880\pi$
$450$	4.01764	−	2.95556i	0.189394	−	0.139326i
$451$	−5.53612	+	15.2104i	−0.260686	+	0.716229i
$452$	−4.84597	+	1.76379i	−0.227935	+	0.0829616i
$453$	−3.06672	+	14.6412i	−0.144087	+	0.687903i
$454$	3.48246	+	19.7500i	0.163440	+	0.926915i
$455$	−34.5855			−1.62139
$456$	−3.26050	+	6.80949i	−0.152687	+	0.318884i
$457$	−21.3688			−0.999591			−0.499796	−	0.866143i	$-0.666592\pi$
$457$	−21.3688			−0.999591			−0.499796	+	0.866143i	$0.666592\pi$
$458$	2.86638	+	16.2560i	0.133937	+	0.759594i
$459$	−6.30004	−	3.00364i	−0.294061	−	0.140198i
$460$	−9.25496	+	3.36853i	−0.431515	+	0.157059i
$461$	9.40832	−	25.8492i	0.438189	−	1.20392i	−0.502480	−	0.864589i	$-0.667579\pi$
$461$	9.40832	−	25.8492i	0.438189	−	1.20392i	0.940669	−	0.339326i	$-0.110199\pi$
$462$	−13.7141	−	0.438189i	−0.638039	−	0.0203864i
$463$	−4.52654	+	7.84019i	−0.210366	+	0.364365i	−0.951829	−	0.306629i	$-0.900799\pi$
$463$	−4.52654	+	7.84019i	−0.210366	+	0.364365i	0.741463	+	0.670994i	$0.234132\pi$
$464$	3.80775	+	6.59522i	0.176770	+	0.306175i
$465$	31.3645	−	16.7963i	1.45450	−	0.778911i
$466$	−6.10825	−	1.07705i	−0.282959	−	0.0498934i
$467$	−17.7092	+	10.2244i	−0.819486	+	0.473130i	−0.850239	−	0.526397i	$-0.823543\pi$
$467$	−17.7092	+	10.2244i	−0.819486	+	0.473130i	0.0307535	+	0.999527i	$0.490209\pi$
$468$	−8.76117	+	9.18082i	−0.404985	+	0.424384i
$469$	9.27865	−	11.0579i	0.428448	−	0.510605i
$470$	−15.1949	−	5.53049i	−0.700888	−	0.255102i
$471$	5.05488	+	3.13783i	0.232916	+	0.144584i
$472$	−6.80843	+	5.71295i	−0.313383	+	0.262960i
$473$	30.7880	−	5.42876i	1.41564	−	0.249615i
$474$	13.5901	−	10.6828i	0.624214	−	0.490678i
$475$	−0.788217	−	7.20391i	−0.0361659	−	0.330538i
$476$		−	4.25459i		−	0.195009i
$477$	−11.0398	−	0.706200i	−0.505478	−	0.0323347i
$478$	−0.370124	−	0.441096i	−0.0169291	−	0.0201753i
$479$	−3.36367	−	9.24160i	−0.153690	−	0.422259i	0.838822	−	0.544405i	$-0.183245\pi$
$479$	−3.36367	−	9.24160i	−0.153690	−	0.422259i	−0.992512	+	0.122146i	$0.961022\pi$
$480$	4.24783	−	1.39414i	0.193886	−	0.0636337i
$481$	13.3011	+	11.1609i	0.606477	+	0.508895i
$482$	−1.47079	−	0.849159i	−0.0669925	−	0.0386781i
$483$	−19.4327	−	7.78437i	−0.884220	−	0.354201i
$484$	0.823985	−	4.67305i	0.0374539	−	0.212411i
$485$	−0.245123	+	1.39016i	−0.0111305	+	0.0631239i
$486$	11.7916	−	10.1960i	0.534876	−	0.462502i
$487$	−6.75564	−	3.90037i	−0.306127	−	0.176743i	0.339065	−	0.940763i	$-0.389889\pi$
$487$	−6.75564	−	3.90037i	−0.306127	−	0.176743i	−0.645192	+	0.764020i	$0.723223\pi$
$488$	0.108668	+	0.0911835i	0.00491918	+	0.00412768i
$489$	−4.14062	−	12.6161i	−0.187245	−	0.570519i
$490$	2.67780	+	7.35721i	0.120971	+	0.332365i
$491$	18.0754	+	21.5414i	0.815729	+	0.972148i	0.999942	−	0.0107379i	$-0.00341805\pi$
$491$	18.0754	+	21.5414i	0.815729	+	0.972148i	−0.184213	+	0.982886i	$0.558974\pi$
$492$	7.47622	−	8.35287i	0.337054	−	0.376577i
$493$			10.2291i			0.460694i
$494$	5.15788	+	17.7026i	0.232064	+	0.796477i
$495$	4.57363	−	18.8187i	0.205569	−	0.845836i
$496$	7.83721	−	1.38191i	0.351901	−	0.0620497i
$497$	−22.1881	+	18.6181i	−0.995274	+	0.835134i
$498$	13.0066	−	20.9529i	0.582839	−	0.938922i
$499$	−12.8477	−	4.67618i	−0.575142	−	0.209334i	0.0380402	−	0.999276i	$-0.487888\pi$
$499$	−12.8477	−	4.67618i	−0.575142	−	0.209334i	−0.613182	+	0.789942i	$0.710111\pi$
$500$	5.53735	−	6.59916i	0.247638	−	0.295123i
$501$	4.02173	−	0.577385i	0.179677	−	0.0257957i
$502$	−5.19486	+	2.99925i	−0.231858	+	0.133863i
$503$	−25.8762	−	4.56267i	−1.15376	−	0.203439i	−0.436144	−	0.899877i	$-0.643656\pi$
$503$	−25.8762	−	4.56267i	−1.15376	−	0.203439i	−0.717618	+	0.696437i	$0.754767\pi$
$504$	8.70382	+	3.81349i	0.387699	+	0.169866i
$505$	15.1858	+	26.3026i	0.675761	+	1.17045i
$506$	−4.77142	+	8.26433i	−0.212115	+	0.367394i
$507$	−0.270702	+	8.47225i	−0.0120223	+	0.376266i
$508$	−2.68037	+	7.36426i	−0.118922	+	0.326736i
$509$	−25.0043	+	9.10082i	−1.10830	+	0.403387i	−0.830368	−	0.557215i	$-0.811870\pi$
$509$	−25.0043	+	9.10082i	−1.10830	+	0.403387i	−0.277928	+	0.960602i	$0.589648\pi$
$510$	5.87753	+	1.23110i	0.260261	+	0.0545140i
$511$	−1.20392	−	6.82777i	−0.0532583	−	0.302043i
$512$	1.00000			0.0441942
$513$	−4.22622	−	22.2517i	−0.186592	−	0.982437i
$514$	18.6091			0.820813
$515$	3.50661	+	19.8869i	0.154520	+	0.876324i
$516$	−21.1913	−	4.43871i	−0.932897	−	0.195403i
$517$	−14.7226	+	5.35860i	−0.647501	+	0.235671i
$518$	4.44685	−	12.2176i	0.195383	−	0.536811i
$519$	0.825191	−	25.8263i	0.0362219	−	1.13365i
$520$	5.45938	−	9.45593i	0.239410	−	0.414670i
$521$	−10.2977	−	17.8362i	−0.451151	−	0.781417i	0.547307	−	0.836932i	$-0.315653\pi$
$521$	−10.2977	−	17.8362i	−0.451151	−	0.781417i	−0.998458	+	0.0555154i	$0.982320\pi$
$522$	−20.9261	−	9.16855i	−0.915909	−	0.401296i
$523$	7.47024	+	1.31720i	0.326651	+	0.0575973i	0.334569	−	0.942371i	$-0.391409\pi$
$523$	7.47024	+	1.31720i	0.326651	+	0.0575973i	−0.00791816	+	0.999969i	$0.502520\pi$
$524$	3.89818	−	2.25062i	0.170293	−	0.0983186i
$525$	−9.02874	+	1.29622i	−0.394046	+	0.0565719i
$526$	1.37946	−	1.64398i	0.0601475	−	0.0716810i
$527$	10.0446	+	3.65594i	0.437550	+	0.159255i
$528$	2.28460	−	3.68037i	0.0994246	−	0.160168i
$529$	6.46604	−	5.42566i	0.281132	−	0.235898i
$530$	9.37344	−	1.65279i	0.407156	−	0.0717926i
$531$	6.29687	−	25.9091i	0.273261	−	1.12436i
$532$	11.1354	−	8.16305i	0.482779	−	0.353913i
$533$		−	27.3778i		−	1.18586i
$534$	−19.2250	+	21.4793i	−0.831946	+	0.929498i
$535$	9.38920	+	11.1896i	0.405931	+	0.483769i
$536$	1.55865	+	4.28235i	0.0673234	+	0.184970i
$537$	0.105287	+	0.320799i	0.00454345	+	0.0138435i
$538$	19.9247	+	16.7188i	0.859015	+	0.720799i
$539$	6.56971	+	3.79302i	0.282977	+	0.163377i
$540$	−7.78668	+	10.9205i	−0.335085	+	0.469942i
$541$	7.39225	−	41.9235i	0.317818	−	1.80243i	−0.238148	−	0.971229i	$-0.576540\pi$
$541$	7.39225	−	41.9235i	0.317818	−	1.80243i	0.555966	−	0.831205i	$-0.312349\pi$
$542$	−0.855325	+	4.85079i	−0.0367394	+	0.208359i
$543$	11.4368	+	4.58137i	0.490802	+	0.196605i
$544$	1.16324	+	0.671595i	0.0498734	+	0.0287944i
$545$	32.6353	+	27.3842i	1.39794	+	1.17301i
$546$	22.0506	−	7.23704i	0.943678	−	0.309717i
$547$	−0.418676	−	1.15030i	−0.0179013	−	0.0491833i	0.930420	−	0.366495i	$-0.119442\pi$
$547$	−0.418676	−	1.15030i	−0.0179013	−	0.0491833i	−0.948321	+	0.317311i	$0.897220\pi$
$548$	5.05673	+	6.02638i	0.216013	+	0.257434i
$549$	−0.424701	−	0.0271675i	−0.0181258	−	0.00115948i
$550$			4.15800i			0.177298i
$551$	−26.7721	+	19.6259i	−1.14053	+	0.836093i
$552$	5.19579	−	4.08427i	0.221148	−	0.173838i
$553$	−31.1323	+	5.48946i	−1.32388	+	0.233436i
$554$	1.29599	−	1.08747i	0.0550615	−	0.0462021i
$555$	15.5914	+	9.67838i	0.661816	+	0.410824i
$556$	7.07526	+	2.57518i	0.300058	+	0.109212i
$557$	−13.8808	+	16.5425i	−0.588147	+	0.700927i	−0.975249	−	0.221110i	$-0.929032\pi$
$557$	−13.8808	+	16.5425i	−0.588147	+	0.700927i	0.387101	+	0.922037i	$0.373476\pi$
$558$	−16.4824	+	17.2718i	−0.697754	+	0.731175i
$559$	−45.7937	+	26.4390i	−1.93687	+	1.11825i
$560$	−8.05179	−	1.41975i	−0.340250	−	0.0599953i
$561$	5.12926	−	2.74682i	0.216557	−	0.115971i
$562$	−14.9153	−	25.8341i	−0.629166	−	1.08975i
$563$	−13.0149	+	22.5424i	−0.548512	+	0.950051i	0.449865	+	0.893097i	$0.351472\pi$
$563$	−13.0149	+	22.5424i	−0.548512	+	0.950051i	−0.998377	+	0.0569541i	$0.981861\pi$
$564$	10.8450	+	0.346516i	0.456658	+	0.0145909i
$565$	−4.55268	+	12.5084i	−0.191533	+	0.526231i
$566$	−22.1991	+	8.07982i	−0.933099	+	0.339620i
$567$	−27.8125	+	6.25748i	−1.16802	+	0.262789i
$568$	−1.58788	−	9.00529i	−0.0666258	−	0.377854i
$569$	−4.80544			−0.201455			−0.100727	−	0.994914i	$-0.532117\pi$
$569$	−4.80544			−0.201455			−0.100727	+	0.994914i	$0.532117\pi$
$570$	8.05478	+	17.7450i	0.337377	+	0.743258i
$571$	−46.6475			−1.95214			−0.976068	−	0.217466i	$-0.930221\pi$
$571$	−46.6475			−1.95214			−0.976068	+	0.217466i	$0.930221\pi$
$572$	−1.83710	−	10.4187i	−0.0768129	−	0.435628i
$573$	3.99403	−	19.0683i	0.166853	−	0.796591i
$574$	−19.2642	+	7.01161i	−0.804074	+	0.292659i
$575$	−2.16968	+	5.96115i	−0.0904820	+	0.248597i
$576$	−2.41655	+	1.77772i	−0.100690	+	0.0740717i
$577$	23.3103	−	40.3745i	0.970418	−	1.68081i	0.276125	−	0.961122i	$-0.410950\pi$
$577$	23.3103	−	40.3745i	0.970418	−	1.68081i	0.694293	−	0.719692i	$-0.255717\pi$
$578$	−7.59792	−	13.1600i	−0.316032	−	0.547383i
$579$	13.1869	+	24.6245i	0.548028	+	1.02336i
$580$	19.3584	+	3.41342i	0.803816	+	0.141734i
$581$	−39.0582	+	22.5503i	−1.62041	+	0.935543i
$582$	−0.134610	−	0.937613i	−0.00557976	−	0.0388653i
$583$	5.92793	−	7.06463i	0.245510	−	0.292587i
$584$	2.05680	+	0.748615i	0.0851112	+	0.0309779i
$585$	3.61714	+	32.5560i	0.149550	+	1.34602i
$586$	−7.10127	+	5.95867i	−0.293351	+	0.246150i
$587$	−14.9298	+	2.63253i	−0.616220	+	0.108656i	−0.473041	−	0.881040i	$-0.656844\pi$
$587$	−14.9298	+	2.63253i	−0.616220	+	0.108656i	−0.143180	+	0.989697i	$0.545733\pi$
$588$	−3.24678	−	4.13038i	−0.133895	−	0.170334i
$589$	9.70350	+	33.3038i	0.399826	+	1.37226i
$590$			22.9411i			0.944469i
$591$	29.5051	+	26.4085i	1.21368	+	1.08630i
$592$	2.63844	+	3.14437i	0.108439	+	0.129233i
$593$	0.398860	+	1.09586i	0.0163792	+	0.0450015i	0.947613	−	0.319421i	$-0.103489\pi$
$593$	0.398860	+	1.09586i	0.0163792	+	0.0450015i	−0.931234	+	0.364423i	$0.881266\pi$
$594$	1.02182	+	12.9552i	0.0419259	+	0.531558i
$595$	−8.41264	−	7.05905i	−0.344885	−	0.289393i
$596$	−11.8513	−	6.84233i	−0.485447	−	0.280273i
$597$	−0.215044	+	0.536831i	−0.00880116	+	0.0219710i
$598$	2.80280	−	15.8955i	0.114615	−	0.650014i
$599$	4.45202	−	25.2486i	0.181905	−	1.03163i	−0.747964	−	0.663739i	$-0.768968\pi$
$599$	4.45202	−	25.2486i	0.181905	−	1.03163i	0.929868	−	0.367892i	$-0.119921\pi$
$600$	1.07080	−	2.67313i	0.0437154	−	0.109130i
$601$	−26.4639	−	15.2789i	−1.07948	−	0.623240i	−0.148726	−	0.988878i	$-0.547517\pi$
$601$	−26.4639	−	15.2789i	−1.07948	−	0.623240i	−0.930757	+	0.365639i	$0.880851\pi$
$602$	30.3317	+	25.4513i	1.23623	+	1.03732i
$603$	−11.3794	−	7.57767i	−0.463404	−	0.308587i
$604$	2.95387	+	8.11568i	0.120191	+	0.330222i
$605$	−7.87294	−	9.38261i	−0.320081	−	0.381457i
$606$	−15.1858	−	13.5921i	−0.616882	−	0.552139i
$607$			7.82667i			0.317675i	0.987305	+	0.158837i	$0.0507745\pi$
$607$			7.82667i			0.317675i	−0.987305	+	0.158837i	$0.949225\pi$
$608$	0.474100	+	4.33304i	0.0192273	+	0.175728i
$609$	25.8205	+	32.8475i	1.04630	+	1.33105i
$610$	0.360596	−	0.0635828i	0.0146001	−	0.00257439i
$611$	20.3001	−	17.0338i	0.821254	−	0.689114i
$612$	−4.00493	+	0.444968i	−0.161890	+	0.0179868i
$613$	30.3824	+	11.0583i	1.22713	+	0.446640i	0.872615	−	0.488408i	$-0.162422\pi$
$613$	30.3824	+	11.0583i	1.22713	+	0.446640i	0.354519	+	0.935049i	$0.384645\pi$
$614$	−1.76414	+	2.10242i	−0.0711948	+	0.0848466i
$615$	−4.11197	−	28.6415i	−0.165810	−	1.15494i
$616$	−6.86057	+	3.96095i	−0.276420	+	0.159591i
$617$	24.5040	+	4.32072i	0.986495	+	0.173946i	0.643545	−	0.765408i	$-0.277463\pi$
$617$	24.5040	+	4.32072i	0.986495	+	0.173946i	0.342950	+	0.939354i	$0.388574\pi$
$618$	−6.39705	−	11.9455i	−0.257327	−	0.480519i
$619$	−3.60285	−	6.24032i	−0.144811	−	0.250820i	0.784492	−	0.620140i	$-0.212924\pi$
$619$	−3.60285	−	6.24032i	−0.144811	−	0.250820i	−0.929302	+	0.369320i	$0.879591\pi$
$620$	10.2707	−	17.7894i	0.412482	−	0.714439i
$621$	−5.29519	+	19.1065i	−0.212489	+	0.766718i
$622$	−7.83109	+	21.5157i	−0.313998	+	0.862702i
$623$	49.5376	−	18.0302i	1.98468	−	0.722366i
$624$	−1.50206	+	7.17117i	−0.0601307	+	0.287077i
$625$	−5.30472	−	30.0846i	−0.212189	−	1.20338i
$626$	−13.4317			−0.536841
$627$	17.0303	+	8.15441i	0.680126	+	0.325656i
$628$	3.43500			0.137072
$629$	0.957388	+	5.42961i	0.0381735	+	0.216493i
$630$	21.9815	−	10.8829i	0.875762	−	0.433587i
$631$	23.7099	−	8.62969i	0.943876	−	0.343543i	0.176180	−	0.984358i	$-0.443626\pi$
$631$	23.7099	−	8.62969i	0.943876	−	0.343543i	0.767695	+	0.640815i	$0.221404\pi$
$632$	3.41343	−	9.37832i	0.135779	−	0.373049i
$633$	−4.44044	−	0.141879i	−0.176492	−	0.00563919i
$634$	−10.3856	+	17.9884i	−0.412465	+	0.714411i
$635$	10.1142	+	17.5184i	0.401372	+	0.695196i
$636$	−5.63035	+	3.01516i	−0.223258	+	0.119559i
$637$	−12.6361	−	2.22808i	−0.500659	−	0.0882796i
$638$	16.4945	−	9.52308i	0.653022	−	0.377022i
$639$	19.8461	+	18.9389i	0.785099	+	0.749212i
$640$	1.65916	−	1.97731i	0.0655840	−	0.0781600i
$641$	−8.36361	−	3.04411i	−0.330343	−	0.120235i	0.171524	−	0.985180i	$-0.445131\pi$
$641$	−8.36361	−	3.04411i	−0.330343	−	0.120235i	−0.501867	+	0.864945i	$0.667353\pi$
$642$	−8.32768	−	5.16943i	−0.328667	−	0.204021i
$643$	5.41716	−	4.54553i	0.213632	−	0.179258i	−0.529692	−	0.848190i	$-0.677693\pi$
$643$	5.41716	−	4.54553i	0.213632	−	0.179258i	0.743324	+	0.668932i	$0.233248\pi$
$644$	−11.9026	+	2.09874i	−0.469027	+	0.0827021i
$645$	−43.9365	+	34.5373i	−1.73000	+	1.35990i
$646$	−2.35856	+	5.35875i	−0.0927962	+	0.210837i
$647$		−	7.87198i		−	0.309479i	−0.987955	−	0.154740i	$-0.950546\pi$
$647$		−	7.87198i		−	0.309479i	0.987955	−	0.154740i	$-0.0494539\pi$
$648$	2.67942	−	8.59190i	0.105257	−	0.337522i
$649$	14.2879	+	17.0277i	0.560850	+	0.668395i
$650$	−2.40536	−	6.60868i	−0.0943461	−	0.259214i
$651$	41.4837	−	13.6150i	1.62587	−	0.533614i
$652$	−5.87262	−	4.92772i	−0.229990	−	0.192984i
$653$	−1.40402	−	0.810613i	−0.0549437	−	0.0317217i	0.472277	−	0.881450i	$-0.343432\pi$
$653$	−1.40402	−	0.810613i	−0.0549437	−	0.0317217i	−0.527220	+	0.849729i	$0.676766\pi$
$654$	−26.5373	−	10.6303i	−1.03769	−	0.415679i
$655$	2.01754	−	11.4420i	0.0788318	−	0.447077i
$656$	1.12387	−	6.37378i	0.0438797	−	0.248854i
$657$	−6.30120	+	1.84736i	−0.245833	+	0.0720723i
$658$	−17.1847	−	9.92160i	−0.669930	−	0.386784i
$659$	−9.29693	−	7.80105i	−0.362157	−	0.303886i	0.443493	−	0.896278i	$-0.353739\pi$
$659$	−9.29693	−	7.80105i	−0.362157	−	0.303886i	−0.805650	+	0.592392i	$0.798184\pi$
$660$	−3.48672	−	10.6237i	−0.135720	−	0.413527i
$661$	−10.0965	−	27.7400i	−0.392710	−	1.07896i	−0.965759	−	0.259440i	$-0.916462\pi$
$661$	−10.0965	−	27.7400i	−0.392710	−	1.07896i	0.573050	−	0.819521i	$-0.305760\pi$
$662$	5.78451	+	6.89371i	0.224821	+	0.267932i
$663$	−6.56338	+	7.33299i	−0.254900	+	0.284790i
$664$		−	14.2384i		−	0.552557i
$665$	2.33447	−	35.5618i	0.0905268	−	1.37903i
$666$	−11.9657	−	2.90812i	−0.463663	−	0.112687i
$667$	28.6166	−	5.04588i	1.10804	−	0.195377i
$668$	1.79695	−	1.50782i	0.0695261	−	0.0583393i
$669$	−6.09740	+	9.82258i	−0.235739	+	0.379763i
$670$	11.0536	+	4.02317i	0.427037	+	0.155429i
$671$	0.228047	−	0.271776i	0.00880367	−	0.0104918i
$672$	5.43064	−	0.779658i	0.209491	−	0.0300760i
$673$	−3.84411	+	2.21940i	−0.148180	+	0.0855516i	−0.572257	−	0.820075i	$-0.693932\pi$
$673$	−3.84411	+	2.21940i	−0.148180	+	0.0855516i	0.424077	+	0.905626i	$0.360599\pi$
$674$	12.6410	+	2.22895i	0.486913	+	0.0858559i
$675$	2.16443	+	8.36335i	0.0833091	+	0.321905i
$676$	2.44698	+	4.23829i	0.0941145	+	0.163011i
$677$	0.610403	−	1.05725i	0.0234597	−	0.0406334i	−0.854057	−	0.520179i	$-0.825865\pi$
$677$	0.610403	−	1.05725i	0.0234597	−	0.0406334i	0.877517	+	0.479546i	$0.159199\pi$
$678$	0.285251	−	8.92758i	0.0109550	−	0.342862i
$679$	−0.592469	+	1.62779i	−0.0227369	+	0.0624690i
$680$	3.25794	−	1.18579i	0.124936	−	0.0454732i
$681$	−33.9980	−	7.12117i	−1.30281	−	0.272884i
$682$	−3.45612	−	19.6006i	−0.132342	−	0.750547i
$683$	40.7336			1.55863			0.779313	−	0.626635i	$-0.215568\pi$
$683$	40.7336			1.55863			0.779313	+	0.626635i	$0.215568\pi$
$684$	−8.84862	−	9.62818i	−0.338335	−	0.368143i
$685$	20.3059			0.775850
$686$	−2.18186	−	12.3739i	−0.0833038	−	0.472439i
$687$	−27.9834	−	5.86136i	−1.06763	−	0.223625i
$688$	−11.7465	+	4.27537i	−0.447830	+	0.162997i
$689$	−5.33497	+	14.6577i	−0.203246	+	0.558414i
$690$	0.544779	−	17.0501i	0.0207394	−	0.649088i
$691$	18.9023	−	32.7397i	0.719077	−	1.24548i	−0.242289	−	0.970204i	$-0.577898\pi$
$691$	18.9023	−	32.7397i	0.719077	−	1.24548i	0.961366	−	0.275274i	$-0.0887686\pi$
$692$	−7.45921	−	12.9197i	−0.283557	−	0.491135i
$693$	9.53743	−	21.7680i	0.362297	−	0.826898i
$694$	13.6351	+	2.40423i	0.517580	+	0.0912633i
$695$	16.8309	−	9.71733i	0.638433	−	0.368599i
$696$	−13.0566	+	1.87449i	−0.494908	+	0.0710522i
$697$	5.58792	−	6.65943i	0.211658	−	0.252244i
$698$	−19.3873	−	7.05640i	−0.733820	−	0.267088i
$699$	5.66589	−	9.12744i	0.214304	−	0.345231i
$700$	−4.03414	+	3.38504i	−0.152476	+	0.127943i
$701$	23.1182	−	4.07636i	0.873162	−	0.153962i	0.280929	−	0.959729i	$-0.409358\pi$
$701$	23.1182	−	4.07636i	0.873162	−	0.153962i	0.592233	+	0.805767i	$0.298246\pi$
$702$	−9.11853	−	19.9997i	−0.344157	−	0.754841i
$703$	−12.3738	+	12.9232i	−0.466687	+	0.487408i
$704$		−	2.50097i		−	0.0942589i
$705$	18.6788	−	20.8690i	0.703483	−	0.785973i
$706$	14.6560	+	17.4664i	0.551587	+	0.657356i
$707$	12.7474	+	35.0231i	0.479414	+	1.31718i
$708$	−4.80043	−	14.6265i	−0.180411	−	0.549696i
$709$	21.3882	+	17.9469i	0.803252	+	0.674009i	0.948987	−	0.315315i	$-0.102110\pi$
$709$	21.3882	+	17.9469i	0.803252	+	0.674009i	−0.145735	+	0.989324i	$0.546555\pi$
$710$	−20.4408	−	11.8015i	−0.767128	−	0.442902i
$711$	8.42332	+	28.7313i	0.315899	+	1.07751i
$712$	−2.89001	+	16.3901i	−0.108308	+	0.614243i
$713$	5.27289	−	29.9041i	0.197471	−	1.11992i
$714$	6.84074	+	2.74026i	0.256008	+	0.102552i
$715$	−23.6490	−	13.6538i	−0.884423	−	0.510622i
$716$	0.149328	+	0.125301i	0.00558063	+	0.00468271i
$717$	0.947601	−	0.311004i	0.0353888	−	0.0116147i
$718$	2.53893	+	6.97566i	0.0947521	+	0.260329i
$719$	−26.4940	−	31.5743i	−0.988060	−	1.17752i	−0.984115	−	0.177532i	$-0.943189\pi$
$719$	−26.4940	−	31.5743i	−0.988060	−	1.17752i	−0.00394505	−	0.999992i	$-0.501256\pi$
$720$	−0.494335	+	7.72778i	−0.0184228	+	0.287997i
$721$			24.7809i			0.922889i
$722$	−18.5505	+	4.10859i	−0.690377	+	0.152906i
$723$	2.31261	−	1.81788i	0.0860069	−	0.0676077i
$724$	7.00507	−	1.23518i	0.260341	−	0.0459052i
$725$	9.69903	−	8.13846i	0.360213	−	0.302255i
$726$	6.98285	+	4.33462i	0.259158	+	0.160873i
$727$	4.13772	+	1.50601i	0.153460	+	0.0558548i	0.417608	−	0.908627i	$-0.362869\pi$
$727$	4.13772	+	1.50601i	0.153460	+	0.0558548i	−0.264148	+	0.964482i	$0.585091\pi$
$728$	8.61274	−	10.2643i	0.319209	−	0.380419i
$729$	8.79906	+	25.5260i	0.325891	+	0.945407i
$730$	4.89281	−	2.82486i	0.181091	−	0.104553i
$731$	−16.5352	−	2.91561i	−0.611578	−	0.107838i
$732$	−0.216599	+	0.115993i	−0.00800574	+	0.00428723i
$733$	11.3991	+	19.7438i	0.421034	+	0.729253i	0.996041	−	0.0888960i	$-0.0283339\pi$
$733$	11.3991	+	19.7438i	0.421034	+	0.729253i	−0.575007	+	0.818149i	$0.695001\pi$
$734$	9.92532	−	17.1912i	0.366350	−	0.634537i
$735$	−13.5540	−	0.433071i	−0.499945	−	0.0159741i
$736$	1.30503	−	3.58554i	0.0481040	−	0.132165i
$737$	10.7100	−	3.89814i	0.394510	−	0.143590i
$738$	8.61491	+	17.4005i	0.317119	+	0.640520i
$739$	−8.91510	−	50.5600i	−0.327947	−	1.85988i	−0.488098	−	0.872789i	$-0.662309\pi$
$739$	−8.91510	−	50.5600i	−0.327947	−	1.85988i	0.160151	−	0.987093i	$-0.448802\pi$
$740$	10.5950			0.389479
$741$	−31.7851	−	3.10865i	−1.16765	−	0.114199i
$742$	11.6801			0.428791
$743$	−0.154876	−	0.878343i	−0.00568183	−	0.0322233i	0.981835	−	0.189737i	$-0.0607634\pi$
$743$	−0.154876	−	0.878343i	−0.00568183	−	0.0322233i	−0.987517	+	0.157513i	$0.949652\pi$
$744$	−2.82583	+	13.4911i	−0.103600	+	0.494607i
$745$	−33.1925	+	12.0811i	−1.21608	+	0.442617i
$746$	−6.52210	+	17.9193i	−0.238791	+	0.656073i
$747$	25.3119	+	34.4078i	0.926114	+	1.25891i
$748$	1.67964	−	2.90922i	0.0614137	−	0.106372i
$749$	8.96255	+	15.5236i	0.327484	+	0.567220i
$750$	7.04398	+	13.1535i	0.257210	+	0.480300i
$751$	−10.0009	−	1.76342i	−0.364936	−	0.0643481i	−0.0118266	−	0.999930i	$-0.503765\pi$
$751$	−10.0009	−	1.76342i	−0.364936	−	0.0643481i	−0.353110	+	0.935582i	$0.614876\pi$
$752$	5.42528	−	3.13228i	0.197839	−	0.114223i
$753$	−1.47648	−	10.2843i	−0.0538058	−	0.374780i
$754$	−20.7071	+	24.6778i	−0.754108	+	0.898711i
$755$	20.9481	+	7.62450i	0.762381	+	0.277484i
$756$	−11.7374	+	11.5382i	−0.426885	+	0.419642i
$757$	16.0181	−	13.4408i	0.582187	−	0.488513i	−0.303478	−	0.952839i	$-0.598148\pi$
$757$	16.0181	−	13.4408i	0.582187	−	0.488513i	0.885664	+	0.464326i	$0.153703\pi$
$758$	29.6323	−	5.22497i	1.07629	−	0.189780i
$759$	−10.2146	−	12.9945i	−0.370768	−	0.471672i
$760$	9.35436	+	6.25176i	0.339318	+	0.226775i
$761$			23.9282i			0.867396i	0.901058	+	0.433698i	$0.142791\pi$
$761$			23.9282i			0.867396i	−0.901058	+	0.433698i	$0.857209\pi$
$762$	−10.1142	−	9.05274i	−0.366401	−	0.327946i
$763$	33.6048	+	40.0486i	1.21657	+	1.44986i
$764$	−3.84705	−	10.5697i	−0.139181	−	0.382397i
$765$	−5.76497	+	8.65725i	−0.208433	+	0.313003i
$766$	−4.60213	−	3.86165i	−0.166282	−	0.139527i
$767$	−32.5594	−	18.7982i	−1.17565	−	0.678764i
$768$	−0.644072	+	1.60785i	−0.0232409	+	0.0580182i
$769$	−3.21910	+	18.2564i	−0.116084	+	0.658344i	0.870124	+	0.492833i	$0.164039\pi$
$769$	−3.21910	+	18.2564i	−0.116084	+	0.658344i	−0.986208	+	0.165511i	$0.947073\pi$
$770$	−3.55075	+	20.1373i	−0.127960	+	0.725698i
$771$	−11.9856	+	29.9206i	−0.431651	+	1.07756i

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(-1.69526 - 0.355087i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.882820 + 2.42553i) q^{5} +(0.0553136 - 1.73117i) q^{6} +(-1.58376 + 2.74316i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.74783 + 1.20393i) q^{9} +O(q^{10})\)	\(q+(0.173648 + 0.984808i) q^{2} +(-1.69526 - 0.355087i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.882820 + 2.42553i) q^{5} +(0.0553136 - 1.73117i) q^{6} +(-1.58376 + 2.74316i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(2.74783 + 1.20393i) q^{9} +(-2.54198 - 0.448219i) q^{10} +(-2.16590 + 1.25049i) q^{11} +(1.71447 - 0.246141i) q^{12} +(2.71907 - 3.24046i) q^{13} +(-2.97650 - 1.08336i) q^{14} +(2.35788 - 3.79843i) q^{15} +(0.766044 - 0.642788i) q^{16} +(1.32278 - 0.233243i) q^{17} +(-0.708487 + 2.91514i) q^{18} +(3.14841 + 3.01455i) q^{19} -2.58119i q^{20} +(3.65896 - 4.08800i) q^{21} +(-1.60759 - 1.91586i) q^{22} +(-1.30503 - 3.58554i) q^{23} +(0.540116 + 1.64568i) q^{24} +(-1.27359 - 1.06867i) q^{25} +(3.66340 + 2.11506i) q^{26} +(-4.23078 - 3.01670i) q^{27} +(0.550036 - 3.11941i) q^{28} +(-1.32242 + 7.49981i) q^{29} +(4.15016 + 1.66247i) q^{30} +(6.89193 + 3.97906i) q^{31} +(0.766044 + 0.642788i) q^{32} +(4.11581 - 1.35082i) q^{33} +(0.459398 + 1.26219i) q^{34} +(-5.25543 - 6.26318i) q^{35} +(-2.99388 - 0.191514i) q^{36} +4.10469i q^{37} +(-2.42204 + 3.62405i) q^{38} +(-5.76019 + 4.52793i) q^{39} +(2.54198 - 0.448219i) q^{40} +(4.95792 - 4.16019i) q^{41} +(4.66127 + 2.89350i) q^{42} +(-11.7465 - 4.27537i) q^{43} +(1.60759 - 1.91586i) q^{44} +(-5.34601 + 5.60207i) q^{45} +(3.30445 - 1.90782i) q^{46} +(6.16940 + 1.08783i) q^{47} +(-1.52689 + 0.817681i) q^{48} +(-1.51662 - 2.62686i) q^{49} +(0.831277 - 1.43981i) q^{50} +(-2.32529 - 0.0742967i) q^{51} +(-1.44679 + 3.97502i) q^{52} +(-3.46508 + 1.26118i) q^{53} +(2.23620 - 4.69035i) q^{54} +(-1.12098 - 6.35742i) q^{55} +3.16753 q^{56} +(-4.26694 - 6.22842i) q^{57} -7.61550 q^{58} +(-1.54335 - 8.75275i) q^{59} +(-0.916549 + 4.37580i) q^{60} +(-0.133301 + 0.0485177i) q^{61} +(-2.72184 + 7.47818i) q^{62} +(-7.65449 + 5.63098i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(5.45938 + 9.45593i) q^{65} +(2.04500 + 3.81871i) q^{66} +(-4.48795 - 0.791347i) q^{67} +(-1.16324 + 0.671595i) q^{68} +(0.939187 + 6.54182i) q^{69} +(5.25543 - 6.26318i) q^{70} +(8.59275 + 3.12750i) q^{71} +(-0.331277 - 2.98165i) q^{72} +(-1.67672 + 1.40694i) q^{73} +(-4.04233 + 0.712771i) q^{74} +(1.77960 + 2.26391i) q^{75} +(-3.98957 - 1.75594i) q^{76} -7.92190i q^{77} +(-5.45938 - 4.88641i) q^{78} +(6.41515 + 7.64528i) q^{79} +(0.882820 + 2.42553i) q^{80} +(6.10110 + 6.61639i) q^{81} +(4.95792 + 4.16019i) q^{82} +(12.3308 + 7.11920i) q^{83} +(-2.04012 + 5.09290i) q^{84} +(-0.602044 + 3.41436i) q^{85} +(2.17066 - 12.3104i) q^{86} +(4.90493 - 12.2446i) q^{87} +(2.16590 + 1.25049i) q^{88} +(-12.7492 - 10.6978i) q^{89} +(-6.44529 - 4.29200i) q^{90} +(4.58274 + 12.5910i) q^{91} +(2.45265 + 2.92296i) q^{92} +(-10.2707 - 9.19278i) q^{93} +6.26457i q^{94} +(-10.0914 + 4.97524i) q^{95} +(-1.07040 - 1.36171i) q^{96} +(0.538573 - 0.0949649i) q^{97} +(2.32360 - 1.94973i) q^{98} +(-7.45703 + 0.828515i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18q + 3q^{3} - 9q^{8} - 3q^{9} + O(q^{10}) \)	\( 18q + 3q^{3} - 9q^{8} - 3q^{9} - 12q^{13} - 12q^{14} + 18q^{15} + 6q^{17} - 6q^{19} - 24q^{22} + 3q^{24} - 18q^{25} + 18q^{26} - 6q^{27} + 6q^{28} - 6q^{29} - 24q^{33} - 6q^{34} - 24q^{35} + 3q^{38} + 6q^{39} + 3q^{41} - 6q^{43} + 24q^{44} - 54q^{45} + 18q^{46} + 30q^{47} + 21q^{49} + 3q^{50} + 42q^{51} - 6q^{52} - 60q^{53} + 54q^{54} + 30q^{55} + 12q^{57} + 12q^{58} + 3q^{59} + 24q^{60} + 54q^{61} + 6q^{62} - 18q^{63} - 9q^{64} + 24q^{65} - 27q^{66} - 15q^{67} - 27q^{68} + 30q^{69} + 24q^{70} + 36q^{71} + 6q^{72} - 42q^{73} + 6q^{74} - 24q^{78} - 6q^{79} - 3q^{81} + 3q^{82} + 36q^{83} - 30q^{84} - 6q^{86} - 60q^{89} - 18q^{91} - 66q^{93} + 6q^{95} + 9q^{97} + 12q^{98} - 102q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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