LMFDB - Embedded newform 966.2.s.a.727.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(97,966)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("966.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.s (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			727.8
Character	$\chi$	$=$	966.727
Dual form			966.2.s.a.97.8

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 + 0.281733i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.486537 + 3.38394i) q^{5} +(0.540641 - 0.841254i) q^{6} +(2.17047 - 1.51296i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.959493 + 0.281733i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.486537 + 3.38394i) q^{5} +(0.540641 - 0.841254i) q^{6} +(2.17047 - 1.51296i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-1.42020 - 3.10979i) q^{10} +(-1.18221 + 4.02625i) q^{11} +(-0.281733 + 0.959493i) q^{12} +(5.10604 - 2.33185i) q^{13} +(-1.65630 + 2.06317i) q^{14} +(-2.58371 - 2.23880i) q^{15} +(0.415415 - 0.909632i) q^{16} +(4.84822 + 3.11576i) q^{17} +(0.142315 + 0.989821i) q^{18} +(2.05496 - 1.32064i) q^{19} +(2.23880 + 2.58371i) q^{20} +(-0.649553 + 2.56478i) q^{21} -4.19622i q^{22} +(1.32147 - 4.61018i) q^{23} -1.00000i q^{24} +(-6.41687 + 1.88416i) q^{25} +(-4.24225 + 3.67593i) q^{26} +(0.540641 + 0.841254i) q^{27} +(1.00795 - 2.44623i) q^{28} +(-2.02436 - 1.30098i) q^{29} +(3.10979 + 1.42020i) q^{30} +(3.22425 + 2.79383i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(-1.74317 - 3.81702i) q^{33} +(-5.52964 - 1.62365i) q^{34} +(6.17579 + 6.60863i) q^{35} +(-0.415415 - 0.909632i) q^{36} +(6.12410 + 0.880512i) q^{37} +(-1.59965 + 1.84609i) q^{38} +(-2.33185 + 5.10604i) q^{39} +(-2.87603 - 1.84831i) q^{40} +(5.88440 - 0.846049i) q^{41} +(-0.0993397 - 2.64389i) q^{42} +(-8.91476 + 7.72469i) q^{43} +(1.18221 + 4.02625i) q^{44} +3.41874 q^{45} +(0.0309001 + 4.79573i) q^{46} -13.0620i q^{47} +(0.281733 + 0.959493i) q^{48} +(2.42189 - 6.56768i) q^{49} +(5.62611 - 3.61568i) q^{50} +(-5.70442 + 0.820172i) q^{51} +(3.03478 - 4.72221i) q^{52} +(-7.56384 - 3.45429i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(-14.1998 - 2.04162i) q^{55} +(-0.277936 + 2.63111i) q^{56} +(-0.688197 + 2.34378i) q^{57} +(2.30889 + 0.677951i) q^{58} +(-11.9487 + 5.45679i) q^{59} +(-3.38394 - 0.486537i) q^{60} +(-1.76314 + 2.03477i) q^{61} +(-3.88076 - 1.77228i) q^{62} +(-1.18867 - 2.36370i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(10.3751 + 16.1440i) q^{65} +(2.74794 + 3.17130i) q^{66} +(2.40633 + 8.19519i) q^{67} +5.76308 q^{68} +(2.02033 + 4.34951i) q^{69} +(-7.78749 - 4.60101i) q^{70} +(4.91437 - 1.44299i) q^{71} +(0.654861 + 0.755750i) q^{72} +(6.49806 + 10.1112i) q^{73} +(-6.12410 + 0.880512i) q^{74} +(3.61568 - 5.62611i) q^{75} +(1.01475 - 2.22199i) q^{76} +(3.52560 + 10.5275i) q^{77} +(0.798856 - 5.55616i) q^{78} +(-5.00149 + 2.28410i) q^{79} +(3.28025 + 0.963170i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-5.40768 + 2.46961i) q^{82} +(-1.67622 + 11.6584i) q^{83} +(0.840184 + 2.50880i) q^{84} +(-8.18470 + 17.9220i) q^{85} +(6.37736 - 9.92336i) q^{86} +(2.38187 - 0.342461i) q^{87} +(-2.26865 - 3.53009i) q^{88} +(1.92781 + 2.22482i) q^{89} +(-3.28025 + 0.963170i) q^{90} +(7.55450 - 12.7864i) q^{91} +(-1.38076 - 4.59277i) q^{92} -4.26630 q^{93} +(3.68000 + 12.5329i) q^{94} +(5.46878 + 6.31131i) q^{95} +(-0.540641 - 0.841254i) q^{96} +(-0.0367847 - 0.255843i) q^{97} +(-0.473456 + 6.98397i) q^{98} +(3.81702 + 1.74317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9}+O(q^{10}) $ 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9	$ 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9} - 22 q^{14} - 16 q^{16} + 16 q^{18} - 36 q^{23} + 96 q^{25} + 22 q^{28} - 20 q^{29} - 16 q^{32} - 50 q^{35} + 16 q^{36} + 22 q^{37} + 4 q^{39} - 110 q^{43} + 8 q^{46} - 36 q^{50} + 22 q^{51} - 88 q^{53} + 22 q^{57} + 24 q^{58} - 16 q^{64} - 72 q^{70} + 48 q^{71} + 16 q^{72} - 22 q^{74} + 24 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} + 22 q^{84} + 76 q^{85} + 44 q^{86} - 44 q^{88} + 8 q^{92} - 14 q^{95} + 22 q^{98} - 22 q^{99}+O(q^{100}) $ 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9 - 22 * q^14 - 16 * q^16 + 16 * q^18 - 36 * q^23 + 96 * q^25 + 22 * q^28 - 20 * q^29 - 16 * q^32 - 50 * q^35 + 16 * q^36 + 22 * q^37 + 4 * q^39 - 110 * q^43 + 8 * q^46 - 36 * q^50 + 22 * q^51 - 88 * q^53 + 22 * q^57 + 24 * q^58 - 16 * q^64 - 72 * q^70 + 48 * q^71 + 16 * q^72 - 22 * q^74 + 24 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 + 22 * q^84 + 76 * q^85 + 44 * q^86 - 44 * q^88 + 8 * q^92 - 14 * q^95 + 22 * q^98 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$-1$	$e\left(\frac{21}{22}\right)$

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 $

$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$2$	−0.959493	+	0.281733i	−0.678464	+	0.199215i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$4$	0.841254	−	0.540641i	0.420627	−	0.270320i
$5$	0.486537	+	3.38394i	0.217586	+	1.51334i	0.746911	+	0.664925i	$0.231536\pi$
$5$	0.486537	+	3.38394i	0.217586	+	1.51334i	−0.529325	+	0.848419i	$0.677555\pi$
$6$	0.540641	−	0.841254i	0.220716	−	0.343440i
$7$	2.17047	−	1.51296i	0.820361	−	0.571846i
$7$	2.17047	−	1.51296i	0.820361	−	0.571846i
$8$	−0.654861	+	0.755750i	−0.231528	+	0.267198i
$9$	0.142315	−	0.989821i	0.0474383	−	0.329940i
$10$	−1.42020	−	3.10979i	−0.449105	−	0.983403i
$11$	−1.18221	+	4.02625i	−0.356451	+	1.21396i	0.564878	+	0.825175i	$0.308923\pi$
$11$	−1.18221	+	4.02625i	−0.356451	+	1.21396i	−0.921329	+	0.388785i	$0.872895\pi$
$12$	−0.281733	+	0.959493i	−0.0813292	+	0.276982i
$13$	5.10604	−	2.33185i	1.41616	−	0.646738i	0.447308	−	0.894380i	$-0.352383\pi$
$13$	5.10604	−	2.33185i	1.41616	−	0.646738i	0.968852	+	0.247642i	$0.0796556\pi$
$14$	−1.65630	+	2.06317i	−0.442665	+	0.551405i
$15$	−2.58371	−	2.23880i	−0.667111	−	0.578055i
$16$	0.415415	−	0.909632i	0.103854	−	0.227408i
$17$	4.84822	+	3.11576i	1.17586	+	0.755682i	0.974622	−	0.223859i	$-0.0718654\pi$
$17$	4.84822	+	3.11576i	1.17586	+	0.755682i	0.201243	+	0.979541i	$0.435502\pi$
$18$	0.142315	+	0.989821i	0.0335439	+	0.233303i
$19$	2.05496	−	1.32064i	0.471439	−	0.302976i	−0.283264	−	0.959042i	$-0.591417\pi$
$19$	2.05496	−	1.32064i	0.471439	−	0.302976i	0.754703	+	0.656066i	$0.227781\pi$
$20$	2.23880	+	2.58371i	0.500610	+	0.577735i
$21$	−0.649553	+	2.56478i	−0.141744	+	0.559680i
$22$		−	4.19622i		−	0.894638i
$23$	1.32147	−	4.61018i	0.275545	−	0.961288i
$23$	1.32147	−	4.61018i	0.275545	−	0.961288i
$24$		−	1.00000i		−	0.204124i
$25$	−6.41687	+	1.88416i	−1.28337	+	0.376832i
$26$	−4.24225	+	3.67593i	−0.831973	+	0.720909i
$27$	0.540641	+	0.841254i	0.104046	+	0.161899i
$28$	1.00795	−	2.44623i	0.190484	−	0.462294i
$29$	−2.02436	−	1.30098i	−0.375915	−	0.241586i	0.339017	−	0.940780i	$-0.389906\pi$
$29$	−2.02436	−	1.30098i	−0.375915	−	0.241586i	−0.714931	+	0.699195i	$0.753542\pi$
$30$	3.10979	+	1.42020i	0.567768	+	0.259291i
$31$	3.22425	+	2.79383i	0.579093	+	0.501787i	0.894439	−	0.447190i	$-0.147575\pi$
$31$	3.22425	+	2.79383i	0.579093	+	0.501787i	−0.315346	+	0.948977i	$0.602121\pi$
$32$	−0.142315	+	0.989821i	−0.0251579	+	0.174977i
$33$	−1.74317	−	3.81702i	−0.303448	−	0.664458i
$34$	−5.52964	−	1.62365i	−0.948325	−	0.278453i
$35$	6.17579	+	6.60863i	1.04390	+	1.11706i
$36$	−0.415415	−	0.909632i	−0.0692358	−	0.151605i
$37$	6.12410	+	0.880512i	1.00680	+	0.144755i	0.625933	−	0.779877i	$-0.284718\pi$
$37$	6.12410	+	0.880512i	1.00680	+	0.144755i	0.380862	+	0.924632i	$0.375627\pi$
$38$	−1.59965	+	1.84609i	−0.259497	+	0.299476i
$39$	−2.33185	+	5.10604i	−0.373395	+	0.817620i
$40$	−2.87603	−	1.84831i	−0.454740	−	0.292243i
$41$	5.88440	−	0.846049i	0.918989	−	0.132131i	0.333443	−	0.942770i	$-0.391789\pi$
$41$	5.88440	−	0.846049i	0.918989	−	0.132131i	0.585546	+	0.810640i	$0.300880\pi$
$42$	−0.0993397	−	2.64389i	−0.0153285	−	0.407960i
$43$	−8.91476	+	7.72469i	−1.35949	+	1.17800i	−0.393529	+	0.919312i	$0.628746\pi$
$43$	−8.91476	+	7.72469i	−1.35949	+	1.17800i	−0.965960	+	0.258692i	$0.916709\pi$
$44$	1.18221	+	4.02625i	0.178225	+	0.606980i
$45$	3.41874			0.509635
$46$	0.0309001	+	4.79573i	0.00455597	+	0.707092i
$47$		−	13.0620i		−	1.90529i	−0.304080	−	0.952646i	$-0.598349\pi$
$47$		−	13.0620i		−	1.90529i	0.304080	−	0.952646i	$-0.401651\pi$
$48$	0.281733	+	0.959493i	0.0406646	+	0.138491i
$49$	2.42189	−	6.56768i	0.345984	−	0.938240i
$50$	5.62611	−	3.61568i	0.795652	−	0.511334i
$51$	−5.70442	+	0.820172i	−0.798779	+	0.114847i
$52$	3.03478	−	4.72221i	0.420848	−	0.654852i
$53$	−7.56384	−	3.45429i	−1.03897	−	0.474484i	−0.178480	−	0.983944i	$-0.557118\pi$
$53$	−7.56384	−	3.45429i	−1.03897	−	0.474484i	−0.860494	+	0.509460i	$0.829845\pi$
$54$	−0.755750	−	0.654861i	−0.102844	−	0.0891153i
$55$	−14.1998	−	2.04162i	−1.91470	−	0.275292i
$56$	−0.277936	+	2.63111i	−0.0371407	+	0.351597i
$57$	−0.688197	+	2.34378i	−0.0911539	+	0.310442i
$58$	2.30889	+	0.677951i	0.303172	+	0.0890194i
$59$	−11.9487	+	5.45679i	−1.55559	+	0.710414i	−0.993196	−	0.116456i	$-0.962847\pi$
$59$	−11.9487	+	5.45679i	−1.55559	+	0.710414i	−0.562393	+	0.826870i	$0.690119\pi$
$60$	−3.38394	−	0.486537i	−0.436865	−	0.0628117i
$61$	−1.76314	+	2.03477i	−0.225746	+	0.260525i	−0.857312	−	0.514797i	$-0.827867\pi$
$61$	−1.76314	+	2.03477i	−0.225746	+	0.260525i	0.631566	+	0.775322i	$0.282413\pi$
$62$	−3.88076	−	1.77228i	−0.492857	−	0.225080i
$63$	−1.18867	−	2.36370i	−0.149759	−	0.297798i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	10.3751	+	16.1440i	1.28687	+	2.00241i
$66$	2.74794	+	3.17130i	0.338248	+	0.390359i
$67$	2.40633	+	8.19519i	0.293979	+	1.00120i	0.965541	+	0.260253i	$0.0838059\pi$
$67$	2.40633	+	8.19519i	0.293979	+	1.00120i	−0.671561	+	0.740949i	$0.734376\pi$
$68$	5.76308			0.698877
$69$	2.02033	+	4.34951i	0.243219	+	0.523620i
$70$	−7.78749	−	4.60101i	−0.930783	−	0.549926i
$71$	4.91437	−	1.44299i	0.583228	−	0.171251i	0.0232087	−	0.999731i	$-0.492612\pi$
$71$	4.91437	−	1.44299i	0.583228	−	0.171251i	0.560020	+	0.828479i	$0.310794\pi$
$72$	0.654861	+	0.755750i	0.0771761	+	0.0890659i
$73$	6.49806	+	10.1112i	0.760540	+	1.18342i	0.978254	+	0.207411i	$0.0665036\pi$
$73$	6.49806	+	10.1112i	0.760540	+	1.18342i	−0.217714	+	0.976013i	$0.569860\pi$
$74$	−6.12410	+	0.880512i	−0.711912	+	0.102357i
$75$	3.61568	−	5.62611i	0.417503	−	0.649647i
$76$	1.01475	−	2.22199i	0.116399	−	0.254879i
$77$	3.52560	+	10.5275i	0.401780	+	1.19972i
$78$	0.798856	−	5.55616i	0.0904526	−	0.629112i
$79$	−5.00149	+	2.28410i	−0.562711	+	0.256982i	−0.676400	−	0.736535i	$-0.736461\pi$
$79$	−5.00149	+	2.28410i	−0.562711	+	0.256982i	0.113688	+	0.993516i	$0.463733\pi$
$80$	3.28025	+	0.963170i	0.366744	+	0.107686i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−5.40768	+	2.46961i	−0.597178	+	0.272722i
$83$	−1.67622	+	11.6584i	−0.183989	+	1.27967i	0.663224	+	0.748421i	$0.269188\pi$
$83$	−1.67622	+	11.6584i	−0.183989	+	1.27967i	−0.847213	+	0.531253i	$0.821721\pi$
$84$	0.840184	+	2.50880i	0.0916716	+	0.273733i
$85$	−8.18470	+	17.9220i	−0.887756	+	1.94391i
$86$	6.37736	−	9.92336i	0.687688	−	1.07006i
$87$	2.38187	−	0.342461i	0.255363	−	0.0367157i
$88$	−2.26865	−	3.53009i	−0.241839	−	0.376309i
$89$	1.92781	+	2.22482i	0.204348	+	0.235830i	0.848668	−	0.528926i	$-0.177405\pi$
$89$	1.92781	+	2.22482i	0.204348	+	0.235830i	−0.644320	+	0.764756i	$0.722860\pi$
$90$	−3.28025	+	0.963170i	−0.345769	+	0.101527i
$91$	7.55450	−	12.7864i	0.791927	−	1.34038i
$92$	−1.38076	−	4.59277i	−0.143954	−	0.478829i
$93$	−4.26630			−0.442394
$94$	3.68000	+	12.5329i	0.379563	+	1.29267i
$95$	5.46878	+	6.31131i	0.561085	+	0.647526i
$96$	−0.540641	−	0.841254i	−0.0551789	−	0.0858601i
$97$	−0.0367847	−	0.255843i	−0.00373492	−	0.0259770i	0.987869	−	0.155291i	$-0.0496315\pi$
$97$	−0.0367847	−	0.255843i	−0.00373492	−	0.0259770i	−0.991604	+	0.129314i	$0.958722\pi$
$98$	−0.473456	+	6.98397i	−0.0478263	+	0.705488i
$99$	3.81702	+	1.74317i	0.383625	+	0.175196i
$100$	−4.37956	+	5.05428i	−0.437956	+	0.505428i
$101$	−4.93319	−	0.709286i	−0.490871	−	0.0705766i	−0.107565	−	0.994198i	$-0.534305\pi$
$101$	−4.93319	−	0.709286i	−0.490871	−	0.0705766i	−0.383306	+	0.923621i	$0.625214\pi$
$102$	5.24229	−	2.39407i	0.519064	−	0.237048i
$103$	−9.38679	−	2.75621i	−0.924908	−	0.271577i	−0.215604	−	0.976481i	$-0.569172\pi$
$103$	−9.38679	−	2.75621i	−0.924908	−	0.271577i	−0.709303	+	0.704903i	$0.750990\pi$
$104$	−1.58145	+	5.38592i	−0.155074	+	0.528133i
$105$	−8.99508	−	0.950189i	−0.877830	−	0.0927289i
$106$	8.23064	+	1.18339i	0.799431	+	0.114941i
$107$	−0.416049	−	0.360508i	−0.0402209	−	0.0348516i	0.634518	−	0.772908i	$-0.281198\pi$
$107$	−0.416049	−	0.360508i	−0.0402209	−	0.0348516i	−0.674739	+	0.738056i	$0.735744\pi$
$108$	0.909632	+	0.415415i	0.0875294	+	0.0399733i
$109$	1.75688	−	2.73376i	0.168279	−	0.261847i	−0.746864	−	0.664977i	$-0.768441\pi$
$109$	1.75688	−	2.73376i	0.168279	−	0.261847i	0.915143	+	0.403130i	$0.132078\pi$
$110$	14.1998	−	2.04162i	1.35390	−	0.194661i
$111$	−5.20490	+	3.34498i	−0.494027	+	0.317492i
$112$	−0.474593	−	2.60284i	−0.0448448	−	0.245945i
$113$	−0.773756	−	2.63517i	−0.0727888	−	0.247896i	0.915059	−	0.403320i	$-0.132144\pi$
$113$	−0.773756	−	2.63517i	−0.0727888	−	0.247896i	−0.987848	+	0.155424i	$0.950326\pi$
$114$		−	2.44273i		−	0.228783i
$115$	16.2435	+	2.22874i	1.51471	+	0.207831i
$116$	−2.40637			−0.223425
$117$	−1.58145	−	5.38592i	−0.146205	−	0.497928i
$118$	9.92734	−	8.60209i	0.913886	−	0.791887i
$119$	15.2369	−	0.572503i	1.39677	−	0.0524813i
$120$	3.38394	−	0.486537i	0.308910	−	0.0444146i
$121$	−5.55926	−	3.57272i	−0.505387	−	0.324793i
$122$	1.11846	−	2.44908i	0.101260	−	0.221729i
$123$	−3.89309	+	4.49286i	−0.351028	+	0.405108i
$124$	4.22287	+	0.607157i	0.379225	+	0.0545243i
$125$	−2.39696	−	5.24861i	−0.214391	−	0.469450i
$126$	1.80645	+	1.93306i	0.160932	+	0.172211i
$127$	−9.85567	−	2.89388i	−0.874549	−	0.256791i	−0.186500	−	0.982455i	$-0.559714\pi$
$127$	−9.85567	−	2.89388i	−0.874549	−	0.256791i	−0.688049	+	0.725664i	$0.741533\pi$
$128$	0.415415	+	0.909632i	0.0367178	+	0.0804009i
$129$	1.67874	−	11.6759i	0.147804	−	1.02800i
$130$	−14.5031	−	12.5670i	−1.27201	−	1.10220i
$131$	2.41379	+	1.10234i	0.210894	+	0.0963121i	0.518061	−	0.855343i	$-0.326654\pi$
$131$	2.41379	+	1.10234i	0.210894	+	0.0963121i	−0.307167	+	0.951656i	$0.599381\pi$
$132$	−3.53009	−	2.26865i	−0.307255	−	0.197461i
$133$	2.46214	−	5.97548i	0.213495	−	0.518140i
$134$	−4.61770	−	7.18529i	−0.398909	−	0.620714i
$135$	−2.58371	+	2.23880i	−0.222370	+	0.192685i
$136$	−5.52964	+	1.62365i	−0.474163	+	0.139227i
$137$			9.20582i			0.786507i	0.919430	+	0.393253i	$0.128650\pi$
$137$			9.20582i			0.786507i	−0.919430	+	0.393253i	$0.871350\pi$
$138$	−3.16389	−	3.60414i	−0.269328	−	0.306805i
$139$		−	8.78081i		−	0.744779i	−0.928077	−	0.372389i	$-0.878539\pi$
$139$		−	8.78081i		−	0.744779i	0.928077	−	0.372389i	$-0.121461\pi$
$140$	8.76830	+	2.22065i	0.741057	+	0.187679i
$141$	8.55381	+	9.87162i	0.720361	+	0.831341i
$142$	−4.30877	+	2.76908i	−0.361584	+	0.232376i
$143$	3.35218	+	23.3149i	0.280323	+	1.94969i
$144$	−0.841254	−	0.540641i	−0.0701045	−	0.0450534i
$145$	3.41751	−	7.48330i	0.283809	−	0.621454i
$146$	−9.08349	−	7.87089i	−0.751755	−	0.651399i
$147$	2.47058	+	6.54952i	0.203770	+	0.540196i
$148$	5.62796	−	2.57020i	0.462615	−	0.211269i
$149$	−3.23160	+	11.0058i	−0.264743	+	0.901633i	0.714618	+	0.699515i	$0.246601\pi$
$149$	−3.23160	+	11.0058i	−0.264743	+	0.901633i	−0.979361	+	0.202118i	$0.935218\pi$
$150$	−1.88416	+	6.41687i	−0.153841	+	0.523935i
$151$	−0.980304	−	2.14657i	−0.0797760	−	0.174685i	0.865541	−	0.500838i	$-0.166975\pi$
$151$	−0.980304	−	2.14657i	−0.0797760	−	0.174685i	−0.945317	+	0.326153i	$0.894248\pi$
$152$	−0.347637	+	2.41787i	−0.0281971	+	0.196115i
$153$	3.77402	−	4.35545i	0.305111	−	0.352117i
$154$	−6.34873	−	9.10778i	−0.511595	−	0.733926i
$155$	−7.88544	+	12.2700i	−0.633373	+	0.985548i
$156$	0.798856	+	5.55616i	0.0639596	+	0.444849i
$157$	−8.16813	+	5.24934i	−0.651888	+	0.418943i	−0.824356	−	0.566072i	$-0.808462\pi$
$157$	−8.16813	+	5.24934i	−0.651888	+	0.418943i	0.172468	+	0.985015i	$0.444826\pi$
$158$	4.15539	−	3.60066i	0.330585	−	0.286453i
$159$	7.97845	−	2.34269i	0.632732	−	0.185787i
$160$	−3.41874			−0.270275
$161$	−4.10682	−	12.0056i	−0.323663	−	0.946172i
$162$	1.00000			0.0785674
$163$	−4.89531	+	1.43739i	−0.383431	+	0.112585i	−0.467767	−	0.883852i	$-0.654941\pi$
$163$	−4.89531	+	1.43739i	−0.383431	+	0.112585i	0.0843361	+	0.996437i	$0.473123\pi$
$164$	4.49286	−	3.89309i	0.350834	−	0.303999i
$165$	12.0684	−	7.75592i	0.939527	−	0.603798i
$166$	−1.67622	−	11.6584i	−0.130100	−	0.904867i
$167$	9.19501	−	14.3077i	0.711531	−	1.10716i	−0.277681	−	0.960673i	$-0.589566\pi$
$167$	9.19501	−	14.3077i	0.711531	−	1.10716i	0.989212	−	0.146491i	$-0.0467980\pi$
$168$	−1.51296	−	2.17047i	−0.116728	−	0.167455i
$169$	12.1209	−	13.9883i	0.932376	−	1.07602i
$170$	2.80395	−	19.5019i	0.215053	−	1.49573i
$171$	−1.01475	−	2.22199i	−0.0775996	−	0.169920i
$172$	−3.32330	+	11.3181i	−0.253399	+	0.862998i
$173$	4.83190	−	16.4559i	0.367362	−	1.25112i	−0.543850	−	0.839183i	$-0.683034\pi$
$173$	4.83190	−	16.4559i	0.367362	−	1.25112i	0.911212	−	0.411938i	$-0.135148\pi$
$174$	−2.18891	+	0.999640i	−0.165941	+	0.0757825i
$175$	−11.0770	+	13.7980i	−0.837339	+	1.04303i
$176$	3.17130	+	2.74794i	0.239045	+	0.207134i
$177$	5.45679	−	11.9487i	0.410158	−	0.898120i
$178$	−2.47653	−	1.59157i	−0.185624	−	0.119293i
$179$	−3.53687	−	24.5995i	−0.264358	−	1.83865i	−0.499038	−	0.866580i	$-0.666313\pi$
$179$	−3.53687	−	24.5995i	−0.264358	−	1.83865i	0.234680	−	0.972073i	$-0.424596\pi$
$180$	2.87603	−	1.84831i	0.214366	−	0.137765i
$181$	−6.23930	−	7.20054i	−0.463764	−	0.535212i	0.474903	−	0.880038i	$-0.342483\pi$
$181$	−6.23930	−	7.20054i	−0.463764	−	0.535212i	−0.938666	+	0.344826i	$0.887938\pi$
$182$	−3.64613	+	14.3969i	−0.270269	+	1.06717i
$183$		−	2.69238i		−	0.199027i
$184$	2.61876	+	4.01772i	0.193058	+	0.296190i
$185$			21.1520i			1.55512i
$186$	4.09348	−	1.20195i	0.300149	−	0.0881316i
$187$	−18.2764	+	15.8366i	−1.33651	+	1.15809i
$188$	−7.06187	−	10.9885i	−0.515040	−	0.801417i
$189$	2.44623	+	1.00795i	0.177937	+	0.0733174i
$190$	−7.02536	−	4.51492i	−0.509673	−	0.327547i
$191$	−7.84626	−	3.58327i	−0.567735	−	0.259276i	0.110801	−	0.993843i	$-0.464658\pi$
$191$	−7.84626	−	3.58327i	−0.567735	−	0.259276i	−0.678537	+	0.734566i	$0.737386\pi$
$192$	0.755750	+	0.654861i	0.0545415	+	0.0472605i
$193$	0.886195	−	6.16362i	0.0637897	−	0.443667i	−0.932748	−	0.360528i	$-0.882596\pi$
$193$	0.886195	−	6.16362i	0.0637897	−	0.443667i	0.996538	−	0.0831390i	$-0.0264945\pi$
$194$	0.107374	+	0.235116i	0.00770901	+	0.0168804i
$195$	−18.4130	−	5.40656i	−1.31859	−	0.387172i
$196$	−1.51333	−	6.83446i	−0.108095	−	0.488176i
$197$	−4.24207	−	9.28883i	−0.302235	−	0.661802i	0.696193	−	0.717855i	$-0.254876\pi$
$197$	−4.24207	−	9.28883i	−0.302235	−	0.661802i	−0.998428	+	0.0560527i	$0.982149\pi$
$198$	−4.15351	−	0.597185i	−0.295177	−	0.0424401i
$199$	9.48167	−	10.9424i	0.672138	−	0.775688i	−0.312571	−	0.949894i	$-0.601190\pi$
$199$	9.48167	−	10.9424i	0.672138	−	0.775688i	0.984709	+	0.174206i	$0.0557358\pi$
$200$	2.77820	−	6.08341i	0.196448	−	0.430162i
$201$	−7.18529	−	4.61770i	−0.506811	−	0.325708i
$202$	4.93319	−	0.709286i	0.347098	−	0.0499052i
$203$	−6.36215	+	0.239048i	−0.446536	+	0.0167779i
$204$	−4.35545	+	3.77402i	−0.304942	+	0.264234i
$205$	5.72596	+	19.5008i	0.399918	+	1.36200i
$206$	9.78307			0.681619
$207$	−4.37519	−	1.96411i	−0.304097	−	0.136515i
$208$		−	5.61330i		−	0.389212i
$209$	2.88783	+	9.83504i	0.199755	+	0.680304i
$210$	8.89842	−	1.62251i	0.614049	−	0.111964i
$211$	12.7949	−	8.22281i	0.880840	−	0.566082i	−0.0202102	−	0.999796i	$-0.506434\pi$
$211$	12.7949	−	8.22281i	0.880840	−	0.566082i	0.901051	+	0.433714i	$0.142797\pi$
$212$	−8.23064	+	1.18339i	−0.565283	+	0.0812754i
$213$	−2.76908	+	4.30877i	−0.189734	+	0.295232i
$214$	0.500763	+	0.228691i	0.0342314	+	0.0156330i
$215$	−30.4772	−	26.4087i	−2.07853	−	1.80106i
$216$	−0.989821	−	0.142315i	−0.0673488	−	0.00968330i
$217$	11.2251	+	1.18576i	0.762010	+	0.0804943i
$218$	−0.915526	+	3.11799i	−0.0620072	+	0.211177i
$219$	−11.5323	−	3.38619i	−0.779282	−	0.228818i
$220$	−13.0494	+	5.95946i	−0.879790	+	0.401787i
$221$	32.0206	+	4.60387i	2.15394	+	0.309690i
$222$	4.05167	−	4.67588i	0.271930	−	0.313824i
$223$	5.75594	+	2.62865i	0.385446	+	0.176027i	0.598707	−	0.800968i	$-0.295681\pi$
$223$	5.75594	+	2.62865i	0.385446	+	0.176027i	−0.213261	+	0.976995i	$0.568409\pi$
$224$	1.18867	+	2.36370i	0.0794215	+	0.157931i
$225$	0.951769	+	6.61970i	0.0634512	+	0.441313i
$226$	1.48483	+	2.31044i	0.0987692	+	0.153688i
$227$	7.94394	+	9.16780i	0.527258	+	0.608488i	0.955433	−	0.295208i	$-0.0953889\pi$
$227$	7.94394	+	9.16780i	0.527258	+	0.608488i	−0.428175	+	0.903696i	$0.640843\pi$
$228$	0.688197	+	2.34378i	0.0455769	+	0.155221i
$229$	−4.53323			−0.299565			−0.149782	−	0.988719i	$-0.547857\pi$
$229$	−4.53323			−0.299565			−0.149782	+	0.988719i	$0.547857\pi$
$230$	−16.2134	+	2.43787i	−1.06908	+	0.160748i
$231$	−9.55852	−	5.64737i	−0.628904	−	0.371570i
$232$	2.30889	−	0.677951i	0.151586	−	0.0445097i
$233$	−8.13667	−	9.39022i	−0.533051	−	0.615174i	0.423799	−	0.905756i	$-0.360696\pi$
$233$	−8.13667	−	9.39022i	−0.533051	−	0.615174i	−0.956850	+	0.290583i	$0.906151\pi$
$234$	3.03478	+	4.72221i	0.198390	+	0.308700i
$235$	44.2011	−	6.35516i	2.88336	−	0.414565i
$236$	−7.10173	+	11.0505i	−0.462283	+	0.719327i
$237$	2.28410	−	5.00149i	0.148368	−	0.324882i
$238$	−14.4584	+	4.84205i	−0.937202	+	0.313864i
$239$	4.28723	−	29.8183i	0.277318	−	1.92879i	−0.0842582	−	0.996444i	$-0.526852\pi$
$239$	4.28723	−	29.8183i	0.277318	−	1.92879i	0.361576	−	0.932343i	$-0.382239\pi$
$240$	−3.10979	+	1.42020i	−0.200736	+	0.0916732i
$241$	−11.3452	−	3.33124i	−0.730807	−	0.214584i	−0.104901	−	0.994483i	$-0.533452\pi$
$241$	−11.3452	−	3.33124i	−0.730807	−	0.214584i	−0.625906	+	0.779898i	$0.715271\pi$
$242$	6.34062	+	1.86177i	0.407590	+	0.119679i
$243$	0.909632	−	0.415415i	0.0583529	−	0.0266489i
$244$	−0.383166	+	2.66498i	−0.0245297	+	0.170608i
$245$	23.4030	+	5.00011i	1.49516	+	0.319445i
$246$	2.46961	−	5.40768i	0.157456	−	0.344781i
$247$	7.41315	−	11.5351i	0.471687	−	0.733960i
$248$	−4.22287	+	0.607157i	−0.268153	+	0.0385545i
$249$	−6.36782	−	9.90852i	−0.403544	−	0.627927i
$250$	3.77857	+	4.36070i	0.238978	+	0.275795i
$251$	−3.80959	+	1.11860i	−0.240459	+	0.0706052i	−0.399742	−	0.916628i	$-0.630900\pi$
$251$	−3.80959	+	1.11860i	−0.240459	+	0.0706052i	0.159282	+	0.987233i	$0.449082\pi$
$252$	−2.27789	−	1.34582i	−0.143493	−	0.0847789i
$253$	16.9995	+	10.7708i	1.06875	+	0.677152i
$254$	10.2717			0.644507
$255$	−5.55083	−	18.9044i	−0.347606	−	1.18384i
$256$	−0.654861	−	0.755750i	−0.0409288	−	0.0472343i
$257$	11.4909	+	17.8801i	0.716781	+	1.11533i	0.988244	+	0.152884i	$0.0488560\pi$
$257$	11.4909	+	17.8801i	0.716781	+	1.11533i	−0.271463	+	0.962449i	$0.587508\pi$
$258$	1.67874	+	11.6759i	0.104513	+	0.726907i
$259$	14.6244	−	7.35440i	0.908714	−	0.456980i
$260$	17.4562	+	7.97198i	1.08259	+	0.494401i
$261$	−1.57583	+	1.81861i	−0.0975417	+	0.112569i
$262$	−2.62658	−	0.377646i	−0.162271	−	0.0233310i
$263$	−26.4581	+	12.0830i	−1.63147	+	0.745069i	−0.999551	−	0.0299615i	$-0.990462\pi$
$263$	−26.4581	+	12.0830i	−1.63147	+	0.745069i	−0.631923	+	0.775031i	$0.717734\pi$
$264$	4.02625	+	1.18221i	0.247798	+	0.0727602i
$265$	8.00903	−	27.2762i	0.491991	−	1.67557i
$266$	−0.678922	+	6.42710i	−0.0416274	+	0.394071i
$267$	−2.91389	−	0.418954i	−0.178327	−	0.0256396i
$268$	6.45498	+	5.59328i	0.394301	+	0.341664i
$269$	13.8557	+	6.32766i	0.844794	+	0.385804i	0.790308	−	0.612710i	$-0.209921\pi$
$269$	13.8557	+	6.32766i	0.844794	+	0.385804i	0.0544862	+	0.998515i	$0.482648\pi$
$270$	1.84831	−	2.87603i	0.112485	−	0.175029i
$271$	−14.5629	+	2.09382i	−0.884630	+	0.127191i	−0.569630	−	0.821901i	$-0.692914\pi$
$271$	−14.5629	+	2.09382i	−0.884630	+	0.127191i	−0.315000	+	0.949092i	$0.602005\pi$
$272$	4.84822	−	3.11576i	0.293966	−	0.188921i
$273$	2.66403	+	14.6105i	0.161234	+	0.884268i
$274$	−2.59358	−	8.83292i	−0.156684	−	0.533616i
$275$		−	28.0634i		−	1.69229i
$276$	4.05113	+	2.56677i	0.243850	+	0.154502i
$277$	28.6678			1.72248			0.861241	−	0.508197i	$-0.169688\pi$
$277$	28.6678			1.72248			0.861241	+	0.508197i	$0.169688\pi$
$278$	2.47384	+	8.42513i	0.148371	+	0.505306i
$279$	3.22425	−	2.79383i	0.193031	−	0.167262i
$280$	−9.03875	+	0.339616i	−0.540169	+	0.0202960i
$281$	−6.26913	+	0.901365i	−0.373985	+	0.0537710i	−0.326745	−	0.945113i	$-0.605952\pi$
$281$	−6.26913	+	0.901365i	−0.373985	+	0.0537710i	−0.0472404	+	0.998884i	$0.515043\pi$
$282$	−10.9885	−	7.06187i	−0.654354	−	0.420528i
$283$	−4.36849	+	9.56567i	−0.259680	+	0.568620i	−0.993899	−	0.110293i	$-0.964821\pi$
$283$	−4.36849	+	9.56567i	−0.259680	+	0.568620i	0.734219	+	0.678912i	$0.237548\pi$
$284$	3.35409	−	3.87083i	0.199029	−	0.229691i
$285$	−8.26605	−	1.18848i	−0.489639	−	0.0703994i
$286$	−9.78496	−	21.4261i	−0.578597	−	1.26695i
$287$	11.4919	−	10.7392i	0.678344	−	0.633915i
$288$	0.959493	+	0.281733i	0.0565387	+	0.0166013i
$289$	6.73518	+	14.7480i	0.396187	+	0.867529i
$290$	−1.17079	+	8.14299i	−0.0687509	+	0.478173i
$291$	0.195342	+	0.169265i	0.0114511	+	0.00992247i
$292$	10.9330	+	4.99295i	0.639807	+	0.292190i
$293$	−6.65028	−	4.27387i	−0.388513	−	0.249682i	0.331773	−	0.943359i	$-0.392353\pi$
$293$	−6.65028	−	4.27387i	−0.388513	−	0.249682i	−0.720286	+	0.693677i	$0.755990\pi$
$294$	−4.21571	−	5.58818i	−0.245865	−	0.325909i
$295$	−24.2789	−	37.7788i	−1.41357	−	2.19957i
$296$	−4.67588	+	4.05167i	−0.271780	+	0.235499i
$297$	−4.02625	+	1.18221i	−0.233627	+	0.0685990i
$298$		−	11.4705i		−	0.664466i
$299$	−4.00278	−	26.6212i	−0.231487	−	1.53954i
$300$		−	6.68777i		−	0.386118i
$301$	−7.66208	+	30.2539i	−0.441635	+	1.74381i
$302$	1.54535	+	1.78343i	0.0889251	+	0.102625i
$303$	4.19274	−	2.69451i	0.240867	−	0.154796i
$304$	−0.347637	−	2.41787i	−0.0199383	−	0.138674i
$305$	−7.74336	−	4.97635i	−0.443383	−	0.284945i
$306$	−2.39407	+	5.24229i	−0.136860	+	0.299682i
$307$	10.5436	+	9.13605i	0.601753	+	0.521422i	0.901603	−	0.432564i	$-0.142391\pi$
$307$	10.5436	+	9.13605i	0.601753	+	0.521422i	−0.299850	+	0.953986i	$0.596937\pi$
$308$	8.65752	+	6.95021i	0.493308	+	0.396025i
$309$	8.89899	−	4.06403i	0.506246	−	0.231195i
$310$	4.10917	−	13.9945i	0.233385	−	0.794836i
$311$	6.33844	−	21.5868i	0.359420	−	1.22407i	−0.559234	−	0.829010i	$-0.688905\pi$
$311$	6.33844	−	21.5868i	0.359420	−	1.22407i	0.918654	−	0.395063i	$-0.129277\pi$
$312$	−2.33185	−	5.10604i	−0.132015	−	0.289072i
$313$	0.614941	−	4.27701i	0.0347585	−	0.241751i	−0.965034	−	0.262125i	$-0.915577\pi$
$313$	0.614941	−	4.27701i	0.0347585	−	0.241751i	0.999792	+	0.0203742i	$0.00648577\pi$
$314$	6.35836	−	7.33793i	0.358823	−	0.414104i
$315$	7.42027	−	5.17242i	0.418085	−	0.291433i
$316$	−2.97264	+	4.62552i	−0.167224	+	0.260206i
$317$	3.83259	+	26.6563i	0.215260	+	1.49717i	0.755218	+	0.655474i	$0.227531\pi$
$317$	3.83259	+	26.6563i	0.215260	+	1.49717i	−0.539958	+	0.841692i	$0.681560\pi$
$318$	−6.99526	+	4.49558i	−0.392275	+	0.252100i
$319$	7.63129	−	6.61255i	0.427270	−	0.370232i
$320$	3.28025	−	0.963170i	0.183372	−	0.0538428i
$321$	0.550511			0.0307265
$322$	7.32283	+	10.3622i	0.408085	+	0.577465i
$323$	14.0777			0.783302
$324$	−0.959493	+	0.281733i	−0.0533052	+	0.0156518i
$325$	−28.3712	+	24.5838i	−1.57375	+	1.36366i
$326$	4.29206	−	2.75834i	0.237715	−	0.152770i
$327$	0.462470	+	3.21655i	0.0255747	+	0.177876i
$328$	−3.21406	+	5.00118i	−0.177467	+	0.276144i
$329$	−19.7624	−	28.3508i	−1.08953	−	1.56303i
$330$	−9.39450	+	10.8418i	−0.517150	+	0.596823i
$331$	4.64921	−	32.3360i	0.255544	−	1.77735i	−0.308127	−	0.951345i	$-0.599702\pi$
$331$	4.64921	−	32.3360i	0.255544	−	1.77735i	0.563670	−	0.826000i	$-0.309389\pi$
$332$	4.89287	+	10.7139i	0.268531	+	0.588001i
$333$	1.74310	−	5.93645i	0.0955213	−	0.325316i
$334$	−4.79160	+	16.3187i	−0.262185	+	0.892919i
$335$	−26.5613	+	12.1301i	−1.45120	+	0.662740i
$336$	2.06317	+	1.65630i	0.112555	+	0.0903586i
$337$	2.39677	+	2.07682i	0.130561	+	0.113131i	0.717693	−	0.696359i	$-0.245198\pi$
$337$	2.39677	+	2.07682i	0.130561	+	0.113131i	−0.587133	+	0.809491i	$0.699743\pi$
$338$	−7.68896	+	16.8365i	−0.418224	+	0.915784i
$339$	2.31044	+	1.48483i	0.125486	+	0.0806447i
$340$	2.80395	+	19.5019i	0.152066	+	1.05764i
$341$	−15.0604	+	9.67874i	−0.815567	+	0.524133i
$342$	1.59965	+	1.84609i	0.0864991	+	0.0998253i
$343$	−4.68002	−	17.9192i	−0.252697	−	0.967545i
$344$		−	11.7959i		−	0.635994i
$345$	−13.7355	+	8.95287i	−0.739496	+	0.482006i
$346$			17.1506i			0.922024i
$347$	−27.4399	+	8.05707i	−1.47305	+	0.432526i	−0.917089	−	0.398683i	$-0.869467\pi$
$347$	−27.4399	+	8.05707i	−1.47305	+	0.432526i	−0.555960	+	0.831209i	$0.687649\pi$
$348$	1.81861	−	1.57583i	0.0974877	−	0.0844736i
$349$	−14.7544	−	22.9584i	−0.789787	−	1.22893i	−0.969470	−	0.245208i	$-0.921144\pi$
$349$	−14.7544	−	22.9584i	−0.789787	−	1.22893i	0.179683	−	0.983724i	$-0.442493\pi$
$350$	6.74092	−	16.3598i	0.360317	−	0.874469i
$351$	4.72221	+	3.03478i	0.252053	+	0.161984i
$352$	−3.81702	−	1.74317i	−0.203448	−	0.0929115i
$353$	23.0775	+	19.9968i	1.22829	+	1.06432i	0.995784	+	0.0917257i	$0.0292383\pi$
$353$	23.0775	+	19.9968i	1.22829	+	1.06432i	0.232507	+	0.972595i	$0.425307\pi$
$354$	−1.86941	+	13.0021i	−0.0993582	+	0.691051i
$355$	7.27401	+	15.9279i	0.386064	+	0.845363i
$356$	2.82461	+	0.829380i	0.149704	+	0.0439570i
$357$	−11.1404	+	10.4107i	−0.589612	+	0.550995i
$358$	10.3241	+	22.6066i	0.545645	+	1.19480i
$359$	13.6865	+	1.96782i	0.722344	+	0.103857i	0.493674	−	0.869647i	$-0.335653\pi$
$359$	13.6865	+	1.96782i	0.722344	+	0.103857i	0.228669	+	0.973504i	$0.426563\pi$
$360$	−2.23880	+	2.58371i	−0.117995	+	0.136173i
$361$	−5.41413	+	11.8553i	−0.284954	+	0.623963i
$362$	8.01519	+	5.15105i	0.421269	+	0.270733i
$363$	6.54104	−	0.940459i	0.343316	−	0.0493613i
$364$	−0.557623	−	14.8409i	−0.0292274	−	0.777875i
$365$	−31.0541	+	26.9085i	−1.62544	+	1.40845i
$366$	0.758532	+	2.58332i	0.0396491	+	0.135032i
$367$	23.3513			1.21893			0.609463	−	0.792814i	$-0.291385\pi$
$367$	23.3513			1.21893			0.609463	+	0.792814i	$0.291385\pi$
$368$	−3.64461	−	3.11718i	−0.189988	−	0.162494i
$369$		−	5.94491i		−	0.309480i
$370$	−5.95920	−	20.2952i	−0.309804	−	1.05510i
$371$	−21.6433	+	3.94637i	−1.12367	+	0.204885i
$372$	−3.58904	+	2.30653i	−0.186083	+	0.119588i
$373$	32.8566	−	4.72406i	1.70125	−	0.244603i	0.777852	−	0.628448i	$-0.216309\pi$
$373$	32.8566	−	4.72406i	1.70125	−	0.244603i	0.923397	+	0.383845i	$0.125400\pi$
$374$	13.0744	−	20.3442i	0.676062	−	1.05197i
$375$	5.24861	+	2.39696i	0.271037	+	0.123778i
$376$	9.87162	+	8.55381i	0.509090	+	0.441129i
$377$	−13.3702	−	1.92234i	−0.688598	−	0.0990054i
$378$	−2.63111	−	0.277936i	−0.135330	−	0.0142955i
$379$	−3.98847	+	13.5835i	−0.204874	+	0.697736i	0.791385	+	0.611318i	$0.209360\pi$
$379$	−3.98847	+	13.5835i	−0.204874	+	0.697736i	−0.996259	+	0.0864182i	$0.972458\pi$
$380$	8.01278	+	2.35276i	0.411047	+	0.120694i
$381$	9.34351	−	4.26704i	0.478682	−	0.218607i
$382$	8.53795	+	1.22757i	0.436840	+	0.0628081i
$383$	1.80036	−	2.07772i	0.0919939	−	0.106167i	−0.707886	−	0.706327i	$-0.750351\pi$
$383$	1.80036	−	2.07772i	0.0919939	−	0.106167i	0.799880	+	0.600160i	$0.204896\pi$
$384$	−0.909632	−	0.415415i	−0.0464195	−	0.0211991i
$385$	−33.9091	+	17.0524i	−1.72817	+	0.869073i
$386$	0.886195	+	6.16362i	0.0451062	+	0.313720i
$387$	6.37736	+	9.92336i	0.324179	+	0.504433i
$388$	−0.169265	−	0.195342i	−0.00859311	−	0.00991698i
$389$	0.413340	+	1.40771i	0.0209572	+	0.0713736i	0.969308	−	0.245851i	$-0.0790673\pi$
$389$	0.413340	+	1.40771i	0.0209572	+	0.0713736i	−0.948350	+	0.317224i	$0.897249\pi$
$390$	19.1904			0.971743
$391$	20.7709	−	18.2338i	1.05043	−	0.922121i
$392$	3.37752	+	6.13126i	0.170591	+	0.309675i
$393$	−2.54611	+	0.747604i	−0.128434	+	0.0377116i
$394$	6.68720	+	7.71744i	0.336896	+	0.388799i
$395$	−10.1627	−	15.8134i	−0.511340	−	0.795660i
$396$	4.15351	−	0.597185i	0.208722	−	0.0300097i
$397$	−15.9099	+	24.7564i	−0.798497	+	1.24249i	0.167995	+	0.985788i	$0.446271\pi$
$397$	−15.9099	+	24.7564i	−0.798497	+	1.24249i	−0.966492	+	0.256698i	$0.917365\pi$
$398$	−6.01476	+	13.1705i	−0.301493	+	0.660177i
$399$	2.05234	+	6.12833i	0.102746	+	0.306800i
$400$	−0.951769	+	6.61970i	−0.0475884	+	0.330985i
$401$	25.0675	−	11.4480i	1.25181	−	0.571684i	0.324470	−	0.945896i	$-0.394814\pi$
$401$	25.0675	−	11.4480i	1.25181	−	0.571684i	0.927343	+	0.374212i	$0.122087\pi$
$402$	8.19519	+	2.40633i	0.408739	+	0.120017i
$403$	22.9779	+	6.74693i	1.14461	+	0.336088i
$404$	−4.53353	+	2.07040i	−0.225552	+	0.103006i
$405$	0.486537	−	3.38394i	0.0241762	−	0.168149i
$406$	6.03709	−	2.02179i	0.299616	−	0.100340i
$407$	−10.7852	+	23.6162i	−0.534600	+	1.17061i
$408$	3.11576	−	4.84822i	0.154253	−	0.240022i
$409$	20.2142	−	2.90636i	0.999528	−	0.143710i	0.376921	−	0.926245i	$-0.376983\pi$
$409$	20.2142	−	2.90636i	0.999528	−	0.143710i	0.622607	+	0.782535i	$0.286074\pi$
$410$	−10.9880	−	17.0977i	−0.542660	−	0.844396i
$411$	−6.02853	−	6.95730i	−0.297366	−	0.343178i
$412$	−9.38679	+	2.75621i	−0.462454	+	0.135789i
$413$	−17.6784	+	29.9218i	−0.869897	+	1.47235i
$414$	4.75132	+	0.651918i	0.233514	+	0.0320400i
$415$	−40.2668			−1.97662
$416$	1.58145	+	5.38592i	0.0775369	+	0.264066i
$417$	5.75021	+	6.63609i	0.281589	+	0.324971i
$418$	−5.54170	−	8.62306i	−0.271054	−	0.421767i
$419$	−1.01359	−	7.04964i	−0.0495169	−	0.344398i	−0.999486	−	0.0320541i	$-0.989795\pi$
$419$	−1.01359	−	7.04964i	−0.0495169	−	0.344398i	0.949969	−	0.312343i	$-0.101114\pi$
$420$	−8.08086	+	4.06376i	−0.394305	+	0.198291i
$421$	−14.0594	−	6.42070i	−0.685212	−	0.312926i	0.0422173	−	0.999108i	$-0.486558\pi$
$421$	−14.0594	−	6.42070i	−0.685212	−	0.312926i	−0.727429	+	0.686183i	$0.759285\pi$
$422$	−9.96003	+	11.4945i	−0.484847	+	0.559543i
$423$	−12.9291	−	1.85892i	−0.628633	−	0.0903838i
$424$	7.56384	−	3.45429i	0.367333	−	0.167755i
$425$	−36.9809	−	10.8586i	−1.79384	−	0.526719i
$426$	1.44299	−	4.91437i	0.0699130	−	0.238102i
$427$	−0.748309	+	7.08396i	−0.0362132	+	0.342817i
$428$	−0.544908	−	0.0783459i	−0.0263391	−	0.00378699i
$429$	−17.8014	−	15.4250i	−0.859461	−	0.744727i
$430$	36.6829	+	16.7525i	1.76901	+	0.807878i
$431$	−7.37331	+	11.4731i	−0.355160	+	0.552640i	−0.972158	−	0.234325i	$-0.924712\pi$
$431$	−7.37331	+	11.4731i	−0.355160	+	0.552640i	0.616998	+	0.786964i	$0.288348\pi$
$432$	0.989821	−	0.142315i	0.0476228	−	0.00684713i
$433$	−3.73448	+	2.40001i	−0.179468	+	0.115337i	−0.627290	−	0.778786i	$-0.715836\pi$
$433$	−3.73448	+	2.40001i	−0.179468	+	0.115337i	0.447822	+	0.894122i	$0.352200\pi$
$434$	−11.1045	+	2.02475i	−0.533032	+	0.0971913i
$435$	2.31774	+	7.89349i	0.111127	+	0.378464i
$436$		−	3.24963i		−	0.155629i
$437$	−3.37283	−	11.2189i	−0.161344	−	0.536672i
$438$	12.0192			0.574298
$439$	8.50185	+	28.9546i	0.405771	+	1.38193i	0.868614	+	0.495489i	$0.165011\pi$
$439$	8.50185	+	28.9546i	0.405771	+	1.38193i	−0.462843	+	0.886440i	$0.653171\pi$
$440$	10.8418	−	9.39450i	0.516864	−	0.447865i
$441$	−6.15616	−	3.33192i	−0.293151	−	0.158663i
$442$	−32.0206	+	4.60387i	−1.52307	+	0.218984i
$443$	−0.746061	−	0.479464i	−0.0354464	−	0.0227800i	0.522798	−	0.852457i	$-0.324888\pi$
$443$	−0.746061	−	0.479464i	−0.0354464	−	0.0227800i	−0.558244	+	0.829677i	$0.688525\pi$
$444$	−2.57020	+	5.62796i	−0.121976	+	0.267091i
$445$	−6.59069	+	7.60607i	−0.312429	+	0.360562i
$446$	−6.26336	−	0.900535i	−0.296579	−	0.0426416i
$447$	−4.76500	−	10.4339i	−0.225377	−	0.493507i
$448$	−1.80645	−	1.93306i	−0.0853469	−	0.0913286i
$449$	4.24432	+	1.24625i	0.200302	+	0.0588139i	0.380345	−	0.924845i	$-0.375805\pi$
$449$	4.24432	+	1.24625i	0.200302	+	0.0588139i	−0.180043	+	0.983659i	$0.557624\pi$
$450$	−2.77820	−	6.08341i	−0.130966	−	0.286775i
$451$	−3.55021	+	24.6923i	−0.167173	+	1.16271i
$452$	−2.07561	−	1.79852i	−0.0976283	−	0.0845954i
$453$	2.14657	+	0.980304i	0.100854	+	0.0460587i
$454$	−10.2050	−	6.55837i	−0.478945	−	0.307800i
$455$	46.9441	+	19.3429i	2.20077	+	0.906809i
$456$	−1.32064	−	2.05496i	−0.0618446	−	0.0962321i
$457$	−26.3690	+	22.8489i	−1.23349	+	1.06882i	−0.238266	+	0.971200i	$0.576579\pi$
$457$	−26.3690	+	22.8489i	−1.23349	+	1.06882i	−0.995223	+	0.0976249i	$0.968875\pi$
$458$	4.34961	−	1.27716i	0.203244	−	0.0596778i
$459$			5.76308i			0.268998i
$460$	14.8699	−	6.90697i	0.693310	−	0.322039i
$461$		−	2.83378i		−	0.131982i	−0.997820	−	0.0659912i	$-0.978979\pi$
$461$		−	2.83378i		−	0.131982i	0.997820	−	0.0659912i	$-0.0210209\pi$
$462$	10.7624	+	2.72567i	0.500711	+	0.126810i
$463$	−1.85686	−	2.14293i	−0.0862954	−	0.0995902i	0.710960	−	0.703233i	$-0.248261\pi$
$463$	−1.85686	−	2.14293i	−0.0862954	−	0.0995902i	−0.797255	+	0.603643i	$0.793715\pi$
$464$	−2.02436	+	1.30098i	−0.0939787	+	0.0603964i
$465$	−2.07571	−	14.4369i	−0.0962588	−	0.669495i
$466$	10.4526	+	6.71748i	0.484208	+	0.311181i
$467$	4.82791	−	10.5716i	0.223409	−	0.489197i	−0.764424	−	0.644713i	$-0.776977\pi$
$467$	4.82791	−	10.5716i	0.223409	−	0.489197i	0.987833	+	0.155516i	$0.0497040\pi$
$468$	−4.24225	−	3.67593i	−0.196098	−	0.169920i
$469$	17.6219	+	14.1467i	0.813703	+	0.653236i
$470$	−40.6202	+	18.5506i	−1.87367	+	0.855677i
$471$	2.73548	−	9.31618i	0.126044	−	0.429267i
$472$	3.70077	−	12.6037i	0.170342	−	0.580131i
$473$	−20.5624	−	45.0253i	−0.945458	−	2.07026i
$474$	−0.782499	+	5.44240i	−0.0359414	+	0.249978i
$475$	−10.6981	+	12.3462i	−0.490862	+	0.566484i
$476$	12.5086	−	8.71933i	0.573331	−	0.399650i
$477$	−4.49558	+	6.99526i	−0.205838	+	0.320291i
$478$	4.28723	+	29.8183i	0.196093	+	1.36386i
$479$	−8.56831	+	5.50652i	−0.391496	+	0.251599i	−0.721549	−	0.692363i	$-0.756570\pi$
$479$	−8.56831	+	5.50652i	−0.391496	+	0.251599i	0.330053	+	0.943962i	$0.392933\pi$
$480$	2.58371	−	2.23880i	0.117930	−	0.102187i
$481$	33.3231	−	9.78454i	1.51940	−	0.446137i
$482$	11.8241			0.538574
$483$	10.9657	+	6.38382i	0.498957	+	0.290474i
$484$	−6.60830			−0.300377
$485$	0.847861	−	0.248955i	0.0384994	−	0.0113044i
$486$	−0.755750	+	0.654861i	−0.0342815	+	0.0297051i
$487$	−30.0034	+	19.2820i	−1.35958	+	0.873751i	−0.998276	−	0.0586966i	$-0.981306\pi$
$487$	−30.0034	+	19.2820i	−1.35958	+	0.873751i	−0.361306	+	0.932447i	$0.617669\pi$
$488$	−0.383166	−	2.66498i	−0.0173451	−	0.120638i
$489$	2.75834	−	4.29206i	0.124736	−	0.194094i
$490$	−23.8637	+	1.79581i	−1.07805	+	0.0811266i
$491$	19.0466	−	21.9809i	0.859560	−	0.991985i	−0.140438	−	0.990089i	$-0.544851\pi$
$491$	19.0466	−	21.9809i	0.859560	−	0.991985i	0.999998	−	0.00189570i	$-0.000603422\pi$
$492$	−0.846049	+	5.88440i	−0.0381428	+	0.265289i
$493$	−5.76101	−	12.6149i	−0.259463	−	0.568144i
$494$	−3.86305	+	13.1564i	−0.173807	+	0.591932i
$495$	−4.04168	+	13.7647i	−0.181660	+	0.618677i
$496$	3.88076	−	1.77228i	0.174251	−	0.0795779i
$497$	8.48331	−	10.5672i	0.380528	−	0.474005i
$498$	8.90143	+	7.71313i	0.398882	+	0.345634i
$499$	10.9410	−	23.9575i	0.489786	−	1.07248i	−0.489869	−	0.871796i	$-0.662955\pi$
$499$	10.9410	−	23.9575i	0.489786	−	1.07248i	0.979655	−	0.200687i	$-0.0643173\pi$
$500$	−4.85406	−	3.11952i	−0.217080	−	0.139509i
$501$	2.42044	+	16.8345i	0.108137	+	0.752110i
$502$	3.34013	−	2.14657i	0.149077	−	0.0958061i
$503$	−27.0463	−	31.2131i	−1.20594	−	1.39173i	−0.897812	−	0.440379i	$-0.854844\pi$
$503$	−27.0463	−	31.2131i	−1.20594	−	1.39173i	−0.308125	−	0.951346i	$-0.599701\pi$
$504$	2.56478	+	0.649553i	0.114244	+	0.0289334i
$505$		−	17.0387i		−	0.758213i
$506$	−19.3453	−	5.54517i	−0.860005	−	0.246513i
$507$			18.5091i			0.822018i
$508$	−9.85567	+	2.89388i	−0.437274	+	0.128395i
$509$	12.6597	−	10.9697i	0.561130	−	0.486222i	−0.327497	−	0.944852i	$-0.606205\pi$
$509$	12.6597	−	10.9697i	0.561130	−	0.486222i	0.888627	+	0.458630i	$0.151660\pi$
$510$	10.6520	+	16.5748i	0.471677	+	0.733943i
$511$	29.4017	+	12.1147i	1.30065	+	0.535922i
$512$	0.841254	+	0.540641i	0.0371785	+	0.0238932i
$513$	2.22199	+	1.01475i	0.0981031	+	0.0448022i
$514$	−16.0628	−	13.9185i	−0.708501	−	0.613919i
$515$	4.75983	−	33.1053i	0.209743	−	1.45879i
$516$	−4.90020	−	10.7299i	−0.215719	−	0.472360i
$517$	52.5910	+	15.4421i	2.31295	+	0.679143i
$518$	−11.9600	+	11.1767i	−0.525492	+	0.491074i
$519$	7.12464	+	15.6008i	0.312737	+	0.684798i
$520$	−18.9951	−	2.73108i	−0.832989	−	0.119766i
$521$	7.49635	−	8.65125i	0.328421	−	0.379018i	−0.567393	−	0.823447i	$-0.692048\pi$
$521$	7.49635	−	8.65125i	0.328421	−	0.379018i	0.895814	+	0.444429i	$0.146593\pi$
$522$	0.999640	−	2.18891i	0.0437531	−	0.0958058i
$523$	−26.1091	−	16.7793i	−1.14167	−	0.733708i	−0.173708	−	0.984797i	$-0.555575\pi$
$523$	−26.1091	−	16.7793i	−1.14167	−	0.733708i	−0.967964	+	0.251089i	$0.919211\pi$
$524$	2.62658	−	0.377646i	0.114743	−	0.0164975i
$525$	−0.664361	−	17.6817i	−0.0289951	−	0.771692i
$526$	21.9822	−	19.0476i	0.958468	−	0.830517i
$527$	6.92697	+	23.5911i	0.301743	+	1.02764i
$528$	−4.19622			−0.182617
$529$	−19.5075	−	12.1844i	−0.848150	−	0.529756i
$530$			28.4278i			1.23482i
$531$	3.70077	+	12.6037i	0.160600	+	0.546953i
$532$	−1.15930	−	6.35803i	−0.0502621	−	0.275656i
$533$	28.0731	−	18.0415i	1.21598	−	0.781463i
$534$	2.91389	−	0.418954i	0.126096	−	0.0181299i
$535$	1.01751	−	1.58328i	0.0439910	−	0.0684513i
$536$	−7.76932	−	3.54813i	−0.335584	−	0.153256i
$537$	18.7822	+	16.2749i	0.810513	+	0.702314i
$538$	−15.0771	−	2.16776i	−0.650020	−	0.0934588i
$539$	23.5799	+	17.5155i	1.01566	+	0.754447i
$540$	−0.963170	+	3.28025i	−0.0414482	+	0.141160i
$541$	8.82821	+	2.59220i	0.379554	+	0.111447i	0.465944	−	0.884814i	$-0.345715\pi$
$541$	8.82821	+	2.59220i	0.379554	+	0.111447i	−0.0863896	+	0.996261i	$0.527533\pi$
$542$	13.3831	−	6.11184i	0.574852	−	0.262526i
$543$	9.43070	+	1.35593i	0.404710	+	0.0581885i
$544$	−3.77402	+	4.35545i	−0.161810	+	0.186738i
$545$	10.1057	+	4.61510i	0.432879	+	0.197689i
$546$	−6.67237	−	13.2681i	−0.285551	−	0.567823i
$547$	3.83088	+	26.6443i	0.163797	+	1.13923i	0.891395	+	0.453227i	$0.149727\pi$
$547$	3.83088	+	26.6443i	0.163797	+	1.13923i	−0.727599	+	0.686003i	$0.759364\pi$
$548$	4.97704	+	7.74443i	0.212609	+	0.330826i
$549$	1.76314	+	2.03477i	0.0752488	+	0.0868417i
$550$	7.90637	+	26.9266i	0.337129	+	1.14815i
$551$	−5.87810			−0.250416
$552$	−4.61018	−	1.32147i	−0.196222	−	0.0562453i
$553$	−7.39982	+	12.5246i	−0.314672	+	0.532602i
$554$	−27.5066	+	8.07666i	−1.16864	+	0.343144i
$555$	−13.8516	−	15.9856i	−0.587968	−	0.678551i
$556$	−4.74727	−	7.38689i	−0.201329	−	0.313274i
$557$	−22.9957	+	3.30628i	−0.974360	+	0.140092i	−0.611063	−	0.791582i	$-0.709258\pi$
$557$	−22.9957	+	3.30628i	−0.974360	+	0.140092i	−0.363297	+	0.931674i	$0.618349\pi$
$558$	−2.30653	+	3.58904i	−0.0976434	+	0.151936i
$559$	−27.5063	+	60.2304i	−1.16339	+	2.54747i
$560$	8.57694	−	2.87237i	0.362442	−	0.121380i
$561$	3.44163	−	23.9370i	0.145306	−	1.01062i
$562$	5.76125	−	2.63107i	0.243024	−	0.110985i
$563$	12.2458	+	3.59568i	0.516098	+	0.151540i	0.529401	−	0.848372i	$-0.322417\pi$
$563$	12.2458	+	3.59568i	0.516098	+	0.151540i	−0.0133036	+	0.999912i	$0.504235\pi$
$564$	12.5329	+	3.68000i	0.527731	+	0.154956i
$565$	8.54080	−	3.90045i	0.359314	−	0.164093i
$566$	1.49658	−	10.4089i	0.0629059	−	0.437520i
$567$	−2.50880	+	0.840184i	−0.105360	+	0.0352844i
$568$	−2.12769	+	4.65899i	−0.0892759	+	0.195487i
$569$	−1.41611	+	2.20350i	−0.0593662	+	0.0923757i	−0.869668	−	0.493638i	$-0.835667\pi$
$569$	−1.41611	+	2.20350i	−0.0593662	+	0.0923757i	0.810302	+	0.586013i	$0.199303\pi$
$570$	8.26605	−	1.18848i	0.346227	−	0.0497799i
$571$	−1.06765	−	1.66130i	−0.0446798	−	0.0695231i	0.818195	−	0.574941i	$-0.194975\pi$
$571$	−1.06765	−	1.66130i	−0.0446798	−	0.0695231i	−0.862875	+	0.505418i	$0.831338\pi$
$572$	15.4250	+	17.8014i	0.644953	+	0.744315i
$573$	8.27635	−	2.43016i	0.345749	−	0.101521i
$574$	−8.00080	+	13.5418i	−0.333947	+	0.565225i
$575$	0.206653	+	32.0727i	0.00861802	+	1.33753i
$576$	−1.00000			−0.0416667
$577$	−3.94519	−	13.4361i	−0.164240	−	0.559352i	−0.999948	−	0.0101773i	$-0.996760\pi$
$577$	−3.94519	−	13.4361i	−0.164240	−	0.559352i	0.835708	−	0.549174i	$-0.185058\pi$
$578$	−10.6174	−	12.2531i	−0.441624	−	0.509661i
$579$	3.36657	+	5.23849i	0.139910	+	0.217704i
$580$	−1.17079	−	8.14299i	−0.0486142	−	0.338119i
$581$	14.0005	+	27.8403i	0.580839	+	1.15501i
$582$	−0.235116	−	0.107374i	−0.00974589	−	0.00445080i
$583$	22.8499	−	26.3702i	0.946347	−	1.09214i
$584$	−11.8968	−	1.71051i	−0.492295	−	0.0707813i
$585$	17.4562	−	7.97198i	0.721725	−	0.329601i
$586$	7.58498	+	2.22715i	0.313333	+	0.0920028i
$587$	−0.405781	+	1.38196i	−0.0167484	+	0.0570397i	−0.967443	−	0.253088i	$-0.918554\pi$
$587$	−0.405781	+	1.38196i	−0.0167484	+	0.0570397i	0.950695	+	0.310128i	$0.100372\pi$
$588$	5.61932	+	4.17412i	0.231737	+	0.172138i
$589$	10.3153	+	1.48312i	0.425036	+	0.0611110i
$590$	33.9390	+	29.4083i	1.39725	+	1.21072i
$591$	9.28883	+	4.24207i	0.382092	+	0.174495i
$592$	3.34498	−	5.20490i	0.137478	−	0.213920i
$593$	43.0486	−	6.18945i	1.76779	−	0.254170i	0.819842	−	0.572589i	$-0.194061\pi$
$593$	43.0486	−	6.18945i	1.76779	−	0.254170i	0.947950	+	0.318419i	$0.103152\pi$
$594$	3.53009	−	2.26865i	0.144841	−	0.0930839i
$595$	9.35065	+	51.2823i	0.383339	+	2.10237i
$596$	3.23160	+	11.0058i	0.132372	+	0.450816i
$597$			14.4789i			0.592582i
$598$	11.3407	+	24.4151i	0.463756	+	0.998409i
$599$	−35.8933			−1.46656			−0.733280	−	0.679927i	$-0.762011\pi$
$599$	−35.8933			−1.46656			−0.733280	+	0.679927i	$0.762011\pi$
$600$	1.88416	+	6.41687i	0.0769206	+	0.261967i
$601$	−11.9109	+	10.3208i	−0.485854	+	0.420995i	−0.863035	−	0.505145i	$-0.831439\pi$
$601$	−11.9109	+	10.3208i	−0.485854	+	0.420995i	0.377181	+	0.926140i	$0.376894\pi$
$602$	−1.17180	−	31.1871i	−0.0477592	−	1.27109i
$603$	8.45423	−	1.21553i	0.344283	−	0.0495004i
$604$	−1.98521	−	1.27581i	−0.0807769	−	0.0519121i
$605$	9.38508	−	20.5505i	0.381558	−	0.835495i
$606$	−3.26377	+	3.76660i	−0.132582	+	0.153008i
$607$	21.8467	+	3.14108i	0.886729	+	0.127492i	0.570604	−	0.821225i	$-0.306709\pi$
$607$	21.8467	+	3.14108i	0.886729	+	0.127492i	0.316125	+	0.948718i	$0.397618\pi$
$608$	1.01475	+	2.22199i	0.0411534	+	0.0901134i
$609$	4.65165	−	4.34699i	0.188494	−	0.176149i
$610$	8.83170	+	2.59322i	0.357585	+	0.104996i
$611$	−30.4587	−	66.6952i	−1.23223	−	2.69820i
$612$	0.820172	−	5.70442i	0.0331535	−	0.230588i
$613$	−21.8072	−	18.8960i	−0.880783	−	0.763203i	0.0917957	−	0.995778i	$-0.470739\pi$
$613$	−21.8072	−	18.8960i	−0.880783	−	0.763203i	−0.972578	+	0.232575i	$0.925285\pi$
$614$	−12.6904	−	5.79551i	−0.512143	−	0.233888i
$615$	−17.0977	−	10.9880i	−0.689446	−	0.443080i
$616$	−10.2649	−	4.22957i	−0.413586	−	0.170414i
$617$	2.65397	+	4.12966i	0.106845	+	0.166254i	0.890559	−	0.454868i	$-0.150314\pi$
$617$	2.65397	+	4.12966i	0.106845	+	0.166254i	−0.783714	+	0.621122i	$0.786677\pi$
$618$	−7.39355	+	6.40655i	−0.297412	+	0.257709i
$619$	0.375863	−	0.110363i	0.0151072	−	0.00443588i	−0.274170	−	0.961681i	$-0.588403\pi$
$619$	0.375863	−	0.110363i	0.0151072	−	0.00443588i	0.289277	+	0.957245i	$0.406585\pi$
$620$			14.5853i			0.585762i
$621$	4.59277	−	1.38076i	0.184301	−	0.0554081i
$622$			22.4981i			0.902091i
$623$	7.55033	+	1.91219i	0.302498	+	0.0766103i
$624$	3.67593	+	4.24225i	0.147155	+	0.169826i
$625$	−11.5358	+	7.41359i	−0.461431	+	0.296544i
$626$	0.614941	+	4.27701i	0.0245780	+	0.170944i
$627$	−8.62306	−	5.54170i	−0.344372	−	0.221314i
$628$	−4.03346	+	8.83205i	−0.160953	+	0.352437i
$629$	26.9475	+	23.3501i	1.07447	+	0.931030i
$630$	−5.66246	+	7.05343i	−0.225598	+	0.281016i
$631$	20.6124	−	9.41335i	0.820565	−	0.374740i	0.0395236	−	0.999219i	$-0.487416\pi$
$631$	20.6124	−	9.41335i	0.820565	−	0.374740i	0.781042	+	0.624479i	$0.214689\pi$
$632$	1.54907	−	5.27564i	0.0616186	−	0.209854i
$633$	−4.28498	+	14.5933i	−0.170313	+	0.580031i
$634$	−11.1873	−	24.4967i	−0.444304	−	0.972890i
$635$	4.99758	−	34.7590i	0.198323	−	1.37937i
$636$	5.44535	−	6.28427i	0.215922	−	0.249187i
$637$	−2.94859	−	39.1823i	−0.116827	−	1.55246i
$638$	−5.45920	+	8.49468i	−0.216132	+	0.336308i
$639$	−0.728914	−	5.06971i	−0.0288354	−	0.200555i
$640$	−2.87603	+	1.84831i	−0.113685	+	0.0730608i
$641$	−8.60913	+	7.45986i	−0.340040	+	0.294647i	−0.808094	−	0.589053i	$-0.799501\pi$
$641$	−8.60913	+	7.45986i	−0.340040	+	0.294647i	0.468054	+	0.883700i	$0.344955\pi$
$642$	−0.528212	+	0.155097i	−0.0208468	+	0.00612119i
$643$	−15.5338			−0.612593			−0.306296	−	0.951936i	$-0.599090\pi$
$643$	−15.5338			−0.612593			−0.306296	+	0.951936i	$0.599090\pi$
$644$	−9.94559	−	7.87942i	−0.391911	−	0.310493i
$645$	40.3272			1.58788
$646$	−13.5074	+	3.96614i	−0.531442	+	0.156046i
$647$	−1.00253	+	0.868696i	−0.0394135	+	0.0341520i	−0.674345	−	0.738417i	$-0.735574\pi$
$647$	−1.00253	+	0.868696i	−0.0394135	+	0.0341520i	0.634931	+	0.772569i	$0.281028\pi$
$648$	0.841254	−	0.540641i	0.0330476	−	0.0212384i
$649$	−7.84448	−	54.5595i	−0.307923	−	2.14165i
$650$	20.2959	−	31.5810i	0.796070	−	1.23871i
$651$	−9.25987	+	6.45475i	−0.362923	+	0.252981i
$652$	−3.34109	+	3.85582i	−0.130847	+	0.151006i
$653$	−2.23383	+	15.5366i	−0.0874165	+	0.607995i	0.898275	+	0.439434i	$0.144821\pi$
$653$	−2.23383	+	15.5366i	−0.0874165	+	0.607995i	−0.985691	+	0.168561i	$0.946088\pi$
$654$	−1.34994	−	2.95596i	−0.0527870	−	0.115587i
$655$	−2.55586	+	8.70447i	−0.0998658	+	0.340112i
$656$	1.67487	−	5.70410i	0.0653929	−	0.222708i
$657$	10.9330	−	4.99295i	0.426538	−	0.194793i
$658$	26.9492	+	21.6347i	1.05059	+	0.843407i
$659$	38.1584	+	33.0645i	1.48644	+	1.28801i	0.861969	+	0.506961i	$0.169231\pi$
$659$	38.1584	+	33.0645i	1.48644	+	1.28801i	0.624472	+	0.781047i	$0.285314\pi$
$660$	5.95946	−	13.0494i	0.231972	−	0.507947i
$661$	4.62430	+	2.97186i	0.179865	+	0.115592i	0.627475	−	0.778637i	$-0.284088\pi$
$661$	4.62430	+	2.97186i	0.179865	+	0.115592i	−0.447610	+	0.894229i	$0.647725\pi$
$662$	4.64921	+	32.3360i	0.180697	+	1.25677i
$663$	−27.2145	+	17.4897i	−1.05692	+	0.679243i
$664$	−7.71313	−	8.90143i	−0.299328	−	0.345442i
$665$	21.4186	+	5.42445i	0.830578	+	0.210351i
$666$			6.18707i			0.239744i
$667$	−8.67287	+	7.61347i	−0.335815	+	0.294795i
$668$		−	17.0076i		−	0.658044i
$669$	−6.07145	+	1.78274i	−0.234736	+	0.0689246i
$670$	22.0679	−	19.1219i	0.852557	−	0.738745i
$671$	−6.10807	−	9.50435i	−0.235800	−	0.366911i
$672$	−2.44623	−	1.00795i	−0.0943654	−	0.0388824i
$673$	−19.7699	−	12.7054i	−0.762075	−	0.489756i	0.100966	−	0.994890i	$-0.467807\pi$
$673$	−19.7699	−	12.7054i	−0.762075	−	0.489756i	−0.863041	+	0.505134i	$0.831443\pi$
$674$	−2.88480	−	1.31744i	−0.111118	−	0.0507460i
$675$	−5.05428	−	4.37956i	−0.194539	−	0.168569i
$676$	2.63412	−	18.3207i	0.101312	−	0.704643i
$677$	−15.4554	−	33.8426i	−0.594000	−	1.30068i	−0.932995	−	0.359890i	$-0.882814\pi$
$677$	−15.4554	−	33.8426i	−0.594000	−	1.30068i	0.338995	−	0.940788i	$-0.389913\pi$
$678$	−2.63517	−	0.773756i	−0.101203	−	0.0297159i
$679$	−0.466922	−	0.499647i	−0.0179188	−	0.0191747i
$680$	−8.18470	−	17.9220i	−0.313869	−	0.687277i
$681$	−12.0073	−	1.72638i	−0.460119	−	0.0661551i
$682$	11.7235	−	13.5297i	0.448918	−	0.518078i
$683$	−11.5204	+	25.2261i	−0.440816	+	0.965252i	0.550632	+	0.834748i	$0.314387\pi$
$683$	−11.5204	+	25.2261i	−0.440816	+	0.965252i	−0.991448	+	0.130504i	$0.958341\pi$
$684$	−2.05496	−	1.32064i	−0.0785732	−	0.0504959i
$685$	−31.1520	+	4.47897i	−1.19025	+	0.171133i
$686$	9.53886	+	15.8748i	0.364195	+	0.606104i
$687$	3.42599	−	2.96864i	0.130710	−	0.113261i
$688$	3.32330	+	11.3181i	0.126699	+	0.431499i
$689$	−46.6761			−1.77822
$690$	10.6568	−	12.4600i	0.405699	−	0.474342i
$691$		−	23.7105i		−	0.901990i	−0.892526	−	0.450995i	$-0.851069\pi$
$691$		−	23.7105i		−	0.901990i	0.892526	−	0.450995i	$-0.148931\pi$
$692$	−4.83190	−	16.4559i	−0.183681	−	0.625560i
$693$	10.9221	−	1.99150i	0.414896	−	0.0756507i
$694$	24.0584	−	15.4614i	0.913245	−	0.586907i
$695$	29.7137	−	4.27219i	1.12711	−	0.162053i
$696$	−1.30098	+	2.02436i	−0.0493135	+	0.0767333i
$697$	31.1649	+	14.2325i	1.18046	+	0.539096i
$698$	20.6249	+	17.8716i	0.780664	+	0.676449i
$699$	12.2986	+	1.76827i	0.465175	+	0.0668820i
$700$	−1.85877	+	17.5963i	−0.0702549	+	0.665076i
$701$	9.34579	−	31.8289i	0.352986	−	1.20216i	−0.571391	−	0.820678i	$-0.693596\pi$
$701$	9.34579	−	31.8289i	0.352986	−	1.20216i	0.924377	−	0.381481i	$-0.124586\pi$
$702$	−5.38592	−	1.58145i	−0.203278	−	0.0596879i
$703$	13.7476	−	6.27831i	0.518500	−	0.236791i
$704$	4.15351	+	0.597185i	0.156541	+	0.0225073i
$705$	−29.2432	+	33.7485i	−1.10136	+	1.27104i
$706$	−27.7764	−	12.6851i	−1.04538	−	0.477409i
$707$	−11.7805	+	5.92425i	−0.443050	+	0.222804i
$708$	−1.86941	−	13.0021i	−0.0702569	−	0.488647i
$709$	−10.3581	−	16.1176i	−0.389008	−	0.605308i	0.590422	−	0.807095i	$-0.298962\pi$
$709$	−10.3581	−	16.1176i	−0.389008	−	0.605308i	−0.979429	+	0.201787i	$0.935325\pi$
$710$	−11.4668	−	13.2333i	−0.430340	−	0.496639i
$711$	1.54907	+	5.27564i	0.0580946	+	0.197852i
$712$	−2.94385			−0.110326
$713$	17.1408	−	11.1724i	0.641928	−	0.418410i
$714$	7.75609	−	13.1276i	0.290264	−	0.491290i
$715$	−77.2653	+	22.6871i	−2.88956	+	0.848451i
$716$	−16.2749	−	18.7822i	−0.608222	−	0.701925i
$717$	16.2868	+	25.3427i	0.608241	+	0.946441i
$718$	−13.6865	+	1.96782i	−0.510774	+	0.0734382i
$719$	−16.0956	+	25.0453i	−0.600266	+	0.934032i	0.399584	+	0.916697i	$0.369155\pi$
$719$	−16.0956	+	25.0453i	−0.600266	+	0.934032i	−0.999850	+	0.0173354i	$0.994482\pi$
$720$	1.42020	−	3.10979i	0.0529275	−	0.115895i
$721$	−24.5438	+	8.21958i	−0.914059	+	0.306113i
$722$	1.85480	−	12.9004i	0.0690285	−	0.480103i
$723$	10.7556	−	4.91192i	0.400005	−	0.182676i
$724$	−9.14174	−	2.68426i	−0.339750	−	0.0997596i
$725$	15.4413	+	4.53398i	0.573476	+	0.168388i
$726$	−6.01112	+	2.74519i	−0.223094	+	0.101883i
$727$	3.08269	−	21.4406i	0.114331	−	0.795187i	−0.849293	−	0.527922i	$-0.822971\pi$
$727$	3.08269	−	21.4406i	0.114331	−	0.795187i	0.963623	−	0.267264i	$-0.0861197\pi$
$728$	4.71621	+	14.0827i	0.174794	+	0.521938i
$729$	−0.415415	+	0.909632i	−0.0153857	+	0.0336901i
$730$	22.2152	−	34.5674i	0.822220	−	1.27940i
$731$	−67.2890	+	9.67469i	−2.48877	+	0.357831i
$732$	−1.45561	−	2.26498i	−0.0538009	−	0.0837159i
$733$	−21.0314	−	24.2715i	−0.776812	−	0.896489i	0.220063	−	0.975486i	$-0.429374\pi$
$733$	−21.0314	−	24.2715i	−0.776812	−	0.896489i	−0.996875	+	0.0789970i	$0.974828\pi$
$734$	−22.4054	+	6.57882i	−0.826998	+	0.242828i
$735$	−20.9612	+	11.5469i	−0.773164	+	0.425913i
$736$	4.37519	+	1.96411i	0.161272	+	0.0723981i
$737$	−35.8407			−1.32021
$738$	1.67487	+	5.70410i	0.0616530	+	0.209971i
$739$	14.4467	+	16.6724i	0.531431	+	0.613304i	0.956456	−	0.291878i	$-0.0942801\pi$
$739$	14.4467	+	16.6724i	0.531431	+	0.613304i	−0.425025	+	0.905182i	$0.639735\pi$
$740$	11.4356	+	17.7942i	0.420382	+	0.654127i
$741$	1.95139	+	13.5722i	0.0716861	+	0.498588i
$742$	19.6548	−	9.88414i	0.721550	−	0.362858i
$743$	−13.8678	−	6.33320i	−0.508759	−	0.232342i	0.144461	−	0.989510i	$-0.453855\pi$
$743$	−13.8678	−	6.33320i	−0.508759	−	0.232342i	−0.653220	+	0.757168i	$0.726582\pi$
$744$	2.79383	−	3.22425i	0.102427	−	0.118207i
$745$	−38.8154	−	5.58081i	−1.42209	−	0.204465i
$746$	−30.1947	+	13.7895i	−1.10551	+	0.504868i
$747$	11.3012	+	3.31832i	0.413488	+	0.121411i
$748$	−6.81319	+	23.2036i	−0.249115	+	0.848408i
$749$	−1.44846	−	0.153007i	−0.0529255	−	0.00559074i
$750$	−5.71131	−	0.821162i	−0.208547	−	0.0299846i
$751$	37.6621	+	32.6344i	1.37431	+	1.19085i	0.959761	+	0.280819i	$0.0906060\pi$
$751$	37.6621	+	32.6344i	1.37431	+	1.19085i	0.414549	+	0.910027i	$0.363939\pi$
$752$	−11.8816	−	5.42616i	−0.433279	−	0.197872i
$753$	2.14657	−	3.34013i	0.0782254	−	0.121721i
$754$	13.3702	−	1.92234i	0.486912	−	0.0700074i
$755$	6.78690	−	4.36167i	0.247001	−	0.158738i
$756$	2.60284	−	0.474593i	0.0946643	−	0.0172608i
$757$	5.60849	+	19.1008i	0.203844	+	0.694230i	0.996426	+	0.0844646i	$0.0269180\pi$
$757$	5.60849	+	19.1008i	0.203844	+	0.694230i	−0.792582	+	0.609765i	$0.791264\pi$
$758$		−	14.1569i		−	0.514203i
$759$	−19.9007	+	2.99228i	−0.722349	+	0.108613i
$760$	−8.35106			−0.302925
$761$	6.57568	+	22.3947i	0.238368	+	0.811808i	0.988591	+	0.150623i	$0.0481280\pi$
$761$	6.57568	+	22.3947i	0.238368	+	0.811808i	−0.750223	+	0.661185i	$0.770054\pi$
$762$	−7.76287	+	6.72656i	−0.281219	+	0.243678i
$763$	−0.322817	−	8.59164i	−0.0116868	−	0.311038i
$764$	−8.53795	+	1.22757i	−0.308892	+	0.0444120i
$765$	16.5748	+	10.6520i	0.599262	+	0.385123i
$766$	−1.14207	+	2.50078i	−0.0412646	+	0.0903568i
$767$	−48.2861	+	55.7251i	−1.74351	+	2.01212i
$768$	0.989821	+	0.142315i	0.0357171	+	0.00513534i
$769$	19.6926	+	43.1207i	0.710132	+	1.55497i	0.827238	+	0.561852i	$0.189911\pi$
$769$	19.6926	+	43.1207i	0.710132	+	1.55497i	−0.117106	+	0.993119i	$0.537362\pi$
$770$	27.7313	−	25.9150i	0.999367	−	0.933912i
$771$	−20.3932	−	5.98799i	−0.734444	−	0.215652i
$772$	−2.58679	−	5.66428i	−0.0931007	−	0.203862i
$773$	3.66820	−	25.5129i	0.131936	−	0.917636i	−0.811091	−	0.584920i	$-0.801126\pi$
$773$	3.66820	−	25.5129i	0.131936	−	0.917636i	0.943027	−	0.332716i	$-0.107965\pi$
$774$	−8.91476	−	7.72469i	−0.320435	−	0.277658i
$775$	−25.9536	−	11.8526i	−0.932282	−	0.425759i
$776$	0.217442	+	0.139742i	0.00780573	+	0.00501644i
$777$	−6.23624	+	15.1350i	−0.223724	+	0.542965i
$778$	−0.793194	−	1.23423i	−0.0284374	−	0.0442495i
$779$	10.9749	−	9.50977i	0.393215	−	0.340723i
$780$	−18.4130	+	5.40656i	−0.659293	+	0.193586i
$781$			21.4924i			0.769058i
$782$	−14.7925	+	23.3470i	−0.528980	+	0.834888i
$783$		−	2.40637i		−	0.0859965i
$784$	−4.96808	−	4.93134i	−0.177432	−	0.176119i
$785$	−21.7376	−	25.0865i	−0.775847	−	0.895375i
$786$	2.23235	−	1.43464i	0.0796251	−	0.0511720i
$787$	−5.07560	−	35.3016i	−0.180926	−	1.25837i	−0.854580	−	0.519319i	$-0.826185\pi$
$787$	−5.07560	−	35.3016i	−0.180926	−	1.25837i	0.673654	−	0.739046i	$-0.264724\pi$
$788$	−8.59058	−	5.52083i	−0.306027	−	0.196671i
$789$	12.0830	−	26.4581i	0.430166	−	0.941932i
$790$	14.2062	+	12.3097i	0.505433	+	0.437960i
$791$	−5.66633	−	4.54890i	−0.201471	−	0.161740i
$792$	−3.81702	+	1.74317i	−0.135632	+	0.0619410i
$793$	−4.25786	+	14.5010i	−0.151201	+	0.514944i
$794$	8.29081	−	28.2359i	0.294230	−	1.00205i
$795$	11.8093	+	25.8588i	0.418833	+	0.917117i
$796$	2.06056	−	14.3315i	0.0730348	−	0.507968i
$797$	3.78252	−	4.36526i	0.133984	−	0.154626i	−0.684793	−	0.728738i	$-0.740107\pi$
$797$	3.78252	−	4.36526i	0.133984	−	0.154626i	0.818777	+	0.574112i	$0.194653\pi$
$798$	−3.69576	−	5.30188i	−0.130828	−	0.187684i
$799$	40.6981	−	63.3275i	1.43980	−	2.24037i
$800$	−0.951769	−	6.61970i	−0.0336501	−	0.234042i
$801$	2.47653	−	1.59157i	0.0875038	−	0.0562353i
$802$	−20.8269	+	18.0466i	−0.735422	+	0.637247i
$803$	−48.3922	+	14.2092i	−1.70772	+	0.501433i
$804$	−8.54117			−0.301224
$805$	38.6281	−	19.7384i	1.36146	−	0.695687i
$806$	−23.9480			−0.843532
$807$	−14.6151	+	4.29139i	−0.514477	+	0.151064i
$808$	3.76660	−	3.26377i	0.132508	−	0.114819i
$809$	−31.6096	+	20.3142i	−1.11133	+	0.714211i	−0.961583	−	0.274513i	$-0.911483\pi$
$809$	−31.6096	+	20.3142i	−1.11133	+	0.714211i	−0.149751	+	0.988724i	$0.547847\pi$
$810$	0.486537	+	3.38394i	0.0170952	+	0.118900i
$811$	−0.0768858	+	0.119637i	−0.00269983	+	0.00420101i	−0.842601	−	0.538539i	$-0.818977\pi$
$811$	−0.0768858	+	0.119637i	−0.00269983	+	0.00420101i	0.839901	+	0.542740i	$0.182613\pi$
$812$	−5.22295	+	3.64074i	−0.183289	+	0.127765i
$813$	9.63471	−	11.1190i	0.337904	−	0.389962i
$814$	3.69483	−	25.6981i	0.129504	−	0.900718i
$815$	−7.24581	−	15.8661i	−0.253810	−	0.555765i
$816$	−1.62365	+	5.52964i	−0.0568391	+	0.193576i
$817$	−8.11792	+	27.6471i	−0.284010	+	0.967249i
$818$	−18.5766	+	8.48363i	−0.649514	+	0.296623i
$819$	−11.5812	−	9.29731i	−0.404679	−	0.324874i
$820$	15.3599	+	13.3094i	0.536392	+	0.464786i
$821$	19.5197	−	42.7422i	0.681242	−	1.49171i	−0.180079	−	0.983652i	$-0.557635\pi$
$821$	19.5197	−	42.7422i	0.681242	−	1.49171i	0.861322	−	0.508060i	$-0.169637\pi$
$822$	7.74443	+	4.97704i	0.270118	+	0.173594i
$823$	−3.71772	−	25.8573i	−0.129592	−	0.901330i	−0.946072	−	0.323957i	$-0.894987\pi$
$823$	−3.71772	−	25.8573i	−0.129592	−	0.901330i	0.816480	−	0.577373i	$-0.195922\pi$
$824$	8.23004	−	5.28913i	0.286707	−	0.184255i
$825$	18.3776	+	21.2089i	0.639826	+	0.738399i
$826$	8.53237	−	33.6903i	0.296879	−	1.17224i
$827$			0.195469i			0.00679712i	0.999994	+	0.00339856i	$0.00108180\pi$
$827$			0.195469i			0.00679712i	−0.999994	+	0.00339856i	$0.998918\pi$
$828$	−4.74252	+	0.713089i	−0.164814	+	0.0247816i
$829$		−	54.0371i		−	1.87679i	−0.345570	−	0.938393i	$-0.612314\pi$
$829$		−	54.0371i		−	1.87679i	0.345570	−	0.938393i	$-0.387686\pi$
$830$	38.6357	−	11.3445i	1.34107	−	0.393773i
$831$	−21.6657	+	18.7734i	−0.751574	+	0.651243i
$832$	−3.03478	−	4.72221i	−0.105212	−	0.163713i
$833$	32.2052	−	24.2955i	1.11584	−	0.841790i
$834$	−7.38689	−	4.74727i	−0.255787	−	0.164384i
$835$	52.8902	+	24.1541i	1.83034	+	0.835888i
$836$	7.74662	+	6.71248i	0.267922	+	0.232156i
$837$	−0.607157	+	4.22287i	−0.0209864	+	0.145964i
$838$	2.95864	+	6.47852i	0.102205	+	0.223797i
$839$	−11.6717	−	3.42713i	−0.402953	−	0.118318i	0.0739749	−	0.997260i	$-0.476432\pi$
$839$	−11.6717	−	3.42713i	−0.402953	−	0.118318i	−0.476928	+	0.878942i	$0.658250\pi$
$840$	6.60863	−	6.17579i	0.228019	−	0.213085i
$841$	−9.64154	−	21.1120i	−0.332467	−	0.728001i
$842$	15.2988	+	2.19963i	0.527231	+	0.0758044i
$843$	4.14763	−	4.78662i	0.142852	−	0.164860i
$844$	6.31821	−	13.8349i	0.217482	−	0.476218i
$845$	53.2327	+	34.2106i	1.83126	+	1.17688i
$846$	12.9291	−	1.85892i	0.444511	−	0.0639110i
$847$	−17.4716	+	0.656467i	−0.600331	+	0.0225565i
$848$	−6.28427	+	5.44535i	−0.215803	+	0.186994i
$849$	−2.96269	−	10.0900i	−0.101679	−	0.346288i
$850$	38.5422			1.32199
$851$	12.1521	−	27.0696i	0.416569	−	0.927934i
$852$			5.12184i			0.175471i
$853$	−10.0861	−	34.3502i	−0.345342	−	1.17613i	−0.930832	−	0.365447i	$-0.880916\pi$
$853$	−10.0861	−	34.3502i	−0.345342	−	1.17613i	0.585490	−	0.810680i	$-0.300902\pi$
$854$	−1.27778	−	7.00783i	−0.0437249	−	0.239803i
$855$	7.02536	−	4.51492i	0.240262	−	0.154407i
$856$	0.544908	−	0.0783459i	0.0186246	−	0.00267781i
$857$	−8.44220	+	13.1363i	−0.288380	+	0.448728i	−0.954973	−	0.296694i	$-0.904116\pi$
$857$	−8.44220	+	13.1363i	−0.288380	+	0.448728i	0.666592	+	0.745422i	$0.267752\pi$
$858$	21.4261	+	9.78496i	0.731474	+	0.334053i
$859$	24.1108	+	20.8921i	0.822650	+	0.712830i	0.960698	−	0.277595i	$-0.0895375\pi$
$859$	24.1108	+	20.8921i	0.822650	+	0.712830i	−0.138048	+	0.990425i	$0.544083\pi$
$860$	−39.9167	−	5.73915i	−1.36115	−	0.195704i
$861$	−1.65230	+	15.6417i	−0.0563103	+	0.533069i
$862$	3.84230	−	13.0857i	0.130869	−	0.445699i
$863$	49.0974	+	14.4163i	1.67130	+	0.490737i	0.974095	−	0.226140i	$-0.0726106\pi$
$863$	49.0974	+	14.4163i	1.67130	+	0.490737i	0.697200	+	0.716876i	$0.254429\pi$
$864$	−0.909632	+	0.415415i	−0.0309463	+	0.0141327i
$865$	58.0368	+	8.34443i	1.97331	+	0.283719i
$866$	2.90705	−	3.35491i	0.0987856	−	0.114005i
$867$	−14.7480	−	6.73518i	−0.500868	−	0.228739i
$868$	10.0842	−	5.07123i	0.342281	−	0.172129i
$869$	−3.28354	−	22.8375i	−0.111386	−	0.774710i
$870$	−4.44771	−	6.92077i	−0.150791	−	0.234636i
$871$	31.3967	+	36.2337i	1.06384	+	1.22773i
$872$	0.915526	+	3.11799i	0.0310036	+	0.105589i
$873$	−0.258474			−0.00874803
$874$	6.39693	+	9.81421i	0.216380	+	0.331971i
$875$	−13.1435	−	7.76545i	−0.444331	−	0.262520i
$876$	−11.5323	+	3.38619i	−0.389641	+	0.114409i
$877$	14.6276	+	16.8812i	0.493940	+	0.570037i	0.946914	−	0.321487i	$-0.104182\pi$
$877$	14.6276	+	16.8812i	0.493940	+	0.570037i	−0.452974	+	0.891524i	$0.649637\pi$
$878$	−16.3149	−	25.3865i	−0.550602	−	0.856753i
$879$	7.82474	−	1.12503i	0.263922	−	0.0379462i
$880$	−7.75592	+	12.0684i	−0.261452	+	0.406827i
$881$	10.0245	−	21.9506i	0.337734	−	0.739533i	−0.662219	−	0.749311i	$-0.730385\pi$
$881$	10.0245	−	21.9506i	0.337734	−	0.739533i	0.999952	+	0.00977738i	$0.00311229\pi$
$882$	6.84550	+	1.46256i	0.230500	+	0.0492469i
$883$	1.46605	−	10.1966i	0.0493364	−	0.343142i	−0.950170	−	0.311732i	$-0.899091\pi$
$883$	1.46605	−	10.1966i	0.0493364	−	0.343142i	0.999507	−	0.0314104i	$-0.00999989\pi$
$884$	29.4265	−	13.4386i	0.989721	−	0.451990i
$885$	43.0886	+	12.6520i	1.44841	+	0.425291i
$886$	0.850921	+	0.249853i	0.0285872	+	0.00839397i
$887$	21.1039	−	9.63783i	0.708600	−	0.323607i	−0.0283086	−	0.999599i	$-0.509012\pi$
$887$	21.1039	−	9.63783i	0.708600	−	0.323607i	0.736909	+	0.675992i	$0.236285\pi$
$888$	0.880512	−	6.12410i	0.0295481	−	0.205511i
$889$	−25.7698	+	8.63016i	−0.864291	+	0.289446i
$890$	4.18085	−	9.15478i	0.140142	−	0.306869i
$891$	2.26865	−	3.53009i	0.0760026	−	0.118262i
$892$	6.26336	−	0.900535i	0.209713	−	0.0301522i
$893$	−17.2502	−	26.8419i	−0.577257	−	0.898230i
$894$	7.51156	+	8.66880i	0.251224	+	0.289928i
$895$	81.5224	−	23.9371i	2.72499	−	0.800130i
$896$	2.27789	+	1.34582i	0.0760988	+	0.0449608i
$897$	20.4583	+	17.4977i	0.683082	+	0.584231i
$898$	−4.42350			−0.147614
$899$	−2.89234	−	9.85041i	−0.0964650	−	0.328530i
$900$	4.37956	+	5.05428i	0.145985	+	0.168476i
$901$	−25.9084	−	40.3143i	−0.863134	−	1.34306i
$902$	−3.55021	−	24.6923i	−0.118209	−	0.822162i
$903$	−14.0215	−	27.8820i	−0.466606	−	0.927854i
$904$	2.49823	+	1.14090i	0.0830900	+	0.0379459i
$905$	21.3305	−	24.6168i	0.709051	−	0.818289i
$906$	−2.33580	−	0.335837i	−0.0776017	−	0.0111574i
$907$	−4.99960	+	2.28324i	−0.166009	+	0.0758138i	−0.496686	−	0.867930i	$-0.665450\pi$
$907$	−4.99960	+	2.28324i	−0.166009	+	0.0758138i	0.330677	+	0.943744i	$0.392723\pi$
$908$	11.6394	+	3.41762i	0.386265	+	0.113418i
$909$	−1.40413	+	4.78204i	−0.0465721	+	0.158610i
$910$	−50.4921	−	5.33369i	−1.67380	−	0.176810i
$911$	−38.3692	−	5.51666i	−1.27123	−	0.182775i	−0.526519	−	0.850164i	$-0.676503\pi$
$911$	−38.3692	−	5.51666i	−1.27123	−	0.182775i	−0.744710	+	0.667389i	$0.767412\pi$
$912$	1.84609	+	1.59965i	0.0611302	+	0.0529697i
$913$	−44.9579	−	20.5316i	−1.48789	−	0.679497i
$914$	18.8636	−	29.3523i	0.623952	−	0.970889i
$915$	9.11086	−	1.30994i	0.301196	−	0.0433054i
$916$	−3.81360	+	2.45085i	−0.126005	+	0.0809784i
$917$	6.90687	−	1.25938i	0.228085	−	0.0415883i
$918$	−1.62365	−	5.52964i	−0.0535884	−	0.182505i
$919$			25.1981i			0.831208i	0.909546	+	0.415604i	$0.136430\pi$
$919$			25.1981i			0.831208i	−0.909546	+	0.415604i	$0.863570\pi$
$920$	−12.3216	+	10.8165i	−0.406231	+	0.356610i
$921$	−13.9511			−0.459706
$922$	0.798369	+	2.71899i	0.0262929	+	0.0895453i
$923$	21.7281	−	18.8275i	0.715190	−	0.619715i
$924$	−11.0943	+	0.416852i	−0.364977	+	0.0137134i
$925$	−40.9565	+	5.88866i	−1.34664	+	0.193618i
$926$	2.38537	+	1.53299i	0.0783882	+	0.0503770i
$927$	−4.06403	+	8.89899i	−0.133480	+	0.292281i
$928$	1.57583	−	1.81861i	0.0517293	−	0.0596988i
$929$	−57.4585	−	8.26129i	−1.88515	−	0.271044i	−0.899134	−	0.437674i	$-0.855802\pi$
$929$	−57.4585	−	8.26129i	−1.88515	−	0.271044i	−0.986019	+	0.166630i	$0.946711\pi$
$930$	6.05897	+	13.2673i	0.198682	+	0.435052i
$931$	−3.69667	−	16.6947i	−0.121153	−	0.547148i
$932$	−11.9217	−	3.50054i	−0.390509	−	0.114664i
$933$	9.34605	+	20.4650i	0.305976	+	0.669994i
$934$	−1.65397	+	11.5036i	−0.0541195	+	0.376409i
$935$	−62.4824	−	54.1413i	−2.04339	−	1.77061i
$936$	5.10604	+	2.33185i	0.166896	+	0.0762188i
$937$	13.2657	+	8.52534i	0.433371	+	0.278511i	0.739084	−	0.673613i	$-0.235259\pi$
$937$	13.2657	+	8.52534i	0.433371	+	0.278511i	−0.305713	+	0.952124i	$0.598895\pi$
$938$	−20.8937	−	8.60905i	−0.682202	−	0.281095i
$939$	2.33610	+	3.63505i	0.0762359	+	0.118625i
$940$	33.7485	−	29.2432i	1.10075	−	0.953809i
$941$	44.1808	−	12.9727i	1.44025	−	0.422897i	0.533948	−	0.845517i	$-0.320708\pi$
$941$	44.1808	−	12.9727i	1.44025	−	0.422897i	0.906307	+	0.422621i	$0.138890\pi$
$942$			9.70948i			0.316352i
$943$	3.87560	−	28.2461i	0.126207	−	0.919821i
$944$			13.1358i			0.427533i
$945$	−2.22065	+	8.76830i	−0.0722378	+	0.285233i
$946$	32.4145	+	37.4084i	1.05389	+	1.21625i
$947$	−26.7278	+	17.1769i	−0.868537	+	0.558175i	−0.897305	−	0.441411i	$-0.854478\pi$
$947$	−26.7278	+	17.1769i	−0.868537	+	0.558175i	0.0287681	+	0.999586i	$0.490842\pi$
$948$	−0.782499	−	5.44240i	−0.0254144	−	0.176761i
$949$	56.7570	+	36.4755i	1.84241	+	1.18405i
$950$	6.78639	−	14.8601i	0.220180	−	0.482126i
$951$	−20.3526	−	17.6357i	−0.659979	−	0.571875i
$952$	−9.54540	+	11.8902i	−0.309368	+	0.385364i
$953$	4.70861	−	2.15035i	0.152527	−	0.0696567i	−0.337689	−	0.941258i	$-0.609645\pi$
$953$	4.70861	−	2.15035i	0.152527	−	0.0696567i	0.490216	+	0.871601i	$0.336918\pi$
$954$	2.34269	−	7.97845i	0.0758472	−	0.258312i
$955$	8.30806	−	28.2947i	0.268843	−	0.915594i
$956$	−12.5144	−	27.4026i	−0.404743	−	0.886264i
$957$	−1.43705	+	9.99487i	−0.0464531	+	0.323088i
$958$	6.66986	−	7.69743i	0.215494	−	0.248693i
$959$	13.9281	+	19.9810i	0.449761	+	0.645219i
$960$	−1.84831	+	2.87603i	−0.0596539	+	0.0928233i
$961$	−1.82145	−	12.6684i	−0.0587564	−	0.408659i
$962$	−29.2166	+	18.7764i	−0.941982	+	0.605375i
$963$	−0.416049	+	0.360508i	−0.0134070	+	0.0116172i
$964$	−11.3452	+	3.33124i	−0.365403	+	0.107292i
$965$	21.2885			0.685301
$966$	−12.3201	−	3.03583i	−0.396391	−	0.0976762i
$967$	26.2525			0.844222			0.422111	−	0.906544i	$-0.361289\pi$
$967$	26.2525			0.844222			0.422111	+	0.906544i	$0.361289\pi$
$968$	6.34062	−	1.86177i	0.203795	−	0.0598397i
$969$	−10.6392	+	9.21891i	−0.341780	+	0.296154i
$970$	−0.743378	+	0.477740i	−0.0238684	+	0.0153393i
$971$	−4.68660	−	32.5960i	−0.150400	−	1.04606i	−0.915550	−	0.402204i	$-0.868244\pi$
$971$	−4.68660	−	32.5960i	−0.150400	−	1.04606i	0.765150	−	0.643852i	$-0.222665\pi$
$972$	0.540641	−	0.841254i	0.0173411	−	0.0269832i
$973$	−13.2850	−	19.0585i	−0.425899	−	0.610987i
$974$	23.3557	−	26.9539i	0.748363	−	0.863657i
$975$	5.34256	−	37.1583i	0.171099	−	1.19002i
$976$	1.11846	+	2.44908i	0.0358009	+	0.0783930i
$977$	8.65037	−	29.4605i	0.276750	−	0.942524i	−0.697412	−	0.716671i	$-0.745665\pi$
$977$	8.65037	−	29.4605i	0.276750	−	0.942524i	0.974161	−	0.225853i	$-0.0725168\pi$
$978$	−1.43739	+	4.89531i	−0.0459628	+	0.156535i
$979$	−11.2368	+	5.13165i	−0.359128	+	0.164008i
$980$	22.3911	−	8.44625i	0.715258	−	0.269806i
$981$	−2.45590	−	2.12805i	−0.0784110	−	0.0679435i
$982$	−12.0823	+	26.4566i	−0.385562	+	0.844263i
$983$	35.8954	+	23.0686i	1.14489	+	0.735774i	0.968615	−	0.248568i	$-0.0799599\pi$
$983$	35.8954	+	23.0686i	1.14489	+	0.735774i	0.176272	+	0.984342i	$0.443596\pi$
$984$	−0.846049	−	5.88440i	−0.0269711	−	0.187588i
$985$	29.3689	−	18.8743i	0.935772	−	0.601384i
$986$	9.08166	+	10.4808i	0.289219	+	0.333777i
$987$	33.5012	+	8.48448i	1.06635	+	0.270064i
$988$		−	13.7118i		−	0.436230i
$989$	23.8316	+	51.3065i	0.757801	+	1.63145i
$990$		−	14.3458i		−	0.455939i
$991$	26.7326	−	7.84941i	0.849191	−	0.249345i	0.171949	−	0.985106i	$-0.444993\pi$
$991$	26.7326	−	7.84941i	0.849191	−	0.249345i	0.677241	+	0.735761i	$0.263175\pi$
$992$	−3.22425	+	2.79383i	−0.102370	+	0.0887042i
$993$	17.6619	+	27.4825i	0.560484	+	0.872130i
$994$	−5.16254	+	12.5292i	−0.163746	+	0.397402i
$995$	41.6417	+	26.7615i	1.32013	+	0.848397i
$996$	−10.7139	−	4.89287i	−0.339483	−	0.155037i
$997$	18.8972	+	16.3745i	0.598479	+	0.518585i	0.900580	−	0.434691i	$-0.143142\pi$
$997$	18.8972	+	16.3745i	0.598479	+	0.518585i	−0.302101	+	0.953276i	$0.597688\pi$
$998$	−3.74822	+	26.0694i	−0.118648	+	0.825214i
$999$	2.57020	+	5.62796i	0.0813176	+	0.178061i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.s.a.727.8	yes	160
7.6	odd	2	inner	966.2.s.a.727.9	yes	160
23.5	odd	22	inner	966.2.s.a.97.9	yes	160
161.97	even	22	inner	966.2.s.a.97.8	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.a.97.8	✓	160	161.97	even	22	inner
966.2.s.a.97.9	yes	160	23.5	odd	22	inner
966.2.s.a.727.8	yes	160	1.1	even	1	trivial
966.2.s.a.727.9	yes	160	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 + 0.281733i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.486537 + 3.38394i) q^{5} +(0.540641 - 0.841254i) q^{6} +(2.17047 - 1.51296i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.959493 + 0.281733i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(0.841254 - 0.540641i) q^{4} +(0.486537 + 3.38394i) q^{5} +(0.540641 - 0.841254i) q^{6} +(2.17047 - 1.51296i) q^{7} +(-0.654861 + 0.755750i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-1.42020 - 3.10979i) q^{10} +(-1.18221 + 4.02625i) q^{11} +(-0.281733 + 0.959493i) q^{12} +(5.10604 - 2.33185i) q^{13} +(-1.65630 + 2.06317i) q^{14} +(-2.58371 - 2.23880i) q^{15} +(0.415415 - 0.909632i) q^{16} +(4.84822 + 3.11576i) q^{17} +(0.142315 + 0.989821i) q^{18} +(2.05496 - 1.32064i) q^{19} +(2.23880 + 2.58371i) q^{20} +(-0.649553 + 2.56478i) q^{21} -4.19622i q^{22} +(1.32147 - 4.61018i) q^{23} -1.00000i q^{24} +(-6.41687 + 1.88416i) q^{25} +(-4.24225 + 3.67593i) q^{26} +(0.540641 + 0.841254i) q^{27} +(1.00795 - 2.44623i) q^{28} +(-2.02436 - 1.30098i) q^{29} +(3.10979 + 1.42020i) q^{30} +(3.22425 + 2.79383i) q^{31} +(-0.142315 + 0.989821i) q^{32} +(-1.74317 - 3.81702i) q^{33} +(-5.52964 - 1.62365i) q^{34} +(6.17579 + 6.60863i) q^{35} +(-0.415415 - 0.909632i) q^{36} +(6.12410 + 0.880512i) q^{37} +(-1.59965 + 1.84609i) q^{38} +(-2.33185 + 5.10604i) q^{39} +(-2.87603 - 1.84831i) q^{40} +(5.88440 - 0.846049i) q^{41} +(-0.0993397 - 2.64389i) q^{42} +(-8.91476 + 7.72469i) q^{43} +(1.18221 + 4.02625i) q^{44} +3.41874 q^{45} +(0.0309001 + 4.79573i) q^{46} -13.0620i q^{47} +(0.281733 + 0.959493i) q^{48} +(2.42189 - 6.56768i) q^{49} +(5.62611 - 3.61568i) q^{50} +(-5.70442 + 0.820172i) q^{51} +(3.03478 - 4.72221i) q^{52} +(-7.56384 - 3.45429i) q^{53} +(-0.755750 - 0.654861i) q^{54} +(-14.1998 - 2.04162i) q^{55} +(-0.277936 + 2.63111i) q^{56} +(-0.688197 + 2.34378i) q^{57} +(2.30889 + 0.677951i) q^{58} +(-11.9487 + 5.45679i) q^{59} +(-3.38394 - 0.486537i) q^{60} +(-1.76314 + 2.03477i) q^{61} +(-3.88076 - 1.77228i) q^{62} +(-1.18867 - 2.36370i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(10.3751 + 16.1440i) q^{65} +(2.74794 + 3.17130i) q^{66} +(2.40633 + 8.19519i) q^{67} +5.76308 q^{68} +(2.02033 + 4.34951i) q^{69} +(-7.78749 - 4.60101i) q^{70} +(4.91437 - 1.44299i) q^{71} +(0.654861 + 0.755750i) q^{72} +(6.49806 + 10.1112i) q^{73} +(-6.12410 + 0.880512i) q^{74} +(3.61568 - 5.62611i) q^{75} +(1.01475 - 2.22199i) q^{76} +(3.52560 + 10.5275i) q^{77} +(0.798856 - 5.55616i) q^{78} +(-5.00149 + 2.28410i) q^{79} +(3.28025 + 0.963170i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-5.40768 + 2.46961i) q^{82} +(-1.67622 + 11.6584i) q^{83} +(0.840184 + 2.50880i) q^{84} +(-8.18470 + 17.9220i) q^{85} +(6.37736 - 9.92336i) q^{86} +(2.38187 - 0.342461i) q^{87} +(-2.26865 - 3.53009i) q^{88} +(1.92781 + 2.22482i) q^{89} +(-3.28025 + 0.963170i) q^{90} +(7.55450 - 12.7864i) q^{91} +(-1.38076 - 4.59277i) q^{92} -4.26630 q^{93} +(3.68000 + 12.5329i) q^{94} +(5.46878 + 6.31131i) q^{95} +(-0.540641 - 0.841254i) q^{96} +(-0.0367847 - 0.255843i) q^{97} +(-0.473456 + 6.98397i) q^{98} +(3.81702 + 1.74317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9}+O(q^{10}) \) 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9	\( 160 q - 16 q^{2} - 16 q^{4} - 16 q^{8} + 16 q^{9} - 22 q^{14} - 16 q^{16} + 16 q^{18} - 36 q^{23} + 96 q^{25} + 22 q^{28} - 20 q^{29} - 16 q^{32} - 50 q^{35} + 16 q^{36} + 22 q^{37} + 4 q^{39} - 110 q^{43} + 8 q^{46} - 36 q^{50} + 22 q^{51} - 88 q^{53} + 22 q^{57} + 24 q^{58} - 16 q^{64} - 72 q^{70} + 48 q^{71} + 16 q^{72} - 22 q^{74} + 24 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} + 22 q^{84} + 76 q^{85} + 44 q^{86} - 44 q^{88} + 8 q^{92} - 14 q^{95} + 22 q^{98} - 22 q^{99}+O(q^{100}) \) 160 * q - 16 * q^2 - 16 * q^4 - 16 * q^8 + 16 * q^9 - 22 * q^14 - 16 * q^16 + 16 * q^18 - 36 * q^23 + 96 * q^25 + 22 * q^28 - 20 * q^29 - 16 * q^32 - 50 * q^35 + 16 * q^36 + 22 * q^37 + 4 * q^39 - 110 * q^43 + 8 * q^46 - 36 * q^50 + 22 * q^51 - 88 * q^53 + 22 * q^57 + 24 * q^58 - 16 * q^64 - 72 * q^70 + 48 * q^71 + 16 * q^72 - 22 * q^74 + 24 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 + 22 * q^84 + 76 * q^85 + 44 * q^86 - 44 * q^88 + 8 * q^92 - 14 * q^95 + 22 * q^98 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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