LMFDB - Embedded newform 966.2.s.a.97.8

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			97.8
Character	$\chi$	$=$	966.97
Dual form			966.2.s.a.727.8

$q$-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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

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

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	−0.529325	−	0.848419i	$-0.677555\pi$
$5$	0.486537	−	3.38394i	0.217586	−	1.51334i	0.746911	−	0.664925i	$-0.231536\pi$
$6$	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	−0.921329	−	0.388785i	$-0.872895\pi$
$11$	−1.18221	−	4.02625i	−0.356451	−	1.21396i	0.564878	−	0.825175i	$-0.308923\pi$
$12$	−0.281733	−	0.959493i	−0.0813292	−	0.276982i
$13$	5.10604	+	2.33185i	1.41616	+	0.646738i	0.968852	−	0.247642i	$-0.0796556\pi$
$13$	5.10604	+	2.33185i	1.41616	+	0.646738i	0.447308	+	0.894380i	$0.352383\pi$
$14$	−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	0.201243	−	0.979541i	$-0.435502\pi$
$17$	4.84822	−	3.11576i	1.17586	−	0.755682i	0.974622	+	0.223859i	$0.0718654\pi$
$18$	0.142315	−	0.989821i	0.0335439	−	0.233303i
$19$	2.05496	+	1.32064i	0.471439	+	0.302976i	0.754703	−	0.656066i	$-0.227781\pi$
$19$	2.05496	+	1.32064i	0.471439	+	0.302976i	−0.283264	+	0.959042i	$0.591417\pi$
$20$	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	−0.714931	−	0.699195i	$-0.753542\pi$
$29$	−2.02436	+	1.30098i	−0.375915	+	0.241586i	0.339017	+	0.940780i	$0.389906\pi$
$30$	3.10979	−	1.42020i	0.567768	−	0.259291i
$31$	3.22425	−	2.79383i	0.579093	−	0.501787i	−0.315346	−	0.948977i	$-0.602121\pi$
$31$	3.22425	−	2.79383i	0.579093	−	0.501787i	0.894439	+	0.447190i	$0.147575\pi$
$32$	−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	0.380862	−	0.924632i	$-0.375627\pi$
$37$	6.12410	−	0.880512i	1.00680	−	0.144755i	0.625933	+	0.779877i	$0.284718\pi$
$38$	−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	0.585546	−	0.810640i	$-0.300880\pi$
$41$	5.88440	+	0.846049i	0.918989	+	0.132131i	0.333443	+	0.942770i	$0.391789\pi$
$42$	−0.0993397	+	2.64389i	−0.0153285	+	0.407960i
$43$	−8.91476	−	7.72469i	−1.35949	−	1.17800i	−0.965960	−	0.258692i	$-0.916709\pi$
$43$	−8.91476	−	7.72469i	−1.35949	−	1.17800i	−0.393529	−	0.919312i	$-0.628746\pi$
$44$	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	$0.401651\pi$
$47$			13.0620i			1.90529i	−0.304080	+	0.952646i	$0.598349\pi$
$48$	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	−0.860494	−	0.509460i	$-0.829845\pi$
$53$	−7.56384	+	3.45429i	−1.03897	+	0.474484i	−0.178480	+	0.983944i	$0.557118\pi$
$54$	−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	−0.562393	−	0.826870i	$-0.690119\pi$
$59$	−11.9487	−	5.45679i	−1.55559	−	0.710414i	−0.993196	+	0.116456i	$0.962847\pi$
$60$	−3.38394	+	0.486537i	−0.436865	+	0.0628117i
$61$	−1.76314	−	2.03477i	−0.225746	−	0.260525i	0.631566	−	0.775322i	$-0.282413\pi$
$61$	−1.76314	−	2.03477i	−0.225746	−	0.260525i	−0.857312	+	0.514797i	$0.827867\pi$
$62$	−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	−0.671561	−	0.740949i	$-0.734376\pi$
$67$	2.40633	−	8.19519i	0.293979	−	1.00120i	0.965541	−	0.260253i	$-0.0838059\pi$
$68$	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	0.560020	−	0.828479i	$-0.310794\pi$
$71$	4.91437	+	1.44299i	0.583228	+	0.171251i	0.0232087	+	0.999731i	$0.492612\pi$
$72$	0.654861	−	0.755750i	0.0771761	−	0.0890659i
$73$	6.49806	−	10.1112i	0.760540	−	1.18342i	−0.217714	−	0.976013i	$-0.569860\pi$
$73$	6.49806	−	10.1112i	0.760540	−	1.18342i	0.978254	−	0.207411i	$-0.0665036\pi$
$74$	−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	0.113688	−	0.993516i	$-0.463733\pi$
$79$	−5.00149	−	2.28410i	−0.562711	−	0.256982i	−0.676400	+	0.736535i	$0.736461\pi$
$80$	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	−0.847213	−	0.531253i	$-0.821721\pi$
$83$	−1.67622	−	11.6584i	−0.183989	−	1.27967i	0.663224	−	0.748421i	$-0.269188\pi$
$84$	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	−0.644320	−	0.764756i	$-0.722860\pi$
$89$	1.92781	−	2.22482i	0.204348	−	0.235830i	0.848668	+	0.528926i	$0.177405\pi$
$90$	−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	−0.991604	−	0.129314i	$-0.958722\pi$
$97$	−0.0367847	+	0.255843i	−0.00373492	+	0.0259770i	0.987869	+	0.155291i	$0.0496315\pi$
$98$	−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	−0.383306	−	0.923621i	$-0.625214\pi$
$101$	−4.93319	+	0.709286i	−0.490871	+	0.0705766i	−0.107565	+	0.994198i	$0.534305\pi$
$102$	5.24229	+	2.39407i	0.519064	+	0.237048i
$103$	−9.38679	+	2.75621i	−0.924908	+	0.271577i	−0.709303	−	0.704903i	$-0.750990\pi$
$103$	−9.38679	+	2.75621i	−0.924908	+	0.271577i	−0.215604	+	0.976481i	$0.569172\pi$
$104$	−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	−0.674739	−	0.738056i	$-0.735744\pi$
$107$	−0.416049	+	0.360508i	−0.0402209	+	0.0348516i	0.634518	+	0.772908i	$0.281198\pi$
$108$	0.909632	−	0.415415i	0.0875294	−	0.0399733i
$109$	1.75688	+	2.73376i	0.168279	+	0.261847i	0.915143	−	0.403130i	$-0.132078\pi$
$109$	1.75688	+	2.73376i	0.168279	+	0.261847i	−0.746864	+	0.664977i	$0.768441\pi$
$110$	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	−0.987848	−	0.155424i	$-0.950326\pi$
$113$	−0.773756	+	2.63517i	−0.0727888	+	0.247896i	0.915059	+	0.403320i	$0.132144\pi$
$114$			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	−0.688049	−	0.725664i	$-0.741533\pi$
$127$	−9.85567	+	2.89388i	−0.874549	+	0.256791i	−0.186500	+	0.982455i	$0.559714\pi$
$128$	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	−0.307167	−	0.951656i	$-0.599381\pi$
$131$	2.41379	−	1.10234i	0.210894	−	0.0963121i	0.518061	+	0.855343i	$0.326654\pi$
$132$	−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	$-0.871350\pi$
$137$		−	9.20582i		−	0.786507i	0.919430	−	0.393253i	$-0.128650\pi$
$138$	−3.16389	+	3.60414i	−0.269328	+	0.306805i
$139$			8.78081i			0.744779i	0.928077	+	0.372389i	$0.121461\pi$
$139$			8.78081i			0.744779i	−0.928077	+	0.372389i	$0.878539\pi$
$140$	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	−0.979361	−	0.202118i	$-0.935218\pi$
$149$	−3.23160	−	11.0058i	−0.264743	−	0.901633i	0.714618	−	0.699515i	$-0.246601\pi$
$150$	−1.88416	−	6.41687i	−0.153841	−	0.523935i
$151$	−0.980304	+	2.14657i	−0.0797760	+	0.174685i	−0.945317	−	0.326153i	$-0.894248\pi$
$151$	−0.980304	+	2.14657i	−0.0797760	+	0.174685i	0.865541	+	0.500838i	$0.166975\pi$
$152$	−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	0.172468	−	0.985015i	$-0.444826\pi$
$157$	−8.16813	−	5.24934i	−0.651888	−	0.418943i	−0.824356	+	0.566072i	$0.808462\pi$
$158$	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	0.0843361	−	0.996437i	$-0.473123\pi$
$163$	−4.89531	−	1.43739i	−0.383431	−	0.112585i	−0.467767	+	0.883852i	$0.654941\pi$
$164$	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	0.989212	+	0.146491i	$0.0467980\pi$
$167$	9.19501	+	14.3077i	0.711531	+	1.10716i	−0.277681	+	0.960673i	$0.589566\pi$
$168$	−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	0.911212	+	0.411938i	$0.135148\pi$
$173$	4.83190	+	16.4559i	0.367362	+	1.25112i	−0.543850	+	0.839183i	$0.683034\pi$
$174$	−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	0.234680	+	0.972073i	$0.424596\pi$
$179$	−3.53687	+	24.5995i	−0.264358	+	1.83865i	−0.499038	+	0.866580i	$0.666313\pi$
$180$	2.87603	+	1.84831i	0.214366	+	0.137765i
$181$	−6.23930	+	7.20054i	−0.463764	+	0.535212i	−0.938666	−	0.344826i	$-0.887938\pi$
$181$	−6.23930	+	7.20054i	−0.463764	+	0.535212i	0.474903	+	0.880038i	$0.342483\pi$
$182$	−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	−0.678537	−	0.734566i	$-0.737386\pi$
$191$	−7.84626	+	3.58327i	−0.567735	+	0.259276i	0.110801	+	0.993843i	$0.464658\pi$
$192$	0.755750	−	0.654861i	0.0545415	−	0.0472605i
$193$	0.886195	+	6.16362i	0.0637897	+	0.443667i	0.996538	+	0.0831390i	$0.0264945\pi$
$193$	0.886195	+	6.16362i	0.0637897	+	0.443667i	−0.932748	+	0.360528i	$0.882596\pi$
$194$	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	−0.998428	−	0.0560527i	$-0.982149\pi$
$197$	−4.24207	+	9.28883i	−0.302235	+	0.661802i	0.696193	+	0.717855i	$0.254876\pi$
$198$	−4.15351	+	0.597185i	−0.295177	+	0.0424401i
$199$	9.48167	+	10.9424i	0.672138	+	0.775688i	0.984709	−	0.174206i	$-0.0557358\pi$
$199$	9.48167	+	10.9424i	0.672138	+	0.775688i	−0.312571	+	0.949894i	$0.601190\pi$
$200$	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	0.901051	−	0.433714i	$-0.142797\pi$
$211$	12.7949	+	8.22281i	0.880840	+	0.566082i	−0.0202102	+	0.999796i	$0.506434\pi$
$212$	−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	−0.213261	−	0.976995i	$-0.568409\pi$
$223$	5.75594	−	2.62865i	0.385446	−	0.176027i	0.598707	+	0.800968i	$0.295681\pi$
$224$	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	−0.428175	−	0.903696i	$-0.640843\pi$
$227$	7.94394	−	9.16780i	0.527258	−	0.608488i	0.955433	+	0.295208i	$0.0953889\pi$
$228$	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	−0.956850	−	0.290583i	$-0.906151\pi$
$233$	−8.13667	+	9.39022i	−0.533051	+	0.615174i	0.423799	+	0.905756i	$0.360696\pi$
$234$	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	0.361576	+	0.932343i	$0.382239\pi$
$239$	4.28723	+	29.8183i	0.277318	+	1.92879i	−0.0842582	+	0.996444i	$0.526852\pi$
$240$	−3.10979	−	1.42020i	−0.200736	−	0.0916732i
$241$	−11.3452	+	3.33124i	−0.730807	+	0.214584i	−0.625906	−	0.779898i	$-0.715271\pi$
$241$	−11.3452	+	3.33124i	−0.730807	+	0.214584i	−0.104901	+	0.994483i	$0.533452\pi$
$242$	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	0.159282	−	0.987233i	$-0.449082\pi$
$251$	−3.80959	−	1.11860i	−0.240459	−	0.0706052i	−0.399742	+	0.916628i	$0.630900\pi$
$252$	−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	−0.271463	−	0.962449i	$-0.587508\pi$
$257$	11.4909	−	17.8801i	0.716781	−	1.11533i	0.988244	−	0.152884i	$-0.0488560\pi$
$258$	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	−0.631923	−	0.775031i	$-0.717734\pi$
$263$	−26.4581	−	12.0830i	−1.63147	−	0.745069i	−0.999551	+	0.0299615i	$0.990462\pi$
$264$	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	0.0544862	−	0.998515i	$-0.482648\pi$
$269$	13.8557	−	6.32766i	0.844794	−	0.385804i	0.790308	+	0.612710i	$0.209921\pi$
$270$	1.84831	+	2.87603i	0.112485	+	0.175029i
$271$	−14.5629	−	2.09382i	−0.884630	−	0.127191i	−0.315000	−	0.949092i	$-0.602005\pi$
$271$	−14.5629	−	2.09382i	−0.884630	−	0.127191i	−0.569630	+	0.821901i	$0.692914\pi$
$272$	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	−0.0472404	−	0.998884i	$-0.515043\pi$
$281$	−6.26913	−	0.901365i	−0.373985	−	0.0537710i	−0.326745	+	0.945113i	$0.605952\pi$
$282$	−10.9885	+	7.06187i	−0.654354	+	0.420528i
$283$	−4.36849	−	9.56567i	−0.259680	−	0.568620i	0.734219	−	0.678912i	$-0.237548\pi$
$283$	−4.36849	−	9.56567i	−0.259680	−	0.568620i	−0.993899	+	0.110293i	$0.964821\pi$
$284$	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	−0.720286	−	0.693677i	$-0.755990\pi$
$293$	−6.65028	+	4.27387i	−0.388513	+	0.249682i	0.331773	+	0.943359i	$0.392353\pi$
$294$	−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	−0.299850	−	0.953986i	$-0.596937\pi$
$307$	10.5436	−	9.13605i	0.601753	−	0.521422i	0.901603	+	0.432564i	$0.142391\pi$
$308$	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	0.918654	+	0.395063i	$0.129277\pi$
$311$	6.33844	+	21.5868i	0.359420	+	1.22407i	−0.559234	+	0.829010i	$0.688905\pi$
$312$	−2.33185	+	5.10604i	−0.132015	+	0.289072i
$313$	0.614941	+	4.27701i	0.0347585	+	0.241751i	0.999792	−	0.0203742i	$-0.00648577\pi$
$313$	0.614941	+	4.27701i	0.0347585	+	0.241751i	−0.965034	+	0.262125i	$0.915577\pi$
$314$	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	−0.539958	−	0.841692i	$-0.681560\pi$
$317$	3.83259	−	26.6563i	0.215260	−	1.49717i	0.755218	−	0.655474i	$-0.227531\pi$
$318$	−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	0.563670	+	0.826000i	$0.309389\pi$
$331$	4.64921	+	32.3360i	0.255544	+	1.77735i	−0.308127	+	0.951345i	$0.599702\pi$
$332$	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	−0.587133	−	0.809491i	$-0.699743\pi$
$337$	2.39677	−	2.07682i	0.130561	−	0.113131i	0.717693	+	0.696359i	$0.245198\pi$
$338$	−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	−0.555960	−	0.831209i	$-0.687649\pi$
$347$	−27.4399	−	8.05707i	−1.47305	−	0.432526i	−0.917089	+	0.398683i	$0.869467\pi$
$348$	1.81861	+	1.57583i	0.0974877	+	0.0844736i
$349$	−14.7544	+	22.9584i	−0.789787	+	1.22893i	0.179683	+	0.983724i	$0.442493\pi$
$349$	−14.7544	+	22.9584i	−0.789787	+	1.22893i	−0.969470	+	0.245208i	$0.921144\pi$
$350$	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	0.232507	−	0.972595i	$-0.425307\pi$
$353$	23.0775	−	19.9968i	1.22829	−	1.06432i	0.995784	−	0.0917257i	$-0.0292383\pi$
$354$	−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	0.228669	−	0.973504i	$-0.426563\pi$
$359$	13.6865	−	1.96782i	0.722344	−	0.103857i	0.493674	+	0.869647i	$0.335653\pi$
$360$	−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	0.923397	−	0.383845i	$-0.125400\pi$
$373$	32.8566	+	4.72406i	1.70125	+	0.244603i	0.777852	+	0.628448i	$0.216309\pi$
$374$	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	−0.996259	−	0.0864182i	$-0.972458\pi$
$379$	−3.98847	−	13.5835i	−0.204874	−	0.697736i	0.791385	−	0.611318i	$-0.209360\pi$
$380$	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	0.799880	−	0.600160i	$-0.204896\pi$
$383$	1.80036	+	2.07772i	0.0919939	+	0.106167i	−0.707886	+	0.706327i	$0.750351\pi$
$384$	−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	−0.948350	−	0.317224i	$-0.897249\pi$
$389$	0.413340	−	1.40771i	0.0209572	−	0.0713736i	0.969308	+	0.245851i	$0.0790673\pi$
$390$	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	−0.966492	−	0.256698i	$-0.917365\pi$
$397$	−15.9099	−	24.7564i	−0.798497	−	1.24249i	0.167995	−	0.985788i	$-0.446271\pi$
$398$	−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	0.927343	−	0.374212i	$-0.122087\pi$
$401$	25.0675	+	11.4480i	1.25181	+	0.571684i	0.324470	+	0.945896i	$0.394814\pi$
$402$	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	0.622607	−	0.782535i	$-0.286074\pi$
$409$	20.2142	+	2.90636i	0.999528	+	0.143710i	0.376921	+	0.926245i	$0.376983\pi$
$410$	−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	0.949969	+	0.312343i	$0.101114\pi$
$419$	−1.01359	+	7.04964i	−0.0495169	+	0.344398i	−0.999486	+	0.0320541i	$0.989795\pi$
$420$	−8.08086	−	4.06376i	−0.394305	−	0.198291i
$421$	−14.0594	+	6.42070i	−0.685212	+	0.312926i	−0.727429	−	0.686183i	$-0.759285\pi$
$421$	−14.0594	+	6.42070i	−0.685212	+	0.312926i	0.0422173	+	0.999108i	$0.486558\pi$
$422$	−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	0.616998	−	0.786964i	$-0.288348\pi$
$431$	−7.37331	−	11.4731i	−0.355160	−	0.552640i	−0.972158	+	0.234325i	$0.924712\pi$
$432$	0.989821	+	0.142315i	0.0476228	+	0.00684713i
$433$	−3.73448	−	2.40001i	−0.179468	−	0.115337i	0.447822	−	0.894122i	$-0.352200\pi$
$433$	−3.73448	−	2.40001i	−0.179468	−	0.115337i	−0.627290	+	0.778786i	$0.715836\pi$
$434$	−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	−0.462843	−	0.886440i	$-0.653171\pi$
$439$	8.50185	−	28.9546i	0.405771	−	1.38193i	0.868614	−	0.495489i	$-0.165011\pi$
$440$	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	−0.558244	−	0.829677i	$-0.688525\pi$
$443$	−0.746061	+	0.479464i	−0.0354464	+	0.0227800i	0.522798	+	0.852457i	$0.324888\pi$
$444$	−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	−0.180043	−	0.983659i	$-0.557624\pi$
$449$	4.24432	−	1.24625i	0.200302	−	0.0588139i	0.380345	+	0.924845i	$0.375805\pi$
$450$	−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	−0.995223	−	0.0976249i	$-0.968875\pi$
$457$	−26.3690	−	22.8489i	−1.23349	−	1.06882i	−0.238266	−	0.971200i	$-0.576579\pi$
$458$	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	$0.0210209\pi$
$461$			2.83378i			0.131982i	−0.997820	+	0.0659912i	$0.978979\pi$
$462$	10.7624	−	2.72567i	0.500711	−	0.126810i
$463$	−1.85686	+	2.14293i	−0.0862954	+	0.0995902i	−0.797255	−	0.603643i	$-0.793715\pi$
$463$	−1.85686	+	2.14293i	−0.0862954	+	0.0995902i	0.710960	+	0.703233i	$0.248261\pi$
$464$	−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	0.987833	−	0.155516i	$-0.0497040\pi$
$467$	4.82791	+	10.5716i	0.223409	+	0.489197i	−0.764424	+	0.644713i	$0.776977\pi$
$468$	−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	0.330053	−	0.943962i	$-0.392933\pi$
$479$	−8.56831	−	5.50652i	−0.391496	−	0.251599i	−0.721549	+	0.692363i	$0.756570\pi$
$480$	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	−0.361306	−	0.932447i	$-0.617669\pi$
$487$	−30.0034	−	19.2820i	−1.35958	−	0.873751i	−0.998276	+	0.0586966i	$0.981306\pi$
$488$	−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	0.999998	+	0.00189570i	$0.000603422\pi$
$491$	19.0466	+	21.9809i	0.859560	+	0.991985i	−0.140438	+	0.990089i	$0.544851\pi$
$492$	−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	0.979655	+	0.200687i	$0.0643173\pi$
$499$	10.9410	+	23.9575i	0.489786	+	1.07248i	−0.489869	+	0.871796i	$0.662955\pi$
$500$	−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	−0.308125	+	0.951346i	$0.599701\pi$
$503$	−27.0463	+	31.2131i	−1.20594	+	1.39173i	−0.897812	+	0.440379i	$0.854844\pi$
$504$	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	0.888627	−	0.458630i	$-0.151660\pi$
$509$	12.6597	+	10.9697i	0.561130	+	0.486222i	−0.327497	+	0.944852i	$0.606205\pi$
$510$	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	0.895814	−	0.444429i	$-0.146593\pi$
$521$	7.49635	+	8.65125i	0.328421	+	0.379018i	−0.567393	+	0.823447i	$0.692048\pi$
$522$	0.999640	+	2.18891i	0.0437531	+	0.0958058i
$523$	−26.1091	+	16.7793i	−1.14167	+	0.733708i	−0.967964	−	0.251089i	$-0.919211\pi$
$523$	−26.1091	+	16.7793i	−1.14167	+	0.733708i	−0.173708	+	0.984797i	$0.555575\pi$
$524$	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	−0.0863896	−	0.996261i	$-0.527533\pi$
$541$	8.82821	−	2.59220i	0.379554	−	0.111447i	0.465944	+	0.884814i	$0.345715\pi$
$542$	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	−0.727599	−	0.686003i	$-0.759364\pi$
$547$	3.83088	−	26.6443i	0.163797	−	1.13923i	0.891395	−	0.453227i	$-0.149727\pi$
$548$	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	−0.363297	−	0.931674i	$-0.618349\pi$
$557$	−22.9957	−	3.30628i	−0.974360	−	0.140092i	−0.611063	+	0.791582i	$0.709258\pi$
$558$	−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	−0.0133036	−	0.999912i	$-0.504235\pi$
$563$	12.2458	−	3.59568i	0.516098	−	0.151540i	0.529401	+	0.848372i	$0.322417\pi$
$564$	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	0.810302	−	0.586013i	$-0.199303\pi$
$569$	−1.41611	−	2.20350i	−0.0593662	−	0.0923757i	−0.869668	+	0.493638i	$0.835667\pi$
$570$	8.26605	+	1.18848i	0.346227	+	0.0497799i
$571$	−1.06765	+	1.66130i	−0.0446798	+	0.0695231i	−0.862875	−	0.505418i	$-0.831338\pi$
$571$	−1.06765	+	1.66130i	−0.0446798	+	0.0695231i	0.818195	+	0.574941i	$0.194975\pi$
$572$	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	0.835708	+	0.549174i	$0.185058\pi$
$577$	−3.94519	+	13.4361i	−0.164240	+	0.559352i	−0.999948	+	0.0101773i	$0.996760\pi$
$578$	−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	0.950695	−	0.310128i	$-0.100372\pi$
$587$	−0.405781	−	1.38196i	−0.0167484	−	0.0570397i	−0.967443	+	0.253088i	$0.918554\pi$
$588$	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	0.947950	−	0.318419i	$-0.103152\pi$
$593$	43.0486	+	6.18945i	1.76779	+	0.254170i	0.819842	+	0.572589i	$0.194061\pi$
$594$	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	0.377181	−	0.926140i	$-0.376894\pi$
$601$	−11.9109	−	10.3208i	−0.485854	−	0.420995i	−0.863035	+	0.505145i	$0.831439\pi$
$602$	−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	0.316125	−	0.948718i	$-0.397618\pi$
$607$	21.8467	−	3.14108i	0.886729	−	0.127492i	0.570604	+	0.821225i	$0.306709\pi$
$608$	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	−0.972578	−	0.232575i	$-0.925285\pi$
$613$	−21.8072	+	18.8960i	−0.880783	+	0.763203i	0.0917957	+	0.995778i	$0.470739\pi$
$614$	−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	−0.783714	−	0.621122i	$-0.786677\pi$
$617$	2.65397	−	4.12966i	0.106845	−	0.166254i	0.890559	+	0.454868i	$0.150314\pi$
$618$	−7.39355	−	6.40655i	−0.297412	−	0.257709i
$619$	0.375863	+	0.110363i	0.0151072	+	0.00443588i	0.289277	−	0.957245i	$-0.406585\pi$
$619$	0.375863	+	0.110363i	0.0151072	+	0.00443588i	−0.274170	+	0.961681i	$0.588403\pi$
$620$		−	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	0.781042	−	0.624479i	$-0.214689\pi$
$631$	20.6124	+	9.41335i	0.820565	+	0.374740i	0.0395236	+	0.999219i	$0.487416\pi$
$632$	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	0.468054	−	0.883700i	$-0.344955\pi$
$641$	−8.60913	−	7.45986i	−0.340040	−	0.294647i	−0.808094	+	0.589053i	$0.799501\pi$
$642$	−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	0.634931	−	0.772569i	$-0.281028\pi$
$647$	−1.00253	−	0.868696i	−0.0394135	−	0.0341520i	−0.674345	+	0.738417i	$0.735574\pi$
$648$	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	−0.985691	−	0.168561i	$-0.946088\pi$
$653$	−2.23383	−	15.5366i	−0.0874165	−	0.607995i	0.898275	−	0.439434i	$-0.144821\pi$
$654$	−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	0.624472	−	0.781047i	$-0.285314\pi$
$659$	38.1584	−	33.0645i	1.48644	−	1.28801i	0.861969	−	0.506961i	$-0.169231\pi$
$660$	5.95946	+	13.0494i	0.231972	+	0.507947i
$661$	4.62430	−	2.97186i	0.179865	−	0.115592i	−0.447610	−	0.894229i	$-0.647725\pi$
$661$	4.62430	−	2.97186i	0.179865	−	0.115592i	0.627475	+	0.778637i	$0.284088\pi$
$662$	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	−0.863041	−	0.505134i	$-0.831443\pi$
$673$	−19.7699	+	12.7054i	−0.762075	+	0.489756i	0.100966	+	0.994890i	$0.467807\pi$
$674$	−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	0.338995	+	0.940788i	$0.389913\pi$
$677$	−15.4554	+	33.8426i	−0.594000	+	1.30068i	−0.932995	+	0.359890i	$0.882814\pi$
$678$	−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	−0.991448	−	0.130504i	$-0.958341\pi$
$683$	−11.5204	−	25.2261i	−0.440816	−	0.965252i	0.550632	−	0.834748i	$-0.314387\pi$
$684$	−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	$0.148931\pi$
$691$			23.7105i			0.901990i	−0.892526	+	0.450995i	$0.851069\pi$
$692$	−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	0.924377	+	0.381481i	$0.124586\pi$
$701$	9.34579	+	31.8289i	0.352986	+	1.20216i	−0.571391	+	0.820678i	$0.693596\pi$
$702$	−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	−0.979429	−	0.201787i	$-0.935325\pi$
$709$	−10.3581	+	16.1176i	−0.389008	+	0.605308i	0.590422	+	0.807095i	$0.298962\pi$
$710$	−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	−0.999850	−	0.0173354i	$-0.994482\pi$
$719$	−16.0956	−	25.0453i	−0.600266	−	0.934032i	0.399584	−	0.916697i	$-0.369155\pi$
$720$	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	0.963623	+	0.267264i	$0.0861197\pi$
$727$	3.08269	+	21.4406i	0.114331	+	0.795187i	−0.849293	+	0.527922i	$0.822971\pi$
$728$	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	−0.996875	−	0.0789970i	$-0.974828\pi$
$733$	−21.0314	+	24.2715i	−0.776812	+	0.896489i	0.220063	+	0.975486i	$0.429374\pi$
$734$	−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	−0.425025	−	0.905182i	$-0.639735\pi$
$739$	14.4467	−	16.6724i	0.531431	−	0.613304i	0.956456	+	0.291878i	$0.0942801\pi$
$740$	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	−0.653220	−	0.757168i	$-0.726582\pi$
$743$	−13.8678	+	6.33320i	−0.508759	+	0.232342i	0.144461	+	0.989510i	$0.453855\pi$
$744$	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	0.414549	−	0.910027i	$-0.363939\pi$
$751$	37.6621	−	32.6344i	1.37431	−	1.19085i	0.959761	−	0.280819i	$-0.0906060\pi$
$752$	−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	−0.792582	−	0.609765i	$-0.791264\pi$
$757$	5.60849	−	19.1008i	0.203844	−	0.694230i	0.996426	−	0.0844646i	$-0.0269180\pi$
$758$			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	−0.750223	−	0.661185i	$-0.770054\pi$
$761$	6.57568	−	22.3947i	0.238368	−	0.811808i	0.988591	−	0.150623i	$-0.0481280\pi$
$762$	−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	−0.117106	−	0.993119i	$-0.537362\pi$
$769$	19.6926	−	43.1207i	0.710132	−	1.55497i	0.827238	−	0.561852i	$-0.189911\pi$
$770$	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	0.943027	+	0.332716i	$0.107965\pi$
$773$	3.66820	+	25.5129i	0.131936	+	0.917636i	−0.811091	+	0.584920i	$0.801126\pi$
$774$	−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	0.673654	+	0.739046i	$0.264724\pi$
$787$	−5.07560	+	35.3016i	−0.180926	+	1.25837i	−0.854580	+	0.519319i	$0.826185\pi$
$788$	−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	0.818777	−	0.574112i	$-0.194653\pi$
$797$	3.78252	+	4.36526i	0.133984	+	0.154626i	−0.684793	+	0.728738i	$0.740107\pi$
$798$	−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	−0.149751	−	0.988724i	$-0.547847\pi$
$809$	−31.6096	−	20.3142i	−1.11133	−	0.714211i	−0.961583	+	0.274513i	$0.911483\pi$
$810$	0.486537	−	3.38394i	0.0170952	−	0.118900i
$811$	−0.0768858	−	0.119637i	−0.00269983	−	0.00420101i	0.839901	−	0.542740i	$-0.182613\pi$
$811$	−0.0768858	−	0.119637i	−0.00269983	−	0.00420101i	−0.842601	+	0.538539i	$0.818977\pi$
$812$	−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	0.861322	+	0.508060i	$0.169637\pi$
$821$	19.5197	+	42.7422i	0.681242	+	1.49171i	−0.180079	+	0.983652i	$0.557635\pi$
$822$	7.74443	−	4.97704i	0.270118	−	0.173594i
$823$	−3.71772	+	25.8573i	−0.129592	+	0.901330i	0.816480	+	0.577373i	$0.195922\pi$
$823$	−3.71772	+	25.8573i	−0.129592	+	0.901330i	−0.946072	+	0.323957i	$0.894987\pi$
$824$	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	$-0.998918\pi$
$827$		−	0.195469i		−	0.00679712i	0.999994	−	0.00339856i	$-0.00108180\pi$
$828$	−4.74252	−	0.713089i	−0.164814	−	0.0247816i
$829$			54.0371i			1.87679i	0.345570	+	0.938393i	$0.387686\pi$
$829$			54.0371i			1.87679i	−0.345570	+	0.938393i	$0.612314\pi$
$830$	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	−0.476928	−	0.878942i	$-0.658250\pi$
$839$	−11.6717	+	3.42713i	−0.402953	+	0.118318i	0.0739749	+	0.997260i	$0.476432\pi$
$840$	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	0.585490	+	0.810680i	$0.300902\pi$
$853$	−10.0861	+	34.3502i	−0.345342	+	1.17613i	−0.930832	+	0.365447i	$0.880916\pi$
$854$	−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	0.666592	−	0.745422i	$-0.267752\pi$
$857$	−8.44220	−	13.1363i	−0.288380	−	0.448728i	−0.954973	+	0.296694i	$0.904116\pi$
$858$	21.4261	−	9.78496i	0.731474	−	0.334053i
$859$	24.1108	−	20.8921i	0.822650	−	0.712830i	−0.138048	−	0.990425i	$-0.544083\pi$
$859$	24.1108	−	20.8921i	0.822650	−	0.712830i	0.960698	+	0.277595i	$0.0895375\pi$
$860$	−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	0.697200	−	0.716876i	$-0.254429\pi$
$863$	49.0974	−	14.4163i	1.67130	−	0.490737i	0.974095	+	0.226140i	$0.0726106\pi$
$864$	−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	−0.452974	−	0.891524i	$-0.649637\pi$
$877$	14.6276	−	16.8812i	0.493940	−	0.570037i	0.946914	+	0.321487i	$0.104182\pi$
$878$	−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	0.999952	−	0.00977738i	$-0.00311229\pi$
$881$	10.0245	+	21.9506i	0.337734	+	0.739533i	−0.662219	+	0.749311i	$0.730385\pi$
$882$	6.84550	−	1.46256i	0.230500	−	0.0492469i
$883$	1.46605	+	10.1966i	0.0493364	+	0.343142i	0.999507	+	0.0314104i	$0.00999989\pi$
$883$	1.46605	+	10.1966i	0.0493364	+	0.343142i	−0.950170	+	0.311732i	$0.899091\pi$
$884$	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	0.736909	−	0.675992i	$-0.236285\pi$
$887$	21.1039	+	9.63783i	0.708600	+	0.323607i	−0.0283086	+	0.999599i	$0.509012\pi$
$888$	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	0.330677	−	0.943744i	$-0.392723\pi$
$907$	−4.99960	−	2.28324i	−0.166009	−	0.0758138i	−0.496686	+	0.867930i	$0.665450\pi$
$908$	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	−0.744710	−	0.667389i	$-0.767412\pi$
$911$	−38.3692	+	5.51666i	−1.27123	+	0.182775i	−0.526519	+	0.850164i	$0.676503\pi$
$912$	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	$-0.863570\pi$
$919$		−	25.1981i		−	0.831208i	0.909546	−	0.415604i	$-0.136430\pi$
$920$	−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	−0.986019	−	0.166630i	$-0.946711\pi$
$929$	−57.4585	+	8.26129i	−1.88515	+	0.271044i	−0.899134	+	0.437674i	$0.855802\pi$
$930$	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	−0.305713	−	0.952124i	$-0.598895\pi$
$937$	13.2657	−	8.52534i	0.433371	−	0.278511i	0.739084	+	0.673613i	$0.235259\pi$
$938$	−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	0.906307	−	0.422621i	$-0.138890\pi$
$941$	44.1808	+	12.9727i	1.44025	+	0.422897i	0.533948	+	0.845517i	$0.320708\pi$
$942$		−	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	0.0287681	−	0.999586i	$-0.490842\pi$
$947$	−26.7278	−	17.1769i	−0.868537	−	0.558175i	−0.897305	+	0.441411i	$0.854478\pi$
$948$	−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	0.490216	−	0.871601i	$-0.336918\pi$
$953$	4.70861	+	2.15035i	0.152527	+	0.0696567i	−0.337689	+	0.941258i	$0.609645\pi$
$954$	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	0.765150	+	0.643852i	$0.222665\pi$
$971$	−4.68660	+	32.5960i	−0.150400	+	1.04606i	−0.915550	+	0.402204i	$0.868244\pi$
$972$	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	0.974161	+	0.225853i	$0.0725168\pi$
$977$	8.65037	+	29.4605i	0.276750	+	0.942524i	−0.697412	+	0.716671i	$0.745665\pi$
$978$	−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	0.176272	−	0.984342i	$-0.443596\pi$
$983$	35.8954	−	23.0686i	1.14489	−	0.735774i	0.968615	+	0.248568i	$0.0799599\pi$
$984$	−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	0.677241	−	0.735761i	$-0.263175\pi$
$991$	26.7326	+	7.84941i	0.849191	+	0.249345i	0.171949	+	0.985106i	$0.444993\pi$
$992$	−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	−0.302101	−	0.953276i	$-0.597688\pi$
$997$	18.8972	−	16.3745i	0.598479	−	0.518585i	0.900580	+	0.434691i	$0.143142\pi$
$998$	−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.97.8	✓	160
7.6	odd	2	inner	966.2.s.a.97.9	yes	160
23.14	odd	22	inner	966.2.s.a.727.9	yes	160
161.83	even	22	inner	966.2.s.a.727.8	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.a.97.8	✓	160	1.1	even	1	trivial
966.2.s.a.97.9	yes	160	7.6	odd	2	inner
966.2.s.a.727.8	yes	160	161.83	even	22	inner
966.2.s.a.727.9	yes	160	23.14	odd	22	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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