LMFDB - Embedded newform 350.2.r.a.237.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(13,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([19, 10]))

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

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

chi := DirichletCharacter("350.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.r (of order $20$, degree $8$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			237.8
Character	$\chi$	$=$	350.237
Dual form			350.2.r.a.223.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 - 0.987688i) q^{2} +(0.617062 - 1.21105i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(0.811760 - 2.08352i) q^{5} +(-1.29267 - 0.420015i) q^{6} +(-2.31097 - 1.28818i) q^{7} +(0.453990 + 0.891007i) q^{8} +(0.677473 + 0.932462i) q^{9} +O(q^{10})$	\(q+(-0.156434 - 0.987688i) q^{2} +(0.617062 - 1.21105i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(0.811760 - 2.08352i) q^{5} +(-1.29267 - 0.420015i) q^{6} +(-2.31097 - 1.28818i) q^{7} +(0.453990 + 0.891007i) q^{8} +(0.677473 + 0.932462i) q^{9} +(-2.18485 - 0.475832i) q^{10} +(-4.81995 - 3.50190i) q^{11} +(-0.212625 + 1.34246i) q^{12} +(1.61047 + 0.255074i) q^{13} +(-0.910801 + 2.48404i) q^{14} +(-2.02234 - 2.26874i) q^{15} +(0.809017 - 0.587785i) q^{16} +(2.42058 + 4.75065i) q^{17} +(0.815002 - 0.815002i) q^{18} +(1.73740 - 5.34717i) q^{19} +(-0.128187 + 2.23239i) q^{20} +(-2.98606 + 2.00383i) q^{21} +(-2.70478 + 5.30843i) q^{22} +(-1.83314 + 0.290341i) q^{23} +1.35920 q^{24} +(-3.68209 - 3.38263i) q^{25} -1.63055i q^{26} +(5.57469 - 0.882944i) q^{27} +(2.59594 + 0.510998i) q^{28} +(-2.97363 + 0.966190i) q^{29} +(-1.92445 + 2.35235i) q^{30} +(1.10078 + 0.357665i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-7.21519 + 3.67632i) q^{33} +(4.31350 - 3.13394i) q^{34} +(-4.55989 + 3.76927i) q^{35} +(-0.932462 - 0.677473i) q^{36} +(7.09927 + 1.12441i) q^{37} +(-5.55313 - 0.879530i) q^{38} +(1.30267 - 1.79297i) q^{39} +(2.22496 - 0.222614i) q^{40} +(-6.46859 - 8.90326i) q^{41} +(2.44628 + 2.63583i) q^{42} +(0.690468 - 0.690468i) q^{43} +(5.66619 + 1.84106i) q^{44} +(2.49275 - 0.654593i) q^{45} +(0.573532 + 1.76515i) q^{46} +(8.35310 + 4.25612i) q^{47} +(-0.212625 - 1.34246i) q^{48} +(3.68120 + 5.95388i) q^{49} +(-2.76498 + 4.16592i) q^{50} +7.24693 q^{51} +(-1.61047 + 0.255074i) q^{52} +(-0.302307 - 0.154033i) q^{53} +(-1.74415 - 5.36793i) q^{54} +(-11.2089 + 7.19975i) q^{55} +(0.0986133 - 2.64391i) q^{56} +(-5.40362 - 5.40362i) q^{57} +(1.41947 + 2.78587i) q^{58} +(-3.15395 + 2.29148i) q^{59} +(2.62444 + 1.53276i) q^{60} +(5.66916 - 7.80293i) q^{61} +(0.181062 - 1.14318i) q^{62} +(-0.364448 - 3.02760i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(1.83877 - 3.14839i) q^{65} +(4.75977 + 6.55126i) q^{66} +(5.08240 - 2.58961i) q^{67} +(-3.77014 - 3.77014i) q^{68} +(-0.779542 + 2.39918i) q^{69} +(4.43618 + 3.91411i) q^{70} +(0.221677 + 0.682250i) q^{71} +(-0.523263 + 1.02696i) q^{72} +(0.0825063 + 0.520924i) q^{73} -7.18776i q^{74} +(-6.36862 + 2.37191i) q^{75} +5.62235i q^{76} +(6.62772 + 14.3017i) q^{77} +(-1.97468 - 1.00615i) q^{78} +(10.8557 - 3.52724i) q^{79} +(-0.567934 - 2.16274i) q^{80} +(1.30213 - 4.00755i) q^{81} +(-7.78173 + 7.78173i) q^{82} +(13.4402 - 6.84812i) q^{83} +(2.22070 - 2.82850i) q^{84} +(11.8630 - 1.18693i) q^{85} +(-0.789980 - 0.573954i) q^{86} +(-0.664806 + 4.19742i) q^{87} +(0.932003 - 5.88444i) q^{88} +(10.4873 + 7.61946i) q^{89} +(-1.03649 - 2.35966i) q^{90} +(-3.39318 - 2.66404i) q^{91} +(1.65370 - 0.842601i) q^{92} +(1.11240 - 1.11240i) q^{93} +(2.89701 - 8.91607i) q^{94} +(-9.73058 - 7.96053i) q^{95} +(-1.29267 + 0.420015i) q^{96} +(-2.62217 - 1.33606i) q^{97} +(5.30472 - 4.56727i) q^{98} -6.86687i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{7}+O(q^{10}) $ 160 * q + 8 * q^7	$ 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) $ 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{9}{20}\right)$

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 $

$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$3$	0.617062	−	1.21105i	0.356261	−	0.699201i	−0.641426	−	0.767185i	$-0.721657\pi$
$3$	0.617062	−	1.21105i	0.356261	−	0.699201i	0.997686	+	0.0679839i	$0.0216567\pi$
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	0.811760	−	2.08352i	0.363030	−	0.931777i
$5$	0.811760	−	2.08352i	0.363030	−	0.931777i
$6$	−1.29267	−	0.420015i	−0.527731	−	0.171470i
$7$	−2.31097	−	1.28818i	−0.873466	−	0.486885i
$7$	−2.31097	−	1.28818i	−0.873466	−	0.486885i
$8$	0.453990	+	0.891007i	0.160510	+	0.315018i
$9$	0.677473	+	0.932462i	0.225824	+	0.310821i
$10$	−2.18485	−	0.475832i	−0.690911	−	0.150471i
$11$	−4.81995	−	3.50190i	−1.45327	−	1.05586i	−0.985053	−	0.172249i	$-0.944897\pi$
$11$	−4.81995	−	3.50190i	−1.45327	−	1.05586i	−0.468217	−	0.883614i	$-0.655103\pi$
$12$	−0.212625	+	1.34246i	−0.0613796	+	0.387535i
$13$	1.61047	+	0.255074i	0.446665	+	0.0707447i	0.375715	−	0.926735i	$-0.377397\pi$
$13$	1.61047	+	0.255074i	0.446665	+	0.0707447i	0.0709494	+	0.997480i	$0.477397\pi$
$14$	−0.910801	+	2.48404i	−0.243422	+	0.663887i
$15$	−2.02234	−	2.26874i	−0.522167	−	0.585787i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	2.42058	+	4.75065i	0.587076	+	1.15220i	0.973244	+	0.229773i	$0.0737984\pi$
$17$	2.42058	+	4.75065i	0.587076	+	1.15220i	−0.386168	+	0.922428i	$0.626202\pi$
$18$	0.815002	−	0.815002i	0.192098	−	0.192098i
$19$	1.73740	−	5.34717i	0.398587	−	1.22673i	−0.527545	−	0.849527i	$-0.676887\pi$
$19$	1.73740	−	5.34717i	0.398587	−	1.22673i	0.926132	−	0.377199i	$-0.123113\pi$
$20$	−0.128187	+	2.23239i	−0.0286635	+	0.499178i
$21$	−2.98606	+	2.00383i	−0.651612	+	0.437271i
$22$	−2.70478	+	5.30843i	−0.576661	+	1.13176i
$23$	−1.83314	+	0.290341i	−0.382236	+	0.0605402i	−0.344596	−	0.938751i	$-0.611984\pi$
$23$	−1.83314	+	0.290341i	−0.382236	+	0.0605402i	−0.0376400	+	0.999291i	$0.511984\pi$
$24$	1.35920			0.277445
$25$	−3.68209	−	3.38263i	−0.736418	−	0.676526i
$26$		−	1.63055i		−	0.319777i
$27$	5.57469	−	0.882944i	1.07285	−	0.169923i
$28$	2.59594	+	0.510998i	0.490586	+	0.0965696i
$29$	−2.97363	+	0.966190i	−0.552189	+	0.179417i	−0.571804	−	0.820391i	$-0.693756\pi$
$29$	−2.97363	+	0.966190i	−0.552189	+	0.179417i	0.0196147	+	0.999808i	$0.493756\pi$
$30$	−1.92445	+	2.35235i	−0.351354	+	0.429479i
$31$	1.10078	+	0.357665i	0.197706	+	0.0642386i	0.406196	−	0.913786i	$-0.366855\pi$
$31$	1.10078	+	0.357665i	0.197706	+	0.0642386i	−0.208490	+	0.978024i	$0.566855\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−7.21519	+	3.67632i	−1.25600	+	0.639966i
$34$	4.31350	−	3.13394i	0.739759	−	0.537466i
$35$	−4.55989	+	3.76927i	−0.770763	+	0.637122i
$36$	−0.932462	−	0.677473i	−0.155410	−	0.112912i
$37$	7.09927	+	1.12441i	1.16711	+	0.184852i	0.709767	−	0.704436i	$-0.248800\pi$
$37$	7.09927	+	1.12441i	1.16711	+	0.184852i	0.457346	+	0.889289i	$0.348800\pi$
$38$	−5.55313	−	0.879530i	−0.900837	−	0.142679i
$39$	1.30267	−	1.79297i	0.208594	−	0.287105i
$40$	2.22496	−	0.222614i	0.351797	−	0.0351984i
$41$	−6.46859	−	8.90326i	−1.01022	−	1.39046i	−0.918836	−	0.394640i	$-0.870869\pi$
$41$	−6.46859	−	8.90326i	−1.01022	−	1.39046i	−0.0913888	−	0.995815i	$-0.529131\pi$
$42$	2.44628	+	2.63583i	0.377469	+	0.406718i
$43$	0.690468	−	0.690468i	0.105295	−	0.105295i	−0.652496	−	0.757792i	$-0.726278\pi$
$43$	0.690468	−	0.690468i	0.105295	−	0.105295i	0.757792	+	0.652496i	$0.226278\pi$
$44$	5.66619	+	1.84106i	0.854211	+	0.277550i
$45$	2.49275	−	0.654593i	0.371597	−	0.0975809i
$46$	0.573532	+	1.76515i	0.0845627	+	0.260257i
$47$	8.35310	+	4.25612i	1.21843	+	0.620819i	0.940503	−	0.339785i	$-0.110354\pi$
$47$	8.35310	+	4.25612i	1.21843	+	0.620819i	0.277922	+	0.960604i	$0.410354\pi$
$48$	−0.212625	−	1.34246i	−0.0306898	−	0.193768i
$49$	3.68120	+	5.95388i	0.525886	+	0.850555i
$50$	−2.76498	+	4.16592i	−0.391027	+	0.589150i
$51$	7.24693			1.01477
$52$	−1.61047	+	0.255074i	−0.223332	+	0.0353724i
$53$	−0.302307	−	0.154033i	−0.0415251	−	0.0211581i	0.433105	−	0.901344i	$-0.357418\pi$
$53$	−0.302307	−	0.154033i	−0.0415251	−	0.0211581i	−0.474630	+	0.880186i	$0.657418\pi$
$54$	−1.74415	−	5.36793i	−0.237348	−	0.730483i
$55$	−11.2089	+	7.19975i	−1.51141	+	0.970815i
$56$	0.0986133	−	2.64391i	0.0131778	−	0.353308i
$57$	−5.40362	−	5.40362i	−0.715727	−	0.715727i
$58$	1.41947	+	2.78587i	0.186386	+	0.365803i
$59$	−3.15395	+	2.29148i	−0.410609	+	0.298325i	−0.773848	−	0.633371i	$-0.781671\pi$
$59$	−3.15395	+	2.29148i	−0.410609	+	0.298325i	0.363239	+	0.931696i	$0.381671\pi$
$60$	2.62444	+	1.53276i	0.338814	+	0.197879i
$61$	5.66916	−	7.80293i	0.725862	−	0.999063i	−0.273447	−	0.961887i	$-0.588164\pi$
$61$	5.66916	−	7.80293i	0.725862	−	0.999063i	0.999309	−	0.0371763i	$-0.0118363\pi$
$62$	0.181062	−	1.14318i	0.0229949	−	0.145184i
$63$	−0.364448	−	3.02760i	−0.0459161	−	0.381442i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	1.83877	−	3.14839i	0.228071	−	0.390510i
$66$	4.75977	+	6.55126i	0.585887	+	0.806404i
$67$	5.08240	−	2.58961i	0.620914	−	0.316372i	−0.115083	−	0.993356i	$-0.536713\pi$
$67$	5.08240	−	2.58961i	0.620914	−	0.316372i	0.735998	+	0.676984i	$0.236713\pi$
$68$	−3.77014	−	3.77014i	−0.457196	−	0.457196i
$69$	−0.779542	+	2.39918i	−0.0938459	+	0.288828i
$70$	4.43618	+	3.91411i	0.530225	+	0.467826i
$71$	0.221677	+	0.682250i	0.0263082	+	0.0809682i	0.963349	−	0.268253i	$-0.0864462\pi$
$71$	0.221677	+	0.682250i	0.0263082	+	0.0809682i	−0.937040	+	0.349221i	$0.886446\pi$
$72$	−0.523263	+	1.02696i	−0.0616672	+	0.121029i
$73$	0.0825063	+	0.520924i	0.00965663	+	0.0609696i	0.992046	−	0.125875i	$-0.0401739\pi$
$73$	0.0825063	+	0.520924i	0.00965663	+	0.0609696i	−0.982389	+	0.186845i	$0.940174\pi$
$74$		−	7.18776i		−	0.835560i
$75$	−6.36862	+	2.37191i	−0.735385	+	0.273885i
$76$			5.62235i			0.644928i
$77$	6.62772	+	14.3017i	0.755299	+	1.62984i
$78$	−1.97468	−	1.00615i	−0.223588	−	0.113924i
$79$	10.8557	−	3.52724i	1.22136	−	0.396845i	0.373786	−	0.927515i	$-0.378060\pi$
$79$	10.8557	−	3.52724i	1.22136	−	0.396845i	0.847579	+	0.530670i	$0.178060\pi$
$80$	−0.567934	−	2.16274i	−0.0634969	−	0.241802i
$81$	1.30213	−	4.00755i	0.144681	−	0.445283i
$82$	−7.78173	+	7.78173i	−0.859348	+	0.859348i
$83$	13.4402	−	6.84812i	1.47525	−	0.751679i	0.482965	−	0.875640i	$-0.339560\pi$
$83$	13.4402	−	6.84812i	1.47525	−	0.751679i	0.992287	+	0.123961i	$0.0395598\pi$
$84$	2.22070	−	2.82850i	0.242298	−	0.308614i
$85$	11.8630	−	1.18693i	1.28672	−	0.128740i
$86$	−0.789980	−	0.573954i	−0.0851857	−	0.0618911i
$87$	−0.664806	+	4.19742i	−0.0712747	+	0.450011i
$88$	0.932003	−	5.88444i	0.0993519	−	0.627283i
$89$	10.4873	+	7.61946i	1.11165	+	0.807661i	0.982923	−	0.184019i	$-0.0589107\pi$
$89$	10.4873	+	7.61946i	1.11165	+	0.807661i	0.128728	+	0.991680i	$0.458911\pi$
$90$	−1.03649	−	2.35966i	−0.109255	−	0.248730i
$91$	−3.39318	−	2.66404i	−0.355702	−	0.279267i
$92$	1.65370	−	0.842601i	0.172410	−	0.0878473i
$93$	1.11240	−	1.11240i	0.115351	−	0.115351i
$94$	2.89701	−	8.91607i	0.298803	−	0.919622i
$95$	−9.73058	−	7.96053i	−0.998336	−	0.816733i
$96$	−1.29267	+	0.420015i	−0.131933	+	0.0428676i
$97$	−2.62217	−	1.33606i	−0.266241	−	0.135656i	0.315775	−	0.948834i	$-0.397736\pi$
$97$	−2.62217	−	1.33606i	−0.266241	−	0.135656i	−0.582015	+	0.813178i	$0.697736\pi$
$98$	5.30472	−	4.56727i	0.535857	−	0.461364i
$99$		−	6.86687i		−	0.690146i
$100$	4.54717	+	2.07924i	0.454717	+	0.207924i
$101$		−	7.48889i		−	0.745172i	−0.927998	−	0.372586i	$-0.878471\pi$
$101$		−	7.48889i		−	0.745172i	0.927998	−	0.372586i	$-0.121529\pi$
$102$	−1.13367	−	7.15771i	−0.112250	−	0.708719i
$103$	−6.62187	+	12.9962i	−0.652472	+	1.28055i	0.293393	+	0.955992i	$0.405215\pi$
$103$	−6.62187	+	12.9962i	−0.652472	+	1.28055i	−0.945866	+	0.324558i	$0.894785\pi$
$104$	0.503867	+	1.55074i	0.0494082	+	0.152063i
$105$	1.75104	+	7.84814i	0.170884	+	0.765900i
$106$	−0.104845	+	0.322681i	−0.0101835	+	0.0313416i
$107$	−3.67576	−	3.67576i	−0.355349	−	0.355349i	0.506746	−	0.862095i	$-0.330848\pi$
$107$	−3.67576	−	3.67576i	−0.355349	−	0.355349i	−0.862095	+	0.506746i	$0.830848\pi$
$108$	−5.02900	+	2.56240i	−0.483916	+	0.246567i
$109$	5.92099	+	8.14954i	0.567128	+	0.780584i	0.992211	−	0.124570i	$-0.0397552\pi$
$109$	5.92099	+	8.14954i	0.567128	+	0.780584i	−0.425083	+	0.905154i	$0.639755\pi$
$110$	8.86457	+	9.94462i	0.845204	+	0.948183i
$111$	5.74241	−	7.90375i	0.545046	−	0.750191i
$112$	−2.62679	+	0.316200i	−0.248208	+	0.0298781i
$113$	0.478487	−	3.02105i	0.0450122	−	0.284196i	−0.954907	−	0.296905i	$-0.904045\pi$
$113$	0.478487	−	3.02105i	0.0450122	−	0.284196i	0.999919	+	0.0127090i	$0.00404550\pi$
$114$	−4.49178	+	6.18241i	−0.420694	+	0.579036i
$115$	−0.883138	+	4.05506i	−0.0823531	+	0.378137i
$116$	2.52952	−	1.83780i	0.234860	−	0.170636i
$117$	0.853205	+	1.67451i	0.0788789	+	0.154809i
$118$	2.75665	+	2.75665i	0.253771	+	0.253771i
$119$	0.525784	−	14.0968i	0.0481986	−	1.29225i
$120$	1.10334	−	2.83191i	0.100721	−	0.258517i
$121$	7.56945	+	23.2964i	0.688131	+	2.11785i
$122$	−8.59372	−	4.37872i	−0.778039	−	0.396431i
$123$	−14.7738	+	2.33995i	−1.33211	+	0.210986i
$124$	−1.15743			−0.103940
$125$	−10.0367	+	4.92582i	−0.897714	+	0.440579i
$126$	−2.93331	+	0.833582i	−0.261320	+	0.0742614i
$127$	2.45972	+	15.5301i	0.218265	+	1.37807i	0.816775	+	0.576956i	$0.195760\pi$
$127$	2.45972	+	15.5301i	0.218265	+	1.37807i	−0.598510	+	0.801115i	$0.704240\pi$
$128$	0.891007	+	0.453990i	0.0787546	+	0.0401275i
$129$	−0.410131	−	1.26225i	−0.0361100	−	0.111135i
$130$	−3.39727	−	1.32361i	−0.297961	−	0.116088i
$131$	−9.30330	−	3.02283i	−0.812833	−	0.264106i	−0.127036	−	0.991898i	$-0.540546\pi$
$131$	−9.30330	−	3.02283i	−0.812833	−	0.264106i	−0.685797	+	0.727792i	$0.740546\pi$
$132$	5.72601	−	5.72601i	0.498385	−	0.498385i
$133$	−10.9032	+	10.1191i	−0.945427	+	0.877437i
$134$	−3.35279	−	4.61473i	−0.289637	−	0.398652i
$135$	2.68568	−	12.3317i	0.231146	−	1.06134i
$136$	−3.13394	+	4.31350i	−0.268733	+	0.369879i
$137$	−21.2216	−	3.36117i	−1.81308	−	0.287164i	−0.844446	−	0.535641i	$-0.820070\pi$
$137$	−21.2216	−	3.36117i	−1.81308	−	0.287164i	−0.968638	+	0.248477i	$0.920070\pi$
$138$	2.49159	+	0.394630i	0.212099	+	0.0335931i
$139$	7.61407	+	5.53195i	0.645817	+	0.469214i	0.861844	−	0.507174i	$-0.169310\pi$
$139$	7.61407	+	5.53195i	0.645817	+	0.469214i	−0.216026	+	0.976388i	$0.569310\pi$
$140$	3.17195	−	4.99387i	0.268079	−	0.422059i
$141$	10.3088	−	7.48976i	0.868155	−	0.630751i
$142$	0.639173	−	0.325675i	0.0536382	−	0.0273300i
$143$	−6.86916	−	6.86916i	−0.574428	−	0.574428i
$144$	1.09618	+	0.356169i	0.0913479	+	0.0296807i
$145$	−0.400797	+	6.97992i	−0.0332844	+	0.579651i
$146$	0.501604	−	0.162981i	0.0415130	−	0.0134884i
$147$	9.48200	−	0.784213i	0.782062	−	0.0646808i
$148$	−7.09927	+	1.12441i	−0.583556	+	0.0924262i
$149$			3.65897i			0.299754i	0.988705	+	0.149877i	$0.0478878\pi$
$149$			3.65897i			0.299754i	−0.988705	+	0.149877i	$0.952112\pi$
$150$	3.33898	+	5.91917i	0.272627	+	0.483298i
$151$	−4.17791			−0.339993			−0.169997	−	0.985445i	$-0.554376\pi$
$151$	−4.17791			−0.339993			−0.169997	+	0.985445i	$0.554376\pi$
$152$	5.55313	−	0.879530i	0.450418	−	0.0713393i
$153$	−2.78992	+	5.47553i	−0.225552	+	0.442671i
$154$	13.0889	−	8.78341i	1.05473	−	0.707787i
$155$	1.63877	−	2.00316i	0.131629	−	0.160898i
$156$	−0.684853	+	2.10776i	−0.0548322	+	0.168756i
$157$	1.79889	−	1.79889i	0.143567	−	0.143567i	−0.631670	−	0.775237i	$-0.717630\pi$
$157$	1.79889	−	1.79889i	0.143567	−	0.143567i	0.775237	+	0.631670i	$0.217630\pi$
$158$	−5.18202	−	10.1703i	−0.412259	−	0.809105i
$159$	−0.373084	+	0.271062i	−0.0295875	+	0.0214966i
$160$	−2.04727	+	0.899269i	−0.161851	+	0.0710934i
$161$	4.61035	+	1.69044i	0.363346	+	0.133225i
$162$	−4.16191	−	0.659181i	−0.326990	−	0.0517902i
$163$	−1.46304	+	9.23725i	−0.114594	+	0.723517i	0.861756	+	0.507322i	$0.169365\pi$
$163$	−1.46304	+	9.23725i	−0.114594	+	0.723517i	−0.976350	+	0.216195i	$0.930635\pi$
$164$	8.90326	+	6.46859i	0.695228	+	0.505112i
$165$	1.80268	+	18.0173i	0.140339	+	1.40264i
$166$	−8.86631	−	12.2034i	−0.688159	−	0.947170i
$167$	5.22912	+	10.2627i	0.404641	+	0.794153i	0.999956	−	0.00933920i	$-0.00297280\pi$
$167$	5.22912	+	10.2627i	0.404641	+	0.794153i	−0.595315	+	0.803492i	$0.702973\pi$
$168$	−3.14107	−	1.75088i	−0.242339	−	0.135084i
$169$	−9.83518	−	3.19564i	−0.756552	−	0.245819i
$170$	−3.02810	−	11.5313i	−0.232244	−	0.884407i
$171$	6.16308	−	2.00251i	0.471303	−	0.153136i
$172$	−0.443308	+	0.870040i	−0.0338019	+	0.0663399i
$173$	−1.22737	−	7.74930i	−0.0933150	−	0.589168i	−0.989392	−	0.145270i	$-0.953595\pi$
$173$	−1.22737	−	7.74930i	−0.0933150	−	0.589168i	0.896077	−	0.443898i	$-0.146405\pi$
$174$	4.24974			0.322172
$175$	4.15179	+	12.5604i	0.313846	+	0.949474i
$176$	−5.95779			−0.449085
$177$	0.828918	+	5.23358i	0.0623053	+	0.393380i
$178$	5.88508	−	11.5501i	0.441105	−	0.865718i
$179$	−20.5502	+	6.67716i	−1.53599	+	0.499074i	−0.950267	−	0.311435i	$-0.899190\pi$
$179$	−20.5502	+	6.67716i	−1.53599	+	0.499074i	−0.585725	+	0.810510i	$0.699190\pi$
$180$	−2.16846	+	1.39286i	−0.161628	+	0.103817i
$181$	−5.66546	−	1.84082i	−0.421110	−	0.136827i	0.0907936	−	0.995870i	$-0.471060\pi$
$181$	−5.66546	−	1.84082i	−0.421110	−	0.136827i	−0.511904	+	0.859043i	$0.671060\pi$
$182$	−2.10043	+	3.76815i	−0.155694	+	0.279314i
$183$	−5.95154	−	11.6805i	−0.439950	−	0.863451i
$184$	−1.09092	−	1.50153i	−0.0804239	−	0.110694i
$185$	8.10564	−	13.8787i	0.595938	−	1.02038i
$186$	−1.27272	−	0.924688i	−0.0933207	−	0.0678014i
$187$	4.96924	−	31.3745i	0.363386	−	2.29433i
$188$	−9.25949	−	1.46656i	−0.675317	−	0.106960i
$189$	−14.0204	−	5.14072i	−1.01983	−	0.373933i
$190$	−6.34032	+	10.8561i	−0.459976	+	0.787583i
$191$	−8.26785	+	6.00695i	−0.598241	+	0.434647i	−0.845254	−	0.534365i	$-0.820551\pi$
$191$	−8.26785	+	6.00695i	−0.598241	+	0.434647i	0.247013	+	0.969012i	$0.420551\pi$
$192$	0.617062	+	1.21105i	0.0445326	+	0.0874002i
$193$	9.57725	−	9.57725i	0.689386	−	0.689386i	−0.272711	−	0.962096i	$-0.587920\pi$
$193$	9.57725	−	9.57725i	0.689386	−	0.689386i	0.962096	+	0.272711i	$0.0879201\pi$
$194$	−0.909414	+	2.79889i	−0.0652921	+	0.200949i
$195$	−2.67823	−	4.16959i	−0.191792	−	0.298591i
$196$	−5.34088	−	4.52493i	−0.381492	−	0.323209i
$197$	−2.92294	+	5.73659i	−0.208251	+	0.408715i	−0.971380	−	0.237531i	$-0.923662\pi$
$197$	−2.92294	+	5.73659i	−0.208251	+	0.408715i	0.763129	+	0.646246i	$0.223662\pi$
$198$	−6.78232	+	1.07421i	−0.481999	+	0.0763411i
$199$	−9.68857			−0.686804			−0.343402	−	0.939188i	$-0.611579\pi$
$199$	−9.68857			−0.686804			−0.343402	+	0.939188i	$0.611579\pi$
$200$	1.34231	−	4.81645i	0.0949158	−	0.340575i
$201$		−	7.75301i		−	0.546855i
$202$	−7.39669	+	1.17152i	−0.520429	+	0.0824279i
$203$	8.11660	+	1.59772i	0.569674	+	0.112138i
$204$	−6.89224	+	2.23942i	−0.482553	+	0.156791i
$205$	−23.8010	+	6.25013i	−1.66234	+	0.436528i
$206$	13.8720	+	4.50730i	0.966511	+	0.314038i
$207$	−1.51263	−	1.51263i	−0.105135	−	0.105135i
$208$	1.45283	−	0.740253i	0.100735	−	0.0513273i
$209$	−27.0995	+	19.6889i	−1.87451	+	1.36191i
$210$	7.47759	−	2.95720i	0.516003	−	0.204066i
$211$	−14.8980	−	10.8240i	−1.02562	−	0.745155i	−0.0581909	−	0.998305i	$-0.518533\pi$
$211$	−14.8980	−	10.8240i	−1.02562	−	0.745155i	−0.967427	+	0.253151i	$0.918533\pi$
$212$	0.335110	+	0.0530762i	0.0230154	+	0.00364529i
$213$	0.963029	+	0.152529i	0.0659857	+	0.0104511i
$214$	−3.05549	+	4.20552i	−0.208869	+	0.287484i
$215$	−0.878108	−	1.99910i	−0.0598865	−	0.136337i
$216$	3.31756	+	4.56624i	0.225732	+	0.310693i
$217$	−2.08314	−	2.24456i	−0.141413	−	0.152370i
$218$	7.12296	−	7.12296i	0.482428	−	0.482428i
$219$	0.681778	+	0.221523i	0.0460703	+	0.0149691i
$220$	8.43546	−	10.3111i	0.568719	−	0.695175i
$221$	2.68651	+	8.26821i	0.180714	+	0.556180i
$222$	−8.70476	−	4.43530i	−0.584225	−	0.297678i
$223$	0.760933	+	4.80434i	0.0509559	+	0.321723i	0.999979	+	0.00651555i	$0.00207398\pi$
$223$	0.760933	+	4.80434i	0.0509559	+	0.321723i	−0.949023	+	0.315207i	$0.897926\pi$
$224$	0.723227	+	2.54498i	0.0483226	+	0.170044i
$225$	0.659657	−	5.72506i	0.0439771	−	0.381670i
$226$	−3.05870			−0.203462
$227$	−17.4106	+	2.75758i	−1.15559	+	0.183027i	−0.704667	−	0.709538i	$-0.748903\pi$
$227$	−17.4106	+	2.75758i	−1.15559	+	0.183027i	−0.450918	+	0.892565i	$0.648903\pi$
$228$	6.80896	+	3.46934i	0.450935	+	0.229763i
$229$	8.52891	+	26.2493i	0.563606	+	1.73460i	0.672057	+	0.740500i	$0.265411\pi$
$229$	8.52891	+	26.2493i	0.563606	+	1.73460i	−0.108451	+	0.994102i	$0.534589\pi$
$230$	4.14329	+	0.237914i	0.273201	+	0.0156876i
$231$	21.4099	+	0.798551i	1.40867	+	0.0525408i
$232$	−2.21088	−	2.21088i	−0.145151	−	0.145151i
$233$	−1.37113	−	2.69100i	−0.0898259	−	0.176293i	0.841723	−	0.539910i	$-0.181542\pi$
$233$	−1.37113	−	2.69100i	−0.0898259	−	0.176293i	−0.931549	+	0.363617i	$0.881542\pi$
$234$	1.52042	−	1.10465i	0.0993932	−	0.0722134i
$235$	15.6484	−	13.9489i	1.02079	−	0.909925i
$236$	2.29148	−	3.15395i	0.149163	−	0.205305i
$237$	2.42698	−	15.3234i	0.157650	−	0.995360i
$238$	−14.0055	+	1.68591i	−0.907839	+	0.109281i
$239$	9.56006	−	13.1583i	0.618389	−	0.851139i	−0.378846	−	0.925460i	$-0.623679\pi$
$239$	9.56006	−	13.1583i	0.618389	−	0.851139i	0.997234	+	0.0743207i	$0.0236789\pi$
$240$	−2.96964	−	0.646748i	−0.191690	−	0.0417474i
$241$	14.3738	+	19.7839i	0.925901	+	1.27439i	0.961437	+	0.275025i	$0.0886861\pi$
$241$	14.3738	+	19.7839i	0.925901	+	1.27439i	−0.0355360	+	0.999368i	$0.511314\pi$
$242$	21.8254	−	11.1206i	1.40299	−	0.714860i
$243$	7.92326	+	7.92326i	0.508277	+	0.508277i
$244$	−2.98046	+	9.17290i	−0.190804	+	0.587235i
$245$	15.3933	−	2.83673i	0.983440	−	0.181232i
$246$	4.62227	+	14.2259i	0.294705	+	0.907010i
$247$	4.16196	−	8.16831i	0.264819	−	0.519737i
$248$	0.181062	+	1.14318i	0.0114974	+	0.0725920i
$249$		−	20.5025i		−	1.29929i
$250$	6.43527	+	9.14261i	0.407002	+	0.578229i
$251$		−	7.20994i		−	0.455087i	−0.973768	−	0.227544i	$-0.926931\pi$
$251$		−	7.20994i		−	0.455087i	0.973768	−	0.227544i	$-0.0730695\pi$
$252$	1.28219	+	2.76680i	0.0807704	+	0.174292i
$253$	9.85238	+	5.02004i	0.619414	+	0.315607i
$254$	14.9541	−	4.85888i	0.938303	−	0.304873i
$255$	5.88277	−	15.0991i	0.368393	−	0.945543i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	10.3664	−	10.3664i	0.646640	−	0.646640i	−0.305539	−	0.952179i	$-0.598837\pi$
$257$	10.3664	−	10.3664i	0.646640	−	0.646640i	0.952179	+	0.305539i	$0.0988368\pi$
$258$	−1.18256	+	0.602542i	−0.0736227	+	0.0375126i
$259$	−14.9578	−	11.7436i	−0.929432	−	0.729712i
$260$	−0.775866	+	3.56251i	−0.0481172	+	0.220937i
$261$	−2.91549	−	2.11823i	−0.180464	−	0.131115i
$262$	−1.53025	+	9.66164i	−0.0945394	+	0.596898i
$263$	−4.14119	+	26.1464i	−0.255357	+	1.61226i	0.443009	+	0.896517i	$0.353911\pi$
$263$	−4.14119	+	26.1464i	−0.255357	+	1.61226i	−0.698366	+	0.715741i	$0.746089\pi$
$264$	−6.55126	−	4.75977i	−0.403202	−	0.292943i
$265$	−0.566331	+	0.504824i	−0.0347895	+	0.0310111i
$266$	11.7002	+	9.18598i	0.717383	+	0.563229i
$267$	15.6989	−	7.99898i	0.960755	−	0.489529i
$268$	−4.03342	+	4.03342i	−0.246380	+	0.246380i
$269$	−5.90962	+	18.1879i	−0.360316	+	1.10894i	0.592547	+	0.805536i	$0.298122\pi$
$269$	−5.90962	+	18.1879i	−0.360316	+	1.10894i	−0.952863	+	0.303402i	$0.901878\pi$
$270$	−12.6000	−	0.723510i	−0.766812	−	0.0440314i
$271$	−12.8101	+	4.16226i	−0.778159	+	0.252839i	−0.671054	−	0.741409i	$-0.734158\pi$
$271$	−12.8101	+	4.16226i	−0.778159	+	0.252839i	−0.107105	+	0.994248i	$0.534158\pi$
$272$	4.75065	+	2.42058i	0.288050	+	0.146769i
$273$	−5.32010	+	2.46544i	−0.321987	+	0.149215i
$274$			21.4861i			1.29802i
$275$	5.90187	+	29.1984i	0.355896	+	1.76073i
$276$		−	2.52265i		−	0.151846i
$277$	0.754029	+	4.76075i	0.0453052	+	0.286046i	0.999931	−	0.0117628i	$-0.00374431\pi$
$277$	0.754029	+	4.76075i	0.0453052	+	0.286046i	−0.954626	+	0.297809i	$0.903744\pi$
$278$	4.27274	−	8.38572i	0.256262	−	0.502942i
$279$	0.412240	+	1.26875i	0.0246802	+	0.0759578i
$280$	−5.42859	−	2.35168i	−0.324420	−	0.140540i
$281$	8.70036	−	26.7770i	0.519020	−	1.59738i	−0.256826	−	0.966458i	$-0.582677\pi$
$281$	8.70036	−	26.7770i	0.519020	−	1.59738i	0.775846	−	0.630922i	$-0.217323\pi$
$282$	−9.01019	−	9.01019i	−0.536549	−	0.536549i
$283$	19.4277	−	9.89890i	1.15486	−	0.588429i	0.231675	−	0.972793i	$-0.425579\pi$
$283$	19.4277	−	9.89890i	1.15486	−	0.588429i	0.923181	+	0.384365i	$0.125579\pi$
$284$	−0.421654	−	0.580357i	−0.0250206	−	0.0344378i
$285$	−15.6450	+	6.87210i	−0.926729	+	0.407068i
$286$	−5.71001	+	7.85916i	−0.337640	+	0.464722i
$287$	3.47979	+	28.9079i	0.205405	+	1.70638i
$288$	0.180304	−	1.13840i	0.0106245	−	0.0670807i
$289$	−6.71713	+	9.24533i	−0.395125	+	0.543843i
$290$	6.95669	−	0.696038i	0.408511	−	0.0408727i
$291$	−3.23608	+	2.35115i	−0.189702	+	0.137827i
$292$	−0.239443	−	0.469932i	−0.0140123	−	0.0275007i
$293$	19.9864	+	19.9864i	1.16762	+	1.16762i	0.982767	+	0.184850i	$0.0591800\pi$
$293$	19.9864	+	19.9864i	1.16762	+	1.16762i	0.184850	+	0.982767i	$0.440820\pi$
$294$	−2.25787	−	9.24258i	−0.131682	−	0.539038i
$295$	2.21409	+	8.43144i	0.128909	+	0.490897i
$296$	2.22114	+	6.83597i	0.129101	+	0.397333i
$297$	−29.9617	−	15.2663i	−1.73856	−	0.885838i
$298$	3.61392	−	0.572389i	0.209349	−	0.0331576i
$299$	−3.02628			−0.175014
$300$	5.32396	−	4.22384i	0.307379	−	0.243863i
$301$	−2.48510	+	0.706209i	−0.143239	+	0.0407052i
$302$	0.653569	+	4.12647i	0.0376087	+	0.237452i
$303$	−9.06943	−	4.62111i	−0.521025	−	0.265476i
$304$	−1.73740	−	5.34717i	−0.0996469	−	0.306682i
$305$	−11.6556	−	18.1459i	−0.667395	−	1.03903i
$306$	5.84456	+	1.89901i	0.334111	+	0.108559i
$307$	15.0098	−	15.0098i	0.856656	−	0.856656i	−0.134287	−	0.990943i	$-0.542874\pi$
$307$	15.0098	−	15.0098i	0.856656	−	0.856656i	0.990943	+	0.134287i	$0.0428743\pi$
$308$	−10.7228	−	11.5537i	−0.610989	−	0.658333i
$309$	11.6529	+	16.0389i	0.662911	+	0.912419i
$310$	−2.23486	−	1.30523i	−0.126931	−	0.0741323i
$311$	−6.64346	+	9.14394i	−0.376716	+	0.518505i	−0.954711	−	0.297535i	$-0.903835\pi$
$311$	−6.64346	+	9.14394i	−0.376716	+	0.518505i	0.577995	+	0.816041i	$0.303835\pi$
$312$	2.18895	+	0.346695i	0.123925	+	0.0196277i
$313$	4.11916	+	0.652411i	0.232829	+	0.0368764i	0.271758	−	0.962366i	$-0.412395\pi$
$313$	4.11916	+	0.652411i	0.232829	+	0.0368764i	−0.0389297	+	0.999242i	$0.512395\pi$
$314$	−2.05815	−	1.49533i	−0.116148	−	0.0843864i
$315$	−6.60391	−	1.69835i	−0.372088	−	0.0956913i
$316$	−9.23443	+	6.70920i	−0.519477	+	0.377422i
$317$	24.5182	−	12.4927i	1.37708	−	0.701657i	0.400396	−	0.916342i	$-0.368872\pi$
$317$	24.5182	−	12.4927i	1.37708	−	0.701657i	0.976683	+	0.214685i	$0.0688724\pi$
$318$	0.326088	+	0.326088i	0.0182861	+	0.0182861i
$319$	17.7162	+	5.75636i	0.991919	+	0.322294i
$320$	1.20846	+	1.88139i	0.0675550	+	0.105173i
$321$	−6.71971	+	2.18337i	−0.375058	+	0.121864i
$322$	0.948407	−	4.81803i	0.0528527	−	0.268498i
$323$	29.6081	−	4.68946i	1.64744	−	0.260928i
$324$			4.21378i			0.234099i
$325$	−5.06709	−	6.38684i	−0.281071	−	0.354278i
$326$	9.35239			0.517981
$327$	13.5231	−	2.14185i	0.747831	−	0.118445i
$328$	4.99618	−	9.80555i	0.275868	−	0.541421i
$329$	−13.8212	−	20.5961i	−0.761986	−	1.13550i
$330$	17.5135	−	4.59901i	0.964084	−	0.253167i
$331$	9.24636	−	28.4574i	0.508226	−	1.56416i	−0.287052	−	0.957915i	$-0.592675\pi$
$331$	9.24636	−	28.4574i	0.508226	−	1.56416i	0.795278	−	0.606244i	$-0.207325\pi$
$332$	−10.6662	+	10.6662i	−0.585383	+	0.585383i
$333$	3.76109	+	7.38156i	0.206107	+	0.404507i
$334$	9.31835	−	6.77018i	0.509878	−	0.370448i
$335$	−1.26982	−	12.6914i	−0.0693775	−	0.693407i
$336$	−1.23796	+	3.37629i	−0.0675361	+	0.184192i
$337$	14.9784	+	2.37234i	0.815923	+	0.129230i	0.550428	−	0.834883i	$-0.314465\pi$
$337$	14.9784	+	2.37234i	0.815923	+	0.129230i	0.265495	+	0.964112i	$0.414465\pi$
$338$	−1.61774	+	10.2140i	−0.0879934	+	0.555568i
$339$	−3.36339	−	2.44365i	−0.182674	−	0.132721i
$340$	−10.9156	+	4.79470i	−0.591981	+	0.260029i
$341$	−4.05320	−	5.57876i	−0.219493	−	0.302107i
$342$	−2.94197	−	5.77394i	−0.159084	−	0.312219i
$343$	−0.837510	−	18.5013i	−0.0452213	−	0.998977i
$344$	0.928677	+	0.301746i	0.0500709	+	0.0162690i
$345$	4.36594	+	3.57175i	0.235054	+	0.192297i
$346$	−7.46189	+	2.42451i	−0.401153	+	0.130343i
$347$	−12.4828	+	24.4989i	−0.670113	+	1.31517i	0.266170	+	0.963926i	$0.414242\pi$
$347$	−12.4828	+	24.4989i	−0.670113	+	1.31517i	−0.936283	+	0.351245i	$0.885758\pi$
$348$	−0.664806	−	4.19742i	−0.0356373	−	0.225005i
$349$	−1.71513			−0.0918089			−0.0459045	−	0.998946i	$-0.514617\pi$
$349$	−1.71513			−0.0918089			−0.0459045	+	0.998946i	$0.514617\pi$
$350$	11.7562	−	6.06555i	0.628397	−	0.324217i
$351$	9.20310			0.491225
$352$	0.932003	+	5.88444i	0.0496759	+	0.313642i
$353$	−7.12953	+	13.9925i	−0.379467	+	0.744745i	−0.999197	−	0.0400696i	$-0.987242\pi$
$353$	−7.12953	+	13.9925i	−0.379467	+	0.744745i	0.619730	+	0.784815i	$0.287242\pi$
$354$	5.03948	−	1.63743i	0.267845	−	0.0870282i
$355$	1.60143	+	0.0919563i	0.0849950	+	0.00488053i
$356$	−12.3285	−	4.00579i	−0.653412	−	0.212306i
$357$	−16.7475	−	9.33533i	−0.886370	−	0.494078i
$358$	9.80971	+	19.2526i	0.518459	+	1.01753i
$359$	−7.82544	−	10.7708i	−0.413011	−	0.568461i	0.550939	−	0.834546i	$-0.314270\pi$
$359$	−7.82544	−	10.7708i	−0.413011	−	0.568461i	−0.963950	+	0.266085i	$0.914270\pi$
$360$	1.71493	+	1.92388i	0.0903847	+	0.101397i
$361$	−10.2024	−	7.41247i	−0.536968	−	0.390130i
$362$	−0.931883	+	5.88368i	−0.0489787	+	0.309239i
$363$	32.8839	+	5.20830i	1.72596	+	0.273365i
$364$	4.05034	+	1.48510i	0.212295	+	0.0778406i
$365$	1.15233	+	0.250962i	0.0603157	+	0.0131359i
$366$	−10.6057	+	7.70550i	−0.554370	+	0.402773i
$367$	2.08983	+	4.10151i	0.109088	+	0.214097i	0.939097	−	0.343653i	$-0.111665\pi$
$367$	2.08983	+	4.10151i	0.109088	+	0.214097i	−0.830009	+	0.557751i	$0.811665\pi$
$368$	−1.31238	+	1.31238i	−0.0684127	+	0.0684127i
$369$	3.91965	−	12.0634i	0.204049	−	0.627998i
$370$	−14.9758	−	5.83474i	−0.778556	−	0.303334i
$371$	0.500202	+	0.745391i	0.0259692	+	0.0386988i
$372$	−0.714206	+	1.40171i	−0.0370298	+	0.0726752i
$373$	−6.56014	+	1.03902i	−0.339671	+	0.0537987i	−0.323940	−	0.946078i	$-0.605008\pi$
$373$	−6.56014	+	1.03902i	−0.339671	+	0.0537987i	−0.0157313	+	0.999876i	$0.505008\pi$
$374$	−31.7656			−1.64256
$375$	−0.227870	+	15.1946i	−0.0117671	+	0.784644i
$376$			9.37491i			0.483474i
$377$	−5.03539	+	0.797528i	−0.259336	+	0.0410748i
$378$	−2.88417	+	14.6519i	−0.148345	+	0.753614i
$379$	−2.35273	+	0.764448i	−0.120852	+	0.0392670i	−0.368818	−	0.929501i	$-0.620238\pi$
$379$	−2.35273	+	0.764448i	−0.120852	+	0.0392670i	0.247967	+	0.968769i	$0.420238\pi$
$380$	11.7143	+	4.56400i	0.600929	+	0.234128i
$381$	20.3255	+	6.60417i	1.04131	+	0.338342i
$382$	7.22637	+	7.22637i	0.369733	+	0.369733i
$383$	−3.67963	+	1.87487i	−0.188020	+	0.0958011i	−0.545467	−	0.838133i	$-0.683648\pi$
$383$	−3.67963	+	1.87487i	−0.188020	+	0.0958011i	0.357446	+	0.933934i	$0.383648\pi$
$384$	1.09961	−	0.798915i	0.0561144	−	0.0407695i
$385$	35.1781	−	2.19939i	1.79284	−	0.112091i
$386$	−10.9576	−	7.96113i	−0.557725	−	0.405211i
$387$	1.11161	+	0.176062i	0.0565063	+	0.00894971i
$388$	2.90669	+	0.460375i	0.147565	+	0.0233720i
$389$	12.3490	−	16.9969i	0.626119	−	0.861779i	−0.371661	−	0.928368i	$-0.621212\pi$
$389$	12.3490	−	16.9969i	0.626119	−	0.861779i	0.997780	+	0.0665891i	$0.0212117\pi$
$390$	−3.69929	+	3.29752i	−0.187321	+	0.166977i
$391$	−5.81656	−	8.00581i	−0.294156	−	0.404871i
$392$	−3.63372	+	5.98298i	−0.183531	+	0.302186i
$393$	−9.40152	+	9.40152i	−0.474244	+	0.474244i
$394$	6.12321	+	1.98955i	0.308483	+	0.100232i
$395$	1.46318	−	25.4814i	0.0736204	−	1.28211i
$396$	2.12198	+	6.53078i	0.106633	+	0.328184i
$397$	−14.9504	−	7.61763i	−0.750341	−	0.382318i	0.0366131	−	0.999330i	$-0.488343\pi$
$397$	−14.9504	−	7.61763i	−0.750341	−	0.382318i	−0.786954	+	0.617012i	$0.788343\pi$
$398$	1.51563	+	9.56929i	0.0759715	+	0.479665i
$399$	5.52681	+	19.4485i	0.276687	+	0.973641i
$400$	−4.96714	−	0.572327i	−0.248357	−	0.0286164i
$401$	−8.59958			−0.429443			−0.214721	−	0.976675i	$-0.568884\pi$
$401$	−8.59958			−0.429443			−0.214721	+	0.976675i	$0.568884\pi$
$402$	−7.65756	+	1.21284i	−0.381924	+	0.0604909i
$403$	1.68155	+	0.856790i	0.0837638	+	0.0426798i
$404$	2.31419	+	7.12235i	0.115135	+	0.354350i
$405$	−7.29278	−	5.96618i	−0.362381	−	0.296462i
$406$	0.308330	−	8.26661i	0.0153022	−	0.410265i
$407$	−30.2806	−	30.2806i	−1.50095	−	1.50095i
$408$	3.29004	+	6.45706i	0.162881	+	0.319672i
$409$	21.1120	−	15.3387i	1.04392	−	0.758452i	0.0728726	−	0.997341i	$-0.476783\pi$
$409$	21.1120	−	15.3387i	1.04392	−	0.758452i	0.971047	+	0.238889i	$0.0767834\pi$
$410$	9.89648	+	22.5303i	0.488752	+	1.11269i
$411$	−17.1656	+	23.6264i	−0.846716	+	1.16541i
$412$	2.28174	−	14.4064i	0.112413	−	0.709750i
$413$	10.2405	−	1.23270i	0.503903	−	0.0606574i
$414$	−1.25738	+	1.73064i	−0.0617970	+	0.0850563i
$415$	−3.35797	−	33.5619i	−0.164836	−	1.64749i
$416$	−0.958411	−	1.31914i	−0.0469900	−	0.0646762i
$417$	11.3978	−	5.80749i	0.558154	−	0.284394i
$418$	23.6858	+	23.6858i	1.15851	+	1.15851i
$419$	−7.09643	+	21.8406i	−0.346683	+	1.06698i	0.613993	+	0.789311i	$0.289562\pi$
$419$	−7.09643	+	21.8406i	−0.346683	+	1.06698i	−0.960677	+	0.277670i	$0.910438\pi$
$420$	−4.09055	−	6.92292i	−0.199598	−	0.337804i
$421$	11.1424	+	34.2929i	0.543049	+	1.67133i	0.725584	+	0.688133i	$0.241570\pi$
$421$	11.1424	+	34.2929i	0.543049	+	1.67133i	−0.182535	+	0.983199i	$0.558430\pi$
$422$	−8.36019	+	16.4078i	−0.406967	+	0.798719i
$423$	1.69034	+	10.6724i	0.0821869	+	0.518908i
$424$		−	0.339287i		−	0.0164772i
$425$	7.15691	−	25.6802i	0.347161	−	1.24567i
$426$		−	0.975033i		−	0.0472405i
$427$	−23.1528	+	10.7295i	−1.12044	+	0.519237i
$428$	4.63173	+	2.35998i	0.223883	+	0.114074i
$429$	−12.5576	+	4.08021i	−0.606287	+	0.196994i
$430$	−1.83712	+	1.18002i	−0.0885937	+	0.0569058i
$431$	−5.48754	+	16.8889i	−0.264325	+	0.813510i	0.727523	+	0.686084i	$0.240672\pi$
$431$	−5.48754	+	16.8889i	−0.264325	+	0.813510i	−0.991848	+	0.127426i	$0.959328\pi$
$432$	3.99104	−	3.99104i	0.192019	−	0.192019i
$433$	25.8485	−	13.1704i	1.24220	−	0.632931i	0.295589	−	0.955315i	$-0.404484\pi$
$433$	25.8485	−	13.1704i	1.24220	−	0.632931i	0.946609	+	0.322384i	$0.104484\pi$
$434$	−1.89105	+	2.40862i	−0.0907731	+	0.115617i
$435$	8.20573	+	4.79243i	0.393435	+	0.229779i
$436$	−8.14954	−	5.92099i	−0.390292	−	0.283564i
$437$	−1.63240	+	10.3065i	−0.0780881	+	0.493029i
$438$	0.112142	−	0.708038i	0.00535836	−	0.0338314i
$439$	−13.9532	−	10.1376i	−0.665948	−	0.483840i	0.202718	−	0.979237i	$-0.435022\pi$
$439$	−13.9532	−	10.1376i	−0.665948	−	0.483840i	−0.868666	+	0.495397i	$0.835022\pi$
$440$	−11.5038	−	6.71860i	−0.548421	−	0.320296i
$441$	−3.05786	+	7.46618i	−0.145612	+	0.355532i
$442$	7.74616	−	3.94686i	0.368447	−	0.187733i
$443$	−6.26838	+	6.26838i	−0.297820	+	0.297820i	−0.840159	−	0.542339i	$-0.817539\pi$
$443$	−6.26838	+	6.26838i	−0.297820	+	0.297820i	0.542339	+	0.840159i	$0.317539\pi$
$444$	−3.01897	+	9.29142i	−0.143274	+	0.440951i
$445$	24.3884	−	15.6653i	1.15612	−	0.742605i
$446$	4.62616	−	1.50313i	0.219055	−	0.0711753i
$447$	4.43120	+	2.25781i	0.209589	+	0.106791i
$448$	2.40051	−	1.11245i	0.113414	−	0.0525581i
$449$		−	5.67123i		−	0.267642i	−0.991006	−	0.133821i	$-0.957275\pi$
$449$		−	5.67123i		−	0.267642i	0.991006	−	0.133821i	$-0.0427247\pi$
$450$	−5.75776	+	0.244061i	−0.271424	+	0.0115051i
$451$			65.5656i			3.08737i
$452$	0.478487	+	3.02105i	0.0225061	+	0.142098i
$453$	−2.57803	+	5.05967i	−0.121126	+	0.237724i
$454$	5.44725	+	16.7649i	0.255652	+	0.786816i
$455$	−8.30502	+	4.90719i	−0.389345	+	0.230053i
$456$	2.36147	−	7.26786i	0.110586	−	0.340349i
$457$	−20.4834	−	20.4834i	−0.958174	−	0.958174i	0.0409857	−	0.999160i	$-0.486950\pi$
$457$	−20.4834	−	20.4834i	−0.958174	−	0.958174i	−0.999160	+	0.0409857i	$0.986950\pi$
$458$	24.5919	−	12.5302i	1.14910	−	0.585498i
$459$	17.6885	+	24.3462i	0.825629	+	1.13638i
$460$	−0.413169	−	4.12950i	−0.0192641	−	0.192539i
$461$	6.63679	−	9.13476i	0.309106	−	0.425448i	−0.625996	−	0.779826i	$-0.715307\pi$
$461$	6.63679	−	9.13476i	0.309106	−	0.425448i	0.935102	+	0.354378i	$0.115307\pi$
$462$	−2.56052	−	21.2712i	−0.119126	−	0.989626i
$463$	−1.81310	+	11.4475i	−0.0842621	+	0.532010i	0.909063	+	0.416659i	$0.136799\pi$
$463$	−1.81310	+	11.4475i	−0.0842621	+	0.532010i	−0.993325	+	0.115351i	$0.963201\pi$
$464$	−1.83780	+	2.52952i	−0.0853179	+	0.117430i
$465$	−1.41471	−	3.22071i	−0.0656054	−	0.149357i
$466$	−2.44338	+	1.77522i	−0.113187	+	0.0822354i
$467$	9.70348	+	19.0441i	0.449023	+	0.881258i	0.998940	+	0.0460381i	$0.0146596\pi$
$467$	9.70348	+	19.0441i	0.449023	+	0.881258i	−0.549916	+	0.835220i	$0.685340\pi$
$468$	−1.32890	−	1.32890i	−0.0614284	−	0.0614284i
$469$	−15.0812	−	0.562502i	−0.696384	−	0.0259739i
$470$	−16.2251	−	13.2737i	−0.748408	−	0.612269i
$471$	−1.06852	−	3.28857i	−0.0492348	−	0.151529i
$472$	−3.47359	−	1.76988i	−0.159885	−	0.0814653i
$473$	−5.74597	+	0.910072i	−0.264200	+	0.0418452i
$474$	−15.5144			−0.712599
$475$	−24.4848	+	13.8118i	−1.12344	+	0.633729i
$476$	3.85609	+	13.5693i	0.176743	+	0.621947i
$477$	−0.0611749	−	0.386243i	−0.00280101	−	0.0176849i
$478$	−14.4918	−	7.38395i	−0.662840	−	0.337734i
$479$	−6.67716	−	20.5502i	−0.305087	−	0.938962i	−0.979645	−	0.200739i	$-0.935666\pi$
$479$	−6.67716	−	20.5502i	−0.305087	−	0.938962i	0.674558	−	0.738222i	$-0.264334\pi$
$480$	−0.174231	+	3.03426i	−0.00795253	+	0.138494i
$481$	11.1464	+	3.62167i	0.508231	+	0.165134i
$482$	17.2918	−	17.2918i	0.787618	−	0.787618i
$483$	4.89208	−	4.54027i	0.222597	−	0.206589i
$484$	−14.3979	−	19.8171i	−0.654452	−	0.900776i
$485$	−4.91228	+	4.37877i	−0.223055	+	0.198830i
$486$	6.58624	−	9.06518i	0.298758	−	0.411205i
$487$	−1.08093	−	0.171202i	−0.0489815	−	0.00775791i	0.131896	−	0.991264i	$-0.457894\pi$
$487$	−1.08093	−	0.171202i	−0.0489815	−	0.00775791i	−0.180877	+	0.983506i	$0.557894\pi$
$488$	9.52621	+	1.50880i	0.431231	+	0.0683003i
$489$	10.2840	+	7.47177i	0.465059	+	0.337885i
$490$	−5.20984	−	14.7600i	−0.235357	−	0.666789i
$491$	−23.7470	+	17.2532i	−1.07169	+	0.778626i	−0.976215	−	0.216806i	$-0.930436\pi$
$491$	−23.7470	+	17.2532i	−1.07169	+	0.778626i	−0.0954718	+	0.995432i	$0.530436\pi$
$492$	13.3277	−	6.79079i	0.600858	−	0.306152i
$493$	−11.7879	−	11.7879i	−0.530901	−	0.530901i
$494$	−8.71882	−	2.83292i	−0.392278	−	0.127459i
$495$	−14.3072	−	5.57425i	−0.643063	−	0.250544i
$496$	1.10078	−	0.357665i	0.0494265	−	0.0160597i
$497$	0.366570	−	1.86222i	0.0164429	−	0.0835321i
$498$	−20.2501	+	3.20729i	−0.907427	+	0.143722i
$499$		−	29.1579i		−	1.30529i	−0.757665	−	0.652644i	$-0.773660\pi$
$499$		−	29.1579i		−	1.30529i	0.757665	−	0.652644i	$-0.226340\pi$
$500$	8.02335	−	7.78626i	0.358815	−	0.348212i
$501$	15.6554			0.699431
$502$	−7.12117	+	1.12788i	−0.317834	+	0.0503399i
$503$	16.5895	−	32.5587i	0.739689	−	1.45172i	−0.146894	−	0.989152i	$-0.546928\pi$
$503$	16.5895	−	32.5587i	0.739689	−	1.45172i	0.886583	−	0.462570i	$-0.153072\pi$
$504$	2.53216	−	1.69923i	0.112791	−	0.0756896i
$505$	−15.6032	−	6.07918i	−0.694335	−	0.270520i
$506$	3.41698	−	10.5164i	0.151903	−	0.467511i
$507$	−9.93900	+	9.93900i	−0.441407	+	0.441407i
$508$	−7.13839	−	14.0099i	−0.316715	−	0.621588i
$509$	−11.9492	+	8.68160i	−0.529639	+	0.384805i	−0.820223	−	0.572044i	$-0.806150\pi$
$509$	−11.9492	+	8.68160i	−0.529639	+	0.384805i	0.290584	+	0.956850i	$0.406150\pi$
$510$	−15.8335	−	3.44832i	−0.701118	−	0.152694i
$511$	0.480372	−	1.31012i	0.0212504	−	0.0579565i
$512$	−0.987688	−	0.156434i	−0.0436501	−	0.00691349i
$513$	4.96422	−	31.3429i	0.219176	−	1.38382i
$514$	−11.8605	−	8.61713i	−0.523143	−	0.380085i
$515$	21.7024	+	24.3465i	0.956320	+	1.07284i
$516$	0.780116	+	1.07374i	0.0343427	+	0.0472687i
$517$	−25.3571	−	49.7660i	−1.11520	−	2.18871i
$518$	−9.25911	+	16.6107i	−0.406822	+	0.729834i
$519$	−10.1422	−	3.29539i	−0.445192	−	0.144652i
$520$	3.64002	+	0.209015i	0.159625	+	0.00916591i
$521$	20.3486	−	6.61167i	0.891489	−	0.289662i	0.172770	−	0.984962i	$-0.444728\pi$
$521$	20.3486	−	6.61167i	0.891489	−	0.289662i	0.718720	+	0.695300i	$0.244728\pi$
$522$	−1.63607	+	3.21096i	−0.0716086	+	0.140540i
$523$	−1.17567	−	7.42288i	−0.0514084	−	0.324580i	−0.999968	−	0.00798177i	$-0.997459\pi$
$523$	−1.17567	−	7.42288i	−0.0514084	−	0.324580i	0.948560	−	0.316598i	$-0.102541\pi$
$524$	9.78207			0.427332
$525$	17.7732	+	2.72248i	0.775685	+	0.118819i
$526$	26.4723			1.15425
$527$	0.965382	+	6.09518i	0.0420527	+	0.265510i
$528$	−3.67632	+	7.21519i	−0.159991	+	0.314001i
$529$	−18.5982	+	6.04292i	−0.808617	+	0.262736i
$530$	0.587203	+	0.480387i	0.0255065	+	0.0208667i
$531$	−4.27343	−	1.38852i	−0.185451	−	0.0602568i
$532$	7.24258	−	12.9931i	0.314006	−	0.563323i
$533$	−8.14650	−	15.9884i	−0.352864	−	0.692535i
$534$	−10.3563	−	14.2543i	−0.448163	−	0.616843i
$535$	−10.6423	+	4.67468i	−0.460109	+	0.202104i
$536$	4.61473	+	3.35279i	0.199326	+	0.144819i
$537$	−4.59435	+	29.0076i	−0.198261	+	1.25177i
$538$	18.8885	+	2.99164i	0.814340	+	0.128979i
$539$	3.10669	−	41.5886i	0.133815	−	1.79135i
$540$	1.25647	+	12.5581i	0.0540700	+	0.540413i
$541$	−5.08408	+	3.69380i	−0.218582	+	0.158809i	−0.691688	−	0.722197i	$-0.743133\pi$
$541$	−5.08408	+	3.69380i	−0.218582	+	0.158809i	0.473106	+	0.881005i	$0.343133\pi$
$542$	6.11496	+	12.0013i	0.262660	+	0.515499i
$543$	−5.72527	+	5.72527i	−0.245695	+	0.245695i
$544$	1.64761	−	5.07082i	0.0706407	−	0.217410i
$545$	21.7861	−	5.72101i	0.933215	−	0.245061i
$546$	3.26733	+	4.86892i	0.139829	+	0.208370i
$547$	−8.95628	+	17.5777i	−0.382943	+	0.751568i	−0.999357	−	0.0358543i	$-0.988585\pi$
$547$	−8.95628	+	17.5777i	−0.382943	+	0.751568i	0.616414	+	0.787422i	$0.288585\pi$
$548$	21.2216	−	3.36117i	0.906542	−	0.143582i
$549$	11.1167			0.474447
$550$	27.9157	−	10.3968i	1.19033	−	0.443323i
$551$			17.5792i			0.748898i
$552$	−2.49159	+	0.394630i	−0.106049	+	0.0167966i
$553$	−29.6310	−	5.83273i	−1.26004	−	0.248033i
$554$	4.58418	−	1.48949i	0.194763	−	0.0632824i
$555$	−11.8062	−	18.3804i	−0.501143	−	0.780203i
$556$	−8.95088	−	2.90832i	−0.379602	−	0.123340i
$557$	4.46365	+	4.46365i	0.189131	+	0.189131i	0.795320	−	0.606189i	$-0.207303\pi$
$557$	4.46365	+	4.46365i	0.189131	+	0.189131i	−0.606189	+	0.795320i	$0.707303\pi$
$558$	1.18864	−	0.605641i	0.0503190	−	0.0256388i
$559$	1.28810	−	0.935859i	0.0544808	−	0.0395826i
$560$	−1.47351	+	5.72964i	−0.0622673	+	0.242121i
$561$	−34.9299	−	25.3780i	−1.47474	−	1.07146i
$562$	−27.8083	−	4.40441i	−1.17302	−	0.185789i
$563$	−34.7486	−	5.50364i	−1.46448	−	0.231951i	−0.627257	−	0.778813i	$-0.715822\pi$
$563$	−34.7486	−	5.50364i	−1.46448	−	0.231951i	−0.837223	+	0.546862i	$0.815822\pi$
$564$	−7.48976	+	10.3088i	−0.315376	+	0.434077i
$565$	−5.90599	−	3.44930i	−0.248467	−	0.145113i
$566$	−12.8162	−	17.6400i	−0.538705	−	0.741463i
$567$	−8.17162	+	7.58396i	−0.343176	+	0.318496i
$568$	−0.507251	+	0.507251i	−0.0212838	+	0.0212838i
$569$	14.5883	+	4.74002i	0.611573	+	0.198712i	0.598395	−	0.801201i	$-0.295805\pi$
$569$	14.5883	+	4.74002i	0.611573	+	0.198712i	0.0131775	+	0.999913i	$0.495805\pi$
$570$	9.23491	+	14.3773i	0.386808	+	0.602201i
$571$	−1.38510	−	4.26289i	−0.0579644	−	0.178396i	0.917882	−	0.396853i	$-0.129898\pi$
$571$	−1.38510	−	4.26289i	−0.0579644	−	0.178396i	−0.975847	+	0.218457i	$0.929898\pi$
$572$	8.65564	+	4.41027i	0.361911	+	0.184403i
$573$	2.17295	+	13.7195i	0.0907762	+	0.573139i
$574$	28.0076	−	7.95914i	1.16902	−	0.332208i
$575$	7.73190	+	5.13177i	0.322443	+	0.214010i
$576$	−1.15259			−0.0480244
$577$	−9.58997	+	1.51890i	−0.399236	+	0.0632327i	−0.352824	−	0.935690i	$-0.614779\pi$
$577$	−9.58997	+	1.51890i	−0.399236	+	0.0632327i	−0.0464116	+	0.998922i	$0.514779\pi$
$578$	10.1823	+	5.18814i	0.423528	+	0.215798i
$579$	−5.68879	−	17.5083i	−0.236418	−	0.727621i
$580$	−1.77573	−	6.76215i	−0.0737333	−	0.280783i
$581$	−39.8815	−	1.48751i	−1.65456	−	0.0617123i
$582$	2.82844	+	2.82844i	0.117242	+	0.117242i
$583$	0.917697	+	1.80108i	0.0380071	+	0.0745931i
$584$	−0.426690	+	0.310008i	−0.0176565	+	0.0128282i
$585$	4.18147	−	0.418369i	0.172882	−	0.0172974i
$586$	16.6138	−	22.8669i	0.686308	−	0.944622i
$587$	0.595336	−	3.75880i	0.0245721	−	0.155142i	−0.972351	−	0.233522i	$-0.924975\pi$
$587$	0.595336	−	3.75880i	0.0245721	−	0.155142i	0.996924	+	0.0783801i	$0.0249748\pi$
$588$	−8.77558	+	3.67593i	−0.361899	+	0.151593i
$589$	3.82500	−	5.26466i	0.157606	−	0.216927i
$590$	7.98128	−	3.50580i	0.328584	−	0.144331i
$591$	5.14368	+	7.07967i	0.211583	+	0.291219i
$592$	6.40434	−	3.26318i	0.263217	−	0.134116i
$593$	−25.3593	−	25.3593i	−1.04138	−	1.04138i	−0.999106	−	0.0422775i	$-0.986539\pi$
$593$	−25.3593	−	25.3593i	−1.04138	−	1.04138i	−0.0422775	−	0.999106i	$-0.513461\pi$
$594$	−10.3913	+	31.9810i	−0.426359	+	1.31220i
$595$	−28.9440	−	12.5387i	−1.18659	−	0.514035i
$596$	−1.13068	−	3.47989i	−0.0463146	−	0.142542i
$597$	−5.97845	+	11.7334i	−0.244682	+	0.480215i
$598$	0.473414	+	2.98902i	0.0193593	+	0.122230i
$599$			18.9357i			0.773691i	0.922145	+	0.386845i	$0.126435\pi$
$599$			18.9357i			0.773691i	−0.922145	+	0.386845i	$0.873565\pi$
$600$	−5.00468	−	4.59766i	−0.204315	−	0.187699i
$601$		−	41.9840i		−	1.71256i	−0.516509	−	0.856282i	$-0.672769\pi$
$601$		−	41.9840i		−	1.71256i	0.516509	−	0.856282i	$-0.327231\pi$
$602$	1.08627	+	2.34403i	0.0442730	+	0.0955354i
$603$	5.85791	+	2.98475i	0.238553	+	0.121549i
$604$	3.97343	−	1.29105i	0.161677	−	0.0525319i
$605$	54.6829	+	3.13997i	2.22318	+	0.127658i
$606$	−3.14544	+	9.68068i	−0.127775	+	0.393251i
$607$	16.9378	−	16.9378i	0.687484	−	0.687484i	−0.274191	−	0.961675i	$-0.588410\pi$
$607$	16.9378	−	16.9378i	0.687484	−	0.687484i	0.961675	+	0.274191i	$0.0884102\pi$
$608$	−5.00955	+	2.55249i	−0.203164	+	0.103517i
$609$	6.94337	−	8.84374i	0.281359	−	0.358366i
$610$	−16.0992	+	14.3507i	−0.651837	+	0.581043i
$611$	12.3668	+	8.98502i	0.500308	+	0.363495i
$612$	0.961342	−	6.06968i	0.0388600	−	0.245352i
$613$	−1.01201	+	6.38955i	−0.0408745	+	0.258071i	−0.999660	−	0.0260580i	$-0.991705\pi$
$613$	−1.01201	+	6.38955i	−0.0408745	+	0.258071i	0.958786	+	0.284129i	$0.0917045\pi$
$614$	−17.1731	−	12.4770i	−0.693049	−	0.503530i
$615$	−7.11749	+	32.6810i	−0.287005	+	1.31783i
$616$	−9.73403	+	12.3982i	−0.392195	+	0.499538i
$617$	3.24015	−	1.65094i	0.130443	−	0.0664642i	−0.387551	−	0.921848i	$-0.626679\pi$
$617$	3.24015	−	1.65094i	0.130443	−	0.0664642i	0.517994	+	0.855384i	$0.326679\pi$
$618$	14.0185	−	14.0185i	0.563906	−	0.563906i
$619$	5.93776	−	18.2745i	0.238659	−	0.734516i	−0.757956	−	0.652305i	$-0.773802\pi$
$619$	5.93776	−	18.2745i	0.238659	−	0.734516i	0.996615	−	0.0822104i	$-0.0261980\pi$
$620$	−0.939555	+	2.41153i	−0.0377334	+	0.0968492i
$621$	−9.96282	+	3.23712i	−0.399794	+	0.129901i
$622$	10.0706	+	5.13124i	0.403795	+	0.205744i
$623$	−14.4206	−	31.1179i	−0.577751	−	1.24671i
$624$		−	2.21623i		−	0.0887203i
$625$	2.11561	+	24.9103i	0.0846242	+	0.996413i
$626$		−	4.17051i		−	0.166687i
$627$	7.12226	+	44.9682i	0.284436	+	1.79586i
$628$	−1.15496	+	2.26673i	−0.0460877	+	0.0904523i
$629$	11.8426	+	36.4479i	0.472197	+	1.45327i
$630$	−0.644364	+	6.78828i	−0.0256721	+	0.270452i
$631$	−7.15494	+	22.0206i	−0.284834	+	0.876628i	0.701615	+	0.712556i	$0.252463\pi$
$631$	−7.15494	+	22.0206i	−0.284834	+	0.876628i	−0.986448	+	0.164071i	$0.947537\pi$
$632$	8.07119	+	8.07119i	0.321055	+	0.321055i
$633$	−22.3014	+	11.3631i	−0.886401	+	0.451644i
$634$	−16.1743	−	22.2621i	−0.642365	−	0.884140i
$635$	34.3539	+	7.48182i	1.36329	+	0.296907i
$636$	0.271062	−	0.373084i	0.0107483	−	0.0147938i
$637$	4.40979	+	10.5275i	0.174722	+	0.417116i
$638$	2.91406	−	18.3986i	0.115369	−	0.728408i
$639$	−0.485993	+	0.668912i	−0.0192256	+	0.0264617i
$640$	1.66918	−	1.48790i	0.0659802	−	0.0588143i
$641$	15.8739	−	11.5331i	0.626982	−	0.455529i	−0.228371	−	0.973574i	$-0.573340\pi$
$641$	15.8739	−	11.5331i	0.626982	−	0.455529i	0.855353	+	0.518045i	$0.173340\pi$
$642$	3.20768	+	6.29543i	0.126597	+	0.248461i
$643$	14.4643	+	14.4643i	0.570418	+	0.570418i	0.932245	−	0.361827i	$-0.117847\pi$
$643$	14.4643	+	14.4643i	0.570418	+	0.570418i	−0.361827	+	0.932245i	$0.617847\pi$
$644$	−4.90707	−	0.183025i	−0.193366	−	0.00721220i
$645$	−2.96286	−	0.170131i	−0.116662	−	0.00669892i
$646$	−9.26344	−	28.5099i	−0.364465	−	1.12171i
$647$	37.2934	+	19.0019i	1.46615	+	0.747043i	0.991126	−	0.132928i	$-0.0424380\pi$
$647$	37.2934	+	19.0019i	1.46615	+	0.747043i	0.475028	+	0.879971i	$0.342438\pi$
$648$	4.16191	−	0.659181i	0.163495	−	0.0258951i
$649$	23.2264			0.911717
$650$	−5.51554	+	6.00382i	−0.216337	+	0.235489i
$651$	−4.00370	+	1.13776i	−0.156917	+	0.0445924i
$652$	−1.46304	−	9.23725i	−0.0572969	−	0.361759i
$653$	7.94302	+	4.04717i	0.310834	+	0.158378i	0.602448	−	0.798158i	$-0.294192\pi$
$653$	7.94302	+	4.04717i	0.310834	+	0.158378i	−0.291614	+	0.956536i	$0.594192\pi$
$654$	−4.23097	−	13.0216i	−0.165444	−	0.509184i
$655$	−13.8502	+	16.9298i	−0.541171	+	0.661502i
$656$	−10.4664	−	3.40074i	−0.408644	−	0.132777i
$657$	−0.429846	+	0.429846i	−0.0167699	+	0.0167699i
$658$	−18.1804	+	16.8729i	−0.708745	+	0.657776i
$659$	24.6441	+	33.9197i	0.959998	+	1.32132i	0.946940	+	0.321409i	$0.104157\pi$
$659$	24.6441	+	33.9197i	0.959998	+	1.32132i	0.0130579	+	0.999915i	$0.495843\pi$
$660$	−7.28210	−	16.5784i	−0.283455	−	0.645313i
$661$	−2.34888	+	3.23296i	−0.0913610	+	0.125748i	−0.852251	−	0.523134i	$-0.824763\pi$
$661$	−2.34888	+	3.23296i	−0.0913610	+	0.125748i	0.760890	+	0.648881i	$0.224763\pi$
$662$	−29.5535	−	4.68081i	−1.14863	−	0.181925i
$663$	11.6710	+	1.84850i	0.453263	+	0.0717898i
$664$	12.2034	+	8.86631i	0.473585	+	0.344080i
$665$	12.2326	+	30.9313i	0.474358	+	1.19946i
$666$	6.70232	−	4.86952i	0.259710	−	0.188690i
$667$	5.17055	−	2.63453i	0.200204	−	0.102009i
$668$	−8.14454	−	8.14454i	−0.315122	−	0.315122i
$669$	6.28785	+	2.04305i	0.243103	+	0.0789888i
$670$	−12.3365	+	3.23956i	−0.476602	+	0.125155i
$671$	−54.6502	+	17.7569i	−2.10975	+	0.685498i
$672$	3.52838	+	0.694547i	0.136110	+	0.0267927i
$673$	−4.58403	+	0.726039i	−0.176701	+	0.0279868i	−0.244158	−	0.969735i	$-0.578512\pi$
$673$	−4.58403	+	0.726039i	−0.176701	+	0.0279868i	0.0674566	+	0.997722i	$0.478512\pi$
$674$		−	15.1651i		−	0.584137i
$675$	−23.5132	−	15.6060i	−0.905023	−	0.600677i
$676$	10.3413			0.397743
$677$	−0.637385	+	0.100952i	−0.0244967	+	0.00387989i	−0.168671	−	0.985672i	$-0.553947\pi$
$677$	−0.637385	+	0.100952i	−0.0244967	+	0.00387989i	0.144174	+	0.989552i	$0.453947\pi$
$678$	−1.88741	+	3.70425i	−0.0724855	+	0.142261i
$679$	4.33868	+	6.46542i	0.166503	+	0.248120i
$680$	6.44324	+	10.0311i	0.247087	+	0.384677i
$681$	−7.40388	+	22.7868i	−0.283717	+	0.873192i
$682$	−4.87601	+	4.87601i	−0.186712	+	0.186712i
$683$	7.62173	+	14.9585i	0.291638	+	0.572371i	0.989614	−	0.143750i	$-0.0459160\pi$
$683$	7.62173	+	14.9585i	0.291638	+	0.572371i	−0.697976	+	0.716121i	$0.745916\pi$
$684$	−5.24263	+	3.80899i	−0.200457	+	0.145641i
$685$	−24.2299	+	41.4871i	−0.925777	+	1.58514i
$686$	−18.1425	+	3.72144i	−0.692684	+	0.142085i
$687$	37.0521	+	5.86848i	1.41363	+	0.223896i
$688$	0.152753	−	0.964447i	0.00582367	−	0.0367692i
$689$	−0.447567	−	0.325177i	−0.0170510	−	0.0123882i
$690$	2.84479	−	4.87094i	0.108299	−	0.185433i
$691$	8.78001	+	12.0846i	0.334007	+	0.459722i	0.942679	−	0.333700i	$-0.108297\pi$
$691$	8.78001	+	12.0846i	0.334007	+	0.459722i	−0.608672	+	0.793422i	$0.708297\pi$
$692$	3.56196	+	6.99074i	0.135405	+	0.265748i
$693$	−8.84574	+	15.8692i	−0.336022	+	0.602819i
$694$	26.1501	+	8.49667i	0.992642	+	0.322529i
$695$	17.7067	−	11.3734i	0.671654	−	0.431419i
$696$	−4.04174	+	1.31324i	−0.153202	+	0.0497783i
$697$	26.6385	−	52.2810i	1.00901	−	1.98029i
$698$	0.268306	+	1.69402i	0.0101555	+	0.0641195i
$699$	−4.10502			−0.155266
$700$	−7.82995	−	10.6626i	−0.295944	−	0.403010i
$701$	33.4167			1.26213			0.631066	−	0.775729i	$-0.282618\pi$
$701$	33.4167			1.26213			0.631066	+	0.775729i	$0.282618\pi$
$702$	−1.43968	−	9.08979i	−0.0543373	−	0.343072i
$703$	18.3467	−	36.0075i	0.691960	−	1.35805i
$704$	5.66619	−	1.84106i	0.213553	−	0.0693875i
$705$	−7.23680	−	27.5584i	−0.272554	−	1.03791i
$706$	14.9355	+	4.85285i	0.562106	+	0.182639i
$707$	−9.64701	+	17.3066i	−0.362813	+	0.650883i
$708$	−2.40561	−	4.72128i	−0.0904085	−	0.177437i
$709$	7.84667	+	10.8000i	0.294688	+	0.405603i	0.930530	−	0.366216i	$-0.119347\pi$
$709$	7.84667	+	10.8000i	0.294688	+	0.405603i	−0.635842	+	0.771819i	$0.719347\pi$
$710$	−0.159695	−	1.59610i	−0.00599323	−	0.0599005i
$711$	10.6435	+	7.73294i	0.399162	+	0.290008i
$712$	−2.02786	+	12.8034i	−0.0759973	+	0.479828i
$713$	−2.12173	−	0.336049i	−0.0794594	−	0.0125851i
$714$	−6.60051	+	18.0016i	−0.247018	+	0.673695i
$715$	−19.8881	+	8.73590i	−0.743773	+	0.326704i
$716$	17.4810	−	12.7007i	0.653297	−	0.474648i
$717$	−10.0362	−	19.6972i	−0.374810	−	0.735606i
$718$	−9.41402	+	9.41402i	−0.351328	+	0.351328i
$719$	2.58856	−	7.96677i	0.0965370	−	0.297110i	−0.891114	−	0.453779i	$-0.850076\pi$
$719$	2.58856	−	7.96677i	0.0965370	−	0.297110i	0.987651	+	0.156669i	$0.0500755\pi$
$720$	1.63192	−	1.99478i	0.0608179	−	0.0743409i
$721$	32.0443	−	21.5036i	1.19339	−	0.800837i
$722$	−5.72520	+	11.2363i	−0.213070	+	0.418174i
$723$	32.8289	−	5.19959i	1.22092	−	0.193375i
$724$	5.95702			0.221391
$725$	14.2174	+	6.50109i	0.528022	+	0.241444i
$726$		−	33.2938i		−	1.23565i
$727$	2.93765	−	0.465278i	0.108951	−	0.0172562i	−0.101721	−	0.994813i	$-0.532435\pi$
$727$	2.93765	−	0.465278i	0.108951	−	0.0172562i	0.210672	+	0.977557i	$0.432435\pi$
$728$	0.833207	−	4.23279i	0.0308807	−	0.156878i
$729$	26.5073	−	8.61273i	0.981750	−	0.318990i
$730$	0.0676081	−	1.17740i	0.00250229	−	0.0435776i
$731$	4.95150	+	1.60884i	0.183138	+	0.0595051i
$732$	9.26974	+	9.26974i	0.342619	+	0.342619i
$733$	−28.3015	+	14.4203i	−1.04534	+	0.532627i	−0.890344	−	0.455288i	$-0.849536\pi$
$733$	−28.3015	+	14.4203i	−1.04534	+	0.532627i	−0.154995	+	0.987915i	$0.549536\pi$
$734$	3.72410	−	2.70572i	0.137459	−	0.0998698i
$735$	6.06318	−	20.3925i	0.223644	−	0.752189i
$736$	1.50153	+	1.09092i	0.0553470	+	0.0402119i
$737$	−33.5655	−	5.31625i	−1.23640	−	0.195827i
$738$	−12.5281	−	1.98425i	−0.461165	−	0.0730414i
$739$	3.15963	−	4.34885i	0.116229	−	0.159975i	−0.746939	−	0.664893i	$-0.768477\pi$
$739$	3.15963	−	4.34885i	0.116229	−	0.159975i	0.863167	+	0.504918i	$0.168477\pi$
$740$	−3.42017	+	15.7042i	−0.125728	+	0.577298i
$741$	−7.32406	−	10.0807i	−0.269056	−	0.370324i
$742$	0.657965	−	0.610648i	0.0241547	−	0.0224176i
$743$	−25.0013	+	25.0013i	−0.917209	+	0.917209i	−0.996826	−	0.0796167i	$-0.974630\pi$
$743$	−25.0013	+	25.0013i	−0.917209	+	0.917209i	0.0796167	+	0.996826i	$0.474630\pi$
$744$	1.49618	+	0.486137i	0.0548525	+	0.0178227i
$745$	7.62353	+	2.97020i	0.279304	+	0.108820i
$746$	2.05247	+	6.31684i	0.0751461	+	0.231276i
$747$	15.4910	+	7.89305i	0.566785	+	0.288792i
$748$	4.96924	+	31.3745i	0.181693	+	1.14717i
$749$	3.75956	+	13.2296i	0.137371	+	0.483400i
$750$	15.0431	−	2.15189i	0.549298	−	0.0785759i
$751$	19.8749			0.725245			0.362623	−	0.931936i	$-0.381881\pi$
$751$	19.8749			0.725245			0.362623	+	0.931936i	$0.381881\pi$
$752$	9.25949	−	1.46656i	0.337659	−	0.0534799i
$753$	−8.73162	−	4.44898i	−0.318198	−	0.162130i
$754$	1.57542	+	4.84864i	0.0573734	+	0.176577i
$755$	−3.39146	+	8.70475i	−0.123428	+	0.316798i
$756$	14.9227	+	0.556591i	0.542734	+	0.0202430i
$757$	−14.4148	−	14.4148i	−0.523914	−	0.523914i	0.394837	−	0.918751i	$-0.370801\pi$
$757$	−14.4148	−	14.4148i	−0.523914	−	0.523914i	−0.918751	+	0.394837i	$0.870801\pi$
$758$	1.12308	+	2.20418i	0.0407922	+	0.0800593i
$759$	12.1591	−	8.83408i	0.441346	−	0.320657i
$760$	2.67529	−	12.2840i	0.0970431	−	0.445588i
$761$	1.99875	−	2.75104i	0.0724546	−	0.0997252i	−0.771252	−	0.636530i	$-0.780369\pi$
$761$	1.99875	−	2.75104i	0.0724546	−	0.0997252i	0.843706	+	0.536805i	$0.180369\pi$
$762$	3.34324	−	21.1084i	0.121113	−	0.764677i
$763$	−3.18520	−	26.4606i	−0.115312	−	0.957940i
$764$	6.00695	−	8.26785i	0.217324	−	0.299120i
$765$	9.14363	+	10.2577i	0.330588	+	0.370867i
$766$	2.42740	+	3.34103i	0.0877056	+	0.120716i
$767$	−5.66384	+	2.88587i	−0.204510	+	0.104203i
$768$	−0.961097	−	0.961097i	−0.0346806	−	0.0346806i
$769$	−3.60312	+	11.0893i	−0.129932	+	0.399889i	−0.994767	−	0.102166i	$-0.967423\pi$
$769$	−3.60312	+	11.0893i	−0.129932	+	0.399889i	0.864836	+	0.502055i	$0.167423\pi$
$770$	−7.67537	−	34.4009i	−0.276601	−	1.23972i
$771$	−6.15756	−	18.9510i	−0.221759	−	0.682504i
$772$	−6.14897	+	12.0680i	−0.221306	+	0.434338i
$773$	0.980775	+	6.19237i	0.0352760	+	0.222724i	0.999028	−	0.0440749i	$-0.0140340\pi$
$773$	0.980775	+	6.19237i	0.0352760	+	0.222724i	−0.963752	+	0.266799i	$0.914034\pi$
$774$		−	1.12547i		−	0.0404540i
$775$	−2.84333	−	5.04049i	−0.102135	−	0.181060i
$776$		−	2.94293i		−	0.105645i
$777$	−23.4520	+	10.8681i	−0.841336	+	0.389892i
$778$	−18.7195	−	9.53806i	−0.671126	−	0.341956i
$779$	−58.8458	+	19.1202i	−2.10837	+	0.685051i
$780$	3.83562	+	3.13790i	0.137337	+	0.112355i
$781$	1.32070	−	4.06470i	0.0472584	−	0.145447i
$782$	−6.99733	+	6.99733i	−0.250224	+	0.250224i
$783$	−15.7240	+	8.01176i	−0.561929	+	0.286317i
$784$	6.47776	+	2.65304i	0.231349	+	0.0947513i
$785$	−2.28775	−	5.20827i	−0.0816532	−	0.185891i
$786$	10.7565	+	7.81505i	0.383671	+	0.278754i
$787$	−1.39187	+	8.78789i	−0.0496146	+	0.313255i	0.950383	+	0.311082i	$0.100691\pi$
$787$	−1.39187	+	8.78789i	−0.0496146	+	0.313255i	−0.999998	+	0.00217231i	$0.999309\pi$
$788$	1.00718	−	6.35906i	0.0358792	−	0.226532i
$789$	29.1093	+	21.1492i	1.03632	+	0.752930i
$790$	−25.3965	+	2.54100i	−0.903568	+	0.0904048i
$791$	−4.99741	+	6.36518i	−0.177687	+	0.226320i
$792$	6.11842	−	3.11749i	0.217409	−	0.110775i
$793$	11.1204	−	11.1204i	0.394895	−	0.394895i
$794$	−5.18508	+	15.9580i	−0.184012	+	0.566329i
$795$	0.261907	+	0.997365i	0.00928888	+	0.0353729i
$796$	9.21438	−	2.99393i	0.326595	−	0.106117i
$797$	1.27167	+	0.647947i	0.0450448	+	0.0229515i	0.476368	−	0.879246i	$-0.341953\pi$
$797$	1.27167	+	0.647947i	0.0450448	+	0.0229515i	−0.431323	+	0.902198i	$0.641953\pi$
$798$	18.3444	−	8.50118i	0.649386	−	0.300938i
$799$			49.9849i			1.76834i
$800$	0.211751	+	4.99551i	0.00748651	+	0.176618i
$801$			14.9410i			0.527914i
$802$	1.34527	+	8.49371i	0.0475032	+	0.299923i
$803$	1.42655	−	2.79976i	0.0503418	−	0.0988013i
$804$	2.39581	+	7.37355i	0.0844938	+	0.260045i
$805$	7.26455	−	8.23351i	0.256042	−	0.290193i
$806$	0.583190	−	1.79487i	0.0205420	−	0.0632218i
$807$	18.3799	+	18.3799i	0.647004	+	0.647004i
$808$	6.67265	−	3.39988i	0.234743	−	0.119607i
$809$	6.06560	+	8.34858i	0.213255	+	0.293521i	0.902222	−	0.431273i	$-0.141935\pi$
$809$	6.06560	+	8.34858i	0.213255	+	0.293521i	−0.688966	+	0.724793i	$0.741935\pi$
$810$	−4.75188	+	8.13631i	−0.166964	+	0.285881i
$811$	17.0885	−	23.5203i	0.600058	−	0.825909i	−0.395655	−	0.918399i	$-0.629483\pi$
$811$	17.0885	−	23.5203i	0.600058	−	0.825909i	0.995714	+	0.0924898i	$0.0294826\pi$
$812$	−8.21307	+	0.988649i	−0.288222	+	0.0346948i
$813$	−2.86392	+	18.0821i	−0.100442	+	0.634166i
$814$	−25.1708	+	34.6447i	−0.882237	+	1.21430i
$815$	18.0583	+	10.5467i	0.632556	+	0.369434i
$816$	5.86289	−	4.25964i	0.205242	−	0.149117i
$817$	−2.49243	−	4.89167i	−0.0871991	−	0.171138i
$818$	−18.4525	−	18.4525i	−0.645178	−	0.645178i
$819$	0.185329	−	4.96883i	0.00647591	−	0.173625i
$820$	20.7047	−	13.2991i	0.723041	−	0.464426i
$821$	−13.8903	−	42.7500i	−0.484775	−	1.49198i	−0.832306	−	0.554316i	$-0.812980\pi$
$821$	−13.8903	−	42.7500i	−0.484775	−	1.49198i	0.347531	−	0.937668i	$-0.387020\pi$
$822$	26.0208	+	13.2583i	0.907581	+	0.462435i
$823$	42.6365	−	6.75295i	1.48621	−	0.235393i	0.640057	−	0.768327i	$-0.278911\pi$
$823$	42.6365	−	6.75295i	1.48621	−	0.235393i	0.846157	+	0.532934i	$0.178911\pi$
$824$	−14.5859			−0.508125
$825$	39.0027	+	10.8698i	1.35790	+	0.378437i
$826$	−2.81950	−	9.92161i	−0.0981029	−	0.345217i
$827$	−0.896247	−	5.65868i	−0.0311656	−	0.196772i	0.967193	−	0.254042i	$-0.0817602\pi$
$827$	−0.896247	−	5.65868i	−0.0311656	−	0.196772i	−0.998359	+	0.0572706i	$0.981760\pi$
$828$	1.90603	+	0.971171i	0.0662391	+	0.0337505i
$829$	−4.63396	−	14.2619i	−0.160944	−	0.495335i	0.837770	−	0.546023i	$-0.183859\pi$
$829$	−4.63396	−	14.2619i	−0.160944	−	0.495335i	−0.998715	+	0.0506876i	$0.983859\pi$
$830$	−32.6234	+	8.56687i	−1.13237	+	0.297360i
$831$	6.23080	+	2.02451i	0.216144	+	0.0702295i
$832$	−1.15297	+	1.15297i	−0.0399721	+	0.0399721i
$833$	−19.3742	+	31.8999i	−0.671276	+	1.10527i
$834$	−7.51900	−	10.3490i	−0.260362	−	0.358357i
$835$	25.6273	−	2.56409i	0.886871	−	0.0887342i
$836$	19.6889	−	27.0995i	0.680955	−	0.937255i
$837$	6.45231	+	1.02195i	0.223024	+	0.0353236i
$838$	22.6818	+	3.59244i	0.783529	+	0.124099i
$839$	−19.3537	−	14.0613i	−0.668165	−	0.485450i	0.201245	−	0.979541i	$-0.435501\pi$
$839$	−19.3537	−	14.0613i	−0.668165	−	0.485450i	−0.869410	+	0.494091i	$0.835501\pi$
$840$	−6.19779	+	5.12317i	−0.213844	+	0.176766i
$841$	−15.5526	+	11.2996i	−0.536295	+	0.389641i
$842$	32.1276	−	16.3698i	1.10719	−	0.564142i
$843$	−27.0596	−	27.0596i	−0.931984	−	0.931984i
$844$	17.5136	+	5.69051i	0.602843	+	0.195876i
$845$	−14.6420	+	17.8977i	−0.503699	+	0.615699i
$846$	10.2765	−	3.33905i	0.353315	−	0.114799i
$847$	12.5170	−	63.5881i	0.430090	−	2.18491i
$848$	−0.335110	+	0.0530762i	−0.0115077	+	0.00182264i
$849$		−	29.6362i		−	1.01711i
$850$	−26.4837	−	3.05152i	−0.908382	−	0.104666i
$851$	−13.3404			−0.457303
$852$	−0.963029	+	0.152529i	−0.0329928	+	0.00522555i
$853$	−16.8368	+	33.0442i	−0.576482	+	1.13141i	0.400141	+	0.916454i	$0.368961\pi$
$853$	−16.8368	+	33.0442i	−0.576482	+	1.13141i	−0.976624	+	0.214957i	$0.931039\pi$
$854$	14.2193	+	21.1893i	0.486575	+	0.725084i
$855$	0.830684	−	14.4664i	0.0284088	−	0.494742i
$856$	1.60637	−	4.94389i	0.0549045	−	0.168979i
$857$	−10.7092	+	10.7092i	−0.365818	+	0.365818i	−0.865949	−	0.500132i	$-0.833285\pi$
$857$	−10.7092	+	10.7092i	−0.365818	+	0.365818i	0.500132	+	0.865949i	$0.333285\pi$
$858$	5.99442	+	11.7647i	0.204646	+	0.401641i
$859$	24.4059	−	17.7319i	0.832717	−	0.605005i	−0.0876095	−	0.996155i	$-0.527923\pi$
$859$	24.4059	−	17.7319i	0.832717	−	0.605005i	0.920327	+	0.391150i	$0.127923\pi$
$860$	1.45288	+	1.62990i	0.0495430	+	0.0555792i
$861$	37.1562	+	13.6238i	1.26628	+	0.464296i
$862$	17.5394	+	2.77797i	0.597395	+	0.0946181i
$863$	4.99541	−	31.5398i	0.170046	−	1.07363i	−0.744049	−	0.668125i	$-0.767097\pi$
$863$	4.99541	−	31.5398i	0.170046	−	1.07363i	0.914094	−	0.405501i	$-0.132903\pi$
$864$	−4.56624	−	3.31756i	−0.155347	−	0.112866i
$865$	−17.1421	−	3.73332i	−0.582850	−	0.126937i
$866$	−17.0519	−	23.4699i	−0.579447	−	0.797540i
$867$	7.05170	+	13.8397i	0.239488	+	0.470022i
$868$	2.67479	+	1.49097i	0.0907883	+	0.0506069i
$869$	−64.6761	−	21.0145i	−2.19399	−	0.712869i
$870$	3.44977	−	8.85441i	0.116958	−	0.300193i
$871$	8.84561	−	2.87411i	0.299722	−	0.0973856i
$872$	−4.57322	+	8.97545i	−0.154869	+	0.303947i
$873$	−0.530622	−	3.35022i	−0.0179588	−	0.113388i
$874$	10.4350			0.352970
$875$	29.5400	+	1.54566i	0.998634	+	0.0522528i
$876$	−0.716864			−0.0242206
$877$	1.25565	+	7.92789i	0.0424004	+	0.267706i	0.999777	−	0.0211384i	$-0.00672906\pi$
$877$	1.25565	+	7.92789i	0.0424004	+	0.267706i	−0.957376	+	0.288844i	$0.906729\pi$
$878$	−7.83000	+	15.3672i	−0.264250	+	0.518619i
$879$	36.5374	−	11.8717i	1.23238	−	0.400423i
$880$	−4.83629	+	12.4132i	−0.163031	+	0.418447i
$881$	−14.5178	−	4.71711i	−0.489116	−	0.158923i	0.0540679	−	0.998537i	$-0.482781\pi$
$881$	−14.5178	−	4.71711i	−0.489116	−	0.158923i	−0.543184	+	0.839614i	$0.682781\pi$
$882$	7.85261	+	1.85224i	0.264411	+	0.0623682i
$883$	3.51560	+	6.89976i	0.118309	+	0.232195i	0.942565	−	0.334022i	$-0.108406\pi$
$883$	3.51560	+	6.89976i	0.118309	+	0.232195i	−0.824256	+	0.566218i	$0.808406\pi$
$884$	−5.11004	−	7.03336i	−0.171869	−	0.236558i
$885$	11.5771	+	2.52135i	0.389161	+	0.0847541i
$886$	7.17180	+	5.21062i	0.240941	+	0.175054i
$887$	4.95437	−	31.2807i	0.166352	−	1.05030i	−0.753332	−	0.657641i	$-0.771554\pi$
$887$	4.95437	−	31.2807i	0.166352	−	1.05030i	0.919683	−	0.392661i	$-0.128446\pi$
$888$	9.64930	+	1.52830i	0.323809	+	0.0512863i
$889$	14.3211	−	39.0582i	0.480315	−	1.30997i
$890$	−19.2876	−	21.6376i	−0.646522	−	0.725294i
$891$	−20.3102	+	14.7562i	−0.680418	+	0.494353i
$892$	−2.20831	−	4.33406i	−0.0739398	−	0.145115i
$893$	37.2709	−	37.2709i	1.24722	−	1.24722i
$894$	1.53682	−	4.72985i	0.0513990	−	0.158190i
$895$	−2.76983	+	48.2369i	−0.0925853	+	1.61238i
$896$	−1.47427	−	2.19693i	−0.0492520	−	0.0733944i
$897$	−1.86740	+	3.66498i	−0.0623507	+	0.122370i
$898$	−5.60140	+	0.887175i	−0.186921	+	0.0296054i
$899$	−3.61889			−0.120697
$900$	1.14177	+	5.64870i	0.0380590	+	0.188290i
$901$		−	1.80900i		−	0.0602666i
$902$	64.7584	−	10.2567i	2.15622	−	0.341512i
$903$	−0.678203	+	3.44536i	−0.0225692	+	0.114654i
$904$	2.90900	−	0.945192i	0.0967519	−	0.0314366i
$905$	−8.43437	+	10.3098i	−0.280368	+	0.342709i
$906$	5.40067	+	1.75478i	0.179425	+	0.0582988i
$907$	−22.9088	−	22.9088i	−0.760673	−	0.760673i	0.215771	−	0.976444i	$-0.430774\pi$
$907$	−22.9088	−	22.9088i	−0.760673	−	0.760673i	−0.976444	+	0.215771i	$0.930774\pi$
$908$	15.7064	−	8.00280i	0.521234	−	0.265582i
$909$	6.98310	−	5.07352i	0.231615	−	0.168278i
$910$	6.14596	+	7.43512i	0.203737	+	0.246472i
$911$	47.2701	+	34.3437i	1.56613	+	1.13786i	0.930749	+	0.365659i	$0.119156\pi$
$911$	47.2701	+	34.3437i	1.56613	+	1.13786i	0.635380	+	0.772200i	$0.280844\pi$
$912$	−7.54779	−	1.19545i	−0.249932	−	0.0395854i
$913$	−88.7625	−	14.0586i	−2.93761	−	0.465272i
$914$	−17.0269	+	23.4355i	−0.563201	+	0.775179i
$915$	−29.1678	+	2.91833i	−0.964259	+	0.0964771i
$916$	−16.2229	−	22.3290i	−0.536021	−	0.737770i
$917$	17.6058	+	18.9700i	0.581393	+	0.626444i
$918$	21.2793	−	21.2793i	0.702322	−	0.702322i
$919$	20.2705	+	6.58628i	0.668662	+	0.217261i	0.623625	−	0.781724i	$-0.285659\pi$
$919$	20.2705	+	6.58628i	0.668662	+	0.217261i	0.0450371	+	0.998985i	$0.485659\pi$
$920$	−4.01402	+	1.05408i	−0.132338	+	0.0347519i
$921$	−8.91569	−	27.4397i	−0.293782	−	0.904168i
$922$	−10.0605	−	5.12609i	−0.331325	−	0.168819i
$923$	0.182980	+	1.15529i	0.00602285	+	0.0380268i
$924$	−20.6088	+	5.85655i	−0.677979	+	0.192666i
$925$	−22.3367	−	28.1544i	−0.734426	−	0.925711i
$926$	11.5902			0.380877
$927$	−16.6046	+	2.62991i	−0.545366	+	0.0863774i
$928$	2.78587	+	1.41947i	0.0914507	+	0.0465965i
$929$	12.2370	+	37.6617i	0.401484	+	1.23564i	0.923796	+	0.382886i	$0.125070\pi$
$929$	12.2370	+	37.6617i	0.401484	+	1.23564i	−0.522312	+	0.852755i	$0.674930\pi$
$930$	−2.95975	+	1.90112i	−0.0970540	+	0.0623401i
$931$	38.2322	−	9.33974i	1.25301	−	0.306098i
$932$	2.13559	+	2.13559i	0.0699536	+	0.0699536i
$933$	6.97436	+	13.6880i	0.228330	+	0.448124i
$934$	17.2917	−	12.5632i	0.565802	−	0.411079i
$935$	−61.3355	−	35.8221i	−2.00589	−	1.17151i
$936$	−1.10465	+	1.52042i	−0.0361067	+	0.0496966i
$937$	−5.04733	+	31.8676i	−0.164889	+	1.04107i	0.756943	+	0.653480i	$0.226692\pi$
$937$	−5.04733	+	31.8676i	−0.164889	+	1.04107i	−0.921833	+	0.387588i	$0.873308\pi$
$938$	1.80364	+	14.9835i	0.0588909	+	0.489229i
$939$	3.33188	−	4.58594i	0.108732	−	0.149656i
$940$	−10.5721	+	18.1018i	−0.344823	+	0.590416i
$941$	−32.2067	−	44.3287i	−1.04991	−	1.44508i	−0.888888	−	0.458124i	$-0.848521\pi$
$941$	−32.2067	−	44.3287i	−1.04991	−	1.44508i	−0.161020	−	0.986951i	$-0.551479\pi$
$942$	−3.08093	+	1.56981i	−0.100382	+	0.0511472i
$943$	14.4428	+	14.4428i	0.470322	+	0.470322i
$944$	−1.20470	+	3.70769i	−0.0392097	+	0.120675i
$945$	−22.0919	+	25.0386i	−0.718651	+	0.814506i
$946$	1.79774	+	5.53286i	0.0584494	+	0.179889i
$947$	−19.3498	+	37.9762i	−0.628785	+	1.23406i	0.328388	+	0.944543i	$0.393495\pi$
$947$	−19.3498	+	37.9762i	−0.628785	+	1.23406i	−0.957173	+	0.289517i	$0.906505\pi$
$948$	2.42698	+	15.3234i	0.0788248	+	0.497680i
$949$			0.859979i			0.0279161i
$950$	17.4720	+	22.0227i	0.566867	+	0.714511i
$951$		−	37.4016i		−	1.21283i
$952$	12.7990	−	5.93132i	0.414818	−	0.192235i
$953$	−7.36421	−	3.75225i	−0.238550	−	0.121547i	0.330629	−	0.943761i	$-0.392739\pi$
$953$	−7.36421	−	3.75225i	−0.238550	−	0.121547i	−0.569179	+	0.822213i	$0.692739\pi$
$954$	−0.371918	+	0.120843i	−0.0120413	+	0.00391245i
$955$	5.80407	+	22.1024i	0.187815	+	0.715217i
$956$	−5.02602	+	15.4685i	−0.162553	+	0.500287i
$957$	17.9033	−	17.9033i	0.578731	−	0.578731i
$958$	−19.2526	+	9.80971i	−0.622024	+	0.316937i
$959$	44.7128	+	35.1047i	1.44385	+	1.13359i
$960$	3.02416	−	0.302576i	0.0976042	−	0.00976560i
$961$	−23.9957	−	17.4339i	−0.774056	−	0.562385i
$962$	1.83341	−	11.5757i	0.0591115	−	0.373215i
$963$	0.937278	−	5.91774i	0.0302034	−	0.190696i
$964$	−19.7839	−	14.3738i	−0.637197	−	0.462951i
$965$	−12.1799	−	27.7288i	−0.392086	−	0.892622i
$966$	−5.24966	−	4.12159i	−0.168905	−	0.132610i
$967$	−37.9221	+	19.3223i	−1.21949	+	0.621363i	−0.940782	−	0.339012i	$-0.889907\pi$
$967$	−37.9221	+	19.3223i	−1.21949	+	0.621363i	−0.278711	+	0.960375i	$0.589907\pi$
$968$	−17.3207	+	17.3207i	−0.556710	+	0.556710i
$969$	12.5908	−	38.7506i	0.404476	−	1.24485i
$970$	5.09331	+	4.16681i	0.163536	+	0.133788i
$971$	−3.47355	+	1.12862i	−0.111471	+	0.0362193i	−0.364222	−	0.931312i	$-0.618665\pi$
$971$	−3.47355	+	1.12862i	−0.111471	+	0.0362193i	0.252750	+	0.967532i	$0.418665\pi$
$972$	−9.98389	−	5.08704i	−0.320233	−	0.163167i
$973$	−10.4698	−	22.5925i	−0.335646	−	0.724281i
$974$			1.09440i			0.0350669i
$975$	−10.8615	+	2.19543i	−0.347846	+	0.0703101i
$976$		−	9.64496i		−	0.308728i
$977$	−1.33523	−	8.43031i	−0.0427178	−	0.269709i	0.957080	−	0.289824i	$-0.0935968\pi$
$977$	−1.33523	−	8.43031i	−0.0427178	−	0.269709i	−0.999798	+	0.0201148i	$0.993597\pi$
$978$	5.77101	−	11.3262i	0.184536	−	0.362173i
$979$	−23.8656	−	73.4509i	−0.762749	−	2.34750i
$980$	−13.7633	+	7.45467i	−0.439652	+	0.238131i
$981$	−3.58783	+	11.0422i	−0.114550	+	0.352550i
$982$	20.7556	+	20.7556i	0.662339	+	0.662339i
$983$	−0.849462	+	0.432822i	−0.0270936	+	0.0138049i	−0.467485	−	0.884001i	$-0.654840\pi$
$983$	−0.849462	+	0.432822i	−0.0270936	+	0.0138049i	0.440391	+	0.897806i	$0.354840\pi$
$984$	−8.79209	−	12.1013i	−0.280281	−	0.385774i
$985$	9.57957	+	10.7467i	0.305230	+	0.342419i
$986$	−9.79876	+	13.4868i	−0.312056	+	0.429508i
$987$	−33.4714	+	4.02912i	−1.06541	+	0.128248i
$988$	−1.43411	+	9.05464i	−0.0456253	+	0.288067i
$989$	−1.06525	+	1.46619i	−0.0338731	+	0.0466223i
$990$	−3.26747	+	15.0031i	−0.103847	+	0.476830i
$991$	5.65735	−	4.11031i	0.179712	−	0.130568i	−0.494293	−	0.869296i	$-0.664573\pi$
$991$	5.65735	−	4.11031i	0.179712	−	0.130568i	0.674004	+	0.738727i	$0.264573\pi$
$992$	−0.525462	−	1.03128i	−0.0166834	−	0.0327431i
$993$	−28.7578	−	28.7578i	−0.912601	−	0.912601i
$994$	−1.89664	−	0.0707413i	−0.0601577	−	0.00224378i
$995$	−7.86479	+	20.1863i	−0.249331	+	0.639949i
$996$	6.33562	+	19.4990i	0.200752	+	0.617850i
$997$	37.5523	+	19.1338i	1.18929	+	0.605975i	0.932738	−	0.360555i	$-0.117413\pi$
$997$	37.5523	+	19.1338i	1.18929	+	0.605975i	0.256555	+	0.966530i	$0.417413\pi$
$998$	−28.7989	+	4.56130i	−0.911614	+	0.144385i
$999$	40.5690			1.28355

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.r.a.237.8	yes	160
7.6	odd	2	inner	350.2.r.a.237.3	yes	160
25.23	odd	20	inner	350.2.r.a.223.3	✓	160
175.48	even	20	inner	350.2.r.a.223.8	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.r.a.223.3	✓	160	25.23	odd	20	inner
350.2.r.a.223.8	yes	160	175.48	even	20	inner
350.2.r.a.237.3	yes	160	7.6	odd	2	inner
350.2.r.a.237.8	yes	160	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.r (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 - 0.987688i) q^{2} +(0.617062 - 1.21105i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(0.811760 - 2.08352i) q^{5} +(-1.29267 - 0.420015i) q^{6} +(-2.31097 - 1.28818i) q^{7} +(0.453990 + 0.891007i) q^{8} +(0.677473 + 0.932462i) q^{9} +O(q^{10})\)	\(q+(-0.156434 - 0.987688i) q^{2} +(0.617062 - 1.21105i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(0.811760 - 2.08352i) q^{5} +(-1.29267 - 0.420015i) q^{6} +(-2.31097 - 1.28818i) q^{7} +(0.453990 + 0.891007i) q^{8} +(0.677473 + 0.932462i) q^{9} +(-2.18485 - 0.475832i) q^{10} +(-4.81995 - 3.50190i) q^{11} +(-0.212625 + 1.34246i) q^{12} +(1.61047 + 0.255074i) q^{13} +(-0.910801 + 2.48404i) q^{14} +(-2.02234 - 2.26874i) q^{15} +(0.809017 - 0.587785i) q^{16} +(2.42058 + 4.75065i) q^{17} +(0.815002 - 0.815002i) q^{18} +(1.73740 - 5.34717i) q^{19} +(-0.128187 + 2.23239i) q^{20} +(-2.98606 + 2.00383i) q^{21} +(-2.70478 + 5.30843i) q^{22} +(-1.83314 + 0.290341i) q^{23} +1.35920 q^{24} +(-3.68209 - 3.38263i) q^{25} -1.63055i q^{26} +(5.57469 - 0.882944i) q^{27} +(2.59594 + 0.510998i) q^{28} +(-2.97363 + 0.966190i) q^{29} +(-1.92445 + 2.35235i) q^{30} +(1.10078 + 0.357665i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-7.21519 + 3.67632i) q^{33} +(4.31350 - 3.13394i) q^{34} +(-4.55989 + 3.76927i) q^{35} +(-0.932462 - 0.677473i) q^{36} +(7.09927 + 1.12441i) q^{37} +(-5.55313 - 0.879530i) q^{38} +(1.30267 - 1.79297i) q^{39} +(2.22496 - 0.222614i) q^{40} +(-6.46859 - 8.90326i) q^{41} +(2.44628 + 2.63583i) q^{42} +(0.690468 - 0.690468i) q^{43} +(5.66619 + 1.84106i) q^{44} +(2.49275 - 0.654593i) q^{45} +(0.573532 + 1.76515i) q^{46} +(8.35310 + 4.25612i) q^{47} +(-0.212625 - 1.34246i) q^{48} +(3.68120 + 5.95388i) q^{49} +(-2.76498 + 4.16592i) q^{50} +7.24693 q^{51} +(-1.61047 + 0.255074i) q^{52} +(-0.302307 - 0.154033i) q^{53} +(-1.74415 - 5.36793i) q^{54} +(-11.2089 + 7.19975i) q^{55} +(0.0986133 - 2.64391i) q^{56} +(-5.40362 - 5.40362i) q^{57} +(1.41947 + 2.78587i) q^{58} +(-3.15395 + 2.29148i) q^{59} +(2.62444 + 1.53276i) q^{60} +(5.66916 - 7.80293i) q^{61} +(0.181062 - 1.14318i) q^{62} +(-0.364448 - 3.02760i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(1.83877 - 3.14839i) q^{65} +(4.75977 + 6.55126i) q^{66} +(5.08240 - 2.58961i) q^{67} +(-3.77014 - 3.77014i) q^{68} +(-0.779542 + 2.39918i) q^{69} +(4.43618 + 3.91411i) q^{70} +(0.221677 + 0.682250i) q^{71} +(-0.523263 + 1.02696i) q^{72} +(0.0825063 + 0.520924i) q^{73} -7.18776i q^{74} +(-6.36862 + 2.37191i) q^{75} +5.62235i q^{76} +(6.62772 + 14.3017i) q^{77} +(-1.97468 - 1.00615i) q^{78} +(10.8557 - 3.52724i) q^{79} +(-0.567934 - 2.16274i) q^{80} +(1.30213 - 4.00755i) q^{81} +(-7.78173 + 7.78173i) q^{82} +(13.4402 - 6.84812i) q^{83} +(2.22070 - 2.82850i) q^{84} +(11.8630 - 1.18693i) q^{85} +(-0.789980 - 0.573954i) q^{86} +(-0.664806 + 4.19742i) q^{87} +(0.932003 - 5.88444i) q^{88} +(10.4873 + 7.61946i) q^{89} +(-1.03649 - 2.35966i) q^{90} +(-3.39318 - 2.66404i) q^{91} +(1.65370 - 0.842601i) q^{92} +(1.11240 - 1.11240i) q^{93} +(2.89701 - 8.91607i) q^{94} +(-9.73058 - 7.96053i) q^{95} +(-1.29267 + 0.420015i) q^{96} +(-2.62217 - 1.33606i) q^{97} +(5.30472 - 4.56727i) q^{98} -6.86687i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{7}+O(q^{10}) \) 160 * q + 8 * q^7	\( 160 q + 8 q^{7} + 16 q^{15} + 40 q^{16} - 8 q^{18} - 24 q^{22} - 32 q^{23} + 12 q^{28} - 40 q^{29} - 56 q^{30} + 28 q^{35} + 40 q^{36} - 32 q^{37} + 40 q^{39} - 112 q^{43} - 32 q^{50} + 112 q^{53} - 152 q^{57} + 16 q^{58} + 8 q^{60} - 100 q^{63} - 8 q^{65} - 16 q^{67} - 56 q^{70} - 8 q^{72} - 144 q^{77} + 40 q^{78} + 40 q^{81} - 60 q^{84} + 48 q^{85} - 16 q^{88} + 8 q^{92} + 56 q^{93} - 104 q^{95} - 32 q^{98}+O(q^{100}) \) 160 * q + 8 * q^7 + 16 * q^15 + 40 * q^16 - 8 * q^18 - 24 * q^22 - 32 * q^23 + 12 * q^28 - 40 * q^29 - 56 * q^30 + 28 * q^35 + 40 * q^36 - 32 * q^37 + 40 * q^39 - 112 * q^43 - 32 * q^50 + 112 * q^53 - 152 * q^57 + 16 * q^58 + 8 * q^60 - 100 * q^63 - 8 * q^65 - 16 * q^67 - 56 * q^70 - 8 * q^72 - 144 * q^77 + 40 * q^78 + 40 * q^81 - 60 * q^84 + 48 * q^85 - 16 * q^88 + 8 * q^92 + 56 * q^93 - 104 * q^95 - 32 * q^98

Introduction

L-functions

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Database

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