LMFDB - Embedded newform 350.2.r.a.27.3

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			27.3
Character	$\chi$	$=$	350.27
Dual form			350.2.r.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.987688 - 0.156434i) q^{2} +(-2.10001 + 1.07001i) q^{3} +(0.951057 + 0.309017i) q^{4} +(0.797761 - 2.08892i) q^{5} +(2.24154 - 0.728320i) q^{6} +(-1.08017 + 2.41521i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(1.50176 - 2.06699i) q^{9} +O(q^{10})$	\(q+(-0.987688 - 0.156434i) q^{2} +(-2.10001 + 1.07001i) q^{3} +(0.951057 + 0.309017i) q^{4} +(0.797761 - 2.08892i) q^{5} +(2.24154 - 0.728320i) q^{6} +(-1.08017 + 2.41521i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(1.50176 - 2.06699i) q^{9} +(-1.11472 + 1.93840i) q^{10} +(0.551427 - 0.400635i) q^{11} +(-2.32787 + 0.368699i) q^{12} +(0.328023 + 2.07105i) q^{13} +(1.44469 - 2.21650i) q^{14} +(0.559852 + 5.24035i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-6.23787 - 3.17835i) q^{17} +(-1.80662 + 1.80662i) q^{18} +(-0.345752 - 1.06411i) q^{19} +(1.40423 - 1.74016i) q^{20} +(-0.315937 - 6.22774i) q^{21} +(-0.607311 + 0.309440i) q^{22} +(-0.0765451 + 0.483287i) q^{23} +2.35689 q^{24} +(-3.72715 - 3.33291i) q^{25} -2.09687i q^{26} +(0.164093 - 1.03604i) q^{27} +(-1.77364 + 1.96321i) q^{28} +(-9.03749 - 2.93646i) q^{29} +(0.266812 - 5.26341i) q^{30} +(-8.02789 + 2.60842i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.729317 + 1.43137i) q^{33} +(5.66386 + 4.11504i) q^{34} +(4.18346 + 4.18314i) q^{35} +(2.06699 - 1.50176i) q^{36} +(-1.23657 - 7.80742i) q^{37} +(0.175031 + 1.10510i) q^{38} +(-2.90489 - 3.99824i) q^{39} +(-1.65916 + 1.49906i) q^{40} +(2.11305 - 2.90836i) q^{41} +(-0.662186 + 6.20049i) q^{42} +(-4.78087 + 4.78087i) q^{43} +(0.648241 - 0.210626i) q^{44} +(-3.11973 - 4.78601i) q^{45} +(0.151205 - 0.465362i) q^{46} +(-1.07194 - 2.10380i) q^{47} +(-2.32787 - 0.368699i) q^{48} +(-4.66649 - 5.21765i) q^{49} +(3.15988 + 3.87494i) q^{50} +16.5004 q^{51} +(-0.328023 + 2.07105i) q^{52} +(2.68033 + 5.26044i) q^{53} +(-0.324145 + 0.997617i) q^{54} +(-0.396986 - 1.47150i) q^{55} +(2.05892 - 1.66158i) q^{56} +(1.86469 + 1.86469i) q^{57} +(8.46686 + 4.31408i) q^{58} +(5.96916 + 4.33685i) q^{59} +(-1.08691 + 5.15687i) q^{60} +(5.54322 + 7.62959i) q^{61} +(8.33710 - 1.32047i) q^{62} +(3.37007 + 5.85975i) q^{63} +(0.587785 + 0.809017i) q^{64} +(4.58794 + 0.966994i) q^{65} +(0.944253 - 1.29965i) q^{66} +(-5.54454 + 10.8818i) q^{67} +(-4.95040 - 4.95040i) q^{68} +(-0.356375 - 1.09681i) q^{69} +(-3.47757 - 4.78607i) q^{70} +(0.647222 - 1.99194i) q^{71} +(-2.27647 + 1.15992i) q^{72} +(3.14934 + 0.498806i) q^{73} +7.90474i q^{74} +(11.3933 + 3.01106i) q^{75} -1.11888i q^{76} +(0.371986 + 1.76456i) q^{77} +(2.24366 + 4.40344i) q^{78} +(-12.6057 - 4.09584i) q^{79} +(1.87324 - 1.22106i) q^{80} +(3.13254 + 9.64095i) q^{81} +(-2.54200 + 2.54200i) q^{82} +(3.09428 - 6.07287i) q^{83} +(1.62400 - 6.02056i) q^{84} +(-11.6156 + 10.4948i) q^{85} +(5.46990 - 3.97412i) q^{86} +(22.1208 - 3.50359i) q^{87} +(-0.673209 + 0.106626i) q^{88} +(8.39461 - 6.09904i) q^{89} +(2.33262 + 5.21512i) q^{90} +(-5.35635 - 1.44484i) q^{91} +(-0.222143 + 0.435979i) q^{92} +(14.0676 - 14.0676i) q^{93} +(0.729635 + 2.24559i) q^{94} +(-2.49868 - 0.126662i) q^{95} +(2.24154 + 0.728320i) q^{96} +(-5.76530 - 11.3150i) q^{97} +(3.79281 + 5.88342i) q^{98} -1.74145i 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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.987688	−	0.156434i	−0.698401	−	0.110616i
$2$	−0.987688	−	0.156434i	−0.698401	−	0.110616i
$3$	−2.10001	+	1.07001i	−1.21244	+	0.617769i	−0.938932	−	0.344101i	$-0.888184\pi$
$3$	−2.10001	+	1.07001i	−1.21244	+	0.617769i	−0.273507	+	0.961870i	$0.588184\pi$
$4$	0.951057	+	0.309017i	0.475528	+	0.154508i
$5$	0.797761	−	2.08892i	0.356770	−	0.934192i
$5$	0.797761	−	2.08892i	0.356770	−	0.934192i
$6$	2.24154	−	0.728320i	0.915104	−	0.297335i
$7$	−1.08017	+	2.41521i	−0.408264	+	0.912864i
$7$	−1.08017	+	2.41521i	−0.408264	+	0.912864i
$8$	−0.891007	−	0.453990i	−0.315018	−	0.160510i
$9$	1.50176	−	2.06699i	0.500586	−	0.688997i
$10$	−1.11472	+	1.93840i	−0.352505	+	0.612977i
$11$	0.551427	−	0.400635i	0.166261	−	0.120796i	−0.501543	−	0.865133i	$-0.667234\pi$
$11$	0.551427	−	0.400635i	0.166261	−	0.120796i	0.667805	+	0.744337i	$0.267234\pi$
$12$	−2.32787	+	0.368699i	−0.672000	+	0.106434i
$13$	0.328023	+	2.07105i	0.0909771	+	0.574407i	0.990498	+	0.137529i	$0.0439159\pi$
$13$	0.328023	+	2.07105i	0.0909771	+	0.574407i	−0.899521	+	0.436878i	$0.856084\pi$
$14$	1.44469	−	2.21650i	0.386109	−	0.592385i
$15$	0.559852	+	5.24035i	0.144553	+	1.35305i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	−6.23787	−	3.17835i	−1.51290	−	0.770863i	−0.516557	−	0.856253i	$-0.672787\pi$
$17$	−6.23787	−	3.17835i	−1.51290	−	0.770863i	−0.996348	+	0.0853893i	$0.972787\pi$
$18$	−1.80662	+	1.80662i	−0.425823	+	0.425823i
$19$	−0.345752	−	1.06411i	−0.0793209	−	0.244125i	0.903531	−	0.428524i	$-0.140966\pi$
$19$	−0.345752	−	1.06411i	−0.0793209	−	0.244125i	−0.982851	+	0.184399i	$0.940966\pi$
$20$	1.40423	−	1.74016i	0.313995	−	0.389111i
$21$	−0.315937	−	6.22774i	−0.0689432	−	1.35900i
$22$	−0.607311	+	0.309440i	−0.129479	+	0.0659729i
$23$	−0.0765451	+	0.483287i	−0.0159608	+	0.100772i	−0.994383	−	0.105845i	$-0.966245\pi$
$23$	−0.0765451	+	0.483287i	−0.0159608	+	0.100772i	0.978422	+	0.206617i	$0.0662454\pi$
$24$	2.35689			0.481099
$25$	−3.72715	−	3.33291i	−0.745431	−	0.666583i
$26$		−	2.09687i		−	0.411230i
$27$	0.164093	−	1.03604i	0.0315797	−	0.199386i
$28$	−1.77364	+	1.96321i	−0.335186	+	0.371012i
$29$	−9.03749	−	2.93646i	−1.67822	−	0.545287i	−0.693655	−	0.720308i	$-0.744001\pi$
$29$	−9.03749	−	2.93646i	−1.67822	−	0.545287i	−0.984565	+	0.175021i	$0.944001\pi$
$30$	0.266812	−	5.26341i	0.0487130	−	0.960963i
$31$	−8.02789	+	2.60842i	−1.44185	+	0.468486i	−0.922474	−	0.386059i	$-0.873836\pi$
$31$	−8.02789	+	2.60842i	−1.44185	+	0.468486i	−0.519377	+	0.854545i	$0.673836\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−0.729317	+	1.43137i	−0.126958	+	0.249169i
$34$	5.66386	+	4.11504i	0.971345	+	0.705723i
$35$	4.18346	+	4.18314i	0.707134	+	0.707079i
$36$	2.06699	−	1.50176i	0.344498	−	0.250293i
$37$	−1.23657	−	7.80742i	−0.203291	−	1.28353i	−0.852422	−	0.522855i	$-0.824867\pi$
$37$	−1.23657	−	7.80742i	−0.203291	−	1.28353i	0.649130	−	0.760677i	$-0.275133\pi$
$38$	0.175031	+	1.10510i	0.0283938	+	0.179271i
$39$	−2.90489	−	3.99824i	−0.465155	−	0.640231i
$40$	−1.65916	+	1.49906i	−0.262336	+	0.237023i
$41$	2.11305	−	2.90836i	0.330003	−	0.454210i	−0.611485	−	0.791256i	$-0.709428\pi$
$41$	2.11305	−	2.90836i	0.330003	−	0.454210i	0.941488	+	0.337046i	$0.109428\pi$
$42$	−0.662186	+	6.20049i	−0.102177	+	0.956757i
$43$	−4.78087	+	4.78087i	−0.729076	+	0.729076i	−0.970436	−	0.241360i	$-0.922407\pi$
$43$	−4.78087	+	4.78087i	−0.729076	+	0.729076i	0.241360	+	0.970436i	$0.422407\pi$
$44$	0.648241	−	0.210626i	0.0977260	−	0.0317531i
$45$	−3.11973	−	4.78601i	−0.465062	−	0.713456i
$46$	0.151205	−	0.465362i	0.0222940	−	0.0686139i
$47$	−1.07194	−	2.10380i	−0.156358	−	0.306871i	0.799517	−	0.600644i	$-0.205089\pi$
$47$	−1.07194	−	2.10380i	−0.156358	−	0.306871i	−0.955875	+	0.293773i	$0.905089\pi$
$48$	−2.32787	−	0.368699i	−0.336000	−	0.0532171i
$49$	−4.66649	−	5.21765i	−0.666641	−	0.745379i
$50$	3.15988	+	3.87494i	0.446875	+	0.547999i
$51$	16.5004			2.31052
$52$	−0.328023	+	2.07105i	−0.0454886	+	0.287203i
$53$	2.68033	+	5.26044i	0.368171	+	0.722577i	0.998557	−	0.0537053i	$-0.0171032\pi$
$53$	2.68033	+	5.26044i	0.368171	+	0.722577i	−0.630386	+	0.776282i	$0.717103\pi$
$54$	−0.324145	+	0.997617i	−0.0441106	+	0.135758i
$55$	−0.396986	−	1.47150i	−0.0535296	−	0.198416i
$56$	2.05892	−	1.66158i	0.275134	−	0.222038i
$57$	1.86469	+	1.86469i	0.246984	+	0.246984i
$58$	8.46686	+	4.31408i	1.11175	+	0.566466i
$59$	5.96916	+	4.33685i	0.777119	+	0.564610i	0.904113	−	0.427294i	$-0.140533\pi$
$59$	5.96916	+	4.33685i	0.777119	+	0.564610i	−0.126994	+	0.991903i	$0.540533\pi$
$60$	−1.08691	+	5.15687i	−0.140319	+	0.665749i
$61$	5.54322	+	7.62959i	0.709737	+	0.976869i	0.999803	+	0.0198624i	$0.00632281\pi$
$61$	5.54322	+	7.62959i	0.709737	+	0.976869i	−0.290066	+	0.957007i	$0.593677\pi$
$62$	8.33710	−	1.32047i	1.05881	−	0.167699i
$63$	3.37007	+	5.85975i	0.424589	+	0.738259i
$64$	0.587785	+	0.809017i	0.0734732	+	0.101127i
$65$	4.58794	+	0.966994i	0.569064	+	0.119941i
$66$	0.944253	−	1.29965i	0.116230	−	0.159976i
$67$	−5.54454	+	10.8818i	−0.677374	+	1.32942i	0.254653	+	0.967032i	$0.418039\pi$
$67$	−5.54454	+	10.8818i	−0.677374	+	1.32942i	−0.932027	+	0.362389i	$0.881961\pi$
$68$	−4.95040	−	4.95040i	−0.600324	−	0.600324i
$69$	−0.356375	−	1.09681i	−0.0429025	−	0.132040i
$70$	−3.47757	−	4.78607i	−0.415649	−	0.572045i
$71$	0.647222	−	1.99194i	0.0768111	−	0.236400i	−0.905277	−	0.424821i	$-0.860337\pi$
$71$	0.647222	−	1.99194i	0.0768111	−	0.236400i	0.982088	+	0.188421i	$0.0603370\pi$
$72$	−2.27647	+	1.15992i	−0.268284	+	0.136698i
$73$	3.14934	+	0.498806i	0.368602	+	0.0583808i	0.337988	−	0.941150i	$-0.390254\pi$
$73$	3.14934	+	0.498806i	0.368602	+	0.0583808i	0.0306141	+	0.999531i	$0.490254\pi$
$74$			7.90474i			0.918907i
$75$	11.3933	+	3.01106i	1.31558	+	0.347688i
$76$		−	1.11888i		−	0.128344i
$77$	0.371986	+	1.76456i	0.0423917	+	0.201091i
$78$	2.24366	+	4.40344i	0.254045	+	0.498591i
$79$	−12.6057	−	4.09584i	−1.41825	−	0.460818i	−0.503205	−	0.864167i	$-0.667846\pi$
$79$	−12.6057	−	4.09584i	−1.41825	−	0.460818i	−0.915046	+	0.403349i	$0.867846\pi$
$80$	1.87324	−	1.22106i	0.209434	−	0.136518i
$81$	3.13254	+	9.64095i	0.348060	+	1.07122i
$82$	−2.54200	+	2.54200i	−0.280717	+	0.280717i
$83$	3.09428	−	6.07287i	0.339642	−	0.666584i	−0.656502	−	0.754324i	$-0.727965\pi$
$83$	3.09428	−	6.07287i	0.339642	−	0.666584i	0.996143	+	0.0877404i	$0.0279646\pi$
$84$	1.62400	−	6.02056i	0.177193	−	0.656897i
$85$	−11.6156	+	10.4948i	−1.25989	+	1.13832i
$86$	5.46990	−	3.97412i	0.589835	−	0.428540i
$87$	22.1208	−	3.50359i	2.37160	−	0.375625i
$88$	−0.673209	+	0.106626i	−0.0717643	+	0.0113664i
$89$	8.39461	−	6.09904i	0.889827	−	0.646497i	−0.0460059	−	0.998941i	$-0.514649\pi$
$89$	8.39461	−	6.09904i	0.889827	−	0.646497i	0.935833	+	0.352444i	$0.114649\pi$
$90$	2.33262	+	5.21512i	0.245880	+	0.549722i
$91$	−5.35635	−	1.44484i	−0.561498	−	0.151460i
$92$	−0.222143	+	0.435979i	−0.0231600	+	0.0454540i
$93$	14.0676	−	14.0676i	1.45874	−	1.45874i
$94$	0.729635	+	2.24559i	0.0752561	+	0.231614i
$95$	−2.49868	−	0.126662i	−0.256359	−	0.0129953i
$96$	2.24154	+	0.728320i	0.228776	+	0.0743338i
$97$	−5.76530	−	11.3150i	−0.585378	−	1.14887i	−0.973804	−	0.227389i	$-0.926981\pi$
$97$	−5.76530	−	11.3150i	−0.585378	−	1.14887i	0.388426	−	0.921480i	$-0.373019\pi$
$98$	3.79281	+	5.88342i	0.383132	+	0.594315i
$99$		−	1.74145i		−	0.175022i
$100$	−2.51481	−	4.32154i	−0.251481	−	0.432154i
$101$			8.29455i			0.825338i	0.910881	+	0.412669i	$0.135403\pi$
$101$			8.29455i			0.825338i	−0.910881	+	0.412669i	$0.864597\pi$
$102$	−16.2973	−	2.58123i	−1.61367	−	0.255580i
$103$	8.31971	−	4.23910i	0.819765	−	0.417691i	0.00678098	−	0.999977i	$-0.497842\pi$
$103$	8.31971	−	4.23910i	0.819765	−	0.417691i	0.812984	+	0.582286i	$0.197842\pi$
$104$	0.647968	−	1.99424i	0.0635385	−	0.195551i
$105$	−13.2613	−	4.30828i	−1.29417	−	0.420445i
$106$	−1.82441	−	5.61497i	−0.177203	−	0.545374i
$107$	−6.58799	−	6.58799i	−0.636885	−	0.636885i	0.312901	−	0.949786i	$-0.398699\pi$
$107$	−6.58799	−	6.58799i	−0.636885	−	0.636885i	−0.949786	+	0.312901i	$0.898699\pi$
$108$	0.476216	−	0.934627i	0.0458239	−	0.0899345i
$109$	2.21573	−	3.04968i	0.212228	−	0.292107i	−0.689610	−	0.724181i	$-0.742218\pi$
$109$	2.21573	−	3.04968i	0.212228	−	0.292107i	0.901838	+	0.432074i	$0.142218\pi$
$110$	0.161906	+	1.51548i	0.0154372	+	0.144495i
$111$	10.9508	+	15.0725i	1.03940	+	1.43062i
$112$	−2.29350	+	1.31904i	−0.216715	+	0.124638i
$113$	−4.55040	+	0.720713i	−0.428066	+	0.0677989i	−0.366750	−	0.930319i	$-0.619530\pi$
$113$	−4.55040	+	0.720713i	−0.428066	+	0.0677989i	−0.0613155	+	0.998118i	$0.519530\pi$
$114$	−1.55003	−	2.13344i	−0.145174	−	0.199815i
$115$	0.948481	+	0.545444i	0.0884464	+	0.0508629i
$116$	−7.68775	−	5.58547i	−0.713789	−	0.518598i
$117$	4.77346	+	2.43220i	0.441306	+	0.224857i
$118$	−5.21724	−	5.21724i	−0.480286	−	0.480286i
$119$	14.4143	−	11.6326i	1.32136	−	1.06636i
$120$	1.88024	−	4.92335i	0.171641	−	0.449439i
$121$	−3.25562	+	10.0198i	−0.295966	+	0.910889i
$122$	−4.28145	−	8.40281i	−0.387624	−	0.760755i
$123$	−1.32545	+	8.36856i	−0.119512	+	0.754568i
$124$	−8.44102			−0.758026
$125$	−9.93556	+	5.12685i	−0.888664	+	0.458559i
$126$	−2.41191	−	6.31480i	−0.214870	−	0.562567i
$127$	0.341436	+	0.0540782i	0.0302975	+	0.00479866i	0.171565	−	0.985173i	$-0.445118\pi$
$127$	0.341436	+	0.0540782i	0.0302975	+	0.00479866i	−0.141267	+	0.989971i	$0.545118\pi$
$128$	−0.453990	−	0.891007i	−0.0401275	−	0.0787546i
$129$	4.92429	−	15.1554i	0.433560	−	1.33436i
$130$	−4.38019	−	1.67280i	−0.384168	−	0.146714i
$131$	−1.08493	+	0.352514i	−0.0947906	+	0.0307993i	−0.356028	−	0.934475i	$-0.615869\pi$
$131$	−1.08493	+	0.352514i	−0.0947906	+	0.0307993i	0.261238	+	0.965274i	$0.415869\pi$
$132$	−1.13594	+	1.13594i	−0.0988707	+	0.0988707i
$133$	2.94353	+	0.314356i	0.255237	+	0.0272582i
$134$	7.17857	−	9.88045i	0.620134	−	0.853541i
$135$	−2.03330	−	1.16929i	−0.174999	−	0.100637i
$136$	4.11504	+	5.66386i	0.352862	+	0.485672i
$137$	0.224997	+	1.42058i	0.0192228	+	0.121368i	0.995434	−	0.0954548i	$-0.0304306\pi$
$137$	0.224997	+	1.42058i	0.0192228	+	0.121368i	−0.976211	+	0.216823i	$0.930431\pi$
$138$	0.180409	+	1.13905i	0.0153574	+	0.0969628i
$139$	−16.1373	+	11.7244i	−1.36875	+	0.994454i	−0.370914	+	0.928667i	$0.620956\pi$
$139$	−16.1373	+	11.7244i	−1.36875	+	0.994454i	−0.997834	+	0.0657866i	$0.979044\pi$
$140$	2.68605	+	5.27116i	0.227013	+	0.445494i
$141$	4.50216	+	3.27101i	0.379150	+	0.275469i
$142$	−0.950862	+	1.86617i	−0.0797945	+	0.156606i
$143$	1.01062	+	1.01062i	0.0845120	+	0.0845120i
$144$	2.42989	−	0.789520i	0.202491	−	0.0657933i
$145$	−13.3438	+	16.5360i	−1.10814	+	1.37324i
$146$	−3.03253	−	0.985330i	−0.250974	−	0.0815465i
$147$	15.3826	+	5.96394i	1.26873	+	0.491897i
$148$	1.23657	−	7.80742i	0.101646	−	0.641766i
$149$			16.3091i			1.33609i	0.744120	+	0.668046i	$0.232869\pi$
$149$			16.3091i			1.33609i	−0.744120	+	0.668046i	$0.767131\pi$
$150$	−10.7820	−	4.75629i	−0.880345	−	0.388350i
$151$	−0.441335			−0.0359154			−0.0179577	−	0.999839i	$-0.505716\pi$
$151$	−0.441335			−0.0359154			−0.0179577	+	0.999839i	$0.505716\pi$
$152$	−0.175031	+	1.10510i	−0.0141969	+	0.0896356i
$153$	−15.9374	+	8.12050i	−1.28846	+	0.656504i
$154$	−0.0913674	−	1.80103i	−0.00736259	−	0.145131i
$155$	−0.955565	+	18.8505i	−0.0767528	+	1.51411i
$156$	−1.52719	−	4.70021i	−0.122273	−	0.376318i
$157$	−2.06860	+	2.06860i	−0.165092	+	0.165092i	−0.784818	−	0.619726i	$-0.787244\pi$
$157$	−2.06860	+	2.06860i	−0.165092	+	0.165092i	0.619726	+	0.784818i	$0.287244\pi$
$158$	11.8098	+	6.01738i	0.939535	+	0.478717i
$159$	−11.2574	−	8.17899i	−0.892771	−	0.648636i
$160$	−2.04119	+	0.912985i	−0.161370	+	0.0721778i
$161$	−1.08456	−	0.706902i	−0.0854751	−	0.0557117i
$162$	−1.58579	−	10.0123i	−0.124592	−	0.786640i
$163$	22.3392	−	3.53819i	1.74974	−	0.277132i	0.802269	−	0.596963i	$-0.203626\pi$
$163$	22.3392	−	3.53819i	1.74974	−	0.277132i	0.947475	+	0.319831i	$0.103626\pi$
$164$	2.90836	−	2.11305i	0.227105	−	0.165001i
$165$	2.40818	+	2.66537i	0.187477	+	0.207499i
$166$	−4.00619	+	5.51405i	−0.310941	+	0.427973i
$167$	−4.79322	−	2.44227i	−0.370911	−	0.188988i	0.258592	−	0.965987i	$-0.416741\pi$
$167$	−4.79322	−	2.44227i	−0.370911	−	0.188988i	−0.629503	+	0.776998i	$0.716741\pi$
$168$	−2.54583	+	5.69239i	−0.196415	+	0.439178i
$169$	8.18207	−	2.65852i	0.629390	−	0.204501i
$170$	13.1144	−	8.54853i	1.00583	−	0.655642i
$171$	−2.71875	−	0.883376i	−0.207908	−	0.0675534i
$172$	−6.02425	+	3.06951i	−0.459345	+	0.234048i
$173$	−0.280390	−	0.0444095i	−0.0213177	−	0.00337639i	0.145767	−	0.989319i	$-0.453435\pi$
$173$	−0.280390	−	0.0444095i	−0.0213177	−	0.00337639i	−0.167084	+	0.985943i	$0.553435\pi$
$174$	−22.3966			−1.69788
$175$	12.0756	−	5.40176i	0.912832	−	0.408335i
$176$	0.681601			0.0513776
$177$	−17.1757	−	2.72037i	−1.29101	−	0.204475i
$178$	−9.24536	+	4.71075i	−0.692969	+	0.353085i
$179$	−22.9849	−	7.46826i	−1.71798	−	0.558204i	−0.726347	−	0.687328i	$-0.758783\pi$
$179$	−22.9849	−	7.46826i	−1.71798	−	0.558204i	−0.991628	+	0.129124i	$0.958783\pi$
$180$	−1.48808	−	5.51582i	−0.110915	−	0.411125i
$181$	8.98251	−	2.91859i	0.667664	−	0.216937i	0.0444777	−	0.999010i	$-0.485838\pi$
$181$	8.98251	−	2.91859i	0.667664	−	0.216937i	0.623187	+	0.782073i	$0.285838\pi$
$182$	5.06438	+	2.26497i	0.375397	+	0.167890i
$183$	−19.8045	−	10.0909i	−1.46399	−	0.745941i
$184$	0.287610	−	0.395861i	0.0212029	−	0.0291833i
$185$	−17.2955	−	3.64536i	−1.27159	−	0.268012i
$186$	−16.0950	+	11.6937i	−1.18015	+	0.857426i
$187$	−4.71308	+	0.746479i	−0.344655	+	0.0545880i
$188$	−0.369365	−	2.33208i	−0.0269387	−	0.170084i
$189$	2.32501	+	1.51542i	0.169120	+	0.110230i
$190$	2.44810	+	0.515982i	0.177604	+	0.0374333i
$191$	1.61890	+	1.17620i	0.117140	+	0.0851071i	0.644813	−	0.764341i	$-0.276935\pi$
$191$	1.61890	+	1.17620i	0.117140	+	0.0851071i	−0.527673	+	0.849448i	$0.676935\pi$
$192$	−2.10001	−	1.07001i	−0.151555	−	0.0772211i
$193$	9.52612	−	9.52612i	0.685705	−	0.685705i	−0.275574	−	0.961280i	$-0.588868\pi$
$193$	9.52612	−	9.52612i	0.685705	−	0.685705i	0.961280	+	0.275574i	$0.0888680\pi$
$194$	3.92426	+	12.0776i	0.281745	+	0.867123i
$195$	−10.6694	+	2.87844i	−0.764052	+	0.206129i
$196$	−2.82575	−	6.40431i	−0.201839	−	0.457451i
$197$	21.8493	−	11.1328i	1.55670	−	0.793177i	0.557385	−	0.830254i	$-0.311805\pi$
$197$	21.8493	−	11.1328i	1.55670	−	0.793177i	0.999312	+	0.0370770i	$0.0118047\pi$
$198$	−0.272423	+	1.72001i	−0.0193602	+	0.122236i
$199$	22.9721			1.62845			0.814226	−	0.580548i	$-0.197162\pi$
$199$	22.9721			1.62845			0.814226	+	0.580548i	$0.197162\pi$
$200$	1.80781	+	4.66174i	0.127831	+	0.329635i
$201$		−	28.7845i		−	2.03030i
$202$	1.29755	−	8.19243i	0.0912955	−	0.576417i
$203$	16.8541	−	18.6556i	1.18293	−	1.30936i
$204$	15.6928	+	5.09891i	1.09872	+	0.356995i
$205$	−4.38962	−	6.73417i	−0.306585	−	0.470335i
$206$	−8.88042	+	2.88542i	−0.618728	+	0.201037i
$207$	0.883997	+	0.883997i	0.0614420	+	0.0614420i
$208$	−0.951959	+	1.86832i	−0.0660065	+	0.129545i
$209$	−0.616978	−	0.448261i	−0.0426773	−	0.0310069i
$210$	12.4241	+	6.32976i	0.857341	+	0.436795i
$211$	−7.63176	+	5.54480i	−0.525392	+	0.381720i	−0.818631	−	0.574320i	$-0.805267\pi$
$211$	−7.63176	+	5.54480i	−0.525392	+	0.381720i	0.293239	+	0.956039i	$0.405267\pi$
$212$	0.923578	+	5.83124i	0.0634316	+	0.400491i
$213$	0.772223	+	4.87562i	0.0529119	+	0.334072i
$214$	5.47630	+	7.53747i	0.374352	+	0.515251i
$215$	6.17285	+	13.8008i	0.420985	+	0.941209i
$216$	−0.616561	+	0.848623i	−0.0419517	+	0.0577415i
$217$	2.37157	−	22.2066i	0.160992	−	1.50748i
$218$	−2.66552	+	2.66552i	−0.180532	+	0.180532i
$219$	−7.14735	+	2.32232i	−0.482973	+	0.156928i
$220$	0.0771606	−	1.52215i	0.00520216	−	0.102623i
$221$	4.53637	−	13.9615i	0.305150	−	0.939154i
$222$	−8.45813	−	16.6000i	−0.567672	−	1.11412i
$223$	−7.32232	−	1.15974i	−0.490339	−	0.0776620i	−0.0936309	−	0.995607i	$-0.529847\pi$
$223$	−7.32232	−	1.15974i	−0.490339	−	0.0776620i	−0.396708	+	0.917945i	$0.629847\pi$
$224$	2.47160	−	0.944020i	0.165141	−	0.0630750i
$225$	−12.4864	+	2.69877i	−0.832425	+	0.179918i
$226$	4.60712			0.306461
$227$	−4.33172	+	27.3494i	−0.287506	+	1.81524i	0.245798	+	0.969321i	$0.420950\pi$
$227$	−4.33172	+	27.3494i	−0.287506	+	1.81524i	−0.533305	+	0.845923i	$0.679050\pi$
$228$	1.19721	+	2.34965i	0.0792869	+	0.155609i
$229$	−2.09144	+	6.43679i	−0.138206	+	0.425355i	−0.996075	−	0.0885138i	$-0.971788\pi$
$229$	−2.09144	+	6.43679i	−0.138206	+	0.425355i	0.857869	+	0.513869i	$0.171788\pi$
$230$	−0.851478	−	0.687104i	−0.0561448	−	0.0453063i
$231$	−2.66927	−	3.30757i	−0.175625	−	0.217622i
$232$	6.71934	+	6.71934i	0.441146	+	0.441146i
$233$	0.0784881	+	0.0399917i	0.00514193	+	0.00261994i	0.456560	−	0.889693i	$-0.349082\pi$
$233$	0.0784881	+	0.0399917i	0.00514193	+	0.00261994i	−0.451418	+	0.892313i	$0.649082\pi$
$234$	−4.33421	−	3.14899i	−0.283336	−	0.205856i
$235$	−5.24981	+	0.560863i	−0.342460	+	0.0365867i
$236$	4.33685	+	5.96916i	0.282305	+	0.388559i
$237$	30.8546	−	4.88689i	2.00422	−	0.317438i
$238$	−16.0566	+	9.23450i	−1.04079	+	0.598584i
$239$	−6.42564	−	8.84414i	−0.415640	−	0.572080i	0.548942	−	0.835860i	$-0.315031\pi$
$239$	−6.42564	−	8.84414i	−0.415640	−	0.572080i	−0.964583	+	0.263780i	$0.915031\pi$
$240$	−2.62727	+	4.56861i	−0.169590	+	0.294902i
$241$	−8.71673	+	11.9975i	−0.561494	+	0.772830i	−0.991515	−	0.129989i	$-0.958506\pi$
$241$	−8.71673	+	11.9975i	−0.561494	+	0.772830i	0.430022	+	0.902818i	$0.358506\pi$
$242$	4.78298	−	9.38713i	0.307462	−	0.603427i
$243$	−14.6691	−	14.6691i	−0.941021	−	0.941021i
$244$	2.91424	+	8.96912i	0.186565	+	0.574189i
$245$	−14.6220	+	5.58546i	−0.934165	+	0.356842i
$246$	2.61826	−	8.05818i	0.166934	−	0.513771i
$247$	2.09042	−	1.06512i	0.133011	−	0.0677723i
$248$	8.33710	+	1.32047i	0.529406	+	0.0838497i
$249$			16.0640i			1.01801i
$250$	10.6153	−	3.50946i	0.671368	−	0.221958i
$251$		−	20.9762i		−	1.32400i	−0.749502	−	0.662002i	$-0.769707\pi$
$251$		−	20.9762i		−	1.32400i	0.749502	−	0.662002i	$-0.230293\pi$
$252$	1.39437	+	6.61436i	0.0878369	+	0.416666i
$253$	0.151412	+	0.297164i	0.00951922	+	0.0186825i
$254$	−0.328773	−	0.106825i	−0.0206290	−	0.00670278i
$255$	13.1634	−	34.4680i	0.824324	−	2.15847i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−6.63127	+	6.63127i	−0.413647	+	0.413647i	−0.883007	−	0.469360i	$-0.844485\pi$
$257$	−6.63127	+	6.63127i	−0.413647	+	0.413647i	0.469360	+	0.883007i	$0.344485\pi$
$258$	−7.23450	+	14.1985i	−0.450400	+	0.883960i
$259$	20.1923	+	5.44672i	1.25469	+	0.338443i
$260$	4.06458	+	2.33742i	0.252074	+	0.144961i
$261$	−19.6417	+	14.2706i	−1.21579	+	0.883325i
$262$	1.12672	−	0.178454i	0.0696087	−	0.0110249i
$263$	−12.1117	+	1.91830i	−0.746839	+	0.118288i	−0.518243	−	0.855234i	$-0.673414\pi$
$263$	−12.1117	+	1.91830i	−0.746839	+	0.118288i	−0.228596	+	0.973521i	$0.573414\pi$
$264$	1.29965	−	0.944253i	0.0799881	−	0.0581148i
$265$	13.1269	−	1.40241i	0.806378	−	0.0861493i
$266$	−2.85812	−	0.770956i	−0.175242	−	0.0472703i
$267$	−11.1027	+	21.7903i	−0.679476	+	1.33355i
$268$	−8.63583	+	8.63583i	−0.527517	+	0.527517i
$269$	4.66244	+	14.3495i	0.284274	+	0.874905i	0.986615	+	0.163065i	$0.0521380\pi$
$269$	4.66244	+	14.3495i	0.284274	+	0.874905i	−0.702342	+	0.711840i	$0.747862\pi$
$270$	1.82535	+	1.47297i	0.111087	+	0.0896423i
$271$	−25.0124	−	8.12701i	−1.51939	−	0.493680i	−0.573789	−	0.819003i	$-0.694527\pi$
$271$	−25.0124	−	8.12701i	−1.51939	−	0.493680i	−0.945603	+	0.325323i	$0.894527\pi$
$272$	−3.17835	−	6.23787i	−0.192716	−	0.378226i
$273$	12.7944	−	2.69716i	0.774349	−	0.163240i
$274$		−	1.43829i		−	0.0868900i
$275$	−3.39053	−	0.344630i	−0.204457	−	0.0207820i
$276$		−	1.15325i		−	0.0694177i
$277$	4.71048	+	0.746067i	0.283025	+	0.0448268i	0.296333	−	0.955085i	$-0.404236\pi$
$277$	4.71048	+	0.746067i	0.283025	+	0.0448268i	−0.0133079	+	0.999911i	$0.504236\pi$
$278$	17.7727	−	9.05566i	1.06594	−	0.543122i
$279$	−6.66435	+	20.5108i	−0.398984	+	1.22795i
$280$	−1.82839	−	5.62646i	−0.109267	−	0.336245i
$281$	−8.83598	−	27.1944i	−0.527110	−	1.62228i	−0.760104	−	0.649801i	$-0.774852\pi$
$281$	−8.83598	−	27.1944i	−0.527110	−	1.62228i	0.232994	−	0.972478i	$-0.425148\pi$
$282$	−3.93503	−	3.93503i	−0.234328	−	0.234328i
$283$	2.69409	−	5.28744i	0.160147	−	0.314306i	−0.796965	−	0.604026i	$-0.793562\pi$
$283$	2.69409	−	5.28744i	0.160147	−	0.314306i	0.957111	+	0.289720i	$0.0935622\pi$
$284$	1.23109	−	1.69445i	0.0730517	−	0.100547i
$285$	5.38276	−	2.40761i	0.318847	−	0.142614i
$286$	−0.840079	−	1.15627i	−0.0496749	−	0.0683716i
$287$	4.74187	+	8.24497i	0.279904	+	0.486685i
$288$	−2.52349	+	0.399681i	−0.148698	+	0.0235514i
$289$	18.8167	+	25.8990i	1.10686	+	1.52347i
$290$	15.7663	−	14.2450i	0.925828	−	0.836493i
$291$	24.2143	+	17.5927i	1.41947	+	1.03131i
$292$	2.84106	+	1.44759i	0.166260	+	0.0847139i
$293$	−2.65754	−	2.65754i	−0.155255	−	0.155255i	0.625205	−	0.780461i	$-0.285015\pi$
$293$	−2.65754	−	2.65754i	−0.155255	−	0.155255i	−0.780461	+	0.625205i	$0.785015\pi$
$294$	−14.2602	−	8.29687i	−0.831673	−	0.483884i
$295$	13.8213	−	9.00932i	0.804707	−	0.524543i
$296$	−2.44270	+	7.51786i	−0.141979	+	0.436966i
$297$	−0.324589	−	0.637042i	−0.0188346	−	0.0369649i
$298$	2.55130	−	16.1083i	0.147793	−	0.933128i
$299$	−1.02602			−0.0593363
$300$	9.90519	+	6.38441i	0.571877	+	0.368604i
$301$	−6.38268	−	16.7109i	−0.367891	−	0.963203i
$302$	0.435902	+	0.0690401i	0.0250833	+	0.00397281i
$303$	−8.87522	−	17.4186i	−0.509868	−	1.00067i
$304$	0.345752	−	1.06411i	0.0198302	−	0.0610312i
$305$	20.3598	−	5.49274i	1.16580	−	0.314514i
$306$	17.0115	−	5.52737i	0.972482	−	0.315979i
$307$	−8.48013	+	8.48013i	−0.483986	+	0.483986i	−0.906402	−	0.422416i	$-0.861182\pi$
$307$	−8.48013	+	8.48013i	−0.483986	+	0.483986i	0.422416	+	0.906402i	$0.361182\pi$
$308$	−0.191501	+	1.79315i	−0.0109118	+	0.102174i
$309$	−12.9356	+	17.8043i	−0.735879	+	1.01285i
$310$	3.89267	−	18.4689i	0.221089	−	1.04896i
$311$	−3.86135	−	5.31469i	−0.218957	−	0.301368i	0.685382	−	0.728184i	$-0.259635\pi$
$311$	−3.86135	−	5.31469i	−0.218957	−	0.301368i	−0.904339	+	0.426816i	$0.859635\pi$
$312$	0.773114	+	4.88125i	0.0437690	+	0.276346i
$313$	2.25526	+	14.2391i	0.127475	+	0.804843i	0.965727	+	0.259560i	$0.0835777\pi$
$313$	2.25526	+	14.2391i	0.127475	+	0.804843i	−0.838252	+	0.545283i	$0.816422\pi$
$314$	2.36673	−	1.71953i	0.133562	−	0.0970387i
$315$	14.9290	−	2.36512i	0.841157	−	0.133260i
$316$	−10.7230	−	7.79075i	−0.603218	−	0.438264i
$317$	5.48718	−	10.7692i	0.308191	−	0.604859i	−0.684015	−	0.729468i	$-0.739768\pi$
$317$	5.48718	−	10.7692i	0.308191	−	0.604859i	0.992206	+	0.124609i	$0.0397677\pi$
$318$	9.83934	+	9.83934i	0.551763	+	0.551763i
$319$	−6.15996	+	2.00149i	−0.344891	+	0.112062i
$320$	2.15888	−	0.582433i	0.120685	−	0.0325590i
$321$	20.8840	+	6.78563i	1.16563	+	0.378737i
$322$	0.960621	+	0.867861i	0.0535333	+	0.0483640i
$323$	−1.22538	+	7.73673i	−0.0681818	+	0.430483i
$324$			10.1371i			0.563172i
$325$	5.68005	−	8.81241i	0.315073	−	0.488824i
$326$	−22.6177			−1.25268
$327$	−1.38985	+	8.77520i	−0.0768591	+	0.485269i
$328$	−3.20311	+	1.63207i	−0.176862	+	0.0901158i
$329$	6.23899	−	0.316508i	0.343967	−	0.0174496i
$330$	−1.96158	−	3.00928i	−0.107981	−	0.165655i
$331$	8.36256	+	25.7373i	0.459648	+	1.41465i	0.865591	+	0.500752i	$0.166943\pi$
$331$	8.36256	+	25.7373i	0.459648	+	1.41465i	−0.405943	+	0.913899i	$0.633057\pi$
$332$	4.81946	−	4.81946i	0.264502	−	0.264502i
$333$	−17.9949	−	9.16886i	−0.986114	−	0.502450i
$334$	4.35216	+	3.16203i	0.238139	+	0.173018i
$335$	18.3079	+	20.2632i	1.00027	+	1.10709i
$336$	3.40498	−	5.22405i	0.185757	−	0.284995i
$337$	2.67414	+	16.8839i	0.145670	+	0.919723i	0.946938	+	0.321417i	$0.104159\pi$
$337$	2.67414	+	16.8839i	0.145670	+	0.919723i	−0.801268	+	0.598306i	$0.795841\pi$
$338$	−8.49722	+	1.34583i	−0.462188	+	0.0732034i
$339$	8.78470	−	6.38246i	0.477119	−	0.346648i
$340$	−14.2902	+	6.39174i	−0.774995	+	0.346641i
$341$	−3.38177	+	4.65460i	−0.183133	+	0.252061i
$342$	2.54709	+	1.29781i	0.137731	+	0.0701773i
$343$	17.6423	−	5.63462i	0.952595	−	0.304241i
$344$	6.43026	−	2.08932i	0.346696	−	0.112648i
$345$	−2.57545	−	0.130554i	−0.138657	−	0.00702879i
$346$	0.269991	+	0.0877254i	0.0145148	+	0.00471615i
$347$	13.7190	−	6.99019i	0.736475	−	0.375253i	−0.0451674	−	0.998979i	$-0.514382\pi$
$347$	13.7190	−	6.99019i	0.736475	−	0.375253i	0.781643	+	0.623727i	$0.214382\pi$
$348$	22.1208	+	3.50359i	1.18580	+	0.187812i
$349$	17.3703			0.929810			0.464905	−	0.885361i	$-0.346089\pi$
$349$	17.3703			0.929810			0.464905	+	0.885361i	$0.346089\pi$
$350$	−12.7720	+	3.44621i	−0.682691	+	0.184208i
$351$	2.19952			0.117402
$352$	−0.673209	−	0.106626i	−0.0358822	−	0.00568318i
$353$	−32.5937	+	16.6073i	−1.73479	+	0.883919i	−0.763572	+	0.645723i	$0.776556\pi$
$353$	−32.5937	+	16.6073i	−1.73479	+	0.883919i	−0.971217	+	0.238196i	$0.923444\pi$
$354$	16.5387	+	5.37375i	0.879023	+	0.285612i
$355$	−3.64468	−	2.94109i	−0.193439	−	0.156097i
$356$	9.86846	−	3.20646i	0.523027	−	0.169942i
$357$	−17.8232	+	39.8520i	−0.943303	+	2.10919i
$358$	21.5337	+	10.9720i	1.13809	+	0.579886i
$359$	−3.94570	+	5.43079i	−0.208246	+	0.286626i	−0.900345	−	0.435176i	$-0.856686\pi$
$359$	−3.94570	+	5.43079i	−0.208246	+	0.286626i	0.692099	+	0.721802i	$0.256686\pi$
$360$	0.606896	+	5.68069i	0.0319862	+	0.299399i
$361$	14.3585	−	10.4321i	0.755712	−	0.549057i
$362$	−9.32849	+	1.47749i	−0.490294	+	0.0776550i
$363$	−3.88440	−	24.5251i	−0.203878	−	1.28724i
$364$	−4.64771	−	3.02932i	−0.243606	−	0.158780i
$365$	3.55438	−	6.18078i	0.186045	−	0.323517i
$366$	17.9821	+	13.0648i	0.939941	+	0.682907i
$367$	−0.261710	−	0.133348i	−0.0136611	−	0.00696070i	0.447147	−	0.894461i	$-0.352440\pi$
$367$	−0.261710	−	0.133348i	−0.0136611	−	0.00696070i	−0.460808	+	0.887500i	$0.652440\pi$
$368$	−0.345995	+	0.345995i	−0.0180362	+	0.0180362i
$369$	−2.83827	−	8.73531i	−0.147755	−	0.454742i
$370$	16.5124	+	6.30610i	0.858436	+	0.327838i
$371$	−15.6003	+	0.791411i	−0.809925	+	0.0410880i
$372$	17.7262	−	9.03195i	0.919060	−	0.468285i
$373$	−1.84613	+	11.6560i	−0.0955888	+	0.603524i	0.892667	+	0.450716i	$0.148831\pi$
$373$	−1.84613	+	11.6560i	−0.0955888	+	0.603524i	−0.988256	+	0.152807i	$0.951169\pi$
$374$	4.77183			0.246746
$375$	15.3790	−	21.3975i	0.794167	−	1.10496i
$376$			2.36115i			0.121767i
$377$	3.11706	−	19.6803i	0.160537	−	1.01359i
$378$	−2.05932	−	1.86047i	−0.105920	−	0.0956923i
$379$	17.8488	+	5.79941i	0.916829	+	0.297896i	0.729165	−	0.684337i	$-0.239908\pi$
$379$	17.8488	+	5.79941i	0.916829	+	0.297896i	0.187664	+	0.982233i	$0.439908\pi$
$380$	−2.33724	−	0.892596i	−0.119898	−	0.0457892i
$381$	−0.774882	+	0.251774i	−0.0396984	+	0.0128988i
$382$	−1.41497	−	1.41497i	−0.0723964	−	0.0723964i
$383$	−1.76408	+	3.46219i	−0.0901400	+	0.176910i	−0.931675	−	0.363293i	$-0.881652\pi$
$383$	−1.76408	+	3.46219i	−0.0901400	+	0.176910i	0.841535	+	0.540203i	$0.181652\pi$
$384$	1.90677	+	1.38535i	0.0973042	+	0.0706957i
$385$	3.98278	+	0.630653i	0.202981	+	0.0321410i
$386$	−10.8991	+	7.91863i	−0.554747	+	0.403047i
$387$	2.70231	+	17.0617i	0.137366	+	0.867296i
$388$	−1.98659	−	12.5428i	−0.100854	−	0.636765i
$389$	−1.88595	−	2.59579i	−0.0956214	−	0.131612i	0.758526	−	0.651643i	$-0.225920\pi$
$389$	−1.88595	−	2.59579i	−0.0956214	−	0.131612i	−0.854147	+	0.520032i	$0.825920\pi$
$390$	10.9883	−	1.17394i	0.556416	−	0.0594446i
$391$	2.01353	−	2.77139i	0.101829	−	0.140155i
$392$	1.78910	+	6.76750i	0.0903634	+	0.341811i
$393$	1.90116	−	1.90116i	0.0959009	−	0.0959009i
$394$	−23.3218	+	7.57773i	−1.17494	+	0.381760i
$395$	−18.6122	+	23.0648i	−0.936482	+	1.16051i
$396$	0.538137	−	1.65622i	0.0270424	−	0.0832280i
$397$	−7.01993	−	13.7774i	−0.352320	−	0.691468i	0.645035	−	0.764153i	$-0.276843\pi$
$397$	−7.01993	−	13.7774i	−0.352320	−	0.691468i	−0.997355	+	0.0726858i	$0.976843\pi$
$398$	−22.6893	−	3.59364i	−1.13731	−	0.180133i
$399$	−6.51780	+	2.48945i	−0.326298	+	0.124628i
$400$	−1.05629	−	4.88715i	−0.0528146	−	0.244358i
$401$	−24.3376			−1.21536			−0.607681	−	0.794181i	$-0.707900\pi$
$401$	−24.3376			−1.21536			−0.607681	+	0.794181i	$0.707900\pi$
$402$	−4.50289	+	28.4301i	−0.224584	+	1.41797i
$403$	−8.03550	−	15.7706i	−0.400277	−	0.785588i
$404$	−2.56316	+	7.88858i	−0.127522	+	0.392472i
$405$	22.6382	+	1.14757i	1.12490	+	0.0570232i
$406$	−19.5650	+	15.7893i	−0.970996	+	0.783611i
$407$	−3.80980	−	3.80980i	−0.188845	−	0.188845i
$408$	−14.7020	−	7.49103i	−0.727856	−	0.370861i
$409$	−22.8425	−	16.5960i	−1.12949	−	0.820621i	−0.143868	−	0.989597i	$-0.545954\pi$
$409$	−22.8425	−	16.5960i	−1.12949	−	0.820621i	−0.985620	+	0.168975i	$0.945954\pi$
$410$	3.28212	+	7.33795i	0.162093	+	0.362395i
$411$	−1.99252	−	2.74247i	−0.0982840	−	0.135276i
$412$	9.22247	−	1.46070i	0.454358	−	0.0719633i
$413$	−16.9221	+	9.73227i	−0.832682	+	0.478894i
$414$	−0.734826	−	1.01140i	−0.0361147	−	0.0497077i
$415$	−10.2172	−	11.3084i	−0.501544	−	0.555107i
$416$	1.23251	−	1.69640i	0.0604287	−	0.0831730i
$417$	21.3432	−	41.8884i	1.04518	−	2.05128i
$418$	0.539259	+	0.539259i	0.0263760	+	0.0263760i
$419$	−4.07219	−	12.5329i	−0.198939	−	0.612273i	−0.999908	−	0.0135662i	$-0.995682\pi$
$419$	−4.07219	−	12.5329i	−0.198939	−	0.612273i	0.800969	−	0.598706i	$-0.204318\pi$
$420$	−11.2809	−	8.19538i	−0.550451	−	0.399894i
$421$	−11.2107	+	34.5030i	−0.546376	+	1.68157i	0.171320	+	0.985215i	$0.445197\pi$
$421$	−11.2107	+	34.5030i	−0.546376	+	1.68157i	−0.717696	+	0.696357i	$0.754803\pi$
$422$	8.40520	−	4.28266i	0.409159	−	0.208477i
$423$	−5.95832	−	0.943706i	−0.289704	−	0.0458845i
$424$		−	5.90393i		−	0.286720i
$425$	12.6563	+	32.6365i	0.613921	+	1.58310i
$426$		−	4.93640i		−	0.239169i
$427$	−24.4147	+	5.14683i	−1.18151	+	0.249073i
$428$	−4.22975	−	8.30136i	−0.204453	−	0.401261i
$429$	−3.20367	−	1.04093i	−0.154675	−	0.0502568i
$430$	−3.93793	−	14.5966i	−0.189904	−	0.703909i
$431$	4.83539	+	14.8818i	0.232913	+	0.716831i	0.997391	+	0.0721825i	$0.0229964\pi$
$431$	4.83539	+	14.8818i	0.232913	+	0.716831i	−0.764479	+	0.644649i	$0.777004\pi$
$432$	0.741724	−	0.741724i	0.0356862	−	0.0356862i
$433$	15.8697	−	31.1461i	0.762651	−	1.49679i	−0.102202	−	0.994764i	$-0.532589\pi$
$433$	15.8697	−	31.1461i	0.762651	−	1.49679i	0.864854	−	0.502024i	$-0.167411\pi$
$434$	−5.81624	+	21.5622i	−0.279188	+	1.03502i
$435$	10.3284	−	49.0036i	0.495209	−	2.34954i
$436$	3.04968	−	2.21573i	0.146053	−	0.106114i
$437$	0.540738	−	0.0856445i	0.0258670	−	0.00409693i
$438$	7.42265	−	1.17563i	0.354668	−	0.0561739i
$439$	0.957762	−	0.695855i	0.0457115	−	0.0332113i	−0.564695	−	0.825300i	$-0.691006\pi$
$439$	0.957762	−	0.695855i	0.0457115	−	0.0332113i	0.610406	+	0.792088i	$0.291006\pi$
$440$	−0.314327	+	1.49134i	−0.0149850	+	0.0710969i
$441$	−17.7928	+	1.80994i	−0.847275	+	0.0861874i
$442$	−6.66459	+	13.0800i	−0.317002	+	0.622152i
$443$	−14.3319	+	14.3319i	−0.680931	+	0.680931i	−0.960210	−	0.279279i	$-0.909904\pi$
$443$	−14.3319	+	14.3319i	−0.680931	+	0.680931i	0.279279	+	0.960210i	$0.409904\pi$
$444$	5.75718	+	17.7188i	0.273224	+	0.840896i
$445$	−6.04350	−	22.4012i	−0.286489	−	1.06192i
$446$	7.05074	+	2.29093i	0.333862	+	0.108478i
$447$	−17.4508	−	34.2492i	−0.825396	−	1.61993i
$448$	−2.58885	+	0.545753i	−0.122312	+	0.0257844i
$449$		−	20.1363i		−	0.950289i	−0.879908	−	0.475144i	$-0.842396\pi$
$449$		−	20.1363i		−	0.950289i	0.879908	−	0.475144i	$-0.157604\pi$
$450$	12.7548	−	0.712239i	0.601269	−	0.0335753i
$451$		−	2.45031i		−	0.115381i
$452$	−4.55040	−	0.720713i	−0.214033	−	0.0338995i
$453$	0.926807	−	0.472232i	0.0435452	−	0.0221874i
$454$	8.55678	−	26.3351i	0.401590	−	1.23597i
$455$	−7.29123	+	10.0363i	−0.341818	+	0.470511i
$456$	−0.814900	−	2.50800i	−0.0381612	−	0.117448i
$457$	−16.7198	−	16.7198i	−0.782118	−	0.782118i	0.198070	−	0.980188i	$-0.436533\pi$
$457$	−16.7198	−	16.7198i	−0.782118	−	0.782118i	−0.980188	+	0.198070i	$0.936533\pi$
$458$	3.07263	−	6.03037i	0.143574	−	0.281781i
$459$	−4.31649	+	5.94115i	−0.201477	+	0.277309i
$460$	0.733508	+	0.811845i	0.0342000	+	0.0378525i
$461$	23.6838	+	32.5980i	1.10306	+	1.51824i	0.831258	+	0.555887i	$0.187621\pi$
$461$	23.6838	+	32.5980i	1.10306	+	1.51824i	0.271807	+	0.962352i	$0.412379\pi$
$462$	2.11899	+	3.68441i	0.0985841	+	0.171414i
$463$	−7.65675	+	1.21271i	−0.355840	+	0.0563594i	−0.331795	−	0.943351i	$-0.607654\pi$
$463$	−7.65675	+	1.21271i	−0.355840	+	0.0563594i	−0.0240443	+	0.999711i	$0.507654\pi$
$464$	−5.58547	−	7.68775i	−0.259299	−	0.356895i
$465$	−18.1635	−	40.6086i	−0.842310	−	1.88318i
$466$	−0.0712657	−	0.0517776i	−0.00330132	−	0.00239855i
$467$	8.88875	+	4.52905i	0.411323	+	0.209579i	0.647393	−	0.762157i	$-0.275859\pi$
$467$	8.88875	+	4.52905i	0.411323	+	0.209579i	−0.236070	+	0.971736i	$0.575859\pi$
$468$	3.78824	+	3.78824i	0.175111	+	0.175111i
$469$	−20.2928	−	25.1454i	−0.937033	−	1.16111i
$470$	5.27292	+	0.267294i	0.243222	+	0.0123293i
$471$	2.13066	−	6.55749i	0.0981755	−	0.302153i
$472$	−3.34967	−	6.57410i	−0.154181	−	0.302598i
$473$	−0.720916	+	4.55168i	−0.0331477	+	0.209287i
$474$	−31.2392			−1.43486
$475$	−2.25793	+	5.11848i	−0.103601	+	0.234852i
$476$	17.3035	−	6.60901i	0.793105	−	0.302923i
$477$	14.8985	+	2.35969i	0.682154	+	0.108043i
$478$	4.96301	+	9.74045i	0.227003	+	0.445518i
$479$	4.88164	−	15.0241i	0.223048	−	0.686471i	−0.775436	−	0.631426i	$-0.782470\pi$
$479$	4.88164	−	15.0241i	0.223048	−	0.686471i	0.998484	−	0.0550445i	$-0.0175301\pi$
$480$	3.30961	−	4.10136i	0.151062	−	0.187201i
$481$	15.7640	−	5.12202i	0.718775	−	0.233544i
$482$	10.4862	−	10.4862i	0.477635	−	0.477635i
$483$	3.03397	+	0.324015i	0.138050	+	0.0147432i
$484$	−6.19256	+	8.52333i	−0.281480	+	0.387424i
$485$	−28.2355	+	3.01654i	−1.28211	+	0.136974i
$486$	12.1937	+	16.7832i	0.553118	+	0.761302i
$487$	5.27652	+	33.3146i	0.239102	+	1.50963i	0.756562	+	0.653922i	$0.226877\pi$
$487$	5.27652	+	33.3146i	0.239102	+	1.50963i	−0.517460	+	0.855707i	$0.673123\pi$
$488$	−1.47529	−	9.31459i	−0.0667830	−	0.421652i
$489$	−43.1266	+	31.3333i	−1.95025	+	1.41694i
$490$	15.3157	−	3.22931i	0.691894	−	0.145885i
$491$	−14.5027	−	10.5369i	−0.654499	−	0.475522i	0.210302	−	0.977637i	$-0.432555\pi$
$491$	−14.5027	−	10.5369i	−0.654499	−	0.475522i	−0.864801	+	0.502115i	$0.832555\pi$
$492$	−3.84660	+	7.54939i	−0.173418	+	0.340353i
$493$	47.0415	+	47.0415i	2.11864	+	2.11864i
$494$	−2.23131	+	0.724997i	−0.100391	+	0.0326191i
$495$	−3.63774	−	1.38926i	−0.163504	−	0.0624426i
$496$	−8.02789	−	2.60842i	−0.360463	−	0.117121i
$497$	4.11186	+	3.71480i	0.184442	+	0.166632i
$498$	2.51296	−	15.8662i	0.112608	−	0.710981i
$499$		−	6.38982i		−	0.286047i	−0.989719	−	0.143024i	$-0.954317\pi$
$499$		−	6.38982i		−	0.286047i	0.989719	−	0.143024i	$-0.0456825\pi$
$500$	−11.0336	+	1.80566i	−0.493436	+	0.0807517i
$501$	12.6790			0.566458
$502$	−3.28140	+	20.7179i	−0.146456	+	0.924686i
$503$	−14.4802	+	7.37805i	−0.645642	+	0.328971i	−0.745966	−	0.665984i	$-0.768012\pi$
$503$	−14.4802	+	7.37805i	−0.645642	+	0.328971i	0.100324	+	0.994955i	$0.468012\pi$
$504$	−0.342485	−	6.75106i	−0.0152555	−	0.300716i
$505$	17.3266	+	6.61707i	0.771025	+	0.294456i
$506$	−0.103062	−	0.317191i	−0.00458165	−	0.0141009i
$507$	−14.3378	+	14.3378i	−0.636763	+	0.636763i
$508$	0.308014	+	0.156941i	0.0136659	+	0.00696313i
$509$	−18.4433	−	13.3999i	−0.817486	−	0.593938i	0.0985052	−	0.995137i	$-0.468594\pi$
$509$	−18.4433	−	13.3999i	−0.817486	−	0.593938i	−0.915991	+	0.401198i	$0.868594\pi$
$510$	−18.3933	+	31.9844i	−0.814470	+	1.41629i
$511$	−4.60653	+	7.06752i	−0.203781	+	0.312649i
$512$	−0.156434	−	0.987688i	−0.00691349	−	0.0436501i
$513$	−1.15920	+	0.183600i	−0.0511801	+	0.00810613i
$514$	7.58698	−	5.51227i	0.334647	−	0.243136i
$515$	−2.21800	−	20.7610i	−0.0977366	−	0.914838i
$516$	9.36657	−	12.8920i	0.412340	−	0.567537i
$517$	−1.43395	−	0.730634i	−0.0630651	−	0.0321333i
$518$	−19.0916	−	8.53843i	−0.838837	−	0.375157i
$519$	0.636340	−	0.206759i	0.0279322	−	0.00907573i
$520$	−3.64888	−	2.94448i	−0.160014	−	0.129124i
$521$	−28.7564	−	9.34352i	−1.25984	−	0.409347i	−0.398403	−	0.917211i	$-0.630435\pi$
$521$	−28.7564	−	9.34352i	−1.25984	−	0.409347i	−0.861438	+	0.507864i	$0.830435\pi$
$522$	21.6323	−	11.0222i	0.946821	−	0.482429i
$523$	−11.3190	−	1.79275i	−0.494946	−	0.0783917i	−0.0960284	−	0.995379i	$-0.530614\pi$
$523$	−11.3190	−	1.79275i	−0.494946	−	0.0783917i	−0.398917	+	0.916987i	$0.630614\pi$
$524$	−1.14076			−0.0498343
$525$	−19.5790	+	24.2647i	−0.854497	+	1.05900i
$526$	12.2627			0.534678
$527$	58.3673	+	9.24448i	2.54252	+	0.402696i
$528$	−1.43137	+	0.729317i	−0.0622922	+	0.0317395i
$529$	21.6466	+	7.03340i	0.941156	+	0.305800i
$530$	−13.1847	−	0.668354i	−0.572705	−	0.0290314i
$531$	17.9285	−	5.82531i	0.778029	−	0.252797i
$532$	2.70232	+	1.20857i	0.117161	+	0.0523982i
$533$	6.71651	+	3.42223i	0.290924	+	0.148233i
$534$	14.3748	−	19.7852i	0.622058	−	0.856189i
$535$	−19.0174	+	8.50613i	−0.822195	+	0.367752i
$536$	9.88045	−	7.17857i	0.426770	−	0.310067i
$537$	56.2596	−	8.91065i	2.42778	−	0.384523i
$538$	−2.36028	−	14.9022i	−0.101759	−	0.642480i
$539$	−4.66360	−	1.00760i	−0.200875	−	0.0434002i
$540$	−1.57245	−	1.74039i	−0.0676675	−	0.0748943i
$541$	−31.0910	−	22.5889i	−1.33670	−	0.971173i	−0.999558	−	0.0297207i	$-0.990538\pi$
$541$	−31.0910	−	22.5889i	−1.33670	−	0.971173i	−0.337147	−	0.941452i	$-0.609462\pi$
$542$	23.4331	+	11.9397i	1.00654	+	0.512856i
$543$	−15.7404	+	15.7404i	−0.675486	+	0.675486i
$544$	2.16340	+	6.65827i	0.0927552	+	0.285471i
$545$	−4.60292	−	7.06139i	−0.197167	−	0.302477i
$546$	−13.0588	+	0.662479i	−0.558863	+	0.0283515i
$547$	−25.1216	+	12.8001i	−1.07412	+	0.547293i	−0.899311	−	0.437309i	$-0.855932\pi$
$547$	−25.1216	+	12.8001i	−1.07412	+	0.547293i	−0.174812	+	0.984602i	$0.555932\pi$
$548$	−0.224997	+	1.42058i	−0.00961141	+	0.0606841i
$549$	24.0949			1.02834
$550$	3.29488	+	0.870783i	0.140494	+	0.0371303i
$551$			10.6322i			0.452947i
$552$	−0.180409	+	1.13905i	−0.00767870	+	0.0484814i
$553$	23.5085	−	26.0212i	0.999685	−	1.10653i
$554$	−4.53577	−	1.47376i	−0.192707	−	0.0626142i
$555$	40.2213	−	10.8511i	1.70730	−	0.460603i
$556$	−18.9705	+	6.16390i	−0.804530	+	0.261408i
$557$	20.3672	+	20.3672i	0.862985	+	0.862985i	0.991684	−	0.128699i	$-0.0410800\pi$
$557$	20.3672	+	20.3672i	0.862985	+	0.862985i	−0.128699	+	0.991684i	$0.541080\pi$
$558$	9.79090	−	19.2157i	0.414482	−	0.813466i
$559$	−11.4697	−	8.33320i	−0.485115	−	0.352457i
$560$	0.925705	+	5.84321i	0.0391182	+	0.246921i
$561$	9.09877	−	6.61064i	0.384150	−	0.279101i
$562$	4.47306	+	28.2418i	0.188685	+	1.19131i
$563$	−5.04756	−	31.8691i	−0.212729	−	1.34312i	−0.830612	−	0.556851i	$-0.812009\pi$
$563$	−5.04756	−	31.8691i	−0.212729	−	1.34312i	0.617883	−	0.786270i	$-0.287991\pi$
$564$	3.27101	+	4.50216i	0.137734	+	0.189575i
$565$	−2.12462	+	10.0804i	−0.0893836	+	0.424084i
$566$	−3.48806	+	4.80090i	−0.146614	+	0.201797i
$567$	−26.6686	−	2.84809i	−1.11998	−	0.119609i
$568$	−1.48100	+	1.48100i	−0.0621415	+	0.0621415i
$569$	19.5816	−	6.36246i	0.820905	−	0.266728i	0.131696	−	0.991290i	$-0.457958\pi$
$569$	19.5816	−	6.36246i	0.820905	−	0.266728i	0.689210	+	0.724562i	$0.257958\pi$
$570$	−5.69313	+	1.53592i	−0.238459	+	0.0643325i
$571$	11.3099	−	34.8083i	0.473305	−	1.45668i	−0.374926	−	0.927055i	$-0.622332\pi$
$571$	11.3099	−	34.8083i	0.473305	−	1.45668i	0.848231	−	0.529627i	$-0.177668\pi$
$572$	0.648856	+	1.27345i	0.0271300	+	0.0532457i
$573$	−4.65826	−	0.737795i	−0.194601	−	0.0308218i
$574$	−3.39369	−	8.88526i	−0.141650	−	0.370863i
$575$	1.89605	−	1.54617i	0.0790707	−	0.0644796i
$576$	2.55494			0.106456
$577$	2.90398	−	18.3350i	0.120894	−	0.763296i	−0.850527	−	0.525932i	$-0.823717\pi$
$577$	2.90398	−	18.3350i	0.120894	−	0.763296i	0.971421	−	0.237364i	$-0.0762834\pi$
$578$	−14.5335	−	28.5237i	−0.604516	−	1.18643i
$579$	−9.81190	+	30.1979i	−0.407769	+	1.25498i
$580$	−17.8006	+	11.6032i	−0.739129	+	0.481796i
$581$	11.3249	+	14.0330i	0.469837	+	0.582189i
$582$	−21.1641	−	21.1641i	−0.877281	−	0.877281i
$583$	3.58552	+	1.82691i	0.148497	+	0.0756630i
$584$	−2.57963	−	1.87421i	−0.106746	−	0.0775553i
$585$	8.88874	−	8.03105i	0.367504	−	0.332043i
$586$	2.20909	+	3.04056i	0.0912568	+	0.125604i
$587$	5.28293	−	0.836733i	0.218050	−	0.0345357i	−0.0464537	−	0.998920i	$-0.514792\pi$
$587$	5.28293	−	0.836733i	0.218050	−	0.0345357i	0.264503	+	0.964385i	$0.414792\pi$
$588$	12.7867	+	10.4255i	0.527316	+	0.429941i
$589$	5.55131	+	7.64073i	0.228738	+	0.314831i
$590$	−15.0605	+	6.73627i	−0.620031	+	0.277328i
$591$	−33.9715	+	46.7578i	−1.39740	+	1.92336i
$592$	3.58868	−	7.04318i	0.147494	−	0.289473i
$593$	−20.8458	−	20.8458i	−0.856035	−	0.856035i	0.134833	−	0.990868i	$-0.456950\pi$
$593$	−20.8458	−	20.8458i	−0.856035	−	0.856035i	−0.990868	+	0.134833i	$0.956950\pi$
$594$	0.220938	+	0.679976i	0.00906518	+	0.0278998i
$595$	−12.8004	−	39.3904i	−0.524765	−	1.61485i
$596$	−5.03978	+	15.5109i	−0.206438	+	0.635350i
$597$	−48.2416	+	24.5803i	−1.97440	+	1.00601i
$598$	1.01339	+	0.160505i	0.0414406	+	0.00656354i
$599$		−	34.1312i		−	1.39456i	−0.716797	−	0.697282i	$-0.754393\pi$
$599$		−	34.1312i		−	1.39456i	0.716797	−	0.697282i	$-0.245607\pi$
$600$	−8.78450	−	7.85532i	−0.358626	−	0.320692i
$601$		−	1.31870i		−	0.0537908i	−0.999638	−	0.0268954i	$-0.991438\pi$
$601$		−	1.31870i		−	0.0537908i	0.999638	−	0.0268954i	$-0.00856211\pi$
$602$	3.68993	+	17.5037i	0.150390	+	0.713396i
$603$	14.1660	+	27.8023i	0.576883	+	1.13220i
$604$	−0.419735	−	0.136380i	−0.0170788	−	0.00554923i
$605$	18.3333	+	14.7941i	0.745354	+	0.601467i
$606$	6.04108	+	18.5925i	0.245402	+	0.755270i
$607$	18.2793	−	18.2793i	0.741933	−	0.741933i	−0.231016	−	0.972950i	$-0.574205\pi$
$607$	18.2793	−	18.2793i	0.741933	−	0.741933i	0.972950	+	0.231016i	$0.0742051\pi$
$608$	−0.507959	+	0.996926i	−0.0206005	+	0.0404307i
$609$	−15.4322	+	57.2109i	−0.625345	+	2.31830i
$610$	−20.9683	+	2.24015i	−0.848984	+	0.0907011i
$611$	4.00546	−	2.91014i	0.162044	−	0.117732i
$612$	−17.6667	+	2.79813i	−0.714135	+	0.113108i
$613$	33.9264	−	5.37342i	1.37028	−	0.217030i	0.572460	−	0.819932i	$-0.305989\pi$
$613$	33.9264	−	5.37342i	1.37028	−	0.217030i	0.797815	+	0.602902i	$0.205989\pi$
$614$	9.70231	−	7.04914i	0.391553	−	0.284480i
$615$	16.4238	+	9.44487i	0.662273	+	0.380854i
$616$	0.469653	−	1.74112i	0.0189229	−	0.0701515i
$617$	5.61404	−	11.0182i	0.226013	−	0.443575i	−0.749955	−	0.661489i	$-0.769925\pi$
$617$	5.61404	−	11.0182i	0.226013	−	0.443575i	0.975968	+	0.217913i	$0.0699250\pi$
$618$	15.5615	−	15.5615i	0.625976	−	0.625976i
$619$	−0.219264	−	0.674825i	−0.00881296	−	0.0271235i	0.946553	−	0.322547i	$-0.104539\pi$
$619$	−0.219264	−	0.674825i	−0.00881296	−	0.0271235i	−0.955366	+	0.295424i	$0.904539\pi$
$620$	−6.73392	+	17.6326i	−0.270441	+	0.708142i
$621$	0.488145	+	0.158608i	0.0195886	+	0.00636471i
$622$	2.98241	+	5.85331i	0.119584	+	0.234696i
$623$	5.66290	+	26.8627i	0.226879	+	1.07623i
$624$		−	4.94210i		−	0.197842i
$625$	2.78336	+	24.8446i	0.111334	+	0.993783i
$626$		−	14.4166i		−	0.576204i
$627$	1.77530	+	0.281180i	0.0708987	+	0.0112292i
$628$	−2.60659	+	1.32812i	−0.104014	+	0.0529978i
$629$	−17.1011	+	52.6319i	−0.681867	+	2.09857i
$630$	−15.1152		0.000585696i	−0.602205		2.33347e-5i
$631$	4.88687	+	15.0402i	0.194543	+	0.598743i	0.999982	+	0.00606307i	$0.00192995\pi$
$631$	4.88687	+	15.0402i	0.194543	+	0.598743i	−0.805438	+	0.592680i	$0.798070\pi$
$632$	9.37228	+	9.37228i	0.372809	+	0.372809i
$633$	10.0938	−	19.8101i	0.401191	−	0.787382i
$634$	−7.10430	+	9.77823i	−0.282148	+	0.388343i
$635$	0.385349	−	0.670090i	0.0152921	−	0.0265917i
$636$	−8.17899	−	11.2574i	−0.324318	−	0.446385i
$637$	9.27533	−	11.3761i	0.367502	−	0.450736i
$638$	6.39722	−	1.01322i	0.253268	−	0.0401138i
$639$	−3.14536	−	4.32921i	−0.124428	−	0.171261i
$640$	−2.22342	+	0.237538i	−0.0878882	+	0.00938953i
$641$	−27.2869	−	19.8251i	−1.07777	−	0.783044i	−0.100475	−	0.994940i	$-0.532036\pi$
$641$	−27.2869	−	19.8251i	−1.07777	−	0.783044i	−0.977292	+	0.211896i	$0.932036\pi$
$642$	−19.5654	−	9.96907i	−0.772185	−	0.393448i
$643$	−22.2277	−	22.2277i	−0.876573	−	0.876573i	0.116605	−	0.993178i	$-0.462799\pi$
$643$	−22.2277	−	22.2277i	−0.876573	−	0.876573i	−0.993178	+	0.116605i	$0.962799\pi$
$644$	−0.813031	−	1.00745i	−0.0320379	−	0.0396991i
$645$	−27.7300	−	22.3769i	−1.09187	−	0.881088i
$646$	2.42058	−	7.44978i	0.0952365	−	0.293108i
$647$	−2.44425	−	4.79711i	−0.0960933	−	0.188594i	0.837956	−	0.545738i	$-0.183751\pi$
$647$	−2.44425	−	4.79711i	−0.0960933	−	0.188594i	−0.934049	+	0.357144i	$0.883751\pi$
$648$	1.58579	−	10.0123i	0.0622958	−	0.393320i
$649$	5.02905			0.197407
$650$	−6.98869	+	7.81536i	−0.274119	+	0.306543i
$651$	18.7809	+	49.1715i	0.736080	+	1.92718i
$652$	22.3392	+	3.53819i	0.874872	+	0.138566i
$653$	13.7177	+	26.9225i	0.536815	+	1.05356i	0.987015	+	0.160630i	$0.0513527\pi$
$653$	13.7177	+	26.9225i	0.536815	+	1.05356i	−0.450200	+	0.892928i	$0.648647\pi$
$654$	2.74549	−	8.44974i	0.107357	−	0.330411i
$655$	−0.129140	+	2.54755i	−0.00504591	+	0.0995409i
$656$	3.41899	−	1.11090i	0.133489	−	0.0433732i
$657$	5.76057	−	5.76057i	0.224741	−	0.224741i
$658$	−6.21169	−	0.663382i	−0.242157	−	0.0258613i
$659$	5.57908	−	7.67894i	0.217330	−	0.299129i	−0.686407	−	0.727218i	$-0.740813\pi$
$659$	5.57908	−	7.67894i	0.217330	−	0.299129i	0.903737	+	0.428089i	$0.140813\pi$
$660$	1.46667	+	3.27909i	0.0570902	+	0.127638i
$661$	−5.07681	−	6.98763i	−0.197465	−	0.271787i	0.698790	−	0.715327i	$-0.253722\pi$
$661$	−5.07681	−	6.98763i	−0.197465	−	0.271787i	−0.896255	+	0.443540i	$0.853722\pi$
$662$	−4.23340	−	26.7286i	−0.164536	−	1.03884i
$663$	5.41251	+	34.1732i	0.210204	+	1.32718i
$664$	−5.51405	+	4.00619i	−0.213987	+	0.155470i
$665$	3.00490	−	5.89801i	0.116525	−	0.228715i
$666$	16.3390	+	11.8710i	0.633124	+	0.459992i
$667$	2.11093	−	4.14293i	0.0817354	−	0.160415i
$668$	−3.80392	−	3.80392i	−0.147178	−	0.147178i
$669$	16.6178	−	5.39947i	0.642483	−	0.208755i
$670$	−14.9127	−	22.8777i	−0.576127	−	0.883842i
$671$	6.11336	+	1.98635i	0.236004	+	0.0766822i
$672$	−4.18028	+	4.62708i	−0.161258	+	0.178493i
$673$	0.685214	−	4.32627i	0.0264131	−	0.166766i	−0.970956	−	0.239259i	$-0.923096\pi$
$673$	0.685214	−	4.32627i	0.0264131	−	0.166766i	0.997369	+	0.0724932i	$0.0230956\pi$
$674$		−	17.0943i		−	0.658449i
$675$	−4.06464	+	3.31458i	−0.156448	+	0.127578i
$676$	8.60314			0.330890
$677$	−4.86916	+	30.7426i	−0.187137	+	1.18154i	0.697963	+	0.716134i	$0.254090\pi$
$677$	−4.86916	+	30.7426i	−0.187137	+	1.18154i	−0.885100	+	0.465402i	$0.845910\pi$
$678$	−9.67498	+	4.92965i	−0.371566	+	0.189322i
$679$	33.5557	−	1.70230i	1.28775	−	0.0653283i
$680$	15.1142	−	4.07756i	0.579602	−	0.156367i
$681$	−20.1674	−	62.0689i	−0.772817	−	2.37849i
$682$	4.06827	−	4.06827i	0.155782	−	0.155782i
$683$	−18.0210	−	9.18217i	−0.689555	−	0.351346i	0.0738468	−	0.997270i	$-0.476472\pi$
$683$	−18.0210	−	9.18217i	−0.689555	−	0.351346i	−0.763402	+	0.645924i	$0.776472\pi$
$684$	−2.31271	−	1.68028i	−0.0884286	−	0.0642471i
$685$	3.14696	+	0.663281i	0.120239	+	0.0253427i
$686$	−18.3066	+	2.80538i	−0.698947	+	0.107110i
$687$	−2.49537	−	15.7552i	−0.0952044	−	0.601097i
$688$	−6.67793	+	1.05768i	−0.254594	+	0.0403237i
$689$	−10.0154	+	7.27665i	−0.381558	+	0.277218i
$690$	2.52331	+	0.531835i	0.0960609	+	0.0202466i
$691$	24.2363	−	33.3585i	0.921994	−	1.26902i	−0.0409074	−	0.999163i	$-0.513025\pi$
$691$	24.2363	−	33.3585i	0.921994	−	1.26902i	0.962902	−	0.269853i	$-0.0869751\pi$
$692$	−0.252944	−	0.128881i	−0.00961548	−	0.00489933i
$693$	4.20597	+	1.88105i	0.159771	+	0.0714553i
$694$	−14.6436	+	4.75800i	−0.555864	+	0.180611i
$695$	11.6177	+	43.0628i	0.440683	+	1.63346i
$696$	−21.3004	−	6.92091i	−0.807389	−	0.262337i
$697$	−22.4247	+	11.4260i	−0.849397	+	0.432789i
$698$	−17.1564	−	2.71731i	−0.649380	−	0.102852i
$699$	−0.207617			−0.00785279
$700$	13.1538	−	1.40581i	0.497169	−	0.0531345i
$701$	−14.1201			−0.533309			−0.266654	−	0.963792i	$-0.585918\pi$
$701$	−14.1201			−0.533309			−0.266654	+	0.963792i	$0.585918\pi$
$702$	−2.17244	−	0.344081i	−0.0819936	−	0.0129865i
$703$	−7.88044	+	4.01529i	−0.297217	+	0.151439i
$704$	0.648241	+	0.210626i	0.0244315	+	0.00793827i
$705$	10.4245	−	6.79515i	0.392610	−	0.255920i
$706$	34.7904	−	11.3041i	1.30935	−	0.425435i
$707$	−20.0331	−	8.95948i	−0.753421	−	0.336956i
$708$	−15.4945	−	7.89482i	−0.582317	−	0.296705i
$709$	19.1687	−	26.3834i	0.719895	−	0.990850i	−0.279633	−	0.960107i	$-0.590213\pi$
$709$	19.1687	−	26.3834i	0.719895	−	0.990850i	0.999527	−	0.0307428i	$-0.00978727\pi$
$710$	3.13972	+	3.47503i	0.117831	+	0.130416i
$711$	−27.3967	+	19.9049i	−1.02746	+	0.746492i
$712$	−10.2486	+	1.62321i	−0.384081	+	0.0608325i
$713$	−0.646119	−	4.07943i	−0.0241973	−	0.152776i
$714$	23.8380	−	36.5732i	0.892114	−	1.36872i
$715$	2.91733	−	1.30486i	0.109102	−	0.0487992i
$716$	−19.5522	−	14.2055i	−0.730699	−	0.530884i
$717$	22.9572	+	11.6973i	0.857352	+	0.436843i
$718$	4.74668	−	4.74668i	0.177145	−	0.177145i
$719$	−15.0912	−	46.4460i	−0.562808	−	1.73214i	−0.674377	−	0.738387i	$-0.735588\pi$
$719$	−15.0912	−	46.4460i	−0.562808	−	1.73214i	0.111569	−	0.993757i	$-0.464412\pi$
$720$	0.289232	−	5.70570i	0.0107790	−	0.212639i
$721$	1.25167	+	24.6728i	0.0466145	+	0.918862i
$722$	−15.8137	+	8.05748i	−0.588524	+	0.299868i
$723$	5.46773	−	34.5219i	0.203347	−	1.28388i
$724$	9.44477			0.351012
$725$	23.8971	+	41.0658i	0.887518	+	1.52515i
$726$			24.8309i			0.921559i
$727$	2.67766	−	16.9061i	0.0993088	−	0.627011i	−0.886958	−	0.461850i	$-0.847186\pi$
$727$	2.67766	−	16.9061i	0.0993088	−	0.627011i	0.986267	−	0.165161i	$-0.0528143\pi$
$728$	4.11660	+	3.71909i	0.152571	+	0.137839i
$729$	17.5782	+	5.71152i	0.651046	+	0.211538i
$730$	−4.47751	+	5.54865i	−0.165720	+	0.205365i
$731$	45.0177	−	14.6271i	1.66504	−	0.541004i
$732$	−15.7170	−	15.7170i	−0.580915	−	0.580915i
$733$	−19.6225	+	38.5113i	−0.724774	+	1.42245i	0.174318	+	0.984689i	$0.444228\pi$
$733$	−19.6225	+	38.5113i	−0.724774	+	1.42245i	−0.899092	+	0.437760i	$0.855772\pi$
$734$	0.237627	+	0.172646i	0.00877099	+	0.00637250i
$735$	24.7298	−	27.3751i	0.912172	−	1.00975i
$736$	0.395861	−	0.287610i	0.0145916	−	0.0106014i
$737$	1.30221	+	8.22184i	0.0479676	+	0.302855i
$738$	1.43683	+	9.07177i	0.0528903	+	0.333936i
$739$	−13.7834	−	18.9712i	−0.507030	−	0.697867i	0.476385	−	0.879237i	$-0.341947\pi$
$739$	−13.7834	−	18.9712i	−0.507030	−	0.697867i	−0.983415	+	0.181370i	$0.941947\pi$
$740$	−15.3226	−	8.81156i	−0.563269	−	0.323919i
$741$	−3.25021	+	4.47354i	−0.119400	+	0.164339i
$742$	15.5320	+	1.65875i	0.570198	+	0.0608947i
$743$	−10.2624	+	10.2624i	−0.376491	+	0.376491i	−0.869835	−	0.493344i	$-0.835775\pi$
$743$	−10.2624	+	10.2624i	−0.376491	+	0.376491i	0.493344	+	0.869835i	$0.335775\pi$
$744$	−18.9209	+	6.14776i	−0.693672	+	0.225388i
$745$	34.0683	+	13.0108i	1.24817	+	0.476677i
$746$	3.64679	−	11.2237i	0.133519	−	0.410928i
$747$	−7.90571	−	15.5158i	−0.289255	−	0.567694i
$748$	−4.71308	−	0.746479i	−0.172327	−	0.0272940i
$749$	23.0275	−	8.79527i	0.841407	−	0.321372i
$750$	−18.5370	+	18.7283i	−0.676874	+	0.683860i
$751$	13.8608			0.505786			0.252893	−	0.967494i	$-0.418618\pi$
$751$	13.8608			0.505786			0.252893	+	0.967494i	$0.418618\pi$
$752$	0.369365	−	2.33208i	0.0134694	−	0.0850422i
$753$	22.4446	+	44.0501i	0.817928	+	1.60527i
$754$	−6.15737	+	18.9504i	−0.224238	+	0.690134i
$755$	−0.352080	+	0.921913i	−0.0128135	+	0.0335519i
$756$	1.74293	+	2.15971i	0.0633897	+	0.0785480i
$757$	−17.7480	−	17.7480i	−0.645061	−	0.645061i	0.306734	−	0.951795i	$-0.400764\pi$
$757$	−17.7480	−	17.7480i	−0.645061	−	0.645061i	−0.951795	+	0.306734i	$0.900764\pi$
$758$	−16.7218	−	8.52017i	−0.607363	−	0.309467i
$759$	−0.635934	−	0.462033i	−0.0230830	−	0.0167707i
$760$	2.16883	+	1.24723i	0.0786718	+	0.0452419i
$761$	−7.73640	−	10.6482i	−0.280444	−	0.385998i	0.645437	−	0.763814i	$-0.276675\pi$
$761$	−7.73640	−	10.6482i	−0.280444	−	0.385998i	−0.925881	+	0.377815i	$0.876675\pi$
$762$	0.804728	−	0.127456i	0.0291522	−	0.00461726i
$763$	4.97228	+	8.64561i	0.180009	+	0.312992i
$764$	1.17620	+	1.61890i	0.0425535	+	0.0585699i
$765$	4.24883	+	39.7701i	0.153617	+	1.43789i
$766$	2.28396	−	3.14361i	0.0825229	−	0.113583i
$767$	−7.02383	+	13.7850i	−0.253616	+	0.497749i
$768$	−1.66657	−	1.66657i	−0.0601373	−	0.0601373i
$769$	10.7363	+	33.0428i	0.387159	+	1.19155i	0.934902	+	0.354907i	$0.115487\pi$
$769$	10.7363	+	33.0428i	0.387159	+	1.19155i	−0.547742	+	0.836647i	$0.684513\pi$
$770$	−3.83509	−	1.24593i	−0.138207	−	0.0449003i
$771$	6.83020	−	21.0212i	0.245984	−	0.757060i
$772$	12.0036	−	6.11615i	0.432020	−	0.220125i
$773$	36.4132	+	5.76728i	1.30969	+	0.207435i	0.771954	−	0.635678i	$-0.219279\pi$
$773$	36.4132	+	5.76728i	1.30969	+	0.207435i	0.537737	+	0.843113i	$0.319279\pi$
$774$		−	17.2744i		−	0.620915i
$775$	38.6148	+	17.0343i	1.38708	+	0.611890i
$776$			12.6992i			0.455874i
$777$	−48.2319	+	10.1677i	−1.73031	+	0.364765i
$778$	1.45666	+	2.85885i	0.0522238	+	0.102495i
$779$	−3.82542	−	1.24296i	−0.137060	−	0.0445335i
$780$	−11.0367	−	0.559470i	−0.395177	−	0.0200322i
$781$	−0.441147	−	1.35771i	−0.0157855	−	0.0485827i
$782$	−2.42228	+	2.42228i	−0.0866207	+	0.0866207i
$783$	−4.52528	+	8.88136i	−0.161720	+	0.317394i
$784$	−0.708406	−	6.96406i	−0.0253002	−	0.248717i
$785$	2.67088	+	5.97138i	0.0953280	+	0.213128i
$786$	−2.17516	+	1.58035i	−0.0775855	+	0.0563692i
$787$	5.21005	−	0.825192i	0.185718	−	0.0294149i	−0.0628824	−	0.998021i	$-0.520029\pi$
$787$	5.21005	−	0.825192i	0.185718	−	0.0294149i	0.248601	+	0.968606i	$0.420029\pi$
$788$	24.2201	−	3.83609i	0.862806	−	0.136655i
$789$	23.3820	−	16.9880i	0.832422	−	0.604790i
$790$	21.9912	−	19.8692i	0.782411	−	0.706914i
$791$	3.17451	−	11.7687i	0.112873	−	0.418446i
$792$	−0.790601	+	1.55164i	−0.0280928	+	0.0551352i
$793$	−13.9830	+	13.9830i	−0.496551	+	0.496551i
$794$	4.77825	+	14.7059i	0.169574	+	0.521894i
$795$	−26.0660	+	16.9909i	−0.924464	+	0.602606i
$796$	21.8478	+	7.09878i	0.774375	+	0.251610i
$797$	−2.98721	−	5.86272i	−0.105812	−	0.207668i	0.832029	−	0.554731i	$-0.187179\pi$
$797$	−2.98721	−	5.86272i	−0.105812	−	0.207668i	−0.937842	+	0.347063i	$0.887179\pi$
$798$	6.82699	−	1.43919i	0.241673	−	0.0509468i
$799$			16.5302i			0.584797i
$800$	0.278769	+	4.99222i	0.00985598	+	0.176502i
$801$		−	26.5109i		−	0.936715i
$802$	24.0380	+	3.80724i	0.848811	+	0.134438i
$803$	1.93647	−	0.986679i	0.0683364	−	0.0348192i
$804$	8.89490	−	27.3757i	0.313699	−	0.965466i
$805$	−2.34188	+	1.70161i	−0.0825404	+	0.0599740i
$806$	5.46951	+	16.8334i	0.192655	+	0.592932i
$807$	−25.1452	−	25.1452i	−0.885154	−	0.885154i
$808$	3.76565	−	7.39049i	0.132475	−	0.259997i
$809$	18.8295	−	25.9166i	0.662011	−	0.911180i	−0.337535	−	0.941313i	$-0.609593\pi$
$809$	18.8295	−	25.9166i	0.662011	−	0.911180i	0.999546	+	0.0301328i	$0.00959302\pi$
$810$	−22.1799	−	4.67483i	−0.779324	−	0.164257i
$811$	8.05779	+	11.0906i	0.282947	+	0.389444i	0.926707	−	0.375784i	$-0.122626\pi$
$811$	8.05779	+	11.0906i	0.282947	+	0.389444i	−0.643760	+	0.765228i	$0.722626\pi$
$812$	21.7941	−	12.5343i	0.764824	−	0.439867i
$813$	61.2220	−	9.69662i	2.14715	−	0.340075i
$814$	3.16691	+	4.35888i	0.111000	+	0.152779i
$815$	10.4304	−	49.4874i	0.365361	−	1.73347i
$816$	13.3491	+	9.69870i	0.467313	+	0.339522i
$817$	6.74039	+	3.43440i	0.235816	+	0.120154i
$818$	19.9651	+	19.9651i	0.698062	+	0.698062i
$819$	−11.0304	+	8.90173i	−0.385433	+	0.311052i
$820$	−2.09381	−	7.76104i	−0.0731189	−	0.271027i
$821$	0.574596	−	1.76843i	0.0200536	−	0.0617185i	−0.940529	−	0.339714i	$-0.889670\pi$
$821$	0.574596	−	1.76843i	0.0200536	−	0.0617185i	0.960583	+	0.277995i	$0.0896699\pi$
$822$	1.53898	+	3.02041i	0.0536779	+	0.105349i
$823$	0.337840	−	2.13304i	0.0117764	−	0.0743531i	−0.981100	−	0.193500i	$-0.938016\pi$
$823$	0.337840	−	2.13304i	0.0117764	−	0.0743531i	0.992877	+	0.119147i	$0.0380160\pi$
$824$	−9.33743			−0.325285
$825$	7.48890	−	2.90417i	0.260730	−	0.101110i
$826$	18.2362	−	6.96525i	0.634519	−	0.242352i
$827$	−26.5021	−	4.19751i	−0.921567	−	0.145962i	−0.322416	−	0.946598i	$-0.604495\pi$
$827$	−26.5021	−	4.19751i	−0.921567	−	0.145962i	−0.599151	+	0.800636i	$0.704495\pi$
$828$	0.567561	+	1.11390i	0.0197241	+	0.0387107i
$829$	8.61595	−	26.5172i	0.299244	−	0.920979i	−0.682518	−	0.730868i	$-0.739115\pi$
$829$	8.61595	−	26.5172i	0.299244	−	0.920979i	0.981763	−	0.190111i	$-0.0608847\pi$
$830$	8.32241	+	12.7675i	0.288875	+	0.443166i
$831$	−10.6903	+	3.47350i	−0.370843	+	0.120494i
$832$	−1.48271	+	1.48271i	−0.0514037	+	0.0514037i
$833$	12.5254	+	47.3788i	0.433978	+	1.64158i
$834$	−27.6332	+	38.0339i	−0.956861	+	1.31701i
$835$	−8.92555	+	8.06430i	−0.308881	+	0.279077i
$836$	−0.448261	−	0.616978i	−0.0155034	−	0.0213386i
$837$	1.38511	+	8.74525i	0.0478765	+	0.302280i
$838$	2.06147	+	13.0156i	0.0712125	+	0.449618i
$839$	−6.05589	+	4.39986i	−0.209073	+	0.151900i	−0.687394	−	0.726285i	$-0.741245\pi$
$839$	−6.05589	+	4.39986i	−0.209073	+	0.151900i	0.478321	+	0.878185i	$0.341245\pi$
$840$	9.85997	+	9.85921i	0.340201	+	0.340175i
$841$	49.5919	+	36.0306i	1.71007	+	1.24244i
$842$	16.4701	−	32.3245i	0.567598	−	1.11397i
$843$	47.6538	+	47.6538i	1.64128	+	1.64128i
$844$	−8.97167	+	2.91507i	−0.308818	+	0.100341i
$845$	0.973918	−	19.2125i	0.0335038	−	0.660931i
$846$	5.73734	+	1.86417i	0.197254	+	0.0640916i
$847$	−20.6833	−	18.6860i	−0.710686	−	0.642060i
$848$	−0.923578	+	5.83124i	−0.0317158	+	0.200246i
$849$			13.9864i			0.480011i
$850$	−7.39502	−	34.2146i	−0.253647	−	1.17355i
$851$	3.86788			0.132589
$852$	−0.772223	+	4.87562i	−0.0264559	+	0.167036i
$853$	−4.71105	+	2.40040i	−0.161303	+	0.0821881i	−0.532778	−	0.846255i	$-0.678852\pi$
$853$	−4.71105	+	2.40040i	−0.161303	+	0.0821881i	0.371475	+	0.928443i	$0.378852\pi$
$854$	24.9192	−	1.26417i	0.852718	−	0.0432589i
$855$	−4.01421	+	4.97452i	−0.137283	+	0.170125i
$856$	2.87906	+	8.86083i	0.0984042	+	0.302857i
$857$	−16.4350	+	16.4350i	−0.561408	+	0.561408i	−0.929707	−	0.368300i	$-0.879940\pi$
$857$	−16.4350	+	16.4350i	−0.561408	+	0.561408i	0.368300	+	0.929707i	$0.379940\pi$
$858$	3.00139	+	1.52928i	0.102466	+	0.0522089i
$859$	19.4475	+	14.1295i	0.663542	+	0.482091i	0.867857	−	0.496814i	$-0.165497\pi$
$859$	19.4475	+	14.1295i	0.663542	+	0.482091i	−0.204315	+	0.978905i	$0.565497\pi$
$860$	1.60604	+	15.0329i	0.0547654	+	0.512617i
$861$	−18.7801	−	12.2407i	−0.640025	−	0.417161i
$862$	−2.44783	−	15.4550i	−0.0833735	−	0.526400i
$863$	−53.5466	+	8.48096i	−1.82275	+	0.288695i	−0.971670	−	0.236342i	$-0.924051\pi$
$863$	−53.5466	+	8.48096i	−1.82275	+	0.288695i	−0.851079	+	0.525037i	$0.824051\pi$
$864$	−0.848623	+	0.616561i	−0.0288708	+	0.0209758i
$865$	−0.316452	+	0.550284i	−0.0107597	+	0.0187102i
$866$	−20.5467	+	28.2801i	−0.698205	+	0.960997i
$867$	−67.2273	−	34.2540i	−2.28316	−	1.16333i
$868$	9.11770	−	20.3868i	0.309475	−	0.691974i
$869$	−8.59205	+	2.79173i	−0.291465	+	0.0947028i
$870$	−17.8671	+	46.7846i	−0.605751	+	1.58614i
$871$	−24.3555	−	7.91358i	−0.825254	−	0.268141i
$872$	−3.35875	+	1.71137i	−0.113742	+	0.0579543i
$873$	−32.0462	−	5.07561i	−1.08460	−	0.171784i
$874$	−0.547479			−0.0185187
$875$	−1.65036	−	29.5343i	−0.0557925	−	0.998442i
$876$	−7.51517			−0.253914
$877$	24.3569	+	3.85775i	0.822474	+	0.130267i	0.553467	−	0.832871i	$-0.313305\pi$
$877$	24.3569	+	3.85775i	0.822474	+	0.130267i	0.269007	+	0.963138i	$0.413305\pi$
$878$	−1.05483	+	0.537461i	−0.0355986	+	0.0181384i
$879$	8.42445	+	2.73727i	0.284150	+	0.0923258i
$880$	0.543755	−	1.42381i	0.0183300	−	0.0479965i
$881$	−4.72492	+	1.53522i	−0.159187	+	0.0517229i	−0.387526	−	0.921859i	$-0.626670\pi$
$881$	−4.72492	+	1.53522i	−0.159187	+	0.0517229i	0.228340	+	0.973582i	$0.426670\pi$
$882$	17.8568	+	0.995750i	0.601271	+	0.0335287i
$883$	24.7034	+	12.5870i	0.831336	+	0.423587i	0.817229	−	0.576313i	$-0.195509\pi$
$883$	24.7034	+	12.5870i	0.831336	+	0.423587i	0.0141077	+	0.999900i	$0.495509\pi$
$884$	8.62870	−	11.8764i	0.290215	−	0.399446i
$885$	−19.3848	+	33.7085i	−0.651612	+	1.13310i
$886$	16.3975	−	11.9135i	0.550884	−	0.400241i
$887$	8.24861	−	1.30645i	0.276961	−	0.0438664i	−0.0164086	−	0.999865i	$-0.505223\pi$
$887$	8.24861	−	1.30645i	0.276961	−	0.0438664i	0.293370	+	0.955999i	$0.405223\pi$
$888$	−2.91447	−	18.4012i	−0.0978033	−	0.617505i
$889$	−0.499418	+	0.766227i	−0.0167499	+	0.0256984i
$890$	2.46477	+	23.0708i	0.0826193	+	0.773337i
$891$	5.58987	+	4.06127i	0.187268	+	0.136058i
$892$	−6.60556	−	3.36570i	−0.221170	−	0.112692i
$893$	−1.86806	+	1.86806i	−0.0625122	+	0.0625122i
$894$	11.8782	+	36.5574i	0.397267	+	1.22266i
$895$	−33.9371	+	42.0558i	−1.13439	+	1.40577i
$896$	2.64235	−	0.134048i	0.0882748	−	0.00447824i
$897$	2.15465	−	1.09785i	0.0719417	−	0.0366561i
$898$	−3.15000	+	19.8883i	−0.105117	+	0.663683i
$899$	80.2114			2.67520
$900$	−12.7092	−	1.29183i	−0.423641	−	0.0430609i
$901$		−	41.3329i		−	1.37700i
$902$	−0.383313	+	2.42014i	−0.0127629	+	0.0805819i
$903$	31.2845	+	28.2636i	1.04108	+	0.940553i
$904$	4.38163	+	1.42368i	0.145731	+	0.0473509i
$905$	1.06919	−	21.0921i	0.0355412	−	0.701124i
$906$	−0.989270	+	0.321433i	−0.0328663	+	0.0106789i
$907$	−33.5991	−	33.5991i	−1.11564	−	1.11564i	−0.992374	−	0.123267i	$-0.960663\pi$
$907$	−33.5991	−	33.5991i	−1.11564	−	1.11564i	−0.123267	−	0.992374i	$-0.539337\pi$
$908$	−12.5711	+	24.6723i	−0.417188	+	0.818778i
$909$	17.1447	+	12.4564i	0.568655	+	0.413152i
$910$	8.77149	−	8.77217i	0.290772	−	0.290795i
$911$	41.2515	−	29.9710i	1.36672	−	0.992982i	0.368738	−	0.929533i	$-0.379790\pi$
$911$	41.2515	−	29.9710i	1.36672	−	0.992982i	0.997985	−	0.0634488i	$-0.0202100\pi$
$912$	0.412529	+	2.60460i	0.0136602	+	0.0862471i
$913$	−0.726734	−	4.58842i	−0.0240514	−	0.151854i
$914$	13.8984	+	19.1295i	0.459717	+	0.632747i
$915$	−36.8783	+	33.3199i	−1.21916	+	1.10152i
$916$	−3.97816	+	5.47546i	−0.131442	+	0.180914i
$917$	0.320505	−	3.00110i	0.0105840	−	0.0991051i
$918$	5.19275	−	5.19275i	0.171386	−	0.171386i
$919$	28.9477	−	9.40569i	0.954898	−	0.310265i	0.210193	−	0.977660i	$-0.432591\pi$
$919$	28.9477	−	9.40569i	0.954898	−	0.310265i	0.744704	+	0.667395i	$0.232591\pi$
$920$	−0.597477	−	0.916596i	−0.0196982	−	0.0302193i
$921$	8.73453	−	26.8821i	0.287813	−	0.885796i
$922$	−18.2928	−	35.9016i	−0.602441	−	1.18236i
$923$	4.33772	+	0.687028i	0.142778	+	0.0226138i
$924$	−1.51653	−	3.97053i	−0.0498901	−	0.130621i
$925$	−21.4126	+	33.2209i	−0.704041	+	1.09229i
$926$	7.75220			0.254753
$927$	3.73199	−	23.5629i	0.122575	−	0.773906i
$928$	4.31408	+	8.46686i	0.141617	+	0.277938i
$929$	−11.6829	+	35.9562i	−0.383302	+	1.17968i	0.554402	+	0.832249i	$0.312947\pi$
$929$	−11.6829	+	35.9562i	−0.383302	+	1.17968i	−0.937704	+	0.347434i	$0.887053\pi$
$930$	11.5872	+	42.9500i	0.379961	+	1.40839i
$931$	−3.93874	+	6.76969i	−0.129087	+	0.221868i
$932$	0.0622885	+	0.0622885i	0.00204033	+	0.00204033i
$933$	13.7956	+	7.02921i	0.451648	+	0.230126i
$934$	−8.07082	−	5.86379i	−0.264085	−	0.191869i
$935$	−2.20058	+	10.4408i	−0.0719667	+	0.341449i
$936$	−3.14899	−	4.33421i	−0.102928	−	0.141668i
$937$	−24.9171	+	3.94648i	−0.814007	+	0.128926i	−0.549539	−	0.835468i	$-0.685196\pi$
$937$	−24.9171	+	3.94648i	−0.814007	+	0.128926i	−0.264468	+	0.964394i	$0.585196\pi$
$938$	16.1093	+	28.0103i	0.525988	+	0.914568i
$939$	−19.9720	−	27.4891i	−0.651762	−	0.897074i
$940$	−5.16619	−	1.08887i	−0.168502	−	0.0355150i
$941$	15.4825	−	21.3098i	0.504715	−	0.694681i	−0.478302	−	0.878195i	$-0.658748\pi$
$941$	15.4825	−	21.3098i	0.504715	−	0.694681i	0.983017	+	0.183515i	$0.0587475\pi$
$942$	−3.13024	+	6.14344i	−0.101989	+	0.200164i
$943$	1.24383	+	1.24383i	0.0405047	+	0.0405047i
$944$	2.28002	+	7.01717i	0.0742082	+	0.228389i
$945$	5.02038	−	3.64782i	0.163313	−	0.118664i
$946$	1.42408	−	4.38287i	0.0463008	−	0.142499i
$947$	26.7663	−	13.6381i	0.869789	−	0.443180i	0.0386556	−	0.999253i	$-0.487692\pi$
$947$	26.7663	−	13.6381i	0.869789	−	0.443180i	0.831134	+	0.556073i	$0.187692\pi$
$948$	30.8546	+	4.88689i	1.00211	+	0.158719i
$949$			6.68607i			0.217039i
$950$	3.03084	−	4.70225i	0.0983335	−	0.152561i
$951$			28.4867i			0.923745i
$952$	−18.1243	+	3.82077i	−0.587413	+	0.123832i
$953$	−15.2544	−	29.9384i	−0.494138	−	0.969801i	−0.994574	−	0.104027i	$-0.966827\pi$
$953$	−15.2544	−	29.9384i	−0.494138	−	0.969801i	0.500436	−	0.865773i	$-0.333173\pi$
$954$	−14.3459	−	4.66127i	−0.464466	−	0.150914i
$955$	3.74849	−	2.44343i	0.121298	−	0.0790675i
$956$	−3.37816	−	10.3969i	−0.109258	−	0.336260i
$957$	10.7943	−	10.7943i	0.348932	−	0.348932i
$958$	−7.17183	+	14.0755i	−0.231711	+	0.454759i
$959$	−3.67403	−	0.991043i	−0.118641	−	0.0320024i
$960$	−3.91046	+	3.53313i	−0.126210	+	0.114031i
$961$	32.5636	−	23.6588i	1.05044	−	0.763188i
$962$	−16.3711	+	2.59293i	−0.527827	+	0.0835996i
$963$	−23.5109	+	3.72376i	−0.757628	+	0.119996i
$964$	−11.9975	+	8.71673i	−0.386415	+	0.280747i
$965$	−12.2997	−	27.4989i	−0.395942	−	0.885220i
$966$	−2.94593	−	0.794643i	−0.0947837	−	0.0255672i
$967$	−22.5389	+	44.2350i	−0.724801	+	1.42250i	0.174269	+	0.984698i	$0.444244\pi$
$967$	−22.5389	+	44.2350i	−0.724801	+	1.42250i	−0.899070	+	0.437805i	$0.855756\pi$
$968$	7.44967	−	7.44967i	0.239441	−	0.239441i
$969$	−5.70505	−	17.5583i	−0.183273	−	0.564055i
$970$	28.3598	+	1.43761i	0.910578	+	0.0461588i
$971$	17.3918	+	5.65093i	0.558129	+	0.181347i	0.574479	−	0.818519i	$-0.305205\pi$
$971$	17.3918	+	5.65093i	0.558129	+	0.181347i	−0.0163503	+	0.999866i	$0.505205\pi$
$972$	−9.41812	−	18.4841i	−0.302086	−	0.592878i
$973$	−10.8860	−	51.6393i	−0.348990	−	1.65548i
$974$		−	33.7299i		−	1.08077i
$975$	−2.49882	+	24.5838i	−0.0800261	+	0.787312i
$976$			9.43069i			0.301869i
$977$	−35.5311	−	5.62758i	−1.13674	−	0.180042i	−0.440433	−	0.897785i	$-0.645175\pi$
$977$	−35.5311	−	5.62758i	−1.13674	−	0.180042i	−0.696308	+	0.717743i	$0.745175\pi$
$978$	47.4973	−	24.2011i	1.51880	−	0.773865i
$979$	2.18552	−	6.72635i	0.0698496	−	0.214975i
$980$	−15.6323	+	0.793646i	−0.499357	+	0.0253521i
$981$	−2.97619	−	9.15977i	−0.0950224	−	0.292449i
$982$	12.6759	+	12.6759i	0.404503	+	0.404503i
$983$	−18.2070	+	35.7332i	−0.580712	+	1.13971i	0.394594	+	0.918856i	$0.370885\pi$
$983$	−18.2070	+	35.7332i	−0.580712	+	1.13971i	−0.975306	+	0.220857i	$0.929115\pi$
$984$	4.98023	−	6.85470i	0.158764	−	0.218520i
$985$	−5.82492	−	54.5227i	−0.185597	−	1.73724i
$986$	−39.1035	−	53.8213i	−1.24531	−	1.71402i
$987$	−12.7632	+	7.34043i	−0.406259	+	0.233648i
$988$	2.31725	−	0.367017i	0.0737217	−	0.0116764i
$989$	−1.94458	−	2.67648i	−0.0618340	−	0.0851072i
$990$	3.37563	+	1.94123i	0.107285	+	0.0616962i
$991$	−39.7091	−	28.8503i	−1.26140	−	0.916461i	−0.262575	−	0.964911i	$-0.584572\pi$
$991$	−39.7091	−	28.8503i	−1.26140	−	0.916461i	−0.998826	+	0.0484500i	$0.984572\pi$
$992$	7.52100	+	3.83214i	0.238792	+	0.121671i
$993$	−45.1005	−	45.1005i	−1.43122	−	1.43122i
$994$	−3.48011	−	4.31230i	−0.110382	−	0.136778i
$995$	18.3263	−	47.9869i	0.580982	−	1.52129i
$996$	−4.96404	+	15.2777i	−0.157292	+	0.484094i
$997$	18.9035	+	37.1002i	0.598679	+	1.17497i	0.969229	+	0.246161i	$0.0791694\pi$
$997$	18.9035	+	37.1002i	0.598679	+	1.17497i	−0.370550	+	0.928813i	$0.620831\pi$
$998$	−0.999587	+	6.31115i	−0.0316414	+	0.199776i
$999$	−8.29173			−0.262339

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.r.a.27.3	yes	160
7.6	odd	2	inner	350.2.r.a.27.8	yes	160
25.13	odd	20	inner	350.2.r.a.13.8	yes	160
175.13	even	20	inner	350.2.r.a.13.3	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.r.a.13.3	✓	160	175.13	even	20	inner
350.2.r.a.13.8	yes	160	25.13	odd	20	inner
350.2.r.a.27.3	yes	160	1.1	even	1	trivial
350.2.r.a.27.8	yes	160	7.6	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.987688 - 0.156434i) q^{2} +(-2.10001 + 1.07001i) q^{3} +(0.951057 + 0.309017i) q^{4} +(0.797761 - 2.08892i) q^{5} +(2.24154 - 0.728320i) q^{6} +(-1.08017 + 2.41521i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(1.50176 - 2.06699i) q^{9} +O(q^{10})\)	\(q+(-0.987688 - 0.156434i) q^{2} +(-2.10001 + 1.07001i) q^{3} +(0.951057 + 0.309017i) q^{4} +(0.797761 - 2.08892i) q^{5} +(2.24154 - 0.728320i) q^{6} +(-1.08017 + 2.41521i) q^{7} +(-0.891007 - 0.453990i) q^{8} +(1.50176 - 2.06699i) q^{9} +(-1.11472 + 1.93840i) q^{10} +(0.551427 - 0.400635i) q^{11} +(-2.32787 + 0.368699i) q^{12} +(0.328023 + 2.07105i) q^{13} +(1.44469 - 2.21650i) q^{14} +(0.559852 + 5.24035i) q^{15} +(0.809017 + 0.587785i) q^{16} +(-6.23787 - 3.17835i) q^{17} +(-1.80662 + 1.80662i) q^{18} +(-0.345752 - 1.06411i) q^{19} +(1.40423 - 1.74016i) q^{20} +(-0.315937 - 6.22774i) q^{21} +(-0.607311 + 0.309440i) q^{22} +(-0.0765451 + 0.483287i) q^{23} +2.35689 q^{24} +(-3.72715 - 3.33291i) q^{25} -2.09687i q^{26} +(0.164093 - 1.03604i) q^{27} +(-1.77364 + 1.96321i) q^{28} +(-9.03749 - 2.93646i) q^{29} +(0.266812 - 5.26341i) q^{30} +(-8.02789 + 2.60842i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.729317 + 1.43137i) q^{33} +(5.66386 + 4.11504i) q^{34} +(4.18346 + 4.18314i) q^{35} +(2.06699 - 1.50176i) q^{36} +(-1.23657 - 7.80742i) q^{37} +(0.175031 + 1.10510i) q^{38} +(-2.90489 - 3.99824i) q^{39} +(-1.65916 + 1.49906i) q^{40} +(2.11305 - 2.90836i) q^{41} +(-0.662186 + 6.20049i) q^{42} +(-4.78087 + 4.78087i) q^{43} +(0.648241 - 0.210626i) q^{44} +(-3.11973 - 4.78601i) q^{45} +(0.151205 - 0.465362i) q^{46} +(-1.07194 - 2.10380i) q^{47} +(-2.32787 - 0.368699i) q^{48} +(-4.66649 - 5.21765i) q^{49} +(3.15988 + 3.87494i) q^{50} +16.5004 q^{51} +(-0.328023 + 2.07105i) q^{52} +(2.68033 + 5.26044i) q^{53} +(-0.324145 + 0.997617i) q^{54} +(-0.396986 - 1.47150i) q^{55} +(2.05892 - 1.66158i) q^{56} +(1.86469 + 1.86469i) q^{57} +(8.46686 + 4.31408i) q^{58} +(5.96916 + 4.33685i) q^{59} +(-1.08691 + 5.15687i) q^{60} +(5.54322 + 7.62959i) q^{61} +(8.33710 - 1.32047i) q^{62} +(3.37007 + 5.85975i) q^{63} +(0.587785 + 0.809017i) q^{64} +(4.58794 + 0.966994i) q^{65} +(0.944253 - 1.29965i) q^{66} +(-5.54454 + 10.8818i) q^{67} +(-4.95040 - 4.95040i) q^{68} +(-0.356375 - 1.09681i) q^{69} +(-3.47757 - 4.78607i) q^{70} +(0.647222 - 1.99194i) q^{71} +(-2.27647 + 1.15992i) q^{72} +(3.14934 + 0.498806i) q^{73} +7.90474i q^{74} +(11.3933 + 3.01106i) q^{75} -1.11888i q^{76} +(0.371986 + 1.76456i) q^{77} +(2.24366 + 4.40344i) q^{78} +(-12.6057 - 4.09584i) q^{79} +(1.87324 - 1.22106i) q^{80} +(3.13254 + 9.64095i) q^{81} +(-2.54200 + 2.54200i) q^{82} +(3.09428 - 6.07287i) q^{83} +(1.62400 - 6.02056i) q^{84} +(-11.6156 + 10.4948i) q^{85} +(5.46990 - 3.97412i) q^{86} +(22.1208 - 3.50359i) q^{87} +(-0.673209 + 0.106626i) q^{88} +(8.39461 - 6.09904i) q^{89} +(2.33262 + 5.21512i) q^{90} +(-5.35635 - 1.44484i) q^{91} +(-0.222143 + 0.435979i) q^{92} +(14.0676 - 14.0676i) q^{93} +(0.729635 + 2.24559i) q^{94} +(-2.49868 - 0.126662i) q^{95} +(2.24154 + 0.728320i) q^{96} +(-5.76530 - 11.3150i) q^{97} +(3.79281 + 5.88342i) q^{98} -1.74145i 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

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