LMFDB - Embedded newform 350.2.r.a.13.3

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			13.3
Character	$\chi$	$=$	350.13
Dual form			350.2.r.a.27.3

$q$-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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{19}{20}\right)$

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	−0.273507	−	0.961870i	$-0.588184\pi$
$3$	−2.10001	−	1.07001i	−1.21244	−	0.617769i	−0.938932	+	0.344101i	$0.888184\pi$
$4$	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	0.667805	−	0.744337i	$-0.267234\pi$
$11$	0.551427	+	0.400635i	0.166261	+	0.120796i	−0.501543	+	0.865133i	$0.667234\pi$
$12$	−2.32787	−	0.368699i	−0.672000	−	0.106434i
$13$	0.328023	−	2.07105i	0.0909771	−	0.574407i	−0.899521	−	0.436878i	$-0.856084\pi$
$13$	0.328023	−	2.07105i	0.0909771	−	0.574407i	0.990498	−	0.137529i	$-0.0439159\pi$
$14$	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	−0.996348	−	0.0853893i	$-0.972787\pi$
$17$	−6.23787	+	3.17835i	−1.51290	+	0.770863i	−0.516557	+	0.856253i	$0.672787\pi$
$18$	−1.80662	−	1.80662i	−0.425823	−	0.425823i
$19$	−0.345752	+	1.06411i	−0.0793209	+	0.244125i	−0.982851	−	0.184399i	$-0.940966\pi$
$19$	−0.345752	+	1.06411i	−0.0793209	+	0.244125i	0.903531	+	0.428524i	$0.140966\pi$
$20$	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	0.978422	−	0.206617i	$-0.0662454\pi$
$23$	−0.0765451	−	0.483287i	−0.0159608	−	0.100772i	−0.994383	+	0.105845i	$0.966245\pi$
$24$	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	−0.984565	−	0.175021i	$-0.944001\pi$
$29$	−9.03749	+	2.93646i	−1.67822	+	0.545287i	−0.693655	+	0.720308i	$0.744001\pi$
$30$	0.266812	+	5.26341i	0.0487130	+	0.960963i
$31$	−8.02789	−	2.60842i	−1.44185	−	0.468486i	−0.519377	−	0.854545i	$-0.673836\pi$
$31$	−8.02789	−	2.60842i	−1.44185	−	0.468486i	−0.922474	+	0.386059i	$0.873836\pi$
$32$	−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	0.649130	+	0.760677i	$0.275133\pi$
$37$	−1.23657	+	7.80742i	−0.203291	+	1.28353i	−0.852422	+	0.522855i	$0.824867\pi$
$38$	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	0.941488	−	0.337046i	$-0.109428\pi$
$41$	2.11305	+	2.90836i	0.330003	+	0.454210i	−0.611485	+	0.791256i	$0.709428\pi$
$42$	−0.662186	−	6.20049i	−0.102177	−	0.956757i
$43$	−4.78087	−	4.78087i	−0.729076	−	0.729076i	0.241360	−	0.970436i	$-0.422407\pi$
$43$	−4.78087	−	4.78087i	−0.729076	−	0.729076i	−0.970436	+	0.241360i	$0.922407\pi$
$44$	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	−0.955875	−	0.293773i	$-0.905089\pi$
$47$	−1.07194	+	2.10380i	−0.156358	+	0.306871i	0.799517	+	0.600644i	$0.205089\pi$
$48$	−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	−0.630386	−	0.776282i	$-0.717103\pi$
$53$	2.68033	−	5.26044i	0.368171	−	0.722577i	0.998557	+	0.0537053i	$0.0171032\pi$
$54$	−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	−0.126994	−	0.991903i	$-0.540533\pi$
$59$	5.96916	−	4.33685i	0.777119	−	0.564610i	0.904113	+	0.427294i	$0.140533\pi$
$60$	−1.08691	−	5.15687i	−0.140319	−	0.665749i
$61$	5.54322	−	7.62959i	0.709737	−	0.976869i	−0.290066	−	0.957007i	$-0.593677\pi$
$61$	5.54322	−	7.62959i	0.709737	−	0.976869i	0.999803	−	0.0198624i	$-0.00632281\pi$
$62$	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	−0.932027	−	0.362389i	$-0.881961\pi$
$67$	−5.54454	−	10.8818i	−0.677374	−	1.32942i	0.254653	−	0.967032i	$-0.418039\pi$
$68$	−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	0.982088	−	0.188421i	$-0.0603370\pi$
$71$	0.647222	+	1.99194i	0.0768111	+	0.236400i	−0.905277	+	0.424821i	$0.860337\pi$
$72$	−2.27647	−	1.15992i	−0.268284	−	0.136698i
$73$	3.14934	−	0.498806i	0.368602	−	0.0583808i	0.0306141	−	0.999531i	$-0.490254\pi$
$73$	3.14934	−	0.498806i	0.368602	−	0.0583808i	0.337988	+	0.941150i	$0.390254\pi$
$74$		−	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	−0.915046	−	0.403349i	$-0.867846\pi$
$79$	−12.6057	+	4.09584i	−1.41825	+	0.460818i	−0.503205	+	0.864167i	$0.667846\pi$
$80$	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	0.996143	−	0.0877404i	$-0.0279646\pi$
$83$	3.09428	+	6.07287i	0.339642	+	0.666584i	−0.656502	+	0.754324i	$0.727965\pi$
$84$	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	0.935833	−	0.352444i	$-0.114649\pi$
$89$	8.39461	+	6.09904i	0.889827	+	0.646497i	−0.0460059	+	0.998941i	$0.514649\pi$
$90$	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	0.388426	+	0.921480i	$0.373019\pi$
$97$	−5.76530	+	11.3150i	−0.585378	+	1.14887i	−0.973804	+	0.227389i	$0.926981\pi$
$98$	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	$-0.864597\pi$
$101$		−	8.29455i		−	0.825338i	0.910881	−	0.412669i	$-0.135403\pi$
$102$	−16.2973	+	2.58123i	−1.61367	+	0.255580i
$103$	8.31971	+	4.23910i	0.819765	+	0.417691i	0.812984	−	0.582286i	$-0.197842\pi$
$103$	8.31971	+	4.23910i	0.819765	+	0.417691i	0.00678098	+	0.999977i	$0.497842\pi$
$104$	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	−0.949786	−	0.312901i	$-0.898699\pi$
$107$	−6.58799	+	6.58799i	−0.636885	+	0.636885i	0.312901	+	0.949786i	$0.398699\pi$
$108$	0.476216	+	0.934627i	0.0458239	+	0.0899345i
$109$	2.21573	+	3.04968i	0.212228	+	0.292107i	0.901838	−	0.432074i	$-0.142218\pi$
$109$	2.21573	+	3.04968i	0.212228	+	0.292107i	−0.689610	+	0.724181i	$0.742218\pi$
$110$	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	−0.0613155	−	0.998118i	$-0.519530\pi$
$113$	−4.55040	−	0.720713i	−0.428066	−	0.0677989i	−0.366750	+	0.930319i	$0.619530\pi$
$114$	−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	−0.141267	−	0.989971i	$-0.545118\pi$
$127$	0.341436	−	0.0540782i	0.0302975	−	0.00479866i	0.171565	+	0.985173i	$0.445118\pi$
$128$	−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	0.261238	−	0.965274i	$-0.415869\pi$
$131$	−1.08493	−	0.352514i	−0.0947906	−	0.0307993i	−0.356028	+	0.934475i	$0.615869\pi$
$132$	−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	−0.976211	−	0.216823i	$-0.930431\pi$
$137$	0.224997	−	1.42058i	0.0192228	−	0.121368i	0.995434	+	0.0954548i	$0.0304306\pi$
$138$	0.180409	−	1.13905i	0.0153574	−	0.0969628i
$139$	−16.1373	−	11.7244i	−1.36875	−	0.994454i	−0.997834	−	0.0657866i	$-0.979044\pi$
$139$	−16.1373	−	11.7244i	−1.36875	−	0.994454i	−0.370914	−	0.928667i	$-0.620956\pi$
$140$	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	$-0.767131\pi$
$149$		−	16.3091i		−	1.33609i	0.744120	−	0.668046i	$-0.232869\pi$
$150$	−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	0.619726	−	0.784818i	$-0.287244\pi$
$157$	−2.06860	−	2.06860i	−0.165092	−	0.165092i	−0.784818	+	0.619726i	$0.787244\pi$
$158$	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	0.947475	−	0.319831i	$-0.103626\pi$
$163$	22.3392	+	3.53819i	1.74974	+	0.277132i	0.802269	+	0.596963i	$0.203626\pi$
$164$	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	−0.629503	−	0.776998i	$-0.716741\pi$
$167$	−4.79322	+	2.44227i	−0.370911	+	0.188988i	0.258592	+	0.965987i	$0.416741\pi$
$168$	−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	−0.167084	−	0.985943i	$-0.553435\pi$
$173$	−0.280390	+	0.0444095i	−0.0213177	+	0.00337639i	0.145767	+	0.989319i	$0.453435\pi$
$174$	−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	−0.991628	−	0.129124i	$-0.958783\pi$
$179$	−22.9849	+	7.46826i	−1.71798	+	0.558204i	−0.726347	+	0.687328i	$0.758783\pi$
$180$	−1.48808	+	5.51582i	−0.110915	+	0.411125i
$181$	8.98251	+	2.91859i	0.667664	+	0.216937i	0.623187	−	0.782073i	$-0.285838\pi$
$181$	8.98251	+	2.91859i	0.667664	+	0.216937i	0.0444777	+	0.999010i	$0.485838\pi$
$182$	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	−0.527673	−	0.849448i	$-0.676935\pi$
$191$	1.61890	−	1.17620i	0.117140	−	0.0851071i	0.644813	+	0.764341i	$0.276935\pi$
$192$	−2.10001	+	1.07001i	−0.151555	+	0.0772211i
$193$	9.52612	+	9.52612i	0.685705	+	0.685705i	0.961280	−	0.275574i	$-0.0888680\pi$
$193$	9.52612	+	9.52612i	0.685705	+	0.685705i	−0.275574	+	0.961280i	$0.588868\pi$
$194$	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	0.999312	−	0.0370770i	$-0.0118047\pi$
$197$	21.8493	+	11.1328i	1.55670	+	0.793177i	0.557385	+	0.830254i	$0.311805\pi$
$198$	−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	0.293239	−	0.956039i	$-0.405267\pi$
$211$	−7.63176	−	5.54480i	−0.525392	−	0.381720i	−0.818631	+	0.574320i	$0.805267\pi$
$212$	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	−0.396708	−	0.917945i	$-0.629847\pi$
$223$	−7.32232	+	1.15974i	−0.490339	+	0.0776620i	−0.0936309	+	0.995607i	$0.529847\pi$
$224$	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	−0.533305	−	0.845923i	$-0.679050\pi$
$227$	−4.33172	−	27.3494i	−0.287506	−	1.81524i	0.245798	−	0.969321i	$-0.420950\pi$
$228$	1.19721	−	2.34965i	0.0792869	−	0.155609i
$229$	−2.09144	−	6.43679i	−0.138206	−	0.425355i	0.857869	−	0.513869i	$-0.171788\pi$
$229$	−2.09144	−	6.43679i	−0.138206	−	0.425355i	−0.996075	+	0.0885138i	$0.971788\pi$
$230$	−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	−0.451418	−	0.892313i	$-0.649082\pi$
$233$	0.0784881	−	0.0399917i	0.00514193	−	0.00261994i	0.456560	+	0.889693i	$0.349082\pi$
$234$	−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	−0.964583	−	0.263780i	$-0.915031\pi$
$239$	−6.42564	+	8.84414i	−0.415640	+	0.572080i	0.548942	+	0.835860i	$0.315031\pi$
$240$	−2.62727	−	4.56861i	−0.169590	−	0.294902i
$241$	−8.71673	−	11.9975i	−0.561494	−	0.772830i	0.430022	−	0.902818i	$-0.358506\pi$
$241$	−8.71673	−	11.9975i	−0.561494	−	0.772830i	−0.991515	+	0.129989i	$0.958506\pi$
$242$	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	$0.230293\pi$
$251$			20.9762i			1.32400i	−0.749502	+	0.662002i	$0.769707\pi$
$252$	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	0.469360	−	0.883007i	$-0.344485\pi$
$257$	−6.63127	−	6.63127i	−0.413647	−	0.413647i	−0.883007	+	0.469360i	$0.844485\pi$
$258$	−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	−0.228596	−	0.973521i	$-0.573414\pi$
$263$	−12.1117	−	1.91830i	−0.746839	−	0.118288i	−0.518243	+	0.855234i	$0.673414\pi$
$264$	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	−0.702342	−	0.711840i	$-0.747862\pi$
$269$	4.66244	−	14.3495i	0.284274	−	0.874905i	0.986615	−	0.163065i	$-0.0521380\pi$
$270$	1.82535	−	1.47297i	0.111087	−	0.0896423i
$271$	−25.0124	+	8.12701i	−1.51939	+	0.493680i	−0.945603	−	0.325323i	$-0.894527\pi$
$271$	−25.0124	+	8.12701i	−1.51939	+	0.493680i	−0.573789	+	0.819003i	$0.694527\pi$
$272$	−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	−0.0133079	−	0.999911i	$-0.504236\pi$
$277$	4.71048	−	0.746067i	0.283025	−	0.0448268i	0.296333	+	0.955085i	$0.404236\pi$
$278$	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	0.232994	+	0.972478i	$0.425148\pi$
$281$	−8.83598	+	27.1944i	−0.527110	+	1.62228i	−0.760104	+	0.649801i	$0.774852\pi$
$282$	−3.93503	+	3.93503i	−0.234328	+	0.234328i
$283$	2.69409	+	5.28744i	0.160147	+	0.314306i	0.957111	−	0.289720i	$-0.0935622\pi$
$283$	2.69409	+	5.28744i	0.160147	+	0.314306i	−0.796965	+	0.604026i	$0.793562\pi$
$284$	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	−0.780461	−	0.625205i	$-0.785015\pi$
$293$	−2.65754	+	2.65754i	−0.155255	+	0.155255i	0.625205	+	0.780461i	$0.285015\pi$
$294$	−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	0.422416	−	0.906402i	$-0.361182\pi$
$307$	−8.48013	−	8.48013i	−0.483986	−	0.483986i	−0.906402	+	0.422416i	$0.861182\pi$
$308$	−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	−0.904339	−	0.426816i	$-0.859635\pi$
$311$	−3.86135	+	5.31469i	−0.218957	+	0.301368i	0.685382	+	0.728184i	$0.259635\pi$
$312$	0.773114	−	4.88125i	0.0437690	−	0.276346i
$313$	2.25526	−	14.2391i	0.127475	−	0.804843i	−0.838252	−	0.545283i	$-0.816422\pi$
$313$	2.25526	−	14.2391i	0.127475	−	0.804843i	0.965727	−	0.259560i	$-0.0835777\pi$
$314$	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	0.992206	−	0.124609i	$-0.0397677\pi$
$317$	5.48718	+	10.7692i	0.308191	+	0.604859i	−0.684015	+	0.729468i	$0.739768\pi$
$318$	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	−0.405943	−	0.913899i	$-0.633057\pi$
$331$	8.36256	−	25.7373i	0.459648	−	1.41465i	0.865591	−	0.500752i	$-0.166943\pi$
$332$	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	−0.801268	−	0.598306i	$-0.795841\pi$
$337$	2.67414	−	16.8839i	0.145670	−	0.919723i	0.946938	−	0.321417i	$-0.104159\pi$
$338$	−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	0.781643	−	0.623727i	$-0.214382\pi$
$347$	13.7190	+	6.99019i	0.736475	+	0.375253i	−0.0451674	+	0.998979i	$0.514382\pi$
$348$	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	−0.971217	−	0.238196i	$-0.923444\pi$
$353$	−32.5937	−	16.6073i	−1.73479	−	0.883919i	−0.763572	−	0.645723i	$-0.776556\pi$
$354$	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	0.692099	−	0.721802i	$-0.256686\pi$
$359$	−3.94570	−	5.43079i	−0.208246	−	0.286626i	−0.900345	+	0.435176i	$0.856686\pi$
$360$	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	−0.460808	−	0.887500i	$-0.652440\pi$
$367$	−0.261710	+	0.133348i	−0.0136611	+	0.00696070i	0.447147	+	0.894461i	$0.352440\pi$
$368$	−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	−0.988256	−	0.152807i	$-0.951169\pi$
$373$	−1.84613	−	11.6560i	−0.0955888	−	0.603524i	0.892667	−	0.450716i	$-0.148831\pi$
$374$	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	0.187664	−	0.982233i	$-0.439908\pi$
$379$	17.8488	−	5.79941i	0.916829	−	0.297896i	0.729165	+	0.684337i	$0.239908\pi$
$380$	−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	0.841535	−	0.540203i	$-0.181652\pi$
$383$	−1.76408	−	3.46219i	−0.0901400	−	0.176910i	−0.931675	+	0.363293i	$0.881652\pi$
$384$	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	−0.854147	−	0.520032i	$-0.825920\pi$
$389$	−1.88595	+	2.59579i	−0.0956214	+	0.131612i	0.758526	+	0.651643i	$0.225920\pi$
$390$	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	−0.997355	−	0.0726858i	$-0.976843\pi$
$397$	−7.01993	+	13.7774i	−0.352320	+	0.691468i	0.645035	+	0.764153i	$0.276843\pi$
$398$	−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	−0.985620	−	0.168975i	$-0.945954\pi$
$409$	−22.8425	+	16.5960i	−1.12949	+	0.820621i	−0.143868	+	0.989597i	$0.545954\pi$
$410$	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	0.800969	+	0.598706i	$0.204318\pi$
$419$	−4.07219	+	12.5329i	−0.198939	+	0.612273i	−0.999908	+	0.0135662i	$0.995682\pi$
$420$	−11.2809	+	8.19538i	−0.550451	+	0.399894i
$421$	−11.2107	−	34.5030i	−0.546376	−	1.68157i	−0.717696	−	0.696357i	$-0.754803\pi$
$421$	−11.2107	−	34.5030i	−0.546376	−	1.68157i	0.171320	−	0.985215i	$-0.445197\pi$
$422$	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	−0.764479	−	0.644649i	$-0.777004\pi$
$431$	4.83539	−	14.8818i	0.232913	−	0.716831i	0.997391	−	0.0721825i	$-0.0229964\pi$
$432$	0.741724	+	0.741724i	0.0356862	+	0.0356862i
$433$	15.8697	+	31.1461i	0.762651	+	1.49679i	0.864854	+	0.502024i	$0.167411\pi$
$433$	15.8697	+	31.1461i	0.762651	+	1.49679i	−0.102202	+	0.994764i	$0.532589\pi$
$434$	−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	0.610406	−	0.792088i	$-0.291006\pi$
$439$	0.957762	+	0.695855i	0.0457115	+	0.0332113i	−0.564695	+	0.825300i	$0.691006\pi$
$440$	−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	0.279279	−	0.960210i	$-0.409904\pi$
$443$	−14.3319	−	14.3319i	−0.680931	−	0.680931i	−0.960210	+	0.279279i	$0.909904\pi$
$444$	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	$0.157604\pi$
$449$			20.1363i			0.950289i	−0.879908	+	0.475144i	$0.842396\pi$
$450$	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	−0.980188	−	0.198070i	$-0.936533\pi$
$457$	−16.7198	+	16.7198i	−0.782118	+	0.782118i	0.198070	+	0.980188i	$0.436533\pi$
$458$	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	0.271807	−	0.962352i	$-0.412379\pi$
$461$	23.6838	−	32.5980i	1.10306	−	1.51824i	0.831258	−	0.555887i	$-0.187621\pi$
$462$	2.11899	−	3.68441i	0.0985841	−	0.171414i
$463$	−7.65675	−	1.21271i	−0.355840	−	0.0563594i	−0.0240443	−	0.999711i	$-0.507654\pi$
$463$	−7.65675	−	1.21271i	−0.355840	−	0.0563594i	−0.331795	+	0.943351i	$0.607654\pi$
$464$	−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	−0.236070	−	0.971736i	$-0.575859\pi$
$467$	8.88875	−	4.52905i	0.411323	−	0.209579i	0.647393	+	0.762157i	$0.275859\pi$
$468$	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	0.998484	+	0.0550445i	$0.0175301\pi$
$479$	4.88164	+	15.0241i	0.223048	+	0.686471i	−0.775436	+	0.631426i	$0.782470\pi$
$480$	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	−0.517460	−	0.855707i	$-0.673123\pi$
$487$	5.27652	−	33.3146i	0.239102	−	1.50963i	0.756562	−	0.653922i	$-0.226877\pi$
$488$	−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	−0.864801	−	0.502115i	$-0.832555\pi$
$491$	−14.5027	+	10.5369i	−0.654499	+	0.475522i	0.210302	+	0.977637i	$0.432555\pi$
$492$	−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	$0.0456825\pi$
$499$			6.38982i			0.286047i	−0.989719	+	0.143024i	$0.954317\pi$
$500$	−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	0.100324	−	0.994955i	$-0.468012\pi$
$503$	−14.4802	−	7.37805i	−0.645642	−	0.328971i	−0.745966	+	0.665984i	$0.768012\pi$
$504$	−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	−0.915991	−	0.401198i	$-0.868594\pi$
$509$	−18.4433	+	13.3999i	−0.817486	+	0.593938i	0.0985052	+	0.995137i	$0.468594\pi$
$510$	−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	−0.861438	−	0.507864i	$-0.830435\pi$
$521$	−28.7564	+	9.34352i	−1.25984	+	0.409347i	−0.398403	+	0.917211i	$0.630435\pi$
$522$	21.6323	+	11.0222i	0.946821	+	0.482429i
$523$	−11.3190	+	1.79275i	−0.494946	+	0.0783917i	−0.398917	−	0.916987i	$-0.630614\pi$
$523$	−11.3190	+	1.79275i	−0.494946	+	0.0783917i	−0.0960284	+	0.995379i	$0.530614\pi$
$524$	−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	−0.337147	+	0.941452i	$0.609462\pi$
$541$	−31.0910	+	22.5889i	−1.33670	+	0.971173i	−0.999558	+	0.0297207i	$0.990538\pi$
$542$	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	−0.174812	−	0.984602i	$-0.555932\pi$
$547$	−25.1216	−	12.8001i	−1.07412	−	0.547293i	−0.899311	+	0.437309i	$0.855932\pi$
$548$	−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	−0.128699	−	0.991684i	$-0.541080\pi$
$557$	20.3672	−	20.3672i	0.862985	−	0.862985i	0.991684	+	0.128699i	$0.0410800\pi$
$558$	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	0.617883	+	0.786270i	$0.287991\pi$
$563$	−5.04756	+	31.8691i	−0.212729	+	1.34312i	−0.830612	+	0.556851i	$0.812009\pi$
$564$	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	0.689210	−	0.724562i	$-0.257958\pi$
$569$	19.5816	+	6.36246i	0.820905	+	0.266728i	0.131696	+	0.991290i	$0.457958\pi$
$570$	−5.69313	−	1.53592i	−0.238459	−	0.0643325i
$571$	11.3099	+	34.8083i	0.473305	+	1.45668i	0.848231	+	0.529627i	$0.177668\pi$
$571$	11.3099	+	34.8083i	0.473305	+	1.45668i	−0.374926	+	0.927055i	$0.622332\pi$
$572$	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	0.971421	+	0.237364i	$0.0762834\pi$
$577$	2.90398	+	18.3350i	0.120894	+	0.763296i	−0.850527	+	0.525932i	$0.823717\pi$
$578$	−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	0.264503	−	0.964385i	$-0.414792\pi$
$587$	5.28293	+	0.836733i	0.218050	+	0.0345357i	−0.0464537	+	0.998920i	$0.514792\pi$
$588$	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	−0.990868	−	0.134833i	$-0.956950\pi$
$593$	−20.8458	+	20.8458i	−0.856035	+	0.856035i	0.134833	+	0.990868i	$0.456950\pi$
$594$	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	$0.245607\pi$
$599$			34.1312i			1.39456i	−0.716797	+	0.697282i	$0.754393\pi$
$600$	−8.78450	+	7.85532i	−0.358626	+	0.320692i
$601$			1.31870i			0.0537908i	0.999638	+	0.0268954i	$0.00856211\pi$
$601$			1.31870i			0.0537908i	−0.999638	+	0.0268954i	$0.991438\pi$
$602$	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	0.972950	−	0.231016i	$-0.0742051\pi$
$607$	18.2793	+	18.2793i	0.741933	+	0.741933i	−0.231016	+	0.972950i	$0.574205\pi$
$608$	−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	0.797815	−	0.602902i	$-0.205989\pi$
$613$	33.9264	+	5.37342i	1.37028	+	0.217030i	0.572460	+	0.819932i	$0.305989\pi$
$614$	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	0.975968	−	0.217913i	$-0.0699250\pi$
$617$	5.61404	+	11.0182i	0.226013	+	0.443575i	−0.749955	+	0.661489i	$0.769925\pi$
$618$	15.5615	+	15.5615i	0.625976	+	0.625976i
$619$	−0.219264	+	0.674825i	−0.00881296	+	0.0271235i	−0.955366	−	0.295424i	$-0.904539\pi$
$619$	−0.219264	+	0.674825i	−0.00881296	+	0.0271235i	0.946553	+	0.322547i	$0.104539\pi$
$620$	−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	−0.805438	−	0.592680i	$-0.798070\pi$
$631$	4.88687	−	15.0402i	0.194543	−	0.598743i	0.999982	−	0.00606307i	$-0.00192995\pi$
$632$	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	−0.977292	−	0.211896i	$-0.932036\pi$
$641$	−27.2869	+	19.8251i	−1.07777	+	0.783044i	−0.100475	+	0.994940i	$0.532036\pi$
$642$	−19.5654	+	9.96907i	−0.772185	+	0.393448i
$643$	−22.2277	+	22.2277i	−0.876573	+	0.876573i	−0.993178	−	0.116605i	$-0.962799\pi$
$643$	−22.2277	+	22.2277i	−0.876573	+	0.876573i	0.116605	+	0.993178i	$0.462799\pi$
$644$	−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	−0.934049	−	0.357144i	$-0.883751\pi$
$647$	−2.44425	+	4.79711i	−0.0960933	+	0.188594i	0.837956	+	0.545738i	$0.183751\pi$
$648$	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	−0.450200	−	0.892928i	$-0.648647\pi$
$653$	13.7177	−	26.9225i	0.536815	−	1.05356i	0.987015	−	0.160630i	$-0.0513527\pi$
$654$	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	0.903737	−	0.428089i	$-0.140813\pi$
$659$	5.57908	+	7.67894i	0.217330	+	0.299129i	−0.686407	+	0.727218i	$0.740813\pi$
$660$	1.46667	−	3.27909i	0.0570902	−	0.127638i
$661$	−5.07681	+	6.98763i	−0.197465	+	0.271787i	−0.896255	−	0.443540i	$-0.853722\pi$
$661$	−5.07681	+	6.98763i	−0.197465	+	0.271787i	0.698790	+	0.715327i	$0.253722\pi$
$662$	−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	0.997369	−	0.0724932i	$-0.0230956\pi$
$673$	0.685214	+	4.32627i	0.0264131	+	0.166766i	−0.970956	+	0.239259i	$0.923096\pi$
$674$			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	−0.885100	−	0.465402i	$-0.845910\pi$
$677$	−4.86916	−	30.7426i	−0.187137	−	1.18154i	0.697963	−	0.716134i	$-0.254090\pi$
$678$	−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	−0.763402	−	0.645924i	$-0.776472\pi$
$683$	−18.0210	+	9.18217i	−0.689555	+	0.351346i	0.0738468	+	0.997270i	$0.476472\pi$
$684$	−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	0.962902	+	0.269853i	$0.0869751\pi$
$691$	24.2363	+	33.3585i	0.921994	+	1.26902i	−0.0409074	+	0.999163i	$0.513025\pi$
$692$	−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	0.999527	+	0.0307428i	$0.00978727\pi$
$709$	19.1687	+	26.3834i	0.719895	+	0.990850i	−0.279633	+	0.960107i	$0.590213\pi$
$710$	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	0.111569	+	0.993757i	$0.464412\pi$
$719$	−15.0912	+	46.4460i	−0.562808	+	1.73214i	−0.674377	+	0.738387i	$0.735588\pi$
$720$	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	0.986267	+	0.165161i	$0.0528143\pi$
$727$	2.67766	+	16.9061i	0.0993088	+	0.627011i	−0.886958	+	0.461850i	$0.847186\pi$
$728$	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	−0.899092	−	0.437760i	$-0.855772\pi$
$733$	−19.6225	−	38.5113i	−0.724774	−	1.42245i	0.174318	−	0.984689i	$-0.444228\pi$
$734$	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	−0.983415	−	0.181370i	$-0.941947\pi$
$739$	−13.7834	+	18.9712i	−0.507030	+	0.697867i	0.476385	+	0.879237i	$0.341947\pi$
$740$	−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	0.493344	−	0.869835i	$-0.335775\pi$
$743$	−10.2624	−	10.2624i	−0.376491	−	0.376491i	−0.869835	+	0.493344i	$0.835775\pi$
$744$	−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	−0.951795	−	0.306734i	$-0.900764\pi$
$757$	−17.7480	+	17.7480i	−0.645061	+	0.645061i	0.306734	+	0.951795i	$0.400764\pi$
$758$	−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	−0.925881	−	0.377815i	$-0.876675\pi$
$761$	−7.73640	+	10.6482i	−0.280444	+	0.385998i	0.645437	+	0.763814i	$0.276675\pi$
$762$	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	−0.547742	−	0.836647i	$-0.684513\pi$
$769$	10.7363	−	33.0428i	0.387159	−	1.19155i	0.934902	−	0.354907i	$-0.115487\pi$
$770$	−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	0.537737	−	0.843113i	$-0.319279\pi$
$773$	36.4132	−	5.76728i	1.30969	−	0.207435i	0.771954	+	0.635678i	$0.219279\pi$
$774$			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	0.248601	−	0.968606i	$-0.420029\pi$
$787$	5.21005	+	0.825192i	0.185718	+	0.0294149i	−0.0628824	+	0.998021i	$0.520029\pi$
$788$	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	−0.937842	−	0.347063i	$-0.887179\pi$
$797$	−2.98721	+	5.86272i	−0.105812	+	0.207668i	0.832029	+	0.554731i	$0.187179\pi$
$798$	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	0.999546	−	0.0301328i	$-0.00959302\pi$
$809$	18.8295	+	25.9166i	0.662011	+	0.911180i	−0.337535	+	0.941313i	$0.609593\pi$
$810$	−22.1799	+	4.67483i	−0.779324	+	0.164257i
$811$	8.05779	−	11.0906i	0.282947	−	0.389444i	−0.643760	−	0.765228i	$-0.722626\pi$
$811$	8.05779	−	11.0906i	0.282947	−	0.389444i	0.926707	+	0.375784i	$0.122626\pi$
$812$	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	0.960583	−	0.277995i	$-0.0896699\pi$
$821$	0.574596	+	1.76843i	0.0200536	+	0.0617185i	−0.940529	+	0.339714i	$0.889670\pi$
$822$	1.53898	−	3.02041i	0.0536779	−	0.105349i
$823$	0.337840	+	2.13304i	0.0117764	+	0.0743531i	0.992877	−	0.119147i	$-0.0380160\pi$
$823$	0.337840	+	2.13304i	0.0117764	+	0.0743531i	−0.981100	+	0.193500i	$0.938016\pi$
$824$	−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	−0.599151	−	0.800636i	$-0.704495\pi$
$827$	−26.5021	+	4.19751i	−0.921567	+	0.145962i	−0.322416	+	0.946598i	$0.604495\pi$
$828$	0.567561	−	1.11390i	0.0197241	−	0.0387107i
$829$	8.61595	+	26.5172i	0.299244	+	0.920979i	0.981763	+	0.190111i	$0.0608847\pi$
$829$	8.61595	+	26.5172i	0.299244	+	0.920979i	−0.682518	+	0.730868i	$0.739115\pi$
$830$	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	0.478321	−	0.878185i	$-0.341245\pi$
$839$	−6.05589	−	4.39986i	−0.209073	−	0.151900i	−0.687394	+	0.726285i	$0.741245\pi$
$840$	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	0.371475	−	0.928443i	$-0.378852\pi$
$853$	−4.71105	−	2.40040i	−0.161303	−	0.0821881i	−0.532778	+	0.846255i	$0.678852\pi$
$854$	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	0.368300	−	0.929707i	$-0.379940\pi$
$857$	−16.4350	−	16.4350i	−0.561408	−	0.561408i	−0.929707	+	0.368300i	$0.879940\pi$
$858$	3.00139	−	1.52928i	0.102466	−	0.0522089i
$859$	19.4475	−	14.1295i	0.663542	−	0.482091i	−0.204315	−	0.978905i	$-0.565497\pi$
$859$	19.4475	−	14.1295i	0.663542	−	0.482091i	0.867857	+	0.496814i	$0.165497\pi$
$860$	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	−0.851079	−	0.525037i	$-0.824051\pi$
$863$	−53.5466	−	8.48096i	−1.82275	−	0.288695i	−0.971670	+	0.236342i	$0.924051\pi$
$864$	−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	0.269007	−	0.963138i	$-0.413305\pi$
$877$	24.3569	−	3.85775i	0.822474	−	0.130267i	0.553467	+	0.832871i	$0.313305\pi$
$878$	−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	0.228340	−	0.973582i	$-0.426670\pi$
$881$	−4.72492	−	1.53522i	−0.159187	−	0.0517229i	−0.387526	+	0.921859i	$0.626670\pi$
$882$	17.8568	−	0.995750i	0.601271	−	0.0335287i
$883$	24.7034	−	12.5870i	0.831336	−	0.423587i	0.0141077	−	0.999900i	$-0.495509\pi$
$883$	24.7034	−	12.5870i	0.831336	−	0.423587i	0.817229	+	0.576313i	$0.195509\pi$
$884$	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	0.293370	−	0.955999i	$-0.405223\pi$
$887$	8.24861	+	1.30645i	0.276961	+	0.0438664i	−0.0164086	+	0.999865i	$0.505223\pi$
$888$	−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	−0.123267	+	0.992374i	$0.539337\pi$
$907$	−33.5991	+	33.5991i	−1.11564	+	1.11564i	−0.992374	+	0.123267i	$0.960663\pi$
$908$	−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	0.997985	+	0.0634488i	$0.0202100\pi$
$911$	41.2515	+	29.9710i	1.36672	+	0.992982i	0.368738	+	0.929533i	$0.379790\pi$
$912$	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	0.744704	−	0.667395i	$-0.232591\pi$
$919$	28.9477	+	9.40569i	0.954898	+	0.310265i	0.210193	+	0.977660i	$0.432591\pi$
$920$	−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	−0.937704	−	0.347434i	$-0.887053\pi$
$929$	−11.6829	−	35.9562i	−0.383302	−	1.17968i	0.554402	−	0.832249i	$-0.312947\pi$
$930$	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	−0.264468	−	0.964394i	$-0.585196\pi$
$937$	−24.9171	−	3.94648i	−0.814007	−	0.128926i	−0.549539	+	0.835468i	$0.685196\pi$
$938$	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	0.983017	−	0.183515i	$-0.0587475\pi$
$941$	15.4825	+	21.3098i	0.504715	+	0.694681i	−0.478302	+	0.878195i	$0.658748\pi$
$942$	−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	0.831134	−	0.556073i	$-0.187692\pi$
$947$	26.7663	+	13.6381i	0.869789	+	0.443180i	0.0386556	+	0.999253i	$0.487692\pi$
$948$	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	0.500436	+	0.865773i	$0.333173\pi$
$953$	−15.2544	+	29.9384i	−0.494138	+	0.969801i	−0.994574	+	0.104027i	$0.966827\pi$
$954$	−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	−0.899070	−	0.437805i	$-0.855756\pi$
$967$	−22.5389	−	44.2350i	−0.724801	−	1.42250i	0.174269	−	0.984698i	$-0.444244\pi$
$968$	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	−0.0163503	−	0.999866i	$-0.505205\pi$
$971$	17.3918	−	5.65093i	0.558129	−	0.181347i	0.574479	+	0.818519i	$0.305205\pi$
$972$	−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	−0.696308	−	0.717743i	$-0.745175\pi$
$977$	−35.5311	+	5.62758i	−1.13674	+	0.180042i	−0.440433	+	0.897785i	$0.645175\pi$
$978$	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	−0.975306	−	0.220857i	$-0.929115\pi$
$983$	−18.2070	−	35.7332i	−0.580712	−	1.13971i	0.394594	−	0.918856i	$-0.370885\pi$
$984$	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	−0.998826	−	0.0484500i	$-0.984572\pi$
$991$	−39.7091	+	28.8503i	−1.26140	+	0.916461i	−0.262575	+	0.964911i	$0.584572\pi$
$992$	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	−0.370550	−	0.928813i	$-0.620831\pi$
$997$	18.9035	−	37.1002i	0.598679	−	1.17497i	0.969229	−	0.246161i	$-0.0791694\pi$
$998$	−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.13.3	✓	160
7.6	odd	2	inner	350.2.r.a.13.8	yes	160
25.2	odd	20	inner	350.2.r.a.27.8	yes	160
175.27	even	20	inner	350.2.r.a.27.3	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.r.a.13.3	✓	160	1.1	even	1	trivial
350.2.r.a.13.8	yes	160	7.6	odd	2	inner
350.2.r.a.27.3	yes	160	175.27	even	20	inner
350.2.r.a.27.8	yes	160	25.2	odd	20	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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more