LMFDB - Embedded newform 209.2.f.a.191.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [209,2,Mod(20,209)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("209.20"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(209, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([6, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	209.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.66887340224$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	209.191
Dual form			209.2.f.a.58.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.80902 - 1.31433i) q^{2} +(-0.381966 + 1.17557i) q^{3} +(0.927051 + 2.85317i) q^{4} +(-0.500000 + 0.363271i) q^{5} +(2.23607 - 1.62460i) q^{6} +(-0.809017 - 2.48990i) q^{7} +(0.690983 - 2.12663i) q^{8} +(1.19098 + 0.865300i) q^{9} +1.38197 q^{10} +(-3.30902 + 0.224514i) q^{11} -3.70820 q^{12} +(-5.23607 - 3.80423i) q^{13} +(-1.80902 + 5.56758i) q^{14} +(-0.236068 - 0.726543i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-6.54508 + 4.75528i) q^{17} +(-1.01722 - 3.13068i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-1.50000 - 1.08981i) q^{20} +3.23607 q^{21} +(6.28115 + 3.94298i) q^{22} +1.61803 q^{23} +(2.23607 + 1.62460i) q^{24} +(-1.42705 + 4.39201i) q^{25} +(4.47214 + 13.7638i) q^{26} +(-4.47214 + 3.24920i) q^{27} +(6.35410 - 4.61653i) q^{28} +(-0.145898 - 0.449028i) q^{29} +(-0.527864 + 1.62460i) q^{30} +(-6.47214 - 4.70228i) q^{31} -6.70820 q^{32} +(1.00000 - 3.97574i) q^{33} +18.0902 q^{34} +(1.30902 + 0.951057i) q^{35} +(-1.36475 + 4.20025i) q^{36} +(-0.618034 - 1.90211i) q^{37} +(-1.80902 + 1.31433i) q^{38} +(6.47214 - 4.70228i) q^{39} +(0.427051 + 1.31433i) q^{40} +(-0.527864 + 1.62460i) q^{41} +(-5.85410 - 4.25325i) q^{42} +8.09017 q^{43} +(-3.70820 - 9.23305i) q^{44} -0.909830 q^{45} +(-2.92705 - 2.12663i) q^{46} +(1.97214 - 6.06961i) q^{47} +(0.381966 + 1.17557i) q^{48} +(0.118034 - 0.0857567i) q^{49} +(8.35410 - 6.06961i) q^{50} +(-3.09017 - 9.51057i) q^{51} +(6.00000 - 18.4661i) q^{52} +(-8.47214 - 6.15537i) q^{53} +12.3607 q^{54} +(1.57295 - 1.31433i) q^{55} -5.85410 q^{56} +(1.00000 + 0.726543i) q^{57} +(-0.326238 + 1.00406i) q^{58} +(1.09017 + 3.35520i) q^{59} +(1.85410 - 1.34708i) q^{60} +(-5.16312 + 3.75123i) q^{61} +(5.52786 + 17.0130i) q^{62} +(1.19098 - 3.66547i) q^{63} +(10.5172 + 7.64121i) q^{64} +4.00000 q^{65} +(-7.03444 + 5.87785i) q^{66} +0.472136 q^{67} +(-19.6353 - 14.2658i) q^{68} +(-0.618034 + 1.90211i) q^{69} +(-1.11803 - 3.44095i) q^{70} +(1.38197 - 1.00406i) q^{71} +(2.66312 - 1.93487i) q^{72} +(3.85410 + 11.8617i) q^{73} +(-1.38197 + 4.25325i) q^{74} +(-4.61803 - 3.35520i) q^{75} +3.00000 q^{76} +(3.23607 + 8.05748i) q^{77} -17.8885 q^{78} +(12.0902 + 8.78402i) q^{79} +(-0.190983 + 0.587785i) q^{80} +(-0.746711 - 2.29814i) q^{81} +(3.09017 - 2.24514i) q^{82} +(8.35410 - 6.06961i) q^{83} +(3.00000 + 9.23305i) q^{84} +(1.54508 - 4.75528i) q^{85} +(-14.6353 - 10.6331i) q^{86} +0.583592 q^{87} +(-1.80902 + 7.19218i) q^{88} +1.23607 q^{89} +(1.64590 + 1.19581i) q^{90} +(-5.23607 + 16.1150i) q^{91} +(1.50000 + 4.61653i) q^{92} +(8.00000 - 5.81234i) q^{93} +(-11.5451 + 8.38800i) q^{94} +(0.190983 + 0.587785i) q^{95} +(2.56231 - 7.88597i) q^{96} +(-8.23607 - 5.98385i) q^{97} -0.326238 q^{98} +(-4.13525 - 2.59590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} - 6 q^{3} - 3 q^{4} - 2 q^{5} - q^{7} + 5 q^{8} + 7 q^{9} + 10 q^{10} - 11 q^{11} + 12 q^{12} - 12 q^{13} - 5 q^{14} + 8 q^{15} + q^{16} - 15 q^{17} + 25 q^{18} - q^{19} - 6 q^{20} + 4 q^{21}+ \cdots + 17 q^{99}+O(q^{100}) $ 4 * q - 5 * q^2 - 6 * q^3 - 3 * q^4 - 2 * q^5 - q^7 + 5 * q^8 + 7 * q^9 + 10 * q^10 - 11 * q^11 + 12 * q^12 - 12 * q^13 - 5 * q^14 + 8 * q^15 + q^16 - 15 * q^17 + 25 * q^18 - q^19 - 6 * q^20 + 4 * q^21 + 5 * q^22 + 2 * q^23 + q^25 + 12 * q^28 - 14 * q^29 - 20 * q^30 - 8 * q^31 + 4 * q^33 + 50 * q^34 + 3 * q^35 - 39 * q^36 + 2 * q^37 - 5 * q^38 + 8 * q^39 - 5 * q^40 - 20 * q^41 - 10 * q^42 + 10 * q^43 + 12 * q^44 - 26 * q^45 - 5 * q^46 - 10 * q^47 + 6 * q^48 - 4 * q^49 + 20 * q^50 + 10 * q^51 + 24 * q^52 - 16 * q^53 - 40 * q^54 + 13 * q^55 - 10 * q^56 + 4 * q^57 + 30 * q^58 - 18 * q^59 - 6 * q^60 - 5 * q^61 + 40 * q^62 + 7 * q^63 + 13 * q^64 + 16 * q^65 + 30 * q^66 - 16 * q^67 - 45 * q^68 + 2 * q^69 + 10 * q^71 - 5 * q^72 + 2 * q^73 - 10 * q^74 - 14 * q^75 + 12 * q^76 + 4 * q^77 + 26 * q^79 - 3 * q^80 - 41 * q^81 - 10 * q^82 + 20 * q^83 + 12 * q^84 - 5 * q^85 - 25 * q^86 + 56 * q^87 - 5 * q^88 - 4 * q^89 + 20 * q^90 - 12 * q^91 + 6 * q^92 + 32 * q^93 - 35 * q^94 + 3 * q^95 - 30 * q^96 - 24 * q^97 + 30 * q^98 + 17 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/209\mathbb{Z}\right)^\times$.

$n$	$78$	$134$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.80902	−	1.31433i	−1.27917	−	0.929370i	−0.279641	−	0.960105i	$-0.590215\pi$
$2$	−1.80902	−	1.31433i	−1.27917	−	0.929370i	−0.999528	+	0.0307347i	$0.990215\pi$
$3$	−0.381966	+	1.17557i	−0.220528	+	0.678716i	0.778187	+	0.628033i	$0.216140\pi$
$3$	−0.381966	+	1.17557i	−0.220528	+	0.678716i	−0.998715	+	0.0506828i	$0.983860\pi$
$4$	0.927051	+	2.85317i	0.463525	+	1.42658i
$5$	−0.500000	+	0.363271i	−0.223607	+	0.162460i	−0.693949	−	0.720024i	$-0.744131\pi$
$5$	−0.500000	+	0.363271i	−0.223607	+	0.162460i	0.470342	+	0.882484i	$0.344131\pi$
$6$	2.23607	−	1.62460i	0.912871	−	0.663240i
$7$	−0.809017	−	2.48990i	−0.305780	−	0.941093i	−0.979385	−	0.202002i	$-0.935255\pi$
$7$	−0.809017	−	2.48990i	−0.305780	−	0.941093i	0.673605	−	0.739091i	$-0.264745\pi$
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$	1.19098	+	0.865300i	0.396994	+	0.288433i
$10$	1.38197			0.437016
$11$	−3.30902	+	0.224514i	−0.997706	+	0.0676935i
$11$	−3.30902	+	0.224514i	−0.997706	+	0.0676935i
$12$	−3.70820			−1.07047
$13$	−5.23607	−	3.80423i	−1.45222	−	1.05510i	−0.985305	−	0.170802i	$-0.945364\pi$
$13$	−5.23607	−	3.80423i	−1.45222	−	1.05510i	−0.466919	−	0.884300i	$-0.654636\pi$
$14$	−1.80902	+	5.56758i	−0.483480	+	1.48800i
$15$	−0.236068	−	0.726543i	−0.0609525	−	0.187592i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−6.54508	+	4.75528i	−1.58742	+	1.15333i	−0.679903	+	0.733302i	$0.737978\pi$
$17$	−6.54508	+	4.75528i	−1.58742	+	1.15333i	−0.907513	+	0.420023i	$0.862022\pi$
$18$	−1.01722	−	3.13068i	−0.239761	−	0.737909i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$19$	0.309017	−	0.951057i	0.0708934	−	0.218187i
$20$	−1.50000	−	1.08981i	−0.335410	−	0.243690i
$21$	3.23607			0.706168
$22$	6.28115	+	3.94298i	1.33915	+	0.840647i
$23$	1.61803			0.337383			0.168692	−	0.985669i	$-0.446046\pi$
$23$	1.61803			0.337383			0.168692	+	0.985669i	$0.446046\pi$
$24$	2.23607	+	1.62460i	0.456435	+	0.331620i
$25$	−1.42705	+	4.39201i	−0.285410	+	0.878402i
$26$	4.47214	+	13.7638i	0.877058	+	2.69931i
$27$	−4.47214	+	3.24920i	−0.860663	+	0.625308i
$28$	6.35410	−	4.61653i	1.20081	−	0.872441i
$29$	−0.145898	−	0.449028i	−0.0270926	−	0.0833824i	0.936596	−	0.350411i	$-0.113958\pi$
$29$	−0.145898	−	0.449028i	−0.0270926	−	0.0833824i	−0.963689	+	0.267029i	$0.913958\pi$
$30$	−0.527864	+	1.62460i	−0.0963743	+	0.296610i
$31$	−6.47214	−	4.70228i	−1.16243	−	0.844555i	−0.172347	−	0.985036i	$-0.555135\pi$
$31$	−6.47214	−	4.70228i	−1.16243	−	0.844555i	−0.990083	+	0.140482i	$0.955135\pi$
$32$	−6.70820			−1.18585
$33$	1.00000	−	3.97574i	0.174078	−	0.692087i
$34$	18.0902			3.10244
$35$	1.30902	+	0.951057i	0.221264	+	0.160758i
$36$	−1.36475	+	4.20025i	−0.227458	+	0.700042i
$37$	−0.618034	−	1.90211i	−0.101604	−	0.312705i	0.887314	−	0.461165i	$-0.152568\pi$
$37$	−0.618034	−	1.90211i	−0.101604	−	0.312705i	−0.988918	+	0.148460i	$0.952568\pi$
$38$	−1.80902	+	1.31433i	−0.293461	+	0.213212i
$39$	6.47214	−	4.70228i	1.03637	−	0.752968i
$40$	0.427051	+	1.31433i	0.0675227	+	0.207813i
$41$	−0.527864	+	1.62460i	−0.0824385	+	0.253720i	−0.983777	−	0.179396i	$-0.942586\pi$
$41$	−0.527864	+	1.62460i	−0.0824385	+	0.253720i	0.901338	+	0.433115i	$0.142586\pi$
$42$	−5.85410	−	4.25325i	−0.903308	−	0.656291i
$43$	8.09017			1.23374			0.616870	−	0.787065i	$-0.288401\pi$
$43$	8.09017			1.23374			0.616870	+	0.787065i	$0.288401\pi$
$44$	−3.70820	−	9.23305i	−0.559033	−	1.39193i
$45$	−0.909830			−0.135629
$46$	−2.92705	−	2.12663i	−0.431570	−	0.313554i
$47$	1.97214	−	6.06961i	0.287666	−	0.885344i	−0.697921	−	0.716174i	$-0.745892\pi$
$47$	1.97214	−	6.06961i	0.287666	−	0.885344i	0.985587	−	0.169169i	$-0.0541085\pi$
$48$	0.381966	+	1.17557i	0.0551320	+	0.169679i
$49$	0.118034	−	0.0857567i	0.0168620	−	0.0122510i
$50$	8.35410	−	6.06961i	1.18145	−	0.858373i
$51$	−3.09017	−	9.51057i	−0.432710	−	1.33175i
$52$	6.00000	−	18.4661i	0.832050	−	2.56079i
$53$	−8.47214	−	6.15537i	−1.16374	−	0.845505i	−0.173491	−	0.984835i	$-0.555505\pi$
$53$	−8.47214	−	6.15537i	−1.16374	−	0.845505i	−0.990246	+	0.139331i	$0.955505\pi$
$54$	12.3607			1.68208
$55$	1.57295	−	1.31433i	0.212096	−	0.177224i
$56$	−5.85410			−0.782287
$57$	1.00000	+	0.726543i	0.132453	+	0.0962329i
$58$	−0.326238	+	1.00406i	−0.0428371	+	0.131839i
$59$	1.09017	+	3.35520i	0.141928	+	0.436810i	0.996603	−	0.0823536i	$-0.0262437\pi$
$59$	1.09017	+	3.35520i	0.141928	+	0.436810i	−0.854675	+	0.519163i	$0.826244\pi$
$60$	1.85410	−	1.34708i	0.239364	−	0.173908i
$61$	−5.16312	+	3.75123i	−0.661070	+	0.480295i	−0.867024	−	0.498266i	$-0.833970\pi$
$61$	−5.16312	+	3.75123i	−0.661070	+	0.480295i	0.205954	+	0.978562i	$0.433970\pi$
$62$	5.52786	+	17.0130i	0.702039	+	2.16066i
$63$	1.19098	−	3.66547i	0.150050	−	0.461806i
$64$	10.5172	+	7.64121i	1.31465	+	0.955151i
$65$	4.00000			0.496139
$66$	−7.03444	+	5.87785i	−0.865880	+	0.723514i
$67$	0.472136			0.0576806			0.0288403	−	0.999584i	$-0.490819\pi$
$67$	0.472136			0.0576806			0.0288403	+	0.999584i	$0.490819\pi$
$68$	−19.6353	−	14.2658i	−2.38112	−	1.72999i
$69$	−0.618034	+	1.90211i	−0.0744025	+	0.228988i
$70$	−1.11803	−	3.44095i	−0.133631	−	0.411273i
$71$	1.38197	−	1.00406i	0.164009	−	0.119160i	−0.502753	−	0.864430i	$-0.667680\pi$
$71$	1.38197	−	1.00406i	0.164009	−	0.119160i	0.666762	+	0.745270i	$0.267680\pi$
$72$	2.66312	−	1.93487i	0.313852	−	0.228027i
$73$	3.85410	+	11.8617i	0.451089	+	1.38831i	0.875667	+	0.482916i	$0.160422\pi$
$73$	3.85410	+	11.8617i	0.451089	+	1.38831i	−0.424578	+	0.905391i	$0.639578\pi$
$74$	−1.38197	+	4.25325i	−0.160650	+	0.494431i
$75$	−4.61803	−	3.35520i	−0.533245	−	0.387425i
$76$	3.00000			0.344124
$77$	3.23607	+	8.05748i	0.368784	+	0.918235i
$78$	−17.8885			−2.02548
$79$	12.0902	+	8.78402i	1.36025	+	0.988280i	0.998429	+	0.0560323i	$0.0178450\pi$
$79$	12.0902	+	8.78402i	1.36025	+	0.988280i	0.361821	+	0.932247i	$0.382155\pi$
$80$	−0.190983	+	0.587785i	−0.0213525	+	0.0657164i
$81$	−0.746711	−	2.29814i	−0.0829679	−	0.255349i
$82$	3.09017	−	2.24514i	0.341252	−	0.247934i
$83$	8.35410	−	6.06961i	0.916982	−	0.666226i	−0.0257891	−	0.999667i	$-0.508210\pi$
$83$	8.35410	−	6.06961i	0.916982	−	0.666226i	0.942771	+	0.333441i	$0.108210\pi$
$84$	3.00000	+	9.23305i	0.327327	+	1.00741i
$85$	1.54508	−	4.75528i	0.167588	−	0.515783i
$86$	−14.6353	−	10.6331i	−1.57816	−	1.14660i
$87$	0.583592			0.0625676
$88$	−1.80902	+	7.19218i	−0.192842	+	0.766689i
$89$	1.23607			0.131023			0.0655115	−	0.997852i	$-0.479132\pi$
$89$	1.23607			0.131023			0.0655115	+	0.997852i	$0.479132\pi$
$90$	1.64590	+	1.19581i	0.173493	+	0.126050i
$91$	−5.23607	+	16.1150i	−0.548889	+	1.68931i
$92$	1.50000	+	4.61653i	0.156386	+	0.481306i
$93$	8.00000	−	5.81234i	0.829561	−	0.602712i
$94$	−11.5451	+	8.38800i	−1.19078	+	0.865156i
$95$	0.190983	+	0.587785i	0.0195944	+	0.0603055i
$96$	2.56231	−	7.88597i	0.261514	−	0.804858i
$97$	−8.23607	−	5.98385i	−0.836246	−	0.607568i	0.0850735	−	0.996375i	$-0.472887\pi$
$97$	−8.23607	−	5.98385i	−0.836246	−	0.607568i	−0.921319	+	0.388806i	$0.872887\pi$
$98$	−0.326238			−0.0329550
$99$	−4.13525	−	2.59590i	−0.415609	−	0.260898i
$100$	−13.8541			−1.38541
$101$	6.97214	+	5.06555i	0.693753	+	0.504041i	0.877892	−	0.478859i	$-0.158949\pi$
$101$	6.97214	+	5.06555i	0.693753	+	0.504041i	−0.184138	+	0.982900i	$0.558949\pi$
$102$	−6.90983	+	21.2663i	−0.684175	+	2.10567i
$103$	0.708204	+	2.17963i	0.0697814	+	0.214765i	0.979866	−	0.199658i	$-0.0639832\pi$
$103$	0.708204	+	2.17963i	0.0697814	+	0.214765i	−0.910084	+	0.414423i	$0.863983\pi$
$104$	−11.7082	+	8.50651i	−1.14808	+	0.834132i
$105$	−1.61803	+	1.17557i	−0.157904	+	0.114724i
$106$	7.23607	+	22.2703i	0.702829	+	2.16309i
$107$	−0.236068	+	0.726543i	−0.0228216	+	0.0702375i	−0.961819	−	0.273687i	$-0.911757\pi$
$107$	−0.236068	+	0.726543i	−0.0228216	+	0.0702375i	0.938997	+	0.343925i	$0.111757\pi$
$108$	−13.4164	−	9.74759i	−1.29099	−	0.937962i
$109$	−6.94427			−0.665141			−0.332570	−	0.943078i	$-0.607916\pi$
$109$	−6.94427			−0.665141			−0.332570	+	0.943078i	$0.607916\pi$
$110$	−4.57295	+	0.310271i	−0.436014	+	0.0295832i
$111$	2.47214			0.234645
$112$	−2.11803	−	1.53884i	−0.200135	−	0.145407i
$113$	−2.09017	+	6.43288i	−0.196627	+	0.605155i	0.803327	+	0.595538i	$0.203061\pi$
$113$	−2.09017	+	6.43288i	−0.196627	+	0.605155i	−0.999954	+	0.00961656i	$0.996939\pi$
$114$	−0.854102	−	2.62866i	−0.0799940	−	0.246196i
$115$	−0.809017	+	0.587785i	−0.0754412	+	0.0548113i
$116$	1.14590	−	0.832544i	0.106394	−	0.0772997i
$117$	−2.94427	−	9.06154i	−0.272198	−	0.837739i
$118$	2.43769	−	7.50245i	0.224408	−	0.690657i
$119$	17.1353	+	12.4495i	1.57079	+	1.14124i
$120$	−1.70820			−0.155937
$121$	10.8992	−	1.48584i	0.990835	−	0.135076i
$122$	14.2705			1.29199
$123$	−1.70820	−	1.24108i	−0.154024	−	0.111905i
$124$	7.41641	−	22.8254i	0.666013	−	2.04978i
$125$	−1.83688	−	5.65334i	−0.164296	−	0.505650i
$126$	−6.97214	+	5.06555i	−0.621127	+	0.451275i
$127$	−1.61803	+	1.17557i	−0.143577	+	0.104315i	−0.657255	−	0.753668i	$-0.728283\pi$
$127$	−1.61803	+	1.17557i	−0.143577	+	0.104315i	0.513678	+	0.857983i	$0.328283\pi$
$128$	−4.83688	−	14.8864i	−0.427524	−	1.31578i
$129$	−3.09017	+	9.51057i	−0.272074	+	0.837359i
$130$	−7.23607	−	5.25731i	−0.634645	−	0.461097i
$131$	−18.0344			−1.57568			−0.787838	−	0.615882i	$-0.788800\pi$
$131$	−18.0344			−1.57568			−0.787838	+	0.615882i	$0.788800\pi$
$132$	12.2705	−	0.832544i	1.06801	−	0.0724636i
$133$	−2.61803			−0.227012
$134$	−0.854102	−	0.620541i	−0.0737832	−	0.0536066i
$135$	1.05573	−	3.24920i	0.0908626	−	0.279646i
$136$	5.59017	+	17.2048i	0.479353	+	1.47530i
$137$	−1.50000	+	1.08981i	−0.128154	+	0.0931091i	−0.650016	−	0.759921i	$-0.725238\pi$
$137$	−1.50000	+	1.08981i	−0.128154	+	0.0931091i	0.521862	+	0.853030i	$0.325238\pi$
$138$	3.61803	−	2.62866i	0.307988	−	0.223766i
$139$	−6.20820	−	19.1069i	−0.526573	−	1.62063i	−0.761184	−	0.648536i	$-0.775382\pi$
$139$	−6.20820	−	19.1069i	−0.526573	−	1.62063i	0.234611	−	0.972089i	$-0.424618\pi$
$140$	−1.50000	+	4.61653i	−0.126773	+	0.390168i
$141$	6.38197	+	4.63677i	0.537458	+	0.390486i
$142$	−3.81966			−0.320539
$143$	18.1803	+	11.4127i	1.52032	+	0.954376i
$144$	1.47214			0.122678
$145$	0.236068	+	0.171513i	0.0196044	+	0.0142434i
$146$	8.61803	−	26.5236i	0.713234	−	2.19511i
$147$	0.0557281	+	0.171513i	0.00459638	+	0.0141462i
$148$	4.85410	−	3.52671i	0.399005	−	0.289894i
$149$	−14.0902	+	10.2371i	−1.15431	+	0.838657i	−0.989048	−	0.147593i	$-0.952847\pi$
$149$	−14.0902	+	10.2371i	−1.15431	+	0.838657i	−0.165264	+	0.986249i	$0.552847\pi$
$150$	3.94427	+	12.1392i	0.322048	+	0.991163i
$151$	0.854102	−	2.62866i	0.0695058	−	0.213917i	−0.910270	−	0.414015i	$-0.864126\pi$
$151$	0.854102	−	2.62866i	0.0695058	−	0.213917i	0.979776	+	0.200098i	$0.0641261\pi$
$152$	−1.80902	−	1.31433i	−0.146731	−	0.106606i
$153$	−11.9098			−0.962853
$154$	4.73607	−	18.8294i	0.381643	−	1.51731i
$155$	4.94427			0.397133
$156$	19.4164	+	14.1068i	1.55456	+	1.12945i
$157$	−1.71885	+	5.29007i	−0.137179	+	0.422193i	−0.995923	−	0.0902121i	$-0.971245\pi$
$157$	−1.71885	+	5.29007i	−0.137179	+	0.422193i	0.858744	+	0.512405i	$0.171245\pi$
$158$	−10.3262	−	31.7809i	−0.821511	−	2.52835i
$159$	10.4721	−	7.60845i	0.830494	−	0.603390i
$160$	3.35410	−	2.43690i	0.265165	−	0.192654i
$161$	−1.30902	−	4.02874i	−0.103165	−	0.317509i
$162$	−1.66970	+	5.13880i	−0.131184	+	0.403742i
$163$	−5.11803	−	3.71847i	−0.400875	−	0.291253i	0.369022	−	0.929421i	$-0.379693\pi$
$163$	−5.11803	−	3.71847i	−0.400875	−	0.291253i	−0.769897	+	0.638168i	$0.779693\pi$
$164$	−5.12461			−0.400165
$165$	0.944272	+	2.35114i	0.0735115	+	0.183036i
$166$	−23.0902			−1.79214
$167$	1.47214	+	1.06957i	0.113917	+	0.0827658i	0.643285	−	0.765627i	$-0.277571\pi$
$167$	1.47214	+	1.06957i	0.113917	+	0.0827658i	−0.529368	+	0.848392i	$0.677571\pi$
$168$	2.23607	−	6.88191i	0.172516	−	0.530951i
$169$	8.92705	+	27.4746i	0.686696	+	2.11343i
$170$	−9.04508	+	6.57164i	−0.693726	+	0.504022i
$171$	1.19098	−	0.865300i	0.0910767	−	0.0661711i
$172$	7.50000	+	23.0826i	0.571870	+	1.76003i
$173$	5.70820	−	17.5680i	0.433987	−	1.33567i	−0.460135	−	0.887849i	$-0.652199\pi$
$173$	5.70820	−	17.5680i	0.433987	−	1.33567i	0.894121	−	0.447825i	$-0.147801\pi$
$174$	−1.05573	−	0.767031i	−0.0800345	−	0.0581485i
$175$	12.0902			0.913931
$176$	−2.54508	+	2.12663i	−0.191843	+	0.160301i
$177$	−4.36068			−0.327769
$178$	−2.23607	−	1.62460i	−0.167600	−	0.121769i
$179$	5.00000	−	15.3884i	0.373718	−	1.15018i	−0.570622	−	0.821213i	$-0.693298\pi$
$179$	5.00000	−	15.3884i	0.373718	−	1.15018i	0.944340	−	0.328972i	$-0.106702\pi$
$180$	−0.843459	−	2.59590i	−0.0628677	−	0.193487i
$181$	−2.00000	+	1.45309i	−0.148659	+	0.108007i	−0.659629	−	0.751592i	$-0.729286\pi$
$181$	−2.00000	+	1.45309i	−0.148659	+	0.108007i	0.510970	+	0.859599i	$0.329286\pi$
$182$	30.6525	−	22.2703i	2.27211	−	1.65079i
$183$	−2.43769	−	7.50245i	−0.180200	−	0.554597i
$184$	1.11803	−	3.44095i	0.0824226	−	0.253671i
$185$	1.00000	+	0.726543i	0.0735215	+	0.0534165i
$186$	−22.1115			−1.62129
$187$	20.5902	−	17.2048i	1.50570	−	1.25814i
$188$	19.1459			1.39636
$189$	11.7082	+	8.50651i	0.851647	+	0.618757i
$190$	0.427051	−	1.31433i	0.0309815	−	0.0953514i
$191$	−4.04508	−	12.4495i	−0.292692	−	0.900814i	−0.983987	−	0.178241i	$-0.942959\pi$
$191$	−4.04508	−	12.4495i	−0.292692	−	0.900814i	0.691295	−	0.722573i	$-0.257041\pi$
$192$	−13.0000	+	9.44505i	−0.938194	+	0.681638i
$193$	−10.7082	+	7.77997i	−0.770793	+	0.560014i	−0.902202	−	0.431314i	$-0.858050\pi$
$193$	−10.7082	+	7.77997i	−0.770793	+	0.560014i	0.131408	+	0.991328i	$0.458050\pi$
$194$	7.03444	+	21.6498i	0.505043	+	1.55436i
$195$	−1.52786	+	4.70228i	−0.109413	+	0.336737i
$196$	0.354102	+	0.257270i	0.0252930	+	0.0183764i
$197$	−12.4721			−0.888603			−0.444301	−	0.895877i	$-0.646548\pi$
$197$	−12.4721			−0.888603			−0.444301	+	0.895877i	$0.646548\pi$
$198$	4.06888	+	10.1311i	0.289163	+	0.719986i
$199$	−23.5623			−1.67029			−0.835144	−	0.550032i	$-0.814616\pi$
$199$	−23.5623			−1.67029			−0.835144	+	0.550032i	$0.814616\pi$
$200$	8.35410	+	6.06961i	0.590724	+	0.429186i
$201$	−0.180340	+	0.555029i	−0.0127202	+	0.0391487i
$202$	−5.95492	−	18.3273i	−0.418986	−	1.28951i
$203$	−1.00000	+	0.726543i	−0.0701862	+	0.0509933i
$204$	24.2705	−	17.6336i	1.69928	−	1.23460i
$205$	−0.326238	−	1.00406i	−0.0227854	−	0.0701264i
$206$	1.58359	−	4.87380i	0.110334	−	0.339573i
$207$	1.92705	+	1.40008i	0.133939	+	0.0973126i
$208$	−6.47214			−0.448762
$209$	−0.809017	+	3.21644i	−0.0559609	+	0.222486i
$210$	4.47214			0.308607
$211$	7.47214	+	5.42882i	0.514403	+	0.373736i	0.814491	−	0.580176i	$-0.197016\pi$
$211$	7.47214	+	5.42882i	0.514403	+	0.373736i	−0.300088	+	0.953911i	$0.597016\pi$
$212$	9.70820	−	29.8788i	0.666762	−	2.05208i
$213$	0.652476	+	2.00811i	0.0447069	+	0.137594i
$214$	1.38197	−	1.00406i	0.0944693	−	0.0686359i
$215$	−4.04508	+	2.93893i	−0.275873	+	0.200433i
$216$	3.81966	+	11.7557i	0.259895	+	0.799874i
$217$	−6.47214	+	19.9192i	−0.439357	+	1.35220i
$218$	12.5623	+	9.12705i	0.850827	+	0.618162i
$219$	−15.4164			−1.04174
$220$	5.20820	+	3.26944i	0.351137	+	0.220426i
$221$	52.3607			3.52216
$222$	−4.47214	−	3.24920i	−0.300150	−	0.218072i
$223$	−2.76393	+	8.50651i	−0.185087	+	0.569638i	−0.999950	−	0.0100153i	$-0.996812\pi$
$223$	−2.76393	+	8.50651i	−0.185087	+	0.569638i	0.814863	+	0.579653i	$0.196812\pi$
$224$	5.42705	+	16.7027i	0.362610	+	1.11600i
$225$	−5.50000	+	3.99598i	−0.366667	+	0.266399i
$226$	12.2361	−	8.89002i	0.813931	−	0.591356i
$227$	−5.29180	−	16.2865i	−0.351229	−	1.08097i	−0.958164	−	0.286220i	$-0.907601\pi$
$227$	−5.29180	−	16.2865i	−0.351229	−	1.08097i	0.606935	−	0.794751i	$-0.292399\pi$
$228$	−1.14590	+	3.52671i	−0.0758890	+	0.233562i
$229$	−0.0729490	−	0.0530006i	−0.00482061	−	0.00350238i	0.585372	−	0.810765i	$-0.300948\pi$
$229$	−0.0729490	−	0.0530006i	−0.00482061	−	0.00350238i	−0.590193	+	0.807262i	$0.700948\pi$
$230$	2.23607			0.147442
$231$	−10.7082	+	0.726543i	−0.704548	+	0.0478030i
$232$	−1.05573			−0.0693119
$233$	2.73607	+	1.98787i	0.179246	+	0.130230i	0.673790	−	0.738923i	$-0.264665\pi$
$233$	2.73607	+	1.98787i	0.179246	+	0.130230i	−0.494545	+	0.869152i	$0.664665\pi$
$234$	−6.58359	+	20.2622i	−0.430383	+	1.32458i
$235$	1.21885	+	3.75123i	0.0795088	+	0.244703i
$236$	−8.56231	+	6.22088i	−0.557359	+	0.404945i
$237$	−14.9443	+	10.8576i	−0.970735	+	0.705280i
$238$	−14.6353	−	45.0427i	−0.948663	−	2.91968i
$239$	−6.68034	+	20.5600i	−0.432115	+	1.32991i	0.463899	+	0.885888i	$0.346450\pi$
$239$	−6.68034	+	20.5600i	−0.432115	+	1.32991i	−0.896014	+	0.444026i	$0.853550\pi$
$240$	−0.618034	−	0.449028i	−0.0398939	−	0.0289846i
$241$	15.5279			1.00024			0.500119	−	0.865957i	$-0.333290\pi$
$241$	15.5279			1.00024			0.500119	+	0.865957i	$0.333290\pi$
$242$	−21.6697	−	11.6372i	−1.39298	−	0.748067i
$243$	−13.5967			−0.872232
$244$	−15.4894	−	11.2537i	−0.991604	−	0.720443i
$245$	−0.0278640	+	0.0857567i	−0.00178017	+	0.00547880i
$246$	1.45898	+	4.49028i	0.0930212	+	0.286290i
$247$	−5.23607	+	3.80423i	−0.333163	+	0.242057i
$248$	−14.4721	+	10.5146i	−0.918982	+	0.667679i
$249$	3.94427	+	12.1392i	0.249958	+	0.769292i
$250$	−4.10739	+	12.6412i	−0.259774	+	0.799503i
$251$	−6.39919	−	4.64928i	−0.403913	−	0.293460i	0.367220	−	0.930134i	$-0.380310\pi$
$251$	−6.39919	−	4.64928i	−0.403913	−	0.293460i	−0.771133	+	0.636674i	$0.780310\pi$
$252$	11.5623			0.728357
$253$	−5.35410	+	0.363271i	−0.336610	+	0.0228387i
$254$	4.47214			0.280607
$255$	5.00000	+	3.63271i	0.313112	+	0.227489i
$256$	−2.78115	+	8.55951i	−0.173822	+	0.534969i
$257$	4.00000	+	12.3107i	0.249513	+	0.767922i	0.994861	+	0.101247i	$0.0322833\pi$
$257$	4.00000	+	12.3107i	0.249513	+	0.767922i	−0.745348	+	0.666675i	$0.767717\pi$
$258$	18.0902	−	13.1433i	1.12624	−	0.818265i
$259$	−4.23607	+	3.07768i	−0.263216	+	0.191238i
$260$	3.70820	+	11.4127i	0.229973	+	0.707784i
$261$	0.214782	−	0.661030i	0.0132947	−	0.0409167i
$262$	32.6246	+	23.7032i	2.01556	+	1.46439i
$263$		0			0			−	1.00000i	$-0.5\pi$
$263$		0			0				1.00000i	$0.5\pi$
$264$	−7.76393	−	4.87380i	−0.477837	−	0.299961i
$265$	6.47214			0.397580
$266$	4.73607	+	3.44095i	0.290387	+	0.210978i
$267$	−0.472136	+	1.45309i	−0.0288943	+	0.0889274i
$268$	0.437694	+	1.34708i	0.0267364	+	0.0822862i
$269$	−15.3262	+	11.1352i	−0.934457	+	0.678923i	−0.947080	−	0.320997i	$-0.895982\pi$
$269$	−15.3262	+	11.1352i	−0.934457	+	0.678923i	0.0126229	+	0.999920i	$0.495982\pi$
$270$	−6.18034	+	4.49028i	−0.376124	+	0.273270i
$271$	−4.02786	−	12.3965i	−0.244675	−	0.753033i	−0.995690	−	0.0927473i	$-0.970435\pi$
$271$	−4.02786	−	12.3965i	−0.244675	−	0.753033i	0.751014	−	0.660286i	$-0.229565\pi$
$272$	−2.50000	+	7.69421i	−0.151585	+	0.466530i
$273$	−16.9443	−	12.3107i	−1.02551	−	0.745080i
$274$	4.14590			0.250463
$275$	3.73607	−	14.8536i	0.225293	−	0.895708i
$276$	−6.00000			−0.361158
$277$	−4.85410	−	3.52671i	−0.291655	−	0.211900i	0.432330	−	0.901715i	$-0.357691\pi$
$277$	−4.85410	−	3.52671i	−0.291655	−	0.211900i	−0.723985	+	0.689816i	$0.757691\pi$
$278$	−13.8820	+	42.7243i	−0.832585	+	2.56243i
$279$	−3.63932	−	11.2007i	−0.217880	−	0.670567i
$280$	2.92705	−	2.12663i	0.174925	−	0.127090i
$281$	3.61803	−	2.62866i	0.215834	−	0.156812i	−0.474615	−	0.880193i	$-0.657413\pi$
$281$	3.61803	−	2.62866i	0.215834	−	0.156812i	0.690449	+	0.723381i	$0.257413\pi$
$282$	−5.45085	−	16.7760i	−0.324593	−	0.998996i
$283$	−5.37132	+	16.5312i	−0.319292	+	0.982680i	0.654660	+	0.755924i	$0.272812\pi$
$283$	−5.37132	+	16.5312i	−0.319292	+	0.982680i	−0.973952	+	0.226756i	$0.927188\pi$
$284$	4.14590	+	3.01217i	0.246014	+	0.178739i
$285$	−0.763932			−0.0452514
$286$	−17.8885	−	44.5407i	−1.05777	−	2.63374i
$287$	4.47214			0.263982
$288$	−7.98936	−	5.80461i	−0.470777	−	0.342040i
$289$	14.9721	−	46.0795i	0.880714	−	2.71056i
$290$	−0.201626	−	0.620541i	−0.0118399	−	0.0364394i
$291$	10.1803	−	7.39645i	0.596782	−	0.433588i
$292$	−30.2705	+	21.9928i	−1.77145	+	1.28703i
$293$	−2.32624	−	7.15942i	−0.135900	−	0.418258i	0.859829	−	0.510583i	$-0.170570\pi$
$293$	−2.32624	−	7.15942i	−0.135900	−	0.418258i	−0.995729	+	0.0923246i	$0.970570\pi$
$294$	0.124612	−	0.383516i	0.00726751	−	0.0223671i
$295$	−1.76393	−	1.28157i	−0.102700	−	0.0746160i
$296$	−4.47214			−0.259938
$297$	14.0689	−	11.7557i	0.816359	−	0.682135i
$298$	38.9443			2.25598
$299$	−8.47214	−	6.15537i	−0.489956	−	0.355974i
$300$	5.29180	−	16.2865i	0.305522	−	0.940300i
$301$	−6.54508	−	20.1437i	−0.377252	−	1.16106i
$302$	−5.00000	+	3.63271i	−0.287718	+	0.209039i
$303$	−8.61803	+	6.26137i	−0.495093	+	0.359706i
$304$	−0.309017	−	0.951057i	−0.0177233	−	0.0545468i
$305$	1.21885	−	3.75123i	0.0697910	−	0.214795i
$306$	21.5451	+	15.6534i	1.23165	+	0.894846i
$307$	9.88854			0.564369			0.282185	−	0.959360i	$-0.408941\pi$
$307$	9.88854			0.564369			0.282185	+	0.959360i	$0.408941\pi$
$308$	−19.9894	+	16.7027i	−1.13900	+	0.951727i
$309$	−2.83282			−0.161153
$310$	−8.94427	−	6.49839i	−0.508001	−	0.369084i
$311$	5.73607	−	17.6538i	0.325263	−	1.00106i	−0.646059	−	0.763287i	$-0.723584\pi$
$311$	5.73607	−	17.6538i	0.325263	−	1.00106i	0.971322	−	0.237768i	$-0.0764158\pi$
$312$	−5.52786	−	17.0130i	−0.312954	−	0.963172i
$313$	7.78115	−	5.65334i	0.439817	−	0.319546i	−0.345745	−	0.938328i	$-0.612374\pi$
$313$	7.78115	−	5.65334i	0.439817	−	0.319546i	0.785562	+	0.618783i	$0.212374\pi$
$314$	10.0623	−	7.31069i	0.567849	−	0.412566i
$315$	0.736068	+	2.26538i	0.0414727	+	0.127640i
$316$	−13.8541	+	42.6385i	−0.779354	+	2.39861i
$317$	15.8541	+	11.5187i	0.890455	+	0.646953i	0.935997	−	0.352009i	$-0.114501\pi$
$317$	15.8541	+	11.5187i	0.890455	+	0.646953i	−0.0455416	+	0.998962i	$0.514501\pi$
$318$	−28.9443			−1.62311
$319$	0.583592	+	1.45309i	0.0326749	+	0.0813571i
$320$	−8.03444			−0.449139
$321$	−0.763932	−	0.555029i	−0.0426385	−	0.0309787i
$322$	−2.92705	+	9.00854i	−0.163118	+	0.502026i
$323$	2.50000	+	7.69421i	0.139104	+	0.428117i
$324$	5.86475	−	4.26099i	0.325819	−	0.236721i
$325$	24.1803	−	17.5680i	1.34128	−	0.974500i
$326$	4.37132	+	13.4535i	0.242105	+	0.745123i
$327$	2.65248	−	8.16348i	0.146682	−	0.451442i
$328$	3.09017	+	2.24514i	0.170626	+	0.123967i
$329$	−16.7082			−0.921153
$330$	1.38197	−	5.49434i	0.0760747	−	0.302453i
$331$	−23.7082			−1.30312			−0.651560	−	0.758597i	$-0.725885\pi$
$331$	−23.7082			−1.30312			−0.651560	+	0.758597i	$0.725885\pi$
$332$	25.0623	+	18.2088i	1.37547	+	0.999339i
$333$	0.909830	−	2.80017i	0.0498584	−	0.153448i
$334$	−1.25735	−	3.86974i	−0.0687994	−	0.211743i
$335$	−0.236068	+	0.171513i	−0.0128978	+	0.00937078i
$336$	2.61803	−	1.90211i	0.142825	−	0.103769i
$337$	6.00000	+	18.4661i	0.326841	+	1.00591i	0.970603	+	0.240687i	$0.0773727\pi$
$337$	6.00000	+	18.4661i	0.326841	+	1.00591i	−0.643762	+	0.765226i	$0.722627\pi$
$338$	19.9615	−	61.4352i	1.08576	−	3.34163i
$339$	−6.76393	−	4.91428i	−0.367366	−	0.266907i
$340$	15.0000			0.813489
$341$	22.4721	+	14.1068i	1.21693	+	0.763929i
$342$	−3.29180			−0.178000
$343$	−15.1353	−	10.9964i	−0.817227	−	0.593750i
$344$	5.59017	−	17.2048i	0.301402	−	0.927619i
$345$	−0.381966	−	1.17557i	−0.0205644	−	0.0632906i
$346$	−33.4164	+	24.2784i	−1.79648	+	1.30522i
$347$	7.16312	−	5.20431i	0.384536	−	0.279382i	−0.378677	−	0.925529i	$-0.623621\pi$
$347$	7.16312	−	5.20431i	0.384536	−	0.279382i	0.763213	+	0.646147i	$0.223621\pi$
$348$	0.541020	+	1.66509i	0.0290017	+	0.0892580i
$349$	−0.663119	+	2.04087i	−0.0354959	+	0.109245i	−0.967235	−	0.253884i	$-0.918292\pi$
$349$	−0.663119	+	2.04087i	−0.0354959	+	0.109245i	0.931739	+	0.363130i	$0.118292\pi$
$350$	−21.8713	−	15.8904i	−1.16907	−	0.849380i
$351$	35.7771			1.90964
$352$	22.1976	−	1.50609i	1.18313	−	0.0802746i
$353$	0.909830			0.0484254			0.0242127	−	0.999707i	$-0.492292\pi$
$353$	0.909830			0.0484254			0.0242127	+	0.999707i	$0.492292\pi$
$354$	7.88854	+	5.73136i	0.419271	+	0.304618i
$355$	−0.326238	+	1.00406i	−0.0173149	+	0.0532898i
$356$	1.14590	+	3.52671i	0.0607325	+	0.186915i
$357$	−21.1803	+	15.3884i	−1.12098	+	0.814441i
$358$	−29.2705	+	21.2663i	−1.54699	+	1.12396i
$359$	0.680340	+	2.09387i	0.0359070	+	0.110510i	0.967404	−	0.253240i	$-0.0814962\pi$
$359$	0.680340	+	2.09387i	0.0359070	+	0.110510i	−0.931497	+	0.363750i	$0.881496\pi$
$360$	−0.628677	+	1.93487i	−0.0331342	+	0.101977i
$361$	−0.809017	−	0.587785i	−0.0425798	−	0.0309361i
$362$	5.52786			0.290538
$363$	−2.41641	+	13.3803i	−0.126829	+	0.702284i
$364$	−50.8328			−2.66436
$365$	−6.23607	−	4.53077i	−0.326411	−	0.237151i
$366$	−5.45085	+	16.7760i	−0.284920	+	0.876895i
$367$	5.66312	+	17.4293i	0.295612	+	0.909801i	0.983015	+	0.183525i	$0.0587508\pi$
$367$	5.66312	+	17.4293i	0.295612	+	0.909801i	−0.687403	+	0.726277i	$0.741249\pi$
$368$	1.30902	−	0.951057i	0.0682372	−	0.0495772i
$369$	−2.03444	+	1.47811i	−0.105909	+	0.0769473i
$370$	−0.854102	−	2.62866i	−0.0444026	−	0.136657i
$371$	−8.47214	+	26.0746i	−0.439851	+	1.35372i
$372$	24.0000	+	17.4370i	1.24434	+	0.904067i
$373$	−23.2361			−1.20312			−0.601559	−	0.798828i	$-0.705454\pi$
$373$	−23.2361			−1.20312			−0.601559	+	0.798828i	$0.705454\pi$
$374$	−59.8607	+	4.06150i	−3.09532	+	0.210015i
$375$	7.34752			0.379425
$376$	−11.5451	−	8.38800i	−0.595392	−	0.432578i
$377$	−0.944272	+	2.90617i	−0.0486325	+	0.149675i
$378$	−10.0000	−	30.7768i	−0.514344	−	1.58299i
$379$	8.61803	−	6.26137i	0.442679	−	0.321625i	−0.344020	−	0.938962i	$-0.611789\pi$
$379$	8.61803	−	6.26137i	0.442679	−	0.321625i	0.786698	+	0.617338i	$0.211789\pi$
$380$	−1.50000	+	1.08981i	−0.0769484	+	0.0559063i
$381$	−0.763932	−	2.35114i	−0.0391374	−	0.120453i
$382$	−9.04508	+	27.8379i	−0.462787	+	1.42431i
$383$	5.76393	+	4.18774i	0.294523	+	0.213984i	0.725227	−	0.688510i	$-0.241735\pi$
$383$	5.76393	+	4.18774i	0.294523	+	0.213984i	−0.430704	+	0.902493i	$0.641735\pi$
$384$	19.3475			0.987324
$385$	−4.54508	−	2.85317i	−0.231639	−	0.145411i
$386$	29.5967			1.50643
$387$	9.63525	+	7.00042i	0.489788	+	0.355851i
$388$	9.43769	−	29.0462i	0.479126	−	1.47460i
$389$	0.555728	+	1.71036i	0.0281765	+	0.0867185i	0.964156	−	0.265336i	$-0.0854830\pi$
$389$	0.555728	+	1.71036i	0.0281765	+	0.0867185i	−0.935979	+	0.352055i	$0.885483\pi$
$390$	8.94427	−	6.49839i	0.452911	−	0.329059i
$391$	−10.5902	+	7.69421i	−0.535568	+	0.389113i
$392$	−0.100813	−	0.310271i	−0.00509183	−	0.0156710i
$393$	6.88854	−	21.2008i	0.347481	−	1.06944i
$394$	22.5623	+	16.3925i	1.13667	+	0.825841i
$395$	−9.23607			−0.464717
$396$	3.57295	−	14.2051i	0.179547	−	0.713834i
$397$	6.56231			0.329353			0.164676	−	0.986348i	$-0.447342\pi$
$397$	6.56231			0.329353			0.164676	+	0.986348i	$0.447342\pi$
$398$	42.6246	+	30.9686i	2.13658	+	1.55232i
$399$	1.00000	−	3.07768i	0.0500626	−	0.154077i
$400$	1.42705	+	4.39201i	0.0713525	+	0.219601i
$401$	−9.47214	+	6.88191i	−0.473016	+	0.343666i	−0.798615	−	0.601842i	$-0.794434\pi$
$401$	−9.47214	+	6.88191i	−0.473016	+	0.343666i	0.325600	+	0.945508i	$0.394434\pi$
$402$	1.05573	−	0.767031i	0.0526549	−	0.0382560i
$403$	16.0000	+	49.2429i	0.797017	+	2.45297i
$404$	−7.98936	+	24.5887i	−0.397485	+	1.22333i
$405$	1.20820	+	0.877812i	0.0600361	+	0.0436188i
$406$	2.76393			0.137172
$407$	2.47214	+	6.15537i	0.122539	+	0.305110i
$408$	−22.3607			−1.10702
$409$	−13.8541	−	10.0656i	−0.685041	−	0.497712i	0.189985	−	0.981787i	$-0.439156\pi$
$409$	−13.8541	−	10.0656i	−0.685041	−	0.497712i	−0.875026	+	0.484075i	$0.839156\pi$
$410$	−0.729490	+	2.24514i	−0.0360270	+	0.110880i
$411$	−0.708204	−	2.17963i	−0.0349331	−	0.107513i
$412$	−5.56231	+	4.04125i	−0.274035	+	0.199098i
$413$	7.47214	−	5.42882i	0.367680	−	0.267135i
$414$	−1.64590	−	5.06555i	−0.0808915	−	0.248958i
$415$	−1.97214	+	6.06961i	−0.0968083	+	0.297945i
$416$	35.1246	+	25.5195i	1.72213	+	1.25120i
$417$	24.8328			1.21607
$418$	5.69098	−	4.75528i	0.278355	−	0.232588i
$419$	−7.14590			−0.349100			−0.174550	−	0.984648i	$-0.555847\pi$
$419$	−7.14590			−0.349100			−0.174550	+	0.984648i	$0.555847\pi$
$420$	−4.85410	−	3.52671i	−0.236856	−	0.172086i
$421$	4.09017	−	12.5882i	0.199343	−	0.613514i	−0.800556	−	0.599258i	$-0.795462\pi$
$421$	4.09017	−	12.5882i	0.199343	−	0.613514i	0.999898	−	0.0142554i	$-0.00453777\pi$
$422$	−6.38197	−	19.6417i	−0.310669	−	0.956142i
$423$	7.60081	−	5.52231i	0.369564	−	0.268504i
$424$	−18.9443	+	13.7638i	−0.920015	+	0.668430i
$425$	−11.5451	−	35.5321i	−0.560019	−	1.72356i
$426$	1.45898	−	4.49028i	0.0706878	−	0.217555i
$427$	13.5172	+	9.82084i	0.654144	+	0.475264i
$428$	−2.29180			−0.110778
$429$	−20.3607	+	17.0130i	−0.983023	+	0.821396i
$430$	11.1803			0.539164
$431$	13.7984	+	10.0251i	0.664644	+	0.482892i	0.868228	−	0.496165i	$-0.165259\pi$
$431$	13.7984	+	10.0251i	0.664644	+	0.482892i	−0.203584	+	0.979058i	$0.565259\pi$
$432$	−1.70820	+	5.25731i	−0.0821860	+	0.252942i
$433$	8.38197	+	25.7970i	0.402812	+	1.23973i	0.922709	+	0.385498i	$0.125970\pi$
$433$	8.38197	+	25.7970i	0.402812	+	1.23973i	−0.519897	+	0.854229i	$0.674030\pi$
$434$	37.8885	−	27.5276i	1.81871	−	1.32137i
$435$	−0.291796	+	0.212002i	−0.0139906	+	0.0101647i
$436$	−6.43769	−	19.8132i	−0.308310	−	0.948879i
$437$	0.500000	−	1.53884i	0.0239182	−	0.0736128i
$438$	27.8885	+	20.2622i	1.33257	+	0.968166i
$439$	−8.76393			−0.418280			−0.209140	−	0.977886i	$-0.567066\pi$
$439$	−8.76393			−0.418280			−0.209140	+	0.977886i	$0.567066\pi$
$440$	−1.70820	−	4.25325i	−0.0814354	−	0.202766i
$441$	0.214782			0.0102277
$442$	−94.7214	−	68.8191i	−4.50544	−	3.27339i
$443$	0.989357	−	3.04493i	0.0470058	−	0.144669i	−0.924799	−	0.380456i	$-0.875767\pi$
$443$	0.989357	−	3.04493i	0.0470058	−	0.144669i	0.971805	+	0.235787i	$0.0757669\pi$
$444$	2.29180	+	7.05342i	0.108764	+	0.334741i
$445$	−0.618034	+	0.449028i	−0.0292976	+	0.0212860i
$446$	16.1803	−	11.7557i	0.766161	−	0.556649i
$447$	−6.65248	−	20.4742i	−0.314651	−	0.968397i
$448$	10.5172	−	32.3687i	0.496892	−	1.52928i
$449$	−19.0344	−	13.8293i	−0.898291	−	0.652647i	0.0397356	−	0.999210i	$-0.487348\pi$
$449$	−19.0344	−	13.8293i	−0.898291	−	0.652647i	−0.938026	+	0.346564i	$0.887348\pi$
$450$	15.2016			0.716612
$451$	1.38197	−	5.49434i	0.0650742	−	0.258718i
$452$	−20.2918			−0.954446
$453$	2.76393	+	2.00811i	0.129861	+	0.0943494i
$454$	−11.8328	+	36.4177i	−0.555342	+	1.70917i
$455$	−3.23607	−	9.95959i	−0.151709	−	0.466913i
$456$	2.23607	−	1.62460i	0.104713	−	0.0760788i
$457$	25.3885	−	18.4459i	1.18763	−	0.862861i	0.194615	−	0.980880i	$-0.437654\pi$
$457$	25.3885	−	18.4459i	1.18763	−	0.862861i	0.993011	+	0.118019i	$0.0376544\pi$
$458$	0.0623059	+	0.191758i	0.00291136	+	0.00896026i
$459$	13.8197	−	42.5325i	0.645046	−	1.98525i
$460$	−2.42705	−	1.76336i	−0.113162	−	0.0822169i
$461$	−34.5066			−1.60713			−0.803566	−	0.595216i	$-0.797067\pi$
$461$	−34.5066			−1.60713			−0.803566	+	0.595216i	$0.797067\pi$
$462$	20.3262	+	12.7598i	0.945662	+	0.593638i
$463$	5.38197			0.250121			0.125061	−	0.992149i	$-0.460087\pi$
$463$	5.38197			0.250121			0.125061	+	0.992149i	$0.460087\pi$
$464$	−0.381966	−	0.277515i	−0.0177323	−	0.0128833i
$465$	−1.88854	+	5.81234i	−0.0875791	+	0.269541i
$466$	−2.33688	−	7.19218i	−0.108254	−	0.333171i
$467$	−8.06231	+	5.85761i	−0.373079	+	0.271058i	−0.758487	−	0.651689i	$-0.774061\pi$
$467$	−8.06231	+	5.85761i	−0.373079	+	0.271058i	0.385408	+	0.922746i	$0.374061\pi$
$468$	23.1246	−	16.8010i	1.06894	−	0.776627i
$469$	−0.381966	−	1.17557i	−0.0176376	−	0.0542828i
$470$	2.72542	−	8.38800i	0.125714	−	0.386909i
$471$	−5.56231	−	4.04125i	−0.256298	−	0.186211i
$472$	7.88854			0.363100
$473$	−26.7705	+	1.81636i	−1.23091	+	0.0835162i
$474$	41.3050			1.89720
$475$	3.73607	+	2.71441i	0.171423	+	0.124546i
$476$	−19.6353	+	60.4311i	−0.899980	+	2.76985i
$477$	−4.76393	−	14.6619i	−0.218125	−	0.671321i
$478$	39.1074	−	28.4132i	1.78873	−	1.29959i
$479$	−2.54508	+	1.84911i	−0.116288	+	0.0844881i	−0.644409	−	0.764681i	$-0.722897\pi$
$479$	−2.54508	+	1.84911i	−0.116288	+	0.0844881i	0.528121	+	0.849169i	$0.322897\pi$
$480$	1.58359	+	4.87380i	0.0722808	+	0.222457i
$481$	−4.00000	+	12.3107i	−0.182384	+	0.561321i
$482$	−28.0902	−	20.4087i	−1.27947	−	0.929591i
$483$	5.23607			0.238249
$484$	14.3435	+	29.7198i	0.651975	+	1.35090i
$485$	6.29180			0.285696
$486$	24.5967	+	17.8706i	1.11573	+	0.810626i
$487$	−7.20163	+	22.1643i	−0.326337	+	1.00436i	0.644497	+	0.764607i	$0.277067\pi$
$487$	−7.20163	+	22.1643i	−0.326337	+	1.00436i	−0.970834	+	0.239754i	$0.922933\pi$
$488$	4.40983	+	13.5721i	0.199624	+	0.614378i
$489$	6.32624	−	4.59628i	0.286082	−	0.207851i
$490$	0.163119	−	0.118513i	0.00736896	−	0.00535387i
$491$	−4.89919	−	15.0781i	−0.221097	−	0.680467i	−0.998664	−	0.0516673i	$-0.983546\pi$
$491$	−4.89919	−	15.0781i	−0.221097	−	0.680467i	0.777567	−	0.628800i	$-0.216454\pi$
$492$	1.95743	−	6.02434i	0.0882476	−	0.271598i
$493$	3.09017	+	2.24514i	0.139174	+	0.101116i
$494$	14.4721			0.651132
$495$	3.01064	−	0.204270i	0.135318	−	0.00918123i
$496$	−8.00000			−0.359211
$497$	−3.61803	−	2.62866i	−0.162291	−	0.117911i
$498$	8.81966	−	27.1441i	0.395218	−	1.21636i
$499$	−1.10081	−	3.38795i	−0.0492792	−	0.151666i	0.923389	−	0.383866i	$-0.125408\pi$
$499$	−1.10081	−	3.38795i	−0.0492792	−	0.151666i	−0.972668	+	0.232200i	$0.925408\pi$
$500$	14.4271	−	10.4819i	0.645197	−	0.468763i
$501$	−1.81966	+	1.32206i	−0.0812964	+	0.0590653i
$502$	5.46556	+	16.8213i	0.243940	+	0.750770i
$503$	8.65248	−	26.6296i	0.385795	−	1.18735i	−0.550107	−	0.835094i	$-0.685413\pi$
$503$	8.65248	−	26.6296i	0.385795	−	1.18735i	0.935902	−	0.352260i	$-0.114587\pi$
$504$	−6.97214	−	5.06555i	−0.310564	−	0.225638i
$505$	−5.32624			−0.237014
$506$	10.1631	+	6.37988i	0.451806	+	0.283620i
$507$	−35.7082			−1.58586
$508$	−4.85410	−	3.52671i	−0.215366	−	0.156473i
$509$	−2.29180	+	7.05342i	−0.101582	+	0.312637i	−0.988913	−	0.148496i	$-0.952557\pi$
$509$	−2.29180	+	7.05342i	−0.101582	+	0.312637i	0.887331	+	0.461133i	$0.152557\pi$
$510$	−4.27051	−	13.1433i	−0.189101	−	0.581994i
$511$	26.4164	−	19.1926i	1.16859	−	0.849033i
$512$	−9.04508	+	6.57164i	−0.399740	+	0.290428i
$513$	1.70820	+	5.25731i	0.0754190	+	0.232116i
$514$	8.94427	−	27.5276i	0.394515	−	1.21419i
$515$	−1.14590	−	0.832544i	−0.0504943	−	0.0366863i
$516$	−30.0000			−1.32068
$517$	−5.16312	+	20.5272i	−0.227074	+	0.902786i
$518$	11.7082			0.514429
$519$	18.4721	+	13.4208i	0.810837	+	0.589107i
$520$	2.76393	−	8.50651i	0.121206	−	0.373035i
$521$	−7.38197	−	22.7194i	−0.323410	−	0.995353i	−0.972153	−	0.234346i	$-0.924705\pi$
$521$	−7.38197	−	22.7194i	−0.323410	−	0.995353i	0.648743	−	0.761007i	$-0.275295\pi$
$522$	−1.25735	+	0.913521i	−0.0550329	+	0.0399837i
$523$	−26.6525	+	19.3642i	−1.16543	+	0.846735i	−0.990455	−	0.137837i	$-0.955985\pi$
$523$	−26.6525	+	19.3642i	−1.16543	+	0.846735i	−0.174976	+	0.984573i	$0.555985\pi$
$524$	−16.7188	−	51.4553i	−0.730366	−	2.24784i
$525$	−4.61803	+	14.2128i	−0.201548	+	0.620300i
$526$		0			0
$527$	64.7214			2.81931
$528$	−1.52786	−	3.80423i	−0.0664917	−	0.165558i
$529$	−20.3820			−0.886172
$530$	−11.7082	−	8.50651i	−0.508572	−	0.369499i
$531$	−1.60488	+	4.93931i	−0.0696458	+	0.214348i
$532$	−2.42705	−	7.46969i	−0.105226	−	0.323852i
$533$	8.94427	−	6.49839i	0.387419	−	0.281477i
$534$	2.76393	−	2.00811i	0.119607	−	0.0868996i
$535$	−0.145898	−	0.449028i	−0.00630772	−	0.0194132i
$536$	0.326238	−	1.00406i	0.0140913	−	0.0433687i
$537$	16.1803	+	11.7557i	0.698233	+	0.507296i
$538$	42.3607			1.82630
$539$	−0.371323	+	0.310271i	−0.0159940	+	0.0133643i
$540$	10.2492			0.441056
$541$	18.2533	+	13.2618i	0.784770	+	0.570169i	0.906407	−	0.422406i	$-0.138814\pi$
$541$	18.2533	+	13.2618i	0.784770	+	0.570169i	−0.121637	+	0.992575i	$0.538814\pi$
$542$	−9.00658	+	27.7194i	−0.386866	+	1.19065i
$543$	−0.944272	−	2.90617i	−0.0405226	−	0.124716i
$544$	43.9058	−	31.8994i	1.88244	−	1.36768i
$545$	3.47214	−	2.52265i	0.148730	−	0.108059i
$546$	14.4721	+	44.5407i	0.619350	+	1.90616i
$547$	−10.9443	+	33.6830i	−0.467943	+	1.44018i	0.387300	+	0.921954i	$0.373408\pi$
$547$	−10.9443	+	33.6830i	−0.467943	+	1.44018i	−0.855243	+	0.518227i	$0.826592\pi$
$548$	−4.50000	−	3.26944i	−0.192230	−	0.139664i
$549$	−9.39512			−0.400974
$550$	−26.2812	+	21.9601i	−1.12063	+	0.936380i
$551$	−0.472136			−0.0201137
$552$	3.61803	+	2.62866i	0.153994	+	0.111883i
$553$	12.0902	−	37.2097i	0.514126	−	1.58232i
$554$	4.14590	+	12.7598i	0.176142	+	0.542110i
$555$	−1.23607	+	0.898056i	−0.0524682	+	0.0381204i
$556$	48.7599	−	35.4261i	2.06788	−	1.50240i
$557$	−6.07953	−	18.7109i	−0.257598	−	0.792805i	−0.993307	−	0.115507i	$-0.963151\pi$
$557$	−6.07953	−	18.7109i	−0.257598	−	0.792805i	0.735709	−	0.677298i	$-0.236849\pi$
$558$	−8.13777	+	25.0455i	−0.344499	+	1.06026i
$559$	−42.3607	−	30.7768i	−1.79167	−	1.30172i
$560$	1.61803			0.0683744
$561$	12.3607	+	30.7768i	0.521868	+	1.29940i
$562$	−10.0000			−0.421825
$563$	−24.4164	−	17.7396i	−1.02903	−	0.747633i	−0.0609148	−	0.998143i	$-0.519402\pi$
$563$	−24.4164	−	17.7396i	−1.02903	−	0.747633i	−0.968114	+	0.250510i	$0.919402\pi$
$564$	−7.31308	+	22.5074i	−0.307936	+	0.947731i
$565$	−1.29180	−	3.97574i	−0.0543463	−	0.167261i
$566$	31.4443	−	22.8456i	1.32170	−	0.960272i
$567$	−5.11803	+	3.71847i	−0.214937	+	0.156161i
$568$	−1.18034	−	3.63271i	−0.0495260	−	0.152425i
$569$	−9.97871	+	30.7113i	−0.418329	+	1.28749i	0.490909	+	0.871211i	$0.336665\pi$
$569$	−9.97871	+	30.7113i	−0.418329	+	1.28749i	−0.909239	+	0.416275i	$0.863335\pi$
$570$	1.38197	+	1.00406i	0.0578842	+	0.0420553i
$571$	−5.67376			−0.237440			−0.118720	−	0.992928i	$-0.537879\pi$
$571$	−5.67376			−0.237440			−0.118720	+	0.992928i	$0.537879\pi$
$572$	−15.7082	+	62.4517i	−0.656793	+	2.61124i
$573$	16.1803			0.675943
$574$	−8.09017	−	5.87785i	−0.337677	−	0.245337i
$575$	−2.30902	+	7.10642i	−0.0962927	+	0.296358i
$576$	5.91390	+	18.2011i	0.246412	+	0.758379i
$577$	27.7984	−	20.1967i	1.15726	−	0.840800i	0.167832	−	0.985816i	$-0.446323\pi$
$577$	27.7984	−	20.1967i	1.15726	−	0.840800i	0.989429	+	0.145016i	$0.0463233\pi$
$578$	−87.6484	+	63.6803i	−3.64569	+	2.64875i
$579$	−5.05573	−	15.5599i	−0.210109	−	0.646649i
$580$	−0.270510	+	0.832544i	−0.0112323	+	0.0345695i
$581$	−21.8713	−	15.8904i	−0.907375	−	0.659247i
$582$	−28.1378			−1.16635
$583$	29.4164	+	18.4661i	1.21830	+	0.764788i
$584$	27.8885			1.15404
$585$	4.76393	+	3.46120i	0.196964	+	0.143103i
$586$	−5.20163	+	16.0090i	−0.214877	+	0.661324i
$587$	−6.00000	−	18.4661i	−0.247647	−	0.762178i	−0.995190	−	0.0979646i	$-0.968767\pi$
$587$	−6.00000	−	18.4661i	−0.247647	−	0.762178i	0.747543	−	0.664213i	$-0.231233\pi$
$588$	−0.437694	+	0.318003i	−0.0180502	+	0.0131142i
$589$	−6.47214	+	4.70228i	−0.266680	+	0.193754i
$590$	1.50658	+	4.63677i	0.0620248	+	0.190893i
$591$	4.76393	−	14.6619i	0.195962	−	0.603109i
$592$	−1.61803	−	1.17557i	−0.0665008	−	0.0483157i
$593$	24.2705			0.996670			0.498335	−	0.866984i	$-0.333945\pi$
$593$	24.2705			0.996670			0.498335	+	0.866984i	$0.333945\pi$
$594$	−40.9017	+	2.77515i	−1.67822	+	0.113866i
$595$	−13.0902			−0.536645
$596$	−42.2705	−	30.7113i	−1.73147	−	1.25798i
$597$	9.00000	−	27.6992i	0.368345	−	1.13365i
$598$	7.23607	+	22.2703i	0.295905	+	0.910701i
$599$	−6.76393	+	4.91428i	−0.276367	+	0.200792i	−0.717331	−	0.696732i	$-0.754637\pi$
$599$	−6.76393	+	4.91428i	−0.276367	+	0.200792i	0.440964	+	0.897525i	$0.354637\pi$
$600$	−10.3262	+	7.50245i	−0.421567	+	0.306286i
$601$	−12.0344	−	37.0382i	−0.490895	−	1.51082i	−0.823258	−	0.567668i	$-0.807846\pi$
$601$	−12.0344	−	37.0382i	−0.490895	−	1.51082i	0.332362	−	0.943152i	$-0.392154\pi$
$602$	−14.6353	+	45.0427i	−0.596488	+	1.83580i
$603$	0.562306	+	0.408539i	0.0228989	+	0.0166370i
$604$	8.29180			0.337388
$605$	−4.90983	+	4.70228i	−0.199613	+	0.191175i
$606$	23.8197			0.967608
$607$	2.14590	+	1.55909i	0.0870993	+	0.0632814i	0.630483	−	0.776203i	$-0.282857\pi$
$607$	2.14590	+	1.55909i	0.0870993	+	0.0632814i	−0.543383	+	0.839485i	$0.682857\pi$
$608$	−2.07295	+	6.37988i	−0.0840692	+	0.258738i
$609$	−0.472136	−	1.45309i	−0.0191319	−	0.0588820i
$610$	−7.13525	+	5.18407i	−0.288898	+	0.209897i
$611$	−33.4164	+	24.2784i	−1.35188	+	0.982201i
$612$	−11.0410	−	33.9808i	−0.446307	−	1.37359i
$613$	11.7361	−	36.1199i	0.474015	−	1.45887i	−0.373266	−	0.927724i	$-0.621762\pi$
$613$	11.7361	−	36.1199i	0.474015	−	1.45887i	0.847281	−	0.531145i	$-0.178238\pi$
$614$	−17.8885	−	12.9968i	−0.721923	−	0.524508i
$615$	1.30495			0.0526207
$616$	19.3713	−	1.31433i	0.780493	−	0.0529558i
$617$	−33.4164			−1.34529			−0.672647	−	0.739964i	$-0.734843\pi$
$617$	−33.4164			−1.34529			−0.672647	+	0.739964i	$0.734843\pi$
$618$	5.12461	+	3.72325i	0.206142	+	0.149771i
$619$	−1.68034	+	5.17155i	−0.0675386	+	0.207862i	−0.979130	−	0.203235i	$-0.934854\pi$
$619$	−1.68034	+	5.17155i	−0.0675386	+	0.207862i	0.911591	+	0.411097i	$0.134854\pi$
$620$	4.58359	+	14.1068i	0.184081	+	0.566545i
$621$	−7.23607	+	5.25731i	−0.290373	+	0.210969i
$622$	−33.5795	+	24.3970i	−1.34642	+	0.978229i
$623$	−1.00000	−	3.07768i	−0.0400642	−	0.123305i
$624$	2.47214	−	7.60845i	0.0989646	−	0.304582i
$625$	−15.7082	−	11.4127i	−0.628328	−	0.456507i
$626$	−21.5066			−0.859576
$627$	−3.47214	−	2.17963i	−0.138664	−	0.0870459i
$628$	−16.6869			−0.665881
$629$	13.0902	+	9.51057i	0.521939	+	0.379211i
$630$	1.64590	−	5.06555i	0.0655741	−	0.201816i
$631$	7.81966	+	24.0664i	0.311296	+	0.958070i	0.977252	+	0.212079i	$0.0680235\pi$
$631$	7.81966	+	24.0664i	0.311296	+	0.958070i	−0.665957	+	0.745990i	$0.731976\pi$
$632$	27.0344	−	19.6417i	1.07537	−	0.781304i
$633$	−9.23607	+	6.71040i	−0.367101	+	0.266714i
$634$	−13.5410	−	41.6750i	−0.537783	−	1.65512i
$635$	0.381966	−	1.17557i	0.0151579	−	0.0466511i
$636$	31.4164	+	22.8254i	1.24574	+	0.905084i
$637$	−0.944272			−0.0374134
$638$	0.854102	−	3.39569i	0.0338142	−	0.134437i
$639$	2.51471			0.0994803
$640$	7.82624	+	5.68609i	0.309359	+	0.224763i
$641$	−0.652476	+	2.00811i	−0.0257712	+	0.0793157i	−0.963115	−	0.269090i	$-0.913277\pi$
$641$	−0.652476	+	2.00811i	−0.0257712	+	0.0793157i	0.937344	+	0.348406i	$0.113277\pi$
$642$	0.652476	+	2.00811i	0.0257512	+	0.0792539i
$643$	−36.4336	+	26.4706i	−1.43680	+	1.04390i	−0.448103	+	0.893982i	$0.647900\pi$
$643$	−36.4336	+	26.4706i	−1.43680	+	1.04390i	−0.988699	+	0.149916i	$0.952100\pi$
$644$	10.2812	−	7.46969i	0.405134	−	0.294347i
$645$	−1.90983	−	5.87785i	−0.0751995	−	0.231440i
$646$	5.59017	−	17.2048i	0.219942	−	0.676913i
$647$	17.7082	+	12.8658i	0.696181	+	0.505805i	0.878686	−	0.477400i	$-0.158421\pi$
$647$	17.7082	+	12.8658i	0.696181	+	0.505805i	−0.182505	+	0.983205i	$0.558421\pi$
$648$	−5.40325			−0.212260
$649$	−4.36068	−	10.8576i	−0.171172	−	0.426200i
$650$	−66.8328			−2.62140
$651$	−20.9443	−	15.2169i	−0.820871	−	0.596397i
$652$	5.86475	−	18.0498i	0.229681	−	0.706886i
$653$	4.50000	+	13.8496i	0.176099	+	0.541976i	0.999682	−	0.0252195i	$-0.00802847\pi$
$653$	4.50000	+	13.8496i	0.176099	+	0.541976i	−0.823583	+	0.567195i	$0.808028\pi$
$654$	−15.5279	+	11.2817i	−0.607188	+	0.441148i
$655$	9.01722	−	6.55139i	0.352332	−	0.255984i
$656$	0.527864	+	1.62460i	0.0206096	+	0.0634299i
$657$	−5.67376	+	17.4620i	−0.221355	+	0.681259i
$658$	30.2254	+	21.9601i	1.17831	+	0.856092i
$659$	−6.29180			−0.245094			−0.122547	−	0.992463i	$-0.539106\pi$
$659$	−6.29180			−0.245094			−0.122547	+	0.992463i	$0.539106\pi$
$660$	−5.83282	+	4.87380i	−0.227042	+	0.189712i
$661$	7.12461			0.277115			0.138558	−	0.990354i	$-0.455753\pi$
$661$	7.12461			0.277115			0.138558	+	0.990354i	$0.455753\pi$
$662$	42.8885	+	31.1604i	1.66691	+	1.21108i
$663$	−20.0000	+	61.5537i	−0.776736	+	2.39055i
$664$	−7.13525	−	21.9601i	−0.276902	−	0.852215i
$665$	1.30902	−	0.951057i	0.0507615	−	0.0368804i
$666$	−5.32624	+	3.86974i	−0.206388	+	0.149949i
$667$	−0.236068	−	0.726543i	−0.00914059	−	0.0281318i
$668$	−1.68692	+	5.19180i	−0.0652688	+	0.200877i
$669$	−8.94427	−	6.49839i	−0.345806	−	0.251242i
$670$	0.652476			0.0252073
$671$	16.2426	−	13.5721i	0.627040	−	0.523944i
$672$	−21.7082			−0.837412
$673$	22.4164	+	16.2865i	0.864089	+	0.627797i	0.928994	−	0.370094i	$-0.120675\pi$
$673$	22.4164	+	16.2865i	0.864089	+	0.627797i	−0.0649053	+	0.997891i	$0.520675\pi$
$674$	13.4164	−	41.2915i	0.516781	−	1.59049i
$675$	−7.88854	−	24.2784i	−0.303630	−	0.934478i
$676$	−70.1140	+	50.9408i	−2.69669	+	1.95926i
$677$	0.472136	−	0.343027i	0.0181457	−	0.0131836i	−0.578675	−	0.815558i	$-0.696430\pi$
$677$	0.472136	−	0.343027i	0.0181457	−	0.0131836i	0.596821	+	0.802374i	$0.296430\pi$
$678$	5.77709	+	17.7800i	0.221868	+	0.682839i
$679$	−8.23607	+	25.3480i	−0.316071	+	0.972767i
$680$	−9.04508	−	6.57164i	−0.346863	−	0.252011i
$681$	21.1672			0.811128
$682$	−22.1115	−	55.0553i	−0.846691	−	2.10818i
$683$	38.8328			1.48590			0.742948	−	0.669349i	$-0.233427\pi$
$683$	38.8328			1.48590			0.742948	+	0.669349i	$0.233427\pi$
$684$	3.57295	+	2.59590i	0.136615	+	0.0992567i
$685$	0.354102	−	1.08981i	0.0135295	−	0.0416396i
$686$	12.9271	+	39.7854i	0.493557	+	1.51901i
$687$	0.0901699	−	0.0655123i	0.00344020	−	0.00249945i
$688$	6.54508	−	4.75528i	0.249529	−	0.181293i
$689$	20.9443	+	64.4598i	0.797913	+	2.45572i
$690$	−0.854102	+	2.62866i	−0.0325151	+	0.100071i
$691$	8.11803	+	5.89810i	0.308825	+	0.224374i	0.731392	−	0.681957i	$-0.238871\pi$
$691$	8.11803	+	5.89810i	0.308825	+	0.224374i	−0.422567	+	0.906332i	$0.638871\pi$
$692$	55.4164			2.10662
$693$	−3.11803	+	12.3965i	−0.118444	+	0.470904i
$694$	−19.7984			−0.751536
$695$	10.0451	+	7.29818i	0.381032	+	0.276836i
$696$	0.403252	−	1.24108i	0.0152852	−	0.0470431i
$697$	−4.27051	−	13.1433i	−0.161757	−	0.497837i
$698$	3.88197	−	2.82041i	0.146935	−	0.106754i
$699$	−3.38197	+	2.45714i	−0.127918	+	0.0929377i
$700$	11.2082	+	34.4953i	0.423630	+	1.30380i
$701$	15.9164	−	48.9857i	0.601154	−	1.85016i	0.0798225	−	0.996809i	$-0.474565\pi$
$701$	15.9164	−	48.9857i	0.601154	−	1.85016i	0.521332	−	0.853354i	$-0.325435\pi$
$702$	−64.7214	−	47.0228i	−2.44275	−	1.77476i
$703$	−2.00000			−0.0754314
$704$	−36.5172	−	22.9236i	−1.37629	−	0.863967i
$705$	−4.87539			−0.183618
$706$	−1.64590	−	1.19581i	−0.0619442	−	0.0450051i
$707$	6.97214	−	21.4580i	0.262214	−	0.807012i
$708$	−4.04257	−	12.4418i	−0.151929	−	0.467590i
$709$	2.50000	−	1.81636i	0.0938895	−	0.0682147i	−0.539850	−	0.841761i	$-0.681519\pi$
$709$	2.50000	−	1.81636i	0.0938895	−	0.0682147i	0.633740	+	0.773546i	$0.281519\pi$
$710$	1.90983	−	1.38757i	0.0716746	−	0.0520747i
$711$	6.79837	+	20.9232i	0.254959	+	0.784683i
$712$	0.854102	−	2.62866i	0.0320088	−	0.0985130i
$713$	−10.4721	−	7.60845i	−0.392185	−	0.284939i
$714$	58.5410			2.19084
$715$	−13.2361	+	0.898056i	−0.495001	+	0.0335854i
$716$	48.5410			1.81406
$717$	−21.6180	−	15.7064i	−0.807340	−	0.586567i
$718$	1.52129	−	4.68204i	0.0567739	−	0.174732i
$719$	8.33688	+	25.6583i	0.310913	+	0.956892i	0.977404	+	0.211379i	$0.0677955\pi$
$719$	8.33688	+	25.6583i	0.310913	+	0.956892i	−0.666491	+	0.745513i	$0.732204\pi$
$720$	−0.736068	+	0.534785i	−0.0274316	+	0.0199302i
$721$	4.85410	−	3.52671i	0.180776	−	0.131342i
$722$	0.690983	+	2.12663i	0.0257157	+	0.0791449i
$723$	−5.93112	+	18.2541i	−0.220581	+	0.678877i
$724$	−6.00000	−	4.35926i	−0.222988	−	0.162010i
$725$	2.18034			0.0809758
$726$	21.9574	−	21.0292i	0.814917	−	0.780468i
$727$	−20.8541			−0.773436			−0.386718	−	0.922198i	$-0.626391\pi$
$727$	−20.8541			−0.773436			−0.386718	+	0.922198i	$0.626391\pi$
$728$	30.6525	+	22.2703i	1.13606	+	0.825393i
$729$	7.43363	−	22.8784i	0.275320	−	0.847347i
$730$	5.32624	+	16.3925i	0.197133	+	0.606713i
$731$	−52.9508	+	38.4710i	−1.95846	+	1.42290i
$732$	19.1459	−	13.9103i	0.707653	−	0.514140i
$733$	13.0238	+	40.0831i	0.481045	+	1.48050i	0.837628	+	0.546241i	$0.183942\pi$
$733$	13.0238	+	40.0831i	0.481045	+	1.48050i	−0.356583	+	0.934264i	$0.616058\pi$
$734$	12.6631	−	38.9731i	0.467404	−	1.43852i
$735$	−0.0901699	−	0.0655123i	−0.00332597	−	0.00241646i
$736$	−10.8541			−0.400088
$737$	−1.56231	+	0.106001i	−0.0575483	+	0.00390460i
$738$	5.62306			0.206988
$739$	28.5344	+	20.7315i	1.04966	+	0.762620i	0.972147	−	0.234372i	$-0.0753032\pi$
$739$	28.5344	+	20.7315i	1.04966	+	0.762620i	0.0775093	+	0.996992i	$0.475303\pi$
$740$	−1.14590	+	3.52671i	−0.0421240	+	0.129644i
$741$	−2.47214	−	7.60845i	−0.0908162	−	0.279503i
$742$	49.5967	−	36.0341i	1.82075	−	1.32286i
$743$	22.5623	−	16.3925i	0.827731	−	0.601382i	−0.0911857	−	0.995834i	$-0.529066\pi$
$743$	22.5623	−	16.3925i	0.827731	−	0.601382i	0.918916	+	0.394452i	$0.129066\pi$
$744$	−6.83282	−	21.0292i	−0.250503	−	0.770970i
$745$	3.32624	−	10.2371i	0.121864	−	0.375059i
$746$	42.0344	+	30.5398i	1.53899	+	1.11814i
$747$	15.2016			0.556198
$748$	68.1763	+	42.7975i	2.49277	+	1.56483i
$749$	2.00000			0.0730784
$750$	−13.2918	−	9.65706i	−0.485348	−	0.352626i
$751$	3.47214	−	10.6861i	0.126700	−	0.389943i	−0.867507	−	0.497425i	$-0.834279\pi$
$751$	3.47214	−	10.6861i	0.126700	−	0.389943i	0.994207	+	0.107482i	$0.0342789\pi$
$752$	−1.97214	−	6.06961i	−0.0719164	−	0.221336i
$753$	7.90983	−	5.74683i	0.288250	−	0.209426i
$754$	5.52786	−	4.01623i	0.201313	−	0.146262i
$755$	0.527864	+	1.62460i	0.0192109	+	0.0591252i
$756$	−13.4164	+	41.2915i	−0.487950	+	1.50176i
$757$	−5.14590	−	3.73871i	−0.187031	−	0.135886i	0.490330	−	0.871537i	$-0.336876\pi$
$757$	−5.14590	−	3.73871i	−0.187031	−	0.135886i	−0.677361	+	0.735651i	$0.736876\pi$
$758$	−23.8197			−0.865169
$759$	1.61803	−	6.43288i	0.0587309	−	0.233499i
$760$	1.38197			0.0501292
$761$	−41.5066	−	30.1563i	−1.50461	−	1.09316i	−0.968499	−	0.249019i	$-0.919892\pi$
$761$	−41.5066	−	30.1563i	−1.50461	−	1.09316i	−0.536114	−	0.844146i	$-0.680108\pi$
$762$	−1.70820	+	5.25731i	−0.0618817	+	0.190452i
$763$	5.61803	+	17.2905i	0.203386	+	0.625959i
$764$	31.7705	−	23.0826i	1.14942	−	0.835100i
$765$	5.95492	−	4.32650i	0.215300	−	0.156425i
$766$	−4.92299	−	15.1514i	−0.177875	−	0.547442i
$767$	7.05573	−	21.7153i	0.254768	−	0.784094i
$768$	−9.00000	−	6.53888i	−0.324760	−	0.235952i
$769$	−11.7426			−0.423451			−0.211725	−	0.977329i	$-0.567908\pi$
$769$	−11.7426			−0.423451			−0.211725	+	0.977329i	$0.567908\pi$
$770$	4.47214	+	11.1352i	0.161165	+	0.401283i
$771$	−16.0000			−0.576226
$772$	−32.1246	−	23.3399i	−1.15619	−	0.840021i
$773$	−15.0689	+	46.3773i	−0.541990	+	1.66807i	0.186051	+	0.982540i	$0.440431\pi$
$773$	−15.0689	+	46.3773i	−0.541990	+	1.66807i	−0.728041	+	0.685534i	$0.759569\pi$
$774$	−8.22949	−	25.3278i	−0.295803	−	0.910388i
$775$	29.8885	−	21.7153i	1.07363	−	0.780037i
$776$	−18.4164	+	13.3803i	−0.661111	+	0.480325i
$777$	−2.00000	−	6.15537i	−0.0717496	−	0.220823i
$778$	1.24265	−	3.82447i	0.0445510	−	0.137114i
$779$	1.38197	+	1.00406i	0.0495141	+	0.0359741i
$780$	−14.8328			−0.531100
$781$	−4.34752	+	3.63271i	−0.155567	+	0.129989i
$782$	29.2705			1.04671
$783$	2.11146	+	1.53406i	0.0754573	+	0.0548229i
$784$	0.0450850	−	0.138757i	0.00161018	−	0.00495562i
$785$	−1.06231	−	3.26944i	−0.0379153	−	0.116691i
$786$	−40.3262	+	29.2987i	−1.43839	+	1.04505i
$787$	−12.5623	+	9.12705i	−0.447798	+	0.325344i	−0.788726	−	0.614745i	$-0.789259\pi$
$787$	−12.5623	+	9.12705i	−0.447798	+	0.325344i	0.340928	+	0.940089i	$0.389259\pi$
$788$	−11.5623	−	35.5851i	−0.411890	−	1.26767i
$789$		0			0
$790$	16.7082	+	12.1392i	0.594451	+	0.431894i
$791$	17.7082			0.629631
$792$	−8.37790	+	7.00042i	−0.297696	+	0.248749i
$793$	41.3050			1.46678
$794$	−11.8713	−	8.62502i	−0.421297	−	0.306091i
$795$	−2.47214	+	7.60845i	−0.0876776	+	0.269844i
$796$	−21.8435	−	67.2273i	−0.774221	−	2.38281i
$797$	−12.0902	+	8.78402i	−0.428256	+	0.311146i	−0.780951	−	0.624592i	$-0.785265\pi$
$797$	−12.0902	+	8.78402i	−0.428256	+	0.311146i	0.352695	+	0.935738i	$0.385265\pi$
$798$	−5.85410	+	4.25325i	−0.207233	+	0.150564i
$799$	15.9549	+	49.1042i	0.564444	+	1.73718i
$800$	9.57295	−	29.4625i	0.338455	−	1.04166i
$801$	1.47214	+	1.06957i	0.0520154	+	0.0377914i
$802$	26.1803			0.924460
$803$	−15.4164	−	38.3853i	−0.544033	−	1.35459i
$804$	−1.75078			−0.0617451
$805$	2.11803	+	1.53884i	0.0746509	+	0.0542370i
$806$	35.7771	−	110.111i	1.26019	−	3.87848i
$807$	−7.23607	−	22.2703i	−0.254722	−	0.783953i
$808$	15.5902	−	11.3269i	0.548460	−	0.398480i
$809$	13.5000	−	9.80832i	0.474635	−	0.344842i	−0.324610	−	0.945848i	$-0.605233\pi$
$809$	13.5000	−	9.80832i	0.474635	−	0.344842i	0.799245	+	0.601006i	$0.205233\pi$
$810$	−1.03193	−	3.17595i	−0.0362583	−	0.111592i
$811$	12.5623	−	38.6628i	0.441122	−	1.35763i	−0.445559	−	0.895253i	$-0.646995\pi$
$811$	12.5623	−	38.6628i	0.441122	−	1.35763i	0.886681	−	0.462382i	$-0.153005\pi$
$812$	−3.00000	−	2.17963i	−0.105279	−	0.0764899i
$813$	16.1115			0.565053
$814$	3.61803	−	14.3844i	0.126812	−	0.504172i
$815$	3.90983			0.136955
$816$	−8.09017	−	5.87785i	−0.283213	−	0.205766i
$817$	2.50000	−	7.69421i	0.0874639	−	0.269186i
$818$	11.8328	+	36.4177i	0.413725	+	1.27331i
$819$	−20.1803	+	14.6619i	−0.705158	+	0.512327i
$820$	2.56231	−	1.86162i	0.0894796	−	0.0650107i
$821$	−12.1525	−	37.4015i	−0.424124	−	1.30532i	−0.903830	−	0.427891i	$-0.859257\pi$
$821$	−12.1525	−	37.4015i	−0.424124	−	1.30532i	0.479706	−	0.877429i	$-0.340743\pi$
$822$	−1.58359	+	4.87380i	−0.0552341	+	0.169993i
$823$	8.11803	+	5.89810i	0.282977	+	0.205595i	0.720215	−	0.693751i	$-0.244043\pi$
$823$	8.11803	+	5.89810i	0.282977	+	0.205595i	−0.437238	+	0.899346i	$0.644043\pi$
$824$	5.12461			0.178524
$825$	16.0344	+	10.0656i	0.558248	+	0.350439i
$826$	−20.6525			−0.718592
$827$	29.7082	+	21.5843i	1.03306	+	0.750559i	0.968918	−	0.247382i	$-0.0795704\pi$
$827$	29.7082	+	21.5843i	1.03306	+	0.750559i	0.0641375	+	0.997941i	$0.479570\pi$
$828$	−2.20820	+	6.79615i	−0.0767404	+	0.236183i
$829$	4.74265	+	14.5964i	0.164719	+	0.506953i	0.999015	−	0.0443633i	$-0.0141259\pi$
$829$	4.74265	+	14.5964i	0.164719	+	0.506953i	−0.834297	+	0.551316i	$0.814126\pi$
$830$	11.5451	−	8.38800i	0.400736	−	0.291152i
$831$	6.00000	−	4.35926i	0.208138	−	0.151221i
$832$	−26.0000	−	80.0198i	−0.901388	−	2.77419i
$833$	−0.364745	+	1.12257i	−0.0126377	+	0.0388947i
$834$	−44.9230	−	32.6385i	−1.55556	−	1.13018i
$835$	−1.12461			−0.0389188
$836$	−9.92705	+	0.673542i	−0.343334	+	0.0232949i
$837$	44.2229			1.52857
$838$	12.9271	+	9.39205i	0.446558	+	0.324443i
$839$	3.00000	−	9.23305i	0.103572	−	0.318760i	−0.885821	−	0.464027i	$-0.846404\pi$
$839$	3.00000	−	9.23305i	0.103572	−	0.318760i	0.989393	+	0.145267i	$0.0464040\pi$
$840$	1.38197	+	4.25325i	0.0476824	+	0.146751i
$841$	23.2812	−	16.9147i	0.802798	−	0.583267i
$842$	−23.9443	+	17.3965i	−0.825174	+	0.599524i
$843$	1.70820	+	5.25731i	0.0588337	+	0.181071i
$844$	−8.56231	+	26.3521i	−0.294727	+	0.907076i
$845$	−14.4443	−	10.4944i	−0.496898	−	0.361018i
$846$	−21.0081			−0.722274
$847$	−12.5172	−	25.9358i	−0.430097	−	0.891164i
$848$	−10.4721			−0.359615
$849$	−17.3820	−	12.6287i	−0.596548	−	0.433417i
$850$	−25.8156	+	79.4522i	−0.885468	+	2.72519i
$851$	−1.00000	−	3.07768i	−0.0342796	−	0.105502i
$852$	−5.12461	+	3.72325i	−0.175566	+	0.127556i
$853$	1.78115	−	1.29408i	0.0609855	−	0.0443086i	−0.556875	−	0.830596i	$-0.688000\pi$
$853$	1.78115	−	1.29408i	0.0609855	−	0.0443086i	0.617860	+	0.786288i	$0.288000\pi$
$854$	−11.5451	−	35.5321i	−0.395065	−	1.21588i
$855$	−0.281153	+	0.865300i	−0.00961523	+	0.0295926i
$856$	1.38197	+	1.00406i	0.0472346	+	0.0343180i
$857$	17.2361			0.588773			0.294386	−	0.955686i	$-0.404885\pi$
$857$	17.2361			0.588773			0.294386	+	0.955686i	$0.404885\pi$
$858$	59.1935	−	4.01623i	2.02083	−	0.137112i
$859$	18.7426			0.639491			0.319745	−	0.947503i	$-0.396403\pi$
$859$	18.7426			0.639491			0.319745	+	0.947503i	$0.396403\pi$
$860$	−12.1353	−	8.81678i	−0.413809	−	0.300650i
$861$	−1.70820	+	5.25731i	−0.0582154	+	0.179169i
$862$	−11.7852	−	36.2712i	−0.401406	−	1.23540i
$863$	−10.3820	+	7.54294i	−0.353406	+	0.256765i	−0.750297	−	0.661101i	$-0.770089\pi$
$863$	−10.3820	+	7.54294i	−0.353406	+	0.256765i	0.396890	+	0.917866i	$0.370089\pi$
$864$	30.0000	−	21.7963i	1.02062	−	0.741524i
$865$	3.52786	+	10.8576i	0.119951	+	0.369171i
$866$	18.7426	−	57.6839i	0.636901	−	1.96018i
$867$	48.4508	+	35.2016i	1.64548	+	1.19551i
$868$	−62.8328			−2.13268
$869$	−41.9787	−	26.3521i	−1.42403	−	0.893933i
$870$	0.806504			0.0273431
$871$	−2.47214	−	1.79611i	−0.0837651	−	0.0608589i
$872$	−4.79837	+	14.7679i	−0.162493	+	0.500103i
$873$	−4.63119	−	14.2533i	−0.156742	−	0.482402i
$874$	−2.92705	+	2.12663i	−0.0990090	+	0.0719342i
$875$	−12.5902	+	9.14729i	−0.425625	+	0.309235i
$876$	−14.2918	−	43.9856i	−0.482875	−	1.48614i
$877$	−12.9443	+	39.8384i	−0.437097	+	1.34525i	0.453825	+	0.891091i	$0.350059\pi$
$877$	−12.9443	+	39.8384i	−0.437097	+	1.34525i	−0.890922	+	0.454156i	$0.849941\pi$
$878$	15.8541	+	11.5187i	0.535050	+	0.388737i
$879$	9.30495			0.313848
$880$	0.500000	−	1.98787i	0.0168550	−	0.0670111i
$881$	49.7771			1.67703			0.838516	−	0.544876i	$-0.183423\pi$
$881$	49.7771			1.67703			0.838516	+	0.544876i	$0.183423\pi$
$882$	−0.388544	−	0.282294i	−0.0130830	−	0.00950532i
$883$	10.0451	−	30.9156i	0.338044	−	1.04039i	−0.627159	−	0.778891i	$-0.715782\pi$
$883$	10.0451	−	30.9156i	0.338044	−	1.04039i	0.965203	−	0.261501i	$-0.0842176\pi$
$884$	48.5410	+	149.394i	1.63261	+	5.02466i
$885$	2.18034	−	1.58411i	0.0732913	−	0.0532493i
$886$	−5.79180	+	4.20799i	−0.194579	+	0.141370i
$887$	10.9098	+	33.5770i	0.366316	+	1.12741i	0.949153	+	0.314816i	$0.101943\pi$
$887$	10.9098	+	33.5770i	0.366316	+	1.12741i	−0.582836	+	0.812589i	$0.698057\pi$
$888$	1.70820	−	5.25731i	0.0573236	−	0.176424i
$889$	4.23607	+	3.07768i	0.142073	+	0.103222i
$890$	1.70820			0.0572591
$891$	2.98684	+	7.43694i	0.100063	+	0.249147i
$892$	−26.8328			−0.898429
$893$	−5.16312	−	3.75123i	−0.172777	−	0.125530i
$894$	−14.8754	+	45.7817i	−0.497507	+	1.53117i
$895$	3.09017	+	9.51057i	0.103293	+	0.317903i
$896$	−33.1525	+	24.0867i	−1.10755	+	0.804680i
$897$	10.4721	−	7.60845i	0.349654	−	0.254039i
$898$	16.2574	+	50.0350i	0.542515	+	1.66969i
$899$	−1.16718	+	3.59222i	−0.0389278	+	0.119807i
$900$	−16.5000	−	11.9880i	−0.550000	−	0.399598i
$901$	84.7214			2.82248
$902$	−9.72136	+	8.12299i	−0.323686	+	0.270466i
$903$	26.1803			0.871227
$904$	12.2361	+	8.89002i	0.406966	+	0.295678i
$905$	0.472136	−	1.45309i	0.0156943	−	0.0483022i
$906$	−2.36068	−	7.26543i	−0.0784283	−	0.241378i
$907$	−15.6180	+	11.3472i	−0.518588	+	0.376776i	−0.816072	−	0.577950i	$-0.803853\pi$
$907$	−15.6180	+	11.3472i	−0.518588	+	0.376776i	0.297484	+	0.954727i	$0.403853\pi$
$908$	41.5623	−	30.1968i	1.37929	−	1.00212i
$909$	3.92047	+	12.0660i	0.130034	+	0.400203i
$910$	−7.23607	+	22.2703i	−0.239873	+	0.738254i
$911$	−21.1803	−	15.3884i	−0.701736	−	0.509841i	0.178761	−	0.983892i	$-0.442791\pi$
$911$	−21.1803	−	15.3884i	−0.701736	−	0.509841i	−0.880497	+	0.474051i	$0.842791\pi$
$912$	1.23607			0.0409303
$913$	−26.2812	+	21.9601i	−0.869779	+	0.726772i
$914$	−70.1722			−2.32109
$915$	3.94427	+	2.86568i	0.130394	+	0.0947365i
$916$	0.0835921	−	0.257270i	0.00276196	−	0.00850044i
$917$	14.5902	+	44.9039i	0.481810	+	1.48286i
$918$	−80.9017	+	58.7785i	−2.67015	+	1.93998i
$919$	−42.4787	+	30.8626i	−1.40124	+	1.01806i	−0.406720	+	0.913553i	$0.633327\pi$
$919$	−42.4787	+	30.8626i	−1.40124	+	1.01806i	−0.994524	+	0.104510i	$0.966673\pi$
$920$	0.690983	+	2.12663i	0.0227810	+	0.0701128i
$921$	−3.77709	+	11.6247i	−0.124459	+	0.383046i
$922$	62.4230	+	45.3530i	2.05579	+	1.49362i
$923$	−11.0557			−0.363904
$924$	−12.0000	−	29.8788i	−0.394771	−	0.982940i
$925$	9.23607			0.303680
$926$	−9.73607	−	7.07367i	−0.319947	−	0.232455i
$927$	−1.04257	+	3.20871i	−0.0342426	+	0.105388i
$928$	0.978714	+	3.01217i	0.0321279	+	0.0988794i
$929$	−33.0517	+	24.0134i	−1.08439	+	0.787855i	−0.978443	−	0.206516i	$-0.933787\pi$
$929$	−33.0517	+	24.0134i	−1.08439	+	0.787855i	−0.105947	+	0.994372i	$0.533787\pi$
$930$	11.0557	−	8.03246i	0.362532	−	0.263395i
$931$	−0.0450850	−	0.138757i	−0.00147760	−	0.00454759i
$932$	−3.13525	+	9.64932i	−0.102699	+	0.316074i
$933$	18.5623	+	13.4863i	0.607703	+	0.441522i
$934$	22.2837			0.729144
$935$	−4.04508	+	16.0822i	−0.132288	+	0.525944i
$936$	−21.3050			−0.696374
$937$	7.63525	+	5.54734i	0.249433	+	0.181224i	0.705475	−	0.708734i	$-0.250734\pi$
$937$	7.63525	+	5.54734i	0.249433	+	0.181224i	−0.456043	+	0.889958i	$0.650734\pi$
$938$	−0.854102	+	2.62866i	−0.0278874	+	0.0858286i
$939$	3.67376	+	11.3067i	0.119889	+	0.368979i
$940$	−9.57295	+	6.95515i	−0.312235	+	0.226852i
$941$	8.56231	−	6.22088i	0.279123	−	0.202795i	−0.439412	−	0.898286i	$-0.644813\pi$
$941$	8.56231	−	6.22088i	0.279123	−	0.202795i	0.718535	+	0.695491i	$0.244813\pi$
$942$	4.75078	+	14.6214i	0.154789	+	0.476391i
$943$	−0.854102	+	2.62866i	−0.0278134	+	0.0856008i
$944$	2.85410	+	2.07363i	0.0928931	+	0.0674908i
$945$	−8.94427			−0.290957
$946$	50.8156	+	31.8994i	1.65216	+	1.03714i
$947$	−10.6869			−0.347278			−0.173639	−	0.984809i	$-0.555553\pi$
$947$	−10.6869			−0.347278			−0.173639	+	0.984809i	$0.555553\pi$
$948$	−44.8328	−	32.5729i	−1.45610	−	1.05792i
$949$	24.9443	−	76.7706i	0.809725	−	2.49208i
$950$	−3.19098	−	9.82084i	−0.103529	−	0.318630i
$951$	−19.5967	+	14.2379i	−0.635468	+	0.461695i
$952$	38.3156	−	27.8379i	1.24182	−	0.902232i
$953$	−8.56231	−	26.3521i	−0.277360	−	0.853627i	−0.988585	−	0.150663i	$-0.951859\pi$
$953$	−8.56231	−	26.3521i	−0.277360	−	0.853627i	0.711225	−	0.702965i	$-0.248141\pi$
$954$	−10.6525	+	32.7849i	−0.344887	+	1.06145i
$955$	6.54508	+	4.75528i	0.211794	+	0.153877i
$956$	−64.8541			−2.09753
$957$	−1.93112	+	0.131025i	−0.0624241	+	0.00423542i
$958$	7.03444			0.227273
$959$	3.92705	+	2.85317i	0.126811	+	0.0921337i
$960$	3.06888	−	9.44505i	0.0990478	−	0.304838i
$961$	10.1976	+	31.3849i	0.328954	+	1.01242i
$962$	23.4164	−	17.0130i	0.754975	−	0.548522i
$963$	−0.909830	+	0.661030i	−0.0293189	+	0.0213014i
$964$	14.3951	+	44.3036i	0.463636	+	1.42692i
$965$	2.52786	−	7.77997i	0.0813748	−	0.250446i
$966$	−9.47214	−	6.88191i	−0.304761	−	0.221422i
$967$	−31.1459			−1.00158			−0.500792	−	0.865567i	$-0.666958\pi$
$967$	−31.1459			−1.00158			−0.500792	+	0.865567i	$0.666958\pi$
$968$	4.37132	−	24.2052i	0.140500	−	0.777984i
$969$	−10.0000			−0.321246
$970$	−11.3820	−	8.26948i	−0.365453	−	0.265517i
$971$	5.00000	−	15.3884i	0.160458	−	0.493838i	−0.838215	−	0.545339i	$-0.816401\pi$
$971$	5.00000	−	15.3884i	0.160458	−	0.493838i	0.998673	+	0.0515017i	$0.0164007\pi$
$972$	−12.6049	−	38.7938i	−0.404302	−	1.24431i
$973$	−42.5517	+	30.9156i	−1.36414	+	0.991108i
$974$	42.1591	−	30.6303i	1.35086	−	0.981460i
$975$	11.4164	+	35.1361i	0.365618	+	1.12526i
$976$	−1.97214	+	6.06961i	−0.0631265	+	0.194283i
$977$	−0.909830	−	0.661030i	−0.0291080	−	0.0211482i	0.573136	−	0.819460i	$-0.305727\pi$
$977$	−0.909830	−	0.661030i	−0.0291080	−	0.0211482i	−0.602244	+	0.798312i	$0.705727\pi$
$978$	−17.4853			−0.559118
$979$	−4.09017	+	0.277515i	−0.130722	+	0.00886940i
$980$	−0.270510			−0.00864112
$981$	−8.27051	−	6.00888i	−0.264057	−	0.191849i
$982$	−10.9549	+	33.7158i	−0.349585	+	1.07591i
$983$	−7.36068	−	22.6538i	−0.234769	−	0.722545i	−0.997152	−	0.0754190i	$-0.975971\pi$
$983$	−7.36068	−	22.6538i	−0.234769	−	0.722545i	0.762383	−	0.647126i	$-0.224029\pi$
$984$	−3.81966	+	2.77515i	−0.121766	+	0.0884684i
$985$	6.23607	−	4.53077i	0.198698	−	0.144362i
$986$	−2.63932	−	8.12299i	−0.0840531	−	0.258689i
$987$	6.38197	−	19.6417i	0.203140	−	0.625201i
$988$	−15.7082	−	11.4127i	−0.499745	−	0.363086i
$989$	13.0902			0.416243
$990$	−5.71478	−	3.58744i	−0.181628	−	0.114016i
$991$	−22.6525			−0.719580			−0.359790	−	0.933033i	$-0.617152\pi$
$991$	−22.6525			−0.719580			−0.359790	+	0.933033i	$0.617152\pi$
$992$	43.4164	+	31.5439i	1.37847	+	1.00152i
$993$	9.05573	−	27.8707i	0.287375	−	0.884449i
$994$	3.09017	+	9.51057i	0.0980142	+	0.301657i
$995$	11.7812	−	8.55951i	0.373488	−	0.271355i
$996$	−30.9787	+	22.5074i	−0.981598	+	0.713173i
$997$	11.8090	+	36.3444i	0.373995	+	1.15104i	0.944154	+	0.329505i	$0.106882\pi$
$997$	11.8090	+	36.3444i	0.373995	+	1.15104i	−0.570159	+	0.821535i	$0.693118\pi$
$998$	−2.46149	+	7.57570i	−0.0779172	+	0.239804i
$999$	8.94427	+	6.49839i	0.282984	+	0.205600i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.2.f.a.191.1	yes	4
11.3	even	5	inner	209.2.f.a.58.1	✓	4
11.5	even	5		2299.2.a.g.1.2		2
11.6	odd	10		2299.2.a.h.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.f.a.58.1	✓	4	11.3	even	5	inner
209.2.f.a.191.1	yes	4	1.1	even	1	trivial
2299.2.a.g.1.2		2	11.5	even	5
2299.2.a.h.1.1		2	11.6	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	209.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80902 - 1.31433i) q^{2} +(-0.381966 + 1.17557i) q^{3} +(0.927051 + 2.85317i) q^{4} +(-0.500000 + 0.363271i) q^{5} +(2.23607 - 1.62460i) q^{6} +(-0.809017 - 2.48990i) q^{7} +(0.690983 - 2.12663i) q^{8} +(1.19098 + 0.865300i) q^{9} +1.38197 q^{10} +(-3.30902 + 0.224514i) q^{11} -3.70820 q^{12} +(-5.23607 - 3.80423i) q^{13} +(-1.80902 + 5.56758i) q^{14} +(-0.236068 - 0.726543i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-6.54508 + 4.75528i) q^{17} +(-1.01722 - 3.13068i) q^{18} +(0.309017 - 0.951057i) q^{19} +(-1.50000 - 1.08981i) q^{20} +3.23607 q^{21} +(6.28115 + 3.94298i) q^{22} +1.61803 q^{23} +(2.23607 + 1.62460i) q^{24} +(-1.42705 + 4.39201i) q^{25} +(4.47214 + 13.7638i) q^{26} +(-4.47214 + 3.24920i) q^{27} +(6.35410 - 4.61653i) q^{28} +(-0.145898 - 0.449028i) q^{29} +(-0.527864 + 1.62460i) q^{30} +(-6.47214 - 4.70228i) q^{31} -6.70820 q^{32} +(1.00000 - 3.97574i) q^{33} +18.0902 q^{34} +(1.30902 + 0.951057i) q^{35} +(-1.36475 + 4.20025i) q^{36} +(-0.618034 - 1.90211i) q^{37} +(-1.80902 + 1.31433i) q^{38} +(6.47214 - 4.70228i) q^{39} +(0.427051 + 1.31433i) q^{40} +(-0.527864 + 1.62460i) q^{41} +(-5.85410 - 4.25325i) q^{42} +8.09017 q^{43} +(-3.70820 - 9.23305i) q^{44} -0.909830 q^{45} +(-2.92705 - 2.12663i) q^{46} +(1.97214 - 6.06961i) q^{47} +(0.381966 + 1.17557i) q^{48} +(0.118034 - 0.0857567i) q^{49} +(8.35410 - 6.06961i) q^{50} +(-3.09017 - 9.51057i) q^{51} +(6.00000 - 18.4661i) q^{52} +(-8.47214 - 6.15537i) q^{53} +12.3607 q^{54} +(1.57295 - 1.31433i) q^{55} -5.85410 q^{56} +(1.00000 + 0.726543i) q^{57} +(-0.326238 + 1.00406i) q^{58} +(1.09017 + 3.35520i) q^{59} +(1.85410 - 1.34708i) q^{60} +(-5.16312 + 3.75123i) q^{61} +(5.52786 + 17.0130i) q^{62} +(1.19098 - 3.66547i) q^{63} +(10.5172 + 7.64121i) q^{64} +4.00000 q^{65} +(-7.03444 + 5.87785i) q^{66} +0.472136 q^{67} +(-19.6353 - 14.2658i) q^{68} +(-0.618034 + 1.90211i) q^{69} +(-1.11803 - 3.44095i) q^{70} +(1.38197 - 1.00406i) q^{71} +(2.66312 - 1.93487i) q^{72} +(3.85410 + 11.8617i) q^{73} +(-1.38197 + 4.25325i) q^{74} +(-4.61803 - 3.35520i) q^{75} +3.00000 q^{76} +(3.23607 + 8.05748i) q^{77} -17.8885 q^{78} +(12.0902 + 8.78402i) q^{79} +(-0.190983 + 0.587785i) q^{80} +(-0.746711 - 2.29814i) q^{81} +(3.09017 - 2.24514i) q^{82} +(8.35410 - 6.06961i) q^{83} +(3.00000 + 9.23305i) q^{84} +(1.54508 - 4.75528i) q^{85} +(-14.6353 - 10.6331i) q^{86} +0.583592 q^{87} +(-1.80902 + 7.19218i) q^{88} +1.23607 q^{89} +(1.64590 + 1.19581i) q^{90} +(-5.23607 + 16.1150i) q^{91} +(1.50000 + 4.61653i) q^{92} +(8.00000 - 5.81234i) q^{93} +(-11.5451 + 8.38800i) q^{94} +(0.190983 + 0.587785i) q^{95} +(2.56231 - 7.88597i) q^{96} +(-8.23607 - 5.98385i) q^{97} -0.326238 q^{98} +(-4.13525 - 2.59590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} - 6 q^{3} - 3 q^{4} - 2 q^{5} - q^{7} + 5 q^{8} + 7 q^{9} + 10 q^{10} - 11 q^{11} + 12 q^{12} - 12 q^{13} - 5 q^{14} + 8 q^{15} + q^{16} - 15 q^{17} + 25 q^{18} - q^{19} - 6 q^{20} + 4 q^{21}+ \cdots + 17 q^{99}+O(q^{100}) \) 4 * q - 5 * q^2 - 6 * q^3 - 3 * q^4 - 2 * q^5 - q^7 + 5 * q^8 + 7 * q^9 + 10 * q^10 - 11 * q^11 + 12 * q^12 - 12 * q^13 - 5 * q^14 + 8 * q^15 + q^16 - 15 * q^17 + 25 * q^18 - q^19 - 6 * q^20 + 4 * q^21 + 5 * q^22 + 2 * q^23 + q^25 + 12 * q^28 - 14 * q^29 - 20 * q^30 - 8 * q^31 + 4 * q^33 + 50 * q^34 + 3 * q^35 - 39 * q^36 + 2 * q^37 - 5 * q^38 + 8 * q^39 - 5 * q^40 - 20 * q^41 - 10 * q^42 + 10 * q^43 + 12 * q^44 - 26 * q^45 - 5 * q^46 - 10 * q^47 + 6 * q^48 - 4 * q^49 + 20 * q^50 + 10 * q^51 + 24 * q^52 - 16 * q^53 - 40 * q^54 + 13 * q^55 - 10 * q^56 + 4 * q^57 + 30 * q^58 - 18 * q^59 - 6 * q^60 - 5 * q^61 + 40 * q^62 + 7 * q^63 + 13 * q^64 + 16 * q^65 + 30 * q^66 - 16 * q^67 - 45 * q^68 + 2 * q^69 + 10 * q^71 - 5 * q^72 + 2 * q^73 - 10 * q^74 - 14 * q^75 + 12 * q^76 + 4 * q^77 + 26 * q^79 - 3 * q^80 - 41 * q^81 - 10 * q^82 + 20 * q^83 + 12 * q^84 - 5 * q^85 - 25 * q^86 + 56 * q^87 - 5 * q^88 - 4 * q^89 + 20 * q^90 - 12 * q^91 + 6 * q^92 + 32 * q^93 - 35 * q^94 + 3 * q^95 - 30 * q^96 - 24 * q^97 + 30 * q^98 + 17 * q^99

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