LMFDB - Embedded newform 520.2.by.c.61.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [520,2,Mod(61,520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(520, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 0, 4]))

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

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

chi := DirichletCharacter("520.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 520 = 2^{3} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	520.by (of order $6$, degree $2$, 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:	$4.15222090511$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$52$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.19
Character	$\chi$	$=$	520.61
Dual form			520.2.by.c.341.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.679694 - 1.24017i) q^{2} +(1.76977 + 1.02178i) q^{3} +(-1.07603 + 1.68587i) q^{4} -1.00000i q^{5} +(0.0642740 - 2.88930i) q^{6} +(1.74453 + 3.02162i) q^{7} +(2.82213 + 0.188588i) q^{8} +(0.588053 + 1.01854i) q^{9} +O(q^{10})$	\(q+(-0.679694 - 1.24017i) q^{2} +(1.76977 + 1.02178i) q^{3} +(-1.07603 + 1.68587i) q^{4} -1.00000i q^{5} +(0.0642740 - 2.88930i) q^{6} +(1.74453 + 3.02162i) q^{7} +(2.82213 + 0.188588i) q^{8} +(0.588053 + 1.01854i) q^{9} +(-1.24017 + 0.679694i) q^{10} +(-2.06396 - 1.19163i) q^{11} +(-3.62691 + 1.88413i) q^{12} +(3.56784 + 0.520082i) q^{13} +(2.56157 - 4.21729i) q^{14} +(1.02178 - 1.76977i) q^{15} +(-1.68430 - 3.62810i) q^{16} +(3.52827 + 6.11114i) q^{17} +(0.863461 - 1.42158i) q^{18} +(-5.24350 + 3.02734i) q^{19} +(1.68587 + 1.07603i) q^{20} +7.13008i q^{21} +(-0.0749584 + 3.36960i) q^{22} +(2.62793 - 4.55171i) q^{23} +(4.80183 + 3.21735i) q^{24} -1.00000 q^{25} +(-1.78005 - 4.77822i) q^{26} -3.72722i q^{27} +(-6.97122 - 0.310310i) q^{28} +(8.68828 + 5.01618i) q^{29} +(-2.88930 - 0.0642740i) q^{30} +0.880490 q^{31} +(-3.35464 + 4.55482i) q^{32} +(-2.43516 - 4.21781i) q^{33} +(5.18070 - 8.52935i) q^{34} +(3.02162 - 1.74453i) q^{35} +(-2.34988 - 0.104600i) q^{36} +(-0.869011 - 0.501724i) q^{37} +(7.31838 + 4.44516i) q^{38} +(5.78285 + 4.56596i) q^{39} +(0.188588 - 2.82213i) q^{40} +(0.0213414 - 0.0369644i) q^{41} +(8.84250 - 4.84627i) q^{42} +(-5.46217 + 3.15358i) q^{43} +(4.22982 - 2.19734i) q^{44} +(1.01854 - 0.588053i) q^{45} +(-7.43108 - 0.165308i) q^{46} +0.383051 q^{47} +(0.726278 - 8.14188i) q^{48} +(-2.58678 + 4.48043i) q^{49} +(0.679694 + 1.24017i) q^{50} +14.4204i q^{51} +(-4.71591 + 5.45529i) q^{52} -5.49342i q^{53} +(-4.62238 + 2.53337i) q^{54} +(-1.19163 + 2.06396i) q^{55} +(4.35346 + 8.85640i) q^{56} -12.3730 q^{57} +(0.315539 - 14.1844i) q^{58} +(2.52304 - 1.45668i) q^{59} +(1.88413 + 3.62691i) q^{60} +(10.1022 - 5.83253i) q^{61} +(-0.598464 - 1.09196i) q^{62} +(-2.05175 + 3.55374i) q^{63} +(7.92887 + 1.06444i) q^{64} +(0.520082 - 3.56784i) q^{65} +(-3.57564 + 5.88682i) q^{66} +(1.97003 + 1.13740i) q^{67} +(-14.0991 - 0.627594i) q^{68} +(9.30167 - 5.37032i) q^{69} +(-4.21729 - 2.56157i) q^{70} +(-6.49362 - 11.2473i) q^{71} +(1.46748 + 2.98535i) q^{72} -12.6132 q^{73} +(-0.0315605 + 1.41874i) q^{74} +(-1.76977 - 1.02178i) q^{75} +(0.538490 - 12.0974i) q^{76} -8.31534i q^{77} +(1.73200 - 10.2752i) q^{78} -11.0198 q^{79} +(-3.62810 + 1.68430i) q^{80} +(5.57255 - 9.65193i) q^{81} +(-0.0603478 - 0.00134247i) q^{82} -10.5000i q^{83} +(-12.0204 - 7.67220i) q^{84} +(6.11114 - 3.52827i) q^{85} +(7.62357 + 4.63053i) q^{86} +(10.2508 + 17.7549i) q^{87} +(-5.60005 - 3.75217i) q^{88} +(1.80802 - 3.13158i) q^{89} +(-1.42158 - 0.863461i) q^{90} +(4.65273 + 11.6880i) q^{91} +(4.84585 + 9.32815i) q^{92} +(1.55826 + 0.899664i) q^{93} +(-0.260357 - 0.475048i) q^{94} +(3.02734 + 5.24350i) q^{95} +(-10.5909 + 4.63328i) q^{96} +(-5.26325 - 9.11622i) q^{97} +(7.31471 + 0.162719i) q^{98} -2.80296i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9}+O(q^{10}) $ 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9	$ 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9} - 28 q^{12} - 24 q^{14} + 4 q^{15} - 20 q^{16} + 4 q^{17} - 40 q^{18} - 4 q^{20} + 24 q^{22} + 32 q^{23} + 24 q^{24} - 104 q^{25} - 10 q^{26} + 22 q^{28} - 12 q^{30} - 40 q^{31} + 30 q^{32} + 12 q^{33} - 4 q^{34} + 18 q^{36} + 56 q^{39} - 16 q^{41} - 20 q^{42} - 32 q^{44} - 30 q^{46} - 56 q^{47} - 24 q^{48} - 80 q^{49} - 6 q^{52} - 10 q^{54} + 16 q^{55} - 38 q^{56} + 104 q^{57} - 68 q^{58} - 12 q^{62} + 12 q^{63} - 108 q^{64} + 180 q^{66} - 6 q^{68} + 8 q^{70} - 72 q^{71} - 80 q^{72} + 24 q^{73} + 40 q^{74} - 20 q^{76} - 52 q^{78} - 40 q^{79} - 24 q^{80} - 60 q^{81} + 64 q^{82} - 70 q^{84} + 140 q^{86} - 8 q^{87} + 86 q^{88} + 36 q^{89} - 20 q^{90} + 76 q^{92} + 46 q^{94} - 32 q^{95} + 12 q^{96} + 12 q^{97} - 8 q^{98}+O(q^{100}) $ 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9 - 28 * q^12 - 24 * q^14 + 4 * q^15 - 20 * q^16 + 4 * q^17 - 40 * q^18 - 4 * q^20 + 24 * q^22 + 32 * q^23 + 24 * q^24 - 104 * q^25 - 10 * q^26 + 22 * q^28 - 12 * q^30 - 40 * q^31 + 30 * q^32 + 12 * q^33 - 4 * q^34 + 18 * q^36 + 56 * q^39 - 16 * q^41 - 20 * q^42 - 32 * q^44 - 30 * q^46 - 56 * q^47 - 24 * q^48 - 80 * q^49 - 6 * q^52 - 10 * q^54 + 16 * q^55 - 38 * q^56 + 104 * q^57 - 68 * q^58 - 12 * q^62 + 12 * q^63 - 108 * q^64 + 180 * q^66 - 6 * q^68 + 8 * q^70 - 72 * q^71 - 80 * q^72 + 24 * q^73 + 40 * q^74 - 20 * q^76 - 52 * q^78 - 40 * q^79 - 24 * q^80 - 60 * q^81 + 64 * q^82 - 70 * q^84 + 140 * q^86 - 8 * q^87 + 86 * q^88 + 36 * q^89 - 20 * q^90 + 76 * q^92 + 46 * q^94 - 32 * q^95 + 12 * q^96 + 12 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/520\mathbb{Z}\right)^\times$.

$n$	$41$	$261$	$391$	$417$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$1$

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 $

$2$	−0.679694	−	1.24017i	−0.480616	−	0.876931i
$2$	−0.679694	−	1.24017i	−0.480616	−	0.876931i
$3$	1.76977	+	1.02178i	1.02178	+	0.589923i	0.914618	−	0.404319i	$-0.132492\pi$
$3$	1.76977	+	1.02178i	1.02178	+	0.589923i	0.107158	+	0.994242i	$0.465825\pi$
$4$	−1.07603	+	1.68587i	−0.538017	+	0.842934i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	0.0642740	−	2.88930i	0.0262397	−	1.17955i
$7$	1.74453	+	3.02162i	0.659371	+	1.14206i	0.980779	+	0.195123i	$0.0625106\pi$
$7$	1.74453	+	3.02162i	0.659371	+	1.14206i	−0.321408	+	0.946941i	$0.604156\pi$
$8$	2.82213	+	0.188588i	0.997775	+	0.0666759i
$9$	0.588053	+	1.01854i	0.196018	+	0.339512i
$10$	−1.24017	+	0.679694i	−0.392176	+	0.214938i
$11$	−2.06396	−	1.19163i	−0.622308	−	0.359290i	0.155459	−	0.987842i	$-0.450314\pi$
$11$	−2.06396	−	1.19163i	−0.622308	−	0.359290i	−0.777767	+	0.628553i	$0.783648\pi$
$12$	−3.62691	+	1.88413i	−1.04700	+	0.543902i
$13$	3.56784	+	0.520082i	0.989542	+	0.144245i
$13$	3.56784	+	0.520082i	0.989542	+	0.144245i
$14$	2.56157	−	4.21729i	0.684607	−	1.12712i
$15$	1.02178	−	1.76977i	0.263821	−	0.456952i
$16$	−1.68430	−	3.62810i	−0.421076	−	0.907025i
$17$	3.52827	+	6.11114i	0.855731	+	1.48217i	0.875965	+	0.482374i	$0.160225\pi$
$17$	3.52827	+	6.11114i	0.855731	+	1.48217i	−0.0202343	+	0.999795i	$0.506441\pi$
$18$	0.863461	−	1.42158i	0.203520	−	0.335069i
$19$	−5.24350	+	3.02734i	−1.20294	+	0.694519i	−0.961208	−	0.275824i	$-0.911049\pi$
$19$	−5.24350	+	3.02734i	−1.20294	+	0.694519i	−0.241734	+	0.970343i	$0.577716\pi$
$20$	1.68587	+	1.07603i	0.376972	+	0.240608i
$21$			7.13008i			1.55591i
$22$	−0.0749584	+	3.36960i	−0.0159812	+	0.718402i
$23$	2.62793	−	4.55171i	0.547962	−	0.949098i	−0.450452	−	0.892801i	$-0.648737\pi$
$23$	2.62793	−	4.55171i	0.547962	−	0.949098i	0.998414	−	0.0562974i	$-0.0179295\pi$
$24$	4.80183	+	3.21735i	0.980169	+	0.656738i
$25$	−1.00000			−0.200000
$26$	−1.78005	−	4.77822i	−0.349097	−	0.937087i
$27$		−	3.72722i		−	0.717305i
$28$	−6.97122	−	0.310310i	−1.31744	−	0.0586431i
$29$	8.68828	+	5.01618i	1.61337	+	0.931481i	0.988581	+	0.150689i	$0.0481492\pi$
$29$	8.68828	+	5.01618i	1.61337	+	0.931481i	0.624791	+	0.780792i	$0.285184\pi$
$30$	−2.88930	−	0.0642740i	−0.527512	−	0.0117348i
$31$	0.880490			0.158141			0.0790704	−	0.996869i	$-0.474805\pi$
$31$	0.880490			0.158141			0.0790704	+	0.996869i	$0.474805\pi$
$32$	−3.35464	+	4.55482i	−0.593023	+	0.805186i
$33$	−2.43516	−	4.21781i	−0.423906	−	0.734227i
$34$	5.18070	−	8.52935i	0.888483	−	1.46277i
$35$	3.02162	−	1.74453i	0.510746	−	0.294880i
$36$	−2.34988	−	0.104600i	−0.391647	−	0.0174334i
$37$	−0.869011	−	0.501724i	−0.142865	−	0.0824829i	0.426864	−	0.904316i	$-0.359618\pi$
$37$	−0.869011	−	0.501724i	−0.142865	−	0.0824829i	−0.569728	+	0.821833i	$0.692952\pi$
$38$	7.31838	+	4.44516i	1.18720	+	0.721101i
$39$	5.78285	+	4.56596i	0.925997	+	0.731139i
$40$	0.188588	−	2.82213i	0.0298184	−	0.446218i
$41$	0.0213414	−	0.0369644i	0.00333297	−	0.00577288i	−0.864354	−	0.502884i	$-0.832272\pi$
$41$	0.0213414	−	0.0369644i	0.00333297	−	0.00577288i	0.867687	+	0.497111i	$0.165606\pi$
$42$	8.84250	−	4.84627i	1.36443	−	0.747796i
$43$	−5.46217	+	3.15358i	−0.832973	+	0.480917i	−0.854869	−	0.518843i	$-0.826363\pi$
$43$	−5.46217	+	3.15358i	−0.832973	+	0.480917i	0.0218967	+	0.999760i	$0.493029\pi$
$44$	4.22982	−	2.19734i	0.637670	−	0.331261i
$45$	1.01854	−	0.588053i	0.151835	−	0.0876617i
$46$	−7.43108	−	0.165308i	−1.09565	−	0.0243733i
$47$	0.383051			0.0558738			0.0279369	−	0.999610i	$-0.491106\pi$
$47$	0.383051			0.0558738			0.0279369	+	0.999610i	$0.491106\pi$
$48$	0.726278	−	8.14188i	0.104829	−	1.17518i
$49$	−2.58678	+	4.48043i	−0.369540	+	0.640062i
$50$	0.679694	+	1.24017i	0.0961232	+	0.175386i
$51$			14.4204i			2.01926i
$52$	−4.71591	+	5.45529i	−0.653979	+	0.756513i
$53$		−	5.49342i		−	0.754579i	−0.926095	−	0.377289i	$-0.876856\pi$
$53$		−	5.49342i		−	0.754579i	0.926095	−	0.377289i	$-0.123144\pi$
$54$	−4.62238	+	2.53337i	−0.629027	+	0.344748i
$55$	−1.19163	+	2.06396i	−0.160679	+	0.278305i
$56$	4.35346	+	8.85640i	0.581755	+	1.18349i
$57$	−12.3730			−1.63885
$58$	0.315539	−	14.1844i	0.0414322	−	1.86250i
$59$	2.52304	−	1.45668i	0.328472	−	0.189643i	−0.326691	−	0.945131i	$-0.605934\pi$
$59$	2.52304	−	1.45668i	0.328472	−	0.189643i	0.655162	+	0.755488i	$0.272600\pi$
$60$	1.88413	+	3.62691i	0.243240	+	0.468232i
$61$	10.1022	−	5.83253i	1.29346	−	0.746778i	0.314193	−	0.949359i	$-0.398266\pi$
$61$	10.1022	−	5.83253i	1.29346	−	0.746778i	0.979266	+	0.202581i	$0.0649329\pi$
$62$	−0.598464	−	1.09196i	−0.0760050	−	0.138679i
$63$	−2.05175	+	3.55374i	−0.258497	+	0.447729i
$64$	7.92887	+	1.06444i	0.991109	+	0.133055i
$65$	0.520082	−	3.56784i	0.0645083	−	0.442537i
$66$	−3.57564	+	5.88682i	−0.440131	+	0.724618i
$67$	1.97003	+	1.13740i	0.240678	+	0.138955i	0.615488	−	0.788146i	$-0.288959\pi$
$67$	1.97003	+	1.13740i	0.240678	+	0.138955i	−0.374810	+	0.927101i	$0.622292\pi$
$68$	−14.0991	−	0.627594i	−1.70977	−	0.0761069i
$69$	9.30167	−	5.37032i	1.11979	−	0.646510i
$70$	−4.21729	−	2.56157i	−0.504062	−	0.306166i
$71$	−6.49362	−	11.2473i	−0.770651	−	1.33481i	−0.937207	−	0.348775i	$-0.886598\pi$
$71$	−6.49362	−	11.2473i	−0.770651	−	1.33481i	0.166555	−	0.986032i	$-0.446736\pi$
$72$	1.46748	+	2.98535i	0.172944	+	0.351827i
$73$	−12.6132			−1.47626			−0.738129	−	0.674659i	$-0.764291\pi$
$73$	−12.6132			−1.47626			−0.738129	+	0.674659i	$0.764291\pi$
$74$	−0.0315605	+	1.41874i	−0.00366883	+	0.164925i
$75$	−1.76977	−	1.02178i	−0.204355	−	0.117985i
$76$	0.538490	−	12.0974i	0.0617691	−	1.38766i
$77$		−	8.31534i		−	0.947621i
$78$	1.73200	−	10.2752i	0.196110	−	1.16343i
$79$	−11.0198			−1.23983			−0.619914	−	0.784669i	$-0.712833\pi$
$79$	−11.0198			−1.23983			−0.619914	+	0.784669i	$0.712833\pi$
$80$	−3.62810	+	1.68430i	−0.405634	+	0.188311i
$81$	5.57255	−	9.65193i	0.619172	−	1.07244i
$82$	−0.0603478	−	0.00134247i	−0.00666430	−	0.000148250i
$83$		−	10.5000i		−	1.15252i	−0.817265	−	0.576262i	$-0.804511\pi$
$83$		−	10.5000i		−	1.15252i	0.817265	−	0.576262i	$-0.195489\pi$
$84$	−12.0204	−	7.67220i	−1.31153	−	0.837106i
$85$	6.11114	−	3.52827i	0.662846	−	0.382695i
$86$	7.62357	+	4.63053i	0.822071	+	0.499323i
$87$	10.2508	+	17.7549i	1.09900	+	1.90353i
$88$	−5.60005	−	3.75217i	−0.596967	−	0.399983i
$89$	1.80802	−	3.13158i	0.191650	−	0.331947i	−0.754147	−	0.656705i	$-0.771950\pi$
$89$	1.80802	−	3.13158i	0.191650	−	0.331947i	0.945797	+	0.324758i	$0.105283\pi$
$90$	−1.42158	−	0.863461i	−0.149847	−	0.0910168i
$91$	4.65273	+	11.6880i	0.487738	+	1.22523i
$92$	4.84585	+	9.32815i	0.505215	+	0.972526i
$93$	1.55826	+	0.899664i	0.161584	+	0.0932908i
$94$	−0.260357	−	0.475048i	−0.0268538	−	0.0489975i
$95$	3.02734	+	5.24350i	0.310598	+	0.537972i
$96$	−10.5909	+	4.63328i	−1.08093	+	0.472882i
$97$	−5.26325	−	9.11622i	−0.534402	−	0.925612i	−0.999192	−	0.0401908i	$-0.987203\pi$
$97$	−5.26325	−	9.11622i	−0.534402	−	0.925612i	0.464790	−	0.885421i	$-0.346130\pi$
$98$	7.31471	+	0.162719i	0.738897	+	0.0164371i
$99$		−	2.80296i		−	0.281708i
$100$	1.07603	−	1.68587i	0.107603	−	0.168587i
$101$	−5.69149	−	3.28598i	−0.566324	−	0.326968i	0.189356	−	0.981909i	$-0.439360\pi$
$101$	−5.69149	−	3.28598i	−0.566324	−	0.326968i	−0.755680	+	0.654941i	$0.772693\pi$
$102$	17.8837	−	9.80146i	1.77075	−	0.970489i
$103$	−7.14093			−0.703617			−0.351809	−	0.936072i	$-0.614433\pi$
$103$	−7.14093			−0.703617			−0.351809	+	0.936072i	$0.614433\pi$
$104$	9.97085	+	2.14059i	0.977722	+	0.209903i
$105$	7.13008			0.695825
$106$	−6.81276	+	3.73384i	−0.661714	+	0.362663i
$107$	−0.463463	−	0.267580i	−0.0448046	−	0.0258680i	0.477430	−	0.878670i	$-0.341568\pi$
$107$	−0.463463	−	0.267580i	−0.0448046	−	0.0258680i	−0.522235	+	0.852802i	$0.674902\pi$
$108$	6.28361	+	4.01062i	0.604641	+	0.385922i
$109$			15.7320i			1.50685i	0.657534	+	0.753425i	$0.271600\pi$
$109$			15.7320i			1.50685i	−0.657534	+	0.753425i	$0.728400\pi$
$110$	3.36960	+	0.0749584i	0.321279	+	0.00714701i
$111$	−1.02530	−	1.77587i	−0.0973170	−	0.168558i
$112$	8.02441	−	11.4187i	0.758235	−	1.07896i
$113$	7.53399	+	13.0493i	0.708738	+	1.22757i	0.965325	+	0.261050i	$0.0840686\pi$
$113$	7.53399	+	13.0493i	0.708738	+	1.22757i	−0.256587	+	0.966521i	$0.582598\pi$
$114$	8.40988	+	15.3447i	0.787658	+	1.43716i
$115$	−4.55171	−	2.62793i	−0.424450	−	0.245056i
$116$	−17.8055	+	9.24972i	−1.65320	+	0.858814i
$117$	1.56836	+	3.93982i	0.144995	+	0.364236i
$118$	−3.52142	−	2.13890i	−0.324173	−	0.196901i
$119$	−12.3104	+	21.3222i	−1.12849	+	1.95460i
$120$	3.21735	−	4.80183i	0.293702	−	0.438345i
$121$	−2.66004	−	4.60732i	−0.241822	−	0.418848i
$122$	−14.0997	−	8.56413i	−1.27653	−	0.775360i
$123$	0.0755388	−	0.0436123i	0.00681110	−	0.00393239i
$124$	−0.947437	+	1.48439i	−0.0850823	+	0.133302i
$125$			1.00000i			0.0894427i
$126$	5.80180	+	0.129064i	0.516865	+	0.0114979i
$127$	0.829740	−	1.43715i	0.0736276	−	0.127527i	−0.826861	−	0.562406i	$-0.809876\pi$
$127$	0.829740	−	1.43715i	0.0736276	−	0.127527i	0.900489	+	0.434880i	$0.143209\pi$
$128$	−4.06912	−	10.5566i	−0.359662	−	0.933083i
$129$	−12.8890			−1.13482
$130$	−4.77822	+	1.78005i	−0.419078	+	0.156121i
$131$			4.70582i			0.411149i	0.978641	+	0.205575i	$0.0659063\pi$
$131$			4.70582i			0.411149i	−0.978641	+	0.205575i	$0.934094\pi$
$132$	9.73099	+	0.433155i	0.846974	+	0.0377013i
$133$	−18.2949	−	10.5626i	−1.58637	−	0.915891i
$134$	0.0715471	−	3.21625i	0.00618073	−	0.277842i
$135$	−3.72722			−0.320788
$136$	8.80476	+	17.9118i	0.755002	+	1.53593i
$137$	−9.25873	−	16.0366i	−0.791027	−	1.37010i	−0.925332	−	0.379159i	$-0.876214\pi$
$137$	−9.25873	−	16.0366i	−0.791027	−	1.37010i	0.134305	−	0.990940i	$-0.457120\pi$
$138$	−12.9824	−	7.88546i	−1.10513	−	0.671255i
$139$	−18.5174	+	10.6910i	−1.57063	+	0.906801i	−0.574534	+	0.818481i	$0.694817\pi$
$139$	−18.5174	+	10.6910i	−1.57063	+	0.906801i	−0.996092	+	0.0883203i	$0.971850\pi$
$140$	−0.310310	+	6.97122i	−0.0262260	+	0.589176i
$141$	0.677912	+	0.391393i	0.0570905	+	0.0329612i
$142$	−9.53485	+	15.6979i	−0.800147	+	1.31734i
$143$	−6.74415	−	5.32498i	−0.563974	−	0.445297i
$144$	2.70490	−	3.84904i	0.225408	−	0.320753i
$145$	5.01618	−	8.68828i	0.416571	−	0.721522i
$146$	8.57308	+	15.6424i	0.709513	+	1.29458i
$147$	−9.15600	+	5.28622i	−0.755174	+	0.436000i
$148$	1.78092	−	0.925167i	0.146391	−	0.0760482i
$149$	−8.42259	+	4.86279i	−0.690006	+	0.398375i	−0.803614	−	0.595151i	$-0.797092\pi$
$149$	−8.42259	+	4.86279i	−0.690006	+	0.398375i	0.113608	+	0.993526i	$0.463759\pi$
$150$	−0.0642740	+	2.88930i	−0.00524795	+	0.235911i
$151$	8.27770			0.673630			0.336815	−	0.941571i	$-0.390650\pi$
$151$	8.27770			0.673630			0.336815	+	0.941571i	$0.390650\pi$
$152$	−15.3688	+	7.55469i	−1.24657	+	0.612766i
$153$	−4.14962	+	7.18735i	−0.335477	+	0.581062i
$154$	−10.3124	+	5.65188i	−0.830998	+	0.455442i
$155$		−	0.880490i		−	0.0707227i
$156$	−13.9202	+	4.83600i	−1.11450	+	0.387190i
$157$			14.4625i			1.15423i	0.816661	+	0.577117i	$0.195823\pi$
$157$			14.4625i			1.15423i	−0.816661	+	0.577117i	$0.804177\pi$
$158$	7.49011	+	13.6665i	0.595881	+	1.08724i
$159$	5.61304	−	9.72207i	0.445143	−	0.771010i
$160$	4.55482	+	3.35464i	0.360090	+	0.265208i
$161$	18.3380			1.44524
$162$	−15.7576	−	0.350536i	−1.23804	−	0.0275407i
$163$	8.68415	−	5.01379i	0.680195	−	0.392711i	−0.119734	−	0.992806i	$-0.538204\pi$
$163$	8.68415	−	5.01379i	0.680195	−	0.392711i	0.799928	+	0.600095i	$0.204871\pi$
$164$	0.0393531	+	0.0757538i	0.00307296	+	0.00591538i
$165$	−4.21781	+	2.43516i	−0.328356	+	0.189577i
$166$	−13.0218	+	7.13678i	−1.01068	+	0.553922i
$167$	−4.33615	+	7.51044i	−0.335542	+	0.581175i	−0.983589	−	0.180425i	$-0.942253\pi$
$167$	−4.33615	+	7.51044i	−0.335542	+	0.581175i	0.648047	+	0.761600i	$0.275586\pi$
$168$	−1.34465	+	20.1220i	−0.103742	+	1.55245i
$169$	12.4590	+	3.71115i	0.958387	+	0.285473i
$170$	−8.52935	−	5.18070i	−0.654171	−	0.397342i
$171$	−6.16691	−	3.56047i	−0.471596	−	0.272276i
$172$	0.560946	−	12.6019i	0.0427718	−	0.960882i
$173$	6.01490	−	3.47270i	0.457304	−	0.264025i	−0.253606	−	0.967308i	$-0.581617\pi$
$173$	6.01490	−	3.47270i	0.457304	−	0.264025i	0.710910	+	0.703283i	$0.248283\pi$
$174$	15.0517	−	24.7807i	1.14107	−	1.87862i
$175$	−1.74453	−	3.02162i	−0.131874	−	0.228413i
$176$	−0.847009	+	9.49533i	−0.0638457	+	0.715737i
$177$	5.95359			0.447499
$178$	−5.11259	−	0.113732i	−0.383205	−	0.00852457i
$179$	−15.0535	−	8.69116i	−1.12515	−	0.649608i	−0.182442	−	0.983217i	$-0.558400\pi$
$179$	−15.0535	−	8.69116i	−1.12515	−	0.649608i	−0.942712	+	0.333609i	$0.891734\pi$
$180$	−0.104600	+	2.34988i	−0.00779645	+	0.175150i
$181$		−	8.89990i		−	0.661525i	−0.943714	−	0.330762i	$-0.892694\pi$
$181$		−	8.89990i		−	0.661525i	0.943714	−	0.330762i	$-0.107306\pi$
$182$	11.3326	−	13.7144i	0.840028	−	1.01658i
$183$	23.8381			1.76217
$184$	8.27478	−	12.3499i	0.610025	−	0.910450i
$185$	−0.501724	+	0.869011i	−0.0368875	+	0.0638909i
$186$	0.0565926	−	2.54400i	0.00414957	−	0.186535i
$187$		−	16.8176i		−	1.22982i
$188$	−0.412176	+	0.645774i	−0.0300610	+	0.0470979i
$189$	11.2622	−	6.50226i	0.819208	−	0.472970i
$190$	4.44516	−	7.31838i	0.322486	−	0.530931i
$191$	7.43546	+	12.8786i	0.538011	+	0.931862i	0.999011	+	0.0444620i	$0.0141574\pi$
$191$	7.43546	+	12.8786i	0.538011	+	0.931862i	−0.461000	+	0.887400i	$0.652509\pi$
$192$	12.9446	+	9.98534i	0.934199	+	0.720630i
$193$	6.07185	−	10.5167i	0.437061	−	0.757012i	−0.560400	−	0.828222i	$-0.689353\pi$
$193$	6.07185	−	10.5167i	0.437061	−	0.757012i	0.997461	+	0.0712098i	$0.0226860\pi$
$194$	−7.72825	+	12.7236i	−0.554856	+	0.913498i
$195$	4.56596	−	5.78285i	0.326975	−	0.414118i
$196$	−4.76996	−	9.18206i	−0.340711	−	0.655862i
$197$	−12.8090	−	7.39528i	−0.912604	−	0.526892i	−0.0313360	−	0.999509i	$-0.509976\pi$
$197$	−12.8090	−	7.39528i	−0.912604	−	0.526892i	−0.881268	+	0.472617i	$0.843310\pi$
$198$	−3.47614	+	1.90516i	−0.247039	+	0.135394i
$199$	−11.8881	−	20.5907i	−0.842723	−	1.45964i	−0.887584	−	0.460645i	$-0.847618\pi$
$199$	−11.8881	−	20.5907i	−0.842723	−	1.45964i	0.0448616	−	0.998993i	$-0.485715\pi$
$200$	−2.82213	−	0.188588i	−0.199555	−	0.0133352i
$201$	2.32433	+	4.02586i	0.163946	+	0.283962i
$202$	−0.206702	+	9.29187i	−0.0145435	+	0.653773i
$203$			35.0035i			2.45677i
$204$	−24.3109	−	15.5168i	−1.70210	−	1.08640i
$205$	−0.0369644	−	0.0213414i	−0.00258171	−	0.00149055i
$206$	4.85365	+	8.85596i	0.338170	+	0.617024i
$207$	6.18145			0.429641
$208$	−4.12243	−	13.8205i	−0.285839	−	0.958278i
$209$	14.4299			0.998134
$210$	−4.84627	−	8.84250i	−0.334424	−	0.610190i
$211$	13.7004	+	7.90994i	0.943175	+	0.544543i	0.890954	−	0.454093i	$-0.150037\pi$
$211$	13.7004	+	7.90994i	0.943175	+	0.544543i	0.0522212	+	0.998636i	$0.483370\pi$
$212$	9.26118	+	5.91110i	0.636060	+	0.405976i
$213$		−	26.5401i		−	1.81850i
$214$	−0.0168319	+	0.756644i	−0.00115061	+	0.0517231i
$215$	3.15358	+	5.46217i	0.215073	+	0.372517i
$216$	0.702910	−	10.5187i	0.0478270	−	0.715708i
$217$	1.53604	+	2.66050i	0.104273	+	0.180607i
$218$	19.5103	−	10.6929i	1.32140	−	0.724216i
$219$	−22.3224	−	12.8878i	−1.50841	−	0.870878i
$220$	−2.19734	−	4.22982i	−0.148144	−	0.285175i
$221$	9.41002	+	23.6386i	0.632986	+	1.59010i
$222$	−1.50549	+	2.47859i	−0.101042	+	0.166352i
$223$	2.62637	−	4.54900i	0.175874	−	0.304624i	−0.764589	−	0.644518i	$-0.777058\pi$
$223$	2.62637	−	4.54900i	0.175874	−	0.304624i	0.940464	+	0.339895i	$0.110391\pi$
$224$	−19.6152	−	2.19043i	−1.31060	−	0.146354i
$225$	−0.588053	−	1.01854i	−0.0392035	−	0.0679025i
$226$	11.0625	−	18.2129i	0.735864	−	1.21150i
$227$	8.26860	−	4.77388i	0.548806	−	0.316853i	−0.199834	−	0.979830i	$-0.564040\pi$
$227$	8.26860	−	4.77388i	0.548806	−	0.316853i	0.748640	+	0.662976i	$0.230707\pi$
$228$	13.3138	−	20.8593i	0.881729	−	1.38144i
$229$		−	8.52399i		−	0.563281i	−0.959520	−	0.281641i	$-0.909121\pi$
$229$		−	8.52399i		−	0.563281i	0.959520	−	0.281641i	$-0.0908786\pi$
$230$	−0.165308	+	7.43108i	−0.0109001	+	0.489991i
$231$	8.49641	−	14.7162i	0.559023	−	0.968256i
$232$	23.5735	+	15.7948i	1.54767	+	1.03698i
$233$	5.62441			0.368467			0.184234	−	0.982882i	$-0.441020\pi$
$233$	5.62441			0.368467			0.184234	+	0.982882i	$0.441020\pi$
$234$	3.82003	−	4.62290i	0.249723	−	0.302208i
$235$		−	0.383051i		−	0.0249875i
$236$	−0.259108	+	5.82094i	−0.0168665	+	0.378911i
$237$	−19.5026	−	11.2598i	−1.26683	−	0.731403i
$238$	34.8103	+	0.774372i	2.25642	+	0.0501951i
$239$	0.582389			0.0376716			0.0188358	−	0.999823i	$-0.494004\pi$
$239$	0.582389			0.0376716			0.0188358	+	0.999823i	$0.494004\pi$
$240$	−8.14188	−	0.726278i	−0.525556	−	0.0468810i
$241$	−1.82448	−	3.16009i	−0.117525	−	0.203560i	0.801261	−	0.598315i	$-0.204163\pi$
$241$	−1.82448	−	3.16009i	−0.117525	−	0.203560i	−0.918786	+	0.394755i	$0.870829\pi$
$242$	−3.90584	+	6.43047i	−0.251077	+	0.413366i
$243$	10.0406	−	5.79695i	0.644106	−	0.371875i
$244$	−1.03747	+	23.3070i	−0.0664169	+	1.49208i
$245$	4.48043	+	2.58678i	0.286244	+	0.165263i
$246$	−0.105430	−	0.0640378i	−0.00672196	−	0.00408290i
$247$	−20.2825	+	8.07402i	−1.29054	+	0.513738i
$248$	2.48486	+	0.166050i	0.157789	+	0.0105442i
$249$	10.7286	−	18.5826i	0.679900	−	1.17762i
$250$	1.24017	−	0.679694i	0.0784351	−	0.0429876i
$251$	8.00658	−	4.62260i	0.505371	−	0.291776i	−0.225558	−	0.974230i	$-0.572421\pi$
$251$	8.00658	−	4.62260i	0.505371	−	0.291776i	0.730929	+	0.682454i	$0.239087\pi$
$252$	−3.78338	−	7.28293i	−0.238331	−	0.458781i
$253$	−10.8479	+	6.26304i	−0.682002	+	0.393754i
$254$	−2.34628	−	0.0521941i	−0.147219	−	0.00327495i
$255$	14.4204			0.903041
$256$	−10.3262	+	12.2217i	−0.645390	+	0.763854i
$257$	5.67462	−	9.82873i	0.353973	−	0.613100i	−0.632969	−	0.774178i	$-0.718164\pi$
$257$	5.67462	−	9.82873i	0.353973	−	0.613100i	0.986942	+	0.161078i	$0.0514971\pi$
$258$	8.76059	+	15.9846i	0.545410	+	0.995155i
$259$		−	3.50109i		−	0.217547i
$260$	5.45529	+	4.71591i	0.338323	+	0.292468i
$261$			11.7991i			0.730346i
$262$	5.83600	−	3.19851i	0.360549	−	0.197605i
$263$	−4.40154	+	7.62370i	−0.271411	+	0.470097i	−0.969223	−	0.246183i	$-0.920824\pi$
$263$	−4.40154	+	7.62370i	−0.271411	+	0.470097i	0.697812	+	0.716280i	$0.254157\pi$
$264$	−6.07691	−	12.3625i	−0.374008	−	0.760858i
$265$	−5.49342			−0.337458
$266$	−0.664430	+	29.8681i	−0.0407388	+	1.83133i
$267$	6.39955	−	3.69478i	0.391646	−	0.226117i
$268$	−4.03732	+	2.09734i	−0.246619	+	0.128115i
$269$	18.0685	−	10.4319i	1.10166	−	0.636041i	0.165001	−	0.986293i	$-0.447237\pi$
$269$	18.0685	−	10.4319i	1.10166	−	0.636041i	0.936655	+	0.350252i	$0.113904\pi$
$270$	2.53337	+	4.62238i	0.154176	+	0.281309i
$271$	9.39153	−	16.2666i	0.570495	−	0.988126i	−0.426020	−	0.904714i	$-0.640085\pi$
$271$	9.39153	−	16.2666i	0.570495	−	0.988126i	0.996515	−	0.0834123i	$-0.0265819\pi$
$272$	16.2292	−	23.0939i	0.984037	−	1.40028i
$273$	−3.70823	+	25.4390i	−0.224432	+	1.53964i
$274$	−13.5950	+	22.3824i	−0.821302	+	1.35217i
$275$	2.06396	+	1.19163i	0.124462	+	0.0718579i
$276$	−0.955250	+	21.4600i	−0.0574993	+	1.29174i
$277$	9.71213	−	5.60730i	0.583545	−	0.336910i	−0.178996	−	0.983850i	$-0.557285\pi$
$277$	9.71213	−	5.60730i	0.583545	−	0.336910i	0.762541	+	0.646940i	$0.223952\pi$
$278$	25.8448	+	15.6981i	1.55007	+	0.941508i
$279$	0.517775	+	0.896812i	0.0309984	+	0.0536907i
$280$	8.85640	−	4.35346i	0.529271	−	0.260169i
$281$	−21.2506			−1.26770			−0.633851	−	0.773455i	$-0.718527\pi$
$281$	−21.2506			−1.26770			−0.633851	+	0.773455i	$0.718527\pi$
$282$	0.0246202	−	1.10675i	0.00146611	−	0.0659061i
$283$	8.57726	+	4.95208i	0.509865	+	0.294371i	0.732778	−	0.680468i	$-0.238223\pi$
$283$	8.57726	+	4.95208i	0.509865	+	0.294371i	−0.222913	+	0.974838i	$0.571557\pi$
$284$	25.9488	+	1.15506i	1.53978	+	0.0685401i
$285$			12.3730i			0.732916i
$286$	−2.01991	+	11.9832i	−0.119440	+	0.708583i
$287$	0.148923			0.00879066
$288$	−6.61196	−	0.738356i	−0.389613	−	0.0435081i
$289$	−16.3974	+	28.4011i	−0.964551	+	1.67065i
$290$	−14.1844	−	0.315539i	−0.832936	−	0.0185291i
$291$		−	21.5115i		−	1.26102i
$292$	13.5722	−	21.2641i	0.794252	−	1.24439i
$293$	12.7181	−	7.34282i	0.743001	−	0.428972i	−0.0801583	−	0.996782i	$-0.525543\pi$
$293$	12.7181	−	7.34282i	0.743001	−	0.428972i	0.823160	+	0.567810i	$0.192209\pi$
$294$	12.7791	+	7.76197i	0.745290	+	0.452687i
$295$	−1.45668	−	2.52304i	−0.0848110	−	0.146897i
$296$	−2.35785	−	1.57982i	−0.137047	−	0.0918249i
$297$	−4.44147	+	7.69285i	−0.257720	+	0.446384i
$298$	11.7555	+	7.14023i	0.680975	+	0.413622i
$299$	11.7433	−	14.8731i	0.679134	−	0.860132i
$300$	3.62691	−	1.88413i	0.209400	−	0.108780i
$301$	−19.0578	−	11.0031i	−1.09848	−	0.634205i
$302$	−5.62630	−	10.2657i	−0.323757	−	0.590727i
$303$	−6.71508	−	11.6309i	−0.385771	−	0.668175i
$304$	19.8151	+	13.9250i	1.13648	+	0.798654i
$305$	−5.83253	−	10.1022i	−0.333969	−	0.578452i
$306$	11.7340	+	0.261028i	0.670787	+	0.0149220i
$307$			14.9995i			0.856064i	0.903764	+	0.428032i	$0.140793\pi$
$307$			14.9995i			0.856064i	−0.903764	+	0.428032i	$0.859207\pi$
$308$	14.0186	+	8.94758i	0.798782	+	0.509836i
$309$	−12.6378	−	7.29644i	−0.718939	−	0.415080i
$310$	−1.09196	+	0.598464i	−0.0620189	+	0.0339905i
$311$	14.9535			0.847933			0.423967	−	0.905678i	$-0.360637\pi$
$311$	14.9535			0.847933			0.423967	+	0.905678i	$0.360637\pi$
$312$	15.4589	+	13.9763i	0.875187	+	0.791254i
$313$	19.3552			1.09402			0.547009	−	0.837127i	$-0.315766\pi$
$313$	19.3552			1.09402			0.547009	+	0.837127i	$0.315766\pi$
$314$	17.9360	−	9.83008i	1.01218	−	0.554744i
$315$	3.55374	+	2.05175i	0.200231	+	0.115603i
$316$	11.8577	−	18.5780i	0.667049	−	1.04509i
$317$		−	3.01712i		−	0.169458i	−0.996404	−	0.0847292i	$-0.972997\pi$
$317$		−	3.01712i		−	0.169458i	0.996404	−	0.0847292i	$-0.0270025\pi$
$318$	−15.8721	−	0.353084i	−0.890066	−	0.0197999i
$319$	−11.9548	−	20.7064i	−0.669343	−	1.15934i
$320$	1.06444	−	7.92887i	0.0595041	−	0.443237i
$321$	−0.546814	−	0.947110i	−0.0305202	−	0.0528625i
$322$	−12.4643	−	22.7423i	−0.694606	−	1.26738i
$323$	−37.0010	−	21.3625i	−2.05879	−	1.18864i
$324$	10.2756	+	19.7804i	0.570869	+	1.09891i
$325$	−3.56784	−	0.520082i	−0.197908	−	0.0288490i
$326$	−12.1205	−	7.36196i	−0.671293	−	0.407741i
$327$	−16.0745	+	27.8419i	−0.888925	+	1.53966i
$328$	0.0671994	−	0.100294i	0.00371047	−	0.00553780i
$329$	0.668245	+	1.15743i	0.0368415	+	0.0638114i
$330$	5.88682	+	3.57564i	0.324059	+	0.196832i
$331$	−14.1812	+	8.18752i	−0.779470	+	0.450027i	−0.836242	−	0.548360i	$-0.815252\pi$
$331$	−14.1812	+	8.18752i	−0.779470	+	0.450027i	0.0567727	+	0.998387i	$0.481919\pi$
$332$	17.7016	+	11.2983i	0.971502	+	0.620077i
$333$		−	1.18016i		−	0.0646724i
$334$	12.2615	+	0.272762i	0.670917	+	0.0149249i
$335$	1.13740	−	1.97003i	0.0621427	−	0.107634i
$336$	25.8687	−	12.0092i	1.41125	−	0.655157i
$337$	−16.0409			−0.873806			−0.436903	−	0.899509i	$-0.643925\pi$
$337$	−16.0409			−0.873806			−0.436903	+	0.899509i	$0.643925\pi$
$338$	−3.86588	−	17.9737i	−0.210276	−	0.977642i
$339$			30.7922i			1.67240i
$340$	−0.627594	+	14.0991i	−0.0340361	+	0.764632i
$341$	−1.81730	−	1.04922i	−0.0984122	−	0.0568183i
$342$	−0.223968	+	10.0680i	−0.0121108	+	0.544417i
$343$	6.37257			0.344087
$344$	−16.0097	+	7.86973i	−0.863185	+	0.424308i
$345$	−5.37032	−	9.30167i	−0.289128	−	0.500785i
$346$	−8.39502	−	5.09911i	−0.451319	−	0.274130i
$347$	−4.67687	+	2.70019i	−0.251068	+	0.144954i	−0.620253	−	0.784402i	$-0.712970\pi$
$347$	−4.67687	+	2.70019i	−0.251068	+	0.144954i	0.369185	+	0.929356i	$0.379637\pi$
$348$	−40.9627	−	1.82337i	−2.19583	−	0.0977431i
$349$	0.784046	+	0.452669i	0.0419690	+	0.0242308i	0.520838	−	0.853656i	$-0.325620\pi$
$349$	0.784046	+	0.452669i	0.0419690	+	0.0242308i	−0.478869	+	0.877887i	$0.658953\pi$
$350$	−2.56157	+	4.21729i	−0.136921	+	0.225423i
$351$	1.93846	−	13.2982i	0.103468	−	0.709803i
$352$	12.3515	−	5.40348i	0.658338	−	0.288006i
$353$	−3.71403	+	6.43289i	−0.197678	+	0.342388i	−0.947775	−	0.318940i	$-0.896673\pi$
$353$	−3.71403	+	6.43289i	−0.197678	+	0.342388i	0.750097	+	0.661328i	$0.230007\pi$
$354$	−4.04662	−	7.38345i	−0.215075	−	0.392426i
$355$	−11.2473	+	6.49362i	−0.596944	+	0.344646i
$356$	3.33395	+	6.41777i	0.176699	+	0.340141i
$357$	−43.5729	+	25.1568i	−2.30612	+	1.33144i
$358$	−0.546710	+	24.5762i	−0.0288945	+	1.29889i
$359$	22.5231			1.18873			0.594363	−	0.804197i	$-0.297404\pi$
$359$	22.5231			1.18873			0.594363	+	0.804197i	$0.297404\pi$
$360$	2.98535	−	1.46748i	0.157342	−	0.0773429i
$361$	8.82955	−	15.2932i	0.464713	−	0.804907i
$362$	−11.0374	+	6.04921i	−0.580111	+	0.317939i
$363$		−	10.8719i		−	0.570625i
$364$	−24.7108	−	4.73275i	−1.29520	−	0.248063i
$365$			12.6132i			0.660203i
$366$	−16.2026	−	29.5633i	−0.846925	−	1.54530i
$367$	−0.130420	+	0.225895i	−0.00680788	+	0.0117916i	−0.869409	−	0.494093i	$-0.835500\pi$
$367$	−0.130420	+	0.225895i	−0.00680788	+	0.0117916i	0.862601	+	0.505884i	$0.168834\pi$
$368$	−20.9403	−	1.86793i	−1.09159	−	0.0973728i
$369$	0.0501996			0.00261328
$370$	1.41874	+	0.0315605i	0.0737567	+	0.00164075i
$371$	16.5990	−	9.58344i	0.861777	−	0.497547i
$372$	−3.19346	+	1.65896i	−0.165573	+	0.0860130i
$373$	−0.852861	+	0.492399i	−0.0441595	+	0.0254955i	−0.521917	−	0.852996i	$-0.674783\pi$
$373$	−0.852861	+	0.492399i	−0.0441595	+	0.0254955i	0.477758	+	0.878492i	$0.341450\pi$
$374$	−20.8566	+	11.4308i	−1.07847	+	0.591072i
$375$	−1.02178	+	1.76977i	−0.0527643	+	0.0913904i
$376$	1.08102	+	0.0722389i	0.0557494	+	0.00372544i
$377$	28.3896	+	22.4156i	1.46214	+	1.15446i
$378$	−15.7188	−	9.54753i	−0.808486	−	0.491072i
$379$	3.45822	+	1.99661i	0.177637	+	0.102559i	0.586182	−	0.810179i	$-0.300630\pi$
$379$	3.45822	+	1.99661i	0.177637	+	0.102559i	−0.408545	+	0.912738i	$0.633964\pi$
$380$	−12.0974	−	0.538490i	−0.620582	−	0.0276240i
$381$	2.93690	−	1.69562i	0.150462	−	0.0868691i
$382$	10.9178	−	17.9747i	0.558602	−	0.919666i
$383$	−6.63716	−	11.4959i	−0.339143	−	0.587413i	0.645129	−	0.764074i	$-0.276804\pi$
$383$	−6.63716	−	11.4959i	−0.339143	−	0.587413i	−0.984272	+	0.176661i	$0.943470\pi$
$384$	3.58511	−	22.8405i	0.182952	−	1.16557i
$385$	−8.31534			−0.423789
$386$	−17.1695	−	0.381945i	−0.873906	−	0.0194405i
$387$	−6.42408	−	3.70895i	−0.326555	−	0.188536i
$388$	21.0322	+	0.936205i	1.06775	+	0.0475286i
$389$			2.56323i			0.129961i	0.997887	+	0.0649804i	$0.0206985\pi$
$389$			2.56323i			0.129961i	−0.997887	+	0.0649804i	$0.979302\pi$
$390$	−10.2752	−	1.73200i	−0.520303	−	0.0877030i
$391$	37.0882			1.87563
$392$	−8.14519	+	12.1565i	−0.411394	+	0.613998i
$393$	−4.80829	+	8.32820i	−0.242546	+	0.420102i
$394$	−0.465194	+	20.9118i	−0.0234361	+	1.05352i
$395$			11.0198i			0.554468i
$396$	4.72543	+	3.01608i	0.237462	+	0.151564i
$397$	−1.49953	+	0.865755i	−0.0752594	+	0.0434510i	−0.537157	−	0.843482i	$-0.680502\pi$
$397$	−1.49953	+	0.865755i	−0.0752594	+	0.0434510i	0.461898	+	0.886933i	$0.347169\pi$
$398$	−17.4557	+	28.7386i	−0.874977	+	1.44054i
$399$	−21.5852	−	37.3866i	−1.08061	−	1.87167i
$400$	1.68430	+	3.62810i	0.0842152	+	0.181405i
$401$	−14.4435	+	25.0169i	−0.721273	+	1.24928i	0.239216	+	0.970966i	$0.423109\pi$
$401$	−14.4435	+	25.0169i	−0.721273	+	1.24928i	−0.960490	+	0.278316i	$0.910224\pi$
$402$	3.41291	−	5.61892i	0.170221	−	0.280246i
$403$	3.14145	+	0.457927i	0.156487	+	0.0228110i
$404$	11.6640	−	6.05928i	0.580304	−	0.301460i
$405$	−9.65193	−	5.57255i	−0.479608	−	0.276902i
$406$	43.4102	−	23.7917i	2.15441	−	1.18076i
$407$	1.19574	+	2.07108i	0.0592705	+	0.102659i
$408$	−2.71952	+	40.6963i	−0.134636	+	2.01477i
$409$	18.2807	+	31.6631i	0.903924	+	1.56564i	0.822355	+	0.568974i	$0.192660\pi$
$409$	18.2807	+	31.6631i	0.903924	+	1.56564i	0.0815684	+	0.996668i	$0.474007\pi$
$410$	−0.00134247	+	0.0603478i	−6.62996e−5	+	0.00298036i
$411$		−	37.8414i		−	1.86658i
$412$	7.68388	−	12.0387i	0.378558	−	0.593103i
$413$	8.80304	+	5.08244i	0.433169	+	0.250090i
$414$	−4.20149	−	7.66604i	−0.206492	−	0.376765i
$415$	−10.5000			−0.515425
$416$	−14.3377	+	14.5062i	−0.702965	+	0.711225i
$417$	−43.6953			−2.13977
$418$	−9.80788	−	17.8954i	−0.479719	−	0.875295i
$419$	−5.61460	−	3.24159i	−0.274291	−	0.158362i	0.356545	−	0.934278i	$-0.383955\pi$
$419$	−5.61460	−	3.24159i	−0.274291	−	0.158362i	−0.630836	+	0.775916i	$0.717288\pi$
$420$	−7.67220	+	12.0204i	−0.374365	+	0.586534i
$421$			36.8759i			1.79722i	0.438746	+	0.898611i	$0.355423\pi$
$421$			36.8759i			1.79722i	−0.438746	+	0.898611i	$0.644577\pi$
$422$	0.497568	−	22.3672i	0.0242212	−	1.08882i
$423$	0.225254	+	0.390152i	0.0109522	+	0.0189698i
$424$	1.03599	−	15.5031i	0.0503122	−	0.752899i
$425$	−3.52827	−	6.11114i	−0.171146	−	0.296434i
$426$	−32.9142	+	18.0391i	−1.59470	+	0.873999i
$427$	35.2473	+	20.3500i	1.70574	+	0.984808i
$428$	0.949807	−	0.493412i	0.0459106	−	0.0238500i
$429$	−6.49465	−	16.3150i	−0.313565	−	0.787695i
$430$	4.63053	−	7.62357i	0.223304	−	0.367641i
$431$	−1.99546	+	3.45625i	−0.0961181	+	0.166481i	−0.910075	−	0.414444i	$-0.863976\pi$
$431$	−1.99546	+	3.45625i	−0.0961181	+	0.166481i	0.813957	+	0.580926i	$0.197309\pi$
$432$	−13.5227	+	6.27778i	−0.650613	+	0.302040i
$433$	−5.08236	−	8.80290i	−0.244242	−	0.423040i	0.717676	−	0.696377i	$-0.245206\pi$
$433$	−5.08236	−	8.80290i	−0.244242	−	0.423040i	−0.961918	+	0.273337i	$0.911873\pi$
$434$	2.25543	−	3.71328i	0.108264	−	0.178243i
$435$	17.7549	−	10.2508i	0.851284	−	0.491489i
$436$	−26.5220	−	16.9281i	−1.27017	−	0.810710i
$437$			31.8226i			1.52228i
$438$	−0.810698	+	36.4433i	−0.0387366	+	1.74133i
$439$	3.70025	−	6.40901i	0.176603	−	0.305886i	−0.764112	−	0.645084i	$-0.776822\pi$
$439$	3.70025	−	6.40901i	0.176603	−	0.305886i	0.940715	+	0.339198i	$0.110156\pi$
$440$	−3.75217	+	5.60005i	−0.178878	+	0.266972i
$441$	−6.08465			−0.289745
$442$	22.9199	−	27.7370i	1.09019	−	1.31931i
$443$		−	27.0150i		−	1.28352i	−0.766905	−	0.641761i	$-0.778204\pi$
$443$		−	27.0150i		−	1.28352i	0.766905	−	0.641761i	$-0.221796\pi$
$444$	4.09714	+	0.182376i	0.194441	+	0.00865517i
$445$	−3.13158	−	1.80802i	−0.148451	−	0.0857083i
$446$	−7.42665	−	0.165209i	−0.351662	−	0.00782289i
$447$	−19.8747			−0.940042
$448$	10.6158	+	25.8150i	0.501551	+	1.21964i
$449$	8.83061	+	15.2951i	0.416742	+	0.721818i	0.995610	−	0.0936032i	$-0.0298385\pi$
$449$	8.83061	+	15.2951i	0.416742	+	0.721818i	−0.578868	+	0.815422i	$0.696505\pi$
$450$	−0.863461	+	1.42158i	−0.0407040	+	0.0670138i
$451$	−0.0880958	+	0.0508621i	−0.00414827	+	0.00239501i
$452$	−30.1062	−	1.34012i	−1.41607	−	0.0630337i
$453$	14.6496	+	8.45796i	0.688299	+	0.397389i
$454$	−11.5405	−	7.00968i	−0.541623	−	0.328980i
$455$	11.6880	−	4.65273i	0.547940	−	0.218123i
$456$	−34.9184	−	2.33341i	−1.63520	−	0.109272i
$457$	−16.3582	+	28.3333i	−0.765205	+	1.32537i	0.174933	+	0.984580i	$0.444029\pi$
$457$	−16.3582	+	28.3333i	−0.765205	+	1.32537i	−0.940138	+	0.340794i	$0.889304\pi$
$458$	−10.5712	+	5.79370i	−0.493959	+	0.270722i
$459$	22.7776	−	13.1506i	1.06317	−	0.613820i
$460$	9.32815	−	4.84585i	0.434927	−	0.225939i
$461$	29.7478	−	17.1749i	1.38549	−	0.799914i	0.392689	−	0.919671i	$-0.371545\pi$
$461$	29.7478	−	17.1749i	1.38549	−	0.799914i	0.992803	+	0.119757i	$0.0382115\pi$
$462$	−24.0255	−	0.534460i	−1.11777	−	0.0248653i
$463$	−25.0290			−1.16320			−0.581599	−	0.813476i	$-0.697573\pi$
$463$	−25.0290			−1.16320			−0.581599	+	0.813476i	$0.697573\pi$
$464$	3.56550	−	39.9707i	0.165524	−	1.85559i
$465$	0.899664	−	1.55826i	0.0417209	−	0.0722627i
$466$	−3.82287	−	6.97521i	−0.177091	−	0.323120i
$467$		−	13.8070i		−	0.638912i	−0.947601	−	0.319456i	$-0.896500\pi$
$467$		−	13.8070i		−	0.638912i	0.947601	−	0.319456i	$-0.103500\pi$
$468$	−8.32962	−	1.59533i	−0.385037	−	0.0737442i
$469$			7.93691i			0.366492i
$470$	−0.475048	+	0.260357i	−0.0219123	+	0.0120094i
$471$	−14.7775	+	25.5953i	−0.680909	+	1.17937i
$472$	7.39506	−	3.63512i	0.340385	−	0.167320i
$473$	15.0316			0.691154
$474$	−0.708289	+	31.8397i	−0.0325328	+	1.46244i
$475$	5.24350	−	3.02734i	0.240588	−	0.138904i
$476$	−22.7000	−	43.6970i	−1.04045	−	2.00285i
$477$	5.59525	−	3.23042i	0.256189	−	0.147911i
$478$	−0.395846	−	0.722260i	−0.0181056	−	0.0330354i
$479$	−17.9705	+	31.1258i	−0.821094	+	1.42218i	0.0837750	+	0.996485i	$0.473302\pi$
$479$	−17.9705	+	31.1258i	−0.821094	+	1.42218i	−0.904869	+	0.425691i	$0.860031\pi$
$480$	4.63328	+	10.5909i	0.211479	+	0.483408i
$481$	−2.83956	−	2.24203i	−0.129473	−	0.102228i
$482$	−2.67896	+	4.41056i	−0.122023	+	0.200895i
$483$	32.4541	+	18.7374i	1.47671	+	0.852580i
$484$	10.6296	+	0.473157i	0.483165	+	0.0215071i
$485$	−9.11622	+	5.26325i	−0.413946	+	0.238992i
$486$	−14.0137	−	8.51190i	−0.635676	−	0.386108i
$487$	18.0009	+	31.1784i	0.815697	+	1.41283i	0.908826	+	0.417175i	$0.136980\pi$
$487$	18.0009	+	31.1784i	0.815697	+	1.41283i	−0.0931288	+	0.995654i	$0.529687\pi$
$488$	29.6098	−	14.5550i	1.34037	−	0.658874i
$489$	20.4919			0.926676
$490$	0.162719	−	7.31471i	0.00735090	−	0.330445i
$491$	9.64168	+	5.56663i	0.435123	+	0.251218i	0.701527	−	0.712643i	$-0.252502\pi$
$491$	9.64168	+	5.56663i	0.435123	+	0.251218i	−0.266404	+	0.963862i	$0.585835\pi$
$492$	−0.00775758	+	0.174277i	−0.000349739	+	0.00785700i
$493$			70.7937i			3.18839i
$494$	23.7990	+	19.6658i	1.07077	+	0.884807i
$495$	−2.80296			−0.125984
$496$	−1.48301	−	3.19451i	−0.0665893	−	0.143438i
$497$	22.6567	−	39.2425i	1.01629	−	1.76027i
$498$	−30.3377	−	0.674877i	−1.35946	−	0.0302419i
$499$			6.16997i			0.276206i	0.990418	+	0.138103i	$0.0441004\pi$
$499$			6.16997i			0.276206i	−0.990418	+	0.138103i	$0.955900\pi$
$500$	−1.68587	−	1.07603i	−0.0753943	−	0.0481217i
$501$	−15.3480	+	8.86115i	−0.685697	+	0.395887i
$502$	−11.1748	−	6.78755i	−0.498757	−	0.302943i
$503$	−12.6989	−	21.9952i	−0.566218	−	0.980718i	−0.996935	−	0.0782314i	$-0.975073\pi$
$503$	−12.6989	−	21.9952i	−0.566218	−	0.980718i	0.430717	−	0.902487i	$-0.358261\pi$
$504$	−6.46051	+	9.64219i	−0.287774	+	0.429497i
$505$	−3.28598	+	5.69149i	−0.146224	+	0.253268i
$506$	15.1405	+	9.19628i	0.673076	+	0.408825i
$507$	18.2576	+	19.2982i	0.810850	+	0.857063i
$508$	1.53002	+	2.94526i	0.0678837	+	0.130675i
$509$	−20.3510	−	11.7497i	−0.902043	−	0.520795i	−0.0241803	−	0.999708i	$-0.507698\pi$
$509$	−20.3510	−	11.7497i	−0.902043	−	0.520795i	−0.877862	+	0.478913i	$0.841031\pi$
$510$	−9.80146	−	17.8837i	−0.434016	−	0.791905i
$511$	−22.0041	−	38.1121i	−0.973402	−	1.68598i
$512$	22.1756	+	4.49928i	0.980032	+	0.198842i
$513$	11.2836	+	19.5437i	0.498182	+	0.862876i
$514$	−16.0463	−	0.356957i	−0.707771	−	0.0157447i
$515$			7.14093i			0.314667i
$516$	13.8690	−	21.7292i	0.610550	−	0.956575i
$517$	−0.790603	−	0.456455i	−0.0347707	−	0.0200749i
$518$	−4.34194	+	2.37967i	−0.190774	+	0.104557i
$519$	14.1933			0.623017
$520$	2.14059	−	9.97085i	0.0938713	−	0.437251i
$521$	36.9801			1.62013			0.810063	−	0.586343i	$-0.199433\pi$
$521$	36.9801			1.62013			0.810063	+	0.586343i	$0.199433\pi$
$522$	14.6329	−	8.01978i	0.640464	−	0.351016i
$523$	22.3786	+	12.9203i	0.978549	+	0.564966i	0.901832	−	0.432087i	$-0.142223\pi$
$523$	22.3786	+	12.9203i	0.978549	+	0.564966i	0.0767174	+	0.997053i	$0.475556\pi$
$524$	−7.93339	−	5.06361i	−0.346572	−	0.221205i
$525$		−	7.13008i		−	0.311182i
$526$	12.4464	+	0.276876i	0.542687	+	0.0120723i
$527$	3.10661	+	5.38080i	0.135326	+	0.234391i
$528$	−11.2011	+	15.9391i	−0.487466	+	0.693659i
$529$	−2.31207	−	4.00462i	−0.100525	−	0.174114i
$530$	3.73384	+	6.81276i	0.162188	+	0.295927i
$531$	2.96736	+	1.71321i	0.128772	+	0.0743468i
$532$	37.4930	−	19.4771i	1.62553	−	0.844441i
$533$	0.0953675	−	0.120784i	0.00413082	−	0.00523174i
$534$	−8.93188	−	5.42520i	−0.386520	−	0.234771i
$535$	−0.267580	+	0.463463i	−0.0115685	+	0.0200372i
$536$	5.34519	+	3.58141i	0.230877	+	0.154694i
$537$	−17.7608	−	30.7627i	−0.766437	−	1.32751i
$538$	−25.2183	−	15.3175i	−1.08724	−	0.660385i
$539$	10.6780	−	6.16496i	0.459935	−	0.265544i
$540$	4.01062	−	6.28361i	0.172589	−	0.270403i
$541$		−	29.8178i		−	1.28197i	−0.767555	−	0.640983i	$-0.778527\pi$
$541$		−	29.8178i		−	1.28197i	0.767555	−	0.640983i	$-0.221473\pi$
$542$	−26.5567	−	0.590766i	−1.14071	−	0.0253756i
$543$	9.09371	−	15.7508i	0.390248	−	0.675930i
$544$	−39.6712	−	4.43008i	−1.70089	−	0.189938i
$545$	15.7320			0.673884
$546$	34.0691	−	12.6919i	1.45802	−	0.543164i
$547$		−	14.5745i		−	0.623161i	−0.950220	−	0.311581i	$-0.899142\pi$
$547$		−	14.5745i		−	0.623161i	0.950220	−	0.311581i	$-0.100858\pi$
$548$	36.9983	+	1.64690i	1.58049	+	0.0703523i
$549$	11.8813	+	6.85967i	0.507081	+	0.292763i
$550$	0.0749584	−	3.36960i	0.00319624	−	0.143680i
$551$	−60.7427			−2.58772
$552$	27.2633	−	13.4016i	1.16040	−	0.570409i
$553$	−19.2245	−	33.2977i	−0.817507	−	1.41596i
$554$	−13.5553	−	8.23343i	−0.575908	−	0.349805i
$555$	−1.77587	+	1.02530i	−0.0753814	+	0.0435215i
$556$	1.90168	−	42.7218i	0.0806490	−	1.81181i
$557$	10.6265	+	6.13521i	0.450259	+	0.259957i	0.707940	−	0.706273i	$-0.249625\pi$
$557$	10.6265	+	6.13521i	0.450259	+	0.259957i	−0.257681	+	0.966230i	$0.582958\pi$
$558$	0.760270	−	1.25169i	0.0321848	−	0.0529881i
$559$	−21.1283	+	8.41072i	−0.893631	+	0.355736i
$560$	−11.4187	−	8.02441i	−0.482526	−	0.339093i
$561$	17.1838	−	29.7632i	0.725499	−	1.25660i
$562$	14.4439	+	26.3543i	0.609278	+	1.11169i
$563$	−32.8090	+	18.9423i	−1.38274	+	0.798323i	−0.992483	−	0.122384i	$-0.960946\pi$
$563$	−32.8090	+	18.9423i	−1.38274	+	0.798323i	−0.390254	+	0.920707i	$0.627613\pi$
$564$	−1.38929	+	0.721719i	−0.0584998	+	0.0303898i
$565$	13.0493	−	7.53399i	0.548986	−	0.316957i
$566$	0.311507	−	14.0031i	0.0130936	−	0.588596i
$567$	38.8859			1.63306
$568$	−16.2048	−	32.9659i	−0.679937	−	1.38322i
$569$	−9.35584	+	16.2048i	−0.392217	+	0.679340i	−0.992742	−	0.120266i	$-0.961625\pi$
$569$	−9.35584	+	16.2048i	−0.392217	+	0.679340i	0.600524	+	0.799607i	$0.294959\pi$
$570$	15.3447	−	8.40988i	0.642717	−	0.352251i
$571$			33.2301i			1.39063i	0.718703	+	0.695317i	$0.244736\pi$
$571$			33.2301i			1.39063i	−0.718703	+	0.695317i	$0.755264\pi$
$572$	16.2341	−	5.63990i	0.678784	−	0.235816i
$573$			30.3895i			1.26954i
$574$	−0.101222	−	0.184690i	−0.00422493	−	0.00770880i
$575$	−2.62793	+	4.55171i	−0.109592	+	0.189820i
$576$	3.57842	+	8.70179i	0.149101	+	0.362575i
$577$	12.6607			0.527070			0.263535	−	0.964650i	$-0.415112\pi$
$577$	12.6607			0.527070			0.263535	+	0.964650i	$0.415112\pi$
$578$	46.3673	+	1.03146i	1.92862	+	0.0429032i
$579$	21.4915	−	12.4081i	0.893157	−	0.515665i
$580$	9.24972	+	17.8055i	0.384074	+	0.739333i
$581$	31.7270	−	18.3176i	1.31626	−	0.759941i
$582$	−26.6778	+	14.6212i	−1.10583	+	0.606068i
$583$	−6.54611	+	11.3382i	−0.271112	+	0.469580i
$584$	−35.5960	−	2.37869i	−1.47297	−	0.0984309i
$585$	3.93982	−	1.56836i	0.162891	−	0.0648436i
$586$	−17.7508	−	10.7818i	−0.733277	−	0.445390i
$587$	−30.0961	−	17.3760i	−1.24220	−	0.717184i	−0.272658	−	0.962111i	$-0.587903\pi$
$587$	−30.0961	−	17.3760i	−1.24220	−	0.717184i	−0.969542	+	0.244927i	$0.921236\pi$
$588$	0.940290	−	21.1240i	0.0387769	−	0.871137i
$589$	−4.61685	+	2.66554i	−0.190234	+	0.109832i
$590$	−2.13890	+	3.52142i	−0.0880570	+	0.144974i
$591$	−15.1126	−	26.1759i	−0.621651	−	1.07673i
$592$	−0.356625	+	3.99791i	−0.0146572	+	0.164313i
$593$	−18.4953			−0.759513			−0.379756	−	0.925086i	$-0.623992\pi$
$593$	−18.4953			−0.759513			−0.379756	+	0.925086i	$0.623992\pi$
$594$	12.5593	+	0.279387i	0.515313	+	0.0114634i
$595$	21.3222	+	12.3104i	0.874123	+	0.504675i
$596$	0.864972	−	19.4319i	0.0354307	−	0.795962i
$597$		−	48.5878i		−	1.98856i
$598$	−26.4270	−	4.45457i	−1.08068	−	0.182161i
$599$	17.5151			0.715649			0.357825	−	0.933789i	$-0.383519\pi$
$599$	17.5151			0.715649			0.357825	+	0.933789i	$0.383519\pi$
$600$	−4.80183	−	3.21735i	−0.196034	−	0.131348i
$601$	−14.5946	+	25.2786i	−0.595326	+	1.03114i	0.398174	+	0.917310i	$0.369644\pi$
$601$	−14.5946	+	25.2786i	−0.595326	+	1.03114i	−0.993501	+	0.113826i	$0.963689\pi$
$602$	−0.692138	+	31.1136i	−0.0282094	+	1.26810i
$603$			2.67540i			0.108951i
$604$	−8.90708	+	13.9551i	−0.362424	+	0.567826i
$605$	−4.60732	+	2.66004i	−0.187314	+	0.108146i
$606$	−9.86002	+	16.2332i	−0.400536	+	0.659430i
$607$	7.67574	+	13.2948i	0.311549	+	0.539618i	0.978698	−	0.205306i	$-0.0658189\pi$
$607$	7.67574	+	13.2948i	0.311549	+	0.539618i	−0.667149	+	0.744924i	$0.732486\pi$
$608$	3.80111	−	34.0388i	0.154155	−	1.38046i
$609$	−35.7658	+	61.9481i	−1.44930	+	2.51026i
$610$	−8.56413	+	14.0997i	−0.346752	+	0.570882i
$611$	1.36667	+	0.199218i	0.0552894	+	0.00805950i
$612$	−7.65179	−	14.7295i	−0.309305	−	0.595406i
$613$	−23.1875	−	13.3873i	−0.936533	−	0.540708i	−0.0476615	−	0.998864i	$-0.515177\pi$
$613$	−23.1875	−	13.3873i	−0.936533	−	0.540708i	−0.888872	+	0.458156i	$0.848510\pi$
$614$	18.6018	−	10.1950i	0.750709	−	0.411438i
$615$	−0.0436123	−	0.0755388i	−0.00175862	−	0.00304602i
$616$	1.56817	−	23.4670i	0.0631835	−	0.945512i
$617$	−10.6475	−	18.4420i	−0.428651	−	0.742446i	0.568102	−	0.822958i	$-0.307678\pi$
$617$	−10.6475	−	18.4420i	−0.428651	−	0.742446i	−0.996754	+	0.0805120i	$0.974344\pi$
$618$	−0.458976	+	20.6323i	−0.0184627	+	0.829954i
$619$			15.5205i			0.623820i	0.950112	+	0.311910i	$0.100969\pi$
$619$			15.5205i			0.623820i	−0.950112	+	0.311910i	$0.899031\pi$
$620$	1.48439	+	0.947437i	0.0596146	+	0.0380500i
$621$	−16.9653	−	9.79490i	−0.680792	−	0.393056i
$622$	−10.1638	−	18.5448i	−0.407530	−	0.743579i
$623$	12.6166			0.505473
$624$	6.82569	−	28.6712i	0.273246	−	1.14777i
$625$	1.00000			0.0400000
$626$	−13.1556	−	24.0037i	−0.525803	−	0.959379i
$627$	25.5375	+	14.7441i	1.01987	+	0.588822i
$628$	−24.3819	−	15.5622i	−0.972944	−	0.620998i
$629$		−	7.08086i		−	0.282333i
$630$	0.129064	−	5.80180i	0.00514202	−	0.231149i
$631$	20.5741	+	35.6355i	0.819044	+	1.41863i	0.906388	+	0.422447i	$0.138829\pi$
$631$	20.5741	+	35.6355i	0.819044	+	1.41863i	−0.0873440	+	0.996178i	$0.527838\pi$
$632$	−31.0995	−	2.07821i	−1.23707	−	0.0826668i
$633$	16.1644	+	27.9975i	0.642476	+	1.11280i
$634$	−3.74173	+	2.05072i	−0.148603	+	0.0814444i
$635$	−1.43715	−	0.829740i	−0.0570317	−	0.0329272i
$636$	10.3503	+	19.9241i	0.410417	+	0.790043i
$637$	−11.5594	+	14.6401i	−0.458001	+	0.580064i
$638$	−17.5538	+	28.9000i	−0.694961	+	1.14416i
$639$	7.63718	−	13.2280i	0.302122	−	0.523291i
$640$	−10.5566	+	4.06912i	−0.417287	+	0.160846i
$641$	3.01464	+	5.22151i	0.119071	+	0.206237i	0.919400	−	0.393324i	$-0.128675\pi$
$641$	3.01464	+	5.22151i	0.119071	+	0.206237i	−0.800329	+	0.599561i	$0.795342\pi$
$642$	−0.802910	+	1.32189i	−0.0316883	+	0.0521707i
$643$	−19.5618	+	11.2940i	−0.771442	+	0.445392i	−0.833389	−	0.552687i	$-0.813602\pi$
$643$	−19.5618	+	11.2940i	−0.771442	+	0.445392i	0.0619470	+	0.998079i	$0.480269\pi$
$644$	−19.7323	+	30.9155i	−0.777564	+	1.21824i
$645$			12.8890i			0.507505i
$646$	−1.34379	+	60.4074i	−0.0528708	+	2.37670i
$647$	8.37197	−	14.5007i	0.329136	−	0.570081i	−0.653205	−	0.757182i	$-0.726576\pi$
$647$	8.37197	−	14.5007i	0.329136	−	0.570081i	0.982341	+	0.187101i	$0.0599092\pi$
$648$	17.5467	−	26.1881i	0.689300	−	1.02877i
$649$	−6.94327			−0.272547
$650$	1.78005	+	4.77822i	0.0698194	+	0.187417i
$651$			6.27797i			0.246053i
$652$	−0.891833	+	20.0353i	−0.0349269	+	0.784644i
$653$	−6.93196	−	4.00217i	−0.271268	−	0.156617i	0.358196	−	0.933647i	$-0.383392\pi$
$653$	−6.93196	−	4.00217i	−0.271268	−	0.156617i	−0.629464	+	0.777030i	$0.716725\pi$
$654$	45.4544	+	1.01116i	1.77741	+	0.0395393i
$655$	4.70582			0.183871
$656$	−0.170056	−	0.0151695i	−0.00663958	−	0.000592269i
$657$	−7.41720	−	12.8470i	−0.289373	−	0.501208i
$658$	0.981211	−	1.61544i	0.0382516	−	0.0629763i
$659$	−36.4531	+	21.0462i	−1.42001	+	0.819844i	−0.996299	−	0.0859530i	$-0.972607\pi$
$659$	−36.4531	+	21.0462i	−1.42001	+	0.819844i	−0.423712	+	0.905797i	$0.639273\pi$
$660$	0.433155	−	9.73099i	0.0168606	−	0.378778i
$661$	−4.19530	−	2.42216i	−0.163178	−	0.0942110i	0.416187	−	0.909279i	$-0.363366\pi$
$661$	−4.19530	−	2.42216i	−0.163178	−	0.0942110i	−0.579365	+	0.815068i	$0.696700\pi$
$662$	19.7928	+	12.0221i	0.769268	+	0.467251i
$663$	−7.49980	+	51.4498i	−0.291268	+	1.99814i
$664$	1.98017	−	29.6324i	0.0768457	−	1.14996i
$665$	−10.5626	+	18.2949i	−0.409599	+	0.709446i
$666$	−1.46360	+	0.802147i	−0.0567132	+	0.0310826i
$667$	45.6644	−	26.3644i	1.76813	−	1.02083i
$668$	−7.99576	−	15.3917i	−0.309365	−	0.595521i
$669$	9.29612	−	5.36712i	0.359409	−	0.207505i
$670$	−3.21625	−	0.0715471i	−0.124255	−	0.00276411i
$671$	−27.8008			−1.07324
$672$	−32.4762	−	23.9189i	−1.25280	−	0.922691i
$673$	7.73165	−	13.3916i	0.298033	−	0.516209i	−0.677653	−	0.735382i	$-0.737003\pi$
$673$	7.73165	−	13.3916i	0.298033	−	0.516209i	0.975686	+	0.219173i	$0.0703361\pi$
$674$	10.9029	+	19.8935i	0.419965	+	0.766268i
$675$			3.72722i			0.143461i
$676$	−19.6628	+	17.0110i	−0.756263	+	0.654268i
$677$			8.96039i			0.344376i	0.985064	+	0.172188i	$0.0550836\pi$
$677$			8.96039i			0.344376i	−0.985064	+	0.172188i	$0.944916\pi$
$678$	38.1875	−	20.9293i	1.46658	−	0.803784i
$679$	18.3638	−	31.8071i	0.704739	−	1.22064i
$680$	17.9118	−	8.80476i	0.686888	−	0.337647i
$681$	19.5113			0.747676
$682$	−0.0660002	+	2.96690i	−0.00252728	+	0.113609i
$683$	−10.8867	+	6.28541i	−0.416566	+	0.240505i	−0.693607	−	0.720353i	$-0.743980\pi$
$683$	−10.8867	+	6.28541i	−0.416566	+	0.240505i	0.277041	+	0.960858i	$0.410646\pi$
$684$	12.6383	−	6.56542i	0.483237	−	0.251035i
$685$	−16.0366	+	9.25873i	−0.612727	+	0.353758i
$686$	−4.33140	−	7.90306i	−0.165373	−	0.301740i
$687$	8.70961	−	15.0855i	0.332292	−	0.575547i
$688$	20.6415	+	14.5057i	0.786949	+	0.553025i
$689$	2.85703	−	19.5997i	0.108844	−	0.746687i
$690$	−7.88546	+	12.9824i	−0.300194	+	0.494231i
$691$	−1.93692	−	1.11828i	−0.0736840	−	0.0425415i	0.462705	−	0.886512i	$-0.346879\pi$
$691$	−1.93692	−	1.11828i	−0.0736840	−	0.0425415i	−0.536389	+	0.843971i	$0.680212\pi$
$692$	−0.617710	+	13.8771i	−0.0234818	+	0.527527i
$693$	8.46948	−	4.88986i	0.321729	−	0.185750i
$694$	6.52753	+	3.96480i	0.247782	+	0.150502i
$695$	10.6910	+	18.5174i	0.405534	+	0.702405i
$696$	25.5808	+	52.0400i	0.969638	+	1.97257i
$697$	0.301193			0.0114085
$698$	0.0284748	−	1.28003i	0.00107779	−	0.0484497i
$699$	9.95389	+	5.74688i	0.376491	+	0.217367i
$700$	6.97122	+	0.310310i	0.263487	+	0.0117286i
$701$		−	36.5121i		−	1.37904i	−0.724265	−	0.689522i	$-0.757821\pi$
$701$		−	36.5121i		−	1.37904i	0.724265	−	0.689522i	$-0.242179\pi$
$702$	−17.8095	+	6.63465i	−0.672177	+	0.250409i
$703$	6.07555			0.229144
$704$	−15.0965	−	11.6452i	−0.568969	−	0.438896i
$705$	0.391393	−	0.677912i	0.0147407	−	0.0255316i
$706$	10.5023	+	0.233628i	0.395258	+	0.00879270i
$707$		−	22.9300i		−	0.862372i
$708$	−6.40626	+	10.0370i	−0.240762	+	0.377212i
$709$	23.7712	−	13.7243i	0.892745	−	0.515426i	0.0179054	−	0.999840i	$-0.494300\pi$
$709$	23.7712	−	13.7243i	0.892745	−	0.515426i	0.874839	+	0.484413i	$0.160967\pi$
$710$	15.6979	+	9.53485i	0.589131	+	0.357836i
$711$	−6.48025	−	11.2241i	−0.243028	−	0.420937i
$712$	5.69305	−	8.49677i	0.213356	−	0.318430i
$713$	2.31387	−	4.00774i	0.0866551	−	0.150091i
$714$	60.8150	+	36.9388i	2.27594	+	1.38240i
$715$	−5.32498	+	6.74415i	−0.199143	+	0.252217i
$716$	30.8503	−	16.0263i	1.15293	−	0.598931i
$717$	1.03069	+	0.595071i	0.0384920	+	0.0222233i
$718$	−15.3088	−	27.9325i	−0.571320	−	1.04243i
$719$	2.55537	+	4.42604i	0.0952993	+	0.165063i	0.909734	−	0.415193i	$-0.136286\pi$
$719$	2.55537	+	4.42604i	0.0952993	+	0.165063i	−0.814434	+	0.580256i	$0.802953\pi$
$720$	−3.84904	−	2.70490i	−0.143445	−	0.100806i
$721$	−12.4576	−	21.5772i	−0.463945	−	0.803576i
$722$	−24.9676	−	0.555416i	−0.929197	−	0.0206704i
$723$		−	7.45684i		−	0.277323i
$724$	15.0041	+	9.57659i	0.557622	+	0.355911i
$725$	−8.68828	−	5.01618i	−0.322674	−	0.186296i
$726$	−13.4829	+	7.38953i	−0.500399	+	0.274251i
$727$	−41.6588			−1.54504			−0.772519	−	0.634992i	$-0.781003\pi$
$727$	−41.6588			−1.54504			−0.772519	+	0.634992i	$0.781003\pi$
$728$	10.9264	+	33.8624i	0.404960	+	1.25502i
$729$	−9.74253			−0.360834
$730$	15.6424	−	8.57308i	0.578953	−	0.317304i
$731$	−38.5440	−	22.2534i	−1.42560	−	0.823071i
$732$	−25.6506	+	40.1880i	−0.948075	+	1.48539i
$733$			9.05871i			0.334591i	0.985907	+	0.167296i	$0.0535034\pi$
$733$			9.05871i			0.334591i	−0.985907	+	0.167296i	$0.946497\pi$
$734$	0.368793	+	0.00820398i	0.0136124	+	0.000302814i
$735$	5.28622	+	9.15600i	0.194985	+	0.337724i
$736$	11.9164	+	27.2391i	0.439246	+	1.00405i
$737$	−2.71071	−	4.69509i	−0.0998504	−	0.172946i
$738$	−0.0341203	−	0.0622559i	−0.00125599	−	0.00229167i
$739$	23.1813	+	13.3837i	0.852737	+	0.492328i	0.861573	−	0.507633i	$-0.169479\pi$
$739$	23.1813	+	13.3837i	0.852737	+	0.492328i	−0.00883653	+	0.999961i	$0.502813\pi$
$740$	−0.925167	−	1.78092i	−0.0340098	−	0.0654681i
$741$	−44.1451	−	6.43500i	−1.62171	−	0.236396i
$742$	−23.1673	−	14.0717i	−0.850498	−	0.516590i
$743$	−9.53612	+	16.5170i	−0.349846	+	0.605951i	−0.986222	−	0.165428i	$-0.947099\pi$
$743$	−9.53612	+	16.5170i	−0.349846	+	0.605951i	0.636376	+	0.771379i	$0.280433\pi$
$744$	4.22796	+	2.83284i	0.155005	+	0.103857i
$745$	4.86279	+	8.42259i	0.178159	+	0.308580i
$746$	1.19034	+	0.723010i	0.0435815	+	0.0264713i
$747$	10.6946	−	6.17455i	0.391296	−	0.225915i
$748$	28.3522	+	18.0962i	1.03666	+	0.661664i
$749$		−	1.86721i		−	0.0682263i
$750$	2.88930	+	0.0642740i	0.105502	+	0.00234695i
$751$	−7.10450	+	12.3053i	−0.259247	+	0.449029i	−0.966040	−	0.258391i	$-0.916808\pi$
$751$	−7.10450	+	12.3053i	−0.259247	+	0.449029i	0.706794	+	0.707420i	$0.250141\pi$
$752$	−0.645175	−	1.38975i	−0.0235271	−	0.0506789i
$753$	18.8930			0.688501
$754$	8.50284	−	50.4436i	0.309655	−	1.83705i
$755$		−	8.27770i		−	0.301256i
$756$	−1.15659	+	25.9833i	−0.0420649	+	0.945004i
$757$	2.19423	+	1.26684i	0.0797508	+	0.0460441i	0.539345	−	0.842085i	$-0.318672\pi$
$757$	2.19423	+	1.26684i	0.0797508	+	0.0460441i	−0.459594	+	0.888129i	$0.652005\pi$
$758$	0.125595	−	5.64586i	0.00456181	−	0.205067i
$759$	−25.5977			−0.929138
$760$	7.55469	+	15.3688i	0.274037	+	0.557484i
$761$	−10.2838	−	17.8120i	−0.372786	−	0.645685i	0.617207	−	0.786801i	$-0.288264\pi$
$761$	−10.2838	−	17.8120i	−0.372786	−	0.645685i	−0.989993	+	0.141116i	$0.954931\pi$
$762$	−4.09904	−	2.48974i	−0.148493	−	0.0901939i
$763$	−47.5360	+	27.4449i	−1.72092	+	0.993573i
$764$	−29.7124	−	1.32259i	−1.07496	−	0.0478496i
$765$	7.18735	+	4.14962i	0.259859	+	0.150030i
$766$	−9.74561	+	16.0449i	−0.352123	+	0.579725i
$767$	9.75940	−	3.88501i	0.352392	−	0.140280i
$768$	−30.7628	+	11.0784i	−1.11006	+	0.399757i
$769$	−0.601911	+	1.04254i	−0.0217055	+	0.0375950i	−0.876674	−	0.481085i	$-0.840243\pi$
$769$	−0.601911	+	1.04254i	−0.0217055	+	0.0375950i	0.854969	+	0.518680i	$0.173576\pi$
$770$	5.65188	+	10.3124i	0.203680	+	0.371634i
$771$	20.0855	−	11.5964i	0.723363	−	0.417634i
$772$	11.1963	+	21.5527i	0.402965	+	0.775699i
$773$	17.9592	−	10.3687i	0.645947	−	0.372938i	−0.140955	−	0.990016i	$-0.545017\pi$
$773$	17.9592	−	10.3687i	0.645947	−	0.372938i	0.786902	+	0.617078i	$0.211684\pi$
$774$	−0.233308	+	10.4879i	−0.00838609	+	0.376979i
$775$	−0.880490			−0.0316281
$776$	−13.1344	−	26.7198i	−0.471497	−	0.959184i
$777$	3.57733	−	6.19612i	0.128336	−	0.222284i
$778$	3.17883	−	1.74221i	0.113967	−	0.0624612i
$779$			0.258431i			0.00925925i
$780$	4.83600	+	13.9202i	0.173156	+	0.498421i
$781$			30.9520i			1.10755i
$782$	−25.2086	−	45.9956i	−0.901459	−	1.64480i
$783$	18.6964	−	32.3831i	0.668156	−	1.15728i
$784$	20.6124	+	1.83868i	0.736157	+	0.0656672i
$785$	14.4625			0.516190
$786$	13.5965	+	0.302461i	0.484972	+	0.0107884i
$787$	25.5338	−	14.7420i	0.910182	−	0.525494i	0.0296924	−	0.999559i	$-0.490547\pi$
$787$	25.5338	−	14.7420i	0.910182	−	0.525494i	0.880490	+	0.474065i	$0.157214\pi$
$788$	26.2504	−	13.6367i	0.935132	−	0.485788i
$789$	−15.5794	+	8.99479i	−0.554642	+	0.320223i
$790$	13.6665	−	7.49011i	0.486231	−	0.266486i
$791$	−26.2866	+	45.5297i	−0.934643	+	1.61885i
$792$	0.528605	−	7.91033i	0.0187832	−	0.281081i
$793$	39.0766	−	15.5556i	1.38765	−	0.552394i
$794$	2.09290	+	1.27122i	0.0742744	+	0.0451140i
$795$	−9.72207	−	5.61304i	−0.344806	−	0.199074i
$796$	47.5052	+	2.11460i	1.68378	+	0.0749500i
$797$	−27.9101	+	16.1139i	−0.988627	+	0.570784i	−0.904863	−	0.425702i	$-0.860027\pi$
$797$	−27.9101	+	16.1139i	−0.988627	+	0.570784i	−0.0837631	+	0.996486i	$0.526694\pi$
$798$	−31.6944	+	52.1807i	−1.12197	+	1.84718i
$799$	1.35151	+	2.34088i	0.0478129	+	0.0828144i
$800$	3.35464	−	4.55482i	0.118605	−	0.161037i
$801$	4.25284			0.150267
$802$	40.8422	+	0.908555i	1.44219	+	0.0320822i
$803$	26.0331	+	15.0302i	0.918688	+	0.530405i
$804$	−9.28813	−	0.413443i	−0.327567	−	0.0145810i
$805$		−	18.3380i		−	0.646331i
$806$	−1.56732	−	4.20718i	−0.0552064	−	0.148192i
$807$	42.6361			1.50086
$808$	−15.4424	−	10.3468i	−0.543263	−	0.364000i
$809$	21.2438	−	36.7953i	0.746891	−	1.29365i	−0.202416	−	0.979300i	$-0.564879\pi$
$809$	21.2438	−	36.7953i	0.746891	−	1.29365i	0.949306	−	0.314353i	$-0.101787\pi$
$810$	−0.350536	+	15.7576i	−0.0123166	+	0.553667i
$811$		−	2.02287i		−	0.0710326i	−0.999369	−	0.0355163i	$-0.988692\pi$
$811$		−	2.02287i		−	0.0710326i	0.999369	−	0.0355163i	$-0.0113076\pi$
$812$	−59.0113	−	37.6650i	−2.07089	−	1.32178i
$813$	33.2417	−	19.1921i	1.16584	−	0.673096i
$814$	1.75575	−	2.89061i	0.0615390	−	0.101316i
$815$	−5.01379	−	8.68415i	−0.175626	−	0.304192i
$816$	52.3187	−	24.2884i	1.83152	−	0.850262i
$817$	19.0939	−	33.0717i	0.668012	−	1.15703i
$818$	26.8423	−	44.1924i	0.938520	−	1.54515i
$819$	−9.16857	+	11.6121i	−0.320376	+	0.405760i
$820$	0.0757538	−	0.0393531i	0.00264544	−	0.00137427i
$821$	29.1336	+	16.8203i	1.01677	+	0.587032i	0.913167	−	0.407586i	$-0.133629\pi$
$821$	29.1336	+	16.8203i	1.01677	+	0.587032i	0.103603	+	0.994619i	$0.466963\pi$
$822$	−46.9297	+	25.7206i	−1.63686	+	0.897107i
$823$	15.7932	+	27.3547i	0.550517	+	0.953524i	0.998237	+	0.0593498i	$0.0189027\pi$
$823$	15.7932	+	27.3547i	0.550517	+	0.953524i	−0.447720	+	0.894174i	$0.647764\pi$
$824$	−20.1527	−	1.34669i	−0.702051	−	0.0469143i
$825$	2.43516	+	4.21781i	0.0847813	+	0.146845i
$826$	0.319706	−	14.3717i	0.0111240	−	0.500057i
$827$		−	37.6983i		−	1.31090i	−0.755240	−	0.655449i	$-0.772479\pi$
$827$		−	37.6983i		−	1.31090i	0.755240	−	0.655449i	$-0.227521\pi$
$828$	−6.65145	+	10.4211i	−0.231154	+	0.362159i
$829$	−1.65066	−	0.953007i	−0.0573297	−	0.0330993i	0.471061	−	0.882101i	$-0.343871\pi$
$829$	−1.65066	−	0.953007i	−0.0573297	−	0.0330993i	−0.528391	+	0.849001i	$0.677204\pi$
$830$	7.13678	+	13.0218i	0.247721	+	0.451992i
$831$	22.9176			0.795003
$832$	27.7354	+	7.92142i	0.961551	+	0.274626i
$833$	−36.5074			−1.26491
$834$	29.6994	+	54.1896i	1.02841	+	1.87643i
$835$	7.51044	+	4.33615i	0.259909	+	0.150059i
$836$	−15.5270	+	24.3268i	−0.537013	+	0.841361i
$837$		−	3.28178i		−	0.113435i
$838$	−0.203910	+	9.16634i	−0.00704394	+	0.316646i
$839$	0.736770	+	1.27612i	0.0254361	+	0.0440567i	0.878463	−	0.477810i	$-0.158569\pi$
$839$	0.736770	+	1.27612i	0.0254361	+	0.0440567i	−0.853027	+	0.521867i	$0.825236\pi$
$840$	20.1220	+	1.34465i	0.694276	+	0.0463948i
$841$	35.8241	+	62.0491i	1.23531	+	2.13963i
$842$	45.7323	−	25.0643i	1.57604	−	0.863774i
$843$	−37.6085	−	21.7133i	−1.29531	−	0.747846i
$844$	−28.0772	+	14.5857i	−0.966458	+	0.502062i
$845$	3.71115	−	12.4590i	0.127667	−	0.428604i
$846$	0.330750	−	0.544537i	0.0113714	−	0.0187216i
$847$	9.28105	−	16.0752i	0.318901	−	0.552352i
$848$	−19.9307	+	9.25259i	−0.684422	+	0.317735i
$849$	10.1198	+	17.5281i	0.347312	+	0.601562i
$850$	−5.18070	+	8.52935i	−0.177697	+	0.292554i
$851$	−4.56741	+	2.63699i	−0.156569	+	0.0903949i
$852$	44.7431	+	28.5580i	1.53287	+	0.978382i
$853$			16.8878i			0.578226i	0.957295	+	0.289113i	$0.0933604\pi$
$853$			16.8878i			0.578226i	−0.957295	+	0.289113i	$0.906640\pi$
$854$	1.28010	−	57.5444i	0.0438042	−	1.96913i
$855$	−3.56047	+	6.16691i	−0.121765	+	0.210904i
$856$	−1.25749	−	0.842551i	−0.0429802	−	0.0287978i
$857$	−10.9536			−0.374168			−0.187084	−	0.982344i	$-0.559904\pi$
$857$	−10.9536			−0.374168			−0.187084	+	0.982344i	$0.559904\pi$
$858$	−15.8190	+	19.1436i	−0.540050	+	0.653553i
$859$		−	20.8225i		−	0.710454i	−0.934780	−	0.355227i	$-0.884404\pi$
$859$		−	20.8225i		−	0.710454i	0.934780	−	0.355227i	$-0.115596\pi$
$860$	−12.6019	−	0.560946i	−0.429720	−	0.0191281i
$861$	0.263560	+	0.152166i	0.00898208	+	0.00518581i
$862$	5.64263	+	0.125523i	0.192189	+	0.00427533i
$863$	−26.2614			−0.893948			−0.446974	−	0.894547i	$-0.647498\pi$
$863$	−26.2614			−0.893948			−0.446974	+	0.894547i	$0.647498\pi$
$864$	16.9768	+	12.5035i	0.577563	+	0.425378i
$865$	−3.47270	−	6.01490i	−0.118075	−	0.204513i
$866$	−7.46263	+	12.2862i	−0.253590	+	0.417504i
$867$	−58.0391	+	33.5089i	−1.97111	+	1.13802i
$868$	−6.13809	−	0.273225i	−0.208340	−	0.00927386i
$869$	22.7445	+	13.1316i	0.771555	+	0.445458i
$870$	−24.7807	−	15.0517i	−0.840143	−	0.510300i
$871$	6.43723	+	5.08264i	0.218117	+	0.172219i
$872$	−2.96686	+	44.3977i	−0.100471	+	1.50350i
$873$	6.19014	−	10.7216i	0.209504	−	0.362872i
$874$	39.4653	−	21.6296i	1.33493	−	0.731632i
$875$	−3.02162	+	1.74453i	−0.102149	+	0.0589759i
$876$	45.7468	−	23.7648i	1.54564	−	0.802940i
$877$	17.3750	−	10.0315i	0.586713	−	0.338739i	−0.177084	−	0.984196i	$-0.556666\pi$
$877$	17.3750	−	10.0315i	0.586713	−	0.338739i	0.763797	+	0.645457i	$0.223333\pi$
$878$	−10.4633	−	0.232761i	−0.353119	−	0.00785530i
$879$	30.0109			1.01224
$880$	9.49533	+	0.847009i	0.320088	+	0.0285527i
$881$	−8.78885	+	15.2227i	−0.296104	+	0.512867i	−0.975241	−	0.221144i	$-0.929021\pi$
$881$	−8.78885	+	15.2227i	−0.296104	+	0.512867i	0.679137	+	0.734011i	$0.262354\pi$
$882$	4.13570	+	7.54599i	0.139256	+	0.254087i
$883$			12.3075i			0.414181i	0.978322	+	0.207091i	$0.0663995\pi$
$883$			12.3075i			0.414181i	−0.978322	+	0.207091i	$0.933601\pi$
$884$	−49.9770	−	9.57186i	−1.68091	−	0.321936i
$885$		−	5.95359i		−	0.200128i
$886$	−33.5031	+	18.3619i	−1.12556	+	0.616881i
$887$	−3.37824	+	5.85129i	−0.113430	+	0.196467i	−0.917151	−	0.398539i	$-0.869517\pi$
$887$	−3.37824	+	5.85129i	−0.113430	+	0.196467i	0.803721	+	0.595006i	$0.202851\pi$
$888$	−2.55862	−	5.20510i	−0.0858617	−	0.174672i
$889$	5.79003			0.194191
$890$	−0.113732	+	5.11259i	−0.00381230	+	0.171374i
$891$	−23.0030	+	13.2808i	−0.770631	+	0.444924i
$892$	4.84296	+	9.32258i	0.162154	+	0.312143i
$893$	−2.00853	+	1.15963i	−0.0672129	+	0.0388054i
$894$	13.5087	+	24.6480i	0.451799	+	0.824352i
$895$	−8.69116	+	15.0535i	−0.290513	+	0.503184i
$896$	24.7994	−	30.7117i	0.828489	−	1.02600i
$897$	35.9799	−	14.3228i	1.20133	−	0.478225i
$898$	12.9663	−	21.3474i	0.432692	−	0.712371i
$899$	7.64994	+	4.41670i	0.255140	+	0.147305i
$900$	2.34988	+	0.104600i	0.0783295	+	0.00348668i
$901$	33.5710	−	19.3822i	1.11841	−	0.645716i
$902$	0.122956	+	0.0746829i	0.00409398	+	0.00248667i
$903$	−22.4853	−	38.9457i	−0.748264	−	1.29603i
$904$	18.8010	+	38.2476i	0.625312	+	1.27209i
$905$	−8.89990			−0.295843
$906$	0.532041	−	23.9168i	0.0176759	−	0.794582i
$907$	−15.0802	−	8.70658i	−0.500731	−	0.289097i	0.228284	−	0.973595i	$-0.426688\pi$
$907$	−15.0802	−	8.70658i	−0.500731	−	0.289097i	−0.729015	+	0.684497i	$0.760022\pi$
$908$	−0.849157	+	19.0766i	−0.0281803	+	0.633080i
$909$		−	7.72933i		−	0.256366i
$910$	−13.7144	−	11.3326i	−0.454628	−	0.375672i
$911$	36.0194			1.19337			0.596687	−	0.802474i	$-0.296483\pi$
$911$	36.0194			1.19337			0.596687	+	0.802474i	$0.296483\pi$
$912$	20.8400	+	44.8907i	0.690081	+	1.48648i
$913$	−12.5121	+	21.6716i	−0.414090	+	0.717225i
$914$	46.2566	+	1.02900i	1.53003	+	0.0340363i
$915$		−	23.8381i		−	0.788065i
$916$	14.3703	+	9.17210i	0.474809	+	0.303055i
$917$	−14.2192	+	8.20944i	−0.469558	+	0.271100i
$918$	−31.7908	−	19.3096i	−1.04925	−	0.637313i
$919$	−9.74994	−	16.8874i	−0.321621	−	0.557064i	0.659202	−	0.751966i	$-0.270894\pi$
$919$	−9.74994	−	16.8874i	−0.321621	−	0.557064i	−0.980823	+	0.194902i	$0.937561\pi$
$920$	−12.3499	−	8.27478i	−0.407166	−	0.272811i
$921$	−15.3261	+	26.5456i	−0.505012	+	0.874706i
$922$	−41.5191	−	25.2186i	−1.36736	−	0.830530i
$923$	−17.3187	−	43.5058i	−0.570053	−	1.43201i
$924$	15.6672	+	30.1590i	0.515413	+	0.992157i
$925$	0.869011	+	0.501724i	0.0285729	+	0.0164966i
$926$	17.0121	+	31.0402i	0.559052	+	1.02004i
$927$	−4.19925	−	7.27331i	−0.137921	−	0.238887i
$928$	−51.9938	+	22.7460i	−1.70678	+	0.746675i
$929$	19.0928	+	33.0697i	0.626414	+	1.08498i	0.988266	+	0.152745i	$0.0488113\pi$
$929$	19.0928	+	33.0697i	0.626414	+	1.08498i	−0.361852	+	0.932236i	$0.617855\pi$
$930$	−2.54400	−	0.0565926i	−0.0834212	−	0.00185574i
$931$		−	31.3242i		−	1.02661i
$932$	−6.05205	+	9.48201i	−0.198241	+	0.310594i
$933$	26.4642	+	15.2791i	0.866398	+	0.500215i
$934$	−17.1230	+	9.38454i	−0.560282	+	0.307071i
$935$	−16.8176			−0.549993
$936$	3.68311	+	11.4145i	0.120386	+	0.373093i
$937$	−27.1203			−0.885981			−0.442991	−	0.896526i	$-0.646083\pi$
$937$	−27.1203			−0.885981			−0.442991	+	0.896526i	$0.646083\pi$
$938$	9.84310	−	5.39467i	0.321389	−	0.176142i
$939$	34.2541	+	19.7766i	1.11784	+	0.645386i
$940$	0.645774	+	0.412176i	0.0210628	+	0.0134437i
$941$		−	0.410385i		−	0.0133782i	−0.999978	−	0.00668908i	$-0.997871\pi$
$941$		−	0.410385i		−	0.0133782i	0.999978	−	0.00668908i	$-0.00212922\pi$
$942$	41.7866	+	0.929564i	1.36148	+	0.0302868i
$943$	−0.112168	−	0.194280i	−0.00365268	−	0.00632663i
$944$	−9.53454	−	6.70035i	−0.310323	−	0.218078i
$945$	−6.50226	−	11.2622i	−0.211518	−	0.366361i
$946$	−10.2169	−	18.6417i	−0.332180	−	0.606095i
$947$	−11.6051	−	6.70020i	−0.377115	−	0.217727i	0.299447	−	0.954113i	$-0.403198\pi$
$947$	−11.6051	−	6.70020i	−0.377115	−	0.217727i	−0.676562	+	0.736385i	$0.736531\pi$
$948$	39.9680	−	20.7628i	1.29810	−	0.674345i
$949$	−45.0018	−	6.55988i	−1.46082	−	0.212943i
$950$	−7.31838	−	4.44516i	−0.237440	−	0.144220i
$951$	3.08282	−	5.33960i	0.0999673	−	0.173148i
$952$	−38.7626	+	57.8524i	−1.25630	+	1.87501i
$953$	−27.3747	−	47.4144i	−0.886754	−	1.53590i	−0.843690	−	0.536830i	$-0.819622\pi$
$953$	−27.3747	−	47.4144i	−0.886754	−	1.53590i	−0.0430634	−	0.999072i	$-0.513712\pi$
$954$	−7.80931	−	4.74335i	−0.252836	−	0.153572i
$955$	12.8786	−	7.43546i	0.416741	−	0.240606i
$956$	−0.626670	+	0.981831i	−0.0202680	+	0.0317547i
$957$		−	48.8607i		−	1.57944i
$958$	50.8157	+	1.13042i	1.64178	+	0.0365222i
$959$	32.3043	−	55.9527i	1.04316	−	1.80681i
$960$	9.98534	−	12.9446i	0.322276	−	0.417786i
$961$	−30.2247			−0.974992
$962$	−0.850463	+	5.04542i	−0.0274200	+	0.162671i
$963$		−	0.629405i		−	0.0202823i
$964$	7.29071	+	0.324531i	0.234818	+	0.0104524i
$965$	−10.5167	−	6.07185i	−0.338546	−	0.195460i
$966$	1.17866	−	52.9842i	0.0379227	−	1.70474i
$967$	−0.190690			−0.00613219			−0.00306609	−	0.999995i	$-0.500976\pi$
$967$	−0.190690			−0.00613219			−0.00306609	+	0.999995i	$0.500976\pi$
$968$	−6.63810	−	13.5041i	−0.213357	−	0.434039i
$969$	−43.6554	−	75.6134i	−1.40241	−	2.42905i
$970$	12.7236	+	7.72825i	0.408529	+	0.248139i
$971$	−28.3310	+	16.3569i	−0.909184	+	0.524918i	−0.880169	−	0.474661i	$-0.842571\pi$
$971$	−28.3310	+	16.3569i	−0.909184	+	0.524918i	−0.0290158	+	0.999579i	$0.509237\pi$
$972$	−1.03114	+	23.1649i	−0.0330738	+	0.743014i
$973$	−64.6084	−	37.3017i	−2.07125	−	1.19584i
$974$	26.4314	−	43.5159i	0.846917	−	1.39434i
$975$	−5.78285	−	4.56596i	−0.185199	−	0.146228i
$976$	−38.1762	−	26.8282i	−1.22199	−	0.858749i
$977$	27.5494	−	47.7169i	0.881382	−	1.52660i	0.0315767	−	0.999501i	$-0.489947\pi$
$977$	27.5494	−	47.7169i	0.881382	−	1.52660i	0.849805	−	0.527097i	$-0.176720\pi$
$978$	−13.9282	−	25.4134i	−0.445375	−	0.812631i
$979$	−7.46337	+	4.30898i	−0.238530	+	0.137715i
$980$	−9.18206	+	4.76996i	−0.293310	+	0.152371i
$981$	−16.0236	+	9.25123i	−0.511594	+	0.295369i
$982$	0.350164	−	15.7409i	0.0111742	−	0.502313i
$983$	33.1360			1.05687			0.528437	−	0.848972i	$-0.322778\pi$
$983$	33.1360			1.05687			0.528437	+	0.848972i	$0.322778\pi$
$984$	0.221405	−	0.108834i	0.00705814	−	0.00346950i
$985$	−7.39528	+	12.8090i	−0.235633	+	0.408129i
$986$	87.7961	−	48.1180i	2.79600	−	1.53239i
$987$			2.73119i			0.0869346i
$988$	8.21288	−	42.8815i	0.261287	−	1.36424i
$989$			33.1496i			1.05410i
$990$	1.90516	+	3.47614i	0.0605498	+	0.110479i
$991$	−4.88394	+	8.45924i	−0.155144	+	0.268717i	−0.933111	−	0.359588i	$-0.882917\pi$
$991$	−4.88394	+	8.45924i	−0.155144	+	0.268717i	0.777968	+	0.628304i	$0.216251\pi$
$992$	−2.95373	+	4.01047i	−0.0937811	+	0.127333i
$993$	−33.4633			−1.06192
$994$	−64.0668	−	1.42520i	−2.03208	−	0.0452045i
$995$	−20.5907	+	11.8881i	−0.652770	+	0.376877i
$996$	19.7834	+	38.0825i	0.626860	+	1.20669i
$997$	1.45497	−	0.840027i	0.0460793	−	0.0266039i	−0.476783	−	0.879021i	$-0.658197\pi$
$997$	1.45497	−	0.840027i	0.0460793	−	0.0266039i	0.522863	+	0.852417i	$0.324864\pi$
$998$	7.65180	−	4.19369i	0.242213	−	0.132749i
$999$	−1.87004	+	3.23900i	−0.0591653	+	0.102477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	520.2.by.c.61.19	✓	104
8.5	even	2	inner	520.2.by.c.61.52	yes	104
13.3	even	3	inner	520.2.by.c.341.52	yes	104
104.29	even	6	inner	520.2.by.c.341.19	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
520.2.by.c.61.19	✓	104	1.1	even	1	trivial
520.2.by.c.61.52	yes	104	8.5	even	2	inner
520.2.by.c.341.19	yes	104	104.29	even	6	inner
520.2.by.c.341.52	yes	104	13.3	even	3	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:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.by (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.679694 - 1.24017i) q^{2} +(1.76977 + 1.02178i) q^{3} +(-1.07603 + 1.68587i) q^{4} -1.00000i q^{5} +(0.0642740 - 2.88930i) q^{6} +(1.74453 + 3.02162i) q^{7} +(2.82213 + 0.188588i) q^{8} +(0.588053 + 1.01854i) q^{9} +O(q^{10})\)	\(q+(-0.679694 - 1.24017i) q^{2} +(1.76977 + 1.02178i) q^{3} +(-1.07603 + 1.68587i) q^{4} -1.00000i q^{5} +(0.0642740 - 2.88930i) q^{6} +(1.74453 + 3.02162i) q^{7} +(2.82213 + 0.188588i) q^{8} +(0.588053 + 1.01854i) q^{9} +(-1.24017 + 0.679694i) q^{10} +(-2.06396 - 1.19163i) q^{11} +(-3.62691 + 1.88413i) q^{12} +(3.56784 + 0.520082i) q^{13} +(2.56157 - 4.21729i) q^{14} +(1.02178 - 1.76977i) q^{15} +(-1.68430 - 3.62810i) q^{16} +(3.52827 + 6.11114i) q^{17} +(0.863461 - 1.42158i) q^{18} +(-5.24350 + 3.02734i) q^{19} +(1.68587 + 1.07603i) q^{20} +7.13008i q^{21} +(-0.0749584 + 3.36960i) q^{22} +(2.62793 - 4.55171i) q^{23} +(4.80183 + 3.21735i) q^{24} -1.00000 q^{25} +(-1.78005 - 4.77822i) q^{26} -3.72722i q^{27} +(-6.97122 - 0.310310i) q^{28} +(8.68828 + 5.01618i) q^{29} +(-2.88930 - 0.0642740i) q^{30} +0.880490 q^{31} +(-3.35464 + 4.55482i) q^{32} +(-2.43516 - 4.21781i) q^{33} +(5.18070 - 8.52935i) q^{34} +(3.02162 - 1.74453i) q^{35} +(-2.34988 - 0.104600i) q^{36} +(-0.869011 - 0.501724i) q^{37} +(7.31838 + 4.44516i) q^{38} +(5.78285 + 4.56596i) q^{39} +(0.188588 - 2.82213i) q^{40} +(0.0213414 - 0.0369644i) q^{41} +(8.84250 - 4.84627i) q^{42} +(-5.46217 + 3.15358i) q^{43} +(4.22982 - 2.19734i) q^{44} +(1.01854 - 0.588053i) q^{45} +(-7.43108 - 0.165308i) q^{46} +0.383051 q^{47} +(0.726278 - 8.14188i) q^{48} +(-2.58678 + 4.48043i) q^{49} +(0.679694 + 1.24017i) q^{50} +14.4204i q^{51} +(-4.71591 + 5.45529i) q^{52} -5.49342i q^{53} +(-4.62238 + 2.53337i) q^{54} +(-1.19163 + 2.06396i) q^{55} +(4.35346 + 8.85640i) q^{56} -12.3730 q^{57} +(0.315539 - 14.1844i) q^{58} +(2.52304 - 1.45668i) q^{59} +(1.88413 + 3.62691i) q^{60} +(10.1022 - 5.83253i) q^{61} +(-0.598464 - 1.09196i) q^{62} +(-2.05175 + 3.55374i) q^{63} +(7.92887 + 1.06444i) q^{64} +(0.520082 - 3.56784i) q^{65} +(-3.57564 + 5.88682i) q^{66} +(1.97003 + 1.13740i) q^{67} +(-14.0991 - 0.627594i) q^{68} +(9.30167 - 5.37032i) q^{69} +(-4.21729 - 2.56157i) q^{70} +(-6.49362 - 11.2473i) q^{71} +(1.46748 + 2.98535i) q^{72} -12.6132 q^{73} +(-0.0315605 + 1.41874i) q^{74} +(-1.76977 - 1.02178i) q^{75} +(0.538490 - 12.0974i) q^{76} -8.31534i q^{77} +(1.73200 - 10.2752i) q^{78} -11.0198 q^{79} +(-3.62810 + 1.68430i) q^{80} +(5.57255 - 9.65193i) q^{81} +(-0.0603478 - 0.00134247i) q^{82} -10.5000i q^{83} +(-12.0204 - 7.67220i) q^{84} +(6.11114 - 3.52827i) q^{85} +(7.62357 + 4.63053i) q^{86} +(10.2508 + 17.7549i) q^{87} +(-5.60005 - 3.75217i) q^{88} +(1.80802 - 3.13158i) q^{89} +(-1.42158 - 0.863461i) q^{90} +(4.65273 + 11.6880i) q^{91} +(4.84585 + 9.32815i) q^{92} +(1.55826 + 0.899664i) q^{93} +(-0.260357 - 0.475048i) q^{94} +(3.02734 + 5.24350i) q^{95} +(-10.5909 + 4.63328i) q^{96} +(-5.26325 - 9.11622i) q^{97} +(7.31471 + 0.162719i) q^{98} -2.80296i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9}+O(q^{10}) \) 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9	\( 104 q + 2 q^{6} - 4 q^{7} + 12 q^{8} + 60 q^{9} - 28 q^{12} - 24 q^{14} + 4 q^{15} - 20 q^{16} + 4 q^{17} - 40 q^{18} - 4 q^{20} + 24 q^{22} + 32 q^{23} + 24 q^{24} - 104 q^{25} - 10 q^{26} + 22 q^{28} - 12 q^{30} - 40 q^{31} + 30 q^{32} + 12 q^{33} - 4 q^{34} + 18 q^{36} + 56 q^{39} - 16 q^{41} - 20 q^{42} - 32 q^{44} - 30 q^{46} - 56 q^{47} - 24 q^{48} - 80 q^{49} - 6 q^{52} - 10 q^{54} + 16 q^{55} - 38 q^{56} + 104 q^{57} - 68 q^{58} - 12 q^{62} + 12 q^{63} - 108 q^{64} + 180 q^{66} - 6 q^{68} + 8 q^{70} - 72 q^{71} - 80 q^{72} + 24 q^{73} + 40 q^{74} - 20 q^{76} - 52 q^{78} - 40 q^{79} - 24 q^{80} - 60 q^{81} + 64 q^{82} - 70 q^{84} + 140 q^{86} - 8 q^{87} + 86 q^{88} + 36 q^{89} - 20 q^{90} + 76 q^{92} + 46 q^{94} - 32 q^{95} + 12 q^{96} + 12 q^{97} - 8 q^{98}+O(q^{100}) \) 104 * q + 2 * q^6 - 4 * q^7 + 12 * q^8 + 60 * q^9 - 28 * q^12 - 24 * q^14 + 4 * q^15 - 20 * q^16 + 4 * q^17 - 40 * q^18 - 4 * q^20 + 24 * q^22 + 32 * q^23 + 24 * q^24 - 104 * q^25 - 10 * q^26 + 22 * q^28 - 12 * q^30 - 40 * q^31 + 30 * q^32 + 12 * q^33 - 4 * q^34 + 18 * q^36 + 56 * q^39 - 16 * q^41 - 20 * q^42 - 32 * q^44 - 30 * q^46 - 56 * q^47 - 24 * q^48 - 80 * q^49 - 6 * q^52 - 10 * q^54 + 16 * q^55 - 38 * q^56 + 104 * q^57 - 68 * q^58 - 12 * q^62 + 12 * q^63 - 108 * q^64 + 180 * q^66 - 6 * q^68 + 8 * q^70 - 72 * q^71 - 80 * q^72 + 24 * q^73 + 40 * q^74 - 20 * q^76 - 52 * q^78 - 40 * q^79 - 24 * q^80 - 60 * q^81 + 64 * q^82 - 70 * q^84 + 140 * q^86 - 8 * q^87 + 86 * q^88 + 36 * q^89 - 20 * q^90 + 76 * q^92 + 46 * q^94 - 32 * q^95 + 12 * q^96 + 12 * q^97 - 8 * q^98

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