LMFDB - Embedded newform 504.2.cz.b.187.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(187,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 4, 5]))

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

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

chi := DirichletCharacter("504.187");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cz (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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$90$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			187.10
Character	$\chi$	$=$	504.187
Dual form			504.2.cz.b.283.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33390 + 0.469805i) q^{2} +(0.0180886 + 1.73196i) q^{3} +(1.55857 - 1.25334i) q^{4} +4.13478 q^{5} +(-0.837810 - 2.30175i) q^{6} +(-1.26742 + 2.32242i) q^{7} +(-1.49014 + 2.40405i) q^{8} +(-2.99935 + 0.0626575i) q^{9} +O(q^{10})$	\(q+(-1.33390 + 0.469805i) q^{2} +(0.0180886 + 1.73196i) q^{3} +(1.55857 - 1.25334i) q^{4} +4.13478 q^{5} +(-0.837810 - 2.30175i) q^{6} +(-1.26742 + 2.32242i) q^{7} +(-1.49014 + 2.40405i) q^{8} +(-2.99935 + 0.0626575i) q^{9} +(-5.51537 + 1.94254i) q^{10} -4.32492 q^{11} +(2.19893 + 2.67670i) q^{12} +(0.641757 + 1.11156i) q^{13} +(0.599527 - 3.69331i) q^{14} +(0.0747925 + 7.16125i) q^{15} +(0.858263 - 3.90684i) q^{16} +(-2.26685 + 1.30876i) q^{17} +(3.97138 - 1.49269i) q^{18} +(1.98530 + 1.14621i) q^{19} +(6.44433 - 5.18229i) q^{20} +(-4.04526 - 2.15311i) q^{21} +(5.76901 - 2.03187i) q^{22} +9.07493i q^{23} +(-4.19067 - 2.53738i) q^{24} +12.0964 q^{25} +(-1.37825 - 1.18120i) q^{26} +(-0.162774 - 5.19360i) q^{27} +(0.935428 + 5.20816i) q^{28} +(-1.34755 - 0.778011i) q^{29} +(-3.46415 - 9.51724i) q^{30} +(3.20286 - 5.54751i) q^{31} +(0.690615 + 5.61454i) q^{32} +(-0.0782320 - 7.49058i) q^{33} +(2.40888 - 2.81073i) q^{34} +(-5.24051 + 9.60269i) q^{35} +(-4.59615 + 3.85686i) q^{36} +(3.81526 + 2.20274i) q^{37} +(-3.18668 - 0.596228i) q^{38} +(-1.91356 + 1.13160i) q^{39} +(-6.16141 + 9.94022i) q^{40} +(0.171501 - 0.0990159i) q^{41} +(6.40750 + 0.971548i) q^{42} +(-1.95206 + 3.38106i) q^{43} +(-6.74068 + 5.42061i) q^{44} +(-12.4016 + 0.259075i) q^{45} +(-4.26344 - 12.1050i) q^{46} +(-1.57995 - 2.73655i) q^{47} +(6.78200 + 1.41580i) q^{48} +(-3.78728 - 5.88698i) q^{49} +(-16.1353 + 5.68293i) q^{50} +(-2.30773 - 3.90241i) q^{51} +(2.39338 + 0.928093i) q^{52} +(-4.24135 + 2.44875i) q^{53} +(2.65710 + 6.85126i) q^{54} -17.8826 q^{55} +(-3.69459 - 6.50769i) q^{56} +(-1.94928 + 3.45918i) q^{57} +(2.16301 + 0.404700i) q^{58} +(4.47816 + 2.58546i) q^{59} +(9.09207 + 11.0675i) q^{60} +(4.40409 + 7.62810i) q^{61} +(-1.66604 + 8.90453i) q^{62} +(3.65592 - 7.04516i) q^{63} +(-3.55895 - 7.16477i) q^{64} +(2.65352 + 4.59603i) q^{65} +(3.62346 + 9.95491i) q^{66} +(1.06600 - 1.84636i) q^{67} +(-1.89270 + 4.88093i) q^{68} +(-15.7174 + 0.164153i) q^{69} +(2.47891 - 15.2710i) q^{70} -4.81184i q^{71} +(4.31882 - 7.30396i) q^{72} +(10.0900 - 5.82545i) q^{73} +(-6.12403 - 1.14581i) q^{74} +(0.218807 + 20.9504i) q^{75} +(4.53082 - 0.701811i) q^{76} +(5.48150 - 10.0443i) q^{77} +(2.02086 - 2.40844i) q^{78} +(7.50245 - 4.33154i) q^{79} +(3.54873 - 16.1539i) q^{80} +(8.99215 - 0.375863i) q^{81} +(-0.182246 + 0.212649i) q^{82} +(-4.89916 - 2.82853i) q^{83} +(-9.00339 + 1.71433i) q^{84} +(-9.37290 + 5.41145i) q^{85} +(1.01541 - 5.42707i) q^{86} +(1.32311 - 2.34798i) q^{87} +(6.44475 - 10.3973i) q^{88} +(7.48220 + 4.31985i) q^{89} +(16.4208 - 6.17192i) q^{90} +(-3.39488 + 0.0816202i) q^{91} +(11.3740 + 14.1439i) q^{92} +(9.66598 + 5.44686i) q^{93} +(3.39313 + 2.90801i) q^{94} +(8.20876 + 4.73933i) q^{95} +(-9.71164 + 1.29768i) q^{96} +(-5.28964 - 3.05398i) q^{97} +(7.81758 + 6.07334i) q^{98} +(12.9719 - 0.270989i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) $ 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9	$ 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9} + 16 q^{11} - 3 q^{12} + 7 q^{14} - 7 q^{16} - 18 q^{17} - 13 q^{18} - 6 q^{19} - 36 q^{20} - 16 q^{22} - 24 q^{24} + 156 q^{25} - 6 q^{26} + 16 q^{28} - 8 q^{30} + 13 q^{32} - 36 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 42 q^{41} + 31 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} + 9 q^{48} + 20 q^{49} + 15 q^{50} - 42 q^{51} - 12 q^{54} - 40 q^{56} - 26 q^{57} - 38 q^{58} + 18 q^{59} - 38 q^{60} - 8 q^{64} - 12 q^{65} - 21 q^{66} - 14 q^{67} - 42 q^{70} + 5 q^{72} + 18 q^{73} - 98 q^{74} - 48 q^{75} + 12 q^{76} - 33 q^{78} - 63 q^{80} + 8 q^{81} - 54 q^{82} - 6 q^{83} - 77 q^{84} + 26 q^{86} - 58 q^{88} - 66 q^{89} + 51 q^{90} + 2 q^{91} - 60 q^{92} + 9 q^{94} - 30 q^{96} + 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) $ 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9 + 16 * q^11 - 3 * q^12 + 7 * q^14 - 7 * q^16 - 18 * q^17 - 13 * q^18 - 6 * q^19 - 36 * q^20 - 16 * q^22 - 24 * q^24 + 156 * q^25 - 6 * q^26 + 16 * q^28 - 8 * q^30 + 13 * q^32 - 36 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 42 * q^41 + 31 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 + 9 * q^48 + 20 * q^49 + 15 * q^50 - 42 * q^51 - 12 * q^54 - 40 * q^56 - 26 * q^57 - 38 * q^58 + 18 * q^59 - 38 * q^60 - 8 * q^64 - 12 * q^65 - 21 * q^66 - 14 * q^67 - 42 * q^70 + 5 * q^72 + 18 * q^73 - 98 * q^74 - 48 * q^75 + 12 * q^76 - 33 * q^78 - 63 * q^80 + 8 * q^81 - 54 * q^82 - 6 * q^83 - 77 * q^84 + 26 * q^86 - 58 * q^88 - 66 * q^89 + 51 * q^90 + 2 * q^91 - 60 * q^92 + 9 * q^94 - 30 * q^96 + 6 * q^97 + 31 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.33390	+	0.469805i	−0.943208	+	0.332202i
$2$	−1.33390	+	0.469805i	−0.943208	+	0.332202i
$3$	0.0180886	+	1.73196i	0.0104435	+	0.999945i
$3$	0.0180886	+	1.73196i	0.0104435	+	0.999945i
$4$	1.55857	−	1.25334i	0.779284	−	0.626671i
$5$	4.13478			1.84913			0.924564	−	0.381027i	$-0.124429\pi$
$5$	4.13478			1.84913			0.924564	+	0.381027i	$0.124429\pi$
$6$	−0.837810	−	2.30175i	−0.342034	−	0.939687i
$7$	−1.26742	+	2.32242i	−0.479040	+	0.877793i
$7$	−1.26742	+	2.32242i	−0.479040	+	0.877793i
$8$	−1.49014	+	2.40405i	−0.526845	+	0.849961i
$9$	−2.99935	+	0.0626575i	−0.999782	+	0.0208858i
$10$	−5.51537	+	1.94254i	−1.74411	+	0.614284i
$11$	−4.32492			−1.30401			−0.652007	−	0.758213i	$-0.726073\pi$
$11$	−4.32492			−1.30401			−0.652007	+	0.758213i	$0.726073\pi$
$12$	2.19893	+	2.67670i	0.634776	+	0.772696i
$13$	0.641757	+	1.11156i	0.177991	+	0.308290i	0.941192	−	0.337871i	$-0.109707\pi$
$13$	0.641757	+	1.11156i	0.177991	+	0.308290i	−0.763201	+	0.646161i	$0.776373\pi$
$14$	0.599527	−	3.69331i	0.160230	−	0.987080i
$15$	0.0747925	+	7.16125i	0.0193113	+	1.84903i
$16$	0.858263	−	3.90684i	0.214566	−	0.976710i
$17$	−2.26685	+	1.30876i	−0.549791	+	0.317422i	−0.749038	−	0.662527i	$-0.769484\pi$
$17$	−2.26685	+	1.30876i	−0.549791	+	0.317422i	0.199247	+	0.979949i	$0.436151\pi$
$18$	3.97138	−	1.49269i	0.936064	−	0.351829i
$19$	1.98530	+	1.14621i	0.455459	+	0.262959i	0.710133	−	0.704068i	$-0.248635\pi$
$19$	1.98530	+	1.14621i	0.455459	+	0.262959i	−0.254674	+	0.967027i	$0.581968\pi$
$20$	6.44433	−	5.18229i	1.44099	−	1.15880i
$21$	−4.04526	−	2.15311i	−0.882748	−	0.469847i
$22$	5.76901	−	2.03187i	1.22996	−	0.433196i
$23$			9.07493i			1.89225i	0.323796	+	0.946127i	$0.395041\pi$
$23$			9.07493i			1.89225i	−0.323796	+	0.946127i	$0.604959\pi$
$24$	−4.19067	−	2.53738i	−0.855417	−	0.517940i
$25$	12.0964			2.41927
$26$	−1.37825	−	1.18120i	−0.270298	−	0.231653i
$27$	−0.162774	−	5.19360i	−0.0313259	−	0.999509i
$28$	0.935428	+	5.20816i	0.176779	+	0.984251i
$29$	−1.34755	−	0.778011i	−0.250235	−	0.144473i	0.369637	−	0.929176i	$-0.379482\pi$
$29$	−1.34755	−	0.778011i	−0.250235	−	0.144473i	−0.619872	+	0.784703i	$0.712815\pi$
$30$	−3.46415	−	9.51724i	−0.632465	−	1.73760i
$31$	3.20286	−	5.54751i	0.575250	−	0.996363i	−0.420764	−	0.907170i	$-0.638238\pi$
$31$	3.20286	−	5.54751i	0.575250	−	0.996363i	0.996014	−	0.0891925i	$-0.0284286\pi$
$32$	0.690615	+	5.61454i	0.122085	+	0.992520i
$33$	−0.0782320	−	7.49058i	−0.0136184	−	1.30394i
$34$	2.40888	−	2.81073i	0.413119	−	0.482037i
$35$	−5.24051	+	9.60269i	−0.885807	+	1.62315i
$36$	−4.59615	+	3.85686i	−0.766025	+	0.642811i
$37$	3.81526	+	2.20274i	0.627225	+	0.362129i	0.779677	−	0.626182i	$-0.215383\pi$
$37$	3.81526	+	2.20274i	0.627225	+	0.362129i	−0.152452	+	0.988311i	$0.548717\pi$
$38$	−3.18668	−	0.596228i	−0.516948	−	0.0967210i
$39$	−1.91356	+	1.13160i	−0.306414	+	0.181201i
$40$	−6.16141	+	9.94022i	−0.974204	+	1.57169i
$41$	0.171501	−	0.0990159i	0.0267839	−	0.0154637i	−0.486548	−	0.873654i	$-0.661744\pi$
$41$	0.171501	−	0.0990159i	0.0267839	−	0.0154637i	0.513332	+	0.858190i	$0.328411\pi$
$42$	6.40750	+	0.971548i	0.988699	+	0.149913i
$43$	−1.95206	+	3.38106i	−0.297686	+	0.515607i	−0.975606	−	0.219529i	$-0.929548\pi$
$43$	−1.95206	+	3.38106i	−0.297686	+	0.515607i	0.677920	+	0.735135i	$0.262881\pi$
$44$	−6.74068	+	5.42061i	−1.01620	+	0.817188i
$45$	−12.4016	+	0.259075i	−1.84872	+	0.0386206i
$46$	−4.26344	−	12.1050i	−0.628611	−	1.78479i
$47$	−1.57995	−	2.73655i	−0.230459	−	0.399167i	0.727484	−	0.686124i	$-0.240689\pi$
$47$	−1.57995	−	2.73655i	−0.230459	−	0.399167i	−0.957943	+	0.286958i	$0.907356\pi$
$48$	6.78200	+	1.41580i	0.978897	+	0.204354i
$49$	−3.78728	−	5.88698i	−0.541040	−	0.840997i
$50$	−16.1353	+	5.68293i	−2.28188	+	0.803688i
$51$	−2.30773	−	3.90241i	−0.323147	−	0.546446i
$52$	2.39338	+	0.928093i	0.331902	+	0.128703i
$53$	−4.24135	+	2.44875i	−0.582594	+	0.336361i	−0.762164	−	0.647384i	$-0.775863\pi$
$53$	−4.24135	+	2.44875i	−0.582594	+	0.336361i	0.179569	+	0.983745i	$0.442530\pi$
$54$	2.65710	+	6.85126i	0.361586	+	0.932339i
$55$	−17.8826			−2.41129
$56$	−3.69459	−	6.50769i	−0.493710	−	0.869627i
$57$	−1.94928	+	3.45918i	−0.258188	+	0.458180i
$58$	2.16301	+	0.404700i	0.284017	+	0.0531397i
$59$	4.47816	+	2.58546i	0.583006	+	0.336599i	0.762327	−	0.647192i	$-0.224057\pi$
$59$	4.47816	+	2.58546i	0.583006	+	0.336599i	−0.179321	+	0.983791i	$0.557390\pi$
$60$	9.09207	+	11.0675i	1.17378	+	1.42881i
$61$	4.40409	+	7.62810i	0.563886	+	0.976679i	0.997152	+	0.0754128i	$0.0240275\pi$
$61$	4.40409	+	7.62810i	0.563886	+	0.976679i	−0.433267	+	0.901266i	$0.642639\pi$
$62$	−1.66604	+	8.90453i	−0.211587	+	1.13088i
$63$	3.65592	−	7.04516i	0.460603	−	0.887607i
$64$	−3.55895	−	7.16477i	−0.444868	−	0.895596i
$65$	2.65352	+	4.59603i	0.329129	+	0.570068i
$66$	3.62346	+	9.95491i	0.446017	+	1.22536i
$67$	1.06600	−	1.84636i	0.130232	−	0.225569i	−0.793534	−	0.608526i	$-0.791761\pi$
$67$	1.06600	−	1.84636i	0.130232	−	0.225569i	0.923766	+	0.382957i	$0.125094\pi$
$68$	−1.89270	+	4.88093i	−0.229524	+	0.591900i
$69$	−15.7174	+	0.164153i	−1.89215	+	0.0197617i
$70$	2.47891	−	15.2710i	0.296286	−	1.82524i
$71$		−	4.81184i		−	0.571060i	−0.958370	−	0.285530i	$-0.907830\pi$
$71$		−	4.81184i		−	0.571060i	0.958370	−	0.285530i	$-0.0921696\pi$
$72$	4.31882	−	7.30396i	0.508978	−	0.860779i
$73$	10.0900	−	5.82545i	1.18094	−	0.681817i	0.224710	−	0.974426i	$-0.427857\pi$
$73$	10.0900	−	5.82545i	1.18094	−	0.681817i	0.956232	+	0.292609i	$0.0945233\pi$
$74$	−6.12403	−	1.14581i	−0.711904	−	0.133197i
$75$	0.218807	+	20.9504i	0.0252656	+	2.41914i
$76$	4.53082	−	0.701811i	0.519721	−	0.0805032i
$77$	5.48150	−	10.0443i	0.624675	−	1.14465i
$78$	2.02086	−	2.40844i	0.228817	−	0.272702i
$79$	7.50245	−	4.33154i	0.844091	−	0.487336i	−0.0145616	−	0.999894i	$-0.504635\pi$
$79$	7.50245	−	4.33154i	0.844091	−	0.487336i	0.858653	+	0.512558i	$0.171302\pi$
$80$	3.54873	−	16.1539i	0.396760	−	1.80606i
$81$	8.99215	−	0.375863i	0.999128	−	0.0417625i
$82$	−0.182246	+	0.212649i	−0.0201257	+	0.0234831i
$83$	−4.89916	−	2.82853i	−0.537753	−	0.310472i	0.206415	−	0.978465i	$-0.433820\pi$
$83$	−4.89916	−	2.82853i	−0.537753	−	0.310472i	−0.744168	+	0.667993i	$0.767154\pi$
$84$	−9.00339	+	1.71433i	−0.982351	+	0.187049i
$85$	−9.37290	+	5.41145i	−1.01663	+	0.586954i
$86$	1.01541	−	5.42707i	0.109494	−	0.585216i
$87$	1.32311	−	2.34798i	0.141852	−	0.251730i
$88$	6.44475	−	10.3973i	0.687013	−	1.10836i
$89$	7.48220	+	4.31985i	0.793111	+	0.457903i	0.841057	−	0.540947i	$-0.181934\pi$
$89$	7.48220	+	4.31985i	0.793111	+	0.457903i	−0.0479453	+	0.998850i	$0.515267\pi$
$90$	16.4208	−	6.17192i	1.73090	−	0.650577i
$91$	−3.39488	+	0.0816202i	−0.355880	+	0.00855612i
$92$	11.3740	+	14.1439i	1.18582	+	1.47460i
$93$	9.66598	+	5.44686i	1.00232	+	0.564813i
$94$	3.39313	+	2.90801i	0.349975	+	0.299939i
$95$	8.20876	+	4.73933i	0.842202	+	0.486245i
$96$	−9.71164	+	1.29768i	−0.991191	+	0.132443i
$97$	−5.28964	−	3.05398i	−0.537082	−	0.310084i	0.206814	−	0.978380i	$-0.433691\pi$
$97$	−5.28964	−	3.05398i	−0.537082	−	0.310084i	−0.743895	+	0.668296i	$0.767024\pi$
$98$	7.81758	+	6.07334i	0.789695	+	0.613500i
$99$	12.9719	−	0.270989i	1.30373	−	0.0272354i
$100$	18.8530	−	15.1609i	1.88530	−	1.51609i
$101$	−1.77444			−0.176563			−0.0882816	−	0.996096i	$-0.528138\pi$
$101$	−1.77444			−0.176563			−0.0882816	+	0.996096i	$0.528138\pi$
$102$	4.91164	+	4.12123i	0.486325	+	0.408063i
$103$	13.0004			1.28097			0.640483	−	0.767972i	$-0.278734\pi$
$103$	13.0004			1.28097			0.640483	+	0.767972i	$0.278734\pi$
$104$	−3.62855	−	0.113559i	−0.355809	−	0.0111354i
$105$	−16.7262	−	8.90263i	−1.63231	−	0.868807i
$106$	4.50710	−	5.25898i	0.437768	−	0.510798i
$107$	2.20389	−	3.81725i	0.213058	−	0.369027i	−0.739612	−	0.673034i	$-0.764991\pi$
$107$	2.20389	−	3.81725i	0.213058	−	0.369027i	0.952670	+	0.304006i	$0.0983243\pi$
$108$	−6.76306	−	7.89057i	−0.650776	−	0.759270i
$109$	−9.98683	+	5.76590i	−0.956565	+	0.552273i	−0.895114	−	0.445837i	$-0.852906\pi$
$109$	−9.98683	+	5.76590i	−0.956565	+	0.552273i	−0.0614507	+	0.998110i	$0.519573\pi$
$110$	23.8535	−	8.40132i	2.27435	−	0.801035i
$111$	−3.74604	+	6.64771i	−0.355558	+	0.630973i
$112$	7.98554	+	6.94486i	0.754563	+	0.656228i
$113$	−4.45447	−	7.71536i	−0.419041	−	0.725800i	0.576802	−	0.816884i	$-0.304300\pi$
$113$	−4.45447	−	7.71536i	−0.419041	−	0.725800i	−0.995843	+	0.0910836i	$0.970967\pi$
$114$	0.974998	−	5.52998i	0.0913170	−	0.517930i
$115$			37.5228i			3.49902i
$116$	−3.07537	+	0.476365i	−0.285541	+	0.0442294i
$117$	−1.99450	−	3.29373i	−0.184391	−	0.304505i
$118$	−7.18807	−	1.34489i	−0.661715	−	0.123807i
$119$	−0.166452	−	6.92333i	−0.0152586	−	0.634661i
$120$	−17.3275	−	10.4915i	−1.58178	−	0.957737i
$121$	7.70496			0.700451
$122$	−9.45832	−	8.10605i	−0.856316	−	0.733887i
$123$	0.174593	+	0.295240i	0.0157426	+	0.0266209i
$124$	−1.96107	−	12.6604i	−0.176109	−	1.13694i
$125$	29.3419			2.62442
$126$	−1.56677	+	11.1151i	−0.139579	+	0.990211i
$127$		−	1.69119i		−	0.150069i	−0.997181	−	0.0750343i	$-0.976093\pi$
$127$		−	1.69119i		−	0.150069i	0.997181	−	0.0750343i	$-0.0239066\pi$
$128$	8.11331	+	7.88506i	0.717122	+	0.696947i
$129$	−5.89116	−	3.31972i	−0.518688	−	0.292285i
$130$	−5.69876	−	4.88400i	−0.499815	−	0.428355i
$131$		−	17.6471i		−	1.54184i	−0.636933	−	0.770919i	$-0.719797\pi$
$131$		−	17.6471i		−	1.54184i	0.636933	−	0.770919i	$-0.280203\pi$
$132$	−9.51019	−	11.5765i	−0.827756	−	1.00761i
$133$	−5.17820	+	3.15797i	−0.449007	+	0.273830i
$134$	−0.554501	+	2.96366i	−0.0479016	+	0.256021i
$135$	−0.673035	−	21.4744i	−0.0579256	−	1.84822i
$136$	0.231586	−	7.39987i	0.0198583	−	0.634534i
$137$	3.18383			0.272013			0.136006	−	0.990708i	$-0.456573\pi$
$137$	3.18383			0.272013			0.136006	+	0.990708i	$0.456573\pi$
$138$	20.8883	−	7.60306i	1.77813	−	0.647216i
$139$	−14.1864	+	8.19051i	−1.20327	+	0.694710i	−0.961281	−	0.275568i	$-0.911134\pi$
$139$	−14.1864	+	8.19051i	−1.20327	+	0.694710i	−0.241991	+	0.970278i	$0.577801\pi$
$140$	3.86779	+	21.5346i	0.326888	+	1.82001i
$141$	4.71101	−	2.78590i	0.396738	−	0.234615i
$142$	2.26062	+	6.41850i	0.189707	+	0.538628i
$143$	−2.77555	−	4.80739i	−0.232103	−	0.402014i
$144$	−2.32944	+	11.7717i	−0.194120	+	0.980978i
$145$	−5.57183	−	3.21690i	−0.462716	−	0.267149i
$146$	−10.7222	+	12.5109i	−0.887373	+	1.03541i
$147$	10.1275	−	6.66590i	0.835300	−	0.549794i
$148$	8.70713	−	1.34871i	0.715722	−	0.110863i
$149$			5.87943i			0.481662i	0.970567	+	0.240831i	$0.0774199\pi$
$149$			5.87943i			0.481662i	−0.970567	+	0.240831i	$0.922580\pi$
$150$	−10.1345	−	27.8429i	−0.827475	−	2.27336i
$151$			10.3821i			0.844882i	0.906390	+	0.422441i	$0.138827\pi$
$151$			10.3821i			0.844882i	−0.906390	+	0.422441i	$0.861173\pi$
$152$	−5.71394	+	3.06474i	−0.463461	+	0.248584i
$153$	6.71705	−	4.06747i	0.543042	−	0.328836i
$154$	−2.59291	+	15.9733i	−0.208942	+	1.28716i
$155$	13.2431	−	22.9377i	1.06371	−	1.84240i
$156$	−1.56412	+	4.16202i	−0.125230	+	0.333228i
$157$	4.88984	−	8.46946i	0.390252	−	0.675936i	−0.602231	−	0.798322i	$-0.705721\pi$
$157$	4.88984	−	8.46946i	0.390252	−	0.675936i	0.992483	+	0.122386i	$0.0390545\pi$
$158$	−7.97252	+	9.30252i	−0.634260	+	0.740068i
$159$	−4.31784	−	7.30154i	−0.342427	−	0.579050i
$160$	2.85554	+	23.2149i	0.225750	+	1.83530i
$161$	−21.0758	−	11.5018i	−1.66101	−	0.906466i
$162$	−11.8180	+	4.72592i	−0.928512	+	0.371303i
$163$	6.46593	−	11.1993i	0.506451	−	0.877198i	−0.493522	−	0.869734i	$-0.664291\pi$
$163$	6.46593	−	11.1993i	0.506451	−	0.877198i	0.999972	−	0.00746457i	$-0.00237607\pi$
$164$	0.143194	−	0.369272i	0.0111816	−	0.0288353i
$165$	−0.323472	−	30.9719i	−0.0251822	−	2.41116i
$166$	7.86384	+	1.47132i	0.610352	+	0.114197i
$167$	6.76297	+	11.7138i	0.523335	+	0.906442i	0.999631	+	0.0271574i	$0.00864552\pi$
$167$	6.76297	+	11.7138i	0.523335	+	0.906442i	−0.476297	+	0.879285i	$0.658021\pi$
$168$	11.2042	−	6.51658i	0.864423	−	0.502765i
$169$	5.67630	−	9.83163i	0.436638	−	0.756279i
$170$	9.96017	−	11.6218i	0.763910	−	0.891348i
$171$	−6.02642	−	3.31349i	−0.460852	−	0.253389i
$172$	1.19522	+	7.71620i	0.0911345	+	0.588355i
$173$	5.43617	+	9.41572i	0.413304	+	0.715864i	0.995249	−	0.0973647i	$-0.0310413\pi$
$173$	5.43617	+	9.41572i	0.413304	+	0.715864i	−0.581945	+	0.813228i	$0.697708\pi$
$174$	−0.661796	+	3.75356i	−0.0501706	+	0.284557i
$175$	−15.3312	+	28.0929i	−1.15893	+	2.12362i
$176$	−3.71192	+	16.8968i	−0.279797	+	1.27364i
$177$	−4.39691	+	7.80274i	−0.330492	+	0.586490i
$178$	−12.0100	−	2.24707i	−0.900186	−	0.168425i
$179$	0.0546462	+	0.0946501i	0.00408445	+	0.00707448i	0.868060	−	0.496459i	$-0.165367\pi$
$179$	0.0546462	+	0.0946501i	0.00408445	+	0.00707448i	−0.863976	+	0.503533i	$0.832033\pi$
$180$	−19.0040	+	15.9473i	−1.41648	+	1.18864i
$181$	−6.95290			−0.516805			−0.258402	−	0.966037i	$-0.583196\pi$
$181$	−6.95290			−0.516805			−0.258402	+	0.966037i	$0.583196\pi$
$182$	4.49007	−	1.70380i	0.332826	−	0.126294i
$183$	−13.1319	+	7.76567i	−0.970736	+	0.574055i
$184$	−21.8166	−	13.5229i	−1.60834	−	0.996925i
$185$	15.7752	+	9.10784i	1.15982	+	0.669622i
$186$	−15.4524	−	2.72443i	−1.13302	−	0.199765i
$187$	9.80394	−	5.66031i	0.716935	−	0.413923i
$188$	−5.89229	−	2.28488i	−0.429740	−	0.166642i
$189$	12.2680	+	6.20446i	0.892368	+	0.451308i
$190$	−13.1762	−	2.46527i	−0.955903	−	0.178849i
$191$	17.3398	−	10.0111i	1.25466	−	0.724380i	0.282631	−	0.959229i	$-0.408793\pi$
$191$	17.3398	−	10.0111i	1.25466	−	0.724380i	0.972032	+	0.234849i	$0.0754595\pi$
$192$	12.3447	−	6.29354i	0.890901	−	0.454197i
$193$	2.13070	−	3.69047i	0.153371	−	0.265646i	−0.779094	−	0.626907i	$-0.784320\pi$
$193$	2.13070	−	3.69047i	0.153371	−	0.265646i	0.932465	+	0.361261i	$0.117654\pi$
$194$	8.49061	+	1.58859i	0.609590	+	0.114054i
$195$	−7.91213	+	4.67892i	−0.566599	+	0.335064i
$196$	−13.2811	−	4.42848i	−0.948652	−	0.316320i
$197$		−	9.24136i		−	0.658420i	−0.944257	−	0.329210i	$-0.893218\pi$
$197$		−	9.24136i		−	0.658420i	0.944257	−	0.329210i	$-0.106782\pi$
$198$	−17.1759	+	6.45575i	−1.22064	+	0.458790i
$199$	11.3696	+	19.6928i	0.805971	+	1.39598i	0.915633	+	0.402014i	$0.131690\pi$
$199$	11.3696	+	19.6928i	0.805971	+	1.39598i	−0.109662	+	0.993969i	$0.534977\pi$
$200$	−18.0253	+	29.0803i	−1.27458	+	2.05629i
$201$	3.21709	+	1.81286i	0.226916	+	0.127869i
$202$	2.36692	−	0.833639i	0.166536	−	0.0586547i
$203$	3.51479	−	2.14352i	0.246690	−	0.150446i
$204$	−8.48780	−	3.18979i	−0.594265	−	0.223330i
$205$	0.709116	−	0.409408i	0.0495268	−	0.0285943i
$206$	−17.3412	+	6.10764i	−1.20822	+	0.425540i
$207$	−0.568612	−	27.2188i	−0.0395213	−	1.89184i
$208$	4.89346	−	1.55323i	0.339301	−	0.107697i
$209$	−8.58626	−	4.95728i	−0.593924	−	0.342902i
$210$	26.4936	+	4.01713i	1.82823	+	0.277208i
$211$	6.35436	+	11.0061i	0.437452	+	0.757689i	0.997492	−	0.0707762i	$-0.0225476\pi$
$211$	6.35436	+	11.0061i	0.437452	+	0.757689i	−0.560040	+	0.828466i	$0.689214\pi$
$212$	−3.54131	+	9.13240i	−0.243218	+	0.627216i
$213$	8.33389	−	0.0870396i	0.571029	−	0.00596386i
$214$	−1.14640	+	6.12722i	−0.0783665	+	0.418848i
$215$	−8.07131	+	13.9799i	−0.550459	+	0.953423i
$216$	12.7283	+	7.34789i	0.866048	+	0.499961i
$217$	8.82429	+	14.4694i	0.599032	+	0.982248i
$218$	10.6126	−	12.3830i	0.718774	−	0.838681i
$219$	10.2719	+	17.3700i	0.694113	+	1.17376i
$220$	−27.8712	+	22.4130i	−1.87908	+	1.51108i
$221$	−2.90953	−	1.67982i	−0.195716	−	0.112997i
$222$	1.87371	−	10.6273i	0.125755	−	0.713256i
$223$	8.50455	−	14.7303i	0.569507	−	0.986414i	−0.427108	−	0.904201i	$-0.640468\pi$
$223$	8.50455	−	14.7303i	0.569507	−	0.986414i	0.996615	−	0.0822138i	$-0.0261990\pi$
$224$	−13.9146	−	5.51209i	−0.929710	−	0.368292i
$225$	−36.2812	+	0.757928i	−2.41875	+	0.0505285i
$226$	9.56652	+	8.19878i	0.636355	+	0.545374i
$227$			10.9658i			0.727825i	0.931433	+	0.363912i	$0.118559\pi$
$227$			10.9658i			0.727825i	−0.931433	+	0.363912i	$0.881441\pi$
$228$	1.29746	+	7.83449i	0.0859265	+	0.518852i
$229$	6.00658			0.396926			0.198463	−	0.980108i	$-0.436405\pi$
$229$	6.00658			0.396926			0.198463	+	0.980108i	$0.436405\pi$
$230$	−17.6284	−	50.0516i	−1.16238	−	3.30030i
$231$	17.4954	+	9.31203i	1.15111	+	0.612687i
$232$	3.87843	−	2.08025i	0.254631	−	0.136575i
$233$	14.4408	−	25.0122i	0.946047	−	1.63860i	0.192404	−	0.981316i	$-0.438371\pi$
$233$	14.4408	−	25.0122i	0.946047	−	1.63860i	0.753642	−	0.657285i	$-0.228295\pi$
$234$	4.20787	+	3.45647i	0.275077	+	0.225957i
$235$	−6.53273	−	11.3150i	−0.426148	−	0.738111i
$236$	10.2200	−	1.58304i	0.665264	−	0.103047i
$237$	7.63775	+	12.9156i	0.496125	+	0.838956i
$238$	3.47464	+	9.15682i	0.225228	+	0.593548i
$239$	1.47156	−	0.849605i	0.0951872	−	0.0549564i	−0.451651	−	0.892195i	$-0.649165\pi$
$239$	1.47156	−	0.849605i	0.0951872	−	0.0549564i	0.546838	+	0.837238i	$0.315831\pi$
$240$	28.0420	+	5.85404i	1.81011	+	0.377876i
$241$		−	21.0026i		−	1.35290i	−0.736490	−	0.676448i	$-0.763518\pi$
$241$		−	21.0026i		−	1.35290i	0.736490	−	0.676448i	$-0.236482\pi$
$242$	−10.2776	+	3.61982i	−0.660671	+	0.232691i
$243$	0.813634	+	15.5672i	0.0521946	+	0.998637i
$244$	16.4247	+	6.36908i	1.05148	+	0.407739i
$245$	−15.6596	−	24.3413i	−1.00045	−	1.55511i
$246$	−0.371595	−	0.311796i	−0.0236920	−	0.0198794i
$247$			2.94236i			0.187218i
$248$	8.56380	+	15.9664i	0.543802	+	1.01387i
$249$	4.81028	−	8.53630i	0.304839	−	0.540966i
$250$	−39.1391	+	13.7850i	−2.47537	+	0.871837i
$251$		−	6.69266i		−	0.422437i	−0.977439	−	0.211219i	$-0.932257\pi$
$251$		−	6.69266i		−	0.422437i	0.977439	−	0.211219i	$-0.0677432\pi$
$252$	−3.13200	−	15.5625i	−0.197298	−	0.980344i
$253$		−	39.2484i		−	2.46752i
$254$	0.794528	+	2.25587i	0.0498531	+	0.141546i
$255$	−9.54194	−	16.1356i	−0.597539	−	1.01045i
$256$	−14.5268	−	6.70619i	−0.907923	−	0.419137i
$257$			24.4467i			1.52494i	0.647022	+	0.762471i	$0.276014\pi$
$257$			24.4467i			1.52494i	−0.647022	+	0.762471i	$0.723986\pi$
$258$	9.41782	+	1.66047i	0.586328	+	0.103376i
$259$	−9.95124	+	6.06884i	−0.618340	+	0.377099i
$260$	9.89610	+	3.83745i	0.613730	+	0.237989i
$261$	4.09053	+	2.24909i	0.253197	+	0.139215i
$262$	8.29071	+	23.5395i	0.512202	+	1.45427i
$263$		−	2.47949i		−	0.152892i	−0.997074	−	0.0764458i	$-0.975643\pi$
$263$		−	2.47949i		−	0.152892i	0.997074	−	0.0764458i	$-0.0243572\pi$
$264$	18.1243	+	10.9740i	1.11548	+	0.675400i
$265$	−17.5370	+	10.1250i	−1.07729	+	0.621975i
$266$	5.42356	−	6.64515i	0.332540	−	0.407440i
$267$	−7.34645	+	13.0370i	−0.449595	+	0.797850i
$268$	−0.652695	−	4.21373i	−0.0398697	−	0.257395i
$269$	5.95410	+	10.3128i	0.363028	+	0.628782i	0.988458	−	0.151498i	$-0.0484097\pi$
$269$	5.95410	+	10.3128i	0.363028	+	0.628782i	−0.625430	+	0.780280i	$0.715076\pi$
$270$	10.9865	+	28.3284i	0.668619	+	1.72401i
$271$	−0.560776	+	0.971293i	−0.0340647	+	0.0590018i	−0.882555	−	0.470209i	$-0.844179\pi$
$271$	−0.560776	+	0.971293i	−0.0340647	+	0.0590018i	0.848490	+	0.529211i	$0.177512\pi$
$272$	3.16758	+	9.97947i	0.192063	+	0.605094i
$273$	−0.202771	−	5.87830i	−0.0122723	−	0.355771i
$274$	−4.24690	+	1.49578i	−0.256565	+	0.0903632i
$275$	−52.3159			−3.15477
$276$	−24.2909	+	19.9551i	−1.46214	+	1.20116i
$277$		−	8.83901i		−	0.531084i	−0.964099	−	0.265542i	$-0.914449\pi$
$277$		−	8.83901i		−	0.531084i	0.964099	−	0.265542i	$-0.0855510\pi$
$278$	15.0752	−	17.5901i	0.904153	−	1.05499i
$279$	−9.25888	+	16.8396i	−0.554315	+	1.00816i
$280$	−15.2763	−	26.9078i	−0.912932	−	1.60805i
$281$	−12.6269	+	21.8704i	−0.753255	+	1.30468i	0.192982	+	0.981202i	$0.438184\pi$
$281$	−12.6269	+	21.8704i	−0.753255	+	1.30468i	−0.946237	+	0.323473i	$0.895149\pi$
$282$	−4.97517	+	5.92936i	−0.296267	+	0.353088i
$283$	−17.3279	−	10.0043i	−1.03004	−	0.594691i	−0.113040	−	0.993590i	$-0.536059\pi$
$283$	−17.3279	−	10.0043i	−1.03004	−	0.594691i	−0.916995	+	0.398899i	$0.869392\pi$
$284$	−6.03088	−	7.49957i	−0.357867	−	0.445018i
$285$	−8.05983	+	14.3030i	−0.477423	+	0.847234i
$286$	5.96083	+	5.10860i	0.352472	+	0.302078i
$287$	0.0125931	+	0.523791i	0.000743345	+	0.0309184i
$288$	−2.42319	−	16.7967i	−0.142788	−	0.989753i
$289$	−5.07427	+	8.78889i	−0.298486	+	0.516994i
$290$	8.94357	+	1.67334i	0.525185	+	0.0982620i
$291$	5.19367	−	9.21667i	0.304458	−	0.540291i
$292$	8.42462	−	21.7256i	0.493013	−	1.27139i
$293$	0.492008	+	0.852182i	0.0287434	+	0.0497850i	0.880039	−	0.474901i	$-0.157516\pi$
$293$	0.492008	+	0.852182i	0.0287434	+	0.0497850i	−0.851296	+	0.524686i	$0.824183\pi$
$294$	−10.3774	+	13.6496i	−0.605220	+	0.796059i
$295$	18.5162	+	10.6903i	1.07805	+	0.622414i
$296$	−10.9808	+	5.88969i	−0.638246	+	0.342331i
$297$	0.703986	+	22.4619i	0.0408494	+	1.30337i
$298$	−2.76219	−	7.84256i	−0.160009	−	0.454308i
$299$	−10.0873	+	5.82390i	−0.583363	+	0.336805i
$300$	26.5990	+	32.3783i	1.53570	+	1.86936i
$301$	−5.37817	−	8.81872i	−0.309992	−	0.508303i
$302$	−4.87755	−	13.8486i	−0.280672	−	0.796900i
$303$	−0.0320972	−	3.07325i	−0.00184393	−	0.176554i
$304$	6.18198	−	6.77249i	0.354561	−	0.388429i
$305$	18.2099	+	31.5405i	1.04270	+	1.80600i
$306$	−7.04895	+	8.58130i	−0.402961	+	0.490560i
$307$			6.74344i			0.384869i	0.981310	+	0.192434i	$0.0616382\pi$
$307$			6.74344i			0.384869i	−0.981310	+	0.192434i	$0.938362\pi$
$308$	−4.04566	−	22.5249i	−0.230523	−	1.28348i
$309$	0.235159	+	22.5161i	0.0133777	+	1.28090i
$310$	−6.88869	+	36.8182i	−0.391251	+	2.09114i
$311$	15.2969	−	26.4949i	0.867405	−	1.50239i	0.00276682	−	0.999996i	$-0.499119\pi$
$311$	15.2969	−	26.4949i	0.867405	−	1.50239i	0.864639	−	0.502394i	$-0.167547\pi$
$312$	0.131044	−	6.28654i	0.00741888	−	0.355905i
$313$	10.9046	−	6.29580i	0.616367	−	0.355860i	−0.159086	−	0.987265i	$-0.550855\pi$
$313$	10.9046	−	6.29580i	0.616367	−	0.355860i	0.775453	+	0.631405i	$0.217521\pi$
$314$	−2.54356	+	13.5947i	−0.143541	+	0.767191i
$315$	15.1164	−	29.1301i	0.851713	−	1.64130i
$316$	6.26416	−	16.1541i	0.352387	−	0.908741i
$317$	−27.2450	+	15.7299i	−1.53023	+	0.883480i	−0.530881	+	0.847446i	$0.678139\pi$
$317$	−27.2450	+	15.7299i	−1.53023	+	0.883480i	−0.999351	+	0.0360334i	$0.988528\pi$
$318$	9.18986	+	7.71097i	0.515342	+	0.432410i
$319$	5.82807	+	3.36484i	0.326309	+	0.188395i
$320$	−14.7154	−	29.6247i	−0.822619	−	1.65607i
$321$	6.65118	+	3.74799i	0.371232	+	0.209193i
$322$	33.5166	+	5.44066i	1.86780	+	0.303196i
$323$	−6.00049			−0.333876
$324$	13.5438	−	11.8561i	0.752432	−	0.658670i
$325$	7.76293	+	13.4458i	0.430610	+	0.745838i
$326$	−3.36340	+	17.9765i	−0.186281	+	0.995624i
$327$	−10.1669	−	17.1925i	−0.562233	−	0.950745i
$328$	−0.0175209	+	0.559844i	−0.000967428	+	0.0309122i
$329$	8.35788	−	0.200941i	0.460785	−	0.0110783i
$330$	14.9822	+	41.1613i	0.824743	+	2.26586i
$331$	−9.02430	−	15.6306i	−0.496021	−	0.859133i	0.503969	−	0.863722i	$-0.331873\pi$
$331$	−9.02430	−	15.6306i	−0.496021	−	0.859133i	−0.999989	+	0.00458901i	$0.998539\pi$
$332$	−11.1808	+	1.73187i	−0.613626	+	0.0950488i
$333$	−11.5813	−	6.36773i	−0.634652	−	0.348949i
$334$	−14.5243	−	12.4478i	−0.794735	−	0.681111i
$335$	4.40765	−	7.63428i	0.240816	−	0.417105i
$336$	−11.8837	+	13.9562i	−0.648312	+	0.761375i
$337$	14.0051	+	24.2576i	0.762908	+	1.32140i	0.941346	+	0.337444i	$0.109562\pi$
$337$	14.0051	+	24.2576i	0.762908	+	1.32140i	−0.178438	+	0.983951i	$0.557104\pi$
$338$	−2.95265	+	15.7811i	−0.160603	+	0.858381i
$339$	13.2821	−	7.85450i	0.721384	−	0.426598i
$340$	−7.82590	+	20.1816i	−0.424419	+	1.09450i
$341$	−13.8521	+	23.9926i	−0.750134	+	1.29927i
$342$	9.59532	+	1.58862i	0.518855	+	0.0859030i
$343$	18.4721	−	1.33439i	0.997401	−	0.0720501i
$344$	−5.21941	−	9.73111i	−0.281412	−	0.524666i
$345$	−64.9878	+	0.678737i	−3.49883	+	0.0365419i
$346$	−11.6748	−	10.0057i	−0.627643	−	0.537908i
$347$	16.9270	−	29.3184i	0.908689	−	1.57390i	0.0928018	−	0.995685i	$-0.470418\pi$
$347$	16.9270	−	29.3184i	0.908689	−	1.57390i	0.815887	−	0.578211i	$-0.196249\pi$
$348$	−0.880673	−	5.31779i	−0.0472090	−	0.285063i
$349$	−3.27919	+	5.67973i	−0.175531	+	0.304029i	−0.940345	−	0.340223i	$-0.889498\pi$
$349$	−3.27919	+	5.67973i	−0.175531	+	0.304029i	0.764814	+	0.644251i	$0.222831\pi$
$350$	7.25210	−	44.6757i	0.387641	−	2.38802i
$351$	5.66852	−	3.51396i	0.302563	−	0.187561i
$352$	−2.98686	−	24.2824i	−0.159200	−	1.29426i
$353$			23.6201i			1.25717i	0.777740	+	0.628587i	$0.216366\pi$
$353$			23.6201i			1.25717i	−0.777740	+	0.628587i	$0.783634\pi$
$354$	2.19926	−	12.4737i	0.116890	−	0.662972i
$355$		−	19.8959i		−	1.05596i
$356$	17.0758	−	2.64499i	0.905014	−	0.140184i
$357$	11.9879	−	0.413521i	0.634467	−	0.0218858i
$358$	−0.117360	−	0.100580i	−0.00620264	−	0.00531584i
$359$	−20.1609	−	11.6399i	−1.06405	−	0.614329i	−0.137500	−	0.990502i	$-0.543907\pi$
$359$	−20.1609	−	11.6399i	−1.06405	−	0.614329i	−0.926550	+	0.376172i	$0.877240\pi$
$360$	17.8574	−	30.2002i	0.941166	−	1.59169i
$361$	−6.87239	−	11.9033i	−0.361705	−	0.626491i
$362$	9.27445	−	3.26650i	0.487454	−	0.171684i
$363$	0.139372	+	13.3446i	0.00731515	+	0.700412i
$364$	−5.18885	+	4.38216i	−0.271969	+	0.229687i
$365$	41.7198	−	24.0869i	2.18371	−	1.26077i
$366$	13.8682	−	16.5280i	0.724904	−	0.863934i
$367$	−35.0257			−1.82833			−0.914164	−	0.405344i	$-0.867152\pi$
$367$	−35.0257			−1.82833			−0.914164	+	0.405344i	$0.867152\pi$
$368$	35.4543	+	7.78868i	1.84818	+	0.406013i
$369$	−0.508185	+	0.307729i	−0.0264551	+	0.0160197i
$370$	−25.3215	−	4.73765i	−1.31640	−	0.246299i
$371$	−0.311437	−	12.9538i	−0.0161690	−	0.672528i
$372$	21.8919	−	3.62549i	1.13504	−	0.187973i
$373$			1.25485i			0.0649735i	0.999472	+	0.0324867i	$0.0103427\pi$
$373$			1.25485i			0.0649735i	−0.999472	+	0.0324867i	$0.989657\pi$
$374$	−10.4182	+	12.1562i	−0.538713	+	0.628583i
$375$	0.530755	+	50.8189i	0.0274081	+	2.62428i
$376$	8.93316	+	0.279572i	0.460693	+	0.0144178i
$377$		−	1.99718i		−	0.102860i
$378$	−19.2792	−	2.51253i	−0.991615	−	0.129231i
$379$	−24.9135			−1.27972			−0.639861	−	0.768491i	$-0.721008\pi$
$379$	−24.9135			−1.27972			−0.639861	+	0.768491i	$0.721008\pi$
$380$	18.7339	−	2.90183i	0.961030	−	0.148861i
$381$	2.92906	−	0.0305913i	0.150060	−	0.00156724i
$382$	−18.4262	+	21.5001i	−0.942768	+	1.10004i
$383$	1.94864			0.0995710			0.0497855	−	0.998760i	$-0.484146\pi$
$383$	1.94864			0.0995710			0.0497855	+	0.998760i	$0.484146\pi$
$384$	−13.5098	+	14.1945i	−0.689420	+	0.724362i
$385$	22.6648	−	41.5309i	1.15510	−	2.11661i
$386$	−1.10833	+	5.92373i	−0.0564125	+	0.301510i
$387$	5.64304	−	10.2633i	0.286852	−	0.521712i
$388$	−12.0719	+	1.86991i	−0.612860	+	0.0949302i
$389$		−	5.44098i		−	0.275868i	−0.990441	−	0.137934i	$-0.955954\pi$
$389$		−	5.44098i		−	0.275868i	0.990441	−	0.137934i	$-0.0440463\pi$
$390$	8.35580	−	9.95836i	0.423112	−	0.504261i
$391$	−11.8769	−	20.5715i	−0.600643	−	1.04034i
$392$	19.7962	−	0.332395i	0.999859	−	0.0167885i
$393$	30.5641	−	0.319213i	1.54175	−	0.0161022i
$394$	4.34163	+	12.3270i	0.218728	+	0.621027i
$395$	31.0209	−	17.9099i	1.56083	−	0.901147i
$396$	19.8780	−	16.6806i	0.998907	−	0.838234i
$397$	−12.8854	+	22.3181i	−0.646698	+	1.12011i	0.337209	+	0.941430i	$0.390517\pi$
$397$	−12.8854	+	22.3181i	−0.646698	+	1.12011i	−0.983907	+	0.178684i	$0.942816\pi$
$398$	−24.4177	−	20.9266i	−1.22395	−	1.04896i
$399$	−5.56312	−	8.91129i	−0.278505	−	0.446123i
$400$	10.3819	−	47.2586i	0.519093	−	2.36293i
$401$	26.0659			1.30167			0.650833	−	0.759221i	$-0.274420\pi$
$401$	26.0659			1.30167			0.650833	+	0.759221i	$0.274420\pi$
$402$	−5.14297	−	0.906764i	−0.256508	−	0.0452253i
$403$	8.22182			0.409558
$404$	−2.76558	+	2.22398i	−0.137593	+	0.110647i
$405$	37.1805	−	1.55411i	1.84751	−	0.0772243i
$406$	−3.68133	+	4.51050i	−0.182701	+	0.223852i
$407$	−16.5007	−	9.52669i	−0.817910	−	0.472220i
$408$	12.8204	+	0.267243i	0.634706	+	0.0132305i
$409$	−0.474018	−	0.273674i	−0.0234387	−	0.0135323i	0.488235	−	0.872712i	$-0.337641\pi$
$409$	−0.474018	−	0.273674i	−0.0234387	−	0.0135323i	−0.511674	+	0.859180i	$0.670974\pi$
$410$	−0.753547	+	0.879255i	−0.0372150	+	0.0434233i
$411$	0.0575912	+	5.51425i	0.00284076	+	0.271998i
$412$	20.2620	−	16.2939i	0.998236	−	0.802745i
$413$	−11.6803	+	7.12329i	−0.574748	+	0.350514i
$414$	13.5460	+	36.0400i	0.665750	+	1.77127i
$415$	−20.2569	−	11.6953i	−0.994374	−	0.574102i
$416$	−5.79767	+	4.37083i	−0.284254	+	0.214297i
$417$	−14.4422	−	24.4220i	−0.707238	−	1.19595i
$418$	13.7822	+	2.57864i	0.674107	+	0.126125i
$419$	11.0422	−	6.37520i	0.539446	−	0.311449i	−0.205409	−	0.978676i	$-0.565852\pi$
$419$	11.0422	−	6.37520i	0.539446	−	0.311449i	0.744854	+	0.667227i	$0.232519\pi$
$420$	−37.2270	+	7.08837i	−1.81649	+	0.345877i
$421$	−14.7249	−	8.50144i	−0.717649	−	0.414335i	0.0962379	−	0.995358i	$-0.469319\pi$
$421$	−14.7249	−	8.50144i	−0.717649	−	0.414335i	−0.813887	+	0.581024i	$0.802652\pi$
$422$	−13.6468	−	11.6957i	−0.664314	−	0.569336i
$423$	4.91028	+	8.10886i	0.238746	+	0.394267i
$424$	0.433306	−	13.8454i	0.0210432	−	0.672393i
$425$	−27.4206	+	15.8313i	−1.33010	+	0.767931i
$426$	−11.0757	+	4.03140i	−0.536618	+	0.195322i
$427$	−23.2975	+	0.560122i	−1.12745	+	0.0271062i
$428$	−1.34941	−	8.71167i	−0.0652263	−	0.421095i
$429$	8.27599	−	4.89409i	0.399568	−	0.236289i
$430$	4.19847	−	22.4397i	0.202468	−	1.08214i
$431$	15.7970	−	9.12038i	0.760912	−	0.439313i	−0.0687108	−	0.997637i	$-0.521889\pi$
$431$	15.7970	−	9.12038i	0.760912	−	0.439313i	0.829623	+	0.558324i	$0.188555\pi$
$432$	−20.4303	−	3.82155i	−0.982952	−	0.183864i
$433$			0.0374331i			0.00179892i	1.00000		0.000899459i	$0.000286307\pi$
$433$			0.0374331i			0.00179892i	−1.00000		0.000899459i	$0.999714\pi$
$434$	−18.5685	−	15.1550i	−0.891317	−	0.727465i
$435$	5.47074	−	9.70836i	0.262302	−	0.465480i
$436$	−8.33850	+	21.5035i	−0.399342	+	1.02983i
$437$	−10.4018	+	18.0164i	−0.497586	+	0.861843i
$438$	−21.8622	−	18.3440i	−1.04462	−	0.876512i
$439$	−2.88974	−	5.00518i	−0.137920	−	0.238884i	0.788789	−	0.614664i	$-0.210708\pi$
$439$	−2.88974	−	5.00518i	−0.137920	−	0.238884i	−0.926709	+	0.375780i	$0.877375\pi$
$440$	26.6476	−	42.9907i	1.27037	−	2.04950i
$441$	11.7282	+	17.4198i	0.558487	+	0.829513i
$442$	4.67020	+	0.873795i	0.222139	+	0.0415622i
$443$	5.40666	+	9.36461i	0.256878	+	0.444926i	0.965404	−	0.260759i	$-0.0839728\pi$
$443$	5.40666	+	9.36461i	0.256878	+	0.444926i	−0.708526	+	0.705685i	$0.750639\pi$
$444$	2.49341	+	15.0560i	0.118332	+	0.714525i
$445$	30.9372	+	17.8616i	1.46656	+	0.846721i
$446$	−4.42383	+	23.6442i	−0.209474	+	1.11959i
$447$	−10.1829	+	0.106351i	−0.481636	+	0.00503023i
$448$	21.1503	+	0.815409i	0.999258	+	0.0385244i
$449$	32.7907			1.54749			0.773744	−	0.633498i	$-0.218381\pi$
$449$	32.7907			1.54749			0.773744	+	0.633498i	$0.218381\pi$
$450$	48.0393	−	18.0561i	2.26460	−	0.851171i
$451$	−0.741726	+	0.428236i	−0.0349265	+	0.0201648i
$452$	−16.6126	−	6.44194i	−0.781390	−	0.303003i
$453$	−17.9813	+	0.187798i	−0.844836	+	0.00882351i
$454$	−5.15178	−	14.6272i	−0.241785	−	0.686490i
$455$	−14.0371	+	0.337481i	−0.658067	+	0.0158214i
$456$	−5.41136	−	9.84085i	−0.253410	−	0.460840i
$457$	9.75756	+	16.9006i	0.456439	+	0.790576i	0.998770	−	0.0495893i	$-0.0157913\pi$
$457$	9.75756	+	16.9006i	0.456439	+	0.790576i	−0.542330	+	0.840165i	$0.682458\pi$
$458$	−8.01217	+	2.82192i	−0.374384	+	0.131860i
$459$	7.16619	+	11.5601i	0.334489	+	0.539578i
$460$	47.0289	+	58.4818i	2.19274	+	2.72673i
$461$	5.74958	−	9.95857i	0.267785	−	0.463817i	−0.700505	−	0.713648i	$-0.747042\pi$
$461$	5.74958	−	9.95857i	0.267785	−	0.463817i	0.968289	+	0.249831i	$0.0803751\pi$
$462$	−27.7120	−	4.20187i	−1.28928	−	0.195489i
$463$	5.14291	−	2.96926i	0.239011	−	0.137993i	−0.375711	−	0.926737i	$-0.622601\pi$
$463$	5.14291	−	2.96926i	0.239011	−	0.137993i	0.614722	+	0.788744i	$0.289268\pi$
$464$	−4.19612	+	4.59694i	−0.194800	+	0.213407i
$465$	39.9667	+	22.5216i	1.85341	+	1.04441i
$466$	−7.51169	+	40.1480i	−0.347972	+	1.85982i
$467$	−32.5590	−	18.7979i	−1.50665	−	0.869865i	−0.999970	−	0.00773005i	$-0.997539\pi$
$467$	−32.5590	−	18.7979i	−1.50665	−	0.869865i	−0.506679	−	0.862135i	$-0.669127\pi$
$468$	−7.23673	−	2.63371i	−0.334518	−	0.121743i
$469$	2.93696	+	4.81581i	0.135616	+	0.222373i
$470$	14.0298	+	12.0240i	0.647149	+	0.554625i
$471$	14.7572	+	8.31580i	0.679975	+	0.383172i
$472$	−12.8887	+	6.91301i	−0.593250	+	0.318197i
$473$	8.44249	−	14.6228i	0.388186	−	0.672358i
$474$	−16.2558	−	13.6398i	−0.746652	−	0.626496i
$475$	24.0149	+	13.8650i	1.10188	+	0.636170i
$476$	−8.93674	−	10.5819i	−0.409615	−	0.485019i
$477$	12.5678	−	7.61039i	0.575442	−	0.348456i
$478$	−1.56376	+	1.82463i	−0.0715248	+	0.0834567i
$479$	−26.8661			−1.22754			−0.613772	−	0.789483i	$-0.710349\pi$
$479$	−26.8661			−1.22754			−0.613772	+	0.789483i	$0.710349\pi$
$480$	−40.1555	+	5.36560i	−1.83284	+	0.244905i
$481$			5.65450i			0.257823i
$482$	9.86712	+	28.0153i	0.449435	+	1.27606i
$483$	19.5393	−	36.7104i	0.889070	−	1.67038i
$484$	12.0087	−	9.65695i	0.545850	−	0.438952i
$485$	−21.8715	−	12.6275i	−0.993133	−	0.573385i
$486$	−8.39885	−	20.3828i	−0.380980	−	0.924583i
$487$	−2.83137	+	1.63469i	−0.128301	+	0.0740749i	−0.562777	−	0.826609i	$-0.690267\pi$
$487$	−2.83137	+	1.63469i	−0.128301	+	0.0740749i	0.434476	+	0.900684i	$0.356934\pi$
$488$	−24.9011	−	0.779303i	−1.12722	−	0.0352774i
$489$	19.5137	+	10.9961i	0.882439	+	0.497262i
$490$	32.3239	+	25.1119i	1.46025	+	1.13444i
$491$	6.51562	+	11.2854i	0.294046	+	0.509302i	0.974762	−	0.223245i	$-0.0716648\pi$
$491$	6.51562	+	11.2854i	0.294046	+	0.509302i	−0.680717	+	0.732547i	$0.738332\pi$
$492$	0.642153	+	0.241327i	0.0289505	+	0.0108798i
$493$	4.07293			0.183436
$494$	−1.38233	−	3.92481i	−0.0621942	−	0.176585i
$495$	53.6361	−	1.12048i	2.41076	−	0.0503617i
$496$	−18.9243	−	17.2743i	−0.849728	−	0.775638i
$497$	11.1751	+	6.09863i	0.501272	+	0.273561i
$498$	−2.40602	+	13.6464i	−0.107816	+	0.611512i
$499$	23.0415			1.03148			0.515740	−	0.856745i	$-0.327517\pi$
$499$	23.0415			1.03148			0.515740	+	0.856745i	$0.327517\pi$
$500$	45.7313	−	36.7755i	2.04517	−	1.64465i
$501$	−20.1655	+	11.9251i	−0.900927	+	0.532772i
$502$	3.14424	+	8.92733i	0.140334	+	0.398446i
$503$	−12.1910			−0.543570			−0.271785	−	0.962358i	$-0.587614\pi$
$503$	−12.1910			−0.543570			−0.271785	+	0.962358i	$0.587614\pi$
$504$	11.4891	+	19.2873i	0.511765	+	0.859126i
$505$	−7.33690			−0.326488
$506$	18.4391	+	52.3533i	0.819716	+	2.32739i
$507$	17.1306	+	9.65326i	0.760798	+	0.428716i
$508$	−2.11964	−	2.63583i	−0.0940437	−	0.116946i
$509$	−3.13469			−0.138943			−0.0694714	−	0.997584i	$-0.522131\pi$
$509$	−3.13469			−0.138943			−0.0694714	+	0.997584i	$0.522131\pi$
$510$	20.3085	+	17.0404i	0.899277	+	0.754560i
$511$	0.740894	+	30.8165i	0.0327752	+	1.36324i
$512$	22.5278	+	2.12063i	0.995599	+	0.0937195i
$513$	5.62982	−	10.4974i	0.248563	−	0.463473i
$514$	−11.4852	−	32.6094i	−0.506589	−	1.43834i
$515$	53.7537			2.36867
$516$	−13.3425	+	2.20964i	−0.587371	+	0.0972740i
$517$	6.83315	+	11.8354i	0.300522	+	0.520519i
$518$	10.4228	−	12.7704i	0.457950	−	0.561097i
$519$	−16.2093	+	9.58552i	−0.711508	+	0.420758i
$520$	−15.0032	−	0.469541i	−0.657935	−	0.0205907i
$521$	−17.1860	+	9.92234i	−0.752932	+	0.434706i	−0.826752	−	0.562566i	$-0.809814\pi$
$521$	−17.1860	+	9.92234i	−0.752932	+	0.434706i	0.0738202	+	0.997272i	$0.476481\pi$
$522$	−6.51298	−	1.07831i	−0.285065	−	0.0471961i
$523$	8.62552	+	4.97995i	0.377168	+	0.217758i	0.676585	−	0.736364i	$-0.263459\pi$
$523$	8.62552	+	4.97995i	0.377168	+	0.217758i	−0.299418	+	0.954122i	$0.596792\pi$
$524$	−22.1179	−	27.5043i	−0.966226	−	1.20153i
$525$	−48.9329	−	26.0448i	−2.13561	−	1.13669i
$526$	1.16487	+	3.30738i	0.0507909	+	0.144209i
$527$			16.7671i			0.730389i
$528$	−29.3316	−	6.12325i	−1.27649	−	0.266480i
$529$	−59.3543			−2.58062
$530$	18.6358	−	21.7447i	0.809489	−	0.944530i
$531$	−13.5935	−	7.47411i	−0.589909	−	0.324349i
$532$	−4.11256	+	11.4120i	−0.178302	+	0.494771i
$533$	0.220123	+	0.127088i	0.00953460	+	0.00550480i
$534$	3.67458	−	20.8414i	0.159014	−	0.901895i
$535$	9.11259	−	15.7835i	0.393972	−	0.682379i
$536$	2.85026	+	5.31405i	0.123112	+	0.229532i
$537$	−0.162941	+	0.0963570i	−0.00703144	+	0.00415811i
$538$	−12.7872	−	10.9590i	−0.551293	−	0.472474i
$539$	16.3797	+	25.4607i	0.705524	+	1.09667i
$540$	−27.9637	−	32.6257i	−1.20337	−	1.40399i
$541$	21.5113	+	12.4195i	0.924841	+	0.533957i	0.885176	−	0.465256i	$-0.154038\pi$
$541$	21.5113	+	12.4195i	0.924841	+	0.533957i	0.0396649	+	0.999213i	$0.487371\pi$
$542$	0.291700	−	1.55906i	0.0125296	−	0.0669674i
$543$	−0.125768	−	12.0421i	−0.00539724	−	0.516776i
$544$	−8.91363	−	11.8234i	−0.382169	−	0.506926i
$545$	−41.2933	+	23.8407i	−1.76881	+	1.02122i
$546$	3.03213	+	7.74579i	0.129763	+	0.331489i
$547$	−15.1654	+	26.2672i	−0.648426	+	1.12311i	0.335073	+	0.942192i	$0.391239\pi$
$547$	−15.1654	+	26.2672i	−0.648426	+	1.12311i	−0.983499	+	0.180914i	$0.942094\pi$
$548$	4.96221	−	3.99043i	0.211975	−	0.170463i
$549$	−13.6873	−	22.6034i	−0.584161	−	0.964688i
$550$	69.7840	−	24.5782i	2.97560	−	1.04802i
$551$	−1.78353	−	3.08917i	−0.0759810	−	0.131603i
$552$	23.0265	−	38.0300i	0.980074	−	1.61867i
$553$	0.550895	+	22.9137i	0.0234265	+	0.974391i
$554$	4.15261	+	11.7903i	0.176427	+	0.500923i
$555$	−15.4890	+	27.4868i	−0.657473	+	1.16675i
$556$	−11.8449	+	30.5459i	−0.502336	+	1.29543i
$557$	−33.0650	+	19.0901i	−1.40101	+	0.808872i	−0.994496	−	0.104774i	$-0.966588\pi$
$557$	−33.0650	+	19.0901i	−1.40101	+	0.808872i	−0.406511	+	0.913646i	$0.633255\pi$
$558$	4.43909	−	26.8122i	0.187922	−	1.13505i
$559$	−5.01098			−0.211942
$560$	33.0184	+	28.7154i	1.39528	+	1.21345i
$561$	9.98074	+	16.8776i	0.421387	+	0.712573i
$562$	6.56814	−	35.1050i	0.277060	−	1.48081i
$563$	−20.1650	−	11.6423i	−0.849855	−	0.490664i	0.0107468	−	0.999942i	$-0.496579\pi$
$563$	−20.1650	−	11.6423i	−0.849855	−	0.490664i	−0.860602	+	0.509278i	$0.829912\pi$
$564$	3.85073	−	10.2465i	0.162145	−	0.431456i
$565$	−18.4182	−	31.9013i	−0.774860	−	1.34210i
$566$	27.8137	+	5.20393i	1.16910	+	0.218738i
$567$	−10.5239	+	21.3599i	−0.441964	+	0.897033i
$568$	11.5679	+	7.17032i	0.485379	+	0.300860i
$569$	−20.4075	−	35.3468i	−0.855526	−	1.48181i	−0.876156	−	0.482027i	$-0.839901\pi$
$569$	−20.4075	−	35.3468i	−0.855526	−	1.48181i	0.0206305	−	0.999787i	$-0.493433\pi$
$570$	4.03140	−	22.8652i	0.168857	−	0.957719i
$571$	−4.34151	+	7.51971i	−0.181687	+	0.314690i	−0.942455	−	0.334333i	$-0.891489\pi$
$571$	−4.34151	+	7.51971i	−0.181687	+	0.314690i	0.760768	+	0.649023i	$0.224822\pi$
$572$	−10.3512	−	4.01393i	−0.432805	−	0.167831i
$573$	17.6525	+	29.8507i	0.737443	+	1.24703i
$574$	−0.262877	−	0.692768i	−0.0109723	−	0.0289156i
$575$			109.774i			4.57788i
$576$	11.1234	+	21.2666i	0.463477	+	0.886109i
$577$	−2.25486	+	1.30185i	−0.0938712	+	0.0541965i	−0.546201	−	0.837654i	$-0.683926\pi$
$577$	−2.25486	+	1.30185i	−0.0938712	+	0.0541965i	0.452330	+	0.891851i	$0.350593\pi$
$578$	2.63949	−	14.1074i	0.109788	−	0.586790i
$579$	6.43028	+	3.62352i	0.267233	+	0.150588i
$580$	−12.7160	+	1.96966i	−0.528001	+	0.0817858i
$581$	12.7783	−	7.79297i	0.530135	−	0.323307i
$582$	−2.59779	+	14.7341i	−0.107682	+	0.610748i
$583$	18.3435	−	10.5906i	0.759711	−	0.438619i
$584$	−1.03081	+	32.9376i	−0.0426554	+	1.36297i
$585$	−8.24680	−	13.6188i	−0.340963	−	0.563069i
$586$	−1.05665	−	0.905577i	−0.0436497	−	0.0374090i
$587$	−22.9961	−	13.2768i	−0.949152	−	0.547993i	−0.0563344	−	0.998412i	$-0.517941\pi$
$587$	−22.9961	−	13.2768i	−0.949152	−	0.547993i	−0.892817	+	0.450419i	$0.851275\pi$
$588$	7.42970	−	23.0825i	0.306396	−	0.951904i
$589$	12.7173	−	7.34231i	0.524005	−	0.302535i
$590$	−29.7210	−	5.56081i	−1.22360	−	0.228935i
$591$	16.0056	−	0.167164i	0.658384	−	0.00687620i
$592$	11.8803	−	13.0151i	0.488276	−	0.534916i
$593$	6.26385	+	3.61643i	0.257225	+	0.148509i	0.623068	−	0.782168i	$-0.285886\pi$
$593$	6.26385	+	3.61643i	0.257225	+	0.148509i	−0.365843	+	0.930677i	$0.619219\pi$
$594$	−11.4918	−	29.6312i	−0.471513	−	1.21578i
$595$	−0.688241	−	28.6264i	−0.0282151	−	1.17357i
$596$	7.36895	+	9.16349i	0.301844	+	0.375351i
$597$	−33.9014	+	20.0479i	−1.38749	+	0.820506i
$598$	10.7193	−	12.5075i	0.438346	−	0.511471i
$599$	0.237738	+	0.137258i	0.00971370	+	0.00560821i	0.504849	−	0.863208i	$-0.331548\pi$
$599$	0.237738	+	0.137258i	0.00971370	+	0.00560821i	−0.495135	+	0.868816i	$0.664882\pi$
$600$	−50.6919	−	30.6930i	−2.06949	−	1.25304i
$601$	−25.9289	−	14.9701i	−1.05766	−	0.610642i	−0.132878	−	0.991132i	$-0.542422\pi$
$601$	−25.9289	−	14.9701i	−1.05766	−	0.610642i	−0.924785	+	0.380491i	$0.875755\pi$
$602$	11.3170	+	9.23659i	0.461247	+	0.376455i
$603$	−3.08160	+	5.60466i	−0.125492	+	0.228239i
$604$	13.0123	+	16.1812i	0.529464	+	0.658403i
$605$	31.8583			1.29522
$606$	1.48664	+	4.08432i	0.0603907	+	0.165914i
$607$	−22.9565			−0.931777			−0.465889	−	0.884843i	$-0.654265\pi$
$607$	−22.9565			−0.931777			−0.465889	+	0.884843i	$0.654265\pi$
$608$	−5.06438	+	11.9381i	−0.205388	+	0.484155i
$609$	3.77606	+	6.04869i	0.153014	+	0.245105i
$610$	−39.1080	−	33.5167i	−1.58344	−	1.35705i
$611$	2.02789	−	3.51240i	0.0820395	−	0.142097i
$612$	5.37104	−	14.7582i	0.217112	−	0.596565i
$613$	−0.368525	+	0.212768i	−0.0148846	+	0.00859363i	−0.507424	−	0.861697i	$-0.669402\pi$
$613$	−0.368525	+	0.212768i	−0.0148846	+	0.00859363i	0.492539	+	0.870290i	$0.336069\pi$
$614$	−3.16810	−	8.99506i	−0.127854	−	0.363011i
$615$	0.721904	+	1.22075i	0.0291100	+	0.0492255i
$616$	15.9788	+	28.1453i	0.643804	+	1.13400i
$617$	−12.0934	−	20.9465i	−0.486864	−	0.843273i	0.513022	−	0.858375i	$-0.328526\pi$
$617$	−12.0934	−	20.9465i	−0.486864	−	0.843273i	−0.999886	+	0.0151024i	$0.995193\pi$
$618$	−10.8918	−	29.9237i	−0.438134	−	1.20371i
$619$			23.6089i			0.948924i	0.880276	+	0.474462i	$0.157357\pi$
$619$			23.6089i			0.948924i	−0.880276	+	0.474462i	$0.842643\pi$
$620$	−8.10857	−	52.3481i	−0.325648	−	2.10235i
$621$	47.1316	−	1.47716i	1.89132	−	0.0592765i
$622$	−7.95700	+	42.5281i	−0.319047	+	1.70522i
$623$	−19.5156	+	11.9017i	−0.781877	+	0.476833i
$624$	2.77865	+	8.44717i	0.111235	+	0.338157i
$625$	60.8403			2.43361
$626$	−11.5879	+	13.5210i	−0.463145	+	0.540408i
$627$	8.43048	−	14.9607i	0.336681	−	0.597473i
$628$	−2.99399	−	19.3289i	−0.119473	−	0.771306i
$629$	−11.5315			−0.459790
$630$	−6.47826	+	45.9584i	−0.258100	+	1.83103i
$631$		−	21.0121i		−	0.836479i	−0.908337	−	0.418240i	$-0.862647\pi$
$631$		−	21.0121i		−	0.836479i	0.908337	−	0.418240i	$-0.137353\pi$
$632$	−0.766466	+	24.4909i	−0.0304884	+	0.974196i
$633$	−18.9471	+	11.2046i	−0.753079	+	0.445341i
$634$	28.9521	−	33.7819i	1.14983	−	1.34165i
$635$		−	6.99268i		−	0.277496i
$636$	−15.8810	−	5.96821i	−0.629722	−	0.236655i
$637$	4.11319	−	7.98778i	0.162970	−	0.316488i
$638$	−9.35486	−	1.75029i	−0.370363	−	0.0692948i
$639$	0.301498	+	14.4324i	0.0119271	+	0.570935i
$640$	33.5467	+	32.6029i	1.32605	+	1.28874i
$641$	−15.7767			−0.623140			−0.311570	−	0.950223i	$-0.600855\pi$
$641$	−15.7767			−0.623140			−0.311570	+	0.950223i	$0.600855\pi$
$642$	−10.6328	−	1.87469i	−0.419644	−	0.0739880i
$643$	−18.5270	+	10.6966i	−0.730634	+	0.421832i	−0.818654	−	0.574287i	$-0.805279\pi$
$643$	−18.5270	+	10.6966i	−0.730634	+	0.421832i	0.0880203	+	0.996119i	$0.471946\pi$
$644$	−47.2637	+	8.48895i	−1.86245	+	0.334511i
$645$	−24.3586	−	13.7263i	−0.959120	−	0.540472i
$646$	8.00404	−	2.81906i	0.314915	−	0.110914i
$647$	−0.659843	−	1.14288i	−0.0259411	−	0.0449313i	0.852763	−	0.522297i	$-0.174925\pi$
$647$	−0.659843	−	1.14288i	−0.0259411	−	0.0449313i	−0.878705	+	0.477366i	$0.841592\pi$
$648$	−12.4960	+	22.1777i	−0.490889	+	0.871222i
$649$	−19.3677	−	11.1819i	−0.760248	−	0.438929i
$650$	−16.6718	−	14.2882i	−0.653924	−	0.560431i
$651$	−24.9008	+	15.5450i	−0.975939	+	0.609257i
$652$	−3.95900	−	25.5589i	−0.155046	−	1.00096i
$653$		−	17.1849i		−	0.672498i	−0.941773	−	0.336249i	$-0.890842\pi$
$653$		−	17.1849i		−	0.672498i	0.941773	−	0.336249i	$-0.109158\pi$
$654$	21.6387	+	18.1565i	0.846142	+	0.709976i
$655$		−	72.9670i		−	2.85106i
$656$	−0.239646	−	0.755006i	−0.00935662	−	0.0294780i
$657$	−29.8983	+	18.1047i	−1.16644	+	0.706333i
$658$	−11.0542	+	4.19461i	−0.430936	+	0.163523i
$659$	10.3636	−	17.9502i	0.403707	−	0.699241i	−0.590463	−	0.807065i	$-0.701055\pi$
$659$	10.3636	−	17.9502i	0.403707	−	0.699241i	0.994170	+	0.107824i	$0.0343882\pi$
$660$	−39.3225	−	47.8663i	−1.53063	−	1.86319i
$661$	4.44476	−	7.69856i	0.172881	−	0.299439i	−0.766545	−	0.642191i	$-0.778026\pi$
$661$	4.44476	−	7.69856i	0.172881	−	0.299439i	0.939426	+	0.342752i	$0.111359\pi$
$662$	19.3808	+	16.6099i	0.753256	+	0.645562i
$663$	2.85674	−	5.06956i	0.110947	−	0.196886i
$664$	14.1004	−	7.56293i	0.547201	−	0.293499i
$665$	−21.4107	+	13.0575i	−0.830271	+	0.506347i
$666$	18.4399	+	3.05295i	0.714530	+	0.118299i
$667$	7.06039	−	12.2290i	0.273379	−	0.473507i
$668$	25.2220	+	9.78044i	0.975867	+	0.378417i
$669$	25.6661	+	14.4631i	0.992308	+	0.559174i
$670$	−2.29274	+	12.2541i	−0.0885762	+	0.473416i
$671$	−19.0473	−	32.9910i	−0.735314	−	1.27360i
$672$	9.29500	−	24.1992i	0.358563	−	0.933506i
$673$	7.82591	−	13.5549i	0.301667	−	0.522502i	−0.674847	−	0.737958i	$-0.735790\pi$
$673$	7.82591	−	13.5549i	0.301667	−	0.522502i	0.976514	+	0.215456i	$0.0691236\pi$
$674$	−30.0777	−	25.7775i	−1.15855	−	0.992911i
$675$	−1.96898	−	62.8237i	−0.0757859	−	2.41809i
$676$	−3.47552	−	22.4376i	−0.133674	−	0.862985i
$677$	−2.57124	−	4.45352i	−0.0988209	−	0.171163i	0.812376	−	0.583134i	$-0.198174\pi$
$677$	−2.57124	−	4.45352i	−0.0988209	−	0.171163i	−0.911197	+	0.411971i	$0.864840\pi$
$678$	−14.0269	+	16.7171i	−0.538699	+	0.642016i
$679$	13.7968	−	8.41410i	0.529474	−	0.322903i
$680$	0.957556	−	30.5968i	0.0367206	−	1.17333i
$681$	−18.9923	+	0.198356i	−0.727785	+	0.00760103i
$682$	7.20549	−	38.5114i	0.275912	−	1.47468i
$683$	15.9748	+	27.6691i	0.611258	+	1.05873i	0.991029	+	0.133649i	$0.0426694\pi$
$683$	15.9748	+	27.6691i	0.611258	+	1.05873i	−0.379771	+	0.925080i	$0.623997\pi$
$684$	−13.5455	+	2.38886i	−0.517926	+	0.0913404i
$685$	13.1644			0.502987
$686$	−24.0130	+	10.4582i	−0.916822	+	0.399297i
$687$	0.108651	+	10.4031i	0.00414529	+	0.396905i
$688$	11.5339	+	10.5282i	0.439725	+	0.401384i
$689$	−5.44383	−	3.14300i	−0.207394	−	0.119739i
$690$	86.3683	−	31.4370i	3.28798	−	1.19678i
$691$	3.67189	−	2.11997i	0.139685	−	0.0806474i	−0.428529	−	0.903528i	$-0.640968\pi$
$691$	3.67189	−	2.11997i	0.139685	−	0.0806474i	0.568214	+	0.822881i	$0.307635\pi$
$692$	20.2738	+	7.86165i	0.770692	+	0.298855i
$693$	−15.8116	+	30.4698i	−0.600632	+	1.15745i
$694$	−8.80496	+	47.0602i	−0.334232	+	1.78638i
$695$	−58.6575	+	33.8659i	−2.22501	+	1.28461i
$696$	3.67305	+	6.67964i	0.139227	+	0.253191i
$697$	−0.259177	+	0.448908i	−0.00981703	+	0.0170036i
$698$	1.70574	−	9.11675i	0.0645634	−	0.345074i
$699$	43.5812	+	24.5584i	1.64839	+	0.928882i
$700$	11.3153	+	62.9999i	0.427678	+	2.38117i
$701$			8.66802i			0.327387i	0.986511	+	0.163693i	$0.0523408\pi$
$701$			8.66802i			0.327387i	−0.986511	+	0.163693i	$0.947659\pi$
$702$	−5.91035	+	7.35036i	−0.223072	+	0.277422i
$703$	5.04962	+	8.74620i	0.190450	+	0.329869i
$704$	15.3922	+	30.9871i	0.580114	+	1.16787i
$705$	19.4790	−	11.5191i	0.733620	−	0.433834i
$706$	−11.0969	−	31.5069i	−0.417635	−	1.18578i
$707$	2.24896	−	4.12099i	0.0845809	−	0.154986i
$708$	2.92663	+	17.6719i	0.109989	+	0.664152i
$709$	−4.60956	+	2.66133i	−0.173116	+	0.0999484i	−0.584054	−	0.811715i	$-0.698534\pi$
$709$	−4.60956	+	2.66133i	−0.173116	+	0.0999484i	0.410938	+	0.911663i	$0.365201\pi$
$710$	9.34717	+	26.5390i	0.350793	+	0.995993i
$711$	−22.2310	+	13.4619i	−0.833729	+	0.504859i
$712$	−21.5347	+	11.5504i	−0.807047	+	0.432870i
$713$	50.3433	+	29.0657i	1.88537	+	1.08852i
$714$	−15.7964	+	6.18357i	−0.591164	+	0.231414i
$715$	−11.4763	−	19.8775i	−0.429188	−	0.743376i
$716$	0.203799	+	0.0790280i	0.00761632	+	0.00295341i
$717$	1.49810	+	2.53331i	0.0559475	+	0.0946081i
$718$	32.3610	+	6.05474i	1.20770	+	0.225961i
$719$	4.34250	−	7.52143i	0.161948	−	0.280502i	−0.773619	−	0.633651i	$-0.781556\pi$
$719$	4.34250	−	7.52143i	0.161948	−	0.280502i	0.935567	+	0.353149i	$0.114889\pi$
$720$	−9.63169	+	48.6735i	−0.358952	+	1.81395i
$721$	−16.4770	+	30.1924i	−0.613635	+	1.12442i
$722$	14.7593	+	12.6491i	0.549285	+	0.470753i
$723$	36.3756	−	0.379909i	1.35282	−	0.0141290i
$724$	−10.8366	+	8.71436i	−0.402737	+	0.323867i
$725$	−16.3005	−	9.41111i	−0.605386	−	0.349520i
$726$	−6.45529	−	17.7349i	−0.239578	−	0.658205i
$727$	−18.3777	+	31.8311i	−0.681590	+	1.18055i	0.292905	+	0.956141i	$0.405378\pi$
$727$	−18.3777	+	31.8311i	−0.681590	+	1.18055i	−0.974495	+	0.224407i	$0.927955\pi$
$728$	4.86263	−	8.28309i	0.180221	−	0.306992i
$729$	−26.9470	+	1.69077i	−0.998037	+	0.0626210i
$730$	−44.3338	+	51.7296i	−1.64087	+	1.91460i
$731$		−	10.2191i		−	0.377968i
$732$	−10.7339	+	28.5621i	−0.396735	+	1.05568i
$733$	−24.0020			−0.886535			−0.443267	−	0.896389i	$-0.646181\pi$
$733$	−24.0020			−0.886535			−0.443267	+	0.896389i	$0.646181\pi$
$734$	46.7207	−	16.4552i	1.72449	−	0.607374i
$735$	41.8749	−	27.5620i	1.54458	−	1.01664i
$736$	−50.9515	+	6.26729i	−1.87810	+	0.231015i
$737$	−4.61035	+	7.98536i	−0.169824	+	0.294144i
$738$	0.533295	−	0.649226i	0.0196309	−	0.0238984i
$739$	5.42035	+	9.38831i	0.199391	+	0.345355i	0.948331	−	0.317283i	$-0.102770\pi$
$739$	5.42035	+	9.38831i	0.199391	+	0.345355i	−0.748940	+	0.662637i	$0.769437\pi$
$740$	36.0020	−	5.57661i	1.32346	−	0.205000i
$741$	−5.09604	+	0.0532233i	−0.187208	+	0.00195521i
$742$	6.50118	+	17.1327i	0.238666	+	0.628962i
$743$	−23.6520	+	13.6555i	−0.867709	+	0.500972i	−0.866586	−	0.499027i	$-0.833691\pi$
$743$	−23.6520	+	13.6555i	−0.867709	+	0.500972i	−0.00112274	+	0.999999i	$0.500357\pi$
$744$	−27.4982	+	15.1209i	−1.00813	+	0.554360i
$745$			24.3101i			0.890654i
$746$	−0.589533	−	1.67384i	−0.0215843	−	0.0612835i
$747$	14.8715	+	8.17678i	0.544120	+	0.299173i
$748$	8.18579	−	21.1097i	0.299302	−	0.771846i
$749$	6.07200	+	9.95643i	0.221866	+	0.363800i
$750$	−24.5829	−	67.5378i	−0.897641	−	2.46613i
$751$			18.6076i			0.679002i	0.940606	+	0.339501i	$0.110258\pi$
$751$			18.6076i			0.679002i	−0.940606	+	0.339501i	$0.889742\pi$
$752$	−12.0473	+	3.82392i	−0.439319	+	0.139444i
$753$	11.5914	−	0.121061i	0.422414	−	0.00441172i
$754$	0.938282	+	2.66403i	0.0341702	+	0.0970182i
$755$			42.9276i			1.56230i
$756$	26.8969	−	5.70600i	0.978230	−	0.207525i
$757$		−	2.81436i		−	0.102290i	−0.998691	−	0.0511449i	$-0.983713\pi$
$757$		−	2.81436i		−	0.102290i	0.998691	−	0.0511449i	$-0.0162870\pi$
$758$	33.2321	−	11.7045i	1.20704	−	0.425126i
$759$	67.9765	−	0.709950i	2.46739	−	0.0257695i
$760$	−23.6258	+	12.6720i	−0.856999	+	0.459663i
$761$			4.83042i			0.175103i	0.996160	+	0.0875513i	$0.0279042\pi$
$761$			4.83042i			0.175103i	−0.996160	+	0.0875513i	$0.972096\pi$
$762$	−3.89270	+	1.41689i	−0.141018	+	0.0513286i
$763$	−0.733320	−	30.5015i	−0.0265480	−	1.10423i
$764$	14.4778	−	37.3357i	0.523790	−	1.35076i
$765$	27.7735	−	16.8181i	1.00415	−	0.608059i
$766$	−2.59929	+	0.915481i	−0.0939162	+	0.0330777i
$767$			6.63696i			0.239647i
$768$	11.3521	−	25.2810i	0.409632	−	0.912251i
$769$	36.9610	−	21.3394i	1.33285	−	0.769520i	0.347113	−	0.937823i	$-0.387162\pi$
$769$	36.9610	−	21.3394i	1.33285	−	0.769520i	0.985735	+	0.168303i	$0.0538287\pi$
$770$	−10.7211	+	66.0460i	−0.386361	+	2.38013i
$771$	−42.3406	+	0.442208i	−1.52486	+	0.0159257i
$772$	−1.30460	−	8.42235i	−0.0469535	−	0.303127i
$773$	6.93491	+	12.0116i	0.249431	+	0.432028i	0.963368	−	0.268182i	$-0.0864229\pi$
$773$	6.93491	+	12.0116i	0.249431	+	0.432028i	−0.713937	+	0.700210i	$0.753090\pi$
$774$	−2.70550	+	16.3413i	−0.0972474	+	0.587376i
$775$	38.7429	−	67.1048i	1.39169	−	2.41047i
$776$	15.2242	−	8.16572i	0.546518	−	0.293132i
$777$	−10.6910	−	17.1253i	−0.383537	−	0.614368i
$778$	2.55620	+	7.25771i	0.0916441	+	0.260201i
$779$	0.453973			0.0162653
$780$	−6.46730	+	17.2090i	−0.231566	+	0.616182i
$781$			20.8108i			0.744670i
$782$	25.5072	+	21.8604i	0.912136	+	0.781727i
$783$	−3.82133	+	7.12530i	−0.136563	+	0.254637i
$784$	−26.2499	+	9.74373i	−0.937498	+	0.347990i
$785$	20.2184	−	35.0193i	0.721626	−	1.24989i
$786$	−40.6194	+	14.7849i	−1.44885	+	0.527362i
$787$	13.5726	+	7.83613i	0.483810	+	0.279328i	0.722003	−	0.691890i	$-0.243222\pi$
$787$	13.5726	+	7.83613i	0.483810	+	0.279328i	−0.238193	+	0.971218i	$0.576555\pi$
$788$	−11.5826	−	14.4033i	−0.412613	−	0.513096i
$789$	4.29436	−	0.0448505i	0.152883	−	0.00159672i
$790$	−32.9646	+	38.4638i	−1.17283	+	1.36848i
$791$	23.5640	−	0.566529i	0.837840	−	0.0201435i
$792$	−18.6786	+	31.5890i	−0.663714	+	1.12247i
$793$	−5.65271	+	9.79078i	−0.200734	+	0.347681i
$794$	6.70261	−	35.8237i	0.237867	−	1.27133i
$795$	−17.8533	−	30.1902i	−0.633191	−	1.07074i
$796$	42.4021	+	16.4425i	1.50290	+	0.582788i
$797$	14.7425	+	25.5348i	0.522208	+	0.904490i	0.999666	+	0.0258360i	$0.00822476\pi$
$797$	14.7425	+	25.5348i	0.522208	+	0.904490i	−0.477458	+	0.878654i	$0.658442\pi$
$798$	11.6072	+	9.27317i	0.410891	+	0.328267i
$799$	7.16300	+	4.13556i	0.253409	+	0.146306i
$800$	8.35394	+	67.9155i	0.295356	+	2.40118i
$801$	−22.7124	−	12.4879i	−0.802502	−	0.441238i
$802$	−34.7692	+	12.2459i	−1.22774	+	0.432416i
$803$	−43.6384	+	25.1946i	−1.53996	+	0.889099i
$804$	7.28619	−	1.20666i	0.256964	−	0.0425556i
$805$	−87.1437	−	47.5572i	−3.07141	−	1.67617i
$806$	−10.9671	+	3.86265i	−0.386299	+	0.136056i
$807$	−17.7536	+	10.4988i	−0.624957	+	0.369575i
$808$	2.64417	−	4.26584i	0.0930215	−	0.150072i
$809$	6.94512	+	12.0293i	0.244177	+	0.422928i	0.961900	−	0.273401i	$-0.0881487\pi$
$809$	6.94512	+	12.0293i	0.244177	+	0.422928i	−0.717723	+	0.696329i	$0.754815\pi$
$810$	−48.8649	+	19.5406i	−1.71694	+	0.686587i
$811$			6.98818i			0.245388i	0.992445	+	0.122694i	$0.0391534\pi$
$811$			6.98818i			0.245388i	−0.992445	+	0.122694i	$0.960847\pi$
$812$	2.79147	−	7.74606i	0.0979613	−	0.271833i
$813$	−1.69238	−	0.953671i	−0.0593544	−	0.0334467i
$814$	26.4859	+	4.95552i	0.928332	+	0.173691i
$815$	26.7352	−	46.3067i	0.936492	−	1.62205i
$816$	−17.2267	+	5.66663i	−0.603055	+	0.198372i
$817$	−7.75083	+	4.47494i	−0.271167	+	0.156558i
$818$	0.760865	+	0.142358i	0.0266030	+	0.00497743i
$819$	10.1773	−	0.457522i	0.355624	−	0.0159871i
$820$	0.592076	−	1.52686i	0.0206762	−	0.0533201i
$821$	46.7385	−	26.9845i	1.63119	−	0.941765i	0.647458	−	0.762102i	$-0.275832\pi$
$821$	46.7385	−	26.9845i	1.63119	−	0.941765i	0.983728	−	0.179664i	$-0.0575010\pi$
$822$	−2.66744	−	7.32839i	−0.0930377	−	0.255607i
$823$	−24.9917	−	14.4289i	−0.871155	−	0.502962i	−0.00342303	−	0.999994i	$-0.501090\pi$
$823$	−24.9917	−	14.4289i	−0.871155	−	0.502962i	−0.867732	+	0.497033i	$0.834423\pi$
$824$	−19.3724	+	31.2536i	−0.674871	+	1.08877i
$825$	−0.946323	−	90.6088i	−0.0329467	−	3.15459i
$826$	12.2337	−	14.9892i	0.425665	−	0.521540i
$827$	−4.23478			−0.147258			−0.0736288	−	0.997286i	$-0.523458\pi$
$827$	−4.23478			−0.147258			−0.0736288	+	0.997286i	$0.523458\pi$
$828$	−35.0008	−	41.7097i	−1.21636	−	1.44951i
$829$	11.3908	+	19.7294i	0.395617	+	0.685229i	0.993180	−	0.116593i	$-0.0371973\pi$
$829$	11.3908	+	19.7294i	0.395617	+	0.685229i	−0.597562	+	0.801822i	$0.703864\pi$
$830$	32.5152	+	6.08360i	1.12862	+	0.211165i
$831$	15.3088	−	0.159886i	0.531056	−	0.00554637i
$832$	5.68006	−	8.55401i	0.196921	−	0.296557i
$833$	16.2899	+	8.38821i	0.564410	+	0.290634i
$834$	30.7380	+	25.7915i	1.06437	+	0.893086i
$835$	27.9634	+	48.4340i	0.967712	+	1.67613i
$836$	−19.5954	+	3.03528i	−0.677723	+	0.104977i
$837$	−29.3329	−	15.7314i	−1.01389	−	0.543756i
$838$	−11.7340	+	13.6915i	−0.405346	+	0.472966i
$839$	18.1968	−	31.5177i	0.628222	−	1.08811i	−0.359686	−	0.933073i	$-0.617116\pi$
$839$	18.1968	−	31.5177i	0.628222	−	1.08811i	0.987908	−	0.155040i	$-0.0495505\pi$
$840$	46.3269	−	26.9446i	1.59843	−	0.929676i
$841$	−13.2894	−	23.0179i	−0.458255	−	0.793721i
$842$	23.6356	+	4.42221i	0.814535	+	0.152400i
$843$	−38.1069	−	21.4736i	−1.31247	−	0.739588i
$844$	23.6981	+	9.18951i	0.815722	+	0.316316i
$845$	23.4702	−	40.6516i	0.807400	−	1.39846i
$846$	−10.3594	−	8.50953i	−0.356163	−	0.292564i
$847$	−9.76543	+	17.8942i	−0.335544	+	0.614851i
$848$	5.92666	+	18.6719i	0.203522	+	0.641197i
$849$	17.0135	−	30.1921i	0.583901	−	1.03619i
$850$	29.1387	−	33.9997i	0.999449	−	1.16618i
$851$	−19.9897	+	34.6232i	−0.685239	+	1.18687i
$852$	12.8798	−	10.5809i	0.441256	−	0.362495i
$853$	20.4122	−	35.3549i	0.698899	−	1.21053i	−0.269950	−	0.962874i	$-0.587007\pi$
$853$	20.4122	−	35.3549i	0.698899	−	1.21053i	0.968849	−	0.247654i	$-0.0796596\pi$
$854$	30.8133	−	11.6924i	1.05441	−	0.400107i
$855$	−24.9179	−	13.7006i	−0.852173	−	0.468549i
$856$	5.89276	+	10.9865i	0.201410	+	0.375512i
$857$		−	43.8043i		−	1.49633i	−0.663514	−	0.748164i	$-0.730936\pi$
$857$		−	43.8043i		−	1.49633i	0.663514	−	0.748164i	$-0.269064\pi$
$858$	−8.74006	+	10.4163i	−0.298381	+	0.355607i
$859$		−	43.0076i		−	1.46740i	−0.679473	−	0.733700i	$-0.737792\pi$
$859$		−	43.0076i		−	1.46740i	0.679473	−	0.733700i	$-0.262208\pi$
$860$	4.94195	+	31.9048i	0.168519	+	1.08794i
$861$	−0.906956	+	0.0312853i	−0.0309090	+	0.00106620i
$862$	−16.7867	+	19.5871i	−0.571758	+	0.667140i
$863$	2.45117	+	1.41519i	0.0834389	+	0.0481735i	0.541139	−	0.840933i	$-0.317993\pi$
$863$	2.45117	+	1.41519i	0.0834389	+	0.0481735i	−0.457700	+	0.889107i	$0.651327\pi$
$864$	29.0473	−	4.50068i	0.988208	−	0.153116i
$865$	22.4773	+	38.9319i	0.764252	+	1.32372i
$866$	−0.0175862	−	0.0499319i	−0.000597604	−	0.00169675i
$867$	−15.3138	−	8.62943i	−0.520083	−	0.293071i
$868$	31.8884	+	11.4917i	1.08236	+	0.390054i
$869$	−32.4475	+	18.7336i	−1.10071	+	0.635493i
$870$	−2.73638	+	15.5201i	−0.0927719	+	0.526182i
$871$	2.73644			0.0927207
$872$	1.02028	−	32.6009i	0.0345509	−	1.10401i
$873$	16.0568	+	8.82849i	0.543441	+	0.298799i
$874$	5.41073	−	28.9189i	0.183021	−	0.978197i
$875$	−37.1886	+	68.1442i	−1.25720	+	2.30370i
$876$	37.7801	+	14.1981i	1.27647	+	0.479709i
$877$			35.6911i			1.20520i	0.798043	+	0.602601i	$0.205869\pi$
$877$			35.6911i			1.20520i	−0.798043	+	0.602601i	$0.794131\pi$
$878$	6.20607	+	5.31878i	0.209445	+	0.179500i
$879$	−1.46704	+	0.867550i	−0.0494821	+	0.0292618i
$880$	−15.3480	+	69.8644i	−0.517380	+	2.35513i
$881$		−	45.7341i		−	1.54082i	−0.637548	−	0.770411i	$-0.720051\pi$
$881$		−	45.7341i		−	1.54082i	0.637548	−	0.770411i	$-0.279949\pi$
$882$	−23.8282	−	17.7262i	−0.802336	−	0.596873i
$883$	48.9258			1.64648			0.823242	−	0.567690i	$-0.192163\pi$
$883$	48.9258			1.64648			0.823242	+	0.567690i	$0.192163\pi$
$884$	−6.64009	+	1.02853i	−0.223330	+	0.0345932i
$885$	−18.1802	+	32.2626i	−0.611122	+	1.08449i
$886$	−11.6115	−	9.95136i	−0.390095	−	0.334322i
$887$	21.3038			0.715313			0.357656	−	0.933853i	$-0.383576\pi$
$887$	21.3038			0.715313			0.357656	+	0.933853i	$0.383576\pi$
$888$	−10.3993	−	18.9117i	−0.348978	−	0.634636i
$889$	3.92765	+	2.14345i	0.131729	+	0.0718889i
$890$	−49.6585	−	9.29111i	−1.66456	−	0.311439i
$891$	−38.8903	+	1.62558i	−1.30288	+	0.0544589i
$892$	−5.20722	−	33.6173i	−0.174351	−	1.12559i
$893$		−	7.24383i		−	0.242405i
$894$	13.5330	−	4.92585i	0.452612	−	0.164745i
$895$	0.225950	+	0.391357i	0.00755267	+	0.0130816i
$896$	−28.5954	+	8.84884i	−0.955306	+	0.295619i
$897$	−10.2692	−	17.3654i	−0.342879	−	0.579814i
$898$	−43.7394	+	15.4052i	−1.45960	+	0.514079i
$899$	−8.63205	+	4.98372i	−0.287895	+	0.166216i
$900$	−55.5967	+	46.6541i	−1.85322	+	1.55514i
$901$	6.40966	−	11.1019i	0.213537	−	0.369857i
$902$	0.788200	−	0.919690i	0.0262442	−	0.0306223i
$903$	15.1764	−	9.47427i	0.505038	−	0.315284i
$904$	25.1859	+	0.788218i	0.837672	+	0.0262157i
$905$	−28.7487			−0.955638
$906$	23.8970	−	8.69821i	0.793925	−	0.288979i
$907$	−49.8060			−1.65378			−0.826890	−	0.562364i	$-0.809892\pi$
$907$	−49.8060			−1.65378			−0.826890	+	0.562364i	$0.809892\pi$
$908$	13.7439	+	17.0909i	0.456107	+	0.567182i
$909$	5.32215	−	0.111182i	0.176525	−	0.00368767i
$910$	18.5655	−	7.04484i	0.615439	−	0.233534i
$911$	51.2355	+	29.5808i	1.69751	+	0.980057i	0.948112	+	0.317936i	$0.102990\pi$
$911$	51.2355	+	29.5808i	1.69751	+	0.980057i	0.749397	+	0.662121i	$0.230344\pi$
$912$	11.8415	+	10.5844i	0.392111	+	0.350485i
$913$	21.1885	+	12.2332i	0.701237	+	0.404859i
$914$	−20.9556	−	17.9595i	−0.693148	−	0.594048i
$915$	−54.2974	+	32.1093i	−1.79502	+	1.06150i
$916$	9.36166	−	7.52831i	0.309318	−	0.248742i
$917$	40.9841	+	22.3664i	1.35341	+	0.738603i
$918$	−14.9899	−	12.0532i	−0.494742	−	0.397816i
$919$	2.66770	+	1.54020i	0.0879994	+	0.0508065i	0.543354	−	0.839504i	$-0.317154\pi$
$919$	2.66770	+	1.54020i	0.0879994	+	0.0508065i	−0.455355	+	0.890310i	$0.650488\pi$
$920$	−90.2068	−	55.9143i	−2.97403	−	1.84344i
$921$	−11.6793	+	0.121980i	−0.384848	+	0.00401937i
$922$	−2.99077	+	15.9849i	−0.0984959	+	0.526435i
$923$	5.34862	−	3.08803i	0.176052	−	0.101644i
$924$	38.9390	−	7.41434i	1.28100	−	0.243914i
$925$	46.1508	+	26.6452i	1.51743	+	0.876088i
$926$	−5.46514	+	6.37685i	−0.179596	+	0.209556i
$927$	−38.9926	+	0.814571i	−1.28069	+	0.0267540i
$928$	3.43753	−	8.10320i	0.112842	−	0.266001i
$929$	−18.6172	+	10.7486i	−0.610810	+	0.352651i	−0.773282	−	0.634062i	$-0.781386\pi$
$929$	−18.6172	+	10.7486i	−0.610810	+	0.352651i	0.162472	+	0.986713i	$0.448053\pi$
$930$	−63.8922	−	11.2649i	−2.09511	−	0.369391i
$931$	−0.771162	−	16.0284i	−0.0252738	−	0.525311i
$932$	−8.84189	−	57.0824i	−0.289626	−	1.86980i
$933$	46.1648	+	26.0142i	1.51137	+	0.851668i
$934$	52.2617	+	9.77816i	1.71006	+	0.319951i
$935$	40.5371	−	23.4041i	1.32570	−	0.765396i
$936$	10.8904	+	0.113247i	0.355963	+	0.00370158i
$937$			17.6261i			0.575820i	0.957657	+	0.287910i	$0.0929604\pi$
$937$			17.6261i			0.575820i	−0.957657	+	0.287910i	$0.907040\pi$
$938$	−6.18009	−	5.04400i	−0.201787	−	0.164692i
$939$	11.1013	+	18.7725i	0.362277	+	0.612617i
$940$	−24.3633	−	9.44747i	−0.794643	−	0.308142i
$941$	−13.7771	+	23.8627i	−0.449121	+	0.777900i	−0.998329	−	0.0577853i	$-0.981596\pi$
$941$	−13.7771	+	23.8627i	−0.449121	+	0.777900i	0.549208	+	0.835686i	$0.314929\pi$
$942$	−23.5914	−	4.15943i	−0.768649	−	0.135522i
$943$	0.898562	+	1.55635i	0.0292612	+	0.0506819i
$944$	13.9444	−	15.2764i	0.453852	−	0.497205i
$945$	50.7256	+	25.6540i	1.65010	+	0.834526i
$946$	−4.39155	+	23.4717i	−0.142782	+	0.763130i
$947$	7.13268	+	12.3542i	0.231781	+	0.401456i	0.958332	−	0.285656i	$-0.0922115\pi$
$947$	7.13268	+	12.3542i	0.231781	+	0.401456i	−0.726551	+	0.687112i	$0.758878\pi$
$948$	28.0916	+	10.5570i	0.912372	+	0.342877i
$949$	12.9506	+	7.47705i	0.420395	+	0.242715i
$950$	−38.5473	−	7.21220i	−1.25064	−	0.233995i
$951$	−27.7363	−	46.9026i	−0.899412	−	1.52092i
$952$	16.8921	+	9.91660i	0.547476	+	0.321399i
$953$	−22.2354			−0.720274			−0.360137	−	0.932899i	$-0.617270\pi$
$953$	−22.2354			−0.720274			−0.360137	+	0.932899i	$0.617270\pi$
$954$	−13.1888	+	16.0559i	−0.427004	+	0.519829i
$955$	71.6961	−	41.3938i	2.32003	−	1.33947i
$956$	1.22868	−	3.16853i	0.0397383	−	0.102478i
$957$	−5.72233	+	10.1548i	−0.184977	+	0.328259i
$958$	35.8367	−	12.6218i	1.15783	−	0.407793i
$959$	−4.03525	+	7.39419i	−0.130305	+	0.238771i
$960$	51.0425	−	26.0224i	1.64739	−	0.839869i
$961$	−5.01659	−	8.68899i	−0.161826	−	0.280290i
$962$	−2.65651	−	7.54253i	−0.0856493	−	0.243181i
$963$	−6.37105	+	11.5873i	−0.205304	+	0.373397i
$964$	−26.3235	−	32.7340i	−0.847822	−	1.05429i
$965$	8.80995	−	15.2593i	0.283602	−	0.491214i
$966$	−8.81672	+	58.1476i	−0.283673	+	1.87087i
$967$	1.33682	−	0.771816i	0.0429894	−	0.0248199i	−0.478351	−	0.878169i	$-0.658765\pi$
$967$	1.33682	−	0.771816i	0.0429894	−	0.0248199i	0.521341	+	0.853349i	$0.325432\pi$
$968$	−11.4815	+	18.5231i	−0.369029	+	0.595356i
$969$	−0.108541	−	10.3926i	−0.00348683	−	0.333858i
$970$	35.1068	+	6.56848i	1.12721	+	0.210901i
$971$	9.12179	+	5.26647i	0.292732	+	0.169009i	0.639173	−	0.769063i	$-0.279277\pi$
$971$	9.12179	+	5.26647i	0.292732	+	0.169009i	−0.346441	+	0.938072i	$0.612610\pi$
$972$	20.7792	+	23.2428i	0.666492	+	0.745512i
$973$	−1.04169	−	43.3276i	−0.0333950	−	1.38902i
$974$	3.00877	−	3.51070i	0.0964071	−	0.112490i
$975$	−23.1471	+	13.6883i	−0.741300	+	0.438375i
$976$	33.5816	−	10.6591i	1.07492	−	0.341191i
$977$	8.77022	−	15.1905i	0.280584	−	0.485986i	−0.690945	−	0.722908i	$-0.742805\pi$
$977$	8.77022	−	15.1905i	0.280584	−	0.485986i	0.971529	+	0.236922i	$0.0761385\pi$
$978$	−31.1953	−	5.50009i	−0.997516	−	0.175873i
$979$	−32.3599	−	18.6830i	−1.03423	−	0.597112i
$980$	−54.9145	−	18.3108i	−1.75418	−	0.584916i
$981$	29.5927	−	17.9197i	0.944821	−	0.572131i
$982$	−13.9931	−	11.9925i	−0.446538	−	0.382695i
$983$	−40.7523			−1.29980			−0.649898	−	0.760022i	$-0.725188\pi$
$983$	−40.7523			−1.29980			−0.649898	+	0.760022i	$0.725188\pi$
$984$	−0.969943	−	0.0202185i	−0.0309206	−	0.000644543i
$985$		−	38.2110i		−	1.21750i
$986$	−5.43288	+	1.91348i	−0.173018	+	0.0609377i
$987$	0.499205	+	14.4719i	0.0158899	+	0.460644i
$988$	3.68779	+	4.58587i	0.117324	+	0.145896i
$989$	−30.6829	−	17.7148i	−0.975659	−	0.563297i
$990$	−71.0186	+	26.6931i	−2.25712	+	0.848361i
$991$	31.7444	−	18.3276i	1.00839	−	0.582196i	0.0976723	−	0.995219i	$-0.468860\pi$
$991$	31.7444	−	18.3276i	1.00839	−	0.582196i	0.910721	+	0.413023i	$0.135527\pi$
$992$	33.3587	+	14.1514i	1.05914	+	0.449307i
$993$	26.9082	−	15.9124i	0.853906	−	0.504966i
$994$	−17.7716	−	2.88483i	−0.563682	−	0.0915011i
$995$	47.0109	+	81.4252i	1.49034	+	2.58135i
$996$	−3.20177	−	19.3333i	−0.101452	−	0.612600i
$997$	−18.4513			−0.584359			−0.292179	−	0.956364i	$-0.594380\pi$
$997$	−18.4513			−0.584359			−0.292179	+	0.956364i	$0.594380\pi$
$998$	−30.7350	+	10.8250i	−0.972901	+	0.342660i
$999$	10.8191	−	20.1735i	0.342302	−	0.638261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cz.b.187.10	yes	180
7.3	odd	6		504.2.bf.b.115.51	✓	180
8.3	odd	2	inner	504.2.cz.b.187.70	yes	180
9.4	even	3		504.2.bf.b.355.51	yes	180
56.3	even	6		504.2.bf.b.115.52	yes	180
63.31	odd	6	inner	504.2.cz.b.283.70	yes	180
72.67	odd	6		504.2.bf.b.355.52	yes	180
504.283	even	6	inner	504.2.cz.b.283.10	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bf.b.115.51	✓	180	7.3	odd	6
504.2.bf.b.115.52	yes	180	56.3	even	6
504.2.bf.b.355.51	yes	180	9.4	even	3
504.2.bf.b.355.52	yes	180	72.67	odd	6
504.2.cz.b.187.10	yes	180	1.1	even	1	trivial
504.2.cz.b.187.70	yes	180	8.3	odd	2	inner
504.2.cz.b.283.10	yes	180	504.283	even	6	inner
504.2.cz.b.283.70	yes	180	63.31	odd	6	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cz (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33390 + 0.469805i) q^{2} +(0.0180886 + 1.73196i) q^{3} +(1.55857 - 1.25334i) q^{4} +4.13478 q^{5} +(-0.837810 - 2.30175i) q^{6} +(-1.26742 + 2.32242i) q^{7} +(-1.49014 + 2.40405i) q^{8} +(-2.99935 + 0.0626575i) q^{9} +O(q^{10})\)	\(q+(-1.33390 + 0.469805i) q^{2} +(0.0180886 + 1.73196i) q^{3} +(1.55857 - 1.25334i) q^{4} +4.13478 q^{5} +(-0.837810 - 2.30175i) q^{6} +(-1.26742 + 2.32242i) q^{7} +(-1.49014 + 2.40405i) q^{8} +(-2.99935 + 0.0626575i) q^{9} +(-5.51537 + 1.94254i) q^{10} -4.32492 q^{11} +(2.19893 + 2.67670i) q^{12} +(0.641757 + 1.11156i) q^{13} +(0.599527 - 3.69331i) q^{14} +(0.0747925 + 7.16125i) q^{15} +(0.858263 - 3.90684i) q^{16} +(-2.26685 + 1.30876i) q^{17} +(3.97138 - 1.49269i) q^{18} +(1.98530 + 1.14621i) q^{19} +(6.44433 - 5.18229i) q^{20} +(-4.04526 - 2.15311i) q^{21} +(5.76901 - 2.03187i) q^{22} +9.07493i q^{23} +(-4.19067 - 2.53738i) q^{24} +12.0964 q^{25} +(-1.37825 - 1.18120i) q^{26} +(-0.162774 - 5.19360i) q^{27} +(0.935428 + 5.20816i) q^{28} +(-1.34755 - 0.778011i) q^{29} +(-3.46415 - 9.51724i) q^{30} +(3.20286 - 5.54751i) q^{31} +(0.690615 + 5.61454i) q^{32} +(-0.0782320 - 7.49058i) q^{33} +(2.40888 - 2.81073i) q^{34} +(-5.24051 + 9.60269i) q^{35} +(-4.59615 + 3.85686i) q^{36} +(3.81526 + 2.20274i) q^{37} +(-3.18668 - 0.596228i) q^{38} +(-1.91356 + 1.13160i) q^{39} +(-6.16141 + 9.94022i) q^{40} +(0.171501 - 0.0990159i) q^{41} +(6.40750 + 0.971548i) q^{42} +(-1.95206 + 3.38106i) q^{43} +(-6.74068 + 5.42061i) q^{44} +(-12.4016 + 0.259075i) q^{45} +(-4.26344 - 12.1050i) q^{46} +(-1.57995 - 2.73655i) q^{47} +(6.78200 + 1.41580i) q^{48} +(-3.78728 - 5.88698i) q^{49} +(-16.1353 + 5.68293i) q^{50} +(-2.30773 - 3.90241i) q^{51} +(2.39338 + 0.928093i) q^{52} +(-4.24135 + 2.44875i) q^{53} +(2.65710 + 6.85126i) q^{54} -17.8826 q^{55} +(-3.69459 - 6.50769i) q^{56} +(-1.94928 + 3.45918i) q^{57} +(2.16301 + 0.404700i) q^{58} +(4.47816 + 2.58546i) q^{59} +(9.09207 + 11.0675i) q^{60} +(4.40409 + 7.62810i) q^{61} +(-1.66604 + 8.90453i) q^{62} +(3.65592 - 7.04516i) q^{63} +(-3.55895 - 7.16477i) q^{64} +(2.65352 + 4.59603i) q^{65} +(3.62346 + 9.95491i) q^{66} +(1.06600 - 1.84636i) q^{67} +(-1.89270 + 4.88093i) q^{68} +(-15.7174 + 0.164153i) q^{69} +(2.47891 - 15.2710i) q^{70} -4.81184i q^{71} +(4.31882 - 7.30396i) q^{72} +(10.0900 - 5.82545i) q^{73} +(-6.12403 - 1.14581i) q^{74} +(0.218807 + 20.9504i) q^{75} +(4.53082 - 0.701811i) q^{76} +(5.48150 - 10.0443i) q^{77} +(2.02086 - 2.40844i) q^{78} +(7.50245 - 4.33154i) q^{79} +(3.54873 - 16.1539i) q^{80} +(8.99215 - 0.375863i) q^{81} +(-0.182246 + 0.212649i) q^{82} +(-4.89916 - 2.82853i) q^{83} +(-9.00339 + 1.71433i) q^{84} +(-9.37290 + 5.41145i) q^{85} +(1.01541 - 5.42707i) q^{86} +(1.32311 - 2.34798i) q^{87} +(6.44475 - 10.3973i) q^{88} +(7.48220 + 4.31985i) q^{89} +(16.4208 - 6.17192i) q^{90} +(-3.39488 + 0.0816202i) q^{91} +(11.3740 + 14.1439i) q^{92} +(9.66598 + 5.44686i) q^{93} +(3.39313 + 2.90801i) q^{94} +(8.20876 + 4.73933i) q^{95} +(-9.71164 + 1.29768i) q^{96} +(-5.28964 - 3.05398i) q^{97} +(7.81758 + 6.07334i) q^{98} +(12.9719 - 0.270989i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9}+O(q^{10}) \) 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9	\( 180 q + 3 q^{2} + q^{4} + 6 q^{6} - 8 q^{9} + 16 q^{11} - 3 q^{12} + 7 q^{14} - 7 q^{16} - 18 q^{17} - 13 q^{18} - 6 q^{19} - 36 q^{20} - 16 q^{22} - 24 q^{24} + 156 q^{25} - 6 q^{26} + 16 q^{28} - 8 q^{30} + 13 q^{32} - 36 q^{33} + 12 q^{34} - 12 q^{35} + 2 q^{36} + 42 q^{41} + 31 q^{42} + 14 q^{43} - 21 q^{44} - 12 q^{46} + 9 q^{48} + 20 q^{49} + 15 q^{50} - 42 q^{51} - 12 q^{54} - 40 q^{56} - 26 q^{57} - 38 q^{58} + 18 q^{59} - 38 q^{60} - 8 q^{64} - 12 q^{65} - 21 q^{66} - 14 q^{67} - 42 q^{70} + 5 q^{72} + 18 q^{73} - 98 q^{74} - 48 q^{75} + 12 q^{76} - 33 q^{78} - 63 q^{80} + 8 q^{81} - 54 q^{82} - 6 q^{83} - 77 q^{84} + 26 q^{86} - 58 q^{88} - 66 q^{89} + 51 q^{90} + 2 q^{91} - 60 q^{92} + 9 q^{94} - 30 q^{96} + 6 q^{97} + 31 q^{98} + 4 q^{99}+O(q^{100}) \) 180 * q + 3 * q^2 + q^4 + 6 * q^6 - 8 * q^9 + 16 * q^11 - 3 * q^12 + 7 * q^14 - 7 * q^16 - 18 * q^17 - 13 * q^18 - 6 * q^19 - 36 * q^20 - 16 * q^22 - 24 * q^24 + 156 * q^25 - 6 * q^26 + 16 * q^28 - 8 * q^30 + 13 * q^32 - 36 * q^33 + 12 * q^34 - 12 * q^35 + 2 * q^36 + 42 * q^41 + 31 * q^42 + 14 * q^43 - 21 * q^44 - 12 * q^46 + 9 * q^48 + 20 * q^49 + 15 * q^50 - 42 * q^51 - 12 * q^54 - 40 * q^56 - 26 * q^57 - 38 * q^58 + 18 * q^59 - 38 * q^60 - 8 * q^64 - 12 * q^65 - 21 * q^66 - 14 * q^67 - 42 * q^70 + 5 * q^72 + 18 * q^73 - 98 * q^74 - 48 * q^75 + 12 * q^76 - 33 * q^78 - 63 * q^80 + 8 * q^81 - 54 * q^82 - 6 * q^83 - 77 * q^84 + 26 * q^86 - 58 * q^88 - 66 * q^89 + 51 * q^90 + 2 * q^91 - 60 * q^92 + 9 * q^94 - 30 * q^96 + 6 * q^97 + 31 * q^98 + 4 * q^99

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