LMFDB - Embedded newform 552.2.bb.a.469.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			469.1
Character	$\chi$	$=$	552.469
Dual form			552.2.bb.a.133.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41218 + 0.0757292i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(1.98853 - 0.213887i) q^{4} +(3.85438 - 0.554176i) q^{5} +(1.01767 - 0.982016i) q^{6} +(-1.25415 + 2.74620i) q^{7} +(-2.79197 + 0.452638i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-1.41218 + 0.0757292i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(1.98853 - 0.213887i) q^{4} +(3.85438 - 0.554176i) q^{5} +(1.01767 - 0.982016i) q^{6} +(-1.25415 + 2.74620i) q^{7} +(-2.79197 + 0.452638i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-5.40113 + 1.07449i) q^{10} +(-1.60389 + 5.46234i) q^{11} +(-1.36276 + 1.46386i) q^{12} +(-3.38420 + 1.54551i) q^{13} +(1.56312 - 3.97311i) q^{14} +(-2.55004 + 2.94290i) q^{15} +(3.90850 - 0.850642i) q^{16} +(1.64292 + 1.05584i) q^{17} +(-0.126016 + 1.40859i) q^{18} +(-3.00727 - 4.67940i) q^{19} +(7.54602 - 1.92640i) q^{20} +(-0.850557 - 2.89673i) q^{21} +(1.85133 - 7.83529i) q^{22} +(-1.61443 + 4.51593i) q^{23} +(1.81362 - 2.17044i) q^{24} +(9.75166 - 2.86335i) q^{25} +(4.66208 - 2.43883i) q^{26} +(0.540641 + 0.841254i) q^{27} +(-1.90653 + 5.72914i) q^{28} +(-1.71503 + 2.66864i) q^{29} +(3.37826 - 4.34903i) q^{30} +(3.99509 - 4.61058i) q^{31} +(-5.45511 + 1.49725i) q^{32} +(-2.36493 - 5.17848i) q^{33} +(-2.40007 - 1.36663i) q^{34} +(-3.31208 + 11.2799i) q^{35} +(0.0712873 - 1.99873i) q^{36} +(-7.51457 - 1.08043i) q^{37} +(4.60119 + 6.38044i) q^{38} +(1.54551 - 3.38420i) q^{39} +(-10.5105 + 3.29188i) q^{40} +(0.522287 + 3.63258i) q^{41} +(1.42051 + 4.02630i) q^{42} +(-1.49601 + 1.29630i) q^{43} +(-2.02105 + 11.2051i) q^{44} -3.89401i q^{45} +(1.93788 - 6.49959i) q^{46} +7.25176 q^{47} +(-2.39680 + 3.20240i) q^{48} +(-1.38470 - 1.59802i) q^{49} +(-13.5543 + 4.78206i) q^{50} +(-1.93307 + 0.277933i) q^{51} +(-6.39902 + 3.79714i) q^{52} +(0.107335 + 0.0490182i) q^{53} +(-0.827192 - 1.14706i) q^{54} +(-3.15489 + 21.9428i) q^{55} +(2.25851 - 8.23499i) q^{56} +(5.33710 + 1.56711i) q^{57} +(2.21985 - 3.89849i) q^{58} +(-9.04524 + 4.13082i) q^{59} +(-4.44138 + 6.39747i) q^{60} +(5.86982 + 5.08623i) q^{61} +(-5.29265 + 6.81354i) q^{62} +(2.53976 + 1.63221i) q^{63} +(7.59024 - 2.52751i) q^{64} +(-12.1875 + 7.83244i) q^{65} +(3.73189 + 7.13388i) q^{66} +(1.13181 + 3.85458i) q^{67} +(3.49283 + 1.74817i) q^{68} +(-1.73720 - 4.47014i) q^{69} +(3.82305 - 16.1801i) q^{70} +(11.6410 - 3.41810i) q^{71} +(0.0506913 + 2.82797i) q^{72} +(-7.29684 + 4.68940i) q^{73} +(10.6938 + 0.956697i) q^{74} +(-5.49472 + 8.54995i) q^{75} +(-6.98091 - 8.66192i) q^{76} +(-12.9892 - 11.2552i) q^{77} +(-1.92627 + 4.89616i) q^{78} +(-6.89632 - 15.1008i) q^{79} +(14.5935 - 5.44470i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-1.01266 - 5.09032i) q^{82} +(13.4677 + 1.93636i) q^{83} +(-2.31093 - 5.57831i) q^{84} +(6.91756 + 3.15915i) q^{85} +(2.01447 - 1.94390i) q^{86} +(-0.451454 - 3.13993i) q^{87} +(2.00555 - 15.9767i) q^{88} +(6.52652 + 7.53201i) q^{89} +(0.294891 + 5.49907i) q^{90} -11.2320i q^{91} +(-2.24444 + 9.32537i) q^{92} +6.10068i q^{93} +(-10.2408 + 0.549170i) q^{94} +(-14.1844 - 16.3696i) q^{95} +(3.14221 - 4.70389i) q^{96} +(1.36658 + 9.50478i) q^{97} +(2.07646 + 2.15184i) q^{98} +(5.17848 + 2.36493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	−1.41218	+	0.0757292i	−0.998565	+	0.0535486i
$2$	−1.41218	+	0.0757292i	−0.998565	+	0.0535486i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$3$	−0.755750	+	0.654861i	−0.436332	+	0.378084i
$4$	1.98853	−	0.213887i	0.994265	−	0.106944i
$5$	3.85438	−	0.554176i	1.72373	−	0.247835i	0.791880	−	0.610677i	$-0.209103\pi$
$5$	3.85438	−	0.554176i	1.72373	−	0.247835i	0.931851	+	0.362842i	$0.118193\pi$
$6$	1.01767	−	0.982016i	0.415460	−	0.400907i
$7$	−1.25415	+	2.74620i	−0.474023	+	1.03797i	0.510041	+	0.860150i	$0.329630\pi$
$7$	−1.25415	+	2.74620i	−0.474023	+	1.03797i	−0.984064	+	0.177815i	$0.943097\pi$
$8$	−2.79197	+	0.452638i	−0.987112	+	0.160032i
$9$	0.142315	−	0.989821i	0.0474383	−	0.329940i
$10$	−5.40113	+	1.07449i	−1.70799	+	0.339783i
$11$	−1.60389	+	5.46234i	−0.483590	+	1.64696i	0.250657	+	0.968076i	$0.419353\pi$
$11$	−1.60389	+	5.46234i	−0.483590	+	1.64696i	−0.734248	+	0.678882i	$0.762465\pi$
$12$	−1.36276	+	1.46386i	−0.393396	+	0.422579i
$13$	−3.38420	+	1.54551i	−0.938608	+	0.428648i	−0.825162	−	0.564896i	$-0.808916\pi$
$13$	−3.38420	+	1.54551i	−0.938608	+	0.428648i	−0.113446	+	0.993544i	$0.536189\pi$
$14$	1.56312	−	3.97311i	0.417761	−	1.06186i
$15$	−2.55004	+	2.94290i	−0.658417	+	0.759853i
$16$	3.90850	−	0.850642i	0.977126	−	0.212661i
$17$	1.64292	+	1.05584i	0.398467	+	0.256079i	0.724494	−	0.689281i	$-0.242074\pi$
$17$	1.64292	+	1.05584i	0.398467	+	0.256079i	−0.326027	+	0.945361i	$0.605710\pi$
$18$	−0.126016	+	1.40859i	−0.0297024	+	0.332007i
$19$	−3.00727	−	4.67940i	−0.689915	−	1.07353i	−0.992716	−	0.120475i	$-0.961558\pi$
$19$	−3.00727	−	4.67940i	−0.689915	−	1.07353i	0.302801	−	0.953054i	$-0.402078\pi$
$20$	7.54602	−	1.92640i	1.68734	−	0.430756i
$21$	−0.850557	−	2.89673i	−0.185607	−	0.632118i
$22$	1.85133	−	7.83529i	0.394704	−	1.67049i
$23$	−1.61443	+	4.51593i	−0.336631	+	0.941637i
$23$	−1.61443	+	4.51593i	−0.336631	+	0.941637i
$24$	1.81362	−	2.17044i	0.370203	−	0.443038i
$25$	9.75166	−	2.86335i	1.95033	−	0.572669i
$26$	4.66208	−	2.43883i	0.914308	−	0.478294i
$27$	0.540641	+	0.841254i	0.104046	+	0.161899i
$28$	−1.90653	+	5.72914i	−0.360301	+	1.08271i
$29$	−1.71503	+	2.66864i	−0.318474	+	0.495554i	−0.963173	−	0.268881i	$-0.913346\pi$
$29$	−1.71503	+	2.66864i	−0.318474	+	0.495554i	0.644700	+	0.764436i	$0.276982\pi$
$30$	3.37826	−	4.34903i	0.616783	−	0.794021i
$31$	3.99509	−	4.61058i	0.717540	−	0.828085i	−0.273469	−	0.961881i	$-0.588171\pi$
$31$	3.99509	−	4.61058i	0.717540	−	0.828085i	0.991009	+	0.133796i	$0.0427166\pi$
$32$	−5.45511	+	1.49725i	−0.964337	+	0.264679i
$33$	−2.36493	−	5.17848i	−0.411682	−	0.901458i
$34$	−2.40007	−	1.36663i	−0.411608	−	0.234374i
$35$	−3.31208	+	11.2799i	−0.559844	+	1.90665i
$36$	0.0712873	−	1.99873i	0.0118812	−	0.333122i
$37$	−7.51457	−	1.08043i	−1.23539	−	0.177622i	−0.506491	−	0.862245i	$-0.669058\pi$
$37$	−7.51457	−	1.08043i	−1.23539	−	0.177622i	−0.728897	+	0.684623i	$0.759967\pi$
$38$	4.60119	+	6.38044i	0.746411	+	1.03504i
$39$	1.54551	−	3.38420i	0.247480	−	0.541906i
$40$	−10.5105	+	3.29188i	−1.66185	+	0.520492i
$41$	0.522287	+	3.63258i	0.0815674	+	0.567314i	0.989090	+	0.147311i	$0.0470619\pi$
$41$	0.522287	+	3.63258i	0.0815674	+	0.567314i	−0.907523	+	0.420003i	$0.862029\pi$
$42$	1.42051	+	4.02630i	0.219189	+	0.621272i
$43$	−1.49601	+	1.29630i	−0.228139	+	0.197684i	−0.761428	−	0.648250i	$-0.775501\pi$
$43$	−1.49601	+	1.29630i	−0.228139	+	0.197684i	0.533289	+	0.845933i	$0.320956\pi$
$44$	−2.02105	+	11.2051i	−0.304685	+	1.68923i
$45$		−	3.89401i		−	0.580485i
$46$	1.93788	−	6.49959i	0.285725	−	0.958312i
$47$	7.25176			1.05778			0.528889	−	0.848691i	$-0.322609\pi$
$47$	7.25176			1.05778			0.528889	+	0.848691i	$0.322609\pi$
$48$	−2.39680	+	3.20240i	−0.345948	+	0.462226i
$49$	−1.38470	−	1.59802i	−0.197814	−	0.228289i
$50$	−13.5543	+	4.78206i	−1.91687	+	0.676285i
$51$	−1.93307	+	0.277933i	−0.270683	+	0.0389184i
$52$	−6.39902	+	3.79714i	−0.887384	+	0.526568i
$53$	0.107335	+	0.0490182i	0.0147436	+	0.00673316i	0.422773	−	0.906236i	$-0.361057\pi$
$53$	0.107335	+	0.0490182i	0.0147436	+	0.00673316i	−0.408030	+	0.912969i	$0.633784\pi$
$54$	−0.827192	−	1.14706i	−0.112567	−	0.156095i
$55$	−3.15489	+	21.9428i	−0.425406	+	2.95876i
$56$	2.25851	−	8.23499i	0.301806	−	1.10045i
$57$	5.33710	+	1.56711i	0.706916	+	0.207569i
$58$	2.21985	−	3.89849i	0.291480	−	0.511897i
$59$	−9.04524	+	4.13082i	−1.17759	+	0.537787i	−0.905443	−	0.424468i	$-0.860461\pi$
$59$	−9.04524	+	4.13082i	−1.17759	+	0.537787i	−0.272147	+	0.962256i	$0.587734\pi$
$60$	−4.44138	+	6.39747i	−0.573379	+	0.825909i
$61$	5.86982	+	5.08623i	0.751554	+	0.651225i	0.943949	−	0.330092i	$-0.107080\pi$
$61$	5.86982	+	5.08623i	0.751554	+	0.651225i	−0.192395	+	0.981318i	$0.561625\pi$
$62$	−5.29265	+	6.81354i	−0.672168	+	0.865320i
$63$	2.53976	+	1.63221i	0.319980	+	0.205639i
$64$	7.59024	−	2.52751i	0.948780	−	0.315938i
$65$	−12.1875	+	7.83244i	−1.51167	+	0.971494i
$66$	3.73189	+	7.13388i	0.459363	+	0.878120i
$67$	1.13181	+	3.85458i	0.138272	+	0.470912i	0.999291	−	0.0376620i	$-0.0119910\pi$
$67$	1.13181	+	3.85458i	0.138272	+	0.470912i	−0.861018	+	0.508574i	$0.830173\pi$
$68$	3.49283	+	1.74817i	0.423568	+	0.211997i
$69$	−1.73720	−	4.47014i	−0.209135	−	0.538141i
$70$	3.82305	−	16.1801i	0.456942	−	1.93390i
$71$	11.6410	−	3.41810i	1.38153	−	0.405654i	0.495229	−	0.868762i	$-0.335084\pi$
$71$	11.6410	−	3.41810i	1.38153	−	0.405654i	0.886302	+	0.463108i	$0.153266\pi$
$72$	0.0506913	+	2.82797i	0.00597403	+	0.333280i
$73$	−7.29684	+	4.68940i	−0.854031	+	0.548852i	−0.892830	−	0.450395i	$-0.851283\pi$
$73$	−7.29684	+	4.68940i	−0.854031	+	0.548852i	0.0387986	+	0.999247i	$0.487647\pi$
$74$	10.6938	+	0.956697i	1.24313	+	0.111214i
$75$	−5.49472	+	8.54995i	−0.634476	+	0.987264i
$76$	−6.98091	−	8.66192i	−0.800765	−	0.993590i
$77$	−12.9892	−	11.2552i	−1.48025	−	1.28265i
$78$	−1.92627	+	4.89616i	−0.218107	+	0.554381i
$79$	−6.89632	−	15.1008i	−0.775896	−	1.69898i	−0.713219	−	0.700942i	$-0.752763\pi$
$79$	−6.89632	−	15.1008i	−0.775896	−	1.69898i	−0.0626774	−	0.998034i	$-0.519964\pi$
$80$	14.5935	−	5.44470i	1.63160	−	0.608736i
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$	−1.01266	−	5.09032i	−0.111829	−	0.562132i
$83$	13.4677	+	1.93636i	1.47827	+	0.212543i	0.833792	−	0.552078i	$-0.186165\pi$
$83$	13.4677	+	1.93636i	1.47827	+	0.212543i	0.644479	+	0.764622i	$0.277074\pi$
$84$	−2.31093	−	5.57831i	−0.252143	−	0.608644i
$85$	6.91756	+	3.15915i	0.750315	+	0.342657i
$86$	2.01447	−	1.94390i	0.217226	−	0.209617i
$87$	−0.451454	−	3.13993i	−0.0484010	−	0.336636i
$88$	2.00555	−	15.9767i	0.213792	−	1.70312i
$89$	6.52652	+	7.53201i	0.691810	+	0.798392i	0.987622	−	0.156855i	$-0.0501355\pi$
$89$	6.52652	+	7.53201i	0.691810	+	0.798392i	−0.295811	+	0.955246i	$0.595590\pi$
$90$	0.294891	+	5.49907i	0.0310842	+	0.579653i
$91$		−	11.2320i		−	1.17743i
$92$	−2.24444	+	9.32537i	−0.233999	+	0.972237i
$93$			6.10068i			0.632611i
$94$	−10.2408	+	0.549170i	−1.05626	+	0.0566425i
$95$	−14.1844	−	16.3696i	−1.45529	−	1.67949i
$96$	3.14221	−	4.70389i	0.320700	−	0.480088i
$97$	1.36658	+	9.50478i	0.138755	+	0.965064i	0.933617	+	0.358273i	$0.116634\pi$
$97$	1.36658	+	9.50478i	0.138755	+	0.965064i	−0.794862	+	0.606791i	$0.792457\pi$
$98$	2.07646	+	2.15184i	0.209754	+	0.217369i
$99$	5.17848	+	2.36493i	0.520457	+	0.237685i
$100$	18.7790	−	7.77961i	1.87790	−	0.777961i
$101$	10.5684	+	1.51951i	1.05159	+	0.151196i	0.646373	−	0.763022i	$-0.276285\pi$
$101$	10.5684	+	1.51951i	1.05159	+	0.151196i	0.405222	+	0.914218i	$0.367194\pi$
$102$	2.70880	−	0.538882i	0.268211	−	0.0533573i
$103$	6.93105	+	2.03514i	0.682936	+	0.200528i	0.604756	−	0.796411i	$-0.293271\pi$
$103$	6.93105	+	2.03514i	0.682936	+	0.200528i	0.0781806	+	0.996939i	$0.475089\pi$
$104$	8.74904	−	5.84685i	0.857914	−	0.573331i
$105$	−4.88367	−	10.6937i	−0.476597	−	1.04360i
$106$	−0.155289	−	0.0610943i	−0.0150830	−	0.00593400i
$107$	−2.95017	−	2.55634i	−0.285204	−	0.247130i	0.500495	−	0.865739i	$-0.333151\pi$
$107$	−2.95017	−	2.55634i	−0.285204	−	0.247130i	−0.785699	+	0.618609i	$0.787697\pi$
$108$	1.25501	+	1.55722i	0.120764	+	0.149844i
$109$	6.58022	−	10.2390i	0.630271	−	0.980720i	−0.368425	−	0.929658i	$-0.620103\pi$
$109$	6.58022	−	10.2390i	0.630271	−	0.980720i	0.998695	−	0.0510626i	$-0.0162608\pi$
$110$	2.79358	−	31.2262i	0.266358	−	2.97730i
$111$	6.38667	−	4.10446i	0.606196	−	0.389578i
$112$	−2.56581	+	11.8004i	−0.242446	+	1.11503i
$113$	−5.71964	+	1.67944i	−0.538058	+	0.157988i	−0.539461	−	0.842011i	$-0.681372\pi$
$113$	−5.71964	+	1.67944i	−0.538058	+	0.157988i	0.00140237	+	0.999999i	$0.499554\pi$
$114$	−7.65565	−	1.80888i	−0.717017	−	0.169417i
$115$	−3.72000	+	18.3008i	−0.346891	+	1.70656i
$116$	−2.83961	+	5.67350i	−0.263651	+	0.526771i
$117$	1.04816	+	3.56970i	0.0969024	+	0.330019i
$118$	12.4607	−	6.51847i	1.14710	−	0.600074i
$119$	−4.96001	+	3.18761i	−0.454684	+	0.292208i
$120$	5.78757	−	9.37074i	0.528330	−	0.855428i
$121$	−18.0109	−	11.5749i	−1.63736	−	1.05226i
$122$	−8.67445	−	6.73818i	−0.785348	−	0.610046i
$123$	−2.77355	−	2.40330i	−0.250083	−	0.216698i
$124$	6.95822	−	10.0228i	0.624866	−	0.900072i
$125$	18.2892	−	8.35240i	1.63584	−	0.747061i
$126$	−3.71022	−	2.11264i	−0.330533	−	0.188209i
$127$	2.79077	+	0.819444i	0.247641	+	0.0727139i	0.403197	−	0.915113i	$-0.367899\pi$
$127$	2.79077	+	0.819444i	0.247641	+	0.0727139i	−0.155556	+	0.987827i	$0.549717\pi$
$128$	−10.5274	+	4.14411i	−0.930500	+	0.366291i
$129$	0.281713	−	1.95935i	0.0248034	−	0.172512i
$130$	16.6179	−	11.9838i	1.45748	−	1.05105i
$131$	−7.64125	−	3.48964i	−0.667619	−	0.304891i	0.0526227	−	0.998614i	$-0.483242\pi$
$131$	−7.64125	−	3.48964i	−0.667619	−	0.304891i	−0.720242	+	0.693723i	$0.755969\pi$
$132$	−5.81035	−	9.79174i	−0.505726	−	0.852262i
$133$	16.6221	−	2.38990i	1.44132	−	0.207231i
$134$	−1.89022	−	5.35767i	−0.163291	−	0.462832i
$135$	2.55004	+	2.94290i	0.219472	+	0.253284i
$136$	−5.06491	−	2.20423i	−0.434312	−	0.189011i
$137$	18.2565			1.55976			0.779879	−	0.625930i	$-0.215281\pi$
$137$	18.2565			1.55976			0.779879	+	0.625930i	$0.215281\pi$
$138$	2.79177	+	6.18110i	0.237651	+	0.526170i
$139$			4.80626i			0.407662i	0.979006	+	0.203831i	$0.0653392\pi$
$139$			4.80626i			0.407662i	−0.979006	+	0.203831i	$0.934661\pi$
$140$	−4.17354	+	23.1388i	−0.352729	+	1.95559i
$141$	−5.48052	+	4.74889i	−0.461543	+	0.399929i
$142$	−16.1804	+	5.70855i	−1.35783	+	0.479051i
$143$	−3.01424	−	20.9645i	−0.252063	−	1.75314i
$144$	−0.285746	−	3.98978i	−0.0238121	−	0.332482i
$145$	−5.13149	+	11.2364i	−0.426147	+	0.933131i
$146$	9.94937	−	7.17488i	0.823415	−	0.593797i
$147$	2.09297	+	0.300923i	0.172625	+	0.0248197i
$148$	−15.1740	−	0.541202i	−1.24730	−	0.0444865i
$149$	2.47073	−	8.41454i	0.202410	−	0.689346i	−0.794243	−	0.607600i	$-0.792132\pi$
$149$	2.47073	−	8.41454i	0.202410	−	0.689346i	0.996653	−	0.0817457i	$-0.0260495\pi$
$150$	7.11208	−	12.4902i	0.580699	−	1.01982i
$151$	6.06182	+	13.2735i	0.493304	+	1.08019i	0.978588	+	0.205829i	$0.0659891\pi$
$151$	6.06182	+	13.2735i	0.493304	+	1.08019i	−0.485284	+	0.874357i	$0.661284\pi$
$152$	10.5143	+	11.7036i	0.852822	+	0.949285i
$153$	1.27891	−	1.47594i	0.103393	−	0.119322i
$154$	19.1954	+	14.9107i	1.54681	+	1.20154i
$155$	12.8435	−	19.9849i	1.03162	−	1.60523i
$156$	2.34946	−	7.06015i	0.188107	−	0.565264i
$157$	0.0636165	+	0.0989892i	0.00507715	+	0.00790020i	0.843783	−	0.536685i	$-0.180324\pi$
$157$	0.0636165	+	0.0989892i	0.00507715	+	0.00790020i	−0.838706	+	0.544585i	$0.816687\pi$
$158$	10.8824	+	20.8029i	0.865761	+	1.65499i
$159$	−0.113218	+	0.0332439i	−0.00897879	+	0.00263641i
$160$	−20.1963	+	8.79407i	−1.59666	+	0.695232i
$161$	−10.3769	−	10.0972i	−0.817815	−	0.795769i
$162$	1.37632	+	0.325197i	0.108134	+	0.0255499i
$163$	0.839209	+	2.85808i	0.0657319	+	0.223862i	0.985808	−	0.167878i	$-0.0536914\pi$
$163$	0.839209	+	2.85808i	0.0657319	+	0.223862i	−0.920076	+	0.391740i	$0.871873\pi$
$164$	1.81555	+	7.11179i	0.141770	+	0.555337i
$165$	−11.9851	−	18.6493i	−0.933042	−	1.45184i
$166$	−19.1655	−	1.71460i	−1.48753	−	0.133079i
$167$	−2.84155	−	1.82615i	−0.219886	−	0.141312i	0.426061	−	0.904694i	$-0.359901\pi$
$167$	−2.84155	−	1.82615i	−0.219886	−	0.141312i	−0.645947	+	0.763382i	$0.723537\pi$
$168$	3.68590	+	7.70260i	0.284373	+	0.594268i
$169$	0.551016	−	0.635907i	0.0423859	−	0.0489159i
$170$	−10.0081	−	3.93744i	−0.767588	−	0.301988i
$171$	−5.05975	+	2.31071i	−0.386929	+	0.176705i
$172$	−2.69760	+	2.89771i	−0.205690	+	0.220948i
$173$	−0.910661	+	3.10143i	−0.0692363	+	0.235797i	−0.986840	−	0.161699i	$-0.948303\pi$
$173$	−0.910661	+	3.10143i	−0.0692363	+	0.235797i	0.917604	+	0.397496i	$0.130121\pi$
$174$	0.875321	+	4.39998i	0.0663579	+	0.333561i
$175$	−4.36670	+	30.3711i	−0.330091	+	2.29584i
$176$	−1.62231	+	22.7139i	−0.122286	+	1.71213i
$177$	4.13082	−	9.04524i	0.310492	−	0.679882i
$178$	−9.78705	−	10.1423i	−0.733570	−	0.760201i
$179$	−6.48367	+	0.932211i	−0.484612	+	0.0696767i	−0.380291	−	0.924867i	$-0.624176\pi$
$179$	−6.48367	+	0.932211i	−0.484612	+	0.0696767i	−0.104321	+	0.994544i	$0.533267\pi$
$180$	−0.832880	−	7.74337i	−0.0620792	−	0.577156i
$181$	4.55834	−	3.94982i	0.338819	−	0.293588i	−0.468787	−	0.883311i	$-0.655309\pi$
$181$	4.55834	−	3.94982i	0.338819	−	0.293588i	0.807605	+	0.589723i	$0.200763\pi$
$182$	0.850589	+	15.8616i	0.0630498	+	1.17574i
$183$	−7.76689			−0.574145
$184$	2.46336	−	13.3391i	0.181601	−	0.983372i
$185$	−29.5628			−2.17350
$186$	−0.461999	−	8.61528i	−0.0338754	−	0.631703i
$187$	−8.40243	+	7.28074i	−0.614446	+	0.532421i
$188$	14.4203	−	1.55106i	1.05171	−	0.113123i
$189$	−2.98829	+	0.429651i	−0.217366	+	0.0312525i
$190$	21.2706	+	22.0428i	1.54313	+	1.59915i
$191$	3.23235	−	7.07787i	0.233885	−	0.512137i	−0.755903	−	0.654683i	$-0.772802\pi$
$191$	3.23235	−	7.07787i	0.233885	−	0.512137i	0.989788	+	0.142547i	$0.0455292\pi$
$192$	−4.08115	+	6.88071i	−0.294532	+	0.496573i
$193$	2.94362	−	20.4733i	0.211886	−	1.47370i	−0.554963	−	0.831875i	$-0.687268\pi$
$193$	2.94362	−	20.4733i	0.211886	−	1.47370i	0.766849	−	0.641827i	$-0.221823\pi$
$194$	−2.64965	−	13.3190i	−0.190234	−	0.956249i
$195$	4.08155	−	13.9005i	0.292286	−	0.995434i
$196$	−3.09530	−	2.88155i	−0.221093	−	0.205825i
$197$	10.0059	−	4.56954i	0.712890	−	0.325566i	−0.0257476	−	0.999668i	$-0.508197\pi$
$197$	10.0059	−	4.56954i	0.712890	−	0.325566i	0.738638	+	0.674102i	$0.235469\pi$
$198$	−7.49207	−	2.94756i	−0.532438	−	0.209474i
$199$	11.1071	−	12.8183i	0.787365	−	0.908667i	−0.210253	−	0.977647i	$-0.567429\pi$
$199$	11.1071	−	12.8183i	0.787365	−	0.908667i	0.997618	+	0.0689796i	$0.0219743\pi$
$200$	−25.9303	+	12.4084i	−1.83355	+	0.877404i
$201$	−3.37958	−	2.17192i	−0.238377	−	0.153196i
$202$	−15.0396	−	1.34549i	−1.05818	−	0.0946681i
$203$	−5.17772	−	8.05669i	−0.363405	−	0.565469i
$204$	−3.78451	+	0.966136i	−0.264969	+	0.0676431i
$205$	4.02618	+	13.7119i	0.281201	+	0.957681i
$206$	−9.94204	−	2.34911i	−0.692695	−	0.163670i
$207$	4.24021	+	2.24068i	0.294715	+	0.155738i
$208$	−11.9125	+	8.91939i	−0.825982	+	0.618448i
$209$	30.3838	−	8.92149i	2.10169	−	0.617113i
$210$	7.70646	+	14.7317i	0.531797	+	1.01658i
$211$	8.82972	+	13.7393i	0.607863	+	0.945853i	0.999667	+	0.0258045i	$0.00821474\pi$
$211$	8.82972	+	13.7393i	0.607863	+	0.945853i	−0.391804	+	0.920049i	$0.628149\pi$
$212$	0.223923	+	0.0745165i	0.0153791	+	0.00511782i
$213$	−6.55929	+	10.2065i	−0.449435	+	0.699335i
$214$	4.35977	+	3.38661i	0.298028	+	0.231504i
$215$	−5.04781	+	5.82548i	−0.344258	+	0.397294i
$216$	−1.89024	−	2.10404i	−0.128614	−	0.143162i
$217$	7.65114	+	16.7537i	0.519393	+	1.13731i
$218$	−8.51709	+	14.9577i	−0.576850	+	1.01306i
$219$	2.44368	−	8.32243i	0.165129	−	0.562377i
$220$	−1.58033	+	44.3086i	−0.106546	+	2.98729i
$221$	−7.19179	−	1.03402i	−0.483772	−	0.0695560i
$222$	−8.70832	+	6.27991i	−0.584464	+	0.421480i
$223$	3.79160	−	8.30245i	0.253905	−	0.555973i	−0.739162	−	0.673528i	$-0.764778\pi$
$223$	3.79160	−	8.30245i	0.253905	−	0.555973i	0.993066	+	0.117554i	$0.0375055\pi$
$224$	2.72976	−	16.8586i	0.182390	−	1.12641i
$225$	−1.44640	−	10.0599i	−0.0964264	−	0.670660i
$226$	7.95000	−	2.80482i	0.528826	−	0.186574i
$227$	−5.74712	+	4.97991i	−0.381450	+	0.330528i	−0.824389	−	0.566024i	$-0.808481\pi$
$227$	−5.74712	+	4.97991i	−0.381450	+	0.330528i	0.442939	+	0.896552i	$0.353936\pi$
$228$	10.9482	+	1.97472i	0.725060	+	0.130779i
$229$		−	20.9859i		−	1.38679i	−0.720559	−	0.693394i	$-0.756115\pi$
$229$		−	20.9859i		−	1.38679i	0.720559	−	0.693394i	$-0.243885\pi$
$230$	3.86742	−	26.1258i	0.255010	−	1.72268i
$231$	17.1871			1.13083
$232$	3.58040	−	8.22707i	0.235065	−	0.540134i
$233$	−1.74396	−	2.01264i	−0.114251	−	0.131852i	0.695743	−	0.718290i	$-0.255075\pi$
$233$	−1.74396	−	2.01264i	−0.114251	−	0.131852i	−0.809994	+	0.586438i	$0.800530\pi$
$234$	−1.75053	−	4.96170i	−0.114435	−	0.324357i
$235$	27.9510	−	4.01875i	1.82332	−	0.262155i
$236$	−17.1032	+	10.1489i	−1.11332	+	0.660639i
$237$	15.1008	+	6.89632i	0.980904	+	0.447964i
$238$	6.76306	−	4.87711i	0.438384	−	0.316136i
$239$	−1.62750	+	11.3195i	−0.105274	+	0.732200i	0.866992	+	0.498323i	$0.166050\pi$
$239$	−1.62750	+	11.3195i	−0.105274	+	0.732200i	−0.972266	+	0.233877i	$0.924859\pi$
$240$	−7.46348	+	13.6715i	−0.481765	+	0.882492i
$241$	9.75154	+	2.86331i	0.628152	+	0.184442i	0.580287	−	0.814412i	$-0.302940\pi$
$241$	9.75154	+	2.86331i	0.628152	+	0.184442i	0.0478646	+	0.998854i	$0.484758\pi$
$242$	26.3113	+	14.9820i	1.69135	+	0.963077i
$243$	0.909632	−	0.415415i	0.0583529	−	0.0266489i
$244$	12.7602	+	8.85864i	0.816888	+	0.567117i
$245$	−6.22273	−	5.39202i	−0.397555	−	0.344484i
$246$	4.09877	+	3.18386i	0.261328	+	0.202996i
$247$	17.4093	+	11.1883i	1.10773	+	0.711892i
$248$	−9.06727	+	14.6810i	−0.575772	+	0.932242i
$249$	−11.4463	+	7.35606i	−0.725377	+	0.466171i
$250$	−25.1952	+	13.1802i	−1.59349	+	0.833586i
$251$	−4.03742	−	13.7502i	−0.254840	−	0.867905i	−0.983172	−	0.182681i	$-0.941523\pi$
$251$	−4.03742	−	13.7502i	−0.254840	−	0.867905i	0.728333	−	0.685224i	$-0.240296\pi$
$252$	5.39950	+	2.70247i	0.340137	+	0.170240i
$253$	−22.0782	−	16.0616i	−1.38804	−	1.00978i
$254$	−4.00314	−	0.945863i	−0.251179	−	0.0593487i
$255$	−7.29675	+	2.14252i	−0.456940	+	0.134170i
$256$	14.5528	−	6.64948i	0.909551	−	0.415592i
$257$	18.1718	−	11.6783i	1.13353	−	0.728473i	0.167233	−	0.985917i	$-0.446517\pi$
$257$	18.1718	−	11.6783i	1.13353	−	0.728473i	0.966293	+	0.257445i	$0.0828805\pi$
$258$	−0.249450	+	2.78830i	−0.0155301	+	0.173592i
$259$	12.3915	−	19.2815i	0.769968	−	1.19809i
$260$	−22.5600	+	18.1818i	−1.39911	+	1.12759i
$261$	2.39740	+	2.07736i	0.148396	+	0.128586i
$262$	11.0551	+	4.34935i	0.682988	+	0.268704i
$263$	−6.36540	−	13.9383i	−0.392507	−	0.859471i	−0.997975	−	0.0636014i	$-0.979741\pi$
$263$	−6.36540	−	13.9383i	−0.392507	−	0.859471i	0.605468	−	0.795870i	$-0.292986\pi$
$264$	8.94681	+	13.3877i	0.550638	+	0.823958i
$265$	0.440874	+	0.129452i	0.0270827	+	0.00795218i
$266$	−23.2925	+	4.63376i	−1.42816	+	0.284114i
$267$	−9.86484	−	1.41835i	−0.603718	−	0.0868016i
$268$	3.07508	+	7.42287i	0.187840	+	0.453424i
$269$	0.0984245	+	0.0449490i	0.00600105	+	0.00274059i	0.418413	−	0.908257i	$-0.362586\pi$
$269$	0.0984245	+	0.0449490i	0.00600105	+	0.00274059i	−0.412412	+	0.910997i	$0.635314\pi$
$270$	−3.82399	−	3.96281i	−0.232720	−	0.241169i
$271$	−0.270311	−	1.88006i	−0.0164202	−	0.114205i	0.979963	−	0.199180i	$-0.0638280\pi$
$271$	−0.270311	−	1.88006i	−0.0164202	−	0.114205i	−0.996383	+	0.0849752i	$0.972919\pi$
$272$	7.31951	+	2.72922i	0.443810	+	0.165483i
$273$	7.35539	+	8.48857i	0.445168	+	0.513752i
$274$	−25.7815	+	1.38255i	−1.55752	+	0.0835229i
$275$			57.8594i			3.48905i
$276$	−4.41058	−	8.51744i	−0.265486	−	0.512690i
$277$		−	8.41580i		−	0.505656i	−0.967511	−	0.252828i	$-0.918639\pi$
$277$		−	8.41580i		−	0.505656i	0.967511	−	0.252828i	$-0.0813607\pi$
$278$	−0.363974	−	6.78733i	−0.0218297	−	0.407077i
$279$	−3.99509	−	4.61058i	−0.239180	−	0.276028i
$280$	4.14153	−	32.9924i	0.247504	−	1.97167i
$281$	1.87374	+	13.0321i	0.111778	+	0.777431i	0.966189	+	0.257834i	$0.0830088\pi$
$281$	1.87374	+	13.0321i	0.111778	+	0.777431i	−0.854412	+	0.519597i	$0.826082\pi$
$282$	7.37987	−	7.12135i	0.439465	−	0.424070i
$283$	−6.02237	−	2.75032i	−0.357993	−	0.163490i	0.228296	−	0.973592i	$-0.426684\pi$
$283$	−6.02237	−	2.75032i	−0.357993	−	0.163490i	−0.586289	+	0.810102i	$0.699412\pi$
$284$	22.4174	−	9.28686i	1.33023	−	0.551073i
$285$	21.4397	+	3.08256i	1.26998	+	0.182595i
$286$	5.84428	+	29.3775i	0.345580	+	1.73713i
$287$	−10.6308	−	3.12149i	−0.627517	−	0.184256i
$288$	0.705668	+	5.61267i	0.0415819	+	0.330730i
$289$	−5.47767	−	11.9944i	−0.322216	−	0.705554i
$290$	6.39568	−	16.2565i	0.375568	−	0.954612i
$291$	−7.25710	−	6.28831i	−0.425419	−	0.368627i
$292$	−13.5070	+	10.8857i	−0.790437	+	0.637038i
$293$	−5.46947	+	8.51067i	−0.319530	+	0.497198i	−0.963448	−	0.267896i	$-0.913672\pi$
$293$	−5.46947	+	8.51067i	−0.319530	+	0.497198i	0.643918	+	0.765095i	$0.277308\pi$
$294$	−2.97844	−	0.266460i	−0.173706	−	0.0155403i
$295$	−32.5746	+	20.9344i	−1.89657	+	1.21885i
$296$	21.4695	−	0.384841i	1.24789	−	0.0223684i
$297$	−5.46234	+	1.60389i	−0.316957	+	0.0930670i
$298$	−2.85190	+	12.0700i	−0.165206	+	0.699196i
$299$	−1.51588	−	17.7779i	−0.0876657	−	1.02812i
$300$	−9.09770	+	18.1771i	−0.525256	+	1.04945i
$301$	−1.68368	−	5.73408i	−0.0970456	−	0.330507i
$302$	−9.56561	−	18.2856i	−0.550439	−	1.05222i
$303$	−8.98212	+	5.77246i	−0.516010	+	0.331619i
$304$	−15.7344	−	15.7314i	−0.902431	−	0.902255i
$305$	25.4432	+	16.3513i	1.45687	+	0.936276i
$306$	−1.69428	+	2.18115i	−0.0968556	+	0.124688i
$307$	−16.2054	−	14.0420i	−0.924890	−	0.801422i	0.0555058	−	0.998458i	$-0.482323\pi$
$307$	−16.2054	−	14.0420i	−0.924890	−	0.801422i	−0.980396	+	0.197036i	$0.936868\pi$
$308$	−28.2367	−	19.6030i	−1.60893	−	1.11699i
$309$	−6.57087	+	3.00082i	−0.373804	+	0.170710i
$310$	−16.6240	+	29.1950i	−0.944179	+	1.65817i
$311$	−9.56784	−	2.80937i	−0.542543	−	0.159305i	−0.00103301	−	0.999999i	$-0.500329\pi$
$311$	−9.56784	−	2.80937i	−0.542543	−	0.159305i	−0.541510	+	0.840695i	$0.682147\pi$
$312$	−2.78321	+	10.1482i	−0.157568	+	0.574526i
$313$	−2.69372	+	18.7352i	−0.152258	+	1.05898i	0.760165	+	0.649730i	$0.225118\pi$
$313$	−2.69372	+	18.7352i	−0.152258	+	1.05898i	−0.912423	+	0.409248i	$0.865791\pi$
$314$	−0.0973346	−	0.134973i	−0.00549291	−	0.00761699i
$315$	10.6937	+	4.88367i	0.602524	+	0.275163i
$316$	−16.9434	−	28.5534i	−0.953141	−	1.60625i
$317$	−27.3958	+	3.93892i	−1.53870	+	0.221232i	−0.858892	−	0.512156i	$-0.828847\pi$
$317$	−27.3958	+	3.93892i	−1.53870	+	0.221232i	−0.679810	+	0.733388i	$0.737938\pi$
$318$	0.157368	−	0.0555204i	0.00882473	−	0.00311343i
$319$	−11.8263	−	13.6483i	−0.662146	−	0.764158i
$320$	27.8550	−	13.9483i	1.55714	−	0.779733i
$321$	3.90364			0.217880
$322$	15.4188	+	13.4732i	0.859254	+	0.750834i
$323$		−	10.8631i		−	0.604439i
$324$	−1.96824	−	0.355010i	−0.109347	−	0.0197228i
$325$	−28.5762	+	24.7615i	−1.58513	+	1.37352i
$326$	−1.40156	−	3.97259i	−0.0776251	−	0.220021i
$327$	1.73213	+	12.0473i	0.0957873	+	0.666215i
$328$	−3.10245	−	9.90567i	−0.171304	−	0.546949i
$329$	−9.09477	+	19.9148i	−0.501411	+	1.09794i
$330$	18.3375	+	25.4286i	1.00945	+	1.39980i
$331$	22.6918	+	3.26259i	1.24725	+	0.179328i	0.734143	−	0.678994i	$-0.237584\pi$
$331$	22.6918	+	3.26259i	1.24725	+	0.179328i	0.513111	+	0.858322i	$0.328493\pi$
$332$	27.1951	+	0.969948i	1.49252	+	0.0532328i
$333$	−2.13887	+	7.28432i	−0.117209	+	0.399178i
$334$	4.15108	+	2.36368i	0.227137	+	0.129335i
$335$	6.49853	+	14.2298i	0.355053	+	0.777457i
$336$	−5.78848	−	10.5984i	−0.315788	−	0.578188i
$337$	5.45133	−	6.29117i	0.296953	−	0.342702i	−0.587592	−	0.809158i	$-0.699924\pi$
$337$	5.45133	−	6.29117i	0.296953	−	0.342702i	0.884545	+	0.466456i	$0.154469\pi$
$338$	−0.729980	+	0.939746i	−0.0397057	+	0.0511154i
$339$	3.22282	−	5.01480i	0.175039	−	0.272367i
$340$	14.4315	+	4.80248i	0.782657	+	0.260451i
$341$	18.7769	+	29.2174i	1.01683	+	1.58221i
$342$	6.97032	−	3.64632i	0.376912	−	0.197171i
$343$	−14.1520	+	4.15540i	−0.764137	+	0.224371i
$344$	3.59006	−	4.29638i	0.193563	−	0.231645i
$345$	−9.17308	−	16.2669i	−0.493862	−	0.875780i
$346$	1.05115	−	4.44875i	0.0565103	−	0.239166i
$347$	6.51026	+	22.1719i	0.349489	+	1.19025i	0.927375	+	0.374132i	$0.122059\pi$
$347$	6.51026	+	22.1719i	0.349489	+	1.19025i	−0.577886	+	0.816117i	$0.696122\pi$
$348$	−1.56932	−	6.14729i	−0.0841245	−	0.329529i
$349$	2.06629	+	3.21520i	0.110606	+	0.172106i	0.892144	−	0.451752i	$-0.149201\pi$
$349$	2.06629	+	3.21520i	0.110606	+	0.172106i	−0.781538	+	0.623858i	$0.785564\pi$
$350$	3.86661	−	43.2202i	0.206679	−	2.31022i
$351$	−3.12981	−	2.01140i	−0.167057	−	0.107361i
$352$	0.570890	−	32.1991i	0.0304286	−	1.71622i
$353$	−12.6010	+	14.5423i	−0.670684	+	0.774011i	−0.984483	−	0.175479i	$-0.943853\pi$
$353$	−12.6010	+	14.5423i	−0.670684	+	0.774011i	0.313799	+	0.949489i	$0.398398\pi$
$354$	−5.14850	+	13.0864i	−0.273639	+	0.695533i
$355$	42.9745	−	19.6258i	2.28085	−	1.04163i
$356$	14.5892	+	13.5817i	0.773226	+	0.719828i
$357$	1.66109	−	5.65715i	0.0879142	−	0.299408i
$358$	9.08554	−	1.80746i	0.480186	−	0.0955271i
$359$	1.66448	−	11.5767i	0.0878476	−	0.610994i	−0.897574	−	0.440864i	$-0.854672\pi$
$359$	1.66448	−	11.5767i	0.0878476	−	0.610994i	0.985422	−	0.170130i	$-0.0544188\pi$
$360$	1.76258	+	10.8720i	0.0928960	+	0.573004i
$361$	−4.96026	+	10.8615i	−0.261066	+	0.571656i
$362$	−6.13810	+	5.92308i	−0.322611	+	0.311310i
$363$	21.1917	−	3.04691i	1.11228	−	0.159921i
$364$	−2.40238	−	22.3351i	−0.125919	−	1.17068i
$365$	−25.5261	+	22.1184i	−1.33609	+	1.15773i
$366$	10.9683	−	0.588180i	0.573321	−	0.0307447i
$367$	−19.3094			−1.00794			−0.503971	−	0.863720i	$-0.668128\pi$
$367$	−19.3094			−1.00794			−0.503971	+	0.863720i	$0.668128\pi$
$368$	−2.46856	+	19.0238i	−0.128682	+	0.991686i
$369$	3.66994			0.191049
$370$	41.7481	−	2.23876i	2.17038	−	0.116388i
$371$	−0.269227	+	0.233287i	−0.0139776	+	0.0121116i
$372$	1.30486	+	12.1314i	0.0676536	+	0.628983i
$373$	20.4441	−	2.93942i	1.05856	−	0.152197i	0.409018	−	0.912526i	$-0.365871\pi$
$373$	20.4441	−	2.93942i	1.05856	−	0.152197i	0.649538	+	0.760329i	$0.274962\pi$
$374$	11.3144	−	10.9181i	0.585054	−	0.564560i
$375$	−8.35240	+	18.2892i	−0.431316	+	0.944451i
$376$	−20.2467	+	3.28242i	−1.04415	+	0.169278i
$377$	1.67959	−	11.6818i	0.0865034	−	0.601645i
$378$	4.18748	−	0.833048i	0.215381	−	0.0428474i
$379$	−4.62379	+	15.7472i	−0.237508	+	0.808878i	0.751336	+	0.659920i	$0.229410\pi$
$379$	−4.62379	+	15.7472i	−0.237508	+	0.808878i	−0.988844	+	0.148957i	$0.952408\pi$
$380$	−31.7073	−	29.5177i	−1.62655	−	1.51422i
$381$	−2.64574	+	1.20827i	−0.135546	+	0.0619016i
$382$	−4.02868	+	10.2400i	−0.206125	+	0.523926i
$383$	21.2678	−	24.5444i	1.08674	−	1.25416i	0.121552	−	0.992585i	$-0.461213\pi$
$383$	21.2678	−	24.5444i	1.08674	−	1.25416i	0.965183	−	0.261574i	$-0.0842417\pi$
$384$	5.24227	−	10.0259i	0.267519	−	0.511632i
$385$	−56.3025	−	36.1834i	−2.86944	−	1.84408i
$386$	−2.60651	+	29.1350i	−0.132668	+	1.48293i
$387$	1.07020	+	1.66526i	0.0544013	+	0.0846501i
$388$	4.75044	+	18.6082i	0.241167	+	0.944690i
$389$	1.32795	+	4.52259i	0.0673299	+	0.229305i	0.986283	−	0.165062i	$-0.0527823\pi$
$389$	1.32795	+	4.52259i	0.0673299	+	0.229305i	−0.918953	+	0.394366i	$0.870964\pi$
$390$	−4.71123	+	19.9391i	−0.238562	+	1.00966i
$391$	−7.42048	+	5.71474i	−0.375270	+	0.289007i
$392$	4.58936	+	3.83487i	0.231798	+	0.193690i
$393$	8.06010	−	2.36666i	0.406578	−	0.119382i
$394$	−13.7841	+	7.21077i	−0.694434	+	0.363273i
$395$	−34.9495	−	54.3825i	−1.75850	−	2.73628i
$396$	10.8034	+	3.59513i	0.542891	+	0.180662i
$397$	8.12523	−	12.6431i	0.407794	−	0.634539i	−0.575236	−	0.817988i	$-0.695090\pi$
$397$	8.12523	−	12.6431i	0.407794	−	0.634539i	0.983029	+	0.183448i	$0.0587260\pi$
$398$	−14.7146	+	18.9430i	−0.737577	+	0.949526i
$399$	−10.9971	+	12.6913i	−0.550544	+	0.635362i
$400$	35.6787	−	19.4866i	1.78394	−	0.974329i
$401$	4.61653	+	10.1088i	0.230539	+	0.504809i	0.989181	−	0.146698i	$-0.0468644\pi$
$401$	4.61653	+	10.1088i	0.230539	+	0.504809i	−0.758643	+	0.651507i	$0.774137\pi$
$402$	4.93706	+	2.81122i	0.246238	+	0.140211i
$403$	−6.39448	+	21.7776i	−0.318532	+	1.08482i
$404$	21.3406	+	0.761139i	1.06173	+	0.0378681i
$405$	−3.85438	−	0.554176i	−0.191526	−	0.0275372i
$406$	7.92202	+	10.9854i	0.393163	+	0.545197i
$407$	17.9542	−	39.3143i	0.889958	−	1.94874i
$408$	5.27127	−	1.65096i	0.260967	−	0.0817347i
$409$	1.81190	+	12.6021i	0.0895929	+	0.623132i	0.984303	+	0.176485i	$0.0564728\pi$
$409$	1.81190	+	12.6021i	0.0895929	+	0.623132i	−0.894710	+	0.446647i	$0.852618\pi$
$410$	−6.72410	−	19.0588i	−0.332080	−	0.941249i
$411$	−13.7973	+	11.9555i	−0.680573	+	0.589720i
$412$	14.2179	+	2.56447i	0.700465	+	0.126343i
$413$		−	30.0207i		−	1.47722i
$414$	−6.15764	−	2.84314i	−0.302631	−	0.139733i
$415$	52.9827			2.60082
$416$	16.1472	−	13.4979i	0.791680	−	0.661791i
$417$	−3.14743	−	3.63233i	−0.154130	−	0.177876i
$418$	−42.2319	+	14.8997i	−2.06563	+	0.728770i
$419$	−3.86040	+	0.555042i	−0.188593	+	0.0271156i	−0.235964	−	0.971762i	$-0.575825\pi$
$419$	−3.86040	+	0.555042i	−0.188593	+	0.0271156i	0.0473710	+	0.998877i	$0.484916\pi$
$420$	−11.9986	−	20.2203i	−0.585470	−	0.986648i
$421$	−19.4450	−	8.88025i	−0.947693	−	0.432797i	−0.119246	−	0.992865i	$-0.538048\pi$
$421$	−19.4450	−	8.88025i	−0.947693	−	0.432797i	−0.828447	+	0.560068i	$0.810775\pi$
$422$	−13.5097	−	18.7338i	−0.657640	−	0.911946i
$423$	1.03203	−	7.17795i	0.0501792	−	0.349004i
$424$	−0.321863	−	0.0882736i	−0.0156311	−	0.00428695i
$425$	19.0445	+	5.59196i	0.923792	+	0.271250i
$426$	8.49000	−	14.9101i	0.411342	−	0.722398i
$427$	−21.3294	+	9.74082i	−1.03220	+	0.471391i
$428$	−6.41327	−	4.45235i	−0.309997	−	0.215212i
$429$	16.0068	+	13.8700i	0.772817	+	0.669650i
$430$	6.68727	−	8.60892i	0.322489	−	0.415159i
$431$	−8.06951	−	5.18596i	−0.388695	−	0.249799i	0.331669	−	0.943396i	$-0.392388\pi$
$431$	−8.06951	−	5.18596i	−0.388695	−	0.249799i	−0.720363	+	0.693597i	$0.756025\pi$
$432$	2.82870	+	2.82815i	0.136096	+	0.136070i
$433$	13.4856	−	8.66666i	0.648076	−	0.416493i	−0.174887	−	0.984589i	$-0.555956\pi$
$433$	13.4856	−	8.66666i	0.648076	−	0.416493i	0.822963	+	0.568095i	$0.192320\pi$
$434$	−12.0736	−	23.0799i	−0.579550	−	1.10787i
$435$	−3.48015	−	11.8523i	−0.166860	−	0.568275i
$436$	10.8950	−	21.7680i	0.521774	−	1.04250i
$437$	25.9869	−	6.02606i	1.24312	−	0.288266i
$438$	−2.82068	+	11.9379i	−0.134777	+	0.570413i
$439$	26.3039	−	7.72351i	1.25542	−	0.368623i	0.414629	−	0.909990i	$-0.363911\pi$
$439$	26.3039	−	7.72351i	1.25542	−	0.368623i	0.840786	+	0.541367i	$0.182093\pi$
$440$	−1.12375	−	62.6917i	−0.0535725	−	2.98871i
$441$	−1.77882	+	1.14318i	−0.0847057	+	0.0544371i
$442$	10.2344	+	0.915604i	0.486803	+	0.0435508i
$443$	15.1465	−	23.5684i	0.719632	−	1.11977i	−0.268067	−	0.963400i	$-0.586385\pi$
$443$	15.1465	−	23.5684i	0.719632	−	1.11977i	0.987699	−	0.156368i	$-0.0499787\pi$
$444$	11.8222	−	9.52787i	0.561056	−	0.452173i
$445$	29.3298	+	25.4144i	1.39036	+	1.20476i
$446$	−4.72571	+	12.0117i	−0.223769	+	0.568772i
$447$	3.64310	+	7.97727i	0.172313	+	0.377312i
$448$	−2.57824	+	24.0142i	−0.121810	+	1.13456i
$449$	−9.15670	−	2.68865i	−0.432131	−	0.126885i	0.0584308	−	0.998291i	$-0.481390\pi$
$449$	−9.15670	−	2.68865i	−0.432131	−	0.126885i	−0.490562	+	0.871406i	$0.663208\pi$
$450$	2.80441	+	14.0969i	0.132201	+	0.664534i
$451$	−20.6801	−	2.97335i	−0.973787	−	0.140009i
$452$	−11.0145	+	4.56297i	−0.518077	+	0.214624i
$453$	−13.2735	−	6.06182i	−0.623646	−	0.284809i
$454$	7.73887	−	7.46777i	0.363203	−	0.350480i
$455$	−6.22450	−	43.2923i	−0.291809	−	2.02958i
$456$	−15.6104	−	1.95957i	−0.731023	−	0.0917652i
$457$	−5.92227	−	6.83467i	−0.277032	−	0.319712i	0.600134	−	0.799900i	$-0.295114\pi$
$457$	−5.92227	−	6.83467i	−0.277032	−	0.319712i	−0.877166	+	0.480187i	$0.840569\pi$
$458$	1.58924	+	29.6360i	0.0742605	+	1.38480i
$459$			1.95294i			0.0911556i
$460$	−3.48302	+	37.1873i	−0.162397	+	1.73387i
$461$			27.4262i			1.27737i	0.769469	+	0.638684i	$0.220521\pi$
$461$			27.4262i			1.27737i	−0.769469	+	0.638684i	$0.779479\pi$
$462$	−24.2714	+	1.30157i	−1.12921	+	0.0605543i
$463$	0.445319	+	0.513926i	0.0206957	+	0.0238841i	0.766003	−	0.642837i	$-0.222243\pi$
$463$	0.445319	+	0.513926i	0.0206957	+	0.0238841i	−0.745307	+	0.666721i	$0.767697\pi$
$464$	−4.43315	+	11.8893i	−0.205804	+	0.551946i
$465$	3.38085	+	23.5143i	0.156783	+	1.09045i
$466$	2.61521	+	2.71014i	0.121147	+	0.125545i
$467$	−1.68925	−	0.771455i	−0.0781692	−	0.0356987i	0.375947	−	0.926641i	$-0.377318\pi$
$467$	−1.68925	−	0.771455i	−0.0781692	−	0.0356987i	−0.454116	+	0.890943i	$0.650045\pi$
$468$	2.84781	+	6.87428i	0.131640	+	0.317764i
$469$	−12.0049	−	1.72604i	−0.554334	−	0.0797013i
$470$	−39.1677	+	7.79193i	−1.80667	+	0.359415i
$471$	−0.112902	−	0.0331511i	−0.00520226	−	0.00152752i
$472$	23.3843	−	15.6274i	1.07635	−	0.719308i
$473$	−4.68139	−	10.2508i	−0.215251	−	0.471333i
$474$	−21.8474	−	8.59530i	−1.00348	−	0.394795i
$475$	−42.7246	−	37.0211i	−1.96034	−	1.69865i
$476$	−9.18135	+	7.39954i	−0.420827	+	0.339157i
$477$	0.0637945	−	0.0992663i	0.00292095	−	0.00454509i
$478$	1.44112	−	16.1085i	0.0659151	−	0.736787i
$479$	−10.4438	+	6.71181i	−0.477189	+	0.306670i	−0.757035	−	0.653374i	$-0.773353\pi$
$479$	−10.4438	+	6.71181i	−0.477189	+	0.306670i	0.279846	+	0.960045i	$0.409716\pi$
$480$	9.50448	−	19.8719i	0.433818	−	0.907024i
$481$	27.1006	−	7.95747i	1.23568	−	0.362829i
$482$	−13.9878	−	3.30505i	−0.637127	−	0.150541i
$483$	14.4546	+	0.835506i	0.657707	+	0.0380168i
$484$	−38.2910	−	19.1648i	−1.74050	−	0.871125i
$485$	10.5346	+	35.8777i	0.478353	+	1.62912i
$486$	−1.25311	+	0.655528i	−0.0568422	+	0.0297354i
$487$	−11.4736	+	7.37362i	−0.519917	+	0.334130i	−0.774139	−	0.633015i	$-0.781817\pi$
$487$	−11.4736	+	7.37362i	−0.519917	+	0.334130i	0.254222	+	0.967146i	$0.418181\pi$
$488$	−18.6906	−	11.5437i	−0.846084	−	0.522560i
$489$	−2.50588	−	1.61043i	−0.113320	−	0.0728262i
$490$	9.19597	+	7.14329i	0.415432	+	0.322701i
$491$	2.75873	+	2.39045i	0.124500	+	0.107880i	0.714885	−	0.699242i	$-0.246479\pi$
$491$	2.75873	+	2.39045i	0.124500	+	0.107880i	−0.590386	+	0.807121i	$0.701024\pi$
$492$	−6.02933	−	4.18580i	−0.271823	−	0.188711i
$493$	−5.63533	+	2.57357i	−0.253802	+	0.115908i
$494$	−25.4324	−	14.4815i	−1.14426	−	0.651554i
$495$	21.2704	+	6.24556i	0.956035	+	0.280717i
$496$	11.6929	−	21.4189i	0.525026	−	0.961736i
$497$	−5.21272	+	36.2553i	−0.233822	+	1.62627i
$498$	15.6072	−	11.2549i	0.699373	−	0.504345i
$499$	31.1371	+	14.2198i	1.39389	+	0.636568i	0.963899	−	0.266267i	$-0.0857901\pi$
$499$	31.1371	+	14.2198i	1.39389	+	0.636568i	0.429989	+	0.902834i	$0.358517\pi$
$500$	34.5822	−	20.5208i	1.54656	−	0.917719i
$501$	3.34337	−	0.480705i	0.149371	−	0.0214763i
$502$	6.74287	+	19.1121i	0.300949	+	0.853013i
$503$	8.78972	+	10.1439i	0.391914	+	0.452293i	0.917078	−	0.398708i	$-0.130541\pi$
$503$	8.78972	+	10.1439i	0.391914	+	0.452293i	−0.525164	+	0.851001i	$0.675996\pi$
$504$	−7.82975	−	3.40748i	−0.348765	−	0.151781i
$505$	41.5767			1.85014
$506$	32.3948	+	21.0100i	1.44012	+	0.934007i
$507$			0.841425i			0.0373690i
$508$	5.72480	+	1.03258i	0.253997	+	0.0458133i
$509$	18.0971	−	15.6812i	0.802139	−	0.695058i	−0.153968	−	0.988076i	$-0.549205\pi$
$509$	18.0971	−	15.6812i	0.802139	−	0.695058i	0.956107	+	0.293018i	$0.0946597\pi$
$510$	10.1421	−	3.57821i	0.449100	−	0.158446i
$511$	−3.72670	−	25.9198i	−0.164860	−	1.14662i
$512$	−20.0477	+	10.4924i	−0.885992	+	0.463701i
$513$	2.31071	−	5.05975i	0.102020	−	0.223394i
$514$	−24.7775	+	17.8681i	−1.09289	+	0.788126i
$515$	27.8427	+	4.00318i	1.22690	+	0.176401i
$516$	0.141113	−	3.95649i	0.00621217	−	0.174175i
$517$	−11.6310	+	39.6116i	−0.511531	+	1.74212i
$518$	−16.0389	+	28.1674i	−0.704707	+	1.23760i
$519$	−1.34277	−	2.94026i	−0.0589411	−	0.129063i
$520$	30.4819	−	27.3845i	1.33672	−	1.20089i
$521$	−12.8737	+	14.8571i	−0.564008	+	0.650900i	−0.964089	−	0.265580i	$-0.914436\pi$
$521$	−12.8737	+	14.8571i	−0.564008	+	0.650900i	0.400081	+	0.916480i	$0.368982\pi$
$522$	−3.54290	−	2.75207i	−0.155068	−	0.120455i
$523$	13.0659	−	20.3309i	0.571331	−	0.889009i	−0.428564	−	0.903512i	$-0.640980\pi$
$523$	13.0659	−	20.3309i	0.571331	−	0.889009i	0.999895	+	0.0145030i	$0.00461661\pi$
$524$	−15.9412	−	5.30489i	−0.696397	−	0.231745i
$525$	−16.5887	−	25.8125i	−0.723989	−	1.12655i
$526$	10.0447	+	19.2014i	0.437968	+	0.837220i
$527$	11.4317	−	3.35664i	0.497971	−	0.146218i
$528$	−13.6484	−	18.2284i	−0.593970	−	0.793290i
$529$	−17.7872	−	14.5813i	−0.773359	−	0.633969i
$530$	−0.632398	−	0.149423i	−0.0274696	−	0.00649054i
$531$	2.80151	+	9.54105i	0.121575	+	0.414046i
$532$	32.5424	−	8.30765i	1.41089	−	0.360182i
$533$	−7.38172	−	11.4862i	−0.319738	−	0.497522i
$534$	14.0384	+	1.25592i	0.607500	+	0.0543488i
$535$	−12.7877	−	8.21818i	−0.552862	−	0.355303i
$536$	−4.90470	−	10.2496i	−0.211851	−	0.442715i
$537$	4.28956	−	4.95042i	0.185108	−	0.213626i
$538$	−0.142397	−	0.0560226i	−0.00613919	−	0.00241531i
$539$	10.9498	−	5.00063i	0.471643	−	0.215392i
$540$	5.70027	+	5.30663i	0.245301	+	0.228361i
$541$	−5.95085	+	20.2667i	−0.255847	+	0.871334i	0.726957	+	0.686683i	$0.240934\pi$
$541$	−5.95085	+	20.2667i	−0.255847	+	0.871334i	−0.982804	+	0.184652i	$0.940884\pi$
$542$	0.524105	+	2.63452i	0.0225122	+	0.113162i
$543$	−0.858379	+	5.97016i	−0.0368366	+	0.256204i
$544$	−10.5432	−	3.29987i	−0.452035	−	0.141481i
$545$	19.6884	−	43.1117i	0.843360	−	1.84670i
$546$	−11.0300	−	11.4304i	−0.472040	−	0.489176i
$547$	−4.35546	+	0.626220i	−0.186226	+	0.0267752i	−0.234797	−	0.972044i	$-0.575442\pi$
$547$	−4.35546	+	0.626220i	−0.186226	+	0.0267752i	0.0485708	+	0.998820i	$0.484533\pi$
$548$	36.3036	−	3.90483i	1.55081	−	0.166806i
$549$	5.86982	−	5.08623i	0.250518	−	0.217075i
$550$	−4.38164	−	81.7081i	−0.186834	−	3.48405i
$551$	17.6452			0.751712
$552$	6.87358	+	11.6942i	0.292559	+	0.497738i
$553$	50.1188			2.13127
$554$	0.637322	+	11.8847i	0.0270772	+	0.504931i
$555$	22.3420	−	19.3595i	0.948367	−	0.821765i
$556$	1.02800	+	9.55739i	0.0435968	+	0.405324i
$557$	31.4295	−	4.51888i	1.33171	−	0.191471i	0.560554	−	0.828118i	$-0.310588\pi$
$557$	31.4295	−	4.51888i	1.33171	−	0.191471i	0.771155	+	0.636647i	$0.219679\pi$
$558$	5.99096	+	6.20845i	0.253618	+	0.262825i
$559$	3.05935	−	6.69904i	0.129397	−	0.283339i
$560$	−3.35012	+	46.9050i	−0.141568	+	1.98210i
$561$	1.58226	−	11.0048i	0.0668029	−	0.464625i
$562$	−3.63297	−	18.2619i	−0.153248	−	0.770330i
$563$	7.57781	−	25.8076i	0.319366	−	1.08766i	−0.630807	−	0.775940i	$-0.717276\pi$
$563$	7.57781	−	25.8076i	0.319366	−	1.08766i	0.950173	−	0.311722i	$-0.100906\pi$
$564$	−9.88244	+	10.6155i	−0.416126	+	0.446994i
$565$	−21.1149	+	9.64287i	−0.888312	+	0.405679i
$566$	8.71298	+	3.42790i	0.366234	+	0.144085i
$567$	1.97704	−	2.28162i	0.0830278	−	0.0958192i
$568$	−30.9542	+	14.8124i	−1.29881	+	0.621515i
$569$	−30.6195	−	19.6780i	−1.28364	−	0.824943i	−0.292305	−	0.956325i	$-0.594422\pi$
$569$	−30.6195	−	19.6780i	−1.28364	−	0.824943i	−0.991332	+	0.131382i	$0.958058\pi$
$570$	−30.5102	−	2.72953i	−1.27793	−	0.114328i
$571$	−10.7851	−	16.7819i	−0.451342	−	0.702302i	0.538790	−	0.842440i	$-0.318882\pi$
$571$	−10.7851	−	16.7819i	−0.451342	−	0.702302i	−0.990132	+	0.140138i	$0.955245\pi$
$572$	−10.4779	−	41.0438i	−0.438105	−	1.71613i
$573$	2.19217	+	7.46584i	0.0915791	+	0.311890i
$574$	15.2491	+	3.60306i	0.636483	+	0.150389i
$575$	−2.81268	+	48.6605i	−0.117297	+	2.02928i
$576$	−1.42158	−	7.87268i	−0.0592323	−	0.328028i
$577$	−42.2701	+	12.4116i	−1.75973	+	0.516703i	−0.992238	−	0.124356i	$-0.960314\pi$
$577$	−42.2701	+	12.4116i	−1.75973	+	0.516703i	−0.767492	+	0.641059i	$0.778495\pi$
$578$	8.64380	+	16.5235i	0.359535	+	0.687287i
$579$	11.1825	+	17.4004i	0.464730	+	0.723135i
$580$	−7.80080	+	23.4415i	−0.323911	+	0.973354i
$581$	−22.2081	+	34.5565i	−0.921347	+	1.43364i
$582$	10.7246	+	8.33068i	0.444548	+	0.345318i
$583$	−0.439907	+	0.507679i	−0.0182191	+	0.0210259i
$584$	18.2500	−	16.3955i	0.755190	−	0.678451i
$585$	6.01825	+	13.1781i	0.248824	+	0.544849i
$586$	7.07940	−	12.4328i	0.292447	−	0.513595i
$587$	−1.70045	+	5.79121i	−0.0701852	+	0.239029i	−0.987113	−	0.160024i	$-0.948843\pi$
$587$	−1.70045	+	5.79121i	−0.0701852	+	0.239029i	0.916928	+	0.399053i	$0.130661\pi$
$588$	4.22629	+	0.150736i	0.174289	+	0.00621625i
$589$	−33.5891	−	4.82938i	−1.38401	−	0.198991i
$590$	44.4160	−	32.0301i	1.82858	−	1.31866i
$591$	−4.56954	+	10.0059i	−0.187966	+	0.411587i
$592$	−30.2898	+	2.16934i	−1.24490	+	0.0891592i
$593$	5.40278	+	37.5771i	0.221865	+	1.54311i	0.730974	+	0.682406i	$0.239066\pi$
$593$	5.40278	+	37.5771i	0.221865	+	1.54311i	−0.509108	+	0.860702i	$0.670025\pi$
$594$	7.59237	−	2.67864i	0.311519	−	0.109906i
$595$	−17.3513	+	15.0350i	−0.711333	+	0.616374i
$596$	3.11336	−	17.2610i	0.127528	−	0.707039i
$597$			16.9611i			0.694171i
$598$	3.48701	+	24.9909i	0.142595	+	1.02195i
$599$	−31.8417			−1.30102			−0.650508	−	0.759499i	$-0.725444\pi$
$599$	−31.8417			−1.30102			−0.650508	+	0.759499i	$0.725444\pi$
$600$	11.4711	−	26.3584i	0.468305	−	1.07608i
$601$	23.8772	+	27.5558i	0.973971	+	1.12402i	0.992258	+	0.124190i	$0.0396333\pi$
$601$	23.8772	+	27.5558i	0.973971	+	1.12402i	−0.0182870	+	0.999833i	$0.505821\pi$
$602$	2.81190	+	7.97008i	0.114605	+	0.324836i
$603$	3.97642	−	0.571723i	0.161932	−	0.0232824i
$604$	14.8932	+	25.0983i	0.605994	+	1.02124i
$605$	−75.8354	−	34.6329i	−3.08315	−	1.40803i
$606$	12.2473	−	8.83199i	0.497511	−	0.358775i
$607$	−0.226882	+	1.57800i	−0.00920885	+	0.0640490i	−0.993908	−	0.110216i	$-0.964846\pi$
$607$	−0.226882	+	1.57800i	−0.00920885	+	0.0640490i	0.984699	+	0.174265i	$0.0557549\pi$
$608$	23.4112	+	21.0240i	0.949451	+	0.852637i
$609$	9.18907	+	2.69815i	0.372360	+	0.109335i
$610$	−37.1688	−	21.1643i	−1.50492	−	0.856919i
$611$	−24.5414	+	11.2077i	−0.992839	+	0.453415i
$612$	2.22746	−	3.20849i	0.0900398	−	0.129695i
$613$	−15.2902	−	13.2490i	−0.617565	−	0.535123i	0.288924	−	0.957352i	$-0.406702\pi$
$613$	−15.2902	−	13.2490i	−0.617565	−	0.535123i	−0.906489	+	0.422229i	$0.861248\pi$
$614$	23.9484	+	18.6027i	0.966478	+	0.750746i
$615$	−12.0222	−	7.72618i	−0.484781	−	0.311550i
$616$	41.3599	+	25.5448i	1.66644	+	1.02923i
$617$	−37.4792	+	24.0864i	−1.50886	+	0.969684i	−0.515220	+	0.857058i	$0.672290\pi$
$617$	−37.4792	+	24.0864i	−1.50886	+	0.969684i	−0.993637	+	0.112626i	$0.964074\pi$
$618$	9.05203	−	4.73531i	0.364126	−	0.190482i
$619$	−1.56632	−	5.33440i	−0.0629557	−	0.214407i	0.922007	−	0.387172i	$-0.126548\pi$
$619$	−1.56632	−	5.33440i	−0.0629557	−	0.214407i	−0.984963	+	0.172765i	$0.944730\pi$
$620$	21.2652	−	42.4877i	0.854032	−	1.70635i
$621$	−4.67187	+	1.08335i	−0.187476	+	0.0434735i
$622$	13.7243	+	3.24279i	0.550295	+	0.130024i
$623$	−28.8696	+	8.47688i	−1.15664	+	0.339619i
$624$	3.16190	−	14.5418i	0.126577	−	0.582140i
$625$	23.1151	−	14.8552i	0.924603	−	0.594206i
$626$	2.38523	−	26.6616i	0.0953328	−	1.06561i
$627$	−17.1202	+	26.6396i	−0.683716	+	1.06388i
$628$	0.147676	+	0.183236i	0.00589291	+	0.00731192i
$629$	−11.2051	−	9.70926i	−0.446776	−	0.387134i
$630$	−15.4714	−	6.08681i	−0.616394	−	0.242504i
$631$	13.6194	+	29.8223i	0.542180	+	1.18721i	0.960339	+	0.278834i	$0.0899480\pi$
$631$	13.6194	+	29.8223i	0.542180	+	1.18721i	−0.418160	+	0.908374i	$0.637325\pi$
$632$	26.0895	+	39.0396i	1.03779	+	1.55291i
$633$	−15.6704	−	4.60124i	−0.622842	−	0.182883i
$634$	38.3897	−	7.63715i	1.52465	−	0.303310i
$635$	11.2108	+	1.61187i	0.444887	+	0.0639651i
$636$	−0.218028	+	0.0903224i	−0.00864535	+	0.00358152i
$637$	7.15585	+	3.26797i	0.283525	+	0.129482i
$638$	17.7345	+	18.3783i	0.702116	+	0.727604i
$639$	−1.72663	−	12.0089i	−0.0683042	−	0.475066i
$640$	−38.2801	+	21.8070i	−1.51315	+	0.861997i
$641$	10.5813	+	12.2115i	0.417938	+	0.482326i	0.925208	−	0.379461i	$-0.123891\pi$
$641$	10.5813	+	12.2115i	0.417938	+	0.482326i	−0.507270	+	0.861787i	$0.669345\pi$
$642$	−5.51265	+	0.295619i	−0.217567	+	0.0116672i
$643$			40.5526i			1.59924i	0.600506	+	0.799620i	$0.294966\pi$
$643$			40.5526i			1.59924i	−0.600506	+	0.799620i	$0.705034\pi$
$644$	−22.7945	−	17.8591i	−0.898227	−	0.703745i
$645$		−	7.70821i		−	0.303511i
$646$	0.822653	+	15.3407i	0.0323669	+	0.603572i
$647$	20.5909	+	23.7632i	0.809513	+	0.934228i	0.998863	−	0.0476815i	$-0.0151833\pi$
$647$	20.5909	+	23.7632i	0.809513	+	0.934228i	−0.189349	+	0.981910i	$0.560638\pi$
$648$	2.80640	+	0.352287i	0.110246	+	0.0138391i
$649$	−8.05641	−	56.0336i	−0.316242	−	2.19951i
$650$	38.4798	−	37.1318i	1.50930	−	1.45643i
$651$	−16.7537	−	7.65114i	−0.656628	−	0.299872i
$652$	2.28010	+	5.50389i	0.0892956	+	0.215549i
$653$	32.8372	+	4.72127i	1.28502	+	0.184758i	0.750766	−	0.660568i	$-0.229685\pi$
$653$	32.8372	+	4.72127i	1.28502	+	0.184758i	0.534251	+	0.845326i	$0.320594\pi$
$654$	−3.35842	−	16.8818i	−0.131325	−	0.660130i
$655$	−31.3862	−	9.21581i	−1.22636	−	0.360091i
$656$	5.13139	+	13.7537i	0.200347	+	0.536991i
$657$	3.60322	+	7.88994i	0.140575	+	0.307816i
$658$	11.3354	−	28.8121i	0.441899	−	1.12321i
$659$	23.6595	+	20.5011i	0.921644	+	0.798609i	0.979858	−	0.199695i	$-0.0639952\pi$
$659$	23.6595	+	20.5011i	0.921644	+	0.798609i	−0.0582142	+	0.998304i	$0.518541\pi$
$660$	−27.8217	−	34.5211i	−1.08296	−	1.34373i
$661$	−19.5073	+	30.3540i	−0.758746	+	1.18063i	0.219988	+	0.975502i	$0.429398\pi$
$661$	−19.5073	+	30.3540i	−0.758746	+	1.18063i	−0.978735	+	0.205130i	$0.934238\pi$
$662$	−32.2921	−	2.88895i	−1.25507	−	0.112282i
$663$	6.11234	−	3.92816i	0.237383	−	0.152557i
$664$	−38.4779	+	0.689715i	−1.49323	+	0.0267661i
$665$	62.7436	−	18.4232i	2.43309	−	0.714420i
$666$	2.46884	−	10.4488i	0.0956657	−	0.404882i
$667$	−9.28261	−	12.0533i	−0.359424	−	0.466705i
$668$	−6.04109	−	3.02359i	−0.233737	−	0.116986i
$669$	2.57145	+	8.75755i	0.0994179	+	0.338586i
$670$	−10.2547	−	19.6030i	−0.396175	−	0.757329i
$671$	−37.1973	+	23.9052i	−1.43598	+	0.922851i
$672$	8.97701	+	14.5285i	0.346296	+	0.560448i
$673$	6.36366	+	4.08968i	0.245301	+	0.157645i	0.657514	−	0.753442i	$-0.271608\pi$
$673$	6.36366	+	4.08968i	0.245301	+	0.157645i	−0.412213	+	0.911087i	$0.635244\pi$
$674$	−7.22186	+	9.29711i	−0.278176	+	0.358111i
$675$	7.68095	+	6.65558i	0.295640	+	0.256173i
$676$	0.959700	−	1.38238i	0.0369116	−	0.0531683i
$677$	−21.8389	+	9.97350i	−0.839338	+	0.383313i	−0.788230	−	0.615380i	$-0.789002\pi$
$677$	−21.8389	+	9.97350i	−0.839338	+	0.383313i	−0.0511077	+	0.998693i	$0.516275\pi$
$678$	−4.17144	+	7.32588i	−0.160203	+	0.281349i
$679$	−27.8159	−	8.16748i	−1.06748	−	0.313439i
$680$	−20.7436	−	5.68910i	−0.795481	−	0.218167i
$681$	1.08224	−	7.52712i	0.0414714	−	0.288440i
$682$	−28.7290	−	39.8384i	−1.10009	−	1.52549i
$683$	−9.29565	−	4.24518i	−0.355688	−	0.162437i	0.229554	−	0.973296i	$-0.426273\pi$
$683$	−9.29565	−	4.24518i	−0.355688	−	0.162437i	−0.585242	+	0.810859i	$0.699001\pi$
$684$	−9.56724	+	5.67714i	−0.365813	+	0.217071i
$685$	70.3675	−	10.1173i	2.68860	−	0.386563i
$686$	19.6706	−	6.93992i	0.751025	−	0.264967i
$687$	13.7428	+	15.8601i	0.524322	+	0.605100i
$688$	−4.74447	+	6.33916i	−0.180881	+	0.241678i
$689$	−0.439001			−0.0167246
$690$	14.1860	+	22.2772i	0.540050	+	0.848078i
$691$		−	6.79301i		−	0.258418i	−0.991617	−	0.129209i	$-0.958756\pi$
$691$		−	6.79301i		−	0.258418i	0.991617	−	0.129209i	$-0.0412439\pi$
$692$	−1.14752	+	6.36206i	−0.0436222	+	0.241849i
$693$	−12.9892	+	11.2552i	−0.493417	+	0.427549i
$694$	−10.8727	−	30.8178i	−0.412724	−	1.16983i
$695$	2.66351	+	18.5251i	0.101033	+	0.702699i
$696$	2.68170	+	8.56227i	0.101650	+	0.324552i
$697$	−2.97736	+	6.51950i	−0.112775	+	0.246944i
$698$	−3.16146	−	4.38398i	−0.119663	−	0.165936i
$699$	2.63599	+	0.378998i	0.0997024	+	0.0143350i
$700$	−2.18733	+	61.3277i	−0.0826735	+	2.31797i
$701$	9.39986	−	32.0130i	0.355028	−	1.20911i	−0.567562	−	0.823331i	$-0.692113\pi$
$701$	9.39986	−	32.0130i	0.355028	−	1.20911i	0.922590	−	0.385783i	$-0.126069\pi$
$702$	4.57218	+	2.60346i	0.172566	+	0.0982611i
$703$	17.5426	+	38.4129i	0.661631	+	1.44877i
$704$	1.63221	+	45.5143i	0.0615162	+	1.71538i
$705$	−18.4923	+	21.3412i	−0.696459	+	0.803756i
$706$	16.6937	−	21.4907i	0.628275	−	0.808814i
$707$	−17.4272	+	27.1172i	−0.655417	+	1.01985i
$708$	6.27961	−	18.8703i	0.236002	−	0.709188i
$709$	1.77776	+	2.76625i	0.0667652	+	0.103889i	0.873031	−	0.487665i	$-0.162151\pi$
$709$	1.77776	+	2.76625i	0.0667652	+	0.103889i	−0.806266	+	0.591554i	$0.798515\pi$
$710$	−59.2017	+	30.9697i	−2.22180	+	1.16227i
$711$	−15.9286	+	4.67705i	−0.597368	+	0.175403i
$712$	−21.6312	−	18.0750i	−0.810662	−	0.677390i
$713$	14.3713	+	25.4850i	0.538209	+	0.954421i
$714$	−1.91735	+	8.11474i	−0.0717552	+	0.303686i
$715$	−23.2360	−	79.1347i	−0.868978	−	2.95947i
$716$	−12.6936	+	3.24050i	−0.474382	+	0.121103i
$717$	−6.18273	−	9.62052i	−0.230898	−	0.359285i
$718$	−1.47385	+	16.4745i	−0.0550037	+	0.614821i
$719$	25.7893	+	16.5738i	0.961778	+	0.618097i	0.924490	−	0.381207i	$-0.124492\pi$
$719$	25.7893	+	16.5738i	0.961778	+	0.618097i	0.0372885	+	0.999305i	$0.488128\pi$
$720$	−3.31241	−	15.2198i	−0.123446	−	0.567207i
$721$	−14.2814	+	16.4817i	−0.531869	+	0.613809i
$722$	6.18227	−	15.7140i	0.230080	−	0.584815i
$723$	−9.24479	+	4.22196i	−0.343818	+	0.157016i
$724$	8.21958	−	8.82932i	0.305478	−	0.328139i
$725$	−9.08317	+	30.9344i	−0.337340	+	1.14888i
$726$	−29.6958	+	5.90762i	−1.10212	+	0.219252i
$727$	5.15522	−	35.8553i	0.191196	−	1.32980i	−0.637651	−	0.770326i	$-0.720094\pi$
$727$	5.15522	−	35.8553i	0.191196	−	1.32980i	0.828847	−	0.559475i	$-0.188997\pi$
$728$	5.08402	+	31.3594i	0.188426	+	1.16226i
$729$	−0.415415	+	0.909632i	−0.0153857	+	0.0336901i
$730$	34.3725	−	33.1684i	1.27218	−	1.22762i
$731$	−3.82651	+	0.550169i	−0.141529	+	0.0203487i
$732$	−15.4447	+	1.66124i	−0.570852	+	0.0614011i
$733$	19.5151	−	16.9099i	0.720806	−	0.624582i	−0.215198	−	0.976570i	$-0.569040\pi$
$733$	19.5151	−	16.9099i	0.720806	−	0.624582i	0.936004	+	0.351988i	$0.114494\pi$
$734$	27.2684	−	1.46229i	1.00650	−	0.0539739i
$735$	8.23385			0.303710
$736$	2.04540	−	27.0521i	0.0753944	−	0.997154i
$737$	−22.8703			−0.842439
$738$	−5.18263	+	0.277921i	−0.190775	+	0.0102304i
$739$	4.71447	−	4.08511i	0.173425	−	0.150273i	−0.563824	−	0.825895i	$-0.690670\pi$
$739$	4.71447	−	4.08511i	0.173425	−	0.150273i	0.737248	+	0.675622i	$0.236125\pi$
$740$	−58.7864	+	6.32309i	−2.16103	+	0.232442i
$741$	−20.4838	+	2.94513i	−0.752492	+	0.108192i
$742$	0.362532	−	0.349832i	0.0133090	−	0.0128427i
$743$	−0.888458	+	1.94545i	−0.0325944	+	0.0713717i	−0.925229	−	0.379409i	$-0.876127\pi$
$743$	−0.888458	+	1.94545i	−0.0325944	+	0.0713717i	0.892635	+	0.450781i	$0.148854\pi$
$744$	−2.76140	−	17.0329i	−0.101238	−	0.624457i
$745$	4.86000	−	33.8020i	0.178057	−	1.23841i
$746$	−28.6483	+	5.69922i	−1.04889	+	0.208663i
$747$	3.83331	−	13.0550i	0.140253	−	0.477659i
$748$	−15.1512	+	16.2752i	−0.553984	+	0.595078i
$749$	10.7202	−	4.89573i	0.391706	−	0.178886i
$750$	10.4101	−	26.4603i	0.380123	−	0.966192i
$751$	−16.2840	+	18.7927i	−0.594211	+	0.685757i	−0.970598	−	0.240706i	$-0.922621\pi$
$751$	−16.2840	+	18.7927i	−0.594211	+	0.685757i	0.376387	+	0.926463i	$0.377166\pi$
$752$	28.3435	−	6.16865i	1.03358	−	0.224948i
$753$	12.0557	+	7.74775i	0.439336	+	0.282344i
$754$	−1.48724	+	16.6241i	−0.0541621	+	0.605414i
$755$	30.7205	+	47.8020i	1.11803	+	1.73969i
$756$	−5.85041	+	1.49353i	−0.212777	+	0.0543192i
$757$	4.83247	+	16.4579i	0.175639	+	0.598172i	0.999507	+	0.0313905i	$0.00999355\pi$
$757$	4.83247	+	16.4579i	0.175639	+	0.598172i	−0.823868	+	0.566782i	$0.808188\pi$
$758$	5.33712	−	22.5881i	0.193853	−	0.820435i
$759$	27.2037	−	2.31959i	0.987431	−	0.0841959i
$760$	47.0119	+	39.2832i	1.70530	+	1.42495i
$761$	−42.2218	+	12.3974i	−1.53054	+	0.449406i	−0.935215	−	0.354080i	$-0.884794\pi$
$761$	−42.2218	+	12.3974i	−1.53054	+	0.449406i	−0.595323	+	0.803487i	$0.702976\pi$
$762$	3.64478	−	1.90666i	0.132036	−	0.0690711i
$763$	19.8658	+	30.9118i	0.719191	+	1.11908i
$764$	4.91377	−	14.7659i	0.177774	−	0.534212i
$765$	4.11146	−	6.39756i	0.148650	−	0.231304i
$766$	−28.1754	+	36.2718i	−1.01802	+	1.31055i
$767$	24.2267	−	27.9591i	0.874774	−	1.00954i
$768$	−6.64380	+	14.5554i	−0.239738	+	0.525223i
$769$	−20.9024	−	45.7698i	−0.753758	−	1.65050i	−0.759492	−	0.650516i	$-0.774553\pi$
$769$	−20.9024	−	45.7698i	−0.753758	−	1.65050i	0.00573425	−	0.999984i	$-0.498175\pi$
$770$	82.2496	+	46.8339i	2.96407	+	1.68778i
$771$	−6.08567	+	20.7259i	−0.219170	+	0.746424i
$772$	1.47450	−	41.3414i	0.0530683	−	1.48791i
$773$	−8.32916	−	1.19755i	−0.299579	−	0.0430729i	−0.00911360	−	0.999958i	$-0.502901\pi$
$773$	−8.32916	−	1.19755i	−0.299579	−	0.0430729i	−0.290465	+	0.956886i	$0.593810\pi$
$774$	−1.63743	−	2.27061i	−0.0588562	−	0.0816155i
$775$	25.7571	−	56.4002i	0.925222	−	2.02595i
$776$	−8.11768	−	25.9185i	−0.291408	−	0.930421i
$777$	3.26185	+	22.6866i	0.117018	+	0.813879i
$778$	−2.21781	−	6.28617i	−0.0795122	−	0.225370i
$779$	15.4277	−	13.3681i	0.552753	−	0.478964i
$780$	5.14315	−	28.5145i	0.184154	−	1.02098i
$781$			69.0693i			2.47149i
$782$	10.0463	−	8.63221i	0.359256	−	0.308687i
$783$	−3.17222			−0.113366
$784$	−6.77143	−	5.06800i	−0.241837	−	0.181000i
$785$	0.300060	+	0.346287i	0.0107096	+	0.0123595i
$786$	−11.2031	+	3.95255i	−0.399602	+	0.140983i
$787$	52.6154	−	7.56496i	1.87554	−	0.269662i	0.892226	−	0.451589i	$-0.149143\pi$
$787$	52.6154	−	7.56496i	1.87554	−	0.269662i	0.983312	+	0.181928i	$0.0582336\pi$
$788$	18.9197	−	11.2268i	0.673985	−	0.399938i
$789$	13.9383	+	6.36540i	0.496216	+	0.226614i
$790$	53.4735	+	74.1515i	1.90250	+	2.63819i
$791$	2.56120	−	17.8135i	0.0910657	−	0.633376i
$792$	−15.5287	−	4.25886i	−0.551787	−	0.151332i
$793$	−27.7255	−	8.14094i	−0.984561	−	0.289093i
$794$	−10.5169	+	18.4697i	−0.373230	+	0.655466i
$795$	−0.417963	+	0.190877i	−0.0148236	+	0.00676972i
$796$	19.3452	−	27.8653i	0.685673	−	0.987660i
$797$	−33.9996	−	29.4609i	−1.20433	−	1.04356i	−0.997879	−	0.0651003i	$-0.979263\pi$
$797$	−33.9996	−	29.4609i	−1.20433	−	1.04356i	−0.206451	−	0.978457i	$-0.566191\pi$
$798$	14.5688	−	18.7553i	0.515732	−	0.663931i
$799$	11.9141	+	7.65671i	0.421490	+	0.270875i
$800$	−48.9093	+	30.2206i	−1.72920	+	1.06846i
$801$	8.38417	−	5.38818i	0.296240	−	0.190382i
$802$	−7.28493	−	13.9259i	−0.257240	−	0.491740i
$803$	−13.9118	−	47.3791i	−0.490935	−	1.67197i
$804$	−7.18494	−	3.59608i	−0.253393	−	0.126824i
$805$	−45.5922	−	33.1677i	−1.60691	−	1.16901i
$806$	7.38099	−	31.2382i	0.259984	−	1.10032i
$807$	−0.103820	+	0.0304842i	−0.00365462	+	0.00107309i
$808$	−30.1945	+	0.541235i	−1.06224	+	0.0190406i
$809$	−6.18254	+	3.97328i	−0.217367	+	0.139693i	−0.644793	−	0.764357i	$-0.723057\pi$
$809$	−6.18254	+	3.97328i	−0.217367	+	0.139693i	0.427427	+	0.904050i	$0.359420\pi$
$810$	5.48506	+	0.490710i	0.192725	+	0.0172418i
$811$	−5.27062	+	8.20125i	−0.185077	+	0.287985i	−0.921377	−	0.388670i	$-0.872935\pi$
$811$	−5.27062	+	8.20125i	−0.185077	+	0.287985i	0.736300	+	0.676655i	$0.236571\pi$
$812$	−12.0193	−	14.9135i	−0.421794	−	0.523362i
$813$	1.43546	+	1.24384i	0.0503439	+	0.0436232i
$814$	−22.3774	+	56.8786i	−0.784329	+	1.99360i
$815$	4.81851	+	10.5511i	0.168785	+	0.369588i
$816$	−7.31898	+	2.73065i	−0.256215	+	0.0955919i
$817$	10.5648	+	3.10211i	0.369616	+	0.108529i
$818$	−3.51309	−	17.6592i	−0.122832	−	0.617440i
$819$	−11.1177	−	1.59848i	−0.388482	−	0.0558553i
$820$	10.9390	+	26.4054i	0.382006	+	0.922117i
$821$	40.0929	+	18.3098i	1.39925	+	0.639017i	0.965114	−	0.261830i	$-0.0843259\pi$
$821$	40.0929	+	18.3098i	1.39925	+	0.639017i	0.434138	+	0.900847i	$0.357053\pi$
$822$	18.5790	−	17.9282i	0.648018	−	0.625317i
$823$	−2.66065	−	18.5052i	−0.0927443	−	0.645051i	−0.982173	−	0.187978i	$-0.939807\pi$
$823$	−2.66065	−	18.5052i	−0.0927443	−	0.645051i	0.889429	−	0.457073i	$-0.151102\pi$
$824$	−20.2725	−	2.54480i	−0.706225	−	0.0886523i
$825$	−37.8898	−	43.7272i	−1.31915	−	1.52239i
$826$	2.27344	+	42.3947i	0.0791031	+	1.47510i
$827$			34.3308i			1.19380i	0.802316	+	0.596900i	$0.203601\pi$
$827$			34.3308i			1.19380i	−0.802316	+	0.596900i	$0.796399\pi$
$828$	8.91103	+	3.54873i	0.309680	+	0.123327i
$829$			37.2469i			1.29364i	0.762643	+	0.646820i	$0.223901\pi$
$829$			37.2469i			1.29364i	−0.762643	+	0.646820i	$0.776099\pi$
$830$	−74.8213	+	4.01234i	−2.59709	+	0.139270i
$831$	5.51118	+	6.36024i	0.191181	+	0.220634i
$832$	−21.7806	+	20.2844i	−0.755106	+	0.703235i
$833$	−0.587686	−	4.08745i	−0.0203621	−	0.141622i
$834$	4.71983	+	4.89117i	0.163434	+	0.169367i
$835$	−11.9644	−	5.46396i	−0.414046	−	0.189088i
$836$	58.5109	−	24.2394i	2.02364	−	0.838336i
$837$	6.03858	+	0.868217i	0.208724	+	0.0300100i
$838$	5.40957	−	1.07617i	0.186871	−	0.0371756i
$839$	−36.0964	−	10.5989i	−1.24619	−	0.365913i	−0.408850	−	0.912602i	$-0.634070\pi$
$839$	−36.0964	−	10.5989i	−1.24619	−	0.365913i	−0.837336	+	0.546688i	$0.815888\pi$
$840$	18.4755	+	27.6461i	0.637464	+	0.953881i
$841$	7.86672	+	17.2257i	0.271266	+	0.593990i
$842$	28.1325	+	11.0680i	0.969509	+	0.381428i
$843$	−9.95030	−	8.62198i	−0.342706	−	0.296957i
$844$	20.4968	+	25.4325i	0.705530	+	0.875422i
$845$	1.77142	−	2.75639i	0.0609388	−	0.0948226i
$846$	−0.913841	+	10.2147i	−0.0314185	+	0.351190i
$847$	54.3753	−	34.9449i	1.86836	−	1.20072i
$848$	0.461215	+	0.100284i	0.0158382	+	0.00344377i
$849$	6.35248	−	1.86526i	0.218017	−	0.0640155i
$850$	−27.3178	−	6.45465i	−0.936992	−	0.221393i
$851$	17.0109	−	32.1910i	0.583126	−	1.10349i
$852$	−10.8603	+	21.6988i	−0.372068	+	0.743388i
$853$	−3.19366	−	10.8766i	−0.109349	−	0.372408i	0.886577	−	0.462580i	$-0.153076\pi$
$853$	−3.19366	−	10.8766i	−0.109349	−	0.372408i	−0.995926	+	0.0901726i	$0.971258\pi$
$854$	29.3834	−	15.3711i	1.00548	−	0.525988i
$855$	−18.2217	+	11.7104i	−0.623168	+	0.400486i
$856$	9.39389	+	5.80187i	0.321077	+	0.198304i
$857$	−8.27635	−	5.31889i	−0.282715	−	0.181690i	0.391596	−	0.920137i	$-0.371923\pi$
$857$	−8.27635	−	5.31889i	−0.282715	−	0.181690i	−0.674311	+	0.738447i	$0.735559\pi$
$858$	−23.6550	−	18.3748i	−0.807567	−	0.627306i
$859$	−26.5365	−	22.9940i	−0.905414	−	0.784546i	0.0716634	−	0.997429i	$-0.477169\pi$
$859$	−26.5365	−	22.9940i	−0.905414	−	0.784546i	−0.977078	+	0.212883i	$0.931715\pi$
$860$	−8.79172	+	12.6638i	−0.299795	+	0.431832i
$861$	10.0784	−	4.60264i	0.343470	−	0.156858i
$862$	11.7884	+	6.71243i	0.401513	+	0.228626i
$863$	45.5479	+	13.3741i	1.55047	+	0.455258i	0.941240	−	0.337737i	$-0.109662\pi$
$863$	45.5479	+	13.3741i	1.55047	+	0.455258i	0.609227	+	0.792996i	$0.291480\pi$
$864$	−4.20882	−	3.77966i	−0.143187	−	0.128587i
$865$	−1.79130	+	12.4587i	−0.0609059	+	0.423610i
$866$	−18.3878	+	13.2602i	−0.624843	+	0.450599i
$867$	11.9944	+	5.47767i	0.407352	+	0.186031i
$868$	18.7979	+	31.6787i	0.638043	+	1.07524i
$869$	93.5467	−	13.4500i	3.17336	−	0.456260i
$870$	5.81218	+	16.4741i	0.197051	+	0.558524i
$871$	−9.78757	−	11.2955i	−0.331639	−	0.382732i
$872$	−13.7372	+	31.5655i	−0.465201	+	1.06894i
$873$	9.60252			0.324996
$874$	−36.2419	+	10.4779i	−1.22590	+	0.354420i
$875$			60.7009i			2.05207i
$876$	3.07928	−	17.0721i	0.104039	−	0.576812i
$877$	11.5984	−	10.0501i	0.391649	−	0.339366i	−0.436671	−	0.899621i	$-0.643842\pi$
$877$	11.5984	−	10.0501i	0.391649	−	0.339366i	0.828320	+	0.560255i	$0.189297\pi$
$878$	−36.5610	+	12.8990i	−1.23388	+	0.435320i
$879$	−1.43975	−	10.0137i	−0.0485615	−	0.337753i
$880$	6.33452	+	88.4471i	0.213537	+	2.98155i
$881$	4.60859	−	10.0914i	0.155267	−	0.339988i	−0.815973	−	0.578091i	$-0.803798\pi$
$881$	4.60859	−	10.0914i	0.155267	−	0.339988i	0.971240	+	0.238102i	$0.0765253\pi$
$882$	2.42545	−	1.74909i	0.0816692	−	0.0588948i
$883$	−25.5823	−	3.67818i	−0.860913	−	0.123781i	−0.302304	−	0.953212i	$-0.597756\pi$
$883$	−25.5823	−	3.67818i	−0.860913	−	0.123781i	−0.558609	+	0.829431i	$0.688665\pi$
$884$	−14.5223	−	0.517955i	−0.488437	−	0.0174207i
$885$	10.9091	−	37.1530i	0.366705	−	1.24888i
$886$	−19.6048	+	34.4300i	−0.658637	+	1.15670i
$887$	−0.979877	−	2.14563i	−0.0329010	−	0.0720432i	0.892468	−	0.451111i	$-0.148972\pi$
$887$	−0.979877	−	2.14563i	−0.0329010	−	0.0720432i	−0.925369	+	0.379068i	$0.876245\pi$
$888$	−15.9736	+	14.3504i	−0.536038	+	0.481568i
$889$	−5.75039	+	6.63630i	−0.192862	+	0.222574i
$890$	−43.3436	−	33.6687i	−1.45288	−	1.12858i
$891$	3.07784	−	4.78921i	0.103111	−	0.160445i
$892$	5.76393	−	17.3207i	0.192991	−	0.579938i
$893$	−21.8080	−	33.9339i	−0.729777	−	1.13556i
$894$	−5.74884	−	10.9895i	−0.192270	−	0.367543i
$895$	−24.4739	+	7.18619i	−0.818073	+	0.240208i
$896$	1.82238	−	34.1077i	0.0608813	−	1.13946i
$897$	12.7877	+	12.4430i	0.426969	+	0.415459i
$898$	13.1346	+	3.10344i	0.438306	+	0.103563i
$899$	5.45228	+	18.5688i	0.181844	+	0.619303i
$900$	−5.02788	−	19.6951i	−0.167596	−	0.656502i
$901$	0.124587	+	0.193861i	0.00415060	+	0.00645846i
$902$	29.4293	+	2.63283i	0.979888	+	0.0876636i
$903$	5.02747	+	3.23096i	0.167304	+	0.107519i
$904$	15.2089	−	7.27787i	0.505841	−	0.242058i
$905$	15.3807	−	17.7502i	0.511271	−	0.590038i
$906$	19.2038	+	7.55522i	0.638002	+	0.251005i
$907$	6.30944	−	2.88142i	0.209501	−	0.0956761i	−0.307901	−	0.951419i	$-0.599626\pi$
$907$	6.30944	−	2.88142i	0.209501	−	0.0956761i	0.517402	+	0.855742i	$0.326899\pi$
$908$	−10.3632	+	11.1319i	−0.343914	+	0.369426i
$909$	3.00808	−	10.2446i	0.0997717	−	0.339791i
$910$	12.0686	+	60.6654i	0.400071	+	2.01104i
$911$	5.30671	−	36.9090i	0.175819	−	1.22285i	−0.690490	−	0.723342i	$-0.742605\pi$
$911$	5.30671	−	36.9090i	0.175819	−	1.22285i	0.866309	−	0.499508i	$-0.166486\pi$
$912$	22.1931	+	1.58511i	0.734888	+	0.0524883i
$913$	−32.1777	+	70.4594i	−1.06493	+	2.33187i
$914$	8.88093	+	9.20332i	0.293755	+	0.304419i
$915$	−29.9365	+	4.30422i	−0.989671	+	0.142293i
$916$	−4.48861	−	41.7311i	−0.148308	−	1.37883i
$917$	19.1665	−	16.6079i	0.632934	−	0.548440i
$918$	−0.147895	−	2.75792i	−0.00488126	−	0.0910249i
$919$	10.1194			0.333807			0.166903	−	0.985973i	$-0.446623\pi$
$919$	10.1194			0.333807			0.166903	+	0.985973i	$0.446623\pi$
$920$	2.10250	−	52.7791i	0.0693174	−	1.74008i
$921$	21.4428			0.706564
$922$	−2.07697	−	38.7309i	−0.0684012	−	1.27553i
$923$	−34.1127	+	29.5588i	−1.12283	+	0.972941i
$924$	34.1771	−	3.67610i	1.12434	−	0.120935i
$925$	−76.3732	+	10.9808i	−2.51114	+	0.361047i
$926$	−0.667792	−	0.692034i	−0.0219450	−	0.0227417i
$927$	3.00082	−	6.57087i	0.0985597	−	0.215816i
$928$	5.36006	−	17.1256i	0.175953	−	0.562175i
$929$	0.889657	−	6.18770i	0.0291887	−	0.203012i	−0.970009	−	0.243070i	$-0.921845\pi$
$929$	0.889657	−	6.18770i	0.0291887	−	0.203012i	0.999197	+	0.0400586i	$0.0127545\pi$
$930$	−6.55510	−	32.9505i	−0.214950	−	1.08049i
$931$	−3.31364	+	11.2852i	−0.108600	+	0.369859i
$932$	−3.89839	−	3.62918i	−0.127696	−	0.118878i
$933$	9.07064	−	4.14242i	0.296959	−	0.135617i
$934$	2.44396	+	0.961511i	0.0799687	+	0.0314616i
$935$	−28.3513	+	32.7192i	−0.927188	+	1.07003i
$936$	−4.54222	−	9.49208i	−0.148467	−	0.310258i
$937$	−6.93428	−	4.45639i	−0.226533	−	0.145584i	0.422451	−	0.906386i	$-0.361170\pi$
$937$	−6.93428	−	4.45639i	−0.226533	−	0.145584i	−0.648985	+	0.760802i	$0.724806\pi$
$938$	17.0838	+	1.52837i	0.557807	+	0.0499031i
$939$	−10.2332	−	15.9232i	−0.333948	−	0.519632i
$940$	54.7219	−	13.9698i	1.78483	−	0.455644i
$941$	8.61543	+	29.3415i	0.280855	+	0.956505i	0.972234	+	0.234012i	$0.0751855\pi$
$941$	8.61543	+	29.3415i	0.280855	+	0.956505i	−0.691379	+	0.722493i	$0.742996\pi$
$942$	0.161949	+	0.0382655i	0.00527660	+	0.00124676i
$943$	−17.2477	−	3.50593i	−0.561662	−	0.114169i
$944$	−31.8395	+	23.8396i	−1.03629	+	0.775913i
$945$	−11.2799	+	3.31208i	−0.366935	+	0.107742i
$946$	7.38728	+	14.1215i	0.240181	+	0.459131i
$947$	−18.1830	−	28.2933i	−0.590868	−	0.919409i	−0.999976	−	0.00692289i	$-0.997796\pi$
$947$	−18.1830	−	28.2933i	−0.590868	−	0.919409i	0.409108	−	0.912486i	$-0.365840\pi$
$948$	31.5035	+	10.4837i	1.02319	+	0.340493i
$949$	17.4465	−	27.1472i	0.566336	−	0.881236i
$950$	63.1387	+	49.0451i	2.04849	+	1.59123i
$951$	18.1249	−	20.9173i	0.587741	−	0.678289i
$952$	12.4054	−	11.1448i	0.402061	−	0.361205i
$953$	−24.6719	−	54.0239i	−0.799200	−	1.75000i	−0.648198	−	0.761471i	$-0.724477\pi$
$953$	−24.6719	−	54.0239i	−0.799200	−	1.75000i	−0.151002	−	0.988533i	$-0.548250\pi$
$954$	−0.0825723	+	0.145013i	−0.00267338	+	0.00469498i
$955$	8.53633	−	29.0721i	0.276229	−	0.940750i
$956$	−0.815237	+	22.8573i	−0.0263666	+	0.739259i
$957$	17.8755	+	2.57010i	0.577832	+	0.0830796i
$958$	14.2403	−	10.2692i	0.460082	−	0.331783i
$959$	−22.8963	+	50.1360i	−0.739361	+	1.61897i
$960$	−11.9172	+	28.7825i	−0.384626	+	0.928953i
$961$	−0.884949	−	6.15495i	−0.0285467	−	0.198547i
$962$	−37.6685	+	13.2897i	−1.21448	+	0.428478i
$963$	−2.95017	+	2.55634i	−0.0950679	+	0.0823768i
$964$	20.0037	+	3.60805i	0.644275	+	0.116207i
$965$		−	80.5433i		−	2.59278i
$966$	−20.4758	−	0.0852541i	−0.658799	−	0.00274301i
$967$	36.6072			1.17721			0.588604	−	0.808422i	$-0.299678\pi$
$967$	36.6072			1.17721			0.588604	+	0.808422i	$0.299678\pi$
$968$	55.5252	+	24.1644i	1.78465	+	0.776674i
$969$	7.11381	+	8.20978i	0.228529	+	0.263736i
$970$	−17.5938	−	49.8681i	−0.564904	−	1.60117i
$971$	−38.6522	+	5.55735i	−1.24041	+	0.178344i	−0.731118	−	0.682251i	$-0.761001\pi$
$971$	−38.6522	+	5.55735i	−1.24041	+	0.178344i	−0.509290	+	0.860595i	$0.670092\pi$
$972$	1.71998	−	1.02062i	0.0551683	−	0.0327365i
$973$	−13.1989	−	6.02775i	−0.423139	−	0.193241i
$974$	15.6444	−	11.2818i	0.501279	−	0.361492i
$975$	5.38118	−	37.4269i	0.172336	−	1.19862i
$976$	27.2688	+	14.8864i	0.872853	+	0.476503i
$977$	−20.8857	−	6.13259i	−0.668193	−	0.196199i	−0.0699946	−	0.997547i	$-0.522298\pi$
$977$	−20.8857	−	6.13259i	−0.668193	−	0.196199i	−0.598198	+	0.801348i	$0.704116\pi$
$978$	3.66072	+	2.08446i	0.117057	+	0.0666536i
$979$	−51.6102	+	23.5696i	−1.64947	+	0.753288i
$980$	−13.5274	−	9.39124i	−0.432116	−	0.299992i
$981$	−9.19834	−	7.97041i	−0.293680	−	0.254475i
$982$	−4.07686	−	3.16684i	−0.130098	−	0.101058i
$983$	42.4381	+	27.2733i	1.35357	+	0.869884i	0.997903	−	0.0647296i	$-0.0206185\pi$
$983$	42.4381	+	27.2733i	1.35357	+	0.869884i	0.355664	+	0.934614i	$0.384255\pi$
$984$	8.83151	+	5.45453i	0.281538	+	0.173884i
$985$	36.0342	−	23.1578i	1.14814	−	0.737868i
$986$	7.76323	−	4.06111i	0.247232	−	0.129332i
$987$	−6.16803	−	21.0064i	−0.196331	−	0.668641i
$988$	37.0119	+	18.5246i	1.17751	+	0.589346i
$989$	−3.43880	−	8.84865i	−0.109347	−	0.281371i
$990$	−30.5107	−	7.20909i	−0.969695	−	0.229120i
$991$	−18.6397	+	5.47311i	−0.592109	+	0.173859i	−0.564041	−	0.825747i	$-0.690754\pi$
$991$	−18.6397	+	5.47311i	−0.592109	+	0.173859i	−0.0280687	+	0.999606i	$0.508936\pi$
$992$	−14.8905	+	31.1329i	−0.472773	+	0.988471i
$993$	−19.2859	+	12.3943i	−0.612018	+	0.393320i
$994$	4.61574	−	51.5939i	0.146402	−	1.63646i
$995$	35.7075	−	55.5620i	1.13201	−	1.76143i
$996$	−21.1879	+	17.0760i	−0.671363	+	0.541072i
$997$	−28.4937	−	24.6899i	−0.902405	−	0.781938i	0.0741408	−	0.997248i	$-0.476379\pi$
$997$	−28.4937	−	24.6899i	−0.902405	−	0.781938i	−0.976546	+	0.215309i	$0.930924\pi$
$998$	−45.0482	−	17.7231i	−1.42598	−	0.561013i
$999$	−3.15377	−	6.90579i	−0.0997808	−	0.218489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.469.1	yes	480
8.5	even	2	inner	552.2.bb.a.469.8	yes	480
23.18	even	11	inner	552.2.bb.a.133.8	yes	480
184.133	even	22	inner	552.2.bb.a.133.1	✓	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.133.1	✓	480	184.133	even	22	inner
552.2.bb.a.133.8	yes	480	23.18	even	11	inner
552.2.bb.a.469.1	yes	480	1.1	even	1	trivial
552.2.bb.a.469.8	yes	480	8.5	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41218 + 0.0757292i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(1.98853 - 0.213887i) q^{4} +(3.85438 - 0.554176i) q^{5} +(1.01767 - 0.982016i) q^{6} +(-1.25415 + 2.74620i) q^{7} +(-2.79197 + 0.452638i) q^{8} +(0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-1.41218 + 0.0757292i) q^{2} +(-0.755750 + 0.654861i) q^{3} +(1.98853 - 0.213887i) q^{4} +(3.85438 - 0.554176i) q^{5} +(1.01767 - 0.982016i) q^{6} +(-1.25415 + 2.74620i) q^{7} +(-2.79197 + 0.452638i) q^{8} +(0.142315 - 0.989821i) q^{9} +(-5.40113 + 1.07449i) q^{10} +(-1.60389 + 5.46234i) q^{11} +(-1.36276 + 1.46386i) q^{12} +(-3.38420 + 1.54551i) q^{13} +(1.56312 - 3.97311i) q^{14} +(-2.55004 + 2.94290i) q^{15} +(3.90850 - 0.850642i) q^{16} +(1.64292 + 1.05584i) q^{17} +(-0.126016 + 1.40859i) q^{18} +(-3.00727 - 4.67940i) q^{19} +(7.54602 - 1.92640i) q^{20} +(-0.850557 - 2.89673i) q^{21} +(1.85133 - 7.83529i) q^{22} +(-1.61443 + 4.51593i) q^{23} +(1.81362 - 2.17044i) q^{24} +(9.75166 - 2.86335i) q^{25} +(4.66208 - 2.43883i) q^{26} +(0.540641 + 0.841254i) q^{27} +(-1.90653 + 5.72914i) q^{28} +(-1.71503 + 2.66864i) q^{29} +(3.37826 - 4.34903i) q^{30} +(3.99509 - 4.61058i) q^{31} +(-5.45511 + 1.49725i) q^{32} +(-2.36493 - 5.17848i) q^{33} +(-2.40007 - 1.36663i) q^{34} +(-3.31208 + 11.2799i) q^{35} +(0.0712873 - 1.99873i) q^{36} +(-7.51457 - 1.08043i) q^{37} +(4.60119 + 6.38044i) q^{38} +(1.54551 - 3.38420i) q^{39} +(-10.5105 + 3.29188i) q^{40} +(0.522287 + 3.63258i) q^{41} +(1.42051 + 4.02630i) q^{42} +(-1.49601 + 1.29630i) q^{43} +(-2.02105 + 11.2051i) q^{44} -3.89401i q^{45} +(1.93788 - 6.49959i) q^{46} +7.25176 q^{47} +(-2.39680 + 3.20240i) q^{48} +(-1.38470 - 1.59802i) q^{49} +(-13.5543 + 4.78206i) q^{50} +(-1.93307 + 0.277933i) q^{51} +(-6.39902 + 3.79714i) q^{52} +(0.107335 + 0.0490182i) q^{53} +(-0.827192 - 1.14706i) q^{54} +(-3.15489 + 21.9428i) q^{55} +(2.25851 - 8.23499i) q^{56} +(5.33710 + 1.56711i) q^{57} +(2.21985 - 3.89849i) q^{58} +(-9.04524 + 4.13082i) q^{59} +(-4.44138 + 6.39747i) q^{60} +(5.86982 + 5.08623i) q^{61} +(-5.29265 + 6.81354i) q^{62} +(2.53976 + 1.63221i) q^{63} +(7.59024 - 2.52751i) q^{64} +(-12.1875 + 7.83244i) q^{65} +(3.73189 + 7.13388i) q^{66} +(1.13181 + 3.85458i) q^{67} +(3.49283 + 1.74817i) q^{68} +(-1.73720 - 4.47014i) q^{69} +(3.82305 - 16.1801i) q^{70} +(11.6410 - 3.41810i) q^{71} +(0.0506913 + 2.82797i) q^{72} +(-7.29684 + 4.68940i) q^{73} +(10.6938 + 0.956697i) q^{74} +(-5.49472 + 8.54995i) q^{75} +(-6.98091 - 8.66192i) q^{76} +(-12.9892 - 11.2552i) q^{77} +(-1.92627 + 4.89616i) q^{78} +(-6.89632 - 15.1008i) q^{79} +(14.5935 - 5.44470i) q^{80} +(-0.959493 - 0.281733i) q^{81} +(-1.01266 - 5.09032i) q^{82} +(13.4677 + 1.93636i) q^{83} +(-2.31093 - 5.57831i) q^{84} +(6.91756 + 3.15915i) q^{85} +(2.01447 - 1.94390i) q^{86} +(-0.451454 - 3.13993i) q^{87} +(2.00555 - 15.9767i) q^{88} +(6.52652 + 7.53201i) q^{89} +(0.294891 + 5.49907i) q^{90} -11.2320i q^{91} +(-2.24444 + 9.32537i) q^{92} +6.10068i q^{93} +(-10.2408 + 0.549170i) q^{94} +(-14.1844 - 16.3696i) q^{95} +(3.14221 - 4.70389i) q^{96} +(1.36658 + 9.50478i) q^{97} +(2.07646 + 2.15184i) q^{98} +(5.17848 + 2.36493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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