LMFDB - Embedded newform 930.2.bj.a.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(277,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 5, 6]))

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

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

chi := DirichletCharacter("930.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bj (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			277.1
Character	$\chi$	$=$	930.277
Dual form			930.2.bj.a.883.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 - 0.987688i) q^{2} +(0.987688 + 0.156434i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-2.22990 + 0.166033i) q^{5} -1.00000i q^{6} +(0.154498 - 0.303220i) q^{7} +(0.453990 + 0.891007i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})$	\(q+(-0.156434 - 0.987688i) q^{2} +(0.987688 + 0.156434i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-2.22990 + 0.166033i) q^{5} -1.00000i q^{6} +(0.154498 - 0.303220i) q^{7} +(0.453990 + 0.891007i) q^{8} +(0.951057 + 0.309017i) q^{9} +(0.512821 + 2.17647i) q^{10} +(-2.41650 + 0.785169i) q^{11} +(-0.987688 + 0.156434i) q^{12} +(4.89912 + 0.775944i) q^{13} +(-0.323656 - 0.105162i) q^{14} +(-2.22841 - 0.184844i) q^{15} +(0.809017 - 0.587785i) q^{16} +(2.48584 + 4.87873i) q^{17} +(0.156434 - 0.987688i) q^{18} +(0.655605 - 0.902363i) q^{19} +(2.06945 - 0.846982i) q^{20} +(0.200030 - 0.275318i) q^{21} +(1.15353 + 2.26392i) q^{22} +(-3.48726 + 1.77685i) q^{23} +(0.309017 + 0.951057i) q^{24} +(4.94487 - 0.740472i) q^{25} -4.96018i q^{26} +(0.891007 + 0.453990i) q^{27} +(-0.0532365 + 0.336122i) q^{28} +(8.19721 + 5.95562i) q^{29} +(0.166033 + 2.22990i) q^{30} +(1.85820 - 5.24853i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.50958 + 0.397478i) q^{33} +(4.42979 - 3.21843i) q^{34} +(-0.294171 + 0.701801i) q^{35} -1.00000 q^{36} +(-1.31249 + 1.31249i) q^{37} +(-0.993813 - 0.506373i) q^{38} +(4.71741 + 1.53278i) q^{39} +(-1.16029 - 1.91147i) q^{40} +(-1.09726 - 0.797206i) q^{41} +(-0.303220 - 0.154498i) q^{42} +(-0.491121 - 3.10082i) q^{43} +(2.05560 - 1.49348i) q^{44} +(-2.17206 - 0.531169i) q^{45} +(2.30050 + 3.16637i) q^{46} +(10.5935 + 1.67785i) q^{47} +(0.891007 - 0.453990i) q^{48} +(4.04642 + 5.56943i) q^{49} +(-1.50490 - 4.76815i) q^{50} +(1.69203 + 5.20754i) q^{51} +(-4.89912 + 0.775944i) q^{52} +(2.15975 - 1.10045i) q^{53} +(0.309017 - 0.951057i) q^{54} +(5.25818 - 2.15206i) q^{55} +0.340312 q^{56} +(0.788695 - 0.788695i) q^{57} +(4.59997 - 9.02795i) q^{58} +(2.01003 + 2.76657i) q^{59} +(2.17647 - 0.512821i) q^{60} -5.32633i q^{61} +(-5.47460 - 1.01427i) q^{62} +(0.240637 - 0.240637i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-11.0533 - 0.916859i) q^{65} +(0.785169 + 2.41650i) q^{66} +(3.72573 + 3.72573i) q^{67} +(-3.87178 - 3.87178i) q^{68} +(-3.72229 + 1.20945i) q^{69} +(0.739179 + 0.180763i) q^{70} +(-2.41732 + 7.43973i) q^{71} +(0.156434 + 0.987688i) q^{72} +(0.826578 - 1.62225i) q^{73} +(1.50165 + 1.09102i) q^{74} +(4.99982 + 0.0421920i) q^{75} +(-0.344672 + 1.06079i) q^{76} +(-0.135266 + 0.854039i) q^{77} +(0.775944 - 4.89912i) q^{78} +(-3.58408 + 11.0307i) q^{79} +(-1.70643 + 1.44502i) q^{80} +(0.809017 + 0.587785i) q^{81} +(-0.615742 + 1.20846i) q^{82} +(-0.526454 - 3.32390i) q^{83} +(-0.105162 + 0.323656i) q^{84} +(-6.35319 - 10.4663i) q^{85} +(-2.98581 + 0.970150i) q^{86} +(7.16462 + 7.16462i) q^{87} +(-1.79666 - 1.79666i) q^{88} +(-0.109811 - 0.337963i) q^{89} +(-0.184844 + 2.22841i) q^{90} +(0.992187 - 1.36563i) q^{91} +(2.76751 - 2.76751i) q^{92} +(2.65637 - 4.89323i) q^{93} -10.7256i q^{94} +(-1.31211 + 2.12103i) q^{95} +(-0.587785 - 0.809017i) q^{96} +(0.469620 - 0.921681i) q^{97} +(4.86786 - 4.86786i) q^{98} -2.54086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{7}+O(q^{10}) $ 128 * q - 16 * q^7	$ 128 q - 16 q^{7} - 4 q^{10} + 4 q^{15} + 32 q^{16} - 12 q^{17} - 40 q^{19} + 40 q^{21} + 16 q^{22} - 32 q^{24} - 8 q^{25} - 4 q^{28} + 8 q^{29} + 20 q^{31} + 4 q^{33} + 24 q^{35} - 128 q^{36} + 64 q^{37} - 16 q^{38} - 24 q^{41} + 4 q^{42} + 24 q^{43} - 8 q^{44} + 20 q^{46} + 108 q^{47} - 100 q^{49} - 24 q^{50} + 16 q^{53} - 32 q^{54} + 12 q^{55} + 16 q^{57} - 40 q^{58} - 16 q^{62} - 4 q^{63} + 36 q^{65} - 12 q^{66} - 32 q^{67} + 8 q^{68} - 32 q^{70} + 24 q^{71} + 60 q^{73} - 16 q^{74} + 24 q^{75} - 24 q^{76} - 20 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 8 q^{83} - 132 q^{85} - 20 q^{87} - 4 q^{88} + 136 q^{89} - 40 q^{91} - 64 q^{93} + 108 q^{95} + 64 q^{97} - 16 q^{98} - 8 q^{99}+O(q^{100}) $ 128 * q - 16 * q^7 - 4 * q^10 + 4 * q^15 + 32 * q^16 - 12 * q^17 - 40 * q^19 + 40 * q^21 + 16 * q^22 - 32 * q^24 - 8 * q^25 - 4 * q^28 + 8 * q^29 + 20 * q^31 + 4 * q^33 + 24 * q^35 - 128 * q^36 + 64 * q^37 - 16 * q^38 - 24 * q^41 + 4 * q^42 + 24 * q^43 - 8 * q^44 + 20 * q^46 + 108 * q^47 - 100 * q^49 - 24 * q^50 + 16 * q^53 - 32 * q^54 + 12 * q^55 + 16 * q^57 - 40 * q^58 - 16 * q^62 - 4 * q^63 + 36 * q^65 - 12 * q^66 - 32 * q^67 + 8 * q^68 - 32 * q^70 + 24 * q^71 + 60 * q^73 - 16 * q^74 + 24 * q^75 - 24 * q^76 - 20 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 8 * q^83 - 132 * q^85 - 20 * q^87 - 4 * q^88 + 136 * q^89 - 40 * q^91 - 64 * q^93 + 108 * q^95 + 64 * q^97 - 16 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$2$	−0.156434	−	0.987688i	−0.110616	−	0.698401i
$3$	0.987688	+	0.156434i	0.570242	+	0.0903175i
$3$	0.987688	+	0.156434i	0.570242	+	0.0903175i
$4$	−0.951057	+	0.309017i	−0.475528	+	0.154508i
$5$	−2.22990	+	0.166033i	−0.997239	+	0.0742522i
$5$	−2.22990	+	0.166033i	−0.997239	+	0.0742522i
$6$		−	1.00000i		−	0.408248i
$7$	0.154498	−	0.303220i	0.0583949	−	0.114606i	−0.859965	−	0.510354i	$-0.829514\pi$
$7$	0.154498	−	0.303220i	0.0583949	−	0.114606i	0.918359	+	0.395747i	$0.129514\pi$
$8$	0.453990	+	0.891007i	0.160510	+	0.315018i
$9$	0.951057	+	0.309017i	0.317019	+	0.103006i
$10$	0.512821	+	2.17647i	0.162168	+	0.688260i
$11$	−2.41650	+	0.785169i	−0.728603	+	0.236737i	−0.649749	−	0.760149i	$-0.725126\pi$
$11$	−2.41650	+	0.785169i	−0.728603	+	0.236737i	−0.0788537	+	0.996886i	$0.525126\pi$
$12$	−0.987688	+	0.156434i	−0.285121	+	0.0451587i
$13$	4.89912	+	0.775944i	1.35877	+	0.215208i	0.792933	−	0.609309i	$-0.208553\pi$
$13$	4.89912	+	0.775944i	1.35877	+	0.215208i	0.565837	+	0.824517i	$0.308553\pi$
$14$	−0.323656	−	0.105162i	−0.0865006	−	0.0281058i
$15$	−2.22841	−	0.184844i	−0.575374	−	0.0477264i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	2.48584	+	4.87873i	0.602904	+	1.18327i	0.967683	+	0.252172i	$0.0811448\pi$
$17$	2.48584	+	4.87873i	0.602904	+	1.18327i	−0.364778	+	0.931094i	$0.618855\pi$
$18$	0.156434	−	0.987688i	0.0368720	−	0.232800i
$19$	0.655605	−	0.902363i	0.150406	−	0.207016i	−0.727165	−	0.686463i	$-0.759162\pi$
$19$	0.655605	−	0.902363i	0.150406	−	0.207016i	0.877571	+	0.479446i	$0.159162\pi$
$20$	2.06945	−	0.846982i	0.462743	−	0.189391i
$21$	0.200030	−	0.275318i	0.0436502	−	0.0600793i
$22$	1.15353	+	2.26392i	0.245933	+	0.482670i
$23$	−3.48726	+	1.77685i	−0.727145	+	0.370499i	−0.778048	−	0.628205i	$-0.783790\pi$
$23$	−3.48726	+	1.77685i	−0.727145	+	0.370499i	0.0509033	+	0.998704i	$0.483790\pi$
$24$	0.309017	+	0.951057i	0.0630778	+	0.194134i
$25$	4.94487	−	0.740472i	0.988973	−	0.148094i
$26$		−	4.96018i		−	0.972772i
$27$	0.891007	+	0.453990i	0.171474	+	0.0873705i
$28$	−0.0532365	+	0.336122i	−0.0100608	+	0.0635211i
$29$	8.19721	+	5.95562i	1.52218	+	1.10593i	0.960392	+	0.278651i	$0.0898873\pi$
$29$	8.19721	+	5.95562i	1.52218	+	1.10593i	0.561791	+	0.827279i	$0.310113\pi$
$30$	0.166033	+	2.22990i	0.0303133	+	0.407121i
$31$	1.85820	−	5.24853i	0.333742	−	0.942664i
$31$	1.85820	−	5.24853i	0.333742	−	0.942664i
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−2.50958	+	0.397478i	−0.436862	+	0.0691921i
$34$	4.42979	−	3.21843i	0.759704	−	0.551957i
$35$	−0.294171	+	0.701801i	−0.0497239	+	0.118626i
$36$	−1.00000			−0.166667
$37$	−1.31249	+	1.31249i	−0.215773	+	0.215773i	−0.806714	−	0.590942i	$-0.798756\pi$
$37$	−1.31249	+	1.31249i	−0.215773	+	0.215773i	0.590942	+	0.806714i	$0.298756\pi$
$38$	−0.993813	−	0.506373i	−0.161218	−	0.0821446i
$39$	4.71741	+	1.53278i	0.755391	+	0.245441i
$40$	−1.16029	−	1.91147i	−0.183458	−	0.302231i
$41$	−1.09726	−	0.797206i	−0.171363	−	0.124503i	0.498798	−	0.866718i	$-0.333775\pi$
$41$	−1.09726	−	0.797206i	−0.171363	−	0.124503i	−0.670161	+	0.742216i	$0.733775\pi$
$42$	−0.303220	−	0.154498i	−0.0467879	−	0.0238396i
$43$	−0.491121	−	3.10082i	−0.0748953	−	0.472870i	−0.996419	−	0.0845490i	$-0.973055\pi$
$43$	−0.491121	−	3.10082i	−0.0748953	−	0.472870i	0.921524	−	0.388321i	$-0.126945\pi$
$44$	2.05560	−	1.49348i	0.309893	−	0.225151i
$45$	−2.17206	−	0.531169i	−0.323792	−	0.0791820i
$46$	2.30050	+	3.16637i	0.339190	+	0.466856i
$47$	10.5935	+	1.67785i	1.54522	+	0.244739i	0.870066	−	0.492934i	$-0.164076\pi$
$47$	10.5935	+	1.67785i	1.54522	+	0.244739i	0.675157	+	0.737674i	$0.264076\pi$
$48$	0.891007	−	0.453990i	0.128606	−	0.0655279i
$49$	4.04642	+	5.56943i	0.578061	+	0.795632i
$50$	−1.50490	−	4.76815i	−0.212825	−	0.674318i
$51$	1.69203	+	5.20754i	0.236932	+	0.729201i
$52$	−4.89912	+	0.775944i	−0.679385	+	0.107604i
$53$	2.15975	−	1.10045i	0.296664	−	0.151158i	−0.299323	−	0.954152i	$-0.596761\pi$
$53$	2.15975	−	1.10045i	0.296664	−	0.151158i	0.595987	+	0.802994i	$0.296761\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	5.25818	−	2.15206i	0.709013	−	0.290184i
$56$	0.340312			0.0454761
$57$	0.788695	−	0.788695i	0.104465	−	0.104465i
$58$	4.59997	−	9.02795i	0.604006	−	1.18543i
$59$	2.01003	+	2.76657i	0.261683	+	0.360176i	0.919560	−	0.392949i	$-0.128545\pi$
$59$	2.01003	+	2.76657i	0.261683	+	0.360176i	−0.657877	+	0.753126i	$0.728545\pi$
$60$	2.17647	−	0.512821i	0.280981	−	0.0662049i
$61$		−	5.32633i		−	0.681967i	−0.940069	−	0.340984i	$-0.889240\pi$
$61$		−	5.32633i		−	0.681967i	0.940069	−	0.340984i	$-0.110760\pi$
$62$	−5.47460	−	1.01427i	−0.695275	−	0.128812i
$63$	0.240637	−	0.240637i	0.0303174	−	0.0303174i
$64$	−0.587785	+	0.809017i	−0.0734732	+	0.101127i
$65$	−11.0533	−	0.916859i	−1.37100	−	0.113722i
$66$	0.785169	+	2.41650i	0.0966476	+	0.297451i
$67$	3.72573	+	3.72573i	0.455170	+	0.455170i	0.897066	−	0.441896i	$-0.145694\pi$
$67$	3.72573	+	3.72573i	0.455170	+	0.455170i	−0.441896	+	0.897066i	$0.645694\pi$
$68$	−3.87178	−	3.87178i	−0.469523	−	0.469523i
$69$	−3.72229	+	1.20945i	−0.448111	+	0.145600i
$70$	0.739179	+	0.180763i	0.0883488	+	0.0216053i
$71$	−2.41732	+	7.43973i	−0.286883	+	0.882934i	0.698946	+	0.715175i	$0.253653\pi$
$71$	−2.41732	+	7.43973i	−0.286883	+	0.882934i	−0.985828	+	0.167759i	$0.946347\pi$
$72$	0.156434	+	0.987688i	0.0184360	+	0.116400i
$73$	0.826578	−	1.62225i	0.0967436	−	0.189870i	−0.837563	−	0.546341i	$-0.816020\pi$
$73$	0.826578	−	1.62225i	0.0967436	−	0.189870i	0.934306	+	0.356471i	$0.116020\pi$
$74$	1.50165	+	1.09102i	0.174564	+	0.126828i
$75$	4.99982	+	0.0421920i	0.577330	+	0.00487192i
$76$	−0.344672	+	1.06079i	−0.0395366	+	0.121681i
$77$	−0.135266	+	0.854039i	−0.0154150	+	0.0973268i
$78$	0.775944	−	4.89912i	0.0878583	−	0.554716i
$79$	−3.58408	+	11.0307i	−0.403241	+	1.24105i	0.519114	+	0.854705i	$0.326262\pi$
$79$	−3.58408	+	11.0307i	−0.403241	+	1.24105i	−0.922355	+	0.386343i	$0.873738\pi$
$80$	−1.70643	+	1.44502i	−0.190785	+	0.161558i
$81$	0.809017	+	0.587785i	0.0898908	+	0.0653095i
$82$	−0.615742	+	1.20846i	−0.0679973	+	0.133452i
$83$	−0.526454	−	3.32390i	−0.0577858	−	0.364845i	−0.999589	−	0.0286795i	$-0.990870\pi$
$83$	−0.526454	−	3.32390i	−0.0577858	−	0.364845i	0.941803	−	0.336166i	$-0.109130\pi$
$84$	−0.105162	+	0.323656i	−0.0114741	+	0.0353137i
$85$	−6.35319	−	10.4663i	−0.689100	−	1.13523i
$86$	−2.98581	+	0.970150i	−0.321969	+	0.104614i
$87$	7.16462	+	7.16462i	0.768128	+	0.768128i
$88$	−1.79666	−	1.79666i	−0.191525	−	0.191525i
$89$	−0.109811	−	0.337963i	−0.0116399	−	0.0358240i	0.945068	−	0.326874i	$-0.105995\pi$
$89$	−0.109811	−	0.337963i	−0.0116399	−	0.0358240i	−0.956708	+	0.291050i	$0.905995\pi$
$90$	−0.184844	+	2.22841i	−0.0194842	+	0.234896i
$91$	0.992187	−	1.36563i	0.104009	−	0.143157i
$92$	2.76751	−	2.76751i	0.288533	−	0.288533i
$93$	2.65637	−	4.89323i	0.275453	−	0.507404i
$94$		−	10.7256i		−	1.10626i
$95$	−1.31211	+	2.12103i	−0.134620	+	0.217613i
$96$	−0.587785	−	0.809017i	−0.0599906	−	0.0825700i
$97$	0.469620	−	0.921681i	0.0476827	−	0.0935825i	−0.865936	−	0.500155i	$-0.833276\pi$
$97$	0.469620	−	0.921681i	0.0476827	−	0.0935825i	0.913618	+	0.406573i	$0.133276\pi$
$98$	4.86786	−	4.86786i	0.491728	−	0.491728i
$99$	−2.54086			−0.255366
$100$	−4.47403	+	2.23228i	−0.447403	+	0.223228i
$101$	−0.538351	+	1.65687i	−0.0535679	+	0.164865i	−0.974261	−	0.225422i	$-0.927624\pi$
$101$	−0.538351	+	1.65687i	−0.0535679	+	0.164865i	0.920693	+	0.390287i	$0.127624\pi$
$102$	4.87873	−	2.48584i	0.483066	−	0.246135i
$103$	−5.78900	+	0.916888i	−0.570407	+	0.0903436i	−0.434974	−	0.900443i	$-0.643243\pi$
$103$	−5.78900	+	0.916888i	−0.570407	+	0.0903436i	−0.135433	+	0.990787i	$0.543243\pi$
$104$	1.53278	+	4.71741i	0.150302	+	0.462581i
$105$	−0.400335	+	0.647142i	−0.0390687	+	0.0631546i
$106$	−1.42476	−	1.96101i	−0.138385	−	0.190470i
$107$	−16.7392	+	8.52905i	−1.61824	+	0.824534i	−0.619006	+	0.785386i	$0.712464\pi$
$107$	−16.7392	+	8.52905i	−1.61824	+	0.824534i	−0.999233	+	0.0391476i	$0.987536\pi$
$108$	−0.987688	−	0.156434i	−0.0950404	−	0.0150529i
$109$	6.50548	+	8.95402i	0.623112	+	0.857640i	0.997575	−	0.0696020i	$-0.0221729\pi$
$109$	6.50548	+	8.95402i	0.623112	+	0.857640i	−0.374463	+	0.927242i	$0.622173\pi$
$110$	−2.94813	−	4.85679i	−0.281093	−	0.463077i
$111$	−1.50165	+	1.09102i	−0.142531	+	0.103555i
$112$	−0.0532365	−	0.336122i	−0.00503038	−	0.0317605i
$113$	−11.9833	−	6.10578i	−1.12729	−	0.574384i	−0.212038	−	0.977261i	$-0.568010\pi$
$113$	−11.9833	−	6.10578i	−1.12729	−	0.574384i	−0.915254	+	0.402878i	$0.868010\pi$
$114$	−0.902363	−	0.655605i	−0.0845141	−	0.0614031i
$115$	7.48122	−	4.54119i	0.697627	−	0.423468i
$116$	−9.63639	−	3.13105i	−0.894717	−	0.290711i
$117$	4.41956	+	2.25188i	0.408588	+	0.208186i
$118$	2.41807	−	2.41807i	0.222601	−	0.222601i
$119$	1.86339			0.170816
$120$	−0.846982	−	2.06945i	−0.0773185	−	0.188914i
$121$	−3.67620	+	2.67091i	−0.334200	+	0.242810i
$122$	−5.26076	+	0.833222i	−0.476287	+	0.0754364i
$123$	−0.959040	−	0.959040i	−0.0864738	−	0.0864738i
$124$	−0.145367	+	5.56587i	−0.0130543	+	0.499830i
$125$	−10.9036	+	2.47219i	−0.975247	+	0.221119i
$126$	−0.275318	−	0.200030i	−0.0245273	−	0.0178201i
$127$	2.27054	−	14.3356i	0.201478	−	1.27208i	−0.654893	−	0.755722i	$-0.727286\pi$
$127$	2.27054	−	14.3356i	0.201478	−	1.27208i	0.856371	−	0.516361i	$-0.172714\pi$
$128$	0.891007	+	0.453990i	0.0787546	+	0.0401275i
$129$		−	3.13947i		−	0.276415i
$130$	0.823554	+	11.0607i	0.0722304	+	0.970087i
$131$	−3.99739	−	12.3027i	−0.349254	−	1.07489i	−0.959267	−	0.282501i	$-0.908836\pi$
$131$	−3.99739	−	12.3027i	−0.349254	−	1.07489i	0.610013	−	0.792391i	$-0.291164\pi$
$132$	2.26392	−	1.15353i	0.197049	−	0.100402i
$133$	−0.172325	−	0.338206i	−0.0149424	−	0.0293262i
$134$	3.09703	−	4.26269i	0.267542	−	0.368240i
$135$	−2.06223	−	0.864415i	−0.177488	−	0.0743970i
$136$	−3.21843	+	4.42979i	−0.275978	+	0.379852i
$137$	1.49216	−	9.42113i	0.127484	−	0.804901i	−0.838235	−	0.545310i	$-0.816412\pi$
$137$	1.49216	−	9.42113i	0.127484	−	0.804901i	0.965719	−	0.259592i	$-0.0835879\pi$
$138$	1.77685	+	3.48726i	0.151255	+	0.296856i
$139$	4.55635	−	3.31038i	0.386464	−	0.280783i	−0.377541	−	0.925993i	$-0.623230\pi$
$139$	4.55635	−	3.31038i	0.386464	−	0.280783i	0.764005	+	0.645210i	$0.223230\pi$
$140$	0.0629045	−	0.758356i	0.00531640	−	0.0640928i
$141$	10.2006	+	3.31438i	0.859047	+	0.279121i
$142$	7.72629	+	1.22372i	0.648376	+	0.102693i
$143$	−12.4480	+	1.97156i	−1.04095	+	0.164871i
$144$	0.951057	−	0.309017i	0.0792547	−	0.0257514i
$145$	−19.2677	−	11.9194i	−1.60010	−	0.989852i
$146$	−1.73158	−	0.562625i	−0.143307	−	0.0465632i
$147$	3.12536	+	6.13386i	0.257775	+	0.505912i
$148$	0.842673	−	1.65384i	0.0692673	−	0.135945i
$149$		−	11.6258i		−	0.952423i	−0.879331	−	0.476212i	$-0.842010\pi$
$149$		−	11.6258i		−	0.952423i	0.879331	−	0.476212i	$-0.157990\pi$
$150$	−0.740472	−	4.94487i	−0.0604593	−	0.403747i
$151$	10.9805	−	3.56779i	0.893582	−	0.290342i	0.173996	−	0.984746i	$-0.444332\pi$
$151$	10.9805	−	3.56779i	0.893582	−	0.290342i	0.719585	+	0.694404i	$0.244332\pi$
$152$	1.10165	+	0.174484i	0.0893556	+	0.0141525i
$153$	0.856561	+	5.40811i	0.0692489	+	0.437220i
$154$	0.864685			0.0696783
$155$	−3.27216	+	12.0122i	−0.262826	+	0.964843i
$156$	−4.96018			−0.397132
$157$	0.996417	+	6.29113i	0.0795227	+	0.502087i	0.995013	+	0.0997464i	$0.0318032\pi$
$157$	0.996417	+	6.29113i	0.0795227	+	0.502087i	−0.915490	+	0.402340i	$0.868197\pi$
$158$	11.4555	+	1.81438i	0.911354	+	0.144344i
$159$	2.30530	−	0.749039i	0.182822	−	0.0594026i
$160$	1.69418	+	1.45937i	0.133936	+	0.115373i
$161$			1.33193i			0.104971i
$162$	0.453990	−	0.891007i	0.0356689	−	0.0700041i
$163$	−9.45329	−	18.5531i	−0.740439	−	1.45319i	−0.885923	−	0.463833i	$-0.846474\pi$
$163$	−9.45329	−	18.5531i	−0.740439	−	1.45319i	0.145483	−	0.989361i	$-0.453526\pi$
$164$	1.28991	+	0.419116i	0.100725	+	0.0327275i
$165$	5.53010	−	1.30301i	0.430518	−	0.101439i
$166$	−3.20062	+	1.03994i	−0.248416	+	0.0807154i
$167$	9.11061	−	1.44298i	0.705000	−	0.111661i	0.206368	−	0.978475i	$-0.433836\pi$
$167$	9.11061	−	1.44298i	0.705000	−	0.111661i	0.498632	+	0.866813i	$0.333836\pi$
$168$	0.336122	+	0.0532365i	0.0259324	+	0.00410728i
$169$	11.0355	+	3.58565i	0.848885	+	0.275819i
$170$	−9.34361	+	7.91226i	−0.716622	+	0.606843i
$171$	0.902363	−	0.655605i	0.0690055	−	0.0501354i
$172$	1.42529	+	2.79729i	0.108677	+	0.213291i
$173$	−0.860920	+	5.43564i	−0.0654546	+	0.413264i	0.933105	+	0.359605i	$0.117088\pi$
$173$	−0.860920	+	5.43564i	−0.0654546	+	0.413264i	−0.998559	+	0.0536592i	$0.982912\pi$
$174$	5.95562	−	8.19721i	0.451494	−	0.621429i
$175$	0.539448	−	1.61378i	0.0407784	−	0.121991i
$176$	−1.49348	+	2.05560i	−0.112575	+	0.154947i
$177$	1.55250	+	3.04694i	0.116693	+	0.229022i
$178$	−0.316624	+	0.161328i	−0.0237320	+	0.0120920i
$179$	4.84172	+	14.9013i	0.361887	+	1.11377i	0.951908	+	0.306385i	$0.0991196\pi$
$179$	4.84172	+	14.9013i	0.361887	+	1.11377i	−0.590021	+	0.807388i	$0.700880\pi$
$180$	2.22990	−	0.166033i	0.166207	−	0.0123754i
$181$			15.2263i			1.13176i	0.824487	+	0.565881i	$0.191464\pi$
$181$			15.2263i			1.13176i	−0.824487	+	0.565881i	$0.808536\pi$
$182$	−1.50403	−	0.766340i	−0.111486	−	0.0568049i
$183$	0.833222	−	5.26076i	0.0615936	−	0.388886i
$184$	−3.16637	−	2.30050i	−0.233428	−	0.169595i
$185$	2.70881	−	3.14464i	0.199155	−	0.231199i
$186$	−5.24853	−	1.85820i	−0.384841	−	0.136250i
$187$	−9.83766	−	9.83766i	−0.719401	−	0.719401i
$188$	−10.5935	+	1.67785i	−0.772612	+	0.122370i
$189$	0.275318	−	0.200030i	0.0200264	−	0.0145501i
$190$	2.30017	+	0.964153i	0.166872	+	0.0699470i
$191$	4.92026			0.356017			0.178009	−	0.984029i	$-0.443035\pi$
$191$	4.92026			0.356017			0.178009	+	0.984029i	$0.443035\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	20.9245	+	10.6615i	1.50618	+	0.767435i	0.995716	−	0.0924662i	$-0.0294750\pi$
$193$	20.9245	+	10.6615i	1.50618	+	0.767435i	0.510460	+	0.859901i	$0.329475\pi$
$194$	−0.983798	−	0.319655i	−0.0706326	−	0.0229499i
$195$	−10.7738	−	2.63470i	−0.771530	−	0.188674i
$196$	−5.56943	−	4.04642i	−0.397816	−	0.289030i
$197$	−21.3900	−	10.8987i	−1.52397	−	0.776503i	−0.526683	−	0.850062i	$-0.676564\pi$
$197$	−21.3900	−	10.8987i	−1.52397	−	0.776503i	−0.997291	+	0.0735585i	$0.976564\pi$
$198$	0.397478	+	2.50958i	0.0282475	+	0.178348i
$199$	−9.45333	+	6.86825i	−0.670129	+	0.486877i	−0.870068	−	0.492931i	$-0.835925\pi$
$199$	−9.45333	+	6.86825i	−0.670129	+	0.486877i	0.199939	+	0.979808i	$0.435925\pi$
$200$	2.90469	+	4.06974i	0.205392	+	0.287774i
$201$	3.09703	+	4.26269i	0.218447	+	0.300667i
$202$	1.72069	+	0.272531i	0.121067	+	0.0191752i
$203$	3.07232	−	1.56542i	0.215634	−	0.109871i
$204$	−3.21843	−	4.42979i	−0.225335	−	0.310148i
$205$	2.57914	+	1.59550i	0.180135	+	0.111435i
$206$	1.81120	+	5.57430i	0.126192	+	0.388380i
$207$	−3.86566	+	0.612261i	−0.268682	+	0.0425551i
$208$	4.41956	−	2.25188i	0.306441	−	0.156140i
$209$	−0.875764	+	2.69532i	−0.0605779	+	0.186439i
$210$	0.701801	+	0.294171i	0.0484288	+	0.0202997i
$211$	−18.9565			−1.30502			−0.652509	−	0.757781i	$-0.726283\pi$
$211$	−18.9565			−1.30502			−0.652509	+	0.757781i	$0.726283\pi$
$212$	−1.71398	+	1.71398i	−0.117717	+	0.117717i
$213$	−3.55138	+	6.96998i	−0.243337	+	0.477575i
$214$	11.0426	+	15.1989i	0.754858	+	1.03897i
$215$	1.60999	+	6.83296i	0.109800	+	0.466004i
$216$			1.00000i			0.0680414i
$217$	−1.30437	−	1.37433i	−0.0885465	−	0.0932958i
$218$	7.82610	−	7.82610i	0.530051	−	0.530051i
$219$	1.07018	−	1.47297i	0.0723158	−	0.0995342i
$220$	−4.33580	+	3.67160i	−0.292320	+	0.247539i
$221$	8.39278	+	25.8303i	0.564560	+	1.73754i
$222$	1.31249	+	1.31249i	0.0880888	+	0.0880888i
$223$	13.6351	+	13.6351i	0.913075	+	0.913075i	0.996513	−	0.0834375i	$-0.0265899\pi$
$223$	13.6351	+	13.6351i	0.913075	+	0.913075i	−0.0834375	+	0.996513i	$0.526590\pi$
$224$	−0.323656	+	0.105162i	−0.0216252	+	0.00702644i
$225$	4.93167	+	0.823817i	0.328778	+	0.0549211i
$226$	−4.15601	+	12.7909i	−0.276454	+	0.850838i
$227$	−4.24976	−	26.8319i	−0.282067	−	1.78090i	−0.568383	−	0.822764i	$-0.692431\pi$
$227$	−4.24976	−	26.8319i	−0.282067	−	1.78090i	0.286317	−	0.958135i	$-0.407569\pi$
$228$	−0.506373	+	0.993813i	−0.0335354	+	0.0658169i
$229$	8.46477	+	6.15002i	0.559368	+	0.406405i	0.831228	−	0.555932i	$-0.187639\pi$
$229$	8.46477	+	6.15002i	0.559368	+	0.406405i	−0.271860	+	0.962337i	$0.587639\pi$
$230$	−5.65560	−	6.67871i	−0.372919	−	0.440381i
$231$	−0.267202	+	0.822364i	−0.0175806	+	0.0541076i
$232$	−1.58504	+	10.0076i	−0.104063	+	0.657028i
$233$	2.18912	−	13.8215i	0.143414	−	0.905479i	−0.806106	−	0.591772i	$-0.798429\pi$
$233$	2.18912	−	13.8215i	0.143414	−	0.905479i	0.949520	−	0.313708i	$-0.101571\pi$
$234$	1.53278	−	4.71741i	0.100201	−	0.308387i
$235$	−23.9010	−	1.98255i	−1.55913	−	0.129328i
$236$	−2.76657	−	2.01003i	−0.180088	−	0.130842i
$237$	−5.26554	+	10.3342i	−0.342033	+	0.671278i
$238$	−0.291498	−	1.84045i	−0.0188950	−	0.119298i
$239$	−0.109174	+	0.336004i	−0.00706189	+	0.0217343i	−0.954525	−	0.298130i	$-0.903637\pi$
$239$	−0.109174	+	0.336004i	−0.00706189	+	0.0217343i	0.947463	+	0.319864i	$0.103637\pi$
$240$	−1.91147	+	1.16029i	−0.123385	+	0.0748962i
$241$	−25.8165	+	8.38830i	−1.66299	+	0.540338i	−0.981495	−	0.191486i	$-0.938669\pi$
$241$	−25.8165	+	8.38830i	−1.66299	+	0.540338i	−0.681494	+	0.731824i	$0.738669\pi$
$242$	3.21311	+	3.21311i	0.206547	+	0.206547i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	1.64593	+	5.06564i	0.105370	+	0.324295i
$245$	−9.94781	−	11.7474i	−0.635542	−	0.750514i
$246$	−0.797206	+	1.09726i	−0.0508280	+	0.0699587i
$247$	3.91207	−	3.91207i	0.248919	−	0.248919i
$248$	5.52008	−	0.727116i	0.350526	−	0.0461719i
$249$		−	3.36533i		−	0.213269i
$250$	4.14745	+	10.3826i	0.262308	+	0.656654i
$251$	−6.69515	−	9.21508i	−0.422594	−	0.581651i	0.543639	−	0.839319i	$-0.317046\pi$
$251$	−6.69515	−	9.21508i	−0.422594	−	0.581651i	−0.966234	+	0.257668i	$0.917046\pi$
$252$	−0.154498	+	0.303220i	−0.00973248	+	0.0191011i
$253$	7.03185	−	7.03185i	0.442089	−	0.442089i
$254$	−14.5143			−0.910711
$255$	−4.63767	−	11.3313i	−0.290422	−	0.709595i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−21.4858	+	10.9475i	−1.34024	+	0.682889i	−0.969327	−	0.245777i	$-0.920957\pi$
$257$	−21.4858	+	10.9475i	−1.34024	+	0.682889i	−0.370918	+	0.928665i	$0.620957\pi$
$258$	−3.10082	+	0.491121i	−0.193049	+	0.0305759i
$259$	0.195196	+	0.600753i	0.0121289	+	0.0373289i
$260$	10.7957	−	2.54369i	0.669520	−	0.157753i
$261$	5.95562	+	8.19721i	0.368644	+	0.507394i
$262$	−11.5259	+	5.87275i	−0.712073	+	0.362819i
$263$	6.78367	+	1.07443i	0.418299	+	0.0662521i	0.362036	−	0.932164i	$-0.382082\pi$
$263$	6.78367	+	1.07443i	0.418299	+	0.0662521i	0.0562627	+	0.998416i	$0.482082\pi$
$264$	−1.49348	−	2.05560i	−0.0919174	−	0.126513i
$265$	−4.63330	+	2.81247i	−0.284621	+	0.172768i
$266$	−0.307085	+	0.223110i	−0.0188286	+	0.0136798i
$267$	−0.0555898	−	0.350980i	−0.00340204	−	0.0214797i
$268$	−4.69469	−	2.39206i	−0.286774	−	0.146119i
$269$	−2.26705	−	1.64711i	−0.138224	−	0.100426i	0.516524	−	0.856273i	$-0.327226\pi$
$269$	−2.26705	−	1.64711i	−0.138224	−	0.100426i	−0.654749	+	0.755847i	$0.727226\pi$
$270$	−0.531169	+	2.17206i	−0.0323259	+	0.132188i
$271$	−5.47291	−	1.77826i	−0.332456	−	0.108021i	0.138033	−	0.990428i	$-0.455922\pi$
$271$	−5.47291	−	1.77826i	−0.332456	−	0.108021i	−0.470488	+	0.882406i	$0.655922\pi$
$272$	4.87873	+	2.48584i	0.295817	+	0.150726i
$273$	1.19360	−	1.19360i	0.0722401	−	0.0722401i
$274$	−9.53856			−0.576246
$275$	−11.3679	+	5.67191i	−0.685509	+	0.342029i
$276$	3.16637	−	2.30050i	0.190593	−	0.138474i
$277$	7.72225	−	1.22308i	0.463985	−	0.0734880i	0.0799347	−	0.996800i	$-0.474529\pi$
$277$	7.72225	−	1.22308i	0.463985	−	0.0734880i	0.384051	+	0.923312i	$0.374529\pi$
$278$	−3.98240	−	3.98240i	−0.238848	−	0.238848i
$279$	3.38914	−	4.41744i	0.202902	−	0.264465i
$280$	−0.758860	+	0.0565029i	−0.0453505	+	0.00337670i
$281$	25.8484	+	18.7799i	1.54198	+	1.12032i	0.949076	+	0.315048i	$0.102021\pi$
$281$	25.8484	+	18.7799i	1.54198	+	1.12032i	0.592909	+	0.805269i	$0.297979\pi$
$282$	1.67785	−	10.5935i	0.0999144	−	0.630835i
$283$	−19.2139	−	9.78999i	−1.14215	−	0.581954i	−0.222593	−	0.974911i	$-0.571452\pi$
$283$	−19.2139	−	9.78999i	−1.14215	−	0.581954i	−0.919557	+	0.392957i	$0.871452\pi$
$284$		−	7.82260i		−	0.464186i
$285$	−1.62776	+	1.88966i	−0.0964200	+	0.111934i
$286$	3.89458	+	11.9863i	0.230291	+	0.708764i
$287$	−0.411254	+	0.209544i	−0.0242755	+	0.0123690i
$288$	−0.453990	−	0.891007i	−0.0267516	−	0.0525031i
$289$	−7.63028	+	10.5022i	−0.448840	+	0.617775i
$290$	−8.75851	+	20.8951i	−0.514318	+	1.22700i
$291$	0.608021	−	0.836869i	0.0356428	−	0.0490581i
$292$	−0.284819	+	1.79828i	−0.0166678	+	0.105236i
$293$	−13.5678	−	26.6282i	−0.792637	−	1.55564i	−0.830934	−	0.556371i	$-0.812193\pi$
$293$	−13.5678	−	26.6282i	−0.792637	−	1.55564i	0.0382967	−	0.999266i	$-0.487807\pi$
$294$	5.56943	−	4.04642i	0.324815	−	0.235992i
$295$	−4.94149	−	5.83542i	−0.287705	−	0.339751i
$296$	−1.76530	−	0.573581i	−0.102606	−	0.0333387i
$297$	−2.50958	−	0.397478i	−0.145621	−	0.0230640i
$298$	−11.4827	+	1.81868i	−0.665174	+	0.105353i
$299$	−18.4632	+	5.99907i	−1.06776	+	0.346935i
$300$	−4.76815	+	1.50490i	−0.275289	+	0.0868856i
$301$	−1.01611	−	0.330153i	−0.0585675	−	0.0190297i
$302$	−5.24159	−	10.2872i	−0.301620	−	0.591962i
$303$	−0.790915	+	1.55226i	−0.0454369	+	0.0891749i
$304$		−	1.11538i		−	0.0639716i
$305$	0.884347	+	11.8772i	0.0506375	+	0.680085i
$306$	5.20754	−	1.69203i	0.297695	−	0.0967270i
$307$	7.62791	+	1.20814i	0.435348	+	0.0689523i	0.370262	−	0.928927i	$-0.379268\pi$
$307$	7.62791	+	1.20814i	0.435348	+	0.0689523i	0.0650857	+	0.997880i	$0.479268\pi$
$308$	−0.135266	−	0.854039i	−0.00770752	−	0.0486634i
$309$	−5.86116			−0.333430
$310$	12.3762	+	1.35275i	0.702920	+	0.0768312i
$311$	−7.31404			−0.414741			−0.207371	−	0.978262i	$-0.566491\pi$
$311$	−7.31404			−0.414741			−0.207371	+	0.978262i	$0.566491\pi$
$312$	0.775944	+	4.89912i	0.0439292	+	0.277358i
$313$	9.06035	+	1.43502i	0.512122	+	0.0811121i	0.407147	−	0.913363i	$-0.366524\pi$
$313$	9.06035	+	1.43502i	0.512122	+	0.0811121i	0.104975	+	0.994475i	$0.466524\pi$
$314$	6.05780	−	1.96830i	0.341861	−	0.111078i
$315$	−0.496641	+	0.576548i	−0.0279826	+	0.0324848i
$316$		−	11.5983i		−	0.652457i
$317$	5.87793	−	11.5361i	0.330138	−	0.647932i	−0.664955	−	0.746884i	$-0.731549\pi$
$317$	5.87793	−	11.5361i	0.330138	−	0.647932i	0.995092	+	0.0989522i	$0.0315491\pi$
$318$	−1.10045	−	2.15975i	−0.0617099	−	0.121113i
$319$	−24.4847	−	7.95557i	−1.37088	−	0.445427i
$320$	1.17638	−	1.90161i	0.0657614	−	0.106304i
$321$	−17.8673	+	5.80545i	−0.997258	+	0.324029i
$322$	1.31553	−	0.208359i	0.0733116	−	0.0116114i
$323$	6.03212	+	0.955393i	0.335636	+	0.0531595i
$324$	−0.951057	−	0.309017i	−0.0528365	−	0.0171676i
$325$	24.8000	+	0.209280i	1.37566	+	0.0116088i
$326$	−16.8459	+	12.2393i	−0.933008	+	0.677870i
$327$	5.02467	+	9.86146i	0.277865	+	0.545340i
$328$	0.212170	−	1.33959i	0.0117151	−	0.0739665i
$329$	2.14544	−	2.95294i	0.118282	−	0.162801i
$330$	−2.15206	−	5.25818i	−0.118467	−	0.289453i
$331$	9.50814	−	13.0868i	0.522615	−	0.719317i	−0.463368	−	0.886166i	$-0.653359\pi$
$331$	9.50814	−	13.0868i	0.522615	−	0.719317i	0.985982	+	0.166849i	$0.0533592\pi$
$332$	1.52783	+	2.99853i	0.0838505	+	0.164566i
$333$	−1.65384	+	0.842673i	−0.0906298	+	0.0461782i
$334$	−2.85043	−	8.77271i	−0.155968	−	0.480021i
$335$	−8.92658	−	7.68939i	−0.487711	−	0.420116i
$336$		−	0.340312i		−	0.0185655i
$337$	12.2043	+	6.21839i	0.664809	+	0.338737i	0.753619	−	0.657311i	$-0.228306\pi$
$337$	12.2043	+	6.21839i	0.664809	+	0.338737i	−0.0888099	+	0.996049i	$0.528306\pi$
$338$	1.81517	−	11.4606i	0.0987325	−	0.623372i
$339$	−10.8806	−	7.90521i	−0.590952	−	0.429352i
$340$	9.27651	+	7.99083i	0.503090	+	0.433363i
$341$	−0.369356	+	14.1421i	−0.0200018	+	0.765837i
$342$	−0.788695	−	0.788695i	−0.0426477	−	0.0426477i
$343$	4.66678	−	0.739145i	0.251982	−	0.0399101i
$344$	2.53989	−	1.84533i	0.136941	−	0.0994938i
$345$	8.09951	−	3.31496i	0.436063	−	0.178471i
$346$	5.50339			0.295864
$347$	21.5766	−	21.5766i	1.15829	−	1.15829i	0.173448	−	0.984843i	$-0.444509\pi$
$347$	21.5766	−	21.5766i	1.15829	−	1.15829i	0.984843	−	0.173448i	$-0.0554907\pi$
$348$	−9.02795	−	4.59997i	−0.483949	−	0.246584i
$349$	33.0019	+	10.7230i	1.76655	+	0.573988i	0.997845	−	0.0656129i	$-0.0209002\pi$
$349$	33.0019	+	10.7230i	1.76655	+	0.573988i	0.768707	+	0.639601i	$0.220900\pi$
$350$	−1.67830	−	0.280355i	−0.0897091	−	0.0149856i
$351$	4.01287	+	2.91552i	0.214191	+	0.155619i
$352$	2.26392	+	1.15353i	0.120668	+	0.0614832i
$353$	1.18077	+	7.45512i	0.0628463	+	0.396796i	0.998980	+	0.0451520i	$0.0143772\pi$
$353$	1.18077	+	7.45512i	0.0628463	+	0.396796i	−0.936134	+	0.351644i	$0.885623\pi$
$354$	2.76657	−	2.01003i	0.147041	−	0.106832i
$355$	4.15512	−	16.9912i	0.220531	−	0.901798i
$356$	0.208873	+	0.287489i	0.0110702	+	0.0152369i
$357$	1.84045	+	0.291498i	0.0974067	+	0.0154277i
$358$	13.9604	−	7.11318i	0.737830	−	0.375943i
$359$	5.30300	+	7.29895i	0.279881	+	0.385224i	0.925695	−	0.378272i	$-0.123481\pi$
$359$	5.30300	+	7.29895i	0.279881	+	0.385224i	−0.645813	+	0.763496i	$0.723481\pi$
$360$	−0.512821	−	2.17647i	−0.0270281	−	0.114710i
$361$	5.48688	+	16.8869i	0.288783	+	0.888783i
$362$	15.0388	−	2.38192i	0.790424	−	0.125191i
$363$	−4.04876	+	2.06295i	−0.212505	+	0.108277i
$364$	−0.521623	+	1.60539i	−0.0273405	+	0.0841454i
$365$	−1.57383	+	3.75469i	−0.0823783	+	0.196529i
$366$	−5.32633			−0.278412
$367$	22.6119	−	22.6119i	1.18033	−	1.18033i	0.200675	−	0.979658i	$-0.435687\pi$
$367$	22.6119	−	22.6119i	1.18033	−	1.18033i	0.979658	−	0.200675i	$-0.0643134\pi$
$368$	−1.77685	+	3.48726i	−0.0926247	+	0.181786i
$369$	−0.797206	−	1.09726i	−0.0415009	−	0.0571211i
$370$	−3.52968	−	2.18353i	−0.183499	−	0.113516i
$371$		−	0.824895i		−	0.0428264i
$372$	−1.01427	+	5.47460i	−0.0525875	+	0.283845i
$373$	−15.8467	+	15.8467i	−0.820510	+	0.820510i	−0.986181	−	0.165671i	$-0.947021\pi$
$373$	−15.8467	+	15.8467i	−0.820510	+	0.820510i	0.165671	+	0.986181i	$0.447021\pi$
$374$	−8.17759	+	11.2555i	−0.422853	+	0.582008i
$375$	−11.1561	+	0.736051i	−0.576098	+	0.0380095i
$376$	3.31438	+	10.2006i	0.170926	+	0.526057i
$377$	35.5378	+	35.5378i	1.83029	+	1.83029i
$378$	−0.240637	−	0.240637i	−0.0123770	−	0.0123770i
$379$	−5.48973	+	1.78372i	−0.281988	+	0.0916236i	−0.446597	−	0.894735i	$-0.647364\pi$
$379$	−5.48973	+	1.78372i	−0.281988	+	0.0916236i	0.164608	+	0.986359i	$0.447364\pi$
$380$	0.592457	−	2.42268i	0.0303924	−	0.124281i
$381$	4.48518	−	13.8040i	0.229783	−	0.707198i
$382$	−0.769698	−	4.85968i	−0.0393812	−	0.248643i
$383$	−8.84141	+	17.3523i	−0.451775	+	0.886659i	0.546998	+	0.837134i	$0.315771\pi$
$383$	−8.84141	+	17.3523i	−0.451775	+	0.886659i	−0.998773	+	0.0495246i	$0.984229\pi$
$384$	0.809017	+	0.587785i	0.0412850	+	0.0299953i
$385$	0.159832	−	1.92688i	0.00814577	−	0.0982027i
$386$	7.25698	−	22.3347i	0.369371	−	1.13681i
$387$	0.491121	−	3.10082i	0.0249651	−	0.157623i
$388$	−0.161820	+	1.02169i	−0.00821517	+	0.0518685i
$389$	−2.89089	+	8.89724i	−0.146574	+	0.451108i	−0.997210	−	0.0746469i	$-0.976217\pi$
$389$	−2.89089	+	8.89724i	−0.146574	+	0.451108i	0.850636	+	0.525755i	$0.176217\pi$
$390$	−0.916859	+	11.0533i	−0.0464269	+	0.559708i
$391$	−17.3375	−	12.5965i	−0.876797	−	0.637030i
$392$	−3.12536	+	6.13386i	−0.157854	+	0.309807i
$393$	−2.02361	−	12.7766i	−0.102078	−	0.644493i
$394$	−7.41843	+	22.8316i	−0.373735	+	1.15024i
$395$	6.16068	−	25.1923i	0.309977	−	1.26756i
$396$	2.41650	−	0.785169i	0.121434	−	0.0394562i
$397$	−6.33091	−	6.33091i	−0.317739	−	0.317739i	0.530159	−	0.847898i	$-0.322132\pi$
$397$	−6.33091	−	6.33091i	−0.317739	−	0.317739i	−0.847898	+	0.530159i	$0.822132\pi$
$398$	8.26251	+	8.26251i	0.414162	+	0.414162i
$399$	−0.117296	−	0.361000i	−0.00587214	−	0.0180726i
$400$	3.56524	−	3.50557i	0.178262	−	0.175279i
$401$	11.9688	−	16.4736i	0.597691	−	0.822651i	−0.397804	−	0.917471i	$-0.630227\pi$
$401$	11.9688	−	16.4736i	0.597691	−	0.822651i	0.995494	+	0.0948196i	$0.0302274\pi$
$402$	3.72573	−	3.72573i	0.185822	−	0.185822i
$403$	13.1761	−	24.2713i	0.656348	−	1.20904i
$404$		−	1.74214i		−	0.0866747i
$405$	−1.90161	−	1.17638i	−0.0944920	−	0.0584546i
$406$	−2.02677	−	2.78961i	−0.100587	−	0.138446i
$407$	2.14111	−	4.20217i	0.106131	−	0.208294i
$408$	−3.87178	+	3.87178i	−0.191682	+	0.191682i
$409$	−15.0783			−0.745573			−0.372787	−	0.927917i	$-0.621598\pi$
$409$	−15.0783			−0.745573			−0.372787	+	0.927917i	$0.621598\pi$
$410$	1.17240	−	2.79698i	0.0579005	−	0.138133i
$411$	2.94758	−	9.07171i	0.145393	−	0.447475i
$412$	5.22233	−	2.66091i	0.257286	−	0.131094i
$413$	1.14942	−	0.182051i	0.0565595	−	0.00895814i
$414$	1.20945	+	3.72229i	0.0594410	+	0.182941i
$415$	1.72581	+	7.32454i	0.0847169	+	0.359547i
$416$	−2.91552	−	4.01287i	−0.142945	−	0.196747i
$417$	5.01811	−	2.55686i	0.245738	−	0.125210i
$418$	2.79914	+	0.443340i	0.136910	+	0.0216845i
$419$	−4.36730	−	6.01107i	−0.213357	−	0.293660i	0.688903	−	0.724854i	$-0.258093\pi$
$419$	−4.36730	−	6.01107i	−0.213357	−	0.293660i	−0.902259	+	0.431194i	$0.858093\pi$
$420$	0.180763	−	0.739179i	0.00882033	−	0.0360682i
$421$	5.60445	−	4.07187i	0.273144	−	0.198451i	−0.442777	−	0.896632i	$-0.646007\pi$
$421$	5.60445	−	4.07187i	0.273144	−	0.198451i	0.715922	+	0.698181i	$0.246007\pi$
$422$	2.96545	+	18.7231i	0.144356	+	0.911425i
$423$	9.55655	+	4.86931i	0.464656	+	0.236754i
$424$	1.96101	+	1.42476i	0.0952350	+	0.0691923i
$425$	15.9047	+	22.2840i	0.771491	+	1.08093i
$426$	7.43973	+	2.41732i	0.360456	+	0.117119i
$427$	−1.61505	−	0.822910i	−0.0781578	−	0.0398234i
$428$	13.2843	−	13.2843i	0.642121	−	0.642121i
$429$	−12.6031			−0.608485
$430$	6.49698	−	2.65908i	0.313312	−	0.128232i
$431$	17.4286	−	12.6626i	0.839505	−	0.609936i	−0.0827276	−	0.996572i	$-0.526363\pi$
$431$	17.4286	−	12.6626i	0.839505	−	0.609936i	0.922232	+	0.386636i	$0.126363\pi$
$432$	0.987688	−	0.156434i	0.0475202	−	0.00752646i
$433$	−12.1240	−	12.1240i	−0.582644	−	0.582644i	0.352985	−	0.935629i	$-0.385167\pi$
$433$	−12.1240	−	12.1240i	−0.582644	−	0.582644i	−0.935629	+	0.352985i	$0.885167\pi$
$434$	−1.15336	+	1.50331i	−0.0553632	+	0.0721610i
$435$	−17.1659	−	14.7868i	−0.823043	−	0.708972i
$436$	−8.95402	−	6.50548i	−0.428820	−	0.311556i
$437$	−0.682905	+	4.31169i	−0.0326678	+	0.206256i
$438$	−1.62225	−	0.826578i	−0.0775141	−	0.0394954i
$439$			21.5817i			1.03004i	0.857178	+	0.515020i	$0.172216\pi$
$439$			21.5817i			1.03004i	−0.857178	+	0.515020i	$0.827784\pi$
$440$	4.30467	+	3.70806i	0.205217	+	0.176775i
$441$	2.12733	+	6.54725i	0.101301	+	0.311774i
$442$	24.1994	−	12.3302i	1.15105	−	0.586488i
$443$	−13.9197	−	27.3190i	−0.661346	−	1.29797i	−0.941176	−	0.337916i	$-0.890278\pi$
$443$	−13.9197	−	27.3190i	−0.661346	−	1.29797i	0.279830	−	0.960050i	$-0.409722\pi$
$444$	1.09102	−	1.50165i	0.0517773	−	0.0712654i
$445$	0.300980	+	0.735390i	0.0142678	+	0.0348608i
$446$	11.3343	−	15.6003i	0.536692	−	0.738694i
$447$	1.81868	−	11.4827i	0.0860205	−	0.543112i
$448$	0.154498	+	0.303220i	0.00729936	+	0.0143258i
$449$	27.6889	−	20.1172i	1.30672	−	0.949388i	0.306724	−	0.951799i	$-0.400767\pi$
$449$	27.6889	−	20.1172i	1.30672	−	0.949388i	0.999997	+	0.00241013i	$0.000767167\pi$
$450$	0.0421920	−	4.99982i	0.00198895	−	0.235694i
$451$	3.27747	+	1.06492i	0.154330	+	0.0501449i
$452$	13.2836	+	2.10391i	0.624806	+	0.0989596i
$453$	11.4035	−	1.80613i	0.535781	−	0.0848594i
$454$	−25.8368	+	8.39488i	−1.21258	+	0.393991i
$455$	−1.98573	+	3.20994i	−0.0930926	+	0.150484i
$456$	1.06079	+	0.344672i	0.0496761	+	0.0161408i
$457$	−10.2828	−	20.1811i	−0.481008	−	0.944030i	−0.996212	−	0.0869629i	$-0.972284\pi$
$457$	−10.2828	−	20.1811i	−0.481008	−	0.944030i	0.515204	−	0.857068i	$-0.327716\pi$
$458$	4.75012	−	9.32263i	0.221958	−	0.435618i
$459$			5.47553i			0.255576i
$460$	−5.71176	+	6.63075i	−0.266312	+	0.309160i
$461$	31.3602	−	10.1895i	1.46059	−	0.474575i	0.532340	−	0.846531i	$-0.321313\pi$
$461$	31.3602	−	10.1895i	1.46059	−	0.474575i	0.928250	+	0.371956i	$0.121313\pi$
$462$	0.854039	+	0.135266i	0.0397335	+	0.00629317i
$463$	−1.37604	−	8.68800i	−0.0639502	−	0.403766i	−0.998811	−	0.0487510i	$-0.984476\pi$
$463$	−1.37604	−	8.68800i	−0.0639502	−	0.403766i	0.934861	−	0.355015i	$-0.115524\pi$
$464$	10.1323			0.470380
$465$	−5.11100	+	11.3524i	−0.237017	+	0.526456i
$466$	−13.9938			−0.648252
$467$	1.77127	+	11.1833i	0.0819645	+	0.517504i	0.994175	+	0.107781i	$0.0343745\pi$
$467$	1.77127	+	11.1833i	0.0819645	+	0.517504i	−0.912210	+	0.409723i	$0.865625\pi$
$468$	−4.89912	−	0.775944i	−0.226462	−	0.0358680i
$469$	1.70533	−	0.554097i	0.0787450	−	0.0255858i
$470$	1.78080	+	23.9169i	0.0821421	+	1.10320i
$471$			6.36955i			0.293493i
$472$	−1.55250	+	3.04694i	−0.0714594	+	0.140247i
$473$	3.62146	+	7.10752i	0.166515	+	0.326804i
$474$	11.0307	+	3.58408i	0.506656	+	0.164622i
$475$	2.57371	−	4.94752i	0.118090	−	0.227008i
$476$	−1.77219	+	0.575818i	−0.0812280	+	0.0263926i
$477$	2.39410	−	0.379188i	0.109618	−	0.0173618i
$478$	0.348945	+	0.0552675i	0.0159604	+	0.00252788i
$479$	23.3351	+	7.58202i	1.06621	+	0.346431i	0.789009	−	0.614382i	$-0.210595\pi$
$479$	23.3351	+	7.58202i	1.06621	+	0.346431i	0.277197	+	0.960813i	$0.410595\pi$
$480$	1.44502	+	1.70643i	0.0659560	+	0.0778876i
$481$	−7.44848	+	5.41164i	−0.339621	+	0.246749i
$482$	12.3236	+	24.1865i	0.561326	+	1.10166i
$483$	−0.208359	+	1.31553i	−0.00948068	+	0.0598587i
$484$	2.67091	−	3.67620i	0.121405	−	0.167100i
$485$	−0.894174	+	2.13322i	−0.0406023	+	0.0968647i
$486$	0.587785	−	0.809017i	0.0266625	−	0.0366978i
$487$	−2.17315	−	4.26505i	−0.0984748	−	0.193268i	0.836513	−	0.547946i	$-0.184590\pi$
$487$	−2.17315	−	4.26505i	−0.0984748	−	0.193268i	−0.934988	+	0.354679i	$0.884590\pi$
$488$	4.74580	−	2.41811i	0.214832	−	0.109462i
$489$	−6.43456	−	19.8035i	−0.290981	−	0.895547i
$490$	−10.0466	+	11.6630i	−0.453858	+	0.526882i
$491$		−	18.2397i		−	0.823146i	−0.911377	−	0.411573i	$-0.864979\pi$
$491$		−	18.2397i		−	0.823146i	0.911377	−	0.411573i	$-0.135021\pi$
$492$	1.20846	+	0.615742i	0.0544817	+	0.0277598i
$493$	−8.67894	+	54.7967i	−0.390880	+	2.46792i
$494$	−4.47589	−	3.25192i	−0.201380	−	0.146311i
$495$	5.66585	−	0.421866i	0.254661	−	0.0189615i
$496$	−1.58170	−	5.33837i	−0.0710202	−	0.239700i
$497$	1.88240	+	1.88240i	0.0844374	+	0.0844374i
$498$	−3.32390	+	0.526454i	−0.148947	+	0.0235910i
$499$	−8.58173	+	6.23499i	−0.384171	+	0.279117i	−0.763063	−	0.646324i	$-0.776305\pi$
$499$	−8.58173	+	6.23499i	−0.384171	+	0.279117i	0.378892	+	0.925441i	$0.376305\pi$
$500$	9.60598	−	5.72058i	0.429593	−	0.255832i
$501$	9.22417			0.412106
$502$	−8.05428	+	8.05428i	−0.359480	+	0.359480i
$503$	22.8037	+	11.6191i	1.01677	+	0.518070i	0.881223	−	0.472701i	$-0.156721\pi$
$503$	22.8037	+	11.6191i	1.01677	+	0.518070i	0.135546	+	0.990771i	$0.456721\pi$
$504$	0.323656	+	0.105162i	0.0144168	+	0.00468429i
$505$	0.925370	−	3.78404i	0.0411784	−	0.168387i
$506$	−8.04530	−	5.84525i	−0.357657	−	0.259853i
$507$	10.3387	+	5.26784i	0.459159	+	0.233953i
$508$	2.27054	+	14.3356i	0.100739	+	0.636041i
$509$	29.2660	−	21.2630i	1.29719	−	0.942465i	0.297268	−	0.954794i	$-0.403924\pi$
$509$	29.2660	−	21.2630i	1.29719	−	0.942465i	0.999924	+	0.0123288i	$0.00392447\pi$
$510$	−10.4663	+	6.35319i	−0.463457	+	0.281324i
$511$	−0.364194	−	0.501270i	−0.0161110	−	0.0221749i
$512$	−0.987688	−	0.156434i	−0.0436501	−	0.00691349i
$513$	0.993813	−	0.506373i	0.0438779	−	0.0223569i
$514$	14.1739	+	19.5087i	0.625183	+	0.860490i
$515$	12.7566	−	3.00573i	0.562124	−	0.132448i
$516$	0.970150	+	2.98581i	0.0427085	+	0.131443i
$517$	−26.9167	+	4.26318i	−1.18379	+	0.187494i
$518$	0.562821	−	0.286772i	0.0247289	−	0.0126000i
$519$	−1.70064	+	5.23404i	−0.0746499	+	0.229749i
$520$	−4.20119	−	10.2648i	−0.184234	−	0.450143i
$521$	22.8766			1.00224			0.501121	−	0.865377i	$-0.332921\pi$
$521$	22.8766			1.00224			0.501121	+	0.865377i	$0.332921\pi$
$522$	7.16462	−	7.16462i	0.313587	−	0.313587i
$523$	11.4191	−	22.4112i	0.499322	−	0.979975i	−0.494519	−	0.869167i	$-0.664656\pi$
$523$	11.4191	−	22.4112i	0.499322	−	0.979975i	0.993842	−	0.110809i	$-0.0353441\pi$
$524$	7.60349	+	10.4653i	0.332160	+	0.457179i
$525$	0.785258	−	1.50953i	0.0342714	−	0.0658812i
$526$		−	6.86823i		−	0.299469i
$527$	30.2254	−	3.98135i	1.31664	−	0.173430i
$528$	−1.79666	+	1.79666i	−0.0781896	+	0.0781896i
$529$	−4.51525	+	6.21471i	−0.196315	+	0.270205i
$530$	3.50265	+	4.13629i	0.152145	+	0.179669i
$531$	1.05673	+	3.25229i	0.0458584	+	0.141138i
$532$	0.268402	+	0.268402i	0.0116367	+	0.0116367i
$533$	−4.75702	−	4.75702i	−0.206049	−	0.206049i
$534$	−0.337963	+	0.109811i	−0.0146251	+	0.00475198i
$535$	35.9106	−	21.7981i	1.55255	−	0.942416i
$536$	−1.62820	+	5.01109i	−0.0703277	+	0.216446i
$537$	2.45104	+	15.4752i	0.105770	+	0.667805i
$538$	−1.27218	+	2.49680i	−0.0548478	+	0.107645i
$539$	−14.1511	−	10.2814i	−0.609532	−	0.442851i
$540$	2.22841	+	0.184844i	0.0958957	+	0.00795441i
$541$	13.6064	−	41.8760i	0.584983	−	1.80039i	−0.0143567	−	0.999897i	$-0.504570\pi$
$541$	13.6064	−	41.8760i	0.584983	−	1.80039i	0.599340	−	0.800495i	$-0.295430\pi$
$542$	−0.900211	+	5.68371i	−0.0386674	+	0.244136i
$543$	−2.38192	+	15.0388i	−0.102218	+	0.645379i
$544$	1.69203	−	5.20754i	0.0725452	−	0.223271i
$545$	−15.9932	−	18.8864i	−0.685073	−	0.809005i
$546$	−1.36563	−	0.992187i	−0.0584435	−	0.0424617i
$547$	−5.11457	+	10.0379i	−0.218683	+	0.429190i	−0.974120	−	0.226032i	$-0.927425\pi$
$547$	−5.11457	+	10.0379i	−0.218683	+	0.429190i	0.755437	+	0.655221i	$0.227425\pi$
$548$	1.49216	+	9.42113i	0.0637419	+	0.402451i
$549$	1.64593	−	5.06564i	0.0702465	−	0.216196i
$550$	7.38041	+	10.3406i	0.314702	+	0.440927i
$551$	10.7483	−	3.49232i	0.457892	−	0.148778i
$552$	−2.76751	−	2.76751i	−0.117793	−	0.117793i
$553$	2.79099	+	2.79099i	0.118685	+	0.118685i
$554$	−2.41605	−	7.43585i	−0.102648	−	0.315919i
$555$	3.16739	−	2.68217i	0.134448	−	0.113852i
$556$	−3.31038	+	4.55635i	−0.140391	+	0.193232i
$557$	−17.4477	+	17.4477i	−0.739284	+	0.739284i	−0.972439	−	0.233156i	$-0.925095\pi$
$557$	−17.4477	+	17.4477i	−0.739284	+	0.739284i	0.233156	+	0.972439i	$0.425095\pi$
$558$	−4.89323	−	2.65637i	−0.207147	−	0.112453i
$559$		−	15.5724i		−	0.658640i
$560$	0.174519	+	0.740678i	0.00737478	+	0.0312993i
$561$	−8.17759	−	11.2555i	−0.345258	−	0.475207i
$562$	14.5052	−	28.4680i	0.611863	−	1.20085i
$563$	8.85903	−	8.85903i	0.373363	−	0.373363i	−0.495337	−	0.868701i	$-0.664956\pi$
$563$	8.85903	−	8.85903i	0.373363	−	0.373363i	0.868701	+	0.495337i	$0.164956\pi$
$564$	−10.7256			−0.451628
$565$	27.7352	+	11.6256i	1.16683	+	0.489094i
$566$	−6.66374	+	20.5089i	−0.280098	+	0.862052i
$567$	0.303220	−	0.154498i	0.0127340	−	0.00648832i
$568$	−7.72629	+	1.22372i	−0.324188	+	0.0513463i
$569$	−9.06686	−	27.9049i	−0.380102	−	1.16984i	−0.939971	−	0.341254i	$-0.889148\pi$
$569$	−9.06686	−	27.9049i	−0.380102	−	1.16984i	0.559869	−	0.828581i	$-0.310852\pi$
$570$	2.12103	+	1.31211i	0.0888401	+	0.0549582i
$571$	−23.4416	−	32.2646i	−0.981001	−	1.35023i	−0.936289	−	0.351231i	$-0.885763\pi$
$571$	−23.4416	−	32.2646i	−0.981001	−	1.35023i	−0.0447119	−	0.999000i	$-0.514237\pi$
$572$	11.2295	−	5.72170i	0.469528	−	0.239236i
$573$	4.85968	+	0.769698i	0.203016	+	0.0321546i
$574$	0.271299	+	0.373411i	0.0113238	+	0.0155859i
$575$	−15.9283	+	11.3685i	−0.664258	+	0.474099i
$576$	−0.809017	+	0.587785i	−0.0337090	+	0.0244911i
$577$	−6.99141	−	44.1420i	−0.291056	−	1.83766i	−0.507858	−	0.861441i	$-0.669562\pi$
$577$	−6.99141	−	44.1420i	−0.291056	−	1.83766i	0.216801	−	0.976216i	$-0.430438\pi$
$578$	11.5665	+	5.89343i	0.481104	+	0.245135i
$579$	18.9990	+	13.8036i	0.789572	+	0.573658i
$580$	22.0080	+	5.38196i	0.913833	+	0.223474i
$581$	−1.08921	−	0.353905i	−0.0451880	−	0.0146825i
$582$	−0.921681	−	0.469620i	−0.0382049	−	0.0194664i
$583$	−4.35499	+	4.35499i	−0.180365	+	0.180365i
$584$	1.82069			0.0753408
$585$	−10.2290	−	4.28766i	−0.422918	−	0.177273i
$586$	−24.1779	+	17.5663i	−0.998781	+	0.725657i
$587$	−44.1280	+	6.98919i	−1.82136	+	0.288475i	−0.971237	−	0.238114i	$-0.923471\pi$
$587$	−44.1280	+	6.98919i	−1.82136	+	0.288475i	−0.850120	+	0.526589i	$0.823471\pi$
$588$	−4.86786	−	4.86786i	−0.200747	−	0.200747i
$589$	−3.51784	−	5.11774i	−0.144950	−	0.210873i
$590$	−4.99056	+	5.79352i	−0.205458	+	0.238515i
$591$	−19.4217	−	14.1107i	−0.798902	−	0.580436i
$592$	−0.290365	+	1.83329i	−0.0119339	+	0.0753479i
$593$	−21.1681	−	10.7857i	−0.869271	−	0.442915i	−0.0383225	−	0.999265i	$-0.512201\pi$
$593$	−21.1681	−	10.7857i	−0.869271	−	0.442915i	−0.830948	+	0.556350i	$0.812201\pi$
$594$			2.54086i			0.104253i
$595$	−4.15516	+	0.309383i	−0.170345	+	0.0126835i
$596$	3.59257	+	11.0568i	0.147158	+	0.452904i
$597$	−10.4114	+	5.30486i	−0.426109	+	0.217114i
$598$	8.81350	+	17.2975i	0.360411	+	0.707346i
$599$	−20.5860	+	28.3342i	−0.841121	+	1.15770i	0.144629	+	0.989486i	$0.453801\pi$
$599$	−20.5860	+	28.3342i	−0.841121	+	1.15770i	−0.985750	+	0.168218i	$0.946199\pi$
$600$	2.23228	+	4.47403i	0.0911324	+	0.182651i
$601$	9.31758	−	12.8245i	0.380072	−	0.523124i	−0.575532	−	0.817780i	$-0.695205\pi$
$601$	9.31758	−	12.8245i	0.380072	−	0.523124i	0.955604	+	0.294655i	$0.0952048\pi$
$602$	−0.167134	+	1.05525i	−0.00681189	+	0.0430086i
$603$	2.39206	+	4.69469i	0.0974124	+	0.191183i
$604$	−9.34059	+	6.78633i	−0.380063	+	0.276132i
$605$	7.75407	−	6.56623i	0.315248	−	0.266955i
$606$	1.65687	+	0.538351i	0.0673059	+	0.0218690i
$607$	−34.4355	−	5.45405i	−1.39769	−	0.221373i	−0.588301	−	0.808642i	$-0.700203\pi$
$607$	−34.4355	−	5.45405i	−1.39769	−	0.221373i	−0.809392	+	0.587269i	$0.800203\pi$
$608$	−1.10165	+	0.174484i	−0.0446778	+	0.00707627i
$609$	3.27938	−	1.06553i	0.132887	−	0.0431776i
$610$	11.5926	−	2.73146i	0.469371	−	0.110593i
$611$	50.5970	+	16.4399i	2.04693	+	0.665089i
$612$	−2.48584	−	4.87873i	−0.100484	−	0.197211i
$613$	−3.03672	+	5.95990i	−0.122652	+	0.240718i	−0.944166	−	0.329470i	$-0.893130\pi$
$613$	−3.03672	+	5.95990i	−0.122652	+	0.240718i	0.821514	+	0.570188i	$0.193130\pi$
$614$		−	7.72299i		−	0.311675i
$615$	2.29779	+	1.97933i	0.0926559	+	0.0798142i
$616$	−0.822364	+	0.267202i	−0.0331340	+	0.0107659i
$617$	−20.3273	−	3.21953i	−0.818347	−	0.129613i	−0.266794	−	0.963754i	$-0.585964\pi$
$617$	−20.3273	−	3.21953i	−0.818347	−	0.129613i	−0.551553	+	0.834140i	$0.685964\pi$
$618$	0.916888	+	5.78900i	0.0368826	+	0.232868i
$619$	−13.2128			−0.531068			−0.265534	−	0.964102i	$-0.585548\pi$
$619$	−13.2128			−0.531068			−0.265534	+	0.964102i	$0.585548\pi$
$620$	−0.599965	−	12.4354i	−0.0240952	−	0.499419i
$621$	−3.91385			−0.157057
$622$	1.14417	+	7.22400i	0.0458770	+	0.289656i
$623$	−0.119443	−	0.0189179i	−0.00478537	−	0.000757929i
$624$	4.71741	−	1.53278i	0.188848	−	0.0613603i
$625$	23.9034	−	7.32307i	0.956136	−	0.292923i
$626$		−	9.17329i		−	0.366639i
$627$	−1.28662	+	2.52514i	−0.0513828	+	0.100844i
$628$	−2.89171	−	5.67531i	−0.115392	−	0.226470i
$629$	−9.66595	−	3.14066i	−0.385407	−	0.125226i
$630$	0.647142	+	0.400335i	0.0257828	+	0.0159497i
$631$	−20.2029	+	6.56433i	−0.804266	+	0.261322i	−0.682167	−	0.731196i	$-0.738962\pi$
$631$	−20.2029	+	6.56433i	−0.804266	+	0.261322i	−0.122099	+	0.992518i	$0.538962\pi$
$632$	−11.4555	+	1.81438i	−0.455677	+	0.0721722i
$633$	−18.7231	−	2.96545i	−0.744176	−	0.117866i
$634$	−12.3136	−	4.00092i	−0.489035	−	0.158897i
$635$	−2.68288	+	32.3440i	−0.106467	+	1.28353i
$636$	−1.96101	+	1.42476i	−0.0777590	+	0.0564952i
$637$	15.5023	+	30.4251i	0.614225	+	1.20548i
$638$	−4.02737	+	25.4278i	−0.159445	+	1.00670i
$639$	−4.59801	+	6.32861i	−0.181894	+	0.250356i
$640$	−2.06223	−	0.864415i	−0.0815167	−	0.0341690i
$641$	−11.3950	+	15.6839i	−0.450077	+	0.619478i	−0.972414	−	0.233261i	$-0.925060\pi$
$641$	−11.3950	+	15.6839i	−0.450077	+	0.619478i	0.522337	+	0.852739i	$0.325060\pi$
$642$	8.52905	+	16.7392i	0.336615	+	0.660643i
$643$	11.3432	−	5.77967i	0.447334	−	0.227928i	−0.215787	−	0.976441i	$-0.569232\pi$
$643$	11.3432	−	5.77967i	0.447334	−	0.227928i	0.663121	+	0.748513i	$0.269232\pi$
$644$	−0.411588	−	1.26674i	−0.0162189	−	0.0499165i
$645$	0.521255	+	7.00069i	0.0205244	+	0.275652i
$646$		−	6.10731i		−	0.240289i
$647$	2.32619	+	1.18525i	0.0914519	+	0.0465971i	0.499118	−	0.866534i	$-0.333657\pi$
$647$	2.32619	+	1.18525i	0.0914519	+	0.0465971i	−0.407666	+	0.913131i	$0.633657\pi$
$648$	−0.156434	+	0.987688i	−0.00614533	+	0.0388001i
$649$	−7.02946	−	5.10720i	−0.275930	−	0.200475i
$650$	−3.67288	−	24.5274i	−0.144062	−	0.962045i
$651$	−1.07332	−	1.56146i	−0.0420667	−	0.0611985i
$652$	14.7239	+	14.7239i	0.576631	+	0.576631i
$653$	−14.7959	+	2.34344i	−0.579007	+	0.0917057i	−0.439067	−	0.898454i	$-0.644691\pi$
$653$	−14.7959	+	2.34344i	−0.579007	+	0.0917057i	−0.139940	+	0.990160i	$0.544691\pi$
$654$	8.95402	−	6.50548i	0.350130	−	0.254384i
$655$	10.9564	+	26.7701i	0.428103	+	1.04599i
$656$	−1.35629			−0.0529542
$657$	1.28742	−	1.28742i	0.0502272	−	0.0502272i
$658$	−3.25221	−	1.65708i	−0.126784	−	0.0645998i
$659$	7.70370	+	2.50308i	0.300094	+	0.0975063i	0.455194	−	0.890392i	$-0.349570\pi$
$659$	7.70370	+	2.50308i	0.300094	+	0.0975063i	−0.155100	+	0.987899i	$0.549570\pi$
$660$	−4.85679	+	2.94813i	−0.189050	+	0.114756i
$661$	−2.34962	−	1.70710i	−0.0913897	−	0.0663985i	0.541152	−	0.840925i	$-0.317988\pi$
$661$	−2.34962	−	1.70710i	−0.0913897	−	0.0663985i	−0.632542	+	0.774526i	$0.717988\pi$
$662$	−14.4131	−	7.34385i	−0.560181	−	0.285427i
$663$	4.24870	+	26.8252i	0.165006	+	1.04181i
$664$	2.72261	−	1.97809i	0.105658	−	0.0767649i
$665$	0.440419	+	0.725553i	0.0170787	+	0.0281357i
$666$	1.09102	+	1.50165i	0.0422760	+	0.0581879i
$667$	−39.1681	−	6.20361i	−1.51659	−	0.240205i
$668$	−8.21880	+	4.18769i	−0.317995	+	0.162026i
$669$	11.3343	+	15.6003i	0.438207	+	0.603141i
$670$	−6.19830	+	10.0196i	−0.239461	+	0.387089i
$671$	4.18207	+	12.8711i	0.161447	+	0.496883i
$672$	−0.336122	+	0.0532365i	−0.0129662	+	0.00205364i
$673$	−21.2729	+	10.8391i	−0.820011	+	0.417817i	−0.813075	−	0.582159i	$-0.802208\pi$
$673$	−21.2729	+	10.8391i	−0.820011	+	0.417817i	−0.00693666	+	0.999976i	$0.502208\pi$
$674$	4.23266	−	13.0268i	0.163036	−	0.501773i
$675$	4.74208	+	1.58516i	0.182523	+	0.0610127i
$676$	−11.6034			−0.446285
$677$	7.98051	−	7.98051i	0.306716	−	0.306716i	−0.536918	−	0.843634i	$-0.680412\pi$
$677$	7.98051	−	7.98051i	0.306716	−	0.306716i	0.843634	+	0.536918i	$0.180412\pi$
$678$	−6.10578	+	11.9833i	−0.234491	+	0.460215i
$679$	−0.206917	−	0.284796i	−0.00794073	−	0.0109295i
$680$	6.44128	−	10.4123i	0.247012	−	0.399295i
$681$		−	27.1664i		−	1.04102i
$682$	14.0258	−	1.84750i	0.537074	−	0.0707445i
$683$	−9.08107	+	9.08107i	−0.347478	+	0.347478i	−0.859169	−	0.511692i	$-0.829019\pi$
$683$	−9.08107	+	9.08107i	−0.347478	+	0.347478i	0.511692	+	0.859169i	$0.329019\pi$
$684$	−0.655605	+	0.902363i	−0.0250677	+	0.0345027i
$685$	−1.76314	+	21.2559i	−0.0673662	+	0.812145i
$686$	−1.46009	−	4.49370i	−0.0557465	−	0.171570i
$687$	7.39848	+	7.39848i	0.282270	+	0.282270i
$688$	−2.21994	−	2.21994i	−0.0846345	−	0.0846345i
$689$	11.4347	−	3.71537i	0.435628	−	0.141544i
$690$	−4.54119	−	7.48122i	−0.172880	−	0.284805i
$691$	−3.29881	+	10.1527i	−0.125493	+	0.386227i	−0.993991	−	0.109466i	$-0.965086\pi$
$691$	−3.29881	+	10.1527i	−0.125493	+	0.386227i	0.868498	+	0.495693i	$0.165086\pi$
$692$	−0.860920	−	5.43564i	−0.0327273	−	0.206632i
$693$	−0.392559	+	0.770440i	−0.0149121	+	0.0292666i
$694$	−24.6862	−	17.9356i	−0.937077	−	0.680826i
$695$	−9.61055	+	8.13831i	−0.364549	+	0.308704i
$696$	−3.13105	+	9.63639i	−0.118682	+	0.365267i
$697$	1.16174	−	7.33496i	0.0440042	−	0.277831i
$698$	5.42832	−	34.2731i	0.205465	−	1.29725i
$699$	4.32433	−	13.3089i	0.163561	−	0.503390i
$700$	−0.0143584	+	1.70150i	−0.000542698	+	0.0643106i
$701$	28.2700	+	20.5393i	1.06774	+	0.775760i	0.975505	−	0.219977i	$-0.0705981\pi$
$701$	28.2700	+	20.5393i	1.06774	+	0.775760i	0.0922375	+	0.995737i	$0.470598\pi$
$702$	2.25188	−	4.41956i	0.0849916	−	0.166805i
$703$	0.323868	+	2.04482i	0.0122149	+	0.0771220i
$704$	0.785169	−	2.41650i	0.0295922	−	0.0910753i
$705$	−23.2966	−	5.69709i	−0.877401	−	0.214565i
$706$	7.17862	−	2.33247i	0.270171	−	0.0877838i
$707$	0.419223	+	0.419223i	0.0157665	+	0.0157665i
$708$	−2.41807	−	2.41807i	−0.0908765	−	0.0908765i
$709$	−1.71509	−	5.27851i	−0.0644116	−	0.198238i	0.913672	−	0.406453i	$-0.133235\pi$
$709$	−1.71509	−	5.27851i	−0.0644116	−	0.198238i	−0.978083	+	0.208215i	$0.933235\pi$
$710$	−17.4320	−	1.44596i	−0.654211	−	0.0542658i
$711$	−6.81733	+	9.38325i	−0.255670	+	0.351899i
$712$	0.251274	−	0.251274i	0.00941690	−	0.00941690i
$713$	2.84582	+	21.6048i	0.106577	+	0.809104i
$714$		−	1.86339i		−	0.0697355i
$715$	27.4303	−	6.46315i	1.02584	−	0.241708i
$716$	−9.20949	−	12.6758i	−0.344175	−	0.473716i
$717$	−0.160393	+	0.314788i	−0.00598997	+	0.0117560i
$718$	6.37952	−	6.37952i	0.238081	−	0.238081i
$719$	−17.9507			−0.669448			−0.334724	−	0.942316i	$-0.608643\pi$
$719$	−17.9507			−0.669448			−0.334724	+	0.942316i	$0.608643\pi$
$720$	−2.06945	+	0.846982i	−0.0771238	+	0.0315652i
$721$	−0.616372	+	1.89700i	−0.0229549	+	0.0706479i
$722$	15.8206	−	8.06102i	0.588783	−	0.300000i
$723$	−26.8109	+	4.24643i	−0.997108	+	0.157926i
$724$	−4.70519	−	14.4811i	−0.174867	−	0.538185i
$725$	44.9441	+	23.3799i	1.66918	+	0.868309i
$726$	2.67091	+	3.67620i	0.0991269	+	0.136436i
$727$	30.6305	−	15.6070i	1.13602	−	0.578832i	0.218231	−	0.975897i	$-0.429971\pi$
$727$	30.6305	−	15.6070i	1.13602	−	0.578832i	0.917790	+	0.397065i	$0.129971\pi$
$728$	1.66723	+	0.264063i	0.0617915	+	0.00978682i
$729$	0.587785	+	0.809017i	0.0217698	+	0.0299636i
$730$	3.95466	+	0.967096i	0.146369	+	0.0357938i
$731$	13.9072	−	10.1042i	0.514377	−	0.373717i
$732$	0.833222	+	5.26076i	0.0307968	+	0.194443i
$733$	8.22058	+	4.18860i	0.303634	+	0.154709i	0.599169	−	0.800623i	$-0.295498\pi$
$733$	8.22058	+	4.18860i	0.303634	+	0.154709i	−0.295535	+	0.955332i	$0.595498\pi$
$734$	−25.8708	−	18.7962i	−0.954909	−	0.693782i
$735$	−7.98764	−	13.1589i	−0.294628	−	0.485375i
$736$	3.72229	+	1.20945i	0.137205	+	0.0445807i
$737$	−11.9286	−	6.07790i	−0.439394	−	0.223882i
$738$	−0.959040	+	0.959040i	−0.0353028	+	0.0353028i
$739$	−39.8147			−1.46461			−0.732304	−	0.680978i	$-0.761555\pi$
$739$	−39.8147			−1.46461			−0.732304	+	0.680978i	$0.761555\pi$
$740$	−1.60448	+	3.82780i	−0.0589819	+	0.140713i
$741$	4.47589	−	3.25192i	0.164426	−	0.119462i
$742$	−0.814739	+	0.129042i	−0.0299100	+	0.00473728i
$743$	5.07780	+	5.07780i	0.186286	+	0.186286i	0.794088	−	0.607802i	$-0.207949\pi$
$743$	5.07780	+	5.07780i	0.186286	+	0.186286i	−0.607802	+	0.794088i	$0.707949\pi$
$744$	5.56587	+	0.145367i	0.204055	+	0.00532940i
$745$	1.93027	+	25.9243i	0.0707195	+	0.949794i
$746$	18.1305	+	13.1726i	0.663806	+	0.482283i
$747$	0.526454	−	3.32390i	0.0192619	−	0.121615i
$748$	12.3962	+	6.31617i	0.453249	+	0.230942i
$749$			6.39338i			0.233609i
$750$	2.47219	+	10.9036i	0.0902714	+	0.398143i
$751$	−3.56010	−	10.9568i	−0.129910	−	0.399821i	0.864854	−	0.502024i	$-0.167411\pi$
$751$	−3.56010	−	10.9568i	−0.129910	−	0.399821i	−0.994764	+	0.102203i	$0.967411\pi$
$752$	9.55655	−	4.86931i	0.348492	−	0.177565i
$753$	−5.17117	−	10.1490i	−0.188448	−	0.369850i
$754$	29.5410	−	40.6596i	1.07582	−	1.48074i
$755$	−23.8930	+	9.77892i	−0.869557	+	0.355891i
$756$	−0.200030	+	0.275318i	−0.00727503	+	0.0100132i
$757$	0.661206	−	4.17469i	0.0240320	−	0.151732i	−0.972754	−	0.231838i	$-0.925526\pi$
$757$	0.661206	−	4.17469i	0.0240320	−	0.151732i	0.996786	+	0.0801064i	$0.0255260\pi$
$758$	2.62054	+	5.14311i	0.0951824	+	0.186806i
$759$	8.04530	−	5.84525i	0.292026	−	0.212169i
$760$	−2.48554	−	0.206171i	−0.0901598	−	0.00747863i
$761$	46.8841	+	15.2336i	1.69955	+	0.552217i	0.988539	−	0.150966i	$-0.0482385\pi$
$761$	46.8841	+	15.2336i	1.69955	+	0.552217i	0.711009	+	0.703183i	$0.248238\pi$
$762$	−14.3356	−	2.27054i	−0.519326	−	0.0822531i
$763$	3.72012	−	0.589210i	0.134678	−	0.0213308i
$764$	−4.67944	+	1.52044i	−0.169296	+	0.0550077i
$765$	−2.80797	−	11.9173i	−0.101522	−	0.430871i
$766$	18.5217	+	6.01807i	0.669217	+	0.217442i
$767$	7.70066	+	15.1134i	0.278055	+	0.545713i
$768$	0.453990	−	0.891007i	0.0163820	−	0.0321514i
$769$			32.2324i			1.16233i	0.813785	+	0.581166i	$0.197403\pi$
$769$			32.2324i			1.16233i	−0.813785	+	0.581166i	$0.802597\pi$
$770$	−1.92816	+	0.143566i	−0.0694859	+	0.00517376i
$771$	−22.9338	+	7.45165i	−0.825941	+	0.268364i
$772$	−23.1950	−	3.67372i	−0.834805	−	0.132220i
$773$	3.03499	+	19.1622i	0.109161	+	0.689215i	0.980201	+	0.198004i	$0.0634458\pi$
$773$	3.03499	+	19.1622i	0.109161	+	0.689215i	−0.871040	+	0.491212i	$0.836554\pi$
$774$	−3.13947			−0.112846
$775$	5.30215	−	27.3292i	0.190459	−	0.981695i
$776$	1.03443			0.0371338
$777$	0.0988147	+	0.623892i	0.00354496	+	0.0223820i
$778$	9.23993	+	1.46346i	0.331268	+	0.0524676i
$779$	−1.43874	+	0.467475i	−0.0515482	+	0.0167490i
$780$	11.0607	−	0.823554i	0.396036	−	0.0294879i
$781$		−	19.8761i		−	0.711224i
$782$	−9.72919	+	19.0946i	−0.347915	+	0.682822i
$783$	4.59997	+	9.02795i	0.164390	+	0.322633i
$784$	6.54725	+	2.12733i	0.233830	+	0.0759761i
$785$	−3.26644	−	13.8631i	−0.116584	−	0.494796i
$786$	−12.3027	+	3.99739i	−0.438823	+	0.142582i
$787$	−27.2806	+	4.32082i	−0.972449	+	0.154021i	−0.622390	−	0.782707i	$-0.713838\pi$
$787$	−27.2806	+	4.32082i	−0.972449	+	0.154021i	−0.350059	+	0.936728i	$0.613838\pi$
$788$	23.7110	+	3.75545i	0.844669	+	0.133782i
$789$	6.53208	+	2.12240i	0.232548	+	0.0755595i
$790$	−25.8459	−	2.14388i	−0.919556	−	0.0762758i
$791$	−3.70279	+	2.69024i	−0.131656	+	0.0956538i
$792$	−1.15353	−	2.26392i	−0.0409888	−	0.0804450i
$793$	4.13294	−	26.0943i	0.146765	−	0.926637i
$794$	−5.26259	+	7.24333i	−0.186762	+	0.257056i
$795$	−5.01622	+	2.05303i	−0.177907	+	0.0728136i
$796$	6.86825	−	9.45333i	0.243439	−	0.335064i
$797$	3.09893	+	6.08199i	0.109770	+	0.215435i	0.939356	−	0.342943i	$-0.111424\pi$
$797$	3.09893	+	6.08199i	0.109770	+	0.215435i	−0.829586	+	0.558378i	$0.811424\pi$
$798$	−0.338206	+	0.172325i	−0.0119724	+	0.00610023i
$799$	18.1480	+	55.8538i	0.642030	+	1.97597i
$800$	−4.02014	−	2.97296i	−0.142133	−	0.105110i
$801$		−	0.355356i		−	0.0125559i
$802$	−18.1431	−	9.24436i	−0.640654	−	0.326430i
$803$	−0.723686	+	4.56917i	−0.0255383	+	0.161243i
$804$	−4.26269	−	3.09703i	−0.150334	−	0.109224i
$805$	−0.221144	−	2.97006i	−0.00779430	−	0.104681i
$806$	−26.0337	−	9.21701i	−0.916997	−	0.324655i
$807$	−1.98147	−	1.98147i	−0.0697512	−	0.0697512i
$808$	−1.72069	+	0.272531i	−0.0605337	+	0.00958759i
$809$	−16.3056	+	11.8467i	−0.573275	+	0.416508i	−0.836293	−	0.548282i	$-0.815282\pi$
$809$	−16.3056	+	11.8467i	−0.573275	+	0.416508i	0.263019	+	0.964791i	$0.415282\pi$
$810$	−0.864415	+	2.06223i	−0.0303724	+	0.0724593i
$811$	−7.77298			−0.272946			−0.136473	−	0.990644i	$-0.543577\pi$
$811$	−7.77298			−0.272946			−0.136473	+	0.990644i	$0.543577\pi$
$812$	−2.43820	+	2.43820i	−0.0855642	+	0.0855642i
$813$	−5.12735	−	2.61251i	−0.179824	−	0.0916249i
$814$	−4.48538	−	1.45739i	−0.157213	−	0.0510815i
$815$	24.1603	+	39.8020i	0.846298	+	1.39420i
$816$	4.42979	+	3.21843i	0.155074	+	0.112668i
$817$	−3.12005	−	1.58974i	−0.109157	−	0.0556181i
$818$	2.35876	+	14.8926i	0.0824722	+	0.520709i
$819$	1.36563	−	0.992187i	0.0477189	−	0.0346698i
$820$	−2.94594	−	0.720418i	−0.102877	−	0.0251581i
$821$	−17.6561	−	24.3015i	−0.616201	−	0.848128i	0.380868	−	0.924629i	$-0.375625\pi$
$821$	−17.6561	−	24.3015i	−0.616201	−	0.848128i	−0.997069	+	0.0765012i	$0.975625\pi$
$822$	−9.42113	−	1.49216i	−0.328600	−	0.0520451i
$823$	23.7797	−	12.1164i	0.828910	−	0.422351i	0.0125687	−	0.999921i	$-0.495999\pi$
$823$	23.7797	−	12.1164i	0.828910	−	0.422351i	0.816341	+	0.577571i	$0.195999\pi$
$824$	−3.44510	−	4.74178i	−0.120016	−	0.165188i
$825$	−12.1152	+	3.82375i	−0.421797	+	0.133126i
$826$	−0.359619	−	1.10679i	−0.0125127	−	0.0385103i
$827$	−50.8487	+	8.05364i	−1.76818	+	0.280053i	−0.953836	−	0.300327i	$-0.902904\pi$
$827$	−50.8487	+	8.05364i	−1.76818	+	0.280053i	−0.814346	+	0.580380i	$0.802904\pi$
$828$	3.48726	−	1.77685i	0.121191	−	0.0617498i
$829$	4.39888	−	13.5384i	0.152780	−	0.470207i	−0.845150	−	0.534530i	$-0.820489\pi$
$829$	4.39888	−	13.5384i	0.152780	−	0.470207i	0.997929	+	0.0643228i	$0.0204887\pi$
$830$	6.96438	−	2.85038i	0.241737	−	0.0989380i
$831$	7.81851			0.271221
$832$	−3.50738	+	3.50738i	−0.121596	+	0.121596i
$833$	−17.1130	+	33.5861i	−0.592929	+	1.16369i
$834$	−3.31038	−	4.55635i	−0.114629	−	0.157773i
$835$	−20.0761	+	4.73035i	−0.694763	+	0.163701i
$836$		−	2.83403i		−	0.0980170i
$837$	4.03845	−	3.83287i	0.139589	−	0.132483i
$838$	−5.25387	+	5.25387i	−0.181492	+	0.181492i
$839$	9.36415	−	12.8886i	0.323286	−	0.444965i	−0.616181	−	0.787605i	$-0.711321\pi$
$839$	9.36415	−	12.8886i	0.323286	−	0.444965i	0.939467	+	0.342639i	$0.111321\pi$
$840$	−0.758356	−	0.0629045i	−0.0261658	−	0.00217041i
$841$	22.7633	+	70.0582i	0.784941	+	2.41580i
$842$	−4.89847	−	4.89847i	−0.168813	−	0.168813i
$843$	22.5923	+	22.5923i	0.778120	+	0.778120i
$844$	18.0287	−	5.85787i	0.620573	−	0.201636i
$845$	−25.2034	−	6.16337i	−0.867022	−	0.212027i
$846$	3.31438	−	10.2006i	0.113951	−	0.350705i
$847$	0.241908	+	1.52735i	0.00831206	+	0.0524803i
$848$	1.10045	−	2.15975i	0.0377895	−	0.0741660i
$849$	−17.4459	−	12.6752i	−0.598741	−	0.435011i
$850$	19.5216	−	19.1949i	0.669585	−	0.658378i
$851$	2.24491	−	6.90912i	0.0769545	−	0.236841i
$852$	1.22372	−	7.72629i	0.0419241	−	0.264698i
$853$	−6.04076	+	38.1398i	−0.206832	+	1.30588i	0.637662	+	0.770317i	$0.279902\pi$
$853$	−6.04076	+	38.1398i	−0.206832	+	1.30588i	−0.844493	+	0.535566i	$0.820098\pi$
$854$	−0.560129	+	1.72390i	−0.0191672	+	0.0589906i
$855$	−1.90332	+	1.61175i	−0.0650923	+	0.0551208i
$856$	−15.1989	−	11.0426i	−0.519487	−	0.377429i
$857$	−1.37471	+	2.69802i	−0.0469591	+	0.0921625i	−0.913294	−	0.407302i	$-0.866470\pi$
$857$	−1.37471	+	2.69802i	−0.0469591	+	0.0921625i	0.866335	+	0.499464i	$0.166470\pi$
$858$	1.97156	+	12.4480i	0.0673081	+	0.424967i
$859$	−3.26552	+	10.0502i	−0.111418	+	0.342910i	−0.991183	−	0.132499i	$-0.957700\pi$
$859$	−3.26552	+	10.0502i	−0.111418	+	0.342910i	0.879765	+	0.475409i	$0.157700\pi$
$860$	−3.64269	−	6.00102i	−0.124215	−	0.204633i
$861$	−0.438970	+	0.142630i	−0.0149601	+	0.00486082i
$862$	−15.2331	−	15.2331i	−0.518842	−	0.518842i
$863$	−18.1794	−	18.1794i	−0.618833	−	0.618833i	0.326399	−	0.945232i	$-0.394165\pi$
$863$	−18.1794	−	18.1794i	−0.618833	−	0.618833i	−0.945232	+	0.326399i	$0.894165\pi$
$864$	−0.309017	−	0.951057i	−0.0105130	−	0.0323556i
$865$	1.01727	−	12.2638i	0.0345881	−	0.416983i
$866$	−10.0782	+	13.8714i	−0.342470	+	0.471369i
$867$	−9.17924	+	9.17924i	−0.311743	+	0.311743i
$868$	1.66522	+	0.903995i	0.0565214	+	0.0306836i
$869$		−	29.4698i		−	0.999693i
$870$	−11.9194	+	19.2677i	−0.404106	+	0.653238i
$871$	15.3618	+	21.1437i	0.520515	+	0.716428i
$872$	−5.02467	+	9.86146i	−0.170157	+	0.333951i
$873$	0.731450	−	0.731450i	0.0247558	−	0.0247558i
$874$	4.36544			0.147663
$875$	−0.934970	+	3.68814i	−0.0316078	+	0.124682i
$876$	−0.562625	+	1.73158i	−0.0190093	+	0.0585048i
$877$	−36.0935	+	18.3906i	−1.21879	+	0.621006i	−0.940599	−	0.339519i	$-0.889736\pi$
$877$	−36.0935	+	18.3906i	−1.21879	+	0.621006i	−0.278193	+	0.960525i	$0.589736\pi$
$878$	21.3160	−	3.37613i	0.719381	−	0.113939i
$879$	−9.23515	−	28.4229i	−0.311494	−	0.958679i
$880$	2.98901	−	4.83174i	0.100759	−	0.162878i
$881$	−26.1657	−	36.0141i	−0.881546	−	1.21334i	−0.975990	−	0.217814i	$-0.930107\pi$
$881$	−26.1657	−	36.0141i	−0.881546	−	1.21334i	0.0944438	−	0.995530i	$-0.469893\pi$
$882$	6.13386	−	3.12536i	0.206538	−	0.105236i
$883$	12.0174	+	1.90337i	0.404417	+	0.0640534i	0.355330	−	0.934741i	$-0.384369\pi$
$883$	12.0174	+	1.90337i	0.404417	+	0.0640534i	0.0490876	+	0.998794i	$0.484369\pi$
$884$	−15.9640	−	21.9726i	−0.536928	−	0.739018i
$885$	−3.96779	−	6.53660i	−0.133376	−	0.219725i
$886$	−24.8051	+	18.0220i	−0.833345	+	0.605461i
$887$	−3.62309	−	22.8753i	−0.121652	−	0.768078i	−0.970794	−	0.239914i	$-0.922881\pi$
$887$	−3.62309	−	22.8753i	−0.121652	−	0.768078i	0.849142	−	0.528164i	$-0.177119\pi$
$888$	−1.65384	−	0.842673i	−0.0554992	−	0.0282783i
$889$	−3.99606	−	2.90331i	−0.134024	−	0.0973738i
$890$	0.679253	−	0.412315i	0.0227686	−	0.0138208i
$891$	−2.41650	−	0.785169i	−0.0809559	−	0.0263042i
$892$	−17.1813	−	8.75429i	−0.575271	−	0.293115i
$893$	8.45920	−	8.45920i	0.283076	−	0.283076i
$894$	−11.6258			−0.388825
$895$	−13.2706	−	32.4244i	−0.443588	−	1.08383i
$896$	0.275318	−	0.200030i	0.00919773	−	0.00668254i
$897$	−19.1744	+	3.03692i	−0.640214	+	0.101400i
$898$	−24.2010	−	24.2010i	−0.807598	−	0.807598i
$899$	46.4903	−	31.9566i	1.55054	−	1.06581i
$900$	−4.94487	+	0.740472i	−0.164829	+	0.0246824i
$901$	10.7376	+	7.80129i	0.357720	+	0.259899i
$902$	0.539095	−	3.40371i	0.0179499	−	0.113331i
$903$	−0.951950	−	0.485043i	−0.0316789	−	0.0161412i
$904$		−	13.4491i		−	0.447312i
$905$	−2.52807	−	33.9531i	−0.0840358	−	1.12864i
$906$	−3.56779	−	10.9805i	−0.118532	−	0.364803i
$907$	51.2602	−	26.1184i	1.70207	−	0.867246i	0.716576	−	0.697509i	$-0.245708\pi$
$907$	51.2602	−	26.1184i	1.70207	−	0.867246i	0.985489	−	0.169736i	$-0.0542917\pi$
$908$	12.3333	+	24.2054i	0.409295	+	0.803286i
$909$	−1.02400	+	1.40942i	−0.0339641	+	0.0467475i
$910$	3.48106	+	1.45914i	0.115396	+	0.0483700i
$911$	4.15830	−	5.72341i	0.137771	−	0.189625i	−0.734557	−	0.678547i	$-0.762610\pi$
$911$	4.15830	−	5.72341i	0.137771	−	0.189625i	0.872327	+	0.488922i	$0.162610\pi$
$912$	0.174484	−	1.10165i	0.00577775	−	0.0364793i
$913$	3.88200	+	7.61885i	0.128475	+	0.252147i
$914$	−18.3240	+	13.3132i	−0.606105	+	0.440361i
$915$	−0.984540	+	11.8693i	−0.0325479	+	0.392386i
$916$	−9.95094	−	3.23325i	−0.328788	−	0.106830i
$917$	−4.34802	−	0.688658i	−0.143584	−	0.0227415i
$918$	5.40811	−	0.856561i	0.178494	−	0.0282707i
$919$	−40.3165	+	13.0996i	−1.32992	+	0.432117i	−0.885890	−	0.463896i	$-0.846451\pi$
$919$	−40.3165	+	13.0996i	−1.32992	+	0.432117i	−0.444029	+	0.896012i	$0.646451\pi$
$920$	7.44263	+	4.60416i	0.245376	+	0.151795i
$921$	7.34500	+	2.38654i	0.242026	+	0.0786390i
$922$	−14.9699	−	29.3801i	−0.493008	−	0.967583i
$923$	−17.6155	+	34.5724i	−0.579822	+	1.13796i
$924$		−	0.864685i		−	0.0284460i
$925$	−5.51824	+	7.46197i	−0.181439	+	0.245348i
$926$	−8.36578	+	2.71821i	−0.274916	+	0.0893258i
$927$	−5.78900	−	0.916888i	−0.190136	−	0.0301145i
$928$	−1.58504	−	10.0076i	−0.0520315	−	0.328514i
$929$	9.15970			0.300520			0.150260	−	0.988647i	$-0.451989\pi$
$929$	9.15970			0.300520			0.150260	+	0.988647i	$0.451989\pi$
$930$	12.0122	+	3.27216i	0.393896	+	0.107298i
$931$	7.67850			0.251653
$932$	2.18912	+	13.8215i	0.0717069	+	0.452740i
$933$	−7.22400	−	1.14417i	−0.236503	−	0.0374584i
$934$	10.7686	−	3.49892i	0.352358	−	0.114488i
$935$	23.5703	+	20.3036i	0.770832	+	0.663998i
$936$			4.96018i			0.162129i
$937$	−15.0232	+	29.4848i	−0.490788	+	0.963226i	0.504234	+	0.863567i	$0.331775\pi$
$937$	−15.0232	+	29.4848i	−0.490788	+	0.963226i	−0.995022	+	0.0996585i	$0.968225\pi$
$938$	−0.814048	−	1.59766i	−0.0265796	−	0.0521654i
$939$	8.72432	+	2.83470i	0.284707	+	0.0925071i
$940$	23.3439	−	5.50030i	0.761393	−	0.179400i
$941$	−55.8702	+	18.1533i	−1.82132	+	0.591781i	−0.821549	+	0.570137i	$0.806890\pi$
$941$	−55.8702	+	18.1533i	−1.82132	+	0.591781i	−0.999766	+	0.0216440i	$0.993110\pi$
$942$	6.29113	−	0.996417i	0.204976	−	0.0324650i
$943$	5.24295	+	0.830402i	0.170734	+	0.0270416i
$944$	3.25229	+	1.05673i	0.105853	+	0.0343938i
$945$	−0.580719	+	0.491758i	−0.0188908	+	0.0159969i
$946$	6.45349	−	4.68874i	0.209821	−	0.152444i
$947$	−1.58531	−	3.11134i	−0.0515155	−	0.101105i	0.863814	−	0.503812i	$-0.168069\pi$
$947$	−1.58531	−	3.11134i	−0.0515155	−	0.101105i	−0.915329	+	0.402707i	$0.868069\pi$
$948$	1.81438	−	11.4555i	0.0589283	−	0.372059i
$949$	5.30827	−	7.30621i	0.172314	−	0.237170i
$950$	−5.28923	−	1.76806i	−0.171605	−	0.0573633i
$951$	7.61021	−	10.4746i	0.246778	−	0.339661i
$952$	0.845960	+	1.66029i	0.0274177	+	0.0538103i
$953$	−19.3232	+	9.84566i	−0.625940	+	0.318932i	−0.738032	−	0.674766i	$-0.764245\pi$
$953$	−19.3232	+	9.84566i	−0.625940	+	0.318932i	0.112092	+	0.993698i	$0.464245\pi$
$954$	−0.749039	−	2.30530i	−0.0242510	−	0.0746370i
$955$	−10.9717	+	0.816924i	−0.355034	+	0.0264350i
$956$		−	0.353295i		−	0.0114264i
$957$	−22.9388	−	11.6879i	−0.741505	−	0.377816i
$958$	3.83826	−	24.2338i	0.124009	−	0.782960i
$959$	−2.62614	−	1.90800i	−0.0848024	−	0.0616126i
$960$	1.45937	−	1.69418i	0.0471010	−	0.0546793i
$961$	−24.0942	−	19.5056i	−0.777232	−	0.629214i
$962$	6.51021	+	6.51021i	0.209898	+	0.209898i
$963$	−18.5555	+	2.93891i	−0.597944	+	0.0947050i
$964$	21.9609	−	15.9555i	0.707312	−	0.513892i
$965$	−48.4295	−	20.3000i	−1.55900	−	0.653480i
$966$	1.33193			0.0428541
$967$	13.7802	−	13.7802i	0.443142	−	0.443142i	−0.449925	−	0.893067i	$-0.648549\pi$
$967$	13.7802	−	13.7802i	0.443142	−	0.443142i	0.893067	+	0.449925i	$0.148549\pi$
$968$	−4.04876	−	2.06295i	−0.130132	−	0.0663056i
$969$	5.80840	+	1.88726i	0.186593	+	0.0606276i
$970$	2.24684	+	0.549455i	0.0721417	+	0.0176419i
$971$	−32.0048	−	23.2528i	−1.02708	−	0.746219i	−0.0593597	−	0.998237i	$-0.518906\pi$
$971$	−32.0048	−	23.2528i	−1.02708	−	0.746219i	−0.967723	+	0.252018i	$0.918906\pi$
$972$	−0.891007	−	0.453990i	−0.0285790	−	0.0145618i
$973$	−0.299826	−	1.89302i	−0.00961197	−	0.0606876i
$974$	−3.87258	+	2.81360i	−0.124086	+	0.0901534i
$975$	24.4620	+	4.08628i	0.783410	+	0.130866i
$976$	−3.13074	−	4.30909i	−0.100213	−	0.137931i
$977$	49.9593	+	7.91277i	1.59834	+	0.253152i	0.891095	−	0.453818i	$-0.149938\pi$
$977$	49.9593	+	7.91277i	1.59834	+	0.253152i	0.707244	+	0.706970i	$0.249938\pi$
$978$	−18.5531	+	9.45329i	−0.593264	+	0.302283i
$979$	0.530716	+	0.730469i	0.0169618	+	0.0233459i
$980$	13.0911	+	8.09839i	0.418179	+	0.258694i
$981$	3.42013	+	10.5261i	0.109196	+	0.336072i
$982$	−18.0151	+	2.85332i	−0.574886	+	0.0910530i
$983$	39.0518	−	19.8979i	1.24556	−	0.634645i	0.298105	−	0.954533i	$-0.403645\pi$
$983$	39.0518	−	19.8979i	1.24556	−	0.634645i	0.947455	+	0.319888i	$0.103645\pi$
$984$	0.419116	−	1.28991i	0.0133609	−	0.0411207i
$985$	49.5070	+	20.7516i	1.57742	+	0.661201i
$986$	55.4797			1.76683
$987$	2.58097	−	2.58097i	0.0821531	−	0.0821531i
$988$	−2.51170	+	4.92950i	−0.0799079	+	0.156828i
$989$	7.22236	+	9.94072i	0.229658	+	0.316097i
$990$	−1.30301	−	5.53010i	−0.0414123	−	0.175758i
$991$		−	32.5456i		−	1.03385i	−0.856032	−	0.516923i	$-0.827077\pi$
$991$		−	32.5456i		−	1.03385i	0.856032	−	0.516923i	$-0.172923\pi$
$992$	−5.02522	+	2.39733i	−0.159551	+	0.0761152i
$993$	11.4383	−	11.4383i	0.362984	−	0.362984i
$994$	1.56476	−	2.15370i	0.0496310	−	0.0683113i
$995$	19.9396	−	16.8850i	0.632127	−	0.535292i
$996$	1.03994	+	3.20062i	0.0329519	+	0.101416i
$997$	11.6059	+	11.6059i	0.367564	+	0.367564i	0.866588	−	0.499024i	$-0.166308\pi$
$997$	11.6059	+	11.6059i	0.367564	+	0.367564i	−0.499024	+	0.866588i	$0.666308\pi$
$998$	7.50071	+	7.50071i	0.237431	+	0.237431i
$999$	−1.76530	+	0.573581i	−0.0558516	+	0.0181473i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bj.a.277.1	✓	128
5.3	odd	4		930.2.bj.b.463.1	yes	128
31.15	odd	10		930.2.bj.b.697.1	yes	128
155.108	even	20	inner	930.2.bj.a.883.1	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bj.a.277.1	✓	128	1.1	even	1	trivial
930.2.bj.a.883.1	yes	128	155.108	even	20	inner
930.2.bj.b.463.1	yes	128	5.3	odd	4
930.2.bj.b.697.1	yes	128	31.15	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 - 0.987688i) q^{2} +(0.987688 + 0.156434i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-2.22990 + 0.166033i) q^{5} -1.00000i q^{6} +(0.154498 - 0.303220i) q^{7} +(0.453990 + 0.891007i) q^{8} +(0.951057 + 0.309017i) q^{9} +O(q^{10})\)	\(q+(-0.156434 - 0.987688i) q^{2} +(0.987688 + 0.156434i) q^{3} +(-0.951057 + 0.309017i) q^{4} +(-2.22990 + 0.166033i) q^{5} -1.00000i q^{6} +(0.154498 - 0.303220i) q^{7} +(0.453990 + 0.891007i) q^{8} +(0.951057 + 0.309017i) q^{9} +(0.512821 + 2.17647i) q^{10} +(-2.41650 + 0.785169i) q^{11} +(-0.987688 + 0.156434i) q^{12} +(4.89912 + 0.775944i) q^{13} +(-0.323656 - 0.105162i) q^{14} +(-2.22841 - 0.184844i) q^{15} +(0.809017 - 0.587785i) q^{16} +(2.48584 + 4.87873i) q^{17} +(0.156434 - 0.987688i) q^{18} +(0.655605 - 0.902363i) q^{19} +(2.06945 - 0.846982i) q^{20} +(0.200030 - 0.275318i) q^{21} +(1.15353 + 2.26392i) q^{22} +(-3.48726 + 1.77685i) q^{23} +(0.309017 + 0.951057i) q^{24} +(4.94487 - 0.740472i) q^{25} -4.96018i q^{26} +(0.891007 + 0.453990i) q^{27} +(-0.0532365 + 0.336122i) q^{28} +(8.19721 + 5.95562i) q^{29} +(0.166033 + 2.22990i) q^{30} +(1.85820 - 5.24853i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-2.50958 + 0.397478i) q^{33} +(4.42979 - 3.21843i) q^{34} +(-0.294171 + 0.701801i) q^{35} -1.00000 q^{36} +(-1.31249 + 1.31249i) q^{37} +(-0.993813 - 0.506373i) q^{38} +(4.71741 + 1.53278i) q^{39} +(-1.16029 - 1.91147i) q^{40} +(-1.09726 - 0.797206i) q^{41} +(-0.303220 - 0.154498i) q^{42} +(-0.491121 - 3.10082i) q^{43} +(2.05560 - 1.49348i) q^{44} +(-2.17206 - 0.531169i) q^{45} +(2.30050 + 3.16637i) q^{46} +(10.5935 + 1.67785i) q^{47} +(0.891007 - 0.453990i) q^{48} +(4.04642 + 5.56943i) q^{49} +(-1.50490 - 4.76815i) q^{50} +(1.69203 + 5.20754i) q^{51} +(-4.89912 + 0.775944i) q^{52} +(2.15975 - 1.10045i) q^{53} +(0.309017 - 0.951057i) q^{54} +(5.25818 - 2.15206i) q^{55} +0.340312 q^{56} +(0.788695 - 0.788695i) q^{57} +(4.59997 - 9.02795i) q^{58} +(2.01003 + 2.76657i) q^{59} +(2.17647 - 0.512821i) q^{60} -5.32633i q^{61} +(-5.47460 - 1.01427i) q^{62} +(0.240637 - 0.240637i) q^{63} +(-0.587785 + 0.809017i) q^{64} +(-11.0533 - 0.916859i) q^{65} +(0.785169 + 2.41650i) q^{66} +(3.72573 + 3.72573i) q^{67} +(-3.87178 - 3.87178i) q^{68} +(-3.72229 + 1.20945i) q^{69} +(0.739179 + 0.180763i) q^{70} +(-2.41732 + 7.43973i) q^{71} +(0.156434 + 0.987688i) q^{72} +(0.826578 - 1.62225i) q^{73} +(1.50165 + 1.09102i) q^{74} +(4.99982 + 0.0421920i) q^{75} +(-0.344672 + 1.06079i) q^{76} +(-0.135266 + 0.854039i) q^{77} +(0.775944 - 4.89912i) q^{78} +(-3.58408 + 11.0307i) q^{79} +(-1.70643 + 1.44502i) q^{80} +(0.809017 + 0.587785i) q^{81} +(-0.615742 + 1.20846i) q^{82} +(-0.526454 - 3.32390i) q^{83} +(-0.105162 + 0.323656i) q^{84} +(-6.35319 - 10.4663i) q^{85} +(-2.98581 + 0.970150i) q^{86} +(7.16462 + 7.16462i) q^{87} +(-1.79666 - 1.79666i) q^{88} +(-0.109811 - 0.337963i) q^{89} +(-0.184844 + 2.22841i) q^{90} +(0.992187 - 1.36563i) q^{91} +(2.76751 - 2.76751i) q^{92} +(2.65637 - 4.89323i) q^{93} -10.7256i q^{94} +(-1.31211 + 2.12103i) q^{95} +(-0.587785 - 0.809017i) q^{96} +(0.469620 - 0.921681i) q^{97} +(4.86786 - 4.86786i) q^{98} -2.54086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{7}+O(q^{10}) \) 128 * q - 16 * q^7	\( 128 q - 16 q^{7} - 4 q^{10} + 4 q^{15} + 32 q^{16} - 12 q^{17} - 40 q^{19} + 40 q^{21} + 16 q^{22} - 32 q^{24} - 8 q^{25} - 4 q^{28} + 8 q^{29} + 20 q^{31} + 4 q^{33} + 24 q^{35} - 128 q^{36} + 64 q^{37} - 16 q^{38} - 24 q^{41} + 4 q^{42} + 24 q^{43} - 8 q^{44} + 20 q^{46} + 108 q^{47} - 100 q^{49} - 24 q^{50} + 16 q^{53} - 32 q^{54} + 12 q^{55} + 16 q^{57} - 40 q^{58} - 16 q^{62} - 4 q^{63} + 36 q^{65} - 12 q^{66} - 32 q^{67} + 8 q^{68} - 32 q^{70} + 24 q^{71} + 60 q^{73} - 16 q^{74} + 24 q^{75} - 24 q^{76} - 20 q^{77} - 56 q^{79} + 32 q^{81} - 16 q^{82} - 8 q^{83} - 132 q^{85} - 20 q^{87} - 4 q^{88} + 136 q^{89} - 40 q^{91} - 64 q^{93} + 108 q^{95} + 64 q^{97} - 16 q^{98} - 8 q^{99}+O(q^{100}) \) 128 * q - 16 * q^7 - 4 * q^10 + 4 * q^15 + 32 * q^16 - 12 * q^17 - 40 * q^19 + 40 * q^21 + 16 * q^22 - 32 * q^24 - 8 * q^25 - 4 * q^28 + 8 * q^29 + 20 * q^31 + 4 * q^33 + 24 * q^35 - 128 * q^36 + 64 * q^37 - 16 * q^38 - 24 * q^41 + 4 * q^42 + 24 * q^43 - 8 * q^44 + 20 * q^46 + 108 * q^47 - 100 * q^49 - 24 * q^50 + 16 * q^53 - 32 * q^54 + 12 * q^55 + 16 * q^57 - 40 * q^58 - 16 * q^62 - 4 * q^63 + 36 * q^65 - 12 * q^66 - 32 * q^67 + 8 * q^68 - 32 * q^70 + 24 * q^71 + 60 * q^73 - 16 * q^74 + 24 * q^75 - 24 * q^76 - 20 * q^77 - 56 * q^79 + 32 * q^81 - 16 * q^82 - 8 * q^83 - 132 * q^85 - 20 * q^87 - 4 * q^88 + 136 * q^89 - 40 * q^91 - 64 * q^93 + 108 * q^95 + 64 * q^97 - 16 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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