LMFDB - Embedded newform 403.2.be.a.398.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(57,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 2]))

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

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

chi := DirichletCharacter("403.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.be (of order $12$, degree $4$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			398.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	403.398
Dual form			403.2.be.a.161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 0.366025i) q^{2} +(2.36603 + 1.36603i) q^{3} -1.73205i q^{4} +(0.366025 - 1.36603i) q^{5} +(0.366025 + 1.36603i) q^{6} +(-0.767949 - 2.86603i) q^{7} +(1.36603 - 1.36603i) q^{8} +(2.23205 + 3.86603i) q^{9} +O(q^{10})$	\(q+(0.366025 + 0.366025i) q^{2} +(2.36603 + 1.36603i) q^{3} -1.73205i q^{4} +(0.366025 - 1.36603i) q^{5} +(0.366025 + 1.36603i) q^{6} +(-0.767949 - 2.86603i) q^{7} +(1.36603 - 1.36603i) q^{8} +(2.23205 + 3.86603i) q^{9} +(0.633975 - 0.366025i) q^{10} +(-0.232051 + 0.866025i) q^{11} +(2.36603 - 4.09808i) q^{12} +(-1.59808 + 3.23205i) q^{13} +(0.767949 - 1.33013i) q^{14} +(2.73205 - 2.73205i) q^{15} -2.46410 q^{16} +(-0.598076 + 2.23205i) q^{18} +(4.96410 - 1.33013i) q^{19} +(-2.36603 - 0.633975i) q^{20} +(2.09808 - 7.83013i) q^{21} +(-0.401924 + 0.232051i) q^{22} -6.19615 q^{23} +(5.09808 - 1.36603i) q^{24} +(2.59808 + 1.50000i) q^{25} +(-1.76795 + 0.598076i) q^{26} +4.00000i q^{27} +(-4.96410 + 1.33013i) q^{28} +8.46410i q^{29} +2.00000 q^{30} +(4.33013 + 3.50000i) q^{31} +(-3.63397 - 3.63397i) q^{32} +(-1.73205 + 1.73205i) q^{33} -4.19615 q^{35} +(6.69615 - 3.86603i) q^{36} +(-4.73205 + 1.26795i) q^{37} +(2.30385 + 1.33013i) q^{38} +(-8.19615 + 5.46410i) q^{39} +(-1.36603 - 2.36603i) q^{40} +(-1.53590 + 5.73205i) q^{41} +(3.63397 - 2.09808i) q^{42} +(-2.09808 + 3.63397i) q^{43} +(1.50000 + 0.401924i) q^{44} +(6.09808 - 1.63397i) q^{45} +(-2.26795 - 2.26795i) q^{46} +(1.53590 - 1.53590i) q^{47} +(-5.83013 - 3.36603i) q^{48} +(-1.56218 + 0.901924i) q^{49} +(0.401924 + 1.50000i) q^{50} +(5.59808 + 2.76795i) q^{52} +(-5.76795 + 3.33013i) q^{53} +(-1.46410 + 1.46410i) q^{54} +(1.09808 + 0.633975i) q^{55} +(-4.96410 - 2.86603i) q^{56} +(13.5622 + 3.63397i) q^{57} +(-3.09808 + 3.09808i) q^{58} +(0.562178 + 2.09808i) q^{59} +(-4.73205 - 4.73205i) q^{60} -3.19615i q^{61} +(0.303848 + 2.86603i) q^{62} +(9.36603 - 9.36603i) q^{63} +2.26795i q^{64} +(3.83013 + 3.36603i) q^{65} -1.26795 q^{66} +(2.86603 - 10.6962i) q^{67} +(-14.6603 - 8.46410i) q^{69} +(-1.53590 - 1.53590i) q^{70} +(-0.330127 + 1.23205i) q^{71} +(8.33013 + 2.23205i) q^{72} +(2.83013 - 10.5622i) q^{73} +(-2.19615 - 1.26795i) q^{74} +(4.09808 + 7.09808i) q^{75} +(-2.30385 - 8.59808i) q^{76} +2.66025 q^{77} +(-5.00000 - 1.00000i) q^{78} +(-10.7321 - 6.19615i) q^{79} +(-0.901924 + 3.36603i) q^{80} +(1.23205 - 2.13397i) q^{81} +(-2.66025 + 1.53590i) q^{82} +(15.5622 + 4.16987i) q^{83} +(-13.5622 - 3.63397i) q^{84} +(-2.09808 + 0.562178i) q^{86} +(-11.5622 + 20.0263i) q^{87} +(0.866025 + 1.50000i) q^{88} +(-2.26795 - 2.26795i) q^{89} +(2.83013 + 1.63397i) q^{90} +(10.4904 + 2.09808i) q^{91} +10.7321i q^{92} +(5.46410 + 14.1962i) q^{93} +1.12436 q^{94} -7.26795i q^{95} +(-3.63397 - 13.5622i) q^{96} +(-8.46410 - 8.46410i) q^{97} +(-0.901924 - 0.241670i) q^{98} +(-3.86603 + 1.03590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{3} - 2 q^{5} - 2 q^{6} - 10 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 - 2 * q^6 - 10 * q^7 + 2 * q^8 + 2 * q^9	$ 4 q - 2 q^{2} + 6 q^{3} - 2 q^{5} - 2 q^{6} - 10 q^{7} + 2 q^{8} + 2 q^{9} + 6 q^{10} + 6 q^{11} + 6 q^{12} + 4 q^{13} + 10 q^{14} + 4 q^{15} + 4 q^{16} + 8 q^{18} + 6 q^{19} - 6 q^{20} - 2 q^{21} - 12 q^{22} - 4 q^{23} + 10 q^{24} - 14 q^{26} - 6 q^{28} + 8 q^{30} - 18 q^{32} + 4 q^{35} + 6 q^{36} - 12 q^{37} + 30 q^{38} - 12 q^{39} - 2 q^{40} - 20 q^{41} + 18 q^{42} + 2 q^{43} + 6 q^{44} + 14 q^{45} - 16 q^{46} + 20 q^{47} - 6 q^{48} + 18 q^{49} + 12 q^{50} + 12 q^{52} - 30 q^{53} + 8 q^{54} - 6 q^{55} - 6 q^{56} + 30 q^{57} - 2 q^{58} - 22 q^{59} - 12 q^{60} + 22 q^{62} + 34 q^{63} - 2 q^{65} - 12 q^{66} + 8 q^{67} - 24 q^{69} - 20 q^{70} + 16 q^{71} + 16 q^{72} - 6 q^{73} + 12 q^{74} + 6 q^{75} - 30 q^{76} - 24 q^{77} - 20 q^{78} - 36 q^{79} - 14 q^{80} - 2 q^{81} + 24 q^{82} + 38 q^{83} - 30 q^{84} + 2 q^{86} - 22 q^{87} - 16 q^{89} - 6 q^{90} - 10 q^{91} + 8 q^{93} - 44 q^{94} - 18 q^{96} - 20 q^{97} - 14 q^{98} - 12 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 - 2 * q^6 - 10 * q^7 + 2 * q^8 + 2 * q^9 + 6 * q^10 + 6 * q^11 + 6 * q^12 + 4 * q^13 + 10 * q^14 + 4 * q^15 + 4 * q^16 + 8 * q^18 + 6 * q^19 - 6 * q^20 - 2 * q^21 - 12 * q^22 - 4 * q^23 + 10 * q^24 - 14 * q^26 - 6 * q^28 + 8 * q^30 - 18 * q^32 + 4 * q^35 + 6 * q^36 - 12 * q^37 + 30 * q^38 - 12 * q^39 - 2 * q^40 - 20 * q^41 + 18 * q^42 + 2 * q^43 + 6 * q^44 + 14 * q^45 - 16 * q^46 + 20 * q^47 - 6 * q^48 + 18 * q^49 + 12 * q^50 + 12 * q^52 - 30 * q^53 + 8 * q^54 - 6 * q^55 - 6 * q^56 + 30 * q^57 - 2 * q^58 - 22 * q^59 - 12 * q^60 + 22 * q^62 + 34 * q^63 - 2 * q^65 - 12 * q^66 + 8 * q^67 - 24 * q^69 - 20 * q^70 + 16 * q^71 + 16 * q^72 - 6 * q^73 + 12 * q^74 + 6 * q^75 - 30 * q^76 - 24 * q^77 - 20 * q^78 - 36 * q^79 - 14 * q^80 - 2 * q^81 + 24 * q^82 + 38 * q^83 - 30 * q^84 + 2 * q^86 - 22 * q^87 - 16 * q^89 - 6 * q^90 - 10 * q^91 + 8 * q^93 - 44 * q^94 - 18 * q^96 - 20 * q^97 - 14 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.366025	+	0.366025i	0.258819	+	0.258819i	0.824574	−	0.565755i	$-0.191415\pi$
$2$	0.366025	+	0.366025i	0.258819	+	0.258819i	−0.565755	+	0.824574i	$0.691415\pi$
$3$	2.36603	+	1.36603i	1.36603	+	0.788675i	0.990418	−	0.138104i	$-0.0441007\pi$
$3$	2.36603	+	1.36603i	1.36603	+	0.788675i	0.375608	+	0.926779i	$0.377434\pi$
$4$		−	1.73205i		−	0.866025i
$5$	0.366025	−	1.36603i	0.163692	−	0.610905i	−0.834512	−	0.550990i	$-0.814250\pi$
$5$	0.366025	−	1.36603i	0.163692	−	0.610905i	0.998203	−	0.0599153i	$-0.0190830\pi$
$6$	0.366025	+	1.36603i	0.149429	+	0.557678i
$7$	−0.767949	−	2.86603i	−0.290258	−	1.08326i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−0.767949	−	2.86603i	−0.290258	−	1.08326i	0.654654	−	0.755929i	$-0.272814\pi$
$8$	1.36603	−	1.36603i	0.482963	−	0.482963i
$9$	2.23205	+	3.86603i	0.744017	+	1.28868i
$10$	0.633975	−	0.366025i	0.200480	−	0.115747i
$11$	−0.232051	+	0.866025i	−0.0699660	+	0.261116i	−0.992045	−	0.125886i	$-0.959823\pi$
$11$	−0.232051	+	0.866025i	−0.0699660	+	0.261116i	0.922079	+	0.387002i	$0.126489\pi$
$12$	2.36603	−	4.09808i	0.683013	−	1.18301i
$13$	−1.59808	+	3.23205i	−0.443227	+	0.896410i
$13$	−1.59808	+	3.23205i	−0.443227	+	0.896410i
$14$	0.767949	−	1.33013i	0.205243	−	0.355491i
$15$	2.73205	−	2.73205i	0.705412	−	0.705412i
$16$	−2.46410			−0.616025
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−0.598076	+	2.23205i	−0.140968	+	0.526099i
$19$	4.96410	−	1.33013i	1.13884	−	0.305152i	0.360357	−	0.932814i	$-0.382655\pi$
$19$	4.96410	−	1.33013i	1.13884	−	0.305152i	0.778486	+	0.627662i	$0.215988\pi$
$20$	−2.36603	−	0.633975i	−0.529059	−	0.141761i
$21$	2.09808	−	7.83013i	0.457838	−	1.70867i
$22$	−0.401924	+	0.232051i	−0.0856904	+	0.0494734i
$23$	−6.19615			−1.29199			−0.645994	−	0.763343i	$-0.723557\pi$
$23$	−6.19615			−1.29199			−0.645994	+	0.763343i	$0.723557\pi$
$24$	5.09808	−	1.36603i	1.04064	−	0.278839i
$25$	2.59808	+	1.50000i	0.519615	+	0.300000i
$26$	−1.76795	+	0.598076i	−0.346723	+	0.117292i
$27$			4.00000i			0.769800i
$28$	−4.96410	+	1.33013i	−0.938127	+	0.251370i
$29$			8.46410i			1.57174i	0.618389	+	0.785872i	$0.287786\pi$
$29$			8.46410i			1.57174i	−0.618389	+	0.785872i	$0.712214\pi$
$30$	2.00000			0.365148
$31$	4.33013	+	3.50000i	0.777714	+	0.628619i
$31$	4.33013	+	3.50000i	0.777714	+	0.628619i
$32$	−3.63397	−	3.63397i	−0.642402	−	0.642402i
$33$	−1.73205	+	1.73205i	−0.301511	+	0.301511i
$34$		0			0
$35$	−4.19615			−0.709279
$36$	6.69615	−	3.86603i	1.11603	−	0.644338i
$37$	−4.73205	+	1.26795i	−0.777944	+	0.208450i	−0.625878	−	0.779921i	$-0.715259\pi$
$37$	−4.73205	+	1.26795i	−0.777944	+	0.208450i	−0.152066	+	0.988370i	$0.548593\pi$
$38$	2.30385	+	1.33013i	0.373733	+	0.215775i
$39$	−8.19615	+	5.46410i	−1.31243	+	0.874957i
$40$	−1.36603	−	2.36603i	−0.215988	−	0.374101i
$41$	−1.53590	+	5.73205i	−0.239867	+	0.895196i	0.736027	+	0.676952i	$0.236700\pi$
$41$	−1.53590	+	5.73205i	−0.239867	+	0.895196i	−0.975894	+	0.218244i	$0.929967\pi$
$42$	3.63397	−	2.09808i	0.560734	−	0.323740i
$43$	−2.09808	+	3.63397i	−0.319954	+	0.554176i	−0.980478	−	0.196629i	$-0.937001\pi$
$43$	−2.09808	+	3.63397i	−0.319954	+	0.554176i	0.660524	+	0.750805i	$0.270334\pi$
$44$	1.50000	+	0.401924i	0.226134	+	0.0605923i
$45$	6.09808	−	1.63397i	0.909048	−	0.243579i
$46$	−2.26795	−	2.26795i	−0.334391	−	0.334391i
$47$	1.53590	−	1.53590i	0.224034	−	0.224034i	−0.586161	−	0.810195i	$-0.699361\pi$
$47$	1.53590	−	1.53590i	0.224034	−	0.224034i	0.810195	+	0.586161i	$0.199361\pi$
$48$	−5.83013	−	3.36603i	−0.841506	−	0.485844i
$49$	−1.56218	+	0.901924i	−0.223168	+	0.128846i
$50$	0.401924	+	1.50000i	0.0568406	+	0.212132i
$51$		0			0
$52$	5.59808	+	2.76795i	0.776313	+	0.383845i
$53$	−5.76795	+	3.33013i	−0.792289	+	0.457428i	−0.840768	−	0.541396i	$-0.817896\pi$
$53$	−5.76795	+	3.33013i	−0.792289	+	0.457428i	0.0484789	+	0.998824i	$0.484563\pi$
$54$	−1.46410	+	1.46410i	−0.199239	+	0.199239i
$55$	1.09808	+	0.633975i	0.148065	+	0.0854851i
$56$	−4.96410	−	2.86603i	−0.663356	−	0.382989i
$57$	13.5622	+	3.63397i	1.79635	+	0.481332i
$58$	−3.09808	+	3.09808i	−0.406797	+	0.406797i
$59$	0.562178	+	2.09808i	0.0731893	+	0.273146i	0.992817	−	0.119646i	$-0.0381759\pi$
$59$	0.562178	+	2.09808i	0.0731893	+	0.273146i	−0.919627	+	0.392792i	$0.871509\pi$
$60$	−4.73205	−	4.73205i	−0.610905	−	0.610905i
$61$		−	3.19615i		−	0.409225i	−0.978843	−	0.204613i	$-0.934407\pi$
$61$		−	3.19615i		−	0.409225i	0.978843	−	0.204613i	$-0.0655935\pi$
$62$	0.303848	+	2.86603i	0.0385887	+	0.363986i
$63$	9.36603	−	9.36603i	1.18001	−	1.18001i
$64$			2.26795i			0.283494i
$65$	3.83013	+	3.36603i	0.475069	+	0.417504i
$66$	−1.26795			−0.156074
$67$	2.86603	−	10.6962i	0.350141	−	1.30674i	−0.536350	−	0.843996i	$-0.680197\pi$
$67$	2.86603	−	10.6962i	0.350141	−	1.30674i	0.886490	−	0.462747i	$-0.153136\pi$
$68$		0			0
$69$	−14.6603	−	8.46410i	−1.76489	−	1.01896i
$70$	−1.53590	−	1.53590i	−0.183575	−	0.183575i
$71$	−0.330127	+	1.23205i	−0.0391789	+	0.146218i	−0.982745	−	0.184968i	$-0.940782\pi$
$71$	−0.330127	+	1.23205i	−0.0391789	+	0.146218i	0.943566	+	0.331185i	$0.107449\pi$
$72$	8.33013	+	2.23205i	0.981715	+	0.263050i
$73$	2.83013	−	10.5622i	0.331241	−	1.23621i	−0.576646	−	0.816994i	$-0.695639\pi$
$73$	2.83013	−	10.5622i	0.331241	−	1.23621i	0.907887	−	0.419215i	$-0.137695\pi$
$74$	−2.19615	−	1.26795i	−0.255298	−	0.147396i
$75$	4.09808	+	7.09808i	0.473205	+	0.819615i
$76$	−2.30385	−	8.59808i	−0.264269	−	0.986267i
$77$	2.66025			0.303164
$78$	−5.00000	−	1.00000i	−0.566139	−	0.113228i
$79$	−10.7321	−	6.19615i	−1.20745	−	0.697122i	−0.245249	−	0.969460i	$-0.578870\pi$
$79$	−10.7321	−	6.19615i	−1.20745	−	0.697122i	−0.962201	+	0.272339i	$0.912203\pi$
$80$	−0.901924	+	3.36603i	−0.100838	+	0.376333i
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$	−2.66025	+	1.53590i	−0.293776	+	0.169612i
$83$	15.5622	+	4.16987i	1.70817	+	0.457703i	0.974975	−	0.222314i	$-0.0713612\pi$
$83$	15.5622	+	4.16987i	1.70817	+	0.457703i	0.733196	+	0.680017i	$0.238028\pi$
$84$	−13.5622	−	3.63397i	−1.47975	−	0.396499i
$85$		0			0
$86$	−2.09808	+	0.562178i	−0.226241	+	0.0606212i
$87$	−11.5622	+	20.0263i	−1.23960	+	2.14704i
$88$	0.866025	+	1.50000i	0.0923186	+	0.159901i
$89$	−2.26795	−	2.26795i	−0.240402	−	0.240402i	0.576614	−	0.817016i	$-0.304374\pi$
$89$	−2.26795	−	2.26795i	−0.240402	−	0.240402i	−0.817016	+	0.576614i	$0.804374\pi$
$90$	2.83013	+	1.63397i	0.298322	+	0.172236i
$91$	10.4904	+	2.09808i	1.09969	+	0.219938i
$92$			10.7321i			1.11889i
$93$	5.46410	+	14.1962i	0.566601	+	1.47207i
$94$	1.12436			0.115968
$95$		−	7.26795i		−	0.745676i
$96$	−3.63397	−	13.5622i	−0.370891	−	1.38418i
$97$	−8.46410	−	8.46410i	−0.859399	−	0.859399i	0.131868	−	0.991267i	$-0.457903\pi$
$97$	−8.46410	−	8.46410i	−0.859399	−	0.859399i	−0.991267	+	0.131868i	$0.957903\pi$
$98$	−0.901924	−	0.241670i	−0.0911081	−	0.0244123i
$99$	−3.86603	+	1.03590i	−0.388550	+	0.104112i
$100$	2.59808	−	4.50000i	0.259808	−	0.450000i
$101$		−	3.92820i		−	0.390871i	−0.980717	−	0.195435i	$-0.937388\pi$
$101$		−	3.92820i		−	0.390871i	0.980717	−	0.195435i	$-0.0626120\pi$
$102$		0			0
$103$	−10.5622	+	6.09808i	−1.04072	+	0.600861i	−0.920038	−	0.391830i	$-0.871842\pi$
$103$	−10.5622	+	6.09808i	−1.04072	+	0.600861i	−0.120685	+	0.992691i	$0.538509\pi$
$104$	2.23205	+	6.59808i	0.218871	+	0.646995i
$105$	−9.92820	−	5.73205i	−0.968893	−	0.559391i
$106$	−3.33013	−	0.892305i	−0.323451	−	0.0866683i
$107$	5.83013	−	10.0981i	0.563620	−	0.976218i	−0.433557	−	0.901126i	$-0.642742\pi$
$107$	5.83013	−	10.0981i	0.563620	−	0.976218i	0.997177	−	0.0750917i	$-0.0239250\pi$
$108$	6.92820			0.666667
$109$	−9.92820	−	9.92820i	−0.950949	−	0.950949i	0.0479026	−	0.998852i	$-0.484746\pi$
$109$	−9.92820	−	9.92820i	−0.950949	−	0.950949i	−0.998852	+	0.0479026i	$0.984746\pi$
$110$	0.169873	+	0.633975i	0.0161968	+	0.0604471i
$111$	−12.9282	−	3.46410i	−1.22709	−	0.328798i
$112$	1.89230	+	7.06218i	0.178806	+	0.667313i
$113$	−3.46410	−	6.00000i	−0.325875	−	0.564433i	0.655814	−	0.754923i	$-0.272326\pi$
$113$	−3.46410	−	6.00000i	−0.325875	−	0.564433i	−0.981689	+	0.190490i	$0.938992\pi$
$114$	3.63397	+	6.29423i	0.340353	+	0.589509i
$115$	−2.26795	+	8.46410i	−0.211487	+	0.789282i
$116$	14.6603			1.36117
$117$	−16.0622	+	1.03590i	−1.48495	+	0.0957688i
$118$	−0.562178	+	0.973721i	−0.0517527	+	0.0896382i
$119$		0			0
$120$		−	7.46410i		−	0.681376i
$121$	8.83013	+	5.09808i	0.802739	+	0.463461i
$122$	1.16987	−	1.16987i	0.105915	−	0.105915i
$123$	−11.4641	+	11.4641i	−1.03368	+	1.03368i
$124$	6.06218	−	7.50000i	0.544400	−	0.673520i
$125$	8.00000	−	8.00000i	0.715542	−	0.715542i
$126$	6.85641			0.610817
$127$	3.19615	−	5.53590i	0.283613	−	0.491232i	−0.688659	−	0.725085i	$-0.741800\pi$
$127$	3.19615	−	5.53590i	0.283613	−	0.491232i	0.972272	+	0.233854i	$0.0751337\pi$
$128$	−8.09808	+	8.09808i	−0.715776	+	0.715776i
$129$	−9.92820	+	5.73205i	−0.874130	+	0.504679i
$130$	0.169873	+	2.63397i	0.0148988	+	0.231015i
$131$	−8.66025	+	15.0000i	−0.756650	+	1.31056i	0.187900	+	0.982188i	$0.439832\pi$
$131$	−8.66025	+	15.0000i	−0.756650	+	1.31056i	−0.944550	+	0.328368i	$0.893501\pi$
$132$	3.00000	+	3.00000i	0.261116	+	0.261116i
$133$	−7.62436	−	13.2058i	−0.661115	−	1.14509i
$134$	4.96410	−	2.86603i	0.428833	−	0.247587i
$135$	5.46410	+	1.46410i	0.470275	+	0.126010i
$136$		0			0
$137$	−0.464102	+	1.73205i	−0.0396509	+	0.147979i	−0.982913	−	0.184069i	$-0.941073\pi$
$137$	−0.464102	+	1.73205i	−0.0396509	+	0.147979i	0.943262	+	0.332048i	$0.107740\pi$
$138$	−2.26795	−	8.46410i	−0.193061	−	0.720512i
$139$			19.3205i			1.63874i	0.573262	+	0.819372i	$0.305678\pi$
$139$			19.3205i			1.63874i	−0.573262	+	0.819372i	$0.694322\pi$
$140$			7.26795i			0.614254i
$141$	5.73205	−	1.53590i	0.482726	−	0.129346i
$142$	−0.571797	+	0.330127i	−0.0479841	+	0.0277036i
$143$	−2.42820	−	2.13397i	−0.203057	−	0.178452i
$144$	−5.50000	−	9.52628i	−0.458333	−	0.793857i
$145$	11.5622	+	3.09808i	0.960187	+	0.257281i
$146$	4.90192	−	2.83013i	0.405686	−	0.234223i
$147$	−4.92820			−0.406471
$148$	2.19615	+	8.19615i	0.180523	+	0.673720i
$149$	−15.6603	+	4.19615i	−1.28294	+	0.343762i	−0.834974	−	0.550289i	$-0.814517\pi$
$149$	−15.6603	+	4.19615i	−1.28294	+	0.343762i	−0.447964	+	0.894052i	$0.647851\pi$
$150$	−1.09808	+	4.09808i	−0.0896575	+	0.334607i
$151$	6.90192	+	6.90192i	0.561671	+	0.561671i	0.929782	−	0.368111i	$-0.119995\pi$
$151$	6.90192	+	6.90192i	0.561671	+	0.561671i	−0.368111	+	0.929782i	$0.619995\pi$
$152$	4.96410	−	8.59808i	0.402642	−	0.697396i
$153$		0			0
$154$	0.973721	+	0.973721i	0.0784646	+	0.0784646i
$155$	6.36603	−	4.63397i	0.511331	−	0.372210i
$156$	9.46410	+	14.1962i	0.757735	+	1.13660i
$157$	4.66025			0.371929			0.185964	−	0.982556i	$-0.440459\pi$
$157$	4.66025			0.371929			0.185964	+	0.982556i	$0.440459\pi$
$158$	−1.66025	−	6.19615i	−0.132083	−	0.492939i
$159$	−18.1962			−1.44305
$160$	−6.29423	+	3.63397i	−0.497602	+	0.287291i
$161$	4.75833	+	17.7583i	0.375009	+	1.39955i
$162$	1.23205	−	0.330127i	0.0967991	−	0.0259372i
$163$	2.56218	−	2.56218i	0.200685	−	0.200685i	−0.599608	−	0.800294i	$-0.704677\pi$
$163$	2.56218	−	2.56218i	0.200685	−	0.200685i	0.800294	+	0.599608i	$0.204677\pi$
$164$	9.92820	+	2.66025i	0.775262	+	0.207731i
$165$	1.73205	+	3.00000i	0.134840	+	0.233550i
$166$	4.16987	+	7.22243i	0.323645	+	0.560569i
$167$	5.96410	−	1.59808i	0.461516	−	0.123663i	−0.0205668	−	0.999788i	$-0.506547\pi$
$167$	5.96410	−	1.59808i	0.461516	−	0.123663i	0.482083	+	0.876126i	$0.339880\pi$
$168$	−7.83013	−	13.5622i	−0.604107	−	1.04634i
$169$	−7.89230	−	10.3301i	−0.607100	−	0.794625i
$170$		0			0
$171$	16.2224	+	16.2224i	1.24056	+	1.24056i
$172$	6.29423	+	3.63397i	0.479930	+	0.277088i
$173$	18.9282	−	10.9282i	1.43908	−	0.830856i	0.441299	−	0.897360i	$-0.354518\pi$
$173$	18.9282	−	10.9282i	1.43908	−	0.830856i	0.997786	+	0.0665045i	$0.0211847\pi$
$174$	−11.5622	+	3.09808i	−0.876526	+	0.234865i
$175$	2.30385	−	8.59808i	0.174155	−	0.649953i
$176$	0.571797	−	2.13397i	0.0431008	−	0.160854i
$177$	−1.53590	+	5.73205i	−0.115445	+	0.430847i
$178$		−	1.66025i		−	0.124441i
$179$	−1.56218	+	2.70577i	−0.116763	+	0.202239i	−0.918483	−	0.395461i	$-0.870585\pi$
$179$	−1.56218	+	2.70577i	−0.116763	+	0.202239i	0.801720	+	0.597699i	$0.203918\pi$
$180$	−2.83013	−	10.5622i	−0.210945	−	0.787258i
$181$	−9.50000	−	16.4545i	−0.706129	−	1.22305i	−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−9.50000	−	16.4545i	−0.706129	−	1.22305i	0.260153	−	0.965567i	$-0.416227\pi$
$182$	3.07180	+	4.60770i	0.227697	+	0.341545i
$183$	4.36603	−	7.56218i	0.322746	−	0.559012i
$184$	−8.46410	+	8.46410i	−0.623982	+	0.623982i
$185$			6.92820i			0.509372i
$186$	−3.19615	+	7.19615i	−0.234353	+	0.527647i
$187$		0			0
$188$	−2.66025	−	2.66025i	−0.194019	−	0.194019i
$189$	11.4641	−	3.07180i	0.833891	−	0.223440i
$190$	2.66025	−	2.66025i	0.192995	−	0.192995i
$191$	2.83013	+	4.90192i	0.204781	+	0.354691i	0.950063	−	0.312059i	$-0.101019\pi$
$191$	2.83013	+	4.90192i	0.204781	+	0.354691i	−0.745282	+	0.666749i	$0.767685\pi$
$192$	−3.09808	+	5.36603i	−0.223584	+	0.387260i
$193$	−1.43782	−	5.36603i	−0.103497	−	0.386255i	0.894674	−	0.446720i	$-0.147408\pi$
$193$	−1.43782	−	5.36603i	−0.103497	−	0.386255i	−0.998170	+	0.0604655i	$0.980741\pi$
$194$		−	6.19615i		−	0.444858i
$195$	4.46410	+	13.1962i	0.319681	+	0.944996i
$196$	1.56218	+	2.70577i	0.111584	+	0.193269i
$197$	5.09808	+	1.36603i	0.363223	+	0.0973253i	0.435815	−	0.900036i	$-0.356460\pi$
$197$	5.09808	+	1.36603i	0.363223	+	0.0973253i	−0.0725917	+	0.997362i	$0.523127\pi$
$198$	−1.79423	−	1.03590i	−0.127510	−	0.0736181i
$199$	−6.66025	−	11.5359i	−0.472133	−	0.817758i	0.527359	−	0.849643i	$-0.323182\pi$
$199$	−6.66025	−	11.5359i	−0.472133	−	0.817758i	−0.999492	+	0.0318846i	$0.989849\pi$
$200$	5.59808	−	1.50000i	0.395844	−	0.106066i
$201$	21.3923	−	21.3923i	1.50890	−	1.50890i
$202$	1.43782	−	1.43782i	0.101165	−	0.101165i
$203$	24.2583	−	6.50000i	1.70260	−	0.456211i
$204$		0			0
$205$	7.26795	+	4.19615i	0.507616	+	0.293072i
$206$	−6.09808	−	1.63397i	−0.424873	−	0.113844i
$207$	−13.8301	−	23.9545i	−0.961260	−	1.66495i
$208$	3.93782	−	7.96410i	0.273039	−	0.552211i
$209$			4.60770i			0.318721i
$210$	−1.53590	−	5.73205i	−0.105987	−	0.395549i
$211$	1.63397	−	2.83013i	0.112487	−	0.194834i	−0.804285	−	0.594244i	$-0.797452\pi$
$211$	1.63397	−	2.83013i	0.112487	−	0.194834i	0.916773	+	0.399410i	$0.130785\pi$
$212$	5.76795	+	9.99038i	0.396144	+	0.686142i
$213$	−2.46410	+	2.46410i	−0.168837	+	0.168837i
$214$	5.83013	−	1.56218i	0.398539	−	0.106788i
$215$	4.19615	+	4.19615i	0.286175	+	0.286175i
$216$	5.46410	+	5.46410i	0.371785	+	0.371785i
$217$	6.70577	−	15.0981i	0.455217	−	1.02492i
$218$		−	7.26795i		−	0.492248i
$219$	21.1244	−	21.1244i	1.42745	−	1.42745i
$220$	1.09808	−	1.90192i	0.0740323	−	0.128228i
$221$		0			0
$222$	−3.46410	−	6.00000i	−0.232495	−	0.402694i
$223$	1.37564	+	5.13397i	0.0921200	+	0.343796i	0.996567	−	0.0827894i	$-0.0263829\pi$
$223$	1.37564	+	5.13397i	0.0921200	+	0.343796i	−0.904447	+	0.426586i	$0.859716\pi$
$224$	−7.62436	+	13.2058i	−0.509424	+	0.882348i
$225$			13.3923i			0.892820i
$226$	0.928203	−	3.46410i	0.0617432	−	0.230429i
$227$	3.09808	−	11.5622i	0.205627	−	0.767409i	−0.783631	−	0.621226i	$-0.786635\pi$
$227$	3.09808	−	11.5622i	0.205627	−	0.767409i	0.989258	−	0.146182i	$-0.0466986\pi$
$228$	6.29423	−	23.4904i	0.416845	−	1.55569i
$229$	0.901924	−	0.241670i	0.0596008	−	0.0159700i	−0.228895	−	0.973451i	$-0.573511\pi$
$229$	0.901924	−	0.241670i	0.0596008	−	0.0159700i	0.288496	+	0.957481i	$0.406845\pi$
$230$	−3.92820	+	2.26795i	−0.259018	+	0.149544i
$231$	6.29423	+	3.63397i	0.414130	+	0.239098i
$232$	11.5622	+	11.5622i	0.759094	+	0.759094i
$233$		−	6.92820i		−	0.453882i	−0.973909	−	0.226941i	$-0.927128\pi$
$233$		−	6.92820i		−	0.453882i	0.973909	−	0.226941i	$-0.0728724\pi$
$234$	−6.25833	−	5.50000i	−0.409120	−	0.359546i
$235$	−1.53590	−	2.66025i	−0.100191	−	0.173536i
$236$	3.63397	−	0.973721i	0.236552	−	0.0633838i
$237$	−16.9282	−	29.3205i	−1.09960	−	1.90457i
$238$		0			0
$239$	6.96410	+	1.86603i	0.450470	+	0.120703i	0.476919	−	0.878947i	$-0.341753\pi$
$239$	6.96410	+	1.86603i	0.450470	+	0.120703i	−0.0264492	+	0.999650i	$0.508420\pi$
$240$	−6.73205	+	6.73205i	−0.434552	+	0.434552i
$241$	2.83013	−	0.758330i	0.182305	−	0.0488483i	−0.166512	−	0.986039i	$-0.553250\pi$
$241$	2.83013	−	0.758330i	0.182305	−	0.0488483i	0.348816	+	0.937191i	$0.386584\pi$
$242$	1.36603	+	5.09808i	0.0878114	+	0.327717i
$243$	16.2224	−	9.36603i	1.04067	−	0.600831i
$244$	−5.53590			−0.354400
$245$	0.660254	+	2.46410i	0.0421821	+	0.157426i
$246$	−8.39230			−0.535074
$247$	−3.63397	+	18.1699i	−0.231224	+	1.15612i
$248$	10.6962	−	1.13397i	0.679206	−	0.0720075i
$249$	31.1244	+	31.1244i	1.97243	+	1.97243i
$250$	5.85641			0.370392
$251$	−14.1244	+	24.4641i	−0.891521	+	1.54416i	−0.0534698	+	0.998569i	$0.517028\pi$
$251$	−14.1244	+	24.4641i	−0.891521	+	1.54416i	−0.838052	+	0.545591i	$0.816305\pi$
$252$	−16.2224	−	16.2224i	−1.02192	−	1.02192i
$253$	1.43782	−	5.36603i	0.0903951	−	0.337359i
$254$	3.19615	−	0.856406i	0.200544	−	0.0537357i
$255$		0			0
$256$	−1.39230			−0.0870191
$257$	−6.40192	+	3.69615i	−0.399341	+	0.230560i	−0.686200	−	0.727413i	$-0.740722\pi$
$257$	−6.40192	+	3.69615i	−0.399341	+	0.230560i	0.286859	+	0.957973i	$0.407389\pi$
$258$	−5.73205	−	1.53590i	−0.356862	−	0.0956209i
$259$	7.26795	+	12.5885i	0.451608	+	0.782209i
$260$	5.83013	−	6.63397i	0.361569	−	0.411422i
$261$	−32.7224	+	18.8923i	−2.02547	+	1.16940i
$262$	−8.66025	+	2.32051i	−0.535032	+	0.143361i
$263$			19.5167i			1.20345i	0.798704	+	0.601724i	$0.205519\pi$
$263$			19.5167i			1.20345i	−0.798704	+	0.601724i	$0.794481\pi$
$264$			4.73205i			0.291238i
$265$	2.43782	+	9.09808i	0.149754	+	0.558890i
$266$	2.04294	−	7.62436i	0.125261	−	0.467479i
$267$	−2.26795	−	8.46410i	−0.138796	−	0.517995i
$268$	−18.5263	−	4.96410i	−1.13167	−	0.303231i
$269$	−15.4019	+	8.89230i	−0.939072	+	0.542173i	−0.889669	−	0.456606i	$-0.849065\pi$
$269$	−15.4019	+	8.89230i	−0.939072	+	0.542173i	−0.0494026	+	0.998779i	$0.515732\pi$
$270$	1.46410	+	2.53590i	0.0891024	+	0.154330i
$271$	−6.46410	−	6.46410i	−0.392666	−	0.392666i	0.482970	−	0.875637i	$-0.339558\pi$
$271$	−6.46410	−	6.46410i	−0.392666	−	0.392666i	−0.875637	+	0.482970i	$0.839558\pi$
$272$		0			0
$273$	21.9545	+	19.2942i	1.32875	+	1.16774i
$274$	−0.803848	+	0.464102i	−0.0485622	+	0.0280374i
$275$	−1.90192	+	1.90192i	−0.114690	+	0.114690i
$276$	−14.6603	+	25.3923i	−0.882444	+	1.52844i
$277$	26.3923			1.58576			0.792880	−	0.609378i	$-0.208581\pi$
$277$	26.3923			1.58576			0.792880	+	0.609378i	$0.208581\pi$
$278$	−7.07180	+	7.07180i	−0.424138	+	0.424138i
$279$	−3.86603	+	24.5526i	−0.231453	+	1.46992i
$280$	−5.73205	+	5.73205i	−0.342556	+	0.342556i
$281$	−21.3923	+	21.3923i	−1.27616	+	1.27616i	−0.333357	+	0.942801i	$0.608182\pi$
$281$	−21.3923	+	21.3923i	−1.27616	+	1.27616i	−0.942801	+	0.333357i	$0.891818\pi$
$282$	2.66025	+	1.53590i	0.158416	+	0.0914614i
$283$			7.12436i			0.423499i	0.977324	+	0.211749i	$0.0679161\pi$
$283$			7.12436i			0.423499i	−0.977324	+	0.211749i	$0.932084\pi$
$284$	2.13397	+	0.571797i	0.126628	+	0.0339299i
$285$	9.92820	−	17.1962i	0.588096	−	1.01861i
$286$	−0.107695	−	1.66987i	−0.00636815	−	0.0987417i
$287$	17.6077			1.03935
$288$	5.93782	−	22.1603i	0.349890	−	1.30581i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	3.09808	+	5.36603i	0.181925	+	0.315104i
$291$	−8.46410	−	31.5885i	−0.496174	−	1.85175i
$292$	−18.2942	−	4.90192i	−1.07059	−	0.286863i
$293$	7.26795	+	27.1244i	0.424598	+	1.58462i	0.764799	+	0.644269i	$0.222838\pi$
$293$	7.26795	+	27.1244i	0.424598	+	1.58462i	−0.340201	+	0.940353i	$0.610495\pi$
$294$	−1.80385	−	1.80385i	−0.105203	−	0.105203i
$295$	3.07180			0.178847
$296$	−4.73205	+	8.19615i	−0.275045	+	0.476392i
$297$	−3.46410	−	0.928203i	−0.201008	−	0.0538598i
$298$	−7.26795	−	4.19615i	−0.421021	−	0.243077i
$299$	9.90192	−	20.0263i	0.572643	−	1.15815i
$300$	12.2942	−	7.09808i	0.709808	−	0.409808i
$301$	12.0263	+	3.22243i	0.693183	+	0.185738i
$302$			5.05256i			0.290742i
$303$	5.36603	−	9.29423i	0.308270	−	0.533939i
$304$	−12.2321	+	3.27757i	−0.701556	+	0.187981i
$305$	−4.36603	−	1.16987i	−0.249998	−	0.0669867i
$306$		0			0
$307$	−6.02628	−	22.4904i	−0.343938	−	1.28359i	−0.893848	−	0.448370i	$-0.852005\pi$
$307$	−6.02628	−	22.4904i	−0.343938	−	1.28359i	0.549910	−	0.835224i	$-0.314662\pi$
$308$		−	4.60770i		−	0.262548i
$309$	−33.3205			−1.89554
$310$	4.02628	+	0.633975i	0.228677	+	0.0360073i
$311$		−	13.0718i		−	0.741234i	−0.928786	−	0.370617i	$-0.879146\pi$
$311$		−	13.0718i		−	0.741234i	0.928786	−	0.370617i	$-0.120854\pi$
$312$	−3.73205	+	18.6603i	−0.211286	+	1.05643i
$313$	−19.3301	−	11.1603i	−1.09260	−	0.630815i	−0.158335	−	0.987385i	$-0.550613\pi$
$313$	−19.3301	−	11.1603i	−1.09260	−	0.630815i	−0.934268	+	0.356571i	$0.883946\pi$
$314$	1.70577	+	1.70577i	0.0962622	+	0.0962622i
$315$	−9.36603	−	16.2224i	−0.527716	−	0.914030i
$316$	−10.7321	+	18.5885i	−0.603725	+	1.04568i
$317$	−16.3923	+	4.39230i	−0.920684	+	0.246696i	−0.687878	−	0.725827i	$-0.741457\pi$
$317$	−16.3923	+	4.39230i	−0.920684	+	0.246696i	−0.232806	+	0.972523i	$0.574791\pi$
$318$	−6.66025	−	6.66025i	−0.373489	−	0.373489i
$319$	−7.33013	−	1.96410i	−0.410408	−	0.109969i
$320$	3.09808	+	0.830127i	0.173188	+	0.0464055i
$321$	27.5885	−	15.9282i	1.53984	−	0.889026i
$322$	−4.75833	+	8.24167i	−0.265171	+	0.459290i
$323$		0			0
$324$	−3.69615	−	2.13397i	−0.205342	−	0.118554i
$325$	−9.00000	+	6.00000i	−0.499230	+	0.332820i
$326$	1.87564			0.103882
$327$	−9.92820	−	37.0526i	−0.549031	−	2.04901i
$328$	5.73205	+	9.92820i	0.316500	+	0.548193i
$329$	−5.58142	−	3.22243i	−0.307713	−	0.177658i
$330$	−0.464102	+	1.73205i	−0.0255480	+	0.0953463i
$331$	15.1603	+	4.06218i	0.833283	+	0.223277i	0.650145	−	0.759810i	$-0.274708\pi$
$331$	15.1603	+	4.06218i	0.833283	+	0.223277i	0.183138	+	0.983087i	$0.441375\pi$
$332$	7.22243	−	26.9545i	0.396382	−	1.47932i
$333$	−15.4641	−	15.4641i	−0.847428	−	0.847428i
$334$	2.76795	+	1.59808i	0.151455	+	0.0874428i
$335$	−13.5622	−	7.83013i	−0.740981	−	0.427806i
$336$	−5.16987	+	19.2942i	−0.282040	+	1.05259i
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$	0.892305	−	6.66987i	0.0485350	−	0.362793i
$339$		−	18.9282i		−	1.02804i
$340$		0			0
$341$	−4.03590	+	2.93782i	−0.218556	+	0.159092i
$342$			11.8756i			0.642161i
$343$	−10.9019	−	10.9019i	−0.588649	−	0.588649i
$344$	2.09808	+	7.83013i	0.113121	+	0.422172i
$345$	−16.9282	+	16.9282i	−0.911384	+	0.911384i
$346$	10.9282	+	2.92820i	0.587504	+	0.157421i
$347$	16.2224	+	9.36603i	0.870866	+	0.502795i	0.867636	−	0.497200i	$-0.165639\pi$
$347$	16.2224	+	9.36603i	0.870866	+	0.502795i	0.00322992	+	0.999995i	$0.498972\pi$
$348$	34.6865	+	20.0263i	1.85939	+	1.07352i
$349$	−20.1244	+	20.1244i	−1.07723	+	1.07723i	−0.0804755	+	0.996757i	$0.525644\pi$
$349$	−20.1244	+	20.1244i	−1.07723	+	1.07723i	−0.996757	+	0.0804755i	$0.974356\pi$
$350$	3.99038	−	2.30385i	0.213295	−	0.123146i
$351$	−12.9282	−	6.39230i	−0.690056	−	0.341196i
$352$	3.99038	−	2.30385i	0.212688	−	0.122795i
$353$	−6.09808	−	22.7583i	−0.324568	−	1.21130i	−0.914746	−	0.404030i	$-0.867609\pi$
$353$	−6.09808	−	22.7583i	−0.324568	−	1.21130i	0.590178	−	0.807273i	$-0.299058\pi$
$354$	−2.66025	+	1.53590i	−0.141391	+	0.0816321i
$355$	1.56218	+	0.901924i	0.0829118	+	0.0478691i
$356$	−3.92820	+	3.92820i	−0.208194	+	0.208194i
$357$		0			0
$358$	−1.56218	+	0.418584i	−0.0825637	+	0.0221229i
$359$	25.2583	+	6.76795i	1.33308	+	0.357199i	0.853864	−	0.520496i	$-0.174253\pi$
$359$	25.2583	+	6.76795i	1.33308	+	0.357199i	0.479220	+	0.877695i	$0.340920\pi$
$360$	6.09808	−	10.5622i	0.321397	−	0.556676i
$361$	6.41858	−	3.70577i	0.337820	−	0.195041i
$362$	2.54552	−	9.50000i	0.133789	−	0.499309i
$363$	13.9282	+	24.1244i	0.731041	+	1.26620i
$364$	3.63397	−	18.1699i	0.190472	−	0.952360i
$365$	−13.3923	−	7.73205i	−0.700985	−	0.404714i
$366$	4.36603	−	1.16987i	0.228216	−	0.0611502i
$367$	17.1962	−	9.92820i	0.897632	−	0.518248i	0.0212007	−	0.999775i	$-0.493251\pi$
$367$	17.1962	−	9.92820i	0.897632	−	0.518248i	0.876431	+	0.481527i	$0.159918\pi$
$368$	15.2679			0.795897
$369$	−25.5885	+	6.85641i	−1.33208	+	0.356930i
$370$	−2.53590	+	2.53590i	−0.131835	+	0.131835i
$371$	13.9737	+	13.9737i	0.725479	+	0.725479i
$372$	24.5885	−	9.46410i	1.27485	−	0.490691i
$373$	35.5885			1.84270			0.921350	−	0.388734i	$-0.127087\pi$
$373$	35.5885			1.84270			0.921350	+	0.388734i	$0.127087\pi$
$374$		0			0
$375$	29.8564	−	8.00000i	1.54178	−	0.413118i
$376$		−	4.19615i		−	0.216400i
$377$	−27.3564	−	13.5263i	−1.40893	−	0.696639i
$378$	5.32051	+	3.07180i	0.273657	+	0.157996i
$379$	2.59808	−	0.696152i	0.133454	−	0.0357589i	−0.191474	−	0.981498i	$-0.561327\pi$
$379$	2.59808	−	0.696152i	0.133454	−	0.0357589i	0.324928	+	0.945739i	$0.394660\pi$
$380$	−12.5885			−0.645774
$381$	15.1244	−	8.73205i	0.774844	−	0.447357i
$382$	−0.758330	+	2.83013i	−0.0387996	+	0.144802i
$383$	−7.56218	−	2.02628i	−0.386409	−	0.103538i	0.0603842	−	0.998175i	$-0.480767\pi$
$383$	−7.56218	−	2.02628i	−0.386409	−	0.103538i	−0.446793	+	0.894637i	$0.647434\pi$
$384$	−30.2224	+	8.09808i	−1.54228	+	0.413253i
$385$	0.973721	−	3.63397i	0.0496254	−	0.185204i
$386$	1.43782	−	2.49038i	0.0731832	−	0.126757i
$387$	−18.7321			−0.952204
$388$	−14.6603	+	14.6603i	−0.744262	+	0.744262i
$389$	−7.69615	+	13.3301i	−0.390210	+	0.675864i	−0.992477	−	0.122431i	$-0.960931\pi$
$389$	−7.69615	+	13.3301i	−0.390210	+	0.675864i	0.602267	+	0.798295i	$0.294264\pi$
$390$	−3.19615	+	6.46410i	−0.161843	+	0.327323i
$391$		0			0
$392$	−0.901924	+	3.36603i	−0.0455540	+	0.170010i
$393$	−40.9808	+	23.6603i	−2.06721	+	1.19350i
$394$	1.36603	+	2.36603i	0.0688194	+	0.119199i
$395$	−12.3923	+	12.3923i	−0.623525	+	0.623525i
$396$	1.79423	+	6.69615i	0.0901634	+	0.336494i
$397$	3.63397	+	13.5622i	0.182384	+	0.680666i	0.995175	+	0.0981115i	$0.0312802\pi$
$397$	3.63397	+	13.5622i	0.182384	+	0.680666i	−0.812791	+	0.582555i	$0.802053\pi$
$398$	1.78461	−	6.66025i	0.0894544	−	0.333848i
$399$		−	41.6603i		−	2.08562i
$400$	−6.40192	−	3.69615i	−0.320096	−	0.184808i
$401$	−17.9282	−	17.9282i	−0.895292	−	0.895292i	0.0997234	−	0.995015i	$-0.468204\pi$
$401$	−17.9282	−	17.9282i	−0.895292	−	0.895292i	−0.995015	+	0.0997234i	$0.968204\pi$
$402$	15.6603			0.781062
$403$	−18.2321	+	8.40192i	−0.908203	+	0.418530i
$404$	−6.80385			−0.338504
$405$	−2.46410	−	2.46410i	−0.122442	−	0.122442i
$406$	11.2583	+	6.50000i	0.558742	+	0.322590i
$407$		−	4.39230i		−	0.217718i
$408$		0			0
$409$	−9.63397	−	35.9545i	−0.476369	−	1.77783i	−0.616125	−	0.787649i	$-0.711298\pi$
$409$	−9.63397	−	35.9545i	−0.476369	−	1.77783i	0.139755	−	0.990186i	$-0.455368\pi$
$410$	1.12436	+	4.19615i	0.0555280	+	0.207233i
$411$	−3.46410	+	3.46410i	−0.170872	+	0.170872i
$412$	10.5622	+	18.2942i	0.520361	+	0.901292i
$413$	5.58142	−	3.22243i	0.274644	−	0.158566i
$414$	3.70577	−	13.8301i	0.182129	−	0.679714i
$415$	11.3923	−	19.7321i	0.559226	−	0.968608i
$416$	17.5526	−	5.93782i	0.860585	−	0.291126i
$417$	−26.3923	+	45.7128i	−1.29244	+	2.23857i
$418$	−1.68653	+	1.68653i	−0.0824910	+	0.0824910i
$419$	30.0000			1.46560			0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000			1.46560			0.732798	+	0.680446i	$0.238214\pi$
$420$	−9.92820	+	17.1962i	−0.484447	+	0.839086i
$421$	3.43782	−	12.8301i	0.167549	−	0.625302i	−0.830152	−	0.557537i	$-0.811746\pi$
$421$	3.43782	−	12.8301i	0.167549	−	0.625302i	0.997701	−	0.0677651i	$-0.0215869\pi$
$422$	1.63397	−	0.437822i	0.0795406	−	0.0213128i
$423$	9.36603	+	2.50962i	0.455392	+	0.122022i
$424$	−3.33013	+	12.4282i	−0.161725	+	0.603567i
$425$		0			0
$426$	−1.80385			−0.0873967
$427$	−9.16025	+	2.45448i	−0.443296	+	0.118781i
$428$	−17.4904	−	10.0981i	−0.845429	−	0.488109i
$429$	−2.83013	−	8.36603i	−0.136640	−	0.403916i
$430$			3.07180i			0.148135i
$431$	35.4545	−	9.50000i	1.70778	−	0.457599i	0.732903	−	0.680333i	$-0.238165\pi$
$431$	35.4545	−	9.50000i	1.70778	−	0.457599i	0.974879	+	0.222734i	$0.0714982\pi$
$432$		−	9.85641i		−	0.474217i
$433$	−13.7321			−0.659920			−0.329960	−	0.943995i	$-0.607035\pi$
$433$	−13.7321			−0.659920			−0.329960	+	0.943995i	$0.607035\pi$
$434$	7.98076	−	3.07180i	0.383089	−	0.147451i
$435$	23.1244	+	23.1244i	1.10873	+	1.10873i
$436$	−17.1962	+	17.1962i	−0.823546	+	0.823546i
$437$	−30.7583	+	8.24167i	−1.47137	+	0.394253i
$438$	15.4641			0.738903
$439$	−0.464102	+	0.267949i	−0.0221504	+	0.0127885i	−0.511034	−	0.859560i	$-0.670737\pi$
$439$	−0.464102	+	0.267949i	−0.0221504	+	0.0127885i	0.488884	+	0.872349i	$0.337404\pi$
$440$	2.36603	−	0.633975i	0.112796	−	0.0302236i
$441$	−6.97372	−	4.02628i	−0.332082	−	0.191728i
$442$		0			0
$443$	2.80385	+	4.85641i	0.133215	+	0.230735i	0.924914	−	0.380176i	$-0.124137\pi$
$443$	2.80385	+	4.85641i	0.133215	+	0.230735i	−0.791699	+	0.610911i	$0.790803\pi$
$444$	−6.00000	+	22.3923i	−0.284747	+	1.06269i
$445$	−3.92820	+	2.26795i	−0.186215	+	0.107511i
$446$	−1.37564	+	2.38269i	−0.0651386	+	0.112823i
$447$	−42.7846	−	11.4641i	−2.02364	−	0.542233i
$448$	6.50000	−	1.74167i	0.307096	−	0.0822862i
$449$	−9.66025	−	9.66025i	−0.455896	−	0.455896i	0.441410	−	0.897306i	$-0.354478\pi$
$449$	−9.66025	−	9.66025i	−0.455896	−	0.455896i	−0.897306	+	0.441410i	$0.854478\pi$
$450$	−4.90192	+	4.90192i	−0.231079	+	0.231079i
$451$	−4.60770	−	2.66025i	−0.216968	−	0.125266i
$452$	−10.3923	+	6.00000i	−0.488813	+	0.282216i
$453$	6.90192	+	25.7583i	0.324281	+	1.21023i
$454$	5.36603	−	3.09808i	0.251840	−	0.145400i
$455$	6.70577	−	13.5622i	0.314371	−	0.635805i
$456$	23.4904	−	13.5622i	1.10004	−	0.635107i
$457$	12.0000	−	12.0000i	0.561336	−	0.561336i	−0.368351	−	0.929687i	$-0.620077\pi$
$457$	12.0000	−	12.0000i	0.561336	−	0.561336i	0.929687	+	0.368351i	$0.120077\pi$
$458$	0.418584	+	0.241670i	0.0195592	+	0.0112925i
$459$		0			0
$460$	14.6603	+	3.92820i	0.683538	+	0.183153i
$461$	−0.196152	+	0.196152i	−0.00913573	+	0.00913573i	−0.711660	−	0.702524i	$-0.752056\pi$
$461$	−0.196152	+	0.196152i	−0.00913573	+	0.00913573i	0.702524	+	0.711660i	$0.252056\pi$
$462$	0.973721	+	3.63397i	0.0453016	+	0.169068i
$463$	−6.66025	−	6.66025i	−0.309528	−	0.309528i	0.535198	−	0.844726i	$-0.320237\pi$
$463$	−6.66025	−	6.66025i	−0.309528	−	0.309528i	−0.844726	+	0.535198i	$0.820237\pi$
$464$		−	20.8564i		−	0.968234i
$465$	21.3923	−	2.26795i	0.992044	−	0.105174i
$466$	2.53590	−	2.53590i	0.117473	−	0.117473i
$467$		−	18.3923i		−	0.851094i	−0.904936	−	0.425547i	$-0.860082\pi$
$467$		−	18.3923i		−	0.851094i	0.904936	−	0.425547i	$-0.139918\pi$
$468$	1.79423	+	27.8205i	0.0829382	+	1.28600i
$469$	−32.8564			−1.51717
$470$	0.411543	−	1.53590i	0.0189831	−	0.0708457i
$471$	11.0263	+	6.36603i	0.508064	+	0.293331i
$472$	3.63397	+	2.09808i	0.167267	+	0.0965718i
$473$	−2.66025	−	2.66025i	−0.122319	−	0.122319i
$474$	4.53590	−	16.9282i	0.208341	−	0.777538i
$475$	14.8923	+	3.99038i	0.683306	+	0.183091i
$476$		0			0
$477$	−25.7487	−	14.8660i	−1.17895	−	0.680669i
$478$	1.86603	+	3.23205i	0.0853500	+	0.147831i
$479$	−1.64359	−	6.13397i	−0.0750977	−	0.280268i	0.918158	−	0.396215i	$-0.129677\pi$
$479$	−1.64359	−	6.13397i	−0.0750977	−	0.280268i	−0.993255	+	0.115947i	$0.963010\pi$
$480$	−19.8564			−0.906317
$481$	3.46410	−	17.3205i	0.157949	−	0.789747i
$482$	1.31347	+	0.758330i	0.0598268	+	0.0345410i
$483$	−13.0000	+	48.5167i	−0.591520	+	2.20758i
$484$	8.83013	−	15.2942i	0.401369	−	0.695192i
$485$	−14.6603	+	8.46410i	−0.665688	+	0.384335i
$486$	9.36603	+	2.50962i	0.424852	+	0.113839i
$487$	13.8301	+	3.70577i	0.626703	+	0.167925i	0.558173	−	0.829725i	$-0.311503\pi$
$487$	13.8301	+	3.70577i	0.626703	+	0.167925i	0.0685298	+	0.997649i	$0.478169\pi$
$488$	−4.36603	−	4.36603i	−0.197641	−	0.197641i
$489$	9.56218	−	2.56218i	0.432417	−	0.115866i
$490$	−0.660254	+	1.14359i	−0.0298272	+	0.0516623i
$491$	2.09808	+	3.63397i	0.0946849	+	0.163999i	0.909477	−	0.415754i	$-0.136482\pi$
$491$	2.09808	+	3.63397i	0.0946849	+	0.163999i	−0.814792	+	0.579753i	$0.803149\pi$
$492$	19.8564	+	19.8564i	0.895196	+	0.895196i
$493$		0			0
$494$	−7.98076	+	5.32051i	−0.359071	+	0.239381i
$495$			5.66025i			0.254409i
$496$	−10.6699	−	8.62436i	−0.479091	−	0.387245i
$497$	3.78461			0.169763
$498$			22.7846i			1.02100i
$499$	−3.55256	−	13.2583i	−0.159034	−	0.593524i	−0.998726	−	0.0504609i	$-0.983931\pi$
$499$	−3.55256	−	13.2583i	−0.159034	−	0.593524i	0.839692	−	0.543063i	$-0.182736\pi$
$500$	−13.8564	−	13.8564i	−0.619677	−	0.619677i
$501$	16.2942	+	4.36603i	0.727972	+	0.195060i
$502$	−14.1244	+	3.78461i	−0.630401	+	0.168915i
$503$	−7.19615	+	12.4641i	−0.320861	+	0.555747i	−0.980666	−	0.195690i	$-0.937305\pi$
$503$	−7.19615	+	12.4641i	−0.320861	+	0.555747i	0.659805	+	0.751437i	$0.270639\pi$
$504$		−	25.5885i		−	1.13980i
$505$	−5.36603	−	1.43782i	−0.238785	−	0.0639822i
$506$	2.49038	−	1.43782i	0.110711	−	0.0639190i
$507$	−4.56218	−	35.2224i	−0.202613	−	1.56428i
$508$	−9.58846	−	5.53590i	−0.425419	−	0.245616i
$509$	20.7583	+	5.56218i	0.920097	+	0.246539i	0.687627	−	0.726064i	$-0.258653\pi$
$509$	20.7583	+	5.56218i	0.920097	+	0.246539i	0.232470	+	0.972604i	$0.425319\pi$
$510$		0			0
$511$	−32.4449			−1.43528
$512$	15.6865	+	15.6865i	0.693253	+	0.693253i
$513$	5.32051	+	19.8564i	0.234906	+	0.876682i
$514$	−3.69615	−	0.990381i	−0.163030	−	0.0436838i
$515$	4.46410	+	16.6603i	0.196712	+	0.734139i
$516$	9.92820	+	17.1962i	0.437065	+	0.757018i
$517$	0.973721	+	1.68653i	0.0428242	+	0.0741737i
$518$	−1.94744	+	7.26795i	−0.0855657	+	0.319335i
$519$	59.7128			2.62110
$520$	9.83013	−	0.633975i	0.431080	−	0.0278016i
$521$	−15.9282	+	27.5885i	−0.697827	+	1.20867i	0.271391	+	0.962469i	$0.412516\pi$
$521$	−15.9282	+	27.5885i	−0.697827	+	1.20867i	−0.969218	+	0.246203i	$0.920817\pi$
$522$	−18.8923	−	5.06218i	−0.826894	−	0.221566i
$523$		−	22.4449i		−	0.981445i	−0.871316	−	0.490723i	$-0.836733\pi$
$523$		−	22.4449i		−	0.981445i	0.871316	−	0.490723i	$-0.163267\pi$
$524$	25.9808	+	15.0000i	1.13497	+	0.655278i
$525$	17.1962	−	17.1962i	0.750502	−	0.750502i
$526$	−7.14359	+	7.14359i	−0.311475	+	0.311475i
$527$		0			0
$528$	4.26795	−	4.26795i	0.185739	−	0.185739i
$529$	15.3923			0.669231
$530$	−2.43782	+	4.22243i	−0.105892	+	0.183411i
$531$	−6.85641	+	6.85641i	−0.297543	+	0.297543i
$532$	−22.8731	+	13.2058i	−0.991673	+	0.572543i
$533$	−16.0718	−	14.1244i	−0.696147	−	0.611794i
$534$	2.26795	−	3.92820i	0.0981438	−	0.169990i
$535$	−11.6603	−	11.6603i	−0.504117	−	0.504117i
$536$	−10.6962	−	18.5263i	−0.462003	−	0.800213i
$537$	−7.39230	+	4.26795i	−0.319002	+	0.184176i
$538$	−8.89230	−	2.38269i	−0.383374	−	0.102725i
$539$	−0.418584	−	1.56218i	−0.0180297	−	0.0672878i
$540$	2.53590	−	9.46410i	0.109128	−	0.407270i
$541$	−5.87564	−	21.9282i	−0.252614	−	0.942767i	−0.969402	−	0.245477i	$-0.921056\pi$
$541$	−5.87564	−	21.9282i	−0.252614	−	0.942767i	0.716789	−	0.697290i	$-0.245611\pi$
$542$		−	4.73205i		−	0.203259i
$543$		−	51.9090i		−	2.22763i
$544$		0			0
$545$	−17.1962	+	9.92820i	−0.736602	+	0.425278i
$546$	0.973721	+	15.0981i	0.0416714	+	0.646138i
$547$	1.26795	+	2.19615i	0.0542136	+	0.0939007i	0.891859	−	0.452314i	$-0.149401\pi$
$547$	1.26795	+	2.19615i	0.0542136	+	0.0939007i	−0.837645	+	0.546215i	$0.816068\pi$
$548$	3.00000	+	0.803848i	0.128154	+	0.0343387i
$549$	12.3564	−	7.13397i	0.527359	−	0.304471i
$550$	−1.39230			−0.0593681
$551$	11.2583	+	42.0167i	0.479621	+	1.78997i
$552$	−31.5885	+	8.46410i	−1.34449	+	0.360256i
$553$	−9.51666	+	35.5167i	−0.404690	+	1.51032i
$554$	9.66025	+	9.66025i	0.410425	+	0.410425i
$555$	−9.46410	+	16.3923i	−0.401729	+	0.695815i
$556$	33.4641			1.41919
$557$	−6.46410	−	6.46410i	−0.273893	−	0.273893i	0.556772	−	0.830665i	$-0.312040\pi$
$557$	−6.46410	−	6.46410i	−0.273893	−	0.273893i	−0.830665	+	0.556772i	$0.812040\pi$
$558$	−10.4019	+	7.57180i	−0.440349	+	0.320540i
$559$	−8.39230	−	12.5885i	−0.354957	−	0.532435i
$560$	10.3397			0.436934
$561$		0			0
$562$	−15.6603			−0.660588
$563$	27.8827	−	16.0981i	1.17512	−	0.678453i	0.220236	−	0.975447i	$-0.429317\pi$
$563$	27.8827	−	16.0981i	1.17512	−	0.678453i	0.954879	+	0.296994i	$0.0959840\pi$
$564$	−2.66025	−	9.92820i	−0.112017	−	0.418053i
$565$	−9.46410	+	2.53590i	−0.398158	+	0.106686i
$566$	−2.60770	+	2.60770i	−0.109610	+	0.109610i
$567$	−7.06218	−	1.89230i	−0.296584	−	0.0794693i
$568$	1.23205	+	2.13397i	0.0516957	+	0.0895396i
$569$	20.0622	+	34.7487i	0.841050	+	1.45674i	0.889008	+	0.457892i	$0.151395\pi$
$569$	20.0622	+	34.7487i	0.841050	+	1.45674i	−0.0479574	+	0.998849i	$0.515271\pi$
$570$	9.92820	−	2.66025i	0.415847	−	0.111426i
$571$	14.7583	+	25.5622i	0.617617	+	1.06974i	0.989919	+	0.141632i	$0.0452351\pi$
$571$	14.7583	+	25.5622i	0.617617	+	1.06974i	−0.372302	+	0.928111i	$0.621432\pi$
$572$	−3.69615	+	4.20577i	−0.154544	+	0.175852i
$573$			15.4641i			0.646022i
$574$	6.44486	+	6.44486i	0.269003	+	0.269003i
$575$	−16.0981	−	9.29423i	−0.671336	−	0.387596i
$576$	−8.76795	+	5.06218i	−0.365331	+	0.210924i
$577$	5.56218	−	1.49038i	0.231556	−	0.0620454i	−0.141175	−	0.989985i	$-0.545088\pi$
$577$	5.56218	−	1.49038i	0.231556	−	0.0620454i	0.372731	+	0.927939i	$0.378421\pi$
$578$	−2.27757	+	8.50000i	−0.0947343	+	0.353553i
$579$	3.92820	−	14.6603i	0.163251	−	0.609259i
$580$	5.36603	−	20.0263i	0.222812	−	0.831546i
$581$		−	47.8038i		−	1.98324i
$582$	8.46410	−	14.6603i	0.350848	−	0.607687i
$583$	−1.54552	−	5.76795i	−0.0640088	−	0.238884i
$584$	−10.5622	−	18.2942i	−0.437066	−	0.757021i
$585$	−4.46410	+	22.3205i	−0.184568	+	0.922839i
$586$	−7.26795	+	12.5885i	−0.300236	+	0.520024i
$587$	−20.2942	+	20.2942i	−0.837632	+	0.837632i	−0.988547	−	0.150914i	$-0.951778\pi$
$587$	−20.2942	+	20.2942i	−0.837632	+	0.837632i	0.150914	+	0.988547i	$0.451778\pi$
$588$			8.53590i			0.352015i
$589$	26.1506	+	11.6147i	1.07752	+	0.478577i
$590$	1.12436	+	1.12436i	0.0462890	+	0.0462890i
$591$	10.1962	+	10.1962i	0.419414	+	0.419414i
$592$	11.6603	−	3.12436i	0.479233	−	0.128410i
$593$	19.8564	−	19.8564i	0.815405	−	0.815405i	−0.170033	−	0.985438i	$-0.554388\pi$
$593$	19.8564	−	19.8564i	0.815405	−	0.815405i	0.985438	+	0.170033i	$0.0543876\pi$
$594$	−0.928203	−	1.60770i	−0.0380846	−	0.0659645i
$595$		0			0
$596$	7.26795	+	27.1244i	0.297707	+	1.11106i
$597$		−	36.3923i		−	1.48944i
$598$	10.9545	−	3.70577i	0.447962	−	0.151540i
$599$	−19.5622	−	33.8827i	−0.799289	−	1.38441i	−0.920080	−	0.391731i	$-0.871876\pi$
$599$	−19.5622	−	33.8827i	−0.799289	−	1.38441i	0.120791	−	0.992678i	$-0.461457\pi$
$600$	15.2942	+	4.09808i	0.624384	+	0.167303i
$601$	34.4545	+	19.8923i	1.40543	+	0.811424i	0.994943	−	0.100443i	$-0.0320261\pi$
$601$	34.4545	+	19.8923i	1.40543	+	0.811424i	0.410485	+	0.911867i	$0.365359\pi$
$602$	3.22243	+	5.58142i	0.131337	+	0.227482i
$603$	47.7487	−	12.7942i	1.94448	−	0.521021i
$604$	11.9545	−	11.9545i	0.486421	−	0.486421i
$605$	10.1962	−	10.1962i	0.414533	−	0.414533i
$606$	5.36603	−	1.43782i	0.217980	−	0.0584075i
$607$	22.6865	+	39.2942i	0.920818	+	1.59490i	0.798152	+	0.602455i	$0.205811\pi$
$607$	22.6865	+	39.2942i	0.920818	+	1.59490i	0.122665	+	0.992448i	$0.460856\pi$
$608$	−22.8731	−	13.2058i	−0.927625	−	0.535565i
$609$	66.2750	+	17.7583i	2.68560	+	0.719604i
$610$	−1.16987	−	2.02628i	−0.0473668	−	0.0820417i
$611$	2.50962	+	7.41858i	0.101528	+	0.300124i
$612$		0			0
$613$	5.92820	+	22.1244i	0.239438	+	0.893594i	0.976098	+	0.217331i	$0.0697351\pi$
$613$	5.92820	+	22.1244i	0.239438	+	0.893594i	−0.736660	+	0.676263i	$0.763598\pi$
$614$	6.02628	−	10.4378i	0.243201	−	0.421236i
$615$	11.4641	+	19.8564i	0.462277	+	0.800688i
$616$	3.63397	−	3.63397i	0.146417	−	0.146417i
$617$	−32.8564	+	8.80385i	−1.32275	+	0.354430i	−0.850007	−	0.526771i	$-0.823402\pi$
$617$	−32.8564	+	8.80385i	−1.32275	+	0.354430i	−0.472742	+	0.881201i	$0.656736\pi$
$618$	−12.1962	−	12.1962i	−0.490601	−	0.490601i
$619$	−0.366025	−	0.366025i	−0.0147118	−	0.0147118i	0.699713	−	0.714424i	$-0.253311\pi$
$619$	−0.366025	−	0.366025i	−0.0147118	−	0.0147118i	−0.714424	+	0.699713i	$0.753311\pi$
$620$	−8.02628	−	11.0263i	−0.322343	−	0.442826i
$621$		−	24.7846i		−	0.994572i
$622$	4.78461	−	4.78461i	0.191845	−	0.191845i
$623$	−4.75833	+	8.24167i	−0.190638	+	0.330196i
$624$	20.1962	−	13.4641i	0.808493	−	0.538995i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−2.99038	−	11.1603i	−0.119520	−	0.446053i
$627$	−6.29423	+	10.9019i	−0.251367	+	0.435381i
$628$		−	8.07180i		−	0.322100i
$629$		0			0
$630$	2.50962	−	9.36603i	0.0999856	−	0.373151i
$631$	10.0263	−	37.4186i	0.399140	−	1.48961i	−0.415473	−	0.909605i	$-0.636384\pi$
$631$	10.0263	−	37.4186i	0.399140	−	1.48961i	0.814613	−	0.580005i	$-0.196949\pi$
$632$	−23.1244	+	6.19615i	−0.919837	+	0.246470i
$633$	7.73205	−	4.46410i	0.307321	−	0.177432i
$634$	−7.60770	−	4.39230i	−0.302140	−	0.174441i
$635$	−6.39230	−	6.39230i	−0.253671	−	0.253671i
$636$			31.5167i			1.24972i
$637$	−0.418584	−	6.49038i	−0.0165849	−	0.257158i
$638$	−1.96410	−	3.40192i	−0.0777595	−	0.134683i
$639$	−5.50000	+	1.47372i	−0.217577	+	0.0582995i
$640$	8.09808	+	14.0263i	0.320105	+	0.554437i
$641$	−20.4282	−	35.3827i	−0.806866	−	1.39753i	−0.915024	−	0.403398i	$-0.867829\pi$
$641$	−20.4282	−	35.3827i	−0.806866	−	1.39753i	0.108159	−	0.994134i	$-0.465504\pi$
$642$	15.9282	+	4.26795i	0.628636	+	0.168443i
$643$	−0.607695	+	0.607695i	−0.0239652	+	0.0239652i	−0.718988	−	0.695023i	$-0.755394\pi$
$643$	−0.607695	+	0.607695i	−0.0239652	+	0.0239652i	0.695023	+	0.718988i	$0.255394\pi$
$644$	30.7583	−	8.24167i	1.21205	−	0.324767i
$645$	4.19615	+	15.6603i	0.165223	+	0.616622i
$646$		0			0
$647$	−46.7321			−1.83723			−0.918613	−	0.395158i	$-0.870690\pi$
$647$	−46.7321			−1.83723			−0.918613	+	0.395158i	$0.870690\pi$
$648$	−1.23205	−	4.59808i	−0.0483995	−	0.180629i
$649$	−1.94744			−0.0764438
$650$	−5.49038	−	1.09808i	−0.215350	−	0.0430701i
$651$	36.4904	−	26.5622i	1.43017	−	1.04105i
$652$	−4.43782	−	4.43782i	−0.173799	−	0.173799i
$653$	37.9808			1.48630			0.743151	−	0.669124i	$-0.233330\pi$
$653$	37.9808			1.48630			0.743151	+	0.669124i	$0.233330\pi$
$654$	9.92820	−	17.1962i	0.388223	−	0.672423i
$655$	17.3205	+	17.3205i	0.676768	+	0.676768i
$656$	3.78461	−	14.1244i	0.147764	−	0.551463i
$657$	47.1506	−	12.6340i	1.83952	−	0.492898i
$658$	−0.863448	−	3.22243i	−0.0336607	−	0.125623i
$659$	−28.5885			−1.11365			−0.556824	−	0.830630i	$-0.687980\pi$
$659$	−28.5885			−1.11365			−0.556824	+	0.830630i	$0.687980\pi$
$660$	5.19615	−	3.00000i	0.202260	−	0.116775i
$661$	−11.4641	−	3.07180i	−0.445902	−	0.119479i	0.0288793	−	0.999583i	$-0.490806\pi$
$661$	−11.4641	−	3.07180i	−0.445902	−	0.119479i	−0.474781	+	0.880104i	$0.657473\pi$
$662$	4.06218	+	7.03590i	0.157881	+	0.273458i
$663$		0			0
$664$	26.9545	−	15.5622i	1.04604	−	0.603930i
$665$	−20.8301	+	5.58142i	−0.807758	+	0.216438i
$666$		−	11.3205i		−	0.438661i
$667$		−	52.4449i		−	2.03067i
$668$	−2.76795	−	10.3301i	−0.107095	−	0.399685i
$669$	−3.75833	+	14.0263i	−0.145305	+	0.542287i
$670$	−2.09808	−	7.83013i	−0.0810558	−	0.302504i
$671$	2.76795	+	0.741670i	0.106855	+	0.0286318i
$672$	−36.0788	+	20.8301i	−1.39177	+	0.803540i
$673$	3.07180	+	5.32051i	0.118409	+	0.205091i	0.919137	−	0.393937i	$-0.128887\pi$
$673$	3.07180	+	5.32051i	0.118409	+	0.205091i	−0.800728	+	0.599028i	$0.795554\pi$
$674$	−4.75833	−	4.75833i	−0.183284	−	0.183284i
$675$	−6.00000	+	10.3923i	−0.230940	+	0.400000i
$676$	−17.8923	+	13.6699i	−0.688166	+	0.525764i
$677$	11.4282	−	6.59808i	0.439222	−	0.253585i	−0.264046	−	0.964510i	$-0.585057\pi$
$677$	11.4282	−	6.59808i	0.439222	−	0.253585i	0.703267	+	0.710925i	$0.251724\pi$
$678$	6.92820	−	6.92820i	0.266076	−	0.266076i
$679$	−17.7583	+	30.7583i	−0.681502	+	1.18040i
$680$		0			0
$681$	23.1244	−	23.1244i	0.886127	−	0.886127i
$682$	−2.55256	−	0.401924i	−0.0977425	−	0.0153905i
$683$	−16.8827	+	16.8827i	−0.645998	+	0.645998i	−0.952023	−	0.306025i	$-0.901001\pi$
$683$	−16.8827	+	16.8827i	−0.645998	+	0.645998i	0.306025	+	0.952023i	$0.401001\pi$
$684$	28.0981	−	28.0981i	1.07436	−	1.07436i
$685$	2.19615	+	1.26795i	0.0839107	+	0.0484458i
$686$		−	7.98076i		−	0.304707i
$687$	2.46410	+	0.660254i	0.0940113	+	0.0251903i
$688$	5.16987	−	8.95448i	0.197100	−	0.341386i
$689$	−1.54552	−	23.9641i	−0.0588795	−	0.912960i
$690$	−12.3923			−0.471767
$691$	−0.356406	+	1.33013i	−0.0135583	+	0.0506004i	−0.972374	−	0.233430i	$-0.925005\pi$
$691$	−0.356406	+	1.33013i	−0.0135583	+	0.0506004i	0.958815	+	0.284030i	$0.0916717\pi$
$692$	−18.9282	−	32.7846i	−0.719542	−	1.24628i
$693$	5.93782	+	10.2846i	0.225559	+	0.390680i
$694$	2.50962	+	9.36603i	0.0952638	+	0.355529i
$695$	26.3923	+	7.07180i	1.00112	+	0.268249i
$696$	11.5622	+	43.1506i	0.438263	+	1.63562i
$697$		0			0
$698$	−14.7321			−0.557616
$699$	9.46410	−	16.3923i	0.357965	−	0.620014i
$700$	−14.8923	−	3.99038i	−0.562876	−	0.150822i
$701$	6.92820	+	4.00000i	0.261675	+	0.151078i	0.625098	−	0.780546i	$-0.285059\pi$
$701$	6.92820	+	4.00000i	0.261675	+	0.151078i	−0.363424	+	0.931624i	$0.618392\pi$
$702$	−2.39230	−	7.07180i	−0.0902917	−	0.266908i
$703$	−21.8038	+	12.5885i	−0.822348	+	0.474783i
$704$	−1.96410	−	0.526279i	−0.0740249	−	0.0198349i
$705$		−	8.39230i		−	0.316072i
$706$	6.09808	−	10.5622i	0.229504	−	0.397513i
$707$	−11.2583	+	3.01666i	−0.423413	+	0.113453i
$708$	9.92820	+	2.66025i	0.373125	+	0.0999785i
$709$	−16.5167	−	16.5167i	−0.620296	−	0.620296i	0.325311	−	0.945607i	$-0.394531\pi$
$709$	−16.5167	−	16.5167i	−0.620296	−	0.620296i	−0.945607	+	0.325311i	$0.894531\pi$
$710$	0.241670	+	0.901924i	0.00906970	+	0.0338486i
$711$		−	55.3205i		−	2.07468i
$712$	−6.19615			−0.232211
$713$	−26.8301	−	21.6865i	−1.00480	−	0.812167i
$714$		0			0
$715$	−3.80385	+	2.53590i	−0.142256	+	0.0948372i
$716$	4.68653	+	2.70577i	0.175144	+	0.101119i
$717$	13.9282	+	13.9282i	0.520158	+	0.520158i
$718$	6.76795	+	11.7224i	0.252578	+	0.437477i
$719$	11.4641	−	19.8564i	0.427539	−	0.740519i	−0.569115	−	0.822258i	$-0.692714\pi$
$719$	11.4641	−	19.8564i	0.427539	−	0.740519i	0.996654	+	0.0817390i	$0.0260474\pi$
$720$	−15.0263	+	4.02628i	−0.559996	+	0.150051i
$721$	25.5885	+	25.5885i	0.952964	+	0.952964i
$722$	3.70577	+	0.992958i	0.137915	+	0.0369541i
$723$	7.73205	+	2.07180i	0.287558	+	0.0770510i
$724$	−28.5000	+	16.4545i	−1.05919	+	0.611526i
$725$	−12.6962	+	21.9904i	−0.471523	+	0.816702i
$726$	−3.73205	+	13.9282i	−0.138509	+	0.516924i
$727$	14.1962	+	8.19615i	0.526506	+	0.303978i	0.739593	−	0.673055i	$-0.235018\pi$
$727$	14.1962	+	8.19615i	0.526506	+	0.303978i	−0.213086	+	0.977033i	$0.568352\pi$
$728$	17.1962	−	11.4641i	0.637332	−	0.424888i
$729$	43.7846			1.62165
$730$	−2.07180	−	7.73205i	−0.0766806	−	0.286176i
$731$		0			0
$732$	−13.0981	−	7.56218i	−0.484119	−	0.279506i
$733$	2.31347	−	8.63397i	0.0854498	−	0.318903i	−0.909949	−	0.414720i	$-0.863880\pi$
$733$	2.31347	−	8.63397i	0.0854498	−	0.318903i	0.995399	+	0.0958167i	$0.0305463\pi$
$734$	9.92820	+	2.66025i	0.366457	+	0.0981918i
$735$	−1.80385	+	6.73205i	−0.0665359	+	0.248315i
$736$	22.5167	+	22.5167i	0.829975	+	0.829975i
$737$	8.59808	+	4.96410i	0.316714	+	0.182855i
$738$	−11.8756	−	6.85641i	−0.437149	−	0.252388i
$739$	5.34936	−	19.9641i	0.196780	−	0.734391i	−0.795019	−	0.606584i	$-0.792539\pi$
$739$	5.34936	−	19.9641i	0.196780	−	0.734391i	0.991799	−	0.127807i	$-0.0407939\pi$
$740$	12.0000			0.441129
$741$	−33.4186	+	38.0263i	−1.22766	+	1.39693i
$742$			10.2295i			0.375536i
$743$	−15.5359	+	15.5359i	−0.569957	+	0.569957i	−0.932116	−	0.362159i	$-0.882040\pi$
$743$	−15.5359	+	15.5359i	−0.569957	+	0.569957i	0.362159	+	0.932116i	$0.382040\pi$
$744$	26.8564	+	11.9282i	0.984604	+	0.437309i
$745$			22.9282i			0.840024i
$746$	13.0263	+	13.0263i	0.476926	+	0.476926i
$747$	18.6147	+	69.4711i	0.681078	+	2.54182i
$748$		0			0
$749$	−33.4186	−	8.95448i	−1.22109	−	0.327190i
$750$	13.8564	+	8.00000i	0.505964	+	0.292119i
$751$	39.1244	+	22.5885i	1.42767	+	0.824265i	0.996936	−	0.0782156i	$-0.0249223\pi$
$751$	39.1244	+	22.5885i	1.42767	+	0.824265i	0.430732	+	0.902480i	$0.358256\pi$
$752$	−3.78461	+	3.78461i	−0.138011	+	0.138011i
$753$	−66.8372	+	38.5885i	−2.43568	+	1.40624i
$754$	−5.06218	−	14.9641i	−0.184354	−	0.544960i
$755$	11.9545	−	6.90192i	0.435068	−	0.251187i
$756$	−5.32051	−	19.8564i	−0.193505	−	0.722171i
$757$	29.7846	−	17.1962i	1.08254	−	0.625005i	0.150960	−	0.988540i	$-0.451764\pi$
$757$	29.7846	−	17.1962i	1.08254	−	0.625005i	0.931580	+	0.363535i	$0.118430\pi$
$758$	1.20577	+	0.696152i	0.0437956	+	0.0252854i
$759$	10.7321	−	10.7321i	0.389549	−	0.389549i
$760$	−9.92820	−	9.92820i	−0.360134	−	0.360134i
$761$	−26.3923	+	7.07180i	−0.956720	+	0.256352i	−0.703212	−	0.710981i	$-0.748251\pi$
$761$	−26.3923	+	7.07180i	−0.956720	+	0.256352i	−0.253509	+	0.967333i	$0.581585\pi$
$762$	8.73205	+	2.33975i	0.316329	+	0.0847601i
$763$	−20.8301	+	36.0788i	−0.754101	+	1.30614i
$764$	8.49038	−	4.90192i	0.307171	−	0.177345i
$765$		0			0
$766$	−2.02628	−	3.50962i	−0.0732125	−	0.126808i
$767$	−7.67949	−	1.53590i	−0.277290	−	0.0554581i
$768$	−3.29423	−	1.90192i	−0.118870	−	0.0686298i
$769$	−9.63397	+	2.58142i	−0.347410	+	0.0930882i	−0.428305	−	0.903634i	$-0.640889\pi$
$769$	−9.63397	+	2.58142i	−0.347410	+	0.0930882i	0.0808946	+	0.996723i	$0.474222\pi$
$770$	1.68653	−	0.973721i	0.0607784	−	0.0350905i
$771$	−20.1962			−0.727347
$772$	−9.29423	+	2.49038i	−0.334507	+	0.0896308i
$773$	21.1962	−	21.1962i	0.762373	−	0.762373i	−0.214378	−	0.976751i	$-0.568772\pi$
$773$	21.1962	−	21.1962i	0.762373	−	0.762373i	0.976751	+	0.214378i	$0.0687725\pi$
$774$	−6.85641	−	6.85641i	−0.246448	−	0.246448i
$775$	6.00000	+	15.5885i	0.215526	+	0.559954i
$776$	−23.1244			−0.830116
$777$			39.7128i			1.42469i
$778$	−7.69615	+	2.06218i	−0.275920	+	0.0739327i
$779$			30.4974i			1.09268i
$780$	22.8564	−	7.73205i	0.818391	−	0.276852i
$781$	−0.990381	−	0.571797i	−0.0354386	−	0.0204605i
$782$		0			0
$783$	−33.8564			−1.20993
$784$	3.84936	−	2.22243i	0.137477	−	0.0793726i
$785$	1.70577	−	6.36603i	0.0608816	−	0.227213i
$786$	−23.6603	−	6.33975i	−0.843933	−	0.226131i
$787$	−43.3827	+	11.6244i	−1.54643	+	0.414364i	−0.928335	−	0.371744i	$-0.878760\pi$
$787$	−43.3827	+	11.6244i	−1.54643	+	0.414364i	−0.618090	+	0.786107i	$0.712093\pi$
$788$	2.36603	−	8.83013i	0.0842862	−	0.314560i
$789$	−26.6603	+	46.1769i	−0.949130	+	1.64394i
$790$	−9.07180			−0.322760
$791$	−14.5359	+	14.5359i	−0.516837	+	0.516837i
$792$	−3.86603	+	6.69615i	−0.137373	+	0.237937i
$793$	10.3301	+	5.10770i	0.366834	+	0.181380i
$794$	−3.63397	+	6.29423i	−0.128965	+	0.223374i
$795$	−6.66025	+	24.8564i	−0.236215	+	0.881566i
$796$	−19.9808	+	11.5359i	−0.708199	+	0.408879i
$797$	−18.8923	−	32.7224i	−0.669200	−	1.15909i	−0.978128	−	0.208003i	$-0.933304\pi$
$797$	−18.8923	−	32.7224i	−0.669200	−	1.15909i	0.308928	−	0.951085i	$-0.400030\pi$
$798$	15.2487	−	15.2487i	0.539799	−	0.539799i
$799$		0			0
$800$	−3.99038	−	14.8923i	−0.141081	−	0.526522i
$801$	3.70577	−	13.8301i	0.130937	−	0.488664i
$802$		−	13.1244i		−	0.463437i
$803$	8.49038	+	4.90192i	0.299619	+	0.172985i
$804$	−37.0526	−	37.0526i	−1.30674	−	1.30674i
$805$	26.0000			0.916380
$806$	−9.74871	−	3.59808i	−0.343384	−	0.126737i
$807$	−48.5885			−1.71039
$808$	−5.36603	−	5.36603i	−0.188776	−	0.188776i
$809$	−26.4449	−	15.2679i	−0.929752	−	0.536793i	−0.0430188	−	0.999074i	$-0.513698\pi$
$809$	−26.4449	−	15.2679i	−0.929752	−	0.536793i	−0.886733	+	0.462282i	$0.847031\pi$
$810$		−	1.80385i		−	0.0633807i
$811$	−8.64359	+	32.2583i	−0.303518	+	1.13274i	0.630696	+	0.776030i	$0.282769\pi$
$811$	−8.64359	+	32.2583i	−0.303518	+	1.13274i	−0.934214	+	0.356713i	$0.883897\pi$
$812$	−11.2583	−	42.0167i	−0.395090	−	1.47450i
$813$	−6.46410	−	24.1244i	−0.226706	−	0.846078i
$814$	1.60770	−	1.60770i	0.0563497	−	0.0563497i
$815$	−2.56218	−	4.43782i	−0.0897492	−	0.155450i
$816$		0			0
$817$	−5.58142	+	20.8301i	−0.195269	+	0.728754i
$818$	9.63397	−	16.6865i	0.336844	−	0.583431i
$819$	15.3038	+	45.2391i	0.534760	+	1.58078i
$820$	7.26795	−	12.5885i	0.253808	−	0.439608i
$821$	37.1769	−	37.1769i	1.29748	−	1.29748i	0.367433	−	0.930050i	$-0.380237\pi$
$821$	37.1769	−	37.1769i	1.29748	−	1.29748i	0.930050	−	0.367433i	$-0.119763\pi$
$822$	−2.53590			−0.0884496
$823$	8.39230	−	14.5359i	0.292537	−	0.506690i	−0.681872	−	0.731472i	$-0.738834\pi$
$823$	8.39230	−	14.5359i	0.292537	−	0.506690i	0.974409	+	0.224782i	$0.0721671\pi$
$824$	−6.09808	+	22.7583i	−0.212437	+	0.792824i
$825$	−7.09808	+	1.90192i	−0.247123	+	0.0662165i
$826$	3.22243	+	0.863448i	0.112123	+	0.0300432i
$827$	0.169873	−	0.633975i	0.00590706	−	0.0220455i	−0.962909	−	0.269825i	$-0.913034\pi$
$827$	0.169873	−	0.633975i	0.00590706	−	0.0220455i	0.968816	+	0.247779i	$0.0797008\pi$
$828$	−41.4904	+	23.9545i	−1.44189	+	0.832476i
$829$	−18.7846			−0.652416			−0.326208	−	0.945298i	$-0.605771\pi$
$829$	−18.7846			−0.652416			−0.326208	+	0.945298i	$0.605771\pi$
$830$	11.3923	−	3.05256i	0.395433	−	0.105956i
$831$	62.4449	+	36.0526i	2.16619	+	1.25065i
$832$	−7.33013	−	3.62436i	−0.254126	−	0.125652i
$833$		0			0
$834$	−26.3923	+	7.07180i	−0.913891	+	0.244876i
$835$		−	8.73205i		−	0.302185i
$836$	7.98076			0.276020
$837$	−14.0000	+	17.3205i	−0.483911	+	0.598684i
$838$	10.9808	+	10.9808i	0.379324	+	0.379324i
$839$	−4.70577	+	4.70577i	−0.162461	+	0.162461i	−0.783656	−	0.621195i	$-0.786648\pi$
$839$	−4.70577	+	4.70577i	−0.162461	+	0.162461i	0.621195	+	0.783656i	$0.286648\pi$
$840$	−21.3923	+	5.73205i	−0.738105	+	0.197775i
$841$	−42.6410			−1.47038
$842$	5.95448	−	3.43782i	0.205205	−	0.118475i
$843$	−79.8372	+	21.3923i	−2.74974	+	0.736790i
$844$	−4.90192	−	2.83013i	−0.168731	−	0.0974170i
$845$	−17.0000	+	7.00000i	−0.584818	+	0.240807i
$846$	2.50962	+	4.34679i	0.0862825	+	0.149446i
$847$	7.83013	−	29.2224i	0.269046	−	1.00409i
$848$	14.2128	−	8.20577i	0.488070	−	0.281787i
$849$	−9.73205	+	16.8564i	−0.334003	+	0.578510i
$850$		0			0
$851$	29.3205	−	7.85641i	1.00509	−	0.269314i
$852$	4.26795	+	4.26795i	0.146218	+	0.146218i
$853$	−24.4641	+	24.4641i	−0.837635	+	0.837635i	−0.988547	−	0.150912i	$-0.951779\pi$
$853$	−24.4641	+	24.4641i	−0.837635	+	0.837635i	0.150912	+	0.988547i	$0.451779\pi$
$854$	−4.25129	−	2.45448i	−0.145476	−	0.0839907i
$855$	28.0981	−	16.2224i	0.960934	−	0.554795i
$856$	−5.83013	−	21.7583i	−0.199270	−	0.743684i
$857$	−25.4545	+	14.6962i	−0.869509	+	0.502011i	−0.867185	−	0.497986i	$-0.834073\pi$
$857$	−25.4545	+	14.6962i	−0.869509	+	0.502011i	−0.00232367	+	0.999997i	$0.500740\pi$
$858$	2.02628	−	4.09808i	0.0691760	−	0.139906i
$859$	22.6865	−	13.0981i	0.774055	−	0.446901i	−0.0602645	−	0.998182i	$-0.519194\pi$
$859$	22.6865	−	13.0981i	0.774055	−	0.446901i	0.834319	+	0.551282i	$0.185861\pi$
$860$	7.26795	−	7.26795i	0.247835	−	0.247835i
$861$	41.6603	+	24.0526i	1.41978	+	0.819709i
$862$	16.4545	+	9.50000i	0.560442	+	0.323571i
$863$	−12.3301	−	3.30385i	−0.419722	−	0.112464i	0.0427754	−	0.999085i	$-0.486380\pi$
$863$	−12.3301	−	3.30385i	−0.419722	−	0.112464i	−0.462498	+	0.886620i	$0.653047\pi$
$864$	14.5359	−	14.5359i	0.494521	−	0.494521i
$865$	−8.00000	−	29.8564i	−0.272008	−	1.01515i
$866$	−5.02628	−	5.02628i	−0.170800	−	0.170800i
$867$			46.4449i			1.57735i
$868$	−26.1506	−	11.6147i	−0.887610	−	0.394230i
$869$	7.85641	−	7.85641i	0.266510	−	0.266510i
$870$			16.9282i			0.573920i
$871$	29.9904	+	26.3564i	1.01619	+	0.893053i
$872$	−27.1244			−0.918547
$873$	13.8301	−	51.6147i	0.468079	−	1.74689i
$874$	−14.2750	−	8.24167i	−0.482859	−	0.278779i
$875$	−29.0718	−	16.7846i	−0.982806	−	0.567423i
$876$	−36.5885	−	36.5885i	−1.23621	−	1.23621i
$877$	−2.63397	+	9.83013i	−0.0889430	+	0.331940i	−0.996032	−	0.0889999i	$-0.971633\pi$
$877$	−2.63397	+	9.83013i	−0.0889430	+	0.331940i	0.907089	+	0.420940i	$0.138300\pi$
$878$	−0.267949	−	0.0717968i	−0.00904285	−	0.00242302i
$879$	−19.8564	+	74.1051i	−0.669740	+	2.49950i
$880$	−2.70577	−	1.56218i	−0.0912115	−	0.0526610i
$881$	9.72243	+	16.8397i	0.327557	+	0.567345i	0.982027	−	0.188743i	$-0.0604413\pi$
$881$	9.72243	+	16.8397i	0.327557	+	0.567345i	−0.654469	+	0.756088i	$0.727108\pi$
$882$	−1.07884	−	4.02628i	−0.0363264	−	0.135572i
$883$	30.1962			1.01618			0.508091	−	0.861304i	$-0.330351\pi$
$883$	30.1962			1.01618			0.508091	+	0.861304i	$0.330351\pi$
$884$		0			0
$885$	7.26795	+	4.19615i	0.244309	+	0.141052i
$886$	−0.751289	+	2.80385i	−0.0252400	+	0.0941971i
$887$	−1.43782	+	2.49038i	−0.0482773	+	0.0836188i	−0.889154	−	0.457608i	$-0.848706\pi$
$887$	−1.43782	+	2.49038i	−0.0482773	+	0.0836188i	0.840877	+	0.541226i	$0.182040\pi$
$888$	−22.3923	+	12.9282i	−0.751437	+	0.433842i
$889$	−18.3205	−	4.90897i	−0.614450	−	0.164641i
$890$	−2.26795	−	0.607695i	−0.0760218	−	0.0203700i
$891$	1.56218	+	1.56218i	0.0523349	+	0.0523349i
$892$	8.89230	−	2.38269i	0.297736	−	0.0797782i
$893$	5.58142	−	9.66730i	0.186775	−	0.323504i
$894$	−11.4641	−	19.8564i	−0.383417	−	0.664098i
$895$	3.12436	+	3.12436i	0.104436	+	0.104436i
$896$	29.4282	+	16.9904i	0.983127	+	0.567609i
$897$	50.7846	−	33.8564i	1.69565	−	1.13043i
$898$		−	7.07180i		−	0.235989i
$899$	−29.6244	+	36.6506i	−0.988028	+	1.22237i
$900$	23.1962			0.773205
$901$		0			0
$902$	−0.712813	−	2.66025i	−0.0237341	−	0.0885768i
$903$	24.0526	+	24.0526i	0.800419	+	0.800419i
$904$	−12.9282	−	3.46410i	−0.429986	−	0.115214i
$905$	−25.9545	+	6.95448i	−0.862756	+	0.231175i
$906$	−6.90192	+	11.9545i	−0.229301	+	0.397161i
$907$			4.87564i			0.161893i	0.996718	+	0.0809466i	$0.0257943\pi$
$907$			4.87564i			0.161893i	−0.996718	+	0.0809466i	$0.974206\pi$
$908$	−20.0263	−	5.36603i	−0.664595	−	0.178078i
$909$	15.1865	−	8.76795i	0.503706	−	0.290815i
$910$	7.41858	−	2.50962i	0.245924	−	0.0831931i
$911$	19.0526	+	11.0000i	0.631239	+	0.364446i	0.781232	−	0.624241i	$-0.214592\pi$
$911$	19.0526	+	11.0000i	0.631239	+	0.364446i	−0.149992	+	0.988687i	$0.547925\pi$
$912$	−33.4186	−	8.95448i	−1.10660	−	0.296513i
$913$	−7.22243	+	12.5096i	−0.239028	+	0.414008i
$914$	8.78461			0.290569
$915$	−8.73205	−	8.73205i	−0.288673	−	0.288673i
$916$	−0.418584	−	1.56218i	−0.0138304	−	0.0516158i
$917$	49.6410	+	13.3013i	1.63929	+	0.439247i
$918$		0			0
$919$	11.6340	+	20.1506i	0.383769	+	0.664708i	0.991598	−	0.129360i	$-0.0412924\pi$
$919$	11.6340	+	20.1506i	0.383769	+	0.664708i	−0.607828	+	0.794069i	$0.707959\pi$
$920$	8.46410	+	14.6603i	0.279053	+	0.483334i
$921$	16.4641	−	61.4449i	0.542511	−	2.02468i
$922$	−0.143594			−0.00472900
$923$	−3.45448	−	3.03590i	−0.113706	−	0.0999278i
$924$	6.29423	−	10.9019i	0.207065	−	0.358647i
$925$	−14.1962	−	3.80385i	−0.466767	−	0.125070i
$926$		−	4.87564i		−	0.160224i
$927$	−47.1506	−	27.2224i	−1.54863	−	0.894102i
$928$	30.7583	−	30.7583i	1.00969	−	1.00969i
$929$	−14.3205	+	14.3205i	−0.469841	+	0.469841i	−0.901863	−	0.432022i	$-0.857800\pi$
$929$	−14.3205	+	14.3205i	−0.469841	+	0.469841i	0.432022	+	0.901863i	$0.357800\pi$
$930$	8.66025	+	7.00000i	0.283981	+	0.229539i
$931$	−6.55514	+	6.55514i	−0.214836	+	0.214836i
$932$	−12.0000			−0.393073
$933$	17.8564	−	30.9282i	0.584593	−	1.01254i
$934$	6.73205	−	6.73205i	0.220279	−	0.220279i
$935$		0			0
$936$	−20.5263	+	23.3564i	−0.670922	+	0.763428i
$937$	0.500000	−	0.866025i	0.0163343	−	0.0282918i	−0.857743	−	0.514079i	$-0.828134\pi$
$937$	0.500000	−	0.866025i	0.0163343	−	0.0282918i	0.874077	+	0.485787i	$0.161467\pi$
$938$	−12.0263	−	12.0263i	−0.392672	−	0.392672i
$939$	−30.4904	−	52.8109i	−0.995016	−	1.72342i
$940$	−4.60770	+	2.66025i	−0.150286	+	0.0867679i
$941$	27.0263	+	7.24167i	0.881032	+	0.236072i	0.670852	−	0.741591i	$-0.265929\pi$
$941$	27.0263	+	7.24167i	0.881032	+	0.236072i	0.210179	+	0.977663i	$0.432595\pi$
$942$	1.70577	+	6.36603i	0.0555770	+	0.207416i
$943$	9.51666	−	35.5167i	0.309905	−	1.15658i
$944$	−1.38526	−	5.16987i	−0.0450865	−	0.168265i
$945$		−	16.7846i		−	0.546003i
$946$		−	1.94744i		−	0.0633168i
$947$	23.1603	−	6.20577i	0.752607	−	0.201660i	0.137933	−	0.990442i	$-0.455954\pi$
$947$	23.1603	−	6.20577i	0.752607	−	0.201660i	0.614674	+	0.788781i	$0.289287\pi$
$948$	−50.7846	+	29.3205i	−1.64941	+	0.952286i
$949$	29.6147	+	26.0263i	0.961335	+	0.844849i
$950$	3.99038	+	6.91154i	0.129465	+	0.224240i
$951$	−44.7846	−	12.0000i	−1.45224	−	0.389127i
$952$		0			0
$953$	15.3397			0.496903			0.248452	−	0.968644i	$-0.420078\pi$
$953$	15.3397			0.496903			0.248452	+	0.968644i	$0.420078\pi$
$954$	−3.98334	−	14.8660i	−0.128965	−	0.481305i
$955$	7.73205	−	2.07180i	0.250203	−	0.0670418i
$956$	3.23205	−	12.0622i	0.104532	−	0.390119i
$957$	−14.6603	−	14.6603i	−0.473899	−	0.473899i
$958$	1.64359	−	2.84679i	0.0531021	−	0.0919755i
$959$	5.32051			0.171808
$960$	6.19615	+	6.19615i	0.199980	+	0.199980i
$961$	6.50000	+	30.3109i	0.209677	+	0.977771i
$962$	7.60770	−	5.07180i	0.245282	−	0.163521i
$963$	52.0526			1.67737
$964$	−1.31347	−	4.90192i	−0.0423039	−	0.157880i
$965$	−7.85641			−0.252907
$966$	−22.5167	+	13.0000i	−0.724462	+	0.418268i
$967$	2.17949	+	8.13397i	0.0700877	+	0.261571i	0.992075	−	0.125650i	$-0.0401017\pi$
$967$	2.17949	+	8.13397i	0.0700877	+	0.261571i	−0.921987	+	0.387221i	$0.873435\pi$
$968$	19.0263	−	5.09808i	0.611528	−	0.163858i
$969$		0			0
$970$	−8.46410	−	2.26795i	−0.271766	−	0.0728195i
$971$	−27.5167	−	47.6603i	−0.883052	−	1.52949i	−0.847931	−	0.530107i	$-0.822152\pi$
$971$	−27.5167	−	47.6603i	−0.883052	−	1.52949i	−0.0351211	−	0.999383i	$-0.511182\pi$
$972$	−16.2224	−	28.0981i	−0.520335	−	0.901246i
$973$	55.3731	−	14.8372i	1.77518	−	0.475658i
$974$	3.70577	+	6.41858i	0.118741	+	0.205665i
$975$	−29.4904	+	1.90192i	−0.944448	+	0.0609103i
$976$			7.87564i			0.252093i
$977$	11.2679	+	11.2679i	0.360494	+	0.360494i	0.863995	−	0.503501i	$-0.167955\pi$
$977$	11.2679	+	11.2679i	0.360494	+	0.360494i	−0.503501	+	0.863995i	$0.667955\pi$
$978$	4.43782	+	2.56218i	0.141906	+	0.0819294i
$979$	2.49038	−	1.43782i	0.0795929	−	0.0459530i
$980$	4.26795	−	1.14359i	0.136335	−	0.0365308i
$981$	16.2224	−	60.5429i	0.517942	−	1.93299i
$982$	−0.562178	+	2.09808i	−0.0179398	+	0.0669523i
$983$	−5.76795	+	21.5263i	−0.183969	+	0.686582i	0.810880	+	0.585213i	$0.198989\pi$
$983$	−5.76795	+	21.5263i	−0.183969	+	0.686582i	−0.994849	+	0.101369i	$0.967678\pi$
$984$			31.3205i			0.998461i
$985$	3.73205	−	6.46410i	0.118913	−	0.205963i
$986$		0			0
$987$	−8.80385	−	15.2487i	−0.280230	−	0.485372i
$988$	31.4711	+	6.29423i	1.00123	+	0.200246i
$989$	13.0000	−	22.5167i	0.413376	−	0.715988i
$990$	−2.07180	+	2.07180i	−0.0658460	+	0.0658460i
$991$			3.85641i			0.122503i	0.998122	+	0.0612514i	$0.0195091\pi$
$991$			3.85641i			0.122503i	−0.998122	+	0.0612514i	$0.980491\pi$
$992$	−3.01666	−	28.4545i	−0.0957791	−	0.903431i
$993$	30.3205	+	30.3205i	0.962192	+	0.962192i
$994$	1.38526	+	1.38526i	0.0439379	+	0.0439379i
$995$	−18.1962	+	4.87564i	−0.576857	+	0.154568i
$996$	53.9090	−	53.9090i	1.70817	−	1.70817i
$997$	20.5885	+	35.6603i	0.652043	+	1.12937i	0.982626	+	0.185595i	$0.0594212\pi$
$997$	20.5885	+	35.6603i	0.652043	+	1.12937i	−0.330583	+	0.943777i	$0.607245\pi$
$998$	3.55256	−	6.15321i	0.112454	−	0.194777i
$999$	−5.07180	−	18.9282i	−0.160465	−	0.598862i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.be.a.398.1	yes	4
13.5	odd	4		403.2.be.b.57.1	yes	4
31.6	odd	6		403.2.be.b.99.1	yes	4
403.161	even	12	inner	403.2.be.a.161.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.be.a.161.1	✓	4	403.161	even	12	inner
403.2.be.a.398.1	yes	4	1.1	even	1	trivial
403.2.be.b.57.1	yes	4	13.5	odd	4
403.2.be.b.99.1	yes	4	31.6	odd	6

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.be (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 0.366025i) q^{2} +(2.36603 + 1.36603i) q^{3} -1.73205i q^{4} +(0.366025 - 1.36603i) q^{5} +(0.366025 + 1.36603i) q^{6} +(-0.767949 - 2.86603i) q^{7} +(1.36603 - 1.36603i) q^{8} +(2.23205 + 3.86603i) q^{9} +O(q^{10})\)	\(q+(0.366025 + 0.366025i) q^{2} +(2.36603 + 1.36603i) q^{3} -1.73205i q^{4} +(0.366025 - 1.36603i) q^{5} +(0.366025 + 1.36603i) q^{6} +(-0.767949 - 2.86603i) q^{7} +(1.36603 - 1.36603i) q^{8} +(2.23205 + 3.86603i) q^{9} +(0.633975 - 0.366025i) q^{10} +(-0.232051 + 0.866025i) q^{11} +(2.36603 - 4.09808i) q^{12} +(-1.59808 + 3.23205i) q^{13} +(0.767949 - 1.33013i) q^{14} +(2.73205 - 2.73205i) q^{15} -2.46410 q^{16} +(-0.598076 + 2.23205i) q^{18} +(4.96410 - 1.33013i) q^{19} +(-2.36603 - 0.633975i) q^{20} +(2.09808 - 7.83013i) q^{21} +(-0.401924 + 0.232051i) q^{22} -6.19615 q^{23} +(5.09808 - 1.36603i) q^{24} +(2.59808 + 1.50000i) q^{25} +(-1.76795 + 0.598076i) q^{26} +4.00000i q^{27} +(-4.96410 + 1.33013i) q^{28} +8.46410i q^{29} +2.00000 q^{30} +(4.33013 + 3.50000i) q^{31} +(-3.63397 - 3.63397i) q^{32} +(-1.73205 + 1.73205i) q^{33} -4.19615 q^{35} +(6.69615 - 3.86603i) q^{36} +(-4.73205 + 1.26795i) q^{37} +(2.30385 + 1.33013i) q^{38} +(-8.19615 + 5.46410i) q^{39} +(-1.36603 - 2.36603i) q^{40} +(-1.53590 + 5.73205i) q^{41} +(3.63397 - 2.09808i) q^{42} +(-2.09808 + 3.63397i) q^{43} +(1.50000 + 0.401924i) q^{44} +(6.09808 - 1.63397i) q^{45} +(-2.26795 - 2.26795i) q^{46} +(1.53590 - 1.53590i) q^{47} +(-5.83013 - 3.36603i) q^{48} +(-1.56218 + 0.901924i) q^{49} +(0.401924 + 1.50000i) q^{50} +(5.59808 + 2.76795i) q^{52} +(-5.76795 + 3.33013i) q^{53} +(-1.46410 + 1.46410i) q^{54} +(1.09808 + 0.633975i) q^{55} +(-4.96410 - 2.86603i) q^{56} +(13.5622 + 3.63397i) q^{57} +(-3.09808 + 3.09808i) q^{58} +(0.562178 + 2.09808i) q^{59} +(-4.73205 - 4.73205i) q^{60} -3.19615i q^{61} +(0.303848 + 2.86603i) q^{62} +(9.36603 - 9.36603i) q^{63} +2.26795i q^{64} +(3.83013 + 3.36603i) q^{65} -1.26795 q^{66} +(2.86603 - 10.6962i) q^{67} +(-14.6603 - 8.46410i) q^{69} +(-1.53590 - 1.53590i) q^{70} +(-0.330127 + 1.23205i) q^{71} +(8.33013 + 2.23205i) q^{72} +(2.83013 - 10.5622i) q^{73} +(-2.19615 - 1.26795i) q^{74} +(4.09808 + 7.09808i) q^{75} +(-2.30385 - 8.59808i) q^{76} +2.66025 q^{77} +(-5.00000 - 1.00000i) q^{78} +(-10.7321 - 6.19615i) q^{79} +(-0.901924 + 3.36603i) q^{80} +(1.23205 - 2.13397i) q^{81} +(-2.66025 + 1.53590i) q^{82} +(15.5622 + 4.16987i) q^{83} +(-13.5622 - 3.63397i) q^{84} +(-2.09808 + 0.562178i) q^{86} +(-11.5622 + 20.0263i) q^{87} +(0.866025 + 1.50000i) q^{88} +(-2.26795 - 2.26795i) q^{89} +(2.83013 + 1.63397i) q^{90} +(10.4904 + 2.09808i) q^{91} +10.7321i q^{92} +(5.46410 + 14.1962i) q^{93} +1.12436 q^{94} -7.26795i q^{95} +(-3.63397 - 13.5622i) q^{96} +(-8.46410 - 8.46410i) q^{97} +(-0.901924 - 0.241670i) q^{98} +(-3.86603 + 1.03590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{3} - 2 q^{5} - 2 q^{6} - 10 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 - 2 * q^6 - 10 * q^7 + 2 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} + 6 q^{3} - 2 q^{5} - 2 q^{6} - 10 q^{7} + 2 q^{8} + 2 q^{9} + 6 q^{10} + 6 q^{11} + 6 q^{12} + 4 q^{13} + 10 q^{14} + 4 q^{15} + 4 q^{16} + 8 q^{18} + 6 q^{19} - 6 q^{20} - 2 q^{21} - 12 q^{22} - 4 q^{23} + 10 q^{24} - 14 q^{26} - 6 q^{28} + 8 q^{30} - 18 q^{32} + 4 q^{35} + 6 q^{36} - 12 q^{37} + 30 q^{38} - 12 q^{39} - 2 q^{40} - 20 q^{41} + 18 q^{42} + 2 q^{43} + 6 q^{44} + 14 q^{45} - 16 q^{46} + 20 q^{47} - 6 q^{48} + 18 q^{49} + 12 q^{50} + 12 q^{52} - 30 q^{53} + 8 q^{54} - 6 q^{55} - 6 q^{56} + 30 q^{57} - 2 q^{58} - 22 q^{59} - 12 q^{60} + 22 q^{62} + 34 q^{63} - 2 q^{65} - 12 q^{66} + 8 q^{67} - 24 q^{69} - 20 q^{70} + 16 q^{71} + 16 q^{72} - 6 q^{73} + 12 q^{74} + 6 q^{75} - 30 q^{76} - 24 q^{77} - 20 q^{78} - 36 q^{79} - 14 q^{80} - 2 q^{81} + 24 q^{82} + 38 q^{83} - 30 q^{84} + 2 q^{86} - 22 q^{87} - 16 q^{89} - 6 q^{90} - 10 q^{91} + 8 q^{93} - 44 q^{94} - 18 q^{96} - 20 q^{97} - 14 q^{98} - 12 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 - 2 * q^6 - 10 * q^7 + 2 * q^8 + 2 * q^9 + 6 * q^10 + 6 * q^11 + 6 * q^12 + 4 * q^13 + 10 * q^14 + 4 * q^15 + 4 * q^16 + 8 * q^18 + 6 * q^19 - 6 * q^20 - 2 * q^21 - 12 * q^22 - 4 * q^23 + 10 * q^24 - 14 * q^26 - 6 * q^28 + 8 * q^30 - 18 * q^32 + 4 * q^35 + 6 * q^36 - 12 * q^37 + 30 * q^38 - 12 * q^39 - 2 * q^40 - 20 * q^41 + 18 * q^42 + 2 * q^43 + 6 * q^44 + 14 * q^45 - 16 * q^46 + 20 * q^47 - 6 * q^48 + 18 * q^49 + 12 * q^50 + 12 * q^52 - 30 * q^53 + 8 * q^54 - 6 * q^55 - 6 * q^56 + 30 * q^57 - 2 * q^58 - 22 * q^59 - 12 * q^60 + 22 * q^62 + 34 * q^63 - 2 * q^65 - 12 * q^66 + 8 * q^67 - 24 * q^69 - 20 * q^70 + 16 * q^71 + 16 * q^72 - 6 * q^73 + 12 * q^74 + 6 * q^75 - 30 * q^76 - 24 * q^77 - 20 * q^78 - 36 * q^79 - 14 * q^80 - 2 * q^81 + 24 * q^82 + 38 * q^83 - 30 * q^84 + 2 * q^86 - 22 * q^87 - 16 * q^89 - 6 * q^90 - 10 * q^91 + 8 * q^93 - 44 * q^94 - 18 * q^96 - 20 * q^97 - 14 * q^98 - 12 * q^99

Introduction

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