LMFDB - Embedded newform 403.2.be.b.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.b.161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 1.36603i) q^{2} +(0.633975 + 0.366025i) q^{3} +1.73205i q^{4} +(0.366025 - 1.36603i) q^{5} +(-0.366025 - 1.36603i) q^{6} +(1.13397 + 4.23205i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(-1.23205 - 2.13397i) q^{9} +O(q^{10})$	\(q+(-1.36603 - 1.36603i) q^{2} +(0.633975 + 0.366025i) q^{3} +1.73205i q^{4} +(0.366025 - 1.36603i) q^{5} +(-0.366025 - 1.36603i) q^{6} +(1.13397 + 4.23205i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(-1.23205 - 2.13397i) q^{9} +(-2.36603 + 1.36603i) q^{10} +(0.866025 - 3.23205i) q^{11} +(-0.633975 + 1.09808i) q^{12} +(1.59808 - 3.23205i) q^{13} +(4.23205 - 7.33013i) q^{14} +(0.732051 - 0.732051i) q^{15} +4.46410 q^{16} +(-1.23205 + 4.59808i) q^{18} +(7.33013 - 1.96410i) q^{19} +(2.36603 + 0.633975i) q^{20} +(-0.830127 + 3.09808i) q^{21} +(-5.59808 + 3.23205i) q^{22} -4.19615 q^{23} +(-0.366025 + 0.0980762i) q^{24} +(2.59808 + 1.50000i) q^{25} +(-6.59808 + 2.23205i) q^{26} -4.00000i q^{27} +(-7.33013 + 1.96410i) q^{28} -1.53590i q^{29} -2.00000 q^{30} +(3.50000 - 4.33013i) q^{31} +(-5.36603 - 5.36603i) q^{32} +(1.73205 - 1.73205i) q^{33} +6.19615 q^{35} +(3.69615 - 2.13397i) q^{36} +(-4.73205 + 1.26795i) q^{37} +(-12.6962 - 7.33013i) q^{38} +(2.19615 - 1.46410i) q^{39} +(0.366025 + 0.633975i) q^{40} +(2.26795 - 8.46410i) q^{41} +(5.36603 - 3.09808i) q^{42} +(-3.09808 + 5.36603i) q^{43} +(5.59808 + 1.50000i) q^{44} +(-3.36603 + 0.901924i) q^{45} +(5.73205 + 5.73205i) q^{46} +(8.46410 - 8.46410i) q^{47} +(2.83013 + 1.63397i) q^{48} +(-10.5622 + 6.09808i) q^{49} +(-1.50000 - 5.59808i) q^{50} +(5.59808 + 2.76795i) q^{52} +(-9.23205 + 5.33013i) q^{53} +(-5.46410 + 5.46410i) q^{54} +(-4.09808 - 2.36603i) q^{55} +(-1.96410 - 1.13397i) q^{56} +(5.36603 + 1.43782i) q^{57} +(-2.09808 + 2.09808i) q^{58} +(3.09808 + 11.5622i) q^{59} +(1.26795 + 1.26795i) q^{60} -7.19615i q^{61} +(-10.6962 + 1.13397i) q^{62} +(7.63397 - 7.63397i) q^{63} +5.73205i q^{64} +(-3.83013 - 3.36603i) q^{65} -4.73205 q^{66} +(-0.303848 + 1.13397i) q^{67} +(-2.66025 - 1.53590i) q^{69} +(-8.46410 - 8.46410i) q^{70} +(-2.23205 + 8.33013i) q^{71} +(1.23205 + 0.330127i) q^{72} +(-1.56218 + 5.83013i) q^{73} +(8.19615 + 4.73205i) q^{74} +(1.09808 + 1.90192i) q^{75} +(3.40192 + 12.6962i) q^{76} +14.6603 q^{77} +(-5.00000 - 1.00000i) q^{78} +(-7.26795 - 4.19615i) q^{79} +(1.63397 - 6.09808i) q^{80} +(-2.23205 + 3.86603i) q^{81} +(-14.6603 + 8.46410i) q^{82} +(12.8301 + 3.43782i) q^{83} +(-5.36603 - 1.43782i) q^{84} +(11.5622 - 3.09808i) q^{86} +(0.562178 - 0.973721i) q^{87} +(0.866025 + 1.50000i) q^{88} +(5.73205 + 5.73205i) q^{89} +(5.83013 + 3.36603i) q^{90} +(15.4904 + 3.09808i) q^{91} -7.26795i q^{92} +(3.80385 - 1.46410i) q^{93} -23.1244 q^{94} -10.7321i q^{95} +(-1.43782 - 5.36603i) q^{96} +(-1.53590 - 1.53590i) q^{97} +(22.7583 + 6.09808i) q^{98} +(-7.96410 + 2.13397i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 6 q^{3} - 2 q^{5} + 2 q^{6} + 8 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 + 8 * q^7 + 2 * q^8 + 2 * q^9	$ 4 q - 2 q^{2} + 6 q^{3} - 2 q^{5} + 2 q^{6} + 8 q^{7} + 2 q^{8} + 2 q^{9} - 6 q^{10} - 6 q^{12} - 4 q^{13} + 10 q^{14} - 4 q^{15} + 4 q^{16} + 2 q^{18} + 12 q^{19} + 6 q^{20} + 14 q^{21} - 12 q^{22} + 4 q^{23} + 2 q^{24} - 16 q^{26} - 12 q^{28} - 8 q^{30} + 14 q^{31} - 18 q^{32} + 4 q^{35} - 6 q^{36} - 12 q^{37} - 30 q^{38} - 12 q^{39} - 2 q^{40} + 16 q^{41} + 18 q^{42} - 2 q^{43} + 12 q^{44} - 10 q^{45} + 16 q^{46} + 20 q^{47} - 6 q^{48} - 18 q^{49} - 6 q^{50} + 12 q^{52} - 30 q^{53} - 8 q^{54} - 6 q^{55} + 6 q^{56} + 18 q^{57} + 2 q^{58} + 2 q^{59} + 12 q^{60} - 22 q^{62} + 34 q^{63} + 2 q^{65} - 12 q^{66} - 22 q^{67} + 24 q^{69} - 20 q^{70} - 2 q^{71} - 2 q^{72} + 18 q^{73} + 12 q^{74} - 6 q^{75} + 24 q^{76} + 24 q^{77} - 20 q^{78} - 36 q^{79} + 10 q^{80} - 2 q^{81} - 24 q^{82} + 34 q^{83} - 18 q^{84} + 22 q^{86} - 22 q^{87} + 16 q^{89} + 6 q^{90} + 10 q^{91} + 36 q^{93} - 44 q^{94} - 30 q^{96} - 20 q^{97} + 46 q^{98} - 18 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 + 2 * q^6 + 8 * q^7 + 2 * q^8 + 2 * q^9 - 6 * q^10 - 6 * q^12 - 4 * q^13 + 10 * q^14 - 4 * q^15 + 4 * q^16 + 2 * q^18 + 12 * q^19 + 6 * q^20 + 14 * q^21 - 12 * q^22 + 4 * q^23 + 2 * q^24 - 16 * q^26 - 12 * q^28 - 8 * q^30 + 14 * q^31 - 18 * q^32 + 4 * q^35 - 6 * q^36 - 12 * q^37 - 30 * q^38 - 12 * q^39 - 2 * q^40 + 16 * q^41 + 18 * q^42 - 2 * q^43 + 12 * q^44 - 10 * q^45 + 16 * q^46 + 20 * q^47 - 6 * q^48 - 18 * q^49 - 6 * q^50 + 12 * q^52 - 30 * q^53 - 8 * q^54 - 6 * q^55 + 6 * q^56 + 18 * q^57 + 2 * q^58 + 2 * q^59 + 12 * q^60 - 22 * q^62 + 34 * q^63 + 2 * q^65 - 12 * q^66 - 22 * q^67 + 24 * q^69 - 20 * q^70 - 2 * q^71 - 2 * q^72 + 18 * q^73 + 12 * q^74 - 6 * q^75 + 24 * q^76 + 24 * q^77 - 20 * q^78 - 36 * q^79 + 10 * q^80 - 2 * q^81 - 24 * q^82 + 34 * q^83 - 18 * q^84 + 22 * q^86 - 22 * q^87 + 16 * q^89 + 6 * q^90 + 10 * q^91 + 36 * q^93 - 44 * q^94 - 30 * q^96 - 20 * q^97 + 46 * q^98 - 18 * 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 $

$2$	−1.36603	−	1.36603i	−0.965926	−	0.965926i	0.0335125	−	0.999438i	$-0.489331\pi$
$2$	−1.36603	−	1.36603i	−0.965926	−	0.965926i	−0.999438	+	0.0335125i	$0.989331\pi$
$3$	0.633975	+	0.366025i	0.366025	+	0.211325i	0.671721	−	0.740805i	$-0.265556\pi$
$3$	0.633975	+	0.366025i	0.366025	+	0.211325i	−0.305695	+	0.952129i	$0.598889\pi$
$4$			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
$7$	1.13397	+	4.23205i	0.428602	+	1.59956i	0.755929	+	0.654654i	$0.227186\pi$
$7$	1.13397	+	4.23205i	0.428602	+	1.59956i	−0.327327	+	0.944911i	$0.606148\pi$
$8$	−0.366025	+	0.366025i	−0.129410	+	0.129410i
$9$	−1.23205	−	2.13397i	−0.410684	−	0.711325i
$10$	−2.36603	+	1.36603i	−0.748203	+	0.431975i
$11$	0.866025	−	3.23205i	0.261116	−	0.974500i	−0.703468	−	0.710727i	$-0.748366\pi$
$11$	0.866025	−	3.23205i	0.261116	−	0.974500i	0.964585	−	0.263773i	$-0.0849671\pi$
$12$	−0.633975	+	1.09808i	−0.183013	+	0.316987i
$13$	1.59808	−	3.23205i	0.443227	−	0.896410i
$13$	1.59808	−	3.23205i	0.443227	−	0.896410i
$14$	4.23205	−	7.33013i	1.13106	−	1.95906i
$15$	0.732051	−	0.732051i	0.189015	−	0.189015i
$16$	4.46410			1.11603
$17$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$17$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$18$	−1.23205	+	4.59808i	−0.290397	+	1.08378i
$19$	7.33013	−	1.96410i	1.68165	−	0.450596i	0.713433	−	0.700723i	$-0.247139\pi$
$19$	7.33013	−	1.96410i	1.68165	−	0.450596i	0.968213	+	0.250127i	$0.0804724\pi$
$20$	2.36603	+	0.633975i	0.529059	+	0.141761i
$21$	−0.830127	+	3.09808i	−0.181149	+	0.676056i
$22$	−5.59808	+	3.23205i	−1.19351	+	0.689076i
$23$	−4.19615			−0.874958			−0.437479	−	0.899229i	$-0.644129\pi$
$23$	−4.19615			−0.874958			−0.437479	+	0.899229i	$0.644129\pi$
$24$	−0.366025	+	0.0980762i	−0.0747146	+	0.0200197i
$25$	2.59808	+	1.50000i	0.519615	+	0.300000i
$26$	−6.59808	+	2.23205i	−1.29399	+	0.437741i
$27$		−	4.00000i		−	0.769800i
$28$	−7.33013	+	1.96410i	−1.38526	+	0.371180i
$29$		−	1.53590i		−	0.285209i	−0.989780	−	0.142605i	$-0.954452\pi$
$29$		−	1.53590i		−	0.285209i	0.989780	−	0.142605i	$-0.0455477\pi$
$30$	−2.00000			−0.365148
$31$	3.50000	−	4.33013i	0.628619	−	0.777714i
$31$	3.50000	−	4.33013i	0.628619	−	0.777714i
$32$	−5.36603	−	5.36603i	−0.948588	−	0.948588i
$33$	1.73205	−	1.73205i	0.301511	−	0.301511i
$34$		0			0
$35$	6.19615			1.04734
$36$	3.69615	−	2.13397i	0.616025	−	0.355662i
$37$	−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	$0.548593\pi$
$38$	−12.6962	−	7.33013i	−2.05959	−	1.18910i
$39$	2.19615	−	1.46410i	0.351666	−	0.234444i
$40$	0.366025	+	0.633975i	0.0578737	+	0.100240i
$41$	2.26795	−	8.46410i	0.354194	−	1.32187i	−0.527301	−	0.849678i	$-0.676796\pi$
$41$	2.26795	−	8.46410i	0.354194	−	1.32187i	0.881496	−	0.472192i	$-0.156537\pi$
$42$	5.36603	−	3.09808i	0.827996	−	0.478044i
$43$	−3.09808	+	5.36603i	−0.472452	+	0.818311i	−0.999503	−	0.0315225i	$-0.989964\pi$
$43$	−3.09808	+	5.36603i	−0.472452	+	0.818311i	0.527051	+	0.849834i	$0.323298\pi$
$44$	5.59808	+	1.50000i	0.843942	+	0.226134i
$45$	−3.36603	+	0.901924i	−0.501777	+	0.134451i
$46$	5.73205	+	5.73205i	0.845145	+	0.845145i
$47$	8.46410	−	8.46410i	1.23462	−	1.23462i	0.272445	−	0.962171i	$-0.412168\pi$
$47$	8.46410	−	8.46410i	1.23462	−	1.23462i	0.962171	−	0.272445i	$-0.0878322\pi$
$48$	2.83013	+	1.63397i	0.408494	+	0.235844i
$49$	−10.5622	+	6.09808i	−1.50888	+	0.871154i
$50$	−1.50000	−	5.59808i	−0.212132	−	0.791688i
$51$		0			0
$52$	5.59808	+	2.76795i	0.776313	+	0.383845i
$53$	−9.23205	+	5.33013i	−1.26812	+	0.732149i	−0.974632	−	0.223814i	$-0.928149\pi$
$53$	−9.23205	+	5.33013i	−1.26812	+	0.732149i	−0.293488	+	0.955963i	$0.594816\pi$
$54$	−5.46410	+	5.46410i	−0.743570	+	0.743570i
$55$	−4.09808	−	2.36603i	−0.552584	−	0.319035i
$56$	−1.96410	−	1.13397i	−0.262464	−	0.151534i
$57$	5.36603	+	1.43782i	0.710747	+	0.190444i
$58$	−2.09808	+	2.09808i	−0.275491	+	0.275491i
$59$	3.09808	+	11.5622i	0.403335	+	1.50527i	0.807106	+	0.590407i	$0.201033\pi$
$59$	3.09808	+	11.5622i	0.403335	+	1.50527i	−0.403770	+	0.914860i	$0.632301\pi$
$60$	1.26795	+	1.26795i	0.163692	+	0.163692i
$61$		−	7.19615i		−	0.921373i	−0.887563	−	0.460686i	$-0.847603\pi$
$61$		−	7.19615i		−	0.921373i	0.887563	−	0.460686i	$-0.152397\pi$
$62$	−10.6962	+	1.13397i	−1.35841	+	0.144015i
$63$	7.63397	−	7.63397i	0.961790	−	0.961790i
$64$			5.73205i			0.716506i
$65$	−3.83013	−	3.36603i	−0.475069	−	0.417504i
$66$	−4.73205			−0.582475
$67$	−0.303848	+	1.13397i	−0.0371209	+	0.138537i	−0.981999	−	0.188884i	$-0.939513\pi$
$67$	−0.303848	+	1.13397i	−0.0371209	+	0.138537i	0.944878	+	0.327421i	$0.106180\pi$
$68$		0			0
$69$	−2.66025	−	1.53590i	−0.320257	−	0.184900i
$70$	−8.46410	−	8.46410i	−1.01165	−	1.01165i
$71$	−2.23205	+	8.33013i	−0.264896	+	0.988604i	0.697418	+	0.716664i	$0.254332\pi$
$71$	−2.23205	+	8.33013i	−0.264896	+	0.988604i	−0.962314	+	0.271940i	$0.912335\pi$
$72$	1.23205	+	0.330127i	0.145199	+	0.0389058i
$73$	−1.56218	+	5.83013i	−0.182839	+	0.682365i	0.812244	+	0.583318i	$0.198246\pi$
$73$	−1.56218	+	5.83013i	−0.182839	+	0.682365i	−0.995083	+	0.0990465i	$0.968421\pi$
$74$	8.19615	+	4.73205i	0.952783	+	0.550090i
$75$	1.09808	+	1.90192i	0.126795	+	0.219615i
$76$	3.40192	+	12.6962i	0.390227	+	1.45635i
$77$	14.6603			1.67069
$78$	−5.00000	−	1.00000i	−0.566139	−	0.113228i
$79$	−7.26795	−	4.19615i	−0.817708	−	0.472104i	0.0319173	−	0.999491i	$-0.489839\pi$
$79$	−7.26795	−	4.19615i	−0.817708	−	0.472104i	−0.849626	+	0.527386i	$0.823172\pi$
$80$	1.63397	−	6.09808i	0.182684	−	0.681786i
$81$	−2.23205	+	3.86603i	−0.248006	+	0.429558i
$82$	−14.6603	+	8.46410i	−1.61895	+	0.934704i
$83$	12.8301	+	3.43782i	1.40829	+	0.377350i	0.881314	−	0.472531i	$-0.156659\pi$
$83$	12.8301	+	3.43782i	1.40829	+	0.377350i	0.526975	+	0.849881i	$0.323326\pi$
$84$	−5.36603	−	1.43782i	−0.585481	−	0.156879i
$85$		0			0
$86$	11.5622	−	3.09808i	1.24678	−	0.334074i
$87$	0.562178	−	0.973721i	0.0602718	−	0.104394i
$88$	0.866025	+	1.50000i	0.0923186	+	0.159901i
$89$	5.73205	+	5.73205i	0.607596	+	0.607596i	0.942317	−	0.334721i	$-0.108642\pi$
$89$	5.73205	+	5.73205i	0.607596	+	0.607596i	−0.334721	+	0.942317i	$0.608642\pi$
$90$	5.83013	+	3.36603i	0.614549	+	0.354810i
$91$	15.4904	+	3.09808i	1.62383	+	0.324767i
$92$		−	7.26795i		−	0.757736i
$93$	3.80385	−	1.46410i	0.394441	−	0.151820i
$94$	−23.1244			−2.38510
$95$		−	10.7321i		−	1.10109i
$96$	−1.43782	−	5.36603i	−0.146747	−	0.547668i
$97$	−1.53590	−	1.53590i	−0.155947	−	0.155947i	0.624821	−	0.780768i	$-0.285172\pi$
$97$	−1.53590	−	1.53590i	−0.155947	−	0.155947i	−0.780768	+	0.624821i	$0.785172\pi$
$98$	22.7583	+	6.09808i	2.29894	+	0.615999i
$99$	−7.96410	+	2.13397i	−0.800422	+	0.214473i
$100$	−2.59808	+	4.50000i	−0.259808	+	0.450000i
$101$			9.92820i			0.987893i	0.869492	+	0.493947i	$0.164446\pi$
$101$			9.92820i			0.987893i	−0.869492	+	0.493947i	$0.835554\pi$
$102$		0			0
$103$	−1.56218	+	0.901924i	−0.153926	+	0.0888692i	−0.574985	−	0.818164i	$-0.694992\pi$
$103$	−1.56218	+	0.901924i	−0.153926	+	0.0888692i	0.421059	+	0.907033i	$0.361659\pi$
$104$	0.598076	+	1.76795i	0.0586462	+	0.173362i
$105$	3.92820	+	2.26795i	0.383353	+	0.221329i
$106$	19.8923	+	5.33013i	1.93211	+	0.517708i
$107$	−2.83013	+	4.90192i	−0.273599	+	0.473887i	−0.969781	−	0.243979i	$-0.921547\pi$
$107$	−2.83013	+	4.90192i	−0.273599	+	0.473887i	0.696182	+	0.717865i	$0.254881\pi$
$108$	6.92820			0.666667
$109$	3.92820	+	3.92820i	0.376254	+	0.376254i	0.869749	−	0.493495i	$-0.164281\pi$
$109$	3.92820	+	3.92820i	0.376254	+	0.376254i	−0.493495	+	0.869749i	$0.664281\pi$
$110$	2.36603	+	8.83013i	0.225592	+	0.841920i
$111$	−3.46410	−	0.928203i	−0.328798	−	0.0881012i
$112$	5.06218	+	18.8923i	0.478331	+	1.78516i
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	0.981689	−	0.190490i	$-0.0610077\pi$
$113$	3.46410	+	6.00000i	0.325875	+	0.564433i	−0.655814	+	0.754923i	$0.727674\pi$
$114$	−5.36603	−	9.29423i	−0.502574	−	0.870484i
$115$	−1.53590	+	5.73205i	−0.143223	+	0.534516i
$116$	2.66025			0.246998
$117$	−8.86603	+	0.571797i	−0.819664	+	0.0528626i
$118$	11.5622	−	20.0263i	1.06438	−	1.84357i
$119$		0			0
$120$			0.535898i			0.0489206i
$121$	−0.169873	−	0.0980762i	−0.0154430	−	0.00891602i
$122$	−9.83013	+	9.83013i	−0.889978	+	0.889978i
$123$	4.53590	−	4.53590i	0.408988	−	0.408988i
$124$	7.50000	+	6.06218i	0.673520	+	0.544400i
$125$	8.00000	−	8.00000i	0.715542	−	0.715542i
$126$	−20.8564			−1.85804
$127$	7.19615	−	12.4641i	0.638555	−	1.10601i	−0.347195	−	0.937793i	$-0.612866\pi$
$127$	7.19615	−	12.4641i	0.638555	−	1.10601i	0.985750	−	0.168217i	$-0.0538010\pi$
$128$	−2.90192	+	2.90192i	−0.256496	+	0.256496i
$129$	−3.92820	+	2.26795i	−0.345859	+	0.199682i
$130$	0.633975	+	9.83013i	0.0556033	+	0.862159i
$131$	8.66025	−	15.0000i	0.756650	−	1.31056i	−0.187900	−	0.982188i	$-0.560168\pi$
$131$	8.66025	−	15.0000i	0.756650	−	1.31056i	0.944550	−	0.328368i	$-0.106499\pi$
$132$	3.00000	+	3.00000i	0.261116	+	0.261116i
$133$	16.6244	+	28.7942i	1.44151	+	2.49678i
$134$	1.96410	−	1.13397i	0.169673	−	0.0979605i
$135$	−5.46410	−	1.46410i	−0.470275	−	0.126010i
$136$		0			0
$137$	1.73205	−	6.46410i	0.147979	−	0.552265i	−0.851626	−	0.524151i	$-0.824383\pi$
$137$	1.73205	−	6.46410i	0.147979	−	0.552265i	0.999605	−	0.0281149i	$-0.00895043\pi$
$138$	1.53590	+	5.73205i	0.130744	+	0.487945i
$139$			15.3205i			1.29947i	0.760161	+	0.649734i	$0.225120\pi$
$139$			15.3205i			1.29947i	−0.760161	+	0.649734i	$0.774880\pi$
$140$			10.7321i			0.907024i
$141$	8.46410	−	2.26795i	0.712806	−	0.190996i
$142$	14.4282	−	8.33013i	1.21079	−	0.699049i
$143$	−9.06218	−	7.96410i	−0.757817	−	0.665992i
$144$	−5.50000	−	9.52628i	−0.458333	−	0.793857i
$145$	−2.09808	−	0.562178i	−0.174236	−	0.0466863i
$146$	10.0981	−	5.83013i	0.835723	−	0.482505i
$147$	−8.92820			−0.736386
$148$	−2.19615	−	8.19615i	−0.180523	−	0.673720i
$149$	−6.19615	+	1.66025i	−0.507609	+	0.136013i	−0.503529	−	0.863978i	$-0.667965\pi$
$149$	−6.19615	+	1.66025i	−0.507609	+	0.136013i	−0.00407966	+	0.999992i	$0.501299\pi$
$150$	1.09808	−	4.09808i	0.0896575	−	0.334607i
$151$	−12.0981	−	12.0981i	−0.984527	−	0.984527i	0.0153546	−	0.999882i	$-0.495112\pi$
$151$	−12.0981	−	12.0981i	−0.984527	−	0.984527i	−0.999882	+	0.0153546i	$0.995112\pi$
$152$	−1.96410	+	3.40192i	−0.159310	+	0.275932i
$153$		0			0
$154$	−20.0263	−	20.0263i	−1.61376	−	1.61376i
$155$	−4.63397	−	6.36603i	−0.372210	−	0.511331i
$156$	2.53590	+	3.80385i	0.203034	+	0.304552i
$157$	−12.6603			−1.01040			−0.505199	−	0.863003i	$-0.668581\pi$
$157$	−12.6603			−1.01040			−0.505199	+	0.863003i	$0.668581\pi$
$158$	4.19615	+	15.6603i	0.333828	+	1.24586i
$159$	−7.80385			−0.618885
$160$	−9.29423	+	5.36603i	−0.734773	+	0.424222i
$161$	−4.75833	−	17.7583i	−0.375009	−	1.39955i
$162$	8.33013	−	2.23205i	0.654477	−	0.175366i
$163$	−9.56218	+	9.56218i	−0.748968	+	0.748968i	−0.974285	−	0.225318i	$-0.927658\pi$
$163$	−9.56218	+	9.56218i	−0.748968	+	0.748968i	0.225318	+	0.974285i	$0.427658\pi$
$164$	14.6603	+	3.92820i	1.14477	+	0.306741i
$165$	−1.73205	−	3.00000i	−0.134840	−	0.233550i
$166$	−12.8301	−	22.2224i	−0.995811	−	1.72480i
$167$	−3.59808	+	0.964102i	−0.278427	+	0.0746044i	−0.395331	−	0.918539i	$-0.629370\pi$
$167$	−3.59808	+	0.964102i	−0.278427	+	0.0746044i	0.116903	+	0.993143i	$0.462703\pi$
$168$	−0.830127	−	1.43782i	−0.0640457	−	0.110930i
$169$	−7.89230	−	10.3301i	−0.607100	−	0.794625i
$170$		0			0
$171$	−13.2224	−	13.2224i	−1.01114	−	1.01114i
$172$	−9.29423	−	5.36603i	−0.708678	−	0.409156i
$173$	−5.07180	+	2.92820i	−0.385602	+	0.222627i	−0.680253	−	0.732978i	$-0.738130\pi$
$173$	−5.07180	+	2.92820i	−0.385602	+	0.222627i	0.294651	+	0.955605i	$0.404797\pi$
$174$	−2.09808	+	0.562178i	−0.159055	+	0.0426186i
$175$	−3.40192	+	12.6962i	−0.257161	+	0.959739i
$176$	3.86603	−	14.4282i	0.291413	−	1.08757i
$177$	−2.26795	+	8.46410i	−0.170470	+	0.636201i
$178$		−	15.6603i		−	1.17379i
$179$	−10.5622	+	18.2942i	−0.789454	+	1.36737i	0.136847	+	0.990592i	$0.456303\pi$
$179$	−10.5622	+	18.2942i	−0.789454	+	1.36737i	−0.926302	+	0.376783i	$0.877030\pi$
$180$	−1.56218	−	5.83013i	−0.116438	−	0.434552i
$181$	9.50000	+	16.4545i	0.706129	+	1.22305i	0.966282	+	0.257485i	$0.0828937\pi$
$181$	9.50000	+	16.4545i	0.706129	+	1.22305i	−0.260153	+	0.965567i	$0.583773\pi$
$182$	−16.9282	−	25.3923i	−1.25480	−	1.88220i
$183$	2.63397	−	4.56218i	0.194709	−	0.337246i
$184$	1.53590	−	1.53590i	0.113228	−	0.113228i
$185$			6.92820i			0.509372i
$186$	−7.19615	−	3.19615i	−0.527647	−	0.234353i
$187$		0			0
$188$	14.6603	+	14.6603i	1.06921	+	1.06921i
$189$	16.9282	−	4.53590i	1.23135	−	0.329938i
$190$	−14.6603	+	14.6603i	−1.06357	+	1.06357i
$191$	−5.83013	−	10.0981i	−0.421853	−	0.730671i	0.574268	−	0.818668i	$-0.305287\pi$
$191$	−5.83013	−	10.0981i	−0.421853	−	0.730671i	−0.996121	+	0.0879965i	$0.971954\pi$
$192$	−2.09808	+	3.63397i	−0.151416	+	0.262260i
$193$	3.63397	+	13.5622i	0.261579	+	0.976227i	0.964311	+	0.264772i	$0.0852967\pi$
$193$	3.63397	+	13.5622i	0.261579	+	0.976227i	−0.702732	+	0.711455i	$0.748037\pi$
$194$			4.19615i			0.301266i
$195$	−1.19615	−	3.53590i	−0.0856583	−	0.253211i
$196$	−10.5622	−	18.2942i	−0.754441	−	1.30673i
$197$	−0.366025	−	0.0980762i	−0.0260782	−	0.00698764i	0.245756	−	0.969332i	$-0.420964\pi$
$197$	−0.366025	−	0.0980762i	−0.0260782	−	0.00698764i	−0.271835	+	0.962344i	$0.587630\pi$
$198$	13.7942	+	7.96410i	0.980313	+	0.565984i
$199$	−10.6603	−	18.4641i	−0.755685	−	1.30889i	−0.945033	−	0.326975i	$-0.893971\pi$
$199$	−10.6603	−	18.4641i	−0.755685	−	1.30889i	0.189348	−	0.981910i	$-0.439363\pi$
$200$	−1.50000	+	0.401924i	−0.106066	+	0.0284203i
$201$	−0.607695	+	0.607695i	−0.0428635	+	0.0428635i
$202$	13.5622	−	13.5622i	0.954232	−	0.954232i
$203$	6.50000	−	1.74167i	0.456211	−	0.122241i
$204$		0			0
$205$	−10.7321	−	6.19615i	−0.749559	−	0.432758i
$206$	3.36603	+	0.901924i	0.234522	+	0.0628400i
$207$	5.16987	+	8.95448i	0.359331	+	0.622380i
$208$	7.13397	−	14.4282i	0.494652	−	1.00042i
$209$		−	25.3923i		−	1.75642i
$210$	−2.26795	−	8.46410i	−0.156503	−	0.584079i
$211$	3.36603	−	5.83013i	0.231727	−	0.401362i	−0.726590	−	0.687072i	$-0.758896\pi$
$211$	3.36603	−	5.83013i	0.231727	−	0.401362i	0.958316	+	0.285709i	$0.0922291\pi$
$212$	−9.23205	−	15.9904i	−0.634060	−	1.09822i
$213$	−4.46410	+	4.46410i	−0.305875	+	0.305875i
$214$	10.5622	−	2.83013i	0.722016	−	0.193464i
$215$	6.19615	+	6.19615i	0.422574	+	0.422574i
$216$	1.46410	+	1.46410i	0.0996195	+	0.0996195i
$217$	22.2942	+	9.90192i	1.51343	+	0.672186i
$218$		−	10.7321i		−	0.726866i
$219$	−3.12436	+	3.12436i	−0.211124	+	0.211124i
$220$	4.09808	−	7.09808i	0.276292	−	0.478552i
$221$		0			0
$222$	3.46410	+	6.00000i	0.232495	+	0.402694i
$223$	6.86603	+	25.6244i	0.459783	+	1.71593i	0.673632	+	0.739067i	$0.264733\pi$
$223$	6.86603	+	25.6244i	0.459783	+	1.71593i	−0.213849	+	0.976867i	$0.568600\pi$
$224$	16.6244	−	28.7942i	1.11076	−	1.92390i
$225$		−	7.39230i		−	0.492820i
$226$	3.46410	−	12.9282i	0.230429	−	0.859971i
$227$	0.562178	−	2.09808i	0.0373131	−	0.139254i	−0.944757	−	0.327773i	$-0.893702\pi$
$227$	0.562178	−	2.09808i	0.0373131	−	0.139254i	0.982070	+	0.188519i	$0.0603686\pi$
$228$	−2.49038	+	9.29423i	−0.164930	+	0.615525i
$229$	22.7583	−	6.09808i	1.50391	−	0.402972i	0.589504	−	0.807765i	$-0.299323\pi$
$229$	22.7583	−	6.09808i	1.50391	−	0.402972i	0.914408	+	0.404793i	$0.132656\pi$
$230$	9.92820	−	5.73205i	0.654646	−	0.377960i
$231$	9.29423	+	5.36603i	0.611515	+	0.353059i
$232$	0.562178	+	0.562178i	0.0369088	+	0.0369088i
$233$			6.92820i			0.453882i	0.973909	+	0.226941i	$0.0728724\pi$
$233$			6.92820i			0.453882i	−0.973909	+	0.226941i	$0.927128\pi$
$234$	12.8923	+	11.3301i	0.842796	+	0.740674i
$235$	−8.46410	−	14.6603i	−0.552137	−	0.956330i
$236$	−20.0263	+	5.36603i	−1.30360	+	0.349299i
$237$	−3.07180	−	5.32051i	−0.199535	−	0.345604i
$238$		0			0
$239$	0.133975	+	0.0358984i	0.00866610	+	0.00232207i	0.263149	−	0.964755i	$-0.415239\pi$
$239$	0.133975	+	0.0358984i	0.00866610	+	0.00232207i	−0.254483	+	0.967077i	$0.581905\pi$
$240$	3.26795	−	3.26795i	0.210945	−	0.210945i
$241$	−21.7583	+	5.83013i	−1.40158	+	0.375551i	−0.878911	−	0.476986i	$-0.841729\pi$
$241$	−21.7583	+	5.83013i	−1.40158	+	0.375551i	−0.522666	+	0.852537i	$0.675063\pi$
$242$	0.0980762	+	0.366025i	0.00630458	+	0.0235290i
$243$	−13.2224	+	7.63397i	−0.848219	+	0.489720i
$244$	12.4641			0.797932
$245$	4.46410	+	16.6603i	0.285201	+	1.06438i
$246$	−12.3923			−0.790104
$247$	5.36603	−	26.8301i	0.341432	−	1.70716i
$248$	0.303848	+	2.86603i	0.0192943	+	0.181993i
$249$	6.87564	+	6.87564i	0.435726	+	0.435726i
$250$	−21.8564			−1.38232
$251$	−10.1244	+	17.5359i	−0.639044	+	1.10686i	0.346599	+	0.938013i	$0.387336\pi$
$251$	−10.1244	+	17.5359i	−0.639044	+	1.10686i	−0.985643	+	0.168843i	$0.945997\pi$
$252$	13.2224	+	13.2224i	0.832935	+	0.832935i
$253$	−3.63397	+	13.5622i	−0.228466	+	0.852647i
$254$	−26.8564	+	7.19615i	−1.68512	+	0.451527i
$255$		0			0
$256$	19.3923			1.21202
$257$	11.5981	−	6.69615i	0.723468	−	0.417695i	−0.0925597	−	0.995707i	$-0.529505\pi$
$257$	11.5981	−	6.69615i	0.723468	−	0.417695i	0.816028	+	0.578013i	$0.196172\pi$
$258$	8.46410	+	2.26795i	0.526952	+	0.141196i
$259$	−10.7321	−	18.5885i	−0.666857	−	1.15503i
$260$	5.83013	−	6.63397i	0.361569	−	0.411422i
$261$	−3.27757	+	1.89230i	−0.202876	+	0.117131i
$262$	−32.3205	+	8.66025i	−1.99677	+	0.535032i
$263$			25.5167i			1.57342i	0.617320	+	0.786712i	$0.288218\pi$
$263$			25.5167i			1.57342i	−0.617320	+	0.786712i	$0.711782\pi$
$264$			1.26795i			0.0780369i
$265$	3.90192	+	14.5622i	0.239693	+	0.894547i
$266$	16.6244	−	62.0429i	1.01930	−	3.80410i
$267$	1.53590	+	5.73205i	0.0939955	+	0.350796i
$268$	−1.96410	−	0.526279i	−0.119977	−	0.0321476i
$269$	−20.5981	+	11.8923i	−1.25589	+	0.725087i	−0.972272	−	0.233852i	$-0.924867\pi$
$269$	−20.5981	+	11.8923i	−1.25589	+	0.725087i	−0.283615	+	0.958938i	$0.591534\pi$
$270$	5.46410	+	9.46410i	0.332535	+	0.575967i
$271$	−0.464102	−	0.464102i	−0.0281922	−	0.0281922i	0.692870	−	0.721062i	$-0.256346\pi$
$271$	−0.464102	−	0.464102i	−0.0281922	−	0.0281922i	−0.721062	+	0.692870i	$0.756346\pi$
$272$		0			0
$273$	8.68653	+	7.63397i	0.525733	+	0.462029i
$274$	−11.1962	+	6.46410i	−0.676384	+	0.390511i
$275$	7.09808	−	7.09808i	0.428030	−	0.428030i
$276$	2.66025	−	4.60770i	0.160128	−	0.277351i
$277$	−5.60770			−0.336934			−0.168467	−	0.985707i	$-0.553882\pi$
$277$	−5.60770			−0.336934			−0.168467	+	0.985707i	$0.553882\pi$
$278$	20.9282	−	20.9282i	1.25519	−	1.25519i
$279$	−13.5526	−	2.13397i	−0.811370	−	0.127758i
$280$	−2.26795	+	2.26795i	−0.135536	+	0.135536i
$281$	−0.607695	+	0.607695i	−0.0362521	+	0.0362521i	−0.725000	−	0.688748i	$-0.758160\pi$
$281$	−0.607695	+	0.607695i	−0.0362521	+	0.0362521i	0.688748	+	0.725000i	$0.258160\pi$
$282$	−14.6603	−	8.46410i	−0.873005	−	0.504030i
$283$		−	17.1244i		−	1.01794i	−0.860785	−	0.508969i	$-0.830027\pi$
$283$		−	17.1244i		−	1.01794i	0.860785	−	0.508969i	$-0.169973\pi$
$284$	−14.4282	−	3.86603i	−0.856156	−	0.229406i
$285$	3.92820	−	6.80385i	0.232687	−	0.403025i
$286$	1.50000	+	23.2583i	0.0886969	+	1.37529i
$287$	38.3923			2.26623
$288$	−4.83975	+	18.0622i	−0.285185	+	1.06432i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	2.09808	+	3.63397i	0.123203	+	0.213394i
$291$	−0.411543	−	1.53590i	−0.0241251	−	0.0900360i
$292$	−10.0981	−	2.70577i	−0.590945	−	0.158343i
$293$	−2.87564	−	10.7321i	−0.167997	−	0.626973i	−0.997639	−	0.0686773i	$-0.978122\pi$
$293$	−2.87564	−	10.7321i	−0.167997	−	0.626973i	0.829642	−	0.558296i	$-0.188545\pi$
$294$	12.1962	+	12.1962i	0.711294	+	0.711294i
$295$	16.9282			0.985598
$296$	1.26795	−	2.19615i	0.0736980	−	0.127649i
$297$	−12.9282	−	3.46410i	−0.750170	−	0.201008i
$298$	10.7321	+	6.19615i	0.621691	+	0.358933i
$299$	−6.70577	+	13.5622i	−0.387805	+	0.784321i
$300$	−3.29423	+	1.90192i	−0.190192	+	0.109808i
$301$	−26.2224	−	7.02628i	−1.51144	−	0.404988i
$302$			33.0526i			1.90196i
$303$	−3.63397	+	6.29423i	−0.208766	+	0.361594i
$304$	32.7224	−	8.76795i	1.87676	−	0.502876i
$305$	−9.83013	−	2.63397i	−0.562871	−	0.150821i
$306$		0			0
$307$	−3.49038	−	13.0263i	−0.199207	−	0.743449i	−0.991138	−	0.132839i	$-0.957591\pi$
$307$	−3.49038	−	13.0263i	−0.199207	−	0.743449i	0.791931	−	0.610610i	$-0.209076\pi$
$308$			25.3923i			1.44686i
$309$	−1.32051			−0.0751211
$310$	−2.36603	+	15.0263i	−0.134381	+	0.853435i
$311$		−	26.9282i		−	1.52696i	−0.645832	−	0.763479i	$-0.723490\pi$
$311$		−	26.9282i		−	1.52696i	0.645832	−	0.763479i	$-0.276510\pi$
$312$	−0.267949	+	1.33975i	−0.0151696	+	0.0758482i
$313$	−10.6699	−	6.16025i	−0.603097	−	0.348198i	0.167162	−	0.985929i	$-0.446540\pi$
$313$	−10.6699	−	6.16025i	−0.603097	−	0.348198i	−0.770259	+	0.637731i	$0.779873\pi$
$314$	17.2942	+	17.2942i	0.975970	+	0.975970i
$315$	−7.63397	−	13.2224i	−0.430126	−	0.745000i
$316$	7.26795	−	12.5885i	0.408854	−	0.708156i
$317$	−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	$0.574791\pi$
$318$	10.6603	+	10.6603i	0.597797	+	0.597797i
$319$	−4.96410	−	1.33013i	−0.277936	−	0.0744728i
$320$	7.83013	+	2.09808i	0.437717	+	0.117286i
$321$	−3.58846	+	2.07180i	−0.200288	+	0.115636i
$322$	−17.7583	+	30.7583i	−0.989633	+	1.71409i
$323$		0			0
$324$	−6.69615	−	3.86603i	−0.372008	−	0.214779i
$325$	9.00000	−	6.00000i	0.499230	−	0.332820i
$326$	26.1244			1.44689
$327$	1.05256	+	3.92820i	0.0582066	+	0.217230i
$328$	2.26795	+	3.92820i	0.125227	+	0.216899i
$329$	45.4186	+	26.2224i	2.50401	+	1.44569i
$330$	−1.73205	+	6.46410i	−0.0953463	+	0.355837i
$331$	−8.06218	−	2.16025i	−0.443137	−	0.118738i	0.0303492	−	0.999539i	$-0.490338\pi$
$331$	−8.06218	−	2.16025i	−0.443137	−	0.118738i	−0.473487	+	0.880801i	$0.657005\pi$
$332$	−5.95448	+	22.2224i	−0.326795	+	1.21961i
$333$	8.53590	+	8.53590i	0.467764	+	0.467764i
$334$	6.23205	+	3.59808i	0.341003	+	0.196878i
$335$	1.43782	+	0.830127i	0.0785566	+	0.0453547i
$336$	−3.70577	+	13.8301i	−0.202166	+	0.754495i
$337$	13.0000			0.708155			0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000			0.708155			0.354078	+	0.935216i	$0.384795\pi$
$338$	−3.33013	+	24.8923i	−0.181135	+	1.35396i
$339$			5.07180i			0.275462i
$340$		0			0
$341$	−10.9641	−	15.0622i	−0.593739	−	0.815663i
$342$			36.1244i			1.95338i
$343$	−16.0981	−	16.0981i	−0.869214	−	0.869214i
$344$	−0.830127	−	3.09808i	−0.0447574	−	0.167037i
$345$	−3.07180	+	3.07180i	−0.165380	+	0.165380i
$346$	10.9282	+	2.92820i	0.587504	+	0.157421i
$347$	−13.2224	−	7.63397i	−0.709817	−	0.409813i	0.101176	−	0.994869i	$-0.467739\pi$
$347$	−13.2224	−	7.63397i	−0.709817	−	0.409813i	−0.810993	+	0.585055i	$0.801073\pi$
$348$	1.68653	+	0.973721i	0.0904077	+	0.0521969i
$349$	4.12436	−	4.12436i	0.220772	−	0.220772i	−0.588052	−	0.808823i	$-0.700105\pi$
$349$	4.12436	−	4.12436i	0.220772	−	0.220772i	0.808823	+	0.588052i	$0.200105\pi$
$350$	21.9904	−	12.6962i	1.17544	−	0.678638i
$351$	−12.9282	−	6.39230i	−0.690056	−	0.341196i
$352$	−21.9904	+	12.6962i	−1.17209	+	0.676707i
$353$	−0.241670	−	0.901924i	−0.0128628	−	0.0480046i	0.959196	−	0.282741i	$-0.0912438\pi$
$353$	−0.241670	−	0.901924i	−0.0128628	−	0.0480046i	−0.972059	+	0.234737i	$0.924577\pi$
$354$	14.6603	−	8.46410i	0.779184	−	0.449862i
$355$	10.5622	+	6.09808i	0.560582	+	0.323652i
$356$	−9.92820	+	9.92820i	−0.526194	+	0.526194i
$357$		0			0
$358$	39.4186	−	10.5622i	2.08334	−	0.558228i
$359$	−10.2321	−	2.74167i	−0.540027	−	0.144700i	−0.0215124	−	0.999769i	$-0.506848\pi$
$359$	−10.2321	−	2.74167i	−0.540027	−	0.144700i	−0.518515	+	0.855069i	$0.673515\pi$
$360$	0.901924	−	1.56218i	0.0475356	−	0.0823340i
$361$	33.4186	−	19.2942i	1.75887	−	1.01549i
$362$	9.50000	−	35.4545i	0.499309	−	1.86345i
$363$	−0.0717968	−	0.124356i	−0.00376835	−	0.00652698i
$364$	−5.36603	+	26.8301i	−0.281256	+	1.40628i
$365$	7.39230	+	4.26795i	0.386931	+	0.223395i
$366$	−9.83013	+	2.63397i	−0.513829	+	0.137680i
$367$	6.80385	−	3.92820i	0.355158	−	0.205051i	−0.311797	−	0.950149i	$-0.600931\pi$
$367$	6.80385	−	3.92820i	0.355158	−	0.205051i	0.666955	+	0.745098i	$0.267597\pi$
$368$	−18.7321			−0.976476
$369$	−20.8564	+	5.58846i	−1.08574	+	0.290923i
$370$	9.46410	−	9.46410i	0.492015	−	0.492015i
$371$	−33.0263	−	33.0263i	−1.71464	−	1.71464i
$372$	2.53590	+	6.58846i	0.131480	+	0.341596i
$373$	4.41154			0.228421			0.114211	−	0.993457i	$-0.463566\pi$
$373$	4.41154			0.228421			0.114211	+	0.993457i	$0.463566\pi$
$374$		0			0
$375$	8.00000	−	2.14359i	0.413118	−	0.110695i
$376$			6.19615i			0.319542i
$377$	−4.96410	−	2.45448i	−0.255664	−	0.126412i
$378$	−29.3205	−	16.9282i	−1.50808	−	0.870693i
$379$	9.69615	−	2.59808i	0.498058	−	0.133454i	−0.00104063	−	0.999999i	$-0.500331\pi$
$379$	9.69615	−	2.59808i	0.498058	−	0.133454i	0.499099	+	0.866545i	$0.333665\pi$
$380$	18.5885			0.953568
$381$	9.12436	−	5.26795i	0.467455	−	0.269885i
$382$	−5.83013	+	21.7583i	−0.298295	+	1.11325i
$383$	17.0263	+	4.56218i	0.870002	+	0.233116i	0.666089	−	0.745873i	$-0.267967\pi$
$383$	17.0263	+	4.56218i	0.870002	+	0.233116i	0.203914	+	0.978989i	$0.434634\pi$
$384$	−2.90192	+	0.777568i	−0.148088	+	0.0396801i
$385$	5.36603	−	20.0263i	0.273478	−	1.02063i
$386$	13.5622	−	23.4904i	0.690297	−	1.19563i
$387$	15.2679			0.776113
$388$	2.66025	−	2.66025i	0.135054	−	0.135054i
$389$	−2.69615	+	4.66987i	−0.136700	+	0.236772i	−0.926246	−	0.376920i	$-0.876983\pi$
$389$	−2.69615	+	4.66987i	−0.136700	+	0.236772i	0.789545	+	0.613692i	$0.210316\pi$
$390$	−3.19615	+	6.46410i	−0.161843	+	0.327323i
$391$		0			0
$392$	1.63397	−	6.09808i	0.0825282	−	0.307999i
$393$	10.9808	−	6.33975i	0.553906	−	0.319798i
$394$	0.366025	+	0.633975i	0.0184401	+	0.0319392i
$395$	−8.39230	+	8.39230i	−0.422263	+	0.422263i
$396$	−3.69615	−	13.7942i	−0.185739	−	0.693186i
$397$	−1.43782	−	5.36603i	−0.0721622	−	0.269313i	0.920413	−	0.390948i	$-0.127853\pi$
$397$	−1.43782	−	5.36603i	−0.0721622	−	0.269313i	−0.992575	+	0.121635i	$0.961186\pi$
$398$	−10.6603	+	39.7846i	−0.534350	+	1.99422i
$399$			24.3397i			1.21851i
$400$	11.5981	+	6.69615i	0.579904	+	0.334808i
$401$	4.07180	+	4.07180i	0.203336	+	0.203336i	0.801428	−	0.598092i	$-0.204074\pi$
$401$	4.07180	+	4.07180i	0.203336	+	0.203336i	−0.598092	+	0.801428i	$0.704074\pi$
$402$	1.66025			0.0828059
$403$	−8.40192	−	18.2321i	−0.418530	−	0.908203i
$404$	−17.1962			−0.855541
$405$	4.46410	+	4.46410i	0.221823	+	0.221823i
$406$	−11.2583	−	6.50000i	−0.558742	−	0.322590i
$407$			16.3923i			0.812536i
$408$		0			0
$409$	−3.04552	−	11.3660i	−0.150591	−	0.562014i	−0.999443	−	0.0333824i	$-0.989372\pi$
$409$	−3.04552	−	11.3660i	−0.150591	−	0.562014i	0.848852	−	0.528631i	$-0.177295\pi$
$410$	6.19615	+	23.1244i	0.306006	+	1.14203i
$411$	3.46410	−	3.46410i	0.170872	−	0.170872i
$412$	−1.56218	−	2.70577i	−0.0769630	−	0.133304i
$413$	−45.4186	+	26.2224i	−2.23490	+	1.29032i
$414$	5.16987	−	19.2942i	0.254085	−	0.948260i
$415$	9.39230	−	16.2679i	0.461050	−	0.798562i
$416$	−25.9186	+	8.76795i	−1.27076	+	0.429884i
$417$	−5.60770	+	9.71281i	−0.274610	+	0.475638i
$418$	−34.6865	+	34.6865i	−1.69657	+	1.69657i
$419$	30.0000			1.46560			0.732798	−	0.680446i	$-0.238214\pi$
$419$	30.0000			1.46560			0.732798	+	0.680446i	$0.238214\pi$
$420$	−3.92820	+	6.80385i	−0.191677	+	0.331994i
$421$	−4.16987	+	15.5622i	−0.203227	+	0.758454i	0.786755	+	0.617265i	$0.211759\pi$
$421$	−4.16987	+	15.5622i	−0.203227	+	0.758454i	−0.989983	+	0.141189i	$0.954907\pi$
$422$	−12.5622	+	3.36603i	−0.611517	+	0.163856i
$423$	−28.4904	−	7.63397i	−1.38525	−	0.371177i
$424$	1.42820	−	5.33013i	0.0693597	−	0.258854i
$425$		0			0
$426$	12.1962			0.590906
$427$	30.4545	−	8.16025i	1.47380	−	0.394902i
$428$	−8.49038	−	4.90192i	−0.410398	−	0.236943i
$429$	−2.83013	−	8.36603i	−0.136640	−	0.403916i
$430$		−	16.9282i		−	0.816350i
$431$	−9.50000	+	2.54552i	−0.457599	+	0.122613i	−0.480253	−	0.877130i	$-0.659455\pi$
$431$	−9.50000	+	2.54552i	−0.457599	+	0.122613i	0.0226539	+	0.999743i	$0.492788\pi$
$432$		−	17.8564i		−	0.859117i
$433$	10.2679			0.493446			0.246723	−	0.969086i	$-0.420646\pi$
$433$	10.2679			0.493446			0.246723	+	0.969086i	$0.420646\pi$
$434$	−16.9282	−	43.9808i	−0.812580	−	2.11114i
$435$	−1.12436	−	1.12436i	−0.0539087	−	0.0539087i
$436$	−6.80385	+	6.80385i	−0.325845	+	0.325845i
$437$	−30.7583	+	8.24167i	−1.47137	+	0.394253i
$438$	8.53590			0.407861
$439$	−6.46410	+	3.73205i	−0.308515	+	0.178121i	−0.646262	−	0.763116i	$-0.723669\pi$
$439$	−6.46410	+	3.73205i	−0.308515	+	0.178121i	0.337747	+	0.941237i	$0.390335\pi$
$440$	2.36603	−	0.633975i	0.112796	−	0.0302236i
$441$	26.0263	+	15.0263i	1.23935	+	0.715537i
$442$		0			0
$443$	13.1962	+	22.8564i	0.626968	+	1.08594i	0.988157	+	0.153448i	$0.0490377\pi$
$443$	13.1962	+	22.8564i	0.626968	+	1.08594i	−0.361189	+	0.932493i	$0.617629\pi$
$444$	1.60770	−	6.00000i	0.0762978	−	0.284747i
$445$	9.92820	−	5.73205i	0.470642	−	0.271725i
$446$	25.6244	−	44.3827i	1.21335	−	2.10158i
$447$	−4.53590	−	1.21539i	−0.214541	−	0.0574860i
$448$	−24.2583	+	6.50000i	−1.14610	+	0.307096i
$449$	−7.66025	−	7.66025i	−0.361510	−	0.361510i	0.502859	−	0.864369i	$-0.332282\pi$
$449$	−7.66025	−	7.66025i	−0.361510	−	0.361510i	−0.864369	+	0.502859i	$0.832282\pi$
$450$	−10.0981	+	10.0981i	−0.476028	+	0.476028i
$451$	−25.3923	−	14.6603i	−1.19568	−	0.690324i
$452$	−10.3923	+	6.00000i	−0.488813	+	0.282216i
$453$	−3.24167	−	12.0981i	−0.152307	−	0.568417i
$454$	−3.63397	+	2.09808i	−0.170551	+	0.0984676i
$455$	9.90192	−	20.0263i	0.464209	−	0.938846i
$456$	−2.49038	+	1.43782i	−0.116623	+	0.0673322i
$457$	−12.0000	+	12.0000i	−0.561336	+	0.561336i	−0.929687	−	0.368351i	$-0.879923\pi$
$457$	−12.0000	+	12.0000i	−0.561336	+	0.561336i	0.368351	+	0.929687i	$0.379923\pi$
$458$	−39.4186	−	22.7583i	−1.84191	−	1.06343i
$459$		0			0
$460$	−9.92820	−	2.66025i	−0.462905	−	0.124035i
$461$	−10.1962	+	10.1962i	−0.474882	+	0.474882i	−0.903490	−	0.428608i	$-0.859004\pi$
$461$	−10.1962	+	10.1962i	−0.474882	+	0.474882i	0.428608	+	0.903490i	$0.359004\pi$
$462$	−5.36603	−	20.0263i	−0.249650	−	0.931707i
$463$	−10.6603	−	10.6603i	−0.495424	−	0.495424i	0.414586	−	0.910010i	$-0.363926\pi$
$463$	−10.6603	−	10.6603i	−0.495424	−	0.495424i	−0.910010	+	0.414586i	$0.863926\pi$
$464$		−	6.85641i		−	0.318301i
$465$	−0.607695	−	5.73205i	−0.0281812	−	0.265817i
$466$	9.46410	−	9.46410i	0.438416	−	0.438416i
$467$			2.39230i			0.110703i	0.998467	+	0.0553513i	$0.0176279\pi$
$467$			2.39230i			0.110703i	−0.998467	+	0.0553513i	$0.982372\pi$
$468$	−0.990381	−	15.3564i	−0.0457804	−	0.709850i
$469$	−5.14359			−0.237509
$470$	−8.46410	+	31.5885i	−0.390420	+	1.45707i
$471$	−8.02628	−	4.63397i	−0.369831	−	0.213522i
$472$	−5.36603	−	3.09808i	−0.246991	−	0.142601i
$473$	14.6603	+	14.6603i	0.674079	+	0.674079i
$474$	−3.07180	+	11.4641i	−0.141092	+	0.526564i
$475$	21.9904	+	5.89230i	1.00899	+	0.270357i
$476$		0			0
$477$	22.7487	+	13.1340i	1.04159	+	0.601363i
$478$	−0.133975	−	0.232051i	−0.00612786	−	0.0106138i
$479$	7.86603	+	29.3564i	0.359408	+	1.34133i	0.874846	+	0.484402i	$0.160963\pi$
$479$	7.86603	+	29.3564i	0.359408	+	1.34133i	−0.515438	+	0.856927i	$0.672371\pi$
$480$	−7.85641			−0.358594
$481$	−3.46410	+	17.3205i	−0.157949	+	0.789747i
$482$	37.6865	+	21.7583i	1.71657	+	0.991065i
$483$	3.48334	−	13.0000i	0.158497	−	0.591520i
$484$	0.169873	−	0.294229i	0.00772150	−	0.0133740i
$485$	−2.66025	+	1.53590i	−0.120796	+	0.0697416i
$486$	28.4904	+	7.63397i	1.29235	+	0.346284i
$487$	19.2942	+	5.16987i	0.874305	+	0.234269i	0.667948	−	0.744208i	$-0.267173\pi$
$487$	19.2942	+	5.16987i	0.874305	+	0.234269i	0.206357	+	0.978477i	$0.433839\pi$
$488$	2.63397	+	2.63397i	0.119234	+	0.119234i
$489$	−9.56218	+	2.56218i	−0.432417	+	0.115866i
$490$	16.6603	−	28.8564i	0.752634	−	1.30360i
$491$	3.09808	+	5.36603i	0.139814	+	0.242165i	0.927426	−	0.374006i	$-0.122016\pi$
$491$	3.09808	+	5.36603i	0.139814	+	0.242165i	−0.787612	+	0.616172i	$0.788683\pi$
$492$	7.85641	+	7.85641i	0.354194	+	0.354194i
$493$		0			0
$494$	−43.9808	+	29.3205i	−1.97879	+	1.31919i
$495$			11.6603i			0.524089i
$496$	15.6244	−	19.3301i	0.701554	−	0.867948i
$497$	−37.7846			−1.69487
$498$		−	18.7846i		−	0.841758i
$499$	9.25833	+	34.5526i	0.414460	+	1.54678i	0.785915	+	0.618334i	$0.212192\pi$
$499$	9.25833	+	34.5526i	0.414460	+	1.54678i	−0.371455	+	0.928451i	$0.621141\pi$
$500$	13.8564	+	13.8564i	0.619677	+	0.619677i
$501$	−2.63397	−	0.705771i	−0.117677	−	0.0315315i
$502$	37.7846	−	10.1244i	1.68641	−	0.451872i
$503$	3.19615	−	5.53590i	0.142509	−	0.246834i	−0.785932	−	0.618313i	$-0.787816\pi$
$503$	3.19615	−	5.53590i	0.142509	−	0.246834i	0.928441	+	0.371480i	$0.121150\pi$
$504$			5.58846i			0.248930i
$505$	13.5622	+	3.63397i	0.603509	+	0.161710i
$506$	23.4904	−	13.5622i	1.04427	−	0.602912i
$507$	−1.22243	−	9.43782i	−0.0542901	−	0.419148i
$508$	21.5885	+	12.4641i	0.957833	+	0.553005i
$509$	−6.56218	−	1.75833i	−0.290863	−	0.0779366i	0.110437	−	0.993883i	$-0.464775\pi$
$509$	−6.56218	−	1.75833i	−0.290863	−	0.0779366i	−0.401300	+	0.915947i	$0.631442\pi$
$510$		0			0
$511$	−26.4449			−1.16985
$512$	−20.6865	−	20.6865i	−0.914224	−	0.914224i
$513$	−7.85641	−	29.3205i	−0.346869	−	1.29453i
$514$	−24.9904	−	6.69615i	−1.10228	−	0.295355i
$515$	0.660254	+	2.46410i	0.0290943	+	0.108581i
$516$	−3.92820	−	6.80385i	−0.172930	−	0.299523i
$517$	−20.0263	−	34.6865i	−0.880755	−	1.52551i
$518$	−10.7321	+	40.0526i	−0.471539	+	1.75981i
$519$	−4.28719			−0.188187
$520$	2.63397	−	0.169873i	0.115507	−	0.00744942i
$521$	−2.07180	+	3.58846i	−0.0907671	+	0.157213i	−0.907834	−	0.419329i	$-0.862265\pi$
$521$	−2.07180	+	3.58846i	−0.0907671	+	0.157213i	0.817067	+	0.576543i	$0.195599\pi$
$522$	7.06218	+	1.89230i	0.309103	+	0.0828239i
$523$		−	36.4449i		−	1.59362i	−0.604228	−	0.796811i	$-0.706518\pi$
$523$		−	36.4449i		−	1.59362i	0.604228	−	0.796811i	$-0.293482\pi$
$524$	25.9808	+	15.0000i	1.13497	+	0.655278i
$525$	−6.80385	+	6.80385i	−0.296944	+	0.296944i
$526$	34.8564	−	34.8564i	1.51981	−	1.51981i
$527$		0			0
$528$	7.73205	−	7.73205i	0.336494	−	0.336494i
$529$	−5.39230			−0.234448
$530$	14.5622	−	25.2224i	0.632541	−	1.09559i
$531$	20.8564	−	20.8564i	0.905091	−	0.905091i
$532$	−49.8731	+	28.7942i	−2.16227	+	1.24839i
$533$	−23.7321	−	20.8564i	−1.02795	−	0.903391i
$534$	5.73205	−	9.92820i	0.248050	−	0.429635i
$535$	5.66025	+	5.66025i	0.244714	+	0.244714i
$536$	−0.303848	−	0.526279i	−0.0131242	−	0.0227318i
$537$	−13.3923	+	7.73205i	−0.577921	+	0.333663i
$538$	44.3827	+	11.8923i	1.91347	+	0.512714i
$539$	10.5622	+	39.4186i	0.454945	+	1.69788i
$540$	2.53590	−	9.46410i	0.109128	−	0.407270i
$541$	8.07180	+	30.1244i	0.347034	+	1.29515i	0.890218	+	0.455534i	$0.150552\pi$
$541$	8.07180	+	30.1244i	0.347034	+	1.29515i	−0.543185	+	0.839613i	$0.682782\pi$
$542$			1.26795i			0.0544631i
$543$			13.9090i			0.596891i
$544$		0			0
$545$	6.80385	−	3.92820i	0.291445	−	0.168266i
$546$	−1.43782	−	22.2942i	−0.0615331	−	0.954105i
$547$	4.73205	+	8.19615i	0.202328	+	0.350442i	0.949278	−	0.314438i	$-0.101816\pi$
$547$	4.73205	+	8.19615i	0.202328	+	0.350442i	−0.746950	+	0.664880i	$0.768483\pi$
$548$	11.1962	+	3.00000i	0.478276	+	0.128154i
$549$	−15.3564	+	8.86603i	−0.655395	+	0.378393i
$550$	−19.3923			−0.826891
$551$	−3.01666	−	11.2583i	−0.128514	−	0.479621i
$552$	1.53590	−	0.411543i	0.0653722	−	0.0175164i
$553$	9.51666	−	35.5167i	0.404690	−	1.51032i
$554$	7.66025	+	7.66025i	0.325453	+	0.325453i
$555$	−2.53590	+	4.39230i	−0.107643	+	0.186443i
$556$	−26.5359			−1.12537
$557$	−0.464102	−	0.464102i	−0.0196646	−	0.0196646i	0.697206	−	0.716871i	$-0.254426\pi$
$557$	−0.464102	−	0.464102i	−0.0196646	−	0.0196646i	−0.716871	+	0.697206i	$0.754426\pi$
$558$	15.5981	+	21.4282i	0.660319	+	0.907128i
$559$	12.3923	+	18.5885i	0.524139	+	0.786208i
$560$	27.6603			1.16886
$561$		0			0
$562$	1.66025			0.0700336
$563$	18.8827	−	10.9019i	0.795810	−	0.459461i	−0.0461937	−	0.998932i	$-0.514709\pi$
$563$	18.8827	−	10.9019i	0.795810	−	0.459461i	0.842004	+	0.539471i	$0.181376\pi$
$564$	3.92820	+	14.6603i	0.165407	+	0.617308i
$565$	9.46410	−	2.53590i	0.398158	−	0.106686i
$566$	−23.3923	+	23.3923i	−0.983252	+	0.983252i
$567$	−18.8923	−	5.06218i	−0.793402	−	0.212591i
$568$	−2.23205	−	3.86603i	−0.0936548	−	0.162215i
$569$	−7.93782	−	13.7487i	−0.332771	−	0.576376i	0.650283	−	0.759692i	$-0.274650\pi$
$569$	−7.93782	−	13.7487i	−0.332771	−	0.576376i	−0.983054	+	0.183316i	$0.941317\pi$
$570$	−14.6603	+	3.92820i	−0.614050	+	0.164534i
$571$	7.75833	+	13.4378i	0.324676	+	0.562355i	0.981447	−	0.191735i	$-0.0614114\pi$
$571$	7.75833	+	13.4378i	0.324676	+	0.562355i	−0.656771	+	0.754090i	$0.728078\pi$
$572$	13.7942	−	15.6962i	0.576766	−	0.656289i
$573$		−	8.53590i		−	0.356592i
$574$	−52.4449	−	52.4449i	−2.18901	−	2.18901i
$575$	−10.9019	−	6.29423i	−0.454642	−	0.262487i
$576$	12.2321	−	7.06218i	0.509669	−	0.294257i
$577$	24.4904	−	6.56218i	1.01955	−	0.273187i	0.289934	−	0.957047i	$-0.406367\pi$
$577$	24.4904	−	6.56218i	1.01955	−	0.273187i	0.729614	+	0.683860i	$0.239700\pi$
$578$	8.50000	−	31.7224i	0.353553	−	1.31948i
$579$	−2.66025	+	9.92820i	−0.110556	+	0.412602i
$580$	0.973721	−	3.63397i	0.0404315	−	0.150893i
$581$			58.1962i			2.41438i
$582$	−1.53590	+	2.66025i	−0.0636650	+	0.110271i
$583$	9.23205	+	34.4545i	0.382352	+	1.42696i
$584$	−1.56218	−	2.70577i	−0.0646434	−	0.111966i
$585$	−2.46410	+	12.3205i	−0.101878	+	0.509390i
$586$	−10.7321	+	18.5885i	−0.443337	+	0.767882i
$587$	4.70577	−	4.70577i	0.194228	−	0.194228i	−0.603292	−	0.797520i	$-0.706145\pi$
$587$	4.70577	−	4.70577i	0.194228	−	0.194228i	0.797520	+	0.603292i	$0.206145\pi$
$588$		−	15.4641i		−	0.637729i
$589$	17.1506	−	38.6147i	0.706680	−	1.59109i
$590$	−23.1244	−	23.1244i	−0.952015	−	0.952015i
$591$	−0.196152	−	0.196152i	−0.00806863	−	0.00806863i
$592$	−21.1244	+	5.66025i	−0.868206	+	0.232635i
$593$	−7.85641	+	7.85641i	−0.322624	+	0.322624i	−0.849773	−	0.527149i	$-0.823261\pi$
$593$	−7.85641	+	7.85641i	−0.322624	+	0.322624i	0.527149	+	0.849773i	$0.323261\pi$
$594$	12.9282	+	22.3923i	0.530451	+	0.918767i
$595$		0			0
$596$	−2.87564	−	10.7321i	−0.117791	−	0.439602i
$597$		−	15.6077i		−	0.638780i
$598$	27.6865	−	9.36603i	1.13219	−	0.383005i
$599$	−7.43782	−	12.8827i	−0.303901	−	0.526372i	0.673115	−	0.739538i	$-0.264956\pi$
$599$	−7.43782	−	12.8827i	−0.303901	−	0.526372i	−0.977016	+	0.213166i	$0.931623\pi$
$600$	−1.09808	−	0.294229i	−0.0448288	−	0.0120118i
$601$	1.54552	+	0.892305i	0.0630430	+	0.0363979i	0.531190	−	0.847253i	$-0.321745\pi$
$601$	1.54552	+	0.892305i	0.0630430	+	0.0363979i	−0.468147	+	0.883650i	$0.655078\pi$
$602$	26.2224	+	45.4186i	1.06875	+	1.85112i
$603$	2.79423	−	0.748711i	0.113790	−	0.0304899i
$604$	20.9545	−	20.9545i	0.852626	−	0.852626i
$605$	−0.196152	+	0.196152i	−0.00797473	+	0.00797473i
$606$	13.5622	−	3.63397i	0.550926	−	0.147620i
$607$	−13.6865	−	23.7058i	−0.555519	−	0.962188i	−0.997863	−	0.0653420i	$-0.979186\pi$
$607$	−13.6865	−	23.7058i	−0.555519	−	0.962188i	0.442344	−	0.896846i	$-0.354147\pi$
$608$	−49.8731	−	28.7942i	−2.02262	−	1.16776i
$609$	4.75833	+	1.27499i	0.192817	+	0.0516652i
$610$	9.83013	+	17.0263i	0.398010	+	0.689374i
$611$	−13.8301	−	40.8827i	−0.559507	−	1.65394i
$612$		0			0
$613$	−2.12436	−	7.92820i	−0.0858019	−	0.320217i	0.909663	−	0.415347i	$-0.136340\pi$
$613$	−2.12436	−	7.92820i	−0.0858019	−	0.320217i	−0.995465	+	0.0951302i	$0.969673\pi$
$614$	−13.0263	+	22.5622i	−0.525698	+	0.910535i
$615$	−4.53590	−	7.85641i	−0.182905	−	0.316801i
$616$	−5.36603	+	5.36603i	−0.216203	+	0.216203i
$617$	19.1962	−	5.14359i	0.772808	−	0.207073i	0.149196	−	0.988808i	$-0.452331\pi$
$617$	19.1962	−	5.14359i	0.772808	−	0.207073i	0.623612	+	0.781734i	$0.285665\pi$
$618$	1.80385	+	1.80385i	0.0725614	+	0.0725614i
$619$	−1.36603	−	1.36603i	−0.0549052	−	0.0549052i	0.679121	−	0.734026i	$-0.262361\pi$
$619$	−1.36603	−	1.36603i	−0.0549052	−	0.0549052i	−0.734026	+	0.679121i	$0.762361\pi$
$620$	11.0263	−	8.02628i	0.442826	−	0.322343i
$621$			16.7846i			0.673543i
$622$	−36.7846	+	36.7846i	−1.47493	+	1.47493i
$623$	−17.7583	+	30.7583i	−0.711472	+	1.23231i
$624$	9.80385	−	6.53590i	0.392468	−	0.261645i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	6.16025	+	22.9904i	0.246213	+	0.918880i
$627$	9.29423	−	16.0981i	0.371176	−	0.642895i
$628$		−	21.9282i		−	0.875031i
$629$		0			0
$630$	−7.63397	+	28.4904i	−0.304145	+	1.13508i
$631$	−2.41858	+	9.02628i	−0.0962823	+	0.359331i	−0.997211	−	0.0746372i	$-0.976220\pi$
$631$	−2.41858	+	9.02628i	−0.0962823	+	0.359331i	0.900928	+	0.433968i	$0.142887\pi$
$632$	4.19615	−	1.12436i	0.166914	−	0.0447245i
$633$	4.26795	−	2.46410i	0.169636	−	0.0979392i
$634$	28.3923	+	16.3923i	1.12760	+	0.651022i
$635$	−14.3923	−	14.3923i	−0.571141	−	0.571141i
$636$		−	13.5167i		−	0.535970i
$637$	2.83013	+	43.8827i	0.112134	+	1.73870i
$638$	4.96410	+	8.59808i	0.196531	+	0.340401i
$639$	20.5263	−	5.50000i	0.812007	−	0.217577i
$640$	2.90192	+	5.02628i	0.114709	+	0.198681i
$641$	6.57180	+	11.3827i	0.259570	+	0.449589i	0.966127	−	0.258068i	$-0.0830857\pi$
$641$	6.57180	+	11.3827i	0.259570	+	0.449589i	−0.706557	+	0.707657i	$0.749752\pi$
$642$	7.73205	+	2.07180i	0.305160	+	0.0817673i
$643$	21.3923	−	21.3923i	0.843630	−	0.843630i	−0.145699	−	0.989329i	$-0.546543\pi$
$643$	21.3923	−	21.3923i	0.843630	−	0.843630i	0.989329	+	0.145699i	$0.0465431\pi$
$644$	30.7583	−	8.24167i	1.21205	−	0.324767i
$645$	1.66025	+	6.19615i	0.0653724	+	0.243973i
$646$		0			0
$647$	43.2679			1.70104			0.850519	−	0.525944i	$-0.176288\pi$
$647$	43.2679			1.70104			0.850519	+	0.525944i	$0.176288\pi$
$648$	−0.598076	−	2.23205i	−0.0234947	−	0.0876832i
$649$	40.0526			1.57220
$650$	−20.4904	−	4.09808i	−0.803699	−	0.160740i
$651$	10.5096	+	14.4378i	0.411904	+	0.565863i
$652$	−16.5622	−	16.5622i	−0.648625	−	0.648625i
$653$	−13.9808			−0.547109			−0.273555	−	0.961856i	$-0.588199\pi$
$653$	−13.9808			−0.547109			−0.273555	+	0.961856i	$0.588199\pi$
$654$	3.92820	−	6.80385i	0.153605	−	0.266051i
$655$	−17.3205	−	17.3205i	−0.676768	−	0.676768i
$656$	10.1244	−	37.7846i	0.395290	−	1.47524i
$657$	14.3660	−	3.84936i	0.560472	−	0.150178i
$658$	−26.2224	−	97.8634i	−1.02226	−	3.81511i
$659$	2.58846			0.100832			0.0504160	−	0.998728i	$-0.483945\pi$
$659$	2.58846			0.100832			0.0504160	+	0.998728i	$0.483945\pi$
$660$	5.19615	−	3.00000i	0.202260	−	0.116775i
$661$	16.9282	+	4.53590i	0.658431	+	0.176426i	0.572538	−	0.819878i	$-0.305959\pi$
$661$	16.9282	+	4.53590i	0.658431	+	0.176426i	0.0858930	+	0.996304i	$0.472626\pi$
$662$	8.06218	+	13.9641i	0.313345	+	0.542730i
$663$		0			0
$664$	−5.95448	+	3.43782i	−0.231079	+	0.133413i
$665$	45.4186	−	12.1699i	1.76126	−	0.471927i
$666$		−	23.3205i		−	0.903651i
$667$			6.44486i			0.249546i
$668$	−1.66987	−	6.23205i	−0.0646093	−	0.241125i
$669$	−5.02628	+	18.7583i	−0.194327	+	0.725239i
$670$	−0.830127	−	3.09808i	−0.0320706	−	0.119689i
$671$	−23.2583	−	6.23205i	−0.897878	−	0.240586i
$672$	21.0788	−	12.1699i	0.813134	−	0.469463i
$673$	−16.9282	−	29.3205i	−0.652534	−	1.13022i	−0.982506	−	0.186232i	$-0.940373\pi$
$673$	−16.9282	−	29.3205i	−0.652534	−	1.13022i	0.329972	−	0.943991i	$-0.392961\pi$
$674$	−17.7583	−	17.7583i	−0.684025	−	0.684025i
$675$	6.00000	−	10.3923i	0.230940	−	0.400000i
$676$	17.8923	−	13.6699i	0.688166	−	0.525764i
$677$	−2.42820	+	1.40192i	−0.0933234	+	0.0538803i	−0.545935	−	0.837827i	$-0.683826\pi$
$677$	−2.42820	+	1.40192i	−0.0933234	+	0.0538803i	0.452612	+	0.891708i	$0.350492\pi$
$678$	6.92820	−	6.92820i	0.266076	−	0.266076i
$679$	4.75833	−	8.24167i	0.182608	−	0.316286i
$680$		0			0
$681$	1.12436	−	1.12436i	0.0430854	−	0.0430854i
$682$	−5.59808	+	35.5526i	−0.214361	+	1.36138i
$683$	29.8827	−	29.8827i	1.14343	−	1.14343i	0.155611	−	0.987818i	$-0.450265\pi$
$683$	29.8827	−	29.8827i	1.14343	−	1.14343i	0.987818	−	0.155611i	$-0.0497346\pi$
$684$	22.9019	−	22.9019i	0.875677	−	0.875677i
$685$	−8.19615	−	4.73205i	−0.313159	−	0.180802i
$686$			43.9808i			1.67919i
$687$	16.6603	+	4.46410i	0.635628	+	0.170316i
$688$	−13.8301	+	23.9545i	−0.527269	+	0.913256i
$689$	2.47372	+	38.3564i	0.0942412	+	1.46126i
$690$	8.39230			0.319490
$691$	−7.33013	+	27.3564i	−0.278851	+	1.04069i	0.674365	+	0.738398i	$0.264417\pi$
$691$	−7.33013	+	27.3564i	−0.278851	+	1.04069i	−0.953216	+	0.302289i	$0.902249\pi$
$692$	−5.07180	−	8.78461i	−0.192801	−	0.333941i
$693$	−18.0622	−	31.2846i	−0.686125	−	1.18840i
$694$	7.63397	+	28.4904i	0.289782	+	1.08148i
$695$	20.9282	+	5.60770i	0.793852	+	0.212712i
$696$	0.150635	+	0.562178i	0.00570981	+	0.0213093i
$697$		0			0
$698$	−11.2679			−0.426498
$699$	−2.53590	+	4.39230i	−0.0959165	+	0.166132i
$700$	−21.9904	−	5.89230i	−0.831158	−	0.222708i
$701$	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	$0.618392\pi$
$702$	8.92820	+	26.3923i	0.336973	+	0.996113i
$703$	−32.1962	+	18.5885i	−1.21430	+	0.701077i
$704$	18.5263	+	4.96410i	0.698235	+	0.187092i
$705$		−	12.3923i		−	0.466721i
$706$	−0.901924	+	1.56218i	−0.0339443	+	0.0587933i
$707$	−42.0167	+	11.2583i	−1.58020	+	0.423413i
$708$	−14.6603	−	3.92820i	−0.550966	−	0.147631i
$709$	−28.5167	−	28.5167i	−1.07097	−	1.07097i	−0.997282	−	0.0736840i	$-0.976524\pi$
$709$	−28.5167	−	28.5167i	−1.07097	−	1.07097i	−0.0736840	−	0.997282i	$-0.523476\pi$
$710$	−6.09808	−	22.7583i	−0.228857	−	0.854105i
$711$			20.6795i			0.775542i
$712$	−4.19615			−0.157257
$713$	−14.6865	+	18.1699i	−0.550015	+	0.680467i
$714$		0			0
$715$	−14.1962	+	9.46410i	−0.530906	+	0.353937i
$716$	−31.6865	−	18.2942i	−1.18418	−	0.683687i
$717$	0.0717968	+	0.0717968i	0.00268130	+	0.00268130i
$718$	10.2321	+	17.7224i	0.381857	+	0.661395i
$719$	−4.53590	+	7.85641i	−0.169160	+	0.292995i	−0.938125	−	0.346297i	$-0.887439\pi$
$719$	−4.53590	+	7.85641i	−0.169160	+	0.292995i	0.768964	+	0.639292i	$0.220772\pi$
$720$	−15.0263	+	4.02628i	−0.559996	+	0.150051i
$721$	−5.58846	−	5.58846i	−0.208125	−	0.208125i
$722$	−72.0070	−	19.2942i	−2.67982	−	0.718057i
$723$	−15.9282	−	4.26795i	−0.592376	−	0.158727i
$724$	−28.5000	+	16.4545i	−1.05919	+	0.611526i
$725$	2.30385	−	3.99038i	0.0855628	−	0.148199i
$726$	−0.0717968	+	0.267949i	−0.00266463	+	0.00994453i
$727$	−3.80385	−	2.19615i	−0.141077	−	0.0814508i	0.427800	−	0.903873i	$-0.359289\pi$
$727$	−3.80385	−	2.19615i	−0.141077	−	0.0814508i	−0.568877	+	0.822423i	$0.692622\pi$
$728$	−6.80385	+	4.53590i	−0.252167	+	0.168112i
$729$	2.21539			0.0820515
$730$	−4.26795	−	15.9282i	−0.157964	−	0.589529i
$731$		0			0
$732$	7.90192	+	4.56218i	0.292064	+	0.168623i
$733$	−10.3660	+	38.6865i	−0.382878	+	1.42892i	0.458607	+	0.888639i	$0.348349\pi$
$733$	−10.3660	+	38.6865i	−0.382878	+	1.42892i	−0.841485	+	0.540281i	$0.818318\pi$
$734$	−14.6603	−	3.92820i	−0.541120	−	0.144993i
$735$	−3.26795	+	12.1962i	−0.120540	+	0.449862i
$736$	22.5167	+	22.5167i	0.829975	+	0.829975i
$737$	3.40192	+	1.96410i	0.125311	+	0.0723486i
$738$	36.1244	+	20.8564i	1.32976	+	0.767735i
$739$	13.0359	−	48.6506i	0.479533	−	1.78964i	−0.123974	−	0.992285i	$-0.539564\pi$
$739$	13.0359	−	48.6506i	0.479533	−	1.78964i	0.603508	−	0.797357i	$-0.293769\pi$
$740$	−12.0000			−0.441129
$741$	13.2224	−	15.0455i	0.485738	−	0.552711i
$742$			90.2295i			3.31243i
$743$	22.4641	−	22.4641i	0.824128	−	0.824128i	−0.162569	−	0.986697i	$-0.551978\pi$
$743$	22.4641	−	22.4641i	0.824128	−	0.824128i	0.986697	+	0.162569i	$0.0519781\pi$
$744$	−0.856406	+	1.92820i	−0.0313974	+	0.0706914i
$745$			9.07180i			0.332365i
$746$	−6.02628	−	6.02628i	−0.220638	−	0.220638i
$747$	−8.47114	−	31.6147i	−0.309943	−	1.15672i
$748$		0			0
$749$	−23.9545	−	6.41858i	−0.875278	−	0.234530i
$750$	−13.8564	−	8.00000i	−0.505964	−	0.292119i
$751$	−14.8756	−	8.58846i	−0.542820	−	0.313397i	0.203401	−	0.979096i	$-0.434800\pi$
$751$	−14.8756	−	8.58846i	−0.542820	−	0.313397i	−0.746221	+	0.665698i	$0.768134\pi$
$752$	37.7846	−	37.7846i	1.37786	−	1.37786i
$753$	−12.8372	+	7.41154i	−0.467812	+	0.270092i
$754$	3.42820	+	10.1340i	0.124848	+	0.369058i
$755$	−20.9545	+	12.0981i	−0.762612	+	0.440294i
$756$	7.85641	+	29.3205i	0.285735	+	1.06638i
$757$	−11.7846	+	6.80385i	−0.428319	+	0.247290i	−0.698630	−	0.715483i	$-0.746207\pi$
$757$	−11.7846	+	6.80385i	−0.428319	+	0.247290i	0.270311	+	0.962773i	$0.412873\pi$
$758$	−16.7942	−	9.69615i	−0.609994	−	0.352180i
$759$	−7.26795	+	7.26795i	−0.263810	+	0.263810i
$760$	3.92820	+	3.92820i	0.142491	+	0.142491i
$761$	−20.9282	+	5.60770i	−0.758647	+	0.203279i	−0.617350	−	0.786689i	$-0.711794\pi$
$761$	−20.9282	+	5.60770i	−0.758647	+	0.203279i	−0.141297	+	0.989967i	$0.545127\pi$
$762$	−19.6603	−	5.26795i	−0.712216	−	0.190838i
$763$	−12.1699	+	21.0788i	−0.440579	+	0.763105i
$764$	17.4904	−	10.0981i	0.632780	−	0.365336i
$765$		0			0
$766$	−17.0263	−	29.4904i	−0.615184	−	1.06553i
$767$	42.3205	+	8.46410i	1.52810	+	0.305621i
$768$	12.2942	+	7.09808i	0.443630	+	0.256130i
$769$	42.4186	−	11.3660i	1.52965	−	0.409869i	0.606747	−	0.794895i	$-0.292474\pi$
$769$	42.4186	−	11.3660i	1.52965	−	0.409869i	0.922906	+	0.385025i	$0.125807\pi$
$770$	−34.6865	+	20.0263i	−1.25002	+	0.721697i
$771$	9.80385			0.353077
$772$	−23.4904	+	6.29423i	−0.845437	+	0.226534i
$773$	−10.8038	+	10.8038i	−0.388587	+	0.388587i	−0.874183	−	0.485596i	$-0.838603\pi$
$773$	−10.8038	+	10.8038i	−0.388587	+	0.388587i	0.485596	+	0.874183i	$0.338603\pi$
$774$	−20.8564	−	20.8564i	−0.749668	−	0.749668i
$775$	15.5885	−	6.00000i	0.559954	−	0.215526i
$776$	1.12436			0.0403620
$777$		−	15.7128i		−	0.563694i
$778$	10.0622	−	2.69615i	0.360747	−	0.0966617i
$779$		−	66.4974i		−	2.38252i
$780$	6.12436	−	2.07180i	0.219287	−	0.0741822i
$781$	24.9904	+	14.4282i	0.894226	+	0.516282i
$782$		0			0
$783$	−6.14359			−0.219554
$784$	−47.1506	+	27.2224i	−1.68395	+	0.972230i
$785$	−4.63397	+	17.2942i	−0.165394	+	0.617257i
$786$	−23.6603	−	6.33975i	−0.843933	−	0.226131i
$787$	12.6244	−	3.38269i	0.450010	−	0.120580i	−0.0266942	−	0.999644i	$-0.508498\pi$
$787$	12.6244	−	3.38269i	0.450010	−	0.120580i	0.476704	+	0.879064i	$0.341831\pi$
$788$	0.169873	−	0.633975i	0.00605147	−	0.0225844i
$789$	−9.33975	+	16.1769i	−0.332504	+	0.575913i
$790$	22.9282			0.815749
$791$	−21.4641	+	21.4641i	−0.763176	+	0.763176i
$792$	2.13397	−	3.69615i	0.0758275	−	0.131337i
$793$	−23.2583	−	11.5000i	−0.825928	−	0.408377i
$794$	−5.36603	+	9.29423i	−0.190433	+	0.329840i
$795$	−2.85641	+	10.6603i	−0.101306	+	0.378080i
$796$	31.9808	−	18.4641i	1.13353	−	0.654443i
$797$	−1.89230	−	3.27757i	−0.0670289	−	0.116097i	0.830563	−	0.556924i	$-0.188019\pi$
$797$	−1.89230	−	3.27757i	−0.0670289	−	0.116097i	−0.897592	+	0.440827i	$0.854685\pi$
$798$	33.2487	−	33.2487i	1.17699	−	1.17699i
$799$		0			0
$800$	−5.89230	−	21.9904i	−0.208324	−	0.777477i
$801$	5.16987	−	19.2942i	0.182668	−	0.681728i
$802$		−	11.1244i		−	0.392815i
$803$	17.4904	+	10.0981i	0.617222	+	0.356353i
$804$	−1.05256	−	1.05256i	−0.0371209	−	0.0371209i
$805$	−26.0000			−0.916380
$806$	−13.4282	+	36.3827i	−0.472988	+	1.28153i
$807$	−17.4115			−0.612915
$808$	−3.63397	−	3.63397i	−0.127843	−	0.127843i
$809$	32.4449	+	18.7321i	1.14070	+	0.658584i	0.946604	−	0.322399i	$-0.104489\pi$
$809$	32.4449	+	18.7321i	1.14070	+	0.658584i	0.194097	+	0.980982i	$0.437822\pi$
$810$		−	12.1962i		−	0.428529i
$811$	9.74167	−	36.3564i	0.342076	−	1.27665i	−0.553915	−	0.832574i	$-0.686867\pi$
$811$	9.74167	−	36.3564i	0.342076	−	1.27665i	0.895991	−	0.444073i	$-0.146467\pi$
$812$	3.01666	+	11.2583i	0.105864	+	0.395090i
$813$	−0.124356	−	0.464102i	−0.00436134	−	0.0162768i
$814$	22.3923	−	22.3923i	0.784850	−	0.784850i
$815$	9.56218	+	16.5622i	0.334948	+	0.580148i
$816$		0			0
$817$	−12.1699	+	45.4186i	−0.425770	+	1.58900i
$818$	−11.3660	+	19.6865i	−0.397404	+	0.688324i
$819$	−12.4737	−	36.8731i	−0.435867	−	1.28845i
$820$	10.7321	−	18.5885i	0.374779	−	0.649137i
$821$	25.1769	−	25.1769i	0.878680	−	0.878680i	−0.114718	−	0.993398i	$-0.536596\pi$
$821$	25.1769	−	25.1769i	0.878680	−	0.878680i	0.993398	+	0.114718i	$0.0365964\pi$
$822$	−9.46410			−0.330098
$823$	12.3923	−	21.4641i	0.431969	−	0.748192i	−0.565074	−	0.825040i	$-0.691152\pi$
$823$	12.3923	−	21.4641i	0.431969	−	0.748192i	0.997043	+	0.0768486i	$0.0244858\pi$
$824$	0.241670	−	0.901924i	0.00841896	−	0.0314200i
$825$	7.09808	−	1.90192i	0.247123	−	0.0662165i
$826$	97.8634	+	26.2224i	3.40510	+	0.912395i
$827$	2.36603	−	8.83013i	0.0822748	−	0.307054i	−0.912509	−	0.409056i	$-0.865858\pi$
$827$	2.36603	−	8.83013i	0.0822748	−	0.307054i	0.994784	+	0.102002i	$0.0325248\pi$
$828$	−15.5096	+	8.95448i	−0.538997	+	0.311190i
$829$	−22.7846			−0.791342			−0.395671	−	0.918392i	$-0.629488\pi$
$829$	−22.7846			−0.791342			−0.395671	+	0.918392i	$0.629488\pi$
$830$	−35.0526	+	9.39230i	−1.21669	+	0.326012i
$831$	−3.55514	−	2.05256i	−0.123326	−	0.0712025i
$832$	18.5263	+	9.16025i	0.642283	+	0.317575i
$833$		0			0
$834$	20.9282	−	5.60770i	0.724684	−	0.194179i
$835$			5.26795i			0.182305i
$836$	43.9808			1.52111
$837$	−17.3205	−	14.0000i	−0.598684	−	0.483911i
$838$	−40.9808	−	40.9808i	−1.41566	−	1.41566i
$839$	−20.2942	+	20.2942i	−0.700635	+	0.700635i	−0.964547	−	0.263912i	$-0.914987\pi$
$839$	−20.2942	+	20.2942i	−0.700635	+	0.700635i	0.263912	+	0.964547i	$0.414987\pi$
$840$	−2.26795	+	0.607695i	−0.0782517	+	0.0209675i
$841$	26.6410			0.918656
$842$	26.9545	−	15.5622i	0.928913	−	0.536308i
$843$	−0.607695	+	0.162831i	−0.0209301	+	0.00560821i
$844$	10.0981	+	5.83013i	0.347590	+	0.200681i
$845$	−17.0000	+	7.00000i	−0.584818	+	0.240807i
$846$	28.4904	+	49.3468i	0.979519	+	1.69658i
$847$	0.222432	−	0.830127i	0.00764285	−	0.0285235i
$848$	−41.2128	+	23.7942i	−1.41525	+	0.817097i
$849$	6.26795	−	10.8564i	0.215115	−	0.372591i
$850$		0			0
$851$	19.8564	−	5.32051i	0.680669	−	0.182385i
$852$	−7.73205	−	7.73205i	−0.264896	−	0.264896i
$853$	−17.5359	+	17.5359i	−0.600418	+	0.600418i	−0.940423	−	0.340006i	$-0.889571\pi$
$853$	−17.5359	+	17.5359i	−0.600418	+	0.600418i	0.340006	+	0.940423i	$0.389571\pi$
$854$	−52.7487	−	30.4545i	−1.80502	−	1.04213i
$855$	−22.9019	+	13.2224i	−0.783229	+	0.452198i
$856$	−0.758330	−	2.83013i	−0.0259192	−	0.0967318i
$857$	−7.45448	+	4.30385i	−0.254640	+	0.147017i	−0.621887	−	0.783107i	$-0.713634\pi$
$857$	−7.45448	+	4.30385i	−0.254640	+	0.147017i	0.367247	+	0.930124i	$0.380300\pi$
$858$	−7.56218	+	15.2942i	−0.258168	+	0.522136i
$859$	−13.6865	+	7.90192i	−0.466978	+	0.269610i	−0.714974	−	0.699151i	$-0.753562\pi$
$859$	−13.6865	+	7.90192i	−0.466978	+	0.269610i	0.247996	+	0.968761i	$0.420228\pi$
$860$	−10.7321	+	10.7321i	−0.365960	+	0.365960i
$861$	24.3397	+	14.0526i	0.829496	+	0.478910i
$862$	16.4545	+	9.50000i	0.560442	+	0.323571i
$863$	−13.6962	−	3.66987i	−0.466222	−	0.124924i	0.0180576	−	0.999837i	$-0.494252\pi$
$863$	−13.6962	−	3.66987i	−0.466222	−	0.124924i	−0.484280	+	0.874913i	$0.660918\pi$
$864$	−21.4641	+	21.4641i	−0.730224	+	0.730224i
$865$	2.14359	+	8.00000i	0.0728844	+	0.272008i
$866$	−14.0263	−	14.0263i	−0.476632	−	0.476632i
$867$			12.4449i			0.422650i
$868$	−17.1506	+	38.6147i	−0.582130	+	1.31067i
$869$	−19.8564	+	19.8564i	−0.673582	+	0.673582i
$870$			3.07180i			0.104144i
$871$	3.17949	+	2.79423i	0.107733	+	0.0946788i
$872$	−2.87564			−0.0973816
$873$	−1.38526	+	5.16987i	−0.0468841	+	0.174974i
$874$	53.2750	+	30.7583i	1.80205	+	1.04042i
$875$	42.9282	+	24.7846i	1.45124	+	0.837873i
$876$	−5.41154	−	5.41154i	−0.182839	−	0.182839i
$877$	1.16987	−	4.36603i	0.0395038	−	0.147430i	−0.943357	−	0.331779i	$-0.892351\pi$
$877$	1.16987	−	4.36603i	0.0395038	−	0.147430i	0.982861	+	0.184349i	$0.0590177\pi$
$878$	13.9282	+	3.73205i	0.470054	+	0.125951i
$879$	2.10512	−	7.85641i	0.0710039	−	0.264990i
$880$	−18.2942	−	10.5622i	−0.616698	−	0.356051i
$881$	19.7224	+	34.1603i	0.664466	+	1.15089i	0.979430	+	0.201785i	$0.0646741\pi$
$881$	19.7224	+	34.1603i	0.664466	+	1.15089i	−0.314964	+	0.949104i	$0.601993\pi$
$882$	−15.0263	−	56.0788i	−0.505961	−	1.88827i
$883$	−19.8038			−0.666453			−0.333226	−	0.942847i	$-0.608137\pi$
$883$	−19.8038			−0.666453			−0.333226	+	0.942847i	$0.608137\pi$
$884$		0			0
$885$	10.7321	+	6.19615i	0.360754	+	0.208281i
$886$	13.1962	−	49.2487i	0.443333	−	1.65454i
$887$	−13.5622	+	23.4904i	−0.455373	+	0.788730i	−0.998710	−	0.0507854i	$-0.983828\pi$
$887$	−13.5622	+	23.4904i	−0.455373	+	0.788730i	0.543336	+	0.839515i	$0.317161\pi$
$888$	1.60770	−	0.928203i	0.0539507	−	0.0311485i
$889$	60.9090	+	16.3205i	2.04282	+	0.547372i
$890$	−21.3923	−	5.73205i	−0.717072	−	0.192139i
$891$	10.5622	+	10.5622i	0.353846	+	0.353846i
$892$	−44.3827	+	11.8923i	−1.48604	+	0.398184i
$893$	45.4186	−	78.6673i	1.51987	−	2.63250i
$894$	4.53590	+	7.85641i	0.151703	+	0.262758i
$895$	21.1244	+	21.1244i	0.706109	+	0.706109i
$896$	−15.5718	−	8.99038i	−0.520217	−	0.300348i
$897$	−9.21539	+	6.14359i	−0.307693	+	0.205129i
$898$			20.9282i			0.698383i
$899$	−6.65064	−	5.37564i	−0.221811	−	0.179288i
$900$	12.8038			0.426795
$901$		0			0
$902$	14.6603	+	54.7128i	0.488133	+	1.82174i
$903$	−14.0526	−	14.0526i	−0.467640	−	0.467640i
$904$	−3.46410	−	0.928203i	−0.115214	−	0.0308716i
$905$	25.9545	−	6.95448i	0.862756	−	0.231175i
$906$	−12.0981	+	20.9545i	−0.401932	+	0.696166i
$907$			29.1244i			0.967058i	0.875328	+	0.483529i	$0.160645\pi$
$907$			29.1244i			0.967058i	−0.875328	+	0.483529i	$0.839355\pi$
$908$	3.63397	+	0.973721i	0.120598	+	0.0323141i
$909$	21.1865	−	12.2321i	0.702713	−	0.405712i
$910$	−40.8827	+	13.8301i	−1.35525	+	0.458464i
$911$	−19.0526	−	11.0000i	−0.631239	−	0.364446i	0.149992	−	0.988687i	$-0.452075\pi$
$911$	−19.0526	−	11.0000i	−0.631239	−	0.364446i	−0.781232	+	0.624241i	$0.785408\pi$
$912$	23.9545	+	6.41858i	0.793212	+	0.212541i
$913$	22.2224	−	38.4904i	0.735455	−	1.27385i
$914$	32.7846			1.08442
$915$	−5.26795	−	5.26795i	−0.174153	−	0.174153i
$916$	10.5622	+	39.4186i	0.348984	+	1.30243i
$917$	73.3013	+	19.6410i	2.42062	+	0.648603i
$918$		0			0
$919$	13.3660	+	23.1506i	0.440904	+	0.763669i	0.997757	−	0.0669425i	$-0.0213244\pi$
$919$	13.3660	+	23.1506i	0.440904	+	0.763669i	−0.556852	+	0.830612i	$0.687991\pi$
$920$	−1.53590	−	2.66025i	−0.0506371	−	0.0877060i
$921$	2.55514	−	9.53590i	0.0841946	−	0.314219i
$922$	27.8564			0.917402
$923$	23.3564	+	20.5263i	0.768785	+	0.675631i
$924$	−9.29423	+	16.0981i	−0.305758	+	0.529588i
$925$	−14.1962	−	3.80385i	−0.466767	−	0.125070i
$926$			29.1244i			0.957086i
$927$	3.84936	+	2.22243i	0.126430	+	0.0729942i
$928$	−8.24167	+	8.24167i	−0.270546	+	0.270546i
$929$	−20.3205	+	20.3205i	−0.666694	+	0.666694i	−0.956949	−	0.290255i	$-0.906260\pi$
$929$	−20.3205	+	20.3205i	−0.666694	+	0.666694i	0.290255	+	0.956949i	$0.406260\pi$
$930$	−7.00000	+	8.66025i	−0.229539	+	0.283981i
$931$	−65.4449	+	65.4449i	−2.14487	+	2.14487i
$932$	−12.0000			−0.393073
$933$	9.85641	−	17.0718i	0.322684	−	0.558906i
$934$	3.26795	−	3.26795i	0.106931	−	0.106931i
$935$		0			0
$936$	3.03590	−	3.45448i	0.0992314	−	0.112913i
$937$	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	$0.161467\pi$
$938$	7.02628	+	7.02628i	0.229416	+	0.229416i
$939$	−4.50962	−	7.81089i	−0.147166	−	0.254899i
$940$	25.3923	−	14.6603i	0.828206	−	0.478165i
$941$	29.7583	+	7.97372i	0.970094	+	0.259936i	0.708867	−	0.705342i	$-0.249206\pi$
$941$	29.7583	+	7.97372i	0.970094	+	0.259936i	0.261226	+	0.965278i	$0.415873\pi$
$942$	4.63397	+	17.2942i	0.150983	+	0.563476i
$943$	−9.51666	+	35.5167i	−0.309905	+	1.15658i
$944$	13.8301	+	51.6147i	0.450132	+	1.67992i
$945$		−	24.7846i		−	0.806243i
$946$		−	40.0526i		−	1.30222i
$947$	21.7942	−	5.83975i	0.708217	−	0.189766i	0.113309	−	0.993560i	$-0.463855\pi$
$947$	21.7942	−	5.83975i	0.708217	−	0.189766i	0.594908	+	0.803794i	$0.297188\pi$
$948$	9.21539	−	5.32051i	0.299302	−	0.172802i
$949$	16.3468	+	14.3660i	0.530639	+	0.466341i
$950$	−21.9904	−	38.0885i	−0.713462	−	1.23575i
$951$	−12.0000	−	3.21539i	−0.389127	−	0.104266i
$952$		0			0
$953$	−32.6603			−1.05797			−0.528985	−	0.848631i	$-0.677427\pi$
$953$	−32.6603			−1.05797			−0.528985	+	0.848631i	$0.677427\pi$
$954$	−13.1340	−	49.0167i	−0.425228	−	1.58697i
$955$	−15.9282	+	4.26795i	−0.515425	+	0.138108i
$956$	−0.0621778	+	0.232051i	−0.00201097	+	0.00750506i
$957$	−2.66025	−	2.66025i	−0.0859938	−	0.0859938i
$958$	29.3564	−	50.8468i	0.948462	−	1.64279i
$959$	29.3205			0.946809
$960$	4.19615	+	4.19615i	0.135430	+	0.135430i
$961$	−6.50000	−	30.3109i	−0.209677	−	0.977771i
$962$	28.3923	−	18.9282i	0.915405	−	0.610270i
$963$	13.9474			0.449450
$964$	−10.0981	−	37.6865i	−0.325237	−	1.21380i
$965$	19.8564			0.639200
$966$	−22.5167	+	13.0000i	−0.724462	+	0.418268i
$967$	9.86603	+	36.8205i	0.317270	+	1.18407i	0.921858	+	0.387529i	$0.126671\pi$
$967$	9.86603	+	36.8205i	0.317270	+	1.18407i	−0.604588	+	0.796539i	$0.706662\pi$
$968$	0.0980762	−	0.0262794i	0.00315229	−	0.000844653i
$969$		0			0
$970$	5.73205	+	1.53590i	0.184045	+	0.0493147i
$971$	17.5167	+	30.3397i	0.562136	+	0.973649i	0.997310	+	0.0733021i	$0.0233537\pi$
$971$	17.5167	+	30.3397i	0.562136	+	0.973649i	−0.435173	+	0.900347i	$0.643313\pi$
$972$	−13.2224	−	22.9019i	−0.424110	−	0.734580i
$973$	−64.8372	+	17.3731i	−2.07858	+	0.556955i
$974$	−19.2942	−	33.4186i	−0.618227	−	1.07080i
$975$	7.90192	−	0.509619i	0.253064	−	0.0163209i
$976$		−	32.1244i		−	1.02828i
$977$	14.7321	+	14.7321i	0.471320	+	0.471320i	0.902342	−	0.431022i	$-0.141847\pi$
$977$	14.7321	+	14.7321i	0.471320	+	0.471320i	−0.431022	+	0.902342i	$0.641847\pi$
$978$	16.5622	+	9.56218i	0.529600	+	0.305765i
$979$	23.4904	−	13.5622i	0.750756	−	0.433449i
$980$	−28.8564	+	7.73205i	−0.921784	+	0.246991i
$981$	3.54294	−	13.2224i	0.113117	−	0.422160i
$982$	3.09808	−	11.5622i	0.0988636	−	0.368964i
$983$	−2.47372	+	9.23205i	−0.0788994	+	0.294457i	−0.994089	−	0.108567i	$-0.965374\pi$
$983$	−2.47372	+	9.23205i	−0.0788994	+	0.294457i	0.915190	+	0.403023i	$0.132041\pi$
$984$			3.32051i			0.105854i
$985$	−0.267949	+	0.464102i	−0.00853757	+	0.0147875i
$986$		0			0
$987$	19.1962	+	33.2487i	0.611020	+	1.05832i
$988$	46.4711	+	9.29423i	1.47844	+	0.295689i
$989$	13.0000	−	22.5167i	0.413376	−	0.715988i
$990$	15.9282	−	15.9282i	0.506232	−	0.506232i
$991$			23.8564i			0.757824i	0.925433	+	0.378912i	$0.123702\pi$
$991$			23.8564i			0.757824i	−0.925433	+	0.378912i	$0.876298\pi$
$992$	−42.0167	+	4.45448i	−1.33403	+	0.141430i
$993$	−4.32051	−	4.32051i	−0.137107	−	0.137107i
$994$	51.6147	+	51.6147i	1.63712	+	1.63712i
$995$	−29.1244	+	7.80385i	−0.923304	+	0.247399i
$996$	−11.9090	+	11.9090i	−0.377350	+	0.377350i
$997$	−10.5885	−	18.3397i	−0.335340	−	0.580826i	0.648210	−	0.761461i	$-0.275518\pi$
$997$	−10.5885	−	18.3397i	−0.335340	−	0.580826i	−0.983550	+	0.180636i	$0.942184\pi$
$998$	34.5526	−	59.8468i	1.09374	−	1.89442i
$999$	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.b.398.1	yes	4
13.5	odd	4		403.2.be.a.57.1	✓	4
31.6	odd	6		403.2.be.a.99.1	yes	4
403.161	even	12	inner	403.2.be.b.161.1	yes	4

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

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)

\(f(q)\)	\(=\)	\(q+(-1.36603 - 1.36603i) q^{2} +(0.633975 + 0.366025i) q^{3} +1.73205i q^{4} +(0.366025 - 1.36603i) q^{5} +(-0.366025 - 1.36603i) q^{6} +(1.13397 + 4.23205i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(-1.23205 - 2.13397i) q^{9} +O(q^{10})\)	\(q+(-1.36603 - 1.36603i) q^{2} +(0.633975 + 0.366025i) q^{3} +1.73205i q^{4} +(0.366025 - 1.36603i) q^{5} +(-0.366025 - 1.36603i) q^{6} +(1.13397 + 4.23205i) q^{7} +(-0.366025 + 0.366025i) q^{8} +(-1.23205 - 2.13397i) q^{9} +(-2.36603 + 1.36603i) q^{10} +(0.866025 - 3.23205i) q^{11} +(-0.633975 + 1.09808i) q^{12} +(1.59808 - 3.23205i) q^{13} +(4.23205 - 7.33013i) q^{14} +(0.732051 - 0.732051i) q^{15} +4.46410 q^{16} +(-1.23205 + 4.59808i) q^{18} +(7.33013 - 1.96410i) q^{19} +(2.36603 + 0.633975i) q^{20} +(-0.830127 + 3.09808i) q^{21} +(-5.59808 + 3.23205i) q^{22} -4.19615 q^{23} +(-0.366025 + 0.0980762i) q^{24} +(2.59808 + 1.50000i) q^{25} +(-6.59808 + 2.23205i) q^{26} -4.00000i q^{27} +(-7.33013 + 1.96410i) q^{28} -1.53590i q^{29} -2.00000 q^{30} +(3.50000 - 4.33013i) q^{31} +(-5.36603 - 5.36603i) q^{32} +(1.73205 - 1.73205i) q^{33} +6.19615 q^{35} +(3.69615 - 2.13397i) q^{36} +(-4.73205 + 1.26795i) q^{37} +(-12.6962 - 7.33013i) q^{38} +(2.19615 - 1.46410i) q^{39} +(0.366025 + 0.633975i) q^{40} +(2.26795 - 8.46410i) q^{41} +(5.36603 - 3.09808i) q^{42} +(-3.09808 + 5.36603i) q^{43} +(5.59808 + 1.50000i) q^{44} +(-3.36603 + 0.901924i) q^{45} +(5.73205 + 5.73205i) q^{46} +(8.46410 - 8.46410i) q^{47} +(2.83013 + 1.63397i) q^{48} +(-10.5622 + 6.09808i) q^{49} +(-1.50000 - 5.59808i) q^{50} +(5.59808 + 2.76795i) q^{52} +(-9.23205 + 5.33013i) q^{53} +(-5.46410 + 5.46410i) q^{54} +(-4.09808 - 2.36603i) q^{55} +(-1.96410 - 1.13397i) q^{56} +(5.36603 + 1.43782i) q^{57} +(-2.09808 + 2.09808i) q^{58} +(3.09808 + 11.5622i) q^{59} +(1.26795 + 1.26795i) q^{60} -7.19615i q^{61} +(-10.6962 + 1.13397i) q^{62} +(7.63397 - 7.63397i) q^{63} +5.73205i q^{64} +(-3.83013 - 3.36603i) q^{65} -4.73205 q^{66} +(-0.303848 + 1.13397i) q^{67} +(-2.66025 - 1.53590i) q^{69} +(-8.46410 - 8.46410i) q^{70} +(-2.23205 + 8.33013i) q^{71} +(1.23205 + 0.330127i) q^{72} +(-1.56218 + 5.83013i) q^{73} +(8.19615 + 4.73205i) q^{74} +(1.09808 + 1.90192i) q^{75} +(3.40192 + 12.6962i) q^{76} +14.6603 q^{77} +(-5.00000 - 1.00000i) q^{78} +(-7.26795 - 4.19615i) q^{79} +(1.63397 - 6.09808i) q^{80} +(-2.23205 + 3.86603i) q^{81} +(-14.6603 + 8.46410i) q^{82} +(12.8301 + 3.43782i) q^{83} +(-5.36603 - 1.43782i) q^{84} +(11.5622 - 3.09808i) q^{86} +(0.562178 - 0.973721i) q^{87} +(0.866025 + 1.50000i) q^{88} +(5.73205 + 5.73205i) q^{89} +(5.83013 + 3.36603i) q^{90} +(15.4904 + 3.09808i) q^{91} -7.26795i q^{92} +(3.80385 - 1.46410i) q^{93} -23.1244 q^{94} -10.7321i q^{95} +(-1.43782 - 5.36603i) q^{96} +(-1.53590 - 1.53590i) q^{97} +(22.7583 + 6.09808i) q^{98} +(-7.96410 + 2.13397i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 6 q^{3} - 2 q^{5} + 2 q^{6} + 8 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 + 2 * q^6 + 8 * q^7 + 2 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} + 6 q^{3} - 2 q^{5} + 2 q^{6} + 8 q^{7} + 2 q^{8} + 2 q^{9} - 6 q^{10} - 6 q^{12} - 4 q^{13} + 10 q^{14} - 4 q^{15} + 4 q^{16} + 2 q^{18} + 12 q^{19} + 6 q^{20} + 14 q^{21} - 12 q^{22} + 4 q^{23} + 2 q^{24} - 16 q^{26} - 12 q^{28} - 8 q^{30} + 14 q^{31} - 18 q^{32} + 4 q^{35} - 6 q^{36} - 12 q^{37} - 30 q^{38} - 12 q^{39} - 2 q^{40} + 16 q^{41} + 18 q^{42} - 2 q^{43} + 12 q^{44} - 10 q^{45} + 16 q^{46} + 20 q^{47} - 6 q^{48} - 18 q^{49} - 6 q^{50} + 12 q^{52} - 30 q^{53} - 8 q^{54} - 6 q^{55} + 6 q^{56} + 18 q^{57} + 2 q^{58} + 2 q^{59} + 12 q^{60} - 22 q^{62} + 34 q^{63} + 2 q^{65} - 12 q^{66} - 22 q^{67} + 24 q^{69} - 20 q^{70} - 2 q^{71} - 2 q^{72} + 18 q^{73} + 12 q^{74} - 6 q^{75} + 24 q^{76} + 24 q^{77} - 20 q^{78} - 36 q^{79} + 10 q^{80} - 2 q^{81} - 24 q^{82} + 34 q^{83} - 18 q^{84} + 22 q^{86} - 22 q^{87} + 16 q^{89} + 6 q^{90} + 10 q^{91} + 36 q^{93} - 44 q^{94} - 30 q^{96} - 20 q^{97} + 46 q^{98} - 18 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 6 * q^3 - 2 * q^5 + 2 * q^6 + 8 * q^7 + 2 * q^8 + 2 * q^9 - 6 * q^10 - 6 * q^12 - 4 * q^13 + 10 * q^14 - 4 * q^15 + 4 * q^16 + 2 * q^18 + 12 * q^19 + 6 * q^20 + 14 * q^21 - 12 * q^22 + 4 * q^23 + 2 * q^24 - 16 * q^26 - 12 * q^28 - 8 * q^30 + 14 * q^31 - 18 * q^32 + 4 * q^35 - 6 * q^36 - 12 * q^37 - 30 * q^38 - 12 * q^39 - 2 * q^40 + 16 * q^41 + 18 * q^42 - 2 * q^43 + 12 * q^44 - 10 * q^45 + 16 * q^46 + 20 * q^47 - 6 * q^48 - 18 * q^49 - 6 * q^50 + 12 * q^52 - 30 * q^53 - 8 * q^54 - 6 * q^55 + 6 * q^56 + 18 * q^57 + 2 * q^58 + 2 * q^59 + 12 * q^60 - 22 * q^62 + 34 * q^63 + 2 * q^65 - 12 * q^66 - 22 * q^67 + 24 * q^69 - 20 * q^70 - 2 * q^71 - 2 * q^72 + 18 * q^73 + 12 * q^74 - 6 * q^75 + 24 * q^76 + 24 * q^77 - 20 * q^78 - 36 * q^79 + 10 * q^80 - 2 * q^81 - 24 * q^82 + 34 * q^83 - 18 * q^84 + 22 * q^86 - 22 * q^87 + 16 * q^89 + 6 * q^90 + 10 * q^91 + 36 * q^93 - 44 * q^94 - 30 * q^96 - 20 * q^97 + 46 * q^98 - 18 * q^99

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