LMFDB - Embedded newform 403.2.be.b.57.1

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			57.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	403.57
Dual form			403.2.be.b.99.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 - 0.366025i) q^{2} +(2.36603 + 1.36603i) q^{3} +1.73205i q^{4} +(-1.36603 - 0.366025i) q^{5} +(1.36603 - 0.366025i) q^{6} +(2.86603 - 0.767949i) q^{7} +(1.36603 + 1.36603i) q^{8} +(2.23205 + 3.86603i) q^{9} +O(q^{10})$	\(q+(0.366025 - 0.366025i) q^{2} +(2.36603 + 1.36603i) q^{3} +1.73205i q^{4} +(-1.36603 - 0.366025i) q^{5} +(1.36603 - 0.366025i) q^{6} +(2.86603 - 0.767949i) q^{7} +(1.36603 + 1.36603i) q^{8} +(2.23205 + 3.86603i) q^{9} +(-0.633975 + 0.366025i) q^{10} +(-0.866025 - 0.232051i) q^{11} +(-2.36603 + 4.09808i) q^{12} +(-3.59808 - 0.232051i) q^{13} +(0.767949 - 1.33013i) q^{14} +(-2.73205 - 2.73205i) q^{15} -2.46410 q^{16} +(2.23205 + 0.598076i) q^{18} +(-1.33013 - 4.96410i) q^{19} +(0.633975 - 2.36603i) q^{20} +(7.83013 + 2.09808i) q^{21} +(-0.401924 + 0.232051i) q^{22} +6.19615 q^{23} +(1.36603 + 5.09808i) q^{24} +(-2.59808 - 1.50000i) q^{25} +(-1.40192 + 1.23205i) q^{26} +4.00000i q^{27} +(1.33013 + 4.96410i) q^{28} +8.46410i q^{29} -2.00000 q^{30} +(3.50000 - 4.33013i) q^{31} +(-3.63397 + 3.63397i) q^{32} +(-1.73205 - 1.73205i) q^{33} -4.19615 q^{35} +(-6.69615 + 3.86603i) q^{36} +(-1.26795 - 4.73205i) q^{37} +(-2.30385 - 1.33013i) q^{38} +(-8.19615 - 5.46410i) q^{39} +(-1.36603 - 2.36603i) q^{40} +(5.73205 + 1.53590i) q^{41} +(3.63397 - 2.09808i) q^{42} +(2.09808 - 3.63397i) q^{43} +(0.401924 - 1.50000i) q^{44} +(-1.63397 - 6.09808i) 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} +(-1.50000 + 0.401924i) q^{50} +(0.401924 - 6.23205i) 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} +(3.63397 - 13.5622i) q^{57} +(3.09808 + 3.09808i) q^{58} +(-2.09808 + 0.562178i) 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} +(4.83013 + 1.63397i) q^{65} -1.26795 q^{66} +(-10.6962 - 2.86603i) q^{67} +(14.6603 + 8.46410i) q^{69} +(-1.53590 + 1.53590i) q^{70} +(1.23205 + 0.330127i) q^{71} +(-2.23205 + 8.33013i) q^{72} +(10.5622 + 2.83013i) q^{73} +(-2.19615 - 1.26795i) q^{74} +(-4.09808 - 7.09808i) q^{75} +(8.59808 - 2.30385i) q^{76} -2.66025 q^{77} +(-5.00000 + 1.00000i) q^{78} +(-10.7321 - 6.19615i) q^{79} +(3.36603 + 0.901924i) q^{80} +(1.23205 - 2.13397i) q^{81} +(2.66025 - 1.53590i) q^{82} +(4.16987 - 15.5622i) q^{83} +(-3.63397 + 13.5622i) q^{84} +(-0.562178 - 2.09808i) 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} +(14.1962 - 5.46410i) q^{93} +1.12436 q^{94} +7.26795i q^{95} +(-13.5622 + 3.63397i) q^{96} +(-8.46410 + 8.46410i) q^{97} +(0.241670 - 0.901924i) q^{98} +(-1.03590 - 3.86603i) 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 $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{6}\right)$

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	−0.565755	−	0.824574i	$-0.691415\pi$
$2$	0.366025	−	0.366025i	0.258819	−	0.258819i	0.824574	+	0.565755i	$0.191415\pi$
$3$	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
$5$	−1.36603	−	0.366025i	−0.610905	−	0.163692i	−0.0599153	−	0.998203i	$-0.519083\pi$
$5$	−1.36603	−	0.366025i	−0.610905	−	0.163692i	−0.550990	+	0.834512i	$0.685750\pi$
$6$	1.36603	−	0.366025i	0.557678	−	0.149429i
$7$	2.86603	−	0.767949i	1.08326	−	0.290258i	0.327327	−	0.944911i	$-0.393852\pi$
$7$	2.86603	−	0.767949i	1.08326	−	0.290258i	0.755929	+	0.654654i	$0.227186\pi$
$8$	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
$11$	−0.866025	−	0.232051i	−0.261116	−	0.0699660i	0.125886	−	0.992045i	$-0.459823\pi$
$11$	−0.866025	−	0.232051i	−0.261116	−	0.0699660i	−0.387002	+	0.922079i	$0.626489\pi$
$12$	−2.36603	+	4.09808i	−0.683013	+	1.18301i
$13$	−3.59808	−	0.232051i	−0.997927	−	0.0643593i
$13$	−3.59808	−	0.232051i	−0.997927	−	0.0643593i
$14$	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	$0.166667\pi$
$18$	2.23205	+	0.598076i	0.526099	+	0.140968i
$19$	−1.33013	−	4.96410i	−0.305152	−	1.13884i	−0.932814	−	0.360357i	$-0.882655\pi$
$19$	−1.33013	−	4.96410i	−0.305152	−	1.13884i	0.627662	−	0.778486i	$-0.284012\pi$
$20$	0.633975	−	2.36603i	0.141761	−	0.529059i
$21$	7.83013	+	2.09808i	1.70867	+	0.457838i
$22$	−0.401924	+	0.232051i	−0.0856904	+	0.0494734i
$23$	6.19615			1.29199			0.645994	−	0.763343i	$-0.276443\pi$
$23$	6.19615			1.29199			0.645994	+	0.763343i	$0.276443\pi$
$24$	1.36603	+	5.09808i	0.278839	+	1.04064i
$25$	−2.59808	−	1.50000i	−0.519615	−	0.300000i
$26$	−1.40192	+	1.23205i	−0.274940	+	0.241625i
$27$			4.00000i			0.769800i
$28$	1.33013	+	4.96410i	0.251370	+	0.938127i
$29$			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
$31$	3.50000	−	4.33013i	0.628619	−	0.777714i
$31$	3.50000	−	4.33013i	0.628619	−	0.777714i
$32$	−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
$37$	−1.26795	−	4.73205i	−0.208450	−	0.777944i	−0.988370	−	0.152066i	$-0.951407\pi$
$37$	−1.26795	−	4.73205i	−0.208450	−	0.777944i	0.779921	−	0.625878i	$-0.215259\pi$
$38$	−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
$41$	5.73205	+	1.53590i	0.895196	+	0.239867i	0.676952	−	0.736027i	$-0.263300\pi$
$41$	5.73205	+	1.53590i	0.895196	+	0.239867i	0.218244	+	0.975894i	$0.429967\pi$
$42$	3.63397	−	2.09808i	0.560734	−	0.323740i
$43$	2.09808	−	3.63397i	0.319954	−	0.554176i	−0.660524	−	0.750805i	$-0.729666\pi$
$43$	2.09808	−	3.63397i	0.319954	−	0.554176i	0.980478	+	0.196629i	$0.0629993\pi$
$44$	0.401924	−	1.50000i	0.0605923	−	0.226134i
$45$	−1.63397	−	6.09808i	−0.243579	−	0.909048i
$46$	2.26795	−	2.26795i	0.334391	−	0.334391i
$47$	1.53590	+	1.53590i	0.224034	+	0.224034i	0.810195	−	0.586161i	$-0.199361\pi$
$47$	1.53590	+	1.53590i	0.224034	+	0.224034i	−0.586161	+	0.810195i	$0.699361\pi$
$48$	−5.83013	−	3.36603i	−0.841506	−	0.485844i
$49$	1.56218	−	0.901924i	0.223168	−	0.128846i
$50$	−1.50000	+	0.401924i	−0.212132	+	0.0568406i
$51$		0			0
$52$	0.401924	−	6.23205i	0.0557368	−	0.864230i
$53$	−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
$57$	3.63397	−	13.5622i	0.481332	−	1.79635i
$58$	3.09808	+	3.09808i	0.406797	+	0.406797i
$59$	−2.09808	+	0.562178i	−0.273146	+	0.0731893i	−0.392792	−	0.919627i	$-0.628491\pi$
$59$	−2.09808	+	0.562178i	−0.273146	+	0.0731893i	0.119646	+	0.992817i	$0.461824\pi$
$60$	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
$65$	4.83013	+	1.63397i	0.599104	+	0.202670i
$66$	−1.26795			−0.156074
$67$	−10.6962	−	2.86603i	−1.30674	−	0.350141i	−0.462747	−	0.886490i	$-0.653136\pi$
$67$	−10.6962	−	2.86603i	−1.30674	−	0.350141i	−0.843996	+	0.536350i	$0.819803\pi$
$68$		0			0
$69$	14.6603	+	8.46410i	1.76489	+	1.01896i
$70$	−1.53590	+	1.53590i	−0.183575	+	0.183575i
$71$	1.23205	+	0.330127i	0.146218	+	0.0391789i	0.331185	−	0.943566i	$-0.392551\pi$
$71$	1.23205	+	0.330127i	0.146218	+	0.0391789i	−0.184968	+	0.982745i	$0.559218\pi$
$72$	−2.23205	+	8.33013i	−0.263050	+	0.981715i
$73$	10.5622	+	2.83013i	1.23621	+	0.331241i	0.816994	−	0.576646i	$-0.195639\pi$
$73$	10.5622	+	2.83013i	1.23621	+	0.331241i	0.419215	+	0.907887i	$0.362305\pi$
$74$	−2.19615	−	1.26795i	−0.255298	−	0.147396i
$75$	−4.09808	−	7.09808i	−0.473205	−	0.819615i
$76$	8.59808	−	2.30385i	0.986267	−	0.264269i
$77$	−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	$0.912203\pi$
$80$	3.36603	+	0.901924i	0.376333	+	0.100838i
$81$	1.23205	−	2.13397i	0.136895	−	0.237108i
$82$	2.66025	−	1.53590i	0.293776	−	0.169612i
$83$	4.16987	−	15.5622i	0.457703	−	1.70817i	−0.222314	−	0.974975i	$-0.571361\pi$
$83$	4.16987	−	15.5622i	0.457703	−	1.70817i	0.680017	−	0.733196i	$-0.261972\pi$
$84$	−3.63397	+	13.5622i	−0.396499	+	1.47975i
$85$		0			0
$86$	−0.562178	−	2.09808i	−0.0606212	−	0.226241i
$87$	−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	$-0.695626\pi$
$89$	2.26795	−	2.26795i	0.240402	−	0.240402i	0.817016	+	0.576614i	$0.195626\pi$
$90$	−2.83013	−	1.63397i	−0.298322	−	0.172236i
$91$	−10.4904	+	2.09808i	−1.09969	+	0.219938i
$92$			10.7321i			1.11889i
$93$	14.1962	−	5.46410i	1.47207	−	0.566601i
$94$	1.12436			0.115968
$95$			7.26795i			0.745676i
$96$	−13.5622	+	3.63397i	−1.38418	+	0.370891i
$97$	−8.46410	+	8.46410i	−0.859399	+	0.859399i	−0.991267	−	0.131868i	$-0.957903\pi$
$97$	−8.46410	+	8.46410i	−0.859399	+	0.859399i	0.131868	+	0.991267i	$0.457903\pi$
$98$	0.241670	−	0.901924i	0.0244123	−	0.0911081i
$99$	−1.03590	−	3.86603i	−0.104112	−	0.388550i
$100$	2.59808	−	4.50000i	0.259808	−	0.450000i
$101$			3.92820i			0.390871i	0.980717	+	0.195435i	$0.0626120\pi$
$101$			3.92820i			0.390871i	−0.980717	+	0.195435i	$0.937388\pi$
$102$		0			0
$103$	10.5622	−	6.09808i	1.04072	−	0.600861i	0.120685	−	0.992691i	$-0.461491\pi$
$103$	10.5622	−	6.09808i	1.04072	−	0.600861i	0.920038	+	0.391830i	$0.128158\pi$
$104$	−4.59808	−	5.23205i	−0.450878	−	0.513045i
$105$	−9.92820	−	5.73205i	−0.968893	−	0.559391i
$106$	−0.892305	+	3.33013i	−0.0866683	+	0.323451i
$107$	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	−0.998852	−	0.0479026i	$-0.984746\pi$
$109$	−9.92820	+	9.92820i	−0.950949	+	0.950949i	0.0479026	+	0.998852i	$0.484746\pi$
$110$	0.633975	−	0.169873i	0.0604471	−	0.0161968i
$111$	3.46410	−	12.9282i	0.328798	−	1.22709i
$112$	−7.06218	+	1.89230i	−0.667313	+	0.178806i
$113$	−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
$115$	−8.46410	−	2.26795i	−0.789282	−	0.211487i
$116$	−14.6603			−1.36117
$117$	−7.13397	−	14.4282i	−0.659536	−	1.33389i
$118$	−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
$124$	7.50000	+	6.06218i	0.673520	+	0.544400i
$125$	8.00000	+	8.00000i	0.715542	+	0.715542i
$126$	6.85641			0.610817
$127$	−3.19615	+	5.53590i	−0.283613	+	0.491232i	−0.972272	−	0.233854i	$-0.924866\pi$
$127$	−3.19615	+	5.53590i	−0.283613	+	0.491232i	0.688659	+	0.725085i	$0.258200\pi$
$128$	−8.09808	−	8.09808i	−0.715776	−	0.715776i
$129$	9.92820	−	5.73205i	0.874130	−	0.504679i
$130$	2.36603	−	1.16987i	0.207514	−	0.102605i
$131$	−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
$135$	1.46410	−	5.46410i	0.126010	−	0.470275i
$136$		0			0
$137$	−1.73205	−	0.464102i	−0.147979	−	0.0396509i	0.184069	−	0.982913i	$-0.441073\pi$
$137$	−1.73205	−	0.464102i	−0.147979	−	0.0396509i	−0.332048	+	0.943262i	$0.607740\pi$
$138$	8.46410	−	2.26795i	0.720512	−	0.193061i
$139$			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
$141$	1.53590	+	5.73205i	0.129346	+	0.482726i
$142$	0.571797	−	0.330127i	0.0479841	−	0.0277036i
$143$	3.06218	+	1.03590i	0.256072	+	0.0866262i
$144$	−5.50000	−	9.52628i	−0.458333	−	0.793857i
$145$	3.09808	−	11.5622i	0.257281	−	0.960187i
$146$	4.90192	−	2.83013i	0.405686	−	0.234223i
$147$	4.92820			0.406471
$148$	8.19615	−	2.19615i	0.673720	−	0.180523i
$149$	4.19615	+	15.6603i	0.343762	+	1.28294i	0.894052	+	0.447964i	$0.147851\pi$
$149$	4.19615	+	15.6603i	0.343762	+	1.28294i	−0.550289	+	0.834974i	$0.685483\pi$
$150$	−4.09808	−	1.09808i	−0.334607	−	0.0896575i
$151$	−6.90192	+	6.90192i	−0.561671	+	0.561671i	−0.929782	−	0.368111i	$-0.880005\pi$
$151$	−6.90192	+	6.90192i	−0.561671	+	0.561671i	0.368111	+	0.929782i	$0.380005\pi$
$152$	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	$0.440459\pi$
$158$	−6.19615	+	1.66025i	−0.492939	+	0.132083i
$159$	−18.1962			−1.44305
$160$	6.29423	−	3.63397i	0.497602	−	0.287291i
$161$	17.7583	−	4.75833i	1.39955	−	0.375009i
$162$	−0.330127	−	1.23205i	−0.0259372	−	0.0967991i
$163$	2.56218	+	2.56218i	0.200685	+	0.200685i	0.800294	−	0.599608i	$-0.204677\pi$
$163$	2.56218	+	2.56218i	0.200685	+	0.200685i	−0.599608	+	0.800294i	$0.704677\pi$
$164$	−2.66025	+	9.92820i	−0.207731	+	0.775262i
$165$	1.73205	+	3.00000i	0.134840	+	0.233550i
$166$	−4.16987	−	7.22243i	−0.323645	−	0.560569i
$167$	1.59808	+	5.96410i	0.123663	+	0.461516i	0.999788	−	0.0205668i	$-0.00654708\pi$
$167$	1.59808	+	5.96410i	0.123663	+	0.461516i	−0.876126	+	0.482083i	$0.839880\pi$
$168$	7.83013	+	13.5622i	0.604107	+	1.04634i
$169$	12.8923	+	1.66987i	0.991716	+	0.128452i
$170$		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	−0.997786	−	0.0665045i	$-0.978815\pi$
$173$	−18.9282	+	10.9282i	−1.43908	+	0.830856i	−0.441299	+	0.897360i	$0.645482\pi$
$174$	3.09808	+	11.5622i	0.234865	+	0.876526i
$175$	−8.59808	−	2.30385i	−0.649953	−	0.174155i
$176$	2.13397	+	0.571797i	0.160854	+	0.0431008i
$177$	−5.73205	−	1.53590i	−0.430847	−	0.115445i
$178$		−	1.66025i		−	0.124441i
$179$	1.56218	−	2.70577i	0.116763	−	0.202239i	−0.801720	−	0.597699i	$-0.796082\pi$
$179$	1.56218	−	2.70577i	0.116763	−	0.202239i	0.918483	+	0.395461i	$0.129415\pi$
$180$	10.5622	−	2.83013i	0.787258	−	0.210945i
$181$	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	$0.583773\pi$
$182$	−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
$189$	3.07180	+	11.4641i	0.223440	+	0.833891i
$190$	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
$193$	5.36603	−	1.43782i	0.386255	−	0.103497i	−0.0604655	−	0.998170i	$-0.519259\pi$
$193$	5.36603	−	1.43782i	0.386255	−	0.103497i	0.446720	+	0.894674i	$0.352592\pi$
$194$			6.19615i			0.444858i
$195$	9.19615	+	10.4641i	0.658550	+	0.749350i
$196$	1.56218	+	2.70577i	0.111584	+	0.193269i
$197$	1.36603	−	5.09808i	0.0973253	−	0.363223i	−0.900036	−	0.435815i	$-0.856460\pi$
$197$	1.36603	−	5.09808i	0.0973253	−	0.363223i	0.997362	+	0.0725917i	$0.0231270\pi$
$198$	−1.79423	−	1.03590i	−0.127510	−	0.0736181i
$199$	6.66025	+	11.5359i	0.472133	+	0.817758i	0.999492	−	0.0318846i	$-0.0101509\pi$
$199$	6.66025	+	11.5359i	0.472133	+	0.817758i	−0.527359	+	0.849643i	$0.676818\pi$
$200$	−1.50000	−	5.59808i	−0.106066	−	0.395844i
$201$	−21.3923	−	21.3923i	−1.50890	−	1.50890i
$202$	1.43782	+	1.43782i	0.101165	+	0.101165i
$203$	6.50000	+	24.2583i	0.456211	+	1.70260i
$204$		0			0
$205$	−7.26795	−	4.19615i	−0.507616	−	0.293072i
$206$	1.63397	−	6.09808i	0.113844	−	0.424873i
$207$	13.8301	+	23.9545i	0.961260	+	1.66495i
$208$	8.86603	+	0.571797i	0.614748	+	0.0396470i
$209$			4.60770i			0.318721i
$210$	−5.73205	+	1.53590i	−0.395549	+	0.105987i
$211$	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
$214$	−1.56218	−	5.83013i	−0.106788	−	0.398539i
$215$	−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
$223$	5.13397	−	1.37564i	0.343796	−	0.0921200i	−0.0827894	−	0.996567i	$-0.526383\pi$
$223$	5.13397	−	1.37564i	0.343796	−	0.0921200i	0.426586	+	0.904447i	$0.359716\pi$
$224$	−7.62436	+	13.2058i	−0.509424	+	0.882348i
$225$		−	13.3923i		−	0.892820i
$226$	−3.46410	−	0.928203i	−0.230429	−	0.0617432i
$227$	−11.5622	−	3.09808i	−0.767409	−	0.205627i	−0.146182	−	0.989258i	$-0.546699\pi$
$227$	−11.5622	−	3.09808i	−0.767409	−	0.205627i	−0.621226	+	0.783631i	$0.713365\pi$
$228$	23.4904	+	6.29423i	1.55569	+	0.416845i
$229$	0.241670	+	0.901924i	0.0159700	+	0.0596008i	0.973451	−	0.228895i	$-0.0735114\pi$
$229$	0.241670	+	0.901924i	0.0159700	+	0.0596008i	−0.957481	+	0.288496i	$0.906845\pi$
$230$	−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	$0.0728724\pi$
$233$			6.92820i			0.453882i	−0.973909	+	0.226941i	$0.927128\pi$
$234$	−7.89230	−	2.66987i	−0.515936	−	0.174535i
$235$	−1.53590	−	2.66025i	−0.100191	−	0.173536i
$236$	−0.973721	−	3.63397i	−0.0633838	−	0.236552i
$237$	−16.9282	−	29.3205i	−1.09960	−	1.90457i
$238$		0			0
$239$	1.86603	−	6.96410i	0.120703	−	0.450470i	−0.878947	−	0.476919i	$-0.841753\pi$
$239$	1.86603	−	6.96410i	0.120703	−	0.450470i	0.999650	+	0.0264492i	$0.00842001\pi$
$240$	6.73205	+	6.73205i	0.434552	+	0.434552i
$241$	0.758330	+	2.83013i	0.0488483	+	0.182305i	0.986039	−	0.166512i	$-0.0532504\pi$
$241$	0.758330	+	2.83013i	0.0488483	+	0.182305i	−0.937191	+	0.348816i	$0.886584\pi$
$242$	−5.09808	+	1.36603i	−0.327717	+	0.0878114i
$243$	16.2224	−	9.36603i	1.04067	−	0.600831i
$244$	5.53590			0.354400
$245$	−2.46410	+	0.660254i	−0.157426	+	0.0421821i
$246$	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	$-0.482972\pi$
$251$	14.1244	−	24.4641i	0.891521	−	1.54416i	0.838052	−	0.545591i	$-0.183695\pi$
$252$	−16.2224	+	16.2224i	−1.02192	+	1.02192i
$253$	−5.36603	−	1.43782i	−0.337359	−	0.0903951i
$254$	0.856406	+	3.19615i	0.0537357	+	0.200544i
$255$		0			0
$256$	−1.39230			−0.0870191
$257$	6.40192	−	3.69615i	0.399341	−	0.230560i	−0.286859	−	0.957973i	$-0.592611\pi$
$257$	6.40192	−	3.69615i	0.399341	−	0.230560i	0.686200	+	0.727413i	$0.259278\pi$
$258$	1.53590	−	5.73205i	0.0956209	−	0.356862i
$259$	−7.26795	−	12.5885i	−0.451608	−	0.782209i
$260$	−2.83013	+	8.36603i	−0.175517	+	0.518839i
$261$	−32.7224	+	18.8923i	−2.02547	+	1.16940i
$262$	2.32051	+	8.66025i	0.143361	+	0.535032i
$263$			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
$265$	9.09808	−	2.43782i	0.558890	−	0.149754i
$266$	−7.62436	−	2.04294i	−0.467479	−	0.125261i
$267$	8.46410	−	2.26795i	0.517995	−	0.138796i
$268$	4.96410	−	18.5263i	0.303231	−	1.13167i
$269$	−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	$-0.660442\pi$
$271$	6.46410	−	6.46410i	0.392666	−	0.392666i	0.875637	+	0.482970i	$0.160442\pi$
$272$		0			0
$273$	−27.6865	−	9.36603i	−1.67567	−	0.566858i
$274$	−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	$-0.791419\pi$
$277$	−26.3923			−1.58576			−0.792880	+	0.609378i	$0.791419\pi$
$278$	7.07180	+	7.07180i	0.424138	+	0.424138i
$279$	24.5526	+	3.86603i	1.46992	+	0.231453i
$280$	−5.73205	−	5.73205i	−0.342556	−	0.342556i
$281$	−21.3923	−	21.3923i	−1.27616	−	1.27616i	−0.942801	−	0.333357i	$-0.891818\pi$
$281$	−21.3923	−	21.3923i	−1.27616	−	1.27616i	−0.333357	−	0.942801i	$-0.608182\pi$
$282$	2.66025	+	1.53590i	0.158416	+	0.0914614i
$283$		−	7.12436i		−	0.423499i	−0.977324	−	0.211749i	$-0.932084\pi$
$283$		−	7.12436i		−	0.423499i	0.977324	−	0.211749i	$-0.0679161\pi$
$284$	−0.571797	+	2.13397i	−0.0339299	+	0.126628i
$285$	−9.92820	+	17.1962i	−0.588096	+	1.01861i
$286$	1.50000	−	0.741670i	0.0886969	−	0.0438559i
$287$	17.6077			1.03935
$288$	−22.1603	−	5.93782i	−1.30581	−	0.349890i
$289$	8.50000	+	14.7224i	0.500000	+	0.866025i
$290$	−3.09808	−	5.36603i	−0.181925	−	0.315104i
$291$	−31.5885	+	8.46410i	−1.85175	+	0.496174i
$292$	−4.90192	+	18.2942i	−0.286863	+	1.07059i
$293$	−27.1244	+	7.26795i	−1.58462	+	0.424598i	−0.940353	−	0.340201i	$-0.889505\pi$
$293$	−27.1244	+	7.26795i	−1.58462	+	0.424598i	−0.644269	+	0.764799i	$0.722838\pi$
$294$	1.80385	−	1.80385i	0.105203	−	0.105203i
$295$	3.07180			0.178847
$296$	4.73205	−	8.19615i	0.275045	−	0.476392i
$297$	0.928203	−	3.46410i	0.0538598	−	0.201008i
$298$	7.26795	+	4.19615i	0.421021	+	0.243077i
$299$	−22.2942	−	1.43782i	−1.28931	−	0.0831514i
$300$	12.2942	−	7.09808i	0.709808	−	0.409808i
$301$	3.22243	−	12.0263i	0.185738	−	0.693183i
$302$			5.05256i			0.290742i
$303$	−5.36603	+	9.29423i	−0.308270	+	0.533939i
$304$	3.27757	+	12.2321i	0.187981	+	0.701556i
$305$	−1.16987	+	4.36603i	−0.0669867	+	0.249998i
$306$		0			0
$307$	22.4904	−	6.02628i	1.28359	−	0.343938i	0.448370	−	0.893848i	$-0.352005\pi$
$307$	22.4904	−	6.02628i	1.28359	−	0.343938i	0.835224	+	0.549910i	$0.185338\pi$
$308$		−	4.60770i		−	0.262548i
$309$	33.3205			1.89554
$310$	−0.633975	+	4.02628i	−0.0360073	+	0.228677i
$311$			13.0718i			0.741234i	0.928786	+	0.370617i	$0.120854\pi$
$311$			13.0718i			0.741234i	−0.928786	+	0.370617i	$0.879146\pi$
$312$	−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
$317$	4.39230	+	16.3923i	0.246696	+	0.920684i	0.972523	+	0.232806i	$0.0747907\pi$
$317$	4.39230	+	16.3923i	0.246696	+	0.920684i	−0.725827	+	0.687878i	$0.758543\pi$
$318$	−6.66025	+	6.66025i	−0.373489	+	0.373489i
$319$	1.96410	−	7.33013i	0.109969	−	0.410408i
$320$	−0.830127	+	3.09808i	−0.0464055	+	0.173188i
$321$	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
$327$	−37.0526	+	9.92820i	−2.04901	+	0.549031i
$328$	5.73205	+	9.92820i	0.316500	+	0.548193i
$329$	5.58142	+	3.22243i	0.307713	+	0.177658i
$330$	1.73205	+	0.464102i	0.0953463	+	0.0255480i
$331$	4.06218	−	15.1603i	0.223277	−	0.833283i	−0.759810	−	0.650145i	$-0.774708\pi$
$331$	4.06218	−	15.1603i	0.223277	−	0.833283i	0.983087	−	0.183138i	$-0.0586254\pi$
$332$	26.9545	+	7.22243i	1.47932	+	0.396382i
$333$	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
$336$	−19.2942	−	5.16987i	−1.05259	−	0.282040i
$337$	13.0000			0.708155			0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000			0.708155			0.354078	+	0.935216i	$0.384795\pi$
$338$	5.33013	−	4.10770i	0.289921	−	0.223429i
$339$		−	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
$344$	7.83013	−	2.09808i	0.422172	−	0.113121i
$345$	−16.9282	−	16.9282i	−0.911384	−	0.911384i
$346$	−2.92820	+	10.9282i	−0.157421	+	0.587504i
$347$	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	−0.996757	−	0.0804755i	$-0.974356\pi$
$349$	−20.1244	−	20.1244i	−1.07723	−	1.07723i	−0.0804755	−	0.996757i	$-0.525644\pi$
$350$	−3.99038	+	2.30385i	−0.213295	+	0.123146i
$351$	0.928203	−	14.3923i	0.0495438	−	0.768204i
$352$	3.99038	−	2.30385i	0.212688	−	0.122795i
$353$	−22.7583	+	6.09808i	−1.21130	+	0.324568i	−0.807273	−	0.590178i	$-0.799058\pi$
$353$	−22.7583	+	6.09808i	−1.21130	+	0.324568i	−0.404030	+	0.914746i	$0.632391\pi$
$354$	−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
$358$	−0.418584	−	1.56218i	−0.0221229	−	0.0825637i
$359$	−6.76795	+	25.2583i	−0.357199	+	1.33308i	0.520496	+	0.853864i	$0.325747\pi$
$359$	−6.76795	+	25.2583i	−0.357199	+	1.33308i	−0.877695	+	0.479220i	$0.840920\pi$
$360$	6.09808	−	10.5622i	0.321397	−	0.556676i
$361$	−6.41858	+	3.70577i	−0.337820	+	0.195041i
$362$	9.50000	+	2.54552i	0.499309	+	0.133789i
$363$	−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
$366$	−1.16987	−	4.36603i	−0.0611502	−	0.228216i
$367$	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
$369$	6.85641	+	25.5885i	0.356930	+	1.33208i
$370$	2.53590	+	2.53590i	0.131835	+	0.131835i
$371$	−13.9737	+	13.9737i	−0.725479	+	0.725479i
$372$	9.46410	+	24.5885i	0.490691	+	1.27485i
$373$	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
$375$	8.00000	+	29.8564i	0.413118	+	1.54178i
$376$			4.19615i			0.216400i
$377$	1.96410	−	30.4545i	0.101156	−	1.56849i
$378$	5.32051	+	3.07180i	0.273657	+	0.157996i
$379$	−0.696152	−	2.59808i	−0.0357589	−	0.133454i	0.945739	−	0.324928i	$-0.105340\pi$
$379$	−0.696152	−	2.59808i	−0.0357589	−	0.133454i	−0.981498	+	0.191474i	$0.938673\pi$
$380$	−12.5885			−0.645774
$381$	−15.1244	+	8.73205i	−0.774844	+	0.447357i
$382$	2.83013	+	0.758330i	0.144802	+	0.0387996i
$383$	−2.02628	+	7.56218i	−0.103538	+	0.386409i	−0.998175	−	0.0603842i	$-0.980767\pi$
$383$	−2.02628	+	7.56218i	−0.103538	+	0.386409i	0.894637	+	0.446793i	$0.147434\pi$
$384$	−8.09808	−	30.2224i	−0.413253	−	1.54228i
$385$	3.63397	+	0.973721i	0.185204	+	0.0496254i
$386$	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	−0.602267	−	0.798295i	$-0.705736\pi$
$389$	7.69615	−	13.3301i	0.390210	−	0.675864i	0.992477	+	0.122431i	$0.0390689\pi$
$390$	7.19615	+	0.464102i	0.364391	+	0.0235007i
$391$		0			0
$392$	3.36603	+	0.901924i	0.170010	+	0.0455540i
$393$	−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
$396$	6.69615	−	1.79423i	0.336494	−	0.0901634i
$397$	−13.5622	+	3.63397i	−0.680666	+	0.182384i	−0.582555	−	0.812791i	$-0.697947\pi$
$397$	−13.5622	+	3.63397i	−0.680666	+	0.182384i	−0.0981115	+	0.995175i	$0.531280\pi$
$398$	6.66025	+	1.78461i	0.333848	+	0.0894544i
$399$		−	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	$-0.531796\pi$
$401$	17.9282	−	17.9282i	0.895292	−	0.895292i	0.995015	+	0.0997234i	$0.0317958\pi$
$402$	−15.6603			−0.781062
$403$	−13.5981	+	14.7679i	−0.677368	+	0.735644i
$404$	−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
$409$	−35.9545	+	9.63397i	−1.77783	+	0.476369i	−0.990186	−	0.139755i	$-0.955368\pi$
$409$	−35.9545	+	9.63397i	−1.77783	+	0.476369i	−0.787649	+	0.616125i	$0.788702\pi$
$410$	−4.19615	+	1.12436i	−0.207233	+	0.0555280i
$411$	−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
$414$	13.8301	+	3.70577i	0.679714	+	0.182129i
$415$	−11.3923	+	19.7321i	−0.559226	+	0.968608i
$416$	13.9186	−	12.2321i	0.682415	−	0.599726i
$417$	−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
$421$	−12.8301	−	3.43782i	−0.625302	−	0.167549i	−0.0677651	−	0.997701i	$-0.521587\pi$
$421$	−12.8301	−	3.43782i	−0.625302	−	0.167549i	−0.557537	+	0.830152i	$0.688254\pi$
$422$	−0.437822	−	1.63397i	−0.0213128	−	0.0795406i
$423$	−2.50962	+	9.36603i	−0.122022	+	0.455392i
$424$	−12.4282	−	3.33013i	−0.603567	−	0.161725i
$425$		0			0
$426$	1.80385			0.0873967
$427$	−2.45448	−	9.16025i	−0.118781	−	0.443296i
$428$	17.4904	+	10.0981i	0.845429	+	0.488109i
$429$	5.83013	+	6.63397i	0.281481	+	0.320291i
$430$			3.07180i			0.148135i
$431$	−9.50000	−	35.4545i	−0.457599	−	1.70778i	−0.680333	−	0.732903i	$-0.738165\pi$
$431$	−9.50000	−	35.4545i	−0.457599	−	1.70778i	0.222734	−	0.974879i	$-0.428502\pi$
$432$		−	9.85641i		−	0.474217i
$433$	13.7321			0.659920			0.329960	−	0.943995i	$-0.392965\pi$
$433$	13.7321			0.659920			0.329960	+	0.943995i	$0.392965\pi$
$434$	−3.07180	−	7.98076i	−0.147451	−	0.383089i
$435$	23.1244	−	23.1244i	1.10873	−	1.10873i
$436$	−17.1962	−	17.1962i	−0.823546	−	0.823546i
$437$	−8.24167	−	30.7583i	−0.394253	−	1.47137i
$438$	15.4641			0.738903
$439$	0.464102	−	0.267949i	0.0221504	−	0.0127885i	−0.488884	−	0.872349i	$-0.662596\pi$
$439$	0.464102	−	0.267949i	0.0221504	−	0.0127885i	0.511034	+	0.859560i	$0.329263\pi$
$440$	0.633975	+	2.36603i	0.0302236	+	0.112796i
$441$	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	$0.790803\pi$
$444$	22.3923	+	6.00000i	1.06269	+	0.284747i
$445$	−3.92820	+	2.26795i	−0.186215	+	0.107511i
$446$	1.37564	−	2.38269i	0.0651386	−	0.112823i
$447$	−11.4641	+	42.7846i	−0.542233	+	2.02364i
$448$	−1.74167	−	6.50000i	−0.0822862	−	0.307096i
$449$	9.66025	−	9.66025i	0.455896	−	0.455896i	−0.441410	−	0.897306i	$-0.645522\pi$
$449$	9.66025	−	9.66025i	0.455896	−	0.455896i	0.897306	+	0.441410i	$0.145522\pi$
$450$	−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
$453$	−25.7583	+	6.90192i	−1.21023	+	0.324281i
$454$	−5.36603	+	3.09808i	−0.251840	+	0.145400i
$455$	15.0981	+	0.973721i	0.707809	+	0.0456487i
$456$	23.4904	−	13.5622i	1.10004	−	0.635107i
$457$	−12.0000	−	12.0000i	−0.561336	−	0.561336i	0.368351	−	0.929687i	$-0.379923\pi$
$457$	−12.0000	−	12.0000i	−0.561336	−	0.561336i	−0.929687	+	0.368351i	$0.879923\pi$
$458$	0.418584	+	0.241670i	0.0195592	+	0.0112925i
$459$		0			0
$460$	3.92820	−	14.6603i	0.183153	−	0.683538i
$461$	0.196152	+	0.196152i	0.00913573	+	0.00913573i	0.711660	−	0.702524i	$-0.247944\pi$
$461$	0.196152	+	0.196152i	0.00913573	+	0.00913573i	−0.702524	+	0.711660i	$0.747944\pi$
$462$	−3.63397	+	0.973721i	−0.169068	+	0.0453016i
$463$	6.66025	−	6.66025i	0.309528	−	0.309528i	−0.535198	−	0.844726i	$-0.679763\pi$
$463$	6.66025	−	6.66025i	0.309528	−	0.309528i	0.844726	+	0.535198i	$0.179763\pi$
$464$		−	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	$0.139918\pi$
$467$			18.3923i			0.851094i	−0.904936	+	0.425547i	$0.860082\pi$
$468$	24.9904	−	12.3564i	1.15518	−	0.571175i
$469$	−32.8564			−1.51717
$470$	−1.53590	−	0.411543i	−0.0708457	−	0.0189831i
$471$	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
$474$	−16.9282	−	4.53590i	−0.777538	−	0.208341i
$475$	−3.99038	+	14.8923i	−0.183091	+	0.683306i
$476$		0			0
$477$	−25.7487	−	14.8660i	−1.17895	−	0.680669i
$478$	−1.86603	−	3.23205i	−0.0853500	−	0.147831i
$479$	6.13397	−	1.64359i	0.280268	−	0.0750977i	−0.115947	−	0.993255i	$-0.536990\pi$
$479$	6.13397	−	1.64359i	0.280268	−	0.0750977i	0.396215	+	0.918158i	$0.370323\pi$
$480$	19.8564			0.906317
$481$	3.46410	+	17.3205i	0.157949	+	0.789747i
$482$	1.31347	+	0.758330i	0.0598268	+	0.0345410i
$483$	48.5167	+	13.0000i	2.20758	+	0.591520i
$484$	8.83013	−	15.2942i	0.401369	−	0.695192i
$485$	14.6603	−	8.46410i	0.665688	−	0.384335i
$486$	2.50962	−	9.36603i	0.113839	−	0.424852i
$487$	3.70577	−	13.8301i	0.167925	−	0.626703i	−0.829725	−	0.558173i	$-0.811503\pi$
$487$	3.70577	−	13.8301i	0.167925	−	0.626703i	0.997649	−	0.0685298i	$-0.0218308\pi$
$488$	4.36603	−	4.36603i	0.197641	−	0.197641i
$489$	2.56218	+	9.56218i	0.115866	+	0.432417i
$490$	−0.660254	+	1.14359i	−0.0298272	+	0.0516623i
$491$	−2.09808	−	3.63397i	−0.0946849	−	0.163999i	0.814792	−	0.579753i	$-0.196851\pi$
$491$	−2.09808	−	3.63397i	−0.0946849	−	0.163999i	−0.909477	+	0.415754i	$0.863518\pi$
$492$	−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
$496$	−8.62436	+	10.6699i	−0.387245	+	0.479091i
$497$	3.78461			0.169763
$498$		−	22.7846i		−	1.02100i
$499$	−13.2583	+	3.55256i	−0.593524	+	0.159034i	−0.543063	−	0.839692i	$-0.682736\pi$
$499$	−13.2583	+	3.55256i	−0.593524	+	0.159034i	−0.0504609	+	0.998726i	$0.516069\pi$
$500$	−13.8564	+	13.8564i	−0.619677	+	0.619677i
$501$	−4.36603	+	16.2942i	−0.195060	+	0.727972i
$502$	−3.78461	−	14.1244i	−0.168915	−	0.630401i
$503$	−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
$505$	1.43782	−	5.36603i	0.0639822	−	0.238785i
$506$	−2.49038	+	1.43782i	−0.110711	+	0.0639190i
$507$	28.2224	+	21.5622i	1.25340	+	0.957610i
$508$	−9.58846	−	5.53590i	−0.425419	−	0.245616i
$509$	5.56218	−	20.7583i	0.246539	−	0.920097i	−0.726064	−	0.687627i	$-0.758653\pi$
$509$	5.56218	−	20.7583i	0.246539	−	0.920097i	0.972604	−	0.232470i	$-0.0746808\pi$
$510$		0			0
$511$	32.4449			1.43528
$512$	15.6865	−	15.6865i	0.693253	−	0.693253i
$513$	19.8564	−	5.32051i	0.876682	−	0.234906i
$514$	0.990381	−	3.69615i	0.0436838	−	0.163030i
$515$	−16.6603	+	4.46410i	−0.734139	+	0.196712i
$516$	9.92820	+	17.1962i	0.437065	+	0.757018i
$517$	−0.973721	−	1.68653i	−0.0428242	−	0.0741737i
$518$	−7.26795	−	1.94744i	−0.319335	−	0.0855657i
$519$	−59.7128			−2.62110
$520$	4.36603	+	8.83013i	0.191463	+	0.387227i
$521$	−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	$0.920817\pi$
$522$	−5.06218	+	18.8923i	−0.221566	+	0.826894i
$523$		−	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
$533$	−20.2679	−	6.85641i	−0.877902	−	0.296984i
$534$	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
$538$	−2.38269	+	8.89230i	−0.102725	+	0.383374i
$539$	−1.56218	+	0.418584i	−0.0672878	+	0.0180297i
$540$	9.46410	+	2.53590i	0.407270	+	0.109128i
$541$	21.9282	−	5.87564i	0.942767	−	0.252614i	0.245477	−	0.969402i	$-0.421056\pi$
$541$	21.9282	−	5.87564i	0.942767	−	0.252614i	0.697290	+	0.716789i	$0.254389\pi$
$542$		−	4.73205i		−	0.203259i
$543$			51.9090i			2.22763i
$544$		0			0
$545$	17.1962	−	9.92820i	0.736602	−	0.425278i
$546$	−13.5622	+	6.70577i	−0.580408	+	0.286981i
$547$	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	$0.816068\pi$
$548$	0.803848	−	3.00000i	0.0343387	−	0.128154i
$549$	12.3564	−	7.13397i	0.527359	−	0.304471i
$550$	1.39230			0.0593681
$551$	42.0167	−	11.2583i	1.78997	−	0.479621i
$552$	8.46410	+	31.5885i	0.360256	+	1.34449i
$553$	−35.5167	−	9.51666i	−1.51032	−	0.404690i
$554$	−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	$-0.687960\pi$
$557$	6.46410	−	6.46410i	0.273893	−	0.273893i	0.830665	+	0.556772i	$0.187960\pi$
$558$	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	−0.954879	−	0.296994i	$-0.904016\pi$
$563$	−27.8827	+	16.0981i	−1.17512	+	0.678453i	−0.220236	+	0.975447i	$0.570683\pi$
$564$	−9.92820	+	2.66025i	−0.418053	+	0.112017i
$565$	2.53590	+	9.46410i	0.106686	+	0.398158i
$566$	−2.60770	−	2.60770i	−0.109610	−	0.109610i
$567$	1.89230	−	7.06218i	0.0794693	−	0.296584i
$568$	1.23205	+	2.13397i	0.0516957	+	0.0895396i
$569$	−20.0622	−	34.7487i	−0.841050	−	1.45674i	−0.889008	−	0.457892i	$-0.848605\pi$
$569$	−20.0622	−	34.7487i	−0.841050	−	1.45674i	0.0479574	−	0.998849i	$-0.484729\pi$
$570$	2.66025	+	9.92820i	0.111426	+	0.415847i
$571$	−14.7583	−	25.5622i	−0.617617	−	1.06974i	−0.989919	−	0.141632i	$-0.954765\pi$
$571$	−14.7583	−	25.5622i	−0.617617	−	1.06974i	0.372302	−	0.928111i	$-0.378568\pi$
$572$	−1.79423	+	5.30385i	−0.0750205	+	0.221765i
$573$			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
$577$	−1.49038	−	5.56218i	−0.0620454	−	0.231556i	0.927939	−	0.372731i	$-0.121579\pi$
$577$	−1.49038	−	5.56218i	−0.0620454	−	0.231556i	−0.989985	+	0.141175i	$0.954912\pi$
$578$	8.50000	+	2.27757i	0.353553	+	0.0947343i
$579$	14.6603	+	3.92820i	0.609259	+	0.163251i
$580$	20.0263	+	5.36603i	0.831546	+	0.222812i
$581$		−	47.8038i		−	1.98324i
$582$	−8.46410	+	14.6603i	−0.350848	+	0.607687i
$583$	5.76795	−	1.54552i	0.238884	−	0.0640088i
$584$	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	$-0.0482218\pi$
$587$	20.2942	+	20.2942i	0.837632	+	0.837632i	−0.150914	+	0.988547i	$0.548222\pi$
$588$			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
$592$	3.12436	+	11.6603i	0.128410	+	0.479233i
$593$	19.8564	+	19.8564i	0.815405	+	0.815405i	0.985438	−	0.170033i	$-0.0543876\pi$
$593$	19.8564	+	19.8564i	0.815405	+	0.815405i	−0.170033	+	0.985438i	$0.554388\pi$
$594$	−0.928203	−	1.60770i	−0.0380846	−	0.0659645i
$595$		0			0
$596$	−27.1244	+	7.26795i	−1.11106	+	0.297707i
$597$			36.3923i			1.48944i
$598$	−8.68653	+	7.63397i	−0.355219	+	0.312176i
$599$	−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	$-0.461457\pi$
$600$	4.09808	−	15.2942i	0.167303	−	0.624384i
$601$	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
$603$	−12.7942	−	47.7487i	−0.521021	−	1.94448i
$604$	−11.9545	−	11.9545i	−0.486421	−	0.486421i
$605$	10.1962	+	10.1962i	0.414533	+	0.414533i
$606$	1.43782	+	5.36603i	0.0584075	+	0.217980i
$607$	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
$609$	−17.7583	+	66.2750i	−0.719604	+	2.68560i
$610$	1.16987	+	2.02628i	0.0473668	+	0.0820417i
$611$	−5.16987	−	5.88269i	−0.209151	−	0.237988i
$612$		0			0
$613$	22.1244	−	5.92820i	0.893594	−	0.239438i	0.217331	−	0.976098i	$-0.430265\pi$
$613$	22.1244	−	5.92820i	0.893594	−	0.239438i	0.676263	+	0.736660i	$0.263598\pi$
$614$	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
$617$	8.80385	+	32.8564i	0.354430	+	1.32275i	0.881201	+	0.472742i	$0.156736\pi$
$617$	8.80385	+	32.8564i	0.354430	+	1.32275i	−0.526771	+	0.850007i	$0.676598\pi$
$618$	12.1962	−	12.1962i	0.490601	−	0.490601i
$619$	0.366025	−	0.366025i	0.0147118	−	0.0147118i	−0.699713	−	0.714424i	$-0.746689\pi$
$619$	0.366025	−	0.366025i	0.0147118	−	0.0147118i	0.714424	+	0.699713i	$0.246689\pi$
$620$	−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
$626$	−11.1603	+	2.99038i	−0.446053	+	0.119520i
$627$	−6.29423	+	10.9019i	−0.251367	+	0.435381i
$628$			8.07180i			0.322100i
$629$		0			0
$630$	−9.36603	−	2.50962i	−0.373151	−	0.0999856i
$631$	37.4186	+	10.0263i	1.48961	+	0.399140i	0.909605	−	0.415473i	$-0.136384\pi$
$631$	37.4186	+	10.0263i	1.48961	+	0.399140i	0.580005	+	0.814613i	$0.303051\pi$
$632$	−6.19615	−	23.1244i	−0.246470	−	0.919837i
$633$	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
$637$	−5.83013	+	2.88269i	−0.230998	+	0.114216i
$638$	−1.96410	−	3.40192i	−0.0777595	−	0.134683i
$639$	1.47372	+	5.50000i	0.0582995	+	0.217577i
$640$	8.09808	+	14.0263i	0.320105	+	0.554437i
$641$	20.4282	+	35.3827i	0.806866	+	1.39753i	0.915024	+	0.403398i	$0.132171\pi$
$641$	20.4282	+	35.3827i	0.806866	+	1.39753i	−0.108159	+	0.994134i	$0.534496\pi$
$642$	4.26795	−	15.9282i	0.168443	−	0.628636i
$643$	0.607695	+	0.607695i	0.0239652	+	0.0239652i	0.718988	−	0.695023i	$-0.244606\pi$
$643$	0.607695	+	0.607695i	0.0239652	+	0.0239652i	−0.695023	+	0.718988i	$0.744606\pi$
$644$	8.24167	+	30.7583i	0.324767	+	1.21205i
$645$	−15.6603	+	4.19615i	−0.616622	+	0.165223i
$646$		0			0
$647$	46.7321			1.83723			0.918613	−	0.395158i	$-0.129310\pi$
$647$	46.7321			1.83723			0.918613	+	0.395158i	$0.129310\pi$
$648$	4.59808	−	1.23205i	0.180629	−	0.0483995i
$649$	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
$656$	−14.1244	−	3.78461i	−0.551463	−	0.147764i
$657$	12.6340	+	47.1506i	0.492898	+	1.83952i
$658$	3.22243	−	0.863448i	0.125623	−	0.0336607i
$659$	−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
$661$	3.07180	−	11.4641i	0.119479	−	0.445902i	−0.880104	−	0.474781i	$-0.842527\pi$
$661$	3.07180	−	11.4641i	0.119479	−	0.445902i	0.999583	+	0.0288793i	$0.00919386\pi$
$662$	−4.06218	−	7.03590i	−0.157881	−	0.273458i
$663$		0			0
$664$	26.9545	−	15.5622i	1.04604	−	0.603930i
$665$	5.58142	+	20.8301i	0.216438	+	0.807758i
$666$		−	11.3205i		−	0.438661i
$667$			52.4449i			2.03067i
$668$	−10.3301	+	2.76795i	−0.399685	+	0.107095i
$669$	14.0263	+	3.75833i	0.542287	+	0.145305i
$670$	7.83013	−	2.09808i	0.302504	−	0.0810558i
$671$	−0.741670	+	2.76795i	−0.0286318	+	0.106855i
$672$	−36.0788	+	20.8301i	−1.39177	+	0.803540i
$673$	−3.07180	−	5.32051i	−0.118409	−	0.205091i	0.800728	−	0.599028i	$-0.204446\pi$
$673$	−3.07180	−	5.32051i	−0.118409	−	0.205091i	−0.919137	+	0.393937i	$0.871113\pi$
$674$	4.75833	−	4.75833i	0.183284	−	0.183284i
$675$	6.00000	−	10.3923i	0.230940	−	0.400000i
$676$	−2.89230	+	22.3301i	−0.111242	+	0.858851i
$677$	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
$682$	−0.401924	+	2.55256i	−0.0153905	+	0.0977425i
$683$	−16.8827	−	16.8827i	−0.645998	−	0.645998i	0.306025	−	0.952023i	$-0.401001\pi$
$683$	−16.8827	−	16.8827i	−0.645998	−	0.645998i	−0.952023	+	0.306025i	$0.901001\pi$
$684$	28.0981	+	28.0981i	1.07436	+	1.07436i
$685$	2.19615	+	1.26795i	0.0839107	+	0.0484458i
$686$			7.98076i			0.304707i
$687$	−0.660254	+	2.46410i	−0.0251903	+	0.0940113i
$688$	−5.16987	+	8.95448i	−0.197100	+	0.341386i
$689$	21.5263	−	10.6436i	0.820086	−	0.405489i
$690$	−12.3923			−0.471767
$691$	1.33013	+	0.356406i	0.0506004	+	0.0135583i	0.284030	−	0.958815i	$-0.408328\pi$
$691$	1.33013	+	0.356406i	0.0506004	+	0.0135583i	−0.233430	+	0.972374i	$0.574995\pi$
$692$	−18.9282	−	32.7846i	−0.719542	−	1.24628i
$693$	−5.93782	−	10.2846i	−0.225559	−	0.390680i
$694$	9.36603	−	2.50962i	0.355529	−	0.0952638i
$695$	7.07180	−	26.3923i	0.268249	−	1.00112i
$696$	−43.1506	+	11.5622i	−1.63562	+	0.438263i
$697$		0			0
$698$	−14.7321			−0.557616
$699$	−9.46410	+	16.3923i	−0.357965	+	0.620014i
$700$	3.99038	−	14.8923i	0.150822	−	0.562876i
$701$	−6.92820	−	4.00000i	−0.261675	−	0.151078i	0.363424	−	0.931624i	$-0.381608\pi$
$701$	−6.92820	−	4.00000i	−0.261675	−	0.151078i	−0.625098	+	0.780546i	$0.714941\pi$
$702$	−4.92820	−	5.60770i	−0.186003	−	0.211649i
$703$	−21.8038	+	12.5885i	−0.822348	+	0.474783i
$704$	−0.526279	+	1.96410i	−0.0198349	+	0.0740249i
$705$		−	8.39230i		−	0.316072i
$706$	−6.09808	+	10.5622i	−0.229504	+	0.397513i
$707$	3.01666	+	11.2583i	0.113453	+	0.423413i
$708$	2.66025	−	9.92820i	0.0999785	−	0.373125i
$709$	16.5167	−	16.5167i	0.620296	−	0.620296i	−0.325311	−	0.945607i	$-0.605469\pi$
$709$	16.5167	−	16.5167i	0.620296	−	0.620296i	0.945607	+	0.325311i	$0.105469\pi$
$710$	−0.901924	+	0.241670i	−0.0338486	+	0.00906970i
$711$		−	55.3205i		−	2.07468i
$712$	6.19615			0.232211
$713$	21.6865	−	26.8301i	0.812167	−	1.00480i
$714$		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	−0.996654	−	0.0817390i	$-0.973953\pi$
$719$	−11.4641	+	19.8564i	−0.427539	+	0.740519i	0.569115	+	0.822258i	$0.307286\pi$
$720$	4.02628	+	15.0263i	0.150051	+	0.559996i
$721$	25.5885	−	25.5885i	0.952964	−	0.952964i
$722$	−0.992958	+	3.70577i	−0.0369541	+	0.137915i
$723$	−2.07180	+	7.73205i	−0.0770510	+	0.287558i
$724$	−28.5000	+	16.4545i	−1.05919	+	0.611526i
$725$	12.6962	−	21.9904i	0.471523	−	0.816702i
$726$	−13.9282	−	3.73205i	−0.516924	−	0.138509i
$727$	−14.1962	−	8.19615i	−0.526506	−	0.303978i	0.213086	−	0.977033i	$-0.431648\pi$
$727$	−14.1962	−	8.19615i	−0.526506	−	0.303978i	−0.739593	+	0.673055i	$0.764982\pi$
$728$	−17.1962	−	11.4641i	−0.637332	−	0.424888i
$729$	43.7846			1.62165
$730$	−7.73205	+	2.07180i	−0.286176	+	0.0766806i
$731$		0			0
$732$	13.0981	+	7.56218i	0.484119	+	0.279506i
$733$	−8.63397	−	2.31347i	−0.318903	−	0.0854498i	0.0958167	−	0.995399i	$-0.469454\pi$
$733$	−8.63397	−	2.31347i	−0.318903	−	0.0854498i	−0.414720	+	0.909949i	$0.636120\pi$
$734$	2.66025	−	9.92820i	0.0981918	−	0.366457i
$735$	−6.73205	−	1.80385i	−0.248315	−	0.0665359i
$736$	−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
$739$	19.9641	+	5.34936i	0.734391	+	0.196780i	0.606584	−	0.795019i	$-0.292539\pi$
$739$	19.9641	+	5.34936i	0.734391	+	0.196780i	0.127807	+	0.991799i	$0.459206\pi$
$740$	−12.0000			−0.441129
$741$	−16.2224	+	47.9545i	−0.595946	+	1.76165i
$742$			10.2295i			0.375536i
$743$	15.5359	+	15.5359i	0.569957	+	0.569957i	0.932116	−	0.362159i	$-0.117960\pi$
$743$	15.5359	+	15.5359i	0.569957	+	0.569957i	−0.362159	+	0.932116i	$0.617960\pi$
$744$	26.8564	+	11.9282i	0.984604	+	0.437309i
$745$		−	22.9282i		−	0.840024i
$746$	13.0263	−	13.0263i	0.476926	−	0.476926i
$747$	69.4711	−	18.6147i	2.54182	−	0.681078i
$748$		0			0
$749$	8.95448	−	33.4186i	0.327190	−	1.22109i
$750$	13.8564	+	8.00000i	0.505964	+	0.292119i
$751$	−39.1244	−	22.5885i	−1.42767	−	0.824265i	−0.430732	−	0.902480i	$-0.641744\pi$
$751$	−39.1244	−	22.5885i	−1.42767	−	0.824265i	−0.996936	+	0.0782156i	$0.975078\pi$
$752$	−3.78461	−	3.78461i	−0.138011	−	0.138011i
$753$	66.8372	−	38.5885i	2.43568	−	1.40624i
$754$	−10.4282	−	11.8660i	−0.379773	−	0.432135i
$755$	11.9545	−	6.90192i	0.435068	−	0.251187i
$756$	−19.8564	+	5.32051i	−0.722171	+	0.193505i
$757$	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
$761$	−7.07180	−	26.3923i	−0.256352	−	0.956720i	−0.967333	−	0.253509i	$-0.918415\pi$
$761$	−7.07180	−	26.3923i	−0.256352	−	0.956720i	0.710981	−	0.703212i	$-0.248251\pi$
$762$	−2.33975	+	8.73205i	−0.0847601	+	0.316329i
$763$	−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
$769$	2.58142	+	9.63397i	0.0930882	+	0.347410i	0.996723	−	0.0808946i	$-0.0257777\pi$
$769$	2.58142	+	9.63397i	0.0930882	+	0.347410i	−0.903634	+	0.428305i	$0.859111\pi$
$770$	1.68653	−	0.973721i	0.0607784	−	0.0350905i
$771$	20.1962			0.727347
$772$	2.49038	+	9.29423i	0.0896308	+	0.334507i
$773$	−21.1962	−	21.1962i	−0.762373	−	0.762373i	0.214378	−	0.976751i	$-0.431228\pi$
$773$	−21.1962	−	21.1962i	−0.762373	−	0.762373i	−0.976751	+	0.214378i	$0.931228\pi$
$774$	6.85641	−	6.85641i	0.246448	−	0.246448i
$775$	−15.5885	+	6.00000i	−0.559954	+	0.215526i
$776$	−23.1244			−0.830116
$777$		−	39.7128i		−	1.42469i
$778$	−2.06218	−	7.69615i	−0.0739327	−	0.275920i
$779$		−	30.4974i		−	1.09268i
$780$	−18.1244	+	15.9282i	−0.648956	+	0.570321i
$781$	−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
$785$	−6.36603	−	1.70577i	−0.227213	−	0.0608816i
$786$	−6.33975	+	23.6603i	−0.226131	+	0.843933i
$787$	−11.6244	−	43.3827i	−0.414364	−	1.54643i	−0.786107	−	0.618090i	$-0.787907\pi$
$787$	−11.6244	−	43.3827i	−0.414364	−	1.54643i	0.371744	−	0.928335i	$-0.378760\pi$
$788$	8.83013	+	2.36603i	0.314560	+	0.0842862i
$789$	−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
$793$	−0.741670	+	11.5000i	−0.0263375	+	0.408377i
$794$	−3.63397	+	6.29423i	−0.128965	+	0.223374i
$795$	24.8564	+	6.66025i	0.881566	+	0.236215i
$796$	−19.9808	+	11.5359i	−0.708199	+	0.408879i
$797$	18.8923	+	32.7224i	0.669200	+	1.15909i	0.978128	+	0.208003i	$0.0666963\pi$
$797$	18.8923	+	32.7224i	0.669200	+	1.15909i	−0.308928	+	0.951085i	$0.599970\pi$
$798$	−15.2487	−	15.2487i	−0.539799	−	0.539799i
$799$		0			0
$800$	14.8923	−	3.99038i	0.526522	−	0.141081i
$801$	13.8301	+	3.70577i	0.488664	+	0.130937i
$802$		−	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
$806$	0.428203	+	10.3827i	0.0150828	+	0.365715i
$807$	−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
$811$	32.2583	+	8.64359i	1.13274	+	0.303518i	0.776030	−	0.630696i	$-0.217231\pi$
$811$	32.2583	+	8.64359i	1.13274	+	0.303518i	0.356713	+	0.934214i	$0.383897\pi$
$812$	−42.0167	+	11.2583i	−1.47450	+	0.395090i
$813$	24.1244	−	6.46410i	0.846078	−	0.226706i
$814$	1.60770	+	1.60770i	0.0563497	+	0.0563497i
$815$	−2.56218	−	4.43782i	−0.0897492	−	0.155450i
$816$		0			0
$817$	−20.8301	−	5.58142i	−0.728754	−	0.195269i
$818$	−9.63397	+	16.6865i	−0.336844	+	0.583431i
$819$	−31.5263	−	35.8731i	−1.10162	−	1.25351i
$820$	7.26795	−	12.5885i	0.253808	−	0.439608i
$821$	−37.1769	−	37.1769i	−1.29748	−	1.29748i	−0.930050	−	0.367433i	$-0.880237\pi$
$821$	−37.1769	−	37.1769i	−1.29748	−	1.29748i	−0.367433	−	0.930050i	$-0.619763\pi$
$822$	−2.53590			−0.0884496
$823$	−8.39230	+	14.5359i	−0.292537	+	0.506690i	−0.974409	−	0.224782i	$-0.927833\pi$
$823$	−8.39230	+	14.5359i	−0.292537	+	0.506690i	0.681872	+	0.731472i	$0.261166\pi$
$824$	22.7583	+	6.09808i	0.792824	+	0.212437i
$825$	1.90192	+	7.09808i	0.0662165	+	0.247123i
$826$	−0.863448	+	3.22243i	−0.0300432	+	0.112123i
$827$	0.633975	+	0.169873i	0.0220455	+	0.00590706i	0.269825	−	0.962909i	$-0.413034\pi$
$827$	0.633975	+	0.169873i	0.0220455	+	0.00590706i	−0.247779	+	0.968816i	$0.579701\pi$
$828$	−41.4904	+	23.9545i	−1.44189	+	0.832476i
$829$	18.7846			0.652416			0.326208	−	0.945298i	$-0.394229\pi$
$829$	18.7846			0.652416			0.326208	+	0.945298i	$0.394229\pi$
$830$	3.05256	+	11.3923i	0.105956	+	0.395433i
$831$	−62.4449	−	36.0526i	−2.16619	−	1.25065i
$832$	−0.526279	+	8.16025i	−0.0182455	+	0.282906i
$833$		0			0
$834$	7.07180	+	26.3923i	0.244876	+	0.913891i
$835$		−	8.73205i		−	0.302185i
$836$	−7.98076			−0.276020
$837$	17.3205	+	14.0000i	0.598684	+	0.483911i
$838$	10.9808	−	10.9808i	0.379324	−	0.379324i
$839$	−4.70577	−	4.70577i	−0.162461	−	0.162461i	0.621195	−	0.783656i	$-0.286648\pi$
$839$	−4.70577	−	4.70577i	−0.162461	−	0.162461i	−0.783656	+	0.621195i	$0.786648\pi$
$840$	−5.73205	−	21.3923i	−0.197775	−	0.738105i
$841$	−42.6410			−1.47038
$842$	−5.95448	+	3.43782i	−0.205205	+	0.118475i
$843$	−21.3923	−	79.8372i	−0.736790	−	2.74974i
$844$	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
$847$	−29.2224	−	7.83013i	−1.00409	−	0.269046i
$848$	14.2128	−	8.20577i	0.488070	−	0.281787i
$849$	9.73205	−	16.8564i	0.334003	−	0.578510i
$850$		0			0
$851$	−7.85641	−	29.3205i	−0.269314	−	1.00509i
$852$	−4.26795	+	4.26795i	−0.146218	+	0.146218i
$853$	−24.4641	−	24.4641i	−0.837635	−	0.837635i	0.150912	−	0.988547i	$-0.451779\pi$
$853$	−24.4641	−	24.4641i	−0.837635	−	0.837635i	−0.988547	+	0.150912i	$0.951779\pi$
$854$	−4.25129	−	2.45448i	−0.145476	−	0.0839907i
$855$	−28.0981	+	16.2224i	−0.960934	+	0.554795i
$856$	21.7583	−	5.83013i	0.743684	−	0.199270i
$857$	25.4545	−	14.6962i	0.869509	−	0.502011i	0.00232367	−	0.999997i	$-0.499260\pi$
$857$	25.4545	−	14.6962i	0.869509	−	0.502011i	0.867185	+	0.497986i	$0.165927\pi$
$858$	4.56218	+	0.294229i	0.155750	+	0.0100448i
$859$	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
$863$	−3.30385	+	12.3301i	−0.112464	+	0.419722i	−0.999085	−	0.0427754i	$-0.986380\pi$
$863$	−3.30385	+	12.3301i	−0.112464	+	0.419722i	0.886620	+	0.462498i	$0.153047\pi$
$864$	−14.5359	−	14.5359i	−0.494521	−	0.494521i
$865$	29.8564	−	8.00000i	1.01515	−	0.272008i
$866$	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
$871$	37.8205	+	12.7942i	1.28150	+	0.433516i
$872$	−27.1244			−0.918547
$873$	−51.6147	−	13.8301i	−1.74689	−	0.468079i
$874$	−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
$877$	9.83013	+	2.63397i	0.331940	+	0.0889430i	0.420940	−	0.907089i	$-0.361700\pi$
$877$	9.83013	+	2.63397i	0.331940	+	0.0889430i	−0.0889999	+	0.996032i	$0.528367\pi$
$878$	0.0717968	−	0.267949i	0.00242302	−	0.00904285i
$879$	−74.1051	−	19.8564i	−2.49950	−	0.669740i
$880$	−2.70577	−	1.56218i	−0.0912115	−	0.0526610i
$881$	−9.72243	−	16.8397i	−0.327557	−	0.567345i	0.654469	−	0.756088i	$-0.272892\pi$
$881$	−9.72243	−	16.8397i	−0.327557	−	0.567345i	−0.982027	+	0.188743i	$0.939559\pi$
$882$	4.02628	−	1.07884i	0.135572	−	0.0363264i
$883$	−30.1962			−1.01618			−0.508091	−	0.861304i	$-0.669649\pi$
$883$	−30.1962			−1.01618			−0.508091	+	0.861304i	$0.669649\pi$
$884$		0			0
$885$	7.26795	+	4.19615i	0.244309	+	0.141052i
$886$	2.80385	+	0.751289i	0.0941971	+	0.0252400i
$887$	−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
$889$	−4.90897	+	18.3205i	−0.164641	+	0.614450i
$890$	−0.607695	+	2.26795i	−0.0203700	+	0.0760218i
$891$	−1.56218	+	1.56218i	−0.0523349	+	0.0523349i
$892$	2.38269	+	8.89230i	0.0797782	+	0.297736i
$893$	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
$899$	36.6506	+	29.6244i	1.22237	+	0.988028i
$900$	23.1962			0.773205
$901$		0			0
$902$	−2.66025	+	0.712813i	−0.0885768	+	0.0237341i
$903$	24.0526	−	24.0526i	0.800419	−	0.800419i
$904$	3.46410	−	12.9282i	0.115214	−	0.429986i
$905$	−6.95448	−	25.9545i	−0.231175	−	0.862756i
$906$	−6.90192	+	11.9545i	−0.229301	+	0.397161i
$907$		−	4.87564i		−	0.161893i	−0.996718	−	0.0809466i	$-0.974206\pi$
$907$		−	4.87564i		−	0.161893i	0.996718	−	0.0809466i	$-0.0257943\pi$
$908$	5.36603	−	20.0263i	0.178078	−	0.664595i
$909$	−15.1865	+	8.76795i	−0.503706	+	0.290815i
$910$	5.88269	−	5.16987i	0.195009	−	0.171380i
$911$	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	$0.547925\pi$
$912$	−8.95448	+	33.4186i	−0.296513	+	1.10660i
$913$	−7.22243	+	12.5096i	−0.239028	+	0.414008i
$914$	−8.78461			−0.290569
$915$	−8.73205	+	8.73205i	−0.288673	+	0.288673i
$916$	−1.56218	+	0.418584i	−0.0516158	+	0.0138304i
$917$	−13.3013	+	49.6410i	−0.439247	+	1.63929i
$918$		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
$921$	61.4449	+	16.4641i	2.02468	+	0.542511i
$922$	0.143594			0.00472900
$923$	−4.35641	−	1.47372i	−0.143393	−	0.0485081i
$924$	6.29423	−	10.9019i	0.207065	−	0.358647i
$925$	−3.80385	+	14.1962i	−0.125070	+	0.466767i
$926$		−	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	$-0.142200\pi$
$929$	14.3205	+	14.3205i	0.469841	+	0.469841i	−0.432022	+	0.901863i	$0.642200\pi$
$930$	−7.00000	+	8.66025i	−0.229539	+	0.283981i
$931$	−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
$936$	9.96410	−	29.4545i	0.325687	−	0.962750i
$937$	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
$941$	7.24167	−	27.0263i	0.236072	−	0.881032i	−0.741591	−	0.670852i	$-0.765929\pi$
$941$	7.24167	−	27.0263i	0.236072	−	0.881032i	0.977663	−	0.210179i	$-0.0674048\pi$
$942$	6.36603	−	1.70577i	0.207416	−	0.0555770i
$943$	35.5167	+	9.51666i	1.15658	+	0.309905i
$944$	5.16987	−	1.38526i	0.168265	−	0.0450865i
$945$		−	16.7846i		−	0.546003i
$946$			1.94744i			0.0633168i
$947$	6.20577	+	23.1603i	0.201660	+	0.752607i	0.990442	+	0.137933i	$0.0440458\pi$
$947$	6.20577	+	23.1603i	0.201660	+	0.752607i	−0.788781	+	0.614674i	$0.789287\pi$
$948$	50.7846	−	29.3205i	1.64941	−	0.952286i
$949$	−37.3468	−	12.6340i	−1.21233	−	0.410116i
$950$	3.99038	+	6.91154i	0.129465	+	0.224240i
$951$	−12.0000	+	44.7846i	−0.389127	+	1.45224i
$952$		0			0
$953$	−15.3397			−0.496903			−0.248452	−	0.968644i	$-0.579922\pi$
$953$	−15.3397			−0.496903			−0.248452	+	0.968644i	$0.579922\pi$
$954$	−14.8660	+	3.98334i	−0.481305	+	0.128965i
$955$	−2.07180	−	7.73205i	−0.0670418	−	0.250203i
$956$	12.0622	+	3.23205i	0.390119	+	0.104532i
$957$	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
$964$	−4.90192	+	1.31347i	−0.157880	+	0.0423039i
$965$	−7.85641			−0.252907
$966$	22.5167	−	13.0000i	0.724462	−	0.418268i
$967$	8.13397	−	2.17949i	0.261571	−	0.0700877i	−0.125650	−	0.992075i	$-0.540102\pi$
$967$	8.13397	−	2.17949i	0.261571	−	0.0700877i	0.387221	+	0.921987i	$0.373435\pi$
$968$	−5.09808	−	19.0263i	−0.163858	−	0.611528i
$969$		0			0
$970$	2.26795	−	8.46410i	0.0728195	−	0.271766i
$971$	−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
$973$	14.8372	+	55.3731i	0.475658	+	1.77518i
$974$	−3.70577	−	6.41858i	−0.118741	−	0.205665i
$975$	13.0981	+	26.4904i	0.419474	+	0.848371i
$976$			7.87564i			0.252093i
$977$	11.2679	−	11.2679i	0.360494	−	0.360494i	−0.503501	−	0.863995i	$-0.667955\pi$
$977$	11.2679	−	11.2679i	0.360494	−	0.360494i	0.863995	+	0.503501i	$0.167955\pi$
$978$	4.43782	+	2.56218i	0.141906	+	0.0819294i
$979$	−2.49038	+	1.43782i	−0.0795929	+	0.0459530i
$980$	−1.14359	−	4.26795i	−0.0365308	−	0.136335i
$981$	−60.5429	−	16.2224i	−1.93299	−	0.517942i
$982$	−2.09808	−	0.562178i	−0.0669523	−	0.0179398i
$983$	−21.5263	−	5.76795i	−0.686582	−	0.183969i	−0.101369	−	0.994849i	$-0.532322\pi$
$983$	−21.5263	−	5.76795i	−0.686582	−	0.183969i	−0.585213	+	0.810880i	$0.698989\pi$
$984$			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
$995$	−4.87564	−	18.1962i	−0.154568	−	0.576857i
$996$	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
$999$	18.9282	−	5.07180i	0.598862	−	0.160465i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.be.a.161.1	✓	4	31.6	odd	6
403.2.be.a.398.1	yes	4	13.8	odd	4
403.2.be.b.57.1	yes	4	1.1	even	1	trivial
403.2.be.b.99.1	yes	4	403.99	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.366025 - 0.366025i) q^{2} +(2.36603 + 1.36603i) q^{3} +1.73205i q^{4} +(-1.36603 - 0.366025i) q^{5} +(1.36603 - 0.366025i) q^{6} +(2.86603 - 0.767949i) q^{7} +(1.36603 + 1.36603i) q^{8} +(2.23205 + 3.86603i) q^{9} +O(q^{10})\)	\(q+(0.366025 - 0.366025i) q^{2} +(2.36603 + 1.36603i) q^{3} +1.73205i q^{4} +(-1.36603 - 0.366025i) q^{5} +(1.36603 - 0.366025i) q^{6} +(2.86603 - 0.767949i) q^{7} +(1.36603 + 1.36603i) q^{8} +(2.23205 + 3.86603i) q^{9} +(-0.633975 + 0.366025i) q^{10} +(-0.866025 - 0.232051i) q^{11} +(-2.36603 + 4.09808i) q^{12} +(-3.59808 - 0.232051i) q^{13} +(0.767949 - 1.33013i) q^{14} +(-2.73205 - 2.73205i) q^{15} -2.46410 q^{16} +(2.23205 + 0.598076i) q^{18} +(-1.33013 - 4.96410i) q^{19} +(0.633975 - 2.36603i) q^{20} +(7.83013 + 2.09808i) q^{21} +(-0.401924 + 0.232051i) q^{22} +6.19615 q^{23} +(1.36603 + 5.09808i) q^{24} +(-2.59808 - 1.50000i) q^{25} +(-1.40192 + 1.23205i) q^{26} +4.00000i q^{27} +(1.33013 + 4.96410i) q^{28} +8.46410i q^{29} -2.00000 q^{30} +(3.50000 - 4.33013i) q^{31} +(-3.63397 + 3.63397i) q^{32} +(-1.73205 - 1.73205i) q^{33} -4.19615 q^{35} +(-6.69615 + 3.86603i) q^{36} +(-1.26795 - 4.73205i) q^{37} +(-2.30385 - 1.33013i) q^{38} +(-8.19615 - 5.46410i) q^{39} +(-1.36603 - 2.36603i) q^{40} +(5.73205 + 1.53590i) q^{41} +(3.63397 - 2.09808i) q^{42} +(2.09808 - 3.63397i) q^{43} +(0.401924 - 1.50000i) q^{44} +(-1.63397 - 6.09808i) 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} +(-1.50000 + 0.401924i) q^{50} +(0.401924 - 6.23205i) 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} +(3.63397 - 13.5622i) q^{57} +(3.09808 + 3.09808i) q^{58} +(-2.09808 + 0.562178i) 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} +(4.83013 + 1.63397i) q^{65} -1.26795 q^{66} +(-10.6962 - 2.86603i) q^{67} +(14.6603 + 8.46410i) q^{69} +(-1.53590 + 1.53590i) q^{70} +(1.23205 + 0.330127i) q^{71} +(-2.23205 + 8.33013i) q^{72} +(10.5622 + 2.83013i) q^{73} +(-2.19615 - 1.26795i) q^{74} +(-4.09808 - 7.09808i) q^{75} +(8.59808 - 2.30385i) q^{76} -2.66025 q^{77} +(-5.00000 + 1.00000i) q^{78} +(-10.7321 - 6.19615i) q^{79} +(3.36603 + 0.901924i) q^{80} +(1.23205 - 2.13397i) q^{81} +(2.66025 - 1.53590i) q^{82} +(4.16987 - 15.5622i) q^{83} +(-3.63397 + 13.5622i) q^{84} +(-0.562178 - 2.09808i) 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} +(14.1962 - 5.46410i) q^{93} +1.12436 q^{94} +7.26795i q^{95} +(-13.5622 + 3.63397i) q^{96} +(-8.46410 + 8.46410i) q^{97} +(0.241670 - 0.901924i) q^{98} +(-1.03590 - 3.86603i) 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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