LMFDB - Embedded newform 252.2.bi.b.139.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(139,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2, 3]))

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

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

chi := DirichletCharacter("252.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bi (of order $6$, degree $2$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			139.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	252.139
Dual form			252.2.bi.b.223.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} -1.73205 q^{3} +(1.73205 + 1.00000i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} -1.73205 q^{3} +(1.73205 + 1.00000i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +(1.73205 + 1.73205i) q^{10} +(0.866025 - 0.500000i) q^{11} +(-3.00000 - 1.73205i) q^{12} +(-1.50000 - 0.866025i) q^{13} +(-3.09808 + 2.09808i) q^{14} +(-2.59808 - 1.50000i) q^{15} +(2.00000 + 3.46410i) q^{16} +3.46410i q^{17} +(4.09808 + 1.09808i) q^{18} +6.92820 q^{19} +(1.73205 + 3.00000i) q^{20} +(3.00000 - 3.46410i) q^{21} +(1.36603 - 0.366025i) q^{22} +(-4.33013 - 2.50000i) q^{23} +(-3.46410 - 3.46410i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(-1.73205 - 1.73205i) q^{26} -5.19615 q^{27} +(-5.00000 + 1.73205i) q^{28} +(-2.50000 - 4.33013i) q^{29} +(-3.00000 - 3.00000i) q^{30} +(4.33013 - 7.50000i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-1.50000 + 0.866025i) q^{33} +(-1.26795 + 4.73205i) q^{34} +(-4.33013 + 1.50000i) q^{35} +(5.19615 + 3.00000i) q^{36} +(9.46410 + 2.53590i) q^{38} +(2.59808 + 1.50000i) q^{39} +(1.26795 + 4.73205i) q^{40} +(-7.50000 - 4.33013i) q^{41} +(5.36603 - 3.63397i) q^{42} +(-0.866025 + 0.500000i) q^{43} +2.00000 q^{44} +(4.50000 + 2.59808i) q^{45} +(-5.00000 - 5.00000i) q^{46} +(-2.59808 - 4.50000i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(-1.00000 - 6.92820i) q^{49} +(-0.732051 - 2.73205i) q^{50} -6.00000i q^{51} +(-1.73205 - 3.00000i) q^{52} +4.00000 q^{53} +(-7.09808 - 1.90192i) q^{54} +1.73205 q^{55} +(-7.46410 + 0.535898i) q^{56} -12.0000 q^{57} +(-1.83013 - 6.83013i) q^{58} +(-4.33013 + 7.50000i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(4.50000 - 2.59808i) q^{61} +(8.66025 - 8.66025i) q^{62} +(-5.19615 + 6.00000i) q^{63} +8.00000i q^{64} +(-1.50000 - 2.59808i) q^{65} +(-2.36603 + 0.633975i) q^{66} +(12.9904 + 7.50000i) q^{67} +(-3.46410 + 6.00000i) q^{68} +(7.50000 + 4.33013i) q^{69} +(-6.46410 + 0.464102i) q^{70} -4.00000i q^{71} +(6.00000 + 6.00000i) q^{72} -10.3923i q^{73} +(1.73205 + 3.00000i) q^{75} +(12.0000 + 6.92820i) q^{76} +(-0.500000 + 2.59808i) q^{77} +(3.00000 + 3.00000i) q^{78} +(-2.59808 + 1.50000i) q^{79} +6.92820i q^{80} +9.00000 q^{81} +(-8.66025 - 8.66025i) q^{82} +(0.866025 + 1.50000i) q^{83} +(8.66025 - 3.00000i) q^{84} +(-3.00000 + 5.19615i) q^{85} +(-1.36603 + 0.366025i) q^{86} +(4.33013 + 7.50000i) q^{87} +(2.73205 + 0.732051i) q^{88} +17.3205i q^{89} +(5.19615 + 5.19615i) q^{90} +(4.33013 - 1.50000i) q^{91} +(-5.00000 - 8.66025i) q^{92} +(-7.50000 + 12.9904i) q^{93} +(-1.90192 - 7.09808i) q^{94} +(10.3923 + 6.00000i) q^{95} +(-2.53590 - 9.46410i) q^{96} +(4.50000 - 2.59808i) q^{97} +(1.16987 - 9.83013i) q^{98} +(2.59808 - 1.50000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 6 q^{5} - 6 q^{6} + 8 q^{8} + 12 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 6 * q^5 - 6 * q^6 + 8 * q^8 + 12 * q^9	$ 4 q + 2 q^{2} + 6 q^{5} - 6 q^{6} + 8 q^{8} + 12 q^{9} - 12 q^{12} - 6 q^{13} - 2 q^{14} + 8 q^{16} + 6 q^{18} + 12 q^{21} + 2 q^{22} - 4 q^{25} - 20 q^{28} - 10 q^{29} - 12 q^{30} - 8 q^{32} - 6 q^{33} - 12 q^{34} + 24 q^{38} + 12 q^{40} - 30 q^{41} + 18 q^{42} + 8 q^{44} + 18 q^{45} - 20 q^{46} - 4 q^{49} + 4 q^{50} + 16 q^{53} - 18 q^{54} - 16 q^{56} - 48 q^{57} + 10 q^{58} - 12 q^{60} + 18 q^{61} - 6 q^{65} - 6 q^{66} + 30 q^{69} - 12 q^{70} + 24 q^{72} + 48 q^{76} - 2 q^{77} + 12 q^{78} + 36 q^{81} - 12 q^{85} - 2 q^{86} + 4 q^{88} - 20 q^{92} - 30 q^{93} - 18 q^{94} - 24 q^{96} + 18 q^{97} + 22 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 6 * q^5 - 6 * q^6 + 8 * q^8 + 12 * q^9 - 12 * q^12 - 6 * q^13 - 2 * q^14 + 8 * q^16 + 6 * q^18 + 12 * q^21 + 2 * q^22 - 4 * q^25 - 20 * q^28 - 10 * q^29 - 12 * q^30 - 8 * q^32 - 6 * q^33 - 12 * q^34 + 24 * q^38 + 12 * q^40 - 30 * q^41 + 18 * q^42 + 8 * q^44 + 18 * q^45 - 20 * q^46 - 4 * q^49 + 4 * q^50 + 16 * q^53 - 18 * q^54 - 16 * q^56 - 48 * q^57 + 10 * q^58 - 12 * q^60 + 18 * q^61 - 6 * q^65 - 6 * q^66 + 30 * q^69 - 12 * q^70 + 24 * q^72 + 48 * q^76 - 2 * q^77 + 12 * q^78 + 36 * q^81 - 12 * q^85 - 2 * q^86 + 4 * q^88 - 20 * q^92 - 30 * q^93 - 18 * q^94 - 24 * q^96 + 18 * q^97 + 22 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.36603	+	0.366025i	0.965926	+	0.258819i
$2$	1.36603	+	0.366025i	0.965926	+	0.258819i
$3$	−1.73205			−1.00000
$3$	−1.73205			−1.00000
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	0.796387	−	0.604787i	$-0.206742\pi$
$5$	1.50000	+	0.866025i	0.670820	+	0.387298i	−0.125567	+	0.992085i	$0.540075\pi$
$6$	−2.36603	−	0.633975i	−0.965926	−	0.258819i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$7$	−1.73205	+	2.00000i	−0.654654	+	0.755929i
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	3.00000			1.00000
$10$	1.73205	+	1.73205i	0.547723	+	0.547723i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i	−0.363727	−	0.931505i	$-0.618496\pi$
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i	0.624844	+	0.780750i	$0.285163\pi$
$12$	−3.00000	−	1.73205i	−0.866025	−	0.500000i
$13$	−1.50000	−	0.866025i	−0.416025	−	0.240192i	0.277350	−	0.960769i	$-0.410544\pi$
$13$	−1.50000	−	0.866025i	−0.416025	−	0.240192i	−0.693375	+	0.720577i	$0.743877\pi$
$14$	−3.09808	+	2.09808i	−0.827996	+	0.560734i
$15$	−2.59808	−	1.50000i	−0.670820	−	0.387298i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$			3.46410i			0.840168i	0.907485	+	0.420084i	$0.137999\pi$
$17$			3.46410i			0.840168i	−0.907485	+	0.420084i	$0.862001\pi$
$18$	4.09808	+	1.09808i	0.965926	+	0.258819i
$19$	6.92820			1.58944			0.794719	−	0.606977i	$-0.207618\pi$
$19$	6.92820			1.58944			0.794719	+	0.606977i	$0.207618\pi$
$20$	1.73205	+	3.00000i	0.387298	+	0.670820i
$21$	3.00000	−	3.46410i	0.654654	−	0.755929i
$22$	1.36603	−	0.366025i	0.291238	−	0.0780369i
$23$	−4.33013	−	2.50000i	−0.902894	−	0.521286i	−0.0247559	−	0.999694i	$-0.507881\pi$
$23$	−4.33013	−	2.50000i	−0.902894	−	0.521286i	−0.878138	+	0.478407i	$0.841214\pi$
$24$	−3.46410	−	3.46410i	−0.707107	−	0.707107i
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$	−1.73205	−	1.73205i	−0.339683	−	0.339683i
$27$	−5.19615			−1.00000
$28$	−5.00000	+	1.73205i	−0.944911	+	0.327327i
$29$	−2.50000	−	4.33013i	−0.464238	−	0.804084i	0.534928	−	0.844897i	$-0.320339\pi$
$29$	−2.50000	−	4.33013i	−0.464238	−	0.804084i	−0.999167	+	0.0408130i	$0.987005\pi$
$30$	−3.00000	−	3.00000i	−0.547723	−	0.547723i
$31$	4.33013	−	7.50000i	0.777714	−	1.34704i	−0.155543	−	0.987829i	$-0.549713\pi$
$31$	4.33013	−	7.50000i	0.777714	−	1.34704i	0.933257	−	0.359211i	$-0.116954\pi$
$32$	1.46410	+	5.46410i	0.258819	+	0.965926i
$33$	−1.50000	+	0.866025i	−0.261116	+	0.150756i
$34$	−1.26795	+	4.73205i	−0.217451	+	0.811540i
$35$	−4.33013	+	1.50000i	−0.731925	+	0.253546i
$36$	5.19615	+	3.00000i	0.866025	+	0.500000i
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	9.46410	+	2.53590i	1.53528	+	0.411377i
$39$	2.59808	+	1.50000i	0.416025	+	0.240192i
$40$	1.26795	+	4.73205i	0.200480	+	0.748203i
$41$	−7.50000	−	4.33013i	−1.17130	−	0.676252i	−0.217317	−	0.976101i	$-0.569730\pi$
$41$	−7.50000	−	4.33013i	−1.17130	−	0.676252i	−0.953987	+	0.299849i	$0.903064\pi$
$42$	5.36603	−	3.63397i	0.827996	−	0.560734i
$43$	−0.866025	+	0.500000i	−0.132068	+	0.0762493i	−0.564578	−	0.825380i	$-0.690961\pi$
$43$	−0.866025	+	0.500000i	−0.132068	+	0.0762493i	0.432511	+	0.901629i	$0.357628\pi$
$44$	2.00000			0.301511
$45$	4.50000	+	2.59808i	0.670820	+	0.387298i
$46$	−5.00000	−	5.00000i	−0.737210	−	0.737210i
$47$	−2.59808	−	4.50000i	−0.378968	−	0.656392i	0.611944	−	0.790901i	$-0.290388\pi$
$47$	−2.59808	−	4.50000i	−0.378968	−	0.656392i	−0.990912	+	0.134509i	$0.957054\pi$
$48$	−3.46410	−	6.00000i	−0.500000	−	0.866025i
$49$	−1.00000	−	6.92820i	−0.142857	−	0.989743i
$50$	−0.732051	−	2.73205i	−0.103528	−	0.386370i
$51$		−	6.00000i		−	0.840168i
$52$	−1.73205	−	3.00000i	−0.240192	−	0.416025i
$53$	4.00000			0.549442			0.274721	−	0.961524i	$-0.411414\pi$
$53$	4.00000			0.549442			0.274721	+	0.961524i	$0.411414\pi$
$54$	−7.09808	−	1.90192i	−0.965926	−	0.258819i
$55$	1.73205			0.233550
$56$	−7.46410	+	0.535898i	−0.997433	+	0.0716124i
$57$	−12.0000			−1.58944
$58$	−1.83013	−	6.83013i	−0.240307	−	0.896840i
$59$	−4.33013	+	7.50000i	−0.563735	+	0.976417i	0.433432	+	0.901186i	$0.357303\pi$
$59$	−4.33013	+	7.50000i	−0.563735	+	0.976417i	−0.997166	+	0.0752304i	$0.976031\pi$
$60$	−3.00000	−	5.19615i	−0.387298	−	0.670820i
$61$	4.50000	−	2.59808i	0.576166	−	0.332650i	−0.183442	−	0.983030i	$-0.558724\pi$
$61$	4.50000	−	2.59808i	0.576166	−	0.332650i	0.759608	+	0.650381i	$0.225391\pi$
$62$	8.66025	−	8.66025i	1.09985	−	1.09985i
$63$	−5.19615	+	6.00000i	−0.654654	+	0.755929i
$64$			8.00000i			1.00000i
$65$	−1.50000	−	2.59808i	−0.186052	−	0.322252i
$66$	−2.36603	+	0.633975i	−0.291238	+	0.0780369i
$67$	12.9904	+	7.50000i	1.58703	+	0.916271i	0.993793	+	0.111241i	$0.0354825\pi$
$67$	12.9904	+	7.50000i	1.58703	+	0.916271i	0.593234	+	0.805030i	$0.297851\pi$
$68$	−3.46410	+	6.00000i	−0.420084	+	0.727607i
$69$	7.50000	+	4.33013i	0.902894	+	0.521286i
$70$	−6.46410	+	0.464102i	−0.772608	+	0.0554708i
$71$		−	4.00000i		−	0.474713i	−0.971423	−	0.237356i	$-0.923719\pi$
$71$		−	4.00000i		−	0.474713i	0.971423	−	0.237356i	$-0.0762809\pi$
$72$	6.00000	+	6.00000i	0.707107	+	0.707107i
$73$		−	10.3923i		−	1.21633i	−0.793812	−	0.608164i	$-0.791906\pi$
$73$		−	10.3923i		−	1.21633i	0.793812	−	0.608164i	$-0.208094\pi$
$74$		0			0
$75$	1.73205	+	3.00000i	0.200000	+	0.346410i
$76$	12.0000	+	6.92820i	1.37649	+	0.794719i
$77$	−0.500000	+	2.59808i	−0.0569803	+	0.296078i
$78$	3.00000	+	3.00000i	0.339683	+	0.339683i
$79$	−2.59808	+	1.50000i	−0.292306	+	0.168763i	−0.638982	−	0.769222i	$-0.720644\pi$
$79$	−2.59808	+	1.50000i	−0.292306	+	0.168763i	0.346675	+	0.937985i	$0.387311\pi$
$80$			6.92820i			0.774597i
$81$	9.00000			1.00000
$82$	−8.66025	−	8.66025i	−0.956365	−	0.956365i
$83$	0.866025	+	1.50000i	0.0950586	+	0.164646i	0.909633	−	0.415413i	$-0.136363\pi$
$83$	0.866025	+	1.50000i	0.0950586	+	0.164646i	−0.814574	+	0.580059i	$0.803029\pi$
$84$	8.66025	−	3.00000i	0.944911	−	0.327327i
$85$	−3.00000	+	5.19615i	−0.325396	+	0.563602i
$86$	−1.36603	+	0.366025i	−0.147302	+	0.0394695i
$87$	4.33013	+	7.50000i	0.464238	+	0.804084i
$88$	2.73205	+	0.732051i	0.291238	+	0.0780369i
$89$			17.3205i			1.83597i	0.396615	+	0.917985i	$0.370185\pi$
$89$			17.3205i			1.83597i	−0.396615	+	0.917985i	$0.629815\pi$
$90$	5.19615	+	5.19615i	0.547723	+	0.547723i
$91$	4.33013	−	1.50000i	0.453921	−	0.157243i
$92$	−5.00000	−	8.66025i	−0.521286	−	0.902894i
$93$	−7.50000	+	12.9904i	−0.777714	+	1.34704i
$94$	−1.90192	−	7.09808i	−0.196168	−	0.732111i
$95$	10.3923	+	6.00000i	1.06623	+	0.615587i
$96$	−2.53590	−	9.46410i	−0.258819	−	0.965926i
$97$	4.50000	−	2.59808i	0.456906	−	0.263795i	−0.253837	−	0.967247i	$-0.581693\pi$
$97$	4.50000	−	2.59808i	0.456906	−	0.263795i	0.710742	+	0.703452i	$0.248359\pi$
$98$	1.16987	−	9.83013i	0.118175	−	0.992993i
$99$	2.59808	−	1.50000i	0.261116	−	0.150756i
$100$		−	4.00000i		−	0.400000i
$101$	−10.5000	+	6.06218i	−1.04479	+	0.603209i	−0.921186	−	0.389123i	$-0.872778\pi$
$101$	−10.5000	+	6.06218i	−1.04479	+	0.603209i	−0.123603	+	0.992332i	$0.539445\pi$
$102$	2.19615	−	8.19615i	0.217451	−	0.811540i
$103$	−4.33013	+	7.50000i	−0.426660	+	0.738997i	−0.996574	−	0.0827075i	$-0.973643\pi$
$103$	−4.33013	+	7.50000i	−0.426660	+	0.738997i	0.569914	+	0.821705i	$0.306977\pi$
$104$	−1.26795	−	4.73205i	−0.124333	−	0.464016i
$105$	7.50000	−	2.59808i	0.731925	−	0.253546i
$106$	5.46410	+	1.46410i	0.530720	+	0.142206i
$107$		−	2.00000i		−	0.193347i	−0.995316	−	0.0966736i	$-0.969180\pi$
$107$		−	2.00000i		−	0.193347i	0.995316	−	0.0966736i	$-0.0308203\pi$
$108$	−9.00000	−	5.19615i	−0.866025	−	0.500000i
$109$	12.0000			1.14939			0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000			1.14939			0.574696	+	0.818367i	$0.305120\pi$
$110$	2.36603	+	0.633975i	0.225592	+	0.0604471i
$111$		0			0
$112$	−10.3923	−	2.00000i	−0.981981	−	0.188982i
$113$	−9.50000	+	16.4545i	−0.893685	+	1.54791i	−0.0582609	+	0.998301i	$0.518556\pi$
$113$	−9.50000	+	16.4545i	−0.893685	+	1.54791i	−0.835424	+	0.549606i	$0.814778\pi$
$114$	−16.3923	−	4.39230i	−1.53528	−	0.411377i
$115$	−4.33013	−	7.50000i	−0.403786	−	0.699379i
$116$		−	10.0000i		−	0.928477i
$117$	−4.50000	−	2.59808i	−0.416025	−	0.240192i
$118$	−8.66025	+	8.66025i	−0.797241	+	0.797241i
$119$	−6.92820	−	6.00000i	−0.635107	−	0.550019i
$120$	−2.19615	−	8.19615i	−0.200480	−	0.748203i
$121$	−5.00000	+	8.66025i	−0.454545	+	0.787296i
$122$	7.09808	−	1.90192i	0.642630	−	0.172192i
$123$	12.9904	+	7.50000i	1.17130	+	0.676252i
$124$	15.0000	−	8.66025i	1.34704	−	0.777714i
$125$		−	12.1244i		−	1.08444i
$126$	−9.29423	+	6.29423i	−0.827996	+	0.560734i
$127$		−	18.0000i		−	1.59724i	−0.601834	−	0.798621i	$-0.705563\pi$
$127$		−	18.0000i		−	1.59724i	0.601834	−	0.798621i	$-0.294437\pi$
$128$	−2.92820	+	10.9282i	−0.258819	+	0.965926i
$129$	1.50000	−	0.866025i	0.132068	−	0.0762493i
$130$	−1.09808	−	4.09808i	−0.0963077	−	0.359425i
$131$	6.06218	−	10.5000i	0.529655	−	0.917389i	−0.469747	−	0.882801i	$-0.655655\pi$
$131$	6.06218	−	10.5000i	0.529655	−	0.917389i	0.999402	−	0.0345880i	$-0.0110119\pi$
$132$	−3.46410			−0.301511
$133$	−12.0000	+	13.8564i	−1.04053	+	1.20150i
$134$	15.0000	+	15.0000i	1.29580	+	1.29580i
$135$	−7.79423	−	4.50000i	−0.670820	−	0.387298i
$136$	−6.92820	+	6.92820i	−0.594089	+	0.594089i
$137$	−2.50000	−	4.33013i	−0.213589	−	0.369948i	0.739246	−	0.673436i	$-0.235182\pi$
$137$	−2.50000	−	4.33013i	−0.213589	−	0.369948i	−0.952835	+	0.303488i	$0.901849\pi$
$138$	8.66025	+	8.66025i	0.737210	+	0.737210i
$139$	−4.33013	+	7.50000i	−0.367277	+	0.636142i	−0.989139	−	0.146985i	$-0.953043\pi$
$139$	−4.33013	+	7.50000i	−0.367277	+	0.636142i	0.621862	+	0.783127i	$0.286376\pi$
$140$	−9.00000	−	1.73205i	−0.760639	−	0.146385i
$141$	4.50000	+	7.79423i	0.378968	+	0.656392i
$142$	1.46410	−	5.46410i	0.122865	−	0.458537i
$143$	−1.73205			−0.144841
$144$	6.00000	+	10.3923i	0.500000	+	0.866025i
$145$		−	8.66025i		−	0.719195i
$146$	3.80385	−	14.1962i	0.314809	−	1.17488i
$147$	1.73205	+	12.0000i	0.142857	+	0.989743i
$148$		0			0
$149$	3.50000	−	6.06218i	0.286731	−	0.496633i	−0.686296	−	0.727322i	$-0.740765\pi$
$149$	3.50000	−	6.06218i	0.286731	−	0.496633i	0.973028	+	0.230689i	$0.0740980\pi$
$150$	1.26795	+	4.73205i	0.103528	+	0.386370i
$151$	−9.52628	+	5.50000i	−0.775238	+	0.447584i	−0.834740	−	0.550645i	$-0.814382\pi$
$151$	−9.52628	+	5.50000i	−0.775238	+	0.447584i	0.0595022	+	0.998228i	$0.481049\pi$
$152$	13.8564	+	13.8564i	1.12390	+	1.12390i
$153$			10.3923i			0.840168i
$154$	−1.63397	+	3.36603i	−0.131669	+	0.271242i
$155$	12.9904	−	7.50000i	1.04341	−	0.602414i
$156$	3.00000	+	5.19615i	0.240192	+	0.416025i
$157$	−4.50000	−	2.59808i	−0.359139	−	0.207349i	0.309564	−	0.950879i	$-0.399817\pi$
$157$	−4.50000	−	2.59808i	−0.359139	−	0.207349i	−0.668703	+	0.743530i	$0.733150\pi$
$158$	−4.09808	+	1.09808i	−0.326025	+	0.0873583i
$159$	−6.92820			−0.549442
$160$	−2.53590	+	9.46410i	−0.200480	+	0.748203i
$161$	12.5000	−	4.33013i	0.985138	−	0.341262i
$162$	12.2942	+	3.29423i	0.965926	+	0.258819i
$163$			6.00000i			0.469956i	0.972001	+	0.234978i	$0.0755019\pi$
$163$			6.00000i			0.469956i	−0.972001	+	0.234978i	$0.924498\pi$
$164$	−8.66025	−	15.0000i	−0.676252	−	1.17130i
$165$	−3.00000			−0.233550
$166$	0.633975	+	2.36603i	0.0492060	+	0.183639i
$167$	6.06218	−	10.5000i	0.469105	−	0.812514i	−0.530271	−	0.847828i	$-0.677910\pi$
$167$	6.06218	−	10.5000i	0.469105	−	0.812514i	0.999376	+	0.0353139i	$0.0112431\pi$
$168$	12.9282	−	0.928203i	0.997433	−	0.0716124i
$169$	−5.00000	−	8.66025i	−0.384615	−	0.666173i
$170$	−6.00000	+	6.00000i	−0.460179	+	0.460179i
$171$	20.7846			1.58944
$172$	−2.00000			−0.152499
$173$	7.50000	−	4.33013i	0.570214	−	0.329213i	−0.187021	−	0.982356i	$-0.559883\pi$
$173$	7.50000	−	4.33013i	0.570214	−	0.329213i	0.757235	+	0.653143i	$0.226550\pi$
$174$	3.16987	+	11.8301i	0.240307	+	0.896840i
$175$	5.19615	+	1.00000i	0.392792	+	0.0755929i
$176$	3.46410	+	2.00000i	0.261116	+	0.150756i
$177$	7.50000	−	12.9904i	0.563735	−	0.976417i
$178$	−6.33975	+	23.6603i	−0.475184	+	1.77341i
$179$			2.00000i			0.149487i	0.997203	+	0.0747435i	$0.0238138\pi$
$179$			2.00000i			0.149487i	−0.997203	+	0.0747435i	$0.976186\pi$
$180$	5.19615	+	9.00000i	0.387298	+	0.670820i
$181$			17.3205i			1.28742i	0.765268	+	0.643712i	$0.222606\pi$
$181$			17.3205i			1.28742i	−0.765268	+	0.643712i	$0.777394\pi$
$182$	6.46410	−	0.464102i	0.479151	−	0.0344015i
$183$	−7.79423	+	4.50000i	−0.576166	+	0.332650i
$184$	−3.66025	−	13.6603i	−0.269838	−	1.00705i
$185$		0			0
$186$	−15.0000	+	15.0000i	−1.09985	+	1.09985i
$187$	1.73205	+	3.00000i	0.126660	+	0.219382i
$188$		−	10.3923i		−	0.757937i
$189$	9.00000	−	10.3923i	0.654654	−	0.755929i
$190$	12.0000	+	12.0000i	0.870572	+	0.870572i
$191$	−4.33013	+	2.50000i	−0.313317	+	0.180894i	−0.648410	−	0.761291i	$-0.724566\pi$
$191$	−4.33013	+	2.50000i	−0.313317	+	0.180894i	0.335093	+	0.942185i	$0.391232\pi$
$192$		−	13.8564i		−	1.00000i
$193$	−4.50000	+	7.79423i	−0.323917	+	0.561041i	−0.981293	−	0.192522i	$-0.938333\pi$
$193$	−4.50000	+	7.79423i	−0.323917	+	0.561041i	0.657376	+	0.753563i	$0.271667\pi$
$194$	7.09808	−	1.90192i	0.509612	−	0.136550i
$195$	2.59808	+	4.50000i	0.186052	+	0.322252i
$196$	5.19615	−	13.0000i	0.371154	−	0.928571i
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	4.09808	−	1.09808i	0.291238	−	0.0780369i
$199$	−17.3205			−1.22782			−0.613909	−	0.789377i	$-0.710404\pi$
$199$	−17.3205			−1.22782			−0.613909	+	0.789377i	$0.710404\pi$
$200$	1.46410	−	5.46410i	0.103528	−	0.386370i
$201$	−22.5000	−	12.9904i	−1.58703	−	0.916271i
$202$	−16.5622	+	4.43782i	−1.16531	+	0.312244i
$203$	12.9904	+	2.50000i	0.911746	+	0.175466i
$204$	6.00000	−	10.3923i	0.420084	−	0.727607i
$205$	−7.50000	−	12.9904i	−0.523823	−	0.907288i
$206$	−8.66025	+	8.66025i	−0.603388	+	0.603388i
$207$	−12.9904	−	7.50000i	−0.902894	−	0.521286i
$208$		−	6.92820i		−	0.480384i
$209$	6.00000	−	3.46410i	0.415029	−	0.239617i
$210$	11.1962	−	0.803848i	0.772608	−	0.0554708i
$211$	−0.866025	−	0.500000i	−0.0596196	−	0.0344214i	0.469894	−	0.882723i	$-0.344292\pi$
$211$	−0.866025	−	0.500000i	−0.0596196	−	0.0344214i	−0.529514	+	0.848301i	$0.677626\pi$
$212$	6.92820	+	4.00000i	0.475831	+	0.274721i
$213$			6.92820i			0.474713i
$214$	0.732051	−	2.73205i	0.0500420	−	0.186759i
$215$	−1.73205			−0.118125
$216$	−10.3923	−	10.3923i	−0.707107	−	0.707107i
$217$	7.50000	+	21.6506i	0.509133	+	1.46974i
$218$	16.3923	+	4.39230i	1.11023	+	0.297484i
$219$			18.0000i			1.21633i
$220$	3.00000	+	1.73205i	0.202260	+	0.116775i
$221$	3.00000	−	5.19615i	0.201802	−	0.349531i
$222$		0			0
$223$	0.866025	+	1.50000i	0.0579934	+	0.100447i	0.893565	−	0.448935i	$-0.148196\pi$
$223$	0.866025	+	1.50000i	0.0579934	+	0.100447i	−0.835571	+	0.549382i	$0.814863\pi$
$224$	−13.4641	−	6.53590i	−0.899608	−	0.436698i
$225$	−3.00000	−	5.19615i	−0.200000	−	0.346410i
$226$	−19.0000	+	19.0000i	−1.26386	+	1.26386i
$227$	2.59808	+	4.50000i	0.172440	+	0.298675i	0.939272	−	0.343172i	$-0.111501\pi$
$227$	2.59808	+	4.50000i	0.172440	+	0.298675i	−0.766832	+	0.641848i	$0.778168\pi$
$228$	−20.7846	−	12.0000i	−1.37649	−	0.794719i
$229$	1.50000	+	0.866025i	0.0991228	+	0.0572286i	0.548742	−	0.835992i	$-0.315107\pi$
$229$	1.50000	+	0.866025i	0.0991228	+	0.0572286i	−0.449619	+	0.893220i	$0.648440\pi$
$230$	−3.16987	−	11.8301i	−0.209015	−	0.780055i
$231$	0.866025	−	4.50000i	0.0569803	−	0.296078i
$232$	3.66025	−	13.6603i	0.240307	−	0.896840i
$233$	−14.0000			−0.917170			−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000			−0.917170			−0.458585	+	0.888650i	$0.651644\pi$
$234$	−5.19615	−	5.19615i	−0.339683	−	0.339683i
$235$		−	9.00000i		−	0.587095i
$236$	−15.0000	+	8.66025i	−0.976417	+	0.563735i
$237$	4.50000	−	2.59808i	0.292306	−	0.168763i
$238$	−7.26795	−	10.7321i	−0.471111	−	0.695656i
$239$	−21.6506	−	12.5000i	−1.40046	−	0.808558i	−0.406023	−	0.913863i	$-0.633085\pi$
$239$	−21.6506	−	12.5000i	−1.40046	−	0.808558i	−0.994440	+	0.105305i	$0.966418\pi$
$240$		−	12.0000i		−	0.774597i
$241$	25.5000	−	14.7224i	1.64260	−	0.948355i	0.662695	−	0.748890i	$-0.269413\pi$
$241$	25.5000	−	14.7224i	1.64260	−	0.948355i	0.979905	−	0.199465i	$-0.0639205\pi$
$242$	−10.0000	+	10.0000i	−0.642824	+	0.642824i
$243$	−15.5885			−1.00000
$244$	10.3923			0.665299
$245$	4.50000	−	11.2583i	0.287494	−	0.719268i
$246$	15.0000	+	15.0000i	0.956365	+	0.956365i
$247$	−10.3923	−	6.00000i	−0.661247	−	0.381771i
$248$	23.6603	−	6.33975i	1.50243	−	0.402574i
$249$	−1.50000	−	2.59808i	−0.0950586	−	0.164646i
$250$	4.43782	−	16.5622i	0.280673	−	1.04748i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	−15.0000	+	5.19615i	−0.944911	+	0.327327i
$253$	−5.00000			−0.314347
$254$	6.58846	−	24.5885i	0.413397	−	1.54282i
$255$	5.19615	−	9.00000i	0.325396	−	0.563602i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	25.5000	+	14.7224i	1.59065	+	0.918360i	0.993196	+	0.116454i	$0.0371528\pi$
$257$	25.5000	+	14.7224i	1.59065	+	0.918360i	0.597450	+	0.801906i	$0.296181\pi$
$258$	2.36603	−	0.633975i	0.147302	−	0.0394695i
$259$		0			0
$260$		−	6.00000i		−	0.372104i
$261$	−7.50000	−	12.9904i	−0.464238	−	0.804084i
$262$	12.1244	−	12.1244i	0.749045	−	0.749045i
$263$	−16.4545	+	9.50000i	−1.01463	+	0.585795i	−0.912543	−	0.408981i	$-0.865884\pi$
$263$	−16.4545	+	9.50000i	−1.01463	+	0.585795i	−0.102084	+	0.994776i	$0.532551\pi$
$264$	−4.73205	−	1.26795i	−0.291238	−	0.0780369i
$265$	6.00000	+	3.46410i	0.368577	+	0.212798i
$266$	−21.4641	+	14.5359i	−1.31605	+	0.891253i
$267$		−	30.0000i		−	1.83597i
$268$	15.0000	+	25.9808i	0.916271	+	1.58703i
$269$		−	10.3923i		−	0.633630i	−0.948487	−	0.316815i	$-0.897387\pi$
$269$		−	10.3923i		−	0.633630i	0.948487	−	0.316815i	$-0.102613\pi$
$270$	−9.00000	−	9.00000i	−0.547723	−	0.547723i
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	−12.0000	+	6.92820i	−0.727607	+	0.420084i
$273$	−7.50000	+	2.59808i	−0.453921	+	0.157243i
$274$	−1.83013	−	6.83013i	−0.110562	−	0.412623i
$275$	−1.73205	−	1.00000i	−0.104447	−	0.0603023i
$276$	8.66025	+	15.0000i	0.521286	+	0.902894i
$277$	−11.5000	−	19.9186i	−0.690968	−	1.19679i	−0.971521	−	0.236953i	$-0.923851\pi$
$277$	−11.5000	−	19.9186i	−0.690968	−	1.19679i	0.280553	−	0.959839i	$-0.409482\pi$
$278$	−8.66025	+	8.66025i	−0.519408	+	0.519408i
$279$	12.9904	−	22.5000i	0.777714	−	1.34704i
$280$	−11.6603	−	5.66025i	−0.696833	−	0.338265i
$281$	−0.500000	−	0.866025i	−0.0298275	−	0.0516627i	0.850726	−	0.525609i	$-0.176162\pi$
$281$	−0.500000	−	0.866025i	−0.0298275	−	0.0516627i	−0.880554	+	0.473946i	$0.842829\pi$
$282$	3.29423	+	12.2942i	0.196168	+	0.732111i
$283$	−7.79423	+	13.5000i	−0.463319	+	0.802492i	−0.999124	−	0.0418500i	$-0.986675\pi$
$283$	−7.79423	+	13.5000i	−0.463319	+	0.802492i	0.535805	+	0.844342i	$0.320008\pi$
$284$	4.00000	−	6.92820i	0.237356	−	0.411113i
$285$	−18.0000	−	10.3923i	−1.06623	−	0.615587i
$286$	−2.36603	−	0.633975i	−0.139906	−	0.0374877i
$287$	21.6506	−	7.50000i	1.27800	−	0.442711i
$288$	4.39230	+	16.3923i	0.258819	+	0.965926i
$289$	5.00000			0.294118
$290$	3.16987	−	11.8301i	0.186141	−	0.694689i
$291$	−7.79423	+	4.50000i	−0.456906	+	0.263795i
$292$	10.3923	−	18.0000i	0.608164	−	1.05337i
$293$	−22.5000	−	12.9904i	−1.31446	−	0.758906i	−0.331632	−	0.943409i	$-0.607599\pi$
$293$	−22.5000	−	12.9904i	−1.31446	−	0.758906i	−0.982832	+	0.184503i	$0.940933\pi$
$294$	−2.02628	+	17.0263i	−0.118175	+	0.992993i
$295$	−12.9904	+	7.50000i	−0.756329	+	0.436667i
$296$		0			0
$297$	−4.50000	+	2.59808i	−0.261116	+	0.150756i
$298$	7.00000	−	7.00000i	0.405499	−	0.405499i
$299$	4.33013	+	7.50000i	0.250418	+	0.433736i
$300$			6.92820i			0.400000i
$301$	0.500000	−	2.59808i	0.0288195	−	0.149751i
$302$	−15.0263	+	4.02628i	−0.864665	+	0.231686i
$303$	18.1865	−	10.5000i	1.04479	−	0.603209i
$304$	13.8564	+	24.0000i	0.794719	+	1.37649i
$305$	9.00000			0.515339
$306$	−3.80385	+	14.1962i	−0.217451	+	0.811540i
$307$	−13.8564			−0.790827			−0.395413	−	0.918503i	$-0.629399\pi$
$307$	−13.8564			−0.790827			−0.395413	+	0.918503i	$0.629399\pi$
$308$	−3.46410	+	4.00000i	−0.197386	+	0.227921i
$309$	7.50000	−	12.9904i	0.426660	−	0.738997i
$310$	20.4904	−	5.49038i	1.16378	−	0.311833i
$311$	−12.9904	+	22.5000i	−0.736617	+	1.27586i	0.217393	+	0.976084i	$0.430245\pi$
$311$	−12.9904	+	22.5000i	−0.736617	+	1.27586i	−0.954010	+	0.299774i	$0.903089\pi$
$312$	2.19615	+	8.19615i	0.124333	+	0.464016i
$313$	7.50000	−	4.33013i	0.423925	−	0.244753i	−0.272830	−	0.962062i	$-0.587960\pi$
$313$	7.50000	−	4.33013i	0.423925	−	0.244753i	0.696755	+	0.717309i	$0.254626\pi$
$314$	−5.19615	−	5.19615i	−0.293236	−	0.293236i
$315$	−12.9904	+	4.50000i	−0.731925	+	0.253546i
$316$	−6.00000			−0.337526
$317$	11.5000	+	19.9186i	0.645904	+	1.11874i	0.984092	+	0.177660i	$0.0568529\pi$
$317$	11.5000	+	19.9186i	0.645904	+	1.11874i	−0.338188	+	0.941079i	$0.609814\pi$
$318$	−9.46410	−	2.53590i	−0.530720	−	0.142206i
$319$	−4.33013	−	2.50000i	−0.242441	−	0.139973i
$320$	−6.92820	+	12.0000i	−0.387298	+	0.670820i
$321$			3.46410i			0.193347i
$322$	18.6603	−	1.33975i	1.03990	−	0.0746611i
$323$			24.0000i			1.33540i
$324$	15.5885	+	9.00000i	0.866025	+	0.500000i
$325$			3.46410i			0.192154i
$326$	−2.19615	+	8.19615i	−0.121634	+	0.453943i
$327$	−20.7846			−1.14939
$328$	−6.33975	−	23.6603i	−0.350054	−	1.30642i
$329$	13.5000	+	2.59808i	0.744279	+	0.143237i
$330$	−4.09808	−	1.09808i	−0.225592	−	0.0604471i
$331$	25.1147	−	14.5000i	1.38043	−	0.796992i	0.388221	−	0.921567i	$-0.373090\pi$
$331$	25.1147	−	14.5000i	1.38043	−	0.796992i	0.992210	+	0.124574i	$0.0397566\pi$
$332$			3.46410i			0.190117i
$333$		0			0
$334$	12.1244	−	12.1244i	0.663415	−	0.663415i
$335$	12.9904	+	22.5000i	0.709740	+	1.22931i
$336$	18.0000	+	3.46410i	0.981981	+	0.188982i
$337$	−7.50000	+	12.9904i	−0.408551	+	0.707631i	−0.994728	−	0.102552i	$-0.967299\pi$
$337$	−7.50000	+	12.9904i	−0.408551	+	0.707631i	0.586177	+	0.810183i	$0.300632\pi$
$338$	−3.66025	−	13.6603i	−0.199092	−	0.743020i
$339$	16.4545	−	28.5000i	0.893685	−	1.54791i
$340$	−10.3923	+	6.00000i	−0.563602	+	0.325396i
$341$		−	8.66025i		−	0.468979i
$342$	28.3923	+	7.60770i	1.53528	+	0.411377i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$	−2.73205	−	0.732051i	−0.147302	−	0.0394695i
$345$	7.50000	+	12.9904i	0.403786	+	0.699379i
$346$	11.8301	−	3.16987i	0.635992	−	0.170413i
$347$	−4.33013	−	2.50000i	−0.232453	−	0.134207i	0.379250	−	0.925294i	$-0.376182\pi$
$347$	−4.33013	−	2.50000i	−0.232453	−	0.134207i	−0.611703	+	0.791087i	$0.709515\pi$
$348$			17.3205i			0.928477i
$349$	−22.5000	+	12.9904i	−1.20440	+	0.695359i	−0.961530	−	0.274700i	$-0.911421\pi$
$349$	−22.5000	+	12.9904i	−1.20440	+	0.695359i	−0.242867	+	0.970059i	$0.578088\pi$
$350$	6.73205	+	3.26795i	0.359843	+	0.174679i
$351$	7.79423	+	4.50000i	0.416025	+	0.240192i
$352$	4.00000	+	4.00000i	0.213201	+	0.213201i
$353$	−7.50000	+	4.33013i	−0.399185	+	0.230469i	−0.686132	−	0.727477i	$-0.740693\pi$
$353$	−7.50000	+	4.33013i	−0.399185	+	0.230469i	0.286947	+	0.957946i	$0.407359\pi$
$354$	15.0000	−	15.0000i	0.797241	−	0.797241i
$355$	3.46410	−	6.00000i	0.183855	−	0.318447i
$356$	−17.3205	+	30.0000i	−0.917985	+	1.59000i
$357$	12.0000	+	10.3923i	0.635107	+	0.550019i
$358$	−0.732051	+	2.73205i	−0.0386901	+	0.144393i
$359$			10.0000i			0.527780i	0.964553	+	0.263890i	$0.0850056\pi$
$359$			10.0000i			0.527780i	−0.964553	+	0.263890i	$0.914994\pi$
$360$	3.80385	+	14.1962i	0.200480	+	0.748203i
$361$	29.0000			1.52632
$362$	−6.33975	+	23.6603i	−0.333210	+	1.24356i
$363$	8.66025	−	15.0000i	0.454545	−	0.787296i
$364$	9.00000	+	1.73205i	0.471728	+	0.0907841i
$365$	9.00000	−	15.5885i	0.471082	−	0.815937i
$366$	−12.2942	+	3.29423i	−0.642630	+	0.172192i
$367$	−11.2583	−	19.5000i	−0.587680	−	1.01789i	−0.994535	−	0.104399i	$-0.966708\pi$
$367$	−11.2583	−	19.5000i	−0.587680	−	1.01789i	0.406855	−	0.913493i	$-0.366625\pi$
$368$		−	20.0000i		−	1.04257i
$369$	−22.5000	−	12.9904i	−1.17130	−	0.676252i
$370$		0			0
$371$	−6.92820	+	8.00000i	−0.359694	+	0.415339i
$372$	−25.9808	+	15.0000i	−1.34704	+	0.777714i
$373$	−0.500000	+	0.866025i	−0.0258890	+	0.0448411i	−0.878680	−	0.477412i	$-0.841575\pi$
$373$	−0.500000	+	0.866025i	−0.0258890	+	0.0448411i	0.852791	+	0.522253i	$0.174908\pi$
$374$	1.26795	+	4.73205i	0.0655641	+	0.244689i
$375$			21.0000i			1.08444i
$376$	3.80385	−	14.1962i	0.196168	−	0.732111i
$377$			8.66025i			0.446026i
$378$	16.0981	−	10.9019i	0.827996	−	0.560734i
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$	12.0000	+	20.7846i	0.615587	+	1.06623i
$381$			31.1769i			1.59724i
$382$	−6.83013	+	1.83013i	−0.349460	+	0.0936374i
$383$	−0.866025	+	1.50000i	−0.0442518	+	0.0766464i	−0.887303	−	0.461187i	$-0.847424\pi$
$383$	−0.866025	+	1.50000i	−0.0442518	+	0.0766464i	0.843051	+	0.537833i	$0.180757\pi$
$384$	5.07180	−	18.9282i	0.258819	−	0.965926i
$385$	−3.00000	+	3.46410i	−0.152894	+	0.176547i
$386$	−9.00000	+	9.00000i	−0.458088	+	0.458088i
$387$	−2.59808	+	1.50000i	−0.132068	+	0.0762493i
$388$	10.3923			0.527589
$389$	8.50000	+	14.7224i	0.430967	+	0.746457i	0.996957	−	0.0779554i	$-0.0248392\pi$
$389$	8.50000	+	14.7224i	0.430967	+	0.746457i	−0.565990	+	0.824412i	$0.691506\pi$
$390$	1.90192	+	7.09808i	0.0963077	+	0.359425i
$391$	8.66025	−	15.0000i	0.437968	−	0.758583i
$392$	11.8564	−	15.8564i	0.598839	−	0.800869i
$393$	−10.5000	+	18.1865i	−0.529655	+	0.917389i
$394$	2.73205	+	0.732051i	0.137639	+	0.0368802i
$395$	−5.19615			−0.261447
$396$	6.00000			0.301511
$397$			17.3205i			0.869291i	0.900602	+	0.434646i	$0.143126\pi$
$397$			17.3205i			0.869291i	−0.900602	+	0.434646i	$0.856874\pi$
$398$	−23.6603	−	6.33975i	−1.18598	−	0.317783i
$399$	20.7846	−	24.0000i	1.04053	−	1.20150i
$400$	4.00000	−	6.92820i	0.200000	−	0.346410i
$401$	−2.50000	+	4.33013i	−0.124844	+	0.216236i	−0.921672	−	0.387970i	$-0.873176\pi$
$401$	−2.50000	+	4.33013i	−0.124844	+	0.216236i	0.796828	+	0.604206i	$0.206510\pi$
$402$	−25.9808	−	25.9808i	−1.29580	−	1.29580i
$403$	−12.9904	+	7.50000i	−0.647097	+	0.373602i
$404$	−24.2487			−1.20642
$405$	13.5000	+	7.79423i	0.670820	+	0.387298i
$406$	16.8301	+	8.16987i	0.835265	+	0.405464i
$407$		0			0
$408$	12.0000	−	12.0000i	0.594089	−	0.594089i
$409$	13.5000	+	7.79423i	0.667532	+	0.385400i	0.795141	−	0.606425i	$-0.207397\pi$
$409$	13.5000	+	7.79423i	0.667532	+	0.385400i	−0.127609	+	0.991825i	$0.540730\pi$
$410$	−5.49038	−	20.4904i	−0.271151	−	1.01195i
$411$	4.33013	+	7.50000i	0.213589	+	0.369948i
$412$	−15.0000	+	8.66025i	−0.738997	+	0.426660i
$413$	−7.50000	−	21.6506i	−0.369051	−	1.06536i
$414$	−15.0000	−	15.0000i	−0.737210	−	0.737210i
$415$			3.00000i			0.147264i
$416$	2.53590	−	9.46410i	0.124333	−	0.464016i
$417$	7.50000	−	12.9904i	0.367277	−	0.636142i
$418$	9.46410	−	2.53590i	0.462904	−	0.124035i
$419$	−12.9904	+	22.5000i	−0.634622	+	1.09920i	0.351974	+	0.936010i	$0.385511\pi$
$419$	−12.9904	+	22.5000i	−0.634622	+	1.09920i	−0.986595	+	0.163187i	$0.947823\pi$
$420$	15.5885	+	3.00000i	0.760639	+	0.146385i
$421$	5.50000	+	9.52628i	0.268054	+	0.464282i	0.968359	−	0.249561i	$-0.0802862\pi$
$421$	5.50000	+	9.52628i	0.268054	+	0.464282i	−0.700306	+	0.713843i	$0.746953\pi$
$422$	−1.00000	−	1.00000i	−0.0486792	−	0.0486792i
$423$	−7.79423	−	13.5000i	−0.378968	−	0.656392i
$424$	8.00000	+	8.00000i	0.388514	+	0.388514i
$425$	6.00000	−	3.46410i	0.291043	−	0.168034i
$426$	−2.53590	+	9.46410i	−0.122865	+	0.458537i
$427$	−2.59808	+	13.5000i	−0.125730	+	0.653311i
$428$	2.00000	−	3.46410i	0.0966736	−	0.167444i
$429$	3.00000			0.144841
$430$	−2.36603	−	0.633975i	−0.114100	−	0.0305730i
$431$		−	26.0000i		−	1.25238i	−0.779672	−	0.626188i	$-0.784614\pi$
$431$		−	26.0000i		−	1.25238i	0.779672	−	0.626188i	$-0.215386\pi$
$432$	−10.3923	−	18.0000i	−0.500000	−	0.866025i
$433$		−	17.3205i		−	0.832370i	−0.909280	−	0.416185i	$-0.863367\pi$
$433$		−	17.3205i		−	0.832370i	0.909280	−	0.416185i	$-0.136633\pi$
$434$	2.32051	+	32.3205i	0.111388	+	1.55143i
$435$			15.0000i			0.719195i
$436$	20.7846	+	12.0000i	0.995402	+	0.574696i
$437$	−30.0000	−	17.3205i	−1.43509	−	0.828552i
$438$	−6.58846	+	24.5885i	−0.314809	+	1.17488i
$439$	9.52628	+	16.5000i	0.454665	+	0.787502i	0.998669	−	0.0515804i	$-0.0164258\pi$
$439$	9.52628	+	16.5000i	0.454665	+	0.787502i	−0.544004	+	0.839082i	$0.683092\pi$
$440$	3.46410	+	3.46410i	0.165145	+	0.165145i
$441$	−3.00000	−	20.7846i	−0.142857	−	0.989743i
$442$	6.00000	−	6.00000i	0.285391	−	0.285391i
$443$	30.3109	−	17.5000i	1.44011	−	0.831450i	0.442257	−	0.896888i	$-0.354178\pi$
$443$	30.3109	−	17.5000i	1.44011	−	0.831450i	0.997857	+	0.0654382i	$0.0208445\pi$
$444$		0			0
$445$	−15.0000	+	25.9808i	−0.711068	+	1.23161i
$446$	0.633975	+	2.36603i	0.0300196	+	0.112035i
$447$	−6.06218	+	10.5000i	−0.286731	+	0.496633i
$448$	−16.0000	−	13.8564i	−0.755929	−	0.654654i
$449$	−20.0000			−0.943858			−0.471929	−	0.881636i	$-0.656442\pi$
$449$	−20.0000			−0.943858			−0.471929	+	0.881636i	$0.656442\pi$
$450$	−2.19615	−	8.19615i	−0.103528	−	0.386370i
$451$	−8.66025			−0.407795
$452$	−32.9090	+	19.0000i	−1.54791	+	0.893685i
$453$	16.5000	−	9.52628i	0.775238	−	0.447584i
$454$	1.90192	+	7.09808i	0.0892617	+	0.333129i
$455$	7.79423	+	1.50000i	0.365399	+	0.0703211i
$456$	−24.0000	−	24.0000i	−1.12390	−	1.12390i
$457$	7.50000	+	12.9904i	0.350835	+	0.607664i	0.986396	−	0.164386i	$-0.0525644\pi$
$457$	7.50000	+	12.9904i	0.350835	+	0.607664i	−0.635561	+	0.772051i	$0.719231\pi$
$458$	1.73205	+	1.73205i	0.0809334	+	0.0809334i
$459$		−	18.0000i		−	0.840168i
$460$		−	17.3205i		−	0.807573i
$461$	10.5000	−	6.06218i	0.489034	−	0.282344i	−0.235140	−	0.971962i	$-0.575555\pi$
$461$	10.5000	−	6.06218i	0.489034	−	0.282344i	0.724174	+	0.689618i	$0.242221\pi$
$462$	2.83013	−	5.83013i	0.131669	−	0.271242i
$463$	33.7750	+	19.5000i	1.56966	+	0.906242i	0.996208	+	0.0870004i	$0.0277281\pi$
$463$	33.7750	+	19.5000i	1.56966	+	0.906242i	0.573449	+	0.819242i	$0.305605\pi$
$464$	10.0000	−	17.3205i	0.464238	−	0.804084i
$465$	−22.5000	+	12.9904i	−1.04341	+	0.602414i
$466$	−19.1244	−	5.12436i	−0.885919	−	0.237381i
$467$	20.7846			0.961797			0.480899	−	0.876776i	$-0.340311\pi$
$467$	20.7846			0.961797			0.480899	+	0.876776i	$0.340311\pi$
$468$	−5.19615	−	9.00000i	−0.240192	−	0.416025i
$469$	−37.5000	+	12.9904i	−1.73159	+	0.599840i
$470$	3.29423	−	12.2942i	0.151951	−	0.567090i
$471$	7.79423	+	4.50000i	0.359139	+	0.207349i
$472$	−23.6603	+	6.33975i	−1.08905	+	0.291810i
$473$	−0.500000	+	0.866025i	−0.0229900	+	0.0398199i
$474$	7.09808	−	1.90192i	0.326025	−	0.0873583i
$475$	−6.92820	−	12.0000i	−0.317888	−	0.550598i
$476$	−6.00000	−	17.3205i	−0.275010	−	0.793884i
$477$	12.0000			0.549442
$478$	−25.0000	−	25.0000i	−1.14347	−	1.14347i
$479$	16.4545	+	28.5000i	0.751825	+	1.30220i	0.946938	+	0.321417i	$0.104159\pi$
$479$	16.4545	+	28.5000i	0.751825	+	1.30220i	−0.195113	+	0.980781i	$0.562507\pi$
$480$	4.39230	−	16.3923i	0.200480	−	0.748203i
$481$		0			0
$482$	40.2224	−	10.7776i	1.83208	−	0.490905i
$483$	−21.6506	+	7.50000i	−0.985138	+	0.341262i
$484$	−17.3205	+	10.0000i	−0.787296	+	0.454545i
$485$	9.00000			0.408669
$486$	−21.2942	−	5.70577i	−0.965926	−	0.258819i
$487$		−	10.0000i		−	0.453143i	−0.973995	−	0.226572i	$-0.927248\pi$
$487$		−	10.0000i		−	0.453143i	0.973995	−	0.226572i	$-0.0727517\pi$
$488$	14.1962	+	3.80385i	0.642630	+	0.172192i
$489$		−	10.3923i		−	0.469956i
$490$	10.2679	−	13.7321i	0.463859	−	0.620351i
$491$	−16.4545	−	9.50000i	−0.742580	−	0.428729i	0.0804264	−	0.996761i	$-0.474372\pi$
$491$	−16.4545	−	9.50000i	−0.742580	−	0.428729i	−0.823007	+	0.568032i	$0.807705\pi$
$492$	15.0000	+	25.9808i	0.676252	+	1.17130i
$493$	15.0000	−	8.66025i	0.675566	−	0.390038i
$494$	−12.0000	−	12.0000i	−0.539906	−	0.539906i
$495$	5.19615			0.233550
$496$	34.6410			1.55543
$497$	8.00000	+	6.92820i	0.358849	+	0.310772i
$498$	−1.09808	−	4.09808i	−0.0492060	−	0.183639i
$499$	−6.06218	−	3.50000i	−0.271380	−	0.156682i	0.358134	−	0.933670i	$-0.383413\pi$
$499$	−6.06218	−	3.50000i	−0.271380	−	0.156682i	−0.629515	+	0.776989i	$0.716746\pi$
$500$	12.1244	−	21.0000i	0.542218	−	0.939149i
$501$	−10.5000	+	18.1865i	−0.469105	+	0.812514i
$502$		0			0
$503$	−17.3205			−0.772283			−0.386142	−	0.922440i	$-0.626192\pi$
$503$	−17.3205			−0.772283			−0.386142	+	0.922440i	$0.626192\pi$
$504$	−22.3923	+	1.60770i	−0.997433	+	0.0716124i
$505$	−21.0000			−0.934488
$506$	−6.83013	−	1.83013i	−0.303636	−	0.0813591i
$507$	8.66025	+	15.0000i	0.384615	+	0.666173i
$508$	18.0000	−	31.1769i	0.798621	−	1.38325i
$509$	22.5000	+	12.9904i	0.997295	+	0.575789i	0.907447	−	0.420167i	$-0.138028\pi$
$509$	22.5000	+	12.9904i	0.997295	+	0.575789i	0.0898481	+	0.995955i	$0.471362\pi$
$510$	10.3923	−	10.3923i	0.460179	−	0.460179i
$511$	20.7846	+	18.0000i	0.919457	+	0.796273i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	−36.0000			−1.58944
$514$	29.4449	+	29.4449i	1.29876	+	1.29876i
$515$	−12.9904	+	7.50000i	−0.572425	+	0.330489i
$516$	3.46410			0.152499
$517$	−4.50000	−	2.59808i	−0.197910	−	0.114263i
$518$		0			0
$519$	−12.9904	+	7.50000i	−0.570214	+	0.329213i
$520$	2.19615	−	8.19615i	0.0963077	−	0.359425i
$521$		0			0		1.00000			$0$
$521$		0			0		−1.00000			$\pi$
$522$	−5.49038	−	20.4904i	−0.240307	−	0.896840i
$523$	24.2487			1.06032			0.530161	−	0.847897i	$-0.322131\pi$
$523$	24.2487			1.06032			0.530161	+	0.847897i	$0.322131\pi$
$524$	21.0000	−	12.1244i	0.917389	−	0.529655i
$525$	−9.00000	−	1.73205i	−0.392792	−	0.0755929i
$526$	−25.9545	+	6.95448i	−1.13167	+	0.303230i
$527$	25.9808	+	15.0000i	1.13174	+	0.653410i
$528$	−6.00000	−	3.46410i	−0.261116	−	0.150756i
$529$	1.00000	+	1.73205i	0.0434783	+	0.0753066i
$530$	6.92820	+	6.92820i	0.300942	+	0.300942i
$531$	−12.9904	+	22.5000i	−0.563735	+	0.976417i
$532$	−34.6410	+	12.0000i	−1.50188	+	0.520266i
$533$	7.50000	+	12.9904i	0.324861	+	0.562676i
$534$	10.9808	−	40.9808i	0.475184	−	1.77341i
$535$	1.73205	−	3.00000i	0.0748831	−	0.129701i
$536$	10.9808	+	40.9808i	0.474297	+	1.77010i
$537$		−	3.46410i		−	0.149487i
$538$	3.80385	−	14.1962i	0.163996	−	0.612040i
$539$	−4.33013	−	5.50000i	−0.186512	−	0.236902i
$540$	−9.00000	−	15.5885i	−0.387298	−	0.670820i
$541$	26.0000			1.11783			0.558914	−	0.829226i	$-0.311218\pi$
$541$	26.0000			1.11783			0.558914	+	0.829226i	$0.311218\pi$
$542$		0			0
$543$		−	30.0000i		−	1.28742i
$544$	−18.9282	+	5.07180i	−0.811540	+	0.217451i
$545$	18.0000	+	10.3923i	0.771035	+	0.445157i
$546$	−11.1962	+	0.803848i	−0.479151	+	0.0344015i
$547$	−23.3827	+	13.5000i	−0.999771	+	0.577218i	−0.908181	−	0.418578i	$-0.862529\pi$
$547$	−23.3827	+	13.5000i	−0.999771	+	0.577218i	−0.0915908	+	0.995797i	$0.529195\pi$
$548$		−	10.0000i		−	0.427179i
$549$	13.5000	−	7.79423i	0.576166	−	0.332650i
$550$	−2.00000	−	2.00000i	−0.0852803	−	0.0852803i
$551$	−17.3205	−	30.0000i	−0.737878	−	1.27804i
$552$	6.33975	+	23.6603i	0.269838	+	1.00705i
$553$	1.50000	−	7.79423i	0.0637865	−	0.331444i
$554$	−8.41858	−	31.4186i	−0.357671	−	1.33485i
$555$		0			0
$556$	−15.0000	+	8.66025i	−0.636142	+	0.367277i
$557$	−40.0000			−1.69485			−0.847427	−	0.530912i	$-0.821850\pi$
$557$	−40.0000			−1.69485			−0.847427	+	0.530912i	$0.821850\pi$
$558$	25.9808	−	25.9808i	1.09985	−	1.09985i
$559$	1.73205			0.0732579
$560$	−13.8564	−	12.0000i	−0.585540	−	0.507093i
$561$	−3.00000	−	5.19615i	−0.126660	−	0.219382i
$562$	−0.366025	−	1.36603i	−0.0154398	−	0.0576223i
$563$	0.866025	−	1.50000i	0.0364986	−	0.0632175i	−0.847199	−	0.531276i	$-0.821713\pi$
$563$	0.866025	−	1.50000i	0.0364986	−	0.0632175i	0.883698	+	0.468058i	$0.155046\pi$
$564$			18.0000i			0.757937i
$565$	−28.5000	+	16.4545i	−1.19900	+	0.692245i
$566$	−15.5885	+	15.5885i	−0.655232	+	0.655232i
$567$	−15.5885	+	18.0000i	−0.654654	+	0.755929i
$568$	8.00000	−	8.00000i	0.335673	−	0.335673i
$569$	−3.50000	−	6.06218i	−0.146728	−	0.254140i	0.783289	−	0.621658i	$-0.213541\pi$
$569$	−3.50000	−	6.06218i	−0.146728	−	0.254140i	−0.930016	+	0.367519i	$0.880207\pi$
$570$	−20.7846	−	20.7846i	−0.870572	−	0.870572i
$571$	−7.79423	−	4.50000i	−0.326178	−	0.188319i	0.327965	−	0.944690i	$-0.393637\pi$
$571$	−7.79423	−	4.50000i	−0.326178	−	0.188319i	−0.654143	+	0.756371i	$0.726971\pi$
$572$	−3.00000	−	1.73205i	−0.125436	−	0.0724207i
$573$	7.50000	−	4.33013i	0.313317	−	0.180894i
$574$	32.3205	−	2.32051i	1.34903	−	0.0968561i
$575$			10.0000i			0.417029i
$576$			24.0000i			1.00000i
$577$		−	38.1051i		−	1.58634i	−0.609002	−	0.793168i	$-0.708430\pi$
$577$		−	38.1051i		−	1.58634i	0.609002	−	0.793168i	$-0.291570\pi$
$578$	6.83013	+	1.83013i	0.284096	+	0.0761232i
$579$	7.79423	−	13.5000i	0.323917	−	0.561041i
$580$	8.66025	−	15.0000i	0.359597	−	0.622841i
$581$	−4.50000	−	0.866025i	−0.186691	−	0.0359288i
$582$	−12.2942	+	3.29423i	−0.509612	+	0.136550i
$583$	3.46410	−	2.00000i	0.143468	−	0.0828315i
$584$	20.7846	−	20.7846i	0.860073	−	0.860073i
$585$	−4.50000	−	7.79423i	−0.186052	−	0.322252i
$586$	−25.9808	−	25.9808i	−1.07326	−	1.07326i
$587$	−12.9904	−	22.5000i	−0.536170	−	0.928674i	−0.999106	−	0.0422823i	$-0.986537\pi$
$587$	−12.9904	−	22.5000i	−0.536170	−	0.928674i	0.462935	−	0.886392i	$-0.346796\pi$
$588$	−9.00000	+	22.5167i	−0.371154	+	0.928571i
$589$	30.0000	−	51.9615i	1.23613	−	2.14104i
$590$	−20.4904	+	5.49038i	−0.843576	+	0.226035i
$591$	−3.46410			−0.142494
$592$		0			0
$593$			31.1769i			1.28028i	0.768257	+	0.640141i	$0.221124\pi$
$593$			31.1769i			1.28028i	−0.768257	+	0.640141i	$0.778876\pi$
$594$	−7.09808	+	1.90192i	−0.291238	+	0.0780369i
$595$	−5.19615	−	15.0000i	−0.213021	−	0.614940i
$596$	12.1244	−	7.00000i	0.496633	−	0.286731i
$597$	30.0000			1.22782
$598$	3.16987	+	11.8301i	0.129626	+	0.483770i
$599$	14.7224	+	8.50000i	0.601542	+	0.347301i	0.769648	−	0.638468i	$-0.220432\pi$
$599$	14.7224	+	8.50000i	0.601542	+	0.347301i	−0.168106	+	0.985769i	$0.553765\pi$
$600$	−2.53590	+	9.46410i	−0.103528	+	0.386370i
$601$	4.50000	−	2.59808i	0.183559	−	0.105978i	−0.405405	−	0.914137i	$-0.632869\pi$
$601$	4.50000	−	2.59808i	0.183559	−	0.105978i	0.588964	+	0.808160i	$0.299536\pi$
$602$	1.63397	−	3.36603i	0.0665958	−	0.137189i
$603$	38.9711	+	22.5000i	1.58703	+	0.916271i
$604$	−22.0000			−0.895167
$605$	−15.0000	+	8.66025i	−0.609837	+	0.352089i
$606$	28.6865	−	7.68653i	1.16531	−	0.312244i
$607$	−4.33013	+	7.50000i	−0.175754	+	0.304416i	−0.940422	−	0.340009i	$-0.889570\pi$
$607$	−4.33013	+	7.50000i	−0.175754	+	0.304416i	0.764668	+	0.644425i	$0.222903\pi$
$608$	10.1436	+	37.8564i	0.411377	+	1.53528i
$609$	−22.5000	−	4.33013i	−0.911746	−	0.175466i
$610$	12.2942	+	3.29423i	0.497779	+	0.133379i
$611$			9.00000i			0.364101i
$612$	−10.3923	+	18.0000i	−0.420084	+	0.727607i
$613$	−40.0000			−1.61558			−0.807792	−	0.589467i	$-0.799338\pi$
$613$	−40.0000			−1.61558			−0.807792	+	0.589467i	$0.799338\pi$
$614$	−18.9282	−	5.07180i	−0.763880	−	0.204681i
$615$	12.9904	+	22.5000i	0.523823	+	0.907288i
$616$	−6.19615	+	4.19615i	−0.249650	+	0.169068i
$617$	17.5000	−	30.3109i	0.704523	−	1.22027i	−0.262340	−	0.964976i	$-0.584494\pi$
$617$	17.5000	−	30.3109i	0.704523	−	1.22027i	0.966863	−	0.255295i	$-0.0821725\pi$
$618$	15.0000	−	15.0000i	0.603388	−	0.603388i
$619$	−4.33013	−	7.50000i	−0.174042	−	0.301450i	0.765787	−	0.643094i	$-0.222350\pi$
$619$	−4.33013	−	7.50000i	−0.174042	−	0.301450i	−0.939829	+	0.341644i	$0.889016\pi$
$620$	30.0000			1.20483
$621$	22.5000	+	12.9904i	0.902894	+	0.521286i
$622$	−25.9808	+	25.9808i	−1.04173	+	1.04173i
$623$	−34.6410	−	30.0000i	−1.38786	−	1.20192i
$624$			12.0000i			0.480384i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	11.8301	−	3.16987i	0.472827	−	0.126694i
$627$	−10.3923	+	6.00000i	−0.415029	+	0.239617i
$628$	−5.19615	−	9.00000i	−0.207349	−	0.359139i
$629$		0			0
$630$	−19.3923	+	1.39230i	−0.772608	+	0.0554708i
$631$			6.00000i			0.238856i	0.992843	+	0.119428i	$0.0381061\pi$
$631$			6.00000i			0.238856i	−0.992843	+	0.119428i	$0.961894\pi$
$632$	−8.19615	−	2.19615i	−0.326025	−	0.0873583i
$633$	1.50000	+	0.866025i	0.0596196	+	0.0344214i
$634$	8.41858	+	31.4186i	0.334345	+	1.24779i
$635$	15.5885	−	27.0000i	0.618609	−	1.07146i
$636$	−12.0000	−	6.92820i	−0.475831	−	0.274721i
$637$	−4.50000	+	11.2583i	−0.178296	+	0.446071i
$638$	−5.00000	−	5.00000i	−0.197952	−	0.197952i
$639$		−	12.0000i		−	0.474713i
$640$	−13.8564	+	13.8564i	−0.547723	+	0.547723i
$641$	2.50000	+	4.33013i	0.0987441	+	0.171030i	0.911165	−	0.412042i	$-0.135184\pi$
$641$	2.50000	+	4.33013i	0.0987441	+	0.171030i	−0.812421	+	0.583071i	$0.801851\pi$
$642$	−1.26795	+	4.73205i	−0.0500420	+	0.186759i
$643$	0.866025	−	1.50000i	0.0341527	−	0.0591542i	−0.848444	−	0.529285i	$-0.822460\pi$
$643$	0.866025	−	1.50000i	0.0341527	−	0.0591542i	0.882597	+	0.470131i	$0.155793\pi$
$644$	25.9808	+	5.00000i	1.02379	+	0.197028i
$645$	3.00000			0.118125
$646$	−8.78461	+	32.7846i	−0.345626	+	1.28989i
$647$	34.6410			1.36188			0.680939	−	0.732340i	$-0.261572\pi$
$647$	34.6410			1.36188			0.680939	+	0.732340i	$0.261572\pi$
$648$	18.0000	+	18.0000i	0.707107	+	0.707107i
$649$			8.66025i			0.339945i
$650$	−1.26795	+	4.73205i	−0.0497331	+	0.185606i
$651$	−12.9904	−	37.5000i	−0.509133	−	1.46974i
$652$	−6.00000	+	10.3923i	−0.234978	+	0.406994i
$653$	0.500000	−	0.866025i	0.0195665	−	0.0338902i	−0.856076	−	0.516849i	$-0.827105\pi$
$653$	0.500000	−	0.866025i	0.0195665	−	0.0338902i	0.875643	+	0.482959i	$0.160438\pi$
$654$	−28.3923	−	7.60770i	−1.11023	−	0.297484i
$655$	18.1865	−	10.5000i	0.710607	−	0.410269i
$656$		−	34.6410i		−	1.35250i
$657$		−	31.1769i		−	1.21633i
$658$	17.4904	+	8.49038i	0.681846	+	0.330990i
$659$	14.7224	−	8.50000i	0.573505	−	0.331113i	−0.185043	−	0.982730i	$-0.559243\pi$
$659$	14.7224	−	8.50000i	0.573505	−	0.331113i	0.758548	+	0.651617i	$0.225909\pi$
$660$	−5.19615	−	3.00000i	−0.202260	−	0.116775i
$661$	7.50000	+	4.33013i	0.291716	+	0.168422i	0.638716	−	0.769443i	$-0.279466\pi$
$661$	7.50000	+	4.33013i	0.291716	+	0.168422i	−0.346999	+	0.937865i	$0.612799\pi$
$662$	39.6147	−	10.6147i	1.53967	−	0.412553i
$663$	−5.19615	+	9.00000i	−0.201802	+	0.349531i
$664$	−1.26795	+	4.73205i	−0.0492060	+	0.183639i
$665$	−30.0000	+	10.3923i	−1.16335	+	0.402996i
$666$		0			0
$667$			25.0000i			0.968004i
$668$	21.0000	−	12.1244i	0.812514	−	0.469105i
$669$	−1.50000	−	2.59808i	−0.0579934	−	0.100447i
$670$	9.50962	+	35.4904i	0.367389	+	1.37111i
$671$	2.59808	−	4.50000i	0.100298	−	0.173721i
$672$	23.3205	+	11.3205i	0.899608	+	0.436698i
$673$	19.5000	+	33.7750i	0.751670	+	1.30193i	0.947013	+	0.321195i	$0.104085\pi$
$673$	19.5000	+	33.7750i	0.751670	+	1.30193i	−0.195343	+	0.980735i	$0.562582\pi$
$674$	−15.0000	+	15.0000i	−0.577778	+	0.577778i
$675$	5.19615	+	9.00000i	0.200000	+	0.346410i
$676$		−	20.0000i		−	0.769231i
$677$	−4.50000	+	2.59808i	−0.172949	+	0.0998522i	−0.583976	−	0.811771i	$-0.698504\pi$
$677$	−4.50000	+	2.59808i	−0.172949	+	0.0998522i	0.411027	+	0.911623i	$0.365170\pi$
$678$	32.9090	−	32.9090i	1.26386	−	1.26386i
$679$	−2.59808	+	13.5000i	−0.0997050	+	0.518082i
$680$	−16.3923	+	4.39230i	−0.628616	+	0.168437i
$681$	−4.50000	−	7.79423i	−0.172440	−	0.298675i
$682$	3.16987	−	11.8301i	0.121381	−	0.452999i
$683$		−	14.0000i		−	0.535695i	−0.963461	−	0.267848i	$-0.913688\pi$
$683$		−	14.0000i		−	0.535695i	0.963461	−	0.267848i	$-0.0863124\pi$
$684$	36.0000	+	20.7846i	1.37649	+	0.794719i
$685$		−	8.66025i		−	0.330891i
$686$	17.6340	+	19.3660i	0.673268	+	0.739398i
$687$	−2.59808	−	1.50000i	−0.0991228	−	0.0572286i
$688$	−3.46410	−	2.00000i	−0.132068	−	0.0762493i
$689$	−6.00000	−	3.46410i	−0.228582	−	0.131972i
$690$	5.49038	+	20.4904i	0.209015	+	0.780055i
$691$	4.33013	+	7.50000i	0.164726	+	0.285313i	0.936558	−	0.350513i	$-0.113993\pi$
$691$	4.33013	+	7.50000i	0.164726	+	0.285313i	−0.771832	+	0.635826i	$0.780659\pi$
$692$	17.3205			0.658427
$693$	−1.50000	+	7.79423i	−0.0569803	+	0.296078i
$694$	−5.00000	−	5.00000i	−0.189797	−	0.189797i
$695$	−12.9904	+	7.50000i	−0.492753	+	0.284491i
$696$	−6.33975	+	23.6603i	−0.240307	+	0.896840i
$697$	15.0000	−	25.9808i	0.568166	−	0.984092i
$698$	−35.4904	+	9.50962i	−1.34333	+	0.359944i
$699$	24.2487			0.917170
$700$	8.00000	+	6.92820i	0.302372	+	0.261861i
$701$	44.0000			1.66186			0.830929	−	0.556379i	$-0.187810\pi$
$701$	44.0000			1.66186			0.830929	+	0.556379i	$0.187810\pi$
$702$	9.00000	+	9.00000i	0.339683	+	0.339683i
$703$		0			0
$704$	4.00000	+	6.92820i	0.150756	+	0.261116i
$705$			15.5885i			0.587095i
$706$	−11.8301	+	3.16987i	−0.445233	+	0.119300i
$707$	6.06218	−	31.5000i	0.227992	−	1.18468i
$708$	25.9808	−	15.0000i	0.976417	−	0.563735i
$709$	−7.50000	−	12.9904i	−0.281668	−	0.487864i	0.690127	−	0.723688i	$-0.257554\pi$
$709$	−7.50000	−	12.9904i	−0.281668	−	0.487864i	−0.971796	+	0.235824i	$0.924221\pi$
$710$	6.92820	−	6.92820i	0.260011	−	0.260011i
$711$	−7.79423	+	4.50000i	−0.292306	+	0.168763i
$712$	−34.6410	+	34.6410i	−1.29823	+	1.29823i
$713$	−37.5000	+	21.6506i	−1.40439	+	0.810823i
$714$	12.5885	+	18.5885i	0.471111	+	0.695656i
$715$	−2.59808	−	1.50000i	−0.0971625	−	0.0560968i
$716$	−2.00000	+	3.46410i	−0.0747435	+	0.129460i
$717$	37.5000	+	21.6506i	1.40046	+	0.808558i
$718$	−3.66025	+	13.6603i	−0.136599	+	0.509796i
$719$	−34.6410			−1.29189			−0.645946	−	0.763383i	$-0.723537\pi$
$719$	−34.6410			−1.29189			−0.645946	+	0.763383i	$0.723537\pi$
$720$			20.7846i			0.774597i
$721$	−7.50000	−	21.6506i	−0.279315	−	0.806312i
$722$	39.6147	+	10.6147i	1.47431	+	0.395040i
$723$	−44.1673	+	25.5000i	−1.64260	+	0.948355i
$724$	−17.3205	+	30.0000i	−0.643712	+	1.11494i
$725$	−5.00000	+	8.66025i	−0.185695	+	0.321634i
$726$	17.3205	−	17.3205i	0.642824	−	0.642824i
$727$	−14.7224	−	25.5000i	−0.546025	−	0.945743i	−0.998542	−	0.0539868i	$-0.982807\pi$
$727$	−14.7224	−	25.5000i	−0.546025	−	0.945743i	0.452517	−	0.891756i	$-0.350526\pi$
$728$	11.6603	+	5.66025i	0.432158	+	0.209783i
$729$	27.0000			1.00000
$730$	18.0000	−	18.0000i	0.666210	−	0.666210i
$731$	−1.73205	−	3.00000i	−0.0640622	−	0.110959i
$732$	−18.0000			−0.665299
$733$	−19.5000	−	11.2583i	−0.720249	−	0.415836i	0.0945954	−	0.995516i	$-0.469844\pi$
$733$	−19.5000	−	11.2583i	−0.720249	−	0.415836i	−0.814844	+	0.579680i	$0.803178\pi$
$734$	−8.24167	−	30.7583i	−0.304206	−	1.13531i
$735$	−7.79423	+	19.5000i	−0.287494	+	0.719268i
$736$	7.32051	−	27.3205i	0.269838	−	1.00705i
$737$	15.0000			0.552532
$738$	−25.9808	−	25.9808i	−0.956365	−	0.956365i
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$		0			0
$741$	18.0000	+	10.3923i	0.661247	+	0.381771i
$742$	−12.3923	+	8.39230i	−0.454936	+	0.308091i
$743$	25.1147	+	14.5000i	0.921370	+	0.531953i	0.884072	−	0.467351i	$-0.154791\pi$
$743$	25.1147	+	14.5000i	0.921370	+	0.531953i	0.0372984	+	0.999304i	$0.488125\pi$
$744$	−40.9808	+	10.9808i	−1.50243	+	0.402574i
$745$	10.5000	−	6.06218i	0.384690	−	0.222101i
$746$	−1.00000	+	1.00000i	−0.0366126	+	0.0366126i
$747$	2.59808	+	4.50000i	0.0950586	+	0.164646i
$748$			6.92820i			0.253320i
$749$	4.00000	+	3.46410i	0.146157	+	0.126576i
$750$	−7.68653	+	28.6865i	−0.280673	+	1.04748i
$751$	−30.3109	−	17.5000i	−1.10606	−	0.638584i	−0.168254	−	0.985744i	$-0.553813\pi$
$751$	−30.3109	−	17.5000i	−1.10606	−	0.638584i	−0.937806	+	0.347160i	$0.887146\pi$
$752$	10.3923	−	18.0000i	0.378968	−	0.656392i
$753$		0			0
$754$	−3.16987	+	11.8301i	−0.115440	+	0.430828i
$755$	−19.0526			−0.693394
$756$	25.9808	−	9.00000i	0.944911	−	0.327327i
$757$	30.0000			1.09037			0.545184	−	0.838316i	$-0.316460\pi$
$757$	30.0000			1.09037			0.545184	+	0.838316i	$0.316460\pi$
$758$	2.92820	−	10.9282i	0.106357	−	0.396930i
$759$	8.66025			0.314347
$760$	8.78461	+	32.7846i	0.318651	+	1.18922i
$761$	−19.5000	−	11.2583i	−0.706874	−	0.408114i	0.103028	−	0.994678i	$-0.467147\pi$
$761$	−19.5000	−	11.2583i	−0.706874	−	0.408114i	−0.809903	+	0.586564i	$0.800480\pi$
$762$	−11.4115	+	42.5885i	−0.413397	+	1.54282i
$763$	−20.7846	+	24.0000i	−0.752453	+	0.868858i
$764$	−10.0000			−0.361787
$765$	−9.00000	+	15.5885i	−0.325396	+	0.563602i
$766$	−1.73205	+	1.73205i	−0.0625815	+	0.0625815i
$767$	12.9904	−	7.50000i	0.469055	−	0.270809i
$768$	13.8564	−	24.0000i	0.500000	−	0.866025i
$769$	−22.5000	−	12.9904i	−0.811371	−	0.468445i	0.0360609	−	0.999350i	$-0.488519\pi$
$769$	−22.5000	−	12.9904i	−0.811371	−	0.468445i	−0.847432	+	0.530904i	$0.821852\pi$
$770$	−5.36603	+	3.63397i	−0.193378	+	0.130959i
$771$	−44.1673	−	25.5000i	−1.59065	−	0.918360i
$772$	−15.5885	+	9.00000i	−0.561041	+	0.323917i
$773$		−	24.2487i		−	0.872166i	−0.899907	−	0.436083i	$-0.856365\pi$
$773$		−	24.2487i		−	0.872166i	0.899907	−	0.436083i	$-0.143635\pi$
$774$	−4.09808	+	1.09808i	−0.147302	+	0.0394695i
$775$	−17.3205			−0.622171
$776$	14.1962	+	3.80385i	0.509612	+	0.136550i
$777$		0			0
$778$	6.22243	+	23.2224i	0.223085	+	0.832565i
$779$	−51.9615	−	30.0000i	−1.86171	−	1.07486i
$780$			10.3923i			0.372104i
$781$	−2.00000	−	3.46410i	−0.0715656	−	0.123955i
$782$	17.3205	−	17.3205i	0.619380	−	0.619380i
$783$	12.9904	+	22.5000i	0.464238	+	0.804084i
$784$	22.0000	−	17.3205i	0.785714	−	0.618590i
$785$	−4.50000	−	7.79423i	−0.160612	−	0.278188i
$786$	−21.0000	+	21.0000i	−0.749045	+	0.749045i
$787$	6.06218	−	10.5000i	0.216093	−	0.374285i	−0.737517	−	0.675329i	$-0.764002\pi$
$787$	6.06218	−	10.5000i	0.216093	−	0.374285i	0.953610	+	0.301044i	$0.0973351\pi$
$788$	3.46410	+	2.00000i	0.123404	+	0.0712470i
$789$	28.5000	−	16.4545i	1.01463	−	0.585795i
$790$	−7.09808	−	1.90192i	−0.252538	−	0.0676674i
$791$	−16.4545	−	47.5000i	−0.585054	−	1.68891i
$792$	8.19615	+	2.19615i	0.291238	+	0.0780369i
$793$	−9.00000			−0.319599
$794$	−6.33975	+	23.6603i	−0.224989	+	0.839671i
$795$	−10.3923	−	6.00000i	−0.368577	−	0.212798i
$796$	−30.0000	−	17.3205i	−1.06332	−	0.613909i
$797$	4.50000	+	2.59808i	0.159398	+	0.0920286i	0.577577	−	0.816336i	$-0.303998\pi$
$797$	4.50000	+	2.59808i	0.159398	+	0.0920286i	−0.418179	+	0.908365i	$0.637332\pi$
$798$	37.1769	−	25.1769i	1.31605	−	0.891253i
$799$	15.5885	−	9.00000i	0.551480	−	0.318397i
$800$	8.00000	−	8.00000i	0.282843	−	0.282843i
$801$			51.9615i			1.83597i
$802$	−5.00000	+	5.00000i	−0.176556	+	0.176556i
$803$	−5.19615	−	9.00000i	−0.183368	−	0.317603i
$804$	−25.9808	−	45.0000i	−0.916271	−	1.58703i
$805$	22.5000	+	4.33013i	0.793021	+	0.152617i
$806$	−20.4904	+	5.49038i	−0.721743	+	0.193390i
$807$			18.0000i			0.633630i
$808$	−33.1244	−	8.87564i	−1.16531	−	0.312244i
$809$	8.00000			0.281265			0.140633	−	0.990062i	$-0.455086\pi$
$809$	8.00000			0.281265			0.140633	+	0.990062i	$0.455086\pi$
$810$	15.5885	+	15.5885i	0.547723	+	0.547723i
$811$	20.7846			0.729846			0.364923	−	0.931038i	$-0.381095\pi$
$811$	20.7846			0.729846			0.364923	+	0.931038i	$0.381095\pi$
$812$	20.0000	+	17.3205i	0.701862	+	0.607831i
$813$		0			0
$814$		0			0
$815$	−5.19615	+	9.00000i	−0.182013	+	0.315256i
$816$	20.7846	−	12.0000i	0.727607	−	0.420084i
$817$	−6.00000	+	3.46410i	−0.209913	+	0.121194i
$818$	15.5885	+	15.5885i	0.545038	+	0.545038i
$819$	12.9904	−	4.50000i	0.453921	−	0.157243i
$820$		−	30.0000i		−	1.04765i
$821$	−20.5000	−	35.5070i	−0.715455	−	1.23920i	−0.962784	−	0.270273i	$-0.912886\pi$
$821$	−20.5000	−	35.5070i	−0.715455	−	1.23920i	0.247329	−	0.968932i	$-0.420447\pi$
$822$	3.16987	+	11.8301i	0.110562	+	0.412623i
$823$	−7.79423	−	4.50000i	−0.271690	−	0.156860i	0.357966	−	0.933735i	$-0.383471\pi$
$823$	−7.79423	−	4.50000i	−0.271690	−	0.156860i	−0.629655	+	0.776875i	$0.716804\pi$
$824$	−23.6603	+	6.33975i	−0.824244	+	0.220856i
$825$	3.00000	+	1.73205i	0.104447	+	0.0603023i
$826$	−2.32051	−	32.3205i	−0.0807408	−	1.12457i
$827$			50.0000i			1.73867i	0.494223	+	0.869335i	$0.335453\pi$
$827$			50.0000i			1.73867i	−0.494223	+	0.869335i	$0.664547\pi$
$828$	−15.0000	−	25.9808i	−0.521286	−	0.902894i
$829$		−	10.3923i		−	0.360940i	−0.983581	−	0.180470i	$-0.942238\pi$
$829$		−	10.3923i		−	0.360940i	0.983581	−	0.180470i	$-0.0577618\pi$
$830$	−1.09808	+	4.09808i	−0.0381148	+	0.142246i
$831$	19.9186	+	34.5000i	0.690968	+	1.19679i
$832$	6.92820	−	12.0000i	0.240192	−	0.416025i
$833$	24.0000	−	3.46410i	0.831551	−	0.120024i
$834$	15.0000	−	15.0000i	0.519408	−	0.519408i
$835$	18.1865	−	10.5000i	0.629371	−	0.363367i
$836$	13.8564			0.479234
$837$	−22.5000	+	38.9711i	−0.777714	+	1.34704i
$838$	−25.9808	+	25.9808i	−0.897491	+	0.897491i
$839$	0.866025	+	1.50000i	0.0298985	+	0.0517858i	0.880587	−	0.473884i	$-0.157148\pi$
$839$	0.866025	+	1.50000i	0.0298985	+	0.0517858i	−0.850689	+	0.525669i	$0.823815\pi$
$840$	20.1962	+	9.80385i	0.696833	+	0.338265i
$841$	2.00000	−	3.46410i	0.0689655	−	0.119452i
$842$	4.02628	+	15.0263i	0.138755	+	0.517840i
$843$	0.866025	+	1.50000i	0.0298275	+	0.0516627i
$844$	−1.00000	−	1.73205i	−0.0344214	−	0.0596196i
$845$		−	17.3205i		−	0.595844i
$846$	−5.70577	−	21.2942i	−0.196168	−	0.732111i
$847$	−8.66025	−	25.0000i	−0.297570	−	0.859010i
$848$	8.00000	+	13.8564i	0.274721	+	0.475831i
$849$	13.5000	−	23.3827i	0.463319	−	0.802492i
$850$	9.46410	−	2.53590i	0.324616	−	0.0869806i
$851$		0			0
$852$	−6.92820	+	12.0000i	−0.237356	+	0.411113i
$853$	34.5000	−	19.9186i	1.18126	−	0.681999i	0.224952	−	0.974370i	$-0.427777\pi$
$853$	34.5000	−	19.9186i	1.18126	−	0.681999i	0.956305	+	0.292370i	$0.0944440\pi$
$854$	−8.49038	+	17.4904i	−0.290535	+	0.598509i
$855$	31.1769	+	18.0000i	1.06623	+	0.615587i
$856$	4.00000	−	4.00000i	0.136717	−	0.136717i
$857$	−25.5000	+	14.7224i	−0.871063	+	0.502909i	−0.867701	−	0.497086i	$-0.834403\pi$
$857$	−25.5000	+	14.7224i	−0.871063	+	0.502909i	−0.00336193	+	0.999994i	$0.501070\pi$
$858$	4.09808	+	1.09808i	0.139906	+	0.0374877i
$859$	18.1865	−	31.5000i	0.620517	−	1.07477i	−0.368873	−	0.929480i	$-0.620256\pi$
$859$	18.1865	−	31.5000i	0.620517	−	1.07477i	0.989390	−	0.145286i	$-0.0464103\pi$
$860$	−3.00000	−	1.73205i	−0.102299	−	0.0590624i
$861$	−37.5000	+	12.9904i	−1.27800	+	0.442711i
$862$	9.51666	−	35.5167i	0.324139	−	1.20970i
$863$		−	10.0000i		−	0.340404i	−0.985409	−	0.170202i	$-0.945558\pi$
$863$		−	10.0000i		−	0.340404i	0.985409	−	0.170202i	$-0.0544420\pi$
$864$	−7.60770	−	28.3923i	−0.258819	−	0.965926i
$865$	15.0000			0.510015
$866$	6.33975	−	23.6603i	0.215433	−	0.804008i
$867$	−8.66025			−0.294118
$868$	−8.66025	+	45.0000i	−0.293948	+	1.52740i
$869$	−1.50000	+	2.59808i	−0.0508840	+	0.0881337i
$870$	−5.49038	+	20.4904i	−0.186141	+	0.694689i
$871$	−12.9904	−	22.5000i	−0.440162	−	0.762383i
$872$	24.0000	+	24.0000i	0.812743	+	0.812743i
$873$	13.5000	−	7.79423i	0.456906	−	0.263795i
$874$	−34.6410	−	34.6410i	−1.17175	−	1.17175i
$875$	24.2487	+	21.0000i	0.819756	+	0.709930i
$876$	−18.0000	+	31.1769i	−0.608164	+	1.05337i
$877$	−12.5000	+	21.6506i	−0.422095	+	0.731090i	−0.996144	−	0.0877308i	$-0.972038\pi$
$877$	−12.5000	+	21.6506i	−0.422095	+	0.731090i	0.574049	+	0.818821i	$0.305372\pi$
$878$	6.97372	+	26.0263i	0.235352	+	0.878344i
$879$	38.9711	+	22.5000i	1.31446	+	0.758906i
$880$	3.46410	+	6.00000i	0.116775	+	0.202260i
$881$			31.1769i			1.05038i	0.850986	+	0.525188i	$0.176005\pi$
$881$			31.1769i			1.05038i	−0.850986	+	0.525188i	$0.823995\pi$
$882$	3.50962	−	29.4904i	0.118175	−	0.992993i
$883$			26.0000i			0.874970i	0.899226	+	0.437485i	$0.144131\pi$
$883$			26.0000i			0.874970i	−0.899226	+	0.437485i	$0.855869\pi$
$884$	10.3923	−	6.00000i	0.349531	−	0.201802i
$885$	22.5000	−	12.9904i	0.756329	−	0.436667i
$886$	47.8109	−	12.8109i	1.60624	−	0.430390i
$887$	4.33013	−	7.50000i	0.145391	−	0.251825i	−0.784127	−	0.620600i	$-0.786889\pi$
$887$	4.33013	−	7.50000i	0.145391	−	0.251825i	0.929519	+	0.368774i	$0.120223\pi$
$888$		0			0
$889$	36.0000	+	31.1769i	1.20740	+	1.04564i
$890$	−30.0000	+	30.0000i	−1.00560	+	1.00560i
$891$	7.79423	−	4.50000i	0.261116	−	0.150756i
$892$			3.46410i			0.115987i
$893$	−18.0000	−	31.1769i	−0.602347	−	1.04330i
$894$	−12.1244	+	12.1244i	−0.405499	+	0.405499i
$895$	−1.73205	+	3.00000i	−0.0578961	+	0.100279i
$896$	−16.7846	−	24.7846i	−0.560734	−	0.827996i
$897$	−7.50000	−	12.9904i	−0.250418	−	0.433736i
$898$	−27.3205	−	7.32051i	−0.911697	−	0.244289i
$899$	−43.3013			−1.44418
$900$		−	12.0000i		−	0.400000i
$901$			13.8564i			0.461624i
$902$	−11.8301	−	3.16987i	−0.393900	−	0.105545i
$903$	−0.866025	+	4.50000i	−0.0288195	+	0.149751i
$904$	−51.9090	+	13.9090i	−1.72647	+	0.462605i
$905$	−15.0000	+	25.9808i	−0.498617	+	0.863630i
$906$	26.0263	−	6.97372i	0.864665	−	0.231686i
$907$	19.9186	−	11.5000i	0.661386	−	0.381851i	−0.131419	−	0.991327i	$-0.541953\pi$
$907$	19.9186	−	11.5000i	0.661386	−	0.381851i	0.792805	+	0.609476i	$0.208620\pi$
$908$			10.3923i			0.344881i
$909$	−31.5000	+	18.1865i	−1.04479	+	0.603209i
$910$	10.0981	+	4.90192i	0.334748	+	0.162497i
$911$	35.5070	−	20.5000i	1.17640	−	0.679195i	0.221222	−	0.975224i	$-0.428996\pi$
$911$	35.5070	−	20.5000i	1.17640	−	0.679195i	0.955179	+	0.296028i	$0.0956623\pi$
$912$	−24.0000	−	41.5692i	−0.794719	−	1.37649i
$913$	1.50000	+	0.866025i	0.0496428	+	0.0286613i
$914$	5.49038	+	20.4904i	0.181606	+	0.677762i
$915$	−15.5885			−0.515339
$916$	1.73205	+	3.00000i	0.0572286	+	0.0991228i
$917$	10.5000	+	30.3109i	0.346741	+	1.00095i
$918$	6.58846	−	24.5885i	0.217451	−	0.811540i
$919$			50.0000i			1.64935i	0.565608	+	0.824674i	$0.308641\pi$
$919$			50.0000i			1.64935i	−0.565608	+	0.824674i	$0.691359\pi$
$920$	6.33975	−	23.6603i	0.209015	−	0.780055i
$921$	24.0000			0.790827
$922$	16.5622	−	4.43782i	0.545446	−	0.146152i
$923$	−3.46410	+	6.00000i	−0.114022	+	0.197492i
$924$	6.00000	−	6.92820i	0.197386	−	0.227921i
$925$		0			0
$926$	39.0000	+	39.0000i	1.28162	+	1.28162i
$927$	−12.9904	+	22.5000i	−0.426660	+	0.738997i
$928$	20.0000	−	20.0000i	0.656532	−	0.656532i
$929$	22.5000	−	12.9904i	0.738201	−	0.426201i	−0.0832138	−	0.996532i	$-0.526518\pi$
$929$	22.5000	−	12.9904i	0.738201	−	0.426201i	0.821415	+	0.570331i	$0.193185\pi$
$930$	−35.4904	+	9.50962i	−1.16378	+	0.311833i
$931$	−6.92820	−	48.0000i	−0.227063	−	1.57314i
$932$	−24.2487	−	14.0000i	−0.794293	−	0.458585i
$933$	22.5000	−	38.9711i	0.736617	−	1.27586i
$934$	28.3923	+	7.60770i	0.929025	+	0.248931i
$935$			6.00000i			0.196221i
$936$	−3.80385	−	14.1962i	−0.124333	−	0.464016i
$937$		−	38.1051i		−	1.24484i	−0.782683	−	0.622420i	$-0.786150\pi$
$937$		−	38.1051i		−	1.24484i	0.782683	−	0.622420i	$-0.213850\pi$
$938$	−55.9808	+	4.01924i	−1.82784	+	0.131233i
$939$	−12.9904	+	7.50000i	−0.423925	+	0.244753i
$940$	9.00000	−	15.5885i	0.293548	−	0.508439i
$941$	−4.50000	−	2.59808i	−0.146696	−	0.0846949i	0.424856	−	0.905261i	$-0.360325\pi$
$941$	−4.50000	−	2.59808i	−0.146696	−	0.0846949i	−0.571551	+	0.820566i	$0.693658\pi$
$942$	9.00000	+	9.00000i	0.293236	+	0.293236i
$943$	21.6506	+	37.5000i	0.705042	+	1.22117i
$944$	−34.6410			−1.12747
$945$	22.5000	−	7.79423i	0.731925	−	0.253546i
$946$	−1.00000	+	1.00000i	−0.0325128	+	0.0325128i
$947$	−30.3109	+	17.5000i	−0.984972	+	0.568674i	−0.903767	−	0.428024i	$-0.859210\pi$
$947$	−30.3109	+	17.5000i	−0.984972	+	0.568674i	−0.0812041	+	0.996697i	$0.525877\pi$
$948$	10.3923			0.337526
$949$	−9.00000	+	15.5885i	−0.292152	+	0.506023i
$950$	−5.07180	−	18.9282i	−0.164551	−	0.614112i
$951$	−19.9186	−	34.5000i	−0.645904	−	1.11874i
$952$	−1.85641	−	25.8564i	−0.0601665	−	0.838011i
$953$	−40.0000			−1.29573			−0.647864	−	0.761756i	$-0.724337\pi$
$953$	−40.0000			−1.29573			−0.647864	+	0.761756i	$0.724337\pi$
$954$	16.3923	+	4.39230i	0.530720	+	0.142206i
$955$	−8.66025			−0.280239
$956$	−25.0000	−	43.3013i	−0.808558	−	1.40046i
$957$	7.50000	+	4.33013i	0.242441	+	0.139973i
$958$	12.0455	+	44.9545i	0.389173	+	1.45241i
$959$	12.9904	+	2.50000i	0.419481	+	0.0807292i
$960$	12.0000	−	20.7846i	0.387298	−	0.670820i
$961$	−22.0000	−	38.1051i	−0.709677	−	1.22920i
$962$		0			0
$963$		−	6.00000i		−	0.193347i
$964$	58.8897			1.89671
$965$	−13.5000	+	7.79423i	−0.434580	+	0.250905i
$966$	−32.3205	+	2.32051i	−1.03990	+	0.0746611i
$967$	12.9904	+	7.50000i	0.417742	+	0.241184i	0.694111	−	0.719868i	$-0.255798\pi$
$967$	12.9904	+	7.50000i	0.417742	+	0.241184i	−0.276368	+	0.961052i	$0.589131\pi$
$968$	−27.3205	+	7.32051i	−0.878114	+	0.235290i
$969$		−	41.5692i		−	1.33540i
$970$	12.2942	+	3.29423i	0.394744	+	0.105771i
$971$	3.46410			0.111168			0.0555842	−	0.998454i	$-0.482298\pi$
$971$	3.46410			0.111168			0.0555842	+	0.998454i	$0.482298\pi$
$972$	−27.0000	−	15.5885i	−0.866025	−	0.500000i
$973$	−7.50000	−	21.6506i	−0.240439	−	0.694087i
$974$	3.66025	−	13.6603i	0.117282	−	0.437703i
$975$		−	6.00000i		−	0.192154i
$976$	18.0000	+	10.3923i	0.576166	+	0.332650i
$977$	2.50000	−	4.33013i	0.0799821	−	0.138533i	−0.823260	−	0.567665i	$-0.807847\pi$
$977$	2.50000	−	4.33013i	0.0799821	−	0.138533i	0.903242	+	0.429132i	$0.141180\pi$
$978$	3.80385	−	14.1962i	0.121634	−	0.453943i
$979$	8.66025	+	15.0000i	0.276783	+	0.479402i
$980$	19.0526	−	15.0000i	0.608612	−	0.479157i
$981$	36.0000			1.14939
$982$	−19.0000	−	19.0000i	−0.606314	−	0.606314i
$983$	−0.866025	−	1.50000i	−0.0276219	−	0.0478426i	0.851884	−	0.523731i	$-0.175460\pi$
$983$	−0.866025	−	1.50000i	−0.0276219	−	0.0478426i	−0.879506	+	0.475888i	$0.842127\pi$
$984$	10.9808	+	40.9808i	0.350054	+	1.30642i
$985$	3.00000	+	1.73205i	0.0955879	+	0.0551877i
$986$	23.6603	−	6.33975i	0.753496	−	0.201899i
$987$	−23.3827	−	4.50000i	−0.744279	−	0.143237i
$988$	−12.0000	−	20.7846i	−0.381771	−	0.661247i
$989$	5.00000			0.158991
$990$	7.09808	+	1.90192i	0.225592	+	0.0604471i
$991$			34.0000i			1.08005i	0.841650	+	0.540023i	$0.181584\pi$
$991$			34.0000i			1.08005i	−0.841650	+	0.540023i	$0.818416\pi$
$992$	47.3205	+	12.6795i	1.50243	+	0.402574i
$993$	−43.5000	+	25.1147i	−1.38043	+	0.796992i
$994$	8.39230	+	12.3923i	0.266188	+	0.393060i
$995$	−25.9808	−	15.0000i	−0.823646	−	0.475532i
$996$		−	6.00000i		−	0.190117i
$997$	−22.5000	+	12.9904i	−0.712582	+	0.411409i	−0.812016	−	0.583635i	$-0.801630\pi$
$997$	−22.5000	+	12.9904i	−0.712582	+	0.411409i	0.0994342	+	0.995044i	$0.468297\pi$
$998$	−7.00000	−	7.00000i	−0.221581	−	0.221581i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bi.b.139.2	yes	4
3.2	odd	2		756.2.bi.a.307.1		4
4.3	odd	2	inner	252.2.bi.b.139.1	yes	4
7.6	odd	2		252.2.bi.a.139.2	yes	4
9.2	odd	6		756.2.bi.b.559.2		4
9.7	even	3		252.2.bi.a.223.1	yes	4
12.11	even	2		756.2.bi.a.307.2		4
21.20	even	2		756.2.bi.b.307.1		4
28.27	even	2		252.2.bi.a.139.1	✓	4
36.7	odd	6		252.2.bi.a.223.2	yes	4
36.11	even	6		756.2.bi.b.559.1		4
63.20	even	6		756.2.bi.a.559.2		4
63.34	odd	6	inner	252.2.bi.b.223.1	yes	4
84.83	odd	2		756.2.bi.b.307.2		4
252.83	odd	6		756.2.bi.a.559.1		4
252.223	even	6	inner	252.2.bi.b.223.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.a.139.1	✓	4	28.27	even	2
252.2.bi.a.139.2	yes	4	7.6	odd	2
252.2.bi.a.223.1	yes	4	9.7	even	3
252.2.bi.a.223.2	yes	4	36.7	odd	6
252.2.bi.b.139.1	yes	4	4.3	odd	2	inner
252.2.bi.b.139.2	yes	4	1.1	even	1	trivial
252.2.bi.b.223.1	yes	4	63.34	odd	6	inner
252.2.bi.b.223.2	yes	4	252.223	even	6	inner
756.2.bi.a.307.1		4	3.2	odd	2
756.2.bi.a.307.2		4	12.11	even	2
756.2.bi.a.559.1		4	252.83	odd	6
756.2.bi.a.559.2		4	63.20	even	6
756.2.bi.b.307.1		4	21.20	even	2
756.2.bi.b.307.2		4	84.83	odd	2
756.2.bi.b.559.1		4	36.11	even	6
756.2.bi.b.559.2		4	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} -1.73205 q^{3} +(1.73205 + 1.00000i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(1.36603 + 0.366025i) q^{2} -1.73205 q^{3} +(1.73205 + 1.00000i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-2.36603 - 0.633975i) q^{6} +(-1.73205 + 2.00000i) q^{7} +(2.00000 + 2.00000i) q^{8} +3.00000 q^{9} +(1.73205 + 1.73205i) q^{10} +(0.866025 - 0.500000i) q^{11} +(-3.00000 - 1.73205i) q^{12} +(-1.50000 - 0.866025i) q^{13} +(-3.09808 + 2.09808i) q^{14} +(-2.59808 - 1.50000i) q^{15} +(2.00000 + 3.46410i) q^{16} +3.46410i q^{17} +(4.09808 + 1.09808i) q^{18} +6.92820 q^{19} +(1.73205 + 3.00000i) q^{20} +(3.00000 - 3.46410i) q^{21} +(1.36603 - 0.366025i) q^{22} +(-4.33013 - 2.50000i) q^{23} +(-3.46410 - 3.46410i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(-1.73205 - 1.73205i) q^{26} -5.19615 q^{27} +(-5.00000 + 1.73205i) q^{28} +(-2.50000 - 4.33013i) q^{29} +(-3.00000 - 3.00000i) q^{30} +(4.33013 - 7.50000i) q^{31} +(1.46410 + 5.46410i) q^{32} +(-1.50000 + 0.866025i) q^{33} +(-1.26795 + 4.73205i) q^{34} +(-4.33013 + 1.50000i) q^{35} +(5.19615 + 3.00000i) q^{36} +(9.46410 + 2.53590i) q^{38} +(2.59808 + 1.50000i) q^{39} +(1.26795 + 4.73205i) q^{40} +(-7.50000 - 4.33013i) q^{41} +(5.36603 - 3.63397i) q^{42} +(-0.866025 + 0.500000i) q^{43} +2.00000 q^{44} +(4.50000 + 2.59808i) q^{45} +(-5.00000 - 5.00000i) q^{46} +(-2.59808 - 4.50000i) q^{47} +(-3.46410 - 6.00000i) q^{48} +(-1.00000 - 6.92820i) q^{49} +(-0.732051 - 2.73205i) q^{50} -6.00000i q^{51} +(-1.73205 - 3.00000i) q^{52} +4.00000 q^{53} +(-7.09808 - 1.90192i) q^{54} +1.73205 q^{55} +(-7.46410 + 0.535898i) q^{56} -12.0000 q^{57} +(-1.83013 - 6.83013i) q^{58} +(-4.33013 + 7.50000i) q^{59} +(-3.00000 - 5.19615i) q^{60} +(4.50000 - 2.59808i) q^{61} +(8.66025 - 8.66025i) q^{62} +(-5.19615 + 6.00000i) q^{63} +8.00000i q^{64} +(-1.50000 - 2.59808i) q^{65} +(-2.36603 + 0.633975i) q^{66} +(12.9904 + 7.50000i) q^{67} +(-3.46410 + 6.00000i) q^{68} +(7.50000 + 4.33013i) q^{69} +(-6.46410 + 0.464102i) q^{70} -4.00000i q^{71} +(6.00000 + 6.00000i) q^{72} -10.3923i q^{73} +(1.73205 + 3.00000i) q^{75} +(12.0000 + 6.92820i) q^{76} +(-0.500000 + 2.59808i) q^{77} +(3.00000 + 3.00000i) q^{78} +(-2.59808 + 1.50000i) q^{79} +6.92820i q^{80} +9.00000 q^{81} +(-8.66025 - 8.66025i) q^{82} +(0.866025 + 1.50000i) q^{83} +(8.66025 - 3.00000i) q^{84} +(-3.00000 + 5.19615i) q^{85} +(-1.36603 + 0.366025i) q^{86} +(4.33013 + 7.50000i) q^{87} +(2.73205 + 0.732051i) q^{88} +17.3205i q^{89} +(5.19615 + 5.19615i) q^{90} +(4.33013 - 1.50000i) q^{91} +(-5.00000 - 8.66025i) q^{92} +(-7.50000 + 12.9904i) q^{93} +(-1.90192 - 7.09808i) q^{94} +(10.3923 + 6.00000i) q^{95} +(-2.53590 - 9.46410i) q^{96} +(4.50000 - 2.59808i) q^{97} +(1.16987 - 9.83013i) q^{98} +(2.59808 - 1.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 6 q^{5} - 6 q^{6} + 8 q^{8} + 12 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 6 * q^5 - 6 * q^6 + 8 * q^8 + 12 * q^9	\( 4 q + 2 q^{2} + 6 q^{5} - 6 q^{6} + 8 q^{8} + 12 q^{9} - 12 q^{12} - 6 q^{13} - 2 q^{14} + 8 q^{16} + 6 q^{18} + 12 q^{21} + 2 q^{22} - 4 q^{25} - 20 q^{28} - 10 q^{29} - 12 q^{30} - 8 q^{32} - 6 q^{33} - 12 q^{34} + 24 q^{38} + 12 q^{40} - 30 q^{41} + 18 q^{42} + 8 q^{44} + 18 q^{45} - 20 q^{46} - 4 q^{49} + 4 q^{50} + 16 q^{53} - 18 q^{54} - 16 q^{56} - 48 q^{57} + 10 q^{58} - 12 q^{60} + 18 q^{61} - 6 q^{65} - 6 q^{66} + 30 q^{69} - 12 q^{70} + 24 q^{72} + 48 q^{76} - 2 q^{77} + 12 q^{78} + 36 q^{81} - 12 q^{85} - 2 q^{86} + 4 q^{88} - 20 q^{92} - 30 q^{93} - 18 q^{94} - 24 q^{96} + 18 q^{97} + 22 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 6 * q^5 - 6 * q^6 + 8 * q^8 + 12 * q^9 - 12 * q^12 - 6 * q^13 - 2 * q^14 + 8 * q^16 + 6 * q^18 + 12 * q^21 + 2 * q^22 - 4 * q^25 - 20 * q^28 - 10 * q^29 - 12 * q^30 - 8 * q^32 - 6 * q^33 - 12 * q^34 + 24 * q^38 + 12 * q^40 - 30 * q^41 + 18 * q^42 + 8 * q^44 + 18 * q^45 - 20 * q^46 - 4 * q^49 + 4 * q^50 + 16 * q^53 - 18 * q^54 - 16 * q^56 - 48 * q^57 + 10 * q^58 - 12 * q^60 + 18 * q^61 - 6 * q^65 - 6 * q^66 + 30 * q^69 - 12 * q^70 + 24 * q^72 + 48 * q^76 - 2 * q^77 + 12 * q^78 + 36 * q^81 - 12 * q^85 - 2 * q^86 + 4 * q^88 - 20 * q^92 - 30 * q^93 - 18 * q^94 - 24 * q^96 + 18 * q^97 + 22 * q^98

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