LMFDB - Embedded newform 252.2.bj.a.115.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(103,252)]

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, 5]))

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

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

chi := DirichletCharacter("252.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bj (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:	$1$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	252.115
Dual form			252.2.bj.a.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(-0.866025 - 1.50000i) q^{3} -2.00000i q^{4} +(-3.00000 - 1.73205i) q^{5} +(2.36603 + 0.633975i) q^{6} +(2.59808 + 0.500000i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(-0.866025 - 1.50000i) q^{3} -2.00000i q^{4} +(-3.00000 - 1.73205i) q^{5} +(2.36603 + 0.633975i) q^{6} +(2.59808 + 0.500000i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(4.73205 - 1.26795i) q^{10} +(-1.73205 + 1.00000i) q^{11} +(-3.00000 + 1.73205i) q^{12} +(-4.50000 + 2.59808i) q^{13} +(-3.09808 + 2.09808i) q^{14} +6.00000i q^{15} -4.00000 q^{16} +(-4.50000 - 2.59808i) q^{17} +(-1.09808 - 4.09808i) q^{18} +(0.866025 + 1.50000i) q^{19} +(-3.46410 + 6.00000i) q^{20} +(-1.50000 - 4.33013i) q^{21} +(0.732051 - 2.73205i) q^{22} +(3.46410 + 2.00000i) q^{23} +(1.26795 - 4.73205i) q^{24} +(3.50000 + 6.06218i) q^{25} +(1.90192 - 7.09808i) q^{26} +5.19615 q^{27} +(1.00000 - 5.19615i) q^{28} +(-2.50000 + 4.33013i) q^{29} +(-6.00000 - 6.00000i) q^{30} -5.19615 q^{31} +(4.00000 - 4.00000i) q^{32} +(3.00000 + 1.73205i) q^{33} +(7.09808 - 1.90192i) q^{34} +(-6.92820 - 6.00000i) q^{35} +(5.19615 + 3.00000i) q^{36} +(-1.50000 - 2.59808i) q^{37} +(-2.36603 - 0.633975i) q^{38} +(7.79423 + 4.50000i) q^{39} +(-2.53590 - 9.46410i) q^{40} +(-1.50000 + 0.866025i) q^{41} +(5.83013 + 2.83013i) q^{42} +(-9.52628 - 5.50000i) q^{43} +(2.00000 + 3.46410i) q^{44} +(9.00000 - 5.19615i) q^{45} +(-5.46410 + 1.46410i) q^{46} -1.73205 q^{47} +(3.46410 + 6.00000i) q^{48} +(6.50000 + 2.59808i) q^{49} +(-9.56218 - 2.56218i) q^{50} +9.00000i q^{51} +(5.19615 + 9.00000i) q^{52} +(-0.500000 + 0.866025i) q^{53} +(-5.19615 + 5.19615i) q^{54} +6.92820 q^{55} +(4.19615 + 6.19615i) q^{56} +(1.50000 - 2.59808i) q^{57} +(-1.83013 - 6.83013i) q^{58} +1.73205 q^{59} +12.0000 q^{60} -5.19615i q^{61} +(5.19615 - 5.19615i) q^{62} +(-5.19615 + 6.00000i) q^{63} +8.00000i q^{64} +18.0000 q^{65} +(-4.73205 + 1.26795i) q^{66} -9.00000i q^{67} +(-5.19615 + 9.00000i) q^{68} -6.92820i q^{69} +(12.9282 - 0.928203i) q^{70} +2.00000i q^{71} +(-8.19615 + 2.19615i) q^{72} +(-10.5000 - 6.06218i) q^{73} +(4.09808 + 1.09808i) q^{74} +(6.06218 - 10.5000i) q^{75} +(3.00000 - 1.73205i) q^{76} +(-5.00000 + 1.73205i) q^{77} +(-12.2942 + 3.29423i) q^{78} +3.00000i q^{79} +(12.0000 + 6.92820i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(0.633975 - 2.36603i) q^{82} +(2.59808 - 4.50000i) q^{83} +(-8.66025 + 3.00000i) q^{84} +(9.00000 + 15.5885i) q^{85} +(15.0263 - 4.02628i) q^{86} +8.66025 q^{87} +(-5.46410 - 1.46410i) q^{88} +(7.50000 - 4.33013i) q^{89} +(-3.80385 + 14.1962i) q^{90} +(-12.9904 + 4.50000i) q^{91} +(4.00000 - 6.92820i) q^{92} +(4.50000 + 7.79423i) q^{93} +(1.73205 - 1.73205i) q^{94} -6.00000i q^{95} +(-9.46410 - 2.53590i) q^{96} +(-1.50000 - 0.866025i) q^{97} +(-9.09808 + 3.90192i) q^{98} -6.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 12 q^{5} + 6 q^{6} + 8 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 12 * q^5 + 6 * q^6 + 8 * q^8 - 6 * q^9	$ 4 q - 4 q^{2} - 12 q^{5} + 6 q^{6} + 8 q^{8} - 6 q^{9} + 12 q^{10} - 12 q^{12} - 18 q^{13} - 2 q^{14} - 16 q^{16} - 18 q^{17} + 6 q^{18} - 6 q^{21} - 4 q^{22} + 12 q^{24} + 14 q^{25} + 18 q^{26} + 4 q^{28} - 10 q^{29} - 24 q^{30} + 16 q^{32} + 12 q^{33} + 18 q^{34} - 6 q^{37} - 6 q^{38} - 24 q^{40} - 6 q^{41} + 6 q^{42} + 8 q^{44} + 36 q^{45} - 8 q^{46} + 26 q^{49} - 14 q^{50} - 2 q^{53} - 4 q^{56} + 6 q^{57} + 10 q^{58} + 48 q^{60} + 72 q^{65} - 12 q^{66} + 24 q^{70} - 12 q^{72} - 42 q^{73} + 6 q^{74} + 12 q^{76} - 20 q^{77} - 18 q^{78} + 48 q^{80} - 18 q^{81} + 6 q^{82} + 36 q^{85} + 22 q^{86} - 8 q^{88} + 30 q^{89} - 36 q^{90} + 16 q^{92} + 18 q^{93} - 24 q^{96} - 6 q^{97} - 26 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 12 * q^5 + 6 * q^6 + 8 * q^8 - 6 * q^9 + 12 * q^10 - 12 * q^12 - 18 * q^13 - 2 * q^14 - 16 * q^16 - 18 * q^17 + 6 * q^18 - 6 * q^21 - 4 * q^22 + 12 * q^24 + 14 * q^25 + 18 * q^26 + 4 * q^28 - 10 * q^29 - 24 * q^30 + 16 * q^32 + 12 * q^33 + 18 * q^34 - 6 * q^37 - 6 * q^38 - 24 * q^40 - 6 * q^41 + 6 * q^42 + 8 * q^44 + 36 * q^45 - 8 * q^46 + 26 * q^49 - 14 * q^50 - 2 * q^53 - 4 * q^56 + 6 * q^57 + 10 * q^58 + 48 * q^60 + 72 * q^65 - 12 * q^66 + 24 * q^70 - 12 * q^72 - 42 * q^73 + 6 * q^74 + 12 * q^76 - 20 * q^77 - 18 * q^78 + 48 * q^80 - 18 * q^81 + 6 * q^82 + 36 * q^85 + 22 * q^86 - 8 * q^88 + 30 * q^89 - 36 * q^90 + 16 * q^92 + 18 * q^93 - 24 * q^96 - 6 * q^97 - 26 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i
$3$	−0.866025	−	1.50000i	−0.500000	−	0.866025i
$4$		−	2.00000i		−	1.00000i
$5$	−3.00000	−	1.73205i	−1.34164	−	0.774597i	−0.354593	−	0.935021i	$-0.615380\pi$
$5$	−3.00000	−	1.73205i	−1.34164	−	0.774597i	−0.987048	+	0.160424i	$0.948714\pi$
$6$	2.36603	+	0.633975i	0.965926	+	0.258819i
$7$	2.59808	+	0.500000i	0.981981	+	0.188982i
$7$	2.59808	+	0.500000i	0.981981	+	0.188982i
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$10$	4.73205	−	1.26795i	1.49641	−	0.400961i
$11$	−1.73205	+	1.00000i	−0.522233	+	0.301511i	−0.737848	−	0.674967i	$-0.764158\pi$
$11$	−1.73205	+	1.00000i	−0.522233	+	0.301511i	0.215615	+	0.976478i	$0.430824\pi$
$12$	−3.00000	+	1.73205i	−0.866025	+	0.500000i
$13$	−4.50000	+	2.59808i	−1.24808	+	0.720577i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−4.50000	+	2.59808i	−1.24808	+	0.720577i	−0.277350	+	0.960769i	$0.589456\pi$
$14$	−3.09808	+	2.09808i	−0.827996	+	0.560734i
$15$			6.00000i			1.54919i
$16$	−4.00000			−1.00000
$17$	−4.50000	−	2.59808i	−1.09141	−	0.630126i	−0.157459	−	0.987526i	$-0.550330\pi$
$17$	−4.50000	−	2.59808i	−1.09141	−	0.630126i	−0.933952	+	0.357400i	$0.883663\pi$
$18$	−1.09808	−	4.09808i	−0.258819	−	0.965926i
$19$	0.866025	+	1.50000i	0.198680	+	0.344124i	0.948101	−	0.317970i	$-0.103001\pi$
$19$	0.866025	+	1.50000i	0.198680	+	0.344124i	−0.749421	+	0.662094i	$0.769668\pi$
$20$	−3.46410	+	6.00000i	−0.774597	+	1.34164i
$21$	−1.50000	−	4.33013i	−0.327327	−	0.944911i
$22$	0.732051	−	2.73205i	0.156074	−	0.582475i
$23$	3.46410	+	2.00000i	0.722315	+	0.417029i	0.815604	−	0.578610i	$-0.196405\pi$
$23$	3.46410	+	2.00000i	0.722315	+	0.417029i	−0.0932891	+	0.995639i	$0.529738\pi$
$24$	1.26795	−	4.73205i	0.258819	−	0.965926i
$25$	3.50000	+	6.06218i	0.700000	+	1.21244i
$26$	1.90192	−	7.09808i	0.372998	−	1.39205i
$27$	5.19615			1.00000
$28$	1.00000	−	5.19615i	0.188982	−	0.981981i
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	−0.999167	−	0.0408130i	$-0.987005\pi$
$29$	−2.50000	+	4.33013i	−0.464238	+	0.804084i	0.534928	+	0.844897i	$0.320339\pi$
$30$	−6.00000	−	6.00000i	−1.09545	−	1.09545i
$31$	−5.19615			−0.933257			−0.466628	−	0.884454i	$-0.654531\pi$
$31$	−5.19615			−0.933257			−0.466628	+	0.884454i	$0.654531\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$	3.00000	+	1.73205i	0.522233	+	0.301511i
$34$	7.09808	−	1.90192i	1.21731	−	0.326177i
$35$	−6.92820	−	6.00000i	−1.17108	−	1.01419i
$36$	5.19615	+	3.00000i	0.866025	+	0.500000i
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	0.715981	−	0.698119i	$-0.245980\pi$
$37$	−1.50000	−	2.59808i	−0.246598	−	0.427121i	−0.962580	+	0.270998i	$0.912646\pi$
$38$	−2.36603	−	0.633975i	−0.383820	−	0.102844i
$39$	7.79423	+	4.50000i	1.24808	+	0.720577i
$40$	−2.53590	−	9.46410i	−0.400961	−	1.49641i
$41$	−1.50000	+	0.866025i	−0.234261	+	0.135250i	−0.612536	−	0.790443i	$-0.709851\pi$
$41$	−1.50000	+	0.866025i	−0.234261	+	0.135250i	0.378275	+	0.925693i	$0.376517\pi$
$42$	5.83013	+	2.83013i	0.899608	+	0.436698i
$43$	−9.52628	−	5.50000i	−1.45274	−	0.838742i	−0.454108	−	0.890947i	$-0.650042\pi$
$43$	−9.52628	−	5.50000i	−1.45274	−	0.838742i	−0.998636	+	0.0522047i	$0.983375\pi$
$44$	2.00000	+	3.46410i	0.301511	+	0.522233i
$45$	9.00000	−	5.19615i	1.34164	−	0.774597i
$46$	−5.46410	+	1.46410i	−0.805638	+	0.215870i
$47$	−1.73205			−0.252646			−0.126323	−	0.991989i	$-0.540318\pi$
$47$	−1.73205			−0.252646			−0.126323	+	0.991989i	$0.540318\pi$
$48$	3.46410	+	6.00000i	0.500000	+	0.866025i
$49$	6.50000	+	2.59808i	0.928571	+	0.371154i
$50$	−9.56218	−	2.56218i	−1.35230	−	0.362347i
$51$			9.00000i			1.26025i
$52$	5.19615	+	9.00000i	0.720577	+	1.24808i
$53$	−0.500000	+	0.866025i	−0.0686803	+	0.118958i	−0.898321	−	0.439340i	$-0.855212\pi$
$53$	−0.500000	+	0.866025i	−0.0686803	+	0.118958i	0.829640	+	0.558298i	$0.188546\pi$
$54$	−5.19615	+	5.19615i	−0.707107	+	0.707107i
$55$	6.92820			0.934199
$56$	4.19615	+	6.19615i	0.560734	+	0.827996i
$57$	1.50000	−	2.59808i	0.198680	−	0.344124i
$58$	−1.83013	−	6.83013i	−0.240307	−	0.896840i
$59$	1.73205			0.225494			0.112747	−	0.993624i	$-0.464035\pi$
$59$	1.73205			0.225494			0.112747	+	0.993624i	$0.464035\pi$
$60$	12.0000			1.54919
$61$		−	5.19615i		−	0.665299i	−0.943051	−	0.332650i	$-0.892057\pi$
$61$		−	5.19615i		−	0.665299i	0.943051	−	0.332650i	$-0.107943\pi$
$62$	5.19615	−	5.19615i	0.659912	−	0.659912i
$63$	−5.19615	+	6.00000i	−0.654654	+	0.755929i
$64$			8.00000i			1.00000i
$65$	18.0000			2.23263
$66$	−4.73205	+	1.26795i	−0.582475	+	0.156074i
$67$		−	9.00000i		−	1.09952i	−0.835321	−	0.549762i	$-0.814718\pi$
$67$		−	9.00000i		−	1.09952i	0.835321	−	0.549762i	$-0.185282\pi$
$68$	−5.19615	+	9.00000i	−0.630126	+	1.09141i
$69$		−	6.92820i		−	0.834058i
$70$	12.9282	−	0.928203i	1.54522	−	0.110942i
$71$			2.00000i			0.237356i	0.992933	+	0.118678i	$0.0378657\pi$
$71$			2.00000i			0.237356i	−0.992933	+	0.118678i	$0.962134\pi$
$72$	−8.19615	+	2.19615i	−0.965926	+	0.258819i
$73$	−10.5000	−	6.06218i	−1.22893	−	0.709524i	−0.262126	−	0.965034i	$-0.584423\pi$
$73$	−10.5000	−	6.06218i	−1.22893	−	0.709524i	−0.966807	+	0.255510i	$0.917757\pi$
$74$	4.09808	+	1.09808i	0.476392	+	0.127649i
$75$	6.06218	−	10.5000i	0.700000	−	1.21244i
$76$	3.00000	−	1.73205i	0.344124	−	0.198680i
$77$	−5.00000	+	1.73205i	−0.569803	+	0.197386i
$78$	−12.2942	+	3.29423i	−1.39205	+	0.372998i
$79$			3.00000i			0.337526i	0.985657	+	0.168763i	$0.0539773\pi$
$79$			3.00000i			0.337526i	−0.985657	+	0.168763i	$0.946023\pi$
$80$	12.0000	+	6.92820i	1.34164	+	0.774597i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	0.633975	−	2.36603i	0.0700108	−	0.261284i
$83$	2.59808	−	4.50000i	0.285176	−	0.493939i	−0.687476	−	0.726207i	$-0.741281\pi$
$83$	2.59808	−	4.50000i	0.285176	−	0.493939i	0.972652	+	0.232268i	$0.0746146\pi$
$84$	−8.66025	+	3.00000i	−0.944911	+	0.327327i
$85$	9.00000	+	15.5885i	0.976187	+	1.69081i
$86$	15.0263	−	4.02628i	1.62033	−	0.434165i
$87$	8.66025			0.928477
$88$	−5.46410	−	1.46410i	−0.582475	−	0.156074i
$89$	7.50000	−	4.33013i	0.794998	−	0.458993i	−0.0467209	−	0.998908i	$-0.514877\pi$
$89$	7.50000	−	4.33013i	0.794998	−	0.458993i	0.841719	+	0.539915i	$0.181544\pi$
$90$	−3.80385	+	14.1962i	−0.400961	+	1.49641i
$91$	−12.9904	+	4.50000i	−1.36176	+	0.471728i
$92$	4.00000	−	6.92820i	0.417029	−	0.722315i
$93$	4.50000	+	7.79423i	0.466628	+	0.808224i
$94$	1.73205	−	1.73205i	0.178647	−	0.178647i
$95$		−	6.00000i		−	0.615587i
$96$	−9.46410	−	2.53590i	−0.965926	−	0.258819i
$97$	−1.50000	−	0.866025i	−0.152302	−	0.0879316i	0.421912	−	0.906637i	$-0.361359\pi$
$97$	−1.50000	−	0.866025i	−0.152302	−	0.0879316i	−0.574214	+	0.818705i	$0.694692\pi$
$98$	−9.09808	+	3.90192i	−0.919044	+	0.394154i
$99$		−	6.00000i		−	0.603023i
$100$	12.1244	−	7.00000i	1.21244	−	0.700000i
$101$	−15.0000	+	8.66025i	−1.49256	+	0.861727i	−0.999964	−	0.00853278i	$-0.997284\pi$
$101$	−15.0000	+	8.66025i	−1.49256	+	0.861727i	−0.492592	+	0.870260i	$0.663951\pi$
$102$	−9.00000	−	9.00000i	−0.891133	−	0.891133i
$103$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$103$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$104$	−14.1962	−	3.80385i	−1.39205	−	0.372998i
$105$	−3.00000	+	15.5885i	−0.292770	+	1.52128i
$106$	−0.366025	−	1.36603i	−0.0355515	−	0.132680i
$107$	6.06218	−	3.50000i	0.586053	−	0.338358i	−0.177482	−	0.984124i	$-0.556795\pi$
$107$	6.06218	−	3.50000i	0.586053	−	0.338358i	0.763535	+	0.645766i	$0.223462\pi$
$108$		−	10.3923i		−	1.00000i
$109$	−1.50000	+	2.59808i	−0.143674	+	0.248851i	−0.928877	−	0.370387i	$-0.879225\pi$
$109$	−1.50000	+	2.59808i	−0.143674	+	0.248851i	0.785203	+	0.619238i	$0.212558\pi$
$110$	−6.92820	+	6.92820i	−0.660578	+	0.660578i
$111$	−2.59808	+	4.50000i	−0.246598	+	0.427121i
$112$	−10.3923	−	2.00000i	−0.981981	−	0.188982i
$113$	−9.50000	−	16.4545i	−0.893685	−	1.54791i	−0.835424	−	0.549606i	$-0.814778\pi$
$113$	−9.50000	−	16.4545i	−0.893685	−	1.54791i	−0.0582609	−	0.998301i	$-0.518556\pi$
$114$	1.09808	+	4.09808i	0.102844	+	0.383820i
$115$	−6.92820	−	12.0000i	−0.646058	−	1.11901i
$116$	8.66025	+	5.00000i	0.804084	+	0.464238i
$117$		−	15.5885i		−	1.44115i
$118$	−1.73205	+	1.73205i	−0.159448	+	0.159448i
$119$	−10.3923	−	9.00000i	−0.952661	−	0.825029i
$120$	−12.0000	+	12.0000i	−1.09545	+	1.09545i
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$	5.19615	+	5.19615i	0.470438	+	0.470438i
$123$	2.59808	+	1.50000i	0.234261	+	0.135250i
$124$			10.3923i			0.933257i
$125$		−	6.92820i		−	0.619677i
$126$	−0.803848	−	11.1962i	−0.0716124	−	0.997433i
$127$			6.00000i			0.532414i	0.963916	+	0.266207i	$0.0857705\pi$
$127$			6.00000i			0.532414i	−0.963916	+	0.266207i	$0.914230\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$			19.0526i			1.67748i
$130$	−18.0000	+	18.0000i	−1.57870	+	1.57870i
$131$	6.92820	−	12.0000i	0.605320	−	1.04844i	−0.386681	−	0.922214i	$-0.626379\pi$
$131$	6.92820	−	12.0000i	0.605320	−	1.04844i	0.992001	−	0.126231i	$-0.0402882\pi$
$132$	3.46410	−	6.00000i	0.301511	−	0.522233i
$133$	1.50000	+	4.33013i	0.130066	+	0.375470i
$134$	9.00000	+	9.00000i	0.777482	+	0.777482i
$135$	−15.5885	−	9.00000i	−1.34164	−	0.774597i
$136$	−3.80385	−	14.1962i	−0.326177	−	1.21731i
$137$	−4.00000	−	6.92820i	−0.341743	−	0.591916i	0.643013	−	0.765855i	$-0.277684\pi$
$137$	−4.00000	−	6.92820i	−0.341743	−	0.591916i	−0.984757	+	0.173939i	$0.944351\pi$
$138$	6.92820	+	6.92820i	0.589768	+	0.589768i
$139$	11.2583	+	19.5000i	0.954919	+	1.65397i	0.734553	+	0.678551i	$0.237392\pi$
$139$	11.2583	+	19.5000i	0.954919	+	1.65397i	0.220366	+	0.975417i	$0.429275\pi$
$140$	−12.0000	+	13.8564i	−1.01419	+	1.17108i
$141$	1.50000	+	2.59808i	0.126323	+	0.218797i
$142$	−2.00000	−	2.00000i	−0.167836	−	0.167836i
$143$	5.19615	−	9.00000i	0.434524	−	0.752618i
$144$	6.00000	−	10.3923i	0.500000	−	0.866025i
$145$	15.0000	−	8.66025i	1.24568	−	0.719195i
$146$	16.5622	−	4.43782i	1.37070	−	0.367277i
$147$	−1.73205	−	12.0000i	−0.142857	−	0.989743i
$148$	−5.19615	+	3.00000i	−0.427121	+	0.246598i
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	−0.772399	−	0.635138i	$-0.780943\pi$
$149$	2.00000	−	3.46410i	0.163846	−	0.283790i	0.936245	+	0.351348i	$0.114277\pi$
$150$	4.43782	+	16.5622i	0.362347	+	1.35230i
$151$	−12.1244	+	7.00000i	−0.986666	+	0.569652i	−0.904276	−	0.426948i	$-0.859589\pi$
$151$	−12.1244	+	7.00000i	−0.986666	+	0.569652i	−0.0823900	+	0.996600i	$0.526255\pi$
$152$	−1.26795	+	4.73205i	−0.102844	+	0.383820i
$153$	13.5000	−	7.79423i	1.09141	−	0.630126i
$154$	3.26795	−	6.73205i	0.263339	−	0.542484i
$155$	15.5885	+	9.00000i	1.25210	+	0.722897i
$156$	9.00000	−	15.5885i	0.720577	−	1.24808i
$157$		−	12.1244i		−	0.967629i	−0.875171	−	0.483814i	$-0.839251\pi$
$157$		−	12.1244i		−	0.967629i	0.875171	−	0.483814i	$-0.160749\pi$
$158$	−3.00000	−	3.00000i	−0.238667	−	0.238667i
$159$	1.73205			0.137361
$160$	−18.9282	+	5.07180i	−1.49641	+	0.400961i
$161$	8.00000	+	6.92820i	0.630488	+	0.546019i
$162$	12.2942	+	3.29423i	0.965926	+	0.258819i
$163$	−7.79423	+	4.50000i	−0.610491	+	0.352467i	−0.773158	−	0.634214i	$-0.781324\pi$
$163$	−7.79423	+	4.50000i	−0.610491	+	0.352467i	0.162667	+	0.986681i	$0.447991\pi$
$164$	1.73205	+	3.00000i	0.135250	+	0.234261i
$165$	−6.00000	−	10.3923i	−0.467099	−	0.809040i
$166$	1.90192	+	7.09808i	0.147618	+	0.550918i
$167$	2.59808	+	4.50000i	0.201045	+	0.348220i	0.948865	−	0.315681i	$-0.102233\pi$
$167$	2.59808	+	4.50000i	0.201045	+	0.348220i	−0.747820	+	0.663901i	$0.768900\pi$
$168$	5.66025	−	11.6603i	0.436698	−	0.899608i
$169$	7.00000	−	12.1244i	0.538462	−	0.932643i
$170$	−24.5885	−	6.58846i	−1.88585	−	0.505312i
$171$	−5.19615			−0.397360
$172$	−11.0000	+	19.0526i	−0.838742	+	1.45274i
$173$			19.0526i			1.44854i	0.689517	+	0.724270i	$0.257823\pi$
$173$			19.0526i			1.44854i	−0.689517	+	0.724270i	$0.742177\pi$
$174$	−8.66025	+	8.66025i	−0.656532	+	0.656532i
$175$	6.06218	+	17.5000i	0.458258	+	1.32288i
$176$	6.92820	−	4.00000i	0.522233	−	0.301511i
$177$	−1.50000	−	2.59808i	−0.112747	−	0.195283i
$178$	−3.16987	+	11.8301i	−0.237592	+	0.886706i
$179$	−4.33013	−	2.50000i	−0.323649	−	0.186859i	0.329369	−	0.944201i	$-0.393164\pi$
$179$	−4.33013	−	2.50000i	−0.323649	−	0.186859i	−0.653018	+	0.757343i	$0.726497\pi$
$180$	−10.3923	−	18.0000i	−0.774597	−	1.34164i
$181$			17.3205i			1.28742i	0.765268	+	0.643712i	$0.222606\pi$
$181$			17.3205i			1.28742i	−0.765268	+	0.643712i	$0.777394\pi$
$182$	8.49038	−	17.4904i	0.629349	−	1.29647i
$183$	−7.79423	+	4.50000i	−0.576166	+	0.332650i
$184$	2.92820	+	10.9282i	0.215870	+	0.805638i
$185$			10.3923i			0.764057i
$186$	−12.2942	−	3.29423i	−0.901457	−	0.241545i
$187$	10.3923			0.759961
$188$			3.46410i			0.252646i
$189$	13.5000	+	2.59808i	0.981981	+	0.188982i
$190$	6.00000	+	6.00000i	0.435286	+	0.435286i
$191$			7.00000i			0.506502i	0.967401	+	0.253251i	$0.0814999\pi$
$191$			7.00000i			0.506502i	−0.967401	+	0.253251i	$0.918500\pi$
$192$	12.0000	−	6.92820i	0.866025	−	0.500000i
$193$	−9.00000			−0.647834			−0.323917	−	0.946085i	$-0.605000\pi$
$193$	−9.00000			−0.647834			−0.323917	+	0.946085i	$0.605000\pi$
$194$	2.36603	−	0.633975i	0.169871	−	0.0455167i
$195$	−15.5885	−	27.0000i	−1.11631	−	1.93351i
$196$	5.19615	−	13.0000i	0.371154	−	0.928571i
$197$	−10.0000			−0.712470			−0.356235	−	0.934396i	$-0.615940\pi$
$197$	−10.0000			−0.712470			−0.356235	+	0.934396i	$0.615940\pi$
$198$	6.00000	+	6.00000i	0.426401	+	0.426401i
$199$	0.866025	−	1.50000i	0.0613909	−	0.106332i	−0.833696	−	0.552223i	$-0.813780\pi$
$199$	0.866025	−	1.50000i	0.0613909	−	0.106332i	0.895087	+	0.445891i	$0.147113\pi$
$200$	−5.12436	+	19.1244i	−0.362347	+	1.35230i
$201$	−13.5000	+	7.79423i	−0.952217	+	0.549762i
$202$	6.33975	−	23.6603i	0.446063	−	1.66473i
$203$	−8.66025	+	10.0000i	−0.607831	+	0.701862i
$204$	18.0000			1.26025
$205$	6.00000			0.419058
$206$		0			0
$207$	−10.3923	+	6.00000i	−0.722315	+	0.417029i
$208$	18.0000	−	10.3923i	1.24808	−	0.720577i
$209$	−3.00000	−	1.73205i	−0.207514	−	0.119808i
$210$	−12.5885	−	18.5885i	−0.868686	−	1.28273i
$211$	21.6506	−	12.5000i	1.49049	−	0.860535i	0.490550	−	0.871413i	$-0.336796\pi$
$211$	21.6506	−	12.5000i	1.49049	−	0.860535i	0.999941	+	0.0108774i	$0.00346244\pi$
$212$	1.73205	+	1.00000i	0.118958	+	0.0686803i
$213$	3.00000	−	1.73205i	0.205557	−	0.118678i
$214$	−2.56218	+	9.56218i	−0.175147	+	0.653657i
$215$	19.0526	+	33.0000i	1.29937	+	2.25058i
$216$	10.3923	+	10.3923i	0.707107	+	0.707107i
$217$	−13.5000	−	2.59808i	−0.916440	−	0.176369i
$218$	−1.09808	−	4.09808i	−0.0743711	−	0.277557i
$219$			21.0000i			1.41905i
$220$		−	13.8564i		−	0.934199i
$221$	27.0000			1.81622
$222$	−1.90192	−	7.09808i	−0.127649	−	0.476392i
$223$	7.79423	−	13.5000i	0.521940	−	0.904027i	−0.477734	−	0.878504i	$-0.658542\pi$
$223$	7.79423	−	13.5000i	0.521940	−	0.904027i	0.999674	−	0.0255224i	$-0.00812491\pi$
$224$	12.3923	−	8.39230i	0.827996	−	0.560734i
$225$	−21.0000			−1.40000
$226$	25.9545	+	6.95448i	1.72647	+	0.462605i
$227$	3.46410	+	6.00000i	0.229920	+	0.398234i	0.957784	−	0.287488i	$-0.0928200\pi$
$227$	3.46410	+	6.00000i	0.229920	+	0.398234i	−0.727864	+	0.685722i	$0.759487\pi$
$228$	−5.19615	−	3.00000i	−0.344124	−	0.198680i
$229$	3.00000	+	1.73205i	0.198246	+	0.114457i	0.595837	−	0.803105i	$-0.296820\pi$
$229$	3.00000	+	1.73205i	0.198246	+	0.114457i	−0.397591	+	0.917563i	$0.630154\pi$
$230$	18.9282	+	5.07180i	1.24809	+	0.334424i
$231$	6.92820	+	6.00000i	0.455842	+	0.394771i
$232$	−13.6603	+	3.66025i	−0.896840	+	0.240307i
$233$	−0.500000	−	0.866025i	−0.0327561	−	0.0567352i	0.849183	−	0.528099i	$-0.177095\pi$
$233$	−0.500000	−	0.866025i	−0.0327561	−	0.0567352i	−0.881939	+	0.471364i	$0.843762\pi$
$234$	15.5885	+	15.5885i	1.01905	+	1.01905i
$235$	5.19615	+	3.00000i	0.338960	+	0.195698i
$236$		−	3.46410i		−	0.225494i
$237$	4.50000	−	2.59808i	0.292306	−	0.168763i
$238$	19.3923	−	1.39230i	1.25702	−	0.0902497i
$239$	−9.52628	+	5.50000i	−0.616204	+	0.355765i	−0.775390	−	0.631483i	$-0.782446\pi$
$239$	−9.52628	+	5.50000i	−0.616204	+	0.355765i	0.159186	+	0.987249i	$0.449113\pi$
$240$		−	24.0000i		−	1.54919i
$241$	−3.00000	+	1.73205i	−0.193247	+	0.111571i	−0.593502	−	0.804833i	$-0.702255\pi$
$241$	−3.00000	+	1.73205i	−0.193247	+	0.111571i	0.400255	+	0.916404i	$0.368922\pi$
$242$	−2.56218	−	9.56218i	−0.164703	−	0.614680i
$243$	−7.79423	+	13.5000i	−0.500000	+	0.866025i
$244$	−10.3923			−0.665299
$245$	−15.0000	−	19.0526i	−0.958315	−	1.21722i
$246$	−4.09808	+	1.09808i	−0.261284	+	0.0700108i
$247$	−7.79423	−	4.50000i	−0.495935	−	0.286328i
$248$	−10.3923	−	10.3923i	−0.659912	−	0.659912i
$249$	−9.00000			−0.570352
$250$	6.92820	+	6.92820i	0.438178	+	0.438178i
$251$	−3.46410			−0.218652			−0.109326	−	0.994006i	$-0.534869\pi$
$251$	−3.46410			−0.218652			−0.109326	+	0.994006i	$0.534869\pi$
$252$	12.0000	+	10.3923i	0.755929	+	0.654654i
$253$	−8.00000			−0.502956
$254$	−6.00000	−	6.00000i	−0.376473	−	0.376473i
$255$	15.5885	−	27.0000i	0.976187	−	1.69081i
$256$	16.0000			1.00000
$257$	−12.0000	−	6.92820i	−0.748539	−	0.432169i	0.0766265	−	0.997060i	$-0.475585\pi$
$257$	−12.0000	−	6.92820i	−0.748539	−	0.432169i	−0.825166	+	0.564890i	$0.808918\pi$
$258$	−19.0526	−	19.0526i	−1.18616	−	1.18616i
$259$	−2.59808	−	7.50000i	−0.161437	−	0.466027i
$260$		−	36.0000i		−	2.23263i
$261$	−7.50000	−	12.9904i	−0.464238	−	0.804084i
$262$	5.07180	+	18.9282i	0.313337	+	1.16939i
$263$	22.5167	−	13.0000i	1.38844	−	0.801614i	0.395298	−	0.918553i	$-0.370641\pi$
$263$	22.5167	−	13.0000i	1.38844	−	0.801614i	0.993139	+	0.116939i	$0.0373081\pi$
$264$	2.53590	+	9.46410i	0.156074	+	0.582475i
$265$	3.00000	−	1.73205i	0.184289	−	0.106399i
$266$	−5.83013	−	2.83013i	−0.357468	−	0.173526i
$267$	−12.9904	−	7.50000i	−0.794998	−	0.458993i
$268$	−18.0000			−1.09952
$269$	25.5000	+	14.7224i	1.55476	+	0.897643i	0.997743	+	0.0671428i	$0.0213883\pi$
$269$	25.5000	+	14.7224i	1.55476	+	0.897643i	0.557019	+	0.830500i	$0.311945\pi$
$270$	24.5885	−	6.58846i	1.49641	−	0.400961i
$271$	2.59808	+	4.50000i	0.157822	+	0.273356i	0.934083	−	0.357056i	$-0.116219\pi$
$271$	2.59808	+	4.50000i	0.157822	+	0.273356i	−0.776261	+	0.630412i	$0.782886\pi$
$272$	18.0000	+	10.3923i	1.09141	+	0.630126i
$273$	18.0000	+	15.5885i	1.08941	+	0.943456i
$274$	10.9282	+	2.92820i	0.660197	+	0.176899i
$275$	−12.1244	−	7.00000i	−0.731126	−	0.422116i
$276$	−13.8564			−0.834058
$277$	2.00000	+	3.46410i	0.120168	+	0.208138i	0.919834	−	0.392308i	$-0.128323\pi$
$277$	2.00000	+	3.46410i	0.120168	+	0.208138i	−0.799666	+	0.600446i	$0.794990\pi$
$278$	−30.7583	−	8.24167i	−1.84476	−	0.494303i
$279$	7.79423	−	13.5000i	0.466628	−	0.808224i
$280$	−1.85641	−	25.8564i	−0.110942	−	1.54522i
$281$	2.50000	−	4.33013i	0.149137	−	0.258314i	−0.781771	−	0.623565i	$-0.785684\pi$
$281$	2.50000	−	4.33013i	0.149137	−	0.258314i	0.930909	+	0.365251i	$0.119017\pi$
$282$	−4.09808	−	1.09808i	−0.244037	−	0.0653895i
$283$	8.66025			0.514799			0.257399	−	0.966305i	$-0.417134\pi$
$283$	8.66025			0.514799			0.257399	+	0.966305i	$0.417134\pi$
$284$	4.00000			0.237356
$285$	−9.00000	+	5.19615i	−0.533114	+	0.307794i
$286$	3.80385	+	14.1962i	0.224926	+	0.839436i
$287$	−4.33013	+	1.50000i	−0.255599	+	0.0885422i
$288$	4.39230	+	16.3923i	0.258819	+	0.965926i
$289$	5.00000	+	8.66025i	0.294118	+	0.509427i
$290$	−6.33975	+	23.6603i	−0.372283	+	1.38938i
$291$			3.00000i			0.175863i
$292$	−12.1244	+	21.0000i	−0.709524	+	1.22893i
$293$	−4.50000	+	2.59808i	−0.262893	+	0.151781i	−0.625653	−	0.780101i	$-0.715168\pi$
$293$	−4.50000	+	2.59808i	−0.262893	+	0.151781i	0.362761	+	0.931882i	$0.381834\pi$
$294$	13.7321	+	10.2679i	0.800869	+	0.598839i
$295$	−5.19615	−	3.00000i	−0.302532	−	0.174667i
$296$	2.19615	−	8.19615i	0.127649	−	0.476392i
$297$	−9.00000	+	5.19615i	−0.522233	+	0.301511i
$298$	1.46410	+	5.46410i	0.0848131	+	0.316527i
$299$	−20.7846			−1.20201
$300$	−21.0000	−	12.1244i	−1.21244	−	0.700000i
$301$	−22.0000	−	19.0526i	−1.26806	−	1.09817i
$302$	5.12436	−	19.1244i	0.294874	−	1.10048i
$303$	25.9808	+	15.0000i	1.49256	+	0.861727i
$304$	−3.46410	−	6.00000i	−0.198680	−	0.344124i
$305$	−9.00000	+	15.5885i	−0.515339	+	0.892592i
$306$	−5.70577	+	21.2942i	−0.326177	+	1.21731i
$307$	−17.3205			−0.988534			−0.494267	−	0.869310i	$-0.664563\pi$
$307$	−17.3205			−0.988534			−0.494267	+	0.869310i	$0.664563\pi$
$308$	3.46410	+	10.0000i	0.197386	+	0.569803i
$309$		0			0
$310$	−24.5885	+	6.58846i	−1.39653	+	0.374199i
$311$	−22.5167			−1.27680			−0.638401	−	0.769704i	$-0.720404\pi$
$311$	−22.5167			−1.27680			−0.638401	+	0.769704i	$0.720404\pi$
$312$	6.58846	+	24.5885i	0.372998	+	1.39205i
$313$		−	22.5167i		−	1.27272i	−0.771393	−	0.636358i	$-0.780440\pi$
$313$		−	22.5167i		−	1.27272i	0.771393	−	0.636358i	$-0.219560\pi$
$314$	12.1244	+	12.1244i	0.684217	+	0.684217i
$315$	25.9808	−	9.00000i	1.46385	−	0.507093i
$316$	6.00000			0.337526
$317$	19.0000			1.06715			0.533573	−	0.845754i	$-0.320849\pi$
$317$	19.0000			1.06715			0.533573	+	0.845754i	$0.320849\pi$
$318$	−1.73205	+	1.73205i	−0.0971286	+	0.0971286i
$319$		−	10.0000i		−	0.559893i
$320$	13.8564	−	24.0000i	0.774597	−	1.34164i
$321$	−10.5000	−	6.06218i	−0.586053	−	0.338358i
$322$	−14.9282	+	1.07180i	−0.831916	+	0.0597289i
$323$		−	9.00000i		−	0.500773i
$324$	−15.5885	+	9.00000i	−0.866025	+	0.500000i
$325$	−31.5000	−	18.1865i	−1.74731	−	1.00881i
$326$	3.29423	−	12.2942i	0.182450	−	0.680914i
$327$	5.19615			0.287348
$328$	−4.73205	−	1.26795i	−0.261284	−	0.0700108i
$329$	−4.50000	−	0.866025i	−0.248093	−	0.0477455i
$330$	16.3923	+	4.39230i	0.902367	+	0.241788i
$331$		−	1.00000i		−	0.0549650i	−0.999622	−	0.0274825i	$-0.991251\pi$
$331$		−	1.00000i		−	0.0549650i	0.999622	−	0.0274825i	$-0.00874905\pi$
$332$	−9.00000	−	5.19615i	−0.493939	−	0.285176i
$333$	9.00000			0.493197
$334$	−7.09808	−	1.90192i	−0.388389	−	0.104069i
$335$	−15.5885	+	27.0000i	−0.851688	+	1.47517i
$336$	6.00000	+	17.3205i	0.327327	+	0.944911i
$337$	13.5000	+	23.3827i	0.735392	+	1.27374i	0.954551	+	0.298047i	$0.0963352\pi$
$337$	13.5000	+	23.3827i	0.735392	+	1.27374i	−0.219159	+	0.975689i	$0.570331\pi$
$338$	5.12436	+	19.1244i	0.278728	+	1.04023i
$339$	−16.4545	+	28.5000i	−0.893685	+	1.54791i
$340$	31.1769	−	18.0000i	1.69081	−	0.976187i
$341$	9.00000	−	5.19615i	0.487377	−	0.281387i
$342$	5.19615	−	5.19615i	0.280976	−	0.280976i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$	−8.05256	−	30.0526i	−0.434165	−	1.62033i
$345$	−12.0000	+	20.7846i	−0.646058	+	1.11901i
$346$	−19.0526	−	19.0526i	−1.02427	−	1.02427i
$347$			29.0000i			1.55680i	0.627768	+	0.778401i	$0.283969\pi$
$347$			29.0000i			1.55680i	−0.627768	+	0.778401i	$0.716031\pi$
$348$		−	17.3205i		−	0.928477i
$349$	−13.5000	−	7.79423i	−0.722638	−	0.417215i	0.0930846	−	0.995658i	$-0.470327\pi$
$349$	−13.5000	−	7.79423i	−0.722638	−	0.417215i	−0.815723	+	0.578443i	$0.803661\pi$
$350$	−23.5622	−	11.4378i	−1.25945	−	0.611377i
$351$	−23.3827	+	13.5000i	−1.24808	+	0.720577i
$352$	−2.92820	+	10.9282i	−0.156074	+	0.582475i
$353$	9.00000	−	5.19615i	0.479022	−	0.276563i	−0.240987	−	0.970528i	$-0.577471\pi$
$353$	9.00000	−	5.19615i	0.479022	−	0.276563i	0.720009	+	0.693965i	$0.244138\pi$
$354$	4.09808	+	1.09808i	0.217810	+	0.0583621i
$355$	3.46410	−	6.00000i	0.183855	−	0.318447i
$356$	−8.66025	−	15.0000i	−0.458993	−	0.794998i
$357$	−4.50000	+	23.3827i	−0.238165	+	1.23754i
$358$	6.83013	−	1.83013i	0.360983	−	0.0967252i
$359$	−14.7224	+	8.50000i	−0.777020	+	0.448613i	−0.835373	−	0.549683i	$-0.814748\pi$
$359$	−14.7224	+	8.50000i	−0.777020	+	0.448613i	0.0583530	+	0.998296i	$0.481415\pi$
$360$	28.3923	+	7.60770i	1.49641	+	0.400961i
$361$	8.00000	−	13.8564i	0.421053	−	0.729285i
$362$	−17.3205	−	17.3205i	−0.910346	−	0.910346i
$363$	12.1244			0.636364
$364$	9.00000	+	25.9808i	0.471728	+	1.36176i
$365$	21.0000	+	36.3731i	1.09919	+	1.90385i
$366$	3.29423	−	12.2942i	0.172192	−	0.642630i
$367$	17.3205	+	30.0000i	0.904123	+	1.56599i	0.822090	+	0.569358i	$0.192808\pi$
$367$	17.3205	+	30.0000i	0.904123	+	1.56599i	0.0820332	+	0.996630i	$0.473859\pi$
$368$	−13.8564	−	8.00000i	−0.722315	−	0.417029i
$369$		−	5.19615i		−	0.270501i
$370$	−10.3923	−	10.3923i	−0.540270	−	0.540270i
$371$	−1.73205	+	2.00000i	−0.0899236	+	0.103835i
$372$	15.5885	−	9.00000i	0.808224	−	0.466628i
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	−0.303902	−	0.952703i	$-0.598289\pi$
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	0.977016	−	0.213165i	$-0.0683772\pi$
$374$	−10.3923	+	10.3923i	−0.537373	+	0.537373i
$375$	−10.3923	+	6.00000i	−0.536656	+	0.309839i
$376$	−3.46410	−	3.46410i	−0.178647	−	0.178647i
$377$		−	25.9808i		−	1.33808i
$378$	−16.0981	+	10.9019i	−0.827996	+	0.560734i
$379$		−	14.0000i		−	0.719132i	−0.933120	−	0.359566i	$-0.882925\pi$
$379$		−	14.0000i		−	0.719132i	0.933120	−	0.359566i	$-0.117075\pi$
$380$	−12.0000			−0.615587
$381$	9.00000	−	5.19615i	0.461084	−	0.266207i
$382$	−7.00000	−	7.00000i	−0.358151	−	0.358151i
$383$	3.46410	−	6.00000i	0.177007	−	0.306586i	−0.763847	−	0.645398i	$-0.776692\pi$
$383$	3.46410	−	6.00000i	0.177007	−	0.306586i	0.940854	+	0.338812i	$0.110025\pi$
$384$	−5.07180	+	18.9282i	−0.258819	+	0.965926i
$385$	18.0000	+	3.46410i	0.917365	+	0.176547i
$386$	9.00000	−	9.00000i	0.458088	−	0.458088i
$387$	28.5788	−	16.5000i	1.45274	−	0.838742i
$388$	−1.73205	+	3.00000i	−0.0879316	+	0.152302i
$389$	16.0000	+	27.7128i	0.811232	+	1.40510i	0.912002	+	0.410186i	$0.134536\pi$
$389$	16.0000	+	27.7128i	0.811232	+	1.40510i	−0.100770	+	0.994910i	$0.532131\pi$
$390$	42.5885	+	11.4115i	2.15655	+	0.577846i
$391$	−10.3923	−	18.0000i	−0.525561	−	0.910299i
$392$	7.80385	+	18.1962i	0.394154	+	0.919044i
$393$	−24.0000			−1.21064
$394$	10.0000	−	10.0000i	0.503793	−	0.503793i
$395$	5.19615	−	9.00000i	0.261447	−	0.452839i
$396$	−12.0000			−0.603023
$397$	−16.5000	+	9.52628i	−0.828111	+	0.478110i	−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−16.5000	+	9.52628i	−0.828111	+	0.478110i	0.0250943	+	0.999685i	$0.492011\pi$
$398$	0.633975	+	2.36603i	0.0317783	+	0.118598i
$399$	5.19615	−	6.00000i	0.260133	−	0.300376i
$400$	−14.0000	−	24.2487i	−0.700000	−	1.21244i
$401$	−4.00000	+	6.92820i	−0.199750	+	0.345978i	−0.948447	−	0.316934i	$-0.897346\pi$
$401$	−4.00000	+	6.92820i	−0.199750	+	0.345978i	0.748697	+	0.662912i	$0.230680\pi$
$402$	5.70577	−	21.2942i	0.284578	−	1.06206i
$403$	23.3827	−	13.5000i	1.16477	−	0.672483i
$404$	17.3205	+	30.0000i	0.861727	+	1.49256i
$405$			31.1769i			1.54919i
$406$	−1.33975	−	18.6603i	−0.0664905	−	0.926093i
$407$	5.19615	+	3.00000i	0.257564	+	0.148704i
$408$	−18.0000	+	18.0000i	−0.891133	+	0.891133i
$409$			15.5885i			0.770800i	0.922750	+	0.385400i	$0.125936\pi$
$409$			15.5885i			0.770800i	−0.922750	+	0.385400i	$0.874064\pi$
$410$	−6.00000	+	6.00000i	−0.296319	+	0.296319i
$411$	−6.92820	+	12.0000i	−0.341743	+	0.591916i
$412$		0			0
$413$	4.50000	+	0.866025i	0.221431	+	0.0426143i
$414$	4.39230	−	16.3923i	0.215870	−	0.805638i
$415$	−15.5885	+	9.00000i	−0.765207	+	0.441793i
$416$	−7.60770	+	28.3923i	−0.372998	+	1.39205i
$417$	19.5000	−	33.7750i	0.954919	−	1.65397i
$418$	4.73205	−	1.26795i	0.231452	−	0.0620174i
$419$	−7.79423	−	13.5000i	−0.380773	−	0.659518i	0.610400	−	0.792093i	$-0.291009\pi$
$419$	−7.79423	−	13.5000i	−0.380773	−	0.659518i	−0.991173	+	0.132575i	$0.957675\pi$
$420$	31.1769	+	6.00000i	1.52128	+	0.292770i
$421$	11.5000	−	19.9186i	0.560476	−	0.970772i	−0.436979	−	0.899472i	$-0.643952\pi$
$421$	11.5000	−	19.9186i	0.560476	−	0.970772i	0.997455	−	0.0713008i	$-0.0227150\pi$
$422$	−9.15064	+	34.1506i	−0.445446	+	1.66243i
$423$	2.59808	−	4.50000i	0.126323	−	0.218797i
$424$	−2.73205	+	0.732051i	−0.132680	+	0.0355515i
$425$		−	36.3731i		−	1.76435i
$426$	−1.26795	+	4.73205i	−0.0614323	+	0.229269i
$427$	2.59808	−	13.5000i	0.125730	−	0.653311i
$428$	−7.00000	−	12.1244i	−0.338358	−	0.586053i
$429$	−18.0000			−0.869048
$430$	−52.0526	−	13.9474i	−2.51020	−	0.672605i
$431$	4.33013	+	2.50000i	0.208575	+	0.120421i	0.600649	−	0.799513i	$-0.294909\pi$
$431$	4.33013	+	2.50000i	0.208575	+	0.120421i	−0.392074	+	0.919934i	$0.628242\pi$
$432$	−20.7846			−1.00000
$433$			27.7128i			1.33179i	0.746044	+	0.665896i	$0.231951\pi$
$433$			27.7128i			1.33179i	−0.746044	+	0.665896i	$0.768049\pi$
$434$	16.0981	−	10.9019i	0.772732	−	0.523309i
$435$	−25.9808	−	15.0000i	−1.24568	−	0.719195i
$436$	5.19615	+	3.00000i	0.248851	+	0.143674i
$437$			6.92820i			0.331421i
$438$	−21.0000	−	21.0000i	−1.00342	−	1.00342i
$439$	12.1244			0.578664			0.289332	−	0.957229i	$-0.406567\pi$
$439$	12.1244			0.578664			0.289332	+	0.957229i	$0.406567\pi$
$440$	13.8564	+	13.8564i	0.660578	+	0.660578i
$441$	−16.5000	+	12.9904i	−0.785714	+	0.618590i
$442$	−27.0000	+	27.0000i	−1.28426	+	1.28426i
$443$		−	31.0000i		−	1.47285i	−0.676517	−	0.736427i	$-0.736511\pi$
$443$		−	31.0000i		−	1.47285i	0.676517	−	0.736427i	$-0.263489\pi$
$444$	9.00000	+	5.19615i	0.427121	+	0.246598i
$445$	−30.0000			−1.42214
$446$	5.70577	+	21.2942i	0.270176	+	1.00831i
$447$	−6.92820			−0.327693
$448$	−4.00000	+	20.7846i	−0.188982	+	0.981981i
$449$	−26.0000			−1.22702			−0.613508	−	0.789689i	$-0.710242\pi$
$449$	−26.0000			−1.22702			−0.613508	+	0.789689i	$0.710242\pi$
$450$	21.0000	−	21.0000i	0.989949	−	0.989949i
$451$	1.73205	−	3.00000i	0.0815591	−	0.141264i
$452$	−32.9090	+	19.0000i	−1.54791	+	0.893685i
$453$	21.0000	+	12.1244i	0.986666	+	0.569652i
$454$	−9.46410	−	2.53590i	−0.444172	−	0.119016i
$455$	46.7654	+	9.00000i	2.19239	+	0.421927i
$456$	8.19615	−	2.19615i	0.383820	−	0.102844i
$457$	3.00000			0.140334			0.0701670	−	0.997535i	$-0.477647\pi$
$457$	3.00000			0.140334			0.0701670	+	0.997535i	$0.477647\pi$
$458$	−4.73205	+	1.26795i	−0.221114	+	0.0592474i
$459$	−23.3827	−	13.5000i	−1.09141	−	0.630126i
$460$	−24.0000	+	13.8564i	−1.11901	+	0.646058i
$461$	−28.5000	−	16.4545i	−1.32738	−	0.766362i	−0.342484	−	0.939524i	$-0.611268\pi$
$461$	−28.5000	−	16.4545i	−1.32738	−	0.766362i	−0.984893	+	0.173162i	$0.944602\pi$
$462$	−12.9282	+	0.928203i	−0.601474	+	0.0431839i
$463$	28.5788	−	16.5000i	1.32817	−	0.766820i	0.343155	−	0.939279i	$-0.388505\pi$
$463$	28.5788	−	16.5000i	1.32817	−	0.766820i	0.985017	+	0.172459i	$0.0551712\pi$
$464$	10.0000	−	17.3205i	0.464238	−	0.804084i
$465$		−	31.1769i		−	1.44579i
$466$	1.36603	+	0.366025i	0.0632799	+	0.0169558i
$467$	−0.866025	−	1.50000i	−0.0400749	−	0.0694117i	0.845292	−	0.534304i	$-0.179426\pi$
$467$	−0.866025	−	1.50000i	−0.0400749	−	0.0694117i	−0.885367	+	0.464892i	$0.846093\pi$
$468$	−31.1769			−1.44115
$469$	4.50000	−	23.3827i	0.207791	−	1.07971i
$470$	−8.19615	+	2.19615i	−0.378060	+	0.101301i
$471$	−18.1865	+	10.5000i	−0.837991	+	0.483814i
$472$	3.46410	+	3.46410i	0.159448	+	0.159448i
$473$	22.0000			1.01156
$474$	−1.90192	+	7.09808i	−0.0873583	+	0.326025i
$475$	−6.06218	+	10.5000i	−0.278152	+	0.481773i
$476$	−18.0000	+	20.7846i	−0.825029	+	0.952661i
$477$	−1.50000	−	2.59808i	−0.0686803	−	0.118958i
$478$	4.02628	−	15.0263i	0.184158	−	0.687286i
$479$	−10.3923	−	18.0000i	−0.474837	−	0.822441i	0.524748	−	0.851258i	$-0.324159\pi$
$479$	−10.3923	−	18.0000i	−0.474837	−	0.822441i	−0.999585	+	0.0288165i	$0.990826\pi$
$480$	24.0000	+	24.0000i	1.09545	+	1.09545i
$481$	13.5000	+	7.79423i	0.615547	+	0.355386i
$482$	1.26795	−	4.73205i	0.0577535	−	0.215539i
$483$	3.46410	−	18.0000i	0.157622	−	0.819028i
$484$	12.1244	+	7.00000i	0.551107	+	0.318182i
$485$	3.00000	+	5.19615i	0.136223	+	0.235945i
$486$	−5.70577	−	21.2942i	−0.258819	−	0.965926i
$487$	−19.9186	−	11.5000i	−0.902597	−	0.521115i	−0.0245553	−	0.999698i	$-0.507817\pi$
$487$	−19.9186	−	11.5000i	−0.902597	−	0.521115i	−0.878042	+	0.478584i	$0.841150\pi$
$488$	10.3923	−	10.3923i	0.470438	−	0.470438i
$489$	13.5000	+	7.79423i	0.610491	+	0.352467i
$490$	34.0526	+	4.05256i	1.53834	+	0.183076i
$491$	16.4545	−	9.50000i	0.742580	−	0.428729i	−0.0804264	−	0.996761i	$-0.525628\pi$
$491$	16.4545	−	9.50000i	0.742580	−	0.428729i	0.823007	+	0.568032i	$0.192295\pi$
$492$	3.00000	−	5.19615i	0.135250	−	0.234261i
$493$	22.5000	−	12.9904i	1.01335	−	0.585057i
$494$	12.2942	−	3.29423i	0.553143	−	0.148214i
$495$	−10.3923	+	18.0000i	−0.467099	+	0.809040i
$496$	20.7846			0.933257
$497$	−1.00000	+	5.19615i	−0.0448561	+	0.233079i
$498$	9.00000	−	9.00000i	0.403300	−	0.403300i
$499$	1.73205	+	1.00000i	0.0775372	+	0.0447661i	0.538267	−	0.842774i	$-0.319079\pi$
$499$	1.73205	+	1.00000i	0.0775372	+	0.0447661i	−0.460730	+	0.887540i	$0.652412\pi$
$500$	−13.8564			−0.619677
$501$	4.50000	−	7.79423i	0.201045	−	0.348220i
$502$	3.46410	−	3.46410i	0.154610	−	0.154610i
$503$	−41.5692			−1.85348			−0.926740	−	0.375703i	$-0.877401\pi$
$503$	−41.5692			−1.85348			−0.926740	+	0.375703i	$0.877401\pi$
$504$	−22.3923	+	1.60770i	−0.997433	+	0.0716124i
$505$	60.0000			2.66996
$506$	8.00000	−	8.00000i	0.355643	−	0.355643i
$507$	−24.2487			−1.07692
$508$	12.0000			0.532414
$509$	6.00000	+	3.46410i	0.265945	+	0.153544i	0.627044	−	0.778984i	$-0.284265\pi$
$509$	6.00000	+	3.46410i	0.265945	+	0.153544i	−0.361098	+	0.932528i	$0.617598\pi$
$510$	11.4115	+	42.5885i	0.505312	+	1.88585i
$511$	−24.2487	−	21.0000i	−1.07270	−	0.928985i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	4.50000	+	7.79423i	0.198680	+	0.344124i
$514$	18.9282	−	5.07180i	0.834887	−	0.223707i
$515$		0			0
$516$	38.1051			1.67748
$517$	3.00000	−	1.73205i	0.131940	−	0.0761755i
$518$	10.0981	+	4.90192i	0.443684	+	0.215378i
$519$	28.5788	−	16.5000i	1.25447	−	0.724270i
$520$	36.0000	+	36.0000i	1.57870	+	1.57870i
$521$	−19.5000	−	11.2583i	−0.854311	−	0.493236i	0.00779240	−	0.999970i	$-0.497520\pi$
$521$	−19.5000	−	11.2583i	−0.854311	−	0.493236i	−0.862103	+	0.506733i	$0.830853\pi$
$522$	20.4904	+	5.49038i	0.896840	+	0.240307i
$523$	−16.4545	−	28.5000i	−0.719504	−	1.24622i	−0.961196	−	0.275865i	$-0.911036\pi$
$523$	−16.4545	−	28.5000i	−0.719504	−	1.24622i	0.241692	−	0.970353i	$-0.422298\pi$
$524$	−24.0000	−	13.8564i	−1.04844	−	0.605320i
$525$	21.0000	−	24.2487i	0.916515	−	1.05830i
$526$	−9.51666	+	35.5167i	−0.414946	+	1.54860i
$527$	23.3827	+	13.5000i	1.01857	+	0.588069i
$528$	−12.0000	−	6.92820i	−0.522233	−	0.301511i
$529$	−3.50000	−	6.06218i	−0.152174	−	0.263573i
$530$	−1.26795	+	4.73205i	−0.0550762	+	0.205547i
$531$	−2.59808	+	4.50000i	−0.112747	+	0.195283i
$532$	8.66025	−	3.00000i	0.375470	−	0.130066i
$533$	4.50000	−	7.79423i	0.194917	−	0.337606i
$534$	20.4904	−	5.49038i	0.886706	−	0.237592i
$535$	−24.2487			−1.04836
$536$	18.0000	−	18.0000i	0.777482	−	0.777482i
$537$			8.66025i			0.373718i
$538$	−40.2224	+	10.7776i	−1.73411	+	0.464654i
$539$	−13.8564	+	2.00000i	−0.596838	+	0.0861461i
$540$	−18.0000	+	31.1769i	−0.774597	+	1.34164i
$541$	−20.5000	−	35.5070i	−0.881364	−	1.52657i	−0.849825	−	0.527064i	$-0.823293\pi$
$541$	−20.5000	−	35.5070i	−0.881364	−	1.52657i	−0.0315385	−	0.999503i	$-0.510041\pi$
$542$	−7.09808	−	1.90192i	−0.304888	−	0.0816946i
$543$	25.9808	−	15.0000i	1.11494	−	0.643712i
$544$	−28.3923	+	7.60770i	−1.21731	+	0.326177i
$545$	9.00000	−	5.19615i	0.385518	−	0.222579i
$546$	−33.5885	+	2.41154i	−1.43745	+	0.103205i
$547$	2.59808	+	1.50000i	0.111086	+	0.0641354i	0.554513	−	0.832175i	$-0.312904\pi$
$547$	2.59808	+	1.50000i	0.111086	+	0.0641354i	−0.443428	+	0.896310i	$0.646238\pi$
$548$	−13.8564	+	8.00000i	−0.591916	+	0.341743i
$549$	13.5000	+	7.79423i	0.576166	+	0.332650i
$550$	19.1244	−	5.12436i	0.815465	−	0.218503i
$551$	−8.66025			−0.368939
$552$	13.8564	−	13.8564i	0.589768	−	0.589768i
$553$	−1.50000	+	7.79423i	−0.0637865	+	0.331444i
$554$	−5.46410	−	1.46410i	−0.232147	−	0.0622037i
$555$	15.5885	−	9.00000i	0.661693	−	0.382029i
$556$	39.0000	−	22.5167i	1.65397	−	0.954919i
$557$	−2.50000	+	4.33013i	−0.105928	+	0.183473i	−0.914117	−	0.405450i	$-0.867115\pi$
$557$	−2.50000	+	4.33013i	−0.105928	+	0.183473i	0.808189	+	0.588924i	$0.200448\pi$
$558$	5.70577	+	21.2942i	0.241545	+	0.901457i
$559$	57.1577			2.41751
$560$	27.7128	+	24.0000i	1.17108	+	1.01419i
$561$	−9.00000	−	15.5885i	−0.379980	−	0.658145i
$562$	1.83013	+	6.83013i	0.0771992	+	0.288112i
$563$	−22.5167			−0.948964			−0.474482	−	0.880265i	$-0.657365\pi$
$563$	−22.5167			−0.948964			−0.474482	+	0.880265i	$0.657365\pi$
$564$	5.19615	−	3.00000i	0.218797	−	0.126323i
$565$			65.8179i			2.76898i
$566$	−8.66025	+	8.66025i	−0.364018	+	0.364018i
$567$	−7.79423	−	22.5000i	−0.327327	−	0.944911i
$568$	−4.00000	+	4.00000i	−0.167836	+	0.167836i
$569$	1.00000			0.0419222			0.0209611	−	0.999780i	$-0.493327\pi$
$569$	1.00000			0.0419222			0.0209611	+	0.999780i	$0.493327\pi$
$570$	3.80385	−	14.1962i	0.159326	−	0.594611i
$571$			27.0000i			1.12991i	0.825120	+	0.564957i	$0.191107\pi$
$571$			27.0000i			1.12991i	−0.825120	+	0.564957i	$0.808893\pi$
$572$	−18.0000	−	10.3923i	−0.752618	−	0.434524i
$573$	10.5000	−	6.06218i	0.438644	−	0.253251i
$574$	2.83013	−	5.83013i	0.118127	−	0.243345i
$575$			28.0000i			1.16768i
$576$	−20.7846	−	12.0000i	−0.866025	−	0.500000i
$577$	19.5000	+	11.2583i	0.811796	+	0.468690i	0.847579	−	0.530669i	$-0.178059\pi$
$577$	19.5000	+	11.2583i	0.811796	+	0.468690i	−0.0357834	+	0.999360i	$0.511393\pi$
$578$	−13.6603	−	3.66025i	−0.568192	−	0.152246i
$579$	7.79423	+	13.5000i	0.323917	+	0.561041i
$580$	−17.3205	−	30.0000i	−0.719195	−	1.24568i
$581$	9.00000	−	10.3923i	0.373383	−	0.431145i
$582$	−3.00000	−	3.00000i	−0.124354	−	0.124354i
$583$		−	2.00000i		−	0.0828315i
$584$	−8.87564	−	33.1244i	−0.367277	−	1.37070i
$585$	−27.0000	+	46.7654i	−1.11631	+	1.93351i
$586$	1.90192	−	7.09808i	0.0785677	−	0.293219i
$587$	−16.4545	+	28.5000i	−0.679149	+	1.17632i	0.296088	+	0.955161i	$0.404318\pi$
$587$	−16.4545	+	28.5000i	−0.679149	+	1.17632i	−0.975237	+	0.221160i	$0.929016\pi$
$588$	−24.0000	+	3.46410i	−0.989743	+	0.142857i
$589$	−4.50000	−	7.79423i	−0.185419	−	0.321156i
$590$	8.19615	−	2.19615i	0.337430	−	0.0904142i
$591$	8.66025	+	15.0000i	0.356235	+	0.617018i
$592$	6.00000	+	10.3923i	0.246598	+	0.427121i
$593$	−13.5000	+	7.79423i	−0.554379	+	0.320071i	−0.750886	−	0.660432i	$-0.770373\pi$
$593$	−13.5000	+	7.79423i	−0.554379	+	0.320071i	0.196508	+	0.980502i	$0.437040\pi$
$594$	3.80385	−	14.1962i	0.156074	−	0.582475i
$595$	15.5885	+	45.0000i	0.639064	+	1.84482i
$596$	−6.92820	−	4.00000i	−0.283790	−	0.163846i
$597$	−3.00000			−0.122782
$598$	20.7846	−	20.7846i	0.849946	−	0.849946i
$599$		−	23.0000i		−	0.939755i	−0.882732	−	0.469877i	$-0.844298\pi$
$599$		−	23.0000i		−	0.939755i	0.882732	−	0.469877i	$-0.155702\pi$
$600$	33.1244	−	8.87564i	1.35230	−	0.362347i
$601$	1.50000	+	0.866025i	0.0611863	+	0.0353259i	0.530281	−	0.847822i	$-0.322086\pi$
$601$	1.50000	+	0.866025i	0.0611863	+	0.0353259i	−0.469095	+	0.883148i	$0.655420\pi$
$602$	41.0526	−	2.94744i	1.67318	−	0.120129i
$603$	23.3827	+	13.5000i	0.952217	+	0.549762i
$604$	14.0000	+	24.2487i	0.569652	+	0.986666i
$605$	21.0000	−	12.1244i	0.853771	−	0.492925i
$606$	−40.9808	+	10.9808i	−1.66473	+	0.446063i
$607$	−13.8564	+	24.0000i	−0.562414	+	0.974130i	0.434871	+	0.900493i	$0.356794\pi$
$607$	−13.8564	+	24.0000i	−0.562414	+	0.974130i	−0.997285	+	0.0736371i	$0.976539\pi$
$608$	9.46410	+	2.53590i	0.383820	+	0.102844i
$609$	22.5000	+	4.33013i	0.911746	+	0.175466i
$610$	−6.58846	−	24.5885i	−0.266759	−	0.995558i
$611$	7.79423	−	4.50000i	0.315321	−	0.182051i
$612$	−15.5885	−	27.0000i	−0.630126	−	1.09141i
$613$	−5.50000	+	9.52628i	−0.222143	+	0.384763i	−0.955458	−	0.295126i	$-0.904638\pi$
$613$	−5.50000	+	9.52628i	−0.222143	+	0.384763i	0.733316	+	0.679888i	$0.237972\pi$
$614$	17.3205	−	17.3205i	0.698999	−	0.698999i
$615$	−5.19615	−	9.00000i	−0.209529	−	0.362915i
$616$	−13.4641	−	6.53590i	−0.542484	−	0.263339i
$617$	−6.50000	−	11.2583i	−0.261680	−	0.453243i	0.705008	−	0.709199i	$-0.250943\pi$
$617$	−6.50000	−	11.2583i	−0.261680	−	0.453243i	−0.966689	+	0.255956i	$0.917610\pi$
$618$		0			0
$619$	6.92820	+	12.0000i	0.278468	+	0.482321i	0.971004	−	0.239062i	$-0.0768400\pi$
$619$	6.92820	+	12.0000i	0.278468	+	0.482321i	−0.692536	+	0.721383i	$0.743507\pi$
$620$	18.0000	−	31.1769i	0.722897	−	1.25210i
$621$	18.0000	+	10.3923i	0.722315	+	0.417029i
$622$	22.5167	−	22.5167i	0.902836	−	0.902836i
$623$	21.6506	−	7.50000i	0.867414	−	0.300481i
$624$	−31.1769	−	18.0000i	−1.24808	−	0.720577i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	22.5167	+	22.5167i	0.899947	+	0.899947i
$627$			6.00000i			0.239617i
$628$	−24.2487			−0.967629
$629$			15.5885i			0.621552i
$630$	−16.9808	+	34.9808i	−0.676530	+	1.39367i
$631$		−	30.0000i		−	1.19428i	−0.802137	−	0.597141i	$-0.796303\pi$
$631$		−	30.0000i		−	1.19428i	0.802137	−	0.597141i	$-0.203697\pi$
$632$	−6.00000	+	6.00000i	−0.238667	+	0.238667i
$633$	−37.5000	−	21.6506i	−1.49049	−	0.860535i
$634$	−19.0000	+	19.0000i	−0.754586	+	0.754586i
$635$	10.3923	−	18.0000i	0.412406	−	0.714308i
$636$		−	3.46410i		−	0.137361i
$637$	−36.0000	+	5.19615i	−1.42637	+	0.205879i
$638$	10.0000	+	10.0000i	0.395904	+	0.395904i
$639$	−5.19615	−	3.00000i	−0.205557	−	0.118678i
$640$	10.1436	+	37.8564i	0.400961	+	1.49641i
$641$	−2.00000	−	3.46410i	−0.0789953	−	0.136824i	0.823821	−	0.566849i	$-0.191838\pi$
$641$	−2.00000	−	3.46410i	−0.0789953	−	0.136824i	−0.902817	+	0.430026i	$0.858505\pi$
$642$	16.5622	−	4.43782i	0.653657	−	0.175147i
$643$	7.79423	+	13.5000i	0.307374	+	0.532388i	0.977787	−	0.209600i	$-0.0672163\pi$
$643$	7.79423	+	13.5000i	0.307374	+	0.532388i	−0.670413	+	0.741988i	$0.733883\pi$
$644$	13.8564	−	16.0000i	0.546019	−	0.630488i
$645$	33.0000	−	57.1577i	1.29937	−	2.25058i
$646$	9.00000	+	9.00000i	0.354100	+	0.354100i
$647$	7.79423	−	13.5000i	0.306423	−	0.530740i	−0.671154	−	0.741318i	$-0.734201\pi$
$647$	7.79423	−	13.5000i	0.306423	−	0.530740i	0.977577	+	0.210578i	$0.0675346\pi$
$648$	6.58846	−	24.5885i	0.258819	−	0.965926i
$649$	−3.00000	+	1.73205i	−0.117760	+	0.0679889i
$650$	49.6865	−	13.3135i	1.94887	−	0.522197i
$651$	7.79423	+	22.5000i	0.305480	+	0.881845i
$652$	9.00000	+	15.5885i	0.352467	+	0.610491i
$653$	−13.0000	+	22.5167i	−0.508729	+	0.881145i	0.491220	+	0.871036i	$0.336551\pi$
$653$	−13.0000	+	22.5167i	−0.508729	+	0.881145i	−0.999949	+	0.0101092i	$0.996782\pi$
$654$	−5.19615	+	5.19615i	−0.203186	+	0.203186i
$655$	−41.5692	+	24.0000i	−1.62424	+	0.937758i
$656$	6.00000	−	3.46410i	0.234261	−	0.135250i
$657$	31.5000	−	18.1865i	1.22893	−	0.709524i
$658$	5.36603	−	3.63397i	0.209189	−	0.141667i
$659$	16.4545	+	9.50000i	0.640976	+	0.370067i	0.784990	−	0.619508i	$-0.212668\pi$
$659$	16.4545	+	9.50000i	0.640976	+	0.370067i	−0.144015	+	0.989576i	$0.546001\pi$
$660$	−20.7846	+	12.0000i	−0.809040	+	0.467099i
$661$			12.1244i			0.471583i	0.971804	+	0.235791i	$0.0757682\pi$
$661$			12.1244i			0.471583i	−0.971804	+	0.235791i	$0.924232\pi$
$662$	1.00000	+	1.00000i	0.0388661	+	0.0388661i
$663$	−23.3827	−	40.5000i	−0.908108	−	1.57289i
$664$	14.1962	−	3.80385i	0.550918	−	0.147618i
$665$	3.00000	−	15.5885i	0.116335	−	0.604494i
$666$	−9.00000	+	9.00000i	−0.348743	+	0.348743i
$667$	−17.3205	+	10.0000i	−0.670653	+	0.387202i
$668$	9.00000	−	5.19615i	0.348220	−	0.201045i
$669$	−27.0000			−1.04388
$670$	−11.4115	−	42.5885i	−0.440866	−	1.64534i
$671$	5.19615	+	9.00000i	0.200595	+	0.347441i
$672$	−23.3205	−	11.3205i	−0.899608	−	0.436698i
$673$	−19.5000	+	33.7750i	−0.751670	+	1.30193i	0.195343	+	0.980735i	$0.437418\pi$
$673$	−19.5000	+	33.7750i	−0.751670	+	1.30193i	−0.947013	+	0.321195i	$0.895915\pi$
$674$	−36.8827	−	9.88269i	−1.42067	−	0.380667i
$675$	18.1865	+	31.5000i	0.700000	+	1.21244i
$676$	−24.2487	−	14.0000i	−0.932643	−	0.538462i
$677$			22.5167i			0.865386i	0.901541	+	0.432693i	$0.142437\pi$
$677$			22.5167i			0.865386i	−0.901541	+	0.432693i	$0.857563\pi$
$678$	−12.0455	−	44.9545i	−0.462605	−	1.72647i
$679$	−3.46410	−	3.00000i	−0.132940	−	0.115129i
$680$	−13.1769	+	49.1769i	−0.505312	+	1.88585i
$681$	6.00000	−	10.3923i	0.229920	−	0.398234i
$682$	−3.80385	+	14.1962i	−0.145657	+	0.543599i
$683$	40.7032	+	23.5000i	1.55746	+	0.899203i	0.997499	+	0.0706868i	$0.0225191\pi$
$683$	40.7032	+	23.5000i	1.55746	+	0.899203i	0.559966	+	0.828516i	$0.310814\pi$
$684$			10.3923i			0.397360i
$685$			27.7128i			1.05885i
$686$	−25.5885	+	5.58846i	−0.976972	+	0.213368i
$687$		−	6.00000i		−	0.228914i
$688$	38.1051	+	22.0000i	1.45274	+	0.838742i
$689$		−	5.19615i		−	0.197958i
$690$	−8.78461	−	32.7846i	−0.334424	−	1.24809i
$691$	−29.4449			−1.12014			−0.560068	−	0.828447i	$-0.689225\pi$
$691$	−29.4449			−1.12014			−0.560068	+	0.828447i	$0.689225\pi$
$692$	38.1051			1.44854
$693$	3.00000	−	15.5885i	0.113961	−	0.592157i
$694$	−29.0000	−	29.0000i	−1.10082	−	1.10082i
$695$		−	78.0000i		−	2.95871i
$696$	17.3205	+	17.3205i	0.656532	+	0.656532i
$697$	9.00000			0.340899
$698$	21.2942	−	5.70577i	0.805998	−	0.215967i
$699$	−0.866025	+	1.50000i	−0.0327561	+	0.0567352i
$700$	35.0000	−	12.1244i	1.32288	−	0.458258i
$701$	−16.0000			−0.604312			−0.302156	−	0.953259i	$-0.597706\pi$
$701$	−16.0000			−0.604312			−0.302156	+	0.953259i	$0.597706\pi$
$702$	9.88269	−	36.8827i	0.372998	−	1.39205i
$703$	2.59808	−	4.50000i	0.0979883	−	0.169721i
$704$	−8.00000	−	13.8564i	−0.301511	−	0.522233i
$705$		−	10.3923i		−	0.391397i
$706$	−3.80385	+	14.1962i	−0.143160	+	0.534279i
$707$	−43.3013	+	15.0000i	−1.62851	+	0.564133i
$708$	−5.19615	+	3.00000i	−0.195283	+	0.112747i
$709$	−33.0000			−1.23934			−0.619671	−	0.784862i	$-0.712734\pi$
$709$	−33.0000			−1.23934			−0.619671	+	0.784862i	$0.712734\pi$
$710$	2.53590	+	9.46410i	0.0951706	+	0.355181i
$711$	−7.79423	−	4.50000i	−0.292306	−	0.168763i
$712$	23.6603	+	6.33975i	0.886706	+	0.237592i
$713$	−18.0000	−	10.3923i	−0.674105	−	0.389195i
$714$	−18.8827	−	27.8827i	−0.706667	−	1.04348i
$715$	−31.1769	+	18.0000i	−1.16595	+	0.673162i
$716$	−5.00000	+	8.66025i	−0.186859	+	0.323649i
$717$	16.5000	+	9.52628i	0.616204	+	0.355765i
$718$	6.22243	−	23.2224i	0.232219	−	0.866653i
$719$	−9.52628	−	16.5000i	−0.355270	−	0.615346i	0.631894	−	0.775055i	$-0.282278\pi$
$719$	−9.52628	−	16.5000i	−0.355270	−	0.615346i	−0.987164	+	0.159709i	$0.948944\pi$
$720$	−36.0000	+	20.7846i	−1.34164	+	0.774597i
$721$		0			0
$722$	5.85641	+	21.8564i	0.217953	+	0.813411i
$723$	5.19615	+	3.00000i	0.193247	+	0.111571i
$724$	34.6410			1.28742
$725$	−35.0000			−1.29987
$726$	−12.1244	+	12.1244i	−0.449977	+	0.449977i
$727$	4.33013	−	7.50000i	0.160596	−	0.278160i	−0.774487	−	0.632590i	$-0.781992\pi$
$727$	4.33013	−	7.50000i	0.160596	−	0.278160i	0.935082	+	0.354430i	$0.115325\pi$
$728$	−34.9808	−	16.9808i	−1.29647	−	0.629349i
$729$	27.0000			1.00000
$730$	−57.3731	−	15.3731i	−2.12347	−	0.568983i
$731$	28.5788	+	49.5000i	1.05703	+	1.83082i
$732$	9.00000	+	15.5885i	0.332650	+	0.576166i
$733$	−18.0000	−	10.3923i	−0.664845	−	0.383849i	0.129275	−	0.991609i	$-0.458735\pi$
$733$	−18.0000	−	10.3923i	−0.664845	−	0.383849i	−0.794121	+	0.607760i	$0.792068\pi$
$734$	−47.3205	−	12.6795i	−1.74663	−	0.468009i
$735$	−15.5885	+	39.0000i	−0.574989	+	1.43854i
$736$	21.8564	−	5.85641i	0.805638	−	0.215870i
$737$	9.00000	+	15.5885i	0.331519	+	0.574208i
$738$	5.19615	+	5.19615i	0.191273	+	0.191273i
$739$	44.1673	+	25.5000i	1.62472	+	0.938033i	0.985634	+	0.168898i	$0.0540208\pi$
$739$	44.1673	+	25.5000i	1.62472	+	0.938033i	0.639087	+	0.769135i	$0.279313\pi$
$740$	20.7846			0.764057
$741$			15.5885i			0.572656i
$742$	−0.267949	−	3.73205i	−0.00983672	−	0.137008i
$743$	−25.1147	+	14.5000i	−0.921370	+	0.531953i	−0.884072	−	0.467351i	$-0.845209\pi$
$743$	−25.1147	+	14.5000i	−0.921370	+	0.531953i	−0.0372984	+	0.999304i	$0.511875\pi$
$744$	−6.58846	+	24.5885i	−0.241545	+	0.901457i
$745$	−12.0000	+	6.92820i	−0.439646	+	0.253830i
$746$	9.51666	+	35.5167i	0.348430	+	1.30036i
$747$	7.79423	+	13.5000i	0.285176	+	0.493939i
$748$		−	20.7846i		−	0.759961i
$749$	17.5000	−	6.06218i	0.639436	−	0.221507i
$750$	4.39230	−	16.3923i	0.160384	−	0.598562i
$751$	−1.73205	−	1.00000i	−0.0632034	−	0.0364905i	0.468065	−	0.883694i	$-0.344951\pi$
$751$	−1.73205	−	1.00000i	−0.0632034	−	0.0364905i	−0.531269	+	0.847203i	$0.678285\pi$
$752$	6.92820			0.252646
$753$	3.00000	+	5.19615i	0.109326	+	0.189358i
$754$	25.9808	+	25.9808i	0.946164	+	0.946164i
$755$	48.4974			1.76500
$756$	5.19615	−	27.0000i	0.188982	−	0.981981i
$757$	−24.0000			−0.872295			−0.436147	−	0.899875i	$-0.643657\pi$
$757$	−24.0000			−0.872295			−0.436147	+	0.899875i	$0.643657\pi$
$758$	14.0000	+	14.0000i	0.508503	+	0.508503i
$759$	6.92820	+	12.0000i	0.251478	+	0.435572i
$760$	12.0000	−	12.0000i	0.435286	−	0.435286i
$761$	−9.00000	−	5.19615i	−0.326250	−	0.188360i	0.327925	−	0.944704i	$-0.393651\pi$
$761$	−9.00000	−	5.19615i	−0.326250	−	0.188360i	−0.654175	+	0.756343i	$0.726984\pi$
$762$	−3.80385	+	14.1962i	−0.137799	+	0.514272i
$763$	−5.19615	+	6.00000i	−0.188113	+	0.217215i
$764$	14.0000			0.506502
$765$	−54.0000			−1.95237
$766$	2.53590	+	9.46410i	0.0916257	+	0.341952i
$767$	−7.79423	+	4.50000i	−0.281433	+	0.162486i
$768$	−13.8564	−	24.0000i	−0.500000	−	0.866025i
$769$	7.50000	−	4.33013i	0.270457	−	0.156148i	−0.358638	−	0.933477i	$-0.616759\pi$
$769$	7.50000	−	4.33013i	0.270457	−	0.156148i	0.629095	+	0.777328i	$0.283426\pi$
$770$	−21.4641	+	14.5359i	−0.773513	+	0.523837i
$771$			24.0000i			0.864339i
$772$			18.0000i			0.647834i
$773$	1.50000	+	0.866025i	0.0539513	+	0.0311488i	0.526733	−	0.850031i	$-0.323417\pi$
$773$	1.50000	+	0.866025i	0.0539513	+	0.0311488i	−0.472782	+	0.881180i	$0.656750\pi$
$774$	−12.0788	+	45.0788i	−0.434165	+	1.62033i
$775$	−18.1865	−	31.5000i	−0.653280	−	1.13151i
$776$	−1.26795	−	4.73205i	−0.0455167	−	0.169871i
$777$	−9.00000	+	10.3923i	−0.322873	+	0.372822i
$778$	−43.7128	−	11.7128i	−1.56718	−	0.419925i
$779$	−2.59808	−	1.50000i	−0.0930857	−	0.0537431i
$780$	−54.0000	+	31.1769i	−1.93351	+	1.11631i
$781$	−2.00000	−	3.46410i	−0.0715656	−	0.123955i
$782$	28.3923	+	7.60770i	1.01531	+	0.272051i
$783$	−12.9904	+	22.5000i	−0.464238	+	0.804084i
$784$	−26.0000	−	10.3923i	−0.928571	−	0.371154i
$785$	−21.0000	+	36.3731i	−0.749522	+	1.29821i
$786$	24.0000	−	24.0000i	0.856052	−	0.856052i
$787$	−50.2295			−1.79049			−0.895244	−	0.445577i	$-0.852999\pi$
$787$	−50.2295			−1.79049			−0.895244	+	0.445577i	$0.852999\pi$
$788$			20.0000i			0.712470i
$789$	−39.0000	−	22.5167i	−1.38844	−	0.801614i
$790$	3.80385	+	14.1962i	0.135335	+	0.505076i
$791$	−16.4545	−	47.5000i	−0.585054	−	1.68891i
$792$	12.0000	−	12.0000i	0.426401	−	0.426401i
$793$	13.5000	+	23.3827i	0.479399	+	0.830344i
$794$	6.97372	−	26.0263i	0.247488	−	0.923638i
$795$	−5.19615	−	3.00000i	−0.184289	−	0.106399i
$796$	−3.00000	−	1.73205i	−0.106332	−	0.0613909i
$797$	22.5000	−	12.9904i	0.796991	−	0.460143i	−0.0454270	−	0.998968i	$-0.514465\pi$
$797$	22.5000	−	12.9904i	0.796991	−	0.460143i	0.842418	+	0.538825i	$0.181132\pi$
$798$	0.803848	+	11.1962i	0.0284559	+	0.396339i
$799$	7.79423	+	4.50000i	0.275740	+	0.159199i
$800$	38.2487	+	10.2487i	1.35230	+	0.362347i
$801$			25.9808i			0.917985i
$802$	−2.92820	−	10.9282i	−0.103398	−	0.385888i
$803$	24.2487			0.855718
$804$	15.5885	+	27.0000i	0.549762	+	0.952217i
$805$	−12.0000	−	34.6410i	−0.422944	−	1.22094i
$806$	−9.88269	+	36.8827i	−0.348103	+	1.29914i
$807$		−	51.0000i		−	1.79529i
$808$	−47.3205	−	12.6795i	−1.66473	−	0.446063i
$809$	−11.5000	+	19.9186i	−0.404318	+	0.700300i	−0.994242	−	0.107159i	$-0.965825\pi$
$809$	−11.5000	+	19.9186i	−0.404318	+	0.700300i	0.589923	+	0.807459i	$0.299158\pi$
$810$	−31.1769	−	31.1769i	−1.09545	−	1.09545i
$811$	6.92820			0.243282			0.121641	−	0.992574i	$-0.461184\pi$
$811$	6.92820			0.243282			0.121641	+	0.992574i	$0.461184\pi$
$812$	20.0000	+	17.3205i	0.701862	+	0.607831i
$813$	4.50000	−	7.79423i	0.157822	−	0.273356i
$814$	−8.19615	+	2.19615i	−0.287275	+	0.0769751i
$815$	31.1769			1.09208
$816$		−	36.0000i		−	1.26025i
$817$		−	19.0526i		−	0.666565i
$818$	−15.5885	−	15.5885i	−0.545038	−	0.545038i
$819$	7.79423	−	40.5000i	0.272352	−	1.41518i
$820$		−	12.0000i		−	0.419058i
$821$	−55.0000			−1.91951			−0.959757	−	0.280833i	$-0.909389\pi$
$821$	−55.0000			−1.91951			−0.959757	+	0.280833i	$0.909389\pi$
$822$	−5.07180	−	18.9282i	−0.176899	−	0.660197i
$823$		−	21.0000i		−	0.732014i	−0.930612	−	0.366007i	$-0.880725\pi$
$823$		−	21.0000i		−	0.732014i	0.930612	−	0.366007i	$-0.119275\pi$
$824$		0			0
$825$			24.2487i			0.844232i
$826$	−5.36603	+	3.63397i	−0.186708	+	0.126442i
$827$		−	10.0000i		−	0.347734i	−0.984769	−	0.173867i	$-0.944374\pi$
$827$		−	10.0000i		−	0.347734i	0.984769	−	0.173867i	$-0.0556263\pi$
$828$	12.0000	+	20.7846i	0.417029	+	0.722315i
$829$	10.5000	+	6.06218i	0.364680	+	0.210548i	0.671132	−	0.741338i	$-0.265808\pi$
$829$	10.5000	+	6.06218i	0.364680	+	0.210548i	−0.306452	+	0.951886i	$0.599142\pi$
$830$	6.58846	−	24.5885i	0.228689	−	0.853478i
$831$	3.46410	−	6.00000i	0.120168	−	0.208138i
$832$	−20.7846	−	36.0000i	−0.720577	−	1.24808i
$833$	−22.5000	−	28.5788i	−0.779579	−	0.990198i
$834$	14.2750	+	53.2750i	0.494303	+	1.84476i
$835$		−	18.0000i		−	0.622916i
$836$	−3.46410	+	6.00000i	−0.119808	+	0.207514i
$837$	−27.0000			−0.933257
$838$	21.2942	+	5.70577i	0.735597	+	0.197103i
$839$	−9.52628	+	16.5000i	−0.328884	+	0.569643i	−0.982291	−	0.187364i	$-0.940006\pi$
$839$	−9.52628	+	16.5000i	−0.328884	+	0.569643i	0.653407	+	0.757007i	$0.273339\pi$
$840$	−37.1769	+	25.1769i	−1.28273	+	0.868686i
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$	8.41858	+	31.4186i	0.290124	+	1.08276i
$843$	−8.66025			−0.298275
$844$	−25.0000	−	43.3013i	−0.860535	−	1.49049i
$845$	−42.0000	+	24.2487i	−1.44484	+	0.834181i
$846$	1.90192	+	7.09808i	0.0653895	+	0.244037i
$847$	−12.1244	+	14.0000i	−0.416598	+	0.481046i
$848$	2.00000	−	3.46410i	0.0686803	−	0.118958i
$849$	−7.50000	−	12.9904i	−0.257399	−	0.445829i
$850$	36.3731	+	36.3731i	1.24759	+	1.24759i
$851$		−	12.0000i		−	0.411355i
$852$	−3.46410	−	6.00000i	−0.118678	−	0.205557i
$853$	22.5000	+	12.9904i	0.770385	+	0.444782i	0.833012	−	0.553255i	$-0.186614\pi$
$853$	22.5000	+	12.9904i	0.770385	+	0.444782i	−0.0626267	+	0.998037i	$0.519948\pi$
$854$	10.9019	+	16.0981i	0.373056	+	0.550865i
$855$	15.5885	+	9.00000i	0.533114	+	0.307794i
$856$	19.1244	+	5.12436i	0.653657	+	0.175147i
$857$	21.0000	−	12.1244i	0.717346	−	0.414160i	−0.0964289	−	0.995340i	$-0.530742\pi$
$857$	21.0000	−	12.1244i	0.717346	−	0.414160i	0.813775	+	0.581180i	$0.197409\pi$
$858$	18.0000	−	18.0000i	0.614510	−	0.614510i
$859$	−13.8564	+	24.0000i	−0.472774	+	0.818869i	−0.999515	−	0.0311570i	$-0.990081\pi$
$859$	−13.8564	+	24.0000i	−0.472774	+	0.818869i	0.526740	+	0.850026i	$0.323414\pi$
$860$	66.0000	−	38.1051i	2.25058	−	1.29937i
$861$	6.00000	+	5.19615i	0.204479	+	0.177084i
$862$	−6.83013	+	1.83013i	−0.232635	+	0.0623344i
$863$	30.3109	−	17.5000i	1.03179	−	0.595707i	0.114296	−	0.993447i	$-0.463539\pi$
$863$	30.3109	−	17.5000i	1.03179	−	0.595707i	0.917498	+	0.397740i	$0.130205\pi$
$864$	20.7846	−	20.7846i	0.707107	−	0.707107i
$865$	33.0000	−	57.1577i	1.12203	−	1.94342i
$866$	−27.7128	−	27.7128i	−0.941720	−	0.941720i
$867$	8.66025	−	15.0000i	0.294118	−	0.509427i
$868$	−5.19615	+	27.0000i	−0.176369	+	0.916440i
$869$	−3.00000	−	5.19615i	−0.101768	−	0.176267i
$870$	40.9808	−	10.9808i	1.38938	−	0.372283i
$871$	23.3827	+	40.5000i	0.792292	+	1.37229i
$872$	−8.19615	+	2.19615i	−0.277557	+	0.0743711i
$873$	4.50000	−	2.59808i	0.152302	−	0.0879316i
$874$	−6.92820	−	6.92820i	−0.234350	−	0.234350i
$875$	3.46410	−	18.0000i	0.117108	−	0.608511i
$876$	42.0000			1.41905
$877$	−8.00000	+	13.8564i	−0.270141	+	0.467898i	−0.968898	−	0.247462i	$-0.920404\pi$
$877$	−8.00000	+	13.8564i	−0.270141	+	0.467898i	0.698757	+	0.715359i	$0.253737\pi$
$878$	−12.1244	+	12.1244i	−0.409177	+	0.409177i
$879$	7.79423	+	4.50000i	0.262893	+	0.151781i
$880$	−27.7128			−0.934199
$881$			24.2487i			0.816960i	0.912767	+	0.408480i	$0.133941\pi$
$881$			24.2487i			0.816960i	−0.912767	+	0.408480i	$0.866059\pi$
$882$	3.50962	−	29.4904i	0.118175	−	0.992993i
$883$			14.0000i			0.471138i	0.971858	+	0.235569i	$0.0756953\pi$
$883$			14.0000i			0.471138i	−0.971858	+	0.235569i	$0.924305\pi$
$884$		−	54.0000i		−	1.81622i
$885$			10.3923i			0.349334i
$886$	31.0000	+	31.0000i	1.04147	+	1.04147i
$887$	19.0526	−	33.0000i	0.639722	−	1.10803i	−0.345771	−	0.938319i	$-0.612383\pi$
$887$	19.0526	−	33.0000i	0.639722	−	1.10803i	0.985494	−	0.169713i	$-0.0542840\pi$
$888$	−14.1962	+	3.80385i	−0.476392	+	0.127649i
$889$	−3.00000	+	15.5885i	−0.100617	+	0.522820i
$890$	30.0000	−	30.0000i	1.00560	−	1.00560i
$891$	15.5885	+	9.00000i	0.522233	+	0.301511i
$892$	−27.0000	−	15.5885i	−0.904027	−	0.521940i
$893$	−1.50000	−	2.59808i	−0.0501956	−	0.0869413i
$894$	6.92820	−	6.92820i	0.231714	−	0.231714i
$895$	8.66025	+	15.0000i	0.289480	+	0.501395i
$896$	−16.7846	−	24.7846i	−0.560734	−	0.827996i
$897$	18.0000	+	31.1769i	0.601003	+	1.04097i
$898$	26.0000	−	26.0000i	0.867631	−	0.867631i
$899$	12.9904	−	22.5000i	0.433253	−	0.750417i
$900$			42.0000i			1.40000i
$901$	4.50000	−	2.59808i	0.149917	−	0.0865545i
$902$	1.26795	+	4.73205i	0.0422181	+	0.157560i
$903$	−9.52628	+	49.5000i	−0.317015	+	1.64726i
$904$	13.9090	−	51.9090i	0.462605	−	1.72647i
$905$	30.0000	−	51.9615i	0.997234	−	1.72726i
$906$	−33.1244	+	8.87564i	−1.10048	+	0.294874i
$907$	1.73205	−	1.00000i	0.0575118	−	0.0332045i	−0.470968	−	0.882150i	$-0.656095\pi$
$907$	1.73205	−	1.00000i	0.0575118	−	0.0332045i	0.528480	+	0.848946i	$0.322762\pi$
$908$	12.0000	−	6.92820i	0.398234	−	0.229920i
$909$		−	51.9615i		−	1.72345i
$910$	−55.7654	+	37.7654i	−1.84860	+	1.25191i
$911$	11.2583	+	6.50000i	0.373005	+	0.215355i	0.674771	−	0.738028i	$-0.264243\pi$
$911$	11.2583	+	6.50000i	0.373005	+	0.215355i	−0.301765	+	0.953382i	$0.597576\pi$
$912$	−6.00000	+	10.3923i	−0.198680	+	0.344124i
$913$			10.3923i			0.343935i
$914$	−3.00000	+	3.00000i	−0.0992312	+	0.0992312i
$915$	31.1769			1.03068
$916$	3.46410	−	6.00000i	0.114457	−	0.198246i
$917$	24.0000	−	27.7128i	0.792550	−	0.915158i
$918$	36.8827	−	9.88269i	1.21731	−	0.326177i
$919$	4.33013	−	2.50000i	0.142838	−	0.0824674i	−0.426878	−	0.904309i	$-0.640387\pi$
$919$	4.33013	−	2.50000i	0.142838	−	0.0824674i	0.569716	+	0.821842i	$0.307053\pi$
$920$	10.1436	−	37.8564i	0.334424	−	1.24809i
$921$	15.0000	+	25.9808i	0.494267	+	0.856095i
$922$	44.9545	−	12.0455i	1.48050	−	0.396698i
$923$	−5.19615	−	9.00000i	−0.171033	−	0.296239i
$924$	12.0000	−	13.8564i	0.394771	−	0.455842i
$925$	10.5000	−	18.1865i	0.345238	−	0.597970i
$926$	−12.0788	+	45.0788i	−0.396935	+	1.48138i
$927$		0			0
$928$	7.32051	+	27.3205i	0.240307	+	0.896840i
$929$			22.5167i			0.738748i	0.929281	+	0.369374i	$0.120428\pi$
$929$			22.5167i			0.738748i	−0.929281	+	0.369374i	$0.879572\pi$
$930$	31.1769	+	31.1769i	1.02233	+	1.02233i
$931$	1.73205	+	12.0000i	0.0567657	+	0.393284i
$932$	−1.73205	+	1.00000i	−0.0567352	+	0.0327561i
$933$	19.5000	+	33.7750i	0.638401	+	1.10574i
$934$	2.36603	+	0.633975i	0.0774187	+	0.0207443i
$935$	−31.1769	−	18.0000i	−1.01959	−	0.588663i
$936$	31.1769	−	31.1769i	1.01905	−	1.01905i
$937$		−	3.46410i		−	0.113167i	−0.998398	−	0.0565836i	$-0.981979\pi$
$937$		−	3.46410i		−	0.113167i	0.998398	−	0.0565836i	$-0.0180208\pi$
$938$	18.8827	+	27.8827i	0.616542	+	0.910402i
$939$	−33.7750	+	19.5000i	−1.10221	+	0.636358i
$940$	6.00000	−	10.3923i	0.195698	−	0.338960i
$941$		−	25.9808i		−	0.846949i	−0.905908	−	0.423474i	$-0.860810\pi$
$941$		−	25.9808i		−	0.846949i	0.905908	−	0.423474i	$-0.139190\pi$
$942$	7.68653	−	28.6865i	0.250441	−	0.934658i
$943$	−6.92820			−0.225613
$944$	−6.92820			−0.225494
$945$	−36.0000	−	31.1769i	−1.17108	−	1.01419i
$946$	−22.0000	+	22.0000i	−0.715282	+	0.715282i
$947$			43.0000i			1.39731i	0.715458	+	0.698656i	$0.246218\pi$
$947$			43.0000i			1.39731i	−0.715458	+	0.698656i	$0.753782\pi$
$948$	−5.19615	−	9.00000i	−0.168763	−	0.292306i
$949$	63.0000			2.04507
$950$	−4.43782	−	16.5622i	−0.143982	−	0.537348i
$951$	−16.4545	−	28.5000i	−0.533573	−	0.924176i
$952$	−2.78461	−	38.7846i	−0.0902497	−	1.25702i
$953$	44.0000			1.42530			0.712650	−	0.701520i	$-0.247495\pi$
$953$	44.0000			1.42530			0.712650	+	0.701520i	$0.247495\pi$
$954$	4.09808	+	1.09808i	0.132680	+	0.0355515i
$955$	12.1244	−	21.0000i	0.392335	−	0.679544i
$956$	11.0000	+	19.0526i	0.355765	+	0.616204i
$957$	−15.0000	+	8.66025i	−0.484881	+	0.279946i
$958$	28.3923	+	7.60770i	0.917314	+	0.245793i
$959$	−6.92820	−	20.0000i	−0.223723	−	0.645834i
$960$	−48.0000			−1.54919
$961$	−4.00000			−0.129032
$962$	−21.2942	+	5.70577i	−0.686553	+	0.183961i
$963$			21.0000i			0.676716i
$964$	3.46410	+	6.00000i	0.111571	+	0.193247i
$965$	27.0000	+	15.5885i	0.869161	+	0.501810i
$966$	14.5359	+	21.4641i	0.467685	+	0.690596i
$967$	−49.3634	+	28.5000i	−1.58742	+	0.916498i	−0.593691	+	0.804693i	$0.702330\pi$
$967$	−49.3634	+	28.5000i	−1.58742	+	0.916498i	−0.993730	+	0.111805i	$0.964337\pi$
$968$	−19.1244	+	5.12436i	−0.614680	+	0.164703i
$969$	−13.5000	+	7.79423i	−0.433682	+	0.250387i
$970$	−8.19615	−	2.19615i	−0.263163	−	0.0705142i
$971$	2.59808	+	4.50000i	0.0833762	+	0.144412i	0.904698	−	0.426053i	$-0.140096\pi$
$971$	2.59808	+	4.50000i	0.0833762	+	0.144412i	−0.821322	+	0.570465i	$0.806763\pi$
$972$	27.0000	+	15.5885i	0.866025	+	0.500000i
$973$	19.5000	+	56.2917i	0.625141	+	1.80463i
$974$	31.4186	−	8.41858i	1.00672	−	0.269749i
$975$			63.0000i			2.01761i
$976$			20.7846i			0.665299i
$977$	−47.0000			−1.50366			−0.751832	−	0.659355i	$-0.770829\pi$
$977$	−47.0000			−1.50366			−0.751832	+	0.659355i	$0.770829\pi$
$978$	−21.2942	+	5.70577i	−0.680914	+	0.182450i
$979$	−8.66025	+	15.0000i	−0.276783	+	0.479402i
$980$	−38.1051	+	30.0000i	−1.21722	+	0.958315i
$981$	−4.50000	−	7.79423i	−0.143674	−	0.248851i
$982$	−6.95448	+	25.9545i	−0.221926	+	0.828241i
$983$	−8.66025	−	15.0000i	−0.276219	−	0.478426i	0.694223	−	0.719760i	$-0.255748\pi$
$983$	−8.66025	−	15.0000i	−0.276219	−	0.478426i	−0.970442	+	0.241334i	$0.922415\pi$
$984$	2.19615	+	8.19615i	0.0700108	+	0.261284i
$985$	30.0000	+	17.3205i	0.955879	+	0.551877i
$986$	−9.50962	+	35.4904i	−0.302848	+	1.13024i
$987$	2.59808	+	7.50000i	0.0826977	+	0.238728i
$988$	−9.00000	+	15.5885i	−0.286328	+	0.495935i
$989$	−22.0000	−	38.1051i	−0.699559	−	1.21167i
$990$	−7.60770	−	28.3923i	−0.241788	−	0.902367i
$991$	−42.4352	−	24.5000i	−1.34800	−	0.778268i	−0.360034	−	0.932939i	$-0.617235\pi$
$991$	−42.4352	−	24.5000i	−1.34800	−	0.778268i	−0.987966	+	0.154671i	$0.950568\pi$
$992$	−20.7846	+	20.7846i	−0.659912	+	0.659912i
$993$	−1.50000	+	0.866025i	−0.0476011	+	0.0274825i
$994$	−4.19615	−	6.19615i	−0.133094	−	0.196530i
$995$	−5.19615	+	3.00000i	−0.164729	+	0.0951064i
$996$			18.0000i			0.570352i
$997$	21.0000	−	12.1244i	0.665077	−	0.383982i	−0.129132	−	0.991627i	$-0.541219\pi$
$997$	21.0000	−	12.1244i	0.665077	−	0.383982i	0.794209	+	0.607645i	$0.207886\pi$
$998$	−2.73205	+	0.732051i	−0.0864816	+	0.0231727i
$999$	−7.79423	−	13.5000i	−0.246598	−	0.427121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bj.a.115.2	yes	4
3.2	odd	2		756.2.bj.a.451.1		4
4.3	odd	2	inner	252.2.bj.a.115.1	yes	4
7.5	odd	6		252.2.n.a.187.2	yes	4
9.4	even	3		252.2.n.a.31.1	✓	4
9.5	odd	6		756.2.n.a.199.2		4
12.11	even	2		756.2.bj.a.451.2		4
21.5	even	6		756.2.n.a.19.1		4
28.19	even	6		252.2.n.a.187.1	yes	4
36.23	even	6		756.2.n.a.199.1		4
36.31	odd	6		252.2.n.a.31.2	yes	4
63.5	even	6		756.2.bj.a.523.1		4
63.40	odd	6	inner	252.2.bj.a.103.2	yes	4
84.47	odd	6		756.2.n.a.19.2		4
252.103	even	6	inner	252.2.bj.a.103.1	yes	4
252.131	odd	6		756.2.bj.a.523.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.a.31.1	✓	4	9.4	even	3
252.2.n.a.31.2	yes	4	36.31	odd	6
252.2.n.a.187.1	yes	4	28.19	even	6
252.2.n.a.187.2	yes	4	7.5	odd	6
252.2.bj.a.103.1	yes	4	252.103	even	6	inner
252.2.bj.a.103.2	yes	4	63.40	odd	6	inner
252.2.bj.a.115.1	yes	4	4.3	odd	2	inner
252.2.bj.a.115.2	yes	4	1.1	even	1	trivial
756.2.n.a.19.1		4	21.5	even	6
756.2.n.a.19.2		4	84.47	odd	6
756.2.n.a.199.1		4	36.23	even	6
756.2.n.a.199.2		4	9.5	odd	6
756.2.bj.a.451.1		4	3.2	odd	2
756.2.bj.a.451.2		4	12.11	even	2
756.2.bj.a.523.1		4	63.5	even	6
756.2.bj.a.523.2		4	252.131	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.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-0.866025 - 1.50000i) q^{3} -2.00000i q^{4} +(-3.00000 - 1.73205i) q^{5} +(2.36603 + 0.633975i) q^{6} +(2.59808 + 0.500000i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(-0.866025 - 1.50000i) q^{3} -2.00000i q^{4} +(-3.00000 - 1.73205i) q^{5} +(2.36603 + 0.633975i) q^{6} +(2.59808 + 0.500000i) q^{7} +(2.00000 + 2.00000i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(4.73205 - 1.26795i) q^{10} +(-1.73205 + 1.00000i) q^{11} +(-3.00000 + 1.73205i) q^{12} +(-4.50000 + 2.59808i) q^{13} +(-3.09808 + 2.09808i) q^{14} +6.00000i q^{15} -4.00000 q^{16} +(-4.50000 - 2.59808i) q^{17} +(-1.09808 - 4.09808i) q^{18} +(0.866025 + 1.50000i) q^{19} +(-3.46410 + 6.00000i) q^{20} +(-1.50000 - 4.33013i) q^{21} +(0.732051 - 2.73205i) q^{22} +(3.46410 + 2.00000i) q^{23} +(1.26795 - 4.73205i) q^{24} +(3.50000 + 6.06218i) q^{25} +(1.90192 - 7.09808i) q^{26} +5.19615 q^{27} +(1.00000 - 5.19615i) q^{28} +(-2.50000 + 4.33013i) q^{29} +(-6.00000 - 6.00000i) q^{30} -5.19615 q^{31} +(4.00000 - 4.00000i) q^{32} +(3.00000 + 1.73205i) q^{33} +(7.09808 - 1.90192i) q^{34} +(-6.92820 - 6.00000i) q^{35} +(5.19615 + 3.00000i) q^{36} +(-1.50000 - 2.59808i) q^{37} +(-2.36603 - 0.633975i) q^{38} +(7.79423 + 4.50000i) q^{39} +(-2.53590 - 9.46410i) q^{40} +(-1.50000 + 0.866025i) q^{41} +(5.83013 + 2.83013i) q^{42} +(-9.52628 - 5.50000i) q^{43} +(2.00000 + 3.46410i) q^{44} +(9.00000 - 5.19615i) q^{45} +(-5.46410 + 1.46410i) q^{46} -1.73205 q^{47} +(3.46410 + 6.00000i) q^{48} +(6.50000 + 2.59808i) q^{49} +(-9.56218 - 2.56218i) q^{50} +9.00000i q^{51} +(5.19615 + 9.00000i) q^{52} +(-0.500000 + 0.866025i) q^{53} +(-5.19615 + 5.19615i) q^{54} +6.92820 q^{55} +(4.19615 + 6.19615i) q^{56} +(1.50000 - 2.59808i) q^{57} +(-1.83013 - 6.83013i) q^{58} +1.73205 q^{59} +12.0000 q^{60} -5.19615i q^{61} +(5.19615 - 5.19615i) q^{62} +(-5.19615 + 6.00000i) q^{63} +8.00000i q^{64} +18.0000 q^{65} +(-4.73205 + 1.26795i) q^{66} -9.00000i q^{67} +(-5.19615 + 9.00000i) q^{68} -6.92820i q^{69} +(12.9282 - 0.928203i) q^{70} +2.00000i q^{71} +(-8.19615 + 2.19615i) q^{72} +(-10.5000 - 6.06218i) q^{73} +(4.09808 + 1.09808i) q^{74} +(6.06218 - 10.5000i) q^{75} +(3.00000 - 1.73205i) q^{76} +(-5.00000 + 1.73205i) q^{77} +(-12.2942 + 3.29423i) q^{78} +3.00000i q^{79} +(12.0000 + 6.92820i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(0.633975 - 2.36603i) q^{82} +(2.59808 - 4.50000i) q^{83} +(-8.66025 + 3.00000i) q^{84} +(9.00000 + 15.5885i) q^{85} +(15.0263 - 4.02628i) q^{86} +8.66025 q^{87} +(-5.46410 - 1.46410i) q^{88} +(7.50000 - 4.33013i) q^{89} +(-3.80385 + 14.1962i) q^{90} +(-12.9904 + 4.50000i) q^{91} +(4.00000 - 6.92820i) q^{92} +(4.50000 + 7.79423i) q^{93} +(1.73205 - 1.73205i) q^{94} -6.00000i q^{95} +(-9.46410 - 2.53590i) q^{96} +(-1.50000 - 0.866025i) q^{97} +(-9.09808 + 3.90192i) q^{98} -6.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 12 q^{5} + 6 q^{6} + 8 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 12 * q^5 + 6 * q^6 + 8 * q^8 - 6 * q^9	\( 4 q - 4 q^{2} - 12 q^{5} + 6 q^{6} + 8 q^{8} - 6 q^{9} + 12 q^{10} - 12 q^{12} - 18 q^{13} - 2 q^{14} - 16 q^{16} - 18 q^{17} + 6 q^{18} - 6 q^{21} - 4 q^{22} + 12 q^{24} + 14 q^{25} + 18 q^{26} + 4 q^{28} - 10 q^{29} - 24 q^{30} + 16 q^{32} + 12 q^{33} + 18 q^{34} - 6 q^{37} - 6 q^{38} - 24 q^{40} - 6 q^{41} + 6 q^{42} + 8 q^{44} + 36 q^{45} - 8 q^{46} + 26 q^{49} - 14 q^{50} - 2 q^{53} - 4 q^{56} + 6 q^{57} + 10 q^{58} + 48 q^{60} + 72 q^{65} - 12 q^{66} + 24 q^{70} - 12 q^{72} - 42 q^{73} + 6 q^{74} + 12 q^{76} - 20 q^{77} - 18 q^{78} + 48 q^{80} - 18 q^{81} + 6 q^{82} + 36 q^{85} + 22 q^{86} - 8 q^{88} + 30 q^{89} - 36 q^{90} + 16 q^{92} + 18 q^{93} - 24 q^{96} - 6 q^{97} - 26 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 12 * q^5 + 6 * q^6 + 8 * q^8 - 6 * q^9 + 12 * q^10 - 12 * q^12 - 18 * q^13 - 2 * q^14 - 16 * q^16 - 18 * q^17 + 6 * q^18 - 6 * q^21 - 4 * q^22 + 12 * q^24 + 14 * q^25 + 18 * q^26 + 4 * q^28 - 10 * q^29 - 24 * q^30 + 16 * q^32 + 12 * q^33 + 18 * q^34 - 6 * q^37 - 6 * q^38 - 24 * q^40 - 6 * q^41 + 6 * q^42 + 8 * q^44 + 36 * q^45 - 8 * q^46 + 26 * q^49 - 14 * q^50 - 2 * q^53 - 4 * q^56 + 6 * q^57 + 10 * q^58 + 48 * q^60 + 72 * q^65 - 12 * q^66 + 24 * q^70 - 12 * q^72 - 42 * q^73 + 6 * q^74 + 12 * q^76 - 20 * q^77 - 18 * q^78 + 48 * q^80 - 18 * q^81 + 6 * q^82 + 36 * q^85 + 22 * q^86 - 8 * q^88 + 30 * q^89 - 36 * q^90 + 16 * q^92 + 18 * q^93 - 24 * q^96 - 6 * q^97 - 26 * q^98

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