LMFDB - Embedded newform 784.2.x.f.557.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			557.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	784.557
Dual form			784.2.x.f.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 0.366025i) q^{2} +(1.36603 - 0.366025i) q^{3} +(1.73205 + 1.00000i) q^{4} +(1.36603 + 0.366025i) q^{5} +2.00000 q^{6} +(2.00000 + 2.00000i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(1.36603 + 0.366025i) q^{2} +(1.36603 - 0.366025i) q^{3} +(1.73205 + 1.00000i) q^{4} +(1.36603 + 0.366025i) q^{5} +2.00000 q^{6} +(2.00000 + 2.00000i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.73205 + 1.00000i) q^{10} +(0.366025 + 1.36603i) q^{11} +(2.73205 + 0.732051i) q^{12} +(-1.00000 - 1.00000i) q^{13} +2.00000 q^{15} +(2.00000 + 3.46410i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-1.36603 + 0.366025i) q^{18} +(1.09808 - 4.09808i) q^{19} +(2.00000 + 2.00000i) q^{20} +2.00000i q^{22} +(-5.19615 + 3.00000i) q^{23} +(3.46410 + 2.00000i) q^{24} +(-2.59808 - 1.50000i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(-4.00000 + 4.00000i) q^{27} +(3.00000 + 3.00000i) q^{29} +(2.73205 + 0.732051i) q^{30} +(4.00000 - 6.92820i) q^{31} +(1.46410 + 5.46410i) q^{32} +(1.00000 + 1.73205i) q^{33} +(2.00000 - 2.00000i) q^{34} -2.00000 q^{36} +(-4.09808 - 1.09808i) q^{37} +(3.00000 - 5.19615i) q^{38} +(-1.73205 - 1.00000i) q^{39} +(2.00000 + 3.46410i) q^{40} +(5.00000 - 5.00000i) q^{43} +(-0.732051 + 2.73205i) q^{44} +(-1.36603 + 0.366025i) q^{45} +(-8.19615 + 2.19615i) q^{46} +(-4.00000 - 6.92820i) q^{47} +(4.00000 + 4.00000i) q^{48} +(-3.00000 - 3.00000i) q^{50} +(0.732051 - 2.73205i) q^{51} +(-0.732051 - 2.73205i) q^{52} +(-1.83013 - 6.83013i) q^{53} +(-6.92820 + 4.00000i) q^{54} +2.00000i q^{55} -6.00000i q^{57} +(3.00000 + 5.19615i) q^{58} +(-1.09808 - 4.09808i) q^{59} +(3.46410 + 2.00000i) q^{60} +(-3.29423 + 12.2942i) q^{61} +(8.00000 - 8.00000i) q^{62} +8.00000i q^{64} +(-1.00000 - 1.73205i) q^{65} +(0.732051 + 2.73205i) q^{66} +(6.83013 - 1.83013i) q^{67} +(3.46410 - 2.00000i) q^{68} +(-6.00000 + 6.00000i) q^{69} +10.0000i q^{71} +(-2.73205 - 0.732051i) q^{72} +(-3.46410 - 2.00000i) q^{73} +(-5.19615 - 3.00000i) q^{74} +(-4.09808 - 1.09808i) q^{75} +(6.00000 - 6.00000i) q^{76} +(-2.00000 - 2.00000i) q^{78} +(1.46410 + 5.46410i) q^{80} +(-2.50000 + 4.33013i) q^{81} +(-1.00000 - 1.00000i) q^{83} +(2.00000 - 2.00000i) q^{85} +(8.66025 - 5.00000i) q^{86} +(5.19615 + 3.00000i) q^{87} +(-2.00000 + 3.46410i) q^{88} +(-3.46410 + 2.00000i) q^{89} -2.00000 q^{90} -12.0000 q^{92} +(2.92820 - 10.9282i) q^{93} +(-2.92820 - 10.9282i) q^{94} +(3.00000 - 5.19615i) q^{95} +(4.00000 + 6.92820i) q^{96} -2.00000 q^{97} +(-1.00000 - 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 8 q^{6} + 8 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 8 * q^6 + 8 * q^8	$ 4 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 8 q^{6} + 8 q^{8} - 2 q^{11} + 4 q^{12} - 4 q^{13} + 8 q^{15} + 8 q^{16} + 4 q^{17} - 2 q^{18} - 6 q^{19} + 8 q^{20} - 4 q^{26} - 16 q^{27} + 12 q^{29} + 4 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{33} + 8 q^{34} - 8 q^{36} - 6 q^{37} + 12 q^{38} + 8 q^{40} + 20 q^{43} + 4 q^{44} - 2 q^{45} - 12 q^{46} - 16 q^{47} + 16 q^{48} - 12 q^{50} - 4 q^{51} + 4 q^{52} + 10 q^{53} + 12 q^{58} + 6 q^{59} + 18 q^{61} + 32 q^{62} - 4 q^{65} - 4 q^{66} + 10 q^{67} - 24 q^{69} - 4 q^{72} - 6 q^{75} + 24 q^{76} - 8 q^{78} - 8 q^{80} - 10 q^{81} - 4 q^{83} + 8 q^{85} - 8 q^{88} - 8 q^{90} - 48 q^{92} - 16 q^{93} + 16 q^{94} + 12 q^{95} + 16 q^{96} - 8 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 8 * q^6 + 8 * q^8 - 2 * q^11 + 4 * q^12 - 4 * q^13 + 8 * q^15 + 8 * q^16 + 4 * q^17 - 2 * q^18 - 6 * q^19 + 8 * q^20 - 4 * q^26 - 16 * q^27 + 12 * q^29 + 4 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^33 + 8 * q^34 - 8 * q^36 - 6 * q^37 + 12 * q^38 + 8 * q^40 + 20 * q^43 + 4 * q^44 - 2 * q^45 - 12 * q^46 - 16 * q^47 + 16 * q^48 - 12 * q^50 - 4 * q^51 + 4 * q^52 + 10 * q^53 + 12 * q^58 + 6 * q^59 + 18 * q^61 + 32 * q^62 - 4 * q^65 - 4 * q^66 + 10 * q^67 - 24 * q^69 - 4 * q^72 - 6 * q^75 + 24 * q^76 - 8 * q^78 - 8 * q^80 - 10 * q^81 - 4 * q^83 + 8 * q^85 - 8 * q^88 - 8 * q^90 - 48 * q^92 - 16 * q^93 + 16 * q^94 + 12 * q^95 + 16 * q^96 - 8 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.36603	+	0.366025i	0.965926	+	0.258819i
$2$	1.36603	+	0.366025i	0.965926	+	0.258819i
$3$	1.36603	−	0.366025i	0.788675	−	0.211325i	0.158069	−	0.987428i	$-0.449473\pi$
$3$	1.36603	−	0.366025i	0.788675	−	0.211325i	0.630606	+	0.776103i	$0.282806\pi$
$4$	1.73205	+	1.00000i	0.866025	+	0.500000i
$5$	1.36603	+	0.366025i	0.610905	+	0.163692i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	1.36603	+	0.366025i	0.610905	+	0.163692i	0.0599153	+	0.998203i	$0.480917\pi$
$6$	2.00000			0.816497
$7$		0			0
$7$		0			0
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	1.73205	+	1.00000i	0.547723	+	0.316228i
$11$	0.366025	+	1.36603i	0.110361	+	0.411872i	0.998898	−	0.0469323i	$-0.0149445\pi$
$11$	0.366025	+	1.36603i	0.110361	+	0.411872i	−0.888537	+	0.458804i	$0.848278\pi$
$12$	2.73205	+	0.732051i	0.788675	+	0.211325i
$13$	−1.00000	−	1.00000i	−0.277350	−	0.277350i	0.554700	−	0.832050i	$-0.312833\pi$
$13$	−1.00000	−	1.00000i	−0.277350	−	0.277350i	−0.832050	+	0.554700i	$0.812833\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$	−1.36603	+	0.366025i	−0.321975	+	0.0862730i
$19$	1.09808	−	4.09808i	0.251916	−	0.940163i	−0.717864	−	0.696183i	$-0.754880\pi$
$19$	1.09808	−	4.09808i	0.251916	−	0.940163i	0.969780	−	0.243980i	$-0.0784532\pi$
$20$	2.00000	+	2.00000i	0.447214	+	0.447214i
$21$		0			0
$22$			2.00000i			0.426401i
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.931831	−	0.362892i	$-0.881789\pi$
$23$	−5.19615	+	3.00000i	−1.08347	+	0.625543i	−0.151642	+	0.988436i	$0.548456\pi$
$24$	3.46410	+	2.00000i	0.707107	+	0.408248i
$25$	−2.59808	−	1.50000i	−0.519615	−	0.300000i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$	−4.00000	+	4.00000i	−0.769800	+	0.769800i
$28$		0			0
$29$	3.00000	+	3.00000i	0.557086	+	0.557086i	0.928477	−	0.371391i	$-0.121119\pi$
$29$	3.00000	+	3.00000i	0.557086	+	0.557086i	−0.371391	+	0.928477i	$0.621119\pi$
$30$	2.73205	+	0.732051i	0.498802	+	0.133654i
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$	1.46410	+	5.46410i	0.258819	+	0.965926i
$33$	1.00000	+	1.73205i	0.174078	+	0.301511i
$34$	2.00000	−	2.00000i	0.342997	−	0.342997i
$35$		0			0
$36$	−2.00000			−0.333333
$37$	−4.09808	−	1.09808i	−0.673720	−	0.180523i	−0.0942898	−	0.995545i	$-0.530058\pi$
$37$	−4.09808	−	1.09808i	−0.673720	−	0.180523i	−0.579430	+	0.815022i	$0.696725\pi$
$38$	3.00000	−	5.19615i	0.486664	−	0.842927i
$39$	−1.73205	−	1.00000i	−0.277350	−	0.160128i
$40$	2.00000	+	3.46410i	0.316228	+	0.547723i
$41$		0			0		1.00000			$0$
$41$		0			0		−1.00000			$\pi$
$42$		0			0
$43$	5.00000	−	5.00000i	0.762493	−	0.762493i	−0.214280	−	0.976772i	$-0.568740\pi$
$43$	5.00000	−	5.00000i	0.762493	−	0.762493i	0.976772	+	0.214280i	$0.0687403\pi$
$44$	−0.732051	+	2.73205i	−0.110361	+	0.411872i
$45$	−1.36603	+	0.366025i	−0.203635	+	0.0545638i
$46$	−8.19615	+	2.19615i	−1.20846	+	0.323805i
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	−0.995066	−	0.0992202i	$-0.968365\pi$
$47$	−4.00000	−	6.92820i	−0.583460	−	1.01058i	0.411606	−	0.911362i	$-0.364968\pi$
$48$	4.00000	+	4.00000i	0.577350	+	0.577350i
$49$		0			0
$50$	−3.00000	−	3.00000i	−0.424264	−	0.424264i
$51$	0.732051	−	2.73205i	0.102508	−	0.382564i
$52$	−0.732051	−	2.73205i	−0.101517	−	0.378867i
$53$	−1.83013	−	6.83013i	−0.251387	−	0.938190i	−0.970065	−	0.242846i	$-0.921919\pi$
$53$	−1.83013	−	6.83013i	−0.251387	−	0.938190i	0.718677	−	0.695344i	$-0.244748\pi$
$54$	−6.92820	+	4.00000i	−0.942809	+	0.544331i
$55$			2.00000i			0.269680i
$56$		0			0
$57$		−	6.00000i		−	0.794719i
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	−1.09808	−	4.09808i	−0.142957	−	0.533524i	−0.999838	−	0.0180090i	$-0.994267\pi$
$59$	−1.09808	−	4.09808i	−0.142957	−	0.533524i	0.856880	−	0.515515i	$-0.172399\pi$
$60$	3.46410	+	2.00000i	0.447214	+	0.258199i
$61$	−3.29423	+	12.2942i	−0.421783	+	1.57411i	0.349067	+	0.937098i	$0.386499\pi$
$61$	−3.29423	+	12.2942i	−0.421783	+	1.57411i	−0.770850	+	0.637017i	$0.780168\pi$
$62$	8.00000	−	8.00000i	1.01600	−	1.01600i
$63$		0			0
$64$			8.00000i			1.00000i
$65$	−1.00000	−	1.73205i	−0.124035	−	0.214834i
$66$	0.732051	+	2.73205i	0.0901092	+	0.336292i
$67$	6.83013	−	1.83013i	0.834433	−	0.223586i	0.183786	−	0.982966i	$-0.441165\pi$
$67$	6.83013	−	1.83013i	0.834433	−	0.223586i	0.650647	+	0.759381i	$0.274498\pi$
$68$	3.46410	−	2.00000i	0.420084	−	0.242536i
$69$	−6.00000	+	6.00000i	−0.722315	+	0.722315i
$70$		0			0
$71$			10.0000i			1.18678i	0.804914	+	0.593391i	$0.202211\pi$
$71$			10.0000i			1.18678i	−0.804914	+	0.593391i	$0.797789\pi$
$72$	−2.73205	−	0.732051i	−0.321975	−	0.0862730i
$73$	−3.46410	−	2.00000i	−0.405442	−	0.234082i	0.283387	−	0.959006i	$-0.408542\pi$
$73$	−3.46410	−	2.00000i	−0.405442	−	0.234082i	−0.688830	+	0.724923i	$0.741875\pi$
$74$	−5.19615	−	3.00000i	−0.604040	−	0.348743i
$75$	−4.09808	−	1.09808i	−0.473205	−	0.126795i
$76$	6.00000	−	6.00000i	0.688247	−	0.688247i
$77$		0			0
$78$	−2.00000	−	2.00000i	−0.226455	−	0.226455i
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	1.46410	+	5.46410i	0.163692	+	0.610905i
$81$	−2.50000	+	4.33013i	−0.277778	+	0.481125i
$82$		0			0
$83$	−1.00000	−	1.00000i	−0.109764	−	0.109764i	0.650092	−	0.759856i	$-0.274731\pi$
$83$	−1.00000	−	1.00000i	−0.109764	−	0.109764i	−0.759856	+	0.650092i	$0.774731\pi$
$84$		0			0
$85$	2.00000	−	2.00000i	0.216930	−	0.216930i
$86$	8.66025	−	5.00000i	0.933859	−	0.539164i
$87$	5.19615	+	3.00000i	0.557086	+	0.321634i
$88$	−2.00000	+	3.46410i	−0.213201	+	0.369274i
$89$	−3.46410	+	2.00000i	−0.367194	+	0.212000i	−0.672232	−	0.740341i	$-0.734664\pi$
$89$	−3.46410	+	2.00000i	−0.367194	+	0.212000i	0.305038	+	0.952340i	$0.401331\pi$
$90$	−2.00000			−0.210819
$91$		0			0
$92$	−12.0000			−1.25109
$93$	2.92820	−	10.9282i	0.303641	−	1.13320i
$94$	−2.92820	−	10.9282i	−0.302021	−	1.12716i
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$	4.00000	+	6.92820i	0.408248	+	0.707107i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	−1.00000	−	1.00000i	−0.100504	−	0.100504i
$100$	−3.00000	−	5.19615i	−0.300000	−	0.519615i
$101$	4.02628	+	15.0263i	0.400630	+	1.49517i	0.811976	+	0.583691i	$0.198392\pi$
$101$	4.02628	+	15.0263i	0.400630	+	1.49517i	−0.411346	+	0.911479i	$0.634941\pi$
$102$	2.00000	−	3.46410i	0.198030	−	0.342997i
$103$	−5.19615	+	3.00000i	−0.511992	+	0.295599i	−0.733652	−	0.679525i	$-0.762186\pi$
$103$	−5.19615	+	3.00000i	−0.511992	+	0.295599i	0.221660	+	0.975124i	$0.428852\pi$
$104$		−	4.00000i		−	0.392232i
$105$		0			0
$106$		−	10.0000i		−	0.971286i
$107$	9.56218	+	2.56218i	0.924411	+	0.247695i	0.689470	−	0.724315i	$-0.257844\pi$
$107$	9.56218	+	2.56218i	0.924411	+	0.247695i	0.234941	+	0.972010i	$0.424510\pi$
$108$	−10.9282	+	2.92820i	−1.05157	+	0.281766i
$109$	−4.09808	+	1.09808i	−0.392525	+	0.105177i	−0.449682	−	0.893189i	$-0.648463\pi$
$109$	−4.09808	+	1.09808i	−0.392525	+	0.105177i	0.0571579	+	0.998365i	$0.481796\pi$
$110$	−0.732051	+	2.73205i	−0.0697983	+	0.260491i
$111$	−6.00000			−0.569495
$112$		0			0
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$	2.19615	−	8.19615i	0.205689	−	0.767640i
$115$	−8.19615	+	2.19615i	−0.764295	+	0.204792i
$116$	2.19615	+	8.19615i	0.203908	+	0.760994i
$117$	1.36603	+	0.366025i	0.126289	+	0.0338391i
$118$		−	6.00000i		−	0.552345i
$119$		0			0
$120$	4.00000	+	4.00000i	0.365148	+	0.365148i
$121$	7.79423	−	4.50000i	0.708566	−	0.409091i
$122$	−9.00000	+	15.5885i	−0.814822	+	1.41131i
$123$		0			0
$124$	13.8564	−	8.00000i	1.24434	−	0.718421i
$125$	−8.00000	−	8.00000i	−0.715542	−	0.715542i
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	−2.92820	+	10.9282i	−0.258819	+	0.965926i
$129$	5.00000	−	8.66025i	0.440225	−	0.762493i
$130$	−0.732051	−	2.73205i	−0.0642051	−	0.239617i
$131$	4.02628	−	15.0263i	0.351778	−	1.31285i	−0.532714	−	0.846296i	$-0.678828\pi$
$131$	4.02628	−	15.0263i	0.351778	−	1.31285i	0.884491	−	0.466557i	$-0.154506\pi$
$132$			4.00000i			0.348155i
$133$		0			0
$134$	10.0000			0.863868
$135$	−6.92820	+	4.00000i	−0.596285	+	0.344265i
$136$	5.46410	−	1.46410i	0.468543	−	0.125546i
$137$	6.92820	+	4.00000i	0.591916	+	0.341743i	0.765855	−	0.643013i	$-0.222316\pi$
$137$	6.92820	+	4.00000i	0.591916	+	0.341743i	−0.173939	+	0.984757i	$0.555649\pi$
$138$	−10.3923	+	6.00000i	−0.884652	+	0.510754i
$139$	−3.00000	+	3.00000i	−0.254457	+	0.254457i	−0.822795	−	0.568338i	$-0.807586\pi$
$139$	−3.00000	+	3.00000i	−0.254457	+	0.254457i	0.568338	+	0.822795i	$0.307586\pi$
$140$		0			0
$141$	−8.00000	−	8.00000i	−0.673722	−	0.673722i
$142$	−3.66025	+	13.6603i	−0.307162	+	1.14634i
$143$	1.00000	−	1.73205i	0.0836242	−	0.144841i
$144$	−3.46410	−	2.00000i	−0.288675	−	0.166667i
$145$	3.00000	+	5.19615i	0.249136	+	0.431517i
$146$	−4.00000	−	4.00000i	−0.331042	−	0.331042i
$147$		0			0
$148$	−6.00000	−	6.00000i	−0.493197	−	0.493197i
$149$	−9.56218	−	2.56218i	−0.783364	−	0.209902i	−0.155097	−	0.987899i	$-0.549569\pi$
$149$	−9.56218	−	2.56218i	−0.783364	−	0.209902i	−0.628267	+	0.777997i	$0.716236\pi$
$150$	−5.19615	−	3.00000i	−0.424264	−	0.244949i
$151$	−8.66025	−	5.00000i	−0.704761	−	0.406894i	0.104357	−	0.994540i	$-0.466722\pi$
$151$	−8.66025	−	5.00000i	−0.704761	−	0.406894i	−0.809118	+	0.587646i	$0.800055\pi$
$152$	10.3923	−	6.00000i	0.842927	−	0.486664i
$153$			2.00000i			0.161690i
$154$		0			0
$155$	8.00000	−	8.00000i	0.642575	−	0.642575i
$156$	−2.00000	−	3.46410i	−0.160128	−	0.277350i
$157$	−20.4904	+	5.49038i	−1.63531	+	0.438180i	−0.955448	−	0.295160i	$-0.904627\pi$
$157$	−20.4904	+	5.49038i	−1.63531	+	0.438180i	−0.679862	+	0.733340i	$0.737961\pi$
$158$		0			0
$159$	−5.00000	−	8.66025i	−0.396526	−	0.686803i
$160$			8.00000i			0.632456i
$161$		0			0
$162$	−5.00000	+	5.00000i	−0.392837	+	0.392837i
$163$	−0.366025	+	1.36603i	−0.0286693	+	0.106995i	−0.978778	−	0.204924i	$-0.934305\pi$
$163$	−0.366025	+	1.36603i	−0.0286693	+	0.106995i	0.950109	+	0.311919i	$0.100972\pi$
$164$		0			0
$165$	0.732051	+	2.73205i	0.0569901	+	0.212690i
$166$	−1.00000	−	1.73205i	−0.0776151	−	0.134433i
$167$			2.00000i			0.154765i	0.997001	+	0.0773823i	$0.0246562\pi$
$167$			2.00000i			0.154765i	−0.997001	+	0.0773823i	$0.975344\pi$
$168$		0			0
$169$		−	11.0000i		−	0.846154i
$170$	3.46410	−	2.00000i	0.265684	−	0.153393i
$171$	1.09808	+	4.09808i	0.0839720	+	0.313388i
$172$	13.6603	−	3.66025i	1.04158	−	0.279092i
$173$	−0.366025	+	1.36603i	−0.0278284	+	0.103857i	−0.978443	−	0.206516i	$-0.933787\pi$
$173$	−0.366025	+	1.36603i	−0.0278284	+	0.103857i	0.950615	+	0.310373i	$0.100454\pi$
$174$	6.00000	+	6.00000i	0.454859	+	0.454859i
$175$		0			0
$176$	−4.00000	+	4.00000i	−0.301511	+	0.301511i
$177$	−3.00000	−	5.19615i	−0.225494	−	0.390567i
$178$	−5.46410	+	1.46410i	−0.409552	+	0.109739i
$179$	23.2224	−	6.22243i	1.73573	−	0.465086i	0.754237	−	0.656603i	$-0.228007\pi$
$179$	23.2224	−	6.22243i	1.73573	−	0.465086i	0.981489	+	0.191516i	$0.0613405\pi$
$180$	−2.73205	−	0.732051i	−0.203635	−	0.0545638i
$181$	−9.00000	+	9.00000i	−0.668965	+	0.668965i	−0.957476	−	0.288512i	$-0.906840\pi$
$181$	−9.00000	+	9.00000i	−0.668965	+	0.668965i	0.288512	+	0.957476i	$0.406840\pi$
$182$		0			0
$183$			18.0000i			1.33060i
$184$	−16.3923	−	4.39230i	−1.20846	−	0.323805i
$185$	−5.19615	−	3.00000i	−0.382029	−	0.220564i
$186$	8.00000	−	13.8564i	0.586588	−	1.01600i
$187$	2.73205	+	0.732051i	0.199787	+	0.0535329i
$188$		−	16.0000i		−	1.16692i
$189$		0			0
$190$	6.00000	−	6.00000i	0.435286	−	0.435286i
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	0.973674	−	0.227946i	$-0.0732010\pi$
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	−0.684244	+	0.729253i	$0.739868\pi$
$192$	2.92820	+	10.9282i	0.211325	+	0.788675i
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	0.496119	+	0.868255i	$0.334758\pi$
$193$	−7.00000	+	12.1244i	−0.503871	+	0.872730i	−0.999990	+	0.00447566i	$0.998575\pi$
$194$	−2.73205	−	0.732051i	−0.196150	−	0.0525582i
$195$	−2.00000	−	2.00000i	−0.143223	−	0.143223i
$196$		0			0
$197$	−17.0000	+	17.0000i	−1.21120	+	1.21120i	−0.240567	+	0.970632i	$0.577334\pi$
$197$	−17.0000	+	17.0000i	−1.21120	+	1.21120i	−0.970632	+	0.240567i	$0.922666\pi$
$198$	−1.00000	−	1.73205i	−0.0710669	−	0.123091i
$199$	12.1244	+	7.00000i	0.859473	+	0.496217i	0.863836	−	0.503774i	$-0.168055\pi$
$199$	12.1244	+	7.00000i	0.859473	+	0.496217i	−0.00436292	+	0.999990i	$0.501389\pi$
$200$	−2.19615	−	8.19615i	−0.155291	−	0.579555i
$201$	8.66025	−	5.00000i	0.610847	−	0.352673i
$202$			22.0000i			1.54791i
$203$		0			0
$204$	4.00000	−	4.00000i	0.280056	−	0.280056i
$205$		0			0
$206$	−8.19615	+	2.19615i	−0.571053	+	0.153013i
$207$	3.00000	−	5.19615i	0.208514	−	0.361158i
$208$	1.46410	−	5.46410i	0.101517	−	0.378867i
$209$	6.00000			0.415029
$210$		0			0
$211$	−9.00000	−	9.00000i	−0.619586	−	0.619586i	0.325840	−	0.945425i	$-0.394353\pi$
$211$	−9.00000	−	9.00000i	−0.619586	−	0.619586i	−0.945425	+	0.325840i	$0.894353\pi$
$212$	3.66025	−	13.6603i	0.251387	−	0.938190i
$213$	3.66025	+	13.6603i	0.250796	+	0.935985i
$214$	12.1244	+	7.00000i	0.828804	+	0.478510i
$215$	8.66025	−	5.00000i	0.590624	−	0.340997i
$216$	−16.0000			−1.08866
$217$		0			0
$218$	−6.00000			−0.406371
$219$	−5.46410	−	1.46410i	−0.369230	−	0.0989348i
$220$	−2.00000	+	3.46410i	−0.134840	+	0.233550i
$221$	−2.73205	+	0.732051i	−0.183778	+	0.0492431i
$222$	−8.19615	−	2.19615i	−0.550090	−	0.147396i
$223$	24.0000			1.60716			0.803579	−	0.595198i	$-0.202926\pi$
$223$	24.0000			1.60716			0.803579	+	0.595198i	$0.202926\pi$
$224$		0			0
$225$	3.00000			0.200000
$226$	−8.19615	−	2.19615i	−0.545200	−	0.146086i
$227$	−20.4904	+	5.49038i	−1.35999	+	0.364409i	−0.863814	−	0.503810i	$-0.831931\pi$
$227$	−20.4904	+	5.49038i	−1.35999	+	0.364409i	−0.496180	+	0.868220i	$0.665264\pi$
$228$	6.00000	−	10.3923i	0.397360	−	0.688247i
$229$	−9.56218	−	2.56218i	−0.631886	−	0.169313i	−0.0713609	−	0.997451i	$-0.522734\pi$
$229$	−9.56218	−	2.56218i	−0.631886	−	0.169313i	−0.560526	+	0.828137i	$0.689401\pi$
$230$	−12.0000			−0.791257
$231$		0			0
$232$			12.0000i			0.787839i
$233$	3.46410	−	2.00000i	0.226941	−	0.131024i	−0.382219	−	0.924072i	$-0.624840\pi$
$233$	3.46410	−	2.00000i	0.226941	−	0.131024i	0.609160	+	0.793047i	$0.291507\pi$
$234$	1.73205	+	1.00000i	0.113228	+	0.0653720i
$235$	−2.92820	−	10.9282i	−0.191015	−	0.712877i
$236$	2.19615	−	8.19615i	0.142957	−	0.533524i
$237$		0			0
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	4.00000	+	6.92820i	0.258199	+	0.447214i
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	−0.415768	−	0.909471i	$-0.636487\pi$
$241$	9.00000	−	15.5885i	0.579741	−	1.00414i	0.995509	−	0.0946700i	$-0.0301796\pi$
$242$	12.2942	−	3.29423i	0.790303	−	0.211761i
$243$	2.56218	−	9.56218i	0.164364	−	0.613414i
$244$	−18.0000	+	18.0000i	−1.15233	+	1.15233i
$245$		0			0
$246$		0			0
$247$	−5.19615	+	3.00000i	−0.330623	+	0.190885i
$248$	21.8564	−	5.85641i	1.38788	−	0.371882i
$249$	−1.73205	−	1.00000i	−0.109764	−	0.0633724i
$250$	−8.00000	−	13.8564i	−0.505964	−	0.876356i
$251$	21.0000	−	21.0000i	1.32551	−	1.32551i	0.416265	−	0.909243i	$-0.363339\pi$
$251$	21.0000	−	21.0000i	1.32551	−	1.32551i	0.909243	−	0.416265i	$-0.136661\pi$
$252$		0			0
$253$	−6.00000	−	6.00000i	−0.377217	−	0.377217i
$254$	10.9282	+	2.92820i	0.685696	+	0.183732i
$255$	2.00000	−	3.46410i	0.125245	−	0.216930i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	11.0000	+	19.0526i	0.686161	+	1.18847i	0.973070	+	0.230508i	$0.0740389\pi$
$257$	11.0000	+	19.0526i	0.686161	+	1.18847i	−0.286909	+	0.957958i	$0.592628\pi$
$258$	10.0000	−	10.0000i	0.622573	−	0.622573i
$259$		0			0
$260$		−	4.00000i		−	0.248069i
$261$	−4.09808	−	1.09808i	−0.253665	−	0.0679692i
$262$	11.0000	−	19.0526i	0.679582	−	1.17707i
$263$	5.19615	+	3.00000i	0.320408	+	0.184988i	0.651575	−	0.758585i	$-0.274109\pi$
$263$	5.19615	+	3.00000i	0.320408	+	0.184988i	−0.331166	+	0.943572i	$0.607442\pi$
$264$	−1.46410	+	5.46410i	−0.0901092	+	0.336292i
$265$		−	10.0000i		−	0.614295i
$266$		0			0
$267$	−4.00000	+	4.00000i	−0.244796	+	0.244796i
$268$	13.6603	+	3.66025i	0.834433	+	0.223586i
$269$	−4.09808	+	1.09808i	−0.249864	+	0.0669509i	−0.381577	−	0.924337i	$-0.624619\pi$
$269$	−4.09808	+	1.09808i	−0.249864	+	0.0669509i	0.131713	+	0.991288i	$0.457952\pi$
$270$	−10.9282	+	2.92820i	−0.665069	+	0.178205i
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$	8.00000			0.485071
$273$		0			0
$274$	8.00000	+	8.00000i	0.483298	+	0.483298i
$275$	1.09808	−	4.09808i	0.0662165	−	0.247123i
$276$	−16.3923	+	4.39230i	−0.986701	+	0.264386i
$277$	1.09808	+	4.09808i	0.0659770	+	0.246230i	0.991036	−	0.133593i	$-0.0426516\pi$
$277$	1.09808	+	4.09808i	0.0659770	+	0.246230i	−0.925059	+	0.379823i	$0.875985\pi$
$278$	−5.19615	+	3.00000i	−0.311645	+	0.179928i
$279$			8.00000i			0.478947i
$280$		0			0
$281$			20.0000i			1.19310i	0.802576	+	0.596550i	$0.203462\pi$
$281$			20.0000i			1.19310i	−0.802576	+	0.596550i	$0.796538\pi$
$282$	−8.00000	−	13.8564i	−0.476393	−	0.825137i
$283$	−5.49038	−	20.4904i	−0.326369	−	1.21803i	−0.912928	−	0.408120i	$-0.866184\pi$
$283$	−5.49038	−	20.4904i	−0.326369	−	1.21803i	0.586559	−	0.809907i	$-0.300482\pi$
$284$	−10.0000	+	17.3205i	−0.593391	+	1.02778i
$285$	2.19615	−	8.19615i	0.130089	−	0.485498i
$286$	2.00000	−	2.00000i	0.118262	−	0.118262i
$287$		0			0
$288$	−4.00000	−	4.00000i	−0.235702	−	0.235702i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	2.19615	+	8.19615i	0.128963	+	0.481295i
$291$	−2.73205	+	0.732051i	−0.160156	+	0.0429136i
$292$	−4.00000	−	6.92820i	−0.234082	−	0.405442i
$293$	15.0000	−	15.0000i	0.876309	−	0.876309i	−0.116841	−	0.993151i	$-0.537277\pi$
$293$	15.0000	−	15.0000i	0.876309	−	0.876309i	0.993151	+	0.116841i	$0.0372769\pi$
$294$		0			0
$295$		−	6.00000i		−	0.349334i
$296$	−6.00000	−	10.3923i	−0.348743	−	0.604040i
$297$	−6.92820	−	4.00000i	−0.402015	−	0.232104i
$298$	−12.1244	−	7.00000i	−0.702345	−	0.405499i
$299$	8.19615	+	2.19615i	0.473996	+	0.127007i
$300$	−6.00000	−	6.00000i	−0.346410	−	0.346410i
$301$		0			0
$302$	−10.0000	−	10.0000i	−0.575435	−	0.575435i
$303$	11.0000	+	19.0526i	0.631933	+	1.09454i
$304$	16.3923	−	4.39230i	0.940163	−	0.251916i
$305$	−9.00000	+	15.5885i	−0.515339	+	0.892592i
$306$	−0.732051	+	2.73205i	−0.0418486	+	0.156181i
$307$	−5.00000	−	5.00000i	−0.285365	−	0.285365i	0.549879	−	0.835244i	$-0.314674\pi$
$307$	−5.00000	−	5.00000i	−0.285365	−	0.285365i	−0.835244	+	0.549879i	$0.814674\pi$
$308$		0			0
$309$	−6.00000	+	6.00000i	−0.341328	+	0.341328i
$310$	13.8564	−	8.00000i	0.786991	−	0.454369i
$311$	25.9808	+	15.0000i	1.47323	+	0.850572i	0.999546	−	0.0301210i	$-0.00958925\pi$
$311$	25.9808	+	15.0000i	1.47323	+	0.850572i	0.473688	+	0.880693i	$0.342923\pi$
$312$	−1.46410	−	5.46410i	−0.0828884	−	0.309344i
$313$	−13.8564	+	8.00000i	−0.783210	+	0.452187i	−0.837567	−	0.546335i	$-0.816023\pi$
$313$	−13.8564	+	8.00000i	−0.783210	+	0.452187i	0.0543564	+	0.998522i	$0.482689\pi$
$314$	−30.0000			−1.69300
$315$		0			0
$316$		0			0
$317$	−1.83013	+	6.83013i	−0.102790	+	0.383618i	−0.998085	−	0.0618557i	$-0.980298\pi$
$317$	−1.83013	+	6.83013i	−0.102790	+	0.383618i	0.895295	+	0.445474i	$0.146965\pi$
$318$	−3.66025	−	13.6603i	−0.205257	−	0.766029i
$319$	−3.00000	+	5.19615i	−0.167968	+	0.290929i
$320$	−2.92820	+	10.9282i	−0.163692	+	0.610905i
$321$	14.0000			0.781404
$322$		0			0
$323$	−6.00000	−	6.00000i	−0.333849	−	0.333849i
$324$	−8.66025	+	5.00000i	−0.481125	+	0.277778i
$325$	1.09808	+	4.09808i	0.0609103	+	0.227320i
$326$	−1.00000	+	1.73205i	−0.0553849	+	0.0959294i
$327$	−5.19615	+	3.00000i	−0.287348	+	0.165900i
$328$		0			0
$329$		0			0
$330$			4.00000i			0.220193i
$331$	−1.36603	−	0.366025i	−0.0750835	−	0.0201186i	0.221082	−	0.975255i	$-0.429041\pi$
$331$	−1.36603	−	0.366025i	−0.0750835	−	0.0201186i	−0.296165	+	0.955137i	$0.595708\pi$
$332$	−0.732051	−	2.73205i	−0.0401765	−	0.149941i
$333$	4.09808	−	1.09808i	0.224573	−	0.0601742i
$334$	−0.732051	+	2.73205i	−0.0400560	+	0.149491i
$335$	10.0000			0.546358
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$	4.02628	−	15.0263i	0.219001	−	0.817322i
$339$	−8.19615	+	2.19615i	−0.445154	+	0.119279i
$340$	5.46410	−	1.46410i	0.296333	−	0.0794021i
$341$	10.9282	+	2.92820i	0.591795	+	0.158571i
$342$			6.00000i			0.324443i
$343$		0			0
$344$	20.0000			1.07833
$345$	−10.3923	+	6.00000i	−0.559503	+	0.323029i
$346$	−1.00000	+	1.73205i	−0.0537603	+	0.0931156i
$347$	4.75833	+	17.7583i	0.255441	+	0.953317i	0.967845	+	0.251548i	$0.0809396\pi$
$347$	4.75833	+	17.7583i	0.255441	+	0.953317i	−0.712404	+	0.701769i	$0.752394\pi$
$348$	6.00000	+	10.3923i	0.321634	+	0.557086i
$349$	3.00000	+	3.00000i	0.160586	+	0.160586i	0.782826	−	0.622240i	$-0.213777\pi$
$349$	3.00000	+	3.00000i	0.160586	+	0.160586i	−0.622240	+	0.782826i	$0.713777\pi$
$350$		0			0
$351$	8.00000			0.427008
$352$	−6.92820	+	4.00000i	−0.369274	+	0.213201i
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	−0.775077	−	0.631867i	$-0.782289\pi$
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	0.934751	+	0.355303i	$0.115622\pi$
$354$	−2.19615	−	8.19615i	−0.116724	−	0.435621i
$355$	−3.66025	+	13.6603i	−0.194266	+	0.725011i
$356$	−8.00000			−0.423999
$357$		0			0
$358$	34.0000			1.79696
$359$	22.5167	−	13.0000i	1.18838	−	0.686114i	0.230445	−	0.973085i	$-0.425982\pi$
$359$	22.5167	−	13.0000i	1.18838	−	0.686114i	0.957939	+	0.286972i	$0.0926486\pi$
$360$	−3.46410	−	2.00000i	−0.182574	−	0.105409i
$361$	0.866025	+	0.500000i	0.0455803	+	0.0263158i
$362$	−15.5885	+	9.00000i	−0.819311	+	0.473029i
$363$	9.00000	−	9.00000i	0.472377	−	0.472377i
$364$		0			0
$365$	−4.00000	−	4.00000i	−0.209370	−	0.209370i
$366$	−6.58846	+	24.5885i	−0.344384	+	1.28526i
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	−0.951336	−	0.308155i	$-0.900289\pi$
$367$	−4.00000	+	6.92820i	−0.208798	+	0.361649i	0.742538	+	0.669804i	$0.233622\pi$
$368$	−20.7846	−	12.0000i	−1.08347	−	0.625543i
$369$		0			0
$370$	−6.00000	−	6.00000i	−0.311925	−	0.311925i
$371$		0			0
$372$	16.0000	−	16.0000i	0.829561	−	0.829561i
$373$	6.83013	+	1.83013i	0.353651	+	0.0947604i	0.431271	−	0.902223i	$-0.358065\pi$
$373$	6.83013	+	1.83013i	0.353651	+	0.0947604i	−0.0776200	+	0.996983i	$0.524732\pi$
$374$	3.46410	+	2.00000i	0.179124	+	0.103418i
$375$	−13.8564	−	8.00000i	−0.715542	−	0.413118i
$376$	5.85641	−	21.8564i	0.302021	−	1.12716i
$377$		−	6.00000i		−	0.309016i
$378$		0			0
$379$	−3.00000	+	3.00000i	−0.154100	+	0.154100i	−0.779946	−	0.625847i	$-0.784754\pi$
$379$	−3.00000	+	3.00000i	−0.154100	+	0.154100i	0.625847	+	0.779946i	$0.284754\pi$
$380$	10.3923	−	6.00000i	0.533114	−	0.307794i
$381$	10.9282	−	2.92820i	0.559869	−	0.150016i
$382$	2.92820	+	10.9282i	0.149820	+	0.559136i
$383$	8.00000	+	13.8564i	0.408781	+	0.708029i	0.994753	−	0.102302i	$-0.0326207\pi$
$383$	8.00000	+	13.8564i	0.408781	+	0.708029i	−0.585973	+	0.810331i	$0.699287\pi$
$384$			16.0000i			0.816497i
$385$		0			0
$386$	−14.0000	+	14.0000i	−0.712581	+	0.712581i
$387$	−1.83013	+	6.83013i	−0.0930306	+	0.347195i
$388$	−3.46410	−	2.00000i	−0.175863	−	0.101535i
$389$	−4.75833	−	17.7583i	−0.241257	−	0.900383i	−0.975228	−	0.221202i	$-0.929002\pi$
$389$	−4.75833	−	17.7583i	−0.241257	−	0.900383i	0.733971	−	0.679181i	$-0.237665\pi$
$390$	−2.00000	−	3.46410i	−0.101274	−	0.175412i
$391$			12.0000i			0.606866i
$392$		0			0
$393$		−	22.0000i		−	1.10975i
$394$	−29.4449	+	17.0000i	−1.48341	+	0.856448i
$395$		0			0
$396$	−0.732051	−	2.73205i	−0.0367869	−	0.137291i
$397$	−1.83013	+	6.83013i	−0.0918514	+	0.342794i	−0.996523	−	0.0833147i	$-0.973449\pi$
$397$	−1.83013	+	6.83013i	−0.0918514	+	0.342794i	0.904672	+	0.426109i	$0.140116\pi$
$398$	14.0000	+	14.0000i	0.701757	+	0.701757i
$399$		0			0
$400$		−	12.0000i		−	0.600000i
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	0.998350	−	0.0574304i	$-0.0182907\pi$
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	−0.548911	+	0.835881i	$0.684957\pi$
$402$	13.6603	−	3.66025i	0.681312	−	0.182557i
$403$	−10.9282	+	2.92820i	−0.544373	+	0.145864i
$404$	−8.05256	+	30.0526i	−0.400630	+	1.49517i
$405$	−5.00000	+	5.00000i	−0.248452	+	0.248452i
$406$		0			0
$407$		−	6.00000i		−	0.297409i
$408$	6.92820	−	4.00000i	0.342997	−	0.198030i
$409$	−13.8564	−	8.00000i	−0.685155	−	0.395575i	0.116639	−	0.993174i	$-0.462788\pi$
$409$	−13.8564	−	8.00000i	−0.685155	−	0.395575i	−0.801795	+	0.597600i	$0.796121\pi$
$410$		0			0
$411$	10.9282	+	2.92820i	0.539049	+	0.144438i
$412$	−12.0000			−0.591198
$413$		0			0
$414$	6.00000	−	6.00000i	0.294884	−	0.294884i
$415$	−1.00000	−	1.73205i	−0.0490881	−	0.0850230i
$416$	4.00000	−	6.92820i	0.196116	−	0.339683i
$417$	−3.00000	+	5.19615i	−0.146911	+	0.254457i
$418$	8.19615	+	2.19615i	0.400887	+	0.107417i
$419$	3.00000	+	3.00000i	0.146560	+	0.146560i	0.776579	−	0.630020i	$-0.216953\pi$
$419$	3.00000	+	3.00000i	0.146560	+	0.146560i	−0.630020	+	0.776579i	$0.716953\pi$
$420$		0			0
$421$	−9.00000	+	9.00000i	−0.438633	+	0.438633i	−0.891552	−	0.452919i	$-0.850383\pi$
$421$	−9.00000	+	9.00000i	−0.438633	+	0.438633i	0.452919	+	0.891552i	$0.350383\pi$
$422$	−9.00000	−	15.5885i	−0.438113	−	0.758834i
$423$	6.92820	+	4.00000i	0.336861	+	0.194487i
$424$	10.0000	−	17.3205i	0.485643	−	0.841158i
$425$	−5.19615	+	3.00000i	−0.252050	+	0.145521i
$426$			20.0000i			0.969003i
$427$		0			0
$428$	14.0000	+	14.0000i	0.676716	+	0.676716i
$429$	0.732051	−	2.73205i	0.0353437	−	0.131905i
$430$	13.6603	−	3.66025i	0.658756	−	0.176513i
$431$	−16.0000	+	27.7128i	−0.770693	+	1.33488i	0.166491	+	0.986043i	$0.446756\pi$
$431$	−16.0000	+	27.7128i	−0.770693	+	1.33488i	−0.937184	+	0.348836i	$0.886577\pi$
$432$	−21.8564	−	5.85641i	−1.05157	−	0.281766i
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$	6.00000	+	6.00000i	0.287678	+	0.287678i
$436$	−8.19615	−	2.19615i	−0.392525	−	0.105177i
$437$	6.58846	+	24.5885i	0.315169	+	1.17623i
$438$	−6.92820	−	4.00000i	−0.331042	−	0.191127i
$439$	−12.1244	+	7.00000i	−0.578664	+	0.334092i	−0.760602	−	0.649218i	$-0.775096\pi$
$439$	−12.1244	+	7.00000i	−0.578664	+	0.334092i	0.181938	+	0.983310i	$0.441763\pi$
$440$	−4.00000	+	4.00000i	−0.190693	+	0.190693i
$441$		0			0
$442$	−4.00000			−0.190261
$443$	20.4904	+	5.49038i	0.973527	+	0.260856i	0.710316	−	0.703882i	$-0.248552\pi$
$443$	20.4904	+	5.49038i	0.973527	+	0.260856i	0.263211	+	0.964738i	$0.415218\pi$
$444$	−10.3923	−	6.00000i	−0.493197	−	0.284747i
$445$	−5.46410	+	1.46410i	−0.259023	+	0.0694051i
$446$	32.7846	+	8.78461i	1.55240	+	0.415963i
$447$	−14.0000			−0.662177
$448$		0			0
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$	4.09808	+	1.09808i	0.193185	+	0.0517638i
$451$		0			0
$452$	−10.3923	−	6.00000i	−0.488813	−	0.282216i
$453$	−13.6603	−	3.66025i	−0.641815	−	0.171974i
$454$	−30.0000			−1.40797
$455$		0			0
$456$	12.0000	−	12.0000i	0.561951	−	0.561951i
$457$	27.7128	−	16.0000i	1.29635	−	0.748448i	0.316579	−	0.948566i	$-0.397466\pi$
$457$	27.7128	−	16.0000i	1.29635	−	0.748448i	0.979772	+	0.200118i	$0.0641325\pi$
$458$	−12.1244	−	7.00000i	−0.566534	−	0.327089i
$459$	2.92820	+	10.9282i	0.136677	+	0.510085i
$460$	−16.3923	−	4.39230i	−0.764295	−	0.204792i
$461$	11.0000	+	11.0000i	0.512321	+	0.512321i	0.915237	−	0.402916i	$-0.132003\pi$
$461$	11.0000	+	11.0000i	0.512321	+	0.512321i	−0.402916	+	0.915237i	$0.632003\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$	−4.39230	+	16.3923i	−0.203908	+	0.760994i
$465$	8.00000	−	13.8564i	0.370991	−	0.642575i
$466$	5.46410	−	1.46410i	0.253120	−	0.0678232i
$467$	−1.83013	+	6.83013i	−0.0846882	+	0.316061i	−0.995255	−	0.0973014i	$-0.968979\pi$
$467$	−1.83013	+	6.83013i	−0.0846882	+	0.316061i	0.910567	+	0.413362i	$0.135646\pi$
$468$	2.00000	+	2.00000i	0.0924500	+	0.0924500i
$469$		0			0
$470$		−	16.0000i		−	0.738025i
$471$	−25.9808	+	15.0000i	−1.19713	+	0.691164i
$472$	6.00000	−	10.3923i	0.276172	−	0.478345i
$473$	8.66025	+	5.00000i	0.398199	+	0.229900i
$474$		0			0
$475$	−9.00000	+	9.00000i	−0.412948	+	0.412948i
$476$		0			0
$477$	5.00000	+	5.00000i	0.228934	+	0.228934i
$478$		0			0
$479$	20.0000	−	34.6410i	0.913823	−	1.58279i	0.105208	−	0.994450i	$-0.466449\pi$
$479$	20.0000	−	34.6410i	0.913823	−	1.58279i	0.808615	−	0.588338i	$-0.200218\pi$
$480$	2.92820	+	10.9282i	0.133654	+	0.498802i
$481$	3.00000	+	5.19615i	0.136788	+	0.236924i
$482$	18.0000	−	18.0000i	0.819878	−	0.819878i
$483$		0			0
$484$	18.0000			0.818182
$485$	−2.73205	−	0.732051i	−0.124056	−	0.0332407i
$486$	7.00000	−	12.1244i	0.317526	−	0.549972i
$487$	−1.73205	−	1.00000i	−0.0784867	−	0.0453143i	0.460243	−	0.887793i	$-0.347762\pi$
$487$	−1.73205	−	1.00000i	−0.0784867	−	0.0453143i	−0.538730	+	0.842479i	$0.681096\pi$
$488$	−31.1769	+	18.0000i	−1.41131	+	0.814822i
$489$			2.00000i			0.0904431i
$490$		0			0
$491$	−19.0000	+	19.0000i	−0.857458	+	0.857458i	−0.991038	−	0.133580i	$-0.957353\pi$
$491$	−19.0000	+	19.0000i	−0.857458	+	0.857458i	0.133580	+	0.991038i	$0.457353\pi$
$492$		0			0
$493$	8.19615	−	2.19615i	0.369136	−	0.0989097i
$494$	−8.19615	+	2.19615i	−0.368762	+	0.0988096i
$495$	−1.00000	−	1.73205i	−0.0449467	−	0.0778499i
$496$	32.0000			1.43684
$497$		0			0
$498$	−2.00000	−	2.00000i	−0.0896221	−	0.0896221i
$499$	8.41858	−	31.4186i	0.376868	−	1.40649i	−0.473729	−	0.880671i	$-0.657092\pi$
$499$	8.41858	−	31.4186i	0.376868	−	1.40649i	0.850597	−	0.525818i	$-0.176241\pi$
$500$	−5.85641	−	21.8564i	−0.261906	−	0.977448i
$501$	0.732051	+	2.73205i	0.0327056	+	0.122059i
$502$	36.3731	−	21.0000i	1.62341	−	0.937276i
$503$		−	6.00000i		−	0.267527i	−0.991013	−	0.133763i	$-0.957294\pi$
$503$		−	6.00000i		−	0.267527i	0.991013	−	0.133763i	$-0.0427062\pi$
$504$		0			0
$505$			22.0000i			0.978987i
$506$	−6.00000	−	10.3923i	−0.266733	−	0.461994i
$507$	−4.02628	−	15.0263i	−0.178813	−	0.667340i
$508$	13.8564	+	8.00000i	0.614779	+	0.354943i
$509$	8.41858	−	31.4186i	0.373147	−	1.39260i	−0.482886	−	0.875683i	$-0.660411\pi$
$509$	8.41858	−	31.4186i	0.373147	−	1.39260i	0.856033	−	0.516921i	$-0.172922\pi$
$510$	4.00000	−	4.00000i	0.177123	−	0.177123i
$511$		0			0
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	12.0000	+	20.7846i	0.529813	+	0.917663i
$514$	8.05256	+	30.0526i	0.355183	+	1.32556i
$515$	−8.19615	+	2.19615i	−0.361166	+	0.0967740i
$516$	17.3205	−	10.0000i	0.762493	−	0.440225i
$517$	8.00000	−	8.00000i	0.351840	−	0.351840i
$518$		0			0
$519$			2.00000i			0.0877903i
$520$	1.46410	−	5.46410i	0.0642051	−	0.239617i
$521$	34.6410	+	20.0000i	1.51765	+	0.876216i	0.999785	+	0.0207541i	$0.00660670\pi$
$521$	34.6410	+	20.0000i	1.51765	+	0.876216i	0.517866	+	0.855462i	$0.326727\pi$
$522$	−5.19615	−	3.00000i	−0.227429	−	0.131306i
$523$	−34.1506	−	9.15064i	−1.49330	−	0.400129i	−0.582452	−	0.812865i	$-0.697907\pi$
$523$	−34.1506	−	9.15064i	−1.49330	−	0.400129i	−0.910851	+	0.412736i	$0.864573\pi$
$524$	22.0000	−	22.0000i	0.961074	−	0.961074i
$525$		0			0
$526$	6.00000	+	6.00000i	0.261612	+	0.261612i
$527$	−8.00000	−	13.8564i	−0.348485	−	0.603595i
$528$	−4.00000	+	6.92820i	−0.174078	+	0.301511i
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$	3.66025	−	13.6603i	0.158991	−	0.593364i
$531$	3.00000	+	3.00000i	0.130189	+	0.130189i
$532$		0			0
$533$		0			0
$534$	−6.92820	+	4.00000i	−0.299813	+	0.173097i
$535$	12.1244	+	7.00000i	0.524182	+	0.302636i
$536$	17.3205	+	10.0000i	0.748132	+	0.431934i
$537$	29.4449	−	17.0000i	1.27064	−	0.733604i
$538$	−6.00000			−0.258678
$539$		0			0
$540$	−16.0000			−0.688530
$541$	−3.29423	+	12.2942i	−0.141630	+	0.528570i	0.858252	+	0.513228i	$0.171550\pi$
$541$	−3.29423	+	12.2942i	−0.141630	+	0.528570i	−0.999882	+	0.0153422i	$0.995116\pi$
$542$	2.92820	+	10.9282i	0.125777	+	0.469407i
$543$	−9.00000	+	15.5885i	−0.386227	+	0.668965i
$544$	10.9282	+	2.92820i	0.468543	+	0.125546i
$545$	−6.00000			−0.257012
$546$		0			0
$547$	−5.00000	−	5.00000i	−0.213785	−	0.213785i	0.592088	−	0.805873i	$-0.298304\pi$
$547$	−5.00000	−	5.00000i	−0.213785	−	0.213785i	−0.805873	+	0.592088i	$0.798304\pi$
$548$	8.00000	+	13.8564i	0.341743	+	0.591916i
$549$	−3.29423	−	12.2942i	−0.140594	−	0.524705i
$550$	3.00000	−	5.19615i	0.127920	−	0.221565i
$551$	15.5885	−	9.00000i	0.664091	−	0.383413i
$552$	−24.0000			−1.02151
$553$		0			0
$554$			6.00000i			0.254916i
$555$	−8.19615	−	2.19615i	−0.347907	−	0.0932215i
$556$	−8.19615	+	2.19615i	−0.347594	+	0.0931376i
$557$	34.1506	−	9.15064i	1.44701	−	0.387725i	0.552027	−	0.833827i	$-0.313855\pi$
$557$	34.1506	−	9.15064i	1.44701	−	0.387725i	0.894982	+	0.446102i	$0.147188\pi$
$558$	−2.92820	+	10.9282i	−0.123961	+	0.462628i
$559$	−10.0000			−0.422955
$560$		0			0
$561$	4.00000			0.168880
$562$	−7.32051	+	27.3205i	−0.308797	+	1.15245i
$563$	−25.9545	+	6.95448i	−1.09385	+	0.293096i	−0.760258	−	0.649621i	$-0.774928\pi$
$563$	−25.9545	+	6.95448i	−1.09385	+	0.293096i	−0.333593	+	0.942717i	$0.608261\pi$
$564$	−5.85641	−	21.8564i	−0.246599	−	0.920321i
$565$	−8.19615	−	2.19615i	−0.344815	−	0.0923928i
$566$		−	30.0000i		−	1.26099i
$567$		0			0
$568$	−20.0000	+	20.0000i	−0.839181	+	0.839181i
$569$	−20.7846	+	12.0000i	−0.871336	+	0.503066i	−0.867792	−	0.496928i	$-0.834461\pi$
$569$	−20.7846	+	12.0000i	−0.871336	+	0.503066i	−0.00354413	+	0.999994i	$0.501128\pi$
$570$	6.00000	−	10.3923i	0.251312	−	0.435286i
$571$	0.366025	+	1.36603i	0.0153177	+	0.0571664i	0.973162	−	0.230123i	$-0.0739127\pi$
$571$	0.366025	+	1.36603i	0.0153177	+	0.0571664i	−0.957844	+	0.287289i	$0.907246\pi$
$572$	3.46410	−	2.00000i	0.144841	−	0.0836242i
$573$	8.00000	+	8.00000i	0.334205	+	0.334205i
$574$		0			0
$575$	18.0000			0.750652
$576$	−4.00000	−	6.92820i	−0.166667	−	0.288675i
$577$	−9.00000	+	15.5885i	−0.374675	+	0.648956i	−0.990278	−	0.139100i	$-0.955579\pi$
$577$	−9.00000	+	15.5885i	−0.374675	+	0.648956i	0.615603	+	0.788056i	$0.288912\pi$
$578$	4.75833	+	17.7583i	0.197920	+	0.738649i
$579$	−5.12436	+	19.1244i	−0.212961	+	0.794781i
$580$			12.0000i			0.498273i
$581$		0			0
$582$	−4.00000			−0.165805
$583$	8.66025	−	5.00000i	0.358671	−	0.207079i
$584$	−2.92820	−	10.9282i	−0.121170	−	0.452212i
$585$	1.73205	+	1.00000i	0.0716115	+	0.0413449i
$586$	25.9808	−	15.0000i	1.07326	−	0.619644i
$587$	−7.00000	+	7.00000i	−0.288921	+	0.288921i	−0.836653	−	0.547733i	$-0.815491\pi$
$587$	−7.00000	+	7.00000i	−0.288921	+	0.288921i	0.547733	+	0.836653i	$0.315491\pi$
$588$		0			0
$589$	−24.0000	−	24.0000i	−0.988903	−	0.988903i
$590$	2.19615	−	8.19615i	0.0904142	−	0.337430i
$591$	−17.0000	+	29.4449i	−0.699287	+	1.21120i
$592$	−4.39230	−	16.3923i	−0.180523	−	0.673720i
$593$	−17.0000	−	29.4449i	−0.698106	−	1.20916i	−0.969122	−	0.246581i	$-0.920693\pi$
$593$	−17.0000	−	29.4449i	−0.698106	−	1.20916i	0.271016	−	0.962575i	$-0.412640\pi$
$594$	−8.00000	−	8.00000i	−0.328244	−	0.328244i
$595$		0			0
$596$	−14.0000	−	14.0000i	−0.573462	−	0.573462i
$597$	19.1244	+	5.12436i	0.782708	+	0.209726i
$598$	10.3923	+	6.00000i	0.424973	+	0.245358i
$599$	12.1244	+	7.00000i	0.495388	+	0.286012i	0.726807	−	0.686842i	$-0.241004\pi$
$599$	12.1244	+	7.00000i	0.495388	+	0.286012i	−0.231419	+	0.972854i	$0.574337\pi$
$600$	−6.00000	−	10.3923i	−0.244949	−	0.424264i
$601$		−	20.0000i		−	0.815817i	−0.913023	−	0.407909i	$-0.866258\pi$
$601$		−	20.0000i		−	0.815817i	0.913023	−	0.407909i	$-0.133742\pi$
$602$		0			0
$603$	−5.00000	+	5.00000i	−0.203616	+	0.203616i
$604$	−10.0000	−	17.3205i	−0.406894	−	0.704761i
$605$	12.2942	−	3.29423i	0.499831	−	0.133929i
$606$	8.05256	+	30.0526i	0.327113	+	1.22080i
$607$	16.0000	+	27.7128i	0.649420	+	1.12483i	0.983262	+	0.182199i	$0.0583216\pi$
$607$	16.0000	+	27.7128i	0.649420	+	1.12483i	−0.333842	+	0.942629i	$0.608345\pi$
$608$	24.0000			0.973329
$609$		0			0
$610$	−18.0000	+	18.0000i	−0.728799	+	0.728799i
$611$	−2.92820	+	10.9282i	−0.118462	+	0.442108i
$612$	−2.00000	+	3.46410i	−0.0808452	+	0.140028i
$613$	−9.15064	−	34.1506i	−0.369591	−	1.37933i	−0.861090	−	0.508453i	$-0.830218\pi$
$613$	−9.15064	−	34.1506i	−0.369591	−	1.37933i	0.491499	−	0.870878i	$-0.336449\pi$
$614$	−5.00000	−	8.66025i	−0.201784	−	0.349499i
$615$		0			0
$616$		0			0
$617$			12.0000i			0.483102i	0.970388	+	0.241551i	$0.0776561\pi$
$617$			12.0000i			0.483102i	−0.970388	+	0.241551i	$0.922344\pi$
$618$	−10.3923	+	6.00000i	−0.418040	+	0.241355i
$619$	6.22243	+	23.2224i	0.250101	+	0.933388i	0.970751	+	0.240089i	$0.0771768\pi$
$619$	6.22243	+	23.2224i	0.250101	+	0.933388i	−0.720650	+	0.693299i	$0.756157\pi$
$620$	21.8564	−	5.85641i	0.877774	−	0.235199i
$621$	8.78461	−	32.7846i	0.352514	−	1.31560i
$622$	30.0000	+	30.0000i	1.20289	+	1.20289i
$623$		0			0
$624$		−	8.00000i		−	0.320256i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−21.8564	+	5.85641i	−0.873558	+	0.234069i
$627$	8.19615	−	2.19615i	0.327323	−	0.0877059i
$628$	−40.9808	−	10.9808i	−1.63531	−	0.438180i
$629$	−6.00000	+	6.00000i	−0.239236	+	0.239236i
$630$		0			0
$631$			10.0000i			0.398094i	0.979990	+	0.199047i	$0.0637846\pi$
$631$			10.0000i			0.398094i	−0.979990	+	0.199047i	$0.936215\pi$
$632$		0			0
$633$	−15.5885	−	9.00000i	−0.619586	−	0.357718i
$634$	−5.00000	+	8.66025i	−0.198575	+	0.343943i
$635$	10.9282	+	2.92820i	0.433673	+	0.116202i
$636$		−	20.0000i		−	0.793052i
$637$		0			0
$638$	−6.00000	+	6.00000i	−0.237542	+	0.237542i
$639$	−5.00000	−	8.66025i	−0.197797	−	0.342594i
$640$	−8.00000	+	13.8564i	−0.316228	+	0.547723i
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	−0.631721	−	0.775196i	$-0.717651\pi$
$641$	9.00000	−	15.5885i	0.355479	−	0.615707i	0.987200	+	0.159489i	$0.0509845\pi$
$642$	19.1244	+	5.12436i	0.754778	+	0.202242i
$643$	−21.0000	−	21.0000i	−0.828159	−	0.828159i	0.159103	−	0.987262i	$-0.449140\pi$
$643$	−21.0000	−	21.0000i	−0.828159	−	0.828159i	−0.987262	+	0.159103i	$0.949140\pi$
$644$		0			0
$645$	10.0000	−	10.0000i	0.393750	−	0.393750i
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$	−36.3731	−	21.0000i	−1.42997	−	0.825595i	−0.432855	−	0.901464i	$-0.642494\pi$
$647$	−36.3731	−	21.0000i	−1.42997	−	0.825595i	−0.997118	+	0.0758684i	$0.975827\pi$
$648$	−13.6603	+	3.66025i	−0.536625	+	0.143788i
$649$	5.19615	−	3.00000i	0.203967	−	0.117760i
$650$			6.00000i			0.235339i
$651$		0			0
$652$	−2.00000	+	2.00000i	−0.0783260	+	0.0783260i
$653$	6.95448	−	25.9545i	0.272150	−	1.01568i	−0.685577	−	0.728000i	$-0.740450\pi$
$653$	6.95448	−	25.9545i	0.272150	−	1.01568i	0.957727	−	0.287678i	$-0.0928832\pi$
$654$	−8.19615	+	2.19615i	−0.320495	+	0.0858764i
$655$	11.0000	−	19.0526i	0.429806	−	0.744445i
$656$		0			0
$657$	4.00000			0.156055
$658$		0			0
$659$	−17.0000	−	17.0000i	−0.662226	−	0.662226i	0.293678	−	0.955904i	$-0.405121\pi$
$659$	−17.0000	−	17.0000i	−0.662226	−	0.662226i	−0.955904	+	0.293678i	$0.905121\pi$
$660$	−1.46410	+	5.46410i	−0.0569901	+	0.212690i
$661$	−3.29423	−	12.2942i	−0.128131	−	0.478190i	0.871801	−	0.489860i	$-0.162952\pi$
$661$	−3.29423	−	12.2942i	−0.128131	−	0.478190i	−0.999932	+	0.0116697i	$0.996285\pi$
$662$	−1.73205	−	1.00000i	−0.0673181	−	0.0388661i
$663$	−3.46410	+	2.00000i	−0.134535	+	0.0776736i
$664$		−	4.00000i		−	0.155230i
$665$		0			0
$666$	6.00000			0.232495
$667$	−24.5885	−	6.58846i	−0.952069	−	0.255106i
$668$	−2.00000	+	3.46410i	−0.0773823	+	0.134030i
$669$	32.7846	−	8.78461i	1.26753	−	0.339633i
$670$	13.6603	+	3.66025i	0.527742	+	0.141408i
$671$	−18.0000			−0.694882
$672$		0			0
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$	24.5885	+	6.58846i	0.947112	+	0.253778i
$675$	16.3923	−	4.39230i	0.630940	−	0.169060i
$676$	11.0000	−	19.0526i	0.423077	−	0.732791i
$677$	−4.09808	−	1.09808i	−0.157502	−	0.0422025i	0.179206	−	0.983811i	$-0.442647\pi$
$677$	−4.09808	−	1.09808i	−0.157502	−	0.0422025i	−0.336708	+	0.941609i	$0.609314\pi$
$678$	−12.0000			−0.460857
$679$		0			0
$680$	8.00000			0.306786
$681$	−25.9808	+	15.0000i	−0.995585	+	0.574801i
$682$	13.8564	+	8.00000i	0.530589	+	0.306336i
$683$	1.83013	+	6.83013i	0.0700279	+	0.261348i	0.992060	−	0.125766i	$-0.0401388\pi$
$683$	1.83013	+	6.83013i	0.0700279	+	0.261348i	−0.922032	+	0.387113i	$0.873472\pi$
$684$	−2.19615	+	8.19615i	−0.0839720	+	0.313388i
$685$	8.00000	+	8.00000i	0.305664	+	0.305664i
$686$		0			0
$687$	−14.0000			−0.534133
$688$	27.3205	+	7.32051i	1.04158	+	0.279092i
$689$	−5.00000	+	8.66025i	−0.190485	+	0.329929i
$690$	−16.3923	+	4.39230i	−0.624044	+	0.167212i
$691$	−3.29423	+	12.2942i	−0.125318	+	0.467694i	−0.999851	−	0.0172725i	$-0.994502\pi$
$691$	−3.29423	+	12.2942i	−0.125318	+	0.467694i	0.874532	+	0.484967i	$0.161168\pi$
$692$	−2.00000	+	2.00000i	−0.0760286	+	0.0760286i
$693$		0			0
$694$			26.0000i			0.986947i
$695$	−5.19615	+	3.00000i	−0.197101	+	0.113796i
$696$	4.39230	+	16.3923i	0.166490	+	0.621349i
$697$		0			0
$698$	3.00000	+	5.19615i	0.113552	+	0.196677i
$699$	4.00000	−	4.00000i	0.151294	−	0.151294i
$700$		0			0
$701$	31.0000	+	31.0000i	1.17085	+	1.17085i	0.982006	+	0.188847i	$0.0604752\pi$
$701$	31.0000	+	31.0000i	1.17085	+	1.17085i	0.188847	+	0.982006i	$0.439525\pi$
$702$	10.9282	+	2.92820i	0.412458	+	0.110518i
$703$	−9.00000	+	15.5885i	−0.339441	+	0.587930i
$704$	−10.9282	+	2.92820i	−0.411872	+	0.110361i
$705$	−8.00000	−	13.8564i	−0.301297	−	0.521862i
$706$	6.00000	−	6.00000i	0.225813	−	0.225813i
$707$		0			0
$708$		−	12.0000i		−	0.450988i
$709$	−36.8827	−	9.88269i	−1.38516	−	0.371152i	−0.512166	−	0.858886i	$-0.671157\pi$
$709$	−36.8827	−	9.88269i	−1.38516	−	0.371152i	−0.872992	+	0.487734i	$0.837823\pi$
$710$	−10.0000	+	17.3205i	−0.375293	+	0.650027i
$711$		0			0
$712$	−10.9282	−	2.92820i	−0.409552	−	0.109739i
$713$			48.0000i			1.79761i
$714$		0			0
$715$	2.00000	−	2.00000i	0.0747958	−	0.0747958i
$716$	46.4449	+	12.4449i	1.73573	+	0.465086i
$717$		0			0
$718$	35.5167	−	9.51666i	1.32547	−	0.355159i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$	−4.00000	−	4.00000i	−0.149071	−	0.149071i
$721$		0			0
$722$	1.00000	+	1.00000i	0.0372161	+	0.0372161i
$723$	6.58846	−	24.5885i	0.245027	−	0.914455i
$724$	−24.5885	+	6.58846i	−0.913823	+	0.244858i
$725$	−3.29423	−	12.2942i	−0.122345	−	0.456596i
$726$	15.5885	−	9.00000i	0.578542	−	0.334021i
$727$			2.00000i			0.0741759i	0.999312	+	0.0370879i	$0.0118082\pi$
$727$			2.00000i			0.0741759i	−0.999312	+	0.0370879i	$0.988192\pi$
$728$		0			0
$729$		−	29.0000i		−	1.07407i
$730$	−4.00000	−	6.92820i	−0.148047	−	0.256424i
$731$	−3.66025	−	13.6603i	−0.135379	−	0.505243i
$732$	−18.0000	+	31.1769i	−0.665299	+	1.15233i
$733$	−7.68653	+	28.6865i	−0.283909	+	1.05956i	0.665725	+	0.746198i	$0.268123\pi$
$733$	−7.68653	+	28.6865i	−0.283909	+	1.05956i	−0.949633	+	0.313364i	$0.898544\pi$
$734$	−8.00000	+	8.00000i	−0.295285	+	0.295285i
$735$		0			0
$736$	−24.0000	−	24.0000i	−0.884652	−	0.884652i
$737$	5.00000	+	8.66025i	0.184177	+	0.319005i
$738$		0			0
$739$	−31.4186	+	8.41858i	−1.15575	+	0.309683i	−0.785268	−	0.619156i	$-0.787475\pi$
$739$	−31.4186	+	8.41858i	−1.15575	+	0.309683i	−0.370484	+	0.928839i	$0.620808\pi$
$740$	−6.00000	−	10.3923i	−0.220564	−	0.382029i
$741$	−6.00000	+	6.00000i	−0.220416	+	0.220416i
$742$		0			0
$743$		−	46.0000i		−	1.68758i	−0.536676	−	0.843788i	$-0.680320\pi$
$743$		−	46.0000i		−	1.68758i	0.536676	−	0.843788i	$-0.319680\pi$
$744$	27.7128	−	16.0000i	1.01600	−	0.586588i
$745$	−12.1244	−	7.00000i	−0.444202	−	0.256460i
$746$	8.66025	+	5.00000i	0.317074	+	0.183063i
$747$	1.36603	+	0.366025i	0.0499803	+	0.0133922i
$748$	4.00000	+	4.00000i	0.146254	+	0.146254i
$749$		0			0
$750$	−16.0000	−	16.0000i	−0.584237	−	0.584237i
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	−0.995018	−	0.0996961i	$-0.968213\pi$
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	0.411170	−	0.911559i	$-0.365120\pi$
$752$	16.0000	−	27.7128i	0.583460	−	1.01058i
$753$	21.0000	−	36.3731i	0.765283	−	1.32551i
$754$	2.19615	−	8.19615i	0.0799792	−	0.298486i
$755$	−10.0000	−	10.0000i	−0.363937	−	0.363937i
$756$		0			0
$757$	23.0000	−	23.0000i	0.835949	−	0.835949i	−0.152374	−	0.988323i	$-0.548692\pi$
$757$	23.0000	−	23.0000i	0.835949	−	0.835949i	0.988323	+	0.152374i	$0.0486917\pi$
$758$	−5.19615	+	3.00000i	−0.188733	+	0.108965i
$759$	−10.3923	−	6.00000i	−0.377217	−	0.217786i
$760$	16.3923	−	4.39230i	0.594611	−	0.159326i
$761$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$761$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$762$	16.0000			0.579619
$763$		0			0
$764$			16.0000i			0.578860i
$765$	−0.732051	+	2.73205i	−0.0264674	+	0.0987775i
$766$	5.85641	+	21.8564i	0.211601	+	0.789704i
$767$	−3.00000	+	5.19615i	−0.108324	+	0.187622i
$768$	−5.85641	+	21.8564i	−0.211325	+	0.788675i
$769$	−50.0000			−1.80305			−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000			−1.80305			−0.901523	+	0.432731i	$0.857550\pi$
$770$		0			0
$771$	22.0000	+	22.0000i	0.792311	+	0.792311i
$772$	−24.2487	+	14.0000i	−0.872730	+	0.503871i
$773$	−1.83013	−	6.83013i	−0.0658251	−	0.245663i	0.925172	−	0.379549i	$-0.123921\pi$
$773$	−1.83013	−	6.83013i	−0.0658251	−	0.245663i	−0.990997	+	0.133887i	$0.957254\pi$
$774$	−5.00000	+	8.66025i	−0.179721	+	0.311286i
$775$	−20.7846	+	12.0000i	−0.746605	+	0.431053i
$776$	−4.00000	−	4.00000i	−0.143592	−	0.143592i
$777$		0			0
$778$		−	26.0000i		−	0.932145i
$779$		0			0
$780$	−1.46410	−	5.46410i	−0.0524232	−	0.195646i
$781$	−13.6603	+	3.66025i	−0.488802	+	0.130974i
$782$	−4.39230	+	16.3923i	−0.157069	+	0.586188i
$783$	−24.0000			−0.857690
$784$		0			0
$785$	−30.0000			−1.07075
$786$	8.05256	−	30.0526i	0.287225	−	1.07194i
$787$	−20.4904	+	5.49038i	−0.730403	+	0.195711i	−0.604809	−	0.796371i	$-0.706750\pi$
$787$	−20.4904	+	5.49038i	−0.730403	+	0.195711i	−0.125594	+	0.992082i	$0.540084\pi$
$788$	−46.4449	+	12.4449i	−1.65453	+	0.443330i
$789$	8.19615	+	2.19615i	0.291791	+	0.0781851i
$790$		0			0
$791$		0			0
$792$		−	4.00000i		−	0.142134i
$793$	15.5885	−	9.00000i	0.553562	−	0.319599i
$794$	−5.00000	+	8.66025i	−0.177443	+	0.307341i
$795$	−3.66025	−	13.6603i	−0.129816	−	0.484479i
$796$	14.0000	+	24.2487i	0.496217	+	0.859473i
$797$	−25.0000	−	25.0000i	−0.885545	−	0.885545i	0.108546	−	0.994091i	$-0.465381\pi$
$797$	−25.0000	−	25.0000i	−0.885545	−	0.885545i	−0.994091	+	0.108546i	$0.965381\pi$
$798$		0			0
$799$	−16.0000			−0.566039
$800$	4.39230	−	16.3923i	0.155291	−	0.579555i
$801$	2.00000	−	3.46410i	0.0706665	−	0.122398i
$802$	6.58846	+	24.5885i	0.232647	+	0.868249i
$803$	1.46410	−	5.46410i	0.0516670	−	0.192824i
$804$	20.0000			0.705346
$805$		0			0
$806$	−16.0000			−0.563576
$807$	−5.19615	+	3.00000i	−0.182913	+	0.105605i
$808$	−22.0000	+	38.1051i	−0.773957	+	1.34053i
$809$	−13.8564	−	8.00000i	−0.487165	−	0.281265i	0.236232	−	0.971697i	$-0.424087\pi$
$809$	−13.8564	−	8.00000i	−0.487165	−	0.281265i	−0.723398	+	0.690432i	$0.757421\pi$
$810$	−8.66025	+	5.00000i	−0.304290	+	0.175682i
$811$	−39.0000	+	39.0000i	−1.36948	+	1.36948i	−0.508288	+	0.861187i	$0.669722\pi$
$811$	−39.0000	+	39.0000i	−1.36948	+	1.36948i	−0.861187	+	0.508288i	$0.830278\pi$
$812$		0			0
$813$	8.00000	+	8.00000i	0.280572	+	0.280572i
$814$	2.19615	−	8.19615i	0.0769751	−	0.287275i
$815$	−1.00000	+	1.73205i	−0.0350285	+	0.0606711i
$816$	10.9282	−	2.92820i	0.382564	−	0.102508i
$817$	−15.0000	−	25.9808i	−0.524784	−	0.908952i
$818$	−16.0000	−	16.0000i	−0.559427	−	0.559427i
$819$		0			0
$820$		0			0
$821$	−15.0263	−	4.02628i	−0.524421	−	0.140518i	−0.0131101	−	0.999914i	$-0.504173\pi$
$821$	−15.0263	−	4.02628i	−0.524421	−	0.140518i	−0.511311	+	0.859396i	$0.670840\pi$
$822$	13.8564	+	8.00000i	0.483298	+	0.279032i
$823$	−29.4449	−	17.0000i	−1.02638	−	0.592583i	−0.110437	−	0.993883i	$-0.535225\pi$
$823$	−29.4449	−	17.0000i	−1.02638	−	0.592583i	−0.915947	+	0.401300i	$0.868558\pi$
$824$	−16.3923	−	4.39230i	−0.571053	−	0.153013i
$825$		−	6.00000i		−	0.208893i
$826$		0			0
$827$	33.0000	−	33.0000i	1.14752	−	1.14752i	0.160484	−	0.987038i	$-0.448695\pi$
$827$	33.0000	−	33.0000i	1.14752	−	1.14752i	0.987038	−	0.160484i	$-0.0513055\pi$
$828$	10.3923	−	6.00000i	0.361158	−	0.208514i
$829$	−31.4186	+	8.41858i	−1.09121	+	0.292390i	−0.759182	−	0.650879i	$-0.774401\pi$
$829$	−31.4186	+	8.41858i	−1.09121	+	0.292390i	−0.332031	+	0.943268i	$0.607734\pi$
$830$	−0.732051	−	2.73205i	−0.0254099	−	0.0948309i
$831$	3.00000	+	5.19615i	0.104069	+	0.180253i
$832$	8.00000	−	8.00000i	0.277350	−	0.277350i
$833$		0			0
$834$	−6.00000	+	6.00000i	−0.207763	+	0.207763i
$835$	−0.732051	+	2.73205i	−0.0253337	+	0.0945465i
$836$	10.3923	+	6.00000i	0.359425	+	0.207514i
$837$	11.7128	+	43.7128i	0.404854	+	1.51094i
$838$	3.00000	+	5.19615i	0.103633	+	0.179498i
$839$		−	14.0000i		−	0.483334i	−0.970359	−	0.241667i	$-0.922306\pi$
$839$		−	14.0000i		−	0.483334i	0.970359	−	0.241667i	$-0.0776941\pi$
$840$		0			0
$841$		−	11.0000i		−	0.379310i
$842$	−15.5885	+	9.00000i	−0.537214	+	0.310160i
$843$	7.32051	+	27.3205i	0.252132	+	0.940968i
$844$	−6.58846	−	24.5885i	−0.226784	−	0.846370i
$845$	4.02628	−	15.0263i	0.138508	−	0.516920i
$846$	8.00000	+	8.00000i	0.275046	+	0.275046i
$847$		0			0
$848$	20.0000	−	20.0000i	0.686803	−	0.686803i
$849$	−15.0000	−	25.9808i	−0.514799	−	0.891657i
$850$	−8.19615	+	2.19615i	−0.281126	+	0.0753274i
$851$	24.5885	−	6.58846i	0.842881	−	0.225849i
$852$	−7.32051	+	27.3205i	−0.250796	+	0.935985i
$853$	−5.00000	+	5.00000i	−0.171197	+	0.171197i	−0.787505	−	0.616308i	$-0.788628\pi$
$853$	−5.00000	+	5.00000i	−0.171197	+	0.171197i	0.616308	+	0.787505i	$0.288628\pi$
$854$		0			0
$855$			6.00000i			0.205196i
$856$	14.0000	+	24.2487i	0.478510	+	0.828804i
$857$	6.92820	+	4.00000i	0.236663	+	0.136637i	0.613642	−	0.789584i	$-0.289704\pi$
$857$	6.92820	+	4.00000i	0.236663	+	0.136637i	−0.376979	+	0.926222i	$0.623037\pi$
$858$	2.00000	−	3.46410i	0.0682789	−	0.118262i
$859$	4.09808	+	1.09808i	0.139825	+	0.0374659i	0.328053	−	0.944659i	$-0.393608\pi$
$859$	4.09808	+	1.09808i	0.139825	+	0.0374659i	−0.188228	+	0.982125i	$0.560274\pi$
$860$	20.0000			0.681994
$861$		0			0
$862$	−32.0000	+	32.0000i	−1.08992	+	1.08992i
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	0.586235	−	0.810141i	$-0.300609\pi$
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	−0.994720	+	0.102624i	$0.967276\pi$
$864$	−27.7128	−	16.0000i	−0.942809	−	0.544331i
$865$	−1.00000	+	1.73205i	−0.0340010	+	0.0588915i
$866$	19.1244	+	5.12436i	0.649872	+	0.174133i
$867$	13.0000	+	13.0000i	0.441503	+	0.441503i
$868$		0			0
$869$		0			0
$870$	6.00000	+	10.3923i	0.203419	+	0.352332i
$871$	−8.66025	−	5.00000i	−0.293442	−	0.169419i
$872$	−10.3923	−	6.00000i	−0.351928	−	0.203186i
$873$	1.73205	−	1.00000i	0.0586210	−	0.0338449i
$874$			36.0000i			1.21772i
$875$		0			0
$876$	−8.00000	−	8.00000i	−0.270295	−	0.270295i
$877$	−1.83013	+	6.83013i	−0.0617990	+	0.230637i	−0.989917	−	0.141649i	$-0.954759\pi$
$877$	−1.83013	+	6.83013i	−0.0617990	+	0.230637i	0.928118	+	0.372286i	$0.121426\pi$
$878$	−19.1244	+	5.12436i	−0.645416	+	0.172939i
$879$	15.0000	−	25.9808i	0.505937	−	0.876309i
$880$	−6.92820	+	4.00000i	−0.233550	+	0.134840i
$881$	2.00000			0.0673817			0.0336909	−	0.999432i	$-0.489274\pi$
$881$	2.00000			0.0673817			0.0336909	+	0.999432i	$0.489274\pi$
$882$		0			0
$883$	−21.0000	−	21.0000i	−0.706706	−	0.706706i	0.259135	−	0.965841i	$-0.416563\pi$
$883$	−21.0000	−	21.0000i	−0.706706	−	0.706706i	−0.965841	+	0.259135i	$0.916563\pi$
$884$	−5.46410	−	1.46410i	−0.183778	−	0.0492431i
$885$	−2.19615	−	8.19615i	−0.0738229	−	0.275511i
$886$	25.9808	+	15.0000i	0.872841	+	0.503935i
$887$	1.73205	−	1.00000i	0.0581566	−	0.0335767i	−0.470640	−	0.882325i	$-0.655977\pi$
$887$	1.73205	−	1.00000i	0.0581566	−	0.0335767i	0.528796	+	0.848749i	$0.322644\pi$
$888$	−12.0000	−	12.0000i	−0.402694	−	0.402694i
$889$		0			0
$890$	−8.00000			−0.268161
$891$	−6.83013	−	1.83013i	−0.228818	−	0.0613116i
$892$	41.5692	+	24.0000i	1.39184	+	0.803579i
$893$	−32.7846	+	8.78461i	−1.09710	+	0.293966i
$894$	−19.1244	−	5.12436i	−0.639614	−	0.171384i
$895$	34.0000			1.13649
$896$		0			0
$897$	12.0000			0.400668
$898$	40.9808	+	10.9808i	1.36755	+	0.366433i
$899$	32.7846	−	8.78461i	1.09343	−	0.292983i
$900$	5.19615	+	3.00000i	0.173205	+	0.100000i
$901$	−13.6603	−	3.66025i	−0.455089	−	0.121941i
$902$		0			0
$903$		0			0
$904$	−12.0000	−	12.0000i	−0.399114	−	0.399114i
$905$	−15.5885	+	9.00000i	−0.518178	+	0.299170i
$906$	−17.3205	−	10.0000i	−0.575435	−	0.332228i
$907$	−9.88269	−	36.8827i	−0.328149	−	1.22467i	−0.911108	−	0.412168i	$-0.864772\pi$
$907$	−9.88269	−	36.8827i	−0.328149	−	1.22467i	0.582959	−	0.812502i	$-0.301895\pi$
$908$	−40.9808	−	10.9808i	−1.35999	−	0.364409i
$909$	−11.0000	−	11.0000i	−0.364847	−	0.364847i
$910$		0			0
$911$	−8.00000			−0.265052			−0.132526	−	0.991180i	$-0.542309\pi$
$911$	−8.00000			−0.265052			−0.132526	+	0.991180i	$0.542309\pi$
$912$	20.7846	−	12.0000i	0.688247	−	0.397360i
$913$	1.00000	−	1.73205i	0.0330952	−	0.0573225i
$914$	43.7128	−	11.7128i	1.44589	−	0.387425i
$915$	−6.58846	+	24.5885i	−0.217808	+	0.812869i
$916$	−14.0000	−	14.0000i	−0.462573	−	0.462573i
$917$		0			0
$918$			16.0000i			0.528079i
$919$	22.5167	−	13.0000i	0.742756	−	0.428830i	−0.0803145	−	0.996770i	$-0.525592\pi$
$919$	22.5167	−	13.0000i	0.742756	−	0.428830i	0.823071	+	0.567939i	$0.192259\pi$
$920$	−20.7846	−	12.0000i	−0.685248	−	0.395628i
$921$	−8.66025	−	5.00000i	−0.285365	−	0.164756i
$922$	11.0000	+	19.0526i	0.362266	+	0.627463i
$923$	10.0000	−	10.0000i	0.329154	−	0.329154i
$924$		0			0
$925$	9.00000	+	9.00000i	0.295918	+	0.295918i
$926$	−21.8564	−	5.85641i	−0.718246	−	0.192453i
$927$	3.00000	−	5.19615i	0.0985329	−	0.170664i
$928$	−12.0000	+	20.7846i	−0.393919	+	0.682288i
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	0.507825	−	0.861460i	$-0.330450\pi$
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	−0.999959	+	0.00905914i	$0.997116\pi$
$930$	16.0000	−	16.0000i	0.524661	−	0.524661i
$931$		0			0
$932$	8.00000			0.262049
$933$	40.9808	+	10.9808i	1.34165	+	0.359494i
$934$	−5.00000	+	8.66025i	−0.163605	+	0.283372i
$935$	3.46410	+	2.00000i	0.113288	+	0.0654070i
$936$	2.00000	+	3.46410i	0.0653720	+	0.113228i
$937$		−	28.0000i		−	0.914720i	−0.889282	−	0.457360i	$-0.848795\pi$
$937$		−	28.0000i		−	0.914720i	0.889282	−	0.457360i	$-0.151205\pi$
$938$		0			0
$939$	−16.0000	+	16.0000i	−0.522140	+	0.522140i
$940$	5.85641	−	21.8564i	0.191015	−	0.712877i
$941$	39.6147	−	10.6147i	1.29140	−	0.346031i	0.453210	−	0.891404i	$-0.350279\pi$
$941$	39.6147	−	10.6147i	1.29140	−	0.346031i	0.838193	+	0.545373i	$0.183612\pi$
$942$	−40.9808	+	10.9808i	−1.33523	+	0.357773i
$943$		0			0
$944$	12.0000	−	12.0000i	0.390567	−	0.390567i
$945$		0			0
$946$	10.0000	+	10.0000i	0.325128	+	0.325128i
$947$	−1.83013	+	6.83013i	−0.0594711	+	0.221949i	−0.989265	−	0.146131i	$-0.953318\pi$
$947$	−1.83013	+	6.83013i	−0.0594711	+	0.221949i	0.929794	+	0.368080i	$0.119985\pi$
$948$		0			0
$949$	1.46410	+	5.46410i	0.0475267	+	0.177372i
$950$	−15.5885	+	9.00000i	−0.505756	+	0.291999i
$951$			10.0000i			0.324272i
$952$		0			0
$953$			24.0000i			0.777436i	0.921357	+	0.388718i	$0.127082\pi$
$953$			24.0000i			0.777436i	−0.921357	+	0.388718i	$0.872918\pi$
$954$	5.00000	+	8.66025i	0.161881	+	0.280386i
$955$	2.92820	+	10.9282i	0.0947544	+	0.353628i
$956$		0			0
$957$	−2.19615	+	8.19615i	−0.0709915	+	0.264944i
$958$	40.0000	−	40.0000i	1.29234	−	1.29234i
$959$		0			0
$960$			16.0000i			0.516398i
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	2.19615	+	8.19615i	0.0708068	+	0.264255i
$963$	−9.56218	+	2.56218i	−0.308137	+	0.0825650i
$964$	31.1769	−	18.0000i	1.00414	−	0.579741i
$965$	−14.0000	+	14.0000i	−0.450676	+	0.450676i
$966$		0			0
$967$			2.00000i			0.0643157i	0.999483	+	0.0321578i	$0.0102379\pi$
$967$			2.00000i			0.0643157i	−0.999483	+	0.0321578i	$0.989762\pi$
$968$	24.5885	+	6.58846i	0.790303	+	0.211761i
$969$	−10.3923	−	6.00000i	−0.333849	−	0.192748i
$970$	−3.46410	−	2.00000i	−0.111226	−	0.0642161i
$971$	25.9545	+	6.95448i	0.832919	+	0.223180i	0.649987	−	0.759946i	$-0.274774\pi$
$971$	25.9545	+	6.95448i	0.832919	+	0.223180i	0.182932	+	0.983126i	$0.441441\pi$
$972$	14.0000	−	14.0000i	0.449050	−	0.449050i
$973$		0			0
$974$	−2.00000	−	2.00000i	−0.0640841	−	0.0640841i
$975$	3.00000	+	5.19615i	0.0960769	+	0.166410i
$976$	−49.1769	+	13.1769i	−1.57411	+	0.421783i
$977$	1.00000	−	1.73205i	0.0319928	−	0.0554132i	−0.849586	−	0.527451i	$-0.823148\pi$
$977$	1.00000	−	1.73205i	0.0319928	−	0.0554132i	0.881579	+	0.472037i	$0.156481\pi$
$978$	−0.732051	+	2.73205i	−0.0234084	+	0.0873614i
$979$	−4.00000	−	4.00000i	−0.127841	−	0.127841i
$980$		0			0
$981$	3.00000	−	3.00000i	0.0957826	−	0.0957826i
$982$	−32.9090	+	19.0000i	−1.05017	+	0.606314i
$983$	−29.4449	−	17.0000i	−0.939145	−	0.542216i	−0.0494530	−	0.998776i	$-0.515748\pi$
$983$	−29.4449	−	17.0000i	−0.939145	−	0.542216i	−0.889692	+	0.456561i	$0.849081\pi$
$984$		0			0
$985$	−29.4449	+	17.0000i	−0.938191	+	0.541665i
$986$	12.0000			0.382158
$987$		0			0
$988$	−12.0000			−0.381771
$989$	−10.9808	+	40.9808i	−0.349168	+	1.30311i
$990$	−0.732051	−	2.73205i	−0.0232661	−	0.0868303i
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	0.491698	+	0.870766i	$0.336377\pi$
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	−0.999954	+	0.00956046i	$0.996957\pi$
$992$	43.7128	+	11.7128i	1.38788	+	0.371882i
$993$	−2.00000			−0.0634681
$994$		0			0
$995$	14.0000	+	14.0000i	0.443830	+	0.443830i
$996$	−2.00000	−	3.46410i	−0.0633724	−	0.109764i
$997$	−13.5429	−	50.5429i	−0.428909	−	1.60071i	−0.755235	−	0.655454i	$-0.772477\pi$
$997$	−13.5429	−	50.5429i	−0.428909	−	1.60071i	0.326326	−	0.945257i	$-0.394189\pi$
$998$	23.0000	−	39.8372i	0.728052	−	1.26102i
$999$	20.7846	−	12.0000i	0.657596	−	0.379663i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.f.557.1		4
7.2	even	3	inner	784.2.x.f.765.1		4
7.3	odd	6		784.2.m.b.589.1		2
7.4	even	3		16.2.e.a.13.1	yes	2
7.5	odd	6		784.2.x.c.765.1		4
7.6	odd	2		784.2.x.c.557.1		4
16.5	even	4	inner	784.2.x.f.165.1		4
21.11	odd	6		144.2.k.a.109.1		2
28.11	odd	6		64.2.e.a.17.1		2
35.4	even	6		400.2.l.c.301.1		2
35.18	odd	12		400.2.q.b.349.1		2
35.32	odd	12		400.2.q.a.349.1		2
56.11	odd	6		128.2.e.a.33.1		2
56.53	even	6		128.2.e.b.33.1		2
84.11	even	6		576.2.k.a.145.1		2
112.5	odd	12		784.2.x.c.373.1		4
112.11	odd	12		64.2.e.a.49.1		2
112.37	even	12	inner	784.2.x.f.373.1		4
112.53	even	12		16.2.e.a.5.1	✓	2
112.67	odd	12		128.2.e.a.97.1		2
112.69	odd	4		784.2.x.c.165.1		4
112.101	odd	12		784.2.m.b.197.1		2
112.109	even	12		128.2.e.b.97.1		2
140.39	odd	6		1600.2.l.a.401.1		2
140.67	even	12		1600.2.q.b.849.1		2
140.123	even	12		1600.2.q.a.849.1		2
168.11	even	6		1152.2.k.a.289.1		2
168.53	odd	6		1152.2.k.b.289.1		2
224.11	odd	24		1024.2.a.e.1.2		2
224.53	even	24		1024.2.a.b.1.1		2
224.67	odd	24		1024.2.b.b.513.2		2
224.109	even	24		1024.2.b.e.513.2		2
224.123	odd	24		1024.2.a.e.1.1		2
224.165	even	24		1024.2.a.b.1.2		2
224.179	odd	24		1024.2.b.b.513.1		2
224.221	even	24		1024.2.b.e.513.1		2
336.11	even	12		576.2.k.a.433.1		2
336.53	odd	12		144.2.k.a.37.1		2
336.179	even	12		1152.2.k.a.865.1		2
336.221	odd	12		1152.2.k.b.865.1		2
560.53	odd	12		400.2.q.a.149.1		2
560.123	even	12		1600.2.q.b.49.1		2
560.277	odd	12		400.2.q.b.149.1		2
560.347	even	12		1600.2.q.a.49.1		2
560.389	even	12		400.2.l.c.101.1		2
560.459	odd	12		1600.2.l.a.1201.1		2
672.11	even	24		9216.2.a.s.1.1		2
672.53	odd	24		9216.2.a.d.1.1		2
672.347	even	24		9216.2.a.s.1.2		2
672.389	odd	24		9216.2.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.2.e.a.5.1	✓	2	112.53	even	12
16.2.e.a.13.1	yes	2	7.4	even	3
64.2.e.a.17.1		2	28.11	odd	6
64.2.e.a.49.1		2	112.11	odd	12
128.2.e.a.33.1		2	56.11	odd	6
128.2.e.a.97.1		2	112.67	odd	12
128.2.e.b.33.1		2	56.53	even	6
128.2.e.b.97.1		2	112.109	even	12
144.2.k.a.37.1		2	336.53	odd	12
144.2.k.a.109.1		2	21.11	odd	6
400.2.l.c.101.1		2	560.389	even	12
400.2.l.c.301.1		2	35.4	even	6
400.2.q.a.149.1		2	560.53	odd	12
400.2.q.a.349.1		2	35.32	odd	12
400.2.q.b.149.1		2	560.277	odd	12
400.2.q.b.349.1		2	35.18	odd	12
576.2.k.a.145.1		2	84.11	even	6
576.2.k.a.433.1		2	336.11	even	12
784.2.m.b.197.1		2	112.101	odd	12
784.2.m.b.589.1		2	7.3	odd	6
784.2.x.c.165.1		4	112.69	odd	4
784.2.x.c.373.1		4	112.5	odd	12
784.2.x.c.557.1		4	7.6	odd	2
784.2.x.c.765.1		4	7.5	odd	6
784.2.x.f.165.1		4	16.5	even	4	inner
784.2.x.f.373.1		4	112.37	even	12	inner
784.2.x.f.557.1		4	1.1	even	1	trivial
784.2.x.f.765.1		4	7.2	even	3	inner
1024.2.a.b.1.1		2	224.53	even	24
1024.2.a.b.1.2		2	224.165	even	24
1024.2.a.e.1.1		2	224.123	odd	24
1024.2.a.e.1.2		2	224.11	odd	24
1024.2.b.b.513.1		2	224.179	odd	24
1024.2.b.b.513.2		2	224.67	odd	24
1024.2.b.e.513.1		2	224.221	even	24
1024.2.b.e.513.2		2	224.109	even	24
1152.2.k.a.289.1		2	168.11	even	6
1152.2.k.a.865.1		2	336.179	even	12
1152.2.k.b.289.1		2	168.53	odd	6
1152.2.k.b.865.1		2	336.221	odd	12
1600.2.l.a.401.1		2	140.39	odd	6
1600.2.l.a.1201.1		2	560.459	odd	12
1600.2.q.a.49.1		2	560.347	even	12
1600.2.q.a.849.1		2	140.123	even	12
1600.2.q.b.49.1		2	560.123	even	12
1600.2.q.b.849.1		2	140.67	even	12
9216.2.a.d.1.1		2	672.53	odd	24
9216.2.a.d.1.2		2	672.389	odd	24
9216.2.a.s.1.1		2	672.11	even	24
9216.2.a.s.1.2		2	672.347	even	24

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 0.366025i) q^{2} +(1.36603 - 0.366025i) q^{3} +(1.73205 + 1.00000i) q^{4} +(1.36603 + 0.366025i) q^{5} +2.00000 q^{6} +(2.00000 + 2.00000i) q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(1.36603 + 0.366025i) q^{2} +(1.36603 - 0.366025i) q^{3} +(1.73205 + 1.00000i) q^{4} +(1.36603 + 0.366025i) q^{5} +2.00000 q^{6} +(2.00000 + 2.00000i) q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.73205 + 1.00000i) q^{10} +(0.366025 + 1.36603i) q^{11} +(2.73205 + 0.732051i) q^{12} +(-1.00000 - 1.00000i) q^{13} +2.00000 q^{15} +(2.00000 + 3.46410i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-1.36603 + 0.366025i) q^{18} +(1.09808 - 4.09808i) q^{19} +(2.00000 + 2.00000i) q^{20} +2.00000i q^{22} +(-5.19615 + 3.00000i) q^{23} +(3.46410 + 2.00000i) q^{24} +(-2.59808 - 1.50000i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(-4.00000 + 4.00000i) q^{27} +(3.00000 + 3.00000i) q^{29} +(2.73205 + 0.732051i) q^{30} +(4.00000 - 6.92820i) q^{31} +(1.46410 + 5.46410i) q^{32} +(1.00000 + 1.73205i) q^{33} +(2.00000 - 2.00000i) q^{34} -2.00000 q^{36} +(-4.09808 - 1.09808i) q^{37} +(3.00000 - 5.19615i) q^{38} +(-1.73205 - 1.00000i) q^{39} +(2.00000 + 3.46410i) q^{40} +(5.00000 - 5.00000i) q^{43} +(-0.732051 + 2.73205i) q^{44} +(-1.36603 + 0.366025i) q^{45} +(-8.19615 + 2.19615i) q^{46} +(-4.00000 - 6.92820i) q^{47} +(4.00000 + 4.00000i) q^{48} +(-3.00000 - 3.00000i) q^{50} +(0.732051 - 2.73205i) q^{51} +(-0.732051 - 2.73205i) q^{52} +(-1.83013 - 6.83013i) q^{53} +(-6.92820 + 4.00000i) q^{54} +2.00000i q^{55} -6.00000i q^{57} +(3.00000 + 5.19615i) q^{58} +(-1.09808 - 4.09808i) q^{59} +(3.46410 + 2.00000i) q^{60} +(-3.29423 + 12.2942i) q^{61} +(8.00000 - 8.00000i) q^{62} +8.00000i q^{64} +(-1.00000 - 1.73205i) q^{65} +(0.732051 + 2.73205i) q^{66} +(6.83013 - 1.83013i) q^{67} +(3.46410 - 2.00000i) q^{68} +(-6.00000 + 6.00000i) q^{69} +10.0000i q^{71} +(-2.73205 - 0.732051i) q^{72} +(-3.46410 - 2.00000i) q^{73} +(-5.19615 - 3.00000i) q^{74} +(-4.09808 - 1.09808i) q^{75} +(6.00000 - 6.00000i) q^{76} +(-2.00000 - 2.00000i) q^{78} +(1.46410 + 5.46410i) q^{80} +(-2.50000 + 4.33013i) q^{81} +(-1.00000 - 1.00000i) q^{83} +(2.00000 - 2.00000i) q^{85} +(8.66025 - 5.00000i) q^{86} +(5.19615 + 3.00000i) q^{87} +(-2.00000 + 3.46410i) q^{88} +(-3.46410 + 2.00000i) q^{89} -2.00000 q^{90} -12.0000 q^{92} +(2.92820 - 10.9282i) q^{93} +(-2.92820 - 10.9282i) q^{94} +(3.00000 - 5.19615i) q^{95} +(4.00000 + 6.92820i) q^{96} -2.00000 q^{97} +(-1.00000 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 8 q^{6} + 8 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 8 * q^6 + 8 * q^8	\( 4 q + 2 q^{2} + 2 q^{3} + 2 q^{5} + 8 q^{6} + 8 q^{8} - 2 q^{11} + 4 q^{12} - 4 q^{13} + 8 q^{15} + 8 q^{16} + 4 q^{17} - 2 q^{18} - 6 q^{19} + 8 q^{20} - 4 q^{26} - 16 q^{27} + 12 q^{29} + 4 q^{30} + 16 q^{31} - 8 q^{32} + 4 q^{33} + 8 q^{34} - 8 q^{36} - 6 q^{37} + 12 q^{38} + 8 q^{40} + 20 q^{43} + 4 q^{44} - 2 q^{45} - 12 q^{46} - 16 q^{47} + 16 q^{48} - 12 q^{50} - 4 q^{51} + 4 q^{52} + 10 q^{53} + 12 q^{58} + 6 q^{59} + 18 q^{61} + 32 q^{62} - 4 q^{65} - 4 q^{66} + 10 q^{67} - 24 q^{69} - 4 q^{72} - 6 q^{75} + 24 q^{76} - 8 q^{78} - 8 q^{80} - 10 q^{81} - 4 q^{83} + 8 q^{85} - 8 q^{88} - 8 q^{90} - 48 q^{92} - 16 q^{93} + 16 q^{94} + 12 q^{95} + 16 q^{96} - 8 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 + 2 * q^5 + 8 * q^6 + 8 * q^8 - 2 * q^11 + 4 * q^12 - 4 * q^13 + 8 * q^15 + 8 * q^16 + 4 * q^17 - 2 * q^18 - 6 * q^19 + 8 * q^20 - 4 * q^26 - 16 * q^27 + 12 * q^29 + 4 * q^30 + 16 * q^31 - 8 * q^32 + 4 * q^33 + 8 * q^34 - 8 * q^36 - 6 * q^37 + 12 * q^38 + 8 * q^40 + 20 * q^43 + 4 * q^44 - 2 * q^45 - 12 * q^46 - 16 * q^47 + 16 * q^48 - 12 * q^50 - 4 * q^51 + 4 * q^52 + 10 * q^53 + 12 * q^58 + 6 * q^59 + 18 * q^61 + 32 * q^62 - 4 * q^65 - 4 * q^66 + 10 * q^67 - 24 * q^69 - 4 * q^72 - 6 * q^75 + 24 * q^76 - 8 * q^78 - 8 * q^80 - 10 * q^81 - 4 * q^83 + 8 * q^85 - 8 * q^88 - 8 * q^90 - 48 * q^92 - 16 * q^93 + 16 * q^94 + 12 * q^95 + 16 * q^96 - 8 * q^97 - 4 * q^99

Introduction

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Database

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