LMFDB - Embedded newform 784.2.x.c.765.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(165,784)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [4,2,-2,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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			765.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	784.765
Dual form			784.2.x.c.165.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.366025 - 1.36603i) q^{2} +(0.366025 - 1.36603i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.366025 + 1.36603i) q^{5} -2.00000 q^{6} +(2.00000 + 2.00000i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.73205 - 1.00000i) q^{10} +(-1.36603 - 0.366025i) q^{11} +(0.732051 + 2.73205i) q^{12} +(1.00000 + 1.00000i) q^{13} +2.00000 q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(0.366025 - 1.36603i) q^{18} +(4.09808 - 1.09808i) 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} +(-0.732051 - 2.73205i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(-2.00000 + 2.00000i) q^{34} -2.00000 q^{36} +(1.09808 + 4.09808i) 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} +(2.73205 - 0.732051i) q^{44} +(-0.366025 + 1.36603i) q^{45} +(2.19615 - 8.19615i) q^{46} +(4.00000 - 6.92820i) q^{47} +(-4.00000 - 4.00000i) q^{48} +(-3.00000 - 3.00000i) q^{50} +(-2.73205 + 0.732051i) q^{51} +(-2.73205 - 0.732051i) q^{52} +(6.83013 + 1.83013i) q^{53} +(-6.92820 - 4.00000i) q^{54} -2.00000i q^{55} -6.00000i q^{57} +(3.00000 - 5.19615i) q^{58} +(-4.09808 - 1.09808i) q^{59} +(-3.46410 + 2.00000i) q^{60} +(-12.2942 + 3.29423i) q^{61} +(-8.00000 + 8.00000i) q^{62} +8.00000i q^{64} +(-1.00000 + 1.73205i) q^{65} +(2.73205 + 0.732051i) q^{66} +(-1.83013 + 6.83013i) q^{67} +(3.46410 + 2.00000i) q^{68} +(6.00000 - 6.00000i) q^{69} +10.0000i q^{71} +(0.732051 + 2.73205i) q^{72} +(-3.46410 + 2.00000i) q^{73} +(5.19615 - 3.00000i) q^{74} +(-1.09808 - 4.09808i) q^{75} +(-6.00000 + 6.00000i) q^{76} +(-2.00000 - 2.00000i) q^{78} +(5.46410 + 1.46410i) 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} +(-10.9282 + 2.92820i) q^{93} +(-10.9282 - 2.92820i) 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} - 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}+ \cdots - 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

Character values

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

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

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 $

$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$2$	−0.366025	−	1.36603i	−0.258819	−	0.965926i
$3$	0.366025	−	1.36603i	0.211325	−	0.788675i	−0.776103	−	0.630606i	$-0.782806\pi$
$3$	0.366025	−	1.36603i	0.211325	−	0.788675i	0.987428	−	0.158069i	$-0.0505269\pi$
$4$	−1.73205	+	1.00000i	−0.866025	+	0.500000i
$5$	0.366025	+	1.36603i	0.163692	+	0.610905i	0.998203	+	0.0599153i	$0.0190830\pi$
$5$	0.366025	+	1.36603i	0.163692	+	0.610905i	−0.834512	+	0.550990i	$0.814250\pi$
$6$	−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
$11$	−1.36603	−	0.366025i	−0.411872	−	0.110361i	0.0469323	−	0.998898i	$-0.485055\pi$
$11$	−1.36603	−	0.366025i	−0.411872	−	0.110361i	−0.458804	+	0.888537i	$0.651722\pi$
$12$	0.732051	+	2.73205i	0.211325	+	0.788675i
$13$	1.00000	+	1.00000i	0.277350	+	0.277350i	0.832050	−	0.554700i	$-0.187167\pi$
$13$	1.00000	+	1.00000i	0.277350	+	0.277350i	−0.554700	+	0.832050i	$0.687167\pi$
$14$		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	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	0.366025	−	1.36603i	0.0862730	−	0.321975i
$19$	4.09808	−	1.09808i	0.940163	−	0.251916i	0.243980	−	0.969780i	$-0.421547\pi$
$19$	4.09808	−	1.09808i	0.940163	−	0.251916i	0.696183	+	0.717864i	$0.254880\pi$
$20$	−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	$-0.118211\pi$
$23$	5.19615	+	3.00000i	1.08347	+	0.625543i	0.151642	+	0.988436i	$0.451544\pi$
$24$	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	$0.621119\pi$
$30$	−0.732051	−	2.73205i	−0.133654	−	0.498802i
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	−5.46410	−	1.46410i	−0.965926	−	0.258819i
$33$	−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
$37$	1.09808	+	4.09808i	0.180523	+	0.673720i	0.995545	+	0.0942898i	$0.0300580\pi$
$37$	1.09808	+	4.09808i	0.180523	+	0.673720i	−0.815022	+	0.579430i	$0.803275\pi$
$38$	−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	$0.0687403\pi$
$44$	2.73205	−	0.732051i	0.411872	−	0.110361i
$45$	−0.366025	+	1.36603i	−0.0545638	+	0.203635i
$46$	2.19615	−	8.19615i	0.323805	−	1.20846i
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	−0.411606	−	0.911362i	$-0.635032\pi$
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	0.995066	−	0.0992202i	$-0.0316348\pi$
$48$	−4.00000	−	4.00000i	−0.577350	−	0.577350i
$49$		0			0
$50$	−3.00000	−	3.00000i	−0.424264	−	0.424264i
$51$	−2.73205	+	0.732051i	−0.382564	+	0.102508i
$52$	−2.73205	−	0.732051i	−0.378867	−	0.101517i
$53$	6.83013	+	1.83013i	0.938190	+	0.251387i	0.695344	−	0.718677i	$-0.255252\pi$
$53$	6.83013	+	1.83013i	0.938190	+	0.251387i	0.242846	+	0.970065i	$0.421919\pi$
$54$	−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
$59$	−4.09808	−	1.09808i	−0.533524	−	0.142957i	−0.0180090	−	0.999838i	$-0.505733\pi$
$59$	−4.09808	−	1.09808i	−0.533524	−	0.142957i	−0.515515	+	0.856880i	$0.672399\pi$
$60$	−3.46410	+	2.00000i	−0.447214	+	0.258199i
$61$	−12.2942	+	3.29423i	−1.57411	+	0.421783i	−0.937098	−	0.349067i	$-0.886499\pi$
$61$	−12.2942	+	3.29423i	−1.57411	+	0.421783i	−0.637017	+	0.770850i	$0.719832\pi$
$62$	−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
$66$	2.73205	+	0.732051i	0.336292	+	0.0901092i
$67$	−1.83013	+	6.83013i	−0.223586	+	0.834433i	0.759381	+	0.650647i	$0.225502\pi$
$67$	−1.83013	+	6.83013i	−0.223586	+	0.834433i	−0.982966	+	0.183786i	$0.941165\pi$
$68$	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	$0.797789\pi$
$72$	0.732051	+	2.73205i	0.0862730	+	0.321975i
$73$	−3.46410	+	2.00000i	−0.405442	+	0.234082i	−0.688830	−	0.724923i	$-0.741875\pi$
$73$	−3.46410	+	2.00000i	−0.405442	+	0.234082i	0.283387	+	0.959006i	$0.408542\pi$
$74$	5.19615	−	3.00000i	0.604040	−	0.348743i
$75$	−1.09808	−	4.09808i	−0.126795	−	0.473205i
$76$	−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	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$	5.46410	+	1.46410i	0.610905	+	0.163692i
$81$	−2.50000	−	4.33013i	−0.277778	−	0.481125i
$82$		0			0
$83$	1.00000	+	1.00000i	0.109764	+	0.109764i	0.759856	−	0.650092i	$-0.225269\pi$
$83$	1.00000	+	1.00000i	0.109764	+	0.109764i	−0.650092	+	0.759856i	$0.725269\pi$
$84$		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	0.305038	−	0.952340i	$-0.401331\pi$
$89$	−3.46410	−	2.00000i	−0.367194	−	0.212000i	−0.672232	+	0.740341i	$0.734664\pi$
$90$	2.00000			0.210819
$91$		0			0
$92$	−12.0000			−1.25109
$93$	−10.9282	+	2.92820i	−1.13320	+	0.303641i
$94$	−10.9282	−	2.92820i	−1.12716	−	0.302021i
$95$	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	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$		0			0
$99$	−1.00000	−	1.00000i	−0.100504	−	0.100504i
$100$	−3.00000	+	5.19615i	−0.300000	+	0.519615i
$101$	15.0263	+	4.02628i	1.49517	+	0.400630i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	15.0263	+	4.02628i	1.49517	+	0.400630i	0.583691	+	0.811976i	$0.301608\pi$
$102$	2.00000	+	3.46410i	0.198030	+	0.342997i
$103$	−5.19615	−	3.00000i	−0.511992	−	0.295599i	0.221660	−	0.975124i	$-0.428852\pi$
$103$	−5.19615	−	3.00000i	−0.511992	−	0.295599i	−0.733652	+	0.679525i	$0.762186\pi$
$104$			4.00000i			0.392232i
$105$		0			0
$106$		−	10.0000i		−	0.971286i
$107$	−2.56218	−	9.56218i	−0.247695	−	0.924411i	−0.972010	−	0.234941i	$-0.924510\pi$
$107$	−2.56218	−	9.56218i	−0.247695	−	0.924411i	0.724315	−	0.689470i	$-0.242156\pi$
$108$	−2.92820	+	10.9282i	−0.281766	+	1.05157i
$109$	1.09808	−	4.09808i	0.105177	−	0.392525i	−0.893189	−	0.449682i	$-0.851537\pi$
$109$	1.09808	−	4.09808i	0.105177	−	0.392525i	0.998365	+	0.0571579i	$0.0182038\pi$
$110$	−2.73205	+	0.732051i	−0.260491	+	0.0697983i
$111$	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	$0.591070\pi$
$114$	−8.19615	+	2.19615i	−0.767640	+	0.205689i
$115$	−2.19615	+	8.19615i	−0.204792	+	0.764295i
$116$	−8.19615	−	2.19615i	−0.760994	−	0.203908i
$117$	0.366025	+	1.36603i	0.0338391	+	0.126289i
$118$			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	$0.384500\pi$
$128$	10.9282	−	2.92820i	0.965926	−	0.258819i
$129$	−5.00000	−	8.66025i	−0.440225	−	0.762493i
$130$	2.73205	+	0.732051i	0.239617	+	0.0642051i
$131$	15.0263	−	4.02628i	1.31285	−	0.351778i	0.466557	−	0.884491i	$-0.345494\pi$
$131$	15.0263	−	4.02628i	1.31285	−	0.351778i	0.846296	+	0.532714i	$0.178828\pi$
$132$		−	4.00000i		−	0.348155i
$133$		0			0
$134$	10.0000			0.863868
$135$	6.92820	+	4.00000i	0.596285	+	0.344265i
$136$	1.46410	−	5.46410i	0.125546	−	0.468543i
$137$	−6.92820	+	4.00000i	−0.591916	+	0.341743i	−0.765855	−	0.643013i	$-0.777684\pi$
$137$	−6.92820	+	4.00000i	−0.591916	+	0.341743i	0.173939	+	0.984757i	$0.444351\pi$
$138$	−10.3923	−	6.00000i	−0.884652	−	0.510754i
$139$	3.00000	−	3.00000i	0.254457	−	0.254457i	−0.568338	−	0.822795i	$-0.692414\pi$
$139$	3.00000	−	3.00000i	0.254457	−	0.254457i	0.822795	+	0.568338i	$0.192414\pi$
$140$		0			0
$141$	−8.00000	−	8.00000i	−0.673722	−	0.673722i
$142$	13.6603	−	3.66025i	1.14634	−	0.307162i
$143$	−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
$149$	2.56218	+	9.56218i	0.209902	+	0.783364i	0.987899	+	0.155097i	$0.0495689\pi$
$149$	2.56218	+	9.56218i	0.209902	+	0.783364i	−0.777997	+	0.628267i	$0.783764\pi$
$150$	−5.19615	+	3.00000i	−0.424264	+	0.244949i
$151$	8.66025	−	5.00000i	0.704761	−	0.406894i	−0.104357	−	0.994540i	$-0.533278\pi$
$151$	8.66025	−	5.00000i	0.704761	−	0.406894i	0.809118	+	0.587646i	$0.199945\pi$
$152$	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
$157$	−5.49038	+	20.4904i	−0.438180	+	1.63531i	0.295160	+	0.955448i	$0.404627\pi$
$157$	−5.49038	+	20.4904i	−0.438180	+	1.63531i	−0.733340	+	0.679862i	$0.762039\pi$
$158$		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
$163$	1.36603	−	0.366025i	0.106995	−	0.0286693i	−0.204924	−	0.978778i	$-0.565695\pi$
$163$	1.36603	−	0.366025i	0.106995	−	0.0286693i	0.311919	+	0.950109i	$0.399028\pi$
$164$		0			0
$165$	−2.73205	−	0.732051i	−0.212690	−	0.0569901i
$166$	1.00000	−	1.73205i	0.0776151	−	0.134433i
$167$		−	2.00000i		−	0.154765i	−0.997001	−	0.0773823i	$-0.975344\pi$
$167$		−	2.00000i		−	0.154765i	0.997001	−	0.0773823i	$-0.0246562\pi$
$168$		0			0
$169$		−	11.0000i		−	0.846154i
$170$	−3.46410	−	2.00000i	−0.265684	−	0.153393i
$171$	4.09808	+	1.09808i	0.313388	+	0.0839720i
$172$	−3.66025	+	13.6603i	−0.279092	+	1.04158i
$173$	−1.36603	+	0.366025i	−0.103857	+	0.0278284i	−0.310373	−	0.950615i	$-0.600454\pi$
$173$	−1.36603	+	0.366025i	−0.103857	+	0.0278284i	0.206516	+	0.978443i	$0.433787\pi$
$174$	−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
$178$	−1.46410	+	5.46410i	−0.109739	+	0.409552i
$179$	−6.22243	+	23.2224i	−0.465086	+	1.73573i	0.191516	+	0.981489i	$0.438660\pi$
$179$	−6.22243	+	23.2224i	−0.465086	+	1.73573i	−0.656603	+	0.754237i	$0.728007\pi$
$180$	−0.732051	−	2.73205i	−0.0545638	−	0.203635i
$181$	9.00000	−	9.00000i	0.668965	−	0.668965i	−0.288512	−	0.957476i	$-0.593160\pi$
$181$	9.00000	−	9.00000i	0.668965	−	0.668965i	0.957476	+	0.288512i	$0.0931604\pi$
$182$		0			0
$183$			18.0000i			1.33060i
$184$	4.39230	+	16.3923i	0.323805	+	1.20846i
$185$	−5.19615	+	3.00000i	−0.382029	+	0.220564i
$186$	8.00000	+	13.8564i	0.586588	+	1.01600i
$187$	0.732051	+	2.73205i	0.0535329	+	0.199787i
$188$			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	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$	10.9282	+	2.92820i	0.788675	+	0.211325i
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	−0.732051	−	2.73205i	−0.0525582	−	0.196150i
$195$	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	−0.00436292	−	0.999990i	$-0.501389\pi$
$199$	12.1244	−	7.00000i	0.859473	−	0.496217i	0.863836	+	0.503774i	$0.168055\pi$
$200$	8.19615	+	2.19615i	0.579555	+	0.155291i
$201$	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
$206$	−2.19615	+	8.19615i	−0.153013	+	0.571053i
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	5.46410	−	1.46410i	0.378867	−	0.101517i
$209$	−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	$0.894353\pi$
$212$	−13.6603	+	3.66025i	−0.938190	+	0.251387i
$213$	13.6603	+	3.66025i	0.935985	+	0.250796i
$214$	−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
$219$	1.46410	+	5.46410i	0.0989348	+	0.369230i
$220$	2.00000	+	3.46410i	0.134840	+	0.233550i
$221$	0.732051	−	2.73205i	0.0492431	−	0.183778i
$222$	−2.19615	−	8.19615i	−0.147396	−	0.550090i
$223$	−24.0000			−1.60716			−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000			−1.60716			−0.803579	+	0.595198i	$0.797074\pi$
$224$		0			0
$225$	3.00000			0.200000
$226$	2.19615	+	8.19615i	0.146086	+	0.545200i
$227$	−5.49038	+	20.4904i	−0.364409	+	1.35999i	0.503810	+	0.863814i	$0.331931\pi$
$227$	−5.49038	+	20.4904i	−0.364409	+	1.35999i	−0.868220	+	0.496180i	$0.834736\pi$
$228$	6.00000	+	10.3923i	0.397360	+	0.688247i
$229$	−2.56218	−	9.56218i	−0.169313	−	0.631886i	−0.997451	−	0.0713609i	$-0.977266\pi$
$229$	−2.56218	−	9.56218i	−0.169313	−	0.631886i	0.828137	−	0.560526i	$-0.189401\pi$
$230$	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	$-0.375160\pi$
$233$	−3.46410	−	2.00000i	−0.226941	−	0.131024i	−0.609160	+	0.793047i	$0.708493\pi$
$234$	1.73205	−	1.00000i	0.113228	−	0.0653720i
$235$	10.9282	+	2.92820i	0.712877	+	0.191015i
$236$	8.19615	−	2.19615i	0.533524	−	0.142957i
$237$		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	−0.995509	−	0.0946700i	$-0.969820\pi$
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	0.415768	−	0.909471i	$-0.363513\pi$
$242$	−3.29423	+	12.2942i	−0.211761	+	0.790303i
$243$	9.56218	−	2.56218i	0.613414	−	0.164364i
$244$	18.0000	−	18.0000i	1.15233	−	1.15233i
$245$		0			0
$246$		0			0
$247$	5.19615	+	3.00000i	0.330623	+	0.190885i
$248$	5.85641	−	21.8564i	0.371882	−	1.38788i
$249$	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	$0.636661\pi$
$251$	−21.0000	+	21.0000i	−1.32551	+	1.32551i	−0.909243	+	0.416265i	$0.863339\pi$
$252$		0			0
$253$	−6.00000	−	6.00000i	−0.377217	−	0.377217i
$254$	−2.92820	−	10.9282i	−0.183732	−	0.685696i
$255$	−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	0.286909	+	0.957958i	$0.407372\pi$
$257$	−11.0000	+	19.0526i	−0.686161	+	1.18847i	−0.973070	+	0.230508i	$0.925961\pi$
$258$	−10.0000	+	10.0000i	−0.622573	+	0.622573i
$259$		0			0
$260$		−	4.00000i		−	0.248069i
$261$	1.09808	+	4.09808i	0.0679692	+	0.253665i
$262$	−11.0000	−	19.0526i	−0.679582	−	1.17707i
$263$	−5.19615	+	3.00000i	−0.320408	+	0.184988i	−0.651575	−	0.758585i	$-0.725891\pi$
$263$	−5.19615	+	3.00000i	−0.320408	+	0.184988i	0.331166	+	0.943572i	$0.392558\pi$
$264$	−5.46410	+	1.46410i	−0.336292	+	0.0901092i
$265$			10.0000i			0.614295i
$266$		0			0
$267$	−4.00000	+	4.00000i	−0.244796	+	0.244796i
$268$	−3.66025	−	13.6603i	−0.223586	−	0.834433i
$269$	−1.09808	+	4.09808i	−0.0669509	+	0.249864i	−0.991288	−	0.131713i	$-0.957952\pi$
$269$	−1.09808	+	4.09808i	−0.0669509	+	0.249864i	0.924337	+	0.381577i	$0.124619\pi$
$270$	2.92820	−	10.9282i	0.178205	−	0.665069i
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	−0.961563	−	0.274586i	$-0.911459\pi$
$271$	−4.00000	+	6.92820i	−0.242983	+	0.420858i	0.718580	+	0.695444i	$0.244792\pi$
$272$	−8.00000			−0.485071
$273$		0			0
$274$	8.00000	+	8.00000i	0.483298	+	0.483298i
$275$	−4.09808	+	1.09808i	−0.247123	+	0.0662165i
$276$	−4.39230	+	16.3923i	−0.264386	+	0.986701i
$277$	−4.09808	−	1.09808i	−0.246230	−	0.0659770i	0.133593	−	0.991036i	$-0.457348\pi$
$277$	−4.09808	−	1.09808i	−0.246230	−	0.0659770i	−0.379823	+	0.925059i	$0.624015\pi$
$278$	−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
$283$	−20.4904	−	5.49038i	−1.21803	−	0.326369i	−0.408120	−	0.912928i	$-0.633816\pi$
$283$	−20.4904	−	5.49038i	−1.21803	−	0.326369i	−0.809907	+	0.586559i	$0.800482\pi$
$284$	−10.0000	−	17.3205i	−0.593391	−	1.02778i
$285$	8.19615	−	2.19615i	0.485498	−	0.130089i
$286$	−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
$290$	8.19615	+	2.19615i	0.481295	+	0.128963i
$291$	0.732051	−	2.73205i	0.0429136	−	0.160156i
$292$	4.00000	−	6.92820i	0.234082	−	0.405442i
$293$	−15.0000	+	15.0000i	−0.876309	+	0.876309i	−0.993151	−	0.116841i	$-0.962723\pi$
$293$	−15.0000	+	15.0000i	−0.876309	+	0.876309i	0.116841	+	0.993151i	$0.462723\pi$
$294$		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
$299$	2.19615	+	8.19615i	0.127007	+	0.473996i
$300$	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
$304$	4.39230	−	16.3923i	0.251916	−	0.940163i
$305$	−9.00000	−	15.5885i	−0.515339	−	0.892592i
$306$	−2.73205	+	0.732051i	−0.156181	+	0.0418486i
$307$	5.00000	+	5.00000i	0.285365	+	0.285365i	0.835244	−	0.549879i	$-0.185326\pi$
$307$	5.00000	+	5.00000i	0.285365	+	0.285365i	−0.549879	+	0.835244i	$0.685326\pi$
$308$		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	0.473688	−	0.880693i	$-0.342923\pi$
$311$	25.9808	−	15.0000i	1.47323	−	0.850572i	0.999546	+	0.0301210i	$0.00958925\pi$
$312$	5.46410	+	1.46410i	0.309344	+	0.0828884i
$313$	−13.8564	−	8.00000i	−0.783210	−	0.452187i	0.0543564	−	0.998522i	$-0.482689\pi$
$313$	−13.8564	−	8.00000i	−0.783210	−	0.452187i	−0.837567	+	0.546335i	$0.816023\pi$
$314$	30.0000			1.69300
$315$		0			0
$316$		0			0
$317$	6.83013	−	1.83013i	0.383618	−	0.102790i	−0.0618557	−	0.998085i	$-0.519702\pi$
$317$	6.83013	−	1.83013i	0.383618	−	0.102790i	0.445474	+	0.895295i	$0.353035\pi$
$318$	−13.6603	−	3.66025i	−0.766029	−	0.205257i
$319$	−3.00000	−	5.19615i	−0.167968	−	0.290929i
$320$	−10.9282	+	2.92820i	−0.610905	+	0.163692i
$321$	−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
$325$	4.09808	+	1.09808i	0.227320	+	0.0609103i
$326$	−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
$331$	0.366025	+	1.36603i	0.0201186	+	0.0750835i	0.975255	−	0.221082i	$-0.0709588\pi$
$331$	0.366025	+	1.36603i	0.0201186	+	0.0750835i	−0.955137	+	0.296165i	$0.904292\pi$
$332$	−2.73205	−	0.732051i	−0.149941	−	0.0401765i
$333$	−1.09808	+	4.09808i	−0.0601742	+	0.224573i
$334$	−2.73205	+	0.732051i	−0.149491	+	0.0400560i
$335$	−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	$0.336901\pi$
$338$	−15.0263	+	4.02628i	−0.817322	+	0.219001i
$339$	−2.19615	+	8.19615i	−0.119279	+	0.445154i
$340$	−1.46410	+	5.46410i	−0.0794021	+	0.296333i
$341$	2.92820	+	10.9282i	0.158571	+	0.591795i
$342$		−	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
$347$	−17.7583	−	4.75833i	−0.953317	−	0.255441i	−0.251548	−	0.967845i	$-0.580940\pi$
$347$	−17.7583	−	4.75833i	−0.953317	−	0.255441i	−0.701769	+	0.712404i	$0.747606\pi$
$348$	−6.00000	+	10.3923i	−0.321634	+	0.557086i
$349$	−3.00000	−	3.00000i	−0.160586	−	0.160586i	0.622240	−	0.782826i	$-0.286223\pi$
$349$	−3.00000	−	3.00000i	−0.160586	−	0.160586i	−0.782826	+	0.622240i	$0.786223\pi$
$350$		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	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$	8.19615	+	2.19615i	0.435621	+	0.116724i
$355$	−13.6603	+	3.66025i	−0.725011	+	0.194266i
$356$	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	$-0.574018\pi$
$359$	−22.5167	−	13.0000i	−1.18838	−	0.686114i	−0.957939	+	0.286972i	$0.907351\pi$
$360$	−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
$366$	24.5885	−	6.58846i	1.28526	−	0.344384i
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	0.951336	−	0.308155i	$-0.0997115\pi$
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	−0.742538	+	0.669804i	$0.766378\pi$
$368$	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
$373$	−1.83013	−	6.83013i	−0.0947604	−	0.353651i	0.902223	−	0.431271i	$-0.141935\pi$
$373$	−1.83013	−	6.83013i	−0.0947604	−	0.353651i	−0.996983	+	0.0776200i	$0.975268\pi$
$374$	3.46410	−	2.00000i	0.179124	−	0.103418i
$375$	13.8564	−	8.00000i	0.715542	−	0.413118i
$376$	21.8564	−	5.85641i	1.12716	−	0.302021i
$377$			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
$381$	2.92820	−	10.9282i	0.150016	−	0.559869i
$382$	−10.9282	−	2.92820i	−0.559136	−	0.149820i
$383$	−8.00000	+	13.8564i	−0.408781	+	0.708029i	−0.994753	−	0.102302i	$-0.967379\pi$
$383$	−8.00000	+	13.8564i	−0.408781	+	0.708029i	0.585973	+	0.810331i	$0.300713\pi$
$384$		−	16.0000i		−	0.816497i
$385$		0			0
$386$	−14.0000	+	14.0000i	−0.712581	+	0.712581i
$387$	6.83013	−	1.83013i	0.347195	−	0.0930306i
$388$	−3.46410	+	2.00000i	−0.175863	+	0.101535i
$389$	17.7583	+	4.75833i	0.900383	+	0.241257i	0.679181	−	0.733971i	$-0.262335\pi$
$389$	17.7583	+	4.75833i	0.900383	+	0.241257i	0.221202	+	0.975228i	$0.429002\pi$
$390$	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
$396$	2.73205	+	0.732051i	0.137291	+	0.0367869i
$397$	−6.83013	+	1.83013i	−0.342794	+	0.0918514i	−0.426109	−	0.904672i	$-0.640116\pi$
$397$	−6.83013	+	1.83013i	−0.342794	+	0.0918514i	0.0833147	+	0.996523i	$0.473449\pi$
$398$	−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	−0.548911	−	0.835881i	$-0.684957\pi$
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	0.998350	+	0.0574304i	$0.0182907\pi$
$402$	3.66025	−	13.6603i	0.182557	−	0.681312i
$403$	2.92820	−	10.9282i	0.145864	−	0.544373i
$404$	−30.0526	+	8.05256i	−1.49517	+	0.400630i
$405$	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	−0.801795	−	0.597600i	$-0.796121\pi$
$409$	−13.8564	+	8.00000i	−0.685155	+	0.395575i	0.116639	+	0.993174i	$0.462788\pi$
$410$		0			0
$411$	2.92820	+	10.9282i	0.144438	+	0.539049i
$412$	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
$418$	2.19615	+	8.19615i	0.107417	+	0.400887i
$419$	−3.00000	−	3.00000i	−0.146560	−	0.146560i	0.630020	−	0.776579i	$-0.283047\pi$
$419$	−3.00000	−	3.00000i	−0.146560	−	0.146560i	−0.776579	+	0.630020i	$0.783047\pi$
$420$		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
$429$	−2.73205	+	0.732051i	−0.131905	+	0.0353437i
$430$	3.66025	−	13.6603i	0.176513	−	0.658756i
$431$	−16.0000	−	27.7128i	−0.770693	−	1.33488i	−0.937184	−	0.348836i	$-0.886577\pi$
$431$	−16.0000	−	27.7128i	−0.770693	−	1.33488i	0.166491	−	0.986043i	$-0.446756\pi$
$432$	−5.85641	−	21.8564i	−0.281766	−	1.05157i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$	6.00000	+	6.00000i	0.287678	+	0.287678i
$436$	2.19615	+	8.19615i	0.105177	+	0.392525i
$437$	24.5885	+	6.58846i	1.17623	+	0.315169i
$438$	6.92820	−	4.00000i	0.331042	−	0.191127i
$439$	−12.1244	−	7.00000i	−0.578664	−	0.334092i	0.181938	−	0.983310i	$-0.441763\pi$
$439$	−12.1244	−	7.00000i	−0.578664	−	0.334092i	−0.760602	+	0.649218i	$0.775096\pi$
$440$	4.00000	−	4.00000i	0.190693	−	0.190693i
$441$		0			0
$442$	−4.00000			−0.190261
$443$	−5.49038	−	20.4904i	−0.260856	−	0.973527i	−0.964738	−	0.263211i	$-0.915218\pi$
$443$	−5.49038	−	20.4904i	−0.260856	−	0.973527i	0.703882	−	0.710316i	$-0.251448\pi$
$444$	−10.3923	+	6.00000i	−0.493197	+	0.284747i
$445$	1.46410	−	5.46410i	0.0694051	−	0.259023i
$446$	8.78461	+	32.7846i	0.415963	+	1.55240i
$447$	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	$0.249646\pi$
$450$	−1.09808	−	4.09808i	−0.0517638	−	0.193185i
$451$		0			0
$452$	10.3923	−	6.00000i	0.488813	−	0.282216i
$453$	−3.66025	−	13.6603i	−0.171974	−	0.641815i
$454$	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	$-0.602534\pi$
$457$	−27.7128	−	16.0000i	−1.29635	−	0.748448i	−0.979772	+	0.200118i	$0.935868\pi$
$458$	−12.1244	+	7.00000i	−0.566534	+	0.327089i
$459$	−10.9282	−	2.92820i	−0.510085	−	0.136677i
$460$	−4.39230	−	16.3923i	−0.204792	−	0.764295i
$461$	−11.0000	−	11.0000i	−0.512321	−	0.512321i	0.402916	−	0.915237i	$-0.367997\pi$
$461$	−11.0000	−	11.0000i	−0.512321	−	0.512321i	−0.915237	+	0.402916i	$0.867997\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$	16.3923	−	4.39230i	0.760994	−	0.203908i
$465$	−8.00000	−	13.8564i	−0.370991	−	0.642575i
$466$	−1.46410	+	5.46410i	−0.0678232	+	0.253120i
$467$	−6.83013	+	1.83013i	−0.316061	+	0.0846882i	−0.413362	−	0.910567i	$-0.635646\pi$
$467$	−6.83013	+	1.83013i	−0.316061	+	0.0846882i	0.0973014	+	0.995255i	$0.468979\pi$
$468$	−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	−0.808615	−	0.588338i	$-0.799782\pi$
$479$	−20.0000	−	34.6410i	−0.913823	−	1.58279i	−0.105208	−	0.994450i	$-0.533551\pi$
$480$	−10.9282	−	2.92820i	−0.498802	−	0.133654i
$481$	−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
$485$	0.732051	+	2.73205i	0.0332407	+	0.124056i
$486$	−7.00000	−	12.1244i	−0.317526	−	0.549972i
$487$	1.73205	−	1.00000i	0.0784867	−	0.0453143i	−0.460243	−	0.887793i	$-0.652238\pi$
$487$	1.73205	−	1.00000i	0.0784867	−	0.0453143i	0.538730	+	0.842479i	$0.318904\pi$
$488$	−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
$493$	2.19615	−	8.19615i	0.0989097	−	0.369136i
$494$	2.19615	−	8.19615i	0.0988096	−	0.368762i
$495$	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
$499$	−31.4186	+	8.41858i	−1.40649	+	0.376868i	−0.880671	−	0.473729i	$-0.842908\pi$
$499$	−31.4186	+	8.41858i	−1.40649	+	0.376868i	−0.525818	+	0.850597i	$0.676241\pi$
$500$	−21.8564	−	5.85641i	−0.977448	−	0.261906i
$501$	−2.73205	−	0.732051i	−0.122059	−	0.0327056i
$502$	36.3731	+	21.0000i	1.62341	+	0.937276i
$503$			6.00000i			0.267527i	0.991013	+	0.133763i	$0.0427062\pi$
$503$			6.00000i			0.267527i	−0.991013	+	0.133763i	$0.957294\pi$
$504$		0			0
$505$			22.0000i			0.978987i
$506$	−6.00000	+	10.3923i	−0.266733	+	0.461994i
$507$	−15.0263	−	4.02628i	−0.667340	−	0.178813i
$508$	−13.8564	+	8.00000i	−0.614779	+	0.354943i
$509$	31.4186	−	8.41858i	1.39260	−	0.373147i	0.516921	−	0.856033i	$-0.327078\pi$
$509$	31.4186	−	8.41858i	1.39260	−	0.373147i	0.875683	+	0.482886i	$0.160411\pi$
$510$	−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
$514$	30.0526	+	8.05256i	1.32556	+	0.355183i
$515$	2.19615	−	8.19615i	0.0967740	−	0.361166i
$516$	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
$520$	−5.46410	+	1.46410i	−0.239617	+	0.0642051i
$521$	34.6410	−	20.0000i	1.51765	−	0.876216i	0.517866	−	0.855462i	$-0.326727\pi$
$521$	34.6410	−	20.0000i	1.51765	−	0.876216i	0.999785	−	0.0207541i	$-0.00660670\pi$
$522$	5.19615	−	3.00000i	0.227429	−	0.131306i
$523$	−9.15064	−	34.1506i	−0.400129	−	1.49330i	−0.812865	−	0.582452i	$-0.802093\pi$
$523$	−9.15064	−	34.1506i	−0.400129	−	1.49330i	0.412736	−	0.910851i	$-0.364573\pi$
$524$	−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
$530$	13.6603	−	3.66025i	0.593364	−	0.158991i
$531$	−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
$541$	12.2942	−	3.29423i	0.528570	−	0.141630i	0.0153422	−	0.999882i	$-0.495116\pi$
$541$	12.2942	−	3.29423i	0.528570	−	0.141630i	0.513228	+	0.858252i	$0.328450\pi$
$542$	10.9282	+	2.92820i	0.469407	+	0.125777i
$543$	−9.00000	−	15.5885i	−0.386227	−	0.668965i
$544$	2.92820	+	10.9282i	0.125546	+	0.468543i
$545$	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
$549$	−12.2942	−	3.29423i	−0.524705	−	0.140594i
$550$	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
$555$	2.19615	+	8.19615i	0.0932215	+	0.347907i
$556$	−2.19615	+	8.19615i	−0.0931376	+	0.347594i
$557$	−9.15064	+	34.1506i	−0.387725	+	1.44701i	0.446102	+	0.894982i	$0.352812\pi$
$557$	−9.15064	+	34.1506i	−0.387725	+	1.44701i	−0.833827	+	0.552027i	$0.813855\pi$
$558$	−10.9282	+	2.92820i	−0.462628	+	0.123961i
$559$	10.0000			0.422955
$560$		0			0
$561$	4.00000			0.168880
$562$	27.3205	−	7.32051i	1.15245	−	0.308797i
$563$	−6.95448	+	25.9545i	−0.293096	+	1.09385i	0.649621	+	0.760258i	$0.274928\pi$
$563$	−6.95448	+	25.9545i	−0.293096	+	1.09385i	−0.942717	+	0.333593i	$0.891739\pi$
$564$	21.8564	+	5.85641i	0.920321	+	0.246599i
$565$	−2.19615	−	8.19615i	−0.0923928	−	0.344815i
$566$			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	$-0.165539\pi$
$569$	20.7846	+	12.0000i	0.871336	+	0.503066i	0.00354413	+	0.999994i	$0.498872\pi$
$570$	−6.00000	−	10.3923i	−0.251312	−	0.435286i
$571$	−1.36603	−	0.366025i	−0.0571664	−	0.0153177i	0.230123	−	0.973162i	$-0.426087\pi$
$571$	−1.36603	−	0.366025i	−0.0571664	−	0.0153177i	−0.287289	+	0.957844i	$0.592754\pi$
$572$	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	$-0.0444210\pi$
$577$	9.00000	+	15.5885i	0.374675	+	0.648956i	−0.615603	+	0.788056i	$0.711088\pi$
$578$	−17.7583	−	4.75833i	−0.738649	−	0.197920i
$579$	−19.1244	+	5.12436i	−0.794781	+	0.212961i
$580$		−	12.0000i		−	0.498273i
$581$		0			0
$582$	−4.00000			−0.165805
$583$	−8.66025	−	5.00000i	−0.358671	−	0.207079i
$584$	−10.9282	−	2.92820i	−0.452212	−	0.121170i
$585$	−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	−0.547733	−	0.836653i	$-0.684509\pi$
$587$	7.00000	−	7.00000i	0.288921	−	0.288921i	0.836653	+	0.547733i	$0.184509\pi$
$588$		0			0
$589$	−24.0000	−	24.0000i	−0.988903	−	0.988903i
$590$	−8.19615	+	2.19615i	−0.337430	+	0.0904142i
$591$	17.0000	+	29.4449i	0.699287	+	1.21120i
$592$	16.3923	+	4.39230i	0.673720	+	0.180523i
$593$	17.0000	−	29.4449i	0.698106	−	1.20916i	−0.271016	−	0.962575i	$-0.587360\pi$
$593$	17.0000	−	29.4449i	0.698106	−	1.20916i	0.969122	−	0.246581i	$-0.0793071\pi$
$594$	8.00000	+	8.00000i	0.328244	+	0.328244i
$595$		0			0
$596$	−14.0000	−	14.0000i	−0.573462	−	0.573462i
$597$	−5.12436	−	19.1244i	−0.209726	−	0.782708i
$598$	10.3923	−	6.00000i	0.424973	−	0.245358i
$599$	−12.1244	+	7.00000i	−0.495388	+	0.286012i	−0.726807	−	0.686842i	$-0.758996\pi$
$599$	−12.1244	+	7.00000i	−0.495388	+	0.286012i	0.231419	+	0.972854i	$0.425663\pi$
$600$	6.00000	−	10.3923i	0.244949	−	0.424264i
$601$			20.0000i			0.815817i	0.913023	+	0.407909i	$0.133742\pi$
$601$			20.0000i			0.815817i	−0.913023	+	0.407909i	$0.866258\pi$
$602$		0			0
$603$	−5.00000	+	5.00000i	−0.203616	+	0.203616i
$604$	−10.0000	+	17.3205i	−0.406894	+	0.704761i
$605$	3.29423	−	12.2942i	0.133929	−	0.499831i
$606$	−30.0526	−	8.05256i	−1.22080	−	0.327113i
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	0.333842	+	0.942629i	$0.391655\pi$
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	−0.983262	+	0.182199i	$0.941678\pi$
$608$	−24.0000			−0.973329
$609$		0			0
$610$	−18.0000	+	18.0000i	−0.728799	+	0.728799i
$611$	10.9282	−	2.92820i	0.442108	−	0.118462i
$612$	2.00000	+	3.46410i	0.0808452	+	0.140028i
$613$	34.1506	+	9.15064i	1.37933	+	0.369591i	0.870878	−	0.491499i	$-0.163551\pi$
$613$	34.1506	+	9.15064i	1.37933	+	0.369591i	0.508453	+	0.861090i	$0.330218\pi$
$614$	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
$619$	23.2224	+	6.22243i	0.933388	+	0.250101i	0.693299	−	0.720650i	$-0.256157\pi$
$619$	23.2224	+	6.22243i	0.933388	+	0.250101i	0.240089	+	0.970751i	$0.422823\pi$
$620$	−5.85641	+	21.8564i	−0.235199	+	0.877774i
$621$	32.7846	−	8.78461i	1.31560	−	0.352514i
$622$	−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
$626$	−5.85641	+	21.8564i	−0.234069	+	0.873558i
$627$	−2.19615	+	8.19615i	−0.0877059	+	0.327323i
$628$	−10.9808	−	40.9808i	−0.438180	−	1.63531i
$629$	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
$635$	2.92820	+	10.9282i	0.116202	+	0.433673i
$636$			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	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$	5.12436	+	19.1244i	0.202242	+	0.754778i
$643$	21.0000	+	21.0000i	0.828159	+	0.828159i	0.987262	−	0.159103i	$-0.0508601\pi$
$643$	21.0000	+	21.0000i	0.828159	+	0.828159i	−0.159103	+	0.987262i	$0.550860\pi$
$644$		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	−0.997118	−	0.0758684i	$-0.975827\pi$
$647$	−36.3731	+	21.0000i	−1.42997	+	0.825595i	−0.432855	+	0.901464i	$0.642494\pi$
$648$	3.66025	−	13.6603i	0.143788	−	0.536625i
$649$	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
$653$	−25.9545	+	6.95448i	−1.01568	+	0.272150i	−0.728000	−	0.685577i	$-0.759550\pi$
$653$	−25.9545	+	6.95448i	−1.01568	+	0.272150i	−0.287678	+	0.957727i	$0.592883\pi$
$654$	−2.19615	+	8.19615i	−0.0858764	+	0.320495i
$655$	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	$0.905121\pi$
$660$	5.46410	−	1.46410i	0.212690	−	0.0569901i
$661$	−12.2942	−	3.29423i	−0.478190	−	0.128131i	0.0116697	−	0.999932i	$-0.496285\pi$
$661$	−12.2942	−	3.29423i	−0.478190	−	0.128131i	−0.489860	+	0.871801i	$0.662952\pi$
$662$	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
$667$	6.58846	+	24.5885i	0.255106	+	0.952069i
$668$	2.00000	+	3.46410i	0.0773823	+	0.134030i
$669$	−8.78461	+	32.7846i	−0.339633	+	1.26753i
$670$	3.66025	+	13.6603i	0.141408	+	0.527742i
$671$	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	$0.413032\pi$
$674$	−6.58846	−	24.5885i	−0.253778	−	0.947112i
$675$	4.39230	−	16.3923i	0.169060	−	0.630940i
$676$	11.0000	+	19.0526i	0.423077	+	0.732791i
$677$	−1.09808	−	4.09808i	−0.0422025	−	0.157502i	0.941609	−	0.336708i	$-0.109314\pi$
$677$	−1.09808	−	4.09808i	−0.0422025	−	0.157502i	−0.983811	+	0.179206i	$0.942647\pi$
$678$	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
$683$	−6.83013	−	1.83013i	−0.261348	−	0.0700279i	0.125766	−	0.992060i	$-0.459861\pi$
$683$	−6.83013	−	1.83013i	−0.261348	−	0.0700279i	−0.387113	+	0.922032i	$0.626528\pi$
$684$	−8.19615	+	2.19615i	−0.313388	+	0.0839720i
$685$	−8.00000	−	8.00000i	−0.305664	−	0.305664i
$686$		0			0
$687$	−14.0000			−0.534133
$688$	−7.32051	−	27.3205i	−0.279092	−	1.04158i
$689$	5.00000	+	8.66025i	0.190485	+	0.329929i
$690$	4.39230	−	16.3923i	0.167212	−	0.624044i
$691$	−12.2942	+	3.29423i	−0.467694	+	0.125318i	−0.484967	−	0.874532i	$-0.661168\pi$
$691$	−12.2942	+	3.29423i	−0.467694	+	0.125318i	0.0172725	+	0.999851i	$0.494502\pi$
$692$	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
$696$	16.3923	+	4.39230i	0.621349	+	0.166490i
$697$		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	$0.439525\pi$
$702$	−2.92820	−	10.9282i	−0.110518	−	0.412458i
$703$	9.00000	+	15.5885i	0.339441	+	0.587930i
$704$	2.92820	−	10.9282i	0.110361	−	0.411872i
$705$	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
$709$	9.88269	+	36.8827i	0.371152	+	1.38516i	0.858886	+	0.512166i	$0.171157\pi$
$709$	9.88269	+	36.8827i	0.371152	+	1.38516i	−0.487734	+	0.872992i	$0.662177\pi$
$710$	10.0000	+	17.3205i	0.375293	+	0.650027i
$711$		0			0
$712$	−2.92820	−	10.9282i	−0.109739	−	0.409552i
$713$		−	48.0000i		−	1.79761i
$714$		0			0
$715$	2.00000	−	2.00000i	0.0747958	−	0.0747958i
$716$	−12.4449	−	46.4449i	−0.465086	−	1.73573i
$717$		0			0
$718$	−9.51666	+	35.5167i	−0.355159	+	1.32547i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$	4.00000	+	4.00000i	0.149071	+	0.149071i
$721$		0			0
$722$	1.00000	+	1.00000i	0.0372161	+	0.0372161i
$723$	−24.5885	+	6.58846i	−0.914455	+	0.245027i
$724$	−6.58846	+	24.5885i	−0.244858	+	0.913823i
$725$	12.2942	+	3.29423i	0.456596	+	0.122345i
$726$	15.5885	+	9.00000i	0.578542	+	0.334021i
$727$		−	2.00000i		−	0.0741759i	−0.999312	−	0.0370879i	$-0.988192\pi$
$727$		−	2.00000i		−	0.0741759i	0.999312	−	0.0370879i	$-0.0118082\pi$
$728$		0			0
$729$		−	29.0000i		−	1.07407i
$730$	−4.00000	+	6.92820i	−0.148047	+	0.256424i
$731$	−13.6603	−	3.66025i	−0.505243	−	0.135379i
$732$	−18.0000	−	31.1769i	−0.665299	−	1.15233i
$733$	−28.6865	+	7.68653i	−1.05956	+	0.283909i	−0.746198	−	0.665725i	$-0.768123\pi$
$733$	−28.6865	+	7.68653i	−1.05956	+	0.283909i	−0.313364	+	0.949633i	$0.601456\pi$
$734$	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
$739$	8.41858	−	31.4186i	0.309683	−	1.15575i	−0.619156	−	0.785268i	$-0.712525\pi$
$739$	8.41858	−	31.4186i	0.309683	−	1.15575i	0.928839	−	0.370484i	$-0.120808\pi$
$740$	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
$747$	0.366025	+	1.36603i	0.0133922	+	0.0499803i
$748$	−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	0.411170	+	0.911559i	$0.365120\pi$
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	−0.995018	+	0.0996961i	$0.968213\pi$
$752$	−16.0000	−	27.7128i	−0.583460	−	1.01058i
$753$	21.0000	+	36.3731i	0.765283	+	1.32551i
$754$	8.19615	−	2.19615i	0.298486	−	0.0799792i
$755$	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
$760$	−4.39230	+	16.3923i	−0.159326	+	0.594611i
$761$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$761$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$762$	−16.0000			−0.579619
$763$		0			0
$764$			16.0000i			0.578860i
$765$	2.73205	−	0.732051i	0.0987775	−	0.0264674i
$766$	21.8564	+	5.85641i	0.789704	+	0.211601i
$767$	−3.00000	−	5.19615i	−0.108324	−	0.187622i
$768$	−21.8564	+	5.85641i	−0.788675	+	0.211325i
$769$	50.0000			1.80305			0.901523	−	0.432731i	$-0.142450\pi$
$769$	50.0000			1.80305			0.901523	+	0.432731i	$0.142450\pi$
$770$		0			0
$771$	22.0000	+	22.0000i	0.792311	+	0.792311i
$772$	24.2487	+	14.0000i	0.872730	+	0.503871i
$773$	−6.83013	−	1.83013i	−0.245663	−	0.0658251i	0.133887	−	0.990997i	$-0.457254\pi$
$773$	−6.83013	−	1.83013i	−0.245663	−	0.0658251i	−0.379549	+	0.925172i	$0.623921\pi$
$774$	−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
$780$	−5.46410	−	1.46410i	−0.195646	−	0.0524232i
$781$	3.66025	−	13.6603i	0.130974	−	0.488802i
$782$	−16.3923	+	4.39230i	−0.586188	+	0.157069i
$783$	24.0000			0.857690
$784$		0			0
$785$	−30.0000			−1.07075
$786$	−30.0526	+	8.05256i	−1.07194	+	0.287225i
$787$	−5.49038	+	20.4904i	−0.195711	+	0.730403i	0.796371	+	0.604809i	$0.206750\pi$
$787$	−5.49038	+	20.4904i	−0.195711	+	0.730403i	−0.992082	+	0.125594i	$0.959916\pi$
$788$	12.4449	−	46.4449i	0.443330	−	1.65453i
$789$	2.19615	+	8.19615i	0.0781851	+	0.291791i
$790$		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
$795$	13.6603	+	3.66025i	0.484479	+	0.129816i
$796$	−14.0000	+	24.2487i	−0.496217	+	0.859473i
$797$	25.0000	+	25.0000i	0.885545	+	0.885545i	0.994091	−	0.108546i	$-0.0346195\pi$
$797$	25.0000	+	25.0000i	0.885545	+	0.885545i	−0.108546	+	0.994091i	$0.534619\pi$
$798$		0			0
$799$	−16.0000			−0.566039
$800$	−16.3923	+	4.39230i	−0.579555	+	0.155291i
$801$	−2.00000	−	3.46410i	−0.0706665	−	0.122398i
$802$	−24.5885	−	6.58846i	−0.868249	−	0.232647i
$803$	5.46410	−	1.46410i	0.192824	−	0.0516670i
$804$	−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	$-0.575913\pi$
$809$	13.8564	−	8.00000i	0.487165	−	0.281265i	0.723398	+	0.690432i	$0.242579\pi$
$810$	−8.66025	−	5.00000i	−0.304290	−	0.175682i
$811$	39.0000	−	39.0000i	1.36948	−	1.36948i	0.508288	−	0.861187i	$-0.330278\pi$
$811$	39.0000	−	39.0000i	1.36948	−	1.36948i	0.861187	−	0.508288i	$-0.169722\pi$
$812$		0			0
$813$	8.00000	+	8.00000i	0.280572	+	0.280572i
$814$	−8.19615	+	2.19615i	−0.287275	+	0.0769751i
$815$	1.00000	+	1.73205i	0.0350285	+	0.0606711i
$816$	−2.92820	+	10.9282i	−0.102508	+	0.382564i
$817$	15.0000	−	25.9808i	0.524784	−	0.908952i
$818$	16.0000	+	16.0000i	0.559427	+	0.559427i
$819$		0			0
$820$		0			0
$821$	4.02628	+	15.0263i	0.140518	+	0.524421i	0.999914	+	0.0131101i	$0.00417319\pi$
$821$	4.02628	+	15.0263i	0.140518	+	0.524421i	−0.859396	+	0.511311i	$0.829160\pi$
$822$	13.8564	−	8.00000i	0.483298	−	0.279032i
$823$	29.4449	−	17.0000i	1.02638	−	0.592583i	0.110437	−	0.993883i	$-0.464775\pi$
$823$	29.4449	−	17.0000i	1.02638	−	0.592583i	0.915947	+	0.401300i	$0.131442\pi$
$824$	−4.39230	−	16.3923i	−0.153013	−	0.571053i
$825$			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
$829$	−8.41858	+	31.4186i	−0.292390	+	1.09121i	0.650879	+	0.759182i	$0.274401\pi$
$829$	−8.41858	+	31.4186i	−0.292390	+	1.09121i	−0.943268	+	0.332031i	$0.892266\pi$
$830$	2.73205	+	0.732051i	0.0948309	+	0.0254099i
$831$	−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
$835$	2.73205	−	0.732051i	0.0945465	−	0.0253337i
$836$	10.3923	−	6.00000i	0.359425	−	0.207514i
$837$	−43.7128	−	11.7128i	−1.51094	−	0.404854i
$838$	−3.00000	+	5.19615i	−0.103633	+	0.179498i
$839$			14.0000i			0.483334i	0.970359	+	0.241667i	$0.0776941\pi$
$839$			14.0000i			0.483334i	−0.970359	+	0.241667i	$0.922306\pi$
$840$		0			0
$841$		−	11.0000i		−	0.379310i
$842$	15.5885	+	9.00000i	0.537214	+	0.310160i
$843$	27.3205	+	7.32051i	0.940968	+	0.252132i
$844$	24.5885	+	6.58846i	0.846370	+	0.226784i
$845$	15.0263	−	4.02628i	0.516920	−	0.138508i
$846$	−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
$850$	−2.19615	+	8.19615i	−0.0753274	+	0.281126i
$851$	−6.58846	+	24.5885i	−0.225849	+	0.842881i
$852$	−27.3205	+	7.32051i	−0.935985	+	0.250796i
$853$	5.00000	−	5.00000i	0.171197	−	0.171197i	−0.616308	−	0.787505i	$-0.711372\pi$
$853$	5.00000	−	5.00000i	0.171197	−	0.171197i	0.787505	+	0.616308i	$0.211372\pi$
$854$		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	−0.376979	−	0.926222i	$-0.623037\pi$
$857$	6.92820	−	4.00000i	0.236663	−	0.136637i	0.613642	+	0.789584i	$0.289704\pi$
$858$	2.00000	+	3.46410i	0.0682789	+	0.118262i
$859$	1.09808	+	4.09808i	0.0374659	+	0.139825i	0.982125	−	0.188228i	$-0.0602744\pi$
$859$	1.09808	+	4.09808i	0.0374659	+	0.139825i	−0.944659	+	0.328053i	$0.893608\pi$
$860$	−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	−0.994720	−	0.102624i	$-0.967276\pi$
$863$	−12.0000	+	20.7846i	−0.408485	+	0.707516i	0.586235	+	0.810141i	$0.300609\pi$
$864$	−27.7128	+	16.0000i	−0.942809	+	0.544331i
$865$	−1.00000	−	1.73205i	−0.0340010	−	0.0588915i
$866$	5.12436	+	19.1244i	0.174133	+	0.649872i
$867$	−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
$877$	6.83013	−	1.83013i	0.230637	−	0.0617990i	−0.141649	−	0.989917i	$-0.545241\pi$
$877$	6.83013	−	1.83013i	0.230637	−	0.0617990i	0.372286	+	0.928118i	$0.378574\pi$
$878$	−5.12436	+	19.1244i	−0.172939	+	0.645416i
$879$	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	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$		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	$0.916563\pi$
$884$	1.46410	+	5.46410i	0.0492431	+	0.183778i
$885$	−8.19615	−	2.19615i	−0.275511	−	0.0738229i
$886$	−25.9808	+	15.0000i	−0.872841	+	0.503935i
$887$	1.73205	+	1.00000i	0.0581566	+	0.0335767i	0.528796	−	0.848749i	$-0.322644\pi$
$887$	1.73205	+	1.00000i	0.0581566	+	0.0335767i	−0.470640	+	0.882325i	$0.655977\pi$
$888$	12.0000	+	12.0000i	0.402694	+	0.402694i
$889$		0			0
$890$	−8.00000			−0.268161
$891$	1.83013	+	6.83013i	0.0613116	+	0.228818i
$892$	41.5692	−	24.0000i	1.39184	−	0.803579i
$893$	8.78461	−	32.7846i	0.293966	−	1.09710i
$894$	−5.12436	−	19.1244i	−0.171384	−	0.639614i
$895$	−34.0000			−1.13649
$896$		0			0
$897$	12.0000			0.400668
$898$	−10.9808	−	40.9808i	−0.366433	−	1.36755i
$899$	8.78461	−	32.7846i	0.292983	−	1.09343i
$900$	−5.19615	+	3.00000i	−0.173205	+	0.100000i
$901$	−3.66025	−	13.6603i	−0.121941	−	0.455089i
$902$		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
$907$	36.8827	+	9.88269i	1.22467	+	0.328149i	0.812502	−	0.582959i	$-0.198105\pi$
$907$	36.8827	+	9.88269i	1.22467	+	0.328149i	0.412168	+	0.911108i	$0.364772\pi$
$908$	−10.9808	−	40.9808i	−0.364409	−	1.35999i
$909$	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
$914$	−11.7128	+	43.7128i	−0.387425	+	1.44589i
$915$	−24.5885	+	6.58846i	−0.812869	+	0.217808i
$916$	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	$-0.474408\pi$
$919$	−22.5167	−	13.0000i	−0.742756	−	0.428830i	−0.823071	+	0.567939i	$0.807741\pi$
$920$	−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
$926$	5.85641	+	21.8564i	0.192453	+	0.718246i
$927$	−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	$-0.669550\pi$
$929$	15.0000	−	25.9808i	0.492134	−	0.852401i	0.999959	+	0.00905914i	$0.00288365\pi$
$930$	−16.0000	+	16.0000i	−0.524661	+	0.524661i
$931$		0			0
$932$	8.00000			0.262049
$933$	−10.9808	−	40.9808i	−0.359494	−	1.34165i
$934$	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	$0.151205\pi$
$937$			28.0000i			0.914720i	−0.889282	+	0.457360i	$0.848795\pi$
$938$		0			0
$939$	−16.0000	+	16.0000i	−0.522140	+	0.522140i
$940$	−21.8564	+	5.85641i	−0.712877	+	0.191015i
$941$	10.6147	−	39.6147i	0.346031	−	1.29140i	−0.545373	−	0.838193i	$-0.683612\pi$
$941$	10.6147	−	39.6147i	0.346031	−	1.29140i	0.891404	−	0.453210i	$-0.149721\pi$
$942$	10.9808	−	40.9808i	0.357773	−	1.33523i
$943$		0			0
$944$	−12.0000	+	12.0000i	−0.390567	+	0.390567i
$945$		0			0
$946$	10.0000	+	10.0000i	0.325128	+	0.325128i
$947$	6.83013	−	1.83013i	0.221949	−	0.0594711i	−0.146131	−	0.989265i	$-0.546682\pi$
$947$	6.83013	−	1.83013i	0.221949	−	0.0594711i	0.368080	+	0.929794i	$0.380015\pi$
$948$		0			0
$949$	−5.46410	−	1.46410i	−0.177372	−	0.0475267i
$950$	−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
$955$	10.9282	+	2.92820i	0.353628	+	0.0947544i
$956$		0			0
$957$	−8.19615	+	2.19615i	−0.264944	+	0.0709915i
$958$	−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
$962$	8.19615	+	2.19615i	0.264255	+	0.0708068i
$963$	2.56218	−	9.56218i	0.0825650	−	0.308137i
$964$	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	$0.989762\pi$
$968$	−6.58846	−	24.5885i	−0.211761	−	0.790303i
$969$	−10.3923	+	6.00000i	−0.333849	+	0.192748i
$970$	3.46410	−	2.00000i	0.111226	−	0.0642161i
$971$	6.95448	+	25.9545i	0.223180	+	0.832919i	0.983126	+	0.182932i	$0.0585589\pi$
$971$	6.95448	+	25.9545i	0.223180	+	0.832919i	−0.759946	+	0.649987i	$0.774774\pi$
$972$	−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
$976$	−13.1769	+	49.1769i	−0.421783	+	1.57411i
$977$	1.00000	+	1.73205i	0.0319928	+	0.0554132i	0.881579	−	0.472037i	$-0.156481\pi$
$977$	1.00000	+	1.73205i	0.0319928	+	0.0554132i	−0.849586	+	0.527451i	$0.823148\pi$
$978$	−2.73205	+	0.732051i	−0.0873614	+	0.0234084i
$979$	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	−0.889692	−	0.456561i	$-0.849081\pi$
$983$	−29.4449	+	17.0000i	−0.939145	+	0.542216i	−0.0494530	+	0.998776i	$0.515748\pi$
$984$		0			0
$985$	−29.4449	−	17.0000i	−0.938191	−	0.541665i
$986$	−12.0000			−0.382158
$987$		0			0
$988$	−12.0000			−0.381771
$989$	40.9808	−	10.9808i	1.30311	−	0.349168i
$990$	−2.73205	−	0.732051i	−0.0868303	−	0.0232661i
$991$	−16.0000	−	27.7128i	−0.508257	−	0.880327i	−0.999954	−	0.00956046i	$-0.996957\pi$
$991$	−16.0000	−	27.7128i	−0.508257	−	0.880327i	0.491698	−	0.870766i	$-0.336377\pi$
$992$	11.7128	+	43.7128i	0.371882	+	1.38788i
$993$	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
$997$	−50.5429	−	13.5429i	−1.60071	−	0.428909i	−0.655454	−	0.755235i	$-0.727523\pi$
$997$	−50.5429	−	13.5429i	−1.60071	−	0.428909i	−0.945257	+	0.326326i	$0.894189\pi$
$998$	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.c.765.1		4
7.2	even	3		784.2.m.b.589.1		2
7.3	odd	6		784.2.x.f.557.1		4
7.4	even	3	inner	784.2.x.c.557.1		4
7.5	odd	6		16.2.e.a.13.1	yes	2
7.6	odd	2		784.2.x.f.765.1		4
16.5	even	4	inner	784.2.x.c.373.1		4
21.5	even	6		144.2.k.a.109.1		2
28.19	even	6		64.2.e.a.17.1		2
35.12	even	12		400.2.q.a.349.1		2
35.19	odd	6		400.2.l.c.301.1		2
35.33	even	12		400.2.q.b.349.1		2
56.5	odd	6		128.2.e.b.33.1		2
56.19	even	6		128.2.e.a.33.1		2
84.47	odd	6		576.2.k.a.145.1		2
112.5	odd	12		16.2.e.a.5.1	✓	2
112.19	even	12		128.2.e.a.97.1		2
112.37	even	12		784.2.m.b.197.1		2
112.53	even	12	inner	784.2.x.c.165.1		4
112.61	odd	12		128.2.e.b.97.1		2
112.69	odd	4		784.2.x.f.373.1		4
112.75	even	12		64.2.e.a.49.1		2
112.101	odd	12		784.2.x.f.165.1		4
140.19	even	6		1600.2.l.a.401.1		2
140.47	odd	12		1600.2.q.b.849.1		2
140.103	odd	12		1600.2.q.a.849.1		2
168.5	even	6		1152.2.k.b.289.1		2
168.131	odd	6		1152.2.k.a.289.1		2
224.5	odd	24		1024.2.a.b.1.2		2
224.19	even	24		1024.2.b.b.513.1		2
224.61	odd	24		1024.2.b.e.513.1		2
224.75	even	24		1024.2.a.e.1.2		2
224.117	odd	24		1024.2.a.b.1.1		2
224.131	even	24		1024.2.b.b.513.2		2
224.173	odd	24		1024.2.b.e.513.2		2
224.187	even	24		1024.2.a.e.1.1		2
336.5	even	12		144.2.k.a.37.1		2
336.131	odd	12		1152.2.k.a.865.1		2
336.173	even	12		1152.2.k.b.865.1		2
336.299	odd	12		576.2.k.a.433.1		2
560.117	even	12		400.2.q.b.149.1		2
560.187	odd	12		1600.2.q.a.49.1		2
560.229	odd	12		400.2.l.c.101.1		2
560.299	even	12		1600.2.l.a.1201.1		2
560.453	even	12		400.2.q.a.149.1		2
560.523	odd	12		1600.2.q.b.49.1		2
672.5	even	24		9216.2.a.d.1.2		2
672.299	odd	24		9216.2.a.s.1.1		2
672.341	even	24		9216.2.a.d.1.1		2
672.635	odd	24		9216.2.a.s.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.2.e.a.5.1	✓	2	112.5	odd	12
16.2.e.a.13.1	yes	2	7.5	odd	6
64.2.e.a.17.1		2	28.19	even	6
64.2.e.a.49.1		2	112.75	even	12
128.2.e.a.33.1		2	56.19	even	6
128.2.e.a.97.1		2	112.19	even	12
128.2.e.b.33.1		2	56.5	odd	6
128.2.e.b.97.1		2	112.61	odd	12
144.2.k.a.37.1		2	336.5	even	12
144.2.k.a.109.1		2	21.5	even	6
400.2.l.c.101.1		2	560.229	odd	12
400.2.l.c.301.1		2	35.19	odd	6
400.2.q.a.149.1		2	560.453	even	12
400.2.q.a.349.1		2	35.12	even	12
400.2.q.b.149.1		2	560.117	even	12
400.2.q.b.349.1		2	35.33	even	12
576.2.k.a.145.1		2	84.47	odd	6
576.2.k.a.433.1		2	336.299	odd	12
784.2.m.b.197.1		2	112.37	even	12
784.2.m.b.589.1		2	7.2	even	3
784.2.x.c.165.1		4	112.53	even	12	inner
784.2.x.c.373.1		4	16.5	even	4	inner
784.2.x.c.557.1		4	7.4	even	3	inner
784.2.x.c.765.1		4	1.1	even	1	trivial
784.2.x.f.165.1		4	112.101	odd	12
784.2.x.f.373.1		4	112.69	odd	4
784.2.x.f.557.1		4	7.3	odd	6
784.2.x.f.765.1		4	7.6	odd	2
1024.2.a.b.1.1		2	224.117	odd	24
1024.2.a.b.1.2		2	224.5	odd	24
1024.2.a.e.1.1		2	224.187	even	24
1024.2.a.e.1.2		2	224.75	even	24
1024.2.b.b.513.1		2	224.19	even	24
1024.2.b.b.513.2		2	224.131	even	24
1024.2.b.e.513.1		2	224.61	odd	24
1024.2.b.e.513.2		2	224.173	odd	24
1152.2.k.a.289.1		2	168.131	odd	6
1152.2.k.a.865.1		2	336.131	odd	12
1152.2.k.b.289.1		2	168.5	even	6
1152.2.k.b.865.1		2	336.173	even	12
1600.2.l.a.401.1		2	140.19	even	6
1600.2.l.a.1201.1		2	560.299	even	12
1600.2.q.a.49.1		2	560.187	odd	12
1600.2.q.a.849.1		2	140.103	odd	12
1600.2.q.b.49.1		2	560.523	odd	12
1600.2.q.b.849.1		2	140.47	odd	12
9216.2.a.d.1.1		2	672.341	even	24
9216.2.a.d.1.2		2	672.5	even	24
9216.2.a.s.1.1		2	672.299	odd	24
9216.2.a.s.1.2		2	672.635	odd	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 $\F_{q}$
Belyi maps

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+(-0.366025 - 1.36603i) q^{2} +(0.366025 - 1.36603i) q^{3} +(-1.73205 + 1.00000i) q^{4} +(0.366025 + 1.36603i) q^{5} -2.00000 q^{6} +(2.00000 + 2.00000i) q^{8} +(0.866025 + 0.500000i) q^{9} +(1.73205 - 1.00000i) q^{10} +(-1.36603 - 0.366025i) q^{11} +(0.732051 + 2.73205i) q^{12} +(1.00000 + 1.00000i) q^{13} +2.00000 q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(0.366025 - 1.36603i) q^{18} +(4.09808 - 1.09808i) 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} +(-0.732051 - 2.73205i) q^{30} +(-4.00000 - 6.92820i) q^{31} +(-5.46410 - 1.46410i) q^{32} +(-1.00000 + 1.73205i) q^{33} +(-2.00000 + 2.00000i) q^{34} -2.00000 q^{36} +(1.09808 + 4.09808i) 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} +(2.73205 - 0.732051i) q^{44} +(-0.366025 + 1.36603i) q^{45} +(2.19615 - 8.19615i) q^{46} +(4.00000 - 6.92820i) q^{47} +(-4.00000 - 4.00000i) q^{48} +(-3.00000 - 3.00000i) q^{50} +(-2.73205 + 0.732051i) q^{51} +(-2.73205 - 0.732051i) q^{52} +(6.83013 + 1.83013i) q^{53} +(-6.92820 - 4.00000i) q^{54} -2.00000i q^{55} -6.00000i q^{57} +(3.00000 - 5.19615i) q^{58} +(-4.09808 - 1.09808i) q^{59} +(-3.46410 + 2.00000i) q^{60} +(-12.2942 + 3.29423i) q^{61} +(-8.00000 + 8.00000i) q^{62} +8.00000i q^{64} +(-1.00000 + 1.73205i) q^{65} +(2.73205 + 0.732051i) q^{66} +(-1.83013 + 6.83013i) q^{67} +(3.46410 + 2.00000i) q^{68} +(6.00000 - 6.00000i) q^{69} +10.0000i q^{71} +(0.732051 + 2.73205i) q^{72} +(-3.46410 + 2.00000i) q^{73} +(5.19615 - 3.00000i) q^{74} +(-1.09808 - 4.09808i) q^{75} +(-6.00000 + 6.00000i) q^{76} +(-2.00000 - 2.00000i) q^{78} +(5.46410 + 1.46410i) 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} +(-10.9282 + 2.92820i) q^{93} +(-10.9282 - 2.92820i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{3} - 2 q^{5} - 8 q^{6} + 8 q^{8} - 2 q^{11} - 4 q^{12} + 4 q^{13} + 8 q^{15} + 8 q^{16} - 4 q^{17} - 2 q^{18} + 6 q^{19} - 8 q^{20} + 4 q^{26} + 16 q^{27} + 12 q^{29} + 4 q^{30} - 16 q^{31}+ \cdots - 4 q^{99}+O(q^{100}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more