LMFDB - Embedded newform 930.2.s.a.439.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(439,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("930.439");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.s (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			439.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	930.439
Dual form			930.2.s.a.769.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(2.23205 - 0.133975i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(2.23205 - 0.133975i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.133975 - 2.23205i) q^{10} +(2.50000 + 4.33013i) q^{11} +(0.866025 + 0.500000i) q^{12} +(1.73205 - 1.00000i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(-2.00000 - 1.00000i) q^{15} +1.00000 q^{16} +(2.59808 + 1.50000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(2.00000 - 3.46410i) q^{19} +(-2.23205 + 0.133975i) q^{20} +(1.00000 + 1.73205i) q^{21} +(4.33013 - 2.50000i) q^{22} -3.00000i q^{23} +(0.500000 - 0.866025i) q^{24} +(4.96410 - 0.598076i) q^{25} +(-1.00000 - 1.73205i) q^{26} -1.00000i q^{27} +(1.73205 + 1.00000i) q^{28} +2.00000 q^{29} +(-1.00000 + 2.00000i) q^{30} +(-2.00000 + 5.19615i) q^{31} -1.00000i q^{32} -5.00000i q^{33} +(1.50000 - 2.59808i) q^{34} +(-4.00000 - 2.00000i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.33013 + 2.50000i) q^{37} +(-3.46410 - 2.00000i) q^{38} -2.00000 q^{39} +(0.133975 + 2.23205i) q^{40} +(1.73205 - 1.00000i) q^{42} +(-0.866025 - 0.500000i) q^{43} +(-2.50000 - 4.33013i) q^{44} +(1.23205 + 1.86603i) q^{45} -3.00000 q^{46} -9.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(-0.598076 - 4.96410i) q^{50} +(-1.50000 - 2.59808i) q^{51} +(-1.73205 + 1.00000i) q^{52} +(6.92820 - 4.00000i) q^{53} -1.00000 q^{54} +(6.16025 + 9.33013i) q^{55} +(1.00000 - 1.73205i) q^{56} +(-3.46410 + 2.00000i) q^{57} -2.00000i q^{58} +(2.00000 - 3.46410i) q^{59} +(2.00000 + 1.00000i) q^{60} -2.00000 q^{61} +(5.19615 + 2.00000i) q^{62} -2.00000i q^{63} -1.00000 q^{64} +(3.73205 - 2.46410i) q^{65} -5.00000 q^{66} +(6.06218 - 3.50000i) q^{67} +(-2.59808 - 1.50000i) q^{68} +(-1.50000 + 2.59808i) q^{69} +(-2.00000 + 4.00000i) q^{70} +(-0.866025 + 0.500000i) q^{72} +(-5.19615 + 3.00000i) q^{73} +(2.50000 - 4.33013i) q^{74} +(-4.59808 - 1.96410i) q^{75} +(-2.00000 + 3.46410i) q^{76} -10.0000i q^{77} +2.00000i q^{78} +(2.50000 - 4.33013i) q^{79} +(2.23205 - 0.133975i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.19615 + 3.00000i) q^{83} +(-1.00000 - 1.73205i) q^{84} +(6.00000 + 3.00000i) q^{85} +(-0.500000 + 0.866025i) q^{86} +(-1.73205 - 1.00000i) q^{87} +(-4.33013 + 2.50000i) q^{88} +(1.86603 - 1.23205i) q^{90} -4.00000 q^{91} +3.00000i q^{92} +(4.33013 - 3.50000i) q^{93} -9.00000 q^{94} +(4.00000 - 8.00000i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(-2.59808 + 1.50000i) q^{98} +(-2.50000 + 4.33013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q - 4 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^9	$ 4 q - 4 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{9} - 4 q^{10} + 10 q^{11} - 4 q^{14} - 8 q^{15} + 4 q^{16} + 8 q^{19} - 2 q^{20} + 4 q^{21} + 2 q^{24} + 6 q^{25} - 4 q^{26} + 8 q^{29} - 4 q^{30} - 8 q^{31} + 6 q^{34} - 16 q^{35} - 2 q^{36} - 8 q^{39} + 4 q^{40} - 10 q^{44} - 2 q^{45} - 12 q^{46} - 6 q^{49} + 8 q^{50} - 6 q^{51} - 4 q^{54} - 10 q^{55} + 4 q^{56} + 8 q^{59} + 8 q^{60} - 8 q^{61} - 4 q^{64} + 8 q^{65} - 20 q^{66} - 6 q^{69} - 8 q^{70} + 10 q^{74} - 8 q^{75} - 8 q^{76} + 10 q^{79} + 2 q^{80} - 2 q^{81} - 4 q^{84} + 24 q^{85} - 2 q^{86} + 4 q^{90} - 16 q^{91} - 36 q^{94} + 16 q^{95} - 2 q^{96} - 10 q^{99}+O(q^{100}) $ 4 * q - 4 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^9 - 4 * q^10 + 10 * q^11 - 4 * q^14 - 8 * q^15 + 4 * q^16 + 8 * q^19 - 2 * q^20 + 4 * q^21 + 2 * q^24 + 6 * q^25 - 4 * q^26 + 8 * q^29 - 4 * q^30 - 8 * q^31 + 6 * q^34 - 16 * q^35 - 2 * q^36 - 8 * q^39 + 4 * q^40 - 10 * q^44 - 2 * q^45 - 12 * q^46 - 6 * q^49 + 8 * q^50 - 6 * q^51 - 4 * q^54 - 10 * q^55 + 4 * q^56 + 8 * q^59 + 8 * q^60 - 8 * q^61 - 4 * q^64 + 8 * q^65 - 20 * q^66 - 6 * q^69 - 8 * q^70 + 10 * q^74 - 8 * q^75 - 8 * q^76 + 10 * q^79 + 2 * q^80 - 2 * q^81 - 4 * q^84 + 24 * q^85 - 2 * q^86 + 4 * q^90 - 16 * q^91 - 36 * q^94 + 16 * q^95 - 2 * q^96 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−1.00000			−0.500000
$5$	2.23205	−	0.133975i	0.998203	−	0.0599153i
$5$	2.23205	−	0.133975i	0.998203	−	0.0599153i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	0.135583	−	0.990766i	$-0.456709\pi$
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	−0.790237	+	0.612801i	$0.790043\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.133975	−	2.23205i	−0.0423665	−	0.705836i
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	0.945979	+	0.324227i	$0.105104\pi$
$11$	2.50000	+	4.33013i	0.753778	+	1.30558i	−0.192201	+	0.981356i	$0.561563\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	1.73205	−	1.00000i	0.480384	−	0.277350i	−0.240192	−	0.970725i	$-0.577210\pi$
$13$	1.73205	−	1.00000i	0.480384	−	0.277350i	0.720577	+	0.693375i	$0.243877\pi$
$14$	−1.00000	+	1.73205i	−0.267261	+	0.462910i
$15$	−2.00000	−	1.00000i	−0.516398	−	0.258199i
$16$	1.00000			0.250000
$17$	2.59808	+	1.50000i	0.630126	+	0.363803i	0.780801	−	0.624780i	$-0.214811\pi$
$17$	2.59808	+	1.50000i	0.630126	+	0.363803i	−0.150675	+	0.988583i	$0.548145\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	−2.23205	+	0.133975i	−0.499102	+	0.0299576i
$21$	1.00000	+	1.73205i	0.218218	+	0.377964i
$22$	4.33013	−	2.50000i	0.923186	−	0.533002i
$23$		−	3.00000i		−	0.625543i	−0.949828	−	0.312772i	$-0.898743\pi$
$23$		−	3.00000i		−	0.625543i	0.949828	−	0.312772i	$-0.101257\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	4.96410	−	0.598076i	0.992820	−	0.119615i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$		−	1.00000i		−	0.192450i
$28$	1.73205	+	1.00000i	0.327327	+	0.188982i
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$	−1.00000	+	2.00000i	−0.182574	+	0.365148i
$31$	−2.00000	+	5.19615i	−0.359211	+	0.933257i
$31$	−2.00000	+	5.19615i	−0.359211	+	0.933257i
$32$		−	1.00000i		−	0.176777i
$33$		−	5.00000i		−	0.870388i
$34$	1.50000	−	2.59808i	0.257248	−	0.445566i
$35$	−4.00000	−	2.00000i	−0.676123	−	0.338062i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	4.33013	+	2.50000i	0.711868	+	0.410997i	0.811752	−	0.584002i	$-0.198514\pi$
$37$	4.33013	+	2.50000i	0.711868	+	0.410997i	−0.0998840	+	0.994999i	$0.531847\pi$
$38$	−3.46410	−	2.00000i	−0.561951	−	0.324443i
$39$	−2.00000			−0.320256
$40$	0.133975	+	2.23205i	0.0211832	+	0.352918i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$	1.73205	−	1.00000i	0.267261	−	0.154303i
$43$	−0.866025	−	0.500000i	−0.132068	−	0.0762493i	0.432511	−	0.901629i	$-0.357628\pi$
$43$	−0.866025	−	0.500000i	−0.132068	−	0.0762493i	−0.564578	+	0.825380i	$0.690961\pi$
$44$	−2.50000	−	4.33013i	−0.376889	−	0.652791i
$45$	1.23205	+	1.86603i	0.183663	+	0.278171i
$46$	−3.00000			−0.442326
$47$		−	9.00000i		−	1.31278i	−0.754420	−	0.656392i	$-0.772082\pi$
$47$		−	9.00000i		−	1.31278i	0.754420	−	0.656392i	$-0.227918\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$	−0.598076	−	4.96410i	−0.0845807	−	0.702030i
$51$	−1.50000	−	2.59808i	−0.210042	−	0.363803i
$52$	−1.73205	+	1.00000i	−0.240192	+	0.138675i
$53$	6.92820	−	4.00000i	0.951662	−	0.549442i	0.0580651	−	0.998313i	$-0.481507\pi$
$53$	6.92820	−	4.00000i	0.951662	−	0.549442i	0.893597	+	0.448871i	$0.148174\pi$
$54$	−1.00000			−0.136083
$55$	6.16025	+	9.33013i	0.830648	+	1.25807i
$56$	1.00000	−	1.73205i	0.133631	−	0.231455i
$57$	−3.46410	+	2.00000i	−0.458831	+	0.264906i
$58$		−	2.00000i		−	0.262613i
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$	2.00000	+	1.00000i	0.258199	+	0.129099i
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$	5.19615	+	2.00000i	0.659912	+	0.254000i
$63$		−	2.00000i		−	0.251976i
$64$	−1.00000			−0.125000
$65$	3.73205	−	2.46410i	0.462904	−	0.305634i
$66$	−5.00000			−0.615457
$67$	6.06218	−	3.50000i	0.740613	−	0.427593i	−0.0816792	−	0.996659i	$-0.526028\pi$
$67$	6.06218	−	3.50000i	0.740613	−	0.427593i	0.822292	+	0.569066i	$0.192695\pi$
$68$	−2.59808	−	1.50000i	−0.315063	−	0.181902i
$69$	−1.50000	+	2.59808i	−0.180579	+	0.312772i
$70$	−2.00000	+	4.00000i	−0.239046	+	0.478091i
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−5.19615	+	3.00000i	−0.608164	+	0.351123i	−0.772246	−	0.635323i	$-0.780867\pi$
$73$	−5.19615	+	3.00000i	−0.608164	+	0.351123i	0.164083	+	0.986447i	$0.447534\pi$
$74$	2.50000	−	4.33013i	0.290619	−	0.503367i
$75$	−4.59808	−	1.96410i	−0.530940	−	0.226795i
$76$	−2.00000	+	3.46410i	−0.229416	+	0.397360i
$77$		−	10.0000i		−	1.13961i
$78$			2.00000i			0.226455i
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	−0.690426	−	0.723403i	$-0.742577\pi$
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	0.971698	+	0.236225i	$0.0759104\pi$
$80$	2.23205	−	0.133975i	0.249551	−	0.0149788i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−5.19615	+	3.00000i	−0.570352	+	0.329293i	−0.757290	−	0.653079i	$-0.773477\pi$
$83$	−5.19615	+	3.00000i	−0.570352	+	0.329293i	0.186938	+	0.982372i	$0.440144\pi$
$84$	−1.00000	−	1.73205i	−0.109109	−	0.188982i
$85$	6.00000	+	3.00000i	0.650791	+	0.325396i
$86$	−0.500000	+	0.866025i	−0.0539164	+	0.0933859i
$87$	−1.73205	−	1.00000i	−0.185695	−	0.107211i
$88$	−4.33013	+	2.50000i	−0.461593	+	0.266501i
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	1.86603	−	1.23205i	0.196696	−	0.129870i
$91$	−4.00000			−0.419314
$92$			3.00000i			0.312772i
$93$	4.33013	−	3.50000i	0.449013	−	0.362933i
$94$	−9.00000			−0.928279
$95$	4.00000	−	8.00000i	0.410391	−	0.820783i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$		0			0		1.00000			$0$
$97$		0			0		−1.00000			$\pi$
$98$	−2.59808	+	1.50000i	−0.262445	+	0.151523i
$99$	−2.50000	+	4.33013i	−0.251259	+	0.435194i
$100$	−4.96410	+	0.598076i	−0.496410	+	0.0598076i
$101$	17.0000			1.69156			0.845782	−	0.533529i	$-0.179135\pi$
$101$	17.0000			1.69156			0.845782	+	0.533529i	$0.179135\pi$
$102$	−2.59808	+	1.50000i	−0.257248	+	0.148522i
$103$	−13.8564	+	8.00000i	−1.36531	+	0.788263i	−0.990325	−	0.138767i	$-0.955686\pi$
$103$	−13.8564	+	8.00000i	−1.36531	+	0.788263i	−0.374987	+	0.927030i	$0.622353\pi$
$104$	1.00000	+	1.73205i	0.0980581	+	0.169842i
$105$	2.46410	+	3.73205i	0.240472	+	0.364211i
$106$	−4.00000	−	6.92820i	−0.388514	−	0.672927i
$107$	−13.8564	−	8.00000i	−1.33955	−	0.773389i	−0.352809	−	0.935695i	$-0.614773\pi$
$107$	−13.8564	−	8.00000i	−1.33955	−	0.773389i	−0.986740	+	0.162306i	$0.948107\pi$
$108$			1.00000i			0.0962250i
$109$	8.00000			0.766261			0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000			0.766261			0.383131	+	0.923694i	$0.374846\pi$
$110$	9.33013	−	6.16025i	0.889593	−	0.587357i
$111$	−2.50000	−	4.33013i	−0.237289	−	0.410997i
$112$	−1.73205	−	1.00000i	−0.163663	−	0.0944911i
$113$	6.06218	−	3.50000i	0.570282	−	0.329252i	−0.186980	−	0.982364i	$-0.559870\pi$
$113$	6.06218	−	3.50000i	0.570282	−	0.329252i	0.757262	+	0.653111i	$0.226537\pi$
$114$	2.00000	+	3.46410i	0.187317	+	0.324443i
$115$	−0.401924	−	6.69615i	−0.0374796	−	0.624419i
$116$	−2.00000			−0.185695
$117$	1.73205	+	1.00000i	0.160128	+	0.0924500i
$118$	−3.46410	−	2.00000i	−0.318896	−	0.184115i
$119$	−3.00000	−	5.19615i	−0.275010	−	0.476331i
$120$	1.00000	−	2.00000i	0.0912871	−	0.182574i
$121$	−7.00000	+	12.1244i	−0.636364	+	1.10221i
$122$			2.00000i			0.181071i
$123$		0			0
$124$	2.00000	−	5.19615i	0.179605	−	0.466628i
$125$	11.0000	−	2.00000i	0.983870	−	0.178885i
$126$	−2.00000			−0.178174
$127$	1.73205	+	1.00000i	0.153695	+	0.0887357i	0.574875	−	0.818241i	$-0.305051\pi$
$127$	1.73205	+	1.00000i	0.153695	+	0.0887357i	−0.421180	+	0.906977i	$0.638384\pi$
$128$			1.00000i			0.0883883i
$129$	0.500000	+	0.866025i	0.0440225	+	0.0762493i
$130$	−2.46410	−	3.73205i	−0.216116	−	0.327323i
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	0.326546	+	0.945181i	$0.394115\pi$
$131$	−7.50000	+	12.9904i	−0.655278	+	1.13497i	−0.981824	+	0.189794i	$0.939218\pi$
$132$			5.00000i			0.435194i
$133$	−6.92820	+	4.00000i	−0.600751	+	0.346844i
$134$	−3.50000	−	6.06218i	−0.302354	−	0.523692i
$135$	−0.133975	−	2.23205i	−0.0115307	−	0.192104i
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	−4.33013	+	2.50000i	−0.369948	+	0.213589i	−0.673436	−	0.739246i	$-0.735182\pi$
$137$	−4.33013	+	2.50000i	−0.369948	+	0.213589i	0.303488	+	0.952835i	$0.401849\pi$
$138$	2.59808	+	1.50000i	0.221163	+	0.127688i
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$	4.00000	+	2.00000i	0.338062	+	0.169031i
$141$	−4.50000	+	7.79423i	−0.378968	+	0.656392i
$142$		0			0
$143$	8.66025	+	5.00000i	0.724207	+	0.418121i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	4.46410	−	0.267949i	0.370723	−	0.0222520i
$146$	3.00000	+	5.19615i	0.248282	+	0.430037i
$147$			3.00000i			0.247436i
$148$	−4.33013	−	2.50000i	−0.355934	−	0.205499i
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$	−1.96410	+	4.59808i	−0.160368	+	0.375431i
$151$	−9.00000			−0.732410			−0.366205	−	0.930534i	$-0.619343\pi$
$151$	−9.00000			−0.732410			−0.366205	+	0.930534i	$0.619343\pi$
$152$	3.46410	+	2.00000i	0.280976	+	0.162221i
$153$			3.00000i			0.242536i
$154$	−10.0000			−0.805823
$155$	−3.76795	+	11.8660i	−0.302649	+	0.953102i
$156$	2.00000			0.160128
$157$			2.00000i			0.159617i	0.996810	+	0.0798087i	$0.0254309\pi$
$157$			2.00000i			0.159617i	−0.996810	+	0.0798087i	$0.974569\pi$
$158$	−4.33013	−	2.50000i	−0.344486	−	0.198889i
$159$	−8.00000			−0.634441
$160$	−0.133975	−	2.23205i	−0.0105916	−	0.176459i
$161$	−3.00000	+	5.19615i	−0.236433	+	0.409514i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$			25.0000i			1.95815i	0.203497	+	0.979076i	$0.434769\pi$
$163$			25.0000i			1.95815i	−0.203497	+	0.979076i	$0.565231\pi$
$164$		0			0
$165$	−0.669873	−	11.1603i	−0.0521495	−	0.868825i
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$167$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$168$	−1.73205	+	1.00000i	−0.133631	+	0.0771517i
$169$	−4.50000	+	7.79423i	−0.346154	+	0.599556i
$170$	3.00000	−	6.00000i	0.230089	−	0.460179i
$171$	4.00000			0.305888
$172$	0.866025	+	0.500000i	0.0660338	+	0.0381246i
$173$	−5.19615	+	3.00000i	−0.395056	+	0.228086i	−0.684349	−	0.729155i	$-0.739913\pi$
$173$	−5.19615	+	3.00000i	−0.395056	+	0.228086i	0.289292	+	0.957241i	$0.406580\pi$
$174$	−1.00000	+	1.73205i	−0.0758098	+	0.131306i
$175$	−9.19615	−	3.92820i	−0.695164	−	0.296944i
$176$	2.50000	+	4.33013i	0.188445	+	0.326396i
$177$	−3.46410	+	2.00000i	−0.260378	+	0.150329i
$178$		0			0
$179$	2.50000	−	4.33013i	0.186859	−	0.323649i	−0.757343	−	0.653018i	$-0.773503\pi$
$179$	2.50000	−	4.33013i	0.186859	−	0.323649i	0.944201	+	0.329369i	$0.106836\pi$
$180$	−1.23205	−	1.86603i	−0.0918316	−	0.139085i
$181$	8.00000	+	13.8564i	0.594635	+	1.02994i	0.993598	+	0.112972i	$0.0360369\pi$
$181$	8.00000	+	13.8564i	0.594635	+	1.02994i	−0.398963	+	0.916967i	$0.630630\pi$
$182$			4.00000i			0.296500i
$183$	1.73205	+	1.00000i	0.128037	+	0.0739221i
$184$	3.00000			0.221163
$185$	10.0000	+	5.00000i	0.735215	+	0.367607i
$186$	−3.50000	−	4.33013i	−0.256632	−	0.317500i
$187$			15.0000i			1.09691i
$188$			9.00000i			0.656392i
$189$	−1.00000	+	1.73205i	−0.0727393	+	0.125988i
$190$	−8.00000	−	4.00000i	−0.580381	−	0.290191i
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	0.995610	+	0.0935936i	$0.0298354\pi$
$191$	8.00000	+	13.8564i	0.578860	+	1.00261i	−0.416751	+	0.909021i	$0.636831\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	3.46410	+	2.00000i	0.249351	+	0.143963i	0.619467	−	0.785022i	$-0.287349\pi$
$193$	3.46410	+	2.00000i	0.249351	+	0.143963i	−0.370116	+	0.928986i	$0.620682\pi$
$194$		0			0
$195$	−4.46410	+	0.267949i	−0.319681	+	0.0191882i
$196$	1.50000	+	2.59808i	0.107143	+	0.185577i
$197$	−1.73205	+	1.00000i	−0.123404	+	0.0712470i	−0.560431	−	0.828201i	$-0.689365\pi$
$197$	−1.73205	+	1.00000i	−0.123404	+	0.0712470i	0.437028	+	0.899448i	$0.356031\pi$
$198$	4.33013	+	2.50000i	0.307729	+	0.177667i
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$	0.598076	+	4.96410i	0.0422904	+	0.351015i
$201$	−7.00000			−0.493742
$202$		−	17.0000i		−	1.19612i
$203$	−3.46410	−	2.00000i	−0.243132	−	0.140372i
$204$	1.50000	+	2.59808i	0.105021	+	0.181902i
$205$		0			0
$206$	8.00000	+	13.8564i	0.557386	+	0.965422i
$207$	2.59808	−	1.50000i	0.180579	−	0.104257i
$208$	1.73205	−	1.00000i	0.120096	−	0.0693375i
$209$	20.0000			1.38343
$210$	3.73205	−	2.46410i	0.257536	−	0.170039i
$211$	−7.00000	+	12.1244i	−0.481900	+	0.834675i	−0.999784	−	0.0207756i	$-0.993386\pi$
$211$	−7.00000	+	12.1244i	−0.481900	+	0.834675i	0.517884	+	0.855451i	$0.326720\pi$
$212$	−6.92820	+	4.00000i	−0.475831	+	0.274721i
$213$		0			0
$214$	−8.00000	+	13.8564i	−0.546869	+	0.947204i
$215$	−2.00000	−	1.00000i	−0.136399	−	0.0681994i
$216$	1.00000			0.0680414
$217$	8.66025	−	7.00000i	0.587896	−	0.475191i
$218$		−	8.00000i		−	0.541828i
$219$	6.00000			0.405442
$220$	−6.16025	−	9.33013i	−0.415324	−	0.629037i
$221$	6.00000			0.403604
$222$	−4.33013	+	2.50000i	−0.290619	+	0.167789i
$223$	−3.46410	−	2.00000i	−0.231973	−	0.133930i	0.379509	−	0.925188i	$-0.376093\pi$
$223$	−3.46410	−	2.00000i	−0.231973	−	0.133930i	−0.611482	+	0.791258i	$0.709426\pi$
$224$	−1.00000	+	1.73205i	−0.0668153	+	0.115728i
$225$	3.00000	+	4.00000i	0.200000	+	0.266667i
$226$	−3.50000	−	6.06218i	−0.232817	−	0.403250i
$227$	−15.5885	+	9.00000i	−1.03464	+	0.597351i	−0.918311	−	0.395860i	$-0.870447\pi$
$227$	−15.5885	+	9.00000i	−1.03464	+	0.597351i	−0.116331	+	0.993210i	$0.537113\pi$
$228$	3.46410	−	2.00000i	0.229416	−	0.132453i
$229$	1.00000	−	1.73205i	0.0660819	−	0.114457i	−0.831092	−	0.556136i	$-0.812283\pi$
$229$	1.00000	−	1.73205i	0.0660819	−	0.114457i	0.897173	+	0.441679i	$0.145617\pi$
$230$	−6.69615	+	0.401924i	−0.441531	+	0.0265021i
$231$	−5.00000	+	8.66025i	−0.328976	+	0.569803i
$232$			2.00000i			0.131306i
$233$		−	19.0000i		−	1.24473i	−0.782727	−	0.622366i	$-0.786172\pi$
$233$		−	19.0000i		−	1.24473i	0.782727	−	0.622366i	$-0.213828\pi$
$234$	1.00000	−	1.73205i	0.0653720	−	0.113228i
$235$	−1.20577	−	20.0885i	−0.0786559	−	1.31043i
$236$	−2.00000	+	3.46410i	−0.130189	+	0.225494i
$237$	−4.33013	+	2.50000i	−0.281272	+	0.162392i
$238$	−5.19615	+	3.00000i	−0.336817	+	0.194461i
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	0.752536	−	0.658551i	$-0.228830\pi$
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	−0.946590	+	0.322440i	$0.895497\pi$
$240$	−2.00000	−	1.00000i	−0.129099	−	0.0645497i
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	0.415768	+	0.909471i	$0.363513\pi$
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	−0.995509	+	0.0946700i	$0.969820\pi$
$242$	12.1244	+	7.00000i	0.779383	+	0.449977i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	2.00000			0.128037
$245$	−3.69615	−	5.59808i	−0.236139	−	0.357648i
$246$		0			0
$247$		−	8.00000i		−	0.509028i
$248$	−5.19615	−	2.00000i	−0.329956	−	0.127000i
$249$	6.00000			0.380235
$250$	−2.00000	−	11.0000i	−0.126491	−	0.695701i
$251$	12.5000	−	21.6506i	0.788993	−	1.36658i	−0.137591	−	0.990489i	$-0.543936\pi$
$251$	12.5000	−	21.6506i	0.788993	−	1.36658i	0.926584	−	0.376087i	$-0.122731\pi$
$252$			2.00000i			0.125988i
$253$	12.9904	−	7.50000i	0.816698	−	0.471521i
$254$	1.00000	−	1.73205i	0.0627456	−	0.108679i
$255$	−3.69615	−	5.59808i	−0.231462	−	0.350565i
$256$	1.00000			0.0625000
$257$	−19.9186	+	11.5000i	−1.24249	+	0.717350i	−0.969600	−	0.244696i	$-0.921312\pi$
$257$	−19.9186	+	11.5000i	−1.24249	+	0.717350i	−0.272887	+	0.962046i	$0.587979\pi$
$258$	0.866025	−	0.500000i	0.0539164	−	0.0311286i
$259$	−5.00000	−	8.66025i	−0.310685	−	0.538122i
$260$	−3.73205	+	2.46410i	−0.231452	+	0.152817i
$261$	1.00000	+	1.73205i	0.0618984	+	0.107211i
$262$	12.9904	+	7.50000i	0.802548	+	0.463352i
$263$		−	17.0000i		−	1.04826i	−0.851637	−	0.524132i	$-0.824390\pi$
$263$		−	17.0000i		−	1.04826i	0.851637	−	0.524132i	$-0.175610\pi$
$264$	5.00000			0.307729
$265$	14.9282	−	9.85641i	0.917032	−	0.605474i
$266$	4.00000	+	6.92820i	0.245256	+	0.424795i
$267$		0			0
$268$	−6.06218	+	3.50000i	−0.370306	+	0.213797i
$269$	2.50000	+	4.33013i	0.152428	+	0.264013i	0.932119	−	0.362151i	$-0.117958\pi$
$269$	2.50000	+	4.33013i	0.152428	+	0.264013i	−0.779692	+	0.626164i	$0.784624\pi$
$270$	−2.23205	+	0.133975i	−0.135838	+	0.00815343i
$271$	32.0000			1.94386			0.971931	−	0.235267i	$-0.0755965\pi$
$271$	32.0000			1.94386			0.971931	+	0.235267i	$0.0755965\pi$
$272$	2.59808	+	1.50000i	0.157532	+	0.0909509i
$273$	3.46410	+	2.00000i	0.209657	+	0.121046i
$274$	2.50000	+	4.33013i	0.151031	+	0.261593i
$275$	15.0000	+	20.0000i	0.904534	+	1.20605i
$276$	1.50000	−	2.59808i	0.0902894	−	0.156386i
$277$		−	7.00000i		−	0.420589i	−0.977638	−	0.210295i	$-0.932558\pi$
$277$		−	7.00000i		−	0.420589i	0.977638	−	0.210295i	$-0.0674423\pi$
$278$		−	14.0000i		−	0.839664i
$279$	−5.50000	+	0.866025i	−0.329276	+	0.0518476i
$280$	2.00000	−	4.00000i	0.119523	−	0.239046i
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$	7.79423	+	4.50000i	0.464140	+	0.267971i
$283$			17.0000i			1.01055i	0.862960	+	0.505273i	$0.168608\pi$
$283$			17.0000i			1.01055i	−0.862960	+	0.505273i	$0.831392\pi$
$284$		0			0
$285$	−7.46410	+	4.92820i	−0.442135	+	0.291922i
$286$	5.00000	−	8.66025i	0.295656	−	0.512092i
$287$		0			0
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	−0.267949	−	4.46410i	−0.0157345	−	0.262141i
$291$		0			0
$292$	5.19615	−	3.00000i	0.304082	−	0.175562i
$293$	−24.2487	−	14.0000i	−1.41662	−	0.817889i	−0.420624	−	0.907235i	$-0.638189\pi$
$293$	−24.2487	−	14.0000i	−1.41662	−	0.817889i	−0.996001	+	0.0893462i	$0.971522\pi$
$294$	3.00000			0.174964
$295$	4.00000	−	8.00000i	0.232889	−	0.465778i
$296$	−2.50000	+	4.33013i	−0.145310	+	0.251684i
$297$	4.33013	−	2.50000i	0.251259	−	0.145065i
$298$	−8.66025	−	5.00000i	−0.501675	−	0.289642i
$299$	−3.00000	−	5.19615i	−0.173494	−	0.300501i
$300$	4.59808	+	1.96410i	0.265470	+	0.113397i
$301$	1.00000	+	1.73205i	0.0576390	+	0.0998337i
$302$			9.00000i			0.517892i
$303$	−14.7224	−	8.50000i	−0.845782	−	0.488312i
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	−4.46410	+	0.267949i	−0.255614	+	0.0153427i
$306$	3.00000			0.171499
$307$	−6.92820	−	4.00000i	−0.395413	−	0.228292i	0.289090	−	0.957302i	$-0.406647\pi$
$307$	−6.92820	−	4.00000i	−0.395413	−	0.228292i	−0.684503	+	0.729010i	$0.739981\pi$
$308$			10.0000i			0.569803i
$309$	16.0000			0.910208
$310$	11.8660	+	3.76795i	0.673945	+	0.214005i
$311$	−26.0000			−1.47432			−0.737162	−	0.675716i	$-0.763835\pi$
$311$	−26.0000			−1.47432			−0.737162	+	0.675716i	$0.763835\pi$
$312$		−	2.00000i		−	0.113228i
$313$	−20.7846	−	12.0000i	−1.17482	−	0.678280i	−0.220006	−	0.975499i	$-0.570608\pi$
$313$	−20.7846	−	12.0000i	−1.17482	−	0.678280i	−0.954810	+	0.297218i	$0.903941\pi$
$314$	2.00000			0.112867
$315$	−0.267949	−	4.46410i	−0.0150972	−	0.251524i
$316$	−2.50000	+	4.33013i	−0.140636	+	0.243589i
$317$	8.66025	+	5.00000i	0.486408	+	0.280828i	0.723083	−	0.690761i	$-0.242724\pi$
$317$	8.66025	+	5.00000i	0.486408	+	0.280828i	−0.236675	+	0.971589i	$0.576058\pi$
$318$			8.00000i			0.448618i
$319$	5.00000	+	8.66025i	0.279946	+	0.484881i
$320$	−2.23205	+	0.133975i	−0.124775	+	0.00748941i
$321$	8.00000	+	13.8564i	0.446516	+	0.773389i
$322$	5.19615	+	3.00000i	0.289570	+	0.167183i
$323$	10.3923	−	6.00000i	0.578243	−	0.333849i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	8.00000	−	6.00000i	0.443760	−	0.332820i
$326$	25.0000			1.38462
$327$	−6.92820	−	4.00000i	−0.383131	−	0.221201i
$328$		0			0
$329$	−9.00000	+	15.5885i	−0.496186	+	0.859419i
$330$	−11.1603	+	0.669873i	−0.614352	+	0.0368753i
$331$	−15.0000	−	25.9808i	−0.824475	−	1.42803i	−0.902320	−	0.431066i	$-0.858137\pi$
$331$	−15.0000	−	25.9808i	−0.824475	−	1.42803i	0.0778456	−	0.996965i	$-0.475196\pi$
$332$	5.19615	−	3.00000i	0.285176	−	0.164646i
$333$			5.00000i			0.273998i
$334$		0			0
$335$	13.0622	−	8.62436i	0.713663	−	0.471199i
$336$	1.00000	+	1.73205i	0.0545545	+	0.0944911i
$337$		−	2.00000i		−	0.108947i	−0.998515	−	0.0544735i	$-0.982652\pi$
$337$		−	2.00000i		−	0.108947i	0.998515	−	0.0544735i	$-0.0173480\pi$
$338$	7.79423	+	4.50000i	0.423950	+	0.244768i
$339$	−7.00000			−0.380188
$340$	−6.00000	−	3.00000i	−0.325396	−	0.162698i
$341$	−27.5000	+	4.33013i	−1.48921	+	0.234490i
$342$		−	4.00000i		−	0.216295i
$343$			20.0000i			1.07990i
$344$	0.500000	−	0.866025i	0.0269582	−	0.0466930i
$345$	−3.00000	+	6.00000i	−0.161515	+	0.323029i
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	5.19615	+	3.00000i	0.278944	+	0.161048i	0.632945	−	0.774197i	$-0.281846\pi$
$347$	5.19615	+	3.00000i	0.278944	+	0.161048i	−0.354001	+	0.935245i	$0.615179\pi$
$348$	1.73205	+	1.00000i	0.0928477	+	0.0536056i
$349$	−28.0000			−1.49881			−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000			−1.49881			−0.749403	+	0.662114i	$0.769659\pi$
$350$	−3.92820	+	9.19615i	−0.209971	+	0.491555i
$351$	−1.00000	−	1.73205i	−0.0533761	−	0.0924500i
$352$	4.33013	−	2.50000i	0.230797	−	0.133250i
$353$	26.8468	+	15.5000i	1.42891	+	0.824982i	0.997035	−	0.0769515i	$-0.0245187\pi$
$353$	26.8468	+	15.5000i	1.42891	+	0.824982i	0.431875	+	0.901933i	$0.357852\pi$
$354$	2.00000	+	3.46410i	0.106299	+	0.184115i
$355$		0			0
$356$		0			0
$357$			6.00000i			0.317554i
$358$	−4.33013	−	2.50000i	−0.228854	−	0.132129i
$359$	−18.0000	−	31.1769i	−0.950004	−	1.64545i	−0.745409	−	0.666608i	$-0.767746\pi$
$359$	−18.0000	−	31.1769i	−0.950004	−	1.64545i	−0.204595	−	0.978847i	$-0.565588\pi$
$360$	−1.86603	+	1.23205i	−0.0983482	+	0.0649348i
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	13.8564	−	8.00000i	0.728277	−	0.420471i
$363$	12.1244	−	7.00000i	0.636364	−	0.367405i
$364$	4.00000			0.209657
$365$	−11.1962	+	7.39230i	−0.586033	+	0.386931i
$366$	1.00000	−	1.73205i	0.0522708	−	0.0905357i
$367$	−25.9808	+	15.0000i	−1.35618	+	0.782994i	−0.989107	−	0.147197i	$-0.952975\pi$
$367$	−25.9808	+	15.0000i	−1.35618	+	0.782994i	−0.367078	+	0.930190i	$0.619642\pi$
$368$		−	3.00000i		−	0.156386i
$369$		0			0
$370$	5.00000	−	10.0000i	0.259938	−	0.519875i
$371$	−16.0000			−0.830679
$372$	−4.33013	+	3.50000i	−0.224507	+	0.181467i
$373$			31.0000i			1.60512i	0.596572	+	0.802560i	$0.296529\pi$
$373$			31.0000i			1.60512i	−0.596572	+	0.802560i	$0.703471\pi$
$374$	15.0000			0.775632
$375$	−10.5263	−	3.76795i	−0.543575	−	0.194576i
$376$	9.00000			0.464140
$377$	3.46410	−	2.00000i	0.178410	−	0.103005i
$378$	1.73205	+	1.00000i	0.0890871	+	0.0514344i
$379$	17.0000	−	29.4449i	0.873231	−	1.51248i	0.0145964	−	0.999893i	$-0.495354\pi$
$379$	17.0000	−	29.4449i	0.873231	−	1.51248i	0.858635	−	0.512588i	$-0.171313\pi$
$380$	−4.00000	+	8.00000i	−0.205196	+	0.410391i
$381$	−1.00000	−	1.73205i	−0.0512316	−	0.0887357i
$382$	13.8564	−	8.00000i	0.708955	−	0.409316i
$383$	18.1865	−	10.5000i	0.929288	−	0.536525i	0.0427020	−	0.999088i	$-0.486403\pi$
$383$	18.1865	−	10.5000i	0.929288	−	0.536525i	0.886586	+	0.462563i	$0.153070\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	−1.33975	−	22.3205i	−0.0682798	−	1.13756i
$386$	2.00000	−	3.46410i	0.101797	−	0.176318i
$387$		−	1.00000i		−	0.0508329i
$388$		0			0
$389$	−12.5000	+	21.6506i	−0.633775	+	1.09773i	0.352998	+	0.935624i	$0.385162\pi$
$389$	−12.5000	+	21.6506i	−0.633775	+	1.09773i	−0.986773	+	0.162107i	$0.948171\pi$
$390$	0.267949	+	4.46410i	0.0135681	+	0.226049i
$391$	4.50000	−	7.79423i	0.227575	−	0.394171i
$392$	2.59808	−	1.50000i	0.131223	−	0.0757614i
$393$	12.9904	−	7.50000i	0.655278	−	0.378325i
$394$	1.00000	+	1.73205i	0.0503793	+	0.0872595i
$395$	5.00000	−	10.0000i	0.251577	−	0.503155i
$396$	2.50000	−	4.33013i	0.125630	−	0.217597i
$397$	−23.3827	−	13.5000i	−1.17354	−	0.677546i	−0.219031	−	0.975718i	$-0.570290\pi$
$397$	−23.3827	−	13.5000i	−1.17354	−	0.677546i	−0.954512	+	0.298172i	$0.903623\pi$
$398$	13.8564	−	8.00000i	0.694559	−	0.401004i
$399$	8.00000			0.400501
$400$	4.96410	−	0.598076i	0.248205	−	0.0299038i
$401$	−28.0000			−1.39825			−0.699127	−	0.714998i	$-0.746428\pi$
$401$	−28.0000			−1.39825			−0.699127	+	0.714998i	$0.746428\pi$
$402$			7.00000i			0.349128i
$403$	1.73205	+	11.0000i	0.0862796	+	0.547949i
$404$	−17.0000			−0.845782
$405$	−1.00000	+	2.00000i	−0.0496904	+	0.0993808i
$406$	−2.00000	+	3.46410i	−0.0992583	+	0.171920i
$407$			25.0000i			1.23920i
$408$	2.59808	−	1.50000i	0.128624	−	0.0742611i
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	0.371750	+	0.928333i	$0.378758\pi$
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	−0.989835	+	0.142222i	$0.954575\pi$
$410$		0			0
$411$	5.00000			0.246632
$412$	13.8564	−	8.00000i	0.682656	−	0.394132i
$413$	−6.92820	+	4.00000i	−0.340915	+	0.196827i
$414$	−1.50000	−	2.59808i	−0.0737210	−	0.127688i
$415$	−11.1962	+	7.39230i	−0.549598	+	0.362874i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	−12.1244	−	7.00000i	−0.593732	−	0.342791i
$418$		−	20.0000i		−	0.978232i
$419$	−39.0000			−1.90527			−0.952637	−	0.304109i	$-0.901641\pi$
$419$	−39.0000			−1.90527			−0.952637	+	0.304109i	$0.901641\pi$
$420$	−2.46410	−	3.73205i	−0.120236	−	0.182105i
$421$	−8.00000	−	13.8564i	−0.389896	−	0.675320i	0.602539	−	0.798089i	$-0.294156\pi$
$421$	−8.00000	−	13.8564i	−0.389896	−	0.675320i	−0.992435	+	0.122769i	$0.960822\pi$
$422$	12.1244	+	7.00000i	0.590204	+	0.340755i
$423$	7.79423	−	4.50000i	0.378968	−	0.218797i
$424$	4.00000	+	6.92820i	0.194257	+	0.336463i
$425$	13.7942	+	5.89230i	0.669118	+	0.285819i
$426$		0			0
$427$	3.46410	+	2.00000i	0.167640	+	0.0967868i
$428$	13.8564	+	8.00000i	0.669775	+	0.386695i
$429$	−5.00000	−	8.66025i	−0.241402	−	0.418121i
$430$	−1.00000	+	2.00000i	−0.0482243	+	0.0964486i
$431$	−5.00000	+	8.66025i	−0.240842	+	0.417150i	−0.960954	−	0.276707i	$-0.910757\pi$
$431$	−5.00000	+	8.66025i	−0.240842	+	0.417150i	0.720113	+	0.693857i	$0.244090\pi$
$432$		−	1.00000i		−	0.0481125i
$433$		−	38.0000i		−	1.82616i	−0.407777	−	0.913082i	$-0.633696\pi$
$433$		−	38.0000i		−	1.82616i	0.407777	−	0.913082i	$-0.366304\pi$
$434$	−7.00000	−	8.66025i	−0.336011	−	0.415705i
$435$	−4.00000	−	2.00000i	−0.191785	−	0.0958927i
$436$	−8.00000			−0.383131
$437$	−10.3923	−	6.00000i	−0.497131	−	0.287019i
$438$		−	6.00000i		−	0.286691i
$439$	−0.500000	−	0.866025i	−0.0238637	−	0.0413331i	0.853847	−	0.520524i	$-0.174263\pi$
$439$	−0.500000	−	0.866025i	−0.0238637	−	0.0413331i	−0.877711	+	0.479191i	$0.840930\pi$
$440$	−9.33013	+	6.16025i	−0.444796	+	0.293679i
$441$	1.50000	−	2.59808i	0.0714286	−	0.123718i
$442$		−	6.00000i		−	0.285391i
$443$	−1.73205	+	1.00000i	−0.0822922	+	0.0475114i	−0.540581	−	0.841292i	$-0.681796\pi$
$443$	−1.73205	+	1.00000i	−0.0822922	+	0.0475114i	0.458289	+	0.888803i	$0.348462\pi$
$444$	2.50000	+	4.33013i	0.118645	+	0.205499i
$445$		0			0
$446$	−2.00000	+	3.46410i	−0.0947027	+	0.164030i
$447$	−8.66025	+	5.00000i	−0.409616	+	0.236492i
$448$	1.73205	+	1.00000i	0.0818317	+	0.0472456i
$449$	24.0000			1.13263			0.566315	−	0.824189i	$-0.308369\pi$
$449$	24.0000			1.13263			0.566315	+	0.824189i	$0.308369\pi$
$450$	4.00000	−	3.00000i	0.188562	−	0.141421i
$451$		0			0
$452$	−6.06218	+	3.50000i	−0.285141	+	0.164626i
$453$	7.79423	+	4.50000i	0.366205	+	0.211428i
$454$	9.00000	+	15.5885i	0.422391	+	0.731603i
$455$	−8.92820	+	0.535898i	−0.418561	+	0.0251233i
$456$	−2.00000	−	3.46410i	−0.0936586	−	0.162221i
$457$			16.0000i			0.748448i	0.927338	+	0.374224i	$0.122091\pi$
$457$			16.0000i			0.748448i	−0.927338	+	0.374224i	$0.877909\pi$
$458$	−1.73205	−	1.00000i	−0.0809334	−	0.0467269i
$459$	1.50000	−	2.59808i	0.0700140	−	0.121268i
$460$	0.401924	+	6.69615i	0.0187398	+	0.312210i
$461$	3.00000			0.139724			0.0698620	−	0.997557i	$-0.477744\pi$
$461$	3.00000			0.139724			0.0698620	+	0.997557i	$0.477744\pi$
$462$	8.66025	+	5.00000i	0.402911	+	0.232621i
$463$		−	18.0000i		−	0.836531i	−0.908325	−	0.418265i	$-0.862638\pi$
$463$		−	18.0000i		−	0.836531i	0.908325	−	0.418265i	$-0.137362\pi$
$464$	2.00000			0.0928477
$465$	9.19615	−	8.39230i	0.426461	−	0.389184i
$466$	−19.0000			−0.880158
$467$		−	8.00000i		−	0.370196i	−0.982720	−	0.185098i	$-0.940740\pi$
$467$		−	8.00000i		−	0.370196i	0.982720	−	0.185098i	$-0.0592602\pi$
$468$	−1.73205	−	1.00000i	−0.0800641	−	0.0462250i
$469$	−14.0000			−0.646460
$470$	−20.0885	+	1.20577i	−0.926611	+	0.0556181i
$471$	1.00000	−	1.73205i	0.0460776	−	0.0798087i
$472$	3.46410	+	2.00000i	0.159448	+	0.0920575i
$473$		−	5.00000i		−	0.229900i
$474$	2.50000	+	4.33013i	0.114829	+	0.198889i
$475$	7.85641	−	18.3923i	0.360477	−	0.843897i
$476$	3.00000	+	5.19615i	0.137505	+	0.238165i
$477$	6.92820	+	4.00000i	0.317221	+	0.183147i
$478$	−5.19615	+	3.00000i	−0.237666	+	0.137217i
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	−0.969920	−	0.243426i	$-0.921729\pi$
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	0.695773	+	0.718262i	$0.255062\pi$
$480$	−1.00000	+	2.00000i	−0.0456435	+	0.0912871i
$481$	10.0000			0.455961
$482$	15.5885	+	9.00000i	0.710035	+	0.409939i
$483$	5.19615	−	3.00000i	0.236433	−	0.136505i
$484$	7.00000	−	12.1244i	0.318182	−	0.551107i
$485$		0			0
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	10.3923	−	6.00000i	0.470920	−	0.271886i	−0.245705	−	0.969345i	$-0.579019\pi$
$487$	10.3923	−	6.00000i	0.470920	−	0.271886i	0.716625	+	0.697459i	$0.245686\pi$
$488$		−	2.00000i		−	0.0905357i
$489$	12.5000	−	21.6506i	0.565270	−	0.979076i
$490$	−5.59808	+	3.69615i	−0.252895	+	0.166975i
$491$	−1.50000	−	2.59808i	−0.0676941	−	0.117250i	0.830192	−	0.557478i	$-0.188231\pi$
$491$	−1.50000	−	2.59808i	−0.0676941	−	0.117250i	−0.897886	+	0.440228i	$0.854898\pi$
$492$		0			0
$493$	5.19615	+	3.00000i	0.234023	+	0.135113i
$494$	−8.00000			−0.359937
$495$	−5.00000	+	10.0000i	−0.224733	+	0.449467i
$496$	−2.00000	+	5.19615i	−0.0898027	+	0.233314i
$497$		0			0
$498$		−	6.00000i		−	0.268866i
$499$	9.00000	−	15.5885i	0.402895	−	0.697835i	−0.591179	−	0.806541i	$-0.701337\pi$
$499$	9.00000	−	15.5885i	0.402895	−	0.697835i	0.994074	+	0.108705i	$0.0346705\pi$
$500$	−11.0000	+	2.00000i	−0.491935	+	0.0894427i
$501$		0			0
$502$	−21.6506	−	12.5000i	−0.966315	−	0.557902i
$503$	38.1051	+	22.0000i	1.69902	+	0.980932i	0.946688	+	0.322151i	$0.104406\pi$
$503$	38.1051	+	22.0000i	1.69902	+	0.980932i	0.752335	+	0.658781i	$0.228928\pi$
$504$	2.00000			0.0890871
$505$	37.9449	−	2.27757i	1.68852	−	0.101350i
$506$	−7.50000	−	12.9904i	−0.333416	−	0.577493i
$507$	7.79423	−	4.50000i	0.346154	−	0.199852i
$508$	−1.73205	−	1.00000i	−0.0768473	−	0.0443678i
$509$	−20.5000	−	35.5070i	−0.908647	−	1.57382i	−0.815946	−	0.578128i	$-0.803783\pi$
$509$	−20.5000	−	35.5070i	−0.908647	−	1.57382i	−0.0927004	−	0.995694i	$-0.529550\pi$
$510$	−5.59808	+	3.69615i	−0.247887	+	0.163668i
$511$	12.0000			0.530849
$512$		−	1.00000i		−	0.0441942i
$513$	−3.46410	−	2.00000i	−0.152944	−	0.0883022i
$514$	11.5000	+	19.9186i	0.507243	+	0.878571i
$515$	−29.8564	+	19.7128i	−1.31563	+	0.868650i
$516$	−0.500000	−	0.866025i	−0.0220113	−	0.0381246i
$517$	38.9711	−	22.5000i	1.71395	−	0.989549i
$518$	−8.66025	+	5.00000i	−0.380510	+	0.219687i
$519$	6.00000			0.263371
$520$	2.46410	+	3.73205i	0.108058	+	0.163661i
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	−0.598714	−	0.800963i	$-0.704321\pi$
$521$	9.00000	−	15.5885i	0.394297	−	0.682943i	0.993011	+	0.118020i	$0.0376547\pi$
$522$	1.73205	−	1.00000i	0.0758098	−	0.0437688i
$523$			29.0000i			1.26808i	0.773300	+	0.634041i	$0.218605\pi$
$523$			29.0000i			1.26808i	−0.773300	+	0.634041i	$0.781395\pi$
$524$	7.50000	−	12.9904i	0.327639	−	0.567487i
$525$	6.00000	+	8.00000i	0.261861	+	0.349149i
$526$	−17.0000			−0.741235
$527$	−12.9904	+	10.5000i	−0.565870	+	0.457387i
$528$		−	5.00000i		−	0.217597i
$529$	14.0000			0.608696
$530$	−9.85641	−	14.9282i	−0.428135	−	0.648440i
$531$	4.00000			0.173585
$532$	6.92820	−	4.00000i	0.300376	−	0.173422i
$533$		0			0
$534$		0			0
$535$	−32.0000	−	16.0000i	−1.38348	−	0.691740i
$536$	3.50000	+	6.06218i	0.151177	+	0.261846i
$537$	−4.33013	+	2.50000i	−0.186859	+	0.107883i
$538$	4.33013	−	2.50000i	0.186685	−	0.107783i
$539$	7.50000	−	12.9904i	0.323048	−	0.559535i
$540$	0.133975	+	2.23205i	0.00576535	+	0.0960522i
$541$	3.00000	−	5.19615i	0.128980	−	0.223400i	−0.794302	−	0.607524i	$-0.792163\pi$
$541$	3.00000	−	5.19615i	0.128980	−	0.223400i	0.923282	+	0.384124i	$0.125496\pi$
$542$		−	32.0000i		−	1.37452i
$543$		−	16.0000i		−	0.686626i
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$	17.8564	−	1.07180i	0.764884	−	0.0459107i
$546$	2.00000	−	3.46410i	0.0855921	−	0.148250i
$547$	−37.2391	+	21.5000i	−1.59223	+	0.919274i	−0.599305	+	0.800521i	$0.704556\pi$
$547$	−37.2391	+	21.5000i	−1.59223	+	0.919274i	−0.992924	+	0.118753i	$0.962110\pi$
$548$	4.33013	−	2.50000i	0.184974	−	0.106795i
$549$	−1.00000	−	1.73205i	−0.0426790	−	0.0739221i
$550$	20.0000	−	15.0000i	0.852803	−	0.639602i
$551$	4.00000	−	6.92820i	0.170406	−	0.295151i
$552$	−2.59808	−	1.50000i	−0.110581	−	0.0638442i
$553$	−8.66025	+	5.00000i	−0.368271	+	0.212622i
$554$	−7.00000			−0.297402
$555$	−6.16025	−	9.33013i	−0.261488	−	0.396042i
$556$	−14.0000			−0.593732
$557$		−	28.0000i		−	1.18640i	−0.805056	−	0.593199i	$-0.797865\pi$
$557$		−	28.0000i		−	1.18640i	0.805056	−	0.593199i	$-0.202135\pi$
$558$	0.866025	+	5.50000i	0.0366618	+	0.232834i
$559$	−2.00000			−0.0845910
$560$	−4.00000	−	2.00000i	−0.169031	−	0.0845154i
$561$	7.50000	−	12.9904i	0.316650	−	0.548454i
$562$			6.00000i			0.253095i
$563$	29.4449	−	17.0000i	1.24095	−	0.716465i	0.271665	−	0.962392i	$-0.412426\pi$
$563$	29.4449	−	17.0000i	1.24095	−	0.716465i	0.969288	+	0.245927i	$0.0790925\pi$
$564$	4.50000	−	7.79423i	0.189484	−	0.328196i
$565$	13.0622	−	8.62436i	0.549530	−	0.362829i
$566$	17.0000			0.714563
$567$	1.73205	−	1.00000i	0.0727393	−	0.0419961i
$568$		0			0
$569$	−12.0000	−	20.7846i	−0.503066	−	0.871336i	−0.999994	−	0.00354413i	$-0.998872\pi$
$569$	−12.0000	−	20.7846i	−0.503066	−	0.871336i	0.496928	−	0.867792i	$-0.334461\pi$
$570$	4.92820	+	7.46410i	0.206420	+	0.312637i
$571$	−7.00000	−	12.1244i	−0.292941	−	0.507388i	0.681563	−	0.731760i	$-0.261301\pi$
$571$	−7.00000	−	12.1244i	−0.292941	−	0.507388i	−0.974504	+	0.224371i	$0.927967\pi$
$572$	−8.66025	−	5.00000i	−0.362103	−	0.209061i
$573$		−	16.0000i		−	0.668410i
$574$		0			0
$575$	−1.79423	−	14.8923i	−0.0748245	−	0.621052i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−32.9090	−	19.0000i	−1.37002	−	0.790980i	−0.379088	−	0.925361i	$-0.623762\pi$
$577$	−32.9090	−	19.0000i	−1.37002	−	0.790980i	−0.990930	+	0.134380i	$0.957096\pi$
$578$	−6.92820	+	4.00000i	−0.288175	+	0.166378i
$579$	−2.00000	−	3.46410i	−0.0831172	−	0.143963i
$580$	−4.46410	+	0.267949i	−0.185362	+	0.0111260i
$581$	12.0000			0.497844
$582$		0			0
$583$	34.6410	+	20.0000i	1.43468	+	0.828315i
$584$	−3.00000	−	5.19615i	−0.124141	−	0.215018i
$585$	4.00000	+	2.00000i	0.165380	+	0.0826898i
$586$	−14.0000	+	24.2487i	−0.578335	+	1.00171i
$587$		−	6.00000i		−	0.247647i	−0.992304	−	0.123823i	$-0.960484\pi$
$587$		−	6.00000i		−	0.247647i	0.992304	−	0.123823i	$-0.0395156\pi$
$588$		−	3.00000i		−	0.123718i
$589$	14.0000	+	17.3205i	0.576860	+	0.713679i
$590$	−8.00000	−	4.00000i	−0.329355	−	0.164677i
$591$	2.00000			0.0822690
$592$	4.33013	+	2.50000i	0.177967	+	0.102749i
$593$			14.0000i			0.574911i	0.957794	+	0.287456i	$0.0928094\pi$
$593$			14.0000i			0.574911i	−0.957794	+	0.287456i	$0.907191\pi$
$594$	−2.50000	−	4.33013i	−0.102576	−	0.177667i
$595$	−7.39230	−	11.1962i	−0.303055	−	0.458997i
$596$	−5.00000	+	8.66025i	−0.204808	+	0.354738i
$597$		−	16.0000i		−	0.654836i
$598$	−5.19615	+	3.00000i	−0.212486	+	0.122679i
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	0.999938	−	0.0111569i	$-0.00355143\pi$
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$600$	1.96410	−	4.59808i	0.0801841	−	0.187716i
$601$	13.5000	−	23.3827i	0.550676	−	0.953800i	−0.447549	−	0.894259i	$-0.647703\pi$
$601$	13.5000	−	23.3827i	0.550676	−	0.953800i	0.998226	−	0.0595404i	$-0.0189635\pi$
$602$	1.73205	−	1.00000i	0.0705931	−	0.0407570i
$603$	6.06218	+	3.50000i	0.246871	+	0.142531i
$604$	9.00000			0.366205
$605$	−14.0000	+	28.0000i	−0.569181	+	1.13836i
$606$	−8.50000	+	14.7224i	−0.345289	+	0.598058i
$607$	27.7128	−	16.0000i	1.12483	−	0.649420i	0.182199	−	0.983262i	$-0.441678\pi$
$607$	27.7128	−	16.0000i	1.12483	−	0.649420i	0.942629	+	0.333842i	$0.108345\pi$
$608$	−3.46410	−	2.00000i	−0.140488	−	0.0811107i
$609$	2.00000	+	3.46410i	0.0810441	+	0.140372i
$610$	0.267949	+	4.46410i	0.0108489	+	0.180746i
$611$	−9.00000	−	15.5885i	−0.364101	−	0.630641i
$612$		−	3.00000i		−	0.121268i
$613$	−19.0526	−	11.0000i	−0.769526	−	0.444286i	0.0631797	−	0.998002i	$-0.479876\pi$
$613$	−19.0526	−	11.0000i	−0.769526	−	0.444286i	−0.832705	+	0.553716i	$0.813209\pi$
$614$	−4.00000	+	6.92820i	−0.161427	+	0.279600i
$615$		0			0
$616$	10.0000			0.402911
$617$	18.1865	+	10.5000i	0.732162	+	0.422714i	0.819213	−	0.573490i	$-0.194411\pi$
$617$	18.1865	+	10.5000i	0.732162	+	0.422714i	−0.0870504	+	0.996204i	$0.527744\pi$
$618$		−	16.0000i		−	0.643614i
$619$	−40.0000			−1.60774			−0.803868	−	0.594808i	$-0.797228\pi$
$619$	−40.0000			−1.60774			−0.803868	+	0.594808i	$0.797228\pi$
$620$	3.76795	−	11.8660i	0.151324	−	0.476551i
$621$	−3.00000			−0.120386
$622$			26.0000i			1.04251i
$623$		0			0
$624$	−2.00000			−0.0800641
$625$	24.2846	−	5.93782i	0.971384	−	0.237513i
$626$	−12.0000	+	20.7846i	−0.479616	+	0.830720i
$627$	−17.3205	−	10.0000i	−0.691714	−	0.399362i
$628$		−	2.00000i		−	0.0798087i
$629$	7.50000	+	12.9904i	0.299045	+	0.517960i
$630$	−4.46410	+	0.267949i	−0.177854	+	0.0106754i
$631$	20.5000	+	35.5070i	0.816092	+	1.41351i	0.908541	+	0.417796i	$0.137197\pi$
$631$	20.5000	+	35.5070i	0.816092	+	1.41351i	−0.0924489	+	0.995717i	$0.529469\pi$
$632$	4.33013	+	2.50000i	0.172243	+	0.0994447i
$633$	12.1244	−	7.00000i	0.481900	−	0.278225i
$634$	5.00000	−	8.66025i	0.198575	−	0.343943i
$635$	4.00000	+	2.00000i	0.158735	+	0.0793676i
$636$	8.00000			0.317221
$637$	−5.19615	−	3.00000i	−0.205879	−	0.118864i
$638$	8.66025	−	5.00000i	0.342863	−	0.197952i
$639$		0			0
$640$	0.133975	+	2.23205i	0.00529581	+	0.0882296i
$641$	1.00000	+	1.73205i	0.0394976	+	0.0684119i	0.885098	−	0.465404i	$-0.154091\pi$
$641$	1.00000	+	1.73205i	0.0394976	+	0.0684119i	−0.845601	+	0.533816i	$0.820758\pi$
$642$	13.8564	−	8.00000i	0.546869	−	0.315735i
$643$			28.0000i			1.10421i	0.833774	+	0.552106i	$0.186176\pi$
$643$			28.0000i			1.10421i	−0.833774	+	0.552106i	$0.813824\pi$
$644$	3.00000	−	5.19615i	0.118217	−	0.204757i
$645$	1.23205	+	1.86603i	0.0485120	+	0.0734747i
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$		−	8.00000i		−	0.314512i	−0.987558	−	0.157256i	$-0.949735\pi$
$647$		−	8.00000i		−	0.314512i	0.987558	−	0.157256i	$-0.0502649\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	20.0000			0.785069
$650$	−6.00000	−	8.00000i	−0.235339	−	0.313786i
$651$	−11.0000	+	1.73205i	−0.431124	+	0.0678844i
$652$		−	25.0000i		−	0.979076i
$653$			48.0000i			1.87839i	0.343391	+	0.939193i	$0.388424\pi$
$653$			48.0000i			1.87839i	−0.343391	+	0.939193i	$0.611576\pi$
$654$	−4.00000	+	6.92820i	−0.156412	+	0.270914i
$655$	−15.0000	+	30.0000i	−0.586098	+	1.17220i
$656$		0			0
$657$	−5.19615	−	3.00000i	−0.202721	−	0.117041i
$658$	15.5885	+	9.00000i	0.607701	+	0.350857i
$659$	−27.0000			−1.05177			−0.525885	−	0.850555i	$-0.676266\pi$
$659$	−27.0000			−1.05177			−0.525885	+	0.850555i	$0.676266\pi$
$660$	0.669873	+	11.1603i	0.0260748	+	0.434412i
$661$	25.0000	+	43.3013i	0.972387	+	1.68422i	0.688301	+	0.725426i	$0.258357\pi$
$661$	25.0000	+	43.3013i	0.972387	+	1.68422i	0.284087	+	0.958799i	$0.408310\pi$
$662$	−25.9808	+	15.0000i	−1.00977	+	0.582992i
$663$	−5.19615	−	3.00000i	−0.201802	−	0.116510i
$664$	−3.00000	−	5.19615i	−0.116423	−	0.201650i
$665$	−14.9282	+	9.85641i	−0.578891	+	0.382215i
$666$	5.00000			0.193746
$667$		−	6.00000i		−	0.232321i
$668$		0			0
$669$	2.00000	+	3.46410i	0.0773245	+	0.133930i
$670$	−8.62436	−	13.0622i	−0.333188	−	0.504636i
$671$	−5.00000	−	8.66025i	−0.193023	−	0.334325i
$672$	1.73205	−	1.00000i	0.0668153	−	0.0385758i
$673$	−13.8564	+	8.00000i	−0.534125	+	0.308377i	−0.742695	−	0.669630i	$-0.766453\pi$
$673$	−13.8564	+	8.00000i	−0.534125	+	0.308377i	0.208569	+	0.978008i	$0.433119\pi$
$674$	−2.00000			−0.0770371
$675$	−0.598076	−	4.96410i	−0.0230200	−	0.191068i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−31.1769	+	18.0000i	−1.19823	+	0.691796i	−0.960159	−	0.279453i	$-0.909847\pi$
$677$	−31.1769	+	18.0000i	−1.19823	+	0.691796i	−0.238067	+	0.971249i	$0.576514\pi$
$678$			7.00000i			0.268833i
$679$		0			0
$680$	−3.00000	+	6.00000i	−0.115045	+	0.230089i
$681$	18.0000			0.689761
$682$	4.33013	+	27.5000i	0.165809	+	1.05303i
$683$			6.00000i			0.229584i	0.993390	+	0.114792i	$0.0366201\pi$
$683$			6.00000i			0.229584i	−0.993390	+	0.114792i	$0.963380\pi$
$684$	−4.00000			−0.152944
$685$	−9.33013	+	6.16025i	−0.356486	+	0.235371i
$686$	20.0000			0.763604
$687$	−1.73205	+	1.00000i	−0.0660819	+	0.0381524i
$688$	−0.866025	−	0.500000i	−0.0330169	−	0.0190623i
$689$	8.00000	−	13.8564i	0.304776	−	0.527887i
$690$	6.00000	+	3.00000i	0.228416	+	0.114208i
$691$	−9.00000	−	15.5885i	−0.342376	−	0.593013i	0.642497	−	0.766288i	$-0.277898\pi$
$691$	−9.00000	−	15.5885i	−0.342376	−	0.593013i	−0.984873	+	0.173275i	$0.944565\pi$
$692$	5.19615	−	3.00000i	0.197528	−	0.114043i
$693$	8.66025	−	5.00000i	0.328976	−	0.189934i
$694$	3.00000	−	5.19615i	0.113878	−	0.197243i
$695$	31.2487	−	1.87564i	1.18533	−	0.0711472i
$696$	1.00000	−	1.73205i	0.0379049	−	0.0656532i
$697$		0			0
$698$			28.0000i			1.05982i
$699$	−9.50000	+	16.4545i	−0.359323	+	0.622366i
$700$	9.19615	+	3.92820i	0.347582	+	0.148472i
$701$	−5.50000	+	9.52628i	−0.207732	+	0.359803i	−0.951000	−	0.309192i	$-0.899942\pi$
$701$	−5.50000	+	9.52628i	−0.207732	+	0.359803i	0.743268	+	0.668994i	$0.233275\pi$
$702$	−1.73205	+	1.00000i	−0.0653720	+	0.0377426i
$703$	17.3205	−	10.0000i	0.653255	−	0.377157i
$704$	−2.50000	−	4.33013i	−0.0942223	−	0.163198i
$705$	−9.00000	+	18.0000i	−0.338960	+	0.677919i
$706$	15.5000	−	26.8468i	0.583350	−	1.01039i
$707$	−29.4449	−	17.0000i	−1.10739	−	0.639351i
$708$	3.46410	−	2.00000i	0.130189	−	0.0751646i
$709$	8.00000			0.300446			0.150223	−	0.988652i	$-0.452001\pi$
$709$	8.00000			0.300446			0.150223	+	0.988652i	$0.452001\pi$
$710$		0			0
$711$	5.00000			0.187515
$712$		0			0
$713$	15.5885	+	6.00000i	0.583792	+	0.224702i
$714$	6.00000			0.224544
$715$	20.0000	+	10.0000i	0.747958	+	0.373979i
$716$	−2.50000	+	4.33013i	−0.0934294	+	0.161824i
$717$			6.00000i			0.224074i
$718$	−31.1769	+	18.0000i	−1.16351	+	0.671754i
$719$	−15.0000	+	25.9808i	−0.559406	+	0.968919i	0.438141	+	0.898906i	$0.355637\pi$
$719$	−15.0000	+	25.9808i	−0.559406	+	0.968919i	−0.997546	+	0.0700124i	$0.977696\pi$
$720$	1.23205	+	1.86603i	0.0459158	+	0.0695427i
$721$	32.0000			1.19174
$722$	2.59808	−	1.50000i	0.0966904	−	0.0558242i
$723$	15.5885	−	9.00000i	0.579741	−	0.334714i
$724$	−8.00000	−	13.8564i	−0.297318	−	0.514969i
$725$	9.92820	−	1.19615i	0.368724	−	0.0444240i
$726$	−7.00000	−	12.1244i	−0.259794	−	0.449977i
$727$	8.66025	+	5.00000i	0.321191	+	0.185440i	0.651923	−	0.758285i	$-0.273962\pi$
$727$	8.66025	+	5.00000i	0.321191	+	0.185440i	−0.330732	+	0.943725i	$0.607296\pi$
$728$		−	4.00000i		−	0.148250i
$729$	−1.00000			−0.0370370
$730$	7.39230	+	11.1962i	0.273601	+	0.414388i
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$	−1.73205	−	1.00000i	−0.0640184	−	0.0369611i
$733$	−35.5070	+	20.5000i	−1.31148	+	0.757185i	−0.982342	−	0.187096i	$-0.940092\pi$
$733$	−35.5070	+	20.5000i	−1.31148	+	0.757185i	−0.329141	+	0.944281i	$0.606759\pi$
$734$	15.0000	+	25.9808i	0.553660	+	0.958967i
$735$	0.401924	+	6.69615i	0.0148252	+	0.246991i
$736$	−3.00000			−0.110581
$737$	30.3109	+	17.5000i	1.11652	+	0.644621i
$738$		0			0
$739$	20.0000	+	34.6410i	0.735712	+	1.27429i	0.954410	+	0.298498i	$0.0964856\pi$
$739$	20.0000	+	34.6410i	0.735712	+	1.27429i	−0.218698	+	0.975793i	$0.570181\pi$
$740$	−10.0000	−	5.00000i	−0.367607	−	0.183804i
$741$	−4.00000	+	6.92820i	−0.146944	+	0.254514i
$742$			16.0000i			0.587378i
$743$			11.0000i			0.403551i	0.979432	+	0.201775i	$0.0646711\pi$
$743$			11.0000i			0.403551i	−0.979432	+	0.201775i	$0.935329\pi$
$744$	3.50000	+	4.33013i	0.128316	+	0.158750i
$745$	10.0000	−	20.0000i	0.366372	−	0.732743i
$746$	31.0000			1.13499
$747$	−5.19615	−	3.00000i	−0.190117	−	0.109764i
$748$		−	15.0000i		−	0.548454i
$749$	16.0000	+	27.7128i	0.584627	+	1.01260i
$750$	−3.76795	+	10.5263i	−0.137586	+	0.384365i
$751$	19.5000	−	33.7750i	0.711565	−	1.23247i	−0.252704	−	0.967544i	$-0.581320\pi$
$751$	19.5000	−	33.7750i	0.711565	−	1.23247i	0.964269	−	0.264923i	$-0.0853467\pi$
$752$		−	9.00000i		−	0.328196i
$753$	−21.6506	+	12.5000i	−0.788993	+	0.455525i
$754$	−2.00000	−	3.46410i	−0.0728357	−	0.126155i
$755$	−20.0885	+	1.20577i	−0.731094	+	0.0438825i
$756$	1.00000	−	1.73205i	0.0363696	−	0.0629941i
$757$	14.7224	−	8.50000i	0.535096	−	0.308938i	−0.207993	−	0.978130i	$-0.566693\pi$
$757$	14.7224	−	8.50000i	0.535096	−	0.308938i	0.743089	+	0.669193i	$0.233360\pi$
$758$	−29.4449	−	17.0000i	−1.06949	−	0.617468i
$759$	−15.0000			−0.544466
$760$	8.00000	+	4.00000i	0.290191	+	0.145095i
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$	−1.73205	+	1.00000i	−0.0627456	+	0.0362262i
$763$	−13.8564	−	8.00000i	−0.501636	−	0.289619i
$764$	−8.00000	−	13.8564i	−0.289430	−	0.501307i
$765$	0.401924	+	6.69615i	0.0145316	+	0.242100i
$766$	−10.5000	−	18.1865i	−0.379380	−	0.657106i
$767$		−	8.00000i		−	0.288863i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	−0.596643	−	0.802507i	$-0.703499\pi$
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	0.993313	+	0.115454i	$0.0368323\pi$
$770$	−22.3205	+	1.33975i	−0.804375	+	0.0482811i
$771$	23.0000			0.828325
$772$	−3.46410	−	2.00000i	−0.124676	−	0.0719816i
$773$		−	18.0000i		−	0.647415i	−0.946157	−	0.323708i	$-0.895071\pi$
$773$		−	18.0000i		−	0.647415i	0.946157	−	0.323708i	$-0.104929\pi$
$774$	−1.00000			−0.0359443
$775$	−6.82051	+	26.9904i	−0.245000	+	0.969523i
$776$		0			0
$777$			10.0000i			0.358748i
$778$	21.6506	+	12.5000i	0.776213	+	0.448147i
$779$		0			0
$780$	4.46410	−	0.267949i	0.159840	−	0.00959412i
$781$		0			0
$782$	−7.79423	−	4.50000i	−0.278721	−	0.160920i
$783$		−	2.00000i		−	0.0714742i
$784$	−1.50000	−	2.59808i	−0.0535714	−	0.0927884i
$785$	0.267949	+	4.46410i	0.00956352	+	0.159331i
$786$	−7.50000	−	12.9904i	−0.267516	−	0.463352i
$787$	−14.7224	−	8.50000i	−0.524798	−	0.302992i	0.214097	−	0.976812i	$-0.431319\pi$
$787$	−14.7224	−	8.50000i	−0.524798	−	0.302992i	−0.738896	+	0.673820i	$0.764652\pi$
$788$	1.73205	−	1.00000i	0.0617018	−	0.0356235i
$789$	−8.50000	+	14.7224i	−0.302608	+	0.524132i
$790$	−10.0000	−	5.00000i	−0.355784	−	0.177892i
$791$	−14.0000			−0.497783
$792$	−4.33013	−	2.50000i	−0.153864	−	0.0888336i
$793$	−3.46410	+	2.00000i	−0.123014	+	0.0710221i
$794$	−13.5000	+	23.3827i	−0.479097	+	0.829820i
$795$	−17.8564	+	1.07180i	−0.633301	+	0.0380127i
$796$	−8.00000	−	13.8564i	−0.283552	−	0.491127i
$797$	32.9090	−	19.0000i	1.16570	−	0.673015i	0.213033	−	0.977045i	$-0.431666\pi$
$797$	32.9090	−	19.0000i	1.16570	−	0.673015i	0.952662	+	0.304030i	$0.0983325\pi$
$798$		−	8.00000i		−	0.283197i
$799$	13.5000	−	23.3827i	0.477596	−	0.827220i
$800$	−0.598076	−	4.96410i	−0.0211452	−	0.175507i
$801$		0			0
$802$			28.0000i			0.988714i
$803$	−25.9808	−	15.0000i	−0.916841	−	0.529339i
$804$	7.00000			0.246871
$805$	−6.00000	+	12.0000i	−0.211472	+	0.422944i
$806$	11.0000	−	1.73205i	0.387458	−	0.0610089i
$807$		−	5.00000i		−	0.176008i
$808$			17.0000i			0.598058i
$809$	−13.0000	+	22.5167i	−0.457056	+	0.791644i	−0.998804	−	0.0488972i	$-0.984429\pi$
$809$	−13.0000	+	22.5167i	−0.457056	+	0.791644i	0.541748	+	0.840541i	$0.317763\pi$
$810$	2.00000	+	1.00000i	0.0702728	+	0.0351364i
$811$	−5.00000	−	8.66025i	−0.175574	−	0.304103i	0.764786	−	0.644284i	$-0.222845\pi$
$811$	−5.00000	−	8.66025i	−0.175574	−	0.304103i	−0.940360	+	0.340182i	$0.889511\pi$
$812$	3.46410	+	2.00000i	0.121566	+	0.0701862i
$813$	−27.7128	−	16.0000i	−0.971931	−	0.561144i
$814$	25.0000			0.876250
$815$	3.34936	+	55.8013i	0.117323	+	1.95463i
$816$	−1.50000	−	2.59808i	−0.0525105	−	0.0909509i
$817$	−3.46410	+	2.00000i	−0.121194	+	0.0699711i
$818$	21.6506	+	12.5000i	0.756997	+	0.437052i
$819$	−2.00000	−	3.46410i	−0.0698857	−	0.121046i
$820$		0			0
$821$	−17.0000			−0.593304			−0.296652	−	0.954986i	$-0.595870\pi$
$821$	−17.0000			−0.593304			−0.296652	+	0.954986i	$0.595870\pi$
$822$		−	5.00000i		−	0.174395i
$823$	1.73205	+	1.00000i	0.0603755	+	0.0348578i	0.529884	−	0.848070i	$-0.322235\pi$
$823$	1.73205	+	1.00000i	0.0603755	+	0.0348578i	−0.469508	+	0.882928i	$0.655569\pi$
$824$	−8.00000	−	13.8564i	−0.278693	−	0.482711i
$825$	−2.99038	−	24.8205i	−0.104112	−	0.864139i
$826$	4.00000	+	6.92820i	0.139178	+	0.241063i
$827$	−12.1244	+	7.00000i	−0.421605	+	0.243414i	−0.695764	−	0.718271i	$-0.744934\pi$
$827$	−12.1244	+	7.00000i	−0.421605	+	0.243414i	0.274159	+	0.961684i	$0.411601\pi$
$828$	−2.59808	+	1.50000i	−0.0902894	+	0.0521286i
$829$	−32.0000			−1.11141			−0.555703	−	0.831381i	$-0.687551\pi$
$829$	−32.0000			−1.11141			−0.555703	+	0.831381i	$0.687551\pi$
$830$	7.39230	+	11.1962i	0.256591	+	0.388624i
$831$	−3.50000	+	6.06218i	−0.121414	+	0.210295i
$832$	−1.73205	+	1.00000i	−0.0600481	+	0.0346688i
$833$		−	9.00000i		−	0.311832i
$834$	−7.00000	+	12.1244i	−0.242390	+	0.419832i
$835$		0			0
$836$	−20.0000			−0.691714
$837$	5.19615	+	2.00000i	0.179605	+	0.0691301i
$838$			39.0000i			1.34723i
$839$	−18.0000			−0.621429			−0.310715	−	0.950503i	$-0.600568\pi$
$839$	−18.0000			−0.621429			−0.310715	+	0.950503i	$0.600568\pi$
$840$	−3.73205	+	2.46410i	−0.128768	+	0.0850196i
$841$	−25.0000			−0.862069
$842$	−13.8564	+	8.00000i	−0.477523	+	0.275698i
$843$	5.19615	+	3.00000i	0.178965	+	0.103325i
$844$	7.00000	−	12.1244i	0.240950	−	0.417338i
$845$	−9.00000	+	18.0000i	−0.309609	+	0.619219i
$846$	−4.50000	−	7.79423i	−0.154713	−	0.267971i
$847$	24.2487	−	14.0000i	0.833196	−	0.481046i
$848$	6.92820	−	4.00000i	0.237915	−	0.137361i
$849$	8.50000	−	14.7224i	0.291719	−	0.505273i
$850$	5.89230	−	13.7942i	0.202104	−	0.473138i
$851$	7.50000	−	12.9904i	0.257097	−	0.445305i
$852$		0			0
$853$			6.00000i			0.205436i	0.994711	+	0.102718i	$0.0327539\pi$
$853$			6.00000i			0.205436i	−0.994711	+	0.102718i	$0.967246\pi$
$854$	2.00000	−	3.46410i	0.0684386	−	0.118539i
$855$	8.92820	−	0.535898i	0.305338	−	0.0183273i
$856$	8.00000	−	13.8564i	0.273434	−	0.473602i
$857$	−6.06218	+	3.50000i	−0.207080	+	0.119558i	−0.599954	−	0.800035i	$-0.704814\pi$
$857$	−6.06218	+	3.50000i	−0.207080	+	0.119558i	0.392874	+	0.919592i	$0.371481\pi$
$858$	−8.66025	+	5.00000i	−0.295656	+	0.170697i
$859$	9.00000	+	15.5885i	0.307076	+	0.531871i	0.977721	−	0.209907i	$-0.0673161\pi$
$859$	9.00000	+	15.5885i	0.307076	+	0.531871i	−0.670645	+	0.741778i	$0.733983\pi$
$860$	2.00000	+	1.00000i	0.0681994	+	0.0340997i
$861$		0			0
$862$	8.66025	+	5.00000i	0.294969	+	0.170301i
$863$	30.3109	−	17.5000i	1.03179	−	0.595707i	0.114296	−	0.993447i	$-0.463539\pi$
$863$	30.3109	−	17.5000i	1.03179	−	0.595707i	0.917498	+	0.397740i	$0.130205\pi$
$864$	−1.00000			−0.0340207
$865$	−11.1962	+	7.39230i	−0.380681	+	0.251346i
$866$	−38.0000			−1.29129
$867$			8.00000i			0.271694i
$868$	−8.66025	+	7.00000i	−0.293948	+	0.237595i
$869$	25.0000			0.848067
$870$	−2.00000	+	4.00000i	−0.0678064	+	0.135613i
$871$	7.00000	−	12.1244i	0.237186	−	0.410818i
$872$			8.00000i			0.270914i
$873$		0			0
$874$	−6.00000	+	10.3923i	−0.202953	+	0.351525i
$875$	−21.0526	−	7.53590i	−0.711706	−	0.254760i
$876$	−6.00000			−0.202721
$877$	−2.59808	+	1.50000i	−0.0877308	+	0.0506514i	−0.543224	−	0.839588i	$-0.682796\pi$
$877$	−2.59808	+	1.50000i	−0.0877308	+	0.0506514i	0.455493	+	0.890239i	$0.349463\pi$
$878$	−0.866025	+	0.500000i	−0.0292269	+	0.0168742i
$879$	14.0000	+	24.2487i	0.472208	+	0.817889i
$880$	6.16025	+	9.33013i	0.207662	+	0.314519i
$881$	−6.00000	−	10.3923i	−0.202145	−	0.350126i	0.747074	−	0.664741i	$-0.231458\pi$
$881$	−6.00000	−	10.3923i	−0.202145	−	0.350126i	−0.949219	+	0.314615i	$0.898125\pi$
$882$	−2.59808	−	1.50000i	−0.0874818	−	0.0505076i
$883$		−	7.00000i		−	0.235569i	−0.993039	−	0.117784i	$-0.962421\pi$
$883$		−	7.00000i		−	0.235569i	0.993039	−	0.117784i	$-0.0375792\pi$
$884$	−6.00000			−0.201802
$885$	−7.46410	+	4.92820i	−0.250903	+	0.165660i
$886$	1.00000	+	1.73205i	0.0335957	+	0.0581894i
$887$	−42.4352	−	24.5000i	−1.42484	−	0.822629i	−0.428129	−	0.903718i	$-0.640827\pi$
$887$	−42.4352	−	24.5000i	−1.42484	−	0.822629i	−0.996707	+	0.0810881i	$0.974160\pi$
$888$	4.33013	−	2.50000i	0.145310	−	0.0838945i
$889$	−2.00000	−	3.46410i	−0.0670778	−	0.116182i
$890$		0			0
$891$	−5.00000			−0.167506
$892$	3.46410	+	2.00000i	0.115987	+	0.0669650i
$893$	−31.1769	−	18.0000i	−1.04330	−	0.602347i
$894$	5.00000	+	8.66025i	0.167225	+	0.289642i
$895$	5.00000	−	10.0000i	0.167132	−	0.334263i
$896$	1.00000	−	1.73205i	0.0334077	−	0.0578638i
$897$			6.00000i			0.200334i
$898$		−	24.0000i		−	0.800890i
$899$	−4.00000	+	10.3923i	−0.133407	+	0.346603i
$900$	−3.00000	−	4.00000i	−0.100000	−	0.133333i
$901$	24.0000			0.799556
$902$		0			0
$903$		−	2.00000i		−	0.0665558i
$904$	3.50000	+	6.06218i	0.116408	+	0.201625i
$905$	19.7128	+	29.8564i	0.655276	+	0.992461i
$906$	4.50000	−	7.79423i	0.149502	−	0.258946i
$907$			20.0000i			0.664089i	0.943264	+	0.332045i	$0.107738\pi$
$907$			20.0000i			0.664089i	−0.943264	+	0.332045i	$0.892262\pi$
$908$	15.5885	−	9.00000i	0.517321	−	0.298675i
$909$	8.50000	+	14.7224i	0.281927	+	0.488312i
$910$	0.535898	+	8.92820i	0.0177649	+	0.295967i
$911$	15.0000	−	25.9808i	0.496972	−	0.860781i	−0.503022	−	0.864274i	$-0.667778\pi$
$911$	15.0000	−	25.9808i	0.496972	−	0.860781i	0.999994	+	0.00349271i	$0.00111177\pi$
$912$	−3.46410	+	2.00000i	−0.114708	+	0.0662266i
$913$	−25.9808	−	15.0000i	−0.859838	−	0.496428i
$914$	16.0000			0.529233
$915$	4.00000	+	2.00000i	0.132236	+	0.0661180i
$916$	−1.00000	+	1.73205i	−0.0330409	+	0.0572286i
$917$	25.9808	−	15.0000i	0.857960	−	0.495344i
$918$	−2.59808	−	1.50000i	−0.0857493	−	0.0495074i
$919$	15.5000	+	26.8468i	0.511298	+	0.885594i	0.999914	+	0.0130951i	$0.00416842\pi$
$919$	15.5000	+	26.8468i	0.511298	+	0.885594i	−0.488616	+	0.872499i	$0.662498\pi$
$920$	6.69615	−	0.401924i	0.220766	−	0.0132510i
$921$	4.00000	+	6.92820i	0.131804	+	0.228292i
$922$		−	3.00000i		−	0.0987997i
$923$		0			0
$924$	5.00000	−	8.66025i	0.164488	−	0.284901i
$925$	22.9904	+	9.82051i	0.755919	+	0.322896i
$926$	−18.0000			−0.591517
$927$	−13.8564	−	8.00000i	−0.455104	−	0.262754i
$928$		−	2.00000i		−	0.0656532i
$929$	50.0000			1.64045			0.820223	−	0.572043i	$-0.193849\pi$
$929$	50.0000			1.64045			0.820223	+	0.572043i	$0.193849\pi$
$930$	−8.39230	−	9.19615i	−0.275195	−	0.301554i
$931$	−12.0000			−0.393284
$932$			19.0000i			0.622366i
$933$	22.5167	+	13.0000i	0.737162	+	0.425601i
$934$	−8.00000			−0.261768
$935$	2.00962	+	33.4808i	0.0657216	+	1.09494i
$936$	−1.00000	+	1.73205i	−0.0326860	+	0.0566139i
$937$	−15.5885	−	9.00000i	−0.509253	−	0.294017i	0.223274	−	0.974756i	$-0.428326\pi$
$937$	−15.5885	−	9.00000i	−0.509253	−	0.294017i	−0.732526	+	0.680739i	$0.761659\pi$
$938$			14.0000i			0.457116i
$939$	12.0000	+	20.7846i	0.391605	+	0.678280i
$940$	1.20577	+	20.0885i	0.0393279	+	0.655213i
$941$	−19.5000	−	33.7750i	−0.635682	−	1.10103i	−0.986370	−	0.164541i	$-0.947386\pi$
$941$	−19.5000	−	33.7750i	−0.635682	−	1.10103i	0.350688	−	0.936492i	$-0.385948\pi$
$942$	−1.73205	−	1.00000i	−0.0564333	−	0.0325818i
$943$		0			0
$944$	2.00000	−	3.46410i	0.0650945	−	0.112747i
$945$	−2.00000	+	4.00000i	−0.0650600	+	0.130120i
$946$	−5.00000			−0.162564
$947$	1.73205	+	1.00000i	0.0562841	+	0.0324956i	0.527878	−	0.849320i	$-0.322988\pi$
$947$	1.73205	+	1.00000i	0.0562841	+	0.0324956i	−0.471594	+	0.881816i	$0.656321\pi$
$948$	4.33013	−	2.50000i	0.140636	−	0.0811962i
$949$	−6.00000	+	10.3923i	−0.194768	+	0.337348i
$950$	−18.3923	−	7.85641i	−0.596725	−	0.254895i
$951$	−5.00000	−	8.66025i	−0.162136	−	0.280828i
$952$	5.19615	−	3.00000i	0.168408	−	0.0972306i
$953$			26.0000i			0.842223i	0.907009	+	0.421111i	$0.138360\pi$
$953$			26.0000i			0.842223i	−0.907009	+	0.421111i	$0.861640\pi$
$954$	4.00000	−	6.92820i	0.129505	−	0.224309i
$955$	19.7128	+	29.8564i	0.637892	+	0.966131i
$956$	3.00000	+	5.19615i	0.0970269	+	0.168056i
$957$		−	10.0000i		−	0.323254i
$958$	10.3923	+	6.00000i	0.335760	+	0.193851i
$959$	10.0000			0.322917
$960$	2.00000	+	1.00000i	0.0645497	+	0.0322749i
$961$	−23.0000	−	20.7846i	−0.741935	−	0.670471i
$962$		−	10.0000i		−	0.322413i
$963$		−	16.0000i		−	0.515593i
$964$	9.00000	−	15.5885i	0.289870	−	0.502070i
$965$	8.00000	+	4.00000i	0.257529	+	0.128765i
$966$	−3.00000	−	5.19615i	−0.0965234	−	0.167183i
$967$	8.66025	+	5.00000i	0.278495	+	0.160789i	0.632742	−	0.774363i	$-0.281929\pi$
$967$	8.66025	+	5.00000i	0.278495	+	0.160789i	−0.354247	+	0.935152i	$0.615263\pi$
$968$	−12.1244	−	7.00000i	−0.389692	−	0.224989i
$969$	−12.0000			−0.385496
$970$		0			0
$971$	−11.5000	−	19.9186i	−0.369053	−	0.639218i	0.620365	−	0.784313i	$-0.286984\pi$
$971$	−11.5000	−	19.9186i	−0.369053	−	0.639218i	−0.989418	+	0.145095i	$0.953651\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	−24.2487	−	14.0000i	−0.777378	−	0.448819i
$974$	−6.00000	−	10.3923i	−0.192252	−	0.332991i
$975$	−9.92820	+	1.19615i	−0.317957	+	0.0383075i
$976$	−2.00000			−0.0640184
$977$			50.0000i			1.59964i	0.600239	+	0.799821i	$0.295072\pi$
$977$			50.0000i			1.59964i	−0.600239	+	0.799821i	$0.704928\pi$
$978$	−21.6506	−	12.5000i	−0.692311	−	0.399706i
$979$		0			0
$980$	3.69615	+	5.59808i	0.118069	+	0.178824i
$981$	4.00000	+	6.92820i	0.127710	+	0.221201i
$982$	−2.59808	+	1.50000i	−0.0829079	+	0.0478669i
$983$	−13.8564	+	8.00000i	−0.441951	+	0.255160i	−0.704425	−	0.709779i	$-0.748795\pi$
$983$	−13.8564	+	8.00000i	−0.441951	+	0.255160i	0.262474	+	0.964939i	$0.415462\pi$
$984$		0			0
$985$	−3.73205	+	2.46410i	−0.118913	+	0.0785128i
$986$	3.00000	−	5.19615i	0.0955395	−	0.165479i
$987$	15.5885	−	9.00000i	0.496186	−	0.286473i
$988$			8.00000i			0.254514i
$989$	−1.50000	+	2.59808i	−0.0476972	+	0.0826140i
$990$	10.0000	+	5.00000i	0.317821	+	0.158910i
$991$	48.0000			1.52477			0.762385	−	0.647124i	$-0.224028\pi$
$991$	48.0000			1.52477			0.762385	+	0.647124i	$0.224028\pi$
$992$	5.19615	+	2.00000i	0.164978	+	0.0635001i
$993$			30.0000i			0.952021i
$994$		0			0
$995$	19.7128	+	29.8564i	0.624938	+	0.946512i
$996$	−6.00000			−0.190117
$997$	−15.5885	+	9.00000i	−0.493691	+	0.285033i	−0.726105	−	0.687584i	$-0.758671\pi$
$997$	−15.5885	+	9.00000i	−0.493691	+	0.285033i	0.232413	+	0.972617i	$0.425338\pi$
$998$	−15.5885	−	9.00000i	−0.493444	−	0.284890i
$999$	2.50000	−	4.33013i	0.0790965	−	0.136999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.s.a.439.1	✓	4
5.4	even	2	inner	930.2.s.a.439.2	yes	4
31.25	even	3	inner	930.2.s.a.769.1	yes	4
155.149	even	6	inner	930.2.s.a.769.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.s.a.439.1	✓	4	1.1	even	1	trivial
930.2.s.a.439.2	yes	4	5.4	even	2	inner
930.2.s.a.769.1	yes	4	31.25	even	3	inner
930.2.s.a.769.2	yes	4	155.149	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(2.23205 - 0.133975i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-0.866025 - 0.500000i) q^{3} -1.00000 q^{4} +(2.23205 - 0.133975i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.73205 - 1.00000i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.133975 - 2.23205i) q^{10} +(2.50000 + 4.33013i) q^{11} +(0.866025 + 0.500000i) q^{12} +(1.73205 - 1.00000i) q^{13} +(-1.00000 + 1.73205i) q^{14} +(-2.00000 - 1.00000i) q^{15} +1.00000 q^{16} +(2.59808 + 1.50000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(2.00000 - 3.46410i) q^{19} +(-2.23205 + 0.133975i) q^{20} +(1.00000 + 1.73205i) q^{21} +(4.33013 - 2.50000i) q^{22} -3.00000i q^{23} +(0.500000 - 0.866025i) q^{24} +(4.96410 - 0.598076i) q^{25} +(-1.00000 - 1.73205i) q^{26} -1.00000i q^{27} +(1.73205 + 1.00000i) q^{28} +2.00000 q^{29} +(-1.00000 + 2.00000i) q^{30} +(-2.00000 + 5.19615i) q^{31} -1.00000i q^{32} -5.00000i q^{33} +(1.50000 - 2.59808i) q^{34} +(-4.00000 - 2.00000i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.33013 + 2.50000i) q^{37} +(-3.46410 - 2.00000i) q^{38} -2.00000 q^{39} +(0.133975 + 2.23205i) q^{40} +(1.73205 - 1.00000i) q^{42} +(-0.866025 - 0.500000i) q^{43} +(-2.50000 - 4.33013i) q^{44} +(1.23205 + 1.86603i) q^{45} -3.00000 q^{46} -9.00000i q^{47} +(-0.866025 - 0.500000i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(-0.598076 - 4.96410i) q^{50} +(-1.50000 - 2.59808i) q^{51} +(-1.73205 + 1.00000i) q^{52} +(6.92820 - 4.00000i) q^{53} -1.00000 q^{54} +(6.16025 + 9.33013i) q^{55} +(1.00000 - 1.73205i) q^{56} +(-3.46410 + 2.00000i) q^{57} -2.00000i q^{58} +(2.00000 - 3.46410i) q^{59} +(2.00000 + 1.00000i) q^{60} -2.00000 q^{61} +(5.19615 + 2.00000i) q^{62} -2.00000i q^{63} -1.00000 q^{64} +(3.73205 - 2.46410i) q^{65} -5.00000 q^{66} +(6.06218 - 3.50000i) q^{67} +(-2.59808 - 1.50000i) q^{68} +(-1.50000 + 2.59808i) q^{69} +(-2.00000 + 4.00000i) q^{70} +(-0.866025 + 0.500000i) q^{72} +(-5.19615 + 3.00000i) q^{73} +(2.50000 - 4.33013i) q^{74} +(-4.59808 - 1.96410i) q^{75} +(-2.00000 + 3.46410i) q^{76} -10.0000i q^{77} +2.00000i q^{78} +(2.50000 - 4.33013i) q^{79} +(2.23205 - 0.133975i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-5.19615 + 3.00000i) q^{83} +(-1.00000 - 1.73205i) q^{84} +(6.00000 + 3.00000i) q^{85} +(-0.500000 + 0.866025i) q^{86} +(-1.73205 - 1.00000i) q^{87} +(-4.33013 + 2.50000i) q^{88} +(1.86603 - 1.23205i) q^{90} -4.00000 q^{91} +3.00000i q^{92} +(4.33013 - 3.50000i) q^{93} -9.00000 q^{94} +(4.00000 - 8.00000i) q^{95} +(-0.500000 + 0.866025i) q^{96} +(-2.59808 + 1.50000i) q^{98} +(-2.50000 + 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q - 4 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^9	\( 4 q - 4 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{9} - 4 q^{10} + 10 q^{11} - 4 q^{14} - 8 q^{15} + 4 q^{16} + 8 q^{19} - 2 q^{20} + 4 q^{21} + 2 q^{24} + 6 q^{25} - 4 q^{26} + 8 q^{29} - 4 q^{30} - 8 q^{31} + 6 q^{34} - 16 q^{35} - 2 q^{36} - 8 q^{39} + 4 q^{40} - 10 q^{44} - 2 q^{45} - 12 q^{46} - 6 q^{49} + 8 q^{50} - 6 q^{51} - 4 q^{54} - 10 q^{55} + 4 q^{56} + 8 q^{59} + 8 q^{60} - 8 q^{61} - 4 q^{64} + 8 q^{65} - 20 q^{66} - 6 q^{69} - 8 q^{70} + 10 q^{74} - 8 q^{75} - 8 q^{76} + 10 q^{79} + 2 q^{80} - 2 q^{81} - 4 q^{84} + 24 q^{85} - 2 q^{86} + 4 q^{90} - 16 q^{91} - 36 q^{94} + 16 q^{95} - 2 q^{96} - 10 q^{99}+O(q^{100}) \) 4 * q - 4 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^9 - 4 * q^10 + 10 * q^11 - 4 * q^14 - 8 * q^15 + 4 * q^16 + 8 * q^19 - 2 * q^20 + 4 * q^21 + 2 * q^24 + 6 * q^25 - 4 * q^26 + 8 * q^29 - 4 * q^30 - 8 * q^31 + 6 * q^34 - 16 * q^35 - 2 * q^36 - 8 * q^39 + 4 * q^40 - 10 * q^44 - 2 * q^45 - 12 * q^46 - 6 * q^49 + 8 * q^50 - 6 * q^51 - 4 * q^54 - 10 * q^55 + 4 * q^56 + 8 * q^59 + 8 * q^60 - 8 * q^61 - 4 * q^64 + 8 * q^65 - 20 * q^66 - 6 * q^69 - 8 * q^70 + 10 * q^74 - 8 * q^75 - 8 * q^76 + 10 * q^79 + 2 * q^80 - 2 * q^81 - 4 * q^84 + 24 * q^85 - 2 * q^86 + 4 * q^90 - 16 * q^91 - 36 * q^94 + 16 * q^95 - 2 * q^96 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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