LMFDB - Embedded newform 930.2.i.c.811.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(211,930)] 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("930.211"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [2,-2,1,2,1,-1,3,-2,-1,-1,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			811.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	930.811
Dual form			930.2.i.c.211.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-2.00000 - 3.46410i) q^{13} +(-1.50000 + 2.59808i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(2.00000 - 3.46410i) q^{17} +(0.500000 + 0.866025i) q^{18} +(0.500000 + 0.866025i) q^{20} +(-1.50000 - 2.59808i) q^{21} +(-1.50000 - 2.59808i) q^{22} +2.00000 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(1.50000 - 2.59808i) q^{28} +1.00000 q^{29} -1.00000 q^{30} +(-3.50000 - 4.33013i) q^{31} -1.00000 q^{32} +3.00000 q^{33} +(-2.00000 + 3.46410i) q^{34} +3.00000 q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.00000 - 5.19615i) q^{37} -4.00000 q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.00000 + 1.73205i) q^{41} +(1.50000 + 2.59808i) q^{42} +(-2.00000 + 3.46410i) q^{43} +(1.50000 + 2.59808i) q^{44} +(0.500000 - 0.866025i) q^{45} -2.00000 q^{46} +4.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-2.00000 - 3.46410i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(1.50000 + 2.59808i) q^{53} +1.00000 q^{54} +(-1.50000 + 2.59808i) q^{55} +(-1.50000 + 2.59808i) q^{56} -1.00000 q^{58} +(4.50000 - 7.79423i) q^{59} +1.00000 q^{60} -2.00000 q^{61} +(3.50000 + 4.33013i) q^{62} -3.00000 q^{63} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{65} -3.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(2.00000 - 3.46410i) q^{68} +(1.00000 - 1.73205i) q^{69} -3.00000 q^{70} +(-2.00000 - 3.46410i) q^{71} +(0.500000 + 0.866025i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(0.500000 + 0.866025i) q^{75} +9.00000 q^{77} +4.00000 q^{78} +(2.00000 - 3.46410i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.00000 - 1.73205i) q^{82} +(-4.50000 - 7.79423i) q^{83} +(-1.50000 - 2.59808i) q^{84} +4.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{87} +(-1.50000 - 2.59808i) q^{88} +10.0000 q^{89} +(-0.500000 + 0.866025i) q^{90} -12.0000 q^{91} +2.00000 q^{92} +(-5.50000 + 0.866025i) q^{93} -4.00000 q^{94} +(-0.500000 + 0.866025i) q^{96} +11.0000 q^{97} +(1.00000 + 1.73205i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} + q^{5} - q^{6} + 3 q^{7} - 2 q^{8} - q^{9} - q^{10} + 3 q^{11} + q^{12} - 4 q^{13} - 3 q^{14} + 2 q^{15} + 2 q^{16} + 4 q^{17} + q^{18} + q^{20} - 3 q^{21} - 3 q^{22}+ \cdots + 3 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 + q^5 - q^6 + 3 * q^7 - 2 * q^8 - q^9 - q^10 + 3 * q^11 + q^12 - 4 * q^13 - 3 * q^14 + 2 * q^15 + 2 * q^16 + 4 * q^17 + q^18 + q^20 - 3 * q^21 - 3 * q^22 + 4 * q^23 - q^24 - q^25 + 4 * q^26 - 2 * q^27 + 3 * q^28 + 2 * q^29 - 2 * q^30 - 7 * q^31 - 2 * q^32 + 6 * q^33 - 4 * q^34 + 6 * q^35 - q^36 + 6 * q^37 - 8 * q^39 - q^40 + 2 * q^41 + 3 * q^42 - 4 * q^43 + 3 * q^44 + q^45 - 4 * q^46 + 8 * q^47 + q^48 - 2 * q^49 + q^50 - 4 * q^51 - 4 * q^52 + 3 * q^53 + 2 * q^54 - 3 * q^55 - 3 * q^56 - 2 * q^58 + 9 * q^59 + 2 * q^60 - 4 * q^61 + 7 * q^62 - 6 * q^63 + 2 * q^64 + 4 * q^65 - 6 * q^66 - 2 * q^67 + 4 * q^68 + 2 * q^69 - 6 * q^70 - 4 * q^71 + q^72 - 2 * q^73 - 6 * q^74 + q^75 + 18 * q^77 + 8 * q^78 + 4 * q^79 + q^80 - q^81 - 2 * q^82 - 9 * q^83 - 3 * q^84 + 8 * q^85 + 4 * q^86 + q^87 - 3 * q^88 + 20 * q^89 - q^90 - 24 * q^91 + 4 * q^92 - 11 * q^93 - 8 * q^94 - q^96 + 22 * q^97 + 2 * q^98 + 3 * q^99

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	1.00000			0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	1.50000	−	2.59808i	0.566947	−	0.981981i	−0.429919	−	0.902867i	$-0.641458\pi$
$7$	1.50000	−	2.59808i	0.566947	−	0.981981i	0.996866	−	0.0791130i	$-0.0252088\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	0.443227	−	0.896410i	$-0.353834\pi$
$14$	−1.50000	+	2.59808i	−0.400892	+	0.694365i
$15$	1.00000			0.258199
$16$	1.00000			0.250000
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	−1.50000	−	2.59808i	−0.327327	−	0.566947i
$22$	−1.50000	−	2.59808i	−0.319801	−	0.553912i
$23$	2.00000			0.417029			0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000			0.417029			0.208514	+	0.978019i	$0.433137\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.00000	+	3.46410i	0.392232	+	0.679366i
$27$	−1.00000			−0.192450
$28$	1.50000	−	2.59808i	0.283473	−	0.490990i
$29$	1.00000			0.185695			0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000			0.185695			0.0928477	+	0.995680i	$0.470403\pi$
$30$	−1.00000			−0.182574
$31$	−3.50000	−	4.33013i	−0.628619	−	0.777714i
$31$	−3.50000	−	4.33013i	−0.628619	−	0.777714i
$32$	−1.00000			−0.176777
$33$	3.00000			0.522233
$34$	−2.00000	+	3.46410i	−0.342997	+	0.594089i
$35$	3.00000			0.507093
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	−0.506772	−	0.862080i	$-0.669162\pi$
$37$	3.00000	−	5.19615i	0.493197	−	0.854242i	0.999969	+	0.00783774i	$0.00249486\pi$
$38$		0			0
$39$	−4.00000			−0.640513
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	0.933486	−	0.358614i	$-0.116751\pi$
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	−0.777312	+	0.629115i	$0.783417\pi$
$42$	1.50000	+	2.59808i	0.231455	+	0.400892i
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	−0.977261	−	0.212041i	$-0.931989\pi$
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	0.672264	+	0.740312i	$0.265322\pi$
$44$	1.50000	+	2.59808i	0.226134	+	0.391675i
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	−2.00000			−0.294884
$47$	4.00000			0.583460			0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000			0.583460			0.291730	+	0.956501i	$0.405769\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−2.00000	−	3.46410i	−0.280056	−	0.485071i
$52$	−2.00000	−	3.46410i	−0.277350	−	0.480384i
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$54$	1.00000			0.136083
$55$	−1.50000	+	2.59808i	−0.202260	+	0.350325i
$56$	−1.50000	+	2.59808i	−0.200446	+	0.347183i
$57$		0			0
$58$	−1.00000			−0.131306
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	−0.408919	−	0.912571i	$-0.634094\pi$
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	0.994769	−	0.102151i	$-0.0325726\pi$
$60$	1.00000			0.129099
$61$	−2.00000			−0.256074			−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000			−0.256074			−0.128037	+	0.991769i	$0.540868\pi$
$62$	3.50000	+	4.33013i	0.444500	+	0.549927i
$63$	−3.00000			−0.377964
$64$	1.00000			0.125000
$65$	2.00000	−	3.46410i	0.248069	−	0.429669i
$66$	−3.00000			−0.369274
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	2.00000	−	3.46410i	0.242536	−	0.420084i
$69$	1.00000	−	1.73205i	0.120386	−	0.208514i
$70$	−3.00000			−0.358569
$71$	−2.00000	−	3.46410i	−0.237356	−	0.411113i	0.722599	−	0.691268i	$-0.242948\pi$
$71$	−2.00000	−	3.46410i	−0.237356	−	0.411113i	−0.959955	+	0.280155i	$0.909614\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	−3.00000	+	5.19615i	−0.348743	+	0.604040i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$		0			0
$77$	9.00000			1.02565
$78$	4.00000			0.452911
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.00000	−	1.73205i	−0.110432	−	0.191273i
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	0.506036	−	0.862512i	$-0.331110\pi$
$83$	−4.50000	−	7.79423i	−0.493939	−	0.855528i	−0.999976	+	0.00698436i	$0.997777\pi$
$84$	−1.50000	−	2.59808i	−0.163663	−	0.283473i
$85$	4.00000			0.433861
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$	0.500000	−	0.866025i	0.0536056	−	0.0928477i
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	10.0000			1.06000			0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000			1.06000			0.529999	+	0.847998i	$0.322192\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	−12.0000			−1.25794
$92$	2.00000			0.208514
$93$	−5.50000	+	0.866025i	−0.570323	+	0.0898027i
$94$	−4.00000			−0.412568
$95$		0			0
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	11.0000			1.11688			0.558440	−	0.829545i	$-0.311400\pi$
$97$	11.0000			1.11688			0.558440	+	0.829545i	$0.311400\pi$
$98$	1.00000	+	1.73205i	0.101015	+	0.174964i
$99$	1.50000	−	2.59808i	0.150756	−	0.261116i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−19.0000			−1.89057			−0.945285	−	0.326245i	$-0.894217\pi$
$101$	−19.0000			−1.89057			−0.945285	+	0.326245i	$0.894217\pi$
$102$	2.00000	+	3.46410i	0.198030	+	0.342997i
$103$	−6.50000	−	11.2583i	−0.640464	−	1.10932i	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−6.50000	−	11.2583i	−0.640464	−	1.10932i	0.344865	−	0.938652i	$-0.387925\pi$
$104$	2.00000	+	3.46410i	0.196116	+	0.339683i
$105$	1.50000	−	2.59808i	0.146385	−	0.253546i
$106$	−1.50000	−	2.59808i	−0.145693	−	0.252347i
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	−0.784366	−	0.620298i	$-0.787012\pi$
$107$	1.50000	−	2.59808i	0.145010	−	0.251166i	0.929377	+	0.369132i	$0.120345\pi$
$108$	−1.00000			−0.0962250
$109$	−4.00000			−0.383131			−0.191565	−	0.981480i	$-0.561356\pi$
$109$	−4.00000			−0.383131			−0.191565	+	0.981480i	$0.561356\pi$
$110$	1.50000	−	2.59808i	0.143019	−	0.247717i
$111$	−3.00000	−	5.19615i	−0.284747	−	0.493197i
$112$	1.50000	−	2.59808i	0.141737	−	0.245495i
$113$	6.00000	+	10.3923i	0.564433	+	0.977626i	0.997102	+	0.0760733i	$0.0242383\pi$
$113$	6.00000	+	10.3923i	0.564433	+	0.977626i	−0.432670	+	0.901553i	$0.642428\pi$
$114$		0			0
$115$	1.00000	+	1.73205i	0.0932505	+	0.161515i
$116$	1.00000			0.0928477
$117$	−2.00000	+	3.46410i	−0.184900	+	0.320256i
$118$	−4.50000	+	7.79423i	−0.414259	+	0.717517i
$119$	−6.00000	−	10.3923i	−0.550019	−	0.952661i
$120$	−1.00000			−0.0912871
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	2.00000			0.181071
$123$	2.00000			0.180334
$124$	−3.50000	−	4.33013i	−0.314309	−	0.388857i
$125$	−1.00000			−0.0894427
$126$	3.00000			0.267261
$127$	6.50000	−	11.2583i	0.576782	−	0.999015i	−0.419064	−	0.907957i	$-0.637642\pi$
$127$	6.50000	−	11.2583i	0.576782	−	0.999015i	0.995846	−	0.0910585i	$-0.0290250\pi$
$128$	−1.00000			−0.0883883
$129$	2.00000	+	3.46410i	0.176090	+	0.304997i
$130$	−2.00000	+	3.46410i	−0.175412	+	0.303822i
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$	3.00000			0.261116
$133$		0			0
$134$	1.00000	+	1.73205i	0.0863868	+	0.149626i
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	−2.00000	+	3.46410i	−0.171499	+	0.297044i
$137$	8.00000	+	13.8564i	0.683486	+	1.18383i	0.973910	+	0.226935i	$0.0728704\pi$
$137$	8.00000	+	13.8564i	0.683486	+	1.18383i	−0.290424	+	0.956898i	$0.593796\pi$
$138$	−1.00000	+	1.73205i	−0.0851257	+	0.147442i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$	3.00000			0.253546
$141$	2.00000	−	3.46410i	0.168430	−	0.291730i
$142$	2.00000	+	3.46410i	0.167836	+	0.290701i
$143$	6.00000	−	10.3923i	0.501745	−	0.869048i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.500000	+	0.866025i	0.0415227	+	0.0719195i
$146$	1.00000	+	1.73205i	0.0827606	+	0.143346i
$147$	−2.00000			−0.164957
$148$	3.00000	−	5.19615i	0.246598	−	0.427121i
$149$	−9.50000	+	16.4545i	−0.778270	+	1.34800i	0.154668	+	0.987967i	$0.450569\pi$
$149$	−9.50000	+	16.4545i	−0.778270	+	1.34800i	−0.932938	+	0.360037i	$0.882764\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	9.00000			0.732410			0.366205	−	0.930534i	$-0.380657\pi$
$151$	9.00000			0.732410			0.366205	+	0.930534i	$0.380657\pi$
$152$		0			0
$153$	−4.00000			−0.323381
$154$	−9.00000			−0.725241
$155$	2.00000	−	5.19615i	0.160644	−	0.417365i
$156$	−4.00000			−0.320256
$157$	22.0000			1.75579			0.877896	−	0.478852i	$-0.158947\pi$
$157$	22.0000			1.75579			0.877896	+	0.478852i	$0.158947\pi$
$158$	−2.00000	+	3.46410i	−0.159111	+	0.275589i
$159$	3.00000			0.237915
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	3.00000	−	5.19615i	0.236433	−	0.409514i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−10.0000			−0.783260			−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000			−0.783260			−0.391630	+	0.920123i	$0.628089\pi$
$164$	1.00000	+	1.73205i	0.0780869	+	0.135250i
$165$	1.50000	+	2.59808i	0.116775	+	0.202260i
$166$	4.50000	+	7.79423i	0.349268	+	0.604949i
$167$	−1.00000	+	1.73205i	−0.0773823	+	0.134030i	−0.902120	−	0.431486i	$-0.857990\pi$
$167$	−1.00000	+	1.73205i	−0.0773823	+	0.134030i	0.824737	+	0.565516i	$0.191323\pi$
$168$	1.50000	+	2.59808i	0.115728	+	0.200446i
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$	−4.00000			−0.306786
$171$		0			0
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$	0.500000	+	0.866025i	0.0380143	+	0.0658427i	0.884407	−	0.466717i	$-0.154563\pi$
$173$	0.500000	+	0.866025i	0.0380143	+	0.0658427i	−0.846392	+	0.532560i	$0.821230\pi$
$174$	−0.500000	+	0.866025i	−0.0379049	+	0.0656532i
$175$	1.50000	+	2.59808i	0.113389	+	0.196396i
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$	−4.50000	−	7.79423i	−0.338241	−	0.585850i
$178$	−10.0000			−0.749532
$179$	−9.50000	+	16.4545i	−0.710063	+	1.22987i	0.254770	+	0.967002i	$0.418000\pi$
$179$	−9.50000	+	16.4545i	−0.710063	+	1.22987i	−0.964833	+	0.262864i	$0.915333\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	0.826465	−	0.562988i	$-0.190348\pi$
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	−0.900794	+	0.434246i	$0.857015\pi$
$182$	12.0000			0.889499
$183$	−1.00000	+	1.73205i	−0.0739221	+	0.128037i
$184$	−2.00000			−0.147442
$185$	6.00000			0.441129
$186$	5.50000	−	0.866025i	0.403280	−	0.0635001i
$187$	12.0000			0.877527
$188$	4.00000			0.291730
$189$	−1.50000	+	2.59808i	−0.109109	+	0.188982i
$190$		0			0
$191$	7.00000	+	12.1244i	0.506502	+	0.877288i	0.999972	+	0.00752447i	$0.00239513\pi$
$191$	7.00000	+	12.1244i	0.506502	+	0.877288i	−0.493469	+	0.869763i	$0.664272\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−10.5000	+	18.1865i	−0.755807	+	1.30910i	0.189166	+	0.981945i	$0.439422\pi$
$193$	−10.5000	+	18.1865i	−0.755807	+	1.30910i	−0.944972	+	0.327150i	$0.893912\pi$
$194$	−11.0000			−0.789754
$195$	−2.00000	−	3.46410i	−0.143223	−	0.248069i
$196$	−1.00000	−	1.73205i	−0.0714286	−	0.123718i
$197$	9.00000	+	15.5885i	0.641223	+	1.11063i	0.985160	+	0.171639i	$0.0549062\pi$
$197$	9.00000	+	15.5885i	0.641223	+	1.11063i	−0.343937	+	0.938993i	$0.611761\pi$
$198$	−1.50000	+	2.59808i	−0.106600	+	0.184637i
$199$	5.50000	+	9.52628i	0.389885	+	0.675300i	0.992434	−	0.122782i	$-0.0391815\pi$
$199$	5.50000	+	9.52628i	0.389885	+	0.675300i	−0.602549	+	0.798082i	$0.705848\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−2.00000			−0.141069
$202$	19.0000			1.33684
$203$	1.50000	−	2.59808i	0.105279	−	0.182349i
$204$	−2.00000	−	3.46410i	−0.140028	−	0.242536i
$205$	−1.00000	+	1.73205i	−0.0698430	+	0.120972i
$206$	6.50000	+	11.2583i	0.452876	+	0.784405i
$207$	−1.00000	−	1.73205i	−0.0695048	−	0.120386i
$208$	−2.00000	−	3.46410i	−0.138675	−	0.240192i
$209$		0			0
$210$	−1.50000	+	2.59808i	−0.103510	+	0.179284i
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	−0.970229	−	0.242190i	$-0.922134\pi$
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	0.694857	+	0.719148i	$0.255467\pi$
$212$	1.50000	+	2.59808i	0.103020	+	0.178437i
$213$	−4.00000			−0.274075
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$	−4.00000			−0.272798
$216$	1.00000			0.0680414
$217$	−16.5000	+	2.59808i	−1.12009	+	0.176369i
$218$	4.00000			0.270914
$219$	−2.00000			−0.135147
$220$	−1.50000	+	2.59808i	−0.101130	+	0.175162i
$221$	−16.0000			−1.07628
$222$	3.00000	+	5.19615i	0.201347	+	0.348743i
$223$	−4.50000	+	7.79423i	−0.301342	+	0.521940i	−0.976440	−	0.215788i	$-0.930768\pi$
$223$	−4.50000	+	7.79423i	−0.301342	+	0.521940i	0.675098	+	0.737728i	$0.264101\pi$
$224$	−1.50000	+	2.59808i	−0.100223	+	0.173591i
$225$	1.00000			0.0666667
$226$	−6.00000	−	10.3923i	−0.399114	−	0.691286i
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$		0			0
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	0.231287	+	0.972886i	$0.425707\pi$
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	−0.958187	+	0.286143i	$0.907627\pi$
$230$	−1.00000	−	1.73205i	−0.0659380	−	0.114208i
$231$	4.50000	−	7.79423i	0.296078	−	0.512823i
$232$	−1.00000			−0.0656532
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$	2.00000	−	3.46410i	0.130744	−	0.226455i
$235$	2.00000	+	3.46410i	0.130466	+	0.225973i
$236$	4.50000	−	7.79423i	0.292925	−	0.507361i
$237$	−2.00000	−	3.46410i	−0.129914	−	0.225018i
$238$	6.00000	+	10.3923i	0.388922	+	0.673633i
$239$	12.0000	+	20.7846i	0.776215	+	1.34444i	0.934109	+	0.356988i	$0.116196\pi$
$239$	12.0000	+	20.7846i	0.776215	+	1.34444i	−0.157893	+	0.987456i	$0.550470\pi$
$240$	1.00000			0.0645497
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	−0.999812	−	0.0193858i	$-0.993829\pi$
$241$	−7.50000	+	12.9904i	−0.483117	+	0.836784i	0.516695	+	0.856170i	$0.327162\pi$
$242$	−1.00000	+	1.73205i	−0.0642824	+	0.111340i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−2.00000			−0.128037
$245$	1.00000	−	1.73205i	0.0638877	−	0.110657i
$246$	−2.00000			−0.127515
$247$		0			0
$248$	3.50000	+	4.33013i	0.222250	+	0.274963i
$249$	−9.00000			−0.570352
$250$	1.00000			0.0632456
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$	−3.00000			−0.188982
$253$	3.00000	+	5.19615i	0.188608	+	0.326679i
$254$	−6.50000	+	11.2583i	−0.407846	+	0.706410i
$255$	2.00000	−	3.46410i	0.125245	−	0.216930i
$256$	1.00000			0.0625000
$257$	−5.00000	−	8.66025i	−0.311891	−	0.540212i	0.666880	−	0.745165i	$-0.267629\pi$
$257$	−5.00000	−	8.66025i	−0.311891	−	0.540212i	−0.978772	+	0.204953i	$0.934296\pi$
$258$	−2.00000	−	3.46410i	−0.124515	−	0.215666i
$259$	−9.00000	−	15.5885i	−0.559233	−	0.968620i
$260$	2.00000	−	3.46410i	0.124035	−	0.214834i
$261$	−0.500000	−	0.866025i	−0.0309492	−	0.0536056i
$262$	6.00000	−	10.3923i	0.370681	−	0.642039i
$263$	−6.00000			−0.369976			−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000			−0.369976			−0.184988	+	0.982741i	$0.559225\pi$
$264$	−3.00000			−0.184637
$265$	−1.50000	+	2.59808i	−0.0921443	+	0.159599i
$266$		0			0
$267$	5.00000	−	8.66025i	0.305995	−	0.529999i
$268$	−1.00000	−	1.73205i	−0.0610847	−	0.105802i
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	0.569789	−	0.821791i	$-0.307025\pi$
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	−0.996586	+	0.0825561i	$0.973692\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	1.00000			0.0607457			0.0303728	−	0.999539i	$-0.490331\pi$
$271$	1.00000			0.0607457			0.0303728	+	0.999539i	$0.490331\pi$
$272$	2.00000	−	3.46410i	0.121268	−	0.210042i
$273$	−6.00000	+	10.3923i	−0.363137	+	0.628971i
$274$	−8.00000	−	13.8564i	−0.483298	−	0.837096i
$275$	−3.00000			−0.180907
$276$	1.00000	−	1.73205i	0.0601929	−	0.104257i
$277$		0			0			−	1.00000i	$-0.5\pi$
$277$		0			0				1.00000i	$0.5\pi$
$278$	−4.00000			−0.239904
$279$	−2.00000	+	5.19615i	−0.119737	+	0.311086i
$280$	−3.00000			−0.179284
$281$	−26.0000			−1.55103			−0.775515	−	0.631329i	$-0.782510\pi$
$281$	−26.0000			−1.55103			−0.775515	+	0.631329i	$0.782510\pi$
$282$	−2.00000	+	3.46410i	−0.119098	+	0.206284i
$283$		0			0			−	1.00000i	$-0.5\pi$
$283$		0			0				1.00000i	$0.5\pi$
$284$	−2.00000	−	3.46410i	−0.118678	−	0.205557i
$285$		0			0
$286$	−6.00000	+	10.3923i	−0.354787	+	0.614510i
$287$	6.00000			0.354169
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	−0.500000	−	0.866025i	−0.0293610	−	0.0508548i
$291$	5.50000	−	9.52628i	0.322416	−	0.558440i
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	−10.5000	+	18.1865i	−0.613417	+	1.06247i	0.377244	+	0.926114i	$0.376872\pi$
$293$	−10.5000	+	18.1865i	−0.613417	+	1.06247i	−0.990660	+	0.136355i	$0.956461\pi$
$294$	2.00000			0.116642
$295$	9.00000			0.524000
$296$	−3.00000	+	5.19615i	−0.174371	+	0.302020i
$297$	−1.50000	−	2.59808i	−0.0870388	−	0.150756i
$298$	9.50000	−	16.4545i	0.550320	−	0.953183i
$299$	−4.00000	−	6.92820i	−0.231326	−	0.400668i
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	6.00000	+	10.3923i	0.345834	+	0.599002i
$302$	−9.00000			−0.517892
$303$	−9.50000	+	16.4545i	−0.545761	+	0.945285i
$304$		0			0
$305$	−1.00000	−	1.73205i	−0.0572598	−	0.0991769i
$306$	4.00000			0.228665
$307$	4.00000	−	6.92820i	0.228292	−	0.395413i	−0.729010	−	0.684503i	$-0.760019\pi$
$307$	4.00000	−	6.92820i	0.228292	−	0.395413i	0.957302	+	0.289090i	$0.0933526\pi$
$308$	9.00000			0.512823
$309$	−13.0000			−0.739544
$310$	−2.00000	+	5.19615i	−0.113592	+	0.295122i
$311$	24.0000			1.36092			0.680458	−	0.732787i	$-0.261781\pi$
$311$	24.0000			1.36092			0.680458	+	0.732787i	$0.261781\pi$
$312$	4.00000			0.226455
$313$	−10.5000	+	18.1865i	−0.593495	+	1.02796i	0.400262	+	0.916401i	$0.368919\pi$
$313$	−10.5000	+	18.1865i	−0.593495	+	1.02796i	−0.993757	+	0.111563i	$0.964414\pi$
$314$	−22.0000			−1.24153
$315$	−1.50000	−	2.59808i	−0.0845154	−	0.146385i
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$	−6.50000	+	11.2583i	−0.365076	+	0.632331i	−0.988788	−	0.149323i	$-0.952290\pi$
$317$	−6.50000	+	11.2583i	−0.365076	+	0.632331i	0.623712	+	0.781654i	$0.285624\pi$
$318$	−3.00000			−0.168232
$319$	1.50000	+	2.59808i	0.0839839	+	0.145464i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	−1.50000	−	2.59808i	−0.0837218	−	0.145010i
$322$	−3.00000	+	5.19615i	−0.167183	+	0.289570i
$323$		0			0
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	4.00000			0.221880
$326$	10.0000			0.553849
$327$	−2.00000	+	3.46410i	−0.110600	+	0.191565i
$328$	−1.00000	−	1.73205i	−0.0552158	−	0.0956365i
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$	−1.50000	−	2.59808i	−0.0825723	−	0.143019i
$331$	15.0000	+	25.9808i	0.824475	+	1.42803i	0.902320	+	0.431066i	$0.141863\pi$
$331$	15.0000	+	25.9808i	0.824475	+	1.42803i	−0.0778456	+	0.996965i	$0.524804\pi$
$332$	−4.50000	−	7.79423i	−0.246970	−	0.427764i
$333$	−6.00000			−0.328798
$334$	1.00000	−	1.73205i	0.0547176	−	0.0947736i
$335$	1.00000	−	1.73205i	0.0546358	−	0.0946320i
$336$	−1.50000	−	2.59808i	−0.0818317	−	0.141737i
$337$	25.0000			1.36184			0.680918	−	0.732359i	$-0.261581\pi$
$337$	25.0000			1.36184			0.680918	+	0.732359i	$0.261581\pi$
$338$	1.50000	−	2.59808i	0.0815892	−	0.141317i
$339$	12.0000			0.651751
$340$	4.00000			0.216930
$341$	6.00000	−	15.5885i	0.324918	−	0.844162i
$342$		0			0
$343$	15.0000			0.809924
$344$	2.00000	−	3.46410i	0.107833	−	0.186772i
$345$	2.00000			0.107676
$346$	−0.500000	−	0.866025i	−0.0268802	−	0.0465578i
$347$	−9.50000	+	16.4545i	−0.509987	+	0.883323i	0.489946	+	0.871753i	$0.337016\pi$
$347$	−9.50000	+	16.4545i	−0.509987	+	0.883323i	−0.999933	+	0.0115703i	$0.996317\pi$
$348$	0.500000	−	0.866025i	0.0268028	−	0.0464238i
$349$	12.0000			0.642345			0.321173	−	0.947021i	$-0.395923\pi$
$349$	12.0000			0.642345			0.321173	+	0.947021i	$0.395923\pi$
$350$	−1.50000	−	2.59808i	−0.0801784	−	0.138873i
$351$	2.00000	+	3.46410i	0.106752	+	0.184900i
$352$	−1.50000	−	2.59808i	−0.0799503	−	0.138478i
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	−0.934751	−	0.355303i	$-0.884378\pi$
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	0.775077	+	0.631867i	$0.217711\pi$
$354$	4.50000	+	7.79423i	0.239172	+	0.414259i
$355$	2.00000	−	3.46410i	0.106149	−	0.183855i
$356$	10.0000			0.529999
$357$	−12.0000			−0.635107
$358$	9.50000	−	16.4545i	0.502091	−	0.869646i
$359$	−15.0000	−	25.9808i	−0.791670	−	1.37121i	−0.924932	−	0.380131i	$-0.875879\pi$
$359$	−15.0000	−	25.9808i	−0.791670	−	1.37121i	0.133263	−	0.991081i	$-0.457455\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	1.00000	+	1.73205i	0.0525588	+	0.0910346i
$363$	−1.00000	−	1.73205i	−0.0524864	−	0.0909091i
$364$	−12.0000			−0.628971
$365$	1.00000	−	1.73205i	0.0523424	−	0.0906597i
$366$	1.00000	−	1.73205i	0.0522708	−	0.0905357i
$367$	−16.0000	−	27.7128i	−0.835193	−	1.44660i	−0.893873	−	0.448320i	$-0.852022\pi$
$367$	−16.0000	−	27.7128i	−0.835193	−	1.44660i	0.0586798	−	0.998277i	$-0.481311\pi$
$368$	2.00000			0.104257
$369$	1.00000	−	1.73205i	0.0520579	−	0.0901670i
$370$	−6.00000			−0.311925
$371$	9.00000			0.467257
$372$	−5.50000	+	0.866025i	−0.285162	+	0.0449013i
$373$	24.0000			1.24267			0.621336	−	0.783544i	$-0.286590\pi$
$373$	24.0000			1.24267			0.621336	+	0.783544i	$0.286590\pi$
$374$	−12.0000			−0.620505
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	−4.00000			−0.206284
$377$	−2.00000	−	3.46410i	−0.103005	−	0.178410i
$378$	1.50000	−	2.59808i	0.0771517	−	0.133631i
$379$	9.00000	−	15.5885i	0.462299	−	0.800725i	−0.536776	−	0.843725i	$-0.680358\pi$
$379$	9.00000	−	15.5885i	0.462299	−	0.800725i	0.999075	+	0.0429994i	$0.0136914\pi$
$380$		0			0
$381$	−6.50000	−	11.2583i	−0.333005	−	0.576782i
$382$	−7.00000	−	12.1244i	−0.358151	−	0.620336i
$383$	−3.00000	−	5.19615i	−0.153293	−	0.265511i	0.779143	−	0.626846i	$-0.215654\pi$
$383$	−3.00000	−	5.19615i	−0.153293	−	0.265511i	−0.932436	+	0.361335i	$0.882321\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	4.50000	+	7.79423i	0.229341	+	0.397231i
$386$	10.5000	−	18.1865i	0.534436	−	0.925670i
$387$	4.00000			0.203331
$388$	11.0000			0.558440
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	−0.321716	−	0.946836i	$-0.604260\pi$
$389$	13.0000	−	22.5167i	0.659126	−	1.14164i	0.980842	−	0.194804i	$-0.0624070\pi$
$390$	2.00000	+	3.46410i	0.101274	+	0.175412i
$391$	4.00000	−	6.92820i	0.202289	−	0.350374i
$392$	1.00000	+	1.73205i	0.0505076	+	0.0874818i
$393$	6.00000	+	10.3923i	0.302660	+	0.524222i
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$	4.00000			0.201262
$396$	1.50000	−	2.59808i	0.0753778	−	0.130558i
$397$	5.00000	−	8.66025i	0.250943	−	0.434646i	−0.712843	−	0.701324i	$-0.752593\pi$
$397$	5.00000	−	8.66025i	0.250943	−	0.434646i	0.963786	+	0.266678i	$0.0859261\pi$
$398$	−5.50000	−	9.52628i	−0.275690	−	0.477509i
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−8.00000			−0.399501			−0.199750	−	0.979847i	$-0.564013\pi$
$401$	−8.00000			−0.399501			−0.199750	+	0.979847i	$0.564013\pi$
$402$	2.00000			0.0997509
$403$	−8.00000	+	20.7846i	−0.398508	+	1.03536i
$404$	−19.0000			−0.945285
$405$	−1.00000			−0.0496904
$406$	−1.50000	+	2.59808i	−0.0744438	+	0.128940i
$407$	18.0000			0.892227
$408$	2.00000	+	3.46410i	0.0990148	+	0.171499i
$409$	6.50000	−	11.2583i	0.321404	−	0.556689i	−0.659374	−	0.751815i	$-0.729178\pi$
$409$	6.50000	−	11.2583i	0.321404	−	0.556689i	0.980778	+	0.195127i	$0.0625118\pi$
$410$	1.00000	−	1.73205i	0.0493865	−	0.0855399i
$411$	16.0000			0.789222
$412$	−6.50000	−	11.2583i	−0.320232	−	0.554658i
$413$	−13.5000	−	23.3827i	−0.664292	−	1.15059i
$414$	1.00000	+	1.73205i	0.0491473	+	0.0851257i
$415$	4.50000	−	7.79423i	0.220896	−	0.382604i
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$	2.00000	−	3.46410i	0.0979404	−	0.169638i
$418$		0			0
$419$	9.00000			0.439679			0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000			0.439679			0.219839	+	0.975536i	$0.429447\pi$
$420$	1.50000	−	2.59808i	0.0731925	−	0.126773i
$421$	17.0000	+	29.4449i	0.828529	+	1.43505i	0.899192	+	0.437555i	$0.144155\pi$
$421$	17.0000	+	29.4449i	0.828529	+	1.43505i	−0.0706626	+	0.997500i	$0.522511\pi$
$422$	4.00000	−	6.92820i	0.194717	−	0.337260i
$423$	−2.00000	−	3.46410i	−0.0972433	−	0.168430i
$424$	−1.50000	−	2.59808i	−0.0728464	−	0.126174i
$425$	2.00000	+	3.46410i	0.0970143	+	0.168034i
$426$	4.00000			0.193801
$427$	−3.00000	+	5.19615i	−0.145180	+	0.251459i
$428$	1.50000	−	2.59808i	0.0725052	−	0.125583i
$429$	−6.00000	−	10.3923i	−0.289683	−	0.501745i
$430$	4.00000			0.192897
$431$	16.0000	−	27.7128i	0.770693	−	1.33488i	−0.166491	−	0.986043i	$-0.553244\pi$
$431$	16.0000	−	27.7128i	0.770693	−	1.33488i	0.937184	−	0.348836i	$-0.113423\pi$
$432$	−1.00000			−0.0481125
$433$	26.0000			1.24948			0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000			1.24948			0.624740	+	0.780833i	$0.285205\pi$
$434$	16.5000	−	2.59808i	0.792025	−	0.124712i
$435$	1.00000			0.0479463
$436$	−4.00000			−0.191565
$437$		0			0
$438$	2.00000			0.0955637
$439$	1.50000	+	2.59808i	0.0715911	+	0.123999i	0.899599	−	0.436717i	$-0.143859\pi$
$439$	1.50000	+	2.59808i	0.0715911	+	0.123999i	−0.828008	+	0.560717i	$0.810526\pi$
$440$	1.50000	−	2.59808i	0.0715097	−	0.123858i
$441$	−1.00000	+	1.73205i	−0.0476190	+	0.0824786i
$442$	16.0000			0.761042
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	−0.876454	−	0.481486i	$-0.840097\pi$
$443$	−18.0000	−	31.1769i	−0.855206	−	1.48126i	0.0212481	−	0.999774i	$-0.493236\pi$
$444$	−3.00000	−	5.19615i	−0.142374	−	0.246598i
$445$	5.00000	+	8.66025i	0.237023	+	0.410535i
$446$	4.50000	−	7.79423i	0.213081	−	0.369067i
$447$	9.50000	+	16.4545i	0.449335	+	0.778270i
$448$	1.50000	−	2.59808i	0.0708683	−	0.122748i
$449$	26.0000			1.22702			0.613508	−	0.789689i	$-0.289758\pi$
$449$	26.0000			1.22702			0.613508	+	0.789689i	$0.289758\pi$
$450$	−1.00000			−0.0471405
$451$	−3.00000	+	5.19615i	−0.141264	+	0.244677i
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$	4.50000	−	7.79423i	0.211428	−	0.366205i
$454$	−1.50000	−	2.59808i	−0.0703985	−	0.121934i
$455$	−6.00000	−	10.3923i	−0.281284	−	0.487199i
$456$		0			0
$457$	−26.0000			−1.21623			−0.608114	−	0.793849i	$-0.708074\pi$
$457$	−26.0000			−1.21623			−0.608114	+	0.793849i	$0.708074\pi$
$458$	11.0000	−	19.0526i	0.513996	−	0.890268i
$459$	−2.00000	+	3.46410i	−0.0933520	+	0.161690i
$460$	1.00000	+	1.73205i	0.0466252	+	0.0807573i
$461$	−9.00000			−0.419172			−0.209586	−	0.977790i	$-0.567212\pi$
$461$	−9.00000			−0.419172			−0.209586	+	0.977790i	$0.567212\pi$
$462$	−4.50000	+	7.79423i	−0.209359	+	0.362620i
$463$	−5.00000			−0.232370			−0.116185	−	0.993228i	$-0.537067\pi$
$463$	−5.00000			−0.232370			−0.116185	+	0.993228i	$0.537067\pi$
$464$	1.00000			0.0464238
$465$	−3.50000	−	4.33013i	−0.162309	−	0.200805i
$466$	6.00000			0.277945
$467$	−27.0000			−1.24941			−0.624705	−	0.780860i	$-0.714781\pi$
$467$	−27.0000			−1.24941			−0.624705	+	0.780860i	$0.714781\pi$
$468$	−2.00000	+	3.46410i	−0.0924500	+	0.160128i
$469$	−6.00000			−0.277054
$470$	−2.00000	−	3.46410i	−0.0922531	−	0.159787i
$471$	11.0000	−	19.0526i	0.506853	−	0.877896i
$472$	−4.50000	+	7.79423i	−0.207129	+	0.358758i
$473$	−12.0000			−0.551761
$474$	2.00000	+	3.46410i	0.0918630	+	0.159111i
$475$		0			0
$476$	−6.00000	−	10.3923i	−0.275010	−	0.476331i
$477$	1.50000	−	2.59808i	0.0686803	−	0.118958i
$478$	−12.0000	−	20.7846i	−0.548867	−	0.950666i
$479$	−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			−0.0456435
$481$	−24.0000			−1.09431
$482$	7.50000	−	12.9904i	0.341616	−	0.591696i
$483$	−3.00000	−	5.19615i	−0.136505	−	0.236433i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	5.50000	+	9.52628i	0.249742	+	0.432566i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−14.5000	−	25.1147i	−0.657058	−	1.13806i	−0.981374	−	0.192109i	$-0.938467\pi$
$487$	−14.5000	−	25.1147i	−0.657058	−	1.13806i	0.324316	−	0.945949i	$-0.394866\pi$
$488$	2.00000			0.0905357
$489$	−5.00000	+	8.66025i	−0.226108	+	0.391630i
$490$	−1.00000	+	1.73205i	−0.0451754	+	0.0782461i
$491$	9.50000	+	16.4545i	0.428729	+	0.742580i	0.996761	−	0.0804264i	$-0.0256282\pi$
$491$	9.50000	+	16.4545i	0.428729	+	0.742580i	−0.568032	+	0.823007i	$0.692295\pi$
$492$	2.00000			0.0901670
$493$	2.00000	−	3.46410i	0.0900755	−	0.156015i
$494$		0			0
$495$	3.00000			0.134840
$496$	−3.50000	−	4.33013i	−0.157155	−	0.194428i
$497$	−12.0000			−0.538274
$498$	9.00000			0.403300
$499$	−11.0000	+	19.0526i	−0.492428	+	0.852910i	−0.999962	−	0.00872186i	$-0.997224\pi$
$499$	−11.0000	+	19.0526i	−0.492428	+	0.852910i	0.507534	+	0.861632i	$0.330557\pi$
$500$	−1.00000			−0.0447214
$501$	1.00000	+	1.73205i	0.0446767	+	0.0773823i
$502$		0			0
$503$	−7.00000	+	12.1244i	−0.312115	+	0.540598i	−0.978820	−	0.204723i	$-0.934371\pi$
$503$	−7.00000	+	12.1244i	−0.312115	+	0.540598i	0.666705	+	0.745321i	$0.267704\pi$
$504$	3.00000			0.133631
$505$	−9.50000	−	16.4545i	−0.422744	−	0.732215i
$506$	−3.00000	−	5.19615i	−0.133366	−	0.230997i
$507$	1.50000	+	2.59808i	0.0666173	+	0.115385i
$508$	6.50000	−	11.2583i	0.288391	−	0.499508i
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	0.982988	−	0.183669i	$-0.0587976\pi$
$509$	7.50000	+	12.9904i	0.332432	+	0.575789i	−0.650556	+	0.759458i	$0.725464\pi$
$510$	−2.00000	+	3.46410i	−0.0885615	+	0.153393i
$511$	−6.00000			−0.265424
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	5.00000	+	8.66025i	0.220541	+	0.381987i
$515$	6.50000	−	11.2583i	0.286424	−	0.496101i
$516$	2.00000	+	3.46410i	0.0880451	+	0.152499i
$517$	6.00000	+	10.3923i	0.263880	+	0.457053i
$518$	9.00000	+	15.5885i	0.395437	+	0.684917i
$519$	1.00000			0.0438951
$520$	−2.00000	+	3.46410i	−0.0877058	+	0.151911i
$521$	12.0000	−	20.7846i	0.525730	−	0.910590i	−0.473821	−	0.880621i	$-0.657126\pi$
$521$	12.0000	−	20.7846i	0.525730	−	0.910590i	0.999551	−	0.0299693i	$-0.00954094\pi$
$522$	0.500000	+	0.866025i	0.0218844	+	0.0379049i
$523$	8.00000			0.349816			0.174908	−	0.984585i	$-0.444037\pi$
$523$	8.00000			0.349816			0.174908	+	0.984585i	$0.444037\pi$
$524$	−6.00000	+	10.3923i	−0.262111	+	0.453990i
$525$	3.00000			0.130931
$526$	6.00000			0.261612
$527$	−22.0000	+	3.46410i	−0.958335	+	0.150899i
$528$	3.00000			0.130558
$529$	−19.0000			−0.826087
$530$	1.50000	−	2.59808i	0.0651558	−	0.112853i
$531$	−9.00000			−0.390567
$532$		0			0
$533$	4.00000	−	6.92820i	0.173259	−	0.300094i
$534$	−5.00000	+	8.66025i	−0.216371	+	0.374766i
$535$	3.00000			0.129701
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	9.50000	+	16.4545i	0.409955	+	0.710063i
$538$	7.00000	+	12.1244i	0.301791	+	0.522718i
$539$	3.00000	−	5.19615i	0.129219	−	0.223814i
$540$	−0.500000	−	0.866025i	−0.0215166	−	0.0372678i
$541$	−5.00000	+	8.66025i	−0.214967	+	0.372333i	−0.953262	−	0.302144i	$-0.902298\pi$
$541$	−5.00000	+	8.66025i	−0.214967	+	0.372333i	0.738296	+	0.674477i	$0.235631\pi$
$542$	−1.00000			−0.0429537
$543$	−2.00000			−0.0858282
$544$	−2.00000	+	3.46410i	−0.0857493	+	0.148522i
$545$	−2.00000	−	3.46410i	−0.0856706	−	0.148386i
$546$	6.00000	−	10.3923i	0.256776	−	0.444750i
$547$	−5.00000	−	8.66025i	−0.213785	−	0.370286i	0.739111	−	0.673583i	$-0.235246\pi$
$547$	−5.00000	−	8.66025i	−0.213785	−	0.370286i	−0.952896	+	0.303298i	$0.901912\pi$
$548$	8.00000	+	13.8564i	0.341743	+	0.591916i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$	3.00000			0.127920
$551$		0			0
$552$	−1.00000	+	1.73205i	−0.0425628	+	0.0737210i
$553$	−6.00000	−	10.3923i	−0.255146	−	0.441926i
$554$		0			0
$555$	3.00000	−	5.19615i	0.127343	−	0.220564i
$556$	4.00000			0.169638
$557$	11.0000			0.466085			0.233042	−	0.972467i	$-0.425132\pi$
$557$	11.0000			0.466085			0.233042	+	0.972467i	$0.425132\pi$
$558$	2.00000	−	5.19615i	0.0846668	−	0.219971i
$559$	16.0000			0.676728
$560$	3.00000			0.126773
$561$	6.00000	−	10.3923i	0.253320	−	0.438763i
$562$	26.0000			1.09674
$563$	−11.5000	−	19.9186i	−0.484667	−	0.839468i	0.515178	−	0.857083i	$-0.327726\pi$
$563$	−11.5000	−	19.9186i	−0.484667	−	0.839468i	−0.999845	+	0.0176152i	$0.994393\pi$
$564$	2.00000	−	3.46410i	0.0842152	−	0.145865i
$565$	−6.00000	+	10.3923i	−0.252422	+	0.437208i
$566$		0			0
$567$	1.50000	+	2.59808i	0.0629941	+	0.109109i
$568$	2.00000	+	3.46410i	0.0839181	+	0.145350i
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	0.821054	−	0.570851i	$-0.193387\pi$
$569$	−2.00000	−	3.46410i	−0.0838444	−	0.145223i	−0.904898	+	0.425628i	$0.860053\pi$
$570$		0			0
$571$	−11.0000	−	19.0526i	−0.460336	−	0.797325i	0.538642	−	0.842535i	$-0.318938\pi$
$571$	−11.0000	−	19.0526i	−0.460336	−	0.797325i	−0.998978	+	0.0452101i	$0.985604\pi$
$572$	6.00000	−	10.3923i	0.250873	−	0.434524i
$573$	14.0000			0.584858
$574$	−6.00000			−0.250435
$575$	−1.00000	+	1.73205i	−0.0417029	+	0.0722315i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	13.0000	−	22.5167i	0.541197	−	0.937381i	−0.457639	−	0.889138i	$-0.651305\pi$
$577$	13.0000	−	22.5167i	0.541197	−	0.937381i	0.998836	−	0.0482425i	$-0.0153620\pi$
$578$	−0.500000	−	0.866025i	−0.0207973	−	0.0360219i
$579$	10.5000	+	18.1865i	0.436365	+	0.755807i
$580$	0.500000	+	0.866025i	0.0207614	+	0.0359597i
$581$	−27.0000			−1.12015
$582$	−5.50000	+	9.52628i	−0.227982	+	0.394877i
$583$	−4.50000	+	7.79423i	−0.186371	+	0.322804i
$584$	1.00000	+	1.73205i	0.0413803	+	0.0716728i
$585$	−4.00000			−0.165380
$586$	10.5000	−	18.1865i	0.433751	−	0.751279i
$587$	11.0000			0.454019			0.227009	−	0.973893i	$-0.427105\pi$
$587$	11.0000			0.454019			0.227009	+	0.973893i	$0.427105\pi$
$588$	−2.00000			−0.0824786
$589$		0			0
$590$	−9.00000			−0.370524
$591$	18.0000			0.740421
$592$	3.00000	−	5.19615i	0.123299	−	0.213561i
$593$	−20.0000			−0.821302			−0.410651	−	0.911793i	$-0.634698\pi$
$593$	−20.0000			−0.821302			−0.410651	+	0.911793i	$0.634698\pi$
$594$	1.50000	+	2.59808i	0.0615457	+	0.106600i
$595$	6.00000	−	10.3923i	0.245976	−	0.426043i
$596$	−9.50000	+	16.4545i	−0.389135	+	0.674002i
$597$	11.0000			0.450200
$598$	4.00000	+	6.92820i	0.163572	+	0.283315i
$599$	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	$0.670218\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	−21.0000	+	36.3731i	−0.856608	+	1.48369i	0.0185374	+	0.999828i	$0.494099\pi$
$601$	−21.0000	+	36.3731i	−0.856608	+	1.48369i	−0.875145	+	0.483860i	$0.839234\pi$
$602$	−6.00000	−	10.3923i	−0.244542	−	0.423559i
$603$	−1.00000	+	1.73205i	−0.0407231	+	0.0705346i
$604$	9.00000			0.366205
$605$	2.00000			0.0813116
$606$	9.50000	−	16.4545i	0.385911	−	0.668418i
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	−0.983262	−	0.182199i	$-0.941678\pi$
$607$	−16.0000	−	27.7128i	−0.649420	−	1.12483i	0.333842	−	0.942629i	$-0.391655\pi$
$608$		0			0
$609$	−1.50000	−	2.59808i	−0.0607831	−	0.105279i
$610$	1.00000	+	1.73205i	0.0404888	+	0.0701287i
$611$	−8.00000	−	13.8564i	−0.323645	−	0.560570i
$612$	−4.00000			−0.161690
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	−0.658012	−	0.753007i	$-0.728603\pi$
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	0.981129	+	0.193352i	$0.0619359\pi$
$614$	−4.00000	+	6.92820i	−0.161427	+	0.279600i
$615$	1.00000	+	1.73205i	0.0403239	+	0.0698430i
$616$	−9.00000			−0.362620
$617$	−21.0000	+	36.3731i	−0.845428	+	1.46432i	0.0398207	+	0.999207i	$0.487321\pi$
$617$	−21.0000	+	36.3731i	−0.845428	+	1.46432i	−0.885249	+	0.465118i	$0.846012\pi$
$618$	13.0000			0.522937
$619$	22.0000			0.884255			0.442127	−	0.896952i	$-0.354224\pi$
$619$	22.0000			0.884255			0.442127	+	0.896952i	$0.354224\pi$
$620$	2.00000	−	5.19615i	0.0803219	−	0.208683i
$621$	−2.00000			−0.0802572
$622$	−24.0000			−0.962312
$623$	15.0000	−	25.9808i	0.600962	−	1.04090i
$624$	−4.00000			−0.160128
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	10.5000	−	18.1865i	0.419664	−	0.726880i
$627$		0			0
$628$	22.0000			0.877896
$629$	−12.0000	−	20.7846i	−0.478471	−	0.828737i
$630$	1.50000	+	2.59808i	0.0597614	+	0.103510i
$631$	−20.5000	−	35.5070i	−0.816092	−	1.41351i	−0.908541	−	0.417796i	$-0.862803\pi$
$631$	−20.5000	−	35.5070i	−0.816092	−	1.41351i	0.0924489	−	0.995717i	$-0.470531\pi$
$632$	−2.00000	+	3.46410i	−0.0795557	+	0.137795i
$633$	4.00000	+	6.92820i	0.158986	+	0.275371i
$634$	6.50000	−	11.2583i	0.258148	−	0.447125i
$635$	13.0000			0.515889
$636$	3.00000			0.118958
$637$	−4.00000	+	6.92820i	−0.158486	+	0.274505i
$638$	−1.50000	−	2.59808i	−0.0593856	−	0.102859i
$639$	−2.00000	+	3.46410i	−0.0791188	+	0.137038i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	5.00000	+	8.66025i	0.197488	+	0.342059i	0.947713	−	0.319123i	$-0.103388\pi$
$641$	5.00000	+	8.66025i	0.197488	+	0.342059i	−0.750225	+	0.661182i	$0.770055\pi$
$642$	1.50000	+	2.59808i	0.0592003	+	0.102538i
$643$	−38.0000			−1.49857			−0.749287	−	0.662246i	$-0.769604\pi$
$643$	−38.0000			−1.49857			−0.749287	+	0.662246i	$0.769604\pi$
$644$	3.00000	−	5.19615i	0.118217	−	0.204757i
$645$	−2.00000	+	3.46410i	−0.0787499	+	0.136399i
$646$		0			0
$647$	−24.0000			−0.943537			−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000			−0.943537			−0.471769	+	0.881722i	$0.656384\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	27.0000			1.05984
$650$	−4.00000			−0.156893
$651$	−6.00000	+	15.5885i	−0.235159	+	0.610960i
$652$	−10.0000			−0.391630
$653$	−29.0000			−1.13486			−0.567429	−	0.823422i	$-0.692062\pi$
$653$	−29.0000			−1.13486			−0.567429	+	0.823422i	$0.692062\pi$
$654$	2.00000	−	3.46410i	0.0782062	−	0.135457i
$655$	−12.0000			−0.468879
$656$	1.00000	+	1.73205i	0.0390434	+	0.0676252i
$657$	−1.00000	+	1.73205i	−0.0390137	+	0.0675737i
$658$	−6.00000	+	10.3923i	−0.233904	+	0.405134i
$659$	−37.0000			−1.44132			−0.720658	−	0.693291i	$-0.756160\pi$
$659$	−37.0000			−1.44132			−0.720658	+	0.693291i	$0.756160\pi$
$660$	1.50000	+	2.59808i	0.0583874	+	0.101130i
$661$	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	$0.408310\pi$
$662$	−15.0000	−	25.9808i	−0.582992	−	1.00977i
$663$	−8.00000	+	13.8564i	−0.310694	+	0.538138i
$664$	4.50000	+	7.79423i	0.174634	+	0.302475i
$665$		0			0
$666$	6.00000			0.232495
$667$	2.00000			0.0774403
$668$	−1.00000	+	1.73205i	−0.0386912	+	0.0670151i
$669$	4.50000	+	7.79423i	0.173980	+	0.301342i
$670$	−1.00000	+	1.73205i	−0.0386334	+	0.0669150i
$671$	−3.00000	−	5.19615i	−0.115814	−	0.200595i
$672$	1.50000	+	2.59808i	0.0578638	+	0.100223i
$673$	9.50000	+	16.4545i	0.366198	+	0.634274i	0.988968	−	0.148132i	$-0.0473259\pi$
$673$	9.50000	+	16.4545i	0.366198	+	0.634274i	−0.622770	+	0.782405i	$0.713993\pi$
$674$	−25.0000			−0.962964
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	16.5000	+	28.5788i	0.634147	+	1.09837i	0.986695	+	0.162581i	$0.0519817\pi$
$677$	16.5000	+	28.5788i	0.634147	+	1.09837i	−0.352549	+	0.935793i	$0.614685\pi$
$678$	−12.0000			−0.460857
$679$	16.5000	−	28.5788i	0.633212	−	1.09676i
$680$	−4.00000			−0.153393
$681$	3.00000			0.114960
$682$	−6.00000	+	15.5885i	−0.229752	+	0.596913i
$683$	23.0000			0.880071			0.440035	−	0.897980i	$-0.354966\pi$
$683$	23.0000			0.880071			0.440035	+	0.897980i	$0.354966\pi$
$684$		0			0
$685$	−8.00000	+	13.8564i	−0.305664	+	0.529426i
$686$	−15.0000			−0.572703
$687$	11.0000	+	19.0526i	0.419676	+	0.726900i
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$	−2.00000			−0.0761387
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	0.500000	+	0.866025i	0.0190071	+	0.0329213i
$693$	−4.50000	−	7.79423i	−0.170941	−	0.296078i
$694$	9.50000	−	16.4545i	0.360615	−	0.624604i
$695$	2.00000	+	3.46410i	0.0758643	+	0.131401i
$696$	−0.500000	+	0.866025i	−0.0189525	+	0.0328266i
$697$	8.00000			0.303022
$698$	−12.0000			−0.454207
$699$	−3.00000	+	5.19615i	−0.113470	+	0.196537i
$700$	1.50000	+	2.59808i	0.0566947	+	0.0981981i
$701$	7.50000	−	12.9904i	0.283271	−	0.490640i	−0.688917	−	0.724840i	$-0.741914\pi$
$701$	7.50000	−	12.9904i	0.283271	−	0.490640i	0.972188	+	0.234200i	$0.0752470\pi$
$702$	−2.00000	−	3.46410i	−0.0754851	−	0.130744i
$703$		0			0
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$	4.00000			0.150649
$706$	3.00000	−	5.19615i	0.112906	−	0.195560i
$707$	−28.5000	+	49.3634i	−1.07185	+	1.85650i
$708$	−4.50000	−	7.79423i	−0.169120	−	0.292925i
$709$	50.0000			1.87779			0.938895	−	0.344204i	$-0.111851\pi$
$709$	50.0000			1.87779			0.938895	+	0.344204i	$0.111851\pi$
$710$	−2.00000	+	3.46410i	−0.0750587	+	0.130005i
$711$	−4.00000			−0.150012
$712$	−10.0000			−0.374766
$713$	−7.00000	−	8.66025i	−0.262152	−	0.324329i
$714$	12.0000			0.449089
$715$	12.0000			0.448775
$716$	−9.50000	+	16.4545i	−0.355032	+	0.614933i
$717$	24.0000			0.896296
$718$	15.0000	+	25.9808i	0.559795	+	0.969593i
$719$	2.00000	−	3.46410i	0.0745874	−	0.129189i	−0.826319	−	0.563202i	$-0.809569\pi$
$719$	2.00000	−	3.46410i	0.0745874	−	0.129189i	0.900907	+	0.434013i	$0.142903\pi$
$720$	0.500000	−	0.866025i	0.0186339	−	0.0322749i
$721$	−39.0000			−1.45244
$722$	−9.50000	−	16.4545i	−0.353553	−	0.612372i
$723$	7.50000	+	12.9904i	0.278928	+	0.483117i
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$	−0.500000	+	0.866025i	−0.0185695	+	0.0321634i
$726$	1.00000	+	1.73205i	0.0371135	+	0.0642824i
$727$	−1.50000	+	2.59808i	−0.0556319	+	0.0963573i	−0.892500	−	0.451047i	$-0.851051\pi$
$727$	−1.50000	+	2.59808i	−0.0556319	+	0.0963573i	0.836868	+	0.547404i	$0.184384\pi$
$728$	12.0000			0.444750
$729$	1.00000			0.0370370
$730$	−1.00000	+	1.73205i	−0.0370117	+	0.0641061i
$731$	8.00000	+	13.8564i	0.295891	+	0.512498i
$732$	−1.00000	+	1.73205i	−0.0369611	+	0.0640184i
$733$	−9.00000	−	15.5885i	−0.332423	−	0.575773i	0.650564	−	0.759452i	$-0.274533\pi$
$733$	−9.00000	−	15.5885i	−0.332423	−	0.575773i	−0.982986	+	0.183679i	$0.941199\pi$
$734$	16.0000	+	27.7128i	0.590571	+	1.02290i
$735$	−1.00000	−	1.73205i	−0.0368856	−	0.0638877i
$736$	−2.00000			−0.0737210
$737$	3.00000	−	5.19615i	0.110506	−	0.191403i
$738$	−1.00000	+	1.73205i	−0.0368105	+	0.0637577i
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	0.680534	−	0.732717i	$-0.261748\pi$
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	−0.974818	+	0.223001i	$0.928415\pi$
$740$	6.00000			0.220564
$741$		0			0
$742$	−9.00000			−0.330400
$743$	50.0000			1.83432			0.917161	−	0.398517i	$-0.130475\pi$
$743$	50.0000			1.83432			0.917161	+	0.398517i	$0.130475\pi$
$744$	5.50000	−	0.866025i	0.201640	−	0.0317500i
$745$	−19.0000			−0.696106
$746$	−24.0000			−0.878702
$747$	−4.50000	+	7.79423i	−0.164646	+	0.285176i
$748$	12.0000			0.438763
$749$	−4.50000	−	7.79423i	−0.164426	−	0.284795i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	5.50000	−	9.52628i	0.200698	−	0.347619i	−0.748056	−	0.663636i	$-0.769012\pi$
$751$	5.50000	−	9.52628i	0.200698	−	0.347619i	0.948753	+	0.316017i	$0.102346\pi$
$752$	4.00000			0.145865
$753$		0			0
$754$	2.00000	+	3.46410i	0.0728357	+	0.126155i
$755$	4.50000	+	7.79423i	0.163772	+	0.283661i
$756$	−1.50000	+	2.59808i	−0.0545545	+	0.0944911i
$757$	26.0000	+	45.0333i	0.944986	+	1.63676i	0.755779	+	0.654827i	$0.227258\pi$
$757$	26.0000	+	45.0333i	0.944986	+	1.63676i	0.189207	+	0.981937i	$0.439408\pi$
$758$	−9.00000	+	15.5885i	−0.326895	+	0.566198i
$759$	6.00000			0.217786
$760$		0			0
$761$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$761$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$762$	6.50000	+	11.2583i	0.235470	+	0.407846i
$763$	−6.00000	+	10.3923i	−0.217215	+	0.376227i
$764$	7.00000	+	12.1244i	0.253251	+	0.438644i
$765$	−2.00000	−	3.46410i	−0.0723102	−	0.125245i
$766$	3.00000	+	5.19615i	0.108394	+	0.187745i
$767$	−36.0000			−1.29988
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−22.5000	+	38.9711i	−0.811371	+	1.40534i	0.100534	+	0.994934i	$0.467945\pi$
$769$	−22.5000	+	38.9711i	−0.811371	+	1.40534i	−0.911905	+	0.410402i	$0.865388\pi$
$770$	−4.50000	−	7.79423i	−0.162169	−	0.280885i
$771$	−10.0000			−0.360141
$772$	−10.5000	+	18.1865i	−0.377903	+	0.654548i
$773$	14.0000			0.503545			0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000			0.503545			0.251773	+	0.967786i	$0.418987\pi$
$774$	−4.00000			−0.143777
$775$	5.50000	−	0.866025i	0.197566	−	0.0311086i
$776$	−11.0000			−0.394877
$777$	−18.0000			−0.645746
$778$	−13.0000	+	22.5167i	−0.466073	+	0.807261i
$779$		0			0
$780$	−2.00000	−	3.46410i	−0.0716115	−	0.124035i
$781$	6.00000	−	10.3923i	0.214697	−	0.371866i
$782$	−4.00000	+	6.92820i	−0.143040	+	0.247752i
$783$	−1.00000			−0.0357371
$784$	−1.00000	−	1.73205i	−0.0357143	−	0.0618590i
$785$	11.0000	+	19.0526i	0.392607	+	0.680015i
$786$	−6.00000	−	10.3923i	−0.214013	−	0.370681i
$787$	−5.00000	+	8.66025i	−0.178231	+	0.308705i	−0.941275	−	0.337642i	$-0.890371\pi$
$787$	−5.00000	+	8.66025i	−0.178231	+	0.308705i	0.763044	+	0.646347i	$0.223704\pi$
$788$	9.00000	+	15.5885i	0.320612	+	0.555316i
$789$	−3.00000	+	5.19615i	−0.106803	+	0.184988i
$790$	−4.00000			−0.142314
$791$	36.0000			1.28001
$792$	−1.50000	+	2.59808i	−0.0533002	+	0.0923186i
$793$	4.00000	+	6.92820i	0.142044	+	0.246028i
$794$	−5.00000	+	8.66025i	−0.177443	+	0.307341i
$795$	1.50000	+	2.59808i	0.0531995	+	0.0921443i
$796$	5.50000	+	9.52628i	0.194942	+	0.337650i
$797$	−11.5000	−	19.9186i	−0.407351	−	0.705552i	0.587241	−	0.809412i	$-0.300214\pi$
$797$	−11.5000	−	19.9186i	−0.407351	−	0.705552i	−0.994592	+	0.103860i	$0.966881\pi$
$798$		0			0
$799$	8.00000	−	13.8564i	0.283020	−	0.490204i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−5.00000	−	8.66025i	−0.176666	−	0.305995i
$802$	8.00000			0.282490
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$	−2.00000			−0.0705346
$805$	6.00000			0.211472
$806$	8.00000	−	20.7846i	0.281788	−	0.732107i
$807$	−14.0000			−0.492823
$808$	19.0000			0.668418
$809$	8.00000	−	13.8564i	0.281265	−	0.487165i	−0.690432	−	0.723398i	$-0.742579\pi$
$809$	8.00000	−	13.8564i	0.281265	−	0.487165i	0.971697	+	0.236232i	$0.0759127\pi$
$810$	1.00000			0.0351364
$811$	15.0000	+	25.9808i	0.526721	+	0.912308i	0.999515	+	0.0311349i	$0.00991216\pi$
$811$	15.0000	+	25.9808i	0.526721	+	0.912308i	−0.472794	+	0.881173i	$0.656755\pi$
$812$	1.50000	−	2.59808i	0.0526397	−	0.0911746i
$813$	0.500000	−	0.866025i	0.0175358	−	0.0303728i
$814$	−18.0000			−0.630900
$815$	−5.00000	−	8.66025i	−0.175142	−	0.303355i
$816$	−2.00000	−	3.46410i	−0.0700140	−	0.121268i
$817$		0			0
$818$	−6.50000	+	11.2583i	−0.227267	+	0.393638i
$819$	6.00000	+	10.3923i	0.209657	+	0.363137i
$820$	−1.00000	+	1.73205i	−0.0349215	+	0.0604858i
$821$	1.00000			0.0349002			0.0174501	−	0.999848i	$-0.494445\pi$
$821$	1.00000			0.0349002			0.0174501	+	0.999848i	$0.494445\pi$
$822$	−16.0000			−0.558064
$823$	10.5000	−	18.1865i	0.366007	−	0.633943i	−0.622930	−	0.782277i	$-0.714058\pi$
$823$	10.5000	−	18.1865i	0.366007	−	0.633943i	0.988937	+	0.148335i	$0.0473913\pi$
$824$	6.50000	+	11.2583i	0.226438	+	0.392203i
$825$	−1.50000	+	2.59808i	−0.0522233	+	0.0904534i
$826$	13.5000	+	23.3827i	0.469725	+	0.813588i
$827$	−4.00000	−	6.92820i	−0.139094	−	0.240917i	0.788060	−	0.615598i	$-0.211086\pi$
$827$	−4.00000	−	6.92820i	−0.139094	−	0.240917i	−0.927154	+	0.374681i	$0.877752\pi$
$828$	−1.00000	−	1.73205i	−0.0347524	−	0.0601929i
$829$	16.0000			0.555703			0.277851	−	0.960624i	$-0.410378\pi$
$829$	16.0000			0.555703			0.277851	+	0.960624i	$0.410378\pi$
$830$	−4.50000	+	7.79423i	−0.156197	+	0.270542i
$831$		0			0
$832$	−2.00000	−	3.46410i	−0.0693375	−	0.120096i
$833$	−8.00000			−0.277184
$834$	−2.00000	+	3.46410i	−0.0692543	+	0.119952i
$835$	−2.00000			−0.0692129
$836$		0			0
$837$	3.50000	+	4.33013i	0.120978	+	0.149671i
$838$	−9.00000			−0.310900
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$	−1.50000	+	2.59808i	−0.0517549	+	0.0896421i
$841$	−28.0000			−0.965517
$842$	−17.0000	−	29.4449i	−0.585859	−	1.01474i
$843$	−13.0000	+	22.5167i	−0.447744	+	0.775515i
$844$	−4.00000	+	6.92820i	−0.137686	+	0.238479i
$845$	−3.00000			−0.103203
$846$	2.00000	+	3.46410i	0.0687614	+	0.119098i
$847$	−3.00000	−	5.19615i	−0.103081	−	0.178542i
$848$	1.50000	+	2.59808i	0.0515102	+	0.0892183i
$849$		0			0
$850$	−2.00000	−	3.46410i	−0.0685994	−	0.118818i
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$	−4.00000			−0.137038
$853$	−44.0000			−1.50653			−0.753266	−	0.657716i	$-0.771523\pi$
$853$	−44.0000			−1.50653			−0.753266	+	0.657716i	$0.771523\pi$
$854$	3.00000	−	5.19615i	0.102658	−	0.177809i
$855$		0			0
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$857$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$858$	6.00000	+	10.3923i	0.204837	+	0.354787i
$859$	11.0000	+	19.0526i	0.375315	+	0.650065i	0.990374	−	0.138416i	$-0.0442012\pi$
$859$	11.0000	+	19.0526i	0.375315	+	0.650065i	−0.615059	+	0.788481i	$0.710868\pi$
$860$	−4.00000			−0.136399
$861$	3.00000	−	5.19615i	0.102240	−	0.177084i
$862$	−16.0000	+	27.7128i	−0.544962	+	0.943902i
$863$	−8.00000	−	13.8564i	−0.272323	−	0.471678i	0.697133	−	0.716942i	$-0.254459\pi$
$863$	−8.00000	−	13.8564i	−0.272323	−	0.471678i	−0.969456	+	0.245264i	$0.921125\pi$
$864$	1.00000			0.0340207
$865$	−0.500000	+	0.866025i	−0.0170005	+	0.0294457i
$866$	−26.0000			−0.883516
$867$	1.00000			0.0339618
$868$	−16.5000	+	2.59808i	−0.560046	+	0.0881845i
$869$	12.0000			0.407072
$870$	−1.00000			−0.0339032
$871$	−4.00000	+	6.92820i	−0.135535	+	0.234753i
$872$	4.00000			0.135457
$873$	−5.50000	−	9.52628i	−0.186147	−	0.322416i
$874$		0			0
$875$	−1.50000	+	2.59808i	−0.0507093	+	0.0878310i
$876$	−2.00000			−0.0675737
$877$	−17.0000	−	29.4449i	−0.574049	−	0.994282i	−0.996144	−	0.0877308i	$-0.972038\pi$
$877$	−17.0000	−	29.4449i	−0.574049	−	0.994282i	0.422095	−	0.906552i	$-0.361295\pi$
$878$	−1.50000	−	2.59808i	−0.0506225	−	0.0876808i
$879$	10.5000	+	18.1865i	0.354156	+	0.613417i
$880$	−1.50000	+	2.59808i	−0.0505650	+	0.0875811i
$881$	−7.00000	−	12.1244i	−0.235836	−	0.408480i	0.723679	−	0.690136i	$-0.242449\pi$
$881$	−7.00000	−	12.1244i	−0.235836	−	0.408480i	−0.959515	+	0.281656i	$0.909116\pi$
$882$	1.00000	−	1.73205i	0.0336718	−	0.0583212i
$883$	2.00000			0.0673054			0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000			0.0673054			0.0336527	+	0.999434i	$0.489286\pi$
$884$	−16.0000			−0.538138
$885$	4.50000	−	7.79423i	0.151266	−	0.262000i
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	17.0000	−	29.4449i	0.570804	−	0.988662i	−0.425679	−	0.904874i	$-0.639965\pi$
$887$	17.0000	−	29.4449i	0.570804	−	0.988662i	0.996484	−	0.0837878i	$-0.0267018\pi$
$888$	3.00000	+	5.19615i	0.100673	+	0.174371i
$889$	−19.5000	−	33.7750i	−0.654009	−	1.13278i
$890$	−5.00000	−	8.66025i	−0.167600	−	0.290292i
$891$	−3.00000			−0.100504
$892$	−4.50000	+	7.79423i	−0.150671	+	0.260970i
$893$		0			0
$894$	−9.50000	−	16.4545i	−0.317728	−	0.550320i
$895$	−19.0000			−0.635100
$896$	−1.50000	+	2.59808i	−0.0501115	+	0.0867956i
$897$	−8.00000			−0.267112
$898$	−26.0000			−0.867631
$899$	−3.50000	−	4.33013i	−0.116732	−	0.144418i
$900$	1.00000			0.0333333
$901$	12.0000			0.399778
$902$	3.00000	−	5.19615i	0.0998891	−	0.173013i
$903$	12.0000			0.399335
$904$	−6.00000	−	10.3923i	−0.199557	−	0.345643i
$905$	1.00000	−	1.73205i	0.0332411	−	0.0575753i
$906$	−4.50000	+	7.79423i	−0.149502	+	0.258946i
$907$	−16.0000			−0.531271			−0.265636	−	0.964073i	$-0.585582\pi$
$907$	−16.0000			−0.531271			−0.265636	+	0.964073i	$0.585582\pi$
$908$	1.50000	+	2.59808i	0.0497792	+	0.0862202i
$909$	9.50000	+	16.4545i	0.315095	+	0.545761i
$910$	6.00000	+	10.3923i	0.198898	+	0.344502i
$911$	14.0000	−	24.2487i	0.463841	−	0.803396i	−0.535308	−	0.844657i	$-0.679804\pi$
$911$	14.0000	−	24.2487i	0.463841	−	0.803396i	0.999148	+	0.0412615i	$0.0131377\pi$
$912$		0			0
$913$	13.5000	−	23.3827i	0.446785	−	0.773854i
$914$	26.0000			0.860004
$915$	−2.00000			−0.0661180
$916$	−11.0000	+	19.0526i	−0.363450	+	0.629514i
$917$	18.0000	+	31.1769i	0.594412	+	1.02955i
$918$	2.00000	−	3.46410i	0.0660098	−	0.114332i
$919$	−21.5000	−	37.2391i	−0.709220	−	1.22840i	−0.965147	−	0.261708i	$-0.915714\pi$
$919$	−21.5000	−	37.2391i	−0.709220	−	1.22840i	0.255927	−	0.966696i	$-0.417619\pi$
$920$	−1.00000	−	1.73205i	−0.0329690	−	0.0571040i
$921$	−4.00000	−	6.92820i	−0.131804	−	0.228292i
$922$	9.00000			0.296399
$923$	−8.00000	+	13.8564i	−0.263323	+	0.456089i
$924$	4.50000	−	7.79423i	0.148039	−	0.256411i
$925$	3.00000	+	5.19615i	0.0986394	+	0.170848i
$926$	5.00000			0.164310
$927$	−6.50000	+	11.2583i	−0.213488	+	0.369772i
$928$	−1.00000			−0.0328266
$929$	16.0000			0.524943			0.262471	−	0.964940i	$-0.415462\pi$
$929$	16.0000			0.524943			0.262471	+	0.964940i	$0.415462\pi$
$930$	3.50000	+	4.33013i	0.114770	+	0.141990i
$931$		0			0
$932$	−6.00000			−0.196537
$933$	12.0000	−	20.7846i	0.392862	−	0.680458i
$934$	27.0000			0.883467
$935$	6.00000	+	10.3923i	0.196221	+	0.339865i
$936$	2.00000	−	3.46410i	0.0653720	−	0.113228i
$937$	29.0000	−	50.2295i	0.947389	−	1.64093i	0.196492	−	0.980505i	$-0.437045\pi$
$937$	29.0000	−	50.2295i	0.947389	−	1.64093i	0.750896	−	0.660420i	$-0.229622\pi$
$938$	6.00000			0.195907
$939$	10.5000	+	18.1865i	0.342655	+	0.593495i
$940$	2.00000	+	3.46410i	0.0652328	+	0.112987i
$941$	8.50000	+	14.7224i	0.277092	+	0.479938i	0.970661	−	0.240453i	$-0.0772960\pi$
$941$	8.50000	+	14.7224i	0.277092	+	0.479938i	−0.693569	+	0.720390i	$0.743963\pi$
$942$	−11.0000	+	19.0526i	−0.358399	+	0.620766i
$943$	2.00000	+	3.46410i	0.0651290	+	0.112807i
$944$	4.50000	−	7.79423i	0.146463	−	0.253681i
$945$	−3.00000			−0.0975900
$946$	12.0000			0.390154
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	0.152106	+	0.988364i	$0.451394\pi$
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	−0.932002	+	0.362454i	$0.881939\pi$
$948$	−2.00000	−	3.46410i	−0.0649570	−	0.112509i
$949$	−4.00000	+	6.92820i	−0.129845	+	0.224899i
$950$		0			0
$951$	6.50000	+	11.2583i	0.210777	+	0.365076i
$952$	6.00000	+	10.3923i	0.194461	+	0.336817i
$953$	2.00000			0.0647864			0.0323932	−	0.999475i	$-0.489687\pi$
$953$	2.00000			0.0647864			0.0323932	+	0.999475i	$0.489687\pi$
$954$	−1.50000	+	2.59808i	−0.0485643	+	0.0841158i
$955$	−7.00000	+	12.1244i	−0.226515	+	0.392335i
$956$	12.0000	+	20.7846i	0.388108	+	0.672222i
$957$	3.00000			0.0969762
$958$	6.00000	−	10.3923i	0.193851	−	0.335760i
$959$	48.0000			1.55000
$960$	1.00000			0.0322749
$961$	−6.50000	+	30.3109i	−0.209677	+	0.977771i
$962$	24.0000			0.773791
$963$	−3.00000			−0.0966736
$964$	−7.50000	+	12.9904i	−0.241559	+	0.418392i
$965$	−21.0000			−0.676014
$966$	3.00000	+	5.19615i	0.0965234	+	0.167183i
$967$	24.0000	−	41.5692i	0.771788	−	1.33678i	−0.164794	−	0.986328i	$-0.552696\pi$
$967$	24.0000	−	41.5692i	0.771788	−	1.33678i	0.936582	−	0.350448i	$-0.113971\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$		0			0
$970$	−5.50000	−	9.52628i	−0.176594	−	0.305870i
$971$	22.5000	+	38.9711i	0.722059	+	1.25064i	0.960173	+	0.279406i	$0.0901376\pi$
$971$	22.5000	+	38.9711i	0.722059	+	1.25064i	−0.238114	+	0.971237i	$0.576529\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	6.00000	−	10.3923i	0.192351	−	0.333162i
$974$	14.5000	+	25.1147i	0.464610	+	0.804728i
$975$	2.00000	−	3.46410i	0.0640513	−	0.110940i
$976$	−2.00000			−0.0640184
$977$	−52.0000			−1.66363			−0.831814	−	0.555055i	$-0.812697\pi$
$977$	−52.0000			−1.66363			−0.831814	+	0.555055i	$0.812697\pi$
$978$	5.00000	−	8.66025i	0.159882	−	0.276924i
$979$	15.0000	+	25.9808i	0.479402	+	0.830349i
$980$	1.00000	−	1.73205i	0.0319438	−	0.0553283i
$981$	2.00000	+	3.46410i	0.0638551	+	0.110600i
$982$	−9.50000	−	16.4545i	−0.303157	−	0.525084i
$983$	7.00000	+	12.1244i	0.223265	+	0.386707i	0.955798	−	0.294025i	$-0.0949950\pi$
$983$	7.00000	+	12.1244i	0.223265	+	0.386707i	−0.732532	+	0.680732i	$0.761662\pi$
$984$	−2.00000			−0.0637577
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$	−2.00000	+	3.46410i	−0.0636930	+	0.110319i
$987$	−6.00000	−	10.3923i	−0.190982	−	0.330791i
$988$		0			0
$989$	−4.00000	+	6.92820i	−0.127193	+	0.220304i
$990$	−3.00000			−0.0953463
$991$	56.0000			1.77890			0.889449	−	0.457034i	$-0.151088\pi$
$991$	56.0000			1.77890			0.889449	+	0.457034i	$0.151088\pi$
$992$	3.50000	+	4.33013i	0.111125	+	0.137482i
$993$	30.0000			0.952021
$994$	12.0000			0.380617
$995$	−5.50000	+	9.52628i	−0.174362	+	0.302003i
$996$	−9.00000			−0.285176
$997$	21.0000	+	36.3731i	0.665077	+	1.15195i	0.979265	+	0.202586i	$0.0649345\pi$
$997$	21.0000	+	36.3731i	0.665077	+	1.15195i	−0.314188	+	0.949361i	$0.601732\pi$
$998$	11.0000	−	19.0526i	0.348199	−	0.603098i
$999$	−3.00000	+	5.19615i	−0.0949158	+	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.i.c.811.1	yes	2
31.25	even	3	inner	930.2.i.c.211.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.i.c.211.1	✓	2	31.25	even	3	inner
930.2.i.c.811.1	yes	2	1.1	even	1	trivial

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(1.50000 - 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(1.50000 + 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} +(-2.00000 - 3.46410i) q^{13} +(-1.50000 + 2.59808i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(2.00000 - 3.46410i) q^{17} +(0.500000 + 0.866025i) q^{18} +(0.500000 + 0.866025i) q^{20} +(-1.50000 - 2.59808i) q^{21} +(-1.50000 - 2.59808i) q^{22} +2.00000 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(2.00000 + 3.46410i) q^{26} -1.00000 q^{27} +(1.50000 - 2.59808i) q^{28} +1.00000 q^{29} -1.00000 q^{30} +(-3.50000 - 4.33013i) q^{31} -1.00000 q^{32} +3.00000 q^{33} +(-2.00000 + 3.46410i) q^{34} +3.00000 q^{35} +(-0.500000 - 0.866025i) q^{36} +(3.00000 - 5.19615i) q^{37} -4.00000 q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.00000 + 1.73205i) q^{41} +(1.50000 + 2.59808i) q^{42} +(-2.00000 + 3.46410i) q^{43} +(1.50000 + 2.59808i) q^{44} +(0.500000 - 0.866025i) q^{45} -2.00000 q^{46} +4.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-2.00000 - 3.46410i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(1.50000 + 2.59808i) q^{53} +1.00000 q^{54} +(-1.50000 + 2.59808i) q^{55} +(-1.50000 + 2.59808i) q^{56} -1.00000 q^{58} +(4.50000 - 7.79423i) q^{59} +1.00000 q^{60} -2.00000 q^{61} +(3.50000 + 4.33013i) q^{62} -3.00000 q^{63} +1.00000 q^{64} +(2.00000 - 3.46410i) q^{65} -3.00000 q^{66} +(-1.00000 - 1.73205i) q^{67} +(2.00000 - 3.46410i) q^{68} +(1.00000 - 1.73205i) q^{69} -3.00000 q^{70} +(-2.00000 - 3.46410i) q^{71} +(0.500000 + 0.866025i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(-3.00000 + 5.19615i) q^{74} +(0.500000 + 0.866025i) q^{75} +9.00000 q^{77} +4.00000 q^{78} +(2.00000 - 3.46410i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.00000 - 1.73205i) q^{82} +(-4.50000 - 7.79423i) q^{83} +(-1.50000 - 2.59808i) q^{84} +4.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{87} +(-1.50000 - 2.59808i) q^{88} +10.0000 q^{89} +(-0.500000 + 0.866025i) q^{90} -12.0000 q^{91} +2.00000 q^{92} +(-5.50000 + 0.866025i) q^{93} -4.00000 q^{94} +(-0.500000 + 0.866025i) q^{96} +11.0000 q^{97} +(1.00000 + 1.73205i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} + q^{5} - q^{6} + 3 q^{7} - 2 q^{8} - q^{9} - q^{10} + 3 q^{11} + q^{12} - 4 q^{13} - 3 q^{14} + 2 q^{15} + 2 q^{16} + 4 q^{17} + q^{18} + q^{20} - 3 q^{21} - 3 q^{22}+ \cdots + 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 + q^5 - q^6 + 3 * q^7 - 2 * q^8 - q^9 - q^10 + 3 * q^11 + q^12 - 4 * q^13 - 3 * q^14 + 2 * q^15 + 2 * q^16 + 4 * q^17 + q^18 + q^20 - 3 * q^21 - 3 * q^22 + 4 * q^23 - q^24 - q^25 + 4 * q^26 - 2 * q^27 + 3 * q^28 + 2 * q^29 - 2 * q^30 - 7 * q^31 - 2 * q^32 + 6 * q^33 - 4 * q^34 + 6 * q^35 - q^36 + 6 * q^37 - 8 * q^39 - q^40 + 2 * q^41 + 3 * q^42 - 4 * q^43 + 3 * q^44 + q^45 - 4 * q^46 + 8 * q^47 + q^48 - 2 * q^49 + q^50 - 4 * q^51 - 4 * q^52 + 3 * q^53 + 2 * q^54 - 3 * q^55 - 3 * q^56 - 2 * q^58 + 9 * q^59 + 2 * q^60 - 4 * q^61 + 7 * q^62 - 6 * q^63 + 2 * q^64 + 4 * q^65 - 6 * q^66 - 2 * q^67 + 4 * q^68 + 2 * q^69 - 6 * q^70 - 4 * q^71 + q^72 - 2 * q^73 - 6 * q^74 + q^75 + 18 * q^77 + 8 * q^78 + 4 * q^79 + q^80 - q^81 - 2 * q^82 - 9 * q^83 - 3 * q^84 + 8 * q^85 + 4 * q^86 + q^87 - 3 * q^88 + 20 * q^89 - q^90 - 24 * q^91 + 4 * q^92 - 11 * q^93 - 8 * q^94 - q^96 + 22 * q^97 + 2 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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