LMFDB - Embedded newform 930.2.i.g.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(211,930)]

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, 0, 2]))

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

//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);

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: 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:	$2$
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			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	930.211
Dual form			930.2.i.g.811.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.00000 - 3.46410i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(-2.00000 - 3.46410i) 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} +(1.00000 - 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(-1.50000 - 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.500000 - 0.866025i) q^{20} +(2.00000 - 3.46410i) q^{21} +(1.50000 - 2.59808i) q^{22} +3.00000 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} -1.00000 q^{27} +(-2.00000 - 3.46410i) q^{28} +2.00000 q^{29} +1.00000 q^{30} +(2.00000 + 5.19615i) q^{31} +1.00000 q^{32} +3.00000 q^{33} +(-1.50000 - 2.59808i) q^{34} -4.00000 q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.500000 - 0.866025i) q^{37} +2.00000 q^{39} +(0.500000 - 0.866025i) q^{40} +(1.00000 - 1.73205i) q^{41} +(2.00000 - 3.46410i) q^{42} +(0.500000 + 0.866025i) q^{43} +(1.50000 - 2.59808i) q^{44} +(0.500000 + 0.866025i) q^{45} +3.00000 q^{46} -1.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.50000 - 2.59808i) q^{51} +(1.00000 - 1.73205i) q^{52} +(-2.00000 + 3.46410i) q^{53} -1.00000 q^{54} +(-1.50000 - 2.59808i) q^{55} +(-2.00000 - 3.46410i) q^{56} +2.00000 q^{58} +(2.00000 + 3.46410i) q^{59} +1.00000 q^{60} +6.00000 q^{61} +(2.00000 + 5.19615i) q^{62} +4.00000 q^{63} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +3.00000 q^{66} +(-5.50000 + 9.52628i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(1.50000 + 2.59808i) q^{69} -4.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(7.00000 - 12.1244i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(0.500000 - 0.866025i) q^{75} -12.0000 q^{77} +2.00000 q^{78} +(6.50000 + 11.2583i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +(-6.00000 + 10.3923i) q^{83} +(2.00000 - 3.46410i) q^{84} -3.00000 q^{85} +(0.500000 + 0.866025i) q^{86} +(1.00000 + 1.73205i) q^{87} +(1.50000 - 2.59808i) q^{88} -8.00000 q^{89} +(0.500000 + 0.866025i) q^{90} -8.00000 q^{91} +3.00000 q^{92} +(-3.50000 + 4.33013i) q^{93} -1.00000 q^{94} +(0.500000 + 0.866025i) q^{96} +14.0000 q^{97} +(-4.50000 + 7.79423i) 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} - 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^5 + q^6 - 4 * q^7 + 2 * q^8 - q^9	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} - 4 q^{7} + 2 q^{8} - q^{9} + q^{10} + 3 q^{11} + q^{12} + 2 q^{13} - 4 q^{14} + 2 q^{15} + 2 q^{16} - 3 q^{17} - q^{18} + q^{20} + 4 q^{21} + 3 q^{22} + 6 q^{23} + q^{24} - q^{25} + 2 q^{26} - 2 q^{27} - 4 q^{28} + 4 q^{29} + 2 q^{30} + 4 q^{31} + 2 q^{32} + 6 q^{33} - 3 q^{34} - 8 q^{35} - q^{36} - q^{37} + 4 q^{39} + q^{40} + 2 q^{41} + 4 q^{42} + q^{43} + 3 q^{44} + q^{45} + 6 q^{46} - 2 q^{47} + q^{48} - 9 q^{49} - q^{50} + 3 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 3 q^{55} - 4 q^{56} + 4 q^{58} + 4 q^{59} + 2 q^{60} + 12 q^{61} + 4 q^{62} + 8 q^{63} + 2 q^{64} - 2 q^{65} + 6 q^{66} - 11 q^{67} - 3 q^{68} + 3 q^{69} - 8 q^{70} - 6 q^{71} - q^{72} + 14 q^{73} - q^{74} + q^{75} - 24 q^{77} + 4 q^{78} + 13 q^{79} + q^{80} - q^{81} + 2 q^{82} - 12 q^{83} + 4 q^{84} - 6 q^{85} + q^{86} + 2 q^{87} + 3 q^{88} - 16 q^{89} + q^{90} - 16 q^{91} + 6 q^{92} - 7 q^{93} - 2 q^{94} + q^{96} + 28 q^{97} - 9 q^{98} + 3 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^5 + q^6 - 4 * q^7 + 2 * q^8 - q^9 + q^10 + 3 * q^11 + q^12 + 2 * q^13 - 4 * q^14 + 2 * q^15 + 2 * q^16 - 3 * q^17 - q^18 + q^20 + 4 * q^21 + 3 * q^22 + 6 * q^23 + q^24 - q^25 + 2 * q^26 - 2 * q^27 - 4 * q^28 + 4 * q^29 + 2 * q^30 + 4 * q^31 + 2 * q^32 + 6 * q^33 - 3 * q^34 - 8 * q^35 - q^36 - q^37 + 4 * q^39 + q^40 + 2 * q^41 + 4 * q^42 + q^43 + 3 * q^44 + q^45 + 6 * q^46 - 2 * q^47 + q^48 - 9 * q^49 - q^50 + 3 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 3 * q^55 - 4 * q^56 + 4 * q^58 + 4 * q^59 + 2 * q^60 + 12 * q^61 + 4 * q^62 + 8 * q^63 + 2 * q^64 - 2 * q^65 + 6 * q^66 - 11 * q^67 - 3 * q^68 + 3 * q^69 - 8 * q^70 - 6 * q^71 - q^72 + 14 * q^73 - q^74 + q^75 - 24 * q^77 + 4 * q^78 + 13 * q^79 + q^80 - q^81 + 2 * q^82 - 12 * q^83 + 4 * q^84 - 6 * q^85 + q^86 + 2 * q^87 + 3 * q^88 - 16 * q^89 + q^90 - 16 * q^91 + 6 * q^92 - 7 * q^93 - 2 * q^94 + q^96 + 28 * q^97 - 9 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	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
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	0.188982	−	0.981981i	$-0.439481\pi$
$8$	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	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$	−2.00000	−	3.46410i	−0.534522	−	0.925820i
$15$	1.00000			0.258199
$16$	1.00000			0.250000
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$19$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	2.00000	−	3.46410i	0.436436	−	0.755929i
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	3.00000			0.625543			0.312772	−	0.949828i	$-0.398743\pi$
$23$	3.00000			0.625543			0.312772	+	0.949828i	$0.398743\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$	−1.00000			−0.192450
$28$	−2.00000	−	3.46410i	−0.377964	−	0.654654i
$29$	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			0.182574
$31$	2.00000	+	5.19615i	0.359211	+	0.933257i
$31$	2.00000	+	5.19615i	0.359211	+	0.933257i
$32$	1.00000			0.176777
$33$	3.00000			0.522233
$34$	−1.50000	−	2.59808i	−0.257248	−	0.445566i
$35$	−4.00000			−0.676123
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	0.821995	−	0.569495i	$-0.192861\pi$
$37$	−0.500000	−	0.866025i	−0.0821995	−	0.142374i	−0.904194	+	0.427121i	$0.859528\pi$
$38$		0			0
$39$	2.00000			0.320256
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	−0.777312	−	0.629115i	$-0.783417\pi$
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	0.933486	+	0.358614i	$0.116751\pi$
$42$	2.00000	−	3.46410i	0.308607	−	0.534522i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	3.00000			0.442326
$47$	−1.00000			−0.145865			−0.0729325	−	0.997337i	$-0.523236\pi$
$47$	−1.00000			−0.145865			−0.0729325	+	0.997337i	$0.523236\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	1.50000	−	2.59808i	0.210042	−	0.363803i
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	−0.970065	−	0.242846i	$-0.921919\pi$
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	0.695344	+	0.718677i	$0.255252\pi$
$54$	−1.00000			−0.136083
$55$	−1.50000	−	2.59808i	−0.202260	−	0.350325i
$56$	−2.00000	−	3.46410i	−0.267261	−	0.462910i
$57$		0			0
$58$	2.00000			0.262613
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$	1.00000			0.129099
$61$	6.00000			0.768221			0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000			0.768221			0.384111	+	0.923287i	$0.374508\pi$
$62$	2.00000	+	5.19615i	0.254000	+	0.659912i
$63$	4.00000			0.503953
$64$	1.00000			0.125000
$65$	−1.00000	−	1.73205i	−0.124035	−	0.214834i
$66$	3.00000			0.369274
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	0.305424	+	0.952217i	$0.401202\pi$
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$	1.50000	+	2.59808i	0.180579	+	0.312772i
$70$	−4.00000			−0.478091
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	−0.0869195	−	0.996215i	$-0.527702\pi$
$73$	7.00000	−	12.1244i	0.819288	−	1.41905i	0.906208	−	0.422833i	$-0.138964\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$		0			0
$77$	−12.0000			−1.36753
$78$	2.00000			0.226455
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	0.956325	+	0.292306i	$0.0944227\pi$
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	−0.225018	+	0.974355i	$0.572244\pi$
$80$	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
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	0.322396	+	0.946605i	$0.395512\pi$
$83$	−6.00000	+	10.3923i	−0.658586	+	1.14070i	−0.980982	+	0.194099i	$0.937822\pi$
$84$	2.00000	−	3.46410i	0.218218	−	0.377964i
$85$	−3.00000			−0.325396
$86$	0.500000	+	0.866025i	0.0539164	+	0.0933859i
$87$	1.00000	+	1.73205i	0.107211	+	0.185695i
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	−8.00000			−0.847998			−0.423999	−	0.905663i	$-0.639374\pi$
$89$	−8.00000			−0.847998			−0.423999	+	0.905663i	$0.639374\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	−8.00000			−0.838628
$92$	3.00000			0.312772
$93$	−3.50000	+	4.33013i	−0.362933	+	0.449013i
$94$	−1.00000			−0.103142
$95$		0			0
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	14.0000			1.42148			0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000			1.42148			0.710742	+	0.703452i	$0.248359\pi$
$98$	−4.50000	+	7.79423i	−0.454569	+	0.787336i
$99$	1.50000	+	2.59808i	0.150756	+	0.261116i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$	1.50000	−	2.59808i	0.148522	−	0.257248i
$103$	3.00000	−	5.19615i	0.295599	−	0.511992i	−0.679525	−	0.733652i	$-0.737814\pi$
$103$	3.00000	−	5.19615i	0.295599	−	0.511992i	0.975124	+	0.221660i	$0.0711475\pi$
$104$	1.00000	−	1.73205i	0.0980581	−	0.169842i
$105$	−2.00000	−	3.46410i	−0.195180	−	0.338062i
$106$	−2.00000	+	3.46410i	−0.194257	+	0.336463i
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	0.605308	−	0.795991i	$-0.293050\pi$
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	−0.992003	+	0.126217i	$0.959717\pi$
$108$	−1.00000			−0.0962250
$109$	12.0000			1.14939			0.574696	−	0.818367i	$-0.305120\pi$
$109$	12.0000			1.14939			0.574696	+	0.818367i	$0.305120\pi$
$110$	−1.50000	−	2.59808i	−0.143019	−	0.247717i
$111$	0.500000	−	0.866025i	0.0474579	−	0.0821995i
$112$	−2.00000	−	3.46410i	−0.188982	−	0.327327i
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	−0.841549	−	0.540181i	$-0.818356\pi$
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	0.888585	+	0.458712i	$0.151689\pi$
$114$		0			0
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$	2.00000			0.185695
$117$	1.00000	+	1.73205i	0.0924500	+	0.160128i
$118$	2.00000	+	3.46410i	0.184115	+	0.318896i
$119$	−6.00000	+	10.3923i	−0.550019	+	0.952661i
$120$	1.00000			0.0912871
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	6.00000			0.543214
$123$	2.00000			0.180334
$124$	2.00000	+	5.19615i	0.179605	+	0.466628i
$125$	−1.00000			−0.0894427
$126$	4.00000			0.356348
$127$	−3.00000	−	5.19615i	−0.266207	−	0.461084i	0.701672	−	0.712500i	$-0.252437\pi$
$127$	−3.00000	−	5.19615i	−0.266207	−	0.461084i	−0.967879	+	0.251416i	$0.919104\pi$
$128$	1.00000			0.0883883
$129$	−0.500000	+	0.866025i	−0.0440225	+	0.0762493i
$130$	−1.00000	−	1.73205i	−0.0877058	−	0.151911i
$131$	−10.5000	−	18.1865i	−0.917389	−	1.58896i	−0.803365	−	0.595487i	$-0.796959\pi$
$131$	−10.5000	−	18.1865i	−0.917389	−	1.58896i	−0.114024	−	0.993478i	$-0.536374\pi$
$132$	3.00000			0.261116
$133$		0			0
$134$	−5.50000	+	9.52628i	−0.475128	+	0.822945i
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	−0.794808	−	0.606861i	$-0.792428\pi$
$137$	1.50000	−	2.59808i	0.128154	−	0.221969i	0.922961	+	0.384893i	$0.125762\pi$
$138$	1.50000	+	2.59808i	0.127688	+	0.221163i
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$	−4.00000			−0.338062
$141$	−0.500000	−	0.866025i	−0.0421076	−	0.0729325i
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	−3.00000	−	5.19615i	−0.250873	−	0.434524i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.00000	−	1.73205i	0.0830455	−	0.143839i
$146$	7.00000	−	12.1244i	0.579324	−	1.00342i
$147$	−9.00000			−0.742307
$148$	−0.500000	−	0.866025i	−0.0410997	−	0.0711868i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	−23.0000			−1.87171			−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−23.0000			−1.87171			−0.935857	+	0.352381i	$0.885372\pi$
$152$		0			0
$153$	3.00000			0.242536
$154$	−12.0000			−0.966988
$155$	5.50000	+	0.866025i	0.441771	+	0.0695608i
$156$	2.00000			0.160128
$157$	18.0000			1.43656			0.718278	−	0.695756i	$-0.244931\pi$
$157$	18.0000			1.43656			0.718278	+	0.695756i	$0.244931\pi$
$158$	6.50000	+	11.2583i	0.517112	+	0.895665i
$159$	−4.00000			−0.317221
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	−6.00000	−	10.3923i	−0.472866	−	0.819028i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	3.00000			0.234978			0.117489	−	0.993074i	$-0.462515\pi$
$163$	3.00000			0.234978			0.117489	+	0.993074i	$0.462515\pi$
$164$	1.00000	−	1.73205i	0.0780869	−	0.135250i
$165$	1.50000	−	2.59808i	0.116775	−	0.202260i
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$	−8.00000	−	13.8564i	−0.619059	−	1.07224i	−0.989658	−	0.143448i	$-0.954181\pi$
$167$	−8.00000	−	13.8564i	−0.619059	−	1.07224i	0.370599	−	0.928793i	$-0.379152\pi$
$168$	2.00000	−	3.46410i	0.154303	−	0.267261i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−3.00000			−0.230089
$171$		0			0
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$	−11.0000	+	19.0526i	−0.836315	+	1.44854i	0.0566411	+	0.998395i	$0.481961\pi$
$173$	−11.0000	+	19.0526i	−0.836315	+	1.44854i	−0.892956	+	0.450145i	$0.851372\pi$
$174$	1.00000	+	1.73205i	0.0758098	+	0.131306i
$175$	−2.00000	+	3.46410i	−0.151186	+	0.261861i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	−2.00000	+	3.46410i	−0.150329	+	0.260378i
$178$	−8.00000			−0.599625
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	0.983742	−	0.179585i	$-0.0574756\pi$
$179$	4.50000	+	7.79423i	0.336346	+	0.582568i	−0.647397	+	0.762153i	$0.724142\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−6.00000	+	10.3923i	−0.445976	+	0.772454i	−0.998120	−	0.0612954i	$-0.980477\pi$
$181$	−6.00000	+	10.3923i	−0.445976	+	0.772454i	0.552143	+	0.833749i	$0.313810\pi$
$182$	−8.00000			−0.592999
$183$	3.00000	+	5.19615i	0.221766	+	0.384111i
$184$	3.00000			0.221163
$185$	−1.00000			−0.0735215
$186$	−3.50000	+	4.33013i	−0.256632	+	0.317500i
$187$	−9.00000			−0.658145
$188$	−1.00000			−0.0729325
$189$	2.00000	+	3.46410i	0.145479	+	0.251976i
$190$		0			0
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	−0.988255	−	0.152813i	$-0.951167\pi$
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	0.626468	+	0.779447i	$0.284500\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	0.899770	−	0.436365i	$-0.143734\pi$
$193$	1.00000	+	1.73205i	0.0719816	+	0.124676i	−0.827788	+	0.561041i	$0.810401\pi$
$194$	14.0000			1.00514
$195$	1.00000	−	1.73205i	0.0716115	−	0.124035i
$196$	−4.50000	+	7.79423i	−0.321429	+	0.556731i
$197$	4.00000	−	6.92820i	0.284988	−	0.493614i	−0.687618	−	0.726073i	$-0.741344\pi$
$197$	4.00000	−	6.92820i	0.284988	−	0.493614i	0.972606	+	0.232458i	$0.0746770\pi$
$198$	1.50000	+	2.59808i	0.106600	+	0.184637i
$199$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$199$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−11.0000			−0.775880
$202$	−3.00000			−0.211079
$203$	−4.00000	−	6.92820i	−0.280745	−	0.486265i
$204$	1.50000	−	2.59808i	0.105021	−	0.181902i
$205$	−1.00000	−	1.73205i	−0.0698430	−	0.120972i
$206$	3.00000	−	5.19615i	0.209020	−	0.362033i
$207$	−1.50000	+	2.59808i	−0.104257	+	0.180579i
$208$	1.00000	−	1.73205i	0.0693375	−	0.120096i
$209$		0			0
$210$	−2.00000	−	3.46410i	−0.138013	−	0.239046i
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	0.970229	−	0.242190i	$-0.0778659\pi$
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	−0.694857	+	0.719148i	$0.744533\pi$
$212$	−2.00000	+	3.46410i	−0.137361	+	0.237915i
$213$	−6.00000			−0.411113
$214$	−4.00000	−	6.92820i	−0.273434	−	0.473602i
$215$	1.00000			0.0681994
$216$	−1.00000			−0.0680414
$217$	14.0000	−	17.3205i	0.950382	−	1.17579i
$218$	12.0000			0.812743
$219$	14.0000			0.946032
$220$	−1.50000	−	2.59808i	−0.101130	−	0.175162i
$221$	−6.00000			−0.403604
$222$	0.500000	−	0.866025i	0.0335578	−	0.0581238i
$223$	13.0000	+	22.5167i	0.870544	+	1.50783i	0.861435	+	0.507869i	$0.169566\pi$
$223$	13.0000	+	22.5167i	0.870544	+	1.50783i	0.00910984	+	0.999959i	$0.497100\pi$
$224$	−2.00000	−	3.46410i	−0.133631	−	0.231455i
$225$	1.00000			0.0666667
$226$	0.500000	−	0.866025i	0.0332595	−	0.0576072i
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$		0			0
$229$	14.0000	+	24.2487i	0.925146	+	1.60240i	0.791326	+	0.611394i	$0.209391\pi$
$229$	14.0000	+	24.2487i	0.925146	+	1.60240i	0.133820	+	0.991006i	$0.457276\pi$
$230$	1.50000	−	2.59808i	0.0989071	−	0.171312i
$231$	−6.00000	−	10.3923i	−0.394771	−	0.683763i
$232$	2.00000			0.131306
$233$	−11.0000			−0.720634			−0.360317	−	0.932830i	$-0.617331\pi$
$233$	−11.0000			−0.720634			−0.360317	+	0.932830i	$0.617331\pi$
$234$	1.00000	+	1.73205i	0.0653720	+	0.113228i
$235$	−0.500000	+	0.866025i	−0.0326164	+	0.0564933i
$236$	2.00000	+	3.46410i	0.130189	+	0.225494i
$237$	−6.50000	+	11.2583i	−0.422220	+	0.731307i
$238$	−6.00000	+	10.3923i	−0.388922	+	0.673633i
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	−0.946590	−	0.322440i	$-0.895497\pi$
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	0.752536	+	0.658551i	$0.228830\pi$
$240$	1.00000			0.0645497
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	6.00000			0.384111
$245$	4.50000	+	7.79423i	0.287494	+	0.497955i
$246$	2.00000			0.127515
$247$		0			0
$248$	2.00000	+	5.19615i	0.127000	+	0.329956i
$249$	−12.0000			−0.760469
$250$	−1.00000			−0.0632456
$251$	−4.50000	−	7.79423i	−0.284037	−	0.491967i	0.688338	−	0.725390i	$-0.258341\pi$
$251$	−4.50000	−	7.79423i	−0.284037	−	0.491967i	−0.972375	+	0.233423i	$0.925007\pi$
$252$	4.00000			0.251976
$253$	4.50000	−	7.79423i	0.282913	−	0.490019i
$254$	−3.00000	−	5.19615i	−0.188237	−	0.326036i
$255$	−1.50000	−	2.59808i	−0.0939336	−	0.162698i
$256$	1.00000			0.0625000
$257$	6.50000	−	11.2583i	0.405459	−	0.702275i	−0.588916	−	0.808194i	$-0.700445\pi$
$257$	6.50000	−	11.2583i	0.405459	−	0.702275i	0.994375	+	0.105919i	$0.0337784\pi$
$258$	−0.500000	+	0.866025i	−0.0311286	+	0.0539164i
$259$	−2.00000	+	3.46410i	−0.124274	+	0.215249i
$260$	−1.00000	−	1.73205i	−0.0620174	−	0.107417i
$261$	−1.00000	+	1.73205i	−0.0618984	+	0.107211i
$262$	−10.5000	−	18.1865i	−0.648692	−	1.12357i
$263$	−23.0000			−1.41824			−0.709120	−	0.705087i	$-0.750908\pi$
$263$	−23.0000			−1.41824			−0.709120	+	0.705087i	$0.750908\pi$
$264$	3.00000			0.184637
$265$	2.00000	+	3.46410i	0.122859	+	0.212798i
$266$		0			0
$267$	−4.00000	−	6.92820i	−0.244796	−	0.423999i
$268$	−5.50000	+	9.52628i	−0.335966	+	0.581910i
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	0.345192	+	0.938532i	$0.387814\pi$
$269$	−10.5000	+	18.1865i	−0.640196	+	1.10885i	−0.985389	+	0.170321i	$0.945520\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$	−1.50000	−	2.59808i	−0.0909509	−	0.157532i
$273$	−4.00000	−	6.92820i	−0.242091	−	0.419314i
$274$	1.50000	−	2.59808i	0.0906183	−	0.156956i
$275$	−3.00000			−0.180907
$276$	1.50000	+	2.59808i	0.0902894	+	0.156386i
$277$	19.0000			1.14160			0.570800	−	0.821089i	$-0.306633\pi$
$277$	19.0000			1.14160			0.570800	+	0.821089i	$0.306633\pi$
$278$	−14.0000			−0.839664
$279$	−5.50000	−	0.866025i	−0.329276	−	0.0518476i
$280$	−4.00000			−0.239046
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$	−0.500000	−	0.866025i	−0.0297746	−	0.0515711i
$283$	11.0000			0.653882			0.326941	−	0.945045i	$-0.393982\pi$
$283$	11.0000			0.653882			0.326941	+	0.945045i	$0.393982\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	−3.00000	−	5.19615i	−0.177394	−	0.307255i
$287$	−8.00000			−0.472225
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	1.00000	−	1.73205i	0.0587220	−	0.101710i
$291$	7.00000	+	12.1244i	0.410347	+	0.710742i
$292$	7.00000	−	12.1244i	0.409644	−	0.709524i
$293$	6.00000	+	10.3923i	0.350524	+	0.607125i	0.986341	−	0.164714i	$-0.0526703\pi$
$293$	6.00000	+	10.3923i	0.350524	+	0.607125i	−0.635818	+	0.771839i	$0.719337\pi$
$294$	−9.00000			−0.524891
$295$	4.00000			0.232889
$296$	−0.500000	−	0.866025i	−0.0290619	−	0.0503367i
$297$	−1.50000	+	2.59808i	−0.0870388	+	0.150756i
$298$	3.00000	+	5.19615i	0.173785	+	0.301005i
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$	0.500000	−	0.866025i	0.0288675	−	0.0500000i
$301$	2.00000	−	3.46410i	0.115278	−	0.199667i
$302$	−23.0000			−1.32350
$303$	−1.50000	−	2.59808i	−0.0861727	−	0.149256i
$304$		0			0
$305$	3.00000	−	5.19615i	0.171780	−	0.297531i
$306$	3.00000			0.171499
$307$	−8.00000	−	13.8564i	−0.456584	−	0.790827i	0.542194	−	0.840254i	$-0.317594\pi$
$307$	−8.00000	−	13.8564i	−0.456584	−	0.790827i	−0.998778	+	0.0494267i	$0.984261\pi$
$308$	−12.0000			−0.683763
$309$	6.00000			0.341328
$310$	5.50000	+	0.866025i	0.312379	+	0.0491869i
$311$	18.0000			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$312$	2.00000			0.113228
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	0.597522	−	0.801852i	$-0.296152\pi$
$313$	−7.00000	−	12.1244i	−0.395663	−	0.685309i	−0.993186	+	0.116543i	$0.962819\pi$
$314$	18.0000			1.01580
$315$	2.00000	−	3.46410i	0.112687	−	0.195180i
$316$	6.50000	+	11.2583i	0.365654	+	0.633331i
$317$	−4.00000	−	6.92820i	−0.224662	−	0.389127i	0.731556	−	0.681782i	$-0.238795\pi$
$317$	−4.00000	−	6.92820i	−0.224662	−	0.389127i	−0.956218	+	0.292655i	$0.905461\pi$
$318$	−4.00000			−0.224309
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	4.00000	−	6.92820i	0.223258	−	0.386695i
$322$	−6.00000	−	10.3923i	−0.334367	−	0.579141i
$323$		0			0
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−2.00000			−0.110940
$326$	3.00000			0.166155
$327$	6.00000	+	10.3923i	0.331801	+	0.574696i
$328$	1.00000	−	1.73205i	0.0552158	−	0.0956365i
$329$	2.00000	+	3.46410i	0.110264	+	0.190982i
$330$	1.50000	−	2.59808i	0.0825723	−	0.143019i
$331$	−12.0000	+	20.7846i	−0.659580	+	1.14243i	0.321145	+	0.947030i	$0.395932\pi$
$331$	−12.0000	+	20.7846i	−0.659580	+	1.14243i	−0.980725	+	0.195395i	$0.937401\pi$
$332$	−6.00000	+	10.3923i	−0.329293	+	0.570352i
$333$	1.00000			0.0547997
$334$	−8.00000	−	13.8564i	−0.437741	−	0.758189i
$335$	5.50000	+	9.52628i	0.300497	+	0.520476i
$336$	2.00000	−	3.46410i	0.109109	−	0.188982i
$337$	16.0000			0.871576			0.435788	−	0.900049i	$-0.356470\pi$
$337$	16.0000			0.871576			0.435788	+	0.900049i	$0.356470\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$	1.00000			0.0543125
$340$	−3.00000			−0.162698
$341$	16.5000	+	2.59808i	0.893525	+	0.140694i
$342$		0			0
$343$	8.00000			0.431959
$344$	0.500000	+	0.866025i	0.0269582	+	0.0466930i
$345$	3.00000			0.161515
$346$	−11.0000	+	19.0526i	−0.591364	+	1.02427i
$347$	−13.0000	−	22.5167i	−0.697877	−	1.20876i	−0.969201	−	0.246270i	$-0.920795\pi$
$347$	−13.0000	−	22.5167i	−0.697877	−	1.20876i	0.271325	−	0.962488i	$-0.412538\pi$
$348$	1.00000	+	1.73205i	0.0536056	+	0.0928477i
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$	−2.00000	+	3.46410i	−0.106904	+	0.185164i
$351$	−1.00000	+	1.73205i	−0.0533761	+	0.0924500i
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	−8.50000	−	14.7224i	−0.452409	−	0.783596i	0.546126	−	0.837703i	$-0.316102\pi$
$353$	−8.50000	−	14.7224i	−0.452409	−	0.783596i	−0.998535	+	0.0541072i	$0.982769\pi$
$354$	−2.00000	+	3.46410i	−0.106299	+	0.184115i
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$	−8.00000			−0.423999
$357$	−12.0000			−0.635107
$358$	4.50000	+	7.79423i	0.237832	+	0.411938i
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	0.353529	+	0.935423i	$0.384981\pi$
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	−0.986865	+	0.161546i	$0.948352\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	9.50000	−	16.4545i	0.500000	−	0.866025i
$362$	−6.00000	+	10.3923i	−0.315353	+	0.546207i
$363$	−1.00000	+	1.73205i	−0.0524864	+	0.0909091i
$364$	−8.00000			−0.419314
$365$	−7.00000	−	12.1244i	−0.366397	−	0.634618i
$366$	3.00000	+	5.19615i	0.156813	+	0.271607i
$367$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$367$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$368$	3.00000			0.156386
$369$	1.00000	+	1.73205i	0.0520579	+	0.0901670i
$370$	−1.00000			−0.0519875
$371$	16.0000			0.830679
$372$	−3.50000	+	4.33013i	−0.181467	+	0.224507i
$373$	3.00000			0.155334			0.0776671	−	0.996979i	$-0.475253\pi$
$373$	3.00000			0.155334			0.0776671	+	0.996979i	$0.475253\pi$
$374$	−9.00000			−0.465379
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	−1.00000			−0.0515711
$377$	2.00000	−	3.46410i	0.103005	−	0.178410i
$378$	2.00000	+	3.46410i	0.102869	+	0.178174i
$379$	11.0000	+	19.0526i	0.565032	+	0.978664i	0.997047	+	0.0767976i	$0.0244695\pi$
$379$	11.0000	+	19.0526i	0.565032	+	0.978664i	−0.432015	+	0.901867i	$0.642197\pi$
$380$		0			0
$381$	3.00000	−	5.19615i	0.153695	−	0.266207i
$382$	−5.00000	+	8.66025i	−0.255822	+	0.443097i
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	−0.991522	−	0.129937i	$-0.958522\pi$
$383$	−7.50000	+	12.9904i	−0.383232	+	0.663777i	0.608290	+	0.793715i	$0.291856\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−6.00000	+	10.3923i	−0.305788	+	0.529641i
$386$	1.00000	+	1.73205i	0.0508987	+	0.0881591i
$387$	−1.00000			−0.0508329
$388$	14.0000			0.710742
$389$	−9.50000	−	16.4545i	−0.481669	−	0.834275i	0.518110	−	0.855314i	$-0.326636\pi$
$389$	−9.50000	−	16.4545i	−0.481669	−	0.834275i	−0.999779	+	0.0210389i	$0.993303\pi$
$390$	1.00000	−	1.73205i	0.0506370	−	0.0877058i
$391$	−4.50000	−	7.79423i	−0.227575	−	0.394171i
$392$	−4.50000	+	7.79423i	−0.227284	+	0.393668i
$393$	10.5000	−	18.1865i	0.529655	−	0.917389i
$394$	4.00000	−	6.92820i	0.201517	−	0.349038i
$395$	13.0000			0.654101
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	−10.5000	−	18.1865i	−0.526980	−	0.912756i	−0.999506	−	0.0314391i	$-0.989991\pi$
$397$	−10.5000	−	18.1865i	−0.526980	−	0.912756i	0.472526	−	0.881317i	$-0.343342\pi$
$398$		0			0
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	10.0000			0.499376			0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000			0.499376			0.249688	+	0.968326i	$0.419672\pi$
$402$	−11.0000			−0.548630
$403$	11.0000	+	1.73205i	0.547949	+	0.0862796i
$404$	−3.00000			−0.149256
$405$	−1.00000			−0.0496904
$406$	−4.00000	−	6.92820i	−0.198517	−	0.343841i
$407$	−3.00000			−0.148704
$408$	1.50000	−	2.59808i	0.0742611	−	0.128624i
$409$	−1.50000	−	2.59808i	−0.0741702	−	0.128467i	0.826555	−	0.562856i	$-0.190297\pi$
$409$	−1.50000	−	2.59808i	−0.0741702	−	0.128467i	−0.900725	+	0.434389i	$0.856964\pi$
$410$	−1.00000	−	1.73205i	−0.0493865	−	0.0855399i
$411$	3.00000			0.147979
$412$	3.00000	−	5.19615i	0.147799	−	0.255996i
$413$	8.00000	−	13.8564i	0.393654	−	0.681829i
$414$	−1.50000	+	2.59808i	−0.0737210	+	0.127688i
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$	−7.00000	−	12.1244i	−0.342791	−	0.593732i
$418$		0			0
$419$	21.0000			1.02592			0.512959	−	0.858413i	$-0.328549\pi$
$419$	21.0000			1.02592			0.512959	+	0.858413i	$0.328549\pi$
$420$	−2.00000	−	3.46410i	−0.0975900	−	0.169031i
$421$	−3.00000	+	5.19615i	−0.146211	+	0.253245i	−0.929824	−	0.368004i	$-0.880041\pi$
$421$	−3.00000	+	5.19615i	−0.146211	+	0.253245i	0.783613	+	0.621249i	$0.213375\pi$
$422$	4.00000	+	6.92820i	0.194717	+	0.337260i
$423$	0.500000	−	0.866025i	0.0243108	−	0.0421076i
$424$	−2.00000	+	3.46410i	−0.0971286	+	0.168232i
$425$	−1.50000	+	2.59808i	−0.0727607	+	0.126025i
$426$	−6.00000			−0.290701
$427$	−12.0000	−	20.7846i	−0.580721	−	1.00584i
$428$	−4.00000	−	6.92820i	−0.193347	−	0.334887i
$429$	3.00000	−	5.19615i	0.144841	−	0.250873i
$430$	1.00000			0.0482243
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	0.959985	+	0.280052i	$0.0903517\pi$
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	−0.237460	+	0.971397i	$0.576315\pi$
$432$	−1.00000			−0.0481125
$433$	−28.0000			−1.34559			−0.672797	−	0.739827i	$-0.734907\pi$
$433$	−28.0000			−1.34559			−0.672797	+	0.739827i	$0.734907\pi$
$434$	14.0000	−	17.3205i	0.672022	−	0.831411i
$435$	2.00000			0.0958927
$436$	12.0000			0.574696
$437$		0			0
$438$	14.0000			0.668946
$439$	13.5000	−	23.3827i	0.644320	−	1.11599i	−0.340138	−	0.940375i	$-0.610474\pi$
$439$	13.5000	−	23.3827i	0.644320	−	1.11599i	0.984458	−	0.175619i	$-0.0561928\pi$
$440$	−1.50000	−	2.59808i	−0.0715097	−	0.123858i
$441$	−4.50000	−	7.79423i	−0.214286	−	0.371154i
$442$	−6.00000			−0.285391
$443$	9.00000	−	15.5885i	0.427603	−	0.740630i	−0.569057	−	0.822298i	$-0.692691\pi$
$443$	9.00000	−	15.5885i	0.427603	−	0.740630i	0.996660	+	0.0816684i	$0.0260248\pi$
$444$	0.500000	−	0.866025i	0.0237289	−	0.0410997i
$445$	−4.00000	+	6.92820i	−0.189618	+	0.328428i
$446$	13.0000	+	22.5167i	0.615568	+	1.06619i
$447$	−3.00000	+	5.19615i	−0.141895	+	0.245770i
$448$	−2.00000	−	3.46410i	−0.0944911	−	0.163663i
$449$	−26.0000			−1.22702			−0.613508	−	0.789689i	$-0.710242\pi$
$449$	−26.0000			−1.22702			−0.613508	+	0.789689i	$0.710242\pi$
$450$	1.00000			0.0471405
$451$	−3.00000	−	5.19615i	−0.141264	−	0.244677i
$452$	0.500000	−	0.866025i	0.0235180	−	0.0407344i
$453$	−11.5000	−	19.9186i	−0.540317	−	0.935857i
$454$		0			0
$455$	−4.00000	+	6.92820i	−0.187523	+	0.324799i
$456$		0			0
$457$	−4.00000			−0.187112			−0.0935561	−	0.995614i	$-0.529823\pi$
$457$	−4.00000			−0.187112			−0.0935561	+	0.995614i	$0.529823\pi$
$458$	14.0000	+	24.2487i	0.654177	+	1.13307i
$459$	1.50000	+	2.59808i	0.0700140	+	0.121268i
$460$	1.50000	−	2.59808i	0.0699379	−	0.121136i
$461$	−21.0000			−0.978068			−0.489034	−	0.872265i	$-0.662651\pi$
$461$	−21.0000			−0.978068			−0.489034	+	0.872265i	$0.662651\pi$
$462$	−6.00000	−	10.3923i	−0.279145	−	0.483494i
$463$	−12.0000			−0.557687			−0.278844	−	0.960337i	$-0.589951\pi$
$463$	−12.0000			−0.557687			−0.278844	+	0.960337i	$0.589951\pi$
$464$	2.00000			0.0928477
$465$	2.00000	+	5.19615i	0.0927478	+	0.240966i
$466$	−11.0000			−0.509565
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$	1.00000	+	1.73205i	0.0462250	+	0.0800641i
$469$	44.0000			2.03173
$470$	−0.500000	+	0.866025i	−0.0230633	+	0.0399468i
$471$	9.00000	+	15.5885i	0.414698	+	0.718278i
$472$	2.00000	+	3.46410i	0.0920575	+	0.159448i
$473$	3.00000			0.137940
$474$	−6.50000	+	11.2583i	−0.298555	+	0.517112i
$475$		0			0
$476$	−6.00000	+	10.3923i	−0.275010	+	0.476331i
$477$	−2.00000	−	3.46410i	−0.0915737	−	0.158610i
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	0.995023	−	0.0996406i	$-0.0317693\pi$
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	−0.583803	+	0.811895i	$0.698436\pi$
$480$	1.00000			0.0456435
$481$	−2.00000			−0.0911922
$482$	−5.00000	−	8.66025i	−0.227744	−	0.394464i
$483$	6.00000	−	10.3923i	0.273009	−	0.472866i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	7.00000	−	12.1244i	0.317854	−	0.550539i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−2.00000	+	3.46410i	−0.0906287	+	0.156973i	−0.907776	−	0.419456i	$-0.862221\pi$
$487$	−2.00000	+	3.46410i	−0.0906287	+	0.156973i	0.817147	+	0.576429i	$0.195554\pi$
$488$	6.00000			0.271607
$489$	1.50000	+	2.59808i	0.0678323	+	0.117489i
$490$	4.50000	+	7.79423i	0.203289	+	0.352107i
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	−0.645675	−	0.763612i	$-0.723424\pi$
$491$	7.50000	−	12.9904i	0.338470	−	0.586248i	0.984145	+	0.177365i	$0.0567572\pi$
$492$	2.00000			0.0901670
$493$	−3.00000	−	5.19615i	−0.135113	−	0.234023i
$494$		0			0
$495$	3.00000			0.134840
$496$	2.00000	+	5.19615i	0.0898027	+	0.233314i
$497$	24.0000			1.07655
$498$	−12.0000			−0.537733
$499$	−4.00000	−	6.92820i	−0.179065	−	0.310149i	0.762496	−	0.646993i	$-0.223974\pi$
$499$	−4.00000	−	6.92820i	−0.179065	−	0.310149i	−0.941560	+	0.336844i	$0.890640\pi$
$500$	−1.00000			−0.0447214
$501$	8.00000	−	13.8564i	0.357414	−	0.619059i
$502$	−4.50000	−	7.79423i	−0.200845	−	0.347873i
$503$	−8.00000	−	13.8564i	−0.356702	−	0.617827i	0.630705	−	0.776022i	$-0.282766\pi$
$503$	−8.00000	−	13.8564i	−0.356702	−	0.617827i	−0.987408	+	0.158196i	$0.949432\pi$
$504$	4.00000			0.178174
$505$	−1.50000	+	2.59808i	−0.0667491	+	0.115613i
$506$	4.50000	−	7.79423i	0.200049	−	0.346496i
$507$	−4.50000	+	7.79423i	−0.199852	+	0.346154i
$508$	−3.00000	−	5.19615i	−0.133103	−	0.230542i
$509$	20.5000	−	35.5070i	0.908647	−	1.57382i	0.0927004	−	0.995694i	$-0.470450\pi$
$509$	20.5000	−	35.5070i	0.908647	−	1.57382i	0.815946	−	0.578128i	$-0.196217\pi$
$510$	−1.50000	−	2.59808i	−0.0664211	−	0.115045i
$511$	−56.0000			−2.47729
$512$	1.00000			0.0441942
$513$		0			0
$514$	6.50000	−	11.2583i	0.286703	−	0.496584i
$515$	−3.00000	−	5.19615i	−0.132196	−	0.228970i
$516$	−0.500000	+	0.866025i	−0.0220113	+	0.0381246i
$517$	−1.50000	+	2.59808i	−0.0659699	+	0.114263i
$518$	−2.00000	+	3.46410i	−0.0878750	+	0.152204i
$519$	−22.0000			−0.965693
$520$	−1.00000	−	1.73205i	−0.0438529	−	0.0759555i
$521$	−12.0000	−	20.7846i	−0.525730	−	0.910590i	−0.999551	−	0.0299693i	$-0.990459\pi$
$521$	−12.0000	−	20.7846i	−0.525730	−	0.910590i	0.473821	−	0.880621i	$-0.342874\pi$
$522$	−1.00000	+	1.73205i	−0.0437688	+	0.0758098i
$523$	27.0000			1.18063			0.590314	−	0.807174i	$-0.299004\pi$
$523$	27.0000			1.18063			0.590314	+	0.807174i	$0.299004\pi$
$524$	−10.5000	−	18.1865i	−0.458695	−	0.794482i
$525$	−4.00000			−0.174574
$526$	−23.0000			−1.00285
$527$	10.5000	−	12.9904i	0.457387	−	0.565870i
$528$	3.00000			0.130558
$529$	−14.0000			−0.608696
$530$	2.00000	+	3.46410i	0.0868744	+	0.150471i
$531$	−4.00000			−0.173585
$532$		0			0
$533$	−2.00000	−	3.46410i	−0.0866296	−	0.150047i
$534$	−4.00000	−	6.92820i	−0.173097	−	0.299813i
$535$	−8.00000			−0.345870
$536$	−5.50000	+	9.52628i	−0.237564	+	0.411473i
$537$	−4.50000	+	7.79423i	−0.194189	+	0.336346i
$538$	−10.5000	+	18.1865i	−0.452687	+	0.784077i
$539$	13.5000	+	23.3827i	0.581486	+	1.00716i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	3.00000	+	5.19615i	0.128980	+	0.223400i	0.923282	−	0.384124i	$-0.125496\pi$
$541$	3.00000	+	5.19615i	0.128980	+	0.223400i	−0.794302	+	0.607524i	$0.792163\pi$
$542$	20.0000			0.859074
$543$	−12.0000			−0.514969
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	6.00000	−	10.3923i	0.257012	−	0.445157i
$546$	−4.00000	−	6.92820i	−0.171184	−	0.296500i
$547$	7.50000	−	12.9904i	0.320677	−	0.555429i	−0.659951	−	0.751309i	$-0.729423\pi$
$547$	7.50000	−	12.9904i	0.320677	−	0.555429i	0.980628	+	0.195880i	$0.0627563\pi$
$548$	1.50000	−	2.59808i	0.0640768	−	0.110984i
$549$	−3.00000	+	5.19615i	−0.128037	+	0.221766i
$550$	−3.00000			−0.127920
$551$		0			0
$552$	1.50000	+	2.59808i	0.0638442	+	0.110581i
$553$	26.0000	−	45.0333i	1.10563	−	1.91501i
$554$	19.0000			0.807233
$555$	−0.500000	−	0.866025i	−0.0212238	−	0.0367607i
$556$	−14.0000			−0.593732
$557$	12.0000			0.508456			0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000			0.508456			0.254228	+	0.967144i	$0.418179\pi$
$558$	−5.50000	−	0.866025i	−0.232834	−	0.0366618i
$559$	2.00000			0.0845910
$560$	−4.00000			−0.169031
$561$	−4.50000	−	7.79423i	−0.189990	−	0.329073i
$562$	30.0000			1.26547
$563$	7.00000	−	12.1244i	0.295015	−	0.510981i	−0.679974	−	0.733237i	$-0.738009\pi$
$563$	7.00000	−	12.1244i	0.295015	−	0.510981i	0.974988	+	0.222256i	$0.0713421\pi$
$564$	−0.500000	−	0.866025i	−0.0210538	−	0.0364662i
$565$	−0.500000	−	0.866025i	−0.0210352	−	0.0364340i
$566$	11.0000			0.462364
$567$	−2.00000	+	3.46410i	−0.0839921	+	0.145479i
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	−0.951592	−	0.307364i	$-0.900553\pi$
$569$	−5.00000	+	8.66025i	−0.209611	+	0.363057i	0.741981	+	0.670421i	$0.233886\pi$
$570$		0			0
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	−3.00000	−	5.19615i	−0.125436	−	0.217262i
$573$	−10.0000			−0.417756
$574$	−8.00000			−0.333914
$575$	−1.50000	−	2.59808i	−0.0625543	−	0.108347i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−12.0000	−	20.7846i	−0.499567	−	0.865275i	0.500433	−	0.865775i	$-0.333174\pi$
$577$	−12.0000	−	20.7846i	−0.499567	−	0.865275i	−1.00000		0.000500448i	$0.999841\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	−1.00000	+	1.73205i	−0.0415586	+	0.0719816i
$580$	1.00000	−	1.73205i	0.0415227	−	0.0719195i
$581$	48.0000			1.99138
$582$	7.00000	+	12.1244i	0.290159	+	0.502571i
$583$	6.00000	+	10.3923i	0.248495	+	0.430405i
$584$	7.00000	−	12.1244i	0.289662	−	0.501709i
$585$	2.00000			0.0826898
$586$	6.00000	+	10.3923i	0.247858	+	0.429302i
$587$	42.0000			1.73353			0.866763	−	0.498721i	$-0.166197\pi$
$587$	42.0000			1.73353			0.866763	+	0.498721i	$0.166197\pi$
$588$	−9.00000			−0.371154
$589$		0			0
$590$	4.00000			0.164677
$591$	8.00000			0.329076
$592$	−0.500000	−	0.866025i	−0.0205499	−	0.0355934i
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$	−1.50000	+	2.59808i	−0.0615457	+	0.106600i
$595$	6.00000	+	10.3923i	0.245976	+	0.426043i
$596$	3.00000	+	5.19615i	0.122885	+	0.212843i
$597$		0			0
$598$	3.00000	−	5.19615i	0.122679	−	0.212486i
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	−0.989210	−	0.146503i	$-0.953198\pi$
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	0.621480	+	0.783430i	$0.286532\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	0.992114	−	0.125336i	$-0.0400009\pi$
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	−0.604601	+	0.796528i	$0.706668\pi$
$602$	2.00000	−	3.46410i	0.0815139	−	0.141186i
$603$	−5.50000	−	9.52628i	−0.223977	−	0.387940i
$604$	−23.0000			−0.935857
$605$	2.00000			0.0813116
$606$	−1.50000	−	2.59808i	−0.0609333	−	0.105540i
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	−0.935713	−	0.352763i	$-0.885242\pi$
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	0.773358	+	0.633970i	$0.218576\pi$
$608$		0			0
$609$	4.00000	−	6.92820i	0.162088	−	0.280745i
$610$	3.00000	−	5.19615i	0.121466	−	0.210386i
$611$	−1.00000	+	1.73205i	−0.0404557	+	0.0700713i
$612$	3.00000			0.121268
$613$	1.00000	+	1.73205i	0.0403896	+	0.0699569i	0.885514	−	0.464614i	$-0.153807\pi$
$613$	1.00000	+	1.73205i	0.0403896	+	0.0699569i	−0.845124	+	0.534570i	$0.820473\pi$
$614$	−8.00000	−	13.8564i	−0.322854	−	0.559199i
$615$	1.00000	−	1.73205i	0.0403239	−	0.0698430i
$616$	−12.0000			−0.483494
$617$	21.5000	+	37.2391i	0.865557	+	1.49919i	0.866493	+	0.499190i	$0.166369\pi$
$617$	21.5000	+	37.2391i	0.865557	+	1.49919i	−0.000935233		1.00000i	$0.500298\pi$
$618$	6.00000			0.241355
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$	5.50000	+	0.866025i	0.220885	+	0.0347804i
$621$	−3.00000			−0.120386
$622$	18.0000			0.721734
$623$	16.0000	+	27.7128i	0.641026	+	1.11029i
$624$	2.00000			0.0800641
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−7.00000	−	12.1244i	−0.279776	−	0.484587i
$627$		0			0
$628$	18.0000			0.718278
$629$	−1.50000	+	2.59808i	−0.0598089	+	0.103592i
$630$	2.00000	−	3.46410i	0.0796819	−	0.138013i
$631$	−6.50000	+	11.2583i	−0.258761	+	0.448187i	−0.965910	−	0.258877i	$-0.916648\pi$
$631$	−6.50000	+	11.2583i	−0.258761	+	0.448187i	0.707149	+	0.707064i	$0.249981\pi$
$632$	6.50000	+	11.2583i	0.258556	+	0.447832i
$633$	−4.00000	+	6.92820i	−0.158986	+	0.275371i
$634$	−4.00000	−	6.92820i	−0.158860	−	0.275154i
$635$	−6.00000			−0.238103
$636$	−4.00000			−0.158610
$637$	9.00000	+	15.5885i	0.356593	+	0.617637i
$638$	3.00000	−	5.19615i	0.118771	−	0.205718i
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−2.00000	+	3.46410i	−0.0789953	+	0.136824i	−0.902817	−	0.430026i	$-0.858505\pi$
$641$	−2.00000	+	3.46410i	−0.0789953	+	0.136824i	0.823821	+	0.566849i	$0.191838\pi$
$642$	4.00000	−	6.92820i	0.157867	−	0.273434i
$643$	−28.0000			−1.10421			−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000			−1.10421			−0.552106	+	0.833774i	$0.686176\pi$
$644$	−6.00000	−	10.3923i	−0.236433	−	0.409514i
$645$	0.500000	+	0.866025i	0.0196875	+	0.0340997i
$646$		0			0
$647$	32.0000			1.25805			0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000			1.25805			0.629025	+	0.777385i	$0.283454\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	12.0000			0.471041
$650$	−2.00000			−0.0784465
$651$	22.0000	+	3.46410i	0.862248	+	0.135769i
$652$	3.00000			0.117489
$653$	−4.00000			−0.156532			−0.0782660	−	0.996933i	$-0.524938\pi$
$653$	−4.00000			−0.156532			−0.0782660	+	0.996933i	$0.524938\pi$
$654$	6.00000	+	10.3923i	0.234619	+	0.406371i
$655$	−21.0000			−0.820538
$656$	1.00000	−	1.73205i	0.0390434	−	0.0676252i
$657$	7.00000	+	12.1244i	0.273096	+	0.473016i
$658$	2.00000	+	3.46410i	0.0779681	+	0.135045i
$659$	9.00000			0.350590			0.175295	−	0.984516i	$-0.443912\pi$
$659$	9.00000			0.350590			0.175295	+	0.984516i	$0.443912\pi$
$660$	1.50000	−	2.59808i	0.0583874	−	0.101130i
$661$	21.0000	−	36.3731i	0.816805	−	1.41475i	−0.0912190	−	0.995831i	$-0.529076\pi$
$661$	21.0000	−	36.3731i	0.816805	−	1.41475i	0.908024	−	0.418917i	$-0.137590\pi$
$662$	−12.0000	+	20.7846i	−0.466393	+	0.807817i
$663$	−3.00000	−	5.19615i	−0.116510	−	0.201802i
$664$	−6.00000	+	10.3923i	−0.232845	+	0.403300i
$665$		0			0
$666$	1.00000			0.0387492
$667$	6.00000			0.232321
$668$	−8.00000	−	13.8564i	−0.309529	−	0.536120i
$669$	−13.0000	+	22.5167i	−0.502609	+	0.870544i
$670$	5.50000	+	9.52628i	0.212484	+	0.368032i
$671$	9.00000	−	15.5885i	0.347441	−	0.601786i
$672$	2.00000	−	3.46410i	0.0771517	−	0.133631i
$673$	−17.0000	+	29.4449i	−0.655302	+	1.13502i	0.326516	+	0.945192i	$0.394125\pi$
$673$	−17.0000	+	29.4449i	−0.655302	+	1.13502i	−0.981818	+	0.189824i	$0.939208\pi$
$674$	16.0000			0.616297
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	17.0000	−	29.4449i	0.653363	−	1.13166i	−0.328938	−	0.944351i	$-0.606691\pi$
$677$	17.0000	−	29.4449i	0.653363	−	1.13166i	0.982301	−	0.187307i	$-0.0599758\pi$
$678$	1.00000			0.0384048
$679$	−28.0000	−	48.4974i	−1.07454	−	1.86116i
$680$	−3.00000			−0.115045
$681$		0			0
$682$	16.5000	+	2.59808i	0.631818	+	0.0994855i
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$		0			0
$685$	−1.50000	−	2.59808i	−0.0573121	−	0.0992674i
$686$	8.00000			0.305441
$687$	−14.0000	+	24.2487i	−0.534133	+	0.925146i
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	4.00000	+	6.92820i	0.152388	+	0.263944i
$690$	3.00000			0.114208
$691$	−25.0000	+	43.3013i	−0.951045	+	1.64726i	−0.207875	+	0.978155i	$0.566655\pi$
$691$	−25.0000	+	43.3013i	−0.951045	+	1.64726i	−0.743170	+	0.669102i	$0.766679\pi$
$692$	−11.0000	+	19.0526i	−0.418157	+	0.724270i
$693$	6.00000	−	10.3923i	0.227921	−	0.394771i
$694$	−13.0000	−	22.5167i	−0.493473	−	0.854721i
$695$	−7.00000	+	12.1244i	−0.265525	+	0.459903i
$696$	1.00000	+	1.73205i	0.0379049	+	0.0656532i
$697$	−6.00000			−0.227266
$698$	14.0000			0.529908
$699$	−5.50000	−	9.52628i	−0.208029	−	0.360317i
$700$	−2.00000	+	3.46410i	−0.0755929	+	0.130931i
$701$	−13.5000	−	23.3827i	−0.509888	−	0.883152i	−0.999934	−	0.0114555i	$-0.996354\pi$
$701$	−13.5000	−	23.3827i	−0.509888	−	0.883152i	0.490046	−	0.871696i	$-0.336980\pi$
$702$	−1.00000	+	1.73205i	−0.0377426	+	0.0653720i
$703$		0			0
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$	−1.00000			−0.0376622
$706$	−8.50000	−	14.7224i	−0.319902	−	0.554086i
$707$	6.00000	+	10.3923i	0.225653	+	0.390843i
$708$	−2.00000	+	3.46410i	−0.0751646	+	0.130189i
$709$	10.0000			0.375558			0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000			0.375558			0.187779	+	0.982211i	$0.439871\pi$
$710$	3.00000	+	5.19615i	0.112588	+	0.195008i
$711$	−13.0000			−0.487538
$712$	−8.00000			−0.299813
$713$	6.00000	+	15.5885i	0.224702	+	0.583792i
$714$	−12.0000			−0.449089
$715$	−6.00000			−0.224387
$716$	4.50000	+	7.79423i	0.168173	+	0.291284i
$717$	−6.00000			−0.224074
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$	14.0000	+	24.2487i	0.522112	+	0.904324i	0.999669	+	0.0257237i	$0.00818900\pi$
$719$	14.0000	+	24.2487i	0.522112	+	0.904324i	−0.477557	+	0.878601i	$0.658478\pi$
$720$	0.500000	+	0.866025i	0.0186339	+	0.0322749i
$721$	−24.0000			−0.893807
$722$	9.50000	−	16.4545i	0.353553	−	0.612372i
$723$	5.00000	−	8.66025i	0.185952	−	0.322078i
$724$	−6.00000	+	10.3923i	−0.222988	+	0.386227i
$725$	−1.00000	−	1.73205i	−0.0371391	−	0.0643268i
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$	−22.0000	−	38.1051i	−0.815935	−	1.41324i	−0.908655	−	0.417548i	$-0.862889\pi$
$727$	−22.0000	−	38.1051i	−0.815935	−	1.41324i	0.0927199	−	0.995692i	$-0.470444\pi$
$728$	−8.00000			−0.296500
$729$	1.00000			0.0370370
$730$	−7.00000	−	12.1244i	−0.259082	−	0.448743i
$731$	1.50000	−	2.59808i	0.0554795	−	0.0960933i
$732$	3.00000	+	5.19615i	0.110883	+	0.192055i
$733$	6.50000	−	11.2583i	0.240083	−	0.415836i	−0.720655	−	0.693294i	$-0.756159\pi$
$733$	6.50000	−	11.2583i	0.240083	−	0.415836i	0.960738	+	0.277458i	$0.0894920\pi$
$734$		0			0
$735$	−4.50000	+	7.79423i	−0.165985	+	0.287494i
$736$	3.00000			0.110581
$737$	16.5000	+	28.5788i	0.607785	+	1.05272i
$738$	1.00000	+	1.73205i	0.0368105	+	0.0637577i
$739$	5.00000	−	8.66025i	0.183928	−	0.318573i	−0.759287	−	0.650756i	$-0.774452\pi$
$739$	5.00000	−	8.66025i	0.183928	−	0.318573i	0.943215	+	0.332184i	$0.107785\pi$
$740$	−1.00000			−0.0367607
$741$		0			0
$742$	16.0000			0.587378
$743$	9.00000			0.330178			0.165089	−	0.986279i	$-0.447209\pi$
$743$	9.00000			0.330178			0.165089	+	0.986279i	$0.447209\pi$
$744$	−3.50000	+	4.33013i	−0.128316	+	0.158750i
$745$	6.00000			0.219823
$746$	3.00000			0.109838
$747$	−6.00000	−	10.3923i	−0.219529	−	0.380235i
$748$	−9.00000			−0.329073
$749$	−16.0000	+	27.7128i	−0.584627	+	1.01260i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	20.5000	+	35.5070i	0.748056	+	1.29567i	0.948753	+	0.316017i	$0.102346\pi$
$751$	20.5000	+	35.5070i	0.748056	+	1.29567i	−0.200698	+	0.979653i	$0.564321\pi$
$752$	−1.00000			−0.0364662
$753$	4.50000	−	7.79423i	0.163989	−	0.284037i
$754$	2.00000	−	3.46410i	0.0728357	−	0.126155i
$755$	−11.5000	+	19.9186i	−0.418528	+	0.724912i
$756$	2.00000	+	3.46410i	0.0727393	+	0.125988i
$757$	−13.5000	+	23.3827i	−0.490666	+	0.849858i	−0.999942	−	0.0107448i	$-0.996580\pi$
$757$	−13.5000	+	23.3827i	−0.490666	+	0.849858i	0.509276	+	0.860603i	$0.329913\pi$
$758$	11.0000	+	19.0526i	0.399538	+	0.692020i
$759$	9.00000			0.326679
$760$		0			0
$761$	−14.0000	−	24.2487i	−0.507500	−	0.879015i	−0.999962	−	0.00868155i	$-0.997237\pi$
$761$	−14.0000	−	24.2487i	−0.507500	−	0.879015i	0.492463	−	0.870334i	$-0.336097\pi$
$762$	3.00000	−	5.19615i	0.108679	−	0.188237i
$763$	−24.0000	−	41.5692i	−0.868858	−	1.50491i
$764$	−5.00000	+	8.66025i	−0.180894	+	0.313317i
$765$	1.50000	−	2.59808i	0.0542326	−	0.0939336i
$766$	−7.50000	+	12.9904i	−0.270986	+	0.469362i
$767$	8.00000			0.288863
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−15.0000	−	25.9808i	−0.540914	−	0.936890i	−0.998852	−	0.0479061i	$-0.984745\pi$
$769$	−15.0000	−	25.9808i	−0.540914	−	0.936890i	0.457938	−	0.888984i	$-0.348588\pi$
$770$	−6.00000	+	10.3923i	−0.216225	+	0.374513i
$771$	13.0000			0.468184
$772$	1.00000	+	1.73205i	0.0359908	+	0.0623379i
$773$	−10.0000			−0.359675			−0.179838	−	0.983696i	$-0.557557\pi$
$773$	−10.0000			−0.359675			−0.179838	+	0.983696i	$0.557557\pi$
$774$	−1.00000			−0.0359443
$775$	3.50000	−	4.33013i	0.125724	−	0.155543i
$776$	14.0000			0.502571
$777$	−4.00000			−0.143499
$778$	−9.50000	−	16.4545i	−0.340592	−	0.589922i
$779$		0			0
$780$	1.00000	−	1.73205i	0.0358057	−	0.0620174i
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$	−4.50000	−	7.79423i	−0.160920	−	0.278721i
$783$	−2.00000			−0.0714742
$784$	−4.50000	+	7.79423i	−0.160714	+	0.278365i
$785$	9.00000	−	15.5885i	0.321224	−	0.556376i
$786$	10.5000	−	18.1865i	0.374523	−	0.648692i
$787$	−8.50000	−	14.7224i	−0.302992	−	0.524798i	0.673820	−	0.738896i	$-0.264652\pi$
$787$	−8.50000	−	14.7224i	−0.302992	−	0.524798i	−0.976812	+	0.214097i	$0.931319\pi$
$788$	4.00000	−	6.92820i	0.142494	−	0.246807i
$789$	−11.5000	−	19.9186i	−0.409411	−	0.709120i
$790$	13.0000			0.462519
$791$	−4.00000			−0.142224
$792$	1.50000	+	2.59808i	0.0533002	+	0.0923186i
$793$	6.00000	−	10.3923i	0.213066	−	0.369042i
$794$	−10.5000	−	18.1865i	−0.372631	−	0.645416i
$795$	−2.00000	+	3.46410i	−0.0709327	+	0.122859i
$796$		0			0
$797$	−20.0000	+	34.6410i	−0.708436	+	1.22705i	0.257001	+	0.966411i	$0.417266\pi$
$797$	−20.0000	+	34.6410i	−0.708436	+	1.22705i	−0.965437	+	0.260637i	$0.916068\pi$
$798$		0			0
$799$	1.50000	+	2.59808i	0.0530662	+	0.0919133i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	4.00000	−	6.92820i	0.141333	−	0.244796i
$802$	10.0000			0.353112
$803$	−21.0000	−	36.3731i	−0.741074	−	1.28358i
$804$	−11.0000			−0.387940
$805$	−12.0000			−0.422944
$806$	11.0000	+	1.73205i	0.387458	+	0.0610089i
$807$	−21.0000			−0.739235
$808$	−3.00000			−0.105540
$809$	−20.0000	−	34.6410i	−0.703163	−	1.21791i	−0.967351	−	0.253442i	$-0.918437\pi$
$809$	−20.0000	−	34.6410i	−0.703163	−	1.21791i	0.264188	−	0.964471i	$-0.414896\pi$
$810$	−1.00000			−0.0351364
$811$	8.00000	−	13.8564i	0.280918	−	0.486564i	−0.690693	−	0.723148i	$-0.742694\pi$
$811$	8.00000	−	13.8564i	0.280918	−	0.486564i	0.971611	+	0.236584i	$0.0760278\pi$
$812$	−4.00000	−	6.92820i	−0.140372	−	0.243132i
$813$	10.0000	+	17.3205i	0.350715	+	0.607457i
$814$	−3.00000			−0.105150
$815$	1.50000	−	2.59808i	0.0525427	−	0.0910066i
$816$	1.50000	−	2.59808i	0.0525105	−	0.0909509i
$817$		0			0
$818$	−1.50000	−	2.59808i	−0.0524463	−	0.0908396i
$819$	4.00000	−	6.92820i	0.139771	−	0.242091i
$820$	−1.00000	−	1.73205i	−0.0349215	−	0.0604858i
$821$	3.00000			0.104701			0.0523504	−	0.998629i	$-0.483329\pi$
$821$	3.00000			0.104701			0.0523504	+	0.998629i	$0.483329\pi$
$822$	3.00000			0.104637
$823$	−27.0000	−	46.7654i	−0.941161	−	1.63014i	−0.763261	−	0.646090i	$-0.776403\pi$
$823$	−27.0000	−	46.7654i	−0.941161	−	1.63014i	−0.177899	−	0.984049i	$-0.556930\pi$
$824$	3.00000	−	5.19615i	0.104510	−	0.181017i
$825$	−1.50000	−	2.59808i	−0.0522233	−	0.0904534i
$826$	8.00000	−	13.8564i	0.278356	−	0.482126i
$827$	−24.0000	+	41.5692i	−0.834562	+	1.44550i	0.0598250	+	0.998209i	$0.480946\pi$
$827$	−24.0000	+	41.5692i	−0.834562	+	1.44550i	−0.894387	+	0.447295i	$0.852388\pi$
$828$	−1.50000	+	2.59808i	−0.0521286	+	0.0902894i
$829$	−10.0000			−0.347314			−0.173657	−	0.984806i	$-0.555558\pi$
$829$	−10.0000			−0.347314			−0.173657	+	0.984806i	$0.555558\pi$
$830$	6.00000	+	10.3923i	0.208263	+	0.360722i
$831$	9.50000	+	16.4545i	0.329551	+	0.570800i
$832$	1.00000	−	1.73205i	0.0346688	−	0.0600481i
$833$	27.0000			0.935495
$834$	−7.00000	−	12.1244i	−0.242390	−	0.419832i
$835$	−16.0000			−0.553703
$836$		0			0
$837$	−2.00000	−	5.19615i	−0.0691301	−	0.179605i
$838$	21.0000			0.725433
$839$	−42.0000			−1.45000			−0.725001	−	0.688748i	$-0.758161\pi$
$839$	−42.0000			−1.45000			−0.725001	+	0.688748i	$0.758161\pi$
$840$	−2.00000	−	3.46410i	−0.0690066	−	0.119523i
$841$	−25.0000			−0.862069
$842$	−3.00000	+	5.19615i	−0.103387	+	0.179071i
$843$	15.0000	+	25.9808i	0.516627	+	0.894825i
$844$	4.00000	+	6.92820i	0.137686	+	0.238479i
$845$	9.00000			0.309609
$846$	0.500000	−	0.866025i	0.0171904	−	0.0297746i
$847$	4.00000	−	6.92820i	0.137442	−	0.238056i
$848$	−2.00000	+	3.46410i	−0.0686803	+	0.118958i
$849$	5.50000	+	9.52628i	0.188760	+	0.326941i
$850$	−1.50000	+	2.59808i	−0.0514496	+	0.0891133i
$851$	−1.50000	−	2.59808i	−0.0514193	−	0.0890609i
$852$	−6.00000			−0.205557
$853$	−42.0000			−1.43805			−0.719026	−	0.694983i	$-0.755412\pi$
$853$	−42.0000			−1.43805			−0.719026	+	0.694983i	$0.755412\pi$
$854$	−12.0000	−	20.7846i	−0.410632	−	0.711235i
$855$		0			0
$856$	−4.00000	−	6.92820i	−0.136717	−	0.236801i
$857$	−17.5000	+	30.3109i	−0.597789	+	1.03540i	0.395358	+	0.918527i	$0.370620\pi$
$857$	−17.5000	+	30.3109i	−0.597789	+	1.03540i	−0.993147	+	0.116873i	$0.962713\pi$
$858$	3.00000	−	5.19615i	0.102418	−	0.177394i
$859$	10.0000	−	17.3205i	0.341196	−	0.590968i	−0.643459	−	0.765480i	$-0.722501\pi$
$859$	10.0000	−	17.3205i	0.341196	−	0.590968i	0.984655	+	0.174512i	$0.0558348\pi$
$860$	1.00000			0.0340997
$861$	−4.00000	−	6.92820i	−0.136320	−	0.236113i
$862$	15.0000	+	25.9808i	0.510902	+	0.884908i
$863$	−22.5000	+	38.9711i	−0.765909	+	1.32659i	0.173856	+	0.984771i	$0.444377\pi$
$863$	−22.5000	+	38.9711i	−0.765909	+	1.32659i	−0.939765	+	0.341822i	$0.888956\pi$
$864$	−1.00000			−0.0340207
$865$	11.0000	+	19.0526i	0.374011	+	0.647806i
$866$	−28.0000			−0.951479
$867$	8.00000			0.271694
$868$	14.0000	−	17.3205i	0.475191	−	0.587896i
$869$	39.0000			1.32298
$870$	2.00000			0.0678064
$871$	11.0000	+	19.0526i	0.372721	+	0.645571i
$872$	12.0000			0.406371
$873$	−7.00000	+	12.1244i	−0.236914	+	0.410347i
$874$		0			0
$875$	2.00000	+	3.46410i	0.0676123	+	0.117108i
$876$	14.0000			0.473016
$877$	−1.50000	+	2.59808i	−0.0506514	+	0.0877308i	−0.890239	−	0.455493i	$-0.849463\pi$
$877$	−1.50000	+	2.59808i	−0.0506514	+	0.0877308i	0.839588	+	0.543224i	$0.182796\pi$
$878$	13.5000	−	23.3827i	0.455603	−	0.789127i
$879$	−6.00000	+	10.3923i	−0.202375	+	0.350524i
$880$	−1.50000	−	2.59808i	−0.0505650	−	0.0875811i
$881$	−6.00000	+	10.3923i	−0.202145	+	0.350126i	−0.949219	−	0.314615i	$-0.898125\pi$
$881$	−6.00000	+	10.3923i	−0.202145	+	0.350126i	0.747074	+	0.664741i	$0.231458\pi$
$882$	−4.50000	−	7.79423i	−0.151523	−	0.262445i
$883$	−33.0000			−1.11054			−0.555269	−	0.831671i	$-0.687385\pi$
$883$	−33.0000			−1.11054			−0.555269	+	0.831671i	$0.687385\pi$
$884$	−6.00000			−0.201802
$885$	2.00000	+	3.46410i	0.0672293	+	0.116445i
$886$	9.00000	−	15.5885i	0.302361	−	0.523704i
$887$	−24.5000	−	42.4352i	−0.822629	−	1.42484i	−0.903718	−	0.428129i	$-0.859173\pi$
$887$	−24.5000	−	42.4352i	−0.822629	−	1.42484i	0.0810881	−	0.996707i	$-0.474160\pi$
$888$	0.500000	−	0.866025i	0.0167789	−	0.0290619i
$889$	−12.0000	+	20.7846i	−0.402467	+	0.697093i
$890$	−4.00000	+	6.92820i	−0.134080	+	0.232234i
$891$	−3.00000			−0.100504
$892$	13.0000	+	22.5167i	0.435272	+	0.753914i
$893$		0			0
$894$	−3.00000	+	5.19615i	−0.100335	+	0.173785i
$895$	9.00000			0.300837
$896$	−2.00000	−	3.46410i	−0.0668153	−	0.115728i
$897$	6.00000			0.200334
$898$	−26.0000			−0.867631
$899$	4.00000	+	10.3923i	0.133407	+	0.346603i
$900$	1.00000			0.0333333
$901$	12.0000			0.399778
$902$	−3.00000	−	5.19615i	−0.0998891	−	0.173013i
$903$	4.00000			0.133112
$904$	0.500000	−	0.866025i	0.0166298	−	0.0288036i
$905$	6.00000	+	10.3923i	0.199447	+	0.345452i
$906$	−11.5000	−	19.9186i	−0.382062	−	0.661751i
$907$	−16.0000			−0.531271			−0.265636	−	0.964073i	$-0.585582\pi$
$907$	−16.0000			−0.531271			−0.265636	+	0.964073i	$0.585582\pi$
$908$		0			0
$909$	1.50000	−	2.59808i	0.0497519	−	0.0861727i
$910$	−4.00000	+	6.92820i	−0.132599	+	0.229668i
$911$	18.0000	+	31.1769i	0.596367	+	1.03294i	0.993352	+	0.115113i	$0.0367229\pi$
$911$	18.0000	+	31.1769i	0.596367	+	1.03294i	−0.396986	+	0.917825i	$0.629944\pi$
$912$		0			0
$913$	18.0000	+	31.1769i	0.595713	+	1.03181i
$914$	−4.00000			−0.132308
$915$	6.00000			0.198354
$916$	14.0000	+	24.2487i	0.462573	+	0.801200i
$917$	−42.0000	+	72.7461i	−1.38696	+	2.40229i
$918$	1.50000	+	2.59808i	0.0495074	+	0.0857493i
$919$	19.5000	−	33.7750i	0.643246	−	1.11413i	−0.341458	−	0.939897i	$-0.610921\pi$
$919$	19.5000	−	33.7750i	0.643246	−	1.11413i	0.984704	−	0.174237i	$-0.0557459\pi$
$920$	1.50000	−	2.59808i	0.0494535	−	0.0856560i
$921$	8.00000	−	13.8564i	0.263609	−	0.456584i
$922$	−21.0000			−0.691598
$923$	6.00000	+	10.3923i	0.197492	+	0.342067i
$924$	−6.00000	−	10.3923i	−0.197386	−	0.341882i
$925$	−0.500000	+	0.866025i	−0.0164399	+	0.0284747i
$926$	−12.0000			−0.394344
$927$	3.00000	+	5.19615i	0.0985329	+	0.170664i
$928$	2.00000			0.0656532
$929$	−36.0000			−1.18112			−0.590561	−	0.806993i	$-0.701093\pi$
$929$	−36.0000			−1.18112			−0.590561	+	0.806993i	$0.701093\pi$
$930$	2.00000	+	5.19615i	0.0655826	+	0.170389i
$931$		0			0
$932$	−11.0000			−0.360317
$933$	9.00000	+	15.5885i	0.294647	+	0.510343i
$934$	−8.00000			−0.261768
$935$	−4.50000	+	7.79423i	−0.147166	+	0.254899i
$936$	1.00000	+	1.73205i	0.0326860	+	0.0566139i
$937$	27.0000	+	46.7654i	0.882052	+	1.52776i	0.849056	+	0.528303i	$0.177171\pi$
$937$	27.0000	+	46.7654i	0.882052	+	1.52776i	0.0329954	+	0.999456i	$0.489495\pi$
$938$	44.0000			1.43665
$939$	7.00000	−	12.1244i	0.228436	−	0.395663i
$940$	−0.500000	+	0.866025i	−0.0163082	+	0.0282466i
$941$	−3.50000	+	6.06218i	−0.114097	+	0.197621i	−0.917418	−	0.397924i	$-0.869731\pi$
$941$	−3.50000	+	6.06218i	−0.114097	+	0.197621i	0.803322	+	0.595545i	$0.203064\pi$
$942$	9.00000	+	15.5885i	0.293236	+	0.507899i
$943$	3.00000	−	5.19615i	0.0976934	−	0.169210i
$944$	2.00000	+	3.46410i	0.0650945	+	0.112747i
$945$	4.00000			0.130120
$946$	3.00000			0.0975384
$947$	17.0000	+	29.4449i	0.552426	+	0.956830i	0.998099	+	0.0616337i	$0.0196311\pi$
$947$	17.0000	+	29.4449i	0.552426	+	0.956830i	−0.445673	+	0.895196i	$0.647036\pi$
$948$	−6.50000	+	11.2583i	−0.211110	+	0.365654i
$949$	−14.0000	−	24.2487i	−0.454459	−	0.787146i
$950$		0			0
$951$	4.00000	−	6.92820i	0.129709	−	0.224662i
$952$	−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	$0.489687\pi$
$954$	−2.00000	−	3.46410i	−0.0647524	−	0.112154i
$955$	5.00000	+	8.66025i	0.161796	+	0.280239i
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$	6.00000			0.193952
$958$	9.00000	+	15.5885i	0.290777	+	0.503640i
$959$	−12.0000			−0.387500
$960$	1.00000			0.0322749
$961$	−23.0000	+	20.7846i	−0.741935	+	0.670471i
$962$	−2.00000			−0.0644826
$963$	8.00000			0.257796
$964$	−5.00000	−	8.66025i	−0.161039	−	0.278928i
$965$	2.00000			0.0643823
$966$	6.00000	−	10.3923i	0.193047	−	0.334367i
$967$	4.00000	+	6.92820i	0.128631	+	0.222796i	0.923147	−	0.384448i	$-0.125608\pi$
$967$	4.00000	+	6.92820i	0.128631	+	0.222796i	−0.794515	+	0.607244i	$0.792275\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$		0			0
$970$	7.00000	−	12.1244i	0.224756	−	0.389290i
$971$	13.5000	−	23.3827i	0.433236	−	0.750386i	−0.563914	−	0.825833i	$-0.690705\pi$
$971$	13.5000	−	23.3827i	0.433236	−	0.750386i	0.997150	+	0.0754473i	$0.0240385\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	28.0000	+	48.4974i	0.897639	+	1.55476i
$974$	−2.00000	+	3.46410i	−0.0640841	+	0.110997i
$975$	−1.00000	−	1.73205i	−0.0320256	−	0.0554700i
$976$	6.00000			0.192055
$977$	−30.0000			−0.959785			−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000			−0.959785			−0.479893	+	0.877327i	$0.659324\pi$
$978$	1.50000	+	2.59808i	0.0479647	+	0.0830773i
$979$	−12.0000	+	20.7846i	−0.383522	+	0.664279i
$980$	4.50000	+	7.79423i	0.143747	+	0.248978i
$981$	−6.00000	+	10.3923i	−0.191565	+	0.331801i
$982$	7.50000	−	12.9904i	0.239335	−	0.414540i
$983$	−28.0000	+	48.4974i	−0.893061	+	1.54683i	−0.0568755	+	0.998381i	$0.518114\pi$
$983$	−28.0000	+	48.4974i	−0.893061	+	1.54683i	−0.836186	+	0.548446i	$0.815220\pi$
$984$	2.00000			0.0637577
$985$	−4.00000	−	6.92820i	−0.127451	−	0.220751i
$986$	−3.00000	−	5.19615i	−0.0955395	−	0.165479i
$987$	−2.00000	+	3.46410i	−0.0636607	+	0.110264i
$988$		0			0
$989$	1.50000	+	2.59808i	0.0476972	+	0.0826140i
$990$	3.00000			0.0953463
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	2.00000	+	5.19615i	0.0635001	+	0.164978i
$993$	−24.0000			−0.761617
$994$	24.0000			0.761234
$995$		0			0
$996$	−12.0000			−0.380235
$997$	−21.0000	+	36.3731i	−0.665077	+	1.15195i	0.314188	+	0.949361i	$0.398268\pi$
$997$	−21.0000	+	36.3731i	−0.665077	+	1.15195i	−0.979265	+	0.202586i	$0.935066\pi$
$998$	−4.00000	−	6.92820i	−0.126618	−	0.219308i
$999$	0.500000	+	0.866025i	0.0158193	+	0.0273998i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.i.g.211.1	✓	2	1.1	even	1	trivial
930.2.i.g.811.1	yes	2	31.5	even	3	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(-2.00000 - 3.46410i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-2.00000 - 3.46410i) 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} +(1.00000 - 1.73205i) q^{13} +(-2.00000 - 3.46410i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(-1.50000 - 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.500000 - 0.866025i) q^{20} +(2.00000 - 3.46410i) q^{21} +(1.50000 - 2.59808i) q^{22} +3.00000 q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} -1.00000 q^{27} +(-2.00000 - 3.46410i) q^{28} +2.00000 q^{29} +1.00000 q^{30} +(2.00000 + 5.19615i) q^{31} +1.00000 q^{32} +3.00000 q^{33} +(-1.50000 - 2.59808i) q^{34} -4.00000 q^{35} +(-0.500000 + 0.866025i) q^{36} +(-0.500000 - 0.866025i) q^{37} +2.00000 q^{39} +(0.500000 - 0.866025i) q^{40} +(1.00000 - 1.73205i) q^{41} +(2.00000 - 3.46410i) q^{42} +(0.500000 + 0.866025i) q^{43} +(1.50000 - 2.59808i) q^{44} +(0.500000 + 0.866025i) q^{45} +3.00000 q^{46} -1.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(1.50000 - 2.59808i) q^{51} +(1.00000 - 1.73205i) q^{52} +(-2.00000 + 3.46410i) q^{53} -1.00000 q^{54} +(-1.50000 - 2.59808i) q^{55} +(-2.00000 - 3.46410i) q^{56} +2.00000 q^{58} +(2.00000 + 3.46410i) q^{59} +1.00000 q^{60} +6.00000 q^{61} +(2.00000 + 5.19615i) q^{62} +4.00000 q^{63} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +3.00000 q^{66} +(-5.50000 + 9.52628i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(1.50000 + 2.59808i) q^{69} -4.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(7.00000 - 12.1244i) q^{73} +(-0.500000 - 0.866025i) q^{74} +(0.500000 - 0.866025i) q^{75} -12.0000 q^{77} +2.00000 q^{78} +(6.50000 + 11.2583i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +(-6.00000 + 10.3923i) q^{83} +(2.00000 - 3.46410i) q^{84} -3.00000 q^{85} +(0.500000 + 0.866025i) q^{86} +(1.00000 + 1.73205i) q^{87} +(1.50000 - 2.59808i) q^{88} -8.00000 q^{89} +(0.500000 + 0.866025i) q^{90} -8.00000 q^{91} +3.00000 q^{92} +(-3.50000 + 4.33013i) q^{93} -1.00000 q^{94} +(0.500000 + 0.866025i) q^{96} +14.0000 q^{97} +(-4.50000 + 7.79423i) q^{98} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} - 4 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^5 + q^6 - 4 * q^7 + 2 * q^8 - q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{5} + q^{6} - 4 q^{7} + 2 q^{8} - q^{9} + q^{10} + 3 q^{11} + q^{12} + 2 q^{13} - 4 q^{14} + 2 q^{15} + 2 q^{16} - 3 q^{17} - q^{18} + q^{20} + 4 q^{21} + 3 q^{22} + 6 q^{23} + q^{24} - q^{25} + 2 q^{26} - 2 q^{27} - 4 q^{28} + 4 q^{29} + 2 q^{30} + 4 q^{31} + 2 q^{32} + 6 q^{33} - 3 q^{34} - 8 q^{35} - q^{36} - q^{37} + 4 q^{39} + q^{40} + 2 q^{41} + 4 q^{42} + q^{43} + 3 q^{44} + q^{45} + 6 q^{46} - 2 q^{47} + q^{48} - 9 q^{49} - q^{50} + 3 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 3 q^{55} - 4 q^{56} + 4 q^{58} + 4 q^{59} + 2 q^{60} + 12 q^{61} + 4 q^{62} + 8 q^{63} + 2 q^{64} - 2 q^{65} + 6 q^{66} - 11 q^{67} - 3 q^{68} + 3 q^{69} - 8 q^{70} - 6 q^{71} - q^{72} + 14 q^{73} - q^{74} + q^{75} - 24 q^{77} + 4 q^{78} + 13 q^{79} + q^{80} - q^{81} + 2 q^{82} - 12 q^{83} + 4 q^{84} - 6 q^{85} + q^{86} + 2 q^{87} + 3 q^{88} - 16 q^{89} + q^{90} - 16 q^{91} + 6 q^{92} - 7 q^{93} - 2 q^{94} + q^{96} + 28 q^{97} - 9 q^{98} + 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^5 + q^6 - 4 * q^7 + 2 * q^8 - q^9 + q^10 + 3 * q^11 + q^12 + 2 * q^13 - 4 * q^14 + 2 * q^15 + 2 * q^16 - 3 * q^17 - q^18 + q^20 + 4 * q^21 + 3 * q^22 + 6 * q^23 + q^24 - q^25 + 2 * q^26 - 2 * q^27 - 4 * q^28 + 4 * q^29 + 2 * q^30 + 4 * q^31 + 2 * q^32 + 6 * q^33 - 3 * q^34 - 8 * q^35 - q^36 - q^37 + 4 * q^39 + q^40 + 2 * q^41 + 4 * q^42 + q^43 + 3 * q^44 + q^45 + 6 * q^46 - 2 * q^47 + q^48 - 9 * q^49 - q^50 + 3 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 3 * q^55 - 4 * q^56 + 4 * q^58 + 4 * q^59 + 2 * q^60 + 12 * q^61 + 4 * q^62 + 8 * q^63 + 2 * q^64 - 2 * q^65 + 6 * q^66 - 11 * q^67 - 3 * q^68 + 3 * q^69 - 8 * q^70 - 6 * q^71 - q^72 + 14 * q^73 - q^74 + q^75 - 24 * q^77 + 4 * q^78 + 13 * q^79 + q^80 - q^81 + 2 * q^82 - 12 * q^83 + 4 * q^84 - 6 * q^85 + q^86 + 2 * q^87 + 3 * q^88 - 16 * q^89 + q^90 - 16 * q^91 + 6 * q^92 - 7 * q^93 - 2 * q^94 + q^96 + 28 * q^97 - 9 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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