LMFDB - Embedded newform 546.2.i.c.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(79,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("546.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.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:	$4.35983195036$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.235
Dual form			546.2.i.c.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +(2.50000 - 0.866025i) q^{14} -4.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.500000 + 0.866025i) q^{19} -4.00000 q^{20} +(-2.00000 - 1.73205i) q^{21} -1.00000 q^{22} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-5.50000 + 9.52628i) q^{25} +(0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +(-2.00000 - 1.73205i) q^{28} -9.00000 q^{29} +(2.00000 + 3.46410i) q^{30} +(4.00000 - 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +3.00000 q^{34} +(-10.0000 + 3.46410i) q^{35} +1.00000 q^{36} +(4.00000 + 6.92820i) q^{37} +(0.500000 - 0.866025i) q^{38} +(0.500000 - 0.866025i) q^{39} +(2.00000 + 3.46410i) q^{40} +(-0.500000 + 2.59808i) q^{42} +10.0000 q^{43} +(0.500000 + 0.866025i) q^{44} +(2.00000 - 3.46410i) q^{45} +(-3.00000 + 5.19615i) q^{46} +(5.50000 + 9.52628i) q^{47} +1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +11.0000 q^{50} +(-1.50000 - 2.59808i) q^{51} +(0.500000 - 0.866025i) q^{52} +(-0.500000 + 0.866025i) q^{53} +(-0.500000 - 0.866025i) q^{54} +4.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} -1.00000 q^{57} +(4.50000 + 7.79423i) q^{58} +(2.50000 - 4.33013i) q^{59} +(2.00000 - 3.46410i) q^{60} +(7.50000 + 12.9904i) q^{61} -8.00000 q^{62} +(2.50000 - 0.866025i) q^{63} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(0.500000 - 0.866025i) q^{66} +(2.50000 - 4.33013i) q^{67} +(-1.50000 - 2.59808i) q^{68} +6.00000 q^{69} +(8.00000 + 6.92820i) q^{70} -15.0000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(4.00000 - 6.92820i) q^{74} +(-5.50000 - 9.52628i) q^{75} -1.00000 q^{76} +(2.00000 + 1.73205i) q^{77} -1.00000 q^{78} +(1.00000 + 1.73205i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} -8.00000 q^{83} +(2.50000 - 0.866025i) q^{84} -12.0000 q^{85} +(-5.00000 - 8.66025i) q^{86} +(4.50000 - 7.79423i) q^{87} +(0.500000 - 0.866025i) q^{88} -4.00000 q^{90} +(0.500000 - 2.59808i) q^{91} +6.00000 q^{92} +(4.00000 + 6.92820i) q^{93} +(5.50000 - 9.52628i) q^{94} +(-2.00000 + 3.46410i) q^{95} +(-0.500000 - 0.866025i) q^{96} +10.0000 q^{97} +(1.00000 + 6.92820i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} + 4 q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - q^3 - q^4 + 4 * q^5 + 2 * q^6 - q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} - q^{3} - q^{4} + 4 q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9} + 4 q^{10} + q^{11} - q^{12} - 2 q^{13} + 5 q^{14} - 8 q^{15} - q^{16} - 3 q^{17} - q^{18} + q^{19} - 8 q^{20} - 4 q^{21} - 2 q^{22} - 6 q^{23} - q^{24} - 11 q^{25} + q^{26} + 2 q^{27} - 4 q^{28} - 18 q^{29} + 4 q^{30} + 8 q^{31} - q^{32} + q^{33} + 6 q^{34} - 20 q^{35} + 2 q^{36} + 8 q^{37} + q^{38} + q^{39} + 4 q^{40} - q^{42} + 20 q^{43} + q^{44} + 4 q^{45} - 6 q^{46} + 11 q^{47} + 2 q^{48} - 13 q^{49} + 22 q^{50} - 3 q^{51} + q^{52} - q^{53} - q^{54} + 8 q^{55} - q^{56} - 2 q^{57} + 9 q^{58} + 5 q^{59} + 4 q^{60} + 15 q^{61} - 16 q^{62} + 5 q^{63} + 2 q^{64} - 4 q^{65} + q^{66} + 5 q^{67} - 3 q^{68} + 12 q^{69} + 16 q^{70} - 30 q^{71} - q^{72} - 2 q^{73} + 8 q^{74} - 11 q^{75} - 2 q^{76} + 4 q^{77} - 2 q^{78} + 2 q^{79} + 4 q^{80} - q^{81} - 16 q^{83} + 5 q^{84} - 24 q^{85} - 10 q^{86} + 9 q^{87} + q^{88} - 8 q^{90} + q^{91} + 12 q^{92} + 8 q^{93} + 11 q^{94} - 4 q^{95} - q^{96} + 20 q^{97} + 2 q^{98} - 2 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 + 4 * q^5 + 2 * q^6 - q^7 + 2 * q^8 - q^9 + 4 * q^10 + q^11 - q^12 - 2 * q^13 + 5 * q^14 - 8 * q^15 - q^16 - 3 * q^17 - q^18 + q^19 - 8 * q^20 - 4 * q^21 - 2 * q^22 - 6 * q^23 - q^24 - 11 * q^25 + q^26 + 2 * q^27 - 4 * q^28 - 18 * q^29 + 4 * q^30 + 8 * q^31 - q^32 + q^33 + 6 * q^34 - 20 * q^35 + 2 * q^36 + 8 * q^37 + q^38 + q^39 + 4 * q^40 - q^42 + 20 * q^43 + q^44 + 4 * q^45 - 6 * q^46 + 11 * q^47 + 2 * q^48 - 13 * q^49 + 22 * q^50 - 3 * q^51 + q^52 - q^53 - q^54 + 8 * q^55 - q^56 - 2 * q^57 + 9 * q^58 + 5 * q^59 + 4 * q^60 + 15 * q^61 - 16 * q^62 + 5 * q^63 + 2 * q^64 - 4 * q^65 + q^66 + 5 * q^67 - 3 * q^68 + 12 * q^69 + 16 * q^70 - 30 * q^71 - q^72 - 2 * q^73 + 8 * q^74 - 11 * q^75 - 2 * q^76 + 4 * q^77 - 2 * q^78 + 2 * q^79 + 4 * q^80 - q^81 - 16 * q^83 + 5 * q^84 - 24 * q^85 - 10 * q^86 + 9 * q^87 + q^88 - 8 * q^90 + q^91 + 12 * q^92 + 8 * q^93 + 11 * q^94 - 4 * q^95 - q^96 + 20 * q^97 + 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.834512	+	0.550990i	$0.185750\pi$
$5$	2.00000	+	3.46410i	0.894427	+	1.54919i	0.0599153	+	0.998203i	$0.480917\pi$
$6$	1.00000			0.408248
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	2.00000	−	3.46410i	0.632456	−	1.09545i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	−0.780750	−	0.624844i	$-0.785163\pi$
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	0.931505	+	0.363727i	$0.118496\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	2.50000	−	0.866025i	0.668153	−	0.231455i
$15$	−4.00000			−1.03280
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	0.917663	−	0.397360i	$-0.130073\pi$
$19$	0.500000	+	0.866025i	0.114708	+	0.198680i	−0.802955	+	0.596040i	$0.796740\pi$
$20$	−4.00000			−0.894427
$21$	−2.00000	−	1.73205i	−0.436436	−	0.377964i
$22$	−1.00000			−0.213201
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−5.50000	+	9.52628i	−1.10000	+	1.90526i
$26$	0.500000	+	0.866025i	0.0980581	+	0.169842i
$27$	1.00000			0.192450
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$	2.00000	+	3.46410i	0.365148	+	0.632456i
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	3.00000			0.514496
$35$	−10.0000	+	3.46410i	−1.69031	+	0.585540i
$36$	1.00000			0.166667
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	0.981236	+	0.192809i	$0.0617599\pi$
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	−0.323640	+	0.946180i	$0.604907\pi$
$38$	0.500000	−	0.866025i	0.0811107	−	0.140488i
$39$	0.500000	−	0.866025i	0.0800641	−	0.138675i
$40$	2.00000	+	3.46410i	0.316228	+	0.547723i
$41$		0			0			−	1.00000i	$-0.5\pi$
$41$		0			0				1.00000i	$0.5\pi$
$42$	−0.500000	+	2.59808i	−0.0771517	+	0.400892i
$43$	10.0000			1.52499			0.762493	−	0.646997i	$-0.223975\pi$
$43$	10.0000			1.52499			0.762493	+	0.646997i	$0.223975\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	2.00000	−	3.46410i	0.298142	−	0.516398i
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	5.50000	+	9.52628i	0.802257	+	1.38955i	0.918127	+	0.396286i	$0.129701\pi$
$47$	5.50000	+	9.52628i	0.802257	+	1.38955i	−0.115870	+	0.993264i	$0.536965\pi$
$48$	1.00000			0.144338
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	11.0000			1.55563
$51$	−1.50000	−	2.59808i	−0.210042	−	0.363803i
$52$	0.500000	−	0.866025i	0.0693375	−	0.120096i
$53$	−0.500000	+	0.866025i	−0.0686803	+	0.118958i	−0.898321	−	0.439340i	$-0.855212\pi$
$53$	−0.500000	+	0.866025i	−0.0686803	+	0.118958i	0.829640	+	0.558298i	$0.188546\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	4.00000			0.539360
$56$	−0.500000	+	2.59808i	−0.0668153	+	0.347183i
$57$	−1.00000			−0.132453
$58$	4.50000	+	7.79423i	0.590879	+	1.02343i
$59$	2.50000	−	4.33013i	0.325472	−	0.563735i	−0.656136	−	0.754643i	$-0.727810\pi$
$59$	2.50000	−	4.33013i	0.325472	−	0.563735i	0.981608	+	0.190909i	$0.0611434\pi$
$60$	2.00000	−	3.46410i	0.258199	−	0.447214i
$61$	7.50000	+	12.9904i	0.960277	+	1.66325i	0.721803	+	0.692099i	$0.243314\pi$
$61$	7.50000	+	12.9904i	0.960277	+	1.66325i	0.238474	+	0.971149i	$0.423353\pi$
$62$	−8.00000			−1.01600
$63$	2.50000	−	0.866025i	0.314970	−	0.109109i
$64$	1.00000			0.125000
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$	0.500000	−	0.866025i	0.0615457	−	0.106600i
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	0.977356	+	0.211604i	$0.0678686\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$	6.00000			0.722315
$70$	8.00000	+	6.92820i	0.956183	+	0.828079i
$71$	−15.0000			−1.78017			−0.890086	−	0.455792i	$-0.849356\pi$
$71$	−15.0000			−1.78017			−0.890086	+	0.455792i	$0.849356\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	4.00000	−	6.92820i	0.464991	−	0.805387i
$75$	−5.50000	−	9.52628i	−0.635085	−	1.10000i
$76$	−1.00000			−0.114708
$77$	2.00000	+	1.73205i	0.227921	+	0.197386i
$78$	−1.00000			−0.113228
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	0.916781	−	0.399390i	$-0.130778\pi$
$79$	1.00000	+	1.73205i	0.112509	+	0.194871i	−0.804272	+	0.594261i	$0.797445\pi$
$80$	2.00000	−	3.46410i	0.223607	−	0.387298i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$	2.50000	−	0.866025i	0.272772	−	0.0944911i
$85$	−12.0000			−1.30158
$86$	−5.00000	−	8.66025i	−0.539164	−	0.933859i
$87$	4.50000	−	7.79423i	0.482451	−	0.835629i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$	−4.00000			−0.421637
$91$	0.500000	−	2.59808i	0.0524142	−	0.272352i
$92$	6.00000			0.625543
$93$	4.00000	+	6.92820i	0.414781	+	0.718421i
$94$	5.50000	−	9.52628i	0.567282	−	0.982561i
$95$	−2.00000	+	3.46410i	−0.205196	+	0.355409i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	10.0000			1.01535			0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000			1.01535			0.507673	+	0.861550i	$0.330506\pi$
$98$	1.00000	+	6.92820i	0.101015	+	0.699854i
$99$	−1.00000			−0.100504
$100$	−5.50000	−	9.52628i	−0.550000	−	0.952628i
$101$	7.00000	−	12.1244i	0.696526	−	1.20642i	−0.273138	−	0.961975i	$-0.588061\pi$
$101$	7.00000	−	12.1244i	0.696526	−	1.20642i	0.969664	−	0.244443i	$-0.0786053\pi$
$102$	−1.50000	+	2.59808i	−0.148522	+	0.257248i
$103$	−3.00000	−	5.19615i	−0.295599	−	0.511992i	0.679525	−	0.733652i	$-0.262186\pi$
$103$	−3.00000	−	5.19615i	−0.295599	−	0.511992i	−0.975124	+	0.221660i	$0.928852\pi$
$104$	−1.00000			−0.0980581
$105$	2.00000	−	10.3923i	0.195180	−	1.01419i
$106$	1.00000			0.0971286
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	0.992003	−	0.126217i	$-0.0402834\pi$
$107$	4.00000	+	6.92820i	0.386695	+	0.669775i	−0.605308	+	0.795991i	$0.706950\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$109$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$110$	−2.00000	−	3.46410i	−0.190693	−	0.330289i
$111$	−8.00000			−0.759326
$112$	2.50000	−	0.866025i	0.236228	−	0.0818317i
$113$	5.00000			0.470360			0.235180	−	0.971952i	$-0.424432\pi$
$113$	5.00000			0.470360			0.235180	+	0.971952i	$0.424432\pi$
$114$	0.500000	+	0.866025i	0.0468293	+	0.0811107i
$115$	12.0000	−	20.7846i	1.11901	−	1.93817i
$116$	4.50000	−	7.79423i	0.417815	−	0.723676i
$117$	0.500000	+	0.866025i	0.0462250	+	0.0800641i
$118$	−5.00000			−0.460287
$119$	−6.00000	−	5.19615i	−0.550019	−	0.476331i
$120$	−4.00000			−0.365148
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	7.50000	−	12.9904i	0.679018	−	1.17609i
$123$		0			0
$124$	4.00000	+	6.92820i	0.359211	+	0.622171i
$125$	−24.0000			−2.14663
$126$	−2.00000	−	1.73205i	−0.178174	−	0.154303i
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−5.00000	+	8.66025i	−0.440225	+	0.762493i
$130$	−2.00000	+	3.46410i	−0.175412	+	0.303822i
$131$	1.00000	+	1.73205i	0.0873704	+	0.151330i	0.906399	−	0.422423i	$-0.138820\pi$
$131$	1.00000	+	1.73205i	0.0873704	+	0.151330i	−0.819028	+	0.573753i	$0.805487\pi$
$132$	−1.00000			−0.0870388
$133$	−2.50000	+	0.866025i	−0.216777	+	0.0750939i
$134$	−5.00000			−0.431934
$135$	2.00000	+	3.46410i	0.172133	+	0.298142i
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	4.00000	−	6.92820i	0.341743	−	0.591916i	−0.643013	−	0.765855i	$-0.722316\pi$
$137$	4.00000	−	6.92820i	0.341743	−	0.591916i	0.984757	+	0.173939i	$0.0556494\pi$
$138$	−3.00000	−	5.19615i	−0.255377	−	0.442326i
$139$	12.0000			1.01783			0.508913	−	0.860818i	$-0.330047\pi$
$139$	12.0000			1.01783			0.508913	+	0.860818i	$0.330047\pi$
$140$	2.00000	−	10.3923i	0.169031	−	0.878310i
$141$	−11.0000			−0.926367
$142$	7.50000	+	12.9904i	0.629386	+	1.09013i
$143$	−0.500000	+	0.866025i	−0.0418121	+	0.0724207i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−18.0000	−	31.1769i	−1.49482	−	2.58910i
$146$	2.00000			0.165521
$147$	5.50000	−	4.33013i	0.453632	−	0.357143i
$148$	−8.00000			−0.657596
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	0.994847	−	0.101391i	$-0.0323294\pi$
$149$	5.00000	+	8.66025i	0.409616	+	0.709476i	−0.585231	+	0.810867i	$0.698996\pi$
$150$	−5.50000	+	9.52628i	−0.449073	+	0.777817i
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	0.162758	+	0.986666i	$0.447961\pi$
$151$	−9.50000	+	16.4545i	−0.773099	+	1.33905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	0.500000	+	0.866025i	0.0405554	+	0.0702439i
$153$	3.00000			0.242536
$154$	0.500000	−	2.59808i	0.0402911	−	0.209359i
$155$	32.0000			2.57030
$156$	0.500000	+	0.866025i	0.0400320	+	0.0693375i
$157$	−7.50000	+	12.9904i	−0.598565	+	1.03675i	0.394468	+	0.918910i	$0.370929\pi$
$157$	−7.50000	+	12.9904i	−0.598565	+	1.03675i	−0.993033	+	0.117836i	$0.962404\pi$
$158$	1.00000	−	1.73205i	0.0795557	−	0.137795i
$159$	−0.500000	−	0.866025i	−0.0396526	−	0.0686803i
$160$	−4.00000			−0.316228
$161$	15.0000	−	5.19615i	1.18217	−	0.409514i
$162$	1.00000			0.0785674
$163$	−6.50000	−	11.2583i	−0.509119	−	0.881820i	−0.999944	−	0.0105623i	$-0.996638\pi$
$163$	−6.50000	−	11.2583i	−0.509119	−	0.881820i	0.490825	−	0.871258i	$-0.336695\pi$
$164$		0			0
$165$	−2.00000	+	3.46410i	−0.155700	+	0.269680i
$166$	4.00000	+	6.92820i	0.310460	+	0.537733i
$167$	3.00000			0.232147			0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000			0.232147			0.116073	+	0.993241i	$0.462969\pi$
$168$	−2.00000	−	1.73205i	−0.154303	−	0.133631i
$169$	1.00000			0.0769231
$170$	6.00000	+	10.3923i	0.460179	+	0.797053i
$171$	0.500000	−	0.866025i	0.0382360	−	0.0662266i
$172$	−5.00000	+	8.66025i	−0.381246	+	0.660338i
$173$	−1.50000	−	2.59808i	−0.114043	−	0.197528i	0.803354	−	0.595502i	$-0.203047\pi$
$173$	−1.50000	−	2.59808i	−0.114043	−	0.197528i	−0.917397	+	0.397974i	$0.869713\pi$
$174$	−9.00000			−0.682288
$175$	−22.0000	−	19.0526i	−1.66304	−	1.44024i
$176$	−1.00000			−0.0753778
$177$	2.50000	+	4.33013i	0.187912	+	0.325472i
$178$		0			0
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	−0.304446	−	0.952529i	$-0.598471\pi$
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	0.977138	−	0.212607i	$-0.0681952\pi$
$180$	2.00000	+	3.46410i	0.149071	+	0.258199i
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	−2.50000	+	0.866025i	−0.185312	+	0.0641941i
$183$	−15.0000			−1.10883
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$	−16.0000	+	27.7128i	−1.17634	+	2.03749i
$186$	4.00000	−	6.92820i	0.293294	−	0.508001i
$187$	1.50000	+	2.59808i	0.109691	+	0.189990i
$188$	−11.0000			−0.802257
$189$	−0.500000	+	2.59808i	−0.0363696	+	0.188982i
$190$	4.00000			0.290191
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	6.00000	−	10.3923i	0.431889	−	0.748054i	−0.565147	−	0.824991i	$-0.691180\pi$
$193$	6.00000	−	10.3923i	0.431889	−	0.748054i	0.997036	+	0.0769360i	$0.0245137\pi$
$194$	−5.00000	−	8.66025i	−0.358979	−	0.621770i
$195$	4.00000			0.286446
$196$	5.50000	−	4.33013i	0.392857	−	0.309295i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	0.500000	+	0.866025i	0.0355335	+	0.0615457i
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	−0.632581	−	0.774494i	$-0.718005\pi$
$199$	5.00000	−	8.66025i	0.354441	−	0.613909i	0.987022	+	0.160585i	$0.0513380\pi$
$200$	−5.50000	+	9.52628i	−0.388909	+	0.673610i
$201$	2.50000	+	4.33013i	0.176336	+	0.305424i
$202$	−14.0000			−0.985037
$203$	4.50000	−	23.3827i	0.315838	−	1.64114i
$204$	3.00000			0.210042
$205$		0			0
$206$	−3.00000	+	5.19615i	−0.209020	+	0.362033i
$207$	−3.00000	+	5.19615i	−0.208514	+	0.361158i
$208$	0.500000	+	0.866025i	0.0346688	+	0.0600481i
$209$	1.00000			0.0691714
$210$	−10.0000	+	3.46410i	−0.690066	+	0.239046i
$211$	18.0000			1.23917			0.619586	−	0.784929i	$-0.287301\pi$
$211$	18.0000			1.23917			0.619586	+	0.784929i	$0.287301\pi$
$212$	−0.500000	−	0.866025i	−0.0343401	−	0.0594789i
$213$	7.50000	−	12.9904i	0.513892	−	0.890086i
$214$	4.00000	−	6.92820i	0.273434	−	0.473602i
$215$	20.0000	+	34.6410i	1.36399	+	2.36250i
$216$	1.00000			0.0680414
$217$	16.0000	+	13.8564i	1.08615	+	0.940634i
$218$		0			0
$219$	−1.00000	−	1.73205i	−0.0675737	−	0.117041i
$220$	−2.00000	+	3.46410i	−0.134840	+	0.233550i
$221$	1.50000	−	2.59808i	0.100901	−	0.174766i
$222$	4.00000	+	6.92820i	0.268462	+	0.464991i
$223$	19.0000			1.27233			0.636167	−	0.771551i	$-0.280519\pi$
$223$	19.0000			1.27233			0.636167	+	0.771551i	$0.280519\pi$
$224$	−2.00000	−	1.73205i	−0.133631	−	0.115728i
$225$	11.0000			0.733333
$226$	−2.50000	−	4.33013i	−0.166298	−	0.288036i
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	−0.595274	−	0.803523i	$-0.702957\pi$
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	0.993508	+	0.113761i	$0.0362899\pi$
$228$	0.500000	−	0.866025i	0.0331133	−	0.0573539i
$229$	−9.00000	−	15.5885i	−0.594737	−	1.03011i	−0.993584	−	0.113097i	$-0.963923\pi$
$229$	−9.00000	−	15.5885i	−0.594737	−	1.03011i	0.398847	−	0.917017i	$-0.369410\pi$
$230$	−24.0000			−1.58251
$231$	−2.50000	+	0.866025i	−0.164488	+	0.0569803i
$232$	−9.00000			−0.590879
$233$	7.50000	+	12.9904i	0.491341	+	0.851028i	0.999950	−	0.00996947i	$-0.00317343\pi$
$233$	7.50000	+	12.9904i	0.491341	+	0.851028i	−0.508609	+	0.860998i	$0.669840\pi$
$234$	0.500000	−	0.866025i	0.0326860	−	0.0566139i
$235$	−22.0000	+	38.1051i	−1.43512	+	2.48570i
$236$	2.50000	+	4.33013i	0.162736	+	0.281867i
$237$	−2.00000			−0.129914
$238$	−1.50000	+	7.79423i	−0.0972306	+	0.505225i
$239$	15.0000			0.970269			0.485135	−	0.874439i	$-0.338771\pi$
$239$	15.0000			0.970269			0.485135	+	0.874439i	$0.338771\pi$
$240$	2.00000	+	3.46410i	0.129099	+	0.223607i
$241$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$241$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$242$	5.00000	−	8.66025i	0.321412	−	0.556702i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−15.0000			−0.960277
$245$	−4.00000	−	27.7128i	−0.255551	−	1.77051i
$246$		0			0
$247$	−0.500000	−	0.866025i	−0.0318142	−	0.0551039i
$248$	4.00000	−	6.92820i	0.254000	−	0.439941i
$249$	4.00000	−	6.92820i	0.253490	−	0.439057i
$250$	12.0000	+	20.7846i	0.758947	+	1.31453i
$251$	−22.0000			−1.38863			−0.694314	−	0.719672i	$-0.744292\pi$
$251$	−22.0000			−1.38863			−0.694314	+	0.719672i	$0.744292\pi$
$252$	−0.500000	+	2.59808i	−0.0314970	+	0.163663i
$253$	−6.00000			−0.377217
$254$	−1.00000	−	1.73205i	−0.0627456	−	0.108679i
$255$	6.00000	−	10.3923i	0.375735	−	0.650791i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$	10.0000			0.622573
$259$	−20.0000	+	6.92820i	−1.24274	+	0.430498i
$260$	4.00000			0.248069
$261$	4.50000	+	7.79423i	0.278543	+	0.482451i
$262$	1.00000	−	1.73205i	0.0617802	−	0.107006i
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$	0.500000	+	0.866025i	0.0307729	+	0.0533002i
$265$	−4.00000			−0.245718
$266$	2.00000	+	1.73205i	0.122628	+	0.106199i
$267$		0			0
$268$	2.50000	+	4.33013i	0.152712	+	0.264505i
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	−0.695606	−	0.718423i	$-0.744864\pi$
$269$	4.50000	−	7.79423i	0.274370	−	0.475223i	0.969976	+	0.243201i	$0.0781974\pi$
$270$	2.00000	−	3.46410i	0.121716	−	0.210819i
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	0.880812	−	0.473466i	$-0.156997\pi$
$271$	0.500000	+	0.866025i	0.0303728	+	0.0526073i	−0.850439	+	0.526073i	$0.823664\pi$
$272$	3.00000			0.181902
$273$	2.00000	+	1.73205i	0.121046	+	0.104828i
$274$	−8.00000			−0.483298
$275$	5.50000	+	9.52628i	0.331662	+	0.574456i
$276$	−3.00000	+	5.19615i	−0.180579	+	0.312772i
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	−0.850613	−	0.525792i	$-0.823769\pi$
$277$	0.500000	−	0.866025i	0.0300421	−	0.0520344i	0.880656	+	0.473757i	$0.157103\pi$
$278$	−6.00000	−	10.3923i	−0.359856	−	0.623289i
$279$	−8.00000			−0.478947
$280$	−10.0000	+	3.46410i	−0.597614	+	0.207020i
$281$	−32.0000			−1.90896			−0.954480	−	0.298275i	$-0.903589\pi$
$281$	−32.0000			−1.90896			−0.954480	+	0.298275i	$0.903589\pi$
$282$	5.50000	+	9.52628i	0.327520	+	0.567282i
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$	7.50000	−	12.9904i	0.445043	−	0.770837i
$285$	−2.00000	−	3.46410i	−0.118470	−	0.205196i
$286$	1.00000			0.0591312
$287$		0			0
$288$	1.00000			0.0589256
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−18.0000	+	31.1769i	−1.05700	+	1.83077i
$291$	−5.00000	+	8.66025i	−0.293105	+	0.507673i
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	14.0000			0.817889			0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000			0.817889			0.408944	+	0.912559i	$0.365897\pi$
$294$	−6.50000	−	2.59808i	−0.379088	−	0.151523i
$295$	20.0000			1.16445
$296$	4.00000	+	6.92820i	0.232495	+	0.402694i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	5.00000	−	8.66025i	0.289642	−	0.501675i
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$	11.0000			0.635085
$301$	−5.00000	+	25.9808i	−0.288195	+	1.49751i
$302$	19.0000			1.09333
$303$	7.00000	+	12.1244i	0.402139	+	0.696526i
$304$	0.500000	−	0.866025i	0.0286770	−	0.0496700i
$305$	−30.0000	+	51.9615i	−1.71780	+	2.97531i
$306$	−1.50000	−	2.59808i	−0.0857493	−	0.148522i
$307$	27.0000			1.54097			0.770486	−	0.637457i	$-0.220014\pi$
$307$	27.0000			1.54097			0.770486	+	0.637457i	$0.220014\pi$
$308$	−2.50000	+	0.866025i	−0.142451	+	0.0493464i
$309$	6.00000			0.341328
$310$	−16.0000	−	27.7128i	−0.908739	−	1.57398i
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	−0.956864	−	0.290537i	$-0.906166\pi$
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	0.730044	+	0.683400i	$0.239499\pi$
$312$	0.500000	−	0.866025i	0.0283069	−	0.0490290i
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	0.993186	−	0.116543i	$-0.0371814\pi$
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	−0.597522	+	0.801852i	$0.703848\pi$
$314$	15.0000			0.846499
$315$	8.00000	+	6.92820i	0.450749	+	0.390360i
$316$	−2.00000			−0.112509
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	0.937892	−	0.346929i	$-0.112775\pi$
$317$	3.00000	+	5.19615i	0.168497	+	0.291845i	−0.769395	+	0.638774i	$0.779442\pi$
$318$	−0.500000	+	0.866025i	−0.0280386	+	0.0485643i
$319$	−4.50000	+	7.79423i	−0.251952	+	0.436393i
$320$	2.00000	+	3.46410i	0.111803	+	0.193649i
$321$	−8.00000			−0.446516
$322$	−12.0000	−	10.3923i	−0.668734	−	0.579141i
$323$	−3.00000			−0.166924
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	5.50000	−	9.52628i	0.305085	−	0.528423i
$326$	−6.50000	+	11.2583i	−0.360002	+	0.623541i
$327$		0			0
$328$		0			0
$329$	−27.5000	+	9.52628i	−1.51612	+	0.525201i
$330$	4.00000			0.220193
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	−0.937829	−	0.347097i	$-0.887167\pi$
$331$	−14.0000	−	24.2487i	−0.769510	−	1.33283i	0.168320	−	0.985732i	$-0.446166\pi$
$332$	4.00000	−	6.92820i	0.219529	−	0.380235i
$333$	4.00000	−	6.92820i	0.219199	−	0.379663i
$334$	−1.50000	−	2.59808i	−0.0820763	−	0.142160i
$335$	20.0000			1.09272
$336$	−0.500000	+	2.59808i	−0.0272772	+	0.141737i
$337$	31.0000			1.68868			0.844339	−	0.535810i	$-0.179994\pi$
$337$	31.0000			1.68868			0.844339	+	0.535810i	$0.179994\pi$
$338$	−0.500000	−	0.866025i	−0.0271964	−	0.0471056i
$339$	−2.50000	+	4.33013i	−0.135781	+	0.235180i
$340$	6.00000	−	10.3923i	0.325396	−	0.563602i
$341$	−4.00000	−	6.92820i	−0.216612	−	0.375183i
$342$	−1.00000			−0.0540738
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	10.0000			0.539164
$345$	12.0000	+	20.7846i	0.646058	+	1.11901i
$346$	−1.50000	+	2.59808i	−0.0806405	+	0.139673i
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	−0.807337	−	0.590091i	$-0.799092\pi$
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	0.914702	+	0.404128i	$0.132425\pi$
$348$	4.50000	+	7.79423i	0.241225	+	0.417815i
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$	−5.50000	+	28.5788i	−0.293987	+	1.52760i
$351$	−1.00000			−0.0533761
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$	2.50000	−	4.33013i	0.132874	−	0.230144i
$355$	−30.0000	−	51.9615i	−1.59223	−	2.75783i
$356$		0			0
$357$	7.50000	−	2.59808i	0.396942	−	0.137505i
$358$	−18.0000			−0.951330
$359$	−4.00000	−	6.92820i	−0.211112	−	0.365657i	0.740951	−	0.671559i	$-0.234375\pi$
$359$	−4.00000	−	6.92820i	−0.211112	−	0.365657i	−0.952063	+	0.305903i	$0.901042\pi$
$360$	2.00000	−	3.46410i	0.105409	−	0.182574i
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	3.50000	+	6.06218i	0.183956	+	0.318621i
$363$	−10.0000			−0.524864
$364$	2.00000	+	1.73205i	0.104828	+	0.0907841i
$365$	−8.00000			−0.418739
$366$	7.50000	+	12.9904i	0.392031	+	0.679018i
$367$	−13.0000	+	22.5167i	−0.678594	+	1.17536i	0.296810	+	0.954937i	$0.404077\pi$
$367$	−13.0000	+	22.5167i	−0.678594	+	1.17536i	−0.975404	+	0.220423i	$0.929256\pi$
$368$	−3.00000	+	5.19615i	−0.156386	+	0.270868i
$369$		0			0
$370$	32.0000			1.66360
$371$	−2.00000	−	1.73205i	−0.103835	−	0.0899236i
$372$	−8.00000			−0.414781
$373$	0.500000	+	0.866025i	0.0258890	+	0.0448411i	0.878680	−	0.477412i	$-0.158425\pi$
$373$	0.500000	+	0.866025i	0.0258890	+	0.0448411i	−0.852791	+	0.522253i	$0.825092\pi$
$374$	1.50000	−	2.59808i	0.0775632	−	0.134343i
$375$	12.0000	−	20.7846i	0.619677	−	1.07331i
$376$	5.50000	+	9.52628i	0.283641	+	0.491280i
$377$	9.00000			0.463524
$378$	2.50000	−	0.866025i	0.128586	−	0.0445435i
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	−2.00000	−	3.46410i	−0.102598	−	0.177705i
$381$	−1.00000	+	1.73205i	−0.0512316	+	0.0887357i
$382$	6.00000	−	10.3923i	0.306987	−	0.531717i
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	0.585973	−	0.810331i	$-0.300713\pi$
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	−0.994753	+	0.102302i	$0.967379\pi$
$384$	1.00000			0.0510310
$385$	−2.00000	+	10.3923i	−0.101929	+	0.529641i
$386$	−12.0000			−0.610784
$387$	−5.00000	−	8.66025i	−0.254164	−	0.440225i
$388$	−5.00000	+	8.66025i	−0.253837	+	0.439658i
$389$	11.5000	−	19.9186i	0.583073	−	1.00991i	−0.412039	−	0.911166i	$-0.635183\pi$
$389$	11.5000	−	19.9186i	0.583073	−	1.00991i	0.995113	−	0.0987463i	$-0.0314832\pi$
$390$	−2.00000	−	3.46410i	−0.101274	−	0.175412i
$391$	18.0000			0.910299
$392$	−6.50000	−	2.59808i	−0.328300	−	0.131223i
$393$	−2.00000			−0.100887
$394$	−9.00000	−	15.5885i	−0.453413	−	0.785335i
$395$	−4.00000	+	6.92820i	−0.201262	+	0.348596i
$396$	0.500000	−	0.866025i	0.0251259	−	0.0435194i
$397$	15.0000	+	25.9808i	0.752828	+	1.30394i	0.946447	+	0.322860i	$0.104644\pi$
$397$	15.0000	+	25.9808i	0.752828	+	1.30394i	−0.193618	+	0.981077i	$0.562022\pi$
$398$	−10.0000			−0.501255
$399$	0.500000	−	2.59808i	0.0250313	−	0.130066i
$400$	11.0000			0.550000
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	−0.948272	−	0.317460i	$-0.897170\pi$
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	0.199207	−	0.979957i	$-0.436163\pi$
$402$	2.50000	−	4.33013i	0.124689	−	0.215967i
$403$	−4.00000	+	6.92820i	−0.199254	+	0.345118i
$404$	7.00000	+	12.1244i	0.348263	+	0.603209i
$405$	−4.00000			−0.198762
$406$	−22.5000	+	7.79423i	−1.11666	+	0.386821i
$407$	8.00000			0.396545
$408$	−1.50000	−	2.59808i	−0.0742611	−	0.128624i
$409$	4.00000	−	6.92820i	0.197787	−	0.342578i	−0.750023	−	0.661411i	$-0.769958\pi$
$409$	4.00000	−	6.92820i	0.197787	−	0.342578i	0.947811	+	0.318834i	$0.103291\pi$
$410$		0			0
$411$	4.00000	+	6.92820i	0.197305	+	0.341743i
$412$	6.00000			0.295599
$413$	10.0000	+	8.66025i	0.492068	+	0.426143i
$414$	6.00000			0.294884
$415$	−16.0000	−	27.7128i	−0.785409	−	1.36037i
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$	−6.00000	+	10.3923i	−0.293821	+	0.508913i
$418$	−0.500000	−	0.866025i	−0.0244558	−	0.0423587i
$419$	−14.0000			−0.683945			−0.341972	−	0.939710i	$-0.611095\pi$
$419$	−14.0000			−0.683945			−0.341972	+	0.939710i	$0.611095\pi$
$420$	8.00000	+	6.92820i	0.390360	+	0.338062i
$421$	−30.0000			−1.46211			−0.731055	−	0.682318i	$-0.760972\pi$
$421$	−30.0000			−1.46211			−0.731055	+	0.682318i	$0.760972\pi$
$422$	−9.00000	−	15.5885i	−0.438113	−	0.758834i
$423$	5.50000	−	9.52628i	0.267419	−	0.463184i
$424$	−0.500000	+	0.866025i	−0.0242821	+	0.0420579i
$425$	−16.5000	−	28.5788i	−0.800368	−	1.38628i
$426$	−15.0000			−0.726752
$427$	−37.5000	+	12.9904i	−1.81475	+	0.628649i
$428$	−8.00000			−0.386695
$429$	−0.500000	−	0.866025i	−0.0241402	−	0.0418121i
$430$	20.0000	−	34.6410i	0.964486	−	1.67054i
$431$	4.00000	−	6.92820i	0.192673	−	0.333720i	−0.753462	−	0.657491i	$-0.771618\pi$
$431$	4.00000	−	6.92820i	0.192673	−	0.333720i	0.946135	+	0.323772i	$0.104951\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−11.0000			−0.528626			−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000			−0.528626			−0.264313	+	0.964437i	$0.585145\pi$
$434$	4.00000	−	20.7846i	0.192006	−	0.997693i
$435$	36.0000			1.72607
$436$		0			0
$437$	3.00000	−	5.19615i	0.143509	−	0.248566i
$438$	−1.00000	+	1.73205i	−0.0477818	+	0.0827606i
$439$	1.00000	+	1.73205i	0.0477274	+	0.0826663i	0.888902	−	0.458097i	$-0.151469\pi$
$439$	1.00000	+	1.73205i	0.0477274	+	0.0826663i	−0.841175	+	0.540763i	$0.818135\pi$
$440$	4.00000			0.190693
$441$	1.00000	+	6.92820i	0.0476190	+	0.329914i
$442$	−3.00000			−0.142695
$443$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$443$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$444$	4.00000	−	6.92820i	0.189832	−	0.328798i
$445$		0			0
$446$	−9.50000	−	16.4545i	−0.449838	−	0.779142i
$447$	−10.0000			−0.472984
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	−4.00000			−0.188772			−0.0943858	−	0.995536i	$-0.530089\pi$
$449$	−4.00000			−0.188772			−0.0943858	+	0.995536i	$0.530089\pi$
$450$	−5.50000	−	9.52628i	−0.259272	−	0.449073i
$451$		0			0
$452$	−2.50000	+	4.33013i	−0.117590	+	0.203672i
$453$	−9.50000	−	16.4545i	−0.446349	−	0.773099i
$454$	−12.0000			−0.563188
$455$	10.0000	−	3.46410i	0.468807	−	0.162400i
$456$	−1.00000			−0.0468293
$457$	−17.0000	−	29.4449i	−0.795226	−	1.37737i	−0.922695	−	0.385530i	$-0.874019\pi$
$457$	−17.0000	−	29.4449i	−0.795226	−	1.37737i	0.127469	−	0.991843i	$-0.459315\pi$
$458$	−9.00000	+	15.5885i	−0.420542	+	0.728401i
$459$	−1.50000	+	2.59808i	−0.0700140	+	0.121268i
$460$	12.0000	+	20.7846i	0.559503	+	0.969087i
$461$	40.0000			1.86299			0.931493	−	0.363760i	$-0.118507\pi$
$461$	40.0000			1.86299			0.931493	+	0.363760i	$0.118507\pi$
$462$	2.00000	+	1.73205i	0.0930484	+	0.0805823i
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$	4.50000	+	7.79423i	0.208907	+	0.361838i
$465$	−16.0000	+	27.7128i	−0.741982	+	1.28515i
$466$	7.50000	−	12.9904i	0.347431	−	0.601768i
$467$	−15.0000	−	25.9808i	−0.694117	−	1.20225i	−0.970477	−	0.241192i	$-0.922462\pi$
$467$	−15.0000	−	25.9808i	−0.694117	−	1.20225i	0.276360	−	0.961054i	$-0.410872\pi$
$468$	−1.00000			−0.0462250
$469$	10.0000	+	8.66025i	0.461757	+	0.399893i
$470$	44.0000			2.02957
$471$	−7.50000	−	12.9904i	−0.345582	−	0.598565i
$472$	2.50000	−	4.33013i	0.115072	−	0.199310i
$473$	5.00000	−	8.66025i	0.229900	−	0.398199i
$474$	1.00000	+	1.73205i	0.0459315	+	0.0795557i
$475$	−11.0000			−0.504715
$476$	7.50000	−	2.59808i	0.343762	−	0.119083i
$477$	1.00000			0.0457869
$478$	−7.50000	−	12.9904i	−0.343042	−	0.594166i
$479$	−2.50000	+	4.33013i	−0.114228	+	0.197849i	−0.917471	−	0.397803i	$-0.869773\pi$
$479$	−2.50000	+	4.33013i	−0.114228	+	0.197849i	0.803243	+	0.595652i	$0.203106\pi$
$480$	2.00000	−	3.46410i	0.0912871	−	0.158114i
$481$	−4.00000	−	6.92820i	−0.182384	−	0.315899i
$482$		0			0
$483$	−3.00000	+	15.5885i	−0.136505	+	0.709299i
$484$	−10.0000			−0.454545
$485$	20.0000	+	34.6410i	0.908153	+	1.57297i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	0.500000	−	0.866025i	0.0226572	−	0.0392434i	−0.854475	−	0.519493i	$-0.826121\pi$
$487$	0.500000	−	0.866025i	0.0226572	−	0.0392434i	0.877132	+	0.480250i	$0.159454\pi$
$488$	7.50000	+	12.9904i	0.339509	+	0.588047i
$489$	13.0000			0.587880
$490$	−22.0000	+	17.3205i	−0.993859	+	0.782461i
$491$	−38.0000			−1.71492			−0.857458	−	0.514554i	$-0.827958\pi$
$491$	−38.0000			−1.71492			−0.857458	+	0.514554i	$0.827958\pi$
$492$		0			0
$493$	13.5000	−	23.3827i	0.608009	−	1.05310i
$494$	−0.500000	+	0.866025i	−0.0224961	+	0.0389643i
$495$	−2.00000	−	3.46410i	−0.0898933	−	0.155700i
$496$	−8.00000			−0.359211
$497$	7.50000	−	38.9711i	0.336421	−	1.74809i
$498$	−8.00000			−0.358489
$499$	−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	$0.890640\pi$
$500$	12.0000	−	20.7846i	0.536656	−	0.929516i
$501$	−1.50000	+	2.59808i	−0.0670151	+	0.116073i
$502$	11.0000	+	19.0526i	0.490954	+	0.850357i
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$	2.50000	−	0.866025i	0.111359	−	0.0385758i
$505$	56.0000			2.49197
$506$	3.00000	+	5.19615i	0.133366	+	0.230997i
$507$	−0.500000	+	0.866025i	−0.0222058	+	0.0384615i
$508$	−1.00000	+	1.73205i	−0.0443678	+	0.0768473i
$509$	−20.0000	−	34.6410i	−0.886484	−	1.53544i	−0.844003	−	0.536339i	$-0.819807\pi$
$509$	−20.0000	−	34.6410i	−0.886484	−	1.53544i	−0.0424816	−	0.999097i	$-0.513526\pi$
$510$	−12.0000			−0.531369
$511$	−4.00000	−	3.46410i	−0.176950	−	0.153243i
$512$	1.00000			0.0441942
$513$	0.500000	+	0.866025i	0.0220755	+	0.0382360i
$514$	3.00000	−	5.19615i	0.132324	−	0.229192i
$515$	12.0000	−	20.7846i	0.528783	−	0.915879i
$516$	−5.00000	−	8.66025i	−0.220113	−	0.381246i
$517$	11.0000			0.483779
$518$	16.0000	+	13.8564i	0.703000	+	0.608816i
$519$	3.00000			0.131685
$520$	−2.00000	−	3.46410i	−0.0877058	−	0.151911i
$521$	−5.00000	+	8.66025i	−0.219054	+	0.379413i	−0.954519	−	0.298150i	$-0.903630\pi$
$521$	−5.00000	+	8.66025i	−0.219054	+	0.379413i	0.735465	+	0.677563i	$0.236964\pi$
$522$	4.50000	−	7.79423i	0.196960	−	0.341144i
$523$	7.00000	+	12.1244i	0.306089	+	0.530161i	0.977503	−	0.210921i	$-0.0676463\pi$
$523$	7.00000	+	12.1244i	0.306089	+	0.530161i	−0.671414	+	0.741082i	$0.734313\pi$
$524$	−2.00000			−0.0873704
$525$	27.5000	−	9.52628i	1.20020	−	0.415761i
$526$	24.0000			1.04645
$527$	12.0000	+	20.7846i	0.522728	+	0.905392i
$528$	0.500000	−	0.866025i	0.0217597	−	0.0376889i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	2.00000	+	3.46410i	0.0868744	+	0.150471i
$531$	−5.00000			−0.216982
$532$	0.500000	−	2.59808i	0.0216777	−	0.112641i
$533$		0			0
$534$		0			0
$535$	−16.0000	+	27.7128i	−0.691740	+	1.19813i
$536$	2.50000	−	4.33013i	0.107984	−	0.187033i
$537$	9.00000	+	15.5885i	0.388379	+	0.672692i
$538$	−9.00000			−0.388018
$539$	−5.50000	+	4.33013i	−0.236902	+	0.186512i
$540$	−4.00000			−0.172133
$541$	14.0000	+	24.2487i	0.601907	+	1.04253i	0.992532	+	0.121984i	$0.0389256\pi$
$541$	14.0000	+	24.2487i	0.601907	+	1.04253i	−0.390625	+	0.920550i	$0.627741\pi$
$542$	0.500000	−	0.866025i	0.0214768	−	0.0371990i
$543$	3.50000	−	6.06218i	0.150199	−	0.260153i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$		0			0
$546$	0.500000	−	2.59808i	0.0213980	−	0.111187i
$547$	−42.0000			−1.79579			−0.897895	−	0.440209i	$-0.854904\pi$
$547$	−42.0000			−1.79579			−0.897895	+	0.440209i	$0.854904\pi$
$548$	4.00000	+	6.92820i	0.170872	+	0.295958i
$549$	7.50000	−	12.9904i	0.320092	−	0.554416i
$550$	5.50000	−	9.52628i	0.234521	−	0.406202i
$551$	−4.50000	−	7.79423i	−0.191706	−	0.332045i
$552$	6.00000			0.255377
$553$	−5.00000	+	1.73205i	−0.212622	+	0.0736543i
$554$	−1.00000			−0.0424859
$555$	−16.0000	−	27.7128i	−0.679162	−	1.17634i
$556$	−6.00000	+	10.3923i	−0.254457	+	0.440732i
$557$	−17.0000	+	29.4449i	−0.720313	+	1.24762i	0.240561	+	0.970634i	$0.422669\pi$
$557$	−17.0000	+	29.4449i	−0.720313	+	1.24762i	−0.960874	+	0.276985i	$0.910665\pi$
$558$	4.00000	+	6.92820i	0.169334	+	0.293294i
$559$	−10.0000			−0.422955
$560$	8.00000	+	6.92820i	0.338062	+	0.292770i
$561$	−3.00000			−0.126660
$562$	16.0000	+	27.7128i	0.674919	+	1.16899i
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	−0.964315	−	0.264758i	$-0.914708\pi$
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	0.711445	+	0.702742i	$0.248041\pi$
$564$	5.50000	−	9.52628i	0.231592	−	0.401129i
$565$	10.0000	+	17.3205i	0.420703	+	0.728679i
$566$	−14.0000			−0.588464
$567$	−2.00000	−	1.73205i	−0.0839921	−	0.0727393i
$568$	−15.0000			−0.629386
$569$	9.50000	+	16.4545i	0.398261	+	0.689808i	0.993511	−	0.113732i	$-0.0362806\pi$
$569$	9.50000	+	16.4545i	0.398261	+	0.689808i	−0.595251	+	0.803540i	$0.702947\pi$
$570$	−2.00000	+	3.46410i	−0.0837708	+	0.145095i
$571$	−8.00000	+	13.8564i	−0.334790	+	0.579873i	−0.983444	−	0.181210i	$-0.941999\pi$
$571$	−8.00000	+	13.8564i	−0.334790	+	0.579873i	0.648655	+	0.761083i	$0.275332\pi$
$572$	−0.500000	−	0.866025i	−0.0209061	−	0.0362103i
$573$	−12.0000			−0.501307
$574$		0			0
$575$	66.0000			2.75239
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	7.00000	−	12.1244i	0.291414	−	0.504744i	−0.682730	−	0.730670i	$-0.739208\pi$
$577$	7.00000	−	12.1244i	0.291414	−	0.504744i	0.974144	+	0.225927i	$0.0725410\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	6.00000	+	10.3923i	0.249351	+	0.431889i
$580$	36.0000			1.49482
$581$	4.00000	−	20.7846i	0.165948	−	0.862291i
$582$	10.0000			0.414513
$583$	0.500000	+	0.866025i	0.0207079	+	0.0358671i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$	−2.00000	+	3.46410i	−0.0826898	+	0.143223i
$586$	−7.00000	−	12.1244i	−0.289167	−	0.500853i
$587$	47.0000			1.93990			0.969949	−	0.243309i	$-0.0782329\pi$
$587$	47.0000			1.93990			0.969949	+	0.243309i	$0.0782329\pi$
$588$	1.00000	+	6.92820i	0.0412393	+	0.285714i
$589$	8.00000			0.329634
$590$	−10.0000	−	17.3205i	−0.411693	−	0.713074i
$591$	−9.00000	+	15.5885i	−0.370211	+	0.641223i
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$	6.00000	+	10.3923i	0.246390	+	0.426761i	0.962522	−	0.271205i	$-0.0874221\pi$
$593$	6.00000	+	10.3923i	0.246390	+	0.426761i	−0.716131	+	0.697966i	$0.754089\pi$
$594$	−1.00000			−0.0410305
$595$	6.00000	−	31.1769i	0.245976	−	1.27813i
$596$	−10.0000			−0.409616
$597$	5.00000	+	8.66025i	0.204636	+	0.354441i
$598$	3.00000	−	5.19615i	0.122679	−	0.212486i
$599$	2.00000	−	3.46410i	0.0817178	−	0.141539i	−0.822270	−	0.569097i	$-0.807293\pi$
$599$	2.00000	−	3.46410i	0.0817178	−	0.141539i	0.903988	+	0.427558i	$0.140626\pi$
$600$	−5.50000	−	9.52628i	−0.224537	−	0.388909i
$601$	17.0000			0.693444			0.346722	−	0.937968i	$-0.387295\pi$
$601$	17.0000			0.693444			0.346722	+	0.937968i	$0.387295\pi$
$602$	25.0000	−	8.66025i	1.01892	−	0.352966i
$603$	−5.00000			−0.203616
$604$	−9.50000	−	16.4545i	−0.386550	−	0.669523i
$605$	−20.0000	+	34.6410i	−0.813116	+	1.40836i
$606$	7.00000	−	12.1244i	0.284356	−	0.492518i
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	0.688274	−	0.725450i	$-0.258368\pi$
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	−0.972396	+	0.233338i	$0.925035\pi$
$608$	−1.00000			−0.0405554
$609$	18.0000	+	15.5885i	0.729397	+	0.631676i
$610$	60.0000			2.42933
$611$	−5.50000	−	9.52628i	−0.222506	−	0.385392i
$612$	−1.50000	+	2.59808i	−0.0606339	+	0.105021i
$613$	12.0000	−	20.7846i	0.484675	−	0.839482i	−0.515170	−	0.857088i	$-0.672271\pi$
$613$	12.0000	−	20.7846i	0.484675	−	0.839482i	0.999845	+	0.0176058i	$0.00560439\pi$
$614$	−13.5000	−	23.3827i	−0.544816	−	0.943648i
$615$		0			0
$616$	2.00000	+	1.73205i	0.0805823	+	0.0697863i
$617$	−30.0000			−1.20775			−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000			−1.20775			−0.603877	+	0.797077i	$0.706378\pi$
$618$	−3.00000	−	5.19615i	−0.120678	−	0.209020i
$619$	22.0000	−	38.1051i	0.884255	−	1.53157i	0.0376891	−	0.999290i	$-0.488000\pi$
$619$	22.0000	−	38.1051i	0.884255	−	1.53157i	0.846566	−	0.532284i	$-0.178666\pi$
$620$	−16.0000	+	27.7128i	−0.642575	+	1.11297i
$621$	−3.00000	−	5.19615i	−0.120386	−	0.208514i
$622$	8.00000			0.320771
$623$		0			0
$624$	−1.00000			−0.0400320
$625$	−20.5000	−	35.5070i	−0.820000	−	1.42028i
$626$	7.00000	−	12.1244i	0.279776	−	0.484587i
$627$	−0.500000	+	0.866025i	−0.0199681	+	0.0345857i
$628$	−7.50000	−	12.9904i	−0.299283	−	0.518373i
$629$	−24.0000			−0.956943
$630$	2.00000	−	10.3923i	0.0796819	−	0.414039i
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$	1.00000	+	1.73205i	0.0397779	+	0.0688973i
$633$	−9.00000	+	15.5885i	−0.357718	+	0.619586i
$634$	3.00000	−	5.19615i	0.119145	−	0.206366i
$635$	4.00000	+	6.92820i	0.158735	+	0.274937i
$636$	1.00000			0.0396526
$637$	6.50000	+	2.59808i	0.257539	+	0.102940i
$638$	9.00000			0.356313
$639$	7.50000	+	12.9904i	0.296695	+	0.513892i
$640$	2.00000	−	3.46410i	0.0790569	−	0.136931i
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$	4.00000	+	6.92820i	0.157867	+	0.273434i
$643$	−49.0000			−1.93237			−0.966186	−	0.257847i	$-0.916987\pi$
$643$	−49.0000			−1.93237			−0.966186	+	0.257847i	$0.916987\pi$
$644$	−3.00000	+	15.5885i	−0.118217	+	0.614271i
$645$	−40.0000			−1.57500
$646$	1.50000	+	2.59808i	0.0590167	+	0.102220i
$647$	−1.00000	+	1.73205i	−0.0393141	+	0.0680939i	−0.885013	−	0.465566i	$-0.845851\pi$
$647$	−1.00000	+	1.73205i	−0.0393141	+	0.0680939i	0.845699	+	0.533660i	$0.179184\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−2.50000	−	4.33013i	−0.0981336	−	0.169972i
$650$	−11.0000			−0.431455
$651$	−20.0000	+	6.92820i	−0.783862	+	0.271538i
$652$	13.0000			0.509119
$653$	−17.0000	−	29.4449i	−0.665261	−	1.15227i	−0.979214	−	0.202828i	$-0.934987\pi$
$653$	−17.0000	−	29.4449i	−0.665261	−	1.15227i	0.313953	−	0.949439i	$-0.398347\pi$
$654$		0			0
$655$	−4.00000	+	6.92820i	−0.156293	+	0.270707i
$656$		0			0
$657$	2.00000			0.0780274
$658$	22.0000	+	19.0526i	0.857649	+	0.742746i
$659$	−36.0000			−1.40236			−0.701180	−	0.712984i	$-0.747343\pi$
$659$	−36.0000			−1.40236			−0.701180	+	0.712984i	$0.747343\pi$
$660$	−2.00000	−	3.46410i	−0.0778499	−	0.134840i
$661$	−8.00000	+	13.8564i	−0.311164	+	0.538952i	−0.978615	−	0.205702i	$-0.934052\pi$
$661$	−8.00000	+	13.8564i	−0.311164	+	0.538952i	0.667451	+	0.744654i	$0.267385\pi$
$662$	−14.0000	+	24.2487i	−0.544125	+	0.942453i
$663$	1.50000	+	2.59808i	0.0582552	+	0.100901i
$664$	−8.00000			−0.310460
$665$	−8.00000	−	6.92820i	−0.310227	−	0.268664i
$666$	−8.00000			−0.309994
$667$	27.0000	+	46.7654i	1.04544	+	1.81076i
$668$	−1.50000	+	2.59808i	−0.0580367	+	0.100523i
$669$	−9.50000	+	16.4545i	−0.367291	+	0.636167i
$670$	−10.0000	−	17.3205i	−0.386334	−	0.669150i
$671$	15.0000			0.579069
$672$	2.50000	−	0.866025i	0.0964396	−	0.0334077i
$673$	−18.0000			−0.693849			−0.346925	−	0.937893i	$-0.612774\pi$
$673$	−18.0000			−0.693849			−0.346925	+	0.937893i	$0.612774\pi$
$674$	−15.5000	−	26.8468i	−0.597038	−	1.03410i
$675$	−5.50000	+	9.52628i	−0.211695	+	0.366667i
$676$	−0.500000	+	0.866025i	−0.0192308	+	0.0333087i
$677$	−0.500000	−	0.866025i	−0.0192166	−	0.0332841i	0.856257	−	0.516550i	$-0.172784\pi$
$677$	−0.500000	−	0.866025i	−0.0192166	−	0.0332841i	−0.875474	+	0.483266i	$0.839451\pi$
$678$	5.00000			0.192024
$679$	−5.00000	+	25.9808i	−0.191882	+	0.997050i
$680$	−12.0000			−0.460179
$681$	6.00000	+	10.3923i	0.229920	+	0.398234i
$682$	−4.00000	+	6.92820i	−0.153168	+	0.265295i
$683$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$683$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$684$	0.500000	+	0.866025i	0.0191180	+	0.0331133i
$685$	32.0000			1.22266
$686$	−18.5000	−	0.866025i	−0.706333	−	0.0330650i
$687$	18.0000			0.686743
$688$	−5.00000	−	8.66025i	−0.190623	−	0.330169i
$689$	0.500000	−	0.866025i	0.0190485	−	0.0329929i
$690$	12.0000	−	20.7846i	0.456832	−	0.791257i
$691$	−2.50000	−	4.33013i	−0.0951045	−	0.164726i	0.814548	−	0.580097i	$-0.196985\pi$
$691$	−2.50000	−	4.33013i	−0.0951045	−	0.164726i	−0.909652	+	0.415371i	$0.863652\pi$
$692$	3.00000			0.114043
$693$	0.500000	−	2.59808i	0.0189934	−	0.0986928i
$694$	−4.00000			−0.151838
$695$	24.0000	+	41.5692i	0.910372	+	1.57681i
$696$	4.50000	−	7.79423i	0.170572	−	0.295439i
$697$		0			0
$698$	5.00000	+	8.66025i	0.189253	+	0.327795i
$699$	−15.0000			−0.567352
$700$	27.5000	−	9.52628i	1.03940	−	0.360060i
$701$	−34.0000			−1.28416			−0.642081	−	0.766637i	$-0.721929\pi$
$701$	−34.0000			−1.28416			−0.642081	+	0.766637i	$0.721929\pi$
$702$	0.500000	+	0.866025i	0.0188713	+	0.0326860i
$703$	−4.00000	+	6.92820i	−0.150863	+	0.261302i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$	−22.0000	−	38.1051i	−0.828568	−	1.43512i
$706$	18.0000			0.677439
$707$	28.0000	+	24.2487i	1.05305	+	0.911967i
$708$	−5.00000			−0.187912
$709$	−15.0000	−	25.9808i	−0.563337	−	0.975728i	−0.997202	−	0.0747503i	$-0.976184\pi$
$709$	−15.0000	−	25.9808i	−0.563337	−	0.975728i	0.433865	−	0.900978i	$-0.357149\pi$
$710$	−30.0000	+	51.9615i	−1.12588	+	1.95008i
$711$	1.00000	−	1.73205i	0.0375029	−	0.0649570i
$712$		0			0
$713$	−48.0000			−1.79761
$714$	−6.00000	−	5.19615i	−0.224544	−	0.194461i
$715$	−4.00000			−0.149592
$716$	9.00000	+	15.5885i	0.336346	+	0.582568i
$717$	−7.50000	+	12.9904i	−0.280093	+	0.485135i
$718$	−4.00000	+	6.92820i	−0.149279	+	0.258558i
$719$	13.0000	+	22.5167i	0.484818	+	0.839730i	0.999848	−	0.0174426i	$-0.00555244\pi$
$719$	13.0000	+	22.5167i	0.484818	+	0.839730i	−0.515030	+	0.857172i	$0.672219\pi$
$720$	−4.00000			−0.149071
$721$	15.0000	−	5.19615i	0.558629	−	0.193515i
$722$	−18.0000			−0.669891
$723$		0			0
$724$	3.50000	−	6.06218i	0.130076	−	0.225299i
$725$	49.5000	−	85.7365i	1.83838	−	3.18417i
$726$	5.00000	+	8.66025i	0.185567	+	0.321412i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$	0.500000	−	2.59808i	0.0185312	−	0.0962911i
$729$	1.00000			0.0370370
$730$	4.00000	+	6.92820i	0.148047	+	0.256424i
$731$	−15.0000	+	25.9808i	−0.554795	+	0.960933i
$732$	7.50000	−	12.9904i	0.277208	−	0.480138i
$733$	−1.00000	−	1.73205i	−0.0369358	−	0.0639748i	0.846967	−	0.531646i	$-0.178426\pi$
$733$	−1.00000	−	1.73205i	−0.0369358	−	0.0639748i	−0.883902	+	0.467671i	$0.845093\pi$
$734$	26.0000			0.959678
$735$	26.0000	+	10.3923i	0.959024	+	0.383326i
$736$	6.00000			0.221163
$737$	−2.50000	−	4.33013i	−0.0920887	−	0.159502i
$738$		0			0
$739$	−2.00000	+	3.46410i	−0.0735712	+	0.127429i	−0.900464	−	0.434930i	$-0.856773\pi$
$739$	−2.00000	+	3.46410i	−0.0735712	+	0.127429i	0.826893	+	0.562360i	$0.190106\pi$
$740$	−16.0000	−	27.7128i	−0.588172	−	1.01874i
$741$	1.00000			0.0367359
$742$	−0.500000	+	2.59808i	−0.0183556	+	0.0953784i
$743$	−5.00000			−0.183432			−0.0917161	−	0.995785i	$-0.529235\pi$
$743$	−5.00000			−0.183432			−0.0917161	+	0.995785i	$0.529235\pi$
$744$	4.00000	+	6.92820i	0.146647	+	0.254000i
$745$	−20.0000	+	34.6410i	−0.732743	+	1.26915i
$746$	0.500000	−	0.866025i	0.0183063	−	0.0317074i
$747$	4.00000	+	6.92820i	0.146352	+	0.253490i
$748$	−3.00000			−0.109691
$749$	−20.0000	+	6.92820i	−0.730784	+	0.253151i
$750$	−24.0000			−0.876356
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$	5.50000	−	9.52628i	0.200564	−	0.347388i
$753$	11.0000	−	19.0526i	0.400862	−	0.694314i
$754$	−4.50000	−	7.79423i	−0.163880	−	0.283849i
$755$	−76.0000			−2.76592
$756$	−2.00000	−	1.73205i	−0.0727393	−	0.0629941i
$757$	−47.0000			−1.70824			−0.854122	−	0.520073i	$-0.825905\pi$
$757$	−47.0000			−1.70824			−0.854122	+	0.520073i	$0.825905\pi$
$758$	10.0000	+	17.3205i	0.363216	+	0.629109i
$759$	3.00000	−	5.19615i	0.108893	−	0.188608i
$760$	−2.00000	+	3.46410i	−0.0725476	+	0.125656i
$761$	8.00000	+	13.8564i	0.290000	+	0.502294i	0.973809	−	0.227366i	$-0.0730114\pi$
$761$	8.00000	+	13.8564i	0.290000	+	0.502294i	−0.683810	+	0.729661i	$0.739678\pi$
$762$	2.00000			0.0724524
$763$		0			0
$764$	−12.0000			−0.434145
$765$	6.00000	+	10.3923i	0.216930	+	0.375735i
$766$	−8.00000	+	13.8564i	−0.289052	+	0.500652i
$767$	−2.50000	+	4.33013i	−0.0902698	+	0.156352i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	22.0000			0.793340			0.396670	−	0.917961i	$-0.370166\pi$
$769$	22.0000			0.793340			0.396670	+	0.917961i	$0.370166\pi$
$770$	10.0000	−	3.46410i	0.360375	−	0.124838i
$771$	−6.00000			−0.216085
$772$	6.00000	+	10.3923i	0.215945	+	0.374027i
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	−0.657542	−	0.753418i	$-0.728404\pi$
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	0.981250	+	0.192740i	$0.0617373\pi$
$774$	−5.00000	+	8.66025i	−0.179721	+	0.311286i
$775$	44.0000	+	76.2102i	1.58053	+	2.73755i
$776$	10.0000			0.358979
$777$	4.00000	−	20.7846i	0.143499	−	0.745644i
$778$	−23.0000			−0.824590
$779$		0			0
$780$	−2.00000	+	3.46410i	−0.0716115	+	0.124035i
$781$	−7.50000	+	12.9904i	−0.268371	+	0.464832i
$782$	−9.00000	−	15.5885i	−0.321839	−	0.557442i
$783$	−9.00000			−0.321634
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$	−60.0000			−2.14149
$786$	1.00000	+	1.73205i	0.0356688	+	0.0617802i
$787$	7.50000	−	12.9904i	0.267346	−	0.463057i	−0.700830	−	0.713329i	$-0.747187\pi$
$787$	7.50000	−	12.9904i	0.267346	−	0.463057i	0.968176	+	0.250272i	$0.0805200\pi$
$788$	−9.00000	+	15.5885i	−0.320612	+	0.555316i
$789$	−12.0000	−	20.7846i	−0.427211	−	0.739952i
$790$	8.00000			0.284627
$791$	−2.50000	+	12.9904i	−0.0888898	+	0.461885i
$792$	−1.00000			−0.0355335
$793$	−7.50000	−	12.9904i	−0.266333	−	0.461302i
$794$	15.0000	−	25.9808i	0.532330	−	0.922023i
$795$	2.00000	−	3.46410i	0.0709327	−	0.122859i
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	54.0000			1.91278			0.956389	−	0.292096i	$-0.0943526\pi$
$797$	54.0000			1.91278			0.956389	+	0.292096i	$0.0943526\pi$
$798$	−2.50000	+	0.866025i	−0.0884990	+	0.0306570i
$799$	−33.0000			−1.16746
$800$	−5.50000	−	9.52628i	−0.194454	−	0.336805i
$801$		0			0
$802$	−15.0000	+	25.9808i	−0.529668	+	0.917413i
$803$	1.00000	+	1.73205i	0.0352892	+	0.0611227i
$804$	−5.00000			−0.176336
$805$	48.0000	+	41.5692i	1.69178	+	1.46512i
$806$	8.00000			0.281788
$807$	4.50000	+	7.79423i	0.158408	+	0.274370i
$808$	7.00000	−	12.1244i	0.246259	−	0.426533i
$809$	1.50000	−	2.59808i	0.0527372	−	0.0913435i	−0.838452	−	0.544976i	$-0.816539\pi$
$809$	1.50000	−	2.59808i	0.0527372	−	0.0913435i	0.891189	+	0.453632i	$0.149872\pi$
$810$	2.00000	+	3.46410i	0.0702728	+	0.121716i
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	18.0000	+	15.5885i	0.631676	+	0.547048i
$813$	−1.00000			−0.0350715
$814$	−4.00000	−	6.92820i	−0.140200	−	0.242833i
$815$	26.0000	−	45.0333i	0.910740	−	1.57745i
$816$	−1.50000	+	2.59808i	−0.0525105	+	0.0909509i
$817$	5.00000	+	8.66025i	0.174928	+	0.302984i
$818$	−8.00000			−0.279713
$819$	−2.50000	+	0.866025i	−0.0873571	+	0.0302614i
$820$		0			0
$821$	−20.0000	−	34.6410i	−0.698005	−	1.20898i	−0.969157	−	0.246443i	$-0.920738\pi$
$821$	−20.0000	−	34.6410i	−0.698005	−	1.20898i	0.271152	−	0.962536i	$-0.412595\pi$
$822$	4.00000	−	6.92820i	0.139516	−	0.241649i
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	−0.829060	−	0.559159i	$-0.811124\pi$
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	0.898776	+	0.438408i	$0.144457\pi$
$824$	−3.00000	−	5.19615i	−0.104510	−	0.181017i
$825$	−11.0000			−0.382971
$826$	2.50000	−	12.9904i	0.0869861	−	0.451993i
$827$	17.0000			0.591148			0.295574	−	0.955320i	$-0.404489\pi$
$827$	17.0000			0.591148			0.295574	+	0.955320i	$0.404489\pi$
$828$	−3.00000	−	5.19615i	−0.104257	−	0.180579i
$829$	−21.5000	+	37.2391i	−0.746726	+	1.29337i	0.202658	+	0.979250i	$0.435042\pi$
$829$	−21.5000	+	37.2391i	−0.746726	+	1.29337i	−0.949384	+	0.314118i	$0.898291\pi$
$830$	−16.0000	+	27.7128i	−0.555368	+	0.961926i
$831$	0.500000	+	0.866025i	0.0173448	+	0.0300421i
$832$	−1.00000			−0.0346688
$833$	16.5000	−	12.9904i	0.571691	−	0.450090i
$834$	12.0000			0.415526
$835$	6.00000	+	10.3923i	0.207639	+	0.359641i
$836$	−0.500000	+	0.866025i	−0.0172929	+	0.0299521i
$837$	4.00000	−	6.92820i	0.138260	−	0.239474i
$838$	7.00000	+	12.1244i	0.241811	+	0.418829i
$839$	5.00000			0.172619			0.0863096	−	0.996268i	$-0.472493\pi$
$839$	5.00000			0.172619			0.0863096	+	0.996268i	$0.472493\pi$
$840$	2.00000	−	10.3923i	0.0690066	−	0.358569i
$841$	52.0000			1.79310
$842$	15.0000	+	25.9808i	0.516934	+	0.895356i
$843$	16.0000	−	27.7128i	0.551069	−	0.954480i
$844$	−9.00000	+	15.5885i	−0.309793	+	0.536577i
$845$	2.00000	+	3.46410i	0.0688021	+	0.119169i
$846$	−11.0000			−0.378188
$847$	−25.0000	+	8.66025i	−0.859010	+	0.297570i
$848$	1.00000			0.0343401
$849$	7.00000	+	12.1244i	0.240239	+	0.416107i
$850$	−16.5000	+	28.5788i	−0.565945	+	0.980246i
$851$	24.0000	−	41.5692i	0.822709	−	1.42497i
$852$	7.50000	+	12.9904i	0.256946	+	0.445043i
$853$	2.00000			0.0684787			0.0342393	−	0.999414i	$-0.489099\pi$
$853$	2.00000			0.0684787			0.0342393	+	0.999414i	$0.489099\pi$
$854$	30.0000	+	25.9808i	1.02658	+	0.889043i
$855$	4.00000			0.136797
$856$	4.00000	+	6.92820i	0.136717	+	0.236801i
$857$	−4.50000	+	7.79423i	−0.153717	+	0.266246i	−0.932591	−	0.360935i	$-0.882458\pi$
$857$	−4.50000	+	7.79423i	−0.153717	+	0.266246i	0.778874	+	0.627180i	$0.215791\pi$
$858$	−0.500000	+	0.866025i	−0.0170697	+	0.0295656i
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	0.926161	−	0.377128i	$-0.123088\pi$
$859$	4.00000	+	6.92820i	0.136478	+	0.236387i	−0.789683	+	0.613515i	$0.789755\pi$
$860$	−40.0000			−1.36399
$861$		0			0
$862$	−8.00000			−0.272481
$863$	2.00000	+	3.46410i	0.0680808	+	0.117919i	0.898056	−	0.439880i	$-0.144979\pi$
$863$	2.00000	+	3.46410i	0.0680808	+	0.117919i	−0.829976	+	0.557800i	$0.811646\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	6.00000	−	10.3923i	0.204006	−	0.353349i
$866$	5.50000	+	9.52628i	0.186898	+	0.323716i
$867$	−8.00000			−0.271694
$868$	−20.0000	+	6.92820i	−0.678844	+	0.235159i
$869$	2.00000			0.0678454
$870$	−18.0000	−	31.1769i	−0.610257	−	1.05700i
$871$	−2.50000	+	4.33013i	−0.0847093	+	0.146721i
$872$		0			0
$873$	−5.00000	−	8.66025i	−0.169224	−	0.293105i
$874$	−6.00000			−0.202953
$875$	12.0000	−	62.3538i	0.405674	−	2.10794i
$876$	2.00000			0.0675737
$877$	−12.0000	−	20.7846i	−0.405211	−	0.701846i	0.589135	−	0.808035i	$-0.299469\pi$
$877$	−12.0000	−	20.7846i	−0.405211	−	0.701846i	−0.994346	+	0.106188i	$0.966135\pi$
$878$	1.00000	−	1.73205i	0.0337484	−	0.0584539i
$879$	−7.00000	+	12.1244i	−0.236104	+	0.408944i
$880$	−2.00000	−	3.46410i	−0.0674200	−	0.116775i
$881$	42.0000			1.41502			0.707508	−	0.706705i	$-0.249819\pi$
$881$	42.0000			1.41502			0.707508	+	0.706705i	$0.249819\pi$
$882$	5.50000	−	4.33013i	0.185195	−	0.145803i
$883$	24.0000			0.807664			0.403832	−	0.914833i	$-0.367678\pi$
$883$	24.0000			0.807664			0.403832	+	0.914833i	$0.367678\pi$
$884$	1.50000	+	2.59808i	0.0504505	+	0.0873828i
$885$	−10.0000	+	17.3205i	−0.336146	+	0.582223i
$886$		0			0
$887$	3.00000	+	5.19615i	0.100730	+	0.174470i	0.911986	−	0.410222i	$-0.134549\pi$
$887$	3.00000	+	5.19615i	0.100730	+	0.174470i	−0.811256	+	0.584692i	$0.801215\pi$
$888$	−8.00000			−0.268462
$889$	−1.00000	+	5.19615i	−0.0335389	+	0.174273i
$890$		0			0
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	−9.50000	+	16.4545i	−0.318084	+	0.550937i
$893$	−5.50000	+	9.52628i	−0.184050	+	0.318785i
$894$	5.00000	+	8.66025i	0.167225	+	0.289642i
$895$	72.0000			2.40669
$896$	2.50000	−	0.866025i	0.0835191	−	0.0289319i
$897$	−6.00000			−0.200334
$898$	2.00000	+	3.46410i	0.0667409	+	0.115599i
$899$	−36.0000	+	62.3538i	−1.20067	+	2.07962i
$900$	−5.50000	+	9.52628i	−0.183333	+	0.317543i
$901$	−1.50000	−	2.59808i	−0.0499722	−	0.0865545i
$902$		0			0
$903$	−20.0000	−	17.3205i	−0.665558	−	0.576390i
$904$	5.00000			0.166298
$905$	−14.0000	−	24.2487i	−0.465376	−	0.806054i
$906$	−9.50000	+	16.4545i	−0.315616	+	0.546664i
$907$	−9.00000	+	15.5885i	−0.298840	+	0.517606i	−0.975871	−	0.218348i	$-0.929933\pi$
$907$	−9.00000	+	15.5885i	−0.298840	+	0.517606i	0.677031	+	0.735955i	$0.263266\pi$
$908$	6.00000	+	10.3923i	0.199117	+	0.344881i
$909$	−14.0000			−0.464351
$910$	−8.00000	−	6.92820i	−0.265197	−	0.229668i
$911$	2.00000			0.0662630			0.0331315	−	0.999451i	$-0.489452\pi$
$911$	2.00000			0.0662630			0.0331315	+	0.999451i	$0.489452\pi$
$912$	0.500000	+	0.866025i	0.0165567	+	0.0286770i
$913$	−4.00000	+	6.92820i	−0.132381	+	0.229290i
$914$	−17.0000	+	29.4449i	−0.562310	+	0.973950i
$915$	−30.0000	−	51.9615i	−0.991769	−	1.71780i
$916$	18.0000			0.594737
$917$	−5.00000	+	1.73205i	−0.165115	+	0.0571974i
$918$	3.00000			0.0990148
$919$	11.0000	+	19.0526i	0.362857	+	0.628486i	0.988430	−	0.151680i	$-0.0484682\pi$
$919$	11.0000	+	19.0526i	0.362857	+	0.628486i	−0.625573	+	0.780165i	$0.715135\pi$
$920$	12.0000	−	20.7846i	0.395628	−	0.685248i
$921$	−13.5000	+	23.3827i	−0.444840	+	0.770486i
$922$	−20.0000	−	34.6410i	−0.658665	−	1.14084i
$923$	15.0000			0.493731
$924$	0.500000	−	2.59808i	0.0164488	−	0.0854704i
$925$	−88.0000			−2.89342
$926$		0			0
$927$	−3.00000	+	5.19615i	−0.0985329	+	0.170664i
$928$	4.50000	−	7.79423i	0.147720	−	0.255858i
$929$	−5.00000	−	8.66025i	−0.164045	−	0.284134i	0.772271	−	0.635293i	$-0.219121\pi$
$929$	−5.00000	−	8.66025i	−0.164045	−	0.284134i	−0.936316	+	0.351160i	$0.885787\pi$
$930$	32.0000			1.04932
$931$	−1.00000	−	6.92820i	−0.0327737	−	0.227063i
$932$	−15.0000			−0.491341
$933$	−4.00000	−	6.92820i	−0.130954	−	0.226819i
$934$	−15.0000	+	25.9808i	−0.490815	+	0.850117i
$935$	−6.00000	+	10.3923i	−0.196221	+	0.339865i
$936$	0.500000	+	0.866025i	0.0163430	+	0.0283069i
$937$	−49.0000			−1.60076			−0.800380	−	0.599493i	$-0.795369\pi$
$937$	−49.0000			−1.60076			−0.800380	+	0.599493i	$0.795369\pi$
$938$	2.50000	−	12.9904i	0.0816279	−	0.424151i
$939$	−14.0000			−0.456873
$940$	−22.0000	−	38.1051i	−0.717561	−	1.24285i
$941$	24.0000	−	41.5692i	0.782378	−	1.35512i	−0.148176	−	0.988961i	$-0.547340\pi$
$941$	24.0000	−	41.5692i	0.782378	−	1.35512i	0.930553	−	0.366157i	$-0.119327\pi$
$942$	−7.50000	+	12.9904i	−0.244363	+	0.423249i
$943$		0			0
$944$	−5.00000			−0.162736
$945$	−10.0000	+	3.46410i	−0.325300	+	0.112687i
$946$	−10.0000			−0.325128
$947$	16.5000	+	28.5788i	0.536178	+	0.928687i	0.999105	+	0.0422912i	$0.0134657\pi$
$947$	16.5000	+	28.5788i	0.536178	+	0.928687i	−0.462927	+	0.886396i	$0.653201\pi$
$948$	1.00000	−	1.73205i	0.0324785	−	0.0562544i
$949$	1.00000	−	1.73205i	0.0324614	−	0.0562247i
$950$	5.50000	+	9.52628i	0.178444	+	0.309073i
$951$	−6.00000			−0.194563
$952$	−6.00000	−	5.19615i	−0.194461	−	0.168408i
$953$	13.0000			0.421111			0.210556	−	0.977582i	$-0.432473\pi$
$953$	13.0000			0.421111			0.210556	+	0.977582i	$0.432473\pi$
$954$	−0.500000	−	0.866025i	−0.0161881	−	0.0280386i
$955$	−24.0000	+	41.5692i	−0.776622	+	1.34515i
$956$	−7.50000	+	12.9904i	−0.242567	+	0.420139i
$957$	−4.50000	−	7.79423i	−0.145464	−	0.251952i
$958$	5.00000			0.161543
$959$	16.0000	+	13.8564i	0.516667	+	0.447447i
$960$	−4.00000			−0.129099
$961$	−16.5000	−	28.5788i	−0.532258	−	0.921898i
$962$	−4.00000	+	6.92820i	−0.128965	+	0.223374i
$963$	4.00000	−	6.92820i	0.128898	−	0.223258i
$964$		0			0
$965$	48.0000			1.54517
$966$	15.0000	−	5.19615i	0.482617	−	0.167183i
$967$	13.0000			0.418052			0.209026	−	0.977910i	$-0.432971\pi$
$967$	13.0000			0.418052			0.209026	+	0.977910i	$0.432971\pi$
$968$	5.00000	+	8.66025i	0.160706	+	0.278351i
$969$	1.50000	−	2.59808i	0.0481869	−	0.0834622i
$970$	20.0000	−	34.6410i	0.642161	−	1.11226i
$971$	−20.0000	−	34.6410i	−0.641831	−	1.11168i	−0.985024	−	0.172418i	$-0.944842\pi$
$971$	−20.0000	−	34.6410i	−0.641831	−	1.11168i	0.343193	−	0.939265i	$-0.388491\pi$
$972$	1.00000			0.0320750
$973$	−6.00000	+	31.1769i	−0.192351	+	0.999486i
$974$	−1.00000			−0.0320421
$975$	5.50000	+	9.52628i	0.176141	+	0.305085i
$976$	7.50000	−	12.9904i	0.240069	−	0.415812i
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	−0.814038	−	0.580812i	$-0.802735\pi$
$977$	3.00000	−	5.19615i	0.0959785	−	0.166240i	0.910017	+	0.414572i	$0.136069\pi$
$978$	−6.50000	−	11.2583i	−0.207847	−	0.360002i
$979$		0			0
$980$	26.0000	+	10.3923i	0.830540	+	0.331970i
$981$		0			0
$982$	19.0000	+	32.9090i	0.606314	+	1.05017i
$983$	2.50000	−	4.33013i	0.0797376	−	0.138110i	−0.823399	−	0.567463i	$-0.807925\pi$
$983$	2.50000	−	4.33013i	0.0797376	−	0.138110i	0.903137	+	0.429353i	$0.141258\pi$
$984$		0			0
$985$	36.0000	+	62.3538i	1.14706	+	1.98676i
$986$	−27.0000			−0.859855
$987$	5.50000	−	28.5788i	0.175067	−	0.909674i
$988$	1.00000			0.0318142
$989$	−30.0000	−	51.9615i	−0.953945	−	1.65228i
$990$	−2.00000	+	3.46410i	−0.0635642	+	0.110096i
$991$	28.0000	−	48.4974i	0.889449	−	1.54057i	0.0489218	−	0.998803i	$-0.484422\pi$
$991$	28.0000	−	48.4974i	0.889449	−	1.54057i	0.840528	−	0.541769i	$-0.182245\pi$
$992$	4.00000	+	6.92820i	0.127000	+	0.219971i
$993$	28.0000			0.888553
$994$	−37.5000	+	12.9904i	−1.18943	+	0.412030i
$995$	40.0000			1.26809
$996$	4.00000	+	6.92820i	0.126745	+	0.219529i
$997$	15.5000	−	26.8468i	0.490890	−	0.850246i	−0.509055	−	0.860734i	$-0.670005\pi$
$997$	15.5000	−	26.8468i	0.490890	−	0.850246i	0.999945	+	0.0104877i	$0.00333839\pi$
$998$	−4.00000	+	6.92820i	−0.126618	+	0.219308i
$999$	4.00000	+	6.92820i	0.126554	+	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.i.c.235.1	yes	2
3.2	odd	2		1638.2.j.f.235.1		2
7.2	even	3	inner	546.2.i.c.79.1	✓	2
7.3	odd	6		3822.2.a.z.1.1		1
7.4	even	3		3822.2.a.ba.1.1		1
21.2	odd	6		1638.2.j.f.1171.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.c.79.1	✓	2	7.2	even	3	inner
546.2.i.c.235.1	yes	2	1.1	even	1	trivial
1638.2.j.f.235.1		2	3.2	odd	2
1638.2.j.f.1171.1		2	21.2	odd	6
3822.2.a.z.1.1		1	7.3	odd	6
3822.2.a.ba.1.1		1	7.4	even	3

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.00000 + 3.46410i) q^{5} +1.00000 q^{6} +(-0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +(2.50000 - 0.866025i) q^{14} -4.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(0.500000 + 0.866025i) q^{19} -4.00000 q^{20} +(-2.00000 - 1.73205i) q^{21} -1.00000 q^{22} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-5.50000 + 9.52628i) q^{25} +(0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +(-2.00000 - 1.73205i) q^{28} -9.00000 q^{29} +(2.00000 + 3.46410i) q^{30} +(4.00000 - 6.92820i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{33} +3.00000 q^{34} +(-10.0000 + 3.46410i) q^{35} +1.00000 q^{36} +(4.00000 + 6.92820i) q^{37} +(0.500000 - 0.866025i) q^{38} +(0.500000 - 0.866025i) q^{39} +(2.00000 + 3.46410i) q^{40} +(-0.500000 + 2.59808i) q^{42} +10.0000 q^{43} +(0.500000 + 0.866025i) q^{44} +(2.00000 - 3.46410i) q^{45} +(-3.00000 + 5.19615i) q^{46} +(5.50000 + 9.52628i) q^{47} +1.00000 q^{48} +(-6.50000 - 2.59808i) q^{49} +11.0000 q^{50} +(-1.50000 - 2.59808i) q^{51} +(0.500000 - 0.866025i) q^{52} +(-0.500000 + 0.866025i) q^{53} +(-0.500000 - 0.866025i) q^{54} +4.00000 q^{55} +(-0.500000 + 2.59808i) q^{56} -1.00000 q^{57} +(4.50000 + 7.79423i) q^{58} +(2.50000 - 4.33013i) q^{59} +(2.00000 - 3.46410i) q^{60} +(7.50000 + 12.9904i) q^{61} -8.00000 q^{62} +(2.50000 - 0.866025i) q^{63} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +(0.500000 - 0.866025i) q^{66} +(2.50000 - 4.33013i) q^{67} +(-1.50000 - 2.59808i) q^{68} +6.00000 q^{69} +(8.00000 + 6.92820i) q^{70} -15.0000 q^{71} +(-0.500000 - 0.866025i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(4.00000 - 6.92820i) q^{74} +(-5.50000 - 9.52628i) q^{75} -1.00000 q^{76} +(2.00000 + 1.73205i) q^{77} -1.00000 q^{78} +(1.00000 + 1.73205i) q^{79} +(2.00000 - 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} -8.00000 q^{83} +(2.50000 - 0.866025i) q^{84} -12.0000 q^{85} +(-5.00000 - 8.66025i) q^{86} +(4.50000 - 7.79423i) q^{87} +(0.500000 - 0.866025i) q^{88} -4.00000 q^{90} +(0.500000 - 2.59808i) q^{91} +6.00000 q^{92} +(4.00000 + 6.92820i) q^{93} +(5.50000 - 9.52628i) q^{94} +(-2.00000 + 3.46410i) q^{95} +(-0.500000 - 0.866025i) q^{96} +10.0000 q^{97} +(1.00000 + 6.92820i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} + 4 q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - q^3 - q^4 + 4 * q^5 + 2 * q^6 - q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - q^{3} - q^{4} + 4 q^{5} + 2 q^{6} - q^{7} + 2 q^{8} - q^{9} + 4 q^{10} + q^{11} - q^{12} - 2 q^{13} + 5 q^{14} - 8 q^{15} - q^{16} - 3 q^{17} - q^{18} + q^{19} - 8 q^{20} - 4 q^{21} - 2 q^{22} - 6 q^{23} - q^{24} - 11 q^{25} + q^{26} + 2 q^{27} - 4 q^{28} - 18 q^{29} + 4 q^{30} + 8 q^{31} - q^{32} + q^{33} + 6 q^{34} - 20 q^{35} + 2 q^{36} + 8 q^{37} + q^{38} + q^{39} + 4 q^{40} - q^{42} + 20 q^{43} + q^{44} + 4 q^{45} - 6 q^{46} + 11 q^{47} + 2 q^{48} - 13 q^{49} + 22 q^{50} - 3 q^{51} + q^{52} - q^{53} - q^{54} + 8 q^{55} - q^{56} - 2 q^{57} + 9 q^{58} + 5 q^{59} + 4 q^{60} + 15 q^{61} - 16 q^{62} + 5 q^{63} + 2 q^{64} - 4 q^{65} + q^{66} + 5 q^{67} - 3 q^{68} + 12 q^{69} + 16 q^{70} - 30 q^{71} - q^{72} - 2 q^{73} + 8 q^{74} - 11 q^{75} - 2 q^{76} + 4 q^{77} - 2 q^{78} + 2 q^{79} + 4 q^{80} - q^{81} - 16 q^{83} + 5 q^{84} - 24 q^{85} - 10 q^{86} + 9 q^{87} + q^{88} - 8 q^{90} + q^{91} + 12 q^{92} + 8 q^{93} + 11 q^{94} - 4 q^{95} - q^{96} + 20 q^{97} + 2 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 + 4 * q^5 + 2 * q^6 - q^7 + 2 * q^8 - q^9 + 4 * q^10 + q^11 - q^12 - 2 * q^13 + 5 * q^14 - 8 * q^15 - q^16 - 3 * q^17 - q^18 + q^19 - 8 * q^20 - 4 * q^21 - 2 * q^22 - 6 * q^23 - q^24 - 11 * q^25 + q^26 + 2 * q^27 - 4 * q^28 - 18 * q^29 + 4 * q^30 + 8 * q^31 - q^32 + q^33 + 6 * q^34 - 20 * q^35 + 2 * q^36 + 8 * q^37 + q^38 + q^39 + 4 * q^40 - q^42 + 20 * q^43 + q^44 + 4 * q^45 - 6 * q^46 + 11 * q^47 + 2 * q^48 - 13 * q^49 + 22 * q^50 - 3 * q^51 + q^52 - q^53 - q^54 + 8 * q^55 - q^56 - 2 * q^57 + 9 * q^58 + 5 * q^59 + 4 * q^60 + 15 * q^61 - 16 * q^62 + 5 * q^63 + 2 * q^64 - 4 * q^65 + q^66 + 5 * q^67 - 3 * q^68 + 12 * q^69 + 16 * q^70 - 30 * q^71 - q^72 - 2 * q^73 + 8 * q^74 - 11 * q^75 - 2 * q^76 + 4 * q^77 - 2 * q^78 + 2 * q^79 + 4 * q^80 - q^81 - 16 * q^83 + 5 * q^84 - 24 * q^85 - 10 * q^86 + 9 * q^87 + q^88 - 8 * q^90 + q^91 + 12 * q^92 + 8 * q^93 + 11 * q^94 - 4 * q^95 - q^96 + 20 * q^97 + 2 * q^98 - 2 * q^99

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