LMFDB - Embedded newform 546.2.q.a.335.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(251,546)]

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([3, 3, 1]))

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

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

chi := DirichletCharacter("546.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
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:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			335.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.335
Dual form			546.2.q.a.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.46410i q^{5} +(1.50000 + 0.866025i) q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.46410i q^{5} +(1.50000 + 0.866025i) q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(3.00000 - 1.73205i) q^{10} +(1.50000 + 2.59808i) q^{11} -1.73205i q^{12} +(-3.50000 - 0.866025i) q^{13} +(2.00000 - 1.73205i) q^{14} +(-3.00000 - 5.19615i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} -3.00000 q^{18} +(3.50000 - 6.06218i) q^{19} +(-3.00000 - 1.73205i) q^{20} +(-3.00000 - 3.46410i) q^{21} +(1.50000 - 2.59808i) q^{22} +(-6.00000 + 3.46410i) q^{23} +(-1.50000 + 0.866025i) q^{24} -7.00000 q^{25} +(1.00000 + 3.46410i) q^{26} +5.19615i q^{27} +(-2.50000 - 0.866025i) q^{28} +(1.50000 - 0.866025i) q^{29} +(-3.00000 + 5.19615i) q^{30} +4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-4.50000 - 2.59808i) q^{33} +3.00000 q^{34} +(-9.00000 + 1.73205i) q^{35} +(1.50000 + 2.59808i) q^{36} +(-6.00000 + 3.46410i) q^{37} -7.00000 q^{38} +(6.00000 - 1.73205i) q^{39} +3.46410i q^{40} +(-4.50000 + 2.59808i) q^{41} +(-1.50000 + 4.33013i) q^{42} +(4.00000 - 6.92820i) q^{43} -3.00000 q^{44} +(9.00000 + 5.19615i) q^{45} +(6.00000 + 3.46410i) q^{46} -8.66025i q^{47} +(1.50000 + 0.866025i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(3.50000 + 6.06218i) q^{50} -5.19615i q^{51} +(2.50000 - 2.59808i) q^{52} +8.66025i q^{53} +(4.50000 - 2.59808i) q^{54} +(-9.00000 + 5.19615i) q^{55} +(0.500000 + 2.59808i) q^{56} +12.1244i q^{57} +(-1.50000 - 0.866025i) q^{58} +(9.00000 + 5.19615i) q^{59} +6.00000 q^{60} +(-4.50000 - 2.59808i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(7.50000 + 2.59808i) q^{63} +1.00000 q^{64} +(3.00000 - 12.1244i) q^{65} +5.19615i q^{66} +(-1.50000 - 2.59808i) q^{68} +(6.00000 - 10.3923i) q^{69} +(6.00000 + 6.92820i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(1.50000 - 2.59808i) q^{72} +4.00000 q^{73} +(6.00000 + 3.46410i) q^{74} +(10.5000 - 6.06218i) q^{75} +(3.50000 + 6.06218i) q^{76} +(-6.00000 + 5.19615i) q^{77} +(-4.50000 - 4.33013i) q^{78} -11.0000 q^{79} +(3.00000 - 1.73205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.50000 + 2.59808i) q^{82} -13.8564i q^{83} +(4.50000 - 0.866025i) q^{84} +(-9.00000 - 5.19615i) q^{85} -8.00000 q^{86} +(-1.50000 + 2.59808i) q^{87} +(1.50000 + 2.59808i) q^{88} +(-7.50000 + 4.33013i) q^{89} -10.3923i q^{90} +(0.500000 - 9.52628i) q^{91} -6.92820i q^{92} +(-6.00000 + 3.46410i) q^{93} +(-7.50000 + 4.33013i) q^{94} +(21.0000 + 12.1244i) q^{95} -1.73205i q^{96} +(-1.00000 + 1.73205i) q^{97} +(5.50000 + 4.33013i) q^{98} +9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 3 q^{3} - q^{4} + 3 q^{6} + q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 - 3 * q^3 - q^4 + 3 * q^6 + q^7 + 2 * q^8 + 3 * q^9	$ 2 q - q^{2} - 3 q^{3} - q^{4} + 3 q^{6} + q^{7} + 2 q^{8} + 3 q^{9} + 6 q^{10} + 3 q^{11} - 7 q^{13} + 4 q^{14} - 6 q^{15} - q^{16} - 3 q^{17} - 6 q^{18} + 7 q^{19} - 6 q^{20} - 6 q^{21} + 3 q^{22} - 12 q^{23} - 3 q^{24} - 14 q^{25} + 2 q^{26} - 5 q^{28} + 3 q^{29} - 6 q^{30} + 8 q^{31} - q^{32} - 9 q^{33} + 6 q^{34} - 18 q^{35} + 3 q^{36} - 12 q^{37} - 14 q^{38} + 12 q^{39} - 9 q^{41} - 3 q^{42} + 8 q^{43} - 6 q^{44} + 18 q^{45} + 12 q^{46} + 3 q^{48} - 13 q^{49} + 7 q^{50} + 5 q^{52} + 9 q^{54} - 18 q^{55} + q^{56} - 3 q^{58} + 18 q^{59} + 12 q^{60} - 9 q^{61} - 4 q^{62} + 15 q^{63} + 2 q^{64} + 6 q^{65} - 3 q^{68} + 12 q^{69} + 12 q^{70} - 6 q^{71} + 3 q^{72} + 8 q^{73} + 12 q^{74} + 21 q^{75} + 7 q^{76} - 12 q^{77} - 9 q^{78} - 22 q^{79} + 6 q^{80} - 9 q^{81} + 9 q^{82} + 9 q^{84} - 18 q^{85} - 16 q^{86} - 3 q^{87} + 3 q^{88} - 15 q^{89} + q^{91} - 12 q^{93} - 15 q^{94} + 42 q^{95} - 2 q^{97} + 11 q^{98} + 18 q^{99}+O(q^{100}) $ 2 * q - q^2 - 3 * q^3 - q^4 + 3 * q^6 + q^7 + 2 * q^8 + 3 * q^9 + 6 * q^10 + 3 * q^11 - 7 * q^13 + 4 * q^14 - 6 * q^15 - q^16 - 3 * q^17 - 6 * q^18 + 7 * q^19 - 6 * q^20 - 6 * q^21 + 3 * q^22 - 12 * q^23 - 3 * q^24 - 14 * q^25 + 2 * q^26 - 5 * q^28 + 3 * q^29 - 6 * q^30 + 8 * q^31 - q^32 - 9 * q^33 + 6 * q^34 - 18 * q^35 + 3 * q^36 - 12 * q^37 - 14 * q^38 + 12 * q^39 - 9 * q^41 - 3 * q^42 + 8 * q^43 - 6 * q^44 + 18 * q^45 + 12 * q^46 + 3 * q^48 - 13 * q^49 + 7 * q^50 + 5 * q^52 + 9 * q^54 - 18 * q^55 + q^56 - 3 * q^58 + 18 * q^59 + 12 * q^60 - 9 * q^61 - 4 * q^62 + 15 * q^63 + 2 * q^64 + 6 * q^65 - 3 * q^68 + 12 * q^69 + 12 * q^70 - 6 * q^71 + 3 * q^72 + 8 * q^73 + 12 * q^74 + 21 * q^75 + 7 * q^76 - 12 * q^77 - 9 * q^78 - 22 * q^79 + 6 * q^80 - 9 * q^81 + 9 * q^82 + 9 * q^84 - 18 * q^85 - 16 * q^86 - 3 * q^87 + 3 * q^88 - 15 * q^89 + q^91 - 12 * q^93 - 15 * q^94 + 42 * q^95 - 2 * q^97 + 11 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$			3.46410i			1.54919i	0.632456	+	0.774597i	$0.282047\pi$
$5$			3.46410i			1.54919i	−0.632456	+	0.774597i	$0.717953\pi$
$6$	1.50000	+	0.866025i	0.612372	+	0.353553i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$7$	0.500000	+	2.59808i	0.188982	+	0.981981i
$8$	1.00000			0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	3.00000	−	1.73205i	0.948683	−	0.547723i
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$		−	1.73205i		−	0.500000i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$14$	2.00000	−	1.73205i	0.534522	−	0.462910i
$15$	−3.00000	−	5.19615i	−0.774597	−	1.34164i
$16$	−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	$0.285189\pi$
$18$	−3.00000			−0.707107
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	0.917663	−	0.397360i	$-0.130073\pi$
$20$	−3.00000	−	1.73205i	−0.670820	−	0.387298i
$21$	−3.00000	−	3.46410i	−0.654654	−	0.755929i
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	−6.00000	+	3.46410i	−1.25109	+	0.722315i	−0.971325	−	0.237754i	$-0.923589\pi$
$23$	−6.00000	+	3.46410i	−1.25109	+	0.722315i	−0.279761	+	0.960070i	$0.590255\pi$
$24$	−1.50000	+	0.866025i	−0.306186	+	0.176777i
$25$	−7.00000			−1.40000
$26$	1.00000	+	3.46410i	0.196116	+	0.679366i
$27$			5.19615i			1.00000i
$28$	−2.50000	−	0.866025i	−0.472456	−	0.163663i
$29$	1.50000	−	0.866025i	0.278543	−	0.160817i	−0.354221	−	0.935162i	$-0.615254\pi$
$29$	1.50000	−	0.866025i	0.278543	−	0.160817i	0.632764	+	0.774345i	$0.281920\pi$
$30$	−3.00000	+	5.19615i	−0.547723	+	0.948683i
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−4.50000	−	2.59808i	−0.783349	−	0.452267i
$34$	3.00000			0.514496
$35$	−9.00000	+	1.73205i	−1.52128	+	0.292770i
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	−6.00000	+	3.46410i	−0.986394	+	0.569495i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−6.00000	+	3.46410i	−0.986394	+	0.569495i	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−7.00000			−1.13555
$39$	6.00000	−	1.73205i	0.960769	−	0.277350i
$40$			3.46410i			0.547723i
$41$	−4.50000	+	2.59808i	−0.702782	+	0.405751i	−0.808383	−	0.588657i	$-0.799657\pi$
$41$	−4.50000	+	2.59808i	−0.702782	+	0.405751i	0.105601	+	0.994409i	$0.466323\pi$
$42$	−1.50000	+	4.33013i	−0.231455	+	0.668153i
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	−0.381246	−	0.924473i	$-0.624505\pi$
$43$	4.00000	−	6.92820i	0.609994	−	1.05654i	0.991241	−	0.132068i	$-0.0421616\pi$
$44$	−3.00000			−0.452267
$45$	9.00000	+	5.19615i	1.34164	+	0.774597i
$46$	6.00000	+	3.46410i	0.884652	+	0.510754i
$47$		−	8.66025i		−	1.26323i	−0.775283	−	0.631614i	$-0.782393\pi$
$47$		−	8.66025i		−	1.26323i	0.775283	−	0.631614i	$-0.217607\pi$
$48$	1.50000	+	0.866025i	0.216506	+	0.125000i
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	3.50000	+	6.06218i	0.494975	+	0.857321i
$51$		−	5.19615i		−	0.727607i
$52$	2.50000	−	2.59808i	0.346688	−	0.360288i
$53$			8.66025i			1.18958i	0.803882	+	0.594789i	$0.202764\pi$
$53$			8.66025i			1.18958i	−0.803882	+	0.594789i	$0.797236\pi$
$54$	4.50000	−	2.59808i	0.612372	−	0.353553i
$55$	−9.00000	+	5.19615i	−1.21356	+	0.700649i
$56$	0.500000	+	2.59808i	0.0668153	+	0.347183i
$57$			12.1244i			1.60591i
$58$	−1.50000	−	0.866025i	−0.196960	−	0.113715i
$59$	9.00000	+	5.19615i	1.17170	+	0.676481i	0.954080	−	0.299552i	$-0.0968372\pi$
$59$	9.00000	+	5.19615i	1.17170	+	0.676481i	0.217620	+	0.976034i	$0.430171\pi$
$60$	6.00000			0.774597
$61$	−4.50000	−	2.59808i	−0.576166	−	0.332650i	0.183442	−	0.983030i	$-0.441276\pi$
$61$	−4.50000	−	2.59808i	−0.576166	−	0.332650i	−0.759608	+	0.650381i	$0.774609\pi$
$62$	−2.00000	−	3.46410i	−0.254000	−	0.439941i
$63$	7.50000	+	2.59808i	0.944911	+	0.327327i
$64$	1.00000			0.125000
$65$	3.00000	−	12.1244i	0.372104	−	1.50384i
$66$			5.19615i			0.639602i
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$	6.00000	−	10.3923i	0.722315	−	1.25109i
$70$	6.00000	+	6.92820i	0.717137	+	0.828079i
$71$	−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	$0.282538\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	4.00000			0.468165			0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000			0.468165			0.234082	+	0.972217i	$0.424791\pi$
$74$	6.00000	+	3.46410i	0.697486	+	0.402694i
$75$	10.5000	−	6.06218i	1.21244	−	0.700000i
$76$	3.50000	+	6.06218i	0.401478	+	0.695379i
$77$	−6.00000	+	5.19615i	−0.683763	+	0.592157i
$78$	−4.50000	−	4.33013i	−0.509525	−	0.490290i
$79$	−11.0000			−1.23760			−0.618798	−	0.785550i	$-0.712380\pi$
$79$	−11.0000			−1.23760			−0.618798	+	0.785550i	$0.712380\pi$
$80$	3.00000	−	1.73205i	0.335410	−	0.193649i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	4.50000	+	2.59808i	0.496942	+	0.286910i
$83$		−	13.8564i		−	1.52094i	−0.649374	−	0.760469i	$-0.724969\pi$
$83$		−	13.8564i		−	1.52094i	0.649374	−	0.760469i	$-0.275031\pi$
$84$	4.50000	−	0.866025i	0.490990	−	0.0944911i
$85$	−9.00000	−	5.19615i	−0.976187	−	0.563602i
$86$	−8.00000			−0.862662
$87$	−1.50000	+	2.59808i	−0.160817	+	0.278543i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	−7.50000	+	4.33013i	−0.794998	+	0.458993i	−0.841719	−	0.539915i	$-0.818456\pi$
$89$	−7.50000	+	4.33013i	−0.794998	+	0.458993i	0.0467209	+	0.998908i	$0.485123\pi$
$90$		−	10.3923i		−	1.09545i
$91$	0.500000	−	9.52628i	0.0524142	−	0.998625i
$92$		−	6.92820i		−	0.722315i
$93$	−6.00000	+	3.46410i	−0.622171	+	0.359211i
$94$	−7.50000	+	4.33013i	−0.773566	+	0.446619i
$95$	21.0000	+	12.1244i	2.15455	+	1.24393i
$96$		−	1.73205i		−	0.176777i
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	5.50000	+	4.33013i	0.555584	+	0.437409i
$99$	9.00000			0.904534
$100$	3.50000	−	6.06218i	0.350000	−	0.606218i
$101$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$101$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$102$	−4.50000	+	2.59808i	−0.445566	+	0.257248i
$103$			3.46410i			0.341328i	0.985329	+	0.170664i	$0.0545913\pi$
$103$			3.46410i			0.341328i	−0.985329	+	0.170664i	$0.945409\pi$
$104$	−3.50000	−	0.866025i	−0.343203	−	0.0849208i
$105$	12.0000	−	10.3923i	1.17108	−	1.01419i
$106$	7.50000	−	4.33013i	0.728464	−	0.420579i
$107$	4.50000	−	2.59808i	0.435031	−	0.251166i	−0.266456	−	0.963847i	$-0.585853\pi$
$107$	4.50000	−	2.59808i	0.435031	−	0.251166i	0.701488	+	0.712681i	$0.252519\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$		−	3.46410i		−	0.331801i	−0.986143	−	0.165900i	$-0.946947\pi$
$109$		−	3.46410i		−	0.331801i	0.986143	−	0.165900i	$-0.0530530\pi$
$110$	9.00000	+	5.19615i	0.858116	+	0.495434i
$111$	6.00000	−	10.3923i	0.569495	−	0.986394i
$112$	2.00000	−	1.73205i	0.188982	−	0.163663i
$113$	12.0000	+	6.92820i	1.12887	+	0.651751i	0.943649	−	0.330947i	$-0.107368\pi$
$113$	12.0000	+	6.92820i	1.12887	+	0.651751i	0.185216	+	0.982698i	$0.440702\pi$
$114$	10.5000	−	6.06218i	0.983415	−	0.567775i
$115$	−12.0000	−	20.7846i	−1.11901	−	1.93817i
$116$			1.73205i			0.160817i
$117$	−7.50000	+	7.79423i	−0.693375	+	0.720577i
$118$		−	10.3923i		−	0.956689i
$119$	−7.50000	−	2.59808i	−0.687524	−	0.238165i
$120$	−3.00000	−	5.19615i	−0.273861	−	0.474342i
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$			5.19615i			0.470438i
$123$	4.50000	−	7.79423i	0.405751	−	0.702782i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$		−	6.92820i		−	0.619677i
$126$	−1.50000	−	7.79423i	−0.133631	−	0.694365i
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	0.987108	−	0.160055i	$-0.0511671\pi$
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	−0.632166	+	0.774833i	$0.717834\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$			13.8564i			1.21999i
$130$	−12.0000	+	3.46410i	−1.05247	+	0.303822i
$131$	6.00000			0.524222			0.262111	−	0.965038i	$-0.415581\pi$
$131$	6.00000			0.524222			0.262111	+	0.965038i	$0.415581\pi$
$132$	4.50000	−	2.59808i	0.391675	−	0.226134i
$133$	17.5000	+	6.06218i	1.51744	+	0.525657i
$134$		0			0
$135$	−18.0000			−1.54919
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$	−12.0000			−1.02151
$139$	4.50000	+	2.59808i	0.381685	+	0.220366i	0.678551	−	0.734553i	$-0.262608\pi$
$139$	4.50000	+	2.59808i	0.381685	+	0.220366i	−0.296866	+	0.954919i	$0.595942\pi$
$140$	3.00000	−	8.66025i	0.253546	−	0.731925i
$141$	7.50000	+	12.9904i	0.631614	+	1.09399i
$142$	6.00000			0.503509
$143$	−3.00000	−	10.3923i	−0.250873	−	0.869048i
$144$	−3.00000			−0.250000
$145$	3.00000	+	5.19615i	0.249136	+	0.431517i
$146$	−2.00000	−	3.46410i	−0.165521	−	0.286691i
$147$	7.50000	−	9.52628i	0.618590	−	0.785714i
$148$		−	6.92820i		−	0.569495i
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	−10.5000	−	6.06218i	−0.857321	−	0.494975i
$151$			8.66025i			0.704761i	0.935857	+	0.352381i	$0.114628\pi$
$151$			8.66025i			0.704761i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	3.50000	−	6.06218i	0.283887	−	0.491708i
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$	7.50000	+	2.59808i	0.604367	+	0.209359i
$155$			13.8564i			1.11297i
$156$	−1.50000	+	6.06218i	−0.120096	+	0.485363i
$157$			13.8564i			1.10586i	0.833227	+	0.552931i	$0.186491\pi$
$157$			13.8564i			1.10586i	−0.833227	+	0.552931i	$0.813509\pi$
$158$	5.50000	+	9.52628i	0.437557	+	0.757870i
$159$	−7.50000	−	12.9904i	−0.594789	−	1.03020i
$160$	−3.00000	−	1.73205i	−0.237171	−	0.136931i
$161$	−12.0000	−	13.8564i	−0.945732	−	1.09204i
$162$	−4.50000	+	7.79423i	−0.353553	+	0.612372i
$163$	21.0000	+	12.1244i	1.64485	+	0.949653i	0.979076	+	0.203497i	$0.0652307\pi$
$163$	21.0000	+	12.1244i	1.64485	+	0.949653i	0.665771	+	0.746156i	$0.268103\pi$
$164$		−	5.19615i		−	0.405751i
$165$	9.00000	−	15.5885i	0.700649	−	1.21356i
$166$	−12.0000	+	6.92820i	−0.931381	+	0.537733i
$167$	−15.0000	+	8.66025i	−1.16073	+	0.670151i	−0.951480	−	0.307711i	$-0.900437\pi$
$167$	−15.0000	+	8.66025i	−1.16073	+	0.670151i	−0.209255	+	0.977861i	$0.567104\pi$
$168$	−3.00000	−	3.46410i	−0.231455	−	0.267261i
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$			10.3923i			0.797053i
$171$	−10.5000	−	18.1865i	−0.802955	−	1.39076i
$172$	4.00000	+	6.92820i	0.304997	+	0.528271i
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$	3.00000			0.227429
$175$	−3.50000	−	18.1865i	−0.264575	−	1.37477i
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	−18.0000			−1.35296
$178$	7.50000	+	4.33013i	0.562149	+	0.324557i
$179$	21.0000	−	12.1244i	1.56961	−	0.906217i	0.573400	−	0.819275i	$-0.305624\pi$
$179$	21.0000	−	12.1244i	1.56961	−	0.906217i	0.996213	−	0.0869415i	$-0.0277093\pi$
$180$	−9.00000	+	5.19615i	−0.670820	+	0.387298i
$181$		−	1.73205i		−	0.128742i	−0.997926	−	0.0643712i	$-0.979496\pi$
$181$		−	1.73205i		−	0.128742i	0.997926	−	0.0643712i	$-0.0205042\pi$
$182$	−8.50000	+	4.33013i	−0.630062	+	0.320970i
$183$	9.00000			0.665299
$184$	−6.00000	+	3.46410i	−0.442326	+	0.255377i
$185$	−12.0000	−	20.7846i	−0.882258	−	1.52811i
$186$	6.00000	+	3.46410i	0.439941	+	0.254000i
$187$	−9.00000			−0.658145
$188$	7.50000	+	4.33013i	0.546994	+	0.315807i
$189$	−13.5000	+	2.59808i	−0.981981	+	0.188982i
$190$		−	24.2487i		−	1.75919i
$191$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$191$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$192$	−1.50000	+	0.866025i	−0.108253	+	0.0625000i
$193$	−10.5000	+	6.06218i	−0.755807	+	0.436365i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	−10.5000	+	6.06218i	−0.755807	+	0.436365i	0.0719816	+	0.997406i	$0.477068\pi$
$194$	2.00000			0.143592
$195$	6.00000	+	20.7846i	0.429669	+	1.48842i
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	−13.5000	−	23.3827i	−0.961835	−	1.66595i	−0.717888	−	0.696159i	$-0.754891\pi$
$197$	−13.5000	−	23.3827i	−0.961835	−	1.66595i	−0.243947	−	0.969788i	$-0.578442\pi$
$198$	−4.50000	−	7.79423i	−0.319801	−	0.553912i
$199$	9.00000	+	5.19615i	0.637993	+	0.368345i	0.783841	−	0.620962i	$-0.213258\pi$
$199$	9.00000	+	5.19615i	0.637993	+	0.368345i	−0.145848	+	0.989307i	$0.546591\pi$
$200$	−7.00000			−0.494975
$201$		0			0
$202$		0			0
$203$	3.00000	+	3.46410i	0.210559	+	0.243132i
$204$	4.50000	+	2.59808i	0.315063	+	0.181902i
$205$	−9.00000	−	15.5885i	−0.628587	−	1.08875i
$206$	3.00000	−	1.73205i	0.209020	−	0.120678i
$207$			20.7846i			1.44463i
$208$	1.00000	+	3.46410i	0.0693375	+	0.240192i
$209$	21.0000			1.45260
$210$	−15.0000	−	5.19615i	−1.03510	−	0.358569i
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	0.944237	+	0.329266i	$0.106801\pi$
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	−0.186966	+	0.982366i	$0.559865\pi$
$212$	−7.50000	−	4.33013i	−0.515102	−	0.297394i
$213$		−	10.3923i		−	0.712069i
$214$	−4.50000	−	2.59808i	−0.307614	−	0.177601i
$215$	24.0000	+	13.8564i	1.63679	+	0.944999i
$216$			5.19615i			0.353553i
$217$	2.00000	+	10.3923i	0.135769	+	0.705476i
$218$	−3.00000	+	1.73205i	−0.203186	+	0.117309i
$219$	−6.00000	+	3.46410i	−0.405442	+	0.234082i
$220$		−	10.3923i		−	0.700649i
$221$	7.50000	−	7.79423i	0.504505	−	0.524297i
$222$	−12.0000			−0.805387
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	0.999128	+	0.0417488i	$0.0132929\pi$
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	−0.463409	+	0.886145i	$0.653374\pi$
$224$	−2.50000	−	0.866025i	−0.167038	−	0.0578638i
$225$	−10.5000	+	18.1865i	−0.700000	+	1.21244i
$226$		−	13.8564i		−	0.921714i
$227$	9.00000	+	5.19615i	0.597351	+	0.344881i	0.767999	−	0.640451i	$-0.221253\pi$
$227$	9.00000	+	5.19615i	0.597351	+	0.344881i	−0.170648	+	0.985332i	$0.554586\pi$
$228$	−10.5000	−	6.06218i	−0.695379	−	0.401478i
$229$	13.0000			0.859064			0.429532	−	0.903052i	$-0.358679\pi$
$229$	13.0000			0.859064			0.429532	+	0.903052i	$0.358679\pi$
$230$	−12.0000	+	20.7846i	−0.791257	+	1.37050i
$231$	4.50000	−	12.9904i	0.296078	−	0.854704i
$232$	1.50000	−	0.866025i	0.0984798	−	0.0568574i
$233$			6.92820i			0.453882i	0.973909	+	0.226941i	$0.0728724\pi$
$233$			6.92820i			0.453882i	−0.973909	+	0.226941i	$0.927128\pi$
$234$	10.5000	+	2.59808i	0.686406	+	0.169842i
$235$	30.0000			1.95698
$236$	−9.00000	+	5.19615i	−0.585850	+	0.338241i
$237$	16.5000	−	9.52628i	1.07179	−	0.618798i
$238$	1.50000	+	7.79423i	0.0972306	+	0.505225i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$	−3.00000	+	5.19615i	−0.193649	+	0.335410i
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	−0.980917	−	0.194429i	$-0.937715\pi$
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	0.658838	+	0.752285i	$0.271048\pi$
$242$	−2.00000			−0.128565
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	4.50000	−	2.59808i	0.288083	−	0.166325i
$245$	−9.00000	−	22.5167i	−0.574989	−	1.43854i
$246$	−9.00000			−0.573819
$247$	−17.5000	+	18.1865i	−1.11350	+	1.15718i
$248$	4.00000			0.254000
$249$	12.0000	+	20.7846i	0.760469	+	1.31717i
$250$	−6.00000	+	3.46410i	−0.379473	+	0.219089i
$251$	−15.0000	+	25.9808i	−0.946792	+	1.63989i	−0.194668	+	0.980869i	$0.562363\pi$
$251$	−15.0000	+	25.9808i	−0.946792	+	1.63989i	−0.752124	+	0.659022i	$0.770970\pi$
$252$	−6.00000	+	5.19615i	−0.377964	+	0.327327i
$253$	−18.0000	−	10.3923i	−1.13165	−	0.653359i
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$	18.0000			1.12720
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	13.5000	+	23.3827i	0.842107	+	1.45857i	0.888110	+	0.459631i	$0.152018\pi$
$257$	13.5000	+	23.3827i	0.842107	+	1.45857i	−0.0460033	+	0.998941i	$0.514648\pi$
$258$	12.0000	−	6.92820i	0.747087	−	0.431331i
$259$	−12.0000	−	13.8564i	−0.745644	−	0.860995i
$260$	9.00000	+	8.66025i	0.558156	+	0.537086i
$261$		−	5.19615i		−	0.321634i
$262$	−3.00000	−	5.19615i	−0.185341	−	0.321019i
$263$	−21.0000	+	12.1244i	−1.29492	+	0.747620i	−0.979521	−	0.201341i	$-0.935470\pi$
$263$	−21.0000	+	12.1244i	−1.29492	+	0.747620i	−0.315394	+	0.948961i	$0.602137\pi$
$264$	−4.50000	−	2.59808i	−0.276956	−	0.159901i
$265$	−30.0000			−1.84289
$266$	−3.50000	−	18.1865i	−0.214599	−	1.11509i
$267$	7.50000	−	12.9904i	0.458993	−	0.794998i
$268$		0			0
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	0.224523	+	0.974469i	$0.427917\pi$
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	−0.956176	+	0.292791i	$0.905416\pi$
$270$	9.00000	+	15.5885i	0.547723	+	0.948683i
$271$	−4.00000	−	6.92820i	−0.242983	−	0.420858i	0.718580	−	0.695444i	$-0.244792\pi$
$271$	−4.00000	−	6.92820i	−0.242983	−	0.420858i	−0.961563	+	0.274586i	$0.911459\pi$
$272$	3.00000			0.181902
$273$	7.50000	+	14.7224i	0.453921	+	0.891042i
$274$	12.0000			0.724947
$275$	−10.5000	−	18.1865i	−0.633174	−	1.09669i
$276$	6.00000	+	10.3923i	0.361158	+	0.625543i
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	−0.519081	−	0.854725i	$-0.673726\pi$
$277$	8.00000	−	13.8564i	0.480673	−	0.832551i	0.999754	+	0.0221745i	$0.00705893\pi$
$278$		−	5.19615i		−	0.311645i
$279$	6.00000	−	10.3923i	0.359211	−	0.622171i
$280$	−9.00000	+	1.73205i	−0.537853	+	0.103510i
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$	7.50000	−	12.9904i	0.446619	−	0.773566i
$283$	−3.00000	+	1.73205i	−0.178331	+	0.102960i	−0.586509	−	0.809943i	$-0.699498\pi$
$283$	−3.00000	+	1.73205i	−0.178331	+	0.102960i	0.408177	+	0.912903i	$0.366165\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$	−42.0000			−2.48787
$286$	−7.50000	+	7.79423i	−0.443484	+	0.460882i
$287$	−9.00000	−	10.3923i	−0.531253	−	0.613438i
$288$	1.50000	+	2.59808i	0.0883883	+	0.153093i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	3.00000	−	5.19615i	0.176166	−	0.305129i
$291$		−	3.46410i		−	0.203069i
$292$	−2.00000	+	3.46410i	−0.117041	+	0.202721i
$293$	−6.00000	−	3.46410i	−0.350524	−	0.202375i	0.314392	−	0.949293i	$-0.398199\pi$
$293$	−6.00000	−	3.46410i	−0.350524	−	0.202375i	−0.664916	+	0.746918i	$0.731533\pi$
$294$	−12.0000	−	1.73205i	−0.699854	−	0.101015i
$295$	−18.0000	+	31.1769i	−1.04800	+	1.81519i
$296$	−6.00000	+	3.46410i	−0.348743	+	0.201347i
$297$	−13.5000	+	7.79423i	−0.783349	+	0.452267i
$298$	−6.00000			−0.347571
$299$	24.0000	−	6.92820i	1.38796	−	0.400668i
$300$			12.1244i			0.700000i
$301$	20.0000	+	6.92820i	1.15278	+	0.399335i
$302$	7.50000	−	4.33013i	0.431577	−	0.249171i
$303$		0			0
$304$	−7.00000			−0.401478
$305$	9.00000	−	15.5885i	0.515339	−	0.892592i
$306$	4.50000	−	7.79423i	0.257248	−	0.445566i
$307$	7.00000			0.399511			0.199756	−	0.979846i	$-0.435985\pi$
$307$	7.00000			0.399511			0.199756	+	0.979846i	$0.435985\pi$
$308$	−1.50000	−	7.79423i	−0.0854704	−	0.444117i
$309$	−3.00000	−	5.19615i	−0.170664	−	0.295599i
$310$	12.0000	−	6.92820i	0.681554	−	0.393496i
$311$	−3.00000			−0.170114			−0.0850572	−	0.996376i	$-0.527107\pi$
$311$	−3.00000			−0.170114			−0.0850572	+	0.996376i	$0.527107\pi$
$312$	6.00000	−	1.73205i	0.339683	−	0.0980581i
$313$		−	20.7846i		−	1.17482i	−0.809291	−	0.587408i	$-0.800148\pi$
$313$		−	20.7846i		−	1.17482i	0.809291	−	0.587408i	$-0.199852\pi$
$314$	12.0000	−	6.92820i	0.677199	−	0.390981i
$315$	−9.00000	+	25.9808i	−0.507093	+	1.46385i
$316$	5.50000	−	9.52628i	0.309399	−	0.535895i
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$	−7.50000	+	12.9904i	−0.420579	+	0.728464i
$319$	4.50000	+	2.59808i	0.251952	+	0.145464i
$320$			3.46410i			0.193649i
$321$	−4.50000	+	7.79423i	−0.251166	+	0.435031i
$322$	−6.00000	+	17.3205i	−0.334367	+	0.965234i
$323$	10.5000	+	18.1865i	0.584236	+	1.01193i
$324$	9.00000			0.500000
$325$	24.5000	+	6.06218i	1.35902	+	0.336269i
$326$		−	24.2487i		−	1.34301i
$327$	3.00000	+	5.19615i	0.165900	+	0.287348i
$328$	−4.50000	+	2.59808i	−0.248471	+	0.143455i
$329$	22.5000	−	4.33013i	1.24047	−	0.238728i
$330$	−18.0000			−0.990867
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$	12.0000	+	6.92820i	0.658586	+	0.380235i
$333$			20.7846i			1.13899i
$334$	15.0000	+	8.66025i	0.820763	+	0.473868i
$335$		0			0
$336$	−1.50000	+	4.33013i	−0.0818317	+	0.236228i
$337$	−19.0000			−1.03500			−0.517498	−	0.855684i	$-0.673136\pi$
$337$	−19.0000			−1.03500			−0.517498	+	0.855684i	$0.673136\pi$
$338$	−0.500000	−	12.9904i	−0.0271964	−	0.706584i
$339$	−24.0000			−1.30350
$340$	9.00000	−	5.19615i	0.488094	−	0.281801i
$341$	6.00000	+	10.3923i	0.324918	+	0.562775i
$342$	−10.5000	+	18.1865i	−0.567775	+	0.983415i
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	4.00000	−	6.92820i	0.215666	−	0.373544i
$345$	36.0000	+	20.7846i	1.93817	+	1.11901i
$346$		0			0
$347$	−13.5000	−	7.79423i	−0.724718	−	0.418416i	0.0917687	−	0.995780i	$-0.470748\pi$
$347$	−13.5000	−	7.79423i	−0.724718	−	0.418416i	−0.816487	+	0.577364i	$0.804081\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$	1.00000	+	1.73205i	0.0535288	+	0.0927146i	0.891548	−	0.452926i	$-0.149620\pi$
$349$	1.00000	+	1.73205i	0.0535288	+	0.0927146i	−0.838019	+	0.545640i	$0.816286\pi$
$350$	−14.0000	+	12.1244i	−0.748331	+	0.648074i
$351$	4.50000	−	18.1865i	0.240192	−	0.970725i
$352$	−3.00000			−0.159901
$353$	18.0000	−	10.3923i	0.958043	−	0.553127i	0.0624731	−	0.998047i	$-0.480101\pi$
$353$	18.0000	−	10.3923i	0.958043	−	0.553127i	0.895570	+	0.444920i	$0.146768\pi$
$354$	9.00000	+	15.5885i	0.478345	+	0.828517i
$355$	−18.0000	−	10.3923i	−0.955341	−	0.551566i
$356$		−	8.66025i		−	0.458993i
$357$	13.5000	−	2.59808i	0.714496	−	0.137505i
$358$	−21.0000	−	12.1244i	−1.10988	−	0.640792i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$	9.00000	+	5.19615i	0.474342	+	0.273861i
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$	−1.50000	+	0.866025i	−0.0788382	+	0.0455173i
$363$			3.46410i			0.181818i
$364$	8.00000	+	5.19615i	0.419314	+	0.272352i
$365$			13.8564i			0.725277i
$366$	−4.50000	−	7.79423i	−0.235219	−	0.407411i
$367$	18.0000	−	10.3923i	0.939592	−	0.542474i	0.0497598	−	0.998761i	$-0.484154\pi$
$367$	18.0000	−	10.3923i	0.939592	−	0.542474i	0.889833	+	0.456287i	$0.150821\pi$
$368$	6.00000	+	3.46410i	0.312772	+	0.180579i
$369$			15.5885i			0.811503i
$370$	−12.0000	+	20.7846i	−0.623850	+	1.08054i
$371$	−22.5000	+	4.33013i	−1.16814	+	0.224809i
$372$		−	6.92820i		−	0.359211i
$373$	10.0000	−	17.3205i	0.517780	−	0.896822i	−0.482006	−	0.876168i	$-0.660092\pi$
$373$	10.0000	−	17.3205i	0.517780	−	0.896822i	0.999787	−	0.0206542i	$-0.00657489\pi$
$374$	4.50000	+	7.79423i	0.232689	+	0.403030i
$375$	6.00000	+	10.3923i	0.309839	+	0.536656i
$376$		−	8.66025i		−	0.446619i
$377$	−6.00000	+	1.73205i	−0.309016	+	0.0892052i
$378$	9.00000	+	10.3923i	0.462910	+	0.534522i
$379$	−9.00000	+	5.19615i	−0.462299	+	0.266908i	−0.713010	−	0.701153i	$-0.752669\pi$
$379$	−9.00000	+	5.19615i	−0.462299	+	0.266908i	0.250711	+	0.968062i	$0.419335\pi$
$380$	−21.0000	+	12.1244i	−1.07728	+	0.621966i
$381$	−12.0000	−	6.92820i	−0.614779	−	0.354943i
$382$		0			0
$383$	−4.50000	−	2.59808i	−0.229939	−	0.132755i	0.380605	−	0.924738i	$-0.375716\pi$
$383$	−4.50000	−	2.59808i	−0.229939	−	0.132755i	−0.610544	+	0.791982i	$0.709049\pi$
$384$	1.50000	+	0.866025i	0.0765466	+	0.0441942i
$385$	−18.0000	−	20.7846i	−0.917365	−	1.05928i
$386$	10.5000	+	6.06218i	0.534436	+	0.308557i
$387$	−12.0000	−	20.7846i	−0.609994	−	1.05654i
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$			20.7846i			1.05382i	0.849921	+	0.526911i	$0.176650\pi$
$389$			20.7846i			1.05382i	−0.849921	+	0.526911i	$0.823350\pi$
$390$	15.0000	−	15.5885i	0.759555	−	0.789352i
$391$		−	20.7846i		−	1.05112i
$392$	−6.50000	+	2.59808i	−0.328300	+	0.131223i
$393$	−9.00000	+	5.19615i	−0.453990	+	0.262111i
$394$	−13.5000	+	23.3827i	−0.680120	+	1.17800i
$395$		−	38.1051i		−	1.91728i
$396$	−4.50000	+	7.79423i	−0.226134	+	0.391675i
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	−0.764730	−	0.644351i	$-0.777127\pi$
$397$	3.50000	−	6.06218i	0.175660	−	0.304252i	0.940389	+	0.340099i	$0.110461\pi$
$398$		−	10.3923i		−	0.520919i
$399$	−31.5000	+	6.06218i	−1.57697	+	0.303488i
$400$	3.50000	+	6.06218i	0.175000	+	0.303109i
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	0.998350	−	0.0574304i	$-0.0182907\pi$
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	−0.548911	+	0.835881i	$0.684957\pi$
$402$		0			0
$403$	−14.0000	−	3.46410i	−0.697390	−	0.172559i
$404$		0			0
$405$	27.0000	−	15.5885i	1.34164	−	0.774597i
$406$	1.50000	−	4.33013i	0.0744438	−	0.214901i
$407$	−18.0000	−	10.3923i	−0.892227	−	0.515127i
$408$		−	5.19615i		−	0.257248i
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	−0.812333	−	0.583193i	$-0.801803\pi$
$409$	2.00000	−	3.46410i	0.0988936	−	0.171289i	0.911227	+	0.411905i	$0.135136\pi$
$410$	−9.00000	+	15.5885i	−0.444478	+	0.769859i
$411$		−	20.7846i		−	1.02523i
$412$	−3.00000	−	1.73205i	−0.147799	−	0.0853320i
$413$	−9.00000	+	25.9808i	−0.442861	+	1.27843i
$414$	18.0000	−	10.3923i	0.884652	−	0.510754i
$415$	48.0000			2.35623
$416$	2.50000	−	2.59808i	0.122573	−	0.127381i
$417$	−9.00000			−0.440732
$418$	−10.5000	−	18.1865i	−0.513572	−	0.889532i
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$	3.00000	+	15.5885i	0.146385	+	0.760639i
$421$			24.2487i			1.18181i	0.806741	+	0.590905i	$0.201229\pi$
$421$			24.2487i			1.18181i	−0.806741	+	0.590905i	$0.798771\pi$
$422$	11.0000	−	19.0526i	0.535472	−	0.927464i
$423$	−22.5000	−	12.9904i	−1.09399	−	0.631614i
$424$			8.66025i			0.420579i
$425$	10.5000	−	18.1865i	0.509325	−	0.882176i
$426$	−9.00000	+	5.19615i	−0.436051	+	0.251754i
$427$	4.50000	−	12.9904i	0.217770	−	0.628649i
$428$			5.19615i			0.251166i
$429$	13.5000	+	12.9904i	0.651786	+	0.627182i
$430$		−	27.7128i		−	1.33643i
$431$	−9.00000	−	15.5885i	−0.433515	−	0.750870i	0.563658	−	0.826008i	$-0.309393\pi$
$431$	−9.00000	−	15.5885i	−0.433515	−	0.750870i	−0.997173	+	0.0751385i	$0.976060\pi$
$432$	4.50000	−	2.59808i	0.216506	−	0.125000i
$433$	15.0000	+	8.66025i	0.720854	+	0.416185i	0.815067	−	0.579367i	$-0.196700\pi$
$433$	15.0000	+	8.66025i	0.720854	+	0.416185i	−0.0942129	+	0.995552i	$0.530033\pi$
$434$	8.00000	−	6.92820i	0.384012	−	0.332564i
$435$	−9.00000	−	5.19615i	−0.431517	−	0.249136i
$436$	3.00000	+	1.73205i	0.143674	+	0.0829502i
$437$			48.4974i			2.31995i
$438$	6.00000	+	3.46410i	0.286691	+	0.165521i
$439$	3.00000	−	1.73205i	0.143182	−	0.0826663i	−0.426698	−	0.904394i	$-0.640323\pi$
$439$	3.00000	−	1.73205i	0.143182	−	0.0826663i	0.569880	+	0.821728i	$0.306990\pi$
$440$	−9.00000	+	5.19615i	−0.429058	+	0.247717i
$441$	−3.00000	+	20.7846i	−0.142857	+	0.989743i
$442$	−10.5000	−	2.59808i	−0.499434	−	0.123578i
$443$		−	29.4449i		−	1.39897i	−0.714648	−	0.699484i	$-0.753413\pi$
$443$		−	29.4449i		−	1.39897i	0.714648	−	0.699484i	$-0.246587\pi$
$444$	6.00000	+	10.3923i	0.284747	+	0.493197i
$445$	−15.0000	−	25.9808i	−0.711068	−	1.23161i
$446$	8.00000	−	13.8564i	0.378811	−	0.656120i
$447$			10.3923i			0.491539i
$448$	0.500000	+	2.59808i	0.0236228	+	0.122748i
$449$	18.0000	−	31.1769i	0.849473	−	1.47133i	−0.0322072	−	0.999481i	$-0.510254\pi$
$449$	18.0000	−	31.1769i	0.849473	−	1.47133i	0.881680	−	0.471848i	$-0.156413\pi$
$450$	21.0000			0.989949
$451$	−13.5000	−	7.79423i	−0.635690	−	0.367016i
$452$	−12.0000	+	6.92820i	−0.564433	+	0.325875i
$453$	−7.50000	−	12.9904i	−0.352381	−	0.610341i
$454$		−	10.3923i		−	0.487735i
$455$	33.0000	+	1.73205i	1.54706	+	0.0811998i
$456$			12.1244i			0.567775i
$457$	−6.00000	+	3.46410i	−0.280668	+	0.162044i	−0.633726	−	0.773558i	$-0.718475\pi$
$457$	−6.00000	+	3.46410i	−0.280668	+	0.162044i	0.353058	+	0.935602i	$0.385142\pi$
$458$	−6.50000	−	11.2583i	−0.303725	−	0.526067i
$459$	−13.5000	−	7.79423i	−0.630126	−	0.363803i
$460$	24.0000			1.11901
$461$	−27.0000	−	15.5885i	−1.25752	−	0.726027i	−0.284925	−	0.958550i	$-0.591969\pi$
$461$	−27.0000	−	15.5885i	−1.25752	−	0.726027i	−0.972591	+	0.232523i	$0.925302\pi$
$462$	−13.5000	+	2.59808i	−0.628077	+	0.120873i
$463$			36.3731i			1.69040i	0.534450	+	0.845200i	$0.320519\pi$
$463$			36.3731i			1.69040i	−0.534450	+	0.845200i	$0.679481\pi$
$464$	−1.50000	−	0.866025i	−0.0696358	−	0.0402042i
$465$	−12.0000	−	20.7846i	−0.556487	−	0.963863i
$466$	6.00000	−	3.46410i	0.277945	−	0.160471i
$467$	6.00000			0.277647			0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000			0.277647			0.138823	+	0.990317i	$0.455668\pi$
$468$	−3.00000	−	10.3923i	−0.138675	−	0.480384i
$469$		0			0
$470$	−15.0000	−	25.9808i	−0.691898	−	1.19840i
$471$	−12.0000	−	20.7846i	−0.552931	−	0.957704i
$472$	9.00000	+	5.19615i	0.414259	+	0.239172i
$473$	24.0000			1.10352
$474$	−16.5000	−	9.52628i	−0.757870	−	0.437557i
$475$	−24.5000	+	42.4352i	−1.12414	+	1.94706i
$476$	6.00000	−	5.19615i	0.275010	−	0.238165i
$477$	22.5000	+	12.9904i	1.03020	+	0.594789i
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	28.5000	−	16.4545i	1.30220	−	0.751825i	0.321417	−	0.946938i	$-0.395841\pi$
$479$	28.5000	−	16.4545i	1.30220	−	0.751825i	0.980781	+	0.195113i	$0.0625074\pi$
$480$	6.00000			0.273861
$481$	24.0000	−	6.92820i	1.09431	−	0.315899i
$482$	10.0000			0.455488
$483$	30.0000	+	10.3923i	1.36505	+	0.472866i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	−6.00000	−	3.46410i	−0.272446	−	0.157297i
$486$		−	15.5885i		−	0.707107i
$487$	7.50000	+	4.33013i	0.339857	+	0.196217i	0.660209	−	0.751082i	$-0.270468\pi$
$487$	7.50000	+	4.33013i	0.339857	+	0.196217i	−0.320352	+	0.947299i	$0.603801\pi$
$488$	−4.50000	−	2.59808i	−0.203705	−	0.117609i
$489$	−42.0000			−1.89931
$490$	−15.0000	+	19.0526i	−0.677631	+	0.860707i
$491$	−9.00000	+	5.19615i	−0.406164	+	0.234499i	−0.689140	−	0.724628i	$-0.742012\pi$
$491$	−9.00000	+	5.19615i	−0.406164	+	0.234499i	0.282976	+	0.959127i	$0.408678\pi$
$492$	4.50000	+	7.79423i	0.202876	+	0.351391i
$493$			5.19615i			0.234023i
$494$	24.5000	+	6.06218i	1.10231	+	0.272750i
$495$			31.1769i			1.40130i
$496$	−2.00000	−	3.46410i	−0.0898027	−	0.155543i
$497$	−15.0000	−	5.19615i	−0.672842	−	0.233079i
$498$	12.0000	−	20.7846i	0.537733	−	0.931381i
$499$		−	41.5692i		−	1.86089i	−0.366427	−	0.930447i	$-0.619419\pi$
$499$		−	41.5692i		−	1.86089i	0.366427	−	0.930447i	$-0.380581\pi$
$500$	6.00000	+	3.46410i	0.268328	+	0.154919i
$501$	15.0000	−	25.9808i	0.670151	−	1.16073i
$502$	30.0000			1.33897
$503$	6.00000	−	10.3923i	0.267527	−	0.463370i	−0.700696	−	0.713460i	$-0.747127\pi$
$503$	6.00000	−	10.3923i	0.267527	−	0.463370i	0.968223	+	0.250090i	$0.0804603\pi$
$504$	7.50000	+	2.59808i	0.334077	+	0.115728i
$505$		0			0
$506$			20.7846i			0.923989i
$507$	−22.5000	+	0.866025i	−0.999260	+	0.0384615i
$508$	−8.00000			−0.354943
$509$	24.0000	−	13.8564i	1.06378	−	0.614174i	0.137305	−	0.990529i	$-0.456156\pi$
$509$	24.0000	−	13.8564i	1.06378	−	0.614174i	0.926476	+	0.376354i	$0.122822\pi$
$510$	−9.00000	−	15.5885i	−0.398527	−	0.690268i
$511$	2.00000	+	10.3923i	0.0884748	+	0.459728i
$512$	1.00000			0.0441942
$513$	31.5000	+	18.1865i	1.39076	+	0.802955i
$514$	13.5000	−	23.3827i	0.595459	−	1.03137i
$515$	−12.0000			−0.528783
$516$	−12.0000	−	6.92820i	−0.528271	−	0.304997i
$517$	22.5000	−	12.9904i	0.989549	−	0.571316i
$518$	−6.00000	+	17.3205i	−0.263625	+	0.761019i
$519$		0			0
$520$	3.00000	−	12.1244i	0.131559	−	0.531688i
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$	−4.50000	+	2.59808i	−0.196960	+	0.113715i
$523$	−28.5000	+	16.4545i	−1.24622	+	0.719504i	−0.970353	−	0.241692i	$-0.922298\pi$
$523$	−28.5000	+	16.4545i	−1.24622	+	0.719504i	−0.275865	+	0.961196i	$0.588964\pi$
$524$	−3.00000	+	5.19615i	−0.131056	+	0.226995i
$525$	21.0000	+	24.2487i	0.916515	+	1.05830i
$526$	21.0000	+	12.1244i	0.915644	+	0.528647i
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$			5.19615i			0.226134i
$529$	12.5000	−	21.6506i	0.543478	−	0.941332i
$530$	15.0000	+	25.9808i	0.651558	+	1.12853i
$531$	27.0000	−	15.5885i	1.17170	−	0.676481i
$532$	−14.0000	+	12.1244i	−0.606977	+	0.525657i
$533$	18.0000	−	5.19615i	0.779667	−	0.225070i
$534$	−15.0000			−0.649113
$535$	9.00000	+	15.5885i	0.389104	+	0.673948i
$536$		0			0
$537$	−21.0000	+	36.3731i	−0.906217	+	1.56961i
$538$	24.0000			1.03471
$539$	−16.5000	−	12.9904i	−0.710705	−	0.559535i
$540$	9.00000	−	15.5885i	0.387298	−	0.670820i
$541$			31.1769i			1.34040i	0.742180	+	0.670200i	$0.233792\pi$
$541$			31.1769i			1.34040i	−0.742180	+	0.670200i	$0.766208\pi$
$542$	−4.00000	+	6.92820i	−0.171815	+	0.297592i
$543$	1.50000	+	2.59808i	0.0643712	+	0.111494i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	12.0000			0.514024
$546$	9.00000	−	13.8564i	0.385164	−	0.592999i
$547$	2.00000			0.0855138			0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000			0.0855138			0.0427569	+	0.999086i	$0.486386\pi$
$548$	−6.00000	−	10.3923i	−0.256307	−	0.443937i
$549$	−13.5000	+	7.79423i	−0.576166	+	0.332650i
$550$	−10.5000	+	18.1865i	−0.447722	+	0.775476i
$551$		−	12.1244i		−	0.516515i
$552$	6.00000	−	10.3923i	0.255377	−	0.442326i
$553$	−5.50000	−	28.5788i	−0.233884	−	1.21530i
$554$	−16.0000			−0.679775
$555$	36.0000	+	20.7846i	1.52811	+	0.882258i
$556$	−4.50000	+	2.59808i	−0.190843	+	0.110183i
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	0.896053	−	0.443947i	$-0.146422\pi$
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	−0.832496	+	0.554031i	$0.813089\pi$
$558$	−12.0000			−0.508001
$559$	−20.0000	+	20.7846i	−0.845910	+	0.879095i
$560$	6.00000	+	6.92820i	0.253546	+	0.292770i
$561$	13.5000	−	7.79423i	0.569970	−	0.329073i
$562$	6.00000	+	10.3923i	0.253095	+	0.438373i
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	0.494238	+	0.869326i	$0.335447\pi$
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	−0.999978	+	0.00664037i	$0.997886\pi$
$564$	−15.0000			−0.631614
$565$	−24.0000	+	41.5692i	−1.00969	+	1.74883i
$566$	3.00000	+	1.73205i	0.126099	+	0.0728035i
$567$	18.0000	−	15.5885i	0.755929	−	0.654654i
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	15.0000	−	8.66025i	0.628833	−	0.363057i	−0.151467	−	0.988462i	$-0.548400\pi$
$569$	15.0000	−	8.66025i	0.628833	−	0.363057i	0.780300	+	0.625406i	$0.215066\pi$
$570$	21.0000	+	36.3731i	0.879593	+	1.52350i
$571$	40.0000			1.67395			0.836974	−	0.547243i	$-0.184323\pi$
$571$	40.0000			1.67395			0.836974	+	0.547243i	$0.184323\pi$
$572$	10.5000	+	2.59808i	0.439027	+	0.108631i
$573$		0			0
$574$	−4.50000	+	12.9904i	−0.187826	+	0.542208i
$575$	42.0000	−	24.2487i	1.75152	−	1.01124i
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−10.0000			−0.416305			−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000			−0.416305			−0.208153	+	0.978096i	$0.566745\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	10.5000	−	18.1865i	0.436365	−	0.755807i
$580$	−6.00000			−0.249136
$581$	36.0000	−	6.92820i	1.49353	−	0.287430i
$582$	−3.00000	+	1.73205i	−0.124354	+	0.0717958i
$583$	−22.5000	+	12.9904i	−0.931855	+	0.538007i
$584$	4.00000			0.165521
$585$	−27.0000	−	25.9808i	−1.11631	−	1.07417i
$586$			6.92820i			0.286201i
$587$	−15.0000	+	8.66025i	−0.619116	+	0.357447i	−0.776525	−	0.630087i	$-0.783019\pi$
$587$	−15.0000	+	8.66025i	−0.619116	+	0.357447i	0.157409	+	0.987534i	$0.449686\pi$
$588$	4.50000	+	11.2583i	0.185577	+	0.464286i
$589$	14.0000	−	24.2487i	0.576860	−	0.999151i
$590$	36.0000			1.48210
$591$	40.5000	+	23.3827i	1.66595	+	0.961835i
$592$	6.00000	+	3.46410i	0.246598	+	0.142374i
$593$		−	8.66025i		−	0.355634i	−0.984064	−	0.177817i	$-0.943096\pi$
$593$		−	8.66025i		−	0.355634i	0.984064	−	0.177817i	$-0.0569035\pi$
$594$	13.5000	+	7.79423i	0.553912	+	0.319801i
$595$	9.00000	−	25.9808i	0.368964	−	1.06511i
$596$	3.00000	+	5.19615i	0.122885	+	0.212843i
$597$	−18.0000			−0.736691
$598$	−18.0000	−	17.3205i	−0.736075	−	0.708288i
$599$		−	3.46410i		−	0.141539i	−0.997493	−	0.0707697i	$-0.977454\pi$
$599$		−	3.46410i		−	0.141539i	0.997493	−	0.0707697i	$-0.0225455\pi$
$600$	10.5000	−	6.06218i	0.428661	−	0.247487i
$601$	27.0000	−	15.5885i	1.10135	−	0.635866i	0.164777	−	0.986331i	$-0.447310\pi$
$601$	27.0000	−	15.5885i	1.10135	−	0.635866i	0.936576	+	0.350464i	$0.113976\pi$
$602$	−4.00000	−	20.7846i	−0.163028	−	0.847117i
$603$		0			0
$604$	−7.50000	−	4.33013i	−0.305171	−	0.176190i
$605$	6.00000	+	3.46410i	0.243935	+	0.140836i
$606$		0			0
$607$	6.00000	+	3.46410i	0.243532	+	0.140604i	0.616799	−	0.787121i	$-0.288429\pi$
$607$	6.00000	+	3.46410i	0.243532	+	0.140604i	−0.373267	+	0.927724i	$0.621762\pi$
$608$	3.50000	+	6.06218i	0.141944	+	0.245854i
$609$	−7.50000	−	2.59808i	−0.303915	−	0.105279i
$610$	−18.0000			−0.728799
$611$	−7.50000	+	30.3109i	−0.303418	+	1.22625i
$612$	−9.00000			−0.363803
$613$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$613$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$614$	−3.50000	−	6.06218i	−0.141249	−	0.244650i
$615$	27.0000	+	15.5885i	1.08875	+	0.628587i
$616$	−6.00000	+	5.19615i	−0.241747	+	0.209359i
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	−0.920074	−	0.391745i	$-0.871871\pi$
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	0.799298	+	0.600935i	$0.205205\pi$
$618$	−3.00000	+	5.19615i	−0.120678	+	0.209020i
$619$	−31.0000			−1.24600			−0.622998	−	0.782224i	$-0.714085\pi$
$619$	−31.0000			−1.24600			−0.622998	+	0.782224i	$0.714085\pi$
$620$	−12.0000	−	6.92820i	−0.481932	−	0.278243i
$621$	−18.0000	−	31.1769i	−0.722315	−	1.25109i
$622$	1.50000	+	2.59808i	0.0601445	+	0.104173i
$623$	−15.0000	−	17.3205i	−0.600962	−	0.693932i
$624$	−4.50000	−	4.33013i	−0.180144	−	0.173344i
$625$	−11.0000			−0.440000
$626$	−18.0000	+	10.3923i	−0.719425	+	0.415360i
$627$	−31.5000	+	18.1865i	−1.25799	+	0.726300i
$628$	−12.0000	−	6.92820i	−0.478852	−	0.276465i
$629$		−	20.7846i		−	0.828737i
$630$	27.0000	−	5.19615i	1.07571	−	0.207020i
$631$	−40.5000	−	23.3827i	−1.61228	−	0.930850i	−0.988841	−	0.148978i	$-0.952402\pi$
$631$	−40.5000	−	23.3827i	−1.61228	−	0.930850i	−0.623439	−	0.781872i	$-0.714265\pi$
$632$	−11.0000			−0.437557
$633$	−33.0000	−	19.0526i	−1.31163	−	0.757271i
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	−24.0000	+	13.8564i	−0.952411	+	0.549875i
$636$	15.0000			0.594789
$637$	25.0000	−	3.46410i	0.990536	−	0.137253i
$638$		−	5.19615i		−	0.205718i
$639$	9.00000	+	15.5885i	0.356034	+	0.616670i
$640$	3.00000	−	1.73205i	0.118585	−	0.0684653i
$641$	−3.00000	−	1.73205i	−0.118493	−	0.0684119i	0.439582	−	0.898202i	$-0.355127\pi$
$641$	−3.00000	−	1.73205i	−0.118493	−	0.0684119i	−0.558075	+	0.829790i	$0.688460\pi$
$642$	9.00000			0.355202
$643$	23.5000	−	40.7032i	0.926750	−	1.60518i	0.138027	−	0.990429i	$-0.455924\pi$
$643$	23.5000	−	40.7032i	0.926750	−	1.60518i	0.788723	−	0.614749i	$-0.210743\pi$
$644$	18.0000	−	3.46410i	0.709299	−	0.136505i
$645$	−48.0000			−1.89000
$646$	10.5000	−	18.1865i	0.413117	−	0.715540i
$647$	10.5000	+	18.1865i	0.412798	+	0.714986i	0.995194	−	0.0979182i	$-0.0312184\pi$
$647$	10.5000	+	18.1865i	0.412798	+	0.714986i	−0.582397	+	0.812905i	$0.697885\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$			31.1769i			1.22380i
$650$	−7.00000	−	24.2487i	−0.274563	−	0.951113i
$651$	−12.0000	−	13.8564i	−0.470317	−	0.543075i
$652$	−21.0000	+	12.1244i	−0.822423	+	0.474826i
$653$	4.50000	−	2.59808i	0.176099	−	0.101671i	−0.409360	−	0.912373i	$-0.634248\pi$
$653$	4.50000	−	2.59808i	0.176099	−	0.101671i	0.585458	+	0.810702i	$0.300915\pi$
$654$	3.00000	−	5.19615i	0.117309	−	0.203186i
$655$			20.7846i			0.812122i
$656$	4.50000	+	2.59808i	0.175695	+	0.101438i
$657$	6.00000	−	10.3923i	0.234082	−	0.405442i
$658$	−15.0000	−	17.3205i	−0.584761	−	0.675224i
$659$	1.50000	+	0.866025i	0.0584317	+	0.0337356i	0.528931	−	0.848665i	$-0.322593\pi$
$659$	1.50000	+	0.866025i	0.0584317	+	0.0337356i	−0.470500	+	0.882400i	$0.655926\pi$
$660$	9.00000	+	15.5885i	0.350325	+	0.606780i
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	0.969442	−	0.245319i	$-0.0788928\pi$
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	−0.697174	+	0.716902i	$0.745559\pi$
$662$		0			0
$663$	−4.50000	+	18.1865i	−0.174766	+	0.706306i
$664$		−	13.8564i		−	0.537733i
$665$	−21.0000	+	60.6218i	−0.814345	+	2.35081i
$666$	18.0000	−	10.3923i	0.697486	−	0.402694i
$667$	−6.00000	+	10.3923i	−0.232321	+	0.402392i
$668$		−	17.3205i		−	0.670151i
$669$	−24.0000	−	13.8564i	−0.927894	−	0.535720i
$670$		0			0
$671$		−	15.5885i		−	0.601786i
$672$	4.50000	−	0.866025i	0.173591	−	0.0334077i
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	0.997586	+	0.0694449i	$0.0221228\pi$
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	−0.438652	+	0.898657i	$0.644544\pi$
$674$	9.50000	+	16.4545i	0.365926	+	0.633803i
$675$		−	36.3731i		−	1.40000i
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$	12.0000	+	20.7846i	0.460857	+	0.798228i
$679$	−5.00000	−	1.73205i	−0.191882	−	0.0664700i
$680$	−9.00000	−	5.19615i	−0.345134	−	0.199263i
$681$	−18.0000			−0.689761
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$	21.0000			0.802955
$685$	−36.0000	−	20.7846i	−1.37549	−	0.794139i
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$	−19.5000	+	11.2583i	−0.743971	+	0.429532i
$688$	−8.00000			−0.304997
$689$	7.50000	−	30.3109i	0.285727	−	1.15475i
$690$		−	41.5692i		−	1.58251i
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$		0			0
$693$	4.50000	+	23.3827i	0.170941	+	0.888235i
$694$			15.5885i			0.591730i
$695$	−9.00000	+	15.5885i	−0.341389	+	0.591304i
$696$	−1.50000	+	2.59808i	−0.0568574	+	0.0984798i
$697$		−	15.5885i		−	0.590455i
$698$	1.00000	−	1.73205i	0.0378506	−	0.0655591i
$699$	−6.00000	−	10.3923i	−0.226941	−	0.393073i
$700$	17.5000	+	6.06218i	0.661438	+	0.229129i
$701$			12.1244i			0.457931i	0.973435	+	0.228965i	$0.0735342\pi$
$701$			12.1244i			0.457931i	−0.973435	+	0.228965i	$0.926466\pi$
$702$	−18.0000	+	5.19615i	−0.679366	+	0.196116i
$703$			48.4974i			1.82911i
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$	−45.0000	+	25.9808i	−1.69480	+	0.978492i
$706$	−18.0000	−	10.3923i	−0.677439	−	0.391120i
$707$		0			0
$708$	9.00000	−	15.5885i	0.338241	−	0.585850i
$709$	21.0000	+	12.1244i	0.788672	+	0.455340i	0.839495	−	0.543368i	$-0.182851\pi$
$709$	21.0000	+	12.1244i	0.788672	+	0.455340i	−0.0508231	+	0.998708i	$0.516184\pi$
$710$			20.7846i			0.780033i
$711$	−16.5000	+	28.5788i	−0.618798	+	1.07179i
$712$	−7.50000	+	4.33013i	−0.281074	+	0.162278i
$713$	−24.0000	+	13.8564i	−0.898807	+	0.518927i
$714$	−9.00000	−	10.3923i	−0.336817	−	0.388922i
$715$	36.0000	−	10.3923i	1.34632	−	0.388650i
$716$			24.2487i			0.906217i
$717$	18.0000	−	10.3923i	0.672222	−	0.388108i
$718$	−12.0000	−	20.7846i	−0.447836	−	0.775675i
$719$	10.5000	−	18.1865i	0.391584	−	0.678243i	−0.601075	−	0.799193i	$-0.705261\pi$
$719$	10.5000	−	18.1865i	0.391584	−	0.678243i	0.992659	+	0.120950i	$0.0385939\pi$
$720$		−	10.3923i		−	0.387298i
$721$	−9.00000	+	1.73205i	−0.335178	+	0.0645049i
$722$	−15.0000	+	25.9808i	−0.558242	+	0.966904i
$723$		−	17.3205i		−	0.644157i
$724$	1.50000	+	0.866025i	0.0557471	+	0.0321856i
$725$	−10.5000	+	6.06218i	−0.389960	+	0.225144i
$726$	3.00000	−	1.73205i	0.111340	−	0.0642824i
$727$			34.6410i			1.28476i	0.766385	+	0.642382i	$0.222054\pi$
$727$			34.6410i			1.28476i	−0.766385	+	0.642382i	$0.777946\pi$
$728$	0.500000	−	9.52628i	0.0185312	−	0.353067i
$729$	−27.0000			−1.00000
$730$	12.0000	−	6.92820i	0.444140	−	0.256424i
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$	−4.50000	+	7.79423i	−0.166325	+	0.288083i
$733$	13.0000			0.480166			0.240083	−	0.970752i	$-0.422825\pi$
$733$	13.0000			0.480166			0.240083	+	0.970752i	$0.422825\pi$
$734$	−18.0000	−	10.3923i	−0.664392	−	0.383587i
$735$	33.0000	+	25.9808i	1.21722	+	0.958315i
$736$		−	6.92820i		−	0.255377i
$737$		0			0
$738$	13.5000	−	7.79423i	0.496942	−	0.286910i
$739$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$739$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$740$	24.0000			0.882258
$741$	10.5000	−	42.4352i	0.385727	−	1.55890i
$742$	15.0000	+	17.3205i	0.550667	+	0.635856i
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	0.805735	−	0.592277i	$-0.201771\pi$
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	−0.915794	+	0.401648i	$0.868437\pi$
$744$	−6.00000	+	3.46410i	−0.219971	+	0.127000i
$745$	18.0000	+	10.3923i	0.659469	+	0.380745i
$746$	−20.0000			−0.732252
$747$	−36.0000	−	20.7846i	−1.31717	−	0.760469i
$748$	4.50000	−	7.79423i	0.164536	−	0.284985i
$749$	9.00000	+	10.3923i	0.328853	+	0.379727i
$750$	6.00000	−	10.3923i	0.219089	−	0.379473i
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	−0.996993	−	0.0774878i	$-0.975310\pi$
$751$	−15.5000	−	26.8468i	−0.565603	−	0.979653i	0.431390	−	0.902165i	$-0.358023\pi$
$752$	−7.50000	+	4.33013i	−0.273497	+	0.157903i
$753$		−	51.9615i		−	1.89358i
$754$	4.50000	+	4.33013i	0.163880	+	0.157694i
$755$	−30.0000			−1.09181
$756$	4.50000	−	12.9904i	0.163663	−	0.472456i
$757$	−10.0000	−	17.3205i	−0.363456	−	0.629525i	0.625071	−	0.780568i	$-0.285070\pi$
$757$	−10.0000	−	17.3205i	−0.363456	−	0.629525i	−0.988527	+	0.151043i	$0.951737\pi$
$758$	9.00000	+	5.19615i	0.326895	+	0.188733i
$759$	36.0000			1.30672
$760$	21.0000	+	12.1244i	0.761750	+	0.439797i
$761$	6.00000	+	3.46410i	0.217500	+	0.125574i	0.604792	−	0.796383i	$-0.293256\pi$
$761$	6.00000	+	3.46410i	0.217500	+	0.125574i	−0.387292	+	0.921957i	$0.626590\pi$
$762$			13.8564i			0.501965i
$763$	9.00000	−	1.73205i	0.325822	−	0.0627044i
$764$		0			0
$765$	−27.0000	+	15.5885i	−0.976187	+	0.563602i
$766$			5.19615i			0.187745i
$767$	−27.0000	−	25.9808i	−0.974913	−	0.938111i
$768$		−	1.73205i		−	0.0625000i
$769$	−20.0000	−	34.6410i	−0.721218	−	1.24919i	−0.960512	−	0.278240i	$-0.910249\pi$
$769$	−20.0000	−	34.6410i	−0.721218	−	1.24919i	0.239293	−	0.970947i	$-0.423084\pi$
$770$	−9.00000	+	25.9808i	−0.324337	+	0.936282i
$771$	−40.5000	−	23.3827i	−1.45857	−	0.842107i
$772$		−	12.1244i		−	0.436365i
$773$	9.00000	+	5.19615i	0.323708	+	0.186893i	0.653044	−	0.757320i	$-0.273492\pi$
$773$	9.00000	+	5.19615i	0.323708	+	0.186893i	−0.329336	+	0.944213i	$0.606825\pi$
$774$	−12.0000	+	20.7846i	−0.431331	+	0.747087i
$775$	−28.0000			−1.00579
$776$	−1.00000	+	1.73205i	−0.0358979	+	0.0621770i
$777$	30.0000	+	10.3923i	1.07624	+	0.372822i
$778$	18.0000	−	10.3923i	0.645331	−	0.372582i
$779$			36.3731i			1.30320i
$780$	−21.0000	−	5.19615i	−0.751921	−	0.186052i
$781$	−18.0000			−0.644091
$782$	−18.0000	+	10.3923i	−0.643679	+	0.371628i
$783$	4.50000	+	7.79423i	0.160817	+	0.278543i
$784$	5.50000	+	4.33013i	0.196429	+	0.154647i
$785$	−48.0000			−1.71319
$786$	9.00000	+	5.19615i	0.321019	+	0.185341i
$787$	−8.50000	+	14.7224i	−0.302992	+	0.524798i	−0.976812	−	0.214097i	$-0.931319\pi$
$787$	−8.50000	+	14.7224i	−0.302992	+	0.524798i	0.673820	+	0.738896i	$0.264652\pi$
$788$	27.0000			0.961835
$789$	21.0000	−	36.3731i	0.747620	−	1.29492i
$790$	−33.0000	+	19.0526i	−1.17409	+	0.677860i
$791$	−12.0000	+	34.6410i	−0.426671	+	1.23169i
$792$	9.00000			0.319801
$793$	13.5000	+	12.9904i	0.479399	+	0.461302i
$794$	−7.00000			−0.248421
$795$	45.0000	−	25.9808i	1.59599	−	0.921443i
$796$	−9.00000	+	5.19615i	−0.318997	+	0.184173i
$797$	6.00000	−	10.3923i	0.212531	−	0.368114i	−0.739975	−	0.672634i	$-0.765163\pi$
$797$	6.00000	−	10.3923i	0.212531	−	0.368114i	0.952506	+	0.304520i	$0.0984960\pi$
$798$	21.0000	+	24.2487i	0.743392	+	0.858395i
$799$	22.5000	+	12.9904i	0.795993	+	0.459567i
$800$	3.50000	−	6.06218i	0.123744	−	0.214330i
$801$			25.9808i			0.917985i
$802$	9.00000	−	15.5885i	0.317801	−	0.550448i
$803$	6.00000	+	10.3923i	0.211735	+	0.366736i
$804$		0			0
$805$	48.0000	−	41.5692i	1.69178	−	1.46512i
$806$	4.00000	+	13.8564i	0.140894	+	0.488071i
$807$		−	41.5692i		−	1.46331i
$808$		0			0
$809$	−42.0000	+	24.2487i	−1.47664	+	0.852539i	−0.999652	−	0.0263699i	$-0.991605\pi$
$809$	−42.0000	+	24.2487i	−1.47664	+	0.852539i	−0.476989	+	0.878909i	$0.658272\pi$
$810$	−27.0000	−	15.5885i	−0.948683	−	0.547723i
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$	−4.50000	+	0.866025i	−0.157919	+	0.0303915i
$813$	12.0000	+	6.92820i	0.420858	+	0.242983i
$814$			20.7846i			0.728500i
$815$	−42.0000	+	72.7461i	−1.47120	+	2.54819i
$816$	−4.50000	+	2.59808i	−0.157532	+	0.0909509i
$817$	−28.0000	−	48.4974i	−0.979596	−	1.69671i
$818$	−4.00000			−0.139857
$819$	−24.0000	−	15.5885i	−0.838628	−	0.544705i
$820$	18.0000			0.628587
$821$	−1.50000	−	2.59808i	−0.0523504	−	0.0906735i	0.838663	−	0.544651i	$-0.183338\pi$
$821$	−1.50000	−	2.59808i	−0.0523504	−	0.0906735i	−0.891013	+	0.453978i	$0.850005\pi$
$822$	−18.0000	+	10.3923i	−0.627822	+	0.362473i
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$			3.46410i			0.120678i
$825$	31.5000	+	18.1865i	1.09669	+	0.633174i
$826$	27.0000	−	5.19615i	0.939450	−	0.180797i
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	−18.0000	−	10.3923i	−0.625543	−	0.361158i
$829$	−13.5000	+	7.79423i	−0.468874	+	0.270705i	−0.715768	−	0.698338i	$-0.753923\pi$
$829$	−13.5000	+	7.79423i	−0.468874	+	0.270705i	0.246894	+	0.969042i	$0.420590\pi$
$830$	−24.0000	−	41.5692i	−0.833052	−	1.44289i
$831$			27.7128i			0.961347i
$832$	−3.50000	−	0.866025i	−0.121341	−	0.0300240i
$833$	3.00000	−	20.7846i	0.103944	−	0.720144i
$834$	4.50000	+	7.79423i	0.155822	+	0.269892i
$835$	−30.0000	−	51.9615i	−1.03819	−	1.79820i
$836$	−10.5000	+	18.1865i	−0.363150	+	0.628994i
$837$			20.7846i			0.718421i
$838$	−6.00000	+	10.3923i	−0.207267	+	0.358996i
$839$	−27.0000	−	15.5885i	−0.932144	−	0.538173i	−0.0446547	−	0.999002i	$-0.514219\pi$
$839$	−27.0000	−	15.5885i	−0.932144	−	0.538173i	−0.887489	+	0.460829i	$0.847552\pi$
$840$	12.0000	−	10.3923i	0.414039	−	0.358569i
$841$	−13.0000	+	22.5167i	−0.448276	+	0.776437i
$842$	21.0000	−	12.1244i	0.723708	−	0.417833i
$843$	18.0000	−	10.3923i	0.619953	−	0.357930i
$844$	−22.0000			−0.757271
$845$	−21.0000	+	39.8372i	−0.722422	+	1.37044i
$846$			25.9808i			0.893237i
$847$	5.00000	+	1.73205i	0.171802	+	0.0595140i
$848$	7.50000	−	4.33013i	0.257551	−	0.148697i
$849$	3.00000	−	5.19615i	0.102960	−	0.178331i
$850$	−21.0000			−0.720294
$851$	24.0000	−	41.5692i	0.822709	−	1.42497i
$852$	9.00000	+	5.19615i	0.308335	+	0.178017i
$853$	35.0000			1.19838			0.599189	−	0.800608i	$-0.295490\pi$
$853$	35.0000			1.19838			0.599189	+	0.800608i	$0.295490\pi$
$854$	−13.5000	+	2.59808i	−0.461960	+	0.0889043i
$855$	63.0000	−	36.3731i	2.15455	−	1.24393i
$856$	4.50000	−	2.59808i	0.153807	−	0.0888004i
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$	4.50000	−	18.1865i	0.153627	−	0.620878i
$859$			39.8372i			1.35923i	0.733571	+	0.679613i	$0.237852\pi$
$859$			39.8372i			1.35923i	−0.733571	+	0.679613i	$0.762148\pi$
$860$	−24.0000	+	13.8564i	−0.818393	+	0.472500i
$861$	22.5000	+	7.79423i	0.766798	+	0.265627i
$862$	−9.00000	+	15.5885i	−0.306541	+	0.530945i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$	−4.50000	−	2.59808i	−0.153093	−	0.0883883i
$865$		0			0
$866$		−	17.3205i		−	0.588575i
$867$	−12.0000	−	6.92820i	−0.407541	−	0.235294i
$868$	−10.0000	−	3.46410i	−0.339422	−	0.117579i
$869$	−16.5000	−	28.5788i	−0.559724	−	0.969471i
$870$			10.3923i			0.352332i
$871$		0			0
$872$		−	3.46410i		−	0.117309i
$873$	3.00000	+	5.19615i	0.101535	+	0.175863i
$874$	42.0000	−	24.2487i	1.42067	−	0.820225i
$875$	18.0000	−	3.46410i	0.608511	−	0.117108i
$876$		−	6.92820i		−	0.234082i
$877$	21.0000	+	12.1244i	0.709120	+	0.409410i	0.810735	−	0.585413i	$-0.199068\pi$
$877$	21.0000	+	12.1244i	0.709120	+	0.409410i	−0.101615	+	0.994824i	$0.532401\pi$
$878$	−3.00000	−	1.73205i	−0.101245	−	0.0584539i
$879$	12.0000			0.404750
$880$	9.00000	+	5.19615i	0.303390	+	0.175162i
$881$	15.0000	+	25.9808i	0.505363	+	0.875314i	0.999981	+	0.00620358i	$0.00197467\pi$
$881$	15.0000	+	25.9808i	0.505363	+	0.875314i	−0.494618	+	0.869111i	$0.664692\pi$
$882$	19.5000	−	7.79423i	0.656599	−	0.262445i
$883$	2.00000			0.0673054			0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000			0.0673054			0.0336527	+	0.999434i	$0.489286\pi$
$884$	3.00000	+	10.3923i	0.100901	+	0.349531i
$885$		−	62.3538i		−	2.09600i
$886$	−25.5000	+	14.7224i	−0.856689	+	0.494610i
$887$	13.5000	+	23.3827i	0.453286	+	0.785114i	0.998588	−	0.0531258i	$-0.0169184\pi$
$887$	13.5000	+	23.3827i	0.453286	+	0.785114i	−0.545302	+	0.838240i	$0.683585\pi$
$888$	6.00000	−	10.3923i	0.201347	−	0.348743i
$889$	−16.0000	+	13.8564i	−0.536623	+	0.464729i
$890$	−15.0000	+	25.9808i	−0.502801	+	0.870877i
$891$	13.5000	−	23.3827i	0.452267	−	0.783349i
$892$	−16.0000			−0.535720
$893$	−52.5000	−	30.3109i	−1.75685	−	1.01432i
$894$	9.00000	−	5.19615i	0.301005	−	0.173785i
$895$	42.0000	+	72.7461i	1.40391	+	2.43164i
$896$	2.00000	−	1.73205i	0.0668153	−	0.0578638i
$897$	−30.0000	+	31.1769i	−1.00167	+	1.04097i
$898$	−36.0000			−1.20134
$899$	6.00000	−	3.46410i	0.200111	−	0.115534i
$900$	−10.5000	−	18.1865i	−0.350000	−	0.606218i
$901$	−22.5000	−	12.9904i	−0.749584	−	0.432772i
$902$			15.5885i			0.519039i
$903$	−36.0000	+	6.92820i	−1.19800	+	0.230556i
$904$	12.0000	+	6.92820i	0.399114	+	0.230429i
$905$	6.00000			0.199447
$906$	−7.50000	+	12.9904i	−0.249171	+	0.431577i
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	0.937018	−	0.349281i	$-0.113574\pi$
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	−0.770996	+	0.636841i	$0.780241\pi$
$908$	−9.00000	+	5.19615i	−0.298675	+	0.172440i
$909$		0			0
$910$	−15.0000	−	29.4449i	−0.497245	−	0.976088i
$911$			48.4974i			1.60679i	0.595446	+	0.803396i	$0.296976\pi$
$911$			48.4974i			1.60679i	−0.595446	+	0.803396i	$0.703024\pi$
$912$	10.5000	−	6.06218i	0.347690	−	0.200739i
$913$	36.0000	−	20.7846i	1.19143	−	0.687870i
$914$	6.00000	+	3.46410i	0.198462	+	0.114582i
$915$			31.1769i			1.03068i
$916$	−6.50000	+	11.2583i	−0.214766	+	0.371986i
$917$	3.00000	+	15.5885i	0.0990687	+	0.514776i
$918$			15.5885i			0.514496i
$919$	−14.5000	+	25.1147i	−0.478311	+	0.828459i	−0.999691	−	0.0248659i	$-0.992084\pi$
$919$	−14.5000	+	25.1147i	−0.478311	+	0.828459i	0.521380	+	0.853325i	$0.325417\pi$
$920$	−12.0000	−	20.7846i	−0.395628	−	0.685248i
$921$	−10.5000	+	6.06218i	−0.345987	+	0.199756i
$922$			31.1769i			1.02676i
$923$	15.0000	−	15.5885i	0.493731	−	0.513100i
$924$	9.00000	+	10.3923i	0.296078	+	0.341882i
$925$	42.0000	−	24.2487i	1.38095	−	0.797293i
$926$	31.5000	−	18.1865i	1.03515	−	0.597647i
$927$	9.00000	+	5.19615i	0.295599	+	0.170664i
$928$			1.73205i			0.0568574i
$929$	−25.5000	−	14.7224i	−0.836628	−	0.483027i	0.0194887	−	0.999810i	$-0.493796\pi$
$929$	−25.5000	−	14.7224i	−0.836628	−	0.483027i	−0.856117	+	0.516783i	$0.827129\pi$
$930$	−12.0000	+	20.7846i	−0.393496	+	0.681554i
$931$	−7.00000	+	48.4974i	−0.229416	+	1.58944i
$932$	−6.00000	−	3.46410i	−0.196537	−	0.113470i
$933$	4.50000	−	2.59808i	0.147323	−	0.0850572i
$934$	−3.00000	−	5.19615i	−0.0981630	−	0.170023i
$935$		−	31.1769i		−	1.01959i
$936$	−7.50000	+	7.79423i	−0.245145	+	0.254762i
$937$		−	38.1051i		−	1.24484i	−0.782683	−	0.622420i	$-0.786150\pi$
$937$		−	38.1051i		−	1.24484i	0.782683	−	0.622420i	$-0.213850\pi$
$938$		0			0
$939$	18.0000	+	31.1769i	0.587408	+	1.01742i
$940$	−15.0000	+	25.9808i	−0.489246	+	0.847399i
$941$			38.1051i			1.24219i	0.783735	+	0.621096i	$0.213312\pi$
$941$			38.1051i			1.24219i	−0.783735	+	0.621096i	$0.786688\pi$
$942$	−12.0000	+	20.7846i	−0.390981	+	0.677199i
$943$	18.0000	−	31.1769i	0.586161	−	1.01526i
$944$		−	10.3923i		−	0.338241i
$945$	−9.00000	−	46.7654i	−0.292770	−	1.52128i
$946$	−12.0000	−	20.7846i	−0.390154	−	0.675766i
$947$	−1.50000	−	2.59808i	−0.0487435	−	0.0844261i	0.840624	−	0.541619i	$-0.182188\pi$
$947$	−1.50000	−	2.59808i	−0.0487435	−	0.0844261i	−0.889368	+	0.457193i	$0.848855\pi$
$948$			19.0526i			0.618798i
$949$	−14.0000	−	3.46410i	−0.454459	−	0.112449i
$950$	49.0000			1.58977
$951$	27.0000	−	15.5885i	0.875535	−	0.505490i
$952$	−7.50000	−	2.59808i	−0.243076	−	0.0842041i
$953$	33.0000	+	19.0526i	1.06897	+	0.617173i	0.927901	−	0.372826i	$-0.121611\pi$
$953$	33.0000	+	19.0526i	1.06897	+	0.617173i	0.141074	+	0.989999i	$0.454945\pi$
$954$		−	25.9808i		−	0.841158i
$955$		0			0
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$	−9.00000			−0.290929
$958$	−28.5000	−	16.4545i	−0.920793	−	0.531620i
$959$	−30.0000	−	10.3923i	−0.968751	−	0.335585i
$960$	−3.00000	−	5.19615i	−0.0968246	−	0.167705i
$961$	−15.0000			−0.483871
$962$	−18.0000	−	17.3205i	−0.580343	−	0.558436i
$963$		−	15.5885i		−	0.502331i
$964$	−5.00000	−	8.66025i	−0.161039	−	0.278928i
$965$	−21.0000	−	36.3731i	−0.676014	−	1.17089i
$966$	−6.00000	−	31.1769i	−0.193047	−	1.00310i
$967$		−	24.2487i		−	0.779786i	−0.920860	−	0.389893i	$-0.872512\pi$
$967$		−	24.2487i		−	0.779786i	0.920860	−	0.389893i	$-0.127488\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$	−31.5000	−	18.1865i	−1.01193	−	0.584236i
$970$			6.92820i			0.222451i
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$	−13.5000	+	7.79423i	−0.433013	+	0.250000i
$973$	−4.50000	+	12.9904i	−0.144263	+	0.416452i
$974$		−	8.66025i		−	0.277492i
$975$	−42.0000	+	12.1244i	−1.34508	+	0.388290i
$976$			5.19615i			0.166325i
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	0.685381	−	0.728184i	$-0.259636\pi$
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	−0.973317	+	0.229465i	$0.926302\pi$
$978$	21.0000	+	36.3731i	0.671506	+	1.16308i
$979$	−22.5000	−	12.9904i	−0.719103	−	0.415174i
$980$	24.0000	+	3.46410i	0.766652	+	0.110657i
$981$	−9.00000	−	5.19615i	−0.287348	−	0.165900i
$982$	9.00000	+	5.19615i	0.287202	+	0.165816i
$983$		−	58.8897i		−	1.87829i	−0.343520	−	0.939145i	$-0.611619\pi$
$983$		−	58.8897i		−	1.87829i	0.343520	−	0.939145i	$-0.388381\pi$
$984$	4.50000	−	7.79423i	0.143455	−	0.248471i
$985$	81.0000	−	46.7654i	2.58087	−	1.49007i
$986$	4.50000	−	2.59808i	0.143309	−	0.0827396i
$987$	−30.0000	+	25.9808i	−0.954911	+	0.826977i
$988$	−7.00000	−	24.2487i	−0.222700	−	0.771454i
$989$			55.4256i			1.76243i
$990$	27.0000	−	15.5885i	0.858116	−	0.495434i
$991$	8.50000	+	14.7224i	0.270011	+	0.467673i	0.968864	−	0.247592i	$-0.0796392\pi$
$991$	8.50000	+	14.7224i	0.270011	+	0.467673i	−0.698853	+	0.715265i	$0.746306\pi$
$992$	−2.00000	+	3.46410i	−0.0635001	+	0.109985i
$993$		0			0
$994$	3.00000	+	15.5885i	0.0951542	+	0.494436i
$995$	−18.0000	+	31.1769i	−0.570638	+	0.988375i
$996$	−24.0000			−0.760469
$997$	19.5000	+	11.2583i	0.617571	+	0.356555i	0.775923	−	0.630828i	$-0.217285\pi$
$997$	19.5000	+	11.2583i	0.617571	+	0.356555i	−0.158352	+	0.987383i	$0.550618\pi$
$998$	−36.0000	+	20.7846i	−1.13956	+	0.657925i
$999$	−18.0000	−	31.1769i	−0.569495	−	0.986394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.q.a.335.1	yes	2
3.2	odd	2		546.2.q.c.335.1	yes	2
7.6	odd	2		546.2.q.b.335.1	yes	2
13.4	even	6		546.2.q.d.251.1	yes	2
21.20	even	2		546.2.q.d.335.1	yes	2
39.17	odd	6		546.2.q.b.251.1	yes	2
91.69	odd	6		546.2.q.c.251.1	yes	2
273.251	even	6	inner	546.2.q.a.251.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.a.251.1	✓	2	273.251	even	6	inner
546.2.q.a.335.1	yes	2	1.1	even	1	trivial
546.2.q.b.251.1	yes	2	39.17	odd	6
546.2.q.b.335.1	yes	2	7.6	odd	2
546.2.q.c.251.1	yes	2	91.69	odd	6
546.2.q.c.335.1	yes	2	3.2	odd	2
546.2.q.d.251.1	yes	2	13.4	even	6
546.2.q.d.335.1	yes	2	21.20	even	2

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.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.46410i q^{5} +(1.50000 + 0.866025i) q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +3.46410i q^{5} +(1.50000 + 0.866025i) q^{6} +(0.500000 + 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(3.00000 - 1.73205i) q^{10} +(1.50000 + 2.59808i) q^{11} -1.73205i q^{12} +(-3.50000 - 0.866025i) q^{13} +(2.00000 - 1.73205i) q^{14} +(-3.00000 - 5.19615i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} -3.00000 q^{18} +(3.50000 - 6.06218i) q^{19} +(-3.00000 - 1.73205i) q^{20} +(-3.00000 - 3.46410i) q^{21} +(1.50000 - 2.59808i) q^{22} +(-6.00000 + 3.46410i) q^{23} +(-1.50000 + 0.866025i) q^{24} -7.00000 q^{25} +(1.00000 + 3.46410i) q^{26} +5.19615i q^{27} +(-2.50000 - 0.866025i) q^{28} +(1.50000 - 0.866025i) q^{29} +(-3.00000 + 5.19615i) q^{30} +4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-4.50000 - 2.59808i) q^{33} +3.00000 q^{34} +(-9.00000 + 1.73205i) q^{35} +(1.50000 + 2.59808i) q^{36} +(-6.00000 + 3.46410i) q^{37} -7.00000 q^{38} +(6.00000 - 1.73205i) q^{39} +3.46410i q^{40} +(-4.50000 + 2.59808i) q^{41} +(-1.50000 + 4.33013i) q^{42} +(4.00000 - 6.92820i) q^{43} -3.00000 q^{44} +(9.00000 + 5.19615i) q^{45} +(6.00000 + 3.46410i) q^{46} -8.66025i q^{47} +(1.50000 + 0.866025i) q^{48} +(-6.50000 + 2.59808i) q^{49} +(3.50000 + 6.06218i) q^{50} -5.19615i q^{51} +(2.50000 - 2.59808i) q^{52} +8.66025i q^{53} +(4.50000 - 2.59808i) q^{54} +(-9.00000 + 5.19615i) q^{55} +(0.500000 + 2.59808i) q^{56} +12.1244i q^{57} +(-1.50000 - 0.866025i) q^{58} +(9.00000 + 5.19615i) q^{59} +6.00000 q^{60} +(-4.50000 - 2.59808i) q^{61} +(-2.00000 - 3.46410i) q^{62} +(7.50000 + 2.59808i) q^{63} +1.00000 q^{64} +(3.00000 - 12.1244i) q^{65} +5.19615i q^{66} +(-1.50000 - 2.59808i) q^{68} +(6.00000 - 10.3923i) q^{69} +(6.00000 + 6.92820i) q^{70} +(-3.00000 + 5.19615i) q^{71} +(1.50000 - 2.59808i) q^{72} +4.00000 q^{73} +(6.00000 + 3.46410i) q^{74} +(10.5000 - 6.06218i) q^{75} +(3.50000 + 6.06218i) q^{76} +(-6.00000 + 5.19615i) q^{77} +(-4.50000 - 4.33013i) q^{78} -11.0000 q^{79} +(3.00000 - 1.73205i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(4.50000 + 2.59808i) q^{82} -13.8564i q^{83} +(4.50000 - 0.866025i) q^{84} +(-9.00000 - 5.19615i) q^{85} -8.00000 q^{86} +(-1.50000 + 2.59808i) q^{87} +(1.50000 + 2.59808i) q^{88} +(-7.50000 + 4.33013i) q^{89} -10.3923i q^{90} +(0.500000 - 9.52628i) q^{91} -6.92820i q^{92} +(-6.00000 + 3.46410i) q^{93} +(-7.50000 + 4.33013i) q^{94} +(21.0000 + 12.1244i) q^{95} -1.73205i q^{96} +(-1.00000 + 1.73205i) q^{97} +(5.50000 + 4.33013i) q^{98} +9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 3 q^{3} - q^{4} + 3 q^{6} + q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 - 3 * q^3 - q^4 + 3 * q^6 + q^7 + 2 * q^8 + 3 * q^9	\( 2 q - q^{2} - 3 q^{3} - q^{4} + 3 q^{6} + q^{7} + 2 q^{8} + 3 q^{9} + 6 q^{10} + 3 q^{11} - 7 q^{13} + 4 q^{14} - 6 q^{15} - q^{16} - 3 q^{17} - 6 q^{18} + 7 q^{19} - 6 q^{20} - 6 q^{21} + 3 q^{22} - 12 q^{23} - 3 q^{24} - 14 q^{25} + 2 q^{26} - 5 q^{28} + 3 q^{29} - 6 q^{30} + 8 q^{31} - q^{32} - 9 q^{33} + 6 q^{34} - 18 q^{35} + 3 q^{36} - 12 q^{37} - 14 q^{38} + 12 q^{39} - 9 q^{41} - 3 q^{42} + 8 q^{43} - 6 q^{44} + 18 q^{45} + 12 q^{46} + 3 q^{48} - 13 q^{49} + 7 q^{50} + 5 q^{52} + 9 q^{54} - 18 q^{55} + q^{56} - 3 q^{58} + 18 q^{59} + 12 q^{60} - 9 q^{61} - 4 q^{62} + 15 q^{63} + 2 q^{64} + 6 q^{65} - 3 q^{68} + 12 q^{69} + 12 q^{70} - 6 q^{71} + 3 q^{72} + 8 q^{73} + 12 q^{74} + 21 q^{75} + 7 q^{76} - 12 q^{77} - 9 q^{78} - 22 q^{79} + 6 q^{80} - 9 q^{81} + 9 q^{82} + 9 q^{84} - 18 q^{85} - 16 q^{86} - 3 q^{87} + 3 q^{88} - 15 q^{89} + q^{91} - 12 q^{93} - 15 q^{94} + 42 q^{95} - 2 q^{97} + 11 q^{98} + 18 q^{99}+O(q^{100}) \) 2 * q - q^2 - 3 * q^3 - q^4 + 3 * q^6 + q^7 + 2 * q^8 + 3 * q^9 + 6 * q^10 + 3 * q^11 - 7 * q^13 + 4 * q^14 - 6 * q^15 - q^16 - 3 * q^17 - 6 * q^18 + 7 * q^19 - 6 * q^20 - 6 * q^21 + 3 * q^22 - 12 * q^23 - 3 * q^24 - 14 * q^25 + 2 * q^26 - 5 * q^28 + 3 * q^29 - 6 * q^30 + 8 * q^31 - q^32 - 9 * q^33 + 6 * q^34 - 18 * q^35 + 3 * q^36 - 12 * q^37 - 14 * q^38 + 12 * q^39 - 9 * q^41 - 3 * q^42 + 8 * q^43 - 6 * q^44 + 18 * q^45 + 12 * q^46 + 3 * q^48 - 13 * q^49 + 7 * q^50 + 5 * q^52 + 9 * q^54 - 18 * q^55 + q^56 - 3 * q^58 + 18 * q^59 + 12 * q^60 - 9 * q^61 - 4 * q^62 + 15 * q^63 + 2 * q^64 + 6 * q^65 - 3 * q^68 + 12 * q^69 + 12 * q^70 - 6 * q^71 + 3 * q^72 + 8 * q^73 + 12 * q^74 + 21 * q^75 + 7 * q^76 - 12 * q^77 - 9 * q^78 - 22 * q^79 + 6 * q^80 - 9 * q^81 + 9 * q^82 + 9 * q^84 - 18 * q^85 - 16 * q^86 - 3 * q^87 + 3 * q^88 - 15 * q^89 + q^91 - 12 * q^93 - 15 * q^94 + 42 * q^95 - 2 * q^97 + 11 * q^98 + 18 * q^99

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