LMFDB - Embedded newform 546.2.q.c.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.c.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	$-0.717953\pi$
$5$		−	3.46410i		−	1.54919i	0.632456	−	0.774597i	$-0.282047\pi$
$6$	−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	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		−	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	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	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	0.279761	−	0.960070i	$-0.409745\pi$
$23$	6.00000	−	3.46410i	1.25109	−	0.722315i	0.971325	+	0.237754i	$0.0764114\pi$
$24$	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	−0.632764	−	0.774345i	$-0.718080\pi$
$29$	−1.50000	+	0.866025i	−0.278543	+	0.160817i	0.354221	+	0.935162i	$0.384746\pi$
$30$	−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	−0.105601	−	0.994409i	$-0.533677\pi$
$41$	4.50000	−	2.59808i	0.702782	−	0.405751i	0.808383	+	0.588657i	$0.200343\pi$
$42$	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	$0.217607\pi$
$47$			8.66025i			1.26323i	−0.775283	+	0.631614i	$0.782393\pi$
$48$	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	$-0.797236\pi$
$53$		−	8.66025i		−	1.18958i	0.803882	−	0.594789i	$-0.202764\pi$
$54$	−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	−0.217620	−	0.976034i	$-0.569829\pi$
$59$	−9.00000	−	5.19615i	−1.17170	−	0.676481i	−0.954080	+	0.299552i	$0.903163\pi$
$60$	−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	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$	−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	$0.275031\pi$
$83$			13.8564i			1.52094i	−0.649374	+	0.760469i	$0.724969\pi$
$84$	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	−0.0467209	−	0.998908i	$-0.514877\pi$
$89$	7.50000	−	4.33013i	0.794998	−	0.458993i	0.841719	+	0.539915i	$0.181544\pi$
$90$		−	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	−0.701488	−	0.712681i	$-0.747481\pi$
$107$	−4.50000	+	2.59808i	−0.435031	+	0.251166i	0.266456	+	0.963847i	$0.414147\pi$
$108$	−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	−0.185216	−	0.982698i	$-0.559298\pi$
$113$	−12.0000	−	6.92820i	−1.12887	−	0.651751i	−0.943649	+	0.330947i	$0.892632\pi$
$114$	−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	$-0.584419\pi$
$131$	−6.00000			−0.524222			−0.262111	+	0.965038i	$0.584419\pi$
$132$	−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	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$	−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	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$	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	0.209255	−	0.977861i	$-0.432896\pi$
$167$	15.0000	−	8.66025i	1.16073	−	0.670151i	0.951480	+	0.307711i	$0.0995628\pi$
$168$	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	$0.694376\pi$
$179$	−21.0000	+	12.1244i	−1.56961	+	0.906217i	−0.996213	+	0.0869415i	$0.972291\pi$
$180$	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	$0.245109\pi$
$197$	13.5000	+	23.3827i	0.961835	+	1.66595i	0.243947	+	0.969788i	$0.421558\pi$
$198$	−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	0.170648	−	0.985332i	$-0.445414\pi$
$227$	−9.00000	−	5.19615i	−0.597351	−	0.344881i	−0.767999	+	0.640451i	$0.778747\pi$
$228$	−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	$-0.927128\pi$
$233$		−	6.92820i		−	0.453882i	0.973909	−	0.226941i	$-0.0728724\pi$
$234$	−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	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$	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	$-0.437637\pi$
$251$	15.0000	−	25.9808i	0.946792	−	1.63989i	0.752124	−	0.659022i	$-0.229030\pi$
$252$	−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	$-0.847982\pi$
$257$	−13.5000	−	23.3827i	−0.842107	−	1.45857i	0.0460033	−	0.998941i	$-0.485352\pi$
$258$	−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	0.315394	−	0.948961i	$-0.397863\pi$
$263$	21.0000	−	12.1244i	1.29492	−	0.747620i	0.979521	+	0.201341i	$0.0645299\pi$
$264$	−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	$-0.572083\pi$
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	0.956176	−	0.292791i	$-0.0945841\pi$
$270$	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	$-0.383483\pi$
$281$	12.0000			0.715860			0.357930	+	0.933748i	$0.383483\pi$
$282$	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	0.664916	−	0.746918i	$-0.268467\pi$
$293$	6.00000	+	3.46410i	0.350524	+	0.202375i	−0.314392	+	0.949293i	$0.601801\pi$
$294$	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	$-0.472893\pi$
$311$	3.00000			0.170114			0.0850572	+	0.996376i	$0.472893\pi$
$312$	−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	$-0.331312\pi$
$317$	18.0000			1.01098			0.505490	+	0.862832i	$0.331312\pi$
$318$	−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	0.816487	−	0.577364i	$-0.195919\pi$
$347$	13.5000	+	7.79423i	0.724718	+	0.418416i	−0.0917687	+	0.995780i	$0.529252\pi$
$348$	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	−0.895570	−	0.444920i	$-0.853232\pi$
$353$	−18.0000	+	10.3923i	−0.958043	+	0.553127i	−0.0624731	+	0.998047i	$0.519899\pi$
$354$	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	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$	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	0.610544	−	0.791982i	$-0.290951\pi$
$383$	4.50000	+	2.59808i	0.229939	+	0.132755i	−0.380605	+	0.924738i	$0.624284\pi$
$384$	−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	$-0.823350\pi$
$389$		−	20.7846i		−	1.05382i	0.849921	−	0.526911i	$-0.176650\pi$
$390$	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	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$		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	0.974546	−	0.224189i	$-0.0719734\pi$
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	−0.681426	+	0.731887i	$0.738640\pi$
$420$	−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	0.997173	−	0.0751385i	$-0.0239399\pi$
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	−0.563658	+	0.826008i	$0.690607\pi$
$432$	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	$0.246587\pi$
$443$			29.4449i			1.39897i	−0.714648	+	0.699484i	$0.753413\pi$
$444$	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	$0.489746\pi$
$449$	−18.0000	+	31.1769i	−0.849473	+	1.47133i	−0.881680	+	0.471848i	$0.843587\pi$
$450$	−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	0.972591	−	0.232523i	$-0.0746981\pi$
$461$	27.0000	+	15.5885i	1.25752	+	0.726027i	0.284925	+	0.958550i	$0.408031\pi$
$462$	−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	$-0.544332\pi$
$467$	−6.00000			−0.277647			−0.138823	+	0.990317i	$0.544332\pi$
$468$	−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	−0.980781	−	0.195113i	$-0.937493\pi$
$479$	−28.5000	+	16.4545i	−1.30220	+	0.751825i	−0.321417	+	0.946938i	$0.604159\pi$
$480$	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	−0.282976	−	0.959127i	$-0.591322\pi$
$491$	9.00000	−	5.19615i	0.406164	−	0.234499i	0.689140	+	0.724628i	$0.257988\pi$
$492$	−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	−0.968223	−	0.250090i	$-0.919540\pi$
$503$	−6.00000	+	10.3923i	−0.267527	+	0.463370i	0.700696	+	0.713460i	$0.252873\pi$
$504$	−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	−0.926476	−	0.376354i	$-0.877178\pi$
$509$	−24.0000	+	13.8564i	−1.06378	+	0.614174i	−0.137305	+	0.990529i	$0.543844\pi$
$510$	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	$-0.479067\pi$
$521$	3.00000			0.131432			0.0657162	+	0.997838i	$0.479067\pi$
$522$	−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	0.832496	−	0.554031i	$-0.186911\pi$
$557$	−1.50000	−	2.59808i	−0.0635570	−	0.110084i	−0.896053	+	0.443947i	$0.853578\pi$
$558$	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	$-0.664553\pi$
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	0.999978	−	0.00664037i	$-0.00211371\pi$
$564$	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	−0.780300	−	0.625406i	$-0.784934\pi$
$569$	−15.0000	+	8.66025i	−0.628833	+	0.363057i	0.151467	+	0.988462i	$0.451600\pi$
$570$	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	−0.157409	−	0.987534i	$-0.550314\pi$
$587$	15.0000	−	8.66025i	0.619116	−	0.357447i	0.776525	+	0.630087i	$0.216981\pi$
$588$	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	$0.0569035\pi$
$593$			8.66025i			0.355634i	−0.984064	+	0.177817i	$0.943096\pi$
$594$	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	$0.0225455\pi$
$599$			3.46410i			0.141539i	−0.997493	+	0.0707697i	$0.977454\pi$
$600$	−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	−0.799298	−	0.600935i	$-0.794795\pi$
$617$	3.00000	−	5.19615i	0.120775	−	0.209189i	0.920074	+	0.391745i	$0.128129\pi$
$618$	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	0.558075	−	0.829790i	$-0.311540\pi$
$641$	3.00000	+	1.73205i	0.118493	+	0.0684119i	−0.439582	+	0.898202i	$0.644873\pi$
$642$	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	0.582397	−	0.812905i	$-0.302115\pi$
$647$	−10.5000	−	18.1865i	−0.412798	−	0.714986i	−0.995194	+	0.0979182i	$0.968782\pi$
$648$	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	−0.585458	−	0.810702i	$-0.699085\pi$
$653$	−4.50000	+	2.59808i	−0.176099	+	0.101671i	0.409360	+	0.912373i	$0.365752\pi$
$654$	−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	0.470500	−	0.882400i	$-0.344074\pi$
$659$	−1.50000	−	0.866025i	−0.0584317	−	0.0337356i	−0.528931	+	0.848665i	$0.677407\pi$
$660$	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	$-0.536783\pi$
$677$	−6.00000			−0.230599			−0.115299	+	0.993331i	$0.536783\pi$
$678$	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	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$	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	$-0.926466\pi$
$701$		−	12.1244i		−	0.457931i	0.973435	−	0.228965i	$-0.0735342\pi$
$702$	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	−0.992659	−	0.120950i	$-0.961406\pi$
$719$	−10.5000	+	18.1865i	−0.391584	+	0.678243i	0.601075	+	0.799193i	$0.294739\pi$
$720$			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	0.915794	−	0.401648i	$-0.131563\pi$
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	−0.805735	+	0.592277i	$0.798229\pi$
$744$	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	0.387292	−	0.921957i	$-0.373410\pi$
$761$	−6.00000	−	3.46410i	−0.217500	−	0.125574i	−0.604792	+	0.796383i	$0.706744\pi$
$762$		−	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	0.329336	−	0.944213i	$-0.393175\pi$
$773$	−9.00000	−	5.19615i	−0.323708	−	0.186893i	−0.653044	+	0.757320i	$0.726508\pi$
$774$	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	−0.952506	−	0.304520i	$-0.901504\pi$
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	0.739975	+	0.672634i	$0.234837\pi$
$798$	−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	0.476989	−	0.878909i	$-0.341728\pi$
$809$	42.0000	−	24.2487i	1.47664	−	0.852539i	0.999652	+	0.0263699i	$0.00839478\pi$
$810$	−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	0.891013	−	0.453978i	$-0.149995\pi$
$821$	1.50000	+	2.59808i	0.0523504	+	0.0906735i	−0.838663	+	0.544651i	$0.816662\pi$
$822$	−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	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$	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	0.887489	−	0.460829i	$-0.152448\pi$
$839$	27.0000	+	15.5885i	0.932144	+	0.538173i	0.0446547	+	0.999002i	$0.485781\pi$
$840$	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	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$	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	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$	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	$-0.998025\pi$
$881$	−15.0000	−	25.9808i	−0.505363	−	0.875314i	0.494618	−	0.869111i	$-0.335308\pi$
$882$	−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	0.545302	−	0.838240i	$-0.316415\pi$
$887$	−13.5000	−	23.3827i	−0.453286	−	0.785114i	−0.998588	+	0.0531258i	$0.983082\pi$
$888$	−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	$-0.703024\pi$
$911$		−	48.4974i		−	1.60679i	0.595446	−	0.803396i	$-0.296976\pi$
$912$	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	0.856117	−	0.516783i	$-0.172871\pi$
$929$	25.5000	+	14.7224i	0.836628	+	0.483027i	−0.0194887	+	0.999810i	$0.506204\pi$
$930$	−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	$-0.786688\pi$
$941$		−	38.1051i		−	1.24219i	0.783735	−	0.621096i	$-0.213312\pi$
$942$	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	0.889368	−	0.457193i	$-0.151145\pi$
$947$	1.50000	+	2.59808i	0.0487435	+	0.0844261i	−0.840624	+	0.541619i	$0.817812\pi$
$948$			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	−0.141074	−	0.989999i	$-0.545055\pi$
$953$	−33.0000	−	19.0526i	−1.06897	−	0.617173i	−0.927901	+	0.372826i	$0.878389\pi$
$954$		−	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	0.973317	−	0.229465i	$-0.0736978\pi$
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	−0.685381	+	0.728184i	$0.740364\pi$
$978$	−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	$0.388381\pi$
$983$			58.8897i			1.87829i	−0.343520	+	0.939145i	$0.611619\pi$
$984$	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.c.335.1	yes	2
3.2	odd	2		546.2.q.a.335.1	yes	2
7.6	odd	2		546.2.q.d.335.1	yes	2
13.4	even	6		546.2.q.b.251.1	yes	2
21.20	even	2		546.2.q.b.335.1	yes	2
39.17	odd	6		546.2.q.d.251.1	yes	2
91.69	odd	6		546.2.q.a.251.1	✓	2
273.251	even	6	inner	546.2.q.c.251.1	yes	2

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