LMFDB - Embedded newform 546.2.q.b.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.b.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.46410i q^{5} +(-1.50000 - 0.866025i) q^{6} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(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} +(2.50000 - 0.866025i) 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} +(-0.500000 + 2.59808i) 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} +(-3.00000 - 8.66025i) 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} +(-4.50000 - 0.866025i) 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} +(5.50000 - 4.33013i) 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} +(2.50000 - 0.866025i) 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} +(1.50000 - 7.79423i) 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} +(1.50000 + 4.33013i) 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} +(9.50000 - 0.866025i) 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} +(-6.50000 - 2.59808i) 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} + 5 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 + 3 * q^3 - q^4 - 3 * q^6 + 5 * q^7 + 2 * q^8 + 3 * q^9	$ 2 q - q^{2} + 3 q^{3} - q^{4} - 3 q^{6} + 5 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} - q^{28} + 3 q^{29} - 6 q^{30} - 8 q^{31} - q^{32} + 9 q^{33} - 6 q^{34} - 6 q^{35} + 3 q^{36} - 12 q^{37} + 14 q^{38} + 12 q^{39} + 9 q^{41} - 9 q^{42} + 8 q^{43} - 6 q^{44} - 18 q^{45} + 12 q^{46} - 3 q^{48} + 11 q^{49} + 7 q^{50} - 5 q^{52} - 9 q^{54} + 18 q^{55} + 5 q^{56} - 3 q^{58} - 18 q^{59} + 12 q^{60} + 9 q^{61} + 4 q^{62} + 3 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} + 3 q^{84} - 18 q^{85} - 16 q^{86} + 3 q^{87} + 3 q^{88} + 15 q^{89} + 19 q^{91} - 12 q^{93} + 15 q^{94} + 42 q^{95} + 2 q^{97} - 13 q^{98} + 18 q^{99}+O(q^{100}) $ 2 * q - q^2 + 3 * q^3 - q^4 - 3 * q^6 + 5 * 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 - q^28 + 3 * q^29 - 6 * q^30 - 8 * q^31 - q^32 + 9 * q^33 - 6 * q^34 - 6 * q^35 + 3 * q^36 - 12 * q^37 + 14 * q^38 + 12 * q^39 + 9 * q^41 - 9 * q^42 + 8 * q^43 - 6 * q^44 - 18 * q^45 + 12 * q^46 - 3 * q^48 + 11 * q^49 + 7 * q^50 - 5 * q^52 - 9 * q^54 + 18 * q^55 + 5 * q^56 - 3 * q^58 - 18 * q^59 + 12 * q^60 + 9 * q^61 + 4 * q^62 + 3 * 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 + 3 * q^84 - 18 * q^85 - 16 * q^86 + 3 * q^87 + 3 * q^88 + 15 * q^89 + 19 * q^91 - 12 * q^93 + 15 * q^94 + 42 * q^95 + 2 * q^97 - 13 * 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
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$	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	−0.624780	−	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	$0.463407\pi$
$19$	−3.50000	+	6.06218i	−0.802955	+	1.39076i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	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
$28$	−0.500000	+	2.59808i	−0.0944911	+	0.490990i
$29$	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	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	4.50000	+	2.59808i	0.783349	+	0.452267i
$34$	−3.00000			−0.514496
$35$	−3.00000	−	8.66025i	−0.507093	−	1.46385i
$36$	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	$0.200343\pi$
$42$	−4.50000	−	0.866025i	−0.694365	−	0.133631i
$43$	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
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	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
$56$	2.50000	−	0.866025i	0.334077	−	0.115728i
$57$			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	0.759608	−	0.650381i	$-0.225391\pi$
$61$	4.50000	+	2.59808i	0.576166	+	0.332650i	−0.183442	+	0.983030i	$0.558724\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$	1.50000	−	7.79423i	0.188982	−	0.981981i
$64$	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	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$	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	$0.724969\pi$
$84$	1.50000	+	4.33013i	0.163663	+	0.472456i
$85$	−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
$91$	9.50000	−	0.866025i	0.995871	−	0.0907841i
$92$		−	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	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$	−6.50000	−	2.59808i	−0.656599	−	0.262445i
$99$	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	$-0.945409\pi$
$103$		−	3.46410i		−	0.341328i	0.985329	−	0.170664i	$-0.0545913\pi$
$104$	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
$119$	1.50000	−	7.79423i	0.137505	−	0.714496i
$120$	−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
$126$	−7.50000	+	2.59808i	−0.668153	+	0.231455i
$127$	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
$133$	−3.50000	+	18.1865i	−0.303488	+	1.57697i
$134$		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	0.296866	−	0.954919i	$-0.404058\pi$
$139$	−4.50000	−	2.59808i	−0.381685	−	0.220366i	−0.678551	+	0.734553i	$0.737392\pi$
$140$	9.00000	+	1.73205i	0.760639	+	0.146385i
$141$	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
$147$	4.50000	−	11.2583i	0.371154	−	0.928571i
$148$		−	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
$154$	1.50000	−	7.79423i	0.120873	−	0.628077i
$155$			13.8564i			1.11297i
$156$	−1.50000	+	6.06218i	−0.120096	+	0.485363i
$157$		−	13.8564i		−	1.10586i	−0.833227	−	0.552931i	$-0.813509\pi$
$157$		−	13.8564i		−	1.10586i	0.833227	−	0.552931i	$-0.186491\pi$
$158$	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
$175$	−17.5000	+	6.06218i	−1.32288	+	0.458258i
$176$	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	$0.0205042\pi$
$181$			1.73205i			0.128742i	−0.997926	+	0.0643712i	$0.979496\pi$
$182$	−5.50000	−	7.79423i	−0.407687	−	0.577747i
$183$	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
$189$	−4.50000	−	12.9904i	−0.327327	−	0.944911i
$190$		−	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	0.145848	−	0.989307i	$-0.453409\pi$
$199$	−9.00000	−	5.19615i	−0.637993	−	0.368345i	−0.783841	+	0.620962i	$0.786742\pi$
$200$	−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
$210$	−3.00000	+	15.5885i	−0.207020	+	1.07571i
$211$	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
$217$	−10.0000	+	3.46410i	−0.678844	+	0.235159i
$218$	−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	$-0.986707\pi$
$223$	−8.00000	−	13.8564i	−0.535720	−	0.927894i	0.463409	−	0.886145i	$-0.346626\pi$
$224$	−0.500000	+	2.59808i	−0.0334077	+	0.173591i
$225$	−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	$-0.641321\pi$
$229$	−13.0000			−0.859064			−0.429532	+	0.903052i	$0.641321\pi$
$230$	12.0000	−	20.7846i	0.791257	−	1.37050i
$231$	13.5000	+	2.59808i	0.888235	+	0.170941i
$232$	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
$238$	−7.50000	+	2.59808i	−0.486153	+	0.168408i
$239$	−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	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	−2.00000			−0.128565
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$	−4.50000	+	2.59808i	−0.288083	+	0.166325i
$245$	−15.0000	−	19.0526i	−0.958315	−	1.21722i
$246$	−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	−0.979521	−	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
$266$	17.5000	−	6.06218i	1.07299	−	0.371696i
$267$	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	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$	−3.00000			−0.181902
$273$	13.5000	−	9.52628i	0.817057	−	0.576557i
$274$	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
$280$	−3.00000	−	8.66025i	−0.179284	−	0.517549i
$281$	−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	−0.408177	−	0.912903i	$-0.633835\pi$
$283$	3.00000	−	1.73205i	0.178331	−	0.102960i	0.586509	+	0.809943i	$0.300502\pi$
$284$	−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
$301$	4.00000	−	20.7846i	0.230556	−	1.19800i
$302$	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	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$	−7.50000	+	2.59808i	−0.427352	+	0.148039i
$309$	−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	$0.199852\pi$
$313$			20.7846i			1.17482i	−0.809291	+	0.587408i	$0.800148\pi$
$314$	−12.0000	+	6.92820i	−0.677199	+	0.390981i
$315$	−27.0000	−	5.19615i	−1.52128	−	0.292770i
$316$	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
$322$	18.0000	+	3.46410i	1.00310	+	0.193047i
$323$	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
$329$	7.50000	+	21.6506i	0.413488	+	1.19364i
$330$	−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
$336$	−4.50000	−	0.866025i	−0.245495	−	0.0472456i
$337$	−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	0.838019	−	0.545640i	$-0.183714\pi$
$349$	−1.00000	−	1.73205i	−0.0535288	−	0.0927146i	−0.891548	+	0.452926i	$0.850380\pi$
$350$	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
$357$	−4.50000	−	12.9904i	−0.238165	−	0.687524i
$358$	−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
$364$	−4.00000	+	8.66025i	−0.209657	+	0.453921i
$365$			13.8564i			0.725277i
$366$	−4.50000	−	7.79423i	−0.235219	−	0.407411i
$367$	−18.0000	+	10.3923i	−0.939592	+	0.542474i	−0.889833	−	0.456287i	$-0.849179\pi$
$367$	−18.0000	+	10.3923i	−0.939592	+	0.542474i	−0.0497598	+	0.998761i	$0.515846\pi$
$368$	6.00000	+	3.46410i	0.312772	+	0.180579i
$369$		−	15.5885i		−	0.811503i
$370$	12.0000	−	20.7846i	0.623850	−	1.08054i
$371$	7.50000	+	21.6506i	0.389381	+	1.12404i
$372$		−	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	$0.176650\pi$
$389$			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
$392$	5.50000	−	4.33013i	0.277792	−	0.218704i
$393$	−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	−0.940389	−	0.340099i	$-0.889539\pi$
$397$	−3.50000	+	6.06218i	−0.175660	+	0.304252i	0.764730	+	0.644351i	$0.222873\pi$
$398$			10.3923i			0.520919i
$399$	10.5000	+	30.3109i	0.525657	+	1.51744i
$400$	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
$406$	−4.50000	−	0.866025i	−0.223331	−	0.0429801i
$407$	−18.0000	−	10.3923i	−0.892227	−	0.515127i
$408$		−	5.19615i		−	0.257248i
$409$	−2.00000	+	3.46410i	−0.0988936	+	0.171289i	−0.911227	−	0.411905i	$-0.864864\pi$
$409$	−2.00000	+	3.46410i	−0.0988936	+	0.171289i	0.812333	+	0.583193i	$0.198197\pi$
$410$	−9.00000	+	15.5885i	−0.444478	+	0.769859i
$411$			20.7846i			1.02523i
$412$	3.00000	+	1.73205i	0.147799	+	0.0853320i
$413$	−27.0000	−	5.19615i	−1.32858	−	0.255686i
$414$	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	$0.738640\pi$
$420$	15.0000	−	5.19615i	0.731925	−	0.253546i
$421$			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
$427$	13.5000	+	2.59808i	0.653311	+	0.125730i
$428$			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	0.0942129	−	0.995552i	$-0.469967\pi$
$433$	−15.0000	−	8.66025i	−0.720854	−	0.416185i	−0.815067	+	0.579367i	$0.803300\pi$
$434$	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	−0.569880	−	0.821728i	$-0.693010\pi$
$439$	−3.00000	+	1.73205i	−0.143182	+	0.0826663i	0.426698	+	0.904394i	$0.359677\pi$
$440$	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
$448$	2.50000	−	0.866025i	0.118114	−	0.0409159i
$449$	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
$455$	−3.00000	−	32.9090i	−0.140642	−	1.54280i
$456$			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	$0.408031\pi$
$462$	−4.50000	−	12.9904i	−0.209359	−	0.604367i
$463$			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
$483$	−6.00000	+	31.1769i	−0.273009	+	1.41860i
$484$	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
$490$	−9.00000	+	22.5167i	−0.406579	+	1.01720i
$491$	−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
$497$	−3.00000	+	15.5885i	−0.134568	+	0.699238i
$498$	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	$0.252873\pi$
$504$	1.50000	−	7.79423i	0.0668153	−	0.347183i
$505$		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
$511$	−10.0000	+	3.46410i	−0.442374	+	0.153243i
$512$	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
$518$	18.0000	+	3.46410i	0.790875	+	0.152204i
$519$		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	0.275865	−	0.961196i	$-0.411036\pi$
$523$	28.5000	−	16.4545i	1.24622	−	0.719504i	0.970353	+	0.241692i	$0.0777024\pi$
$524$	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
$539$	19.5000	+	7.79423i	0.839924	+	0.335721i
$540$	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
$546$	−15.0000	−	6.92820i	−0.641941	−	0.296500i
$547$	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
$553$	−27.5000	+	9.52628i	−1.16942	+	0.405099i
$554$	−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	$-0.664553\pi$
$563$	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	−0.151467	−	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
$574$	−13.5000	−	2.59808i	−0.563479	−	0.108442i
$575$	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	$-0.433255\pi$
$577$	10.0000			0.416305			0.208153	+	0.978096i	$0.433255\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	−10.5000	+	18.1865i	−0.436365	+	0.755807i
$580$	6.00000			0.249136
$581$	12.0000	+	34.6410i	0.497844	+	1.43715i
$582$	−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	$0.216981\pi$
$588$	7.50000	+	9.52628i	0.309295	+	0.392857i
$589$	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
$595$	−27.0000	−	5.19615i	−1.10689	−	0.213021i
$596$	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	−0.936576	−	0.350464i	$-0.886024\pi$
$601$	−27.0000	+	15.5885i	−1.10135	+	0.635866i	−0.164777	+	0.986331i	$0.552690\pi$
$602$	−20.0000	+	6.92820i	−0.815139	+	0.282372i
$603$		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	0.373267	−	0.927724i	$-0.378238\pi$
$607$	−6.00000	−	3.46410i	−0.243532	−	0.140604i	−0.616799	+	0.787121i	$0.711571\pi$
$608$	−3.50000	−	6.06218i	−0.141944	−	0.245854i
$609$	1.50000	−	7.79423i	0.0607831	−	0.315838i
$610$	−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	$-0.285915\pi$
$619$	31.0000			1.24600			0.622998	+	0.782224i	$0.285915\pi$
$620$	−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
$630$	9.00000	+	25.9808i	0.358569	+	1.03510i
$631$	−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
$637$	23.0000	−	10.3923i	0.911293	−	0.411758i
$638$		−	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	$0.544076\pi$
$643$	−23.5000	+	40.7032i	−0.926750	+	1.60518i	−0.788723	+	0.614749i	$0.789257\pi$
$644$	−6.00000	−	17.3205i	−0.236433	−	0.682524i
$645$	−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	−0.409360	−	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	0.697174	−	0.716902i	$-0.254441\pi$
$661$	−7.00000	−	12.1244i	−0.272268	−	0.471583i	−0.969442	+	0.245319i	$0.921107\pi$
$662$		0			0
$663$	4.50000	−	18.1865i	0.174766	−	0.706306i
$664$			13.8564i			0.537733i
$665$	63.0000	+	12.1244i	2.44304	+	0.470162i
$666$	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
$672$	1.50000	+	4.33013i	0.0578638	+	0.167038i
$673$	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
$679$	1.00000	−	5.19615i	0.0383765	−	0.199410i
$680$	−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
$686$	−18.5000	−	0.866025i	−0.706333	−	0.0330650i
$687$	−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	0.932024	−	0.362397i	$-0.118041\pi$
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	−0.779857	+	0.625958i	$0.784708\pi$
$692$		0			0
$693$	22.5000	−	7.79423i	0.854704	−	0.296078i
$694$			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
$700$	3.50000	−	18.1865i	0.132288	−	0.687386i
$701$			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	−0.992659	−	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
$721$	−3.00000	−	8.66025i	−0.111726	−	0.322525i
$722$	−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	$-0.777946\pi$
$727$		−	34.6410i		−	1.28476i	0.766385	−	0.642382i	$-0.222054\pi$
$728$	9.50000	−	0.866025i	0.352093	−	0.0320970i
$729$	−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	$-0.577175\pi$
$733$	−13.0000			−0.480166			−0.240083	+	0.970752i	$0.577175\pi$
$734$	18.0000	+	10.3923i	0.664392	+	0.383587i
$735$	−39.0000	−	15.5885i	−1.43854	−	0.574989i
$736$		−	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
$756$	13.5000	+	2.59808i	0.490990	+	0.0944911i
$757$	−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
$763$	−3.00000	−	8.66025i	−0.108607	−	0.313522i
$764$		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	$0.0897509\pi$
$769$	20.0000	+	34.6410i	0.721218	+	1.24919i	−0.239293	+	0.970947i	$0.576916\pi$
$770$	−27.0000	−	5.19615i	−0.973012	−	0.187256i
$771$	−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
$777$	−6.00000	+	31.1769i	−0.215249	+	1.11847i
$778$	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
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$	−48.0000			−1.71319
$786$	9.00000	+	5.19615i	0.321019	+	0.185341i
$787$	8.50000	−	14.7224i	0.302992	−	0.524798i	−0.673820	−	0.738896i	$-0.735348\pi$
$787$	8.50000	−	14.7224i	0.302992	−	0.524798i	0.976812	+	0.214097i	$0.0686810\pi$
$788$	27.0000			0.961835
$789$	−21.0000	+	36.3731i	−0.747620	+	1.29492i
$790$	33.0000	−	19.0526i	1.17409	−	0.677860i
$791$	36.0000	+	6.92820i	1.28001	+	0.246339i
$792$	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	−0.999652	−	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	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	1.50000	+	4.33013i	0.0526397	+	0.151958i
$813$	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
$819$	12.0000	−	25.9808i	0.419314	−	0.907841i
$820$	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
$826$	9.00000	+	25.9808i	0.313150	+	0.903986i
$827$	−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	−0.246894	−	0.969042i	$-0.579410\pi$
$829$	13.5000	−	7.79423i	0.468874	−	0.270705i	0.715768	+	0.698338i	$0.246077\pi$
$830$	−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
$847$	1.00000	−	5.19615i	0.0343604	−	0.178542i
$848$	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	$-0.704510\pi$
$853$	−35.0000			−1.19838			−0.599189	+	0.800608i	$0.704510\pi$
$854$	−4.50000	−	12.9904i	−0.153987	−	0.444522i
$855$	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	$-0.762148\pi$
$859$		−	39.8372i		−	1.35923i	0.733571	−	0.679613i	$-0.237852\pi$
$860$	24.0000	−	13.8564i	0.818393	−	0.472500i
$861$	4.50000	−	23.3827i	0.153360	−	0.796880i
$862$	−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
$868$	2.00000	−	10.3923i	0.0678844	−	0.352738i
$869$	−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
$875$	6.00000	+	17.3205i	0.202837	+	0.585540i
$876$		−	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	$-0.335308\pi$
$882$	−16.5000	+	12.9904i	−0.555584	+	0.437409i
$883$	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
$903$	−12.0000	−	34.6410i	−0.399335	−	1.15278i
$904$	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
$910$	−27.0000	+	19.0526i	−0.895041	+	0.631586i
$911$			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
$917$	−15.0000	+	5.19615i	−0.495344	+	0.171592i
$918$			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	$0.213850\pi$
$937$			38.1051i			1.24484i	−0.782683	+	0.622420i	$0.786150\pi$
$938$		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
$945$	−45.0000	+	15.5885i	−1.46385	+	0.507093i
$946$	−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
$952$	1.50000	−	7.79423i	0.0486153	−	0.252612i
$953$	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
$959$	−6.00000	+	31.1769i	−0.193750	+	1.00676i
$960$	−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
$966$	30.0000	−	10.3923i	0.965234	−	0.334367i
$967$		−	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
$973$	−13.5000	−	2.59808i	−0.432790	−	0.0832905i
$974$		−	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	$0.388381\pi$
$983$			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
$994$	15.0000	−	5.19615i	0.475771	−	0.164812i
$995$	−18.0000	+	31.1769i	−0.570638	+	0.988375i
$996$	−24.0000			−0.760469
$997$	−19.5000	−	11.2583i	−0.617571	−	0.356555i	0.158352	−	0.987383i	$-0.449382\pi$
$997$	−19.5000	−	11.2583i	−0.617571	−	0.356555i	−0.775923	+	0.630828i	$0.782715\pi$
$998$	−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.b.335.1	yes	2
3.2	odd	2		546.2.q.d.335.1	yes	2
7.6	odd	2		546.2.q.a.335.1	yes	2
13.4	even	6		546.2.q.c.251.1	yes	2
21.20	even	2		546.2.q.c.335.1	yes	2
39.17	odd	6		546.2.q.a.251.1	✓	2
91.69	odd	6		546.2.q.d.251.1	yes	2
273.251	even	6	inner	546.2.q.b.251.1	yes	2

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.46410i q^{5} +(-1.50000 - 0.866025i) q^{6} +(2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(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} +(2.50000 - 0.866025i) 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} +(-0.500000 + 2.59808i) 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} +(-3.00000 - 8.66025i) 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} +(-4.50000 - 0.866025i) 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} +(5.50000 - 4.33013i) 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} +(2.50000 - 0.866025i) 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} +(1.50000 - 7.79423i) 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} +(1.50000 + 4.33013i) 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} +(9.50000 - 0.866025i) 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} +(-6.50000 - 2.59808i) q^{98} +9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 3 q^{3} - q^{4} - 3 q^{6} + 5 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 + 3 * q^3 - q^4 - 3 * q^6 + 5 * q^7 + 2 * q^8 + 3 * q^9	\( 2 q - q^{2} + 3 q^{3} - q^{4} - 3 q^{6} + 5 q^{7} + 2 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} + 7 q^{13} - 4 q^{14} - 6 q^{15} - q^{16} + 3 q^{17} - 6 q^{18} - 7 q^{19} + 6 q^{20} + 6 q^{21} + 3 q^{22} - 12 q^{23} + 3 q^{24} - 14 q^{25} - 2 q^{26} - q^{28} + 3 q^{29} - 6 q^{30} - 8 q^{31} - q^{32} + 9 q^{33} - 6 q^{34} - 6 q^{35} + 3 q^{36} - 12 q^{37} + 14 q^{38} + 12 q^{39} + 9 q^{41} - 9 q^{42} + 8 q^{43} - 6 q^{44} - 18 q^{45} + 12 q^{46} - 3 q^{48} + 11 q^{49} + 7 q^{50} - 5 q^{52} - 9 q^{54} + 18 q^{55} + 5 q^{56} - 3 q^{58} - 18 q^{59} + 12 q^{60} + 9 q^{61} + 4 q^{62} + 3 q^{63} + 2 q^{64} + 6 q^{65} + 3 q^{68} - 12 q^{69} - 12 q^{70} - 6 q^{71} + 3 q^{72} - 8 q^{73} + 12 q^{74} - 21 q^{75} - 7 q^{76} + 12 q^{77} - 9 q^{78} - 22 q^{79} - 6 q^{80} - 9 q^{81} - 9 q^{82} + 3 q^{84} - 18 q^{85} - 16 q^{86} + 3 q^{87} + 3 q^{88} + 15 q^{89} + 19 q^{91} - 12 q^{93} + 15 q^{94} + 42 q^{95} + 2 q^{97} - 13 q^{98} + 18 q^{99}+O(q^{100}) \) 2 * q - q^2 + 3 * q^3 - q^4 - 3 * q^6 + 5 * 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 - q^28 + 3 * q^29 - 6 * q^30 - 8 * q^31 - q^32 + 9 * q^33 - 6 * q^34 - 6 * q^35 + 3 * q^36 - 12 * q^37 + 14 * q^38 + 12 * q^39 + 9 * q^41 - 9 * q^42 + 8 * q^43 - 6 * q^44 - 18 * q^45 + 12 * q^46 - 3 * q^48 + 11 * q^49 + 7 * q^50 - 5 * q^52 - 9 * q^54 + 18 * q^55 + 5 * q^56 - 3 * q^58 - 18 * q^59 + 12 * q^60 + 9 * q^61 + 4 * q^62 + 3 * 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 + 3 * q^84 - 18 * q^85 - 16 * q^86 + 3 * q^87 + 3 * q^88 + 15 * q^89 + 19 * q^91 - 12 * q^93 + 15 * q^94 + 42 * q^95 + 2 * q^97 - 13 * q^98 + 18 * q^99

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