LMFDB - Embedded newform 546.2.i.e.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("546.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.79
Dual form			546.2.i.e.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} -2.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} -2.00000 q^{20} +(2.00000 + 1.73205i) q^{21} -3.00000 q^{22} +(0.500000 + 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +(2.00000 + 1.73205i) q^{28} -1.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} -5.00000 q^{34} +(-1.00000 + 5.19615i) q^{35} +1.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(0.500000 + 0.866025i) q^{38} +(0.500000 + 0.866025i) q^{39} +(-1.00000 + 1.73205i) q^{40} +10.0000 q^{41} +(2.50000 - 0.866025i) q^{42} -10.0000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(1.00000 + 1.73205i) q^{45} +(0.500000 - 0.866025i) q^{47} +1.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +1.00000 q^{50} +(-2.50000 + 4.33013i) q^{51} +(0.500000 + 0.866025i) q^{52} +(1.50000 + 2.59808i) q^{53} +(0.500000 - 0.866025i) q^{54} -6.00000 q^{55} +(2.50000 - 0.866025i) q^{56} +1.00000 q^{57} +(-0.500000 + 0.866025i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(1.00000 + 1.73205i) q^{60} +(2.50000 - 4.33013i) q^{61} -4.00000 q^{62} +(0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(1.50000 + 2.59808i) q^{66} +(-2.50000 - 4.33013i) q^{67} +(-2.50000 + 4.33013i) q^{68} +(4.00000 + 3.46410i) q^{70} -1.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-6.00000 - 10.3923i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(0.500000 - 0.866025i) q^{75} +1.00000 q^{76} +(6.00000 + 5.19615i) q^{77} +1.00000 q^{78} +(3.00000 - 5.19615i) q^{79} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.00000 - 8.66025i) q^{82} +16.0000 q^{83} +(0.500000 - 2.59808i) q^{84} -10.0000 q^{85} +(-5.00000 + 8.66025i) q^{86} +(0.500000 + 0.866025i) q^{87} +(1.50000 + 2.59808i) q^{88} +(7.00000 - 12.1244i) q^{89} +2.00000 q^{90} +(2.50000 - 0.866025i) q^{91} +(-2.00000 + 3.46410i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(1.00000 + 1.73205i) q^{95} +(0.500000 - 0.866025i) q^{96} +4.00000 q^{97} +(-1.00000 - 6.92820i) q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} + 2 q^{5} - 2 q^{6} - 5 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 + 2 * q^5 - 2 * q^6 - 5 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} - q^{3} - q^{4} + 2 q^{5} - 2 q^{6} - 5 q^{7} - 2 q^{8} - q^{9} - 2 q^{10} - 3 q^{11} - q^{12} - 2 q^{13} - q^{14} - 4 q^{15} - q^{16} - 5 q^{17} + q^{18} - q^{19} - 4 q^{20} + 4 q^{21} - 6 q^{22} + q^{24} + q^{25} - q^{26} + 2 q^{27} + 4 q^{28} - 2 q^{29} - 2 q^{30} - 4 q^{31} + q^{32} - 3 q^{33} - 10 q^{34} - 2 q^{35} + 2 q^{36} + 2 q^{37} + q^{38} + q^{39} - 2 q^{40} + 20 q^{41} + 5 q^{42} - 20 q^{43} - 3 q^{44} + 2 q^{45} + q^{47} + 2 q^{48} + 11 q^{49} + 2 q^{50} - 5 q^{51} + q^{52} + 3 q^{53} + q^{54} - 12 q^{55} + 5 q^{56} + 2 q^{57} - q^{58} - 3 q^{59} + 2 q^{60} + 5 q^{61} - 8 q^{62} + q^{63} + 2 q^{64} - 2 q^{65} + 3 q^{66} - 5 q^{67} - 5 q^{68} + 8 q^{70} - 2 q^{71} + q^{72} - 12 q^{73} - 2 q^{74} + q^{75} + 2 q^{76} + 12 q^{77} + 2 q^{78} + 6 q^{79} + 2 q^{80} - q^{81} + 10 q^{82} + 32 q^{83} + q^{84} - 20 q^{85} - 10 q^{86} + q^{87} + 3 q^{88} + 14 q^{89} + 4 q^{90} + 5 q^{91} - 4 q^{93} - q^{94} + 2 q^{95} + q^{96} + 8 q^{97} - 2 q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 + 2 * q^5 - 2 * q^6 - 5 * q^7 - 2 * q^8 - q^9 - 2 * q^10 - 3 * q^11 - q^12 - 2 * q^13 - q^14 - 4 * q^15 - q^16 - 5 * q^17 + q^18 - q^19 - 4 * q^20 + 4 * q^21 - 6 * q^22 + q^24 + q^25 - q^26 + 2 * q^27 + 4 * q^28 - 2 * q^29 - 2 * q^30 - 4 * q^31 + q^32 - 3 * q^33 - 10 * q^34 - 2 * q^35 + 2 * q^36 + 2 * q^37 + q^38 + q^39 - 2 * q^40 + 20 * q^41 + 5 * q^42 - 20 * q^43 - 3 * q^44 + 2 * q^45 + q^47 + 2 * q^48 + 11 * q^49 + 2 * q^50 - 5 * q^51 + q^52 + 3 * q^53 + q^54 - 12 * q^55 + 5 * q^56 + 2 * q^57 - q^58 - 3 * q^59 + 2 * q^60 + 5 * q^61 - 8 * q^62 + q^63 + 2 * q^64 - 2 * q^65 + 3 * q^66 - 5 * q^67 - 5 * q^68 + 8 * q^70 - 2 * q^71 + q^72 - 12 * q^73 - 2 * q^74 + q^75 + 2 * q^76 + 12 * q^77 + 2 * q^78 + 6 * q^79 + 2 * q^80 - q^81 + 10 * q^82 + 32 * q^83 + q^84 - 20 * q^85 - 10 * q^86 + q^87 + 3 * q^88 + 14 * q^89 + 4 * q^90 + 5 * q^91 - 4 * q^93 - q^94 + 2 * q^95 + q^96 + 8 * q^97 - 2 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	−0.550990	−	0.834512i	$-0.685750\pi$
$5$	1.00000	−	1.73205i	0.447214	−	0.774597i	0.998203	+	0.0599153i	$0.0190830\pi$
$6$	−1.00000			−0.408248
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000	−	1.73205i	−0.316228	−	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	$0.982718\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−0.500000	+	2.59808i	−0.133631	+	0.694365i
$15$	−2.00000			−0.516398
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	−0.991838	−	0.127502i	$-0.959304\pi$
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	0.385499	−	0.922708i	$-0.374029\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$	−2.00000			−0.447214
$21$	2.00000	+	1.73205i	0.436436	+	0.377964i
$22$	−3.00000			−0.639602
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	1.00000			0.192450
$28$	2.00000	+	1.73205i	0.377964	+	0.327327i
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$	−5.00000			−0.857493
$35$	−1.00000	+	5.19615i	−0.169031	+	0.878310i
$36$	1.00000			0.166667
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	0.500000	+	0.866025i	0.0811107	+	0.140488i
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$	−1.00000	+	1.73205i	−0.158114	+	0.273861i
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$	2.50000	−	0.866025i	0.385758	−	0.133631i
$43$	−10.0000			−1.52499			−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000			−1.52499			−0.762493	+	0.646997i	$0.776025\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$		0			0
$47$	0.500000	−	0.866025i	0.0729325	−	0.126323i	−0.827253	−	0.561830i	$-0.810098\pi$
$47$	0.500000	−	0.866025i	0.0729325	−	0.126323i	0.900185	+	0.435507i	$0.143431\pi$
$48$	1.00000			0.144338
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$	1.00000			0.141421
$51$	−2.50000	+	4.33013i	−0.350070	+	0.606339i
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−6.00000			−0.809040
$56$	2.50000	−	0.866025i	0.334077	−	0.115728i
$57$	1.00000			0.132453
$58$	−0.500000	+	0.866025i	−0.0656532	+	0.113715i
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	0.751710	−	0.659494i	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$	1.00000	+	1.73205i	0.129099	+	0.223607i
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	−0.660415	−	0.750901i	$-0.729619\pi$
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	0.980507	+	0.196485i	$0.0629528\pi$
$62$	−4.00000			−0.508001
$63$	0.500000	−	2.59808i	0.0629941	−	0.327327i
$64$	1.00000			0.125000
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$	1.50000	+	2.59808i	0.184637	+	0.319801i
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	0.671932	−	0.740613i	$-0.265465\pi$
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	−2.50000	+	4.33013i	−0.303170	+	0.525105i
$69$		0			0
$70$	4.00000	+	3.46410i	0.478091	+	0.414039i
$71$	−1.00000			−0.118678			−0.0593391	−	0.998238i	$-0.518899\pi$
$71$	−1.00000			−0.118678			−0.0593391	+	0.998238i	$0.518899\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−6.00000	−	10.3923i	−0.702247	−	1.21633i	−0.967676	−	0.252197i	$-0.918847\pi$
$73$	−6.00000	−	10.3923i	−0.702247	−	1.21633i	0.265429	−	0.964130i	$-0.414486\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	1.00000			0.114708
$77$	6.00000	+	5.19615i	0.683763	+	0.592157i
$78$	1.00000			0.113228
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	−0.646440	−	0.762964i	$-0.723743\pi$
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	0.983967	+	0.178352i	$0.0570765\pi$
$80$	1.00000	+	1.73205i	0.111803	+	0.193649i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.00000	−	8.66025i	0.552158	−	0.956365i
$83$	16.0000			1.75623			0.878114	−	0.478451i	$-0.158802\pi$
$83$	16.0000			1.75623			0.878114	+	0.478451i	$0.158802\pi$
$84$	0.500000	−	2.59808i	0.0545545	−	0.283473i
$85$	−10.0000			−1.08465
$86$	−5.00000	+	8.66025i	−0.539164	+	0.933859i
$87$	0.500000	+	0.866025i	0.0536056	+	0.0928477i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	−0.209585	−	0.977790i	$-0.567211\pi$
$89$	7.00000	−	12.1244i	0.741999	−	1.28518i	0.951584	−	0.307389i	$-0.0994552\pi$
$90$	2.00000			0.210819
$91$	2.50000	−	0.866025i	0.262071	−	0.0907841i
$92$		0			0
$93$	−2.00000	+	3.46410i	−0.207390	+	0.359211i
$94$	−0.500000	−	0.866025i	−0.0515711	−	0.0893237i
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	4.00000			0.406138			0.203069	−	0.979164i	$-0.434908\pi$
$97$	4.00000			0.406138			0.203069	+	0.979164i	$0.434908\pi$
$98$	−1.00000	−	6.92820i	−0.101015	−	0.699854i
$99$	3.00000			0.301511
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	0.811976	−	0.583691i	$-0.198392\pi$
$101$	−1.00000	−	1.73205i	−0.0995037	−	0.172345i	−0.911479	+	0.411346i	$0.865059\pi$
$102$	2.50000	+	4.33013i	0.247537	+	0.428746i
$103$	1.00000	−	1.73205i	0.0985329	−	0.170664i	−0.812545	−	0.582899i	$-0.801918\pi$
$103$	1.00000	−	1.73205i	0.0985329	−	0.170664i	0.911078	+	0.412235i	$0.135252\pi$
$104$	1.00000			0.0980581
$105$	5.00000	−	1.73205i	0.487950	−	0.169031i
$106$	3.00000			0.291386
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	0.939577	+	0.342337i	$0.111218\pi$
$109$	8.00000	+	13.8564i	0.766261	+	1.32720i	−0.173316	+	0.984866i	$0.555448\pi$
$110$	−3.00000	+	5.19615i	−0.286039	+	0.495434i
$111$	−2.00000			−0.189832
$112$	0.500000	−	2.59808i	0.0472456	−	0.245495i
$113$	15.0000			1.41108			0.705541	−	0.708669i	$-0.250704\pi$
$113$	15.0000			1.41108			0.705541	+	0.708669i	$0.250704\pi$
$114$	0.500000	−	0.866025i	0.0468293	−	0.0811107i
$115$		0			0
$116$	0.500000	+	0.866025i	0.0464238	+	0.0804084i
$117$	0.500000	−	0.866025i	0.0462250	−	0.0800641i
$118$	−3.00000			−0.276172
$119$	10.0000	+	8.66025i	0.916698	+	0.793884i
$120$	2.00000			0.182574
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−2.50000	−	4.33013i	−0.226339	−	0.392031i
$123$	−5.00000	−	8.66025i	−0.450835	−	0.780869i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	12.0000			1.07331
$126$	−2.00000	−	1.73205i	−0.178174	−	0.154303i
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	5.00000	+	8.66025i	0.440225	+	0.762493i
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$	3.00000			0.261116
$133$	0.500000	−	2.59808i	0.0433555	−	0.225282i
$134$	−5.00000			−0.431934
$135$	1.00000	−	1.73205i	0.0860663	−	0.149071i
$136$	2.50000	+	4.33013i	0.214373	+	0.371305i
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	−0.938148	−	0.346235i	$-0.887460\pi$
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	0.169226	−	0.985577i	$-0.445873\pi$
$138$		0			0
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$	5.00000	−	1.73205i	0.422577	−	0.146385i
$141$	−1.00000			−0.0842152
$142$	−0.500000	+	0.866025i	−0.0419591	+	0.0726752i
$143$	1.50000	+	2.59808i	0.125436	+	0.217262i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−1.00000	+	1.73205i	−0.0830455	+	0.143839i
$146$	−12.0000			−0.993127
$147$	−6.50000	−	2.59808i	−0.536111	−	0.214286i
$148$	−2.00000			−0.164399
$149$	−4.00000	+	6.92820i	−0.327693	+	0.567581i	−0.982054	−	0.188602i	$-0.939604\pi$
$149$	−4.00000	+	6.92820i	−0.327693	+	0.567581i	0.654361	+	0.756182i	$0.272938\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−9.50000	−	16.4545i	−0.773099	−	1.33905i	0.162758	−	0.986666i	$-0.447961\pi$
$152$	0.500000	−	0.866025i	0.0405554	−	0.0702439i
$153$	5.00000			0.404226
$154$	7.50000	−	2.59808i	0.604367	−	0.209359i
$155$	−8.00000			−0.642575
$156$	0.500000	−	0.866025i	0.0400320	−	0.0693375i
$157$	−10.5000	−	18.1865i	−0.837991	−	1.45144i	−0.891572	−	0.452880i	$-0.850397\pi$
$157$	−10.5000	−	18.1865i	−0.837991	−	1.45144i	0.0535803	−	0.998564i	$-0.482937\pi$
$158$	−3.00000	−	5.19615i	−0.238667	−	0.413384i
$159$	1.50000	−	2.59808i	0.118958	−	0.206041i
$160$	2.00000			0.158114
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	−9.50000	+	16.4545i	−0.744097	+	1.28881i	0.206518	+	0.978443i	$0.433787\pi$
$163$	−9.50000	+	16.4545i	−0.744097	+	1.28881i	−0.950615	+	0.310372i	$0.899546\pi$
$164$	−5.00000	−	8.66025i	−0.390434	−	0.676252i
$165$	3.00000	+	5.19615i	0.233550	+	0.404520i
$166$	8.00000	−	13.8564i	0.620920	−	1.07547i
$167$	21.0000			1.62503			0.812514	−	0.582941i	$-0.198098\pi$
$167$	21.0000			1.62503			0.812514	+	0.582941i	$0.198098\pi$
$168$	−2.00000	−	1.73205i	−0.154303	−	0.133631i
$169$	1.00000			0.0769231
$170$	−5.00000	+	8.66025i	−0.383482	+	0.664211i
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	5.00000	+	8.66025i	0.381246	+	0.660338i
$173$	−1.50000	+	2.59808i	−0.114043	+	0.197528i	−0.917397	−	0.397974i	$-0.869713\pi$
$173$	−1.50000	+	2.59808i	−0.114043	+	0.197528i	0.803354	+	0.595502i	$0.203047\pi$
$174$	1.00000			0.0758098
$175$	−2.00000	−	1.73205i	−0.151186	−	0.130931i
$176$	3.00000			0.226134
$177$	−1.50000	+	2.59808i	−0.112747	+	0.195283i
$178$	−7.00000	−	12.1244i	−0.524672	−	0.908759i
$179$	−1.00000	−	1.73205i	−0.0747435	−	0.129460i	0.826231	−	0.563331i	$-0.190480\pi$
$179$	−1.00000	−	1.73205i	−0.0747435	−	0.129460i	−0.900975	+	0.433872i	$0.857147\pi$
$180$	1.00000	−	1.73205i	0.0745356	−	0.129099i
$181$	3.00000			0.222988			0.111494	−	0.993765i	$-0.464436\pi$
$181$	3.00000			0.222988			0.111494	+	0.993765i	$0.464436\pi$
$182$	0.500000	−	2.59808i	0.0370625	−	0.192582i
$183$	−5.00000			−0.369611
$184$		0			0
$185$	−2.00000	−	3.46410i	−0.147043	−	0.254686i
$186$	2.00000	+	3.46410i	0.146647	+	0.254000i
$187$	−7.50000	+	12.9904i	−0.548454	+	0.949951i
$188$	−1.00000			−0.0729325
$189$	−2.50000	+	0.866025i	−0.181848	+	0.0629941i
$190$	2.00000			0.145095
$191$	−10.0000	+	17.3205i	−0.723575	+	1.25327i	0.235983	+	0.971757i	$0.424169\pi$
$191$	−10.0000	+	17.3205i	−0.723575	+	1.25327i	−0.959558	+	0.281511i	$0.909164\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	0.999990	+	0.00447566i	$0.00142465\pi$
$193$	7.00000	+	12.1244i	0.503871	+	0.872730i	−0.496119	+	0.868255i	$0.665242\pi$
$194$	2.00000	−	3.46410i	0.143592	−	0.248708i
$195$	2.00000			0.143223
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	−24.0000			−1.70993			−0.854965	−	0.518686i	$-0.826421\pi$
$197$	−24.0000			−1.70993			−0.854965	+	0.518686i	$0.826421\pi$
$198$	1.50000	−	2.59808i	0.106600	−	0.184637i
$199$	10.0000	+	17.3205i	0.708881	+	1.22782i	0.965272	+	0.261245i	$0.0841331\pi$
$199$	10.0000	+	17.3205i	0.708881	+	1.22782i	−0.256391	+	0.966573i	$0.582534\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−2.50000	+	4.33013i	−0.176336	+	0.305424i
$202$	−2.00000			−0.140720
$203$	2.50000	−	0.866025i	0.175466	−	0.0607831i
$204$	5.00000			0.350070
$205$	10.0000	−	17.3205i	0.698430	−	1.20972i
$206$	−1.00000	−	1.73205i	−0.0696733	−	0.120678i
$207$		0			0
$208$	0.500000	−	0.866025i	0.0346688	−	0.0600481i
$209$	3.00000			0.207514
$210$	1.00000	−	5.19615i	0.0690066	−	0.358569i
$211$	−16.0000			−1.10149			−0.550743	−	0.834675i	$-0.685655\pi$
$211$	−16.0000			−1.10149			−0.550743	+	0.834675i	$0.685655\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$	0.500000	+	0.866025i	0.0342594	+	0.0593391i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−10.0000	+	17.3205i	−0.681994	+	1.18125i
$216$	−1.00000			−0.0680414
$217$	8.00000	+	6.92820i	0.543075	+	0.470317i
$218$	16.0000			1.08366
$219$	−6.00000	+	10.3923i	−0.405442	+	0.702247i
$220$	3.00000	+	5.19615i	0.202260	+	0.350325i
$221$	2.50000	+	4.33013i	0.168168	+	0.291276i
$222$	−1.00000	+	1.73205i	−0.0671156	+	0.116248i
$223$	11.0000			0.736614			0.368307	−	0.929704i	$-0.379937\pi$
$223$	11.0000			0.736614			0.368307	+	0.929704i	$0.379937\pi$
$224$	−2.00000	−	1.73205i	−0.133631	−	0.115728i
$225$	−1.00000			−0.0666667
$226$	7.50000	−	12.9904i	0.498893	−	0.864107i
$227$	−4.00000	−	6.92820i	−0.265489	−	0.459841i	0.702202	−	0.711977i	$-0.252200\pi$
$227$	−4.00000	−	6.92820i	−0.265489	−	0.459841i	−0.967692	+	0.252136i	$0.918867\pi$
$228$	−0.500000	−	0.866025i	−0.0331133	−	0.0573539i
$229$	−3.00000	+	5.19615i	−0.198246	+	0.343371i	−0.947960	−	0.318390i	$-0.896858\pi$
$229$	−3.00000	+	5.19615i	−0.198246	+	0.343371i	0.749714	+	0.661762i	$0.230191\pi$
$230$		0			0
$231$	1.50000	−	7.79423i	0.0986928	−	0.512823i
$232$	1.00000			0.0656532
$233$	−5.50000	+	9.52628i	−0.360317	+	0.624087i	−0.988013	−	0.154371i	$-0.950665\pi$
$233$	−5.50000	+	9.52628i	−0.360317	+	0.624087i	0.627696	+	0.778459i	$0.283998\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$	−1.00000	−	1.73205i	−0.0652328	−	0.112987i
$236$	−1.50000	+	2.59808i	−0.0976417	+	0.169120i
$237$	−6.00000			−0.389742
$238$	12.5000	−	4.33013i	0.810255	−	0.280680i
$239$	21.0000			1.35838			0.679189	−	0.733964i	$-0.262332\pi$
$239$	21.0000			1.35838			0.679189	+	0.733964i	$0.262332\pi$
$240$	1.00000	−	1.73205i	0.0645497	−	0.111803i
$241$	−2.00000	−	3.46410i	−0.128831	−	0.223142i	0.794393	−	0.607404i	$-0.207789\pi$
$241$	−2.00000	−	3.46410i	−0.128831	−	0.223142i	−0.923224	+	0.384262i	$0.874456\pi$
$242$	−1.00000	−	1.73205i	−0.0642824	−	0.111340i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−5.00000			−0.320092
$245$	−2.00000	−	13.8564i	−0.127775	−	0.885253i
$246$	−10.0000			−0.637577
$247$	0.500000	−	0.866025i	0.0318142	−	0.0551039i
$248$	2.00000	+	3.46410i	0.127000	+	0.219971i
$249$	−8.00000	−	13.8564i	−0.506979	−	0.878114i
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$	−2.50000	+	0.866025i	−0.157485	+	0.0545545i
$253$		0			0
$254$		0			0
$255$	5.00000	+	8.66025i	0.313112	+	0.542326i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$	10.0000			0.622573
$259$	−1.00000	+	5.19615i	−0.0621370	+	0.322873i
$260$	2.00000			0.124035
$261$	0.500000	−	0.866025i	0.0309492	−	0.0536056i
$262$	−2.00000	−	3.46410i	−0.123560	−	0.214013i
$263$	3.00000	+	5.19615i	0.184988	+	0.320408i	0.943572	−	0.331166i	$-0.107442\pi$
$263$	3.00000	+	5.19615i	0.184988	+	0.320408i	−0.758585	+	0.651575i	$0.774109\pi$
$264$	1.50000	−	2.59808i	0.0923186	−	0.159901i
$265$	6.00000			0.368577
$266$	−2.00000	−	1.73205i	−0.122628	−	0.106199i
$267$	−14.0000			−0.856786
$268$	−2.50000	+	4.33013i	−0.152712	+	0.264505i
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	0.969976	−	0.243201i	$-0.0781974\pi$
$269$	4.50000	+	7.79423i	0.274370	+	0.475223i	−0.695606	+	0.718423i	$0.744864\pi$
$270$	−1.00000	−	1.73205i	−0.0608581	−	0.105409i
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	−0.983312	−	0.181928i	$-0.941766\pi$
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	0.649211	+	0.760609i	$0.275099\pi$
$272$	5.00000			0.303170
$273$	−2.00000	−	1.73205i	−0.121046	−	0.104828i
$274$	−18.0000			−1.08742
$275$	1.50000	−	2.59808i	0.0904534	−	0.156670i
$276$		0			0
$277$	13.5000	+	23.3827i	0.811136	+	1.40493i	0.912069	+	0.410036i	$0.134484\pi$
$277$	13.5000	+	23.3827i	0.811136	+	1.40493i	−0.100933	+	0.994893i	$0.532183\pi$
$278$	1.00000	−	1.73205i	0.0599760	−	0.103882i
$279$	4.00000			0.239474
$280$	1.00000	−	5.19615i	0.0597614	−	0.310530i
$281$	16.0000			0.954480			0.477240	−	0.878773i	$-0.341637\pi$
$281$	16.0000			0.954480			0.477240	+	0.878773i	$0.341637\pi$
$282$	−0.500000	+	0.866025i	−0.0297746	+	0.0515711i
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	0.500000	+	0.866025i	0.0296695	+	0.0513892i
$285$	1.00000	−	1.73205i	0.0592349	−	0.102598i
$286$	3.00000			0.177394
$287$	−25.0000	+	8.66025i	−1.47570	+	0.511199i
$288$	−1.00000			−0.0589256
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$	1.00000	+	1.73205i	0.0587220	+	0.101710i
$291$	−2.00000	−	3.46410i	−0.117242	−	0.203069i
$292$	−6.00000	+	10.3923i	−0.351123	+	0.608164i
$293$	−12.0000			−0.701047			−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000			−0.701047			−0.350524	+	0.936554i	$0.613996\pi$
$294$	−5.50000	+	4.33013i	−0.320767	+	0.252538i
$295$	−6.00000			−0.349334
$296$	−1.00000	+	1.73205i	−0.0581238	+	0.100673i
$297$	−1.50000	−	2.59808i	−0.0870388	−	0.150756i
$298$	4.00000	+	6.92820i	0.231714	+	0.401340i
$299$		0			0
$300$	−1.00000			−0.0577350
$301$	25.0000	−	8.66025i	1.44098	−	0.499169i
$302$	−19.0000			−1.09333
$303$	−1.00000	+	1.73205i	−0.0574485	+	0.0995037i
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$	−5.00000	−	8.66025i	−0.286299	−	0.495885i
$306$	2.50000	−	4.33013i	0.142915	−	0.247537i
$307$	−27.0000			−1.54097			−0.770486	−	0.637457i	$-0.779986\pi$
$307$	−27.0000			−1.54097			−0.770486	+	0.637457i	$0.779986\pi$
$308$	1.50000	−	7.79423i	0.0854704	−	0.444117i
$309$	−2.00000			−0.113776
$310$	−4.00000	+	6.92820i	−0.227185	+	0.393496i
$311$	−7.00000	−	12.1244i	−0.396934	−	0.687509i	0.596412	−	0.802678i	$-0.296592\pi$
$311$	−7.00000	−	12.1244i	−0.396934	−	0.687509i	−0.993346	+	0.115169i	$0.963259\pi$
$312$	−0.500000	−	0.866025i	−0.0283069	−	0.0490290i
$313$	−17.0000	+	29.4449i	−0.960897	+	1.66432i	−0.240640	+	0.970614i	$0.577357\pi$
$313$	−17.0000	+	29.4449i	−0.960897	+	1.66432i	−0.720257	+	0.693708i	$0.755976\pi$
$314$	−21.0000			−1.18510
$315$	−4.00000	−	3.46410i	−0.225374	−	0.195180i
$316$	−6.00000			−0.337526
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	−0.769395	−	0.638774i	$-0.779442\pi$
$317$	3.00000	−	5.19615i	0.168497	−	0.291845i	0.937892	+	0.346929i	$0.112775\pi$
$318$	−1.50000	−	2.59808i	−0.0841158	−	0.145693i
$319$	1.50000	+	2.59808i	0.0839839	+	0.145464i
$320$	1.00000	−	1.73205i	0.0559017	−	0.0968246i
$321$	12.0000			0.669775
$322$		0			0
$323$	5.00000			0.278207
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−0.500000	−	0.866025i	−0.0277350	−	0.0480384i
$326$	9.50000	+	16.4545i	0.526156	+	0.911330i
$327$	8.00000	−	13.8564i	0.442401	−	0.766261i
$328$	−10.0000			−0.552158
$329$	−0.500000	+	2.59808i	−0.0275659	+	0.143237i
$330$	6.00000			0.330289
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	−0.448649	−	0.893708i	$-0.648095\pi$
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	0.998298	−	0.0583130i	$-0.0185721\pi$
$332$	−8.00000	−	13.8564i	−0.439057	−	0.760469i
$333$	1.00000	+	1.73205i	0.0547997	+	0.0949158i
$334$	10.5000	−	18.1865i	0.574534	−	0.995123i
$335$	−10.0000			−0.546358
$336$	−2.50000	+	0.866025i	−0.136386	+	0.0472456i
$337$	−17.0000			−0.926049			−0.463025	−	0.886345i	$-0.653236\pi$
$337$	−17.0000			−0.926049			−0.463025	+	0.886345i	$0.653236\pi$
$338$	0.500000	−	0.866025i	0.0271964	−	0.0471056i
$339$	−7.50000	−	12.9904i	−0.407344	−	0.705541i
$340$	5.00000	+	8.66025i	0.271163	+	0.469668i
$341$	−6.00000	+	10.3923i	−0.324918	+	0.562775i
$342$	−1.00000			−0.0540738
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	10.0000			0.539164
$345$		0			0
$346$	1.50000	+	2.59808i	0.0806405	+	0.139673i
$347$	−1.00000	−	1.73205i	−0.0536828	−	0.0929814i	0.837935	−	0.545770i	$-0.183763\pi$
$347$	−1.00000	−	1.73205i	−0.0536828	−	0.0929814i	−0.891618	+	0.452788i	$0.850429\pi$
$348$	0.500000	−	0.866025i	0.0268028	−	0.0464238i
$349$	36.0000			1.92704			0.963518	−	0.267644i	$-0.0862451\pi$
$349$	36.0000			1.92704			0.963518	+	0.267644i	$0.0862451\pi$
$350$	−2.50000	+	0.866025i	−0.133631	+	0.0462910i
$351$	−1.00000			−0.0533761
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	−7.00000	−	12.1244i	−0.372572	−	0.645314i	0.617388	−	0.786659i	$-0.288191\pi$
$353$	−7.00000	−	12.1244i	−0.372572	−	0.645314i	−0.989960	+	0.141344i	$0.954858\pi$
$354$	1.50000	+	2.59808i	0.0797241	+	0.138086i
$355$	−1.00000	+	1.73205i	−0.0530745	+	0.0919277i
$356$	−14.0000			−0.741999
$357$	2.50000	−	12.9904i	0.132314	−	0.687524i
$358$	−2.00000			−0.105703
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$	−1.00000	−	1.73205i	−0.0527046	−	0.0912871i
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	1.50000	−	2.59808i	0.0788382	−	0.136552i
$363$	−2.00000			−0.104973
$364$	−2.00000	−	1.73205i	−0.104828	−	0.0907841i
$365$	−24.0000			−1.25622
$366$	−2.50000	+	4.33013i	−0.130677	+	0.226339i
$367$	−13.0000	−	22.5167i	−0.678594	−	1.17536i	−0.975404	−	0.220423i	$-0.929256\pi$
$367$	−13.0000	−	22.5167i	−0.678594	−	1.17536i	0.296810	−	0.954937i	$-0.404077\pi$
$368$		0			0
$369$	−5.00000	+	8.66025i	−0.260290	+	0.450835i
$370$	−4.00000			−0.207950
$371$	−6.00000	−	5.19615i	−0.311504	−	0.269771i
$372$	4.00000			0.207390
$373$	−6.50000	+	11.2583i	−0.336557	+	0.582934i	−0.983783	−	0.179364i	$-0.942596\pi$
$373$	−6.50000	+	11.2583i	−0.336557	+	0.582934i	0.647225	+	0.762299i	$0.275929\pi$
$374$	7.50000	+	12.9904i	0.387816	+	0.671717i
$375$	−6.00000	−	10.3923i	−0.309839	−	0.536656i
$376$	−0.500000	+	0.866025i	−0.0257855	+	0.0446619i
$377$	1.00000			0.0515026
$378$	−0.500000	+	2.59808i	−0.0257172	+	0.133631i
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$	1.00000	−	1.73205i	0.0512989	−	0.0888523i
$381$		0			0
$382$	10.0000	+	17.3205i	0.511645	+	0.886194i
$383$	16.0000	−	27.7128i	0.817562	−	1.41606i	−0.0899119	−	0.995950i	$-0.528659\pi$
$383$	16.0000	−	27.7128i	0.817562	−	1.41606i	0.907474	−	0.420109i	$-0.138008\pi$
$384$	−1.00000			−0.0510310
$385$	15.0000	−	5.19615i	0.764471	−	0.264820i
$386$	14.0000			0.712581
$387$	5.00000	−	8.66025i	0.254164	−	0.440225i
$388$	−2.00000	−	3.46410i	−0.101535	−	0.175863i
$389$	−4.50000	−	7.79423i	−0.228159	−	0.395183i	0.729103	−	0.684403i	$-0.239937\pi$
$389$	−4.50000	−	7.79423i	−0.228159	−	0.395183i	−0.957263	+	0.289220i	$0.906604\pi$
$390$	1.00000	−	1.73205i	0.0506370	−	0.0877058i
$391$		0			0
$392$	−5.50000	+	4.33013i	−0.277792	+	0.218704i
$393$	−4.00000			−0.201773
$394$	−12.0000	+	20.7846i	−0.604551	+	1.04711i
$395$	−6.00000	−	10.3923i	−0.301893	−	0.522894i
$396$	−1.50000	−	2.59808i	−0.0753778	−	0.130558i
$397$	−18.0000	+	31.1769i	−0.903394	+	1.56472i	−0.0803356	+	0.996768i	$0.525599\pi$
$397$	−18.0000	+	31.1769i	−0.903394	+	1.56472i	−0.823058	+	0.567957i	$0.807734\pi$
$398$	20.0000			1.00251
$399$	−2.50000	+	0.866025i	−0.125157	+	0.0433555i
$400$	−1.00000			−0.0500000
$401$	18.0000	−	31.1769i	0.898877	−	1.55690i	0.0699455	−	0.997551i	$-0.477717\pi$
$401$	18.0000	−	31.1769i	0.898877	−	1.55690i	0.828932	−	0.559350i	$-0.188949\pi$
$402$	2.50000	+	4.33013i	0.124689	+	0.215967i
$403$	2.00000	+	3.46410i	0.0996271	+	0.172559i
$404$	−1.00000	+	1.73205i	−0.0497519	+	0.0861727i
$405$	−2.00000			−0.0993808
$406$	0.500000	−	2.59808i	0.0248146	−	0.128940i
$407$	−6.00000			−0.297409
$408$	2.50000	−	4.33013i	0.123768	−	0.214373i
$409$	15.0000	+	25.9808i	0.741702	+	1.28467i	0.951720	+	0.306968i	$0.0993146\pi$
$409$	15.0000	+	25.9808i	0.741702	+	1.28467i	−0.210017	+	0.977698i	$0.567352\pi$
$410$	−10.0000	−	17.3205i	−0.493865	−	0.855399i
$411$	−9.00000	+	15.5885i	−0.443937	+	0.768922i
$412$	−2.00000			−0.0985329
$413$	6.00000	+	5.19615i	0.295241	+	0.255686i
$414$		0			0
$415$	16.0000	−	27.7128i	0.785409	−	1.36037i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	−1.00000	−	1.73205i	−0.0489702	−	0.0848189i
$418$	1.50000	−	2.59808i	0.0733674	−	0.127076i
$419$	10.0000			0.488532			0.244266	−	0.969708i	$-0.421453\pi$
$419$	10.0000			0.488532			0.244266	+	0.969708i	$0.421453\pi$
$420$	−4.00000	−	3.46410i	−0.195180	−	0.169031i
$421$	8.00000			0.389896			0.194948	−	0.980814i	$-0.437546\pi$
$421$	8.00000			0.389896			0.194948	+	0.980814i	$0.437546\pi$
$422$	−8.00000	+	13.8564i	−0.389434	+	0.674519i
$423$	0.500000	+	0.866025i	0.0243108	+	0.0421076i
$424$	−1.50000	−	2.59808i	−0.0728464	−	0.126174i
$425$	2.50000	−	4.33013i	0.121268	−	0.210042i
$426$	1.00000			0.0484502
$427$	−2.50000	+	12.9904i	−0.120983	+	0.628649i
$428$	12.0000			0.580042
$429$	1.50000	−	2.59808i	0.0724207	−	0.125436i
$430$	10.0000	+	17.3205i	0.482243	+	0.835269i
$431$	4.00000	+	6.92820i	0.192673	+	0.333720i	0.946135	−	0.323772i	$-0.104951\pi$
$431$	4.00000	+	6.92820i	0.192673	+	0.333720i	−0.753462	+	0.657491i	$0.771618\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−19.0000			−0.913082			−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000			−0.913082			−0.456541	+	0.889702i	$0.650912\pi$
$434$	10.0000	−	3.46410i	0.480015	−	0.166282i
$435$	2.00000			0.0958927
$436$	8.00000	−	13.8564i	0.383131	−	0.663602i
$437$		0			0
$438$	6.00000	+	10.3923i	0.286691	+	0.496564i
$439$	−20.0000	+	34.6410i	−0.954548	+	1.65333i	−0.219149	+	0.975691i	$0.570328\pi$
$439$	−20.0000	+	34.6410i	−0.954548	+	1.65333i	−0.735399	+	0.677634i	$0.763005\pi$
$440$	6.00000			0.286039
$441$	1.00000	+	6.92820i	0.0476190	+	0.329914i
$442$	5.00000			0.237826
$443$	9.00000	−	15.5885i	0.427603	−	0.740630i	−0.569057	−	0.822298i	$-0.692691\pi$
$443$	9.00000	−	15.5885i	0.427603	−	0.740630i	0.996660	+	0.0816684i	$0.0260248\pi$
$444$	1.00000	+	1.73205i	0.0474579	+	0.0821995i
$445$	−14.0000	−	24.2487i	−0.663664	−	1.14950i
$446$	5.50000	−	9.52628i	0.260433	−	0.451082i
$447$	8.00000			0.378387
$448$	−2.50000	+	0.866025i	−0.118114	+	0.0409159i
$449$	−8.00000			−0.377543			−0.188772	−	0.982021i	$-0.560451\pi$
$449$	−8.00000			−0.377543			−0.188772	+	0.982021i	$0.560451\pi$
$450$	−0.500000	+	0.866025i	−0.0235702	+	0.0408248i
$451$	−15.0000	−	25.9808i	−0.706322	−	1.22339i
$452$	−7.50000	−	12.9904i	−0.352770	−	0.611016i
$453$	−9.50000	+	16.4545i	−0.446349	+	0.773099i
$454$	−8.00000			−0.375459
$455$	1.00000	−	5.19615i	0.0468807	−	0.243599i
$456$	−1.00000			−0.0468293
$457$	8.00000	−	13.8564i	0.374224	−	0.648175i	−0.615986	−	0.787757i	$-0.711242\pi$
$457$	8.00000	−	13.8564i	0.374224	−	0.648175i	0.990211	+	0.139581i	$0.0445757\pi$
$458$	3.00000	+	5.19615i	0.140181	+	0.242800i
$459$	−2.50000	−	4.33013i	−0.116690	−	0.202113i
$460$		0			0
$461$	20.0000			0.931493			0.465746	−	0.884918i	$-0.345786\pi$
$461$	20.0000			0.931493			0.465746	+	0.884918i	$0.345786\pi$
$462$	−6.00000	−	5.19615i	−0.279145	−	0.241747i
$463$	8.00000			0.371792			0.185896	−	0.982569i	$-0.440481\pi$
$463$	8.00000			0.371792			0.185896	+	0.982569i	$0.440481\pi$
$464$	0.500000	−	0.866025i	0.0232119	−	0.0402042i
$465$	4.00000	+	6.92820i	0.185496	+	0.321288i
$466$	5.50000	+	9.52628i	0.254783	+	0.441296i
$467$	12.0000	−	20.7846i	0.555294	−	0.961797i	−0.442587	−	0.896726i	$-0.645939\pi$
$467$	12.0000	−	20.7846i	0.555294	−	0.961797i	0.997881	−	0.0650714i	$-0.0207275\pi$
$468$	−1.00000			−0.0462250
$469$	10.0000	+	8.66025i	0.461757	+	0.399893i
$470$	−2.00000			−0.0922531
$471$	−10.5000	+	18.1865i	−0.483814	+	0.837991i
$472$	1.50000	+	2.59808i	0.0690431	+	0.119586i
$473$	15.0000	+	25.9808i	0.689701	+	1.19460i
$474$	−3.00000	+	5.19615i	−0.137795	+	0.238667i
$475$	−1.00000			−0.0458831
$476$	2.50000	−	12.9904i	0.114587	−	0.595413i
$477$	−3.00000			−0.137361
$478$	10.5000	−	18.1865i	0.480259	−	0.831833i
$479$	16.5000	+	28.5788i	0.753904	+	1.30580i	0.945917	+	0.324408i	$0.105165\pi$
$479$	16.5000	+	28.5788i	0.753904	+	1.30580i	−0.192013	+	0.981392i	$0.561502\pi$
$480$	−1.00000	−	1.73205i	−0.0456435	−	0.0790569i
$481$	−1.00000	+	1.73205i	−0.0455961	+	0.0789747i
$482$	−4.00000			−0.182195
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	4.00000	−	6.92820i	0.181631	−	0.314594i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−5.50000	−	9.52628i	−0.249229	−	0.431677i	0.714083	−	0.700061i	$-0.246844\pi$
$487$	−5.50000	−	9.52628i	−0.249229	−	0.431677i	−0.963312	+	0.268384i	$0.913510\pi$
$488$	−2.50000	+	4.33013i	−0.113170	+	0.196016i
$489$	19.0000			0.859210
$490$	−13.0000	−	5.19615i	−0.587280	−	0.234738i
$491$	22.0000			0.992846			0.496423	−	0.868081i	$-0.334646\pi$
$491$	22.0000			0.992846			0.496423	+	0.868081i	$0.334646\pi$
$492$	−5.00000	+	8.66025i	−0.225417	+	0.390434i
$493$	2.50000	+	4.33013i	0.112594	+	0.195019i
$494$	−0.500000	−	0.866025i	−0.0224961	−	0.0389643i
$495$	3.00000	−	5.19615i	0.134840	−	0.233550i
$496$	4.00000			0.179605
$497$	2.50000	−	0.866025i	0.112140	−	0.0388465i
$498$	−16.0000			−0.716977
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	−0.361478	−	0.932381i	$-0.617728\pi$
$499$	14.0000	−	24.2487i	0.626726	−	1.08552i	0.988204	−	0.153141i	$-0.0489388\pi$
$500$	−6.00000	−	10.3923i	−0.268328	−	0.464758i
$501$	−10.5000	−	18.1865i	−0.469105	−	0.812514i
$502$	−9.00000	+	15.5885i	−0.401690	+	0.695747i
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$	−0.500000	+	2.59808i	−0.0222718	+	0.115728i
$505$	−4.00000			−0.177998
$506$		0			0
$507$	−0.500000	−	0.866025i	−0.0222058	−	0.0384615i
$508$		0			0
$509$	14.0000	−	24.2487i	0.620539	−	1.07481i	−0.368846	−	0.929490i	$-0.620247\pi$
$509$	14.0000	−	24.2487i	0.620539	−	1.07481i	0.989385	−	0.145315i	$-0.0464195\pi$
$510$	10.0000			0.442807
$511$	24.0000	+	20.7846i	1.06170	+	0.919457i
$512$	−1.00000			−0.0441942
$513$	−0.500000	+	0.866025i	−0.0220755	+	0.0382360i
$514$	3.00000	+	5.19615i	0.132324	+	0.229192i
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$	5.00000	−	8.66025i	0.220113	−	0.381246i
$517$	−3.00000			−0.131940
$518$	4.00000	+	3.46410i	0.175750	+	0.152204i
$519$	3.00000			0.131685
$520$	1.00000	−	1.73205i	0.0438529	−	0.0759555i
$521$	−21.0000	−	36.3731i	−0.920027	−	1.59353i	−0.799370	−	0.600839i	$-0.794833\pi$
$521$	−21.0000	−	36.3731i	−0.920027	−	1.59353i	−0.120656	−	0.992694i	$-0.538500\pi$
$522$	−0.500000	−	0.866025i	−0.0218844	−	0.0379049i
$523$	−3.00000	+	5.19615i	−0.131181	+	0.227212i	−0.924132	−	0.382073i	$-0.875210\pi$
$523$	−3.00000	+	5.19615i	−0.131181	+	0.227212i	0.792951	+	0.609285i	$0.208544\pi$
$524$	−4.00000			−0.174741
$525$	−0.500000	+	2.59808i	−0.0218218	+	0.113389i
$526$	6.00000			0.261612
$527$	−10.0000	+	17.3205i	−0.435607	+	0.754493i
$528$	−1.50000	−	2.59808i	−0.0652791	−	0.113067i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	3.00000	−	5.19615i	0.130312	−	0.225706i
$531$	3.00000			0.130189
$532$	−2.50000	+	0.866025i	−0.108389	+	0.0375470i
$533$	−10.0000			−0.433148
$534$	−7.00000	+	12.1244i	−0.302920	+	0.524672i
$535$	12.0000	+	20.7846i	0.518805	+	0.898597i
$536$	2.50000	+	4.33013i	0.107984	+	0.187033i
$537$	−1.00000	+	1.73205i	−0.0431532	+	0.0747435i
$538$	9.00000			0.388018
$539$	−19.5000	−	7.79423i	−0.839924	−	0.335721i
$540$	−2.00000			−0.0860663
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	−0.225617	−	0.974216i	$-0.572440\pi$
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	0.956504	−	0.291718i	$-0.0942267\pi$
$542$	5.50000	+	9.52628i	0.236245	+	0.409189i
$543$	−1.50000	−	2.59808i	−0.0643712	−	0.111494i
$544$	2.50000	−	4.33013i	0.107187	−	0.185653i
$545$	32.0000			1.37073
$546$	−2.50000	+	0.866025i	−0.106990	+	0.0370625i
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$	−9.00000	+	15.5885i	−0.384461	+	0.665906i
$549$	2.50000	+	4.33013i	0.106697	+	0.184805i
$550$	−1.50000	−	2.59808i	−0.0639602	−	0.110782i
$551$	0.500000	−	0.866025i	0.0213007	−	0.0368939i
$552$		0			0
$553$	−3.00000	+	15.5885i	−0.127573	+	0.662889i
$554$	27.0000			1.14712
$555$	−2.00000	+	3.46410i	−0.0848953	+	0.147043i
$556$	−1.00000	−	1.73205i	−0.0424094	−	0.0734553i
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	0.609912	−	0.792469i	$-0.291205\pi$
$557$	−9.00000	−	15.5885i	−0.381342	−	0.660504i	−0.991254	+	0.131965i	$0.957871\pi$
$558$	2.00000	−	3.46410i	0.0846668	−	0.146647i
$559$	10.0000			0.422955
$560$	−4.00000	−	3.46410i	−0.169031	−	0.146385i
$561$	15.0000			0.633300
$562$	8.00000	−	13.8564i	0.337460	−	0.584497i
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	−0.999978	−	0.00664037i	$-0.997886\pi$
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	0.494238	−	0.869326i	$-0.335447\pi$
$564$	0.500000	+	0.866025i	0.0210538	+	0.0364662i
$565$	15.0000	−	25.9808i	0.631055	−	1.09302i
$566$	−4.00000			−0.168133
$567$	2.00000	+	1.73205i	0.0839921	+	0.0727393i
$568$	1.00000			0.0419591
$569$	−9.50000	+	16.4545i	−0.398261	+	0.689808i	−0.993511	−	0.113732i	$-0.963719\pi$
$569$	−9.50000	+	16.4545i	−0.398261	+	0.689808i	0.595251	+	0.803540i	$0.297053\pi$
$570$	−1.00000	−	1.73205i	−0.0418854	−	0.0725476i
$571$	−18.0000	−	31.1769i	−0.753277	−	1.30471i	−0.946227	−	0.323505i	$-0.895139\pi$
$571$	−18.0000	−	31.1769i	−0.753277	−	1.30471i	0.192950	−	0.981209i	$-0.438194\pi$
$572$	1.50000	−	2.59808i	0.0627182	−	0.108631i
$573$	20.0000			0.835512
$574$	−5.00000	+	25.9808i	−0.208696	+	1.08442i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−19.0000	−	32.9090i	−0.790980	−	1.37002i	−0.925361	−	0.379088i	$-0.876238\pi$
$577$	−19.0000	−	32.9090i	−0.790980	−	1.37002i	0.134380	−	0.990930i	$-0.457096\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$	7.00000	−	12.1244i	0.290910	−	0.503871i
$580$	2.00000			0.0830455
$581$	−40.0000	+	13.8564i	−1.65948	+	0.574861i
$582$	−4.00000			−0.165805
$583$	4.50000	−	7.79423i	0.186371	−	0.322804i
$584$	6.00000	+	10.3923i	0.248282	+	0.430037i
$585$	−1.00000	−	1.73205i	−0.0413449	−	0.0716115i
$586$	−6.00000	+	10.3923i	−0.247858	+	0.429302i
$587$	31.0000			1.27951			0.639753	−	0.768580i	$-0.279036\pi$
$587$	31.0000			1.27951			0.639753	+	0.768580i	$0.279036\pi$
$588$	1.00000	+	6.92820i	0.0412393	+	0.285714i
$589$	4.00000			0.164817
$590$	−3.00000	+	5.19615i	−0.123508	+	0.213922i
$591$	12.0000	+	20.7846i	0.493614	+	0.854965i
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	−7.00000	+	12.1244i	−0.287456	+	0.497888i	−0.973202	−	0.229953i	$-0.926143\pi$
$593$	−7.00000	+	12.1244i	−0.287456	+	0.497888i	0.685746	+	0.727841i	$0.259476\pi$
$594$	−3.00000			−0.123091
$595$	25.0000	−	8.66025i	1.02490	−	0.355036i
$596$	8.00000			0.327693
$597$	10.0000	−	17.3205i	0.409273	−	0.708881i
$598$		0			0
$599$	19.0000	+	32.9090i	0.776319	+	1.34462i	0.934050	+	0.357142i	$0.116249\pi$
$599$	19.0000	+	32.9090i	0.776319	+	1.34462i	−0.157731	+	0.987482i	$0.550418\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	−19.0000			−0.775026			−0.387513	−	0.921864i	$-0.626666\pi$
$601$	−19.0000			−0.775026			−0.387513	+	0.921864i	$0.626666\pi$
$602$	5.00000	−	25.9808i	0.203785	−	1.05890i
$603$	5.00000			0.203616
$604$	−9.50000	+	16.4545i	−0.386550	+	0.669523i
$605$	−2.00000	−	3.46410i	−0.0813116	−	0.140836i
$606$	1.00000	+	1.73205i	0.0406222	+	0.0703598i
$607$	6.00000	−	10.3923i	0.243532	−	0.421811i	−0.718186	−	0.695852i	$-0.755027\pi$
$607$	6.00000	−	10.3923i	0.243532	−	0.421811i	0.961718	+	0.274041i	$0.0883604\pi$
$608$	−1.00000			−0.0405554
$609$	−2.00000	−	1.73205i	−0.0810441	−	0.0701862i
$610$	−10.0000			−0.404888
$611$	−0.500000	+	0.866025i	−0.0202278	+	0.0350356i
$612$	−2.50000	−	4.33013i	−0.101057	−	0.175035i
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	0.981129	−	0.193352i	$-0.0619359\pi$
$613$	8.00000	+	13.8564i	0.323117	+	0.559655i	−0.658012	+	0.753007i	$0.728603\pi$
$614$	−13.5000	+	23.3827i	−0.544816	+	0.943648i
$615$	−20.0000			−0.806478
$616$	−6.00000	−	5.19615i	−0.241747	−	0.209359i
$617$	34.0000			1.36879			0.684394	−	0.729112i	$-0.260067\pi$
$617$	34.0000			1.36879			0.684394	+	0.729112i	$0.260067\pi$
$618$	−1.00000	+	1.73205i	−0.0402259	+	0.0696733i
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	0.903416	−	0.428765i	$-0.141051\pi$
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	−0.823029	+	0.567999i	$0.807718\pi$
$620$	4.00000	+	6.92820i	0.160644	+	0.278243i
$621$		0			0
$622$	−14.0000			−0.561349
$623$	−7.00000	+	36.3731i	−0.280449	+	1.45726i
$624$	−1.00000			−0.0400320
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	17.0000	+	29.4449i	0.679457	+	1.17685i
$627$	−1.50000	−	2.59808i	−0.0599042	−	0.103757i
$628$	−10.5000	+	18.1865i	−0.418996	+	0.725722i
$629$	−10.0000			−0.398726
$630$	−5.00000	+	1.73205i	−0.199205	+	0.0690066i
$631$	48.0000			1.91085			0.955425	−	0.295234i	$-0.0953977\pi$
$631$	48.0000			1.91085			0.955425	+	0.295234i	$0.0953977\pi$
$632$	−3.00000	+	5.19615i	−0.119334	+	0.206692i
$633$	8.00000	+	13.8564i	0.317971	+	0.550743i
$634$	−3.00000	−	5.19615i	−0.119145	−	0.206366i
$635$		0			0
$636$	−3.00000			−0.118958
$637$	−5.50000	+	4.33013i	−0.217918	+	0.171566i
$638$	3.00000			0.118771
$639$	0.500000	−	0.866025i	0.0197797	−	0.0342594i
$640$	−1.00000	−	1.73205i	−0.0395285	−	0.0684653i
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	−0.993899	−	0.110291i	$-0.964822\pi$
$641$	−15.0000	−	25.9808i	−0.592464	−	1.02618i	0.401435	−	0.915888i	$-0.368512\pi$
$642$	6.00000	−	10.3923i	0.236801	−	0.410152i
$643$	−19.0000			−0.749287			−0.374643	−	0.927169i	$-0.622235\pi$
$643$	−19.0000			−0.749287			−0.374643	+	0.927169i	$0.622235\pi$
$644$		0			0
$645$	20.0000			0.787499
$646$	2.50000	−	4.33013i	0.0983612	−	0.170367i
$647$	19.0000	+	32.9090i	0.746967	+	1.29378i	0.949270	+	0.314462i	$0.101824\pi$
$647$	19.0000	+	32.9090i	0.746967	+	1.29378i	−0.202303	+	0.979323i	$0.564843\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−4.50000	+	7.79423i	−0.176640	+	0.305950i
$650$	−1.00000			−0.0392232
$651$	2.00000	−	10.3923i	0.0783862	−	0.407307i
$652$	19.0000			0.744097
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$	−8.00000	−	13.8564i	−0.312825	−	0.541828i
$655$	−4.00000	−	6.92820i	−0.156293	−	0.270707i
$656$	−5.00000	+	8.66025i	−0.195217	+	0.338126i
$657$	12.0000			0.468165
$658$	2.00000	+	1.73205i	0.0779681	+	0.0675224i
$659$	6.00000			0.233727			0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000			0.233727			0.116863	+	0.993148i	$0.462716\pi$
$660$	3.00000	−	5.19615i	0.116775	−	0.202260i
$661$	13.0000	+	22.5167i	0.505641	+	0.875797i	0.999979	+	0.00652642i	$0.00207744\pi$
$661$	13.0000	+	22.5167i	0.505641	+	0.875797i	−0.494337	+	0.869270i	$0.664589\pi$
$662$	−10.0000	−	17.3205i	−0.388661	−	0.673181i
$663$	2.50000	−	4.33013i	0.0970920	−	0.168168i
$664$	−16.0000			−0.620920
$665$	−4.00000	−	3.46410i	−0.155113	−	0.134332i
$666$	2.00000			0.0774984
$667$		0			0
$668$	−10.5000	−	18.1865i	−0.406257	−	0.703658i
$669$	−5.50000	−	9.52628i	−0.212642	−	0.368307i
$670$	−5.00000	+	8.66025i	−0.193167	+	0.334575i
$671$	−15.0000			−0.579069
$672$	−0.500000	+	2.59808i	−0.0192879	+	0.100223i
$673$	14.0000			0.539660			0.269830	−	0.962908i	$-0.413032\pi$
$673$	14.0000			0.539660			0.269830	+	0.962908i	$0.413032\pi$
$674$	−8.50000	+	14.7224i	−0.327408	+	0.567087i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	1.50000	−	2.59808i	0.0576497	−	0.0998522i	−0.835760	−	0.549095i	$-0.814973\pi$
$677$	1.50000	−	2.59808i	0.0576497	−	0.0998522i	0.893410	+	0.449242i	$0.148306\pi$
$678$	−15.0000			−0.576072
$679$	−10.0000	+	3.46410i	−0.383765	+	0.132940i
$680$	10.0000			0.383482
$681$	−4.00000	+	6.92820i	−0.153280	+	0.265489i
$682$	6.00000	+	10.3923i	0.229752	+	0.397942i
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	0.957685	−	0.287819i	$-0.0929302\pi$
$683$	6.00000	+	10.3923i	0.229584	+	0.397650i	−0.728101	+	0.685470i	$0.759597\pi$
$684$	−0.500000	+	0.866025i	−0.0191180	+	0.0331133i
$685$	−36.0000			−1.37549
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$	6.00000			0.228914
$688$	5.00000	−	8.66025i	0.190623	−	0.330169i
$689$	−1.50000	−	2.59808i	−0.0571454	−	0.0989788i
$690$		0			0
$691$	8.50000	−	14.7224i	0.323355	−	0.560068i	−0.657823	−	0.753173i	$-0.728522\pi$
$691$	8.50000	−	14.7224i	0.323355	−	0.560068i	0.981178	+	0.193105i	$0.0618558\pi$
$692$	3.00000			0.114043
$693$	−7.50000	+	2.59808i	−0.284901	+	0.0986928i
$694$	−2.00000			−0.0759190
$695$	2.00000	−	3.46410i	0.0758643	−	0.131401i
$696$	−0.500000	−	0.866025i	−0.0189525	−	0.0328266i
$697$	−25.0000	−	43.3013i	−0.946943	−	1.64015i
$698$	18.0000	−	31.1769i	0.681310	−	1.18006i
$699$	11.0000			0.416058
$700$	−0.500000	+	2.59808i	−0.0188982	+	0.0981981i
$701$	−50.0000			−1.88847			−0.944237	−	0.329267i	$-0.893198\pi$
$701$	−50.0000			−1.88847			−0.944237	+	0.329267i	$0.893198\pi$
$702$	−0.500000	+	0.866025i	−0.0188713	+	0.0326860i
$703$	1.00000	+	1.73205i	0.0377157	+	0.0653255i
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$	−1.00000	+	1.73205i	−0.0376622	+	0.0652328i
$706$	−14.0000			−0.526897
$707$	4.00000	+	3.46410i	0.150435	+	0.130281i
$708$	3.00000			0.112747
$709$	−10.0000	+	17.3205i	−0.375558	+	0.650485i	−0.990410	−	0.138157i	$-0.955882\pi$
$709$	−10.0000	+	17.3205i	−0.375558	+	0.650485i	0.614852	+	0.788642i	$0.289216\pi$
$710$	1.00000	+	1.73205i	0.0375293	+	0.0650027i
$711$	3.00000	+	5.19615i	0.112509	+	0.194871i
$712$	−7.00000	+	12.1244i	−0.262336	+	0.454379i
$713$		0			0
$714$	−10.0000	−	8.66025i	−0.374241	−	0.324102i
$715$	6.00000			0.224387
$716$	−1.00000	+	1.73205i	−0.0373718	+	0.0647298i
$717$	−10.5000	−	18.1865i	−0.392130	−	0.679189i
$718$		0			0
$719$	9.00000	−	15.5885i	0.335643	−	0.581351i	−0.647965	−	0.761670i	$-0.724380\pi$
$719$	9.00000	−	15.5885i	0.335643	−	0.581351i	0.983608	+	0.180319i	$0.0577130\pi$
$720$	−2.00000			−0.0745356
$721$	−1.00000	+	5.19615i	−0.0372419	+	0.193515i
$722$	18.0000			0.669891
$723$	−2.00000	+	3.46410i	−0.0743808	+	0.128831i
$724$	−1.50000	−	2.59808i	−0.0557471	−	0.0965567i
$725$	−0.500000	−	0.866025i	−0.0185695	−	0.0321634i
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$	12.0000			0.445055			0.222528	−	0.974926i	$-0.428569\pi$
$727$	12.0000			0.445055			0.222528	+	0.974926i	$0.428569\pi$
$728$	−2.50000	+	0.866025i	−0.0926562	+	0.0320970i
$729$	1.00000			0.0370370
$730$	−12.0000	+	20.7846i	−0.444140	+	0.769273i
$731$	25.0000	+	43.3013i	0.924658	+	1.60156i
$732$	2.50000	+	4.33013i	0.0924027	+	0.160046i
$733$	20.0000	−	34.6410i	0.738717	−	1.27950i	−0.214356	−	0.976756i	$-0.568765\pi$
$733$	20.0000	−	34.6410i	0.738717	−	1.27950i	0.953073	−	0.302740i	$-0.0979013\pi$
$734$	−26.0000			−0.959678
$735$	−11.0000	+	8.66025i	−0.405741	+	0.319438i
$736$		0			0
$737$	−7.50000	+	12.9904i	−0.276266	+	0.478507i
$738$	5.00000	+	8.66025i	0.184053	+	0.318788i
$739$	−20.0000	−	34.6410i	−0.735712	−	1.27429i	−0.954410	−	0.298498i	$-0.903514\pi$
$739$	−20.0000	−	34.6410i	−0.735712	−	1.27429i	0.218698	−	0.975793i	$-0.429819\pi$
$740$	−2.00000	+	3.46410i	−0.0735215	+	0.127343i
$741$	−1.00000			−0.0367359
$742$	−7.50000	+	2.59808i	−0.275334	+	0.0953784i
$743$	−3.00000			−0.110059			−0.0550297	−	0.998485i	$-0.517525\pi$
$743$	−3.00000			−0.110059			−0.0550297	+	0.998485i	$0.517525\pi$
$744$	2.00000	−	3.46410i	0.0733236	−	0.127000i
$745$	8.00000	+	13.8564i	0.293097	+	0.507659i
$746$	6.50000	+	11.2583i	0.237982	+	0.412197i
$747$	−8.00000	+	13.8564i	−0.292705	+	0.506979i
$748$	15.0000			0.548454
$749$	6.00000	−	31.1769i	0.219235	−	1.13918i
$750$	−12.0000			−0.438178
$751$	6.00000	−	10.3923i	0.218943	−	0.379221i	−0.735542	−	0.677479i	$-0.763072\pi$
$751$	6.00000	−	10.3923i	0.218943	−	0.379221i	0.954485	+	0.298259i	$0.0964058\pi$
$752$	0.500000	+	0.866025i	0.0182331	+	0.0315807i
$753$	9.00000	+	15.5885i	0.327978	+	0.568075i
$754$	0.500000	−	0.866025i	0.0182089	−	0.0315388i
$755$	−38.0000			−1.38296
$756$	2.00000	+	1.73205i	0.0727393	+	0.0629941i
$757$	−37.0000			−1.34479			−0.672394	−	0.740193i	$-0.734734\pi$
$757$	−37.0000			−1.34479			−0.672394	+	0.740193i	$0.734734\pi$
$758$	14.0000	−	24.2487i	0.508503	−	0.880753i
$759$		0			0
$760$	−1.00000	−	1.73205i	−0.0362738	−	0.0628281i
$761$	−6.00000	+	10.3923i	−0.217500	+	0.376721i	−0.954043	−	0.299670i	$-0.903123\pi$
$761$	−6.00000	+	10.3923i	−0.217500	+	0.376721i	0.736543	+	0.676391i	$0.236457\pi$
$762$		0			0
$763$	−32.0000	−	27.7128i	−1.15848	−	1.00327i
$764$	20.0000			0.723575
$765$	5.00000	−	8.66025i	0.180775	−	0.313112i
$766$	−16.0000	−	27.7128i	−0.578103	−	1.00130i
$767$	1.50000	+	2.59808i	0.0541619	+	0.0938111i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−44.0000			−1.58668			−0.793340	−	0.608778i	$-0.791660\pi$
$769$	−44.0000			−1.58668			−0.793340	+	0.608778i	$0.791660\pi$
$770$	3.00000	−	15.5885i	0.108112	−	0.561769i
$771$	6.00000			0.216085
$772$	7.00000	−	12.1244i	0.251936	−	0.436365i
$773$	−13.0000	−	22.5167i	−0.467578	−	0.809868i	0.531736	−	0.846910i	$-0.321540\pi$
$773$	−13.0000	−	22.5167i	−0.467578	−	0.809868i	−0.999314	+	0.0370420i	$0.988206\pi$
$774$	−5.00000	−	8.66025i	−0.179721	−	0.311286i
$775$	2.00000	−	3.46410i	0.0718421	−	0.124434i
$776$	−4.00000			−0.143592
$777$	5.00000	−	1.73205i	0.179374	−	0.0621370i
$778$	−9.00000			−0.322666
$779$	−5.00000	+	8.66025i	−0.179144	+	0.310286i
$780$	−1.00000	−	1.73205i	−0.0358057	−	0.0620174i
$781$	1.50000	+	2.59808i	0.0536742	+	0.0929665i
$782$		0			0
$783$	−1.00000			−0.0357371
$784$	1.00000	+	6.92820i	0.0357143	+	0.247436i
$785$	−42.0000			−1.49904
$786$	−2.00000	+	3.46410i	−0.0713376	+	0.123560i
$787$	2.50000	+	4.33013i	0.0891154	+	0.154352i	0.907137	−	0.420834i	$-0.138263\pi$
$787$	2.50000	+	4.33013i	0.0891154	+	0.154352i	−0.818022	+	0.575187i	$0.804929\pi$
$788$	12.0000	+	20.7846i	0.427482	+	0.740421i
$789$	3.00000	−	5.19615i	0.106803	−	0.184988i
$790$	−12.0000			−0.426941
$791$	−37.5000	+	12.9904i	−1.33335	+	0.461885i
$792$	−3.00000			−0.106600
$793$	−2.50000	+	4.33013i	−0.0887776	+	0.153767i
$794$	18.0000	+	31.1769i	0.638796	+	1.10643i
$795$	−3.00000	−	5.19615i	−0.106399	−	0.184289i
$796$	10.0000	−	17.3205i	0.354441	−	0.613909i
$797$	2.00000			0.0708436			0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000			0.0708436			0.0354218	+	0.999372i	$0.488723\pi$
$798$	−0.500000	+	2.59808i	−0.0176998	+	0.0919709i
$799$	−5.00000			−0.176887
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	7.00000	+	12.1244i	0.247333	+	0.428393i
$802$	−18.0000	−	31.1769i	−0.635602	−	1.10090i
$803$	−18.0000	+	31.1769i	−0.635206	+	1.10021i
$804$	5.00000			0.176336
$805$		0			0
$806$	4.00000			0.140894
$807$	4.50000	−	7.79423i	0.158408	−	0.274370i
$808$	1.00000	+	1.73205i	0.0351799	+	0.0609333i
$809$	2.50000	+	4.33013i	0.0878953	+	0.152239i	0.906621	−	0.421945i	$-0.138653\pi$
$809$	2.50000	+	4.33013i	0.0878953	+	0.152239i	−0.818726	+	0.574184i	$0.805319\pi$
$810$	−1.00000	+	1.73205i	−0.0351364	+	0.0608581i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	−2.00000	−	1.73205i	−0.0701862	−	0.0607831i
$813$	11.0000			0.385787
$814$	−3.00000	+	5.19615i	−0.105150	+	0.182125i
$815$	19.0000	+	32.9090i	0.665541	+	1.15275i
$816$	−2.50000	−	4.33013i	−0.0875175	−	0.151585i
$817$	5.00000	−	8.66025i	0.174928	−	0.302984i
$818$	30.0000			1.04893
$819$	−0.500000	+	2.59808i	−0.0174714	+	0.0907841i
$820$	−20.0000			−0.698430
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	0.222731	+	0.974880i	$0.428503\pi$
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	−0.955636	+	0.294549i	$0.904831\pi$
$822$	9.00000	+	15.5885i	0.313911	+	0.543710i
$823$	15.0000	+	25.9808i	0.522867	+	0.905632i	0.999646	+	0.0266091i	$0.00847095\pi$
$823$	15.0000	+	25.9808i	0.522867	+	0.905632i	−0.476779	+	0.879023i	$0.658196\pi$
$824$	−1.00000	+	1.73205i	−0.0348367	+	0.0603388i
$825$	−3.00000			−0.104447
$826$	7.50000	−	2.59808i	0.260958	−	0.0903986i
$827$	−35.0000			−1.21707			−0.608535	−	0.793527i	$-0.708242\pi$
$827$	−35.0000			−1.21707			−0.608535	+	0.793527i	$0.708242\pi$
$828$		0			0
$829$	9.50000	+	16.4545i	0.329949	+	0.571488i	0.982501	−	0.186256i	$-0.0596352\pi$
$829$	9.50000	+	16.4545i	0.329949	+	0.571488i	−0.652553	+	0.757743i	$0.726302\pi$
$830$	−16.0000	−	27.7128i	−0.555368	−	0.961926i
$831$	13.5000	−	23.3827i	0.468310	−	0.811136i
$832$	−1.00000			−0.0346688
$833$	−32.5000	−	12.9904i	−1.12606	−	0.450090i
$834$	−2.00000			−0.0692543
$835$	21.0000	−	36.3731i	0.726735	−	1.25874i
$836$	−1.50000	−	2.59808i	−0.0518786	−	0.0898563i
$837$	−2.00000	−	3.46410i	−0.0691301	−	0.119737i
$838$	5.00000	−	8.66025i	0.172722	−	0.299164i
$839$	−9.00000			−0.310715			−0.155357	−	0.987858i	$-0.549653\pi$
$839$	−9.00000			−0.310715			−0.155357	+	0.987858i	$0.549653\pi$
$840$	−5.00000	+	1.73205i	−0.172516	+	0.0597614i
$841$	−28.0000			−0.965517
$842$	4.00000	−	6.92820i	0.137849	−	0.238762i
$843$	−8.00000	−	13.8564i	−0.275535	−	0.477240i
$844$	8.00000	+	13.8564i	0.275371	+	0.476957i
$845$	1.00000	−	1.73205i	0.0344010	−	0.0595844i
$846$	1.00000			0.0343807
$847$	−1.00000	+	5.19615i	−0.0343604	+	0.178542i
$848$	−3.00000			−0.103020
$849$	−2.00000	+	3.46410i	−0.0686398	+	0.118888i
$850$	−2.50000	−	4.33013i	−0.0857493	−	0.148522i
$851$		0			0
$852$	0.500000	−	0.866025i	0.0171297	−	0.0296695i
$853$	−40.0000			−1.36957			−0.684787	−	0.728743i	$-0.740105\pi$
$853$	−40.0000			−1.36957			−0.684787	+	0.728743i	$0.740105\pi$
$854$	10.0000	+	8.66025i	0.342193	+	0.296348i
$855$	−2.00000			−0.0683986
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	0.839268	−	0.543718i	$-0.182984\pi$
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	−0.890507	+	0.454969i	$0.849650\pi$
$858$	−1.50000	−	2.59808i	−0.0512092	−	0.0886969i
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	−0.291858	−	0.956462i	$-0.594273\pi$
$859$	20.0000	−	34.6410i	0.682391	−	1.18194i	0.974249	−	0.225475i	$-0.0723932\pi$
$860$	20.0000			0.681994
$861$	20.0000	+	17.3205i	0.681598	+	0.590281i
$862$	8.00000			0.272481
$863$	22.0000	−	38.1051i	0.748889	−	1.29711i	−0.199467	−	0.979905i	$-0.563921\pi$
$863$	22.0000	−	38.1051i	0.748889	−	1.29711i	0.948356	−	0.317209i	$-0.102746\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	3.00000	+	5.19615i	0.102003	+	0.176674i
$866$	−9.50000	+	16.4545i	−0.322823	+	0.559146i
$867$	8.00000			0.271694
$868$	2.00000	−	10.3923i	0.0678844	−	0.352738i
$869$	−18.0000			−0.610608
$870$	1.00000	−	1.73205i	0.0339032	−	0.0587220i
$871$	2.50000	+	4.33013i	0.0847093	+	0.146721i
$872$	−8.00000	−	13.8564i	−0.270914	−	0.469237i
$873$	−2.00000	+	3.46410i	−0.0676897	+	0.117242i
$874$		0			0
$875$	−30.0000	+	10.3923i	−1.01419	+	0.351324i
$876$	12.0000			0.405442
$877$	−11.0000	+	19.0526i	−0.371444	+	0.643359i	−0.989788	−	0.142548i	$-0.954470\pi$
$877$	−11.0000	+	19.0526i	−0.371444	+	0.643359i	0.618344	+	0.785907i	$0.287804\pi$
$878$	20.0000	+	34.6410i	0.674967	+	1.16908i
$879$	6.00000	+	10.3923i	0.202375	+	0.350524i
$880$	3.00000	−	5.19615i	0.101130	−	0.175162i
$881$	−26.0000			−0.875962			−0.437981	−	0.898984i	$-0.644306\pi$
$881$	−26.0000			−0.875962			−0.437981	+	0.898984i	$0.644306\pi$
$882$	6.50000	+	2.59808i	0.218866	+	0.0874818i
$883$	−38.0000			−1.27880			−0.639401	−	0.768874i	$-0.720818\pi$
$883$	−38.0000			−1.27880			−0.639401	+	0.768874i	$0.720818\pi$
$884$	2.50000	−	4.33013i	0.0840841	−	0.145638i
$885$	3.00000	+	5.19615i	0.100844	+	0.174667i
$886$	−9.00000	−	15.5885i	−0.302361	−	0.523704i
$887$	7.00000	−	12.1244i	0.235037	−	0.407096i	−0.724246	−	0.689541i	$-0.757812\pi$
$887$	7.00000	−	12.1244i	0.235037	−	0.407096i	0.959283	+	0.282445i	$0.0911455\pi$
$888$	2.00000			0.0671156
$889$		0			0
$890$	−28.0000			−0.938562
$891$	−1.50000	+	2.59808i	−0.0502519	+	0.0870388i
$892$	−5.50000	−	9.52628i	−0.184154	−	0.318963i
$893$	0.500000	+	0.866025i	0.0167319	+	0.0289804i
$894$	4.00000	−	6.92820i	0.133780	−	0.231714i
$895$	−4.00000			−0.133705
$896$	−0.500000	+	2.59808i	−0.0167038	+	0.0867956i
$897$		0			0
$898$	−4.00000	+	6.92820i	−0.133482	+	0.231197i
$899$	2.00000	+	3.46410i	0.0667037	+	0.115534i
$900$	0.500000	+	0.866025i	0.0166667	+	0.0288675i
$901$	7.50000	−	12.9904i	0.249861	−	0.432772i
$902$	−30.0000			−0.998891
$903$	−20.0000	−	17.3205i	−0.665558	−	0.576390i
$904$	−15.0000			−0.498893
$905$	3.00000	−	5.19615i	0.0997234	−	0.172726i
$906$	9.50000	+	16.4545i	0.315616	+	0.546664i
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	0.534333	−	0.845274i	$-0.320563\pi$
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	−0.999195	+	0.0401089i	$0.987230\pi$
$908$	−4.00000	+	6.92820i	−0.132745	+	0.229920i
$909$	2.00000			0.0663358
$910$	−4.00000	−	3.46410i	−0.132599	−	0.114834i
$911$	26.0000			0.861418			0.430709	−	0.902491i	$-0.358263\pi$
$911$	26.0000			0.861418			0.430709	+	0.902491i	$0.358263\pi$
$912$	−0.500000	+	0.866025i	−0.0165567	+	0.0286770i
$913$	−24.0000	−	41.5692i	−0.794284	−	1.37574i
$914$	−8.00000	−	13.8564i	−0.264616	−	0.458329i
$915$	−5.00000	+	8.66025i	−0.165295	+	0.286299i
$916$	6.00000			0.198246
$917$	−2.00000	+	10.3923i	−0.0660458	+	0.343184i
$918$	−5.00000			−0.165025
$919$	1.00000	−	1.73205i	0.0329870	−	0.0571351i	−0.849061	−	0.528295i	$-0.822831\pi$
$919$	1.00000	−	1.73205i	0.0329870	−	0.0571351i	0.882048	+	0.471160i	$0.156165\pi$
$920$		0			0
$921$	13.5000	+	23.3827i	0.444840	+	0.770486i
$922$	10.0000	−	17.3205i	0.329332	−	0.570421i
$923$	1.00000			0.0329154
$924$	−7.50000	+	2.59808i	−0.246732	+	0.0854704i
$925$	2.00000			0.0657596
$926$	4.00000	−	6.92820i	0.131448	−	0.227675i
$927$	1.00000	+	1.73205i	0.0328443	+	0.0568880i
$928$	−0.500000	−	0.866025i	−0.0164133	−	0.0284287i
$929$	23.0000	−	39.8372i	0.754606	−	1.30702i	−0.190965	−	0.981597i	$-0.561162\pi$
$929$	23.0000	−	39.8372i	0.754606	−	1.30702i	0.945570	−	0.325418i	$-0.105505\pi$
$930$	8.00000			0.262330
$931$	1.00000	+	6.92820i	0.0327737	+	0.227063i
$932$	11.0000			0.360317
$933$	−7.00000	+	12.1244i	−0.229170	+	0.396934i
$934$	−12.0000	−	20.7846i	−0.392652	−	0.680093i
$935$	15.0000	+	25.9808i	0.490552	+	0.849662i
$936$	−0.500000	+	0.866025i	−0.0163430	+	0.0283069i
$937$	−5.00000			−0.163343			−0.0816714	−	0.996659i	$-0.526026\pi$
$937$	−5.00000			−0.163343			−0.0816714	+	0.996659i	$0.526026\pi$
$938$	12.5000	−	4.33013i	0.408139	−	0.141384i
$939$	34.0000			1.10955
$940$	−1.00000	+	1.73205i	−0.0326164	+	0.0564933i
$941$	12.0000	+	20.7846i	0.391189	+	0.677559i	0.992607	−	0.121376i	$-0.0387306\pi$
$941$	12.0000	+	20.7846i	0.391189	+	0.677559i	−0.601418	+	0.798935i	$0.705397\pi$
$942$	10.5000	+	18.1865i	0.342108	+	0.592549i
$943$		0			0
$944$	3.00000			0.0976417
$945$	−1.00000	+	5.19615i	−0.0325300	+	0.169031i
$946$	30.0000			0.975384
$947$	12.5000	−	21.6506i	0.406195	−	0.703551i	−0.588264	−	0.808669i	$-0.700189\pi$
$947$	12.5000	−	21.6506i	0.406195	−	0.703551i	0.994460	+	0.105118i	$0.0335219\pi$
$948$	3.00000	+	5.19615i	0.0974355	+	0.168763i
$949$	6.00000	+	10.3923i	0.194768	+	0.337348i
$950$	−0.500000	+	0.866025i	−0.0162221	+	0.0280976i
$951$	−6.00000			−0.194563
$952$	−10.0000	−	8.66025i	−0.324102	−	0.280680i
$953$	19.0000			0.615470			0.307735	−	0.951472i	$-0.400429\pi$
$953$	19.0000			0.615470			0.307735	+	0.951472i	$0.400429\pi$
$954$	−1.50000	+	2.59808i	−0.0485643	+	0.0841158i
$955$	20.0000	+	34.6410i	0.647185	+	1.12096i
$956$	−10.5000	−	18.1865i	−0.339594	−	0.588195i
$957$	1.50000	−	2.59808i	0.0484881	−	0.0839839i
$958$	33.0000			1.06618
$959$	36.0000	+	31.1769i	1.16250	+	1.00676i
$960$	−2.00000			−0.0645497
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$	1.00000	+	1.73205i	0.0322413	+	0.0558436i
$963$	−6.00000	−	10.3923i	−0.193347	−	0.334887i
$964$	−2.00000	+	3.46410i	−0.0644157	+	0.111571i
$965$	28.0000			0.901352
$966$		0			0
$967$	−31.0000			−0.996893			−0.498446	−	0.866921i	$-0.666096\pi$
$967$	−31.0000			−0.996893			−0.498446	+	0.866921i	$0.666096\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$	−2.50000	−	4.33013i	−0.0803116	−	0.139104i
$970$	−4.00000	−	6.92820i	−0.128432	−	0.222451i
$971$	7.00000	−	12.1244i	0.224641	−	0.389089i	−0.731571	−	0.681765i	$-0.761212\pi$
$971$	7.00000	−	12.1244i	0.224641	−	0.389089i	0.956212	+	0.292676i	$0.0945458\pi$
$972$	1.00000			0.0320750
$973$	−5.00000	+	1.73205i	−0.160293	+	0.0555270i
$974$	−11.0000			−0.352463
$975$	−0.500000	+	0.866025i	−0.0160128	+	0.0277350i
$976$	2.50000	+	4.33013i	0.0800230	+	0.138604i
$977$	−31.0000	−	53.6936i	−0.991778	−	1.71781i	−0.606715	−	0.794919i	$-0.707513\pi$
$977$	−31.0000	−	53.6936i	−0.991778	−	1.71781i	−0.385063	−	0.922890i	$-0.625820\pi$
$978$	9.50000	−	16.4545i	0.303777	−	0.526156i
$979$	−42.0000			−1.34233
$980$	−11.0000	+	8.66025i	−0.351382	+	0.276642i
$981$	−16.0000			−0.510841
$982$	11.0000	−	19.0526i	0.351024	−	0.607992i
$983$	29.5000	+	51.0955i	0.940904	+	1.62969i	0.763752	+	0.645510i	$0.223355\pi$
$983$	29.5000	+	51.0955i	0.940904	+	1.62969i	0.177152	+	0.984184i	$0.443312\pi$
$984$	5.00000	+	8.66025i	0.159394	+	0.276079i
$985$	−24.0000	+	41.5692i	−0.764704	+	1.32451i
$986$	5.00000			0.159232
$987$	2.50000	−	0.866025i	0.0795759	−	0.0275659i
$988$	−1.00000			−0.0318142
$989$		0			0
$990$	−3.00000	−	5.19615i	−0.0953463	−	0.165145i
$991$	24.0000	+	41.5692i	0.762385	+	1.32049i	0.941618	+	0.336683i	$0.109305\pi$
$991$	24.0000	+	41.5692i	0.762385	+	1.32049i	−0.179233	+	0.983807i	$0.557362\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$	−20.0000			−0.634681
$994$	0.500000	−	2.59808i	0.0158590	−	0.0824060i
$995$	40.0000			1.26809
$996$	−8.00000	+	13.8564i	−0.253490	+	0.439057i
$997$	−9.50000	−	16.4545i	−0.300868	−	0.521119i	0.675465	−	0.737392i	$-0.263943\pi$
$997$	−9.50000	−	16.4545i	−0.300868	−	0.521119i	−0.976333	+	0.216274i	$0.930610\pi$
$998$	−14.0000	−	24.2487i	−0.443162	−	0.767580i
$999$	1.00000	−	1.73205i	0.0316386	−	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.i.e.79.1	✓	2
3.2	odd	2		1638.2.j.a.1171.1		2
7.2	even	3		3822.2.a.k.1.1		1
7.4	even	3	inner	546.2.i.e.235.1	yes	2
7.5	odd	6		3822.2.a.i.1.1		1
21.11	odd	6		1638.2.j.a.235.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.i.e.79.1	✓	2	1.1	even	1	trivial
546.2.i.e.235.1	yes	2	7.4	even	3	inner
1638.2.j.a.235.1		2	21.11	odd	6
1638.2.j.a.1171.1		2	3.2	odd	2
3822.2.a.i.1.1		1	7.5	odd	6
3822.2.a.k.1.1		1	7.2	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.00000 - 1.73205i) q^{5} -1.00000 q^{6} +(-2.50000 + 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.00000 - 1.73205i) q^{10} +(-1.50000 - 2.59808i) q^{11} +(-0.500000 + 0.866025i) q^{12} -1.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} -2.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} -2.00000 q^{20} +(2.00000 + 1.73205i) q^{21} -3.00000 q^{22} +(0.500000 + 0.866025i) q^{24} +(0.500000 + 0.866025i) q^{25} +(-0.500000 + 0.866025i) q^{26} +1.00000 q^{27} +(2.00000 + 1.73205i) q^{28} -1.00000 q^{29} +(-1.00000 + 1.73205i) q^{30} +(-2.00000 - 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} -5.00000 q^{34} +(-1.00000 + 5.19615i) q^{35} +1.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(0.500000 + 0.866025i) q^{38} +(0.500000 + 0.866025i) q^{39} +(-1.00000 + 1.73205i) q^{40} +10.0000 q^{41} +(2.50000 - 0.866025i) q^{42} -10.0000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(1.00000 + 1.73205i) q^{45} +(0.500000 - 0.866025i) q^{47} +1.00000 q^{48} +(5.50000 - 4.33013i) q^{49} +1.00000 q^{50} +(-2.50000 + 4.33013i) q^{51} +(0.500000 + 0.866025i) q^{52} +(1.50000 + 2.59808i) q^{53} +(0.500000 - 0.866025i) q^{54} -6.00000 q^{55} +(2.50000 - 0.866025i) q^{56} +1.00000 q^{57} +(-0.500000 + 0.866025i) q^{58} +(-1.50000 - 2.59808i) q^{59} +(1.00000 + 1.73205i) q^{60} +(2.50000 - 4.33013i) q^{61} -4.00000 q^{62} +(0.500000 - 2.59808i) q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{65} +(1.50000 + 2.59808i) q^{66} +(-2.50000 - 4.33013i) q^{67} +(-2.50000 + 4.33013i) q^{68} +(4.00000 + 3.46410i) q^{70} -1.00000 q^{71} +(0.500000 - 0.866025i) q^{72} +(-6.00000 - 10.3923i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(0.500000 - 0.866025i) q^{75} +1.00000 q^{76} +(6.00000 + 5.19615i) q^{77} +1.00000 q^{78} +(3.00000 - 5.19615i) q^{79} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(5.00000 - 8.66025i) q^{82} +16.0000 q^{83} +(0.500000 - 2.59808i) q^{84} -10.0000 q^{85} +(-5.00000 + 8.66025i) q^{86} +(0.500000 + 0.866025i) q^{87} +(1.50000 + 2.59808i) q^{88} +(7.00000 - 12.1244i) q^{89} +2.00000 q^{90} +(2.50000 - 0.866025i) q^{91} +(-2.00000 + 3.46410i) q^{93} +(-0.500000 - 0.866025i) q^{94} +(1.00000 + 1.73205i) q^{95} +(0.500000 - 0.866025i) q^{96} +4.00000 q^{97} +(-1.00000 - 6.92820i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} + 2 q^{5} - 2 q^{6} - 5 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 + 2 * q^5 - 2 * q^6 - 5 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} + 2 q^{5} - 2 q^{6} - 5 q^{7} - 2 q^{8} - q^{9} - 2 q^{10} - 3 q^{11} - q^{12} - 2 q^{13} - q^{14} - 4 q^{15} - q^{16} - 5 q^{17} + q^{18} - q^{19} - 4 q^{20} + 4 q^{21} - 6 q^{22} + q^{24} + q^{25} - q^{26} + 2 q^{27} + 4 q^{28} - 2 q^{29} - 2 q^{30} - 4 q^{31} + q^{32} - 3 q^{33} - 10 q^{34} - 2 q^{35} + 2 q^{36} + 2 q^{37} + q^{38} + q^{39} - 2 q^{40} + 20 q^{41} + 5 q^{42} - 20 q^{43} - 3 q^{44} + 2 q^{45} + q^{47} + 2 q^{48} + 11 q^{49} + 2 q^{50} - 5 q^{51} + q^{52} + 3 q^{53} + q^{54} - 12 q^{55} + 5 q^{56} + 2 q^{57} - q^{58} - 3 q^{59} + 2 q^{60} + 5 q^{61} - 8 q^{62} + q^{63} + 2 q^{64} - 2 q^{65} + 3 q^{66} - 5 q^{67} - 5 q^{68} + 8 q^{70} - 2 q^{71} + q^{72} - 12 q^{73} - 2 q^{74} + q^{75} + 2 q^{76} + 12 q^{77} + 2 q^{78} + 6 q^{79} + 2 q^{80} - q^{81} + 10 q^{82} + 32 q^{83} + q^{84} - 20 q^{85} - 10 q^{86} + q^{87} + 3 q^{88} + 14 q^{89} + 4 q^{90} + 5 q^{91} - 4 q^{93} - q^{94} + 2 q^{95} + q^{96} + 8 q^{97} - 2 q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 + 2 * q^5 - 2 * q^6 - 5 * q^7 - 2 * q^8 - q^9 - 2 * q^10 - 3 * q^11 - q^12 - 2 * q^13 - q^14 - 4 * q^15 - q^16 - 5 * q^17 + q^18 - q^19 - 4 * q^20 + 4 * q^21 - 6 * q^22 + q^24 + q^25 - q^26 + 2 * q^27 + 4 * q^28 - 2 * q^29 - 2 * q^30 - 4 * q^31 + q^32 - 3 * q^33 - 10 * q^34 - 2 * q^35 + 2 * q^36 + 2 * q^37 + q^38 + q^39 - 2 * q^40 + 20 * q^41 + 5 * q^42 - 20 * q^43 - 3 * q^44 + 2 * q^45 + q^47 + 2 * q^48 + 11 * q^49 + 2 * q^50 - 5 * q^51 + q^52 + 3 * q^53 + q^54 - 12 * q^55 + 5 * q^56 + 2 * q^57 - q^58 - 3 * q^59 + 2 * q^60 + 5 * q^61 - 8 * q^62 + q^63 + 2 * q^64 - 2 * q^65 + 3 * q^66 - 5 * q^67 - 5 * q^68 + 8 * q^70 - 2 * q^71 + q^72 - 12 * q^73 - 2 * q^74 + q^75 + 2 * q^76 + 12 * q^77 + 2 * q^78 + 6 * q^79 + 2 * q^80 - q^81 + 10 * q^82 + 32 * q^83 + q^84 - 20 * q^85 - 10 * q^86 + q^87 + 3 * q^88 + 14 * q^89 + 4 * q^90 + 5 * q^91 - 4 * q^93 - q^94 + 2 * q^95 + q^96 + 8 * q^97 - 2 * q^98 + 6 * q^99

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