LMFDB - Embedded newform 507.2.j.d.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(316,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("507.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.j (of order $6$, degree $2$, not 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			361.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	507.361
Dual form			507.2.j.d.316.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} -3.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} -3.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.73205 + 1.00000i) q^{11} -1.00000 q^{12} +2.00000 q^{14} +(-0.866025 + 0.500000i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.50000 + 6.06218i) q^{17} -1.00000i q^{18} +(-5.19615 - 3.00000i) q^{19} +(-0.866025 - 0.500000i) q^{20} -2.00000i q^{21} +(1.00000 - 1.73205i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(2.59808 - 1.50000i) q^{24} +4.00000 q^{25} -1.00000 q^{27} +(1.73205 - 1.00000i) q^{28} +(0.500000 + 0.866025i) q^{29} +(0.500000 - 0.866025i) q^{30} -4.00000i q^{31} +(4.33013 + 2.50000i) q^{32} +(-1.73205 - 1.00000i) q^{33} -7.00000i q^{34} +(1.00000 - 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(0.866025 - 0.500000i) q^{37} +6.00000 q^{38} +3.00000 q^{40} +(-7.79423 + 4.50000i) q^{41} +(1.00000 + 1.73205i) q^{42} +(3.00000 - 5.19615i) q^{43} -2.00000i q^{44} +(-0.866025 - 0.500000i) q^{45} +(5.19615 + 3.00000i) q^{46} +6.00000i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(-3.46410 + 2.00000i) q^{50} -7.00000 q^{51} -9.00000 q^{53} +(0.866025 - 0.500000i) q^{54} +(-1.00000 - 1.73205i) q^{55} +(-3.00000 + 5.19615i) q^{56} -6.00000i q^{57} +(-0.866025 - 0.500000i) q^{58} -1.00000i q^{60} +(-0.500000 + 0.866025i) q^{61} +(2.00000 + 3.46410i) q^{62} +(1.73205 - 1.00000i) q^{63} -7.00000 q^{64} +2.00000 q^{66} +(1.73205 - 1.00000i) q^{67} +(-3.50000 - 6.06218i) q^{68} +(3.00000 - 5.19615i) q^{69} +2.00000i q^{70} +(5.19615 + 3.00000i) q^{71} +(2.59808 + 1.50000i) q^{72} +11.0000i q^{73} +(-0.500000 + 0.866025i) q^{74} +(2.00000 + 3.46410i) q^{75} +(5.19615 - 3.00000i) q^{76} +4.00000 q^{77} -4.00000 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} +14.0000i q^{83} +(1.73205 + 1.00000i) q^{84} +(-6.06218 - 3.50000i) q^{85} +6.00000i q^{86} +(-0.500000 + 0.866025i) q^{87} +(3.00000 + 5.19615i) q^{88} +(-12.1244 + 7.00000i) q^{89} +1.00000 q^{90} +6.00000 q^{92} +(3.46410 - 2.00000i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(3.00000 - 5.19615i) q^{95} +5.00000i q^{96} +(-1.73205 - 1.00000i) q^{97} +(2.59808 + 1.50000i) q^{98} -2.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} - 2 q^{4} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 - 2 * q^4 - 2 * q^9	$ 4 q + 2 q^{3} - 2 q^{4} - 2 q^{9} - 2 q^{10} - 4 q^{12} + 8 q^{14} + 2 q^{16} - 14 q^{17} + 4 q^{22} - 12 q^{23} + 16 q^{25} - 4 q^{27} + 2 q^{29} + 2 q^{30} + 4 q^{35} - 2 q^{36} + 24 q^{38} + 12 q^{40} + 4 q^{42} + 12 q^{43} - 2 q^{48} - 6 q^{49} - 28 q^{51} - 36 q^{53} - 4 q^{55} - 12 q^{56} - 2 q^{61} + 8 q^{62} - 28 q^{64} + 8 q^{66} - 14 q^{68} + 12 q^{69} - 2 q^{74} + 8 q^{75} + 16 q^{77} - 16 q^{79} - 2 q^{81} + 18 q^{82} - 2 q^{87} + 12 q^{88} + 4 q^{90} + 24 q^{92} - 12 q^{94} + 12 q^{95}+O(q^{100}) $ 4 * q + 2 * q^3 - 2 * q^4 - 2 * q^9 - 2 * q^10 - 4 * q^12 + 8 * q^14 + 2 * q^16 - 14 * q^17 + 4 * q^22 - 12 * q^23 + 16 * q^25 - 4 * q^27 + 2 * q^29 + 2 * q^30 + 4 * q^35 - 2 * q^36 + 24 * q^38 + 12 * q^40 + 4 * q^42 + 12 * q^43 - 2 * q^48 - 6 * q^49 - 28 * q^51 - 36 * q^53 - 4 * q^55 - 12 * q^56 - 2 * q^61 + 8 * q^62 - 28 * q^64 + 8 * q^66 - 14 * q^68 + 12 * q^69 - 2 * q^74 + 8 * q^75 + 16 * q^77 - 16 * q^79 - 2 * q^81 + 18 * q^82 - 2 * q^87 + 12 * q^88 + 4 * q^90 + 24 * q^92 - 12 * q^94 + 12 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i	−0.773893	−	0.633316i	$-0.781693\pi$
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i	0.161521	+	0.986869i	$0.448360\pi$
$3$	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
$5$			1.00000i			0.447214i	0.974679	+	0.223607i	$0.0717831\pi$
$5$			1.00000i			0.447214i	−0.974679	+	0.223607i	$0.928217\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	0.135583	−	0.990766i	$-0.456709\pi$
$7$	−1.73205	−	1.00000i	−0.654654	−	0.377964i	−0.790237	+	0.612801i	$0.790043\pi$
$8$		−	3.00000i		−	1.06066i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−1.73205	+	1.00000i	−0.522233	+	0.301511i	−0.737848	−	0.674967i	$-0.764158\pi$
$11$	−1.73205	+	1.00000i	−0.522233	+	0.301511i	0.215615	+	0.976478i	$0.430824\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	2.00000			0.534522
$15$	−0.866025	+	0.500000i	−0.223607	+	0.129099i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−3.50000	+	6.06218i	−0.848875	+	1.47029i	0.0333386	+	0.999444i	$0.489386\pi$
$17$	−3.50000	+	6.06218i	−0.848875	+	1.47029i	−0.882213	+	0.470850i	$0.843947\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−5.19615	−	3.00000i	−1.19208	−	0.688247i	−0.233301	−	0.972404i	$-0.574953\pi$
$19$	−5.19615	−	3.00000i	−1.19208	−	0.688247i	−0.958778	+	0.284157i	$0.908286\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$		−	2.00000i		−	0.436436i
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	2.59808	−	1.50000i	0.530330	−	0.306186i
$25$	4.00000			0.800000
$26$		0			0
$27$	−1.00000			−0.192450
$28$	1.73205	−	1.00000i	0.327327	−	0.188982i
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$		−	4.00000i		−	0.718421i	−0.933257	−	0.359211i	$-0.883046\pi$
$31$		−	4.00000i		−	0.718421i	0.933257	−	0.359211i	$-0.116954\pi$
$32$	4.33013	+	2.50000i	0.765466	+	0.441942i
$33$	−1.73205	−	1.00000i	−0.301511	−	0.174078i
$34$		−	7.00000i		−	1.20049i
$35$	1.00000	−	1.73205i	0.169031	−	0.292770i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	0.866025	−	0.500000i	0.142374	−	0.0821995i	−0.427121	−	0.904194i	$-0.640472\pi$
$37$	0.866025	−	0.500000i	0.142374	−	0.0821995i	0.569495	+	0.821995i	$0.307139\pi$
$38$	6.00000			0.973329
$39$		0			0
$40$	3.00000			0.474342
$41$	−7.79423	+	4.50000i	−1.21725	+	0.702782i	−0.964330	−	0.264704i	$-0.914726\pi$
$41$	−7.79423	+	4.50000i	−1.21725	+	0.702782i	−0.252924	+	0.967486i	$0.581392\pi$
$42$	1.00000	+	1.73205i	0.154303	+	0.267261i
$43$	3.00000	−	5.19615i	0.457496	−	0.792406i	−0.541332	−	0.840809i	$-0.682080\pi$
$43$	3.00000	−	5.19615i	0.457496	−	0.792406i	0.998828	+	0.0484030i	$0.0154132\pi$
$44$		−	2.00000i		−	0.301511i
$45$	−0.866025	−	0.500000i	−0.129099	−	0.0745356i
$46$	5.19615	+	3.00000i	0.766131	+	0.442326i
$47$			6.00000i			0.875190i	0.899172	+	0.437595i	$0.144170\pi$
$47$			6.00000i			0.875190i	−0.899172	+	0.437595i	$0.855830\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$	−3.46410	+	2.00000i	−0.489898	+	0.282843i
$51$	−7.00000			−0.980196
$52$		0			0
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$	−1.00000	−	1.73205i	−0.134840	−	0.233550i
$56$	−3.00000	+	5.19615i	−0.400892	+	0.694365i
$57$		−	6.00000i		−	0.794719i
$58$	−0.866025	−	0.500000i	−0.113715	−	0.0656532i
$59$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$59$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$60$		−	1.00000i		−	0.129099i
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	0.832240	+	0.554416i	$0.187058\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$	1.73205	−	1.00000i	0.218218	−	0.125988i
$64$	−7.00000			−0.875000
$65$		0			0
$66$	2.00000			0.246183
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	−0.390453	−	0.920623i	$-0.627682\pi$
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	0.602056	+	0.798454i	$0.294348\pi$
$68$	−3.50000	−	6.06218i	−0.424437	−	0.735147i
$69$	3.00000	−	5.19615i	0.361158	−	0.625543i
$70$			2.00000i			0.239046i
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	0.775571	−	0.631260i	$-0.217462\pi$
$71$	5.19615	+	3.00000i	0.616670	+	0.356034i	−0.158901	+	0.987294i	$0.550795\pi$
$72$	2.59808	+	1.50000i	0.306186	+	0.176777i
$73$			11.0000i			1.28745i	0.765256	+	0.643726i	$0.222612\pi$
$73$			11.0000i			1.28745i	−0.765256	+	0.643726i	$0.777388\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$	2.00000	+	3.46410i	0.230940	+	0.400000i
$76$	5.19615	−	3.00000i	0.596040	−	0.344124i
$77$	4.00000			0.455842
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	4.50000	−	7.79423i	0.496942	−	0.860729i
$83$			14.0000i			1.53670i	0.640030	+	0.768350i	$0.278922\pi$
$83$			14.0000i			1.53670i	−0.640030	+	0.768350i	$0.721078\pi$
$84$	1.73205	+	1.00000i	0.188982	+	0.109109i
$85$	−6.06218	−	3.50000i	−0.657536	−	0.379628i
$86$			6.00000i			0.646997i
$87$	−0.500000	+	0.866025i	−0.0536056	+	0.0928477i
$88$	3.00000	+	5.19615i	0.319801	+	0.553912i
$89$	−12.1244	+	7.00000i	−1.28518	+	0.741999i	−0.977790	−	0.209585i	$-0.932789\pi$
$89$	−12.1244	+	7.00000i	−1.28518	+	0.741999i	−0.307389	+	0.951584i	$0.599455\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$	6.00000			0.625543
$93$	3.46410	−	2.00000i	0.359211	−	0.207390i
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$			5.00000i			0.510310i
$97$	−1.73205	−	1.00000i	−0.175863	−	0.101535i	0.409484	−	0.912317i	$-0.365709\pi$
$97$	−1.73205	−	1.00000i	−0.175863	−	0.101535i	−0.585348	+	0.810782i	$0.699042\pi$
$98$	2.59808	+	1.50000i	0.262445	+	0.151523i
$99$		−	2.00000i		−	0.201008i
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$	6.06218	−	3.50000i	0.600245	−	0.346552i
$103$	−6.00000			−0.591198			−0.295599	−	0.955312i	$-0.595519\pi$
$103$	−6.00000			−0.591198			−0.295599	+	0.955312i	$0.595519\pi$
$104$		0			0
$105$	2.00000			0.195180
$106$	7.79423	−	4.50000i	0.757042	−	0.437079i
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	0.973814	−	0.227345i	$-0.0730044\pi$
$107$	3.00000	+	5.19615i	0.290021	+	0.502331i	−0.683793	+	0.729676i	$0.739671\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$			2.00000i			0.191565i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$			2.00000i			0.191565i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$	1.73205	+	1.00000i	0.165145	+	0.0953463i
$111$	0.866025	+	0.500000i	0.0821995	+	0.0474579i
$112$		−	2.00000i		−	0.188982i
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	−0.260955	−	0.965351i	$-0.584038\pi$
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	0.966496	−	0.256681i	$-0.0826291\pi$
$114$	3.00000	+	5.19615i	0.280976	+	0.486664i
$115$	5.19615	−	3.00000i	0.484544	−	0.279751i
$116$	−1.00000			−0.0928477
$117$		0			0
$118$		0			0
$119$	12.1244	−	7.00000i	1.11144	−	0.641689i
$120$	1.50000	+	2.59808i	0.136931	+	0.237171i
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$		−	1.00000i		−	0.0905357i
$123$	−7.79423	−	4.50000i	−0.702782	−	0.405751i
$124$	3.46410	+	2.00000i	0.311086	+	0.179605i
$125$			9.00000i			0.804984i
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	10.0000	+	17.3205i	0.887357	+	1.53695i	0.842989	+	0.537931i	$0.180794\pi$
$127$	10.0000	+	17.3205i	0.887357	+	1.53695i	0.0443678	+	0.999015i	$0.485873\pi$
$128$	−2.59808	+	1.50000i	−0.229640	+	0.132583i
$129$	6.00000			0.528271
$130$		0			0
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$	1.73205	−	1.00000i	0.150756	−	0.0870388i
$133$	6.00000	+	10.3923i	0.520266	+	0.901127i
$134$	−1.00000	+	1.73205i	−0.0863868	+	0.149626i
$135$		−	1.00000i		−	0.0860663i
$136$	18.1865	+	10.5000i	1.55948	+	0.900368i
$137$	2.59808	+	1.50000i	0.221969	+	0.128154i	0.606861	−	0.794808i	$-0.292428\pi$
$137$	2.59808	+	1.50000i	0.221969	+	0.128154i	−0.384893	+	0.922961i	$0.625762\pi$
$138$			6.00000i			0.510754i
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	0.491033	+	0.871141i	$0.336619\pi$
$139$	−6.00000	+	10.3923i	−0.508913	+	0.881464i	−0.999947	+	0.0103230i	$0.996714\pi$
$140$	1.00000	+	1.73205i	0.0845154	+	0.146385i
$141$	−5.19615	+	3.00000i	−0.437595	+	0.252646i
$142$	−6.00000			−0.503509
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	−0.866025	+	0.500000i	−0.0719195	+	0.0415227i
$146$	−5.50000	−	9.52628i	−0.455183	−	0.788400i
$147$	1.50000	−	2.59808i	0.123718	−	0.214286i
$148$			1.00000i			0.0821995i
$149$	2.59808	+	1.50000i	0.212843	+	0.122885i	0.602632	−	0.798019i	$-0.294119\pi$
$149$	2.59808	+	1.50000i	0.212843	+	0.122885i	−0.389789	+	0.920904i	$0.627452\pi$
$150$	−3.46410	−	2.00000i	−0.282843	−	0.163299i
$151$		−	2.00000i		−	0.162758i	−0.996683	−	0.0813788i	$-0.974068\pi$
$151$		−	2.00000i		−	0.162758i	0.996683	−	0.0813788i	$-0.0259324\pi$
$152$	−9.00000	+	15.5885i	−0.729996	+	1.26439i
$153$	−3.50000	−	6.06218i	−0.282958	−	0.490098i
$154$	−3.46410	+	2.00000i	−0.279145	+	0.161165i
$155$	4.00000			0.321288
$156$		0			0
$157$	−3.00000			−0.239426			−0.119713	−	0.992809i	$-0.538197\pi$
$157$	−3.00000			−0.239426			−0.119713	+	0.992809i	$0.538197\pi$
$158$	3.46410	−	2.00000i	0.275589	−	0.159111i
$159$	−4.50000	−	7.79423i	−0.356873	−	0.618123i
$160$	−2.50000	+	4.33013i	−0.197642	+	0.342327i
$161$			12.0000i			0.945732i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	0.629492	−	0.777007i	$-0.283263\pi$
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	−0.358162	+	0.933659i	$0.616597\pi$
$164$		−	9.00000i		−	0.702782i
$165$	1.00000	−	1.73205i	0.0778499	−	0.134840i
$166$	−7.00000	−	12.1244i	−0.543305	−	0.941033i
$167$	13.8564	−	8.00000i	1.07224	−	0.619059i	0.143448	−	0.989658i	$-0.454181\pi$
$167$	13.8564	−	8.00000i	1.07224	−	0.619059i	0.928793	+	0.370599i	$0.120848\pi$
$168$	−6.00000			−0.462910
$169$		0			0
$170$	7.00000			0.536875
$171$	5.19615	−	3.00000i	0.397360	−	0.229416i
$172$	3.00000	+	5.19615i	0.228748	+	0.396203i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		−	1.00000i		−	0.0758098i
$175$	−6.92820	−	4.00000i	−0.523723	−	0.302372i
$176$	−1.73205	−	1.00000i	−0.130558	−	0.0753778i
$177$		0			0
$178$	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	$0.857147\pi$
$180$	0.866025	−	0.500000i	0.0645497	−	0.0372678i
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$		0			0
$183$	−1.00000			−0.0739221
$184$	−15.5885	+	9.00000i	−1.14920	+	0.663489i
$185$	0.500000	+	0.866025i	0.0367607	+	0.0636715i
$186$	−2.00000	+	3.46410i	−0.146647	+	0.254000i
$187$		−	14.0000i		−	1.02378i
$188$	−5.19615	−	3.00000i	−0.378968	−	0.218797i
$189$	1.73205	+	1.00000i	0.125988	+	0.0727393i
$190$			6.00000i			0.435286i
$191$	2.00000	−	3.46410i	0.144715	−	0.250654i	−0.784552	−	0.620063i	$-0.787107\pi$
$191$	2.00000	−	3.46410i	0.144715	−	0.250654i	0.929267	+	0.369410i	$0.120440\pi$
$192$	−3.50000	−	6.06218i	−0.252591	−	0.437500i
$193$	−7.79423	+	4.50000i	−0.561041	+	0.323917i	−0.753563	−	0.657376i	$-0.771667\pi$
$193$	−7.79423	+	4.50000i	−0.561041	+	0.323917i	0.192522	+	0.981293i	$0.438333\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	3.00000			0.214286
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	−0.673550	−	0.739141i	$-0.735232\pi$
$197$	−5.19615	+	3.00000i	−0.370211	+	0.213741i	0.303340	+	0.952882i	$0.401898\pi$
$198$	1.00000	+	1.73205i	0.0710669	+	0.123091i
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	−0.503774	−	0.863836i	$-0.668055\pi$
$199$	7.00000	−	12.1244i	0.496217	−	0.859473i	0.999990	+	0.00436292i	$0.00138876\pi$
$200$		−	12.0000i		−	0.848528i
$201$	1.73205	+	1.00000i	0.122169	+	0.0705346i
$202$	−2.59808	−	1.50000i	−0.182800	−	0.105540i
$203$		−	2.00000i		−	0.140372i
$204$	3.50000	−	6.06218i	0.245049	−	0.424437i
$205$	−4.50000	−	7.79423i	−0.314294	−	0.544373i
$206$	5.19615	−	3.00000i	0.362033	−	0.209020i
$207$	6.00000			0.417029
$208$		0			0
$209$	12.0000			0.830057
$210$	−1.73205	+	1.00000i	−0.119523	+	0.0690066i
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	0.970229	−	0.242190i	$-0.0778659\pi$
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	−0.694857	+	0.719148i	$0.744533\pi$
$212$	4.50000	−	7.79423i	0.309061	−	0.535310i
$213$			6.00000i			0.411113i
$214$	−5.19615	−	3.00000i	−0.355202	−	0.205076i
$215$	5.19615	+	3.00000i	0.354375	+	0.204598i
$216$			3.00000i			0.204124i
$217$	−4.00000	+	6.92820i	−0.271538	+	0.470317i
$218$	−1.00000	−	1.73205i	−0.0677285	−	0.117309i
$219$	−9.52628	+	5.50000i	−0.643726	+	0.371656i
$220$	2.00000			0.134840
$221$		0			0
$222$	−1.00000			−0.0671156
$223$	−13.8564	+	8.00000i	−0.927894	+	0.535720i	−0.886145	−	0.463409i	$-0.846626\pi$
$223$	−13.8564	+	8.00000i	−0.927894	+	0.535720i	−0.0417488	+	0.999128i	$0.513293\pi$
$224$	−5.00000	−	8.66025i	−0.334077	−	0.578638i
$225$	−2.00000	+	3.46410i	−0.133333	+	0.230940i
$226$			15.0000i			0.997785i
$227$	−12.1244	−	7.00000i	−0.804722	−	0.464606i	0.0403978	−	0.999184i	$-0.487137\pi$
$227$	−12.1244	−	7.00000i	−0.804722	−	0.464606i	−0.845120	+	0.534577i	$0.820471\pi$
$228$	5.19615	+	3.00000i	0.344124	+	0.198680i
$229$		−	22.0000i		−	1.45380i	−0.686743	−	0.726900i	$-0.740960\pi$
$229$		−	22.0000i		−	1.45380i	0.686743	−	0.726900i	$-0.259040\pi$
$230$	−3.00000	+	5.19615i	−0.197814	+	0.342624i
$231$	2.00000	+	3.46410i	0.131590	+	0.227921i
$232$	2.59808	−	1.50000i	0.170572	−	0.0984798i
$233$	−10.0000			−0.655122			−0.327561	−	0.944830i	$-0.606227\pi$
$233$	−10.0000			−0.655122			−0.327561	+	0.944830i	$0.606227\pi$
$234$		0			0
$235$	−6.00000			−0.391397
$236$		0			0
$237$	−2.00000	−	3.46410i	−0.129914	−	0.225018i
$238$	−7.00000	+	12.1244i	−0.453743	+	0.785905i
$239$		−	30.0000i		−	1.94054i	−0.242028	−	0.970269i	$-0.577812\pi$
$239$		−	30.0000i		−	1.94054i	0.242028	−	0.970269i	$-0.422188\pi$
$240$	−0.866025	−	0.500000i	−0.0559017	−	0.0322749i
$241$	−6.06218	−	3.50000i	−0.390499	−	0.225455i	0.291877	−	0.956456i	$-0.405720\pi$
$241$	−6.06218	−	3.50000i	−0.390499	−	0.225455i	−0.682376	+	0.731001i	$0.739053\pi$
$242$		−	7.00000i		−	0.449977i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−0.500000	−	0.866025i	−0.0320092	−	0.0554416i
$245$	2.59808	−	1.50000i	0.165985	−	0.0958315i
$246$	9.00000			0.573819
$247$		0			0
$248$	−12.0000			−0.762001
$249$	−12.1244	+	7.00000i	−0.768350	+	0.443607i
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	−0.612159	−	0.790735i	$-0.709699\pi$
$251$	6.00000	−	10.3923i	0.378717	−	0.655956i	0.990876	+	0.134778i	$0.0430322\pi$
$252$			2.00000i			0.125988i
$253$	10.3923	+	6.00000i	0.653359	+	0.377217i
$254$	−17.3205	−	10.0000i	−1.08679	−	0.627456i
$255$		−	7.00000i		−	0.438357i
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−3.50000	−	6.06218i	−0.218324	−	0.378148i	0.735972	−	0.677012i	$-0.236726\pi$
$257$	−3.50000	−	6.06218i	−0.218324	−	0.378148i	−0.954296	+	0.298864i	$0.903392\pi$
$258$	−5.19615	+	3.00000i	−0.323498	+	0.186772i
$259$	−2.00000			−0.124274
$260$		0			0
$261$	−1.00000			−0.0618984
$262$	6.92820	−	4.00000i	0.428026	−	0.247121i
$263$	15.0000	+	25.9808i	0.924940	+	1.60204i	0.791658	+	0.610964i	$0.209218\pi$
$263$	15.0000	+	25.9808i	0.924940	+	1.60204i	0.133281	+	0.991078i	$0.457449\pi$
$264$	−3.00000	+	5.19615i	−0.184637	+	0.319801i
$265$		−	9.00000i		−	0.552866i
$266$	−10.3923	−	6.00000i	−0.637193	−	0.367884i
$267$	−12.1244	−	7.00000i	−0.741999	−	0.428393i
$268$			2.00000i			0.122169i
$269$	7.00000	−	12.1244i	0.426798	−	0.739235i	−0.569789	−	0.821791i	$-0.692975\pi$
$269$	7.00000	−	12.1244i	0.426798	−	0.739235i	0.996586	+	0.0825561i	$0.0263084\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$271$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$272$	−7.00000			−0.424437
$273$		0			0
$274$	−3.00000			−0.181237
$275$	−6.92820	+	4.00000i	−0.417786	+	0.241209i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	−15.5000	+	26.8468i	−0.931305	+	1.61307i	−0.150210	+	0.988654i	$0.547995\pi$
$277$	−15.5000	+	26.8468i	−0.931305	+	1.61307i	−0.781094	+	0.624413i	$0.785338\pi$
$278$		−	12.0000i		−	0.719712i
$279$	3.46410	+	2.00000i	0.207390	+	0.119737i
$280$	−5.19615	−	3.00000i	−0.310530	−	0.179284i
$281$		−	19.0000i		−	1.13344i	−0.823909	−	0.566722i	$-0.808211\pi$
$281$		−	19.0000i		−	1.13344i	0.823909	−	0.566722i	$-0.191789\pi$
$282$	3.00000	−	5.19615i	0.178647	−	0.309426i
$283$	−9.00000	−	15.5885i	−0.534994	−	0.926638i	−0.999164	−	0.0408910i	$-0.986980\pi$
$283$	−9.00000	−	15.5885i	−0.534994	−	0.926638i	0.464169	−	0.885747i	$-0.346353\pi$
$284$	−5.19615	+	3.00000i	−0.308335	+	0.178017i
$285$	6.00000			0.355409
$286$		0			0
$287$	18.0000			1.06251
$288$	−4.33013	+	2.50000i	−0.255155	+	0.147314i
$289$	−16.0000	−	27.7128i	−0.941176	−	1.63017i
$290$	0.500000	−	0.866025i	0.0293610	−	0.0508548i
$291$		−	2.00000i		−	0.117242i
$292$	−9.52628	−	5.50000i	−0.557483	−	0.321863i
$293$	7.79423	+	4.50000i	0.455344	+	0.262893i	0.710084	−	0.704117i	$-0.248657\pi$
$293$	7.79423	+	4.50000i	0.455344	+	0.262893i	−0.254741	+	0.967009i	$0.581990\pi$
$294$			3.00000i			0.174964i
$295$		0			0
$296$	−1.50000	−	2.59808i	−0.0871857	−	0.151010i
$297$	1.73205	−	1.00000i	0.100504	−	0.0580259i
$298$	−3.00000			−0.173785
$299$		0			0
$300$	−4.00000			−0.230940
$301$	−10.3923	+	6.00000i	−0.599002	+	0.345834i
$302$	1.00000	+	1.73205i	0.0575435	+	0.0996683i
$303$	−1.50000	+	2.59808i	−0.0861727	+	0.149256i
$304$		−	6.00000i		−	0.344124i
$305$	−0.866025	−	0.500000i	−0.0495885	−	0.0286299i
$306$	6.06218	+	3.50000i	0.346552	+	0.200082i
$307$			14.0000i			0.799022i	0.916728	+	0.399511i	$0.130820\pi$
$307$			14.0000i			0.799022i	−0.916728	+	0.399511i	$0.869180\pi$
$308$	−2.00000	+	3.46410i	−0.113961	+	0.197386i
$309$	−3.00000	−	5.19615i	−0.170664	−	0.295599i
$310$	−3.46410	+	2.00000i	−0.196748	+	0.113592i
$311$	−18.0000			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	2.59808	−	1.50000i	0.146618	−	0.0846499i
$315$	1.00000	+	1.73205i	0.0563436	+	0.0975900i
$316$	2.00000	−	3.46410i	0.112509	−	0.194871i
$317$			25.0000i			1.40414i	0.712108	+	0.702070i	$0.247741\pi$
$317$			25.0000i			1.40414i	−0.712108	+	0.702070i	$0.752259\pi$
$318$	7.79423	+	4.50000i	0.437079	+	0.252347i
$319$	−1.73205	−	1.00000i	−0.0969762	−	0.0559893i
$320$		−	7.00000i		−	0.391312i
$321$	−3.00000	+	5.19615i	−0.167444	+	0.290021i
$322$	−6.00000	−	10.3923i	−0.334367	−	0.579141i
$323$	36.3731	−	21.0000i	2.02385	−	1.16847i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−4.00000			−0.221540
$327$	−1.73205	+	1.00000i	−0.0957826	+	0.0553001i
$328$	13.5000	+	23.3827i	0.745413	+	1.29109i
$329$	6.00000	−	10.3923i	0.330791	−	0.572946i
$330$			2.00000i			0.110096i
$331$	−3.46410	−	2.00000i	−0.190404	−	0.109930i	0.401768	−	0.915742i	$-0.368396\pi$
$331$	−3.46410	−	2.00000i	−0.190404	−	0.109930i	−0.592172	+	0.805812i	$0.701729\pi$
$332$	−12.1244	−	7.00000i	−0.665410	−	0.384175i
$333$			1.00000i			0.0547997i
$334$	−8.00000	+	13.8564i	−0.437741	+	0.758189i
$335$	1.00000	+	1.73205i	0.0546358	+	0.0946320i
$336$	1.73205	−	1.00000i	0.0944911	−	0.0545545i
$337$	33.0000			1.79762			0.898812	−	0.438334i	$-0.144431\pi$
$337$	33.0000			1.79762			0.898812	+	0.438334i	$0.144431\pi$
$338$		0			0
$339$	15.0000			0.814688
$340$	6.06218	−	3.50000i	0.328768	−	0.189814i
$341$	4.00000	+	6.92820i	0.216612	+	0.375183i
$342$	−3.00000	+	5.19615i	−0.162221	+	0.280976i
$343$			20.0000i			1.07990i
$344$	−15.5885	−	9.00000i	−0.840473	−	0.485247i
$345$	5.19615	+	3.00000i	0.279751	+	0.161515i
$346$		−	6.00000i		−	0.322562i
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	−0.999813	−	0.0193540i	$-0.993839\pi$
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	0.516667	+	0.856186i	$0.327172\pi$
$348$	−0.500000	−	0.866025i	−0.0268028	−	0.0464238i
$349$	−22.5167	+	13.0000i	−1.20529	+	0.695874i	−0.961727	−	0.274011i	$-0.911649\pi$
$349$	−22.5167	+	13.0000i	−1.20529	+	0.695874i	−0.243563	+	0.969885i	$0.578316\pi$
$350$	8.00000			0.427618
$351$		0			0
$352$	−10.0000			−0.533002
$353$	9.52628	−	5.50000i	0.507033	−	0.292735i	−0.224580	−	0.974456i	$-0.572101\pi$
$353$	9.52628	−	5.50000i	0.507033	−	0.292735i	0.731613	+	0.681720i	$0.238768\pi$
$354$		0			0
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$		−	14.0000i		−	0.741999i
$357$	12.1244	+	7.00000i	0.641689	+	0.370479i
$358$	1.73205	+	1.00000i	0.0915417	+	0.0528516i
$359$		−	18.0000i		−	0.950004i	−0.879985	−	0.475002i	$-0.842447\pi$
$359$		−	18.0000i		−	0.950004i	0.879985	−	0.475002i	$-0.157553\pi$
$360$	−1.50000	+	2.59808i	−0.0790569	+	0.136931i
$361$	8.50000	+	14.7224i	0.447368	+	0.774865i
$362$	−6.06218	+	3.50000i	−0.318621	+	0.183956i
$363$	−7.00000			−0.367405
$364$		0			0
$365$	−11.0000			−0.575766
$366$	0.866025	−	0.500000i	0.0452679	−	0.0261354i
$367$	−5.00000	−	8.66025i	−0.260998	−	0.452062i	0.705509	−	0.708700i	$-0.250718\pi$
$367$	−5.00000	−	8.66025i	−0.260998	−	0.452062i	−0.966507	+	0.256639i	$0.917385\pi$
$368$	3.00000	−	5.19615i	0.156386	−	0.270868i
$369$		−	9.00000i		−	0.468521i
$370$	−0.866025	−	0.500000i	−0.0450225	−	0.0259938i
$371$	15.5885	+	9.00000i	0.809312	+	0.467257i
$372$			4.00000i			0.207390i
$373$	5.50000	−	9.52628i	0.284779	−	0.493252i	−0.687776	−	0.725923i	$-0.741413\pi$
$373$	5.50000	−	9.52628i	0.284779	−	0.493252i	0.972556	+	0.232671i	$0.0747464\pi$
$374$	7.00000	+	12.1244i	0.361961	+	0.626936i
$375$	−7.79423	+	4.50000i	−0.402492	+	0.232379i
$376$	18.0000			0.928279
$377$		0			0
$378$	−2.00000			−0.102869
$379$	31.1769	−	18.0000i	1.60145	−	0.924598i	0.610253	−	0.792207i	$-0.291068\pi$
$379$	31.1769	−	18.0000i	1.60145	−	0.924598i	0.991198	−	0.132391i	$-0.0422655\pi$
$380$	3.00000	+	5.19615i	0.153897	+	0.266557i
$381$	−10.0000	+	17.3205i	−0.512316	+	0.887357i
$382$			4.00000i			0.204658i
$383$	6.92820	+	4.00000i	0.354015	+	0.204390i	0.666452	−	0.745548i	$-0.267812\pi$
$383$	6.92820	+	4.00000i	0.354015	+	0.204390i	−0.312437	+	0.949938i	$0.601145\pi$
$384$	−2.59808	−	1.50000i	−0.132583	−	0.0765466i
$385$			4.00000i			0.203859i
$386$	4.50000	−	7.79423i	0.229044	−	0.396716i
$387$	3.00000	+	5.19615i	0.152499	+	0.264135i
$388$	1.73205	−	1.00000i	0.0879316	−	0.0507673i
$389$	−19.0000			−0.963338			−0.481669	−	0.876353i	$-0.659969\pi$
$389$	−19.0000			−0.963338			−0.481669	+	0.876353i	$0.659969\pi$
$390$		0			0
$391$	42.0000			2.12403
$392$	−7.79423	+	4.50000i	−0.393668	+	0.227284i
$393$	−4.00000	−	6.92820i	−0.201773	−	0.349482i
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$		−	4.00000i		−	0.201262i
$396$	1.73205	+	1.00000i	0.0870388	+	0.0502519i
$397$	29.4449	+	17.0000i	1.47780	+	0.853206i	0.999685	−	0.0250943i	$-0.00798860\pi$
$397$	29.4449	+	17.0000i	1.47780	+	0.853206i	0.478110	+	0.878300i	$0.341322\pi$
$398$			14.0000i			0.701757i
$399$	−6.00000	+	10.3923i	−0.300376	+	0.520266i
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	0.866025	−	0.500000i	0.0432472	−	0.0249688i	−0.478220	−	0.878240i	$-0.658718\pi$
$401$	0.866025	−	0.500000i	0.0432472	−	0.0249688i	0.521468	+	0.853271i	$0.325385\pi$
$402$	−2.00000			−0.0997509
$403$		0			0
$404$	−3.00000			−0.149256
$405$	0.866025	−	0.500000i	0.0430331	−	0.0248452i
$406$	1.00000	+	1.73205i	0.0496292	+	0.0859602i
$407$	−1.00000	+	1.73205i	−0.0495682	+	0.0858546i
$408$			21.0000i			1.03965i
$409$	6.06218	+	3.50000i	0.299755	+	0.173064i	0.642333	−	0.766426i	$-0.277967\pi$
$409$	6.06218	+	3.50000i	0.299755	+	0.173064i	−0.342578	+	0.939490i	$0.611300\pi$
$410$	7.79423	+	4.50000i	0.384930	+	0.222239i
$411$			3.00000i			0.147979i
$412$	3.00000	−	5.19615i	0.147799	−	0.255996i
$413$		0			0
$414$	−5.19615	+	3.00000i	−0.255377	+	0.147442i
$415$	−14.0000			−0.687233
$416$		0			0
$417$	−12.0000			−0.587643
$418$	−10.3923	+	6.00000i	−0.508304	+	0.293470i
$419$	−8.00000	−	13.8564i	−0.390826	−	0.676930i	0.601733	−	0.798697i	$-0.294477\pi$
$419$	−8.00000	−	13.8564i	−0.390826	−	0.676930i	−0.992559	+	0.121768i	$0.961144\pi$
$420$	−1.00000	+	1.73205i	−0.0487950	+	0.0845154i
$421$			19.0000i			0.926003i	0.886357	+	0.463002i	$0.153228\pi$
$421$			19.0000i			0.926003i	−0.886357	+	0.463002i	$0.846772\pi$
$422$	−6.92820	−	4.00000i	−0.337260	−	0.194717i
$423$	−5.19615	−	3.00000i	−0.252646	−	0.145865i
$424$			27.0000i			1.31124i
$425$	−14.0000	+	24.2487i	−0.679100	+	1.17624i
$426$	−3.00000	−	5.19615i	−0.145350	−	0.251754i
$427$	1.73205	−	1.00000i	0.0838198	−	0.0483934i
$428$	−6.00000			−0.290021
$429$		0			0
$430$	−6.00000			−0.289346
$431$	25.9808	−	15.0000i	1.25145	−	0.722525i	0.280052	−	0.959985i	$-0.409648\pi$
$431$	25.9808	−	15.0000i	1.25145	−	0.722525i	0.971397	+	0.237460i	$0.0763149\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	9.50000	−	16.4545i	0.456541	−	0.790752i	−0.542234	−	0.840227i	$-0.682422\pi$
$433$	9.50000	−	16.4545i	0.456541	−	0.790752i	0.998775	+	0.0494752i	$0.0157549\pi$
$434$		−	8.00000i		−	0.384012i
$435$	−0.866025	−	0.500000i	−0.0415227	−	0.0239732i
$436$	−1.73205	−	1.00000i	−0.0829502	−	0.0478913i
$437$			36.0000i			1.72211i
$438$	5.50000	−	9.52628i	0.262800	−	0.455183i
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	0.983310	−	0.181938i	$-0.0582371\pi$
$439$	7.00000	+	12.1244i	0.334092	+	0.578664i	−0.649218	+	0.760602i	$0.724904\pi$
$440$	−5.19615	+	3.00000i	−0.247717	+	0.143019i
$441$	3.00000			0.142857
$442$		0			0
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$	−0.866025	+	0.500000i	−0.0410997	+	0.0237289i
$445$	−7.00000	−	12.1244i	−0.331832	−	0.574750i
$446$	8.00000	−	13.8564i	0.378811	−	0.656120i
$447$			3.00000i			0.141895i
$448$	12.1244	+	7.00000i	0.572822	+	0.330719i
$449$	−29.4449	−	17.0000i	−1.38959	−	0.802280i	−0.396320	−	0.918112i	$-0.629713\pi$
$449$	−29.4449	−	17.0000i	−1.38959	−	0.802280i	−0.993269	+	0.115833i	$0.963046\pi$
$450$		−	4.00000i		−	0.188562i
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$	7.50000	+	12.9904i	0.352770	+	0.611016i
$453$	1.73205	−	1.00000i	0.0813788	−	0.0469841i
$454$	14.0000			0.657053
$455$		0			0
$456$	−18.0000			−0.842927
$457$	11.2583	−	6.50000i	0.526642	−	0.304057i	−0.213006	−	0.977051i	$-0.568325\pi$
$457$	11.2583	−	6.50000i	0.526642	−	0.304057i	0.739648	+	0.672994i	$0.234992\pi$
$458$	11.0000	+	19.0526i	0.513996	+	0.890268i
$459$	3.50000	−	6.06218i	0.163366	−	0.282958i
$460$			6.00000i			0.279751i
$461$	16.4545	+	9.50000i	0.766362	+	0.442459i	0.831575	−	0.555412i	$-0.187440\pi$
$461$	16.4545	+	9.50000i	0.766362	+	0.442459i	−0.0652135	+	0.997871i	$0.520773\pi$
$462$	−3.46410	−	2.00000i	−0.161165	−	0.0930484i
$463$		−	26.0000i		−	1.20832i	−0.796862	−	0.604161i	$-0.793508\pi$
$463$		−	26.0000i		−	1.20832i	0.796862	−	0.604161i	$-0.206492\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$	2.00000	+	3.46410i	0.0927478	+	0.160644i
$466$	8.66025	−	5.00000i	0.401179	−	0.231621i
$467$	−6.00000			−0.277647			−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000			−0.277647			−0.138823	+	0.990317i	$0.544332\pi$
$468$		0			0
$469$	−4.00000			−0.184703
$470$	5.19615	−	3.00000i	0.239681	−	0.138380i
$471$	−1.50000	−	2.59808i	−0.0691164	−	0.119713i
$472$		0			0
$473$			12.0000i			0.551761i
$474$	3.46410	+	2.00000i	0.159111	+	0.0918630i
$475$	−20.7846	−	12.0000i	−0.953663	−	0.550598i
$476$			14.0000i			0.641689i
$477$	4.50000	−	7.79423i	0.206041	−	0.356873i
$478$	15.0000	+	25.9808i	0.686084	+	1.18833i
$479$	20.7846	−	12.0000i	0.949673	−	0.548294i	0.0566937	−	0.998392i	$-0.481944\pi$
$479$	20.7846	−	12.0000i	0.949673	−	0.548294i	0.892979	+	0.450098i	$0.148611\pi$
$480$	−5.00000			−0.228218
$481$		0			0
$482$	7.00000			0.318841
$483$	−10.3923	+	6.00000i	−0.472866	+	0.273009i
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$			1.00000i			0.0453609i
$487$	15.5885	+	9.00000i	0.706380	+	0.407829i	0.809719	−	0.586817i	$-0.199619\pi$
$487$	15.5885	+	9.00000i	0.706380	+	0.407829i	−0.103339	+	0.994646i	$0.532953\pi$
$488$	2.59808	+	1.50000i	0.117609	+	0.0679018i
$489$			4.00000i			0.180886i
$490$	−1.50000	+	2.59808i	−0.0677631	+	0.117369i
$491$	3.00000	+	5.19615i	0.135388	+	0.234499i	0.925746	−	0.378147i	$-0.123439\pi$
$491$	3.00000	+	5.19615i	0.135388	+	0.234499i	−0.790358	+	0.612646i	$0.790105\pi$
$492$	7.79423	−	4.50000i	0.351391	−	0.202876i
$493$	−7.00000			−0.315264
$494$		0			0
$495$	2.00000			0.0898933
$496$	3.46410	−	2.00000i	0.155543	−	0.0898027i
$497$	−6.00000	−	10.3923i	−0.269137	−	0.466159i
$498$	7.00000	−	12.1244i	0.313678	−	0.543305i
$499$		−	24.0000i		−	1.07439i	−0.843459	−	0.537194i	$-0.819484\pi$
$499$		−	24.0000i		−	1.07439i	0.843459	−	0.537194i	$-0.180516\pi$
$500$	−7.79423	−	4.50000i	−0.348569	−	0.201246i
$501$	13.8564	+	8.00000i	0.619059	+	0.357414i
$502$			12.0000i			0.535586i
$503$	1.00000	−	1.73205i	0.0445878	−	0.0772283i	−0.842870	−	0.538117i	$-0.819136\pi$
$503$	1.00000	−	1.73205i	0.0445878	−	0.0772283i	0.887458	+	0.460889i	$0.152469\pi$
$504$	−3.00000	−	5.19615i	−0.133631	−	0.231455i
$505$	−2.59808	+	1.50000i	−0.115613	+	0.0667491i
$506$	−12.0000			−0.533465
$507$		0			0
$508$	−20.0000			−0.887357
$509$	−6.06218	+	3.50000i	−0.268701	+	0.155135i	−0.628297	−	0.777973i	$-0.716248\pi$
$509$	−6.06218	+	3.50000i	−0.268701	+	0.155135i	0.359596	+	0.933108i	$0.382915\pi$
$510$	3.50000	+	6.06218i	0.154983	+	0.268438i
$511$	11.0000	−	19.0526i	0.486611	−	0.842836i
$512$			11.0000i			0.486136i
$513$	5.19615	+	3.00000i	0.229416	+	0.132453i
$514$	6.06218	+	3.50000i	0.267391	+	0.154378i
$515$		−	6.00000i		−	0.264392i
$516$	−3.00000	+	5.19615i	−0.132068	+	0.228748i
$517$	−6.00000	−	10.3923i	−0.263880	−	0.457053i
$518$	1.73205	−	1.00000i	0.0761019	−	0.0439375i
$519$	−6.00000			−0.263371
$520$		0			0
$521$	−3.00000			−0.131432			−0.0657162	−	0.997838i	$-0.520933\pi$
$521$	−3.00000			−0.131432			−0.0657162	+	0.997838i	$0.520933\pi$
$522$	0.866025	−	0.500000i	0.0379049	−	0.0218844i
$523$	−7.00000	−	12.1244i	−0.306089	−	0.530161i	0.671414	−	0.741082i	$-0.265687\pi$
$523$	−7.00000	−	12.1244i	−0.306089	−	0.530161i	−0.977503	+	0.210921i	$0.932354\pi$
$524$	4.00000	−	6.92820i	0.174741	−	0.302660i
$525$		−	8.00000i		−	0.349149i
$526$	−25.9808	−	15.0000i	−1.13282	−	0.654031i
$527$	24.2487	+	14.0000i	1.05629	+	0.609850i
$528$		−	2.00000i		−	0.0870388i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$	4.50000	+	7.79423i	0.195468	+	0.338560i
$531$		0			0
$532$	−12.0000			−0.520266
$533$		0			0
$534$	14.0000			0.605839
$535$	−5.19615	+	3.00000i	−0.224649	+	0.129701i
$536$	−3.00000	−	5.19615i	−0.129580	−	0.224440i
$537$	1.00000	−	1.73205i	0.0431532	−	0.0747435i
$538$			14.0000i			0.603583i
$539$	5.19615	+	3.00000i	0.223814	+	0.129219i
$540$	0.866025	+	0.500000i	0.0372678	+	0.0215166i
$541$			45.0000i			1.93470i	0.253442	+	0.967351i	$0.418437\pi$
$541$			45.0000i			1.93470i	−0.253442	+	0.967351i	$0.581563\pi$
$542$		0			0
$543$	3.50000	+	6.06218i	0.150199	+	0.260153i
$544$	−30.3109	+	17.5000i	−1.29957	+	0.750306i
$545$	−2.00000			−0.0856706
$546$		0			0
$547$	−26.0000			−1.11168			−0.555840	−	0.831289i	$-0.687603\pi$
$547$	−26.0000			−1.11168			−0.555840	+	0.831289i	$0.687603\pi$
$548$	−2.59808	+	1.50000i	−0.110984	+	0.0640768i
$549$	−0.500000	−	0.866025i	−0.0213395	−	0.0369611i
$550$	4.00000	−	6.92820i	0.170561	−	0.295420i
$551$		−	6.00000i		−	0.255609i
$552$	−15.5885	−	9.00000i	−0.663489	−	0.383065i
$553$	6.92820	+	4.00000i	0.294617	+	0.170097i
$554$		−	31.0000i		−	1.31706i
$555$	−0.500000	+	0.866025i	−0.0212238	+	0.0367607i
$556$	−6.00000	−	10.3923i	−0.254457	−	0.440732i
$557$	−7.79423	+	4.50000i	−0.330252	+	0.190671i	−0.655953	−	0.754802i	$-0.727733\pi$
$557$	−7.79423	+	4.50000i	−0.330252	+	0.190671i	0.325701	+	0.945473i	$0.394400\pi$
$558$	−4.00000			−0.169334
$559$		0			0
$560$	2.00000			0.0845154
$561$	12.1244	−	7.00000i	0.511891	−	0.295540i
$562$	9.50000	+	16.4545i	0.400733	+	0.694090i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		−	6.00000i		−	0.252646i
$565$	12.9904	+	7.50000i	0.546509	+	0.315527i
$566$	15.5885	+	9.00000i	0.655232	+	0.378298i
$567$			2.00000i			0.0839921i
$568$	9.00000	−	15.5885i	0.377632	−	0.654077i
$569$	11.0000	+	19.0526i	0.461144	+	0.798725i	0.999018	−	0.0443003i	$-0.0141058\pi$
$569$	11.0000	+	19.0526i	0.461144	+	0.798725i	−0.537874	+	0.843025i	$0.680772\pi$
$570$	−5.19615	+	3.00000i	−0.217643	+	0.125656i
$571$	−26.0000			−1.08807			−0.544033	−	0.839064i	$-0.683103\pi$
$571$	−26.0000			−1.08807			−0.544033	+	0.839064i	$0.683103\pi$
$572$		0			0
$573$	4.00000			0.167102
$574$	−15.5885	+	9.00000i	−0.650650	+	0.375653i
$575$	−12.0000	−	20.7846i	−0.500435	−	0.866778i
$576$	3.50000	−	6.06218i	0.145833	−	0.252591i
$577$		−	11.0000i		−	0.457936i	−0.973434	−	0.228968i	$-0.926465\pi$
$577$		−	11.0000i		−	0.457936i	0.973434	−	0.228968i	$-0.0735351\pi$
$578$	27.7128	+	16.0000i	1.15270	+	0.665512i
$579$	−7.79423	−	4.50000i	−0.323917	−	0.187014i
$580$		−	1.00000i		−	0.0415227i
$581$	14.0000	−	24.2487i	0.580818	−	1.00601i
$582$	1.00000	+	1.73205i	0.0414513	+	0.0717958i
$583$	15.5885	−	9.00000i	0.645608	−	0.372742i
$584$	33.0000			1.36555
$585$		0			0
$586$	−9.00000			−0.371787
$587$	−13.8564	+	8.00000i	−0.571915	+	0.330195i	−0.757914	−	0.652355i	$-0.773781\pi$
$587$	−13.8564	+	8.00000i	−0.571915	+	0.330195i	0.185999	+	0.982550i	$0.440448\pi$
$588$	1.50000	+	2.59808i	0.0618590	+	0.107143i
$589$	−12.0000	+	20.7846i	−0.494451	+	0.856415i
$590$		0			0
$591$	−5.19615	−	3.00000i	−0.213741	−	0.123404i
$592$	0.866025	+	0.500000i	0.0355934	+	0.0205499i
$593$			13.0000i			0.533846i	0.963718	+	0.266923i	$0.0860069\pi$
$593$			13.0000i			0.533846i	−0.963718	+	0.266923i	$0.913993\pi$
$594$	−1.00000	+	1.73205i	−0.0410305	+	0.0710669i
$595$	7.00000	+	12.1244i	0.286972	+	0.497050i
$596$	−2.59808	+	1.50000i	−0.106421	+	0.0614424i
$597$	14.0000			0.572982
$598$		0			0
$599$	−16.0000			−0.653742			−0.326871	−	0.945069i	$-0.605994\pi$
$599$	−16.0000			−0.653742			−0.326871	+	0.945069i	$0.605994\pi$
$600$	10.3923	−	6.00000i	0.424264	−	0.244949i
$601$	2.50000	+	4.33013i	0.101977	+	0.176630i	0.912499	−	0.409079i	$-0.134150\pi$
$601$	2.50000	+	4.33013i	0.101977	+	0.176630i	−0.810522	+	0.585708i	$0.800816\pi$
$602$	6.00000	−	10.3923i	0.244542	−	0.423559i
$603$			2.00000i			0.0814463i
$604$	1.73205	+	1.00000i	0.0704761	+	0.0406894i
$605$	−6.06218	−	3.50000i	−0.246463	−	0.142295i
$606$		−	3.00000i		−	0.121867i
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	−0.935713	−	0.352763i	$-0.885242\pi$
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	0.773358	+	0.633970i	$0.218576\pi$
$608$	−15.0000	−	25.9808i	−0.608330	−	1.05366i
$609$	1.73205	−	1.00000i	0.0701862	−	0.0405220i
$610$	1.00000			0.0404888
$611$		0			0
$612$	7.00000			0.282958
$613$	19.9186	−	11.5000i	0.804504	−	0.464481i	−0.0405396	−	0.999178i	$-0.512908\pi$
$613$	19.9186	−	11.5000i	0.804504	−	0.464481i	0.845044	+	0.534697i	$0.179574\pi$
$614$	−7.00000	−	12.1244i	−0.282497	−	0.489299i
$615$	4.50000	−	7.79423i	0.181458	−	0.314294i
$616$		−	12.0000i		−	0.483494i
$617$	11.2583	+	6.50000i	0.453243	+	0.261680i	0.709199	−	0.705008i	$-0.249057\pi$
$617$	11.2583	+	6.50000i	0.453243	+	0.261680i	−0.255956	+	0.966689i	$0.582390\pi$
$618$	5.19615	+	3.00000i	0.209020	+	0.120678i
$619$		−	24.0000i		−	0.964641i	−0.875995	−	0.482321i	$-0.839794\pi$
$619$		−	24.0000i		−	0.964641i	0.875995	−	0.482321i	$-0.160206\pi$
$620$	−2.00000	+	3.46410i	−0.0803219	+	0.139122i
$621$	3.00000	+	5.19615i	0.120386	+	0.208514i
$622$	15.5885	−	9.00000i	0.625040	−	0.360867i
$623$	28.0000			1.12180
$624$		0			0
$625$	11.0000			0.440000
$626$	−5.19615	+	3.00000i	−0.207680	+	0.119904i
$627$	6.00000	+	10.3923i	0.239617	+	0.415029i
$628$	1.50000	−	2.59808i	0.0598565	−	0.103675i
$629$			7.00000i			0.279108i
$630$	−1.73205	−	1.00000i	−0.0690066	−	0.0398410i
$631$	−17.3205	−	10.0000i	−0.689519	−	0.398094i	0.113913	−	0.993491i	$-0.463661\pi$
$631$	−17.3205	−	10.0000i	−0.689519	−	0.398094i	−0.803432	+	0.595397i	$0.796995\pi$
$632$			12.0000i			0.477334i
$633$	−4.00000	+	6.92820i	−0.158986	+	0.275371i
$634$	−12.5000	−	21.6506i	−0.496438	−	0.859857i
$635$	−17.3205	+	10.0000i	−0.687343	+	0.396838i
$636$	9.00000			0.356873
$637$		0			0
$638$	2.00000			0.0791808
$639$	−5.19615	+	3.00000i	−0.205557	+	0.118678i
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	−15.5000	+	26.8468i	−0.612213	+	1.06038i	0.378653	+	0.925539i	$0.376387\pi$
$641$	−15.5000	+	26.8468i	−0.612213	+	1.06038i	−0.990867	+	0.134846i	$0.956946\pi$
$642$		−	6.00000i		−	0.236801i
$643$	−13.8564	−	8.00000i	−0.546443	−	0.315489i	0.201243	−	0.979541i	$-0.435502\pi$
$643$	−13.8564	−	8.00000i	−0.546443	−	0.315489i	−0.747686	+	0.664052i	$0.768835\pi$
$644$	−10.3923	−	6.00000i	−0.409514	−	0.236433i
$645$			6.00000i			0.236250i
$646$	−21.0000	+	36.3731i	−0.826234	+	1.43108i
$647$	−16.0000	−	27.7128i	−0.629025	−	1.08950i	−0.987748	−	0.156059i	$-0.950121\pi$
$647$	−16.0000	−	27.7128i	−0.629025	−	1.08950i	0.358723	−	0.933444i	$-0.383212\pi$
$648$	−2.59808	+	1.50000i	−0.102062	+	0.0589256i
$649$		0			0
$650$		0			0
$651$	−8.00000			−0.313545
$652$	−3.46410	+	2.00000i	−0.135665	+	0.0783260i
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$	1.00000	−	1.73205i	0.0391031	−	0.0677285i
$655$		−	8.00000i		−	0.312586i
$656$	−7.79423	−	4.50000i	−0.304314	−	0.175695i
$657$	−9.52628	−	5.50000i	−0.371656	−	0.214575i
$658$			12.0000i			0.467809i
$659$	4.00000	−	6.92820i	0.155818	−	0.269884i	−0.777539	−	0.628835i	$-0.783532\pi$
$659$	4.00000	−	6.92820i	0.155818	−	0.269884i	0.933357	+	0.358951i	$0.116865\pi$
$660$	1.00000	+	1.73205i	0.0389249	+	0.0674200i
$661$	38.9711	−	22.5000i	1.51580	−	0.875149i	0.515974	−	0.856604i	$-0.327430\pi$
$661$	38.9711	−	22.5000i	1.51580	−	0.875149i	0.999828	−	0.0185442i	$-0.00590313\pi$
$662$	4.00000			0.155464
$663$		0			0
$664$	42.0000			1.62992
$665$	−10.3923	+	6.00000i	−0.402996	+	0.232670i
$666$	−0.500000	−	0.866025i	−0.0193746	−	0.0335578i
$667$	3.00000	−	5.19615i	0.116160	−	0.201196i
$668$			16.0000i			0.619059i
$669$	−13.8564	−	8.00000i	−0.535720	−	0.309298i
$670$	−1.73205	−	1.00000i	−0.0669150	−	0.0386334i
$671$		−	2.00000i		−	0.0772091i
$672$	5.00000	−	8.66025i	0.192879	−	0.334077i
$673$	−14.5000	−	25.1147i	−0.558934	−	0.968102i	−0.997586	−	0.0694449i	$-0.977877\pi$
$673$	−14.5000	−	25.1147i	−0.558934	−	0.968102i	0.438652	−	0.898657i	$-0.355456\pi$
$674$	−28.5788	+	16.5000i	−1.10082	+	0.635556i
$675$	−4.00000			−0.153960
$676$		0			0
$677$	34.0000			1.30673			0.653363	−	0.757045i	$-0.273358\pi$
$677$	34.0000			1.30673			0.653363	+	0.757045i	$0.273358\pi$
$678$	−12.9904	+	7.50000i	−0.498893	+	0.288036i
$679$	2.00000	+	3.46410i	0.0767530	+	0.132940i
$680$	−10.5000	+	18.1865i	−0.402657	+	0.697422i
$681$		−	14.0000i		−	0.536481i
$682$	−6.92820	−	4.00000i	−0.265295	−	0.153168i
$683$	20.7846	+	12.0000i	0.795301	+	0.459167i	0.841825	−	0.539750i	$-0.181481\pi$
$683$	20.7846	+	12.0000i	0.795301	+	0.459167i	−0.0465244	+	0.998917i	$0.514815\pi$
$684$			6.00000i			0.229416i
$685$	−1.50000	+	2.59808i	−0.0573121	+	0.0992674i
$686$	−10.0000	−	17.3205i	−0.381802	−	0.661300i
$687$	19.0526	−	11.0000i	0.726900	−	0.419676i
$688$	6.00000			0.228748
$689$		0			0
$690$	−6.00000			−0.228416
$691$	−36.3731	+	21.0000i	−1.38370	+	0.798878i	−0.992595	−	0.121470i	$-0.961239\pi$
$691$	−36.3731	+	21.0000i	−1.38370	+	0.798878i	−0.391102	+	0.920348i	$0.627906\pi$
$692$	−3.00000	−	5.19615i	−0.114043	−	0.197528i
$693$	−2.00000	+	3.46410i	−0.0759737	+	0.131590i
$694$		−	18.0000i		−	0.683271i
$695$	−10.3923	−	6.00000i	−0.394203	−	0.227593i
$696$	2.59808	+	1.50000i	0.0984798	+	0.0568574i
$697$		−	63.0000i		−	2.38630i
$698$	13.0000	−	22.5167i	0.492057	−	0.852268i
$699$	−5.00000	−	8.66025i	−0.189117	−	0.327561i
$700$	6.92820	−	4.00000i	0.261861	−	0.151186i
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$		0			0
$703$	−6.00000			−0.226294
$704$	12.1244	−	7.00000i	0.456954	−	0.263822i
$705$	−3.00000	−	5.19615i	−0.112987	−	0.195698i
$706$	−5.50000	+	9.52628i	−0.206995	+	0.358526i
$707$		−	6.00000i		−	0.225653i
$708$		0			0
$709$	9.52628	+	5.50000i	0.357767	+	0.206557i	0.668101	−	0.744071i	$-0.267108\pi$
$709$	9.52628	+	5.50000i	0.357767	+	0.206557i	−0.310334	+	0.950628i	$0.600441\pi$
$710$		−	6.00000i		−	0.225176i
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	21.0000	+	36.3731i	0.787008	+	1.36314i
$713$	−20.7846	+	12.0000i	−0.778390	+	0.449404i
$714$	−14.0000			−0.523937
$715$		0			0
$716$	2.00000			0.0747435
$717$	25.9808	−	15.0000i	0.970269	−	0.560185i
$718$	9.00000	+	15.5885i	0.335877	+	0.581756i
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.0613050	+	0.998119i	$0.519526\pi$
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.833744	+	0.552151i	$0.813807\pi$
$720$		−	1.00000i		−	0.0372678i
$721$	10.3923	+	6.00000i	0.387030	+	0.223452i
$722$	−14.7224	−	8.50000i	−0.547912	−	0.316337i
$723$		−	7.00000i		−	0.260333i
$724$	−3.50000	+	6.06218i	−0.130076	+	0.225299i
$725$	2.00000	+	3.46410i	0.0742781	+	0.128654i
$726$	6.06218	−	3.50000i	0.224989	−	0.129897i
$727$	−14.0000			−0.519231			−0.259616	−	0.965712i	$-0.583596\pi$
$727$	−14.0000			−0.519231			−0.259616	+	0.965712i	$0.583596\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	9.52628	−	5.50000i	0.352583	−	0.203564i
$731$	21.0000	+	36.3731i	0.776713	+	1.34531i
$732$	0.500000	−	0.866025i	0.0184805	−	0.0320092i
$733$			15.0000i			0.554038i	0.960864	+	0.277019i	$0.0893464\pi$
$733$			15.0000i			0.554038i	−0.960864	+	0.277019i	$0.910654\pi$
$734$	8.66025	+	5.00000i	0.319656	+	0.184553i
$735$	2.59808	+	1.50000i	0.0958315	+	0.0553283i
$736$		−	30.0000i		−	1.10581i
$737$	−2.00000	+	3.46410i	−0.0736709	+	0.127602i
$738$	4.50000	+	7.79423i	0.165647	+	0.286910i
$739$	−13.8564	+	8.00000i	−0.509716	+	0.294285i	−0.732717	−	0.680534i	$-0.761748\pi$
$739$	−13.8564	+	8.00000i	−0.509716	+	0.294285i	0.223001	+	0.974818i	$0.428415\pi$
$740$	−1.00000			−0.0367607
$741$		0			0
$742$	−18.0000			−0.660801
$743$	31.1769	−	18.0000i	1.14377	−	0.660356i	0.196409	−	0.980522i	$-0.437072\pi$
$743$	31.1769	−	18.0000i	1.14377	−	0.660356i	0.947361	+	0.320166i	$0.103739\pi$
$744$	−6.00000	−	10.3923i	−0.219971	−	0.381000i
$745$	−1.50000	+	2.59808i	−0.0549557	+	0.0951861i
$746$			11.0000i			0.402739i
$747$	−12.1244	−	7.00000i	−0.443607	−	0.256117i
$748$	12.1244	+	7.00000i	0.443310	+	0.255945i
$749$		−	12.0000i		−	0.438470i
$750$	4.50000	−	7.79423i	0.164317	−	0.284605i
$751$	−17.0000	−	29.4449i	−0.620339	−	1.07446i	−0.989423	−	0.145062i	$-0.953662\pi$
$751$	−17.0000	−	29.4449i	−0.620339	−	1.07446i	0.369084	−	0.929396i	$-0.379672\pi$
$752$	−5.19615	+	3.00000i	−0.189484	+	0.109399i
$753$	12.0000			0.437304
$754$		0			0
$755$	2.00000			0.0727875
$756$	−1.73205	+	1.00000i	−0.0629941	+	0.0363696i
$757$	25.0000	+	43.3013i	0.908640	+	1.57381i	0.815955	+	0.578116i	$0.196212\pi$
$757$	25.0000	+	43.3013i	0.908640	+	1.57381i	0.0926859	+	0.995695i	$0.470455\pi$
$758$	−18.0000	+	31.1769i	−0.653789	+	1.13240i
$759$			12.0000i			0.435572i
$760$	−15.5885	−	9.00000i	−0.565453	−	0.326464i
$761$	−43.3013	−	25.0000i	−1.56967	−	0.906249i	−0.996207	−	0.0870179i	$-0.972266\pi$
$761$	−43.3013	−	25.0000i	−1.56967	−	0.906249i	−0.573463	−	0.819231i	$-0.694400\pi$
$762$		−	20.0000i		−	0.724524i
$763$	2.00000	−	3.46410i	0.0724049	−	0.125409i
$764$	2.00000	+	3.46410i	0.0723575	+	0.125327i
$765$	6.06218	−	3.50000i	0.219179	−	0.126543i
$766$	−8.00000			−0.289052
$767$		0			0
$768$	17.0000			0.613435
$769$	−25.9808	+	15.0000i	−0.936890	+	0.540914i	−0.888984	−	0.457938i	$-0.848588\pi$
$769$	−25.9808	+	15.0000i	−0.936890	+	0.540914i	−0.0479061	+	0.998852i	$0.515255\pi$
$770$	−2.00000	−	3.46410i	−0.0720750	−	0.124838i
$771$	3.50000	−	6.06218i	0.126049	−	0.218324i
$772$		−	9.00000i		−	0.323917i
$773$	−12.1244	−	7.00000i	−0.436083	−	0.251773i	0.265852	−	0.964014i	$-0.414347\pi$
$773$	−12.1244	−	7.00000i	−0.436083	−	0.251773i	−0.701935	+	0.712241i	$0.747680\pi$
$774$	−5.19615	−	3.00000i	−0.186772	−	0.107833i
$775$		−	16.0000i		−	0.574737i
$776$	−3.00000	+	5.19615i	−0.107694	+	0.186531i
$777$	−1.00000	−	1.73205i	−0.0358748	−	0.0621370i
$778$	16.4545	−	9.50000i	0.589922	−	0.340592i
$779$	54.0000			1.93475
$780$		0			0
$781$	−12.0000			−0.429394
$782$	−36.3731	+	21.0000i	−1.30070	+	0.750958i
$783$	−0.500000	−	0.866025i	−0.0178685	−	0.0309492i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$		−	3.00000i		−	0.107075i
$786$	6.92820	+	4.00000i	0.247121	+	0.142675i
$787$	−24.2487	−	14.0000i	−0.864373	−	0.499046i	0.00110111	−	0.999999i	$-0.499650\pi$
$787$	−24.2487	−	14.0000i	−0.864373	−	0.499046i	−0.865474	+	0.500953i	$0.832983\pi$
$788$		−	6.00000i		−	0.213741i
$789$	−15.0000	+	25.9808i	−0.534014	+	0.924940i
$790$	2.00000	+	3.46410i	0.0711568	+	0.123247i
$791$	−25.9808	+	15.0000i	−0.923770	+	0.533339i
$792$	−6.00000			−0.213201
$793$		0			0
$794$	−34.0000			−1.20661
$795$	7.79423	−	4.50000i	0.276433	−	0.159599i
$796$	7.00000	+	12.1244i	0.248108	+	0.429736i
$797$	−1.00000	+	1.73205i	−0.0354218	+	0.0613524i	−0.883193	−	0.469010i	$-0.844611\pi$
$797$	−1.00000	+	1.73205i	−0.0354218	+	0.0613524i	0.847771	+	0.530362i	$0.177944\pi$
$798$		−	12.0000i		−	0.424795i
$799$	−36.3731	−	21.0000i	−1.28679	−	0.742927i
$800$	17.3205	+	10.0000i	0.612372	+	0.353553i
$801$		−	14.0000i		−	0.494666i
$802$	−0.500000	+	0.866025i	−0.0176556	+	0.0305804i
$803$	−11.0000	−	19.0526i	−0.388182	−	0.672350i
$804$	−1.73205	+	1.00000i	−0.0610847	+	0.0352673i
$805$	−12.0000			−0.422944
$806$		0			0
$807$	14.0000			0.492823
$808$	7.79423	−	4.50000i	0.274200	−	0.158309i
$809$	−16.5000	−	28.5788i	−0.580109	−	1.00478i	−0.995466	−	0.0951198i	$-0.969677\pi$
$809$	−16.5000	−	28.5788i	−0.580109	−	1.00478i	0.415357	−	0.909659i	$-0.363657\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$			28.0000i			0.983213i	0.870817	+	0.491606i	$0.163590\pi$
$811$			28.0000i			0.983213i	−0.870817	+	0.491606i	$0.836410\pi$
$812$	1.73205	+	1.00000i	0.0607831	+	0.0350931i
$813$		0			0
$814$		−	2.00000i		−	0.0701000i
$815$	−2.00000	+	3.46410i	−0.0700569	+	0.121342i
$816$	−3.50000	−	6.06218i	−0.122525	−	0.212219i
$817$	−31.1769	+	18.0000i	−1.09074	+	0.629740i
$818$	−7.00000			−0.244749
$819$		0			0
$820$	9.00000			0.314294
$821$	−43.3013	+	25.0000i	−1.51122	+	0.872506i	−0.511311	+	0.859396i	$0.670840\pi$
$821$	−43.3013	+	25.0000i	−1.51122	+	0.872506i	−0.999914	+	0.0131101i	$0.995827\pi$
$822$	−1.50000	−	2.59808i	−0.0523185	−	0.0906183i
$823$	−12.0000	+	20.7846i	−0.418294	+	0.724506i	−0.995768	−	0.0919029i	$-0.970705\pi$
$823$	−12.0000	+	20.7846i	−0.418294	+	0.724506i	0.577474	+	0.816409i	$0.304038\pi$
$824$			18.0000i			0.627060i
$825$	−6.92820	−	4.00000i	−0.241209	−	0.139262i
$826$		0			0
$827$			16.0000i			0.556375i	0.960527	+	0.278187i	$0.0897336\pi$
$827$			16.0000i			0.556375i	−0.960527	+	0.278187i	$0.910266\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	8.50000	+	14.7224i	0.295217	+	0.511331i	0.975035	−	0.222049i	$-0.0712747\pi$
$829$	8.50000	+	14.7224i	0.295217	+	0.511331i	−0.679818	+	0.733381i	$0.737941\pi$
$830$	12.1244	−	7.00000i	0.420843	−	0.242974i
$831$	−31.0000			−1.07538
$832$		0			0
$833$	21.0000			0.727607
$834$	10.3923	−	6.00000i	0.359856	−	0.207763i
$835$	8.00000	+	13.8564i	0.276851	+	0.479521i
$836$	−6.00000	+	10.3923i	−0.207514	+	0.359425i
$837$			4.00000i			0.138260i
$838$	13.8564	+	8.00000i	0.478662	+	0.276355i
$839$	−10.3923	−	6.00000i	−0.358782	−	0.207143i	0.309764	−	0.950813i	$-0.399750\pi$
$839$	−10.3923	−	6.00000i	−0.358782	−	0.207143i	−0.668546	+	0.743670i	$0.733083\pi$
$840$		−	6.00000i		−	0.207020i
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	−9.50000	−	16.4545i	−0.327392	−	0.567059i
$843$	16.4545	−	9.50000i	0.566722	−	0.327197i
$844$	−8.00000			−0.275371
$845$		0			0
$846$	6.00000			0.206284
$847$	12.1244	−	7.00000i	0.416598	−	0.240523i
$848$	−4.50000	−	7.79423i	−0.154531	−	0.267655i
$849$	9.00000	−	15.5885i	0.308879	−	0.534994i
$850$		−	28.0000i		−	0.960392i
$851$	−5.19615	−	3.00000i	−0.178122	−	0.102839i
$852$	−5.19615	−	3.00000i	−0.178017	−	0.102778i
$853$			21.0000i			0.719026i	0.933140	+	0.359513i	$0.117057\pi$
$853$			21.0000i			0.719026i	−0.933140	+	0.359513i	$0.882943\pi$
$854$	−1.00000	+	1.73205i	−0.0342193	+	0.0592696i
$855$	3.00000	+	5.19615i	0.102598	+	0.177705i
$856$	15.5885	−	9.00000i	0.532803	−	0.307614i
$857$	31.0000			1.05894			0.529470	−	0.848329i	$-0.322391\pi$
$857$	31.0000			1.05894			0.529470	+	0.848329i	$0.322391\pi$
$858$		0			0
$859$	34.0000			1.16007			0.580033	−	0.814593i	$-0.303040\pi$
$859$	34.0000			1.16007			0.580033	+	0.814593i	$0.303040\pi$
$860$	−5.19615	+	3.00000i	−0.177187	+	0.102299i
$861$	9.00000	+	15.5885i	0.306719	+	0.531253i
$862$	−15.0000	+	25.9808i	−0.510902	+	0.884908i
$863$		−	10.0000i		−	0.340404i	−0.985409	−	0.170202i	$-0.945558\pi$
$863$		−	10.0000i		−	0.340404i	0.985409	−	0.170202i	$-0.0544420\pi$
$864$	−4.33013	−	2.50000i	−0.147314	−	0.0850517i
$865$	−5.19615	−	3.00000i	−0.176674	−	0.102003i
$866$			19.0000i			0.645646i
$867$	16.0000	−	27.7128i	0.543388	−	0.941176i
$868$	−4.00000	−	6.92820i	−0.135769	−	0.235159i
$869$	6.92820	−	4.00000i	0.235023	−	0.135691i
$870$	1.00000			0.0339032
$871$		0			0
$872$	6.00000			0.203186
$873$	1.73205	−	1.00000i	0.0586210	−	0.0338449i
$874$	−18.0000	−	31.1769i	−0.608859	−	1.05457i
$875$	9.00000	−	15.5885i	0.304256	−	0.526986i
$876$		−	11.0000i		−	0.371656i
$877$	14.7224	+	8.50000i	0.497141	+	0.287025i	0.727532	−	0.686074i	$-0.240667\pi$
$877$	14.7224	+	8.50000i	0.497141	+	0.287025i	−0.230391	+	0.973098i	$0.574001\pi$
$878$	−12.1244	−	7.00000i	−0.409177	−	0.236239i
$879$			9.00000i			0.303562i
$880$	1.00000	−	1.73205i	0.0337100	−	0.0583874i
$881$	18.5000	+	32.0429i	0.623281	+	1.07955i	0.988871	+	0.148778i	$0.0475340\pi$
$881$	18.5000	+	32.0429i	0.623281	+	1.07955i	−0.365590	+	0.930776i	$0.619133\pi$
$882$	−2.59808	+	1.50000i	−0.0874818	+	0.0505076i
$883$	−16.0000			−0.538443			−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000			−0.538443			−0.269221	+	0.963078i	$0.586766\pi$
$884$		0			0
$885$		0			0
$886$	3.46410	−	2.00000i	0.116379	−	0.0671913i
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$	1.50000	−	2.59808i	0.0503367	−	0.0871857i
$889$		−	40.0000i		−	1.34156i
$890$	12.1244	+	7.00000i	0.406409	+	0.234641i
$891$	1.73205	+	1.00000i	0.0580259	+	0.0335013i
$892$		−	16.0000i		−	0.535720i
$893$	18.0000	−	31.1769i	0.602347	−	1.04330i
$894$	−1.50000	−	2.59808i	−0.0501675	−	0.0868927i
$895$	1.73205	−	1.00000i	0.0578961	−	0.0334263i
$896$	6.00000			0.200446
$897$		0			0
$898$	34.0000			1.13459
$899$	3.46410	−	2.00000i	0.115534	−	0.0667037i
$900$	−2.00000	−	3.46410i	−0.0666667	−	0.115470i
$901$	31.5000	−	54.5596i	1.04942	−	1.81764i
$902$			18.0000i			0.599334i
$903$	−10.3923	−	6.00000i	−0.345834	−	0.199667i
$904$	−38.9711	−	22.5000i	−1.29616	−	0.748339i
$905$			7.00000i			0.232688i
$906$	−1.00000	+	1.73205i	−0.0332228	+	0.0575435i
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	0.948278	−	0.317441i	$-0.102824\pi$
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	−0.749051	+	0.662512i	$0.769490\pi$
$908$	12.1244	−	7.00000i	0.402361	−	0.232303i
$909$	−3.00000			−0.0995037
$910$		0			0
$911$	−40.0000			−1.32526			−0.662630	−	0.748947i	$-0.730560\pi$
$911$	−40.0000			−1.32526			−0.662630	+	0.748947i	$0.730560\pi$
$912$	5.19615	−	3.00000i	0.172062	−	0.0993399i
$913$	−14.0000	−	24.2487i	−0.463332	−	0.802515i
$914$	−6.50000	+	11.2583i	−0.215001	+	0.372392i
$915$		−	1.00000i		−	0.0330590i
$916$	19.0526	+	11.0000i	0.629514	+	0.363450i
$917$	13.8564	+	8.00000i	0.457579	+	0.264183i
$918$			7.00000i			0.231034i
$919$	−12.0000	+	20.7846i	−0.395843	+	0.685621i	−0.993208	−	0.116348i	$-0.962881\pi$
$919$	−12.0000	+	20.7846i	−0.395843	+	0.685621i	0.597365	+	0.801970i	$0.296214\pi$
$920$	−9.00000	−	15.5885i	−0.296721	−	0.513936i
$921$	−12.1244	+	7.00000i	−0.399511	+	0.230658i
$922$	−19.0000			−0.625732
$923$		0			0
$924$	−4.00000			−0.131590
$925$	3.46410	−	2.00000i	0.113899	−	0.0657596i
$926$	13.0000	+	22.5167i	0.427207	+	0.739943i
$927$	3.00000	−	5.19615i	0.0985329	−	0.170664i
$928$			5.00000i			0.164133i
$929$	−23.3827	−	13.5000i	−0.767161	−	0.442921i	0.0646999	−	0.997905i	$-0.479391\pi$
$929$	−23.3827	−	13.5000i	−0.767161	−	0.442921i	−0.831861	+	0.554984i	$0.812724\pi$
$930$	−3.46410	−	2.00000i	−0.113592	−	0.0655826i
$931$			18.0000i			0.589926i
$932$	5.00000	−	8.66025i	0.163780	−	0.283676i
$933$	−9.00000	−	15.5885i	−0.294647	−	0.510343i
$934$	5.19615	−	3.00000i	0.170023	−	0.0981630i
$935$	14.0000			0.457849
$936$		0			0
$937$	−49.0000			−1.60076			−0.800380	−	0.599493i	$-0.795369\pi$
$937$	−49.0000			−1.60076			−0.800380	+	0.599493i	$0.795369\pi$
$938$	3.46410	−	2.00000i	0.113107	−	0.0653023i
$939$	3.00000	+	5.19615i	0.0979013	+	0.169570i
$940$	3.00000	−	5.19615i	0.0978492	−	0.169480i
$941$			38.0000i			1.23876i	0.785090	+	0.619382i	$0.212617\pi$
$941$			38.0000i			1.23876i	−0.785090	+	0.619382i	$0.787383\pi$
$942$	2.59808	+	1.50000i	0.0846499	+	0.0488726i
$943$	46.7654	+	27.0000i	1.52289	+	0.879241i
$944$		0			0
$945$	−1.00000	+	1.73205i	−0.0325300	+	0.0563436i
$946$	−6.00000	−	10.3923i	−0.195077	−	0.337883i
$947$	−41.5692	+	24.0000i	−1.35082	+	0.779895i	−0.988364	−	0.152106i	$-0.951394\pi$
$947$	−41.5692	+	24.0000i	−1.35082	+	0.779895i	−0.362454	+	0.932002i	$0.618061\pi$
$948$	4.00000			0.129914
$949$		0			0
$950$	24.0000			0.778663
$951$	−21.6506	+	12.5000i	−0.702070	+	0.405340i
$952$	−21.0000	−	36.3731i	−0.680614	−	1.17886i
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	−0.813337	−	0.581793i	$-0.802351\pi$
$953$	3.00000	−	5.19615i	0.0971795	−	0.168320i	0.910516	+	0.413473i	$0.135685\pi$
$954$			9.00000i			0.291386i
$955$	3.46410	+	2.00000i	0.112096	+	0.0647185i
$956$	25.9808	+	15.0000i	0.840278	+	0.485135i
$957$		−	2.00000i		−	0.0646508i
$958$	−12.0000	+	20.7846i	−0.387702	+	0.671520i
$959$	−3.00000	−	5.19615i	−0.0968751	−	0.167793i
$960$	6.06218	−	3.50000i	0.195656	−	0.112962i
$961$	15.0000			0.483871
$962$		0			0
$963$	−6.00000			−0.193347
$964$	6.06218	−	3.50000i	0.195250	−	0.112727i
$965$	−4.50000	−	7.79423i	−0.144860	−	0.250905i
$966$	6.00000	−	10.3923i	0.193047	−	0.334367i
$967$		−	2.00000i		−	0.0643157i	−0.999483	−	0.0321578i	$-0.989762\pi$
$967$		−	2.00000i		−	0.0643157i	0.999483	−	0.0321578i	$-0.0102379\pi$
$968$	18.1865	+	10.5000i	0.584537	+	0.337483i
$969$	36.3731	+	21.0000i	1.16847	+	0.674617i
$970$			2.00000i			0.0642161i
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	0.418101	+	0.908401i	$0.362696\pi$
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	−0.995748	+	0.0921142i	$0.970638\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	20.7846	−	12.0000i	0.666324	−	0.384702i
$974$	−18.0000			−0.576757
$975$		0			0
$976$	−1.00000			−0.0320092
$977$	−28.5788	+	16.5000i	−0.914318	+	0.527882i	−0.881818	−	0.471590i	$-0.843680\pi$
$977$	−28.5788	+	16.5000i	−0.914318	+	0.527882i	−0.0325001	+	0.999472i	$0.510347\pi$
$978$	−2.00000	−	3.46410i	−0.0639529	−	0.110770i
$979$	14.0000	−	24.2487i	0.447442	−	0.774992i
$980$			3.00000i			0.0958315i
$981$	−1.73205	−	1.00000i	−0.0553001	−	0.0319275i
$982$	−5.19615	−	3.00000i	−0.165816	−	0.0957338i
$983$			4.00000i			0.127580i	0.997963	+	0.0637901i	$0.0203188\pi$
$983$			4.00000i			0.127580i	−0.997963	+	0.0637901i	$0.979681\pi$
$984$	−13.5000	+	23.3827i	−0.430364	+	0.745413i
$985$	−3.00000	−	5.19615i	−0.0955879	−	0.165563i
$986$	6.06218	−	3.50000i	0.193059	−	0.111463i
$987$	12.0000			0.381964
$988$		0			0
$989$	−36.0000			−1.14473
$990$	−1.73205	+	1.00000i	−0.0550482	+	0.0317821i
$991$	1.00000	+	1.73205i	0.0317660	+	0.0550204i	0.881471	−	0.472237i	$-0.156554\pi$
$991$	1.00000	+	1.73205i	0.0317660	+	0.0550204i	−0.849705	+	0.527258i	$0.823220\pi$
$992$	10.0000	−	17.3205i	0.317500	−	0.549927i
$993$		−	4.00000i		−	0.126936i
$994$	10.3923	+	6.00000i	0.329624	+	0.190308i
$995$	12.1244	+	7.00000i	0.384368	+	0.221915i
$996$		−	14.0000i		−	0.443607i
$997$	17.5000	−	30.3109i	0.554231	−	0.959955i	−0.443732	−	0.896159i	$-0.646346\pi$
$997$	17.5000	−	30.3109i	0.554231	−	0.959955i	0.997963	−	0.0637961i	$-0.0203207\pi$
$998$	12.0000	+	20.7846i	0.379853	+	0.657925i
$999$	−0.866025	+	0.500000i	−0.0273998	+	0.0158193i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.j.d.361.1		4
13.2	odd	12		507.2.a.b.1.1		1
13.3	even	3		507.2.b.b.337.1		2
13.4	even	6	inner	507.2.j.d.316.1		4
13.5	odd	4		507.2.e.c.484.1		2
13.6	odd	12		507.2.e.c.22.1		2
13.7	odd	12		39.2.e.a.22.1	yes	2
13.8	odd	4		39.2.e.a.16.1	✓	2
13.9	even	3	inner	507.2.j.d.316.2		4
13.10	even	6		507.2.b.b.337.2		2
13.11	odd	12		507.2.a.c.1.1		1
13.12	even	2	inner	507.2.j.d.361.2		4
39.2	even	12		1521.2.a.d.1.1		1
39.8	even	4		117.2.g.b.55.1		2
39.11	even	12		1521.2.a.a.1.1		1
39.20	even	12		117.2.g.b.100.1		2
39.23	odd	6		1521.2.b.c.1351.1		2
39.29	odd	6		1521.2.b.c.1351.2		2
52.7	even	12		624.2.q.c.529.1		2
52.11	even	12		8112.2.a.w.1.1		1
52.15	even	12		8112.2.a.bc.1.1		1
52.47	even	4		624.2.q.c.289.1		2
65.7	even	12		975.2.bb.d.724.1		4
65.8	even	4		975.2.bb.d.874.1		4
65.33	even	12		975.2.bb.d.724.2		4
65.34	odd	4		975.2.i.f.601.1		2
65.47	even	4		975.2.bb.d.874.2		4
65.59	odd	12		975.2.i.f.451.1		2
156.47	odd	4		1872.2.t.j.289.1		2
156.59	odd	12		1872.2.t.j.1153.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.a.16.1	✓	2	13.8	odd	4
39.2.e.a.22.1	yes	2	13.7	odd	12
117.2.g.b.55.1		2	39.8	even	4
117.2.g.b.100.1		2	39.20	even	12
507.2.a.b.1.1		1	13.2	odd	12
507.2.a.c.1.1		1	13.11	odd	12
507.2.b.b.337.1		2	13.3	even	3
507.2.b.b.337.2		2	13.10	even	6
507.2.e.c.22.1		2	13.6	odd	12
507.2.e.c.484.1		2	13.5	odd	4
507.2.j.d.316.1		4	13.4	even	6	inner
507.2.j.d.316.2		4	13.9	even	3	inner
507.2.j.d.361.1		4	1.1	even	1	trivial
507.2.j.d.361.2		4	13.12	even	2	inner
624.2.q.c.289.1		2	52.47	even	4
624.2.q.c.529.1		2	52.7	even	12
975.2.i.f.451.1		2	65.59	odd	12
975.2.i.f.601.1		2	65.34	odd	4
975.2.bb.d.724.1		4	65.7	even	12
975.2.bb.d.724.2		4	65.33	even	12
975.2.bb.d.874.1		4	65.8	even	4
975.2.bb.d.874.2		4	65.47	even	4
1521.2.a.a.1.1		1	39.11	even	12
1521.2.a.d.1.1		1	39.2	even	12
1521.2.b.c.1351.1		2	39.23	odd	6
1521.2.b.c.1351.2		2	39.29	odd	6
1872.2.t.j.289.1		2	156.47	odd	4
1872.2.t.j.1153.1		2	156.59	odd	12
8112.2.a.w.1.1		1	52.11	even	12
8112.2.a.bc.1.1		1	52.15	even	12

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} -3.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.00000i q^{5} +(-0.866025 - 0.500000i) q^{6} +(-1.73205 - 1.00000i) q^{7} -3.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.73205 + 1.00000i) q^{11} -1.00000 q^{12} +2.00000 q^{14} +(-0.866025 + 0.500000i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-3.50000 + 6.06218i) q^{17} -1.00000i q^{18} +(-5.19615 - 3.00000i) q^{19} +(-0.866025 - 0.500000i) q^{20} -2.00000i q^{21} +(1.00000 - 1.73205i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(2.59808 - 1.50000i) q^{24} +4.00000 q^{25} -1.00000 q^{27} +(1.73205 - 1.00000i) q^{28} +(0.500000 + 0.866025i) q^{29} +(0.500000 - 0.866025i) q^{30} -4.00000i q^{31} +(4.33013 + 2.50000i) q^{32} +(-1.73205 - 1.00000i) q^{33} -7.00000i q^{34} +(1.00000 - 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(0.866025 - 0.500000i) q^{37} +6.00000 q^{38} +3.00000 q^{40} +(-7.79423 + 4.50000i) q^{41} +(1.00000 + 1.73205i) q^{42} +(3.00000 - 5.19615i) q^{43} -2.00000i q^{44} +(-0.866025 - 0.500000i) q^{45} +(5.19615 + 3.00000i) q^{46} +6.00000i q^{47} +(-0.500000 + 0.866025i) q^{48} +(-1.50000 - 2.59808i) q^{49} +(-3.46410 + 2.00000i) q^{50} -7.00000 q^{51} -9.00000 q^{53} +(0.866025 - 0.500000i) q^{54} +(-1.00000 - 1.73205i) q^{55} +(-3.00000 + 5.19615i) q^{56} -6.00000i q^{57} +(-0.866025 - 0.500000i) q^{58} -1.00000i q^{60} +(-0.500000 + 0.866025i) q^{61} +(2.00000 + 3.46410i) q^{62} +(1.73205 - 1.00000i) q^{63} -7.00000 q^{64} +2.00000 q^{66} +(1.73205 - 1.00000i) q^{67} +(-3.50000 - 6.06218i) q^{68} +(3.00000 - 5.19615i) q^{69} +2.00000i q^{70} +(5.19615 + 3.00000i) q^{71} +(2.59808 + 1.50000i) q^{72} +11.0000i q^{73} +(-0.500000 + 0.866025i) q^{74} +(2.00000 + 3.46410i) q^{75} +(5.19615 - 3.00000i) q^{76} +4.00000 q^{77} -4.00000 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} +14.0000i q^{83} +(1.73205 + 1.00000i) q^{84} +(-6.06218 - 3.50000i) q^{85} +6.00000i q^{86} +(-0.500000 + 0.866025i) q^{87} +(3.00000 + 5.19615i) q^{88} +(-12.1244 + 7.00000i) q^{89} +1.00000 q^{90} +6.00000 q^{92} +(3.46410 - 2.00000i) q^{93} +(-3.00000 - 5.19615i) q^{94} +(3.00000 - 5.19615i) q^{95} +5.00000i q^{96} +(-1.73205 - 1.00000i) q^{97} +(2.59808 + 1.50000i) q^{98} -2.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} - 2 q^{4} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 - 2 * q^4 - 2 * q^9	\( 4 q + 2 q^{3} - 2 q^{4} - 2 q^{9} - 2 q^{10} - 4 q^{12} + 8 q^{14} + 2 q^{16} - 14 q^{17} + 4 q^{22} - 12 q^{23} + 16 q^{25} - 4 q^{27} + 2 q^{29} + 2 q^{30} + 4 q^{35} - 2 q^{36} + 24 q^{38} + 12 q^{40} + 4 q^{42} + 12 q^{43} - 2 q^{48} - 6 q^{49} - 28 q^{51} - 36 q^{53} - 4 q^{55} - 12 q^{56} - 2 q^{61} + 8 q^{62} - 28 q^{64} + 8 q^{66} - 14 q^{68} + 12 q^{69} - 2 q^{74} + 8 q^{75} + 16 q^{77} - 16 q^{79} - 2 q^{81} + 18 q^{82} - 2 q^{87} + 12 q^{88} + 4 q^{90} + 24 q^{92} - 12 q^{94} + 12 q^{95}+O(q^{100}) \) 4 * q + 2 * q^3 - 2 * q^4 - 2 * q^9 - 2 * q^10 - 4 * q^12 + 8 * q^14 + 2 * q^16 - 14 * q^17 + 4 * q^22 - 12 * q^23 + 16 * q^25 - 4 * q^27 + 2 * q^29 + 2 * q^30 + 4 * q^35 - 2 * q^36 + 24 * q^38 + 12 * q^40 + 4 * q^42 + 12 * q^43 - 2 * q^48 - 6 * q^49 - 28 * q^51 - 36 * q^53 - 4 * q^55 - 12 * q^56 - 2 * q^61 + 8 * q^62 - 28 * q^64 + 8 * q^66 - 14 * q^68 + 12 * q^69 - 2 * q^74 + 8 * q^75 + 16 * q^77 - 16 * q^79 - 2 * q^81 + 18 * q^82 - 2 * q^87 + 12 * q^88 + 4 * q^90 + 24 * q^92 - 12 * q^94 + 12 * q^95

Introduction

L-functions

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