LMFDB - Embedded newform 507.2.e.c.484.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(22,507)]

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, 4]))

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

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

chi := DirichletCharacter("507.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.e (of order $3$, 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:	$2$
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:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			484.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	507.484
Dual form			507.2.e.c.22.1

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

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$	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
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$	3.00000			1.06066
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	2.00000			0.534522
$15$	0.500000	+	0.866025i	0.129099	+	0.223607i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.50000	−	6.06218i	0.848875	−	1.47029i	−0.0333386	−	0.999444i	$-0.510614\pi$
$17$	3.50000	−	6.06218i	0.848875	−	1.47029i	0.882213	−	0.470850i	$-0.156053\pi$
$18$	−1.00000			−0.235702
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	0.284157	+	0.958778i	$0.408286\pi$
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	−0.972404	+	0.233301i	$0.925047\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	2.00000			0.436436
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$	1.50000	+	2.59808i	0.306186	+	0.530330i
$25$	−4.00000			−0.800000
$26$		0			0
$27$	−1.00000			−0.192450
$28$	−1.00000	−	1.73205i	−0.188982	−	0.327327i
$29$	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
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	2.50000	−	4.33013i	0.441942	−	0.765466i
$33$	1.00000	−	1.73205i	0.174078	−	0.301511i
$34$	7.00000			1.20049
$35$	1.00000	−	1.73205i	0.169031	−	0.292770i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−6.00000			−0.973329
$39$		0			0
$40$	3.00000			0.474342
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$	1.00000	+	1.73205i	0.154303	+	0.267261i
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	−0.998828	−	0.0484030i	$-0.984587\pi$
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	0.541332	+	0.840809i	$0.317920\pi$
$44$	−2.00000			−0.301511
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	1.50000	+	2.59808i	0.214286	+	0.371154i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$	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	$0.712106\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−1.00000	−	1.73205i	−0.134840	−	0.233550i
$56$	3.00000	−	5.19615i	0.400892	−	0.694365i
$57$	−6.00000			−0.794719
$58$	−0.500000	+	0.866025i	−0.0656532	+	0.113715i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	1.00000			0.129099
$61$	−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
$63$	1.00000	+	1.73205i	0.125988	+	0.218218i
$64$	7.00000			0.875000
$65$		0			0
$66$	2.00000			0.246183
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$	−3.50000	−	6.06218i	−0.424437	−	0.735147i
$69$	−3.00000	+	5.19615i	−0.361158	+	0.625543i
$70$	2.00000			0.239046
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$	−1.50000	+	2.59808i	−0.176777	+	0.306186i
$73$	−11.0000			−1.28745			−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000			−1.28745			−0.643726	+	0.765256i	$0.722612\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$	3.00000	+	5.19615i	0.344124	+	0.596040i
$77$	−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	$0.572244\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−4.50000	+	7.79423i	−0.496942	+	0.860729i
$83$	14.0000			1.53670			0.768350	−	0.640030i	$-0.221078\pi$
$83$	14.0000			1.53670			0.768350	+	0.640030i	$0.221078\pi$
$84$	1.00000	−	1.73205i	0.109109	−	0.188982i
$85$	3.50000	−	6.06218i	0.379628	−	0.657536i
$86$	−6.00000			−0.646997
$87$	−0.500000	+	0.866025i	−0.0536056	+	0.0928477i
$88$	−3.00000	−	5.19615i	−0.319801	−	0.553912i
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	−0.951584	−	0.307389i	$-0.900545\pi$
$89$	−7.00000	−	12.1244i	−0.741999	−	1.28518i	0.209585	−	0.977790i	$-0.432789\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	6.00000			0.625543
$93$	−2.00000	−	3.46410i	−0.207390	−	0.359211i
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$	5.00000			0.510310
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	−1.50000	+	2.59808i	−0.151523	+	0.262445i
$99$	2.00000			0.201008
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$	3.50000	+	6.06218i	0.346552	+	0.600245i
$103$	6.00000			0.591198			0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000			0.591198			0.295599	+	0.955312i	$0.404481\pi$
$104$		0			0
$105$	2.00000			0.195180
$106$	−4.50000	−	7.79423i	−0.437079	−	0.757042i
$107$	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
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$	1.00000	−	1.73205i	0.0953463	−	0.165145i
$111$	−0.500000	+	0.866025i	−0.0474579	+	0.0821995i
$112$	2.00000			0.188982
$113$	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
$115$	3.00000	+	5.19615i	0.279751	+	0.484544i
$116$	1.00000			0.0928477
$117$		0			0
$118$		0			0
$119$	−7.00000	−	12.1244i	−0.641689	−	1.11144i
$120$	1.50000	+	2.59808i	0.136931	+	0.237171i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−1.00000			−0.0905357
$123$	−4.50000	+	7.79423i	−0.405751	+	0.702782i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$	−9.00000			−0.804984
$126$	−1.00000	+	1.73205i	−0.0890871	+	0.154303i
$127$	−10.0000	−	17.3205i	−0.887357	−	1.53695i	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−10.0000	−	17.3205i	−0.887357	−	1.53695i	−0.0443678	−	0.999015i	$-0.514127\pi$
$128$	−1.50000	−	2.59808i	−0.132583	−	0.229640i
$129$	−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	$0.613642\pi$
$132$	−1.00000	−	1.73205i	−0.0870388	−	0.150756i
$133$	6.00000	+	10.3923i	0.520266	+	0.901127i
$134$	1.00000	−	1.73205i	0.0863868	−	0.149626i
$135$	−1.00000			−0.0860663
$136$	10.5000	−	18.1865i	0.900368	−	1.55948i
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	−0.922961	−	0.384893i	$-0.874238\pi$
$137$	−1.50000	+	2.59808i	−0.128154	+	0.221969i	0.794808	+	0.606861i	$0.207572\pi$
$138$	−6.00000			−0.510754
$139$	−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
$141$	−3.00000	−	5.19615i	−0.252646	−	0.437595i
$142$	6.00000			0.503509
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	0.500000	+	0.866025i	0.0415227	+	0.0719195i
$146$	−5.50000	−	9.52628i	−0.455183	−	0.788400i
$147$	−1.50000	+	2.59808i	−0.123718	+	0.214286i
$148$	1.00000			0.0821995
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$	−9.00000	+	15.5885i	−0.729996	+	1.26439i
$153$	3.50000	+	6.06218i	0.282958	+	0.490098i
$154$	−2.00000	−	3.46410i	−0.161165	−	0.279145i
$155$	−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	$0.538197\pi$
$158$	−2.00000	−	3.46410i	−0.159111	−	0.275589i
$159$	−4.50000	−	7.79423i	−0.356873	−	0.618123i
$160$	2.50000	−	4.33013i	0.197642	−	0.342327i
$161$	12.0000			0.945732
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	−0.933659	−	0.358162i	$-0.883403\pi$
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	0.777007	+	0.629492i	$0.216737\pi$
$164$	9.00000			0.702782
$165$	1.00000	−	1.73205i	0.0778499	−	0.134840i
$166$	7.00000	+	12.1244i	0.543305	+	0.941033i
$167$	8.00000	+	13.8564i	0.619059	+	1.07224i	0.989658	+	0.143448i	$0.0458190\pi$
$167$	8.00000	+	13.8564i	0.619059	+	1.07224i	−0.370599	+	0.928793i	$0.620848\pi$
$168$	6.00000			0.462910
$169$		0			0
$170$	7.00000			0.536875
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$	3.00000	+	5.19615i	0.228748	+	0.396203i
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	−0.729155	−	0.684349i	$-0.760087\pi$
$173$	3.00000	−	5.19615i	0.228086	−	0.395056i	0.957241	+	0.289292i	$0.0934200\pi$
$174$	−1.00000			−0.0758098
$175$	−4.00000	+	6.92820i	−0.302372	+	0.523723i
$176$	1.00000	−	1.73205i	0.0753778	−	0.130558i
$177$		0			0
$178$	7.00000	−	12.1244i	0.524672	−	0.908759i
$179$	1.00000	+	1.73205i	0.0747435	+	0.129460i	0.900975	−	0.433872i	$-0.142853\pi$
$179$	1.00000	+	1.73205i	0.0747435	+	0.129460i	−0.826231	+	0.563331i	$0.809520\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$	−1.00000			−0.0739221
$184$	9.00000	+	15.5885i	0.663489	+	1.14920i
$185$	0.500000	+	0.866025i	0.0367607	+	0.0636715i
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$	−14.0000			−1.02378
$188$	−3.00000	+	5.19615i	−0.218797	+	0.378968i
$189$	−1.00000	+	1.73205i	−0.0727393	+	0.125988i
$190$	−6.00000			−0.435286
$191$	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
$193$	−4.50000	−	7.79423i	−0.323917	−	0.561041i	0.657376	−	0.753563i	$-0.271667\pi$
$193$	−4.50000	−	7.79423i	−0.323917	−	0.561041i	−0.981293	+	0.192522i	$0.938333\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	3.00000			0.214286
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	0.952882	−	0.303340i	$-0.0981018\pi$
$197$	3.00000	+	5.19615i	0.213741	+	0.370211i	−0.739141	+	0.673550i	$0.764768\pi$
$198$	1.00000	+	1.73205i	0.0710669	+	0.123091i
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	−0.999990	−	0.00436292i	$-0.998611\pi$
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	0.503774	+	0.863836i	$0.331945\pi$
$200$	−12.0000			−0.848528
$201$	1.00000	−	1.73205i	0.0705346	−	0.122169i
$202$	1.50000	−	2.59808i	0.105540	−	0.182800i
$203$	2.00000			0.140372
$204$	3.50000	−	6.06218i	0.245049	−	0.424437i
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	3.00000	+	5.19615i	0.209020	+	0.362033i
$207$	−6.00000			−0.417029
$208$		0			0
$209$	12.0000			0.830057
$210$	1.00000	+	1.73205i	0.0690066	+	0.119523i
$211$	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
$213$	6.00000			0.411113
$214$	−3.00000	+	5.19615i	−0.205076	+	0.355202i
$215$	−3.00000	+	5.19615i	−0.204598	+	0.354375i
$216$	−3.00000			−0.204124
$217$	−4.00000	+	6.92820i	−0.271538	+	0.470317i
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$	−5.50000	−	9.52628i	−0.371656	−	0.643726i
$220$	−2.00000			−0.134840
$221$		0			0
$222$	−1.00000			−0.0671156
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	0.999128	+	0.0417488i	$0.0132929\pi$
$223$	8.00000	+	13.8564i	0.535720	+	0.927894i	−0.463409	+	0.886145i	$0.653374\pi$
$224$	−5.00000	−	8.66025i	−0.334077	−	0.578638i
$225$	2.00000	−	3.46410i	0.133333	−	0.230940i
$226$	15.0000			0.997785
$227$	−7.00000	+	12.1244i	−0.464606	+	0.804722i	−0.999184	−	0.0403978i	$-0.987137\pi$
$227$	−7.00000	+	12.1244i	−0.464606	+	0.804722i	0.534577	+	0.845120i	$0.320471\pi$
$228$	−3.00000	+	5.19615i	−0.198680	+	0.344124i
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$	−3.00000	+	5.19615i	−0.197814	+	0.342624i
$231$	−2.00000	−	3.46410i	−0.131590	−	0.227921i
$232$	1.50000	+	2.59808i	0.0984798	+	0.170572i
$233$	10.0000			0.655122			0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000			0.655122			0.327561	+	0.944830i	$0.393773\pi$
$234$		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
$239$	−30.0000			−1.94054			−0.970269	−	0.242028i	$-0.922188\pi$
$239$	−30.0000			−1.94054			−0.970269	+	0.242028i	$0.922188\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	−0.731001	−	0.682376i	$-0.760947\pi$
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	0.956456	+	0.291877i	$0.0942799\pi$
$242$	7.00000			0.449977
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	0.500000	+	0.866025i	0.0320092	+	0.0554416i
$245$	1.50000	+	2.59808i	0.0958315	+	0.165985i
$246$	−9.00000			−0.573819
$247$		0			0
$248$	−12.0000			−0.762001
$249$	7.00000	+	12.1244i	0.443607	+	0.768350i
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	−0.990876	−	0.134778i	$-0.956968\pi$
$251$	−6.00000	+	10.3923i	−0.378717	+	0.655956i	0.612159	+	0.790735i	$0.290301\pi$
$252$	2.00000			0.125988
$253$	6.00000	−	10.3923i	0.377217	−	0.653359i
$254$	10.0000	−	17.3205i	0.627456	−	1.08679i
$255$	7.00000			0.438357
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	3.50000	+	6.06218i	0.218324	+	0.378148i	0.954296	−	0.298864i	$-0.0966077\pi$
$257$	3.50000	+	6.06218i	0.218324	+	0.378148i	−0.735972	+	0.677012i	$0.763274\pi$
$258$	−3.00000	−	5.19615i	−0.186772	−	0.323498i
$259$	2.00000			0.124274
$260$		0			0
$261$	−1.00000			−0.0618984
$262$	−4.00000	−	6.92820i	−0.247121	−	0.428026i
$263$	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
$265$	−9.00000			−0.552866
$266$	−6.00000	+	10.3923i	−0.367884	+	0.637193i
$267$	7.00000	−	12.1244i	0.428393	−	0.741999i
$268$	−2.00000			−0.122169
$269$	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		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$	7.00000			0.424437
$273$		0			0
$274$	−3.00000			−0.181237
$275$	4.00000	+	6.92820i	0.241209	+	0.417786i
$276$	3.00000	+	5.19615i	0.180579	+	0.312772i
$277$	15.5000	−	26.8468i	0.931305	−	1.61307i	0.150210	−	0.988654i	$-0.452005\pi$
$277$	15.5000	−	26.8468i	0.931305	−	1.61307i	0.781094	−	0.624413i	$-0.214662\pi$
$278$	−12.0000			−0.719712
$279$	2.00000	−	3.46410i	0.119737	−	0.207390i
$280$	3.00000	−	5.19615i	0.179284	−	0.310530i
$281$	19.0000			1.13344			0.566722	−	0.823909i	$-0.308211\pi$
$281$	19.0000			1.13344			0.566722	+	0.823909i	$0.308211\pi$
$282$	3.00000	−	5.19615i	0.178647	−	0.309426i
$283$	9.00000	+	15.5885i	0.534994	+	0.926638i	0.999164	+	0.0408910i	$0.0130196\pi$
$283$	9.00000	+	15.5885i	0.534994	+	0.926638i	−0.464169	+	0.885747i	$0.653647\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$	−6.00000			−0.355409
$286$		0			0
$287$	18.0000			1.06251
$288$	2.50000	+	4.33013i	0.147314	+	0.255155i
$289$	−16.0000	−	27.7128i	−0.941176	−	1.63017i
$290$	−0.500000	+	0.866025i	−0.0293610	+	0.0508548i
$291$	−2.00000			−0.117242
$292$	−5.50000	+	9.52628i	−0.321863	+	0.557483i
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	−0.967009	−	0.254741i	$-0.918010\pi$
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	0.704117	+	0.710084i	$0.251343\pi$
$294$	−3.00000			−0.174964
$295$		0			0
$296$	1.50000	+	2.59808i	0.0871857	+	0.151010i
$297$	1.00000	+	1.73205i	0.0580259	+	0.100504i
$298$	3.00000			0.173785
$299$		0			0
$300$	−4.00000			−0.230940
$301$	6.00000	+	10.3923i	0.345834	+	0.599002i
$302$	1.00000	+	1.73205i	0.0575435	+	0.0996683i
$303$	1.50000	−	2.59808i	0.0861727	−	0.149256i
$304$	−6.00000			−0.344124
$305$	−0.500000	+	0.866025i	−0.0286299	+	0.0495885i
$306$	−3.50000	+	6.06218i	−0.200082	+	0.346552i
$307$	−14.0000			−0.799022			−0.399511	−	0.916728i	$-0.630820\pi$
$307$	−14.0000			−0.799022			−0.399511	+	0.916728i	$0.630820\pi$
$308$	−2.00000	+	3.46410i	−0.113961	+	0.197386i
$309$	3.00000	+	5.19615i	0.170664	+	0.295599i
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$	18.0000			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	−1.50000	−	2.59808i	−0.0846499	−	0.146618i
$315$	1.00000	+	1.73205i	0.0563436	+	0.0975900i
$316$	−2.00000	+	3.46410i	−0.112509	+	0.194871i
$317$	25.0000			1.40414			0.702070	−	0.712108i	$-0.252259\pi$
$317$	25.0000			1.40414			0.702070	+	0.712108i	$0.252259\pi$
$318$	4.50000	−	7.79423i	0.252347	−	0.437079i
$319$	1.00000	−	1.73205i	0.0559893	−	0.0969762i
$320$	7.00000			0.391312
$321$	−3.00000	+	5.19615i	−0.167444	+	0.290021i
$322$	6.00000	+	10.3923i	0.334367	+	0.579141i
$323$	21.0000	+	36.3731i	1.16847	+	2.02385i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−4.00000			−0.221540
$327$	1.00000	+	1.73205i	0.0553001	+	0.0957826i
$328$	13.5000	+	23.3827i	0.745413	+	1.29109i
$329$	−6.00000	+	10.3923i	−0.330791	+	0.572946i
$330$	2.00000			0.110096
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	−0.915742	−	0.401768i	$-0.868396\pi$
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	0.805812	+	0.592172i	$0.201729\pi$
$332$	7.00000	−	12.1244i	0.384175	−	0.665410i
$333$	−1.00000			−0.0547997
$334$	−8.00000	+	13.8564i	−0.437741	+	0.758189i
$335$	−1.00000	−	1.73205i	−0.0546358	−	0.0946320i
$336$	1.00000	+	1.73205i	0.0545545	+	0.0944911i
$337$	−33.0000			−1.79762			−0.898812	−	0.438334i	$-0.855569\pi$
$337$	−33.0000			−1.79762			−0.898812	+	0.438334i	$0.855569\pi$
$338$		0			0
$339$	15.0000			0.814688
$340$	−3.50000	−	6.06218i	−0.189814	−	0.328768i
$341$	4.00000	+	6.92820i	0.216612	+	0.375183i
$342$	3.00000	−	5.19615i	0.162221	−	0.280976i
$343$	20.0000			1.07990
$344$	−9.00000	+	15.5885i	−0.485247	+	0.840473i
$345$	−3.00000	+	5.19615i	−0.161515	+	0.279751i
$346$	6.00000			0.322562
$347$	−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
$349$	−13.0000	−	22.5167i	−0.695874	−	1.20529i	−0.969885	−	0.243563i	$-0.921684\pi$
$349$	−13.0000	−	22.5167i	−0.695874	−	1.20529i	0.274011	−	0.961727i	$-0.411649\pi$
$350$	−8.00000			−0.427618
$351$		0			0
$352$	−10.0000			−0.533002
$353$	−5.50000	−	9.52628i	−0.292735	−	0.507033i	0.681720	−	0.731613i	$-0.261232\pi$
$353$	−5.50000	−	9.52628i	−0.292735	−	0.507033i	−0.974456	+	0.224580i	$0.927899\pi$
$354$		0			0
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$	−14.0000			−0.741999
$357$	7.00000	−	12.1244i	0.370479	−	0.641689i
$358$	−1.00000	+	1.73205i	−0.0528516	+	0.0915417i
$359$	18.0000			0.950004			0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000			0.950004			0.475002	+	0.879985i	$0.342447\pi$
$360$	−1.50000	+	2.59808i	−0.0790569	+	0.136931i
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	−3.50000	−	6.06218i	−0.183956	−	0.318621i
$363$	7.00000			0.367405
$364$		0			0
$365$	−11.0000			−0.575766
$366$	−0.500000	−	0.866025i	−0.0261354	−	0.0452679i
$367$	−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
$369$	−9.00000			−0.468521
$370$	−0.500000	+	0.866025i	−0.0259938	+	0.0450225i
$371$	−9.00000	+	15.5885i	−0.467257	+	0.809312i
$372$	−4.00000			−0.207390
$373$	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
$375$	−4.50000	−	7.79423i	−0.232379	−	0.402492i
$376$	−18.0000			−0.928279
$377$		0			0
$378$	−2.00000			−0.102869
$379$	−18.0000	−	31.1769i	−0.924598	−	1.60145i	−0.792207	−	0.610253i	$-0.791068\pi$
$379$	−18.0000	−	31.1769i	−0.924598	−	1.60145i	−0.132391	−	0.991198i	$-0.542266\pi$
$380$	3.00000	+	5.19615i	0.153897	+	0.266557i
$381$	10.0000	−	17.3205i	0.512316	−	0.887357i
$382$	4.00000			0.204658
$383$	4.00000	−	6.92820i	0.204390	−	0.354015i	−0.745548	−	0.666452i	$-0.767812\pi$
$383$	4.00000	−	6.92820i	0.204390	−	0.354015i	0.949938	+	0.312437i	$0.101145\pi$
$384$	1.50000	−	2.59808i	0.0765466	−	0.132583i
$385$	−4.00000			−0.203859
$386$	4.50000	−	7.79423i	0.229044	−	0.396716i
$387$	−3.00000	−	5.19615i	−0.152499	−	0.264135i
$388$	1.00000	+	1.73205i	0.0507673	+	0.0879316i
$389$	19.0000			0.963338			0.481669	−	0.876353i	$-0.340031\pi$
$389$	19.0000			0.963338			0.481669	+	0.876353i	$0.340031\pi$
$390$		0			0
$391$	42.0000			2.12403
$392$	4.50000	+	7.79423i	0.227284	+	0.393668i
$393$	−4.00000	−	6.92820i	−0.201773	−	0.349482i
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$	−4.00000			−0.201262
$396$	1.00000	−	1.73205i	0.0502519	−	0.0870388i
$397$	−17.0000	+	29.4449i	−0.853206	+	1.47780i	0.0250943	+	0.999685i	$0.492011\pi$
$397$	−17.0000	+	29.4449i	−0.853206	+	1.47780i	−0.878300	+	0.478110i	$0.841322\pi$
$398$	−14.0000			−0.701757
$399$	−6.00000	+	10.3923i	−0.300376	+	0.520266i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	0.500000	+	0.866025i	0.0249688	+	0.0432472i	0.878240	−	0.478220i	$-0.158718\pi$
$401$	0.500000	+	0.866025i	0.0249688	+	0.0432472i	−0.853271	+	0.521468i	$0.825385\pi$
$402$	2.00000			0.0997509
$403$		0			0
$404$	−3.00000			−0.149256
$405$	−0.500000	−	0.866025i	−0.0248452	−	0.0430331i
$406$	1.00000	+	1.73205i	0.0496292	+	0.0859602i
$407$	1.00000	−	1.73205i	0.0495682	−	0.0858546i
$408$	21.0000			1.03965
$409$	3.50000	−	6.06218i	0.173064	−	0.299755i	−0.766426	−	0.642333i	$-0.777967\pi$
$409$	3.50000	−	6.06218i	0.173064	−	0.299755i	0.939490	+	0.342578i	$0.111300\pi$
$410$	−4.50000	+	7.79423i	−0.222239	+	0.384930i
$411$	−3.00000			−0.147979
$412$	3.00000	−	5.19615i	0.147799	−	0.255996i
$413$		0			0
$414$	−3.00000	−	5.19615i	−0.147442	−	0.255377i
$415$	14.0000			0.687233
$416$		0			0
$417$	−12.0000			−0.587643
$418$	6.00000	+	10.3923i	0.293470	+	0.508304i
$419$	−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
$421$	19.0000			0.926003			0.463002	−	0.886357i	$-0.346772\pi$
$421$	19.0000			0.926003			0.463002	+	0.886357i	$0.346772\pi$
$422$	−4.00000	+	6.92820i	−0.194717	+	0.337260i
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$	−27.0000			−1.31124
$425$	−14.0000	+	24.2487i	−0.679100	+	1.17624i
$426$	3.00000	+	5.19615i	0.145350	+	0.251754i
$427$	1.00000	+	1.73205i	0.0483934	+	0.0838198i
$428$	6.00000			0.290021
$429$		0			0
$430$	−6.00000			−0.289346
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	−0.959985	−	0.280052i	$-0.909648\pi$
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	0.237460	−	0.971397i	$-0.423685\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−9.50000	+	16.4545i	−0.456541	+	0.790752i	−0.998775	−	0.0494752i	$-0.984245\pi$
$433$	−9.50000	+	16.4545i	−0.456541	+	0.790752i	0.542234	+	0.840227i	$0.317578\pi$
$434$	−8.00000			−0.384012
$435$	−0.500000	+	0.866025i	−0.0239732	+	0.0415227i
$436$	1.00000	−	1.73205i	0.0478913	−	0.0829502i
$437$	−36.0000			−1.72211
$438$	5.50000	−	9.52628i	0.262800	−	0.455183i
$439$	−7.00000	−	12.1244i	−0.334092	−	0.578664i	0.649218	−	0.760602i	$-0.275096\pi$
$439$	−7.00000	−	12.1244i	−0.334092	−	0.578664i	−0.983310	+	0.181938i	$0.941763\pi$
$440$	−3.00000	−	5.19615i	−0.143019	−	0.247717i
$441$	−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	$0.530292\pi$
$444$	0.500000	+	0.866025i	0.0237289	+	0.0410997i
$445$	−7.00000	−	12.1244i	−0.331832	−	0.574750i
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$	3.00000			0.141895
$448$	7.00000	−	12.1244i	0.330719	−	0.572822i
$449$	17.0000	−	29.4449i	0.802280	−	1.38959i	−0.115833	−	0.993269i	$-0.536954\pi$
$449$	17.0000	−	29.4449i	0.802280	−	1.38959i	0.918112	−	0.396320i	$-0.129713\pi$
$450$	4.00000			0.188562
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$	−7.50000	−	12.9904i	−0.352770	−	0.611016i
$453$	1.00000	+	1.73205i	0.0469841	+	0.0813788i
$454$	−14.0000			−0.657053
$455$		0			0
$456$	−18.0000			−0.842927
$457$	−6.50000	−	11.2583i	−0.304057	−	0.526642i	0.672994	−	0.739648i	$-0.265008\pi$
$457$	−6.50000	−	11.2583i	−0.304057	−	0.526642i	−0.977051	+	0.213006i	$0.931675\pi$
$458$	11.0000	+	19.0526i	0.513996	+	0.890268i
$459$	−3.50000	+	6.06218i	−0.163366	+	0.282958i
$460$	6.00000			0.279751
$461$	9.50000	−	16.4545i	0.442459	−	0.766362i	−0.555412	−	0.831575i	$-0.687440\pi$
$461$	9.50000	−	16.4545i	0.442459	−	0.766362i	0.997871	+	0.0652135i	$0.0207728\pi$
$462$	2.00000	−	3.46410i	0.0930484	−	0.161165i
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$	−2.00000	−	3.46410i	−0.0927478	−	0.160644i
$466$	5.00000	+	8.66025i	0.231621	+	0.401179i
$467$	6.00000			0.277647			0.138823	−	0.990317i	$-0.455668\pi$
$467$	6.00000			0.277647			0.138823	+	0.990317i	$0.455668\pi$
$468$		0			0
$469$	−4.00000			−0.184703
$470$	−3.00000	−	5.19615i	−0.138380	−	0.239681i
$471$	−1.50000	−	2.59808i	−0.0691164	−	0.119713i
$472$		0			0
$473$	12.0000			0.551761
$474$	2.00000	−	3.46410i	0.0918630	−	0.159111i
$475$	12.0000	−	20.7846i	0.550598	−	0.953663i
$476$	−14.0000			−0.641689
$477$	4.50000	−	7.79423i	0.206041	−	0.356873i
$478$	−15.0000	−	25.9808i	−0.686084	−	1.18833i
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$	5.00000			0.228218
$481$		0			0
$482$	7.00000			0.318841
$483$	6.00000	+	10.3923i	0.273009	+	0.472866i
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$	1.00000			0.0453609
$487$	9.00000	−	15.5885i	0.407829	−	0.706380i	−0.586817	−	0.809719i	$-0.699619\pi$
$487$	9.00000	−	15.5885i	0.407829	−	0.706380i	0.994646	+	0.103339i	$0.0329526\pi$
$488$	−1.50000	+	2.59808i	−0.0679018	+	0.117609i
$489$	−4.00000			−0.180886
$490$	−1.50000	+	2.59808i	−0.0677631	+	0.117369i
$491$	−3.00000	−	5.19615i	−0.135388	−	0.234499i	0.790358	−	0.612646i	$-0.209895\pi$
$491$	−3.00000	−	5.19615i	−0.135388	−	0.234499i	−0.925746	+	0.378147i	$0.876561\pi$
$492$	4.50000	+	7.79423i	0.202876	+	0.351391i
$493$	7.00000			0.315264
$494$		0			0
$495$	2.00000			0.0898933
$496$	−2.00000	−	3.46410i	−0.0898027	−	0.155543i
$497$	−6.00000	−	10.3923i	−0.269137	−	0.466159i
$498$	−7.00000	+	12.1244i	−0.313678	+	0.543305i
$499$	−24.0000			−1.07439			−0.537194	−	0.843459i	$-0.680516\pi$
$499$	−24.0000			−1.07439			−0.537194	+	0.843459i	$0.680516\pi$
$500$	−4.50000	+	7.79423i	−0.201246	+	0.348569i
$501$	−8.00000	+	13.8564i	−0.357414	+	0.619059i
$502$	−12.0000			−0.535586
$503$	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
$505$	−1.50000	−	2.59808i	−0.0667491	−	0.115613i
$506$	12.0000			0.533465
$507$		0			0
$508$	−20.0000			−0.887357
$509$	3.50000	+	6.06218i	0.155135	+	0.268701i	0.933108	−	0.359596i	$-0.117085\pi$
$509$	3.50000	+	6.06218i	0.155135	+	0.268701i	−0.777973	+	0.628297i	$0.783752\pi$
$510$	3.50000	+	6.06218i	0.154983	+	0.268438i
$511$	−11.0000	+	19.0526i	−0.486611	+	0.842836i
$512$	11.0000			0.486136
$513$	3.00000	−	5.19615i	0.132453	−	0.229416i
$514$	−3.50000	+	6.06218i	−0.154378	+	0.267391i
$515$	6.00000			0.264392
$516$	−3.00000	+	5.19615i	−0.132068	+	0.228748i
$517$	6.00000	+	10.3923i	0.263880	+	0.457053i
$518$	1.00000	+	1.73205i	0.0439375	+	0.0761019i
$519$	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	$0.520933\pi$
$522$	−0.500000	−	0.866025i	−0.0218844	−	0.0379049i
$523$	−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
$525$	−8.00000			−0.349149
$526$	−15.0000	+	25.9808i	−0.654031	+	1.13282i
$527$	−14.0000	+	24.2487i	−0.609850	+	1.05629i
$528$	2.00000			0.0870388
$529$	−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
$535$	3.00000	+	5.19615i	0.129701	+	0.224649i
$536$	−3.00000	−	5.19615i	−0.129580	−	0.224440i
$537$	−1.00000	+	1.73205i	−0.0431532	+	0.0747435i
$538$	14.0000			0.603583
$539$	3.00000	−	5.19615i	0.129219	−	0.223814i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	−45.0000			−1.93470			−0.967351	−	0.253442i	$-0.918437\pi$
$541$	−45.0000			−1.93470			−0.967351	+	0.253442i	$0.918437\pi$
$542$		0			0
$543$	−3.50000	−	6.06218i	−0.150199	−	0.260153i
$544$	−17.5000	−	30.3109i	−0.750306	−	1.29957i
$545$	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	$0.687603\pi$
$548$	1.50000	+	2.59808i	0.0640768	+	0.110984i
$549$	−0.500000	−	0.866025i	−0.0213395	−	0.0369611i
$550$	−4.00000	+	6.92820i	−0.170561	+	0.295420i
$551$	−6.00000			−0.255609
$552$	−9.00000	+	15.5885i	−0.383065	+	0.663489i
$553$	−4.00000	+	6.92820i	−0.170097	+	0.294617i
$554$	31.0000			1.31706
$555$	−0.500000	+	0.866025i	−0.0212238	+	0.0367607i
$556$	6.00000	+	10.3923i	0.254457	+	0.440732i
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	0.754802	−	0.655953i	$-0.227733\pi$
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	−0.945473	+	0.325701i	$0.894400\pi$
$558$	4.00000			0.169334
$559$		0			0
$560$	2.00000			0.0845154
$561$	−7.00000	−	12.1244i	−0.295540	−	0.511891i
$562$	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	$0.166667\pi$
$564$	−6.00000			−0.252646
$565$	7.50000	−	12.9904i	0.315527	−	0.546509i
$566$	−9.00000	+	15.5885i	−0.378298	+	0.655232i
$567$	−2.00000			−0.0839921
$568$	9.00000	−	15.5885i	0.377632	−	0.654077i
$569$	−11.0000	−	19.0526i	−0.461144	−	0.798725i	0.537874	−	0.843025i	$-0.319228\pi$
$569$	−11.0000	−	19.0526i	−0.461144	−	0.798725i	−0.999018	+	0.0443003i	$0.985894\pi$
$570$	−3.00000	−	5.19615i	−0.125656	−	0.217643i
$571$	26.0000			1.08807			0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000			1.08807			0.544033	+	0.839064i	$0.316897\pi$
$572$		0			0
$573$	4.00000			0.167102
$574$	9.00000	+	15.5885i	0.375653	+	0.650650i
$575$	−12.0000	−	20.7846i	−0.500435	−	0.866778i
$576$	−3.50000	+	6.06218i	−0.145833	+	0.252591i
$577$	−11.0000			−0.457936			−0.228968	−	0.973434i	$-0.573535\pi$
$577$	−11.0000			−0.457936			−0.228968	+	0.973434i	$0.573535\pi$
$578$	16.0000	−	27.7128i	0.665512	−	1.15270i
$579$	4.50000	−	7.79423i	0.187014	−	0.323917i
$580$	1.00000			0.0415227
$581$	14.0000	−	24.2487i	0.580818	−	1.00601i
$582$	−1.00000	−	1.73205i	−0.0414513	−	0.0717958i
$583$	9.00000	+	15.5885i	0.372742	+	0.645608i
$584$	−33.0000			−1.36555
$585$		0			0
$586$	−9.00000			−0.371787
$587$	8.00000	+	13.8564i	0.330195	+	0.571915i	0.982550	−	0.185999i	$-0.0595520\pi$
$587$	8.00000	+	13.8564i	0.330195	+	0.571915i	−0.652355	+	0.757914i	$0.726219\pi$
$588$	1.50000	+	2.59808i	0.0618590	+	0.107143i
$589$	12.0000	−	20.7846i	0.494451	−	0.856415i
$590$		0			0
$591$	−3.00000	+	5.19615i	−0.123404	+	0.213741i
$592$	−0.500000	+	0.866025i	−0.0205499	+	0.0355934i
$593$	−13.0000			−0.533846			−0.266923	−	0.963718i	$-0.586007\pi$
$593$	−13.0000			−0.533846			−0.266923	+	0.963718i	$0.586007\pi$
$594$	−1.00000	+	1.73205i	−0.0410305	+	0.0710669i
$595$	−7.00000	−	12.1244i	−0.286972	−	0.497050i
$596$	−1.50000	−	2.59808i	−0.0614424	−	0.106421i
$597$	−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	$0.605994\pi$
$600$	−6.00000	−	10.3923i	−0.244949	−	0.424264i
$601$	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
$603$	2.00000			0.0814463
$604$	1.00000	−	1.73205i	0.0406894	−	0.0704761i
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$	3.00000			0.121867
$607$	−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
$609$	1.00000	+	1.73205i	0.0405220	+	0.0701862i
$610$	−1.00000			−0.0404888
$611$		0			0
$612$	7.00000			0.282958
$613$	−11.5000	−	19.9186i	−0.464481	−	0.804504i	0.534697	−	0.845044i	$-0.320426\pi$
$613$	−11.5000	−	19.9186i	−0.464481	−	0.804504i	−0.999178	+	0.0405396i	$0.987092\pi$
$614$	−7.00000	−	12.1244i	−0.282497	−	0.489299i
$615$	−4.50000	+	7.79423i	−0.181458	+	0.314294i
$616$	−12.0000			−0.483494
$617$	6.50000	−	11.2583i	0.261680	−	0.453243i	−0.705008	−	0.709199i	$-0.749057\pi$
$617$	6.50000	−	11.2583i	0.261680	−	0.453243i	0.966689	+	0.255956i	$0.0823901\pi$
$618$	−3.00000	+	5.19615i	−0.120678	+	0.209020i
$619$	24.0000			0.964641			0.482321	−	0.875995i	$-0.339794\pi$
$619$	24.0000			0.964641			0.482321	+	0.875995i	$0.339794\pi$
$620$	−2.00000	+	3.46410i	−0.0803219	+	0.139122i
$621$	−3.00000	−	5.19615i	−0.120386	−	0.208514i
$622$	9.00000	+	15.5885i	0.360867	+	0.625040i
$623$	−28.0000			−1.12180
$624$		0			0
$625$	11.0000			0.440000
$626$	3.00000	+	5.19615i	0.119904	+	0.207680i
$627$	6.00000	+	10.3923i	0.239617	+	0.415029i
$628$	−1.50000	+	2.59808i	−0.0598565	+	0.103675i
$629$	7.00000			0.279108
$630$	−1.00000	+	1.73205i	−0.0398410	+	0.0690066i
$631$	10.0000	−	17.3205i	0.398094	−	0.689519i	−0.595397	−	0.803432i	$-0.703005\pi$
$631$	10.0000	−	17.3205i	0.398094	−	0.689519i	0.993491	+	0.113913i	$0.0363385\pi$
$632$	−12.0000			−0.477334
$633$	−4.00000	+	6.92820i	−0.158986	+	0.275371i
$634$	12.5000	+	21.6506i	0.496438	+	0.859857i
$635$	−10.0000	−	17.3205i	−0.396838	−	0.687343i
$636$	−9.00000			−0.356873
$637$		0			0
$638$	2.00000			0.0791808
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	15.5000	−	26.8468i	0.612213	−	1.06038i	−0.378653	−	0.925539i	$-0.623613\pi$
$641$	15.5000	−	26.8468i	0.612213	−	1.06038i	0.990867	−	0.134846i	$-0.0430539\pi$
$642$	−6.00000			−0.236801
$643$	−8.00000	+	13.8564i	−0.315489	+	0.546443i	−0.979541	−	0.201243i	$-0.935502\pi$
$643$	−8.00000	+	13.8564i	−0.315489	+	0.546443i	0.664052	+	0.747686i	$0.268835\pi$
$644$	6.00000	−	10.3923i	0.236433	−	0.409514i
$645$	−6.00000			−0.236250
$646$	−21.0000	+	36.3731i	−0.826234	+	1.43108i
$647$	16.0000	+	27.7128i	0.629025	+	1.08950i	0.987748	+	0.156059i	$0.0498790\pi$
$647$	16.0000	+	27.7128i	0.629025	+	1.08950i	−0.358723	+	0.933444i	$0.616788\pi$
$648$	−1.50000	−	2.59808i	−0.0589256	−	0.102062i
$649$		0			0
$650$		0			0
$651$	−8.00000			−0.313545
$652$	2.00000	+	3.46410i	0.0783260	+	0.135665i
$653$	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
$655$	−8.00000			−0.312586
$656$	−4.50000	+	7.79423i	−0.175695	+	0.304314i
$657$	5.50000	−	9.52628i	0.214575	−	0.371656i
$658$	−12.0000			−0.467809
$659$	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
$661$	22.5000	+	38.9711i	0.875149	+	1.51580i	0.856604	+	0.515974i	$0.172570\pi$
$661$	22.5000	+	38.9711i	0.875149	+	1.51580i	0.0185442	+	0.999828i	$0.494097\pi$
$662$	−4.00000			−0.155464
$663$		0			0
$664$	42.0000			1.62992
$665$	6.00000	+	10.3923i	0.232670	+	0.402996i
$666$	−0.500000	−	0.866025i	−0.0193746	−	0.0335578i
$667$	−3.00000	+	5.19615i	−0.116160	+	0.201196i
$668$	16.0000			0.619059
$669$	−8.00000	+	13.8564i	−0.309298	+	0.535720i
$670$	1.00000	−	1.73205i	0.0386334	−	0.0669150i
$671$	2.00000			0.0772091
$672$	5.00000	−	8.66025i	0.192879	−	0.334077i
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	0.997586	+	0.0694449i	$0.0221228\pi$
$673$	14.5000	+	25.1147i	0.558934	+	0.968102i	−0.438652	+	0.898657i	$0.644544\pi$
$674$	−16.5000	−	28.5788i	−0.635556	−	1.10082i
$675$	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	$0.273358\pi$
$678$	7.50000	+	12.9904i	0.288036	+	0.498893i
$679$	2.00000	+	3.46410i	0.0767530	+	0.132940i
$680$	10.5000	−	18.1865i	0.402657	−	0.697422i
$681$	−14.0000			−0.536481
$682$	−4.00000	+	6.92820i	−0.153168	+	0.265295i
$683$	−12.0000	+	20.7846i	−0.459167	+	0.795301i	−0.998917	−	0.0465244i	$-0.985185\pi$
$683$	−12.0000	+	20.7846i	−0.459167	+	0.795301i	0.539750	+	0.841825i	$0.318519\pi$
$684$	−6.00000			−0.229416
$685$	−1.50000	+	2.59808i	−0.0573121	+	0.0992674i
$686$	10.0000	+	17.3205i	0.381802	+	0.661300i
$687$	11.0000	+	19.0526i	0.419676	+	0.726900i
$688$	−6.00000			−0.228748
$689$		0			0
$690$	−6.00000			−0.228416
$691$	21.0000	+	36.3731i	0.798878	+	1.38370i	0.920348	+	0.391102i	$0.127906\pi$
$691$	21.0000	+	36.3731i	0.798878	+	1.38370i	−0.121470	+	0.992595i	$0.538761\pi$
$692$	−3.00000	−	5.19615i	−0.114043	−	0.197528i
$693$	2.00000	−	3.46410i	0.0759737	−	0.131590i
$694$	−18.0000			−0.683271
$695$	−6.00000	+	10.3923i	−0.227593	+	0.394203i
$696$	−1.50000	+	2.59808i	−0.0568574	+	0.0984798i
$697$	63.0000			2.38630
$698$	13.0000	−	22.5167i	0.492057	−	0.852268i
$699$	5.00000	+	8.66025i	0.189117	+	0.327561i
$700$	4.00000	+	6.92820i	0.151186	+	0.261861i
$701$	2.00000			0.0755390			0.0377695	−	0.999286i	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$		0			0
$703$	−6.00000			−0.226294
$704$	−7.00000	−	12.1244i	−0.263822	−	0.456954i
$705$	−3.00000	−	5.19615i	−0.112987	−	0.195698i
$706$	5.50000	−	9.52628i	0.206995	−	0.358526i
$707$	−6.00000			−0.225653
$708$		0			0
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	−0.950628	−	0.310334i	$-0.899559\pi$
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	0.744071	+	0.668101i	$0.232892\pi$
$710$	6.00000			0.225176
$711$	2.00000	−	3.46410i	0.0750059	−	0.129914i
$712$	−21.0000	−	36.3731i	−0.787008	−	1.36314i
$713$	−12.0000	−	20.7846i	−0.449404	−	0.778390i
$714$	14.0000			0.523937
$715$		0			0
$716$	2.00000			0.0747435
$717$	−15.0000	−	25.9808i	−0.560185	−	0.970269i
$718$	9.00000	+	15.5885i	0.335877	+	0.581756i
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.0613050	−	0.998119i	$-0.480474\pi$
$719$	24.0000	−	41.5692i	0.895049	−	1.55027i	0.833744	−	0.552151i	$-0.186193\pi$
$720$	−1.00000			−0.0372678
$721$	6.00000	−	10.3923i	0.223452	−	0.387030i
$722$	8.50000	−	14.7224i	0.316337	−	0.547912i
$723$	7.00000			0.260333
$724$	−3.50000	+	6.06218i	−0.130076	+	0.225299i
$725$	−2.00000	−	3.46410i	−0.0742781	−	0.128654i
$726$	3.50000	+	6.06218i	0.129897	+	0.224989i
$727$	14.0000			0.519231			0.259616	−	0.965712i	$-0.416404\pi$
$727$	14.0000			0.519231			0.259616	+	0.965712i	$0.416404\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−5.50000	−	9.52628i	−0.203564	−	0.352583i
$731$	21.0000	+	36.3731i	0.776713	+	1.34531i
$732$	−0.500000	+	0.866025i	−0.0184805	+	0.0320092i
$733$	15.0000			0.554038			0.277019	−	0.960864i	$-0.410654\pi$
$733$	15.0000			0.554038			0.277019	+	0.960864i	$0.410654\pi$
$734$	5.00000	−	8.66025i	0.184553	−	0.319656i
$735$	−1.50000	+	2.59808i	−0.0553283	+	0.0958315i
$736$	30.0000			1.10581
$737$	−2.00000	+	3.46410i	−0.0736709	+	0.127602i
$738$	−4.50000	−	7.79423i	−0.165647	−	0.286910i
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	0.680534	−	0.732717i	$-0.261748\pi$
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	−0.974818	+	0.223001i	$0.928415\pi$
$740$	1.00000			0.0367607
$741$		0			0
$742$	−18.0000			−0.660801
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	−0.980522	−	0.196409i	$-0.937072\pi$
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	0.320166	−	0.947361i	$-0.396261\pi$
$744$	−6.00000	−	10.3923i	−0.219971	−	0.381000i
$745$	1.50000	−	2.59808i	0.0549557	−	0.0951861i
$746$	11.0000			0.402739
$747$	−7.00000	+	12.1244i	−0.256117	+	0.443607i
$748$	−7.00000	+	12.1244i	−0.255945	+	0.443310i
$749$	12.0000			0.438470
$750$	4.50000	−	7.79423i	0.164317	−	0.284605i
$751$	17.0000	+	29.4449i	0.620339	+	1.07446i	0.989423	+	0.145062i	$0.0463382\pi$
$751$	17.0000	+	29.4449i	0.620339	+	1.07446i	−0.369084	+	0.929396i	$0.620328\pi$
$752$	−3.00000	−	5.19615i	−0.109399	−	0.189484i
$753$	−12.0000			−0.437304
$754$		0			0
$755$	2.00000			0.0727875
$756$	1.00000	+	1.73205i	0.0363696	+	0.0629941i
$757$	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
$759$	12.0000			0.435572
$760$	−9.00000	+	15.5885i	−0.326464	+	0.565453i
$761$	25.0000	−	43.3013i	0.906249	−	1.56967i	0.0870179	−	0.996207i	$-0.472266\pi$
$761$	25.0000	−	43.3013i	0.906249	−	1.56967i	0.819231	−	0.573463i	$-0.194400\pi$
$762$	20.0000			0.724524
$763$	2.00000	−	3.46410i	0.0724049	−	0.125409i
$764$	−2.00000	−	3.46410i	−0.0723575	−	0.125327i
$765$	3.50000	+	6.06218i	0.126543	+	0.219179i
$766$	8.00000			0.289052
$767$		0			0
$768$	17.0000			0.613435
$769$	15.0000	+	25.9808i	0.540914	+	0.936890i	0.998852	+	0.0479061i	$0.0152548\pi$
$769$	15.0000	+	25.9808i	0.540914	+	0.936890i	−0.457938	+	0.888984i	$0.651412\pi$
$770$	−2.00000	−	3.46410i	−0.0720750	−	0.124838i
$771$	−3.50000	+	6.06218i	−0.126049	+	0.218324i
$772$	−9.00000			−0.323917
$773$	−7.00000	+	12.1244i	−0.251773	+	0.436083i	−0.964014	−	0.265852i	$-0.914347\pi$
$773$	−7.00000	+	12.1244i	−0.251773	+	0.436083i	0.712241	+	0.701935i	$0.247680\pi$
$774$	3.00000	−	5.19615i	0.107833	−	0.186772i
$775$	16.0000			0.574737
$776$	−3.00000	+	5.19615i	−0.107694	+	0.186531i
$777$	1.00000	+	1.73205i	0.0358748	+	0.0621370i
$778$	9.50000	+	16.4545i	0.340592	+	0.589922i
$779$	−54.0000			−1.93475
$780$		0			0
$781$	−12.0000			−0.429394
$782$	21.0000	+	36.3731i	0.750958	+	1.30070i
$783$	−0.500000	−	0.866025i	−0.0178685	−	0.0309492i
$784$	−1.50000	+	2.59808i	−0.0535714	+	0.0927884i
$785$	−3.00000			−0.107075
$786$	4.00000	−	6.92820i	0.142675	−	0.247121i
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$	6.00000			0.213741
$789$	−15.0000	+	25.9808i	−0.534014	+	0.924940i
$790$	−2.00000	−	3.46410i	−0.0711568	−	0.123247i
$791$	−15.0000	−	25.9808i	−0.533339	−	0.923770i
$792$	6.00000			0.213201
$793$		0			0
$794$	−34.0000			−1.20661
$795$	−4.50000	−	7.79423i	−0.159599	−	0.276433i
$796$	7.00000	+	12.1244i	0.248108	+	0.429736i
$797$	1.00000	−	1.73205i	0.0354218	−	0.0613524i	−0.847771	−	0.530362i	$-0.822056\pi$
$797$	1.00000	−	1.73205i	0.0354218	−	0.0613524i	0.883193	+	0.469010i	$0.155389\pi$
$798$	−12.0000			−0.424795
$799$	−21.0000	+	36.3731i	−0.742927	+	1.28679i
$800$	−10.0000	+	17.3205i	−0.353553	+	0.612372i
$801$	14.0000			0.494666
$802$	−0.500000	+	0.866025i	−0.0176556	+	0.0305804i
$803$	11.0000	+	19.0526i	0.388182	+	0.672350i
$804$	−1.00000	−	1.73205i	−0.0352673	−	0.0610847i
$805$	12.0000			0.422944
$806$		0			0
$807$	14.0000			0.492823
$808$	−4.50000	−	7.79423i	−0.158309	−	0.274200i
$809$	−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
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$	1.00000	−	1.73205i	0.0350931	−	0.0607831i
$813$		0			0
$814$	2.00000			0.0701000
$815$	−2.00000	+	3.46410i	−0.0700569	+	0.121342i
$816$	3.50000	+	6.06218i	0.122525	+	0.212219i
$817$	−18.0000	−	31.1769i	−0.629740	−	1.09074i
$818$	7.00000			0.244749
$819$		0			0
$820$	9.00000			0.314294
$821$	25.0000	+	43.3013i	0.872506	+	1.51122i	0.859396	+	0.511311i	$0.170840\pi$
$821$	25.0000	+	43.3013i	0.872506	+	1.51122i	0.0131101	+	0.999914i	$0.495827\pi$
$822$	−1.50000	−	2.59808i	−0.0523185	−	0.0906183i
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	−0.577474	−	0.816409i	$-0.695962\pi$
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	0.995768	+	0.0919029i	$0.0292950\pi$
$824$	18.0000			0.627060
$825$	−4.00000	+	6.92820i	−0.139262	+	0.241209i
$826$		0			0
$827$	−16.0000			−0.556375			−0.278187	−	0.960527i	$-0.589734\pi$
$827$	−16.0000			−0.556375			−0.278187	+	0.960527i	$0.589734\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	−8.50000	−	14.7224i	−0.295217	−	0.511331i	0.679818	−	0.733381i	$-0.262059\pi$
$829$	−8.50000	−	14.7224i	−0.295217	−	0.511331i	−0.975035	+	0.222049i	$0.928725\pi$
$830$	7.00000	+	12.1244i	0.242974	+	0.420843i
$831$	31.0000			1.07538
$832$		0			0
$833$	21.0000			0.727607
$834$	−6.00000	−	10.3923i	−0.207763	−	0.359856i
$835$	8.00000	+	13.8564i	0.276851	+	0.479521i
$836$	6.00000	−	10.3923i	0.207514	−	0.359425i
$837$	4.00000			0.138260
$838$	8.00000	−	13.8564i	0.276355	−	0.478662i
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	−0.743670	−	0.668546i	$-0.766917\pi$
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	0.950813	+	0.309764i	$0.100250\pi$
$840$	6.00000			0.207020
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	9.50000	+	16.4545i	0.327392	+	0.567059i
$843$	9.50000	+	16.4545i	0.327197	+	0.566722i
$844$	8.00000			0.275371
$845$		0			0
$846$	6.00000			0.206284
$847$	−7.00000	−	12.1244i	−0.240523	−	0.416598i
$848$	−4.50000	−	7.79423i	−0.154531	−	0.267655i
$849$	−9.00000	+	15.5885i	−0.308879	+	0.534994i
$850$	−28.0000			−0.960392
$851$	−3.00000	+	5.19615i	−0.102839	+	0.178122i
$852$	3.00000	−	5.19615i	0.102778	−	0.178017i
$853$	−21.0000			−0.719026			−0.359513	−	0.933140i	$-0.617057\pi$
$853$	−21.0000			−0.719026			−0.359513	+	0.933140i	$0.617057\pi$
$854$	−1.00000	+	1.73205i	−0.0342193	+	0.0592696i
$855$	−3.00000	−	5.19615i	−0.102598	−	0.177705i
$856$	9.00000	+	15.5885i	0.307614	+	0.532803i
$857$	−31.0000			−1.05894			−0.529470	−	0.848329i	$-0.677609\pi$
$857$	−31.0000			−1.05894			−0.529470	+	0.848329i	$0.677609\pi$
$858$		0			0
$859$	34.0000			1.16007			0.580033	−	0.814593i	$-0.303040\pi$
$859$	34.0000			1.16007			0.580033	+	0.814593i	$0.303040\pi$
$860$	3.00000	+	5.19615i	0.102299	+	0.177187i
$861$	9.00000	+	15.5885i	0.306719	+	0.531253i
$862$	15.0000	−	25.9808i	0.510902	−	0.884908i
$863$	−10.0000			−0.340404			−0.170202	−	0.985409i	$-0.554442\pi$
$863$	−10.0000			−0.340404			−0.170202	+	0.985409i	$0.554442\pi$
$864$	−2.50000	+	4.33013i	−0.0850517	+	0.147314i
$865$	3.00000	−	5.19615i	0.102003	−	0.176674i
$866$	−19.0000			−0.645646
$867$	16.0000	−	27.7128i	0.543388	−	0.941176i
$868$	4.00000	+	6.92820i	0.135769	+	0.235159i
$869$	4.00000	+	6.92820i	0.135691	+	0.235023i
$870$	−1.00000			−0.0339032
$871$		0			0
$872$	6.00000			0.203186
$873$	−1.00000	−	1.73205i	−0.0338449	−	0.0586210i
$874$	−18.0000	−	31.1769i	−0.608859	−	1.05457i
$875$	−9.00000	+	15.5885i	−0.304256	+	0.526986i
$876$	−11.0000			−0.371656
$877$	8.50000	−	14.7224i	0.287025	−	0.497141i	−0.686074	−	0.727532i	$-0.740667\pi$
$877$	8.50000	−	14.7224i	0.287025	−	0.497141i	0.973098	+	0.230391i	$0.0740005\pi$
$878$	7.00000	−	12.1244i	0.236239	−	0.409177i
$879$	−9.00000			−0.303562
$880$	1.00000	−	1.73205i	0.0337100	−	0.0583874i
$881$	−18.5000	−	32.0429i	−0.623281	−	1.07955i	−0.988871	−	0.148778i	$-0.952466\pi$
$881$	−18.5000	−	32.0429i	−0.623281	−	1.07955i	0.365590	−	0.930776i	$-0.380867\pi$
$882$	−1.50000	−	2.59808i	−0.0505076	−	0.0874818i
$883$	16.0000			0.538443			0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000			0.538443			0.269221	+	0.963078i	$0.413234\pi$
$884$		0			0
$885$		0			0
$886$	−2.00000	−	3.46410i	−0.0671913	−	0.116379i
$887$		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
$889$	−40.0000			−1.34156
$890$	7.00000	−	12.1244i	0.234641	−	0.406409i
$891$	−1.00000	+	1.73205i	−0.0335013	+	0.0580259i
$892$	16.0000			0.535720
$893$	18.0000	−	31.1769i	0.602347	−	1.04330i
$894$	1.50000	+	2.59808i	0.0501675	+	0.0868927i
$895$	1.00000	+	1.73205i	0.0334263	+	0.0578961i
$896$	−6.00000			−0.200446
$897$		0			0
$898$	34.0000			1.13459
$899$	−2.00000	−	3.46410i	−0.0667037	−	0.115534i
$900$	−2.00000	−	3.46410i	−0.0666667	−	0.115470i
$901$	−31.5000	+	54.5596i	−1.04942	+	1.81764i
$902$	18.0000			0.599334
$903$	−6.00000	+	10.3923i	−0.199667	+	0.345834i
$904$	22.5000	−	38.9711i	0.748339	−	1.29616i
$905$	−7.00000			−0.232688
$906$	−1.00000	+	1.73205i	−0.0332228	+	0.0575435i
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	0.749051	−	0.662512i	$-0.230510\pi$
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	−0.948278	+	0.317441i	$0.897176\pi$
$908$	7.00000	+	12.1244i	0.232303	+	0.402361i
$909$	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	$0.730560\pi$
$912$	−3.00000	−	5.19615i	−0.0993399	−	0.172062i
$913$	−14.0000	−	24.2487i	−0.463332	−	0.802515i
$914$	6.50000	−	11.2583i	0.215001	−	0.372392i
$915$	−1.00000			−0.0330590
$916$	11.0000	−	19.0526i	0.363450	−	0.629514i
$917$	−8.00000	+	13.8564i	−0.264183	+	0.457579i
$918$	−7.00000			−0.231034
$919$	−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
$921$	−7.00000	−	12.1244i	−0.230658	−	0.399511i
$922$	19.0000			0.625732
$923$		0			0
$924$	−4.00000			−0.131590
$925$	−2.00000	−	3.46410i	−0.0657596	−	0.113899i
$926$	13.0000	+	22.5167i	0.427207	+	0.739943i
$927$	−3.00000	+	5.19615i	−0.0985329	+	0.170664i
$928$	5.00000			0.164133
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	−0.997905	−	0.0646999i	$-0.979391\pi$
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	0.554984	+	0.831861i	$0.312724\pi$
$930$	2.00000	−	3.46410i	0.0655826	−	0.113592i
$931$	−18.0000			−0.589926
$932$	5.00000	−	8.66025i	0.163780	−	0.283676i
$933$	9.00000	+	15.5885i	0.294647	+	0.510343i
$934$	3.00000	+	5.19615i	0.0981630	+	0.170023i
$935$	−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	$0.795369\pi$
$938$	−2.00000	−	3.46410i	−0.0653023	−	0.113107i
$939$	3.00000	+	5.19615i	0.0979013	+	0.169570i
$940$	−3.00000	+	5.19615i	−0.0978492	+	0.169480i
$941$	38.0000			1.23876			0.619382	−	0.785090i	$-0.287383\pi$
$941$	38.0000			1.23876			0.619382	+	0.785090i	$0.287383\pi$
$942$	1.50000	−	2.59808i	0.0488726	−	0.0846499i
$943$	−27.0000	+	46.7654i	−0.879241	+	1.52289i
$944$		0			0
$945$	−1.00000	+	1.73205i	−0.0325300	+	0.0563436i
$946$	6.00000	+	10.3923i	0.195077	+	0.337883i
$947$	−24.0000	−	41.5692i	−0.779895	−	1.35082i	−0.932002	−	0.362454i	$-0.881939\pi$
$947$	−24.0000	−	41.5692i	−0.779895	−	1.35082i	0.152106	−	0.988364i	$-0.451394\pi$
$948$	−4.00000			−0.129914
$949$		0			0
$950$	24.0000			0.778663
$951$	12.5000	+	21.6506i	0.405340	+	0.702070i
$952$	−21.0000	−	36.3731i	−0.680614	−	1.17886i
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	−0.910516	−	0.413473i	$-0.864315\pi$
$953$	−3.00000	+	5.19615i	−0.0971795	+	0.168320i	0.813337	+	0.581793i	$0.197649\pi$
$954$	9.00000			0.291386
$955$	2.00000	−	3.46410i	0.0647185	−	0.112096i
$956$	−15.0000	+	25.9808i	−0.485135	+	0.840278i
$957$	2.00000			0.0646508
$958$	−12.0000	+	20.7846i	−0.387702	+	0.671520i
$959$	3.00000	+	5.19615i	0.0968751	+	0.167793i
$960$	3.50000	+	6.06218i	0.112962	+	0.195656i
$961$	−15.0000			−0.483871
$962$		0			0
$963$	−6.00000			−0.193347
$964$	−3.50000	−	6.06218i	−0.112727	−	0.195250i
$965$	−4.50000	−	7.79423i	−0.144860	−	0.250905i
$966$	−6.00000	+	10.3923i	−0.193047	+	0.334367i
$967$	−2.00000			−0.0643157			−0.0321578	−	0.999483i	$-0.510238\pi$
$967$	−2.00000			−0.0643157			−0.0321578	+	0.999483i	$0.510238\pi$
$968$	10.5000	−	18.1865i	0.337483	−	0.584537i
$969$	−21.0000	+	36.3731i	−0.674617	+	1.16847i
$970$	−2.00000			−0.0642161
$971$	−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
$973$	12.0000	+	20.7846i	0.384702	+	0.666324i
$974$	18.0000			0.576757
$975$		0			0
$976$	−1.00000			−0.0320092
$977$	16.5000	+	28.5788i	0.527882	+	0.914318i	0.999472	+	0.0325001i	$0.0103469\pi$
$977$	16.5000	+	28.5788i	0.527882	+	0.914318i	−0.471590	+	0.881818i	$0.656320\pi$
$978$	−2.00000	−	3.46410i	−0.0639529	−	0.110770i
$979$	−14.0000	+	24.2487i	−0.447442	+	0.774992i
$980$	3.00000			0.0958315
$981$	−1.00000	+	1.73205i	−0.0319275	+	0.0553001i
$982$	3.00000	−	5.19615i	0.0957338	−	0.165816i
$983$	−4.00000			−0.127580			−0.0637901	−	0.997963i	$-0.520319\pi$
$983$	−4.00000			−0.127580			−0.0637901	+	0.997963i	$0.520319\pi$
$984$	−13.5000	+	23.3827i	−0.430364	+	0.745413i
$985$	3.00000	+	5.19615i	0.0955879	+	0.165563i
$986$	3.50000	+	6.06218i	0.111463	+	0.193059i
$987$	−12.0000			−0.381964
$988$		0			0
$989$	−36.0000			−1.14473
$990$	1.00000	+	1.73205i	0.0317821	+	0.0550482i
$991$	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
$993$	−4.00000			−0.126936
$994$	6.00000	−	10.3923i	0.190308	−	0.329624i
$995$	−7.00000	+	12.1244i	−0.221915	+	0.384368i
$996$	14.0000			0.443607
$997$	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
$999$	−0.500000	−	0.866025i	−0.0158193	−	0.0273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.e.c.484.1		2
13.2	odd	12		507.2.b.b.337.2		2
13.3	even	3		507.2.a.b.1.1		1
13.4	even	6		39.2.e.a.22.1	yes	2
13.5	odd	4		507.2.j.d.361.2		4
13.6	odd	12		507.2.j.d.316.1		4
13.7	odd	12		507.2.j.d.316.2		4
13.8	odd	4		507.2.j.d.361.1		4
13.9	even	3	inner	507.2.e.c.22.1		2
13.10	even	6		507.2.a.c.1.1		1
13.11	odd	12		507.2.b.b.337.1		2
13.12	even	2		39.2.e.a.16.1	✓	2
39.2	even	12		1521.2.b.c.1351.1		2
39.11	even	12		1521.2.b.c.1351.2		2
39.17	odd	6		117.2.g.b.100.1		2
39.23	odd	6		1521.2.a.a.1.1		1
39.29	odd	6		1521.2.a.d.1.1		1
39.38	odd	2		117.2.g.b.55.1		2
52.3	odd	6		8112.2.a.bc.1.1		1
52.23	odd	6		8112.2.a.w.1.1		1
52.43	odd	6		624.2.q.c.529.1		2
52.51	odd	2		624.2.q.c.289.1		2
65.4	even	6		975.2.i.f.451.1		2
65.12	odd	4		975.2.bb.d.874.2		4
65.17	odd	12		975.2.bb.d.724.1		4
65.38	odd	4		975.2.bb.d.874.1		4
65.43	odd	12		975.2.bb.d.724.2		4
65.64	even	2		975.2.i.f.601.1		2
156.95	even	6		1872.2.t.j.1153.1		2
156.155	even	2		1872.2.t.j.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.a.16.1	✓	2	13.12	even	2
39.2.e.a.22.1	yes	2	13.4	even	6
117.2.g.b.55.1		2	39.38	odd	2
117.2.g.b.100.1		2	39.17	odd	6
507.2.a.b.1.1		1	13.3	even	3
507.2.a.c.1.1		1	13.10	even	6
507.2.b.b.337.1		2	13.11	odd	12
507.2.b.b.337.2		2	13.2	odd	12
507.2.e.c.22.1		2	13.9	even	3	inner
507.2.e.c.484.1		2	1.1	even	1	trivial
507.2.j.d.316.1		4	13.6	odd	12
507.2.j.d.316.2		4	13.7	odd	12
507.2.j.d.361.1		4	13.8	odd	4
507.2.j.d.361.2		4	13.5	odd	4
624.2.q.c.289.1		2	52.51	odd	2
624.2.q.c.529.1		2	52.43	odd	6
975.2.i.f.451.1		2	65.4	even	6
975.2.i.f.601.1		2	65.64	even	2
975.2.bb.d.724.1		4	65.17	odd	12
975.2.bb.d.724.2		4	65.43	odd	12
975.2.bb.d.874.1		4	65.38	odd	4
975.2.bb.d.874.2		4	65.12	odd	4
1521.2.a.a.1.1		1	39.23	odd	6
1521.2.a.d.1.1		1	39.29	odd	6
1521.2.b.c.1351.1		2	39.2	even	12
1521.2.b.c.1351.2		2	39.11	even	12
1872.2.t.j.289.1		2	156.155	even	2
1872.2.t.j.1153.1		2	156.95	even	6
8112.2.a.w.1.1		1	52.23	odd	6
8112.2.a.bc.1.1		1	52.3	odd	6

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.e (of order \(3\), degree \(2\), not minimal)

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

Introduction

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