LMFDB - Embedded newform 117.2.g.b.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(55,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("117.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.934249703649$
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			100.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	117.100
Dual form			117.2.g.b.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +3.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +3.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-3.50000 - 0.866025i) q^{13} -2.00000 q^{14} +(0.500000 - 0.866025i) q^{16} +(-3.50000 - 6.06218i) q^{17} +(3.00000 + 5.19615i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.00000 + 1.73205i) q^{22} +(-3.00000 + 5.19615i) q^{23} -4.00000 q^{25} +(-2.50000 + 2.59808i) q^{26} +(1.00000 - 1.73205i) q^{28} +(-0.500000 + 0.866025i) q^{29} +4.00000 q^{31} +(2.50000 + 4.33013i) q^{32} -7.00000 q^{34} +(-1.00000 - 1.73205i) q^{35} +(-0.500000 + 0.866025i) q^{37} +6.00000 q^{38} +3.00000 q^{40} +(4.50000 - 7.79423i) q^{41} +(-3.00000 - 5.19615i) q^{43} -2.00000 q^{44} +(3.00000 + 5.19615i) q^{46} -6.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(-1.00000 - 3.46410i) q^{52} +9.00000 q^{53} +(-1.00000 + 1.73205i) q^{55} +(-3.00000 - 5.19615i) q^{56} +(0.500000 + 0.866025i) q^{58} +(-0.500000 - 0.866025i) q^{61} +(2.00000 - 3.46410i) q^{62} +7.00000 q^{64} +(-3.50000 - 0.866025i) q^{65} +(1.00000 - 1.73205i) q^{67} +(3.50000 - 6.06218i) q^{68} -2.00000 q^{70} +(3.00000 + 5.19615i) q^{71} +11.0000 q^{73} +(0.500000 + 0.866025i) q^{74} +(-3.00000 + 5.19615i) q^{76} +4.00000 q^{77} -4.00000 q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{82} +14.0000 q^{83} +(-3.50000 - 6.06218i) q^{85} -6.00000 q^{86} +(-3.00000 + 5.19615i) q^{88} +(-7.00000 + 12.1244i) q^{89} +(2.00000 + 6.92820i) q^{91} -6.00000 q^{92} +(-3.00000 + 5.19615i) q^{94} +(3.00000 + 5.19615i) q^{95} +(1.00000 + 1.73205i) q^{97} +(-1.50000 - 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{4} + 2 q^{5} - 2 q^{7} + 6 q^{8}+O(q^{10}) $ 2 * q + q^2 + q^4 + 2 * q^5 - 2 * q^7 + 6 * q^8	$ 2 q + q^{2} + q^{4} + 2 q^{5} - 2 q^{7} + 6 q^{8} + q^{10} - 2 q^{11} - 7 q^{13} - 4 q^{14} + q^{16} - 7 q^{17} + 6 q^{19} + q^{20} + 2 q^{22} - 6 q^{23} - 8 q^{25} - 5 q^{26} + 2 q^{28} - q^{29} + 8 q^{31} + 5 q^{32} - 14 q^{34} - 2 q^{35} - q^{37} + 12 q^{38} + 6 q^{40} + 9 q^{41} - 6 q^{43} - 4 q^{44} + 6 q^{46} - 12 q^{47} + 3 q^{49} - 4 q^{50} - 2 q^{52} + 18 q^{53} - 2 q^{55} - 6 q^{56} + q^{58} - q^{61} + 4 q^{62} + 14 q^{64} - 7 q^{65} + 2 q^{67} + 7 q^{68} - 4 q^{70} + 6 q^{71} + 22 q^{73} + q^{74} - 6 q^{76} + 8 q^{77} - 8 q^{79} + q^{80} - 9 q^{82} + 28 q^{83} - 7 q^{85} - 12 q^{86} - 6 q^{88} - 14 q^{89} + 4 q^{91} - 12 q^{92} - 6 q^{94} + 6 q^{95} + 2 q^{97} - 3 q^{98}+O(q^{100}) $ 2 * q + q^2 + q^4 + 2 * q^5 - 2 * q^7 + 6 * q^8 + q^10 - 2 * q^11 - 7 * q^13 - 4 * q^14 + q^16 - 7 * q^17 + 6 * q^19 + q^20 + 2 * q^22 - 6 * q^23 - 8 * q^25 - 5 * q^26 + 2 * q^28 - q^29 + 8 * q^31 + 5 * q^32 - 14 * q^34 - 2 * q^35 - q^37 + 12 * q^38 + 6 * q^40 + 9 * q^41 - 6 * q^43 - 4 * q^44 + 6 * q^46 - 12 * q^47 + 3 * q^49 - 4 * q^50 - 2 * q^52 + 18 * q^53 - 2 * q^55 - 6 * q^56 + q^58 - q^61 + 4 * q^62 + 14 * q^64 - 7 * q^65 + 2 * q^67 + 7 * q^68 - 4 * q^70 + 6 * q^71 + 22 * q^73 + q^74 - 6 * q^76 + 8 * q^77 - 8 * q^79 + q^80 - 9 * q^82 + 28 * q^83 - 7 * q^85 - 12 * q^86 - 6 * q^88 - 14 * q^89 + 4 * q^91 - 12 * q^92 - 6 * q^94 + 6 * q^95 + 2 * q^97 - 3 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	0.986869	+	0.161521i	$0.0516399\pi$
$3$		0			0
$3$		0			0
$4$	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			0
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$	3.00000			1.06066
$9$		0			0
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$14$	−2.00000			−0.534522
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	−0.882213	−	0.470850i	$-0.843947\pi$
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	0.0333386	−	0.999444i	$-0.489386\pi$
$18$		0			0
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	0.972404	+	0.233301i	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	0.362892	+	0.931831i	$0.381789\pi$
$23$	−3.00000	+	5.19615i	−0.625543	+	1.08347i	−0.988436	+	0.151642i	$0.951544\pi$
$24$		0			0
$25$	−4.00000			−0.800000
$26$	−2.50000	+	2.59808i	−0.490290	+	0.509525i
$27$		0			0
$28$	1.00000	−	1.73205i	0.188982	−	0.327327i
$29$	−0.500000	+	0.866025i	−0.0928477	+	0.160817i	−0.908708	−	0.417432i	$-0.862930\pi$
$29$	−0.500000	+	0.866025i	−0.0928477	+	0.160817i	0.815861	+	0.578249i	$0.196264\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	2.50000	+	4.33013i	0.441942	+	0.765466i
$33$		0			0
$34$	−7.00000			−1.20049
$35$	−1.00000	−	1.73205i	−0.169031	−	0.292770i
$36$		0			0
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−0.500000	+	0.866025i	−0.0821995	+	0.142374i	0.821995	+	0.569495i	$0.192861\pi$
$38$	6.00000			0.973329
$39$		0			0
$40$	3.00000			0.474342
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	−0.264704	−	0.964330i	$-0.585274\pi$
$41$	4.50000	−	7.79423i	0.702782	−	1.21725i	0.967486	−	0.252924i	$-0.0813924\pi$
$42$		0			0
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	0.541332	−	0.840809i	$-0.317920\pi$
$43$	−3.00000	−	5.19615i	−0.457496	−	0.792406i	−0.998828	+	0.0484030i	$0.984587\pi$
$44$	−2.00000			−0.301511
$45$		0			0
$46$	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			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$		0			0
$52$	−1.00000	−	3.46410i	−0.138675	−	0.480384i
$53$	9.00000			1.23625			0.618123	−	0.786082i	$-0.287894\pi$
$53$	9.00000			1.23625			0.618123	+	0.786082i	$0.287894\pi$
$54$		0			0
$55$	−1.00000	+	1.73205i	−0.134840	+	0.233550i
$56$	−3.00000	−	5.19615i	−0.400892	−	0.694365i
$57$		0			0
$58$	0.500000	+	0.866025i	0.0656532	+	0.113715i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	2.00000	−	3.46410i	0.254000	−	0.439941i
$63$		0			0
$64$	7.00000			0.875000
$65$	−3.50000	−	0.866025i	−0.434122	−	0.107417i
$66$		0			0
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$	3.50000	−	6.06218i	0.424437	−	0.735147i
$69$		0			0
$70$	−2.00000			−0.239046
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	0.987294	−	0.158901i	$-0.0507952\pi$
$71$	3.00000	+	5.19615i	0.356034	+	0.616670i	−0.631260	+	0.775571i	$0.717462\pi$
$72$		0			0
$73$	11.0000			1.28745			0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000			1.28745			0.643726	+	0.765256i	$0.277388\pi$
$74$	0.500000	+	0.866025i	0.0581238	+	0.100673i
$75$		0			0
$76$	−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			0
$82$	−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	$0.221078\pi$
$84$		0			0
$85$	−3.50000	−	6.06218i	−0.379628	−	0.657536i
$86$	−6.00000			−0.646997
$87$		0			0
$88$	−3.00000	+	5.19615i	−0.319801	+	0.553912i
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	0.209585	+	0.977790i	$0.432789\pi$
$89$	−7.00000	+	12.1244i	−0.741999	+	1.28518i	−0.951584	+	0.307389i	$0.900545\pi$
$90$		0			0
$91$	2.00000	+	6.92820i	0.209657	+	0.726273i
$92$	−6.00000			−0.625543
$93$		0			0
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$		0			0
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$	−1.50000	−	2.59808i	−0.151523	−	0.262445i
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$		0			0
$103$	6.00000			0.591198			0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000			0.591198			0.295599	+	0.955312i	$0.404481\pi$
$104$	−10.5000	−	2.59808i	−1.02961	−	0.254762i
$105$		0			0
$106$	4.50000	−	7.79423i	0.437079	−	0.757042i
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	−0.973814	−	0.227345i	$-0.926996\pi$
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	0.683793	+	0.729676i	$0.260329\pi$
$108$		0			0
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	1.00000	+	1.73205i	0.0953463	+	0.165145i
$111$		0			0
$112$	−2.00000			−0.188982
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	−0.966496	−	0.256681i	$-0.917371\pi$
$113$	−7.50000	−	12.9904i	−0.705541	−	1.22203i	0.260955	−	0.965351i	$-0.415962\pi$
$114$		0			0
$115$	−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
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−1.00000			−0.0905357
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	−9.00000			−0.804984
$126$		0			0
$127$	−10.0000	+	17.3205i	−0.887357	+	1.53695i	−0.0443678	+	0.999015i	$0.514127\pi$
$127$	−10.0000	+	17.3205i	−0.887357	+	1.53695i	−0.842989	+	0.537931i	$0.819206\pi$
$128$	−1.50000	+	2.59808i	−0.132583	+	0.229640i
$129$		0			0
$130$	−2.50000	+	2.59808i	−0.219265	+	0.227866i
$131$	8.00000			0.698963			0.349482	−	0.936943i	$-0.386358\pi$
$131$	8.00000			0.698963			0.349482	+	0.936943i	$0.386358\pi$
$132$		0			0
$133$	6.00000	−	10.3923i	0.520266	−	0.901127i
$134$	−1.00000	−	1.73205i	−0.0863868	−	0.149626i
$135$		0			0
$136$	−10.5000	−	18.1865i	−0.900368	−	1.55948i
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	0.794808	−	0.606861i	$-0.207572\pi$
$137$	−1.50000	−	2.59808i	−0.128154	−	0.221969i	−0.922961	+	0.384893i	$0.874238\pi$
$138$		0			0
$139$	−6.00000	−	10.3923i	−0.508913	−	0.881464i	−0.999947	−	0.0103230i	$-0.996714\pi$
$139$	−6.00000	−	10.3923i	−0.508913	−	0.881464i	0.491033	−	0.871141i	$-0.336619\pi$
$140$	1.00000	−	1.73205i	0.0845154	−	0.146385i
$141$		0			0
$142$	6.00000			0.503509
$143$	5.00000	−	5.19615i	0.418121	−	0.434524i
$144$		0			0
$145$	−0.500000	+	0.866025i	−0.0415227	+	0.0719195i
$146$	5.50000	−	9.52628i	0.455183	−	0.788400i
$147$		0			0
$148$	−1.00000			−0.0821995
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	0.920904	−	0.389789i	$-0.127452\pi$
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	−0.798019	+	0.602632i	$0.794119\pi$
$150$		0			0
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$	9.00000	+	15.5885i	0.729996	+	1.26439i
$153$		0			0
$154$	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
$159$		0			0
$160$	2.50000	+	4.33013i	0.197642	+	0.342327i
$161$	12.0000			0.945732
$162$		0			0
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$	9.00000			0.702782
$165$		0			0
$166$	7.00000	−	12.1244i	0.543305	−	0.941033i
$167$	8.00000	−	13.8564i	0.619059	−	1.07224i	−0.370599	−	0.928793i	$-0.620848\pi$
$167$	8.00000	−	13.8564i	0.619059	−	1.07224i	0.989658	−	0.143448i	$-0.0458190\pi$
$168$		0			0
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$	−7.00000			−0.536875
$171$		0			0
$172$	3.00000	−	5.19615i	0.228748	−	0.396203i
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		0			0
$175$	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	$-0.857147\pi$
$179$	−1.00000	+	1.73205i	−0.0747435	+	0.129460i	0.826231	+	0.563331i	$0.190480\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	7.00000	+	1.73205i	0.518875	+	0.128388i
$183$		0			0
$184$	−9.00000	+	15.5885i	−0.663489	+	1.14920i
$185$	−0.500000	+	0.866025i	−0.0367607	+	0.0636715i
$186$		0			0
$187$	14.0000			1.02378
$188$	−3.00000	−	5.19615i	−0.218797	−	0.378968i
$189$		0			0
$190$	6.00000			0.435286
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	0.784552	−	0.620063i	$-0.212893\pi$
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	−0.929267	+	0.369410i	$0.879560\pi$
$192$		0			0
$193$	4.50000	−	7.79423i	0.323917	−	0.561041i	−0.657376	−	0.753563i	$-0.728333\pi$
$193$	4.50000	−	7.79423i	0.323917	−	0.561041i	0.981293	+	0.192522i	$0.0616668\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	3.00000			0.214286
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	−0.739141	−	0.673550i	$-0.764768\pi$
$197$	3.00000	−	5.19615i	0.213741	−	0.370211i	0.952882	+	0.303340i	$0.0981018\pi$
$198$		0			0
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	0.503774	−	0.863836i	$-0.331945\pi$
$199$	−7.00000	−	12.1244i	−0.496217	−	0.859473i	−0.999990	+	0.00436292i	$0.998611\pi$
$200$	−12.0000			−0.848528
$201$		0			0
$202$	−1.50000	−	2.59808i	−0.105540	−	0.182800i
$203$	2.00000			0.140372
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$	3.00000	−	5.19615i	0.209020	−	0.362033i
$207$		0			0
$208$	−2.50000	+	2.59808i	−0.173344	+	0.180144i
$209$	−12.0000			−0.830057
$210$		0			0
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	−0.694857	−	0.719148i	$-0.744533\pi$
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	0.970229	+	0.242190i	$0.0778659\pi$
$212$	4.50000	+	7.79423i	0.309061	+	0.535310i
$213$		0			0
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$	−3.00000	−	5.19615i	−0.204598	−	0.354375i
$216$		0			0
$217$	−4.00000	−	6.92820i	−0.271538	−	0.470317i
$218$	−1.00000	+	1.73205i	−0.0677285	+	0.117309i
$219$		0			0
$220$	−2.00000			−0.134840
$221$	7.00000	+	24.2487i	0.470871	+	1.63114i
$222$		0			0
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	0.463409	+	0.886145i	$0.346626\pi$
$223$	−8.00000	+	13.8564i	−0.535720	+	0.927894i	−0.999128	+	0.0417488i	$0.986707\pi$
$224$	5.00000	−	8.66025i	0.334077	−	0.578638i
$225$		0			0
$226$	−15.0000			−0.997785
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	0.534577	−	0.845120i	$-0.320471\pi$
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	−0.999184	+	0.0403978i	$0.987137\pi$
$228$		0			0
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$	3.00000	+	5.19615i	0.197814	+	0.342624i
$231$		0			0
$232$	−1.50000	+	2.59808i	−0.0984798	+	0.170572i
$233$	−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
$237$		0			0
$238$	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			0
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	0.731001	−	0.682376i	$-0.239053\pi$
$241$	−3.50000	−	6.06218i	−0.225455	−	0.390499i	−0.956456	+	0.291877i	$0.905720\pi$
$242$	7.00000			0.449977
$243$		0			0
$244$	0.500000	−	0.866025i	0.0320092	−	0.0554416i
$245$	1.50000	−	2.59808i	0.0958315	−	0.165985i
$246$		0			0
$247$	−6.00000	−	20.7846i	−0.381771	−	1.32249i
$248$	12.0000			0.762001
$249$		0			0
$250$	−4.50000	+	7.79423i	−0.284605	+	0.492950i
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	0.990876	−	0.134778i	$-0.0430322\pi$
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	−0.612159	+	0.790735i	$0.709699\pi$
$252$		0			0
$253$	−6.00000	−	10.3923i	−0.377217	−	0.653359i
$254$	10.0000	+	17.3205i	0.627456	+	1.08679i
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−3.50000	+	6.06218i	−0.218324	+	0.378148i	−0.954296	−	0.298864i	$-0.903392\pi$
$257$	−3.50000	+	6.06218i	−0.218324	+	0.378148i	0.735972	+	0.677012i	$0.236726\pi$
$258$		0			0
$259$	2.00000			0.124274
$260$	−1.00000	−	3.46410i	−0.0620174	−	0.214834i
$261$		0			0
$262$	4.00000	−	6.92820i	0.247121	−	0.428026i
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.133281	+	0.991078i	$0.542551\pi$
$263$	−15.0000	+	25.9808i	−0.924940	+	1.60204i	−0.791658	+	0.610964i	$0.790782\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$	−6.00000	−	10.3923i	−0.367884	−	0.637193i
$267$		0			0
$268$	2.00000			0.122169
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	0.569789	−	0.821791i	$-0.307025\pi$
$269$	−7.00000	−	12.1244i	−0.426798	−	0.739235i	−0.996586	+	0.0825561i	$0.973692\pi$
$270$		0			0
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$	−7.00000			−0.424437
$273$		0			0
$274$	−3.00000			−0.181237
$275$	4.00000	−	6.92820i	0.241209	−	0.417786i
$276$		0			0
$277$	15.5000	+	26.8468i	0.931305	+	1.61307i	0.781094	+	0.624413i	$0.214662\pi$
$277$	15.5000	+	26.8468i	0.931305	+	1.61307i	0.150210	+	0.988654i	$0.452005\pi$
$278$	−12.0000			−0.719712
$279$		0			0
$280$	−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	$0.308211\pi$
$282$		0			0
$283$	9.00000	−	15.5885i	0.534994	−	0.926638i	−0.464169	−	0.885747i	$-0.653647\pi$
$283$	9.00000	−	15.5885i	0.534994	−	0.926638i	0.999164	−	0.0408910i	$-0.0130196\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	−2.00000	−	6.92820i	−0.118262	−	0.409673i
$287$	−18.0000			−1.06251
$288$		0			0
$289$	−16.0000	+	27.7128i	−0.941176	+	1.63017i
$290$	0.500000	+	0.866025i	0.0293610	+	0.0508548i
$291$		0			0
$292$	5.50000	+	9.52628i	0.321863	+	0.557483i
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	0.704117	−	0.710084i	$-0.251343\pi$
$293$	−4.50000	−	7.79423i	−0.262893	−	0.455344i	−0.967009	+	0.254741i	$0.918010\pi$
$294$		0			0
$295$		0			0
$296$	−1.50000	+	2.59808i	−0.0871857	+	0.151010i
$297$		0			0
$298$	3.00000			0.173785
$299$	15.0000	−	15.5885i	0.867472	−	0.901504i
$300$		0			0
$301$	−6.00000	+	10.3923i	−0.345834	+	0.599002i
$302$	−1.00000	+	1.73205i	−0.0575435	+	0.0996683i
$303$		0			0
$304$	6.00000			0.344124
$305$	−0.500000	−	0.866025i	−0.0286299	−	0.0495885i
$306$		0			0
$307$	14.0000			0.799022			0.399511	−	0.916728i	$-0.369180\pi$
$307$	14.0000			0.799022			0.399511	+	0.916728i	$0.369180\pi$
$308$	2.00000	+	3.46410i	0.113961	+	0.197386i
$309$		0			0
$310$	2.00000	−	3.46410i	0.113592	−	0.196748i
$311$	−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	$0.445762\pi$
$314$	−1.50000	+	2.59808i	−0.0846499	+	0.146618i
$315$		0			0
$316$	−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	$0.252259\pi$
$318$		0			0
$319$	−1.00000	−	1.73205i	−0.0559893	−	0.0969762i
$320$	7.00000			0.391312
$321$		0			0
$322$	6.00000	−	10.3923i	0.334367	−	0.579141i
$323$	21.0000	−	36.3731i	1.16847	−	2.02385i
$324$		0			0
$325$	14.0000	+	3.46410i	0.776580	+	0.192154i
$326$	4.00000			0.221540
$327$		0			0
$328$	13.5000	−	23.3827i	0.745413	−	1.29109i
$329$	6.00000	+	10.3923i	0.330791	+	0.572946i
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	7.00000	+	12.1244i	0.384175	+	0.665410i
$333$		0			0
$334$	−8.00000	−	13.8564i	−0.437741	−	0.758189i
$335$	1.00000	−	1.73205i	0.0546358	−	0.0946320i
$336$		0			0
$337$	−33.0000			−1.79762			−0.898812	−	0.438334i	$-0.855569\pi$
$337$	−33.0000			−1.79762			−0.898812	+	0.438334i	$0.855569\pi$
$338$	11.0000	−	6.92820i	0.598321	−	0.376845i
$339$		0			0
$340$	3.50000	−	6.06218i	0.189814	−	0.328768i
$341$	−4.00000	+	6.92820i	−0.216612	+	0.375183i
$342$		0			0
$343$	−20.0000			−1.07990
$344$	−9.00000	−	15.5885i	−0.485247	−	0.840473i
$345$		0			0
$346$	−6.00000			−0.322562
$347$	9.00000	+	15.5885i	0.483145	+	0.836832i	0.999813	−	0.0193540i	$-0.00616095\pi$
$347$	9.00000	+	15.5885i	0.483145	+	0.836832i	−0.516667	+	0.856186i	$0.672828\pi$
$348$		0			0
$349$	13.0000	−	22.5167i	0.695874	−	1.20529i	−0.274011	−	0.961727i	$-0.588351\pi$
$349$	13.0000	−	22.5167i	0.695874	−	1.20529i	0.969885	−	0.243563i	$-0.0783162\pi$
$350$	8.00000			0.427618
$351$		0			0
$352$	−10.0000			−0.533002
$353$	−5.50000	+	9.52628i	−0.292735	+	0.507033i	−0.974456	−	0.224580i	$-0.927899\pi$
$353$	−5.50000	+	9.52628i	−0.292735	+	0.507033i	0.681720	+	0.731613i	$0.261232\pi$
$354$		0			0
$355$	3.00000	+	5.19615i	0.159223	+	0.275783i
$356$	−14.0000			−0.741999
$357$		0			0
$358$	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	$0.342447\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	−3.50000	+	6.06218i	−0.183956	+	0.318621i
$363$		0			0
$364$	−5.00000	+	5.19615i	−0.262071	+	0.272352i
$365$	11.0000			0.575766
$366$		0			0
$367$	−5.00000	+	8.66025i	−0.260998	+	0.452062i	−0.966507	−	0.256639i	$-0.917385\pi$
$367$	−5.00000	+	8.66025i	−0.260998	+	0.452062i	0.705509	+	0.708700i	$0.250718\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$		0			0
$370$	0.500000	+	0.866025i	0.0259938	+	0.0450225i
$371$	−9.00000	−	15.5885i	−0.467257	−	0.809312i
$372$		0			0
$373$	5.50000	+	9.52628i	0.284779	+	0.493252i	0.972556	−	0.232671i	$-0.0747464\pi$
$373$	5.50000	+	9.52628i	0.284779	+	0.493252i	−0.687776	+	0.725923i	$0.741413\pi$
$374$	7.00000	−	12.1244i	0.361961	−	0.626936i
$375$		0			0
$376$	−18.0000			−0.928279
$377$	2.50000	−	2.59808i	0.128757	−	0.133808i
$378$		0			0
$379$	18.0000	−	31.1769i	0.924598	−	1.60145i	0.132391	−	0.991198i	$-0.457734\pi$
$379$	18.0000	−	31.1769i	0.924598	−	1.60145i	0.792207	−	0.610253i	$-0.208932\pi$
$380$	−3.00000	+	5.19615i	−0.153897	+	0.266557i
$381$		0			0
$382$	−4.00000			−0.204658
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	0.949938	−	0.312437i	$-0.101145\pi$
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	−0.745548	+	0.666452i	$0.767812\pi$
$384$		0			0
$385$	4.00000			0.203859
$386$	−4.50000	−	7.79423i	−0.229044	−	0.396716i
$387$		0			0
$388$	−1.00000	+	1.73205i	−0.0507673	+	0.0879316i
$389$	−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
$392$	4.50000	−	7.79423i	0.227284	−	0.393668i
$393$		0			0
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$	−4.00000			−0.201262
$396$		0			0
$397$	17.0000	+	29.4449i	0.853206	+	1.47780i	0.878300	+	0.478110i	$0.158678\pi$
$397$	17.0000	+	29.4449i	0.853206	+	1.47780i	−0.0250943	+	0.999685i	$0.507989\pi$
$398$	−14.0000			−0.701757
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	0.500000	−	0.866025i	0.0249688	−	0.0432472i	−0.853271	−	0.521468i	$-0.825385\pi$
$401$	0.500000	−	0.866025i	0.0249688	−	0.0432472i	0.878240	+	0.478220i	$0.158718\pi$
$402$		0			0
$403$	−14.0000	−	3.46410i	−0.697390	−	0.172559i
$404$	3.00000			0.149256
$405$		0			0
$406$	1.00000	−	1.73205i	0.0496292	−	0.0859602i
$407$	−1.00000	−	1.73205i	−0.0495682	−	0.0858546i
$408$		0			0
$409$	−3.50000	−	6.06218i	−0.173064	−	0.299755i	0.766426	−	0.642333i	$-0.222033\pi$
$409$	−3.50000	−	6.06218i	−0.173064	−	0.299755i	−0.939490	+	0.342578i	$0.888700\pi$
$410$	−4.50000	−	7.79423i	−0.222239	−	0.384930i
$411$		0			0
$412$	3.00000	+	5.19615i	0.147799	+	0.255996i
$413$		0			0
$414$		0			0
$415$	14.0000			0.687233
$416$	−5.00000	−	17.3205i	−0.245145	−	0.849208i
$417$		0			0
$418$	−6.00000	+	10.3923i	−0.293470	+	0.508304i
$419$	8.00000	−	13.8564i	0.390826	−	0.676930i	−0.601733	−	0.798697i	$-0.705523\pi$
$419$	8.00000	−	13.8564i	0.390826	−	0.676930i	0.992559	+	0.121768i	$0.0388562\pi$
$420$		0			0
$421$	−19.0000			−0.926003			−0.463002	−	0.886357i	$-0.653228\pi$
$421$	−19.0000			−0.926003			−0.463002	+	0.886357i	$0.653228\pi$
$422$	−4.00000	−	6.92820i	−0.194717	−	0.337260i
$423$		0			0
$424$	27.0000			1.31124
$425$	14.0000	+	24.2487i	0.679100	+	1.17624i
$426$		0			0
$427$	−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	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$		0			0
$433$	−9.50000	−	16.4545i	−0.456541	−	0.790752i	0.542234	−	0.840227i	$-0.317578\pi$
$433$	−9.50000	−	16.4545i	−0.456541	−	0.790752i	−0.998775	+	0.0494752i	$0.984245\pi$
$434$	−8.00000			−0.384012
$435$		0			0
$436$	−1.00000	−	1.73205i	−0.0478913	−	0.0829502i
$437$	−36.0000			−1.72211
$438$		0			0
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	−0.983310	−	0.181938i	$-0.941763\pi$
$439$	−7.00000	+	12.1244i	−0.334092	+	0.578664i	0.649218	+	0.760602i	$0.275096\pi$
$440$	−3.00000	+	5.19615i	−0.143019	+	0.247717i
$441$		0			0
$442$	24.5000	+	6.06218i	1.16535	+	0.288348i
$443$	4.00000			0.190046			0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000			0.190046			0.0950229	+	0.995475i	$0.469708\pi$
$444$		0			0
$445$	−7.00000	+	12.1244i	−0.331832	+	0.574750i
$446$	8.00000	+	13.8564i	0.378811	+	0.656120i
$447$		0			0
$448$	−7.00000	−	12.1244i	−0.330719	−	0.572822i
$449$	17.0000	+	29.4449i	0.802280	+	1.38959i	0.918112	+	0.396320i	$0.129713\pi$
$449$	17.0000	+	29.4449i	0.802280	+	1.38959i	−0.115833	+	0.993269i	$0.536954\pi$
$450$		0			0
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$	7.50000	−	12.9904i	0.352770	−	0.611016i
$453$		0			0
$454$	−14.0000			−0.657053
$455$	2.00000	+	6.92820i	0.0937614	+	0.324799i
$456$		0			0
$457$	6.50000	−	11.2583i	0.304057	−	0.526642i	−0.672994	−	0.739648i	$-0.734992\pi$
$457$	6.50000	−	11.2583i	0.304057	−	0.526642i	0.977051	+	0.213006i	$0.0683253\pi$
$458$	−11.0000	+	19.0526i	−0.513996	+	0.890268i
$459$		0			0
$460$	−6.00000			−0.279751
$461$	9.50000	+	16.4545i	0.442459	+	0.766362i	0.997871	−	0.0652135i	$-0.0207728\pi$
$461$	9.50000	+	16.4545i	0.442459	+	0.766362i	−0.555412	+	0.831575i	$0.687440\pi$
$462$		0			0
$463$	−26.0000			−1.20832			−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000			−1.20832			−0.604161	+	0.796862i	$0.706492\pi$
$464$	0.500000	+	0.866025i	0.0232119	+	0.0402042i
$465$		0			0
$466$	−5.00000	+	8.66025i	−0.231621	+	0.401179i
$467$	−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
$470$	−3.00000	+	5.19615i	−0.138380	+	0.239681i
$471$		0			0
$472$		0			0
$473$	12.0000			0.551761
$474$		0			0
$475$	−12.0000	−	20.7846i	−0.550598	−	0.953663i
$476$	−14.0000			−0.641689
$477$		0			0
$478$	−15.0000	+	25.9808i	−0.686084	+	1.18833i
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$		0			0
$481$	2.50000	−	2.59808i	0.113990	−	0.118462i
$482$	−7.00000			−0.318841
$483$		0			0
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$	1.00000	+	1.73205i	0.0454077	+	0.0786484i
$486$		0			0
$487$	−9.00000	−	15.5885i	−0.407829	−	0.706380i	0.586817	−	0.809719i	$-0.300381\pi$
$487$	−9.00000	−	15.5885i	−0.407829	−	0.706380i	−0.994646	+	0.103339i	$0.967047\pi$
$488$	−1.50000	−	2.59808i	−0.0679018	−	0.117609i
$489$		0			0
$490$	−1.50000	−	2.59808i	−0.0677631	−	0.117369i
$491$	3.00000	−	5.19615i	0.135388	−	0.234499i	−0.790358	−	0.612646i	$-0.790105\pi$
$491$	3.00000	−	5.19615i	0.135388	−	0.234499i	0.925746	+	0.378147i	$0.123439\pi$
$492$		0			0
$493$	7.00000			0.315264
$494$	−21.0000	−	5.19615i	−0.944835	−	0.233786i
$495$		0			0
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$	6.00000	−	10.3923i	0.269137	−	0.466159i
$498$		0			0
$499$	24.0000			1.07439			0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000			1.07439			0.537194	+	0.843459i	$0.319484\pi$
$500$	−4.50000	−	7.79423i	−0.201246	−	0.348569i
$501$		0			0
$502$	12.0000			0.535586
$503$	−1.00000	−	1.73205i	−0.0445878	−	0.0772283i	0.842870	−	0.538117i	$-0.180864\pi$
$503$	−1.00000	−	1.73205i	−0.0445878	−	0.0772283i	−0.887458	+	0.460889i	$0.847531\pi$
$504$		0			0
$505$	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	−0.777973	−	0.628297i	$-0.783752\pi$
$509$	3.50000	−	6.06218i	0.155135	−	0.268701i	0.933108	+	0.359596i	$0.117085\pi$
$510$		0			0
$511$	−11.0000	−	19.0526i	−0.486611	−	0.842836i
$512$	11.0000			0.486136
$513$		0			0
$514$	3.50000	+	6.06218i	0.154378	+	0.267391i
$515$	6.00000			0.264392
$516$		0			0
$517$	6.00000	−	10.3923i	0.263880	−	0.457053i
$518$	1.00000	−	1.73205i	0.0439375	−	0.0761019i
$519$		0			0
$520$	−10.5000	−	2.59808i	−0.460455	−	0.113933i
$521$	3.00000			0.131432			0.0657162	−	0.997838i	$-0.479067\pi$
$521$	3.00000			0.131432			0.0657162	+	0.997838i	$0.479067\pi$
$522$		0			0
$523$	−7.00000	+	12.1244i	−0.306089	+	0.530161i	−0.977503	−	0.210921i	$-0.932354\pi$
$523$	−7.00000	+	12.1244i	−0.306089	+	0.530161i	0.671414	+	0.741082i	$0.265687\pi$
$524$	4.00000	+	6.92820i	0.174741	+	0.302660i
$525$		0			0
$526$	15.0000	+	25.9808i	0.654031	+	1.13282i
$527$	−14.0000	−	24.2487i	−0.609850	−	1.05629i
$528$		0			0
$529$	−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
$533$	−22.5000	+	23.3827i	−0.974583	+	1.01282i
$534$		0			0
$535$	−3.00000	+	5.19615i	−0.129701	+	0.224649i
$536$	3.00000	−	5.19615i	0.129580	−	0.224440i
$537$		0			0
$538$	−14.0000			−0.603583
$539$	3.00000	+	5.19615i	0.129219	+	0.223814i
$540$		0			0
$541$	45.0000			1.93470			0.967351	−	0.253442i	$-0.0815627\pi$
$541$	45.0000			1.93470			0.967351	+	0.253442i	$0.0815627\pi$
$542$		0			0
$543$		0			0
$544$	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			0
$550$	−4.00000	−	6.92820i	−0.170561	−	0.295420i
$551$	−6.00000			−0.255609
$552$		0			0
$553$	4.00000	+	6.92820i	0.170097	+	0.294617i
$554$	31.0000			1.31706
$555$		0			0
$556$	6.00000	−	10.3923i	0.254457	−	0.440732i
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	−0.945473	−	0.325701i	$-0.894400\pi$
$557$	−4.50000	+	7.79423i	−0.190671	+	0.330252i	0.754802	+	0.655953i	$0.227733\pi$
$558$		0			0
$559$	6.00000	+	20.7846i	0.253773	+	0.879095i
$560$	−2.00000			−0.0845154
$561$		0			0
$562$	9.50000	−	16.4545i	0.400733	−	0.694090i
$563$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$563$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$564$		0			0
$565$	−7.50000	−	12.9904i	−0.315527	−	0.546509i
$566$	−9.00000	−	15.5885i	−0.378298	−	0.655232i
$567$		0			0
$568$	9.00000	+	15.5885i	0.377632	+	0.654077i
$569$	11.0000	−	19.0526i	0.461144	−	0.798725i	−0.537874	−	0.843025i	$-0.680772\pi$
$569$	11.0000	−	19.0526i	0.461144	−	0.798725i	0.999018	+	0.0443003i	$0.0141058\pi$
$570$		0			0
$571$	26.0000			1.08807			0.544033	−	0.839064i	$-0.316897\pi$
$571$	26.0000			1.08807			0.544033	+	0.839064i	$0.316897\pi$
$572$	7.00000	+	1.73205i	0.292685	+	0.0724207i
$573$		0			0
$574$	−9.00000	+	15.5885i	−0.375653	+	0.650650i
$575$	12.0000	−	20.7846i	0.500435	−	0.866778i
$576$		0			0
$577$	11.0000			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$577$	11.0000			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$578$	16.0000	+	27.7128i	0.665512	+	1.15270i
$579$		0			0
$580$	−1.00000			−0.0415227
$581$	−14.0000	−	24.2487i	−0.580818	−	1.00601i
$582$		0			0
$583$	−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	−0.652355	−	0.757914i	$-0.726219\pi$
$587$	8.00000	−	13.8564i	0.330195	−	0.571915i	0.982550	+	0.185999i	$0.0595520\pi$
$588$		0			0
$589$	12.0000	+	20.7846i	0.494451	+	0.856415i
$590$		0			0
$591$		0			0
$592$	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	$0.586007\pi$
$594$		0			0
$595$	−7.00000	+	12.1244i	−0.286972	+	0.497050i
$596$	−1.50000	+	2.59808i	−0.0614424	+	0.106421i
$597$		0			0
$598$	−6.00000	−	20.7846i	−0.245358	−	0.849946i
$599$	16.0000			0.653742			0.326871	−	0.945069i	$-0.394006\pi$
$599$	16.0000			0.653742			0.326871	+	0.945069i	$0.394006\pi$
$600$		0			0
$601$	2.50000	−	4.33013i	0.101977	−	0.176630i	−0.810522	−	0.585708i	$-0.800816\pi$
$601$	2.50000	−	4.33013i	0.101977	−	0.176630i	0.912499	+	0.409079i	$0.134150\pi$
$602$	6.00000	+	10.3923i	0.244542	+	0.423559i
$603$		0			0
$604$	−1.00000	−	1.73205i	−0.0406894	−	0.0704761i
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$		0			0
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	0.773358	−	0.633970i	$-0.218576\pi$
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$608$	−15.0000	+	25.9808i	−0.608330	+	1.05366i
$609$		0			0
$610$	−1.00000			−0.0404888
$611$	21.0000	+	5.19615i	0.849569	+	0.210214i
$612$		0			0
$613$	11.5000	−	19.9186i	0.464481	−	0.804504i	−0.534697	−	0.845044i	$-0.679574\pi$
$613$	11.5000	−	19.9186i	0.464481	−	0.804504i	0.999178	+	0.0405396i	$0.0129077\pi$
$614$	7.00000	−	12.1244i	0.282497	−	0.489299i
$615$		0			0
$616$	12.0000			0.483494
$617$	6.50000	+	11.2583i	0.261680	+	0.453243i	0.966689	−	0.255956i	$-0.0823901\pi$
$617$	6.50000	+	11.2583i	0.261680	+	0.453243i	−0.705008	+	0.709199i	$0.749057\pi$
$618$		0			0
$619$	−24.0000			−0.964641			−0.482321	−	0.875995i	$-0.660206\pi$
$619$	−24.0000			−0.964641			−0.482321	+	0.875995i	$0.660206\pi$
$620$	2.00000	+	3.46410i	0.0803219	+	0.139122i
$621$		0			0
$622$	−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
$627$		0			0
$628$	−1.50000	−	2.59808i	−0.0598565	−	0.103675i
$629$	7.00000			0.279108
$630$		0			0
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	0.595397	−	0.803432i	$-0.296995\pi$
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	−0.993491	+	0.113913i	$0.963661\pi$
$632$	−12.0000			−0.477334
$633$		0			0
$634$	12.5000	−	21.6506i	0.496438	−	0.859857i
$635$	−10.0000	+	17.3205i	−0.396838	+	0.687343i
$636$		0			0
$637$	−7.50000	+	7.79423i	−0.297161	+	0.308819i
$638$	−2.00000			−0.0791808
$639$		0			0
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	−15.5000	−	26.8468i	−0.612213	−	1.06038i	−0.990867	−	0.134846i	$-0.956946\pi$
$641$	−15.5000	−	26.8468i	−0.612213	−	1.06038i	0.378653	−	0.925539i	$-0.376387\pi$
$642$		0			0
$643$	8.00000	+	13.8564i	0.315489	+	0.546443i	0.979541	−	0.201243i	$-0.0644981\pi$
$643$	8.00000	+	13.8564i	0.315489	+	0.546443i	−0.664052	+	0.747686i	$0.731165\pi$
$644$	6.00000	+	10.3923i	0.236433	+	0.409514i
$645$		0			0
$646$	−21.0000	−	36.3731i	−0.826234	−	1.43108i
$647$	−16.0000	+	27.7128i	−0.629025	+	1.08950i	0.358723	+	0.933444i	$0.383212\pi$
$647$	−16.0000	+	27.7128i	−0.629025	+	1.08950i	−0.987748	+	0.156059i	$0.950121\pi$
$648$		0			0
$649$		0			0
$650$	10.0000	−	10.3923i	0.392232	−	0.407620i
$651$		0			0
$652$	−2.00000	+	3.46410i	−0.0783260	+	0.135665i
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	−0.918736	−	0.394872i	$-0.870789\pi$
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	0.801337	+	0.598213i	$0.204122\pi$
$654$		0			0
$655$	8.00000			0.312586
$656$	−4.50000	−	7.79423i	−0.175695	−	0.304314i
$657$		0			0
$658$	12.0000			0.467809
$659$	−4.00000	−	6.92820i	−0.155818	−	0.269884i	0.777539	−	0.628835i	$-0.216468\pi$
$659$	−4.00000	−	6.92820i	−0.155818	−	0.269884i	−0.933357	+	0.358951i	$0.883135\pi$
$660$		0			0
$661$	−22.5000	+	38.9711i	−0.875149	+	1.51580i	−0.0185442	+	0.999828i	$0.505903\pi$
$661$	−22.5000	+	38.9711i	−0.875149	+	1.51580i	−0.856604	+	0.515974i	$0.827430\pi$
$662$	4.00000			0.155464
$663$		0			0
$664$	42.0000			1.62992
$665$	6.00000	−	10.3923i	0.232670	−	0.402996i
$666$		0			0
$667$	−3.00000	−	5.19615i	−0.116160	−	0.201196i
$668$	16.0000			0.619059
$669$		0			0
$670$	−1.00000	−	1.73205i	−0.0386334	−	0.0669150i
$671$	2.00000			0.0772091
$672$		0			0
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	−0.438652	−	0.898657i	$-0.644544\pi$
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	0.997586	−	0.0694449i	$-0.0221228\pi$
$674$	−16.5000	+	28.5788i	−0.635556	+	1.10082i
$675$		0			0
$676$	0.500000	+	12.9904i	0.0192308	+	0.499630i
$677$	−34.0000			−1.30673			−0.653363	−	0.757045i	$-0.726642\pi$
$677$	−34.0000			−1.30673			−0.653363	+	0.757045i	$0.726642\pi$
$678$		0			0
$679$	2.00000	−	3.46410i	0.0767530	−	0.132940i
$680$	−10.5000	−	18.1865i	−0.402657	−	0.697422i
$681$		0			0
$682$	4.00000	+	6.92820i	0.153168	+	0.265295i
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	0.539750	−	0.841825i	$-0.318519\pi$
$683$	−12.0000	−	20.7846i	−0.459167	−	0.795301i	−0.998917	+	0.0465244i	$0.985185\pi$
$684$		0			0
$685$	−1.50000	−	2.59808i	−0.0573121	−	0.0992674i
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$		0			0
$688$	−6.00000			−0.228748
$689$	−31.5000	−	7.79423i	−1.20005	−	0.296936i
$690$		0			0
$691$	−21.0000	+	36.3731i	−0.798878	+	1.38370i	0.121470	+	0.992595i	$0.461239\pi$
$691$	−21.0000	+	36.3731i	−0.798878	+	1.38370i	−0.920348	+	0.391102i	$0.872094\pi$
$692$	3.00000	−	5.19615i	0.114043	−	0.197528i
$693$		0			0
$694$	18.0000			0.683271
$695$	−6.00000	−	10.3923i	−0.227593	−	0.394203i
$696$		0			0
$697$	−63.0000			−2.38630
$698$	−13.0000	−	22.5167i	−0.492057	−	0.852268i
$699$		0			0
$700$	−4.00000	+	6.92820i	−0.151186	+	0.261861i
$701$	−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
$704$	−7.00000	+	12.1244i	−0.263822	+	0.456954i
$705$		0			0
$706$	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	$-0.100441\pi$
$709$	5.50000	+	9.52628i	0.206557	+	0.357767i	−0.744071	+	0.668101i	$0.767108\pi$
$710$	6.00000			0.225176
$711$		0			0
$712$	−21.0000	+	36.3731i	−0.787008	+	1.36314i
$713$	−12.0000	+	20.7846i	−0.449404	+	0.778390i
$714$		0			0
$715$	5.00000	−	5.19615i	0.186989	−	0.194325i
$716$	−2.00000			−0.0747435
$717$		0			0
$718$	9.00000	−	15.5885i	0.335877	−	0.581756i
$719$	−24.0000	−	41.5692i	−0.895049	−	1.55027i	−0.833744	−	0.552151i	$-0.813807\pi$
$719$	−24.0000	−	41.5692i	−0.895049	−	1.55027i	−0.0613050	−	0.998119i	$-0.519526\pi$
$720$		0			0
$721$	−6.00000	−	10.3923i	−0.223452	−	0.387030i
$722$	8.50000	+	14.7224i	0.316337	+	0.547912i
$723$		0			0
$724$	−3.50000	−	6.06218i	−0.130076	−	0.225299i
$725$	2.00000	−	3.46410i	0.0742781	−	0.128654i
$726$		0			0
$727$	14.0000			0.519231			0.259616	−	0.965712i	$-0.416404\pi$
$727$	14.0000			0.519231			0.259616	+	0.965712i	$0.416404\pi$
$728$	6.00000	+	20.7846i	0.222375	+	0.770329i
$729$		0			0
$730$	5.50000	−	9.52628i	0.203564	−	0.352583i
$731$	−21.0000	+	36.3731i	−0.776713	+	1.34531i
$732$		0			0
$733$	−15.0000			−0.554038			−0.277019	−	0.960864i	$-0.589346\pi$
$733$	−15.0000			−0.554038			−0.277019	+	0.960864i	$0.589346\pi$
$734$	5.00000	+	8.66025i	0.184553	+	0.319656i
$735$		0			0
$736$	−30.0000			−1.10581
$737$	2.00000	+	3.46410i	0.0736709	+	0.127602i
$738$		0			0
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	−0.680534	−	0.732717i	$-0.738252\pi$
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	0.974818	+	0.223001i	$0.0715853\pi$
$740$	−1.00000			−0.0367607
$741$		0			0
$742$	−18.0000			−0.660801
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	0.320166	+	0.947361i	$0.396261\pi$
$743$	−18.0000	+	31.1769i	−0.660356	+	1.14377i	−0.980522	+	0.196409i	$0.937072\pi$
$744$		0			0
$745$	1.50000	+	2.59808i	0.0549557	+	0.0951861i
$746$	11.0000			0.402739
$747$		0			0
$748$	7.00000	+	12.1244i	0.255945	+	0.443310i
$749$	12.0000			0.438470
$750$		0			0
$751$	17.0000	−	29.4449i	0.620339	−	1.07446i	−0.369084	−	0.929396i	$-0.620328\pi$
$751$	17.0000	−	29.4449i	0.620339	−	1.07446i	0.989423	−	0.145062i	$-0.0463382\pi$
$752$	−3.00000	+	5.19615i	−0.109399	+	0.189484i
$753$		0			0
$754$	−1.00000	−	3.46410i	−0.0364179	−	0.126155i
$755$	−2.00000			−0.0727875
$756$		0			0
$757$	25.0000	−	43.3013i	0.908640	−	1.57381i	0.0926859	−	0.995695i	$-0.470455\pi$
$757$	25.0000	−	43.3013i	0.908640	−	1.57381i	0.815955	−	0.578116i	$-0.196212\pi$
$758$	−18.0000	−	31.1769i	−0.653789	−	1.13240i
$759$		0			0
$760$	9.00000	+	15.5885i	0.326464	+	0.565453i
$761$	25.0000	+	43.3013i	0.906249	+	1.56967i	0.819231	+	0.573463i	$0.194400\pi$
$761$	25.0000	+	43.3013i	0.906249	+	1.56967i	0.0870179	+	0.996207i	$0.472266\pi$
$762$		0			0
$763$	2.00000	+	3.46410i	0.0724049	+	0.125409i
$764$	2.00000	−	3.46410i	0.0723575	−	0.125327i
$765$		0			0
$766$	8.00000			0.289052
$767$		0			0
$768$		0			0
$769$	−15.0000	+	25.9808i	−0.540914	+	0.936890i	0.457938	+	0.888984i	$0.348588\pi$
$769$	−15.0000	+	25.9808i	−0.540914	+	0.936890i	−0.998852	+	0.0479061i	$0.984745\pi$
$770$	2.00000	−	3.46410i	0.0720750	−	0.124838i
$771$		0			0
$772$	9.00000			0.323917
$773$	−7.00000	−	12.1244i	−0.251773	−	0.436083i	0.712241	−	0.701935i	$-0.247680\pi$
$773$	−7.00000	−	12.1244i	−0.251773	−	0.436083i	−0.964014	+	0.265852i	$0.914347\pi$
$774$		0			0
$775$	−16.0000			−0.574737
$776$	3.00000	+	5.19615i	0.107694	+	0.186531i
$777$		0			0
$778$	−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			0
$784$	−1.50000	−	2.59808i	−0.0535714	−	0.0927884i
$785$	−3.00000			−0.107075
$786$		0			0
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	0.500953	−	0.865474i	$-0.332983\pi$
$787$	−14.0000	−	24.2487i	−0.499046	−	0.864373i	−0.999999	+	0.00110111i	$0.999650\pi$
$788$	6.00000			0.213741
$789$		0			0
$790$	−2.00000	+	3.46410i	−0.0711568	+	0.123247i
$791$	−15.0000	+	25.9808i	−0.533339	+	0.923770i
$792$		0			0
$793$	1.00000	+	3.46410i	0.0355110	+	0.123014i
$794$	34.0000			1.20661
$795$		0			0
$796$	7.00000	−	12.1244i	0.248108	−	0.429736i
$797$	−1.00000	−	1.73205i	−0.0354218	−	0.0613524i	0.847771	−	0.530362i	$-0.177944\pi$
$797$	−1.00000	−	1.73205i	−0.0354218	−	0.0613524i	−0.883193	+	0.469010i	$0.844611\pi$
$798$		0			0
$799$	21.0000	+	36.3731i	0.742927	+	1.28679i
$800$	−10.0000	−	17.3205i	−0.353553	−	0.612372i
$801$		0			0
$802$	−0.500000	−	0.866025i	−0.0176556	−	0.0305804i
$803$	−11.0000	+	19.0526i	−0.388182	+	0.672350i
$804$		0			0
$805$	12.0000			0.422944
$806$	−10.0000	+	10.3923i	−0.352235	+	0.366053i
$807$		0			0
$808$	4.50000	−	7.79423i	0.158309	−	0.274200i
$809$	16.5000	−	28.5788i	0.580109	−	1.00478i	−0.415357	−	0.909659i	$-0.636343\pi$
$809$	16.5000	−	28.5788i	0.580109	−	1.00478i	0.995466	−	0.0951198i	$-0.0303234\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	1.00000	+	1.73205i	0.0350931	+	0.0607831i
$813$		0			0
$814$	−2.00000			−0.0701000
$815$	2.00000	+	3.46410i	0.0700569	+	0.121342i
$816$		0			0
$817$	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	0.0131101	−	0.999914i	$-0.495827\pi$
$821$	25.0000	−	43.3013i	0.872506	−	1.51122i	0.859396	−	0.511311i	$-0.170840\pi$
$822$		0			0
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	0.995768	−	0.0919029i	$-0.0292950\pi$
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	−0.577474	+	0.816409i	$0.695962\pi$
$824$	18.0000			0.627060
$825$		0			0
$826$		0			0
$827$	−16.0000			−0.556375			−0.278187	−	0.960527i	$-0.589734\pi$
$827$	−16.0000			−0.556375			−0.278187	+	0.960527i	$0.589734\pi$
$828$		0			0
$829$	−8.50000	+	14.7224i	−0.295217	+	0.511331i	−0.975035	−	0.222049i	$-0.928725\pi$
$829$	−8.50000	+	14.7224i	−0.295217	+	0.511331i	0.679818	+	0.733381i	$0.262059\pi$
$830$	7.00000	−	12.1244i	0.242974	−	0.420843i
$831$		0			0
$832$	−24.5000	−	6.06218i	−0.849385	−	0.210168i
$833$	−21.0000			−0.727607
$834$		0			0
$835$	8.00000	−	13.8564i	0.276851	−	0.479521i
$836$	−6.00000	−	10.3923i	−0.207514	−	0.359425i
$837$		0			0
$838$	−8.00000	−	13.8564i	−0.276355	−	0.478662i
$839$	6.00000	+	10.3923i	0.207143	+	0.358782i	0.950813	−	0.309764i	$-0.100250\pi$
$839$	6.00000	+	10.3923i	0.207143	+	0.358782i	−0.743670	+	0.668546i	$0.766917\pi$
$840$		0			0
$841$	14.0000	+	24.2487i	0.482759	+	0.836162i
$842$	−9.50000	+	16.4545i	−0.327392	+	0.567059i
$843$		0			0
$844$	8.00000			0.275371
$845$	11.5000	+	6.06218i	0.395612	+	0.208545i
$846$		0			0
$847$	7.00000	−	12.1244i	0.240523	−	0.416598i
$848$	4.50000	−	7.79423i	0.154531	−	0.267655i
$849$		0			0
$850$	28.0000			0.960392
$851$	−3.00000	−	5.19615i	−0.102839	−	0.178122i
$852$		0			0
$853$	21.0000			0.719026			0.359513	−	0.933140i	$-0.382943\pi$
$853$	21.0000			0.719026			0.359513	+	0.933140i	$0.382943\pi$
$854$	1.00000	+	1.73205i	0.0342193	+	0.0592696i
$855$		0			0
$856$	−9.00000	+	15.5885i	−0.307614	+	0.532803i
$857$	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	$0.303040\pi$
$860$	3.00000	−	5.19615i	0.102299	−	0.177187i
$861$		0			0
$862$	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	$0.554442\pi$
$864$		0			0
$865$	−3.00000	−	5.19615i	−0.102003	−	0.176674i
$866$	−19.0000			−0.645646
$867$		0			0
$868$	4.00000	−	6.92820i	0.135769	−	0.235159i
$869$	4.00000	−	6.92820i	0.135691	−	0.235023i
$870$		0			0
$871$	−5.00000	+	5.19615i	−0.169419	+	0.176065i
$872$	−6.00000			−0.203186
$873$		0			0
$874$	−18.0000	+	31.1769i	−0.608859	+	1.05457i
$875$	9.00000	+	15.5885i	0.304256	+	0.526986i
$876$		0			0
$877$	−8.50000	−	14.7224i	−0.287025	−	0.497141i	0.686074	−	0.727532i	$-0.259333\pi$
$877$	−8.50000	−	14.7224i	−0.287025	−	0.497141i	−0.973098	+	0.230391i	$0.925999\pi$
$878$	7.00000	+	12.1244i	0.236239	+	0.409177i
$879$		0			0
$880$	1.00000	+	1.73205i	0.0337100	+	0.0583874i
$881$	18.5000	−	32.0429i	0.623281	−	1.07955i	−0.365590	−	0.930776i	$-0.619133\pi$
$881$	18.5000	−	32.0429i	0.623281	−	1.07955i	0.988871	−	0.148778i	$-0.0475340\pi$
$882$		0			0
$883$	16.0000			0.538443			0.269221	−	0.963078i	$-0.413234\pi$
$883$	16.0000			0.538443			0.269221	+	0.963078i	$0.413234\pi$
$884$	−17.5000	+	18.1865i	−0.588589	+	0.611679i
$885$		0			0
$886$	2.00000	−	3.46410i	0.0671913	−	0.116379i
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$		0			0
$889$	40.0000			1.34156
$890$	7.00000	+	12.1244i	0.234641	+	0.406409i
$891$		0			0
$892$	−16.0000			−0.535720
$893$	−18.0000	−	31.1769i	−0.602347	−	1.04330i
$894$		0			0
$895$	−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
$900$		0			0
$901$	−31.5000	−	54.5596i	−1.04942	−	1.81764i
$902$	18.0000			0.599334
$903$		0			0
$904$	−22.5000	−	38.9711i	−0.748339	−	1.29616i
$905$	−7.00000			−0.232688
$906$		0			0
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	−0.948278	−	0.317441i	$-0.897176\pi$
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	0.749051	+	0.662512i	$0.230510\pi$
$908$	7.00000	−	12.1244i	0.232303	−	0.402361i
$909$		0			0
$910$	7.00000	+	1.73205i	0.232048	+	0.0574169i
$911$	40.0000			1.32526			0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000			1.32526			0.662630	+	0.748947i	$0.269440\pi$
$912$		0			0
$913$	−14.0000	+	24.2487i	−0.463332	+	0.802515i
$914$	−6.50000	−	11.2583i	−0.215001	−	0.372392i
$915$		0			0
$916$	−11.0000	−	19.0526i	−0.363450	−	0.629514i
$917$	−8.00000	−	13.8564i	−0.264183	−	0.457579i
$918$		0			0
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	0.597365	−	0.801970i	$-0.296214\pi$
$919$	−12.0000	−	20.7846i	−0.395843	−	0.685621i	−0.993208	+	0.116348i	$0.962881\pi$
$920$	−9.00000	+	15.5885i	−0.296721	+	0.513936i
$921$		0			0
$922$	19.0000			0.625732
$923$	−6.00000	−	20.7846i	−0.197492	−	0.684134i
$924$		0			0
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$	−13.0000	+	22.5167i	−0.427207	+	0.739943i
$927$		0			0
$928$	−5.00000			−0.164133
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	0.554984	−	0.831861i	$-0.312724\pi$
$929$	−13.5000	−	23.3827i	−0.442921	−	0.767161i	−0.997905	+	0.0646999i	$0.979391\pi$
$930$		0			0
$931$	18.0000			0.589926
$932$	−5.00000	−	8.66025i	−0.163780	−	0.283676i
$933$		0			0
$934$	−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
$939$		0			0
$940$	−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	$0.287383\pi$
$942$		0			0
$943$	27.0000	+	46.7654i	0.879241	+	1.52289i
$944$		0			0
$945$		0			0
$946$	6.00000	−	10.3923i	0.195077	−	0.337883i
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	0.152106	+	0.988364i	$0.451394\pi$
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	−0.932002	+	0.362454i	$0.881939\pi$
$948$		0			0
$949$	−38.5000	−	9.52628i	−1.24976	−	0.309236i
$950$	−24.0000			−0.778663
$951$		0			0
$952$	−21.0000	+	36.3731i	−0.680614	+	1.17886i
$953$	3.00000	+	5.19615i	0.0971795	+	0.168320i	0.910516	−	0.413473i	$-0.135685\pi$
$953$	3.00000	+	5.19615i	0.0971795	+	0.168320i	−0.813337	+	0.581793i	$0.802351\pi$
$954$		0			0
$955$	−2.00000	−	3.46410i	−0.0647185	−	0.112096i
$956$	−15.0000	−	25.9808i	−0.485135	−	0.840278i
$957$		0			0
$958$	−12.0000	−	20.7846i	−0.387702	−	0.671520i
$959$	−3.00000	+	5.19615i	−0.0968751	+	0.167793i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−1.00000	−	3.46410i	−0.0322413	−	0.111687i
$963$		0			0
$964$	3.50000	−	6.06218i	0.112727	−	0.195250i
$965$	4.50000	−	7.79423i	0.144860	−	0.250905i
$966$		0			0
$967$	2.00000			0.0643157			0.0321578	−	0.999483i	$-0.489762\pi$
$967$	2.00000			0.0643157			0.0321578	+	0.999483i	$0.489762\pi$
$968$	10.5000	+	18.1865i	0.337483	+	0.584537i
$969$		0			0
$970$	2.00000			0.0642161
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	0.995748	+	0.0921142i	$0.0293625\pi$
$971$	18.0000	+	31.1769i	0.577647	+	1.00051i	−0.418101	+	0.908401i	$0.637304\pi$
$972$		0			0
$973$	−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	−0.471590	−	0.881818i	$-0.656320\pi$
$977$	16.5000	−	28.5788i	0.527882	−	0.914318i	0.999472	−	0.0325001i	$-0.0103469\pi$
$978$		0			0
$979$	−14.0000	−	24.2487i	−0.447442	−	0.774992i
$980$	3.00000			0.0958315
$981$		0			0
$982$	−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	$0.520319\pi$
$984$		0			0
$985$	3.00000	−	5.19615i	0.0955879	−	0.165563i
$986$	3.50000	−	6.06218i	0.111463	−	0.193059i
$987$		0			0
$988$	15.0000	−	15.5885i	0.477214	−	0.495935i
$989$	36.0000			1.14473
$990$		0			0
$991$	1.00000	−	1.73205i	0.0317660	−	0.0550204i	−0.849705	−	0.527258i	$-0.823220\pi$
$991$	1.00000	−	1.73205i	0.0317660	−	0.0550204i	0.881471	+	0.472237i	$0.156554\pi$
$992$	10.0000	+	17.3205i	0.317500	+	0.549927i
$993$		0			0
$994$	−6.00000	−	10.3923i	−0.190308	−	0.329624i
$995$	−7.00000	−	12.1244i	−0.221915	−	0.384368i
$996$		0			0
$997$	17.5000	+	30.3109i	0.554231	+	0.959955i	0.997963	+	0.0637961i	$0.0203207\pi$
$997$	17.5000	+	30.3109i	0.554231	+	0.959955i	−0.443732	+	0.896159i	$0.646346\pi$
$998$	12.0000	−	20.7846i	0.379853	−	0.657925i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.g.b.100.1		2
3.2	odd	2		39.2.e.a.22.1	yes	2
4.3	odd	2		1872.2.t.j.1153.1		2
12.11	even	2		624.2.q.c.529.1		2
13.3	even	3	inner	117.2.g.b.55.1		2
13.4	even	6		1521.2.a.d.1.1		1
13.6	odd	12		1521.2.b.c.1351.2		2
13.7	odd	12		1521.2.b.c.1351.1		2
13.9	even	3		1521.2.a.a.1.1		1
15.2	even	4		975.2.bb.d.724.1		4
15.8	even	4		975.2.bb.d.724.2		4
15.14	odd	2		975.2.i.f.451.1		2
39.2	even	12		507.2.j.d.361.1		4
39.5	even	4		507.2.j.d.316.2		4
39.8	even	4		507.2.j.d.316.1		4
39.11	even	12		507.2.j.d.361.2		4
39.17	odd	6		507.2.a.b.1.1		1
39.20	even	12		507.2.b.b.337.2		2
39.23	odd	6		507.2.e.c.484.1		2
39.29	odd	6		39.2.e.a.16.1	✓	2
39.32	even	12		507.2.b.b.337.1		2
39.35	odd	6		507.2.a.c.1.1		1
39.38	odd	2		507.2.e.c.22.1		2
52.3	odd	6		1872.2.t.j.289.1		2
156.35	even	6		8112.2.a.w.1.1		1
156.95	even	6		8112.2.a.bc.1.1		1
156.107	even	6		624.2.q.c.289.1		2
195.29	odd	6		975.2.i.f.601.1		2
195.68	even	12		975.2.bb.d.874.1		4
195.107	even	12		975.2.bb.d.874.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.e.a.16.1	✓	2	39.29	odd	6
39.2.e.a.22.1	yes	2	3.2	odd	2
117.2.g.b.55.1		2	13.3	even	3	inner
117.2.g.b.100.1		2	1.1	even	1	trivial
507.2.a.b.1.1		1	39.17	odd	6
507.2.a.c.1.1		1	39.35	odd	6
507.2.b.b.337.1		2	39.32	even	12
507.2.b.b.337.2		2	39.20	even	12
507.2.e.c.22.1		2	39.38	odd	2
507.2.e.c.484.1		2	39.23	odd	6
507.2.j.d.316.1		4	39.8	even	4
507.2.j.d.316.2		4	39.5	even	4
507.2.j.d.361.1		4	39.2	even	12
507.2.j.d.361.2		4	39.11	even	12
624.2.q.c.289.1		2	156.107	even	6
624.2.q.c.529.1		2	12.11	even	2
975.2.i.f.451.1		2	15.14	odd	2
975.2.i.f.601.1		2	195.29	odd	6
975.2.bb.d.724.1		4	15.2	even	4
975.2.bb.d.724.2		4	15.8	even	4
975.2.bb.d.874.1		4	195.68	even	12
975.2.bb.d.874.2		4	195.107	even	12
1521.2.a.a.1.1		1	13.9	even	3
1521.2.a.d.1.1		1	13.4	even	6
1521.2.b.c.1351.1		2	13.7	odd	12
1521.2.b.c.1351.2		2	13.6	odd	12
1872.2.t.j.289.1		2	52.3	odd	6
1872.2.t.j.1153.1		2	4.3	odd	2
8112.2.a.w.1.1		1	156.35	even	6
8112.2.a.bc.1.1		1	156.95	even	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +3.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{5} +(-1.00000 - 1.73205i) q^{7} +3.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(-3.50000 - 0.866025i) q^{13} -2.00000 q^{14} +(0.500000 - 0.866025i) q^{16} +(-3.50000 - 6.06218i) q^{17} +(3.00000 + 5.19615i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.00000 + 1.73205i) q^{22} +(-3.00000 + 5.19615i) q^{23} -4.00000 q^{25} +(-2.50000 + 2.59808i) q^{26} +(1.00000 - 1.73205i) q^{28} +(-0.500000 + 0.866025i) q^{29} +4.00000 q^{31} +(2.50000 + 4.33013i) q^{32} -7.00000 q^{34} +(-1.00000 - 1.73205i) q^{35} +(-0.500000 + 0.866025i) q^{37} +6.00000 q^{38} +3.00000 q^{40} +(4.50000 - 7.79423i) q^{41} +(-3.00000 - 5.19615i) q^{43} -2.00000 q^{44} +(3.00000 + 5.19615i) q^{46} -6.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +(-2.00000 + 3.46410i) q^{50} +(-1.00000 - 3.46410i) q^{52} +9.00000 q^{53} +(-1.00000 + 1.73205i) q^{55} +(-3.00000 - 5.19615i) q^{56} +(0.500000 + 0.866025i) q^{58} +(-0.500000 - 0.866025i) q^{61} +(2.00000 - 3.46410i) q^{62} +7.00000 q^{64} +(-3.50000 - 0.866025i) q^{65} +(1.00000 - 1.73205i) q^{67} +(3.50000 - 6.06218i) q^{68} -2.00000 q^{70} +(3.00000 + 5.19615i) q^{71} +11.0000 q^{73} +(0.500000 + 0.866025i) q^{74} +(-3.00000 + 5.19615i) q^{76} +4.00000 q^{77} -4.00000 q^{79} +(0.500000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{82} +14.0000 q^{83} +(-3.50000 - 6.06218i) q^{85} -6.00000 q^{86} +(-3.00000 + 5.19615i) q^{88} +(-7.00000 + 12.1244i) q^{89} +(2.00000 + 6.92820i) q^{91} -6.00000 q^{92} +(-3.00000 + 5.19615i) q^{94} +(3.00000 + 5.19615i) q^{95} +(1.00000 + 1.73205i) q^{97} +(-1.50000 - 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{4} + 2 q^{5} - 2 q^{7} + 6 q^{8}+O(q^{10}) \) 2 * q + q^2 + q^4 + 2 * q^5 - 2 * q^7 + 6 * q^8	\( 2 q + q^{2} + q^{4} + 2 q^{5} - 2 q^{7} + 6 q^{8} + q^{10} - 2 q^{11} - 7 q^{13} - 4 q^{14} + q^{16} - 7 q^{17} + 6 q^{19} + q^{20} + 2 q^{22} - 6 q^{23} - 8 q^{25} - 5 q^{26} + 2 q^{28} - q^{29} + 8 q^{31} + 5 q^{32} - 14 q^{34} - 2 q^{35} - q^{37} + 12 q^{38} + 6 q^{40} + 9 q^{41} - 6 q^{43} - 4 q^{44} + 6 q^{46} - 12 q^{47} + 3 q^{49} - 4 q^{50} - 2 q^{52} + 18 q^{53} - 2 q^{55} - 6 q^{56} + q^{58} - q^{61} + 4 q^{62} + 14 q^{64} - 7 q^{65} + 2 q^{67} + 7 q^{68} - 4 q^{70} + 6 q^{71} + 22 q^{73} + q^{74} - 6 q^{76} + 8 q^{77} - 8 q^{79} + q^{80} - 9 q^{82} + 28 q^{83} - 7 q^{85} - 12 q^{86} - 6 q^{88} - 14 q^{89} + 4 q^{91} - 12 q^{92} - 6 q^{94} + 6 q^{95} + 2 q^{97} - 3 q^{98}+O(q^{100}) \) 2 * q + q^2 + q^4 + 2 * q^5 - 2 * q^7 + 6 * q^8 + q^10 - 2 * q^11 - 7 * q^13 - 4 * q^14 + q^16 - 7 * q^17 + 6 * q^19 + q^20 + 2 * q^22 - 6 * q^23 - 8 * q^25 - 5 * q^26 + 2 * q^28 - q^29 + 8 * q^31 + 5 * q^32 - 14 * q^34 - 2 * q^35 - q^37 + 12 * q^38 + 6 * q^40 + 9 * q^41 - 6 * q^43 - 4 * q^44 + 6 * q^46 - 12 * q^47 + 3 * q^49 - 4 * q^50 - 2 * q^52 + 18 * q^53 - 2 * q^55 - 6 * q^56 + q^58 - q^61 + 4 * q^62 + 14 * q^64 - 7 * q^65 + 2 * q^67 + 7 * q^68 - 4 * q^70 + 6 * q^71 + 22 * q^73 + q^74 - 6 * q^76 + 8 * q^77 - 8 * q^79 + q^80 - 9 * q^82 + 28 * q^83 - 7 * q^85 - 12 * q^86 - 6 * q^88 - 14 * q^89 + 4 * q^91 - 12 * q^92 - 6 * q^94 + 6 * q^95 + 2 * q^97 - 3 * q^98

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