LMFDB - Embedded newform 360.2.k.d.181.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(181,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("360.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.k (of order $2$, degree $1$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 3x^{2} + 4 $ x^4 - 3*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.2
Root			$-1.32288 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	360.181
Dual form			360.2.k.d.181.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32288 + 0.500000i) q^{2} +(1.50000 - 1.32288i) q^{4} -1.00000i q^{5} +2.00000 q^{7} +(-1.32288 + 2.50000i) q^{8} +O(q^{10})$	\(q+(-1.32288 + 0.500000i) q^{2} +(1.50000 - 1.32288i) q^{4} -1.00000i q^{5} +2.00000 q^{7} +(-1.32288 + 2.50000i) q^{8} +(0.500000 + 1.32288i) q^{10} -2.00000i q^{11} +(-2.64575 + 1.00000i) q^{14} +(0.500000 - 3.96863i) q^{16} -5.29150i q^{19} +(-1.32288 - 1.50000i) q^{20} +(1.00000 + 2.64575i) q^{22} +5.29150 q^{23} -1.00000 q^{25} +(3.00000 - 2.64575i) q^{28} -6.00000i q^{29} +4.00000 q^{31} +(1.32288 + 5.50000i) q^{32} -2.00000i q^{35} +10.5830i q^{37} +(2.64575 + 7.00000i) q^{38} +(2.50000 + 1.32288i) q^{40} +10.5830 q^{41} -10.5830i q^{43} +(-2.64575 - 3.00000i) q^{44} +(-7.00000 + 2.64575i) q^{46} +5.29150 q^{47} -3.00000 q^{49} +(1.32288 - 0.500000i) q^{50} +2.00000i q^{53} -2.00000 q^{55} +(-2.64575 + 5.00000i) q^{56} +(3.00000 + 7.93725i) q^{58} -10.0000i q^{59} +10.5830i q^{61} +(-5.29150 + 2.00000i) q^{62} +(-4.50000 - 6.61438i) q^{64} +(1.00000 + 2.64575i) q^{70} -10.5830 q^{71} -14.0000 q^{73} +(-5.29150 - 14.0000i) q^{74} +(-7.00000 - 7.93725i) q^{76} -4.00000i q^{77} +4.00000 q^{79} +(-3.96863 - 0.500000i) q^{80} +(-14.0000 + 5.29150i) q^{82} +12.0000i q^{83} +(5.29150 + 14.0000i) q^{86} +(5.00000 + 2.64575i) q^{88} -10.5830 q^{89} +(7.93725 - 7.00000i) q^{92} +(-7.00000 + 2.64575i) q^{94} -5.29150 q^{95} +2.00000 q^{97} +(3.96863 - 1.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{4} + 8 q^{7}+O(q^{10}) $ 4 * q + 6 * q^4 + 8 * q^7	$ 4 q + 6 q^{4} + 8 q^{7} + 2 q^{10} + 2 q^{16} + 4 q^{22} - 4 q^{25} + 12 q^{28} + 16 q^{31} + 10 q^{40} - 28 q^{46} - 12 q^{49} - 8 q^{55} + 12 q^{58} - 18 q^{64} + 4 q^{70} - 56 q^{73} - 28 q^{76} + 16 q^{79} - 56 q^{82} + 20 q^{88} - 28 q^{94} + 8 q^{97}+O(q^{100}) $ 4 * q + 6 * q^4 + 8 * q^7 + 2 * q^10 + 2 * q^16 + 4 * q^22 - 4 * q^25 + 12 * q^28 + 16 * q^31 + 10 * q^40 - 28 * q^46 - 12 * q^49 - 8 * q^55 + 12 * q^58 - 18 * q^64 + 4 * q^70 - 56 * q^73 - 28 * q^76 + 16 * q^79 - 56 * q^82 + 20 * q^88 - 28 * q^94 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$	−1.32288	+	0.500000i	−0.935414	+	0.353553i
$2$	−1.32288	+	0.500000i	−0.935414	+	0.353553i
$3$		0			0
$3$		0			0
$4$	1.50000	−	1.32288i	0.750000	−	0.661438i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$	−1.32288	+	2.50000i	−0.467707	+	0.883883i
$9$		0			0
$10$	0.500000	+	1.32288i	0.158114	+	0.418330i
$11$		−	2.00000i		−	0.603023i	−0.953463	−	0.301511i	$-0.902509\pi$
$11$		−	2.00000i		−	0.603023i	0.953463	−	0.301511i	$-0.0974911\pi$
$12$		0			0
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	−2.64575	+	1.00000i	−0.707107	+	0.267261i
$15$		0			0
$16$	0.500000	−	3.96863i	0.125000	−	0.992157i
$17$		0			0			−	1.00000i	$-0.5\pi$
$17$		0			0				1.00000i	$0.5\pi$
$18$		0			0
$19$		−	5.29150i		−	1.21395i	−0.794719	−	0.606977i	$-0.792382\pi$
$19$		−	5.29150i		−	1.21395i	0.794719	−	0.606977i	$-0.207618\pi$
$20$	−1.32288	−	1.50000i	−0.295804	−	0.335410i
$21$		0			0
$22$	1.00000	+	2.64575i	0.213201	+	0.564076i
$23$	5.29150			1.10335			0.551677	−	0.834058i	$-0.313988\pi$
$23$	5.29150			1.10335			0.551677	+	0.834058i	$0.313988\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$		0			0
$27$		0			0
$28$	3.00000	−	2.64575i	0.566947	−	0.500000i
$29$		−	6.00000i		−	1.11417i	−0.830455	−	0.557086i	$-0.811919\pi$
$29$		−	6.00000i		−	1.11417i	0.830455	−	0.557086i	$-0.188081\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	1.32288	+	5.50000i	0.233854	+	0.972272i
$33$		0			0
$34$		0			0
$35$		−	2.00000i		−	0.338062i
$36$		0			0
$37$			10.5830i			1.73984i	0.493197	+	0.869918i	$0.335828\pi$
$37$			10.5830i			1.73984i	−0.493197	+	0.869918i	$0.664172\pi$
$38$	2.64575	+	7.00000i	0.429198	+	1.13555i
$39$		0			0
$40$	2.50000	+	1.32288i	0.395285	+	0.209165i
$41$	10.5830			1.65279			0.826394	−	0.563093i	$-0.190389\pi$
$41$	10.5830			1.65279			0.826394	+	0.563093i	$0.190389\pi$
$42$		0			0
$43$		−	10.5830i		−	1.61389i	−0.590624	−	0.806947i	$-0.701119\pi$
$43$		−	10.5830i		−	1.61389i	0.590624	−	0.806947i	$-0.298881\pi$
$44$	−2.64575	−	3.00000i	−0.398862	−	0.452267i
$45$		0			0
$46$	−7.00000	+	2.64575i	−1.03209	+	0.390095i
$47$	5.29150			0.771845			0.385922	−	0.922531i	$-0.373883\pi$
$47$	5.29150			0.771845			0.385922	+	0.922531i	$0.373883\pi$
$48$		0			0
$49$	−3.00000			−0.428571
$50$	1.32288	−	0.500000i	0.187083	−	0.0707107i
$51$		0			0
$52$		0			0
$53$			2.00000i			0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$			2.00000i			0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$	−2.64575	+	5.00000i	−0.353553	+	0.668153i
$57$		0			0
$58$	3.00000	+	7.93725i	0.393919	+	1.04221i
$59$		−	10.0000i		−	1.30189i	−0.759125	−	0.650945i	$-0.774373\pi$
$59$		−	10.0000i		−	1.30189i	0.759125	−	0.650945i	$-0.225627\pi$
$60$		0			0
$61$			10.5830i			1.35501i	0.735516	+	0.677507i	$0.236940\pi$
$61$			10.5830i			1.35501i	−0.735516	+	0.677507i	$0.763060\pi$
$62$	−5.29150	+	2.00000i	−0.672022	+	0.254000i
$63$		0			0
$64$	−4.50000	−	6.61438i	−0.562500	−	0.826797i
$65$		0			0
$66$		0			0
$67$		0			0		1.00000			$0$
$67$		0			0		−1.00000			$\pi$
$68$		0			0
$69$		0			0
$70$	1.00000	+	2.64575i	0.119523	+	0.316228i
$71$	−10.5830			−1.25597			−0.627986	−	0.778225i	$-0.716120\pi$
$71$	−10.5830			−1.25597			−0.627986	+	0.778225i	$0.716120\pi$
$72$		0			0
$73$	−14.0000			−1.63858			−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000			−1.63858			−0.819288	+	0.573382i	$0.805631\pi$
$74$	−5.29150	−	14.0000i	−0.615125	−	1.62747i
$75$		0			0
$76$	−7.00000	−	7.93725i	−0.802955	−	0.910465i
$77$		−	4.00000i		−	0.455842i
$78$		0			0
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$	−3.96863	−	0.500000i	−0.443706	−	0.0559017i
$81$		0			0
$82$	−14.0000	+	5.29150i	−1.54604	+	0.584349i
$83$			12.0000i			1.31717i	0.752506	+	0.658586i	$0.228845\pi$
$83$			12.0000i			1.31717i	−0.752506	+	0.658586i	$0.771155\pi$
$84$		0			0
$85$		0			0
$86$	5.29150	+	14.0000i	0.570597	+	1.50966i
$87$		0			0
$88$	5.00000	+	2.64575i	0.533002	+	0.282038i
$89$	−10.5830			−1.12180			−0.560898	−	0.827885i	$-0.689544\pi$
$89$	−10.5830			−1.12180			−0.560898	+	0.827885i	$0.689544\pi$
$90$		0			0
$91$		0			0
$92$	7.93725	−	7.00000i	0.827516	−	0.729800i
$93$		0			0
$94$	−7.00000	+	2.64575i	−0.721995	+	0.272888i
$95$	−5.29150			−0.542897
$96$		0			0
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$	3.96863	−	1.50000i	0.400892	−	0.151523i
$99$		0			0
$100$	−1.50000	+	1.32288i	−0.150000	+	0.132288i
$101$			14.0000i			1.39305i	0.717532	+	0.696526i	$0.245272\pi$
$101$			14.0000i			1.39305i	−0.717532	+	0.696526i	$0.754728\pi$
$102$		0			0
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$		0			0
$105$		0			0
$106$	−1.00000	−	2.64575i	−0.0971286	−	0.256978i
$107$			4.00000i			0.386695i	0.981130	+	0.193347i	$0.0619344\pi$
$107$			4.00000i			0.386695i	−0.981130	+	0.193347i	$0.938066\pi$
$108$		0			0
$109$			10.5830i			1.01367i	0.862044	+	0.506834i	$0.169184\pi$
$109$			10.5830i			1.01367i	−0.862044	+	0.506834i	$0.830816\pi$
$110$	2.64575	−	1.00000i	0.252262	−	0.0953463i
$111$		0			0
$112$	1.00000	−	7.93725i	0.0944911	−	0.750000i
$113$		0			0			−	1.00000i	$-0.5\pi$
$113$		0			0				1.00000i	$0.5\pi$
$114$		0			0
$115$		−	5.29150i		−	0.493435i
$116$	−7.93725	−	9.00000i	−0.736956	−	0.835629i
$117$		0			0
$118$	5.00000	+	13.2288i	0.460287	+	1.21781i
$119$		0			0
$120$		0			0
$121$	7.00000			0.636364
$122$	−5.29150	−	14.0000i	−0.479070	−	1.26750i
$123$		0			0
$124$	6.00000	−	5.29150i	0.538816	−	0.475191i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	6.00000			0.532414			0.266207	−	0.963916i	$-0.414230\pi$
$127$	6.00000			0.532414			0.266207	+	0.963916i	$0.414230\pi$
$128$	9.26013	+	6.50000i	0.818488	+	0.574524i
$129$		0			0
$130$		0			0
$131$			6.00000i			0.524222i	0.965038	+	0.262111i	$0.0844187\pi$
$131$			6.00000i			0.524222i	−0.965038	+	0.262111i	$0.915581\pi$
$132$		0			0
$133$		−	10.5830i		−	0.917663i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−21.1660			−1.80833			−0.904167	−	0.427179i	$-0.859507\pi$
$137$	−21.1660			−1.80833			−0.904167	+	0.427179i	$0.859507\pi$
$138$		0			0
$139$			5.29150i			0.448819i	0.974495	+	0.224410i	$0.0720454\pi$
$139$			5.29150i			0.448819i	−0.974495	+	0.224410i	$0.927955\pi$
$140$	−2.64575	−	3.00000i	−0.223607	−	0.253546i
$141$		0			0
$142$	14.0000	−	5.29150i	1.17485	−	0.444053i
$143$		0			0
$144$		0			0
$145$	−6.00000			−0.498273
$146$	18.5203	−	7.00000i	1.53275	−	0.579324i
$147$		0			0
$148$	14.0000	+	15.8745i	1.15079	+	1.30488i
$149$		−	6.00000i		−	0.491539i	−0.969328	−	0.245770i	$-0.920959\pi$
$149$		−	6.00000i		−	0.491539i	0.969328	−	0.245770i	$-0.0790407\pi$
$150$		0			0
$151$	16.0000			1.30206			0.651031	−	0.759051i	$-0.274337\pi$
$151$	16.0000			1.30206			0.651031	+	0.759051i	$0.274337\pi$
$152$	13.2288	+	7.00000i	1.07299	+	0.567775i
$153$		0			0
$154$	2.00000	+	5.29150i	0.161165	+	0.426401i
$155$		−	4.00000i		−	0.321288i
$156$		0			0
$157$		−	10.5830i		−	0.844616i	−0.906452	−	0.422308i	$-0.861220\pi$
$157$		−	10.5830i		−	0.844616i	0.906452	−	0.422308i	$-0.138780\pi$
$158$	−5.29150	+	2.00000i	−0.420969	+	0.159111i
$159$		0			0
$160$	5.50000	−	1.32288i	0.434813	−	0.104583i
$161$	10.5830			0.834058
$162$		0			0
$163$		−	10.5830i		−	0.828925i	−0.910066	−	0.414462i	$-0.863970\pi$
$163$		−	10.5830i		−	0.828925i	0.910066	−	0.414462i	$-0.136030\pi$
$164$	15.8745	−	14.0000i	1.23959	−	1.09322i
$165$		0			0
$166$	−6.00000	−	15.8745i	−0.465690	−	1.23210i
$167$	15.8745			1.22841			0.614203	−	0.789148i	$-0.289478\pi$
$167$	15.8745			1.22841			0.614203	+	0.789148i	$0.289478\pi$
$168$		0			0
$169$	13.0000			1.00000
$170$		0			0
$171$		0			0
$172$	−14.0000	−	15.8745i	−1.06749	−	1.21042i
$173$			14.0000i			1.06440i	0.846619	+	0.532200i	$0.178635\pi$
$173$			14.0000i			1.06440i	−0.846619	+	0.532200i	$0.821365\pi$
$174$		0			0
$175$	−2.00000			−0.151186
$176$	−7.93725	−	1.00000i	−0.598293	−	0.0753778i
$177$		0			0
$178$	14.0000	−	5.29150i	1.04934	−	0.396615i
$179$			18.0000i			1.34538i	0.739923	+	0.672692i	$0.234862\pi$
$179$			18.0000i			1.34538i	−0.739923	+	0.672692i	$0.765138\pi$
$180$		0			0
$181$			10.5830i			0.786629i	0.919404	+	0.393314i	$0.128672\pi$
$181$			10.5830i			0.786629i	−0.919404	+	0.393314i	$0.871328\pi$
$182$		0			0
$183$		0			0
$184$	−7.00000	+	13.2288i	−0.516047	+	0.975237i
$185$	10.5830			0.778078
$186$		0			0
$187$		0			0
$188$	7.93725	−	7.00000i	0.578884	−	0.510527i
$189$		0			0
$190$	7.00000	−	2.64575i	0.507833	−	0.191943i
$191$	−21.1660			−1.53152			−0.765759	−	0.643127i	$-0.777637\pi$
$191$	−21.1660			−1.53152			−0.765759	+	0.643127i	$0.777637\pi$
$192$		0			0
$193$	−2.00000			−0.143963			−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000			−0.143963			−0.0719816	+	0.997406i	$0.522932\pi$
$194$	−2.64575	+	1.00000i	−0.189954	+	0.0717958i
$195$		0			0
$196$	−4.50000	+	3.96863i	−0.321429	+	0.283473i
$197$			2.00000i			0.142494i	0.997459	+	0.0712470i	$0.0226979\pi$
$197$			2.00000i			0.142494i	−0.997459	+	0.0712470i	$0.977302\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	1.32288	−	2.50000i	0.0935414	−	0.176777i
$201$		0			0
$202$	−7.00000	−	18.5203i	−0.492518	−	1.30308i
$203$		−	12.0000i		−	0.842235i
$204$		0			0
$205$		−	10.5830i		−	0.739149i
$206$	18.5203	−	7.00000i	1.29037	−	0.487713i
$207$		0			0
$208$		0			0
$209$	−10.5830			−0.732042
$210$		0			0
$211$			15.8745i			1.09285i	0.837509	+	0.546423i	$0.184011\pi$
$211$			15.8745i			1.09285i	−0.837509	+	0.546423i	$0.815989\pi$
$212$	2.64575	+	3.00000i	0.181711	+	0.206041i
$213$		0			0
$214$	−2.00000	−	5.29150i	−0.136717	−	0.361720i
$215$	−10.5830			−0.721755
$216$		0			0
$217$	8.00000			0.543075
$218$	−5.29150	−	14.0000i	−0.358386	−	0.948200i
$219$		0			0
$220$	−3.00000	+	2.64575i	−0.202260	+	0.178377i
$221$		0			0
$222$		0			0
$223$	−2.00000			−0.133930			−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000			−0.133930			−0.0669650	+	0.997755i	$0.521332\pi$
$224$	2.64575	+	11.0000i	0.176777	+	0.734968i
$225$		0			0
$226$		0			0
$227$			24.0000i			1.59294i	0.604681	+	0.796468i	$0.293301\pi$
$227$			24.0000i			1.59294i	−0.604681	+	0.796468i	$0.706699\pi$
$228$		0			0
$229$		−	10.5830i		−	0.699345i	−0.936872	−	0.349672i	$-0.886293\pi$
$229$		−	10.5830i		−	0.699345i	0.936872	−	0.349672i	$-0.113707\pi$
$230$	2.64575	+	7.00000i	0.174456	+	0.461566i
$231$		0			0
$232$	15.0000	+	7.93725i	0.984798	+	0.521106i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$		−	5.29150i		−	0.345180i
$236$	−13.2288	−	15.0000i	−0.861119	−	0.976417i
$237$		0			0
$238$		0			0
$239$	10.5830			0.684558			0.342279	−	0.939598i	$-0.388801\pi$
$239$	10.5830			0.684558			0.342279	+	0.939598i	$0.388801\pi$
$240$		0			0
$241$	18.0000			1.15948			0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000			1.15948			0.579741	+	0.814801i	$0.303154\pi$
$242$	−9.26013	+	3.50000i	−0.595264	+	0.224989i
$243$		0			0
$244$	14.0000	+	15.8745i	0.896258	+	1.01626i
$245$			3.00000i			0.191663i
$246$		0			0
$247$		0			0
$248$	−5.29150	+	10.0000i	−0.336011	+	0.635001i
$249$		0			0
$250$	−0.500000	−	1.32288i	−0.0316228	−	0.0836660i
$251$		−	30.0000i		−	1.89358i	−0.321847	−	0.946792i	$-0.604304\pi$
$251$		−	30.0000i		−	1.89358i	0.321847	−	0.946792i	$-0.395696\pi$
$252$		0			0
$253$		−	10.5830i		−	0.665348i
$254$	−7.93725	+	3.00000i	−0.498028	+	0.188237i
$255$		0			0
$256$	−15.5000	−	3.96863i	−0.968750	−	0.248039i
$257$	−21.1660			−1.32030			−0.660150	−	0.751134i	$-0.729507\pi$
$257$	−21.1660			−1.32030			−0.660150	+	0.751134i	$0.729507\pi$
$258$		0			0
$259$			21.1660i			1.31519i
$260$		0			0
$261$		0			0
$262$	−3.00000	−	7.93725i	−0.185341	−	0.490365i
$263$	−15.8745			−0.978864			−0.489432	−	0.872041i	$-0.662796\pi$
$263$	−15.8745			−0.978864			−0.489432	+	0.872041i	$0.662796\pi$
$264$		0			0
$265$	2.00000			0.122859
$266$	5.29150	+	14.0000i	0.324443	+	0.858395i
$267$		0			0
$268$		0			0
$269$			10.0000i			0.609711i	0.952399	+	0.304855i	$0.0986081\pi$
$269$			10.0000i			0.609711i	−0.952399	+	0.304855i	$0.901392\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$		0			0
$273$		0			0
$274$	28.0000	−	10.5830i	1.69154	−	0.639343i
$275$			2.00000i			0.120605i
$276$		0			0
$277$		−	10.5830i		−	0.635871i	−0.948112	−	0.317936i	$-0.897010\pi$
$277$		−	10.5830i		−	0.635871i	0.948112	−	0.317936i	$-0.102990\pi$
$278$	−2.64575	−	7.00000i	−0.158682	−	0.419832i
$279$		0			0
$280$	5.00000	+	2.64575i	0.298807	+	0.158114i
$281$	21.1660			1.26266			0.631329	−	0.775515i	$-0.282510\pi$
$281$	21.1660			1.26266			0.631329	+	0.775515i	$0.282510\pi$
$282$		0			0
$283$			21.1660i			1.25819i	0.777329	+	0.629094i	$0.216574\pi$
$283$			21.1660i			1.25819i	−0.777329	+	0.629094i	$0.783426\pi$
$284$	−15.8745	+	14.0000i	−0.941979	+	0.830747i
$285$		0			0
$286$		0			0
$287$	21.1660			1.24939
$288$		0			0
$289$	−17.0000			−1.00000
$290$	7.93725	−	3.00000i	0.466092	−	0.176166i
$291$		0			0
$292$	−21.0000	+	18.5203i	−1.22893	+	1.08382i
$293$		−	26.0000i		−	1.51894i	−0.650545	−	0.759468i	$-0.725459\pi$
$293$		−	26.0000i		−	1.51894i	0.650545	−	0.759468i	$-0.274541\pi$
$294$		0			0
$295$	−10.0000			−0.582223
$296$	−26.4575	−	14.0000i	−1.53781	−	0.813733i
$297$		0			0
$298$	3.00000	+	7.93725i	0.173785	+	0.459793i
$299$		0			0
$300$		0			0
$301$		−	21.1660i		−	1.21999i
$302$	−21.1660	+	8.00000i	−1.21797	+	0.460348i
$303$		0			0
$304$	−21.0000	−	2.64575i	−1.20443	−	0.151744i
$305$	10.5830			0.605981
$306$		0			0
$307$			10.5830i			0.604004i	0.953307	+	0.302002i	$0.0976549\pi$
$307$			10.5830i			0.604004i	−0.953307	+	0.302002i	$0.902345\pi$
$308$	−5.29150	−	6.00000i	−0.301511	−	0.341882i
$309$		0			0
$310$	2.00000	+	5.29150i	0.113592	+	0.300537i
$311$	−10.5830			−0.600107			−0.300054	−	0.953922i	$-0.597005\pi$
$311$	−10.5830			−0.600107			−0.300054	+	0.953922i	$0.597005\pi$
$312$		0			0
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	5.29150	+	14.0000i	0.298617	+	0.790066i
$315$		0			0
$316$	6.00000	−	5.29150i	0.337526	−	0.297670i
$317$		−	18.0000i		−	1.01098i	−0.862832	−	0.505490i	$-0.831312\pi$
$317$		−	18.0000i		−	1.01098i	0.862832	−	0.505490i	$-0.168688\pi$
$318$		0			0
$319$	−12.0000			−0.671871
$320$	−6.61438	+	4.50000i	−0.369755	+	0.251558i
$321$		0			0
$322$	−14.0000	+	5.29150i	−0.780189	+	0.294884i
$323$		0			0
$324$		0			0
$325$		0			0
$326$	5.29150	+	14.0000i	0.293069	+	0.775388i
$327$		0			0
$328$	−14.0000	+	26.4575i	−0.773021	+	1.46087i
$329$	10.5830			0.583460
$330$		0			0
$331$			26.4575i			1.45424i	0.686512	+	0.727118i	$0.259141\pi$
$331$			26.4575i			1.45424i	−0.686512	+	0.727118i	$0.740859\pi$
$332$	15.8745	+	18.0000i	0.871227	+	0.987878i
$333$		0			0
$334$	−21.0000	+	7.93725i	−1.14907	+	0.434307i
$335$		0			0
$336$		0			0
$337$	6.00000			0.326841			0.163420	−	0.986557i	$-0.447747\pi$
$337$	6.00000			0.326841			0.163420	+	0.986557i	$0.447747\pi$
$338$	−17.1974	+	6.50000i	−0.935414	+	0.353553i
$339$		0			0
$340$		0			0
$341$		−	8.00000i		−	0.433224i
$342$		0			0
$343$	−20.0000			−1.07990
$344$	26.4575	+	14.0000i	1.42649	+	0.754829i
$345$		0			0
$346$	−7.00000	−	18.5203i	−0.376322	−	0.995655i
$347$		−	32.0000i		−	1.71785i	−0.512101	−	0.858925i	$-0.671133\pi$
$347$		−	32.0000i		−	1.71785i	0.512101	−	0.858925i	$-0.328867\pi$
$348$		0			0
$349$		−	10.5830i		−	0.566495i	−0.959047	−	0.283248i	$-0.908588\pi$
$349$		−	10.5830i		−	0.566495i	0.959047	−	0.283248i	$-0.0914118\pi$
$350$	2.64575	−	1.00000i	0.141421	−	0.0534522i
$351$		0			0
$352$	11.0000	−	2.64575i	0.586302	−	0.141019i
$353$		0			0			−	1.00000i	$-0.5\pi$
$353$		0			0				1.00000i	$0.5\pi$
$354$		0			0
$355$			10.5830i			0.561688i
$356$	−15.8745	+	14.0000i	−0.841347	+	0.741999i
$357$		0			0
$358$	−9.00000	−	23.8118i	−0.475665	−	1.25849i
$359$	31.7490			1.67565			0.837824	−	0.545940i	$-0.183827\pi$
$359$	31.7490			1.67565			0.837824	+	0.545940i	$0.183827\pi$
$360$		0			0
$361$	−9.00000			−0.473684
$362$	−5.29150	−	14.0000i	−0.278115	−	0.735824i
$363$		0			0
$364$		0			0
$365$			14.0000i			0.732793i
$366$		0			0
$367$	−18.0000			−0.939592			−0.469796	−	0.882775i	$-0.655673\pi$
$367$	−18.0000			−0.939592			−0.469796	+	0.882775i	$0.655673\pi$
$368$	2.64575	−	21.0000i	0.137919	−	1.09470i
$369$		0			0
$370$	−14.0000	+	5.29150i	−0.727825	+	0.275092i
$371$			4.00000i			0.207670i
$372$		0			0
$373$		−	10.5830i		−	0.547967i	−0.961734	−	0.273984i	$-0.911659\pi$
$373$		−	10.5830i		−	0.547967i	0.961734	−	0.273984i	$-0.0883414\pi$
$374$		0			0
$375$		0			0
$376$	−7.00000	+	13.2288i	−0.360997	+	0.682221i
$377$		0			0
$378$		0			0
$379$		−	15.8745i		−	0.815419i	−0.913112	−	0.407709i	$-0.866328\pi$
$379$		−	15.8745i		−	0.815419i	0.913112	−	0.407709i	$-0.133672\pi$
$380$	−7.93725	+	7.00000i	−0.407173	+	0.359092i
$381$		0			0
$382$	28.0000	−	10.5830i	1.43260	−	0.541474i
$383$	15.8745			0.811149			0.405575	−	0.914062i	$-0.367071\pi$
$383$	15.8745			0.811149			0.405575	+	0.914062i	$0.367071\pi$
$384$		0			0
$385$	−4.00000			−0.203859
$386$	2.64575	−	1.00000i	0.134665	−	0.0508987i
$387$		0			0
$388$	3.00000	−	2.64575i	0.152302	−	0.134318i
$389$			10.0000i			0.507020i	0.967333	+	0.253510i	$0.0815851\pi$
$389$			10.0000i			0.507020i	−0.967333	+	0.253510i	$0.918415\pi$
$390$		0			0
$391$		0			0
$392$	3.96863	−	7.50000i	0.200446	−	0.378807i
$393$		0			0
$394$	−1.00000	−	2.64575i	−0.0503793	−	0.133291i
$395$		−	4.00000i		−	0.201262i
$396$		0			0
$397$			21.1660i			1.06229i	0.847280	+	0.531146i	$0.178238\pi$
$397$			21.1660i			1.06229i	−0.847280	+	0.531146i	$0.821762\pi$
$398$		0			0
$399$		0			0
$400$	−0.500000	+	3.96863i	−0.0250000	+	0.198431i
$401$	31.7490			1.58547			0.792735	−	0.609566i	$-0.208656\pi$
$401$	31.7490			1.58547			0.792735	+	0.609566i	$0.208656\pi$
$402$		0			0
$403$		0			0
$404$	18.5203	+	21.0000i	0.921417	+	1.04479i
$405$		0			0
$406$	6.00000	+	15.8745i	0.297775	+	0.787839i
$407$	21.1660			1.04916
$408$		0			0
$409$	18.0000			0.890043			0.445021	−	0.895520i	$-0.353196\pi$
$409$	18.0000			0.890043			0.445021	+	0.895520i	$0.353196\pi$
$410$	5.29150	+	14.0000i	0.261329	+	0.691411i
$411$		0			0
$412$	−21.0000	+	18.5203i	−1.03460	+	0.912428i
$413$		−	20.0000i		−	0.984136i
$414$		0			0
$415$	12.0000			0.589057
$416$		0			0
$417$		0			0
$418$	14.0000	−	5.29150i	0.684762	−	0.258816i
$419$			14.0000i			0.683945i	0.939710	+	0.341972i	$0.111095\pi$
$419$			14.0000i			0.683945i	−0.939710	+	0.341972i	$0.888905\pi$
$420$		0			0
$421$		−	10.5830i		−	0.515784i	−0.966174	−	0.257892i	$-0.916972\pi$
$421$		−	10.5830i		−	0.515784i	0.966174	−	0.257892i	$-0.0830279\pi$
$422$	−7.93725	−	21.0000i	−0.386379	−	1.02226i
$423$		0			0
$424$	−5.00000	−	2.64575i	−0.242821	−	0.128489i
$425$		0			0
$426$		0			0
$427$			21.1660i			1.02430i
$428$	5.29150	+	6.00000i	0.255774	+	0.290021i
$429$		0			0
$430$	14.0000	−	5.29150i	0.675140	−	0.255179i
$431$	−31.7490			−1.52930			−0.764648	−	0.644448i	$-0.777087\pi$
$431$	−31.7490			−1.52930			−0.764648	+	0.644448i	$0.777087\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	−10.5830	+	4.00000i	−0.508001	+	0.192006i
$435$		0			0
$436$	14.0000	+	15.8745i	0.670478	+	0.760251i
$437$		−	28.0000i		−	1.33942i
$438$		0			0
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$	2.64575	−	5.00000i	0.126131	−	0.238366i
$441$		0			0
$442$		0			0
$443$		−	32.0000i		−	1.52037i	−0.649709	−	0.760183i	$-0.725109\pi$
$443$		−	32.0000i		−	1.52037i	0.649709	−	0.760183i	$-0.274891\pi$
$444$		0			0
$445$			10.5830i			0.501683i
$446$	2.64575	−	1.00000i	0.125280	−	0.0473514i
$447$		0			0
$448$	−9.00000	−	13.2288i	−0.425210	−	0.625000i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$		0			0
$451$		−	21.1660i		−	0.996669i
$452$		0			0
$453$		0			0
$454$	−12.0000	−	31.7490i	−0.563188	−	1.49006i
$455$		0			0
$456$		0			0
$457$	−18.0000			−0.842004			−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000			−0.842004			−0.421002	+	0.907060i	$0.638322\pi$
$458$	5.29150	+	14.0000i	0.247256	+	0.654177i
$459$		0			0
$460$	−7.00000	−	7.93725i	−0.326377	−	0.370076i
$461$			14.0000i			0.652045i	0.945362	+	0.326023i	$0.105709\pi$
$461$			14.0000i			0.652045i	−0.945362	+	0.326023i	$0.894291\pi$
$462$		0			0
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$	−23.8118	−	3.00000i	−1.10543	−	0.139272i
$465$		0			0
$466$		0			0
$467$			28.0000i			1.29569i	0.761774	+	0.647843i	$0.224329\pi$
$467$			28.0000i			1.29569i	−0.761774	+	0.647843i	$0.775671\pi$
$468$		0			0
$469$		0			0
$470$	2.64575	+	7.00000i	0.122039	+	0.322886i
$471$		0			0
$472$	25.0000	+	13.2288i	1.15072	+	0.608903i
$473$	−21.1660			−0.973214
$474$		0			0
$475$			5.29150i			0.242791i
$476$		0			0
$477$		0			0
$478$	−14.0000	+	5.29150i	−0.640345	+	0.242028i
$479$	10.5830			0.483550			0.241775	−	0.970332i	$-0.422270\pi$
$479$	10.5830			0.483550			0.241775	+	0.970332i	$0.422270\pi$
$480$		0			0
$481$		0			0
$482$	−23.8118	+	9.00000i	−1.08460	+	0.409939i
$483$		0			0
$484$	10.5000	−	9.26013i	0.477273	−	0.420915i
$485$		−	2.00000i		−	0.0908153i
$486$		0			0
$487$	30.0000			1.35943			0.679715	−	0.733476i	$-0.262104\pi$
$487$	30.0000			1.35943			0.679715	+	0.733476i	$0.262104\pi$
$488$	−26.4575	−	14.0000i	−1.19768	−	0.633750i
$489$		0			0
$490$	−1.50000	−	3.96863i	−0.0677631	−	0.179284i
$491$		−	22.0000i		−	0.992846i	−0.868081	−	0.496423i	$-0.834646\pi$
$491$		−	22.0000i		−	0.992846i	0.868081	−	0.496423i	$-0.165354\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	2.00000	−	15.8745i	0.0898027	−	0.712786i
$497$	−21.1660			−0.949425
$498$		0			0
$499$		−	5.29150i		−	0.236880i	−0.992961	−	0.118440i	$-0.962211\pi$
$499$		−	5.29150i		−	0.236880i	0.992961	−	0.118440i	$-0.0377894\pi$
$500$	1.32288	+	1.50000i	0.0591608	+	0.0670820i
$501$		0			0
$502$	15.0000	+	39.6863i	0.669483	+	1.77128i
$503$	15.8745			0.707809			0.353905	−	0.935282i	$-0.384854\pi$
$503$	15.8745			0.707809			0.353905	+	0.935282i	$0.384854\pi$
$504$		0			0
$505$	14.0000			0.622992
$506$	5.29150	+	14.0000i	0.235236	+	0.622376i
$507$		0			0
$508$	9.00000	−	7.93725i	0.399310	−	0.352159i
$509$		−	6.00000i		−	0.265945i	−0.991120	−	0.132973i	$-0.957548\pi$
$509$		−	6.00000i		−	0.265945i	0.991120	−	0.132973i	$-0.0424523\pi$
$510$		0			0
$511$	−28.0000			−1.23865
$512$	22.4889	−	2.50000i	0.993878	−	0.110485i
$513$		0			0
$514$	28.0000	−	10.5830i	1.23503	−	0.466796i
$515$			14.0000i			0.616914i
$516$		0			0
$517$		−	10.5830i		−	0.465440i
$518$	−10.5830	−	28.0000i	−0.464991	−	1.23025i
$519$		0			0
$520$		0			0
$521$		0			0			−	1.00000i	$-0.5\pi$
$521$		0			0				1.00000i	$0.5\pi$
$522$		0			0
$523$		−	21.1660i		−	0.925525i	−0.886482	−	0.462763i	$-0.846858\pi$
$523$		−	21.1660i		−	0.925525i	0.886482	−	0.462763i	$-0.153142\pi$
$524$	7.93725	+	9.00000i	0.346741	+	0.393167i
$525$		0			0
$526$	21.0000	−	7.93725i	0.915644	−	0.346081i
$527$		0			0
$528$		0			0
$529$	5.00000			0.217391
$530$	−2.64575	+	1.00000i	−0.114924	+	0.0434372i
$531$		0			0
$532$	−14.0000	−	15.8745i	−0.606977	−	0.688247i
$533$		0			0
$534$		0			0
$535$	4.00000			0.172935
$536$		0			0
$537$		0			0
$538$	−5.00000	−	13.2288i	−0.215565	−	0.570332i
$539$			6.00000i			0.258438i
$540$		0			0
$541$			10.5830i			0.454999i	0.973778	+	0.227499i	$0.0730550\pi$
$541$			10.5830i			0.454999i	−0.973778	+	0.227499i	$0.926945\pi$
$542$	10.5830	−	4.00000i	0.454579	−	0.171815i
$543$		0			0
$544$		0			0
$545$	10.5830			0.453326
$546$		0			0
$547$		−	10.5830i		−	0.452497i	−0.974070	−	0.226248i	$-0.927354\pi$
$547$		−	10.5830i		−	0.452497i	0.974070	−	0.226248i	$-0.0726461\pi$
$548$	−31.7490	+	28.0000i	−1.35625	+	1.19610i
$549$		0			0
$550$	−1.00000	−	2.64575i	−0.0426401	−	0.112815i
$551$	−31.7490			−1.35255
$552$		0			0
$553$	8.00000			0.340195
$554$	5.29150	+	14.0000i	0.224814	+	0.594803i
$555$		0			0
$556$	7.00000	+	7.93725i	0.296866	+	0.336615i
$557$			30.0000i			1.27114i	0.772043	+	0.635570i	$0.219235\pi$
$557$			30.0000i			1.27114i	−0.772043	+	0.635570i	$0.780765\pi$
$558$		0			0
$559$		0			0
$560$	−7.93725	−	1.00000i	−0.335410	−	0.0422577i
$561$		0			0
$562$	−28.0000	+	10.5830i	−1.18111	+	0.446417i
$563$			24.0000i			1.01148i	0.862686	+	0.505740i	$0.168780\pi$
$563$			24.0000i			1.01148i	−0.862686	+	0.505740i	$0.831220\pi$
$564$		0			0
$565$		0			0
$566$	−10.5830	−	28.0000i	−0.444837	−	1.17693i
$567$		0			0
$568$	14.0000	−	26.4575i	0.587427	−	1.11013i
$569$	−10.5830			−0.443663			−0.221831	−	0.975085i	$-0.571203\pi$
$569$	−10.5830			−0.443663			−0.221831	+	0.975085i	$0.571203\pi$
$570$		0			0
$571$		−	37.0405i		−	1.55010i	−0.631901	−	0.775049i	$-0.717725\pi$
$571$		−	37.0405i		−	1.55010i	0.631901	−	0.775049i	$-0.282275\pi$
$572$		0			0
$573$		0			0
$574$	−28.0000	+	10.5830i	−1.16870	+	0.441726i
$575$	−5.29150			−0.220671
$576$		0			0
$577$	10.0000			0.416305			0.208153	−	0.978096i	$-0.433255\pi$
$577$	10.0000			0.416305			0.208153	+	0.978096i	$0.433255\pi$
$578$	22.4889	−	8.50000i	0.935414	−	0.353553i
$579$		0			0
$580$	−9.00000	+	7.93725i	−0.373705	+	0.329577i
$581$			24.0000i			0.995688i
$582$		0			0
$583$	4.00000			0.165663
$584$	18.5203	−	35.0000i	0.766374	−	1.44831i
$585$		0			0
$586$	13.0000	+	34.3948i	0.537025	+	1.42083i
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$		0			0
$589$		−	21.1660i		−	0.872130i
$590$	13.2288	−	5.00000i	0.544619	−	0.205847i
$591$		0			0
$592$	42.0000	+	5.29150i	1.72619	+	0.217479i
$593$	−21.1660			−0.869184			−0.434592	−	0.900627i	$-0.643107\pi$
$593$	−21.1660			−0.869184			−0.434592	+	0.900627i	$0.643107\pi$
$594$		0			0
$595$		0			0
$596$	−7.93725	−	9.00000i	−0.325123	−	0.368654i
$597$		0			0
$598$		0			0
$599$	−31.7490			−1.29723			−0.648615	−	0.761117i	$-0.724651\pi$
$599$	−31.7490			−1.29723			−0.648615	+	0.761117i	$0.724651\pi$
$600$		0			0
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$	10.5830	+	28.0000i	0.431331	+	1.14119i
$603$		0			0
$604$	24.0000	−	21.1660i	0.976546	−	0.861233i
$605$		−	7.00000i		−	0.284590i
$606$		0			0
$607$	−22.0000			−0.892952			−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000			−0.892952			−0.446476	+	0.894795i	$0.647321\pi$
$608$	29.1033	−	7.00000i	1.18029	−	0.283887i
$609$		0			0
$610$	−14.0000	+	5.29150i	−0.566843	+	0.214247i
$611$		0			0
$612$		0			0
$613$			42.3320i			1.70977i	0.518814	+	0.854887i	$0.326374\pi$
$613$			42.3320i			1.70977i	−0.518814	+	0.854887i	$0.673626\pi$
$614$	−5.29150	−	14.0000i	−0.213548	−	0.564994i
$615$		0			0
$616$	10.0000	+	5.29150i	0.402911	+	0.213201i
$617$		0			0			−	1.00000i	$-0.5\pi$
$617$		0			0				1.00000i	$0.5\pi$
$618$		0			0
$619$			5.29150i			0.212683i	0.994330	+	0.106342i	$0.0339137\pi$
$619$			5.29150i			0.212683i	−0.994330	+	0.106342i	$0.966086\pi$
$620$	−5.29150	−	6.00000i	−0.212512	−	0.240966i
$621$		0			0
$622$	14.0000	−	5.29150i	0.561349	−	0.212170i
$623$	−21.1660			−0.847998
$624$		0			0
$625$	1.00000			0.0400000
$626$	7.93725	−	3.00000i	0.317236	−	0.119904i
$627$		0			0
$628$	−14.0000	−	15.8745i	−0.558661	−	0.633462i
$629$		0			0
$630$		0			0
$631$	36.0000			1.43314			0.716569	−	0.697517i	$-0.245712\pi$
$631$	36.0000			1.43314			0.716569	+	0.697517i	$0.245712\pi$
$632$	−5.29150	+	10.0000i	−0.210485	+	0.397779i
$633$		0			0
$634$	9.00000	+	23.8118i	0.357436	+	0.945686i
$635$		−	6.00000i		−	0.238103i
$636$		0			0
$637$		0			0
$638$	15.8745	−	6.00000i	0.628478	−	0.237542i
$639$		0			0
$640$	6.50000	−	9.26013i	0.256935	−	0.366039i
$641$	21.1660			0.836007			0.418004	−	0.908445i	$-0.362730\pi$
$641$	21.1660			0.836007			0.418004	+	0.908445i	$0.362730\pi$
$642$		0			0
$643$			31.7490i			1.25206i	0.779799	+	0.626029i	$0.215321\pi$
$643$			31.7490i			1.25206i	−0.779799	+	0.626029i	$0.784679\pi$
$644$	15.8745	−	14.0000i	0.625543	−	0.551677i
$645$		0			0
$646$		0			0
$647$	−15.8745			−0.624091			−0.312046	−	0.950067i	$-0.601014\pi$
$647$	−15.8745			−0.624091			−0.312046	+	0.950067i	$0.601014\pi$
$648$		0			0
$649$	−20.0000			−0.785069
$650$		0			0
$651$		0			0
$652$	−14.0000	−	15.8745i	−0.548282	−	0.621694i
$653$			18.0000i			0.704394i	0.935926	+	0.352197i	$0.114565\pi$
$653$			18.0000i			0.704394i	−0.935926	+	0.352197i	$0.885435\pi$
$654$		0			0
$655$	6.00000			0.234439
$656$	5.29150	−	42.0000i	0.206598	−	1.63982i
$657$		0			0
$658$	−14.0000	+	5.29150i	−0.545777	+	0.206284i
$659$			30.0000i			1.16863i	0.811525	+	0.584317i	$0.198638\pi$
$659$			30.0000i			1.16863i	−0.811525	+	0.584317i	$0.801362\pi$
$660$		0			0
$661$		−	10.5830i		−	0.411631i	−0.978591	−	0.205816i	$-0.934015\pi$
$661$		−	10.5830i		−	0.411631i	0.978591	−	0.205816i	$-0.0659847\pi$
$662$	−13.2288	−	35.0000i	−0.514150	−	1.36031i
$663$		0			0
$664$	−30.0000	−	15.8745i	−1.16423	−	0.616050i
$665$	−10.5830			−0.410391
$666$		0			0
$667$		−	31.7490i		−	1.22933i
$668$	23.8118	−	21.0000i	0.921305	−	0.812514i
$669$		0			0
$670$		0			0
$671$	21.1660			0.817105
$672$		0			0
$673$	22.0000			0.848038			0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000			0.848038			0.424019	+	0.905653i	$0.360619\pi$
$674$	−7.93725	+	3.00000i	−0.305732	+	0.115556i
$675$		0			0
$676$	19.5000	−	17.1974i	0.750000	−	0.661438i
$677$			22.0000i			0.845529i	0.906240	+	0.422764i	$0.138940\pi$
$677$			22.0000i			0.845529i	−0.906240	+	0.422764i	$0.861060\pi$
$678$		0			0
$679$	4.00000			0.153506
$680$		0			0
$681$		0			0
$682$	4.00000	+	10.5830i	0.153168	+	0.405244i
$683$			12.0000i			0.459167i	0.973289	+	0.229584i	$0.0737364\pi$
$683$			12.0000i			0.459167i	−0.973289	+	0.229584i	$0.926264\pi$
$684$		0			0
$685$			21.1660i			0.808712i
$686$	26.4575	−	10.0000i	1.01015	−	0.381802i
$687$		0			0
$688$	−42.0000	−	5.29150i	−1.60123	−	0.201737i
$689$		0			0
$690$		0			0
$691$		−	15.8745i		−	0.603895i	−0.953325	−	0.301947i	$-0.902363\pi$
$691$		−	15.8745i		−	0.603895i	0.953325	−	0.301947i	$-0.0976367\pi$
$692$	18.5203	+	21.0000i	0.704035	+	0.798300i
$693$		0			0
$694$	16.0000	+	42.3320i	0.607352	+	1.60690i
$695$	5.29150			0.200718
$696$		0			0
$697$		0			0
$698$	5.29150	+	14.0000i	0.200286	+	0.529908i
$699$		0			0
$700$	−3.00000	+	2.64575i	−0.113389	+	0.100000i
$701$		−	22.0000i		−	0.830929i	−0.909610	−	0.415464i	$-0.863619\pi$
$701$		−	22.0000i		−	0.830929i	0.909610	−	0.415464i	$-0.136381\pi$
$702$		0			0
$703$	56.0000			2.11208
$704$	−13.2288	+	9.00000i	−0.498578	+	0.339200i
$705$		0			0
$706$		0			0
$707$			28.0000i			1.05305i
$708$		0			0
$709$			52.9150i			1.98727i	0.112667	+	0.993633i	$0.464061\pi$
$709$			52.9150i			1.98727i	−0.112667	+	0.993633i	$0.535939\pi$
$710$	−5.29150	−	14.0000i	−0.198587	−	0.525411i
$711$		0			0
$712$	14.0000	−	26.4575i	0.524672	−	0.991537i
$713$	21.1660			0.792673
$714$		0			0
$715$		0			0
$716$	23.8118	+	27.0000i	0.889887	+	1.00904i
$717$		0			0
$718$	−42.0000	+	15.8745i	−1.56743	+	0.592431i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	−28.0000			−1.04277
$722$	11.9059	−	4.50000i	0.443091	−	0.167473i
$723$		0			0
$724$	14.0000	+	15.8745i	0.520306	+	0.589971i
$725$			6.00000i			0.222834i
$726$		0			0
$727$	−26.0000			−0.964287			−0.482143	−	0.876092i	$-0.660142\pi$
$727$	−26.0000			−0.964287			−0.482143	+	0.876092i	$0.660142\pi$
$728$		0			0
$729$		0			0
$730$	−7.00000	−	18.5203i	−0.259082	−	0.685466i
$731$		0			0
$732$		0			0
$733$			31.7490i			1.17268i	0.810066	+	0.586338i	$0.199431\pi$
$733$			31.7490i			1.17268i	−0.810066	+	0.586338i	$0.800569\pi$
$734$	23.8118	−	9.00000i	0.878908	−	0.332196i
$735$		0			0
$736$	7.00000	+	29.1033i	0.258023	+	1.07276i
$737$		0			0
$738$		0			0
$739$		−	47.6235i		−	1.75186i	−0.482439	−	0.875930i	$-0.660249\pi$
$739$		−	47.6235i		−	1.75186i	0.482439	−	0.875930i	$-0.339751\pi$
$740$	15.8745	−	14.0000i	0.583559	−	0.514650i
$741$		0			0
$742$	−2.00000	−	5.29150i	−0.0734223	−	0.194257i
$743$	15.8745			0.582379			0.291190	−	0.956665i	$-0.405949\pi$
$743$	15.8745			0.582379			0.291190	+	0.956665i	$0.405949\pi$
$744$		0			0
$745$	−6.00000			−0.219823
$746$	5.29150	+	14.0000i	0.193736	+	0.512576i
$747$		0			0
$748$		0			0
$749$			8.00000i			0.292314i
$750$		0			0
$751$	−52.0000			−1.89751			−0.948753	−	0.316017i	$-0.897654\pi$
$751$	−52.0000			−1.89751			−0.948753	+	0.316017i	$0.897654\pi$
$752$	2.64575	−	21.0000i	0.0964806	−	0.765791i
$753$		0			0
$754$		0			0
$755$		−	16.0000i		−	0.582300i
$756$		0			0
$757$			10.5830i			0.384646i	0.981332	+	0.192323i	$0.0616021\pi$
$757$			10.5830i			0.384646i	−0.981332	+	0.192323i	$0.938398\pi$
$758$	7.93725	+	21.0000i	0.288294	+	0.762754i
$759$		0			0
$760$	7.00000	−	13.2288i	0.253917	−	0.479857i
$761$	−21.1660			−0.767267			−0.383634	−	0.923485i	$-0.625327\pi$
$761$	−21.1660			−0.767267			−0.383634	+	0.923485i	$0.625327\pi$
$762$		0			0
$763$			21.1660i			0.766261i
$764$	−31.7490	+	28.0000i	−1.14864	+	1.01300i
$765$		0			0
$766$	−21.0000	+	7.93725i	−0.758761	+	0.286785i
$767$		0			0
$768$		0			0
$769$	−30.0000			−1.08183			−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000			−1.08183			−0.540914	+	0.841078i	$0.681921\pi$
$770$	5.29150	−	2.00000i	0.190693	−	0.0720750i
$771$		0			0
$772$	−3.00000	+	2.64575i	−0.107972	+	0.0952227i
$773$			42.0000i			1.51064i	0.655359	+	0.755318i	$0.272517\pi$
$773$			42.0000i			1.51064i	−0.655359	+	0.755318i	$0.727483\pi$
$774$		0			0
$775$	−4.00000			−0.143684
$776$	−2.64575	+	5.00000i	−0.0949769	+	0.179490i
$777$		0			0
$778$	−5.00000	−	13.2288i	−0.179259	−	0.474274i
$779$		−	56.0000i		−	2.00641i
$780$		0			0
$781$			21.1660i			0.757379i
$782$		0			0
$783$		0			0
$784$	−1.50000	+	11.9059i	−0.0535714	+	0.425210i
$785$	−10.5830			−0.377724
$786$		0			0
$787$		−	21.1660i		−	0.754487i	−0.926114	−	0.377243i	$-0.876872\pi$
$787$		−	21.1660i		−	0.754487i	0.926114	−	0.377243i	$-0.123128\pi$
$788$	2.64575	+	3.00000i	0.0942510	+	0.106871i
$789$		0			0
$790$	2.00000	+	5.29150i	0.0711568	+	0.188263i
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−10.5830	−	28.0000i	−0.375577	−	0.993683i
$795$		0			0
$796$		0			0
$797$		−	30.0000i		−	1.06265i	−0.847167	−	0.531327i	$-0.821693\pi$
$797$		−	30.0000i		−	1.06265i	0.847167	−	0.531327i	$-0.178307\pi$
$798$		0			0
$799$		0			0
$800$	−1.32288	−	5.50000i	−0.0467707	−	0.194454i
$801$		0			0
$802$	−42.0000	+	15.8745i	−1.48307	+	0.560548i
$803$			28.0000i			0.988099i
$804$		0			0
$805$		−	10.5830i		−	0.373002i
$806$		0			0
$807$		0			0
$808$	−35.0000	−	18.5203i	−1.23130	−	0.651540i
$809$	−21.1660			−0.744157			−0.372079	−	0.928201i	$-0.621355\pi$
$809$	−21.1660			−0.744157			−0.372079	+	0.928201i	$0.621355\pi$
$810$		0			0
$811$		−	26.4575i		−	0.929049i	−0.885560	−	0.464524i	$-0.846225\pi$
$811$		−	26.4575i		−	0.929049i	0.885560	−	0.464524i	$-0.153775\pi$
$812$	−15.8745	−	18.0000i	−0.557086	−	0.631676i
$813$		0			0
$814$	−28.0000	+	10.5830i	−0.981399	+	0.370934i
$815$	−10.5830			−0.370707
$816$		0			0
$817$	−56.0000			−1.95919
$818$	−23.8118	+	9.00000i	−0.832559	+	0.314678i
$819$		0			0
$820$	−14.0000	−	15.8745i	−0.488901	−	0.554362i
$821$		−	10.0000i		−	0.349002i	−0.984657	−	0.174501i	$-0.944169\pi$
$821$		−	10.0000i		−	0.349002i	0.984657	−	0.174501i	$-0.0558313\pi$
$822$		0			0
$823$	−18.0000			−0.627441			−0.313720	−	0.949515i	$-0.601575\pi$
$823$	−18.0000			−0.627441			−0.313720	+	0.949515i	$0.601575\pi$
$824$	18.5203	−	35.0000i	0.645184	−	1.21928i
$825$		0			0
$826$	10.0000	+	26.4575i	0.347945	+	0.920575i
$827$			8.00000i			0.278187i	0.990279	+	0.139094i	$0.0444189\pi$
$827$			8.00000i			0.278187i	−0.990279	+	0.139094i	$0.955581\pi$
$828$		0			0
$829$			10.5830i			0.367563i	0.982967	+	0.183781i	$0.0588339\pi$
$829$			10.5830i			0.367563i	−0.982967	+	0.183781i	$0.941166\pi$
$830$	−15.8745	+	6.00000i	−0.551012	+	0.208263i
$831$		0			0
$832$		0			0
$833$		0			0
$834$		0			0
$835$		−	15.8745i		−	0.549360i
$836$	−15.8745	+	14.0000i	−0.549031	+	0.484200i
$837$		0			0
$838$	−7.00000	−	18.5203i	−0.241811	−	0.639772i
$839$	10.5830			0.365366			0.182683	−	0.983172i	$-0.441522\pi$
$839$	10.5830			0.365366			0.182683	+	0.983172i	$0.441522\pi$
$840$		0			0
$841$	−7.00000			−0.241379
$842$	5.29150	+	14.0000i	0.182357	+	0.482472i
$843$		0			0
$844$	21.0000	+	23.8118i	0.722850	+	0.819635i
$845$		−	13.0000i		−	0.447214i
$846$		0			0
$847$	14.0000			0.481046
$848$	7.93725	+	1.00000i	0.272566	+	0.0343401i
$849$		0			0
$850$		0			0
$851$			56.0000i			1.91966i
$852$		0			0
$853$			42.3320i			1.44942i	0.689054	+	0.724710i	$0.258026\pi$
$853$			42.3320i			1.44942i	−0.689054	+	0.724710i	$0.741974\pi$
$854$	−10.5830	−	28.0000i	−0.362143	−	0.958140i
$855$		0			0
$856$	−10.0000	−	5.29150i	−0.341793	−	0.180860i
$857$		0			0			−	1.00000i	$-0.5\pi$
$857$		0			0				1.00000i	$0.5\pi$
$858$		0			0
$859$			26.4575i			0.902719i	0.892342	+	0.451359i	$0.149061\pi$
$859$			26.4575i			0.902719i	−0.892342	+	0.451359i	$0.850939\pi$
$860$	−15.8745	+	14.0000i	−0.541316	+	0.477396i
$861$		0			0
$862$	42.0000	−	15.8745i	1.43053	−	0.540688i
$863$	−15.8745			−0.540375			−0.270187	−	0.962808i	$-0.587086\pi$
$863$	−15.8745			−0.540375			−0.270187	+	0.962808i	$0.587086\pi$
$864$		0			0
$865$	14.0000			0.476014
$866$	−18.5203	+	7.00000i	−0.629344	+	0.237870i
$867$		0			0
$868$	12.0000	−	10.5830i	0.407307	−	0.359211i
$869$		−	8.00000i		−	0.271381i
$870$		0			0
$871$		0			0
$872$	−26.4575	−	14.0000i	−0.895964	−	0.474100i
$873$		0			0
$874$	14.0000	+	37.0405i	0.473557	+	1.25291i
$875$			2.00000i			0.0676123i
$876$		0			0
$877$		−	10.5830i		−	0.357363i	−0.983907	−	0.178681i	$-0.942817\pi$
$877$		−	10.5830i		−	0.357363i	0.983907	−	0.178681i	$-0.0571831\pi$
$878$	−10.5830	+	4.00000i	−0.357159	+	0.134993i
$879$		0			0
$880$	−1.00000	+	7.93725i	−0.0337100	+	0.267565i
$881$	−31.7490			−1.06965			−0.534826	−	0.844962i	$-0.679623\pi$
$881$	−31.7490			−1.06965			−0.534826	+	0.844962i	$0.679623\pi$
$882$		0			0
$883$		−	10.5830i		−	0.356146i	−0.984017	−	0.178073i	$-0.943014\pi$
$883$		−	10.5830i		−	0.356146i	0.984017	−	0.178073i	$-0.0569864\pi$
$884$		0			0
$885$		0			0
$886$	16.0000	+	42.3320i	0.537531	+	1.42217i
$887$	−5.29150			−0.177671			−0.0888356	−	0.996046i	$-0.528315\pi$
$887$	−5.29150			−0.177671			−0.0888356	+	0.996046i	$0.528315\pi$
$888$		0			0
$889$	12.0000			0.402467
$890$	−5.29150	−	14.0000i	−0.177372	−	0.469281i
$891$		0			0
$892$	−3.00000	+	2.64575i	−0.100447	+	0.0885863i
$893$		−	28.0000i		−	0.936984i
$894$		0			0
$895$	18.0000			0.601674
$896$	18.5203	+	13.0000i	0.618718	+	0.434300i
$897$		0			0
$898$		0			0
$899$		−	24.0000i		−	0.800445i
$900$		0			0
$901$		0			0
$902$	10.5830	+	28.0000i	0.352376	+	0.932298i
$903$		0			0
$904$		0			0
$905$	10.5830			0.351791
$906$		0			0
$907$		−	42.3320i		−	1.40561i	−0.711382	−	0.702806i	$-0.751930\pi$
$907$		−	42.3320i		−	1.40561i	0.711382	−	0.702806i	$-0.248070\pi$
$908$	31.7490	+	36.0000i	1.05363	+	1.19470i
$909$		0			0
$910$		0			0
$911$	31.7490			1.05189			0.525946	−	0.850518i	$-0.323711\pi$
$911$	31.7490			1.05189			0.525946	+	0.850518i	$0.323711\pi$
$912$		0			0
$913$	24.0000			0.794284
$914$	23.8118	−	9.00000i	0.787623	−	0.297694i
$915$		0			0
$916$	−14.0000	−	15.8745i	−0.462573	−	0.524509i
$917$			12.0000i			0.396275i
$918$		0			0
$919$	−20.0000			−0.659739			−0.329870	−	0.944027i	$-0.607005\pi$
$919$	−20.0000			−0.659739			−0.329870	+	0.944027i	$0.607005\pi$
$920$	13.2288	+	7.00000i	0.436139	+	0.230783i
$921$		0			0
$922$	−7.00000	−	18.5203i	−0.230533	−	0.609932i
$923$		0			0
$924$		0			0
$925$		−	10.5830i		−	0.347967i
$926$	−34.3948	+	13.0000i	−1.13028	+	0.427207i
$927$		0			0
$928$	33.0000	−	7.93725i	1.08328	−	0.260553i
$929$	−21.1660			−0.694434			−0.347217	−	0.937785i	$-0.612873\pi$
$929$	−21.1660			−0.694434			−0.347217	+	0.937785i	$0.612873\pi$
$930$		0			0
$931$			15.8745i			0.520266i
$932$		0			0
$933$		0			0
$934$	−14.0000	−	37.0405i	−0.458094	−	1.21200i
$935$		0			0
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$		0			0
$940$	−7.00000	−	7.93725i	−0.228315	−	0.258885i
$941$			46.0000i			1.49956i	0.661689	+	0.749779i	$0.269840\pi$
$941$			46.0000i			1.49956i	−0.661689	+	0.749779i	$0.730160\pi$
$942$		0			0
$943$	56.0000			1.82361
$944$	−39.6863	−	5.00000i	−1.29168	−	0.162736i
$945$		0			0
$946$	28.0000	−	10.5830i	0.910359	−	0.344083i
$947$		−	48.0000i		−	1.55979i	−0.625910	−	0.779895i	$-0.715272\pi$
$947$		−	48.0000i		−	1.55979i	0.625910	−	0.779895i	$-0.284728\pi$
$948$		0			0
$949$		0			0
$950$	−2.64575	−	7.00000i	−0.0858395	−	0.227110i
$951$		0			0
$952$		0			0
$953$	42.3320			1.37127			0.685634	−	0.727946i	$-0.259525\pi$
$953$	42.3320			1.37127			0.685634	+	0.727946i	$0.259525\pi$
$954$		0			0
$955$			21.1660i			0.684916i
$956$	15.8745	−	14.0000i	0.513418	−	0.452792i
$957$		0			0
$958$	−14.0000	+	5.29150i	−0.452319	+	0.170961i
$959$	−42.3320			−1.36697
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$		0			0
$964$	27.0000	−	23.8118i	0.869611	−	0.766925i
$965$			2.00000i			0.0643823i
$966$		0			0
$967$	34.0000			1.09337			0.546683	−	0.837340i	$-0.315890\pi$
$967$	34.0000			1.09337			0.546683	+	0.837340i	$0.315890\pi$
$968$	−9.26013	+	17.5000i	−0.297632	+	0.562471i
$969$		0			0
$970$	1.00000	+	2.64575i	0.0321081	+	0.0849500i
$971$		−	6.00000i		−	0.192549i	−0.995355	−	0.0962746i	$-0.969307\pi$
$971$		−	6.00000i		−	0.192549i	0.995355	−	0.0962746i	$-0.0306927\pi$
$972$		0			0
$973$			10.5830i			0.339276i
$974$	−39.6863	+	15.0000i	−1.27163	+	0.480631i
$975$		0			0
$976$	42.0000	+	5.29150i	1.34439	+	0.169377i
$977$	21.1660			0.677161			0.338580	−	0.940937i	$-0.390053\pi$
$977$	21.1660			0.677161			0.338580	+	0.940937i	$0.390053\pi$
$978$		0			0
$979$			21.1660i			0.676469i
$980$	3.96863	+	4.50000i	0.126773	+	0.143747i
$981$		0			0
$982$	11.0000	+	29.1033i	0.351024	+	0.928722i
$983$	−5.29150			−0.168773			−0.0843864	−	0.996433i	$-0.526893\pi$
$983$	−5.29150			−0.168773			−0.0843864	+	0.996433i	$0.526893\pi$
$984$		0			0
$985$	2.00000			0.0637253
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	56.0000i		−	1.78070i
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	5.29150	+	22.0000i	0.168005	+	0.698501i
$993$		0			0
$994$	28.0000	−	10.5830i	0.888106	−	0.335673i
$995$		0			0
$996$		0			0
$997$		−	42.3320i		−	1.34067i	−0.742059	−	0.670334i	$-0.766151\pi$
$997$		−	42.3320i		−	1.34067i	0.742059	−	0.670334i	$-0.233849\pi$
$998$	2.64575	+	7.00000i	0.0837498	+	0.221581i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.k.d.181.2	yes	4
3.2	odd	2	inner	360.2.k.d.181.3	yes	4
4.3	odd	2		1440.2.k.d.721.2		4
5.2	odd	4		1800.2.d.k.1549.2		4
5.3	odd	4		1800.2.d.o.1549.3		4
5.4	even	2		1800.2.k.n.901.3		4
8.3	odd	2		1440.2.k.d.721.3		4
8.5	even	2	inner	360.2.k.d.181.1	✓	4
12.11	even	2		1440.2.k.d.721.4		4
15.2	even	4		1800.2.d.o.1549.4		4
15.8	even	4		1800.2.d.k.1549.1		4
15.14	odd	2		1800.2.k.n.901.2		4
20.3	even	4		7200.2.d.k.2449.3		4
20.7	even	4		7200.2.d.l.2449.1		4
20.19	odd	2		7200.2.k.o.3601.4		4
24.5	odd	2	inner	360.2.k.d.181.4	yes	4
24.11	even	2		1440.2.k.d.721.1		4
40.3	even	4		7200.2.d.l.2449.4		4
40.13	odd	4		1800.2.d.k.1549.3		4
40.19	odd	2		7200.2.k.o.3601.1		4
40.27	even	4		7200.2.d.k.2449.2		4
40.29	even	2		1800.2.k.n.901.4		4
40.37	odd	4		1800.2.d.o.1549.2		4
60.23	odd	4		7200.2.d.l.2449.3		4
60.47	odd	4		7200.2.d.k.2449.1		4
60.59	even	2		7200.2.k.o.3601.2		4
120.29	odd	2		1800.2.k.n.901.1		4
120.53	even	4		1800.2.d.o.1549.1		4
120.59	even	2		7200.2.k.o.3601.3		4
120.77	even	4		1800.2.d.k.1549.4		4
120.83	odd	4		7200.2.d.k.2449.4		4
120.107	odd	4		7200.2.d.l.2449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.k.d.181.1	✓	4	8.5	even	2	inner
360.2.k.d.181.2	yes	4	1.1	even	1	trivial
360.2.k.d.181.3	yes	4	3.2	odd	2	inner
360.2.k.d.181.4	yes	4	24.5	odd	2	inner
1440.2.k.d.721.1		4	24.11	even	2
1440.2.k.d.721.2		4	4.3	odd	2
1440.2.k.d.721.3		4	8.3	odd	2
1440.2.k.d.721.4		4	12.11	even	2
1800.2.d.k.1549.1		4	15.8	even	4
1800.2.d.k.1549.2		4	5.2	odd	4
1800.2.d.k.1549.3		4	40.13	odd	4
1800.2.d.k.1549.4		4	120.77	even	4
1800.2.d.o.1549.1		4	120.53	even	4
1800.2.d.o.1549.2		4	40.37	odd	4
1800.2.d.o.1549.3		4	5.3	odd	4
1800.2.d.o.1549.4		4	15.2	even	4
1800.2.k.n.901.1		4	120.29	odd	2
1800.2.k.n.901.2		4	15.14	odd	2
1800.2.k.n.901.3		4	5.4	even	2
1800.2.k.n.901.4		4	40.29	even	2
7200.2.d.k.2449.1		4	60.47	odd	4
7200.2.d.k.2449.2		4	40.27	even	4
7200.2.d.k.2449.3		4	20.3	even	4
7200.2.d.k.2449.4		4	120.83	odd	4
7200.2.d.l.2449.1		4	20.7	even	4
7200.2.d.l.2449.2		4	120.107	odd	4
7200.2.d.l.2449.3		4	60.23	odd	4
7200.2.d.l.2449.4		4	40.3	even	4
7200.2.k.o.3601.1		4	40.19	odd	2
7200.2.k.o.3601.2		4	60.59	even	2
7200.2.k.o.3601.3		4	120.59	even	2
7200.2.k.o.3601.4		4	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.k (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32288 + 0.500000i) q^{2} +(1.50000 - 1.32288i) q^{4} -1.00000i q^{5} +2.00000 q^{7} +(-1.32288 + 2.50000i) q^{8} +O(q^{10})\)	\(q+(-1.32288 + 0.500000i) q^{2} +(1.50000 - 1.32288i) q^{4} -1.00000i q^{5} +2.00000 q^{7} +(-1.32288 + 2.50000i) q^{8} +(0.500000 + 1.32288i) q^{10} -2.00000i q^{11} +(-2.64575 + 1.00000i) q^{14} +(0.500000 - 3.96863i) q^{16} -5.29150i q^{19} +(-1.32288 - 1.50000i) q^{20} +(1.00000 + 2.64575i) q^{22} +5.29150 q^{23} -1.00000 q^{25} +(3.00000 - 2.64575i) q^{28} -6.00000i q^{29} +4.00000 q^{31} +(1.32288 + 5.50000i) q^{32} -2.00000i q^{35} +10.5830i q^{37} +(2.64575 + 7.00000i) q^{38} +(2.50000 + 1.32288i) q^{40} +10.5830 q^{41} -10.5830i q^{43} +(-2.64575 - 3.00000i) q^{44} +(-7.00000 + 2.64575i) q^{46} +5.29150 q^{47} -3.00000 q^{49} +(1.32288 - 0.500000i) q^{50} +2.00000i q^{53} -2.00000 q^{55} +(-2.64575 + 5.00000i) q^{56} +(3.00000 + 7.93725i) q^{58} -10.0000i q^{59} +10.5830i q^{61} +(-5.29150 + 2.00000i) q^{62} +(-4.50000 - 6.61438i) q^{64} +(1.00000 + 2.64575i) q^{70} -10.5830 q^{71} -14.0000 q^{73} +(-5.29150 - 14.0000i) q^{74} +(-7.00000 - 7.93725i) q^{76} -4.00000i q^{77} +4.00000 q^{79} +(-3.96863 - 0.500000i) q^{80} +(-14.0000 + 5.29150i) q^{82} +12.0000i q^{83} +(5.29150 + 14.0000i) q^{86} +(5.00000 + 2.64575i) q^{88} -10.5830 q^{89} +(7.93725 - 7.00000i) q^{92} +(-7.00000 + 2.64575i) q^{94} -5.29150 q^{95} +2.00000 q^{97} +(3.96863 - 1.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{4} + 8 q^{7}+O(q^{10}) \) 4 * q + 6 * q^4 + 8 * q^7	\( 4 q + 6 q^{4} + 8 q^{7} + 2 q^{10} + 2 q^{16} + 4 q^{22} - 4 q^{25} + 12 q^{28} + 16 q^{31} + 10 q^{40} - 28 q^{46} - 12 q^{49} - 8 q^{55} + 12 q^{58} - 18 q^{64} + 4 q^{70} - 56 q^{73} - 28 q^{76} + 16 q^{79} - 56 q^{82} + 20 q^{88} - 28 q^{94} + 8 q^{97}+O(q^{100}) \) 4 * q + 6 * q^4 + 8 * q^7 + 2 * q^10 + 2 * q^16 + 4 * q^22 - 4 * q^25 + 12 * q^28 + 16 * q^31 + 10 * q^40 - 28 * q^46 - 12 * q^49 - 8 * q^55 + 12 * q^58 - 18 * q^64 + 4 * q^70 - 56 * q^73 - 28 * q^76 + 16 * q^79 - 56 * q^82 + 20 * q^88 - 28 * q^94 + 8 * q^97

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