LMFDB - Embedded newform 360.2.k.a.181.1

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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			181.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	360.181
Dual form			360.2.k.a.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} -1.00000i q^{5} -4.00000 q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})$	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} -1.00000i q^{5} -4.00000 q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.00000 + 1.00000i) q^{10} -2.00000i q^{11} +6.00000i q^{13} +(4.00000 + 4.00000i) q^{14} -4.00000 q^{16} -6.00000 q^{17} -4.00000i q^{19} +2.00000 q^{20} +(-2.00000 + 2.00000i) q^{22} -8.00000 q^{23} -1.00000 q^{25} +(6.00000 - 6.00000i) q^{26} -8.00000i q^{28} +6.00000i q^{29} -2.00000 q^{31} +(4.00000 + 4.00000i) q^{32} +(6.00000 + 6.00000i) q^{34} +4.00000i q^{35} +2.00000i q^{37} +(-4.00000 + 4.00000i) q^{38} +(-2.00000 - 2.00000i) q^{40} -4.00000 q^{41} +4.00000i q^{43} +4.00000 q^{44} +(8.00000 + 8.00000i) q^{46} +4.00000 q^{47} +9.00000 q^{49} +(1.00000 + 1.00000i) q^{50} -12.0000 q^{52} -10.0000i q^{53} -2.00000 q^{55} +(-8.00000 + 8.00000i) q^{56} +(6.00000 - 6.00000i) q^{58} +2.00000i q^{59} -4.00000i q^{61} +(2.00000 + 2.00000i) q^{62} -8.00000i q^{64} +6.00000 q^{65} -12.0000i q^{67} -12.0000i q^{68} +(4.00000 - 4.00000i) q^{70} -8.00000 q^{71} +10.0000 q^{73} +(2.00000 - 2.00000i) q^{74} +8.00000 q^{76} +8.00000i q^{77} -2.00000 q^{79} +4.00000i q^{80} +(4.00000 + 4.00000i) q^{82} +6.00000i q^{85} +(4.00000 - 4.00000i) q^{86} +(-4.00000 - 4.00000i) q^{88} +4.00000 q^{89} -24.0000i q^{91} -16.0000i q^{92} +(-4.00000 - 4.00000i) q^{94} -4.00000 q^{95} +2.00000 q^{97} +(-9.00000 - 9.00000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 8 q^{7} + 4 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 8 * q^7 + 4 * q^8	$ 2 q - 2 q^{2} - 8 q^{7} + 4 q^{8} - 2 q^{10} + 8 q^{14} - 8 q^{16} - 12 q^{17} + 4 q^{20} - 4 q^{22} - 16 q^{23} - 2 q^{25} + 12 q^{26} - 4 q^{31} + 8 q^{32} + 12 q^{34} - 8 q^{38} - 4 q^{40} - 8 q^{41} + 8 q^{44} + 16 q^{46} + 8 q^{47} + 18 q^{49} + 2 q^{50} - 24 q^{52} - 4 q^{55} - 16 q^{56} + 12 q^{58} + 4 q^{62} + 12 q^{65} + 8 q^{70} - 16 q^{71} + 20 q^{73} + 4 q^{74} + 16 q^{76} - 4 q^{79} + 8 q^{82} + 8 q^{86} - 8 q^{88} + 8 q^{89} - 8 q^{94} - 8 q^{95} + 4 q^{97} - 18 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 8 * q^7 + 4 * q^8 - 2 * q^10 + 8 * q^14 - 8 * q^16 - 12 * q^17 + 4 * q^20 - 4 * q^22 - 16 * q^23 - 2 * q^25 + 12 * q^26 - 4 * q^31 + 8 * q^32 + 12 * q^34 - 8 * q^38 - 4 * q^40 - 8 * q^41 + 8 * q^44 + 16 * q^46 + 8 * q^47 + 18 * q^49 + 2 * q^50 - 24 * q^52 - 4 * q^55 - 16 * q^56 + 12 * q^58 + 4 * q^62 + 12 * q^65 + 8 * q^70 - 16 * q^71 + 20 * q^73 + 4 * q^74 + 16 * q^76 - 4 * q^79 + 8 * q^82 + 8 * q^86 - 8 * q^88 + 8 * q^89 - 8 * q^94 - 8 * q^95 + 4 * q^97 - 18 * q^98

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 $

$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$2$	−1.00000	−	1.00000i	−0.707107	−	0.707107i
$3$		0			0
$3$		0			0
$4$			2.00000i			1.00000i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$		0			0
$7$	−4.00000			−1.51186			−0.755929	−	0.654654i	$-0.772814\pi$
$7$	−4.00000			−1.51186			−0.755929	+	0.654654i	$0.772814\pi$
$8$	2.00000	−	2.00000i	0.707107	−	0.707107i
$9$		0			0
$10$	−1.00000	+	1.00000i	−0.316228	+	0.316228i
$11$		−	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
$13$			6.00000i			1.66410i	0.554700	+	0.832050i	$0.312833\pi$
$13$			6.00000i			1.66410i	−0.554700	+	0.832050i	$0.687167\pi$
$14$	4.00000	+	4.00000i	1.06904	+	1.06904i
$15$		0			0
$16$	−4.00000			−1.00000
$17$	−6.00000			−1.45521			−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000			−1.45521			−0.727607	+	0.685994i	$0.759367\pi$
$18$		0			0
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	2.00000			0.447214
$21$		0			0
$22$	−2.00000	+	2.00000i	−0.426401	+	0.426401i
$23$	−8.00000			−1.66812			−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000			−1.66812			−0.834058	+	0.551677i	$0.813988\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	6.00000	−	6.00000i	1.17670	−	1.17670i
$27$		0			0
$28$		−	8.00000i		−	1.51186i
$29$			6.00000i			1.11417i	0.830455	+	0.557086i	$0.188081\pi$
$29$			6.00000i			1.11417i	−0.830455	+	0.557086i	$0.811919\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$		0			0
$34$	6.00000	+	6.00000i	1.02899	+	1.02899i
$35$			4.00000i			0.676123i
$36$		0			0
$37$			2.00000i			0.328798i	0.986394	+	0.164399i	$0.0525685\pi$
$37$			2.00000i			0.328798i	−0.986394	+	0.164399i	$0.947432\pi$
$38$	−4.00000	+	4.00000i	−0.648886	+	0.648886i
$39$		0			0
$40$	−2.00000	−	2.00000i	−0.316228	−	0.316228i
$41$	−4.00000			−0.624695			−0.312348	−	0.949968i	$-0.601115\pi$
$41$	−4.00000			−0.624695			−0.312348	+	0.949968i	$0.601115\pi$
$42$		0			0
$43$			4.00000i			0.609994i	0.952353	+	0.304997i	$0.0986555\pi$
$43$			4.00000i			0.609994i	−0.952353	+	0.304997i	$0.901344\pi$
$44$	4.00000			0.603023
$45$		0			0
$46$	8.00000	+	8.00000i	1.17954	+	1.17954i
$47$	4.00000			0.583460			0.291730	−	0.956501i	$-0.405769\pi$
$47$	4.00000			0.583460			0.291730	+	0.956501i	$0.405769\pi$
$48$		0			0
$49$	9.00000			1.28571
$50$	1.00000	+	1.00000i	0.141421	+	0.141421i
$51$		0			0
$52$	−12.0000			−1.66410
$53$		−	10.0000i		−	1.37361i	−0.726844	−	0.686803i	$-0.759014\pi$
$53$		−	10.0000i		−	1.37361i	0.726844	−	0.686803i	$-0.240986\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$	−8.00000	+	8.00000i	−1.06904	+	1.06904i
$57$		0			0
$58$	6.00000	−	6.00000i	0.787839	−	0.787839i
$59$			2.00000i			0.260378i	0.991489	+	0.130189i	$0.0415584\pi$
$59$			2.00000i			0.260378i	−0.991489	+	0.130189i	$0.958442\pi$
$60$		0			0
$61$		−	4.00000i		−	0.512148i	−0.966657	−	0.256074i	$-0.917571\pi$
$61$		−	4.00000i		−	0.512148i	0.966657	−	0.256074i	$-0.0824290\pi$
$62$	2.00000	+	2.00000i	0.254000	+	0.254000i
$63$		0			0
$64$		−	8.00000i		−	1.00000i
$65$	6.00000			0.744208
$66$		0			0
$67$		−	12.0000i		−	1.46603i	−0.680211	−	0.733017i	$-0.738112\pi$
$67$		−	12.0000i		−	1.46603i	0.680211	−	0.733017i	$-0.261888\pi$
$68$		−	12.0000i		−	1.45521i
$69$		0			0
$70$	4.00000	−	4.00000i	0.478091	−	0.478091i
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	10.0000			1.17041			0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000			1.17041			0.585206	+	0.810885i	$0.301014\pi$
$74$	2.00000	−	2.00000i	0.232495	−	0.232495i
$75$		0			0
$76$	8.00000			0.917663
$77$			8.00000i			0.911685i
$78$		0			0
$79$	−2.00000			−0.225018			−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000			−0.225018			−0.112509	+	0.993651i	$0.535889\pi$
$80$			4.00000i			0.447214i
$81$		0			0
$82$	4.00000	+	4.00000i	0.441726	+	0.441726i
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$		0			0
$85$			6.00000i			0.650791i
$86$	4.00000	−	4.00000i	0.431331	−	0.431331i
$87$		0			0
$88$	−4.00000	−	4.00000i	−0.426401	−	0.426401i
$89$	4.00000			0.423999			0.212000	−	0.977270i	$-0.432002\pi$
$89$	4.00000			0.423999			0.212000	+	0.977270i	$0.432002\pi$
$90$		0			0
$91$		−	24.0000i		−	2.51588i
$92$		−	16.0000i		−	1.66812i
$93$		0			0
$94$	−4.00000	−	4.00000i	−0.412568	−	0.412568i
$95$	−4.00000			−0.410391
$96$		0			0
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$	−9.00000	−	9.00000i	−0.909137	−	0.909137i
$99$		0			0
$100$		−	2.00000i		−	0.200000i
$101$		−	10.0000i		−	0.995037i	−0.867453	−	0.497519i	$-0.834245\pi$
$101$		−	10.0000i		−	0.995037i	0.867453	−	0.497519i	$-0.165755\pi$
$102$		0			0
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$	12.0000	+	12.0000i	1.17670	+	1.17670i
$105$		0			0
$106$	−10.0000	+	10.0000i	−0.971286	+	0.971286i
$107$		−	20.0000i		−	1.93347i	−0.255774	−	0.966736i	$-0.582330\pi$
$107$		−	20.0000i		−	1.93347i	0.255774	−	0.966736i	$-0.417670\pi$
$108$		0			0
$109$			8.00000i			0.766261i	0.923694	+	0.383131i	$0.125154\pi$
$109$			8.00000i			0.766261i	−0.923694	+	0.383131i	$0.874846\pi$
$110$	2.00000	+	2.00000i	0.190693	+	0.190693i
$111$		0			0
$112$	16.0000			1.51186
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$			8.00000i			0.746004i
$116$	−12.0000			−1.11417
$117$		0			0
$118$	2.00000	−	2.00000i	0.184115	−	0.184115i
$119$	24.0000			2.20008
$120$		0			0
$121$	7.00000			0.636364
$122$	−4.00000	+	4.00000i	−0.362143	+	0.362143i
$123$		0			0
$124$		−	4.00000i		−	0.359211i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	−8.00000	+	8.00000i	−0.707107	+	0.707107i
$129$		0			0
$130$	−6.00000	−	6.00000i	−0.526235	−	0.526235i
$131$			18.0000i			1.57267i	0.617802	+	0.786334i	$0.288023\pi$
$131$			18.0000i			1.57267i	−0.617802	+	0.786334i	$0.711977\pi$
$132$		0			0
$133$			16.0000i			1.38738i
$134$	−12.0000	+	12.0000i	−1.03664	+	1.03664i
$135$		0			0
$136$	−12.0000	+	12.0000i	−1.02899	+	1.02899i
$137$	2.00000			0.170872			0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000			0.170872			0.0854358	+	0.996344i	$0.472772\pi$
$138$		0			0
$139$			4.00000i			0.339276i	0.985506	+	0.169638i	$0.0542598\pi$
$139$			4.00000i			0.339276i	−0.985506	+	0.169638i	$0.945740\pi$
$140$	−8.00000			−0.676123
$141$		0			0
$142$	8.00000	+	8.00000i	0.671345	+	0.671345i
$143$	12.0000			1.00349
$144$		0			0
$145$	6.00000			0.498273
$146$	−10.0000	−	10.0000i	−0.827606	−	0.827606i
$147$		0			0
$148$	−4.00000			−0.328798
$149$			6.00000i			0.491539i	0.969328	+	0.245770i	$0.0790407\pi$
$149$			6.00000i			0.491539i	−0.969328	+	0.245770i	$0.920959\pi$
$150$		0			0
$151$	−2.00000			−0.162758			−0.0813788	−	0.996683i	$-0.525932\pi$
$151$	−2.00000			−0.162758			−0.0813788	+	0.996683i	$0.525932\pi$
$152$	−8.00000	−	8.00000i	−0.648886	−	0.648886i
$153$		0			0
$154$	8.00000	−	8.00000i	0.644658	−	0.644658i
$155$			2.00000i			0.160644i
$156$		0			0
$157$		−	14.0000i		−	1.11732i	−0.829396	−	0.558661i	$-0.811315\pi$
$157$		−	14.0000i		−	1.11732i	0.829396	−	0.558661i	$-0.188685\pi$
$158$	2.00000	+	2.00000i	0.159111	+	0.159111i
$159$		0			0
$160$	4.00000	−	4.00000i	0.316228	−	0.316228i
$161$	32.0000			2.52195
$162$		0			0
$163$			16.0000i			1.25322i	0.779334	+	0.626608i	$0.215557\pi$
$163$			16.0000i			1.25322i	−0.779334	+	0.626608i	$0.784443\pi$
$164$		−	8.00000i		−	0.624695i
$165$		0			0
$166$		0			0
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$		0			0
$169$	−23.0000			−1.76923
$170$	6.00000	−	6.00000i	0.460179	−	0.460179i
$171$		0			0
$172$	−8.00000			−0.609994
$173$			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
$175$	4.00000			0.302372
$176$			8.00000i			0.603023i
$177$		0			0
$178$	−4.00000	−	4.00000i	−0.299813	−	0.299813i
$179$			6.00000i			0.448461i	0.974536	+	0.224231i	$0.0719869\pi$
$179$			6.00000i			0.448461i	−0.974536	+	0.224231i	$0.928013\pi$
$180$		0			0
$181$		−	16.0000i		−	1.18927i	−0.803996	−	0.594635i	$-0.797296\pi$
$181$		−	16.0000i		−	1.18927i	0.803996	−	0.594635i	$-0.202704\pi$
$182$	−24.0000	+	24.0000i	−1.77900	+	1.77900i
$183$		0			0
$184$	−16.0000	+	16.0000i	−1.17954	+	1.17954i
$185$	2.00000			0.147043
$186$		0			0
$187$			12.0000i			0.877527i
$188$			8.00000i			0.583460i
$189$		0			0
$190$	4.00000	+	4.00000i	0.290191	+	0.290191i
$191$	−16.0000			−1.15772			−0.578860	−	0.815427i	$-0.696502\pi$
$191$	−16.0000			−1.15772			−0.578860	+	0.815427i	$0.696502\pi$
$192$		0			0
$193$	−26.0000			−1.87152			−0.935760	−	0.352636i	$-0.885285\pi$
$193$	−26.0000			−1.87152			−0.935760	+	0.352636i	$0.885285\pi$
$194$	−2.00000	−	2.00000i	−0.143592	−	0.143592i
$195$		0			0
$196$			18.0000i			1.28571i
$197$			14.0000i			0.997459i	0.866758	+	0.498729i	$0.166200\pi$
$197$			14.0000i			0.997459i	−0.866758	+	0.498729i	$0.833800\pi$
$198$		0			0
$199$	−6.00000			−0.425329			−0.212664	−	0.977125i	$-0.568214\pi$
$199$	−6.00000			−0.425329			−0.212664	+	0.977125i	$0.568214\pi$
$200$	−2.00000	+	2.00000i	−0.141421	+	0.141421i
$201$		0			0
$202$	−10.0000	+	10.0000i	−0.703598	+	0.703598i
$203$		−	24.0000i		−	1.68447i
$204$		0			0
$205$			4.00000i			0.279372i
$206$	8.00000	+	8.00000i	0.557386	+	0.557386i
$207$		0			0
$208$		−	24.0000i		−	1.66410i
$209$	−8.00000			−0.553372
$210$		0			0
$211$			12.0000i			0.826114i	0.910705	+	0.413057i	$0.135539\pi$
$211$			12.0000i			0.826114i	−0.910705	+	0.413057i	$0.864461\pi$
$212$	20.0000			1.37361
$213$		0			0
$214$	−20.0000	+	20.0000i	−1.36717	+	1.36717i
$215$	4.00000			0.272798
$216$		0			0
$217$	8.00000			0.543075
$218$	8.00000	−	8.00000i	0.541828	−	0.541828i
$219$		0			0
$220$		−	4.00000i		−	0.269680i
$221$		−	36.0000i		−	2.42162i
$222$		0			0
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$	−16.0000	−	16.0000i	−1.06904	−	1.06904i
$225$		0			0
$226$	6.00000	+	6.00000i	0.399114	+	0.399114i
$227$			12.0000i			0.796468i	0.917284	+	0.398234i	$0.130377\pi$
$227$			12.0000i			0.796468i	−0.917284	+	0.398234i	$0.869623\pi$
$228$		0			0
$229$		−	20.0000i		−	1.32164i	−0.750546	−	0.660819i	$-0.770209\pi$
$229$		−	20.0000i		−	1.32164i	0.750546	−	0.660819i	$-0.229791\pi$
$230$	8.00000	−	8.00000i	0.527504	−	0.527504i
$231$		0			0
$232$	12.0000	+	12.0000i	0.787839	+	0.787839i
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$		−	4.00000i		−	0.260931i
$236$	−4.00000			−0.260378
$237$		0			0
$238$	−24.0000	−	24.0000i	−1.55569	−	1.55569i
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	−18.0000			−1.15948			−0.579741	−	0.814801i	$-0.696846\pi$
$241$	−18.0000			−1.15948			−0.579741	+	0.814801i	$0.696846\pi$
$242$	−7.00000	−	7.00000i	−0.449977	−	0.449977i
$243$		0			0
$244$	8.00000			0.512148
$245$		−	9.00000i		−	0.574989i
$246$		0			0
$247$	24.0000			1.52708
$248$	−4.00000	+	4.00000i	−0.254000	+	0.254000i
$249$		0			0
$250$	1.00000	−	1.00000i	0.0632456	−	0.0632456i
$251$			18.0000i			1.13615i	0.822977	+	0.568075i	$0.192312\pi$
$251$			18.0000i			1.13615i	−0.822977	+	0.568075i	$0.807688\pi$
$252$		0			0
$253$			16.0000i			1.00591i
$254$		0			0
$255$		0			0
$256$	16.0000			1.00000
$257$	−22.0000			−1.37232			−0.686161	−	0.727450i	$-0.740706\pi$
$257$	−22.0000			−1.37232			−0.686161	+	0.727450i	$0.740706\pi$
$258$		0			0
$259$		−	8.00000i		−	0.497096i
$260$			12.0000i			0.744208i
$261$		0			0
$262$	18.0000	−	18.0000i	1.11204	−	1.11204i
$263$	12.0000			0.739952			0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000			0.739952			0.369976	+	0.929041i	$0.379366\pi$
$264$		0			0
$265$	−10.0000			−0.614295
$266$	16.0000	−	16.0000i	0.981023	−	0.981023i
$267$		0			0
$268$	24.0000			1.46603
$269$		−	2.00000i		−	0.121942i	−0.998140	−	0.0609711i	$-0.980580\pi$
$269$		−	2.00000i		−	0.121942i	0.998140	−	0.0609711i	$-0.0194197\pi$
$270$		0			0
$271$	−2.00000			−0.121491			−0.0607457	−	0.998153i	$-0.519348\pi$
$271$	−2.00000			−0.121491			−0.0607457	+	0.998153i	$0.519348\pi$
$272$	24.0000			1.45521
$273$		0			0
$274$	−2.00000	−	2.00000i	−0.120824	−	0.120824i
$275$			2.00000i			0.120605i
$276$		0			0
$277$		−	2.00000i		−	0.120168i	−0.998193	−	0.0600842i	$-0.980863\pi$
$277$		−	2.00000i		−	0.120168i	0.998193	−	0.0600842i	$-0.0191369\pi$
$278$	4.00000	−	4.00000i	0.239904	−	0.239904i
$279$		0			0
$280$	8.00000	+	8.00000i	0.478091	+	0.478091i
$281$	28.0000			1.67034			0.835170	−	0.549992i	$-0.185369\pi$
$281$	28.0000			1.67034			0.835170	+	0.549992i	$0.185369\pi$
$282$		0			0
$283$			28.0000i			1.66443i	0.554455	+	0.832214i	$0.312927\pi$
$283$			28.0000i			1.66443i	−0.554455	+	0.832214i	$0.687073\pi$
$284$		−	16.0000i		−	0.949425i
$285$		0			0
$286$	−12.0000	−	12.0000i	−0.709575	−	0.709575i
$287$	16.0000			0.944450
$288$		0			0
$289$	19.0000			1.11765
$290$	−6.00000	−	6.00000i	−0.352332	−	0.352332i
$291$		0			0
$292$			20.0000i			1.17041i
$293$			22.0000i			1.28525i	0.766179	+	0.642627i	$0.222155\pi$
$293$			22.0000i			1.28525i	−0.766179	+	0.642627i	$0.777845\pi$
$294$		0			0
$295$	2.00000			0.116445
$296$	4.00000	+	4.00000i	0.232495	+	0.232495i
$297$		0			0
$298$	6.00000	−	6.00000i	0.347571	−	0.347571i
$299$		−	48.0000i		−	2.77591i
$300$		0			0
$301$		−	16.0000i		−	0.922225i
$302$	2.00000	+	2.00000i	0.115087	+	0.115087i
$303$		0			0
$304$			16.0000i			0.917663i
$305$	−4.00000			−0.229039
$306$		0			0
$307$		−	16.0000i		−	0.913168i	−0.889680	−	0.456584i	$-0.849073\pi$
$307$		−	16.0000i		−	0.913168i	0.889680	−	0.456584i	$-0.150927\pi$
$308$	−16.0000			−0.911685
$309$		0			0
$310$	2.00000	−	2.00000i	0.113592	−	0.113592i
$311$	−32.0000			−1.81455			−0.907277	−	0.420534i	$-0.861843\pi$
$311$	−32.0000			−1.81455			−0.907277	+	0.420534i	$0.861843\pi$
$312$		0			0
$313$	18.0000			1.01742			0.508710	−	0.860938i	$-0.330123\pi$
$313$	18.0000			1.01742			0.508710	+	0.860938i	$0.330123\pi$
$314$	−14.0000	+	14.0000i	−0.790066	+	0.790066i
$315$		0			0
$316$		−	4.00000i		−	0.225018i
$317$		−	6.00000i		−	0.336994i	−0.985702	−	0.168497i	$-0.946109\pi$
$317$		−	6.00000i		−	0.336994i	0.985702	−	0.168497i	$-0.0538913\pi$
$318$		0			0
$319$	12.0000			0.671871
$320$	−8.00000			−0.447214
$321$		0			0
$322$	−32.0000	−	32.0000i	−1.78329	−	1.78329i
$323$			24.0000i			1.33540i
$324$		0			0
$325$		−	6.00000i		−	0.332820i
$326$	16.0000	−	16.0000i	0.886158	−	0.886158i
$327$		0			0
$328$	−8.00000	+	8.00000i	−0.441726	+	0.441726i
$329$	−16.0000			−0.882109
$330$		0			0
$331$		−	4.00000i		−	0.219860i	−0.993939	−	0.109930i	$-0.964937\pi$
$331$		−	4.00000i		−	0.219860i	0.993939	−	0.109930i	$-0.0350627\pi$
$332$		0			0
$333$		0			0
$334$	−12.0000	−	12.0000i	−0.656611	−	0.656611i
$335$	−12.0000			−0.655630
$336$		0			0
$337$	−18.0000			−0.980522			−0.490261	−	0.871576i	$-0.663099\pi$
$337$	−18.0000			−0.980522			−0.490261	+	0.871576i	$0.663099\pi$
$338$	23.0000	+	23.0000i	1.25104	+	1.25104i
$339$		0			0
$340$	−12.0000			−0.650791
$341$			4.00000i			0.216612i
$342$		0			0
$343$	−8.00000			−0.431959
$344$	8.00000	+	8.00000i	0.431331	+	0.431331i
$345$		0			0
$346$	14.0000	−	14.0000i	0.752645	−	0.752645i
$347$		−	20.0000i		−	1.07366i	−0.843692	−	0.536828i	$-0.819622\pi$
$347$		−	20.0000i		−	1.07366i	0.843692	−	0.536828i	$-0.180378\pi$
$348$		0			0
$349$		−	20.0000i		−	1.07058i	−0.844670	−	0.535288i	$-0.820203\pi$
$349$		−	20.0000i		−	1.07058i	0.844670	−	0.535288i	$-0.179797\pi$
$350$	−4.00000	−	4.00000i	−0.213809	−	0.213809i
$351$		0			0
$352$	8.00000	−	8.00000i	0.426401	−	0.426401i
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$		0			0
$355$			8.00000i			0.424596i
$356$			8.00000i			0.423999i
$357$		0			0
$358$	6.00000	−	6.00000i	0.317110	−	0.317110i
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−16.0000	+	16.0000i	−0.840941	+	0.840941i
$363$		0			0
$364$	48.0000			2.51588
$365$		−	10.0000i		−	0.523424i
$366$		0			0
$367$	−12.0000			−0.626395			−0.313197	−	0.949688i	$-0.601400\pi$
$367$	−12.0000			−0.626395			−0.313197	+	0.949688i	$0.601400\pi$
$368$	32.0000			1.66812
$369$		0			0
$370$	−2.00000	−	2.00000i	−0.103975	−	0.103975i
$371$			40.0000i			2.07670i
$372$		0			0
$373$		−	26.0000i		−	1.34623i	−0.739538	−	0.673114i	$-0.764956\pi$
$373$		−	26.0000i		−	1.34623i	0.739538	−	0.673114i	$-0.235044\pi$
$374$	12.0000	−	12.0000i	0.620505	−	0.620505i
$375$		0			0
$376$	8.00000	−	8.00000i	0.412568	−	0.412568i
$377$	−36.0000			−1.85409
$378$		0			0
$379$			12.0000i			0.616399i	0.951322	+	0.308199i	$0.0997264\pi$
$379$			12.0000i			0.616399i	−0.951322	+	0.308199i	$0.900274\pi$
$380$		−	8.00000i		−	0.410391i
$381$		0			0
$382$	16.0000	+	16.0000i	0.818631	+	0.818631i
$383$		0			0			−	1.00000i	$-0.5\pi$
$383$		0			0				1.00000i	$0.5\pi$
$384$		0			0
$385$	8.00000			0.407718
$386$	26.0000	+	26.0000i	1.32337	+	1.32337i
$387$		0			0
$388$			4.00000i			0.203069i
$389$			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
$391$	48.0000			2.42746
$392$	18.0000	−	18.0000i	0.909137	−	0.909137i
$393$		0			0
$394$	14.0000	−	14.0000i	0.705310	−	0.705310i
$395$			2.00000i			0.100631i
$396$		0			0
$397$		−	2.00000i		−	0.100377i	−0.998740	−	0.0501886i	$-0.984018\pi$
$397$		−	2.00000i		−	0.100377i	0.998740	−	0.0501886i	$-0.0159822\pi$
$398$	6.00000	+	6.00000i	0.300753	+	0.300753i
$399$		0			0
$400$	4.00000			0.200000
$401$	−24.0000			−1.19850			−0.599251	−	0.800561i	$-0.704535\pi$
$401$	−24.0000			−1.19850			−0.599251	+	0.800561i	$0.704535\pi$
$402$		0			0
$403$		−	12.0000i		−	0.597763i
$404$	20.0000			0.995037
$405$		0			0
$406$	−24.0000	+	24.0000i	−1.19110	+	1.19110i
$407$	4.00000			0.198273
$408$		0			0
$409$	−30.0000			−1.48340			−0.741702	−	0.670729i	$-0.765981\pi$
$409$	−30.0000			−1.48340			−0.741702	+	0.670729i	$0.765981\pi$
$410$	4.00000	−	4.00000i	0.197546	−	0.197546i
$411$		0			0
$412$		−	16.0000i		−	0.788263i
$413$		−	8.00000i		−	0.393654i
$414$		0			0
$415$		0			0
$416$	−24.0000	+	24.0000i	−1.17670	+	1.17670i
$417$		0			0
$418$	8.00000	+	8.00000i	0.391293	+	0.391293i
$419$			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
$421$			4.00000i			0.194948i	0.995238	+	0.0974740i	$0.0310763\pi$
$421$			4.00000i			0.194948i	−0.995238	+	0.0974740i	$0.968924\pi$
$422$	12.0000	−	12.0000i	0.584151	−	0.584151i
$423$		0			0
$424$	−20.0000	−	20.0000i	−0.971286	−	0.971286i
$425$	6.00000			0.291043
$426$		0			0
$427$			16.0000i			0.774294i
$428$	40.0000			1.93347
$429$		0			0
$430$	−4.00000	−	4.00000i	−0.192897	−	0.192897i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$		0			0
$433$	−10.0000			−0.480569			−0.240285	−	0.970702i	$-0.577241\pi$
$433$	−10.0000			−0.480569			−0.240285	+	0.970702i	$0.577241\pi$
$434$	−8.00000	−	8.00000i	−0.384012	−	0.384012i
$435$		0			0
$436$	−16.0000			−0.766261
$437$			32.0000i			1.53077i
$438$		0			0
$439$	26.0000			1.24091			0.620456	−	0.784241i	$-0.286947\pi$
$439$	26.0000			1.24091			0.620456	+	0.784241i	$0.286947\pi$
$440$	−4.00000	+	4.00000i	−0.190693	+	0.190693i
$441$		0			0
$442$	−36.0000	+	36.0000i	−1.71235	+	1.71235i
$443$			4.00000i			0.190046i	0.995475	+	0.0950229i	$0.0302924\pi$
$443$			4.00000i			0.190046i	−0.995475	+	0.0950229i	$0.969708\pi$
$444$		0			0
$445$		−	4.00000i		−	0.189618i
$446$	−16.0000	−	16.0000i	−0.757622	−	0.757622i
$447$		0			0
$448$			32.0000i			1.51186i
$449$	−24.0000			−1.13263			−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000			−1.13263			−0.566315	+	0.824189i	$0.691631\pi$
$450$		0			0
$451$			8.00000i			0.376705i
$452$		−	12.0000i		−	0.564433i
$453$		0			0
$454$	12.0000	−	12.0000i	0.563188	−	0.563188i
$455$	−24.0000			−1.12514
$456$		0			0
$457$	−18.0000			−0.842004			−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000			−0.842004			−0.421002	+	0.907060i	$0.638322\pi$
$458$	−20.0000	+	20.0000i	−0.934539	+	0.934539i
$459$		0			0
$460$	−16.0000			−0.746004
$461$			2.00000i			0.0931493i	0.998915	+	0.0465746i	$0.0148305\pi$
$461$			2.00000i			0.0931493i	−0.998915	+	0.0465746i	$0.985169\pi$
$462$		0			0
$463$	20.0000			0.929479			0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000			0.929479			0.464739	+	0.885448i	$0.346148\pi$
$464$		−	24.0000i		−	1.11417i
$465$		0			0
$466$	6.00000	+	6.00000i	0.277945	+	0.277945i
$467$		−	32.0000i		−	1.48078i	−0.672176	−	0.740392i	$-0.734640\pi$
$467$		−	32.0000i		−	1.48078i	0.672176	−	0.740392i	$-0.265360\pi$
$468$		0			0
$469$			48.0000i			2.21643i
$470$	−4.00000	+	4.00000i	−0.184506	+	0.184506i
$471$		0			0
$472$	4.00000	+	4.00000i	0.184115	+	0.184115i
$473$	8.00000			0.367840
$474$		0			0
$475$			4.00000i			0.183533i
$476$			48.0000i			2.20008i
$477$		0			0
$478$	16.0000	+	16.0000i	0.731823	+	0.731823i
$479$	32.0000			1.46212			0.731059	−	0.682315i	$-0.239027\pi$
$479$	32.0000			1.46212			0.731059	+	0.682315i	$0.239027\pi$
$480$		0			0
$481$	−12.0000			−0.547153
$482$	18.0000	+	18.0000i	0.819878	+	0.819878i
$483$		0			0
$484$			14.0000i			0.636364i
$485$		−	2.00000i		−	0.0908153i
$486$		0			0
$487$	−24.0000			−1.08754			−0.543772	−	0.839233i	$-0.683004\pi$
$487$	−24.0000			−1.08754			−0.543772	+	0.839233i	$0.683004\pi$
$488$	−8.00000	−	8.00000i	−0.362143	−	0.362143i
$489$		0			0
$490$	−9.00000	+	9.00000i	−0.406579	+	0.406579i
$491$		−	34.0000i		−	1.53440i	−0.641409	−	0.767199i	$-0.721650\pi$
$491$		−	34.0000i		−	1.53440i	0.641409	−	0.767199i	$-0.278350\pi$
$492$		0			0
$493$		−	36.0000i		−	1.62136i
$494$	−24.0000	−	24.0000i	−1.07981	−	1.07981i
$495$		0			0
$496$	8.00000			0.359211
$497$	32.0000			1.43540
$498$		0			0
$499$			20.0000i			0.895323i	0.894203	+	0.447661i	$0.147743\pi$
$499$			20.0000i			0.895323i	−0.894203	+	0.447661i	$0.852257\pi$
$500$	−2.00000			−0.0894427
$501$		0			0
$502$	18.0000	−	18.0000i	0.803379	−	0.803379i
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$	−10.0000			−0.444994
$506$	16.0000	−	16.0000i	0.711287	−	0.711287i
$507$		0			0
$508$		0			0
$509$		−	30.0000i		−	1.32973i	−0.746965	−	0.664863i	$-0.768490\pi$
$509$		−	30.0000i		−	1.32973i	0.746965	−	0.664863i	$-0.231510\pi$
$510$		0			0
$511$	−40.0000			−1.76950
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$		0			0
$514$	22.0000	+	22.0000i	0.970378	+	0.970378i
$515$			8.00000i			0.352522i
$516$		0			0
$517$		−	8.00000i		−	0.351840i
$518$	−8.00000	+	8.00000i	−0.351500	+	0.351500i
$519$		0			0
$520$	12.0000	−	12.0000i	0.526235	−	0.526235i
$521$	24.0000			1.05146			0.525730	−	0.850652i	$-0.323792\pi$
$521$	24.0000			1.05146			0.525730	+	0.850652i	$0.323792\pi$
$522$		0			0
$523$		−	40.0000i		−	1.74908i	−0.484955	−	0.874539i	$-0.661164\pi$
$523$		−	40.0000i		−	1.74908i	0.484955	−	0.874539i	$-0.338836\pi$
$524$	−36.0000			−1.57267
$525$		0			0
$526$	−12.0000	−	12.0000i	−0.523225	−	0.523225i
$527$	12.0000			0.522728
$528$		0			0
$529$	41.0000			1.78261
$530$	10.0000	+	10.0000i	0.434372	+	0.434372i
$531$		0			0
$532$	−32.0000			−1.38738
$533$		−	24.0000i		−	1.03956i
$534$		0			0
$535$	−20.0000			−0.864675
$536$	−24.0000	−	24.0000i	−1.03664	−	1.03664i
$537$		0			0
$538$	−2.00000	+	2.00000i	−0.0862261	+	0.0862261i
$539$		−	18.0000i		−	0.775315i
$540$		0			0
$541$			32.0000i			1.37579i	0.725811	+	0.687894i	$0.241464\pi$
$541$			32.0000i			1.37579i	−0.725811	+	0.687894i	$0.758536\pi$
$542$	2.00000	+	2.00000i	0.0859074	+	0.0859074i
$543$		0			0
$544$	−24.0000	−	24.0000i	−1.02899	−	1.02899i
$545$	8.00000			0.342682
$546$		0			0
$547$			28.0000i			1.19719i	0.801050	+	0.598597i	$0.204275\pi$
$547$			28.0000i			1.19719i	−0.801050	+	0.598597i	$0.795725\pi$
$548$			4.00000i			0.170872i
$549$		0			0
$550$	2.00000	−	2.00000i	0.0852803	−	0.0852803i
$551$	24.0000			1.02243
$552$		0			0
$553$	8.00000			0.340195
$554$	−2.00000	+	2.00000i	−0.0849719	+	0.0849719i
$555$		0			0
$556$	−8.00000			−0.339276
$557$			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
$559$	−24.0000			−1.01509
$560$		−	16.0000i		−	0.676123i
$561$		0			0
$562$	−28.0000	−	28.0000i	−1.18111	−	1.18111i
$563$			36.0000i			1.51722i	0.651546	+	0.758610i	$0.274121\pi$
$563$			36.0000i			1.51722i	−0.651546	+	0.758610i	$0.725879\pi$
$564$		0			0
$565$			6.00000i			0.252422i
$566$	28.0000	−	28.0000i	1.17693	−	1.17693i
$567$		0			0
$568$	−16.0000	+	16.0000i	−0.671345	+	0.671345i
$569$	−32.0000			−1.34151			−0.670755	−	0.741679i	$-0.734030\pi$
$569$	−32.0000			−1.34151			−0.670755	+	0.741679i	$0.734030\pi$
$570$		0			0
$571$			20.0000i			0.836974i	0.908223	+	0.418487i	$0.137439\pi$
$571$			20.0000i			0.836974i	−0.908223	+	0.418487i	$0.862561\pi$
$572$			24.0000i			1.00349i
$573$		0			0
$574$	−16.0000	−	16.0000i	−0.667827	−	0.667827i
$575$	8.00000			0.333623
$576$		0			0
$577$	10.0000			0.416305			0.208153	−	0.978096i	$-0.433255\pi$
$577$	10.0000			0.416305			0.208153	+	0.978096i	$0.433255\pi$
$578$	−19.0000	−	19.0000i	−0.790296	−	0.790296i
$579$		0			0
$580$			12.0000i			0.498273i
$581$		0			0
$582$		0			0
$583$	−20.0000			−0.828315
$584$	20.0000	−	20.0000i	0.827606	−	0.827606i
$585$		0			0
$586$	22.0000	−	22.0000i	0.908812	−	0.908812i
$587$		−	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
$589$			8.00000i			0.329634i
$590$	−2.00000	−	2.00000i	−0.0823387	−	0.0823387i
$591$		0			0
$592$		−	8.00000i		−	0.328798i
$593$	26.0000			1.06769			0.533846	−	0.845582i	$-0.320746\pi$
$593$	26.0000			1.06769			0.533846	+	0.845582i	$0.320746\pi$
$594$		0			0
$595$		−	24.0000i		−	0.983904i
$596$	−12.0000			−0.491539
$597$		0			0
$598$	−48.0000	+	48.0000i	−1.96287	+	1.96287i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	22.0000			0.897399			0.448699	−	0.893683i	$-0.351887\pi$
$601$	22.0000			0.897399			0.448699	+	0.893683i	$0.351887\pi$
$602$	−16.0000	+	16.0000i	−0.652111	+	0.652111i
$603$		0			0
$604$		−	4.00000i		−	0.162758i
$605$		−	7.00000i		−	0.284590i
$606$		0			0
$607$	−4.00000			−0.162355			−0.0811775	−	0.996700i	$-0.525868\pi$
$607$	−4.00000			−0.162355			−0.0811775	+	0.996700i	$0.525868\pi$
$608$	16.0000	−	16.0000i	0.648886	−	0.648886i
$609$		0			0
$610$	4.00000	+	4.00000i	0.161955	+	0.161955i
$611$			24.0000i			0.970936i
$612$		0			0
$613$			26.0000i			1.05013i	0.851062	+	0.525065i	$0.175959\pi$
$613$			26.0000i			1.05013i	−0.851062	+	0.525065i	$0.824041\pi$
$614$	−16.0000	+	16.0000i	−0.645707	+	0.645707i
$615$		0			0
$616$	16.0000	+	16.0000i	0.644658	+	0.644658i
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$		0			0
$619$		−	20.0000i		−	0.803868i	−0.915669	−	0.401934i	$-0.868338\pi$
$619$		−	20.0000i		−	0.803868i	0.915669	−	0.401934i	$-0.131662\pi$
$620$	−4.00000			−0.160644
$621$		0			0
$622$	32.0000	+	32.0000i	1.28308	+	1.28308i
$623$	−16.0000			−0.641026
$624$		0			0
$625$	1.00000			0.0400000
$626$	−18.0000	−	18.0000i	−0.719425	−	0.719425i
$627$		0			0
$628$	28.0000			1.11732
$629$		−	12.0000i		−	0.478471i
$630$		0			0
$631$	−30.0000			−1.19428			−0.597141	−	0.802137i	$-0.703697\pi$
$631$	−30.0000			−1.19428			−0.597141	+	0.802137i	$0.703697\pi$
$632$	−4.00000	+	4.00000i	−0.159111	+	0.159111i
$633$		0			0
$634$	−6.00000	+	6.00000i	−0.238290	+	0.238290i
$635$		0			0
$636$		0			0
$637$			54.0000i			2.13956i
$638$	−12.0000	−	12.0000i	−0.475085	−	0.475085i
$639$		0			0
$640$	8.00000	+	8.00000i	0.316228	+	0.316228i
$641$	4.00000			0.157991			0.0789953	−	0.996875i	$-0.474829\pi$
$641$	4.00000			0.157991			0.0789953	+	0.996875i	$0.474829\pi$
$642$		0			0
$643$		−	24.0000i		−	0.946468i	−0.880937	−	0.473234i	$-0.843087\pi$
$643$		−	24.0000i		−	0.946468i	0.880937	−	0.473234i	$-0.156913\pi$
$644$			64.0000i			2.52195i
$645$		0			0
$646$	24.0000	−	24.0000i	0.944267	−	0.944267i
$647$	12.0000			0.471769			0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$		0			0
$649$	4.00000			0.157014
$650$	−6.00000	+	6.00000i	−0.235339	+	0.235339i
$651$		0			0
$652$	−32.0000			−1.25322
$653$			6.00000i			0.234798i	0.993085	+	0.117399i	$0.0374557\pi$
$653$			6.00000i			0.234798i	−0.993085	+	0.117399i	$0.962544\pi$
$654$		0			0
$655$	18.0000			0.703318
$656$	16.0000			0.624695
$657$		0			0
$658$	16.0000	+	16.0000i	0.623745	+	0.623745i
$659$			18.0000i			0.701180i	0.936529	+	0.350590i	$0.114019\pi$
$659$			18.0000i			0.701180i	−0.936529	+	0.350590i	$0.885981\pi$
$660$		0			0
$661$			28.0000i			1.08907i	0.838737	+	0.544537i	$0.183295\pi$
$661$			28.0000i			1.08907i	−0.838737	+	0.544537i	$0.816705\pi$
$662$	−4.00000	+	4.00000i	−0.155464	+	0.155464i
$663$		0			0
$664$		0			0
$665$	16.0000			0.620453
$666$		0			0
$667$		−	48.0000i		−	1.85857i
$668$			24.0000i			0.928588i
$669$		0			0
$670$	12.0000	+	12.0000i	0.463600	+	0.463600i
$671$	−8.00000			−0.308837
$672$		0			0
$673$	−2.00000			−0.0770943			−0.0385472	−	0.999257i	$-0.512273\pi$
$673$	−2.00000			−0.0770943			−0.0385472	+	0.999257i	$0.512273\pi$
$674$	18.0000	+	18.0000i	0.693334	+	0.693334i
$675$		0			0
$676$		−	46.0000i		−	1.76923i
$677$		−	14.0000i		−	0.538064i	−0.963131	−	0.269032i	$-0.913296\pi$
$677$		−	14.0000i		−	0.538064i	0.963131	−	0.269032i	$-0.0867037\pi$
$678$		0			0
$679$	−8.00000			−0.307012
$680$	12.0000	+	12.0000i	0.460179	+	0.460179i
$681$		0			0
$682$	4.00000	−	4.00000i	0.153168	−	0.153168i
$683$		−	24.0000i		−	0.918334i	−0.888350	−	0.459167i	$-0.848148\pi$
$683$		−	24.0000i		−	0.918334i	0.888350	−	0.459167i	$-0.151852\pi$
$684$		0			0
$685$		−	2.00000i		−	0.0764161i
$686$	8.00000	+	8.00000i	0.305441	+	0.305441i
$687$		0			0
$688$		−	16.0000i		−	0.609994i
$689$	60.0000			2.28582
$690$		0			0
$691$		−	12.0000i		−	0.456502i	−0.973602	−	0.228251i	$-0.926699\pi$
$691$		−	12.0000i		−	0.456502i	0.973602	−	0.228251i	$-0.0733006\pi$
$692$	−28.0000			−1.06440
$693$		0			0
$694$	−20.0000	+	20.0000i	−0.759190	+	0.759190i
$695$	4.00000			0.151729
$696$		0			0
$697$	24.0000			0.909065
$698$	−20.0000	+	20.0000i	−0.757011	+	0.757011i
$699$		0			0
$700$			8.00000i			0.302372i
$701$			2.00000i			0.0755390i	0.999286	+	0.0377695i	$0.0120253\pi$
$701$			2.00000i			0.0755390i	−0.999286	+	0.0377695i	$0.987975\pi$
$702$		0			0
$703$	8.00000			0.301726
$704$	−16.0000			−0.603023
$705$		0			0
$706$	−6.00000	−	6.00000i	−0.225813	−	0.225813i
$707$			40.0000i			1.50435i
$708$		0			0
$709$		−	44.0000i		−	1.65245i	−0.563337	−	0.826227i	$-0.690483\pi$
$709$		−	44.0000i		−	1.65245i	0.563337	−	0.826227i	$-0.309517\pi$
$710$	8.00000	−	8.00000i	0.300235	−	0.300235i
$711$		0			0
$712$	8.00000	−	8.00000i	0.299813	−	0.299813i
$713$	16.0000			0.599205
$714$		0			0
$715$		−	12.0000i		−	0.448775i
$716$	−12.0000			−0.448461
$717$		0			0
$718$	24.0000	+	24.0000i	0.895672	+	0.895672i
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$		0			0
$721$	32.0000			1.19174
$722$	−3.00000	−	3.00000i	−0.111648	−	0.111648i
$723$		0			0
$724$	32.0000			1.18927
$725$		−	6.00000i		−	0.222834i
$726$		0			0
$727$	40.0000			1.48352			0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000			1.48352			0.741759	+	0.670667i	$0.233992\pi$
$728$	−48.0000	−	48.0000i	−1.77900	−	1.77900i
$729$		0			0
$730$	−10.0000	+	10.0000i	−0.370117	+	0.370117i
$731$		−	24.0000i		−	0.887672i
$732$		0			0
$733$		−	6.00000i		−	0.221615i	−0.993842	−	0.110808i	$-0.964656\pi$
$733$		−	6.00000i		−	0.221615i	0.993842	−	0.110808i	$-0.0353437\pi$
$734$	12.0000	+	12.0000i	0.442928	+	0.442928i
$735$		0			0
$736$	−32.0000	−	32.0000i	−1.17954	−	1.17954i
$737$	−24.0000			−0.884051
$738$		0			0
$739$		−	12.0000i		−	0.441427i	−0.975339	−	0.220714i	$-0.929161\pi$
$739$		−	12.0000i		−	0.441427i	0.975339	−	0.220714i	$-0.0708386\pi$
$740$			4.00000i			0.147043i
$741$		0			0
$742$	40.0000	−	40.0000i	1.46845	−	1.46845i
$743$	48.0000			1.76095			0.880475	−	0.474093i	$-0.157224\pi$
$743$	48.0000			1.76095			0.880475	+	0.474093i	$0.157224\pi$
$744$		0			0
$745$	6.00000			0.219823
$746$	−26.0000	+	26.0000i	−0.951928	+	0.951928i
$747$		0			0
$748$	−24.0000			−0.877527
$749$			80.0000i			2.92314i
$750$		0			0
$751$	−10.0000			−0.364905			−0.182453	−	0.983215i	$-0.558404\pi$
$751$	−10.0000			−0.364905			−0.182453	+	0.983215i	$0.558404\pi$
$752$	−16.0000			−0.583460
$753$		0			0
$754$	36.0000	+	36.0000i	1.31104	+	1.31104i
$755$			2.00000i			0.0727875i
$756$		0			0
$757$		−	10.0000i		−	0.363456i	−0.983349	−	0.181728i	$-0.941831\pi$
$757$		−	10.0000i		−	0.363456i	0.983349	−	0.181728i	$-0.0581691\pi$
$758$	12.0000	−	12.0000i	0.435860	−	0.435860i
$759$		0			0
$760$	−8.00000	+	8.00000i	−0.290191	+	0.290191i
$761$	8.00000			0.290000			0.145000	−	0.989432i	$-0.453682\pi$
$761$	8.00000			0.290000			0.145000	+	0.989432i	$0.453682\pi$
$762$		0			0
$763$		−	32.0000i		−	1.15848i
$764$		−	32.0000i		−	1.15772i
$765$		0			0
$766$		0			0
$767$	−12.0000			−0.433295
$768$		0			0
$769$	−18.0000			−0.649097			−0.324548	−	0.945869i	$-0.605212\pi$
$769$	−18.0000			−0.649097			−0.324548	+	0.945869i	$0.605212\pi$
$770$	−8.00000	−	8.00000i	−0.288300	−	0.288300i
$771$		0			0
$772$		−	52.0000i		−	1.87152i
$773$			6.00000i			0.215805i	0.994161	+	0.107903i	$0.0344134\pi$
$773$			6.00000i			0.215805i	−0.994161	+	0.107903i	$0.965587\pi$
$774$		0			0
$775$	2.00000			0.0718421
$776$	4.00000	−	4.00000i	0.143592	−	0.143592i
$777$		0			0
$778$	10.0000	−	10.0000i	0.358517	−	0.358517i
$779$			16.0000i			0.573259i
$780$		0			0
$781$			16.0000i			0.572525i
$782$	−48.0000	−	48.0000i	−1.71648	−	1.71648i
$783$		0			0
$784$	−36.0000			−1.28571
$785$	−14.0000			−0.499681
$786$		0			0
$787$			32.0000i			1.14068i	0.821410	+	0.570338i	$0.193188\pi$
$787$			32.0000i			1.14068i	−0.821410	+	0.570338i	$0.806812\pi$
$788$	−28.0000			−0.997459
$789$		0			0
$790$	2.00000	−	2.00000i	0.0711568	−	0.0711568i
$791$	24.0000			0.853342
$792$		0			0
$793$	24.0000			0.852265
$794$	−2.00000	+	2.00000i	−0.0709773	+	0.0709773i
$795$		0			0
$796$		−	12.0000i		−	0.425329i
$797$		−	18.0000i		−	0.637593i	−0.947823	−	0.318796i	$-0.896721\pi$
$797$		−	18.0000i		−	0.637593i	0.947823	−	0.318796i	$-0.103279\pi$
$798$		0			0
$799$	−24.0000			−0.849059
$800$	−4.00000	−	4.00000i	−0.141421	−	0.141421i
$801$		0			0
$802$	24.0000	+	24.0000i	0.847469	+	0.847469i
$803$		−	20.0000i		−	0.705785i
$804$		0			0
$805$		−	32.0000i		−	1.12785i
$806$	−12.0000	+	12.0000i	−0.422682	+	0.422682i
$807$		0			0
$808$	−20.0000	−	20.0000i	−0.703598	−	0.703598i
$809$	44.0000			1.54696			0.773479	−	0.633822i	$-0.218515\pi$
$809$	44.0000			1.54696			0.773479	+	0.633822i	$0.218515\pi$
$810$		0			0
$811$			52.0000i			1.82597i	0.407997	+	0.912983i	$0.366228\pi$
$811$			52.0000i			1.82597i	−0.407997	+	0.912983i	$0.633772\pi$
$812$	48.0000			1.68447
$813$		0			0
$814$	−4.00000	−	4.00000i	−0.140200	−	0.140200i
$815$	16.0000			0.560456
$816$		0			0
$817$	16.0000			0.559769
$818$	30.0000	+	30.0000i	1.04893	+	1.04893i
$819$		0			0
$820$	−8.00000			−0.279372
$821$		−	46.0000i		−	1.60541i	−0.596376	−	0.802706i	$-0.703393\pi$
$821$		−	46.0000i		−	1.60541i	0.596376	−	0.802706i	$-0.296607\pi$
$822$		0			0
$823$	−48.0000			−1.67317			−0.836587	−	0.547833i	$-0.815453\pi$
$823$	−48.0000			−1.67317			−0.836587	+	0.547833i	$0.815453\pi$
$824$	−16.0000	+	16.0000i	−0.557386	+	0.557386i
$825$		0			0
$826$	−8.00000	+	8.00000i	−0.278356	+	0.278356i
$827$		−	16.0000i		−	0.556375i	−0.960527	−	0.278187i	$-0.910266\pi$
$827$		−	16.0000i		−	0.556375i	0.960527	−	0.278187i	$-0.0897336\pi$
$828$		0			0
$829$			8.00000i			0.277851i	0.990303	+	0.138926i	$0.0443649\pi$
$829$			8.00000i			0.277851i	−0.990303	+	0.138926i	$0.955635\pi$
$830$		0			0
$831$		0			0
$832$	48.0000			1.66410
$833$	−54.0000			−1.87099
$834$		0			0
$835$		−	12.0000i		−	0.415277i
$836$		−	16.0000i		−	0.553372i
$837$		0			0
$838$	14.0000	−	14.0000i	0.483622	−	0.483622i
$839$	−16.0000			−0.552381			−0.276191	−	0.961103i	$-0.589072\pi$
$839$	−16.0000			−0.552381			−0.276191	+	0.961103i	$0.589072\pi$
$840$		0			0
$841$	−7.00000			−0.241379
$842$	4.00000	−	4.00000i	0.137849	−	0.137849i
$843$		0			0
$844$	−24.0000			−0.826114
$845$			23.0000i			0.791224i
$846$		0			0
$847$	−28.0000			−0.962091
$848$			40.0000i			1.37361i
$849$		0			0
$850$	−6.00000	−	6.00000i	−0.205798	−	0.205798i
$851$		−	16.0000i		−	0.548473i
$852$		0			0
$853$		−	46.0000i		−	1.57501i	−0.616308	−	0.787505i	$-0.711372\pi$
$853$		−	46.0000i		−	1.57501i	0.616308	−	0.787505i	$-0.288628\pi$
$854$	16.0000	−	16.0000i	0.547509	−	0.547509i
$855$		0			0
$856$	−40.0000	−	40.0000i	−1.36717	−	1.36717i
$857$	6.00000			0.204956			0.102478	−	0.994735i	$-0.467323\pi$
$857$	6.00000			0.204956			0.102478	+	0.994735i	$0.467323\pi$
$858$		0			0
$859$		−	28.0000i		−	0.955348i	−0.878537	−	0.477674i	$-0.841480\pi$
$859$		−	28.0000i		−	0.955348i	0.878537	−	0.477674i	$-0.158520\pi$
$860$			8.00000i			0.272798i
$861$		0			0
$862$		0			0
$863$	−36.0000			−1.22545			−0.612727	−	0.790295i	$-0.709928\pi$
$863$	−36.0000			−1.22545			−0.612727	+	0.790295i	$0.709928\pi$
$864$		0			0
$865$	14.0000			0.476014
$866$	10.0000	+	10.0000i	0.339814	+	0.339814i
$867$		0			0
$868$			16.0000i			0.543075i
$869$			4.00000i			0.135691i
$870$		0			0
$871$	72.0000			2.43963
$872$	16.0000	+	16.0000i	0.541828	+	0.541828i
$873$		0			0
$874$	32.0000	−	32.0000i	1.08242	−	1.08242i
$875$		−	4.00000i		−	0.135225i
$876$		0			0
$877$			10.0000i			0.337676i	0.985644	+	0.168838i	$0.0540015\pi$
$877$			10.0000i			0.337676i	−0.985644	+	0.168838i	$0.945999\pi$
$878$	−26.0000	−	26.0000i	−0.877457	−	0.877457i
$879$		0			0
$880$	8.00000			0.269680
$881$	−12.0000			−0.404290			−0.202145	−	0.979356i	$-0.564791\pi$
$881$	−12.0000			−0.404290			−0.202145	+	0.979356i	$0.564791\pi$
$882$		0			0
$883$		−	8.00000i		−	0.269221i	−0.990899	−	0.134611i	$-0.957022\pi$
$883$		−	8.00000i		−	0.269221i	0.990899	−	0.134611i	$-0.0429784\pi$
$884$	72.0000			2.42162
$885$		0			0
$886$	4.00000	−	4.00000i	0.134383	−	0.134383i
$887$	20.0000			0.671534			0.335767	−	0.941945i	$-0.391004\pi$
$887$	20.0000			0.671534			0.335767	+	0.941945i	$0.391004\pi$
$888$		0			0
$889$		0			0
$890$	−4.00000	+	4.00000i	−0.134080	+	0.134080i
$891$		0			0
$892$			32.0000i			1.07144i
$893$		−	16.0000i		−	0.535420i
$894$		0			0
$895$	6.00000			0.200558
$896$	32.0000	−	32.0000i	1.06904	−	1.06904i
$897$		0			0
$898$	24.0000	+	24.0000i	0.800890	+	0.800890i
$899$		−	12.0000i		−	0.400222i
$900$		0			0
$901$			60.0000i			1.99889i
$902$	8.00000	−	8.00000i	0.266371	−	0.266371i
$903$		0			0
$904$	−12.0000	+	12.0000i	−0.399114	+	0.399114i
$905$	−16.0000			−0.531858
$906$		0			0
$907$			4.00000i			0.132818i	0.997792	+	0.0664089i	$0.0211542\pi$
$907$			4.00000i			0.132818i	−0.997792	+	0.0664089i	$0.978846\pi$
$908$	−24.0000			−0.796468
$909$		0			0
$910$	24.0000	+	24.0000i	0.795592	+	0.795592i
$911$	−48.0000			−1.59031			−0.795155	−	0.606406i	$-0.792611\pi$
$911$	−48.0000			−1.59031			−0.795155	+	0.606406i	$0.792611\pi$
$912$		0			0
$913$		0			0
$914$	18.0000	+	18.0000i	0.595387	+	0.595387i
$915$		0			0
$916$	40.0000			1.32164
$917$		−	72.0000i		−	2.37765i
$918$		0			0
$919$	−14.0000			−0.461817			−0.230909	−	0.972975i	$-0.574170\pi$
$919$	−14.0000			−0.461817			−0.230909	+	0.972975i	$0.574170\pi$
$920$	16.0000	+	16.0000i	0.527504	+	0.527504i
$921$		0			0
$922$	2.00000	−	2.00000i	0.0658665	−	0.0658665i
$923$		−	48.0000i		−	1.57994i
$924$		0			0
$925$		−	2.00000i		−	0.0657596i
$926$	−20.0000	−	20.0000i	−0.657241	−	0.657241i
$927$		0			0
$928$	−24.0000	+	24.0000i	−0.787839	+	0.787839i
$929$	−16.0000			−0.524943			−0.262471	−	0.964940i	$-0.584538\pi$
$929$	−16.0000			−0.524943			−0.262471	+	0.964940i	$0.584538\pi$
$930$		0			0
$931$		−	36.0000i		−	1.17985i
$932$		−	12.0000i		−	0.393073i
$933$		0			0
$934$	−32.0000	+	32.0000i	−1.04707	+	1.04707i
$935$	12.0000			0.392442
$936$		0			0
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$	48.0000	−	48.0000i	1.56726	−	1.56726i
$939$		0			0
$940$	8.00000			0.260931
$941$			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
$943$	32.0000			1.04206
$944$		−	8.00000i		−	0.260378i
$945$		0			0
$946$	−8.00000	−	8.00000i	−0.260102	−	0.260102i
$947$			48.0000i			1.55979i	0.625910	+	0.779895i	$0.284728\pi$
$947$			48.0000i			1.55979i	−0.625910	+	0.779895i	$0.715272\pi$
$948$		0			0
$949$			60.0000i			1.94768i
$950$	4.00000	−	4.00000i	0.129777	−	0.129777i
$951$		0			0
$952$	48.0000	−	48.0000i	1.55569	−	1.55569i
$953$	−46.0000			−1.49009			−0.745043	−	0.667016i	$-0.767571\pi$
$953$	−46.0000			−1.49009			−0.745043	+	0.667016i	$0.767571\pi$
$954$		0			0
$955$			16.0000i			0.517748i
$956$		−	32.0000i		−	1.03495i
$957$		0			0
$958$	−32.0000	−	32.0000i	−1.03387	−	1.03387i
$959$	−8.00000			−0.258333
$960$		0			0
$961$	−27.0000			−0.870968
$962$	12.0000	+	12.0000i	0.386896	+	0.386896i
$963$		0			0
$964$		−	36.0000i		−	1.15948i
$965$			26.0000i			0.836970i
$966$		0			0
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$	14.0000	−	14.0000i	0.449977	−	0.449977i
$969$		0			0
$970$	−2.00000	+	2.00000i	−0.0642161	+	0.0642161i
$971$			42.0000i			1.34784i	0.738802	+	0.673922i	$0.235392\pi$
$971$			42.0000i			1.34784i	−0.738802	+	0.673922i	$0.764608\pi$
$972$		0			0
$973$		−	16.0000i		−	0.512936i
$974$	24.0000	+	24.0000i	0.769010	+	0.769010i
$975$		0			0
$976$			16.0000i			0.512148i
$977$	34.0000			1.08776			0.543878	−	0.839164i	$-0.316955\pi$
$977$	34.0000			1.08776			0.543878	+	0.839164i	$0.316955\pi$
$978$		0			0
$979$		−	8.00000i		−	0.255681i
$980$	18.0000			0.574989
$981$		0			0
$982$	−34.0000	+	34.0000i	−1.08498	+	1.08498i
$983$	−16.0000			−0.510321			−0.255160	−	0.966899i	$-0.582128\pi$
$983$	−16.0000			−0.510321			−0.255160	+	0.966899i	$0.582128\pi$
$984$		0			0
$985$	14.0000			0.446077
$986$	−36.0000	+	36.0000i	−1.14647	+	1.14647i
$987$		0			0
$988$			48.0000i			1.52708i
$989$		−	32.0000i		−	1.01754i
$990$		0			0
$991$	−46.0000			−1.46124			−0.730619	−	0.682785i	$-0.760768\pi$
$991$	−46.0000			−1.46124			−0.730619	+	0.682785i	$0.760768\pi$
$992$	−8.00000	−	8.00000i	−0.254000	−	0.254000i
$993$		0			0
$994$	−32.0000	−	32.0000i	−1.01498	−	1.01498i
$995$			6.00000i			0.190213i
$996$		0			0
$997$			46.0000i			1.45683i	0.685134	+	0.728417i	$0.259744\pi$
$997$			46.0000i			1.45683i	−0.685134	+	0.728417i	$0.740256\pi$
$998$	20.0000	−	20.0000i	0.633089	−	0.633089i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.k.a.181.1	✓	2
3.2	odd	2		360.2.k.c.181.2	yes	2
4.3	odd	2		1440.2.k.b.721.1		2
5.2	odd	4		1800.2.d.j.1549.1		2
5.3	odd	4		1800.2.d.a.1549.2		2
5.4	even	2		1800.2.k.i.901.2		2
8.3	odd	2		1440.2.k.b.721.2		2
8.5	even	2	inner	360.2.k.a.181.2	yes	2
12.11	even	2		1440.2.k.c.721.2		2
15.2	even	4		1800.2.d.e.1549.2		2
15.8	even	4		1800.2.d.g.1549.1		2
15.14	odd	2		1800.2.k.c.901.1		2
20.3	even	4		7200.2.d.a.2449.1		2
20.7	even	4		7200.2.d.h.2449.2		2
20.19	odd	2		7200.2.k.c.3601.2		2
24.5	odd	2		360.2.k.c.181.1	yes	2
24.11	even	2		1440.2.k.c.721.1		2
40.3	even	4		7200.2.d.h.2449.1		2
40.13	odd	4		1800.2.d.j.1549.2		2
40.19	odd	2		7200.2.k.c.3601.1		2
40.27	even	4		7200.2.d.a.2449.2		2
40.29	even	2		1800.2.k.i.901.1		2
40.37	odd	4		1800.2.d.a.1549.1		2
60.23	odd	4		7200.2.d.b.2449.1		2
60.47	odd	4		7200.2.d.i.2449.2		2
60.59	even	2		7200.2.k.a.3601.1		2
120.29	odd	2		1800.2.k.c.901.2		2
120.53	even	4		1800.2.d.e.1549.1		2
120.59	even	2		7200.2.k.a.3601.2		2
120.77	even	4		1800.2.d.g.1549.2		2
120.83	odd	4		7200.2.d.i.2449.1		2
120.107	odd	4		7200.2.d.b.2449.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.k.a.181.1	✓	2	1.1	even	1	trivial
360.2.k.a.181.2	yes	2	8.5	even	2	inner
360.2.k.c.181.1	yes	2	24.5	odd	2
360.2.k.c.181.2	yes	2	3.2	odd	2
1440.2.k.b.721.1		2	4.3	odd	2
1440.2.k.b.721.2		2	8.3	odd	2
1440.2.k.c.721.1		2	24.11	even	2
1440.2.k.c.721.2		2	12.11	even	2
1800.2.d.a.1549.1		2	40.37	odd	4
1800.2.d.a.1549.2		2	5.3	odd	4
1800.2.d.e.1549.1		2	120.53	even	4
1800.2.d.e.1549.2		2	15.2	even	4
1800.2.d.g.1549.1		2	15.8	even	4
1800.2.d.g.1549.2		2	120.77	even	4
1800.2.d.j.1549.1		2	5.2	odd	4
1800.2.d.j.1549.2		2	40.13	odd	4
1800.2.k.c.901.1		2	15.14	odd	2
1800.2.k.c.901.2		2	120.29	odd	2
1800.2.k.i.901.1		2	40.29	even	2
1800.2.k.i.901.2		2	5.4	even	2
7200.2.d.a.2449.1		2	20.3	even	4
7200.2.d.a.2449.2		2	40.27	even	4
7200.2.d.b.2449.1		2	60.23	odd	4
7200.2.d.b.2449.2		2	120.107	odd	4
7200.2.d.h.2449.1		2	40.3	even	4
7200.2.d.h.2449.2		2	20.7	even	4
7200.2.d.i.2449.1		2	120.83	odd	4
7200.2.d.i.2449.2		2	60.47	odd	4
7200.2.k.a.3601.1		2	60.59	even	2
7200.2.k.a.3601.2		2	120.59	even	2
7200.2.k.c.3601.1		2	40.19	odd	2
7200.2.k.c.3601.2		2	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)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} -1.00000i q^{5} -4.00000 q^{7} +(2.00000 - 2.00000i) q^{8} +O(q^{10})\)	\(q+(-1.00000 - 1.00000i) q^{2} +2.00000i q^{4} -1.00000i q^{5} -4.00000 q^{7} +(2.00000 - 2.00000i) q^{8} +(-1.00000 + 1.00000i) q^{10} -2.00000i q^{11} +6.00000i q^{13} +(4.00000 + 4.00000i) q^{14} -4.00000 q^{16} -6.00000 q^{17} -4.00000i q^{19} +2.00000 q^{20} +(-2.00000 + 2.00000i) q^{22} -8.00000 q^{23} -1.00000 q^{25} +(6.00000 - 6.00000i) q^{26} -8.00000i q^{28} +6.00000i q^{29} -2.00000 q^{31} +(4.00000 + 4.00000i) q^{32} +(6.00000 + 6.00000i) q^{34} +4.00000i q^{35} +2.00000i q^{37} +(-4.00000 + 4.00000i) q^{38} +(-2.00000 - 2.00000i) q^{40} -4.00000 q^{41} +4.00000i q^{43} +4.00000 q^{44} +(8.00000 + 8.00000i) q^{46} +4.00000 q^{47} +9.00000 q^{49} +(1.00000 + 1.00000i) q^{50} -12.0000 q^{52} -10.0000i q^{53} -2.00000 q^{55} +(-8.00000 + 8.00000i) q^{56} +(6.00000 - 6.00000i) q^{58} +2.00000i q^{59} -4.00000i q^{61} +(2.00000 + 2.00000i) q^{62} -8.00000i q^{64} +6.00000 q^{65} -12.0000i q^{67} -12.0000i q^{68} +(4.00000 - 4.00000i) q^{70} -8.00000 q^{71} +10.0000 q^{73} +(2.00000 - 2.00000i) q^{74} +8.00000 q^{76} +8.00000i q^{77} -2.00000 q^{79} +4.00000i q^{80} +(4.00000 + 4.00000i) q^{82} +6.00000i q^{85} +(4.00000 - 4.00000i) q^{86} +(-4.00000 - 4.00000i) q^{88} +4.00000 q^{89} -24.0000i q^{91} -16.0000i q^{92} +(-4.00000 - 4.00000i) q^{94} -4.00000 q^{95} +2.00000 q^{97} +(-9.00000 - 9.00000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 8 q^{7} + 4 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 8 * q^7 + 4 * q^8	\( 2 q - 2 q^{2} - 8 q^{7} + 4 q^{8} - 2 q^{10} + 8 q^{14} - 8 q^{16} - 12 q^{17} + 4 q^{20} - 4 q^{22} - 16 q^{23} - 2 q^{25} + 12 q^{26} - 4 q^{31} + 8 q^{32} + 12 q^{34} - 8 q^{38} - 4 q^{40} - 8 q^{41} + 8 q^{44} + 16 q^{46} + 8 q^{47} + 18 q^{49} + 2 q^{50} - 24 q^{52} - 4 q^{55} - 16 q^{56} + 12 q^{58} + 4 q^{62} + 12 q^{65} + 8 q^{70} - 16 q^{71} + 20 q^{73} + 4 q^{74} + 16 q^{76} - 4 q^{79} + 8 q^{82} + 8 q^{86} - 8 q^{88} + 8 q^{89} - 8 q^{94} - 8 q^{95} + 4 q^{97} - 18 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 8 * q^7 + 4 * q^8 - 2 * q^10 + 8 * q^14 - 8 * q^16 - 12 * q^17 + 4 * q^20 - 4 * q^22 - 16 * q^23 - 2 * q^25 + 12 * q^26 - 4 * q^31 + 8 * q^32 + 12 * q^34 - 8 * q^38 - 4 * q^40 - 8 * q^41 + 8 * q^44 + 16 * q^46 + 8 * q^47 + 18 * q^49 + 2 * q^50 - 24 * q^52 - 4 * q^55 - 16 * q^56 + 12 * q^58 + 4 * q^62 + 12 * q^65 + 8 * q^70 - 16 * q^71 + 20 * q^73 + 4 * q^74 + 16 * q^76 - 4 * q^79 + 8 * q^82 + 8 * q^86 - 8 * q^88 + 8 * q^89 - 8 * q^94 - 8 * q^95 + 4 * q^97 - 18 * q^98

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