LMFDB - Embedded newform 120.9.c.a.89.26

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [120,9,Mod(89,120)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("120.89"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(120, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1, 1])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	120.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$48.8854332073$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			89.26
Character	$\chi$	$=$	120.89
Dual form			120.9.c.a.89.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.827899 + 80.9958i) q^{3} +(-614.183 - 115.775i) q^{5} -2689.51i q^{7} +(-6559.63 + 134.113i) q^{9} -8645.32i q^{11} +10695.3i q^{13} +(8868.83 - 49842.1i) q^{15} -63832.7 q^{17} +127573. q^{19} +(217839. - 2226.64i) q^{21} +65329.8 q^{23} +(363817. + 142215. i) q^{25} +(-16293.3 - 531191. i) q^{27} +326271. i q^{29} +326429. q^{31} +(700235. - 7157.45i) q^{33} +(-311379. + 1.65185e6i) q^{35} +2.55678e6i q^{37} +(-866275. + 8854.64i) q^{39} -3.04601e6i q^{41} +2.76741e6i q^{43} +(4.04434e6 + 677073. i) q^{45} -9.65661e6 q^{47} -1.46867e6 q^{49} +(-52847.1 - 5.17018e6i) q^{51} +5.50516e6 q^{53} +(-1.00092e6 + 5.30981e6i) q^{55} +(105618. + 1.03329e7i) q^{57} +3.10238e6i q^{59} -6.78622e6 q^{61} +(360697. + 1.76422e7i) q^{63} +(1.23825e6 - 6.56888e6i) q^{65} +1.83710e7i q^{67} +(54086.5 + 5.29144e6i) q^{69} +3.17540e7i q^{71} +3.20830e7i q^{73} +(-1.12176e7 + 2.95854e7i) q^{75} -2.32517e7 q^{77} +5.93091e7 q^{79} +(4.30107e7 - 1.75946e6i) q^{81} +7.24238e7 q^{83} +(3.92050e7 + 7.39026e6i) q^{85} +(-2.64266e7 + 270119. i) q^{87} -7.78845e7i q^{89} +2.87652e7 q^{91} +(270250. + 2.64394e7i) q^{93} +(-7.83535e7 - 1.47699e7i) q^{95} +1.59825e8i q^{97} +(1.15945e6 + 5.67101e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2528 q^{9} + 132352 q^{15} + 116176 q^{21} + 56976 q^{25} + 1395648 q^{31} + 6888832 q^{39} - 4287056 q^{45} - 30813552 q^{49} - 22815168 q^{51} - 6062784 q^{55} + 14031936 q^{61} + 2522608 q^{69}+ \cdots - 21719360 q^{99}+O(q^{100}) $ 48 * q + 2528 * q^9 + 132352 * q^15 + 116176 * q^21 + 56976 * q^25 + 1395648 * q^31 + 6888832 * q^39 - 4287056 * q^45 - 30813552 * q^49 - 22815168 * q^51 - 6062784 * q^55 + 14031936 * q^61 + 2522608 * q^69 + 41684416 * q^75 + 19866432 * q^79 - 93539312 * q^81 - 116297664 * q^85 + 16826880 * q^91 - 21719360 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$1$	$-1$

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 $

$2$		0			0
$2$		0			0
$3$	0.827899	+	80.9958i	0.0102210	+	0.999948i
$3$	0.827899	+	80.9958i	0.0102210	+	0.999948i
$4$		0			0
$5$	−614.183	−	115.775i	−0.982693	−	0.185241i
$5$	−614.183	−	115.775i	−0.982693	−	0.185241i
$6$		0			0
$7$		−	2689.51i		−	1.12016i	−0.828438	−	0.560081i	$-0.810770\pi$
$7$		−	2689.51i		−	1.12016i	0.828438	−	0.560081i	$-0.189230\pi$
$8$		0			0
$9$	−6559.63	+	134.113i	−0.999791	+	0.0204409i
$10$		0			0
$11$		−	8645.32i		−	0.590487i	−0.955422	−	0.295244i	$-0.904599\pi$
$11$		−	8645.32i		−	0.590487i	0.955422	−	0.295244i	$-0.0954008\pi$
$12$		0			0
$13$			10695.3i			0.374473i	0.982315	+	0.187236i	$0.0599530\pi$
$13$			10695.3i			0.374473i	−0.982315	+	0.187236i	$0.940047\pi$
$14$		0			0
$15$	8868.83	−	49842.1i	0.175187	−	0.984535i
$16$		0			0
$17$	−63832.7			−0.764272			−0.382136	−	0.924106i	$-0.624811\pi$
$17$	−63832.7			−0.764272			−0.382136	+	0.924106i	$0.624811\pi$
$18$		0			0
$19$	127573.			0.978917			0.489458	−	0.872027i	$-0.337194\pi$
$19$	127573.			0.978917			0.489458	+	0.872027i	$0.337194\pi$
$20$		0			0
$21$	217839.	−	2226.64i	1.12010	−	0.0114492i
$22$		0			0
$23$	65329.8			0.233453			0.116727	−	0.993164i	$-0.462760\pi$
$23$	65329.8			0.233453			0.116727	+	0.993164i	$0.462760\pi$
$24$		0			0
$25$	363817.	+	142215.i	0.931372	+	0.364069i
$26$		0			0
$27$	−16293.3	−	531191.i	−0.0306587	−	0.999530i
$28$		0			0
$29$			326271.i			0.461303i	0.973036	+	0.230651i	$0.0740857\pi$
$29$			326271.i			0.461303i	−0.973036	+	0.230651i	$0.925914\pi$
$30$		0			0
$31$	326429.			0.353462			0.176731	−	0.984259i	$-0.443448\pi$
$31$	326429.			0.353462			0.176731	+	0.984259i	$0.443448\pi$
$32$		0			0
$33$	700235.	−	7157.45i	0.590456	−	0.00603535i
$34$		0			0
$35$	−311379.	+	1.65185e6i	−0.207500	+	1.10078i
$36$		0			0
$37$			2.55678e6i			1.36422i	0.731248	+	0.682112i	$0.238938\pi$
$37$			2.55678e6i			1.36422i	−0.731248	+	0.682112i	$0.761062\pi$
$38$		0			0
$39$	−866275.	+	8854.64i	−0.374453	+	0.00382748i
$40$		0			0
$41$		−	3.04601e6i		−	1.07794i	−0.842324	−	0.538972i	$-0.818813\pi$
$41$		−	3.04601e6i		−	1.07794i	0.842324	−	0.538972i	$-0.181187\pi$
$42$		0			0
$43$			2.76741e6i			0.809467i	0.914435	+	0.404734i	$0.132636\pi$
$43$			2.76741e6i			0.809467i	−0.914435	+	0.404734i	$0.867364\pi$
$44$		0			0
$45$	4.04434e6	+	677073.i	0.986274	+	0.165115i
$46$		0			0
$47$	−9.65661e6			−1.97894			−0.989471	−	0.144729i	$-0.953769\pi$
$47$	−9.65661e6			−1.97894			−0.989471	+	0.144729i	$0.953769\pi$
$48$		0			0
$49$	−1.46867e6			−0.254765
$50$		0			0
$51$	−52847.1	−	5.17018e6i	−0.00781160	−	0.764232i
$52$		0			0
$53$	5.50516e6			0.697696			0.348848	−	0.937179i	$-0.386573\pi$
$53$	5.50516e6			0.697696			0.348848	+	0.937179i	$0.386573\pi$
$54$		0			0
$55$	−1.00092e6	+	5.30981e6i	−0.109382	+	0.580268i
$56$		0			0
$57$	105618.	+	1.03329e7i	0.0100055	+	0.978866i
$58$		0			0
$59$			3.10238e6i			0.256028i	0.991772	+	0.128014i	$0.0408602\pi$
$59$			3.10238e6i			0.256028i	−0.991772	+	0.128014i	$0.959140\pi$
$60$		0			0
$61$	−6.78622e6			−0.490127			−0.245063	−	0.969507i	$-0.578809\pi$
$61$	−6.78622e6			−0.490127			−0.245063	+	0.969507i	$0.578809\pi$
$62$		0			0
$63$	360697.	+	1.76422e7i	0.0228971	+	1.11993i
$64$		0			0
$65$	1.23825e6	−	6.56888e6i	0.0693675	−	0.367992i
$66$		0			0
$67$			1.83710e7i			0.911664i	0.890066	+	0.455832i	$0.150658\pi$
$67$			1.83710e7i			0.911664i	−0.890066	+	0.455832i	$0.849342\pi$
$68$		0			0
$69$	54086.5	+	5.29144e6i	0.00238612	+	0.233441i
$70$		0			0
$71$			3.17540e7i			1.24958i	0.780792	+	0.624791i	$0.214816\pi$
$71$			3.17540e7i			1.24958i	−0.780792	+	0.624791i	$0.785184\pi$
$72$		0			0
$73$			3.20830e7i			1.12975i	0.825175	+	0.564877i	$0.191076\pi$
$73$			3.20830e7i			1.12975i	−0.825175	+	0.564877i	$0.808924\pi$
$74$		0			0
$75$	−1.12176e7	+	2.95854e7i	−0.354531	+	0.935044i
$76$		0			0
$77$	−2.32517e7			−0.661442
$78$		0			0
$79$	5.93091e7			1.52269			0.761347	−	0.648344i	$-0.224538\pi$
$79$	5.93091e7			1.52269			0.761347	+	0.648344i	$0.224538\pi$
$80$		0			0
$81$	4.30107e7	−	1.75946e6i	0.999164	−	0.0408732i
$82$		0			0
$83$	7.24238e7			1.52605			0.763025	−	0.646369i	$-0.223713\pi$
$83$	7.24238e7			1.52605			0.763025	+	0.646369i	$0.223713\pi$
$84$		0			0
$85$	3.92050e7	+	7.39026e6i	0.751045	+	0.141574i
$86$		0			0
$87$	−2.64266e7	+	270119.i	−0.461279	+	0.00471496i
$88$		0			0
$89$		−	7.78845e7i		−	1.24134i	−0.784072	−	0.620670i	$-0.786861\pi$
$89$		−	7.78845e7i		−	1.24134i	0.784072	−	0.620670i	$-0.213139\pi$
$90$		0			0
$91$	2.87652e7			0.419470
$92$		0			0
$93$	270250.	+	2.64394e7i	0.00361272	+	0.353443i
$94$		0			0
$95$	−7.83535e7	−	1.47699e7i	−0.961975	−	0.181335i
$96$		0			0
$97$			1.59825e8i			1.80534i	0.430334	+	0.902670i	$0.358396\pi$
$97$			1.59825e8i			1.80534i	−0.430334	+	0.902670i	$0.641604\pi$
$98$		0			0
$99$	1.15945e6	+	5.67101e7i	0.0120701	+	0.590364i
$100$		0			0
$101$		−	1.50933e7i		−	0.145044i	−0.997367	−	0.0725220i	$-0.976895\pi$
$101$		−	1.50933e7i		−	0.145044i	0.997367	−	0.0725220i	$-0.0231047\pi$
$102$		0			0
$103$			8.06438e7i			0.716510i	0.933624	+	0.358255i	$0.116628\pi$
$103$			8.06438e7i			0.716510i	−0.933624	+	0.358255i	$0.883372\pi$
$104$		0			0
$105$	−1.34051e8	−	2.38528e7i	−1.10284	−	0.196238i
$106$		0			0
$107$	1.45381e8			1.10911			0.554553	−	0.832148i	$-0.312889\pi$
$107$	1.45381e8			1.10911			0.554553	+	0.832148i	$0.312889\pi$
$108$		0			0
$109$	−1.38800e8			−0.983291			−0.491646	−	0.870795i	$-0.663604\pi$
$109$	−1.38800e8			−0.983291			−0.491646	+	0.870795i	$0.663604\pi$
$110$		0			0
$111$	−2.07088e8	+	2.11675e6i	−1.36415	+	0.0139437i
$112$		0			0
$113$	9.43804e7			0.578852			0.289426	−	0.957200i	$-0.406536\pi$
$113$	9.43804e7			0.578852			0.289426	+	0.957200i	$0.406536\pi$
$114$		0			0
$115$	−4.01245e7	−	7.56358e6i	−0.229413	−	0.0432450i
$116$		0			0
$117$	−1.43438e6	−	7.01573e7i	−0.00765455	−	0.374394i
$118$		0			0
$119$			1.71679e8i			0.856109i
$120$		0			0
$121$	1.39617e8			0.651325
$122$		0			0
$123$	2.46714e8	−	2.52179e6i	1.07789	−	0.0110176i
$124$		0			0
$125$	−2.06985e8	−	1.29467e8i	−0.847812	−	0.530296i
$126$		0			0
$127$		−	1.62468e8i		−	0.624531i	−0.949995	−	0.312266i	$-0.898912\pi$
$127$		−	1.62468e8i		−	0.624531i	0.949995	−	0.312266i	$-0.101088\pi$
$128$		0			0
$129$	−2.24148e8	+	2.29113e6i	−0.809425	+	0.00827354i
$130$		0			0
$131$			2.83670e8i			0.963227i	0.876384	+	0.481614i	$0.159949\pi$
$131$			2.83670e8i			0.963227i	−0.876384	+	0.481614i	$0.840051\pi$
$132$		0			0
$133$		−	3.43110e8i		−	1.09655i
$134$		0			0
$135$	−5.14918e7	+	3.28135e8i	−0.155025	+	0.987910i
$136$		0			0
$137$	−2.16033e8			−0.613251			−0.306626	−	0.951830i	$-0.599200\pi$
$137$	−2.16033e8			−0.613251			−0.306626	+	0.951830i	$0.599200\pi$
$138$		0			0
$139$	3.24470e8			0.869191			0.434595	−	0.900626i	$-0.356891\pi$
$139$	3.24470e8			0.869191			0.434595	+	0.900626i	$0.356891\pi$
$140$		0			0
$141$	−7.99470e6	−	7.82144e8i	−0.0202267	−	1.97884i
$142$		0			0
$143$	9.24645e7			0.221121
$144$		0			0
$145$	3.77741e7	−	2.00390e8i	0.0854520	−	0.453319i
$146$		0			0
$147$	−1.21591e6	−	1.18956e8i	−0.00260395	−	0.254752i
$148$		0			0
$149$		−	3.56978e8i		−	0.724263i	−0.932127	−	0.362132i	$-0.882049\pi$
$149$		−	3.56978e8i		−	0.724263i	0.932127	−	0.362132i	$-0.117951\pi$
$150$		0			0
$151$	5.96108e7			0.114661			0.0573307	−	0.998355i	$-0.481741\pi$
$151$	5.96108e7			0.114661			0.0573307	+	0.998355i	$0.481741\pi$
$152$		0			0
$153$	4.18719e8	−	8.56077e6i	0.764112	−	0.0156224i
$154$		0			0
$155$	−2.00487e8	−	3.77925e7i	−0.347344	−	0.0654754i
$156$		0			0
$157$		−	1.08167e9i		−	1.78031i	−0.455655	−	0.890157i	$-0.650595\pi$
$157$		−	1.08167e9i		−	1.78031i	0.455655	−	0.890157i	$-0.349405\pi$
$158$		0			0
$159$	4.55771e6	+	4.45894e8i	0.00713113	+	0.697659i
$160$		0			0
$161$		−	1.75705e8i		−	0.261506i
$162$		0			0
$163$		−	9.33597e8i		−	1.32254i	−0.750147	−	0.661271i	$-0.770017\pi$
$163$		−	9.33597e8i		−	1.32254i	0.750147	−	0.661271i	$-0.229983\pi$
$164$		0			0
$165$	−4.30901e8	−	7.66739e7i	−0.581355	−	0.103446i
$166$		0			0
$167$	−9.37788e8			−1.20570			−0.602849	−	0.797855i	$-0.705968\pi$
$167$	−9.37788e8			−1.20570			−0.602849	+	0.797855i	$0.705968\pi$
$168$		0			0
$169$	7.01341e8			0.859770
$170$		0			0
$171$	−8.36834e8	+	1.71092e7i	−0.978712	+	0.0200099i
$172$		0			0
$173$	1.08766e9			1.21425			0.607123	−	0.794608i	$-0.292323\pi$
$173$	1.08766e9			1.21425			0.607123	+	0.794608i	$0.292323\pi$
$174$		0			0
$175$	3.82488e8	−	9.78490e8i	0.407817	−	1.04329i
$176$		0			0
$177$	−2.51280e8	+	2.56846e6i	−0.256014	+	0.00261685i
$178$		0			0
$179$			1.37206e9i			1.33648i	0.743947	+	0.668239i	$0.232952\pi$
$179$			1.37206e9i			1.33648i	−0.743947	+	0.668239i	$0.767048\pi$
$180$		0			0
$181$	1.36221e9			1.26920			0.634600	−	0.772841i	$-0.281165\pi$
$181$	1.36221e9			1.26920			0.634600	+	0.772841i	$0.281165\pi$
$182$		0			0
$183$	−5.61830e6	−	5.49655e8i	−0.00500957	−	0.490101i
$184$		0			0
$185$	2.96012e8	−	1.57033e9i	0.252710	−	1.34061i
$186$		0			0
$187$			5.51855e8i			0.451293i
$188$		0			0
$189$	−1.42864e9	+	4.38209e7i	−1.11964	+	0.0343427i
$190$		0			0
$191$			1.69573e9i			1.27416i	0.770800	+	0.637078i	$0.219857\pi$
$191$			1.69573e9i			1.27416i	−0.770800	+	0.637078i	$0.780143\pi$
$192$		0			0
$193$			3.55641e8i			0.256320i	0.991754	+	0.128160i	$0.0409071\pi$
$193$			3.55641e8i			0.256320i	−0.991754	+	0.128160i	$0.959093\pi$
$194$		0			0
$195$	5.33077e8	+	9.48549e7i	0.368682	+	0.0656027i
$196$		0			0
$197$	−4.28125e8			−0.284254			−0.142127	−	0.989848i	$-0.545394\pi$
$197$	−4.28125e8			−0.284254			−0.142127	+	0.989848i	$0.545394\pi$
$198$		0			0
$199$	−7.73732e7			−0.0493376			−0.0246688	−	0.999696i	$-0.507853\pi$
$199$	−7.73732e7			−0.0493376			−0.0246688	+	0.999696i	$0.507853\pi$
$200$		0			0
$201$	−1.48798e9	+	1.52094e7i	−0.911616	+	0.00931809i
$202$		0			0
$203$	8.77509e8			0.516734
$204$		0			0
$205$	−3.52653e8	+	1.87081e9i	−0.199679	+	1.05929i
$206$		0			0
$207$	−4.28539e8	+	8.76155e6i	−0.233405	+	0.00477199i
$208$		0			0
$209$		−	1.10291e9i		−	0.578038i
$210$		0			0
$211$	−9.44377e8			−0.476448			−0.238224	−	0.971210i	$-0.576565\pi$
$211$	−9.44377e8			−0.476448			−0.238224	+	0.971210i	$0.576565\pi$
$212$		0			0
$213$	−2.57194e9	+	2.62891e7i	−1.24952	+	0.0127719i
$214$		0			0
$215$	3.20397e8	−	1.69969e9i	0.149946	−	0.795458i
$216$		0			0
$217$		−	8.77935e8i		−	0.395935i
$218$		0			0
$219$	−2.59859e9	+	2.65615e7i	−1.12970	+	0.0115472i
$220$		0			0
$221$		−	6.82711e8i		−	0.286199i
$222$		0			0
$223$			2.69965e9i			1.09166i	0.837895	+	0.545831i	$0.183786\pi$
$223$			2.69965e9i			1.09166i	−0.837895	+	0.545831i	$0.816214\pi$
$224$		0			0
$225$	−2.40558e9	−	8.84082e8i	−0.938619	−	0.344955i
$226$		0			0
$227$	3.36947e9			1.26899			0.634494	−	0.772928i	$-0.281209\pi$
$227$	3.36947e9			1.26899			0.634494	+	0.772928i	$0.281209\pi$
$228$		0			0
$229$	2.89455e9			1.05254			0.526270	−	0.850318i	$-0.323590\pi$
$229$	2.89455e9			1.05254			0.526270	+	0.850318i	$0.323590\pi$
$230$		0			0
$231$	−1.92501e7	−	1.88329e9i	−0.00676058	−	0.661407i
$232$		0			0
$233$	−3.91852e9			−1.32953			−0.664766	−	0.747052i	$-0.731469\pi$
$233$	−3.91852e9			−1.32953			−0.664766	+	0.747052i	$0.731469\pi$
$234$		0			0
$235$	5.93093e9	+	1.11800e9i	1.94469	+	0.366580i
$236$		0			0
$237$	4.91019e7	+	4.80378e9i	0.0155634	+	1.52261i
$238$		0			0
$239$			3.63759e9i			1.11487i	0.830222	+	0.557433i	$0.188214\pi$
$239$			3.63759e9i			1.11487i	−0.830222	+	0.557433i	$0.811786\pi$
$240$		0			0
$241$	5.96625e9			1.76862			0.884308	−	0.466905i	$-0.154631\pi$
$241$	5.96625e9			1.76862			0.884308	+	0.466905i	$0.154631\pi$
$242$		0			0
$243$	1.78117e8	+	3.48223e9i	0.0510835	+	0.998694i
$244$		0			0
$245$	9.02032e8	+	1.70036e8i	0.250356	+	0.0471928i
$246$		0			0
$247$			1.36444e9i			0.366578i
$248$		0			0
$249$	5.99596e7	+	5.86602e9i	0.0155977	+	1.52597i
$250$		0			0
$251$		−	4.21754e9i		−	1.06259i	−0.847188	−	0.531294i	$-0.821706\pi$
$251$		−	4.21754e9i		−	1.06259i	0.847188	−	0.531294i	$-0.178294\pi$
$252$		0			0
$253$		−	5.64797e8i		−	0.137851i
$254$		0			0
$255$	−5.66122e8	+	3.18156e9i	−0.133890	+	0.752452i
$256$		0			0
$257$	5.58045e9			1.27919			0.639597	−	0.768710i	$-0.279101\pi$
$257$	5.58045e9			1.27919			0.639597	+	0.768710i	$0.279101\pi$
$258$		0			0
$259$	6.87648e9			1.52815
$260$		0			0
$261$	−4.37570e7	−	2.14022e9i	−0.00942944	−	0.461206i
$262$		0			0
$263$	−8.48161e9			−1.77278			−0.886391	−	0.462938i	$-0.846795\pi$
$263$	−8.48161e9			−1.77278			−0.886391	+	0.462938i	$0.846795\pi$
$264$		0			0
$265$	−3.38117e9	−	6.37361e8i	−0.685621	−	0.129242i
$266$		0			0
$267$	6.30831e9	−	6.44805e7i	1.24128	−	0.0126877i
$268$		0			0
$269$			8.84324e9i			1.68889i	0.535640	+	0.844446i	$0.320070\pi$
$269$			8.84324e9i			1.68889i	−0.535640	+	0.844446i	$0.679930\pi$
$270$		0			0
$271$	2.38301e8			0.0441823			0.0220911	−	0.999756i	$-0.492968\pi$
$271$	2.38301e8			0.0441823			0.0220911	+	0.999756i	$0.492968\pi$
$272$		0			0
$273$	2.38147e7	+	2.32986e9i	0.00428740	+	0.419449i
$274$		0			0
$275$	1.22949e9	−	3.14532e9i	0.214978	−	0.549963i
$276$		0			0
$277$			5.59173e9i			0.949788i	0.880043	+	0.474894i	$0.157514\pi$
$277$			5.59173e9i			0.949788i	−0.880043	+	0.474894i	$0.842486\pi$
$278$		0			0
$279$	−2.14126e9	+	4.37783e7i	−0.353388	+	0.00722507i
$280$		0			0
$281$			2.97153e7i			0.00476601i	0.999997	+	0.00238301i	$0.000758535\pi$
$281$			2.97153e7i			0.00476601i	−0.999997	+	0.00238301i	$0.999241\pi$
$282$		0			0
$283$		−	9.87692e8i		−	0.153984i	−0.997032	−	0.0769920i	$-0.975468\pi$
$283$		−	9.87692e8i		−	0.153984i	0.997032	−	0.0769920i	$-0.0245316\pi$
$284$		0			0
$285$	1.13143e9	−	6.35853e9i	0.171493	−	0.963778i
$286$		0			0
$287$	−8.19228e9			−1.20747
$288$		0			0
$289$	−2.90114e9			−0.415889
$290$		0			0
$291$	−1.29452e10	+	1.32319e8i	−1.80525	+	0.0184523i
$292$		0			0
$293$	−2.92728e8			−0.0397186			−0.0198593	−	0.999803i	$-0.506322\pi$
$293$	−2.92728e8			−0.0397186			−0.0198593	+	0.999803i	$0.506322\pi$
$294$		0			0
$295$	3.59179e8	−	1.90543e9i	0.0474267	−	0.251597i
$296$		0			0
$297$	−4.59232e9	+	1.40861e8i	−0.590210	+	0.0181035i
$298$		0			0
$299$			6.98723e8i			0.0874219i
$300$		0			0
$301$	7.44297e9			0.906735
$302$		0			0
$303$	1.22250e9	−	1.24958e7i	0.145036	−	0.00148249i
$304$		0			0
$305$	4.16798e9	+	7.85676e8i	0.481644	+	0.0907913i
$306$		0			0
$307$		−	2.25899e9i		−	0.254309i	−0.991883	−	0.127154i	$-0.959416\pi$
$307$		−	2.25899e9i		−	0.254309i	0.991883	−	0.127154i	$-0.0405843\pi$
$308$		0			0
$309$	−6.53180e9	+	6.67649e7i	−0.716472	+	0.00732343i
$310$		0			0
$311$		−	1.39907e10i		−	1.49554i	−0.663957	−	0.747771i	$-0.731124\pi$
$311$		−	1.39907e10i		−	1.49554i	0.663957	−	0.747771i	$-0.268876\pi$
$312$		0			0
$313$			4.23221e9i			0.440951i	0.975393	+	0.220475i	$0.0707609\pi$
$313$			4.23221e9i			0.440951i	−0.975393	+	0.220475i	$0.929239\pi$
$314$		0			0
$315$	1.82100e9	−	1.08773e10i	0.184955	−	1.10479i
$316$		0			0
$317$	8.10394e9			0.802526			0.401263	−	0.915963i	$-0.368571\pi$
$317$	8.10394e9			0.802526			0.401263	+	0.915963i	$0.368571\pi$
$318$		0			0
$319$	2.82072e9			0.272393
$320$		0			0
$321$	1.20361e8	+	1.17753e10i	0.0113362	+	1.10905i
$322$		0			0
$323$	−8.14336e9			−0.748158
$324$		0			0
$325$	−1.52103e9	+	3.89114e9i	−0.136334	+	0.348773i
$326$		0			0
$327$	−1.14912e8	−	1.12422e10i	−0.0100502	−	0.983240i
$328$		0			0
$329$			2.59716e10i			2.21674i
$330$		0			0
$331$	−4.11106e9			−0.342485			−0.171243	−	0.985229i	$-0.554778\pi$
$331$	−4.11106e9			−0.342485			−0.171243	+	0.985229i	$0.554778\pi$
$332$		0			0
$333$	−3.42896e8	−	1.67715e10i	−0.0278859	−	1.36394i
$334$		0			0
$335$	2.12691e9	−	1.12832e10i	0.168877	−	0.895886i
$336$		0			0
$337$		−	1.87362e10i		−	1.45265i	−0.687349	−	0.726327i	$-0.741226\pi$
$337$		−	1.87362e10i		−	1.45265i	0.687349	−	0.726327i	$-0.258774\pi$
$338$		0			0
$339$	7.81374e7	+	7.64441e9i	0.00591644	+	0.578822i
$340$		0			0
$341$		−	2.82209e9i		−	0.208715i
$342$		0			0
$343$		−	1.15545e10i		−	0.834785i
$344$		0			0
$345$	5.79399e8	−	3.25617e9i	0.0408979	−	0.229843i
$346$		0			0
$347$	−1.41417e10			−0.975404			−0.487702	−	0.873010i	$-0.662165\pi$
$347$	−1.41417e10			−0.975404			−0.487702	+	0.873010i	$0.662165\pi$
$348$		0			0
$349$	−8.98906e9			−0.605916			−0.302958	−	0.953004i	$-0.597974\pi$
$349$	−8.98906e9			−0.605916			−0.302958	+	0.953004i	$0.597974\pi$
$350$		0			0
$351$	5.68126e9	−	1.74262e8i	0.374297	−	0.0114808i
$352$		0			0
$353$	2.71489e10			1.74845			0.874224	−	0.485523i	$-0.161371\pi$
$353$	2.71489e10			1.74845			0.874224	+	0.485523i	$0.161371\pi$
$354$		0			0
$355$	3.67632e9	−	1.95027e10i	0.231473	−	1.22795i
$356$		0			0
$357$	−1.39053e10	+	1.42133e8i	−0.856064	+	0.00875027i
$358$		0			0
$359$			1.89024e10i			1.13799i	0.822341	+	0.568995i	$0.192668\pi$
$359$			1.89024e10i			1.13799i	−0.822341	+	0.568995i	$0.807332\pi$
$360$		0			0
$361$	−7.08584e8			−0.0417218
$362$		0			0
$363$	1.15589e8	+	1.13084e10i	0.00665717	+	0.651291i
$364$		0			0
$365$	3.71442e9	−	1.97049e10i	0.209276	−	1.11020i
$366$		0			0
$367$			1.19898e10i			0.660918i	0.943820	+	0.330459i	$0.107204\pi$
$367$			1.19898e10i			0.660918i	−0.943820	+	0.330459i	$0.892796\pi$
$368$		0			0
$369$	4.08508e8	+	1.99807e10i	0.0220341	+	1.07772i
$370$		0			0
$371$		−	1.48062e10i		−	0.781533i
$372$		0			0
$373$		−	2.84938e10i		−	1.47202i	−0.676969	−	0.736011i	$-0.736707\pi$
$373$		−	2.84938e10i		−	1.47202i	0.676969	−	0.736011i	$-0.263293\pi$
$374$		0			0
$375$	1.03149e10	−	1.68721e10i	0.521603	−	0.853188i
$376$		0			0
$377$	−3.48957e9			−0.172745
$378$		0			0
$379$	5.90472e9			0.286182			0.143091	−	0.989710i	$-0.454296\pi$
$379$	5.90472e9			0.286182			0.143091	+	0.989710i	$0.454296\pi$
$380$		0			0
$381$	1.31593e10	−	1.34507e8i	0.624499	−	0.00638332i
$382$		0			0
$383$	1.95451e10			0.908328			0.454164	−	0.890918i	$-0.349938\pi$
$383$	1.95451e10			0.908328			0.454164	+	0.890918i	$0.349938\pi$
$384$		0			0
$385$	1.42808e10	+	2.69197e9i	0.649995	+	0.122526i
$386$		0			0
$387$	−3.71144e8	−	1.81532e10i	−0.0165462	−	0.809298i
$388$		0			0
$389$			1.11276e10i			0.485964i	0.970031	+	0.242982i	$0.0781255\pi$
$389$			1.11276e10i			0.485964i	−0.970031	+	0.242982i	$0.921874\pi$
$390$		0			0
$391$	−4.17018e9			−0.178422
$392$		0			0
$393$	−2.29761e10	+	2.34850e8i	−0.963177	+	0.00984512i
$394$		0			0
$395$	−3.64266e10	−	6.86653e9i	−1.49634	−	0.282065i
$396$		0			0
$397$		−	1.76590e10i		−	0.710895i	−0.934696	−	0.355447i	$-0.884329\pi$
$397$		−	1.76590e10i		−	0.710895i	0.934696	−	0.355447i	$-0.115671\pi$
$398$		0			0
$399$	2.77905e10	−	2.84061e8i	1.09649	−	0.0112078i
$400$		0			0
$401$		−	2.51338e10i		−	0.972031i	−0.873950	−	0.486016i	$-0.838450\pi$
$401$		−	2.51338e10i		−	0.972031i	0.873950	−	0.486016i	$-0.161550\pi$
$402$		0			0
$403$			3.49126e9i			0.132362i
$404$		0			0
$405$	−2.66202e10	−	3.89895e9i	−0.989443	−	0.144920i
$406$		0			0
$407$	2.21042e10			0.805557
$408$		0			0
$409$	−1.15164e10			−0.411551			−0.205776	−	0.978599i	$-0.565972\pi$
$409$	−1.15164e10			−0.411551			−0.205776	+	0.978599i	$0.565972\pi$
$410$		0			0
$411$	−1.78854e8	−	1.74978e10i	−0.00626803	−	0.613219i
$412$		0			0
$413$	8.34388e9			0.286793
$414$		0			0
$415$	−4.44815e10	−	8.38489e9i	−1.49964	−	0.282686i
$416$		0			0
$417$	2.68628e8	+	2.62807e10i	0.00888398	+	0.869146i
$418$		0			0
$419$			5.32510e10i			1.72771i	0.503738	+	0.863856i	$0.331958\pi$
$419$			5.32510e10i			1.72771i	−0.503738	+	0.863856i	$0.668042\pi$
$420$		0			0
$421$	−3.51669e10			−1.11945			−0.559727	−	0.828677i	$-0.689094\pi$
$421$	−3.51669e10			−1.11945			−0.559727	+	0.828677i	$0.689094\pi$
$422$		0			0
$423$	6.33438e10	−	1.29507e9i	1.97853	−	0.0404513i
$424$		0			0
$425$	−2.32234e10	−	9.07794e9i	−0.711821	−	0.278248i
$426$		0			0
$427$			1.82516e10i			0.549022i
$428$		0			0
$429$	7.65512e7	+	7.48923e9i	0.00226008	+	0.221110i
$430$		0			0
$431$		−	3.94186e9i		−	0.114233i	−0.998368	−	0.0571166i	$-0.981809\pi$
$431$		−	3.94186e9i		−	0.114233i	0.998368	−	0.0571166i	$-0.0181907\pi$
$432$		0			0
$433$			3.68544e10i			1.04843i	0.851587	+	0.524213i	$0.175640\pi$
$433$			3.68544e10i			1.04843i	−0.851587	+	0.524213i	$0.824360\pi$
$434$		0			0
$435$	1.62620e10	+	2.89364e9i	0.454169	+	0.0808142i
$436$		0			0
$437$	8.33435e9			0.228531
$438$		0			0
$439$	−5.40882e10			−1.45628			−0.728139	−	0.685429i	$-0.759615\pi$
$439$	−5.40882e10			−1.45628			−0.728139	+	0.685429i	$0.759615\pi$
$440$		0			0
$441$	9.63393e9	−	1.96967e8i	0.254712	−	0.00520762i
$442$		0			0
$443$	−1.65809e10			−0.430520			−0.215260	−	0.976557i	$-0.569060\pi$
$443$	−1.65809e10			−0.430520			−0.215260	+	0.976557i	$0.569060\pi$
$444$		0			0
$445$	−9.01710e9	+	4.78354e10i	−0.229947	+	1.21986i
$446$		0			0
$447$	2.89137e10	−	2.95542e8i	0.724225	−	0.00740268i
$448$		0			0
$449$			7.08627e10i			1.74354i	0.489914	+	0.871771i	$0.337028\pi$
$449$			7.08627e10i			1.74354i	−0.489914	+	0.871771i	$0.662972\pi$
$450$		0			0
$451$	−2.63337e10			−0.636512
$452$		0			0
$453$	4.93517e7	+	4.82822e9i	0.00117195	+	0.114655i
$454$		0			0
$455$	−1.76671e10	−	3.33030e9i	−0.412211	−	0.0777029i
$456$		0			0
$457$			3.73933e10i			0.857291i	0.903473	+	0.428646i	$0.141009\pi$
$457$			3.73933e10i			0.857291i	−0.903473	+	0.428646i	$0.858991\pi$
$458$		0			0
$459$	1.04004e9	+	3.39074e10i	0.0234315	+	0.763912i
$460$		0			0
$461$		−	7.64195e10i		−	1.69200i	−0.533182	−	0.846001i	$-0.679004\pi$
$461$		−	7.64195e10i		−	1.69200i	0.533182	−	0.846001i	$-0.320996\pi$
$462$		0			0
$463$			7.86784e10i			1.71211i	0.516886	+	0.856054i	$0.327091\pi$
$463$			7.86784e10i			1.71211i	−0.516886	+	0.856054i	$0.672909\pi$
$464$		0			0
$465$	2.89505e9	−	1.62699e10i	0.0619218	−	0.347996i
$466$		0			0
$467$	−5.21913e10			−1.09731			−0.548657	−	0.836048i	$-0.684861\pi$
$467$	−5.21913e10			−1.09731			−0.548657	+	0.836048i	$0.684861\pi$
$468$		0			0
$469$	4.94091e10			1.02121
$470$		0			0
$471$	8.76107e10	−	8.95514e8i	1.78022	−	0.0181965i
$472$		0			0
$473$	2.39251e10			0.477980
$474$		0			0
$475$	4.64134e10	+	1.81428e10i	0.911736	+	0.356393i
$476$		0			0
$477$	−3.61118e10	+	7.38311e8i	−0.697550	+	0.0142615i
$478$		0			0
$479$			4.68712e10i			0.890357i	0.895442	+	0.445179i	$0.146860\pi$
$479$			4.68712e10i			0.890357i	−0.895442	+	0.445179i	$0.853140\pi$
$480$		0			0
$481$	−2.73455e10			−0.510865
$482$		0			0
$483$	1.42314e10	−	1.45466e8i	0.261492	−	0.00267284i
$484$		0			0
$485$	1.85038e10	−	9.81621e10i	0.334422	−	1.77409i
$486$		0			0
$487$			3.43558e9i			0.0610779i	0.999534	+	0.0305390i	$0.00972236\pi$
$487$			3.43558e9i			0.0610779i	−0.999534	+	0.0305390i	$0.990278\pi$
$488$		0			0
$489$	7.56174e10	−	7.72924e8i	1.32247	−	0.0135177i
$490$		0			0
$491$			8.87660e10i			1.52729i	0.645638	+	0.763643i	$0.276591\pi$
$491$			8.87660e10i			1.52729i	−0.645638	+	0.763643i	$0.723409\pi$
$492$		0			0
$493$		−	2.08268e10i		−	0.352561i
$494$		0			0
$495$	5.85352e9	−	3.49646e10i	0.0974981	−	0.582382i
$496$		0			0
$497$	8.54026e10			1.39973
$498$		0			0
$499$	−4.27977e10			−0.690269			−0.345134	−	0.938553i	$-0.612167\pi$
$499$	−4.27977e10			−0.690269			−0.345134	+	0.938553i	$0.612167\pi$
$500$		0			0
$501$	−7.76394e8	−	7.59569e10i	−0.0123234	−	1.20564i
$502$		0			0
$503$	−9.23473e10			−1.44262			−0.721311	−	0.692612i	$-0.756460\pi$
$503$	−9.23473e10			−1.44262			−0.721311	+	0.692612i	$0.756460\pi$
$504$		0			0
$505$	−1.74744e9	+	9.27007e9i	−0.0268680	+	0.142534i
$506$		0			0
$507$	5.80639e8	+	5.68056e10i	0.00878769	+	0.859725i
$508$		0			0
$509$		−	1.23059e11i		−	1.83333i	−0.399655	−	0.916666i	$-0.630870\pi$
$509$		−	1.23059e11i		−	1.83333i	0.399655	−	0.916666i	$-0.369130\pi$
$510$		0			0
$511$	8.62877e10			1.26551
$512$		0			0
$513$	−2.07859e9	−	6.77659e10i	−0.0300123	−	0.978457i
$514$		0			0
$515$	9.33656e9	−	4.95301e10i	0.132727	−	0.704109i
$516$		0			0
$517$			8.34845e10i			1.16854i
$518$		0			0
$519$	9.00469e8	+	8.80955e10i	0.0124108	+	1.21418i
$520$		0			0
$521$			1.19451e11i			1.62121i	0.585594	+	0.810604i	$0.300861\pi$
$521$			1.19451e11i			1.62121i	−0.585594	+	0.810604i	$0.699139\pi$
$522$		0			0
$523$			8.52895e10i			1.13996i	0.821659	+	0.569979i	$0.193049\pi$
$523$			8.52895e10i			1.13996i	−0.821659	+	0.569979i	$0.806951\pi$
$524$		0			0
$525$	7.95702e10	+	3.01698e10i	1.04740	+	0.397132i
$526$		0			0
$527$	−2.08369e10			−0.270141
$528$		0			0
$529$	−7.40430e10			−0.945500
$530$		0			0
$531$	−4.16068e8	−	2.03505e10i	−0.00523343	−	0.255974i
$532$		0			0
$533$	3.25780e10			0.403660
$534$		0			0
$535$	−8.92908e10	−	1.68316e10i	−1.08991	−	0.205452i
$536$		0			0
$537$	−1.11131e11	+	1.13593e9i	−1.33641	+	0.0136601i
$538$		0			0
$539$			1.26971e10i			0.150436i
$540$		0			0
$541$	−9.16464e10			−1.06986			−0.534929	−	0.844897i	$-0.679662\pi$
$541$	−9.16464e10			−1.06986			−0.534929	+	0.844897i	$0.679662\pi$
$542$		0			0
$543$	1.12777e9	+	1.10333e11i	0.0129725	+	1.26913i
$544$		0			0
$545$	8.52484e10	+	1.60696e10i	0.966274	+	0.182145i
$546$		0			0
$547$		−	1.44838e11i		−	1.61783i	−0.587926	−	0.808915i	$-0.700055\pi$
$547$		−	1.44838e11i		−	1.61783i	0.587926	−	0.808915i	$-0.299945\pi$
$548$		0			0
$549$	4.45151e10	−	9.10117e8i	0.490024	−	0.0100186i
$550$		0			0
$551$			4.16235e10i			0.451577i
$552$		0			0
$553$		−	1.59512e11i		−	1.70567i
$554$		0			0
$555$	1.27435e11	+	2.26756e10i	1.34313	+	0.238994i
$556$		0			0
$557$	−1.61507e10			−0.167791			−0.0838957	−	0.996475i	$-0.526736\pi$
$557$	−1.61507e10			−0.167791			−0.0838957	+	0.996475i	$0.526736\pi$
$558$		0			0
$559$	−2.95983e10			−0.303123
$560$		0			0
$561$	−4.46979e10	+	4.56880e8i	−0.451269	+	0.00461265i
$562$		0			0
$563$	1.91282e10			0.190388			0.0951942	−	0.995459i	$-0.469653\pi$
$563$	1.91282e10			0.190388			0.0951942	+	0.995459i	$0.469653\pi$
$564$		0			0
$565$	−5.79668e10	−	1.09269e10i	−0.568834	−	0.107227i
$566$		0			0
$567$	−4.73208e9	−	1.15678e11i	−0.0457847	−	1.11923i
$568$		0			0
$569$			9.97367e10i			0.951494i	0.879582	+	0.475747i	$0.157822\pi$
$569$			9.97367e10i			0.951494i	−0.879582	+	0.475747i	$0.842178\pi$
$570$		0			0
$571$	−7.92305e9			−0.0745329			−0.0372664	−	0.999305i	$-0.511865\pi$
$571$	−7.92305e9			−0.0745329			−0.0372664	+	0.999305i	$0.511865\pi$
$572$		0			0
$573$	−1.37347e11	+	1.40389e9i	−1.27409	+	0.0130231i
$574$		0			0
$575$	2.37681e10	+	9.29085e9i	0.217432	+	0.0849932i
$576$		0			0
$577$			3.84287e8i			0.00346699i	0.999998	+	0.00173349i	$0.000551788\pi$
$577$			3.84287e8i			0.00346699i	−0.999998	+	0.00173349i	$0.999448\pi$
$578$		0			0
$579$	−2.88054e10	+	2.94435e8i	−0.256306	+	0.00261984i
$580$		0			0
$581$		−	1.94785e11i		−	1.70943i
$582$		0			0
$583$		−	4.75939e10i		−	0.411981i
$584$		0			0
$585$	−7.24151e9	+	4.32555e10i	−0.0618310	+	0.369333i
$586$		0			0
$587$	9.25816e10			0.779780			0.389890	−	0.920861i	$-0.372513\pi$
$587$	9.25816e10			0.779780			0.389890	+	0.920861i	$0.372513\pi$
$588$		0			0
$589$	4.16437e10			0.346010
$590$		0			0
$591$	−3.54444e8	−	3.46763e10i	−0.00290535	−	0.284239i
$592$		0			0
$593$	−3.60791e10			−0.291767			−0.145884	−	0.989302i	$-0.546603\pi$
$593$	−3.60791e10			−0.291767			−0.145884	+	0.989302i	$0.546603\pi$
$594$		0			0
$595$	1.98762e10	−	1.05442e11i	0.158586	−	0.841292i
$596$		0			0
$597$	−6.40572e7	−	6.26690e9i	−0.000504279	−	0.0493351i
$598$		0			0
$599$		−	6.63438e9i		−	0.0515339i	−0.999668	−	0.0257670i	$-0.991797\pi$
$599$		−	6.63438e9i		−	0.0515339i	0.999668	−	0.0257670i	$-0.00820278\pi$
$600$		0			0
$601$	−8.01880e10			−0.614627			−0.307313	−	0.951608i	$-0.599430\pi$
$601$	−8.01880e10			−0.614627			−0.307313	+	0.951608i	$0.599430\pi$
$602$		0			0
$603$	−2.46379e9	−	1.20507e11i	−0.0186352	−	0.911473i
$604$		0			0
$605$	−8.57506e10	−	1.61642e10i	−0.640052	−	0.120652i
$606$		0			0
$607$		−	7.86480e10i		−	0.579339i	−0.957127	−	0.289670i	$-0.906455\pi$
$607$		−	7.86480e10i		−	0.579339i	0.957127	−	0.289670i	$-0.0935455\pi$
$608$		0			0
$609$	7.26489e8	+	7.10745e10i	0.00528153	+	0.516707i
$610$		0			0
$611$		−	1.03280e11i		−	0.741060i
$612$		0			0
$613$		−	1.23608e11i		−	0.875394i	−0.899123	−	0.437697i	$-0.855794\pi$
$613$		−	1.23608e11i		−	0.875394i	0.899123	−	0.437697i	$-0.144206\pi$
$614$		0			0
$615$	−1.51819e11	−	2.70145e10i	−1.06127	−	0.188841i
$616$		0			0
$617$	1.10181e11			0.760267			0.380134	−	0.924932i	$-0.375878\pi$
$617$	1.10181e11			0.760267			0.380134	+	0.924932i	$0.375878\pi$
$618$		0			0
$619$	−3.94436e10			−0.268667			−0.134333	−	0.990936i	$-0.542889\pi$
$619$	−3.94436e10			−0.268667			−0.134333	+	0.990936i	$0.542889\pi$
$620$		0			0
$621$	−1.06444e9	−	3.47026e10i	−0.00715736	−	0.233344i
$622$		0			0
$623$	−2.09471e11			−1.39050
$624$		0			0
$625$	1.12138e11	+	1.03480e11i	0.734907	+	0.678168i
$626$		0			0
$627$	8.93313e10	−	9.13101e8i	0.578008	−	0.00590811i
$628$		0			0
$629$		−	1.63206e11i		−	1.04264i
$630$		0			0
$631$	1.77147e10			0.111742			0.0558710	−	0.998438i	$-0.482206\pi$
$631$	1.77147e10			0.111742			0.0558710	+	0.998438i	$0.482206\pi$
$632$		0			0
$633$	−7.81849e8	−	7.64906e10i	−0.00486976	−	0.476423i
$634$		0			0
$635$	−1.88098e10	+	9.97854e10i	−0.115689	+	0.613723i
$636$		0			0
$637$		−	1.57079e10i		−	0.0954026i
$638$		0			0
$639$	−4.25861e9	−	2.08294e11i	−0.0255425	−	1.24932i
$640$		0			0
$641$			2.60682e11i			1.54411i	0.635553	+	0.772057i	$0.280772\pi$
$641$			2.60682e11i			1.54411i	−0.635553	+	0.772057i	$0.719228\pi$
$642$		0			0
$643$			1.67181e11i			0.978007i	0.872282	+	0.489004i	$0.162640\pi$
$643$			1.67181e11i			0.978007i	−0.872282	+	0.489004i	$0.837360\pi$
$644$		0			0
$645$	1.37933e11	+	2.45437e10i	0.796949	+	0.141808i
$646$		0			0
$647$	3.14485e10			0.179466			0.0897332	−	0.995966i	$-0.471399\pi$
$647$	3.14485e10			0.179466			0.0897332	+	0.995966i	$0.471399\pi$
$648$		0			0
$649$	2.68211e10			0.151181
$650$		0			0
$651$	7.11090e10	−	7.26842e8i	0.395914	−	0.00404684i
$652$		0			0
$653$	−2.03277e11			−1.11799			−0.558993	−	0.829172i	$-0.688812\pi$
$653$	−2.03277e11			−1.11799			−0.558993	+	0.829172i	$0.688812\pi$
$654$		0			0
$655$	3.28420e10	−	1.74226e11i	0.178429	−	0.946557i
$656$		0			0
$657$	−4.30274e9	−	2.10453e11i	−0.0230932	−	1.12952i
$658$		0			0
$659$		−	1.20844e11i		−	0.640744i	−0.947292	−	0.320372i	$-0.896192\pi$
$659$		−	1.20844e11i		−	0.640744i	0.947292	−	0.320372i	$-0.103808\pi$
$660$		0			0
$661$	1.71943e11			0.900697			0.450349	−	0.892853i	$-0.351300\pi$
$661$	1.71943e11			0.900697			0.450349	+	0.892853i	$0.351300\pi$
$662$		0			0
$663$	5.52967e10	−	5.65216e8i	0.286184	−	0.00292523i
$664$		0			0
$665$	−3.97237e10	+	2.10733e11i	−0.203125	+	1.07757i
$666$		0			0
$667$			2.13152e10i			0.107693i
$668$		0			0
$669$	−2.18660e11	+	2.23504e9i	−1.09161	+	0.0111579i
$670$		0			0
$671$			5.86690e10i			0.289414i
$672$		0			0
$673$		−	2.68936e11i		−	1.31096i	−0.755215	−	0.655478i	$-0.772467\pi$
$673$		−	2.68936e11i		−	1.31096i	0.755215	−	0.655478i	$-0.227533\pi$
$674$		0			0
$675$	6.96153e10	−	1.95574e11i	0.335343	−	0.942096i
$676$		0			0
$677$	2.69671e11			1.28375			0.641873	−	0.766811i	$-0.278158\pi$
$677$	2.69671e11			1.28375			0.641873	+	0.766811i	$0.278158\pi$
$678$		0			0
$679$	4.29852e11			2.02227
$680$		0			0
$681$	2.78958e9	+	2.72912e11i	0.0129703	+	1.26892i
$682$		0			0
$683$	7.06710e10			0.324757			0.162378	−	0.986729i	$-0.448083\pi$
$683$	7.06710e10			0.324757			0.162378	+	0.986729i	$0.448083\pi$
$684$		0			0
$685$	1.32684e11	+	2.50113e10i	0.602638	+	0.113599i
$686$		0			0
$687$	2.39639e9	+	2.34446e11i	0.0107580	+	1.05248i
$688$		0			0
$689$			5.88794e10i			0.261268i
$690$		0			0
$691$	7.39121e10			0.324193			0.162096	−	0.986775i	$-0.448174\pi$
$691$	7.39121e10			0.324193			0.162096	+	0.986775i	$0.448174\pi$
$692$		0			0
$693$	1.52523e11	−	3.11835e9i	0.661304	−	0.0135205i
$694$		0			0
$695$	−1.99284e11	−	3.75656e10i	−0.854148	−	0.161009i
$696$		0			0
$697$			1.94435e11i			0.823841i
$698$		0			0
$699$	−3.24414e9	−	3.17384e11i	−0.0135891	−	1.32946i
$700$		0			0
$701$			1.31322e11i			0.543833i	0.962321	+	0.271917i	$0.0876575\pi$
$701$			1.31322e11i			0.543833i	−0.962321	+	0.271917i	$0.912343\pi$
$702$		0			0
$703$			3.26177e11i			1.33546i
$704$		0			0
$705$	−8.56428e10	+	4.81306e11i	−0.346685	+	1.94834i
$706$		0			0
$707$	−4.05937e10			−0.162473
$708$		0			0
$709$	−1.01201e11			−0.400497			−0.200248	−	0.979745i	$-0.564175\pi$
$709$	−1.01201e11			−0.400497			−0.200248	+	0.979745i	$0.564175\pi$
$710$		0			0
$711$	−3.89046e11	+	7.95409e9i	−1.52238	+	0.0311252i
$712$		0			0
$713$	2.13256e10			0.0825168
$714$		0			0
$715$	−5.67901e10	−	1.07051e10i	−0.217294	−	0.0409606i
$716$		0			0
$717$	−2.94630e11	+	3.01156e9i	−1.11481	+	0.0113950i
$718$		0			0
$719$		−	2.67104e11i		−	0.999458i	−0.866182	−	0.499729i	$-0.833433\pi$
$719$		−	2.67104e11i		−	0.999458i	0.866182	−	0.499729i	$-0.166567\pi$
$720$		0			0
$721$	2.16892e11			0.802607
$722$		0			0
$723$	4.93945e9	+	4.83241e11i	0.0180770	+	1.76852i
$724$		0			0
$725$	−4.64004e10	+	1.18703e11i	−0.167946	+	0.429645i
$726$		0			0
$727$		−	1.03626e11i		−	0.370964i	−0.982648	−	0.185482i	$-0.940615\pi$
$727$		−	1.03626e11i		−	0.370964i	0.982648	−	0.185482i	$-0.0593847\pi$
$728$		0			0
$729$	−2.81899e11	+	1.73097e10i	−0.998120	+	0.0612885i
$730$		0			0
$731$		−	1.76651e11i		−	0.618653i
$732$		0			0
$733$		−	1.48148e11i		−	0.513192i	−0.966519	−	0.256596i	$-0.917399\pi$
$733$		−	1.48148e11i		−	0.513192i	0.966519	−	0.256596i	$-0.0826010\pi$
$734$		0			0
$735$	−1.30254e10	+	7.32016e10i	−0.0446315	+	0.250825i
$736$		0			0
$737$	1.58824e11			0.538326
$738$		0			0
$739$	−2.86587e11			−0.960901			−0.480450	−	0.877022i	$-0.659527\pi$
$739$	−2.86587e11			−0.960901			−0.480450	+	0.877022i	$0.659527\pi$
$740$		0			0
$741$	−1.10514e11	+	1.12962e9i	−0.366559	+	0.00374678i
$742$		0			0
$743$	1.04718e10			0.0343609			0.0171805	−	0.999852i	$-0.494531\pi$
$743$	1.04718e10			0.0343609			0.0171805	+	0.999852i	$0.494531\pi$
$744$		0			0
$745$	−4.13292e10	+	2.19250e11i	−0.134163	+	0.711728i
$746$		0			0
$747$	−4.75073e11	+	9.71295e9i	−1.52573	+	0.0311938i
$748$		0			0
$749$		−	3.91005e11i		−	1.24238i
$750$		0			0
$751$	−2.22488e11			−0.699433			−0.349717	−	0.936855i	$-0.613722\pi$
$751$	−2.22488e11			−0.699433			−0.349717	+	0.936855i	$0.613722\pi$
$752$		0			0
$753$	3.41603e11	−	3.49170e9i	1.06253	−	0.0108607i
$754$		0			0
$755$	−3.66120e10	−	6.90146e9i	−0.112677	−	0.0212399i
$756$		0			0
$757$			3.34747e11i			1.01937i	0.860361	+	0.509686i	$0.170238\pi$
$757$			3.34747e11i			1.01937i	−0.860361	+	0.509686i	$0.829762\pi$
$758$		0			0
$759$	4.57462e10	−	4.67595e8i	0.137844	−	0.00140897i
$760$		0			0
$761$			2.34208e10i			0.0698335i	0.999390	+	0.0349168i	$0.0111166\pi$
$761$			2.34208e10i			0.0698335i	−0.999390	+	0.0349168i	$0.988883\pi$
$762$		0			0
$763$			3.73303e11i			1.10145i
$764$		0			0
$765$	−2.58161e11	−	4.32195e10i	−0.753782	−	0.126192i
$766$		0			0
$767$	−3.31809e10			−0.0958753
$768$		0			0
$769$	4.64303e11			1.32769			0.663845	−	0.747870i	$-0.268924\pi$
$769$	4.64303e11			1.32769			0.663845	+	0.747870i	$0.268924\pi$
$770$		0			0
$771$	4.62005e9	+	4.51993e11i	0.0130746	+	1.27913i
$772$		0			0
$773$	4.73329e11			1.32570			0.662850	−	0.748752i	$-0.269346\pi$
$773$	4.73329e11			1.32570			0.662850	+	0.748752i	$0.269346\pi$
$774$		0			0
$775$	1.18761e11	+	4.64230e10i	0.329204	+	0.128685i
$776$		0			0
$777$	5.69303e9	+	5.56965e11i	0.0156192	+	1.52807i
$778$		0			0
$779$		−	3.88590e11i		−	1.05522i
$780$		0			0
$781$	2.74523e11			0.737862
$782$		0			0
$783$	1.73312e11	−	5.31602e9i	0.461086	−	0.0141429i
$784$		0			0
$785$	−1.25231e11	+	6.64344e11i	−0.329786	+	1.74950i
$786$		0			0
$787$		−	2.83682e11i		−	0.739492i	−0.929133	−	0.369746i	$-0.879445\pi$
$787$		−	2.83682e11i		−	0.739492i	0.929133	−	0.369746i	$-0.120555\pi$
$788$		0			0
$789$	−7.02191e9	−	6.86974e11i	−0.0181196	−	1.77269i
$790$		0			0
$791$		−	2.53837e11i		−	0.648409i
$792$		0			0
$793$		−	7.25807e10i		−	0.183539i
$794$		0			0
$795$	4.88243e10	−	2.74389e11i	0.122227	−	0.686906i
$796$		0			0
$797$	−4.08181e11			−1.01163			−0.505813	−	0.862643i	$-0.668807\pi$
$797$	−4.08181e11			−1.01163			−0.505813	+	0.862643i	$0.668807\pi$
$798$		0			0
$799$	6.16408e11			1.51245
$800$		0			0
$801$	1.04453e10	+	5.10893e11i	0.0253741	+	1.24108i
$802$		0			0
$803$	2.77368e11			0.667105
$804$		0			0
$805$	−2.03423e10	+	1.07915e11i	−0.0484415	+	0.256980i
$806$		0			0
$807$	−7.16265e11	+	7.32131e9i	−1.68880	+	0.0172621i
$808$		0			0
$809$			2.28320e11i			0.533028i	0.963831	+	0.266514i	$0.0858719\pi$
$809$			2.28320e11i			0.533028i	−0.963831	+	0.266514i	$0.914128\pi$
$810$		0			0
$811$	4.30064e11			0.994144			0.497072	−	0.867709i	$-0.334408\pi$
$811$	4.30064e11			0.994144			0.497072	+	0.867709i	$0.334408\pi$
$812$		0			0
$813$	1.97289e8	+	1.93013e10i	0.000451586	+	0.0441800i
$814$		0			0
$815$	−1.08088e11	+	5.73400e11i	−0.244988	+	1.29965i
$816$		0			0
$817$			3.53048e11i			0.792401i
$818$		0			0
$819$	−1.88689e11	+	3.85777e9i	−0.419383	+	0.00857435i
$820$		0			0
$821$			1.77961e11i			0.391699i	0.980634	+	0.195850i	$0.0627464\pi$
$821$			1.77961e11i			0.391699i	−0.980634	+	0.195850i	$0.937254\pi$
$822$		0			0
$823$			4.06602e11i			0.886278i	0.896453	+	0.443139i	$0.146135\pi$
$823$			4.06602e11i			0.886278i	−0.896453	+	0.443139i	$0.853865\pi$
$824$		0			0
$825$	2.55775e11	+	9.69795e10i	0.552132	+	0.209346i
$826$		0			0
$827$	8.21144e11			1.75549			0.877743	−	0.479133i	$-0.159049\pi$
$827$	8.21144e11			1.75549			0.877743	+	0.479133i	$0.159049\pi$
$828$		0			0
$829$	2.41128e11			0.510540			0.255270	−	0.966870i	$-0.417836\pi$
$829$	2.41128e11			0.510540			0.255270	+	0.966870i	$0.417836\pi$
$830$		0			0
$831$	−4.52906e11	+	4.62938e9i	−0.949739	+	0.00970776i
$832$		0			0
$833$	9.37492e10			0.194710
$834$		0			0
$835$	5.75974e11	+	1.08573e11i	1.18483	+	0.223344i
$836$		0			0
$837$	−5.31860e9	−	1.73396e11i	−0.0108367	−	0.353296i
$838$		0			0
$839$		−	5.99608e11i		−	1.21009i	−0.796189	−	0.605047i	$-0.793154\pi$
$839$		−	5.99608e11i		−	1.21009i	0.796189	−	0.605047i	$-0.206846\pi$
$840$		0			0
$841$	3.93794e11			0.787200
$842$		0			0
$843$	−2.40682e9	+	2.46013e7i	−0.00476577	+	4.87133e-5i
$844$		0			0
$845$	−4.30752e11	−	8.11980e10i	−0.844890	−	0.159264i
$846$		0			0
$847$		−	3.75502e11i		−	0.729590i
$848$		0			0
$849$	7.99989e10	−	8.17709e8i	0.153976	−	0.00157387i
$850$		0			0
$851$			1.67034e11i			0.318483i
$852$		0			0
$853$		−	6.49840e11i		−	1.22747i	−0.789513	−	0.613734i	$-0.789667\pi$
$853$		−	6.49840e11i		−	1.22747i	0.789513	−	0.613734i	$-0.210333\pi$
$854$		0			0
$855$	5.15950e11	+	8.63766e10i	0.965481	+	0.161634i
$856$		0			0
$857$	−5.07048e11			−0.939995			−0.469998	−	0.882668i	$-0.655745\pi$
$857$	−5.07048e11			−0.939995			−0.469998	+	0.882668i	$0.655745\pi$
$858$		0			0
$859$	−7.28000e11			−1.33708			−0.668542	−	0.743674i	$-0.733082\pi$
$859$	−7.28000e11			−1.33708			−0.668542	+	0.743674i	$0.733082\pi$
$860$		0			0
$861$	−6.78238e9	−	6.63540e11i	−0.0123415	−	1.20741i
$862$		0			0
$863$	2.68029e11			0.483213			0.241606	−	0.970374i	$-0.422326\pi$
$863$	2.68029e11			0.483213			0.241606	+	0.970374i	$0.422326\pi$
$864$		0			0
$865$	−6.68020e11	−	1.25924e11i	−1.19323	−	0.224928i
$866$		0			0
$867$	−2.40185e9	−	2.34980e11i	−0.00425079	−	0.415867i
$868$		0			0
$869$		−	5.12746e11i		−	0.899132i
$870$		0			0
$871$	−1.96484e11			−0.341393
$872$		0			0
$873$	−2.14346e10	−	1.04840e12i	−0.0369027	−	1.80496i
$874$		0			0
$875$	−3.48203e11	+	5.56690e11i	−0.594018	+	0.949688i
$876$		0			0
$877$		−	3.03544e11i		−	0.513125i	−0.966528	−	0.256563i	$-0.917410\pi$
$877$		−	3.03544e11i		−	0.513125i	0.966528	−	0.256563i	$-0.0825900\pi$
$878$		0			0
$879$	−2.42349e8	−	2.37097e10i	−0.000405962	−	0.0397165i
$880$		0			0
$881$		−	5.01924e11i		−	0.833172i	−0.909096	−	0.416586i	$-0.863226\pi$
$881$		−	5.01924e11i		−	0.833172i	0.909096	−	0.416586i	$-0.136774\pi$
$882$		0			0
$883$			2.24386e11i			0.369108i	0.982822	+	0.184554i	$0.0590840\pi$
$883$			2.24386e11i			0.369108i	−0.982822	+	0.184554i	$0.940916\pi$
$884$		0			0
$885$	1.54629e11	+	2.75145e10i	0.252068	+	0.0448526i
$886$		0			0
$887$	8.33590e11			1.34666			0.673330	−	0.739342i	$-0.264863\pi$
$887$	8.33590e11			1.34666			0.673330	+	0.739342i	$0.264863\pi$
$888$		0			0
$889$	−4.36961e11			−0.699577
$890$		0			0
$891$	−1.52111e10	−	3.71842e11i	−0.0241351	−	0.589994i
$892$		0			0
$893$	−1.23193e12			−1.93722
$894$		0			0
$895$	1.58851e11	−	8.42698e11i	0.247570	−	1.31335i
$896$		0			0
$897$	−5.65936e10	+	5.78472e8i	−0.0874173	+	0.000893537i
$898$		0			0
$899$			1.06504e11i			0.163053i
$900$		0			0
$901$	−3.51409e11			−0.533229
$902$		0			0
$903$	6.16203e9	+	6.02849e11i	0.00926772	+	0.906688i
$904$		0			0
$905$	−8.36648e11	−	1.57710e11i	−1.24723	−	0.235107i
$906$		0			0
$907$		−	2.56833e11i		−	0.379509i	−0.981832	−	0.189755i	$-0.939231\pi$
$907$		−	2.56833e11i		−	0.379509i	0.981832	−	0.189755i	$-0.0607692\pi$
$908$		0			0
$909$	2.02421e9	+	9.90067e10i	0.00296483	+	0.145014i
$910$		0			0
$911$			1.08855e12i			1.58043i	0.612829	+	0.790215i	$0.290031\pi$
$911$			1.08855e12i			1.58043i	−0.612829	+	0.790215i	$0.709969\pi$
$912$		0			0
$913$		−	6.26127e11i		−	0.901113i
$914$		0			0
$915$	−6.01858e10	+	3.38239e11i	−0.0858637	+	0.482547i
$916$		0			0
$917$	7.62935e11			1.07897
$918$		0			0
$919$	1.96591e11			0.275614			0.137807	−	0.990459i	$-0.455995\pi$
$919$	1.96591e11			0.275614			0.137807	+	0.990459i	$0.455995\pi$
$920$		0			0
$921$	1.82969e11	−	1.87022e9i	0.254295	−	0.00259928i
$922$		0			0
$923$	−3.39619e11			−0.467934
$924$		0			0
$925$	−3.63611e11	+	9.30199e11i	−0.496672	+	1.27060i
$926$		0			0
$927$	−1.08153e10	−	5.28993e11i	−0.0146461	−	0.716360i
$928$		0			0
$929$		−	1.41420e12i		−	1.89866i	−0.314285	−	0.949329i	$-0.601765\pi$
$929$		−	1.41420e12i		−	1.89866i	0.314285	−	0.949329i	$-0.398235\pi$
$930$		0			0
$931$	−1.87363e11			−0.249394
$932$		0			0
$933$	1.13319e12	−	1.15829e10i	1.49546	−	0.0152859i
$934$		0			0
$935$	6.38912e10	−	3.38940e11i	0.0835977	−	0.443482i
$936$		0			0
$937$		−	9.48260e11i		−	1.23018i	−0.788457	−	0.615090i	$-0.789120\pi$
$937$		−	9.48260e11i		−	1.23018i	0.788457	−	0.615090i	$-0.210880\pi$
$938$		0			0
$939$	−3.42791e11	+	3.50384e9i	−0.440928	+	0.00450695i
$940$		0			0
$941$			6.15688e11i			0.785239i	0.919701	+	0.392620i	$0.128431\pi$
$941$			6.15688e11i			0.785239i	−0.919701	+	0.392620i	$0.871569\pi$
$942$		0			0
$943$		−	1.98995e11i		−	0.251649i
$944$		0			0
$945$	8.82523e11	+	1.38488e11i	1.10662	+	0.173654i
$946$		0			0
$947$	6.24461e11			0.776435			0.388218	−	0.921568i	$-0.373091\pi$
$947$	6.24461e11			0.776435			0.388218	+	0.921568i	$0.373091\pi$
$948$		0			0
$949$	−3.43138e11			−0.423062
$950$		0			0
$951$	6.70924e9	+	6.56385e11i	0.00820260	+	0.802484i
$952$		0			0
$953$	−7.85330e11			−0.952096			−0.476048	−	0.879419i	$-0.657931\pi$
$953$	−7.85330e11			−0.952096			−0.476048	+	0.879419i	$0.657931\pi$
$954$		0			0
$955$	1.96323e11	−	1.04149e12i	0.236025	−	1.25210i
$956$		0			0
$957$	2.33527e9	+	2.28466e11i	0.00278413	+	0.272379i
$958$		0			0
$959$			5.81024e11i			0.686941i
$960$		0			0
$961$	−7.46335e11			−0.875065
$962$		0			0
$963$	−9.53647e11	+	1.94975e10i	−1.10888	+	0.0226711i
$964$		0			0
$965$	4.11744e10	−	2.18429e11i	0.0474808	−	0.251884i
$966$		0			0
$967$		−	6.73177e9i		−	0.00769881i	−0.999993	−	0.00384940i	$-0.998775\pi$
$967$		−	6.73177e9i		−	0.00769881i	0.999993	−	0.00384940i	$-0.00122531\pi$
$968$		0			0
$969$	−6.74188e9	−	6.59578e11i	−0.00764691	−	0.748119i
$970$		0			0
$971$			1.15007e12i			1.29374i	0.762601	+	0.646869i	$0.223922\pi$
$971$			1.15007e12i			1.29374i	−0.762601	+	0.646869i	$0.776078\pi$
$972$		0			0
$973$		−	8.72665e11i		−	0.973636i
$974$		0			0
$975$	−3.16425e11	−	1.19975e11i	−0.350149	−	0.132762i
$976$		0			0
$977$	1.28466e12			1.40997			0.704983	−	0.709224i	$-0.250955\pi$
$977$	1.28466e12			1.40997			0.704983	+	0.709224i	$0.250955\pi$
$978$		0			0
$979$	−6.73337e11			−0.732996
$980$		0			0
$981$	9.10474e11	−	1.86148e10i	0.983086	−	0.0200993i
$982$		0			0
$983$	9.83890e10			0.105374			0.0526869	−	0.998611i	$-0.483221\pi$
$983$	9.83890e10			0.105374			0.0526869	+	0.998611i	$0.483221\pi$
$984$		0			0
$985$	2.62947e11	+	4.95663e10i	0.279334	+	0.0526553i
$986$		0			0
$987$	−2.10359e12	+	2.15018e10i	−2.21662	+	0.0226572i
$988$		0			0
$989$			1.80794e11i			0.188973i
$990$		0			0
$991$	−1.87647e12			−1.94557			−0.972787	−	0.231703i	$-0.925570\pi$
$991$	−1.87647e12			−1.94557			−0.972787	+	0.231703i	$0.925570\pi$
$992$		0			0
$993$	−3.40354e9	−	3.32979e11i	−0.00350054	−	0.342468i
$994$		0			0
$995$	4.75213e10	+	8.95791e9i	0.0484838	+	0.00913933i
$996$		0			0
$997$			1.13370e12i			1.14741i	0.819063	+	0.573704i	$0.194494\pi$
$997$			1.13370e12i			1.14741i	−0.819063	+	0.573704i	$0.805506\pi$
$998$		0			0
$999$	1.35814e12	−	4.16582e10i	1.36358	−	0.0418253i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.9.c.a.89.26	yes	48
3.2	odd	2	inner	120.9.c.a.89.24	yes	48
4.3	odd	2		240.9.c.f.209.23		48
5.4	even	2	inner	120.9.c.a.89.23	✓	48
12.11	even	2		240.9.c.f.209.25		48
15.14	odd	2	inner	120.9.c.a.89.25	yes	48
20.19	odd	2		240.9.c.f.209.26		48
60.59	even	2		240.9.c.f.209.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.9.c.a.89.23	✓	48	5.4	even	2	inner
120.9.c.a.89.24	yes	48	3.2	odd	2	inner
120.9.c.a.89.25	yes	48	15.14	odd	2	inner
120.9.c.a.89.26	yes	48	1.1	even	1	trivial
240.9.c.f.209.23		48	4.3	odd	2
240.9.c.f.209.24		48	60.59	even	2
240.9.c.f.209.25		48	12.11	even	2
240.9.c.f.209.26		48	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	120.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.827899 + 80.9958i) q^{3} +(-614.183 - 115.775i) q^{5} -2689.51i q^{7} +(-6559.63 + 134.113i) q^{9} -8645.32i q^{11} +10695.3i q^{13} +(8868.83 - 49842.1i) q^{15} -63832.7 q^{17} +127573. q^{19} +(217839. - 2226.64i) q^{21} +65329.8 q^{23} +(363817. + 142215. i) q^{25} +(-16293.3 - 531191. i) q^{27} +326271. i q^{29} +326429. q^{31} +(700235. - 7157.45i) q^{33} +(-311379. + 1.65185e6i) q^{35} +2.55678e6i q^{37} +(-866275. + 8854.64i) q^{39} -3.04601e6i q^{41} +2.76741e6i q^{43} +(4.04434e6 + 677073. i) q^{45} -9.65661e6 q^{47} -1.46867e6 q^{49} +(-52847.1 - 5.17018e6i) q^{51} +5.50516e6 q^{53} +(-1.00092e6 + 5.30981e6i) q^{55} +(105618. + 1.03329e7i) q^{57} +3.10238e6i q^{59} -6.78622e6 q^{61} +(360697. + 1.76422e7i) q^{63} +(1.23825e6 - 6.56888e6i) q^{65} +1.83710e7i q^{67} +(54086.5 + 5.29144e6i) q^{69} +3.17540e7i q^{71} +3.20830e7i q^{73} +(-1.12176e7 + 2.95854e7i) q^{75} -2.32517e7 q^{77} +5.93091e7 q^{79} +(4.30107e7 - 1.75946e6i) q^{81} +7.24238e7 q^{83} +(3.92050e7 + 7.39026e6i) q^{85} +(-2.64266e7 + 270119. i) q^{87} -7.78845e7i q^{89} +2.87652e7 q^{91} +(270250. + 2.64394e7i) q^{93} +(-7.83535e7 - 1.47699e7i) q^{95} +1.59825e8i q^{97} +(1.15945e6 + 5.67101e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2528 q^{9} + 132352 q^{15} + 116176 q^{21} + 56976 q^{25} + 1395648 q^{31} + 6888832 q^{39} - 4287056 q^{45} - 30813552 q^{49} - 22815168 q^{51} - 6062784 q^{55} + 14031936 q^{61} + 2522608 q^{69}+ \cdots - 21719360 q^{99}+O(q^{100}) \) 48 * q + 2528 * q^9 + 132352 * q^15 + 116176 * q^21 + 56976 * q^25 + 1395648 * q^31 + 6888832 * q^39 - 4287056 * q^45 - 30813552 * q^49 - 22815168 * q^51 - 6062784 * q^55 + 14031936 * q^61 + 2522608 * q^69 + 41684416 * q^75 + 19866432 * q^79 - 93539312 * q^81 - 116297664 * q^85 + 16826880 * q^91 - 21719360 * q^99

Introduction

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