LMFDB - Embedded newform 120.9.c.a.89.39

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)

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")

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);

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			89.39
Character	$\chi$	$=$	120.89
Dual form			120.9.c.a.89.40

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(63.1416 - 50.7359i) q^{3} +(94.4932 + 617.816i) q^{5} +2120.56i q^{7} +(1412.73 - 6407.10i) q^{9} +18869.7i q^{11} -1613.52i q^{13} +(37311.9 + 34215.7i) q^{15} -128361. q^{17} +123008. q^{19} +(107589. + 133896. i) q^{21} -463819. q^{23} +(-372767. + 116759. i) q^{25} +(-235868. - 476231. i) q^{27} -867620. i q^{29} -1.29205e6 q^{31} +(957369. + 1.19146e6i) q^{33} +(-1.31012e6 + 200379. i) q^{35} -160257. i q^{37} +(-81863.3 - 101880. i) q^{39} +4.10559e6i q^{41} -1.57070e6i q^{43} +(4.09190e6 + 267382. i) q^{45} +5.70949e6 q^{47} +1.26802e6 q^{49} +(-8.10494e6 + 6.51253e6i) q^{51} -8.30385e6 q^{53} +(-1.16580e7 + 1.78305e6i) q^{55} +(7.76690e6 - 6.24090e6i) q^{57} +1.28620e7i q^{59} +2.79353e6 q^{61} +(1.35867e7 + 2.99579e6i) q^{63} +(996857. - 152467. i) q^{65} -2.02082e7i q^{67} +(-2.92863e7 + 2.35323e7i) q^{69} +2.19500e7i q^{71} +3.05707e7i q^{73} +(-1.76133e7 + 2.62850e7i) q^{75} -4.00143e7 q^{77} -6.31989e7 q^{79} +(-3.90551e7 - 1.81030e7i) q^{81} +3.53309e6 q^{83} +(-1.21293e7 - 7.93036e7i) q^{85} +(-4.40195e7 - 5.47829e7i) q^{87} +9.26111e7i q^{89} +3.42157e6 q^{91} +(-8.15825e7 + 6.55536e7i) q^{93} +(1.16234e7 + 7.59960e7i) q^{95} +1.20124e8i q^{97} +(1.20900e8 + 2.66578e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	63.1416	−	50.7359i	0.779526	−	0.626369i
$3$	63.1416	−	50.7359i	0.779526	−	0.626369i
$4$		0			0
$5$	94.4932	+	617.816i	0.151189	+	0.988505i
$5$	94.4932	+	617.816i	0.151189	+	0.988505i
$6$		0			0
$7$			2120.56i			0.883200i	0.897212	+	0.441600i	$0.145589\pi$
$7$			2120.56i			0.883200i	−0.897212	+	0.441600i	$0.854411\pi$
$8$		0			0
$9$	1412.73	−	6407.10i	0.215323	−	0.976543i
$10$		0			0
$11$			18869.7i			1.28882i	0.764679	+	0.644412i	$0.222898\pi$
$11$			18869.7i			1.28882i	−0.764679	+	0.644412i	$0.777102\pi$
$12$		0			0
$13$		−	1613.52i		−	0.0564938i	−0.999601	−	0.0282469i	$-0.991008\pi$
$13$		−	1613.52i		−	0.0564938i	0.999601	−	0.0282469i	$-0.00899246\pi$
$14$		0			0
$15$	37311.9	+	34215.7i	0.737025	+	0.675865i
$16$		0			0
$17$	−128361.			−1.53687			−0.768437	−	0.639925i	$-0.778965\pi$
$17$	−128361.			−1.53687			−0.768437	+	0.639925i	$0.778965\pi$
$18$		0			0
$19$	123008.			0.943882			0.471941	−	0.881630i	$-0.343554\pi$
$19$	123008.			0.943882			0.471941	+	0.881630i	$0.343554\pi$
$20$		0			0
$21$	107589.	+	133896.i	0.553209	+	0.688478i
$22$		0			0
$23$	−463819.			−1.65744			−0.828719	−	0.559664i	$-0.810930\pi$
$23$	−463819.			−1.65744			−0.828719	+	0.559664i	$0.810930\pi$
$24$		0			0
$25$	−372767.	+	116759.i	−0.954284	+	0.298902i
$26$		0			0
$27$	−235868.	−	476231.i	−0.443827	−	0.896113i
$28$		0			0
$29$		−	867620.i		−	1.22670i	−0.789812	−	0.613349i	$-0.789822\pi$
$29$		−	867620.i		−	1.22670i	0.789812	−	0.613349i	$-0.210178\pi$
$30$		0			0
$31$	−1.29205e6			−1.39905			−0.699527	−	0.714607i	$-0.746606\pi$
$31$	−1.29205e6			−1.39905			−0.699527	+	0.714607i	$0.746606\pi$
$32$		0			0
$33$	957369.	+	1.19146e6i	0.807279	+	1.00467i
$34$		0			0
$35$	−1.31012e6	+	200379.i	−0.873047	+	0.133530i
$36$		0			0
$37$		−	160257.i		−	0.0855088i	−0.999086	−	0.0427544i	$-0.986387\pi$
$37$		−	160257.i		−	0.0855088i	0.999086	−	0.0427544i	$-0.0136133\pi$
$38$		0			0
$39$	−81863.3	−	101880.i	−0.0353860	−	0.0440384i
$40$		0			0
$41$			4.10559e6i			1.45292i	0.687211	+	0.726458i	$0.258835\pi$
$41$			4.10559e6i			1.45292i	−0.687211	+	0.726458i	$0.741165\pi$
$42$		0			0
$43$		−	1.57070e6i		−	0.459430i	−0.973258	−	0.229715i	$-0.926221\pi$
$43$		−	1.57070e6i		−	0.459430i	0.973258	−	0.229715i	$-0.0737795\pi$
$44$		0			0
$45$	4.09190e6	+	267382.i	0.997872	+	0.0652051i
$46$		0			0
$47$	5.70949e6			1.17005			0.585027	−	0.811014i	$-0.301084\pi$
$47$	5.70949e6			1.17005			0.585027	+	0.811014i	$0.301084\pi$
$48$		0			0
$49$	1.26802e6			0.219958
$50$		0			0
$51$	−8.10494e6	+	6.51253e6i	−1.19803	+	0.962651i
$52$		0			0
$53$	−8.30385e6			−1.05239			−0.526194	−	0.850365i	$-0.676381\pi$
$53$	−8.30385e6			−1.05239			−0.526194	+	0.850365i	$0.676381\pi$
$54$		0			0
$55$	−1.16580e7	+	1.78305e6i	−1.27401	+	0.194856i
$56$		0			0
$57$	7.76690e6	−	6.24090e6i	0.735781	−	0.591219i
$58$		0			0
$59$			1.28620e7i			1.06145i	0.847543	+	0.530727i	$0.178081\pi$
$59$			1.28620e7i			1.06145i	−0.847543	+	0.530727i	$0.821919\pi$
$60$		0			0
$61$	2.79353e6			0.201760			0.100880	−	0.994899i	$-0.467834\pi$
$61$	2.79353e6			0.201760			0.100880	+	0.994899i	$0.467834\pi$
$62$		0			0
$63$	1.35867e7	+	2.99579e6i	0.862482	+	0.190173i
$64$		0			0
$65$	996857.	−	152467.i	0.0558443	−	0.00854124i
$66$		0			0
$67$		−	2.02082e7i		−	1.00283i	−0.865206	−	0.501417i	$-0.832812\pi$
$67$		−	2.02082e7i		−	1.00283i	0.865206	−	0.501417i	$-0.167188\pi$
$68$		0			0
$69$	−2.92863e7	+	2.35323e7i	−1.29202	+	1.03817i
$70$		0			0
$71$			2.19500e7i			0.863774i	0.901928	+	0.431887i	$0.142152\pi$
$71$			2.19500e7i			0.863774i	−0.901928	+	0.431887i	$0.857848\pi$
$72$		0			0
$73$			3.05707e7i			1.07650i	0.842785	+	0.538250i	$0.180915\pi$
$73$			3.05707e7i			1.07650i	−0.842785	+	0.538250i	$0.819085\pi$
$74$		0			0
$75$	−1.76133e7	+	2.62850e7i	−0.556666	+	0.830736i
$76$		0			0
$77$	−4.00143e7			−1.13829
$78$		0			0
$79$	−6.31989e7			−1.62256			−0.811281	−	0.584657i	$-0.801229\pi$
$79$	−6.31989e7			−1.62256			−0.811281	+	0.584657i	$0.801229\pi$
$80$		0			0
$81$	−3.90551e7	−	1.81030e7i	−0.907272	−	0.420544i
$82$		0			0
$83$	3.53309e6			0.0744461			0.0372231	−	0.999307i	$-0.488149\pi$
$83$	3.53309e6			0.0744461			0.0372231	+	0.999307i	$0.488149\pi$
$84$		0			0
$85$	−1.21293e7	−	7.93036e7i	−0.232359	−	1.51921i
$86$		0			0
$87$	−4.40195e7	−	5.47829e7i	−0.768366	−	0.956243i
$88$		0			0
$89$			9.26111e7i			1.47606i	0.674770	+	0.738028i	$0.264243\pi$
$89$			9.26111e7i			1.47606i	−0.674770	+	0.738028i	$0.735757\pi$
$90$		0			0
$91$	3.42157e6			0.0498953
$92$		0			0
$93$	−8.15825e7	+	6.55536e7i	−1.09060	+	0.876324i
$94$		0			0
$95$	1.16234e7	+	7.59960e7i	0.142705	+	0.933032i
$96$		0			0
$97$			1.20124e8i			1.35688i	0.734655	+	0.678441i	$0.237344\pi$
$97$			1.20124e8i			1.35688i	−0.734655	+	0.678441i	$0.762656\pi$
$98$		0			0
$99$	1.20900e8	+	2.66578e7i	1.25859	+	0.277513i
$100$		0			0
$101$			4.63058e7i			0.444990i	0.974934	+	0.222495i	$0.0714200\pi$
$101$			4.63058e7i			0.444990i	−0.974934	+	0.222495i	$0.928580\pi$
$102$		0			0
$103$		−	2.76358e7i		−	0.245540i	−0.992435	−	0.122770i	$-0.960822\pi$
$103$		−	2.76358e7i		−	0.245540i	0.992435	−	0.122770i	$-0.0391778\pi$
$104$		0			0
$105$	−7.25565e7	+	7.91222e7i	−0.596924	+	0.650940i
$106$		0			0
$107$	1.46266e8			1.11586			0.557929	−	0.829889i	$-0.311596\pi$
$107$	1.46266e8			1.11586			0.557929	+	0.829889i	$0.311596\pi$
$108$		0			0
$109$	−5.99322e7			−0.424575			−0.212287	−	0.977207i	$-0.568091\pi$
$109$	−5.99322e7			−0.424575			−0.212287	+	0.977207i	$0.568091\pi$
$110$		0			0
$111$	−8.13080e6	−	1.01189e7i	−0.0535601	−	0.0666564i
$112$		0			0
$113$	1.82371e8			1.11851			0.559257	−	0.828994i	$-0.311086\pi$
$113$	1.82371e8			1.11851			0.559257	+	0.828994i	$0.311086\pi$
$114$		0			0
$115$	−4.38278e7	−	2.86555e8i	−0.250587	−	1.63839i
$116$		0			0
$117$	−1.03380e7	−	2.27947e6i	−0.0551686	−	0.0121644i
$118$		0			0
$119$		−	2.72198e8i		−	1.35737i
$120$		0			0
$121$	−1.41705e8			−0.661065
$122$		0			0
$123$	2.08301e8	+	2.59234e8i	0.910062	+	1.13259i
$124$		0			0
$125$	−1.07359e8	−	2.19268e8i	−0.439744	−	0.898123i
$126$		0			0
$127$		−	2.33236e8i		−	0.896564i	−0.893892	−	0.448282i	$-0.852036\pi$
$127$		−	2.33236e8i		−	0.896564i	0.893892	−	0.448282i	$-0.147964\pi$
$128$		0			0
$129$	−7.96910e7	−	9.91766e7i	−0.287773	−	0.358138i
$130$		0			0
$131$			3.10558e8i			1.05453i	0.849702	+	0.527264i	$0.176782\pi$
$131$			3.10558e8i			1.05453i	−0.849702	+	0.527264i	$0.823218\pi$
$132$		0			0
$133$			2.60845e8i			0.833636i
$134$		0			0
$135$	2.71935e8	−	1.90723e8i	0.818710	−	0.574207i
$136$		0			0
$137$	−5.94131e8			−1.68655			−0.843277	−	0.537479i	$-0.819377\pi$
$137$	−5.94131e8			−1.68655			−0.843277	+	0.537479i	$0.819377\pi$
$138$		0			0
$139$	6.69752e8			1.79413			0.897067	−	0.441894i	$-0.145693\pi$
$139$	6.69752e8			1.79413			0.897067	+	0.441894i	$0.145693\pi$
$140$		0			0
$141$	3.60507e8	−	2.89676e8i	0.912089	−	0.732886i
$142$		0			0
$143$	3.04465e7			0.0728105
$144$		0			0
$145$	5.36029e8	−	8.19842e7i	1.21260	−	0.185463i
$146$		0			0
$147$	8.00646e7	−	6.43339e7i	0.171463	−	0.137775i
$148$		0			0
$149$		−	1.67119e7i		−	0.0339062i	−0.999856	−	0.0169531i	$-0.994603\pi$
$149$		−	1.67119e7i		−	0.0339062i	0.999856	−	0.0169531i	$-0.00539661\pi$
$150$		0			0
$151$	1.13964e8			0.219210			0.109605	−	0.993975i	$-0.465041\pi$
$151$	1.13964e8			0.219210			0.109605	+	0.993975i	$0.465041\pi$
$152$		0			0
$153$	−1.81340e8	+	8.22423e8i	−0.330924	+	1.50082i
$154$		0			0
$155$	−1.22090e8	−	7.98252e8i	−0.211522	−	1.38297i
$156$		0			0
$157$		−	1.40513e8i		−	0.231269i	−0.993292	−	0.115634i	$-0.963110\pi$
$157$		−	1.40513e8i		−	0.231269i	0.993292	−	0.115634i	$-0.0368901\pi$
$158$		0			0
$159$	−5.24319e8	+	4.21303e8i	−0.820364	+	0.659183i
$160$		0			0
$161$		−	9.83558e8i		−	1.46385i
$162$		0			0
$163$		−	7.91463e7i		−	0.112119i	−0.998427	−	0.0560596i	$-0.982146\pi$
$163$		−	7.91463e7i		−	0.112119i	0.998427	−	0.0560596i	$-0.0178537\pi$
$164$		0			0
$165$	−6.45638e8	+	7.04063e8i	−0.871071	+	0.949895i
$166$		0			0
$167$	6.28239e8			0.807716			0.403858	−	0.914822i	$-0.367669\pi$
$167$	6.28239e8			0.807716			0.403858	+	0.914822i	$0.367669\pi$
$168$		0			0
$169$	8.13127e8			0.996808
$170$		0			0
$171$	1.73777e8	−	7.88122e8i	0.203239	−	0.921741i
$172$		0			0
$173$	−6.95824e8			−0.776810			−0.388405	−	0.921489i	$-0.626974\pi$
$173$	−6.95824e8			−0.776810			−0.388405	+	0.921489i	$0.626974\pi$
$174$		0			0
$175$	−2.47594e8	−	7.90476e8i	−0.263991	−	0.842823i
$176$		0			0
$177$	6.52566e8	+	8.12129e8i	0.664862	+	0.827431i
$178$		0			0
$179$		−	7.76912e8i		−	0.756763i	−0.925650	−	0.378381i	$-0.876481\pi$
$179$		−	7.76912e8i		−	0.756763i	0.925650	−	0.378381i	$-0.123519\pi$
$180$		0			0
$181$	2.94877e8			0.274743			0.137371	−	0.990520i	$-0.456135\pi$
$181$	2.94877e8			0.274743			0.137371	+	0.990520i	$0.456135\pi$
$182$		0			0
$183$	1.76388e8	−	1.41732e8i	0.157277	−	0.126376i
$184$		0			0
$185$	9.90094e7	−	1.51432e7i	0.0845259	−	0.0129280i
$186$		0			0
$187$		−	2.42213e9i		−	1.98076i
$188$		0			0
$189$	1.00988e9	−	5.00172e8i	0.791447	−	0.391988i
$190$		0			0
$191$			9.31088e8i			0.699612i	0.936822	+	0.349806i	$0.113752\pi$
$191$			9.31088e8i			0.699612i	−0.936822	+	0.349806i	$0.886248\pi$
$192$		0			0
$193$			4.86009e8i			0.350280i	0.984544	+	0.175140i	$0.0560378\pi$
$193$			4.86009e8i			0.350280i	−0.984544	+	0.175140i	$0.943962\pi$
$194$		0			0
$195$	5.52076e7	−	6.02034e7i	0.0381822	−	0.0416373i
$196$		0			0
$197$	8.14587e8			0.540844			0.270422	−	0.962742i	$-0.412837\pi$
$197$	8.14587e8			0.540844			0.270422	+	0.962742i	$0.412837\pi$
$198$		0			0
$199$	−9.60620e7			−0.0612547			−0.0306274	−	0.999531i	$-0.509751\pi$
$199$	−9.60620e7			−0.0612547			−0.0306274	+	0.999531i	$0.509751\pi$
$200$		0			0
$201$	−1.02528e9	−	1.27598e9i	−0.628144	−	0.781735i
$202$		0			0
$203$	1.83984e9			1.08342
$204$		0			0
$205$	−2.53650e9	+	3.87951e8i	−1.43621	+	0.219665i
$206$		0			0
$207$	−6.55253e8	+	2.97174e9i	−0.356885	+	1.61856i
$208$		0			0
$209$			2.32111e9i			1.21650i
$210$		0			0
$211$	1.64760e9			0.831233			0.415617	−	0.909540i	$-0.363566\pi$
$211$	1.64760e9			0.831233			0.415617	+	0.909540i	$0.363566\pi$
$212$		0			0
$213$	1.11365e9	+	1.38596e9i	0.541042	+	0.673335i
$214$		0			0
$215$	9.70403e8	−	1.48421e8i	0.454149	−	0.0694609i
$216$		0			0
$217$		−	2.73988e9i		−	1.23564i
$218$		0			0
$219$	1.55103e9	+	1.93029e9i	0.674287	+	0.839161i
$220$		0			0
$221$			2.07113e8i			0.0868238i
$222$		0			0
$223$		−	4.65964e9i		−	1.88423i	−0.335297	−	0.942113i	$-0.608837\pi$
$223$		−	4.65964e9i		−	1.88423i	0.335297	−	0.942113i	$-0.391163\pi$
$224$		0			0
$225$	2.21464e8	+	2.55330e9i	0.0864119	+	0.996259i
$226$		0			0
$227$	−1.38807e8			−0.0522766			−0.0261383	−	0.999658i	$-0.508321\pi$
$227$	−1.38807e8			−0.0522766			−0.0261383	+	0.999658i	$0.508321\pi$
$228$		0			0
$229$	5.36401e7			0.0195051			0.00975254	−	0.999952i	$-0.496896\pi$
$229$	5.36401e7			0.0195051			0.00975254	+	0.999952i	$0.496896\pi$
$230$		0			0
$231$	−2.52657e9	+	2.03016e9i	−0.887326	+	0.712989i
$232$		0			0
$233$	−2.88612e9			−0.979244			−0.489622	−	0.871935i	$-0.662865\pi$
$233$	−2.88612e9			−0.979244			−0.489622	+	0.871935i	$0.662865\pi$
$234$		0			0
$235$	5.39509e8	+	3.52741e9i	0.176900	+	1.15660i
$236$		0			0
$237$	−3.99048e9	+	3.20645e9i	−1.26483	+	1.01632i
$238$		0			0
$239$			8.01549e8i			0.245662i	0.992428	+	0.122831i	$0.0391974\pi$
$239$			8.01549e8i			0.245662i	−0.992428	+	0.122831i	$0.960803\pi$
$240$		0			0
$241$	−3.63914e9			−1.07878			−0.539388	−	0.842057i	$-0.681344\pi$
$241$	−3.63914e9			−1.07878			−0.539388	+	0.842057i	$0.681344\pi$
$242$		0			0
$243$	−3.38448e9	+	8.38439e8i	−0.970659	+	0.240462i
$244$		0			0
$245$	1.19819e8	+	7.83400e8i	0.0332553	+	0.217430i
$246$		0			0
$247$		−	1.98475e8i		−	0.0533234i
$248$		0			0
$249$	2.23085e8	−	1.79254e8i	0.0580327	−	0.0466308i
$250$		0			0
$251$			4.20935e9i			1.06052i	0.847834	+	0.530262i	$0.177906\pi$
$251$			4.20935e9i			1.06052i	−0.847834	+	0.530262i	$0.822094\pi$
$252$		0			0
$253$		−	8.75211e9i		−	2.13615i
$254$		0			0
$255$	−4.78940e9	−	4.39197e9i	−1.13272	−	1.03872i
$256$		0			0
$257$	−1.29375e9			−0.296563			−0.148281	−	0.988945i	$-0.547374\pi$
$257$	−1.29375e9			−0.296563			−0.148281	+	0.988945i	$0.547374\pi$
$258$		0			0
$259$	3.39835e8			0.0755213
$260$		0			0
$261$	−5.55893e9	−	1.22572e9i	−1.19792	−	0.264136i
$262$		0			0
$263$	−1.94582e9			−0.406706			−0.203353	−	0.979106i	$-0.565184\pi$
$263$	−1.94582e9			−0.406706			−0.203353	+	0.979106i	$0.565184\pi$
$264$		0			0
$265$	−7.84657e8	−	5.13025e9i	−0.159110	−	1.04029i
$266$		0			0
$267$	4.69871e9	+	5.84761e9i	0.924556	+	1.15062i
$268$		0			0
$269$			1.00661e10i			1.92244i	0.275788	+	0.961218i	$0.411061\pi$
$269$			1.00661e10i			1.92244i	−0.275788	+	0.961218i	$0.588939\pi$
$270$		0			0
$271$	−3.90424e9			−0.723868			−0.361934	−	0.932204i	$-0.617883\pi$
$271$	−3.90424e9			−0.723868			−0.361934	+	0.932204i	$0.617883\pi$
$272$		0			0
$273$	2.16043e8	−	1.73596e8i	0.0388947	−	0.0312529i
$274$		0			0
$275$	−2.20320e9	−	7.03399e9i	−0.385232	−	1.22990i
$276$		0			0
$277$			5.08015e9i			0.862893i	0.902138	+	0.431447i	$0.141997\pi$
$277$			5.08015e9i			0.862893i	−0.902138	+	0.431447i	$0.858003\pi$
$278$		0			0
$279$	−1.82533e9	+	8.27832e9i	−0.301248	+	1.36624i
$280$		0			0
$281$		−	2.37851e9i		−	0.381487i	−0.981640	−	0.190744i	$-0.938910\pi$
$281$		−	2.37851e9i		−	0.381487i	0.981640	−	0.190744i	$-0.0610899\pi$
$282$		0			0
$283$		−	2.07541e9i		−	0.323562i	−0.986827	−	0.161781i	$-0.948276\pi$
$283$		−	2.07541e9i		−	0.323562i	0.986827	−	0.161781i	$-0.0517238\pi$
$284$		0			0
$285$	4.58965e9	+	4.20879e9i	0.695665	+	0.637937i
$286$		0			0
$287$	−8.70616e9			−1.28321
$288$		0			0
$289$	9.50087e9			1.36198
$290$		0			0
$291$	6.09459e9	+	7.58482e9i	0.849909	+	1.05773i
$292$		0			0
$293$	9.60092e9			1.30269			0.651347	−	0.758780i	$-0.274204\pi$
$293$	9.60092e9			1.30269			0.651347	+	0.758780i	$0.274204\pi$
$294$		0			0
$295$	−7.94635e9	+	1.21537e9i	−1.04925	+	0.160480i
$296$		0			0
$297$	8.98632e9	−	4.45074e9i	1.15493	−	0.572014i
$298$		0			0
$299$			7.48381e8i			0.0936349i
$300$		0			0
$301$	3.33077e9			0.405769
$302$		0			0
$303$	2.34937e9	+	2.92382e9i	0.278728	+	0.346881i
$304$		0			0
$305$	2.63970e8	+	1.72589e9i	0.0305039	+	0.199440i
$306$		0			0
$307$		−	7.90407e9i		−	0.889810i	−0.895578	−	0.444905i	$-0.853237\pi$
$307$		−	7.90407e9i		−	0.889810i	0.895578	−	0.444905i	$-0.146763\pi$
$308$		0			0
$309$	−1.40213e9	−	1.74497e9i	−0.153799	−	0.191405i
$310$		0			0
$311$		−	1.10579e10i		−	1.18204i	−0.806657	−	0.591020i	$-0.798726\pi$
$311$		−	1.10579e10i		−	1.18204i	0.806657	−	0.591020i	$-0.201274\pi$
$312$		0			0
$313$		−	1.11144e10i		−	1.15800i	−0.815327	−	0.579001i	$-0.803443\pi$
$313$		−	1.11144e10i		−	1.15800i	0.815327	−	0.579001i	$-0.196557\pi$
$314$		0			0
$315$	−5.66999e8	+	8.67713e9i	−0.0575891	+	0.881320i
$316$		0			0
$317$	8.57623e9			0.849296			0.424648	−	0.905359i	$-0.360398\pi$
$317$	8.57623e9			0.849296			0.424648	+	0.905359i	$0.360398\pi$
$318$		0			0
$319$	1.63717e10			1.58100
$320$		0			0
$321$	9.23549e9	−	7.42095e9i	0.869841	−	0.698939i
$322$		0			0
$323$	−1.57894e10			−1.45063
$324$		0			0
$325$	1.88392e8	+	6.01466e8i	0.0168861	+	0.0539111i
$326$		0			0
$327$	−3.78422e9	+	3.04072e9i	−0.330967	+	0.265941i
$328$		0			0
$329$			1.21073e10i			1.03339i
$330$		0			0
$331$	−2.03785e10			−1.69770			−0.848850	−	0.528633i	$-0.822705\pi$
$331$	−2.03785e10			−1.69770			−0.848850	+	0.528633i	$0.822705\pi$
$332$		0			0
$333$	−1.02678e9	−	2.26401e8i	−0.0835030	−	0.0184120i
$334$		0			0
$335$	1.24850e10	−	1.90954e9i	0.991306	−	0.151618i
$336$		0			0
$337$		−	6.68643e9i		−	0.518412i	−0.965822	−	0.259206i	$-0.916539\pi$
$337$		−	6.68643e9i		−	0.518412i	0.965822	−	0.259206i	$-0.0834609\pi$
$338$		0			0
$339$	1.15152e10	−	9.25275e9i	0.871911	−	0.700603i
$340$		0			0
$341$		−	2.43806e10i		−	1.80313i
$342$		0			0
$343$			1.49135e10i			1.07747i
$344$		0			0
$345$	−1.73060e10	−	1.58699e10i	−1.22157	−	1.12021i
$346$		0			0
$347$	1.18843e10			0.819704			0.409852	−	0.912152i	$-0.365580\pi$
$347$	1.18843e10			0.819704			0.409852	+	0.912152i	$0.365580\pi$
$348$		0			0
$349$	2.80203e10			1.88874			0.944368	−	0.328890i	$-0.106674\pi$
$349$	2.80203e10			1.88874			0.944368	+	0.328890i	$0.106674\pi$
$350$		0			0
$351$	−7.68407e8	+	3.80577e8i	−0.0506248	+	0.0250734i
$352$		0			0
$353$	1.58911e10			1.02342			0.511710	−	0.859158i	$-0.329012\pi$
$353$	1.58911e10			1.02342			0.511710	+	0.859158i	$0.329012\pi$
$354$		0			0
$355$	−1.35610e10	+	2.07412e9i	−0.853845	+	0.130593i
$356$		0			0
$357$	−1.38102e10	−	1.71870e10i	−0.850213	−	1.05810i
$358$		0			0
$359$		−	1.24351e10i		−	0.748635i	−0.927301	−	0.374317i	$-0.877877\pi$
$359$		−	1.24351e10i		−	0.748635i	0.927301	−	0.374317i	$-0.122123\pi$
$360$		0			0
$361$	−1.85269e9			−0.109087
$362$		0			0
$363$	−8.94750e9	+	7.18954e9i	−0.515318	+	0.414071i
$364$		0			0
$365$	−1.88871e10	+	2.88873e9i	−1.06413	+	0.162755i
$366$		0			0
$367$			2.24145e10i			1.23556i	0.786351	+	0.617781i	$0.211968\pi$
$367$			2.24145e10i			1.23556i	−0.786351	+	0.617781i	$0.788032\pi$
$368$		0			0
$369$	2.63049e10	+	5.80011e9i	1.41883	+	0.312846i
$370$		0			0
$371$		−	1.76088e10i		−	0.929469i
$372$		0			0
$373$			1.30243e10i			0.672851i	0.941710	+	0.336426i	$0.109218\pi$
$373$			1.30243e10i			0.672851i	−0.941710	+	0.336426i	$0.890782\pi$
$374$		0			0
$375$	−1.79036e10	−	8.39799e9i	−0.905349	−	0.424669i
$376$		0			0
$377$	−1.39992e9			−0.0693007
$378$		0			0
$379$	1.88060e10			0.911466			0.455733	−	0.890117i	$-0.349377\pi$
$379$	1.88060e10			0.911466			0.455733	+	0.890117i	$0.349377\pi$
$380$		0			0
$381$	−1.18335e10	−	1.47269e10i	−0.561580	−	0.698895i
$382$		0			0
$383$	−5.11148e8			−0.0237548			−0.0118774	−	0.999929i	$-0.503781\pi$
$383$	−5.11148e8			−0.0237548			−0.0118774	+	0.999929i	$0.503781\pi$
$384$		0			0
$385$	−3.78108e9	−	2.47215e10i	−0.172097	−	1.12520i
$386$		0			0
$387$	−1.00636e10	−	2.21898e9i	−0.448653	−	0.0989259i
$388$		0			0
$389$			2.64776e10i			1.15633i	0.815921	+	0.578163i	$0.196230\pi$
$389$			2.64776e10i			1.15633i	−0.815921	+	0.578163i	$0.803770\pi$
$390$		0			0
$391$	5.95365e10			2.54728
$392$		0			0
$393$	1.57565e10	+	1.96092e10i	0.660524	+	0.822032i
$394$		0			0
$395$	−5.97187e9	−	3.90453e10i	−0.245314	−	1.60391i
$396$		0			0
$397$			1.10906e10i			0.446472i	0.974764	+	0.223236i	$0.0716621\pi$
$397$			1.10906e10i			0.446472i	−0.974764	+	0.223236i	$0.928338\pi$
$398$		0			0
$399$	1.32342e10	+	1.64702e10i	0.522164	+	0.649841i
$400$		0			0
$401$			2.27708e10i			0.880643i	0.897840	+	0.440322i	$0.145136\pi$
$401$			2.27708e10i			0.880643i	−0.897840	+	0.440322i	$0.854864\pi$
$402$		0			0
$403$			2.08475e9i			0.0790378i
$404$		0			0
$405$	7.49390e9	−	2.58395e10i	0.278540	−	0.960425i
$406$		0			0
$407$	3.02400e9			0.110206
$408$		0			0
$409$	−2.75068e10			−0.982986			−0.491493	−	0.870881i	$-0.663549\pi$
$409$	−2.75068e10			−0.982986			−0.491493	+	0.870881i	$0.663549\pi$
$410$		0			0
$411$	−3.75144e10	+	3.01438e10i	−1.31471	+	1.05641i
$412$		0			0
$413$	−2.72747e10			−0.937475
$414$		0			0
$415$	3.33853e8	+	2.18280e9i	0.0112554	+	0.0735904i
$416$		0			0
$417$	4.22893e10	−	3.39805e10i	1.39858	−	1.12379i
$418$		0			0
$419$			4.36699e10i			1.41686i	0.705782	+	0.708429i	$0.250596\pi$
$419$			4.36699e10i			1.41686i	−0.705782	+	0.708429i	$0.749404\pi$
$420$		0			0
$421$	−4.09807e10			−1.30452			−0.652261	−	0.757995i	$-0.726179\pi$
$421$	−4.09807e10			−1.30452			−0.652261	+	0.757995i	$0.726179\pi$
$422$		0			0
$423$	8.06600e9	−	3.65813e10i	0.251940	−	1.14261i
$424$		0			0
$425$	4.78489e10	−	1.49873e10i	1.46661	−	0.459376i
$426$		0			0
$427$			5.92386e9i			0.178194i
$428$		0			0
$429$	1.92244e9	−	1.54473e9i	0.0567577	−	0.0456062i
$430$		0			0
$431$		−	3.40323e10i		−	0.986239i	−0.869962	−	0.493120i	$-0.835857\pi$
$431$		−	3.40323e10i		−	0.986239i	0.869962	−	0.493120i	$-0.164143\pi$
$432$		0			0
$433$			6.70291e10i			1.90683i	0.301665	+	0.953414i	$0.402458\pi$
$433$			6.70291e10i			1.90683i	−0.301665	+	0.953414i	$0.597542\pi$
$434$		0			0
$435$	2.96862e10	−	3.23725e10i	0.829082	−	0.904107i
$436$		0			0
$437$	−5.70533e10			−1.56443
$438$		0			0
$439$	3.27169e10			0.880874			0.440437	−	0.897783i	$-0.354823\pi$
$439$	3.27169e10			0.880874			0.440437	+	0.897783i	$0.354823\pi$
$440$		0			0
$441$	1.79137e9	−	8.12430e9i	0.0473621	−	0.214799i
$442$		0			0
$443$	6.16171e10			1.59988			0.799938	−	0.600082i	$-0.204866\pi$
$443$	6.16171e10			1.59988			0.799938	+	0.600082i	$0.204866\pi$
$444$		0			0
$445$	−5.72165e10	+	8.75112e9i	−1.45909	+	0.223164i
$446$		0			0
$447$	−8.47892e8	−	1.05521e9i	−0.0212378	−	0.0264308i
$448$		0			0
$449$			3.08295e10i			0.758544i	0.925285	+	0.379272i	$0.123826\pi$
$449$			3.08295e10i			0.758544i	−0.925285	+	0.379272i	$0.876174\pi$
$450$		0			0
$451$	−7.74711e10			−1.87255
$452$		0			0
$453$	7.19589e9	−	5.78208e9i	0.170880	−	0.137307i
$454$		0			0
$455$	3.23315e8	+	2.11390e9i	0.00754362	+	0.0493217i
$456$		0			0
$457$		−	5.77594e9i		−	0.132421i	−0.997806	−	0.0662107i	$-0.978909\pi$
$457$		−	5.77594e9i		−	0.132421i	0.997806	−	0.0662107i	$-0.0210909\pi$
$458$		0			0
$459$	3.02763e10	+	6.11296e10i	0.682106	+	1.37721i
$460$		0			0
$461$			7.19674e10i			1.59343i	0.604358	+	0.796713i	$0.293430\pi$
$461$			7.19674e10i			1.59343i	−0.604358	+	0.796713i	$0.706570\pi$
$462$		0			0
$463$			6.07888e9i			0.132282i	0.997810	+	0.0661409i	$0.0210687\pi$
$463$			6.07888e9i			0.132282i	−0.997810	+	0.0661409i	$0.978931\pi$
$464$		0			0
$465$	−4.82090e10	−	4.42085e10i	−1.03114	−	0.945572i
$466$		0			0
$467$	−2.68395e10			−0.564297			−0.282148	−	0.959371i	$-0.591047\pi$
$467$	−2.68395e10			−0.564297			−0.282148	+	0.959371i	$0.591047\pi$
$468$		0			0
$469$	4.28528e10			0.885702
$470$		0			0
$471$	−7.12904e9	−	8.87221e9i	−0.144860	−	0.180280i
$472$		0			0
$473$	2.96386e10			0.592124
$474$		0			0
$475$	−4.58532e10	+	1.43622e10i	−0.900731	+	0.282129i
$476$		0			0
$477$	−1.17311e10	+	5.32036e10i	−0.226603	+	1.02770i
$478$		0			0
$479$			3.87146e10i			0.735416i	0.929941	+	0.367708i	$0.119857\pi$
$479$			3.87146e10i			0.735416i	−0.929941	+	0.367708i	$0.880143\pi$
$480$		0			0
$481$	−2.58578e8			−0.00483071
$482$		0			0
$483$	−4.99017e10	−	6.21035e10i	−0.916910	−	1.14111i
$484$		0			0
$485$	−7.42144e10	+	1.13509e10i	−1.34128	+	0.205146i
$486$		0			0
$487$		−	6.53324e10i		−	1.16148i	−0.814088	−	0.580741i	$-0.802763\pi$
$487$		−	6.53324e10i		−	1.16148i	0.814088	−	0.580741i	$-0.197237\pi$
$488$		0			0
$489$	−4.01556e9	−	4.99743e9i	−0.0702281	−	0.0873999i
$490$		0			0
$491$		−	4.58946e10i		−	0.789652i	−0.918756	−	0.394826i	$-0.870805\pi$
$491$		−	4.58946e10i		−	0.789652i	0.918756	−	0.394826i	$-0.129195\pi$
$492$		0			0
$493$			1.11369e11i			1.88528i
$494$		0			0
$495$	−5.04540e9	+	7.72127e10i	−0.0840378	+	1.28608i
$496$		0			0
$497$	−4.65463e10			−0.762885
$498$		0			0
$499$	−3.21201e10			−0.518054			−0.259027	−	0.965870i	$-0.583402\pi$
$499$	−3.21201e10			−0.518054			−0.259027	+	0.965870i	$0.583402\pi$
$500$		0			0
$501$	3.96680e10	−	3.18743e10i	0.629636	−	0.505929i
$502$		0			0
$503$	−1.00259e11			−1.56622			−0.783111	−	0.621882i	$-0.786368\pi$
$503$	−1.00259e11			−1.56622			−0.783111	+	0.621882i	$0.786368\pi$
$504$		0			0
$505$	−2.86084e10	+	4.37558e9i	−0.439874	+	0.0672776i
$506$		0			0
$507$	5.13422e10	−	4.12548e10i	0.777039	−	0.624370i
$508$		0			0
$509$		−	1.58469e10i		−	0.236087i	−0.993008	−	0.118044i	$-0.962338\pi$
$509$		−	1.58469e10i		−	0.236087i	0.993008	−	0.118044i	$-0.0376622\pi$
$510$		0			0
$511$	−6.48271e10			−0.950765
$512$		0			0
$513$	−2.90135e10	−	5.85800e10i	−0.418920	−	0.845824i
$514$		0			0
$515$	1.70738e10	−	2.61140e9i	0.242718	−	0.0371231i
$516$		0			0
$517$			1.07736e11i			1.50799i
$518$		0			0
$519$	−4.39354e10	+	3.53032e10i	−0.605544	+	0.486570i
$520$		0			0
$521$			1.15949e11i			1.57368i	0.617154	+	0.786842i	$0.288285\pi$
$521$			1.15949e11i			1.57368i	−0.617154	+	0.786842i	$0.711715\pi$
$522$		0			0
$523$		−	1.09614e10i		−	0.146507i	−0.997313	−	0.0732535i	$-0.976662\pi$
$523$		−	1.09614e10i		−	0.146507i	0.997313	−	0.0732535i	$-0.0233382\pi$
$524$		0			0
$525$	−5.57390e10	−	3.73500e10i	−0.733706	−	0.491647i
$526$		0			0
$527$	1.65850e11			2.15017
$528$		0			0
$529$	1.36817e11			1.74710
$530$		0			0
$531$	8.24082e10	+	1.81706e10i	1.03655	+	0.228555i
$532$		0			0
$533$	6.62445e9			0.0820806
$534$		0			0
$535$	1.38212e10	+	9.03655e10i	0.168706	+	1.10303i
$536$		0			0
$537$	−3.94173e10	−	4.90555e10i	−0.474013	−	0.589917i
$538$		0			0
$539$			2.39270e10i			0.283487i
$540$		0			0
$541$	−1.38686e10			−0.161898			−0.0809491	−	0.996718i	$-0.525795\pi$
$541$	−1.38686e10			−0.161898			−0.0809491	+	0.996718i	$0.525795\pi$
$542$		0			0
$543$	1.86190e10	−	1.49608e10i	0.214169	−	0.172090i
$544$		0			0
$545$	−5.66319e9	−	3.70270e10i	−0.0641911	−	0.419694i
$546$		0			0
$547$			3.53794e10i			0.395186i	0.980284	+	0.197593i	$0.0633124\pi$
$547$			3.53794e10i			0.395186i	−0.980284	+	0.197593i	$0.936688\pi$
$548$		0			0
$549$	3.94652e9	−	1.78984e10i	0.0434435	−	0.197027i
$550$		0			0
$551$		−	1.06724e11i		−	1.15786i
$552$		0			0
$553$		−	1.34017e11i		−	1.43305i
$554$		0			0
$555$	5.48331e9	−	5.97950e9i	0.0577924	−	0.0630221i
$556$		0			0
$557$	−2.28319e10			−0.237204			−0.118602	−	0.992942i	$-0.537841\pi$
$557$	−2.28319e10			−0.237204			−0.118602	+	0.992942i	$0.537841\pi$
$558$		0			0
$559$	−2.53435e9			−0.0259549
$560$		0			0
$561$	−1.22889e11	−	1.52938e11i	−1.24069	−	1.54405i
$562$		0			0
$563$	1.31341e10			0.130728			0.0653638	−	0.997862i	$-0.479179\pi$
$563$	1.31341e10			0.130728			0.0653638	+	0.997862i	$0.479179\pi$
$564$		0			0
$565$	1.72328e10	+	1.12671e11i	0.169107	+	1.10566i
$566$		0			0
$567$	3.83887e10	−	8.28188e10i	0.371425	−	0.801302i
$568$		0			0
$569$			8.76252e9i			0.0835949i	0.999126	+	0.0417974i	$0.0133084\pi$
$569$			8.76252e9i			0.0835949i	−0.999126	+	0.0417974i	$0.986692\pi$
$570$		0			0
$571$	5.82482e10			0.547946			0.273973	−	0.961737i	$-0.411662\pi$
$571$	5.82482e10			0.547946			0.273973	+	0.961737i	$0.411662\pi$
$572$		0			0
$573$	4.72396e10	+	5.87904e10i	0.438215	+	0.545366i
$574$		0			0
$575$	1.72897e11	−	5.41550e10i	1.58167	−	0.495412i
$576$		0			0
$577$		−	4.97998e10i		−	0.449288i	−0.974441	−	0.224644i	$-0.927878\pi$
$577$		−	4.97998e10i		−	0.449288i	0.974441	−	0.224644i	$-0.0721219\pi$
$578$		0			0
$579$	2.46581e10	+	3.06874e10i	0.219405	+	0.273052i
$580$		0			0
$581$			7.49213e9i			0.0657508i
$582$		0			0
$583$		−	1.56691e11i		−	1.35634i
$584$		0			0
$585$	4.31425e8	−	6.60235e9i	0.00368368	−	0.0563735i
$586$		0			0
$587$	−9.62104e10			−0.810344			−0.405172	−	0.914240i	$-0.632788\pi$
$587$	−9.62104e10			−0.810344			−0.405172	+	0.914240i	$0.632788\pi$
$588$		0			0
$589$	−1.58933e11			−1.32054
$590$		0			0
$591$	5.14343e10	−	4.13288e10i	0.421603	−	0.338768i
$592$		0			0
$593$	2.25032e11			1.81981			0.909905	−	0.414818i	$-0.136155\pi$
$593$	2.25032e11			1.81981			0.909905	+	0.414818i	$0.136155\pi$
$594$		0			0
$595$	1.68168e11	−	2.57209e10i	1.34176	−	0.205219i
$596$		0			0
$597$	−6.06552e9	+	4.87380e9i	−0.0477497	+	0.0383681i
$598$		0			0
$599$		−	1.54879e11i		−	1.20305i	−0.798853	−	0.601526i	$-0.794559\pi$
$599$		−	1.54879e11i		−	1.20305i	0.798853	−	0.601526i	$-0.205441\pi$
$600$		0			0
$601$	1.19944e11			0.919346			0.459673	−	0.888088i	$-0.347967\pi$
$601$	1.19944e11			0.919346			0.459673	+	0.888088i	$0.347967\pi$
$602$		0			0
$603$	−1.29476e11	−	2.85488e10i	−0.979310	−	0.215933i
$604$		0			0
$605$	−1.33902e10	−	8.75476e10i	−0.0999459	−	0.653466i
$606$		0			0
$607$			1.26738e11i			0.933584i	0.884367	+	0.466792i	$0.154590\pi$
$607$			1.26738e11i			0.933584i	−0.884367	+	0.466792i	$0.845410\pi$
$608$		0			0
$609$	1.16171e11	−	9.33461e10i	0.844554	−	0.678620i
$610$		0			0
$611$		−	9.21237e9i		−	0.0661008i
$612$		0			0
$613$			2.06214e11i			1.46041i	0.683227	+	0.730207i	$0.260576\pi$
$613$			2.06214e11i			1.46041i	−0.683227	+	0.730207i	$0.739424\pi$
$614$		0			0
$615$	−1.40476e11	+	1.53187e11i	−0.981975	+	1.07084i
$616$		0			0
$617$	6.08519e10			0.419888			0.209944	−	0.977713i	$-0.432672\pi$
$617$	6.08519e10			0.419888			0.209944	+	0.977713i	$0.432672\pi$
$618$		0			0
$619$	1.90502e11			1.29759			0.648795	−	0.760964i	$-0.275273\pi$
$619$	1.90502e11			1.29759			0.648795	+	0.760964i	$0.275273\pi$
$620$		0			0
$621$	1.09400e11	+	2.20885e11i	0.735615	+	1.48525i
$622$		0			0
$623$	−1.96388e11			−1.30365
$624$		0			0
$625$	1.25323e11	−	8.70476e10i	0.821315	−	0.570475i
$626$		0			0
$627$	1.17764e11	+	1.46559e11i	0.761976	+	0.948291i
$628$		0			0
$629$			2.05708e10i			0.131416i
$630$		0			0
$631$	−8.86060e7			−0.000558915			−0.000279457	−	1.00000i	$-0.500089\pi$
$631$	−8.86060e7			−0.000558915			−0.000279457		1.00000i	$0.500089\pi$
$632$		0			0
$633$	1.04032e11	−	8.35927e10i	0.647968	−	0.520659i
$634$		0			0
$635$	1.44097e11	−	2.20392e10i	0.886258	−	0.135551i
$636$		0			0
$637$		−	2.04597e9i		−	0.0124263i
$638$		0			0
$639$	1.40636e11	+	3.10094e10i	0.843513	+	0.185990i
$640$		0			0
$641$			3.50234e10i			0.207456i	0.994606	+	0.103728i	$0.0330772\pi$
$641$			3.50234e10i			0.207456i	−0.994606	+	0.103728i	$0.966923\pi$
$642$		0			0
$643$		−	2.54275e11i		−	1.48751i	−0.668452	−	0.743755i	$-0.733043\pi$
$643$		−	2.54275e11i		−	1.48751i	0.668452	−	0.743755i	$-0.266957\pi$
$644$		0			0
$645$	5.37426e10	−	5.86058e10i	0.310513	−	0.338612i
$646$		0			0
$647$	−1.96848e11			−1.12335			−0.561673	−	0.827360i	$-0.689842\pi$
$647$	−1.96848e11			−1.12335			−0.561673	+	0.827360i	$0.689842\pi$
$648$		0			0
$649$	−2.42702e11			−1.36803
$650$		0			0
$651$	−1.39010e11	−	1.73001e11i	−0.773969	−	0.963217i
$652$		0			0
$653$	−1.90774e11			−1.04922			−0.524611	−	0.851342i	$-0.675789\pi$
$653$	−1.90774e11			−1.04922			−0.524611	+	0.851342i	$0.675789\pi$
$654$		0			0
$655$	−1.91868e11	+	2.93457e10i	−1.04241	+	0.159433i
$656$		0			0
$657$	1.95870e11	+	4.31883e10i	1.05125	+	0.231795i
$658$		0			0
$659$		−	3.23776e11i		−	1.71673i	−0.513038	−	0.858366i	$-0.671480\pi$
$659$		−	3.23776e11i		−	1.71673i	0.513038	−	0.858366i	$-0.328520\pi$
$660$		0			0
$661$	7.51395e10			0.393607			0.196803	−	0.980443i	$-0.436944\pi$
$661$	7.51395e10			0.393607			0.196803	+	0.980443i	$0.436944\pi$
$662$		0			0
$663$	1.05081e10	+	1.30775e10i	0.0543838	+	0.0676815i
$664$		0			0
$665$	−1.61154e11	+	2.46481e10i	−0.824053	+	0.126037i
$666$		0			0
$667$			4.02419e11i			2.03318i
$668$		0			0
$669$	−2.36411e11	−	2.94217e11i	−1.18022	−	1.46880i
$670$		0			0
$671$			5.27130e10i			0.260033i
$672$		0			0
$673$		−	2.54980e11i		−	1.24293i	−0.783444	−	0.621463i	$-0.786539\pi$
$673$		−	2.54980e11i		−	1.24293i	0.783444	−	0.621463i	$-0.213461\pi$
$674$		0			0
$675$	1.43528e11	+	1.49984e11i	0.691387	+	0.722485i
$676$		0			0
$677$	−3.70554e11			−1.76399			−0.881997	−	0.471254i	$-0.843801\pi$
$677$	−3.70554e11			−1.76399			−0.881997	+	0.471254i	$0.843801\pi$
$678$		0			0
$679$	−2.54730e11			−1.19840
$680$		0			0
$681$	−8.76449e9	+	7.04249e9i	−0.0407510	+	0.0327444i
$682$		0			0
$683$	−3.26263e10			−0.149929			−0.0749644	−	0.997186i	$-0.523884\pi$
$683$	−3.26263e10			−0.149929			−0.0749644	+	0.997186i	$0.523884\pi$
$684$		0			0
$685$	−5.61414e10	−	3.67064e11i	−0.254989	−	1.66717i
$686$		0			0
$687$	3.38692e9	−	2.72148e9i	0.0152047	−	0.0122174i
$688$		0			0
$689$			1.33984e10i			0.0594533i
$690$		0			0
$691$	1.73441e11			0.760745			0.380373	−	0.924833i	$-0.375796\pi$
$691$	1.73441e11			0.760745			0.380373	+	0.924833i	$0.375796\pi$
$692$		0			0
$693$	−5.65296e10	+	2.56375e11i	−0.245100	+	1.11159i
$694$		0			0
$695$	6.32871e10	+	4.13783e11i	0.271254	+	1.77351i
$696$		0			0
$697$		−	5.26999e11i		−	2.23295i
$698$		0			0
$699$	−1.82234e11	+	1.46430e11i	−0.763346	+	0.613368i
$700$		0			0
$701$		−	3.03079e11i		−	1.25511i	−0.778571	−	0.627557i	$-0.784055\pi$
$701$		−	3.03079e11i		−	1.25511i	0.778571	−	0.627557i	$-0.215945\pi$
$702$		0			0
$703$		−	1.97129e10i		−	0.0807102i
$704$		0			0
$705$	2.13032e11	+	1.95354e11i	0.862360	+	0.790800i
$706$		0			0
$707$	−9.81943e10			−0.393015
$708$		0			0
$709$	3.41415e11			1.35113			0.675567	−	0.737299i	$-0.263899\pi$
$709$	3.41415e11			1.35113			0.675567	+	0.737299i	$0.263899\pi$
$710$		0			0
$711$	−8.92832e10	+	4.04921e11i	−0.349375	+	1.58450i
$712$		0			0
$713$	5.99280e11			2.31884
$714$		0			0
$715$	2.87699e9	+	1.88103e10i	0.0110082	+	0.0719735i
$716$		0			0
$717$	4.06673e10	+	5.06111e10i	0.153875	+	0.191500i
$718$		0			0
$719$		−	1.16767e11i		−	0.436921i	−0.975846	−	0.218460i	$-0.929897\pi$
$719$		−	1.16767e11i		−	0.436921i	0.975846	−	0.218460i	$-0.0701035\pi$
$720$		0			0
$721$	5.86034e10			0.216861
$722$		0			0
$723$	−2.29782e11	+	1.84635e11i	−0.840934	+	0.675712i
$724$		0			0
$725$	1.01302e11	+	3.23420e11i	0.366663	+	1.17062i
$726$		0			0
$727$		−	4.11351e10i		−	0.147257i	−0.997286	−	0.0736283i	$-0.976542\pi$
$727$		−	4.11351e10i		−	0.147257i	0.997286	−	0.0736283i	$-0.0234579\pi$
$728$		0			0
$729$	−1.71162e11	+	2.24655e11i	−0.606036	+	0.795437i
$730$		0			0
$731$			2.01617e11i			0.706087i
$732$		0			0
$733$			3.64955e11i			1.26422i	0.774878	+	0.632110i	$0.217811\pi$
$733$			3.64955e11i			1.26422i	−0.774878	+	0.632110i	$0.782189\pi$
$734$		0			0
$735$	4.73120e10	+	4.33860e10i	0.162115	+	0.148662i
$736$		0			0
$737$	3.81322e11			1.29248
$738$		0			0
$739$	−3.12470e11			−1.04769			−0.523843	−	0.851815i	$-0.675502\pi$
$739$	−3.12470e11			−1.04769			−0.523843	+	0.851815i	$0.675502\pi$
$740$		0			0
$741$	−1.00698e10	−	1.25320e10i	−0.0334002	−	0.0415670i
$742$		0			0
$743$	−8.05559e10			−0.264327			−0.132164	−	0.991228i	$-0.542192\pi$
$743$	−8.05559e10			−0.264327			−0.132164	+	0.991228i	$0.542192\pi$
$744$		0			0
$745$	1.03248e10	−	1.57916e9i	0.0335165	−	0.00512626i
$746$		0			0
$747$	4.99131e9	−	2.26368e10i	0.0160300	−	0.0726998i
$748$		0			0
$749$			3.10167e11i			0.985525i
$750$		0			0
$751$	−3.97233e10			−0.124878			−0.0624390	−	0.998049i	$-0.519888\pi$
$751$	−3.97233e10			−0.124878			−0.0624390	+	0.998049i	$0.519888\pi$
$752$		0			0
$753$	2.13565e11	+	2.65785e11i	0.664280	+	0.826706i
$754$		0			0
$755$	1.07689e10	+	7.04089e10i	0.0331422	+	0.216690i
$756$		0			0
$757$		−	4.60111e11i		−	1.40113i	−0.713588	−	0.700566i	$-0.752931\pi$
$757$		−	4.60111e11i		−	1.40113i	0.713588	−	0.700566i	$-0.247069\pi$
$758$		0			0
$759$	−4.44046e11	−	5.52623e11i	−1.33802	−	1.66518i
$760$		0			0
$761$			2.08945e11i			0.623007i	0.950245	+	0.311503i	$0.100833\pi$
$761$			2.08945e11i			0.623007i	−0.950245	+	0.311503i	$0.899167\pi$
$762$		0			0
$763$		−	1.27090e11i		−	0.374984i
$764$		0			0
$765$	−5.25241e11	−	3.43215e10i	−1.53360	−	0.100212i
$766$		0			0
$767$	2.07531e10			0.0599655
$768$		0			0
$769$	−3.43585e11			−0.982493			−0.491246	−	0.871021i	$-0.663459\pi$
$769$	−3.43585e11			−0.982493			−0.491246	+	0.871021i	$0.663459\pi$
$770$		0			0
$771$	−8.16892e10	+	6.56394e10i	−0.231178	+	0.185758i
$772$		0			0
$773$	5.64823e11			1.58196			0.790978	−	0.611845i	$-0.209572\pi$
$773$	5.64823e11			1.58196			0.790978	+	0.611845i	$0.209572\pi$
$774$		0			0
$775$	4.81636e11	−	1.50859e11i	1.33509	−	0.418180i
$776$		0			0
$777$	2.14578e10	−	1.72419e10i	0.0588709	−	0.0473042i
$778$		0			0
$779$			5.05019e11i			1.37138i
$780$		0			0
$781$	−4.14188e11			−1.11325
$782$		0			0
$783$	−4.13188e11	+	2.04643e11i	−1.09926	+	0.544441i
$784$		0			0
$785$	8.68110e10	−	1.32775e10i	0.228610	−	0.0349653i
$786$		0			0
$787$		−	5.31289e11i		−	1.38494i	−0.721445	−	0.692472i	$-0.756522\pi$
$787$		−	5.31289e11i		−	1.38494i	0.721445	−	0.692472i	$-0.243478\pi$
$788$		0			0
$789$	−1.22862e11	+	9.87231e10i	−0.317038	+	0.254748i
$790$		0			0
$791$			3.86729e11i			0.987871i
$792$		0			0
$793$		−	4.50742e9i		−	0.0113982i
$794$		0			0
$795$	−3.09832e11	−	2.84122e11i	−0.775636	−	0.711273i
$796$		0			0
$797$	−5.49894e11			−1.36284			−0.681421	−	0.731891i	$-0.738638\pi$
$797$	−5.49894e11			−1.36284			−0.681421	+	0.731891i	$0.738638\pi$
$798$		0			0
$799$	−7.32878e11			−1.79823
$800$		0			0
$801$	5.93368e11	+	1.30835e11i	1.44143	+	0.317829i
$802$		0			0
$803$	−5.76859e11			−1.38742
$804$		0			0
$805$	6.07657e11	−	9.29396e10i	1.44702	−	0.221318i
$806$		0			0
$807$	5.10713e11	+	6.35590e11i	1.20416	+	1.49859i
$808$		0			0
$809$		−	4.15825e11i		−	0.970771i	−0.874300	−	0.485385i	$-0.838679\pi$
$809$		−	4.15825e11i		−	0.970771i	0.874300	−	0.485385i	$-0.161321\pi$
$810$		0			0
$811$	3.62554e11			0.838086			0.419043	−	0.907966i	$-0.362366\pi$
$811$	3.62554e11			0.838086			0.419043	+	0.907966i	$0.362366\pi$
$812$		0			0
$813$	−2.46520e11	+	1.98085e11i	−0.564274	+	0.453409i
$814$		0			0
$815$	4.88978e10	−	7.47879e9i	0.110830	−	0.0169512i
$816$		0			0
$817$		−	1.93208e11i		−	0.433648i
$818$		0			0
$819$	4.83376e9	−	2.19223e10i	0.0107436	−	0.0487249i
$820$		0			0
$821$		−	3.41748e11i		−	0.752200i	−0.926579	−	0.376100i	$-0.877265\pi$
$821$		−	3.41748e11i		−	0.752200i	0.926579	−	0.376100i	$-0.122735\pi$
$822$		0			0
$823$		−	6.08011e10i		−	0.132529i	−0.997802	−	0.0662647i	$-0.978892\pi$
$823$		−	6.08011e10i		−	0.132529i	0.997802	−	0.0662647i	$-0.0211082\pi$
$824$		0			0
$825$	−4.95989e11	−	3.32356e11i	−1.07067	−	0.717444i
$826$		0			0
$827$	5.88464e9			0.0125805			0.00629025	−	0.999980i	$-0.497998\pi$
$827$	5.88464e9			0.0125805			0.00629025	+	0.999980i	$0.497998\pi$
$828$		0			0
$829$	−7.58209e11			−1.60535			−0.802677	−	0.596414i	$-0.796592\pi$
$829$	−7.58209e11			−1.60535			−0.802677	+	0.596414i	$0.796592\pi$
$830$		0			0
$831$	2.57746e11	+	3.20769e11i	0.540490	+	0.672648i
$832$		0			0
$833$	−1.62764e11			−0.338048
$834$		0			0
$835$	5.93643e10	+	3.88136e11i	0.122118	+	0.798431i
$836$		0			0
$837$	3.04754e11	+	6.15317e11i	0.620937	+	1.25371i
$838$		0			0
$839$		−	9.22647e11i		−	1.86203i	−0.364975	−	0.931017i	$-0.618923\pi$
$839$		−	9.22647e11i		−	1.86203i	0.364975	−	0.931017i	$-0.381077\pi$
$840$		0			0
$841$	−2.52518e11			−0.504787
$842$		0			0
$843$	−1.20676e11	−	1.50183e11i	−0.238952	−	0.297379i
$844$		0			0
$845$	7.68350e10	+	5.02363e11i	0.150707	+	0.985350i
$846$		0			0
$847$		−	3.00495e11i		−	0.583852i
$848$		0			0
$849$	−1.05298e11	−	1.31045e11i	−0.202669	−	0.252225i
$850$		0			0
$851$			7.43304e10i			0.141726i
$852$		0			0
$853$			4.96245e11i			0.937346i	0.883372	+	0.468673i	$0.155268\pi$
$853$			4.96245e11i			0.937346i	−0.883372	+	0.468673i	$0.844732\pi$
$854$		0			0
$855$	5.03335e11	+	3.28900e10i	0.941873	+	0.0615459i
$856$		0			0
$857$	−9.48856e11			−1.75905			−0.879523	−	0.475857i	$-0.842138\pi$
$857$	−9.48856e11			−1.75905			−0.879523	+	0.475857i	$0.842138\pi$
$858$		0			0
$859$	4.61338e11			0.847318			0.423659	−	0.905822i	$-0.360746\pi$
$859$	4.61338e11			0.847318			0.423659	+	0.905822i	$0.360746\pi$
$860$		0			0
$861$	−5.49722e11	+	4.41715e11i	−1.00030	+	0.803766i
$862$		0			0
$863$	1.26432e11			0.227937			0.113969	−	0.993484i	$-0.463644\pi$
$863$	1.26432e11			0.227937			0.113969	+	0.993484i	$0.463644\pi$
$864$		0			0
$865$	−6.57506e10	−	4.29891e11i	−0.117445	−	0.767880i
$866$		0			0
$867$	5.99900e11	−	4.82035e11i	1.06170	−	0.853105i
$868$		0			0
$869$		−	1.19254e12i		−	2.09119i
$870$		0			0
$871$	−3.26063e10			−0.0566538
$872$		0			0
$873$	7.69645e11	+	1.69703e11i	1.32505	+	0.292168i
$874$		0			0
$875$	4.64972e11	−	2.27662e11i	0.793222	−	0.388382i
$876$		0			0
$877$			1.15100e11i			0.194570i	0.995257	+	0.0972852i	$0.0310159\pi$
$877$			1.15100e11i			0.194570i	−0.995257	+	0.0972852i	$0.968984\pi$
$878$		0			0
$879$	6.06218e11	−	4.87111e11i	1.01548	−	0.815967i
$880$		0			0
$881$		−	5.84739e10i		−	0.0970640i	−0.998822	−	0.0485320i	$-0.984546\pi$
$881$		−	5.84739e10i		−	0.0970640i	0.998822	−	0.0485320i	$-0.0154543\pi$
$882$		0			0
$883$			4.54543e11i			0.747708i	0.927488	+	0.373854i	$0.121964\pi$
$883$			4.54543e11i			0.747708i	−0.927488	+	0.373854i	$0.878036\pi$
$884$		0			0
$885$	−4.40083e11	+	4.79906e11i	−0.717400	+	0.782318i
$886$		0			0
$887$	−3.50655e11			−0.566481			−0.283241	−	0.959049i	$-0.591410\pi$
$887$	−3.50655e11			−0.566481			−0.283241	+	0.959049i	$0.591410\pi$
$888$		0			0
$889$	4.94592e11			0.791845
$890$		0			0
$891$	3.41598e11	−	7.36956e11i	0.542007	−	1.16931i
$892$		0			0
$893$	7.02311e11			1.10439
$894$		0			0
$895$	4.79988e11	−	7.34129e10i	0.748064	−	0.114414i
$896$		0			0
$897$	3.79698e10	+	4.72540e10i	0.0586500	+	0.0729909i
$898$		0			0
$899$			1.12101e12i			1.71622i
$900$		0			0
$901$	1.06589e12			1.61739
$902$		0			0
$903$	2.10310e11	−	1.68990e11i	0.316308	−	0.254161i
$904$		0			0
$905$	2.78638e10	+	1.82179e11i	0.0415381	+	0.271584i
$906$		0			0
$907$		−	8.28086e10i		−	0.122362i	−0.998127	−	0.0611810i	$-0.980513\pi$
$907$		−	8.28086e10i		−	0.122362i	0.998127	−	0.0611810i	$-0.0194867\pi$
$908$		0			0
$909$	2.96686e11	+	6.54178e10i	0.434551	+	0.0958165i
$910$		0			0
$911$			7.95238e11i			1.15458i	0.816540	+	0.577289i	$0.195890\pi$
$911$			7.95238e11i			1.15458i	−0.816540	+	0.577289i	$0.804110\pi$
$912$		0			0
$913$			6.66682e10i			0.0959479i
$914$		0			0
$915$	1.04232e11	+	9.55827e10i	0.148702	+	0.136362i
$916$		0			0
$917$	−6.58558e11			−0.931359
$918$		0			0
$919$	1.62582e11			0.227935			0.113967	−	0.993484i	$-0.463644\pi$
$919$	1.62582e11			0.227935			0.113967	+	0.993484i	$0.463644\pi$
$920$		0			0
$921$	−4.01020e11	−	4.99076e11i	−0.557350	−	0.693630i
$922$		0			0
$923$	3.54166e10			0.0487978
$924$		0			0
$925$	1.87114e10	+	5.97386e10i	0.0255588	+	0.0815996i
$926$		0			0
$927$	−1.77065e11	−	3.90420e10i	−0.239781	−	0.0528705i
$928$		0			0
$929$		−	1.13990e12i		−	1.53040i	−0.643794	−	0.765199i	$-0.722640\pi$
$929$		−	1.13990e12i		−	1.53040i	0.643794	−	0.765199i	$-0.277360\pi$
$930$		0			0
$931$	1.55976e11			0.207615
$932$		0			0
$933$	−5.61034e11	−	6.98215e11i	−0.740393	−	0.921431i
$934$		0			0
$935$	1.49643e12	−	2.28875e11i	1.95799	−	0.299469i
$936$		0			0
$937$			1.12341e12i			1.45741i	0.684829	+	0.728704i	$0.259877\pi$
$937$			1.12341e12i			1.45741i	−0.684829	+	0.728704i	$0.740123\pi$
$938$		0			0
$939$	−5.63900e11	−	7.01783e11i	−0.725337	−	0.902693i
$940$		0			0
$941$		−	1.49509e12i		−	1.90682i	−0.301682	−	0.953409i	$-0.597548\pi$
$941$		−	1.49509e12i		−	1.90682i	0.301682	−	0.953409i	$-0.402452\pi$
$942$		0			0
$943$		−	1.90425e12i		−	2.40812i
$944$		0			0
$945$	4.04441e11	+	5.76655e11i	0.507140	+	0.723084i
$946$		0			0
$947$	8.53479e11			1.06119			0.530595	−	0.847626i	$-0.321969\pi$
$947$	8.53479e11			1.06119			0.530595	+	0.847626i	$0.321969\pi$
$948$		0			0
$949$	4.93264e10			0.0608156
$950$		0			0
$951$	5.41517e11	−	4.35123e11i	0.662049	−	0.531973i
$952$		0			0
$953$	1.63198e11			0.197853			0.0989264	−	0.995095i	$-0.468459\pi$
$953$	1.63198e11			0.197853			0.0989264	+	0.995095i	$0.468459\pi$
$954$		0			0
$955$	−5.75241e11	+	8.79815e10i	−0.691570	+	0.105774i
$956$		0			0
$957$	1.03374e12	−	8.30633e11i	1.23243	−	0.990287i
$958$		0			0
$959$		−	1.25989e12i		−	1.48956i
$960$		0			0
$961$	8.16515e11			0.957350
$962$		0			0
$963$	2.06635e11	−	9.37142e11i	0.240270	−	1.08968i
$964$		0			0
$965$	−3.00264e11	+	4.59246e10i	−0.346253	+	0.0529585i
$966$		0			0
$967$			1.07651e12i			1.23115i	0.788079	+	0.615575i	$0.211076\pi$
$967$			1.07651e12i			1.23115i	−0.788079	+	0.615575i	$0.788924\pi$
$968$		0			0
$969$	−9.96970e11	+	8.01091e11i	−1.13080	+	0.908629i
$970$		0			0
$971$		−	3.39646e11i		−	0.382075i	−0.981583	−	0.191038i	$-0.938815\pi$
$971$		−	3.39646e11i		−	0.382075i	0.981583	−	0.191038i	$-0.0611853\pi$
$972$		0			0
$973$			1.42025e12i			1.58458i
$974$		0			0
$975$	4.24114e10	+	2.84193e10i	0.0469314	+	0.0314482i
$976$		0			0
$977$	−7.05270e11			−0.774064			−0.387032	−	0.922066i	$-0.626500\pi$
$977$	−7.05270e11			−0.774064			−0.387032	+	0.922066i	$0.626500\pi$
$978$		0			0
$979$	−1.74754e12			−1.90237
$980$		0			0
$981$	−8.46683e10	+	3.83992e11i	−0.0914207	+	0.414616i
$982$		0			0
$983$	−4.75755e11			−0.509529			−0.254765	−	0.967003i	$-0.581998\pi$
$983$	−4.75755e11			−0.509529			−0.254765	+	0.967003i	$0.581998\pi$
$984$		0			0
$985$	7.69729e10	+	5.03264e11i	0.0817698	+	0.534627i
$986$		0			0
$987$	6.14277e11	+	7.64477e11i	0.647285	+	0.805556i
$988$		0			0
$989$			7.28521e11i			0.761478i
$990$		0			0
$991$	6.02162e11			0.624337			0.312168	−	0.950027i	$-0.398945\pi$
$991$	6.02162e11			0.624337			0.312168	+	0.950027i	$0.398945\pi$
$992$		0			0
$993$	−1.28673e12	+	1.03392e12i	−1.32340	+	1.06339i
$994$		0			0
$995$	−9.07721e9	−	5.93486e10i	−0.00926105	−	0.0605506i
$996$		0			0
$997$			1.02815e12i			1.04058i	0.853990	+	0.520289i	$0.174176\pi$
$997$			1.02815e12i			1.04058i	−0.853990	+	0.520289i	$0.825824\pi$
$998$		0			0
$999$	−7.63195e10	+	3.77995e10i	−0.0766255	+	0.0379511i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.9.c.a.89.39	yes	48
3.2	odd	2	inner	120.9.c.a.89.9	✓	48
4.3	odd	2		240.9.c.f.209.10		48
5.4	even	2	inner	120.9.c.a.89.10	yes	48
12.11	even	2		240.9.c.f.209.40		48
15.14	odd	2	inner	120.9.c.a.89.40	yes	48
20.19	odd	2		240.9.c.f.209.39		48
60.59	even	2		240.9.c.f.209.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.9.c.a.89.9	✓	48	3.2	odd	2	inner
120.9.c.a.89.10	yes	48	5.4	even	2	inner
120.9.c.a.89.39	yes	48	1.1	even	1	trivial
120.9.c.a.89.40	yes	48	15.14	odd	2	inner
240.9.c.f.209.9		48	60.59	even	2
240.9.c.f.209.10		48	4.3	odd	2
240.9.c.f.209.39		48	20.19	odd	2
240.9.c.f.209.40		48	12.11	even	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)

\(f(q)\)	\(=\)	\(q+(63.1416 - 50.7359i) q^{3} +(94.4932 + 617.816i) q^{5} +2120.56i q^{7} +(1412.73 - 6407.10i) q^{9} +18869.7i q^{11} -1613.52i q^{13} +(37311.9 + 34215.7i) q^{15} -128361. q^{17} +123008. q^{19} +(107589. + 133896. i) q^{21} -463819. q^{23} +(-372767. + 116759. i) q^{25} +(-235868. - 476231. i) q^{27} -867620. i q^{29} -1.29205e6 q^{31} +(957369. + 1.19146e6i) q^{33} +(-1.31012e6 + 200379. i) q^{35} -160257. i q^{37} +(-81863.3 - 101880. i) q^{39} +4.10559e6i q^{41} -1.57070e6i q^{43} +(4.09190e6 + 267382. i) q^{45} +5.70949e6 q^{47} +1.26802e6 q^{49} +(-8.10494e6 + 6.51253e6i) q^{51} -8.30385e6 q^{53} +(-1.16580e7 + 1.78305e6i) q^{55} +(7.76690e6 - 6.24090e6i) q^{57} +1.28620e7i q^{59} +2.79353e6 q^{61} +(1.35867e7 + 2.99579e6i) q^{63} +(996857. - 152467. i) q^{65} -2.02082e7i q^{67} +(-2.92863e7 + 2.35323e7i) q^{69} +2.19500e7i q^{71} +3.05707e7i q^{73} +(-1.76133e7 + 2.62850e7i) q^{75} -4.00143e7 q^{77} -6.31989e7 q^{79} +(-3.90551e7 - 1.81030e7i) q^{81} +3.53309e6 q^{83} +(-1.21293e7 - 7.93036e7i) q^{85} +(-4.40195e7 - 5.47829e7i) q^{87} +9.26111e7i q^{89} +3.42157e6 q^{91} +(-8.15825e7 + 6.55536e7i) q^{93} +(1.16234e7 + 7.59960e7i) q^{95} +1.20124e8i q^{97} +(1.20900e8 + 2.66578e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2528 q^{9} + 132352 q^{15} + 116176 q^{21} + 56976 q^{25} + 1395648 q^{31} + 6888832 q^{39} - 4287056 q^{45} - 30813552 q^{49} - 22815168 q^{51} - 6062784 q^{55} + 14031936 q^{61} + 2522608 q^{69}+ \cdots - 21719360 q^{99}+O(q^{100}) \) 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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