LMFDB - Embedded newform 240.9.c.f.209.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [240,9,Mod(209,240)] 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("240.209"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(240, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1, 1])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	240.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0,0,0,0,0,0,2528] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$97.7708664147$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.4
Character	$\chi$	$=$	240.209
Dual form			240.9.c.f.209.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-77.3427 + 24.0647i) q^{3} +(-566.843 - 263.275i) q^{5} -3447.79i q^{7} +(5402.78 - 3722.46i) q^{9} +15416.5i q^{11} +9932.71i q^{13} +(50176.8 + 6721.46i) q^{15} -42942.6 q^{17} -44941.3 q^{19} +(82970.2 + 266661. i) q^{21} -296163. q^{23} +(251997. + 298471. i) q^{25} +(-328285. + 417922. i) q^{27} +628329. i q^{29} -1.30083e6 q^{31} +(-370993. - 1.19235e6i) q^{33} +(-907717. + 1.95436e6i) q^{35} -1.56452e6i q^{37} +(-239028. - 768223. i) q^{39} -980599. i q^{41} -5.90146e6i q^{43} +(-4.04256e6 + 687637. i) q^{45} -6.68264e6 q^{47} -6.12246e6 q^{49} +(3.32130e6 - 1.03340e6i) q^{51} +8.16675e6 q^{53} +(4.05877e6 - 8.73872e6i) q^{55} +(3.47588e6 - 1.08150e6i) q^{57} +2.30526e7i q^{59} +6.16910e6 q^{61} +(-1.28343e7 - 1.86276e7i) q^{63} +(2.61504e6 - 5.63029e6i) q^{65} +3.43783e7i q^{67} +(2.29061e7 - 7.12710e6i) q^{69} +4.22081e6i q^{71} +1.17191e7i q^{73} +(-2.66728e7 - 1.70203e7i) q^{75} +5.31528e7 q^{77} -2.04927e7 q^{79} +(1.53333e7 - 4.02233e7i) q^{81} -7.73251e7 q^{83} +(2.43417e7 + 1.13057e7i) q^{85} +(-1.51206e7 - 4.85966e7i) q^{87} +6.91345e7i q^{89} +3.42459e7 q^{91} +(1.00610e8 - 3.13042e7i) q^{93} +(2.54747e7 + 1.18319e7i) q^{95} +7.42781e7i q^{97} +(5.73872e7 + 8.32917e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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
$3$	−77.3427	+	24.0647i	−0.954848	+	0.297096i
$3$	−77.3427	+	24.0647i	−0.954848	+	0.297096i
$4$		0			0
$5$	−566.843	−	263.275i	−0.906949	−	0.421240i
$5$	−566.843	−	263.275i	−0.906949	−	0.421240i
$6$		0			0
$7$		−	3447.79i		−	1.43598i	−0.696053	−	0.717991i	$-0.745062\pi$
$7$		−	3447.79i		−	1.43598i	0.696053	−	0.717991i	$-0.254938\pi$
$8$		0			0
$9$	5402.78	−	3722.46i	0.823468	−	0.567362i
$10$		0			0
$11$			15416.5i			1.05297i	0.850186	+	0.526483i	$0.176490\pi$
$11$			15416.5i			1.05297i	−0.850186	+	0.526483i	$0.823510\pi$
$12$		0			0
$13$			9932.71i			0.347772i	0.984766	+	0.173886i	$0.0556324\pi$
$13$			9932.71i			0.347772i	−0.984766	+	0.173886i	$0.944368\pi$
$14$		0			0
$15$	50176.8	+	6721.46i	0.991147	+	0.132770i
$16$		0			0
$17$	−42942.6			−0.514153			−0.257077	−	0.966391i	$-0.582759\pi$
$17$	−42942.6			−0.514153			−0.257077	+	0.966391i	$0.582759\pi$
$18$		0			0
$19$	−44941.3			−0.344851			−0.172425	−	0.985023i	$-0.555160\pi$
$19$	−44941.3			−0.344851			−0.172425	+	0.985023i	$0.555160\pi$
$20$		0			0
$21$	82970.2	+	266661.i	0.426624	+	1.37114i
$22$		0			0
$23$	−296163.			−1.05833			−0.529164	−	0.848520i	$-0.677494\pi$
$23$	−296163.			−1.05833			−0.529164	+	0.848520i	$0.677494\pi$
$24$		0			0
$25$	251997.	+	298471.i	0.645113	+	0.764087i
$26$		0			0
$27$	−328285.	+	417922.i	−0.617726	+	0.786393i
$28$		0			0
$29$			628329.i			0.888372i	0.895934	+	0.444186i	$0.146507\pi$
$29$			628329.i			0.888372i	−0.895934	+	0.444186i	$0.853493\pi$
$30$		0			0
$31$	−1.30083e6			−1.40856			−0.704279	−	0.709923i	$-0.748730\pi$
$31$	−1.30083e6			−1.40856			−0.704279	+	0.709923i	$0.748730\pi$
$32$		0			0
$33$	−370993.	−	1.19235e6i	−0.312832	−	1.00542i
$34$		0			0
$35$	−907717.	+	1.95436e6i	−0.604893	+	1.30236i
$36$		0			0
$37$		−	1.56452e6i		−	0.834784i	−0.908727	−	0.417392i	$-0.862944\pi$
$37$		−	1.56452e6i		−	0.834784i	0.908727	−	0.417392i	$-0.137056\pi$
$38$		0			0
$39$	−239028.	−	768223.i	−0.103322	−	0.332069i
$40$		0			0
$41$		−	980599.i		−	0.347021i	−0.984832	−	0.173511i	$-0.944489\pi$
$41$		−	980599.i		−	0.347021i	0.984832	−	0.173511i	$-0.0555111\pi$
$42$		0			0
$43$		−	5.90146e6i		−	1.72618i	−0.505052	−	0.863089i	$-0.668527\pi$
$43$		−	5.90146e6i		−	1.72618i	0.505052	−	0.863089i	$-0.331473\pi$
$44$		0			0
$45$	−4.04256e6	+	687637.i	−0.985840	+	0.167691i
$46$		0			0
$47$	−6.68264e6			−1.36948			−0.684741	−	0.728786i	$-0.740085\pi$
$47$	−6.68264e6			−1.36948			−0.684741	+	0.728786i	$0.740085\pi$
$48$		0			0
$49$	−6.12246e6			−1.06204
$50$		0			0
$51$	3.32130e6	−	1.03340e6i	0.490938	−	0.152753i
$52$		0			0
$53$	8.16675e6			1.03501			0.517507	−	0.855679i	$-0.326860\pi$
$53$	8.16675e6			1.03501			0.517507	+	0.855679i	$0.326860\pi$
$54$		0			0
$55$	4.05877e6	−	8.73872e6i	0.443551	−	0.954986i
$56$		0			0
$57$	3.47588e6	−	1.08150e6i	0.329280	−	0.102454i
$58$		0			0
$59$			2.30526e7i			1.90244i	0.308509	+	0.951221i	$0.400170\pi$
$59$			2.30526e7i			1.90244i	−0.308509	+	0.951221i	$0.599830\pi$
$60$		0			0
$61$	6.16910e6			0.445556			0.222778	−	0.974869i	$-0.428487\pi$
$61$	6.16910e6			0.445556			0.222778	+	0.974869i	$0.428487\pi$
$62$		0			0
$63$	−1.28343e7	−	1.86276e7i	−0.814721	−	1.18249i
$64$		0			0
$65$	2.61504e6	−	5.63029e6i	0.146496	−	0.315411i
$66$		0			0
$67$			3.43783e7i			1.70602i	0.521893	+	0.853011i	$0.325226\pi$
$67$			3.43783e7i			1.70602i	−0.521893	+	0.853011i	$0.674774\pi$
$68$		0			0
$69$	2.29061e7	−	7.12710e6i	1.01054	−	0.314424i
$70$		0			0
$71$			4.22081e6i			0.166097i	0.996545	+	0.0830486i	$0.0264657\pi$
$71$			4.22081e6i			0.166097i	−0.996545	+	0.0830486i	$0.973534\pi$
$72$		0			0
$73$			1.17191e7i			0.412671i	0.978481	+	0.206336i	$0.0661538\pi$
$73$			1.17191e7i			0.412671i	−0.978481	+	0.206336i	$0.933846\pi$
$74$		0			0
$75$	−2.66728e7	−	1.70203e7i	−0.842992	−	0.537926i
$76$		0			0
$77$	5.31528e7			1.51204
$78$		0			0
$79$	−2.04927e7			−0.526128			−0.263064	−	0.964778i	$-0.584733\pi$
$79$	−2.04927e7			−0.526128			−0.263064	+	0.964778i	$0.584733\pi$
$80$		0			0
$81$	1.53333e7	−	4.02233e7i	0.356200	−	0.934410i
$82$		0			0
$83$	−7.73251e7			−1.62933			−0.814664	−	0.579934i	$-0.803078\pi$
$83$	−7.73251e7			−1.62933			−0.814664	+	0.579934i	$0.803078\pi$
$84$		0			0
$85$	2.43417e7	+	1.13057e7i	0.466311	+	0.216582i
$86$		0			0
$87$	−1.51206e7	−	4.85966e7i	−0.263932	−	0.848260i
$88$		0			0
$89$			6.91345e7i			1.10188i	0.834545	+	0.550940i	$0.185731\pi$
$89$			6.91345e7i			1.10188i	−0.834545	+	0.550940i	$0.814269\pi$
$90$		0			0
$91$	3.42459e7			0.499394
$92$		0			0
$93$	1.00610e8	−	3.13042e7i	1.34496	−	0.418477i
$94$		0			0
$95$	2.54747e7	+	1.18319e7i	0.312762	+	0.145265i
$96$		0			0
$97$			7.42781e7i			0.839023i	0.907750	+	0.419512i	$0.137799\pi$
$97$			7.42781e7i			0.839023i	−0.907750	+	0.419512i	$0.862201\pi$
$98$		0			0
$99$	5.73872e7	+	8.32917e7i	0.597413	+	0.867084i
$100$		0			0
$101$		−	2.76466e7i		−	0.265678i	−0.991138	−	0.132839i	$-0.957591\pi$
$101$		−	2.76466e7i		−	0.265678i	0.991138	−	0.132839i	$-0.0424093\pi$
$102$		0			0
$103$		−	1.48827e8i		−	1.32231i	−0.750249	−	0.661155i	$-0.770066\pi$
$103$		−	1.48827e8i		−	1.32231i	0.750249	−	0.661155i	$-0.229934\pi$
$104$		0			0
$105$	2.31742e7	−	1.72999e8i	0.190655	−	1.42327i
$106$		0			0
$107$	1.31415e8			1.00256			0.501279	−	0.865285i	$-0.332863\pi$
$107$	1.31415e8			1.00256			0.501279	+	0.865285i	$0.332863\pi$
$108$		0			0
$109$	5.88925e7			0.417209			0.208605	−	0.978000i	$-0.433108\pi$
$109$	5.88925e7			0.417209			0.208605	+	0.978000i	$0.433108\pi$
$110$		0			0
$111$	3.76497e7	+	1.21004e8i	0.248011	+	0.797091i
$112$		0			0
$113$	1.82872e8			1.12159			0.560794	−	0.827955i	$-0.310496\pi$
$113$	1.82872e8			1.12159			0.560794	+	0.827955i	$0.310496\pi$
$114$		0			0
$115$	1.67878e8	+	7.79725e7i	0.959849	+	0.445810i
$116$		0			0
$117$	3.69742e7	+	5.36642e7i	0.197313	+	0.286379i
$118$		0			0
$119$			1.48057e8i			0.738315i
$120$		0			0
$121$	−2.33087e7			−0.108737
$122$		0			0
$123$	2.35979e7	+	7.58421e7i	0.103098	+	0.331352i
$124$		0			0
$125$	−6.42630e7	−	2.35531e8i	−0.263221	−	0.964736i
$126$		0			0
$127$		−	2.39601e7i		−	0.0921028i	−0.998939	−	0.0460514i	$-0.985336\pi$
$127$		−	2.39601e7i		−	0.0921028i	0.998939	−	0.0460514i	$-0.0146638\pi$
$128$		0			0
$129$	1.42017e8	+	4.56434e8i	0.512840	+	1.64824i
$130$		0			0
$131$		−	4.48777e8i		−	1.52386i	−0.647658	−	0.761931i	$-0.724252\pi$
$131$		−	4.48777e8i		−	1.52386i	0.647658	−	0.761931i	$-0.275748\pi$
$132$		0			0
$133$			1.54948e8i			0.495199i
$134$		0			0
$135$	2.96114e8	−	1.50467e8i	0.891507	−	0.453008i
$136$		0			0
$137$	−4.50461e8			−1.27872			−0.639359	−	0.768909i	$-0.720800\pi$
$137$	−4.50461e8			−1.27872			−0.639359	+	0.768909i	$0.720800\pi$
$138$		0			0
$139$	5.30018e8			1.41981			0.709907	−	0.704296i	$-0.248737\pi$
$139$	5.30018e8			1.41981			0.709907	+	0.704296i	$0.248737\pi$
$140$		0			0
$141$	5.16853e8	−	1.60816e8i	1.30765	−	0.406867i
$142$		0			0
$143$	−1.53127e8			−0.366192
$144$		0			0
$145$	1.65423e8	−	3.56164e8i	0.374218	−	0.805709i
$146$		0			0
$147$	4.73527e8	−	1.47335e8i	1.01409	−	0.315528i
$148$		0			0
$149$		−	1.05440e8i		−	0.213924i	−0.994263	−	0.106962i	$-0.965888\pi$
$149$		−	1.05440e8i		−	0.213924i	0.994263	−	0.106962i	$-0.0341123\pi$
$150$		0			0
$151$	5.07757e8			0.976670			0.488335	−	0.872656i	$-0.337604\pi$
$151$	5.07757e8			0.976670			0.488335	+	0.872656i	$0.337604\pi$
$152$		0			0
$153$	−2.32009e8	+	1.59852e8i	−0.423389	+	0.291711i
$154$		0			0
$155$	7.37369e8	+	3.42477e8i	1.27749	+	0.593341i
$156$		0			0
$157$		−	1.07574e9i		−	1.77055i	−0.465063	−	0.885277i	$-0.653968\pi$
$157$		−	1.07574e9i		−	1.77055i	0.465063	−	0.885277i	$-0.346032\pi$
$158$		0			0
$159$	−6.31638e8	+	1.96531e8i	−0.988280	+	0.307498i
$160$		0			0
$161$			1.02111e9i			1.51974i
$162$		0			0
$163$		−	4.12493e8i		−	0.584341i	−0.956366	−	0.292171i	$-0.905623\pi$
$163$		−	4.12493e8i		−	0.584341i	0.956366	−	0.292171i	$-0.0943775\pi$
$164$		0			0
$165$	−1.03621e8	+	7.73549e8i	−0.139802	+	1.04364i
$166$		0			0
$167$	−1.67072e8			−0.214802			−0.107401	−	0.994216i	$-0.534253\pi$
$167$	−1.67072e8			−0.214802			−0.107401	+	0.994216i	$0.534253\pi$
$168$		0			0
$169$	7.17072e8			0.879055
$170$		0			0
$171$	−2.42808e8	+	1.67292e8i	−0.283974	+	0.195655i
$172$		0			0
$173$	−2.69293e8			−0.300636			−0.150318	−	0.988638i	$-0.548030\pi$
$173$	−2.69293e8			−0.300636			−0.150318	+	0.988638i	$0.548030\pi$
$174$		0			0
$175$	1.02907e9	−	8.68834e8i	1.09721	−	0.926371i
$176$		0			0
$177$	−5.54755e8	−	1.78295e9i	−0.565207	−	1.81654i
$178$		0			0
$179$		−	2.01580e8i		−	0.196352i	−0.995169	−	0.0981759i	$-0.968699\pi$
$179$		−	2.01580e8i		−	0.196352i	0.995169	−	0.0981759i	$-0.0313008\pi$
$180$		0			0
$181$	−7.82915e8			−0.729458			−0.364729	−	0.931114i	$-0.618838\pi$
$181$	−7.82915e8			−0.729458			−0.364729	+	0.931114i	$0.618838\pi$
$182$		0			0
$183$	−4.77135e8	+	1.48458e8i	−0.425438	+	0.132373i
$184$		0			0
$185$	−4.11899e8	+	8.86837e8i	−0.351644	+	0.757106i
$186$		0			0
$187$		−	6.62023e8i		−	0.541386i
$188$		0			0
$189$	1.44091e9	+	1.13186e9i	1.12925	+	0.887043i
$190$		0			0
$191$			6.84462e7i			0.0514299i	0.999669	+	0.0257150i	$0.00818623\pi$
$191$			6.84462e7i			0.0514299i	−0.999669	+	0.0257150i	$0.991814\pi$
$192$		0			0
$193$		−	4.40198e8i		−	0.317263i	−0.987338	−	0.158631i	$-0.949292\pi$
$193$		−	4.40198e8i		−	0.317263i	0.987338	−	0.158631i	$-0.0507081\pi$
$194$		0			0
$195$	−6.67624e7	+	4.98392e8i	−0.0461735	+	0.344693i
$196$		0			0
$197$	−4.69489e7			−0.0311717			−0.0155859	−	0.999879i	$-0.504961\pi$
$197$	−4.69489e7			−0.0311717			−0.0155859	+	0.999879i	$0.504961\pi$
$198$		0			0
$199$	2.11868e9			1.35099			0.675496	−	0.737364i	$-0.263930\pi$
$199$	2.11868e9			1.35099			0.675496	+	0.737364i	$0.263930\pi$
$200$		0			0
$201$	−8.27304e8	−	2.65891e9i	−0.506852	−	1.62899i
$202$		0			0
$203$	2.16635e9			1.27569
$204$		0			0
$205$	−2.58167e8	+	5.55846e8i	−0.146179	+	0.314731i
$206$		0			0
$207$	−1.60010e9	+	1.10246e9i	−0.871499	+	0.600455i
$208$		0			0
$209$		−	6.92837e8i		−	0.363116i
$210$		0			0
$211$	1.61141e9			0.812973			0.406487	−	0.913657i	$-0.366754\pi$
$211$	1.61141e9			0.812973			0.406487	+	0.913657i	$0.366754\pi$
$212$		0			0
$213$	−1.01573e8	−	3.26449e8i	−0.0493468	−	0.158598i
$214$		0			0
$215$	−1.55371e9	+	3.34520e9i	−0.727135	+	1.56556i
$216$		0			0
$217$			4.48500e9i			2.02266i
$218$		0			0
$219$	−2.82018e8	−	9.06389e8i	−0.122603	−	0.394038i
$220$		0			0
$221$		−	4.26537e8i		−	0.178808i
$222$		0			0
$223$		−	2.77932e9i		−	1.12388i	−0.827179	−	0.561938i	$-0.810056\pi$
$223$		−	2.77932e9i		−	1.12388i	0.827179	−	0.561938i	$-0.189944\pi$
$224$		0			0
$225$	2.47253e9	+	6.74523e8i	0.964744	+	0.263188i
$226$		0			0
$227$	1.01869e9			0.383653			0.191826	−	0.981429i	$-0.438559\pi$
$227$	1.01869e9			0.383653			0.191826	+	0.981429i	$0.438559\pi$
$228$		0			0
$229$	2.24205e9			0.815274			0.407637	−	0.913144i	$-0.366353\pi$
$229$	2.24205e9			0.815274			0.407637	+	0.913144i	$0.366353\pi$
$230$		0			0
$231$	−4.11098e9	+	1.27911e9i	−1.44377	+	0.449220i
$232$		0			0
$233$	3.96042e9			1.34375			0.671874	−	0.740666i	$-0.265490\pi$
$233$	3.96042e9			1.34375			0.671874	+	0.740666i	$0.265490\pi$
$234$		0			0
$235$	3.78801e9	+	1.75937e9i	1.24205	+	0.576881i
$236$		0			0
$237$	1.58496e9	−	4.93153e8i	0.502373	−	0.156310i
$238$		0			0
$239$		−	3.52028e9i		−	1.07891i	−0.842014	−	0.539456i	$-0.818630\pi$
$239$		−	3.52028e9i		−	1.07891i	0.842014	−	0.539456i	$-0.181370\pi$
$240$		0			0
$241$	−4.28842e9			−1.27125			−0.635623	−	0.772000i	$-0.719257\pi$
$241$	−4.28842e9			−1.27125			−0.635623	+	0.772000i	$0.719257\pi$
$242$		0			0
$243$	−2.17952e8	+	3.47997e9i	−0.0625081	+	0.998044i
$244$		0			0
$245$	3.47047e9	+	1.61189e9i	0.963218	+	0.447375i
$246$		0			0
$247$		−	4.46389e8i		−	0.119929i
$248$		0			0
$249$	5.98053e9	−	1.86081e9i	1.55576	−	0.484066i
$250$		0			0
$251$		−	2.95568e9i		−	0.744667i	−0.928099	−	0.372334i	$-0.878558\pi$
$251$		−	2.95568e9i		−	0.744667i	0.928099	−	0.372334i	$-0.121442\pi$
$252$		0			0
$253$		−	4.56580e9i		−	1.11438i
$254$		0			0
$255$	−2.15472e9	−	2.88637e8i	−0.509602	−	0.0682639i
$256$		0			0
$257$	7.23312e9			1.65803			0.829016	−	0.559225i	$-0.188901\pi$
$257$	7.23312e9			1.65803			0.829016	+	0.559225i	$0.188901\pi$
$258$		0			0
$259$	−5.39413e9			−1.19873
$260$		0			0
$261$	2.33893e9	+	3.39472e9i	0.504029	+	0.731547i
$262$		0			0
$263$	3.25922e8			0.0681225			0.0340613	−	0.999420i	$-0.489156\pi$
$263$	3.25922e8			0.0681225			0.0340613	+	0.999420i	$0.489156\pi$
$264$		0			0
$265$	−4.62927e9	−	2.15010e9i	−0.938704	−	0.435989i
$266$		0			0
$267$	−1.66370e9	−	5.34704e9i	−0.327364	−	1.05213i
$268$		0			0
$269$		−	6.24979e9i		−	1.19359i	−0.802393	−	0.596796i	$-0.796440\pi$
$269$		−	6.24979e9i		−	1.19359i	0.802393	−	0.596796i	$-0.203560\pi$
$270$		0			0
$271$	−3.64533e9			−0.675865			−0.337933	−	0.941170i	$-0.609728\pi$
$271$	−3.64533e9			−0.675865			−0.337933	+	0.941170i	$0.609728\pi$
$272$		0			0
$273$	−2.64867e9	+	8.24119e8i	−0.476845	+	0.148368i
$274$		0			0
$275$	−4.60138e9	+	3.88491e9i	−0.804557	+	0.679282i
$276$		0			0
$277$			1.07672e10i			1.82888i	0.404722	+	0.914440i	$0.367368\pi$
$277$			1.07672e10i			1.82888i	−0.404722	+	0.914440i	$0.632632\pi$
$278$		0			0
$279$	−7.02811e9	+	4.84230e9i	−1.15990	+	0.799163i
$280$		0			0
$281$		−	8.83503e9i		−	1.41704i	−0.705690	−	0.708521i	$-0.749363\pi$
$281$		−	8.83503e9i		−	1.41704i	0.705690	−	0.708521i	$-0.250637\pi$
$282$		0			0
$283$			6.24269e9i			0.973253i	0.873610	+	0.486627i	$0.161773\pi$
$283$			6.24269e9i			0.973253i	−0.873610	+	0.486627i	$0.838227\pi$
$284$		0			0
$285$	−2.25501e9	−	3.02071e8i	−0.341798	−	0.0457857i
$286$		0			0
$287$	−3.38090e9			−0.498316
$288$		0			0
$289$	−5.13169e9			−0.735646
$290$		0			0
$291$	−1.78748e9	−	5.74487e9i	−0.249270	−	0.801139i
$292$		0			0
$293$	−7.75635e9			−1.05242			−0.526208	−	0.850356i	$-0.676387\pi$
$293$	−7.75635e9			−1.05242			−0.526208	+	0.850356i	$0.676387\pi$
$294$		0			0
$295$	6.06917e9	−	1.30672e10i	0.801385	−	1.72542i
$296$		0			0
$297$	−6.44288e9	−	5.06100e9i	−0.828045	−	0.650444i
$298$		0			0
$299$		−	2.94171e9i		−	0.368057i
$300$		0			0
$301$	−2.03470e10			−2.47876
$302$		0			0
$303$	6.65307e8	+	2.13826e9i	0.0789318	+	0.253682i
$304$		0			0
$305$	−3.49691e9	−	1.62417e9i	−0.404097	−	0.187686i
$306$		0			0
$307$			1.05673e10i			1.18963i	0.803862	+	0.594816i	$0.202775\pi$
$307$			1.05673e10i			1.18963i	−0.803862	+	0.594816i	$0.797225\pi$
$308$		0			0
$309$	3.58149e9	+	1.15107e10i	0.392853	+	1.26261i
$310$		0			0
$311$			6.69370e9i			0.715525i	0.933813	+	0.357762i	$0.116460\pi$
$311$			6.69370e9i			0.715525i	−0.933813	+	0.357762i	$0.883540\pi$
$312$		0			0
$313$			1.62994e10i			1.69822i	0.528212	+	0.849112i	$0.322863\pi$
$313$			1.62994e10i			1.69822i	−0.528212	+	0.849112i	$0.677137\pi$
$314$		0			0
$315$	2.37083e9	+	1.39379e10i	0.240801	+	1.41565i
$316$		0			0
$317$	−4.93374e9			−0.488584			−0.244292	−	0.969702i	$-0.578556\pi$
$317$	−4.93374e9			−0.488584			−0.244292	+	0.969702i	$0.578556\pi$
$318$		0			0
$319$	−9.68662e9			−0.935426
$320$		0			0
$321$	−1.01640e10	+	3.16247e9i	−0.957291	+	0.297856i
$322$		0			0
$323$	1.92990e9			0.177306
$324$		0			0
$325$	−2.96463e9	+	2.50302e9i	−0.265728	+	0.224352i
$326$		0			0
$327$	−4.55490e9	+	1.41723e9i	−0.398371	+	0.123951i
$328$		0			0
$329$			2.30403e10i			1.96655i
$330$		0			0
$331$	−4.23300e9			−0.352644			−0.176322	−	0.984333i	$-0.556420\pi$
$331$	−4.23300e9			−0.352644			−0.176322	+	0.984333i	$0.556420\pi$
$332$		0			0
$333$	−5.82386e9	−	8.45275e9i	−0.473625	−	0.687418i
$334$		0			0
$335$	9.05094e9	−	1.94871e10i	0.718645	−	1.54728i
$336$		0			0
$337$		−	1.06509e10i		−	0.825781i	−0.910781	−	0.412891i	$-0.864519\pi$
$337$		−	1.06509e10i		−	0.825781i	0.910781	−	0.412891i	$-0.135481\pi$
$338$		0			0
$339$	−1.41438e10	+	4.40077e9i	−1.07095	+	0.333219i
$340$		0			0
$341$		−	2.00543e10i		−	1.48316i
$342$		0			0
$343$			1.23313e9i			0.0890908i
$344$		0			0
$345$	−1.48605e10	−	1.99065e9i	−1.04896	−	0.140514i
$346$		0			0
$347$	1.74013e10			1.20023			0.600113	−	0.799915i	$-0.295122\pi$
$347$	1.74013e10			1.20023			0.600113	+	0.799915i	$0.295122\pi$
$348$		0			0
$349$	2.62504e10			1.76943			0.884716	−	0.466130i	$-0.154352\pi$
$349$	2.62504e10			1.76943			0.884716	+	0.466130i	$0.154352\pi$
$350$		0			0
$351$	−4.15110e9	−	3.26076e9i	−0.273486	−	0.214828i
$352$		0			0
$353$	1.98518e9			0.127850			0.0639250	−	0.997955i	$-0.479638\pi$
$353$	1.98518e9			0.127850			0.0639250	+	0.997955i	$0.479638\pi$
$354$		0			0
$355$	1.11123e9	−	2.39254e9i	0.0699668	−	0.150642i
$356$		0			0
$357$	−3.56296e9	−	1.14511e10i	−0.219350	−	0.704978i
$358$		0			0
$359$		−	1.57071e10i		−	0.945625i	−0.881163	−	0.472812i	$-0.843239\pi$
$359$		−	1.57071e10i		−	0.945625i	0.881163	−	0.472812i	$-0.156761\pi$
$360$		0			0
$361$	−1.49638e10			−0.881078
$362$		0			0
$363$	1.80276e9	−	5.60918e8i	0.103827	−	0.0323052i
$364$		0			0
$365$	3.08536e9	−	6.64291e9i	0.173834	−	0.374272i
$366$		0			0
$367$			2.67965e10i			1.47711i	0.674193	+	0.738555i	$0.264492\pi$
$367$			2.67965e10i			1.47711i	−0.674193	+	0.738555i	$0.735508\pi$
$368$		0			0
$369$	−3.65024e9	−	5.29796e9i	−0.196887	−	0.285761i
$370$		0			0
$371$		−	2.81573e10i		−	1.48626i
$372$		0			0
$373$		−	6.95289e9i		−	0.359195i	−0.983740	−	0.179597i	$-0.942520\pi$
$373$		−	6.95289e9i		−	0.359195i	0.983740	−	0.179597i	$-0.0574795\pi$
$374$		0			0
$375$	1.06383e10	+	1.66701e10i	0.537955	+	0.842974i
$376$		0			0
$377$	−6.24101e9			−0.308951
$378$		0			0
$379$	−3.74354e10			−1.81437			−0.907185	−	0.420733i	$-0.861773\pi$
$379$	−3.74354e10			−1.81437			−0.907185	+	0.420733i	$0.861773\pi$
$380$		0			0
$381$	5.76593e8	+	1.85313e9i	0.0273633	+	0.0879442i
$382$		0			0
$383$	3.68328e10			1.71175			0.855875	−	0.517183i	$-0.173019\pi$
$383$	3.68328e10			1.71175			0.855875	+	0.517183i	$0.173019\pi$
$384$		0			0
$385$	−3.01293e10	−	1.39938e10i	−1.37134	−	0.636932i
$386$		0			0
$387$	−2.19680e10	−	3.18842e10i	−0.979368	−	1.42145i
$388$		0			0
$389$			2.34598e10i			1.02453i	0.858827	+	0.512266i	$0.171194\pi$
$389$			2.34598e10i			1.02453i	−0.858827	+	0.512266i	$0.828806\pi$
$390$		0			0
$391$	1.27180e10			0.544143
$392$		0			0
$393$	1.07997e10	+	3.47096e10i	0.452733	+	1.45506i
$394$		0			0
$395$	1.16162e10	+	5.39523e9i	0.477172	+	0.221626i
$396$		0			0
$397$			3.58814e9i			0.144446i	0.997388	+	0.0722232i	$0.0230094\pi$
$397$			3.58814e9i			0.144446i	−0.997388	+	0.0722232i	$0.976991\pi$
$398$		0			0
$399$	−3.72879e9	−	1.19841e10i	−0.147122	−	0.472840i
$400$		0			0
$401$		−	4.80248e9i		−	0.185733i	−0.995679	−	0.0928664i	$-0.970397\pi$
$401$		−	4.80248e9i		−	0.185733i	0.995679	−	0.0928664i	$-0.0296029\pi$
$402$		0			0
$403$		−	1.29208e10i		−	0.489857i
$404$		0			0
$405$	−1.92813e10	+	1.87634e10i	−0.716666	+	0.697416i
$406$		0			0
$407$	2.41194e10			0.878999
$408$		0			0
$409$	2.02788e10			0.724685			0.362342	−	0.932045i	$-0.381977\pi$
$409$	2.02788e10			0.724685			0.362342	+	0.932045i	$0.381977\pi$
$410$		0			0
$411$	3.48398e10	−	1.08402e10i	1.22098	−	0.379901i
$412$		0			0
$413$	7.94805e10			2.73187
$414$		0			0
$415$	4.38312e10	+	2.03578e10i	1.47772	+	0.686338i
$416$		0			0
$417$	−4.09930e10	+	1.27547e10i	−1.35571	+	0.421820i
$418$		0			0
$419$			3.60381e10i			1.16925i	0.811305	+	0.584623i	$0.198758\pi$
$419$			3.60381e10i			1.16925i	−0.811305	+	0.584623i	$0.801242\pi$
$420$		0			0
$421$	4.90406e10			1.56109			0.780544	−	0.625101i	$-0.214942\pi$
$421$	4.90406e10			1.56109			0.780544	+	0.625101i	$0.214942\pi$
$422$		0			0
$423$	−3.61048e10	+	2.48759e10i	−1.12773	+	0.776993i
$424$		0			0
$425$	−1.08214e10	−	1.28171e10i	−0.331687	−	0.392858i
$426$		0			0
$427$		−	2.12698e10i		−	0.639811i
$428$		0			0
$429$	1.18433e10	−	3.68497e9i	0.349658	−	0.108794i
$430$		0			0
$431$			5.36301e10i			1.55417i	0.629394	+	0.777087i	$0.283303\pi$
$431$			5.36301e10i			1.55417i	−0.629394	+	0.777087i	$0.716697\pi$
$432$		0			0
$433$		−	1.36877e10i		−	0.389385i	−0.980864	−	0.194692i	$-0.937629\pi$
$433$		−	1.36877e10i		−	0.389385i	0.980864	−	0.194692i	$-0.0623708\pi$
$434$		0			0
$435$	−4.22329e9	+	3.15275e10i	−0.117949	+	0.880508i
$436$		0			0
$437$	1.33100e10			0.364965
$438$		0			0
$439$	−3.05371e10			−0.822186			−0.411093	−	0.911593i	$-0.634853\pi$
$439$	−3.05371e10			−0.822186			−0.411093	+	0.911593i	$0.634853\pi$
$440$		0			0
$441$	−3.30783e10	+	2.27906e10i	−0.874558	+	0.602562i
$442$		0			0
$443$	−1.20943e10			−0.314026			−0.157013	−	0.987597i	$-0.550186\pi$
$443$	−1.20943e10			−0.314026			−0.157013	+	0.987597i	$0.550186\pi$
$444$		0			0
$445$	1.82014e10	−	3.91884e10i	0.464156	−	0.999350i
$446$		0			0
$447$	2.53738e9	+	8.15499e9i	0.0635558	+	0.204265i
$448$		0			0
$449$		−	5.17706e10i		−	1.27379i	−0.770950	−	0.636895i	$-0.780218\pi$
$449$		−	5.17706e10i		−	1.27379i	0.770950	−	0.636895i	$-0.219782\pi$
$450$		0			0
$451$	1.51174e10			0.365401
$452$		0			0
$453$	−3.92713e10	+	1.22190e10i	−0.932571	+	0.290164i
$454$		0			0
$455$	−1.94121e10	−	9.01610e9i	−0.452925	−	0.210365i
$456$		0			0
$457$			3.74702e10i			0.859056i	0.903054	+	0.429528i	$0.141320\pi$
$457$			3.74702e10i			0.859056i	−0.903054	+	0.429528i	$0.858680\pi$
$458$		0			0
$459$	1.40974e10	−	1.79466e10i	0.317606	−	0.404327i
$460$		0			0
$461$			3.52628e10i			0.780752i	0.920655	+	0.390376i	$0.127655\pi$
$461$			3.52628e10i			0.780752i	−0.920655	+	0.390376i	$0.872345\pi$
$462$		0			0
$463$		−	2.30500e10i		−	0.501588i	−0.968040	−	0.250794i	$-0.919308\pi$
$463$		−	2.30500e10i		−	0.501588i	0.968040	−	0.250794i	$-0.0806917\pi$
$464$		0			0
$465$	−6.52717e10	−	8.74350e9i	−1.39609	−	0.187014i
$466$		0			0
$467$	−4.90788e10			−1.03187			−0.515936	−	0.856627i	$-0.672556\pi$
$467$	−4.90788e10			−1.03187			−0.515936	+	0.856627i	$0.672556\pi$
$468$		0			0
$469$	1.18529e11			2.44982
$470$		0			0
$471$	2.58874e10	+	8.32007e10i	0.526024	+	1.69061i
$472$		0			0
$473$	9.09796e10			1.81761
$474$		0			0
$475$	−1.13251e10	−	1.34137e10i	−0.222468	−	0.263496i
$476$		0			0
$477$	4.41231e10	−	3.04004e10i	0.852301	−	0.587227i
$478$		0			0
$479$		−	5.85055e10i		−	1.11136i	−0.831396	−	0.555680i	$-0.812458\pi$
$479$		−	5.85055e10i		−	1.11136i	0.831396	−	0.555680i	$-0.187542\pi$
$480$		0			0
$481$	1.55399e10			0.290314
$482$		0			0
$483$	−2.45727e10	−	7.89753e10i	−0.451508	−	1.45112i
$484$		0			0
$485$	1.95556e10	−	4.21040e10i	0.353430	−	0.760951i
$486$		0			0
$487$		−	6.11680e10i		−	1.08745i	−0.839264	−	0.543724i	$-0.817014\pi$
$487$		−	6.11680e10i		−	1.08745i	0.839264	−	0.543724i	$-0.182986\pi$
$488$		0			0
$489$	9.92654e9	+	3.19033e10i	0.173605	+	0.557957i
$490$		0			0
$491$		−	2.88854e10i		−	0.496996i	−0.968632	−	0.248498i	$-0.920063\pi$
$491$		−	2.88854e10i		−	0.496996i	0.968632	−	0.248498i	$-0.0799370\pi$
$492$		0			0
$493$		−	2.69821e10i		−	0.456760i
$494$		0			0
$495$	−1.06009e10	−	6.23220e10i	−0.176573	−	1.03806i
$496$		0			0
$497$	1.45525e10			0.238513
$498$		0			0
$499$	−5.78459e10			−0.932976			−0.466488	−	0.884527i	$-0.654481\pi$
$499$	−5.78459e10			−0.932976			−0.466488	+	0.884527i	$0.654481\pi$
$500$		0			0
$501$	1.29218e10	−	4.02054e9i	0.205103	−	0.0638166i
$502$		0			0
$503$	5.04066e10			0.787437			0.393719	−	0.919231i	$-0.371188\pi$
$503$	5.04066e10			0.787437			0.393719	+	0.919231i	$0.371188\pi$
$504$		0			0
$505$	−7.27865e9	+	1.56713e10i	−0.111914	+	0.240956i
$506$		0			0
$507$	−5.54603e10	+	1.72562e10i	−0.839363	+	0.261163i
$508$		0			0
$509$			2.55244e10i			0.380263i	0.981759	+	0.190132i	$0.0608915\pi$
$509$			2.55244e10i			0.380263i	−0.981759	+	0.190132i	$0.939108\pi$
$510$		0			0
$511$	4.04051e10			0.592588
$512$		0			0
$513$	1.47536e10	−	1.87820e10i	0.213023	−	0.271188i
$514$		0			0
$515$	−3.91825e10	+	8.43617e10i	−0.557010	+	1.19927i
$516$		0			0
$517$		−	1.03023e11i		−	1.44202i
$518$		0			0
$519$	2.08279e10	−	6.48048e9i	0.287062	−	0.0893177i
$520$		0			0
$521$		−	5.87171e10i		−	0.796919i	−0.917186	−	0.398459i	$-0.869545\pi$
$521$		−	5.87171e10i		−	0.796919i	0.917186	−	0.398459i	$-0.130455\pi$
$522$		0			0
$523$			6.38671e10i			0.853632i	0.904338	+	0.426816i	$0.140365\pi$
$523$			6.38671e10i			0.853632i	−0.904338	+	0.426816i	$0.859635\pi$
$524$		0			0
$525$	−5.86825e10	+	9.19622e10i	−0.772452	+	1.21052i
$526$		0			0
$527$	5.58612e10			0.724215
$528$		0			0
$529$	9.40179e9			0.120057
$530$		0			0
$531$	8.58124e10	+	1.24548e11i	1.07937	+	1.56660i
$532$		0			0
$533$	9.74001e9			0.120684
$534$		0			0
$535$	−7.44917e10	−	3.45983e10i	−0.909270	−	0.422318i
$536$		0			0
$537$	4.85097e9	+	1.55907e10i	0.0583353	+	0.187486i
$538$		0			0
$539$		−	9.43867e10i		−	1.11829i
$540$		0			0
$541$	1.45524e11			1.69881			0.849406	−	0.527740i	$-0.176960\pi$
$541$	1.45524e11			1.69881			0.849406	+	0.527740i	$0.176960\pi$
$542$		0			0
$543$	6.05527e10	−	1.88406e10i	0.696521	−	0.216719i
$544$		0			0
$545$	−3.33828e10	−	1.55049e10i	−0.378387	−	0.175745i
$546$		0			0
$547$			1.45585e11i			1.62617i	0.582144	+	0.813086i	$0.302214\pi$
$547$			1.45585e11i			1.62617i	−0.582144	+	0.813086i	$0.697786\pi$
$548$		0			0
$549$	3.33303e10	−	2.29643e10i	0.366902	−	0.252792i
$550$		0			0
$551$		−	2.82379e10i		−	0.306356i
$552$		0			0
$553$			7.06547e10i			0.755511i
$554$		0			0
$555$	1.05159e10	−	7.85026e10i	0.110834	−	0.827393i
$556$		0			0
$557$	−2.62613e9			−0.0272833			−0.0136416	−	0.999907i	$-0.504342\pi$
$557$	−2.62613e9			−0.0272833			−0.0136416	+	0.999907i	$0.504342\pi$
$558$		0			0
$559$	5.86175e10			0.600316
$560$		0			0
$561$	1.59314e10	+	5.12027e10i	0.160843	+	0.516941i
$562$		0			0
$563$	1.79138e11			1.78301			0.891503	−	0.453014i	$-0.149651\pi$
$563$	1.79138e11			1.78301			0.891503	+	0.453014i	$0.149651\pi$
$564$		0			0
$565$	−1.03660e11	−	4.81457e10i	−1.01722	−	0.472458i
$566$		0			0
$567$	−1.38681e11	−	5.28659e10i	−1.34179	−	0.511497i
$568$		0			0
$569$		−	1.25005e11i		−	1.19256i	−0.802777	−	0.596279i	$-0.796645\pi$
$569$		−	1.25005e11i		−	1.19256i	0.802777	−	0.596279i	$-0.203355\pi$
$570$		0			0
$571$	1.33638e11			1.25714			0.628571	−	0.777752i	$-0.283640\pi$
$571$	1.33638e11			1.25714			0.628571	+	0.777752i	$0.283640\pi$
$572$		0			0
$573$	−1.64714e9	−	5.29381e9i	−0.0152796	−	0.0491078i
$574$		0			0
$575$	−7.46324e10	−	8.83963e10i	−0.682741	−	0.808654i
$576$		0			0
$577$			8.41141e9i			0.0758867i	0.999280	+	0.0379433i	$0.0120806\pi$
$577$			8.41141e9i			0.0758867i	−0.999280	+	0.0379433i	$0.987919\pi$
$578$		0			0
$579$	1.05933e10	+	3.40461e10i	0.0942573	+	0.302937i
$580$		0			0
$581$			2.66601e11i			2.33968i
$582$		0			0
$583$			1.25903e11i			1.08983i
$584$		0			0
$585$	−6.83010e9	−	4.01536e10i	−0.0583181	−	0.342847i
$586$		0			0
$587$	1.54462e11			1.30098			0.650488	−	0.759516i	$-0.274564\pi$
$587$	1.54462e11			1.30098			0.650488	+	0.759516i	$0.274564\pi$
$588$		0			0
$589$	5.84612e10			0.485743
$590$		0			0
$591$	3.63116e9	−	1.12981e9i	0.0297642	−	0.00926098i
$592$		0			0
$593$	−6.76963e10			−0.547452			−0.273726	−	0.961808i	$-0.588256\pi$
$593$	−6.76963e10			−0.547452			−0.273726	+	0.961808i	$0.588256\pi$
$594$		0			0
$595$	3.89798e10	−	8.39252e10i	0.311008	−	0.669614i
$596$		0			0
$597$	−1.63864e11	+	5.09855e10i	−1.28999	+	0.401374i
$598$		0			0
$599$			1.20194e11i			0.933635i	0.884354	+	0.466818i	$0.154600\pi$
$599$			1.20194e11i			0.933635i	−0.884354	+	0.466818i	$0.845400\pi$
$600$		0			0
$601$	−1.53372e11			−1.17557			−0.587783	−	0.809019i	$-0.699999\pi$
$601$	−1.53372e11			−1.17557			−0.587783	+	0.809019i	$0.699999\pi$
$602$		0			0
$603$	1.27972e11	+	1.85738e11i	0.967933	+	1.40486i
$604$		0			0
$605$	1.32124e10	+	6.13660e9i	0.0986188	+	0.0458043i
$606$		0			0
$607$		−	1.46632e11i		−	1.08013i	−0.841625	−	0.540063i	$-0.818401\pi$
$607$		−	1.46632e11i		−	1.08013i	0.841625	−	0.540063i	$-0.181599\pi$
$608$		0			0
$609$	−1.67551e11	+	5.21326e10i	−1.21809	+	0.379001i
$610$		0			0
$611$		−	6.63768e10i		−	0.476268i
$612$		0			0
$613$		−	3.83397e10i		−	0.271523i	−0.990742	−	0.135762i	$-0.956652\pi$
$613$		−	3.83397e10i		−	0.271523i	0.990742	−	0.135762i	$-0.0433481\pi$
$614$		0			0
$615$	6.59106e9	−	4.92033e10i	0.0460739	−	0.343949i
$616$		0			0
$617$	−2.31520e10			−0.159753			−0.0798763	−	0.996805i	$-0.525453\pi$
$617$	−2.31520e10			−0.159753			−0.0798763	+	0.996805i	$0.525453\pi$
$618$		0			0
$619$	−1.13065e11			−0.770129			−0.385065	−	0.922890i	$-0.625821\pi$
$619$	−1.13065e11			−0.770129			−0.385065	+	0.922890i	$0.625821\pi$
$620$		0			0
$621$	9.72260e10	−	1.23773e11i	0.653757	−	0.832262i
$622$		0			0
$623$	2.38361e11			1.58228
$624$		0			0
$625$	−2.55825e10	+	1.50428e11i	−0.167657	+	0.985845i
$626$		0			0
$627$	1.66729e10	+	5.35858e10i	0.107880	+	0.346721i
$628$		0			0
$629$			6.71845e10i			0.429207i
$630$		0			0
$631$	−2.17611e11			−1.37266			−0.686332	−	0.727288i	$-0.740780\pi$
$631$	−2.17611e11			−1.37266			−0.686332	+	0.727288i	$0.740780\pi$
$632$		0			0
$633$	−1.24631e11	+	3.87782e10i	−0.776266	+	0.241531i
$634$		0			0
$635$	−6.30809e9	+	1.35816e10i	−0.0387974	+	0.0835326i
$636$		0			0
$637$		−	6.08126e10i		−	0.369348i
$638$		0			0
$639$	1.57118e10	+	2.28041e10i	0.0942373	+	0.136776i
$640$		0			0
$641$		−	1.22597e11i		−	0.726184i	−0.931753	−	0.363092i	$-0.881721\pi$
$641$		−	1.22597e11i		−	0.726184i	0.931753	−	0.363092i	$-0.118279\pi$
$642$		0			0
$643$			1.86916e10i			0.109346i	0.998504	+	0.0546729i	$0.0174116\pi$
$643$			1.86916e10i			0.109346i	−0.998504	+	0.0546729i	$0.982588\pi$
$644$		0			0
$645$	3.96664e10	−	2.96116e11i	0.229184	−	1.71090i
$646$		0			0
$647$	−4.19998e10			−0.239679			−0.119840	−	0.992793i	$-0.538238\pi$
$647$	−4.19998e10			−0.239679			−0.119840	+	0.992793i	$0.538238\pi$
$648$		0			0
$649$	−3.55389e11			−2.00321
$650$		0			0
$651$	−1.07930e11	−	3.46882e11i	−0.600924	−	1.93134i
$652$		0			0
$653$	2.89608e11			1.59279			0.796394	−	0.604778i	$-0.206738\pi$
$653$	2.89608e11			1.59279			0.796394	+	0.604778i	$0.206738\pi$
$654$		0			0
$655$	−1.18152e11	+	2.54386e11i	−0.641912	+	1.38206i
$656$		0			0
$657$	4.36240e10	+	6.33159e10i	0.234134	+	0.339822i
$658$		0			0
$659$		−	1.18895e11i		−	0.630408i	−0.949024	−	0.315204i	$-0.897927\pi$
$659$		−	1.18895e11i		−	0.630408i	0.949024	−	0.315204i	$-0.102073\pi$
$660$		0			0
$661$	1.86560e11			0.977265			0.488632	−	0.872490i	$-0.337496\pi$
$661$	1.86560e11			0.977265			0.488632	+	0.872490i	$0.337496\pi$
$662$		0			0
$663$	1.02645e10	+	3.29895e10i	0.0531231	+	0.170735i
$664$		0			0
$665$	4.07940e10	−	8.78314e10i	0.208598	−	0.449121i
$666$		0			0
$667$		−	1.86088e11i		−	0.940189i
$668$		0			0
$669$	6.68836e10	+	2.14960e11i	0.333899	+	1.07313i
$670$		0			0
$671$			9.51058e10i			0.469156i
$672$		0			0
$673$			3.70883e10i			0.180791i	0.995906	+	0.0903954i	$0.0288131\pi$
$673$			3.70883e10i			0.180791i	−0.995906	+	0.0903954i	$0.971187\pi$
$674$		0			0
$675$	−2.07465e11	+	7.33151e9i	−0.999376	+	0.0353165i
$676$		0			0
$677$	−1.75040e11			−0.833265			−0.416632	−	0.909075i	$-0.636790\pi$
$677$	−1.75040e11			−0.833265			−0.416632	+	0.909075i	$0.636790\pi$
$678$		0			0
$679$	2.56095e11			1.20482
$680$		0			0
$681$	−7.87881e10	+	2.45145e10i	−0.366330	+	0.113981i
$682$		0			0
$683$	1.12903e11			0.518827			0.259413	−	0.965766i	$-0.416471\pi$
$683$	1.12903e11			0.518827			0.259413	+	0.965766i	$0.416471\pi$
$684$		0			0
$685$	2.55341e11	+	1.18595e11i	1.15973	+	0.538647i
$686$		0			0
$687$	−1.73406e11	+	5.39544e10i	−0.778463	+	0.242214i
$688$		0			0
$689$			8.11180e10i			0.359949i
$690$		0			0
$691$	−2.95392e9			−0.0129565			−0.00647824	−	0.999979i	$-0.502062\pi$
$691$	−2.95392e9			−0.0129565			−0.00647824	+	0.999979i	$0.502062\pi$
$692$		0			0
$693$	2.87172e11	−	1.97859e11i	1.24512	−	0.857874i
$694$		0			0
$695$	−3.00437e11	−	1.39541e11i	−1.28770	−	0.598083i
$696$		0			0
$697$			4.21095e10i			0.178422i
$698$		0			0
$699$	−3.06309e11	+	9.53065e10i	−1.28307	+	0.399221i
$700$		0			0
$701$		−	1.57652e11i		−	0.652871i	−0.945220	−	0.326435i	$-0.894152\pi$
$701$		−	1.57652e11i		−	0.652871i	0.945220	−	0.326435i	$-0.105848\pi$
$702$		0			0
$703$			7.03115e10i			0.287876i
$704$		0			0
$705$	−3.35314e11	−	4.49171e10i	−1.35736	−	0.181826i
$706$		0			0
$707$	−9.53195e10			−0.381509
$708$		0			0
$709$	−3.19657e11			−1.26502			−0.632512	−	0.774551i	$-0.717976\pi$
$709$	−3.19657e11			−1.26502			−0.632512	+	0.774551i	$0.717976\pi$
$710$		0			0
$711$	−1.10718e11	+	7.62835e10i	−0.433250	+	0.298505i
$712$		0			0
$713$	3.85259e11			1.49072
$714$		0			0
$715$	8.67992e10	+	4.03146e10i	0.332117	+	0.154255i
$716$		0			0
$717$	8.47147e10	+	2.72268e11i	0.320540	+	1.03020i
$718$		0			0
$719$			1.87728e11i			0.702447i	0.936292	+	0.351223i	$0.114234\pi$
$719$			1.87728e11i			0.702447i	−0.936292	+	0.351223i	$0.885766\pi$
$720$		0			0
$721$	−5.13125e11			−1.89881
$722$		0			0
$723$	3.31678e11	−	1.03200e11i	1.21385	−	0.377682i
$724$		0			0
$725$	−1.87538e11	+	1.58337e11i	−0.678794	+	0.573101i
$726$		0			0
$727$		−	5.60776e10i		−	0.200748i	−0.994950	−	0.100374i	$-0.967996\pi$
$727$		−	5.60776e10i		−	0.200748i	0.994950	−	0.100374i	$-0.0320040\pi$
$728$		0			0
$729$	−6.68875e10	−	2.74395e11i	−0.236829	−	0.971551i
$730$		0			0
$731$			2.53424e11i			0.887520i
$732$		0			0
$733$			5.18007e11i			1.79440i	0.441623	+	0.897200i	$0.354403\pi$
$733$			5.18007e11i			1.79440i	−0.441623	+	0.897200i	$0.645597\pi$
$734$		0			0
$735$	−3.07205e11	−	4.11519e10i	−1.05264	−	0.141007i
$736$		0			0
$737$	−5.29992e11			−1.79638
$738$		0			0
$739$	3.21137e11			1.07674			0.538372	−	0.842707i	$-0.319040\pi$
$739$	3.21137e11			1.07674			0.538372	+	0.842707i	$0.319040\pi$
$740$		0			0
$741$	1.07422e10	+	3.45249e10i	0.0356305	+	0.114514i
$742$		0			0
$743$	−2.77749e11			−0.911374			−0.455687	−	0.890140i	$-0.650606\pi$
$743$	−2.77749e11			−0.911374			−0.455687	+	0.890140i	$0.650606\pi$
$744$		0			0
$745$	−2.77596e10	+	5.97678e10i	−0.0901133	+	0.194018i
$746$		0			0
$747$	−4.17770e11	+	2.87840e11i	−1.34170	+	0.924419i
$748$		0			0
$749$		−	4.53092e11i		−	1.43966i
$750$		0			0
$751$	−6.78103e10			−0.213175			−0.106587	−	0.994303i	$-0.533992\pi$
$751$	−6.78103e10			−0.213175			−0.106587	+	0.994303i	$0.533992\pi$
$752$		0			0
$753$	7.11276e10	+	2.28600e11i	0.221237	+	0.711044i
$754$		0			0
$755$	−2.87818e11	−	1.33680e11i	−0.885790	−	0.411413i
$756$		0			0
$757$		−	5.07778e11i		−	1.54629i	−0.634231	−	0.773144i	$-0.718683\pi$
$757$		−	5.07778e11i		−	1.54629i	0.634231	−	0.773144i	$-0.281317\pi$
$758$		0			0
$759$	1.09875e11	+	3.53131e11i	0.331078	+	1.06407i
$760$		0			0
$761$		−	3.45584e11i		−	1.03042i	−0.857064	−	0.515210i	$-0.827714\pi$
$761$		−	3.45584e11i		−	1.03042i	0.857064	−	0.515210i	$-0.172286\pi$
$762$		0			0
$763$		−	2.03049e11i		−	0.599104i
$764$		0			0
$765$	1.73598e11	−	2.95289e10i	0.506873	−	0.0862187i
$766$		0			0
$767$	−2.28975e11			−0.661616
$768$		0			0
$769$	−6.28668e11			−1.79769			−0.898847	−	0.438262i	$-0.855594\pi$
$769$	−6.28668e11			−1.79769			−0.898847	+	0.438262i	$0.855594\pi$
$770$		0			0
$771$	−5.59428e11	+	1.74063e11i	−1.58317	+	0.492594i
$772$		0			0
$773$	5.04406e11			1.41274			0.706370	−	0.707843i	$-0.250331\pi$
$773$	5.04406e11			1.41274			0.706370	+	0.707843i	$0.250331\pi$
$774$		0			0
$775$	−3.27807e11	−	3.88262e11i	−0.908680	−	1.07626i
$776$		0			0
$777$	4.17197e11	−	1.29808e11i	1.14461	−	0.356138i
$778$		0			0
$779$			4.40694e10i			0.119671i
$780$		0			0
$781$	−6.50700e10			−0.174895
$782$		0			0
$783$	−2.62592e11	−	2.06271e11i	−0.698610	−	0.548771i
$784$		0			0
$785$	−2.83216e11	+	6.09777e11i	−0.745829	+	1.60580i
$786$		0			0
$787$		−	2.30047e11i		−	0.599676i	−0.953990	−	0.299838i	$-0.903067\pi$
$787$		−	2.30047e11i		−	0.599676i	0.953990	−	0.299838i	$-0.0969327\pi$
$788$		0			0
$789$	−2.52077e10	+	7.84323e9i	−0.0650466	+	0.0202389i
$790$		0			0
$791$		−	6.30504e11i		−	1.61058i
$792$		0			0
$793$			6.12759e10i			0.154952i
$794$		0			0
$795$	4.09782e11	+	5.48925e10i	1.02585	+	0.137418i
$796$		0			0
$797$	−8.94310e10			−0.221643			−0.110822	−	0.993840i	$-0.535348\pi$
$797$	−8.94310e10			−0.221643			−0.110822	+	0.993840i	$0.535348\pi$
$798$		0			0
$799$	2.86970e11			0.704124
$800$		0			0
$801$	2.57351e11	+	3.73518e11i	0.625165	+	0.907364i
$802$		0			0
$803$	−1.80668e11			−0.434529
$804$		0			0
$805$	2.68833e11	−	5.78809e11i	0.640175	−	1.37833i
$806$		0			0
$807$	1.50400e11	+	4.83375e11i	0.354611	+	1.13970i
$808$		0			0
$809$			3.49693e11i			0.816381i	0.912897	+	0.408191i	$0.133840\pi$
$809$			3.49693e11i			0.816381i	−0.912897	+	0.408191i	$0.866160\pi$
$810$		0			0
$811$	−3.68966e11			−0.852911			−0.426455	−	0.904509i	$-0.640238\pi$
$811$	−3.68966e11			−0.852911			−0.426455	+	0.904509i	$0.640238\pi$
$812$		0			0
$813$	2.81940e11	−	8.77240e10i	0.645348	−	0.200797i
$814$		0			0
$815$	−1.08599e11	+	2.33819e11i	−0.246148	+	0.529968i
$816$		0			0
$817$			2.65219e11i			0.595274i
$818$		0			0
$819$	1.85023e11	−	1.27479e11i	0.411235	−	0.283337i
$820$		0			0
$821$		−	7.26326e10i		−	0.159867i	−0.996800	−	0.0799335i	$-0.974529\pi$
$821$		−	7.26326e10i		−	0.159867i	0.996800	−	0.0799335i	$-0.0254708\pi$
$822$		0			0
$823$			1.53874e11i			0.335402i	0.985838	+	0.167701i	$0.0536343\pi$
$823$			1.53874e11i			0.335402i	−0.985838	+	0.167701i	$0.946366\pi$
$824$		0			0
$825$	2.62393e11	−	4.11200e11i	0.566418	−	0.887642i
$826$		0			0
$827$	−1.95841e10			−0.0418679			−0.0209339	−	0.999781i	$-0.506664\pi$
$827$	−1.95841e10			−0.0418679			−0.0209339	+	0.999781i	$0.506664\pi$
$828$		0			0
$829$	4.33352e11			0.917536			0.458768	−	0.888556i	$-0.348291\pi$
$829$	4.33352e11			0.917536			0.458768	+	0.888556i	$0.348291\pi$
$830$		0			0
$831$	−2.59111e11	−	8.32767e11i	−0.543352	−	1.74630i
$832$		0			0
$833$	2.62914e11			0.546052
$834$		0			0
$835$	9.47036e10	+	4.39859e10i	0.194814	+	0.0904830i
$836$		0			0
$837$	4.27044e11	−	5.43646e11i	0.870103	−	1.10768i
$838$		0			0
$839$			1.88670e11i			0.380764i	0.981710	+	0.190382i	$0.0609726\pi$
$839$			1.88670e11i			0.380764i	−0.981710	+	0.190382i	$0.939027\pi$
$840$		0			0
$841$	1.05449e11			0.210794
$842$		0			0
$843$	2.12613e11	+	6.83325e11i	0.420997	+	1.35306i
$844$		0			0
$845$	−4.06467e11	−	1.88787e11i	−0.797258	−	0.370293i
$846$		0			0
$847$			8.03636e10i			0.156144i
$848$		0			0
$849$	−1.50229e11	−	4.82826e11i	−0.289149	−	0.929309i
$850$		0			0
$851$			4.63353e11i			0.883474i
$852$		0			0
$853$			1.04742e12i			1.97845i	0.146418	+	0.989223i	$0.453226\pi$
$853$			1.04742e12i			1.97845i	−0.146418	+	0.989223i	$0.546774\pi$
$854$		0			0
$855$	1.81678e11	−	3.09033e10i	0.339968	−	0.0578283i
$856$		0			0
$857$	−3.08722e11			−0.572328			−0.286164	−	0.958181i	$-0.592380\pi$
$857$	−3.08722e11			−0.572328			−0.286164	+	0.958181i	$0.592380\pi$
$858$		0			0
$859$	7.88671e11			1.44852			0.724258	−	0.689529i	$-0.242182\pi$
$859$	7.88671e11			1.44852			0.724258	+	0.689529i	$0.242182\pi$
$860$		0			0
$861$	2.61488e11	−	8.13605e10i	0.475816	−	0.148047i
$862$		0			0
$863$	9.07738e11			1.63650			0.818252	−	0.574859i	$-0.194943\pi$
$863$	9.07738e11			1.63650			0.818252	+	0.574859i	$0.194943\pi$
$864$		0			0
$865$	1.52647e11	+	7.08983e10i	0.272662	+	0.126640i
$866$		0			0
$867$	3.96899e11	−	1.23493e11i	0.702430	−	0.218557i
$868$		0			0
$869$		−	3.15926e11i		−	0.553995i
$870$		0			0
$871$	−3.41469e11			−0.593307
$872$		0			0
$873$	2.76498e11	+	4.01308e11i	0.476030	+	0.690909i
$874$		0			0
$875$	−8.12062e11	+	2.21565e11i	−1.38534	+	0.377980i
$876$		0			0
$877$			4.01949e11i			0.679473i	0.940521	+	0.339736i	$0.110338\pi$
$877$			4.01949e11i			0.679473i	−0.940521	+	0.339736i	$0.889662\pi$
$878$		0			0
$879$	5.99897e11	−	1.86655e11i	1.00490	−	0.312668i
$880$		0			0
$881$			1.75145e11i			0.290732i	0.989378	+	0.145366i	$0.0464360\pi$
$881$			1.75145e11i			0.290732i	−0.989378	+	0.145366i	$0.953564\pi$
$882$		0			0
$883$			5.11781e11i			0.841863i	0.907093	+	0.420931i	$0.138297\pi$
$883$			5.11781e11i			0.841863i	−0.907093	+	0.420931i	$0.861703\pi$
$884$		0			0
$885$	−1.54947e11	+	1.15671e12i	−0.252587	+	1.88560i
$886$		0			0
$887$	8.96441e11			1.44819			0.724097	−	0.689698i	$-0.242257\pi$
$887$	8.96441e11			1.44819			0.724097	+	0.689698i	$0.242257\pi$
$888$		0			0
$889$	−8.26093e10			−0.132258
$890$		0			0
$891$	6.20101e11	+	2.36385e11i	0.983901	+	0.375067i
$892$		0			0
$893$	3.00327e11			0.472267
$894$		0			0
$895$	−5.30709e10	+	1.14264e11i	−0.0827113	+	0.178081i
$896$		0			0
$897$	7.07914e10	+	2.27519e11i	0.109348	+	0.351438i
$898$		0			0
$899$		−	8.17351e11i		−	1.25132i
$900$		0			0
$901$	−3.50702e11			−0.532156
$902$		0			0
$903$	1.57369e12	−	4.89645e11i	2.36684	−	0.736428i
$904$		0			0
$905$	4.43790e11	+	2.06122e11i	0.661581	+	0.307277i
$906$		0			0
$907$		−	2.04108e11i		−	0.301600i	−0.988564	−	0.150800i	$-0.951815\pi$
$907$		−	2.04108e11i		−	0.301600i	0.988564	−	0.150800i	$-0.0481850\pi$
$908$		0			0
$909$	−1.02913e11	−	1.49368e11i	−0.150736	−	0.218777i
$910$		0			0
$911$		−	4.48465e11i		−	0.651112i	−0.945523	−	0.325556i	$-0.894449\pi$
$911$		−	4.48465e11i		−	0.651112i	0.945523	−	0.325556i	$-0.105551\pi$
$912$		0			0
$913$		−	1.19208e12i		−	1.71563i
$914$		0			0
$915$	3.09546e11	+	4.14654e10i	0.441612	+	0.0591563i
$916$		0			0
$917$	−1.54729e12			−2.18824
$918$		0			0
$919$	1.35717e12			1.90271			0.951357	−	0.308091i	$-0.0996902\pi$
$919$	1.35717e12			1.90271			0.951357	+	0.308091i	$0.0996902\pi$
$920$		0			0
$921$	−2.54300e11	−	8.17306e11i	−0.353434	−	1.13592i
$922$		0			0
$923$	−4.19241e10			−0.0577640
$924$		0			0
$925$	4.66964e11	−	3.94255e11i	0.637847	−	0.538530i
$926$		0			0
$927$	−5.54004e11	−	8.04080e11i	−0.750229	−	1.08888i
$928$		0			0
$929$		−	2.21578e9i		−	0.00297485i	−0.999999	−	0.00148742i	$-0.999527\pi$
$929$		−	2.21578e9i		−	0.00297485i	0.999999	−	0.00148742i	$-0.000473462\pi$
$930$		0			0
$931$	2.75151e11			0.366246
$932$		0			0
$933$	−1.61082e11	−	5.17709e11i	−0.212579	−	0.683217i
$934$		0			0
$935$	−1.74294e11	+	3.75263e11i	−0.228053	+	0.491009i
$936$		0			0
$937$			4.81469e11i			0.624612i	0.949982	+	0.312306i	$0.101101\pi$
$937$			4.81469e11i			0.624612i	−0.949982	+	0.312306i	$0.898899\pi$
$938$		0			0
$939$	−3.92242e11	−	1.26064e12i	−0.504535	−	1.62155i
$940$		0			0
$941$			1.10645e12i			1.41115i	0.708634	+	0.705576i	$0.249312\pi$
$941$			1.10645e12i			1.41115i	−0.708634	+	0.705576i	$0.750688\pi$
$942$		0			0
$943$			2.90418e11i			0.367262i
$944$		0			0
$945$	−5.18778e11	−	1.02094e12i	−0.650510	−	1.28019i
$946$		0			0
$947$	−2.53028e10			−0.0314607			−0.0157304	−	0.999876i	$-0.505007\pi$
$947$	−2.53028e10			−0.0314607			−0.0157304	+	0.999876i	$0.505007\pi$
$948$		0			0
$949$	−1.16403e11			−0.143515
$950$		0			0
$951$	3.81589e11	−	1.18729e11i	0.466524	−	0.145156i
$952$		0			0
$953$	1.38607e11			0.168040			0.0840200	−	0.996464i	$-0.473224\pi$
$953$	1.38607e11			0.168040			0.0840200	+	0.996464i	$0.473224\pi$
$954$		0			0
$955$	1.80202e10	−	3.87983e10i	0.0216644	−	0.0466443i
$956$		0			0
$957$	7.49189e11	−	2.33106e11i	0.893189	−	0.277911i
$958$		0			0
$959$			1.55309e12i			1.83621i
$960$		0			0
$961$	8.39277e11			0.984037
$962$		0			0
$963$	7.10006e11	−	4.89188e11i	0.825576	−	0.568814i
$964$		0			0
$965$	−1.15893e11	+	2.49523e11i	−0.133644	+	0.287741i
$966$		0			0
$967$			7.99682e11i			0.914559i	0.889323	+	0.457279i	$0.151176\pi$
$967$			7.99682e11i			0.914559i	−0.889323	+	0.457279i	$0.848824\pi$
$968$		0			0
$969$	−1.49263e11	+	4.64425e10i	−0.169300	+	0.0526769i
$970$		0			0
$971$			1.34624e12i			1.51442i	0.653174	+	0.757208i	$0.273437\pi$
$971$			1.34624e12i			1.51442i	−0.653174	+	0.757208i	$0.726563\pi$
$972$		0			0
$973$		−	1.82739e12i		−	2.03883i
$974$		0			0
$975$	1.69058e11	−	2.64933e11i	0.187076	−	0.293169i
$976$		0			0
$977$	−1.31472e12			−1.44297			−0.721483	−	0.692432i	$-0.756539\pi$
$977$	−1.31472e12			−1.44297			−0.721483	+	0.692432i	$0.756539\pi$
$978$		0			0
$979$	−1.06581e12			−1.16024
$980$		0			0
$981$	3.18183e11	−	2.19225e11i	0.343559	−	0.236709i
$982$		0			0
$983$	3.43773e11			0.368178			0.184089	−	0.982910i	$-0.441067\pi$
$983$	3.43773e11			0.368178			0.184089	+	0.982910i	$0.441067\pi$
$984$		0			0
$985$	2.66127e10	+	1.23605e10i	0.0282712	+	0.0131308i
$986$		0			0
$987$	−5.54460e11	−	1.78200e12i	−0.584254	−	1.87776i
$988$		0			0
$989$			1.74780e12i			1.82686i
$990$		0			0
$991$	1.03988e11			0.107818			0.0539089	−	0.998546i	$-0.482832\pi$
$991$	1.03988e11			0.107818			0.0539089	+	0.998546i	$0.482832\pi$
$992$		0			0
$993$	3.27391e11	−	1.01866e11i	0.336721	−	0.104769i
$994$		0			0
$995$	−1.20096e12	−	5.57795e11i	−1.22528	−	0.569092i
$996$		0			0
$997$		−	8.41259e11i		−	0.851430i	−0.904857	−	0.425715i	$-0.860023\pi$
$997$		−	8.41259e11i		−	0.851430i	0.904857	−	0.425715i	$-0.139977\pi$
$998$		0			0
$999$	6.53846e11	+	5.13608e11i	0.656468	+	0.515668i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.9.c.f.209.4		48
3.2	odd	2	inner	240.9.c.f.209.46		48
4.3	odd	2		120.9.c.a.89.45	yes	48
5.4	even	2	inner	240.9.c.f.209.45		48
12.11	even	2		120.9.c.a.89.3	✓	48
15.14	odd	2	inner	240.9.c.f.209.3		48
20.19	odd	2		120.9.c.a.89.4	yes	48
60.59	even	2		120.9.c.a.89.46	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.9.c.a.89.3	✓	48	12.11	even	2
120.9.c.a.89.4	yes	48	20.19	odd	2
120.9.c.a.89.45	yes	48	4.3	odd	2
120.9.c.a.89.46	yes	48	60.59	even	2
240.9.c.f.209.3		48	15.14	odd	2	inner
240.9.c.f.209.4		48	1.1	even	1	trivial
240.9.c.f.209.45		48	5.4	even	2	inner
240.9.c.f.209.46		48	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	240.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-77.3427 + 24.0647i) q^{3} +(-566.843 - 263.275i) q^{5} -3447.79i q^{7} +(5402.78 - 3722.46i) q^{9} +15416.5i q^{11} +9932.71i q^{13} +(50176.8 + 6721.46i) q^{15} -42942.6 q^{17} -44941.3 q^{19} +(82970.2 + 266661. i) q^{21} -296163. q^{23} +(251997. + 298471. i) q^{25} +(-328285. + 417922. i) q^{27} +628329. i q^{29} -1.30083e6 q^{31} +(-370993. - 1.19235e6i) q^{33} +(-907717. + 1.95436e6i) q^{35} -1.56452e6i q^{37} +(-239028. - 768223. i) q^{39} -980599. i q^{41} -5.90146e6i q^{43} +(-4.04256e6 + 687637. i) q^{45} -6.68264e6 q^{47} -6.12246e6 q^{49} +(3.32130e6 - 1.03340e6i) q^{51} +8.16675e6 q^{53} +(4.05877e6 - 8.73872e6i) q^{55} +(3.47588e6 - 1.08150e6i) q^{57} +2.30526e7i q^{59} +6.16910e6 q^{61} +(-1.28343e7 - 1.86276e7i) q^{63} +(2.61504e6 - 5.63029e6i) q^{65} +3.43783e7i q^{67} +(2.29061e7 - 7.12710e6i) q^{69} +4.22081e6i q^{71} +1.17191e7i q^{73} +(-2.66728e7 - 1.70203e7i) q^{75} +5.31528e7 q^{77} -2.04927e7 q^{79} +(1.53333e7 - 4.02233e7i) q^{81} -7.73251e7 q^{83} +(2.43417e7 + 1.13057e7i) q^{85} +(-1.51206e7 - 4.85966e7i) q^{87} +6.91345e7i q^{89} +3.42459e7 q^{91} +(1.00610e8 - 3.13042e7i) q^{93} +(2.54747e7 + 1.18319e7i) q^{95} +7.42781e7i q^{97} +(5.73872e7 + 8.32917e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2528 q^{9} - 132352 q^{15} + 116176 q^{21} + 56976 q^{25} - 1395648 q^{31} - 6888832 q^{39} - 4287056 q^{45} - 30813552 q^{49} + 22815168 q^{51} + 6062784 q^{55} + 14031936 q^{61} + 2522608 q^{69}+ \cdots + 21719360 q^{99}+O(q^{100}) \) 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

L-functions

Modular forms

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Database

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