LMFDB - Embedded newform 240.9.c.f.209.19

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)

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")

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);

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			209.19
Character	$\chi$	$=$	240.209
Dual form			240.9.c.f.209.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-24.3113 - 77.2655i) q^{3} +(-547.246 - 301.906i) q^{5} -1536.33i q^{7} +(-5378.92 + 3756.85i) q^{9} -7761.82i q^{11} +24341.2i q^{13} +(-10022.6 + 49622.9i) q^{15} +83979.0 q^{17} +115321. q^{19} +(-118705. + 37350.2i) q^{21} +186279. q^{23} +(208331. + 330433. i) q^{25} +(421044. + 324271. i) q^{27} -907077. i q^{29} +1.08877e6 q^{31} +(-599721. + 188700. i) q^{33} +(-463828. + 840751. i) q^{35} +59293.5i q^{37} +(1.88073e6 - 591765. i) q^{39} -329743. i q^{41} +4.48269e6i q^{43} +(4.07781e6 - 431994. i) q^{45} -473075. q^{47} +3.40449e6 q^{49} +(-2.04164e6 - 6.48868e6i) q^{51} +1.18509e7 q^{53} +(-2.34334e6 + 4.24762e6i) q^{55} +(-2.80360e6 - 8.91032e6i) q^{57} -3.27453e6i q^{59} -2.05184e7 q^{61} +(5.77177e6 + 8.26381e6i) q^{63} +(7.34874e6 - 1.33206e7i) q^{65} +3.13995e7i q^{67} +(-4.52869e6 - 1.43929e7i) q^{69} +9.40161e6i q^{71} -3.64874e7i q^{73} +(2.04663e7 - 2.41301e7i) q^{75} -1.19247e7 q^{77} +4.17263e7 q^{79} +(1.48189e7 - 4.04156e7i) q^{81} +2.83168e7 q^{83} +(-4.59572e7 - 2.53538e7i) q^{85} +(-7.00858e7 + 2.20522e7i) q^{87} +1.11786e7i q^{89} +3.73961e7 q^{91} +(-2.64695e7 - 8.41246e7i) q^{93} +(-6.31088e7 - 3.48160e7i) q^{95} +5.09945e7i q^{97} +(2.91600e7 + 4.17502e7i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−24.3113	−	77.2655i	−0.300140	−	0.953895i
$3$	−24.3113	−	77.2655i	−0.300140	−	0.953895i
$4$		0			0
$5$	−547.246	−	301.906i	−0.875593	−	0.483049i
$5$	−547.246	−	301.906i	−0.875593	−	0.483049i
$6$		0			0
$7$		−	1536.33i		−	0.639872i	−0.947439	−	0.319936i	$-0.896339\pi$
$7$		−	1536.33i		−	0.639872i	0.947439	−	0.319936i	$-0.103661\pi$
$8$		0			0
$9$	−5378.92	+	3756.85i	−0.819832	+	0.572604i
$10$		0			0
$11$		−	7761.82i		−	0.530143i	−0.964229	−	0.265072i	$-0.914604\pi$
$11$		−	7761.82i		−	0.530143i	0.964229	−	0.265072i	$-0.0853956\pi$
$12$		0			0
$13$			24341.2i			0.852252i	0.904664	+	0.426126i	$0.140122\pi$
$13$			24341.2i			0.852252i	−0.904664	+	0.426126i	$0.859878\pi$
$14$		0			0
$15$	−10022.6	+	49622.9i	−0.197978	+	0.980206i
$16$		0			0
$17$	83979.0			1.00548			0.502742	−	0.864437i	$-0.332325\pi$
$17$	83979.0			1.00548			0.502742	+	0.864437i	$0.332325\pi$
$18$		0			0
$19$	115321.			0.884898			0.442449	−	0.896794i	$-0.354110\pi$
$19$	115321.			0.884898			0.442449	+	0.896794i	$0.354110\pi$
$20$		0			0
$21$	−118705.	+	37350.2i	−0.610371	+	0.192051i
$22$		0			0
$23$	186279.			0.665660			0.332830	−	0.942987i	$-0.391996\pi$
$23$	186279.			0.665660			0.332830	+	0.942987i	$0.391996\pi$
$24$		0			0
$25$	208331.	+	330433.i	0.533327	+	0.845909i
$26$		0			0
$27$	421044.	+	324271.i	0.792268	+	0.610173i
$28$		0			0
$29$		−	907077.i		−	1.28249i	−0.767338	−	0.641243i	$-0.778419\pi$
$29$		−	907077.i		−	1.28249i	0.767338	−	0.641243i	$-0.221581\pi$
$30$		0			0
$31$	1.08877e6			1.17894			0.589468	−	0.807792i	$-0.299337\pi$
$31$	1.08877e6			1.17894			0.589468	+	0.807792i	$0.299337\pi$
$32$		0			0
$33$	−599721.	+	188700.i	−0.505701	+	0.159117i
$34$		0			0
$35$	−463828.	+	840751.i	−0.309090	+	0.560267i
$36$		0			0
$37$			59293.5i			0.0316373i	0.999875	+	0.0158187i	$0.00503545\pi$
$37$			59293.5i			0.0316373i	−0.999875	+	0.0158187i	$0.994965\pi$
$38$		0			0
$39$	1.88073e6	−	591765.i	0.812959	−	0.255794i
$40$		0			0
$41$		−	329743.i		−	0.116692i	−0.998296	−	0.0583459i	$-0.981417\pi$
$41$		−	329743.i		−	0.116692i	0.998296	−	0.0583459i	$-0.0185826\pi$
$42$		0			0
$43$			4.48269e6i			1.31119i	0.755113	+	0.655594i	$0.227582\pi$
$43$			4.48269e6i			1.31119i	−0.755113	+	0.655594i	$0.772418\pi$
$44$		0			0
$45$	4.07781e6	−	431994.i	0.994435	−	0.105348i
$46$		0			0
$47$	−473075.			−0.0969480			−0.0484740	−	0.998824i	$-0.515436\pi$
$47$	−473075.			−0.0969480			−0.0484740	+	0.998824i	$0.515436\pi$
$48$		0			0
$49$	3.40449e6			0.590564
$50$		0			0
$51$	−2.04164e6	−	6.48868e6i	−0.301785	−	0.959126i
$52$		0			0
$53$	1.18509e7			1.50192			0.750959	−	0.660349i	$-0.229592\pi$
$53$	1.18509e7			1.50192			0.750959	+	0.660349i	$0.229592\pi$
$54$		0			0
$55$	−2.34334e6	+	4.24762e6i	−0.256085	+	0.464190i
$56$		0			0
$57$	−2.80360e6	−	8.91032e6i	−0.265593	−	0.844100i
$58$		0			0
$59$		−	3.27453e6i		−	0.270234i	−0.990830	−	0.135117i	$-0.956859\pi$
$59$		−	3.27453e6i		−	0.270234i	0.990830	−	0.135117i	$-0.0431411\pi$
$60$		0			0
$61$	−2.05184e7			−1.48192			−0.740958	−	0.671552i	$-0.765628\pi$
$61$	−2.05184e7			−1.48192			−0.740958	+	0.671552i	$0.765628\pi$
$62$		0			0
$63$	5.77177e6	+	8.26381e6i	0.366393	+	0.524588i
$64$		0			0
$65$	7.34874e6	−	1.33206e7i	0.411680	−	0.746226i
$66$		0			0
$67$			3.13995e7i			1.55820i	0.626900	+	0.779100i	$0.284324\pi$
$67$			3.13995e7i			1.55820i	−0.626900	+	0.779100i	$0.715676\pi$
$68$		0			0
$69$	−4.52869e6	−	1.43929e7i	−0.199791	−	0.634970i
$70$		0			0
$71$			9.40161e6i			0.369972i	0.982741	+	0.184986i	$0.0592240\pi$
$71$			9.40161e6i			0.369972i	−0.982741	+	0.184986i	$0.940776\pi$
$72$		0			0
$73$		−	3.64874e7i		−	1.28485i	−0.766350	−	0.642423i	$-0.777929\pi$
$73$		−	3.64874e7i		−	1.28485i	0.766350	−	0.642423i	$-0.222071\pi$
$74$		0			0
$75$	2.04663e7	−	2.41301e7i	0.646836	−	0.762629i
$76$		0			0
$77$	−1.19247e7			−0.339223
$78$		0			0
$79$	4.17263e7			1.07128			0.535639	−	0.844447i	$-0.320071\pi$
$79$	4.17263e7			1.07128			0.535639	+	0.844447i	$0.320071\pi$
$80$		0			0
$81$	1.48189e7	−	4.04156e7i	0.344250	−	0.938878i
$82$		0			0
$83$	2.83168e7			0.596667			0.298334	−	0.954462i	$-0.403569\pi$
$83$	2.83168e7			0.596667			0.298334	+	0.954462i	$0.403569\pi$
$84$		0			0
$85$	−4.59572e7	−	2.53538e7i	−0.880395	−	0.485698i
$86$		0			0
$87$	−7.00858e7	+	2.20522e7i	−1.22336	+	0.384925i
$88$		0			0
$89$			1.11786e7i			0.178167i	0.996024	+	0.0890834i	$0.0283938\pi$
$89$			1.11786e7i			0.178167i	−0.996024	+	0.0890834i	$0.971606\pi$
$90$		0			0
$91$	3.73961e7			0.545332
$92$		0			0
$93$	−2.64695e7	−	8.41246e7i	−0.353845	−	1.12458i
$94$		0			0
$95$	−6.31088e7	−	3.48160e7i	−0.774811	−	0.427449i
$96$		0			0
$97$			5.09945e7i			0.576019i	0.957628	+	0.288009i	$0.0929934\pi$
$97$			5.09945e7i			0.576019i	−0.957628	+	0.288009i	$0.907007\pi$
$98$		0			0
$99$	2.91600e7	+	4.17502e7i	0.303562	+	0.434628i
$100$		0			0
$101$		−	1.60526e7i		−	0.154262i	−0.997021	−	0.0771310i	$-0.975424\pi$
$101$		−	1.60526e7i		−	0.154262i	0.997021	−	0.0771310i	$-0.0245760\pi$
$102$		0			0
$103$			1.14045e8i			1.01327i	0.862159	+	0.506637i	$0.169112\pi$
$103$			1.14045e8i			1.01327i	−0.862159	+	0.506637i	$0.830888\pi$
$104$		0			0
$105$	7.62373e7	+	1.53981e7i	0.627206	+	0.126681i
$106$		0			0
$107$	−1.82935e8			−1.39560			−0.697801	−	0.716292i	$-0.745838\pi$
$107$	−1.82935e8			−1.39560			−0.697801	+	0.716292i	$0.745838\pi$
$108$		0			0
$109$	−5.63846e7			−0.399443			−0.199721	−	0.979853i	$-0.564004\pi$
$109$	−5.63846e7			−0.399443			−0.199721	+	0.979853i	$0.564004\pi$
$110$		0			0
$111$	4.58134e6	−	1.44150e6i	0.0301787	−	0.00949562i
$112$		0			0
$113$	−2.92929e8			−1.79659			−0.898295	−	0.439392i	$-0.855194\pi$
$113$	−2.92929e8			−1.79659			−0.898295	+	0.439392i	$0.855194\pi$
$114$		0			0
$115$	−1.01940e8	−	5.62387e7i	−0.582848	−	0.321547i
$116$		0			0
$117$	−9.14461e7	−	1.30929e8i	−0.488002	−	0.698704i
$118$		0			0
$119$		−	1.29020e8i		−	0.643381i
$120$		0			0
$121$	1.54113e8			0.718948
$122$		0			0
$123$	−2.54778e7	+	8.01649e6i	−0.111312	+	0.0350239i
$124$		0			0
$125$	−1.42484e7	−	2.43724e8i	−0.0583614	−	0.998296i
$126$		0			0
$127$		−	2.62325e8i		−	1.00838i	−0.863593	−	0.504190i	$-0.831791\pi$
$127$		−	2.62325e8i		−	1.00838i	0.863593	−	0.504190i	$-0.168209\pi$
$128$		0			0
$129$	3.46357e8	−	1.08980e8i	1.25074	−	0.393540i
$130$		0			0
$131$		−	4.02961e8i		−	1.36829i	−0.729347	−	0.684144i	$-0.760176\pi$
$131$		−	4.02961e8i		−	1.36829i	0.729347	−	0.684144i	$-0.239824\pi$
$132$		0			0
$133$		−	1.77171e8i		−	0.566221i
$134$		0			0
$135$	−1.32515e8	−	3.04572e8i	−0.398961	−	0.916968i
$136$		0			0
$137$	1.89514e8			0.537971			0.268985	−	0.963144i	$-0.413312\pi$
$137$	1.89514e8			0.537971			0.268985	+	0.963144i	$0.413312\pi$
$138$		0			0
$139$	1.34482e7			0.0360250			0.0180125	−	0.999838i	$-0.494266\pi$
$139$	1.34482e7			0.0360250			0.0180125	+	0.999838i	$0.494266\pi$
$140$		0			0
$141$	1.15011e7	+	3.65524e7i	0.0290979	+	0.0924783i
$142$		0			0
$143$	1.88932e8			0.451815
$144$		0			0
$145$	−2.73852e8	+	4.96394e8i	−0.619504	+	1.12294i
$146$		0			0
$147$	−8.27675e7	−	2.63049e8i	−0.177252	−	0.563336i
$148$		0			0
$149$		−	8.69761e8i		−	1.76463i	−0.470655	−	0.882317i	$-0.655982\pi$
$149$		−	8.69761e8i		−	1.76463i	0.470655	−	0.882317i	$-0.344018\pi$
$150$		0			0
$151$	6.67479e8			1.28390			0.641948	−	0.766749i	$-0.278127\pi$
$151$	6.67479e8			1.28390			0.641948	+	0.766749i	$0.278127\pi$
$152$		0			0
$153$	−4.51716e8	+	3.15497e8i	−0.824328	+	0.575744i
$154$		0			0
$155$	−5.95826e8	−	3.28707e8i	−1.03227	−	0.569484i
$156$		0			0
$157$			7.07110e8i			1.16383i	0.813251	+	0.581914i	$0.197696\pi$
$157$			7.07110e8i			1.16383i	−0.813251	+	0.581914i	$0.802304\pi$
$158$		0			0
$159$	−2.88110e8	−	9.15662e8i	−0.450785	−	1.43267i
$160$		0			0
$161$		−	2.86186e8i		−	0.425937i
$162$		0			0
$163$		−	1.12694e9i		−	1.59643i	−0.602375	−	0.798213i	$-0.705779\pi$
$163$		−	1.12694e9i		−	1.59643i	0.602375	−	0.798213i	$-0.294221\pi$
$164$		0			0
$165$	3.85165e8	+	7.77940e7i	0.519650	+	0.104957i
$166$		0			0
$167$	8.17466e8			1.05100			0.525501	−	0.850793i	$-0.323878\pi$
$167$	8.17466e8			1.05100			0.525501	+	0.850793i	$0.323878\pi$
$168$		0			0
$169$	2.23239e8			0.273667
$170$		0			0
$171$	−6.20301e8	+	4.33243e8i	−0.725468	+	0.506696i
$172$		0			0
$173$	−6.87454e8			−0.767467			−0.383733	−	0.923444i	$-0.625362\pi$
$173$	−6.87454e8			−0.767467			−0.383733	+	0.923444i	$0.625362\pi$
$174$		0			0
$175$	5.07655e8	−	3.20065e8i	0.541273	−	0.341261i
$176$		0			0
$177$	−2.53008e8	+	7.96081e7i	−0.257775	+	0.0811081i
$178$		0			0
$179$			1.62205e8i			0.157998i	0.996875	+	0.0789989i	$0.0251723\pi$
$179$			1.62205e8i			0.157998i	−0.996875	+	0.0789989i	$0.974828\pi$
$180$		0			0
$181$	7.76510e8			0.723491			0.361745	−	0.932277i	$-0.382181\pi$
$181$	7.76510e8			0.723491			0.361745	+	0.932277i	$0.382181\pi$
$182$		0			0
$183$	4.98828e8	+	1.58536e9i	0.444781	+	1.41359i
$184$		0			0
$185$	1.79010e7	−	3.24481e7i	0.0152824	−	0.0277014i
$186$		0			0
$187$		−	6.51830e8i		−	0.533050i
$188$		0			0
$189$	4.98188e8	−	6.46863e8i	0.390433	−	0.506950i
$190$		0			0
$191$		−	1.59755e9i		−	1.20038i	−0.799856	−	0.600192i	$-0.795091\pi$
$191$		−	1.59755e9i		−	1.20038i	0.799856	−	0.600192i	$-0.204909\pi$
$192$		0			0
$193$			1.66557e8i			0.120042i	0.998197	+	0.0600210i	$0.0191168\pi$
$193$			1.66557e8i			0.120042i	−0.998197	+	0.0600210i	$0.980883\pi$
$194$		0			0
$195$	−1.20788e9	−	2.43963e8i	−0.835383	−	0.168727i
$196$		0			0
$197$	−2.58267e8			−0.171476			−0.0857380	−	0.996318i	$-0.527325\pi$
$197$	−2.58267e8			−0.171476			−0.0857380	+	0.996318i	$0.527325\pi$
$198$		0			0
$199$	6.98731e8			0.445551			0.222776	−	0.974870i	$-0.428488\pi$
$199$	6.98731e8			0.445551			0.222776	+	0.974870i	$0.428488\pi$
$200$		0			0
$201$	2.42610e9	−	7.63362e8i	1.48636	−	0.467678i
$202$		0			0
$203$	−1.39357e9			−0.820626
$204$		0			0
$205$	−9.95514e7	+	1.80451e8i	−0.0563679	+	0.102175i
$206$		0			0
$207$	−1.00198e9	+	6.99823e8i	−0.545730	+	0.381159i
$208$		0			0
$209$		−	8.95100e8i		−	0.469122i
$210$		0			0
$211$	2.39920e9			1.21042			0.605210	−	0.796066i	$-0.293089\pi$
$211$	2.39920e9			1.21042			0.605210	+	0.796066i	$0.293089\pi$
$212$		0			0
$213$	7.26420e8	−	2.28565e8i	0.352914	−	0.111043i
$214$		0			0
$215$	1.35335e9	−	2.45313e9i	0.633369	−	1.14807i
$216$		0			0
$217$		−	1.67272e9i		−	0.754368i
$218$		0			0
$219$	−2.81922e9	+	8.87056e8i	−1.22561	+	0.385633i
$220$		0			0
$221$			2.04415e9i			0.856925i
$222$		0			0
$223$		−	1.47178e9i		−	0.595146i	−0.954699	−	0.297573i	$-0.903823\pi$
$223$		−	1.47178e9i		−	0.595146i	0.954699	−	0.297573i	$-0.0961772\pi$
$224$		0			0
$225$	−2.36198e9	−	9.94707e8i	−0.921609	−	0.388119i
$226$		0			0
$227$	−1.08671e9			−0.409272			−0.204636	−	0.978838i	$-0.565601\pi$
$227$	−1.08671e9			−0.409272			−0.204636	+	0.978838i	$0.565601\pi$
$228$		0			0
$229$	−4.17978e9			−1.51989			−0.759943	−	0.649990i	$-0.774773\pi$
$229$	−4.17978e9			−1.51989			−0.759943	+	0.649990i	$0.774773\pi$
$230$		0			0
$231$	2.89906e8	+	9.21371e8i	0.101814	+	0.323584i
$232$		0			0
$233$	2.71753e9			0.922042			0.461021	−	0.887389i	$-0.347483\pi$
$233$	2.71753e9			0.922042			0.461021	+	0.887389i	$0.347483\pi$
$234$		0			0
$235$	2.58888e8	+	1.42824e8i	0.0848870	+	0.0468307i
$236$		0			0
$237$	−1.01442e9	−	3.22401e9i	−0.321533	−	1.02189i
$238$		0			0
$239$			2.95521e9i			0.905726i	0.891580	+	0.452863i	$0.149597\pi$
$239$			2.95521e9i			0.905726i	−0.891580	+	0.452863i	$0.850403\pi$
$240$		0			0
$241$	−4.66821e9			−1.38383			−0.691914	−	0.721980i	$-0.743232\pi$
$241$	−4.66821e9			−1.38383			−0.691914	+	0.721980i	$0.743232\pi$
$242$		0			0
$243$	−3.48300e9	−	1.62430e8i	−0.998914	−	0.0465845i
$244$		0			0
$245$	−1.86309e9	−	1.02783e9i	−0.517094	−	0.285272i
$246$		0			0
$247$			2.80704e9i			0.754156i
$248$		0			0
$249$	−6.88419e8	−	2.18791e9i	−0.179083	−	0.569158i
$250$		0			0
$251$			4.78667e9i			1.20598i	0.797750	+	0.602988i	$0.206023\pi$
$251$			4.78667e9i			1.20598i	−0.797750	+	0.602988i	$0.793977\pi$
$252$		0			0
$253$		−	1.44586e9i		−	0.352895i
$254$		0			0
$255$	−8.41692e8	+	4.16729e9i	−0.199064	+	0.985582i
$256$		0			0
$257$	2.28160e8			0.0523007			0.0261504	−	0.999658i	$-0.491675\pi$
$257$	2.28160e8			0.0523007			0.0261504	+	0.999658i	$0.491675\pi$
$258$		0			0
$259$	9.10944e7			0.0202438
$260$		0			0
$261$	3.40775e9	+	4.87910e9i	0.734355	+	1.05142i
$262$		0			0
$263$	1.74265e9			0.364241			0.182120	−	0.983276i	$-0.441704\pi$
$263$	1.74265e9			0.364241			0.182120	+	0.983276i	$0.441704\pi$
$264$		0			0
$265$	−6.48533e9	−	3.57784e9i	−1.31507	−	0.725500i
$266$		0			0
$267$	8.63719e8	−	2.71766e8i	0.169952	−	0.0534749i
$268$		0			0
$269$		−	7.36671e9i		−	1.40690i	−0.710742	−	0.703452i	$-0.751641\pi$
$269$		−	7.36671e9i		−	1.40690i	0.710742	−	0.703452i	$-0.248359\pi$
$270$		0			0
$271$	1.03021e10			1.91007			0.955037	−	0.296487i	$-0.0958151\pi$
$271$	1.03021e10			1.91007			0.955037	+	0.296487i	$0.0958151\pi$
$272$		0			0
$273$	−9.09148e8	−	2.88943e9i	−0.163676	−	0.520189i
$274$		0			0
$275$	2.56477e9	−	1.61703e9i	0.448453	−	0.282739i
$276$		0			0
$277$			6.13563e9i			1.04217i	0.853504	+	0.521086i	$0.174473\pi$
$277$			6.13563e9i			1.04217i	−0.853504	+	0.521086i	$0.825527\pi$
$278$		0			0
$279$	−5.85642e9	+	4.09036e9i	−0.966530	+	0.675063i
$280$		0			0
$281$			8.53142e9i			1.36835i	0.729320	+	0.684173i	$0.239837\pi$
$281$			8.53142e9i			1.36835i	−0.729320	+	0.684173i	$0.760163\pi$
$282$		0			0
$283$		−	4.57625e8i		−	0.0713451i	−0.999364	−	0.0356726i	$-0.988643\pi$
$283$		−	4.57625e8i		−	0.0713451i	0.999364	−	0.0356726i	$-0.0113573\pi$
$284$		0			0
$285$	−1.15582e9	+	5.72256e9i	−0.175191	+	0.867383i
$286$		0			0
$287$	−5.06595e8			−0.0746678
$288$		0			0
$289$	7.67165e7			0.0109976
$290$		0			0
$291$	3.94012e9	−	1.23974e9i	0.549462	−	0.172886i
$292$		0			0
$293$	1.24237e10			1.68569			0.842847	−	0.538153i	$-0.180878\pi$
$293$	1.24237e10			1.68569			0.842847	+	0.538153i	$0.180878\pi$
$294$		0			0
$295$	−9.88599e8	+	1.79197e9i	−0.130537	+	0.236615i
$296$		0			0
$297$	2.51694e9	−	3.26807e9i	0.323479	−	0.420015i
$298$		0			0
$299$			4.53425e9i			0.567310i
$300$		0			0
$301$	6.88690e9			0.838992
$302$		0			0
$303$	−1.24031e9	+	3.90259e8i	−0.147150	+	0.0463001i
$304$		0			0
$305$	1.12286e10	+	6.19461e9i	1.29755	+	0.715838i
$306$		0			0
$307$			9.95212e9i			1.12037i	0.828367	+	0.560186i	$0.189270\pi$
$307$			9.95212e9i			1.12037i	−0.828367	+	0.560186i	$0.810730\pi$
$308$		0			0
$309$	8.81174e9	−	2.77258e9i	0.966557	−	0.304124i
$310$		0			0
$311$			2.96957e9i			0.317433i	0.987324	+	0.158717i	$0.0507356\pi$
$311$			2.96957e9i			0.317433i	−0.987324	+	0.158717i	$0.949264\pi$
$312$		0			0
$313$			1.22243e10i			1.27364i	0.771012	+	0.636821i	$0.219751\pi$
$313$			1.22243e10i			1.27364i	−0.771012	+	0.636821i	$0.780249\pi$
$314$		0			0
$315$	−6.63685e8	−	6.26486e9i	−0.0674093	−	0.636311i
$316$		0			0
$317$	−1.12216e9			−0.111127			−0.0555634	−	0.998455i	$-0.517695\pi$
$317$	−1.12216e9			−0.111127			−0.0555634	+	0.998455i	$0.517695\pi$
$318$		0			0
$319$	−7.04057e9			−0.679901
$320$		0			0
$321$	4.44739e9	+	1.41346e10i	0.418875	+	1.33126i
$322$		0			0
$323$	9.68453e9			0.889750
$324$		0			0
$325$	−8.04313e9	+	5.07101e9i	−0.720928	+	0.454529i
$326$		0			0
$327$	1.37078e9	+	4.35658e9i	0.119889	+	0.381026i
$328$		0			0
$329$			7.26801e8i			0.0620343i
$330$		0			0
$331$	−1.42650e10			−1.18839			−0.594195	−	0.804321i	$-0.702529\pi$
$331$	−1.42650e10			−1.18839			−0.594195	+	0.804321i	$0.702529\pi$
$332$		0			0
$333$	−2.22757e8	−	3.18935e8i	−0.0181156	−	0.0259373i
$334$		0			0
$335$	9.47969e9	−	1.71832e10i	0.752688	−	1.36435i
$336$		0			0
$337$			1.67909e10i			1.30183i	0.759151	+	0.650914i	$0.225614\pi$
$337$			1.67909e10i			1.30183i	−0.759151	+	0.650914i	$0.774386\pi$
$338$		0			0
$339$	7.12150e9	+	2.26333e10i	0.539228	+	1.71376i
$340$		0			0
$341$		−	8.45086e9i		−	0.625005i
$342$		0			0
$343$		−	1.40871e10i		−	1.01776i
$344$		0			0
$345$	−1.86701e9	+	9.24371e9i	−0.131786	+	0.652484i
$346$		0			0
$347$	2.61649e10			1.80468			0.902342	−	0.431020i	$-0.141846\pi$
$347$	2.61649e10			1.80468			0.902342	+	0.431020i	$0.141846\pi$
$348$		0			0
$349$	−4.75720e8			−0.0320663			−0.0160332	−	0.999871i	$-0.505104\pi$
$349$	−4.75720e8			−0.0320663			−0.0160332	+	0.999871i	$0.505104\pi$
$350$		0			0
$351$	−7.89313e9	+	1.02487e10i	−0.520021	+	0.675212i
$352$		0			0
$353$	−7.48574e8			−0.0482099			−0.0241049	−	0.999709i	$-0.507674\pi$
$353$	−7.48574e8			−0.0482099			−0.0241049	+	0.999709i	$0.507674\pi$
$354$		0			0
$355$	2.83840e9	−	5.14499e9i	0.178715	−	0.323945i
$356$		0			0
$357$	−9.96877e9	+	3.13664e9i	−0.613718	+	0.193104i
$358$		0			0
$359$			2.69368e10i			1.62169i	0.585261	+	0.810845i	$0.300992\pi$
$359$			2.69368e10i			1.62169i	−0.585261	+	0.810845i	$0.699008\pi$
$360$		0			0
$361$	−3.68468e9			−0.216956
$362$		0			0
$363$	−3.74669e9	−	1.19076e10i	−0.215785	−	0.685801i
$364$		0			0
$365$	−1.10158e10	+	1.99676e10i	−0.620644	+	1.12500i
$366$		0			0
$367$		−	2.88998e10i		−	1.59305i	−0.604603	−	0.796527i	$-0.706668\pi$
$367$		−	2.88998e10i		−	1.59305i	0.604603	−	0.796527i	$-0.293332\pi$
$368$		0			0
$369$	1.23880e9	+	1.77366e9i	0.0668182	+	0.0956678i
$370$		0			0
$371$		−	1.82068e10i		−	0.961035i
$372$		0			0
$373$		−	1.68477e10i		−	0.870371i	−0.900341	−	0.435186i	$-0.856683\pi$
$373$		−	1.68477e10i		−	0.870371i	0.900341	−	0.435186i	$-0.143317\pi$
$374$		0			0
$375$	−1.84851e10	+	7.02617e9i	−0.934753	+	0.355299i
$376$		0			0
$377$	2.20793e10			1.09300
$378$		0			0
$379$	−1.47718e10			−0.715942			−0.357971	−	0.933733i	$-0.616531\pi$
$379$	−1.47718e10			−0.715942			−0.357971	+	0.933733i	$0.616531\pi$
$380$		0			0
$381$	−2.02687e10	+	6.37746e9i	−0.961889	+	0.302655i
$382$		0			0
$383$	1.12179e10			0.521335			0.260667	−	0.965429i	$-0.416057\pi$
$383$	1.12179e10			0.521335			0.260667	+	0.965429i	$0.416057\pi$
$384$		0			0
$385$	6.52576e9	+	3.60015e9i	0.297022	+	0.163862i
$386$		0			0
$387$	−1.68408e10	−	2.41120e10i	−0.750791	−	1.07495i
$388$		0			0
$389$		−	3.64224e10i		−	1.59063i	−0.606194	−	0.795316i	$-0.707305\pi$
$389$		−	3.64224e10i		−	1.59063i	0.606194	−	0.795316i	$-0.292695\pi$
$390$		0			0
$391$	1.56435e10			0.669311
$392$		0			0
$393$	−3.11350e10	+	9.79650e9i	−1.30520	+	0.410677i
$394$		0			0
$395$	−2.28346e10	−	1.25974e10i	−0.938003	−	0.517480i
$396$		0			0
$397$		−	1.47854e10i		−	0.595210i	−0.954689	−	0.297605i	$-0.903812\pi$
$397$		−	1.47854e10i		−	0.595210i	0.954689	−	0.297605i	$-0.0961879\pi$
$398$		0			0
$399$	−1.36892e10	+	4.30726e9i	−0.540116	+	0.169945i
$400$		0			0
$401$			3.77306e10i			1.45920i	0.683872	+	0.729602i	$0.260295\pi$
$401$			3.77306e10i			1.45920i	−0.683872	+	0.729602i	$0.739705\pi$
$402$		0			0
$403$			2.65020e10i			1.00475i
$404$		0			0
$405$	−2.03113e10	+	1.76434e10i	−0.754948	+	0.655785i
$406$		0			0
$407$	4.60225e8			0.0167723
$408$		0			0
$409$	3.92354e10			1.40212			0.701060	−	0.713102i	$-0.252711\pi$
$409$	3.92354e10			1.40212			0.701060	+	0.713102i	$0.252711\pi$
$410$		0			0
$411$	−4.60733e9	−	1.46429e10i	−0.161466	−	0.513168i
$412$		0			0
$413$	−5.03076e9			−0.172915
$414$		0			0
$415$	−1.54963e10	−	8.54901e9i	−0.522438	−	0.288220i
$416$		0			0
$417$	−3.26943e8	−	1.03908e9i	−0.0108125	−	0.0343641i
$418$		0			0
$419$			2.13803e10i			0.693677i	0.937925	+	0.346839i	$0.112745\pi$
$419$			2.13803e10i			0.693677i	−0.937925	+	0.346839i	$0.887255\pi$
$420$		0			0
$421$	5.69063e9			0.181147			0.0905736	−	0.995890i	$-0.471130\pi$
$421$	5.69063e9			0.181147			0.0905736	+	0.995890i	$0.471130\pi$
$422$		0			0
$423$	2.54463e9	−	1.77727e9i	0.0794811	−	0.0555128i
$424$		0			0
$425$	1.74954e10	+	2.77495e10i	0.536251	+	0.850548i
$426$		0			0
$427$			3.15230e10i			0.948236i
$428$		0			0
$429$	−4.59318e9	−	1.45979e10i	−0.135608	−	0.430984i
$430$		0			0
$431$		−	1.13346e10i		−	0.328470i	−0.986421	−	0.164235i	$-0.947484\pi$
$431$		−	1.13346e10i		−	0.328470i	0.986421	−	0.164235i	$-0.0525156\pi$
$432$		0			0
$433$		−	4.20265e10i		−	1.19556i	−0.801660	−	0.597780i	$-0.796050\pi$
$433$		−	4.20265e10i		−	1.19556i	0.801660	−	0.597780i	$-0.203950\pi$
$434$		0			0
$435$	4.50119e10	+	9.09132e9i	1.25710	+	0.253904i
$436$		0			0
$437$	2.14818e10			0.589041
$438$		0			0
$439$	−9.92180e9			−0.267136			−0.133568	−	0.991040i	$-0.542643\pi$
$439$	−9.92180e9			−0.267136			−0.133568	+	0.991040i	$0.542643\pi$
$440$		0			0
$441$	−1.83125e10	+	1.27901e10i	−0.484164	+	0.338159i
$442$		0			0
$443$	5.28626e10			1.37257			0.686284	−	0.727334i	$-0.259241\pi$
$443$	5.28626e10			1.37257			0.686284	+	0.727334i	$0.259241\pi$
$444$		0			0
$445$	3.37488e9	−	6.11743e9i	0.0860634	−	0.156002i
$446$		0			0
$447$	−6.72025e10	+	2.11450e10i	−1.68328	+	0.529637i
$448$		0			0
$449$		−	7.83301e10i		−	1.92727i	−0.267216	−	0.963637i	$-0.586104\pi$
$449$		−	7.83301e10i		−	1.92727i	0.267216	−	0.963637i	$-0.413896\pi$
$450$		0			0
$451$	−2.55941e9			−0.0618634
$452$		0			0
$453$	−1.62273e10	−	5.15731e10i	−0.385348	−	1.22470i
$454$		0			0
$455$	−2.04649e10	−	1.12901e10i	−0.477489	−	0.263422i
$456$		0			0
$457$		−	2.09261e10i		−	0.479759i	−0.970803	−	0.239879i	$-0.922892\pi$
$457$		−	2.09261e10i		−	0.479759i	0.970803	−	0.239879i	$-0.0771079\pi$
$458$		0			0
$459$	3.53588e10	+	2.72320e10i	0.796613	+	0.613519i
$460$		0			0
$461$		−	6.62131e10i		−	1.46602i	−0.680217	−	0.733011i	$-0.738114\pi$
$461$		−	6.62131e10i		−	1.46602i	0.680217	−	0.733011i	$-0.261886\pi$
$462$		0			0
$463$		−	9.21885e9i		−	0.200610i	−0.994957	−	0.100305i	$-0.968018\pi$
$463$		−	9.21885e9i		−	0.200610i	0.994957	−	0.100305i	$-0.0319819\pi$
$464$		0			0
$465$	−1.09124e10	+	5.40281e10i	−0.233404	+	1.15560i
$466$		0			0
$467$	−1.06274e10			−0.223438			−0.111719	−	0.993740i	$-0.535636\pi$
$467$	−1.06274e10			−0.223438			−0.111719	+	0.993740i	$0.535636\pi$
$468$		0			0
$469$	4.82400e10			0.997048
$470$		0			0
$471$	5.46353e10	−	1.71908e10i	1.11017	−	0.349311i
$472$		0			0
$473$	3.47939e10			0.695117
$474$		0			0
$475$	2.40249e10	+	3.81058e10i	0.471940	+	0.748543i
$476$		0			0
$477$	−6.37448e10	+	4.45219e10i	−1.23132	+	0.860003i
$478$		0			0
$479$		−	2.18080e10i		−	0.414261i	−0.978313	−	0.207131i	$-0.933587\pi$
$479$		−	2.18080e10i		−	0.414261i	0.978313	−	0.207131i	$-0.0664125\pi$
$480$		0			0
$481$	−1.44327e9			−0.0269630
$482$		0			0
$483$	−2.21123e10	+	6.95757e9i	−0.406299	+	0.127841i
$484$		0			0
$485$	1.53955e10	−	2.79065e10i	0.278245	−	0.504358i
$486$		0			0
$487$			5.62626e10i			1.00024i	0.865956	+	0.500120i	$0.166711\pi$
$487$			5.62626e10i			1.00024i	−0.865956	+	0.500120i	$0.833289\pi$
$488$		0			0
$489$	−8.70733e10	+	2.73973e10i	−1.52282	+	0.479151i
$490$		0			0
$491$		−	9.30039e10i		−	1.60020i	−0.599865	−	0.800101i	$-0.704779\pi$
$491$		−	9.30039e10i		−	1.60020i	0.599865	−	0.800101i	$-0.295221\pi$
$492$		0			0
$493$		−	7.61755e10i		−	1.28952i
$494$		0			0
$495$	−3.35306e9	−	3.16512e10i	−0.0558496	−	0.527193i
$496$		0			0
$497$	1.44440e10			0.236734
$498$		0			0
$499$	1.67310e10			0.269849			0.134924	−	0.990856i	$-0.456921\pi$
$499$	1.67310e10			0.269849			0.134924	+	0.990856i	$0.456921\pi$
$500$		0			0
$501$	−1.98737e10	−	6.31620e10i	−0.315448	−	1.00255i
$502$		0			0
$503$	−5.19116e10			−0.810946			−0.405473	−	0.914107i	$-0.632893\pi$
$503$	−5.19116e10			−0.810946			−0.405473	+	0.914107i	$0.632893\pi$
$504$		0			0
$505$	−4.84636e9	+	8.78469e9i	−0.0745161	+	0.135071i
$506$		0			0
$507$	−5.42722e9	−	1.72487e10i	−0.0821383	−	0.261050i
$508$		0			0
$509$		−	1.26142e11i		−	1.87927i	−0.342176	−	0.939636i	$-0.611164\pi$
$509$		−	1.26142e11i		−	1.87927i	0.342176	−	0.939636i	$-0.388836\pi$
$510$		0			0
$511$	−5.60567e10			−0.822137
$512$		0			0
$513$	4.85551e10	+	3.73952e10i	0.701076	+	0.539941i
$514$		0			0
$515$	3.44308e10	−	6.24106e10i	0.489461	−	0.887216i
$516$		0			0
$517$			3.67193e9i			0.0513963i
$518$		0			0
$519$	1.67129e10	+	5.31165e10i	0.230347	+	0.732083i
$520$		0			0
$521$		−	2.83866e10i		−	0.385268i	−0.981271	−	0.192634i	$-0.938297\pi$
$521$		−	2.83866e10i		−	0.385268i	0.981271	−	0.192634i	$-0.0617030\pi$
$522$		0			0
$523$		−	8.97597e10i		−	1.19971i	−0.800110	−	0.599853i	$-0.795226\pi$
$523$		−	8.97597e10i		−	1.19971i	0.800110	−	0.599853i	$-0.204774\pi$
$524$		0			0
$525$	−3.70718e10	−	3.14430e10i	−0.487985	−	0.413892i
$526$		0			0
$527$	9.14340e10			1.18540
$528$		0			0
$529$	−4.36111e10			−0.556897
$530$		0			0
$531$	1.23019e10	+	1.76134e10i	0.154737	+	0.221547i
$532$		0			0
$533$	8.02633e9			0.0994508
$534$		0			0
$535$	1.00110e11	+	5.52291e10i	1.22198	+	0.674144i
$536$		0			0
$537$	1.25328e10	−	3.94340e9i	0.150713	−	0.0474214i
$538$		0			0
$539$		−	2.64250e10i		−	0.313084i
$540$		0			0
$541$	1.36729e10			0.159615			0.0798073	−	0.996810i	$-0.474569\pi$
$541$	1.36729e10			0.159615			0.0798073	+	0.996810i	$0.474569\pi$
$542$		0			0
$543$	−1.88780e10	−	5.99975e10i	−0.217148	−	0.690134i
$544$		0			0
$545$	3.08562e10	+	1.70228e10i	0.349749	+	0.192950i
$546$		0			0
$547$			9.47576e10i			1.05844i	0.848486	+	0.529218i	$0.177515\pi$
$547$			9.47576e10i			1.05844i	−0.848486	+	0.529218i	$0.822485\pi$
$548$		0			0
$549$	1.10367e11	−	7.70844e10i	1.21492	−	0.848550i
$550$		0			0
$551$		−	1.04605e11i		−	1.13487i
$552$		0			0
$553$		−	6.41055e10i		−	0.685480i
$554$		0			0
$555$	−2.94232e9	−	5.94278e8i	−0.0310111	−	0.00626350i
$556$		0			0
$557$	−1.26174e11			−1.31083			−0.655417	−	0.755267i	$-0.727507\pi$
$557$	−1.26174e11			−1.31083			−0.655417	+	0.755267i	$0.727507\pi$
$558$		0			0
$559$	−1.09114e11			−1.11746
$560$		0			0
$561$	−5.03640e10	+	1.58468e10i	−0.508474	+	0.159989i
$562$		0			0
$563$	4.22072e10			0.420100			0.210050	−	0.977691i	$-0.432637\pi$
$563$	4.22072e10			0.420100			0.210050	+	0.977691i	$0.432637\pi$
$564$		0			0
$565$	1.60304e11	+	8.84371e10i	1.57308	+	0.867842i
$566$		0			0
$567$	−6.20918e10	−	2.27667e10i	−0.600761	−	0.220276i
$568$		0			0
$569$			1.55177e11i			1.48040i	0.672389	+	0.740198i	$0.265268\pi$
$569$			1.55177e11i			1.48040i	−0.672389	+	0.740198i	$0.734732\pi$
$570$		0			0
$571$	−1.78848e11			−1.68244			−0.841219	−	0.540695i	$-0.818161\pi$
$571$	−1.78848e11			−1.68244			−0.841219	+	0.540695i	$0.818161\pi$
$572$		0			0
$573$	−1.23435e11	+	3.88385e10i	−1.14504	+	0.360283i
$574$		0			0
$575$	3.88076e10	+	6.15528e10i	0.355014	+	0.563088i
$576$		0			0
$577$			8.78895e10i			0.792928i	0.918050	+	0.396464i	$0.129763\pi$
$577$			8.78895e10i			0.792928i	−0.918050	+	0.396464i	$0.870237\pi$
$578$		0			0
$579$	1.28691e10	−	4.04922e9i	0.114508	−	0.0360294i
$580$		0			0
$581$		−	4.35040e10i		−	0.381790i
$582$		0			0
$583$		−	9.19842e10i		−	0.796231i
$584$		0			0
$585$	1.05152e10	+	9.92585e10i	0.0897832	+	0.847509i
$586$		0			0
$587$	−4.83034e10			−0.406842			−0.203421	−	0.979091i	$-0.565206\pi$
$587$	−4.83034e10			−0.406842			−0.203421	+	0.979091i	$0.565206\pi$
$588$		0			0
$589$	1.25558e11			1.04324
$590$		0			0
$591$	6.27880e9	+	1.99551e10i	0.0514667	+	0.163570i
$592$		0			0
$593$	2.31582e11			1.87278			0.936389	−	0.350964i	$-0.114146\pi$
$593$	2.31582e11			1.87278			0.936389	+	0.350964i	$0.114146\pi$
$594$		0			0
$595$	−3.89518e10	+	7.06054e10i	−0.310785	+	0.563340i
$596$		0			0
$597$	−1.69871e10	−	5.39878e10i	−0.133728	−	0.425009i
$598$		0			0
$599$		−	5.43950e10i		−	0.422524i	−0.977429	−	0.211262i	$-0.932243\pi$
$599$		−	5.43950e10i		−	0.422524i	0.977429	−	0.211262i	$-0.0677574\pi$
$600$		0			0
$601$	−1.22003e11			−0.935134			−0.467567	−	0.883958i	$-0.654869\pi$
$601$	−1.22003e11			−0.935134			−0.467567	+	0.883958i	$0.654869\pi$
$602$		0			0
$603$	−1.17963e11	−	1.68895e11i	−0.892231	−	1.27746i
$604$		0			0
$605$	−8.43377e10	−	4.65276e10i	−0.629506	−	0.347288i
$606$		0			0
$607$		−	1.16739e11i		−	0.859926i	−0.902847	−	0.429963i	$-0.858527\pi$
$607$		−	1.16739e11i		−	0.859926i	0.902847	−	0.429963i	$-0.141473\pi$
$608$		0			0
$609$	3.38796e10	+	1.07675e11i	0.246302	+	0.782791i
$610$		0			0
$611$		−	1.15152e10i		−	0.0826241i
$612$		0			0
$613$			7.33615e10i			0.519549i	0.965669	+	0.259774i	$0.0836482\pi$
$613$			7.33615e10i			0.519549i	−0.965669	+	0.259774i	$0.916352\pi$
$614$		0			0
$615$	1.63628e10	+	3.30490e9i	0.114382	+	0.0231025i
$616$		0			0
$617$	−7.75475e10			−0.535091			−0.267545	−	0.963545i	$-0.586213\pi$
$617$	−7.75475e10			−0.535091			−0.267545	+	0.963545i	$0.586213\pi$
$618$		0			0
$619$	1.23023e11			0.837961			0.418981	−	0.907995i	$-0.362387\pi$
$619$	1.23023e11			0.837961			0.418981	+	0.907995i	$0.362387\pi$
$620$		0			0
$621$	7.84316e10	+	6.04049e10i	0.527381	+	0.406168i
$622$		0			0
$623$	1.71740e10			0.114004
$624$		0			0
$625$	−6.57845e10	+	1.37679e11i	−0.431125	+	0.902292i
$626$		0			0
$627$	−6.91603e10	+	2.17610e10i	−0.447494	+	0.140802i
$628$		0			0
$629$			4.97941e9i			0.0318108i
$630$		0			0
$631$	9.08957e10			0.573358			0.286679	−	0.958027i	$-0.407449\pi$
$631$	9.08957e10			0.573358			0.286679	+	0.958027i	$0.407449\pi$
$632$		0			0
$633$	−5.83277e10	−	1.85375e11i	−0.363295	−	1.15461i
$634$		0			0
$635$	−7.91974e10	+	1.43556e11i	−0.487097	+	0.882931i
$636$		0			0
$637$			8.28691e10i			0.503309i
$638$		0			0
$639$	−3.53204e10	−	5.05705e10i	−0.211847	−	0.303315i
$640$		0			0
$641$			9.47742e10i			0.561381i	0.959798	+	0.280691i	$0.0905635\pi$
$641$			9.47742e10i			0.561381i	−0.959798	+	0.280691i	$0.909436\pi$
$642$		0			0
$643$		−	3.36793e11i		−	1.97024i	−0.171872	−	0.985119i	$-0.554982\pi$
$643$		−	3.36793e11i		−	1.97024i	0.171872	−	0.985119i	$-0.445018\pi$
$644$		0			0
$645$	−2.22444e11	−	4.49284e10i	−1.28524	−	0.259587i
$646$		0			0
$647$	2.21687e11			1.26509			0.632547	−	0.774522i	$-0.282010\pi$
$647$	2.21687e11			1.26509			0.632547	+	0.774522i	$0.282010\pi$
$648$		0			0
$649$	−2.54163e10			−0.143263
$650$		0			0
$651$	−1.29243e11	+	4.06659e10i	−0.719588	+	0.226416i
$652$		0			0
$653$	9.67862e10			0.532305			0.266153	−	0.963931i	$-0.414247\pi$
$653$	9.67862e10			0.532305			0.266153	+	0.963931i	$0.414247\pi$
$654$		0			0
$655$	−1.21656e11	+	2.20518e11i	−0.660950	+	1.19806i
$656$		0			0
$657$	1.37078e11	+	1.96263e11i	0.735708	+	1.05336i
$658$		0			0
$659$			3.02636e11i			1.60464i	0.596891	+	0.802322i	$0.296402\pi$
$659$			3.02636e11i			1.60464i	−0.596891	+	0.802322i	$0.703598\pi$
$660$		0			0
$661$	−9.96172e10			−0.521829			−0.260915	−	0.965362i	$-0.584024\pi$
$661$	−9.96172e10			−0.521829			−0.260915	+	0.965362i	$0.584024\pi$
$662$		0			0
$663$	1.57942e11	−	4.96959e10i	0.817417	−	0.257197i
$664$		0			0
$665$	−5.34890e10	+	9.69561e10i	−0.273513	+	0.495779i
$666$		0			0
$667$		−	1.68969e11i		−	0.853699i
$668$		0			0
$669$	−1.13718e11	+	3.57809e10i	−0.567707	+	0.178627i
$670$		0			0
$671$			1.59260e11i			0.785627i
$672$		0			0
$673$		−	9.69292e10i		−	0.472492i	−0.971693	−	0.236246i	$-0.924083\pi$
$673$		−	9.69292e10i		−	0.472492i	0.971693	−	0.236246i	$-0.0759171\pi$
$674$		0			0
$675$	−1.94336e10	+	2.06683e11i	−0.0936136	+	0.995609i
$676$		0			0
$677$	5.33776e10			0.254100			0.127050	−	0.991896i	$-0.459449\pi$
$677$	5.33776e10			0.254100			0.127050	+	0.991896i	$0.459449\pi$
$678$		0			0
$679$	7.83445e10			0.368578
$680$		0			0
$681$	2.64194e10	+	8.39655e10i	0.122839	+	0.390402i
$682$		0			0
$683$	8.56243e10			0.393472			0.196736	−	0.980456i	$-0.436966\pi$
$683$	8.56243e10			0.393472			0.196736	+	0.980456i	$0.436966\pi$
$684$		0			0
$685$	−1.03711e11	−	5.72153e10i	−0.471044	−	0.259866i
$686$		0			0
$687$	1.01616e11	+	3.22953e11i	0.456178	+	1.44981i
$688$		0			0
$689$			2.88464e11i			1.28001i
$690$		0			0
$691$	7.57374e10			0.332199			0.166100	−	0.986109i	$-0.446883\pi$
$691$	7.57374e10			0.332199			0.166100	+	0.986109i	$0.446883\pi$
$692$		0			0
$693$	6.41422e10	−	4.47995e10i	0.278106	−	0.194241i
$694$		0			0
$695$	−7.35946e9	−	4.06008e9i	−0.0315433	−	0.0174019i
$696$		0			0
$697$		−	2.76915e10i		−	0.117332i
$698$		0			0
$699$	−6.60667e10	−	2.09971e11i	−0.276741	−	0.879531i
$700$		0			0
$701$		−	3.12777e11i		−	1.29528i	−0.761948	−	0.647638i	$-0.775757\pi$
$701$		−	3.12777e11i		−	1.29528i	0.761948	−	0.647638i	$-0.224243\pi$
$702$		0			0
$703$			6.83777e9i			0.0279958i
$704$		0			0
$705$	4.74147e9	−	2.34754e10i	0.0191936	−	0.0950291i
$706$		0			0
$707$	−2.46621e10			−0.0987078
$708$		0			0
$709$	−3.38964e11			−1.34143			−0.670716	−	0.741715i	$-0.734013\pi$
$709$	−3.38964e11			−1.34143			−0.670716	+	0.741715i	$0.734013\pi$
$710$		0			0
$711$	−2.24443e11	+	1.56760e11i	−0.878268	+	0.613417i
$712$		0			0
$713$	2.02815e11			0.784771
$714$		0			0
$715$	−1.03392e11	−	5.70396e10i	−0.395606	−	0.218249i
$716$		0			0
$717$	2.28336e11	−	7.18450e10i	0.863968	−	0.271844i
$718$		0			0
$719$		−	4.77464e11i		−	1.78659i	−0.449470	−	0.893296i	$-0.648387\pi$
$719$		−	4.77464e11i		−	1.78659i	0.449470	−	0.893296i	$-0.351613\pi$
$720$		0			0
$721$	1.75211e11			0.648365
$722$		0			0
$723$	1.13490e11	+	3.60692e11i	0.415342	+	1.32003i
$724$		0			0
$725$	2.99729e11	−	1.88972e11i	1.08487	−	0.683984i
$726$		0			0
$727$			2.79820e11i			1.00171i	0.865532	+	0.500854i	$0.166981\pi$
$727$			2.79820e11i			1.00171i	−0.865532	+	0.500854i	$0.833019\pi$
$728$		0			0
$729$	7.21260e10	+	2.73065e11i	0.255377	+	0.966842i
$730$		0			0
$731$			3.76452e11i			1.31838i
$732$		0			0
$733$		−	4.61873e11i		−	1.59995i	−0.600033	−	0.799975i	$-0.704846\pi$
$733$		−	4.61873e11i		−	1.59995i	0.600033	−	0.799975i	$-0.295154\pi$
$734$		0			0
$735$	−3.41220e10	+	1.68941e11i	−0.116919	+	0.578875i
$736$		0			0
$737$	2.43717e11			0.826069
$738$		0			0
$739$	3.51955e11			1.18007			0.590036	−	0.807377i	$-0.299113\pi$
$739$	3.51955e11			1.18007			0.590036	+	0.807377i	$0.299113\pi$
$740$		0			0
$741$	2.16888e11	−	6.82429e10i	0.719386	−	0.226352i
$742$		0			0
$743$	3.68777e11			1.21006			0.605032	−	0.796201i	$-0.293160\pi$
$743$	3.68777e11			1.21006			0.605032	+	0.796201i	$0.293160\pi$
$744$		0			0
$745$	−2.62586e11	+	4.75973e11i	−0.852405	+	1.54510i
$746$		0			0
$747$	−1.52314e11	+	1.06382e11i	−0.489167	+	0.341654i
$748$		0			0
$749$			2.81049e11i			0.893006i
$750$		0			0
$751$	3.58921e11			1.12834			0.564169	−	0.825659i	$-0.309197\pi$
$751$	3.58921e11			1.12834			0.564169	+	0.825659i	$0.309197\pi$
$752$		0			0
$753$	3.69845e11	−	1.16370e11i	1.15038	−	0.361961i
$754$		0			0
$755$	−3.65275e11	−	2.01516e11i	−1.12417	−	0.620185i
$756$		0			0
$757$		−	1.44523e11i		−	0.440101i	−0.975488	−	0.220051i	$-0.929378\pi$
$757$		−	1.44523e11i		−	0.440101i	0.975488	−	0.220051i	$-0.0706223\pi$
$758$		0			0
$759$	−1.11716e11	+	3.51509e10i	−0.336625	+	0.105918i
$760$		0			0
$761$			6.00551e11i			1.79065i	0.445410	+	0.895327i	$0.353058\pi$
$761$			6.00551e11i			1.79065i	−0.445410	+	0.895327i	$0.646942\pi$
$762$		0			0
$763$			8.66254e10i			0.255592i
$764$		0			0
$765$	3.42450e11	−	3.62784e10i	0.999889	−	0.105926i
$766$		0			0
$767$	7.97058e10			0.230308
$768$		0			0
$769$	−1.04208e11			−0.297987			−0.148993	−	0.988838i	$-0.547603\pi$
$769$	−1.04208e11			−0.297987			−0.148993	+	0.988838i	$0.547603\pi$
$770$		0			0
$771$	−5.54688e9	−	1.76289e10i	−0.0156975	−	0.0498894i
$772$		0			0
$773$	−4.76449e11			−1.33444			−0.667219	−	0.744861i	$-0.732516\pi$
$773$	−4.76449e11			−1.33444			−0.667219	+	0.744861i	$0.732516\pi$
$774$		0			0
$775$	2.26825e11	+	3.59767e11i	0.628758	+	0.997273i
$776$		0			0
$777$	−2.21462e9	−	7.03846e9i	−0.00607598	−	0.0193105i
$778$		0			0
$779$		−	3.80263e10i		−	0.103260i
$780$		0			0
$781$	7.29736e10			0.196138
$782$		0			0
$783$	2.94139e11	−	3.81919e11i	0.782538	−	1.01607i
$784$		0			0
$785$	2.13481e11	−	3.86963e11i	0.562186	−	1.01904i
$786$		0			0
$787$			1.28735e11i			0.335582i	0.985823	+	0.167791i	$0.0536633\pi$
$787$			1.28735e11i			0.335582i	−0.985823	+	0.167791i	$0.946337\pi$
$788$		0			0
$789$	−4.23662e10	−	1.34647e11i	−0.109323	−	0.347447i
$790$		0			0
$791$			4.50037e11i			1.14959i
$792$		0			0
$793$		−	4.99441e11i		−	1.26296i
$794$		0			0
$795$	−1.18777e11	+	5.88074e11i	−0.297347	+	1.47219i
$796$		0			0
$797$	−7.14430e11			−1.77062			−0.885312	−	0.464997i	$-0.846056\pi$
$797$	−7.14430e11			−1.77062			−0.885312	+	0.464997i	$0.846056\pi$
$798$		0			0
$799$	−3.97284e10			−0.0974797
$800$		0			0
$801$	−4.19963e10	−	6.01287e10i	−0.102019	−	0.146067i
$802$		0			0
$803$	−2.83209e11			−0.681153
$804$		0			0
$805$	−8.64013e10	+	1.56614e11i	−0.205749	+	0.372948i
$806$		0			0
$807$	−5.69193e11	+	1.79094e11i	−1.34204	+	0.422268i
$808$		0			0
$809$			7.05895e11i			1.64796i	0.566621	+	0.823978i	$0.308250\pi$
$809$			7.05895e11i			1.64796i	−0.566621	+	0.823978i	$0.691750\pi$
$810$		0			0
$811$	4.38265e11			1.01310			0.506551	−	0.862210i	$-0.330920\pi$
$811$	4.38265e11			1.01310			0.506551	+	0.862210i	$0.330920\pi$
$812$		0			0
$813$	−2.50458e11	−	7.96000e11i	−0.573289	−	1.82201i
$814$		0			0
$815$	−3.40229e11	+	6.16711e11i	−0.771153	+	1.39782i
$816$		0			0
$817$			5.16947e11i			1.16027i
$818$		0			0
$819$	−2.01151e11	+	1.40492e11i	−0.447081	+	0.312259i
$820$		0			0
$821$		−	4.54620e11i		−	1.00064i	−0.865842	−	0.500318i	$-0.833217\pi$
$821$		−	4.54620e11i		−	1.00064i	0.865842	−	0.500318i	$-0.166783\pi$
$822$		0			0
$823$		−	3.92102e11i		−	0.854673i	−0.904093	−	0.427336i	$-0.859452\pi$
$823$		−	3.92102e11i		−	0.854673i	0.904093	−	0.427336i	$-0.140548\pi$
$824$		0			0
$825$	−1.87293e11	−	1.58856e11i	−0.404302	−	0.342916i
$826$		0			0
$827$	4.22989e11			0.904289			0.452145	−	0.891945i	$-0.350659\pi$
$827$	4.22989e11			0.904289			0.452145	+	0.891945i	$0.350659\pi$
$828$		0			0
$829$	−4.11878e11			−0.872068			−0.436034	−	0.899930i	$-0.643617\pi$
$829$	−4.11878e11			−0.872068			−0.436034	+	0.899930i	$0.643617\pi$
$830$		0			0
$831$	4.74072e11	−	1.49165e11i	0.994124	−	0.312797i
$832$		0			0
$833$	2.85905e11			0.593803
$834$		0			0
$835$	−4.47355e11	−	2.46798e11i	−0.920251	−	0.507686i
$836$		0			0
$837$	4.58421e11	+	3.53057e11i	0.934033	+	0.719355i
$838$		0			0
$839$		−	4.56672e11i		−	0.921630i	−0.887496	−	0.460815i	$-0.847557\pi$
$839$		−	4.56672e11i		−	0.921630i	0.887496	−	0.460815i	$-0.152443\pi$
$840$		0			0
$841$	−3.22543e11			−0.644768
$842$		0			0
$843$	6.59185e11	−	2.07410e11i	1.30526	−	0.410695i
$844$		0			0
$845$	−1.22166e11	−	6.73971e10i	−0.239621	−	0.132195i
$846$		0			0
$847$		−	2.36769e11i		−	0.460035i
$848$		0			0
$849$	−3.53587e10	+	1.11255e10i	−0.0680558	+	0.0214135i
$850$		0			0
$851$			1.10451e10i			0.0210597i
$852$		0			0
$853$			1.75194e11i			0.330920i	0.986216	+	0.165460i	$0.0529109\pi$
$853$			1.75194e11i			0.330920i	−0.986216	+	0.165460i	$0.947089\pi$
$854$		0			0
$855$	4.70256e11	−	4.98178e10i	0.879974	−	0.0932224i
$856$		0			0
$857$	−6.30653e11			−1.16914			−0.584571	−	0.811343i	$-0.698737\pi$
$857$	−6.30653e11			−1.16914			−0.584571	+	0.811343i	$0.698737\pi$
$858$		0			0
$859$	5.02518e11			0.922951			0.461475	−	0.887153i	$-0.347320\pi$
$859$	5.02518e11			0.922951			0.461475	+	0.887153i	$0.347320\pi$
$860$		0			0
$861$	1.23160e10	+	3.91423e10i	0.0224108	+	0.0712253i
$862$		0			0
$863$	−4.96972e11			−0.895961			−0.447981	−	0.894043i	$-0.647857\pi$
$863$	−4.96972e11			−0.895961			−0.447981	+	0.894043i	$0.647857\pi$
$864$		0			0
$865$	3.76206e11	+	2.07546e11i	0.671988	+	0.370724i
$866$		0			0
$867$	−1.86508e9	−	5.92754e9i	−0.00330081	−	0.0104906i
$868$		0			0
$869$		−	3.23872e11i		−	0.567930i
$870$		0			0
$871$	−7.64300e11			−1.32798
$872$		0			0
$873$	−1.91579e11	−	2.74296e11i	−0.329830	−	0.472239i
$874$		0			0
$875$	−3.74442e11	+	2.18902e10i	−0.638781	+	0.0373438i
$876$		0			0
$877$			1.97015e11i			0.333044i	0.986038	+	0.166522i	$0.0532537\pi$
$877$			1.97015e11i			0.333044i	−0.986038	+	0.166522i	$0.946746\pi$
$878$		0			0
$879$	−3.02035e11	−	9.59920e11i	−0.505944	−	1.60798i
$880$		0			0
$881$			1.40330e11i			0.232942i	0.993194	+	0.116471i	$0.0371581\pi$
$881$			1.40330e11i			0.232942i	−0.993194	+	0.116471i	$0.962842\pi$
$882$		0			0
$883$		−	1.03460e12i		−	1.70188i	−0.525266	−	0.850938i	$-0.676034\pi$
$883$		−	1.03460e12i		−	1.70188i	0.525266	−	0.850938i	$-0.323966\pi$
$884$		0			0
$885$	1.62492e11	+	3.28195e10i	0.264886	+	0.0535006i
$886$		0			0
$887$	−7.73307e11			−1.24927			−0.624637	−	0.780915i	$-0.714753\pi$
$887$	−7.73307e11			−1.24927			−0.624637	+	0.780915i	$0.714753\pi$
$888$		0			0
$889$	−4.03018e11			−0.645234
$890$		0			0
$891$	−3.13699e11	−	1.15021e11i	−0.497740	−	0.182502i
$892$		0			0
$893$	−5.45554e10			−0.0857891
$894$		0			0
$895$	4.89705e10	−	8.87657e10i	0.0763207	−	0.138342i
$896$		0			0
$897$	3.50341e11	−	1.10233e11i	0.541154	−	0.170272i
$898$		0			0
$899$		−	9.87601e11i		−	1.51197i
$900$		0			0
$901$	9.95223e11			1.51015
$902$		0			0
$903$	−1.67430e11	−	5.32120e11i	−0.251815	−	0.800311i
$904$		0			0
$905$	−4.24942e11	−	2.34433e11i	−0.633483	−	0.349482i
$906$		0			0
$907$			5.62860e11i			0.831709i	0.909431	+	0.415854i	$0.136517\pi$
$907$			5.62860e11i			0.831709i	−0.909431	+	0.415854i	$0.863483\pi$
$908$		0			0
$909$	6.03071e10	+	8.63454e10i	0.0883309	+	0.126469i
$910$		0			0
$911$			2.29424e11i			0.333093i	0.986034	+	0.166546i	$0.0532616\pi$
$911$			2.29424e11i			0.333093i	−0.986034	+	0.166546i	$0.946738\pi$
$912$		0			0
$913$		−	2.19790e11i		−	0.316319i
$914$		0			0
$915$	2.05648e11	−	1.01818e12i	0.293387	−	1.45258i
$916$		0			0
$917$	−6.19081e11			−0.875528
$918$		0			0
$919$	−1.24790e12			−1.74952			−0.874760	−	0.484556i	$-0.838981\pi$
$919$	−1.24790e12			−1.74952			−0.874760	+	0.484556i	$0.838981\pi$
$920$		0			0
$921$	7.68956e11	−	2.41949e11i	1.06872	−	0.336268i
$922$		0			0
$923$	−2.28846e11			−0.315309
$924$		0			0
$925$	−1.95925e10	+	1.23527e10i	−0.0267623	+	0.0168730i
$926$		0			0
$927$	−4.28450e11	−	6.13438e11i	−0.580204	−	0.830715i
$928$		0			0
$929$		−	1.95910e11i		−	0.263024i	−0.991315	−	0.131512i	$-0.958017\pi$
$929$		−	1.95910e11i		−	0.263024i	0.991315	−	0.131512i	$-0.0419831\pi$
$930$		0			0
$931$	3.92608e11			0.522589
$932$		0			0
$933$	2.29445e11	−	7.21942e10i	0.302798	−	0.0952742i
$934$		0			0
$935$	−1.96791e11	+	3.56711e11i	−0.257490	+	0.466735i
$936$		0			0
$937$			2.83389e10i			0.0367641i	0.999831	+	0.0183821i	$0.00585152\pi$
$937$			2.83389e10i			0.0367641i	−0.999831	+	0.0183821i	$0.994148\pi$
$938$		0			0
$939$	9.44518e11	−	2.97189e11i	1.21492	−	0.382270i
$940$		0			0
$941$		−	1.29493e11i		−	0.165153i	−0.996585	−	0.0825766i	$-0.973685\pi$
$941$		−	1.29493e11i		−	0.165153i	0.996585	−	0.0825766i	$-0.0263149\pi$
$942$		0			0
$943$		−	6.14243e10i		−	0.0776771i
$944$		0			0
$945$	−4.67923e11	+	2.03587e11i	−0.586742	+	0.255284i
$946$		0			0
$947$	1.02713e11			0.127710			0.0638548	−	0.997959i	$-0.479661\pi$
$947$	1.02713e11			0.127710			0.0638548	+	0.997959i	$0.479661\pi$
$948$		0			0
$949$	8.88145e11			1.09501
$950$		0			0
$951$	2.72812e10	+	8.67044e10i	0.0333535	+	0.106003i
$952$		0			0
$953$	−6.30533e11			−0.764428			−0.382214	−	0.924074i	$-0.624838\pi$
$953$	−6.30533e11			−0.764428			−0.382214	+	0.924074i	$0.624838\pi$
$954$		0			0
$955$	−4.82309e11	+	8.74251e11i	−0.579845	+	1.05105i
$956$		0			0
$957$	1.71166e11	+	5.43994e11i	0.204065	+	0.648554i
$958$		0			0
$959$		−	2.91156e11i		−	0.344232i
$960$		0			0
$961$	3.32534e11			0.389891
$962$		0			0
$963$	9.83992e11	−	6.87259e11i	1.14416	−	0.799126i
$964$		0			0
$965$	5.02845e10	−	9.11476e10i	0.0579862	−	0.105108i
$966$		0			0
$967$		−	3.98318e11i		−	0.455538i	−0.973715	−	0.227769i	$-0.926857\pi$
$967$		−	3.98318e11i		−	0.455538i	0.973715	−	0.227769i	$-0.0731431\pi$
$968$		0			0
$969$	−2.35443e11	−	7.48280e11i	−0.267049	−	0.848729i
$970$		0			0
$971$		−	6.28862e10i		−	0.0707422i	−0.999374	−	0.0353711i	$-0.988739\pi$
$971$		−	6.28862e10i		−	0.0707422i	0.999374	−	0.0353711i	$-0.0112613\pi$
$972$		0			0
$973$		−	2.06609e10i		−	0.0230514i
$974$		0			0
$975$	5.87353e11	+	4.98174e11i	0.649952	+	0.551267i
$976$		0			0
$977$	−7.52369e11			−0.825758			−0.412879	−	0.910786i	$-0.635477\pi$
$977$	−7.52369e11			−0.825758			−0.412879	+	0.910786i	$0.635477\pi$
$978$		0			0
$979$	8.67662e10			0.0944539
$980$		0			0
$981$	3.03288e11	−	2.11828e11i	0.327476	−	0.228722i
$982$		0			0
$983$	−1.78809e11			−0.191503			−0.0957514	−	0.995405i	$-0.530525\pi$
$983$	−1.78809e11			−0.191503			−0.0957514	+	0.995405i	$0.530525\pi$
$984$		0			0
$985$	1.41335e11	+	7.79722e10i	0.150143	+	0.0828314i
$986$		0			0
$987$	5.61566e10	−	1.76695e10i	0.0591742	−	0.0186189i
$988$		0			0
$989$			8.35031e11i			0.872806i
$990$		0			0
$991$	6.12252e10			0.0634798			0.0317399	−	0.999496i	$-0.489895\pi$
$991$	6.12252e10			0.0634798			0.0317399	+	0.999496i	$0.489895\pi$
$992$		0			0
$993$	3.46800e11	+	1.10219e12i	0.356683	+	1.13360i
$994$		0			0
$995$	−3.82377e11	−	2.10951e11i	−0.390121	−	0.215223i
$996$		0			0
$997$			1.06525e12i			1.07813i	0.842264	+	0.539066i	$0.181223\pi$
$997$			1.06525e12i			1.07813i	−0.842264	+	0.539066i	$0.818777\pi$
$998$		0			0
$999$	−1.92272e10	+	2.49651e10i	−0.0193043	+	0.0250652i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.9.c.f.209.19		48
3.2	odd	2	inner	240.9.c.f.209.29		48
4.3	odd	2		120.9.c.a.89.30	yes	48
5.4	even	2	inner	240.9.c.f.209.30		48
12.11	even	2		120.9.c.a.89.20	yes	48
15.14	odd	2	inner	240.9.c.f.209.20		48
20.19	odd	2		120.9.c.a.89.19	✓	48
60.59	even	2		120.9.c.a.89.29	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.9.c.a.89.19	✓	48	20.19	odd	2
120.9.c.a.89.20	yes	48	12.11	even	2
120.9.c.a.89.29	yes	48	60.59	even	2
120.9.c.a.89.30	yes	48	4.3	odd	2
240.9.c.f.209.19		48	1.1	even	1	trivial
240.9.c.f.209.20		48	15.14	odd	2	inner
240.9.c.f.209.29		48	3.2	odd	2	inner
240.9.c.f.209.30		48	5.4	even	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)

\(f(q)\)	\(=\)	\(q+(-24.3113 - 77.2655i) q^{3} +(-547.246 - 301.906i) q^{5} -1536.33i q^{7} +(-5378.92 + 3756.85i) q^{9} -7761.82i q^{11} +24341.2i q^{13} +(-10022.6 + 49622.9i) q^{15} +83979.0 q^{17} +115321. q^{19} +(-118705. + 37350.2i) q^{21} +186279. q^{23} +(208331. + 330433. i) q^{25} +(421044. + 324271. i) q^{27} -907077. i q^{29} +1.08877e6 q^{31} +(-599721. + 188700. i) q^{33} +(-463828. + 840751. i) q^{35} +59293.5i q^{37} +(1.88073e6 - 591765. i) q^{39} -329743. i q^{41} +4.48269e6i q^{43} +(4.07781e6 - 431994. i) q^{45} -473075. q^{47} +3.40449e6 q^{49} +(-2.04164e6 - 6.48868e6i) q^{51} +1.18509e7 q^{53} +(-2.34334e6 + 4.24762e6i) q^{55} +(-2.80360e6 - 8.91032e6i) q^{57} -3.27453e6i q^{59} -2.05184e7 q^{61} +(5.77177e6 + 8.26381e6i) q^{63} +(7.34874e6 - 1.33206e7i) q^{65} +3.13995e7i q^{67} +(-4.52869e6 - 1.43929e7i) q^{69} +9.40161e6i q^{71} -3.64874e7i q^{73} +(2.04663e7 - 2.41301e7i) q^{75} -1.19247e7 q^{77} +4.17263e7 q^{79} +(1.48189e7 - 4.04156e7i) q^{81} +2.83168e7 q^{83} +(-4.59572e7 - 2.53538e7i) q^{85} +(-7.00858e7 + 2.20522e7i) q^{87} +1.11786e7i q^{89} +3.73961e7 q^{91} +(-2.64695e7 - 8.41246e7i) q^{93} +(-6.31088e7 - 3.48160e7i) q^{95} +5.09945e7i q^{97} +(2.91600e7 + 4.17502e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2528 q^{9} - 132352 q^{15} + 116176 q^{21} + 56976 q^{25} - 1395648 q^{31} - 6888832 q^{39} - 4287056 q^{45} - 30813552 q^{49} + 22815168 q^{51} + 6062784 q^{55} + 14031936 q^{61} + 2522608 q^{69}+ \cdots + 21719360 q^{99}+O(q^{100}) \) 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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Modular forms

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Database

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