LMFDB - Embedded newform 180.9.c.b.91.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,9,Mod(91,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 0, 0])) N = Newforms(chi, 9, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.91"); S:= CuspForms(chi, 9); N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	180.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$73.3281498110$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.5
Character	$\chi$	$=$	180.91
Dual form			180.9.c.b.91.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-14.6346 - 6.46742i) q^{2} +(172.345 + 189.297i) q^{4} +279.508 q^{5} +1279.81i q^{7} +(-1297.94 - 3884.91i) q^{8} +(-4090.50 - 1807.70i) q^{10} +3918.81i q^{11} +33391.7 q^{13} +(8277.07 - 18729.5i) q^{14} +(-6130.49 + 65248.6i) q^{16} -81036.2 q^{17} -50011.0i q^{19} +(48171.9 + 52910.0i) q^{20} +(25344.6 - 57350.4i) q^{22} -519530. i q^{23} +78125.0 q^{25} +(-488675. - 215958. i) q^{26} +(-242264. + 220568. i) q^{28} +851423. q^{29} -617163. i q^{31} +(511708. - 915241. i) q^{32} +(1.18593e6 + 524095. i) q^{34} +357717. i q^{35} -2.77393e6 q^{37} +(-323442. + 731892. i) q^{38} +(-362786. - 1.08587e6i) q^{40} -1.07328e6 q^{41} +6.23975e6i q^{43} +(-741818. + 675387. i) q^{44} +(-3.36002e6 + 7.60313e6i) q^{46} -3.81873e6i q^{47} +4.12689e6 q^{49} +(-1.14333e6 - 505267. i) q^{50} +(5.75488e6 + 6.32093e6i) q^{52} +7.88378e6 q^{53} +1.09534e6i q^{55} +(4.97195e6 - 1.66112e6i) q^{56} +(-1.24603e7 - 5.50651e6i) q^{58} +6.36280e6i q^{59} -7.65342e6 q^{61} +(-3.99146e6 + 9.03196e6i) q^{62} +(-1.34079e7 + 1.00848e7i) q^{64} +9.33325e6 q^{65} +2.21100e7i q^{67} +(-1.39662e7 - 1.53399e7i) q^{68} +(2.31351e6 - 5.23506e6i) q^{70} -2.48940e6i q^{71} +1.34278e7 q^{73} +(4.05955e7 + 1.79402e7i) q^{74} +(9.46691e6 - 8.61913e6i) q^{76} -5.01533e6 q^{77} -426407. i q^{79} +(-1.71352e6 + 1.82375e7i) q^{80} +(1.57071e7 + 6.94137e6i) q^{82} -7.39202e7i q^{83} -2.26503e7 q^{85} +(4.03551e7 - 9.13164e7i) q^{86} +(1.52243e7 - 5.08639e6i) q^{88} +5.04683e7 q^{89} +4.27349e7i q^{91} +(9.83454e7 - 8.95384e7i) q^{92} +(-2.46974e7 + 5.58857e7i) q^{94} -1.39785e7i q^{95} +5.32622e7 q^{97} +(-6.03955e7 - 2.66903e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 610 q^{4} - 8750 q^{10} - 51392 q^{13} + 11986 q^{16} - 758068 q^{22} + 2500000 q^{25} + 976324 q^{28} - 6117428 q^{34} + 5152064 q^{37} - 96250 q^{40} - 10391752 q^{46} - 11002976 q^{49} + 13976584 q^{52}+ \cdots + 80579520 q^{97}+O(q^{100}) $ 32 * q + 610 * q^4 - 8750 * q^10 - 51392 * q^13 + 11986 * q^16 - 758068 * q^22 + 2500000 * q^25 + 976324 * q^28 - 6117428 * q^34 + 5152064 * q^37 - 96250 * q^40 - 10391752 * q^46 - 11002976 * q^49 + 13976584 * q^52 - 36333948 * q^58 - 7802048 * q^61 + 116259994 * q^64 - 49897500 * q^70 - 94303680 * q^73 + 248840592 * q^76 - 428557904 * q^82 + 106960000 * q^85 + 510719924 * q^88 - 692727576 * q^94 + 80579520 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$	−14.6346	−	6.46742i	−0.914664	−	0.404214i
$2$	−14.6346	−	6.46742i	−0.914664	−	0.404214i
$3$		0			0
$3$		0			0
$4$	172.345	+	189.297i	0.673222	+	0.739440i
$5$	279.508			0.447214
$5$	279.508			0.447214
$6$		0			0
$7$			1279.81i			0.533032i	0.963831	+	0.266516i	$0.0858725\pi$
$7$			1279.81i			0.533032i	−0.963831	+	0.266516i	$0.914128\pi$
$8$	−1297.94	−	3884.91i	−0.316880	−	0.948466i
$9$		0			0
$10$	−4090.50	−	1807.70i	−0.409050	−	0.180770i
$11$			3918.81i			0.267660i	0.991004	+	0.133830i	$0.0427276\pi$
$11$			3918.81i			0.267660i	−0.991004	+	0.133830i	$0.957272\pi$
$12$		0			0
$13$	33391.7			1.16913			0.584567	−	0.811345i	$-0.301264\pi$
$13$	33391.7			1.16913			0.584567	+	0.811345i	$0.301264\pi$
$14$	8277.07	−	18729.5i	0.215459	−	0.487545i
$15$		0			0
$16$	−6130.49	+	65248.6i	−0.0935439	+	0.995615i
$17$	−81036.2			−0.970249			−0.485125	−	0.874445i	$-0.661226\pi$
$17$	−81036.2			−0.970249			−0.485125	+	0.874445i	$0.661226\pi$
$18$		0			0
$19$		−	50011.0i		−	0.383752i	−0.981419	−	0.191876i	$-0.938543\pi$
$19$		−	50011.0i		−	0.383752i	0.981419	−	0.191876i	$-0.0614572\pi$
$20$	48171.9	+	52910.0i	0.301074	+	0.330688i
$21$		0			0
$22$	25344.6	−	57350.4i	0.108192	−	0.244819i
$23$		−	519530.i		−	1.85652i	−0.371933	−	0.928260i	$-0.621305\pi$
$23$		−	519530.i		−	1.85652i	0.371933	−	0.928260i	$-0.378695\pi$
$24$		0			0
$25$	78125.0			0.200000
$26$	−488675.	−	215958.i	−1.06937	−	0.472581i
$27$		0			0
$28$	−242264.	+	220568.i	−0.394145	+	0.358849i
$29$	851423.			1.20380			0.601899	−	0.798573i	$-0.294411\pi$
$29$	851423.			1.20380			0.601899	+	0.798573i	$0.294411\pi$
$30$		0			0
$31$		−	617163.i		−	0.668272i	−0.942525	−	0.334136i	$-0.891555\pi$
$31$		−	617163.i		−	0.668272i	0.942525	−	0.334136i	$-0.108445\pi$
$32$	511708.	−	915241.i	0.488003	−	0.872842i
$33$		0			0
$34$	1.18593e6	+	524095.i	0.887453	+	0.392188i
$35$			357717.i			0.238379i
$36$		0			0
$37$	−2.77393e6			−1.48009			−0.740047	−	0.672555i	$-0.765197\pi$
$37$	−2.77393e6			−1.48009			−0.740047	+	0.672555i	$0.765197\pi$
$38$	−323442.	+	731892.i	−0.155118	+	0.351004i
$39$		0			0
$40$	−362786.	−	1.08587e6i	−0.141713	−	0.424167i
$41$	−1.07328e6			−0.379821			−0.189910	−	0.981801i	$-0.560820\pi$
$41$	−1.07328e6			−0.379821			−0.189910	+	0.981801i	$0.560820\pi$
$42$		0			0
$43$			6.23975e6i			1.82513i	0.408934	+	0.912564i	$0.365901\pi$
$43$			6.23975e6i			1.82513i	−0.408934	+	0.912564i	$0.634099\pi$
$44$	−741818.	+	675387.i	−0.197919	+	0.180195i
$45$		0			0
$46$	−3.36002e6	+	7.60313e6i	−0.750431	+	1.69809i
$47$		−	3.81873e6i		−	0.782578i	−0.920268	−	0.391289i	$-0.872029\pi$
$47$		−	3.81873e6i		−	0.782578i	0.920268	−	0.391289i	$-0.127971\pi$
$48$		0			0
$49$	4.12689e6			0.715877
$50$	−1.14333e6	−	505267.i	−0.182933	−	0.0808428i
$51$		0			0
$52$	5.75488e6	+	6.32093e6i	0.787088	+	0.864505i
$53$	7.88378e6			0.999151			0.499576	−	0.866270i	$-0.333489\pi$
$53$	7.88378e6			0.999151			0.499576	+	0.866270i	$0.333489\pi$
$54$		0			0
$55$			1.09534e6i			0.119701i
$56$	4.97195e6	−	1.66112e6i	0.505562	−	0.168907i
$57$		0			0
$58$	−1.24603e7	−	5.50651e6i	−1.10107	−	0.486592i
$59$			6.36280e6i			0.525098i	0.964919	+	0.262549i	$0.0845631\pi$
$59$			6.36280e6i			0.525098i	−0.964919	+	0.262549i	$0.915437\pi$
$60$		0			0
$61$	−7.65342e6			−0.552759			−0.276380	−	0.961049i	$-0.589135\pi$
$61$	−7.65342e6			−0.552759			−0.276380	+	0.961049i	$0.589135\pi$
$62$	−3.99146e6	+	9.03196e6i	−0.270125	+	0.611245i
$63$		0			0
$64$	−1.34079e7	+	1.00848e7i	−0.799174	+	0.601100i
$65$	9.33325e6			0.522853
$66$		0			0
$67$			2.21100e7i			1.09721i	0.836082	+	0.548605i	$0.184841\pi$
$67$			2.21100e7i			1.09721i	−0.836082	+	0.548605i	$0.815159\pi$
$68$	−1.39662e7	−	1.53399e7i	−0.653193	−	0.717441i
$69$		0			0
$70$	2.31351e6	−	5.23506e6i	0.0963561	−	0.218037i
$71$		−	2.48940e6i		−	0.0979628i	−0.998800	−	0.0489814i	$-0.984402\pi$
$71$		−	2.48940e6i		−	0.0979628i	0.998800	−	0.0489814i	$-0.0155975\pi$
$72$		0			0
$73$	1.34278e7			0.472840			0.236420	−	0.971651i	$-0.424026\pi$
$73$	1.34278e7			0.472840			0.236420	+	0.971651i	$0.424026\pi$
$74$	4.05955e7	+	1.79402e7i	1.35379	+	0.598275i
$75$		0			0
$76$	9.46691e6	−	8.61913e6i	0.283762	−	0.258350i
$77$	−5.01533e6			−0.142671
$78$		0			0
$79$		−	426407.i		−	0.0109475i	−0.999985	−	0.00547376i	$-0.998258\pi$
$79$		−	426407.i		−	0.0109475i	0.999985	−	0.00547376i	$-0.00174236\pi$
$80$	−1.71352e6	+	1.82375e7i	−0.0418341	+	0.445253i
$81$		0			0
$82$	1.57071e7	+	6.94137e6i	0.347409	+	0.153529i
$83$		−	7.39202e7i		−	1.55758i	−0.627283	−	0.778791i	$-0.715833\pi$
$83$		−	7.39202e7i		−	1.55758i	0.627283	−	0.778791i	$-0.284167\pi$
$84$		0			0
$85$	−2.26503e7			−0.433909
$86$	4.03551e7	−	9.13164e7i	0.737742	−	1.66938i
$87$		0			0
$88$	1.52243e7	−	5.08639e6i	0.253866	−	0.0848162i
$89$	5.04683e7			0.804375			0.402188	−	0.915557i	$-0.368250\pi$
$89$	5.04683e7			0.804375			0.402188	+	0.915557i	$0.368250\pi$
$90$		0			0
$91$			4.27349e7i			0.623186i
$92$	9.83454e7	−	8.95384e7i	1.37278	−	1.24985i
$93$		0			0
$94$	−2.46974e7	+	5.58857e7i	−0.316329	+	0.715797i
$95$		−	1.39785e7i		−	0.171619i
$96$		0			0
$97$	5.32622e7			0.601634			0.300817	−	0.953682i	$-0.402741\pi$
$97$	5.32622e7			0.601634			0.300817	+	0.953682i	$0.402741\pi$
$98$	−6.03955e7	−	2.66903e7i	−0.654788	−	0.289368i
$99$		0			0
$100$	1.34644e7	+	1.47888e7i	0.134644	+	0.147888i
$101$	−4.08680e7			−0.392733			−0.196367	−	0.980531i	$-0.562914\pi$
$101$	−4.08680e7			−0.392733			−0.196367	+	0.980531i	$0.562914\pi$
$102$		0			0
$103$		−	2.18144e8i		−	1.93818i	−0.246707	−	0.969090i	$-0.579348\pi$
$103$		−	2.18144e8i		−	1.93818i	0.246707	−	0.969090i	$-0.420652\pi$
$104$	−4.33404e7	−	1.29724e8i	−0.370476	−	1.10888i
$105$		0			0
$106$	−1.15376e8	−	5.09878e7i	−0.913888	−	0.403871i
$107$		−	1.41164e8i		−	1.07693i	−0.842648	−	0.538465i	$-0.819004\pi$
$107$		−	1.41164e8i		−	1.07693i	0.842648	−	0.538465i	$-0.180996\pi$
$108$		0			0
$109$	4.33116e7			0.306830			0.153415	−	0.988162i	$-0.450973\pi$
$109$	4.33116e7			0.306830			0.153415	+	0.988162i	$0.450973\pi$
$110$	7.08404e6	−	1.60299e7i	0.0483849	−	0.109487i
$111$		0			0
$112$	−8.35058e7	−	7.84586e6i	−0.530694	−	0.0498619i
$113$	2.45194e8			1.50382			0.751910	−	0.659266i	$-0.229133\pi$
$113$	2.45194e8			1.50382			0.751910	+	0.659266i	$0.229133\pi$
$114$		0			0
$115$		−	1.45213e8i		−	0.830261i
$116$	1.46738e8	+	1.61172e8i	0.810423	+	0.890136i
$117$		0			0
$118$	4.11509e7	−	9.31172e7i	0.212252	−	0.480288i
$119$		−	1.03711e8i		−	0.517174i
$120$		0			0
$121$	1.99002e8			0.928358
$122$	1.12005e8	+	4.94979e7i	0.505589	+	0.223433i
$123$		0			0
$124$	1.16827e8	−	1.06365e8i	0.494147	−	0.449896i
$125$	2.18366e7			0.0894427
$126$		0			0
$127$		−	6.73587e7i		−	0.258928i	−0.991584	−	0.129464i	$-0.958674\pi$
$127$		−	6.73587e7i		−	0.258928i	0.991584	−	0.129464i	$-0.0413257\pi$
$128$	2.61442e8	−	6.08725e7i	0.973949	−	0.226768i
$129$		0			0
$130$	−1.36589e8	−	6.03621e7i	−0.478235	−	0.211344i
$131$		−	5.91573e7i		−	0.200874i	−0.994943	−	0.100437i	$-0.967976\pi$
$131$		−	5.91573e7i		−	0.200874i	0.994943	−	0.100437i	$-0.0320241\pi$
$132$		0			0
$133$	6.40045e7			0.204552
$134$	1.42995e8	−	3.23572e8i	0.443507	−	1.00358i
$135$		0			0
$136$	1.05180e8	+	3.14819e8i	0.307453	+	0.920248i
$137$	2.22966e8			0.632930			0.316465	−	0.948604i	$-0.397504\pi$
$137$	2.22966e8			0.632930			0.316465	+	0.948604i	$0.397504\pi$
$138$		0			0
$139$		−	2.02348e8i		−	0.542050i	−0.962572	−	0.271025i	$-0.912637\pi$
$139$		−	2.02348e8i		−	0.542050i	0.962572	−	0.271025i	$-0.0873627\pi$
$140$	−6.77147e7	+	6.16508e7i	−0.176267	+	0.160482i
$141$		0			0
$142$	−1.61000e7	+	3.64314e7i	−0.0395979	+	0.0896031i
$143$			1.30856e8i			0.312931i
$144$		0			0
$145$	2.37980e8			0.538354
$146$	−1.96511e8	−	8.68435e7i	−0.432490	−	0.191129i
$147$		0			0
$148$	−4.78073e8	−	5.25097e8i	−0.996432	−	1.09444i
$149$	2.20219e8			0.446797			0.223398	−	0.974727i	$-0.428285\pi$
$149$	2.20219e8			0.446797			0.223398	+	0.974727i	$0.428285\pi$
$150$		0			0
$151$			3.07054e8i			0.590618i	0.955402	+	0.295309i	$0.0954225\pi$
$151$			3.07054e8i			0.590618i	−0.955402	+	0.295309i	$0.904577\pi$
$152$	−1.94288e8	+	6.49113e7i	−0.363976	+	0.121603i
$153$		0			0
$154$	7.33975e7	+	3.24363e7i	0.130496	+	0.0576698i
$155$		−	1.72502e8i		−	0.298860i
$156$		0			0
$157$	6.79416e8			1.11824			0.559122	−	0.829085i	$-0.311138\pi$
$157$	6.79416e8			1.11824			0.559122	+	0.829085i	$0.311138\pi$
$158$	−2.75775e6	+	6.24031e6i	−0.00442514	+	0.0100133i
$159$		0			0
$160$	1.43027e8	−	2.55818e8i	0.218241	−	0.390347i
$161$	6.64899e8			0.989583
$162$		0			0
$163$		−	2.29685e8i		−	0.325373i	−0.986678	−	0.162687i	$-0.947984\pi$
$163$		−	2.29685e8i		−	0.325373i	0.986678	−	0.162687i	$-0.0520160\pi$
$164$	−1.84975e8	−	2.03169e8i	−0.255704	−	0.280855i
$165$		0			0
$166$	−4.78074e8	+	1.08180e9i	−0.629597	+	1.42467i
$167$		−	1.19746e9i		−	1.53956i	−0.638309	−	0.769780i	$-0.720366\pi$
$167$		−	1.19746e9i		−	1.53956i	0.638309	−	0.769780i	$-0.279634\pi$
$168$		0			0
$169$	2.99272e8			0.366876
$170$	3.31479e8	+	1.46489e8i	0.396881	+	0.175392i
$171$		0			0
$172$	−1.18116e9	+	1.07539e9i	−1.34957	+	1.22872i
$173$	−5.29600e8			−0.591240			−0.295620	−	0.955306i	$-0.595526\pi$
$173$	−5.29600e8			−0.591240			−0.295620	+	0.955306i	$0.595526\pi$
$174$		0			0
$175$			9.99851e7i			0.106606i
$176$	−2.55697e8	−	2.40243e7i	−0.266487	−	0.0250380i
$177$		0			0
$178$	−7.38585e8	−	3.26400e8i	−0.735733	−	0.325140i
$179$		−	3.30454e8i		−	0.321884i	−0.986964	−	0.160942i	$-0.948547\pi$
$179$		−	3.30454e8i		−	0.321884i	0.986964	−	0.160942i	$-0.0514531\pi$
$180$		0			0
$181$	6.27215e8			0.584389			0.292195	−	0.956359i	$-0.405615\pi$
$181$	6.27215e8			0.584389			0.292195	+	0.956359i	$0.405615\pi$
$182$	2.76385e8	−	6.25410e8i	0.251900	−	0.570006i
$183$		0			0
$184$	−2.01833e9	+	6.74320e8i	−1.76084	+	0.588294i
$185$	−7.75338e8			−0.661918
$186$		0			0
$187$		−	3.17566e8i		−	0.259697i
$188$	7.22874e8	−	6.58139e8i	0.578670	−	0.526849i
$189$		0			0
$190$	−9.04048e7	+	2.04570e8i	−0.0693709	+	0.156974i
$191$			1.72241e9i			1.29420i	0.762404	+	0.647102i	$0.224019\pi$
$191$			1.72241e9i			1.29420i	−0.762404	+	0.647102i	$0.775981\pi$
$192$		0			0
$193$	1.52665e9			1.10030			0.550149	−	0.835066i	$-0.314571\pi$
$193$	1.52665e9			1.10030			0.550149	+	0.835066i	$0.314571\pi$
$194$	−7.79473e8	−	3.44469e8i	−0.550293	−	0.243189i
$195$		0			0
$196$	7.11248e8	+	7.81207e8i	0.481944	+	0.529349i
$197$	−4.12733e8			−0.274034			−0.137017	−	0.990569i	$-0.543751\pi$
$197$	−4.12733e8			−0.274034			−0.137017	+	0.990569i	$0.543751\pi$
$198$		0			0
$199$			7.19579e8i			0.458845i	0.973327	+	0.229423i	$0.0736838\pi$
$199$			7.19579e8i			0.458845i	−0.973327	+	0.229423i	$0.926316\pi$
$200$	−1.01402e8	−	3.03509e8i	−0.0633761	−	0.189693i
$201$		0			0
$202$	5.98088e8	+	2.64310e8i	0.359219	+	0.158748i
$203$			1.08966e9i			0.641662i
$204$		0			0
$205$	−2.99992e8			−0.169861
$206$	−1.41083e9	+	3.19246e9i	−0.783440	+	1.77278i
$207$		0			0
$208$	−2.04707e8	+	2.17876e9i	−0.109365	+	1.16401i
$209$	1.95984e8			0.102715
$210$		0			0
$211$			1.87773e8i			0.0947333i	0.998878	+	0.0473666i	$0.0150829\pi$
$211$			1.87773e8i			0.0947333i	−0.998878	+	0.0473666i	$0.984917\pi$
$212$	1.35873e9	+	1.49237e9i	0.672651	+	0.738813i
$213$		0			0
$214$	−9.12965e8	+	2.06588e9i	−0.435310	+	0.985030i
$215$			1.74406e9i			0.816222i
$216$		0			0
$217$	7.89851e8			0.356210
$218$	−6.33850e8	−	2.80115e8i	−0.280647	−	0.124025i
$219$		0			0
$220$	−2.07345e8	+	1.88777e8i	−0.0885120	+	0.0805856i
$221$	−2.70593e9			−1.13435
$222$		0			0
$223$		−	3.73114e9i		−	1.50877i	−0.656435	−	0.754383i	$-0.727936\pi$
$223$		−	3.73114e9i		−	1.50877i	0.656435	−	0.754383i	$-0.272064\pi$
$224$	1.17133e9	+	6.54889e8i	0.465252	+	0.260121i
$225$		0			0
$226$	−3.58832e9	−	1.58577e9i	−1.37549	−	0.607865i
$227$		−	1.52473e9i		−	0.574234i	−0.957895	−	0.287117i	$-0.907303\pi$
$227$		−	1.52473e9i		−	0.574234i	0.957895	−	0.287117i	$-0.0926969\pi$
$228$		0			0
$229$	4.21607e9			1.53308			0.766541	−	0.642195i	$-0.221976\pi$
$229$	4.21607e9			1.53308			0.766541	+	0.642195i	$0.221976\pi$
$230$	−9.39155e8	+	2.12514e9i	−0.335603	+	0.759410i
$231$		0			0
$232$	−1.10510e9	−	3.30771e9i	−0.381460	−	1.14176i
$233$	−2.82357e9			−0.958022			−0.479011	−	0.877809i	$-0.659005\pi$
$233$	−2.82357e9			−0.958022			−0.479011	+	0.877809i	$0.659005\pi$
$234$		0			0
$235$		−	1.06737e9i		−	0.349980i
$236$	−1.20446e9	+	1.09660e9i	−0.388278	+	0.353507i
$237$		0			0
$238$	−6.70742e8	+	1.51777e9i	−0.209049	+	0.473040i
$239$			4.33879e9i			1.32977i	0.746946	+	0.664885i	$0.231520\pi$
$239$			4.33879e9i			1.32977i	−0.746946	+	0.664885i	$0.768480\pi$
$240$		0			0
$241$	5.45496e9			1.61705			0.808526	−	0.588461i	$-0.200266\pi$
$241$	5.45496e9			1.61705			0.808526	+	0.588461i	$0.200266\pi$
$242$	−2.91232e9	−	1.28703e9i	−0.849136	−	0.375255i
$243$		0			0
$244$	−1.31903e9	−	1.44877e9i	−0.372130	−	0.408732i
$245$	1.15350e9			0.320150
$246$		0			0
$247$		−	1.66995e9i		−	0.448658i
$248$	−2.39763e9	+	8.01042e8i	−0.633833	+	0.211762i
$249$		0			0
$250$	−3.19571e8	−	1.41227e8i	−0.0818101	−	0.0361540i
$251$			6.01395e9i			1.51518i	0.652729	+	0.757591i	$0.273624\pi$
$251$			6.01395e9i			1.51518i	−0.652729	+	0.757591i	$0.726376\pi$
$252$		0			0
$253$	2.03594e9			0.496916
$254$	−4.35637e8	+	9.85770e8i	−0.104662	+	0.236832i
$255$		0			0
$256$	−4.21980e9	−	8.00013e8i	−0.982499	−	0.186267i
$257$	1.93062e8			0.0442552			0.0221276	−	0.999755i	$-0.492956\pi$
$257$	1.93062e8			0.0442552			0.0221276	+	0.999755i	$0.492956\pi$
$258$		0			0
$259$		−	3.55011e9i		−	0.788937i
$260$	1.60854e9	+	1.76675e9i	0.351996	+	0.386619i
$261$		0			0
$262$	−3.82596e8	+	8.65746e8i	−0.0811960	+	0.183732i
$263$		−	3.41514e9i		−	0.713814i	−0.934140	−	0.356907i	$-0.883831\pi$
$263$		−	3.41514e9i		−	0.713814i	0.934140	−	0.356907i	$-0.116169\pi$
$264$		0			0
$265$	2.20358e9			0.446834
$266$	−9.36682e8	−	4.13944e8i	−0.187096	−	0.0826828i
$267$		0			0
$268$	−4.18535e9	+	3.81055e9i	−0.811321	+	0.738666i
$269$	−1.38303e9			−0.264133			−0.132067	−	0.991241i	$-0.542161\pi$
$269$	−1.38303e9			−0.264133			−0.132067	+	0.991241i	$0.542161\pi$
$270$		0			0
$271$		−	9.60020e9i		−	1.77993i	−0.456028	−	0.889965i	$-0.650728\pi$
$271$		−	9.60020e9i		−	1.77993i	0.456028	−	0.889965i	$-0.349272\pi$
$272$	4.96792e8	−	5.28750e9i	0.0907609	−	0.965995i
$273$		0			0
$274$	−3.26302e9	−	1.44201e9i	−0.578918	−	0.255839i
$275$			3.06157e8i			0.0535320i
$276$		0			0
$277$	1.11200e10			1.88880			0.944399	−	0.328801i	$-0.106645\pi$
$277$	1.11200e10			1.88880			0.944399	+	0.328801i	$0.106645\pi$
$278$	−1.30867e9	+	2.96129e9i	−0.219104	+	0.495794i
$279$		0			0
$280$	1.38970e9	−	4.64296e8i	0.226094	−	0.0755376i
$281$	−6.81089e9			−1.09239			−0.546196	−	0.837657i	$-0.683925\pi$
$281$	−6.81089e9			−1.09239			−0.546196	+	0.837657i	$0.683925\pi$
$282$		0			0
$283$			1.07587e10i			1.67732i	0.544657	+	0.838659i	$0.316660\pi$
$283$			1.07587e10i			1.67732i	−0.544657	+	0.838659i	$0.683340\pi$
$284$	4.71235e8	−	4.29035e8i	0.0724376	−	0.0659507i
$285$		0			0
$286$	8.46299e8	−	1.91502e9i	0.126491	−	0.286227i
$287$		−	1.37360e9i		−	0.202456i
$288$		0			0
$289$	−4.08894e8			−0.0586164
$290$	−3.48275e9	−	1.53912e9i	−0.492414	−	0.217610i
$291$		0			0
$292$	2.31422e9	+	2.54185e9i	0.318327	+	0.349637i
$293$	1.10554e10			1.50004			0.750022	−	0.661413i	$-0.230043\pi$
$293$	1.10554e10			1.50004			0.750022	+	0.661413i	$0.230043\pi$
$294$		0			0
$295$			1.77846e9i			0.234831i
$296$	3.60040e9	+	1.07765e10i	0.469013	+	1.40382i
$297$		0			0
$298$	−3.22283e9	−	1.42425e9i	−0.408669	−	0.180601i
$299$		−	1.73480e10i		−	2.17052i
$300$		0			0
$301$	−7.98569e9			−0.972851
$302$	1.98585e9	−	4.49362e9i	0.238736	−	0.540217i
$303$		0			0
$304$	3.26315e9	+	3.06592e8i	0.382069	+	0.0358977i
$305$	−2.13920e9			−0.247201
$306$		0			0
$307$		−	1.65673e10i		−	1.86508i	−0.361066	−	0.932540i	$-0.617587\pi$
$307$		−	1.65673e10i		−	1.86508i	0.361066	−	0.932540i	$-0.382413\pi$
$308$	−8.64367e8	−	9.49386e8i	−0.0960495	−	0.105497i
$309$		0			0
$310$	−1.11565e9	+	2.52451e9i	−0.120804	+	0.273357i
$311$			1.08723e10i			1.16220i	0.813833	+	0.581099i	$0.197377\pi$
$311$			1.08723e10i			1.16220i	−0.813833	+	0.581099i	$0.802623\pi$
$312$		0			0
$313$	6.57086e9			0.684613			0.342307	−	0.939588i	$-0.388792\pi$
$313$	6.57086e9			0.684613			0.342307	+	0.939588i	$0.388792\pi$
$314$	−9.94300e9	−	4.39407e9i	−1.02282	−	0.452010i
$315$		0			0
$316$	8.07174e7	−	7.34891e7i	0.00809504	−	0.00737012i
$317$	2.30028e9			0.227795			0.113897	−	0.993493i	$-0.463667\pi$
$317$	2.30028e9			0.227795			0.113897	+	0.993493i	$0.463667\pi$
$318$		0			0
$319$			3.33657e9i			0.322209i
$320$	−3.74763e9	+	2.81878e9i	−0.357401	+	0.268820i
$321$		0			0
$322$	−9.73056e9	−	4.30019e9i	−0.905137	−	0.400003i
$323$			4.05270e9i			0.372335i
$324$		0			0
$325$	2.60872e9			0.233827
$326$	−1.48547e9	+	3.36135e9i	−0.131520	+	0.297608i
$327$		0			0
$328$	1.39306e9	+	4.16961e9i	0.120358	+	0.360247i
$329$	4.88725e9			0.417139
$330$		0			0
$331$		−	4.15455e9i		−	0.346108i	−0.984912	−	0.173054i	$-0.944636\pi$
$331$		−	4.15455e9i		−	0.346108i	0.984912	−	0.173054i	$-0.0553636\pi$
$332$	1.39929e10	−	1.27398e10i	1.15174	−	1.04860i
$333$		0			0
$334$	−7.74451e9	+	1.75244e10i	−0.622312	+	1.40818i
$335$			6.17993e9i			0.490687i
$336$		0			0
$337$	7.45299e9			0.577844			0.288922	−	0.957353i	$-0.406703\pi$
$337$	7.45299e9			0.577844			0.288922	+	0.957353i	$0.406703\pi$
$338$	−4.37974e9	−	1.93552e9i	−0.335569	−	0.148297i
$339$		0			0
$340$	−3.90366e9	−	4.28763e9i	−0.292117	−	0.320850i
$341$	2.41855e9			0.178870
$342$		0			0
$343$			1.26595e10i			0.914617i
$344$	2.42409e10	−	8.09883e9i	1.73107	−	0.578347i
$345$		0			0
$346$	7.75050e9	+	3.42515e9i	0.540786	+	0.238987i
$347$		−	1.43423e10i		−	0.989238i	−0.869110	−	0.494619i	$-0.835308\pi$
$347$		−	1.43423e10i		−	0.989238i	0.869110	−	0.494619i	$-0.164692\pi$
$348$		0			0
$349$	−1.53420e10			−1.03414			−0.517071	−	0.855943i	$-0.672978\pi$
$349$	−1.53420e10			−1.03414			−0.517071	+	0.855943i	$0.672978\pi$
$350$	6.46646e8	−	1.46324e9i	0.0430918	−	0.0975090i
$351$		0			0
$352$	3.58666e9	+	2.00529e9i	0.233625	+	0.130619i
$353$	−1.05428e10			−0.678978			−0.339489	−	0.940610i	$-0.610254\pi$
$353$	−1.05428e10			−0.678978			−0.339489	+	0.940610i	$0.610254\pi$
$354$		0			0
$355$		−	6.95808e8i		−	0.0438103i
$356$	8.69795e9	+	9.55348e9i	0.541523	+	0.594787i
$357$		0			0
$358$	−2.13719e9	+	4.83607e9i	−0.130110	+	0.294415i
$359$		−	4.69543e9i		−	0.282681i	−0.989961	−	0.141341i	$-0.954859\pi$
$359$		−	4.69543e9i		−	0.282681i	0.989961	−	0.141341i	$-0.0451413\pi$
$360$		0			0
$361$	1.44825e10			0.852734
$362$	−9.17906e9	−	4.05646e9i	−0.534520	−	0.236218i
$363$		0			0
$364$	−8.08959e9	+	7.36515e9i	−0.460809	+	0.419543i
$365$	3.75319e9			0.211461
$366$		0			0
$367$			4.20349e9i			0.231711i	0.993266	+	0.115855i	$0.0369609\pi$
$367$			4.20349e9i			0.231711i	−0.993266	+	0.115855i	$0.963039\pi$
$368$	3.38986e10	+	3.18498e9i	1.84838	+	0.173666i
$369$		0			0
$370$	1.13468e10	+	5.01444e9i	0.605433	+	0.267557i
$371$			1.00897e10i			0.532579i
$372$		0			0
$373$	−2.03230e10			−1.04991			−0.524956	−	0.851130i	$-0.675918\pi$
$373$	−2.03230e10			−1.04991			−0.524956	+	0.851130i	$0.675918\pi$
$374$	−2.05383e9	+	4.64746e9i	−0.104973	+	0.237536i
$375$		0			0
$376$	−1.48355e10	+	4.95649e9i	−0.742249	+	0.247984i
$377$	2.84304e10			1.40740
$378$		0			0
$379$			2.99459e10i			1.45138i	0.688024	+	0.725688i	$0.258478\pi$
$379$			2.99459e10i			1.45138i	−0.688024	+	0.725688i	$0.741522\pi$
$380$	2.64608e9	−	2.40912e9i	0.126902	−	0.115538i
$381$		0			0
$382$	1.11395e10	−	2.52068e10i	0.523135	−	1.18376i
$383$		−	2.45977e10i		−	1.14314i	−0.820554	−	0.571569i	$-0.806335\pi$
$383$		−	2.45977e10i		−	1.14314i	0.820554	−	0.571569i	$-0.193665\pi$
$384$		0			0
$385$	−1.40183e9			−0.0638046
$386$	−2.23420e10	−	9.87350e9i	−1.00640	−	0.444756i
$387$		0			0
$388$	9.17947e9	+	1.00824e10i	0.405033	+	0.444872i
$389$	2.48604e9			0.108570			0.0542851	−	0.998525i	$-0.482712\pi$
$389$	2.48604e9			0.108570			0.0542851	+	0.998525i	$0.482712\pi$
$390$		0			0
$391$			4.21007e10i			1.80129i
$392$	−5.35646e9	−	1.60326e10i	−0.226847	−	0.678985i
$393$		0			0
$394$	6.04019e9	+	2.66932e9i	0.250649	+	0.110768i
$395$		−	1.19184e8i		−	0.00489588i
$396$		0			0
$397$	−2.18098e10			−0.877992			−0.438996	−	0.898489i	$-0.644666\pi$
$397$	−2.18098e10			−0.877992			−0.438996	+	0.898489i	$0.644666\pi$
$398$	4.65382e9	−	1.05308e10i	0.185472	−	0.419690i
$399$		0			0
$400$	−4.78945e8	+	5.09755e9i	−0.0187088	+	0.199123i
$401$	1.42753e10			0.552088			0.276044	−	0.961145i	$-0.410976\pi$
$401$	1.42753e10			0.552088			0.276044	+	0.961145i	$0.410976\pi$
$402$		0			0
$403$		−	2.06081e10i		−	0.781300i
$404$	−7.04338e9	−	7.73617e9i	−0.264397	−	0.290403i
$405$		0			0
$406$	7.04728e9	−	1.59467e10i	0.259369	−	0.586905i
$407$		−	1.08705e10i		−	0.396162i
$408$		0			0
$409$	−2.26795e10			−0.810474			−0.405237	−	0.914212i	$-0.632811\pi$
$409$	−2.26795e10			−0.810474			−0.405237	+	0.914212i	$0.632811\pi$
$410$	4.39027e9	+	1.94017e9i	0.155366	+	0.0686602i
$411$		0			0
$412$	4.12939e10	−	3.75960e10i	1.43317	−	1.30483i
$413$	−8.14317e9			−0.279894
$414$		0			0
$415$		−	2.06613e10i		−	0.696572i
$416$	1.70868e10	−	3.05614e10i	0.570541	−	1.02047i
$417$		0			0
$418$	−2.86815e9	−	1.26751e9i	−0.0939499	−	0.0415189i
$419$		−	3.50541e10i		−	1.13732i	−0.822572	−	0.568661i	$-0.807462\pi$
$419$		−	3.50541e10i		−	1.13732i	0.822572	−	0.568661i	$-0.192538\pi$
$420$		0			0
$421$	−1.90869e10			−0.607586			−0.303793	−	0.952738i	$-0.598253\pi$
$421$	−1.90869e10			−0.607586			−0.303793	+	0.952738i	$0.598253\pi$
$422$	1.21441e9	−	2.74798e9i	0.0382925	−	0.0866491i
$423$		0			0
$424$	−1.02327e10	−	3.06278e10i	−0.316611	−	0.947660i
$425$	−6.33095e9			−0.194050
$426$		0			0
$427$		−	9.79491e9i		−	0.294638i
$428$	2.67218e10	−	2.43288e10i	0.796326	−	0.725013i
$429$		0			0
$430$	1.12796e10	−	2.55237e10i	0.329928	−	0.746569i
$431$		−	4.67409e10i		−	1.35453i	−0.735740	−	0.677264i	$-0.763166\pi$
$431$		−	4.67409e10i		−	1.35453i	0.735740	−	0.677264i	$-0.236834\pi$
$432$		0			0
$433$	−2.73439e10			−0.777873			−0.388937	−	0.921265i	$-0.627157\pi$
$433$	−2.73439e10			−0.777873			−0.388937	+	0.921265i	$0.627157\pi$
$434$	−1.15592e10	−	5.10830e9i	−0.325813	−	0.143985i
$435$		0			0
$436$	7.46454e9	+	8.19875e9i	0.206565	+	0.226883i
$437$	−2.59822e10			−0.712443
$438$		0			0
$439$		−	1.20747e10i		−	0.325100i	−0.986700	−	0.162550i	$-0.948028\pi$
$439$		−	1.20747e10i		−	0.325100i	0.986700	−	0.162550i	$-0.0519719\pi$
$440$	4.25531e9	−	1.42169e9i	0.113533	−	0.0379310i
$441$		0			0
$442$	3.96003e10	+	1.75004e10i	1.03755	+	0.458521i
$443$			3.74276e10i			0.971801i	0.874014	+	0.485900i	$0.161508\pi$
$443$			3.74276e10i			0.971801i	−0.874014	+	0.485900i	$0.838492\pi$
$444$		0			0
$445$	1.41063e10			0.359728
$446$	−2.41308e10	+	5.46038e10i	−0.609864	+	1.38001i
$447$		0			0
$448$	−1.29066e10	−	1.71596e10i	−0.320405	−	0.425985i
$449$	4.43873e10			1.09213			0.546063	−	0.837744i	$-0.316126\pi$
$449$	4.43873e10			1.09213			0.546063	+	0.837744i	$0.316126\pi$
$450$		0			0
$451$		−	4.20599e9i		−	0.101663i
$452$	4.22579e10	+	4.64144e10i	1.01240	+	1.11198i
$453$		0			0
$454$	−9.86107e9	+	2.23138e10i	−0.232114	+	0.525232i
$455$			1.19448e10i			0.278697i
$456$		0			0
$457$	4.57924e10			1.04985			0.524926	−	0.851148i	$-0.324093\pi$
$457$	4.57924e10			1.04985			0.524926	+	0.851148i	$0.324093\pi$
$458$	−6.17006e10	−	2.72671e10i	−1.40226	−	0.619693i
$459$		0			0
$460$	2.74884e10	−	2.50267e10i	0.613928	−	0.558950i
$461$	6.96170e9			0.154139			0.0770693	−	0.997026i	$-0.475444\pi$
$461$	6.96170e9			0.154139			0.0770693	+	0.997026i	$0.475444\pi$
$462$		0			0
$463$			2.79510e9i			0.0608237i	0.999537	+	0.0304118i	$0.00968188\pi$
$463$			2.79510e9i			0.0608237i	−0.999537	+	0.0304118i	$0.990318\pi$
$464$	−5.21964e9	+	5.55542e10i	−0.112608	+	1.19852i
$465$		0			0
$466$	4.13220e10	+	1.82612e10i	0.876269	+	0.387246i
$467$			2.10272e10i			0.442094i	0.975263	+	0.221047i	$0.0709474\pi$
$467$			2.10272e10i			0.442094i	−0.975263	+	0.221047i	$0.929053\pi$
$468$		0			0
$469$	−2.82966e10			−0.584847
$470$	−6.90312e9	+	1.56205e10i	−0.141467	+	0.320114i
$471$		0			0
$472$	2.47189e10	−	8.25854e9i	0.498037	−	0.166393i
$473$	−2.44524e10			−0.488514
$474$		0			0
$475$		−	3.90711e9i		−	0.0767504i
$476$	1.96321e10	−	1.78740e10i	0.382419	−	0.348173i
$477$		0			0
$478$	2.80608e10	−	6.34965e10i	0.537512	−	1.21629i
$479$			1.01174e11i			1.92188i	0.276749	+	0.960942i	$0.410743\pi$
$479$			1.01174e11i			1.92188i	−0.276749	+	0.960942i	$0.589257\pi$
$480$		0			0
$481$	−9.26263e10			−1.73043
$482$	−7.98314e10	−	3.52796e10i	−1.47906	−	0.653635i
$483$		0			0
$484$	3.42969e10	+	3.76704e10i	0.624991	+	0.686465i
$485$	1.48872e10			0.269059
$486$		0			0
$487$		−	6.69576e10i		−	1.19038i	−0.803587	−	0.595188i	$-0.797078\pi$
$487$		−	6.69576e10i		−	1.19038i	0.803587	−	0.595188i	$-0.202922\pi$
$488$	9.93369e9	+	2.97329e10i	0.175159	+	0.524273i
$489$		0			0
$490$	−1.68811e10	−	7.46018e9i	−0.292830	−	0.129409i
$491$			4.99684e10i			0.859745i	0.902890	+	0.429873i	$0.141442\pi$
$491$			4.99684e10i			0.859745i	−0.902890	+	0.429873i	$0.858558\pi$
$492$		0			0
$493$	−6.89961e10			−1.16798
$494$	−1.08003e10	+	2.44391e10i	−0.181354	+	0.410372i
$495$		0			0
$496$	4.02691e10	+	3.78352e9i	0.665342	+	0.0625128i
$497$	3.18595e9			0.0522173
$498$		0			0
$499$			1.20214e11i			1.93889i	0.245317	+	0.969443i	$0.421108\pi$
$499$			1.20214e11i			1.93889i	−0.245317	+	0.969443i	$0.578892\pi$
$500$	3.76343e9	+	4.13360e9i	0.0602148	+	0.0661376i
$501$		0			0
$502$	3.88948e10	−	8.80119e10i	0.612458	−	1.38588i
$503$		−	2.09154e10i		−	0.326734i	−0.986565	−	0.163367i	$-0.947765\pi$
$503$		−	2.09154e10i		−	0.326734i	0.986565	−	0.163367i	$-0.0522354\pi$
$504$		0			0
$505$	−1.14229e10			−0.175636
$506$	−2.97953e10	−	1.31673e10i	−0.454512	−	0.200861i
$507$		0			0
$508$	1.27508e10	−	1.16089e10i	0.191462	−	0.174316i
$509$	−1.68591e10			−0.251167			−0.125584	−	0.992083i	$-0.540080\pi$
$509$	−1.68591e10			−0.251167			−0.125584	+	0.992083i	$0.540080\pi$
$510$		0			0
$511$			1.71851e10i			0.252039i
$512$	5.65812e10	+	3.89991e10i	0.823365	+	0.567512i
$513$		0			0
$514$	−2.82539e9	−	1.24861e9i	−0.0404787	−	0.0178886i
$515$		−	6.09731e10i		−	0.866781i
$516$		0			0
$517$	1.49649e10			0.209465
$518$	−2.29600e10	+	5.19545e10i	−0.318899	+	0.721613i
$519$		0			0
$520$	−1.21140e10	−	3.62589e10i	−0.165682	−	0.495908i
$521$	−1.13266e11			−1.53726			−0.768630	−	0.639693i	$-0.779061\pi$
$521$	−1.13266e11			−1.53726			−0.768630	+	0.639693i	$0.779061\pi$
$522$		0			0
$523$			6.37613e10i			0.852218i	0.904672	+	0.426109i	$0.140116\pi$
$523$			6.37613e10i			0.852218i	−0.904672	+	0.426109i	$0.859884\pi$
$524$	1.11983e10	−	1.01955e10i	0.148534	−	0.135233i
$525$		0			0
$526$	−2.20871e10	+	4.99793e10i	−0.288534	+	0.652900i
$527$			5.00126e10i			0.648391i
$528$		0			0
$529$	−1.91601e11			−2.44666
$530$	−3.22486e10	−	1.42515e10i	−0.408703	−	0.180617i
$531$		0			0
$532$	1.10308e10	+	1.21158e10i	0.137709	+	0.151254i
$533$	−3.58387e10			−0.444062
$534$		0			0
$535$		−	3.94564e10i		−	0.481618i
$536$	8.58955e10	−	2.86975e10i	1.04067	−	0.347684i
$537$		0			0
$538$	2.02402e10	+	8.94465e9i	0.241593	+	0.106766i
$539$			1.61725e10i			0.191612i
$540$		0			0
$541$	1.34348e9			0.0156835			0.00784176	−	0.999969i	$-0.497504\pi$
$541$	1.34348e9			0.0156835			0.00784176	+	0.999969i	$0.497504\pi$
$542$	−6.20886e10	+	1.40495e11i	−0.719473	+	1.62804i
$543$		0			0
$544$	−4.14669e10	+	7.41677e10i	−0.473484	+	0.846874i
$545$	1.21060e10			0.137219
$546$		0			0
$547$		−	2.97384e10i		−	0.332176i	−0.986111	−	0.166088i	$-0.946886\pi$
$547$		−	2.97384e10i		−	0.332176i	0.986111	−	0.166088i	$-0.0531135\pi$
$548$	3.84270e10	+	4.22066e10i	0.426102	+	0.468014i
$549$		0			0
$550$	1.98005e9	−	4.48050e9i	0.0216384	−	0.0489639i
$551$		−	4.25805e10i		−	0.461960i
$552$		0			0
$553$	5.45720e8			0.00583538
$554$	−1.62737e11	−	7.19177e10i	−1.72762	−	0.763479i
$555$		0			0
$556$	3.83038e10	−	3.48736e10i	0.400814	−	0.364920i
$557$	−1.67715e11			−1.74241			−0.871207	−	0.490917i	$-0.836662\pi$
$557$	−1.67715e11			−1.74241			−0.871207	+	0.490917i	$0.836662\pi$
$558$		0			0
$559$			2.08356e11i			2.13382i
$560$	−2.33406e10	−	2.19298e9i	−0.237334	−	0.0222989i
$561$		0			0
$562$	9.96749e10	+	4.40489e10i	0.999173	+	0.441560i
$563$			1.43083e11i			1.42415i	0.702105	+	0.712074i	$0.252244\pi$
$563$			1.43083e11i			1.42415i	−0.702105	+	0.712074i	$0.747756\pi$
$564$		0			0
$565$	6.85338e10			0.672529
$566$	6.95813e10	−	1.57450e11i	0.677996	−	1.53418i
$567$		0			0
$568$	−9.67110e9	+	3.23109e9i	−0.0929143	+	0.0310425i
$569$	−6.35929e10			−0.606680			−0.303340	−	0.952882i	$-0.598102\pi$
$569$	−6.35929e10			−0.606680			−0.303340	+	0.952882i	$0.598102\pi$
$570$		0			0
$571$			9.56419e10i			0.899712i	0.893101	+	0.449856i	$0.148525\pi$
$571$			9.56419e10i			0.899712i	−0.893101	+	0.449856i	$0.851475\pi$
$572$	−2.47706e10	+	2.25523e10i	−0.231394	+	0.210672i
$573$		0			0
$574$	−8.88363e9	+	2.01021e10i	−0.0818357	+	0.185180i
$575$		−	4.05883e10i		−	0.371304i
$576$		0			0
$577$	1.18749e11			1.07134			0.535670	−	0.844427i	$-0.320059\pi$
$577$	1.18749e11			1.07134			0.535670	+	0.844427i	$0.320059\pi$
$578$	5.98401e9	+	2.64449e9i	0.0536143	+	0.0236936i
$579$		0			0
$580$	4.10146e10	+	4.50488e10i	0.362432	+	0.398081i
$581$	9.46038e10			0.830241
$582$		0			0
$583$			3.08951e10i			0.267433i
$584$	−1.74285e10	−	5.21660e10i	−0.149834	−	0.448473i
$585$		0			0
$586$	−1.61792e11	−	7.14999e10i	−1.37204	−	0.606339i
$587$			1.11850e11i			0.942069i	0.882115	+	0.471034i	$0.156119\pi$
$587$			1.11850e11i			0.942069i	−0.882115	+	0.471034i	$0.843881\pi$
$588$		0			0
$589$	−3.08649e10			−0.256451
$590$	1.15020e10	−	2.60271e10i	0.0949219	−	0.214791i
$591$		0			0
$592$	1.70056e10	−	1.80995e11i	0.138454	−	1.47360i
$593$	1.05296e11			0.851516			0.425758	−	0.904837i	$-0.360007\pi$
$593$	1.05296e11			0.851516			0.425758	+	0.904837i	$0.360007\pi$
$594$		0			0
$595$		−	2.89881e10i		−	0.231287i
$596$	3.79536e10	+	4.16867e10i	0.300793	+	0.330379i
$597$		0			0
$598$	−1.12197e11	+	2.53881e11i	−0.877355	+	1.98530i
$599$		−	9.40591e10i		−	0.730623i	−0.930885	−	0.365312i	$-0.880962\pi$
$599$		−	9.40591e10i		−	0.730623i	0.930885	−	0.365312i	$-0.119038\pi$
$600$		0			0
$601$	4.09050e10			0.313529			0.156765	−	0.987636i	$-0.449894\pi$
$601$	4.09050e10			0.313529			0.156765	+	0.987636i	$0.449894\pi$
$602$	1.16868e11	+	5.16468e10i	0.889832	+	0.393240i
$603$		0			0
$604$	−5.81242e10	+	5.29191e10i	−0.436726	+	0.397617i
$605$	5.56227e10			0.415174
$606$		0			0
$607$		−	6.17741e10i		−	0.455043i	−0.973773	−	0.227521i	$-0.926938\pi$
$607$		−	6.17741e10i		−	0.455043i	0.973773	−	0.227521i	$-0.0730621\pi$
$608$	−4.57721e10	−	2.55910e10i	−0.334955	−	0.187272i
$609$		0			0
$610$	3.13063e10	+	1.38351e10i	0.226106	+	0.0999223i
$611$		−	1.27514e11i		−	0.914940i
$612$		0			0
$613$	−2.30900e11			−1.63524			−0.817620	−	0.575758i	$-0.804707\pi$
$613$	−2.30900e11			−1.63524			−0.817620	+	0.575758i	$0.804707\pi$
$614$	−1.07148e11	+	2.42456e11i	−0.753891	+	1.70592i
$615$		0			0
$616$	6.50961e9	+	1.94841e10i	0.0452097	+	0.135319i
$617$	−4.96773e10			−0.342781			−0.171391	−	0.985203i	$-0.554826\pi$
$617$	−4.96773e10			−0.342781			−0.171391	+	0.985203i	$0.554826\pi$
$618$		0			0
$619$		−	1.90142e11i		−	1.29514i	−0.762008	−	0.647568i	$-0.775786\pi$
$619$		−	1.90142e11i		−	1.29514i	0.762008	−	0.647568i	$-0.224214\pi$
$620$	3.26541e10	−	2.97299e10i	0.220989	−	0.201199i
$621$		0			0
$622$	7.03158e10	−	1.59112e11i	0.469777	−	1.06302i
$623$			6.45898e10i			0.428757i
$624$		0			0
$625$	6.10352e9			0.0400000
$626$	−9.61622e10	−	4.24966e10i	−0.626191	−	0.276730i
$627$		0			0
$628$	1.17094e11	+	1.28611e11i	0.752827	+	0.826875i
$629$	2.24789e11			1.43606
$630$		0			0
$631$		−	5.46424e10i		−	0.344677i	−0.985038	−	0.172339i	$-0.944868\pi$
$631$		−	5.46424e10i		−	0.344677i	0.985038	−	0.172339i	$-0.0551323\pi$
$632$	−1.65655e9	+	5.53451e8i	−0.0103834	+	0.00346906i
$633$		0			0
$634$	−3.36637e10	−	1.48769e10i	−0.208356	−	0.0920778i
$635$		−	1.88273e10i		−	0.115796i
$636$		0			0
$637$	1.37804e11			0.836957
$638$	2.15790e10	−	4.88294e10i	0.130241	−	0.294713i
$639$		0			0
$640$	7.30754e10	−	1.70144e10i	0.435563	−	0.101414i
$641$	−1.04680e11			−0.620055			−0.310028	−	0.950728i	$-0.600338\pi$
$641$	−1.04680e11			−0.620055			−0.310028	+	0.950728i	$0.600338\pi$
$642$		0			0
$643$			1.54907e11i			0.906208i	0.891458	+	0.453104i	$0.149683\pi$
$643$			1.54907e11i			0.906208i	−0.891458	+	0.453104i	$0.850317\pi$
$644$	1.14592e11	+	1.25863e11i	0.666209	+	0.731738i
$645$		0			0
$646$	2.62105e10	−	5.93097e10i	0.150503	−	0.340562i
$647$			2.90218e10i			0.165618i	0.996565	+	0.0828088i	$0.0263891\pi$
$647$			2.90218e10i			0.165618i	−0.996565	+	0.0828088i	$0.973611\pi$
$648$		0			0
$649$	−2.49346e10			−0.140548
$650$	−3.81777e10	−	1.68717e10i	−0.213873	−	0.0945161i
$651$		0			0
$652$	4.34786e10	−	3.95850e10i	0.240594	−	0.219049i
$653$	−3.00413e11			−1.65221			−0.826106	−	0.563515i	$-0.809449\pi$
$653$	−3.00413e11			−1.65221			−0.826106	+	0.563515i	$0.809449\pi$
$654$		0			0
$655$		−	1.65350e10i		−	0.0898335i
$656$	6.57975e9	−	7.00302e10i	0.0355299	−	0.378155i
$657$		0			0
$658$	−7.15231e10	−	3.16079e10i	−0.381542	−	0.168613i
$659$			1.24478e11i			0.660013i	0.943979	+	0.330006i	$0.107051\pi$
$659$			1.24478e11i			0.660013i	−0.943979	+	0.330006i	$0.892949\pi$
$660$		0			0
$661$	−1.42995e10			−0.0749055			−0.0374528	−	0.999298i	$-0.511924\pi$
$661$	−1.42995e10			−0.0749055			−0.0374528	+	0.999298i	$0.511924\pi$
$662$	−2.68692e10	+	6.08003e10i	−0.139902	+	0.316573i
$663$		0			0
$664$	−2.87174e11	+	9.59442e10i	−1.47731	+	0.493567i
$665$	1.78898e10			0.0914784
$666$		0			0
$667$		−	4.42340e11i		−	2.23487i
$668$	2.26676e11	−	2.06377e11i	1.13841	−	1.03647i
$669$		0			0
$670$	3.99682e10	−	9.04410e10i	0.198343	−	0.448814i
$671$		−	2.99923e10i		−	0.147952i
$672$		0			0
$673$	3.61252e11			1.76096			0.880481	−	0.474082i	$-0.157220\pi$
$673$	3.61252e11			1.76096			0.880481	+	0.474082i	$0.157220\pi$
$674$	−1.09072e11	−	4.82016e10i	−0.528534	−	0.233573i
$675$		0			0
$676$	5.15781e10	+	5.66513e10i	0.246989	+	0.271283i
$677$	3.59458e11			1.71117			0.855587	−	0.517659i	$-0.173197\pi$
$677$	3.59458e11			1.71117			0.855587	+	0.517659i	$0.173197\pi$
$678$		0			0
$679$			6.81655e10i			0.320690i
$680$	2.93988e10	+	8.79945e10i	0.137497	+	0.411547i
$681$		0			0
$682$	−3.53946e10	−	1.56418e10i	−0.163606	−	0.0723017i
$683$		−	2.44203e11i		−	1.12220i	−0.827749	−	0.561098i	$-0.810379\pi$
$683$		−	2.44203e11i		−	1.12220i	0.827749	−	0.561098i	$-0.189621\pi$
$684$		0			0
$685$	6.23208e10			0.283055
$686$	8.18742e10	−	1.85267e11i	0.369701	−	0.836568i
$687$		0			0
$688$	−4.07135e11	−	3.82527e10i	−1.81712	−	0.170730i
$689$	2.63253e11			1.16814
$690$		0			0
$691$		−	2.33912e11i		−	1.02598i	−0.858393	−	0.512992i	$-0.828537\pi$
$691$		−	2.33912e11i		−	1.02598i	0.858393	−	0.512992i	$-0.171463\pi$
$692$	−9.12738e10	−	1.00252e11i	−0.398036	−	0.437186i
$693$		0			0
$694$	−9.27577e10	+	2.09894e11i	−0.399864	+	0.904820i
$695$		−	5.65580e10i		−	0.242412i
$696$		0			0
$697$	8.69747e10			0.368521
$698$	2.24524e11	+	9.92231e10i	0.945892	+	0.418014i
$699$		0			0
$700$	−1.89268e10	+	1.72319e10i	−0.0788290	+	0.0717697i
$701$	4.15300e11			1.71985			0.859924	−	0.510422i	$-0.170511\pi$
$701$	4.15300e11			1.71985			0.859924	+	0.510422i	$0.170511\pi$
$702$		0			0
$703$			1.38727e11i			0.567989i
$704$	−3.95204e10	−	5.25431e10i	−0.160891	−	0.213907i
$705$		0			0
$706$	1.54289e11	+	6.81845e10i	0.621037	+	0.274452i
$707$		−	5.23032e10i		−	0.209339i
$708$		0			0
$709$	3.09619e11			1.22530			0.612650	−	0.790355i	$-0.290104\pi$
$709$	3.09619e11			1.22530			0.612650	+	0.790355i	$0.290104\pi$
$710$	−4.50009e9	+	1.01829e10i	−0.0177087	+	0.0400717i
$711$		0			0
$712$	−6.55049e10	−	1.96065e11i	−0.254891	−	0.762922i
$713$	−3.20635e11			−1.24066
$714$		0			0
$715$			3.65753e10i			0.139947i
$716$	6.25538e10	−	5.69520e10i	0.238014	−	0.216699i
$717$		0			0
$718$	−3.03673e10	+	6.87159e10i	−0.114264	+	0.258559i
$719$		−	4.00141e11i		−	1.49726i	−0.662988	−	0.748630i	$-0.730712\pi$
$719$		−	4.00141e11i		−	1.49726i	0.662988	−	0.748630i	$-0.269288\pi$
$720$		0			0
$721$	2.79183e11			1.03311
$722$	−2.11946e11	−	9.36642e10i	−0.779966	−	0.344687i
$723$		0			0
$724$	1.08097e11	+	1.18730e11i	0.393424	+	0.432121i
$725$	6.65174e10			0.240759
$726$		0			0
$727$		−	3.98461e11i		−	1.42642i	−0.700950	−	0.713211i	$-0.747240\pi$
$727$		−	3.98461e11i		−	1.42642i	0.700950	−	0.713211i	$-0.252760\pi$
$728$	1.66022e11	−	5.54675e10i	0.591070	−	0.197475i
$729$		0			0
$730$	−5.49266e10	−	2.42735e10i	−0.193416	−	0.0854754i
$731$		−	5.05645e11i		−	1.77083i
$732$		0			0
$733$	2.50341e11			0.867195			0.433597	−	0.901107i	$-0.357244\pi$
$733$	2.50341e11			0.867195			0.433597	+	0.901107i	$0.357244\pi$
$734$	2.71858e10	−	6.15165e10i	0.0936606	−	0.211937i
$735$		0			0
$736$	−4.75495e11	−	2.65848e11i	−1.62045	−	0.905987i
$737$	−8.66450e10			−0.293679
$738$		0			0
$739$			1.17998e11i			0.395636i	0.980239	+	0.197818i	$0.0633854\pi$
$739$			1.17998e11i			0.395636i	−0.980239	+	0.197818i	$0.936615\pi$
$740$	−1.33626e11	−	1.46769e11i	−0.445618	−	0.489449i
$741$		0			0
$742$	6.52546e10	−	1.47660e11i	0.215276	−	0.487131i
$743$			1.74300e11i			0.571929i	0.958240	+	0.285965i	$0.0923140\pi$
$743$			1.74300e11i			0.571929i	−0.958240	+	0.285965i	$0.907686\pi$
$744$		0			0
$745$	6.15531e10			0.199814
$746$	2.97420e11	+	1.31437e11i	0.960316	+	0.424389i
$747$		0			0
$748$	6.01141e10	−	5.47308e10i	0.192031	−	0.174834i
$749$	1.80662e11			0.574038
$750$		0			0
$751$		−	4.00985e11i		−	1.26057i	−0.776362	−	0.630287i	$-0.782937\pi$
$751$		−	4.00985e11i		−	1.26057i	0.776362	−	0.630287i	$-0.217063\pi$
$752$	2.49167e11	+	2.34107e10i	0.779147	+	0.0732054i
$753$		0			0
$754$	−4.16069e11	−	1.83872e11i	−1.28730	−	0.568891i
$755$			8.58241e10i			0.264132i
$756$		0			0
$757$	5.64071e11			1.71771			0.858855	−	0.512218i	$-0.171176\pi$
$757$	5.64071e11			1.71771			0.858855	+	0.512218i	$0.171176\pi$
$758$	1.93673e11	−	4.38247e11i	0.586666	−	1.32752i
$759$		0			0
$760$	−5.43052e10	+	1.81433e10i	−0.162775	+	0.0543827i
$761$	−3.24502e11			−0.967561			−0.483781	−	0.875189i	$-0.660737\pi$
$761$	−3.24502e11			−0.967561			−0.483781	+	0.875189i	$0.660737\pi$
$762$		0			0
$763$			5.54306e10i			0.163550i
$764$	−3.26046e11	+	2.96848e11i	−0.956986	+	0.871286i
$765$		0			0
$766$	−1.59084e11	+	3.59978e11i	−0.462072	+	1.04559i
$767$			2.12464e11i			0.613910i
$768$		0			0
$769$	−5.53794e11			−1.58359			−0.791796	−	0.610786i	$-0.790854\pi$
$769$	−5.53794e11			−1.58359			−0.791796	+	0.610786i	$0.790854\pi$
$770$	2.05152e10	+	9.06621e9i	0.0583598	+	0.0257907i
$771$		0			0
$772$	2.63110e11	+	2.88990e11i	0.740745	+	0.813605i
$773$	−1.03435e10			−0.0289699			−0.0144850	−	0.999895i	$-0.504611\pi$
$773$	−1.03435e10			−0.0289699			−0.0144850	+	0.999895i	$0.504611\pi$
$774$		0			0
$775$		−	4.82159e10i		−	0.133654i
$776$	−6.91313e10	−	2.06919e11i	−0.190646	−	0.570629i
$777$		0			0
$778$	−3.63823e10	−	1.60783e10i	−0.0993052	−	0.0438856i
$779$			5.36759e10i			0.145757i
$780$		0			0
$781$	9.75549e9			0.0262207
$782$	2.72283e11	−	6.16129e11i	0.728105	−	1.64757i
$783$		0			0
$784$	−2.52999e10	+	2.69274e11i	−0.0669659	+	0.712738i
$785$	1.89902e11			0.500094
$786$		0			0
$787$			3.10807e11i			0.810199i	0.914273	+	0.405100i	$0.132763\pi$
$787$			3.10807e11i			0.810199i	−0.914273	+	0.405100i	$0.867237\pi$
$788$	−7.11323e10	−	7.81289e10i	−0.184485	−	0.202631i
$789$		0			0
$790$	−7.70816e8	+	1.74422e9i	−0.00197898	+	0.00447809i
$791$			3.13801e11i			0.801583i
$792$		0			0
$793$	−2.55560e11			−0.646250
$794$	3.19179e11	+	1.41053e11i	0.803068	+	0.354897i
$795$		0			0
$796$	−1.36214e11	+	1.24016e11i	−0.339289	+	0.308905i
$797$	−3.11127e11			−0.771089			−0.385544	−	0.922689i	$-0.625986\pi$
$797$	−3.11127e11			−0.771089			−0.385544	+	0.922689i	$0.625986\pi$
$798$		0			0
$799$			3.09456e11i			0.759296i
$800$	3.99772e10	−	7.15032e10i	0.0976006	−	0.174568i
$801$		0			0
$802$	−2.08914e11	−	9.23246e10i	−0.504976	−	0.223162i
$803$			5.26212e10i			0.126561i
$804$		0			0
$805$	1.85845e11			0.442555
$806$	−1.33281e11	+	3.01592e11i	−0.315812	+	0.714628i
$807$		0			0
$808$	5.30442e10	+	1.58769e11i	0.124449	+	0.372494i
$809$	6.49886e11			1.51720			0.758601	−	0.651556i	$-0.225883\pi$
$809$	6.49886e11			1.51720			0.758601	+	0.651556i	$0.225883\pi$
$810$		0			0
$811$			5.51208e11i			1.27418i	0.770788	+	0.637091i	$0.219863\pi$
$811$			5.51208e11i			1.27418i	−0.770788	+	0.637091i	$0.780137\pi$
$812$	−2.06269e11	+	1.87797e11i	−0.474471	+	0.431981i
$813$		0			0
$814$	−7.03043e10	+	1.59086e11i	−0.160134	+	0.362356i
$815$		−	6.41989e10i		−	0.145511i
$816$		0			0
$817$	3.12056e11			0.700397
$818$	3.31905e11	+	1.46678e11i	0.741312	+	0.327605i
$819$		0			0
$820$	−5.17020e10	−	5.67874e10i	−0.114354	−	0.125602i
$821$	−6.49196e11			−1.42891			−0.714453	−	0.699684i	$-0.753324\pi$
$821$	−6.49196e11			−1.42891			−0.714453	+	0.699684i	$0.753324\pi$
$822$		0			0
$823$		−	5.51911e11i		−	1.20301i	−0.798869	−	0.601506i	$-0.794568\pi$
$823$		−	5.51911e11i		−	1.20301i	0.798869	−	0.601506i	$-0.205432\pi$
$824$	−8.47470e11	+	2.83138e11i	−1.83830	+	0.614171i
$825$		0			0
$826$	1.19172e11	+	5.26653e10i	0.256009	+	0.113137i
$827$		−	2.53430e11i		−	0.541797i	−0.962608	−	0.270898i	$-0.912679\pi$
$827$		−	2.53430e11i		−	0.541797i	0.962608	−	0.270898i	$-0.0873207\pi$
$828$		0			0
$829$	4.64664e11			0.983833			0.491916	−	0.870642i	$-0.336297\pi$
$829$	4.64664e11			0.983833			0.491916	+	0.870642i	$0.336297\pi$
$830$	−1.33626e11	+	3.02371e11i	−0.281564	+	0.637130i
$831$		0			0
$832$	−4.47712e11	+	3.36748e11i	−0.934342	+	0.702767i
$833$	−3.34427e11			−0.694579
$834$		0			0
$835$		−	3.34701e11i		−	0.688512i
$836$	3.37768e10	+	3.70991e10i	0.0691501	+	0.0759517i
$837$		0			0
$838$	−2.26710e11	+	5.13004e11i	−0.459721	+	1.04027i
$839$		−	8.01655e11i		−	1.61785i	−0.587909	−	0.808927i	$-0.700049\pi$
$839$		−	8.01655e11i		−	1.61785i	0.587909	−	0.808927i	$-0.299951\pi$
$840$		0			0
$841$	2.24674e11			0.449127
$842$	2.79330e11	+	1.23443e11i	0.555738	+	0.245595i
$843$		0			0
$844$	−3.55447e10	+	3.23617e10i	−0.0700496	+	0.0637765i
$845$	8.36492e10			0.164072
$846$		0			0
$847$			2.54684e11i			0.494844i
$848$	−4.83315e10	+	5.14406e11i	−0.0934645	+	0.994770i
$849$		0			0
$850$	9.26512e10	+	4.09449e10i	0.177491	+	0.0784377i
$851$			1.44114e12i			2.74782i
$852$		0			0
$853$	−2.92765e11			−0.552997			−0.276499	−	0.961014i	$-0.589174\pi$
$853$	−2.92765e11			−0.552997			−0.276499	+	0.961014i	$0.589174\pi$
$854$	−6.33478e10	+	1.43345e11i	−0.119097	+	0.269495i
$855$		0			0
$856$	−5.48408e11	+	1.83222e11i	−1.02143	+	0.341258i
$857$	2.44583e11			0.453423			0.226712	−	0.973962i	$-0.427203\pi$
$857$	2.44583e11			0.453423			0.226712	+	0.973962i	$0.427203\pi$
$858$		0			0
$859$			5.81097e9i			0.0106727i	0.999986	+	0.00533637i	$0.00169863\pi$
$859$			5.81097e9i			0.0106727i	−0.999986	+	0.00533637i	$0.998301\pi$
$860$	−3.30145e11	+	3.00580e11i	−0.603547	+	0.549499i
$861$		0			0
$862$	−3.02293e11	+	6.84036e11i	−0.547519	+	1.23894i
$863$			5.81147e11i			1.04771i	0.851806	+	0.523857i	$0.175507\pi$
$863$			5.81147e11i			1.04771i	−0.851806	+	0.523857i	$0.824493\pi$
$864$		0			0
$865$	−1.48028e11			−0.264410
$866$	4.00168e11	+	1.76845e11i	0.711493	+	0.314427i
$867$		0			0
$868$	1.36127e11	+	1.49516e11i	0.239809	+	0.263396i
$869$	1.67101e9			0.00293022
$870$		0			0
$871$			7.38290e11i			1.28279i
$872$	−5.62160e10	−	1.68262e11i	−0.0972285	−	0.291018i
$873$		0			0
$874$	3.80240e11	+	1.68038e11i	0.651646	+	0.287979i
$875$			2.79467e10i			0.0476758i
$876$		0			0
$877$	1.69423e11			0.286401			0.143200	−	0.989694i	$-0.454261\pi$
$877$	1.69423e11			0.286401			0.143200	+	0.989694i	$0.454261\pi$
$878$	−7.80920e10	+	1.76708e11i	−0.131410	+	0.297357i
$879$		0			0
$880$	−7.14695e10	−	6.71498e9i	−0.119176	−	0.0111973i
$881$	−2.75321e11			−0.457020			−0.228510	−	0.973542i	$-0.573385\pi$
$881$	−2.75321e11			−0.457020			−0.228510	+	0.973542i	$0.573385\pi$
$882$		0			0
$883$		−	6.38716e11i		−	1.05067i	−0.850896	−	0.525333i	$-0.823941\pi$
$883$		−	6.38716e11i		−	1.05067i	0.850896	−	0.525333i	$-0.176059\pi$
$884$	−4.66354e11	−	5.12224e11i	−0.763671	−	0.838786i
$885$		0			0
$886$	2.42060e11	−	5.47739e11i	0.392815	−	0.888872i
$887$			2.03717e11i			0.329103i	0.986368	+	0.164552i	$0.0526177\pi$
$887$			2.03717e11i			0.329103i	−0.986368	+	0.164552i	$0.947382\pi$
$888$		0			0
$889$	8.62063e10			0.138017
$890$	−2.06441e11	−	9.12315e10i	−0.329030	−	0.145407i
$891$		0			0
$892$	7.06292e11	−	6.43042e11i	1.11564	−	1.01573i
$893$	−1.90978e11			−0.300316
$894$		0			0
$895$		−	9.23647e10i		−	0.143951i
$896$	7.79051e10	+	3.34596e11i	0.120874	+	0.519146i
$897$		0			0
$898$	−6.49591e11	−	2.87071e11i	−0.998929	−	0.441453i
$899$		−	5.25467e11i		−	0.804464i
$900$		0			0
$901$	−6.38872e11			−0.969426
$902$	−2.72019e10	+	6.15532e10i	−0.0410936	+	0.0929875i
$903$		0			0
$904$	−3.18247e11	−	9.52557e11i	−0.476531	−	1.42632i
$905$	1.75312e11			0.261347
$906$		0			0
$907$		−	4.30286e11i		−	0.635811i	−0.948122	−	0.317906i	$-0.897020\pi$
$907$		−	4.30286e11i		−	0.635811i	0.948122	−	0.317906i	$-0.102980\pi$
$908$	2.88626e11	−	2.62779e11i	0.424612	−	0.386587i
$909$		0			0
$910$	7.72520e10	−	1.74807e11i	0.112653	−	0.254914i
$911$			8.13793e11i			1.18152i	0.806848	+	0.590759i	$0.201172\pi$
$911$			8.13793e11i			1.18152i	−0.806848	+	0.590759i	$0.798828\pi$
$912$		0			0
$913$	2.89680e11			0.416903
$914$	−6.70155e11	−	2.96159e11i	−0.960263	−	0.424365i
$915$		0			0
$916$	7.26617e11	+	7.98087e11i	1.03210	+	1.13362i
$917$	7.57101e10			0.107072
$918$		0			0
$919$		−	4.72727e11i		−	0.662748i	−0.943500	−	0.331374i	$-0.892488\pi$
$919$		−	4.72727e11i		−	0.662748i	0.943500	−	0.331374i	$-0.107512\pi$
$920$	−5.64140e11	+	1.88478e11i	−0.787474	+	0.263093i
$921$		0			0
$922$	−1.01882e11	−	4.50242e10i	−0.140985	−	0.0623050i
$923$		−	8.31252e10i		−	0.114532i
$924$		0			0
$925$	−2.16714e11			−0.296019
$926$	1.80771e10	−	4.09052e10i	0.0245858	−	0.0556333i
$927$		0			0
$928$	4.35680e11	−	7.79257e11i	0.587456	−	1.05072i
$929$	2.08893e11			0.280453			0.140227	−	0.990119i	$-0.455217\pi$
$929$	2.08893e11			0.280453			0.140227	+	0.990119i	$0.455217\pi$
$930$		0			0
$931$		−	2.06390e11i		−	0.274719i
$932$	−4.86628e11	−	5.34493e11i	−0.644962	−	0.708400i
$933$		0			0
$934$	1.35992e11	−	3.07726e11i	0.178701	−	0.404368i
$935$		−	8.87623e10i		−	0.116140i
$936$		0			0
$937$	−1.00252e12			−1.30058			−0.650288	−	0.759688i	$-0.725352\pi$
$937$	−1.00252e12			−1.30058			−0.650288	+	0.759688i	$0.725352\pi$
$938$	4.14110e11	+	1.83006e11i	0.534939	+	0.236403i
$939$		0			0
$940$	2.02049e11	−	1.83955e11i	0.258789	−	0.235614i
$941$	−1.13207e12			−1.44383			−0.721913	−	0.691983i	$-0.756737\pi$
$941$	−1.13207e12			−1.44383			−0.721913	+	0.691983i	$0.756737\pi$
$942$		0			0
$943$			5.57603e11i			0.705145i
$944$	−4.15164e11	−	3.90071e10i	−0.522795	−	0.0491197i
$945$		0			0
$946$	3.57852e11	+	1.58144e11i	0.446826	+	0.197464i
$947$		−	1.05689e12i		−	1.31411i	−0.753844	−	0.657053i	$-0.771803\pi$
$947$		−	1.05689e12i		−	1.31411i	0.753844	−	0.657053i	$-0.228197\pi$
$948$		0			0
$949$	4.48378e11			0.552814
$950$	−2.52689e10	+	5.71791e10i	−0.0310236	+	0.0702009i
$951$		0			0
$952$	−4.02908e11	+	1.34611e11i	−0.490521	+	0.163882i
$953$	−1.31887e12			−1.59893			−0.799464	−	0.600714i	$-0.794883\pi$
$953$	−1.31887e12			−1.59893			−0.799464	+	0.600714i	$0.794883\pi$
$954$		0			0
$955$			4.81428e11i			0.578785i
$956$	−8.21318e11	+	7.47768e11i	−0.983286	+	0.895231i
$957$		0			0
$958$	6.54336e11	−	1.48065e12i	0.776853	−	1.75788i
$959$			2.85353e11i			0.337372i
$960$		0			0
$961$	4.72000e11			0.553412
$962$	1.35555e12	+	5.99053e11i	1.58276	+	0.699464i
$963$		0			0
$964$	9.40135e11	+	1.03261e12i	1.08863	+	1.19571i
$965$	4.26712e11			0.492069
$966$		0			0
$967$			1.10518e12i			1.26395i	0.774990	+	0.631973i	$0.217755\pi$
$967$			1.10518e12i			1.26395i	−0.774990	+	0.631973i	$0.782245\pi$
$968$	−2.58293e11	−	7.73105e11i	−0.294178	−	0.880516i
$969$		0			0
$970$	−2.17869e11	−	9.62821e10i	−0.246099	−	0.108757i
$971$		−	3.17367e11i		−	0.357013i	−0.983939	−	0.178507i	$-0.942873\pi$
$971$		−	3.17367e11i		−	0.357013i	0.983939	−	0.178507i	$-0.0571266\pi$
$972$		0			0
$973$	2.58967e11			0.288930
$974$	−4.33043e11	+	9.79900e11i	−0.481166	+	1.08879i
$975$		0			0
$976$	4.69192e10	−	4.99375e11i	0.0517073	−	0.550336i
$977$	−1.27398e12			−1.39825			−0.699125	−	0.714999i	$-0.746427\pi$
$977$	−1.27398e12			−1.39825			−0.699125	+	0.714999i	$0.746427\pi$
$978$		0			0
$979$			1.97776e11i			0.215299i
$980$	1.98800e11	+	2.18354e11i	0.215532	+	0.236732i
$981$		0			0
$982$	3.23167e11	−	7.31270e11i	0.347521	−	0.786378i
$983$			9.79210e11i			1.04873i	0.851495	+	0.524363i	$0.175696\pi$
$983$			9.79210e11i			1.04873i	−0.851495	+	0.524363i	$0.824304\pi$
$984$		0			0
$985$	−1.15362e11			−0.122552
$986$	1.00973e12	+	4.46227e11i	1.06831	+	0.472115i
$987$		0			0
$988$	3.16116e11	−	2.87807e11i	0.331756	−	0.302046i
$989$	3.24174e12			3.38838
$990$		0			0
$991$		−	1.05272e12i		−	1.09149i	−0.837952	−	0.545744i	$-0.816247\pi$
$991$		−	1.05272e12i		−	1.09149i	0.837952	−	0.545744i	$-0.183753\pi$
$992$	−5.64853e11	−	3.15807e11i	−0.583296	−	0.326119i
$993$		0			0
$994$	−4.66253e10	−	2.06049e10i	−0.0477613	−	0.0211069i
$995$			2.01129e11i			0.205202i
$996$		0			0
$997$	−1.91731e12			−1.94049			−0.970245	−	0.242126i	$-0.922155\pi$
$997$	−1.91731e12			−1.94049			−0.970245	+	0.242126i	$0.922155\pi$
$998$	7.77474e11	−	1.75928e12i	0.783725	−	1.77343i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.9.c.b.91.5	✓	32
3.2	odd	2	inner	180.9.c.b.91.28	yes	32
4.3	odd	2	inner	180.9.c.b.91.6	yes	32
12.11	even	2	inner	180.9.c.b.91.27	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.9.c.b.91.5	✓	32	1.1	even	1	trivial
180.9.c.b.91.6	yes	32	4.3	odd	2	inner
180.9.c.b.91.27	yes	32	12.11	even	2	inner
180.9.c.b.91.28	yes	32	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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	180.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-14.6346 - 6.46742i) q^{2} +(172.345 + 189.297i) q^{4} +279.508 q^{5} +1279.81i q^{7} +(-1297.94 - 3884.91i) q^{8} +(-4090.50 - 1807.70i) q^{10} +3918.81i q^{11} +33391.7 q^{13} +(8277.07 - 18729.5i) q^{14} +(-6130.49 + 65248.6i) q^{16} -81036.2 q^{17} -50011.0i q^{19} +(48171.9 + 52910.0i) q^{20} +(25344.6 - 57350.4i) q^{22} -519530. i q^{23} +78125.0 q^{25} +(-488675. - 215958. i) q^{26} +(-242264. + 220568. i) q^{28} +851423. q^{29} -617163. i q^{31} +(511708. - 915241. i) q^{32} +(1.18593e6 + 524095. i) q^{34} +357717. i q^{35} -2.77393e6 q^{37} +(-323442. + 731892. i) q^{38} +(-362786. - 1.08587e6i) q^{40} -1.07328e6 q^{41} +6.23975e6i q^{43} +(-741818. + 675387. i) q^{44} +(-3.36002e6 + 7.60313e6i) q^{46} -3.81873e6i q^{47} +4.12689e6 q^{49} +(-1.14333e6 - 505267. i) q^{50} +(5.75488e6 + 6.32093e6i) q^{52} +7.88378e6 q^{53} +1.09534e6i q^{55} +(4.97195e6 - 1.66112e6i) q^{56} +(-1.24603e7 - 5.50651e6i) q^{58} +6.36280e6i q^{59} -7.65342e6 q^{61} +(-3.99146e6 + 9.03196e6i) q^{62} +(-1.34079e7 + 1.00848e7i) q^{64} +9.33325e6 q^{65} +2.21100e7i q^{67} +(-1.39662e7 - 1.53399e7i) q^{68} +(2.31351e6 - 5.23506e6i) q^{70} -2.48940e6i q^{71} +1.34278e7 q^{73} +(4.05955e7 + 1.79402e7i) q^{74} +(9.46691e6 - 8.61913e6i) q^{76} -5.01533e6 q^{77} -426407. i q^{79} +(-1.71352e6 + 1.82375e7i) q^{80} +(1.57071e7 + 6.94137e6i) q^{82} -7.39202e7i q^{83} -2.26503e7 q^{85} +(4.03551e7 - 9.13164e7i) q^{86} +(1.52243e7 - 5.08639e6i) q^{88} +5.04683e7 q^{89} +4.27349e7i q^{91} +(9.83454e7 - 8.95384e7i) q^{92} +(-2.46974e7 + 5.58857e7i) q^{94} -1.39785e7i q^{95} +5.32622e7 q^{97} +(-6.03955e7 - 2.66903e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 610 q^{4} - 8750 q^{10} - 51392 q^{13} + 11986 q^{16} - 758068 q^{22} + 2500000 q^{25} + 976324 q^{28} - 6117428 q^{34} + 5152064 q^{37} - 96250 q^{40} - 10391752 q^{46} - 11002976 q^{49} + 13976584 q^{52}+ \cdots + 80579520 q^{97}+O(q^{100}) \) 32 * q + 610 * q^4 - 8750 * q^10 - 51392 * q^13 + 11986 * q^16 - 758068 * q^22 + 2500000 * q^25 + 976324 * q^28 - 6117428 * q^34 + 5152064 * q^37 - 96250 * q^40 - 10391752 * q^46 - 11002976 * q^49 + 13976584 * q^52 - 36333948 * q^58 - 7802048 * q^61 + 116259994 * q^64 - 49897500 * q^70 - 94303680 * q^73 + 248840592 * q^76 - 428557904 * q^82 + 106960000 * q^85 + 510719924 * q^88 - 692727576 * q^94 + 80579520 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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