LMFDB - Embedded newform 432.8.i.c.289.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,8,Mod(145,432)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("432.145");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	432.i (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$134.950331009$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 375 x^{10} - 1820 x^{9} + 50808 x^{8} - 192378 x^{7} + 3002887 x^{6} + \cdots + 754412211 $ x^12 - 6x^11 + 375x^10 - 1820x^9 + 50808x^8 - 192378x^7 + 3002887x^6 - 8342916x^5 + 72369348x^4 - 131054670x^3 + 513267363x^2 - 449098992*x + 754412211
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{21} $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.5
Root			$0.500000 - 9.08282i$ of defining polynomial
Character	$\chi$	$=$	432.289
Dual form			432.8.i.c.145.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(145.304 + 251.673i) q^{5} +(555.940 - 962.916i) q^{7} +(-2245.36 + 3889.07i) q^{11} +(-1218.29 - 2110.14i) q^{13} -15905.4 q^{17} +49949.6 q^{19} +(-34692.5 - 60089.2i) q^{23} +(-3163.73 + 5479.74i) q^{25} +(-47035.8 + 81468.4i) q^{29} +(-9963.58 - 17257.4i) q^{31} +323120. q^{35} +331750. q^{37} +(121133. + 209809. i) q^{41} +(415713. - 720036. i) q^{43} +(80005.3 - 138573. i) q^{47} +(-206366. - 357437. i) q^{49} -311589. q^{53} -1.30503e6 q^{55} +(156177. + 270506. i) q^{59} +(28723.9 - 49751.3i) q^{61} +(354044. - 613221. i) q^{65} +(-2.05100e6 - 3.55243e6i) q^{67} -403110. q^{71} -823496. q^{73} +(2.49656e6 + 4.32418e6i) q^{77} +(489414. - 847689. i) q^{79} +(1.85204e6 - 3.20782e6i) q^{83} +(-2.31111e6 - 4.00296e6i) q^{85} -2.09023e6 q^{89} -2.70918e6 q^{91} +(7.25786e6 + 1.25710e7i) q^{95} +(-1.75125e6 + 3.03325e6i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 180 q^{5} + 84 q^{7} - 8460 q^{11} - 1848 q^{13} - 30564 q^{17} - 24432 q^{19} - 51588 q^{23} + 4746 q^{25} + 414648 q^{29} - 8196 q^{31} + 2210616 q^{35} + 139344 q^{37} + 1731582 q^{41} - 408372 q^{43}+ \cdots + 9977226 q^{97}+O(q^{100}) $ 12 * q + 180 * q^5 + 84 * q^7 - 8460 * q^11 - 1848 * q^13 - 30564 * q^17 - 24432 * q^19 - 51588 * q^23 + 4746 * q^25 + 414648 * q^29 - 8196 * q^31 + 2210616 * q^35 + 139344 * q^37 + 1731582 * q^41 - 408372 * q^43 - 1631484 * q^47 - 179010 * q^49 - 2835648 * q^53 + 16056 * q^55 - 2055636 * q^59 - 2723196 * q^61 + 1387620 * q^65 - 3806556 * q^67 + 2408400 * q^71 - 10670052 * q^73 - 3478824 * q^77 - 6020916 * q^79 + 9605052 * q^83 - 1698624 * q^85 + 24630264 * q^89 - 13570104 * q^91 + 10422072 * q^95 + 9977226 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	145.304	+	251.673i	0.519854	+	0.900413i	0.999734	+	0.0230788i	$0.00734688\pi$
$5$	145.304	+	251.673i	0.519854	+	0.900413i	−0.479880	+	0.877334i	$0.659320\pi$
$6$		0			0
$7$	555.940	−	962.916i	0.612611	−	1.06107i	−0.378188	−	0.925729i	$-0.623453\pi$
$7$	555.940	−	962.916i	0.612611	−	1.06107i	0.990799	−	0.135344i	$-0.0432139\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2245.36	+	3889.07i	−0.508640	+	0.880991i	0.491310	+	0.870985i	$0.336518\pi$
$11$	−2245.36	+	3889.07i	−0.508640	+	0.880991i	−0.999950	+	0.0100060i	$0.996815\pi$
$12$		0			0
$13$	−1218.29	−	2110.14i	−0.153797	−	0.266385i	0.778823	−	0.627244i	$-0.215817\pi$
$13$	−1218.29	−	2110.14i	−0.153797	−	0.266385i	−0.932620	+	0.360859i	$0.882484\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−15905.4			−0.785187			−0.392593	−	0.919712i	$-0.628422\pi$
$17$	−15905.4			−0.785187			−0.392593	+	0.919712i	$0.628422\pi$
$18$		0			0
$19$	49949.6			1.67069			0.835343	−	0.549730i	$-0.185269\pi$
$19$	49949.6			1.67069			0.835343	+	0.549730i	$0.185269\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−34692.5	−	60089.2i	−0.594550	−	1.02979i	−0.993610	−	0.112867i	$-0.963997\pi$
$23$	−34692.5	−	60089.2i	−0.594550	−	1.02979i	0.399060	−	0.916925i	$-0.369337\pi$
$24$		0			0
$25$	−3163.73	+	5479.74i	−0.0404957	+	0.0701406i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−47035.8	+	81468.4i	−0.358126	+	0.620292i	−0.987648	−	0.156691i	$-0.949917\pi$
$29$	−47035.8	+	81468.4i	−0.358126	+	0.620292i	0.629522	+	0.776983i	$0.283251\pi$
$30$		0			0
$31$	−9963.58	−	17257.4i	−0.0600689	−	0.104042i	0.834427	−	0.551118i	$-0.185799\pi$
$31$	−9963.58	−	17257.4i	−0.0600689	−	0.104042i	−0.894496	+	0.447076i	$0.852465\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	323120.			1.27387
$36$		0			0
$37$	331750.			1.07673			0.538363	−	0.842713i	$-0.319043\pi$
$37$	331750.			1.07673			0.538363	+	0.842713i	$0.319043\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	121133.	+	209809.i	0.274486	+	0.475423i	0.970005	−	0.243084i	$-0.0781591\pi$
$41$	121133.	+	209809.i	0.274486	+	0.475423i	−0.695520	+	0.718507i	$0.744826\pi$
$42$		0			0
$43$	415713.	−	720036.i	0.797359	−	1.38107i	−0.123971	−	0.992286i	$-0.539563\pi$
$43$	415713.	−	720036.i	0.797359	−	1.38107i	0.921330	−	0.388781i	$-0.127104\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	80005.3	−	138573.i	0.112403	−	0.194687i	−0.804336	−	0.594175i	$-0.797479\pi$
$47$	80005.3	−	138573.i	0.112403	−	0.194687i	0.916738	+	0.399488i	$0.130812\pi$
$48$		0			0
$49$	−206366.	−	357437.i	−0.250583	−	0.434023i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−311589.			−0.287486			−0.143743	−	0.989615i	$-0.545914\pi$
$53$	−311589.			−0.287486			−0.143743	+	0.989615i	$0.545914\pi$
$54$		0			0
$55$	−1.30503e6			−1.05767
$56$		0			0
$57$		0			0
$58$		0			0
$59$	156177.	+	270506.i	0.0989997	+	0.171473i	0.911271	−	0.411807i	$-0.135102\pi$
$59$	156177.	+	270506.i	0.0989997	+	0.171473i	−0.812271	+	0.583280i	$0.801769\pi$
$60$		0			0
$61$	28723.9	−	49751.3i	0.0162028	−	0.0280640i	−0.857810	−	0.513966i	$-0.828176\pi$
$61$	28723.9	−	49751.3i	0.0162028	−	0.0280640i	0.874013	+	0.485902i	$0.161509\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	354044.	−	613221.i	0.159904	−	0.276962i
$66$		0			0
$67$	−2.05100e6	−	3.55243e6i	−0.833111	−	1.44299i	−0.895559	−	0.444943i	$-0.853224\pi$
$67$	−2.05100e6	−	3.55243e6i	−0.833111	−	1.44299i	0.0624478	−	0.998048i	$-0.480109\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−403110.			−0.133666			−0.0668328	−	0.997764i	$-0.521289\pi$
$71$	−403110.			−0.133666			−0.0668328	+	0.997764i	$0.521289\pi$
$72$		0			0
$73$	−823496.			−0.247760			−0.123880	−	0.992297i	$-0.539534\pi$
$73$	−823496.			−0.247760			−0.123880	+	0.992297i	$0.539534\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.49656e6	+	4.32418e6i	0.623197	+	1.07941i
$78$		0			0
$79$	489414.	−	847689.i	0.111682	−	0.193438i	−0.804767	−	0.593591i	$-0.797710\pi$
$79$	489414.	−	847689.i	0.111682	−	0.193438i	0.916448	+	0.400153i	$0.131043\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.85204e6	−	3.20782e6i	0.355530	−	0.615796i	−0.631678	−	0.775231i	$-0.717634\pi$
$83$	1.85204e6	−	3.20782e6i	0.355530	−	0.615796i	0.987209	+	0.159434i	$0.0509670\pi$
$84$		0			0
$85$	−2.31111e6	−	4.00296e6i	−0.408182	−	0.706993i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.09023e6			−0.314289			−0.157145	−	0.987576i	$-0.550229\pi$
$89$	−2.09023e6			−0.314289			−0.157145	+	0.987576i	$0.550229\pi$
$90$		0			0
$91$	−2.70918e6			−0.376872
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.25786e6	+	1.25710e7i	0.868512	+	1.50431i
$96$		0			0
$97$	−1.75125e6	+	3.03325e6i	−0.194826	+	0.337448i	−0.946843	−	0.321695i	$-0.895747\pi$
$97$	−1.75125e6	+	3.03325e6i	−0.194826	+	0.337448i	0.752018	+	0.659143i	$0.229081\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	277361.	−	480403.i	0.0267868	−	0.0463960i	−0.852321	−	0.523019i	$-0.824806\pi$
$101$	277361.	−	480403.i	0.0267868	−	0.0463960i	0.879108	+	0.476623i	$0.158139\pi$
$102$		0			0
$103$	1.01746e7	+	1.76229e7i	0.917459	+	1.58909i	0.803260	+	0.595628i	$0.203097\pi$
$103$	1.01746e7	+	1.76229e7i	0.917459	+	1.58909i	0.114199	+	0.993458i	$0.463570\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.49941e6			0.512897			0.256449	−	0.966558i	$-0.417448\pi$
$107$	6.49941e6			0.512897			0.256449	+	0.966558i	$0.417448\pi$
$108$		0			0
$109$	2.79312e6			0.206584			0.103292	−	0.994651i	$-0.467062\pi$
$109$	2.79312e6			0.206584			0.103292	+	0.994651i	$0.467062\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.04172e7	+	1.80431e7i	0.679167	+	1.17635i	0.975232	+	0.221184i	$0.0709922\pi$
$113$	1.04172e7	+	1.80431e7i	0.679167	+	1.17635i	−0.296065	+	0.955168i	$0.595674\pi$
$114$		0			0
$115$	1.00819e7	−	1.74624e7i	0.618158	−	1.07068i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.84244e6	+	1.53155e7i	−0.481014	+	0.833140i
$120$		0			0
$121$	−339665.	−	588316.i	−0.0174302	−	0.0301899i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	2.08649e7			0.955500
$126$		0			0
$127$	−8.89911e6			−0.385508			−0.192754	−	0.981247i	$-0.561742\pi$
$127$	−8.89911e6			−0.385508			−0.192754	+	0.981247i	$0.561742\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.35869e6	−	1.10136e7i	−0.247126	−	0.428034i	0.715601	−	0.698509i	$-0.246153\pi$
$131$	−6.35869e6	−	1.10136e7i	−0.247126	−	0.428034i	−0.962727	+	0.270475i	$0.912819\pi$
$132$		0			0
$133$	2.77690e7	−	4.80973e7i	1.02348	−	1.77272i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.45052e7	−	4.24442e7i	0.814209	−	1.41025i	−0.0956855	−	0.995412i	$-0.530504\pi$
$137$	2.45052e7	−	4.24442e7i	0.814209	−	1.41025i	0.909895	−	0.414840i	$-0.136162\pi$
$138$		0			0
$139$	−789537.	−	1.36752e6i	−0.0249357	−	0.0431898i	0.853288	−	0.521439i	$-0.174605\pi$
$139$	−789537.	−	1.36752e6i	−0.0249357	−	0.0431898i	−0.878224	+	0.478250i	$0.841271\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.09420e7			0.312910
$144$		0			0
$145$	−2.73379e7			−0.744692
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.95734e7	−	3.39021e7i	−0.484746	−	0.839605i	0.515100	−	0.857130i	$-0.327755\pi$
$149$	−1.95734e7	−	3.39021e7i	−0.484746	−	0.839605i	−0.999846	+	0.0175249i	$0.994421\pi$
$150$		0			0
$151$	9.19094e6	−	1.59192e7i	0.217240	−	0.376271i	−0.736723	−	0.676195i	$-0.763628\pi$
$151$	9.19094e6	−	1.59192e7i	0.217240	−	0.376271i	0.953963	+	0.299923i	$0.0969611\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.89549e6	−	5.01513e6i	0.0624540	−	0.108174i
$156$		0			0
$157$	3.32168e7	+	5.75332e7i	0.685029	+	1.18650i	0.973428	+	0.228994i	$0.0735437\pi$
$157$	3.32168e7	+	5.75332e7i	0.685029	+	1.18650i	−0.288399	+	0.957510i	$0.593123\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−7.71478e7			−1.45691
$162$		0			0
$163$	3.94682e7			0.713823			0.356912	−	0.934138i	$-0.383830\pi$
$163$	3.94682e7			0.713823			0.356912	+	0.934138i	$0.383830\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−4.86177e7	−	8.42084e7i	−0.807769	−	1.39910i	−0.914406	−	0.404799i	$-0.867342\pi$
$167$	−4.86177e7	−	8.42084e7i	−0.807769	−	1.39910i	0.106637	−	0.994298i	$-0.465992\pi$
$168$		0			0
$169$	2.84058e7	−	4.92003e7i	0.452693	−	0.784087i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.77015e7	−	4.79804e7i	0.406763	−	0.704534i	−0.587762	−	0.809034i	$-0.699991\pi$
$173$	2.77015e7	−	4.79804e7i	0.406763	−	0.704534i	0.994525	+	0.104500i	$0.0333242\pi$
$174$		0			0
$175$	3.51768e6	+	6.09281e6i	0.0496162	+	0.0859378i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.87173e7			1.28649			0.643247	−	0.765659i	$-0.277587\pi$
$179$	9.87173e7			1.28649			0.643247	+	0.765659i	$0.277587\pi$
$180$		0			0
$181$	9.03305e7			1.13230			0.566148	−	0.824304i	$-0.308433\pi$
$181$	9.03305e7			1.13230			0.566148	+	0.824304i	$0.308433\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	4.82045e7	+	8.34927e7i	0.559740	+	0.969499i
$186$		0			0
$187$	3.57133e7	−	6.18572e7i	0.399378	−	0.691743i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	5.20912e7	−	9.02247e7i	0.540938	−	0.936933i	−0.457912	−	0.888998i	$-0.651403\pi$
$191$	5.20912e7	−	9.02247e7i	0.540938	−	0.936933i	0.998850	−	0.0479353i	$-0.0152641\pi$
$192$		0			0
$193$	−6.65147e6	−	1.15207e7i	−0.0665989	−	0.115353i	0.830803	−	0.556566i	$-0.187881\pi$
$193$	−6.65147e6	−	1.15207e7i	−0.0665989	−	0.115353i	−0.897402	+	0.441214i	$0.854548\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	1.71308e8			1.59641			0.798206	−	0.602384i	$-0.205783\pi$
$197$	1.71308e8			1.59641			0.798206	+	0.602384i	$0.205783\pi$
$198$		0			0
$199$	1.24021e8			1.11561			0.557803	−	0.829974i	$-0.311645\pi$
$199$	1.24021e8			1.11561			0.557803	+	0.829974i	$0.311645\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	5.22981e7	+	9.05830e7i	0.438783	+	0.759994i
$204$		0			0
$205$	−3.52021e7	+	6.09719e7i	−0.285385	+	0.494301i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.12155e8	+	1.94258e8i	−0.849778	+	1.47186i
$210$		0			0
$211$	−9.32487e7	−	1.61511e8i	−0.683367	−	1.18363i	−0.973947	−	0.226776i	$-0.927181\pi$
$211$	−9.32487e7	−	1.61511e8i	−0.683367	−	1.18363i	0.290580	−	0.956851i	$-0.406152\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.41618e8			1.65804
$216$		0			0
$217$	−2.21566e7			−0.147195
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.93774e7	+	3.35626e7i	0.120760	+	0.209162i
$222$		0			0
$223$	−2.10250e7	+	3.64164e7i	−0.126961	+	0.219902i	−0.922498	−	0.386003i	$-0.873856\pi$
$223$	−2.10250e7	+	3.64164e7i	−0.126961	+	0.219902i	0.795537	+	0.605905i	$0.207189\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.56517e8	+	2.71095e8i	−0.888117	+	1.53826i	−0.0460190	+	0.998941i	$0.514653\pi$
$227$	−1.56517e8	+	2.71095e8i	−0.888117	+	1.53826i	−0.842098	+	0.539324i	$0.818680\pi$
$228$		0			0
$229$	−8.35576e7	−	1.44726e8i	−0.459792	−	0.796384i	0.539157	−	0.842205i	$-0.318743\pi$
$229$	−8.35576e7	−	1.44726e8i	−0.459792	−	0.796384i	−0.998950	+	0.0458213i	$0.985410\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.55430e8			1.32290			0.661449	−	0.749990i	$-0.269942\pi$
$233$	2.55430e8			1.32290			0.661449	+	0.749990i	$0.269942\pi$
$234$		0			0
$235$	4.65002e7			0.233732
$236$		0			0
$237$		0			0
$238$		0			0
$239$	8.84471e7	+	1.53195e8i	0.419074	+	0.725858i	0.995847	−	0.0910472i	$-0.0290214\pi$
$239$	8.84471e7	+	1.53195e8i	0.419074	+	0.725858i	−0.576772	+	0.816905i	$0.695688\pi$
$240$		0			0
$241$	1.56994e8	−	2.71922e8i	0.722478	−	1.25137i	−0.237526	−	0.971381i	$-0.576336\pi$
$241$	1.56994e8	−	2.71922e8i	0.722478	−	1.25137i	0.960004	−	0.279987i	$-0.0903303\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.99715e7	−	1.03874e8i	0.260533	−	0.451257i
$246$		0			0
$247$	−6.08531e7	−	1.05401e8i	−0.256947	−	0.445045i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.34891e8			0.538425			0.269212	−	0.963081i	$-0.413237\pi$
$251$	1.34891e8			0.538425			0.269212	+	0.963081i	$0.413237\pi$
$252$		0			0
$253$	3.11588e8			1.20965
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.17761e8	+	2.03969e8i	0.432750	+	0.749545i	0.997109	−	0.0759845i	$-0.0242099\pi$
$257$	1.17761e8	+	2.03969e8i	0.432750	+	0.749545i	−0.564359	+	0.825529i	$0.690877\pi$
$258$		0			0
$259$	1.84433e8	−	3.19448e8i	0.659614	−	1.14249i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	8.33326e7	−	1.44336e8i	0.282468	−	0.489249i	−0.689524	−	0.724263i	$-0.742180\pi$
$263$	8.33326e7	−	1.44336e8i	0.282468	−	0.489249i	0.971992	+	0.235014i	$0.0755135\pi$
$264$		0			0
$265$	−4.52750e7	−	7.84186e7i	−0.149451	−	0.258856i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.49508e8			0.468308			0.234154	−	0.972200i	$-0.424768\pi$
$269$	1.49508e8			0.468308			0.234154	+	0.972200i	$0.424768\pi$
$270$		0			0
$271$	−3.02665e8			−0.923783			−0.461892	−	0.886936i	$-0.652829\pi$
$271$	−3.02665e8			−0.923783			−0.461892	+	0.886936i	$0.652829\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−1.42074e7	−	2.46079e7i	−0.0411955	−	0.0713527i
$276$		0			0
$277$	−1.63479e7	+	2.83153e7i	−0.0462148	+	0.0800465i	−0.888207	−	0.459443i	$-0.848049\pi$
$277$	−1.63479e7	+	2.83153e7i	−0.0462148	+	0.0800465i	0.841993	+	0.539489i	$0.181383\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.50968e8	−	4.34689e8i	0.674755	−	1.16871i	−0.301786	−	0.953376i	$-0.597583\pi$
$281$	2.50968e8	−	4.34689e8i	0.674755	−	1.16871i	0.976540	−	0.215334i	$-0.0690840\pi$
$282$		0			0
$283$	1.62635e8	+	2.81691e8i	0.426541	+	0.738790i	0.996563	−	0.0828391i	$-0.0263988\pi$
$283$	1.62635e8	+	2.81691e8i	0.426541	+	0.738790i	−0.570022	+	0.821629i	$0.693065\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.69371e8			0.672611
$288$		0			0
$289$	−1.57357e8			−0.383481
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.17572e7	−	1.24287e8i	−0.166659	−	0.288662i	0.770584	−	0.637338i	$-0.219965\pi$
$293$	−7.17572e7	−	1.24287e8i	−0.166659	−	0.288662i	−0.937243	+	0.348676i	$0.886631\pi$
$294$		0			0
$295$	−4.53860e7	+	7.86109e7i	−0.102931	+	0.178281i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−8.45311e7	+	1.46412e8i	−0.182881	+	0.316758i
$300$		0			0
$301$	−4.62223e8	−	8.00593e8i	−0.976941	−	1.69211i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	1.66947e7			0.0336923
$306$		0			0
$307$	6.60558e8			1.30295			0.651474	−	0.758671i	$-0.274151\pi$
$307$	6.60558e8			1.30295			0.651474	+	0.758671i	$0.274151\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.28703e7	−	9.15740e7i	−0.0996667	−	0.172628i	0.811880	−	0.583824i	$-0.198444\pi$
$311$	−5.28703e7	−	9.15740e7i	−0.0996667	−	0.172628i	−0.911547	+	0.411197i	$0.865111\pi$
$312$		0			0
$313$	5.93605e7	−	1.02815e8i	0.109419	−	0.189519i	−0.806116	−	0.591757i	$-0.798434\pi$
$313$	5.93605e7	−	1.02815e8i	0.109419	−	0.189519i	0.915535	+	0.402238i	$0.131768\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−2.17334e8	+	3.76434e8i	−0.383196	+	0.663715i	−0.991517	−	0.129976i	$-0.958510\pi$
$317$	−2.17334e8	+	3.76434e8i	−0.383196	+	0.663715i	0.608321	+	0.793691i	$0.291843\pi$
$318$		0			0
$319$	−2.11224e8	−	3.65851e8i	−0.364314	−	0.631011i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−7.94468e8			−1.31180
$324$		0			0
$325$	1.54173e7			0.0249125
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−8.89563e7	−	1.54077e8i	−0.137718	−	0.238535i
$330$		0			0
$331$	3.67129e8	−	6.35887e8i	0.556444	−	0.963789i	−0.441346	−	0.897337i	$-0.645499\pi$
$331$	3.67129e8	−	6.35887e8i	0.556444	−	0.963789i	0.997790	−	0.0664518i	$-0.0211678\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	5.96034e8	−	1.03236e9i	0.866192	−	1.50029i
$336$		0			0
$337$	2.35772e8	+	4.08370e8i	0.335574	+	0.581231i	0.983595	−	0.180391i	$-0.0577364\pi$
$337$	2.35772e8	+	4.08370e8i	0.335574	+	0.581231i	−0.648021	+	0.761622i	$0.724403\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	8.94871e7			0.122214
$342$		0			0
$343$	4.56772e8			0.611181
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.53356e8	+	9.58441e8i	0.710970	+	1.23144i	0.964493	+	0.264107i	$0.0850773\pi$
$347$	5.53356e8	+	9.58441e8i	0.710970	+	1.23144i	−0.253523	+	0.967329i	$0.581589\pi$
$348$		0			0
$349$	3.98088e7	−	6.89509e7i	0.0501291	−	0.0868262i	−0.839872	−	0.542784i	$-0.817370\pi$
$349$	3.98088e7	−	6.89509e7i	0.0501291	−	0.0868262i	0.890001	+	0.455958i	$0.150703\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−5.09107e7	+	8.81799e7i	−0.0616024	+	0.106698i	−0.895182	−	0.445701i	$-0.852954\pi$
$353$	−5.09107e7	+	8.81799e7i	−0.0616024	+	0.106698i	0.833579	+	0.552400i	$0.186288\pi$
$354$		0			0
$355$	−5.85734e7	−	1.01452e8i	−0.0694866	−	0.120354i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.69307e7			0.110568			0.0552842	−	0.998471i	$-0.482394\pi$
$359$	9.69307e7			0.110568			0.0552842	+	0.998471i	$0.482394\pi$
$360$		0			0
$361$	1.60109e9			1.79119
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.19657e8	−	2.07252e8i	−0.128799	−	0.223086i
$366$		0			0
$367$	−7.72007e8	+	1.33716e9i	−0.815249	+	1.41205i	0.0939003	+	0.995582i	$0.470067\pi$
$367$	−7.72007e8	+	1.33716e9i	−0.815249	+	1.41205i	−0.909149	+	0.416471i	$0.863267\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.73225e8	+	3.00034e8i	−0.176117	+	0.305043i
$372$		0			0
$373$	6.74772e8	+	1.16874e9i	0.673250	+	1.16610i	0.976977	+	0.213344i	$0.0684355\pi$
$373$	6.74772e8	+	1.16874e9i	0.673250	+	1.16610i	−0.303727	+	0.952759i	$0.598231\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.29213e8			0.220315
$378$		0			0
$379$	−1.61145e9			−1.52048			−0.760238	−	0.649645i	$-0.774918\pi$
$379$	−1.61145e9			−1.52048			−0.760238	+	0.649645i	$0.774918\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−6.32119e8	−	1.09486e9i	−0.574915	−	0.995781i	−0.996051	−	0.0887840i	$-0.971702\pi$
$383$	−6.32119e8	−	1.09486e9i	−0.574915	−	0.995781i	0.421136	−	0.906997i	$-0.361631\pi$
$384$		0			0
$385$	−7.25519e8	+	1.25664e9i	−0.647942	+	1.12227i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.18665e8	+	1.59117e9i	−0.791286	+	1.37055i	0.133885	+	0.990997i	$0.457255\pi$
$389$	−9.18665e8	+	1.59117e9i	−0.791286	+	1.37055i	−0.925171	+	0.379551i	$0.876079\pi$
$390$		0			0
$391$	5.51798e8	+	9.55743e8i	0.466833	+	0.808579i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.84454e8			0.232232
$396$		0			0
$397$	−1.85478e9			−1.48773			−0.743867	−	0.668327i	$-0.767011\pi$
$397$	−1.85478e9			−1.48773			−0.743867	+	0.668327i	$0.767011\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−6.04284e8	−	1.04665e9i	−0.467989	−	0.810580i	0.531342	−	0.847157i	$-0.321688\pi$
$401$	−6.04284e8	−	1.04665e9i	−0.467989	−	0.810580i	−0.999331	+	0.0365770i	$0.988355\pi$
$402$		0			0
$403$	−2.42770e7	+	4.20491e7i	−0.0184769	+	0.0320029i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.44898e8	+	1.29020e9i	−0.547667	+	0.948587i
$408$		0			0
$409$	6.10716e8	+	1.05779e9i	0.441375	+	0.764484i	0.997792	−	0.0664194i	$-0.0211575\pi$
$409$	6.10716e8	+	1.05779e9i	0.441375	+	0.764484i	−0.556417	+	0.830903i	$0.687824\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	3.47299e8			0.242593
$414$		0			0
$415$	1.07643e9			0.739295
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−7.60350e8	−	1.31697e9i	−0.504969	−	0.874632i	−0.999983	−	0.00574729i	$-0.998171\pi$
$419$	−7.60350e8	−	1.31697e9i	−0.504969	−	0.874632i	0.495014	−	0.868885i	$-0.335163\pi$
$420$		0			0
$421$	−5.43681e8	+	9.41684e8i	−0.355105	+	0.615060i	−0.987136	−	0.159883i	$-0.948888\pi$
$421$	−5.43681e8	+	9.41684e8i	−0.355105	+	0.615060i	0.632031	+	0.774943i	$0.282222\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.03203e7	−	8.71573e7i	0.0317967	−	0.0550735i
$426$		0			0
$427$	−3.19375e7	−	5.53174e7i	−0.0198520	−	0.0343846i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−1.33391e9			−0.802521			−0.401261	−	0.915964i	$-0.631428\pi$
$431$	−1.33391e9			−0.802521			−0.401261	+	0.915964i	$0.631428\pi$
$432$		0			0
$433$	−3.41286e8			−0.202027			−0.101014	−	0.994885i	$-0.532209\pi$
$433$	−3.41286e8			−0.202027			−0.101014	+	0.994885i	$0.532209\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−1.73288e9	−	3.00144e9i	−0.993307	−	1.72046i
$438$		0			0
$439$	−6.78117e8	+	1.17453e9i	−0.382541	+	0.662581i	−0.991425	−	0.130679i	$-0.958284\pi$
$439$	−6.78117e8	+	1.17453e9i	−0.382541	+	0.662581i	0.608883	+	0.793260i	$0.291618\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.79697e8	−	1.00407e9i	0.316802	−	0.548717i	−0.663017	−	0.748605i	$-0.730724\pi$
$443$	5.79697e8	−	1.00407e9i	0.316802	−	0.548717i	0.979819	+	0.199887i	$0.0640575\pi$
$444$		0			0
$445$	−3.03718e8	−	5.26055e8i	−0.163384	−	0.282990i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−9.76057e8			−0.508877			−0.254439	−	0.967089i	$-0.581891\pi$
$449$	−9.76057e8			−0.508877			−0.254439	+	0.967089i	$0.581891\pi$
$450$		0			0
$451$	−1.08795e9			−0.558458
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.93654e8	−	6.81828e8i	−0.195918	−	0.339340i
$456$		0			0
$457$	9.44190e8	−	1.63539e9i	0.462757	−	0.801518i	−0.536340	−	0.844002i	$-0.680194\pi$
$457$	9.44190e8	−	1.63539e9i	0.462757	−	0.801518i	0.999097	+	0.0424836i	$0.0135270\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.07086e8	+	1.22471e9i	−0.336139	+	0.582210i	−0.983703	−	0.179801i	$-0.942455\pi$
$461$	−7.07086e8	+	1.22471e9i	−0.336139	+	0.582210i	0.647564	+	0.762011i	$0.275788\pi$
$462$		0			0
$463$	−5.13035e8	−	8.88602e8i	−0.240222	−	0.416077i	0.720555	−	0.693398i	$-0.243887\pi$
$463$	−5.13035e8	−	8.88602e8i	−0.240222	−	0.416077i	−0.960778	+	0.277320i	$0.910554\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.39875e8			0.199858			0.0999288	−	0.994995i	$-0.468139\pi$
$467$	4.39875e8			0.199858			0.0999288	+	0.994995i	$0.468139\pi$
$468$		0			0
$469$	−4.56092e9			−2.04149
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.86685e9	+	3.23347e9i	0.811138	+	1.40493i
$474$		0			0
$475$	−1.58027e8	+	2.73711e8i	−0.0676556	+	0.117183i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−1.23369e9	+	2.13681e9i	−0.512899	+	0.888367i	0.486989	+	0.873408i	$0.338095\pi$
$479$	−1.23369e9	+	2.13681e9i	−0.512899	+	0.888367i	−0.999888	+	0.0149590i	$0.995238\pi$
$480$		0			0
$481$	−4.04168e8	−	7.00040e8i	−0.165598	−	0.286824i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.01785e9			−0.405123
$486$		0			0
$487$	−9.54719e8			−0.374563			−0.187281	−	0.982306i	$-0.559968\pi$
$487$	−9.54719e8			−0.374563			−0.187281	+	0.982306i	$0.559968\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.83801e8	−	1.70399e9i	−0.375079	−	0.649655i	0.615260	−	0.788324i	$-0.289051\pi$
$491$	−9.83801e8	−	1.70399e9i	−0.375079	−	0.649655i	−0.990339	+	0.138669i	$0.955718\pi$
$492$		0			0
$493$	7.48122e8	−	1.29579e9i	0.281196	−	0.487045i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.24105e8	+	3.88161e8i	−0.0818850	+	0.141829i
$498$		0			0
$499$	5.22725e8	+	9.05387e8i	0.188331	+	0.326199i	0.944694	−	0.327953i	$-0.106359\pi$
$499$	5.22725e8	+	9.05387e8i	0.188331	+	0.326199i	−0.756363	+	0.654152i	$0.773026\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.15052e9			0.403093			0.201546	−	0.979479i	$-0.435403\pi$
$503$	1.15052e9			0.403093			0.201546	+	0.979479i	$0.435403\pi$
$504$		0			0
$505$	1.61206e8			0.0557008
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.50094e9	−	4.33176e9i	−0.840603	−	1.45597i	−0.889385	−	0.457158i	$-0.848867\pi$
$509$	−2.50094e9	−	4.33176e9i	−0.840603	−	1.45597i	0.0487822	−	0.998809i	$-0.484466\pi$
$510$		0			0
$511$	−4.57814e8	+	7.92957e8i	−0.151781	+	0.262892i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.95681e9	+	5.12134e9i	−0.953889	+	1.65218i
$516$		0			0
$517$	3.59281e8	+	6.22293e8i	0.114345	+	0.198051i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	1.31851e9			0.408460			0.204230	−	0.978923i	$-0.434531\pi$
$521$	1.31851e9			0.408460			0.204230	+	0.978923i	$0.434531\pi$
$522$		0			0
$523$	−1.46804e9			−0.448727			−0.224363	−	0.974506i	$-0.572030\pi$
$523$	−1.46804e9			−0.448727			−0.224363	+	0.974506i	$0.572030\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	1.58475e8	+	2.74486e8i	0.0471653	+	0.0816927i
$528$		0			0
$529$	−7.04732e8	+	1.22063e9i	−0.206980	+	0.358501i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.95151e8	−	5.11216e8i	0.0844303	−	0.146238i
$534$		0			0
$535$	9.44387e8	+	1.63573e9i	0.266632	+	0.461820i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.85346e9			0.509827
$540$		0			0
$541$	3.28515e9			0.892000			0.446000	−	0.895033i	$-0.352848\pi$
$541$	3.28515e9			0.892000			0.446000	+	0.895033i	$0.352848\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	4.05850e8	+	7.02954e8i	0.107394	+	0.186011i
$546$		0			0
$547$	1.71890e9	−	2.97722e9i	0.449050	−	0.777778i	−0.549274	−	0.835642i	$-0.685096\pi$
$547$	1.71890e9	−	2.97722e9i	0.449050	−	0.777778i	0.998324	+	0.0578644i	$0.0184291\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−2.34942e9	+	4.06931e9i	−0.598315	+	1.03631i
$552$		0			0
$553$	−5.44169e8	−	9.42528e8i	−0.136835	−	0.237004i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.14256e9			1.75130			0.875651	−	0.482945i	$-0.160433\pi$
$557$	7.14256e9			1.75130			0.875651	+	0.482945i	$0.160433\pi$
$558$		0			0
$559$	−2.02584e9			−0.490527
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−2.31348e9	−	4.00706e9i	−0.546369	−	0.946338i	−0.998519	−	0.0543966i	$-0.982676\pi$
$563$	−2.31348e9	−	4.00706e9i	−0.546369	−	0.946338i	0.452151	−	0.891941i	$-0.350657\pi$
$564$		0			0
$565$	−3.02731e9	+	5.24346e9i	−0.706135	+	1.22306i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.82742e9	+	4.89724e9i	−0.643425	+	1.11444i	0.341238	+	0.939977i	$0.389154\pi$
$569$	−2.82742e9	+	4.89724e9i	−0.643425	+	1.11444i	−0.984663	+	0.174468i	$0.944180\pi$
$570$		0			0
$571$	3.84013e9	+	6.65130e9i	0.863216	+	1.49513i	0.868808	+	0.495149i	$0.164887\pi$
$571$	3.84013e9	+	6.65130e9i	0.863216	+	1.49513i	−0.00559216	+	0.999984i	$0.501780\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	4.39031e8			0.0963070
$576$		0			0
$577$	2.51579e9			0.545204			0.272602	−	0.962127i	$-0.412116\pi$
$577$	2.51579e9			0.545204			0.272602	+	0.962127i	$0.412116\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2.05924e9	−	3.56671e9i	−0.435603	−	0.754487i
$582$		0			0
$583$	6.99628e8	−	1.21179e9i	0.146227	−	0.253273i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.25025e9	−	3.89755e9i	0.459196	−	0.795351i	−0.539723	−	0.841843i	$-0.681471\pi$
$587$	2.25025e9	−	3.89755e9i	0.459196	−	0.795351i	0.998919	+	0.0464920i	$0.0148042\pi$
$588$		0			0
$589$	−4.97677e8	−	8.62002e8i	−0.100356	−	0.173822i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−8.41758e9			−1.65766			−0.828831	−	0.559499i	$-0.810993\pi$
$593$	−8.41758e9			−1.65766			−0.828831	+	0.559499i	$0.810993\pi$
$594$		0			0
$595$	−5.13935e9			−1.00023
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.91250e9	−	3.31254e9i	−0.363586	−	0.629749i	0.624963	−	0.780655i	$-0.285114\pi$
$599$	−1.91250e9	−	3.31254e9i	−0.363586	−	0.629749i	−0.988548	+	0.150906i	$0.951781\pi$
$600$		0			0
$601$	3.62512e8	−	6.27889e8i	0.0681179	−	0.117984i	−0.829955	−	0.557830i	$-0.811634\pi$
$601$	3.62512e8	−	6.27889e8i	0.0681179	−	0.117984i	0.898073	+	0.439847i	$0.144967\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	9.87089e7	−	1.70969e8i	0.0181223	−	0.0313887i
$606$		0			0
$607$	−5.42460e9	−	9.39569e9i	−0.984481	−	1.70517i	−0.644218	−	0.764842i	$-0.722817\pi$
$607$	−5.42460e9	−	9.39569e9i	−0.984481	−	1.70517i	−0.340263	−	0.940330i	$-0.610516\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−3.89879e8			−0.0691489
$612$		0			0
$613$	−7.59484e9			−1.33170			−0.665851	−	0.746085i	$-0.731931\pi$
$613$	−7.59484e9			−1.33170			−0.665851	+	0.746085i	$0.731931\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	5.91168e8	+	1.02393e9i	0.101324	+	0.175498i	0.912230	−	0.409678i	$-0.134359\pi$
$617$	5.91168e8	+	1.02393e9i	0.101324	+	0.175498i	−0.810906	+	0.585176i	$0.801025\pi$
$618$		0			0
$619$	−4.81004e9	+	8.33123e9i	−0.815138	+	1.41186i	0.0940908	+	0.995564i	$0.470006\pi$
$619$	−4.81004e9	+	8.33123e9i	−0.815138	+	1.41186i	−0.909229	+	0.416297i	$0.863328\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−1.16204e9	+	2.01272e9i	−0.192537	+	0.333484i
$624$		0			0
$625$	3.27891e9	+	5.67923e9i	0.537216	+	0.930485i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−5.27662e9			−0.845432
$630$		0			0
$631$	4.21153e9			0.667325			0.333662	−	0.942693i	$-0.391715\pi$
$631$	4.21153e9			0.667325			0.333662	+	0.942693i	$0.391715\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.29307e9	−	2.23967e9i	−0.200408	−	0.347116i
$636$		0			0
$637$	−5.02828e8	+	8.70923e8i	−0.0770781	+	0.133503i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−3.96142e9	+	6.86139e9i	−0.594084	+	1.02898i	0.399591	+	0.916694i	$0.369152\pi$
$641$	−3.96142e9	+	6.86139e9i	−0.594084	+	1.02898i	−0.993675	+	0.112291i	$0.964181\pi$
$642$		0			0
$643$	−1.46169e9	−	2.53172e9i	−0.216829	−	0.375558i	0.737008	−	0.675884i	$-0.236238\pi$
$643$	−1.46169e9	−	2.53172e9i	−0.216829	−	0.375558i	−0.953837	+	0.300326i	$0.902905\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.00413e10			1.45755			0.728774	−	0.684754i	$-0.240090\pi$
$647$	1.00413e10			1.45755			0.728774	+	0.684754i	$0.240090\pi$
$648$		0			0
$649$	−1.40269e9			−0.201421
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7.41652e8	+	1.28458e9i	0.104233	+	0.180536i	0.913424	−	0.407008i	$-0.133428\pi$
$653$	7.41652e8	+	1.28458e9i	0.104233	+	0.180536i	−0.809192	+	0.587545i	$0.800095\pi$
$654$		0			0
$655$	1.84788e9	−	3.20062e9i	0.256938	−	0.445030i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.67543e9	−	2.90193e9i	0.228048	−	0.394991i	−0.729181	−	0.684320i	$-0.760099\pi$
$659$	1.67543e9	−	2.90193e9i	0.228048	−	0.394991i	0.957230	+	0.289329i	$0.0934323\pi$
$660$		0			0
$661$	−1.70018e9	−	2.94480e9i	−0.228976	−	0.396598i	0.728529	−	0.685015i	$-0.240204\pi$
$661$	−1.70018e9	−	2.94480e9i	−0.228976	−	0.396598i	−0.957505	+	0.288417i	$0.906871\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.61397e10			2.12824
$666$		0			0
$667$	6.52716e9			0.851695
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.28991e8	+	2.23419e8i	0.0164828	+	0.0285490i
$672$		0			0
$673$	−4.48300e9	+	7.76478e9i	−0.566912	+	0.981921i	0.429957	+	0.902850i	$0.358529\pi$
$673$	−4.48300e9	+	7.76478e9i	−0.566912	+	0.981921i	−0.996869	+	0.0790714i	$0.974804\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7.44416e9	−	1.28937e10i	0.922052	−	1.59704i	0.125816	−	0.992054i	$-0.459845\pi$
$677$	7.44416e9	−	1.28937e10i	0.922052	−	1.59704i	0.796235	−	0.604987i	$-0.206822\pi$
$678$		0			0
$679$	1.94717e9	+	3.37261e9i	0.238705	+	0.413448i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	7.71503e9			0.926542			0.463271	−	0.886217i	$-0.346676\pi$
$683$	7.71503e9			0.926542			0.463271	+	0.886217i	$0.346676\pi$
$684$		0			0
$685$	1.42428e10			1.69308
$686$		0			0
$687$		0			0
$688$		0			0
$689$	3.79606e8	+	6.57496e8i	0.0442146	+	0.0765819i
$690$		0			0
$691$	−1.26498e9	+	2.19101e9i	−0.145851	+	0.252622i	−0.929690	−	0.368342i	$-0.879925\pi$
$691$	−1.26498e9	+	2.19101e9i	−0.145851	+	0.252622i	0.783839	+	0.620964i	$0.213259\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.29445e8	−	3.97411e8i	0.0259258	−	0.0449048i
$696$		0			0
$697$	−1.92667e9	−	3.33709e9i	−0.215522	−	0.373296i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−1.41167e10			−1.54782			−0.773908	−	0.633298i	$-0.781701\pi$
$701$	−1.41167e10			−1.54782			−0.773908	+	0.633298i	$0.781701\pi$
$702$		0			0
$703$	1.65708e10			1.79887
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.08392e8	−	5.34150e8i	−0.0328197	−	0.0568454i
$708$		0			0
$709$	6.46733e9	−	1.12017e10i	0.681496	−	1.18039i	−0.293028	−	0.956104i	$-0.594663\pi$
$709$	6.46733e9	−	1.12017e10i	0.681496	−	1.18039i	0.974524	−	0.224282i	$-0.0720037\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−6.91324e8	+	1.19741e9i	−0.0714279	+	0.123717i
$714$		0			0
$715$	1.58991e9	+	2.75380e9i	0.162668	+	0.281748i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.22962e10			−1.23373			−0.616864	−	0.787070i	$-0.711597\pi$
$719$	−1.22962e10			−1.23373			−0.616864	+	0.787070i	$0.711597\pi$
$720$		0			0
$721$	2.26258e10			2.24818
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.97617e8	−	5.15487e8i	−0.0290051	−	0.0502383i
$726$		0			0
$727$	3.37402e9	−	5.84398e9i	0.325670	−	0.564077i	−0.655978	−	0.754780i	$-0.727744\pi$
$727$	3.37402e9	−	5.84398e9i	0.325670	−	0.564077i	0.981648	+	0.190704i	$0.0610769\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−6.61208e9	+	1.14525e10i	−0.626076	+	1.08440i
$732$		0			0
$733$	−1.87123e9	−	3.24106e9i	−0.175494	−	0.303965i	0.764838	−	0.644223i	$-0.222819\pi$
$733$	−1.87123e9	−	3.24106e9i	−0.175494	−	0.303965i	−0.940332	+	0.340258i	$0.889486\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.84209e10			1.69502
$738$		0			0
$739$	−1.27399e9			−0.116121			−0.0580606	−	0.998313i	$-0.518492\pi$
$739$	−1.27399e9			−0.116121			−0.0580606	+	0.998313i	$0.518492\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−3.62517e9	−	6.27897e9i	−0.324240	−	0.561601i	0.657118	−	0.753788i	$-0.271775\pi$
$743$	−3.62517e9	−	6.27897e9i	−0.324240	−	0.561601i	−0.981358	+	0.192187i	$0.938442\pi$
$744$		0			0
$745$	5.68817e9	−	9.85220e9i	0.503994	−	0.872944i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	3.61328e9	−	6.25838e9i	0.314206	−	0.544221i
$750$		0			0
$751$	−9.82411e9	−	1.70159e10i	−0.846357	−	1.46593i	−0.884437	−	0.466659i	$-0.845458\pi$
$751$	−9.82411e9	−	1.70159e10i	−0.846357	−	1.46593i	0.0380804	−	0.999275i	$-0.487876\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	5.34190e9			0.451733
$756$		0			0
$757$	−1.81025e10			−1.51671			−0.758356	−	0.651841i	$-0.773997\pi$
$757$	−1.81025e10			−1.51671			−0.758356	+	0.651841i	$0.773997\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.43280e9	−	4.21373e9i	−0.200106	−	0.346593i	0.748457	−	0.663184i	$-0.230795\pi$
$761$	−2.43280e9	−	4.21373e9i	−0.200106	−	0.346593i	−0.948562	+	0.316590i	$0.897462\pi$
$762$		0			0
$763$	1.55281e9	−	2.68954e9i	0.126556	−	0.219201i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.80537e8	−	6.59109e8i	0.0304518	−	0.0527440i
$768$		0			0
$769$	3.32352e9	+	5.75651e9i	0.263546	+	0.456475i	0.967182	−	0.254086i	$-0.0817746\pi$
$769$	3.32352e9	+	5.75651e9i	0.263546	+	0.456475i	−0.703636	+	0.710561i	$0.748441\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	1.79263e10			1.39593			0.697963	−	0.716134i	$-0.254090\pi$
$773$	1.79263e10			1.39593			0.697963	+	0.716134i	$0.254090\pi$
$774$		0			0
$775$	1.26088e8			0.00973012
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.05056e9	+	1.04799e10i	0.458579	+	0.794282i
$780$		0			0
$781$	9.05127e8	−	1.56773e9i	0.0679878	−	0.117758i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−9.65303e9	+	1.67195e10i	−0.712229	+	1.23362i
$786$		0			0
$787$	4.95269e9	+	8.57831e9i	0.362184	+	0.627321i	0.988320	−	0.152393i	$-0.0486978\pi$
$787$	4.95269e9	+	8.57831e9i	0.362184	+	0.627321i	−0.626136	+	0.779714i	$0.715365\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	2.31653e10			1.66426
$792$		0			0
$793$	−1.39976e8			−0.00996777
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.18602e10	−	2.05424e10i	−0.829824	−	1.43730i	−0.898176	−	0.439637i	$-0.855107\pi$
$797$	−1.18602e10	−	2.05424e10i	−0.829824	−	1.43730i	0.0683515	−	0.997661i	$-0.478226\pi$
$798$		0			0
$799$	−1.27252e9	+	2.20406e9i	−0.0882571	+	0.152866i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.84904e9	−	3.20263e9i	0.126021	−	0.218275i
$804$		0			0
$805$	−1.12099e10	−	1.94160e10i	−0.757381	−	1.31182i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	2.49700e10			1.65805			0.829027	−	0.559208i	$-0.188895\pi$
$809$	2.49700e10			1.65805			0.829027	+	0.559208i	$0.188895\pi$
$810$		0			0
$811$	1.12321e9			0.0739412			0.0369706	−	0.999316i	$-0.488229\pi$
$811$	1.12321e9			0.0739412			0.0369706	+	0.999316i	$0.488229\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	5.73487e9	+	9.93308e9i	0.371084	+	0.642736i
$816$		0			0
$817$	2.07647e10	−	3.59655e10i	1.33214	−	2.30733i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−7.45639e9	+	1.29148e10i	−0.470249	+	0.814494i	−0.999421	−	0.0340198i	$-0.989169\pi$
$821$	−7.45639e9	+	1.29148e10i	−0.470249	+	0.814494i	0.529173	+	0.848514i	$0.322502\pi$
$822$		0			0
$823$	−1.40501e9	−	2.43356e9i	−0.0878580	−	0.152175i	0.818747	−	0.574154i	$-0.194669\pi$
$823$	−1.40501e9	−	2.43356e9i	−0.0878580	−	0.152175i	−0.906605	+	0.421979i	$0.861336\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.92634e10			1.18430			0.592151	−	0.805827i	$-0.298279\pi$
$827$	1.92634e10			1.18430			0.592151	+	0.805827i	$0.298279\pi$
$828$		0			0
$829$	−3.12798e10			−1.90688			−0.953440	−	0.301582i	$-0.902485\pi$
$829$	−3.12798e10			−1.90688			−0.953440	+	0.301582i	$0.902485\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3.28233e9	+	5.68517e9i	0.196755	+	0.340789i
$834$		0			0
$835$	1.41287e10	−	2.44716e10i	0.839843	−	1.45465i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−7.65355e9	+	1.32563e10i	−0.447400	+	0.774920i	−0.998216	−	0.0597070i	$-0.980983\pi$
$839$	−7.65355e9	+	1.32563e10i	−0.447400	+	0.774920i	0.550816	+	0.834627i	$0.314317\pi$
$840$		0			0
$841$	4.20021e9	+	7.27498e9i	0.243492	+	0.421741i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	1.65099e10			0.941336
$846$		0			0
$847$	−7.55332e8			−0.0427116
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−1.15093e10	−	1.99346e10i	−0.640168	−	1.10880i
$852$		0			0
$853$	−1.59603e10	+	2.76441e10i	−0.880480	+	1.52504i	−0.0296720	+	0.999560i	$0.509446\pi$
$853$	−1.59603e10	+	2.76441e10i	−0.880480	+	1.52504i	−0.850808	+	0.525477i	$0.823887\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−1.48319e10	+	2.56895e10i	−0.804938	+	1.39419i	0.111395	+	0.993776i	$0.464468\pi$
$857$	−1.48319e10	+	2.56895e10i	−0.804938	+	1.39419i	−0.916333	+	0.400417i	$0.868865\pi$
$858$		0			0
$859$	−8.51597e9	−	1.47501e10i	−0.458414	−	0.793997i	0.540463	−	0.841368i	$-0.318249\pi$
$859$	−8.51597e9	−	1.47501e10i	−0.458414	−	0.793997i	−0.998877	+	0.0473709i	$0.984916\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−3.16249e9			−0.167491			−0.0837454	−	0.996487i	$-0.526688\pi$
$863$	−3.16249e9			−0.167491			−0.0837454	+	0.996487i	$0.526688\pi$
$864$		0			0
$865$	1.61005e10			0.845829
$866$		0			0
$867$		0			0
$868$		0			0
$869$	2.19782e9	+	3.80673e9i	0.113611	+	0.196781i
$870$		0			0
$871$	−4.99741e9	+	8.65578e9i	−0.256261	+	0.443856i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	1.15996e10	−	2.00911e10i	0.585349	−	1.01385i
$876$		0			0
$877$	−3.19898e9	−	5.54079e9i	−0.160145	−	0.277379i	0.774776	−	0.632236i	$-0.217863\pi$
$877$	−3.19898e9	−	5.54079e9i	−0.160145	−	0.277379i	−0.934920	+	0.354857i	$0.884529\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	1.45065e10			0.714739			0.357369	−	0.933963i	$-0.383674\pi$
$881$	1.45065e10			0.714739			0.357369	+	0.933963i	$0.383674\pi$
$882$		0			0
$883$	−2.39105e10			−1.16876			−0.584382	−	0.811479i	$-0.698663\pi$
$883$	−2.39105e10			−1.16876			−0.584382	+	0.811479i	$0.698663\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.54012e10	+	2.66757e10i	0.741007	+	1.28346i	0.952037	+	0.305982i	$0.0989849\pi$
$887$	1.54012e10	+	2.66757e10i	0.741007	+	1.28346i	−0.211030	+	0.977480i	$0.567682\pi$
$888$		0			0
$889$	−4.94737e9	+	8.56909e9i	−0.236166	+	0.409052i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.99624e9	−	6.92168e9i	0.187789	−	0.325261i
$894$		0			0
$895$	1.43440e10	+	2.48445e10i	0.668789	+	1.15838i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.87458e9			0.0860488
$900$		0			0
$901$	4.95594e9			0.225730
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.31253e10	+	2.27338e10i	0.588628	+	1.01953i
$906$		0			0
$907$	6.06562e9	−	1.05060e10i	0.269929	−	0.467531i	−0.698914	−	0.715206i	$-0.746333\pi$
$907$	6.06562e9	−	1.05060e10i	0.269929	−	0.467531i	0.968843	+	0.247675i	$0.0796664\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−9.73568e9	+	1.68627e10i	−0.426630	+	0.738945i	−0.996571	−	0.0827403i	$-0.973633\pi$
$911$	−9.73568e9	+	1.68627e10i	−0.426630	+	0.738945i	0.569941	+	0.821686i	$0.306966\pi$
$912$		0			0
$913$	8.31697e9	+	1.44054e10i	0.361674	+	0.626438i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−1.41402e10			−0.605567
$918$		0			0
$919$	−2.10755e10			−0.895721			−0.447861	−	0.894103i	$-0.647814\pi$
$919$	−2.10755e10			−0.895721			−0.447861	+	0.894103i	$0.647814\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	4.91105e8	+	8.50619e8i	0.0205574	+	0.0356065i
$924$		0			0
$925$	−1.04957e9	+	1.81791e9i	−0.0436028	+	0.0755223i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.48141e9	−	6.02997e9i	0.142462	−	0.246752i	−0.785961	−	0.618276i	$-0.787831\pi$
$929$	3.48141e9	−	6.02997e9i	0.142462	−	0.246752i	0.928423	+	0.371524i	$0.121165\pi$
$930$		0			0
$931$	−1.03079e10	−	1.78538e10i	−0.418646	−	0.725116i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.07571e10			0.830472
$936$		0			0
$937$	1.58623e10			0.629908			0.314954	−	0.949107i	$-0.398011\pi$
$937$	1.58623e10			0.629908			0.314954	+	0.949107i	$0.398011\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.62492e10	−	2.81444e10i	−0.635722	−	1.10110i	−0.986362	−	0.164592i	$-0.947369\pi$
$941$	−1.62492e10	−	2.81444e10i	−0.635722	−	1.10110i	0.350640	−	0.936510i	$-0.385964\pi$
$942$		0			0
$943$	8.40483e9	−	1.45576e10i	0.326391	−	0.565326i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.70871e9	+	4.69162e9i	−0.103642	+	0.179514i	−0.913183	−	0.407550i	$-0.866383\pi$
$947$	−2.70871e9	+	4.69162e9i	−0.103642	+	0.179514i	0.809540	+	0.587064i	$0.199716\pi$
$948$		0			0
$949$	1.00326e9	+	1.73769e9i	0.0381049	+	0.0659996i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−2.62658e9			−0.0983028			−0.0491514	−	0.998791i	$-0.515652\pi$
$953$	−2.62658e9			−0.0983028			−0.0491514	+	0.998791i	$0.515652\pi$
$954$		0			0
$955$	3.02762e10			1.12484
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.72468e10	−	4.71928e10i	−0.997586	−	1.72787i
$960$		0			0
$961$	1.35578e10	−	2.34827e10i	0.492783	−	0.853526i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.93296e9	−	3.34799e9i	0.0692433	−	0.119933i
$966$		0			0
$967$	1.95753e10	+	3.39054e10i	0.696171	+	1.20580i	0.969784	+	0.243963i	$0.0784477\pi$
$967$	1.95753e10	+	3.39054e10i	0.696171	+	1.20580i	−0.273614	+	0.961840i	$0.588219\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−2.49003e10			−0.872846			−0.436423	−	0.899742i	$-0.643755\pi$
$971$	−2.49003e10			−0.872846			−0.436423	+	0.899742i	$0.643755\pi$
$972$		0			0
$973$	−1.75574e9			−0.0611034
$974$		0			0
$975$		0			0
$976$		0			0
$977$	2.22902e9	+	3.86078e9i	0.0764686	+	0.132448i	0.901724	−	0.432312i	$-0.142302\pi$
$977$	2.22902e9	+	3.86078e9i	0.0764686	+	0.132448i	−0.825255	+	0.564760i	$0.808969\pi$
$978$		0			0
$979$	4.69332e9	−	8.12906e9i	0.159860	−	0.276886i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	1.32778e10	−	2.29979e10i	0.445851	−	0.772237i	−0.552260	−	0.833672i	$-0.686234\pi$
$983$	1.32778e10	−	2.29979e10i	0.445851	−	0.772237i	0.998111	+	0.0614353i	$0.0195678\pi$
$984$		0			0
$985$	2.48916e10	+	4.31135e10i	0.829901	+	1.43743i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−5.76886e10			−1.89628
$990$		0			0
$991$	−6.89473e9			−0.225040			−0.112520	−	0.993649i	$-0.535892\pi$
$991$	−6.89473e9			−0.225040			−0.112520	+	0.993649i	$0.535892\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	1.80207e10	+	3.12128e10i	0.579951	+	1.00451i
$996$		0			0
$997$	2.56614e8	−	4.44468e8i	0.00820062	−	0.0142039i	−0.861896	−	0.507085i	$-0.830723\pi$
$997$	2.56614e8	−	4.44468e8i	0.00820062	−	0.0142039i	0.870097	+	0.492881i	$0.164056\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.8.i.c.289.5		12
3.2	odd	2		144.8.i.c.97.1		12
4.3	odd	2		27.8.c.a.19.2		12
9.4	even	3	inner	432.8.i.c.145.5		12
9.5	odd	6		144.8.i.c.49.1		12
12.11	even	2		9.8.c.a.7.5	yes	12
36.7	odd	6		81.8.a.c.1.5		6
36.11	even	6		81.8.a.e.1.2		6
36.23	even	6		9.8.c.a.4.5	✓	12
36.31	odd	6		27.8.c.a.10.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.8.c.a.4.5	✓	12	36.23	even	6
9.8.c.a.7.5	yes	12	12.11	even	2
27.8.c.a.10.2		12	36.31	odd	6
27.8.c.a.19.2		12	4.3	odd	2
81.8.a.c.1.5		6	36.7	odd	6
81.8.a.e.1.2		6	36.11	even	6
144.8.i.c.49.1		12	9.5	odd	6
144.8.i.c.97.1		12	3.2	odd	2
432.8.i.c.145.5		12	9.4	even	3	inner
432.8.i.c.289.5		12	1.1	even	1	trivial

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	432.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(145.304 + 251.673i) q^{5} +(555.940 - 962.916i) q^{7} +(-2245.36 + 3889.07i) q^{11} +(-1218.29 - 2110.14i) q^{13} -15905.4 q^{17} +49949.6 q^{19} +(-34692.5 - 60089.2i) q^{23} +(-3163.73 + 5479.74i) q^{25} +(-47035.8 + 81468.4i) q^{29} +(-9963.58 - 17257.4i) q^{31} +323120. q^{35} +331750. q^{37} +(121133. + 209809. i) q^{41} +(415713. - 720036. i) q^{43} +(80005.3 - 138573. i) q^{47} +(-206366. - 357437. i) q^{49} -311589. q^{53} -1.30503e6 q^{55} +(156177. + 270506. i) q^{59} +(28723.9 - 49751.3i) q^{61} +(354044. - 613221. i) q^{65} +(-2.05100e6 - 3.55243e6i) q^{67} -403110. q^{71} -823496. q^{73} +(2.49656e6 + 4.32418e6i) q^{77} +(489414. - 847689. i) q^{79} +(1.85204e6 - 3.20782e6i) q^{83} +(-2.31111e6 - 4.00296e6i) q^{85} -2.09023e6 q^{89} -2.70918e6 q^{91} +(7.25786e6 + 1.25710e7i) q^{95} +(-1.75125e6 + 3.03325e6i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 180 q^{5} + 84 q^{7} - 8460 q^{11} - 1848 q^{13} - 30564 q^{17} - 24432 q^{19} - 51588 q^{23} + 4746 q^{25} + 414648 q^{29} - 8196 q^{31} + 2210616 q^{35} + 139344 q^{37} + 1731582 q^{41} - 408372 q^{43}+ \cdots + 9977226 q^{97}+O(q^{100}) \) 12 * q + 180 * q^5 + 84 * q^7 - 8460 * q^11 - 1848 * q^13 - 30564 * q^17 - 24432 * q^19 - 51588 * q^23 + 4746 * q^25 + 414648 * q^29 - 8196 * q^31 + 2210616 * q^35 + 139344 * q^37 + 1731582 * q^41 - 408372 * q^43 - 1631484 * q^47 - 179010 * q^49 - 2835648 * q^53 + 16056 * q^55 - 2055636 * q^59 - 2723196 * q^61 + 1387620 * q^65 - 3806556 * q^67 + 2408400 * q^71 - 10670052 * q^73 - 3478824 * q^77 - 6020916 * q^79 + 9605052 * q^83 - 1698624 * q^85 + 24630264 * q^89 - 13570104 * q^91 + 10422072 * q^95 + 9977226 * q^97

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