LMFDB - Embedded newform 1584.2.cd.c.17.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1584,2,Mod(17,1584)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1584, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 5, 9]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1584.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1584 = 2^{4} \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1584.cd (of order $10$, degree $4$, 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:	$12.6483036802$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 $ x^16 + 2x^14 - 16x^12 - 72x^10 + 26x^8 + 360x^6 + 725x^4 + 1000*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			17.3
Root			$0.556839 - 1.81878i$ of defining polynomial
Character	$\chi$	$=$	1584.17
Dual form			1584.2.cd.c.1025.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0381457 + 0.0123943i) q^{5} +(-0.145094 - 0.199704i) q^{7} +O(q^{10})$	$q+(0.0381457 + 0.0123943i) q^{5} +(-0.145094 - 0.199704i) q^{7} +(-3.12033 + 1.12407i) q^{11} +(-2.18888 + 0.711209i) q^{13} +(-1.32142 + 4.06692i) q^{17} +(3.64429 - 5.01593i) q^{19} -6.79984i q^{23} +(-4.04378 - 2.93798i) q^{25} +(4.52705 - 3.28909i) q^{29} +(-1.48247 - 4.56258i) q^{31} +(-0.00305951 - 0.00941619i) q^{35} +(3.26102 - 2.36927i) q^{37} +(-7.76893 - 5.64446i) q^{41} -1.03166i q^{43} +(-6.53982 + 9.00129i) q^{47} +(2.14429 - 6.59944i) q^{49} +(-8.52885 + 2.77119i) q^{53} +(-0.132959 + 0.00420408i) q^{55} +(1.63893 + 2.25580i) q^{59} +(8.06923 + 2.62185i) q^{61} -0.0923111 q^{65} -7.94588 q^{67} +(-3.16559 - 1.02856i) q^{71} +(-6.96743 - 9.58984i) q^{73} +(0.677222 + 0.460048i) q^{77} +(2.86363 - 0.930451i) q^{79} +(1.63587 - 5.03470i) q^{83} +(-0.100813 + 0.138757i) q^{85} +8.54422i q^{89} +(0.459624 + 0.333936i) q^{91} +(0.201183 - 0.146168i) q^{95} +(-0.935778 - 2.88003i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 32 q^{25} - 16 q^{31} - 12 q^{37} - 24 q^{49} - 16 q^{55} - 96 q^{67} - 20 q^{73} - 100 q^{85} + 72 q^{91} + 60 q^{97}+O(q^{100}) $ 16 * q - 32 * q^25 - 16 * q^31 - 12 * q^37 - 24 * q^49 - 16 * q^55 - 96 * q^67 - 20 * q^73 - 100 * q^85 + 72 * q^91 + 60 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1584\mathbb{Z}\right)^\times$.

$n$	$145$	$353$	$991$	$1189$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.0381457	+	0.0123943i	0.0170593	+	0.00554289i	0.317534	−	0.948247i	$-0.397145\pi$
$5$	0.0381457	+	0.0123943i	0.0170593	+	0.00554289i	−0.300475	+	0.953790i	$0.597145\pi$
$6$		0			0
$7$	−0.145094	−	0.199704i	−0.0548403	−	0.0754811i	0.780716	−	0.624886i	$-0.214855\pi$
$7$	−0.145094	−	0.199704i	−0.0548403	−	0.0754811i	−0.835556	+	0.549405i	$0.814855\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.12033	+	1.12407i	−0.940815	+	0.338919i
$11$	−3.12033	+	1.12407i	−0.940815	+	0.338919i
$12$		0			0
$13$	−2.18888	+	0.711209i	−0.607085	+	0.197254i	−0.596398	−	0.802689i	$-0.703402\pi$
$13$	−2.18888	+	0.711209i	−0.607085	+	0.197254i	−0.0106874	+	0.999943i	$0.503402\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.32142	+	4.06692i	−0.320492	+	0.986372i	0.652943	+	0.757407i	$0.273534\pi$
$17$	−1.32142	+	4.06692i	−0.320492	+	0.986372i	−0.973435	+	0.228965i	$0.926466\pi$
$18$		0			0
$19$	3.64429	−	5.01593i	0.836057	−	1.15073i	−0.150708	−	0.988578i	$-0.548155\pi$
$19$	3.64429	−	5.01593i	0.836057	−	1.15073i	0.986765	−	0.162156i	$-0.0518447\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	6.79984i		−	1.41786i	−0.705277	−	0.708932i	$-0.749177\pi$
$23$		−	6.79984i		−	1.41786i	0.705277	−	0.708932i	$-0.250823\pi$
$24$		0			0
$25$	−4.04378	−	2.93798i	−0.808757	−	0.587596i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.52705	−	3.28909i	0.840652	−	0.610769i	−0.0819007	−	0.996640i	$-0.526099\pi$
$29$	4.52705	−	3.28909i	0.840652	−	0.610769i	0.922553	+	0.385871i	$0.126099\pi$
$30$		0			0
$31$	−1.48247	−	4.56258i	−0.266260	−	0.819463i	−0.991401	−	0.130863i	$-0.958225\pi$
$31$	−1.48247	−	4.56258i	−0.266260	−	0.819463i	0.725141	−	0.688601i	$-0.241775\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.00305951	−	0.00941619i	−0.000517151	−	0.00159163i
$36$		0			0
$37$	3.26102	−	2.36927i	0.536109	−	0.389506i	−0.286529	−	0.958072i	$-0.592502\pi$
$37$	3.26102	−	2.36927i	0.536109	−	0.389506i	0.822638	+	0.568566i	$0.192502\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−7.76893	−	5.64446i	−1.21330	−	0.881517i	−0.217777	−	0.975999i	$-0.569881\pi$
$41$	−7.76893	−	5.64446i	−1.21330	−	0.881517i	−0.995527	+	0.0944820i	$0.969881\pi$
$42$		0			0
$43$		−	1.03166i		−	0.157327i	−0.996901	−	0.0786636i	$-0.974935\pi$
$43$		−	1.03166i		−	0.157327i	0.996901	−	0.0786636i	$-0.0250653\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−6.53982	+	9.00129i	−0.953931	+	1.31297i	−0.00417211	+	0.999991i	$0.501328\pi$
$47$	−6.53982	+	9.00129i	−0.953931	+	1.31297i	−0.949759	+	0.312982i	$0.898672\pi$
$48$		0			0
$49$	2.14429	−	6.59944i	0.306327	−	0.942778i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−8.52885	+	2.77119i	−1.17153	+	0.380652i	−0.829213	−	0.558933i	$-0.811211\pi$
$53$	−8.52885	+	2.77119i	−1.17153	+	0.380652i	−0.342314	+	0.939585i	$0.611211\pi$
$54$		0			0
$55$	−0.132959	+	0.00420408i	−0.0179282	+	0.000566878i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.63893	+	2.25580i	0.213371	+	0.293680i	0.902265	−	0.431182i	$-0.141903\pi$
$59$	1.63893	+	2.25580i	0.213371	+	0.293680i	−0.688894	+	0.724862i	$0.741903\pi$
$60$		0			0
$61$	8.06923	+	2.62185i	1.03316	+	0.335694i	0.776039	−	0.630685i	$-0.217226\pi$
$61$	8.06923	+	2.62185i	1.03316	+	0.335694i	0.257121	+	0.966379i	$0.417226\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.0923111			−0.0114498
$66$		0			0
$67$	−7.94588			−0.970744			−0.485372	−	0.874308i	$-0.661316\pi$
$67$	−7.94588			−0.970744			−0.485372	+	0.874308i	$0.661316\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−3.16559	−	1.02856i	−0.375687	−	0.122068i	0.115086	−	0.993355i	$-0.463286\pi$
$71$	−3.16559	−	1.02856i	−0.375687	−	0.122068i	−0.490773	+	0.871288i	$0.663286\pi$
$72$		0			0
$73$	−6.96743	−	9.58984i	−0.815476	−	1.12241i	−0.990455	−	0.137834i	$-0.955986\pi$
$73$	−6.96743	−	9.58984i	−0.815476	−	1.12241i	0.174980	−	0.984572i	$-0.444014\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.677222	+	0.460048i	0.0771766	+	0.0524274i
$78$		0			0
$79$	2.86363	−	0.930451i	0.322184	−	0.104684i	−0.143460	−	0.989656i	$-0.545823\pi$
$79$	2.86363	−	0.930451i	0.322184	−	0.104684i	0.465644	+	0.884972i	$0.345823\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	1.63587	−	5.03470i	0.179560	−	0.552630i	−0.820252	−	0.572002i	$-0.806167\pi$
$83$	1.63587	−	5.03470i	0.179560	−	0.552630i	0.999812	+	0.0193724i	$0.00616680\pi$
$84$		0			0
$85$	−0.100813	+	0.138757i	−0.0109347	+	0.0150503i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			8.54422i			0.905686i	0.891590	+	0.452843i	$0.149590\pi$
$89$			8.54422i			0.905686i	−0.891590	+	0.452843i	$0.850410\pi$
$90$		0			0
$91$	0.459624	+	0.333936i	0.0481817	+	0.0350060i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.201183	−	0.146168i	0.0206409	−	0.0149965i
$96$		0			0
$97$	−0.935778	−	2.88003i	−0.0950139	−	0.292423i	0.892243	−	0.451555i	$-0.149130\pi$
$97$	−0.935778	−	2.88003i	−0.0950139	−	0.292423i	−0.987257	+	0.159132i	$0.949130\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.14828	−	6.61172i	−0.213762	−	0.657891i	−0.999239	−	0.0390007i	$-0.987583\pi$
$101$	−2.14828	−	6.61172i	−0.213762	−	0.657891i	0.785477	−	0.618890i	$-0.212417\pi$
$102$		0			0
$103$	10.6138	−	7.71139i	1.04581	−	0.759826i	0.0743996	−	0.997229i	$-0.476296\pi$
$103$	10.6138	−	7.71139i	1.04581	−	0.759826i	0.971411	+	0.237402i	$0.0762960\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.10712	+	0.804368i	0.107029	+	0.0777612i	0.640012	−	0.768365i	$-0.278929\pi$
$107$	1.10712	+	0.804368i	0.107029	+	0.0777612i	−0.532983	+	0.846126i	$0.678929\pi$
$108$		0			0
$109$		−	7.34454i		−	0.703480i	−0.936098	−	0.351740i	$-0.885590\pi$
$109$		−	7.34454i		−	0.703480i	0.936098	−	0.351740i	$-0.114410\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.310669	−	0.427600i	0.0292253	−	0.0402252i	−0.794154	−	0.607716i	$-0.792086\pi$
$113$	0.310669	−	0.427600i	0.0292253	−	0.0402252i	0.823380	+	0.567491i	$0.192086\pi$
$114$		0			0
$115$	0.0842791	−	0.259385i	0.00785907	−	0.0241877i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.00391	−	0.326190i	0.0920284	−	0.0299018i
$120$		0			0
$121$	8.47294	−	7.01493i	0.770267	−	0.637721i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.235715	−	0.324434i	−0.0210830	−	0.0290183i
$126$		0			0
$127$	−12.1468	−	3.94673i	−1.07785	−	0.350215i	−0.284311	−	0.958732i	$-0.591765\pi$
$127$	−12.1468	−	3.94673i	−1.07785	−	0.350215i	−0.793541	+	0.608517i	$0.791765\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−18.1534			−1.58607			−0.793033	−	0.609178i	$-0.791499\pi$
$131$	−18.1534			−1.58607			−0.793033	+	0.609178i	$0.791499\pi$
$132$		0			0
$133$	−1.53047			−0.132708
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−15.2863	−	4.96682i	−1.30600	−	0.424344i	−0.428334	−	0.903621i	$-0.640899\pi$
$137$	−15.2863	−	4.96682i	−1.30600	−	0.424344i	−0.877664	+	0.479276i	$0.840899\pi$
$138$		0			0
$139$	−2.26727	−	3.12062i	−0.192307	−	0.264688i	0.701965	−	0.712211i	$-0.252306\pi$
$139$	−2.26727	−	3.12062i	−0.192307	−	0.264688i	−0.894272	+	0.447523i	$0.852306\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	6.03057	−	4.67966i	0.504302	−	0.391333i
$144$		0			0
$145$	0.213453	−	0.0693552i	0.0177263	−	0.00575964i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.17360	−	9.76734i	0.259992	−	0.800172i	−0.732813	−	0.680430i	$-0.761793\pi$
$149$	3.17360	−	9.76734i	0.259992	−	0.800172i	0.992805	−	0.119742i	$-0.0382068\pi$
$150$		0			0
$151$	−5.15512	+	7.09542i	−0.419518	+	0.577417i	−0.965508	−	0.260375i	$-0.916154\pi$
$151$	−5.15512	+	7.09542i	−0.419518	+	0.577417i	0.545990	+	0.837792i	$0.316154\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	0.192417i		−	0.0154553i
$156$		0			0
$157$	10.5422	+	7.65934i	0.841357	+	0.611282i	0.922749	−	0.385400i	$-0.125937\pi$
$157$	10.5422	+	7.65934i	0.841357	+	0.611282i	−0.0813923	+	0.996682i	$0.525937\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.35796	+	0.986614i	−0.107022	+	0.0777561i
$162$		0			0
$163$	2.83608	+	8.72855i	0.222139	+	0.683673i	0.998569	+	0.0534700i	$0.0170281\pi$
$163$	2.83608	+	8.72855i	0.222139	+	0.683673i	−0.776431	+	0.630203i	$0.782972\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.35141	+	7.23691i	0.181958	+	0.560009i	0.999883	−	0.0153164i	$-0.00487554\pi$
$167$	2.35141	+	7.23691i	0.181958	+	0.560009i	−0.817925	+	0.575325i	$0.804876\pi$
$168$		0			0
$169$	−6.23186	+	4.52771i	−0.479374	+	0.348285i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	13.4462	+	9.76923i	1.02230	+	0.742741i	0.966752	−	0.255715i	$-0.0823109\pi$
$173$	13.4462	+	9.76923i	1.02230	+	0.742741i	0.0555432	+	0.998456i	$0.482311\pi$
$174$		0			0
$175$			1.23384i			0.0932698i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.14376	−	5.70340i	0.309719	−	0.426292i	−0.625574	−	0.780165i	$-0.715135\pi$
$179$	4.14376	−	5.70340i	0.309719	−	0.426292i	0.935294	+	0.353872i	$0.115135\pi$
$180$		0			0
$181$	−6.52756	+	20.0898i	−0.485189	+	1.49326i	0.346517	+	0.938044i	$0.387364\pi$
$181$	−6.52756	+	20.0898i	−0.485189	+	1.49326i	−0.831706	+	0.555216i	$0.812636\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.153759	−	0.0499594i	0.0113046	−	0.00367309i
$186$		0			0
$187$	−0.448220	−	14.1755i	−0.0327771	−	1.03662i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.03400	+	11.0579i	0.581320	+	0.800118i	0.993839	−	0.110831i	$-0.0353511\pi$
$191$	8.03400	+	11.0579i	0.581320	+	0.800118i	−0.412519	+	0.910949i	$0.635351\pi$
$192$		0			0
$193$	−23.8096	−	7.73620i	−1.71385	−	0.556864i	−0.722884	−	0.690969i	$-0.757184\pi$
$193$	−23.8096	−	7.73620i	−1.71385	−	0.556864i	−0.990967	+	0.134105i	$0.957184\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	21.0442			1.49934			0.749668	−	0.661814i	$-0.230213\pi$
$197$	21.0442			1.49934			0.749668	+	0.661814i	$0.230213\pi$
$198$		0			0
$199$	10.3709			0.735176			0.367588	−	0.929989i	$-0.380184\pi$
$199$	10.3709			0.735176			0.367588	+	0.929989i	$0.380184\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.31369	−	0.426845i	−0.0922031	−	0.0299586i
$204$		0			0
$205$	−0.226392	−	0.311602i	−0.0158119	−	0.0217632i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−5.73314	+	19.7478i	−0.396569	+	1.36598i
$210$		0			0
$211$	17.8262	−	5.79210i	1.22721	−	0.398744i	0.377506	−	0.926007i	$-0.376782\pi$
$211$	17.8262	−	5.79210i	1.22721	−	0.398744i	0.849702	+	0.527263i	$0.176782\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.0127867	−	0.0393535i	0.000872048	−	0.00268389i
$216$		0			0
$217$	−0.696069	+	0.958057i	−0.0472523	+	0.0650372i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	9.84179i		−	0.662031i
$222$		0			0
$223$	7.82233	+	5.68326i	0.523822	+	0.380579i	0.818042	−	0.575159i	$-0.195060\pi$
$223$	7.82233	+	5.68326i	0.523822	+	0.380579i	−0.294220	+	0.955738i	$0.595060\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	9.47859	−	6.88660i	0.629116	−	0.457080i	−0.226978	−	0.973900i	$-0.572884\pi$
$227$	9.47859	−	6.88660i	0.629116	−	0.457080i	0.856094	+	0.516820i	$0.172884\pi$
$228$		0			0
$229$	6.32872	+	19.4778i	0.418214	+	1.28713i	0.909345	+	0.416044i	$0.136584\pi$
$229$	6.32872	+	19.4778i	0.418214	+	1.28713i	−0.491131	+	0.871086i	$0.663416\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.98842	+	15.3528i	0.326802	+	1.00579i	0.970621	+	0.240615i	$0.0773492\pi$
$233$	4.98842	+	15.3528i	0.326802	+	1.00579i	−0.643818	+	0.765178i	$0.722651\pi$
$234$		0			0
$235$	−0.361031	+	0.262304i	−0.0235510	+	0.0171108i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−22.9660	−	16.6858i	−1.48555	−	1.07931i	−0.975716	−	0.219038i	$-0.929708\pi$
$239$	−22.9660	−	16.6858i	−1.48555	−	1.07931i	−0.509830	−	0.860275i	$-0.670292\pi$
$240$		0			0
$241$		−	14.3654i		−	0.925357i	−0.886526	−	0.462679i	$-0.846888\pi$
$241$		−	14.3654i		−	0.925357i	0.886526	−	0.462679i	$-0.153112\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.163591	−	0.225163i	0.0104514	−	0.0143852i
$246$		0			0
$247$	−4.40952	+	13.5711i	−0.280571	+	0.863509i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.60298	+	2.14544i	−0.416776	+	0.135419i	−0.509896	−	0.860236i	$-0.670316\pi$
$251$	−6.60298	+	2.14544i	−0.416776	+	0.135419i	0.0931196	+	0.995655i	$0.470316\pi$
$252$		0			0
$253$	7.64348	+	21.2178i	0.480542	+	1.33395i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−6.12372	−	8.42858i	−0.381987	−	0.525760i	0.574122	−	0.818769i	$-0.305343\pi$
$257$	−6.12372	−	8.42858i	−0.381987	−	0.525760i	−0.956110	+	0.293009i	$0.905343\pi$
$258$		0			0
$259$	−0.946307	−	0.307474i	−0.0588007	−	0.0191055i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.26110			0.262751			0.131375	−	0.991333i	$-0.458061\pi$
$263$	4.26110			0.262751			0.131375	+	0.991333i	$0.458061\pi$
$264$		0			0
$265$	−0.359686			−0.0220953
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.5223	−	3.41889i	−0.641553	−	0.208453i	−0.0298672	−	0.999554i	$-0.509508\pi$
$269$	−10.5223	−	3.41889i	−0.641553	−	0.208453i	−0.611686	+	0.791101i	$0.709508\pi$
$270$		0			0
$271$	−9.34327	−	12.8599i	−0.567563	−	0.781184i	0.424700	−	0.905334i	$-0.360379\pi$
$271$	−9.34327	−	12.8599i	−0.567563	−	0.781184i	−0.992263	+	0.124150i	$0.960379\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	15.9204	+	4.62198i	0.960038	+	0.278716i
$276$		0			0
$277$	10.7860	−	3.50458i	0.648066	−	0.210570i	0.0335051	−	0.999439i	$-0.489333\pi$
$277$	10.7860	−	3.50458i	0.648066	−	0.210570i	0.614561	+	0.788869i	$0.289333\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.482158	−	1.48393i	0.0287631	−	0.0885238i	−0.935644	−	0.352944i	$-0.885181\pi$
$281$	0.482158	−	1.48393i	0.0287631	−	0.0885238i	0.964408	+	0.264420i	$0.0851806\pi$
$282$		0			0
$283$	−15.6148	+	21.4919i	−0.928202	+	1.27756i	0.0323551	+	0.999476i	$0.489699\pi$
$283$	−15.6148	+	21.4919i	−0.928202	+	1.27756i	−0.960557	+	0.278084i	$0.910301\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			2.37046i			0.139924i
$288$		0			0
$289$	−1.04038	−	0.755878i	−0.0611986	−	0.0444634i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	21.3051	−	15.4791i	1.24466	−	0.904296i	0.246757	−	0.969077i	$-0.420635\pi$
$293$	21.3051	−	15.4791i	1.24466	−	0.904296i	0.997900	+	0.0647811i	$0.0206349\pi$
$294$		0			0
$295$	0.0345592	+	0.106362i	0.00201211	+	0.00619265i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	4.83611	+	14.8840i	0.279679	+	0.860765i
$300$		0			0
$301$	−0.206028	+	0.149688i	−0.0118752	+	0.00862786i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.275310	+	0.200025i	0.0157642	+	0.0114534i
$306$		0			0
$307$			26.0083i			1.48437i	0.670195	+	0.742185i	$0.266211\pi$
$307$			26.0083i			1.48437i	−0.670195	+	0.742185i	$0.733789\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	7.83210	−	10.7800i	0.444118	−	0.611276i	−0.527003	−	0.849863i	$-0.676684\pi$
$311$	7.83210	−	10.7800i	0.444118	−	0.611276i	0.971121	+	0.238588i	$0.0766844\pi$
$312$		0			0
$313$	−3.47592	+	10.6978i	−0.196471	+	0.604675i	0.803486	+	0.595324i	$0.202976\pi$
$313$	−3.47592	+	10.6978i	−0.196471	+	0.604675i	−0.999956	+	0.00935037i	$0.997024\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.4166	−	3.38455i	0.585053	−	0.190095i	−0.00151019	−	0.999999i	$-0.500481\pi$
$317$	10.4166	−	3.38455i	0.585053	−	0.190095i	0.586563	+	0.809904i	$0.300481\pi$
$318$		0			0
$319$	−10.4287	+	15.3518i	−0.583897	+	0.859535i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	15.5837	+	21.4492i	0.867103	+	1.19346i
$324$		0			0
$325$	10.9409	+	3.55490i	0.606890	+	0.197191i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.74648			0.151419
$330$		0			0
$331$	−4.23285			−0.232659			−0.116329	−	0.993211i	$-0.537113\pi$
$331$	−4.23285			−0.232659			−0.116329	+	0.993211i	$0.537113\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.303101	−	0.0984835i	−0.0165602	−	0.00538073i
$336$		0			0
$337$	−1.56491	−	2.15391i	−0.0852460	−	0.117331i	0.764264	−	0.644903i	$-0.223102\pi$
$337$	−1.56491	−	2.15391i	−0.0852460	−	0.117331i	−0.849510	+	0.527572i	$0.823102\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	9.75446	+	12.5704i	0.528233	+	0.680723i
$342$		0			0
$343$	−3.27243	+	1.06328i	−0.176694	+	0.0574115i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.13066	−	15.7905i	0.275428	−	0.847681i	−0.713678	−	0.700474i	$-0.752972\pi$
$347$	5.13066	−	15.7905i	0.275428	−	0.847681i	0.989106	−	0.147207i	$-0.0470282\pi$
$348$		0			0
$349$	−8.09660	+	11.1440i	−0.433401	+	0.596525i	−0.968730	−	0.248118i	$-0.920188\pi$
$349$	−8.09660	+	11.1440i	−0.433401	+	0.596525i	0.535329	+	0.844644i	$0.320188\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	11.0249i		−	0.586795i	−0.955990	−	0.293398i	$-0.905214\pi$
$353$		−	11.0249i		−	0.586795i	0.955990	−	0.293398i	$-0.0947860\pi$
$354$		0			0
$355$	−0.108005	−	0.0784705i	−0.00573233	−	0.00416478i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	15.3828	−	11.1763i	0.811875	−	0.589862i	−0.102499	−	0.994733i	$-0.532684\pi$
$359$	15.3828	−	11.1763i	0.811875	−	0.589862i	0.914374	+	0.404871i	$0.132684\pi$
$360$		0			0
$361$	−6.00743	−	18.4890i	−0.316180	−	0.973103i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−0.146918	−	0.452167i	−0.00769004	−	0.0236675i
$366$		0			0
$367$	−4.60911	+	3.34872i	−0.240594	+	0.174802i	−0.701548	−	0.712622i	$-0.747507\pi$
$367$	−4.60911	+	3.34872i	−0.240594	+	0.174802i	0.460954	+	0.887424i	$0.347507\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	1.79090	+	1.30117i	0.0929789	+	0.0675531i
$372$		0			0
$373$			22.1594i			1.14737i	0.819076	+	0.573684i	$0.194486\pi$
$373$			22.1594i			1.14737i	−0.819076	+	0.573684i	$0.805514\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−7.56992	+	10.4191i	−0.389871	+	0.536611i
$378$		0			0
$379$	0.117844	−	0.362687i	0.00605325	−	0.0186300i	−0.947984	−	0.318317i	$-0.896882\pi$
$379$	0.117844	−	0.362687i	0.00605325	−	0.0186300i	0.954038	+	0.299687i	$0.0968823\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	12.0446	−	3.91352i	0.615450	−	0.199972i	0.0153308	−	0.999882i	$-0.495120\pi$
$383$	12.0446	−	3.91352i	0.615450	−	0.199972i	0.600119	+	0.799911i	$0.295120\pi$
$384$		0			0
$385$	0.0201311	+	0.0259425i	0.00102598	+	0.00132215i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	13.9885	+	19.2535i	0.709243	+	0.976190i	0.999813	+	0.0193359i	$0.00615519\pi$
$389$	13.9885	+	19.2535i	0.709243	+	0.976190i	−0.290570	+	0.956854i	$0.593845\pi$
$390$		0			0
$391$	27.6544	+	8.98546i	1.39854	+	0.454414i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.120768			0.00607647
$396$		0			0
$397$	5.00497			0.251192			0.125596	−	0.992081i	$-0.459916\pi$
$397$	5.00497			0.251192			0.125596	+	0.992081i	$0.459916\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−4.03643	−	1.31151i	−0.201570	−	0.0654939i	0.206492	−	0.978448i	$-0.433795\pi$
$401$	−4.03643	−	1.31151i	−0.201570	−	0.0654939i	−0.408062	+	0.912954i	$0.633795\pi$
$402$		0			0
$403$	6.48990	+	8.93258i	0.323285	+	0.444963i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.51225	+	11.0585i	−0.372368	+	0.548151i
$408$		0			0
$409$	−11.2278	+	3.64812i	−0.555177	+	0.180388i	−0.573150	−	0.819450i	$-0.694279\pi$
$409$	−11.2278	+	3.64812i	−0.555177	+	0.180388i	0.0179728	+	0.999838i	$0.494279\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.212694	−	0.654604i	0.0104660	−	0.0322109i
$414$		0			0
$415$	0.124803	−	0.171777i	0.00612634	−	0.00843218i
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	20.9795i		−	1.02492i	−0.858712	−	0.512459i	$-0.828735\pi$
$419$		−	20.9795i		−	1.02492i	0.858712	−	0.512459i	$-0.171265\pi$
$420$		0			0
$421$	2.24889	+	1.63391i	0.109604	+	0.0796320i	0.641237	−	0.767343i	$-0.278421\pi$
$421$	2.24889	+	1.63391i	0.109604	+	0.0796320i	−0.531633	+	0.846975i	$0.678421\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	17.2921	−	12.5634i	0.838789	−	0.609416i
$426$		0			0
$427$	−0.647200	−	1.99188i	−0.0313202	−	0.0963936i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	8.63060	+	26.5623i	0.415722	+	1.27946i	0.911604	+	0.411070i	$0.134845\pi$
$431$	8.63060	+	26.5623i	0.415722	+	1.27946i	−0.495882	+	0.868390i	$0.665155\pi$
$432$		0			0
$433$	7.41714	−	5.38887i	0.356445	−	0.258973i	−0.395123	−	0.918628i	$-0.629298\pi$
$433$	7.41714	−	5.38887i	0.356445	−	0.258973i	0.751568	+	0.659656i	$0.229298\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−34.1075	−	24.7806i	−1.63159	−	1.18542i
$438$		0			0
$439$			2.93111i			0.139894i	0.997551	+	0.0699472i	$0.0222831\pi$
$439$			2.93111i			0.139894i	−0.997551	+	0.0699472i	$0.977717\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−21.0670	+	28.9963i	−1.00093	+	1.37766i	−0.0761695	+	0.997095i	$0.524269\pi$
$443$	−21.0670	+	28.9963i	−1.00093	+	1.37766i	−0.924756	+	0.380561i	$0.875731\pi$
$444$		0			0
$445$	−0.105900	+	0.325925i	−0.00502012	+	0.0154503i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−13.5184	+	4.39241i	−0.637974	+	0.207290i	−0.610104	−	0.792321i	$-0.708872\pi$
$449$	−13.5184	+	4.39241i	−0.637974	+	0.207290i	−0.0278700	+	0.999612i	$0.508872\pi$
$450$		0			0
$451$	30.5864	+	8.87978i	1.44026	+	0.418132i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.0133938	+	0.0184349i	0.000627909	+	0.000864243i
$456$		0			0
$457$	19.4009	+	6.30372i	0.907534	+	0.294876i	0.725343	−	0.688387i	$-0.241681\pi$
$457$	19.4009	+	6.30372i	0.907534	+	0.294876i	0.182191	+	0.983263i	$0.441681\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.770354			−0.0358790			−0.0179395	−	0.999839i	$-0.505711\pi$
$461$	−0.770354			−0.0358790			−0.0179395	+	0.999839i	$0.505711\pi$
$462$		0			0
$463$	−37.7948			−1.75647			−0.878236	−	0.478228i	$-0.841279\pi$
$463$	−37.7948			−1.75647			−0.878236	+	0.478228i	$0.841279\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−16.7411	−	5.43950i	−0.774684	−	0.251710i	−0.105115	−	0.994460i	$-0.533521\pi$
$467$	−16.7411	−	5.43950i	−0.774684	−	0.251710i	−0.669569	+	0.742750i	$0.733521\pi$
$468$		0			0
$469$	1.15290	+	1.58683i	0.0532358	+	0.0732728i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.15966	+	3.21913i	0.0533212	+	0.148016i
$474$		0			0
$475$	−29.4734	+	9.57650i	−1.35233	+	0.439400i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−0.743452	+	2.28811i	−0.0339692	+	0.104546i	−0.966603	−	0.256277i	$-0.917504\pi$
$479$	−0.743452	+	2.28811i	−0.0339692	+	0.104546i	0.932634	+	0.360823i	$0.117504\pi$
$480$		0			0
$481$	−5.45293	+	7.50531i	−0.248632	+	0.342213i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	0.121459i		−	0.00551517i
$486$		0			0
$487$	11.8099	+	8.58039i	0.535157	+	0.388815i	0.822283	−	0.569078i	$-0.192700\pi$
$487$	11.8099	+	8.58039i	0.535157	+	0.388815i	−0.287126	+	0.957893i	$0.592700\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	20.2597	−	14.7195i	0.914307	−	0.664283i	−0.0277932	−	0.999614i	$-0.508848\pi$
$491$	20.2597	−	14.7195i	0.914307	−	0.664283i	0.942101	+	0.335331i	$0.108848\pi$
$492$		0			0
$493$	7.39433	+	22.7574i	0.333024	+	1.02494i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.253899	+	0.781420i	0.0113889	+	0.0350515i
$498$		0			0
$499$	18.3740	−	13.3495i	0.822535	−	0.597607i	−0.0949025	−	0.995487i	$-0.530254\pi$
$499$	18.3740	−	13.3495i	0.822535	−	0.597607i	0.917438	+	0.397880i	$0.130254\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	8.41953	+	6.11715i	0.375408	+	0.272750i	0.759450	−	0.650566i	$-0.225468\pi$
$503$	8.41953	+	6.11715i	0.375408	+	0.272750i	−0.384042	+	0.923316i	$0.625468\pi$
$504$		0			0
$505$		−	0.278835i		−	0.0124080i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.75254	−	6.54130i	0.210652	−	0.289938i	−0.690596	−	0.723241i	$-0.742652\pi$
$509$	4.75254	−	6.54130i	0.210652	−	0.289938i	0.901249	+	0.433302i	$0.142652\pi$
$510$		0			0
$511$	−0.904203	+	2.78285i	−0.0399996	+	0.123106i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.500449	−	0.162606i	0.0220524	−	0.00716526i
$516$		0			0
$517$	10.2883	−	35.4382i	0.452481	−	1.55857i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	20.5846	+	28.3323i	0.901828	+	1.24126i	0.969881	+	0.243578i	$0.0783211\pi$
$521$	20.5846	+	28.3323i	0.901828	+	1.24126i	−0.0680535	+	0.997682i	$0.521679\pi$
$522$		0			0
$523$	−41.1766	−	13.3791i	−1.80052	−	0.585026i	−0.800625	−	0.599166i	$-0.795499\pi$
$523$	−41.1766	−	13.3791i	−1.80052	−	0.585026i	−0.999900	+	0.0141400i	$0.995499\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	20.5146			0.893630
$528$		0			0
$529$	−23.2378			−1.01034
$530$		0			0
$531$		0			0
$532$		0			0
$533$	21.0196	+	6.82969i	0.910461	+	0.295827i
$534$		0			0
$535$	0.0322622	+	0.0444051i	0.00139482	+	0.00191980i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.727333	+	23.0028i	0.0313284	+	0.990800i
$540$		0			0
$541$	−0.215252	+	0.0699396i	−0.00925440	+	0.00300694i	−0.313641	−	0.949542i	$-0.601549\pi$
$541$	−0.215252	+	0.0699396i	−0.00925440	+	0.00300694i	0.304386	+	0.952549i	$0.401549\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.0910303	−	0.280163i	0.00389931	−	0.0120008i
$546$		0			0
$547$	9.67686	−	13.3191i	0.413753	−	0.569482i	−0.550376	−	0.834917i	$-0.685516\pi$
$547$	9.67686	−	13.3191i	0.413753	−	0.569482i	0.964129	+	0.265435i	$0.0855157\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	34.6938i		−	1.47801i
$552$		0			0
$553$	−0.601310	−	0.436877i	−0.0255703	−	0.0185779i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	21.2624	−	15.4481i	0.900919	−	0.654556i	−0.0377832	−	0.999286i	$-0.512030\pi$
$557$	21.2624	−	15.4481i	0.900919	−	0.654556i	0.938702	+	0.344730i	$0.112030\pi$
$558$		0			0
$559$	0.733729	+	2.25818i	0.0310334	+	0.0955110i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−11.2376	−	34.5859i	−0.473610	−	1.45762i	−0.847823	−	0.530279i	$-0.822087\pi$
$563$	−11.2376	−	34.5859i	−0.473610	−	1.45762i	0.374213	−	0.927343i	$-0.377913\pi$
$564$		0			0
$565$	0.0171505	−	0.0124606i	0.000721527	−	0.000524220i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−16.3670	−	11.8913i	−0.686138	−	0.498509i	0.189250	−	0.981929i	$-0.439394\pi$
$569$	−16.3670	−	11.8913i	−0.686138	−	0.498509i	−0.875388	+	0.483420i	$0.839394\pi$
$570$		0			0
$571$		−	24.4002i		−	1.02112i	−0.859843	−	0.510558i	$-0.829439\pi$
$571$		−	24.4002i		−	1.02112i	0.859843	−	0.510558i	$-0.170561\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−19.9778	+	27.4971i	−0.833132	+	1.14671i
$576$		0			0
$577$	−5.96494	+	18.3582i	−0.248324	+	0.764262i	0.746748	+	0.665107i	$0.231614\pi$
$577$	−5.96494	+	18.3582i	−0.248324	+	0.764262i	−0.995072	+	0.0991553i	$0.968386\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−1.24281	+	0.403812i	−0.0515603	+	0.0167530i
$582$		0			0
$583$	23.4978	−	18.2340i	0.973180	−	0.755177i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.2480	−	15.4816i	−0.464256	−	0.638994i	0.511128	−	0.859504i	$-0.329228\pi$
$587$	−11.2480	−	15.4816i	−0.464256	−	0.638994i	−0.975385	+	0.220510i	$0.929228\pi$
$588$		0			0
$589$	−28.2882	−	9.19138i	−1.16559	−	0.378724i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−14.9885			−0.615503			−0.307751	−	0.951467i	$-0.599577\pi$
$593$	−14.9885			−0.615503			−0.307751	+	0.951467i	$0.599577\pi$
$594$		0			0
$595$	0.0423378			0.00173568
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−31.7090	−	10.3029i	−1.29560	−	0.420965i	−0.421549	−	0.906806i	$-0.638513\pi$
$599$	−31.7090	−	10.3029i	−1.29560	−	0.420965i	−0.874047	+	0.485841i	$0.838513\pi$
$600$		0			0
$601$	−24.8474	−	34.1996i	−1.01355	−	1.39503i	−0.916630	−	0.399737i	$-0.869102\pi$
$601$	−24.8474	−	34.1996i	−1.01355	−	1.39503i	−0.0969178	−	0.995292i	$-0.530898\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.410151	−	0.162573i	0.0166750	−	0.00660955i
$606$		0			0
$607$	29.3742	−	9.54427i	1.19226	−	0.387390i	0.355354	−	0.934732i	$-0.384360\pi$
$607$	29.3742	−	9.54427i	1.19226	−	0.387390i	0.836909	+	0.547342i	$0.184360\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	7.91306	−	24.3539i	0.320128	−	0.985254i
$612$		0			0
$613$	−9.38958	+	12.9237i	−0.379242	+	0.521981i	−0.955383	−	0.295368i	$-0.904558\pi$
$613$	−9.38958	+	12.9237i	−0.379242	+	0.521981i	0.576142	+	0.817350i	$0.304558\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			2.63374i			0.106030i	0.998594	+	0.0530151i	$0.0168831\pi$
$617$			2.63374i			0.106030i	−0.998594	+	0.0530151i	$0.983117\pi$
$618$		0			0
$619$	16.3822	+	11.9023i	0.658454	+	0.478395i	0.866141	−	0.499800i	$-0.166593\pi$
$619$	16.3822	+	11.9023i	0.658454	+	0.478395i	−0.207686	+	0.978196i	$0.566593\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.70632	−	1.23971i	0.0683622	−	0.0496680i
$624$		0			0
$625$	7.71797	+	23.7535i	0.308719	+	0.950139i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	5.32645	+	16.3931i	0.212379	+	0.653636i
$630$		0			0
$631$	6.82846	−	4.96116i	0.271837	−	0.197501i	−0.443512	−	0.896268i	$-0.646268\pi$
$631$	6.82846	−	4.96116i	0.271837	−	0.197501i	0.715349	+	0.698767i	$0.246268\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.414430	−	0.301101i	−0.0164462	−	0.0119488i
$636$		0			0
$637$			15.9704i			0.632771i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−18.9940	+	26.1429i	−0.750216	+	1.03258i	0.247749	+	0.968824i	$0.420309\pi$
$641$	−18.9940	+	26.1429i	−0.750216	+	1.03258i	−0.997965	+	0.0637599i	$0.979691\pi$
$642$		0			0
$643$	−4.25724	+	13.1024i	−0.167889	+	0.516709i	−0.999238	−	0.0390421i	$-0.987569\pi$
$643$	−4.25724	+	13.1024i	−0.167889	+	0.516709i	0.831349	+	0.555751i	$0.187569\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−8.11003	+	2.63511i	−0.318838	+	0.103597i	−0.464064	−	0.885802i	$-0.653609\pi$
$647$	−8.11003	+	2.63511i	−0.318838	+	0.103597i	0.145226	+	0.989399i	$0.453609\pi$
$648$		0			0
$649$	−7.64968	−	5.19656i	−0.300276	−	0.203983i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	0.710037	+	0.977282i	0.0277859	+	0.0382440i	0.822684	−	0.568499i	$-0.192476\pi$
$653$	0.710037	+	0.977282i	0.0277859	+	0.0382440i	−0.794898	+	0.606743i	$0.792476\pi$
$654$		0			0
$655$	−0.692472	−	0.224998i	−0.0270571	−	0.00879139i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	9.41054			0.366583			0.183291	−	0.983059i	$-0.441325\pi$
$659$	9.41054			0.366583			0.183291	+	0.983059i	$0.441325\pi$
$660$		0			0
$661$	15.1027			0.587425			0.293713	−	0.955894i	$-0.405109\pi$
$661$	15.1027			0.587425			0.293713	+	0.955894i	$0.405109\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.0583807	−	0.0189690i	−0.00226391	−	0.000735588i
$666$		0			0
$667$	−22.3653	−	30.7832i	−0.865988	−	1.19193i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−28.1258	+	0.889320i	−1.08579	+	0.0343318i
$672$		0			0
$673$	39.5629	−	12.8548i	1.52504	−	0.495514i	0.577835	−	0.816153i	$-0.303898\pi$
$673$	39.5629	−	12.8548i	1.52504	−	0.495514i	0.947201	+	0.320639i	$0.103898\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−1.39693	+	4.29931i	−0.0536884	+	0.165236i	−0.974305	−	0.225231i	$-0.927686\pi$
$677$	−1.39693	+	4.29931i	−0.0536884	+	0.165236i	0.920617	+	0.390467i	$0.127686\pi$
$678$		0			0
$679$	−0.439379	+	0.604753i	−0.0168618	+	0.0232083i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			34.7783i			1.33075i	0.746507	+	0.665377i	$0.231729\pi$
$683$			34.7783i			1.33075i	−0.746507	+	0.665377i	$0.768271\pi$
$684$		0			0
$685$	−0.521547	−	0.378926i	−0.0199273	−	0.0144780i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	16.6977	−	12.1316i	0.636132	−	0.462177i
$690$		0			0
$691$	5.52630	+	17.0082i	0.210230	+	0.647023i	0.999458	+	0.0329217i	$0.0104812\pi$
$691$	5.52630	+	17.0082i	0.210230	+	0.647023i	−0.789228	+	0.614101i	$0.789519\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.0478085	−	0.147139i	−0.00181348	−	0.00558132i
$696$		0			0
$697$	33.2216	−	24.1369i	1.25836	−	0.914250i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−14.1345	−	10.2693i	−0.533852	−	0.387866i	0.287945	−	0.957647i	$-0.407028\pi$
$701$	−14.1345	−	10.2693i	−0.533852	−	0.387866i	−0.821797	+	0.569781i	$0.807028\pi$
$702$		0			0
$703$		−	24.9914i		−	0.942568i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.00869	+	1.38834i	−0.0379356	+	0.0522139i
$708$		0			0
$709$	2.57673	−	7.93037i	0.0967713	−	0.297831i	−0.890940	−	0.454121i	$-0.849953\pi$
$709$	2.57673	−	7.93037i	0.0967713	−	0.297831i	0.987711	+	0.156290i	$0.0499533\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−31.0248	+	10.0806i	−1.16189	+	0.377520i
$714$		0			0
$715$	0.288041	−	0.103764i	0.0107721	−	0.00388056i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	13.8736	+	19.0953i	0.517397	+	0.712136i	0.985145	−	0.171726i	$-0.0549344\pi$
$719$	13.8736	+	19.0953i	0.517397	+	0.712136i	−0.467748	+	0.883862i	$0.654934\pi$
$720$		0			0
$721$	−3.08000	−	1.00075i	−0.114705	−	0.0372699i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−27.9697			−1.03877
$726$		0			0
$727$	−1.90462			−0.0706386			−0.0353193	−	0.999376i	$-0.511245\pi$
$727$	−1.90462			−0.0706386			−0.0353193	+	0.999376i	$0.511245\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.19569	+	1.36326i	0.155183	+	0.0504221i
$732$		0			0
$733$	−10.3520	−	14.2482i	−0.382358	−	0.526271i	0.573849	−	0.818961i	$-0.305450\pi$
$733$	−10.3520	−	14.2482i	−0.382358	−	0.526271i	−0.956207	+	0.292690i	$0.905450\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	24.7938	−	8.93171i	0.913291	−	0.329004i
$738$		0			0
$739$	4.54355	−	1.47629i	0.167137	−	0.0543062i	−0.224253	−	0.974531i	$-0.571994\pi$
$739$	4.54355	−	1.47629i	0.167137	−	0.0543062i	0.391390	+	0.920225i	$0.371994\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−0.567901	+	1.74782i	−0.0208343	+	0.0641212i	−0.960933	−	0.276781i	$-0.910732\pi$
$743$	−0.567901	+	1.74782i	−0.0208343	+	0.0641212i	0.940099	+	0.340902i	$0.110732\pi$
$744$		0			0
$745$	0.242118	−	0.333247i	0.00887053	−	0.0122092i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	0.337805i		−	0.0123431i
$750$		0			0
$751$	−30.6978	−	22.3033i	−1.12018	−	0.813857i	−0.135942	−	0.990717i	$-0.543406\pi$
$751$	−30.6978	−	22.3033i	−1.12018	−	0.813857i	−0.984236	+	0.176859i	$0.943406\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.284588	+	0.206765i	−0.0103572	+	0.00752497i
$756$		0			0
$757$	−9.46409	−	29.1275i	−0.343978	−	1.05866i	−0.962128	−	0.272596i	$-0.912118\pi$
$757$	−9.46409	−	29.1275i	−0.343978	−	1.05866i	0.618150	−	0.786060i	$-0.287882\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.53788	−	29.3546i	−0.345748	−	1.06410i	−0.961182	−	0.275914i	$-0.911019\pi$
$761$	−9.53788	−	29.3546i	−0.345748	−	1.06410i	0.615434	−	0.788188i	$-0.288981\pi$
$762$		0			0
$763$	−1.46674	+	1.06565i	−0.0530994	+	0.0385790i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.19177	−	3.77204i	−0.187464	−	0.136200i
$768$		0			0
$769$		−	19.3154i		−	0.696532i	−0.937396	−	0.348266i	$-0.886771\pi$
$769$		−	19.3154i		−	0.696532i	0.937396	−	0.348266i	$-0.113229\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1.72928	+	2.38015i	−0.0621980	+	0.0856082i	−0.838983	−	0.544158i	$-0.816849\pi$
$773$	−1.72928	+	2.38015i	−0.0621980	+	0.0856082i	0.776785	+	0.629766i	$0.216849\pi$
$774$		0			0
$775$	−7.40997	+	22.8056i	−0.266174	+	0.819200i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−56.6245	+	18.3984i	−2.02878	+	0.659191i
$780$		0			0
$781$	11.0339	−	0.348884i	0.394823	−	0.0124840i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.307206	+	0.422833i	0.0109647	+	0.0150916i
$786$		0			0
$787$	7.65190	+	2.48625i	0.272761	+	0.0886254i	0.442204	−	0.896915i	$-0.354197\pi$
$787$	7.65190	+	2.48625i	0.272761	+	0.0886254i	−0.169443	+	0.985540i	$0.554197\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.130470			−0.00463897
$792$		0			0
$793$	−19.5272			−0.693433
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−52.2338	−	16.9718i	−1.85022	−	0.601172i	−0.996799	−	0.0799446i	$-0.974526\pi$
$797$	−52.2338	−	16.9718i	−1.85022	−	0.601172i	−0.853418	−	0.521227i	$-0.825474\pi$
$798$		0			0
$799$	−27.9657	−	38.4914i	−0.989354	−	1.36173i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	32.5203	+	22.0916i	1.14762	+	0.779596i
$804$		0			0
$805$	−0.0640286	+	0.0208041i	−0.00225671	+	0.000733250i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	7.52538	−	23.1607i	0.264578	−	0.814288i	−0.727212	−	0.686413i	$-0.759184\pi$
$809$	7.52538	−	23.1607i	0.264578	−	0.814288i	0.991790	−	0.127875i	$-0.0408156\pi$
$810$		0			0
$811$	12.2026	−	16.7955i	0.428493	−	0.589770i	−0.539114	−	0.842233i	$-0.681241\pi$
$811$	12.2026	−	16.7955i	0.428493	−	0.589770i	0.967607	+	0.252463i	$0.0812407\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$			0.368107i			0.0128942i
$816$		0			0
$817$	−5.17476	−	3.75968i	−0.181042	−	0.131535i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−23.1681	+	16.8326i	−0.808571	+	0.587461i	−0.913416	−	0.407027i	$-0.866565\pi$
$821$	−23.1681	+	16.8326i	−0.808571	+	0.587461i	0.104845	+	0.994489i	$0.466565\pi$
$822$		0			0
$823$	−0.768785	−	2.36608i	−0.0267982	−	0.0824763i	0.936763	−	0.349964i	$-0.113806\pi$
$823$	−0.768785	−	2.36608i	−0.0267982	−	0.0824763i	−0.963561	+	0.267488i	$0.913806\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	7.36490	+	22.6668i	0.256103	+	0.788202i	0.993610	+	0.112864i	$0.0360024\pi$
$827$	7.36490	+	22.6668i	0.256103	+	0.788202i	−0.737508	+	0.675338i	$0.763998\pi$
$828$		0			0
$829$	32.8736	−	23.8841i	1.14175	−	0.829528i	0.154386	−	0.988011i	$-0.450660\pi$
$829$	32.8736	−	23.8841i	1.14175	−	0.829528i	0.987362	+	0.158482i	$0.0506601\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	24.0059	+	17.4413i	0.831755	+	0.604305i
$834$		0			0
$835$			0.305201i			0.0105619i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	33.6349	−	46.2945i	1.16121	−	1.59826i	0.454525	−	0.890734i	$-0.349809\pi$
$839$	33.6349	−	46.2945i	1.16121	−	1.59826i	0.706683	−	0.707531i	$-0.250191\pi$
$840$		0			0
$841$	0.714546	−	2.19915i	0.0246395	−	0.0758327i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.293836	+	0.0954731i	−0.0101083	+	0.00328438i
$846$		0			0
$847$	−2.63028	−	0.674260i	−0.0903776	−	0.0231679i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−16.1107	−	22.1744i	−0.552266	−	0.760130i
$852$		0			0
$853$	−29.0464	−	9.43774i	−0.994529	−	0.323142i	−0.233852	−	0.972272i	$-0.575133\pi$
$853$	−29.0464	−	9.43774i	−0.994529	−	0.323142i	−0.760677	+	0.649130i	$0.775133\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−6.14781			−0.210005			−0.105003	−	0.994472i	$-0.533485\pi$
$857$	−6.14781			−0.210005			−0.105003	+	0.994472i	$0.533485\pi$
$858$		0			0
$859$	27.5988			0.941660			0.470830	−	0.882224i	$-0.343955\pi$
$859$	27.5988			0.941660			0.470830	+	0.882224i	$0.343955\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−40.7061	−	13.2262i	−1.38565	−	0.450226i	−0.481129	−	0.876650i	$-0.659773\pi$
$863$	−40.7061	−	13.2262i	−1.38565	−	0.450226i	−0.904523	+	0.426424i	$0.859773\pi$
$864$		0			0
$865$	0.391832	+	0.539310i	0.0133227	+	0.0183371i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−7.88960	+	6.12224i	−0.267636	+	0.207683i
$870$		0			0
$871$	17.3926	−	5.65118i	0.589324	−	0.191483i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.0305901	+	0.0941467i	−0.00103414	+	0.00318274i
$876$		0			0
$877$	6.60112	−	9.08566i	0.222904	−	0.306801i	−0.682889	−	0.730523i	$-0.739277\pi$
$877$	6.60112	−	9.08566i	0.222904	−	0.306801i	0.905792	+	0.423722i	$0.139277\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	47.3136i		−	1.59403i	−0.603957	−	0.797017i	$-0.706410\pi$
$881$		−	47.3136i		−	1.59403i	0.603957	−	0.797017i	$-0.293590\pi$
$882$		0			0
$883$	14.7740	+	10.7340i	0.497186	+	0.361227i	0.807941	−	0.589263i	$-0.200582\pi$
$883$	14.7740	+	10.7340i	0.497186	+	0.361227i	−0.310755	+	0.950490i	$0.600582\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	32.9354	−	23.9289i	1.10586	−	0.803455i	0.123854	−	0.992300i	$-0.460474\pi$
$887$	32.9354	−	23.9289i	1.10586	−	0.803455i	0.982007	+	0.188845i	$0.0604744\pi$
$888$		0			0
$889$	0.974242	+	2.99841i	0.0326750	+	0.100563i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	21.3169	+	65.6066i	0.713342	+	2.19544i
$894$		0			0
$895$	0.228756	−	0.166201i	0.00764648	−	0.00555549i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−21.7180	−	15.7790i	−0.724335	−	0.526260i
$900$		0			0
$901$		−	38.3480i		−	1.27756i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.497996	+	0.685433i	−0.0165540	+	0.0227846i
$906$		0			0
$907$	−0.365168	+	1.12387i	−0.0121252	+	0.0373176i	−0.956936	−	0.290299i	$-0.906245\pi$
$907$	−0.365168	+	1.12387i	−0.0121252	+	0.0373176i	0.944811	+	0.327616i	$0.106245\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−20.1283	+	6.54007i	−0.666879	+	0.216682i	−0.622842	−	0.782348i	$-0.714022\pi$
$911$	−20.1283	+	6.54007i	−0.666879	+	0.216682i	−0.0440370	+	0.999030i	$0.514022\pi$
$912$		0			0
$913$	0.554880	+	17.5488i	0.0183639	+	0.580779i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.63394	+	3.62530i	0.0869803	+	0.119718i
$918$		0			0
$919$	13.4009	+	4.35422i	0.442055	+	0.143633i	0.521584	−	0.853200i	$-0.325341\pi$
$919$	13.4009	+	4.35422i	0.442055	+	0.143633i	−0.0795283	+	0.996833i	$0.525341\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	7.66061			0.252152
$924$		0			0
$925$	−20.1477			−0.662454
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−32.4174	−	10.5331i	−1.06358	−	0.345578i	−0.275596	−	0.961273i	$-0.588875\pi$
$929$	−32.4174	−	10.5331i	−1.06358	−	0.345578i	−0.787985	+	0.615695i	$0.788875\pi$
$930$		0			0
$931$	−25.2880	−	34.8059i	−0.828780	−	1.14072i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.158598	−	0.546290i	0.00518669	−	0.0178656i
$936$		0			0
$937$	6.41974	−	2.08590i	0.209724	−	0.0681434i	−0.202271	−	0.979330i	$-0.564832\pi$
$937$	6.41974	−	2.08590i	0.209724	−	0.0681434i	0.411995	+	0.911186i	$0.364832\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.2896	−	31.6682i	0.335432	−	1.03235i	−0.631077	−	0.775720i	$-0.717387\pi$
$941$	10.2896	−	31.6682i	0.335432	−	1.03235i	0.966509	−	0.256633i	$-0.0826131\pi$
$942$		0			0
$943$	−38.3814	+	52.8275i	−1.24987	+	1.72030i
$944$		0			0
$945$		0			0
$946$		0			0
$947$			0.751232i			0.0244117i	0.999926	+	0.0122059i	$0.00388535\pi$
$947$			0.751232i			0.0244117i	−0.999926	+	0.0122059i	$0.996115\pi$
$948$		0			0
$949$	22.0712	+	16.0357i	0.716462	+	0.520540i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−3.76491	+	2.73537i	−0.121957	+	0.0886073i	−0.647092	−	0.762412i	$-0.724015\pi$
$953$	−3.76491	+	2.73537i	−0.121957	+	0.0886073i	0.525134	+	0.851019i	$0.324015\pi$
$954$		0			0
$955$	0.169408	+	0.521385i	0.00548192	+	0.0168716i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.22605	+	3.77340i	0.0395913	+	0.121849i
$960$		0			0
$961$	6.46012	−	4.69355i	0.208391	−	0.151405i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.812348	−	0.590205i	−0.0261504	−	0.0189994i
$966$		0			0
$967$		−	21.7529i		−	0.699525i	−0.936838	−	0.349763i	$-0.886262\pi$
$967$		−	21.7529i		−	0.699525i	0.936838	−	0.349763i	$-0.113738\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−3.45215	+	4.75147i	−0.110785	+	0.152482i	−0.860809	−	0.508928i	$-0.830042\pi$
$971$	−3.45215	+	4.75147i	−0.110785	+	0.152482i	0.750024	+	0.661410i	$0.230042\pi$
$972$		0			0
$973$	−0.294236	+	0.905565i	−0.00943277	+	0.0290311i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−0.874965	+	0.284293i	−0.0279926	+	0.00909535i	−0.322980	−	0.946406i	$-0.604685\pi$
$977$	−0.874965	+	0.284293i	−0.0279926	+	0.00909535i	0.294987	+	0.955501i	$0.404685\pi$
$978$		0			0
$979$	−9.60429	−	26.6608i	−0.306954	−	0.852083i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	27.4119	+	37.7293i	0.874304	+	1.20338i	0.977966	+	0.208764i	$0.0669440\pi$
$983$	27.4119	+	37.7293i	0.874304	+	1.20338i	−0.103662	+	0.994613i	$0.533056\pi$
$984$		0			0
$985$	0.802745	+	0.260828i	0.0255776	+	0.00831066i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−7.01515			−0.223069
$990$		0			0
$991$	−6.21090			−0.197296			−0.0986478	−	0.995122i	$-0.531452\pi$
$991$	−6.21090			−0.197296			−0.0986478	+	0.995122i	$0.531452\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.395607	+	0.128540i	0.0125416	+	0.00407500i
$996$		0			0
$997$	−16.7911	−	23.1110i	−0.531781	−	0.731933i	0.455620	−	0.890174i	$-0.349418\pi$
$997$	−16.7911	−	23.1110i	−0.531781	−	0.731933i	−0.987400	+	0.158241i	$0.949418\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1584.2.cd.c.17.3		16
3.2	odd	2	inner	1584.2.cd.c.17.2		16
4.3	odd	2		99.2.j.a.17.2	✓	16
11.2	odd	10	inner	1584.2.cd.c.1025.2		16
12.11	even	2		99.2.j.a.17.3	yes	16
33.2	even	10	inner	1584.2.cd.c.1025.3		16
36.7	odd	6		891.2.u.c.215.2		32
36.11	even	6		891.2.u.c.215.3		32
36.23	even	6		891.2.u.c.512.2		32
36.31	odd	6		891.2.u.c.512.3		32
44.3	odd	10		1089.2.d.g.1088.6		16
44.19	even	10		1089.2.d.g.1088.12		16
44.35	even	10		99.2.j.a.35.3	yes	16
132.35	odd	10		99.2.j.a.35.2	yes	16
132.47	even	10		1089.2.d.g.1088.11		16
132.107	odd	10		1089.2.d.g.1088.5		16
396.79	even	30		891.2.u.c.134.2		32
396.167	odd	30		891.2.u.c.431.2		32
396.211	even	30		891.2.u.c.431.3		32
396.299	odd	30		891.2.u.c.134.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.17.2	✓	16	4.3	odd	2
99.2.j.a.17.3	yes	16	12.11	even	2
99.2.j.a.35.2	yes	16	132.35	odd	10
99.2.j.a.35.3	yes	16	44.35	even	10
891.2.u.c.134.2		32	396.79	even	30
891.2.u.c.134.3		32	396.299	odd	30
891.2.u.c.215.2		32	36.7	odd	6
891.2.u.c.215.3		32	36.11	even	6
891.2.u.c.431.2		32	396.167	odd	30
891.2.u.c.431.3		32	396.211	even	30
891.2.u.c.512.2		32	36.23	even	6
891.2.u.c.512.3		32	36.31	odd	6
1089.2.d.g.1088.5		16	132.107	odd	10
1089.2.d.g.1088.6		16	44.3	odd	10
1089.2.d.g.1088.11		16	132.47	even	10
1089.2.d.g.1088.12		16	44.19	even	10
1584.2.cd.c.17.2		16	3.2	odd	2	inner
1584.2.cd.c.17.3		16	1.1	even	1	trivial
1584.2.cd.c.1025.2		16	11.2	odd	10	inner
1584.2.cd.c.1025.3		16	33.2	even	10	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1584.cd (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0381457 + 0.0123943i) q^{5} +(-0.145094 - 0.199704i) q^{7} +O(q^{10})\)	\(q+(0.0381457 + 0.0123943i) q^{5} +(-0.145094 - 0.199704i) q^{7} +(-3.12033 + 1.12407i) q^{11} +(-2.18888 + 0.711209i) q^{13} +(-1.32142 + 4.06692i) q^{17} +(3.64429 - 5.01593i) q^{19} -6.79984i q^{23} +(-4.04378 - 2.93798i) q^{25} +(4.52705 - 3.28909i) q^{29} +(-1.48247 - 4.56258i) q^{31} +(-0.00305951 - 0.00941619i) q^{35} +(3.26102 - 2.36927i) q^{37} +(-7.76893 - 5.64446i) q^{41} -1.03166i q^{43} +(-6.53982 + 9.00129i) q^{47} +(2.14429 - 6.59944i) q^{49} +(-8.52885 + 2.77119i) q^{53} +(-0.132959 + 0.00420408i) q^{55} +(1.63893 + 2.25580i) q^{59} +(8.06923 + 2.62185i) q^{61} -0.0923111 q^{65} -7.94588 q^{67} +(-3.16559 - 1.02856i) q^{71} +(-6.96743 - 9.58984i) q^{73} +(0.677222 + 0.460048i) q^{77} +(2.86363 - 0.930451i) q^{79} +(1.63587 - 5.03470i) q^{83} +(-0.100813 + 0.138757i) q^{85} +8.54422i q^{89} +(0.459624 + 0.333936i) q^{91} +(0.201183 - 0.146168i) q^{95} +(-0.935778 - 2.88003i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 32 q^{25} - 16 q^{31} - 12 q^{37} - 24 q^{49} - 16 q^{55} - 96 q^{67} - 20 q^{73} - 100 q^{85} + 72 q^{91} + 60 q^{97}+O(q^{100}) \) 16 * q - 32 * q^25 - 16 * q^31 - 12 * q^37 - 24 * q^49 - 16 * q^55 - 96 * q^67 - 20 * q^73 - 100 * q^85 + 72 * q^91 + 60 * q^97

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