LMFDB - Embedded newform 1728.2.z.a.1583.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1728,2,Mod(143,1728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1728, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1728.143"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1728.z (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$13.7981494693$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			1583.7
Character	$\chi$	$=$	1728.1583
Dual form			1728.2.z.a.143.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20583 + 0.323102i) q^{5} +(-0.140266 - 0.242948i) q^{7} +(-3.07444 - 0.823794i) q^{11} +(2.76539 - 0.740984i) q^{13} +3.72031i q^{17} +(4.10860 - 4.10860i) q^{19} +(-1.57595 - 0.909876i) q^{23} +(-2.98049 + 1.72078i) q^{25} +(3.83006 + 1.02626i) q^{29} +(-8.81101 - 5.08704i) q^{31} +(0.247635 + 0.247635i) q^{35} +(1.76964 - 1.76964i) q^{37} +(-2.66819 + 4.62144i) q^{41} +(1.84748 - 6.89490i) q^{43} +(-5.48486 - 9.50006i) q^{47} +(3.46065 - 5.99402i) q^{49} +(-8.58403 - 8.58403i) q^{53} +3.97344 q^{55} +(1.44299 + 5.38532i) q^{59} +(1.66977 - 6.23168i) q^{61} +(-3.09519 + 1.78701i) q^{65} +(1.00652 + 3.75640i) q^{67} -10.6808i q^{71} -9.30419i q^{73} +(0.231101 + 0.862479i) q^{77} +(-8.70990 + 5.02866i) q^{79} +(0.588691 - 2.19703i) q^{83} +(-1.20204 - 4.48608i) q^{85} +1.87637 q^{89} +(-0.567911 - 0.567911i) q^{91} +(-3.62679 + 6.28179i) q^{95} +(9.19070 + 15.9188i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 6 q^{5} + 4 q^{7} - 6 q^{11} - 2 q^{13} + 8 q^{19} - 12 q^{23} + 6 q^{29} - 8 q^{37} + 2 q^{43} - 24 q^{49} + 16 q^{55} - 42 q^{59} - 2 q^{61} + 12 q^{65} + 2 q^{67} + 6 q^{77} + 54 q^{83} + 8 q^{85}+ \cdots - 4 q^{97}+O(q^{100}) $ 88 * q + 6 * q^5 + 4 * q^7 - 6 * q^11 - 2 * q^13 + 8 * q^19 - 12 * q^23 + 6 * q^29 - 8 * q^37 + 2 * q^43 - 24 * q^49 + 16 * q^55 - 42 * q^59 - 2 * q^61 + 12 * q^65 + 2 * q^67 + 6 * q^77 + 54 * q^83 + 8 * q^85 - 20 * q^91 - 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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
$5$	−1.20583	+	0.323102i	−0.539266	+	0.144496i	−0.518164	−	0.855282i	$-0.673384\pi$
$5$	−1.20583	+	0.323102i	−0.539266	+	0.144496i	−0.0211020	+	0.999777i	$0.506717\pi$
$6$		0			0
$7$	−0.140266	−	0.242948i	−0.0530156	−	0.0918256i	0.838300	−	0.545210i	$-0.183550\pi$
$7$	−0.140266	−	0.242948i	−0.0530156	−	0.0918256i	−0.891315	+	0.453384i	$0.850217\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.07444	−	0.823794i	−0.926979	−	0.248383i	−0.236413	−	0.971653i	$-0.575972\pi$
$11$	−3.07444	−	0.823794i	−0.926979	−	0.248383i	−0.690566	+	0.723269i	$0.742639\pi$
$12$		0			0
$13$	2.76539	−	0.740984i	0.766982	−	0.205512i	0.145944	−	0.989293i	$-0.453378\pi$
$13$	2.76539	−	0.740984i	0.766982	−	0.205512i	0.621038	+	0.783781i	$0.286711\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			3.72031i			0.902309i	0.892446	+	0.451154i	$0.148988\pi$
$17$			3.72031i			0.902309i	−0.892446	+	0.451154i	$0.851012\pi$
$18$		0			0
$19$	4.10860	−	4.10860i	0.942577	−	0.942577i	−0.0558614	−	0.998439i	$-0.517791\pi$
$19$	4.10860	−	4.10860i	0.942577	−	0.942577i	0.998439	+	0.0558614i	$0.0177905\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.57595	−	0.909876i	−0.328609	−	0.189722i	0.326615	−	0.945158i	$-0.394092\pi$
$23$	−1.57595	−	0.909876i	−0.328609	−	0.189722i	−0.655223	+	0.755435i	$0.727425\pi$
$24$		0			0
$25$	−2.98049	+	1.72078i	−0.596097	+	0.344157i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.83006	+	1.02626i	0.711224	+	0.190572i	0.596253	−	0.802797i	$-0.296656\pi$
$29$	3.83006	+	1.02626i	0.711224	+	0.190572i	0.114972	+	0.993369i	$0.463322\pi$
$30$		0			0
$31$	−8.81101	−	5.08704i	−1.58250	−	0.913659i	−0.994493	−	0.104807i	$-0.966578\pi$
$31$	−8.81101	−	5.08704i	−1.58250	−	0.913659i	−0.588012	−	0.808852i	$-0.700089\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.247635	+	0.247635i	0.0418579	+	0.0418579i
$36$		0			0
$37$	1.76964	−	1.76964i	0.290928	−	0.290928i	−0.546519	−	0.837447i	$-0.684047\pi$
$37$	1.76964	−	1.76964i	0.290928	−	0.290928i	0.837447	+	0.546519i	$0.184047\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.66819	+	4.62144i	−0.416701	+	0.721747i	−0.995605	−	0.0936482i	$-0.970147\pi$
$41$	−2.66819	+	4.62144i	−0.416701	+	0.721747i	0.578904	+	0.815395i	$0.303480\pi$
$42$		0			0
$43$	1.84748	−	6.89490i	0.281738	−	1.05146i	−0.669452	−	0.742856i	$-0.733471\pi$
$43$	1.84748	−	6.89490i	0.281738	−	1.05146i	0.951190	−	0.308606i	$-0.0998625\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.48486	−	9.50006i	−0.800049	−	1.38573i	−0.919583	−	0.392896i	$-0.871473\pi$
$47$	−5.48486	−	9.50006i	−0.800049	−	1.38573i	0.119534	−	0.992830i	$-0.461860\pi$
$48$		0			0
$49$	3.46065	−	5.99402i	0.494379	−	0.856289i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−8.58403	−	8.58403i	−1.17911	−	1.17911i	−0.979972	−	0.199135i	$-0.936187\pi$
$53$	−8.58403	−	8.58403i	−1.17911	−	1.17911i	−0.199135	−	0.979972i	$-0.563813\pi$
$54$		0			0
$55$	3.97344			0.535778
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.44299	+	5.38532i	0.187862	+	0.701109i	0.994000	+	0.109382i	$0.0348871\pi$
$59$	1.44299	+	5.38532i	0.187862	+	0.701109i	−0.806138	+	0.591727i	$0.798446\pi$
$60$		0			0
$61$	1.66977	−	6.23168i	0.213793	−	0.797885i	−0.772796	−	0.634655i	$-0.781142\pi$
$61$	1.66977	−	6.23168i	0.213793	−	0.797885i	0.986588	−	0.163230i	$-0.0521911\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−3.09519	+	1.78701i	−0.383911	+	0.221651i
$66$		0			0
$67$	1.00652	+	3.75640i	0.122967	+	0.458918i	0.999759	−	0.0219514i	$-0.00698792\pi$
$67$	1.00652	+	3.75640i	0.122967	+	0.458918i	−0.876792	+	0.480869i	$0.840321\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	10.6808i		−	1.26758i	−0.773506	−	0.633789i	$-0.781499\pi$
$71$		−	10.6808i		−	1.26758i	0.773506	−	0.633789i	$-0.218501\pi$
$72$		0			0
$73$		−	9.30419i		−	1.08897i	−0.838770	−	0.544487i	$-0.816725\pi$
$73$		−	9.30419i		−	1.08897i	0.838770	−	0.544487i	$-0.183275\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.231101	+	0.862479i	0.0263364	+	0.0982886i
$78$		0			0
$79$	−8.70990	+	5.02866i	−0.979940	+	0.565769i	−0.902252	−	0.431209i	$-0.858087\pi$
$79$	−8.70990	+	5.02866i	−0.979940	+	0.565769i	−0.0776882	+	0.996978i	$0.524754\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.588691	−	2.19703i	0.0646173	−	0.241155i	−0.926062	−	0.377372i	$-0.876828\pi$
$83$	0.588691	−	2.19703i	0.0646173	−	0.241155i	0.990679	+	0.136217i	$0.0434945\pi$
$84$		0			0
$85$	−1.20204	−	4.48608i	−0.130380	−	0.486584i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.87637			0.198895			0.0994475	−	0.995043i	$-0.468292\pi$
$89$	1.87637			0.198895			0.0994475	+	0.995043i	$0.468292\pi$
$90$		0			0
$91$	−0.567911	−	0.567911i	−0.0595332	−	0.0595332i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.62679	+	6.28179i	−0.372101	+	0.644498i
$96$		0			0
$97$	9.19070	+	15.9188i	0.933175	+	1.61631i	0.777857	+	0.628441i	$0.216307\pi$
$97$	9.19070	+	15.9188i	0.933175	+	1.61631i	0.155317	+	0.987865i	$0.450360\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	4.18566	−	15.6211i	0.416488	−	1.55436i	−0.365347	−	0.930871i	$-0.619050\pi$
$101$	4.18566	−	15.6211i	0.416488	−	1.55436i	0.781836	−	0.623485i	$-0.214284\pi$
$102$		0			0
$103$	−0.0611378	+	0.105894i	−0.00602409	+	0.0104340i	−0.869022	−	0.494774i	$-0.835251\pi$
$103$	−0.0611378	+	0.105894i	−0.00602409	+	0.0104340i	0.862998	+	0.505208i	$0.168584\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.97359	−	5.97359i	0.577489	−	0.577489i	−0.356722	−	0.934211i	$-0.616106\pi$
$107$	5.97359	−	5.97359i	0.577489	−	0.577489i	0.934211	+	0.356722i	$0.116106\pi$
$108$		0			0
$109$	−3.40913	−	3.40913i	−0.326536	−	0.326536i	0.524732	−	0.851268i	$-0.324166\pi$
$109$	−3.40913	−	3.40913i	−0.326536	−	0.326536i	−0.851268	+	0.524732i	$0.824166\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−1.91330	−	1.10464i	−0.179988	−	0.103916i	0.407299	−	0.913295i	$-0.366471\pi$
$113$	−1.91330	−	1.10464i	−0.179988	−	0.103916i	−0.587287	+	0.809379i	$0.699804\pi$
$114$		0			0
$115$	2.19432	+	0.587966i	0.204621	+	0.0548281i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.903842	−	0.521833i	0.0828551	−	0.0478364i
$120$		0			0
$121$	−0.752719	−	0.434583i	−0.0684290	−	0.0395075i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	7.45164	−	7.45164i	0.666495	−	0.666495i
$126$		0			0
$127$			3.63934i			0.322939i	0.986878	+	0.161470i	$0.0516234\pi$
$127$			3.63934i			0.322939i	−0.986878	+	0.161470i	$0.948377\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−14.9890	+	4.01630i	−1.30960	+	0.350906i	−0.845072	−	0.534653i	$-0.820442\pi$
$131$	−14.9890	+	4.01630i	−1.30960	+	0.350906i	−0.464527	+	0.885559i	$0.653776\pi$
$132$		0			0
$133$	−1.57447	−	0.421878i	−0.136524	−	0.0365815i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−10.4065	−	18.0245i	−0.889085	−	1.53994i	−0.840959	−	0.541099i	$-0.818008\pi$
$137$	−10.4065	−	18.0245i	−0.889085	−	1.53994i	−0.0481263	−	0.998841i	$-0.515325\pi$
$138$		0			0
$139$	−0.802043	+	0.214907i	−0.0680284	+	0.0182282i	−0.292673	−	0.956213i	$-0.594545\pi$
$139$	−0.802043	+	0.214907i	−0.0680284	+	0.0182282i	0.224644	+	0.974441i	$0.427878\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−9.11246			−0.762022
$144$		0			0
$145$	−4.95000			−0.411076
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.13681	+	1.37640i	−0.420824	+	0.112759i	−0.463015	−	0.886350i	$-0.653233\pi$
$149$	−5.13681	+	1.37640i	−0.420824	+	0.112759i	0.0421919	+	0.999110i	$0.486566\pi$
$150$		0			0
$151$	1.53487	+	2.65847i	0.124906	+	0.216343i	0.921696	−	0.387913i	$-0.126804\pi$
$151$	1.53487	+	2.65847i	0.124906	+	0.216343i	−0.796790	+	0.604256i	$0.793471\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	12.2683	+	3.28727i	0.985410	+	0.264040i
$156$		0			0
$157$	−5.63885	+	1.51093i	−0.450029	+	0.120585i	−0.476713	−	0.879059i	$-0.658172\pi$
$157$	−5.63885	+	1.51093i	−0.450029	+	0.120585i	0.0266838	+	0.999644i	$0.491505\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			0.510499i			0.0402329i
$162$		0			0
$163$	12.5565	−	12.5565i	0.983500	−	0.983500i	−0.0163656	−	0.999866i	$-0.505210\pi$
$163$	12.5565	−	12.5565i	0.983500	−	0.983500i	0.999866	+	0.0163656i	$0.00520958\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.0834	+	6.97635i	0.935041	+	0.539846i	0.888402	−	0.459066i	$-0.151816\pi$
$167$	12.0834	+	6.97635i	0.935041	+	0.539846i	0.0466388	+	0.998912i	$0.485149\pi$
$168$		0			0
$169$	−4.16000	+	2.40178i	−0.320000	+	0.184752i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.38993	+	0.640380i	0.181703	+	0.0486872i	0.348523	−	0.937300i	$-0.386683\pi$
$173$	2.38993	+	0.640380i	0.181703	+	0.0486872i	−0.166820	+	0.985987i	$0.553350\pi$
$174$		0			0
$175$	0.836121	+	0.482735i	0.0632048	+	0.0364913i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.53870	+	9.53870i	0.712956	+	0.712956i	0.967153	−	0.254197i	$-0.0818111\pi$
$179$	9.53870	+	9.53870i	0.712956	+	0.712956i	−0.254197	+	0.967153i	$0.581811\pi$
$180$		0			0
$181$	−6.83874	+	6.83874i	−0.508320	+	0.508320i	−0.914010	−	0.405691i	$-0.867031\pi$
$181$	−6.83874	+	6.83874i	−0.508320	+	0.508320i	0.405691	+	0.914010i	$0.367031\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.56212	+	2.70567i	−0.114849	+	0.198925i
$186$		0			0
$187$	3.06477	−	11.4379i	0.224118	−	0.836421i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.08629	−	12.2738i	−0.512746	−	0.888102i	−0.999891	−	0.0147810i	$-0.995295\pi$
$191$	−7.08629	−	12.2738i	−0.512746	−	0.888102i	0.487145	−	0.873321i	$-0.338038\pi$
$192$		0			0
$193$	−6.47017	+	11.2067i	−0.465733	+	0.806673i	−0.999234	−	0.0391263i	$-0.987543\pi$
$193$	−6.47017	+	11.2067i	−0.465733	+	0.806673i	0.533501	+	0.845799i	$0.320876\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.02294	+	8.02294i	0.571611	+	0.571611i	0.932578	−	0.360968i	$-0.117553\pi$
$197$	8.02294	+	8.02294i	0.571611	+	0.571611i	−0.360968	+	0.932578i	$0.617553\pi$
$198$		0			0
$199$	−10.9199			−0.774093			−0.387046	−	0.922060i	$-0.626505\pi$
$199$	−10.9199			−0.774093			−0.387046	+	0.922060i	$0.626505\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.287899	−	1.07445i	−0.0202066	−	0.0754119i
$204$		0			0
$205$	1.72420	−	6.43478i	0.120423	−	0.449425i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−16.0163	+	9.24701i	−1.10787	+	0.639629i
$210$		0			0
$211$	4.37047	+	16.3108i	0.300875	+	1.12288i	0.936438	+	0.350833i	$0.114101\pi$
$211$	4.37047	+	16.3108i	0.300875	+	1.12288i	−0.635563	+	0.772049i	$0.719232\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			8.91103i			0.607727i
$216$		0			0
$217$			2.85415i			0.193753i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.75669	+	10.2881i	0.185435	+	0.692054i
$222$		0			0
$223$	12.3586	−	7.13522i	0.827591	−	0.477810i	−0.0254364	−	0.999676i	$-0.508098\pi$
$223$	12.3586	−	7.13522i	0.827591	−	0.477810i	0.853027	+	0.521867i	$0.174764\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.27906	+	8.50557i	−0.151267	+	0.564535i	0.848130	+	0.529789i	$0.177729\pi$
$227$	−2.27906	+	8.50557i	−0.151267	+	0.564535i	−0.999396	+	0.0347459i	$0.988938\pi$
$228$		0			0
$229$	−6.45185	−	24.0786i	−0.426350	−	1.59116i	−0.760957	−	0.648803i	$-0.775270\pi$
$229$	−6.45185	−	24.0786i	−0.426350	−	1.59116i	0.334606	−	0.942358i	$-0.391397\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	6.51295			0.426678			0.213339	−	0.976978i	$-0.431566\pi$
$233$	6.51295			0.426678			0.213339	+	0.976978i	$0.431566\pi$
$234$		0			0
$235$	9.68332	+	9.68332i	0.631670	+	0.631670i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.36907	+	4.10336i	−0.153243	+	0.265424i	−0.932418	−	0.361382i	$-0.882305\pi$
$239$	−2.36907	+	4.10336i	−0.153243	+	0.265424i	0.779175	+	0.626806i	$0.215638\pi$
$240$		0			0
$241$	7.43805	+	12.8831i	0.479127	+	0.829872i	0.999713	−	0.0239367i	$-0.00762000\pi$
$241$	7.43805	+	12.8831i	0.479127	+	0.829872i	−0.520586	+	0.853809i	$0.674287\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.23629	+	8.34594i	−0.142871	+	0.533203i
$246$		0			0
$247$	8.31748	−	14.4063i	0.529228	−	0.916650i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.89508	−	6.89508i	0.435213	−	0.435213i	−0.455184	−	0.890397i	$-0.650427\pi$
$251$	6.89508	−	6.89508i	0.435213	−	0.435213i	0.890397	+	0.455184i	$0.150427\pi$
$252$		0			0
$253$	4.09562	+	4.09562i	0.257489	+	0.257489i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.17437	−	1.25537i	−0.135633	−	0.0783080i	0.430648	−	0.902520i	$-0.358285\pi$
$257$	−2.17437	−	1.25537i	−0.135633	−	0.0783080i	−0.566281	+	0.824212i	$0.691618\pi$
$258$		0			0
$259$	−0.678152	−	0.181710i	−0.0421383	−	0.0112909i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.14718	+	1.81703i	−0.194064	+	0.112043i	−0.593884	−	0.804551i	$-0.702406\pi$
$263$	−3.14718	+	1.81703i	−0.194064	+	0.112043i	0.399820	+	0.916594i	$0.369073\pi$
$264$		0			0
$265$	13.1244	+	7.57740i	0.806228	+	0.465476i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	12.3633	−	12.3633i	0.753802	−	0.753802i	−0.221384	−	0.975187i	$-0.571058\pi$
$269$	12.3633	−	12.3633i	0.753802	−	0.753802i	0.975187	+	0.221384i	$0.0710575\pi$
$270$		0			0
$271$			27.2658i			1.65628i	0.560523	+	0.828139i	$0.310600\pi$
$271$			27.2658i			1.65628i	−0.560523	+	0.828139i	$0.689400\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	10.5809	−	2.83514i	0.638053	−	0.170966i
$276$		0			0
$277$	−16.7042	−	4.47587i	−1.00366	−	0.268929i	−0.280680	−	0.959801i	$-0.590560\pi$
$277$	−16.7042	−	4.47587i	−1.00366	−	0.268929i	−0.722977	+	0.690872i	$0.757227\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	7.04702	+	12.2058i	0.420390	+	0.728137i	0.995978	−	0.0896034i	$-0.0285600\pi$
$281$	7.04702	+	12.2058i	0.420390	+	0.728137i	−0.575588	+	0.817740i	$0.695227\pi$
$282$		0			0
$283$	−0.628767	+	0.168478i	−0.0373763	+	0.0100149i	−0.277459	−	0.960738i	$-0.589492\pi$
$283$	−0.628767	+	0.168478i	−0.0373763	+	0.0100149i	0.240082	+	0.970753i	$0.422826\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.49702			0.0883665
$288$		0			0
$289$	3.15927			0.185839
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.09169	−	2.16816i	0.472722	−	0.126665i	−0.0145900	−	0.999894i	$-0.504644\pi$
$293$	8.09169	−	2.16816i	0.472722	−	0.126665i	0.487312	+	0.873228i	$0.337978\pi$
$294$		0			0
$295$	−3.48002	−	6.02757i	−0.202615	−	0.350939i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−5.03233	−	1.34841i	−0.291027	−	0.0779804i
$300$		0			0
$301$	−1.93424	+	0.518278i	−0.111488	+	0.0298730i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			8.05388i			0.461164i
$306$		0			0
$307$	−10.1250	+	10.1250i	−0.577865	+	0.577865i	−0.934315	−	0.356449i	$-0.883987\pi$
$307$	−10.1250	+	10.1250i	−0.577865	+	0.577865i	0.356449	+	0.934315i	$0.383987\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−13.7848	−	7.95868i	−0.781667	−	0.451295i	0.0553539	−	0.998467i	$-0.482371\pi$
$311$	−13.7848	−	7.95868i	−0.781667	−	0.451295i	−0.837021	+	0.547171i	$0.815705\pi$
$312$		0			0
$313$	−9.90266	+	5.71730i	−0.559732	+	0.323161i	−0.753038	−	0.657977i	$-0.771412\pi$
$313$	−9.90266	+	5.71730i	−0.559732	+	0.323161i	0.193306	+	0.981138i	$0.438079\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−26.3682	−	7.06533i	−1.48098	−	0.396828i	−0.574302	−	0.818644i	$-0.694726\pi$
$317$	−26.3682	−	7.06533i	−1.48098	−	0.396828i	−0.906682	+	0.421815i	$0.861393\pi$
$318$		0			0
$319$	−10.9299	−	6.31036i	−0.611955	−	0.353313i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	15.2853	+	15.2853i	0.850495	+	0.850495i
$324$		0			0
$325$	−6.96714	+	6.96714i	−0.386467	+	0.386467i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.53868	+	2.66507i	−0.0848301	+	0.146930i
$330$		0			0
$331$	−2.97493	+	11.1026i	−0.163517	+	0.610254i	0.834708	+	0.550693i	$0.185637\pi$
$331$	−2.97493	+	11.1026i	−0.163517	+	0.610254i	−0.998225	+	0.0595605i	$0.981030\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.42740	−	4.20439i	−0.132623	−	0.229710i
$336$		0			0
$337$	4.37194	−	7.57242i	0.238155	−	0.412496i	−0.722030	−	0.691862i	$-0.756791\pi$
$337$	4.37194	−	7.57242i	0.238155	−	0.412496i	0.960185	+	0.279366i	$0.0901242\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	22.8983	+	22.8983i	1.24001	+	1.24001i
$342$		0			0
$343$	−3.90537			−0.210870
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.832493	+	3.10690i	0.0446905	+	0.166787i	0.984664	−	0.174459i	$-0.0558176\pi$
$347$	0.832493	+	3.10690i	0.0446905	+	0.166787i	−0.939974	+	0.341246i	$0.889151\pi$
$348$		0			0
$349$	8.57705	−	32.0100i	0.459119	−	1.71346i	−0.216568	−	0.976268i	$-0.569486\pi$
$349$	8.57705	−	32.0100i	0.459119	−	1.71346i	0.675687	−	0.737188i	$-0.263847\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.18886	−	4.15049i	0.382624	−	0.220908i	−0.296335	−	0.955084i	$-0.595765\pi$
$353$	7.18886	−	4.15049i	0.382624	−	0.220908i	0.678959	+	0.734176i	$0.262431\pi$
$354$		0			0
$355$	3.45099	+	12.8793i	0.183160	+	0.683561i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			17.1616i			0.905754i	0.891573	+	0.452877i	$0.149602\pi$
$359$			17.1616i			0.905754i	−0.891573	+	0.452877i	$0.850398\pi$
$360$		0			0
$361$		−	14.7612i		−	0.776903i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	3.00621	+	11.2193i	0.157352	+	0.587246i
$366$		0			0
$367$	1.27977	−	0.738875i	0.0668034	−	0.0385690i	−0.466226	−	0.884666i	$-0.654387\pi$
$367$	1.27977	−	0.738875i	0.0668034	−	0.0385690i	0.533030	+	0.846097i	$0.321053\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.881424	+	3.28952i	−0.0457612	+	0.170783i
$372$		0			0
$373$	8.48049	+	31.6496i	0.439103	+	1.63876i	0.731052	+	0.682322i	$0.239030\pi$
$373$	8.48049	+	31.6496i	0.439103	+	1.63876i	−0.291948	+	0.956434i	$0.594304\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	11.3521			0.584661
$378$		0			0
$379$	−19.2548	−	19.2548i	−0.989053	−	0.989053i	0.0108880	−	0.999941i	$-0.496534\pi$
$379$	−19.2548	−	19.2548i	−0.989053	−	0.989053i	−0.999941	+	0.0108880i	$0.996534\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−3.99635	+	6.92189i	−0.204204	+	0.353692i	−0.949879	−	0.312618i	$-0.898794\pi$
$383$	−3.99635	+	6.92189i	−0.204204	+	0.353692i	0.745675	+	0.666310i	$0.232127\pi$
$384$		0			0
$385$	−0.557338	−	0.965338i	−0.0284046	−	0.0491982i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.21212	−	8.25574i	0.112159	−	0.418583i	−0.886900	−	0.461962i	$-0.847146\pi$
$389$	2.21212	−	8.25574i	0.112159	−	0.418583i	0.999059	+	0.0433793i	$0.0138124\pi$
$390$		0			0
$391$	3.38502	−	5.86303i	0.171188	−	0.296506i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	8.87792	−	8.87792i	0.446697	−	0.446697i
$396$		0			0
$397$	21.9949	+	21.9949i	1.10389	+	1.10389i	0.993936	+	0.109957i	$0.0350713\pi$
$397$	21.9949	+	21.9949i	1.10389	+	1.10389i	0.109957	+	0.993936i	$0.464929\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	15.4215	+	8.90359i	0.770111	+	0.444624i	0.832914	−	0.553402i	$-0.186671\pi$
$401$	15.4215	+	8.90359i	0.770111	+	0.444624i	−0.0628030	+	0.998026i	$0.520004\pi$
$402$		0			0
$403$	−28.1353	−	7.53883i	−1.40152	−	0.375536i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−6.89849	+	3.98284i	−0.341945	+	0.197422i
$408$		0			0
$409$	21.0100	+	12.1301i	1.03888	+	0.599797i	0.919515	−	0.393054i	$-0.128581\pi$
$409$	21.0100	+	12.1301i	1.03888	+	0.599797i	0.119363	+	0.992851i	$0.461915\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	1.10595	−	1.10595i	0.0544202	−	0.0544202i
$414$		0			0
$415$			2.83946i			0.139383i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	11.0392	−	2.95796i	0.539302	−	0.144506i	0.0211217	−	0.999777i	$-0.493276\pi$
$419$	11.0392	−	2.95796i	0.539302	−	0.144506i	0.518180	+	0.855271i	$0.326610\pi$
$420$		0			0
$421$	16.7104	+	4.47753i	0.814413	+	0.218221i	0.641903	−	0.766786i	$-0.278145\pi$
$421$	16.7104	+	4.47753i	0.814413	+	0.218221i	0.172511	+	0.985008i	$0.444812\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−6.40186	−	11.0883i	−0.310536	−	0.537864i
$426$		0			0
$427$	−1.74819	+	0.468425i	−0.0846006	+	0.0226687i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	33.7821			1.62723			0.813613	−	0.581407i	$-0.197498\pi$
$431$	33.7821			1.62723			0.813613	+	0.581407i	$0.197498\pi$
$432$		0			0
$433$	−32.7436			−1.57356			−0.786779	−	0.617235i	$-0.788253\pi$
$433$	−32.7436			−1.57356			−0.786779	+	0.617235i	$0.788253\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.2133	+	2.73664i	−0.488567	+	0.130911i
$438$		0			0
$439$	14.7258	+	25.5058i	0.702824	+	1.21733i	0.967471	+	0.252982i	$0.0814113\pi$
$439$	14.7258	+	25.5058i	0.702824	+	1.21733i	−0.264647	+	0.964345i	$0.585255\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−8.80422	−	2.35908i	−0.418301	−	0.112083i	0.0435282	−	0.999052i	$-0.486140\pi$
$443$	−8.80422	−	2.35908i	−0.418301	−	0.112083i	−0.461830	+	0.886969i	$0.652807\pi$
$444$		0			0
$445$	−2.26259	+	0.606260i	−0.107257	+	0.0287395i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	2.79179i		−	0.131753i	−0.997828	−	0.0658765i	$-0.979016\pi$
$449$		−	2.79179i		−	0.131753i	0.997828	−	0.0658765i	$-0.0209843\pi$
$450$		0			0
$451$	12.0103	−	12.0103i	0.565543	−	0.565543i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.868300	+	0.501313i	0.0407065	+	0.0235019i
$456$		0			0
$457$	1.90950	−	1.10245i	0.0893226	−	0.0515704i	−0.454673	−	0.890658i	$-0.650244\pi$
$457$	1.90950	−	1.10245i	0.0893226	−	0.0515704i	0.543996	+	0.839088i	$0.316911\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	19.1849	+	5.14058i	0.893531	+	0.239421i	0.676236	−	0.736685i	$-0.263610\pi$
$461$	19.1849	+	5.14058i	0.893531	+	0.239421i	0.217295	+	0.976106i	$0.430277\pi$
$462$		0			0
$463$	1.39347	+	0.804523i	0.0647602	+	0.0373893i	0.532031	−	0.846725i	$-0.321429\pi$
$463$	1.39347	+	0.804523i	0.0647602	+	0.0373893i	−0.467270	+	0.884115i	$0.654762\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−9.94383	−	9.94383i	−0.460145	−	0.460145i	0.438558	−	0.898703i	$-0.355489\pi$
$467$	−9.94383	−	9.94383i	−0.460145	−	0.460145i	−0.898703	+	0.438558i	$0.855489\pi$
$468$		0			0
$469$	0.771428	−	0.771428i	0.0356213	−	0.0356213i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−11.3600	+	19.6760i	−0.522331	+	0.904704i
$474$		0			0
$475$	−5.17561	+	19.3156i	−0.237473	+	0.886262i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	14.3867	+	24.9185i	0.657346	+	1.13856i	0.981300	+	0.192483i	$0.0616542\pi$
$479$	14.3867	+	24.9185i	0.657346	+	1.13856i	−0.323955	+	0.946073i	$0.605013\pi$
$480$		0			0
$481$	3.58248	−	6.20504i	0.163347	−	0.282925i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−16.2259	−	16.2259i	−0.736778	−	0.736778i
$486$		0			0
$487$	−43.0194			−1.94939			−0.974697	−	0.223530i	$-0.928242\pi$
$487$	−43.0194			−1.94939			−0.974697	+	0.223530i	$0.928242\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.40962	+	5.26076i	0.0636152	+	0.237415i	0.990411	−	0.138150i	$-0.0441155\pi$
$491$	1.40962	+	5.26076i	0.0636152	+	0.237415i	−0.926796	+	0.375565i	$0.877449\pi$
$492$		0			0
$493$	−3.81801	+	14.2490i	−0.171955	+	0.641744i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.59488	+	1.49815i	−0.116396	+	0.0672013i
$498$		0			0
$499$	4.61454	+	17.2217i	0.206575	+	0.770950i	0.988964	+	0.148159i	$0.0473347\pi$
$499$	4.61454	+	17.2217i	0.206575	+	0.770950i	−0.782388	+	0.622791i	$0.785999\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	0.254767i		−	0.0113595i	−0.999984	−	0.00567974i	$-0.998192\pi$
$503$		−	0.254767i		−	0.0113595i	0.999984	−	0.00567974i	$-0.00180793\pi$
$504$		0			0
$505$			20.1888i			0.898391i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−2.84712	−	10.6256i	−0.126196	−	0.470971i	0.873683	−	0.486495i	$-0.161725\pi$
$509$	−2.84712	−	10.6256i	−0.126196	−	0.470971i	−0.999879	+	0.0155245i	$0.995058\pi$
$510$		0			0
$511$	−2.26043	+	1.30506i	−0.0999956	+	0.0577325i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.0395075	−	0.147444i	0.00174091	−	0.00649716i
$516$		0			0
$517$	9.03680	+	33.7258i	0.397438	+	1.48326i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	8.17552			0.358176			0.179088	−	0.983833i	$-0.442685\pi$
$521$	8.17552			0.358176			0.179088	+	0.983833i	$0.442685\pi$
$522$		0			0
$523$	11.4305	+	11.4305i	0.499820	+	0.499820i	0.911382	−	0.411562i	$-0.135017\pi$
$523$	11.4305	+	11.4305i	0.499820	+	0.499820i	−0.411562	+	0.911382i	$0.635017\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	18.9254	−	32.7797i	0.824403	−	1.42791i
$528$		0			0
$529$	−9.84425	−	17.0507i	−0.428011	−	0.741337i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.95417	+	14.7572i	−0.171274	+	0.639204i
$534$		0			0
$535$	−5.27308	+	9.13325i	−0.227975	+	0.394865i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−15.5774	+	15.5774i	−0.670967	+	0.670967i
$540$		0			0
$541$	9.93863	+	9.93863i	0.427295	+	0.427295i	0.887706	−	0.460411i	$-0.152298\pi$
$541$	9.93863	+	9.93863i	0.427295	+	0.427295i	−0.460411	+	0.887706i	$0.652298\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.21235	+	3.00935i	0.223273	+	0.128906i
$546$		0			0
$547$	−2.81747	−	0.754938i	−0.120466	−	0.0322788i	0.198082	−	0.980185i	$-0.436529\pi$
$547$	−2.81747	−	0.754938i	−0.120466	−	0.0322788i	−0.318548	+	0.947907i	$0.603195\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	19.9527	−	11.5197i	0.850012	−	0.490755i
$552$		0			0
$553$	2.44341	+	1.41070i	0.103904	+	0.0599891i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−11.5964	+	11.5964i	−0.491356	+	0.491356i	−0.908733	−	0.417377i	$-0.862949\pi$
$557$	−11.5964	+	11.5964i	−0.491356	+	0.491356i	0.417377	+	0.908733i	$0.362949\pi$
$558$		0			0
$559$		−	20.4360i		−	0.864352i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.42718	+	1.99011i	−0.313018	+	0.0838730i	−0.411908	−	0.911225i	$-0.635138\pi$
$563$	−7.42718	+	1.99011i	−0.313018	+	0.0838730i	0.0988898	+	0.995098i	$0.468471\pi$
$564$		0			0
$565$	2.66403	+	0.713826i	0.112077	+	0.0300309i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	11.7897	+	20.4204i	0.494250	+	0.856066i	0.999978	−	0.00662697i	$-0.00210945\pi$
$569$	11.7897	+	20.4204i	0.494250	+	0.856066i	−0.505728	+	0.862693i	$0.668776\pi$
$570$		0			0
$571$	7.46185	−	1.99940i	0.312269	−	0.0836722i	−0.0992811	−	0.995059i	$-0.531654\pi$
$571$	7.46185	−	1.99940i	0.312269	−	0.0836722i	0.411550	+	0.911387i	$0.364988\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	6.26280			0.261177
$576$		0			0
$577$	16.4238			0.683733			0.341866	−	0.939749i	$-0.388941\pi$
$577$	16.4238			0.683733			0.341866	+	0.939749i	$0.388941\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.616336	+	0.165147i	−0.0255699	+	0.00685144i
$582$		0			0
$583$	19.3196	+	33.4626i	0.800137	+	1.38588i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−44.0249	−	11.7964i	−1.81710	−	0.486891i	−0.820680	−	0.571388i	$-0.806405\pi$
$587$	−44.0249	−	11.7964i	−1.81710	−	0.486891i	−0.996424	+	0.0844969i	$0.973072\pi$
$588$		0			0
$589$	−57.1015	+	15.3003i	−2.35283	+	0.630438i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	9.66931i		−	0.397071i	−0.980094	−	0.198535i	$-0.936382\pi$
$593$		−	9.66931i		−	0.397071i	0.980094	−	0.198535i	$-0.0636185\pi$
$594$		0			0
$595$	−0.921278	+	0.921278i	−0.0377687	+	0.0377687i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−8.99479	−	5.19314i	−0.367517	−	0.212186i	0.304856	−	0.952398i	$-0.401392\pi$
$599$	−8.99479	−	5.19314i	−0.367517	−	0.212186i	−0.672373	+	0.740212i	$0.734725\pi$
$600$		0			0
$601$	−16.6353	+	9.60440i	−0.678569	+	0.391772i	−0.799316	−	0.600912i	$-0.794804\pi$
$601$	−16.6353	+	9.60440i	−0.678569	+	0.391772i	0.120747	+	0.992683i	$0.461471\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.04807	+	0.280829i	0.0426101	+	0.0114173i
$606$		0			0
$607$	12.1261	+	7.00100i	0.492183	+	0.284162i	0.725480	−	0.688244i	$-0.241618\pi$
$607$	12.1261	+	7.00100i	0.492183	+	0.284162i	−0.233297	+	0.972406i	$0.574951\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−22.2072	−	22.2072i	−0.898406	−	0.898406i
$612$		0			0
$613$	17.8303	−	17.8303i	0.720159	−	0.720159i	−0.248478	−	0.968637i	$-0.579930\pi$
$613$	17.8303	−	17.8303i	0.720159	−	0.720159i	0.968637	+	0.248478i	$0.0799304\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	24.3668	−	42.2045i	0.980970	−	1.69909i	0.322340	−	0.946624i	$-0.395531\pi$
$617$	24.3668	−	42.2045i	0.980970	−	1.69909i	0.658630	−	0.752467i	$-0.271136\pi$
$618$		0			0
$619$	2.99775	−	11.1877i	0.120490	−	0.449673i	−0.879149	−	0.476547i	$-0.841888\pi$
$619$	2.99775	−	11.1877i	0.120490	−	0.449673i	0.999639	+	0.0268731i	$0.00855501\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−0.263191	−	0.455861i	−0.0105445	−	0.0182637i
$624$		0			0
$625$	2.02612	−	3.50934i	0.0810447	−	0.140374i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	6.58363	+	6.58363i	0.262506	+	0.262506i
$630$		0			0
$631$	−1.63509			−0.0650918			−0.0325459	−	0.999470i	$-0.510362\pi$
$631$	−1.63509			−0.0650918			−0.0325459	+	0.999470i	$0.510362\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−1.17588	−	4.38844i	−0.0466633	−	0.174150i
$636$		0			0
$637$	5.12858	−	19.1401i	0.203202	−	0.758359i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	33.5608	−	19.3763i	1.32557	−	0.765319i	0.340960	−	0.940078i	$-0.389248\pi$
$641$	33.5608	−	19.3763i	1.32557	−	0.765319i	0.984611	+	0.174759i	$0.0559148\pi$
$642$		0			0
$643$	−5.22528	−	19.5010i	−0.206065	−	0.769044i	−0.989122	−	0.147095i	$-0.953008\pi$
$643$	−5.22528	−	19.5010i	−0.206065	−	0.769044i	0.783058	−	0.621949i	$-0.213659\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	28.2882i		−	1.11212i	−0.831141	−	0.556062i	$-0.812312\pi$
$647$		−	28.2882i		−	1.11212i	0.831141	−	0.556062i	$-0.187688\pi$
$648$		0			0
$649$		−	17.7456i		−	0.696575i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−0.228971	−	0.854532i	−0.00896033	−	0.0334404i	0.961301	−	0.275500i	$-0.0888436\pi$
$653$	−0.228971	−	0.854532i	−0.00896033	−	0.0334404i	−0.970261	+	0.242060i	$0.922177\pi$
$654$		0			0
$655$	16.7766	−	9.68599i	0.655517	−	0.378463i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	13.0375	−	48.6567i	0.507869	−	1.89539i	0.0671656	−	0.997742i	$-0.478604\pi$
$659$	13.0375	−	48.6567i	0.507869	−	1.89539i	0.440704	−	0.897653i	$-0.354729\pi$
$660$		0			0
$661$	−7.17239	−	26.7677i	−0.278974	−	1.04114i	−0.953131	−	0.302557i	$-0.902160\pi$
$661$	−7.17239	−	26.7677i	−0.278974	−	1.04114i	0.674158	−	0.738587i	$-0.264507\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	2.03486			0.0789086
$666$		0			0
$667$	−5.10222	−	5.10222i	−0.197559	−	0.197559i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−10.2672	+	17.7834i	−0.396363	+	0.686520i
$672$		0			0
$673$	−16.5237	−	28.6198i	−0.636941	−	1.10321i	−0.986100	−	0.166150i	$-0.946866\pi$
$673$	−16.5237	−	28.6198i	−0.636941	−	1.10321i	0.349160	−	0.937063i	$-0.386467\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−2.69118	+	10.0436i	−0.103430	+	0.386007i	−0.998162	−	0.0605961i	$-0.980700\pi$
$677$	−2.69118	+	10.0436i	−0.103430	+	0.386007i	0.894732	+	0.446603i	$0.147367\pi$
$678$		0			0
$679$	2.57829	−	4.46572i	0.0989455	−	0.171379i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−9.18142	+	9.18142i	−0.351317	+	0.351317i	−0.860600	−	0.509282i	$-0.829911\pi$
$683$	−9.18142	+	9.18142i	−0.351317	+	0.351317i	0.509282	+	0.860600i	$0.329911\pi$
$684$		0			0
$685$	18.3723	+	18.3723i	0.701968	+	0.701968i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−30.0988	−	17.3776i	−1.14667	−	0.662033i
$690$		0			0
$691$	−24.3744	−	6.53111i	−0.927247	−	0.248455i	−0.236567	−	0.971615i	$-0.576022\pi$
$691$	−24.3744	−	6.53111i	−0.927247	−	0.248455i	−0.690680	+	0.723160i	$0.742689\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.897694	−	0.518284i	0.0340515	−	0.0196596i
$696$		0			0
$697$	−17.1932	−	9.92649i	−0.651239	−	0.375993i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−32.8695	+	32.8695i	−1.24146	+	1.24146i	−0.282069	+	0.959394i	$0.591021\pi$
$701$	−32.8695	+	32.8695i	−1.24146	+	1.24146i	−0.959394	+	0.282069i	$0.908979\pi$
$702$		0			0
$703$		−	14.5415i		−	0.548443i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−4.38221	+	1.17421i	−0.164810	+	0.0441607i
$708$		0			0
$709$	41.1714	+	11.0318i	1.54622	+	0.414310i	0.928271	−	0.371905i	$-0.121295\pi$
$709$	41.1714	+	11.0318i	1.54622	+	0.414310i	0.617953	+	0.786215i	$0.287962\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	9.25715	+	16.0339i	0.346683	+	0.600473i
$714$		0			0
$715$	10.9881	−	2.94426i	0.410932	−	0.110109i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8.84226			−0.329761			−0.164880	−	0.986314i	$-0.552724\pi$
$719$	−8.84226			−0.329761			−0.164880	+	0.986314i	$0.552724\pi$
$720$		0			0
$721$	0.0343022			0.00127748
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−13.1814	+	3.53195i	−0.489545	+	0.131173i
$726$		0			0
$727$	−11.4146	−	19.7707i	−0.423344	−	0.733254i	0.572920	−	0.819611i	$-0.305811\pi$
$727$	−11.4146	−	19.7707i	−0.423344	−	0.733254i	−0.996264	+	0.0863576i	$0.972477\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	25.6512	+	6.87321i	0.948743	+	0.254215i
$732$		0			0
$733$	−28.8645	+	7.73423i	−1.06614	+	0.285670i	−0.748905	−	0.662678i	$-0.769420\pi$
$733$	−28.8645	+	7.73423i	−1.06614	+	0.285670i	−0.317232	+	0.948348i	$0.602753\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	12.3780i		−	0.455950i
$738$		0			0
$739$	−6.92568	+	6.92568i	−0.254765	+	0.254765i	−0.822921	−	0.568156i	$-0.807657\pi$
$739$	−6.92568	+	6.92568i	−0.254765	+	0.254765i	0.568156	+	0.822921i	$0.307657\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	27.7583	+	16.0262i	1.01835	+	0.587946i	0.913626	−	0.406555i	$-0.133270\pi$
$743$	27.7583	+	16.0262i	1.01835	+	0.587946i	0.104726	+	0.994501i	$0.466603\pi$
$744$		0			0
$745$	5.74942	−	3.31943i	0.210642	−	0.121614i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−2.28916	−	0.613380i	−0.0836442	−	0.0224124i
$750$		0			0
$751$	7.35037	+	4.24374i	0.268219	+	0.154856i	0.628078	−	0.778151i	$-0.283842\pi$
$751$	7.35037	+	4.24374i	0.268219	+	0.154856i	−0.359859	+	0.933007i	$0.617175\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.70975	−	2.70975i	−0.0986179	−	0.0986179i
$756$		0			0
$757$	−15.2511	+	15.2511i	−0.554309	+	0.554309i	−0.927682	−	0.373372i	$-0.878201\pi$
$757$	−15.2511	+	15.2511i	−0.554309	+	0.554309i	0.373372	+	0.927682i	$0.378201\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−1.63439	+	2.83084i	−0.0592465	+	0.102618i	−0.894127	−	0.447813i	$-0.852203\pi$
$761$	−1.63439	+	2.83084i	−0.0592465	+	0.102618i	0.834881	+	0.550431i	$0.185536\pi$
$762$		0			0
$763$	−0.350056	+	1.30643i	−0.0126729	+	0.0472959i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	7.98088	+	13.8233i	0.288173	+	0.499130i
$768$		0			0
$769$	19.1814	−	33.2232i	0.691701	−	1.19806i	−0.279580	−	0.960123i	$-0.590195\pi$
$769$	19.1814	−	33.2232i	0.691701	−	1.19806i	0.971280	−	0.237938i	$-0.0764716\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−20.0548	−	20.0548i	−0.721320	−	0.721320i	0.247554	−	0.968874i	$-0.420373\pi$
$773$	−20.0548	−	20.0548i	−0.721320	−	0.721320i	−0.968874	+	0.247554i	$0.920373\pi$
$774$		0			0
$775$	35.0148			1.25777
$776$		0			0
$777$		0			0
$778$		0			0
$779$	8.02512	+	29.9501i	0.287530	+	1.07308i
$780$		0			0
$781$	−8.79878	+	32.8375i	−0.314845	+	1.17502i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.31134	−	3.64385i	0.225261	−	0.130055i
$786$		0			0
$787$	−2.45116	−	9.14785i	−0.0873744	−	0.326086i	0.908379	−	0.418148i	$-0.137321\pi$
$787$	−2.45116	−	9.14785i	−0.0873744	−	0.326086i	−0.995753	+	0.0920625i	$0.970654\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			0.619775i			0.0220367i
$792$		0			0
$793$		−	18.4703i		−	0.655900i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−7.19855	−	26.8654i	−0.254986	−	0.951620i	−0.968098	−	0.250571i	$-0.919382\pi$
$797$	−7.19855	−	26.8654i	−0.254986	−	0.951620i	0.713112	−	0.701050i	$-0.247285\pi$
$798$		0			0
$799$	35.3432	−	20.4054i	1.25035	−	0.721891i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−7.66474	+	28.6052i	−0.270483	+	1.00946i
$804$		0			0
$805$	−0.164943	−	0.615577i	−0.00581349	−	0.0216962i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−48.8492			−1.71745			−0.858724	−	0.512439i	$-0.828742\pi$
$809$	−48.8492			−1.71745			−0.858724	+	0.512439i	$0.828742\pi$
$810$		0			0
$811$	5.86383	+	5.86383i	0.205907	+	0.205907i	0.802525	−	0.596618i	$-0.203489\pi$
$811$	5.86383	+	5.86383i	0.205907	+	0.205907i	−0.596618	+	0.802525i	$0.703489\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−11.0840	+	19.1981i	−0.388256	+	0.672480i
$816$		0			0
$817$	−20.7378	−	35.9189i	−0.725524	−	1.25664i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	0.828375	−	3.09154i	0.0289105	−	0.107895i	−0.949963	−	0.312363i	$-0.898880\pi$
$821$	0.828375	−	3.09154i	0.0289105	−	0.107895i	0.978873	+	0.204467i	$0.0655462\pi$
$822$		0			0
$823$	20.9908	−	36.3572i	0.731695	−	1.26733i	−0.224464	−	0.974482i	$-0.572063\pi$
$823$	20.9908	−	36.3572i	0.731695	−	1.26733i	0.956158	−	0.292850i	$-0.0946037\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−12.7209	+	12.7209i	−0.442348	+	0.442348i	−0.892800	−	0.450453i	$-0.851263\pi$
$827$	−12.7209	+	12.7209i	−0.442348	+	0.442348i	0.450453	+	0.892800i	$0.351263\pi$
$828$		0			0
$829$	−10.4132	−	10.4132i	−0.361665	−	0.361665i	0.502761	−	0.864425i	$-0.332318\pi$
$829$	−10.4132	−	10.4132i	−0.361665	−	0.361665i	−0.864425	+	0.502761i	$0.832318\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	22.2996	+	12.8747i	0.772637	+	0.446082i
$834$		0			0
$835$	−16.8246	−	4.50815i	−0.582241	−	0.156011i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−25.7863	+	14.8877i	−0.890241	+	0.513981i	−0.874021	−	0.485888i	$-0.838496\pi$
$839$	−25.7863	+	14.8877i	−0.890241	+	0.513981i	−0.0162196	+	0.999868i	$0.505163\pi$
$840$		0			0
$841$	−11.4986	−	6.63872i	−0.396503	−	0.228921i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.24025	−	4.24025i	0.145869	−	0.145869i
$846$		0			0
$847$			0.243829i			0.00837805i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−4.39903	+	1.17872i	−0.150797	+	0.0404059i
$852$		0			0
$853$	−28.4092	−	7.61221i	−0.972711	−	0.260637i	−0.262739	−	0.964867i	$-0.584626\pi$
$853$	−28.4092	−	7.61221i	−0.972711	−	0.260637i	−0.709972	+	0.704230i	$0.751292\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−14.3783	−	24.9039i	−0.491152	−	0.850700i	0.508796	−	0.860887i	$-0.330091\pi$
$857$	−14.3783	−	24.9039i	−0.491152	−	0.850700i	−0.999948	+	0.0101867i	$0.996757\pi$
$858$		0			0
$859$	−9.26004	+	2.48122i	−0.315949	+	0.0846582i	−0.413308	−	0.910591i	$-0.635627\pi$
$859$	−9.26004	+	2.48122i	−0.315949	+	0.0846582i	0.0973599	+	0.995249i	$0.468960\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	38.6895			1.31700			0.658502	−	0.752579i	$-0.271190\pi$
$863$	38.6895			1.31700			0.658502	+	0.752579i	$0.271190\pi$
$864$		0			0
$865$	−3.08877			−0.105021
$866$		0			0
$867$		0			0
$868$		0			0
$869$	30.9207	−	8.28517i	1.04891	−	0.281055i
$870$		0			0
$871$	5.56687	+	9.64210i	0.188626	+	0.326710i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−2.85557	−	0.765148i	−0.0965360	−	0.0258667i
$876$		0			0
$877$	33.8645	−	9.07397i	1.14352	−	0.306406i	0.363157	−	0.931728i	$-0.381699\pi$
$877$	33.8645	−	9.07397i	1.14352	−	0.306406i	0.780367	+	0.625322i	$0.215032\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	15.5358i		−	0.523415i	−0.965147	−	0.261708i	$-0.915714\pi$
$881$		−	15.5358i		−	0.523415i	0.965147	−	0.261708i	$-0.0842856\pi$
$882$		0			0
$883$	35.3696	−	35.3696i	1.19028	−	1.19028i	0.213292	−	0.976988i	$-0.431581\pi$
$883$	35.3696	−	35.3696i	1.19028	−	1.19028i	0.976988	−	0.213292i	$-0.0684187\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−22.5037	−	12.9925i	−0.755599	−	0.436246i	0.0721141	−	0.997396i	$-0.477025\pi$
$887$	−22.5037	−	12.9925i	−0.755599	−	0.436246i	−0.827714	+	0.561151i	$0.810359\pi$
$888$		0			0
$889$	0.884169	−	0.510475i	0.0296541	−	0.0171208i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−61.5670	−	16.4968i	−2.06026	−	0.552045i
$894$		0			0
$895$	−14.5841	−	8.42011i	−0.487492	−	0.281453i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−28.5261	−	28.5261i	−0.951398	−	0.951398i
$900$		0			0
$901$	31.9353	−	31.9353i	1.06392	−	1.06392i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	6.03678	−	10.4560i	0.200669	−	0.347569i
$906$		0			0
$907$	−7.10188	+	26.5046i	−0.235814	+	0.880070i	0.741966	+	0.670437i	$0.233894\pi$
$907$	−7.10188	+	26.5046i	−0.235814	+	0.880070i	−0.977780	+	0.209633i	$0.932773\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	23.4177	+	40.5606i	0.775863	+	1.34383i	0.934308	+	0.356466i	$0.116018\pi$
$911$	23.4177	+	40.5606i	0.775863	+	1.34383i	−0.158445	+	0.987368i	$0.550648\pi$
$912$		0			0
$913$	−3.61980	+	6.26967i	−0.119798	+	0.207496i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.07820	+	3.07820i	0.101651	+	0.101651i
$918$		0			0
$919$	0.421071			0.0138899			0.00694493	−	0.999976i	$-0.497789\pi$
$919$	0.421071			0.0138899			0.00694493	+	0.999976i	$0.497789\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−7.91430	−	29.5366i	−0.260503	−	0.972209i
$924$		0			0
$925$	−2.22922	+	8.31957i	−0.0732964	+	0.273546i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	5.41100	−	3.12404i	0.177529	−	0.102496i	−0.408602	−	0.912713i	$-0.633984\pi$
$929$	5.41100	−	3.12404i	0.177529	−	0.102496i	0.586131	+	0.810216i	$0.300650\pi$
$930$		0			0
$931$	−10.4086	−	38.8455i	−0.341128	−	1.27311i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			14.7824i			0.483437i
$936$		0			0
$937$		−	41.2133i		−	1.34638i	−0.739470	−	0.673189i	$-0.764924\pi$
$937$		−	41.2133i		−	1.34638i	0.739470	−	0.673189i	$-0.235076\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.22526	−	12.0368i	−0.105141	−	0.392390i	0.893221	−	0.449619i	$-0.148440\pi$
$941$	−3.22526	−	12.0368i	−0.105141	−	0.392390i	−0.998361	+	0.0572290i	$0.981773\pi$
$942$		0			0
$943$	8.40987	−	4.85544i	0.273863	−	0.158115i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.96886	−	14.8120i	0.128971	−	0.481325i	−0.870979	−	0.491320i	$-0.836515\pi$
$947$	3.96886	−	14.8120i	0.128971	−	0.481325i	0.999950	+	0.00999447i	$0.00318139\pi$
$948$		0			0
$949$	−6.89426	−	25.7297i	−0.223797	−	0.835222i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−20.0192			−0.648486			−0.324243	−	0.945974i	$-0.605110\pi$
$953$	−20.0192			−0.648486			−0.324243	+	0.945974i	$0.605110\pi$
$954$		0			0
$955$	12.5106	+	12.5106i	0.404833	+	0.404833i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.91935	+	5.05646i	−0.0942707	+	0.163282i
$960$		0			0
$961$	36.2559	+	62.7971i	1.16955	+	2.02571i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	4.18105	−	15.6039i	0.134593	−	0.502307i
$966$		0			0
$967$	16.3485	−	28.3164i	0.525732	−	0.910594i	−0.473819	−	0.880622i	$-0.657125\pi$
$967$	16.3485	−	28.3164i	0.525732	−	0.910594i	0.999551	−	0.0299719i	$-0.00954179\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−12.2406	+	12.2406i	−0.392820	+	0.392820i	−0.875691	−	0.482871i	$-0.839594\pi$
$971$	−12.2406	+	12.2406i	−0.392820	+	0.392820i	0.482871	+	0.875691i	$0.339594\pi$
$972$		0			0
$973$	0.164710	+	0.164710i	0.00528037	+	0.00528037i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−34.1771	−	19.7322i	−1.09342	−	0.631288i	−0.158938	−	0.987289i	$-0.550807\pi$
$977$	−34.1771	−	19.7322i	−1.09342	−	0.631288i	−0.934486	+	0.356000i	$0.884140\pi$
$978$		0			0
$979$	−5.76880	−	1.54575i	−0.184372	−	0.0494022i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	3.78032	−	2.18257i	0.120574	−	0.0696132i	−0.438500	−	0.898731i	$-0.644490\pi$
$983$	3.78032	−	2.18257i	0.120574	−	0.0696132i	0.559074	+	0.829118i	$0.311157\pi$
$984$		0			0
$985$	−12.2666	−	7.08211i	−0.390845	−	0.225655i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.18504	+	9.18504i	−0.292067	+	0.292067i
$990$		0			0
$991$			21.1610i			0.672200i	0.941826	+	0.336100i	$0.109108\pi$
$991$			21.1610i			0.672200i	−0.941826	+	0.336100i	$0.890892\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	13.1676	−	3.52825i	0.417441	−	0.111853i
$996$		0			0
$997$	12.7473	+	3.41563i	0.403712	+	0.108174i	0.454960	−	0.890512i	$-0.349653\pi$
$997$	12.7473	+	3.41563i	0.403712	+	0.108174i	−0.0512486	+	0.998686i	$0.516320\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.z.a.1583.7		88
3.2	odd	2		576.2.y.a.239.6		88
4.3	odd	2		432.2.v.a.179.7		88
9.2	odd	6	inner	1728.2.z.a.1007.7		88
9.7	even	3		576.2.y.a.47.17		88
12.11	even	2		144.2.u.a.131.16	yes	88
16.5	even	4		432.2.v.a.395.1		88
16.11	odd	4	inner	1728.2.z.a.719.7		88
36.7	odd	6		144.2.u.a.83.22	yes	88
36.11	even	6		432.2.v.a.35.1		88
48.5	odd	4		144.2.u.a.59.22	yes	88
48.11	even	4		576.2.y.a.527.17		88
144.11	even	12	inner	1728.2.z.a.143.7		88
144.43	odd	12		576.2.y.a.335.6		88
144.101	odd	12		432.2.v.a.251.7		88
144.133	even	12		144.2.u.a.11.16	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.16	✓	88	144.133	even	12
144.2.u.a.59.22	yes	88	48.5	odd	4
144.2.u.a.83.22	yes	88	36.7	odd	6
144.2.u.a.131.16	yes	88	12.11	even	2
432.2.v.a.35.1		88	36.11	even	6
432.2.v.a.179.7		88	4.3	odd	2
432.2.v.a.251.7		88	144.101	odd	12
432.2.v.a.395.1		88	16.5	even	4
576.2.y.a.47.17		88	9.7	even	3
576.2.y.a.239.6		88	3.2	odd	2
576.2.y.a.335.6		88	144.43	odd	12
576.2.y.a.527.17		88	48.11	even	4
1728.2.z.a.143.7		88	144.11	even	12	inner
1728.2.z.a.719.7		88	16.11	odd	4	inner
1728.2.z.a.1007.7		88	9.2	odd	6	inner
1728.2.z.a.1583.7		88	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1728.z (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20583 + 0.323102i) q^{5} +(-0.140266 - 0.242948i) q^{7} +(-3.07444 - 0.823794i) q^{11} +(2.76539 - 0.740984i) q^{13} +3.72031i q^{17} +(4.10860 - 4.10860i) q^{19} +(-1.57595 - 0.909876i) q^{23} +(-2.98049 + 1.72078i) q^{25} +(3.83006 + 1.02626i) q^{29} +(-8.81101 - 5.08704i) q^{31} +(0.247635 + 0.247635i) q^{35} +(1.76964 - 1.76964i) q^{37} +(-2.66819 + 4.62144i) q^{41} +(1.84748 - 6.89490i) q^{43} +(-5.48486 - 9.50006i) q^{47} +(3.46065 - 5.99402i) q^{49} +(-8.58403 - 8.58403i) q^{53} +3.97344 q^{55} +(1.44299 + 5.38532i) q^{59} +(1.66977 - 6.23168i) q^{61} +(-3.09519 + 1.78701i) q^{65} +(1.00652 + 3.75640i) q^{67} -10.6808i q^{71} -9.30419i q^{73} +(0.231101 + 0.862479i) q^{77} +(-8.70990 + 5.02866i) q^{79} +(0.588691 - 2.19703i) q^{83} +(-1.20204 - 4.48608i) q^{85} +1.87637 q^{89} +(-0.567911 - 0.567911i) q^{91} +(-3.62679 + 6.28179i) q^{95} +(9.19070 + 15.9188i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{5} + 4 q^{7} - 6 q^{11} - 2 q^{13} + 8 q^{19} - 12 q^{23} + 6 q^{29} - 8 q^{37} + 2 q^{43} - 24 q^{49} + 16 q^{55} - 42 q^{59} - 2 q^{61} + 12 q^{65} + 2 q^{67} + 6 q^{77} + 54 q^{83} + 8 q^{85}+ \cdots - 4 q^{97}+O(q^{100}) \) 88 * q + 6 * q^5 + 4 * q^7 - 6 * q^11 - 2 * q^13 + 8 * q^19 - 12 * q^23 + 6 * q^29 - 8 * q^37 + 2 * q^43 - 24 * q^49 + 16 * q^55 - 42 * q^59 - 2 * q^61 + 12 * q^65 + 2 * q^67 + 6 * q^77 + 54 * q^83 + 8 * q^85 - 20 * q^91 - 4 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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