LMFDB - Embedded newform 1728.2.z.a.1583.18

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			1583.18
Character	$\chi$	$=$	1728.1583
Dual form			1728.2.z.a.143.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.70956 - 0.726024i) q^{5} +(0.00424642 + 0.00735502i) q^{7} +(3.00129 + 0.804193i) q^{11} +(6.42317 - 1.72108i) q^{13} -3.37812i q^{17} +(-1.35881 + 1.35881i) q^{19} +(-5.38718 - 3.11029i) q^{23} +(2.48446 - 1.43441i) q^{25} +(-3.27685 - 0.878030i) q^{29} +(6.70211 + 3.86947i) q^{31} +(0.0168459 + 0.0168459i) q^{35} +(0.769697 - 0.769697i) q^{37} +(-2.64756 + 4.58570i) q^{41} +(-1.60713 + 5.99790i) q^{43} +(0.0955284 + 0.165460i) q^{47} +(3.49996 - 6.06212i) q^{49} +(-0.750557 - 0.750557i) q^{53} +8.71603 q^{55} +(-2.43515 - 9.08809i) q^{59} +(-2.64143 + 9.85796i) q^{61} +(16.1544 - 9.32674i) q^{65} +(-2.08238 - 7.77154i) q^{67} +1.02260i q^{71} +7.30911i q^{73} +(0.00682989 + 0.0254895i) q^{77} +(4.36074 - 2.51768i) q^{79} +(3.35017 - 12.5030i) q^{83} +(-2.45259 - 9.15320i) q^{85} +18.1774 q^{89} +(0.0399341 + 0.0399341i) q^{91} +(-2.69525 + 4.66831i) q^{95} +(1.64497 + 2.84917i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.70956	−	0.726024i	1.21175	−	0.324688i	0.404302	−	0.914625i	$-0.367514\pi$
$5$	2.70956	−	0.726024i	1.21175	−	0.324688i	0.807449	+	0.589938i	$0.200848\pi$
$6$		0			0
$7$	0.00424642	+	0.00735502i	0.00160500	+	0.00277994i	0.866827	−	0.498609i	$-0.166156\pi$
$7$	0.00424642	+	0.00735502i	0.00160500	+	0.00277994i	−0.865222	+	0.501389i	$0.832822\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.00129	+	0.804193i	0.904923	+	0.242473i	0.681129	−	0.732163i	$-0.261489\pi$
$11$	3.00129	+	0.804193i	0.904923	+	0.242473i	0.223794	+	0.974637i	$0.428156\pi$
$12$		0			0
$13$	6.42317	−	1.72108i	1.78147	−	0.477342i	0.790616	−	0.612312i	$-0.209760\pi$
$13$	6.42317	−	1.72108i	1.78147	−	0.477342i	0.990850	+	0.134969i	$0.0430936\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	3.37812i		−	0.819314i	−0.912240	−	0.409657i	$-0.865648\pi$
$17$		−	3.37812i		−	0.819314i	0.912240	−	0.409657i	$-0.134352\pi$
$18$		0			0
$19$	−1.35881	+	1.35881i	−0.311733	+	0.311733i	−0.845581	−	0.533848i	$-0.820746\pi$
$19$	−1.35881	+	1.35881i	−0.311733	+	0.311733i	0.533848	+	0.845581i	$0.320746\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.38718	−	3.11029i	−1.12331	−	0.648541i	−0.181062	−	0.983472i	$-0.557954\pi$
$23$	−5.38718	−	3.11029i	−1.12331	−	0.648541i	−0.942243	+	0.334931i	$0.891287\pi$
$24$		0			0
$25$	2.48446	−	1.43441i	0.496893	−	0.286881i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.27685	−	0.878030i	−0.608496	−	0.163046i	−0.0586036	−	0.998281i	$-0.518665\pi$
$29$	−3.27685	−	0.878030i	−0.608496	−	0.163046i	−0.549893	+	0.835235i	$0.685331\pi$
$30$		0			0
$31$	6.70211	+	3.86947i	1.20374	+	0.694977i	0.961384	−	0.275212i	$-0.0887479\pi$
$31$	6.70211	+	3.86947i	1.20374	+	0.694977i	0.242352	+	0.970188i	$0.422081\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.0168459	+	0.0168459i	0.00284747	+	0.00284747i
$36$		0			0
$37$	0.769697	−	0.769697i	0.126537	−	0.126537i	−0.641002	−	0.767539i	$-0.721481\pi$
$37$	0.769697	−	0.769697i	0.126537	−	0.126537i	0.767539	+	0.641002i	$0.221481\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.64756	+	4.58570i	−0.413479	+	0.716166i	−0.995267	−	0.0971739i	$-0.969020\pi$
$41$	−2.64756	+	4.58570i	−0.413479	+	0.716166i	0.581789	+	0.813340i	$0.302353\pi$
$42$		0			0
$43$	−1.60713	+	5.99790i	−0.245086	+	0.914672i	0.728255	+	0.685306i	$0.240332\pi$
$43$	−1.60713	+	5.99790i	−0.245086	+	0.914672i	−0.973340	+	0.229365i	$0.926335\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.0955284	+	0.165460i	0.0139343	+	0.0241348i	0.872908	−	0.487884i	$-0.162231\pi$
$47$	0.0955284	+	0.165460i	0.0139343	+	0.0241348i	−0.858974	+	0.512019i	$0.828898\pi$
$48$		0			0
$49$	3.49996	−	6.06212i	0.499995	−	0.866016i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.750557	−	0.750557i	−0.103097	−	0.103097i	0.653677	−	0.756774i	$-0.273226\pi$
$53$	−0.750557	−	0.750557i	−0.103097	−	0.103097i	−0.756774	+	0.653677i	$0.773226\pi$
$54$		0			0
$55$	8.71603			1.17527
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.43515	−	9.08809i	−0.317029	−	1.18317i	−0.922086	−	0.386986i	$-0.873516\pi$
$59$	−2.43515	−	9.08809i	−0.317029	−	1.18317i	0.605057	−	0.796182i	$-0.293150\pi$
$60$		0			0
$61$	−2.64143	+	9.85796i	−0.338201	+	1.26218i	0.562156	+	0.827031i	$0.309972\pi$
$61$	−2.64143	+	9.85796i	−0.338201	+	1.26218i	−0.900357	+	0.435152i	$0.856695\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	16.1544	−	9.32674i	2.00371	−	1.15684i
$66$		0			0
$67$	−2.08238	−	7.77154i	−0.254403	−	0.949445i	−0.968422	−	0.249318i	$-0.919794\pi$
$67$	−2.08238	−	7.77154i	−0.254403	−	0.949445i	0.714019	−	0.700127i	$-0.246873\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			1.02260i			0.121360i	0.998157	+	0.0606801i	$0.0193269\pi$
$71$			1.02260i			0.121360i	−0.998157	+	0.0606801i	$0.980673\pi$
$72$		0			0
$73$			7.30911i			0.855467i	0.903905	+	0.427734i	$0.140688\pi$
$73$			7.30911i			0.855467i	−0.903905	+	0.427734i	$0.859312\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.00682989	+	0.0254895i	0.000778338	+	0.00290480i
$78$		0			0
$79$	4.36074	−	2.51768i	0.490622	−	0.283261i	−0.234211	−	0.972186i	$-0.575251\pi$
$79$	4.36074	−	2.51768i	0.490622	−	0.283261i	0.724832	+	0.688925i	$0.241917\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.35017	−	12.5030i	0.367729	−	1.37238i	−0.495955	−	0.868348i	$-0.665182\pi$
$83$	3.35017	−	12.5030i	0.367729	−	1.37238i	0.863684	−	0.504034i	$-0.168151\pi$
$84$		0			0
$85$	−2.45259	−	9.15320i	−0.266021	−	0.992804i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	18.1774			1.92680			0.963399	−	0.268070i	$-0.0863859\pi$
$89$	18.1774			1.92680			0.963399	+	0.268070i	$0.0863859\pi$
$90$		0			0
$91$	0.0399341	+	0.0399341i	0.00418623	+	0.00418623i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.69525	+	4.66831i	−0.276527	+	0.478959i
$96$		0			0
$97$	1.64497	+	2.84917i	0.167021	+	0.289289i	0.937371	−	0.348332i	$-0.113252\pi$
$97$	1.64497	+	2.84917i	0.167021	+	0.289289i	−0.770350	+	0.637621i	$0.779918\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.714822	+	2.66775i	−0.0711275	+	0.265451i	−0.992327	−	0.123638i	$-0.960544\pi$
$101$	−0.714822	+	2.66775i	−0.0711275	+	0.265451i	0.921200	+	0.389090i	$0.127210\pi$
$102$		0			0
$103$	−5.52502	+	9.56961i	−0.544396	+	0.942922i	0.454249	+	0.890875i	$0.349908\pi$
$103$	−5.52502	+	9.56961i	−0.544396	+	0.942922i	−0.998645	+	0.0520466i	$0.983426\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.93562	−	1.93562i	0.187124	−	0.187124i	−0.607328	−	0.794451i	$-0.707759\pi$
$107$	1.93562	−	1.93562i	0.187124	−	0.187124i	0.794451	+	0.607328i	$0.207759\pi$
$108$		0			0
$109$	5.98392	+	5.98392i	0.573155	+	0.573155i	0.933009	−	0.359853i	$-0.117173\pi$
$109$	5.98392	+	5.98392i	0.573155	+	0.573155i	−0.359853	+	0.933009i	$0.617173\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−11.7864	−	6.80488i	−1.10877	−	0.640149i	−0.170260	−	0.985399i	$-0.554461\pi$
$113$	−11.7864	−	6.80488i	−1.10877	−	0.640149i	−0.938511	+	0.345250i	$0.887794\pi$
$114$		0			0
$115$	−16.8550	−	4.51629i	−1.57174	−	0.421146i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.0248461	−	0.0143449i	0.00227764	−	0.00131500i
$120$		0			0
$121$	−1.16526	−	0.672766i	−0.105933	−	0.0611605i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−4.22728	+	4.22728i	−0.378100	+	0.378100i
$126$		0			0
$127$		−	7.01184i		−	0.622200i	−0.950377	−	0.311100i	$-0.899303\pi$
$127$		−	7.01184i		−	0.622200i	0.950377	−	0.311100i	$-0.100697\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−8.04427	+	2.15546i	−0.702831	+	0.188323i	−0.592498	−	0.805572i	$-0.701858\pi$
$131$	−8.04427	+	2.15546i	−0.702831	+	0.188323i	−0.110333	+	0.993895i	$0.535192\pi$
$132$		0			0
$133$	−0.0157642	−	0.00422400i	−0.00136693	−	0.000366268i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.71852	+	4.70861i	0.232259	+	0.402284i	0.958472	−	0.285185i	$-0.0920550\pi$
$137$	2.71852	+	4.70861i	0.232259	+	0.402284i	−0.726214	+	0.687469i	$0.758722\pi$
$138$		0			0
$139$	13.5977	−	3.64349i	1.15334	−	0.309037i	0.369038	−	0.929414i	$-0.379687\pi$
$139$	13.5977	−	3.64349i	1.15334	−	0.309037i	0.784303	+	0.620378i	$0.213021\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	20.6619			1.72783
$144$		0			0
$145$	−9.51629			−0.790285
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−9.17223	+	2.45769i	−0.751419	+	0.201342i	−0.614147	−	0.789191i	$-0.710500\pi$
$149$	−9.17223	+	2.45769i	−0.751419	+	0.201342i	−0.137271	+	0.990533i	$0.543833\pi$
$150$		0			0
$151$	2.26744	+	3.92732i	0.184522	+	0.319601i	0.943415	−	0.331614i	$-0.107593\pi$
$151$	2.26744	+	3.92732i	0.184522	+	0.319601i	−0.758893	+	0.651215i	$0.774260\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	20.9691	+	5.61865i	1.68428	+	0.451301i
$156$		0			0
$157$	−19.1085	+	5.12011i	−1.52502	+	0.408629i	−0.921392	−	0.388634i	$-0.872947\pi$
$157$	−19.1085	+	5.12011i	−1.52502	+	0.408629i	−0.603632	+	0.797263i	$0.706280\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	0.0528305i		−	0.00416362i
$162$		0			0
$163$	6.31776	−	6.31776i	0.494845	−	0.494845i	−0.414984	−	0.909829i	$-0.636213\pi$
$163$	6.31776	−	6.31776i	0.494845	−	0.494845i	0.909829	+	0.414984i	$0.136213\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.2973	+	5.94513i	0.796827	+	0.460048i	0.842360	−	0.538915i	$-0.181165\pi$
$167$	10.2973	+	5.94513i	0.796827	+	0.460048i	−0.0455334	+	0.998963i	$0.514499\pi$
$168$		0			0
$169$	27.0366	−	15.6096i	2.07974	−	1.20074i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	0.468462	+	0.125524i	0.0356165	+	0.00954341i	0.276583	−	0.960990i	$-0.410798\pi$
$173$	0.468462	+	0.125524i	0.0356165	+	0.00954341i	−0.240967	+	0.970533i	$0.577464\pi$
$174$		0			0
$175$	0.0211002	+	0.0121822i	0.00159502	+	0.000920887i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−6.91661	−	6.91661i	−0.516971	−	0.516971i	0.399682	−	0.916654i	$-0.369120\pi$
$179$	−6.91661	−	6.91661i	−0.516971	−	0.516971i	−0.916654	+	0.399682i	$0.869120\pi$
$180$		0			0
$181$	−2.19753	+	2.19753i	−0.163341	+	0.163341i	−0.784045	−	0.620704i	$-0.786847\pi$
$181$	−2.19753	+	2.19753i	−0.163341	+	0.163341i	0.620704	+	0.784045i	$0.286847\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.52672	−	2.64436i	0.112247	−	0.194417i
$186$		0			0
$187$	2.71666	−	10.1387i	0.198662	−	0.741416i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.33144	+	10.9664i	0.458127	+	0.793499i	0.998862	−	0.0476936i	$-0.0151871\pi$
$191$	6.33144	+	10.9664i	0.458127	+	0.793499i	−0.540735	+	0.841193i	$0.681854\pi$
$192$		0			0
$193$	4.99499	−	8.65157i	0.359547	−	0.622754i	−0.628338	−	0.777940i	$-0.716265\pi$
$193$	4.99499	−	8.65157i	0.359547	−	0.622754i	0.987885	+	0.155187i	$0.0495979\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.273888	+	0.273888i	0.0195137	+	0.0195137i	0.716796	−	0.697283i	$-0.245608\pi$
$197$	0.273888	+	0.273888i	0.0195137	+	0.0195137i	−0.697283	+	0.716796i	$0.745608\pi$
$198$		0			0
$199$	18.0544			1.27984			0.639920	−	0.768441i	$-0.278967\pi$
$199$	18.0544			1.27984			0.639920	+	0.768441i	$0.278967\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.00745698	−	0.0278298i	−0.000523377	−	0.00195327i
$204$		0			0
$205$	−3.84438	+	14.3474i	−0.268503	+	1.00207i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−5.17094	+	2.98544i	−0.357681	+	0.206507i
$210$		0			0
$211$	−0.625467	−	2.33428i	−0.0430589	−	0.160698i	0.941049	−	0.338271i	$-0.109842\pi$
$211$	−0.625467	−	2.33428i	−0.0430589	−	0.160698i	−0.984108	+	0.177573i	$0.943175\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$			17.4185i			1.18793i
$216$		0			0
$217$			0.0657256i			0.00446175i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.81402	−	21.6982i	−0.391093	−	1.45958i
$222$		0			0
$223$	0.0284597	−	0.0164312i	0.00190581	−	0.00110032i	−0.499047	−	0.866575i	$-0.666316\pi$
$223$	0.0284597	−	0.0164312i	0.00190581	−	0.00110032i	0.500953	+	0.865475i	$0.332983\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.79797	−	17.9063i	0.318453	−	1.18848i	−0.602279	−	0.798285i	$-0.705741\pi$
$227$	4.79797	−	17.9063i	0.318453	−	1.18848i	0.920732	−	0.390196i	$-0.127593\pi$
$228$		0			0
$229$	7.06225	+	26.3567i	0.466687	+	1.74170i	0.651236	+	0.758875i	$0.274251\pi$
$229$	7.06225	+	26.3567i	0.466687	+	1.74170i	−0.184549	+	0.982823i	$0.559082\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−7.42838			−0.486649			−0.243325	−	0.969945i	$-0.578238\pi$
$233$	−7.42838			−0.486649			−0.243325	+	0.969945i	$0.578238\pi$
$234$		0			0
$235$	0.378968	+	0.378968i	0.0247211	+	0.0247211i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−2.67225	+	4.62848i	−0.172854	+	0.299391i	−0.939416	−	0.342778i	$-0.888632\pi$
$239$	−2.67225	+	4.62848i	−0.172854	+	0.299391i	0.766563	+	0.642169i	$0.221965\pi$
$240$		0			0
$241$	−10.9314	−	18.9337i	−0.704151	−	1.21963i	−0.966997	−	0.254788i	$-0.917994\pi$
$241$	−10.9314	−	18.9337i	−0.704151	−	1.21963i	0.262845	−	0.964838i	$-0.415339\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.08211	−	18.9667i	0.324684	−	1.21174i
$246$		0			0
$247$	−6.38925	+	11.0665i	−0.406538	+	0.704145i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−18.4081	+	18.4081i	−1.16191	+	1.16191i	−0.177854	+	0.984057i	$0.556915\pi$
$251$	−18.4081	+	18.4081i	−1.16191	+	1.16191i	−0.984057	+	0.177854i	$0.943085\pi$
$252$		0			0
$253$	−13.6672	−	13.6672i	−0.859251	−	0.859251i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	6.96658	+	4.02216i	0.434563	+	0.250895i	0.701289	−	0.712877i	$-0.252608\pi$
$257$	6.96658	+	4.02216i	0.434563	+	0.250895i	−0.266726	+	0.963773i	$0.585942\pi$
$258$		0			0
$259$	0.00892960	+	0.00239268i	0.000554858	+	0.000148674i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−3.65553	+	2.11052i	−0.225409	+	0.130140i	−0.608452	−	0.793590i	$-0.708209\pi$
$263$	−3.65553	+	2.11052i	−0.225409	+	0.130140i	0.383043	+	0.923730i	$0.374876\pi$
$264$		0			0
$265$	−2.57860	−	1.48876i	−0.158402	−	0.0914535i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−13.7834	+	13.7834i	−0.840386	+	0.840386i	−0.988909	−	0.148523i	$-0.952548\pi$
$269$	−13.7834	+	13.7834i	−0.840386	+	0.840386i	0.148523	+	0.988909i	$0.452548\pi$
$270$		0			0
$271$			14.3202i			0.869889i	0.900457	+	0.434945i	$0.143232\pi$
$271$			14.3202i			0.869889i	−0.900457	+	0.434945i	$0.856768\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.61014	−	2.30708i	0.519211	−	0.139122i
$276$		0			0
$277$	−6.39501	−	1.71354i	−0.384239	−	0.102956i	0.0615286	−	0.998105i	$-0.480402\pi$
$277$	−6.39501	−	1.71354i	−0.384239	−	0.102956i	−0.445767	+	0.895149i	$0.647069\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.84037	+	3.18761i	0.109787	+	0.190157i	0.915684	−	0.401899i	$-0.131650\pi$
$281$	1.84037	+	3.18761i	0.109787	+	0.190157i	−0.805897	+	0.592056i	$0.798316\pi$
$282$		0			0
$283$	−4.19445	+	1.12390i	−0.249334	+	0.0668089i	−0.381321	−	0.924442i	$-0.624531\pi$
$283$	−4.19445	+	1.12390i	−0.249334	+	0.0668089i	0.131987	+	0.991251i	$0.457864\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.0449706			−0.00265453
$288$		0			0
$289$	5.58832			0.328725
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−14.6770	+	3.93269i	−0.857439	+	0.229750i	−0.660649	−	0.750695i	$-0.729719\pi$
$293$	−14.6770	+	3.93269i	−0.857439	+	0.229750i	−0.196791	+	0.980446i	$0.563052\pi$
$294$		0			0
$295$	−13.1963	−	22.8567i	−0.768320	−	1.33077i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−39.9558	−	10.7061i	−2.31071	−	0.619152i
$300$		0			0
$301$	−0.0509393	+	0.0136491i	−0.00293609	+	0.000786723i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			28.6285i			1.63926i
$306$		0			0
$307$	−23.4294	+	23.4294i	−1.33718	+	1.33718i	−0.438408	+	0.898776i	$0.644457\pi$
$307$	−23.4294	+	23.4294i	−1.33718	+	1.33718i	−0.898776	+	0.438408i	$0.855543\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−25.9086	−	14.9583i	−1.46914	−	0.848210i	−0.469741	−	0.882804i	$-0.655653\pi$
$311$	−25.9086	−	14.9583i	−1.46914	−	0.848210i	−0.999401	+	0.0345940i	$0.988986\pi$
$312$		0			0
$313$	−13.0513	+	7.53519i	−0.737705	+	0.425914i	−0.821234	−	0.570591i	$-0.806714\pi$
$313$	−13.0513	+	7.53519i	−0.737705	+	0.425914i	0.0835293	+	0.996505i	$0.473381\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−20.1652	−	5.40325i	−1.13259	−	0.303477i	−0.356623	−	0.934248i	$-0.616072\pi$
$317$	−20.1652	−	5.40325i	−1.13259	−	0.303477i	−0.775969	+	0.630772i	$0.782739\pi$
$318$		0			0
$319$	−9.12868	−	5.27045i	−0.511108	−	0.295088i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	4.59023	+	4.59023i	0.255407	+	0.255407i
$324$		0			0
$325$	13.4894	−	13.4894i	0.748257	−	0.748257i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.000811309		0.00140523i	−4.47289e−5		7.74727e-5i
$330$		0			0
$331$	−4.94242	+	18.4453i	−0.271660	+	1.01385i	0.686387	+	0.727236i	$0.259196\pi$
$331$	−4.94242	+	18.4453i	−0.271660	+	1.01385i	−0.958047	+	0.286612i	$0.907471\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−11.2846	−	19.5456i	−0.616546	−	1.06789i
$336$		0			0
$337$	−9.91944	+	17.1810i	−0.540346	+	0.935907i	0.458538	+	0.888675i	$0.348373\pi$
$337$	−9.91944	+	17.1810i	−0.540346	+	0.935907i	−0.998884	+	0.0472324i	$0.984960\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	17.0032	+	17.0032i	0.920774	+	0.920774i
$342$		0			0
$343$	0.118899			0.00641996
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.60618	+	20.9225i	0.300955	+	1.12318i	0.936372	+	0.351011i	$0.114162\pi$
$347$	5.60618	+	20.9225i	0.300955	+	1.12318i	−0.635416	+	0.772170i	$0.719171\pi$
$348$		0			0
$349$	−0.426410	+	1.59139i	−0.0228252	+	0.0851849i	−0.976399	−	0.215975i	$-0.930707\pi$
$349$	−0.426410	+	1.59139i	−0.0228252	+	0.0851849i	0.953574	+	0.301160i	$0.0973737\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	3.91868	−	2.26245i	0.208570	−	0.120418i	−0.392076	−	0.919933i	$-0.628243\pi$
$353$	3.91868	−	2.26245i	0.208570	−	0.120418i	0.600647	+	0.799514i	$0.294910\pi$
$354$		0			0
$355$	0.742431	+	2.77079i	0.0394042	+	0.147058i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			11.0661i			0.584046i	0.956411	+	0.292023i	$0.0943284\pi$
$359$			11.0661i			0.584046i	−0.956411	+	0.292023i	$0.905672\pi$
$360$		0			0
$361$			15.3073i			0.805645i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	5.30659	+	19.8045i	0.277760	+	1.03661i
$366$		0			0
$367$	4.77772	−	2.75842i	0.249395	−	0.143988i	−0.370092	−	0.928995i	$-0.620674\pi$
$367$	4.77772	−	2.75842i	0.249395	−	0.143988i	0.619487	+	0.785007i	$0.287341\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.00233318	−	0.00870755i	0.000121133	−	0.000452074i
$372$		0			0
$373$	2.18851	+	8.16763i	0.113317	+	0.422904i	0.999155	−	0.0410893i	$-0.0130828\pi$
$373$	2.18851	+	8.16763i	0.113317	+	0.422904i	−0.885839	+	0.463993i	$0.846416\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−22.5589			−1.16184
$378$		0			0
$379$	−20.4820	−	20.4820i	−1.05209	−	1.05209i	−0.998566	−	0.0535254i	$-0.982954\pi$
$379$	−20.4820	−	20.4820i	−1.05209	−	1.05209i	−0.0535254	−	0.998566i	$-0.517046\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.14427	−	3.71398i	0.109567	−	0.189776i	−0.806028	−	0.591878i	$-0.798387\pi$
$383$	2.14427	−	3.71398i	0.109567	−	0.189776i	0.915595	+	0.402102i	$0.131720\pi$
$384$		0			0
$385$	0.0370120	+	0.0641066i	0.00188630	+	0.00326718i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4.19823	−	15.6680i	0.212859	−	0.794400i	−0.774051	−	0.633124i	$-0.781772\pi$
$389$	4.19823	−	15.6680i	0.212859	−	0.794400i	0.986909	−	0.161276i	$-0.0515609\pi$
$390$		0			0
$391$	−10.5069	+	18.1985i	−0.531358	+	0.920339i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	9.98779	−	9.98779i	0.502540	−	0.502540i
$396$		0			0
$397$	−2.22738	−	2.22738i	−0.111789	−	0.111789i	0.649000	−	0.760789i	$-0.275188\pi$
$397$	−2.22738	−	2.22738i	−0.111789	−	0.111789i	−0.760789	+	0.649000i	$0.775188\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−7.43343	−	4.29169i	−0.371208	−	0.214317i	0.302778	−	0.953061i	$-0.402086\pi$
$401$	−7.43343	−	4.29169i	−0.371208	−	0.214317i	−0.673986	+	0.738744i	$0.735419\pi$
$402$		0			0
$403$	49.7085	+	13.3193i	2.47616	+	0.663484i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.92907	−	1.69110i	0.145189	−	0.0838246i
$408$		0			0
$409$	−32.0886	−	18.5263i	−1.58668	−	0.916068i	−0.993850	−	0.110739i	$-0.964678\pi$
$409$	−32.0886	−	18.5263i	−1.58668	−	0.916068i	−0.592828	−	0.805329i	$-0.701988\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.0565024	−	0.0565024i	0.00278030	−	0.00278030i
$414$		0			0
$415$		−	36.3099i		−	1.78238i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−19.9702	+	5.35101i	−0.975609	+	0.261414i	−0.711195	−	0.702995i	$-0.751845\pi$
$419$	−19.9702	+	5.35101i	−0.975609	+	0.261414i	−0.264415	+	0.964409i	$0.585179\pi$
$420$		0			0
$421$	−9.35966	−	2.50791i	−0.456162	−	0.122228i	0.0234192	−	0.999726i	$-0.492545\pi$
$421$	−9.35966	−	2.50791i	−0.456162	−	0.122228i	−0.479581	+	0.877497i	$0.659211\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.84559	−	8.39281i	−0.235046	−	0.407111i
$426$		0			0
$427$	−0.0837222	+	0.0224333i	−0.00405160	+	0.00108562i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−25.3669			−1.22188			−0.610941	−	0.791676i	$-0.709209\pi$
$431$	−25.3669			−1.22188			−0.610941	+	0.791676i	$0.709209\pi$
$432$		0			0
$433$	−10.5243			−0.505764			−0.252882	−	0.967497i	$-0.581378\pi$
$433$	−10.5243			−0.505764			−0.252882	+	0.967497i	$0.581378\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	11.5465	−	3.09387i	0.552343	−	0.148000i
$438$		0			0
$439$	−1.65348	−	2.86391i	−0.0789163	−	0.136687i	0.823866	−	0.566784i	$-0.191813\pi$
$439$	−1.65348	−	2.86391i	−0.0789163	−	0.136687i	−0.902783	+	0.430097i	$0.858479\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−5.42439	−	1.45346i	−0.257721	−	0.0690560i	0.127645	−	0.991820i	$-0.459258\pi$
$443$	−5.42439	−	1.45346i	−0.257721	−	0.0690560i	−0.385366	+	0.922764i	$0.625925\pi$
$444$		0			0
$445$	49.2527	−	13.1972i	2.33480	−	0.625608i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			3.76456i			0.177661i	0.996047	+	0.0888303i	$0.0283129\pi$
$449$			3.76456i			0.177661i	−0.996047	+	0.0888303i	$0.971687\pi$
$450$		0			0
$451$	−11.6339	+	11.6339i	−0.547818	+	0.547818i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.137197	+	0.0792106i	0.00643189	+	0.00371345i
$456$		0			0
$457$	18.4633	−	10.6598i	0.863675	−	0.498643i	−0.00156649	−	0.999999i	$-0.500499\pi$
$457$	18.4633	−	10.6598i	0.863675	−	0.498643i	0.865241	+	0.501356i	$0.167165\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	37.4962	+	10.0471i	1.74637	+	0.467938i	0.983845	−	0.179021i	$-0.0572929\pi$
$461$	37.4962	+	10.0471i	1.74637	+	0.467938i	0.762525	+	0.646959i	$0.223960\pi$
$462$		0			0
$463$	−7.29597	−	4.21233i	−0.339073	−	0.195764i	0.320789	−	0.947151i	$-0.396052\pi$
$463$	−7.29597	−	4.21233i	−0.339073	−	0.195764i	−0.659862	+	0.751387i	$0.729385\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.4539	+	19.4539i	0.900219	+	0.900219i	0.995455	−	0.0952358i	$-0.0303605\pi$
$467$	19.4539	+	19.4539i	0.900219	+	0.900219i	−0.0952358	+	0.995455i	$0.530361\pi$
$468$		0			0
$469$	0.0483172	−	0.0483172i	0.00223108	−	0.00223108i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−9.64695	+	16.7090i	−0.443567	+	0.768281i
$474$		0			0
$475$	−1.42683	+	5.32501i	−0.0654676	+	0.244328i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	10.4276	+	18.0611i	0.476450	+	0.825235i	0.999636	−	0.0269835i	$-0.00859016\pi$
$479$	10.4276	+	18.0611i	0.476450	+	0.825235i	−0.523186	+	0.852218i	$0.675257\pi$
$480$		0			0
$481$	3.61918	−	6.26860i	0.165020	−	0.285824i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.52570	+	6.52570i	0.296317	+	0.296317i
$486$		0			0
$487$	−34.0126			−1.54126			−0.770629	−	0.637284i	$-0.780058\pi$
$487$	−34.0126			−1.54126			−0.770629	+	0.637284i	$0.780058\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	0.378725	+	1.41342i	0.0170916	+	0.0637868i	0.973945	−	0.226785i	$-0.0728213\pi$
$491$	0.378725	+	1.41342i	0.0170916	+	0.0637868i	−0.956853	+	0.290571i	$0.906155\pi$
$492$		0			0
$493$	−2.96609	+	11.0696i	−0.133586	+	0.498550i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−0.00752124	+	0.00434239i	−0.000337374	+	0.000194783i
$498$		0			0
$499$	−9.43390	−	35.2078i	−0.422319	−	1.57612i	−0.769708	−	0.638396i	$-0.779598\pi$
$499$	−9.43390	−	35.2078i	−0.422319	−	1.57612i	0.347389	−	0.937721i	$-0.387068\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			10.8529i			0.483908i	0.970288	+	0.241954i	$0.0777882\pi$
$503$			10.8529i			0.483908i	−0.970288	+	0.241954i	$0.922212\pi$
$504$		0			0
$505$			7.74741i			0.344755i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−1.05732	−	3.94598i	−0.0468650	−	0.174903i	0.938526	−	0.345207i	$-0.112191\pi$
$509$	−1.05732	−	3.94598i	−0.0468650	−	0.174903i	−0.985391	+	0.170305i	$0.945525\pi$
$510$		0			0
$511$	−0.0537587	+	0.0310376i	−0.00237814	+	0.00137302i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−8.02259	+	29.9407i	−0.353517	+	1.31934i
$516$		0			0
$517$	0.153647	+	0.573417i	0.00675737	+	0.0252189i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	13.4286			0.588318			0.294159	−	0.955757i	$-0.404961\pi$
$521$	13.4286			0.588318			0.294159	+	0.955757i	$0.404961\pi$
$522$		0			0
$523$	−23.5806	−	23.5806i	−1.03111	−	1.03111i	−0.999500	−	0.0316083i	$-0.989937\pi$
$523$	−23.5806	−	23.5806i	−1.03111	−	1.03111i	−0.0316083	−	0.999500i	$-0.510063\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	13.0715	−	22.6405i	0.569404	−	0.986237i
$528$		0			0
$529$	7.84782	+	13.5928i	0.341210	+	0.590992i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−9.11332	+	34.0114i	−0.394742	+	1.47320i
$534$		0			0
$535$	3.83937	−	6.64999i	0.165991	−	0.287504i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	15.3795	−	15.3795i	0.662443	−	0.662443i
$540$		0			0
$541$	−31.9545	−	31.9545i	−1.37383	−	1.37383i	−0.854684	−	0.519148i	$-0.826249\pi$
$541$	−31.9545	−	31.9545i	−1.37383	−	1.37383i	−0.519148	−	0.854684i	$-0.673751\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	20.5582	+	11.8693i	0.880618	+	0.508425i
$546$		0			0
$547$	10.3053	+	2.76131i	0.440625	+	0.118065i	0.472309	−	0.881433i	$-0.343421\pi$
$547$	10.3053	+	2.76131i	0.440625	+	0.118065i	−0.0316846	+	0.999498i	$0.510087\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	5.64571	−	3.25955i	0.240515	−	0.138862i
$552$		0			0
$553$	0.0370351	+	0.0213822i	0.00157489	+	0.000909265i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	11.6850	−	11.6850i	0.495109	−	0.495109i	−0.414802	−	0.909912i	$-0.636149\pi$
$557$	11.6850	−	11.6850i	0.495109	−	0.495109i	0.909912	+	0.414802i	$0.136149\pi$
$558$		0			0
$559$			41.2915i			1.74645i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	8.64631	−	2.31677i	0.364398	−	0.0976403i	−0.0719737	−	0.997407i	$-0.522930\pi$
$563$	8.64631	−	2.31677i	0.364398	−	0.0976403i	0.436372	+	0.899766i	$0.356263\pi$
$564$		0			0
$565$	−36.8764	−	9.88100i	−1.55140	−	0.415697i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	6.28570	+	10.8872i	0.263510	+	0.456413i	0.967172	−	0.254122i	$-0.0817864\pi$
$569$	6.28570	+	10.8872i	0.263510	+	0.456413i	−0.703662	+	0.710535i	$0.748453\pi$
$570$		0			0
$571$	−13.9023	+	3.72510i	−0.581791	+	0.155890i	−0.537699	−	0.843137i	$-0.680706\pi$
$571$	−13.9023	+	3.72510i	−0.581791	+	0.155890i	−0.0440924	+	0.999027i	$0.514040\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−17.8457			−0.744216
$576$		0			0
$577$	17.0561			0.710056			0.355028	−	0.934856i	$-0.384471\pi$
$577$	17.0561			0.710056			0.355028	+	0.934856i	$0.384471\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.106186	−	0.0284525i	0.00440534	−	0.00118041i
$582$		0			0
$583$	−1.64905	−	2.85623i	−0.0682965	−	0.118293i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	17.2954	+	4.63428i	0.713856	+	0.191277i	0.597428	−	0.801922i	$-0.296189\pi$
$587$	17.2954	+	4.63428i	0.713856	+	0.191277i	0.116427	+	0.993199i	$0.462856\pi$
$588$		0			0
$589$	−14.3648	+	3.84904i	−0.591891	+	0.158597i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	25.5455i		−	1.04903i	−0.851402	−	0.524514i	$-0.824247\pi$
$593$		−	25.5455i		−	1.04903i	0.851402	−	0.524514i	$-0.175753\pi$
$594$		0			0
$595$	0.0569073	−	0.0569073i	0.00233297	−	0.00233297i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	1.66118	+	0.959083i	0.0678740	+	0.0391871i	0.533553	−	0.845767i	$-0.320857\pi$
$599$	1.66118	+	0.959083i	0.0678740	+	0.0391871i	−0.465679	+	0.884954i	$0.654190\pi$
$600$		0			0
$601$	−7.76786	+	4.48478i	−0.316858	+	0.182938i	−0.649991	−	0.759942i	$-0.725227\pi$
$601$	−7.76786	+	4.48478i	−0.316858	+	0.182938i	0.333133	+	0.942880i	$0.391894\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−3.64579	−	0.976888i	−0.148223	−	0.0397161i
$606$		0			0
$607$	20.1239	+	11.6185i	0.816802	+	0.471581i	0.849312	−	0.527890i	$-0.177017\pi$
$607$	20.1239	+	11.6185i	0.816802	+	0.471581i	−0.0325103	+	0.999471i	$0.510350\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.898366	+	0.898366i	0.0363440	+	0.0363440i
$612$		0			0
$613$	18.6158	−	18.6158i	0.751886	−	0.751886i	−0.222945	−	0.974831i	$-0.571567\pi$
$613$	18.6158	−	18.6158i	0.751886	−	0.751886i	0.974831	+	0.222945i	$0.0715670\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	18.3062	−	31.7073i	0.736981	−	1.27649i	−0.216868	−	0.976201i	$-0.569584\pi$
$617$	18.3062	−	31.7073i	0.736981	−	1.27649i	0.953849	−	0.300288i	$-0.0970827\pi$
$618$		0			0
$619$	−6.87138	+	25.6443i	−0.276184	+	1.03073i	0.678860	+	0.734268i	$0.262474\pi$
$619$	−6.87138	+	25.6443i	−0.276184	+	1.03073i	−0.955044	+	0.296465i	$0.904192\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	0.0771889	+	0.133695i	0.00309251	+	0.00535638i
$624$		0			0
$625$	−15.5570	+	26.9455i	−0.622280	+	1.07782i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.60013	−	2.60013i	−0.103674	−	0.103674i
$630$		0			0
$631$	28.2467			1.12449			0.562243	−	0.826972i	$-0.309939\pi$
$631$	28.2467			1.12449			0.562243	+	0.826972i	$0.309939\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−5.09076	−	18.9990i	−0.202021	−	0.753952i
$636$		0			0
$637$	12.0475	−	44.9617i	0.477338	−	1.78145i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−14.4080	+	8.31845i	−0.569081	+	0.328559i	−0.756782	−	0.653667i	$-0.773230\pi$
$641$	−14.4080	+	8.31845i	−0.569081	+	0.328559i	0.187701	+	0.982226i	$0.439896\pi$
$642$		0			0
$643$	1.52303	+	5.68404i	0.0600626	+	0.224157i	0.989433	−	0.144993i	$-0.0463158\pi$
$643$	1.52303	+	5.68404i	0.0600626	+	0.224157i	−0.929370	+	0.369149i	$0.879649\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	37.4518i		−	1.47238i	−0.676773	−	0.736192i	$-0.736622\pi$
$647$		−	37.4518i		−	1.47238i	0.676773	−	0.736192i	$-0.263378\pi$
$648$		0			0
$649$		−	29.2343i		−	1.14755i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	5.70340	+	21.2854i	0.223191	+	0.832962i	0.983121	+	0.182956i	$0.0585667\pi$
$653$	5.70340	+	21.2854i	0.223191	+	0.832962i	−0.759930	+	0.650005i	$0.774767\pi$
$654$		0			0
$655$	−20.2315	+	11.6807i	−0.790510	+	0.456401i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−6.39350	+	23.8609i	−0.249055	+	0.929487i	0.722246	+	0.691636i	$0.243110\pi$
$659$	−6.39350	+	23.8609i	−0.249055	+	0.929487i	−0.971302	+	0.237851i	$0.923557\pi$
$660$		0			0
$661$	−0.958674	−	3.57782i	−0.0372881	−	0.139161i	0.944772	−	0.327727i	$-0.106283\pi$
$661$	−0.958674	−	3.57782i	−0.0372881	−	0.139161i	−0.982060	+	0.188566i	$0.939616\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−0.0457807			−0.00177530
$666$		0			0
$667$	14.9221	+	14.9221i	0.577785	+	0.577785i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−15.8554	+	27.4624i	−0.612091	+	1.06017i
$672$		0			0
$673$	17.3782	+	30.0999i	0.669880	+	1.16027i	0.977937	+	0.208898i	$0.0669877\pi$
$673$	17.3782	+	30.0999i	0.669880	+	1.16027i	−0.308058	+	0.951368i	$0.599679\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.56283	−	24.4928i	0.252230	−	0.941335i	−0.717381	−	0.696681i	$-0.754659\pi$
$677$	6.56283	−	24.4928i	0.252230	−	0.941335i	0.969611	−	0.244654i	$-0.0786742\pi$
$678$		0			0
$679$	−0.0139705	+	0.0241976i	−0.000536137	+	0.000928617i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.88928	−	1.88928i	0.0722912	−	0.0722912i	−0.670037	−	0.742328i	$-0.733722\pi$
$683$	1.88928	−	1.88928i	0.0722912	−	0.0722912i	0.742328	+	0.670037i	$0.233722\pi$
$684$		0			0
$685$	10.7845	+	10.7845i	0.412056	+	0.412056i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−6.11273	−	3.52918i	−0.232876	−	0.134451i
$690$		0			0
$691$	−19.4017	−	5.19868i	−0.738077	−	0.197767i	−0.129854	−	0.991533i	$-0.541451\pi$
$691$	−19.4017	−	5.19868i	−0.738077	−	0.197767i	−0.608223	+	0.793766i	$0.708117\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	34.1985	−	19.7445i	1.29722	−	0.748951i
$696$		0			0
$697$	15.4910	+	8.94375i	0.586765	+	0.338769i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−10.9010	+	10.9010i	−0.411725	+	0.411725i	−0.882339	−	0.470614i	$-0.844032\pi$
$701$	−10.9010	+	10.9010i	−0.411725	+	0.411725i	0.470614	+	0.882339i	$0.344032\pi$
$702$		0			0
$703$			2.09175i			0.0788918i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.0226568	+	0.00607088i	−0.000852098	+	0.000228319i
$708$		0			0
$709$	15.4807	+	4.14803i	0.581389	+	0.155783i	0.537515	−	0.843254i	$-0.319363\pi$
$709$	15.4807	+	4.14803i	0.581389	+	0.155783i	0.0438741	+	0.999037i	$0.486030\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−24.0703	−	41.6911i	−0.901441	−	1.56134i
$714$		0			0
$715$	55.9845	−	15.0010i	2.09370	−	0.561006i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−21.7763			−0.812119			−0.406060	−	0.913847i	$-0.633097\pi$
$719$	−21.7763			−0.812119			−0.406060	+	0.913847i	$0.633097\pi$
$720$		0			0
$721$	−0.0938463			−0.00349502
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−9.40068	+	2.51890i	−0.349132	+	0.0935497i
$726$		0			0
$727$	2.62325	+	4.54360i	0.0972908	+	0.168513i	0.910562	−	0.413372i	$-0.135649\pi$
$727$	2.62325	+	4.54360i	0.0972908	+	0.168513i	−0.813272	+	0.581884i	$0.802316\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	20.2616	+	5.42908i	0.749403	+	0.200802i
$732$		0			0
$733$	12.7415	−	3.41408i	0.470618	−	0.126102i	−0.0157124	−	0.999877i	$-0.505002\pi$
$733$	12.7415	−	3.41408i	0.470618	−	0.126102i	0.486331	+	0.873775i	$0.338335\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	24.9993i		−	0.920860i
$738$		0			0
$739$	23.2424	−	23.2424i	0.854984	−	0.854984i	−0.135758	−	0.990742i	$-0.543347\pi$
$739$	23.2424	−	23.2424i	0.854984	−	0.854984i	0.990742	+	0.135758i	$0.0433470\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	24.5336	+	14.1645i	0.900049	+	0.519643i	0.877216	−	0.480096i	$-0.159398\pi$
$743$	24.5336	+	14.1645i	0.900049	+	0.519643i	0.0228329	+	0.999739i	$0.492731\pi$
$744$		0			0
$745$	−23.0683	+	13.3185i	−0.845159	+	0.487953i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	0.0224560	+	0.00601707i	0.000820525	+	0.000219859i
$750$		0			0
$751$	−22.5527	−	13.0208i	−0.822960	−	0.475136i	0.0284763	−	0.999594i	$-0.490934\pi$
$751$	−22.5527	−	13.0208i	−0.822960	−	0.475136i	−0.851436	+	0.524458i	$0.824268\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	8.99509	+	8.99509i	0.327365	+	0.327365i
$756$		0			0
$757$	4.87465	−	4.87465i	0.177172	−	0.177172i	−0.612950	−	0.790122i	$-0.710017\pi$
$757$	4.87465	−	4.87465i	0.177172	−	0.177172i	0.790122	+	0.612950i	$0.210017\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	3.18964	−	5.52462i	0.115624	−	0.200267i	−0.802405	−	0.596780i	$-0.796446\pi$
$761$	3.18964	−	5.52462i	0.115624	−	0.200267i	0.918029	+	0.396513i	$0.129780\pi$
$762$		0			0
$763$	−0.0186016	+	0.0694221i	−0.000673423	+	0.00251325i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−31.2827	−	54.1832i	−1.12955	−	1.95644i
$768$		0			0
$769$	−9.57641	+	16.5868i	−0.345334	+	0.598136i	−0.985414	−	0.170172i	$-0.945568\pi$
$769$	−9.57641	+	16.5868i	−0.345334	+	0.598136i	0.640080	+	0.768308i	$0.278901\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−26.0627	−	26.0627i	−0.937411	−	0.937411i	0.0607427	−	0.998153i	$-0.480653\pi$
$773$	−26.0627	−	26.0627i	−0.937411	−	0.937411i	−0.998153	+	0.0607427i	$0.980653\pi$
$774$		0			0
$775$	22.2015			0.797503
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.63358	−	9.82864i	−0.0943577	−	0.352148i
$780$		0			0
$781$	−0.822367	+	3.06912i	−0.0294266	+	0.109822i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−48.0583	+	27.7464i	−1.71527	+	0.990313i
$786$		0			0
$787$	2.96285	+	11.0575i	0.105614	+	0.394158i	0.998414	−	0.0562956i	$-0.0179289\pi$
$787$	2.96285	+	11.0575i	0.105614	+	0.394158i	−0.892800	+	0.450454i	$0.851262\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$		−	0.115586i		−	0.00410975i
$792$		0			0
$793$			67.8655i			2.40997i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1.12000	+	4.17990i	0.0396725	+	0.148060i	0.982921	−	0.184028i	$-0.0589137\pi$
$797$	1.12000	+	4.17990i	0.0396725	+	0.148060i	−0.943249	+	0.332088i	$0.892247\pi$
$798$		0			0
$799$	0.558944	−	0.322706i	0.0197740	−	0.0114165i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.87794	+	21.9368i	−0.207428	+	0.774132i
$804$		0			0
$805$	−0.0383562	−	0.143147i	−0.00135188	−	0.00504528i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−22.7884			−0.801198			−0.400599	−	0.916253i	$-0.631198\pi$
$809$	−22.7884			−0.801198			−0.400599	+	0.916253i	$0.631198\pi$
$810$		0			0
$811$	14.9053	+	14.9053i	0.523396	+	0.523396i	0.918595	−	0.395200i	$-0.129325\pi$
$811$	14.9053	+	14.9053i	0.523396	+	0.523396i	−0.395200	+	0.918595i	$0.629325\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	12.5315	−	21.7052i	0.438959	−	0.760299i
$816$		0			0
$817$	−5.96623	−	10.3338i	−0.208732	−	0.361535i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−11.7591	+	43.8854i	−0.410394	+	1.53161i	0.383492	+	0.923544i	$0.374721\pi$
$821$	−11.7591	+	43.8854i	−0.410394	+	1.53161i	−0.793886	+	0.608067i	$0.791945\pi$
$822$		0			0
$823$	22.8842	−	39.6366i	0.797694	−	1.38165i	−0.123421	−	0.992354i	$-0.539386\pi$
$823$	22.8842	−	39.6366i	0.797694	−	1.38165i	0.921115	−	0.389292i	$-0.127280\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−22.0262	+	22.0262i	−0.765925	+	0.765925i	−0.977386	−	0.211461i	$-0.932178\pi$
$827$	−22.0262	+	22.0262i	−0.765925	+	0.765925i	0.211461	+	0.977386i	$0.432178\pi$
$828$		0			0
$829$	28.3392	+	28.3392i	0.984261	+	0.984261i	0.999878	−	0.0156173i	$-0.00497134\pi$
$829$	28.3392	+	28.3392i	0.984261	+	0.984261i	−0.0156173	+	0.999878i	$0.504971\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−20.4785	−	11.8233i	−0.709539	−	0.409653i
$834$		0			0
$835$	32.2174	+	8.63262i	1.11493	+	0.298744i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	15.8724	−	9.16393i	0.547976	−	0.316374i	−0.200329	−	0.979729i	$-0.564201\pi$
$839$	15.8724	−	9.16393i	0.547976	−	0.316374i	0.748305	+	0.663355i	$0.230868\pi$
$840$		0			0
$841$	−15.1479	−	8.74565i	−0.522342	−	0.301574i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	61.9244	−	61.9244i	2.13026	−	2.13026i
$846$		0			0
$847$		−	0.0114274i		−	0.000392650i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−6.54048	+	1.75252i	−0.224205	+	0.0600755i
$852$		0			0
$853$	−23.7728	−	6.36992i	−0.813967	−	0.218102i	−0.172260	−	0.985052i	$-0.555107\pi$
$853$	−23.7728	−	6.36992i	−0.813967	−	0.218102i	−0.641707	+	0.766950i	$0.721773\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	0.838395	+	1.45214i	0.0286390	+	0.0496043i	0.879990	−	0.474993i	$-0.157549\pi$
$857$	0.838395	+	1.45214i	0.0286390	+	0.0496043i	−0.851351	+	0.524597i	$0.824216\pi$
$858$		0			0
$859$	13.4806	−	3.61213i	0.459954	−	0.123244i	−0.0213994	−	0.999771i	$-0.506812\pi$
$859$	13.4806	−	3.61213i	0.459954	−	0.123244i	0.481353	+	0.876527i	$0.340145\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	31.6409			1.07707			0.538535	−	0.842603i	$-0.318978\pi$
$863$	31.6409			1.07707			0.538535	+	0.842603i	$0.318978\pi$
$864$		0			0
$865$	1.36046			0.0462570
$866$		0			0
$867$		0			0
$868$		0			0
$869$	15.1126	−	4.04940i	0.512658	−	0.137366i
$870$		0			0
$871$	−26.7509	−	46.3340i	−0.906421	−	1.56997i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.0490426	−	0.0131409i	−0.00165794	−	0.000444244i
$876$		0			0
$877$	29.4369	−	7.88760i	0.994014	−	0.266345i	0.275078	−	0.961422i	$-0.411296\pi$
$877$	29.4369	−	7.88760i	0.994014	−	0.266345i	0.718936	+	0.695077i	$0.244630\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			10.2116i			0.344037i	0.985094	+	0.172019i	$0.0550290\pi$
$881$			10.2116i			0.344037i	−0.985094	+	0.172019i	$0.944971\pi$
$882$		0			0
$883$	−7.98299	+	7.98299i	−0.268649	+	0.268649i	−0.828556	−	0.559907i	$-0.810837\pi$
$883$	−7.98299	+	7.98299i	−0.268649	+	0.268649i	0.559907	+	0.828556i	$0.310837\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	9.34850	+	5.39736i	0.313892	+	0.181226i	0.648667	−	0.761073i	$-0.275327\pi$
$887$	9.34850	+	5.39736i	0.313892	+	0.181226i	−0.334775	+	0.942298i	$0.608660\pi$
$888$		0			0
$889$	0.0515723	−	0.0297753i	0.00172968	−	0.000998630i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−0.354635	−	0.0950241i	−0.0118674	−	0.00317986i
$894$		0			0
$895$	−23.7626	−	13.7193i	−0.794295	−	0.458586i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−18.5643	−	18.5643i	−0.619155	−	0.619155i
$900$		0			0
$901$	−2.53547	+	2.53547i	−0.0844688	+	0.0844688i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−4.35887	+	7.54978i	−0.144894	+	0.250963i
$906$		0			0
$907$	2.05717	−	7.67746i	0.0683072	−	0.254926i	−0.923325	−	0.384019i	$-0.874540\pi$
$907$	2.05717	−	7.67746i	0.0683072	−	0.254926i	0.991633	+	0.129093i	$0.0412065\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	17.5142	+	30.3354i	0.580270	+	1.00506i	0.995447	+	0.0953171i	$0.0303865\pi$
$911$	17.5142	+	30.3354i	0.580270	+	1.00506i	−0.415176	+	0.909741i	$0.636280\pi$
$912$		0			0
$913$	20.1096	−	34.8309i	0.665532	−	1.15274i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.0500128	−	0.0500128i	−0.00165157	−	0.00165157i
$918$		0			0
$919$	−25.9311			−0.855387			−0.427694	−	0.903924i	$-0.640674\pi$
$919$	−25.9311			−0.855387			−0.427694	+	0.903924i	$0.640674\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.75998	+	6.56833i	0.0579304	+	0.216199i
$924$		0			0
$925$	0.808226	−	3.01634i	0.0265743	−	0.0991767i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	23.3443	−	13.4779i	0.765903	−	0.442194i	−0.0655082	−	0.997852i	$-0.520867\pi$
$929$	23.3443	−	13.4779i	0.765903	−	0.442194i	0.831411	+	0.555658i	$0.187534\pi$
$930$		0			0
$931$	3.48148	+	12.9931i	0.114101	+	0.425831i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	29.4438i		−	0.962914i
$936$		0			0
$937$		−	5.72005i		−	0.186866i	−0.995626	−	0.0934330i	$-0.970216\pi$
$937$		−	5.72005i		−	0.186866i	0.995626	−	0.0934330i	$-0.0297841\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−6.14201	−	22.9223i	−0.200224	−	0.747245i	−0.990853	−	0.134949i	$-0.956913\pi$
$941$	−6.14201	−	22.9223i	−0.200224	−	0.747245i	0.790629	−	0.612296i	$-0.209754\pi$
$942$		0			0
$943$	28.5257	−	16.4693i	0.928925	−	0.536315i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	14.0030	−	52.2601i	0.455038	−	1.69822i	−0.232940	−	0.972491i	$-0.574834\pi$
$947$	14.0030	−	52.2601i	0.455038	−	1.69822i	0.687977	−	0.725732i	$-0.258499\pi$
$948$		0			0
$949$	12.5796	+	46.9477i	0.408351	+	1.52399i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−2.80246			−0.0907805			−0.0453902	−	0.998969i	$-0.514453\pi$
$953$	−2.80246			−0.0907805			−0.0453902	+	0.998969i	$0.514453\pi$
$954$		0			0
$955$	25.1173	+	25.1173i	0.812775	+	0.812775i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.0230880	+	0.0399895i	−0.000745550	+	0.00129133i
$960$		0			0
$961$	14.4456	+	25.0204i	0.465986	+	0.807111i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	7.25296	−	27.0684i	0.233481	−	0.871363i
$966$		0			0
$967$	7.66141	−	13.2699i	0.246374	−	0.426733i	−0.716143	−	0.697954i	$-0.754094\pi$
$967$	7.66141	−	13.2699i	0.246374	−	0.426733i	0.962517	+	0.271221i	$0.0874275\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	22.7938	−	22.7938i	0.731487	−	0.731487i	−0.239428	−	0.970914i	$-0.576960\pi$
$971$	22.7938	−	22.7938i	0.731487	−	0.731487i	0.970914	+	0.239428i	$0.0769598\pi$
$972$		0			0
$973$	0.0845395	+	0.0845395i	0.00271021	+	0.00271021i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	20.2451	+	11.6885i	0.647699	+	0.373949i	0.787574	−	0.616220i	$-0.211337\pi$
$977$	20.2451	+	11.6885i	0.647699	+	0.373949i	−0.139875	+	0.990169i	$0.544670\pi$
$978$		0			0
$979$	54.5556	+	14.6181i	1.74360	+	0.467197i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−30.2556	+	17.4681i	−0.965005	+	0.557146i	−0.897710	−	0.440587i	$-0.854770\pi$
$983$	−30.2556	+	17.4681i	−0.965005	+	0.557146i	−0.0672949	+	0.997733i	$0.521437\pi$
$984$		0			0
$985$	0.940963	+	0.543265i	0.0299816	+	0.0173099i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	27.3131	−	27.3131i	0.868507	−	0.868507i
$990$		0			0
$991$			58.5560i			1.86009i	0.367440	+	0.930047i	$0.380234\pi$
$991$			58.5560i			1.86009i	−0.367440	+	0.930047i	$0.619766\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	48.9194	−	13.1079i	1.55085	−	0.415549i
$996$		0			0
$997$	43.9362	+	11.7727i	1.39147	+	0.372844i	0.875276	−	0.483624i	$-0.160680\pi$
$997$	43.9362	+	11.7727i	1.39147	+	0.372844i	0.516199	+	0.856469i	$0.327347\pi$
$998$		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.1583.18		88
3.2	odd	2		576.2.y.a.239.5		88
4.3	odd	2		432.2.v.a.179.9		88
9.2	odd	6	inner	1728.2.z.a.1007.18		88
9.7	even	3		576.2.y.a.47.16		88
12.11	even	2		144.2.u.a.131.14	yes	88
16.5	even	4		432.2.v.a.395.17		88
16.11	odd	4	inner	1728.2.z.a.719.18		88
36.7	odd	6		144.2.u.a.83.6	yes	88
36.11	even	6		432.2.v.a.35.17		88
48.5	odd	4		144.2.u.a.59.6	yes	88
48.11	even	4		576.2.y.a.527.16		88
144.11	even	12	inner	1728.2.z.a.143.18		88
144.43	odd	12		576.2.y.a.335.5		88
144.101	odd	12		432.2.v.a.251.9		88
144.133	even	12		144.2.u.a.11.14	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.14	✓	88	144.133	even	12
144.2.u.a.59.6	yes	88	48.5	odd	4
144.2.u.a.83.6	yes	88	36.7	odd	6
144.2.u.a.131.14	yes	88	12.11	even	2
432.2.v.a.35.17		88	36.11	even	6
432.2.v.a.179.9		88	4.3	odd	2
432.2.v.a.251.9		88	144.101	odd	12
432.2.v.a.395.17		88	16.5	even	4
576.2.y.a.47.16		88	9.7	even	3
576.2.y.a.239.5		88	3.2	odd	2
576.2.y.a.335.5		88	144.43	odd	12
576.2.y.a.527.16		88	48.11	even	4
1728.2.z.a.143.18		88	144.11	even	12	inner
1728.2.z.a.719.18		88	16.11	odd	4	inner
1728.2.z.a.1007.18		88	9.2	odd	6	inner
1728.2.z.a.1583.18		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)

\(f(q)\)	\(=\)	\(q+(2.70956 - 0.726024i) q^{5} +(0.00424642 + 0.00735502i) q^{7} +(3.00129 + 0.804193i) q^{11} +(6.42317 - 1.72108i) q^{13} -3.37812i q^{17} +(-1.35881 + 1.35881i) q^{19} +(-5.38718 - 3.11029i) q^{23} +(2.48446 - 1.43441i) q^{25} +(-3.27685 - 0.878030i) q^{29} +(6.70211 + 3.86947i) q^{31} +(0.0168459 + 0.0168459i) q^{35} +(0.769697 - 0.769697i) q^{37} +(-2.64756 + 4.58570i) q^{41} +(-1.60713 + 5.99790i) q^{43} +(0.0955284 + 0.165460i) q^{47} +(3.49996 - 6.06212i) q^{49} +(-0.750557 - 0.750557i) q^{53} +8.71603 q^{55} +(-2.43515 - 9.08809i) q^{59} +(-2.64143 + 9.85796i) q^{61} +(16.1544 - 9.32674i) q^{65} +(-2.08238 - 7.77154i) q^{67} +1.02260i q^{71} +7.30911i q^{73} +(0.00682989 + 0.0254895i) q^{77} +(4.36074 - 2.51768i) q^{79} +(3.35017 - 12.5030i) q^{83} +(-2.45259 - 9.15320i) q^{85} +18.1774 q^{89} +(0.0399341 + 0.0399341i) q^{91} +(-2.69525 + 4.66831i) q^{95} +(1.64497 + 2.84917i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 6 q^{5} + 4 q^{7} - 6 q^{11} - 2 q^{13} + 8 q^{19} - 12 q^{23} + 6 q^{29} - 8 q^{37} + 2 q^{43} - 24 q^{49} + 16 q^{55} - 42 q^{59} - 2 q^{61} + 12 q^{65} + 2 q^{67} + 6 q^{77} + 54 q^{83} + 8 q^{85}+ \cdots - 4 q^{97}+O(q^{100}) \) 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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