LMFDB - Embedded newform 1728.2.bc.e.145.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1728,2,Mod(145,1728)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1728.145"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1728, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [72,0,0,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$13.7981494693$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			145.10
Character	$\chi$	$=$	1728.145
Dual form			1728.2.bc.e.1585.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.00302457 - 0.0112878i) q^{5} +(1.05753 - 0.610563i) q^{7} +(1.83070 + 0.490535i) q^{11} +(5.06759 - 1.35786i) q^{13} +1.54238 q^{17} +(-4.06823 - 4.06823i) q^{19} +(-5.20660 - 3.00603i) q^{23} +(4.33001 - 2.49993i) q^{25} +(-0.798708 + 2.98082i) q^{29} +(-2.92831 + 5.07198i) q^{31} +(-0.0100905 - 0.0100905i) q^{35} +(0.923082 - 0.923082i) q^{37} +(3.20829 + 1.85231i) q^{41} +(4.84015 + 1.29691i) q^{43} +(-1.31218 - 2.27277i) q^{47} +(-2.75442 + 4.77080i) q^{49} +(8.88508 - 8.88508i) q^{53} -0.0221483i q^{55} +(2.35453 + 8.78724i) q^{59} +(3.24737 - 12.1194i) q^{61} +(-0.0306545 - 0.0530952i) q^{65} +(11.8800 - 3.18324i) q^{67} -14.2363i q^{71} +4.32091i q^{73} +(2.23552 - 0.599006i) q^{77} +(0.261880 + 0.453589i) q^{79} +(2.91592 - 10.8824i) q^{83} +(-0.00466503 - 0.0174101i) q^{85} -10.7103i q^{89} +(4.53005 - 4.53005i) q^{91} +(-0.0336169 + 0.0582262i) q^{95} +(8.78820 + 15.2216i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 4 q^{5} - 2 q^{11} - 16 q^{13} + 16 q^{17} - 28 q^{19} - 4 q^{29} - 28 q^{31} - 16 q^{35} + 16 q^{37} + 10 q^{43} - 56 q^{47} + 4 q^{49} + 8 q^{53} - 14 q^{59} - 32 q^{61} + 64 q^{65} + 18 q^{67}+ \cdots + 40 q^{97}+O(q^{100}) $ 72 * q - 4 * q^5 - 2 * q^11 - 16 * q^13 + 16 * q^17 - 28 * q^19 - 4 * q^29 - 28 * q^31 - 16 * q^35 + 16 * q^37 + 10 * q^43 - 56 * q^47 + 4 * q^49 + 8 * q^53 - 14 * q^59 - 32 * q^61 + 64 * q^65 + 18 * q^67 + 36 * q^77 - 44 * q^79 + 20 * q^83 - 8 * q^85 + 80 * q^91 + 48 * q^95 + 40 * q^97

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.00302457	−	0.0112878i	−0.00135263	−	0.00504807i	0.965246	−	0.261342i	$-0.0841651\pi$
$5$	−0.00302457	−	0.0112878i	−0.00135263	−	0.00504807i	−0.966599	+	0.256294i	$0.917498\pi$
$6$		0			0
$7$	1.05753	−	0.610563i	0.399708	−	0.230771i	−0.286650	−	0.958035i	$-0.592542\pi$
$7$	1.05753	−	0.610563i	0.399708	−	0.230771i	0.686358	+	0.727264i	$0.259208\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.83070	+	0.490535i	0.551977	+	0.147902i	0.524018	−	0.851707i	$-0.324432\pi$
$11$	1.83070	+	0.490535i	0.551977	+	0.147902i	0.0279594	+	0.999609i	$0.491099\pi$
$12$		0			0
$13$	5.06759	−	1.35786i	1.40550	−	0.376602i	0.525181	−	0.850991i	$-0.323998\pi$
$13$	5.06759	−	1.35786i	1.40550	−	0.376602i	0.880315	+	0.474389i	$0.157331\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.54238			0.374082			0.187041	−	0.982352i	$-0.440110\pi$
$17$	1.54238			0.374082			0.187041	+	0.982352i	$0.440110\pi$
$18$		0			0
$19$	−4.06823	−	4.06823i	−0.933317	−	0.933317i	0.0645950	−	0.997912i	$-0.479424\pi$
$19$	−4.06823	−	4.06823i	−0.933317	−	0.933317i	−0.997912	+	0.0645950i	$0.979424\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.20660	−	3.00603i	−1.08565	−	0.626801i	−0.153236	−	0.988190i	$-0.548970\pi$
$23$	−5.20660	−	3.00603i	−1.08565	−	0.626801i	−0.932415	+	0.361388i	$0.882303\pi$
$24$		0			0
$25$	4.33001	−	2.49993i	0.866002	−	0.499986i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.798708	+	2.98082i	−0.148316	+	0.553524i	0.851269	+	0.524730i	$0.175834\pi$
$29$	−0.798708	+	2.98082i	−0.148316	+	0.553524i	−0.999585	+	0.0287946i	$0.990833\pi$
$30$		0			0
$31$	−2.92831	+	5.07198i	−0.525939	+	0.910954i	0.473604	+	0.880738i	$0.342953\pi$
$31$	−2.92831	+	5.07198i	−0.525939	+	0.910954i	−0.999543	+	0.0302159i	$0.990381\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−0.0100905	−	0.0100905i	−0.00170561	−	0.00170561i
$36$		0			0
$37$	0.923082	−	0.923082i	0.151754	−	0.151754i	−0.627147	−	0.778901i	$-0.715777\pi$
$37$	0.923082	−	0.923082i	0.151754	−	0.151754i	0.778901	+	0.627147i	$0.215777\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.20829	+	1.85231i	0.501051	+	0.289282i	0.729147	−	0.684357i	$-0.239917\pi$
$41$	3.20829	+	1.85231i	0.501051	+	0.289282i	−0.228096	+	0.973639i	$0.573250\pi$
$42$		0			0
$43$	4.84015	+	1.29691i	0.738115	+	0.197777i	0.608240	−	0.793753i	$-0.291876\pi$
$43$	4.84015	+	1.29691i	0.738115	+	0.197777i	0.129875	+	0.991530i	$0.458542\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.31218	−	2.27277i	−0.191402	−	0.331517i	0.754313	−	0.656515i	$-0.227970\pi$
$47$	−1.31218	−	2.27277i	−0.191402	−	0.331517i	−0.945715	+	0.324997i	$0.894637\pi$
$48$		0			0
$49$	−2.75442	+	4.77080i	−0.393489	+	0.681543i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	8.88508	−	8.88508i	1.22046	−	1.22046i	0.252991	−	0.967469i	$-0.418586\pi$
$53$	8.88508	−	8.88508i	1.22046	−	1.22046i	0.967469	−	0.252991i	$-0.0814144\pi$
$54$		0			0
$55$		−	0.0221483i		−	0.00298648i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.35453	+	8.78724i	0.306534	+	1.14400i	0.931617	+	0.363443i	$0.118399\pi$
$59$	2.35453	+	8.78724i	0.306534	+	1.14400i	−0.625082	+	0.780559i	$0.714935\pi$
$60$		0			0
$61$	3.24737	−	12.1194i	0.415783	−	1.55172i	−0.367478	−	0.930032i	$-0.619779\pi$
$61$	3.24737	−	12.1194i	0.415783	−	1.55172i	0.783262	−	0.621692i	$-0.213555\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.0306545	−	0.0530952i	−0.00380223	−	0.00658565i
$66$		0			0
$67$	11.8800	−	3.18324i	1.45137	−	0.388895i	0.554873	−	0.831935i	$-0.312767\pi$
$67$	11.8800	−	3.18324i	1.45137	−	0.388895i	0.896501	+	0.443041i	$0.146100\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	14.2363i		−	1.68954i	−0.535129	−	0.844771i	$-0.679737\pi$
$71$		−	14.2363i		−	1.68954i	0.535129	−	0.844771i	$-0.320263\pi$
$72$		0			0
$73$			4.32091i			0.505724i	0.967502	+	0.252862i	$0.0813718\pi$
$73$			4.32091i			0.505724i	−0.967502	+	0.252862i	$0.918628\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	2.23552	−	0.599006i	0.254761	−	0.0682630i
$78$		0			0
$79$	0.261880	+	0.453589i	0.0294638	+	0.0510328i	0.880381	−	0.474267i	$-0.157287\pi$
$79$	0.261880	+	0.453589i	0.0294638	+	0.0510328i	−0.850918	+	0.525299i	$0.823953\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.91592	−	10.8824i	0.320064	−	1.19450i	−0.599117	−	0.800661i	$-0.704482\pi$
$83$	2.91592	−	10.8824i	0.320064	−	1.19450i	0.919181	−	0.393834i	$-0.128852\pi$
$84$		0			0
$85$	−0.00466503	−	0.0174101i	−0.000505994	−	0.00188839i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	10.7103i		−	1.13529i	−0.823274	−	0.567644i	$-0.807855\pi$
$89$		−	10.7103i		−	1.13529i	0.823274	−	0.567644i	$-0.192145\pi$
$90$		0			0
$91$	4.53005	−	4.53005i	0.474879	−	0.474879i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0336169	+	0.0582262i	−0.00344902	+	0.00597388i
$96$		0			0
$97$	8.78820	+	15.2216i	0.892306	+	1.54552i	0.837104	+	0.547044i	$0.184247\pi$
$97$	8.78820	+	15.2216i	0.892306	+	1.54552i	0.0552025	+	0.998475i	$0.482420\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.73117	−	1.80361i	−0.669776	−	0.179466i	−0.0921222	−	0.995748i	$-0.529365\pi$
$101$	−6.73117	−	1.80361i	−0.669776	−	0.179466i	−0.577654	+	0.816282i	$0.696032\pi$
$102$		0			0
$103$	2.20609	+	1.27369i	0.217373	+	0.125500i	0.604733	−	0.796428i	$-0.293280\pi$
$103$	2.20609	+	1.27369i	0.217373	+	0.125500i	−0.387360	+	0.921928i	$0.626613\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.52175	−	3.52175i	0.340460	−	0.340460i	−0.516080	−	0.856540i	$-0.672609\pi$
$107$	3.52175	−	3.52175i	0.340460	−	0.340460i	0.856540	+	0.516080i	$0.172609\pi$
$108$		0			0
$109$	3.14334	+	3.14334i	0.301077	+	0.301077i	0.841435	−	0.540358i	$-0.181711\pi$
$109$	3.14334	+	3.14334i	0.301077	+	0.301077i	−0.540358	+	0.841435i	$0.681711\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−7.90904	+	13.6989i	−0.744020	+	1.28868i	0.206631	+	0.978419i	$0.433750\pi$
$113$	−7.90904	+	13.6989i	−0.744020	+	1.28868i	−0.950651	+	0.310262i	$0.899583\pi$
$114$		0			0
$115$	−0.0181839	+	0.0678632i	−0.00169566	+	0.00632828i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.63111	−	0.941721i	0.149523	−	0.0863274i
$120$		0			0
$121$	−6.41543	−	3.70395i	−0.583221	−	0.336723i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−0.0826316	−	0.0826316i	−0.00739079	−	0.00739079i
$126$		0			0
$127$	5.72603			0.508103			0.254052	−	0.967191i	$-0.418237\pi$
$127$	5.72603			0.508103			0.254052	+	0.967191i	$0.418237\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.56224	−	1.75835i	0.573346	−	0.153628i	0.0395151	−	0.999219i	$-0.487419\pi$
$131$	6.56224	−	1.75835i	0.573346	−	0.153628i	0.533831	+	0.845591i	$0.320752\pi$
$132$		0			0
$133$	−6.78618	−	1.81835i	−0.588436	−	0.157671i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	3.64923	−	2.10688i	0.311775	−	0.180003i	−0.335946	−	0.941881i	$-0.609056\pi$
$137$	3.64923	−	2.10688i	0.311775	−	0.180003i	0.647720	+	0.761878i	$0.275722\pi$
$138$		0			0
$139$	4.19392	+	15.6519i	0.355724	+	1.32758i	0.879571	+	0.475767i	$0.157830\pi$
$139$	4.19392	+	15.6519i	0.355724	+	1.32758i	−0.523847	+	0.851812i	$0.675504\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.94332			0.831502
$144$		0			0
$145$	0.0360627			0.00299485
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.00877	−	3.76477i	−0.0826415	−	0.308422i	0.912216	−	0.409710i	$-0.134370\pi$
$149$	−1.00877	−	3.76477i	−0.0826415	−	0.308422i	−0.994857	+	0.101288i	$0.967704\pi$
$150$		0			0
$151$	−13.0073	+	7.50979i	−1.05852	+	0.611138i	−0.925023	−	0.379911i	$-0.875955\pi$
$151$	−13.0073	+	7.50979i	−1.05852	+	0.611138i	−0.133499	+	0.991049i	$0.542621\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.0661085	+	0.0177137i	0.00530996	+	0.00142280i
$156$		0			0
$157$	−9.47288	+	2.53825i	−0.756018	+	0.202574i	−0.616186	−	0.787601i	$-0.711323\pi$
$157$	−9.47288	+	2.53825i	−0.756018	+	0.202574i	−0.139832	+	0.990175i	$0.544656\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−7.34150			−0.578591
$162$		0			0
$163$	−5.22606	−	5.22606i	−0.409336	−	0.409336i	0.472171	−	0.881507i	$-0.343471\pi$
$163$	−5.22606	−	5.22606i	−0.409336	−	0.409336i	−0.881507	+	0.472171i	$0.843471\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−6.31476	−	3.64583i	−0.488651	−	0.282123i	0.235364	−	0.971907i	$-0.424372\pi$
$167$	−6.31476	−	3.64583i	−0.488651	−	0.282123i	−0.724015	+	0.689785i	$0.757705\pi$
$168$		0			0
$169$	12.5783	−	7.26211i	0.967565	−	0.558624i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.14659	−	22.9394i	0.467317	−	1.74405i	−0.181775	−	0.983340i	$-0.558184\pi$
$173$	6.14659	−	22.9394i	0.467317	−	1.74405i	0.649092	−	0.760710i	$-0.275149\pi$
$174$		0			0
$175$	3.05273	−	5.28749i	0.230765	−	0.399697i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	11.4489	+	11.4489i	0.855732	+	0.855732i	0.990832	−	0.135100i	$-0.0431356\pi$
$179$	11.4489	+	11.4489i	0.855732	+	0.855732i	−0.135100	+	0.990832i	$0.543136\pi$
$180$		0			0
$181$	−3.01327	+	3.01327i	−0.223974	+	0.223974i	−0.810170	−	0.586195i	$-0.800625\pi$
$181$	−3.01327	+	3.01327i	−0.223974	+	0.223974i	0.586195	+	0.810170i	$0.300625\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.0132115	−	0.00762768i	−0.000971331	−	0.000560798i
$186$		0			0
$187$	2.82364	+	0.756592i	0.206485	+	0.0553275i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−2.25702	−	3.90928i	−0.163313	−	0.282866i	0.772742	−	0.634720i	$-0.218885\pi$
$191$	−2.25702	−	3.90928i	−0.163313	−	0.282866i	−0.936055	+	0.351854i	$0.885551\pi$
$192$		0			0
$193$	−1.75793	+	3.04482i	−0.126539	+	0.219171i	−0.922333	−	0.386395i	$-0.873720\pi$
$193$	−1.75793	+	3.04482i	−0.126539	+	0.219171i	0.795795	+	0.605566i	$0.207053\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.81922	−	4.81922i	0.343355	−	0.343355i	−0.514272	−	0.857627i	$-0.671938\pi$
$197$	4.81922	−	4.81922i	0.343355	−	0.343355i	0.857627	+	0.514272i	$0.171938\pi$
$198$		0			0
$199$			4.66322i			0.330567i	0.986246	+	0.165284i	$0.0528539\pi$
$199$			4.66322i			0.330567i	−0.986246	+	0.165284i	$0.947146\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.975324	+	3.63996i	0.0684543	+	0.255475i
$204$		0			0
$205$	0.0112049	−	0.0418171i	0.000782581	−	0.00292063i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−5.45211	−	9.44333i	−0.377130	−	0.653209i
$210$		0			0
$211$	17.4452	−	4.67442i	1.20097	−	0.321800i	0.397760	−	0.917490i	$-0.369788\pi$
$211$	17.4452	−	4.67442i	1.20097	−	0.321800i	0.803215	+	0.595689i	$0.203121\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	0.0585574i		−	0.00399358i
$216$		0			0
$217$			7.15167i			0.485487i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.81615	−	2.09433i	0.525771	−	0.140880i
$222$		0			0
$223$	−2.85769	−	4.94966i	−0.191365	−	0.331454i	0.754338	−	0.656486i	$-0.227958\pi$
$223$	−2.85769	−	4.94966i	−0.191365	−	0.331454i	−0.945703	+	0.325032i	$0.894625\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.27233	+	19.6766i	−0.349937	+	1.30598i	0.536802	+	0.843709i	$0.319632\pi$
$227$	−5.27233	+	19.6766i	−0.349937	+	1.30598i	−0.886738	+	0.462272i	$0.847034\pi$
$228$		0			0
$229$	−0.992819	−	3.70525i	−0.0656073	−	0.244850i	0.925332	−	0.379157i	$-0.123786\pi$
$229$	−0.992819	−	3.70525i	−0.0656073	−	0.244850i	−0.990940	+	0.134307i	$0.957119\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			5.33043i			0.349208i	0.984639	+	0.174604i	$0.0558645\pi$
$233$			5.33043i			0.349208i	−0.984639	+	0.174604i	$0.944136\pi$
$234$		0			0
$235$	−0.0216859	+	0.0216859i	−0.00141463	+	0.00141463i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−13.8380	+	23.9681i	−0.895104	+	1.55037i	−0.0614282	+	0.998112i	$0.519566\pi$
$239$	−13.8380	+	23.9681i	−0.895104	+	1.55037i	−0.833676	+	0.552254i	$0.813768\pi$
$240$		0			0
$241$	0.847203	+	1.46740i	0.0545731	+	0.0945234i	0.892021	−	0.451993i	$-0.149287\pi$
$241$	0.847203	+	1.46740i	0.0545731	+	0.0945234i	−0.837448	+	0.546517i	$0.815954\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.0621830	+	0.0166619i	0.00397273	+	0.00106449i
$246$		0			0
$247$	−26.1402	−	15.0921i	−1.66326	−	0.960284i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	0.987980	−	0.987980i	0.0623607	−	0.0623607i	−0.675239	−	0.737599i	$-0.735959\pi$
$251$	0.987980	−	0.987980i	0.0623607	−	0.0623607i	0.737599	+	0.675239i	$0.235959\pi$
$252$		0			0
$253$	−8.05717	−	8.05717i	−0.506550	−	0.506550i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−11.8214	+	20.4753i	−0.737401	+	1.27722i	0.216260	+	0.976336i	$0.430614\pi$
$257$	−11.8214	+	20.4753i	−0.737401	+	1.27722i	−0.953662	+	0.300881i	$0.902719\pi$
$258$		0			0
$259$	0.412584	−	1.53978i	0.0256367	−	0.0956776i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−22.2619	+	12.8529i	−1.37273	+	0.792545i	−0.991271	−	0.131841i	$-0.957911\pi$
$263$	−22.2619	+	12.8529i	−1.37273	+	0.792545i	−0.381458	+	0.924386i	$0.624578\pi$
$264$		0			0
$265$	−0.127167	−	0.0734198i	−0.00781180	−	0.00451015i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	13.6891	+	13.6891i	0.834637	+	0.834637i	0.988147	−	0.153510i	$-0.0490577\pi$
$269$	13.6891	+	13.6891i	0.834637	+	0.834637i	−0.153510	+	0.988147i	$0.549058\pi$
$270$		0			0
$271$	7.11000			0.431902			0.215951	−	0.976404i	$-0.430715\pi$
$271$	7.11000			0.431902			0.215951	+	0.976404i	$0.430715\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	9.15326	−	2.45261i	0.551962	−	0.147898i
$276$		0			0
$277$	−21.7174	−	5.81917i	−1.30487	−	0.349640i	−0.461583	−	0.887097i	$-0.652718\pi$
$277$	−21.7174	−	5.81917i	−1.30487	−	0.349640i	−0.843291	+	0.537457i	$0.819385\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−19.7952	+	11.4288i	−1.18088	+	0.681783i	−0.956218	−	0.292654i	$-0.905462\pi$
$281$	−19.7952	+	11.4288i	−1.18088	+	0.681783i	−0.224664	+	0.974436i	$0.572128\pi$
$282$		0			0
$283$	−1.59958	−	5.96971i	−0.0950851	−	0.354862i	0.901947	−	0.431846i	$-0.142138\pi$
$283$	−1.59958	−	5.96971i	−0.0950851	−	0.354862i	−0.997032	+	0.0769838i	$0.975471\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	4.52381			0.267032
$288$		0			0
$289$	−14.6211			−0.860063
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−1.00950	−	3.76752i	−0.0589758	−	0.220101i	0.930148	−	0.367184i	$-0.119678\pi$
$293$	−1.00950	−	3.76752i	−0.0589758	−	0.220101i	−0.989124	+	0.147083i	$0.953011\pi$
$294$		0			0
$295$	0.0920675	−	0.0531552i	0.00536038	−	0.00309482i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−30.4667	−	8.16352i	−1.76193	−	0.472109i
$300$		0			0
$301$	5.91043	−	1.58370i	0.340672	−	0.0912827i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.146623			−0.00839562
$306$		0			0
$307$	−10.8111	−	10.8111i	−0.617023	−	0.617023i	0.327743	−	0.944767i	$-0.393712\pi$
$307$	−10.8111	−	10.8111i	−0.617023	−	0.617023i	−0.944767	+	0.327743i	$0.893712\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	19.5372	+	11.2798i	1.10785	+	0.639619i	0.938273	−	0.345897i	$-0.112425\pi$
$311$	19.5372	+	11.2798i	1.10785	+	0.639619i	0.169581	+	0.985516i	$0.445759\pi$
$312$		0			0
$313$	−5.17232	+	2.98624i	−0.292357	+	0.168792i	−0.639004	−	0.769203i	$-0.720653\pi$
$313$	−5.17232	+	2.98624i	−0.292357	+	0.168792i	0.346647	+	0.937996i	$0.387320\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.81751	+	17.9792i	−0.270579	+	1.00981i	0.688168	+	0.725551i	$0.258415\pi$
$317$	−4.81751	+	17.9792i	−0.270579	+	1.00981i	−0.958747	+	0.284262i	$0.908252\pi$
$318$		0			0
$319$	−2.92439	+	5.06520i	−0.163735	+	0.283597i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−6.27476	−	6.27476i	−0.349137	−	0.349137i
$324$		0			0
$325$	18.5482	−	18.5482i	1.02887	−	1.02887i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−2.77534	−	1.60234i	−0.153009	−	0.0883400i
$330$		0			0
$331$	10.1869	+	2.72957i	0.559923	+	0.150031i	0.527671	−	0.849449i	$-0.323065\pi$
$331$	10.1869	+	2.72957i	0.559923	+	0.150031i	0.0322521	+	0.999480i	$0.489732\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−0.0718638	−	0.124472i	−0.00392634	−	0.00680062i
$336$		0			0
$337$	12.1222	−	20.9962i	0.660336	−	1.14374i	−0.320192	−	0.947353i	$-0.603747\pi$
$337$	12.1222	−	20.9962i	0.660336	−	1.14374i	0.980527	−	0.196382i	$-0.0629194\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−7.84884	+	7.84884i	−0.425038	+	0.425038i
$342$		0			0
$343$			15.2749i			0.824767i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	4.97570	+	18.5696i	0.267110	+	0.996867i	0.960946	+	0.276735i	$0.0892523\pi$
$347$	4.97570	+	18.5696i	0.267110	+	0.996867i	−0.693837	+	0.720132i	$0.744081\pi$
$348$		0			0
$349$	−4.19134	+	15.6423i	−0.224357	+	0.837313i	0.758304	+	0.651901i	$0.226028\pi$
$349$	−4.19134	+	15.6423i	−0.224357	+	0.837313i	−0.982661	+	0.185411i	$0.940638\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.69391	+	13.3262i	0.409505	+	0.709284i	0.994834	−	0.101512i	$-0.0323680\pi$
$353$	7.69391	+	13.3262i	0.409505	+	0.709284i	−0.585329	+	0.810796i	$0.699035\pi$
$354$		0			0
$355$	−0.160697	+	0.0430587i	−0.00852893	+	0.00228532i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			2.97883i			0.157217i	0.996906	+	0.0786083i	$0.0250476\pi$
$359$			2.97883i			0.157217i	−0.996906	+	0.0786083i	$0.974952\pi$
$360$		0			0
$361$			14.1010i			0.742159i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	0.0487737	−	0.0130689i	0.00255293	−	0.000684056i
$366$		0			0
$367$	−12.5585	−	21.7519i	−0.655547	−	1.13544i	−0.981756	−	0.190143i	$-0.939105\pi$
$367$	−12.5585	−	21.7519i	−0.655547	−	1.13544i	0.326210	−	0.945297i	$-0.394228\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.97131	−	14.8211i	0.206180	−	0.769474i
$372$		0			0
$373$	7.71816	+	28.8046i	0.399631	+	1.49144i	0.813747	+	0.581220i	$0.197424\pi$
$373$	7.71816	+	28.8046i	0.399631	+	1.49144i	−0.414116	+	0.910224i	$0.635909\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			16.1901i			0.833832i
$378$		0			0
$379$	−10.1985	+	10.1985i	−0.523864	+	0.523864i	−0.918736	−	0.394872i	$-0.870789\pi$
$379$	−10.1985	+	10.1985i	−0.523864	+	0.523864i	0.394872	+	0.918736i	$0.370789\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	10.5750	−	18.3164i	0.540356	−	0.935924i	−0.458528	−	0.888680i	$-0.651623\pi$
$383$	10.5750	−	18.3164i	0.540356	−	0.935924i	0.998883	−	0.0472436i	$-0.0150437\pi$
$384$		0			0
$385$	−0.0135230	−	0.0234224i	−0.000689194	−	0.00119372i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−30.3488	−	8.13193i	−1.53874	−	0.412305i	−0.612884	−	0.790173i	$-0.709991\pi$
$389$	−30.3488	−	8.13193i	−1.53874	−	0.412305i	−0.925860	+	0.377867i	$0.876658\pi$
$390$		0			0
$391$	−8.03056	−	4.63645i	−0.406123	−	0.234475i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.00432797	−	0.00432797i	0.000217764	−	0.000217764i
$396$		0			0
$397$	−3.24113	−	3.24113i	−0.162668	−	0.162668i	0.621080	−	0.783747i	$-0.286694\pi$
$397$	−3.24113	−	3.24113i	−0.162668	−	0.162668i	−0.783747	+	0.621080i	$0.786694\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	10.7429	−	18.6073i	0.536476	−	0.929203i	−0.462614	−	0.886560i	$-0.653089\pi$
$401$	10.7429	−	18.6073i	0.536476	−	0.929203i	0.999090	−	0.0426439i	$-0.0135781\pi$
$402$		0			0
$403$	−7.95244	+	29.6789i	−0.396139	+	1.47841i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.14269	−	1.23708i	0.106209	−	0.0613200i
$408$		0			0
$409$	−23.1426	−	13.3614i	−1.14433	−	0.660678i	−0.196829	−	0.980438i	$-0.563064\pi$
$409$	−23.1426	−	13.3614i	−1.14433	−	0.660678i	−0.947499	+	0.319760i	$0.896398\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.85515	+	7.85515i	0.386527	+	0.386527i
$414$		0			0
$415$	−0.131658			−0.00646283
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−8.83989	+	2.36864i	−0.431857	+	0.115716i	−0.468198	−	0.883624i	$-0.655097\pi$
$419$	−8.83989	+	2.36864i	−0.431857	+	0.115716i	0.0363407	+	0.999339i	$0.488430\pi$
$420$		0			0
$421$	−28.9344	−	7.75295i	−1.41018	−	0.377856i	−0.528188	−	0.849127i	$-0.677128\pi$
$421$	−28.9344	−	7.75295i	−1.41018	−	0.377856i	−0.881988	+	0.471272i	$0.843795\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	6.67852	−	3.85585i	0.323956	−	0.187036i
$426$		0			0
$427$	−3.96545	−	14.7993i	−0.191902	−	0.716187i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−7.05544			−0.339849			−0.169924	−	0.985457i	$-0.554352\pi$
$431$	−7.05544			−0.339849			−0.169924	+	0.985457i	$0.554352\pi$
$432$		0			0
$433$	13.1552			0.632201			0.316100	−	0.948726i	$-0.397626\pi$
$433$	13.1552			0.632201			0.316100	+	0.948726i	$0.397626\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	8.95243	+	33.4109i	0.428253	+	1.59826i
$438$		0			0
$439$	12.8757	−	7.43381i	0.614525	−	0.354796i	−0.160209	−	0.987083i	$-0.551217\pi$
$439$	12.8757	−	7.43381i	0.614525	−	0.354796i	0.774734	+	0.632287i	$0.217884\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.97678	−	0.797625i	−0.141431	−	0.0378963i	0.187409	−	0.982282i	$-0.439991\pi$
$443$	−2.97678	−	0.797625i	−0.141431	−	0.0378963i	−0.328840	+	0.944386i	$0.606658\pi$
$444$		0			0
$445$	−0.120896	+	0.0323940i	−0.00573102	+	0.00153562i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	21.8550			1.03140			0.515701	−	0.856769i	$-0.327532\pi$
$449$	21.8550			1.03140			0.515701	+	0.856769i	$0.327532\pi$
$450$		0			0
$451$	4.96480	+	4.96480i	0.233783	+	0.233783i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−0.0648360	−	0.0374331i	−0.00303956	−	0.00175489i
$456$		0			0
$457$	−2.32261	+	1.34096i	−0.108647	+	0.0627275i	−0.553339	−	0.832956i	$-0.686647\pi$
$457$	−2.32261	+	1.34096i	−0.108647	+	0.0627275i	0.444692	+	0.895684i	$0.353313\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−2.74844	+	10.2573i	−0.128008	+	0.477732i	−0.999929	−	0.0119146i	$-0.996207\pi$
$461$	−2.74844	+	10.2573i	−0.128008	+	0.477732i	0.871921	+	0.489646i	$0.162874\pi$
$462$		0			0
$463$	−11.8249	+	20.4814i	−0.549550	+	0.951849i	0.448755	+	0.893655i	$0.351868\pi$
$463$	−11.8249	+	20.4814i	−0.549550	+	0.951849i	−0.998305	+	0.0581943i	$0.981466\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	2.22540	+	2.22540i	0.102979	+	0.102979i	0.756719	−	0.653740i	$-0.226801\pi$
$467$	2.22540	+	2.22540i	0.102979	+	0.102979i	−0.653740	+	0.756719i	$0.726801\pi$
$468$		0			0
$469$	10.6199	−	10.6199i	0.490380	−	0.490380i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	8.22468	+	4.74852i	0.378171	+	0.218337i
$474$		0			0
$475$	−27.7858	−	7.44518i	−1.27490	−	0.341608i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−6.23896	−	10.8062i	−0.285066	−	0.493748i	0.687559	−	0.726128i	$-0.258682\pi$
$479$	−6.23896	−	10.8062i	−0.285066	−	0.493748i	−0.972625	+	0.232380i	$0.925349\pi$
$480$		0			0
$481$	3.42439	−	5.93121i	0.156139	−	0.270440i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	0.145238	−	0.145238i	0.00659494	−	0.00659494i
$486$		0			0
$487$			12.5314i			0.567853i	0.958846	+	0.283927i	$0.0916372\pi$
$487$			12.5314i			0.567853i	−0.958846	+	0.283927i	$0.908363\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−3.93613	−	14.6898i	−0.177635	−	0.662942i	−0.996088	−	0.0883688i	$-0.971835\pi$
$491$	−3.93613	−	14.6898i	−0.177635	−	0.662942i	0.818453	−	0.574574i	$-0.194832\pi$
$492$		0			0
$493$	−1.23191	+	4.59756i	−0.0554825	+	0.207064i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8.69218	−	15.0553i	−0.389898	−	0.675322i
$498$		0			0
$499$	−29.4298	+	7.88570i	−1.31746	+	0.353012i	−0.848026	−	0.529955i	$-0.822209\pi$
$499$	−29.4298	+	7.88570i	−1.31746	+	0.353012i	−0.469434	+	0.882967i	$0.655542\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			1.90106i			0.0847639i	0.999101	+	0.0423820i	$0.0134946\pi$
$503$			1.90106i			0.0847639i	−0.999101	+	0.0423820i	$0.986505\pi$
$504$		0			0
$505$			0.0814355i			0.00362383i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−12.4896	+	3.34659i	−0.553593	+	0.148335i	−0.524761	−	0.851249i	$-0.675845\pi$
$509$	−12.4896	+	3.34659i	−0.553593	+	0.148335i	−0.0288320	+	0.999584i	$0.509179\pi$
$510$		0			0
$511$	2.63819	+	4.56947i	0.116706	+	0.202142i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	0.00770471	−	0.0287544i	0.000339510	−	0.00126707i
$516$		0			0
$517$	−1.28734	−	4.80444i	−0.0566174	−	0.211299i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	1.24885i		−	0.0547130i	−0.999626	−	0.0273565i	$-0.991291\pi$
$521$		−	1.24885i		−	0.0547130i	0.999626	−	0.0273565i	$-0.00870893\pi$
$522$		0			0
$523$	−9.58031	+	9.58031i	−0.418918	+	0.418918i	−0.884831	−	0.465913i	$-0.845726\pi$
$523$	−9.58031	+	9.58031i	−0.418918	+	0.418918i	0.465913	+	0.884831i	$0.345726\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.51656	+	7.82292i	−0.196745	+	0.340772i
$528$		0			0
$529$	6.57248	+	11.3839i	0.285760	+	0.494951i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	18.7735	+	5.03034i	0.813169	+	0.217888i
$534$		0			0
$535$	−0.0504047	−	0.0291012i	−0.00217918	−	0.00125815i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−7.38278	+	7.38278i	−0.317999	+	0.317999i
$540$		0			0
$541$	13.0165	+	13.0165i	0.559622	+	0.559622i	0.929200	−	0.369578i	$-0.120498\pi$
$541$	13.0165	+	13.0165i	0.559622	+	0.559622i	−0.369578	+	0.929200i	$0.620498\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	0.0259743	−	0.0449887i	0.00111262	−	0.00192711i
$546$		0			0
$547$	−2.61540	+	9.76080i	−0.111826	+	0.417341i	−0.999030	−	0.0440366i	$-0.985978\pi$
$547$	−2.61540	+	9.76080i	−0.111826	+	0.417341i	0.887204	+	0.461378i	$0.152645\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	15.3760	−	8.87733i	0.655039	−	0.378187i
$552$		0			0
$553$	0.553890	+	0.319788i	0.0235538	+	0.0135988i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−26.6259	−	26.6259i	−1.12818	−	1.12818i	−0.990474	−	0.137702i	$-0.956029\pi$
$557$	−26.6259	−	26.6259i	−1.12818	−	1.12818i	−0.137702	−	0.990474i	$-0.543971\pi$
$558$		0			0
$559$	26.2889			1.11190
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−21.1660	+	5.67141i	−0.892039	+	0.239021i	−0.675594	−	0.737274i	$-0.736113\pi$
$563$	−21.1660	+	5.67141i	−0.892039	+	0.239021i	−0.216445	+	0.976295i	$0.569446\pi$
$564$		0			0
$565$	0.178552	+	0.0478429i	0.00751174	+	0.00201276i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.15901	+	4.71061i	−0.342044	+	0.197479i	−0.661175	−	0.750231i	$-0.729942\pi$
$569$	−8.15901	+	4.71061i	−0.342044	+	0.197479i	0.319132	+	0.947710i	$0.396609\pi$
$570$		0			0
$571$	−7.61666	−	28.4258i	−0.318747	−	1.18958i	−0.920450	−	0.390861i	$-0.872177\pi$
$571$	−7.61666	−	28.4258i	−0.318747	−	1.18958i	0.601702	−	0.798720i	$-0.294489\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−30.0595			−1.25357
$576$		0			0
$577$	−42.9309			−1.78724			−0.893618	−	0.448828i	$-0.851842\pi$
$577$	−42.9309			−1.78724			−0.893618	+	0.448828i	$0.851842\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.56071	−	13.2888i	−0.147723	−	0.551310i
$582$		0			0
$583$	20.6244	−	11.9075i	0.854175	−	0.493158i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	30.3611	+	8.13523i	1.25314	+	0.335777i	0.823548	−	0.567247i	$-0.191992\pi$
$587$	30.3611	+	8.13523i	1.25314	+	0.335777i	0.429589	+	0.903024i	$0.358658\pi$
$588$		0			0
$589$	32.5470	−	8.72095i	1.34108	−	0.359340i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.434128			−0.0178275			−0.00891374	−	0.999960i	$-0.502837\pi$
$593$	−0.434128			−0.0178275			−0.00891374	+	0.999960i	$0.502837\pi$
$594$		0			0
$595$	−0.0155634	−	0.0155634i	−0.000638037	−	0.000638037i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.46143	+	1.99846i	0.141430	+	0.0816547i	0.569045	−	0.822306i	$-0.307313\pi$
$599$	3.46143	+	1.99846i	0.141430	+	0.0816547i	−0.427615	+	0.903961i	$0.640646\pi$
$600$		0			0
$601$	−3.54563	+	2.04707i	−0.144629	+	0.0835019i	−0.570569	−	0.821250i	$-0.693277\pi$
$601$	−3.54563	+	2.04707i	−0.144629	+	0.0835019i	0.425939	+	0.904752i	$0.359944\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.0224057	+	0.0836192i	−0.000910922	+	0.00339961i
$606$		0			0
$607$	−16.8996	+	29.2709i	−0.685932	+	1.18807i	0.287211	+	0.957867i	$0.407272\pi$
$607$	−16.8996	+	29.2709i	−0.685932	+	1.18807i	−0.973143	+	0.230202i	$0.926061\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−9.73570	−	9.73570i	−0.393864	−	0.393864i
$612$		0			0
$613$	1.73094	−	1.73094i	0.0699119	−	0.0699119i	−0.671286	−	0.741198i	$-0.734258\pi$
$613$	1.73094	−	1.73094i	0.0699119	−	0.0699119i	0.741198	+	0.671286i	$0.234258\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	14.9093	+	8.60788i	0.600225	+	0.346540i	0.769130	−	0.639092i	$-0.220690\pi$
$617$	14.9093	+	8.60788i	0.600225	+	0.346540i	−0.168905	+	0.985632i	$0.554023\pi$
$618$		0			0
$619$	−6.34645	−	1.70053i	−0.255085	−	0.0683499i	0.129010	−	0.991643i	$-0.458820\pi$
$619$	−6.34645	−	1.70053i	−0.255085	−	0.0683499i	−0.384095	+	0.923293i	$0.625487\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−6.53931	−	11.3264i	−0.261992	−	0.453783i
$624$		0			0
$625$	12.4990	−	21.6489i	0.499959	−	0.865954i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.42374	−	1.42374i	0.0567684	−	0.0567684i
$630$		0			0
$631$		−	13.3295i		−	0.530639i	−0.964161	−	0.265319i	$-0.914523\pi$
$631$		−	13.3295i		−	0.530639i	0.964161	−	0.265319i	$-0.0854774\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.0173188	−	0.0646345i	−0.000687274	−	0.00256494i
$636$		0			0
$637$	−7.48023	+	27.9166i	−0.296377	+	1.10610i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−8.26044	−	14.3075i	−0.326268	−	0.565113i	0.655500	−	0.755195i	$-0.272458\pi$
$641$	−8.26044	−	14.3075i	−0.326268	−	0.565113i	−0.981768	+	0.190082i	$0.939124\pi$
$642$		0			0
$643$	24.0050	−	6.43213i	0.946667	−	0.253659i	0.247719	−	0.968832i	$-0.420319\pi$
$643$	24.0050	−	6.43213i	0.946667	−	0.253659i	0.698947	+	0.715173i	$0.253652\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$			26.9660i			1.06014i	0.847954	+	0.530071i	$0.177835\pi$
$647$			26.9660i			1.06014i	−0.847954	+	0.530071i	$0.822165\pi$
$648$		0			0
$649$			17.2418i			0.676800i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.27782	+	1.41419i	−0.206537	+	0.0553414i	−0.360604	−	0.932719i	$-0.617429\pi$
$653$	−5.27782	+	1.41419i	−0.206537	+	0.0553414i	0.154067	+	0.988060i	$0.450763\pi$
$654$		0			0
$655$	−0.0396959	−	0.0687553i	−0.00155105	−	0.00268649i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−0.184661	+	0.689165i	−0.00719337	+	0.0268460i	−0.969429	−	0.245371i	$-0.921090\pi$
$659$	−0.184661	+	0.689165i	−0.00719337	+	0.0268460i	0.962236	+	0.272217i	$0.0877569\pi$
$660$		0			0
$661$	9.89344	+	36.9228i	0.384810	+	1.43613i	0.838466	+	0.544954i	$0.183453\pi$
$661$	9.89344	+	36.9228i	0.384810	+	1.43613i	−0.453656	+	0.891177i	$0.649880\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			0.0821010i			0.00318374i
$666$		0			0
$667$	13.1190	−	13.1190i	0.507970	−	0.507970i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	11.8899	−	20.5940i	0.459006	−	0.795022i
$672$		0			0
$673$	−6.39173	−	11.0708i	−0.246383	−	0.426748i	0.716137	−	0.697960i	$-0.245909\pi$
$673$	−6.39173	−	11.0708i	−0.246383	−	0.426748i	−0.962520	+	0.271212i	$0.912575\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	25.4595	+	6.82184i	0.978487	+	0.262185i	0.712407	−	0.701766i	$-0.247605\pi$
$677$	25.4595	+	6.82184i	0.978487	+	0.262185i	0.266079	+	0.963951i	$0.414272\pi$
$678$		0			0
$679$	18.5875	+	10.7315i	0.713323	+	0.411837i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	9.42670	−	9.42670i	0.360703	−	0.360703i	−0.503369	−	0.864072i	$-0.667906\pi$
$683$	9.42670	−	9.42670i	0.360703	−	0.360703i	0.864072	+	0.503369i	$0.167906\pi$
$684$		0			0
$685$	−0.0348195	−	0.0348195i	−0.00133039	−	0.00133039i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	32.9613	−	57.0906i	1.25572	−	2.17498i
$690$		0			0
$691$	−4.07041	+	15.1910i	−0.154846	+	0.577891i	0.844273	+	0.535913i	$0.180033\pi$
$691$	−4.07041	+	15.1910i	−0.154846	+	0.577891i	−0.999119	+	0.0419780i	$0.986634\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.163992	−	0.0946807i	0.00622056	−	0.00359144i
$696$		0			0
$697$	4.94841	+	2.85696i	0.187434	+	0.108215i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−9.62303	−	9.62303i	−0.363457	−	0.363457i	0.501627	−	0.865084i	$-0.332735\pi$
$701$	−9.62303	−	9.62303i	−0.363457	−	0.363457i	−0.865084	+	0.501627i	$0.832735\pi$
$702$		0			0
$703$	−7.51063			−0.283269
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−8.21961	+	2.20244i	−0.309130	+	0.0828312i
$708$		0			0
$709$	40.3893	+	10.8223i	1.51685	+	0.406439i	0.918704	−	0.394947i	$-0.129237\pi$
$709$	40.3893	+	10.8223i	1.51685	+	0.406439i	0.598148	+	0.801386i	$0.295904\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	30.4931	−	17.6052i	1.14197	−	0.659319i
$714$		0			0
$715$	−0.0300742	−	0.112239i	−0.00112471	−	0.00419749i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	48.7757			1.81903			0.909514	−	0.415674i	$-0.136454\pi$
$719$	48.7757			1.81903			0.909514	+	0.415674i	$0.136454\pi$
$720$		0			0
$721$	3.11067			0.115847
$722$		0			0
$723$		0			0
$724$		0			0
$725$	3.99343	+	14.9037i	0.148312	+	0.553509i
$726$		0			0
$727$	34.9918	−	20.2025i	1.29777	−	0.749270i	0.317755	−	0.948173i	$-0.397071\pi$
$727$	34.9918	−	20.2025i	1.29777	−	0.749270i	0.980019	+	0.198902i	$0.0637377\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	7.46535	+	2.00033i	0.276116	+	0.0739850i
$732$		0			0
$733$	−28.4006	+	7.60991i	−1.04900	+	0.281078i	−0.741838	−	0.670579i	$-0.766046\pi$
$733$	−28.4006	+	7.60991i	−1.04900	+	0.281078i	−0.307161	+	0.951658i	$0.599379\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	23.3102			0.858644
$738$		0			0
$739$	−15.4222	−	15.4222i	−0.567316	−	0.567316i	0.364060	−	0.931376i	$-0.381390\pi$
$739$	−15.4222	−	15.4222i	−0.567316	−	0.567316i	−0.931376	+	0.364060i	$0.881390\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−21.5896	−	12.4647i	−0.792045	−	0.457287i	0.0486373	−	0.998817i	$-0.484512\pi$
$743$	−21.5896	−	12.4647i	−0.792045	−	0.457287i	−0.840682	+	0.541529i	$0.817845\pi$
$744$		0			0
$745$	−0.0394451	+	0.0227736i	−0.00144515	+	0.000834361i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.57409	−	5.87459i	0.0575161	−	0.214653i
$750$		0			0
$751$	21.2809	−	36.8596i	0.776551	−	1.34503i	−0.157368	−	0.987540i	$-0.550301\pi$
$751$	21.2809	−	36.8596i	0.776551	−	1.34503i	0.933919	−	0.357486i	$-0.116366\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.124111	+	0.124111i	0.00451686	+	0.00451686i
$756$		0			0
$757$	1.80855	−	1.80855i	0.0657328	−	0.0657328i	−0.673476	−	0.739209i	$-0.735200\pi$
$757$	1.80855	−	1.80855i	0.0657328	−	0.0657328i	0.739209	+	0.673476i	$0.235200\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−18.5805	−	10.7275i	−0.673543	−	0.388870i	0.123875	−	0.992298i	$-0.460468\pi$
$761$	−18.5805	−	10.7275i	−0.673543	−	0.388870i	−0.797418	+	0.603428i	$0.793801\pi$
$762$		0			0
$763$	5.24337	+	1.40496i	0.189823	+	0.0508629i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	23.8636	+	41.3330i	0.861665	+	1.49245i
$768$		0			0
$769$	−9.98382	+	17.2925i	−0.360026	+	0.623583i	−0.987965	−	0.154680i	$-0.950565\pi$
$769$	−9.98382	+	17.2925i	−0.360026	+	0.623583i	0.627939	+	0.778263i	$0.283899\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−24.8049	+	24.8049i	−0.892171	+	0.892171i	−0.994727	−	0.102557i	$-0.967298\pi$
$773$	−24.8049	+	24.8049i	−0.892171	+	0.892171i	0.102557	+	0.994727i	$0.467298\pi$
$774$		0			0
$775$			29.2823i			1.05185i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5.51646	−	20.5877i	−0.197648	−	0.737631i
$780$		0			0
$781$	6.98342	−	26.0625i	0.249886	−	0.932589i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	0.0573027	+	0.0992512i	0.00204522	+	0.00354243i
$786$		0			0
$787$	−10.3344	+	2.76911i	−0.368383	+	0.0987080i	−0.438261	−	0.898848i	$-0.644406\pi$
$787$	−10.3344	+	2.76911i	−0.368383	+	0.0987080i	0.0698783	+	0.997556i	$0.477739\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			19.3159i			0.686794i
$792$		0			0
$793$		−	65.8254i		−	2.33753i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−46.8027	+	12.5408i	−1.65784	+	0.444216i	−0.961792	−	0.273781i	$-0.911726\pi$
$797$	−46.8027	+	12.5408i	−1.65784	+	0.444216i	−0.696046	+	0.717997i	$0.745059\pi$
$798$		0			0
$799$	−2.02389	−	3.50547i	−0.0716000	−	0.124015i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−2.11956	+	7.91029i	−0.0747975	+	0.279148i
$804$		0			0
$805$	0.0222048	+	0.0828696i	0.000782618	+	0.00292077i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	51.3577i		−	1.80564i	−0.430019	−	0.902820i	$-0.641493\pi$
$809$		−	51.3577i		−	1.80564i	0.430019	−	0.902820i	$-0.358507\pi$
$810$		0			0
$811$	2.55652	−	2.55652i	0.0897715	−	0.0897715i	−0.660795	−	0.750566i	$-0.729781\pi$
$811$	2.55652	−	2.55652i	0.0897715	−	0.0897715i	0.750566	+	0.660795i	$0.229781\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.0431843	+	0.0747975i	−0.00151268	+	0.00262004i
$816$		0			0
$817$	−14.4147	−	24.9670i	−0.504306	−	0.873484i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.179113	−	0.0479933i	−0.00625110	−	0.00167498i	0.255692	−	0.966758i	$-0.417697\pi$
$821$	−0.179113	−	0.0479933i	−0.00625110	−	0.00167498i	−0.261943	+	0.965083i	$0.584363\pi$
$822$		0			0
$823$	16.8590	+	9.73353i	0.587667	+	0.339290i	0.764174	−	0.645010i	$-0.223147\pi$
$823$	16.8590	+	9.73353i	0.587667	+	0.339290i	−0.176508	+	0.984299i	$0.556480\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	7.70731	−	7.70731i	0.268009	−	0.268009i	−0.560288	−	0.828298i	$-0.689310\pi$
$827$	7.70731	−	7.70731i	0.268009	−	0.268009i	0.828298	+	0.560288i	$0.189310\pi$
$828$		0			0
$829$	−23.8166	−	23.8166i	−0.827184	−	0.827184i	0.159942	−	0.987126i	$-0.448869\pi$
$829$	−23.8166	−	23.8166i	−0.827184	−	0.827184i	−0.987126	+	0.159942i	$0.948869\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.24837	+	7.35839i	−0.147197	+	0.254953i
$834$		0			0
$835$	−0.0220541	+	0.0823071i	−0.000763214	+	0.00284835i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	18.6769	−	10.7831i	0.644799	−	0.372275i	−0.141662	−	0.989915i	$-0.545245\pi$
$839$	18.6769	−	10.7831i	0.644799	−	0.372275i	0.786461	+	0.617640i	$0.211911\pi$
$840$		0			0
$841$	16.8674	+	9.73839i	0.581634	+	0.335807i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.120018	−	0.120018i	−0.00412873	−	0.00412873i
$846$		0			0
$847$	−9.04599			−0.310824
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−7.58094	+	2.03131i	−0.259871	+	0.0696323i
$852$		0			0
$853$	38.5967	+	10.3419i	1.32153	+	0.354102i	0.849549	−	0.527510i	$-0.176874\pi$
$853$	38.5967	+	10.3419i	1.32153	+	0.354102i	0.471976	+	0.881611i	$0.343541\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−14.5777	+	8.41643i	−0.497964	+	0.287500i	−0.727872	−	0.685713i	$-0.759491\pi$
$857$	−14.5777	+	8.41643i	−0.497964	+	0.287500i	0.229908	+	0.973212i	$0.426157\pi$
$858$		0			0
$859$	5.55582	+	20.7346i	0.189562	+	0.707455i	0.993608	+	0.112888i	$0.0360100\pi$
$859$	5.55582	+	20.7346i	0.189562	+	0.707455i	−0.804046	+	0.594568i	$0.797323\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	20.3421			0.692455			0.346227	−	0.938151i	$-0.387463\pi$
$863$	20.3421			0.692455			0.346227	+	0.938151i	$0.387463\pi$
$864$		0			0
$865$	−0.277527			−0.00943620
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.256922	+	0.958848i	0.00871550	+	0.0325267i
$870$		0			0
$871$	55.8806	−	32.2627i	1.89344	−	1.09318i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−0.137837	−	0.0369333i	−0.00465974	−	0.00124857i
$876$		0			0
$877$	−18.6156	+	4.98805i	−0.628606	+	0.168434i	−0.559037	−	0.829143i	$-0.688829\pi$
$877$	−18.6156	+	4.98805i	−0.628606	+	0.168434i	−0.0695688	+	0.997577i	$0.522162\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−37.3378			−1.25794			−0.628972	−	0.777428i	$-0.716524\pi$
$881$	−37.3378			−1.25794			−0.628972	+	0.777428i	$0.716524\pi$
$882$		0			0
$883$	16.7468	+	16.7468i	0.563576	+	0.563576i	0.930321	−	0.366745i	$-0.119528\pi$
$883$	16.7468	+	16.7468i	0.563576	+	0.563576i	−0.366745	+	0.930321i	$0.619528\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	36.4841	+	21.0641i	1.22502	+	0.707263i	0.965983	−	0.258606i	$-0.0832630\pi$
$887$	36.4841	+	21.0641i	1.22502	+	0.707263i	0.259033	+	0.965869i	$0.416596\pi$
$888$		0			0
$889$	6.05543	−	3.49611i	0.203093	−	0.117256i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−3.90788	+	14.5844i	−0.130772	+	0.488049i
$894$		0			0
$895$	0.0946055	−	0.163862i	0.00316231	−	0.00547729i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−12.7798	−	12.7798i	−0.426229	−	0.426229i
$900$		0			0
$901$	13.7042	−	13.7042i	0.456552	−	0.456552i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.0431271	+	0.0248994i	0.00143359	+	0.000827685i
$906$		0			0
$907$	−1.02635	−	0.275009i	−0.0340794	−	0.00913154i	0.241739	−	0.970341i	$-0.422282\pi$
$907$	−1.02635	−	0.275009i	−0.0340794	−	0.00913154i	−0.275818	+	0.961210i	$0.588949\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	1.91307	+	3.31354i	0.0633829	+	0.109782i	0.895976	−	0.444103i	$-0.146478\pi$
$911$	1.91307	+	3.31354i	0.0633829	+	0.109782i	−0.832593	+	0.553886i	$0.813144\pi$
$912$		0			0
$913$	10.6764	−	18.4920i	0.353336	−	0.611996i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.86616	−	5.86616i	0.193718	−	0.193718i
$918$		0			0
$919$			5.73779i			0.189272i	0.995512	+	0.0946361i	$0.0301688\pi$
$919$			5.73779i			0.189272i	−0.995512	+	0.0946361i	$0.969831\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−19.3309	−	72.1438i	−0.636284	−	2.37464i
$924$		0			0
$925$	1.68931	−	6.30460i	0.0555442	−	0.207294i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	20.2911	+	35.1451i	0.665728	+	1.15307i	0.979087	+	0.203440i	$0.0652122\pi$
$929$	20.2911	+	35.1451i	0.665728	+	1.15307i	−0.313359	+	0.949635i	$0.601454\pi$
$930$		0			0
$931$	30.6144	−	8.20310i	1.00335	−	0.268846i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	0.0341611i		−	0.00111719i
$936$		0			0
$937$			27.9974i			0.914635i	0.889304	+	0.457317i	$0.151190\pi$
$937$			27.9974i			0.914635i	−0.889304	+	0.457317i	$0.848810\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	36.1343	−	9.68215i	1.17794	−	0.315629i	0.383833	−	0.923402i	$-0.374604\pi$
$941$	36.1343	−	9.68215i	1.17794	−	0.315629i	0.794111	+	0.607773i	$0.207937\pi$
$942$		0			0
$943$	−11.1362	−	19.2885i	−0.362645	−	0.628119i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.92887	+	18.3948i	−0.160167	+	0.597751i	0.838441	+	0.544993i	$0.183468\pi$
$947$	−4.92887	+	18.3948i	−0.160167	+	0.597751i	−0.998607	+	0.0527575i	$0.983199\pi$
$948$		0			0
$949$	5.86717	+	21.8966i	0.190456	+	0.710793i
$950$		0			0
$951$		0			0
$952$		0			0
$953$			2.49861i			0.0809380i	0.999181	+	0.0404690i	$0.0128852\pi$
$953$			2.49861i			0.0809380i	−0.999181	+	0.0404690i	$0.987115\pi$
$954$		0			0
$955$	−0.0373008	+	0.0373008i	−0.00120703	+	0.00120703i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	2.57277	−	4.45617i	0.0830792	−	0.143897i
$960$		0			0
$961$	−1.64996	−	2.85782i	−0.0532246	−	0.0921877i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	0.0396865	+	0.0106340i	0.00127755	+	0.000342319i
$966$		0			0
$967$	3.08638	+	1.78192i	0.0992513	+	0.0573028i	0.548804	−	0.835951i	$-0.315083\pi$
$967$	3.08638	+	1.78192i	0.0992513	+	0.0573028i	−0.449553	+	0.893254i	$0.648417\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.578866	+	0.578866i	−0.0185767	+	0.0185767i	−0.716334	−	0.697757i	$-0.754181\pi$
$971$	−0.578866	+	0.578866i	−0.0185767	+	0.0185767i	0.697757	+	0.716334i	$0.254181\pi$
$972$		0			0
$973$	13.9917	+	13.9917i	0.448553	+	0.448553i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−10.3841	+	17.9859i	−0.332218	+	0.575418i	−0.982946	−	0.183892i	$-0.941130\pi$
$977$	−10.3841	+	17.9859i	−0.332218	+	0.575418i	0.650728	+	0.759310i	$0.274464\pi$
$978$		0			0
$979$	5.25377	−	19.6074i	0.167911	−	0.626654i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	9.13353	−	5.27325i	0.291314	−	0.168190i	−0.347220	−	0.937784i	$-0.612874\pi$
$983$	9.13353	−	5.27325i	0.291314	−	0.168190i	0.638534	+	0.769593i	$0.279541\pi$
$984$		0			0
$985$	−0.0689747	−	0.0398225i	−0.00219772	−	0.00126885i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−21.3022	−	21.3022i	−0.677369	−	0.677369i
$990$		0			0
$991$	24.1374			0.766749			0.383374	−	0.923593i	$-0.374762\pi$
$991$	24.1374			0.766749			0.383374	+	0.923593i	$0.374762\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	0.0526377	−	0.0141042i	0.00166873	−	0.000447134i
$996$		0			0
$997$	−22.4986	−	6.02848i	−0.712538	−	0.190924i	−0.115698	−	0.993284i	$-0.536910\pi$
$997$	−22.4986	−	6.02848i	−0.712538	−	0.190924i	−0.596840	+	0.802361i	$0.703577\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1728.2.bc.e.145.10		72
3.2	odd	2		576.2.bb.e.337.14		72
4.3	odd	2		432.2.y.e.253.6		72
9.2	odd	6		576.2.bb.e.529.4		72
9.7	even	3	inner	1728.2.bc.e.721.9		72
12.11	even	2		144.2.x.e.13.13	✓	72
16.5	even	4	inner	1728.2.bc.e.1009.9		72
16.11	odd	4		432.2.y.e.37.7		72
36.7	odd	6		432.2.y.e.397.7		72
36.11	even	6		144.2.x.e.61.12	yes	72
48.5	odd	4		576.2.bb.e.49.4		72
48.11	even	4		144.2.x.e.85.12	yes	72
144.11	even	12		144.2.x.e.133.13	yes	72
144.43	odd	12		432.2.y.e.181.6		72
144.101	odd	12		576.2.bb.e.241.14		72
144.133	even	12	inner	1728.2.bc.e.1585.10		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.13	✓	72	12.11	even	2
144.2.x.e.61.12	yes	72	36.11	even	6
144.2.x.e.85.12	yes	72	48.11	even	4
144.2.x.e.133.13	yes	72	144.11	even	12
432.2.y.e.37.7		72	16.11	odd	4
432.2.y.e.181.6		72	144.43	odd	12
432.2.y.e.253.6		72	4.3	odd	2
432.2.y.e.397.7		72	36.7	odd	6
576.2.bb.e.49.4		72	48.5	odd	4
576.2.bb.e.241.14		72	144.101	odd	12
576.2.bb.e.337.14		72	3.2	odd	2
576.2.bb.e.529.4		72	9.2	odd	6
1728.2.bc.e.145.10		72	1.1	even	1	trivial
1728.2.bc.e.721.9		72	9.7	even	3	inner
1728.2.bc.e.1009.9		72	16.5	even	4	inner
1728.2.bc.e.1585.10		72	144.133	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.00302457 - 0.0112878i) q^{5} +(1.05753 - 0.610563i) q^{7} +(1.83070 + 0.490535i) q^{11} +(5.06759 - 1.35786i) q^{13} +1.54238 q^{17} +(-4.06823 - 4.06823i) q^{19} +(-5.20660 - 3.00603i) q^{23} +(4.33001 - 2.49993i) q^{25} +(-0.798708 + 2.98082i) q^{29} +(-2.92831 + 5.07198i) q^{31} +(-0.0100905 - 0.0100905i) q^{35} +(0.923082 - 0.923082i) q^{37} +(3.20829 + 1.85231i) q^{41} +(4.84015 + 1.29691i) q^{43} +(-1.31218 - 2.27277i) q^{47} +(-2.75442 + 4.77080i) q^{49} +(8.88508 - 8.88508i) q^{53} -0.0221483i q^{55} +(2.35453 + 8.78724i) q^{59} +(3.24737 - 12.1194i) q^{61} +(-0.0306545 - 0.0530952i) q^{65} +(11.8800 - 3.18324i) q^{67} -14.2363i q^{71} +4.32091i q^{73} +(2.23552 - 0.599006i) q^{77} +(0.261880 + 0.453589i) q^{79} +(2.91592 - 10.8824i) q^{83} +(-0.00466503 - 0.0174101i) q^{85} -10.7103i q^{89} +(4.53005 - 4.53005i) q^{91} +(-0.0336169 + 0.0582262i) q^{95} +(8.78820 + 15.2216i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 4 q^{5} - 2 q^{11} - 16 q^{13} + 16 q^{17} - 28 q^{19} - 4 q^{29} - 28 q^{31} - 16 q^{35} + 16 q^{37} + 10 q^{43} - 56 q^{47} + 4 q^{49} + 8 q^{53} - 14 q^{59} - 32 q^{61} + 64 q^{65} + 18 q^{67}+ \cdots + 40 q^{97}+O(q^{100}) \) 72 * q - 4 * q^5 - 2 * q^11 - 16 * q^13 + 16 * q^17 - 28 * q^19 - 4 * q^29 - 28 * q^31 - 16 * q^35 + 16 * q^37 + 10 * q^43 - 56 * q^47 + 4 * q^49 + 8 * q^53 - 14 * q^59 - 32 * q^61 + 64 * q^65 + 18 * q^67 + 36 * q^77 - 44 * q^79 + 20 * q^83 - 8 * q^85 + 80 * q^91 + 48 * q^95 + 40 * q^97

Introduction

L-functions

Modular forms

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Database

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