LMFDB - Embedded newform 1584.2.cd.c.161.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1584.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			161.3
Root			$-0.0783900 + 1.17295i$ of defining polynomial
Character	$\chi$	$=$	1584.161
Dual form			1584.2.cd.c.305.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.71735 + 2.36373i) q^{5} +(-2.58586 + 0.840196i) q^{7} +(2.71994 + 1.89788i) q^{11} +(-1.67869 + 2.31052i) q^{13} +(-3.60998 + 2.62280i) q^{17} +(1.81761 + 0.590579i) q^{19} -0.816370i q^{23} +(-1.09283 + 3.36340i) q^{25} +(-2.95006 - 9.07936i) q^{29} +(-4.84281 - 3.51851i) q^{31} +(-6.42681 - 4.66935i) q^{35} +(1.83750 + 5.65524i) q^{37} +(-2.60604 + 8.02058i) q^{41} +11.8763i q^{43} +(-7.34041 - 2.38504i) q^{47} +(0.317615 - 0.230761i) q^{49} +(6.14564 - 8.45874i) q^{53} +(0.185009 + 9.68851i) q^{55} +(0.0887332 - 0.0288312i) q^{59} +(1.26024 + 1.73457i) q^{61} -8.34434 q^{65} +1.40778 q^{67} +(-2.12141 - 2.91987i) q^{71} +(-1.67338 + 0.543714i) q^{73} +(-8.62796 - 2.62237i) q^{77} +(4.19260 - 5.77063i) q^{79} +(-6.33808 + 4.60488i) q^{83} +(-12.3992 - 4.02874i) q^{85} -2.06830i q^{89} +(2.39957 - 7.38512i) q^{91} +(1.72551 + 5.31057i) q^{95} +(-1.35141 - 0.981858i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 32 q^{25} - 16 q^{31} - 12 q^{37} - 24 q^{49} - 16 q^{55} - 96 q^{67} - 20 q^{73} - 100 q^{85} + 72 q^{91} + 60 q^{97}+O(q^{100}) $ 16 * q - 32 * q^25 - 16 * q^31 - 12 * q^37 - 24 * q^49 - 16 * q^55 - 96 * q^67 - 20 * q^73 - 100 * q^85 + 72 * q^91 + 60 * q^97

Character values

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

$n$	$145$	$353$	$991$	$1189$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.71735	+	2.36373i	0.768021	+	1.05709i	0.996504	+	0.0835427i	$0.0266235\pi$
$5$	1.71735	+	2.36373i	0.768021	+	1.05709i	−0.228483	+	0.973548i	$0.573376\pi$
$6$		0			0
$7$	−2.58586	+	0.840196i	−0.977363	+	0.317564i	−0.753785	−	0.657122i	$-0.771774\pi$
$7$	−2.58586	+	0.840196i	−0.977363	+	0.317564i	−0.223578	+	0.974686i	$0.571774\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.71994	+	1.89788i	0.820092	+	0.572232i
$11$	2.71994	+	1.89788i	0.820092	+	0.572232i
$12$		0			0
$13$	−1.67869	+	2.31052i	−0.465586	+	0.640824i	−0.975655	−	0.219309i	$-0.929620\pi$
$13$	−1.67869	+	2.31052i	−0.465586	+	0.640824i	0.510070	+	0.860133i	$0.329620\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.60998	+	2.62280i	−0.875549	+	0.636124i	−0.932070	−	0.362278i	$-0.881999\pi$
$17$	−3.60998	+	2.62280i	−0.875549	+	0.636124i	0.0565211	+	0.998401i	$0.481999\pi$
$18$		0			0
$19$	1.81761	+	0.590579i	0.416989	+	0.135488i	0.509995	−	0.860178i	$-0.329647\pi$
$19$	1.81761	+	0.590579i	0.416989	+	0.135488i	−0.0930053	+	0.995666i	$0.529647\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	0.816370i		−	0.170225i	−0.996371	−	0.0851124i	$-0.972875\pi$
$23$		−	0.816370i		−	0.170225i	0.996371	−	0.0851124i	$-0.0271249\pi$
$24$		0			0
$25$	−1.09283	+	3.36340i	−0.218567	+	0.672680i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.95006	−	9.07936i	−0.547813	−	1.68599i	−0.714207	−	0.699935i	$-0.753212\pi$
$29$	−2.95006	−	9.07936i	−0.547813	−	1.68599i	0.166394	−	0.986059i	$-0.446788\pi$
$30$		0			0
$31$	−4.84281	−	3.51851i	−0.869795	−	0.631943i	0.0607369	−	0.998154i	$-0.480655\pi$
$31$	−4.84281	−	3.51851i	−0.869795	−	0.631943i	−0.930532	+	0.366211i	$0.880655\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−6.42681	−	4.66935i	−1.08633	−	0.789265i
$36$		0			0
$37$	1.83750	+	5.65524i	0.302083	+	0.929717i	0.980750	+	0.195270i	$0.0625583\pi$
$37$	1.83750	+	5.65524i	0.302083	+	0.929717i	−0.678666	+	0.734447i	$0.737442\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−2.60604	+	8.02058i	−0.406996	+	1.25260i	0.512221	+	0.858853i	$0.328823\pi$
$41$	−2.60604	+	8.02058i	−0.406996	+	1.25260i	−0.919217	+	0.393751i	$0.871177\pi$
$42$		0			0
$43$			11.8763i			1.81112i	0.424214	+	0.905562i	$0.360550\pi$
$43$			11.8763i			1.81112i	−0.424214	+	0.905562i	$0.639450\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.34041	−	2.38504i	−1.07071	−	0.347894i	−0.279945	−	0.960016i	$-0.590316\pi$
$47$	−7.34041	−	2.38504i	−1.07071	−	0.347894i	−0.790764	+	0.612122i	$0.790316\pi$
$48$		0			0
$49$	0.317615	−	0.230761i	0.0453735	−	0.0329658i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.14564	−	8.45874i	0.844168	−	1.16190i	−0.140950	−	0.990017i	$-0.545016\pi$
$53$	6.14564	−	8.45874i	0.844168	−	1.16190i	0.985118	−	0.171881i	$-0.0549845\pi$
$54$		0			0
$55$	0.185009	+	9.68851i	0.0249466	+	1.30640i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.0887332	−	0.0288312i	0.0115521	−	0.00375350i	−0.303235	−	0.952916i	$-0.598067\pi$
$59$	0.0887332	−	0.0288312i	0.0115521	−	0.00375350i	0.314787	+	0.949162i	$0.398067\pi$
$60$		0			0
$61$	1.26024	+	1.73457i	0.161357	+	0.222089i	0.882038	−	0.471177i	$-0.156171\pi$
$61$	1.26024	+	1.73457i	0.161357	+	0.222089i	−0.720681	+	0.693267i	$0.756171\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−8.34434			−1.03499
$66$		0			0
$67$	1.40778			0.171988			0.0859941	−	0.996296i	$-0.472593\pi$
$67$	1.40778			0.171988			0.0859941	+	0.996296i	$0.472593\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.12141	−	2.91987i	−0.251765	−	0.346525i	0.664363	−	0.747410i	$-0.268703\pi$
$71$	−2.12141	−	2.91987i	−0.251765	−	0.346525i	−0.916128	+	0.400885i	$0.868703\pi$
$72$		0			0
$73$	−1.67338	+	0.543714i	−0.195854	+	0.0636369i	−0.405302	−	0.914183i	$-0.632833\pi$
$73$	−1.67338	+	0.543714i	−0.195854	+	0.0636369i	0.209447	+	0.977820i	$0.432833\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−8.62796	−	2.62237i	−0.983247	−	0.298846i
$78$		0			0
$79$	4.19260	−	5.77063i	0.471705	−	0.649246i	−0.505180	−	0.863014i	$-0.668574\pi$
$79$	4.19260	−	5.77063i	0.471705	−	0.649246i	0.976884	+	0.213768i	$0.0685737\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−6.33808	+	4.60488i	−0.695695	+	0.505452i	−0.878527	−	0.477692i	$-0.841473\pi$
$83$	−6.33808	+	4.60488i	−0.695695	+	0.505452i	0.182833	+	0.983144i	$0.441473\pi$
$84$		0			0
$85$	−12.3992	−	4.02874i	−1.34488	−	0.436978i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	2.06830i		−	0.219240i	−0.993974	−	0.109620i	$-0.965037\pi$
$89$		−	2.06830i		−	0.219240i	0.993974	−	0.109620i	$-0.0349633\pi$
$90$		0			0
$91$	2.39957	−	7.38512i	0.251543	−	0.774171i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.72551	+	5.31057i	0.177034	+	0.544853i
$96$		0			0
$97$	−1.35141	−	0.981858i	−0.137215	−	0.0996926i	0.517060	−	0.855949i	$-0.327026\pi$
$97$	−1.35141	−	0.981858i	−0.137215	−	0.0996926i	−0.654275	+	0.756256i	$0.727026\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.31972	−	5.31809i	−0.728339	−	0.529170i	0.160698	−	0.987004i	$-0.448625\pi$
$101$	−7.31972	−	5.31809i	−0.728339	−	0.529170i	−0.889038	+	0.457834i	$0.848625\pi$
$102$		0			0
$103$	5.12132	+	15.7618i	0.504618	+	1.55306i	0.801411	+	0.598114i	$0.204083\pi$
$103$	5.12132	+	15.7618i	0.504618	+	1.55306i	−0.296793	+	0.954942i	$0.595917\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.19803	+	6.76484i	−0.212492	+	0.653982i	0.786830	+	0.617169i	$0.211721\pi$
$107$	−2.19803	+	6.76484i	−0.212492	+	0.653982i	−0.999322	+	0.0368130i	$0.988279\pi$
$108$		0			0
$109$			8.62045i			0.825690i	0.910801	+	0.412845i	$0.135465\pi$
$109$			8.62045i			0.825690i	−0.910801	+	0.412845i	$0.864535\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	10.8495	+	3.52523i	1.02064	+	0.331626i	0.771083	−	0.636735i	$-0.219715\pi$
$113$	10.8495	+	3.52523i	1.02064	+	0.331626i	0.249556	+	0.968360i	$0.419715\pi$
$114$		0			0
$115$	1.92967	−	1.40199i	0.179943	−	0.130736i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	7.13123	−	9.81529i	0.653719	−	0.899767i
$120$		0			0
$121$	3.79611	+	10.3242i	0.345101	+	0.938566i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	4.06670	−	1.32135i	0.363737	−	0.118185i
$126$		0			0
$127$	1.69463	+	2.33246i	0.150374	+	0.206973i	0.877558	−	0.479470i	$-0.159171\pi$
$127$	1.69463	+	2.33246i	0.150374	+	0.206973i	−0.727184	+	0.686443i	$0.759171\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.10155			−0.183613			−0.0918067	−	0.995777i	$-0.529264\pi$
$131$	−2.10155			−0.183613			−0.0918067	+	0.995777i	$0.529264\pi$
$132$		0			0
$133$	−5.19630			−0.450576
$134$		0			0
$135$		0			0
$136$		0			0
$137$	2.98245	+	4.10498i	0.254808	+	0.350712i	0.917188	−	0.398455i	$-0.130454\pi$
$137$	2.98245	+	4.10498i	0.254808	+	0.350712i	−0.662380	+	0.749168i	$0.730454\pi$
$138$		0			0
$139$	−16.6282	+	5.40283i	−1.41039	+	0.458262i	−0.912535	−	0.409000i	$-0.865878\pi$
$139$	−16.6282	+	5.40283i	−1.41039	+	0.458262i	−0.497852	+	0.867262i	$0.665878\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.95103	+	3.09852i	−0.748523	+	0.259111i
$144$		0			0
$145$	16.3948	−	22.5656i	1.36152	−	1.87397i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.57623	−	3.32483i	0.374900	−	0.272381i	−0.384340	−	0.923192i	$-0.625571\pi$
$149$	4.57623	−	3.32483i	0.374900	−	0.272381i	0.759240	+	0.650811i	$0.225571\pi$
$150$		0			0
$151$	−8.72640	−	2.83538i	−0.710145	−	0.230740i	−0.0683995	−	0.997658i	$-0.521789\pi$
$151$	−8.72640	−	2.83538i	−0.710145	−	0.230740i	−0.641745	+	0.766918i	$0.721789\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$		−	17.4896i		−	1.40480i
$156$		0			0
$157$	−0.943653	+	2.90426i	−0.0753117	+	0.231785i	−0.981625	−	0.190821i	$-0.938885\pi$
$157$	−0.943653	+	2.90426i	−0.0753117	+	0.231785i	0.906313	+	0.422607i	$0.138885\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	0.685911	+	2.11102i	0.0540573	+	0.166371i
$162$		0			0
$163$	6.39488	+	4.64615i	0.500885	+	0.363914i	0.809355	−	0.587320i	$-0.199817\pi$
$163$	6.39488	+	4.64615i	0.500885	+	0.363914i	−0.308470	+	0.951234i	$0.599817\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	13.3065	+	9.66777i	1.02969	+	0.748115i	0.968247	−	0.249996i	$-0.0804292\pi$
$167$	13.3065	+	9.66777i	1.02969	+	0.748115i	0.0614446	+	0.998110i	$0.480429\pi$
$168$		0			0
$169$	1.49672	+	4.60642i	0.115132	+	0.354340i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−4.79669	+	14.7627i	−0.364686	+	1.12239i	0.585492	+	0.810678i	$0.300901\pi$
$173$	−4.79669	+	14.7627i	−0.364686	+	1.12239i	−0.950178	+	0.311709i	$0.899099\pi$
$174$		0			0
$175$		−	9.61547i		−	0.726861i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.93538	+	1.60360i	0.368888	+	0.119859i	0.487594	−	0.873071i	$-0.337875\pi$
$179$	4.93538	+	1.60360i	0.368888	+	0.119859i	−0.118706	+	0.992929i	$0.537875\pi$
$180$		0			0
$181$	−4.29773	+	3.12248i	−0.319448	+	0.232092i	−0.735940	−	0.677047i	$-0.763259\pi$
$181$	−4.29773	+	3.12248i	−0.319448	+	0.232092i	0.416492	+	0.909139i	$0.363259\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−10.2118	+	14.0554i	−0.750788	+	1.03337i
$186$		0			0
$187$	−14.7967	+	0.282553i	−1.08204	+	0.0206624i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	10.3662	−	3.36817i	0.750069	−	0.243712i	0.0910582	−	0.995846i	$-0.470975\pi$
$191$	10.3662	−	3.36817i	0.750069	−	0.243712i	0.659011	+	0.752133i	$0.270975\pi$
$192$		0			0
$193$	9.03216	+	12.4317i	0.650149	+	0.894853i	0.999106	−	0.0422855i	$-0.0134639\pi$
$193$	9.03216	+	12.4317i	0.650149	+	0.894853i	−0.348956	+	0.937139i	$0.613464\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	7.24149			0.515935			0.257967	−	0.966154i	$-0.416947\pi$
$197$	7.24149			0.515935			0.257967	+	0.966154i	$0.416947\pi$
$198$		0			0
$199$	11.3726			0.806181			0.403090	−	0.915160i	$-0.367936\pi$
$199$	11.3726			0.806181			0.403090	+	0.915160i	$0.367936\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	15.2569	+	20.9993i	1.07082	+	1.47386i
$204$		0			0
$205$	−23.4339	+	7.61415i	−1.63670	+	0.531795i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	3.82295	+	5.05595i	0.264439	+	0.349727i
$210$		0			0
$211$	2.17376	−	2.99193i	0.149648	−	0.205973i	−0.727611	−	0.685990i	$-0.759369\pi$
$211$	2.17376	−	2.99193i	0.149648	−	0.205973i	0.877259	+	0.480017i	$0.159369\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−28.0724	+	20.3958i	−1.91452	+	1.39098i
$216$		0			0
$217$	15.4791	+	5.02946i	1.05079	+	0.341422i
$218$		0			0
$219$		0			0
$220$		0			0
$221$		−	12.7438i		−	0.857243i
$222$		0			0
$223$	0.0875209	−	0.269362i	0.00586083	−	0.0180378i	−0.948083	−	0.318022i	$-0.896981\pi$
$223$	0.0875209	−	0.269362i	0.00586083	−	0.0180378i	0.953944	+	0.299984i	$0.0969814\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.64140	−	17.3625i	−0.374433	−	1.15239i	−0.943860	−	0.330345i	$-0.892835\pi$
$227$	−5.64140	−	17.3625i	−0.374433	−	1.15239i	0.569427	−	0.822042i	$-0.307165\pi$
$228$		0			0
$229$	−21.3385	−	15.5033i	−1.41009	−	1.02449i	−0.993310	−	0.115479i	$-0.963160\pi$
$229$	−21.3385	−	15.5033i	−1.41009	−	1.02449i	−0.416777	−	0.909009i	$-0.636840\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−8.73916	−	6.34937i	−0.572521	−	0.415961i	0.263499	−	0.964660i	$-0.415123\pi$
$233$	−8.73916	−	6.34937i	−0.572521	−	0.415961i	−0.836020	+	0.548699i	$0.815123\pi$
$234$		0			0
$235$	−6.96844	−	21.4467i	−0.454571	−	1.39903i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.29393	−	7.06000i	0.148382	−	0.456673i	−0.849048	−	0.528315i	$-0.822824\pi$
$239$	2.29393	−	7.06000i	0.148382	−	0.456673i	0.997430	+	0.0716420i	$0.0228239\pi$
$240$		0			0
$241$			2.66873i			0.171908i	0.996299	+	0.0859539i	$0.0273938\pi$
$241$			2.66873i			0.171908i	−0.996299	+	0.0859539i	$0.972606\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.09091	+	0.354458i	0.0696957	+	0.0226455i
$246$		0			0
$247$	−4.41576	+	3.20824i	−0.280968	+	0.204135i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	14.2630	−	19.6313i	0.900271	−	1.23912i	−0.0701107	−	0.997539i	$-0.522335\pi$
$251$	14.2630	−	19.6313i	0.900271	−	1.23912i	0.970382	−	0.241577i	$-0.0776647\pi$
$252$		0			0
$253$	1.54937	−	2.22047i	0.0974081	−	0.139600i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	15.9360	−	5.17791i	0.994059	−	0.322989i	0.233570	−	0.972340i	$-0.424959\pi$
$257$	15.9360	−	5.17791i	0.994059	−	0.322989i	0.760489	+	0.649351i	$0.224959\pi$
$258$		0			0
$259$	−9.50303	−	13.0798i	−0.590490	−	0.812739i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	10.9146			0.673021			0.336511	−	0.941680i	$-0.390753\pi$
$263$	10.9146			0.673021			0.336511	+	0.941680i	$0.390753\pi$
$264$		0			0
$265$	30.5484			1.87657
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−9.22041	−	12.6908i	−0.562178	−	0.773772i	0.429423	−	0.903103i	$-0.358717\pi$
$269$	−9.22041	−	12.6908i	−0.562178	−	0.773772i	−0.991601	+	0.129331i	$0.958717\pi$
$270$		0			0
$271$	2.76289	−	0.897717i	0.167834	−	0.0545324i	−0.223895	−	0.974613i	$-0.571877\pi$
$271$	2.76289	−	0.897717i	0.167834	−	0.0545324i	0.391728	+	0.920081i	$0.371877\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−9.35577	+	7.07416i	−0.564174	+	0.426588i
$276$		0			0
$277$	12.4111	−	17.0824i	0.745709	−	1.02638i	−0.252561	−	0.967581i	$-0.581273\pi$
$277$	12.4111	−	17.0824i	0.745709	−	1.02638i	0.998270	−	0.0587992i	$-0.0187272\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	2.50015	−	1.81647i	0.149147	−	0.108361i	−0.510709	−	0.859753i	$-0.670617\pi$
$281$	2.50015	−	1.81647i	0.149147	−	0.108361i	0.659856	+	0.751392i	$0.270617\pi$
$282$		0			0
$283$	21.3272	+	6.92961i	1.26777	+	0.411923i	0.864256	−	0.503052i	$-0.167789\pi$
$283$	21.3272	+	6.92961i	1.26777	+	0.411923i	0.403512	+	0.914975i	$0.367789\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	22.9297i		−	1.35350i
$288$		0			0
$289$	0.899570	−	2.76859i	0.0529159	−	0.162858i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	6.40930	+	19.7258i	0.374435	+	1.15239i	0.943859	+	0.330349i	$0.107167\pi$
$293$	6.40930	+	19.7258i	0.374435	+	1.15239i	−0.569423	+	0.822044i	$0.692833\pi$
$294$		0			0
$295$	0.220535	+	0.160228i	0.0128400	+	0.00932883i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.88624	+	1.37043i	0.109084	+	0.0792543i
$300$		0			0
$301$	−9.97845	−	30.7105i	−0.575148	−	1.77012i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.93578	+	5.95772i	−0.110843	+	0.341138i
$306$		0			0
$307$			15.0077i			0.856533i	0.903652	+	0.428267i	$0.140876\pi$
$307$			15.0077i			0.856533i	−0.903652	+	0.428267i	$0.859124\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.95824	+	0.636270i	0.111042	+	0.0360796i	0.364011	−	0.931395i	$-0.381407\pi$
$311$	1.95824	+	0.636270i	0.111042	+	0.0360796i	−0.252969	+	0.967474i	$0.581407\pi$
$312$		0			0
$313$	20.1223	−	14.6197i	1.13738	−	0.826355i	0.150628	−	0.988591i	$-0.451870\pi$
$313$	20.1223	−	14.6197i	1.13738	−	0.826355i	0.986752	+	0.162236i	$0.0518705\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	0.254351	−	0.350085i	0.0142858	−	0.0196627i	−0.801814	−	0.597573i	$-0.796132\pi$
$317$	0.254351	−	0.350085i	0.0142858	−	0.0196627i	0.816100	+	0.577910i	$0.196132\pi$
$318$		0			0
$319$	9.20754	−	30.2941i	0.515523	−	1.69615i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−8.11053	+	2.63527i	−0.451282	+	0.146630i
$324$		0			0
$325$	−5.93668	−	8.17113i	−0.329308	−	0.453253i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	20.9852			1.15695
$330$		0			0
$331$	17.3090			0.951391			0.475696	−	0.879610i	$-0.342196\pi$
$331$	17.3090			0.951391			0.475696	+	0.879610i	$0.342196\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.41766	+	3.32762i	0.132091	+	0.181807i
$336$		0			0
$337$	23.8381	−	7.74548i	1.29855	−	0.421923i	0.423471	−	0.905910i	$-0.360812\pi$
$337$	23.8381	−	7.74548i	1.29855	−	0.421923i	0.875076	+	0.483986i	$0.160812\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−6.49444	−	18.7612i	−0.351694	−	1.01598i
$342$		0			0
$343$	10.5596	−	14.5341i	0.570166	−	0.784766i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	16.8866	−	12.2688i	0.906519	−	0.658625i	−0.0336127	−	0.999435i	$-0.510701\pi$
$347$	16.8866	−	12.2688i	0.906519	−	0.658625i	0.940132	+	0.340810i	$0.110701\pi$
$348$		0			0
$349$	−17.1385	−	5.56865i	−0.917405	−	0.298083i	−0.188003	−	0.982168i	$-0.560202\pi$
$349$	−17.1385	−	5.56865i	−0.917405	−	0.298083i	−0.729402	+	0.684085i	$0.760202\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	16.2953i		−	0.867313i	−0.901078	−	0.433656i	$-0.857223\pi$
$353$		−	16.2953i		−	0.867313i	0.901078	−	0.433656i	$-0.142777\pi$
$354$		0			0
$355$	3.25858	−	10.0289i	0.172947	−	0.532277i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	7.65875	+	23.5712i	0.404213	+	1.24404i	0.921550	+	0.388259i	$0.126923\pi$
$359$	7.65875	+	23.5712i	0.404213	+	1.24404i	−0.517337	+	0.855782i	$0.673077\pi$
$360$		0			0
$361$	−12.4164	−	9.02103i	−0.653494	−	0.474791i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−4.15897	−	3.02167i	−0.217690	−	0.158161i
$366$		0			0
$367$	−2.76683	−	8.51544i	−0.144428	−	0.444502i	0.852509	−	0.522712i	$-0.175080\pi$
$367$	−2.76683	−	8.51544i	−0.144428	−	0.444502i	−0.996937	+	0.0782097i	$0.975080\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−8.78474	+	27.0367i	−0.456081	+	1.40367i
$372$		0			0
$373$			16.9007i			0.875088i	0.899197	+	0.437544i	$0.144152\pi$
$373$			16.9007i			0.875088i	−0.899197	+	0.437544i	$0.855848\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	25.9303	+	8.42527i	1.33548	+	0.433923i
$378$		0			0
$379$	15.9625	−	11.5975i	0.819940	−	0.595722i	−0.0967550	−	0.995308i	$-0.530846\pi$
$379$	15.9625	−	11.5975i	0.819940	−	0.595722i	0.916695	+	0.399587i	$0.130846\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.93889	+	4.04503i	−0.150170	+	0.206691i	−0.877474	−	0.479624i	$-0.840773\pi$
$383$	−2.93889	+	4.04503i	−0.150170	+	0.206691i	0.727304	+	0.686315i	$0.240773\pi$
$384$		0			0
$385$	−8.61865	−	24.8977i	−0.439247	−	1.26890i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−9.37115	+	3.04487i	−0.475136	+	0.154381i	−0.536789	−	0.843716i	$-0.680363\pi$
$389$	−9.37115	+	3.04487i	−0.475136	+	0.154381i	0.0616527	+	0.998098i	$0.480363\pi$
$390$		0			0
$391$	2.14118	+	2.94708i	0.108284	+	0.149040i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	20.8403			1.04859
$396$		0			0
$397$	−19.0245			−0.954812			−0.477406	−	0.878683i	$-0.658423\pi$
$397$	−19.0245			−0.954812			−0.477406	+	0.878683i	$0.658423\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	18.0482	+	24.8413i	0.901286	+	1.24051i	0.970056	+	0.242881i	$0.0780926\pi$
$401$	18.0482	+	24.8413i	0.901286	+	1.24051i	−0.0687699	+	0.997633i	$0.521907\pi$
$402$		0			0
$403$	16.2592	−	5.28293i	0.809928	−	0.263162i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−5.73509	+	18.8693i	−0.284278	+	0.935315i
$408$		0			0
$409$	−6.97905	+	9.60583i	−0.345092	+	0.474978i	−0.945920	−	0.324400i	$-0.894838\pi$
$409$	−6.97905	+	9.60583i	−0.345092	+	0.474978i	0.600828	+	0.799378i	$0.294838\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−0.205228	+	0.149107i	−0.0100986	+	0.00733706i
$414$		0			0
$415$	−21.7694	−	7.07330i	−1.06862	−	0.347215i
$416$		0			0
$417$		0			0
$418$		0			0
$419$			10.0629i			0.491606i	0.969320	+	0.245803i	$0.0790516\pi$
$419$			10.0629i			0.491606i	−0.969320	+	0.245803i	$0.920948\pi$
$420$		0			0
$421$	−1.93337	+	5.95029i	−0.0942265	+	0.289999i	−0.987051	−	0.160405i	$-0.948720\pi$
$421$	−1.93337	+	5.95029i	−0.0942265	+	0.289999i	0.892825	+	0.450404i	$0.148720\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−4.87643	−	15.0081i	−0.236541	−	0.728000i
$426$		0			0
$427$	−4.71618	−	3.42651i	−0.228232	−	0.165820i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−15.8885	−	11.5436i	−0.765321	−	0.556038i	0.135217	−	0.990816i	$-0.456827\pi$
$431$	−15.8885	−	11.5436i	−0.765321	−	0.556038i	−0.900538	+	0.434778i	$0.856827\pi$
$432$		0			0
$433$	9.66882	+	29.7576i	0.464654	+	1.43006i	0.859418	+	0.511274i	$0.170826\pi$
$433$	9.66882	+	29.7576i	0.464654	+	1.43006i	−0.394764	+	0.918783i	$0.629174\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.482131	−	1.48385i	0.0230634	−	0.0709820i
$438$		0			0
$439$			20.1935i			0.963782i	0.876231	+	0.481891i	$0.160050\pi$
$439$			20.1935i			0.963782i	−0.876231	+	0.481891i	$0.839950\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	23.1752	+	7.53009i	1.10109	+	0.357765i	0.802521	−	0.596624i	$-0.203491\pi$
$443$	23.1752	+	7.53009i	1.10109	+	0.357765i	0.298567	+	0.954389i	$0.403491\pi$
$444$		0			0
$445$	4.88890	−	3.55199i	0.231756	−	0.168381i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.94082	+	2.67131i	−0.0915930	+	0.126067i	−0.852354	−	0.522965i	$-0.824826\pi$
$449$	−1.94082	+	2.67131i	−0.0915930	+	0.126067i	0.760761	+	0.649032i	$0.224826\pi$
$450$		0			0
$451$	−22.3104	+	16.8695i	−1.05055	+	0.794354i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	21.5773	−	7.01089i	1.01156	−	0.328675i
$456$		0			0
$457$	−9.17968	−	12.6347i	−0.429407	−	0.591028i	0.538410	−	0.842683i	$-0.319025\pi$
$457$	−9.17968	−	12.6347i	−0.429407	−	0.591028i	−0.967817	+	0.251655i	$0.919025\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	36.5685			1.70316			0.851582	−	0.524221i	$-0.175644\pi$
$461$	36.5685			1.70316			0.851582	+	0.524221i	$0.175644\pi$
$462$		0			0
$463$	−4.45531			−0.207056			−0.103528	−	0.994627i	$-0.533013\pi$
$463$	−4.45531			−0.207056			−0.103528	+	0.994627i	$0.533013\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−24.4676	−	33.6768i	−1.13223	−	1.55838i	−0.783769	−	0.621052i	$-0.786706\pi$
$467$	−24.4676	−	33.6768i	−1.13223	−	1.55838i	−0.348458	−	0.937325i	$-0.613294\pi$
$468$		0			0
$469$	−3.64033	+	1.18282i	−0.168095	+	0.0546173i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−22.5398	+	32.3029i	−1.03638	+	1.48529i
$474$		0			0
$475$	−3.97270	+	5.46796i	−0.182280	+	0.250887i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	2.84896	−	2.06989i	0.130172	−	0.0945756i	−0.520794	−	0.853682i	$-0.674364\pi$
$479$	2.84896	−	2.06989i	0.130172	−	0.0945756i	0.650966	+	0.759107i	$0.274364\pi$
$480$		0			0
$481$	−16.1512	−	5.24783i	−0.736430	−	0.239281i
$482$		0			0
$483$		0			0
$484$		0			0
$485$		−	4.88056i		−	0.221615i
$486$		0			0
$487$	−9.85775	+	30.3390i	−0.446697	+	1.37479i	0.433914	+	0.900954i	$0.357132\pi$
$487$	−9.85775	+	30.3390i	−0.446697	+	1.37479i	−0.880611	+	0.473839i	$0.842868\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	7.54595	+	23.2241i	0.340544	+	1.04809i	0.963926	+	0.266170i	$0.0857581\pi$
$491$	7.54595	+	23.2241i	0.340544	+	1.04809i	−0.623382	+	0.781917i	$0.714242\pi$
$492$		0			0
$493$	34.4630	+	25.0389i	1.55214	+	1.12769i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.93893	+	5.76797i	0.356110	+	0.258729i
$498$		0			0
$499$	7.19057	+	22.1303i	0.321894	+	0.990689i	0.972823	+	0.231550i	$0.0743797\pi$
$499$	7.19057	+	22.1303i	0.321894	+	0.990689i	−0.650929	+	0.759139i	$0.725620\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	11.2856	−	34.7334i	0.503199	−	1.54869i	−0.300579	−	0.953757i	$-0.597180\pi$
$503$	11.2856	−	34.7334i	0.503199	−	1.54869i	0.803778	−	0.594930i	$-0.202820\pi$
$504$		0			0
$505$		−	26.4348i		−	1.17633i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	23.6347	+	7.67938i	1.04759	+	0.340383i	0.781722	−	0.623627i	$-0.214341\pi$
$509$	23.6347	+	7.67938i	1.04759	+	0.340383i	0.265868	+	0.964009i	$0.414341\pi$
$510$		0			0
$511$	3.87030	−	2.81193i	0.171212	−	0.124393i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−28.4615	+	39.1739i	−1.25416	+	1.72621i
$516$		0			0
$517$	−15.4389	−	20.4184i	−0.679003	−	0.897999i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−9.26334	+	3.00984i	−0.405834	+	0.131864i	−0.504819	−	0.863225i	$-0.668441\pi$
$521$	−9.26334	+	3.00984i	−0.405834	+	0.131864i	0.0989844	+	0.995089i	$0.468441\pi$
$522$		0			0
$523$	−19.5526	−	26.9118i	−0.854975	−	1.17677i	−0.982744	−	0.184968i	$-0.940782\pi$
$523$	−19.5526	−	26.9118i	−0.854975	−	1.17677i	0.127769	−	0.991804i	$-0.459218\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	26.7108			1.16354
$528$		0			0
$529$	22.3335			0.971023
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−14.1570	−	19.4854i	−0.613207	−	0.844007i
$534$		0			0
$535$	−19.7650	+	6.42205i	−0.854517	+	0.277649i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	1.30185	−	0.0248597i	0.0560746	−	0.00107078i
$540$		0			0
$541$	−6.85075	+	9.42925i	−0.294537	+	0.405395i	−0.930481	−	0.366340i	$-0.880611\pi$
$541$	−6.85075	+	9.42925i	−0.294537	+	0.405395i	0.635944	+	0.771735i	$0.280611\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−20.3764	+	14.8043i	−0.872829	+	0.634147i
$546$		0			0
$547$	−0.773004	−	0.251164i	−0.0330513	−	0.0107390i	0.292445	−	0.956282i	$-0.405531\pi$
$547$	−0.773004	−	0.251164i	−0.0330513	−	0.0107390i	−0.325496	+	0.945543i	$0.605531\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	18.2450i		−	0.777264i
$552$		0			0
$553$	−5.99302	+	18.4446i	−0.254849	+	0.784345i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−2.14843	−	6.61219i	−0.0910320	−	0.280168i	0.895167	−	0.445730i	$-0.147056\pi$
$557$	−2.14843	−	6.61219i	−0.0910320	−	0.280168i	−0.986199	+	0.165563i	$0.947056\pi$
$558$		0			0
$559$	−27.4405	−	19.9367i	−1.16061	−	0.843233i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−23.2654	−	16.9033i	−0.980519	−	0.712388i	−0.0226941	−	0.999742i	$-0.507224\pi$
$563$	−23.2654	−	16.9033i	−0.980519	−	0.712388i	−0.957824	+	0.287354i	$0.907224\pi$
$564$		0			0
$565$	10.2998	+	31.6994i	0.433314	+	1.33360i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	3.22890	−	9.93752i	0.135362	−	0.416602i	−0.860284	−	0.509815i	$-0.829714\pi$
$569$	3.22890	−	9.93752i	0.135362	−	0.416602i	0.995646	+	0.0932129i	$0.0297137\pi$
$570$		0			0
$571$		−	21.2530i		−	0.889409i	−0.895677	−	0.444704i	$-0.853309\pi$
$571$		−	21.2530i		−	0.889409i	0.895677	−	0.444704i	$-0.146691\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	2.74578	+	0.892157i	0.114507	+	0.0372055i
$576$		0			0
$577$	−12.6856	+	9.21665i	−0.528110	+	0.383694i	−0.819650	−	0.572864i	$-0.805832\pi$
$577$	−12.6856	+	9.21665i	−0.528110	+	0.383694i	0.291541	+	0.956558i	$0.405832\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	12.5204	−	17.2328i	0.519432	−	0.714937i
$582$		0			0
$583$	32.7694	−	11.3436i	1.35717	−	0.469803i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−19.1691	+	6.22843i	−0.791195	+	0.257075i	−0.676613	−	0.736339i	$-0.736553\pi$
$587$	−19.1691	+	6.22843i	−0.791195	+	0.257075i	−0.114582	+	0.993414i	$0.536553\pi$
$588$		0			0
$589$	−6.72441	−	9.25536i	−0.277075	−	0.381360i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−40.5694			−1.66599			−0.832993	−	0.553284i	$-0.813374\pi$
$593$	−40.5694			−1.66599			−0.832993	+	0.553284i	$0.813374\pi$
$594$		0			0
$595$	35.4475			1.45320
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−6.42889	−	8.84861i	−0.262678	−	0.361545i	0.657223	−	0.753696i	$-0.271731\pi$
$599$	−6.42889	−	8.84861i	−0.262678	−	0.361545i	−0.919901	+	0.392151i	$0.871731\pi$
$600$		0			0
$601$	15.5556	−	5.05433i	0.634527	−	0.206170i	0.0259478	−	0.999663i	$-0.491740\pi$
$601$	15.5556	−	5.05433i	0.634527	−	0.206170i	0.608580	+	0.793493i	$0.291740\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−17.8844	+	26.7032i	−0.727104	+	1.08564i
$606$		0			0
$607$	14.0272	−	19.3068i	0.569348	−	0.783641i	−0.423129	−	0.906069i	$-0.639068\pi$
$607$	14.0272	−	19.3068i	0.569348	−	0.783641i	0.992477	+	0.122429i	$0.0390683\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	17.8330	−	12.9564i	0.721445	−	0.524161i
$612$		0			0
$613$	0.0461533	+	0.0149961i	0.00186411	+	0.000605687i	0.309949	−	0.950753i	$-0.399688\pi$
$613$	0.0461533	+	0.0149961i	0.00186411	+	0.000605687i	−0.308085	+	0.951359i	$0.599688\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	8.24561i		−	0.331956i	−0.986129	−	0.165978i	$-0.946922\pi$
$617$		−	8.24561i		−	0.331956i	0.986129	−	0.165978i	$-0.0530780\pi$
$618$		0			0
$619$	0.537464	−	1.65414i	0.0216025	−	0.0664857i	−0.939674	−	0.342071i	$-0.888872\pi$
$619$	0.537464	−	1.65414i	0.0216025	−	0.0664857i	0.961277	+	0.275585i	$0.0888717\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.73778	+	5.34834i	0.0696227	+	0.214277i
$624$		0			0
$625$	24.4126	+	17.7368i	0.976506	+	0.709473i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−21.4659	−	15.5959i	−0.855903	−	0.621850i
$630$		0			0
$631$	8.14182	+	25.0580i	0.324121	+	0.997541i	0.971836	+	0.235659i	$0.0757248\pi$
$631$	8.14182	+	25.0580i	0.324121	+	0.997541i	−0.647715	+	0.761883i	$0.724275\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.60303	+	8.01130i	−0.103298	+	0.317919i
$636$		0			0
$637$			1.12123i			0.0444249i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	8.27017	+	2.68714i	0.326652	+	0.106136i	0.467752	−	0.883860i	$-0.345064\pi$
$641$	8.27017	+	2.68714i	0.326652	+	0.106136i	−0.141100	+	0.989995i	$0.545064\pi$
$642$		0			0
$643$	−17.4877	+	12.7055i	−0.689646	+	0.501057i	−0.876544	−	0.481322i	$-0.840157\pi$
$643$	−17.4877	+	12.7055i	−0.689646	+	0.501057i	0.186897	+	0.982379i	$0.440157\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−17.2616	+	23.7586i	−0.678625	+	0.934048i	−0.999916	−	0.0129330i	$-0.995883\pi$
$647$	−17.2616	+	23.7586i	−0.678625	+	0.934048i	0.321291	+	0.946980i	$0.395883\pi$
$648$		0			0
$649$	0.296067	+	0.0899860i	0.0116216	+	0.00353226i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	22.5339	−	7.32170i	0.881818	−	0.286520i	0.167106	−	0.985939i	$-0.446558\pi$
$653$	22.5339	−	7.32170i	0.881818	−	0.286520i	0.714712	+	0.699419i	$0.246558\pi$
$654$		0			0
$655$	−3.60909	−	4.96749i	−0.141019	−	0.194096i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	34.5941			1.34759			0.673797	−	0.738916i	$-0.264662\pi$
$659$	34.5941			1.34759			0.673797	+	0.738916i	$0.264662\pi$
$660$		0			0
$661$	35.4913			1.38045			0.690225	−	0.723595i	$-0.257512\pi$
$661$	35.4913			1.38045			0.690225	+	0.723595i	$0.257512\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−8.92385	−	12.2826i	−0.346052	−	0.476300i
$666$		0			0
$667$	−7.41211	+	2.40834i	−0.286998	+	0.0932513i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	0.135765	+	7.10971i	0.00524115	+	0.274467i
$672$		0			0
$673$	−12.2854	+	16.9095i	−0.473569	+	0.651812i	−0.977253	−	0.212076i	$-0.931978\pi$
$673$	−12.2854	+	16.9095i	−0.473569	+	0.651812i	0.503684	+	0.863888i	$0.331978\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−19.6090	+	14.2468i	−0.753634	+	0.547547i	−0.896951	−	0.442130i	$-0.854223\pi$
$677$	−19.6090	+	14.2468i	−0.753634	+	0.547547i	0.143317	+	0.989677i	$0.454223\pi$
$678$		0			0
$679$	4.31951	+	1.40350i	0.165768	+	0.0538612i
$680$		0			0
$681$		0			0
$682$		0			0
$683$		−	17.6311i		−	0.674636i	−0.941391	−	0.337318i	$-0.890480\pi$
$683$		−	17.6311i		−	0.674636i	0.941391	−	0.337318i	$-0.109520\pi$
$684$		0			0
$685$	−4.58116	+	14.0994i	−0.175037	+	0.538709i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	9.22748	+	28.3993i	0.351539	+	1.08193i
$690$		0			0
$691$	23.5718	+	17.1259i	0.896713	+	0.651500i	0.937620	−	0.347663i	$-0.113024\pi$
$691$	23.5718	+	17.1259i	0.896713	+	0.651500i	−0.0409063	+	0.999163i	$0.513024\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−41.3272	−	30.0260i	−1.56763	−	1.13895i
$696$		0			0
$697$	−11.6286	−	35.7893i	−0.440466	−	1.35562i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	4.54301	−	13.9820i	0.171587	−	0.528091i	−0.827874	−	0.560914i	$-0.810450\pi$
$701$	4.54301	−	13.9820i	0.171587	−	0.528091i	0.999461	+	0.0328229i	$0.0104497\pi$
$702$		0			0
$703$			11.3642i			0.428611i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	23.3960	+	7.60182i	0.879897	+	0.285896i
$708$		0			0
$709$	−8.72312	+	6.33772i	−0.327604	+	0.238018i	−0.739413	−	0.673252i	$-0.764897\pi$
$709$	−8.72312	+	6.33772i	−0.327604	+	0.238018i	0.411810	+	0.911270i	$0.364897\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−2.87241	+	3.95353i	−0.107572	+	0.148061i
$714$		0			0
$715$	−22.6961	−	15.8366i	−0.848785	−	0.592254i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	30.1960	−	9.81128i	1.12612	−	0.365899i	0.314020	−	0.949416i	$-0.398324\pi$
$719$	30.1960	−	9.81128i	1.12612	−	0.365899i	0.812101	+	0.583517i	$0.198324\pi$
$720$		0			0
$721$	−26.4860	−	36.4549i	−0.986390	−	1.35765i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	33.7614			1.25387
$726$		0			0
$727$	−23.6418			−0.876828			−0.438414	−	0.898773i	$-0.644460\pi$
$727$	−23.6418			−0.876828			−0.438414	+	0.898773i	$0.644460\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−31.1493	−	42.8733i	−1.15210	−	1.58573i
$732$		0			0
$733$	15.6206	−	5.07543i	0.576959	−	0.187465i	−0.00597872	−	0.999982i	$-0.501903\pi$
$733$	15.6206	−	5.07543i	0.576959	−	0.187465i	0.582938	+	0.812517i	$0.301903\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	3.82908	+	2.67181i	0.141046	+	0.0984172i
$738$		0			0
$739$	−20.4813	+	28.1901i	−0.753417	+	1.03699i	0.244316	+	0.969696i	$0.421437\pi$
$739$	−20.4813	+	28.1901i	−0.753417	+	1.03699i	−0.997733	+	0.0672942i	$0.978563\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−42.7101	+	31.0307i	−1.56688	+	1.13841i	−0.636813	+	0.771019i	$0.719748\pi$
$743$	−42.7101	+	31.0307i	−1.56688	+	1.13841i	−0.930068	+	0.367387i	$0.880252\pi$
$744$		0			0
$745$	15.7180	+	5.10708i	0.575862	+	0.187109i
$746$		0			0
$747$		0			0
$748$		0			0
$749$		−	19.3397i		−	0.706657i
$750$		0			0
$751$	−15.8766	+	48.8631i	−0.579345	+	1.78304i	0.0415382	+	0.999137i	$0.486774\pi$
$751$	−15.8766	+	48.8631i	−0.579345	+	1.78304i	−0.620883	+	0.783903i	$0.713226\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−8.28421	−	25.4962i	−0.301493	−	0.927900i
$756$		0			0
$757$	5.71877	+	4.15493i	0.207852	+	0.151013i	0.686841	−	0.726807i	$-0.258997\pi$
$757$	5.71877	+	4.15493i	0.207852	+	0.151013i	−0.478989	+	0.877821i	$0.658997\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−23.5688	−	17.1238i	−0.854370	−	0.620736i	0.0719775	−	0.997406i	$-0.477069\pi$
$761$	−23.5688	−	17.1238i	−0.854370	−	0.620736i	−0.926347	+	0.376670i	$0.877069\pi$
$762$		0			0
$763$	−7.24287	−	22.2913i	−0.262210	−	0.806998i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−0.0823407	+	0.253419i	−0.00297315	+	0.00915042i
$768$		0			0
$769$			44.2408i			1.59536i	0.603079	+	0.797682i	$0.293940\pi$
$769$			44.2408i			1.59536i	−0.603079	+	0.797682i	$0.706060\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−38.0786	−	12.3725i	−1.36959	−	0.445007i	−0.470358	−	0.882476i	$-0.655875\pi$
$773$	−38.0786	−	12.3725i	−1.36959	−	0.445007i	−0.899234	+	0.437468i	$0.855875\pi$
$774$		0			0
$775$	17.1266	−	12.4432i	0.615204	−	0.446972i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−9.47357	+	13.0393i	−0.339426	+	0.467180i
$780$		0			0
$781$	−0.228538	−	11.9680i	−0.00817775	−	0.428250i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−8.48547	+	2.75709i	−0.302859	+	0.0984049i
$786$		0			0
$787$	16.6720	+	22.9470i	0.594292	+	0.817973i	0.995171	−	0.0981579i	$-0.0312950\pi$
$787$	16.6720	+	22.9470i	0.594292	+	0.817973i	−0.400878	+	0.916131i	$0.631295\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−31.0173			−1.10285
$792$		0			0
$793$	−6.12332			−0.217446
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.78371	−	12.0897i	−0.311135	−	0.428241i	0.624600	−	0.780945i	$-0.285262\pi$
$797$	−8.78371	−	12.0897i	−0.311135	−	0.428241i	−0.935735	+	0.352704i	$0.885262\pi$
$798$		0			0
$799$	32.7542	−	10.6425i	1.15876	−	0.376504i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.58339	−	1.69700i	−0.197034	−	0.0598860i
$804$		0			0
$805$	−3.81192	+	5.24666i	−0.134352	+	0.184920i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−24.0892	+	17.5019i	−0.846933	+	0.615333i	−0.924299	−	0.381670i	$-0.875349\pi$
$809$	−24.0892	+	17.5019i	−0.846933	+	0.615333i	0.0773660	+	0.997003i	$0.475349\pi$
$810$		0			0
$811$	−41.9856	−	13.6420i	−1.47432	−	0.479034i	−0.541906	−	0.840439i	$-0.682297\pi$
$811$	−41.9856	−	13.6420i	−1.47432	−	0.479034i	−0.932409	+	0.361405i	$0.882297\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$			23.0948i			0.808975i
$816$		0			0
$817$	−7.01391	+	21.5866i	−0.245386	+	0.755220i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	1.23760	+	3.80893i	0.0431924	+	0.132933i	0.970327	−	0.241795i	$-0.0777362\pi$
$821$	1.23760	+	3.80893i	0.0431924	+	0.132933i	−0.927135	+	0.374728i	$0.877736\pi$
$822$		0			0
$823$	34.1262	+	24.7941i	1.18956	+	0.864268i	0.993218	−	0.116266i	$-0.0370926\pi$
$823$	34.1262	+	24.7941i	1.18956	+	0.864268i	0.196345	+	0.980535i	$0.437093\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−21.5183	−	15.6340i	−0.748266	−	0.543647i	0.147023	−	0.989133i	$-0.453031\pi$
$827$	−21.5183	−	15.6340i	−0.748266	−	0.543647i	−0.895289	+	0.445486i	$0.853031\pi$
$828$		0			0
$829$	3.77976	+	11.6329i	0.131276	+	0.404027i	0.994992	−	0.0999518i	$-0.0318689\pi$
$829$	3.77976	+	11.6329i	0.131276	+	0.404027i	−0.863716	+	0.503979i	$0.831869\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.541343	+	1.66608i	−0.0187564	+	0.0577264i
$834$		0			0
$835$			48.0560i			1.66305i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−9.17434	−	2.98092i	−0.316733	−	0.102913i	0.146336	−	0.989235i	$-0.453252\pi$
$839$	−9.17434	−	2.98092i	−0.316733	−	0.102913i	−0.463069	+	0.886322i	$0.653252\pi$
$840$		0			0
$841$	−50.2704	+	36.5236i	−1.73346	+	1.25943i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−8.31793	+	11.4486i	−0.286146	+	0.393846i
$846$		0			0
$847$	−18.4906	−	23.5075i	−0.635344	−	0.807727i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4.61677	−	1.50008i	0.158261	−	0.0514221i
$852$		0			0
$853$	−6.89976	−	9.49670i	−0.236243	−	0.325161i	0.674391	−	0.738374i	$-0.264406\pi$
$853$	−6.89976	−	9.49670i	−0.236243	−	0.325161i	−0.910634	+	0.413214i	$0.864406\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	48.7738			1.66608			0.833041	−	0.553212i	$-0.186598\pi$
$857$	48.7738			1.66608			0.833041	+	0.553212i	$0.186598\pi$
$858$		0			0
$859$	31.0880			1.06071			0.530355	−	0.847776i	$-0.322059\pi$
$859$	31.0880			1.06071			0.530355	+	0.847776i	$0.322059\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	30.6459	+	42.1805i	1.04320	+	1.43584i	0.894559	+	0.446950i	$0.147490\pi$
$863$	30.6459	+	42.1805i	1.04320	+	1.43584i	0.148641	+	0.988891i	$0.452510\pi$
$864$		0			0
$865$	−43.1325	+	14.0146i	−1.46655	+	0.476511i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	22.3556	−	7.73868i	0.758361	−	0.262517i
$870$		0			0
$871$	−2.36324	+	3.25272i	−0.0800753	+	0.110214i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−9.40572	+	6.83366i	−0.317971	+	0.231020i
$876$		0			0
$877$	16.1564	+	5.24952i	0.545561	+	0.177264i	0.568814	−	0.822466i	$-0.307402\pi$
$877$	16.1564	+	5.24952i	0.545561	+	0.177264i	−0.0232530	+	0.999730i	$0.507402\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	50.3115i		−	1.69504i	−0.530765	−	0.847519i	$-0.678095\pi$
$881$		−	50.3115i		−	1.69504i	0.530765	−	0.847519i	$-0.321905\pi$
$882$		0			0
$883$	−4.44037	+	13.6660i	−0.149430	+	0.459899i	−0.997554	−	0.0698990i	$-0.977732\pi$
$883$	−4.44037	+	13.6660i	−0.149430	+	0.459899i	0.848124	+	0.529798i	$0.177732\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.7625	+	39.2790i	0.428523	+	1.31886i	0.899580	+	0.436756i	$0.143873\pi$
$887$	12.7625	+	39.2790i	0.428523	+	1.31886i	−0.471057	+	0.882103i	$0.656127\pi$
$888$		0			0
$889$	−6.34181	−	4.60760i	−0.212698	−	0.154534i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−11.9335	−	8.67018i	−0.399339	−	0.290136i
$894$		0			0
$895$	4.68529	+	14.4198i	0.156612	+	0.482002i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−17.6592	+	54.3495i	−0.588968	+	1.81266i
$900$		0			0
$901$			46.6547i			1.55429i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−14.7614	−	4.79627i	−0.490685	−	0.159433i
$906$		0			0
$907$	−21.1288	+	15.3510i	−0.701571	+	0.509721i	−0.880444	−	0.474151i	$-0.842755\pi$
$907$	−21.1288	+	15.3510i	−0.701571	+	0.509721i	0.178872	+	0.983872i	$0.442755\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	26.6929	−	36.7397i	0.884377	−	1.21724i	−0.0908128	−	0.995868i	$-0.528946\pi$
$911$	26.6929	−	36.7397i	0.884377	−	1.21724i	0.975189	−	0.221372i	$-0.0710535\pi$
$912$		0			0
$913$	−25.9787	+	0.496082i	−0.859769	+	0.0164179i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.43431	−	1.76572i	0.179457	−	0.0583091i
$918$		0			0
$919$	16.3737	+	22.5365i	0.540119	+	0.743410i	0.988630	−	0.150367i	$-0.0480456\pi$
$919$	16.3737	+	22.5365i	0.540119	+	0.743410i	−0.448511	+	0.893777i	$0.648046\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	10.3076			0.339280
$924$		0			0
$925$	−21.0289			−0.691427
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−29.2450	−	40.2523i	−0.959497	−	1.32063i	−0.947178	−	0.320710i	$-0.896079\pi$
$929$	−29.2450	−	40.2523i	−0.959497	−	1.32063i	−0.0123191	−	0.999924i	$-0.503921\pi$
$930$		0			0
$931$	0.713584	−	0.231857i	0.0233868	−	0.00759882i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−26.0789	−	34.4901i	−0.852872	−	1.12795i
$936$		0			0
$937$	11.9943	−	16.5087i	0.391837	−	0.539317i	−0.566835	−	0.823831i	$-0.691832\pi$
$937$	11.9943	−	16.5087i	0.391837	−	0.539317i	0.958672	+	0.284514i	$0.0918323\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−14.1929	+	10.3117i	−0.462675	+	0.336153i	−0.794580	−	0.607160i	$-0.792309\pi$
$941$	−14.1929	+	10.3117i	−0.462675	+	0.336153i	0.331904	+	0.943313i	$0.392309\pi$
$942$		0			0
$943$	6.54776	+	2.12750i	0.213224	+	0.0692808i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		−	47.0672i		−	1.52948i	−0.644340	−	0.764739i	$-0.722868\pi$
$947$		−	47.0672i		−	1.52948i	0.644340	−	0.764739i	$-0.277132\pi$
$948$		0			0
$949$	1.55283	−	4.77911i	0.0504069	−	0.155136i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	15.9545	+	49.1029i	0.516817	+	1.59060i	0.779952	+	0.625839i	$0.215243\pi$
$953$	15.9545	+	49.1029i	0.516817	+	1.59060i	−0.263136	+	0.964759i	$0.584757\pi$
$954$		0			0
$955$	25.7637	+	18.7185i	0.833695	+	0.605715i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−11.1612	−	8.10907i	−0.360413	−	0.261855i
$960$		0			0
$961$	1.49341	+	4.59623i	0.0481744	+	0.148266i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−13.8738	+	42.6991i	−0.446613	+	1.37453i
$966$		0			0
$967$		−	33.6964i		−	1.08360i	−0.840506	−	0.541802i	$-0.817742\pi$
$967$		−	33.6964i		−	1.08360i	0.840506	−	0.541802i	$-0.182258\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	53.1467	+	17.2684i	1.70556	+	0.554170i	0.989584	−	0.143955i	$-0.0459822\pi$
$971$	53.1467	+	17.2684i	1.70556	+	0.554170i	0.715976	+	0.698125i	$0.245982\pi$
$972$		0			0
$973$	38.4588	−	27.9419i	1.23293	−	0.895777i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.1432	+	16.7137i	−0.388496	+	0.534719i	−0.957810	−	0.287401i	$-0.907209\pi$
$977$	−12.1432	+	16.7137i	−0.388496	+	0.534719i	0.569314	+	0.822120i	$0.307209\pi$
$978$		0			0
$979$	3.92539	−	5.62565i	0.125456	−	0.179797i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−47.6740	+	15.4902i	−1.52056	+	0.494061i	−0.945936	−	0.324354i	$-0.894853\pi$
$983$	−47.6740	+	15.4902i	−1.52056	+	0.494061i	−0.574628	+	0.818415i	$0.694853\pi$
$984$		0			0
$985$	12.4362	+	17.1169i	0.396249	+	0.545390i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	9.69548			0.308298
$990$		0			0
$991$	−45.3068			−1.43922			−0.719609	−	0.694379i	$-0.755679\pi$
$991$	−45.3068			−1.43922			−0.719609	+	0.694379i	$0.755679\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	19.5307	+	26.8817i	0.619164	+	0.852206i
$996$		0			0
$997$	9.77676	−	3.17666i	0.309633	−	0.100606i	−0.150079	−	0.988674i	$-0.547953\pi$
$997$	9.77676	−	3.17666i	0.309633	−	0.100606i	0.459712	+	0.888068i	$0.347953\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1584.2.cd.c.161.3		16
3.2	odd	2	inner	1584.2.cd.c.161.2		16
4.3	odd	2		99.2.j.a.62.3	yes	16
11.8	odd	10	inner	1584.2.cd.c.305.2		16
12.11	even	2		99.2.j.a.62.2	yes	16
33.8	even	10	inner	1584.2.cd.c.305.3		16
36.7	odd	6		891.2.u.c.458.3		32
36.11	even	6		891.2.u.c.458.2		32
36.23	even	6		891.2.u.c.755.3		32
36.31	odd	6		891.2.u.c.755.2		32
44.19	even	10		99.2.j.a.8.2	✓	16
44.27	odd	10		1089.2.d.g.1088.7		16
44.39	even	10		1089.2.d.g.1088.9		16
132.71	even	10		1089.2.d.g.1088.10		16
132.83	odd	10		1089.2.d.g.1088.8		16
132.107	odd	10		99.2.j.a.8.3	yes	16
396.151	even	30		891.2.u.c.701.3		32
396.239	odd	30		891.2.u.c.107.3		32
396.283	even	30		891.2.u.c.107.2		32
396.371	odd	30		891.2.u.c.701.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.j.a.8.2	✓	16	44.19	even	10
99.2.j.a.8.3	yes	16	132.107	odd	10
99.2.j.a.62.2	yes	16	12.11	even	2
99.2.j.a.62.3	yes	16	4.3	odd	2
891.2.u.c.107.2		32	396.283	even	30
891.2.u.c.107.3		32	396.239	odd	30
891.2.u.c.458.2		32	36.11	even	6
891.2.u.c.458.3		32	36.7	odd	6
891.2.u.c.701.2		32	396.371	odd	30
891.2.u.c.701.3		32	396.151	even	30
891.2.u.c.755.2		32	36.31	odd	6
891.2.u.c.755.3		32	36.23	even	6
1089.2.d.g.1088.7		16	44.27	odd	10
1089.2.d.g.1088.8		16	132.83	odd	10
1089.2.d.g.1088.9		16	44.39	even	10
1089.2.d.g.1088.10		16	132.71	even	10
1584.2.cd.c.161.2		16	3.2	odd	2	inner
1584.2.cd.c.161.3		16	1.1	even	1	trivial
1584.2.cd.c.305.2		16	11.8	odd	10	inner
1584.2.cd.c.305.3		16	33.8	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.71735 + 2.36373i) q^{5} +(-2.58586 + 0.840196i) q^{7} +(2.71994 + 1.89788i) q^{11} +(-1.67869 + 2.31052i) q^{13} +(-3.60998 + 2.62280i) q^{17} +(1.81761 + 0.590579i) q^{19} -0.816370i q^{23} +(-1.09283 + 3.36340i) q^{25} +(-2.95006 - 9.07936i) q^{29} +(-4.84281 - 3.51851i) q^{31} +(-6.42681 - 4.66935i) q^{35} +(1.83750 + 5.65524i) q^{37} +(-2.60604 + 8.02058i) q^{41} +11.8763i q^{43} +(-7.34041 - 2.38504i) q^{47} +(0.317615 - 0.230761i) q^{49} +(6.14564 - 8.45874i) q^{53} +(0.185009 + 9.68851i) q^{55} +(0.0887332 - 0.0288312i) q^{59} +(1.26024 + 1.73457i) q^{61} -8.34434 q^{65} +1.40778 q^{67} +(-2.12141 - 2.91987i) q^{71} +(-1.67338 + 0.543714i) q^{73} +(-8.62796 - 2.62237i) q^{77} +(4.19260 - 5.77063i) q^{79} +(-6.33808 + 4.60488i) q^{83} +(-12.3992 - 4.02874i) q^{85} -2.06830i q^{89} +(2.39957 - 7.38512i) q^{91} +(1.72551 + 5.31057i) q^{95} +(-1.35141 - 0.981858i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 32 q^{25} - 16 q^{31} - 12 q^{37} - 24 q^{49} - 16 q^{55} - 96 q^{67} - 20 q^{73} - 100 q^{85} + 72 q^{91} + 60 q^{97}+O(q^{100}) \) 16 * q - 32 * q^25 - 16 * q^31 - 12 * q^37 - 24 * q^49 - 16 * q^55 - 96 * q^67 - 20 * q^73 - 100 * q^85 + 72 * q^91 + 60 * q^97

Introduction

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