LMFDB - Embedded newform 1260.2.ej.a.233.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(53,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 9, 8]))

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

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

chi := DirichletCharacter("1260.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.ej (of order $12$, degree $4$, 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:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			233.13
Character	$\chi$	$=$	1260.233
Dual form			1260.2.ej.a.557.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65096 + 1.50808i) q^{5} +(0.407758 - 2.61414i) q^{7} +O(q^{10})$	$q+(1.65096 + 1.50808i) q^{5} +(0.407758 - 2.61414i) q^{7} +(-3.45539 + 1.99497i) q^{11} +(-4.61757 - 4.61757i) q^{13} +(1.34592 - 5.02305i) q^{17} +(-4.70173 - 2.71454i) q^{19} +(-2.23461 - 8.33968i) q^{23} +(0.451364 + 4.97959i) q^{25} +3.86048 q^{29} +(-0.780027 - 1.35105i) q^{31} +(4.61554 - 3.70092i) q^{35} +(0.0737337 + 0.275178i) q^{37} +3.13961i q^{41} +(2.78010 + 2.78010i) q^{43} +(0.765069 - 0.205000i) q^{47} +(-6.66747 - 2.13187i) q^{49} +(5.99134 + 1.60537i) q^{53} +(-8.71331 - 1.91740i) q^{55} +(5.19648 + 9.00057i) q^{59} +(4.58612 - 7.94339i) q^{61} +(-0.659758 - 14.5871i) q^{65} +(-5.70341 - 1.52822i) q^{67} +0.668930i q^{71} +(-2.89302 + 10.7969i) q^{73} +(3.80617 + 9.84635i) q^{77} +(-13.8981 - 8.02408i) q^{79} +(3.96079 - 3.96079i) q^{83} +(9.79725 - 6.26311i) q^{85} +(5.68967 - 9.85480i) q^{89} +(-13.9538 + 10.1881i) q^{91} +(-3.66862 - 11.5722i) q^{95} +(12.4980 - 12.4980i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7}+O(q^{10}) $ 64 * q - 8 * q^7	$ 64 q - 8 q^{7} + 16 q^{25} + 32 q^{31} + 16 q^{37} - 16 q^{43} + 32 q^{55} + 48 q^{61} + 32 q^{67} + 40 q^{73} + 80 q^{85} + 96 q^{91} + 80 q^{97}+O(q^{100}) $ 64 * q - 8 * q^7 + 16 * q^25 + 32 * q^31 + 16 * q^37 - 16 * q^43 + 32 * q^55 + 48 * q^61 + 32 * q^67 + 40 * q^73 + 80 * q^85 + 96 * q^91 + 80 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$

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
$5$	1.65096	+	1.50808i	0.738334	+	0.674436i
$5$	1.65096	+	1.50808i	0.738334	+	0.674436i
$6$		0			0
$7$	0.407758	−	2.61414i	0.154118	−	0.988052i
$7$	0.407758	−	2.61414i	0.154118	−	0.988052i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.45539	+	1.99497i	−1.04184	+	0.601507i	−0.920354	−	0.391086i	$-0.872099\pi$
$11$	−3.45539	+	1.99497i	−1.04184	+	0.601507i	−0.121486	+	0.992593i	$0.538766\pi$
$12$		0			0
$13$	−4.61757	−	4.61757i	−1.28068	−	1.28068i	−0.940278	−	0.340406i	$-0.889435\pi$
$13$	−4.61757	−	4.61757i	−1.28068	−	1.28068i	−0.340406	−	0.940278i	$-0.610565\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.34592	−	5.02305i	0.326434	−	1.21827i	−0.586428	−	0.810001i	$-0.699466\pi$
$17$	1.34592	−	5.02305i	0.326434	−	1.21827i	0.912862	−	0.408267i	$-0.133867\pi$
$18$		0			0
$19$	−4.70173	−	2.71454i	−1.07865	−	0.622759i	−0.148118	−	0.988970i	$-0.547322\pi$
$19$	−4.70173	−	2.71454i	−1.07865	−	0.622759i	−0.930532	+	0.366211i	$0.880655\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.23461	−	8.33968i	−0.465948	−	1.73894i	−0.653726	−	0.756731i	$-0.726795\pi$
$23$	−2.23461	−	8.33968i	−0.465948	−	1.73894i	0.187777	−	0.982212i	$-0.439872\pi$
$24$		0			0
$25$	0.451364	+	4.97959i	0.0902729	+	0.995917i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.86048			0.716873			0.358436	−	0.933554i	$-0.383310\pi$
$29$	3.86048			0.716873			0.358436	+	0.933554i	$0.383310\pi$
$30$		0			0
$31$	−0.780027	−	1.35105i	−0.140097	−	0.242655i	0.787436	−	0.616396i	$-0.211408\pi$
$31$	−0.780027	−	1.35105i	−0.140097	−	0.242655i	−0.927533	+	0.373741i	$0.878075\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.61554	−	3.70092i	0.780168	−	0.625570i
$36$		0			0
$37$	0.0737337	+	0.275178i	0.0121218	+	0.0452390i	0.971722	−	0.236129i	$-0.0758787\pi$
$37$	0.0737337	+	0.275178i	0.0121218	+	0.0452390i	−0.959600	+	0.281368i	$0.909212\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			3.13961i			0.490324i	0.969482	+	0.245162i	$0.0788412\pi$
$41$			3.13961i			0.490324i	−0.969482	+	0.245162i	$0.921159\pi$
$42$		0			0
$43$	2.78010	+	2.78010i	0.423961	+	0.423961i	0.886565	−	0.462604i	$-0.153085\pi$
$43$	2.78010	+	2.78010i	0.423961	+	0.423961i	−0.462604	+	0.886565i	$0.653085\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.765069	−	0.205000i	0.111597	−	0.0299023i	−0.202588	−	0.979264i	$-0.564935\pi$
$47$	0.765069	−	0.205000i	0.111597	−	0.0299023i	0.314185	+	0.949362i	$0.398269\pi$
$48$		0			0
$49$	−6.66747	−	2.13187i	−0.952495	−	0.304553i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	5.99134	+	1.60537i	0.822973	+	0.220515i	0.645646	−	0.763637i	$-0.276588\pi$
$53$	5.99134	+	1.60537i	0.822973	+	0.220515i	0.177327	+	0.984152i	$0.443255\pi$
$54$		0			0
$55$	−8.71331	−	1.91740i	−1.17490	−	0.258542i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.19648	+	9.00057i	0.676524	+	1.17177i	0.976021	+	0.217677i	$0.0698479\pi$
$59$	5.19648	+	9.00057i	0.676524	+	1.17177i	−0.299497	+	0.954097i	$0.596819\pi$
$60$		0			0
$61$	4.58612	−	7.94339i	0.587192	−	1.01705i	−0.407406	−	0.913247i	$-0.633567\pi$
$61$	4.58612	−	7.94339i	0.587192	−	1.01705i	0.994598	−	0.103799i	$-0.0331000\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.659758	−	14.5871i	−0.0818330	−	1.80931i
$66$		0			0
$67$	−5.70341	−	1.52822i	−0.696782	−	0.186702i	−0.106993	−	0.994260i	$-0.534122\pi$
$67$	−5.70341	−	1.52822i	−0.696782	−	0.186702i	−0.589789	+	0.807557i	$0.700789\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			0.668930i			0.0793874i	0.999212	+	0.0396937i	$0.0126382\pi$
$71$			0.668930i			0.0793874i	−0.999212	+	0.0396937i	$0.987362\pi$
$72$		0			0
$73$	−2.89302	+	10.7969i	−0.338603	+	1.26368i	0.561307	+	0.827608i	$0.310299\pi$
$73$	−2.89302	+	10.7969i	−0.338603	+	1.26368i	−0.899910	+	0.436076i	$0.856368\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.80617	+	9.84635i	0.433754	+	1.12210i
$78$		0			0
$79$	−13.8981	−	8.02408i	−1.56366	−	0.902780i	−0.996882	−	0.0789092i	$-0.974856\pi$
$79$	−13.8981	−	8.02408i	−1.56366	−	0.902780i	−0.566778	−	0.823870i	$-0.691810\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.96079	−	3.96079i	0.434754	−	0.434754i	−0.455488	−	0.890242i	$-0.650535\pi$
$83$	3.96079	−	3.96079i	0.434754	−	0.434754i	0.890242	+	0.455488i	$0.150535\pi$
$84$		0			0
$85$	9.79725	−	6.26311i	1.06266	−	0.679330i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.68967	−	9.85480i	0.603104	−	1.04461i	−0.389244	−	0.921135i	$-0.627264\pi$
$89$	5.68967	−	9.85480i	0.603104	−	1.04461i	0.992348	−	0.123472i	$-0.0394029\pi$
$90$		0			0
$91$	−13.9538	+	10.1881i	−1.46276	+	1.06801i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−3.66862	−	11.5722i	−0.376393	−	1.18728i
$96$		0			0
$97$	12.4980	−	12.4980i	1.26898	−	1.26898i	0.322363	−	0.946616i	$-0.395523\pi$
$97$	12.4980	−	12.4980i	1.26898	−	1.26898i	0.946616	−	0.322363i	$-0.104477\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	2.71835	−	1.56944i	0.270486	−	0.156165i	−0.358623	−	0.933483i	$-0.616754\pi$
$101$	2.71835	−	1.56944i	0.270486	−	0.156165i	0.629108	+	0.777318i	$0.283420\pi$
$102$		0			0
$103$	−1.13664	+	0.304563i	−0.111997	+	0.0300095i	−0.314382	−	0.949297i	$-0.601797\pi$
$103$	−1.13664	+	0.304563i	−0.111997	+	0.0300095i	0.202385	+	0.979306i	$0.435131\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.45218	−	1.46091i	0.527082	−	0.141231i	0.0145417	−	0.999894i	$-0.495371\pi$
$107$	5.45218	−	1.46091i	0.527082	−	0.141231i	0.512541	+	0.858663i	$0.328704\pi$
$108$		0			0
$109$	10.3902	−	5.99877i	0.995198	−	0.574578i	0.0883743	−	0.996087i	$-0.471833\pi$
$109$	10.3902	−	5.99877i	0.995198	−	0.574578i	0.906824	+	0.421509i	$0.138500\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−11.1258	+	11.1258i	−1.04663	+	1.04663i	−0.0477714	+	0.998858i	$0.515212\pi$
$113$	−11.1258	+	11.1258i	−1.04663	+	1.04663i	−0.998858	+	0.0477714i	$0.984788\pi$
$114$		0			0
$115$	8.88768	−	17.1385i	0.828780	−	1.59817i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−12.5821	−	5.56662i	−1.15340	−	0.510291i
$120$		0			0
$121$	2.45983	−	4.26054i	0.223621	−	0.387322i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−6.76445	+	8.90181i	−0.605031	+	0.796202i
$126$		0			0
$127$	−0.899132	+	0.899132i	−0.0797851	+	0.0797851i	−0.745873	−	0.666088i	$-0.767967\pi$
$127$	−0.899132	+	0.899132i	−0.0797851	+	0.0797851i	0.666088	+	0.745873i	$0.267967\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−12.2332	−	7.06285i	−1.06882	−	0.617084i	−0.140962	−	0.990015i	$-0.545019\pi$
$131$	−12.2332	−	7.06285i	−1.06882	−	0.617084i	−0.927859	+	0.372931i	$0.878353\pi$
$132$		0			0
$133$	−9.01337	+	11.1841i	−0.781558	+	0.969785i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	1.50980	−	5.63464i	0.128991	−	0.481400i	−0.870960	−	0.491354i	$-0.836502\pi$
$137$	1.50980	−	5.63464i	0.128991	−	0.481400i	0.999950	+	0.00995439i	$0.00316863\pi$
$138$		0			0
$139$			12.6637i			1.07412i	0.843543	+	0.537062i	$0.180466\pi$
$139$			12.6637i			1.07412i	−0.843543	+	0.537062i	$0.819534\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	25.1675	+	6.74360i	2.10461	+	0.563928i
$144$		0			0
$145$	6.37351	+	5.82193i	0.529291	+	0.483485i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−8.29771	+	14.3721i	−0.679775	+	1.17741i	0.295273	+	0.955413i	$0.404589\pi$
$149$	−8.29771	+	14.3721i	−0.679775	+	1.17741i	−0.975048	+	0.221992i	$0.928744\pi$
$150$		0			0
$151$	−11.5635	−	20.0285i	−0.941022	−	1.62990i	−0.763526	−	0.645777i	$-0.776534\pi$
$151$	−11.5635	−	20.0285i	−0.941022	−	1.62990i	−0.177496	−	0.984121i	$-0.556800\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	0.749696	−	3.40688i	0.0602170	−	0.273647i
$156$		0			0
$157$	−2.95607	−	0.792075i	−0.235920	−	0.0632145i	0.138922	−	0.990303i	$-0.455636\pi$
$157$	−2.95607	−	0.792075i	−0.235920	−	0.0632145i	−0.374842	+	0.927089i	$0.622303\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−22.7123	+	2.44101i	−1.78998	+	0.192379i
$162$		0			0
$163$	−4.78946	+	1.28333i	−0.375140	+	0.100518i	−0.441462	−	0.897280i	$-0.645540\pi$
$163$	−4.78946	+	1.28333i	−0.375140	+	0.100518i	0.0663225	+	0.997798i	$0.478873\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.39463	−	2.39463i	−0.185302	−	0.185302i	0.608360	−	0.793662i	$-0.291828\pi$
$167$	−2.39463	−	2.39463i	−0.185302	−	0.185302i	−0.793662	+	0.608360i	$0.791828\pi$
$168$		0			0
$169$			29.6440i			2.28031i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	4.57805	+	17.0855i	0.348063	+	1.29899i	0.888993	+	0.457920i	$0.151405\pi$
$173$	4.57805	+	17.0855i	0.348063	+	1.29899i	−0.540931	+	0.841067i	$0.681928\pi$
$174$		0			0
$175$	13.2014	+	0.850536i	0.997931	+	0.0642945i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.83087	+	6.63526i	0.286333	+	0.495943i	0.972931	−	0.231094i	$-0.0742304\pi$
$179$	3.83087	+	6.63526i	0.286333	+	0.495943i	−0.686599	+	0.727037i	$0.740897\pi$
$180$		0			0
$181$	0.418252			0.0310884			0.0155442	−	0.999879i	$-0.495052\pi$
$181$	0.418252			0.0310884			0.0155442	+	0.999879i	$0.495052\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.293260	+	0.565506i	−0.0215609	+	0.0415768i
$186$		0			0
$187$	5.37015	+	20.0417i	0.392704	+	1.46559i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.52604	+	2.61311i	0.327493	+	0.189078i	0.654727	−	0.755865i	$-0.272783\pi$
$191$	4.52604	+	2.61311i	0.327493	+	0.189078i	−0.327235	+	0.944943i	$0.606117\pi$
$192$		0			0
$193$	0.559202	−	2.08697i	0.0402522	−	0.150223i	−0.942875	−	0.333147i	$-0.891889\pi$
$193$	0.559202	−	2.08697i	0.0402522	−	0.150223i	0.983127	+	0.182924i	$0.0585561\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−12.1286	−	12.1286i	−0.864128	−	0.864128i	0.127686	−	0.991815i	$-0.459245\pi$
$197$	−12.1286	−	12.1286i	−0.864128	−	0.864128i	−0.991815	+	0.127686i	$0.959245\pi$
$198$		0			0
$199$	6.72138	−	3.88059i	0.476466	−	0.275088i	−0.242477	−	0.970157i	$-0.577960\pi$
$199$	6.72138	−	3.88059i	0.476466	−	0.275088i	0.718943	+	0.695069i	$0.244626\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.57414	−	10.0918i	0.110483	−	0.708308i
$204$		0			0
$205$	−4.73479	+	5.18338i	−0.330692	+	0.362023i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	21.6618			1.49837
$210$		0			0
$211$	9.99314			0.687956			0.343978	−	0.938978i	$-0.388225\pi$
$211$	9.99314			0.687956			0.343978	+	0.938978i	$0.388225\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.397220	+	8.78246i	0.0270902	+	0.598959i
$216$		0			0
$217$	−3.84989	+	1.48820i	−0.261348	+	0.101026i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−29.4092	+	16.9794i	−1.97828	+	1.14216i
$222$		0			0
$223$	−6.14948	−	6.14948i	−0.411799	−	0.411799i	0.470566	−	0.882365i	$-0.344050\pi$
$223$	−6.14948	−	6.14948i	−0.411799	−	0.411799i	−0.882365	+	0.470566i	$0.844050\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	5.11788	−	19.1002i	0.339685	−	1.26772i	−0.559014	−	0.829158i	$-0.688820\pi$
$227$	5.11788	−	19.1002i	0.339685	−	1.26772i	0.898700	−	0.438565i	$-0.144513\pi$
$228$		0			0
$229$	9.06445	+	5.23336i	0.598995	+	0.345830i	0.768646	−	0.639674i	$-0.220931\pi$
$229$	9.06445	+	5.23336i	0.598995	+	0.345830i	−0.169651	+	0.985504i	$0.554264\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.10955	+	11.6050i	0.203713	+	0.760268i	0.989838	+	0.142200i	$0.0454177\pi$
$233$	3.10955	+	11.6050i	0.203713	+	0.760268i	−0.786125	+	0.618068i	$0.787916\pi$
$234$		0			0
$235$	1.57226	+	0.815342i	0.102563	+	0.0531870i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−1.26303			−0.0816985			−0.0408492	−	0.999165i	$-0.513006\pi$
$239$	−1.26303			−0.0816985			−0.0408492	+	0.999165i	$0.513006\pi$
$240$		0			0
$241$	−8.56339	−	14.8322i	−0.551616	−	0.955427i	−0.998158	−	0.0606647i	$-0.980678\pi$
$241$	−8.56339	−	14.8322i	−0.551616	−	0.955427i	0.446542	−	0.894763i	$-0.352655\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.79270	−	13.5747i	−0.497857	−	0.867259i
$246$		0			0
$247$	9.17597	+	34.2452i	0.583853	+	2.17897i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	13.8447i		−	0.873872i	−0.899493	−	0.436936i	$-0.856064\pi$
$251$		−	13.8447i		−	0.873872i	0.899493	−	0.436936i	$-0.143936\pi$
$252$		0			0
$253$	24.3589	+	24.3589i	1.53143	+	1.53143i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	9.22460	−	2.47172i	0.575415	−	0.154182i	0.0406360	−	0.999174i	$-0.487062\pi$
$257$	9.22460	−	2.47172i	0.575415	−	0.154182i	0.534779	+	0.844992i	$0.320395\pi$
$258$		0			0
$259$	0.749420	−	0.0805443i	0.0465667	−	0.00500478i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	26.2837	+	7.04269i	1.62072	+	0.434271i	0.951213	−	0.308534i	$-0.0998382\pi$
$263$	26.2837	+	7.04269i	1.62072	+	0.434271i	0.669508	+	0.742805i	$0.266505\pi$
$264$		0			0
$265$	7.47044	+	11.6859i	0.458906	+	0.717856i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	9.01025	+	15.6062i	0.549365	+	0.951528i	0.998318	+	0.0579725i	$0.0184636\pi$
$269$	9.01025	+	15.6062i	0.549365	+	0.951528i	−0.448953	+	0.893555i	$0.648203\pi$
$270$		0			0
$271$	15.6511	−	27.1086i	0.950739	−	1.64673i	0.206908	−	0.978360i	$-0.433660\pi$
$271$	15.6511	−	27.1086i	0.950739	−	1.64673i	0.743831	−	0.668367i	$-0.233007\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−11.4938	−	16.3060i	−0.693101	−	0.983287i
$276$		0			0
$277$	26.5101	+	7.10337i	1.59284	+	0.426800i	0.942870	−	0.333160i	$-0.108115\pi$
$277$	26.5101	+	7.10337i	1.59284	+	0.426800i	0.649970	+	0.759960i	$0.274782\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			31.5139i			1.87996i	0.341231	+	0.939980i	$0.389156\pi$
$281$			31.5139i			1.87996i	−0.341231	+	0.939980i	$0.610844\pi$
$282$		0			0
$283$	6.28698	−	23.4633i	0.373722	−	1.39475i	−0.481480	−	0.876457i	$-0.659901\pi$
$283$	6.28698	−	23.4633i	0.373722	−	1.39475i	0.855202	−	0.518294i	$-0.173433\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.20738	+	1.28020i	0.484466	+	0.0755678i
$288$		0			0
$289$	−8.69709	−	5.02127i	−0.511593	−	0.295369i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	3.13734	−	3.13734i	0.183285	−	0.183285i	−0.609501	−	0.792786i	$-0.708630\pi$
$293$	3.13734	−	3.13734i	0.183285	−	0.183285i	0.792786	+	0.609501i	$0.208630\pi$
$294$		0			0
$295$	−4.99441	+	22.6963i	−0.290786	+	1.32143i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−28.1906	+	48.8276i	−1.63030	+	2.82377i
$300$		0			0
$301$	8.40117	−	6.13396i	0.484236	−	0.353556i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	19.5508	−	6.19800i	1.11948	−	0.354896i
$306$		0			0
$307$	−8.84326	+	8.84326i	−0.504711	+	0.504711i	−0.912898	−	0.408187i	$-0.866161\pi$
$307$	−8.84326	+	8.84326i	−0.504711	+	0.504711i	0.408187	+	0.912898i	$0.366161\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−24.3630	+	14.0660i	−1.38150	+	0.797609i	−0.992337	−	0.123560i	$-0.960569\pi$
$311$	−24.3630	+	14.0660i	−1.38150	+	0.797609i	−0.389162	+	0.921169i	$0.627235\pi$
$312$		0			0
$313$	19.1002	−	5.11789i	1.07961	−	0.289281i	0.325174	−	0.945654i	$-0.394577\pi$
$313$	19.1002	−	5.11789i	1.07961	−	0.289281i	0.754436	+	0.656374i	$0.227911\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−9.62368	+	2.57866i	−0.540519	+	0.144832i	−0.518742	−	0.854931i	$-0.673599\pi$
$317$	−9.62368	+	2.57866i	−0.540519	+	0.144832i	−0.0217779	+	0.999763i	$0.506933\pi$
$318$		0			0
$319$	−13.3395	+	7.70155i	−0.746867	+	0.431204i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−19.9634	+	19.9634i	−1.11080	+	1.11080i
$324$		0			0
$325$	20.9094	−	25.0778i	1.15984	−	1.39107i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−0.223935	−	2.08359i	−0.0123459	−	0.114872i
$330$		0			0
$331$	−10.8145	+	18.7313i	−0.594419	+	1.02956i	0.399210	+	0.916860i	$0.369285\pi$
$331$	−10.8145	+	18.7313i	−0.594419	+	1.02956i	−0.993629	+	0.112704i	$0.964049\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−7.11143	−	11.1243i	−0.388539	−	0.607783i
$336$		0			0
$337$	6.18409	−	6.18409i	0.336869	−	0.336869i	−0.518319	−	0.855188i	$-0.673442\pi$
$337$	6.18409	−	6.18409i	0.336869	−	0.336869i	0.855188	+	0.518319i	$0.173442\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	5.39060	+	3.11227i	0.291917	+	0.168539i
$342$		0			0
$343$	−8.29173	+	16.5604i	−0.447712	+	0.894178i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.529679	−	1.97679i	0.0284347	−	0.106120i	−0.950250	−	0.311488i	$-0.899173\pi$
$347$	0.529679	−	1.97679i	0.0284347	−	0.106120i	0.978685	+	0.205368i	$0.0658393\pi$
$348$		0			0
$349$		−	9.29551i		−	0.497577i	−0.968558	−	0.248788i	$-0.919968\pi$
$349$		−	9.29551i		−	0.497577i	0.968558	−	0.248788i	$-0.0800324\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−0.753362	−	0.201863i	−0.0400974	−	0.0107441i	0.238715	−	0.971090i	$-0.423274\pi$
$353$	−0.753362	−	0.201863i	−0.0400974	−	0.0107441i	−0.278812	+	0.960346i	$0.589941\pi$
$354$		0			0
$355$	−1.00880	+	1.10438i	−0.0535417	+	0.0586144i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	7.20384	−	12.4774i	0.380204	−	0.658532i	−0.610887	−	0.791718i	$-0.709187\pi$
$359$	7.20384	−	12.4774i	0.380204	−	0.658532i	0.991091	+	0.133185i	$0.0425205\pi$
$360$		0			0
$361$	5.23749	+	9.07161i	0.275658	+	0.477453i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−21.0589	+	13.4624i	−1.10227	+	0.704654i
$366$		0			0
$367$	−2.38784	−	0.639821i	−0.124644	−	0.0333984i	0.195958	−	0.980612i	$-0.437219\pi$
$367$	−2.38784	−	0.639821i	−0.124644	−	0.0333984i	−0.320602	+	0.947214i	$0.603885\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.63969	−	15.0076i	0.344715	−	0.779155i
$372$		0			0
$373$	−23.1949	+	6.21507i	−1.20099	+	0.321804i	−0.803221	−	0.595682i	$-0.796882\pi$
$373$	−23.1949	+	6.21507i	−1.20099	+	0.321804i	−0.397768	+	0.917486i	$0.630215\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−17.8260	−	17.8260i	−0.918088	−	0.918088i
$378$		0			0
$379$			1.60683i			0.0825374i	0.999148	+	0.0412687i	$0.0131400\pi$
$379$			1.60683i			0.0825374i	−0.999148	+	0.0412687i	$0.986860\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.63111	−	9.81943i	−0.134443	−	0.501750i	−1.00000		0.000937706i	$-0.999702\pi$
$383$	−2.63111	−	9.81943i	−0.134443	−	0.501750i	0.865556	−	0.500812i	$-0.166965\pi$
$384$		0			0
$385$	−8.56527	+	21.9960i	−0.436527	+	1.12102i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4.45338	+	7.71348i	0.225795	+	0.391089i	0.956558	−	0.291543i	$-0.0941687\pi$
$389$	4.45338	+	7.71348i	0.225795	+	0.391089i	−0.730763	+	0.682632i	$0.760835\pi$
$390$		0			0
$391$	−44.8982			−2.27060
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−10.8443	−	34.2070i	−0.545636	−	1.72114i
$396$		0			0
$397$	−1.58723	−	5.92364i	−0.0796610	−	0.297299i	0.914589	−	0.404385i	$-0.132514\pi$
$397$	−1.58723	−	5.92364i	−0.0796610	−	0.297299i	−0.994250	+	0.107086i	$0.965848\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−25.8112	−	14.9021i	−1.28895	−	0.744175i	−0.310482	−	0.950579i	$-0.600490\pi$
$401$	−25.8112	−	14.9021i	−1.28895	−	0.744175i	−0.978467	+	0.206404i	$0.933824\pi$
$402$		0			0
$403$	−2.63673	+	9.84039i	−0.131345	+	0.490185i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−0.803751	−	0.803751i	−0.0398405	−	0.0398405i
$408$		0			0
$409$	18.0630	−	10.4287i	0.893160	−	0.515666i	0.0181849	−	0.999835i	$-0.494211\pi$
$409$	18.0630	−	10.4287i	0.893160	−	0.515666i	0.874975	+	0.484169i	$0.160878\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	25.6477	−	9.91428i	1.26204	−	0.487850i
$414$		0			0
$415$	12.5123	−	0.565918i	0.614207	−	0.0277798i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	0.388663			0.0189874			0.00949371	−	0.999955i	$-0.496978\pi$
$419$	0.388663			0.0189874			0.00949371	+	0.999955i	$0.496978\pi$
$420$		0			0
$421$	9.60962			0.468344			0.234172	−	0.972195i	$-0.424762\pi$
$421$	9.60962			0.468344			0.234172	+	0.972195i	$0.424762\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	25.6202	+	4.43491i	1.24276	+	0.215125i
$426$		0			0
$427$	−18.8951	−	15.2277i	−0.914398	−	0.736922i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	17.0734	−	9.85733i	0.822396	−	0.474811i	−0.0288458	−	0.999584i	$-0.509183\pi$
$431$	17.0734	−	9.85733i	0.822396	−	0.474811i	0.851242	+	0.524773i	$0.175850\pi$
$432$		0			0
$433$	2.29281	+	2.29281i	0.110186	+	0.110186i	0.760050	−	0.649865i	$-0.225174\pi$
$433$	2.29281	+	2.29281i	0.110186	+	0.110186i	−0.649865	+	0.760050i	$0.725174\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−12.1319	+	45.2768i	−0.580347	+	2.16588i
$438$		0			0
$439$	16.2466	+	9.37996i	0.775406	+	0.447681i	0.834800	−	0.550554i	$-0.185583\pi$
$439$	16.2466	+	9.37996i	0.775406	+	0.447681i	−0.0593934	+	0.998235i	$0.518917\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.93558	+	10.9557i	0.139474	+	0.520523i	0.999939	+	0.0110143i	$0.00350602\pi$
$443$	2.93558	+	10.9557i	0.139474	+	0.520523i	−0.860466	+	0.509508i	$0.829827\pi$
$444$		0			0
$445$	24.2553	−	7.68942i	1.14981	−	0.364513i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−28.3215			−1.33657			−0.668287	−	0.743903i	$-0.732972\pi$
$449$	−28.3215			−1.33657			−0.668287	+	0.743903i	$0.732972\pi$
$450$		0			0
$451$	−6.26343	−	10.8486i	−0.294933	−	0.510840i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−38.4019	−	4.22332i	−1.80031	−	0.197992i
$456$		0			0
$457$	−8.69278	−	32.4419i	−0.406631	−	1.51757i	−0.801027	−	0.598628i	$-0.795713\pi$
$457$	−8.69278	−	32.4419i	−0.406631	−	1.51757i	0.394396	−	0.918941i	$-0.370954\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	5.09025i		−	0.237077i	−0.992949	−	0.118538i	$-0.962179\pi$
$461$		−	5.09025i		−	0.237077i	0.992949	−	0.118538i	$-0.0378208\pi$
$462$		0			0
$463$	10.1917	+	10.1917i	0.473649	+	0.473649i	0.903093	−	0.429445i	$-0.141291\pi$
$463$	10.1917	+	10.1917i	0.473649	+	0.473649i	−0.429445	+	0.903093i	$0.641291\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	20.1552	−	5.40057i	0.932672	−	0.249909i	0.239678	−	0.970852i	$-0.422958\pi$
$467$	20.1552	−	5.40057i	0.932672	−	0.249909i	0.692994	+	0.720944i	$0.256291\pi$
$468$		0			0
$469$	−6.32060	+	14.2864i	−0.291858	+	0.659683i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−15.1525	−	4.06011i	−0.696715	−	0.186684i
$474$		0			0
$475$	11.3951	−	24.6379i	0.522843	−	1.13046i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.55551	+	11.3545i	0.299529	+	0.518799i	0.976028	−	0.217644i	$-0.0698372\pi$
$479$	6.55551	+	11.3545i	0.299529	+	0.518799i	−0.676499	+	0.736443i	$0.736504\pi$
$480$		0			0
$481$	0.930184	−	1.61113i	0.0424127	−	0.0734610i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	39.4818	−	1.78571i	1.79277	−	0.0810850i
$486$		0			0
$487$	5.34729	+	1.43280i	0.242309	+	0.0649265i	0.377930	−	0.925834i	$-0.376636\pi$
$487$	5.34729	+	1.43280i	0.242309	+	0.0649265i	−0.135621	+	0.990761i	$0.543303\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			43.0848i			1.94439i	0.234176	+	0.972194i	$0.424761\pi$
$491$			43.0848i			1.94439i	−0.234176	+	0.972194i	$0.575239\pi$
$492$		0			0
$493$	5.19590	−	19.3914i	0.234012	−	0.873344i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.74868	+	0.272762i	0.0784389	+	0.0122350i
$498$		0			0
$499$	−19.5051	−	11.2612i	−0.873166	−	0.504123i	−0.00476710	−	0.999989i	$-0.501517\pi$
$499$	−19.5051	−	11.2612i	−0.873166	−	0.504123i	−0.868399	+	0.495866i	$0.834851\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	6.10761	−	6.10761i	0.272325	−	0.272325i	−0.557711	−	0.830035i	$-0.688320\pi$
$503$	6.10761	−	6.10761i	0.272325	−	0.272325i	0.830035	+	0.557711i	$0.188320\pi$
$504$		0			0
$505$	6.85474	+	1.50841i	0.305032	+	0.0671234i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	5.10835	−	8.84791i	0.226423	−	0.392177i	−0.730322	−	0.683103i	$-0.760630\pi$
$509$	5.10835	−	8.84791i	0.226423	−	0.392177i	0.956746	+	0.290926i	$0.0939634\pi$
$510$		0			0
$511$	27.0450	+	11.9653i	1.19640	+	0.529314i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.33586	−	1.21133i	−0.102930	−	0.0533777i
$516$		0			0
$517$	−2.23465	+	2.23465i	−0.0982796	+	0.0982796i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	28.5763	−	16.4985i	1.25195	−	0.722813i	0.280452	−	0.959868i	$-0.409516\pi$
$521$	28.5763	−	16.4985i	1.25195	−	0.722813i	0.971496	+	0.237055i	$0.0761822\pi$
$522$		0			0
$523$	3.86775	−	1.03636i	0.169125	−	0.0453169i	−0.173263	−	0.984876i	$-0.555431\pi$
$523$	3.86775	−	1.03636i	0.169125	−	0.0453169i	0.342388	+	0.939559i	$0.388764\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.83623	+	2.09971i	−0.341352	+	0.0914649i
$528$		0			0
$529$	−44.6382	+	25.7719i	−1.94079	+	1.12052i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	14.4974	−	14.4974i	0.627951	−	0.627951i
$534$		0			0
$535$	11.2045	+	5.81044i	0.484414	+	0.251207i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	27.2917	−	5.93495i	1.17554	−	0.255636i
$540$		0			0
$541$	−2.57808	+	4.46537i	−0.110840	+	0.191981i	−0.916109	−	0.400929i	$-0.868688\pi$
$541$	−2.57808	+	4.46537i	−0.110840	+	0.191981i	0.805269	+	0.592910i	$0.202021\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	26.2005	+	5.76550i	1.12230	+	0.246967i
$546$		0			0
$547$	18.1666	−	18.1666i	0.776746	−	0.776746i	−0.202530	−	0.979276i	$-0.564916\pi$
$547$	18.1666	−	18.1666i	0.776746	−	0.776746i	0.979276	+	0.202530i	$0.0649163\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−18.1509	−	10.4794i	−0.773255	−	0.446439i
$552$		0			0
$553$	−26.6431	+	33.0597i	−1.13298	+	1.40584i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.104939	+	0.391638i	−0.00444641	+	0.0165942i	−0.968113	−	0.250512i	$-0.919401\pi$
$557$	−0.104939	+	0.391638i	−0.00444641	+	0.0165942i	0.963667	+	0.267107i	$0.0860676\pi$
$558$		0			0
$559$		−	25.6746i		−	1.08592i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	19.4319	+	5.20676i	0.818957	+	0.219439i	0.643890	−	0.765118i	$-0.277319\pi$
$563$	19.4319	+	5.20676i	0.818957	+	0.219439i	0.175066	+	0.984557i	$0.443986\pi$
$564$		0			0
$565$	−35.1470	+	1.58966i	−1.47865	+	0.0668774i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	18.5230	−	32.0828i	0.776525	−	1.34498i	−0.157409	−	0.987534i	$-0.550314\pi$
$569$	18.5230	−	32.0828i	0.776525	−	1.34498i	0.933934	−	0.357447i	$-0.116353\pi$
$570$		0			0
$571$	−19.7508	−	34.2093i	−0.826544	−	1.43162i	−0.900734	−	0.434372i	$-0.856970\pi$
$571$	−19.7508	−	34.2093i	−0.826544	−	1.43162i	0.0741896	−	0.997244i	$-0.476363\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	40.5195	−	14.8917i	1.68978	−	0.621025i
$576$		0			0
$577$	−28.5344	−	7.64578i	−1.18790	−	0.318298i	−0.389847	−	0.920880i	$-0.627472\pi$
$577$	−28.5344	−	7.64578i	−1.18790	−	0.318298i	−0.798057	+	0.602582i	$0.794139\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−8.73903	−	11.9691i	−0.362556	−	0.496563i
$582$		0			0
$583$	−23.9051	+	6.40535i	−0.990048	+	0.265283i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	23.7238	+	23.7238i	0.979187	+	0.979187i	0.999788	−	0.0206004i	$-0.00655778\pi$
$587$	23.7238	+	23.7238i	0.979187	+	0.979187i	−0.0206004	+	0.999788i	$0.506558\pi$
$588$		0			0
$589$			8.46967i			0.348987i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.814182	−	3.03857i	−0.0334344	−	0.124779i	0.947192	−	0.320668i	$-0.103907\pi$
$593$	−0.814182	−	3.03857i	−0.0334344	−	0.124779i	−0.980626	+	0.195889i	$0.937241\pi$
$594$		0			0
$595$	−12.3777	−	28.1652i	−0.507438	−	1.15466i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	6.46396	+	11.1959i	0.264110	+	0.457452i	0.967330	−	0.253520i	$-0.0815885\pi$
$599$	6.46396	+	11.1959i	0.264110	+	0.457452i	−0.703220	+	0.710972i	$0.748255\pi$
$600$		0			0
$601$	17.6862			0.721435			0.360717	−	0.932675i	$-0.382532\pi$
$601$	17.6862			0.721435			0.360717	+	0.932675i	$0.382532\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	10.4863	−	3.32438i	0.426330	−	0.135155i
$606$		0			0
$607$	3.41975	+	12.7627i	0.138804	+	0.518022i	0.999953	+	0.00967038i	$0.00307823\pi$
$607$	3.41975	+	12.7627i	0.138804	+	0.518022i	−0.861150	+	0.508351i	$0.830255\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.47937	−	2.58616i	−0.181216	−	0.104625i
$612$		0			0
$613$	7.60801	−	28.3935i	0.307285	−	1.14680i	−0.623676	−	0.781683i	$-0.714362\pi$
$613$	7.60801	−	28.3935i	0.307285	−	1.14680i	0.930961	−	0.365119i	$-0.118972\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−30.5277	−	30.5277i	−1.22900	−	1.22900i	−0.964343	−	0.264654i	$-0.914742\pi$
$617$	−30.5277	−	30.5277i	−1.22900	−	1.22900i	−0.264654	−	0.964343i	$-0.585258\pi$
$618$		0			0
$619$	−10.7393	+	6.20035i	−0.431650	+	0.249213i	−0.700049	−	0.714094i	$-0.746839\pi$
$619$	−10.7393	+	6.20035i	−0.431650	+	0.249213i	0.268399	+	0.963308i	$0.413505\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−23.4418	−	18.8920i	−0.939177	−	0.756891i
$624$		0			0
$625$	−24.5925	+	4.49521i	−0.983702	+	0.179809i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	1.48147			0.0590702
$630$		0			0
$631$	−7.95169			−0.316552			−0.158276	−	0.987395i	$-0.550594\pi$
$631$	−7.95169			−0.316552			−0.158276	+	0.987395i	$0.550594\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−2.84040	+	0.128468i	−0.112718	+	0.00509809i
$636$		0			0
$637$	20.9434	+	40.6316i	0.829809	+	1.60988i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	2.60428	−	1.50358i	0.102863	−	0.0593878i	−0.447686	−	0.894191i	$-0.647752\pi$
$641$	2.60428	−	1.50358i	0.102863	−	0.0593878i	0.550549	+	0.834803i	$0.314418\pi$
$642$		0			0
$643$	15.4015	+	15.4015i	0.607375	+	0.607375i	0.942259	−	0.334884i	$-0.108697\pi$
$643$	15.4015	+	15.4015i	0.607375	+	0.607375i	−0.334884	+	0.942259i	$0.608697\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.340705	−	1.27153i	0.0133945	−	0.0499890i	−0.958905	−	0.283727i	$-0.908429\pi$
$647$	0.340705	−	1.27153i	0.0133945	−	0.0499890i	0.972300	+	0.233738i	$0.0750958\pi$
$648$		0			0
$649$	−35.9118	−	20.7337i	−1.40966	−	0.813867i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−2.10508	−	7.85628i	−0.0823783	−	0.307440i	0.912427	−	0.409240i	$-0.134206\pi$
$653$	−2.10508	−	7.85628i	−0.0823783	−	0.307440i	−0.994805	+	0.101801i	$0.967540\pi$
$654$		0			0
$655$	−9.54522	−	30.1092i	−0.372963	−	1.17646i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−2.11773			−0.0824949			−0.0412475	−	0.999149i	$-0.513133\pi$
$659$	−2.11773			−0.0824949			−0.0412475	+	0.999149i	$0.513133\pi$
$660$		0			0
$661$	−5.70613	−	9.88332i	−0.221943	−	0.384416i	0.733455	−	0.679738i	$-0.237907\pi$
$661$	−5.70613	−	9.88332i	−0.221943	−	0.384416i	−0.955398	+	0.295322i	$0.904573\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−31.7473	+	4.87163i	−1.23111	+	0.188914i
$666$		0			0
$667$	−8.62666	−	32.1951i	−0.334026	−	1.24660i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			36.5967i			1.41280i
$672$		0			0
$673$	−22.0017	−	22.0017i	−0.848101	−	0.848101i	0.141795	−	0.989896i	$-0.454713\pi$
$673$	−22.0017	−	22.0017i	−0.848101	−	0.848101i	−0.989896	+	0.141795i	$0.954713\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	44.8725	−	12.0235i	1.72459	−	0.462102i	0.745664	−	0.666322i	$-0.232132\pi$
$677$	44.8725	−	12.0235i	1.72459	−	0.462102i	0.978925	+	0.204219i	$0.0654656\pi$
$678$		0			0
$679$	−27.5754	−	37.7677i	−1.05825	−	1.44939i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−32.8924	−	8.81350i	−1.25859	−	0.337239i	−0.432943	−	0.901421i	$-0.642525\pi$
$683$	−32.8924	−	8.81350i	−1.25859	−	0.337239i	−0.825651	+	0.564182i	$0.809192\pi$
$684$		0			0
$685$	10.9901	−	7.02569i	0.419912	−	0.268438i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−20.2525	−	35.0784i	−0.771559	−	1.33638i
$690$		0			0
$691$	−10.9241	+	18.9211i	−0.415573	+	0.719793i	−0.995488	−	0.0948834i	$-0.969752\pi$
$691$	−10.9241	+	18.9211i	−0.415573	+	0.719793i	0.579916	+	0.814677i	$0.303086\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−19.0980	+	20.9074i	−0.724428	+	0.793062i
$696$		0			0
$697$	15.7704	+	4.22567i	0.597347	+	0.160059i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			2.96757i			0.112084i	0.998428	+	0.0560418i	$0.0178480\pi$
$701$			2.96757i			0.112084i	−0.998428	+	0.0560418i	$0.982152\pi$
$702$		0			0
$703$	0.400307	−	1.49397i	0.0150979	−	0.0563460i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.99431	−	7.74610i	−0.112612	−	0.291322i
$708$		0			0
$709$	35.0959	+	20.2626i	1.31805	+	0.760978i	0.983415	−	0.181368i	$-0.0580526\pi$
$709$	35.0959	+	20.2626i	1.31805	+	0.760978i	0.334638	+	0.942347i	$0.391386\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−9.52424	+	9.52424i	−0.356686	+	0.356686i
$714$		0			0
$715$	31.3807	+	49.0881i	1.17357	+	1.83579i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−18.9524	+	32.8266i	−0.706806	+	1.22422i	0.259229	+	0.965816i	$0.416531\pi$
$719$	−18.9524	+	32.8266i	−0.706806	+	1.22422i	−0.966036	+	0.258409i	$0.916802\pi$
$720$		0			0
$721$	0.332694	+	3.09553i	0.0123902	+	0.115284i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.74248	+	19.2236i	0.0647142	+	0.713946i
$726$		0			0
$727$	8.38400	−	8.38400i	0.310945	−	0.310945i	−0.534330	−	0.845276i	$-0.679436\pi$
$727$	8.38400	−	8.38400i	0.310945	−	0.310945i	0.845276	+	0.534330i	$0.179436\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	17.7064	−	10.2228i	0.654893	−	0.378103i
$732$		0			0
$733$	33.8136	−	9.06033i	1.24893	−	0.334651i	0.427010	−	0.904247i	$-0.359567\pi$
$733$	33.8136	−	9.06033i	1.24893	−	0.334651i	0.821925	+	0.569596i	$0.192900\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	22.7563	−	6.09753i	0.838238	−	0.224605i
$738$		0			0
$739$	15.1608	−	8.75308i	0.557699	−	0.321987i	−0.194523	−	0.980898i	$-0.562316\pi$
$739$	15.1608	−	8.75308i	0.557699	−	0.321987i	0.752221	+	0.658911i	$0.228982\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.6772	+	10.6772i	−0.391710	+	0.391710i	−0.875297	−	0.483586i	$-0.839334\pi$
$743$	−10.6772	+	10.6772i	−0.391710	+	0.391710i	0.483586	+	0.875297i	$0.339334\pi$
$744$		0			0
$745$	−35.3735	+	11.2141i	−1.29598	+	0.410853i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.59585	−	14.8485i	−0.0583110	−	0.542551i
$750$		0			0
$751$	−2.77825	+	4.81207i	−0.101380	+	0.175595i	−0.912253	−	0.409626i	$-0.865659\pi$
$751$	−2.77825	+	4.81207i	−0.101380	+	0.175595i	0.810874	+	0.585221i	$0.198992\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	11.1138	−	50.5051i	0.404473	−	1.83807i
$756$		0			0
$757$	4.18611	−	4.18611i	0.152147	−	0.152147i	−0.626929	−	0.779076i	$-0.715689\pi$
$757$	4.18611	−	4.18611i	0.152147	−	0.152147i	0.779076	+	0.626929i	$0.215689\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−38.7651	−	22.3810i	−1.40523	−	0.811312i	−0.410310	−	0.911946i	$-0.634579\pi$
$761$	−38.7651	−	22.3810i	−1.40523	−	0.811312i	−0.994923	+	0.100635i	$0.967913\pi$
$762$		0			0
$763$	−11.4450	−	29.6074i	−0.414335	−	1.07186i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	17.5657	−	65.5559i	0.634259	−	2.36709i
$768$		0			0
$769$		−	28.0618i		−	1.01194i	−0.862553	−	0.505968i	$-0.831136\pi$
$769$		−	28.0618i		−	1.01194i	0.862553	−	0.505968i	$-0.168864\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	36.5524	+	9.79419i	1.31470	+	0.352272i	0.846989	−	0.531610i	$-0.178413\pi$
$773$	36.5524	+	9.79419i	1.31470	+	0.352272i	0.467709	+	0.883882i	$0.345079\pi$
$774$		0			0
$775$	6.37558	−	4.49403i	0.229018	−	0.161430i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	8.52260	−	14.7616i	0.305354	−	0.528888i
$780$		0			0
$781$	−1.33450	−	2.31142i	−0.0477521	−	0.0827090i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.68584	−	5.76568i	−0.131553	−	0.205786i
$786$		0			0
$787$	20.9091	+	5.60257i	0.745328	+	0.199710i	0.611445	−	0.791287i	$-0.290589\pi$
$787$	20.9091	+	5.60257i	0.745328	+	0.199710i	0.133883	+	0.990997i	$0.457255\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	24.5478	+	33.6211i	0.872820	+	1.19543i
$792$		0			0
$793$	−57.8559	+	15.5024i	−2.05452	+	0.550508i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	9.92920	+	9.92920i	0.351710	+	0.351710i	0.860746	−	0.509035i	$-0.169998\pi$
$797$	9.92920	+	9.92920i	0.351710	+	0.351710i	−0.509035	+	0.860746i	$0.669998\pi$
$798$		0			0
$799$		−	4.11889i		−	0.145716i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−11.5430	−	43.0791i	−0.407344	−	1.52023i
$804$		0			0
$805$	−41.1784	−	30.2220i	−1.45135	−	1.06519i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	8.79298	+	15.2299i	0.309145	+	0.535455i	0.978176	−	0.207780i	$-0.0666239\pi$
$809$	8.79298	+	15.2299i	0.309145	+	0.535455i	−0.669031	+	0.743235i	$0.733291\pi$
$810$		0			0
$811$	14.2296			0.499669			0.249834	−	0.968289i	$-0.419624\pi$
$811$	14.2296			0.499669			0.249834	+	0.968289i	$0.419624\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−9.84260	−	5.10418i	−0.344771	−	0.178791i
$816$		0			0
$817$	−5.52457	−	20.6180i	−0.193280	−	0.721331i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−24.1320	−	13.9326i	−0.842212	−	0.486252i	0.0158033	−	0.999875i	$-0.494969\pi$
$821$	−24.1320	−	13.9326i	−0.842212	−	0.486252i	−0.858016	+	0.513624i	$0.828303\pi$
$822$		0			0
$823$	−8.71302	+	32.5174i	−0.303717	+	1.13349i	0.630328	+	0.776329i	$0.282921\pi$
$823$	−8.71302	+	32.5174i	−0.303717	+	1.13349i	−0.934044	+	0.357157i	$0.883746\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	16.4123	+	16.4123i	0.570711	+	0.570711i	0.932327	−	0.361616i	$-0.117775\pi$
$827$	16.4123	+	16.4123i	0.570711	+	0.570711i	−0.361616	+	0.932327i	$0.617775\pi$
$828$		0			0
$829$	19.7621	−	11.4096i	0.686365	−	0.396273i	−0.115884	−	0.993263i	$-0.536970\pi$
$829$	19.7621	−	11.4096i	0.686365	−	0.396273i	0.802249	+	0.596990i	$0.203637\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−19.6824	+	30.6217i	−0.681955	+	1.06098i
$834$		0			0
$835$	−0.342144	−	7.56475i	−0.0118404	−	0.261789i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−11.9662			−0.413120			−0.206560	−	0.978434i	$-0.566227\pi$
$839$	−11.9662			−0.413120			−0.206560	+	0.978434i	$0.566227\pi$
$840$		0			0
$841$	−14.0967			−0.486093
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−44.7056	+	48.9411i	−1.53792	+	1.68363i
$846$		0			0
$847$	−10.1346	−	8.16760i	−0.348231	−	0.280642i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	2.13013	−	1.22983i	0.0730199	−	0.0421581i
$852$		0			0
$853$	−21.0778	−	21.0778i	−0.721689	−	0.721689i	0.247260	−	0.968949i	$-0.420470\pi$
$853$	−21.0778	−	21.0778i	−0.721689	−	0.721689i	−0.968949	+	0.247260i	$0.920470\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−10.2355	+	38.1995i	−0.349639	+	1.30487i	0.537460	+	0.843289i	$0.319384\pi$
$857$	−10.2355	+	38.1995i	−0.349639	+	1.30487i	−0.887099	+	0.461580i	$0.847283\pi$
$858$		0			0
$859$	−26.9617	−	15.5664i	−0.919922	−	0.531117i	−0.0363117	−	0.999341i	$-0.511561\pi$
$859$	−26.9617	−	15.5664i	−0.919922	−	0.531117i	−0.883610	+	0.468223i	$0.844894\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.89119	−	7.05803i	−0.0643769	−	0.240258i	0.926238	−	0.376939i	$-0.123023\pi$
$863$	−1.89119	−	7.05803i	−0.0643769	−	0.240258i	−0.990615	+	0.136681i	$0.956357\pi$
$864$		0			0
$865$	−18.2082	+	35.1117i	−0.619097	+	1.19383i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	64.0313			2.17211
$870$		0			0
$871$	19.2792	+	33.3926i	0.653252	+	1.13147i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	20.5123	+	21.3130i	0.693443	+	0.720511i
$876$		0			0
$877$	−6.64534	−	24.8008i	−0.224397	−	0.837462i	−0.982645	−	0.185495i	$-0.940611\pi$
$877$	−6.64534	−	24.8008i	−0.224397	−	0.837462i	0.758248	−	0.651966i	$-0.226056\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	2.90498i		−	0.0978712i	−0.998802	−	0.0489356i	$-0.984417\pi$
$881$		−	2.90498i		−	0.0978712i	0.998802	−	0.0489356i	$-0.0155829\pi$
$882$		0			0
$883$	1.08162	+	1.08162i	0.0363995	+	0.0363995i	0.725072	−	0.688673i	$-0.241806\pi$
$883$	1.08162	+	1.08162i	0.0363995	+	0.0363995i	−0.688673	+	0.725072i	$0.741806\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	28.5630	−	7.65344i	0.959053	−	0.256978i	0.254854	−	0.966980i	$-0.417973\pi$
$887$	28.5630	−	7.65344i	0.959053	−	0.256978i	0.704200	+	0.710002i	$0.251306\pi$
$888$		0			0
$889$	1.98383	+	2.71709i	0.0665355	+	0.0911282i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.15363	−	1.11296i	−0.138996	−	0.0372438i
$894$		0			0
$895$	−3.68190	+	16.7319i	−0.123073	+	0.559284i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.01128	−	5.21569i	−0.100432	−	0.173953i
$900$		0			0
$901$	16.1277	−	27.9341i	0.537293	−	0.930619i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.690519	+	0.630759i	0.0229536	+	0.0209671i
$906$		0			0
$907$	−25.8960	−	6.93882i	−0.859863	−	0.230400i	−0.198164	−	0.980169i	$-0.563498\pi$
$907$	−25.8960	−	6.93882i	−0.859863	−	0.230400i	−0.661699	+	0.749769i	$0.730164\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			11.3305i			0.375398i	0.982227	+	0.187699i	$0.0601029\pi$
$911$			11.3305i			0.375398i	−0.982227	+	0.187699i	$0.939897\pi$
$912$		0			0
$913$	−5.78443	+	21.5878i	−0.191437	+	0.714451i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−23.4515	+	29.0994i	−0.774436	+	0.960947i
$918$		0			0
$919$	30.6984	+	17.7237i	1.01265	+	0.584652i	0.911966	−	0.410267i	$-0.134564\pi$
$919$	30.6984	+	17.7237i	1.01265	+	0.584652i	0.100681	+	0.994919i	$0.467898\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	3.08884	−	3.08884i	0.101670	−	0.101670i
$924$		0			0
$925$	−1.33699	+	0.491369i	−0.0439600	+	0.0161561i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	21.1105	−	36.5644i	0.692613	−	1.19964i	−0.278366	−	0.960475i	$-0.589793\pi$
$929$	21.1105	−	36.5644i	0.692613	−	1.19964i	0.970979	−	0.239165i	$-0.0768738\pi$
$930$		0			0
$931$	25.5615	+	28.1226i	0.837746	+	0.921682i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−21.3586	+	41.1867i	−0.698501	+	1.34695i
$936$		0			0
$937$	−32.2881	+	32.2881i	−1.05481	+	1.05481i	−0.0563972	+	0.998408i	$0.517961\pi$
$937$	−32.2881	+	32.2881i	−1.05481	+	1.05481i	−0.998408	+	0.0563972i	$0.982039\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	35.4853	−	20.4875i	1.15679	−	0.667872i	0.206256	−	0.978498i	$-0.433872\pi$
$941$	35.4853	−	20.4875i	1.15679	−	0.667872i	0.950532	+	0.310626i	$0.100539\pi$
$942$		0			0
$943$	26.1833	−	7.01580i	0.852646	−	0.228466i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−44.0229	+	11.7959i	−1.43055	+	0.383315i	−0.889214	−	0.457491i	$-0.848748\pi$
$947$	−44.0229	+	11.7959i	−1.43055	+	0.383315i	−0.541337	+	0.840806i	$0.682082\pi$
$948$		0			0
$949$	63.2143	−	36.4968i	2.05202	−	1.18474i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−6.20043	+	6.20043i	−0.200851	+	0.200851i	−0.800365	−	0.599513i	$-0.795361\pi$
$953$	−6.20043	+	6.20043i	−0.200851	+	0.200851i	0.599513	+	0.800365i	$0.295361\pi$
$954$		0			0
$955$	3.53154	+	11.1398i	0.114278	+	0.360475i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−14.1141	−	6.24440i	−0.455769	−	0.201642i
$960$		0			0
$961$	14.2831	−	24.7391i	0.460746	−	0.798035i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	4.07055	−	2.60219i	0.131036	−	0.0837674i
$966$		0			0
$967$	16.5609	−	16.5609i	0.532562	−	0.532562i	−0.388772	−	0.921334i	$-0.627101\pi$
$967$	16.5609	−	16.5609i	0.532562	−	0.532562i	0.921334	+	0.388772i	$0.127101\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	29.5825	+	17.0794i	0.949346	+	0.548105i	0.892878	−	0.450299i	$-0.148683\pi$
$971$	29.5825	+	17.0794i	0.949346	+	0.548105i	0.0564686	+	0.998404i	$0.482016\pi$
$972$		0			0
$973$	33.1048	+	5.16374i	1.06129	+	0.165542i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−5.13303	+	19.1567i	−0.164220	+	0.612878i	0.833918	+	0.551888i	$0.186092\pi$
$977$	−5.13303	+	19.1567i	−0.164220	+	0.612878i	−0.998138	+	0.0609900i	$0.980574\pi$
$978$		0			0
$979$			45.4029i			1.45108i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	38.1666	+	10.2267i	1.21732	+	0.326181i	0.809632	−	0.586938i	$-0.199667\pi$
$983$	38.1666	+	10.2267i	1.21732	+	0.326181i	0.407692	+	0.913119i	$0.366334\pi$
$984$		0			0
$985$	−1.73294	−	38.3149i	−0.0552159	−	1.22081i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	16.9727	−	29.3976i	0.539700	−	0.934788i
$990$		0			0
$991$	25.4154	+	44.0207i	0.807346	+	1.39836i	0.914696	+	0.404143i	$0.132430\pi$
$991$	25.4154	+	44.0207i	0.807346	+	1.39836i	−0.107349	+	0.994221i	$0.534236\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	16.9490	+	3.72969i	0.537320	+	0.118239i
$996$		0			0
$997$	3.27003	+	0.876201i	0.103563	+	0.0277496i	0.310228	−	0.950662i	$-0.399595\pi$
$997$	3.27003	+	0.876201i	0.103563	+	0.0277496i	−0.206665	+	0.978412i	$0.566261\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.ej.a.233.13	yes	64
3.2	odd	2	inner	1260.2.ej.a.233.4	yes	64
5.2	odd	4	inner	1260.2.ej.a.737.15	yes	64
7.4	even	3	inner	1260.2.ej.a.53.2	✓	64
15.2	even	4	inner	1260.2.ej.a.737.2	yes	64
21.11	odd	6	inner	1260.2.ej.a.53.15	yes	64
35.32	odd	12	inner	1260.2.ej.a.557.4	yes	64
105.32	even	12	inner	1260.2.ej.a.557.13	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.ej.a.53.2	✓	64	7.4	even	3	inner
1260.2.ej.a.53.15	yes	64	21.11	odd	6	inner
1260.2.ej.a.233.4	yes	64	3.2	odd	2	inner
1260.2.ej.a.233.13	yes	64	1.1	even	1	trivial
1260.2.ej.a.557.4	yes	64	35.32	odd	12	inner
1260.2.ej.a.557.13	yes	64	105.32	even	12	inner
1260.2.ej.a.737.2	yes	64	15.2	even	4	inner
1260.2.ej.a.737.15	yes	64	5.2	odd	4	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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.ej (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.65096 + 1.50808i) q^{5} +(0.407758 - 2.61414i) q^{7} +O(q^{10})\)	\(q+(1.65096 + 1.50808i) q^{5} +(0.407758 - 2.61414i) q^{7} +(-3.45539 + 1.99497i) q^{11} +(-4.61757 - 4.61757i) q^{13} +(1.34592 - 5.02305i) q^{17} +(-4.70173 - 2.71454i) q^{19} +(-2.23461 - 8.33968i) q^{23} +(0.451364 + 4.97959i) q^{25} +3.86048 q^{29} +(-0.780027 - 1.35105i) q^{31} +(4.61554 - 3.70092i) q^{35} +(0.0737337 + 0.275178i) q^{37} +3.13961i q^{41} +(2.78010 + 2.78010i) q^{43} +(0.765069 - 0.205000i) q^{47} +(-6.66747 - 2.13187i) q^{49} +(5.99134 + 1.60537i) q^{53} +(-8.71331 - 1.91740i) q^{55} +(5.19648 + 9.00057i) q^{59} +(4.58612 - 7.94339i) q^{61} +(-0.659758 - 14.5871i) q^{65} +(-5.70341 - 1.52822i) q^{67} +0.668930i q^{71} +(-2.89302 + 10.7969i) q^{73} +(3.80617 + 9.84635i) q^{77} +(-13.8981 - 8.02408i) q^{79} +(3.96079 - 3.96079i) q^{83} +(9.79725 - 6.26311i) q^{85} +(5.68967 - 9.85480i) q^{89} +(-13.9538 + 10.1881i) q^{91} +(-3.66862 - 11.5722i) q^{95} +(12.4980 - 12.4980i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 64 * q - 8 * q^7	\( 64 q - 8 q^{7} + 16 q^{25} + 32 q^{31} + 16 q^{37} - 16 q^{43} + 32 q^{55} + 48 q^{61} + 32 q^{67} + 40 q^{73} + 80 q^{85} + 96 q^{91} + 80 q^{97}+O(q^{100}) \) 64 * q - 8 * q^7 + 16 * q^25 + 32 * q^31 + 16 * q^37 - 16 * q^43 + 32 * q^55 + 48 * q^61 + 32 * q^67 + 40 * q^73 + 80 * q^85 + 96 * q^91 + 80 * q^97

Introduction

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