LMFDB - Embedded newform 1260.2.ej.a.737.2

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			737.2
Character	$\chi$	$=$	1260.737
Dual form			1260.2.ej.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.13152 - 0.675735i) q^{5} +(2.61414 + 0.407758i) q^{7} +O(q^{10})$	$q+(-2.13152 - 0.675735i) q^{5} +(2.61414 + 0.407758i) q^{7} +(3.45539 - 1.99497i) q^{11} +(-4.61757 + 4.61757i) q^{13} +(-5.02305 - 1.34592i) q^{17} +(4.70173 + 2.71454i) q^{19} +(8.33968 - 2.23461i) q^{23} +(4.08677 + 2.88069i) q^{25} +3.86048 q^{29} +(-0.780027 - 1.35105i) q^{31} +(-5.29656 - 2.63561i) q^{35} +(-0.275178 + 0.0737337i) q^{37} -3.13961i q^{41} +(2.78010 - 2.78010i) q^{43} +(-0.205000 - 0.765069i) q^{47} +(6.66747 + 2.13187i) q^{49} +(-1.60537 + 5.99134i) q^{53} +(-8.71331 + 1.91740i) q^{55} +(5.19648 + 9.00057i) q^{59} +(4.58612 - 7.94339i) q^{61} +(12.9627 - 6.72220i) q^{65} +(1.52822 - 5.70341i) q^{67} -0.668930i q^{71} +(10.7969 + 2.89302i) q^{73} +(9.84635 - 3.80617i) q^{77} +(13.8981 + 8.02408i) q^{79} +(3.96079 + 3.96079i) q^{83} +(9.79725 + 6.26311i) q^{85} +(5.68967 - 9.85480i) q^{89} +(-13.9538 + 10.1881i) q^{91} +(-8.18752 - 8.96323i) q^{95} +(12.4980 + 12.4980i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

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

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
$5$	−2.13152	−	0.675735i	−0.953245	−	0.302198i
$5$	−2.13152	−	0.675735i	−0.953245	−	0.302198i
$6$		0			0
$7$	2.61414	+	0.407758i	0.988052	+	0.154118i
$7$	2.61414	+	0.407758i	0.988052	+	0.154118i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.45539	−	1.99497i	1.04184	−	0.601507i	0.121486	−	0.992593i	$-0.461234\pi$
$11$	3.45539	−	1.99497i	1.04184	−	0.601507i	0.920354	+	0.391086i	$0.127901\pi$
$12$		0			0
$13$	−4.61757	+	4.61757i	−1.28068	+	1.28068i	−0.340406	+	0.940278i	$0.610565\pi$
$13$	−4.61757	+	4.61757i	−1.28068	+	1.28068i	−0.940278	+	0.340406i	$0.889435\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−5.02305	−	1.34592i	−1.21827	−	0.326434i	−0.408267	−	0.912862i	$-0.633867\pi$
$17$	−5.02305	−	1.34592i	−1.21827	−	0.326434i	−0.810001	+	0.586428i	$0.800534\pi$
$18$		0			0
$19$	4.70173	+	2.71454i	1.07865	+	0.622759i	0.930532	−	0.366211i	$-0.119345\pi$
$19$	4.70173	+	2.71454i	1.07865	+	0.622759i	0.148118	+	0.988970i	$0.452678\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	8.33968	−	2.23461i	1.73894	−	0.465948i	0.756731	−	0.653726i	$-0.226795\pi$
$23$	8.33968	−	2.23461i	1.73894	−	0.465948i	0.982212	+	0.187777i	$0.0601284\pi$
$24$		0			0
$25$	4.08677	+	2.88069i	0.817353	+	0.576137i
$26$		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
$35$	−5.29656	−	2.63561i	−0.895282	−	0.445500i
$36$		0			0
$37$	−0.275178	+	0.0737337i	−0.0452390	+	0.0121218i	−0.281368	−	0.959600i	$-0.590788\pi$
$37$	−0.275178	+	0.0737337i	−0.0452390	+	0.0121218i	0.236129	+	0.971722i	$0.424121\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	3.13961i		−	0.490324i	−0.969482	−	0.245162i	$-0.921159\pi$
$41$		−	3.13961i		−	0.490324i	0.969482	−	0.245162i	$-0.0788412\pi$
$42$		0			0
$43$	2.78010	−	2.78010i	0.423961	−	0.423961i	−0.462604	−	0.886565i	$-0.653085\pi$
$43$	2.78010	−	2.78010i	0.423961	−	0.423961i	0.886565	+	0.462604i	$0.153085\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.205000	−	0.765069i	−0.0299023	−	0.111597i	0.949362	−	0.314185i	$-0.101731\pi$
$47$	−0.205000	−	0.765069i	−0.0299023	−	0.111597i	−0.979264	+	0.202588i	$0.935065\pi$
$48$		0			0
$49$	6.66747	+	2.13187i	0.952495	+	0.304553i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.60537	+	5.99134i	−0.220515	+	0.822973i	0.763637	+	0.645646i	$0.223412\pi$
$53$	−1.60537	+	5.99134i	−0.220515	+	0.822973i	−0.984152	+	0.177327i	$0.943255\pi$
$54$		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
$65$	12.9627	−	6.72220i	1.60783	−	0.833787i
$66$		0			0
$67$	1.52822	−	5.70341i	0.186702	−	0.696782i	−0.807557	−	0.589789i	$-0.799211\pi$
$67$	1.52822	−	5.70341i	0.186702	−	0.696782i	0.994260	−	0.106993i	$-0.0341224\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	0.668930i		−	0.0793874i	−0.999212	−	0.0396937i	$-0.987362\pi$
$71$		−	0.668930i		−	0.0793874i	0.999212	−	0.0396937i	$-0.0126382\pi$
$72$		0			0
$73$	10.7969	+	2.89302i	1.26368	+	0.338603i	0.827608	−	0.561307i	$-0.189701\pi$
$73$	10.7969	+	2.89302i	1.26368	+	0.338603i	0.436076	+	0.899910i	$0.356368\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.84635	−	3.80617i	1.12210	−	0.433754i
$78$		0			0
$79$	13.8981	+	8.02408i	1.56366	+	0.902780i	0.996882	+	0.0789092i	$0.0251437\pi$
$79$	13.8981	+	8.02408i	1.56366	+	0.902780i	0.566778	+	0.823870i	$0.308190\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.96079	+	3.96079i	0.434754	+	0.434754i	0.890242	−	0.455488i	$-0.150535\pi$
$83$	3.96079	+	3.96079i	0.434754	+	0.434754i	−0.455488	+	0.890242i	$0.650535\pi$
$84$		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
$95$	−8.18752	−	8.96323i	−0.840022	−	0.919608i
$96$		0			0
$97$	12.4980	+	12.4980i	1.26898	+	1.26898i	0.946616	+	0.322363i	$0.104477\pi$
$97$	12.4980	+	12.4980i	1.26898	+	1.26898i	0.322363	+	0.946616i	$0.395523\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.71835	+	1.56944i	−0.270486	+	0.156165i	−0.629108	−	0.777318i	$-0.716580\pi$
$101$	−2.71835	+	1.56944i	−0.270486	+	0.156165i	0.358623	+	0.933483i	$0.383246\pi$
$102$		0			0
$103$	0.304563	+	1.13664i	0.0300095	+	0.111997i	0.979306	−	0.202385i	$-0.0648693\pi$
$103$	0.304563	+	1.13664i	0.0300095	+	0.111997i	−0.949297	+	0.314382i	$0.898203\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.46091	−	5.45218i	−0.141231	−	0.527082i	−0.999894	−	0.0145417i	$-0.995371\pi$
$107$	−1.46091	−	5.45218i	−0.141231	−	0.527082i	0.858663	−	0.512541i	$-0.171296\pi$
$108$		0			0
$109$	−10.3902	+	5.99877i	−0.995198	+	0.574578i	−0.906824	−	0.421509i	$-0.861500\pi$
$109$	−10.3902	+	5.99877i	−0.995198	+	0.574578i	−0.0883743	+	0.996087i	$0.528167\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−11.1258	−	11.1258i	−1.04663	−	1.04663i	−0.998858	−	0.0477714i	$-0.984788\pi$
$113$	−11.1258	−	11.1258i	−1.04663	−	1.04663i	−0.0477714	−	0.998858i	$-0.515212\pi$
$114$		0			0
$115$	−19.2862	−	0.872291i	−1.79845	−	0.0813416i
$116$		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	0.666088	−	0.745873i	$-0.267967\pi$
$127$	−0.899132	−	0.899132i	−0.0797851	−	0.0797851i	−0.745873	+	0.666088i	$0.767967\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	12.2332	+	7.06285i	1.06882	+	0.617084i	0.927859	−	0.372931i	$-0.121647\pi$
$131$	12.2332	+	7.06285i	1.06882	+	0.617084i	0.140962	+	0.990015i	$0.454981\pi$
$132$		0			0
$133$	11.1841	+	9.01337i	0.969785	+	0.781558i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.63464	−	1.50980i	−0.481400	−	0.128991i	0.00995439	−	0.999950i	$-0.496831\pi$
$137$	−5.63464	−	1.50980i	−0.481400	−	0.128991i	−0.491354	+	0.870960i	$0.663498\pi$
$138$		0			0
$139$		−	12.6637i		−	1.07412i	−0.843543	−	0.537062i	$-0.819534\pi$
$139$		−	12.6637i		−	1.07412i	0.843543	−	0.537062i	$-0.180466\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−6.74360	+	25.1675i	−0.563928	+	2.10461i
$144$		0			0
$145$	−8.22869	−	2.60866i	−0.683356	−	0.216637i
$146$		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
$157$	0.792075	−	2.95607i	0.0632145	−	0.235920i	−0.927089	−	0.374842i	$-0.877697\pi$
$157$	0.792075	−	2.95607i	0.0632145	−	0.235920i	0.990303	+	0.138922i	$0.0443637\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	22.7123	−	2.44101i	1.78998	−	0.192379i
$162$		0			0
$163$	1.28333	+	4.78946i	0.100518	+	0.375140i	0.997798	−	0.0663225i	$-0.0211266\pi$
$163$	1.28333	+	4.78946i	0.100518	+	0.375140i	−0.897280	+	0.441462i	$0.854460\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−2.39463	+	2.39463i	−0.185302	+	0.185302i	−0.793662	−	0.608360i	$-0.791828\pi$
$167$	−2.39463	+	2.39463i	−0.185302	+	0.185302i	0.608360	+	0.793662i	$0.291828\pi$
$168$		0			0
$169$		−	29.6440i		−	2.28031i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−17.0855	+	4.57805i	−1.29899	+	0.348063i	−0.841067	−	0.540931i	$-0.818072\pi$
$173$	−17.0855	+	4.57805i	−1.29899	+	0.348063i	−0.457920	+	0.888993i	$0.651405\pi$
$174$		0			0
$175$	9.50876	+	9.19693i	0.718795	+	0.695223i
$176$		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
$185$	0.636372	+	0.0287823i	0.0467870	+	0.00211612i
$186$		0			0
$187$	−20.0417	+	5.37015i	−1.46559	+	0.392704i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.52604	−	2.61311i	−0.327493	−	0.189078i	0.327235	−	0.944943i	$-0.393883\pi$
$191$	−4.52604	−	2.61311i	−0.327493	−	0.189078i	−0.654727	+	0.755865i	$0.727217\pi$
$192$		0			0
$193$	−2.08697	−	0.559202i	−0.150223	−	0.0402522i	0.182924	−	0.983127i	$-0.441444\pi$
$193$	−2.08697	−	0.559202i	−0.150223	−	0.0402522i	−0.333147	+	0.942875i	$0.608111\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−12.1286	+	12.1286i	−0.864128	+	0.864128i	−0.991815	−	0.127686i	$-0.959245\pi$
$197$	−12.1286	+	12.1286i	−0.864128	+	0.864128i	0.127686	+	0.991815i	$0.459245\pi$
$198$		0			0
$199$	−6.72138	+	3.88059i	−0.476466	+	0.275088i	−0.718943	−	0.695069i	$-0.755374\pi$
$199$	−6.72138	+	3.88059i	−0.476466	+	0.275088i	0.242477	+	0.970157i	$0.422040\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	10.0918	+	1.57414i	0.708308	+	0.110483i
$204$		0			0
$205$	−2.12154	+	6.69214i	−0.148175	+	0.467399i
$206$		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
$215$	−7.80445	+	4.04723i	−0.532259	+	0.276019i
$216$		0			0
$217$	−1.48820	−	3.84989i	−0.101026	−	0.261348i
$218$		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	−0.882365	−	0.470566i	$-0.844050\pi$
$223$	−6.14948	+	6.14948i	−0.411799	+	0.411799i	0.470566	+	0.882365i	$0.344050\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−19.1002	−	5.11788i	−1.26772	−	0.339685i	−0.438565	−	0.898700i	$-0.644513\pi$
$227$	−19.1002	−	5.11788i	−1.26772	−	0.339685i	−0.829158	+	0.559014i	$0.811180\pi$
$228$		0			0
$229$	−9.06445	−	5.23336i	−0.598995	−	0.345830i	0.169651	−	0.985504i	$-0.445736\pi$
$229$	−9.06445	−	5.23336i	−0.598995	−	0.345830i	−0.768646	+	0.639674i	$0.779069\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−11.6050	+	3.10955i	−0.760268	+	0.203713i	−0.618068	−	0.786125i	$-0.712084\pi$
$233$	−11.6050	+	3.10955i	−0.760268	+	0.203713i	−0.142200	+	0.989838i	$0.545418\pi$
$234$		0			0
$235$	−0.0800227	+	1.76929i	−0.00522010	+	0.115416i
$236$		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
$245$	−12.7713	−	9.04957i	−0.815926	−	0.578156i
$246$		0			0
$247$	−34.2452	+	9.17597i	−2.17897	+	0.583853i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			13.8447i			0.873872i	0.899493	+	0.436936i	$0.143936\pi$
$251$			13.8447i			0.873872i	−0.899493	+	0.436936i	$0.856064\pi$
$252$		0			0
$253$	24.3589	−	24.3589i	1.53143	−	1.53143i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.47172	−	9.22460i	−0.154182	−	0.575415i	−0.999174	−	0.0406360i	$-0.987062\pi$
$257$	−2.47172	−	9.22460i	−0.154182	−	0.575415i	0.844992	−	0.534779i	$-0.179605\pi$
$258$		0			0
$259$	−0.749420	+	0.0805443i	−0.0465667	+	0.00500478i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−7.04269	+	26.2837i	−0.434271	+	1.62072i	0.308534	+	0.951213i	$0.400162\pi$
$263$	−7.04269	+	26.2837i	−0.434271	+	1.62072i	−0.742805	+	0.669508i	$0.766505\pi$
$264$		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
$275$	19.8683	+	1.80092i	1.19810	+	0.108599i
$276$		0			0
$277$	−7.10337	+	26.5101i	−0.426800	+	1.59284i	0.333160	+	0.942870i	$0.391885\pi$
$277$	−7.10337	+	26.5101i	−0.426800	+	1.59284i	−0.759960	+	0.649970i	$0.774782\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	31.5139i		−	1.87996i	−0.341231	−	0.939980i	$-0.610844\pi$
$281$		−	31.5139i		−	1.87996i	0.341231	−	0.939980i	$-0.389156\pi$
$282$		0			0
$283$	−23.4633	−	6.28698i	−1.39475	−	0.373722i	−0.518294	−	0.855202i	$-0.673433\pi$
$283$	−23.4633	−	6.28698i	−1.39475	−	0.373722i	−0.876457	+	0.481480i	$0.840099\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	1.28020	−	8.20738i	0.0755678	−	0.484466i
$288$		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	0.792786	−	0.609501i	$-0.208630\pi$
$293$	3.13734	+	3.13734i	0.183285	+	0.183285i	−0.609501	+	0.792786i	$0.708630\pi$
$294$		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
$305$	−15.1430	+	13.8325i	−0.867087	+	0.792047i
$306$		0			0
$307$	−8.84326	−	8.84326i	−0.504711	−	0.504711i	0.408187	−	0.912898i	$-0.366161\pi$
$307$	−8.84326	−	8.84326i	−0.504711	−	0.504711i	−0.912898	+	0.408187i	$0.866161\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	24.3630	−	14.0660i	1.38150	−	0.797609i	0.389162	−	0.921169i	$-0.372765\pi$
$311$	24.3630	−	14.0660i	1.38150	−	0.797609i	0.992337	+	0.123560i	$0.0394312\pi$
$312$		0			0
$313$	−5.11789	−	19.1002i	−0.289281	−	1.07961i	−0.945654	−	0.325174i	$-0.894577\pi$
$313$	−5.11789	−	19.1002i	−0.289281	−	1.07961i	0.656374	−	0.754436i	$-0.272089\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.57866	+	9.62368i	0.144832	+	0.540519i	0.999763	+	0.0217779i	$0.00693266\pi$
$317$	2.57866	+	9.62368i	0.144832	+	0.540519i	−0.854931	+	0.518742i	$0.826401\pi$
$318$		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
$325$	−32.1727	+	5.56916i	−1.78462	+	0.308922i
$326$		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	0.855188	−	0.518319i	$-0.173442\pi$
$337$	6.18409	+	6.18409i	0.336869	+	0.336869i	−0.518319	+	0.855188i	$0.673442\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−5.39060	−	3.11227i	−0.291917	−	0.168539i
$342$		0			0
$343$	16.5604	+	8.29173i	0.894178	+	0.447712i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1.97679	−	0.529679i	−0.106120	−	0.0284347i	0.205368	−	0.978685i	$-0.434161\pi$
$347$	−1.97679	−	0.529679i	−0.106120	−	0.0284347i	−0.311488	+	0.950250i	$0.600827\pi$
$348$		0			0
$349$			9.29551i			0.497577i	0.968558	+	0.248788i	$0.0800324\pi$
$349$			9.29551i			0.497577i	−0.968558	+	0.248788i	$0.919968\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	0.201863	−	0.753362i	0.0107441	−	0.0400974i	−0.960346	−	0.278812i	$-0.910059\pi$
$353$	0.201863	−	0.753362i	0.0107441	−	0.0400974i	0.971090	+	0.238715i	$0.0767260\pi$
$354$		0			0
$355$	−0.452019	+	1.42584i	−0.0239907	+	0.0756757i
$356$		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
$367$	0.639821	−	2.38784i	0.0333984	−	0.124644i	−0.947214	−	0.320602i	$-0.896115\pi$
$367$	0.639821	−	2.38784i	0.0333984	−	0.124644i	0.980612	+	0.195958i	$0.0627815\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.63969	+	15.0076i	−0.344715	+	0.779155i
$372$		0			0
$373$	6.21507	+	23.1949i	0.321804	+	1.20099i	0.917486	+	0.397768i	$0.130215\pi$
$373$	6.21507	+	23.1949i	0.321804	+	1.20099i	−0.595682	+	0.803221i	$0.703118\pi$
$374$		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	$-0.986860\pi$
$379$		−	1.60683i		−	0.0825374i	0.999148	−	0.0412687i	$-0.0131400\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.81943	−	2.63111i	0.501750	−	0.134443i	0.000937706	−	1.00000i	$-0.499702\pi$
$383$	9.81943	−	2.63111i	0.501750	−	0.134443i	0.500812	+	0.865556i	$0.333035\pi$
$384$		0			0
$385$	−23.5597	+	1.45942i	−1.20071	+	0.0743789i
$386$		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
$395$	−24.2020	−	26.4949i	−1.21773	−	1.33310i
$396$		0			0
$397$	5.92364	−	1.58723i	0.297299	−	0.0796610i	−0.107086	−	0.994250i	$-0.534152\pi$
$397$	5.92364	−	1.58723i	0.297299	−	0.0796610i	0.404385	+	0.914589i	$0.367486\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	25.8112	+	14.9021i	1.28895	+	0.744175i	0.978467	−	0.206404i	$-0.0661762\pi$
$401$	25.8112	+	14.9021i	1.28895	+	0.744175i	0.310482	+	0.950579i	$0.399510\pi$
$402$		0			0
$403$	9.84039	+	2.63673i	0.490185	+	0.131345i
$404$		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	−0.874975	−	0.484169i	$-0.839122\pi$
$409$	−18.0630	+	10.4287i	−0.893160	+	0.515666i	−0.0181849	+	0.999835i	$0.505789\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	9.91428	+	25.6477i	0.487850	+	1.26204i
$414$		0			0
$415$	−5.76607	−	11.1190i	−0.283045	−	0.545808i
$416$		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
$425$	−16.6508	−	19.9703i	−0.807685	−	0.968702i
$426$		0			0
$427$	15.2277	−	18.8951i	0.736922	−	0.914398i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−17.0734	+	9.85733i	−0.822396	+	0.474811i	−0.851242	−	0.524773i	$-0.824150\pi$
$431$	−17.0734	+	9.85733i	−0.822396	+	0.474811i	0.0288458	+	0.999584i	$0.490817\pi$
$432$		0			0
$433$	2.29281	−	2.29281i	0.110186	−	0.110186i	−0.649865	−	0.760050i	$-0.725174\pi$
$433$	2.29281	−	2.29281i	0.110186	−	0.110186i	0.760050	+	0.649865i	$0.225174\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	45.2768	+	12.1319i	2.16588	+	0.580347i
$438$		0			0
$439$	−16.2466	−	9.37996i	−0.775406	−	0.447681i	0.0593934	−	0.998235i	$-0.481083\pi$
$439$	−16.2466	−	9.37996i	−0.775406	−	0.447681i	−0.834800	+	0.550554i	$0.814417\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.9557	+	2.93558i	−0.520523	+	0.139474i	−0.509508	−	0.860466i	$-0.670173\pi$
$443$	−10.9557	+	2.93558i	−0.520523	+	0.139474i	−0.0110143	+	0.999939i	$0.503506\pi$
$444$		0			0
$445$	−18.7869	+	17.1610i	−0.890584	+	0.813510i
$446$		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
$455$	36.6274	−	12.2871i	1.71712	−	0.576030i
$456$		0			0
$457$	32.4419	−	8.69278i	1.51757	−	0.406631i	0.598628	−	0.801027i	$-0.295713\pi$
$457$	32.4419	−	8.69278i	1.51757	−	0.406631i	0.918941	+	0.394396i	$0.129046\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			5.09025i			0.237077i	0.992949	+	0.118538i	$0.0378208\pi$
$461$			5.09025i			0.237077i	−0.992949	+	0.118538i	$0.962179\pi$
$462$		0			0
$463$	10.1917	−	10.1917i	0.473649	−	0.473649i	−0.429445	−	0.903093i	$-0.641291\pi$
$463$	10.1917	−	10.1917i	0.473649	−	0.473649i	0.903093	+	0.429445i	$0.141291\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.40057	−	20.1552i	−0.249909	−	0.932672i	−0.970852	−	0.239678i	$-0.922958\pi$
$467$	−5.40057	−	20.1552i	−0.249909	−	0.932672i	0.720944	−	0.692994i	$-0.243709\pi$
$468$		0			0
$469$	6.32060	−	14.2864i	0.291858	−	0.659683i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	4.06011	−	15.1525i	0.186684	−	0.696715i
$474$		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
$485$	−18.1944	−	35.0851i	−0.826166	−	1.59313i
$486$		0			0
$487$	−1.43280	+	5.34729i	−0.0649265	+	0.242309i	−0.990761	−	0.135621i	$-0.956697\pi$
$487$	−1.43280	+	5.34729i	−0.0649265	+	0.242309i	0.925834	+	0.377930i	$0.123364\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	43.0848i		−	1.94439i	−0.234176	−	0.972194i	$-0.575239\pi$
$491$		−	43.0848i		−	1.94439i	0.234176	−	0.972194i	$-0.424761\pi$
$492$		0			0
$493$	−19.3914	−	5.19590i	−0.873344	−	0.234012i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.272762	−	1.74868i	0.0122350	−	0.0784389i
$498$		0			0
$499$	19.5051	+	11.2612i	0.873166	+	0.504123i	0.868399	−	0.495866i	$-0.165149\pi$
$499$	19.5051	+	11.2612i	0.873166	+	0.504123i	0.00476710	+	0.999989i	$0.498483\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	6.10761	+	6.10761i	0.272325	+	0.272325i	0.830035	−	0.557711i	$-0.188320\pi$
$503$	6.10761	+	6.10761i	0.272325	+	0.272325i	−0.557711	+	0.830035i	$0.688320\pi$
$504$		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
$515$	0.118888	−	2.62858i	0.00523881	−	0.115829i
$516$		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	−0.971496	−	0.237055i	$-0.923818\pi$
$521$	−28.5763	+	16.4985i	−1.25195	+	0.722813i	−0.280452	+	0.959868i	$0.590484\pi$
$522$		0			0
$523$	−1.03636	−	3.86775i	−0.0453169	−	0.169125i	0.939559	−	0.342388i	$-0.111236\pi$
$523$	−1.03636	−	3.86775i	−0.0453169	−	0.169125i	−0.984876	+	0.173263i	$0.944569\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.09971	+	7.83623i	0.0914649	+	0.341352i
$528$		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
$535$	−0.570273	+	12.6086i	−0.0246550	+	0.545119i
$536$		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	0.979276	−	0.202530i	$-0.0649163\pi$
$547$	18.1666	+	18.1666i	0.776746	+	0.776746i	−0.202530	+	0.979276i	$0.564916\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	18.1509	+	10.4794i	0.773255	+	0.446439i
$552$		0			0
$553$	33.0597	+	26.6431i	1.40584	+	1.13298i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	0.391638	+	0.104939i	0.0165942	+	0.00444641i	0.267107	−	0.963667i	$-0.413932\pi$
$557$	0.391638	+	0.104939i	0.0165942	+	0.00444641i	−0.250512	+	0.968113i	$0.580599\pi$
$558$		0			0
$559$			25.6746i			1.08592i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−5.20676	+	19.4319i	−0.219439	+	0.818957i	0.765118	+	0.643890i	$0.222681\pi$
$563$	−5.20676	+	19.4319i	−0.219439	+	0.818957i	−0.984557	+	0.175066i	$0.943986\pi$
$564$		0			0
$565$	16.1968	+	31.2330i	0.681406	+	1.31398i
$566$		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
$577$	7.64578	−	28.5344i	0.318298	−	1.18790i	−0.602582	−	0.798057i	$-0.705861\pi$
$577$	7.64578	−	28.5344i	0.318298	−	1.18790i	0.920880	−	0.389847i	$-0.127472\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	8.73903	+	11.9691i	0.362556	+	0.496563i
$582$		0			0
$583$	6.40535	+	23.9051i	0.265283	+	0.990048i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	23.7238	−	23.7238i	0.979187	−	0.979187i	−0.0206004	−	0.999788i	$-0.506558\pi$
$587$	23.7238	−	23.7238i	0.979187	−	0.979187i	0.999788	+	0.0206004i	$0.00655778\pi$
$588$		0			0
$589$		−	8.46967i		−	0.348987i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	3.03857	−	0.814182i	0.124779	−	0.0334344i	−0.195889	−	0.980626i	$-0.562759\pi$
$593$	3.03857	−	0.814182i	0.124779	−	0.0334344i	0.320668	+	0.947192i	$0.396093\pi$
$594$		0			0
$595$	23.0576	+	20.3676i	0.945268	+	0.834989i
$596$		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
$605$	−8.12217	+	7.41925i	−0.330213	+	0.301635i
$606$		0			0
$607$	−12.7627	+	3.41975i	−0.518022	+	0.138804i	−0.508351	−	0.861150i	$-0.669745\pi$
$607$	−12.7627	+	3.41975i	−0.518022	+	0.138804i	−0.00967038	+	0.999953i	$0.503078\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	4.47937	+	2.58616i	0.181216	+	0.104625i
$612$		0			0
$613$	−28.3935	−	7.60801i	−1.14680	−	0.307285i	−0.365119	−	0.930961i	$-0.618972\pi$
$613$	−28.3935	−	7.60801i	−1.14680	−	0.307285i	−0.781683	+	0.623676i	$0.785638\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−30.5277	+	30.5277i	−1.22900	+	1.22900i	−0.264654	+	0.964343i	$0.585258\pi$
$617$	−30.5277	+	30.5277i	−1.22900	+	1.22900i	−0.964343	+	0.264654i	$0.914742\pi$
$618$		0			0
$619$	10.7393	−	6.20035i	0.431650	−	0.249213i	−0.268399	−	0.963308i	$-0.586495\pi$
$619$	10.7393	−	6.20035i	0.431650	−	0.249213i	0.700049	+	0.714094i	$0.253161\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	18.8920	−	23.4418i	0.756891	−	0.939177i
$624$		0			0
$625$	8.40330	+	23.5454i	0.336132	+	0.941815i
$626$		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
$635$	1.30894	+	2.52409i	0.0519439	+	0.100166i
$636$		0			0
$637$	−40.6316	+	20.9434i	−1.60988	+	0.829809i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−2.60428	+	1.50358i	−0.102863	+	0.0593878i	−0.550549	−	0.834803i	$-0.685582\pi$
$641$	−2.60428	+	1.50358i	−0.102863	+	0.0593878i	0.447686	+	0.894191i	$0.352248\pi$
$642$		0			0
$643$	15.4015	−	15.4015i	0.607375	−	0.607375i	−0.334884	−	0.942259i	$-0.608697\pi$
$643$	15.4015	−	15.4015i	0.607375	−	0.607375i	0.942259	+	0.334884i	$0.108697\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.27153	−	0.340705i	−0.0499890	−	0.0133945i	0.233738	−	0.972300i	$-0.424904\pi$
$647$	−1.27153	−	0.340705i	−0.0499890	−	0.0133945i	−0.283727	+	0.958905i	$0.591571\pi$
$648$		0			0
$649$	35.9118	+	20.7337i	1.40966	+	0.813867i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	7.85628	−	2.10508i	0.307440	−	0.0823783i	−0.101801	−	0.994805i	$-0.532460\pi$
$653$	7.85628	−	2.10508i	0.307440	−	0.0823783i	0.409240	+	0.912427i	$0.365794\pi$
$654$		0			0
$655$	−21.3027	−	23.3210i	−0.832367	−	0.911227i
$656$		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
$665$	−17.7485	−	26.7697i	−0.688257	−	1.03808i
$666$		0			0
$667$	32.1951	−	8.62666i	1.24660	−	0.334026i
$668$		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	−0.989896	−	0.141795i	$-0.954713\pi$
$673$	−22.0017	+	22.0017i	−0.848101	+	0.848101i	0.141795	+	0.989896i	$0.454713\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.0235	−	44.8725i	−0.462102	−	1.72459i	−0.666322	−	0.745664i	$-0.732132\pi$
$677$	−12.0235	−	44.8725i	−0.462102	−	1.72459i	0.204219	−	0.978925i	$-0.434534\pi$
$678$		0			0
$679$	27.5754	+	37.7677i	1.05825	+	1.44939i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	8.81350	−	32.8924i	0.337239	−	1.25859i	−0.564182	−	0.825651i	$-0.690808\pi$
$683$	8.81350	−	32.8924i	0.337239	−	1.25859i	0.901421	−	0.432943i	$-0.142525\pi$
$684$		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
$695$	−8.55732	+	26.9930i	−0.324598	+	1.02390i
$696$		0			0
$697$	−4.22567	+	15.7704i	−0.160059	+	0.597347i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	2.96757i		−	0.112084i	−0.998428	−	0.0560418i	$-0.982152\pi$
$701$		−	2.96757i		−	0.112084i	0.998428	−	0.0560418i	$-0.0178480\pi$
$702$		0			0
$703$	−1.49397	−	0.400307i	−0.0563460	−	0.0150979i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.74610	+	2.99431i	−0.291322	+	0.112612i
$708$		0			0
$709$	−35.0959	−	20.2626i	−1.31805	−	0.760978i	−0.334638	−	0.942347i	$-0.608614\pi$
$709$	−35.0959	−	20.2626i	−1.31805	−	0.760978i	−0.983415	+	0.181368i	$0.941947\pi$
$710$		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
$725$	15.7769	+	11.1208i	0.585938	+	0.413017i
$726$		0			0
$727$	8.38400	+	8.38400i	0.310945	+	0.310945i	0.845276	−	0.534330i	$-0.179436\pi$
$727$	8.38400	+	8.38400i	0.310945	+	0.310945i	−0.534330	+	0.845276i	$0.679436\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−17.7064	+	10.2228i	−0.654893	+	0.378103i
$732$		0			0
$733$	−9.06033	−	33.8136i	−0.334651	−	1.24893i	−0.904247	−	0.427010i	$-0.859567\pi$
$733$	−9.06033	−	33.8136i	−0.334651	−	1.24893i	0.569596	−	0.821925i	$-0.307100\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.09753	−	22.7563i	−0.224605	−	0.838238i
$738$		0			0
$739$	−15.1608	+	8.75308i	−0.557699	+	0.321987i	−0.752221	−	0.658911i	$-0.771018\pi$
$739$	−15.1608	+	8.75308i	−0.557699	+	0.321987i	0.194523	+	0.980898i	$0.437684\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−10.6772	−	10.6772i	−0.391710	−	0.391710i	0.483586	−	0.875297i	$-0.339334\pi$
$743$	−10.6772	−	10.6772i	−0.391710	−	0.391710i	−0.875297	+	0.483586i	$0.839334\pi$
$744$		0			0
$745$	27.3985	−	25.0273i	1.00380	−	0.916929i
$746$		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	0.779076	−	0.626929i	$-0.215689\pi$
$757$	4.18611	+	4.18611i	0.152147	+	0.152147i	−0.626929	+	0.779076i	$0.715689\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	38.7651	+	22.3810i	1.40523	+	0.811312i	0.994923	−	0.100635i	$-0.0320873\pi$
$761$	38.7651	+	22.3810i	1.40523	+	0.811312i	0.410310	+	0.911946i	$0.365421\pi$
$762$		0			0
$763$	−29.6074	+	11.4450i	−1.07186	+	0.414335i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−65.5559	−	17.5657i	−2.36709	−	0.634259i
$768$		0			0
$769$			28.0618i			1.01194i	0.862553	+	0.505968i	$0.168864\pi$
$769$			28.0618i			1.01194i	−0.862553	+	0.505968i	$0.831136\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−9.79419	+	36.5524i	−0.352272	+	1.31470i	0.531610	+	0.846989i	$0.321587\pi$
$773$	−9.79419	+	36.5524i	−0.352272	+	1.31470i	−0.883882	+	0.467709i	$0.845079\pi$
$774$		0			0
$775$	0.704153	−	7.76843i	0.0252939	−	0.279050i
$776$		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
$787$	−5.60257	+	20.9091i	−0.199710	+	0.745328i	0.791287	+	0.611445i	$0.209411\pi$
$787$	−5.60257	+	20.9091i	−0.199710	+	0.745328i	−0.990997	+	0.133883i	$0.957255\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−24.5478	−	33.6211i	−0.872820	−	1.19543i
$792$		0			0
$793$	15.5024	+	57.8559i	0.550508	+	2.05452i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	9.92920	−	9.92920i	0.351710	−	0.351710i	−0.509035	−	0.860746i	$-0.669998\pi$
$797$	9.92920	−	9.92920i	0.351710	−	0.351710i	0.860746	+	0.509035i	$0.169998\pi$
$798$		0			0
$799$			4.11889i			0.145716i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	43.0791	−	11.5430i	1.52023	−	0.407344i
$804$		0			0
$805$	−50.0612	−	10.1444i	−1.76442	−	0.357543i
$806$		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
$815$	0.500955	−	11.0760i	0.0175477	−	0.387977i
$816$		0			0
$817$	20.6180	−	5.52457i	0.721331	−	0.193280i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	24.1320	+	13.9326i	0.842212	+	0.486252i	0.858016	−	0.513624i	$-0.171697\pi$
$821$	24.1320	+	13.9326i	0.842212	+	0.486252i	−0.0158033	+	0.999875i	$0.505031\pi$
$822$		0			0
$823$	32.5174	+	8.71302i	1.13349	+	0.303717i	0.776329	−	0.630328i	$-0.217079\pi$
$823$	32.5174	+	8.71302i	1.13349	+	0.303717i	0.357157	+	0.934044i	$0.383746\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	16.4123	−	16.4123i	0.570711	−	0.570711i	−0.361616	−	0.932327i	$-0.617775\pi$
$827$	16.4123	−	16.4123i	0.570711	−	0.570711i	0.932327	+	0.361616i	$0.117775\pi$
$828$		0			0
$829$	−19.7621	+	11.4096i	−0.686365	+	0.396273i	−0.802249	−	0.596990i	$-0.796363\pi$
$829$	−19.7621	+	11.4096i	−0.686365	+	0.396273i	0.115884	+	0.993263i	$0.463030\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−30.6217	−	19.6824i	−1.06098	−	0.681955i
$834$		0			0
$835$	6.72233	−	3.48607i	0.232636	−	0.120640i
$836$		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
$845$	−20.0315	+	63.1868i	−0.689103	+	2.17369i
$846$		0			0
$847$	8.16760	−	10.1346i	0.280642	−	0.348231i
$848$		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	−0.968949	−	0.247260i	$-0.920470\pi$
$853$	−21.0778	+	21.0778i	−0.721689	+	0.721689i	0.247260	+	0.968949i	$0.420470\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	38.1995	+	10.2355i	1.30487	+	0.349639i	0.843289	−	0.537460i	$-0.180616\pi$
$857$	38.1995	+	10.2355i	1.30487	+	0.349639i	0.461580	+	0.887099i	$0.347283\pi$
$858$		0			0
$859$	26.9617	+	15.5664i	0.919922	+	0.531117i	0.883610	−	0.468223i	$-0.155106\pi$
$859$	26.9617	+	15.5664i	0.919922	+	0.531117i	0.0363117	+	0.999341i	$0.488439\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	7.05803	−	1.89119i	0.240258	−	0.0643769i	−0.136681	−	0.990615i	$-0.543643\pi$
$863$	7.05803	−	1.89119i	0.240258	−	0.0643769i	0.376939	+	0.926238i	$0.376977\pi$
$864$		0			0
$865$	39.5117	+	1.78706i	1.34344	+	0.0607620i
$866$		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
$875$	−14.0534	−	26.0288i	−0.475093	−	0.879936i
$876$		0			0
$877$	24.8008	−	6.64534i	0.837462	−	0.224397i	0.185495	−	0.982645i	$-0.440611\pi$
$877$	24.8008	−	6.64534i	0.837462	−	0.224397i	0.651966	+	0.758248i	$0.273944\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			2.90498i			0.0978712i	0.998802	+	0.0489356i	$0.0155829\pi$
$881$			2.90498i			0.0978712i	−0.998802	+	0.0489356i	$0.984417\pi$
$882$		0			0
$883$	1.08162	−	1.08162i	0.0363995	−	0.0363995i	−0.688673	−	0.725072i	$-0.741806\pi$
$883$	1.08162	−	1.08162i	0.0363995	−	0.0363995i	0.725072	+	0.688673i	$0.241806\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−7.65344	−	28.5630i	−0.256978	−	0.959053i	−0.966980	−	0.254854i	$-0.917973\pi$
$887$	−7.65344	−	28.5630i	−0.256978	−	0.959053i	0.710002	−	0.704200i	$-0.248694\pi$
$888$		0			0
$889$	−1.98383	−	2.71709i	−0.0665355	−	0.0911282i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	1.11296	−	4.15363i	0.0372438	−	0.138996i
$894$		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
$905$	−0.891513	−	0.282627i	−0.0296349	−	0.00939485i
$906$		0			0
$907$	6.93882	−	25.8960i	0.230400	−	0.859863i	−0.749769	−	0.661699i	$-0.769836\pi$
$907$	6.93882	−	25.8960i	0.230400	−	0.859863i	0.980169	−	0.198164i	$-0.0634978\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	11.3305i		−	0.375398i	−0.982227	−	0.187699i	$-0.939897\pi$
$911$		−	11.3305i		−	0.375398i	0.982227	−	0.187699i	$-0.0601029\pi$
$912$		0			0
$913$	21.5878	+	5.78443i	0.714451	+	0.191437i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	29.0994	+	23.4515i	0.960947	+	0.774436i
$918$		0			0
$919$	−30.6984	−	17.7237i	−1.01265	−	0.584652i	−0.100681	−	0.994919i	$-0.532102\pi$
$919$	−30.6984	−	17.7237i	−1.01265	−	0.584652i	−0.911966	+	0.410267i	$0.865436\pi$
$920$		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
$935$	46.3481	+	2.09627i	1.51574	+	0.0685552i
$936$		0			0
$937$	−32.2881	−	32.2881i	−1.05481	−	1.05481i	−0.998408	−	0.0563972i	$-0.982039\pi$
$937$	−32.2881	−	32.2881i	−1.05481	−	1.05481i	−0.0563972	−	0.998408i	$-0.517961\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−35.4853	+	20.4875i	−1.15679	+	0.667872i	−0.950532	−	0.310626i	$-0.899461\pi$
$941$	−35.4853	+	20.4875i	−1.15679	+	0.667872i	−0.206256	+	0.978498i	$0.566128\pi$
$942$		0			0
$943$	−7.01580	−	26.1833i	−0.228466	−	0.852646i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	11.7959	+	44.0229i	0.383315	+	1.43055i	0.840806	+	0.541337i	$0.182082\pi$
$947$	11.7959	+	44.0229i	0.383315	+	1.43055i	−0.457491	+	0.889214i	$0.651252\pi$
$948$		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	0.599513	−	0.800365i	$-0.295361\pi$
$953$	−6.20043	−	6.20043i	−0.200851	−	0.200851i	−0.800365	+	0.599513i	$0.795361\pi$
$954$		0			0
$955$	7.88158	+	8.62830i	0.255042	+	0.279205i
$956$		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	0.921334	−	0.388772i	$-0.127101\pi$
$967$	16.5609	+	16.5609i	0.532562	+	0.532562i	−0.388772	+	0.921334i	$0.627101\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−29.5825	−	17.0794i	−0.949346	−	0.548105i	−0.0564686	−	0.998404i	$-0.517984\pi$
$971$	−29.5825	−	17.0794i	−0.949346	−	0.548105i	−0.892878	+	0.450299i	$0.851317\pi$
$972$		0			0
$973$	5.16374	−	33.1048i	0.165542	−	1.06129i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	19.1567	+	5.13303i	0.612878	+	0.164220i	0.551888	−	0.833918i	$-0.313908\pi$
$977$	19.1567	+	5.13303i	0.612878	+	0.164220i	0.0609900	+	0.998138i	$0.480574\pi$
$978$		0			0
$979$		−	45.4029i		−	1.45108i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−10.2267	+	38.1666i	−0.326181	+	1.21732i	0.586938	+	0.809632i	$0.300333\pi$
$983$	−10.2267	+	38.1666i	−0.326181	+	1.21732i	−0.913119	+	0.407692i	$0.866334\pi$
$984$		0			0
$985$	34.0481	−	17.6567i	1.08486	−	0.562589i
$986$		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
$997$	−0.876201	+	3.27003i	−0.0277496	+	0.103563i	−0.978412	−	0.206665i	$-0.933739\pi$
$997$	−0.876201	+	3.27003i	−0.0277496	+	0.103563i	0.950662	+	0.310228i	$0.100405\pi$
$998$		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.737.2	yes	64
3.2	odd	2	inner	1260.2.ej.a.737.15	yes	64
5.3	odd	4	inner	1260.2.ej.a.233.4	yes	64
7.4	even	3	inner	1260.2.ej.a.557.13	yes	64
15.8	even	4	inner	1260.2.ej.a.233.13	yes	64
21.11	odd	6	inner	1260.2.ej.a.557.4	yes	64
35.18	odd	12	inner	1260.2.ej.a.53.15	yes	64
105.53	even	12	inner	1260.2.ej.a.53.2	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.ej.a.53.2	✓	64	105.53	even	12	inner
1260.2.ej.a.53.15	yes	64	35.18	odd	12	inner
1260.2.ej.a.233.4	yes	64	5.3	odd	4	inner
1260.2.ej.a.233.13	yes	64	15.8	even	4	inner
1260.2.ej.a.557.4	yes	64	21.11	odd	6	inner
1260.2.ej.a.557.13	yes	64	7.4	even	3	inner
1260.2.ej.a.737.2	yes	64	1.1	even	1	trivial
1260.2.ej.a.737.15	yes	64	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-2.13152 - 0.675735i) q^{5} +(2.61414 + 0.407758i) q^{7} +O(q^{10})\)	\(q+(-2.13152 - 0.675735i) q^{5} +(2.61414 + 0.407758i) q^{7} +(3.45539 - 1.99497i) q^{11} +(-4.61757 + 4.61757i) q^{13} +(-5.02305 - 1.34592i) q^{17} +(4.70173 + 2.71454i) q^{19} +(8.33968 - 2.23461i) q^{23} +(4.08677 + 2.88069i) q^{25} +3.86048 q^{29} +(-0.780027 - 1.35105i) q^{31} +(-5.29656 - 2.63561i) q^{35} +(-0.275178 + 0.0737337i) q^{37} -3.13961i q^{41} +(2.78010 - 2.78010i) q^{43} +(-0.205000 - 0.765069i) q^{47} +(6.66747 + 2.13187i) q^{49} +(-1.60537 + 5.99134i) q^{53} +(-8.71331 + 1.91740i) q^{55} +(5.19648 + 9.00057i) q^{59} +(4.58612 - 7.94339i) q^{61} +(12.9627 - 6.72220i) q^{65} +(1.52822 - 5.70341i) q^{67} -0.668930i q^{71} +(10.7969 + 2.89302i) q^{73} +(9.84635 - 3.80617i) q^{77} +(13.8981 + 8.02408i) q^{79} +(3.96079 + 3.96079i) q^{83} +(9.79725 + 6.26311i) q^{85} +(5.68967 - 9.85480i) q^{89} +(-13.9538 + 10.1881i) q^{91} +(-8.18752 - 8.96323i) q^{95} +(12.4980 + 12.4980i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 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

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