LMFDB - Embedded newform 1260.2.ej.a.737.15

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			737.15
Character	$\chi$	$=$	1260.737
Dual form			1260.2.ej.a.53.15

$q$-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	−0.920354	−	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	−0.340406	+	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	0.810001	−	0.586428i	$-0.199466\pi$
$17$	5.02305	+	1.34592i	1.21827	+	0.326434i	0.408267	+	0.912862i	$0.366133\pi$
$18$		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	−0.982212	−	0.187777i	$-0.939872\pi$
$23$	−8.33968	+	2.23461i	−1.73894	+	0.465948i	−0.756731	+	0.653726i	$0.773205\pi$
$24$		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	$-0.616690\pi$
$29$	−3.86048			−0.716873			−0.358436	+	0.933554i	$0.616690\pi$
$30$		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	$0.0788412\pi$
$41$			3.13961i			0.490324i	−0.969482	+	0.245162i	$0.921159\pi$
$42$		0			0
$43$	2.78010	−	2.78010i	0.423961	−	0.423961i	−0.462604	−	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	0.979264	−	0.202588i	$-0.0649354\pi$
$47$	0.205000	+	0.765069i	0.0299023	+	0.111597i	−0.949362	+	0.314185i	$0.898269\pi$
$48$		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	$-0.776588\pi$
$53$	1.60537	−	5.99134i	0.220515	−	0.822973i	0.984152	−	0.177327i	$-0.0567451\pi$
$54$		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	$-0.930152\pi$
$59$	−5.19648	−	9.00057i	−0.676524	−	1.17177i	0.299497	−	0.954097i	$-0.403181\pi$
$60$		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	$0.0126382\pi$
$71$			0.668930i			0.0793874i	−0.999212	+	0.0396937i	$0.987362\pi$
$72$		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	0.455488	−	0.890242i	$-0.349465\pi$
$83$	−3.96079	−	3.96079i	−0.434754	−	0.434754i	−0.890242	+	0.455488i	$0.849465\pi$
$84$		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	$0.372736\pi$
$89$	−5.68967	+	9.85480i	−0.603104	+	1.04461i	−0.992348	+	0.123472i	$0.960597\pi$
$90$		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	−0.358623	−	0.933483i	$-0.616754\pi$
$101$	2.71835	−	1.56944i	0.270486	−	0.156165i	0.629108	+	0.777318i	$0.283420\pi$
$102$		0			0
$103$	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	$0.00462894\pi$
$107$	1.46091	+	5.45218i	0.141231	+	0.527082i	−0.858663	+	0.512541i	$0.828704\pi$
$108$		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	$0.0152119\pi$
$113$	11.1258	+	11.1258i	1.04663	+	1.04663i	0.0477714	+	0.998858i	$0.484788\pi$
$114$		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	−0.140962	−	0.990015i	$-0.545019\pi$
$131$	−12.2332	−	7.06285i	−1.06882	−	0.617084i	−0.927859	+	0.372931i	$0.878353\pi$
$132$		0			0
$133$	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	0.491354	−	0.870960i	$-0.336502\pi$
$137$	5.63464	+	1.50980i	0.481400	+	0.128991i	−0.00995439	+	0.999950i	$0.503169\pi$
$138$		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	$-0.595411\pi$
$149$	8.29771	−	14.3721i	0.679775	−	1.17741i	0.975048	−	0.221992i	$-0.0712560\pi$
$150$		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	−0.608360	−	0.793662i	$-0.708172\pi$
$167$	2.39463	−	2.39463i	0.185302	−	0.185302i	0.793662	+	0.608360i	$0.208172\pi$
$168$		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	0.457920	−	0.888993i	$-0.348595\pi$
$173$	17.0855	−	4.57805i	1.29899	−	0.348063i	0.841067	+	0.540931i	$0.181928\pi$
$174$		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	0.686599	−	0.727037i	$-0.259103\pi$
$179$	−3.83087	−	6.63526i	−0.286333	−	0.495943i	−0.972931	+	0.231094i	$0.925770\pi$
$180$		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	0.654727	−	0.755865i	$-0.272783\pi$
$191$	4.52604	+	2.61311i	0.327493	+	0.189078i	−0.327235	+	0.944943i	$0.606117\pi$
$192$		0			0
$193$	−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	−0.127686	−	0.991815i	$-0.540755\pi$
$197$	12.1286	−	12.1286i	0.864128	−	0.864128i	0.991815	+	0.127686i	$0.0407550\pi$
$198$		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	0.829158	−	0.559014i	$-0.188820\pi$
$227$	19.1002	+	5.11788i	1.26772	+	0.339685i	0.438565	+	0.898700i	$0.355487\pi$
$228$		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	0.142200	−	0.989838i	$-0.454582\pi$
$233$	11.6050	−	3.10955i	0.760268	−	0.203713i	0.618068	+	0.786125i	$0.287916\pi$
$234$		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	$-0.486994\pi$
$239$	1.26303			0.0816985			0.0408492	+	0.999165i	$0.486994\pi$
$240$		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	$-0.856064\pi$
$251$		−	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
$257$	2.47172	+	9.22460i	0.154182	+	0.575415i	0.999174	+	0.0406360i	$0.0129384\pi$
$257$	2.47172	+	9.22460i	0.154182	+	0.575415i	−0.844992	+	0.534779i	$0.820395\pi$
$258$		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	$-0.599838\pi$
$263$	7.04269	−	26.2837i	0.434271	−	1.62072i	0.742805	−	0.669508i	$-0.233495\pi$
$264$		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	$-0.981536\pi$
$269$	−9.01025	−	15.6062i	−0.549365	−	0.951528i	0.448953	−	0.893555i	$-0.351797\pi$
$270$		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	$0.389156\pi$
$281$			31.5139i			1.87996i	−0.341231	+	0.939980i	$0.610844\pi$
$282$		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	0.609501	−	0.792786i	$-0.291370\pi$
$293$	−3.13734	−	3.13734i	−0.183285	−	0.183285i	−0.792786	+	0.609501i	$0.791370\pi$
$294$		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	−0.992337	−	0.123560i	$-0.960569\pi$
$311$	−24.3630	+	14.0660i	−1.38150	+	0.797609i	−0.389162	+	0.921169i	$0.627235\pi$
$312$		0			0
$313$	−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	$-0.993067\pi$
$317$	−2.57866	−	9.62368i	−0.144832	−	0.540519i	0.854931	−	0.518742i	$-0.173599\pi$
$318$		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	0.311488	−	0.950250i	$-0.399173\pi$
$347$	1.97679	+	0.529679i	0.106120	+	0.0284347i	−0.205368	+	0.978685i	$0.565839\pi$
$348$		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	−0.971090	−	0.238715i	$-0.923274\pi$
$353$	−0.201863	+	0.753362i	−0.0107441	+	0.0400974i	0.960346	+	0.278812i	$0.0899406\pi$
$354$		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	−0.991091	−	0.133185i	$-0.957480\pi$
$359$	−7.20384	+	12.4774i	−0.380204	+	0.658532i	0.610887	+	0.791718i	$0.290813\pi$
$360$		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	−0.500812	−	0.865556i	$-0.666965\pi$
$383$	−9.81943	+	2.63111i	−0.501750	+	0.134443i	−0.000937706		1.00000i	$0.500298\pi$
$384$		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	0.730763	−	0.682632i	$-0.239165\pi$
$389$	−4.45338	−	7.71348i	−0.225795	−	0.391089i	−0.956558	+	0.291543i	$0.905831\pi$
$390$		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	−0.310482	−	0.950579i	$-0.600490\pi$
$401$	−25.8112	−	14.9021i	−1.28895	−	0.744175i	−0.978467	+	0.206404i	$0.933824\pi$
$402$		0			0
$403$	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	$-0.503022\pi$
$419$	−0.388663			−0.0189874			−0.00949371	+	0.999955i	$0.503022\pi$
$420$		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	−0.0288458	−	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	−0.649865	−	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	0.0110143	−	0.999939i	$-0.496494\pi$
$443$	10.9557	−	2.93558i	0.520523	−	0.139474i	0.509508	+	0.860466i	$0.329827\pi$
$444$		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	$-0.267028\pi$
$449$	28.3215			1.33657			0.668287	+	0.743903i	$0.267028\pi$
$450$		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	$-0.962179\pi$
$461$		−	5.09025i		−	0.237077i	0.992949	−	0.118538i	$-0.0378208\pi$
$462$		0			0
$463$	10.1917	−	10.1917i	0.473649	−	0.473649i	−0.429445	−	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	$0.0770419\pi$
$467$	5.40057	+	20.1552i	0.249909	+	0.932672i	−0.720944	+	0.692994i	$0.756291\pi$
$468$		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	0.676499	−	0.736443i	$-0.263496\pi$
$479$	−6.55551	−	11.3545i	−0.299529	−	0.518799i	−0.976028	+	0.217644i	$0.930163\pi$
$480$		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	$0.424761\pi$
$491$			43.0848i			1.94439i	−0.234176	+	0.972194i	$0.575239\pi$
$492$		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	0.557711	−	0.830035i	$-0.311680\pi$
$503$	−6.10761	−	6.10761i	−0.272325	−	0.272325i	−0.830035	+	0.557711i	$0.811680\pi$
$504$		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	−0.956746	−	0.290926i	$-0.906037\pi$
$509$	−5.10835	+	8.84791i	−0.226423	+	0.392177i	0.730322	+	0.683103i	$0.239370\pi$
$510$		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	0.280452	−	0.959868i	$-0.409516\pi$
$521$	28.5763	−	16.4985i	1.25195	−	0.722813i	0.971496	+	0.237055i	$0.0761822\pi$
$522$		0			0
$523$	−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	0.250512	−	0.968113i	$-0.419401\pi$
$557$	−0.391638	−	0.104939i	−0.0165942	−	0.00444641i	−0.267107	+	0.963667i	$0.586068\pi$
$558$		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	$-0.777319\pi$
$563$	5.20676	−	19.4319i	0.219439	−	0.818957i	0.984557	−	0.175066i	$-0.0560140\pi$
$564$		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	$0.449686\pi$
$569$	−18.5230	+	32.0828i	−0.776525	+	1.34498i	−0.933934	+	0.357447i	$0.883647\pi$
$570$		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	−0.999788	−	0.0206004i	$-0.993442\pi$
$587$	−23.7238	+	23.7238i	−0.979187	+	0.979187i	0.0206004	+	0.999788i	$0.493442\pi$
$588$		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	−0.320668	−	0.947192i	$-0.603907\pi$
$593$	−3.03857	+	0.814182i	−0.124779	+	0.0334344i	0.195889	+	0.980626i	$0.437241\pi$
$594$		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	0.703220	−	0.710972i	$-0.251745\pi$
$599$	−6.46396	−	11.1959i	−0.264110	−	0.457452i	−0.967330	+	0.253520i	$0.918412\pi$
$600$		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	$-0.414742\pi$
$617$	30.5277	−	30.5277i	1.22900	−	1.22900i	0.964343	−	0.264654i	$-0.0852577\pi$
$618$		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	−0.447686	−	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	−0.334884	−	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	0.283727	−	0.958905i	$-0.408429\pi$
$647$	1.27153	+	0.340705i	0.0499890	+	0.0133945i	−0.233738	+	0.972300i	$0.575096\pi$
$648$		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	−0.409240	−	0.912427i	$-0.634206\pi$
$653$	−7.85628	+	2.10508i	−0.307440	+	0.0823783i	0.101801	+	0.994805i	$0.467540\pi$
$654$		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	$-0.486867\pi$
$659$	2.11773			0.0824949			0.0412475	+	0.999149i	$0.486867\pi$
$660$		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	$0.267868\pi$
$677$	12.0235	+	44.8725i	0.462102	+	1.72459i	−0.204219	+	0.978925i	$0.565466\pi$
$678$		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	$0.309192\pi$
$683$	−8.81350	+	32.8924i	−0.337239	+	1.25859i	−0.901421	+	0.432943i	$0.857475\pi$
$684$		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	$0.0178480\pi$
$701$			2.96757i			0.112084i	−0.998428	+	0.0560418i	$0.982152\pi$
$702$		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	$-0.583469\pi$
$719$	18.9524	−	32.8266i	0.706806	−	1.22422i	0.966036	−	0.258409i	$-0.0831981\pi$
$720$		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	0.875297	−	0.483586i	$-0.160666\pi$
$743$	10.6772	+	10.6772i	0.391710	+	0.391710i	−0.483586	+	0.875297i	$0.660666\pi$
$744$		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	−0.410310	−	0.911946i	$-0.634579\pi$
$761$	−38.7651	−	22.3810i	−1.40523	−	0.811312i	−0.994923	+	0.100635i	$0.967913\pi$
$762$		0			0
$763$	−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	$-0.678413\pi$
$773$	9.79419	−	36.5524i	0.352272	−	1.31470i	0.883882	−	0.467709i	$-0.154921\pi$
$774$		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	−0.860746	−	0.509035i	$-0.830002\pi$
$797$	−9.92920	+	9.92920i	−0.351710	+	0.351710i	0.509035	+	0.860746i	$0.330002\pi$
$798$		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	0.669031	−	0.743235i	$-0.266709\pi$
$809$	−8.79298	−	15.2299i	−0.309145	−	0.535455i	−0.978176	+	0.207780i	$0.933376\pi$
$810$		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	0.0158033	−	0.999875i	$-0.494969\pi$
$821$	−24.1320	−	13.9326i	−0.842212	−	0.486252i	−0.858016	+	0.513624i	$0.828303\pi$
$822$		0			0
$823$	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	−0.932327	−	0.361616i	$-0.882225\pi$
$827$	−16.4123	+	16.4123i	−0.570711	+	0.570711i	0.361616	+	0.932327i	$0.382225\pi$
$828$		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	$-0.433773\pi$
$839$	11.9662			0.413120			0.206560	+	0.978434i	$0.433773\pi$
$840$		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	−0.461580	−	0.887099i	$-0.652717\pi$
$857$	−38.1995	−	10.2355i	−1.30487	−	0.349639i	−0.843289	+	0.537460i	$0.819384\pi$
$858$		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	−0.376939	−	0.926238i	$-0.623023\pi$
$863$	−7.05803	+	1.89119i	−0.240258	+	0.0643769i	0.136681	+	0.990615i	$0.456357\pi$
$864$		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	$-0.984417\pi$
$881$		−	2.90498i		−	0.0978712i	0.998802	−	0.0489356i	$-0.0155829\pi$
$882$		0			0
$883$	1.08162	−	1.08162i	0.0363995	−	0.0363995i	−0.688673	−	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	$0.0820273\pi$
$887$	7.65344	+	28.5630i	0.256978	+	0.959053i	−0.710002	+	0.704200i	$0.751306\pi$
$888$		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	$0.0601029\pi$
$911$			11.3305i			0.375398i	−0.982227	+	0.187699i	$0.939897\pi$
$912$		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	$0.410207\pi$
$929$	−21.1105	+	36.5644i	−0.692613	+	1.19964i	−0.970979	+	0.239165i	$0.923126\pi$
$930$		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	0.206256	−	0.978498i	$-0.433872\pi$
$941$	35.4853	−	20.4875i	1.15679	−	0.667872i	0.950532	+	0.310626i	$0.100539\pi$
$942$		0			0
$943$	−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	$-0.817918\pi$
$947$	−11.7959	−	44.0229i	−0.383315	−	1.43055i	0.457491	−	0.889214i	$-0.348748\pi$
$948$		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	$-0.204639\pi$
$953$	6.20043	+	6.20043i	0.200851	+	0.200851i	−0.599513	+	0.800365i	$0.704639\pi$
$954$		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	0.892878	−	0.450299i	$-0.148683\pi$
$971$	29.5825	+	17.0794i	0.949346	+	0.548105i	0.0564686	+	0.998404i	$0.482016\pi$
$972$		0			0
$973$	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	−0.0609900	−	0.998138i	$-0.519426\pi$
$977$	−19.1567	−	5.13303i	−0.612878	−	0.164220i	−0.551888	+	0.833918i	$0.686092\pi$
$978$		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	$-0.699667\pi$
$983$	10.2267	−	38.1666i	0.326181	−	1.21732i	0.913119	−	0.407692i	$-0.133666\pi$
$984$		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.737.15	yes	64
3.2	odd	2	inner	1260.2.ej.a.737.2	yes	64
5.3	odd	4	inner	1260.2.ej.a.233.13	yes	64
7.4	even	3	inner	1260.2.ej.a.557.4	yes	64
15.8	even	4	inner	1260.2.ej.a.233.4	yes	64
21.11	odd	6	inner	1260.2.ej.a.557.13	yes	64
35.18	odd	12	inner	1260.2.ej.a.53.2	✓	64
105.53	even	12	inner	1260.2.ej.a.53.15	yes	64

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more