LMFDB - Embedded newform 1260.2.ej.a.233.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1260.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.ej (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			233.11
Character	$\chi$	$=$	1260.233
Dual form			1260.2.ej.a.557.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.11962 + 1.93557i) q^{5} +(-0.988471 + 2.45417i) q^{7} +(-2.72089 + 1.57091i) q^{11} +(-0.380199 - 0.380199i) q^{13} +(0.321846 - 1.20115i) q^{17} +(-5.59110 - 3.22802i) q^{19} +(2.12591 + 7.93400i) q^{23} +(-2.49289 + 4.33422i) q^{25} -4.09991 q^{29} +(2.84794 + 4.93277i) q^{31} +(-5.85693 + 0.834480i) q^{35} +(-2.89360 - 10.7991i) q^{37} -7.39900i q^{41} +(-8.31257 - 8.31257i) q^{43} +(-1.56762 + 0.420044i) q^{47} +(-5.04585 - 4.85174i) q^{49} +(10.7595 + 2.88301i) q^{53} +(-6.08698 - 3.50766i) q^{55} +(5.50159 + 9.52904i) q^{59} +(-3.74059 + 6.47889i) q^{61} +(0.310224 - 1.16158i) q^{65} +(-4.89021 - 1.31033i) q^{67} +15.1301i q^{71} +(-2.51813 + 9.39779i) q^{73} +(-1.16575 - 8.23032i) q^{77} +(3.95167 + 2.28150i) q^{79} +(2.60611 - 2.60611i) q^{83} +(2.68525 - 0.721873i) q^{85} +(-4.35104 + 7.53622i) q^{89} +(1.30889 - 0.557255i) q^{91} +(-0.0118431 - 14.4361i) q^{95} +(2.02356 - 2.02356i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	1.11962	+	1.93557i	0.500710	+	0.865615i
$5$	1.11962	+	1.93557i	0.500710	+	0.865615i
$6$		0			0
$7$	−0.988471	+	2.45417i	−0.373607	+	0.927587i
$7$	−0.988471	+	2.45417i	−0.373607	+	0.927587i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.72089	+	1.57091i	−0.820380	+	0.473647i	−0.850548	−	0.525898i	$-0.823729\pi$
$11$	−2.72089	+	1.57091i	−0.820380	+	0.473647i	0.0301675	+	0.999545i	$0.490396\pi$
$12$		0			0
$13$	−0.380199	−	0.380199i	−0.105448	−	0.105448i	0.652414	−	0.757863i	$-0.273756\pi$
$13$	−0.380199	−	0.380199i	−0.105448	−	0.105448i	−0.757863	+	0.652414i	$0.773756\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.321846	−	1.20115i	0.0780592	−	0.291321i	−0.915850	−	0.401520i	$-0.868482\pi$
$17$	0.321846	−	1.20115i	0.0780592	−	0.291321i	0.993910	+	0.110199i	$0.0351488\pi$
$18$		0			0
$19$	−5.59110	−	3.22802i	−1.28269	−	0.740559i	−0.305347	−	0.952241i	$-0.598773\pi$
$19$	−5.59110	−	3.22802i	−1.28269	−	0.740559i	−0.977339	+	0.211682i	$0.932106\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.12591	+	7.93400i	0.443283	+	1.65435i	0.720431	+	0.693527i	$0.243944\pi$
$23$	2.12591	+	7.93400i	0.443283	+	1.65435i	−0.277148	+	0.960827i	$0.589389\pi$
$24$		0			0
$25$	−2.49289	+	4.33422i	−0.498578	+	0.866845i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−4.09991			−0.761334			−0.380667	−	0.924712i	$-0.624306\pi$
$29$	−4.09991			−0.761334			−0.380667	+	0.924712i	$0.624306\pi$
$30$		0			0
$31$	2.84794	+	4.93277i	0.511505	+	0.885952i	0.999911	+	0.0133360i	$0.00424510\pi$
$31$	2.84794	+	4.93277i	0.511505	+	0.885952i	−0.488406	+	0.872616i	$0.662422\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.85693	+	0.834480i	−0.990002	+	0.141053i
$36$		0			0
$37$	−2.89360	−	10.7991i	−0.475706	−	1.77536i	−0.618693	−	0.785633i	$-0.712337\pi$
$37$	−2.89360	−	10.7991i	−0.475706	−	1.77536i	0.142987	−	0.989725i	$-0.454329\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	7.39900i		−	1.15553i	−0.816203	−	0.577765i	$-0.803925\pi$
$41$		−	7.39900i		−	1.15553i	0.816203	−	0.577765i	$-0.196075\pi$
$42$		0			0
$43$	−8.31257	−	8.31257i	−1.26766	−	1.26766i	−0.947296	−	0.320359i	$-0.896197\pi$
$43$	−8.31257	−	8.31257i	−1.26766	−	1.26766i	−0.320359	−	0.947296i	$-0.603803\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−1.56762	+	0.420044i	−0.228661	+	0.0612697i	−0.371330	−	0.928501i	$-0.621098\pi$
$47$	−1.56762	+	0.420044i	−0.228661	+	0.0612697i	0.142669	+	0.989770i	$0.454432\pi$
$48$		0			0
$49$	−5.04585	−	4.85174i	−0.720836	−	0.693106i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	10.7595	+	2.88301i	1.47793	+	0.396011i	0.905644	−	0.424040i	$-0.139388\pi$
$53$	10.7595	+	2.88301i	1.47793	+	0.396011i	0.572290	+	0.820051i	$0.306055\pi$
$54$		0			0
$55$	−6.08698	−	3.50766i	−0.820768	−	0.472973i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.50159	+	9.52904i	0.716246	+	1.24058i	0.962477	+	0.271364i	$0.0874746\pi$
$59$	5.50159	+	9.52904i	0.716246	+	1.24058i	−0.246231	+	0.969211i	$0.579192\pi$
$60$		0			0
$61$	−3.74059	+	6.47889i	−0.478933	+	0.829537i	−0.999708	−	0.0241574i	$-0.992310\pi$
$61$	−3.74059	+	6.47889i	−0.478933	+	0.829537i	0.520775	+	0.853694i	$0.325643\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.310224	−	1.16158i	0.0384785	−	0.144077i
$66$		0			0
$67$	−4.89021	−	1.31033i	−0.597434	−	0.160082i	−0.0525853	−	0.998616i	$-0.516746\pi$
$67$	−4.89021	−	1.31033i	−0.597434	−	0.160082i	−0.544848	+	0.838535i	$0.683413\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			15.1301i			1.79561i	0.440389	+	0.897807i	$0.354841\pi$
$71$			15.1301i			1.79561i	−0.440389	+	0.897807i	$0.645159\pi$
$72$		0			0
$73$	−2.51813	+	9.39779i	−0.294725	+	1.09993i	0.646711	+	0.762735i	$0.276144\pi$
$73$	−2.51813	+	9.39779i	−0.294725	+	1.09993i	−0.941436	+	0.337192i	$0.890523\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.16575	−	8.23032i	−0.132849	−	0.937932i
$78$		0			0
$79$	3.95167	+	2.28150i	0.444598	+	0.256688i	0.705546	−	0.708664i	$-0.250702\pi$
$79$	3.95167	+	2.28150i	0.444598	+	0.256688i	−0.260948	+	0.965353i	$0.584035\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.60611	−	2.60611i	0.286057	−	0.286057i	−0.549462	−	0.835519i	$-0.685167\pi$
$83$	2.60611	−	2.60611i	0.286057	−	0.286057i	0.835519	+	0.549462i	$0.185167\pi$
$84$		0			0
$85$	2.68525	−	0.721873i	0.291257	−	0.0782982i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.35104	+	7.53622i	−0.461209	+	0.798838i	−0.999022	−	0.0442266i	$-0.985918\pi$
$89$	−4.35104	+	7.53622i	−0.461209	+	0.798838i	0.537812	+	0.843065i	$0.319251\pi$
$90$		0			0
$91$	1.30889	−	0.557255i	0.137209	−	0.0584162i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.0118431	−	14.4361i	−0.00121508	−	1.48112i
$96$		0			0
$97$	2.02356	−	2.02356i	0.205461	−	0.205461i	−0.596874	−	0.802335i	$-0.703591\pi$
$97$	2.02356	−	2.02356i	0.205461	−	0.205461i	0.802335	+	0.596874i	$0.203591\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−12.2993	+	7.10098i	−1.22382	+	0.706574i	−0.965731	−	0.259547i	$-0.916427\pi$
$101$	−12.2993	+	7.10098i	−1.22382	+	0.706574i	−0.258091	+	0.966121i	$0.583093\pi$
$102$		0			0
$103$	−3.45232	+	0.925045i	−0.340167	+	0.0911474i	−0.424858	−	0.905260i	$-0.639676\pi$
$103$	−3.45232	+	0.925045i	−0.340167	+	0.0911474i	0.0846916	+	0.996407i	$0.473009\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.60336	−	0.697568i	0.251676	−	0.0674364i	−0.130775	−	0.991412i	$-0.541747\pi$
$107$	2.60336	−	0.697568i	0.251676	−	0.0674364i	0.382451	+	0.923976i	$0.375080\pi$
$108$		0			0
$109$	4.95186	−	2.85896i	0.474302	−	0.273839i	−0.243737	−	0.969841i	$-0.578373\pi$
$109$	4.95186	−	2.85896i	0.474302	−	0.273839i	0.718039	+	0.696003i	$0.245040\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.976035	−	0.976035i	0.0918177	−	0.0918177i	−0.659706	−	0.751524i	$-0.729319\pi$
$113$	0.976035	−	0.976035i	0.0918177	−	0.0918177i	0.751524	+	0.659706i	$0.229319\pi$
$114$		0			0
$115$	−12.9766	+	12.9979i	−1.21008	+	1.21206i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	2.62968	+	1.97716i	0.241062	+	0.181246i
$120$		0			0
$121$	−0.564495	+	0.977734i	−0.0513177	+	0.0888849i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.1803	+	0.0275163i	−0.999997	+	0.00246114i
$126$		0			0
$127$	−5.69577	+	5.69577i	−0.505417	+	0.505417i	−0.913116	−	0.407699i	$-0.866331\pi$
$127$	−5.69577	+	5.69577i	−0.505417	+	0.505417i	0.407699	+	0.913116i	$0.366331\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	11.1697	+	6.44881i	0.975899	+	0.563435i	0.901029	−	0.433758i	$-0.142813\pi$
$131$	11.1697	+	6.44881i	0.975899	+	0.563435i	0.0748691	+	0.997193i	$0.476146\pi$
$132$		0			0
$133$	13.4487	−	10.5307i	1.16615	−	0.913125i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.19916	+	4.47534i	−0.102451	+	0.382354i	−0.998044	−	0.0625222i	$-0.980086\pi$
$137$	−1.19916	+	4.47534i	−0.102451	+	0.382354i	0.895592	+	0.444876i	$0.146752\pi$
$138$		0			0
$139$			7.85056i			0.665876i	0.942949	+	0.332938i	$0.108040\pi$
$139$			7.85056i			0.665876i	−0.942949	+	0.332938i	$0.891960\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.63174	+	0.437223i	0.136453	+	0.0365624i
$144$		0			0
$145$	−4.59035	−	7.93567i	−0.381208	−	0.659022i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.03231	−	6.98416i	0.330340	−	0.572165i	−0.652239	−	0.758014i	$-0.726170\pi$
$149$	4.03231	−	6.98416i	0.330340	−	0.572165i	0.982578	+	0.185849i	$0.0595034\pi$
$150$		0			0
$151$	3.05240	+	5.28692i	0.248401	+	0.430243i	0.963082	−	0.269207i	$-0.0867616\pi$
$151$	3.05240	+	5.28692i	0.248401	+	0.430243i	−0.714681	+	0.699450i	$0.753428\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.35913	+	11.0352i	−0.510778	+	0.886372i
$156$		0			0
$157$	13.5182	+	3.62219i	1.07887	+	0.289082i	0.754133	−	0.656722i	$-0.228058\pi$
$157$	13.5182	+	3.62219i	1.07887	+	0.289082i	0.324737	+	0.945804i	$0.394724\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−21.5727	−	2.62520i	−1.70017	−	0.206894i
$162$		0			0
$163$	11.3029	−	3.02860i	0.885309	−	0.237218i	0.212613	−	0.977137i	$-0.431803\pi$
$163$	11.3029	−	3.02860i	0.885309	−	0.237218i	0.672696	+	0.739919i	$0.265136\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.72175	−	1.72175i	−0.133233	−	0.133233i	0.637345	−	0.770578i	$-0.280032\pi$
$167$	−1.72175	−	1.72175i	−0.133233	−	0.133233i	−0.770578	+	0.637345i	$0.780032\pi$
$168$		0			0
$169$		−	12.7109i		−	0.977761i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.56749	+	9.58199i	0.195202	+	0.728505i	0.992214	+	0.124542i	$0.0397461\pi$
$173$	2.56749	+	9.58199i	0.195202	+	0.728505i	−0.797012	+	0.603963i	$0.793587\pi$
$174$		0			0
$175$	−8.17275	−	10.4022i	−0.617802	−	0.786334i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	6.39946	+	11.0842i	0.478318	+	0.828471i	0.999691	−	0.0248576i	$-0.00791323\pi$
$179$	6.39946	+	11.0842i	0.478318	+	0.828471i	−0.521373	+	0.853329i	$0.674580\pi$
$180$		0			0
$181$	20.6067			1.53168			0.765841	−	0.643030i	$-0.222323\pi$
$181$	20.6067			1.53168			0.765841	+	0.643030i	$0.222323\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	17.6627	−	17.6917i	1.29859	−	1.30072i
$186$		0			0
$187$	1.01118	+	3.77378i	0.0739450	+	0.275966i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−16.4274	−	9.48434i	−1.18864	−	0.686262i	−0.230644	−	0.973038i	$-0.574083\pi$
$191$	−16.4274	−	9.48434i	−1.18864	−	0.686262i	−0.957998	+	0.286776i	$0.907417\pi$
$192$		0			0
$193$	0.179426	−	0.669626i	0.0129153	−	0.0482007i	−0.959167	−	0.282839i	$-0.908724\pi$
$193$	0.179426	−	0.669626i	0.0129153	−	0.0482007i	0.972083	+	0.234638i	$0.0753905\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.03090	−	2.03090i	−0.144696	−	0.144696i	0.631048	−	0.775744i	$-0.282625\pi$
$197$	−2.03090	−	2.03090i	−0.144696	−	0.144696i	−0.775744	+	0.631048i	$0.782625\pi$
$198$		0			0
$199$	6.05795	−	3.49756i	0.429437	−	0.247936i	−0.269670	−	0.962953i	$-0.586915\pi$
$199$	6.05795	−	3.49756i	0.429437	−	0.247936i	0.699107	+	0.715017i	$0.253581\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.05264	−	10.0618i	0.284439	−	0.706203i
$204$		0			0
$205$	14.3213	−	8.28409i	1.00024	−	0.578586i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	20.2837			1.40305
$210$		0			0
$211$	−23.3394			−1.60675			−0.803375	−	0.595474i	$-0.796964\pi$
$211$	−23.3394			−1.60675			−0.803375	+	0.595474i	$0.796964\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.78265	−	25.3965i	0.462573	−	1.73203i
$216$		0			0
$217$	−14.9209	+	2.11341i	−1.01290	+	0.143468i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.579040	+	0.334309i	−0.0389505	+	0.0224881i
$222$		0			0
$223$	4.20268	+	4.20268i	0.281432	+	0.281432i	0.833680	−	0.552248i	$-0.186230\pi$
$223$	4.20268	+	4.20268i	0.281432	+	0.281432i	−0.552248	+	0.833680i	$0.686230\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	4.13240	−	15.4223i	0.274277	−	1.02362i	−0.682047	−	0.731308i	$-0.738910\pi$
$227$	4.13240	−	15.4223i	0.274277	−	1.02362i	0.956324	−	0.292308i	$-0.0944232\pi$
$228$		0			0
$229$	18.6115	+	10.7453i	1.22988	+	0.710071i	0.967005	−	0.254759i	$-0.0819960\pi$
$229$	18.6115	+	10.7453i	1.22988	+	0.710071i	0.262875	+	0.964830i	$0.415329\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.46192	−	20.3842i	−0.357823	−	1.33541i	−0.876895	−	0.480682i	$-0.840389\pi$
$233$	−5.46192	−	20.3842i	−0.357823	−	1.33541i	0.519072	−	0.854730i	$-0.326277\pi$
$234$		0			0
$235$	−2.56817	−	2.56396i	−0.167529	−	0.167254i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−3.49125			−0.225830			−0.112915	−	0.993605i	$-0.536019\pi$
$239$	−3.49125			−0.225830			−0.112915	+	0.993605i	$0.536019\pi$
$240$		0			0
$241$	11.5764	+	20.0509i	0.745700	+	1.29159i	0.949867	+	0.312654i	$0.101218\pi$
$241$	11.5764	+	20.0509i	0.745700	+	1.29159i	−0.204167	+	0.978936i	$0.565449\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.74145	−	15.1987i	0.239033	−	0.971012i
$246$		0			0
$247$	0.898439	+	3.35302i	0.0571663	+	0.213348i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			20.3285i			1.28313i	0.767071	+	0.641563i	$0.221714\pi$
$251$			20.3285i			1.28313i	−0.767071	+	0.641563i	$0.778286\pi$
$252$		0			0
$253$	−18.2480	−	18.2480i	−1.14724	−	1.14724i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.213922	+	0.0573203i	−0.0133441	+	0.00357554i	−0.265485	−	0.964115i	$-0.585532\pi$
$257$	−0.213922	+	0.0573203i	−0.0133441	+	0.00357554i	0.252141	+	0.967691i	$0.418865\pi$
$258$		0			0
$259$	29.3630	+	3.57319i	1.82453	+	0.222027i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−2.70116	−	0.723773i	−0.166560	−	0.0446297i	0.174575	−	0.984644i	$-0.444145\pi$
$263$	−2.70116	−	0.723773i	−0.166560	−	0.0446297i	−0.341136	+	0.940014i	$0.610812\pi$
$264$		0			0
$265$	6.46633	+	24.0537i	0.397224	+	1.47761i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	5.05513	+	8.75575i	0.308217	+	0.533847i	0.977972	−	0.208734i	$-0.0669344\pi$
$269$	5.05513	+	8.75575i	0.308217	+	0.533847i	−0.669755	+	0.742582i	$0.733601\pi$
$270$		0			0
$271$	−0.417054	+	0.722359i	−0.0253343	+	0.0438802i	−0.878415	−	0.477899i	$-0.841398\pi$
$271$	−0.417054	+	0.722359i	−0.0253343	+	0.0438802i	0.853080	+	0.521780i	$0.174732\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.0257748	−	15.7091i	−0.00155428	−	0.947292i
$276$		0			0
$277$	−0.482749	−	0.129352i	−0.0290056	−	0.00777202i	0.244287	−	0.969703i	$-0.421446\pi$
$277$	−0.482749	−	0.129352i	−0.0290056	−	0.00777202i	−0.273293	+	0.961931i	$0.588113\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			4.50960i			0.269020i	0.990912	+	0.134510i	$0.0429461\pi$
$281$			4.50960i			0.269020i	−0.990912	+	0.134510i	$0.957054\pi$
$282$		0			0
$283$	2.87653	−	10.7354i	0.170992	−	0.638151i	−0.826208	−	0.563366i	$-0.809506\pi$
$283$	2.87653	−	10.7354i	0.170992	−	0.638151i	0.997200	−	0.0747854i	$-0.0238272\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	18.1584	+	7.31370i	1.07186	+	0.431714i
$288$		0			0
$289$	13.3833	+	7.72683i	0.787251	+	0.454519i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	15.3240	−	15.3240i	0.895239	−	0.895239i	−0.0997714	−	0.995010i	$-0.531811\pi$
$293$	15.3240	−	15.3240i	0.895239	−	0.895239i	0.995010	+	0.0997714i	$0.0318112\pi$
$294$		0			0
$295$	−12.2845	+	21.3177i	−0.715228	+	1.24116i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	2.20823	−	3.82477i	0.127705	−	0.221192i
$300$		0			0
$301$	28.6171	−	12.1837i	1.64947	−	0.702256i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−16.7284	+	0.0137237i	−0.957866	+	0.000785814i
$306$		0			0
$307$	−11.4605	+	11.4605i	−0.654087	+	0.654087i	−0.953974	−	0.299888i	$-0.903051\pi$
$307$	−11.4605	+	11.4605i	−0.654087	+	0.654087i	0.299888	+	0.953974i	$0.403051\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	4.38389	−	2.53104i	0.248587	−	0.143522i	−0.370530	−	0.928821i	$-0.620824\pi$
$311$	4.38389	−	2.53104i	0.248587	−	0.143522i	0.619117	+	0.785299i	$0.287491\pi$
$312$		0			0
$313$	8.19791	−	2.19662i	0.463373	−	0.124160i	−0.0195769	−	0.999808i	$-0.506232\pi$
$313$	8.19791	−	2.19662i	0.463373	−	0.124160i	0.482950	+	0.875648i	$0.339565\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−8.11319	+	2.17392i	−0.455682	+	0.122100i	−0.479357	−	0.877620i	$-0.659130\pi$
$317$	−8.11319	+	2.17392i	−0.455682	+	0.122100i	0.0236748	+	0.999720i	$0.492463\pi$
$318$		0			0
$319$	11.1554	−	6.44058i	0.624583	−	0.360603i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−5.67680	+	5.67680i	−0.315866	+	0.315866i
$324$		0			0
$325$	2.59566	−	0.700072i	0.143981	−	0.0388330i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	0.518694	−	4.26241i	0.0285965	−	0.234994i
$330$		0			0
$331$	5.39047	−	9.33657i	0.296287	−	0.513185i	−0.678996	−	0.734142i	$-0.737585\pi$
$331$	5.39047	−	9.33657i	0.296287	−	0.513185i	0.975284	+	0.220957i	$0.0709181\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−2.93895	−	10.9324i	−0.160572	−	0.597302i
$336$		0			0
$337$	14.1629	−	14.1629i	0.771501	−	0.771501i	−0.206868	−	0.978369i	$-0.566327\pi$
$337$	14.1629	−	14.1629i	0.771501	−	0.771501i	0.978369	+	0.206868i	$0.0663271\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−15.4979	−	8.94770i	−0.839257	−	0.484545i
$342$		0			0
$343$	16.8946	−	7.58755i	0.912225	−	0.409689i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	7.21878	−	26.9409i	0.387525	−	1.44626i	−0.446624	−	0.894722i	$-0.647374\pi$
$347$	7.21878	−	26.9409i	0.387525	−	1.44626i	0.834149	−	0.551540i	$-0.185959\pi$
$348$		0			0
$349$		−	26.6684i		−	1.42753i	−0.700387	−	0.713764i	$-0.746989\pi$
$349$		−	26.6684i		−	1.42753i	0.700387	−	0.713764i	$-0.253011\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	31.0566	+	8.32160i	1.65298	+	0.442914i	0.960444	−	0.278472i	$-0.0898279\pi$
$353$	31.0566	+	8.32160i	1.65298	+	0.442914i	0.692533	+	0.721386i	$0.256495\pi$
$354$		0			0
$355$	−29.2855	+	16.9400i	−1.55431	+	0.899083i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−2.46072	+	4.26209i	−0.129872	+	0.224944i	−0.923627	−	0.383293i	$-0.874790\pi$
$359$	−2.46072	+	4.26209i	−0.129872	+	0.224944i	0.793755	+	0.608238i	$0.208123\pi$
$360$		0			0
$361$	11.3403	+	19.6419i	0.596856	+	1.03378i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−21.0095	+	5.64795i	−1.09969	+	0.295627i
$366$		0			0
$367$	−19.9454	−	5.34435i	−1.04114	−	0.278973i	−0.302554	−	0.953132i	$-0.597839\pi$
$367$	−19.9454	−	5.34435i	−1.04114	−	0.278973i	−0.738586	+	0.674160i	$0.764506\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−17.7108	+	23.5559i	−0.919501	+	1.22296i
$372$		0			0
$373$	27.6436	−	7.40708i	1.43133	−	0.383524i	0.541842	−	0.840480i	$-0.317727\pi$
$373$	27.6436	−	7.40708i	1.43133	−	0.383524i	0.889489	+	0.456956i	$0.151060\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.55878	+	1.55878i	0.0802813	+	0.0802813i
$378$		0			0
$379$			10.2503i			0.526522i	0.964725	+	0.263261i	$0.0847980\pi$
$379$			10.2503i			0.526522i	−0.964725	+	0.263261i	$0.915202\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.31099	+	27.2850i	0.373574	+	1.39420i	0.855417	+	0.517939i	$0.173301\pi$
$383$	7.31099	+	27.2850i	0.373574	+	1.39420i	−0.481843	+	0.876257i	$0.660033\pi$
$384$		0			0
$385$	14.6252	−	11.4712i	0.745369	−	0.584628i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.54833	−	2.68179i	−0.0785036	−	0.135972i	0.824101	−	0.566443i	$-0.191681\pi$
$389$	−1.54833	−	2.68179i	−0.0785036	−	0.135972i	−0.902605	+	0.430471i	$0.858348\pi$
$390$		0			0
$391$	10.2141			0.516550
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.00837047	+	10.2032i	0.000421164	+	0.513377i
$396$		0			0
$397$	6.71038	+	25.0435i	0.336785	+	1.25690i	0.901922	+	0.431900i	$0.142157\pi$
$397$	6.71038	+	25.0435i	0.336785	+	1.25690i	−0.565137	+	0.824997i	$0.691177\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−15.1316	−	8.73625i	−0.755638	−	0.436268i	0.0720896	−	0.997398i	$-0.477033\pi$
$401$	−15.1316	−	8.73625i	−0.755638	−	0.436268i	−0.827727	+	0.561131i	$0.810367\pi$
$402$		0			0
$403$	0.792652	−	2.95822i	0.0394848	−	0.147359i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	24.8375	+	24.8375i	1.23115	+	1.23115i
$408$		0			0
$409$	−27.1742	+	15.6890i	−1.34368	+	0.775772i	−0.987345	−	0.158588i	$-0.949306\pi$
$409$	−27.1742	+	15.6890i	−1.34368	+	0.775772i	−0.356332	+	0.934360i	$0.615973\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−28.8240	+	4.08264i	−1.41834	+	0.200894i
$414$		0			0
$415$	7.96217	+	2.12646i	0.390847	+	0.104384i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−24.1134			−1.17802			−0.589008	−	0.808127i	$-0.700481\pi$
$419$	−24.1134			−1.17802			−0.589008	+	0.808127i	$0.700481\pi$
$420$		0			0
$421$	−27.7464			−1.35228			−0.676139	−	0.736774i	$-0.736348\pi$
$421$	−27.7464			−1.35228			−0.676139	+	0.736774i	$0.736348\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	4.40371	+	4.38928i	0.213611	+	0.212912i
$426$		0			0
$427$	−12.2028	−	15.5842i	−0.590535	−	0.754173i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−20.5060	+	11.8391i	−0.987739	+	0.570271i	−0.904598	−	0.426266i	$-0.859829\pi$
$431$	−20.5060	+	11.8391i	−0.987739	+	0.570271i	−0.0831413	+	0.996538i	$0.526495\pi$
$432$		0			0
$433$	12.7820	+	12.7820i	0.614264	+	0.614264i	0.944054	−	0.329790i	$-0.106978\pi$
$433$	12.7820	+	12.7820i	0.614264	+	0.614264i	−0.329790	+	0.944054i	$0.606978\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	13.7250	−	51.2223i	0.656554	−	2.45029i
$438$		0			0
$439$	−21.1416	−	12.2061i	−1.00903	−	0.582565i	−0.0981240	−	0.995174i	$-0.531284\pi$
$439$	−21.1416	−	12.2061i	−1.00903	−	0.582565i	−0.910908	+	0.412609i	$0.864618\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.90926	−	10.8575i	−0.138223	−	0.515855i	−0.999964	−	0.00850631i	$-0.997292\pi$
$443$	−2.90926	−	10.8575i	−0.138223	−	0.515855i	0.861741	−	0.507349i	$-0.169374\pi$
$444$		0			0
$445$	−19.4584	+	0.0159633i	−0.922419	+	0.000756734i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	7.29747			0.344389			0.172194	−	0.985063i	$-0.444914\pi$
$449$	7.29747			0.344389			0.172194	+	0.985063i	$0.444914\pi$
$450$		0			0
$451$	11.6232	+	20.1319i	0.547313	+	0.947974i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.54407	+	1.90953i	0.119268	+	0.0895202i
$456$		0			0
$457$	−1.78721	−	6.66995i	−0.0836020	−	0.312007i	0.911444	−	0.411425i	$-0.134969\pi$
$457$	−1.78721	−	6.66995i	−0.0836020	−	0.312007i	−0.995046	+	0.0994176i	$0.968302\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			2.23973i			0.104315i	0.998639	+	0.0521574i	$0.0166097\pi$
$461$			2.23973i			0.104315i	−0.998639	+	0.0521574i	$0.983390\pi$
$462$		0			0
$463$	−24.7669	−	24.7669i	−1.15101	−	1.15101i	−0.986349	−	0.164665i	$-0.947346\pi$
$463$	−24.7669	−	24.7669i	−1.15101	−	1.15101i	−0.164665	−	0.986349i	$-0.552654\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−23.6447	+	6.33559i	−1.09415	+	0.293176i	−0.760380	−	0.649479i	$-0.774987\pi$
$467$	−23.6447	+	6.33559i	−1.09415	+	0.293176i	−0.333769	+	0.942655i	$0.608320\pi$
$468$		0			0
$469$	8.04958	−	10.7062i	0.371695	−	0.494364i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	35.6759	+	9.55933i	1.64038	+	0.439538i
$474$		0			0
$475$	27.9290	−	16.1860i	1.28147	−	0.742663i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	13.9499	+	24.1620i	0.637388	+	1.10399i	0.986004	+	0.166722i	$0.0533183\pi$
$479$	13.9499	+	24.1620i	0.637388	+	1.10399i	−0.348616	+	0.937266i	$0.613348\pi$
$480$		0			0
$481$	−3.00565	+	5.20594i	−0.137046	+	0.237371i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	6.18236	+	1.65112i	0.280727	+	0.0749737i
$486$		0			0
$487$	23.6119	+	6.32679i	1.06996	+	0.286694i	0.750476	−	0.660898i	$-0.229824\pi$
$487$	23.6119	+	6.32679i	1.06996	+	0.286694i	0.319482	+	0.947592i	$0.396491\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	7.50191i		−	0.338556i	−0.985568	−	0.169278i	$-0.945856\pi$
$491$		−	7.50191i		−	0.338556i	0.985568	−	0.169278i	$-0.0541436\pi$
$492$		0			0
$493$	−1.31954	+	4.92459i	−0.0594291	+	0.221792i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−37.1318	−	14.9557i	−1.66559	−	0.670854i
$498$		0			0
$499$	16.2317	+	9.37137i	0.726630	+	0.419520i	0.817188	−	0.576371i	$-0.195532\pi$
$499$	16.2317	+	9.37137i	0.726630	+	0.419520i	−0.0905579	+	0.995891i	$0.528865\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	16.1780	−	16.1780i	0.721342	−	0.721342i	−0.247537	−	0.968879i	$-0.579621\pi$
$503$	16.1780	−	16.1780i	0.721342	−	0.721342i	0.968879	+	0.247537i	$0.0796210\pi$
$504$		0			0
$505$	−27.5150	−	15.8557i	−1.22440	−	0.705569i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	20.7815	−	35.9945i	0.921122	−	1.59543i	0.123439	−	0.992352i	$-0.460608\pi$
$509$	20.7815	−	35.9945i	0.921122	−	1.59543i	0.797683	−	0.603078i	$-0.206059\pi$
$510$		0			0
$511$	−20.5746	−	15.4693i	−0.910168	−	0.684323i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−5.65578	−	5.64651i	−0.249224	−	0.248815i
$516$		0			0
$517$	3.60549	−	3.60549i	0.158569	−	0.158569i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−0.376731	+	0.217506i	−0.0165049	+	0.00952910i	−0.508230	−	0.861222i	$-0.669700\pi$
$521$	−0.376731	+	0.217506i	−0.0165049	+	0.00952910i	0.491725	+	0.870751i	$0.336367\pi$
$522$		0			0
$523$	−6.73764	+	1.80535i	−0.294616	+	0.0789422i	−0.403100	−	0.915156i	$-0.632067\pi$
$523$	−6.73764	+	1.80535i	−0.294616	+	0.0789422i	0.108483	+	0.994098i	$0.465401\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	6.84158	−	1.83320i	0.298024	−	0.0798553i
$528$		0			0
$529$	−38.5103	+	22.2339i	−1.67436	+	0.966693i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−2.81309	+	2.81309i	−0.121849	+	0.121849i
$534$		0			0
$535$	4.26497	+	4.25798i	0.184391	+	0.184088i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	21.3509	+	5.27449i	0.919647	+	0.227189i
$540$		0			0
$541$	−9.69165	+	16.7864i	−0.416677	+	0.721705i	−0.995603	−	0.0936748i	$-0.970139\pi$
$541$	−9.69165	+	16.7864i	−0.416677	+	0.721705i	0.578926	+	0.815380i	$0.303472\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	11.0779	+	6.38374i	0.474527	+	0.273449i
$546$		0			0
$547$	−6.02367	+	6.02367i	−0.257554	+	0.257554i	−0.824058	−	0.566505i	$-0.808295\pi$
$547$	−6.02367	+	6.02367i	−0.257554	+	0.257554i	0.566505	+	0.824058i	$0.308295\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	22.9230	+	13.2346i	0.976552	+	0.563813i
$552$		0			0
$553$	−9.50528	+	7.44286i	−0.404206	+	0.316502i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−9.72301	+	36.2868i	−0.411977	+	1.53752i	0.378837	+	0.925463i	$0.376324\pi$
$557$	−9.72301	+	36.2868i	−0.411977	+	1.53752i	−0.790814	+	0.612056i	$0.790343\pi$
$558$		0			0
$559$			6.32086i			0.267344i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	36.0264	+	9.65324i	1.51833	+	0.406835i	0.919192	−	0.393810i	$-0.128843\pi$
$563$	36.0264	+	9.65324i	1.51833	+	0.406835i	0.599139	+	0.800645i	$0.295510\pi$
$564$		0			0
$565$	2.98198	+	0.796397i	0.125453	+	0.0335047i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−8.66323	+	15.0052i	−0.363182	+	0.629049i	−0.988483	−	0.151335i	$-0.951643\pi$
$569$	−8.66323	+	15.0052i	−0.363182	+	0.629049i	0.625301	+	0.780384i	$0.284976\pi$
$570$		0			0
$571$	11.0308	+	19.1059i	0.461625	+	0.799558i	0.999042	−	0.0437587i	$-0.0139333\pi$
$571$	11.0308	+	19.1059i	0.461625	+	0.799558i	−0.537417	+	0.843317i	$0.680600\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−39.6874	−	10.5644i	−1.65508	−	0.440568i
$576$		0			0
$577$	−24.1437	−	6.46928i	−1.00512	−	0.269320i	−0.281528	−	0.959553i	$-0.590841\pi$
$577$	−24.1437	−	6.46928i	−1.00512	−	0.269320i	−0.723587	+	0.690233i	$0.757508\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.81976	+	8.97187i	0.158470	+	0.372216i
$582$		0			0
$583$	−33.8044	+	9.05787i	−1.40004	+	0.375139i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.5063	+	11.5063i	0.474915	+	0.474915i	0.903501	−	0.428586i	$-0.140988\pi$
$587$	11.5063	+	11.5063i	0.474915	+	0.474915i	−0.428586	+	0.903501i	$0.640988\pi$
$588$		0			0
$589$		−	36.7728i		−	1.51520i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	12.1729	+	45.4299i	0.499881	+	1.86558i	0.500768	+	0.865581i	$0.333051\pi$
$593$	12.1729	+	45.4299i	0.499881	+	1.86558i	−0.000887582		1.00000i	$0.500283\pi$
$594$		0			0
$595$	−0.882699	+	7.30361i	−0.0361871	+	0.299419i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.48145	+	6.03005i	0.142248	+	0.246381i	0.928343	−	0.371725i	$-0.121234\pi$
$599$	3.48145	+	6.03005i	0.142248	+	0.246381i	−0.786095	+	0.618106i	$0.787900\pi$
$600$		0			0
$601$	−27.5177			−1.12247			−0.561235	−	0.827657i	$-0.689674\pi$
$601$	−27.5177			−1.12247			−0.561235	+	0.827657i	$0.689674\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−2.52450	+	0.00207105i	−0.102635	+	8.42001e-5i
$606$		0			0
$607$	−7.95377	−	29.6839i	−0.322834	−	1.20483i	−0.916472	−	0.400099i	$-0.868976\pi$
$607$	−7.95377	−	29.6839i	−0.322834	−	1.20483i	0.593638	−	0.804732i	$-0.297691\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	0.755709	+	0.436309i	0.0305727	+	0.0176512i
$612$		0			0
$613$	7.47201	−	27.8859i	0.301792	−	1.12630i	−0.633880	−	0.773431i	$-0.718539\pi$
$613$	7.47201	−	27.8859i	0.301792	−	1.12630i	0.935672	−	0.352871i	$-0.114795\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.259882	+	0.259882i	0.0104625	+	0.0104625i	0.712319	−	0.701856i	$-0.247645\pi$
$617$	0.259882	+	0.259882i	0.0104625	+	0.0104625i	−0.701856	+	0.712319i	$0.747645\pi$
$618$		0			0
$619$	16.3858	−	9.46036i	0.658602	−	0.380244i	−0.133142	−	0.991097i	$-0.542507\pi$
$619$	16.3858	−	9.46036i	0.658602	−	0.380244i	0.791744	+	0.610853i	$0.209173\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−14.1943	−	18.1275i	−0.568681	−	0.726263i
$624$		0			0
$625$	−12.5710	−	21.6095i	−0.502839	−	0.864380i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−13.9026			−0.554332
$630$		0			0
$631$	−2.77349			−0.110411			−0.0552055	−	0.998475i	$-0.517581\pi$
$631$	−2.77349			−0.110411			−0.0552055	+	0.998475i	$0.517581\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−17.4017	−	4.64747i	−0.690565	−	0.184429i
$636$		0			0
$637$	0.0738011	+	3.76305i	0.00292411	+	0.149098i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	4.12501	−	2.38158i	0.162928	−	0.0940667i	−0.416319	−	0.909219i	$-0.636680\pi$
$641$	4.12501	−	2.38158i	0.162928	−	0.0940667i	0.579247	+	0.815152i	$0.303347\pi$
$642$		0			0
$643$	−12.2522	−	12.2522i	−0.483178	−	0.483178i	0.422967	−	0.906145i	$-0.360989\pi$
$643$	−12.2522	−	12.2522i	−0.483178	−	0.483178i	−0.906145	+	0.422967i	$0.860989\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.414222	+	1.54590i	−0.0162848	+	0.0607755i	−0.973590	−	0.228303i	$-0.926682\pi$
$647$	−0.414222	+	1.54590i	−0.0162848	+	0.0607755i	0.957305	+	0.289079i	$0.0933489\pi$
$648$		0			0
$649$	−29.9385	−	17.2850i	−1.17519	−	0.678495i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−1.01478	−	3.78720i	−0.0397113	−	0.148205i	0.943224	−	0.332159i	$-0.107777\pi$
$653$	−1.01478	−	3.78720i	−0.0397113	−	0.148205i	−0.982935	+	0.183954i	$0.941110\pi$
$654$		0			0
$655$	0.0236597	+	28.8400i	0.000924462	+	1.12687i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−25.1996			−0.981635			−0.490818	−	0.871262i	$-0.663302\pi$
$659$	−25.1996			−0.981635			−0.490818	+	0.871262i	$0.663302\pi$
$660$		0			0
$661$	17.7559	+	30.7542i	0.690626	+	1.19620i	0.971633	+	0.236494i	$0.0759984\pi$
$661$	17.7559	+	30.7542i	0.690626	+	1.19620i	−0.281007	+	0.959706i	$0.590668\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	35.4404	+	14.2406i	1.37432	+	0.552228i
$666$		0			0
$667$	−8.71603	−	32.5287i	−0.337486	−	1.25952i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	23.5045i		−	0.907380i
$672$		0			0
$673$	9.74176	+	9.74176i	0.375517	+	0.375517i	0.869482	−	0.493965i	$-0.164453\pi$
$673$	9.74176	+	9.74176i	0.375517	+	0.375517i	−0.493965	+	0.869482i	$0.664453\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−24.6209	+	6.59716i	−0.946259	+	0.253549i	−0.698774	−	0.715342i	$-0.746271\pi$
$677$	−24.6209	+	6.59716i	−0.946259	+	0.253549i	−0.247485	+	0.968892i	$0.579604\pi$
$678$		0			0
$679$	2.96592	+	6.96637i	0.113821	+	0.267345i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−1.56677	−	0.419816i	−0.0599510	−	0.0160638i	0.228719	−	0.973493i	$-0.426546\pi$
$683$	−1.56677	−	0.419816i	−0.0599510	−	0.0160638i	−0.288670	+	0.957429i	$0.593213\pi$
$684$		0			0
$685$	−10.0050	+	2.68962i	−0.382270	+	0.102765i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.99464	−	5.18687i	−0.114087	−	0.197604i
$690$		0			0
$691$	6.68922	−	11.5861i	0.254470	−	0.440755i	−0.710281	−	0.703918i	$-0.751432\pi$
$691$	6.68922	−	11.5861i	0.254470	−	0.440755i	0.964751	+	0.263163i	$0.0847657\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−15.1953	+	8.78966i	−0.576392	+	0.333411i
$696$		0			0
$697$	−8.88729	−	2.38134i	−0.336630	−	0.0901998i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			22.6890i			0.856950i	0.903554	+	0.428475i	$0.140949\pi$
$701$			22.6890i			0.856950i	−0.903554	+	0.428475i	$0.859051\pi$
$702$		0			0
$703$	−18.6812	+	69.7193i	−0.704576	+	2.62951i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.26952	−	37.2035i	−0.198181	−	1.39918i
$708$		0			0
$709$	−32.7244	−	18.8934i	−1.22899	−	0.709558i	−0.262172	−	0.965021i	$-0.584439\pi$
$709$	−32.7244	−	18.8934i	−1.22899	−	0.709558i	−0.966819	+	0.255463i	$0.917772\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−33.0822	+	33.0822i	−1.23894	+	1.23894i
$714$		0			0
$715$	0.980653	+	3.64787i	0.0366743	+	0.136423i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−24.5922	+	42.5949i	−0.917133	+	1.58852i	−0.113385	+	0.993551i	$0.536169\pi$
$719$	−24.5922	+	42.5949i	−0.917133	+	1.58852i	−0.803748	+	0.594970i	$0.797164\pi$
$720$		0			0
$721$	1.14230	−	9.38693i	0.0425414	−	0.349588i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	10.2206	−	17.7699i	0.379584	−	0.659958i
$726$		0			0
$727$	20.0541	−	20.0541i	0.743766	−	0.743766i	−0.229534	−	0.973301i	$-0.573720\pi$
$727$	20.0541	−	20.0541i	0.743766	−	0.743766i	0.973301	+	0.229534i	$0.0737203\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−12.6600	+	7.30925i	−0.468247	+	0.270342i
$732$		0			0
$733$	−25.1099	+	6.72817i	−0.927454	+	0.248510i	−0.690769	−	0.723076i	$-0.742728\pi$
$733$	−25.1099	+	6.72817i	−0.927454	+	0.248510i	−0.236685	+	0.971586i	$0.576061\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	15.3641	−	4.11681i	0.565945	−	0.151645i
$738$		0			0
$739$	6.88907	−	3.97740i	0.253418	−	0.146311i	−0.367910	−	0.929861i	$-0.619927\pi$
$739$	6.88907	−	3.97740i	0.253418	−	0.146311i	0.621328	+	0.783550i	$0.286593\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−11.0815	+	11.0815i	−0.406541	+	0.406541i	−0.880531	−	0.473989i	$-0.842814\pi$
$743$	−11.0815	+	11.0815i	−0.406541	+	0.406541i	0.473989	+	0.880531i	$0.342814\pi$
$744$		0			0
$745$	18.0330	−	0.0147939i	0.660679	−	0.000542008i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.861397	+	7.07859i	−0.0314747	+	0.258646i
$750$		0			0
$751$	19.8106	−	34.3130i	0.722899	−	1.25210i	−0.236934	−	0.971526i	$-0.576142\pi$
$751$	19.8106	−	34.3130i	0.722899	−	1.25210i	0.959833	−	0.280572i	$-0.0905243\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−6.81568	+	11.8275i	−0.248048	+	0.430447i
$756$		0			0
$757$	9.30716	−	9.30716i	0.338274	−	0.338274i	−0.517443	−	0.855718i	$-0.673116\pi$
$757$	9.30716	−	9.30716i	0.338274	−	0.338274i	0.855718	+	0.517443i	$0.173116\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	34.5097	+	19.9242i	1.25098	+	0.722252i	0.971303	−	0.237844i	$-0.0764407\pi$
$761$	34.5097	+	19.9242i	1.25098	+	0.722252i	0.279673	+	0.960095i	$0.409774\pi$
$762$		0			0
$763$	2.12159	+	14.9787i	0.0768066	+	0.542265i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.53123	−	5.71463i	0.0552895	−	0.206343i
$768$		0			0
$769$			52.6681i			1.89926i	0.313373	+	0.949630i	$0.398541\pi$
$769$			52.6681i			1.89926i	−0.313373	+	0.949630i	$0.601459\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−41.4276	−	11.1005i	−1.49005	−	0.399257i	−0.580294	−	0.814407i	$-0.697062\pi$
$773$	−41.4276	−	11.1005i	−1.49005	−	0.399257i	−0.909753	+	0.415151i	$0.863729\pi$
$774$		0			0
$775$	−28.4793	+	0.0467278i	−1.02301	+	0.00167851i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−23.8841	+	41.3686i	−0.855738	+	1.48218i
$780$		0			0
$781$	−23.7680	−	41.1674i	−0.850487	−	1.47309i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	8.12426	+	30.2210i	0.289967	+	1.07863i
$786$		0			0
$787$	−1.12663	−	0.301878i	−0.0401599	−	0.0107608i	0.238683	−	0.971097i	$-0.423284\pi$
$787$	−1.12663	−	0.301878i	−0.0401599	−	0.0107608i	−0.278843	+	0.960337i	$0.589951\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.43057	+	3.36013i	0.0508652	+	0.119473i
$792$		0			0
$793$	3.88543	−	1.04110i	0.137976	−	0.0369705i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.61236	−	1.61236i	−0.0571127	−	0.0571127i	0.677974	−	0.735086i	$-0.262858\pi$
$797$	−1.61236	−	1.61236i	−0.0571127	−	0.0571127i	−0.735086	+	0.677974i	$0.762858\pi$
$798$		0			0
$799$			2.01814i			0.0713965i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−7.91150	−	29.5261i	−0.279191	−	1.04195i
$804$		0			0
$805$	−19.0721	−	44.6949i	−0.672202	−	1.57529i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	2.67507	+	4.63335i	0.0940503	+	0.162900i	0.909212	−	0.416334i	$-0.136685\pi$
$809$	2.67507	+	4.63335i	0.0940503	+	0.162900i	−0.815162	+	0.579234i	$0.803352\pi$
$810$		0			0
$811$	19.7244			0.692618			0.346309	−	0.938120i	$-0.387435\pi$
$811$	19.7244			0.692618			0.346309	+	0.938120i	$0.387435\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	18.5170	+	18.4867i	0.648623	+	0.647559i
$816$		0			0
$817$	19.6432	+	73.3096i	0.687230	+	2.56478i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−24.7054	−	14.2636i	−0.862223	−	0.497805i	0.00253295	−	0.999997i	$-0.499194\pi$
$821$	−24.7054	−	14.2636i	−0.862223	−	0.497805i	−0.864756	+	0.502192i	$0.832527\pi$
$822$		0			0
$823$	−0.333167	+	1.24340i	−0.0116135	+	0.0433421i	−0.971489	−	0.237083i	$-0.923809\pi$
$823$	−0.333167	+	1.24340i	−0.0116135	+	0.0433421i	0.959876	+	0.280425i	$0.0904754\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	33.6915	+	33.6915i	1.17157	+	1.17157i	0.981836	+	0.189733i	$0.0607622\pi$
$827$	33.6915	+	33.6915i	1.17157	+	1.17157i	0.189733	+	0.981836i	$0.439238\pi$
$828$		0			0
$829$	20.0337	−	11.5665i	0.695799	−	0.401720i	−0.109982	−	0.993934i	$-0.535079\pi$
$829$	20.0337	−	11.5665i	0.695799	−	0.401720i	0.805781	+	0.592214i	$0.201746\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−7.45164	+	4.49929i	−0.258184	+	0.155891i
$834$		0			0
$835$	1.40486	−	5.26028i	0.0486173	−	0.182040i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	22.8467			0.788756			0.394378	−	0.918948i	$-0.370960\pi$
$839$	22.8467			0.788756			0.394378	+	0.918948i	$0.370960\pi$
$840$		0			0
$841$	−12.1908			−0.420371
$842$		0			0
$843$		0			0
$844$		0			0
$845$	24.6029	−	14.2314i	0.846365	−	0.489575i
$846$		0			0
$847$	−1.84153	−	2.35183i	−0.0632759	−	0.0808097i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	79.5284	−	45.9157i	2.72620	−	1.57397i
$852$		0			0
$853$	−14.3579	−	14.3579i	−0.491604	−	0.491604i	0.417207	−	0.908811i	$-0.363009\pi$
$853$	−14.3579	−	14.3579i	−0.491604	−	0.491604i	−0.908811	+	0.417207i	$0.863009\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−12.0523	+	44.9798i	−0.411699	+	1.53648i	0.379658	+	0.925127i	$0.376042\pi$
$857$	−12.0523	+	44.9798i	−0.411699	+	1.53648i	−0.791357	+	0.611355i	$0.790625\pi$
$858$		0			0
$859$	−14.7100	−	8.49281i	−0.501898	−	0.289771i	0.227599	−	0.973755i	$-0.426912\pi$
$859$	−14.7100	−	8.49281i	−0.501898	−	0.289771i	−0.729497	+	0.683984i	$0.760246\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−7.98905	−	29.8155i	−0.271950	−	1.01493i	−0.957858	−	0.287243i	$-0.907261\pi$
$863$	−7.98905	−	29.8155i	−0.271950	−	1.01493i	0.685907	−	0.727689i	$-0.259406\pi$
$864$		0			0
$865$	−15.6720	+	15.6978i	−0.532865	+	0.533740i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−14.3361			−0.486319
$870$		0			0
$871$	1.36107	+	2.35744i	0.0461180	+	0.0798787i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	10.9839	−	27.4655i	0.371323	−	0.928504i
$876$		0			0
$877$	13.6921	+	51.0998i	0.462351	+	1.72552i	0.665526	+	0.746375i	$0.268207\pi$
$877$	13.6921	+	51.0998i	0.462351	+	1.72552i	−0.203175	+	0.979142i	$0.565126\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	40.0911i		−	1.35070i	−0.737496	−	0.675351i	$-0.763992\pi$
$881$		−	40.0911i		−	1.35070i	0.737496	−	0.675351i	$-0.236008\pi$
$882$		0			0
$883$	−9.29675	−	9.29675i	−0.312860	−	0.312860i	0.533156	−	0.846017i	$-0.321006\pi$
$883$	−9.29675	−	9.29675i	−0.312860	−	0.312860i	−0.846017	+	0.533156i	$0.821006\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.57674	+	0.958383i	−0.120095	+	0.0321794i	−0.318366	−	0.947968i	$-0.603134\pi$
$887$	−3.57674	+	0.958383i	−0.120095	+	0.0321794i	0.198271	+	0.980147i	$0.436467\pi$
$888$		0			0
$889$	−8.34825	−	19.6084i	−0.279991	−	0.657646i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	10.1207	+	2.71182i	0.338675	+	0.0907476i
$894$		0			0
$895$	−14.2893	+	24.7967i	−0.477638	+	0.828864i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−11.6763	−	20.2239i	−0.389426	−	0.674505i
$900$		0			0
$901$	6.92582	−	11.9959i	0.230733	−	0.399641i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	23.0717	+	39.8857i	0.766929	+	1.32585i
$906$		0			0
$907$	11.0009	+	2.94768i	0.365279	+	0.0978763i	0.436790	−	0.899564i	$-0.356115\pi$
$907$	11.0009	+	2.94768i	0.365279	+	0.0978763i	−0.0715107	+	0.997440i	$0.522782\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		−	32.6632i		−	1.08218i	−0.840965	−	0.541090i	$-0.818012\pi$
$911$		−	32.6632i		−	1.08218i	0.840965	−	0.541090i	$-0.181988\pi$
$912$		0			0
$913$	−2.99698	+	11.1849i	−0.0991856	+	0.370166i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−26.8673	+	21.0378i	−0.887238	+	0.694728i
$918$		0			0
$919$	15.2690	+	8.81555i	0.503677	+	0.290798i	0.730231	−	0.683201i	$-0.239413\pi$
$919$	15.2690	+	8.81555i	0.503677	+	0.290798i	−0.226554	+	0.973999i	$0.572746\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	5.75245	−	5.75245i	0.189344	−	0.189344i
$924$		0			0
$925$	54.0191	+	14.3794i	1.77614	+	0.472792i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	10.0115	−	17.3405i	0.328468	−	0.568923i	−0.653740	−	0.756719i	$-0.726801\pi$
$929$	10.0115	−	17.3405i	0.328468	−	0.568923i	0.982208	+	0.187796i	$0.0601343\pi$
$930$		0			0
$931$	12.5503	+	43.4147i	0.411320	+	1.42286i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−6.17229	+	6.18243i	−0.201856	+	0.202187i
$936$		0			0
$937$	5.61057	−	5.61057i	0.183289	−	0.183289i	−0.609498	−	0.792788i	$-0.708629\pi$
$937$	5.61057	−	5.61057i	0.183289	−	0.183289i	0.792788	+	0.609498i	$0.208629\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−10.4386	+	6.02672i	−0.340288	+	0.196466i	−0.660400	−	0.750914i	$-0.729613\pi$
$941$	−10.4386	+	6.02672i	−0.340288	+	0.196466i	0.320111	+	0.947380i	$0.396280\pi$
$942$		0			0
$943$	58.7037	−	15.7296i	1.91166	−	0.512227i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	33.3184	−	8.92765i	1.08270	−	0.290110i	0.327001	−	0.945024i	$-0.393962\pi$
$947$	33.3184	−	8.92765i	1.08270	−	0.290110i	0.755703	+	0.654915i	$0.227295\pi$
$948$		0			0
$949$	4.53042	−	2.61564i	0.147064	−	0.0849072i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	10.1921	−	10.1921i	0.330156	−	0.330156i	−0.522490	−	0.852646i	$-0.674997\pi$
$953$	10.1921	−	10.1921i	0.330156	−	0.330156i	0.852646	+	0.522490i	$0.174997\pi$
$954$		0			0
$955$	−0.0347966	−	42.4152i	−0.00112599	−	1.37252i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−9.79788	−	7.36668i	−0.316390	−	0.237883i
$960$		0			0
$961$	−0.721506	+	1.24969i	−0.0232744	+	0.0403124i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.49700	−	0.402436i	0.0481901	−	0.0129549i
$966$		0			0
$967$	6.82630	−	6.82630i	0.219519	−	0.219519i	−0.588777	−	0.808296i	$-0.700390\pi$
$967$	6.82630	−	6.82630i	0.219519	−	0.219519i	0.808296	+	0.588777i	$0.200390\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	5.92560	+	3.42115i	0.190162	+	0.109790i	0.592058	−	0.805895i	$-0.298316\pi$
$971$	5.92560	+	3.42115i	0.190162	+	0.109790i	−0.401897	+	0.915685i	$0.631649\pi$
$972$		0			0
$973$	−19.2666	−	7.76005i	−0.617658	−	0.248776i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−11.5558	+	43.1269i	−0.369704	+	1.37975i	0.491228	+	0.871031i	$0.336548\pi$
$977$	−11.5558	+	43.1269i	−0.369704	+	1.37975i	−0.860931	+	0.508721i	$0.830118\pi$
$978$		0			0
$979$		−	27.3403i		−	0.873801i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−48.6380	−	13.0325i	−1.55131	−	0.415673i	−0.621411	−	0.783485i	$-0.713440\pi$
$983$	−48.6380	−	13.0325i	−1.55131	−	0.415673i	−0.929900	+	0.367812i	$0.880107\pi$
$984$		0			0
$985$	1.65712	−	6.20480i	0.0528001	−	0.197701i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	48.2802	−	83.6237i	1.53522	−	2.65908i
$990$		0			0
$991$	−22.3110	−	38.6437i	−0.708731	−	1.22756i	−0.965328	−	0.261040i	$-0.915935\pi$
$991$	−22.3110	−	38.6437i	−0.708731	−	1.22756i	0.256597	−	0.966518i	$-0.417399\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	13.5524	+	7.80967i	0.429640	+	0.247583i
$996$		0			0
$997$	−18.1286	−	4.85753i	−0.574137	−	0.153840i	−0.0399439	−	0.999202i	$-0.512718\pi$
$997$	−18.1286	−	4.85753i	−0.574137	−	0.153840i	−0.534193	+	0.845362i	$0.679385\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.ej.a.233.11	yes	64
3.2	odd	2	inner	1260.2.ej.a.233.6	yes	64
5.2	odd	4	inner	1260.2.ej.a.737.16	yes	64
7.4	even	3	inner	1260.2.ej.a.53.1	✓	64
15.2	even	4	inner	1260.2.ej.a.737.1	yes	64
21.11	odd	6	inner	1260.2.ej.a.53.16	yes	64
35.32	odd	12	inner	1260.2.ej.a.557.6	yes	64
105.32	even	12	inner	1260.2.ej.a.557.11	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.ej.a.53.1	✓	64	7.4	even	3	inner
1260.2.ej.a.53.16	yes	64	21.11	odd	6	inner
1260.2.ej.a.233.6	yes	64	3.2	odd	2	inner
1260.2.ej.a.233.11	yes	64	1.1	even	1	trivial
1260.2.ej.a.557.6	yes	64	35.32	odd	12	inner
1260.2.ej.a.557.11	yes	64	105.32	even	12	inner
1260.2.ej.a.737.1	yes	64	15.2	even	4	inner
1260.2.ej.a.737.16	yes	64	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.ej (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.11962 + 1.93557i) q^{5} +(-0.988471 + 2.45417i) q^{7} +(-2.72089 + 1.57091i) q^{11} +(-0.380199 - 0.380199i) q^{13} +(0.321846 - 1.20115i) q^{17} +(-5.59110 - 3.22802i) q^{19} +(2.12591 + 7.93400i) q^{23} +(-2.49289 + 4.33422i) q^{25} -4.09991 q^{29} +(2.84794 + 4.93277i) q^{31} +(-5.85693 + 0.834480i) q^{35} +(-2.89360 - 10.7991i) q^{37} -7.39900i q^{41} +(-8.31257 - 8.31257i) q^{43} +(-1.56762 + 0.420044i) q^{47} +(-5.04585 - 4.85174i) q^{49} +(10.7595 + 2.88301i) q^{53} +(-6.08698 - 3.50766i) q^{55} +(5.50159 + 9.52904i) q^{59} +(-3.74059 + 6.47889i) q^{61} +(0.310224 - 1.16158i) q^{65} +(-4.89021 - 1.31033i) q^{67} +15.1301i q^{71} +(-2.51813 + 9.39779i) q^{73} +(-1.16575 - 8.23032i) q^{77} +(3.95167 + 2.28150i) q^{79} +(2.60611 - 2.60611i) q^{83} +(2.68525 - 0.721873i) q^{85} +(-4.35104 + 7.53622i) q^{89} +(1.30889 - 0.557255i) q^{91} +(-0.0118431 - 14.4361i) q^{95} +(2.02356 - 2.02356i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7} + 16 q^{25} + 32 q^{31} + 16 q^{37} - 16 q^{43} + 32 q^{55} + 48 q^{61} + 32 q^{67} + 40 q^{73} + 80 q^{85} + 96 q^{91} + 80 q^{97}+O(q^{100}) \) 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

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