LMFDB - Embedded newform 1260.2.ej.a.737.1

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			737.1
Character	$\chi$	$=$	1260.737
Dual form			1260.2.ej.a.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.23607 - 0.00183442i) q^{5} +(-2.45417 - 0.988471i) q^{7} +O(q^{10})$	$q+(-2.23607 - 0.00183442i) q^{5} +(-2.45417 - 0.988471i) q^{7} +(2.72089 - 1.57091i) q^{11} +(-0.380199 + 0.380199i) q^{13} +(-1.20115 - 0.321846i) q^{17} +(5.59110 + 3.22802i) q^{19} +(-7.93400 + 2.12591i) q^{23} +(4.99999 + 0.00820379i) q^{25} -4.09991 q^{29} +(2.84794 + 4.93277i) q^{31} +(5.48586 + 2.21479i) q^{35} +(10.7991 - 2.89360i) q^{37} +7.39900i q^{41} +(-8.31257 + 8.31257i) q^{43} +(0.420044 + 1.56762i) q^{47} +(5.04585 + 4.85174i) q^{49} +(-2.88301 + 10.7595i) q^{53} +(-6.08698 + 3.50766i) q^{55} +(5.50159 + 9.52904i) q^{59} +(-3.74059 + 6.47889i) q^{61} +(0.850848 - 0.849453i) q^{65} +(1.31033 - 4.89021i) q^{67} -15.1301i q^{71} +(9.39779 + 2.51813i) q^{73} +(-8.23032 + 1.16575i) q^{77} +(-3.95167 - 2.28150i) q^{79} +(2.60611 + 2.60611i) q^{83} +(2.68525 + 0.721873i) q^{85} +(-4.35104 + 7.53622i) q^{89} +(1.30889 - 0.557255i) q^{91} +(-12.4962 - 7.22833i) q^{95} +(2.02356 + 2.02356i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−2.23607	−	0.00183442i	−1.00000	−	0.000820380i
$5$	−2.23607	−	0.00183442i	−1.00000	−	0.000820380i
$6$		0			0
$7$	−2.45417	−	0.988471i	−0.927587	−	0.373607i
$7$	−2.45417	−	0.988471i	−0.927587	−	0.373607i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.72089	−	1.57091i	0.820380	−	0.473647i	−0.0301675	−	0.999545i	$-0.509604\pi$
$11$	2.72089	−	1.57091i	0.820380	−	0.473647i	0.850548	+	0.525898i	$0.176271\pi$
$12$		0			0
$13$	−0.380199	+	0.380199i	−0.105448	+	0.105448i	−0.757863	−	0.652414i	$-0.773756\pi$
$13$	−0.380199	+	0.380199i	−0.105448	+	0.105448i	0.652414	+	0.757863i	$0.273756\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.20115	−	0.321846i	−0.291321	−	0.0780592i	0.110199	−	0.993910i	$-0.464851\pi$
$17$	−1.20115	−	0.321846i	−0.291321	−	0.0780592i	−0.401520	+	0.915850i	$0.631518\pi$
$18$		0			0
$19$	5.59110	+	3.22802i	1.28269	+	0.740559i	0.977339	−	0.211682i	$-0.0678941\pi$
$19$	5.59110	+	3.22802i	1.28269	+	0.740559i	0.305347	+	0.952241i	$0.401227\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.93400	+	2.12591i	−1.65435	+	0.443283i	−0.960827	−	0.277148i	$-0.910611\pi$
$23$	−7.93400	+	2.12591i	−1.65435	+	0.443283i	−0.693527	+	0.720431i	$0.743944\pi$
$24$		0			0
$25$	4.99999	+	0.00820379i	0.999999	+	0.00164076i
$26$		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
$35$	5.48586	+	2.21479i	0.927280	+	0.374368i
$36$		0			0
$37$	10.7991	−	2.89360i	1.77536	−	0.475706i	0.785633	−	0.618693i	$-0.212337\pi$
$37$	10.7991	−	2.89360i	1.77536	−	0.475706i	0.989725	+	0.142987i	$0.0456707\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			7.39900i			1.15553i	0.816203	+	0.577765i	$0.196075\pi$
$41$			7.39900i			1.15553i	−0.816203	+	0.577765i	$0.803925\pi$
$42$		0			0
$43$	−8.31257	+	8.31257i	−1.26766	+	1.26766i	−0.320359	+	0.947296i	$0.603803\pi$
$43$	−8.31257	+	8.31257i	−1.26766	+	1.26766i	−0.947296	+	0.320359i	$0.896197\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.420044	+	1.56762i	0.0612697	+	0.228661i	0.989770	−	0.142669i	$-0.0455684\pi$
$47$	0.420044	+	1.56762i	0.0612697	+	0.228661i	−0.928501	+	0.371330i	$0.878902\pi$
$48$		0			0
$49$	5.04585	+	4.85174i	0.720836	+	0.693106i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−2.88301	+	10.7595i	−0.396011	+	1.47793i	0.424040	+	0.905644i	$0.360612\pi$
$53$	−2.88301	+	10.7595i	−0.396011	+	1.47793i	−0.820051	+	0.572290i	$0.806055\pi$
$54$		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
$65$	0.850848	−	0.849453i	0.105535	−	0.105362i
$66$		0			0
$67$	1.31033	−	4.89021i	0.160082	−	0.597434i	−0.838535	−	0.544848i	$-0.816587\pi$
$67$	1.31033	−	4.89021i	0.160082	−	0.597434i	0.998616	−	0.0525853i	$-0.0167462\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	15.1301i		−	1.79561i	−0.440389	−	0.897807i	$-0.645159\pi$
$71$		−	15.1301i		−	1.79561i	0.440389	−	0.897807i	$-0.354841\pi$
$72$		0			0
$73$	9.39779	+	2.51813i	1.09993	+	0.294725i	0.762735	−	0.646711i	$-0.223856\pi$
$73$	9.39779	+	2.51813i	1.09993	+	0.294725i	0.337192	+	0.941436i	$0.390523\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−8.23032	+	1.16575i	−0.937932	+	0.132849i
$78$		0			0
$79$	−3.95167	−	2.28150i	−0.444598	−	0.256688i	0.260948	−	0.965353i	$-0.415965\pi$
$79$	−3.95167	−	2.28150i	−0.444598	−	0.256688i	−0.705546	+	0.708664i	$0.749298\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.60611	+	2.60611i	0.286057	+	0.286057i	0.835519	−	0.549462i	$-0.185167\pi$
$83$	2.60611	+	2.60611i	0.286057	+	0.286057i	−0.549462	+	0.835519i	$0.685167\pi$
$84$		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
$95$	−12.4962	−	7.22833i	−1.28208	−	0.741611i
$96$		0			0
$97$	2.02356	+	2.02356i	0.205461	+	0.205461i	0.802335	−	0.596874i	$-0.203591\pi$
$97$	2.02356	+	2.02356i	0.205461	+	0.205461i	−0.596874	+	0.802335i	$0.703591\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	12.2993	−	7.10098i	1.22382	−	0.706574i	0.258091	−	0.966121i	$-0.416907\pi$
$101$	12.2993	−	7.10098i	1.22382	−	0.706574i	0.965731	+	0.259547i	$0.0835732\pi$
$102$		0			0
$103$	0.925045	+	3.45232i	0.0911474	+	0.340167i	0.996407	−	0.0846916i	$-0.0269905\pi$
$103$	0.925045	+	3.45232i	0.0911474	+	0.340167i	−0.905260	+	0.424858i	$0.860324\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−0.697568	−	2.60336i	−0.0674364	−	0.251676i	0.923976	−	0.382451i	$-0.124920\pi$
$107$	−0.697568	−	2.60336i	−0.0674364	−	0.251676i	−0.991412	+	0.130775i	$0.958253\pi$
$108$		0			0
$109$	−4.95186	+	2.85896i	−0.474302	+	0.273839i	−0.718039	−	0.696003i	$-0.754960\pi$
$109$	−4.95186	+	2.85896i	−0.474302	+	0.273839i	0.243737	+	0.969841i	$0.421627\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.976035	+	0.976035i	0.0918177	+	0.0918177i	0.751524	−	0.659706i	$-0.229319\pi$
$113$	0.976035	+	0.976035i	0.0918177	+	0.0918177i	−0.659706	+	0.751524i	$0.729319\pi$
$114$		0			0
$115$	17.7449	−	4.73912i	1.65472	−	0.441925i
$116$		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	0.407699	−	0.913116i	$-0.366331\pi$
$127$	−5.69577	−	5.69577i	−0.505417	−	0.505417i	−0.913116	+	0.407699i	$0.866331\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−11.1697	−	6.44881i	−0.975899	−	0.563435i	−0.0748691	−	0.997193i	$-0.523854\pi$
$131$	−11.1697	−	6.44881i	−0.975899	−	0.563435i	−0.901029	+	0.433758i	$0.857187\pi$
$132$		0			0
$133$	−10.5307	−	13.4487i	−0.913125	−	1.16615i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.47534	+	1.19916i	0.382354	+	0.102451i	0.444876	−	0.895592i	$-0.353248\pi$
$137$	4.47534	+	1.19916i	0.382354	+	0.102451i	−0.0625222	+	0.998044i	$0.519914\pi$
$138$		0			0
$139$		−	7.85056i		−	0.665876i	−0.942949	−	0.332938i	$-0.891960\pi$
$139$		−	7.85056i		−	0.665876i	0.942949	−	0.332938i	$-0.108040\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−0.437223	+	1.63174i	−0.0365624	+	0.136453i
$144$		0			0
$145$	9.16767	+	0.00752097i	0.761333	+	0.000624583i
$146$		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
$157$	−3.62219	+	13.5182i	−0.289082	+	1.07887i	0.656722	+	0.754133i	$0.271942\pi$
$157$	−3.62219	+	13.5182i	−0.289082	+	1.07887i	−0.945804	+	0.324737i	$0.894724\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	21.5727	+	2.62520i	1.70017	+	0.206894i
$162$		0			0
$163$	−3.02860	−	11.3029i	−0.237218	−	0.885309i	−0.977137	−	0.212613i	$-0.931803\pi$
$163$	−3.02860	−	11.3029i	−0.237218	−	0.885309i	0.739919	−	0.672696i	$-0.234864\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.72175	+	1.72175i	−0.133233	+	0.133233i	−0.770578	−	0.637345i	$-0.780032\pi$
$167$	−1.72175	+	1.72175i	−0.133233	+	0.133233i	0.637345	+	0.770578i	$0.280032\pi$
$168$		0			0
$169$			12.7109i			0.977761i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.58199	+	2.56749i	−0.728505	+	0.195202i	−0.603963	−	0.797012i	$-0.706413\pi$
$173$	−9.58199	+	2.56749i	−0.728505	+	0.195202i	−0.124542	+	0.992214i	$0.539746\pi$
$174$		0			0
$175$	−12.2627	−	4.96248i	−0.926973	−	0.375128i
$176$		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
$185$	−24.1528	+	6.45048i	−1.77575	+	0.474249i
$186$		0			0
$187$	−3.77378	+	1.01118i	−0.275966	+	0.0739450i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	16.4274	+	9.48434i	1.18864	+	0.686262i	0.957998	−	0.286776i	$-0.0925835\pi$
$191$	16.4274	+	9.48434i	1.18864	+	0.686262i	0.230644	+	0.973038i	$0.425917\pi$
$192$		0			0
$193$	−0.669626	−	0.179426i	−0.0482007	−	0.0129153i	0.234638	−	0.972083i	$-0.424609\pi$
$193$	−0.669626	−	0.179426i	−0.0482007	−	0.0129153i	−0.282839	+	0.959167i	$0.591276\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−2.03090	+	2.03090i	−0.144696	+	0.144696i	−0.775744	−	0.631048i	$-0.782625\pi$
$197$	−2.03090	+	2.03090i	−0.144696	+	0.144696i	0.631048	+	0.775744i	$0.282625\pi$
$198$		0			0
$199$	−6.05795	+	3.49756i	−0.429437	+	0.247936i	−0.699107	−	0.715017i	$-0.746419\pi$
$199$	−6.05795	+	3.49756i	−0.429437	+	0.247936i	0.269670	+	0.962953i	$0.413085\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	10.0618	+	4.05264i	0.706203	+	0.284439i
$204$		0			0
$205$	0.0135729	−	16.5447i	0.000947973	−	1.15553i
$206$		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
$215$	18.6027	−	18.5722i	1.26869	−	1.26661i
$216$		0			0
$217$	−2.11341	−	14.9209i	−0.143468	−	1.01290i
$218$		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	−0.552248	−	0.833680i	$-0.686230\pi$
$223$	4.20268	−	4.20268i	0.281432	−	0.281432i	0.833680	+	0.552248i	$0.186230\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−15.4223	−	4.13240i	−1.02362	−	0.274277i	−0.292308	−	0.956324i	$-0.594423\pi$
$227$	−15.4223	−	4.13240i	−1.02362	−	0.274277i	−0.731308	+	0.682047i	$0.761090\pi$
$228$		0			0
$229$	−18.6115	−	10.7453i	−1.22988	−	0.710071i	−0.262875	−	0.964830i	$-0.584671\pi$
$229$	−18.6115	−	10.7453i	−1.22988	−	0.710071i	−0.967005	+	0.254759i	$0.918004\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	20.3842	−	5.46192i	1.33541	−	0.357823i	0.480682	−	0.876895i	$-0.340389\pi$
$233$	20.3842	−	5.46192i	1.33541	−	0.357823i	0.854730	+	0.519072i	$0.173723\pi$
$234$		0			0
$235$	−0.936370	−	3.50608i	−0.0610820	−	0.228712i
$236$		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
$245$	−11.2740	−	10.8581i	−0.720267	−	0.693697i
$246$		0			0
$247$	−3.35302	+	0.898439i	−0.213348	+	0.0571663i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	20.3285i		−	1.28313i	−0.767071	−	0.641563i	$-0.778286\pi$
$251$		−	20.3285i		−	1.28313i	0.767071	−	0.641563i	$-0.221714\pi$
$252$		0			0
$253$	−18.2480	+	18.2480i	−1.14724	+	1.14724i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	0.0573203	+	0.213922i	0.00357554	+	0.0133441i	0.967691	−	0.252141i	$-0.0811346\pi$
$257$	0.0573203	+	0.213922i	0.00357554	+	0.0133441i	−0.964115	+	0.265485i	$0.914468\pi$
$258$		0			0
$259$	−29.3630	−	3.57319i	−1.82453	−	0.222027i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	0.723773	−	2.70116i	0.0446297	−	0.166560i	−0.940014	−	0.341136i	$-0.889188\pi$
$263$	0.723773	−	2.70116i	0.0446297	−	0.166560i	0.984644	+	0.174575i	$0.0558552\pi$
$264$		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
$275$	13.6173	−	7.83221i	0.821156	−	0.472300i
$276$		0			0
$277$	0.129352	−	0.482749i	0.00777202	−	0.0290056i	−0.961931	−	0.273293i	$-0.911887\pi$
$277$	0.129352	−	0.482749i	0.00777202	−	0.0290056i	0.969703	+	0.244287i	$0.0785539\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	4.50960i		−	0.269020i	−0.990912	−	0.134510i	$-0.957054\pi$
$281$		−	4.50960i		−	0.269020i	0.990912	−	0.134510i	$-0.0429461\pi$
$282$		0			0
$283$	−10.7354	−	2.87653i	−0.638151	−	0.170992i	−0.0747854	−	0.997200i	$-0.523827\pi$
$283$	−10.7354	−	2.87653i	−0.638151	−	0.170992i	−0.563366	+	0.826208i	$0.690494\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.31370	−	18.1584i	0.431714	−	1.07186i
$288$		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	0.995010	−	0.0997714i	$-0.0318112\pi$
$293$	15.3240	+	15.3240i	0.895239	+	0.895239i	−0.0997714	+	0.995010i	$0.531811\pi$
$294$		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
$305$	8.37609	−	14.4804i	0.479614	−	0.829143i
$306$		0			0
$307$	−11.4605	−	11.4605i	−0.654087	−	0.654087i	0.299888	−	0.953974i	$-0.403051\pi$
$307$	−11.4605	−	11.4605i	−0.654087	−	0.654087i	−0.953974	+	0.299888i	$0.903051\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.38389	+	2.53104i	−0.248587	+	0.143522i	−0.619117	−	0.785299i	$-0.712509\pi$
$311$	−4.38389	+	2.53104i	−0.248587	+	0.143522i	0.370530	+	0.928821i	$0.379176\pi$
$312$		0			0
$313$	−2.19662	−	8.19791i	−0.124160	−	0.463373i	0.875648	−	0.482950i	$-0.160435\pi$
$313$	−2.19662	−	8.19791i	−0.124160	−	0.463373i	−0.999808	+	0.0195769i	$0.993768\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	2.17392	+	8.11319i	0.122100	+	0.455682i	0.999720	−	0.0236748i	$-0.00753663\pi$
$317$	2.17392	+	8.11319i	0.122100	+	0.455682i	−0.877620	+	0.479357i	$0.840870\pi$
$318$		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
$325$	−1.90411	+	1.89787i	−0.105621	+	0.105275i
$326$		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	0.978369	−	0.206868i	$-0.0663271\pi$
$337$	14.1629	+	14.1629i	0.771501	+	0.771501i	−0.206868	+	0.978369i	$0.566327\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	15.4979	+	8.94770i	0.839257	+	0.484545i
$342$		0			0
$343$	−7.58755	−	16.8946i	−0.409689	−	0.912225i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−26.9409	−	7.21878i	−1.44626	−	0.387525i	−0.551540	−	0.834149i	$-0.685959\pi$
$347$	−26.9409	−	7.21878i	−1.44626	−	0.387525i	−0.894722	+	0.446624i	$0.852626\pi$
$348$		0			0
$349$			26.6684i			1.42753i	0.700387	+	0.713764i	$0.253011\pi$
$349$			26.6684i			1.42753i	−0.700387	+	0.713764i	$0.746989\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−8.32160	+	31.0566i	−0.442914	+	1.65298i	0.278472	+	0.960444i	$0.410172\pi$
$353$	−8.32160	+	31.0566i	−0.442914	+	1.65298i	−0.721386	+	0.692533i	$0.756495\pi$
$354$		0			0
$355$	−0.0277551	+	33.8320i	−0.00147309	+	1.79561i
$356$		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
$367$	5.34435	−	19.9454i	0.278973	−	1.04114i	−0.674160	−	0.738586i	$-0.735494\pi$
$367$	5.34435	−	19.9454i	0.278973	−	1.04114i	0.953132	−	0.302554i	$-0.0978393\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	17.7108	−	23.5559i	0.919501	−	1.22296i
$372$		0			0
$373$	−7.40708	−	27.6436i	−0.383524	−	1.43133i	−0.840480	−	0.541842i	$-0.817727\pi$
$373$	−7.40708	−	27.6436i	−0.383524	−	1.43133i	0.456956	−	0.889489i	$-0.348940\pi$
$374$		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	$-0.915202\pi$
$379$		−	10.2503i		−	0.526522i	0.964725	−	0.263261i	$-0.0847980\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−27.2850	+	7.31099i	−1.39420	+	0.373574i	−0.876257	−	0.481843i	$-0.839967\pi$
$383$	−27.2850	+	7.31099i	−1.39420	+	0.373574i	−0.517939	+	0.855417i	$0.673301\pi$
$384$		0			0
$385$	18.4057	−	2.59159i	0.938040	−	0.132080i
$386$		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
$395$	8.83201	+	5.10883i	0.444387	+	0.257053i
$396$		0			0
$397$	−25.0435	+	6.71038i	−1.25690	+	0.336785i	−0.824997	−	0.565137i	$-0.808823\pi$
$397$	−25.0435	+	6.71038i	−1.25690	+	0.336785i	−0.431900	+	0.901922i	$0.642157\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	15.1316	+	8.73625i	0.755638	+	0.436268i	0.827727	−	0.561131i	$-0.189633\pi$
$401$	15.1316	+	8.73625i	0.755638	+	0.436268i	−0.0720896	+	0.997398i	$0.522967\pi$
$402$		0			0
$403$	−2.95822	−	0.792652i	−0.147359	−	0.0394848i
$404$		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	0.356332	−	0.934360i	$-0.384027\pi$
$409$	27.1742	−	15.6890i	1.34368	−	0.775772i	0.987345	+	0.158588i	$0.0506940\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4.08264	−	28.8240i	−0.200894	−	1.41834i
$414$		0			0
$415$	−5.82265	−	5.83221i	−0.285823	−	0.286292i
$416$		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
$425$	−6.00309	−	1.61908i	−0.291192	−	0.0785371i
$426$		0			0
$427$	15.5842	−	12.2028i	0.754173	−	0.590535i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	20.5060	−	11.8391i	0.987739	−	0.570271i	0.0831413	−	0.996538i	$-0.473505\pi$
$431$	20.5060	−	11.8391i	0.987739	−	0.570271i	0.904598	+	0.426266i	$0.140171\pi$
$432$		0			0
$433$	12.7820	−	12.7820i	0.614264	−	0.614264i	−0.329790	−	0.944054i	$-0.606978\pi$
$433$	12.7820	−	12.7820i	0.614264	−	0.614264i	0.944054	+	0.329790i	$0.106978\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−51.2223	−	13.7250i	−2.45029	−	0.656554i
$438$		0			0
$439$	21.1416	+	12.2061i	1.00903	+	0.582565i	0.910908	−	0.412609i	$-0.135382\pi$
$439$	21.1416	+	12.2061i	1.00903	+	0.582565i	0.0981240	+	0.995174i	$0.468716\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.8575	−	2.90926i	0.515855	−	0.138223i	0.00850631	−	0.999964i	$-0.497292\pi$
$443$	10.8575	−	2.90926i	0.515855	−	0.138223i	0.507349	+	0.861741i	$0.330626\pi$
$444$		0			0
$445$	9.74304	−	16.8435i	0.461865	−	0.798459i
$446$		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
$455$	−2.92778	+	1.24366i	−0.137256	+	0.0583037i
$456$		0			0
$457$	6.66995	−	1.78721i	0.312007	−	0.0836020i	−0.0994176	−	0.995046i	$-0.531698\pi$
$457$	6.66995	−	1.78721i	0.312007	−	0.0836020i	0.411425	+	0.911444i	$0.365031\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	2.23973i		−	0.104315i	−0.998639	−	0.0521574i	$-0.983390\pi$
$461$		−	2.23973i		−	0.104315i	0.998639	−	0.0521574i	$-0.0166097\pi$
$462$		0			0
$463$	−24.7669	+	24.7669i	−1.15101	+	1.15101i	−0.164665	+	0.986349i	$0.552654\pi$
$463$	−24.7669	+	24.7669i	−1.15101	+	1.15101i	−0.986349	+	0.164665i	$0.947346\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.33559	+	23.6447i	0.293176	+	1.09415i	0.942655	+	0.333769i	$0.108320\pi$
$467$	6.33559	+	23.6447i	0.293176	+	1.09415i	−0.649479	+	0.760380i	$0.725013\pi$
$468$		0			0
$469$	−8.04958	+	10.7062i	−0.371695	+	0.494364i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−9.55933	+	35.6759i	−0.439538	+	1.64038i
$474$		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
$485$	−4.52110	−	4.52852i	−0.205292	−	0.205629i
$486$		0			0
$487$	−6.32679	+	23.6119i	−0.286694	+	1.06996i	0.660898	+	0.750476i	$0.270176\pi$
$487$	−6.32679	+	23.6119i	−0.286694	+	1.06996i	−0.947592	+	0.319482i	$0.896491\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			7.50191i			0.338556i	0.985568	+	0.169278i	$0.0541436\pi$
$491$			7.50191i			0.338556i	−0.985568	+	0.169278i	$0.945856\pi$
$492$		0			0
$493$	4.92459	+	1.31954i	0.221792	+	0.0594291i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−14.9557	+	37.1318i	−0.670854	+	1.66559i
$498$		0			0
$499$	−16.2317	−	9.37137i	−0.726630	−	0.419520i	0.0905579	−	0.995891i	$-0.471135\pi$
$499$	−16.2317	−	9.37137i	−0.726630	−	0.419520i	−0.817188	+	0.576371i	$0.804468\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	16.1780	+	16.1780i	0.721342	+	0.721342i	0.968879	−	0.247537i	$-0.0796210\pi$
$503$	16.1780	+	16.1780i	0.721342	+	0.721342i	−0.247537	+	0.968879i	$0.579621\pi$
$504$		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
$515$	−2.06213	−	7.72131i	−0.0908683	−	0.340242i
$516$		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	−0.491725	−	0.870751i	$-0.663633\pi$
$521$	0.376731	−	0.217506i	0.0165049	−	0.00952910i	0.508230	+	0.861222i	$0.330300\pi$
$522$		0			0
$523$	1.80535	+	6.73764i	0.0789422	+	0.294616i	0.994098	−	0.108483i	$-0.0345994\pi$
$523$	1.80535	+	6.73764i	0.0789422	+	0.294616i	−0.915156	+	0.403100i	$0.867933\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.83320	−	6.84158i	−0.0798553	−	0.298024i
$528$		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
$535$	1.55503	+	5.82256i	0.0672299	+	0.251731i
$536$		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	0.566505	−	0.824058i	$-0.308295\pi$
$547$	−6.02367	−	6.02367i	−0.257554	−	0.257554i	−0.824058	+	0.566505i	$0.808295\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−22.9230	−	13.2346i	−0.976552	−	0.563813i
$552$		0			0
$553$	7.44286	+	9.50528i	0.316502	+	0.404206i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	36.2868	+	9.72301i	1.53752	+	0.411977i	0.925463	−	0.378837i	$-0.123676\pi$
$557$	36.2868	+	9.72301i	1.53752	+	0.411977i	0.612056	+	0.790814i	$0.290343\pi$
$558$		0			0
$559$		−	6.32086i		−	0.267344i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−9.65324	+	36.0264i	−0.406835	+	1.51833i	0.393810	+	0.919192i	$0.371157\pi$
$563$	−9.65324	+	36.0264i	−0.406835	+	1.51833i	−0.800645	+	0.599139i	$0.795510\pi$
$564$		0			0
$565$	−2.18069	−	2.18427i	−0.0917423	−	0.0918930i
$566$		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
$577$	6.46928	−	24.1437i	0.269320	−	1.00512i	−0.690233	−	0.723587i	$-0.742492\pi$
$577$	6.46928	−	24.1437i	0.269320	−	1.00512i	0.959553	−	0.281528i	$-0.0908413\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.81976	−	8.97187i	−0.158470	−	0.372216i
$582$		0			0
$583$	9.05787	+	33.8044i	0.375139	+	1.40004i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	11.5063	−	11.5063i	0.474915	−	0.474915i	−0.428586	−	0.903501i	$-0.640988\pi$
$587$	11.5063	−	11.5063i	0.474915	−	0.474915i	0.903501	+	0.428586i	$0.140988\pi$
$588$		0			0
$589$			36.7728i			1.51520i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−45.4299	+	12.1729i	−1.86558	+	0.499881i	−1.00000		0.000887582i	$-0.999717\pi$
$593$	−45.4299	+	12.1729i	−1.86558	+	0.499881i	−0.865581	+	0.500768i	$0.833051\pi$
$594$		0			0
$595$	−5.87651	−	4.42589i	−0.240913	−	0.181444i
$596$		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
$605$	1.26404	−	2.18524i	0.0513906	−	0.0888428i
$606$		0			0
$607$	29.6839	−	7.95377i	1.20483	−	0.322834i	0.400099	−	0.916472i	$-0.368976\pi$
$607$	29.6839	−	7.95377i	1.20483	−	0.322834i	0.804732	+	0.593638i	$0.202309\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.755709	−	0.436309i	−0.0305727	−	0.0176512i
$612$		0			0
$613$	−27.8859	−	7.47201i	−1.12630	−	0.301792i	−0.352871	−	0.935672i	$-0.614795\pi$
$613$	−27.8859	−	7.47201i	−1.12630	−	0.301792i	−0.773431	+	0.633880i	$0.781461\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	0.259882	−	0.259882i	0.0104625	−	0.0104625i	−0.701856	−	0.712319i	$-0.747645\pi$
$617$	0.259882	−	0.259882i	0.0104625	−	0.0104625i	0.712319	+	0.701856i	$0.247645\pi$
$618$		0			0
$619$	−16.3858	+	9.46036i	−0.658602	+	0.380244i	−0.791744	−	0.610853i	$-0.790827\pi$
$619$	−16.3858	+	9.46036i	−0.658602	+	0.380244i	0.133142	+	0.991097i	$0.457493\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	18.1275	−	14.1943i	0.726263	−	0.568681i
$624$		0			0
$625$	24.9999	+	0.0820378i	0.999995	+	0.00328151i
$626$		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
$635$	12.7257	+	12.7466i	0.505003	+	0.505832i
$636$		0			0
$637$	−3.76305	+	0.0738011i	−0.149098	+	0.00292411i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−4.12501	+	2.38158i	−0.162928	+	0.0940667i	−0.579247	−	0.815152i	$-0.696653\pi$
$641$	−4.12501	+	2.38158i	−0.162928	+	0.0940667i	0.416319	+	0.909219i	$0.363320\pi$
$642$		0			0
$643$	−12.2522	+	12.2522i	−0.483178	+	0.483178i	−0.906145	−	0.422967i	$-0.860989\pi$
$643$	−12.2522	+	12.2522i	−0.483178	+	0.483178i	0.422967	+	0.906145i	$0.360989\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	1.54590	+	0.414222i	0.0607755	+	0.0162848i	0.289079	−	0.957305i	$-0.406651\pi$
$647$	1.54590	+	0.414222i	0.0607755	+	0.0162848i	−0.228303	+	0.973590i	$0.573318\pi$
$648$		0			0
$649$	29.9385	+	17.2850i	1.17519	+	0.678495i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.78720	−	1.01478i	0.148205	−	0.0397113i	−0.183954	−	0.982935i	$-0.558890\pi$
$653$	3.78720	−	1.01478i	0.148205	−	0.0397113i	0.332159	+	0.943224i	$0.392223\pi$
$654$		0			0
$655$	24.9643	+	14.4405i	0.975436	+	0.564236i
$656$		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
$665$	23.5226	+	30.0916i	0.912168	+	1.16690i
$666$		0			0
$667$	32.5287	−	8.71603i	1.25952	−	0.337486i
$668$		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	−0.493965	−	0.869482i	$-0.664453\pi$
$673$	9.74176	−	9.74176i	0.375517	−	0.375517i	0.869482	+	0.493965i	$0.164453\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	6.59716	+	24.6209i	0.253549	+	0.946259i	0.968892	+	0.247485i	$0.0796041\pi$
$677$	6.59716	+	24.6209i	0.253549	+	0.946259i	−0.715342	+	0.698774i	$0.753729\pi$
$678$		0			0
$679$	−2.96592	−	6.96637i	−0.113821	−	0.267345i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	0.419816	−	1.56677i	0.0160638	−	0.0599510i	−0.957429	−	0.288670i	$-0.906787\pi$
$683$	0.419816	−	1.56677i	0.0160638	−	0.0599510i	0.973493	+	0.228719i	$0.0734537\pi$
$684$		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
$695$	−0.0144013	+	17.5544i	−0.000546271	+	0.665875i
$696$		0			0
$697$	2.38134	−	8.88729i	0.0901998	−	0.336630i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	22.6890i		−	0.856950i	−0.903554	−	0.428475i	$-0.859051\pi$
$701$		−	22.6890i		−	0.856950i	0.903554	−	0.428475i	$-0.140949\pi$
$702$		0			0
$703$	69.7193	+	18.6812i	2.62951	+	0.704576i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−37.2035	+	5.26952i	−1.39918	+	0.198181i
$708$		0			0
$709$	32.7244	+	18.8934i	1.22899	+	0.709558i	0.966819	−	0.255463i	$-0.0822279\pi$
$709$	32.7244	+	18.8934i	1.22899	+	0.709558i	0.262172	+	0.965021i	$0.415561\pi$
$710$		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
$725$	−20.4995	−	0.0336348i	−0.761333	−	0.00124916i
$726$		0			0
$727$	20.0541	+	20.0541i	0.743766	+	0.743766i	0.973301	−	0.229534i	$-0.0737203\pi$
$727$	20.0541	+	20.0541i	0.743766	+	0.743766i	−0.229534	+	0.973301i	$0.573720\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	12.6600	−	7.30925i	0.468247	−	0.270342i
$732$		0			0
$733$	6.72817	+	25.1099i	0.248510	+	0.927454i	0.971586	+	0.236685i	$0.0760610\pi$
$733$	6.72817	+	25.1099i	0.248510	+	0.927454i	−0.723076	+	0.690769i	$0.757272\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−4.11681	−	15.3641i	−0.151645	−	0.565945i
$738$		0			0
$739$	−6.88907	+	3.97740i	−0.253418	+	0.146311i	−0.621328	−	0.783550i	$-0.713407\pi$
$739$	−6.88907	+	3.97740i	−0.253418	+	0.146311i	0.367910	+	0.929861i	$0.380073\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−11.0815	−	11.0815i	−0.406541	−	0.406541i	0.473989	−	0.880531i	$-0.342814\pi$
$743$	−11.0815	−	11.0815i	−0.406541	−	0.406541i	−0.880531	+	0.473989i	$0.842814\pi$
$744$		0			0
$745$	−9.02933	+	15.6097i	−0.330809	+	0.571894i
$746$		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	0.855718	−	0.517443i	$-0.173116\pi$
$757$	9.30716	+	9.30716i	0.338274	+	0.338274i	−0.517443	+	0.855718i	$0.673116\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−34.5097	−	19.9242i	−1.25098	−	0.722252i	−0.279673	−	0.960095i	$-0.590226\pi$
$761$	−34.5097	−	19.9242i	−1.25098	−	0.722252i	−0.971303	+	0.237844i	$0.923559\pi$
$762$		0			0
$763$	14.9787	−	2.12159i	0.542265	−	0.0768066i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.71463	−	1.53123i	−0.206343	−	0.0552895i
$768$		0			0
$769$		−	52.6681i		−	1.89926i	−0.313373	−	0.949630i	$-0.601459\pi$
$769$		−	52.6681i		−	1.89926i	0.313373	−	0.949630i	$-0.398541\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	11.1005	−	41.4276i	0.399257	−	1.49005i	−0.415151	−	0.909753i	$-0.636271\pi$
$773$	11.1005	−	41.4276i	0.399257	−	1.49005i	0.814407	−	0.580294i	$-0.197062\pi$
$774$		0			0
$775$	14.1992	+	24.6872i	0.510051	+	0.886790i
$776$		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
$787$	0.301878	−	1.12663i	0.0107608	−	0.0401599i	−0.960337	−	0.278843i	$-0.910049\pi$
$787$	0.301878	−	1.12663i	0.0107608	−	0.0401599i	0.971097	+	0.238683i	$0.0767157\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−1.43057	−	3.36013i	−0.0508652	−	0.119473i
$792$		0			0
$793$	−1.04110	−	3.88543i	−0.0369705	−	0.137976i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−1.61236	+	1.61236i	−0.0571127	+	0.0571127i	−0.735086	−	0.677974i	$-0.762858\pi$
$797$	−1.61236	+	1.61236i	−0.0571127	+	0.0571127i	0.677974	+	0.735086i	$0.262858\pi$
$798$		0			0
$799$		−	2.01814i		−	0.0713965i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	29.5261	−	7.91150i	1.04195	−	0.279191i
$804$		0			0
$805$	−48.2333	−	5.90969i	−1.70000	−	0.208289i
$806$		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
$815$	6.75141	+	25.2795i	0.236492	+	0.885503i
$816$		0			0
$817$	−73.3096	+	19.6432i	−2.56478	+	0.687230i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	24.7054	+	14.2636i	0.862223	+	0.497805i	0.864756	−	0.502192i	$-0.167473\pi$
$821$	24.7054	+	14.2636i	0.862223	+	0.497805i	−0.00253295	+	0.999997i	$0.500806\pi$
$822$		0			0
$823$	1.24340	+	0.333167i	0.0433421	+	0.0116135i	0.280425	−	0.959876i	$-0.409525\pi$
$823$	1.24340	+	0.333167i	0.0433421	+	0.0116135i	−0.237083	+	0.971489i	$0.576191\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	33.6915	−	33.6915i	1.17157	−	1.17157i	0.189733	−	0.981836i	$-0.439238\pi$
$827$	33.6915	−	33.6915i	1.17157	−	1.17157i	0.981836	−	0.189733i	$-0.0607622\pi$
$828$		0			0
$829$	−20.0337	+	11.5665i	−0.695799	+	0.401720i	−0.805781	−	0.592214i	$-0.798254\pi$
$829$	−20.0337	+	11.5665i	−0.695799	+	0.401720i	0.109982	+	0.993934i	$0.464921\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.49929	−	7.45164i	−0.155891	−	0.258184i
$834$		0			0
$835$	3.85311	−	3.84679i	0.133342	−	0.133124i
$836$		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
$845$	0.0233172	−	28.4224i	0.000802136	−	0.977761i
$846$		0			0
$847$	2.35183	−	1.84153i	0.0808097	−	0.0632759i
$848$		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	−0.908811	−	0.417207i	$-0.863009\pi$
$853$	−14.3579	+	14.3579i	−0.491604	+	0.491604i	0.417207	+	0.908811i	$0.363009\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	44.9798	+	12.0523i	1.53648	+	0.411699i	0.925127	−	0.379658i	$-0.123958\pi$
$857$	44.9798	+	12.0523i	1.53648	+	0.411699i	0.611355	+	0.791357i	$0.290625\pi$
$858$		0			0
$859$	14.7100	+	8.49281i	0.501898	+	0.289771i	0.729497	−	0.683984i	$-0.239754\pi$
$859$	14.7100	+	8.49281i	0.501898	+	0.289771i	−0.227599	+	0.973755i	$0.573088\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	29.8155	−	7.98905i	1.01493	−	0.271950i	0.287243	−	0.957858i	$-0.407261\pi$
$863$	29.8155	−	7.98905i	1.01493	−	0.271950i	0.727689	+	0.685907i	$0.240594\pi$
$864$		0			0
$865$	21.4307	−	5.72349i	0.728665	−	0.194605i
$866$		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
$875$	27.4111	+	11.1189i	0.926665	+	0.375889i
$876$		0			0
$877$	−51.0998	+	13.6921i	−1.72552	+	0.462351i	−0.979142	−	0.203175i	$-0.934874\pi$
$877$	−51.0998	+	13.6921i	−1.72552	+	0.462351i	−0.746375	+	0.665526i	$0.768207\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			40.0911i			1.35070i	0.737496	+	0.675351i	$0.236008\pi$
$881$			40.0911i			1.35070i	−0.737496	+	0.675351i	$0.763992\pi$
$882$		0			0
$883$	−9.29675	+	9.29675i	−0.312860	+	0.312860i	−0.846017	−	0.533156i	$-0.821006\pi$
$883$	−9.29675	+	9.29675i	−0.312860	+	0.312860i	0.533156	+	0.846017i	$0.321006\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	0.958383	+	3.57674i	0.0321794	+	0.120095i	0.980147	−	0.198271i	$-0.0635326\pi$
$887$	0.958383	+	3.57674i	0.0321794	+	0.120095i	−0.947968	+	0.318366i	$0.896866\pi$
$888$		0			0
$889$	8.34825	+	19.6084i	0.279991	+	0.657646i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.71182	+	10.1207i	−0.0907476	+	0.338675i
$894$		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
$905$	−46.0779	−	0.0378014i	−1.53168	−	0.00125656i
$906$		0			0
$907$	−2.94768	+	11.0009i	−0.0978763	+	0.365279i	−0.997440	−	0.0715107i	$-0.977218\pi$
$907$	−2.94768	+	11.0009i	−0.0978763	+	0.365279i	0.899564	+	0.436790i	$0.143885\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			32.6632i			1.08218i	0.840965	+	0.541090i	$0.181988\pi$
$911$			32.6632i			1.08218i	−0.840965	+	0.541090i	$0.818012\pi$
$912$		0			0
$913$	11.1849	+	2.99698i	0.370166	+	0.0991856i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	21.0378	+	26.8673i	0.694728	+	0.887238i
$918$		0			0
$919$	−15.2690	−	8.81555i	−0.503677	−	0.290798i	0.226554	−	0.973999i	$-0.427254\pi$
$919$	−15.2690	−	8.81555i	−0.503677	−	0.290798i	−0.730231	+	0.683201i	$0.760587\pi$
$920$		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
$935$	8.44029	−	2.25415i	0.276027	−	0.0737185i
$936$		0			0
$937$	5.61057	+	5.61057i	0.183289	+	0.183289i	0.792788	−	0.609498i	$-0.208629\pi$
$937$	5.61057	+	5.61057i	0.183289	+	0.183289i	−0.609498	+	0.792788i	$0.708629\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	10.4386	−	6.02672i	0.340288	−	0.196466i	−0.320111	−	0.947380i	$-0.603720\pi$
$941$	10.4386	−	6.02672i	0.340288	−	0.196466i	0.660400	+	0.750914i	$0.270387\pi$
$942$		0			0
$943$	−15.7296	−	58.7037i	−0.512227	−	1.91166i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.92765	−	33.3184i	−0.290110	−	1.08270i	−0.945024	−	0.327001i	$-0.893962\pi$
$947$	−8.92765	−	33.3184i	−0.290110	−	1.08270i	0.654915	−	0.755703i	$-0.272705\pi$
$948$		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	0.852646	−	0.522490i	$-0.174997\pi$
$953$	10.1921	+	10.1921i	0.330156	+	0.330156i	−0.522490	+	0.852646i	$0.674997\pi$
$954$		0			0
$955$	−36.7153	−	21.2377i	−1.18808	−	0.687237i
$956$		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	0.808296	−	0.588777i	$-0.200390\pi$
$967$	6.82630	+	6.82630i	0.219519	+	0.219519i	−0.588777	+	0.808296i	$0.700390\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−5.92560	−	3.42115i	−0.190162	−	0.109790i	0.401897	−	0.915685i	$-0.368351\pi$
$971$	−5.92560	−	3.42115i	−0.190162	−	0.109790i	−0.592058	+	0.805895i	$0.701684\pi$
$972$		0			0
$973$	−7.76005	+	19.2666i	−0.248776	+	0.617658i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	43.1269	+	11.5558i	1.37975	+	0.369704i	0.871031	−	0.491228i	$-0.163452\pi$
$977$	43.1269	+	11.5558i	1.37975	+	0.369704i	0.508721	+	0.860931i	$0.330118\pi$
$978$		0			0
$979$			27.3403i			0.873801i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	13.0325	−	48.6380i	0.415673	−	1.55131i	−0.367812	−	0.929900i	$-0.619893\pi$
$983$	13.0325	−	48.6380i	0.415673	−	1.55131i	0.783485	−	0.621411i	$-0.213440\pi$
$984$		0			0
$985$	4.54496	−	4.53750i	0.144814	−	0.144577i
$986$		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
$997$	4.85753	−	18.1286i	0.153840	−	0.574137i	−0.845362	−	0.534193i	$-0.820615\pi$
$997$	4.85753	−	18.1286i	0.153840	−	0.574137i	0.999202	−	0.0399439i	$-0.0127179\pi$
$998$		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.737.1	yes	64
3.2	odd	2	inner	1260.2.ej.a.737.16	yes	64
5.3	odd	4	inner	1260.2.ej.a.233.6	yes	64
7.4	even	3	inner	1260.2.ej.a.557.11	yes	64
15.8	even	4	inner	1260.2.ej.a.233.11	yes	64
21.11	odd	6	inner	1260.2.ej.a.557.6	yes	64
35.18	odd	12	inner	1260.2.ej.a.53.16	yes	64
105.53	even	12	inner	1260.2.ej.a.53.1	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.ej.a.53.1	✓	64	105.53	even	12	inner
1260.2.ej.a.53.16	yes	64	35.18	odd	12	inner
1260.2.ej.a.233.6	yes	64	5.3	odd	4	inner
1260.2.ej.a.233.11	yes	64	15.8	even	4	inner
1260.2.ej.a.557.6	yes	64	21.11	odd	6	inner
1260.2.ej.a.557.11	yes	64	7.4	even	3	inner
1260.2.ej.a.737.1	yes	64	1.1	even	1	trivial
1260.2.ej.a.737.16	yes	64	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-2.23607 - 0.00183442i) q^{5} +(-2.45417 - 0.988471i) q^{7} +O(q^{10})\)	\(q+(-2.23607 - 0.00183442i) q^{5} +(-2.45417 - 0.988471i) q^{7} +(2.72089 - 1.57091i) q^{11} +(-0.380199 + 0.380199i) q^{13} +(-1.20115 - 0.321846i) q^{17} +(5.59110 + 3.22802i) q^{19} +(-7.93400 + 2.12591i) q^{23} +(4.99999 + 0.00820379i) q^{25} -4.09991 q^{29} +(2.84794 + 4.93277i) q^{31} +(5.48586 + 2.21479i) q^{35} +(10.7991 - 2.89360i) q^{37} +7.39900i q^{41} +(-8.31257 + 8.31257i) q^{43} +(0.420044 + 1.56762i) q^{47} +(5.04585 + 4.85174i) q^{49} +(-2.88301 + 10.7595i) q^{53} +(-6.08698 + 3.50766i) q^{55} +(5.50159 + 9.52904i) q^{59} +(-3.74059 + 6.47889i) q^{61} +(0.850848 - 0.849453i) q^{65} +(1.31033 - 4.89021i) q^{67} -15.1301i q^{71} +(9.39779 + 2.51813i) q^{73} +(-8.23032 + 1.16575i) q^{77} +(-3.95167 - 2.28150i) q^{79} +(2.60611 + 2.60611i) q^{83} +(2.68525 + 0.721873i) q^{85} +(-4.35104 + 7.53622i) q^{89} +(1.30889 - 0.557255i) q^{91} +(-12.4962 - 7.22833i) q^{95} +(2.02356 + 2.02356i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 64 * q - 8 * q^7	\( 64 q - 8 q^{7} + 16 q^{25} + 32 q^{31} + 16 q^{37} - 16 q^{43} + 32 q^{55} + 48 q^{61} + 32 q^{67} + 40 q^{73} + 80 q^{85} + 96 q^{91} + 80 q^{97}+O(q^{100}) \) 64 * q - 8 * q^7 + 16 * q^25 + 32 * q^31 + 16 * q^37 - 16 * q^43 + 32 * q^55 + 48 * q^61 + 32 * q^67 + 40 * q^73 + 80 * q^85 + 96 * q^91 + 80 * q^97

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