LMFDB - Embedded newform 1260.2.ej.a.233.8

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			233.8
Character	$\chi$	$=$	1260.233
Dual form			1260.2.ej.a.557.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.224278 - 2.22479i) q^{5} +(-2.29737 - 1.31229i) q^{7} +O(q^{10})$	$q+(-0.224278 - 2.22479i) q^{5} +(-2.29737 - 1.31229i) q^{7} +(-5.56017 + 3.21017i) q^{11} +(1.53308 + 1.53308i) q^{13} +(0.985913 - 3.67948i) q^{17} +(1.19038 + 0.687268i) q^{19} +(2.18478 + 8.15372i) q^{23} +(-4.89940 + 0.997943i) q^{25} -5.95407 q^{29} +(4.97256 + 8.61273i) q^{31} +(-2.40432 + 5.40548i) q^{35} +(0.642964 + 2.39957i) q^{37} -1.18135i q^{41} +(3.28359 + 3.28359i) q^{43} +(-2.44481 + 0.655086i) q^{47} +(3.55579 + 6.02962i) q^{49} +(-1.80184 - 0.482801i) q^{53} +(8.38898 + 11.6503i) q^{55} +(-3.27774 - 5.67721i) q^{59} +(4.09020 - 7.08443i) q^{61} +(3.06694 - 3.75461i) q^{65} +(9.29378 + 2.49026i) q^{67} -8.06341i q^{71} +(-3.47748 + 12.9781i) q^{73} +(16.9864 - 0.0783798i) q^{77} +(-8.00786 - 4.62334i) q^{79} +(-5.11988 + 5.11988i) q^{83} +(-8.40719 - 1.36823i) q^{85} +(-3.97384 + 6.88289i) q^{89} +(-1.51020 - 5.53388i) q^{91} +(1.26205 - 2.80250i) q^{95} +(-0.537395 + 0.537395i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 8 q^{7}+O(q^{10}) $ 64 * q - 8 * q^7	$ 64 q - 8 q^{7} + 16 q^{25} + 32 q^{31} + 16 q^{37} - 16 q^{43} + 32 q^{55} + 48 q^{61} + 32 q^{67} + 40 q^{73} + 80 q^{85} + 96 q^{91} + 80 q^{97}+O(q^{100}) $ 64 * q - 8 * q^7 + 16 * q^25 + 32 * q^31 + 16 * q^37 - 16 * q^43 + 32 * q^55 + 48 * q^61 + 32 * q^67 + 40 * q^73 + 80 * q^85 + 96 * q^91 + 80 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.224278	−	2.22479i	−0.100300	−	0.994957i
$5$	−0.224278	−	2.22479i	−0.100300	−	0.994957i
$6$		0			0
$7$	−2.29737	−	1.31229i	−0.868323	−	0.495999i
$7$	−2.29737	−	1.31229i	−0.868323	−	0.495999i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−5.56017	+	3.21017i	−1.67645	+	0.967902i	−0.712563	+	0.701609i	$0.752466\pi$
$11$	−5.56017	+	3.21017i	−1.67645	+	0.967902i	−0.963892	+	0.266293i	$0.914201\pi$
$12$		0			0
$13$	1.53308	+	1.53308i	0.425199	+	0.425199i	0.886989	−	0.461790i	$-0.152793\pi$
$13$	1.53308	+	1.53308i	0.425199	+	0.425199i	−0.461790	+	0.886989i	$0.652793\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.985913	−	3.67948i	0.239119	−	0.892405i	−0.737130	−	0.675751i	$-0.763819\pi$
$17$	0.985913	−	3.67948i	0.239119	−	0.892405i	0.976249	−	0.216653i	$-0.0695141\pi$
$18$		0			0
$19$	1.19038	+	0.687268i	0.273093	+	0.157670i	0.630292	−	0.776358i	$-0.282935\pi$
$19$	1.19038	+	0.687268i	0.273093	+	0.157670i	−0.357200	+	0.934028i	$0.616268\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.18478	+	8.15372i	0.455559	+	1.70017i	0.686440	+	0.727187i	$0.259173\pi$
$23$	2.18478	+	8.15372i	0.455559	+	1.70017i	−0.230881	+	0.972982i	$0.574161\pi$
$24$		0			0
$25$	−4.89940	+	0.997943i	−0.979880	+	0.199589i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.95407			−1.10564			−0.552822	−	0.833299i	$-0.686449\pi$
$29$	−5.95407			−1.10564			−0.552822	+	0.833299i	$0.686449\pi$
$30$		0			0
$31$	4.97256	+	8.61273i	0.893098	+	1.54689i	0.836141	+	0.548515i	$0.184807\pi$
$31$	4.97256	+	8.61273i	0.893098	+	1.54689i	0.0569572	+	0.998377i	$0.481860\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.40432	+	5.40548i	−0.406405	+	0.913693i
$36$		0			0
$37$	0.642964	+	2.39957i	0.105703	+	0.394488i	0.998424	−	0.0561216i	$-0.0178735\pi$
$37$	0.642964	+	2.39957i	0.105703	+	0.394488i	−0.892721	+	0.450609i	$0.851207\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	1.18135i		−	0.184496i	−0.995736	−	0.0922482i	$-0.970595\pi$
$41$		−	1.18135i		−	0.184496i	0.995736	−	0.0922482i	$-0.0294053\pi$
$42$		0			0
$43$	3.28359	+	3.28359i	0.500742	+	0.500742i	0.911668	−	0.410926i	$-0.134795\pi$
$43$	3.28359	+	3.28359i	0.500742	+	0.500742i	−0.410926	+	0.911668i	$0.634795\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.44481	+	0.655086i	−0.356613	+	0.0955541i	−0.432677	−	0.901549i	$-0.642431\pi$
$47$	−2.44481	+	0.655086i	−0.356613	+	0.0955541i	0.0760648	+	0.997103i	$0.475764\pi$
$48$		0			0
$49$	3.55579	+	6.02962i	0.507971	+	0.861374i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.80184	−	0.482801i	−0.247501	−	0.0663178i	0.132936	−	0.991125i	$-0.457560\pi$
$53$	−1.80184	−	0.482801i	−0.247501	−	0.0663178i	−0.380437	+	0.924807i	$0.624226\pi$
$54$		0			0
$55$	8.38898	+	11.6503i	1.13117	+	1.57092i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.27774	−	5.67721i	−0.426725	−	0.739109i	0.569855	−	0.821745i	$-0.306999\pi$
$59$	−3.27774	−	5.67721i	−0.426725	−	0.739109i	−0.996580	+	0.0826362i	$0.973666\pi$
$60$		0			0
$61$	4.09020	−	7.08443i	0.523696	−	0.907069i	−0.475923	−	0.879487i	$-0.657886\pi$
$61$	4.09020	−	7.08443i	0.523696	−	0.907069i	0.999620	−	0.0275818i	$-0.00878067\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	3.06694	−	3.75461i	0.380407	−	0.465702i
$66$		0			0
$67$	9.29378	+	2.49026i	1.13542	+	0.304234i	0.777107	−	0.629369i	$-0.216687\pi$
$67$	9.29378	+	2.49026i	1.13542	+	0.304234i	0.358310	+	0.933603i	$0.383353\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	8.06341i		−	0.956951i	−0.878101	−	0.478476i	$-0.841189\pi$
$71$		−	8.06341i		−	0.956951i	0.878101	−	0.478476i	$-0.158811\pi$
$72$		0			0
$73$	−3.47748	+	12.9781i	−0.407008	+	1.51898i	0.393313	+	0.919405i	$0.371329\pi$
$73$	−3.47748	+	12.9781i	−0.407008	+	1.51898i	−0.800321	+	0.599571i	$0.795338\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	16.9864	−	0.0783798i	1.93578	−	0.00893221i
$78$		0			0
$79$	−8.00786	−	4.62334i	−0.900954	−	0.520166i	−0.0234445	−	0.999725i	$-0.507463\pi$
$79$	−8.00786	−	4.62334i	−0.900954	−	0.520166i	−0.877510	+	0.479559i	$0.840797\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−5.11988	+	5.11988i	−0.561980	+	0.561980i	−0.929869	−	0.367890i	$-0.880080\pi$
$83$	−5.11988	+	5.11988i	−0.561980	+	0.561980i	0.367890	+	0.929869i	$0.380080\pi$
$84$		0			0
$85$	−8.40719	−	1.36823i	−0.911888	−	0.148405i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.97384	+	6.88289i	−0.421226	+	0.729585i	−0.996060	−	0.0886851i	$-0.971734\pi$
$89$	−3.97384	+	6.88289i	−0.421226	+	0.729585i	0.574833	+	0.818270i	$0.305067\pi$
$90$		0			0
$91$	−1.51020	−	5.53388i	−0.158312	−	0.580108i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.26205	−	2.80250i	0.129484	−	0.287530i
$96$		0			0
$97$	−0.537395	+	0.537395i	−0.0545642	+	0.0545642i	−0.733862	−	0.679298i	$-0.762284\pi$
$97$	−0.537395	+	0.537395i	−0.0545642	+	0.0545642i	0.679298	+	0.733862i	$0.262284\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.83036	+	4.52086i	−0.779150	+	0.449842i	−0.836129	−	0.548533i	$-0.815186\pi$
$101$	−7.83036	+	4.52086i	−0.779150	+	0.449842i	0.0569791	+	0.998375i	$0.481853\pi$
$102$		0			0
$103$	−14.8104	+	3.96842i	−1.45931	+	0.391020i	−0.899251	−	0.437434i	$-0.855887\pi$
$103$	−14.8104	+	3.96842i	−1.45931	+	0.391020i	−0.560057	+	0.828454i	$0.689221\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−11.5619	+	3.09800i	−1.11773	+	0.299495i	−0.769965	−	0.638086i	$-0.779726\pi$
$107$	−11.5619	+	3.09800i	−1.11773	+	0.299495i	−0.347766	+	0.937581i	$0.613060\pi$
$108$		0			0
$109$	−13.3397	+	7.70171i	−1.27772	+	0.737690i	−0.976428	−	0.215843i	$-0.930750\pi$
$109$	−13.3397	+	7.70171i	−1.27772	+	0.737690i	−0.301288	+	0.953533i	$0.597417\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.29944	+	4.29944i	−0.404457	+	0.404457i	−0.879800	−	0.475343i	$-0.842324\pi$
$113$	−4.29944	+	4.29944i	−0.404457	+	0.404457i	0.475343	+	0.879800i	$0.342324\pi$
$114$		0			0
$115$	17.6503	−	6.68939i	1.64590	−	0.623789i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.09354	+	7.15931i	−0.650264	+	0.656293i
$120$		0			0
$121$	15.1103	−	26.1719i	1.37367	−	2.37926i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	3.31904	+	10.6763i	0.296864	+	0.954920i
$126$		0			0
$127$	−7.73178	+	7.73178i	−0.686085	+	0.686085i	−0.961364	−	0.275280i	$-0.911230\pi$
$127$	−7.73178	+	7.73178i	−0.686085	+	0.686085i	0.275280	+	0.961364i	$0.411230\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.02321	−	2.90015i	−0.438880	−	0.253387i	0.264242	−	0.964456i	$-0.414878\pi$
$131$	−5.02321	−	2.90015i	−0.438880	−	0.253387i	−0.703122	+	0.711069i	$0.748211\pi$
$132$		0			0
$133$	−1.83285	−	3.14104i	−0.158929	−	0.272362i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.303714	−	1.13348i	0.0259480	−	0.0968394i	−0.951737	−	0.306913i	$-0.900704\pi$
$137$	0.303714	−	1.13348i	0.0259480	−	0.0968394i	0.977685	+	0.210074i	$0.0673705\pi$
$138$		0			0
$139$		−	7.86518i		−	0.667116i	−0.942730	−	0.333558i	$-0.891751\pi$
$139$		−	7.86518i		−	0.667116i	0.942730	−	0.333558i	$-0.108249\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−13.4456	−	3.60274i	−1.12438	−	0.301276i
$144$		0			0
$145$	1.33537	+	13.2466i	0.110896	+	1.10007i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.75934	−	3.04726i	0.144131	−	0.249642i	−0.784918	−	0.619600i	$-0.787295\pi$
$149$	1.75934	−	3.04726i	0.144131	−	0.249642i	0.929048	+	0.369959i	$0.120628\pi$
$150$		0			0
$151$	3.82269	+	6.62109i	0.311086	+	0.538816i	0.978598	−	0.205783i	$-0.0659740\pi$
$151$	3.82269	+	6.62109i	0.311086	+	0.538816i	−0.667512	+	0.744599i	$0.732641\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	18.0463	−	12.9946i	1.44951	−	1.04375i
$156$		0			0
$157$	−10.3865	−	2.78306i	−0.828935	−	0.222112i	−0.180686	−	0.983541i	$-0.557832\pi$
$157$	−10.3865	−	2.78306i	−0.828935	−	0.222112i	−0.648249	+	0.761428i	$0.724498\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.68079	−	21.5992i	0.447709	−	1.70225i
$162$		0			0
$163$	12.8465	−	3.44221i	1.00622	−	0.269615i	0.282169	−	0.959365i	$-0.408946\pi$
$163$	12.8465	−	3.44221i	1.00622	−	0.269615i	0.724048	+	0.689750i	$0.242280\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	16.8122	+	16.8122i	1.30097	+	1.30097i	0.927738	+	0.373232i	$0.121751\pi$
$167$	16.8122	+	16.8122i	1.30097	+	1.30097i	0.373232	+	0.927738i	$0.378249\pi$
$168$		0			0
$169$		−	8.29936i		−	0.638412i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.748879	−	2.79486i	−0.0569362	−	0.212489i	0.931597	−	0.363493i	$-0.118416\pi$
$173$	−0.748879	−	2.79486i	−0.0569362	−	0.212489i	−0.988533	+	0.151004i	$0.951749\pi$
$174$		0			0
$175$	12.5653	+	4.13678i	0.949848	+	0.312712i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.68362	+	8.11226i	0.350070	+	0.606339i	0.986261	−	0.165192i	$-0.0528244\pi$
$179$	4.68362	+	8.11226i	0.350070	+	0.606339i	−0.636191	+	0.771531i	$0.719491\pi$
$180$		0			0
$181$	−1.18064			−0.0877561			−0.0438781	−	0.999037i	$-0.513971\pi$
$181$	−1.18064			−0.0877561			−0.0438781	+	0.999037i	$0.513971\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.19435	−	1.96863i	0.381896	−	0.144737i
$186$		0			0
$187$	6.32989	+	23.6235i	0.462888	+	1.72752i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−8.89213	−	5.13388i	−0.643412	−	0.371474i	0.142516	−	0.989793i	$-0.454481\pi$
$191$	−8.89213	−	5.13388i	−0.643412	−	0.371474i	−0.785928	+	0.618318i	$0.787814\pi$
$192$		0			0
$193$	3.78641	−	14.1311i	0.272551	−	1.01718i	−0.684913	−	0.728625i	$-0.740160\pi$
$193$	3.78641	−	14.1311i	0.272551	−	1.01718i	0.957465	−	0.288551i	$-0.0931735\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−14.4253	−	14.4253i	−1.02776	−	1.02776i	−0.999603	−	0.0281591i	$-0.991035\pi$
$197$	−14.4253	−	14.4253i	−1.02776	−	1.02776i	−0.0281591	−	0.999603i	$-0.508965\pi$
$198$		0			0
$199$	8.35907	−	4.82611i	0.592559	−	0.342114i	−0.173550	−	0.984825i	$-0.555524\pi$
$199$	8.35907	−	4.82611i	0.592559	−	0.342114i	0.766109	+	0.642711i	$0.222190\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	13.6787	+	7.81347i	0.960056	+	0.548398i
$204$		0			0
$205$	−2.62827	+	0.264951i	−0.183566	+	0.0185050i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−8.82498			−0.610437
$210$		0			0
$211$	−20.2730			−1.39565			−0.697824	−	0.716270i	$-0.745848\pi$
$211$	−20.2730			−1.39565			−0.697824	+	0.716270i	$0.745848\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.56886	−	8.04173i	0.447992	−	0.548441i
$216$		0			0
$217$	−0.121411	−	26.3120i	−0.00824189	−	1.78618i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	7.15240	−	4.12944i	0.481122	−	0.277776i
$222$		0			0
$223$	−16.9480	−	16.9480i	−1.13492	−	1.13492i	−0.989348	−	0.145573i	$-0.953498\pi$
$223$	−16.9480	−	16.9480i	−1.13492	−	1.13492i	−0.145573	−	0.989348i	$-0.546502\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.83595	+	10.5839i	−0.188229	+	0.702479i	0.805688	+	0.592341i	$0.201796\pi$
$227$	−2.83595	+	10.5839i	−0.188229	+	0.702479i	−0.993916	+	0.110138i	$0.964871\pi$
$228$		0			0
$229$	−22.2072	−	12.8213i	−1.46749	−	0.847259i	−0.468157	−	0.883645i	$-0.655082\pi$
$229$	−22.2072	−	12.8213i	−1.46749	−	0.847259i	−0.999338	+	0.0363868i	$0.988415\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	5.95531	+	22.2255i	0.390146	+	1.45604i	0.829893	+	0.557922i	$0.188401\pi$
$233$	5.95531	+	22.2255i	0.390146	+	1.45604i	−0.439748	+	0.898121i	$0.644932\pi$
$234$		0			0
$235$	2.00575	+	5.29228i	0.130841	+	0.345230i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.15912			0.463085			0.231542	−	0.972825i	$-0.425623\pi$
$239$	7.15912			0.463085			0.231542	+	0.972825i	$0.425623\pi$
$240$		0			0
$241$	11.4613	+	19.8515i	0.738286	+	1.27875i	0.953267	+	0.302130i	$0.0976978\pi$
$241$	11.4613	+	19.8515i	0.738286	+	1.27875i	−0.214981	+	0.976618i	$0.568969\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	12.6172	−	9.26321i	0.806081	−	0.591805i
$246$		0			0
$247$	0.771314	+	2.87858i	0.0490775	+	0.183160i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	11.0773i		−	0.699192i	−0.936901	−	0.349596i	$-0.886319\pi$
$251$		−	11.0773i		−	0.699192i	0.936901	−	0.349596i	$-0.113681\pi$
$252$		0			0
$253$	−38.3226	−	38.3226i	−2.40932	−	2.40932i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	24.2345	−	6.49362i	1.51171	−	0.405061i	0.594705	−	0.803944i	$-0.297269\pi$
$257$	24.2345	−	6.49362i	1.51171	−	0.405061i	0.917002	+	0.398883i	$0.130602\pi$
$258$		0			0
$259$	1.67181	−	6.35646i	0.103881	−	0.394971i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	14.9339	+	4.00153i	0.920864	+	0.246745i	0.687954	−	0.725754i	$-0.258509\pi$
$263$	14.9339	+	4.00153i	0.920864	+	0.246745i	0.232909	+	0.972499i	$0.425176\pi$
$264$		0			0
$265$	−0.670019	+	4.11699i	−0.0411589	+	0.252905i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	13.0155	+	22.5435i	0.793568	+	1.37450i	0.923744	+	0.383010i	$0.125112\pi$
$269$	13.0155	+	22.5435i	0.793568	+	1.37450i	−0.130176	+	0.991491i	$0.541554\pi$
$270$		0			0
$271$	1.50319	−	2.60360i	0.0913123	−	0.158158i	−0.816751	−	0.576990i	$-0.804227\pi$
$271$	1.50319	−	2.60360i	0.0913123	−	0.158158i	0.908064	+	0.418832i	$0.137561\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	24.0379	−	21.2766i	1.44954	−	1.28303i
$276$		0			0
$277$	−0.621618	−	0.166562i	−0.0373494	−	0.0100077i	0.240096	−	0.970749i	$-0.422821\pi$
$277$	−0.621618	−	0.166562i	−0.0373494	−	0.0100077i	−0.277445	+	0.960741i	$0.589488\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	22.2195i		−	1.32550i	−0.748840	−	0.662751i	$-0.769389\pi$
$281$		−	22.2195i		−	1.32550i	0.748840	−	0.662751i	$-0.230611\pi$
$282$		0			0
$283$	−5.30555	+	19.8006i	−0.315382	+	1.17702i	0.608251	+	0.793745i	$0.291871\pi$
$283$	−5.30555	+	19.8006i	−0.315382	+	1.17702i	−0.923633	+	0.383278i	$0.874795\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.55028	+	2.71400i	−0.0915100	+	0.160203i
$288$		0			0
$289$	2.15589	+	1.24471i	0.126817	+	0.0732180i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.76855	−	2.76855i	0.161740	−	0.161740i	−0.621597	−	0.783337i	$-0.713516\pi$
$293$	2.76855	−	2.76855i	0.161740	−	0.161740i	0.783337	+	0.621597i	$0.213516\pi$
$294$		0			0
$295$	−11.8955	+	8.56555i	−0.692581	+	0.498706i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−9.15084	+	15.8497i	−0.529207	+	0.916613i
$300$		0			0
$301$	−3.23459	−	11.8526i	−0.186439	−	0.683173i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−16.6787	−	7.51096i	−0.955021	−	0.430076i
$306$		0			0
$307$	16.3148	−	16.3148i	0.931133	−	0.931133i	−0.0666440	−	0.997777i	$-0.521229\pi$
$307$	16.3148	−	16.3148i	0.931133	−	0.931133i	0.997777	+	0.0666440i	$0.0212292\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−22.1640	+	12.7964i	−1.25680	+	0.725615i	−0.972452	−	0.233105i	$-0.925111\pi$
$311$	−22.1640	+	12.7964i	−1.25680	+	0.725615i	−0.284351	+	0.958720i	$0.591778\pi$
$312$		0			0
$313$	21.7716	−	5.83368i	1.23060	−	0.329739i	0.415789	−	0.909461i	$-0.363506\pi$
$313$	21.7716	−	5.83368i	1.23060	−	0.329739i	0.814814	+	0.579722i	$0.196839\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	20.3754	−	5.45957i	1.14440	−	0.306640i	0.363679	−	0.931524i	$-0.381520\pi$
$317$	20.3754	−	5.45957i	1.14440	−	0.306640i	0.780717	+	0.624884i	$0.214854\pi$
$318$		0			0
$319$	33.1057	−	19.1136i	1.85356	−	1.07015i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.70240	−	3.70240i	0.206007	−	0.206007i
$324$		0			0
$325$	−9.04107	−	5.98123i	−0.501508	−	0.331779i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	6.47630	+	1.70333i	0.357050	+	0.0939076i
$330$		0			0
$331$	6.15236	−	10.6562i	0.338165	−	0.585718i	−0.645923	−	0.763403i	$-0.723527\pi$
$331$	6.15236	−	10.6562i	0.338165	−	0.585718i	0.984088	+	0.177684i	$0.0568606\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3.45592	−	21.2352i	0.188817	−	1.16021i
$336$		0			0
$337$	−17.0712	+	17.0712i	−0.929929	+	0.929929i	−0.997701	−	0.0677716i	$-0.978411\pi$
$337$	−17.0712	+	17.0712i	−0.929929	+	0.929929i	0.0677716	+	0.997701i	$0.478411\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−55.2966	−	31.9255i	−2.99448	−	1.72886i
$342$		0			0
$343$	−0.256362	−	18.5185i	−0.0138422	−	0.999904i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.05196	+	7.65803i	−0.110155	+	0.411105i	−0.998879	−	0.0473385i	$-0.984926\pi$
$347$	−2.05196	+	7.65803i	−0.110155	+	0.411105i	0.888724	+	0.458443i	$0.151593\pi$
$348$		0			0
$349$			5.97100i			0.319620i	0.987148	+	0.159810i	$0.0510882\pi$
$349$			5.97100i			0.319620i	−0.987148	+	0.159810i	$0.948912\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4.73574	+	1.26894i	0.252058	+	0.0675388i	0.382636	−	0.923899i	$-0.375016\pi$
$353$	4.73574	+	1.26894i	0.252058	+	0.0675388i	−0.130577	+	0.991438i	$0.541683\pi$
$354$		0			0
$355$	−17.9394	+	1.80845i	−0.952126	+	0.0959823i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.65561	+	9.79581i	−0.298492	+	0.517003i	−0.975791	−	0.218704i	$-0.929817\pi$
$359$	−5.65561	+	9.79581i	−0.298492	+	0.517003i	0.677299	+	0.735708i	$0.263150\pi$
$360$		0			0
$361$	−8.55532	−	14.8183i	−0.450280	−	0.779908i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	29.6536	+	4.82596i	1.55214	+	0.252602i
$366$		0			0
$367$	−1.16669	−	0.312613i	−0.0609006	−	0.0163183i	0.228240	−	0.973605i	$-0.426703\pi$
$367$	−1.16669	−	0.312613i	−0.0609006	−	0.0163183i	−0.289141	+	0.957287i	$0.593370\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	3.50591	+	3.47370i	0.182018	+	0.180346i
$372$		0			0
$373$	−15.8413	+	4.24465i	−0.820229	+	0.219780i	−0.644447	−	0.764649i	$-0.722912\pi$
$373$	−15.8413	+	4.24465i	−0.820229	+	0.219780i	−0.175783	+	0.984429i	$0.556246\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−9.12805	−	9.12805i	−0.470118	−	0.470118i
$378$		0			0
$379$		−	5.32863i		−	0.273713i	−0.990591	−	0.136857i	$-0.956300\pi$
$379$		−	5.32863i		−	0.273713i	0.990591	−	0.136857i	$-0.0436999\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−0.324341	−	1.21046i	−0.0165730	−	0.0618514i	0.957144	−	0.289612i	$-0.0935263\pi$
$383$	−0.324341	−	1.21046i	−0.0165730	−	0.0618514i	−0.973717	+	0.227761i	$0.926860\pi$
$384$		0			0
$385$	−3.98406	−	37.7737i	−0.203046	−	1.92512i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−4.24901	−	7.35950i	−0.215433	−	0.373142i	0.737973	−	0.674830i	$-0.235783\pi$
$389$	−4.24901	−	7.35950i	−0.215433	−	0.373142i	−0.953407	+	0.301688i	$0.902450\pi$
$390$		0			0
$391$	32.1555			1.62617
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−8.48998	+	18.8527i	−0.427177	+	0.948584i
$396$		0			0
$397$	6.08973	+	22.7272i	0.305635	+	1.14064i	0.932398	+	0.361434i	$0.117713\pi$
$397$	6.08973	+	22.7272i	0.305635	+	1.14064i	−0.626763	+	0.779210i	$0.715621\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	32.6634	+	18.8582i	1.63113	+	0.941734i	0.983745	+	0.179573i	$0.0574717\pi$
$401$	32.6634	+	18.8582i	1.63113	+	0.941734i	0.647387	+	0.762161i	$0.275862\pi$
$402$		0			0
$403$	−5.58065	+	20.8273i	−0.277992	+	1.03748i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−11.2780	−	11.2780i	−0.559031	−	0.559031i
$408$		0			0
$409$	9.32771	−	5.38535i	0.461225	−	0.266289i	−0.251334	−	0.967900i	$-0.580869\pi$
$409$	9.32771	−	5.38535i	0.461225	−	0.266289i	0.712559	+	0.701612i	$0.247536\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.0800296	+	17.3440i	0.00393800	+	0.853441i
$414$		0			0
$415$	12.5389	+	10.2424i	0.615512	+	0.502779i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−28.8526			−1.40954			−0.704770	−	0.709436i	$-0.748950\pi$
$419$	−28.8526			−1.40954			−0.704770	+	0.709436i	$0.748950\pi$
$420$		0			0
$421$	−15.9248			−0.776128			−0.388064	−	0.921632i	$-0.626856\pi$
$421$	−15.9248			−0.776128			−0.388064	+	0.921632i	$0.626856\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.15847	+	19.0111i	−0.0561941	+	0.922175i
$426$		0			0
$427$	−18.6935	+	10.9080i	−0.904643	+	0.527876i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9.67322	+	5.58484i	−0.465943	+	0.269012i	−0.714540	−	0.699595i	$-0.753364\pi$
$431$	−9.67322	+	5.58484i	−0.465943	+	0.269012i	0.248597	+	0.968607i	$0.420031\pi$
$432$		0			0
$433$	11.8082	+	11.8082i	0.567465	+	0.567465i	0.931417	−	0.363953i	$-0.118573\pi$
$433$	11.8082	+	11.8082i	0.567465	+	0.567465i	−0.363953	+	0.931417i	$0.618573\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.00306	+	11.2076i	−0.143656	+	0.536132i
$438$		0			0
$439$	−14.8317	−	8.56307i	−0.707877	−	0.408693i	0.102397	−	0.994744i	$-0.467349\pi$
$439$	−14.8317	−	8.56307i	−0.707877	−	0.408693i	−0.810274	+	0.586051i	$0.800682\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	5.35864	+	19.9987i	0.254597	+	0.950168i	0.968314	+	0.249735i	$0.0803434\pi$
$443$	5.35864	+	19.9987i	0.254597	+	0.950168i	−0.713718	+	0.700434i	$0.752990\pi$
$444$		0			0
$445$	16.2043	+	7.29729i	0.768155	+	0.345925i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	16.1978			0.764420			0.382210	−	0.924075i	$-0.375163\pi$
$449$	16.1978			0.764420			0.382210	+	0.924075i	$0.375163\pi$
$450$		0			0
$451$	3.79234	+	6.56853i	0.178574	+	0.309300i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−11.9730	+	4.60101i	−0.561304	+	0.215699i
$456$		0			0
$457$	0.199776	+	0.745573i	0.00934511	+	0.0348764i	0.970441	−	0.241339i	$-0.0775865\pi$
$457$	0.199776	+	0.745573i	0.00934511	+	0.0348764i	−0.961096	+	0.276215i	$0.910920\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	16.4071i		−	0.764156i	−0.924130	−	0.382078i	$-0.875208\pi$
$461$		−	16.4071i		−	0.764156i	0.924130	−	0.382078i	$-0.124792\pi$
$462$		0			0
$463$	0.487765	+	0.487765i	0.0226684	+	0.0226684i	0.718350	−	0.695682i	$-0.244898\pi$
$463$	0.487765	+	0.487765i	0.0226684	+	0.0226684i	−0.695682	+	0.718350i	$0.744898\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	18.2383	−	4.88694i	0.843968	−	0.226141i	0.189170	−	0.981944i	$-0.439420\pi$
$467$	18.2383	−	4.88694i	0.843968	−	0.226141i	0.654798	+	0.755804i	$0.272754\pi$
$468$		0			0
$469$	−18.0833	−	17.9172i	−0.835009	−	0.827338i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−28.7981	−	7.71644i	−1.32414	−	0.354802i
$474$		0			0
$475$	−6.51802	−	2.17927i	−0.299067	−	0.0999916i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−11.4807	−	19.8851i	−0.524566	−	0.908575i	−0.999591	−	0.0286029i	$-0.990894\pi$
$479$	−11.4807	−	19.8851i	−0.524566	−	0.908575i	0.475025	−	0.879973i	$-0.342439\pi$
$480$		0			0
$481$	−2.69302	+	4.66444i	−0.122791	+	0.212680i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.31612	+	1.07507i	0.0597618	+	0.0488163i
$486$		0			0
$487$	10.9883	+	2.94431i	0.497929	+	0.133420i	0.499039	−	0.866580i	$-0.333687\pi$
$487$	10.9883	+	2.94431i	0.497929	+	0.133420i	−0.00110982	+	0.999999i	$0.500353\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$		−	4.73772i		−	0.213810i	−0.994269	−	0.106905i	$-0.965906\pi$
$491$		−	4.73772i		−	0.213810i	0.994269	−	0.106905i	$-0.0340941\pi$
$492$		0			0
$493$	−5.87020	+	21.9079i	−0.264381	+	0.986682i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−10.5815	+	18.5246i	−0.474647	+	0.830943i
$498$		0			0
$499$	9.91207	+	5.72274i	0.443725	+	0.256185i	0.705176	−	0.709032i	$-0.250868\pi$
$499$	9.91207	+	5.72274i	0.443725	+	0.256185i	−0.261451	+	0.965217i	$0.584201\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	0.173418	−	0.173418i	0.00773234	−	0.00773234i	−0.703230	−	0.710962i	$-0.748260\pi$
$503$	0.173418	−	0.173418i	0.00773234	−	0.00773234i	0.710962	+	0.703230i	$0.248260\pi$
$504$		0			0
$505$	11.8141	+	16.4070i	0.525723	+	0.730101i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	12.2378	−	21.1964i	0.542430	−	0.939516i	−0.456334	−	0.889809i	$-0.650838\pi$
$509$	12.2378	−	21.1964i	0.542430	−	0.939516i	0.998764	−	0.0497073i	$-0.0158288\pi$
$510$		0			0
$511$	25.0201	−	25.2521i	1.10682	−	1.11709i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	12.1506	+	32.0599i	0.535417	+	1.41273i
$516$		0			0
$517$	11.4906	−	11.4906i	0.505358	−	0.505358i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	5.94938	−	3.43488i	0.260647	−	0.150485i	−0.363983	−	0.931406i	$-0.618583\pi$
$521$	5.94938	−	3.43488i	0.260647	−	0.150485i	0.624630	+	0.780921i	$0.285250\pi$
$522$		0			0
$523$	−25.2582	+	6.76790i	−1.10446	+	0.295940i	−0.764580	−	0.644528i	$-0.777054\pi$
$523$	−25.2582	+	6.76790i	−1.10446	+	0.295940i	−0.339882	+	0.940468i	$0.610387\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	36.5929	−	9.80503i	1.59401	−	0.427114i
$528$		0			0
$529$	−41.7913	+	24.1282i	−1.81701	+	1.04905i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	1.81110	−	1.81110i	0.0784476	−	0.0784476i
$534$		0			0
$535$	9.48548	+	25.0280i	0.410093	+	1.08205i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−39.1269	−	22.1110i	−1.68532	−	0.952390i
$540$		0			0
$541$	6.15367	−	10.6585i	0.264567	−	0.458243i	−0.702883	−	0.711305i	$-0.748104\pi$
$541$	6.15367	−	10.6585i	0.264567	−	0.458243i	0.967450	+	0.253062i	$0.0814377\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	20.1265	+	27.9508i	0.862125	+	1.19728i
$546$		0			0
$547$	−0.687016	+	0.687016i	−0.0293747	+	0.0293747i	−0.721642	−	0.692267i	$-0.756612\pi$
$547$	−0.687016	+	0.687016i	−0.0293747	+	0.0293747i	0.692267	+	0.721642i	$0.256612\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−7.08763	−	4.09205i	−0.301943	−	0.174327i
$552$		0			0
$553$	12.3298	+	21.1301i	0.524318	+	0.898544i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.19815	−	34.3280i	0.389738	−	1.45452i	−0.440822	−	0.897594i	$-0.645313\pi$
$557$	9.19815	−	34.3280i	0.389738	−	1.45452i	0.830561	−	0.556928i	$-0.188020\pi$
$558$		0			0
$559$			10.0680i			0.425830i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	11.1589	+	2.99001i	0.470290	+	0.126014i	0.486178	−	0.873860i	$-0.338391\pi$
$563$	11.1589	+	2.99001i	0.470290	+	0.126014i	−0.0158879	+	0.999874i	$0.505057\pi$
$564$		0			0
$565$	10.5296	+	8.60108i	0.442984	+	0.361850i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−3.73569	+	6.47040i	−0.156608	+	0.271253i	−0.933643	−	0.358204i	$-0.883389\pi$
$569$	−3.73569	+	6.47040i	−0.156608	+	0.271253i	0.777035	+	0.629457i	$0.216723\pi$
$570$		0			0
$571$	−11.9995	−	20.7837i	−0.502162	−	0.869770i	−0.999997	−	0.00249810i	$-0.999205\pi$
$571$	−11.9995	−	20.7837i	−0.502162	−	0.869770i	0.497835	−	0.867272i	$-0.334129\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−18.8411	−	37.7681i	−0.785727	−	1.57504i
$576$		0			0
$577$	35.7665	+	9.58360i	1.48898	+	0.398971i	0.909392	−	0.415940i	$-0.136547\pi$
$577$	35.7665	+	9.58360i	1.48898	+	0.398971i	0.579587	+	0.814911i	$0.303214\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	18.4810	−	5.04348i	0.766721	−	0.209239i
$582$		0			0
$583$	11.5684	−	3.09974i	0.479114	−	0.128378i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.12363	+	5.12363i	0.211475	+	0.211475i	0.804894	−	0.593419i	$-0.202222\pi$
$587$	5.12363	+	5.12363i	0.211475	+	0.211475i	−0.593419	+	0.804894i	$0.702222\pi$
$588$		0			0
$589$			13.6699i			0.563260i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	4.61098	+	17.2084i	0.189350	+	0.706665i	0.993657	+	0.112451i	$0.0358701\pi$
$593$	4.61098	+	17.2084i	0.189350	+	0.706665i	−0.804307	+	0.594214i	$0.797463\pi$
$594$		0			0
$595$	17.5189	+	14.1760i	0.718205	+	0.581159i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	4.03317	+	6.98565i	0.164791	+	0.285426i	0.936581	−	0.350451i	$-0.113972\pi$
$599$	4.03317	+	6.98565i	0.164791	+	0.285426i	−0.771790	+	0.635877i	$0.780638\pi$
$600$		0			0
$601$	19.7065			0.803847			0.401923	−	0.915673i	$-0.368342\pi$
$601$	19.7065			0.803847			0.401923	+	0.915673i	$0.368342\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−61.6159	−	27.7476i	−2.50504	−	1.12810i
$606$		0			0
$607$	0.876127	+	3.26975i	0.0355609	+	0.132715i	0.981424	−	0.191850i	$-0.0614487\pi$
$607$	0.876127	+	3.26975i	0.0355609	+	0.132715i	−0.945863	+	0.324565i	$0.894782\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−4.75238	−	2.74379i	−0.192261	−	0.111002i
$612$		0			0
$613$	−6.61440	+	24.6853i	−0.267153	+	0.997029i	0.693766	+	0.720200i	$0.255950\pi$
$613$	−6.61440	+	24.6853i	−0.267153	+	0.997029i	−0.960919	+	0.276828i	$0.910717\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−10.3049	−	10.3049i	−0.414858	−	0.414858i	0.468569	−	0.883427i	$-0.344770\pi$
$617$	−10.3049	−	10.3049i	−0.414858	−	0.414858i	−0.883427	+	0.468569i	$0.844770\pi$
$618$		0			0
$619$	−40.7197	+	23.5095i	−1.63666	+	0.944927i	−0.654690	+	0.755897i	$0.727201\pi$
$619$	−40.7197	+	23.5095i	−1.63666	+	0.944927i	−0.981971	+	0.189030i	$0.939466\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	18.1617	−	10.5977i	0.727634	−	0.424588i
$624$		0			0
$625$	23.0082	−	9.77865i	0.920329	−	0.391146i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	9.46309			0.377318
$630$		0			0
$631$	−28.2257			−1.12365			−0.561823	−	0.827257i	$-0.689900\pi$
$631$	−28.2257			−1.12365			−0.561823	+	0.827257i	$0.689900\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	18.9357	+	15.4675i	0.751439	+	0.613810i
$636$		0			0
$637$	−3.79256	+	14.6952i	−0.150267	+	0.582244i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−14.1061	+	8.14415i	−0.557157	+	0.321675i	−0.752004	−	0.659159i	$-0.770912\pi$
$641$	−14.1061	+	8.14415i	−0.557157	+	0.321675i	0.194847	+	0.980834i	$0.437579\pi$
$642$		0			0
$643$	17.3483	+	17.3483i	0.684152	+	0.684152i	0.960933	−	0.276781i	$-0.0892677\pi$
$643$	17.3483	+	17.3483i	0.684152	+	0.684152i	−0.276781	+	0.960933i	$0.589268\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−11.9573	+	44.6252i	−0.470090	+	1.75440i	0.169349	+	0.985556i	$0.445833\pi$
$647$	−11.9573	+	44.6252i	−0.470090	+	1.75440i	−0.639439	+	0.768842i	$0.720833\pi$
$648$		0			0
$649$	36.4495	+	21.0442i	1.43077	+	0.826055i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.43848	−	20.2967i	−0.212824	−	0.794270i	−0.986921	−	0.161203i	$-0.948462\pi$
$653$	−5.43848	−	20.2967i	−0.212824	−	0.794270i	0.774097	−	0.633067i	$-0.218204\pi$
$654$		0			0
$655$	−5.32564	+	11.8260i	−0.208090	+	0.462082i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−32.6555			−1.27208			−0.636038	−	0.771658i	$-0.719428\pi$
$659$	−32.6555			−1.27208			−0.636038	+	0.771658i	$0.719428\pi$
$660$		0			0
$661$	7.61755	+	13.1940i	0.296288	+	0.513187i	0.975284	−	0.220956i	$-0.0709177\pi$
$661$	7.61755	+	13.1940i	0.296288	+	0.513187i	−0.678995	+	0.734143i	$0.737584\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−6.57708	+	4.78218i	−0.255048	+	0.185445i
$666$		0			0
$667$	−13.0084	−	48.5479i	−0.503686	−	1.87978i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			52.5209i			2.02755i
$672$		0			0
$673$	−13.9179	−	13.9179i	−0.536496	−	0.536496i	0.386002	−	0.922498i	$-0.373856\pi$
$673$	−13.9179	−	13.9179i	−0.536496	−	0.536496i	−0.922498	+	0.386002i	$0.873856\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−15.5379	+	4.16337i	−0.597170	+	0.160011i	−0.544728	−	0.838613i	$-0.683367\pi$
$677$	−15.5379	+	4.16337i	−0.597170	+	0.160011i	−0.0524419	+	0.998624i	$0.516700\pi$
$678$		0			0
$679$	1.93981	−	0.529376i	0.0744431	−	0.0203156i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−20.7681	−	5.56479i	−0.794669	−	0.212931i	−0.161427	−	0.986885i	$-0.551610\pi$
$683$	−20.7681	−	5.56479i	−0.794669	−	0.212931i	−0.633242	+	0.773954i	$0.718276\pi$
$684$		0			0
$685$	−2.58986	−	0.421487i	−0.0989536	−	0.0161042i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−2.02218	−	3.50252i	−0.0770390	−	0.133435i
$690$		0			0
$691$	−2.07439	+	3.59295i	−0.0789136	+	0.136682i	−0.902781	−	0.430100i	$-0.858478\pi$
$691$	−2.07439	+	3.59295i	−0.0789136	+	0.136682i	0.823868	+	0.566782i	$0.191812\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−17.4984	+	1.76399i	−0.663752	+	0.0669118i
$696$		0			0
$697$	−4.34676	−	1.16471i	−0.164645	−	0.0441166i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			20.3268i			0.767732i	0.923389	+	0.383866i	$0.125407\pi$
$701$			20.3268i			0.767732i	−0.923389	+	0.383866i	$0.874593\pi$
$702$		0			0
$703$	−0.883778	+	3.29830i	−0.0333323	+	0.124398i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	23.9219	−	0.110382i	0.899675	−	0.00415134i
$708$		0			0
$709$	0.848324	+	0.489780i	0.0318595	+	0.0183941i	0.515845	−	0.856682i	$-0.327478\pi$
$709$	0.848324	+	0.489780i	0.0318595	+	0.0183941i	−0.483986	+	0.875076i	$0.660811\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−59.3618	+	59.3618i	−2.22312	+	2.22312i
$714$		0			0
$715$	−4.99979	+	30.7217i	−0.186981	+	1.14892i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−18.2451	+	31.6014i	−0.680426	+	1.17853i	0.294425	+	0.955675i	$0.404872\pi$
$719$	−18.2451	+	31.6014i	−0.680426	+	1.17853i	−0.974851	+	0.222858i	$0.928461\pi$
$720$		0			0
$721$	39.2325	+	10.3185i	1.46110	+	0.384283i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	29.1714	−	5.94183i	1.08340	−	0.220674i
$726$		0			0
$727$	−19.5435	+	19.5435i	−0.724829	+	0.724829i	−0.969585	−	0.244756i	$-0.921292\pi$
$727$	−19.5435	+	19.5435i	−0.724829	+	0.724829i	0.244756	+	0.969585i	$0.421292\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	15.3192	−	8.84455i	0.566601	−	0.327128i
$732$		0			0
$733$	11.3962	−	3.05361i	0.420930	−	0.112788i	−0.0421356	−	0.999112i	$-0.513416\pi$
$733$	11.3962	−	3.05361i	0.420930	−	0.112788i	0.463065	+	0.886324i	$0.346749\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−59.6692	+	15.9883i	−2.19794	+	0.588937i
$738$		0			0
$739$	18.7655	−	10.8343i	0.690300	−	0.398545i	−0.113425	−	0.993547i	$-0.536182\pi$
$739$	18.7655	−	10.8343i	0.690300	−	0.398545i	0.803724	+	0.595002i	$0.202849\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−25.6469	+	25.6469i	−0.940893	+	0.940893i	−0.998348	−	0.0574554i	$-0.981701\pi$
$743$	−25.6469	+	25.6469i	−0.940893	+	0.940893i	0.0574554	+	0.998348i	$0.481701\pi$
$744$		0			0
$745$	−7.17411	−	3.23073i	−0.262839	−	0.118365i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	30.6274	+	8.05530i	1.11910	+	0.294334i
$750$		0			0
$751$	−11.3333	+	19.6298i	−0.413557	+	0.716302i	−0.995276	−	0.0970880i	$-0.969047\pi$
$751$	−11.3333	+	19.6298i	−0.413557	+	0.716302i	0.581719	+	0.813390i	$0.302381\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	13.8732	−	9.98965i	0.504897	−	0.363560i
$756$		0			0
$757$	22.5856	−	22.5856i	0.820889	−	0.820889i	−0.165346	−	0.986236i	$-0.552874\pi$
$757$	22.5856	−	22.5856i	0.820889	−	0.820889i	0.986236	+	0.165346i	$0.0528742\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	4.22144	+	2.43725i	0.153027	+	0.0883503i	0.574558	−	0.818464i	$-0.305174\pi$
$761$	4.22144	+	2.43725i	0.153027	+	0.0883503i	−0.421531	+	0.906814i	$0.638507\pi$
$762$		0			0
$763$	40.7532	−	0.188046i	1.47536	−	0.00680772i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.67857	−	13.7286i	0.132825	−	0.495711i
$768$		0			0
$769$			21.6504i			0.780732i	0.920660	+	0.390366i	$0.127652\pi$
$769$			21.6504i			0.780732i	−0.920660	+	0.390366i	$0.872348\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−3.60024	−	0.964680i	−0.129491	−	0.0346971i	0.193491	−	0.981102i	$-0.438019\pi$
$773$	−3.60024	−	0.964680i	−0.129491	−	0.0346971i	−0.322983	+	0.946405i	$0.604686\pi$
$774$		0			0
$775$	−32.9576	−	37.2348i	−1.18387	−	1.33752i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.811907	−	1.40626i	0.0290896	−	0.0503846i
$780$		0			0
$781$	25.8849	+	44.8340i	0.926235	+	1.60429i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.86226	+	23.7320i	−0.137850	+	0.847033i
$786$		0			0
$787$	−26.5026	−	7.10136i	−0.944717	−	0.253136i	−0.246598	−	0.969118i	$-0.579313\pi$
$787$	−26.5026	−	7.10136i	−0.944717	−	0.253136i	−0.698119	+	0.715982i	$0.745979\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	15.5195	−	4.23528i	0.551809	−	0.150589i
$792$		0			0
$793$	17.1316	−	4.59039i	0.608359	−	0.163009i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−27.2650	−	27.2650i	−0.965776	−	0.965776i	0.0336572	−	0.999433i	$-0.489285\pi$
$797$	−27.2650	−	27.2650i	−0.965776	−	0.965776i	−0.999433	+	0.0336572i	$0.989285\pi$
$798$		0			0
$799$			9.64150i			0.341092i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−22.3266	−	83.3239i	−0.787888	−	2.94044i
$804$		0			0
$805$	−49.3277	−	7.79436i	−1.73857	−	0.274715i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.48375	−	2.56993i	−0.0521659	−	0.0903539i	0.838763	−	0.544496i	$-0.183279\pi$
$809$	−1.48375	−	2.56993i	−0.0521659	−	0.0903539i	−0.890929	+	0.454142i	$0.849946\pi$
$810$		0			0
$811$	−22.1671			−0.778394			−0.389197	−	0.921155i	$-0.627247\pi$
$811$	−22.1671			−0.778394			−0.389197	+	0.921155i	$0.627247\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−10.5394	−	27.8088i	−0.369179	−	0.974100i
$816$		0			0
$817$	1.65202	+	6.16543i	0.0577969	+	0.215701i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−26.0088	−	15.0162i	−0.907713	−	0.524068i	−0.0280184	−	0.999607i	$-0.508920\pi$
$821$	−26.0088	−	15.0162i	−0.907713	−	0.524068i	−0.879695	+	0.475539i	$0.842253\pi$
$822$		0			0
$823$	3.32059	−	12.3926i	0.115749	−	0.431980i	−0.883593	−	0.468255i	$-0.844883\pi$
$823$	3.32059	−	12.3926i	0.115749	−	0.431980i	0.999342	+	0.0362756i	$0.0115494\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.13860	−	4.13860i	−0.143913	−	0.143913i	0.631479	−	0.775393i	$-0.282448\pi$
$827$	−4.13860	−	4.13860i	−0.143913	−	0.143913i	−0.775393	+	0.631479i	$0.782448\pi$
$828$		0			0
$829$	24.3610	−	14.0648i	0.846092	−	0.488492i	−0.0132381	−	0.999912i	$-0.504214\pi$
$829$	24.3610	−	14.0648i	0.846092	−	0.488492i	0.859330	+	0.511421i	$0.170881\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	25.6916	−	7.13879i	0.890160	−	0.247344i
$834$		0			0
$835$	33.6331	−	41.1744i	1.16392	−	1.42490i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	56.7938			1.96074			0.980370	−	0.197169i	$-0.0631746\pi$
$839$	56.7938			1.96074			0.980370	+	0.197169i	$0.0631746\pi$
$840$		0			0
$841$	6.45100			0.222448
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−18.4643	+	1.86136i	−0.635193	+	0.0640328i
$846$		0			0
$847$	−69.0591	+	40.2973i	−2.37290	+	1.38463i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−18.1607	+	10.4851i	−0.622542	+	0.359425i
$852$		0			0
$853$	−5.48579	−	5.48579i	−0.187830	−	0.187830i	0.606927	−	0.794757i	$-0.292402\pi$
$853$	−5.48579	−	5.48579i	−0.187830	−	0.187830i	−0.794757	+	0.606927i	$0.792402\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.82019	+	21.7212i	−0.198814	+	0.741983i	0.792433	+	0.609959i	$0.208814\pi$
$857$	−5.82019	+	21.7212i	−0.198814	+	0.741983i	−0.991247	+	0.132024i	$0.957852\pi$
$858$		0			0
$859$	1.08516	+	0.626520i	0.0370253	+	0.0213766i	0.518398	−	0.855139i	$-0.326528\pi$
$859$	1.08516	+	0.626520i	0.0370253	+	0.0213766i	−0.481373	+	0.876516i	$0.659862\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−1.35093	−	5.04175i	−0.0459863	−	0.171623i	0.939113	−	0.343607i	$-0.111649\pi$
$863$	−1.35093	−	5.04175i	−0.0459863	−	0.171623i	−0.985100	+	0.171984i	$0.944982\pi$
$864$		0			0
$865$	−6.05002	+	2.29293i	−0.205707	+	0.0779618i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	59.3667			2.01388
$870$		0			0
$871$	10.4303	+	18.0658i	0.353418	+	0.612137i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	6.38536	−	28.8830i	0.215865	−	0.976423i
$876$		0			0
$877$	−14.2128	−	53.0430i	−0.479933	−	1.79113i	−0.601867	−	0.798596i	$-0.705576\pi$
$877$	−14.2128	−	53.0430i	−0.479933	−	1.79113i	0.121934	−	0.992538i	$-0.461090\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			27.6422i			0.931288i	0.884972	+	0.465644i	$0.154177\pi$
$881$			27.6422i			0.931288i	−0.884972	+	0.465644i	$0.845823\pi$
$882$		0			0
$883$	8.22329	+	8.22329i	0.276736	+	0.276736i	0.831804	−	0.555069i	$-0.187308\pi$
$883$	8.22329	+	8.22329i	0.276736	+	0.276736i	−0.555069	+	0.831804i	$0.687308\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	29.7893	−	7.98203i	1.00023	−	0.268010i	0.278687	−	0.960382i	$-0.410101\pi$
$887$	29.7893	−	7.98203i	1.00023	−	0.268010i	0.721541	+	0.692372i	$0.243434\pi$
$888$		0			0
$889$	27.9091	−	7.61641i	0.936040	−	0.255446i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−3.36049	−	0.900439i	−0.112454	−	0.0301321i
$894$		0			0
$895$	16.9977	−	12.2395i	0.568169	−	0.409121i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−29.6070	−	51.2808i	−0.987448	−	1.71031i
$900$		0			0
$901$	−3.55291	+	6.15382i	−0.118365	+	0.205013i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.264791	+	2.62667i	0.00880195	+	0.0873136i
$906$		0			0
$907$	31.7710	+	8.51300i	1.05494	+	0.282670i	0.744291	−	0.667856i	$-0.232788\pi$
$907$	31.7710	+	8.51300i	1.05494	+	0.282670i	0.310647	+	0.950525i	$0.399454\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			8.90827i			0.295144i	0.989051	+	0.147572i	$0.0471459\pi$
$911$			8.90827i			0.295144i	−0.989051	+	0.147572i	$0.952854\pi$
$912$		0			0
$913$	12.0317	−	44.9031i	0.398192	−	1.48607i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	7.73432	+	13.2546i	0.255410	+	0.437706i
$918$		0			0
$919$	−21.1251	−	12.1966i	−0.696852	−	0.402327i	0.109322	−	0.994006i	$-0.465132\pi$
$919$	−21.1251	−	12.1966i	−0.696852	−	0.402327i	−0.806174	+	0.591679i	$0.798465\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	12.3618	−	12.3618i	0.406894	−	0.406894i
$924$		0			0
$925$	−5.54478	−	11.1148i	−0.182311	−	0.365453i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−19.3772	+	33.5624i	−0.635746	+	1.10115i	0.350610	+	0.936522i	$0.385974\pi$
$929$	−19.3772	+	33.5624i	−0.635746	+	1.10115i	−0.986356	+	0.164624i	$0.947359\pi$
$930$		0			0
$931$	0.0887927	+	9.62135i	0.00291006	+	0.315327i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	51.1377	−	19.3809i	1.67238	−	0.633824i
$936$		0			0
$937$	−21.7681	+	21.7681i	−0.711132	+	0.711132i	−0.966772	−	0.255640i	$-0.917714\pi$
$937$	−21.7681	+	21.7681i	−0.711132	+	0.711132i	0.255640	+	0.966772i	$0.417714\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	40.4091	−	23.3302i	1.31730	−	0.760544i	0.334007	−	0.942571i	$-0.391599\pi$
$941$	40.4091	−	23.3302i	1.31730	−	0.760544i	0.983294	+	0.182027i	$0.0582657\pi$
$942$		0			0
$943$	9.63243	−	2.58100i	0.313675	−	0.0840490i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	21.9780	−	5.88900i	0.714190	−	0.191367i	0.116612	−	0.993178i	$-0.462797\pi$
$947$	21.9780	−	5.88900i	0.714190	−	0.191367i	0.597578	+	0.801811i	$0.296130\pi$
$948$		0			0
$949$	−25.2277	+	14.5652i	−0.818926	+	0.472807i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	17.8617	−	17.8617i	0.578598	−	0.578598i	−0.355919	−	0.934517i	$-0.615832\pi$
$953$	17.8617	−	17.8617i	0.578598	−	0.578598i	0.934517	+	0.355919i	$0.115832\pi$
$954$		0			0
$955$	−9.42750	+	20.9346i	−0.305067	+	0.677427i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−2.18519	+	2.20545i	−0.0705635	+	0.0712177i
$960$		0			0
$961$	−33.9527	+	58.8078i	−1.09525	+	1.89703i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−32.2879	−	5.25468i	−1.03938	−	0.169154i
$966$		0			0
$967$	35.0807	−	35.0807i	1.12812	−	1.12812i	0.137636	−	0.990483i	$-0.456050\pi$
$967$	35.0807	−	35.0807i	1.12812	−	1.12812i	0.990483	−	0.137636i	$-0.0439504\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	4.12273	+	2.38026i	0.132305	+	0.0763862i	0.564692	−	0.825302i	$-0.308995\pi$
$971$	4.12273	+	2.38026i	0.132305	+	0.0763862i	−0.432387	+	0.901688i	$0.642328\pi$
$972$		0			0
$973$	−10.3214	+	18.0692i	−0.330889	+	0.579272i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3.00447	+	11.2128i	−0.0961215	+	0.358730i	−0.997187	−	0.0749525i	$-0.976119\pi$
$977$	−3.00447	+	11.2128i	−0.0961215	+	0.358730i	0.901066	+	0.433683i	$0.142786\pi$
$978$		0			0
$979$		−	51.0268i		−	1.63082i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	47.3664	+	12.6918i	1.51075	+	0.404805i	0.916685	−	0.399611i	$-0.130855\pi$
$983$	47.3664	+	12.6918i	1.51075	+	0.404805i	0.594067	+	0.804415i	$0.297521\pi$
$984$		0			0
$985$	−28.8581	+	35.3287i	−0.919495	+	1.12566i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−19.5995	+	33.9474i	−0.623229	+	1.07946i
$990$		0			0
$991$	−16.9538	−	29.3649i	−0.538556	−	0.932807i	−0.998982	−	0.0451089i	$-0.985637\pi$
$991$	−16.9538	−	29.3649i	−0.538556	−	0.932807i	0.460426	−	0.887698i	$-0.347697\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−12.6119	−	17.5148i	−0.399823	−	0.555257i
$996$		0			0
$997$	57.3937	+	15.3786i	1.81768	+	0.487045i	0.996497	−	0.0836238i	$-0.0266494\pi$
$997$	57.3937	+	15.3786i	1.81768	+	0.487045i	0.821180	+	0.570669i	$0.193316\pi$
$998$		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.233.8	yes	64
3.2	odd	2	inner	1260.2.ej.a.233.9	yes	64
5.2	odd	4	inner	1260.2.ej.a.737.4	yes	64
7.4	even	3	inner	1260.2.ej.a.53.13	yes	64
15.2	even	4	inner	1260.2.ej.a.737.13	yes	64
21.11	odd	6	inner	1260.2.ej.a.53.4	✓	64
35.32	odd	12	inner	1260.2.ej.a.557.9	yes	64
105.32	even	12	inner	1260.2.ej.a.557.8	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.ej.a.53.4	✓	64	21.11	odd	6	inner
1260.2.ej.a.53.13	yes	64	7.4	even	3	inner
1260.2.ej.a.233.8	yes	64	1.1	even	1	trivial
1260.2.ej.a.233.9	yes	64	3.2	odd	2	inner
1260.2.ej.a.557.8	yes	64	105.32	even	12	inner
1260.2.ej.a.557.9	yes	64	35.32	odd	12	inner
1260.2.ej.a.737.4	yes	64	5.2	odd	4	inner
1260.2.ej.a.737.13	yes	64	15.2	even	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)

\(f(q)\)	\(=\)	\(q+(-0.224278 - 2.22479i) q^{5} +(-2.29737 - 1.31229i) q^{7} +O(q^{10})\)	\(q+(-0.224278 - 2.22479i) q^{5} +(-2.29737 - 1.31229i) q^{7} +(-5.56017 + 3.21017i) q^{11} +(1.53308 + 1.53308i) q^{13} +(0.985913 - 3.67948i) q^{17} +(1.19038 + 0.687268i) q^{19} +(2.18478 + 8.15372i) q^{23} +(-4.89940 + 0.997943i) q^{25} -5.95407 q^{29} +(4.97256 + 8.61273i) q^{31} +(-2.40432 + 5.40548i) q^{35} +(0.642964 + 2.39957i) q^{37} -1.18135i q^{41} +(3.28359 + 3.28359i) q^{43} +(-2.44481 + 0.655086i) q^{47} +(3.55579 + 6.02962i) q^{49} +(-1.80184 - 0.482801i) q^{53} +(8.38898 + 11.6503i) q^{55} +(-3.27774 - 5.67721i) q^{59} +(4.09020 - 7.08443i) q^{61} +(3.06694 - 3.75461i) q^{65} +(9.29378 + 2.49026i) q^{67} -8.06341i q^{71} +(-3.47748 + 12.9781i) q^{73} +(16.9864 - 0.0783798i) q^{77} +(-8.00786 - 4.62334i) q^{79} +(-5.11988 + 5.11988i) q^{83} +(-8.40719 - 1.36823i) q^{85} +(-3.97384 + 6.88289i) q^{89} +(-1.51020 - 5.53388i) q^{91} +(1.26205 - 2.80250i) q^{95} +(-0.537395 + 0.537395i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 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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