LMFDB - Embedded newform 1260.2.ej.a.737.9

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			737.9
Character	$\chi$	$=$	1260.737
Dual form			1260.2.ej.a.53.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.260321 + 2.22086i) q^{5} +(2.63286 + 0.260847i) q^{7} +O(q^{10})$	$q+(0.260321 + 2.22086i) q^{5} +(2.63286 + 0.260847i) q^{7} +(3.34307 - 1.93012i) q^{11} +(4.35942 - 4.35942i) q^{13} +(-4.66129 - 1.24899i) q^{17} +(1.57138 + 0.907238i) q^{19} +(2.15233 - 0.576716i) q^{23} +(-4.86447 + 1.15627i) q^{25} -0.529880 q^{29} +(-3.19477 - 5.53350i) q^{31} +(0.106084 + 5.91513i) q^{35} +(9.69597 - 2.59803i) q^{37} +5.31881i q^{41} +(-1.82244 + 1.82244i) q^{43} +(2.59757 + 9.69426i) q^{47} +(6.86392 + 1.37355i) q^{49} +(-0.0180330 + 0.0673002i) q^{53} +(5.15680 + 6.92204i) q^{55} +(-1.07454 - 1.86116i) q^{59} +(1.99772 - 3.46015i) q^{61} +(10.8165 + 8.54682i) q^{65} +(-1.36379 + 5.08972i) q^{67} +8.72093i q^{71} +(-3.55904 - 0.953642i) q^{73} +(9.30530 - 4.20971i) q^{77} +(-0.564269 - 0.325781i) q^{79} +(-4.54026 - 4.54026i) q^{83} +(1.56040 - 10.6772i) q^{85} +(7.34188 - 12.7165i) q^{89} +(12.6149 - 10.3406i) q^{91} +(-1.60579 + 3.72600i) q^{95} +(0.639339 + 0.639339i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.260321	+	2.22086i	0.116419	+	0.993200i
$5$	0.260321	+	2.22086i	0.116419	+	0.993200i
$6$		0			0
$7$	2.63286	+	0.260847i	0.995128	+	0.0985909i
$7$	2.63286	+	0.260847i	0.995128	+	0.0985909i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.34307	−	1.93012i	1.00797	−	0.581953i	0.0973753	−	0.995248i	$-0.468955\pi$
$11$	3.34307	−	1.93012i	1.00797	−	0.581953i	0.910597	+	0.413294i	$0.135622\pi$
$12$		0			0
$13$	4.35942	−	4.35942i	1.20908	−	1.20908i	0.237761	−	0.971324i	$-0.423587\pi$
$13$	4.35942	−	4.35942i	1.20908	−	1.20908i	0.971324	−	0.237761i	$-0.0764134\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−4.66129	−	1.24899i	−1.13053	−	0.302924i	−0.355392	−	0.934717i	$-0.615653\pi$
$17$	−4.66129	−	1.24899i	−1.13053	−	0.302924i	−0.775137	+	0.631793i	$0.782319\pi$
$18$		0			0
$19$	1.57138	+	0.907238i	0.360500	+	0.208135i	0.669300	−	0.742992i	$-0.266594\pi$
$19$	1.57138	+	0.907238i	0.360500	+	0.208135i	−0.308800	+	0.951127i	$0.599927\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	2.15233	−	0.576716i	0.448793	−	0.120254i	−0.0273418	−	0.999626i	$-0.508704\pi$
$23$	2.15233	−	0.576716i	0.448793	−	0.120254i	0.476134	+	0.879373i	$0.342038\pi$
$24$		0			0
$25$	−4.86447	+	1.15627i	−0.972893	+	0.231255i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−0.529880			−0.0983963			−0.0491981	−	0.998789i	$-0.515667\pi$
$29$	−0.529880			−0.0983963			−0.0491981	+	0.998789i	$0.515667\pi$
$30$		0			0
$31$	−3.19477	−	5.53350i	−0.573797	−	0.993845i	−0.996171	−	0.0874239i	$-0.972137\pi$
$31$	−3.19477	−	5.53350i	−0.573797	−	0.993845i	0.422374	−	0.906422i	$-0.361197\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.106084	+	5.91513i	0.0179314	+	0.999839i
$36$		0			0
$37$	9.69597	−	2.59803i	1.59401	−	0.427113i	0.650782	−	0.759265i	$-0.274441\pi$
$37$	9.69597	−	2.59803i	1.59401	−	0.427113i	0.943226	+	0.332152i	$0.107775\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$			5.31881i			0.830659i	0.909671	+	0.415330i	$0.136334\pi$
$41$			5.31881i			0.830659i	−0.909671	+	0.415330i	$0.863666\pi$
$42$		0			0
$43$	−1.82244	+	1.82244i	−0.277920	+	0.277920i	−0.832278	−	0.554358i	$-0.812964\pi$
$43$	−1.82244	+	1.82244i	−0.277920	+	0.277920i	0.554358	+	0.832278i	$0.312964\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.59757	+	9.69426i	0.378894	+	1.41405i	0.847571	+	0.530683i	$0.178064\pi$
$47$	2.59757	+	9.69426i	0.378894	+	1.41405i	−0.468676	+	0.883370i	$0.655269\pi$
$48$		0			0
$49$	6.86392	+	1.37355i	0.980560	+	0.196221i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.0180330	+	0.0673002i	−0.00247703	+	0.00924440i	−0.967153	−	0.254194i	$-0.918190\pi$
$53$	−0.0180330	+	0.0673002i	−0.00247703	+	0.00924440i	0.964676	+	0.263438i	$0.0848565\pi$
$54$		0			0
$55$	5.15680	+	6.92204i	0.695343	+	0.933368i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−1.07454	−	1.86116i	−0.139893	−	0.242302i	0.787563	−	0.616234i	$-0.211343\pi$
$59$	−1.07454	−	1.86116i	−0.139893	−	0.242302i	−0.927456	+	0.373932i	$0.878009\pi$
$60$		0			0
$61$	1.99772	−	3.46015i	0.255782	−	0.443027i	−0.709326	−	0.704881i	$-0.751001\pi$
$61$	1.99772	−	3.46015i	0.255782	−	0.443027i	0.965108	+	0.261854i	$0.0843338\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	10.8165	+	8.54682i	1.34162	+	1.06010i
$66$		0			0
$67$	−1.36379	+	5.08972i	−0.166613	+	0.621808i	0.831216	+	0.555950i	$0.187645\pi$
$67$	−1.36379	+	5.08972i	−0.166613	+	0.621808i	−0.997829	+	0.0658587i	$0.979021\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			8.72093i			1.03498i	0.855688	+	0.517492i	$0.173134\pi$
$71$			8.72093i			1.03498i	−0.855688	+	0.517492i	$0.826866\pi$
$72$		0			0
$73$	−3.55904	−	0.953642i	−0.416554	−	0.111615i	0.0444535	−	0.999011i	$-0.485845\pi$
$73$	−3.55904	−	0.953642i	−0.416554	−	0.111615i	−0.461008	+	0.887396i	$0.652512\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.30530	−	4.20971i	1.06044	−	0.479741i
$78$		0			0
$79$	−0.564269	−	0.325781i	−0.0634852	−	0.0366532i	0.467921	−	0.883770i	$-0.345003\pi$
$79$	−0.564269	−	0.325781i	−0.0634852	−	0.0366532i	−0.531407	+	0.847117i	$0.678336\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−4.54026	−	4.54026i	−0.498358	−	0.498358i	0.412568	−	0.910927i	$-0.364632\pi$
$83$	−4.54026	−	4.54026i	−0.498358	−	0.498358i	−0.910927	+	0.412568i	$0.864632\pi$
$84$		0			0
$85$	1.56040	−	10.6772i	0.169249	−	1.15811i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	7.34188	−	12.7165i	0.778238	−	1.34795i	−0.154718	−	0.987959i	$-0.549447\pi$
$89$	7.34188	−	12.7165i	0.778238	−	1.34795i	0.932956	−	0.359989i	$-0.117220\pi$
$90$		0			0
$91$	12.6149	−	10.3406i	1.32240	−	1.08399i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.60579	+	3.72600i	−0.164750	+	0.382279i
$96$		0			0
$97$	0.639339	+	0.639339i	0.0649150	+	0.0649150i	0.738819	−	0.673904i	$-0.235384\pi$
$97$	0.639339	+	0.639339i	0.0649150	+	0.0649150i	−0.673904	+	0.738819i	$0.735384\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−15.2630	+	8.81210i	−1.51873	+	0.876837i	−0.518969	+	0.854793i	$0.673684\pi$
$101$	−15.2630	+	8.81210i	−1.51873	+	0.876837i	−0.999757	+	0.0220433i	$0.992983\pi$
$102$		0			0
$103$	−1.67334	−	6.24499i	−0.164879	−	0.615338i	−0.998056	−	0.0623302i	$-0.980147\pi$
$103$	−1.67334	−	6.24499i	−0.164879	−	0.615338i	0.833176	−	0.553007i	$-0.186520\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.84530	+	10.6188i	0.275065	+	1.02656i	0.955798	+	0.294026i	$0.0949951\pi$
$107$	2.84530	+	10.6188i	0.275065	+	1.02656i	−0.680732	+	0.732532i	$0.738338\pi$
$108$		0			0
$109$	10.5032	−	6.06404i	1.00603	−	0.580830i	0.0960010	−	0.995381i	$-0.469395\pi$
$109$	10.5032	−	6.06404i	1.00603	−	0.580830i	0.910026	+	0.414551i	$0.136061\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	3.39477	+	3.39477i	0.319353	+	0.319353i	0.848518	−	0.529166i	$-0.177495\pi$
$113$	3.39477	+	3.39477i	0.319353	+	0.319353i	−0.529166	+	0.848518i	$0.677495\pi$
$114$		0			0
$115$	1.84110	+	4.62991i	0.171684	+	0.431741i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−11.9467	−	4.50430i	−1.09516	−	0.412909i
$120$		0			0
$121$	1.95073	−	3.37877i	0.177339	−	0.307161i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−3.83425	−	10.5023i	−0.342946	−	0.939355i
$126$		0			0
$127$	−4.78425	−	4.78425i	−0.424533	−	0.424533i	0.462228	−	0.886761i	$-0.347050\pi$
$127$	−4.78425	−	4.78425i	−0.424533	−	0.424533i	−0.886761	+	0.462228i	$0.847050\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−13.3805	−	7.72525i	−1.16906	−	0.674958i	−0.215603	−	0.976481i	$-0.569172\pi$
$131$	−13.3805	−	7.72525i	−1.16906	−	0.674958i	−0.953459	+	0.301523i	$0.902505\pi$
$132$		0			0
$133$	3.90058	+	2.79852i	0.338223	+	0.242663i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.6905	+	2.86451i	0.913349	+	0.244731i	0.684740	−	0.728787i	$-0.259916\pi$
$137$	10.6905	+	2.86451i	0.913349	+	0.244731i	0.228609	+	0.973518i	$0.426582\pi$
$138$		0			0
$139$			20.5805i			1.74561i	0.488067	+	0.872806i	$0.337702\pi$
$139$			20.5805i			1.74561i	−0.488067	+	0.872806i	$0.662298\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	6.15962	−	22.9880i	0.515093	−	1.92235i
$144$		0			0
$145$	−0.137939	−	1.17679i	−0.0114552	−	0.0977272i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.3596	+	17.9433i	−0.848690	+	1.46997i	0.0336877	+	0.999432i	$0.489275\pi$
$149$	−10.3596	+	17.9433i	−0.848690	+	1.46997i	−0.882378	+	0.470542i	$0.844059\pi$
$150$		0			0
$151$	−3.92687	−	6.80153i	−0.319564	−	0.553501i	0.660833	−	0.750533i	$-0.270203\pi$
$151$	−3.92687	−	6.80153i	−0.319564	−	0.553501i	−0.980397	+	0.197032i	$0.936870\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	11.4575	−	8.53562i	0.920287	−	0.685598i
$156$		0			0
$157$	−5.04041	+	18.8110i	−0.402268	+	1.50129i	0.406771	+	0.913530i	$0.366655\pi$
$157$	−5.04041	+	18.8110i	−0.402268	+	1.50129i	−0.809039	+	0.587755i	$0.800012\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.81723	−	0.956984i	0.458462	−	0.0754209i
$162$		0			0
$163$	6.24395	+	23.3028i	0.489064	+	1.82521i	0.561017	+	0.827804i	$0.310410\pi$
$163$	6.24395	+	23.3028i	0.489064	+	1.82521i	−0.0719528	+	0.997408i	$0.522923\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.51564	+	1.51564i	−0.117284	+	0.117284i	−0.763313	−	0.646029i	$-0.776429\pi$
$167$	−1.51564	+	1.51564i	−0.117284	+	0.117284i	0.646029	+	0.763313i	$0.276429\pi$
$168$		0			0
$169$		−	25.0090i		−	1.92377i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	12.7211	−	3.40860i	0.967165	−	0.259151i	0.259535	−	0.965734i	$-0.416431\pi$
$173$	12.7211	−	3.40860i	0.967165	−	0.259151i	0.707630	+	0.706583i	$0.249764\pi$
$174$		0			0
$175$	−13.1091	+	1.77543i	−0.990953	+	0.134210i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−10.6813	−	18.5006i	−0.798359	−	1.38280i	−0.920685	−	0.390308i	$-0.872369\pi$
$179$	−10.6813	−	18.5006i	−0.798359	−	1.38280i	0.122326	−	0.992490i	$-0.460965\pi$
$180$		0			0
$181$	−2.94599			−0.218974			−0.109487	−	0.993988i	$-0.534921\pi$
$181$	−2.94599			−0.218974			−0.109487	+	0.993988i	$0.534921\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	8.29393	+	20.8571i	0.609782	+	1.53344i
$186$		0			0
$187$	−17.9937	+	4.82140i	−1.31583	+	0.352576i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−18.5035	−	10.6830i	−1.33887	−	0.772994i	−0.352226	−	0.935915i	$-0.614575\pi$
$191$	−18.5035	−	10.6830i	−1.33887	−	0.772994i	−0.986639	+	0.162921i	$0.947909\pi$
$192$		0			0
$193$	20.3001	+	5.43940i	1.46123	+	0.391536i	0.899916	−	0.436064i	$-0.143628\pi$
$193$	20.3001	+	5.43940i	1.46123	+	0.391536i	0.561318	+	0.827600i	$0.310294\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	12.0490	−	12.0490i	0.858452	−	0.858452i	−0.132703	−	0.991156i	$-0.542366\pi$
$197$	12.0490	−	12.0490i	0.858452	−	0.858452i	0.991156	+	0.132703i	$0.0423658\pi$
$198$		0			0
$199$	−14.5176	+	8.38174i	−1.02913	+	0.594166i	−0.916734	−	0.399498i	$-0.869184\pi$
$199$	−14.5176	+	8.38174i	−1.02913	+	0.594166i	−0.112391	+	0.993664i	$0.535851\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.39510	−	0.138218i	−0.0979169	−	0.00970097i
$204$		0			0
$205$	−11.8124	+	1.38460i	−0.825011	+	0.0967045i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	7.00431			0.484499
$210$		0			0
$211$	−27.7646			−1.91140			−0.955698	−	0.294350i	$-0.904897\pi$
$211$	−27.7646			−1.91140			−0.955698	+	0.294350i	$0.904897\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−4.52181	−	3.57297i	−0.308385	−	0.243675i
$216$		0			0
$217$	−6.96798	−	15.4023i	−0.473017	−	1.04557i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−25.7654	+	14.8756i	−1.73317	+	1.00064i
$222$		0			0
$223$	−2.85004	+	2.85004i	−0.190853	+	0.190853i	−0.796065	−	0.605212i	$-0.793088\pi$
$223$	−2.85004	+	2.85004i	−0.190853	+	0.190853i	0.605212	+	0.796065i	$0.293088\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−22.9617	−	6.15257i	−1.52402	−	0.408360i	−0.602958	−	0.797773i	$-0.706011\pi$
$227$	−22.9617	−	6.15257i	−1.52402	−	0.408360i	−0.921063	+	0.389413i	$0.872678\pi$
$228$		0			0
$229$	−15.1865	−	8.76794i	−1.00355	−	0.579402i	−0.0942558	−	0.995548i	$-0.530047\pi$
$229$	−15.1865	−	8.76794i	−1.00355	−	0.579402i	−0.909298	+	0.416146i	$0.863380\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.5867	−	2.83669i	0.693555	−	0.185837i	0.105213	−	0.994450i	$-0.466448\pi$
$233$	10.5867	−	2.83669i	0.693555	−	0.185837i	0.588342	+	0.808612i	$0.299781\pi$
$234$		0			0
$235$	−20.8534	+	8.29246i	−1.36033	+	0.540941i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	20.5953			1.33220			0.666098	−	0.745864i	$-0.267963\pi$
$239$	20.5953			1.33220			0.666098	+	0.745864i	$0.267963\pi$
$240$		0			0
$241$	−2.95404	−	5.11654i	−0.190286	−	0.329585i	0.755059	−	0.655657i	$-0.227608\pi$
$241$	−2.95404	−	5.11654i	−0.190286	−	0.329585i	−0.945345	+	0.326072i	$0.894275\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.26364	+	15.6014i	−0.0807310	+	0.996736i
$246$		0			0
$247$	10.8053	−	2.89528i	0.687527	−	0.184222i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			4.60332i			0.290559i	0.989391	+	0.145279i	$0.0464081\pi$
$251$			4.60332i			0.290559i	−0.989391	+	0.145279i	$0.953592\pi$
$252$		0			0
$253$	6.08226	−	6.08226i	0.382389	−	0.382389i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−0.644695	−	2.40603i	−0.0402150	−	0.150084i	0.942899	−	0.333079i	$-0.108088\pi$
$257$	−0.644695	−	2.40603i	−0.0402150	−	0.150084i	−0.983114	+	0.182995i	$0.941421\pi$
$258$		0			0
$259$	26.2058	−	4.31108i	1.62835	−	0.267878i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	2.54756	−	9.50763i	0.157089	−	0.586265i	−0.841828	−	0.539746i	$-0.818520\pi$
$263$	2.54756	−	9.50763i	0.157089	−	0.586265i	0.998917	−	0.0465196i	$-0.0148130\pi$
$264$		0			0
$265$	−0.154159	−	0.0225293i	−0.00946991	−	0.00138396i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.50721	−	11.2708i	−0.396752	−	0.687194i	0.596571	−	0.802560i	$-0.296529\pi$
$269$	−6.50721	−	11.2708i	−0.396752	−	0.687194i	−0.993323	+	0.115366i	$0.963196\pi$
$270$		0			0
$271$	−11.4095	+	19.7619i	−0.693080	+	1.20045i	0.277744	+	0.960655i	$0.410413\pi$
$271$	−11.4095	+	19.7619i	−0.693080	+	1.20045i	−0.970824	+	0.239794i	$0.922920\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−14.0305	+	13.2545i	−0.846070	+	0.799277i
$276$		0			0
$277$	−5.43032	+	20.2662i	−0.326276	+	1.21768i	0.586746	+	0.809771i	$0.300409\pi$
$277$	−5.43032	+	20.2662i	−0.326276	+	1.21768i	−0.913023	+	0.407909i	$0.866258\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	20.0205i		−	1.19433i	−0.802120	−	0.597163i	$-0.796295\pi$
$281$		−	20.0205i		−	1.19433i	0.802120	−	0.597163i	$-0.203705\pi$
$282$		0			0
$283$	6.09241	+	1.63246i	0.362156	+	0.0970395i	0.435309	−	0.900281i	$-0.356639\pi$
$283$	6.09241	+	1.63246i	0.362156	+	0.0970395i	−0.0731523	+	0.997321i	$0.523306\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.38740	+	14.0037i	−0.0818954	+	0.826612i
$288$		0			0
$289$	5.44524	+	3.14381i	0.320308	+	0.184930i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	6.90593	+	6.90593i	0.403449	+	0.403449i	0.879446	−	0.475998i	$-0.157913\pi$
$293$	6.90593	+	6.90593i	0.403449	+	0.403449i	−0.475998	+	0.879446i	$0.657913\pi$
$294$		0			0
$295$	3.85365	−	2.87090i	0.224368	−	0.167151i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	6.86877	−	11.8971i	0.397231	−	0.688025i
$300$		0			0
$301$	−5.27361	+	4.32286i	−0.303966	+	0.249165i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	8.20457	+	3.53591i	0.469792	+	0.202466i
$306$		0			0
$307$	−8.27428	−	8.27428i	−0.472238	−	0.472238i	0.430400	−	0.902638i	$-0.358373\pi$
$307$	−8.27428	−	8.27428i	−0.472238	−	0.472238i	−0.902638	+	0.430400i	$0.858373\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	2.88146	−	1.66361i	0.163393	−	0.0943349i	−0.416074	−	0.909331i	$-0.636594\pi$
$311$	2.88146	−	1.66361i	0.163393	−	0.0943349i	0.579467	+	0.814996i	$0.303261\pi$
$312$		0			0
$313$	4.11127	+	15.3435i	0.232383	+	0.867265i	0.979311	+	0.202360i	$0.0648612\pi$
$313$	4.11127	+	15.3435i	0.232383	+	0.867265i	−0.746928	+	0.664905i	$0.768472\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.58526	−	17.1124i	−0.257534	−	0.961130i	−0.966663	−	0.256052i	$-0.917578\pi$
$317$	−4.58526	−	17.1124i	−0.257534	−	0.961130i	0.709129	−	0.705079i	$-0.249088\pi$
$318$		0			0
$319$	−1.77142	+	1.02273i	−0.0991808	+	0.0572620i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−6.19154	−	6.19154i	−0.344507	−	0.344507i
$324$		0			0
$325$	−16.1655	+	26.2469i	−0.896703	+	1.45592i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.31032	+	26.2012i	0.237636	+	1.44452i
$330$		0			0
$331$	8.12021	−	14.0646i	0.446327	−	0.773061i	−0.551817	−	0.833965i	$-0.686065\pi$
$331$	8.12021	−	14.0646i	0.446327	−	0.773061i	0.998144	+	0.0609044i	$0.0193985\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−11.6586	−	1.70382i	−0.636977	−	0.0930898i
$336$		0			0
$337$	−16.1092	−	16.1092i	−0.877523	−	0.877523i	0.115755	−	0.993278i	$-0.463071\pi$
$337$	−16.1092	−	16.1092i	−0.877523	−	0.877523i	−0.993278	+	0.115755i	$0.963071\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−21.3606	−	12.3326i	−1.15674	−	0.667846i
$342$		0			0
$343$	17.7135	+	5.40679i	0.956437	+	0.291939i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	22.1906	+	5.94596i	1.19126	+	0.319196i	0.799382	−	0.600823i	$-0.205160\pi$
$347$	22.1906	+	5.94596i	1.19126	+	0.319196i	0.391873	+	0.920019i	$0.371827\pi$
$348$		0			0
$349$		−	23.7988i		−	1.27392i	−0.770897	−	0.636960i	$-0.780191\pi$
$349$		−	23.7988i		−	1.27392i	0.770897	−	0.636960i	$-0.219809\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	7.89564	−	29.4669i	0.420242	−	1.56837i	−0.353856	−	0.935300i	$-0.615130\pi$
$353$	7.89564	−	29.4669i	0.420242	−	1.56837i	0.774098	−	0.633066i	$-0.218204\pi$
$354$		0			0
$355$	−19.3680	+	2.27024i	−1.02795	+	0.120492i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	13.3888	−	23.1901i	0.706634	−	1.22393i	−0.259465	−	0.965752i	$-0.583546\pi$
$359$	13.3888	−	23.1901i	0.706634	−	1.22393i	0.966099	−	0.258173i	$-0.0831204\pi$
$360$		0			0
$361$	−7.85384	−	13.6032i	−0.413360	−	0.715960i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	1.19142	−	8.15240i	0.0623616	−	0.426716i
$366$		0			0
$367$	−8.58794	+	32.0506i	−0.448287	+	1.67303i	0.258822	+	0.965925i	$0.416666\pi$
$367$	−8.58794	+	32.0506i	−0.448287	+	1.67303i	−0.707109	+	0.707104i	$0.750001\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.0650336	+	0.172488i	−0.00337637	+	0.00895515i
$372$		0			0
$373$	1.08581	+	4.05231i	0.0562212	+	0.209820i	0.988322	−	0.152378i	$-0.0486930\pi$
$373$	1.08581	+	4.05231i	0.0562212	+	0.209820i	−0.932101	+	0.362198i	$0.882026\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−2.30997	+	2.30997i	−0.118969	+	0.118969i
$378$		0			0
$379$		−	19.4036i		−	0.996694i	−0.866978	−	0.498347i	$-0.833941\pi$
$379$		−	19.4036i		−	0.996694i	0.866978	−	0.498347i	$-0.166059\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−30.0852	+	8.06130i	−1.53728	+	0.411913i	−0.925386	−	0.379026i	$-0.876259\pi$
$383$	−30.0852	+	8.06130i	−1.53728	+	0.411913i	−0.611895	+	0.790939i	$0.709593\pi$
$384$		0			0
$385$	11.7716	+	19.5699i	0.599934	+	0.997375i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−15.0117	−	26.0011i	−0.761126	−	1.31831i	−0.942271	−	0.334852i	$-0.891314\pi$
$389$	−15.0117	−	26.0011i	−0.761126	−	1.31831i	0.181145	−	0.983456i	$-0.442020\pi$
$390$		0			0
$391$	−10.7530			−0.543801
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.576623	−	1.33797i	0.0290131	−	0.0673206i
$396$		0			0
$397$	−20.1168	+	5.39027i	−1.00963	+	0.270530i	−0.725476	−	0.688248i	$-0.758380\pi$
$397$	−20.1168	+	5.39027i	−1.00963	+	0.270530i	−0.284156	+	0.958778i	$0.591713\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−13.5045	−	7.79683i	−0.674382	−	0.389355i	0.123353	−	0.992363i	$-0.460635\pi$
$401$	−13.5045	−	7.79683i	−0.674382	−	0.389355i	−0.797735	+	0.603008i	$0.793969\pi$
$402$		0			0
$403$	−38.0501	−	10.1955i	−1.89541	−	0.507874i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	27.3998	−	27.3998i	1.35816	−	1.35816i
$408$		0			0
$409$	−0.713481	+	0.411929i	−0.0352794	+	0.0203686i	−0.517536	−	0.855661i	$-0.673151\pi$
$409$	−0.713481	+	0.411929i	−0.0352794	+	0.0203686i	0.482257	+	0.876030i	$0.339817\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.34364	−	5.18046i	−0.115323	−	0.254914i
$414$		0			0
$415$	8.90137	−	11.2652i	0.436951	−	0.552988i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−21.3059			−1.04086			−0.520430	−	0.853904i	$-0.674229\pi$
$419$	−21.3059			−1.04086			−0.520430	+	0.853904i	$0.674229\pi$
$420$		0			0
$421$	−9.61579			−0.468645			−0.234322	−	0.972159i	$-0.575287\pi$
$421$	−9.61579			−0.468645			−0.234322	+	0.972159i	$0.575287\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	24.1189	+	0.685935i	1.16994	+	0.0332727i
$426$		0			0
$427$	6.16229	−	8.58900i	0.298214	−	0.415651i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−21.4716	+	12.3966i	−1.03425	+	0.597124i	−0.918199	−	0.396119i	$-0.870357\pi$
$431$	−21.4716	+	12.3966i	−1.03425	+	0.597124i	−0.116051	+	0.993243i	$0.537023\pi$
$432$		0			0
$433$	−1.18428	+	1.18428i	−0.0569126	+	0.0569126i	−0.734990	−	0.678078i	$-0.762813\pi$
$433$	−1.18428	+	1.18428i	−0.0569126	+	0.0569126i	0.678078	+	0.734990i	$0.262813\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	3.90536	+	1.04644i	0.186819	+	0.0500579i
$438$		0			0
$439$	28.1621	+	16.2594i	1.34410	+	0.776018i	0.987407	−	0.158203i	$-0.0505701\pi$
$439$	28.1621	+	16.2594i	1.34410	+	0.776018i	0.356695	+	0.934221i	$0.383903\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−7.28961	+	1.95325i	−0.346340	+	0.0928015i	−0.427796	−	0.903875i	$-0.640710\pi$
$443$	−7.28961	+	1.95325i	−0.346340	+	0.0928015i	0.0814558	+	0.996677i	$0.474043\pi$
$444$		0			0
$445$	30.1529	+	12.9949i	1.42938	+	0.616019i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−4.80279			−0.226658			−0.113329	−	0.993558i	$-0.536151\pi$
$449$	−4.80279			−0.226658			−0.113329	+	0.993558i	$0.536151\pi$
$450$		0			0
$451$	10.2660	+	17.7812i	0.483405	+	0.837282i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	26.2490	+	25.3240i	1.23057	+	1.18721i
$456$		0			0
$457$	28.6180	−	7.66817i	1.33869	−	0.358702i	0.482744	−	0.875761i	$-0.339640\pi$
$457$	28.6180	−	7.66817i	1.33869	−	0.358702i	0.855949	+	0.517060i	$0.172973\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$			34.5690i			1.61004i	0.593249	+	0.805019i	$0.297845\pi$
$461$			34.5690i			1.61004i	−0.593249	+	0.805019i	$0.702155\pi$
$462$		0			0
$463$	14.1353	−	14.1353i	0.656924	−	0.656924i	−0.297727	−	0.954651i	$-0.596229\pi$
$463$	14.1353	−	14.1353i	0.656924	−	0.656924i	0.954651	+	0.297727i	$0.0962285\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	1.59053	+	5.93593i	0.0736009	+	0.274682i	0.992912	−	0.118848i	$-0.0379202\pi$
$467$	1.59053	+	5.93593i	0.0736009	+	0.274682i	−0.919312	+	0.393531i	$0.871254\pi$
$468$		0			0
$469$	−4.91830	+	13.0448i	−0.227106	+	0.602352i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.57501	+	9.61008i	−0.118399	+	0.441872i
$474$		0			0
$475$	−8.69295	−	2.59628i	−0.398860	−	0.119125i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−10.8482	−	18.7896i	−0.495667	−	0.858520i	0.504321	−	0.863516i	$-0.331743\pi$
$479$	−10.8482	−	18.7896i	−0.495667	−	0.858520i	−0.999988	+	0.00499651i	$0.998410\pi$
$480$		0			0
$481$	30.9429	−	53.5946i	1.41087	−	2.44371i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−1.25345	+	1.58632i	−0.0569162	+	0.0720309i
$486$		0			0
$487$	0.978941	−	3.65346i	0.0443601	−	0.165554i	−0.940192	−	0.340644i	$-0.889355\pi$
$487$	0.978941	−	3.65346i	0.0443601	−	0.165554i	0.984552	+	0.175090i	$0.0560216\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			35.0066i			1.57982i	0.613220	+	0.789912i	$0.289874\pi$
$491$			35.0066i			1.57982i	−0.613220	+	0.789912i	$0.710126\pi$
$492$		0			0
$493$	2.46993	+	0.661815i	0.111240	+	0.0298066i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−2.27483	+	22.9610i	−0.102040	+	1.02994i
$498$		0			0
$499$	33.2567	+	19.2008i	1.48878	+	0.859545i	0.999918	−	0.0128184i	$-0.00408033\pi$
$499$	33.2567	+	19.2008i	1.48878	+	0.859545i	0.488858	+	0.872363i	$0.337414\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−7.66899	−	7.66899i	−0.341943	−	0.341943i	0.515154	−	0.857098i	$-0.327735\pi$
$503$	−7.66899	−	7.66899i	−0.341943	−	0.341943i	−0.857098	+	0.515154i	$0.827735\pi$
$504$		0			0
$505$	−23.5437	−	31.6031i	−1.04768	−	1.40632i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.15889	−	12.3996i	0.317312	−	0.549601i	−0.662614	−	0.748961i	$-0.730553\pi$
$509$	7.15889	−	12.3996i	0.317312	−	0.549601i	0.979926	+	0.199360i	$0.0638864\pi$
$510$		0			0
$511$	−9.12171	−	3.43917i	−0.403521	−	0.152140i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	13.4337	−	5.34196i	0.591958	−	0.235395i
$516$		0			0
$517$	27.3949	+	27.3949i	1.20483	+	1.20483i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	8.94536	−	5.16460i	0.391903	−	0.226265i	−0.291081	−	0.956698i	$-0.594015\pi$
$521$	8.94536	−	5.16460i	0.391903	−	0.226265i	0.682984	+	0.730433i	$0.260682\pi$
$522$		0			0
$523$	−9.42250	−	35.1652i	−0.412017	−	1.53767i	−0.790736	−	0.612157i	$-0.790302\pi$
$523$	−9.42250	−	35.1652i	−0.412017	−	1.53767i	0.378719	−	0.925512i	$-0.376365\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	7.98046	+	29.7835i	0.347634	+	1.29739i
$528$		0			0
$529$	−15.6186	+	9.01743i	−0.679072	+	0.392062i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	23.1869	+	23.1869i	1.00434	+	1.00434i
$534$		0			0
$535$	−22.8422	+	9.08331i	−0.987555	+	0.392706i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	25.5977	−	8.65633i	1.10257	−	0.372854i
$540$		0			0
$541$	−0.616603	+	1.06799i	−0.0265098	+	0.0459164i	−0.878976	−	0.476866i	$-0.841773\pi$
$541$	−0.616603	+	1.06799i	−0.0265098	+	0.0459164i	0.852466	+	0.522782i	$0.175106\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	16.2016	+	21.7476i	0.694001	+	0.931566i
$546$		0			0
$547$	13.8969	+	13.8969i	0.594188	+	0.594188i	0.938760	−	0.344572i	$-0.111976\pi$
$547$	13.8969	+	13.8969i	0.594188	+	0.594188i	−0.344572	+	0.938760i	$0.611976\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.832644	−	0.480727i	−0.0354718	−	0.0204797i
$552$		0			0
$553$	−1.40066	−	1.00492i	−0.0595622	−	0.0427337i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−20.7434	−	5.55819i	−0.878928	−	0.235508i	−0.208983	−	0.977919i	$-0.567015\pi$
$557$	−20.7434	−	5.55819i	−0.878928	−	0.235508i	−0.669944	+	0.742411i	$0.733682\pi$
$558$		0			0
$559$			15.8896i			0.672057i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−8.06309	+	30.0918i	−0.339819	+	1.26822i	0.558731	+	0.829349i	$0.311288\pi$
$563$	−8.06309	+	30.0918i	−0.339819	+	1.26822i	−0.898550	+	0.438871i	$0.855378\pi$
$564$		0			0
$565$	−6.65558	+	8.42304i	−0.280002	+	0.354360i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.95163	+	17.2367i	−0.417194	+	0.722601i	−0.995656	−	0.0931081i	$-0.970320\pi$
$569$	−9.95163	+	17.2367i	−0.417194	+	0.722601i	0.578462	+	0.815709i	$0.303653\pi$
$570$		0			0
$571$	1.67631	+	2.90345i	0.0701512	+	0.121505i	0.898967	−	0.438015i	$-0.144318\pi$
$571$	1.67631	+	2.90345i	0.0701512	+	0.121505i	−0.828816	+	0.559521i	$0.810985\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−9.80311	+	5.29410i	−0.408818	+	0.220779i
$576$		0			0
$577$	6.57214	−	24.5276i	0.273602	−	1.02110i	−0.683171	−	0.730259i	$-0.739400\pi$
$577$	6.57214	−	24.5276i	0.273602	−	1.02110i	0.956773	−	0.290837i	$-0.0939338\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−10.7696	−	13.1382i	−0.446797	−	0.545064i
$582$		0			0
$583$	0.0696119	+	0.259795i	0.00288303	+	0.0107596i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.0794189	+	0.0794189i	−0.00327797	+	0.00327797i	−0.708744	−	0.705466i	$-0.750738\pi$
$587$	−0.0794189	+	0.0794189i	−0.00327797	+	0.00327797i	0.705466	+	0.708744i	$0.250738\pi$
$588$		0			0
$589$		−	11.5937i		−	0.477708i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	19.8265	−	5.31249i	0.814177	−	0.218158i	0.172378	−	0.985031i	$-0.444855\pi$
$593$	19.8265	−	5.31249i	0.814177	−	0.218158i	0.641799	+	0.766873i	$0.278188\pi$
$594$		0			0
$595$	6.89345	−	27.7046i	0.282604	−	1.13578i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	17.5330	+	30.3680i	0.716378	+	1.24080i	0.962426	+	0.271545i	$0.0875345\pi$
$599$	17.5330	+	30.3680i	0.716378	+	1.24080i	−0.246048	+	0.969258i	$0.579132\pi$
$600$		0			0
$601$	35.2747			1.43889			0.719443	−	0.694551i	$-0.244397\pi$
$601$	35.2747			1.43889			0.719443	+	0.694551i	$0.244397\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	8.01160	+	3.45275i	0.325718	+	0.140374i
$606$		0			0
$607$	−24.3142	+	6.51497i	−0.986883	+	0.264435i	−0.715941	−	0.698161i	$-0.754002\pi$
$607$	−24.3142	+	6.51497i	−0.986883	+	0.264435i	−0.270942	+	0.962596i	$0.587335\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	53.5852	+	30.9374i	2.16782	+	1.25159i
$612$		0			0
$613$	22.0777	+	5.91571i	0.891711	+	0.238933i	0.675453	−	0.737403i	$-0.263948\pi$
$613$	22.0777	+	5.91571i	0.891711	+	0.238933i	0.216258	+	0.976336i	$0.430615\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	13.9219	−	13.9219i	0.560474	−	0.560474i	−0.368968	−	0.929442i	$-0.620289\pi$
$617$	13.9219	−	13.9219i	0.560474	−	0.560474i	0.929442	+	0.368968i	$0.120289\pi$
$618$		0			0
$619$	−12.1371	+	7.00734i	−0.487830	+	0.281649i	−0.723674	−	0.690142i	$-0.757548\pi$
$619$	−12.1371	+	7.00734i	−0.487830	+	0.281649i	0.235844	+	0.971791i	$0.424215\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	22.6472	−	31.5657i	0.907342	−	1.26465i
$624$		0			0
$625$	22.3261	−	11.2493i	0.893042	−	0.449973i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−48.4407			−1.93146
$630$		0			0
$631$	5.57174			0.221807			0.110904	−	0.993831i	$-0.464625\pi$
$631$	5.57174			0.221807			0.110904	+	0.993831i	$0.464625\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	9.37972	−	11.8706i	0.372223	−	0.471070i
$636$		0			0
$637$	35.9105	−	23.9348i	1.42283	−	0.948332i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	4.03096	−	2.32727i	0.159213	−	0.0919218i	−0.418277	−	0.908320i	$-0.637366\pi$
$641$	4.03096	−	2.32727i	0.159213	−	0.0919218i	0.577490	+	0.816398i	$0.304032\pi$
$642$		0			0
$643$	−20.4342	+	20.4342i	−0.805845	+	0.805845i	−0.984002	−	0.178157i	$-0.942987\pi$
$643$	−20.4342	+	20.4342i	−0.805845	+	0.805845i	0.178157	+	0.984002i	$0.442987\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−14.6414	−	3.92315i	−0.575613	−	0.154235i	−0.0407433	−	0.999170i	$-0.512973\pi$
$647$	−14.6414	−	3.92315i	−0.575613	−	0.154235i	−0.534870	+	0.844935i	$0.679639\pi$
$648$		0			0
$649$	−7.18452	−	4.14798i	−0.282017	−	0.162823i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−16.5659	+	4.43881i	−0.648272	+	0.173704i	−0.567948	−	0.823065i	$-0.692262\pi$
$653$	−16.5659	+	4.43881i	−0.648272	+	0.173704i	−0.0803246	+	0.996769i	$0.525596\pi$
$654$		0			0
$655$	13.6735	−	31.7274i	0.534267	−	1.23969i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.43550			0.0559190			0.0279595	−	0.999609i	$-0.491099\pi$
$659$	1.43550			0.0559190			0.0279595	+	0.999609i	$0.491099\pi$
$660$		0			0
$661$	2.10565	+	3.64709i	0.0819001	+	0.141855i	0.904066	−	0.427393i	$-0.140568\pi$
$661$	2.10565	+	3.64709i	0.0819001	+	0.141855i	−0.822166	+	0.569248i	$0.807234\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−5.19973	+	9.39117i	−0.201637	+	0.364174i
$666$		0			0
$667$	−1.14048	+	0.305590i	−0.0441595	+	0.0118325i
$668$		0			0
$669$		0			0
$670$		0			0
$671$		−	15.4234i		−	0.595412i
$672$		0			0
$673$	−14.8035	+	14.8035i	−0.570634	+	0.570634i	−0.932305	−	0.361672i	$-0.882206\pi$
$673$	−14.8035	+	14.8035i	−0.570634	+	0.570634i	0.361672	+	0.932305i	$0.382206\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	5.84912	+	21.8292i	0.224800	+	0.838964i	0.982485	+	0.186344i	$0.0596638\pi$
$677$	5.84912	+	21.8292i	0.224800	+	0.838964i	−0.757685	+	0.652621i	$0.773670\pi$
$678$		0			0
$679$	1.51652	+	1.85006i	0.0581987	+	0.0709988i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	7.19365	−	26.8471i	0.275257	−	1.02727i	−0.680411	−	0.732830i	$-0.738199\pi$
$683$	7.19365	−	26.8471i	0.275257	−	1.02727i	0.955669	−	0.294444i	$-0.0951344\pi$
$684$		0			0
$685$	−3.57872	+	24.4878i	−0.136736	+	0.935630i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.214776	+	0.372003i	0.00818232	+	0.0141722i
$690$		0			0
$691$	11.6433	−	20.1668i	0.442932	−	0.767181i	−0.554973	−	0.831868i	$-0.687271\pi$
$691$	11.6433	−	20.1668i	0.442932	−	0.767181i	0.997906	+	0.0646868i	$0.0206048\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−45.7064	+	5.35752i	−1.73374	+	0.203222i
$696$		0			0
$697$	6.64314	−	24.7925i	0.251627	−	0.939085i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	20.5920i		−	0.777747i	−0.921291	−	0.388874i	$-0.872864\pi$
$701$		−	20.5920i		−	0.777747i	0.921291	−	0.388874i	$-0.127136\pi$
$702$		0			0
$703$	17.5931	+	4.71406i	0.663536	+	0.177794i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−42.4840	+	19.2197i	−1.59777	+	0.722832i
$708$		0			0
$709$	11.2705	+	6.50703i	0.423273	+	0.244377i	0.696476	−	0.717580i	$-0.254750\pi$
$709$	11.2705	+	6.50703i	0.423273	+	0.244377i	−0.273204	+	0.961956i	$0.588083\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−10.0675	−	10.0675i	−0.377029	−	0.377029i
$714$		0			0
$715$	52.6567	+	7.69541i	1.96925	+	0.287792i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	0.464750	−	0.804971i	0.0173323	−	0.0300204i	−0.857229	−	0.514935i	$-0.827816\pi$
$719$	0.464750	−	0.804971i	0.0173323	−	0.0300204i	0.874561	+	0.484915i	$0.161149\pi$
$720$		0			0
$721$	−2.77669	−	16.8787i	−0.103409	−	0.628595i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	2.57758	−	0.612687i	0.0957291	−	0.0227546i
$726$		0			0
$727$	17.0935	+	17.0935i	0.633963	+	0.633963i	0.949060	−	0.315096i	$-0.102037\pi$
$727$	17.0935	+	17.0935i	0.633963	+	0.633963i	−0.315096	+	0.949060i	$0.602037\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	10.7711	−	6.21872i	0.398385	−	0.230008i
$732$		0			0
$733$	−0.0964005	−	0.359771i	−0.00356063	−	0.0132885i	0.964123	−	0.265457i	$-0.0855229\pi$
$733$	−0.0964005	−	0.359771i	−0.00356063	−	0.0132885i	−0.967683	+	0.252169i	$0.918856\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.26455	+	19.6476i	0.193922	+	0.723727i
$738$		0			0
$739$	3.86240	−	2.22996i	0.142081	−	0.0820302i	−0.427275	−	0.904122i	$-0.640526\pi$
$739$	3.86240	−	2.22996i	0.142081	−	0.0820302i	0.569355	+	0.822092i	$0.307193\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	17.9724	+	17.9724i	0.659344	+	0.659344i	0.955225	−	0.295881i	$-0.0956131\pi$
$743$	17.9724	+	17.9724i	0.659344	+	0.659344i	−0.295881	+	0.955225i	$0.595613\pi$
$744$		0			0
$745$	−42.5465	−	18.3362i	−1.55878	−	0.671786i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	4.72140	+	28.7000i	0.172516	+	1.04868i
$750$		0			0
$751$	0.282773	−	0.489776i	0.0103185	−	0.0178722i	−0.860820	−	0.508909i	$-0.830049\pi$
$751$	0.282773	−	0.489776i	0.0103185	−	0.0178722i	0.871139	+	0.491037i	$0.163382\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	14.0830	−	10.4916i	0.512534	−	0.381829i
$756$		0			0
$757$	9.83235	+	9.83235i	0.357363	+	0.357363i	0.862840	−	0.505477i	$-0.168684\pi$
$757$	9.83235	+	9.83235i	0.357363	+	0.357363i	−0.505477	+	0.862840i	$0.668684\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−5.51661	−	3.18501i	−0.199977	−	0.115457i	0.396668	−	0.917962i	$-0.370166\pi$
$761$	−5.51661	−	3.18501i	−0.199977	−	0.115457i	−0.596645	+	0.802506i	$0.703500\pi$
$762$		0			0
$763$	29.2353	−	13.2260i	1.05839	−	0.478815i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−12.7979	−	3.42919i	−0.462106	−	0.123821i
$768$		0			0
$769$			10.5325i			0.379813i	0.981802	+	0.189906i	$0.0608185\pi$
$769$			10.5325i			0.379813i	−0.981802	+	0.189906i	$0.939182\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	7.28996	−	27.2065i	0.262202	−	0.978550i	−0.701739	−	0.712434i	$-0.747593\pi$
$773$	7.28996	−	27.2065i	0.262202	−	0.978550i	0.963941	−	0.266116i	$-0.0857404\pi$
$774$		0			0
$775$	21.9391	+	23.2235i	0.788075	+	0.834212i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−4.82543	+	8.35789i	−0.172889	+	0.299452i
$780$		0			0
$781$	16.8324	+	29.1547i	0.602312	+	1.04324i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−43.0889	−	6.29714i	−1.53791	−	0.224755i
$786$		0			0
$787$	7.73346	−	28.8617i	0.275668	−	1.02881i	−0.679724	−	0.733468i	$-0.737901\pi$
$787$	7.73346	−	28.8617i	0.275668	−	1.02881i	0.955392	−	0.295339i	$-0.0954327\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	8.05244	+	9.82346i	0.286312	+	0.349282i
$792$		0			0
$793$	−6.37535	−	23.7931i	−0.226395	−	0.844918i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	18.0036	−	18.0036i	0.637720	−	0.637720i	−0.312273	−	0.949993i	$-0.601090\pi$
$797$	18.0036	−	18.0036i	0.637720	−	0.637720i	0.949993	+	0.312273i	$0.101090\pi$
$798$		0			0
$799$		−	48.4321i		−	1.71340i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−13.7388	+	3.68129i	−0.484830	+	0.129910i
$804$		0			0
$805$	3.63968	+	12.6701i	0.128282	+	0.446564i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	10.1383	+	17.5601i	0.356445	+	0.617380i	0.987364	−	0.158468i	$-0.0506555\pi$
$809$	10.1383	+	17.5601i	0.356445	+	0.617380i	−0.630920	+	0.775848i	$0.717322\pi$
$810$		0			0
$811$	−7.90815			−0.277693			−0.138846	−	0.990314i	$-0.544339\pi$
$811$	−7.90815			−0.277693			−0.138846	+	0.990314i	$0.544339\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−50.1268	+	19.9332i	−1.75586	+	0.698228i
$816$		0			0
$817$	−4.51714	+	1.21036i	−0.158035	+	0.0423453i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	43.8092	+	25.2932i	1.52895	+	0.882740i	0.999406	+	0.0344585i	$0.0109706\pi$
$821$	43.8092	+	25.2932i	1.52895	+	0.882740i	0.529545	+	0.848282i	$0.322363\pi$
$822$		0			0
$823$	−14.4074	−	3.86045i	−0.502210	−	0.134567i	−0.00118453	−	0.999999i	$-0.500377\pi$
$823$	−14.4074	−	3.86045i	−0.502210	−	0.134567i	−0.501025	+	0.865433i	$0.667044\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	27.5761	−	27.5761i	0.958914	−	0.958914i	−0.0402745	−	0.999189i	$-0.512823\pi$
$827$	27.5761	−	27.5761i	0.958914	−	0.958914i	0.999189	+	0.0402745i	$0.0128232\pi$
$828$		0			0
$829$	−17.4701	+	10.0864i	−0.606763	+	0.350315i	−0.771697	−	0.635990i	$-0.780592\pi$
$829$	−17.4701	+	10.0864i	−0.606763	+	0.350315i	0.164935	+	0.986304i	$0.447259\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−30.2792	−	14.9755i	−1.04911	−	0.518869i
$834$		0			0
$835$	−3.76059	−	2.97148i	−0.130141	−	0.102832i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	28.6353			0.988600			0.494300	−	0.869291i	$-0.335424\pi$
$839$	28.6353			0.988600			0.494300	+	0.869291i	$0.335424\pi$
$840$		0			0
$841$	−28.7192			−0.990318
$842$		0			0
$843$		0			0
$844$		0			0
$845$	55.5416	−	6.51037i	1.91069	−	0.223963i
$846$		0			0
$847$	6.01735	−	8.38699i	0.206759	−	0.288180i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	19.3706	−	11.1836i	0.664017	−	0.383370i
$852$		0			0
$853$	8.95864	−	8.95864i	0.306738	−	0.306738i	−0.536905	−	0.843643i	$-0.680407\pi$
$853$	8.95864	−	8.95864i	0.306738	−	0.306738i	0.843643	+	0.536905i	$0.180407\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−17.8054	−	4.77095i	−0.608222	−	0.162973i	−0.0584542	−	0.998290i	$-0.518617\pi$
$857$	−17.8054	−	4.77095i	−0.608222	−	0.162973i	−0.549768	+	0.835317i	$0.685284\pi$
$858$		0			0
$859$	0.245195	+	0.141563i	0.00836594	+	0.00483008i	0.504177	−	0.863600i	$-0.331796\pi$
$859$	0.245195	+	0.141563i	0.00836594	+	0.00483008i	−0.495811	+	0.868430i	$0.665129\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	37.5592	−	10.0640i	1.27853	−	0.342581i	0.445237	−	0.895413i	$-0.353119\pi$
$863$	37.5592	−	10.0640i	1.27853	−	0.342581i	0.833293	+	0.552831i	$0.186453\pi$
$864$		0			0
$865$	10.8816	+	27.3644i	0.369985	+	0.930418i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.51518			−0.0853218
$870$		0			0
$871$	16.2429	+	28.1335i	0.550370	+	0.953268i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−7.35555	−	28.6513i	−0.248663	−	0.968590i
$876$		0			0
$877$	−46.4154	+	12.4370i	−1.56734	+	0.419967i	−0.934977	−	0.354708i	$-0.884580\pi$
$877$	−46.4154	+	12.4370i	−1.56734	+	0.419967i	−0.632360	+	0.774675i	$0.717914\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	58.5090i		−	1.97122i	−0.169039	−	0.985609i	$-0.554066\pi$
$881$		−	58.5090i		−	1.97122i	0.169039	−	0.985609i	$-0.445934\pi$
$882$		0			0
$883$	13.2248	−	13.2248i	0.445048	−	0.445048i	−0.448656	−	0.893704i	$-0.648097\pi$
$883$	13.2248	−	13.2248i	0.445048	−	0.445048i	0.893704	+	0.448656i	$0.148097\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.9654	+	48.3874i	0.435334	+	1.62469i	0.740265	+	0.672315i	$0.234700\pi$
$887$	12.9654	+	48.3874i	0.435334	+	1.62469i	−0.304931	+	0.952374i	$0.598633\pi$
$888$		0			0
$889$	−11.3483	−	13.8442i	−0.380610	−	0.464320i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.71322	+	17.5900i	−0.157722	+	0.588627i
$894$		0			0
$895$	38.3067	−	28.5378i	1.28045	−	0.953914i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	1.69284	+	2.93209i	0.0564595	+	0.0977907i
$900$		0			0
$901$	0.168115	−	0.291183i	0.00560071	−	0.00970071i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.766903	−	6.54265i	−0.0254927	−	0.217485i
$906$		0			0
$907$	−6.56292	+	24.4932i	−0.217918	+	0.813282i	0.767201	+	0.641407i	$0.221649\pi$
$907$	−6.56292	+	24.4932i	−0.217918	+	0.813282i	−0.985119	+	0.171875i	$0.945018\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			49.8629i			1.65203i	0.563647	+	0.826016i	$0.309398\pi$
$911$			49.8629i			1.65203i	−0.563647	+	0.826016i	$0.690602\pi$
$912$		0			0
$913$	−23.9416	−	6.41515i	−0.792353	−	0.212310i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−33.2140	−	23.8298i	−1.09682	−	0.786929i
$918$		0			0
$919$	−4.69174	−	2.70878i	−0.154766	−	0.0893543i	0.420617	−	0.907238i	$-0.361814\pi$
$919$	−4.69174	−	2.70878i	−0.154766	−	0.0893543i	−0.575383	+	0.817884i	$0.695147\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	38.0182	+	38.0182i	1.25138	+	1.25138i
$924$		0			0
$925$	−44.1617	+	23.8492i	−1.45203	+	0.784157i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−11.7139	+	20.2890i	−0.384319	+	0.665660i	−0.991674	−	0.128770i	$-0.958897\pi$
$929$	−11.7139	+	20.2890i	−0.384319	+	0.665660i	0.607355	+	0.794430i	$0.292230\pi$
$930$		0			0
$931$	9.53970	+	8.38557i	0.312651	+	0.274826i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−15.3918	−	38.7065i	−0.503366	−	1.26584i
$936$		0			0
$937$	23.8511	+	23.8511i	0.779183	+	0.779183i	0.979692	−	0.200509i	$-0.0642596\pi$
$937$	23.8511	+	23.8511i	0.779183	+	0.779183i	−0.200509	+	0.979692i	$0.564260\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−16.4465	+	9.49537i	−0.536140	+	0.309540i	−0.743513	−	0.668722i	$-0.766842\pi$
$941$	−16.4465	+	9.49537i	−0.536140	+	0.309540i	0.207373	+	0.978262i	$0.433508\pi$
$942$		0			0
$943$	3.06744	+	11.4479i	0.0998897	+	0.372794i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−2.48186	−	9.26242i	−0.0806495	−	0.300988i	0.913805	−	0.406152i	$-0.133130\pi$
$947$	−2.48186	−	9.26242i	−0.0806495	−	0.300988i	−0.994455	+	0.105164i	$0.966463\pi$
$948$		0			0
$949$	−19.6727	+	11.3580i	−0.638602	+	0.368697i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	23.2105	+	23.2105i	0.751862	+	0.751862i	0.974827	−	0.222965i	$-0.0715734\pi$
$953$	23.2105	+	23.2105i	0.751862	+	0.751862i	−0.222965	+	0.974827i	$0.571573\pi$
$954$		0			0
$955$	18.9086	−	43.8747i	0.611869	−	1.41975i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	27.3994	+	10.3304i	0.884771	+	0.333587i
$960$		0			0
$961$	−4.91306	+	8.50967i	−0.158486	+	0.274505i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.79562	+	46.4998i	−0.218759	+	1.49688i
$966$		0			0
$967$	−13.8682	−	13.8682i	−0.445971	−	0.445971i	0.448042	−	0.894013i	$-0.352122\pi$
$967$	−13.8682	−	13.8682i	−0.445971	−	0.445971i	−0.894013	+	0.448042i	$0.852122\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−33.6878	−	19.4497i	−1.08109	−	0.624170i	−0.149903	−	0.988701i	$-0.547896\pi$
$971$	−33.6878	−	19.4497i	−1.08109	−	0.624170i	−0.931191	+	0.364531i	$0.881229\pi$
$972$		0			0
$973$	−5.36835	+	54.1855i	−0.172101	+	1.73711i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	9.06640	+	2.42933i	0.290060	+	0.0777213i	0.400915	−	0.916115i	$-0.368692\pi$
$977$	9.06640	+	2.42933i	0.290060	+	0.0777213i	−0.110855	+	0.993837i	$0.535359\pi$
$978$		0			0
$979$		−	56.6829i		−	1.81159i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−13.7669	+	51.3787i	−0.439095	+	1.63873i	0.291977	+	0.956425i	$0.405687\pi$
$983$	−13.7669	+	51.3787i	−0.439095	+	1.63873i	−0.731072	+	0.682300i	$0.760980\pi$
$984$		0			0
$985$	29.8957	+	23.6225i	0.952555	+	0.752675i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.87147	+	4.97353i	−0.0913074	+	0.158149i
$990$		0			0
$991$	−30.3683	−	52.5994i	−0.964679	−	1.67087i	−0.710474	−	0.703724i	$-0.751519\pi$
$991$	−30.3683	−	52.5994i	−0.964679	−	1.67087i	−0.254206	−	0.967150i	$-0.581814\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−22.3939	−	30.0596i	−0.709935	−	0.952955i
$996$		0			0
$997$	5.33046	−	19.8936i	0.168817	−	0.630035i	−0.828705	−	0.559686i	$-0.810922\pi$
$997$	5.33046	−	19.8936i	0.168817	−	0.630035i	0.997522	−	0.0703495i	$-0.0224115\pi$
$998$		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.737.9	yes	64
3.2	odd	2	inner	1260.2.ej.a.737.8	yes	64
5.3	odd	4	inner	1260.2.ej.a.233.14	yes	64
7.4	even	3	inner	1260.2.ej.a.557.3	yes	64
15.8	even	4	inner	1260.2.ej.a.233.3	yes	64
21.11	odd	6	inner	1260.2.ej.a.557.14	yes	64
35.18	odd	12	inner	1260.2.ej.a.53.8	✓	64
105.53	even	12	inner	1260.2.ej.a.53.9	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.ej.a.53.8	✓	64	35.18	odd	12	inner
1260.2.ej.a.53.9	yes	64	105.53	even	12	inner
1260.2.ej.a.233.3	yes	64	15.8	even	4	inner
1260.2.ej.a.233.14	yes	64	5.3	odd	4	inner
1260.2.ej.a.557.3	yes	64	7.4	even	3	inner
1260.2.ej.a.557.14	yes	64	21.11	odd	6	inner
1260.2.ej.a.737.8	yes	64	3.2	odd	2	inner
1260.2.ej.a.737.9	yes	64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.260321 + 2.22086i) q^{5} +(2.63286 + 0.260847i) q^{7} +O(q^{10})\)	\(q+(0.260321 + 2.22086i) q^{5} +(2.63286 + 0.260847i) q^{7} +(3.34307 - 1.93012i) q^{11} +(4.35942 - 4.35942i) q^{13} +(-4.66129 - 1.24899i) q^{17} +(1.57138 + 0.907238i) q^{19} +(2.15233 - 0.576716i) q^{23} +(-4.86447 + 1.15627i) q^{25} -0.529880 q^{29} +(-3.19477 - 5.53350i) q^{31} +(0.106084 + 5.91513i) q^{35} +(9.69597 - 2.59803i) q^{37} +5.31881i q^{41} +(-1.82244 + 1.82244i) q^{43} +(2.59757 + 9.69426i) q^{47} +(6.86392 + 1.37355i) q^{49} +(-0.0180330 + 0.0673002i) q^{53} +(5.15680 + 6.92204i) q^{55} +(-1.07454 - 1.86116i) q^{59} +(1.99772 - 3.46015i) q^{61} +(10.8165 + 8.54682i) q^{65} +(-1.36379 + 5.08972i) q^{67} +8.72093i q^{71} +(-3.55904 - 0.953642i) q^{73} +(9.30530 - 4.20971i) q^{77} +(-0.564269 - 0.325781i) q^{79} +(-4.54026 - 4.54026i) q^{83} +(1.56040 - 10.6772i) q^{85} +(7.34188 - 12.7165i) q^{89} +(12.6149 - 10.3406i) q^{91} +(-1.60579 + 3.72600i) q^{95} +(0.639339 + 0.639339i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 64 * q - 8 * q^7	\( 64 q - 8 q^{7} + 16 q^{25} + 32 q^{31} + 16 q^{37} - 16 q^{43} + 32 q^{55} + 48 q^{61} + 32 q^{67} + 40 q^{73} + 80 q^{85} + 96 q^{91} + 80 q^{97}+O(q^{100}) \) 64 * q - 8 * q^7 + 16 * q^25 + 32 * q^31 + 16 * q^37 - 16 * q^43 + 32 * q^55 + 48 * q^61 + 32 * q^67 + 40 * q^73 + 80 * q^85 + 96 * q^91 + 80 * q^97

Introduction

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