LMFDB - Embedded newform 1260.2.ej.a.233.16

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			233.16
Character	$\chi$	$=$	1260.233
Dual form			1260.2.ej.a.557.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.23583 + 0.0326818i) q^{5} +(2.56653 - 0.642608i) q^{7} +O(q^{10})$	$q+(2.23583 + 0.0326818i) q^{5} +(2.56653 - 0.642608i) q^{7} +(2.01809 - 1.16514i) q^{11} +(0.104291 + 0.104291i) q^{13} +(0.977264 - 3.64720i) q^{17} +(0.646098 + 0.373025i) q^{19} +(-0.471152 - 1.75836i) q^{23} +(4.99786 + 0.146142i) q^{25} -7.38009 q^{29} +(0.668412 + 1.15772i) q^{31} +(5.75931 - 1.35288i) q^{35} +(1.78713 + 6.66967i) q^{37} -0.0508439i q^{41} +(-3.06145 - 3.06145i) q^{43} +(-2.78540 + 0.746347i) q^{47} +(6.17411 - 3.29854i) q^{49} +(-0.926031 - 0.248129i) q^{53} +(4.55018 - 2.53911i) q^{55} +(-3.37080 - 5.83840i) q^{59} +(-3.61219 + 6.25649i) q^{61} +(0.229769 + 0.236585i) q^{65} +(9.80215 + 2.62648i) q^{67} -12.8092i q^{71} +(-2.94310 + 10.9838i) q^{73} +(4.43074 - 4.28721i) q^{77} +(9.97215 + 5.75742i) q^{79} +(0.461820 - 0.461820i) q^{83} +(2.30419 - 8.12257i) q^{85} +(-2.21306 + 3.83314i) q^{89} +(0.334684 + 0.200647i) q^{91} +(1.43237 + 0.855136i) q^{95} +(5.18939 - 5.18939i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	2.23583	+	0.0326818i	0.999893	+	0.0146157i
$5$	2.23583	+	0.0326818i	0.999893	+	0.0146157i
$6$		0			0
$7$	2.56653	−	0.642608i	0.970056	−	0.242883i
$7$	2.56653	−	0.642608i	0.970056	−	0.242883i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.01809	−	1.16514i	0.608476	−	0.351304i	−0.163893	−	0.986478i	$-0.552405\pi$
$11$	2.01809	−	1.16514i	0.608476	−	0.351304i	0.772369	+	0.635174i	$0.219072\pi$
$12$		0			0
$13$	0.104291	+	0.104291i	0.0289251	+	0.0289251i	0.721421	−	0.692496i	$-0.243489\pi$
$13$	0.104291	+	0.104291i	0.0289251	+	0.0289251i	−0.692496	+	0.721421i	$0.743489\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.977264	−	3.64720i	0.237021	−	0.884576i	−0.740206	−	0.672380i	$-0.765272\pi$
$17$	0.977264	−	3.64720i	0.237021	−	0.884576i	0.977227	−	0.212195i	$-0.0680613\pi$
$18$		0			0
$19$	0.646098	+	0.373025i	0.148225	+	0.0855778i	0.572278	−	0.820059i	$-0.306060\pi$
$19$	0.646098	+	0.373025i	0.148225	+	0.0855778i	−0.424053	+	0.905637i	$0.639393\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−0.471152	−	1.75836i	−0.0982420	−	0.366644i	0.899249	−	0.437437i	$-0.144114\pi$
$23$	−0.471152	−	1.75836i	−0.0982420	−	0.366644i	−0.997491	+	0.0707930i	$0.977447\pi$
$24$		0			0
$25$	4.99786	+	0.146142i	0.999573	+	0.0292283i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−7.38009			−1.37045			−0.685224	−	0.728332i	$-0.740296\pi$
$29$	−7.38009			−1.37045			−0.685224	+	0.728332i	$0.740296\pi$
$30$		0			0
$31$	0.668412	+	1.15772i	0.120050	+	0.207933i	0.919787	−	0.392417i	$-0.128361\pi$
$31$	0.668412	+	1.15772i	0.120050	+	0.207933i	−0.799737	+	0.600351i	$0.795028\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	5.75931	−	1.35288i	0.973502	−	0.228679i
$36$		0			0
$37$	1.78713	+	6.66967i	0.293803	+	1.09649i	0.942163	+	0.335154i	$0.108788\pi$
$37$	1.78713	+	6.66967i	0.293803	+	1.09649i	−0.648361	+	0.761333i	$0.724545\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$		−	0.0508439i		−	0.00794049i	−0.999992	−	0.00397024i	$-0.998736\pi$
$41$		−	0.0508439i		−	0.00794049i	0.999992	−	0.00397024i	$-0.00126377\pi$
$42$		0			0
$43$	−3.06145	−	3.06145i	−0.466867	−	0.466867i	0.434031	−	0.900898i	$-0.357091\pi$
$43$	−3.06145	−	3.06145i	−0.466867	−	0.466867i	−0.900898	+	0.434031i	$0.857091\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.78540	+	0.746347i	−0.406293	+	0.108866i	−0.456177	−	0.889889i	$-0.650782\pi$
$47$	−2.78540	+	0.746347i	−0.406293	+	0.108866i	0.0498839	+	0.998755i	$0.484115\pi$
$48$		0			0
$49$	6.17411	−	3.29854i	0.882016	−	0.471220i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.926031	−	0.248129i	−0.127200	−	0.0340832i	0.194657	−	0.980871i	$-0.437641\pi$
$53$	−0.926031	−	0.248129i	−0.127200	−	0.0340832i	−0.321857	+	0.946788i	$0.604307\pi$
$54$		0			0
$55$	4.55018	−	2.53911i	0.613546	−	0.342373i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.37080	−	5.83840i	−0.438841	−	0.760095i	0.558760	−	0.829330i	$-0.311277\pi$
$59$	−3.37080	−	5.83840i	−0.438841	−	0.760095i	−0.997600	+	0.0692351i	$0.977944\pi$
$60$		0			0
$61$	−3.61219	+	6.25649i	−0.462493	+	0.801062i	−0.999084	−	0.0427805i	$-0.986378\pi$
$61$	−3.61219	+	6.25649i	−0.462493	+	0.801062i	0.536591	+	0.843842i	$0.319712\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.229769	+	0.236585i	0.0284993	+	0.0293448i
$66$		0			0
$67$	9.80215	+	2.62648i	1.19752	+	0.320875i	0.801855	−	0.597518i	$-0.203846\pi$
$67$	9.80215	+	2.62648i	1.19752	+	0.320875i	0.395668	+	0.918394i	$0.370513\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	12.8092i		−	1.52018i	−0.649820	−	0.760089i	$-0.725156\pi$
$71$		−	12.8092i		−	1.52018i	0.649820	−	0.760089i	$-0.274844\pi$
$72$		0			0
$73$	−2.94310	+	10.9838i	−0.344463	+	1.28555i	0.548775	+	0.835970i	$0.315095\pi$
$73$	−2.94310	+	10.9838i	−0.344463	+	1.28555i	−0.893238	+	0.449584i	$0.851572\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	4.43074	−	4.28721i	0.504930	−	0.488573i
$78$		0			0
$79$	9.97215	+	5.75742i	1.12195	+	0.647761i	0.941899	−	0.335896i	$-0.109039\pi$
$79$	9.97215	+	5.75742i	1.12195	+	0.647761i	0.180055	+	0.983657i	$0.442372\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.461820	−	0.461820i	0.0506913	−	0.0506913i	−0.681307	−	0.731998i	$-0.738588\pi$
$83$	0.461820	−	0.461820i	0.0506913	−	0.0506913i	0.731998	+	0.681307i	$0.238588\pi$
$84$		0			0
$85$	2.30419	−	8.12257i	0.249925	−	0.881017i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−2.21306	+	3.83314i	−0.234584	+	0.406312i	−0.959152	−	0.282892i	$-0.908706\pi$
$89$	−2.21306	+	3.83314i	−0.234584	+	0.406312i	0.724568	+	0.689204i	$0.242040\pi$
$90$		0			0
$91$	0.334684	+	0.200647i	0.0350844	+	0.0210336i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	1.43237	+	0.855136i	0.146959	+	0.0877351i
$96$		0			0
$97$	5.18939	−	5.18939i	0.526903	−	0.526903i	−0.392744	−	0.919648i	$-0.628474\pi$
$97$	5.18939	−	5.18939i	0.526903	−	0.526903i	0.919648	+	0.392744i	$0.128474\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	11.4823	−	6.62933i	1.14253	−	0.659643i	0.195478	−	0.980708i	$-0.437374\pi$
$101$	11.4823	−	6.62933i	1.14253	−	0.659643i	0.947057	+	0.321065i	$0.104041\pi$
$102$		0			0
$103$	9.32463	−	2.49853i	0.918783	−	0.246187i	0.231718	−	0.972783i	$-0.425565\pi$
$103$	9.32463	−	2.49853i	0.918783	−	0.246187i	0.687065	+	0.726596i	$0.258899\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5.94412	−	1.59272i	0.574640	−	0.153974i	0.0402162	−	0.999191i	$-0.487195\pi$
$107$	5.94412	−	1.59272i	0.574640	−	0.153974i	0.534424	+	0.845217i	$0.320529\pi$
$108$		0			0
$109$	−7.23504	+	4.17715i	−0.692991	+	0.400099i	−0.804732	−	0.593639i	$-0.797691\pi$
$109$	−7.23504	+	4.17715i	−0.692991	+	0.400099i	0.111741	+	0.993737i	$0.464357\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−13.3725	+	13.3725i	−1.25798	+	1.25798i	−0.305921	+	0.952057i	$0.598964\pi$
$113$	−13.3725	+	13.3725i	−1.25798	+	1.25798i	−0.952057	+	0.305921i	$0.901036\pi$
$114$		0			0
$115$	−0.995949	−	3.94680i	−0.0928727	−	0.368041i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.164453	−	9.98863i	0.0150754	−	0.915656i
$120$		0			0
$121$	−2.78488	+	4.82356i	−0.253171	+	0.438505i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	11.1696	+	0.490087i	0.999039	+	0.0438347i
$126$		0			0
$127$	7.26806	−	7.26806i	0.644936	−	0.644936i	−0.306828	−	0.951765i	$-0.599268\pi$
$127$	7.26806	−	7.26806i	0.644936	−	0.644936i	0.951765	+	0.306828i	$0.0992678\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.0639933	+	0.0369465i	0.00559112	+	0.00322803i	0.502793	−	0.864407i	$-0.332306\pi$
$131$	0.0639933	+	0.0369465i	0.00559112	+	0.00322803i	−0.497202	+	0.867635i	$0.665639\pi$
$132$		0			0
$133$	1.89794	+	0.542190i	0.164572	+	0.0470139i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−1.18212	+	4.41175i	−0.100996	+	0.376921i	−0.997860	−	0.0653845i	$-0.979173\pi$
$137$	−1.18212	+	4.41175i	−0.100996	+	0.376921i	0.896865	+	0.442305i	$0.145839\pi$
$138$		0			0
$139$			9.00554i			0.763840i	0.924195	+	0.381920i	$0.124737\pi$
$139$			9.00554i			0.763840i	−0.924195	+	0.381920i	$0.875263\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	0.331982	+	0.0889544i	0.0277618	+	0.00743874i
$144$		0			0
$145$	−16.5006	−	0.241194i	−1.37030	−	0.0200301i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−2.58290	+	4.47372i	−0.211599	+	0.366501i	−0.952215	−	0.305428i	$-0.901201\pi$
$149$	−2.58290	+	4.47372i	−0.211599	+	0.366501i	0.740616	+	0.671929i	$0.234534\pi$
$150$		0			0
$151$	−5.89401	−	10.2087i	−0.479647	−	0.830774i	0.520080	−	0.854118i	$-0.325902\pi$
$151$	−5.89401	−	10.2087i	−0.479647	−	0.830774i	−0.999727	+	0.0233437i	$0.992569\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.45662	+	2.61032i	0.116998	+	0.209666i
$156$		0			0
$157$	−19.7061	−	5.28022i	−1.57271	−	0.421407i	−0.636053	−	0.771645i	$-0.719434\pi$
$157$	−19.7061	−	5.28022i	−1.57271	−	0.421407i	−0.936661	+	0.350238i	$0.886101\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−2.33916	−	4.21012i	−0.184352	−	0.331804i
$162$		0			0
$163$	18.1229	−	4.85602i	1.41950	−	0.380353i	0.534192	−	0.845363i	$-0.320616\pi$
$163$	18.1229	−	4.85602i	1.41950	−	0.380353i	0.885305	+	0.465010i	$0.153949\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.95202	+	9.95202i	0.770110	+	0.770110i	0.978126	−	0.208015i	$-0.0667004\pi$
$167$	9.95202	+	9.95202i	0.770110	+	0.770110i	−0.208015	+	0.978126i	$0.566700\pi$
$168$		0			0
$169$		−	12.9782i		−	0.998327i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.60187	+	9.71031i	0.197817	+	0.738261i	0.991520	+	0.129956i	$0.0414837\pi$
$173$	2.60187	+	9.71031i	0.197817	+	0.738261i	−0.793703	+	0.608305i	$0.791850\pi$
$174$		0			0
$175$	12.9211	−	2.83659i	0.976740	−	0.214426i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.319174	+	0.552825i	0.0238562	+	0.0413201i	0.877707	−	0.479198i	$-0.159072\pi$
$179$	0.319174	+	0.552825i	0.0238562	+	0.0413201i	−0.853851	+	0.520518i	$0.825739\pi$
$180$		0			0
$181$	−22.2918			−1.65693			−0.828467	−	0.560038i	$-0.810787\pi$
$181$	−22.2918			−1.65693			−0.828467	+	0.560038i	$0.810787\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.77775	+	14.9706i	0.277745	+	1.10066i
$186$		0			0
$187$	−2.27730	−	8.49902i	−0.166533	−	0.621510i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−17.1487	−	9.90082i	−1.24084	−	0.716398i	−0.271574	−	0.962418i	$-0.587544\pi$
$191$	−17.1487	−	9.90082i	−1.24084	−	0.716398i	−0.969265	+	0.246019i	$0.920877\pi$
$192$		0			0
$193$	−2.54505	+	9.49825i	−0.183197	+	0.683699i	0.811813	+	0.583918i	$0.198481\pi$
$193$	−2.54505	+	9.49825i	−0.183197	+	0.683699i	−0.995009	+	0.0997814i	$0.968186\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.89272	+	4.89272i	0.348592	+	0.348592i	0.859585	−	0.510993i	$-0.170722\pi$
$197$	4.89272	+	4.89272i	0.348592	+	0.348592i	−0.510993	+	0.859585i	$0.670722\pi$
$198$		0			0
$199$	−20.1519	+	11.6347i	−1.42853	+	0.824761i	−0.997005	−	0.0773405i	$-0.975357\pi$
$199$	−20.1519	+	11.6347i	−1.42853	+	0.824761i	−0.431524	+	0.902102i	$0.642024\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−18.9412	+	4.74251i	−1.32941	+	0.332859i
$204$		0			0
$205$	0.00166167	−	0.113678i	0.000116056	−	0.00793964i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	1.73851			0.120255
$210$		0			0
$211$	−19.2223			−1.32332			−0.661659	−	0.749804i	$-0.730148\pi$
$211$	−19.2223			−1.32332			−0.661659	+	0.749804i	$0.730148\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−6.74483	−	6.94494i	−0.459994	−	0.473641i
$216$		0			0
$217$	2.45946	+	2.54180i	0.166959	+	0.172549i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.482290	−	0.278450i	0.0324423	−	0.0187306i
$222$		0			0
$223$	14.5153	+	14.5153i	0.972013	+	0.972013i	0.999619	−	0.0276056i	$-0.00878826\pi$
$223$	14.5153	+	14.5153i	0.972013	+	0.972013i	−0.0276056	+	0.999619i	$0.508788\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.34991	+	27.4302i	−0.487831	+	1.82061i	0.0791306	+	0.996864i	$0.474786\pi$
$227$	−7.34991	+	27.4302i	−0.487831	+	1.82061i	−0.566961	+	0.823744i	$0.691881\pi$
$228$		0			0
$229$	−12.5027	−	7.21845i	−0.826203	−	0.477009i	0.0263477	−	0.999653i	$-0.491612\pi$
$229$	−12.5027	−	7.21845i	−0.826203	−	0.477009i	−0.852551	+	0.522644i	$0.824946\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	0.295018	+	1.10102i	0.0193273	+	0.0721305i	0.974916	−	0.222573i	$-0.0714457\pi$
$233$	0.295018	+	1.10102i	0.0193273	+	0.0721305i	−0.955589	+	0.294704i	$0.904779\pi$
$234$		0			0
$235$	−6.25208	+	1.57767i	−0.407841	+	0.102916i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−27.6642			−1.78945			−0.894724	−	0.446620i	$-0.852628\pi$
$239$	−27.6642			−1.78945			−0.894724	+	0.446620i	$0.852628\pi$
$240$		0			0
$241$	0.322862	+	0.559213i	0.0207974	+	0.0360221i	0.876237	−	0.481881i	$-0.160046\pi$
$241$	0.322862	+	0.559213i	0.0207974	+	0.0360221i	−0.855439	+	0.517903i	$0.826713\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	13.9121	−	7.17319i	0.888809	−	0.458279i
$246$		0			0
$247$	0.0284791	+	0.106285i	0.00181208	+	0.00676278i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	28.3922i		−	1.79210i	−0.443951	−	0.896051i	$-0.646424\pi$
$251$		−	28.3922i		−	1.79210i	0.443951	−	0.896051i	$-0.353576\pi$
$252$		0			0
$253$	−2.99957	−	2.99957i	−0.188581	−	0.188581i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−10.4635	+	2.80368i	−0.652693	+	0.174889i	−0.569946	−	0.821682i	$-0.693036\pi$
$257$	−10.4635	+	2.80368i	−0.652693	+	0.174889i	−0.0827470	+	0.996571i	$0.526369\pi$
$258$		0			0
$259$	8.87271	+	15.9695i	0.551323	+	0.992294i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.20043	+	1.12550i	0.259010	+	0.0694014i	0.385987	−	0.922504i	$-0.373861\pi$
$263$	4.20043	+	1.12550i	0.259010	+	0.0694014i	−0.126978	+	0.991906i	$0.540528\pi$
$264$		0			0
$265$	−2.06234	−	0.585039i	−0.126688	−	0.0359386i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	15.5036	+	26.8531i	0.945273	+	1.63726i	0.755204	+	0.655489i	$0.227538\pi$
$269$	15.5036	+	26.8531i	0.945273	+	1.63726i	0.190068	+	0.981771i	$0.439129\pi$
$270$		0			0
$271$	7.80093	−	13.5116i	0.473873	−	0.820772i	−0.525680	−	0.850683i	$-0.676189\pi$
$271$	7.80093	−	13.5116i	0.473873	−	0.820772i	0.999553	+	0.0299108i	$0.00952233\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	10.2564	−	5.52830i	0.618484	−	0.333369i
$276$		0			0
$277$	−21.4933	−	5.75912i	−1.29141	−	0.346032i	−0.453213	−	0.891402i	$-0.649722\pi$
$277$	−21.4933	−	5.75912i	−1.29141	−	0.346032i	−0.838195	+	0.545370i	$0.816389\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$		−	20.3914i		−	1.21645i	−0.793764	−	0.608226i	$-0.791881\pi$
$281$		−	20.3914i		−	1.21645i	0.793764	−	0.608226i	$-0.208119\pi$
$282$		0			0
$283$	−3.67034	+	13.6979i	−0.218179	+	0.814256i	0.766844	+	0.641834i	$0.221826\pi$
$283$	−3.67034	+	13.6979i	−0.218179	+	0.814256i	−0.985023	+	0.172422i	$0.944841\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−0.0326727	−	0.130492i	−0.00192861	−	0.00770272i
$288$		0			0
$289$	2.37542	+	1.37145i	0.139731	+	0.0806735i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−19.3784	+	19.3784i	−1.13210	+	1.13210i	−0.142268	+	0.989828i	$0.545439\pi$
$293$	−19.3784	+	19.3784i	−1.13210	+	1.13210i	−0.989828	+	0.142268i	$0.954561\pi$
$294$		0			0
$295$	−7.34572	−	13.1638i	−0.427685	−	0.766427i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.134245	−	0.232518i	0.00776357	−	0.0134469i
$300$		0			0
$301$	−9.82461	−	5.88998i	−0.566281	−	0.339493i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−8.28071	+	13.8704i	−0.474152	+	0.794217i
$306$		0			0
$307$	−4.73484	+	4.73484i	−0.270231	+	0.270231i	−0.829193	−	0.558962i	$-0.811200\pi$
$307$	−4.73484	+	4.73484i	−0.270231	+	0.270231i	0.558962	+	0.829193i	$0.311200\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−17.4525	+	10.0762i	−0.989638	+	0.571368i	−0.905166	−	0.425058i	$-0.860254\pi$
$311$	−17.4525	+	10.0762i	−0.989638	+	0.571368i	−0.0844722	+	0.996426i	$0.526920\pi$
$312$		0			0
$313$	−22.1128	+	5.92510i	−1.24989	+	0.334906i	−0.822293	−	0.569065i	$-0.807305\pi$
$313$	−22.1128	+	5.92510i	−1.24989	+	0.334906i	−0.427594	+	0.903971i	$0.640639\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	24.6124	−	6.59488i	1.38237	−	0.370405i	0.510389	−	0.859944i	$-0.329501\pi$
$317$	24.6124	−	6.59488i	1.38237	−	0.370405i	0.871982	+	0.489538i	$0.162835\pi$
$318$		0			0
$319$	−14.8937	+	8.59886i	−0.833885	+	0.481444i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	1.99190	−	1.99190i	0.110833	−	0.110833i
$324$		0			0
$325$	0.505991	+	0.536474i	0.0280673	+	0.0297582i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−6.66920	+	3.70544i	−0.367685	+	0.204288i
$330$		0			0
$331$	4.65524	−	8.06311i	0.255875	−	0.443188i	−0.709258	−	0.704949i	$-0.750970\pi$
$331$	4.65524	−	8.06311i	0.255875	−	0.443188i	0.965133	+	0.261761i	$0.0843031\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	21.8301	+	6.19271i	1.19271	+	0.338344i
$336$		0			0
$337$	21.8402	−	21.8402i	1.18971	−	1.18971i	0.212563	−	0.977147i	$-0.431819\pi$
$337$	21.8402	−	21.8402i	1.18971	−	1.18971i	0.977147	−	0.212563i	$-0.0681811\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.69783	+	1.55759i	0.146096	+	0.0843483i
$342$		0			0
$343$	13.7263	−	12.4333i	0.741153	−	0.671336i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.93531	+	10.9547i	−0.157575	+	0.588080i	0.841296	+	0.540575i	$0.181793\pi$
$347$	−2.93531	+	10.9547i	−0.157575	+	0.588080i	−0.998871	+	0.0475043i	$0.984873\pi$
$348$		0			0
$349$			34.4062i			1.84172i	0.389894	+	0.920860i	$0.372512\pi$
$349$			34.4062i			1.84172i	−0.389894	+	0.920860i	$0.627488\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	4.89720	+	1.31220i	0.260652	+	0.0698414i	0.386778	−	0.922173i	$-0.373588\pi$
$353$	4.89720	+	1.31220i	0.260652	+	0.0698414i	−0.126127	+	0.992014i	$0.540255\pi$
$354$		0			0
$355$	0.418628	−	28.6393i	0.0222185	−	1.52001i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	10.8694	−	18.8263i	0.573664	−	0.993615i	−0.422521	−	0.906353i	$-0.638855\pi$
$359$	10.8694	−	18.8263i	0.573664	−	0.993615i	0.996185	−	0.0872623i	$-0.0278118\pi$
$360$		0			0
$361$	−9.22170	−	15.9725i	−0.485353	−	0.840656i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−6.93923	+	24.4617i	−0.363216	+	1.28038i
$366$		0			0
$367$	−20.6955	−	5.54534i	−1.08030	−	0.289465i	−0.325579	−	0.945515i	$-0.605559\pi$
$367$	−20.6955	−	5.54534i	−1.08030	−	0.289465i	−0.754717	+	0.656050i	$0.772226\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−2.53613	−	0.0417549i	−0.131669	−	0.00216781i
$372$		0			0
$373$	4.14465	−	1.11056i	0.214602	−	0.0575024i	−0.149916	−	0.988699i	$-0.547900\pi$
$373$	4.14465	−	1.11056i	0.214602	−	0.0575024i	0.364518	+	0.931196i	$0.381234\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−0.769678	−	0.769678i	−0.0396404	−	0.0396404i
$378$		0			0
$379$		−	19.1083i		−	0.981527i	−0.871293	−	0.490763i	$-0.836718\pi$
$379$		−	19.1083i		−	0.981527i	0.871293	−	0.490763i	$-0.163282\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.66017	+	32.3202i	0.442514	+	1.65148i	0.722418	+	0.691456i	$0.243031\pi$
$383$	8.66017	+	32.3202i	0.442514	+	1.65148i	−0.279905	+	0.960028i	$0.590303\pi$
$384$		0			0
$385$	10.0465	−	9.44066i	0.512017	−	0.481141i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−0.575383	−	0.996593i	−0.0291731	−	0.0505293i	0.851070	−	0.525052i	$-0.175954\pi$
$389$	−0.575383	−	0.996593i	−0.0291731	−	0.0505293i	−0.880243	+	0.474523i	$0.842621\pi$
$390$		0			0
$391$	−6.87354			−0.347610
$392$		0			0
$393$		0			0
$394$		0			0
$395$	22.1079	+	13.1985i	1.11237	+	0.664090i
$396$		0			0
$397$	4.00655	+	14.9527i	0.201083	+	0.750452i	0.990608	+	0.136734i	$0.0436604\pi$
$397$	4.00655	+	14.9527i	0.201083	+	0.750452i	−0.789525	+	0.613719i	$0.789673\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	4.92522	+	2.84358i	0.245954	+	0.142001i	0.617910	−	0.786249i	$-0.287980\pi$
$401$	4.92522	+	2.84358i	0.245954	+	0.142001i	−0.371956	+	0.928250i	$0.621313\pi$
$402$		0			0
$403$	−0.0510309	+	0.190450i	−0.00254203	+	0.00948698i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	11.3777	+	11.3777i	0.563972	+	0.563972i
$408$		0			0
$409$	−9.24201	+	5.33588i	−0.456988	+	0.263842i	−0.710777	−	0.703417i	$-0.751656\pi$
$409$	−9.24201	+	5.33588i	−0.456988	+	0.263842i	0.253789	+	0.967260i	$0.418323\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−12.4030	−	12.8183i	−0.610314	−	0.630747i
$414$		0			0
$415$	1.04764	−	1.01746i	0.0514268	−	0.0499450i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−29.3200			−1.43237			−0.716187	−	0.697908i	$-0.754114\pi$
$419$	−29.3200			−1.43237			−0.716187	+	0.697908i	$0.754114\pi$
$420$		0			0
$421$	−11.8570			−0.577875			−0.288937	−	0.957348i	$-0.593302\pi$
$421$	−11.8570			−0.577875			−0.288937	+	0.957348i	$0.593302\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.41724	−	18.0854i	0.262775	−	0.877270i
$426$		0			0
$427$	−5.25030	+	18.3787i	−0.254080	+	0.889406i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	17.8028	−	10.2784i	0.857530	−	0.495095i	−0.00565449	−	0.999984i	$-0.501800\pi$
$431$	17.8028	−	10.2784i	0.857530	−	0.495095i	0.863184	+	0.504889i	$0.168467\pi$
$432$		0			0
$433$	0.378779	+	0.378779i	0.0182030	+	0.0182030i	0.716150	−	0.697947i	$-0.245903\pi$
$433$	0.378779	+	0.378779i	0.0182030	+	0.0182030i	−0.697947	+	0.716150i	$0.745903\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	0.351503	−	1.31183i	0.0168147	−	0.0627532i
$438$		0			0
$439$	−5.67969	−	3.27917i	−0.271077	−	0.156506i	0.358300	−	0.933606i	$-0.383356\pi$
$439$	−5.67969	−	3.27917i	−0.271077	−	0.156506i	−0.629377	+	0.777100i	$0.716690\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−8.15225	−	30.4246i	−0.387325	−	1.44552i	−0.834469	−	0.551055i	$-0.814225\pi$
$443$	−8.15225	−	30.4246i	−0.387325	−	1.44552i	0.447144	−	0.894462i	$-0.352441\pi$
$444$		0			0
$445$	−5.07330	+	8.49791i	−0.240498	+	0.402840i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−29.5810			−1.39602			−0.698008	−	0.716090i	$-0.745930\pi$
$449$	−29.5810			−1.39602			−0.698008	+	0.716090i	$0.745930\pi$
$450$		0			0
$451$	−0.0592405	−	0.102607i	−0.00278952	−	0.00483160i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	0.741739	+	0.459551i	0.0347733	+	0.0215441i
$456$		0			0
$457$	−1.98486	−	7.40762i	−0.0928481	−	0.346514i	0.903836	−	0.427878i	$-0.140739\pi$
$457$	−1.98486	−	7.40762i	−0.0928481	−	0.346514i	−0.996684	+	0.0813646i	$0.974072\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$		−	7.60597i		−	0.354245i	−0.984189	−	0.177123i	$-0.943321\pi$
$461$		−	7.60597i		−	0.354245i	0.984189	−	0.177123i	$-0.0566789\pi$
$462$		0			0
$463$	−12.6349	−	12.6349i	−0.587191	−	0.587191i	0.349678	−	0.936870i	$-0.386291\pi$
$463$	−12.6349	−	12.6349i	−0.587191	−	0.587191i	−0.936870	+	0.349678i	$0.886291\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−20.3354	+	5.44885i	−0.941010	+	0.252143i	−0.696543	−	0.717515i	$-0.745280\pi$
$467$	−20.3354	+	5.44885i	−0.941010	+	0.252143i	−0.244467	+	0.969658i	$0.578613\pi$
$468$		0			0
$469$	26.8453	+	0.441981i	1.23960	+	0.0204088i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−9.74531	−	2.61125i	−0.448090	−	0.120065i
$474$		0			0
$475$	3.17460	+	1.95875i	0.145660	+	0.0898736i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.80518	+	11.7869i	0.310937	+	0.538558i	0.978565	−	0.205936i	$-0.0660240\pi$
$479$	6.80518	+	11.7869i	0.310937	+	0.538558i	−0.667629	+	0.744494i	$0.732691\pi$
$480$		0			0
$481$	−0.509205	+	0.881969i	−0.0232178	+	0.0402143i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	11.7722	−	11.4330i	0.534548	−	0.519146i
$486$		0			0
$487$	27.1350	+	7.27081i	1.22961	+	0.329472i	0.814426	−	0.580267i	$-0.197052\pi$
$487$	27.1350	+	7.27081i	1.22961	+	0.329472i	0.415180	+	0.909739i	$0.363719\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$			4.70236i			0.212214i	0.994355	+	0.106107i	$0.0338387\pi$
$491$			4.70236i			0.212214i	−0.994355	+	0.106107i	$0.966161\pi$
$492$		0			0
$493$	−7.21229	+	26.9167i	−0.324825	+	1.21227i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−8.23132	−	32.8752i	−0.369225	−	1.47466i
$498$		0			0
$499$	15.7438	+	9.08967i	0.704788	+	0.406909i	0.809128	−	0.587632i	$-0.199940\pi$
$499$	15.7438	+	9.08967i	0.704788	+	0.406909i	−0.104340	+	0.994542i	$0.533273\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	21.7734	−	21.7734i	0.970828	−	0.970828i	−0.0287581	−	0.999586i	$-0.509155\pi$
$503$	21.7734	−	21.7734i	0.970828	−	0.970828i	0.999586	+	0.0287581i	$0.00915524\pi$
$504$		0			0
$505$	25.8892	−	14.4468i	1.15205	−	0.642873i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.96907	+	13.8028i	−0.353223	+	0.611800i	−0.986812	−	0.161869i	$-0.948248\pi$
$509$	−7.96907	+	13.8028i	−0.353223	+	0.611800i	0.633589	+	0.773670i	$0.281581\pi$
$510$		0			0
$511$	−0.495261	+	30.0814i	−0.0219091	+	1.33072i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	20.9299	−	5.28153i	0.922283	−	0.232732i
$516$		0			0
$517$	−4.75159	+	4.75159i	−0.208975	+	0.208975i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	15.2976	−	8.83206i	0.670199	−	0.386940i	−0.125953	−	0.992036i	$-0.540199\pi$
$521$	15.2976	−	8.83206i	0.670199	−	0.386940i	0.796152	+	0.605097i	$0.206865\pi$
$522$		0			0
$523$	11.8117	−	3.16494i	0.516490	−	0.138393i	0.00884737	−	0.999961i	$-0.497184\pi$
$523$	11.8117	−	3.16494i	0.516490	−	0.138393i	0.507642	+	0.861568i	$0.330517\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.87566	−	1.30643i	0.212387	−	0.0569090i
$528$		0			0
$529$	17.0487	−	9.84309i	0.741249	−	0.427960i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	0.00530257	−	0.00530257i	0.000229680	−	0.000229680i
$534$		0			0
$535$	13.3421	−	3.36679i	0.576829	−	0.145559i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	8.61662	−	13.8505i	0.371144	−	0.596582i
$540$		0			0
$541$	−8.40922	+	14.5652i	−0.361541	+	0.626207i	−0.988215	−	0.153075i	$-0.951082\pi$
$541$	−8.40922	+	14.5652i	−0.361541	+	0.626207i	0.626674	+	0.779281i	$0.284416\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−16.3128	+	9.10294i	−0.698765	+	0.389927i
$546$		0			0
$547$	26.8955	−	26.8955i	1.14997	−	1.14997i	0.163409	−	0.986558i	$-0.447751\pi$
$547$	26.8955	−	26.8955i	1.14997	−	1.14997i	0.986558	−	0.163409i	$-0.0522489\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−4.76826	−	2.75296i	−0.203135	−	0.117280i
$552$		0			0
$553$	29.2935	+	8.36839i	1.24569	+	0.355860i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−4.61005	+	17.2049i	−0.195334	+	0.728996i	0.796846	+	0.604182i	$0.206500\pi$
$557$	−4.61005	+	17.2049i	−0.195334	+	0.728996i	−0.992180	+	0.124814i	$0.960167\pi$
$558$		0			0
$559$		−	0.638564i		−	0.0270084i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−13.9514	−	3.73827i	−0.587982	−	0.157549i	−0.0474513	−	0.998874i	$-0.515110\pi$
$563$	−13.9514	−	3.73827i	−0.587982	−	0.157549i	−0.540531	+	0.841324i	$0.681777\pi$
$564$		0			0
$565$	−30.3356	+	29.4616i	−1.27623	+	1.23946i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−0.938459	+	1.62546i	−0.0393423	+	0.0681428i	−0.885026	−	0.465541i	$-0.845860\pi$
$569$	−0.938459	+	1.62546i	−0.0393423	+	0.0681428i	0.845684	+	0.533684i	$0.179193\pi$
$570$		0			0
$571$	20.0044	+	34.6487i	0.837160	+	1.45000i	0.892260	+	0.451522i	$0.149119\pi$
$571$	20.0044	+	34.6487i	0.837160	+	1.45000i	−0.0551003	+	0.998481i	$0.517548\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−2.09778	−	8.85691i	−0.0874836	−	0.369359i
$576$		0			0
$577$	16.6139	+	4.45168i	0.691646	+	0.185326i	0.587486	−	0.809235i	$-0.300118\pi$
$577$	16.6139	+	4.45168i	0.691646	+	0.185326i	0.104160	+	0.994561i	$0.466785\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	0.888503	−	1.48204i	0.0368613	−	0.0614854i
$582$		0			0
$583$	−2.15792	+	0.578212i	−0.0893718	+	0.0239471i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−2.70958	−	2.70958i	−0.111836	−	0.111836i	0.648974	−	0.760811i	$-0.275198\pi$
$587$	−2.70958	−	2.70958i	−0.111836	−	0.111836i	−0.760811	+	0.648974i	$0.775198\pi$
$588$		0			0
$589$			0.997338i			0.0410946i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−0.993840	−	3.70906i	−0.0408121	−	0.152313i	0.942513	−	0.334170i	$-0.108456\pi$
$593$	−0.993840	−	3.70906i	−0.0408121	−	0.152313i	−0.983325	+	0.181857i	$0.941789\pi$
$594$		0			0
$595$	0.694135	−	22.3275i	0.0284568	−	0.915338i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−20.0255	−	34.6852i	−0.818220	−	1.41720i	−0.906992	−	0.421147i	$-0.861628\pi$
$599$	−20.0255	−	34.6852i	−0.818220	−	1.41720i	0.0887723	−	0.996052i	$-0.471706\pi$
$600$		0			0
$601$	21.3751			0.871908			0.435954	−	0.899969i	$-0.356411\pi$
$601$	21.3751			0.871908			0.435954	+	0.899969i	$0.356411\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−6.38417	+	10.6936i	−0.259553	+	0.434758i
$606$		0			0
$607$	5.09249	+	19.0054i	0.206698	+	0.771406i	0.988925	+	0.148413i	$0.0474166\pi$
$607$	5.09249	+	19.0054i	0.206698	+	0.771406i	−0.782228	+	0.622993i	$0.785917\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−0.368330	−	0.212655i	−0.0149010	−	0.00860312i
$612$		0			0
$613$	3.65554	−	13.6427i	0.147646	−	0.551022i	−0.851978	−	0.523578i	$-0.824597\pi$
$613$	3.65554	−	13.6427i	0.147646	−	0.551022i	0.999623	−	0.0274433i	$-0.00873659\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−12.8139	−	12.8139i	−0.515869	−	0.515869i	0.400450	−	0.916319i	$-0.368854\pi$
$617$	−12.8139	−	12.8139i	−0.515869	−	0.515869i	−0.916319	+	0.400450i	$0.868854\pi$
$618$		0			0
$619$	0.120189	−	0.0693910i	0.00483079	−	0.00278906i	−0.497583	−	0.867417i	$-0.665779\pi$
$619$	0.120189	−	0.0693910i	0.00483079	−	0.00278906i	0.502413	+	0.864628i	$0.332446\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.21668	+	11.2600i	−0.128873	+	0.451121i
$624$		0			0
$625$	24.9573	+	1.46079i	0.998291	+	0.0584317i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	26.0721			1.03956
$630$		0			0
$631$	−24.0417			−0.957086			−0.478543	−	0.878064i	$-0.658835\pi$
$631$	−24.0417			−0.957086			−0.478543	+	0.878064i	$0.658835\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	16.4877	−	16.0126i	0.654294	−	0.635441i
$636$		0			0
$637$	0.987913	+	0.299896i	0.0391425	+	0.0118823i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	22.9415	−	13.2453i	0.906135	−	0.523157i	0.0269495	−	0.999637i	$-0.491421\pi$
$641$	22.9415	−	13.2453i	0.906135	−	0.523157i	0.879186	+	0.476479i	$0.158087\pi$
$642$		0			0
$643$	−7.25605	−	7.25605i	−0.286151	−	0.286151i	0.549405	−	0.835556i	$-0.314854\pi$
$643$	−7.25605	−	7.25605i	−0.286151	−	0.286151i	−0.835556	+	0.549405i	$0.814854\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	7.77230	−	29.0066i	0.305560	−	1.14037i	−0.626901	−	0.779099i	$-0.715677\pi$
$647$	7.77230	−	29.0066i	0.305560	−	1.14037i	0.932462	−	0.361269i	$-0.117656\pi$
$648$		0			0
$649$	−13.6051	−	7.85493i	−0.534048	−	0.308333i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.72386	+	10.1656i	0.106593	+	0.397811i	0.998521	−	0.0543669i	$-0.0173141\pi$
$653$	2.72386	+	10.1656i	0.106593	+	0.397811i	−0.891928	+	0.452177i	$0.850647\pi$
$654$		0			0
$655$	0.141871	+	0.0846976i	0.00554334	+	0.00330941i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−15.1391			−0.589736			−0.294868	−	0.955538i	$-0.595276\pi$
$659$	−15.1391			−0.589736			−0.294868	+	0.955538i	$0.595276\pi$
$660$		0			0
$661$	3.48192	+	6.03087i	0.135431	+	0.234574i	0.925762	−	0.378107i	$-0.123425\pi$
$661$	3.48192	+	6.03087i	0.135431	+	0.234574i	−0.790331	+	0.612680i	$0.790091\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	4.22574	+	1.27427i	0.163867	+	0.0494142i
$666$		0			0
$667$	3.47714	+	12.9769i	0.134636	+	0.502467i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			16.8349i			0.649903i
$672$		0			0
$673$	−19.2321	−	19.2321i	−0.741342	−	0.741342i	0.231494	−	0.972836i	$-0.425639\pi$
$673$	−19.2321	−	19.2321i	−0.741342	−	0.741342i	−0.972836	+	0.231494i	$0.925639\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.82176	+	1.02404i	−0.146882	+	0.0393570i	−0.331511	−	0.943451i	$-0.607558\pi$
$677$	−3.82176	+	1.02404i	−0.146882	+	0.0393570i	0.184629	+	0.982808i	$0.440892\pi$
$678$		0			0
$679$	9.98397	−	16.6535i	0.383149	−	0.639101i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	14.5772	+	3.90594i	0.557780	+	0.149457i	0.526686	−	0.850060i	$-0.323434\pi$
$683$	14.5772	+	3.90594i	0.557780	+	0.149457i	0.0310937	+	0.999516i	$0.490101\pi$
$684$		0			0
$685$	−2.78721	+	9.82528i	−0.106494	+	0.375404i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.0706991	−	0.122454i	−0.00269342	−	0.00466514i
$690$		0			0
$691$	7.85554	−	13.6062i	0.298839	−	0.517604i	−0.677032	−	0.735954i	$-0.736734\pi$
$691$	7.85554	−	13.6062i	0.298839	−	0.517604i	0.975871	+	0.218350i	$0.0700674\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−0.294317	+	20.1348i	−0.0111641	+	0.763758i
$696$		0			0
$697$	−0.185438	−	0.0496879i	−0.00702396	−	0.00188207i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	31.8850i		−	1.20428i	−0.798390	−	0.602140i	$-0.794315\pi$
$701$		−	31.8850i		−	1.20428i	0.798390	−	0.602140i	$-0.205685\pi$
$702$		0			0
$703$	−1.33329	+	4.97591i	−0.0502860	+	0.187670i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	25.2096	−	24.3930i	0.948106	−	0.917392i
$708$		0			0
$709$	37.8083	+	21.8287i	1.41992	+	0.819793i	0.996291	−	0.0860424i	$-0.0274221\pi$
$709$	37.8083	+	21.8287i	1.41992	+	0.819793i	0.423631	+	0.905835i	$0.360755\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	1.72078	−	1.72078i	0.0644435	−	0.0644435i
$714$		0			0
$715$	0.739349	+	0.209737i	0.0276501	+	0.00784371i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	9.67488	−	16.7574i	0.360812	−	0.624945i	−0.627283	−	0.778792i	$-0.715833\pi$
$719$	9.67488	−	16.7574i	0.360812	−	0.624945i	0.988095	+	0.153847i	$0.0491663\pi$
$720$		0			0
$721$	22.3263	−	12.4046i	0.831476	−	0.461972i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−36.8847	−	1.07854i	−1.36986	−	0.0400559i
$726$		0			0
$727$	12.7385	−	12.7385i	0.472446	−	0.472446i	−0.430259	−	0.902705i	$-0.641578\pi$
$727$	12.7385	−	12.7385i	0.472446	−	0.472446i	0.902705	+	0.430259i	$0.141578\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−14.1576	+	8.17388i	−0.523637	+	0.302322i
$732$		0			0
$733$	22.9487	−	6.14909i	0.847631	−	0.227122i	0.191240	−	0.981543i	$-0.438749\pi$
$733$	22.9487	−	6.14909i	0.847631	−	0.227122i	0.656390	+	0.754421i	$0.272082\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	22.8418	−	6.12044i	0.841389	−	0.225449i
$738$		0			0
$739$	−5.89553	+	3.40379i	−0.216871	+	0.125210i	−0.604500	−	0.796605i	$-0.706627\pi$
$739$	−5.89553	+	3.40379i	−0.216871	+	0.125210i	0.387630	+	0.921815i	$0.373294\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−16.4727	+	16.4727i	−0.604323	+	0.604323i	−0.941457	−	0.337134i	$-0.890543\pi$
$743$	−16.4727	+	16.4727i	−0.604323	+	0.604323i	0.337134	+	0.941457i	$0.390543\pi$
$744$		0			0
$745$	−5.92113	+	9.91805i	−0.216934	+	0.363369i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	14.2322	−	7.90751i	0.520035	−	0.288934i
$750$		0			0
$751$	−11.1127	+	19.2478i	−0.405509	+	0.702363i	−0.994381	−	0.105864i	$-0.966239\pi$
$751$	−11.1127	+	19.2478i	−0.405509	+	0.702363i	0.588871	+	0.808227i	$0.299572\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−12.8444	−	23.0176i	−0.467454	−	0.837695i
$756$		0			0
$757$	7.83526	−	7.83526i	0.284777	−	0.284777i	−0.550234	−	0.835011i	$-0.685461\pi$
$757$	7.83526	−	7.83526i	0.284777	−	0.284777i	0.835011	+	0.550234i	$0.185461\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	42.4511	+	24.5091i	1.53885	+	0.888456i	0.998906	+	0.0467553i	$0.0148881\pi$
$761$	42.4511	+	24.5091i	1.53885	+	0.888456i	0.539944	+	0.841701i	$0.318445\pi$
$762$		0			0
$763$	−15.8846	+	15.3701i	−0.575063	+	0.556434i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.257348	−	0.960437i	0.00929231	−	0.0346794i
$768$		0			0
$769$		−	46.8128i		−	1.68811i	−0.536254	−	0.844057i	$-0.680161\pi$
$769$		−	46.8128i		−	1.68811i	0.536254	−	0.844057i	$-0.319839\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	4.60758	+	1.23460i	0.165723	+	0.0444054i	0.340727	−	0.940162i	$-0.389327\pi$
$773$	4.60758	+	1.23460i	0.165723	+	0.0444054i	−0.175003	+	0.984568i	$0.555994\pi$
$774$		0			0
$775$	3.17144	+	5.88383i	0.113922	+	0.211353i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.0189661	−	0.0328502i	0.000679530	−	0.00117698i
$780$		0			0
$781$	−14.9246	−	25.8502i	−0.534044	−	0.924991i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−43.8868	−	12.4497i	−1.56639	−	0.444349i
$786$		0			0
$787$	2.78142	+	0.745278i	0.0991467	+	0.0265663i	0.308051	−	0.951370i	$-0.400323\pi$
$787$	2.78142	+	0.745278i	0.0991467	+	0.0265663i	−0.208905	+	0.977936i	$0.566990\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−25.7276	+	42.9141i	−0.914767	+	1.52585i
$792$		0			0
$793$	−1.02922	+	0.275777i	−0.0365485	+	0.00979314i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	32.0045	+	32.0045i	1.13366	+	1.13366i	0.989564	+	0.144092i	$0.0460262\pi$
$797$	32.0045	+	32.0045i	1.13366	+	1.13366i	0.144092	+	0.989564i	$0.453974\pi$
$798$		0			0
$799$			10.8883i			0.385200i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	6.85826	+	25.5954i	0.242023	+	0.903241i
$804$		0			0
$805$	−5.09237	−	9.48955i	−0.179483	−	0.334463i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	7.21768	+	12.5014i	0.253760	+	0.439526i	0.964558	−	0.263871i	$-0.0849992\pi$
$809$	7.21768	+	12.5014i	0.253760	+	0.439526i	−0.710798	+	0.703396i	$0.751666\pi$
$810$		0			0
$811$	25.5314			0.896529			0.448264	−	0.893901i	$-0.352042\pi$
$811$	25.5314			0.896529			0.448264	+	0.893901i	$0.352042\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	40.6785	−	10.2649i	1.42490	−	0.359565i
$816$		0			0
$817$	−0.836001	−	3.12000i	−0.0292480	−	0.109155i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−16.7388	−	9.66415i	−0.584188	−	0.337281i	0.178608	−	0.983920i	$-0.442841\pi$
$821$	−16.7388	−	9.66415i	−0.584188	−	0.337281i	−0.762796	+	0.646639i	$0.776174\pi$
$822$		0			0
$823$	−2.98221	+	11.1298i	−0.103953	+	0.387959i	−0.998224	−	0.0595669i	$-0.981028\pi$
$823$	−2.98221	+	11.1298i	−0.103953	+	0.387959i	0.894271	+	0.447526i	$0.147695\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	13.6422	+	13.6422i	0.474386	+	0.474386i	0.903331	−	0.428945i	$-0.141115\pi$
$827$	13.6422	+	13.6422i	0.474386	+	0.474386i	−0.428945	+	0.903331i	$0.641115\pi$
$828$		0			0
$829$	11.2056	−	6.46958i	0.389188	−	0.224698i	−0.292620	−	0.956229i	$-0.594527\pi$
$829$	11.2056	−	6.46958i	0.389188	−	0.224698i	0.681808	+	0.731531i	$0.261194\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−5.99670	−	25.7417i	−0.207773	−	0.891899i
$834$		0			0
$835$	21.9258	+	22.5763i	0.758772	+	0.781284i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	8.37176			0.289025			0.144513	−	0.989503i	$-0.453839\pi$
$839$	8.37176			0.289025			0.144513	+	0.989503i	$0.453839\pi$
$840$		0			0
$841$	25.4657			0.878129
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.424152	−	29.0171i	0.0145913	−	0.998220i
$846$		0			0
$847$	−4.04782	+	14.1694i	−0.139085	+	0.486866i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	10.8857	−	6.28486i	0.373157	−	0.215442i
$852$		0			0
$853$	5.83879	+	5.83879i	0.199917	+	0.199917i	0.799964	−	0.600048i	$-0.204852\pi$
$853$	5.83879	+	5.83879i	0.199917	+	0.199917i	−0.600048	+	0.799964i	$0.704852\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	14.3891	−	53.7007i	0.491521	−	1.83438i	−0.0571796	−	0.998364i	$-0.518211\pi$
$857$	14.3891	−	53.7007i	0.491521	−	1.83438i	0.548701	−	0.836019i	$-0.315123\pi$
$858$		0			0
$859$	−34.6355	−	19.9968i	−1.18175	−	0.682282i	−0.225329	−	0.974283i	$-0.572346\pi$
$859$	−34.6355	−	19.9968i	−1.18175	−	0.682282i	−0.956418	+	0.292001i	$0.905679\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	8.61959	+	32.1687i	0.293414	+	1.09504i	0.942469	+	0.334295i	$0.108498\pi$
$863$	8.61959	+	32.1687i	0.293414	+	1.09504i	−0.649054	+	0.760742i	$0.724835\pi$
$864$		0			0
$865$	5.49999	+	21.7956i	0.187005	+	0.741074i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	26.8329			0.910243
$870$		0			0
$871$	0.748358	+	1.29619i	0.0253572	+	0.0439199i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	28.9820	−	5.91985i	0.979770	−	0.200128i
$876$		0			0
$877$	3.32288	+	12.4012i	0.112206	+	0.418757i	0.999063	−	0.0432867i	$-0.0137829\pi$
$877$	3.32288	+	12.4012i	0.112206	+	0.418757i	−0.886857	+	0.462044i	$0.847116\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	35.9760i		−	1.21206i	−0.795441	−	0.606031i	$-0.792761\pi$
$881$		−	35.9760i		−	1.21206i	0.795441	−	0.606031i	$-0.207239\pi$
$882$		0			0
$883$	−10.8203	−	10.8203i	−0.364131	−	0.364131i	0.501200	−	0.865331i	$-0.332892\pi$
$883$	−10.8203	−	10.8203i	−0.364131	−	0.364131i	−0.865331	+	0.501200i	$0.832892\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−49.9917	+	13.3952i	−1.67856	+	0.449768i	−0.967398	−	0.253262i	$-0.918497\pi$
$887$	−49.9917	+	13.3952i	−1.67856	+	0.449768i	−0.711160	+	0.703030i	$0.751830\pi$
$888$		0			0
$889$	13.9832	−	23.3242i	0.468980	−	0.782268i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.07805	−	0.556812i	−0.0695393	−	0.0186330i
$894$		0			0
$895$	0.695551	+	1.24645i	0.0232497	+	0.0416644i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−4.93294	−	8.54411i	−0.164523	−	0.284962i
$900$		0			0
$901$	−1.80995	+	3.13493i	−0.0602983	+	0.104440i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−49.8406	−	0.728534i	−1.65676	−	0.0242173i
$906$		0			0
$907$	16.4643	+	4.41159i	0.546687	+	0.146484i	0.521583	−	0.853200i	$-0.325342\pi$
$907$	16.4643	+	4.41159i	0.546687	+	0.146484i	0.0251041	+	0.999685i	$0.492008\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$			14.0849i			0.466653i	0.972398	+	0.233327i	$0.0749611\pi$
$911$			14.0849i			0.466653i	−0.972398	+	0.233327i	$0.925039\pi$
$912$		0			0
$913$	0.393906	−	1.47008i	0.0130364	−	0.0486525i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.187983	+	0.0537016i	0.00620773	+	0.00177338i
$918$		0			0
$919$	−25.5234	−	14.7359i	−0.841938	−	0.486093i	0.0159844	−	0.999872i	$-0.494912\pi$
$919$	−25.5234	−	14.7359i	−0.841938	−	0.486093i	−0.857923	+	0.513779i	$0.828245\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.33589	−	1.33589i	0.0439713	−	0.0439713i
$924$		0			0
$925$	7.95713	+	33.5953i	0.261629	+	1.10461i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	6.07883	−	10.5288i	0.199440	−	0.345440i	−0.748907	−	0.662675i	$-0.769421\pi$
$929$	6.07883	−	10.5288i	0.199440	−	0.345440i	0.948347	+	0.317235i	$0.102754\pi$
$930$		0			0
$931$	5.21952	+	0.171915i	0.171063	+	0.00563430i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−4.81390	−	19.0768i	−0.157431	−	0.623877i
$936$		0			0
$937$	−11.8563	+	11.8563i	−0.387328	+	0.387328i	−0.873733	−	0.486405i	$-0.838308\pi$
$937$	−11.8563	+	11.8563i	−0.387328	+	0.387328i	0.486405	+	0.873733i	$0.338308\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−39.7659	+	22.9589i	−1.29633	+	0.748438i	−0.979769	−	0.200133i	$-0.935862\pi$
$941$	−39.7659	+	22.9589i	−1.29633	+	0.748438i	−0.316564	+	0.948571i	$0.602529\pi$
$942$		0			0
$943$	−0.0894021	+	0.0239552i	−0.00291133	+	0.000780089i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−45.3291	+	12.1459i	−1.47300	+	0.394688i	−0.903957	−	0.427622i	$-0.859351\pi$
$947$	−45.3291	+	12.1459i	−1.47300	+	0.394688i	−0.569039	+	0.822311i	$0.692685\pi$
$948$		0			0
$949$	−1.45245	+	0.838572i	−0.0471485	+	0.0272212i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	36.1467	−	36.1467i	1.17091	−	1.17091i	0.188913	−	0.981994i	$-0.439503\pi$
$953$	36.1467	−	36.1467i	1.17091	−	1.17091i	0.981994	−	0.188913i	$-0.0604966\pi$
$954$		0			0
$955$	−38.0181	−	22.6970i	−1.23024	−	0.734458i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−0.198927	+	12.0825i	−0.00642368	+	0.390164i
$960$		0			0
$961$	14.6064	−	25.2991i	0.471176	−	0.816100i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−6.00072	+	21.1533i	−0.193170	+	0.680949i
$966$		0			0
$967$	−16.8667	+	16.8667i	−0.542398	+	0.542398i	−0.924231	−	0.381834i	$-0.875293\pi$
$967$	−16.8667	+	16.8667i	−0.542398	+	0.542398i	0.381834	+	0.924231i	$0.375293\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	3.57022	+	2.06127i	0.114574	+	0.0661493i	0.556192	−	0.831054i	$-0.312262\pi$
$971$	3.57022	+	2.06127i	0.114574	+	0.0661493i	−0.441618	+	0.897203i	$0.645595\pi$
$972$		0			0
$973$	5.78703	+	23.1129i	0.185524	+	0.740967i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.70347	+	6.35743i	−0.0544988	+	0.203392i	−0.987807	−	0.155684i	$-0.950242\pi$
$977$	−1.70347	+	6.35743i	−0.0544988	+	0.203392i	0.933308	+	0.359077i	$0.116908\pi$
$978$		0			0
$979$			10.3141i			0.329641i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−7.44635	−	1.99524i	−0.237502	−	0.0636384i	0.138105	−	0.990418i	$-0.455899\pi$
$983$	−7.44635	−	1.99524i	−0.237502	−	0.0636384i	−0.375606	+	0.926779i	$0.622566\pi$
$984$		0			0
$985$	10.7794	+	11.0992i	0.343460	+	0.353650i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.94073	+	6.82555i	−0.125308	+	0.217040i
$990$		0			0
$991$	20.3448	+	35.2382i	0.646273	+	1.11938i	0.984006	+	0.178136i	$0.0570068\pi$
$991$	20.3448	+	35.2382i	0.646273	+	1.11938i	−0.337732	+	0.941242i	$0.609660\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−45.4364	+	25.3546i	−1.44043	+	0.803794i
$996$		0			0
$997$	−33.8780	−	9.07758i	−1.07293	−	0.287490i	−0.321231	−	0.947001i	$-0.604097\pi$
$997$	−33.8780	−	9.07758i	−1.07293	−	0.287490i	−0.751695	+	0.659511i	$0.770763\pi$
$998$		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.233.16	yes	64
3.2	odd	2	inner	1260.2.ej.a.233.1	yes	64
5.2	odd	4	inner	1260.2.ej.a.737.11	yes	64
7.4	even	3	inner	1260.2.ej.a.53.6	✓	64
15.2	even	4	inner	1260.2.ej.a.737.6	yes	64
21.11	odd	6	inner	1260.2.ej.a.53.11	yes	64
35.32	odd	12	inner	1260.2.ej.a.557.1	yes	64
105.32	even	12	inner	1260.2.ej.a.557.16	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1260.2.ej.a.53.6	✓	64	7.4	even	3	inner
1260.2.ej.a.53.11	yes	64	21.11	odd	6	inner
1260.2.ej.a.233.1	yes	64	3.2	odd	2	inner
1260.2.ej.a.233.16	yes	64	1.1	even	1	trivial
1260.2.ej.a.557.1	yes	64	35.32	odd	12	inner
1260.2.ej.a.557.16	yes	64	105.32	even	12	inner
1260.2.ej.a.737.6	yes	64	15.2	even	4	inner
1260.2.ej.a.737.11	yes	64	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.23583 + 0.0326818i) q^{5} +(2.56653 - 0.642608i) q^{7} +O(q^{10})\)	\(q+(2.23583 + 0.0326818i) q^{5} +(2.56653 - 0.642608i) q^{7} +(2.01809 - 1.16514i) q^{11} +(0.104291 + 0.104291i) q^{13} +(0.977264 - 3.64720i) q^{17} +(0.646098 + 0.373025i) q^{19} +(-0.471152 - 1.75836i) q^{23} +(4.99786 + 0.146142i) q^{25} -7.38009 q^{29} +(0.668412 + 1.15772i) q^{31} +(5.75931 - 1.35288i) q^{35} +(1.78713 + 6.66967i) q^{37} -0.0508439i q^{41} +(-3.06145 - 3.06145i) q^{43} +(-2.78540 + 0.746347i) q^{47} +(6.17411 - 3.29854i) q^{49} +(-0.926031 - 0.248129i) q^{53} +(4.55018 - 2.53911i) q^{55} +(-3.37080 - 5.83840i) q^{59} +(-3.61219 + 6.25649i) q^{61} +(0.229769 + 0.236585i) q^{65} +(9.80215 + 2.62648i) q^{67} -12.8092i q^{71} +(-2.94310 + 10.9838i) q^{73} +(4.43074 - 4.28721i) q^{77} +(9.97215 + 5.75742i) q^{79} +(0.461820 - 0.461820i) q^{83} +(2.30419 - 8.12257i) q^{85} +(-2.21306 + 3.83314i) q^{89} +(0.334684 + 0.200647i) q^{91} +(1.43237 + 0.855136i) q^{95} +(5.18939 - 5.18939i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 8 q^{7}+O(q^{10}) \) 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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