LMFDB - Embedded newform 1260.2.bm.b.289.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1260,2,Mod(109,1260)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1260.109"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1260, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.bm (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.2
Root			$2.13746 + 0.656712i$ of defining polynomial
Character	$\chi$	$=$	1260.289
Dual form			1260.2.bm.b.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 2.17945i) q^{5} +(-1.13746 - 2.38876i) q^{7} +(-2.63746 - 4.56821i) q^{11} +2.62685i q^{13} +(0.362541 - 0.209313i) q^{17} +(1.63746 - 2.83616i) q^{19} +(-6.77492 - 3.91150i) q^{23} +(-4.50000 + 2.17945i) q^{25} +4.27492 q^{29} +(-1.63746 - 2.83616i) q^{31} +(4.63746 - 3.67341i) q^{35} +(-8.63746 - 4.98684i) q^{37} +3.72508 q^{41} -2.15068i q^{43} +(-5.63746 - 3.25479i) q^{47} +(-4.41238 + 5.43424i) q^{49} +(4.91238 - 2.83616i) q^{53} +(8.63746 - 8.03231i) q^{55} +(1.63746 + 2.83616i) q^{59} +(6.77492 - 11.7345i) q^{61} +(-5.72508 + 1.31342i) q^{65} +(-3.04983 + 1.76082i) q^{67} +4.54983 q^{71} +(5.63746 - 3.25479i) q^{73} +(-7.91238 + 11.4964i) q^{77} +(3.63746 - 6.30026i) q^{79} +7.40437i q^{83} +(0.637459 + 0.685484i) q^{85} +(3.50000 - 6.06218i) q^{89} +(6.27492 - 2.98793i) q^{91} +(7.00000 + 2.15068i) q^{95} +6.92820i q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} + 3 q^{7} - 3 q^{11} + 9 q^{17} - q^{19} - 12 q^{23} - 18 q^{25} + 2 q^{29} + q^{31} + 11 q^{35} - 27 q^{37} + 30 q^{41} - 15 q^{47} + 5 q^{49} - 3 q^{53} + 27 q^{55} - q^{59} + 12 q^{61}+ \cdots + 28 q^{95}+O(q^{100}) $ 4 * q + 2 * q^5 + 3 * q^7 - 3 * q^11 + 9 * q^17 - q^19 - 12 * q^23 - 18 * q^25 + 2 * q^29 + q^31 + 11 * q^35 - 27 * q^37 + 30 * q^41 - 15 * q^47 + 5 * q^49 - 3 * q^53 + 27 * q^55 - q^59 + 12 * q^61 - 38 * q^65 + 18 * q^67 - 12 * q^71 + 15 * q^73 - 9 * q^77 + 7 * q^79 - 5 * q^85 + 14 * q^89 + 10 * q^91 + 28 * q^95

Character values

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

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

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
$5$	0.500000	+	2.17945i	0.223607	+	0.974679i
$5$	0.500000	+	2.17945i	0.223607	+	0.974679i
$6$		0			0
$7$	−1.13746	−	2.38876i	−0.429919	−	0.902867i
$7$	−1.13746	−	2.38876i	−0.429919	−	0.902867i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.63746	−	4.56821i	−0.795224	−	1.37737i	−0.922697	−	0.385526i	$-0.874020\pi$
$11$	−2.63746	−	4.56821i	−0.795224	−	1.37737i	0.127473	−	0.991842i	$-0.459313\pi$
$12$		0			0
$13$			2.62685i			0.728557i	0.931290	+	0.364278i	$0.118684\pi$
$13$			2.62685i			0.728557i	−0.931290	+	0.364278i	$0.881316\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.362541	−	0.209313i	0.0879292	−	0.0507659i	−0.455391	−	0.890292i	$-0.650500\pi$
$17$	0.362541	−	0.209313i	0.0879292	−	0.0507659i	0.543320	+	0.839526i	$0.317167\pi$
$18$		0			0
$19$	1.63746	−	2.83616i	0.375659	−	0.650660i	−0.614767	−	0.788709i	$-0.710750\pi$
$19$	1.63746	−	2.83616i	0.375659	−	0.650660i	0.990425	+	0.138049i	$0.0440831\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−6.77492	−	3.91150i	−1.41267	−	0.815604i	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−6.77492	−	3.91150i	−1.41267	−	0.815604i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$		0			0
$25$	−4.50000	+	2.17945i	−0.900000	+	0.435890i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	4.27492			0.793832			0.396916	−	0.917855i	$-0.370080\pi$
$29$	4.27492			0.793832			0.396916	+	0.917855i	$0.370080\pi$
$30$		0			0
$31$	−1.63746	−	2.83616i	−0.294096	−	0.509390i	0.680678	−	0.732583i	$-0.261685\pi$
$31$	−1.63746	−	2.83616i	−0.294096	−	0.509390i	−0.974774	+	0.223193i	$0.928352\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.63746	−	3.67341i	0.783874	−	0.620920i
$36$		0			0
$37$	−8.63746	−	4.98684i	−1.41999	−	0.819831i	−0.423692	−	0.905806i	$-0.639266\pi$
$37$	−8.63746	−	4.98684i	−1.41999	−	0.819831i	−0.996297	+	0.0859750i	$0.972599\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.72508			0.581760			0.290880	−	0.956760i	$-0.406052\pi$
$41$	3.72508			0.581760			0.290880	+	0.956760i	$0.406052\pi$
$42$		0			0
$43$		−	2.15068i		−	0.327975i	−0.986462	−	0.163988i	$-0.947564\pi$
$43$		−	2.15068i		−	0.327975i	0.986462	−	0.163988i	$-0.0524357\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.63746	−	3.25479i	−0.822308	−	0.474760i	0.0289038	−	0.999582i	$-0.490798\pi$
$47$	−5.63746	−	3.25479i	−0.822308	−	0.474760i	−0.851212	+	0.524823i	$0.824132\pi$
$48$		0			0
$49$	−4.41238	+	5.43424i	−0.630339	+	0.776320i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.91238	−	2.83616i	0.674767	−	0.389577i	−0.123114	−	0.992393i	$-0.539288\pi$
$53$	4.91238	−	2.83616i	0.674767	−	0.389577i	0.797880	+	0.602816i	$0.205955\pi$
$54$		0			0
$55$	8.63746	−	8.03231i	1.16467	−	1.08308i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.63746	+	2.83616i	0.213179	+	0.369237i	0.952708	−	0.303888i	$-0.0982849\pi$
$59$	1.63746	+	2.83616i	0.213179	+	0.369237i	−0.739529	+	0.673125i	$0.764952\pi$
$60$		0			0
$61$	6.77492	−	11.7345i	0.867439	−	1.50245i	0.00283468	−	0.999996i	$-0.499098\pi$
$61$	6.77492	−	11.7345i	0.867439	−	1.50245i	0.864605	−	0.502453i	$-0.167569\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−5.72508	+	1.31342i	−0.710109	+	0.162910i
$66$		0			0
$67$	−3.04983	+	1.76082i	−0.372597	+	0.215119i	−0.674592	−	0.738191i	$-0.735681\pi$
$67$	−3.04983	+	1.76082i	−0.372597	+	0.215119i	0.301996	+	0.953309i	$0.402347\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.54983			0.539966			0.269983	−	0.962865i	$-0.412982\pi$
$71$	4.54983			0.539966			0.269983	+	0.962865i	$0.412982\pi$
$72$		0			0
$73$	5.63746	−	3.25479i	0.659815	−	0.380944i	−0.132392	−	0.991197i	$-0.542266\pi$
$73$	5.63746	−	3.25479i	0.659815	−	0.380944i	0.792206	+	0.610253i	$0.208932\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−7.91238	+	11.4964i	−0.901699	+	1.31014i
$78$		0			0
$79$	3.63746	−	6.30026i	0.409246	−	0.708835i	−0.585559	−	0.810630i	$-0.699125\pi$
$79$	3.63746	−	6.30026i	0.409246	−	0.708835i	0.994805	+	0.101795i	$0.0324584\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$			7.40437i			0.812736i	0.913710	+	0.406368i	$0.133205\pi$
$83$			7.40437i			0.812736i	−0.913710	+	0.406368i	$0.866795\pi$
$84$		0			0
$85$	0.637459	+	0.685484i	0.0691421	+	0.0743512i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	3.50000	−	6.06218i	0.370999	−	0.642590i	−0.618720	−	0.785611i	$-0.712349\pi$
$89$	3.50000	−	6.06218i	0.370999	−	0.642590i	0.989720	+	0.143022i	$0.0456819\pi$
$90$		0			0
$91$	6.27492	−	2.98793i	0.657790	−	0.313220i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	7.00000	+	2.15068i	0.718185	+	0.220655i
$96$		0			0
$97$			6.92820i			0.703452i	0.936103	+	0.351726i	$0.114405\pi$
$97$			6.92820i			0.703452i	−0.936103	+	0.351726i	$0.885595\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−6.77492	−	11.7345i	−0.674129	−	1.16763i	−0.976723	−	0.214507i	$-0.931186\pi$
$101$	−6.77492	−	11.7345i	−0.674129	−	1.16763i	0.302593	−	0.953120i	$-0.402148\pi$
$102$		0			0
$103$	−9.77492	−	5.64355i	−0.963151	−	0.556076i	−0.0660098	−	0.997819i	$-0.521027\pi$
$103$	−9.77492	−	5.64355i	−0.963151	−	0.556076i	−0.897141	+	0.441743i	$0.854360\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.04983	−	1.76082i	−0.294839	−	0.170225i	0.345283	−	0.938499i	$-0.387783\pi$
$107$	−3.04983	−	1.76082i	−0.294839	−	0.170225i	−0.640122	+	0.768273i	$0.721116\pi$
$108$		0			0
$109$	−5.77492	−	10.0025i	−0.553137	−	0.958061i	−0.998046	−	0.0624852i	$-0.980097\pi$
$109$	−5.77492	−	10.0025i	−0.553137	−	0.958061i	0.444909	−	0.895576i	$-0.353236\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$		−	4.30136i		−	0.404637i	−0.979320	−	0.202319i	$-0.935152\pi$
$113$		−	4.30136i		−	0.404637i	0.979320	−	0.202319i	$-0.0648477\pi$
$114$		0			0
$115$	5.13746	−	16.7213i	0.479070	−	1.55927i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.912376	−	0.627940i	−0.0836374	−	0.0575632i
$120$		0			0
$121$	−8.41238	+	14.5707i	−0.764761	+	1.32461i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−7.00000	−	8.71780i	−0.626099	−	0.779744i
$126$		0			0
$127$			15.6460i			1.38836i	0.719802	+	0.694179i	$0.244232\pi$
$127$			15.6460i			1.38836i	−0.719802	+	0.694179i	$0.755768\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.36254	+	9.28819i	−0.468527	+	0.811513i	−0.999353	−	0.0359678i	$-0.988549\pi$
$131$	−5.36254	+	9.28819i	−0.468527	+	0.811513i	0.530826	+	0.847481i	$0.321882\pi$
$132$		0			0
$133$	−8.63746	−	0.685484i	−0.748963	−	0.0594390i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−18.4622	+	10.6592i	−1.57733	+	0.910674i	−0.582103	+	0.813115i	$0.697770\pi$
$137$	−18.4622	+	10.6592i	−1.57733	+	0.910674i	−0.995230	+	0.0975588i	$0.968897\pi$
$138$		0			0
$139$	−13.0997			−1.11110			−0.555550	−	0.831483i	$-0.687492\pi$
$139$	−13.0997			−1.11110			−0.555550	+	0.831483i	$0.687492\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	12.0000	−	6.92820i	1.00349	−	0.579365i
$144$		0			0
$145$	2.13746	+	9.31697i	0.177506	+	0.773732i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.77492	−	6.53835i	0.309253	−	0.535642i	−0.668946	−	0.743311i	$-0.733254\pi$
$149$	3.77492	−	6.53835i	0.309253	−	0.535642i	0.978199	+	0.207669i	$0.0665876\pi$
$150$		0			0
$151$	6.36254	+	11.0202i	0.517776	+	0.896815i	0.999787	+	0.0206494i	$0.00657337\pi$
$151$	6.36254	+	11.0202i	0.517776	+	0.896815i	−0.482011	+	0.876165i	$0.660093\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.36254	−	4.98684i	0.430730	−	0.400553i
$156$		0			0
$157$	1.91238	−	1.10411i	0.152624	−	0.0881176i	−0.421743	−	0.906715i	$-0.638582\pi$
$157$	1.91238	−	1.10411i	0.152624	−	0.0881176i	0.574367	+	0.818598i	$0.305248\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.63746	+	20.6328i	−0.129050	+	1.62610i
$162$		0			0
$163$	−4.91238	−	2.83616i	−0.384767	−	0.222145i	0.295123	−	0.955459i	$-0.404639\pi$
$163$	−4.91238	−	2.83616i	−0.384767	−	0.222145i	−0.679890	+	0.733314i	$0.737973\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$		−	0.476171i		−	0.0368472i	−0.999830	−	0.0184236i	$-0.994135\pi$
$167$		−	0.476171i		−	0.0368472i	0.999830	−	0.0184236i	$-0.00586474\pi$
$168$		0			0
$169$	6.09967			0.469205
$170$		0			0
$171$		0			0
$172$		0			0
$173$	17.7371	+	10.2405i	1.34853	+	0.778573i	0.988041	−	0.154190i	$-0.0492769\pi$
$173$	17.7371	+	10.2405i	1.34853	+	0.778573i	0.360488	+	0.932764i	$0.382610\pi$
$174$		0			0
$175$	10.3248	+	8.27040i	0.780478	+	0.625183i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	3.63746	+	6.30026i	0.271876	+	0.470904i	0.969342	−	0.245714i	$-0.0790225\pi$
$179$	3.63746	+	6.30026i	0.271876	+	0.470904i	−0.697466	+	0.716618i	$0.745689\pi$
$180$		0			0
$181$	−24.2749			−1.80434			−0.902170	−	0.431380i	$-0.858027\pi$
$181$	−24.2749			−1.80434			−0.902170	+	0.431380i	$0.858027\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.54983	−	21.3183i	0.481553	−	1.56735i
$186$		0			0
$187$	−1.91238	−	1.10411i	−0.139847	−	0.0807406i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.0876242	−	0.151770i	0.00634026	−	0.0109817i	−0.862838	−	0.505481i	$-0.831315\pi$
$191$	0.0876242	−	0.151770i	0.00634026	−	0.0109817i	0.869178	+	0.494499i	$0.164648\pi$
$192$		0			0
$193$	18.4622	−	10.6592i	1.32894	−	0.767263i	0.343803	−	0.939042i	$-0.388285\pi$
$193$	18.4622	−	10.6592i	1.32894	−	0.767263i	0.985136	+	0.171778i	$0.0549513\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			8.60271i			0.612918i	0.951884	+	0.306459i	$0.0991442\pi$
$197$			8.60271i			0.612918i	−0.951884	+	0.306459i	$0.900856\pi$
$198$		0			0
$199$	8.63746	+	14.9605i	0.612293	+	1.06052i	0.990853	+	0.134946i	$0.0430861\pi$
$199$	8.63746	+	14.9605i	0.612293	+	1.06052i	−0.378560	+	0.925577i	$0.623581\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−4.86254	−	10.2118i	−0.341284	−	0.716725i
$204$		0			0
$205$	1.86254	+	8.11863i	0.130086	+	0.567030i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−17.2749			−1.19493
$210$		0			0
$211$	25.6495			1.76578			0.882892	−	0.469576i	$-0.155593\pi$
$211$	25.6495			1.76578			0.882892	+	0.469576i	$0.155593\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4.68729	−	1.07534i	0.319671	−	0.0733375i
$216$		0			0
$217$	−4.91238	+	7.13752i	−0.333474	+	0.484526i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	0.549834	+	0.952341i	0.0369859	+	0.0640614i
$222$		0			0
$223$		−	8.71780i		−	0.583787i	−0.956451	−	0.291893i	$-0.905715\pi$
$223$		−	8.71780i		−	0.583787i	0.956451	−	0.291893i	$-0.0942853\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−16.9124	+	9.76436i	−1.12251	+	0.648084i	−0.942041	−	0.335496i	$-0.891096\pi$
$227$	−16.9124	+	9.76436i	−1.12251	+	0.648084i	−0.180472	+	0.983580i	$0.557763\pi$
$228$		0			0
$229$	1.63746	−	2.83616i	0.108206	−	0.187419i	−0.806837	−	0.590774i	$-0.798823\pi$
$229$	1.63746	−	2.83616i	0.108206	−	0.187419i	0.915044	+	0.403355i	$0.132156\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	12.3625	+	7.13752i	0.809897	+	0.467594i	0.846920	−	0.531720i	$-0.178454\pi$
$233$	12.3625	+	7.13752i	0.809897	+	0.467594i	−0.0370231	+	0.999314i	$0.511788\pi$
$234$		0			0
$235$	4.27492	−	13.9140i	0.278865	−	0.907646i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	0.549834			0.0355658			0.0177829	−	0.999842i	$-0.494339\pi$
$239$	0.549834			0.0355658			0.0177829	+	0.999842i	$0.494339\pi$
$240$		0			0
$241$	−4.91238	−	8.50848i	−0.316434	−	0.548080i	0.663307	−	0.748347i	$-0.269152\pi$
$241$	−4.91238	−	8.50848i	−0.316434	−	0.548080i	−0.979741	+	0.200267i	$0.935819\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−14.0498	−	6.89943i	−0.897611	−	0.440788i
$246$		0			0
$247$	7.45017	+	4.30136i	0.474043	+	0.273689i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	20.5498			1.29709			0.648547	−	0.761175i	$-0.275377\pi$
$251$	20.5498			1.29709			0.648547	+	0.761175i	$0.275377\pi$
$252$		0			0
$253$			41.2657i			2.59435i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	10.0876	+	5.82409i	0.629249	+	0.363297i	0.780461	−	0.625204i	$-0.214984\pi$
$257$	10.0876	+	5.82409i	0.629249	+	0.363297i	−0.151212	+	0.988501i	$0.548318\pi$
$258$		0			0
$259$	−2.08762	+	26.3052i	−0.129719	+	1.63452i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.675248	+	0.389855i	−0.0416376	+	0.0240395i	−0.520674	−	0.853755i	$-0.674319\pi$
$263$	−0.675248	+	0.389855i	−0.0416376	+	0.0240395i	0.479037	+	0.877795i	$0.340986\pi$
$264$		0			0
$265$	8.63746	+	9.28819i	0.530595	+	0.570569i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	7.22508	+	12.5142i	0.440521	+	0.763005i	0.997728	−	0.0673687i	$-0.0214604\pi$
$269$	7.22508	+	12.5142i	0.440521	+	0.763005i	−0.557207	+	0.830374i	$0.688127\pi$
$270$		0			0
$271$	−4.91238	+	8.50848i	−0.298406	+	0.516854i	−0.975771	−	0.218793i	$-0.929788\pi$
$271$	−4.91238	+	8.50848i	−0.298406	+	0.516854i	0.677366	+	0.735646i	$0.263121\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	21.8248	+	14.8087i	1.31608	+	0.893001i
$276$		0			0
$277$	−12.3625	+	7.13752i	−0.742793	+	0.428852i	−0.823084	−	0.567920i	$-0.807748\pi$
$277$	−12.3625	+	7.13752i	−0.742793	+	0.428852i	0.0802909	+	0.996771i	$0.474415\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	9.46221	−	5.46301i	0.562470	−	0.324742i	−0.191666	−	0.981460i	$-0.561389\pi$
$283$	9.46221	−	5.46301i	0.562470	−	0.324742i	0.754136	+	0.656718i	$0.228056\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−4.23713	−	8.89834i	−0.250110	−	0.525252i
$288$		0			0
$289$	−8.41238	+	14.5707i	−0.494846	+	0.857098i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	6.92820i		−	0.404750i	−0.979308	−	0.202375i	$-0.935134\pi$
$293$		−	6.92820i		−	0.404750i	0.979308	−	0.202375i	$-0.0648660\pi$
$294$		0			0
$295$	−5.36254	+	4.98684i	−0.312219	+	0.290345i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	10.2749	−	17.7967i	0.594214	−	1.02921i
$300$		0			0
$301$	−5.13746	+	2.44631i	−0.296118	+	0.141003i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	28.9622	+	8.89834i	1.65837	+	0.509517i
$306$		0			0
$307$		−	26.5145i		−	1.51326i	−0.653843	−	0.756631i	$-0.726844\pi$
$307$		−	26.5145i		−	1.51326i	0.653843	−	0.756631i	$-0.273156\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.91238	−	8.50848i	−0.278555	−	0.482472i	0.692471	−	0.721446i	$-0.256522\pi$
$311$	−4.91238	−	8.50848i	−0.278555	−	0.482472i	−0.971026	+	0.238974i	$0.923189\pi$
$312$		0			0
$313$	29.0120	+	16.7501i	1.63986	+	0.946772i	0.980881	+	0.194609i	$0.0623438\pi$
$313$	29.0120	+	16.7501i	1.63986	+	0.946772i	0.658977	+	0.752163i	$0.270990\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−22.1873	−	12.8098i	−1.24616	−	0.719472i	−0.275821	−	0.961209i	$-0.588950\pi$
$317$	−22.1873	−	12.8098i	−1.24616	−	0.719472i	−0.970342	+	0.241737i	$0.922283\pi$
$318$		0			0
$319$	−11.2749	−	19.5287i	−0.631274	−	1.09340i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	1.37097i		−	0.0762827i
$324$		0			0
$325$	−5.72508	−	11.8208i	−0.317570	−	0.655701i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.36254	+	17.1687i	−0.0751193	+	0.946543i
$330$		0			0
$331$	−8.91238	+	15.4367i	−0.489868	+	0.848477i	−0.999932	−	0.0116596i	$-0.996289\pi$
$331$	−8.91238	+	15.4367i	−0.489868	+	0.848477i	0.510064	+	0.860137i	$0.329622\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.36254	−	5.76655i	−0.292987	−	0.315060i
$336$		0			0
$337$			4.30136i			0.234310i	0.993114	+	0.117155i	$0.0373774\pi$
$337$			4.30136i			0.234310i	−0.993114	+	0.117155i	$0.962623\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−8.63746	+	14.9605i	−0.467745	+	0.810157i
$342$		0			0
$343$	18.0000	+	4.35890i	0.971909	+	0.235358i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.5000	−	6.06218i	0.563670	−	0.325435i	−0.190947	−	0.981600i	$-0.561156\pi$
$347$	10.5000	−	6.06218i	0.563670	−	0.325435i	0.754617	+	0.656165i	$0.227823\pi$
$348$		0			0
$349$	3.72508			0.199399			0.0996996	−	0.995018i	$-0.468212\pi$
$349$	3.72508			0.199399			0.0996996	+	0.995018i	$0.468212\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.08762	+	4.09204i	−0.377236	+	0.217797i	−0.676615	−	0.736337i	$-0.736554\pi$
$353$	−7.08762	+	4.09204i	−0.377236	+	0.217797i	0.299379	+	0.954134i	$0.403221\pi$
$354$		0			0
$355$	2.27492	+	9.91613i	0.120740	+	0.526294i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−18.1873	+	31.5013i	−0.959889	+	1.66258i	−0.237127	+	0.971479i	$0.576206\pi$
$359$	−18.1873	+	31.5013i	−0.959889	+	1.66258i	−0.722762	+	0.691097i	$0.757128\pi$
$360$		0			0
$361$	4.13746	+	7.16629i	0.217761	+	0.377173i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	9.91238	+	10.6592i	0.518837	+	0.557926i
$366$		0			0
$367$	5.22508	−	3.01670i	0.272747	−	0.157471i	−0.357388	−	0.933956i	$-0.616333\pi$
$367$	5.22508	−	3.01670i	0.272747	−	0.157471i	0.630135	+	0.776485i	$0.282999\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−12.3625	−	8.50848i	−0.641831	−	0.441739i
$372$		0			0
$373$	−8.63746	−	4.98684i	−0.447231	−	0.258209i	0.259429	−	0.965762i	$-0.416466\pi$
$373$	−8.63746	−	4.98684i	−0.447231	−	0.258209i	−0.706660	+	0.707553i	$0.749799\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			11.2296i			0.578352i
$378$		0			0
$379$	21.6495			1.11206			0.556030	−	0.831162i	$-0.312324\pi$
$379$	21.6495			1.11206			0.556030	+	0.831162i	$0.312324\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−5.32475	−	3.07425i	−0.272082	−	0.157087i	0.357751	−	0.933817i	$-0.383544\pi$
$383$	−5.32475	−	3.07425i	−0.272082	−	0.157087i	−0.629833	+	0.776730i	$0.716877\pi$
$384$		0			0
$385$	−29.0120	−	11.4964i	−1.47859	−	0.585912i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−16.1873	−	28.0372i	−0.820728	−	1.42154i	−0.905141	−	0.425112i	$-0.860235\pi$
$389$	−16.1873	−	28.0372i	−0.820728	−	1.42154i	0.0844123	−	0.996431i	$-0.473099\pi$
$390$		0			0
$391$	−3.27492			−0.165620
$392$		0			0
$393$		0			0
$394$		0			0
$395$	15.5498	+	4.77753i	0.782397	+	0.240383i
$396$		0			0
$397$	9.36254	+	5.40547i	0.469892	+	0.271293i	0.716195	−	0.697901i	$-0.245882\pi$
$397$	9.36254	+	5.40547i	0.469892	+	0.271293i	−0.246302	+	0.969193i	$0.579216\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$		0			0
$403$	7.45017	−	4.30136i	0.371119	−	0.214266i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			52.6103i			2.60780i
$408$		0			0
$409$	−10.0498	−	17.4068i	−0.496932	−	0.860712i	0.503061	−	0.864251i	$-0.332207\pi$
$409$	−10.0498	−	17.4068i	−0.496932	−	0.860712i	−0.999994	+	0.00353862i	$0.998874\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	4.91238	−	7.13752i	0.241722	−	0.351214i
$414$		0			0
$415$	−16.1375	+	3.70219i	−0.792157	+	0.181733i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−13.0997			−0.639961			−0.319980	−	0.947424i	$-0.603676\pi$
$419$	−13.0997			−0.639961			−0.319980	+	0.947424i	$0.603676\pi$
$420$		0			0
$421$	−4.27492			−0.208347			−0.104173	−	0.994559i	$-0.533220\pi$
$421$	−4.27492			−0.208347			−0.104173	+	0.994559i	$0.533220\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−1.17525	+	1.73205i	−0.0570079	+	0.0840168i
$426$		0			0
$427$	−35.7371	−	2.83616i	−1.72944	−	0.137251i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−9.18729	−	15.9129i	−0.442536	−	0.766495i	0.555341	−	0.831623i	$-0.312588\pi$
$431$	−9.18729	−	15.9129i	−0.442536	−	0.766495i	−0.997877	+	0.0651276i	$0.979255\pi$
$432$		0			0
$433$		−	18.1578i		−	0.872606i	−0.899800	−	0.436303i	$-0.856288\pi$
$433$		−	18.1578i		−	0.872606i	0.899800	−	0.436303i	$-0.143712\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−22.1873	+	12.8098i	−1.06136	+	0.612778i
$438$		0			0
$439$	11.9124	−	20.6328i	0.568547	−	0.984752i	−0.428163	−	0.903701i	$-0.640839\pi$
$439$	11.9124	−	20.6328i	0.568547	−	0.984752i	0.996710	−	0.0810504i	$-0.0258275\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−10.5000	−	6.06218i	−0.498870	−	0.288023i	0.229377	−	0.973338i	$-0.426331\pi$
$443$	−10.5000	−	6.06218i	−0.498870	−	0.288023i	−0.728247	+	0.685315i	$0.759665\pi$
$444$		0			0
$445$	14.9622	+	4.59698i	0.709277	+	0.217918i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−3.17525			−0.149849			−0.0749246	−	0.997189i	$-0.523872\pi$
$449$	−3.17525			−0.149849			−0.0749246	+	0.997189i	$0.523872\pi$
$450$		0			0
$451$	−9.82475	−	17.0170i	−0.462629	−	0.801298i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	9.64950	+	12.1819i	0.452376	+	0.571096i
$456$		0			0
$457$	−1.18729	−	0.685484i	−0.0555392	−	0.0320656i	0.471973	−	0.881613i	$-0.343542\pi$
$457$	−1.18729	−	0.685484i	−0.0555392	−	0.0320656i	−0.527512	+	0.849547i	$0.676875\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$			2.15068i			0.0999505i	0.998750	+	0.0499752i	$0.0159142\pi$
$463$			2.15068i			0.0999505i	−0.998750	+	0.0499752i	$0.984086\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.5997	−	7.85177i	−0.629318	−	0.363337i	0.151170	−	0.988508i	$-0.451696\pi$
$467$	−13.5997	−	7.85177i	−0.629318	−	0.363337i	−0.780488	+	0.625171i	$0.785029\pi$
$468$		0			0
$469$	7.67525	+	5.28247i	0.354410	+	0.243922i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−9.82475	+	5.67232i	−0.451743	+	0.260814i
$474$		0			0
$475$	−1.18729	+	16.3315i	−0.0544767	+	0.749340i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4.91238	−	8.50848i	−0.224452	−	0.388763i	0.731703	−	0.681624i	$-0.238726\pi$
$479$	−4.91238	−	8.50848i	−0.224452	−	0.388763i	−0.956155	+	0.292861i	$0.905393\pi$
$480$		0			0
$481$	13.0997	−	22.6893i	0.597293	−	1.03454i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−15.0997	+	3.46410i	−0.685641	+	0.157297i
$486$		0			0
$487$	−2.53779	+	1.46519i	−0.114998	+	0.0663943i	−0.556396	−	0.830917i	$-0.687816\pi$
$487$	−2.53779	+	1.46519i	−0.114998	+	0.0663943i	0.441398	+	0.897312i	$0.354483\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	28.5498			1.28844			0.644218	−	0.764842i	$-0.277183\pi$
$491$	28.5498			1.28844			0.644218	+	0.764842i	$0.277183\pi$
$492$		0			0
$493$	1.54983	−	0.894797i	0.0698010	−	0.0402996i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5.17525	−	10.8685i	−0.232142	−	0.487518i
$498$		0			0
$499$	0.812707	−	1.40765i	0.0363818	−	0.0630151i	−0.847261	−	0.531177i	$-0.821750\pi$
$499$	0.812707	−	1.40765i	0.0363818	−	0.0630151i	0.883643	+	0.468161i	$0.155083\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$		−	31.7682i		−	1.41647i	−0.705975	−	0.708236i	$-0.749491\pi$
$503$		−	31.7682i		−	1.41647i	0.705975	−	0.708236i	$-0.250509\pi$
$504$		0			0
$505$	22.1873	−	20.6328i	0.987322	−	0.918149i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	7.22508	−	12.5142i	0.320246	−	0.554683i	−0.660293	−	0.751008i	$-0.729568\pi$
$509$	7.22508	−	12.5142i	0.320246	−	0.554683i	0.980539	+	0.196326i	$0.0629010\pi$
$510$		0			0
$511$	−14.1873	−	9.76436i	−0.627609	−	0.431950i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	7.41238	−	24.1257i	0.326628	−	1.06311i
$516$		0			0
$517$			34.3375i			1.51016i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	4.91238	+	8.50848i	0.215215	+	0.372763i	0.953339	−	0.301902i	$-0.0976214\pi$
$521$	4.91238	+	8.50848i	0.215215	+	0.372763i	−0.738124	+	0.674665i	$0.764288\pi$
$522$		0			0
$523$	−6.36254	−	3.67341i	−0.278215	−	0.160627i	0.354400	−	0.935094i	$-0.384685\pi$
$523$	−6.36254	−	3.67341i	−0.278215	−	0.160627i	−0.632615	+	0.774467i	$0.718018\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−1.18729	−	0.685484i	−0.0517193	−	0.0298602i
$528$		0			0
$529$	19.0997	+	33.0816i	0.830420	+	1.43833i
$530$		0			0
$531$		0			0
$532$		0			0
$533$			9.78523i			0.423845i
$534$		0			0
$535$	2.31271	−	7.52737i	0.0999870	−	0.325437i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	36.4622	+	5.82409i	1.57054	+	0.250861i
$540$		0			0
$541$	8.77492	−	15.1986i	0.377263	−	0.653439i	−0.613400	−	0.789773i	$-0.710199\pi$
$541$	8.77492	−	15.1986i	0.377263	−	0.653439i	0.990663	+	0.136334i	$0.0435319\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	18.9124	−	17.5874i	0.810117	−	0.753360i
$546$		0			0
$547$			20.5386i			0.878168i	0.898446	+	0.439084i	$0.144697\pi$
$547$			20.5386i			0.878168i	−0.898446	+	0.439084i	$0.855303\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	7.00000	−	12.1244i	0.298210	−	0.516515i
$552$		0			0
$553$	−19.1873	−	1.52274i	−0.815927	−	0.0647534i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.63746	−	4.98684i	0.365981	−	0.211299i	−0.305720	−	0.952121i	$-0.598897\pi$
$557$	8.63746	−	4.98684i	0.365981	−	0.211299i	0.671701	+	0.740822i	$0.265564\pi$
$558$		0			0
$559$	5.64950			0.238949
$560$		0			0
$561$		0			0
$562$		0			0
$563$	19.5997	−	11.3159i	0.826028	−	0.476907i	−0.0264630	−	0.999650i	$-0.508424\pi$
$563$	19.5997	−	11.3159i	0.826028	−	0.476907i	0.852491	+	0.522743i	$0.175091\pi$
$564$		0			0
$565$	9.37459	−	2.15068i	0.394392	−	0.0904797i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−4.18729	+	7.25260i	−0.175540	+	0.304045i	−0.940348	−	0.340214i	$-0.889501\pi$
$569$	−4.18729	+	7.25260i	−0.175540	+	0.304045i	0.764808	+	0.644259i	$0.222834\pi$
$570$		0			0
$571$	−3.63746	−	6.30026i	−0.152223	−	0.263658i	0.779821	−	0.626002i	$-0.215310\pi$
$571$	−3.63746	−	6.30026i	−0.152223	−	0.263658i	−0.932044	+	0.362344i	$0.881976\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	39.0120	+	2.83616i	1.62691	+	0.118276i
$576$		0			0
$577$	3.36254	−	1.94136i	0.139984	−	0.0808200i	−0.428372	−	0.903602i	$-0.640913\pi$
$577$	3.36254	−	1.94136i	0.139984	−	0.0808200i	0.568357	+	0.822782i	$0.307579\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	17.6873	−	8.42217i	0.733793	−	0.349410i
$582$		0			0
$583$	−25.9124	−	14.9605i	−1.07318	−	0.619601i
$584$		0			0
$585$		0			0
$586$		0			0
$587$			20.8997i			0.862623i	0.902203	+	0.431311i	$0.141949\pi$
$587$			20.8997i			0.862623i	−0.902203	+	0.431311i	$0.858051\pi$
$588$		0			0
$589$	−10.7251			−0.441919
$590$		0			0
$591$		0			0
$592$		0			0
$593$	28.9124	+	16.6926i	1.18729	+	0.685482i	0.957689	−	0.287804i	$-0.0929250\pi$
$593$	28.9124	+	16.6926i	1.18729	+	0.685482i	0.229600	+	0.973285i	$0.426258\pi$
$594$		0			0
$595$	0.912376	−	2.30245i	0.0374038	−	0.0943911i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−2.63746	−	4.56821i	−0.107764	−	0.186652i	0.807100	−	0.590414i	$-0.201036\pi$
$599$	−2.63746	−	4.56821i	−0.107764	−	0.186652i	−0.914864	+	0.403762i	$0.867702\pi$
$600$		0			0
$601$	14.0000			0.571072			0.285536	−	0.958368i	$-0.407828\pi$
$601$	14.0000			0.571072			0.285536	+	0.958368i	$0.407828\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−35.9622	−	11.0490i	−1.46207	−	0.449206i
$606$		0			0
$607$	9.87459	+	5.70109i	0.400797	+	0.231400i	0.686828	−	0.726820i	$-0.259003\pi$
$607$	9.87459	+	5.70109i	0.400797	+	0.231400i	−0.286031	+	0.958220i	$0.592336\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	8.54983	−	14.8087i	0.345889	−	0.599098i
$612$		0			0
$613$	−24.5619	+	14.1808i	−0.992045	+	0.572757i	−0.905885	−	0.423524i	$-0.860793\pi$
$613$	−24.5619	+	14.1808i	−0.992045	+	0.572757i	−0.0861600	+	0.996281i	$0.527460\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		−	31.2920i		−	1.25977i	−0.776689	−	0.629884i	$-0.783102\pi$
$617$		−	31.2920i		−	1.25977i	0.776689	−	0.629884i	$-0.216898\pi$
$618$		0			0
$619$	−4.46221	−	7.72877i	−0.179351	−	0.310646i	0.762307	−	0.647215i	$-0.224067\pi$
$619$	−4.46221	−	7.72877i	−0.179351	−	0.310646i	−0.941659	+	0.336570i	$0.890733\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−18.4622	−	1.46519i	−0.739673	−	0.0587017i
$624$		0			0
$625$	15.5000	−	19.6150i	0.620000	−	0.784602i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−4.17525			−0.166478
$630$		0			0
$631$	33.0997			1.31768			0.658839	−	0.752284i	$-0.271048\pi$
$631$	33.0997			1.31768			0.658839	+	0.752284i	$0.271048\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−34.0997	+	7.82300i	−1.35320	+	0.310446i
$636$		0			0
$637$	−14.2749	−	11.5906i	−0.565593	−	0.459238i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−1.04983	−	1.81837i	−0.0414660	−	0.0718212i	0.844548	−	0.535481i	$-0.179869\pi$
$641$	−1.04983	−	1.81837i	−0.0414660	−	0.0718212i	−0.886014	+	0.463659i	$0.846536\pi$
$642$		0			0
$643$		−	31.4071i		−	1.23857i	−0.785164	−	0.619287i	$-0.787422\pi$
$643$		−	31.4071i		−	1.23857i	0.785164	−	0.619287i	$-0.212578\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	23.3248	−	13.4666i	0.916991	−	0.529425i	0.0343169	−	0.999411i	$-0.489074\pi$
$647$	23.3248	−	13.4666i	0.916991	−	0.529425i	0.882674	+	0.469986i	$0.155741\pi$
$648$		0			0
$649$	8.63746	−	14.9605i	0.339050	−	0.587252i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	24.5619	+	14.1808i	0.961181	+	0.554938i	0.896536	−	0.442970i	$-0.146075\pi$
$653$	24.5619	+	14.1808i	0.961181	+	0.554938i	0.0646444	+	0.997908i	$0.479409\pi$
$654$		0			0
$655$	−22.9244	−	7.04329i	−0.895731	−	0.275204i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−40.5498			−1.57960			−0.789799	−	0.613366i	$-0.789815\pi$
$659$	−40.5498			−1.57960			−0.789799	+	0.613366i	$0.789815\pi$
$660$		0			0
$661$	0.225083	+	0.389855i	0.00875471	+	0.0151636i	0.870370	−	0.492399i	$-0.163880\pi$
$661$	0.225083	+	0.389855i	0.00875471	+	0.0151636i	−0.861615	+	0.507563i	$0.830547\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−2.82475	−	19.1676i	−0.109539	−	0.743289i
$666$		0			0
$667$	−28.9622	−	16.7213i	−1.12142	−	0.647453i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−71.4743			−2.75923
$672$		0			0
$673$		−	31.2920i		−	1.20622i	−0.797659	−	0.603109i	$-0.793928\pi$
$673$		−	31.2920i		−	1.20622i	0.797659	−	0.603109i	$-0.206072\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−40.1873	−	23.2021i	−1.54452	−	0.891731i	−0.998545	−	0.0539317i	$-0.982825\pi$
$677$	−40.1873	−	23.2021i	−1.54452	−	0.891731i	−0.545979	−	0.837799i	$-0.683842\pi$
$678$		0			0
$679$	16.5498	−	7.88054i	0.635124	−	0.302428i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−16.5997	+	9.58382i	−0.635169	+	0.366715i	−0.782751	−	0.622335i	$-0.786184\pi$
$683$	−16.5997	+	9.58382i	−0.635169	+	0.366715i	0.147582	+	0.989050i	$0.452851\pi$
$684$		0			0
$685$	−32.4622	−	34.9079i	−1.24032	−	1.33376i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	7.45017	+	12.9041i	0.283829	+	0.491606i
$690$		0			0
$691$	−15.1873	+	26.3052i	−0.577752	+	1.00070i	0.417985	+	0.908454i	$0.362737\pi$
$691$	−15.1873	+	26.3052i	−0.577752	+	1.00070i	−0.995737	+	0.0922416i	$0.970597\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.54983	−	28.5501i	−0.248449	−	1.08297i
$696$		0			0
$697$	1.35050	−	0.779710i	0.0511537	−	0.0295336i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−8.82475			−0.333306			−0.166653	−	0.986016i	$-0.553296\pi$
$701$	−8.82475			−0.333306			−0.166653	+	0.986016i	$0.553296\pi$
$702$		0			0
$703$	−28.2870	+	16.3315i	−1.06686	+	0.615954i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−20.3248	+	29.5312i	−0.764391	+	1.11063i
$708$		0			0
$709$	−5.22508	+	9.05011i	−0.196232	+	0.339884i	−0.947304	−	0.320337i	$-0.896204\pi$
$709$	−5.22508	+	9.05011i	−0.196232	+	0.339884i	0.751072	+	0.660221i	$0.229537\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$			25.6197i			0.959465i
$714$		0			0
$715$	21.0997	+	22.6893i	0.789083	+	0.848531i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	15.1873	−	26.3052i	0.566390	−	0.981017i	−0.430528	−	0.902577i	$-0.641673\pi$
$719$	15.1873	−	26.3052i	0.566390	−	0.981017i	0.996919	−	0.0784400i	$-0.0249939\pi$
$720$		0			0
$721$	−2.36254	+	29.7693i	−0.0879856	+	1.10867i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−19.2371	+	9.31697i	−0.714449	+	0.346023i
$726$		0			0
$727$		−	3.10302i		−	0.115085i	−0.998343	−	0.0575423i	$-0.981674\pi$
$727$		−	3.10302i		−	0.115085i	0.998343	−	0.0575423i	$-0.0183264\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.450166	−	0.779710i	−0.0166500	−	0.0288386i
$732$		0			0
$733$	−32.6375	−	18.8432i	−1.20549	−	0.695991i	−0.243721	−	0.969845i	$-0.578368\pi$
$733$	−32.6375	−	18.8432i	−1.20549	−	0.695991i	−0.961771	+	0.273854i	$0.911701\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	16.0876	+	9.28819i	0.592595	+	0.342135i
$738$		0			0
$739$	−10.4622	−	18.1211i	−0.384859	−	0.666595i	0.606891	−	0.794785i	$-0.292416\pi$
$739$	−10.4622	−	18.1211i	−0.384859	−	0.666595i	−0.991750	+	0.128190i	$0.959083\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			6.45203i			0.236702i	0.992972	+	0.118351i	$0.0377608\pi$
$743$			6.45203i			0.236702i	−0.992972	+	0.118351i	$0.962239\pi$
$744$		0			0
$745$	16.1375	+	4.95807i	0.591231	+	0.181650i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.737127	+	9.28819i	−0.0269341	+	0.339383i
$750$		0			0
$751$	7.36254	−	12.7523i	0.268663	−	0.465338i	−0.699854	−	0.714286i	$-0.746752\pi$
$751$	7.36254	−	12.7523i	0.268663	−	0.465338i	0.968517	+	0.248948i	$0.0800849\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−20.8368	+	19.3770i	−0.758329	+	0.705200i
$756$		0			0
$757$		−	35.5934i		−	1.29366i	−0.762633	−	0.646831i	$-0.776094\pi$
$757$		−	35.5934i		−	1.29366i	0.762633	−	0.646831i	$-0.223906\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	11.4622	−	19.8531i	0.415505	−	0.719675i	−0.579977	−	0.814633i	$-0.696938\pi$
$761$	11.4622	−	19.8531i	0.415505	−	0.719675i	0.995481	+	0.0949578i	$0.0302716\pi$
$762$		0			0
$763$	−17.3248	+	25.1723i	−0.627198	+	0.911298i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−7.45017	+	4.30136i	−0.269010	+	0.155313i
$768$		0			0
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	34.9124	−	20.1567i	1.25571	−	0.724985i	0.283473	−	0.958980i	$-0.408513\pi$
$773$	34.9124	−	20.1567i	1.25571	−	0.724985i	0.972238	+	0.233995i	$0.0751800\pi$
$774$		0			0
$775$	13.5498	+	9.19397i	0.486724	+	0.330257i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	6.09967	−	10.5649i	0.218543	−	0.378528i
$780$		0			0
$781$	−12.0000	−	20.7846i	−0.429394	−	0.743732i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	3.36254	+	3.61587i	0.120014	+	0.129056i
$786$		0			0
$787$	1.50000	−	0.866025i	0.0534692	−	0.0308705i	−0.473027	−	0.881048i	$-0.656839\pi$
$787$	1.50000	−	0.866025i	0.0534692	−	0.0308705i	0.526496	+	0.850177i	$0.323505\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−10.2749	+	4.89261i	−0.365334	+	0.173961i
$792$		0			0
$793$	30.8248	+	17.7967i	1.09462	+	0.631979i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	46.8229i		−	1.65855i	−0.558839	−	0.829276i	$-0.688753\pi$
$797$		−	46.8229i		−	1.65855i	0.558839	−	0.829276i	$-0.311247\pi$
$798$		0			0
$799$	−2.72508			−0.0964065
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−29.7371	−	17.1687i	−1.04940	−	0.605872i
$804$		0			0
$805$	−45.7870	+	6.74766i	−1.61378	+	0.237824i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	8.59967	+	14.8951i	0.302348	+	0.523683i	0.976667	−	0.214757i	$-0.0688961\pi$
$809$	8.59967	+	14.8951i	0.302348	+	0.523683i	−0.674319	+	0.738440i	$0.735563\pi$
$810$		0			0
$811$	7.45017			0.261611			0.130805	−	0.991408i	$-0.458244\pi$
$811$	7.45017			0.261611			0.130805	+	0.991408i	$0.458244\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	3.72508	−	12.1244i	0.130484	−	0.424698i
$816$		0			0
$817$	−6.09967	−	3.52165i	−0.213400	−	0.123207i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.1873	+	17.6449i	−0.355539	+	0.615812i	−0.987210	−	0.159425i	$-0.949036\pi$
$821$	−10.1873	+	17.6449i	−0.355539	+	0.615812i	0.631671	+	0.775237i	$0.282369\pi$
$822$		0			0
$823$	39.9743	−	23.0791i	1.39341	−	0.804488i	0.399723	−	0.916636i	$-0.369106\pi$
$823$	39.9743	−	23.0791i	1.39341	−	0.804488i	0.993692	+	0.112147i	$0.0357729\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	15.0547i		−	0.523505i	−0.965135	−	0.261752i	$-0.915700\pi$
$827$		−	15.0547i		−	0.523505i	0.965135	−	0.261752i	$-0.0843004\pi$
$828$		0			0
$829$	−25.4622	−	44.1018i	−0.884339	−	1.53172i	−0.846469	−	0.532438i	$-0.821276\pi$
$829$	−25.4622	−	44.1018i	−0.884339	−	1.53172i	−0.0378699	−	0.999283i	$-0.512057\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−0.462210	+	2.89371i	−0.0160146	+	0.100261i
$834$		0			0
$835$	1.03779	−	0.238085i	0.0359142	−	0.00823928i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	41.0997			1.41892			0.709459	−	0.704747i	$-0.248939\pi$
$839$	41.0997			1.41892			0.709459	+	0.704747i	$0.248939\pi$
$840$		0			0
$841$	−10.7251			−0.369830
$842$		0			0
$843$		0			0
$844$		0			0
$845$	3.04983	+	13.2939i	0.104917	+	0.457325i
$846$		0			0
$847$	44.3746	+	3.52165i	1.52473	+	0.121005i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	39.0120	+	67.5708i	1.33732	+	2.31630i
$852$		0			0
$853$			13.1342i			0.449708i	0.974392	+	0.224854i	$0.0721905\pi$
$853$			13.1342i			0.449708i	−0.974392	+	0.224854i	$0.927810\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	32.6375	−	18.8432i	1.11487	−	0.643673i	0.174787	−	0.984606i	$-0.444076\pi$
$857$	32.6375	−	18.8432i	1.11487	−	0.643673i	0.940087	+	0.340933i	$0.110743\pi$
$858$		0			0
$859$	−1.18729	+	2.05645i	−0.0405099	+	0.0701652i	−0.885569	−	0.464507i	$-0.846232\pi$
$859$	−1.18729	+	2.05645i	−0.0405099	+	0.0701652i	0.845060	+	0.534672i	$0.179565\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−14.2251	−	8.21286i	−0.484227	−	0.279569i	0.237949	−	0.971278i	$-0.423525\pi$
$863$	−14.2251	−	8.21286i	−0.484227	−	0.279569i	−0.722177	+	0.691709i	$0.756858\pi$
$864$		0			0
$865$	−13.4502	+	43.7774i	−0.457319	+	1.48848i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−38.3746			−1.30177
$870$		0			0
$871$	−4.62541	−	8.01145i	−0.156726	−	0.271458i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−12.8625	+	26.6375i	−0.434833	+	0.900511i
$876$		0			0
$877$	−19.8127	−	11.4389i	−0.669028	−	0.386263i	0.126681	−	0.991944i	$-0.459568\pi$
$877$	−19.8127	−	11.4389i	−0.669028	−	0.386263i	−0.795708	+	0.605680i	$0.792901\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	43.0241			1.44952			0.724759	−	0.689002i	$-0.241951\pi$
$881$	43.0241			1.44952			0.724759	+	0.689002i	$0.241951\pi$
$882$		0			0
$883$			55.5407i			1.86909i	0.355840	+	0.934547i	$0.384195\pi$
$883$			55.5407i			1.86909i	−0.355840	+	0.934547i	$0.615805\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	33.9743	+	19.6150i	1.14074	+	0.658609i	0.946615	−	0.322367i	$-0.104479\pi$
$887$	33.9743	+	19.6150i	1.14074	+	0.658609i	0.194129	+	0.980976i	$0.437812\pi$
$888$		0			0
$889$	37.3746	−	17.7967i	1.25350	−	0.596881i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−18.4622	+	10.6592i	−0.617814	+	0.356695i
$894$		0			0
$895$	−11.9124	+	11.0778i	−0.398187	+	0.370290i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−7.00000	−	12.1244i	−0.233463	−	0.404370i
$900$		0			0
$901$	1.18729	−	2.05645i	0.0395545	−	0.0685103i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−12.1375	−	52.9060i	−0.403463	−	1.75865i
$906$		0			0
$907$	36.2492	−	20.9285i	1.20363	−	0.694918i	0.242273	−	0.970208i	$-0.422107\pi$
$907$	36.2492	−	20.9285i	1.20363	−	0.694918i	0.961361	+	0.275290i	$0.0887738\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	25.0997			0.831589			0.415795	−	0.909459i	$-0.363504\pi$
$911$	25.0997			0.831589			0.415795	+	0.909459i	$0.363504\pi$
$912$		0			0
$913$	33.8248	−	19.5287i	1.11944	−	0.646307i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	28.2870	+	2.24490i	0.934118	+	0.0741332i
$918$		0			0
$919$	−23.4622	+	40.6377i	−0.773947	+	1.34052i	0.161438	+	0.986883i	$0.448387\pi$
$919$	−23.4622	+	40.6377i	−0.773947	+	1.34052i	−0.935384	+	0.353632i	$0.884946\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$			11.9517i			0.393396i
$924$		0			0
$925$	49.7371	+	3.61587i	1.63535	+	0.118889i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	24.0498	−	41.6555i	0.789049	−	1.36667i	−0.137500	−	0.990502i	$-0.543907\pi$
$929$	24.0498	−	41.6555i	0.789049	−	1.36667i	0.926550	−	0.376172i	$-0.122760\pi$
$930$		0			0
$931$	8.18729	+	21.4125i	0.268328	+	0.701768i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.45017	−	4.71998i	0.0474255	−	0.154360i
$936$		0			0
$937$		−	24.3638i		−	0.795931i	−0.917400	−	0.397965i	$-0.869716\pi$
$937$		−	24.3638i		−	0.795931i	0.917400	−	0.397965i	$-0.130284\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.63746	−	2.83616i	−0.0533796	−	0.0924562i	0.838101	−	0.545515i	$-0.183666\pi$
$941$	−1.63746	−	2.83616i	−0.0533796	−	0.0924562i	−0.891481	+	0.453059i	$0.850333\pi$
$942$		0			0
$943$	−25.2371	−	14.5707i	−0.821834	−	0.474486i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	9.14950	+	5.28247i	0.297319	+	0.171657i	0.641238	−	0.767342i	$-0.278421\pi$
$947$	9.14950	+	5.28247i	0.297319	+	0.171657i	−0.343919	+	0.938999i	$0.611755\pi$
$948$		0			0
$949$	8.54983	+	14.8087i	0.277539	+	0.480712i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	22.6893i		−	0.734978i	−0.930028	−	0.367489i	$-0.880218\pi$
$953$		−	22.6893i		−	0.734978i	0.930028	−	0.367489i	$-0.119782\pi$
$954$		0			0
$955$	0.374586	+	0.115088i	0.0121213	+	0.00372415i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	46.4622	+	31.9775i	1.50034	+	1.03261i
$960$		0			0
$961$	10.1375	−	17.5586i	0.327015	−	0.566406i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	32.4622	+	34.9079i	1.04500	+	1.12372i
$966$		0			0
$967$			2.15068i			0.0691611i	0.999402	+	0.0345806i	$0.0110095\pi$
$967$			2.15068i			0.0691611i	−0.999402	+	0.0345806i	$0.988990\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−18.4622	+	31.9775i	−0.592481	+	1.02621i	0.401417	+	0.915896i	$0.368518\pi$
$971$	−18.4622	+	31.9775i	−0.592481	+	1.02621i	−0.993897	+	0.110311i	$0.964815\pi$
$972$		0			0
$973$	14.9003	+	31.2920i	0.477683	+	1.00318i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−25.9124	+	14.9605i	−0.829010	+	0.478629i	−0.853514	−	0.521070i	$-0.825533\pi$
$977$	−25.9124	+	14.9605i	−0.829010	+	0.478629i	0.0245034	+	0.999700i	$0.492200\pi$
$978$		0			0
$979$	−36.9244			−1.18011
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−39.7749	+	22.9641i	−1.26862	+	0.732440i	−0.974727	−	0.223398i	$-0.928285\pi$
$983$	−39.7749	+	22.9641i	−1.26862	+	0.732440i	−0.293895	+	0.955838i	$0.594952\pi$
$984$		0			0
$985$	−18.7492	+	4.30136i	−0.597398	+	0.137053i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−8.41238	+	14.5707i	−0.267498	+	0.463320i
$990$		0			0
$991$	−16.7371	−	28.9896i	−0.531672	−	0.920884i	−0.999316	−	0.0369667i	$-0.988230\pi$
$991$	−16.7371	−	28.9896i	−0.531672	−	0.920884i	0.467644	−	0.883917i	$-0.345103\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−28.2870	+	26.3052i	−0.896757	+	0.833930i
$996$		0			0
$997$	−0.362541	+	0.209313i	−0.0114818	+	0.00662902i	−0.505730	−	0.862692i	$-0.668777\pi$
$997$	−0.362541	+	0.209313i	−0.0114818	+	0.00662902i	0.494248	+	0.869321i	$0.335443\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.bm.b.289.2		4
3.2	odd	2		140.2.q.b.9.1	yes	4
5.4	even	2		1260.2.bm.a.289.1		4
7.4	even	3		1260.2.bm.a.109.1		4
12.11	even	2		560.2.bw.a.289.1		4
15.2	even	4		700.2.i.f.401.2		8
15.8	even	4		700.2.i.f.401.3		8
15.14	odd	2		140.2.q.a.9.2	✓	4
21.2	odd	6		980.2.e.f.589.3		4
21.5	even	6		980.2.e.c.589.2		4
21.11	odd	6		140.2.q.a.109.2	yes	4
21.17	even	6		980.2.q.g.949.1		4
21.20	even	2		980.2.q.b.569.2		4
35.4	even	6	inner	1260.2.bm.b.109.1		4
60.59	even	2		560.2.bw.e.289.2		4
84.11	even	6		560.2.bw.e.529.2		4
105.2	even	12		4900.2.a.be.1.3		4
105.23	even	12		4900.2.a.be.1.1		4
105.32	even	12		700.2.i.f.501.2		8
105.44	odd	6		980.2.e.f.589.1		4
105.47	odd	12		4900.2.a.bf.1.1		4
105.53	even	12		700.2.i.f.501.3		8
105.59	even	6		980.2.q.b.949.1		4
105.68	odd	12		4900.2.a.bf.1.3		4
105.74	odd	6		140.2.q.b.109.2	yes	4
105.89	even	6		980.2.e.c.589.4		4
105.104	even	2		980.2.q.g.569.1		4
420.179	even	6		560.2.bw.a.529.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.q.a.9.2	✓	4	15.14	odd	2
140.2.q.a.109.2	yes	4	21.11	odd	6
140.2.q.b.9.1	yes	4	3.2	odd	2
140.2.q.b.109.2	yes	4	105.74	odd	6
560.2.bw.a.289.1		4	12.11	even	2
560.2.bw.a.529.2		4	420.179	even	6
560.2.bw.e.289.2		4	60.59	even	2
560.2.bw.e.529.2		4	84.11	even	6
700.2.i.f.401.2		8	15.2	even	4
700.2.i.f.401.3		8	15.8	even	4
700.2.i.f.501.2		8	105.32	even	12
700.2.i.f.501.3		8	105.53	even	12
980.2.e.c.589.2		4	21.5	even	6
980.2.e.c.589.4		4	105.89	even	6
980.2.e.f.589.1		4	105.44	odd	6
980.2.e.f.589.3		4	21.2	odd	6
980.2.q.b.569.2		4	21.20	even	2
980.2.q.b.949.1		4	105.59	even	6
980.2.q.g.569.1		4	105.104	even	2
980.2.q.g.949.1		4	21.17	even	6
1260.2.bm.a.109.1		4	7.4	even	3
1260.2.bm.a.289.1		4	5.4	even	2
1260.2.bm.b.109.1		4	35.4	even	6	inner
1260.2.bm.b.289.2		4	1.1	even	1	trivial
4900.2.a.be.1.1		4	105.23	even	12
4900.2.a.be.1.3		4	105.2	even	12
4900.2.a.bf.1.1		4	105.47	odd	12
4900.2.a.bf.1.3		4	105.68	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 2.17945i) q^{5} +(-1.13746 - 2.38876i) q^{7} +(-2.63746 - 4.56821i) q^{11} +2.62685i q^{13} +(0.362541 - 0.209313i) q^{17} +(1.63746 - 2.83616i) q^{19} +(-6.77492 - 3.91150i) q^{23} +(-4.50000 + 2.17945i) q^{25} +4.27492 q^{29} +(-1.63746 - 2.83616i) q^{31} +(4.63746 - 3.67341i) q^{35} +(-8.63746 - 4.98684i) q^{37} +3.72508 q^{41} -2.15068i q^{43} +(-5.63746 - 3.25479i) q^{47} +(-4.41238 + 5.43424i) q^{49} +(4.91238 - 2.83616i) q^{53} +(8.63746 - 8.03231i) q^{55} +(1.63746 + 2.83616i) q^{59} +(6.77492 - 11.7345i) q^{61} +(-5.72508 + 1.31342i) q^{65} +(-3.04983 + 1.76082i) q^{67} +4.54983 q^{71} +(5.63746 - 3.25479i) q^{73} +(-7.91238 + 11.4964i) q^{77} +(3.63746 - 6.30026i) q^{79} +7.40437i q^{83} +(0.637459 + 0.685484i) q^{85} +(3.50000 - 6.06218i) q^{89} +(6.27492 - 2.98793i) q^{91} +(7.00000 + 2.15068i) q^{95} +6.92820i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} + 3 q^{7} - 3 q^{11} + 9 q^{17} - q^{19} - 12 q^{23} - 18 q^{25} + 2 q^{29} + q^{31} + 11 q^{35} - 27 q^{37} + 30 q^{41} - 15 q^{47} + 5 q^{49} - 3 q^{53} + 27 q^{55} - q^{59} + 12 q^{61}+ \cdots + 28 q^{95}+O(q^{100}) \) 4 * q + 2 * q^5 + 3 * q^7 - 3 * q^11 + 9 * q^17 - q^19 - 12 * q^23 - 18 * q^25 + 2 * q^29 + q^31 + 11 * q^35 - 27 * q^37 + 30 * q^41 - 15 * q^47 + 5 * q^49 - 3 * q^53 + 27 * q^55 - q^59 + 12 * q^61 - 38 * q^65 + 18 * q^67 - 12 * q^71 + 15 * q^73 - 9 * q^77 + 7 * q^79 - 5 * q^85 + 14 * q^89 + 10 * q^91 + 28 * q^95

Introduction

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