LMFDB - Embedded newform 2268.2.k.e.1297.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2268,2,Mod(1297,2268)] 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("2268.1297"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2268, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2268 = 2^{2} \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2268.k (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0,0,0,-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:	$18.1100711784$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 $ x^14 - 5x^12 - 3x^11 + 7x^10 + 30x^9 - 117x^7 + 270x^5 + 189x^4 - 243x^3 - 1215*x^2 + 2187
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{7} $
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1297.3
Root			$-1.73040 + 0.0755709i$ of defining polynomial
Character	$\chi$	$=$	2268.1297
Dual form			2268.2.k.e.1621.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.483929 + 0.838189i) q^{5} +(2.63536 - 0.234242i) q^{7} +(-0.364122 - 0.630678i) q^{11} -3.62132 q^{13} +(3.49948 + 6.06128i) q^{17} +(-0.348050 + 0.602841i) q^{19} +(-3.21898 + 5.57544i) q^{23} +(2.03163 + 3.51888i) q^{25} -6.69454 q^{29} +(-4.58310 - 7.93816i) q^{31} +(-1.07899 + 2.32229i) q^{35} +(0.854506 - 1.48005i) q^{37} +7.24887 q^{41} +0.696101 q^{43} +(-3.83120 + 6.63583i) q^{47} +(6.89026 - 1.23462i) q^{49} +(2.05637 + 3.56174i) q^{53} +0.704836 q^{55} +(2.38809 + 4.13629i) q^{59} +(-2.46287 + 4.26582i) q^{61} +(1.75246 - 3.03535i) q^{65} +(2.91035 + 5.04087i) q^{67} +0.304424 q^{71} +(5.33879 + 9.24705i) q^{73} +(-1.10732 - 1.57677i) q^{77} +(1.61945 - 2.80497i) q^{79} -1.23752 q^{83} -6.77400 q^{85} +(-5.78679 + 10.0230i) q^{89} +(-9.54349 + 0.848265i) q^{91} +(-0.336863 - 0.583464i) q^{95} -2.65866 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{5} - 3 q^{7} + 2 q^{11} - 4 q^{13} + 2 q^{17} + 7 q^{19} + 11 q^{23} - 9 q^{25} - 2 q^{29} - q^{31} - 19 q^{35} + 10 q^{37} + 66 q^{41} - 14 q^{43} - 3 q^{47} + 17 q^{49} - 15 q^{53} - 28 q^{55}+ \cdots + 36 q^{97}+O(q^{100}) $ 14 * q - 2 * q^5 - 3 * q^7 + 2 * q^11 - 4 * q^13 + 2 * q^17 + 7 * q^19 + 11 * q^23 - 9 * q^25 - 2 * q^29 - q^31 - 19 * q^35 + 10 * q^37 + 66 * q^41 - 14 * q^43 - 3 * q^47 + 17 * q^49 - 15 * q^53 - 28 * q^55 - 14 * q^59 - 10 * q^61 + 15 * q^65 + 6 * q^67 + 2 * q^71 + 21 * q^73 + 28 * q^77 - 10 * q^79 + 50 * q^83 - 16 * q^85 - 6 * q^89 + 2 * q^91 - 28 * q^95 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times$.

$n$	$325$	$1135$	$1541$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$5$	−0.483929	+	0.838189i	−0.216419	+	0.374850i	−0.953711	−	0.300725i	$-0.902771\pi$
$5$	−0.483929	+	0.838189i	−0.216419	+	0.374850i	0.737291	+	0.675575i	$0.236105\pi$
$6$		0			0
$7$	2.63536	−	0.234242i	0.996073	−	0.0885351i
$7$	2.63536	−	0.234242i	0.996073	−	0.0885351i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.364122	−	0.630678i	−0.109787	−	0.190156i	0.805897	−	0.592056i	$-0.201683\pi$
$11$	−0.364122	−	0.630678i	−0.109787	−	0.190156i	−0.915684	+	0.401899i	$0.868350\pi$
$12$		0			0
$13$	−3.62132			−1.00437			−0.502187	−	0.864759i	$-0.667471\pi$
$13$	−3.62132			−1.00437			−0.502187	+	0.864759i	$0.667471\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.49948	+	6.06128i	0.848749	+	1.47008i	0.882325	+	0.470641i	$0.155977\pi$
$17$	3.49948	+	6.06128i	0.848749	+	1.47008i	−0.0335755	+	0.999436i	$0.510689\pi$
$18$		0			0
$19$	−0.348050	+	0.602841i	−0.0798483	+	0.138301i	−0.903184	−	0.429253i	$-0.858777\pi$
$19$	−0.348050	+	0.602841i	−0.0798483	+	0.138301i	0.823336	+	0.567554i	$0.192110\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.21898	+	5.57544i	−0.671204	+	1.16256i	0.306359	+	0.951916i	$0.400889\pi$
$23$	−3.21898	+	5.57544i	−0.671204	+	1.16256i	−0.977563	+	0.210643i	$0.932444\pi$
$24$		0			0
$25$	2.03163	+	3.51888i	0.406325	+	0.703776i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.69454			−1.24315			−0.621573	−	0.783356i	$-0.713506\pi$
$29$	−6.69454			−1.24315			−0.621573	+	0.783356i	$0.713506\pi$
$30$		0			0
$31$	−4.58310	−	7.93816i	−0.823149	−	1.42574i	−0.903326	−	0.428956i	$-0.858882\pi$
$31$	−4.58310	−	7.93816i	−0.823149	−	1.42574i	0.0801762	−	0.996781i	$-0.474452\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.07899	+	2.32229i	−0.182382	+	0.392538i
$36$		0			0
$37$	0.854506	−	1.48005i	0.140480	−	0.243318i	−0.787197	−	0.616701i	$-0.788469\pi$
$37$	0.854506	−	1.48005i	0.140480	−	0.243318i	0.927677	+	0.373383i	$0.121802\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	7.24887			1.13208			0.566042	−	0.824376i	$-0.308474\pi$
$41$	7.24887			1.13208			0.566042	+	0.824376i	$0.308474\pi$
$42$		0			0
$43$	0.696101			0.106154			0.0530772	−	0.998590i	$-0.483097\pi$
$43$	0.696101			0.106154			0.0530772	+	0.998590i	$0.483097\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.83120	+	6.63583i	−0.558838	+	0.967936i	0.438756	+	0.898606i	$0.355419\pi$
$47$	−3.83120	+	6.63583i	−0.558838	+	0.967936i	−0.997594	+	0.0693294i	$0.977914\pi$
$48$		0			0
$49$	6.89026	−	1.23462i	0.984323	−	0.176375i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.05637	+	3.56174i	0.282465	+	0.489243i	0.971991	−	0.235017i	$-0.0755147\pi$
$53$	2.05637	+	3.56174i	0.282465	+	0.489243i	−0.689527	+	0.724260i	$0.742181\pi$
$54$		0			0
$55$	0.704836			0.0950401
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.38809	+	4.13629i	0.310903	+	0.538500i	0.978558	−	0.205971i	$-0.0660353\pi$
$59$	2.38809	+	4.13629i	0.310903	+	0.538500i	−0.667655	+	0.744471i	$0.732702\pi$
$60$		0			0
$61$	−2.46287	+	4.26582i	−0.315338	+	0.546182i	−0.979509	−	0.201399i	$-0.935451\pi$
$61$	−2.46287	+	4.26582i	−0.315338	+	0.546182i	0.664171	+	0.747581i	$0.268785\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.75246	−	3.03535i	0.217366	−	0.376489i
$66$		0			0
$67$	2.91035	+	5.04087i	0.355556	+	0.615841i	0.987213	−	0.159407i	$-0.0509583\pi$
$67$	2.91035	+	5.04087i	0.355556	+	0.615841i	−0.631657	+	0.775248i	$0.717625\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.304424			0.0361285			0.0180642	−	0.999837i	$-0.494250\pi$
$71$	0.304424			0.0361285			0.0180642	+	0.999837i	$0.494250\pi$
$72$		0			0
$73$	5.33879	+	9.24705i	0.624858	+	1.08229i	0.988568	+	0.150773i	$0.0481763\pi$
$73$	5.33879	+	9.24705i	0.624858	+	1.08229i	−0.363711	+	0.931512i	$0.618490\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.10732	−	1.57677i	−0.126191	−	0.179690i
$78$		0			0
$79$	1.61945	−	2.80497i	0.182203	−	0.315584i	−0.760428	−	0.649423i	$-0.775011\pi$
$79$	1.61945	−	2.80497i	0.182203	−	0.315584i	0.942630	+	0.333839i	$0.108344\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−1.23752			−0.135835			−0.0679176	−	0.997691i	$-0.521636\pi$
$83$	−1.23752			−0.135835			−0.0679176	+	0.997691i	$0.521636\pi$
$84$		0			0
$85$	−6.77400			−0.734744
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.78679	+	10.0230i	−0.613399	+	1.06244i	0.377264	+	0.926106i	$0.376865\pi$
$89$	−5.78679	+	10.0230i	−0.613399	+	1.06244i	−0.990663	+	0.136333i	$0.956468\pi$
$90$		0			0
$91$	−9.54349	+	0.848265i	−1.00043	+	0.0889223i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−0.336863	−	0.583464i	−0.0345614	−	0.0598622i
$96$		0			0
$97$	−2.65866			−0.269946			−0.134973	−	0.990849i	$-0.543095\pi$
$97$	−2.65866			−0.269946			−0.134973	+	0.990849i	$0.543095\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−0.806969	−	1.39771i	−0.0802964	−	0.139077i	0.823081	−	0.567924i	$-0.192253\pi$
$101$	−0.806969	−	1.39771i	−0.0802964	−	0.139077i	−0.903377	+	0.428847i	$0.858920\pi$
$102$		0			0
$103$	−5.42007	+	9.38783i	−0.534055	+	0.925010i	0.465153	+	0.885230i	$0.345999\pi$
$103$	−5.42007	+	9.38783i	−0.534055	+	0.925010i	−0.999208	+	0.0397803i	$0.987334\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.97630	−	8.61920i	0.481077	−	0.833249i	−0.518688	−	0.854964i	$-0.673579\pi$
$107$	4.97630	−	8.61920i	0.481077	−	0.833249i	0.999764	+	0.0217146i	$0.00691252\pi$
$108$		0			0
$109$	−9.27835	−	16.0706i	−0.888705	−	1.53928i	−0.841407	−	0.540401i	$-0.818272\pi$
$109$	−9.27835	−	16.0706i	−0.888705	−	1.53928i	−0.0472974	−	0.998881i	$-0.515061\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−11.5165			−1.08338			−0.541689	−	0.840579i	$-0.682215\pi$
$113$	−11.5165			−1.08338			−0.541689	+	0.840579i	$0.682215\pi$
$114$		0			0
$115$	−3.11551	−	5.39623i	−0.290523	−	0.503201i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	10.6422	+	15.1539i	0.975570	+	1.38916i
$120$		0			0
$121$	5.23483	−	9.06699i	0.475894	−	0.824272i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−8.77193			−0.784586
$126$		0			0
$127$	9.06977			0.804812			0.402406	−	0.915461i	$-0.368174\pi$
$127$	9.06977			0.804812			0.402406	+	0.915461i	$0.368174\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.54255	+	11.3320i	−0.571625	+	0.990084i	0.424774	+	0.905299i	$0.360354\pi$
$131$	−6.54255	+	11.3320i	−0.571625	+	0.990084i	−0.996399	+	0.0847847i	$0.972980\pi$
$132$		0			0
$133$	−0.776028	+	1.67023i	−0.0672902	+	0.144828i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	10.0382	+	17.3867i	0.857623	+	1.48545i	0.874190	+	0.485584i	$0.161393\pi$
$137$	10.0382	+	17.3867i	0.857623	+	1.48545i	−0.0165668	+	0.999863i	$0.505274\pi$
$138$		0			0
$139$	−0.675665			−0.0573091			−0.0286546	−	0.999589i	$-0.509122\pi$
$139$	−0.675665			−0.0573091			−0.0286546	+	0.999589i	$0.509122\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.31860	+	2.28388i	0.110267	+	0.190988i
$144$		0			0
$145$	3.23968	−	5.61129i	0.269041	−	0.465992i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.7544	+	18.6271i	−0.881034	+	1.52599i	−0.0308402	+	0.999524i	$0.509818\pi$
$149$	−10.7544	+	18.6271i	−0.881034	+	1.52599i	−0.850193	+	0.526471i	$0.823515\pi$
$150$		0			0
$151$	−7.08523	−	12.2720i	−0.576588	−	0.998680i	−0.995867	−	0.0908223i	$-0.971050\pi$
$151$	−7.08523	−	12.2720i	−0.576588	−	0.998680i	0.419279	−	0.907857i	$-0.362283\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	8.87158			0.712582
$156$		0			0
$157$	7.99845	+	13.8537i	0.638346	+	1.10565i	0.985796	+	0.167949i	$0.0537143\pi$
$157$	7.99845	+	13.8537i	0.638346	+	1.10565i	−0.347450	+	0.937699i	$0.612952\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−7.17717	+	15.4473i	−0.565641	+	1.21742i
$162$		0			0
$163$	−10.0904	+	17.4771i	−0.790340	+	1.36891i	0.135417	+	0.990789i	$0.456763\pi$
$163$	−10.0904	+	17.4771i	−0.790340	+	1.36891i	−0.925757	+	0.378120i	$0.876571\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	24.4598			1.89276			0.946378	−	0.323061i	$-0.104712\pi$
$167$	24.4598			1.89276			0.946378	+	0.323061i	$0.104712\pi$
$168$		0			0
$169$	0.113954			0.00876572
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.87800	+	17.1092i	−0.751010	+	1.30079i	0.196323	+	0.980539i	$0.437100\pi$
$173$	−9.87800	+	17.1092i	−0.751010	+	1.30079i	−0.947333	+	0.320249i	$0.896233\pi$
$174$		0			0
$175$	6.17834	+	8.79763i	0.467039	+	0.665038i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−6.32439	−	10.9542i	−0.472707	−	0.818753i	0.526805	−	0.849986i	$-0.323390\pi$
$179$	−6.32439	−	10.9542i	−0.472707	−	0.818753i	−0.999512	+	0.0312332i	$0.990057\pi$
$180$		0			0
$181$	12.5654			0.933975			0.466988	−	0.884264i	$-0.345339\pi$
$181$	12.5654			0.933975			0.466988	+	0.884264i	$0.345339\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.827040	+	1.43248i	0.0608052	+	0.105318i
$186$		0			0
$187$	2.54848	−	4.41409i	0.186363	−	0.322790i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	3.70316	−	6.41407i	0.267951	−	0.464105i	−0.700381	−	0.713769i	$-0.746987\pi$
$191$	3.70316	−	6.41407i	0.267951	−	0.464105i	0.968333	+	0.249663i	$0.0803200\pi$
$192$		0			0
$193$	0.813937	+	1.40978i	0.0585885	+	0.101478i	0.893832	−	0.448402i	$-0.148007\pi$
$193$	0.813937	+	1.40978i	0.0585885	+	0.101478i	−0.835244	+	0.549880i	$0.814673\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.27125			−0.589302			−0.294651	−	0.955605i	$-0.595203\pi$
$197$	−8.27125			−0.589302			−0.294651	+	0.955605i	$0.595203\pi$
$198$		0			0
$199$	5.34411	+	9.25627i	0.378834	+	0.656159i	0.990893	−	0.134653i	$-0.0429919\pi$
$199$	5.34411	+	9.25627i	0.378834	+	0.656159i	−0.612059	+	0.790812i	$0.709659\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−17.6425	+	1.56814i	−1.23826	+	0.110062i
$204$		0			0
$205$	−3.50794	+	6.07593i	−0.245005	+	0.424361i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	0.506931			0.0350652
$210$		0			0
$211$	22.5451			1.55207			0.776034	−	0.630691i	$-0.217228\pi$
$211$	22.5451			1.55207			0.776034	+	0.630691i	$0.217228\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−0.336863	+	0.583464i	−0.0229739	+	0.0397919i
$216$		0			0
$217$	−13.9376	−	19.8464i	−0.946145	−	1.34726i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−12.6727	−	21.9498i	−0.852461	−	1.47651i
$222$		0			0
$223$	−7.40186			−0.495665			−0.247832	−	0.968803i	$-0.579718\pi$
$223$	−7.40186			−0.495665			−0.247832	+	0.968803i	$0.579718\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.299086	+	0.518033i	0.0198511	+	0.0343831i	0.875780	−	0.482710i	$-0.160347\pi$
$227$	0.299086	+	0.518033i	0.0198511	+	0.0343831i	−0.855929	+	0.517093i	$0.827014\pi$
$228$		0			0
$229$	2.01858	−	3.49629i	0.133392	−	0.231041i	−0.791590	−	0.611052i	$-0.790747\pi$
$229$	2.01858	−	3.49629i	0.133392	−	0.231041i	0.924982	+	0.380011i	$0.124080\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−5.59754	+	9.69523i	−0.366707	+	0.635155i	−0.989049	−	0.147591i	$-0.952848\pi$
$233$	−5.59754	+	9.69523i	−0.366707	+	0.635155i	0.622341	+	0.782746i	$0.286182\pi$
$234$		0			0
$235$	−3.70805	−	6.42254i	−0.241887	−	0.418960i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	25.6342			1.65814			0.829069	−	0.559146i	$-0.188871\pi$
$239$	25.6342			1.65814			0.829069	+	0.559146i	$0.188871\pi$
$240$		0			0
$241$	3.29590	+	5.70866i	0.212307	+	0.367727i	0.952436	−	0.304738i	$-0.0985688\pi$
$241$	3.29590	+	5.70866i	0.212307	+	0.367727i	−0.740129	+	0.672465i	$0.765236\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−2.29955	+	6.37281i	−0.146913	+	0.407144i
$246$		0			0
$247$	1.26040	−	2.18308i	0.0801975	−	0.138906i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	25.0438			1.58075			0.790374	−	0.612624i	$-0.209886\pi$
$251$	25.0438			1.58075			0.790374	+	0.612624i	$0.209886\pi$
$252$		0			0
$253$	4.68840			0.294757
$254$		0			0
$255$		0			0
$256$		0			0
$257$	9.07036	−	15.7103i	0.565794	−	0.979984i	−0.431182	−	0.902265i	$-0.641903\pi$
$257$	9.07036	−	15.7103i	0.565794	−	0.979984i	0.996975	−	0.0777184i	$-0.0247635\pi$
$258$		0			0
$259$	1.90524	−	4.10062i	0.118386	−	0.254800i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.40438	−	11.0927i	−0.394911	−	0.684006i	0.598179	−	0.801363i	$-0.295891\pi$
$263$	−6.40438	−	11.0927i	−0.394911	−	0.684006i	−0.993090	+	0.117357i	$0.962558\pi$
$264$		0			0
$265$	−3.98055			−0.244523
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−14.4412	−	25.0129i	−0.880497	−	1.52507i	−0.850789	−	0.525507i	$-0.823876\pi$
$269$	−14.4412	−	25.0129i	−0.880497	−	1.52507i	−0.0297079	−	0.999559i	$-0.509458\pi$
$270$		0			0
$271$	4.59579	−	7.96015i	0.279175	−	0.483544i	−0.692005	−	0.721892i	$-0.743273\pi$
$271$	4.59579	−	7.96015i	0.279175	−	0.483544i	0.971180	+	0.238348i	$0.0766059\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	1.47952	−	2.56260i	0.0892183	−	0.154531i
$276$		0			0
$277$	1.95778	+	3.39098i	0.117632	+	0.203744i	0.918829	−	0.394656i	$-0.129136\pi$
$277$	1.95778	+	3.39098i	0.117632	+	0.203744i	−0.801197	+	0.598401i	$0.795803\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−15.2931			−0.912308			−0.456154	−	0.889901i	$-0.650773\pi$
$281$	−15.2931			−0.912308			−0.456154	+	0.889901i	$0.650773\pi$
$282$		0			0
$283$	−12.4890	−	21.6315i	−0.742392	−	1.28586i	−0.951403	−	0.307947i	$-0.900358\pi$
$283$	−12.4890	−	21.6315i	−0.742392	−	1.28586i	0.209011	−	0.977913i	$-0.432975\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	19.1034	−	1.69799i	1.12764	−	0.100229i
$288$		0			0
$289$	−15.9928	+	27.7003i	−0.940751	+	1.62943i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	8.16183			0.476819			0.238410	−	0.971165i	$-0.423374\pi$
$293$	8.16183			0.476819			0.238410	+	0.971165i	$0.423374\pi$
$294$		0			0
$295$	−4.62266			−0.269142
$296$		0			0
$297$		0			0
$298$		0			0
$299$	11.6570	−	20.1904i	0.674139	−	1.16764i
$300$		0			0
$301$	1.83448	−	0.163056i	0.105738	−	0.00939839i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−2.38371	−	4.12870i	−0.136491	−	0.236409i
$306$		0			0
$307$	18.0692			1.03126			0.515631	−	0.856811i	$-0.327558\pi$
$307$	18.0692			1.03126			0.515631	+	0.856811i	$0.327558\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	5.00384	+	8.66691i	0.283742	+	0.491456i	0.972303	−	0.233723i	$-0.0750907\pi$
$311$	5.00384	+	8.66691i	0.283742	+	0.491456i	−0.688561	+	0.725178i	$0.741757\pi$
$312$		0			0
$313$	−1.49532	+	2.58998i	−0.0845207	+	0.146394i	−0.905187	−	0.425014i	$-0.860269\pi$
$313$	−1.49532	+	2.58998i	−0.0845207	+	0.146394i	0.820666	+	0.571408i	$0.193603\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.9246	−	20.6541i	0.669754	−	1.16005i	−0.308219	−	0.951315i	$-0.599733\pi$
$317$	11.9246	−	20.6541i	0.669754	−	1.16005i	0.977973	−	0.208732i	$-0.0669336\pi$
$318$		0			0
$319$	2.43763	+	4.22210i	0.136481	+	0.236392i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−4.87199			−0.271085
$324$		0			0
$325$	−7.35717	−	12.7430i	−0.408102	−	0.706854i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−8.54221	+	18.3852i	−0.470947	+	1.01361i
$330$		0			0
$331$	8.01886	−	13.8891i	0.440757	−	0.763413i	−0.556989	−	0.830520i	$-0.688044\pi$
$331$	8.01886	−	13.8891i	0.440757	−	0.763413i	0.997746	+	0.0671069i	$0.0213768\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.63360			−0.307797
$336$		0			0
$337$	−33.7970			−1.84104			−0.920520	−	0.390696i	$-0.872234\pi$
$337$	−33.7970			−1.84104			−0.920520	+	0.390696i	$0.872234\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−3.33761	+	5.78092i	−0.180742	+	0.313054i
$342$		0			0
$343$	17.8691	−	4.86767i	0.964842	−	0.262829i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−17.6637	−	30.5944i	−0.948237	−	1.64240i	−0.749136	−	0.662417i	$-0.769531\pi$
$347$	−17.6637	−	30.5944i	−0.948237	−	1.64240i	−0.199102	−	0.979979i	$-0.563802\pi$
$348$		0			0
$349$	11.5069			0.615950			0.307975	−	0.951395i	$-0.400349\pi$
$349$	11.5069			0.615950			0.307975	+	0.951395i	$0.400349\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.4432	−	21.5522i	−0.662283	−	1.14711i	−0.980014	−	0.198926i	$-0.936254\pi$
$353$	−12.4432	−	21.5522i	−0.662283	−	1.14711i	0.317732	−	0.948181i	$-0.397079\pi$
$354$		0			0
$355$	−0.147320	+	0.255165i	−0.00781891	+	0.0135427i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	9.22681	−	15.9813i	0.486972	−	0.843461i	−0.512916	−	0.858439i	$-0.671435\pi$
$359$	9.22681	−	15.9813i	0.486972	−	0.843461i	0.999888	+	0.0149785i	$0.00476798\pi$
$360$		0			0
$361$	9.25772	+	16.0348i	0.487249	+	0.843939i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−10.3344			−0.540925
$366$		0			0
$367$	9.10688	+	15.7736i	0.475375	+	0.823374i	0.999602	−	0.0282046i	$-0.00897899\pi$
$367$	9.10688	+	15.7736i	0.475375	+	0.823374i	−0.524227	+	0.851579i	$0.675646\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.25360	+	8.90479i	0.324671	+	0.462314i
$372$		0			0
$373$	9.09995	−	15.7616i	0.471177	−	0.816103i	−0.528279	−	0.849071i	$-0.677162\pi$
$373$	9.09995	−	15.7616i	0.471177	−	0.816103i	0.999456	+	0.0329676i	$0.0104958\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	24.2431			1.24858
$378$		0			0
$379$	−24.1061			−1.23825			−0.619124	−	0.785293i	$-0.712512\pi$
$379$	−24.1061			−1.23825			−0.619124	+	0.785293i	$0.712512\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	3.21847	−	5.57455i	0.164456	−	0.284846i	−0.772006	−	0.635615i	$-0.780746\pi$
$383$	3.21847	−	5.57455i	0.164456	−	0.284846i	0.936462	+	0.350769i	$0.114080\pi$
$384$		0			0
$385$	1.85750	−	0.165102i	0.0946668	−	0.00841438i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−16.9299	−	29.3234i	−0.858379	−	1.48676i	−0.873475	−	0.486869i	$-0.838139\pi$
$389$	−16.9299	−	29.3234i	−0.858379	−	1.48676i	0.0150964	−	0.999886i	$-0.495194\pi$
$390$		0			0
$391$	−45.0591			−2.27873
$392$		0			0
$393$		0			0
$394$		0			0
$395$	1.56740	+	2.71481i	0.0788643	+	0.136597i
$396$		0			0
$397$	−0.808630	+	1.40059i	−0.0405840	+	0.0702935i	−0.885604	−	0.464441i	$-0.846255\pi$
$397$	−0.808630	+	1.40059i	−0.0405840	+	0.0702935i	0.845020	+	0.534735i	$0.179588\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.87691	+	4.98296i	−0.143666	+	0.248837i	−0.928874	−	0.370395i	$-0.879222\pi$
$401$	−2.87691	+	4.98296i	−0.143666	+	0.248837i	0.785208	+	0.619232i	$0.212556\pi$
$402$		0			0
$403$	16.5969	+	28.7466i	0.826749	+	1.43197i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.24458			−0.0616914
$408$		0			0
$409$	2.88631	+	4.99923i	0.142719	+	0.247196i	0.928520	−	0.371284i	$-0.121082\pi$
$409$	2.88631	+	4.99923i	0.142719	+	0.247196i	−0.785801	+	0.618480i	$0.787749\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.26237	+	10.3412i	0.357358	+	0.508859i
$414$		0			0
$415$	0.598871	−	1.03727i	0.0293974	−	0.0509178i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	18.5806			0.907723			0.453862	−	0.891072i	$-0.350046\pi$
$419$	18.5806			0.907723			0.453862	+	0.891072i	$0.350046\pi$
$420$		0			0
$421$	16.1158			0.785434			0.392717	−	0.919659i	$-0.371535\pi$
$421$	16.1158			0.785434			0.392717	+	0.919659i	$0.371535\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−14.2193	+	24.6285i	−0.689737	+	1.19466i
$426$		0			0
$427$	−5.49132	+	11.8189i	−0.265744	+	0.571956i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	1.82664	+	3.16383i	0.0879860	+	0.152396i	0.906660	−	0.421863i	$-0.138624\pi$
$431$	1.82664	+	3.16383i	0.0879860	+	0.152396i	−0.818674	+	0.574259i	$0.805290\pi$
$432$		0			0
$433$	12.6697			0.608865			0.304432	−	0.952534i	$-0.401533\pi$
$433$	12.6697			0.608865			0.304432	+	0.952534i	$0.401533\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.24073	−	3.88107i	−0.107189	−	0.185657i
$438$		0			0
$439$	−5.85810	+	10.1465i	−0.279592	+	0.484267i	−0.971283	−	0.237926i	$-0.923532\pi$
$439$	−5.85810	+	10.1465i	−0.279592	+	0.484267i	0.691692	+	0.722193i	$0.256866\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	14.8735	−	25.7617i	0.706661	−	1.22397i	−0.259428	−	0.965763i	$-0.583534\pi$
$443$	14.8735	−	25.7617i	0.706661	−	1.22397i	0.966089	−	0.258210i	$-0.0831328\pi$
$444$		0			0
$445$	−5.60079	−	9.70085i	−0.265503	−	0.459865i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	11.0193			0.520034			0.260017	−	0.965604i	$-0.416272\pi$
$449$	11.0193			0.520034			0.260017	+	0.965604i	$0.416272\pi$
$450$		0			0
$451$	−2.63947	−	4.57170i	−0.124288	−	0.215273i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	3.90736	−	8.40974i	0.183180	−	0.394255i
$456$		0			0
$457$	−0.258224	+	0.447257i	−0.0120792	+	0.0209218i	−0.872002	−	0.489503i	$-0.837178\pi$
$457$	−0.258224	+	0.447257i	−0.0120792	+	0.0209218i	0.859923	+	0.510424i	$0.170512\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	7.09925			0.330645			0.165322	−	0.986240i	$-0.447134\pi$
$461$	7.09925			0.330645			0.165322	+	0.986240i	$0.447134\pi$
$462$		0			0
$463$	9.82296			0.456512			0.228256	−	0.973601i	$-0.426698\pi$
$463$	9.82296			0.456512			0.228256	+	0.973601i	$0.426698\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−4.79604	+	8.30698i	−0.221934	+	0.384401i	−0.955395	−	0.295330i	$-0.904570\pi$
$467$	−4.79604	+	8.30698i	−0.221934	+	0.384401i	0.733461	+	0.679731i	$0.237904\pi$
$468$		0			0
$469$	8.85061	+	12.6028i	0.408683	+	0.581943i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−0.253466	−	0.439015i	−0.0116544	−	0.0201859i
$474$		0			0
$475$	−2.82843			−0.129777
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−8.13621	−	14.0923i	−0.371753	−	0.643895i	0.618082	−	0.786113i	$-0.287910\pi$
$479$	−8.13621	−	14.0923i	−0.371753	−	0.643895i	−0.989835	+	0.142218i	$0.954576\pi$
$480$		0			0
$481$	−3.09444	+	5.35973i	−0.141094	+	0.244383i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	1.28660	−	2.22846i	0.0584217	−	0.101189i
$486$		0			0
$487$	−9.50511	−	16.4633i	−0.430718	−	0.746025i	0.566217	−	0.824256i	$-0.308406\pi$
$487$	−9.50511	−	16.4633i	−0.430718	−	0.746025i	−0.996935	+	0.0782307i	$0.975073\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−5.10825			−0.230532			−0.115266	−	0.993335i	$-0.536772\pi$
$491$	−5.10825			−0.230532			−0.115266	+	0.993335i	$0.536772\pi$
$492$		0			0
$493$	−23.4274	−	40.5775i	−1.05512	−	1.82752i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.802268	−	0.0713089i	0.0359866	−	0.00319864i
$498$		0			0
$499$	14.2638	−	24.7056i	0.638536	−	1.10598i	−0.347219	−	0.937784i	$-0.612874\pi$
$499$	14.2638	−	24.7056i	0.638536	−	1.10598i	0.985754	−	0.168192i	$-0.0537928\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	4.05885			0.180975			0.0904877	−	0.995898i	$-0.471157\pi$
$503$	4.05885			0.180975			0.0904877	+	0.995898i	$0.471157\pi$
$504$		0			0
$505$	1.56206			0.0695108
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−8.63023	+	14.9480i	−0.382528	+	0.662558i	−0.991423	−	0.130693i	$-0.958280\pi$
$509$	−8.63023	+	14.9480i	−0.382528	+	0.662558i	0.608895	+	0.793251i	$0.291613\pi$
$510$		0			0
$511$	16.2357	+	23.1188i	0.718224	+	1.02271i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−5.24585	−	9.08608i	−0.231160	−	0.400380i
$516$		0			0
$517$	5.58009			0.245412
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−17.0525	−	29.5358i	−0.747083	−	1.29399i	−0.949215	−	0.314628i	$-0.898120\pi$
$521$	−17.0525	−	29.5358i	−0.747083	−	1.29399i	0.202132	−	0.979358i	$-0.435213\pi$
$522$		0			0
$523$	−9.44847	+	16.3652i	−0.413153	+	0.715602i	−0.995233	−	0.0975299i	$-0.968906\pi$
$523$	−9.44847	+	16.3652i	−0.413153	+	0.715602i	0.582080	+	0.813132i	$0.302239\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	32.0770	−	55.5589i	1.39729	−	2.42019i
$528$		0			0
$529$	−9.22366	−	15.9758i	−0.401029	−	0.694602i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−26.2505			−1.13703
$534$		0			0
$535$	4.81634	+	8.34215i	0.208229	+	0.360663i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−3.28754	−	3.89598i	−0.141605	−	0.167812i
$540$		0			0
$541$	0.564117	−	0.977080i	0.0242533	−	0.0420080i	−0.853644	−	0.520857i	$-0.825613\pi$
$541$	0.564117	−	0.977080i	0.0242533	−	0.0420080i	0.877897	+	0.478849i	$0.158946\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	17.9602			0.769332
$546$		0			0
$547$	−31.6854			−1.35477			−0.677386	−	0.735628i	$-0.736887\pi$
$547$	−31.6854			−1.35477			−0.677386	+	0.735628i	$0.736887\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	2.33004	−	4.03575i	0.0992630	−	0.171929i
$552$		0			0
$553$	3.61080	−	7.77146i	0.153547	−	0.330476i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−13.8135	−	23.9257i	−0.585298	−	1.01377i	−0.994838	−	0.101474i	$-0.967644\pi$
$557$	−13.8135	−	23.9257i	−0.585298	−	1.01377i	0.409540	−	0.912292i	$-0.365689\pi$
$558$		0			0
$559$	−2.52080			−0.106619
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−0.920685	−	1.59467i	−0.0388022	−	0.0672074i	0.845972	−	0.533227i	$-0.179021\pi$
$563$	−0.920685	−	1.59467i	−0.0388022	−	0.0672074i	−0.884774	+	0.466020i	$0.845688\pi$
$564$		0			0
$565$	5.57315	−	9.65298i	0.234464	−	0.406104i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	5.75524	−	9.96837i	0.241272	−	0.417896i	−0.719805	−	0.694177i	$-0.755769\pi$
$569$	5.75524	−	9.96837i	0.241272	−	0.417896i	0.961077	+	0.276281i	$0.0891020\pi$
$570$		0			0
$571$	4.35262	+	7.53896i	0.182152	+	0.315496i	0.942613	−	0.333887i	$-0.108361\pi$
$571$	4.35262	+	7.53896i	0.182152	+	0.315496i	−0.760461	+	0.649383i	$0.775027\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−26.1591			−1.09091
$576$		0			0
$577$	−7.24358	−	12.5462i	−0.301554	−	0.522307i	0.674934	−	0.737878i	$-0.264172\pi$
$577$	−7.24358	−	12.5462i	−0.301554	−	0.522307i	−0.976488	+	0.215571i	$0.930839\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.26131	+	0.289879i	−0.135302	+	0.0120262i
$582$		0			0
$583$	1.49754	−	2.59382i	0.0620218	−	0.107425i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	28.7389			1.18618			0.593091	−	0.805135i	$-0.297907\pi$
$587$	28.7389			1.18618			0.593091	+	0.805135i	$0.297907\pi$
$588$		0			0
$589$	6.38060			0.262908
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.82328	−	11.8183i	0.280199	−	0.485318i	−0.691235	−	0.722630i	$-0.742933\pi$
$593$	6.82328	−	11.8183i	0.280199	−	0.485318i	0.971434	+	0.237312i	$0.0762663\pi$
$594$		0			0
$595$	−17.8519	+	1.58676i	−0.731858	+	0.0650506i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−2.64585	−	4.58275i	−0.108106	−	0.187246i	0.806897	−	0.590693i	$-0.201145\pi$
$599$	−2.64585	−	4.58275i	−0.108106	−	0.187246i	−0.915003	+	0.403447i	$0.867812\pi$
$600$		0			0
$601$	−34.1044			−1.39115			−0.695574	−	0.718454i	$-0.744850\pi$
$601$	−34.1044			−1.39115			−0.695574	+	0.718454i	$0.744850\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5.06657	+	8.77555i	0.205985	+	0.356777i
$606$		0			0
$607$	4.52232	−	7.83289i	0.183555	−	0.317927i	−0.759533	−	0.650468i	$-0.774573\pi$
$607$	4.52232	−	7.83289i	0.183555	−	0.317927i	0.943089	+	0.332541i	$0.107906\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	13.8740	−	24.0305i	0.561282	−	0.972169i
$612$		0			0
$613$	5.97889	+	10.3557i	0.241485	+	0.418264i	0.961137	−	0.276070i	$-0.0890322\pi$
$613$	5.97889	+	10.3557i	0.241485	+	0.418264i	−0.719653	+	0.694334i	$0.755699\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−10.2644			−0.413229			−0.206615	−	0.978422i	$-0.566245\pi$
$617$	−10.2644			−0.413229			−0.206615	+	0.978422i	$0.566245\pi$
$618$		0			0
$619$	21.7803	+	37.7245i	0.875423	+	1.51628i	0.856312	+	0.516460i	$0.172750\pi$
$619$	21.7803	+	37.7245i	0.875423	+	1.51628i	0.0191114	+	0.999817i	$0.493916\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−12.9025	+	27.7698i	−0.516927	+	1.11257i
$624$		0			0
$625$	−5.91314	+	10.2419i	−0.236526	+	0.409674i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	11.9613			0.476929
$630$		0			0
$631$	19.3703			0.771119			0.385559	−	0.922683i	$-0.374008\pi$
$631$	19.3703			0.771119			0.385559	+	0.922683i	$0.374008\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4.38912	+	7.60218i	−0.174177	+	0.301684i
$636$		0			0
$637$	−24.9518	+	4.47097i	−0.988628	+	0.177146i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−2.25008	−	3.89725i	−0.0888728	−	0.153932i	0.818162	−	0.574988i	$-0.194993\pi$
$641$	−2.25008	−	3.89725i	−0.0888728	−	0.153932i	−0.907035	+	0.421055i	$0.861660\pi$
$642$		0			0
$643$	41.8091			1.64879			0.824394	−	0.566016i	$-0.191516\pi$
$643$	41.8091			1.64879			0.824394	+	0.566016i	$0.191516\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	11.9381	+	20.6773i	0.469334	+	0.812910i	0.999385	−	0.0350555i	$-0.0111608\pi$
$647$	11.9381	+	20.6773i	0.469334	+	0.812910i	−0.530052	+	0.847965i	$0.677827\pi$
$648$		0			0
$649$	1.73911	−	3.01223i	0.0682661	−	0.118240i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.16674	−	7.21700i	0.163057	−	0.282423i	−0.772907	−	0.634520i	$-0.781198\pi$
$653$	4.16674	−	7.21700i	0.163057	−	0.282423i	0.935964	+	0.352097i	$0.114531\pi$
$654$		0			0
$655$	−6.33226	−	10.9678i	−0.247422	−	0.428547i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	40.4976			1.57756			0.788781	−	0.614675i	$-0.210713\pi$
$659$	40.4976			1.57756			0.788781	+	0.614675i	$0.210713\pi$
$660$		0			0
$661$	3.88559	+	6.73004i	0.151132	+	0.261768i	0.931644	−	0.363373i	$-0.118375\pi$
$661$	3.88559	+	6.73004i	0.151132	+	0.261768i	−0.780512	+	0.625141i	$0.785042\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−1.02443	−	1.45873i	−0.0397256	−	0.0565672i
$666$		0			0
$667$	21.5496	−	37.3250i	0.834404	−	1.44523i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	3.58714			0.138480
$672$		0			0
$673$	45.5661			1.75644			0.878221	−	0.478254i	$-0.158730\pi$
$673$	45.5661			1.75644			0.878221	+	0.478254i	$0.158730\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−6.54521	+	11.3366i	−0.251553	+	0.435702i	−0.963954	−	0.266071i	$-0.914275\pi$
$677$	−6.54521	+	11.3366i	−0.251553	+	0.435702i	0.712401	+	0.701773i	$0.247608\pi$
$678$		0			0
$679$	−7.00654	+	0.622771i	−0.268886	+	0.0238997i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−12.6506	−	21.9114i	−0.484060	−	0.838417i	0.515772	−	0.856726i	$-0.327505\pi$
$683$	−12.6506	−	21.9114i	−0.484060	−	0.838417i	−0.999832	+	0.0183087i	$0.994172\pi$
$684$		0			0
$685$	−19.4311			−0.742425
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−7.44679	−	12.8982i	−0.283700	−	0.491383i
$690$		0			0
$691$	12.2016	−	21.1337i	0.464170	−	0.803965i	−0.534994	−	0.844856i	$-0.679686\pi$
$691$	12.2016	−	21.1337i	0.464170	−	0.803965i	0.999164	+	0.0408905i	$0.0130195\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	0.326974	−	0.566335i	0.0124028	−	0.0214823i
$696$		0			0
$697$	25.3673	+	43.9375i	0.960855	+	1.66425i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−18.4137			−0.695476			−0.347738	−	0.937592i	$-0.613050\pi$
$701$	−18.4137			−0.695476			−0.347738	+	0.937592i	$0.613050\pi$
$702$		0			0
$703$	0.594823	+	1.03026i	0.0224342	+	0.0388571i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−2.45406	−	3.49445i	−0.0922943	−	0.131422i
$708$		0			0
$709$	6.66501	−	11.5441i	0.250310	−	0.433549i	−0.713301	−	0.700858i	$-0.752801\pi$
$709$	6.66501	−	11.5441i	0.250310	−	0.433549i	0.963611	+	0.267308i	$0.0861342\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	59.0116			2.21000
$714$		0			0
$715$	−2.55244			−0.0954557
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−7.84705	+	13.5915i	−0.292646	+	0.506877i	−0.974434	−	0.224672i	$-0.927869\pi$
$719$	−7.84705	+	13.5915i	−0.292646	+	0.506877i	0.681789	+	0.731549i	$0.261202\pi$
$720$		0			0
$721$	−12.0848	+	26.0099i	−0.450062	+	0.968660i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−13.6008	−	23.5573i	−0.505121	−	0.874896i
$726$		0			0
$727$	25.6775			0.952327			0.476163	−	0.879357i	$-0.342027\pi$
$727$	25.6775			0.952327			0.476163	+	0.879357i	$0.342027\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	2.43599	+	4.21926i	0.0900985	+	0.156055i
$732$		0			0
$733$	−0.586541	+	1.01592i	−0.0216644	+	0.0375238i	−0.876654	−	0.481121i	$-0.840230\pi$
$733$	−0.586541	+	1.01592i	−0.0216644	+	0.0375238i	0.854990	+	0.518645i	$0.173563\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.11944	−	3.67098i	0.0780707	−	0.135222i
$738$		0			0
$739$	11.6114	+	20.1116i	0.427133	+	0.739816i	0.996617	−	0.0821861i	$-0.0261902\pi$
$739$	11.6114	+	20.1116i	0.427133	+	0.739816i	−0.569484	+	0.822003i	$0.692857\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−23.5692			−0.864669			−0.432335	−	0.901713i	$-0.642310\pi$
$743$	−23.5692			−0.864669			−0.432335	+	0.901713i	$0.642310\pi$
$744$		0			0
$745$	−10.4087	−	18.0284i	−0.381346	−	0.660510i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	11.0954	−	23.8804i	0.405416	−	0.872569i
$750$		0			0
$751$	−22.0531	+	38.1971i	−0.804728	+	1.39383i	0.111746	+	0.993737i	$0.464356\pi$
$751$	−22.0531	+	38.1971i	−0.804728	+	1.39383i	−0.916474	+	0.400093i	$0.868978\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	13.7150			0.499139
$756$		0			0
$757$	−2.71020			−0.0985040			−0.0492520	−	0.998786i	$-0.515684\pi$
$757$	−2.71020			−0.0985040			−0.0492520	+	0.998786i	$0.515684\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−14.5248	+	25.1577i	−0.526524	+	0.911966i	0.472999	+	0.881063i	$0.343172\pi$
$761$	−14.5248	+	25.1577i	−0.526524	+	0.911966i	−0.999522	+	0.0309029i	$0.990162\pi$
$762$		0			0
$763$	−28.2162	−	40.1784i	−1.02150	−	1.45456i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−8.64804	−	14.9788i	−0.312263	−	0.540855i
$768$		0			0
$769$	10.5035			0.378766			0.189383	−	0.981903i	$-0.439351\pi$
$769$	10.5035			0.378766			0.189383	+	0.981903i	$0.439351\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−11.9230	−	20.6513i	−0.428841	−	0.742774i	0.567930	−	0.823077i	$-0.307745\pi$
$773$	−11.9230	−	20.6513i	−0.428841	−	0.742774i	−0.996771	+	0.0803029i	$0.974411\pi$
$774$		0			0
$775$	18.6223	−	32.2548i	0.668933	−	1.15863i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−2.52297	+	4.36992i	−0.0903949	+	0.156569i
$780$		0			0
$781$	−0.110847	−	0.191993i	−0.00396643	−	0.00687007i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−15.4827			−0.552602
$786$		0			0
$787$	2.19788	+	3.80684i	0.0783460	+	0.135699i	0.902536	−	0.430613i	$-0.141703\pi$
$787$	2.19788	+	3.80684i	0.0783460	+	0.135699i	−0.824190	+	0.566313i	$0.808369\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−30.3501	+	2.69764i	−1.07912	+	0.0959171i
$792$		0			0
$793$	8.91885	−	15.4479i	0.316717	−	0.548571i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.12471			0.181527			0.0907633	−	0.995872i	$-0.471069\pi$
$797$	5.12471			0.181527			0.0907633	+	0.995872i	$0.471069\pi$
$798$		0			0
$799$	−53.6289			−1.89725
$800$		0			0
$801$		0			0
$802$		0			0
$803$	3.88794	−	6.73410i	0.137202	−	0.237641i
$804$		0			0
$805$	−9.47452	−	13.4912i	−0.333933	−	0.475503i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−16.4612	−	28.5116i	−0.578744	−	1.00241i	−0.995624	−	0.0934519i	$-0.970210\pi$
$809$	−16.4612	−	28.5116i	−0.578744	−	1.00241i	0.416880	−	0.908961i	$-0.363123\pi$
$810$		0			0
$811$	−31.8830			−1.11956			−0.559781	−	0.828640i	$-0.689115\pi$
$811$	−31.8830			−1.11956			−0.559781	+	0.828640i	$0.689115\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−9.76605	−	16.9153i	−0.342090	−	0.592517i
$816$		0			0
$817$	−0.242278	+	0.419638i	−0.00847624	+	0.0146813i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−17.1139	+	29.6421i	−0.597278	+	1.03452i	0.395943	+	0.918275i	$0.370418\pi$
$821$	−17.1139	+	29.6421i	−0.597278	+	1.03452i	−0.993221	+	0.116241i	$0.962916\pi$
$822$		0			0
$823$	−19.1866	−	33.2321i	−0.668802	−	1.15840i	−0.978239	−	0.207480i	$-0.933474\pi$
$823$	−19.1866	−	33.2321i	−0.668802	−	1.15840i	0.309437	−	0.950920i	$-0.399859\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	9.23903			0.321273			0.160636	−	0.987014i	$-0.448645\pi$
$827$	9.23903			0.321273			0.160636	+	0.987014i	$0.448645\pi$
$828$		0			0
$829$	20.8224	+	36.0654i	0.723191	+	1.25260i	0.959714	+	0.280978i	$0.0906589\pi$
$829$	20.8224	+	36.0654i	0.723191	+	1.25260i	−0.236523	+	0.971626i	$0.576008\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	31.5958	+	37.4433i	1.09473	+	1.29733i
$834$		0			0
$835$	−11.8368	+	20.5019i	−0.409629	+	0.709499i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	30.8483			1.06500			0.532500	−	0.846430i	$-0.321253\pi$
$839$	30.8483			1.06500			0.532500	+	0.846430i	$0.321253\pi$
$840$		0			0
$841$	15.8169			0.545410
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−0.0551458	+	0.0955153i	−0.00189707	+	0.00328583i
$846$		0			0
$847$	11.6718	−	25.1210i	0.401048	−	0.863168i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	5.50128	+	9.52849i	0.188581	+	0.326632i
$852$		0			0
$853$	22.8342			0.781827			0.390913	−	0.920428i	$-0.372159\pi$
$853$	22.8342			0.781827			0.390913	+	0.920428i	$0.372159\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	26.6720	+	46.1973i	0.911100	+	1.57807i	0.812513	+	0.582942i	$0.198099\pi$
$857$	26.6720	+	46.1973i	0.911100	+	1.57807i	0.0985862	+	0.995129i	$0.468568\pi$
$858$		0			0
$859$	11.5878	−	20.0707i	0.395372	−	0.684804i	−0.597777	−	0.801663i	$-0.703949\pi$
$859$	11.5878	−	20.0707i	0.395372	−	0.684804i	0.993149	+	0.116859i	$0.0372825\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	4.58456	−	7.94069i	0.156060	−	0.270304i	−0.777384	−	0.629026i	$-0.783454\pi$
$863$	4.58456	−	7.94069i	0.156060	−	0.270304i	0.933445	+	0.358722i	$0.116787\pi$
$864$		0			0
$865$	−9.56049	−	16.5593i	−0.325067	−	0.563032i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.35871			−0.0800138
$870$		0			0
$871$	−10.5393	−	18.2546i	−0.357111	−	0.618534i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−23.1172	+	2.05476i	−0.781505	+	0.0694634i
$876$		0			0
$877$	−18.6190	+	32.2490i	−0.628718	+	1.08897i	0.359091	+	0.933303i	$0.383087\pi$
$877$	−18.6190	+	32.2490i	−0.628718	+	1.08897i	−0.987809	+	0.155670i	$0.950247\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	7.15345			0.241006			0.120503	−	0.992713i	$-0.461549\pi$
$881$	7.15345			0.241006			0.120503	+	0.992713i	$0.461549\pi$
$882$		0			0
$883$	−39.8688			−1.34169			−0.670846	−	0.741596i	$-0.734069\pi$
$883$	−39.8688			−1.34169			−0.670846	+	0.741596i	$0.734069\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	10.6755	−	18.4904i	0.358447	−	0.620848i	−0.629255	−	0.777199i	$-0.716640\pi$
$887$	10.6755	−	18.4904i	0.358447	−	0.620848i	0.987702	+	0.156351i	$0.0499731\pi$
$888$		0			0
$889$	23.9021	−	2.12452i	0.801652	−	0.0712542i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−2.66690	−	4.61921i	−0.0892445	−	0.154576i
$894$		0			0
$895$	12.2422			0.409212
$896$		0			0
$897$		0			0
$898$		0			0
$899$	30.6818	+	53.1424i	1.02329	+	1.77240i
$900$		0			0
$901$	−14.3925	+	24.9285i	−0.479483	+	0.830490i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−6.08073	+	10.5321i	−0.202130	+	0.350100i
$906$		0			0
$907$	11.3012	+	19.5742i	0.375250	+	0.649951i	0.990364	−	0.138486i	$-0.0442237\pi$
$907$	11.3012	+	19.5742i	0.375250	+	0.649951i	−0.615115	+	0.788438i	$0.710890\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−25.5188			−0.845476			−0.422738	−	0.906252i	$-0.638931\pi$
$911$	−25.5188			−0.845476			−0.422738	+	0.906252i	$0.638931\pi$
$912$		0			0
$913$	0.450607	+	0.780475i	0.0149129	+	0.0258300i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−14.5876	+	31.3965i	−0.481723	+	1.03681i
$918$		0			0
$919$	5.71326	−	9.89566i	0.188463	−	0.326428i	−0.756275	−	0.654254i	$-0.772983\pi$
$919$	5.71326	−	9.89566i	0.188463	−	0.326428i	0.944738	+	0.327826i	$0.106316\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−1.10242			−0.0362865
$924$		0			0
$925$	6.94415			0.228322
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−6.79851	+	11.7754i	−0.223052	+	0.386337i	−0.955733	−	0.294235i	$-0.904935\pi$
$929$	−6.79851	+	11.7754i	−0.223052	+	0.386337i	0.732681	+	0.680572i	$0.238269\pi$
$930$		0			0
$931$	−1.65388	+	4.58344i	−0.0542036	+	0.150216i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	2.46656	+	4.27221i	0.0806652	+	0.139716i
$936$		0			0
$937$	−11.1455			−0.364109			−0.182054	−	0.983288i	$-0.558275\pi$
$937$	−11.1455			−0.364109			−0.182054	+	0.983288i	$0.558275\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−20.7310	−	35.9072i	−0.675813	−	1.17054i	−0.976231	−	0.216734i	$-0.930460\pi$
$941$	−20.7310	−	35.9072i	−0.675813	−	1.17054i	0.300418	−	0.953808i	$-0.402874\pi$
$942$		0			0
$943$	−23.3340	+	40.4156i	−0.759859	+	1.31611i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−21.2784	+	36.8552i	−0.691454	+	1.19763i	0.279908	+	0.960027i	$0.409696\pi$
$947$	−21.2784	+	36.8552i	−0.691454	+	1.19763i	−0.971362	+	0.237606i	$0.923637\pi$
$948$		0			0
$949$	−19.3335	−	33.4865i	−0.627590	−	1.08702i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	21.2114			0.687106			0.343553	−	0.939133i	$-0.388370\pi$
$953$	21.2114			0.687106			0.343553	+	0.939133i	$0.388370\pi$
$954$		0			0
$955$	3.58413	+	6.20790i	0.115980	+	0.200883i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	30.5270	+	43.4689i	0.985770	+	1.40368i
$960$		0			0
$961$	−26.5096	+	45.9160i	−0.855150	+	1.48116i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−1.57555			−0.0507188
$966$		0			0
$967$	19.6651			0.632388			0.316194	−	0.948695i	$-0.397595\pi$
$967$	19.6651			0.632388			0.316194	+	0.948695i	$0.397595\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−12.2892	+	21.2855i	−0.394379	+	0.683084i	−0.993022	−	0.117932i	$-0.962374\pi$
$971$	−12.2892	+	21.2855i	−0.394379	+	0.683084i	0.598643	+	0.801016i	$0.295707\pi$
$972$		0			0
$973$	−1.78062	+	0.158269i	−0.0570841	+	0.00507387i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	23.7359	+	41.1117i	0.759378	+	1.31528i	0.943168	+	0.332316i	$0.107830\pi$
$977$	23.7359	+	41.1117i	0.759378	+	1.31528i	−0.183790	+	0.982966i	$0.558837\pi$
$978$		0			0
$979$	8.42839			0.269373
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−13.7720	−	23.8538i	−0.439258	−	0.760817i	0.558374	−	0.829589i	$-0.311425\pi$
$983$	−13.7720	−	23.8538i	−0.439258	−	0.760817i	−0.997632	+	0.0687719i	$0.978092\pi$
$984$		0			0
$985$	4.00269	−	6.93287i	0.127536	−	0.220900i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−2.24073	+	3.88107i	−0.0712512	+	0.123411i
$990$		0			0
$991$	19.2335	+	33.3135i	0.610973	+	1.05824i	0.991077	+	0.133293i	$0.0425551\pi$
$991$	19.2335	+	33.3135i	0.610973	+	1.05824i	−0.380103	+	0.924944i	$0.624112\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−10.3447			−0.327948
$996$		0			0
$997$	16.2272	+	28.1064i	0.513921	+	0.890138i	0.999870	+	0.0161503i	$0.00514103\pi$
$997$	16.2272	+	28.1064i	0.513921	+	0.890138i	−0.485948	+	0.873988i	$0.661526\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2268.2.k.e.1297.3		14
3.2	odd	2		2268.2.k.f.1297.5		14
7.4	even	3	inner	2268.2.k.e.1621.3		14
9.2	odd	6		756.2.i.b.37.5		14
9.4	even	3		252.2.l.b.205.1	yes	14
9.5	odd	6		756.2.l.b.289.3		14
9.7	even	3		252.2.i.b.121.5	yes	14
21.11	odd	6		2268.2.k.f.1621.5		14
36.7	odd	6		1008.2.q.j.625.3		14
36.11	even	6		3024.2.q.j.2305.5		14
36.23	even	6		3024.2.t.j.289.3		14
36.31	odd	6		1008.2.t.j.961.7		14
63.2	odd	6		5292.2.j.h.1765.5		14
63.4	even	3		252.2.i.b.25.5	✓	14
63.5	even	6		5292.2.j.g.3529.3		14
63.11	odd	6		756.2.l.b.361.3		14
63.13	odd	6		1764.2.l.i.961.7		14
63.16	even	3		1764.2.j.g.589.6		14
63.20	even	6		5292.2.i.i.1549.3		14
63.23	odd	6		5292.2.j.h.3529.5		14
63.25	even	3		252.2.l.b.193.1	yes	14
63.31	odd	6		1764.2.i.i.1537.3		14
63.32	odd	6		756.2.i.b.613.5		14
63.34	odd	6		1764.2.i.i.373.3		14
63.38	even	6		5292.2.l.i.361.5		14
63.40	odd	6		1764.2.j.h.1177.2		14
63.41	even	6		5292.2.l.i.3313.5		14
63.47	even	6		5292.2.j.g.1765.3		14
63.52	odd	6		1764.2.l.i.949.7		14
63.58	even	3		1764.2.j.g.1177.6		14
63.59	even	6		5292.2.i.i.2125.3		14
63.61	odd	6		1764.2.j.h.589.2		14
252.11	even	6		3024.2.t.j.1873.3		14
252.67	odd	6		1008.2.q.j.529.3		14
252.95	even	6		3024.2.q.j.2881.5		14
252.151	odd	6		1008.2.t.j.193.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.i.b.25.5	✓	14	63.4	even	3
252.2.i.b.121.5	yes	14	9.7	even	3
252.2.l.b.193.1	yes	14	63.25	even	3
252.2.l.b.205.1	yes	14	9.4	even	3
756.2.i.b.37.5		14	9.2	odd	6
756.2.i.b.613.5		14	63.32	odd	6
756.2.l.b.289.3		14	9.5	odd	6
756.2.l.b.361.3		14	63.11	odd	6
1008.2.q.j.529.3		14	252.67	odd	6
1008.2.q.j.625.3		14	36.7	odd	6
1008.2.t.j.193.7		14	252.151	odd	6
1008.2.t.j.961.7		14	36.31	odd	6
1764.2.i.i.373.3		14	63.34	odd	6
1764.2.i.i.1537.3		14	63.31	odd	6
1764.2.j.g.589.6		14	63.16	even	3
1764.2.j.g.1177.6		14	63.58	even	3
1764.2.j.h.589.2		14	63.61	odd	6
1764.2.j.h.1177.2		14	63.40	odd	6
1764.2.l.i.949.7		14	63.52	odd	6
1764.2.l.i.961.7		14	63.13	odd	6
2268.2.k.e.1297.3		14	1.1	even	1	trivial
2268.2.k.e.1621.3		14	7.4	even	3	inner
2268.2.k.f.1297.5		14	3.2	odd	2
2268.2.k.f.1621.5		14	21.11	odd	6
3024.2.q.j.2305.5		14	36.11	even	6
3024.2.q.j.2881.5		14	252.95	even	6
3024.2.t.j.289.3		14	36.23	even	6
3024.2.t.j.1873.3		14	252.11	even	6
5292.2.i.i.1549.3		14	63.20	even	6
5292.2.i.i.2125.3		14	63.59	even	6
5292.2.j.g.1765.3		14	63.47	even	6
5292.2.j.g.3529.3		14	63.5	even	6
5292.2.j.h.1765.5		14	63.2	odd	6
5292.2.j.h.3529.5		14	63.23	odd	6
5292.2.l.i.361.5		14	63.38	even	6
5292.2.l.i.3313.5		14	63.41	even	6

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:	\( N \)	\(=\)	\( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2268.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.483929 + 0.838189i) q^{5} +(2.63536 - 0.234242i) q^{7} +(-0.364122 - 0.630678i) q^{11} -3.62132 q^{13} +(3.49948 + 6.06128i) q^{17} +(-0.348050 + 0.602841i) q^{19} +(-3.21898 + 5.57544i) q^{23} +(2.03163 + 3.51888i) q^{25} -6.69454 q^{29} +(-4.58310 - 7.93816i) q^{31} +(-1.07899 + 2.32229i) q^{35} +(0.854506 - 1.48005i) q^{37} +7.24887 q^{41} +0.696101 q^{43} +(-3.83120 + 6.63583i) q^{47} +(6.89026 - 1.23462i) q^{49} +(2.05637 + 3.56174i) q^{53} +0.704836 q^{55} +(2.38809 + 4.13629i) q^{59} +(-2.46287 + 4.26582i) q^{61} +(1.75246 - 3.03535i) q^{65} +(2.91035 + 5.04087i) q^{67} +0.304424 q^{71} +(5.33879 + 9.24705i) q^{73} +(-1.10732 - 1.57677i) q^{77} +(1.61945 - 2.80497i) q^{79} -1.23752 q^{83} -6.77400 q^{85} +(-5.78679 + 10.0230i) q^{89} +(-9.54349 + 0.848265i) q^{91} +(-0.336863 - 0.583464i) q^{95} -2.65866 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{5} - 3 q^{7} + 2 q^{11} - 4 q^{13} + 2 q^{17} + 7 q^{19} + 11 q^{23} - 9 q^{25} - 2 q^{29} - q^{31} - 19 q^{35} + 10 q^{37} + 66 q^{41} - 14 q^{43} - 3 q^{47} + 17 q^{49} - 15 q^{53} - 28 q^{55}+ \cdots + 36 q^{97}+O(q^{100}) \) 14 * q - 2 * q^5 - 3 * q^7 + 2 * q^11 - 4 * q^13 + 2 * q^17 + 7 * q^19 + 11 * q^23 - 9 * q^25 - 2 * q^29 - q^31 - 19 * q^35 + 10 * q^37 + 66 * q^41 - 14 * q^43 - 3 * q^47 + 17 * q^49 - 15 * q^53 - 28 * q^55 - 14 * q^59 - 10 * q^61 + 15 * q^65 + 6 * q^67 + 2 * q^71 + 21 * q^73 + 28 * q^77 - 10 * q^79 + 50 * q^83 - 16 * q^85 - 6 * q^89 + 2 * q^91 - 28 * q^95 + 36 * q^97

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