LMFDB - Embedded newform 1980.2.z.b.1081.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1980,2,Mod(181,1980)] 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("1980.181"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1980, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1980.z (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,-2,0,-3,0,0,0,5,0,-8,0,0,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$15.8103796002$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 660)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			1081.1
Root			$-0.762262 - 2.34600i$ of defining polynomial
Character	$\chi$	$=$	1980.1081
Dual form			1980.2.z.b.1621.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 - 0.587785i) q^{5} +(-1.26226 + 3.88484i) q^{7} +(2.91998 + 1.57281i) q^{11} +(-5.72462 + 4.15918i) q^{13} +(0.657715 + 0.477858i) q^{17} +(-2.56691 - 7.90013i) q^{19} -7.02697 q^{23} +(0.309017 + 0.951057i) q^{25} +(2.19613 - 6.75901i) q^{29} +(3.69573 - 2.68510i) q^{31} +(3.30464 - 2.40097i) q^{35} +(-0.971104 + 2.98875i) q^{37} +(-1.96840 - 6.05812i) q^{41} +1.35115 q^{43} +(-0.858221 - 2.64133i) q^{47} +(-7.83558 - 5.69288i) q^{49} +(5.62404 - 4.08610i) q^{53} +(-1.43784 - 2.98875i) q^{55} +(1.34036 - 4.12521i) q^{59} +(8.12278 + 5.90154i) q^{61} +7.07602 q^{65} -3.26304 q^{67} +(-7.22025 - 5.24582i) q^{71} +(0.649380 - 1.99858i) q^{73} +(-9.79590 + 9.35835i) q^{77} +(-10.1631 + 7.38394i) q^{79} +(-11.3050 - 8.21357i) q^{83} +(-0.251225 - 0.773190i) q^{85} -0.800155 q^{89} +(-8.93179 - 27.4892i) q^{91} +(-2.56691 + 7.90013i) q^{95} +(-3.90457 + 2.83683i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{5} - 3 q^{7} + 5 q^{11} - 8 q^{13} - 6 q^{17} + 6 q^{19} - 30 q^{23} - 2 q^{25} - 9 q^{31} + 7 q^{35} - 7 q^{37} - 25 q^{41} - 8 q^{43} + 7 q^{47} - 11 q^{49} - 3 q^{53} + 5 q^{55} - 5 q^{59}+ \cdots + q^{97}+O(q^{100}) $ 8 * q - 2 * q^5 - 3 * q^7 + 5 * q^11 - 8 * q^13 - 6 * q^17 + 6 * q^19 - 30 * q^23 - 2 * q^25 - 9 * q^31 + 7 * q^35 - 7 * q^37 - 25 * q^41 - 8 * q^43 + 7 * q^47 - 11 * q^49 - 3 * q^53 + 5 * q^55 - 5 * q^59 + 13 * q^61 + 2 * q^65 + 18 * q^67 - 5 * q^71 - 15 * q^73 - 29 * q^77 - 50 * q^79 - 13 * q^83 + 4 * q^85 - 32 * q^89 - 15 * q^91 + 6 * q^95 + q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1980\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$991$	$1541$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$		0			0
$7$	−1.26226	+	3.88484i	−0.477090	+	1.46833i	0.366028	+	0.930604i	$0.380718\pi$
$7$	−1.26226	+	3.88484i	−0.477090	+	1.46833i	−0.843118	+	0.537729i	$0.819282\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.91998	+	1.57281i	0.880406	+	0.474220i
$11$	2.91998	+	1.57281i	0.880406	+	0.474220i
$12$		0			0
$13$	−5.72462	+	4.15918i	−1.58772	+	1.15355i	−0.680626	+	0.732631i	$0.738292\pi$
$13$	−5.72462	+	4.15918i	−1.58772	+	1.15355i	−0.907099	+	0.420918i	$0.861708\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.657715	+	0.477858i	0.159519	+	0.115898i	0.664681	−	0.747127i	$-0.268567\pi$
$17$	0.657715	+	0.477858i	0.159519	+	0.115898i	−0.505162	+	0.863024i	$0.668567\pi$
$18$		0			0
$19$	−2.56691	−	7.90013i	−0.588889	−	1.81241i	−0.583058	−	0.812431i	$-0.698144\pi$
$19$	−2.56691	−	7.90013i	−0.588889	−	1.81241i	−0.00583084	−	0.999983i	$-0.501856\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−7.02697			−1.46523			−0.732613	−	0.680646i	$-0.761699\pi$
$23$	−7.02697			−1.46523			−0.732613	+	0.680646i	$0.761699\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.19613	−	6.75901i	0.407812	−	1.25512i	−0.510712	−	0.859752i	$-0.670618\pi$
$29$	2.19613	−	6.75901i	0.407812	−	1.25512i	0.918524	−	0.395364i	$-0.129382\pi$
$30$		0			0
$31$	3.69573	−	2.68510i	0.663772	−	0.482259i	−0.204163	−	0.978937i	$-0.565447\pi$
$31$	3.69573	−	2.68510i	0.663772	−	0.482259i	0.867935	+	0.496678i	$0.165447\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.30464	−	2.40097i	0.558587	−	0.405837i
$36$		0			0
$37$	−0.971104	+	2.98875i	−0.159648	+	0.491348i	−0.998602	−	0.0528553i	$-0.983168\pi$
$37$	−0.971104	+	2.98875i	−0.159648	+	0.491348i	0.838954	+	0.544203i	$0.183168\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.96840	−	6.05812i	−0.307413	−	0.946119i	−0.978766	−	0.204981i	$-0.934287\pi$
$41$	−1.96840	−	6.05812i	−0.307413	−	0.946119i	0.671353	−	0.741138i	$-0.265713\pi$
$42$		0			0
$43$	1.35115			0.206048			0.103024	−	0.994679i	$-0.467148\pi$
$43$	1.35115			0.206048			0.103024	+	0.994679i	$0.467148\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−0.858221	−	2.64133i	−0.125184	−	0.385278i	0.868750	−	0.495251i	$-0.164924\pi$
$47$	−0.858221	−	2.64133i	−0.125184	−	0.385278i	−0.993935	+	0.109972i	$0.964924\pi$
$48$		0			0
$49$	−7.83558	−	5.69288i	−1.11937	−	0.813269i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	5.62404	−	4.08610i	0.772521	−	0.561269i	−0.130204	−	0.991487i	$-0.541563\pi$
$53$	5.62404	−	4.08610i	0.772521	−	0.561269i	0.902725	+	0.430218i	$0.141563\pi$
$54$		0			0
$55$	−1.43784	−	2.98875i	−0.193878	−	0.403003i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.34036	−	4.12521i	0.174500	−	0.537057i	−0.825110	−	0.564972i	$-0.808887\pi$
$59$	1.34036	−	4.12521i	0.174500	−	0.537057i	0.999610	+	0.0279154i	$0.00888689\pi$
$60$		0			0
$61$	8.12278	+	5.90154i	1.04001	+	0.755615i	0.970288	−	0.241951i	$-0.0777873\pi$
$61$	8.12278	+	5.90154i	1.04001	+	0.755615i	0.0697265	+	0.997566i	$0.477787\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	7.07602			0.877672
$66$		0			0
$67$	−3.26304			−0.398644			−0.199322	−	0.979934i	$-0.563874\pi$
$67$	−3.26304			−0.398644			−0.199322	+	0.979934i	$0.563874\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.22025	−	5.24582i	−0.856886	−	0.622564i	0.0701500	−	0.997536i	$-0.477652\pi$
$71$	−7.22025	−	5.24582i	−0.856886	−	0.622564i	−0.927036	+	0.374972i	$0.877652\pi$
$72$		0			0
$73$	0.649380	−	1.99858i	0.0760041	−	0.233917i	−0.905835	−	0.423630i	$-0.860756\pi$
$73$	0.649380	−	1.99858i	0.0760041	−	0.233917i	0.981840	+	0.189713i	$0.0607558\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−9.79590	+	9.35835i	−1.11635	+	1.06648i
$78$		0			0
$79$	−10.1631	+	7.38394i	−1.14344	+	0.830758i	−0.987595	−	0.157024i	$-0.949810\pi$
$79$	−10.1631	+	7.38394i	−1.14344	+	0.830758i	−0.155845	+	0.987781i	$0.549810\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−11.3050	−	8.21357i	−1.24089	−	0.901557i	−0.243229	−	0.969969i	$-0.578207\pi$
$83$	−11.3050	−	8.21357i	−1.24089	−	0.901557i	−0.997657	+	0.0684118i	$0.978207\pi$
$84$		0			0
$85$	−0.251225	−	0.773190i	−0.0272491	−	0.0838642i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.800155			−0.0848163			−0.0424081	−	0.999100i	$-0.513503\pi$
$89$	−0.800155			−0.0848163			−0.0424081	+	0.999100i	$0.513503\pi$
$90$		0			0
$91$	−8.93179	−	27.4892i	−0.936306	−	2.88165i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.56691	+	7.90013i	−0.263359	+	0.810536i
$96$		0			0
$97$	−3.90457	+	2.83683i	−0.396449	+	0.288037i	−0.768093	−	0.640338i	$-0.778794\pi$
$97$	−3.90457	+	2.83683i	−0.396449	+	0.288037i	0.371644	+	0.928375i	$0.378794\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−11.1326	+	8.08827i	−1.10773	+	0.804813i	−0.982305	−	0.187290i	$-0.940030\pi$
$101$	−11.1326	+	8.08827i	−1.10773	+	0.804813i	−0.125426	+	0.992103i	$0.540030\pi$
$102$		0			0
$103$	1.93554	−	5.95699i	0.190715	−	0.586959i	−0.809285	−	0.587416i	$-0.800145\pi$
$103$	1.93554	−	5.95699i	0.190715	−	0.586959i	1.00000		0.000456502i	$0.000145309\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.523263	+	1.61044i	0.0505857	+	0.155687i	0.973158	−	0.230137i	$-0.0739173\pi$
$107$	0.523263	+	1.61044i	0.0505857	+	0.155687i	−0.922573	+	0.385824i	$0.873917\pi$
$108$		0			0
$109$	−7.19732			−0.689378			−0.344689	−	0.938717i	$-0.612016\pi$
$109$	−7.19732			−0.689378			−0.344689	+	0.938717i	$0.612016\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−4.98521	−	15.3429i	−0.468969	−	1.44334i	−0.853921	−	0.520403i	$-0.825782\pi$
$113$	−4.98521	−	15.3429i	−0.468969	−	1.44334i	0.384951	−	0.922937i	$-0.374218\pi$
$114$		0			0
$115$	5.68494	+	4.13035i	0.530123	+	0.385157i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.68661	+	1.95194i	−0.246281	+	0.178934i
$120$		0			0
$121$	6.05253	+	9.18514i	0.550230	+	0.835013i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$		0			0
$127$	0.858474	+	0.623718i	0.0761773	+	0.0553460i	0.625222	−	0.780447i	$-0.285008\pi$
$127$	0.858474	+	0.623718i	0.0761773	+	0.0553460i	−0.549045	+	0.835793i	$0.685008\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.42227			−0.124264			−0.0621322	−	0.998068i	$-0.519790\pi$
$131$	−1.42227			−0.124264			−0.0621322	+	0.998068i	$0.519790\pi$
$132$		0			0
$133$	33.9309			2.94218
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.87592	−	3.54257i	−0.416578	−	0.302662i	0.359681	−	0.933075i	$-0.382885\pi$
$137$	−4.87592	−	3.54257i	−0.416578	−	0.302662i	−0.776260	+	0.630413i	$0.782885\pi$
$138$		0			0
$139$	−4.69265	+	14.4425i	−0.398026	+	1.22500i	0.528554	+	0.848899i	$0.322734\pi$
$139$	−4.69265	+	14.4425i	−0.398026	+	1.22500i	−0.926580	+	0.376098i	$0.877266\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−23.2574	+	3.14096i	−1.94488	+	0.262661i
$144$		0			0
$145$	−5.74955	+	4.17730i	−0.477475	+	0.346906i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	4.61533	+	3.35323i	0.378103	+	0.274708i	0.760563	−	0.649264i	$-0.224923\pi$
$149$	4.61533	+	3.35323i	0.378103	+	0.274708i	−0.382460	+	0.923972i	$0.624923\pi$
$150$		0			0
$151$	−0.254179	−	0.782284i	−0.0206848	−	0.0636614i	0.940181	−	0.340675i	$-0.110655\pi$
$151$	−0.254179	−	0.782284i	−0.0206848	−	0.0636614i	−0.960866	+	0.277013i	$0.910655\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.56817			−0.366924
$156$		0			0
$157$	−1.52905	−	4.70594i	−0.122032	−	0.375575i	0.871317	−	0.490721i	$-0.163266\pi$
$157$	−1.52905	−	4.70594i	−0.122032	−	0.375575i	−0.993349	+	0.115146i	$0.963266\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.86988	−	27.2987i	0.699045	−	2.15144i
$162$		0			0
$163$	7.75826	−	5.63671i	0.607674	−	0.441501i	−0.240921	−	0.970545i	$-0.577449\pi$
$163$	7.75826	−	5.63671i	0.607674	−	0.441501i	0.848594	+	0.529044i	$0.177449\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−18.1574	+	13.1922i	−1.40507	+	1.02084i	−0.411049	+	0.911613i	$0.634837\pi$
$167$	−18.1574	+	13.1922i	−1.40507	+	1.02084i	−0.994017	+	0.109226i	$0.965163\pi$
$168$		0			0
$169$	11.4553	−	35.2557i	0.881176	−	2.71198i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	2.14359	+	6.59729i	0.162974	+	0.501583i	0.998881	−	0.0472880i	$-0.0150579\pi$
$173$	2.14359	+	6.59729i	0.162974	+	0.501583i	−0.835907	+	0.548871i	$0.815058\pi$
$174$		0			0
$175$	−4.08477			−0.308779
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.33574	+	16.4217i	0.398812	+	1.22742i	0.925953	+	0.377639i	$0.123264\pi$
$179$	5.33574	+	16.4217i	0.398812	+	1.22742i	−0.527141	+	0.849778i	$0.676736\pi$
$180$		0			0
$181$	4.25830	+	3.09384i	0.316517	+	0.229963i	0.734688	−	0.678405i	$-0.237329\pi$
$181$	4.25830	+	3.09384i	0.316517	+	0.229963i	−0.418171	+	0.908368i	$0.637329\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.54238	−	1.84715i	0.186920	−	0.135805i
$186$		0			0
$187$	1.16893	+	2.42979i	0.0854808	+	0.177684i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−4.96007	+	15.2655i	−0.358898	+	1.10457i	0.594817	+	0.803861i	$0.297225\pi$
$191$	−4.96007	+	15.2655i	−0.358898	+	1.10457i	−0.953715	+	0.300713i	$0.902775\pi$
$192$		0			0
$193$	−5.19639	−	3.77540i	−0.374044	−	0.271759i	0.384842	−	0.922983i	$-0.374256\pi$
$193$	−5.19639	−	3.77540i	−0.374044	−	0.271759i	−0.758886	+	0.651224i	$0.774256\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	14.3571			1.02290			0.511449	−	0.859314i	$-0.329109\pi$
$197$	14.3571			1.02290			0.511449	+	0.859314i	$0.329109\pi$
$198$		0			0
$199$	−15.1413			−1.07334			−0.536669	−	0.843793i	$-0.680317\pi$
$199$	−15.1413			−1.07334			−0.536669	+	0.843793i	$0.680317\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	23.4856	+	17.0633i	1.64836	+	1.19761i
$204$		0			0
$205$	−1.96840	+	6.05812i	−0.137479	+	0.423117i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	4.93010	−	27.1054i	0.341022	−	1.87492i
$210$		0			0
$211$	−2.70076	+	1.96222i	−0.185928	+	0.135085i	−0.676856	−	0.736116i	$-0.736658\pi$
$211$	−2.70076	+	1.96222i	−0.185928	+	0.135085i	0.490928	+	0.871200i	$0.336658\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.09310	−	0.794184i	−0.0745489	−	0.0541629i
$216$		0			0
$217$	5.76623	+	17.7466i	0.391437	+	1.20472i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−5.75267			−0.386966
$222$		0			0
$223$	−7.55931	−	23.2652i	−0.506209	−	1.55795i	−0.798729	−	0.601691i	$-0.794494\pi$
$223$	−7.55931	−	23.2652i	−0.506209	−	1.55795i	0.292521	−	0.956259i	$-0.405506\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.65630	−	11.2529i	0.242677	−	0.746883i	−0.753333	−	0.657639i	$-0.771555\pi$
$227$	3.65630	−	11.2529i	0.242677	−	0.746883i	0.996010	−	0.0892435i	$-0.0284449\pi$
$228$		0			0
$229$	−3.44953	+	2.50623i	−0.227952	+	0.165617i	−0.695899	−	0.718140i	$-0.744994\pi$
$229$	−3.44953	+	2.50623i	−0.227952	+	0.165617i	0.467947	+	0.883756i	$0.344994\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−20.7086	+	15.0457i	−1.35666	+	0.985674i	−0.358015	+	0.933716i	$0.616546\pi$
$233$	−20.7086	+	15.0457i	−1.35666	+	0.985674i	−0.998649	+	0.0519580i	$0.983454\pi$
$234$		0			0
$235$	−0.858221	+	2.64133i	−0.0559842	+	0.172302i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.26716	+	22.3660i	0.470074	+	1.44674i	0.852488	+	0.522747i	$0.175093\pi$
$239$	7.26716	+	22.3660i	0.470074	+	1.44674i	−0.382414	+	0.923991i	$0.624907\pi$
$240$		0			0
$241$	13.3232			0.858223			0.429112	−	0.903251i	$-0.358827\pi$
$241$	13.3232			0.858223			0.429112	+	0.903251i	$0.358827\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	2.99293	+	9.21128i	0.191211	+	0.588487i
$246$		0			0
$247$	47.5526	+	34.5490i	3.02570	+	2.19830i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−11.0134	+	8.00174i	−0.695163	+	0.505065i	−0.878353	−	0.478012i	$-0.841357\pi$
$251$	−11.0134	+	8.00174i	−0.695163	+	0.505065i	0.183191	+	0.983077i	$0.441357\pi$
$252$		0			0
$253$	−20.5186	−	11.0521i	−1.28999	−	0.694840i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	8.50577	−	26.1781i	0.530576	−	1.63294i	−0.222444	−	0.974946i	$-0.571403\pi$
$257$	8.50577	−	26.1781i	0.530576	−	1.63294i	0.753019	−	0.657998i	$-0.228597\pi$
$258$		0			0
$259$	−10.3850	−	7.54517i	−0.645295	−	0.468834i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−0.977108			−0.0602510			−0.0301255	−	0.999546i	$-0.509591\pi$
$263$	−0.977108			−0.0602510			−0.0301255	+	0.999546i	$0.509591\pi$
$264$		0			0
$265$	−6.95169			−0.427039
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−10.7562	−	7.81485i	−0.655818	−	0.476480i	0.209430	−	0.977824i	$-0.432839\pi$
$269$	−10.7562	−	7.81485i	−0.655818	−	0.476480i	−0.865248	+	0.501344i	$0.832839\pi$
$270$		0			0
$271$	−4.87363	+	14.9995i	−0.296052	+	0.911154i	0.686814	+	0.726833i	$0.259009\pi$
$271$	−4.87363	+	14.9995i	−0.296052	+	0.911154i	−0.982866	+	0.184321i	$0.940991\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−0.593510	+	3.26309i	−0.0357900	+	0.196772i
$276$		0			0
$277$	4.25189	−	3.08918i	0.255471	−	0.185611i	−0.452677	−	0.891675i	$-0.649531\pi$
$277$	4.25189	−	3.08918i	0.255471	−	0.185611i	0.708148	+	0.706064i	$0.249531\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	20.7021	+	15.0410i	1.23498	+	0.897268i	0.997254	−	0.0740630i	$-0.0235966\pi$
$281$	20.7021	+	15.0410i	1.23498	+	0.897268i	0.237730	+	0.971331i	$0.423597\pi$
$282$		0			0
$283$	2.54739	+	7.84007i	0.151427	+	0.466044i	0.997781	−	0.0665762i	$-0.0212075\pi$
$283$	2.54739	+	7.84007i	0.151427	+	0.466044i	−0.846355	+	0.532620i	$0.821208\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	26.0195			1.53588
$288$		0			0
$289$	−5.04905	−	15.5394i	−0.297003	−	0.914081i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	7.20757	−	22.1826i	0.421071	−	1.29592i	−0.485637	−	0.874161i	$-0.661412\pi$
$293$	7.20757	−	22.1826i	0.421071	−	1.29592i	0.906707	−	0.421761i	$-0.138588\pi$
$294$		0			0
$295$	−3.50911	+	2.54952i	−0.204309	+	0.148439i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	40.2268	−	29.2265i	2.32637	−	1.69021i
$300$		0			0
$301$	−1.70550	+	5.24899i	−0.0983035	+	0.302547i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−3.10262	−	9.54890i	−0.177656	−	0.546768i
$306$		0			0
$307$	−25.3339			−1.44588			−0.722941	−	0.690910i	$-0.757210\pi$
$307$	−25.3339			−1.44588			−0.722941	+	0.690910i	$0.757210\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.34470	−	28.7600i	−0.529889	−	1.63083i	−0.754440	−	0.656369i	$-0.772092\pi$
$311$	−9.34470	−	28.7600i	−0.529889	−	1.63083i	0.224551	−	0.974462i	$-0.427908\pi$
$312$		0			0
$313$	11.0326	+	8.01563i	0.623598	+	0.453070i	0.854176	−	0.519983i	$-0.174062\pi$
$313$	11.0326	+	8.01563i	0.623598	+	0.453070i	−0.230579	+	0.973054i	$0.574062\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−10.3686	+	7.53320i	−0.582356	+	0.423107i	−0.839573	−	0.543247i	$-0.817195\pi$
$317$	−10.3686	+	7.53320i	−0.582356	+	0.423107i	0.257217	+	0.966354i	$0.417195\pi$
$318$		0			0
$319$	17.0433	−	16.2820i	0.954242	−	0.911619i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	2.08684	−	6.42265i	0.116115	−	0.357366i
$324$		0			0
$325$	−5.72462	−	4.15918i	−0.317545	−	0.230710i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	11.3445			0.625441
$330$		0			0
$331$	−14.8785			−0.817795			−0.408898	−	0.912580i	$-0.634087\pi$
$331$	−14.8785			−0.817795			−0.408898	+	0.912580i	$0.634087\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.63986	+	1.91797i	0.144231	+	0.104790i
$336$		0			0
$337$	2.17130	−	6.68257i	0.118278	−	0.364023i	−0.874338	−	0.485317i	$-0.838704\pi$
$337$	2.17130	−	6.68257i	0.118278	−	0.364023i	0.992617	+	0.121294i	$0.0387044\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	15.0146	−	2.02776i	0.813086	−	0.109809i
$342$		0			0
$343$	8.87400	−	6.44734i	0.479151	−	0.348124i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	0.198657	+	0.144333i	0.0106645	+	0.00774818i	0.593105	−	0.805125i	$-0.297902\pi$
$347$	0.198657	+	0.144333i	0.0106645	+	0.00774818i	−0.582440	+	0.812874i	$0.697902\pi$
$348$		0			0
$349$	−1.46454	−	4.50738i	−0.0783948	−	0.241274i	0.904177	−	0.427158i	$-0.140485\pi$
$349$	−1.46454	−	4.50738i	−0.0783948	−	0.241274i	−0.982572	+	0.185884i	$0.940485\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−17.8806			−0.951689			−0.475845	−	0.879529i	$-0.657858\pi$
$353$	−17.8806			−0.951689			−0.475845	+	0.879529i	$0.657858\pi$
$354$		0			0
$355$	2.75789	+	8.48791i	0.146374	+	0.450492i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.98411	+	6.10646i	−0.104717	+	0.322287i	−0.989664	−	0.143406i	$-0.954195\pi$
$359$	−1.98411	+	6.10646i	−0.104717	+	0.322287i	0.884947	+	0.465692i	$0.154195\pi$
$360$		0			0
$361$	−40.4517	+	29.3899i	−2.12904	+	1.54683i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.70010	+	1.23519i	−0.0889872	+	0.0646530i
$366$		0			0
$367$	−4.50292	+	13.8586i	−0.235050	+	0.723411i	0.762064	+	0.647501i	$0.224186\pi$
$367$	−4.50292	+	13.8586i	−0.235050	+	0.723411i	−0.997115	+	0.0759093i	$0.975814\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	8.77486	+	27.0062i	0.455568	+	1.40209i
$372$		0			0
$373$	−7.39686			−0.382995			−0.191497	−	0.981493i	$-0.561334\pi$
$373$	−7.39686			−0.382995			−0.191497	+	0.981493i	$0.561334\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15.5399	+	47.8269i	0.800345	+	2.46321i
$378$		0			0
$379$	3.56116	+	2.58733i	0.182924	+	0.132902i	0.675479	−	0.737379i	$-0.263937\pi$
$379$	3.56116	+	2.58733i	0.182924	+	0.132902i	−0.492555	+	0.870281i	$0.663937\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	24.6605	−	17.9169i	1.26009	−	0.915511i	0.261330	−	0.965249i	$-0.415839\pi$
$383$	24.6605	−	17.9169i	1.26009	−	0.915511i	0.998762	+	0.0497387i	$0.0158388\pi$
$384$		0			0
$385$	13.4258	−	1.81318i	0.684240	−	0.0924082i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	1.90292	−	5.85659i	0.0964819	−	0.296941i	−0.891155	−	0.453699i	$-0.850104\pi$
$389$	1.90292	−	5.85659i	0.0964819	−	0.296941i	0.987637	+	0.156758i	$0.0501042\pi$
$390$		0			0
$391$	−4.62174	−	3.35789i	−0.233732	−	0.169816i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	12.5623			0.632078
$396$		0			0
$397$	29.7981			1.49552			0.747761	−	0.663968i	$-0.231129\pi$
$397$	29.7981			1.49552			0.747761	+	0.663968i	$0.231129\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.00433382	+	0.00314870i	0.000216421	+	0.000157239i	0.587893	−	0.808938i	$-0.299957\pi$
$401$	0.00433382	+	0.00314870i	0.000216421	+	0.000157239i	−0.587677	+	0.809096i	$0.699957\pi$
$402$		0			0
$403$	−9.98881	+	30.7424i	−0.497578	+	1.53139i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−7.53634	+	7.19972i	−0.373563	+	0.356877i
$408$		0			0
$409$	2.52320	−	1.83321i	0.124764	−	0.0906465i	−0.523653	−	0.851932i	$-0.675431\pi$
$409$	2.52320	−	1.83321i	0.124764	−	0.0906465i	0.648417	+	0.761285i	$0.275431\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	14.3339	+	10.4142i	0.705326	+	0.512449i
$414$		0			0
$415$	4.31813	+	13.2898i	0.211969	+	0.652373i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−30.8785			−1.50851			−0.754256	−	0.656580i	$-0.772002\pi$
$419$	−30.8785			−1.50851			−0.754256	+	0.656580i	$0.772002\pi$
$420$		0			0
$421$	2.15309	+	6.62653i	0.104935	+	0.322957i	0.989715	−	0.143052i	$-0.0456915\pi$
$421$	2.15309	+	6.62653i	0.104935	+	0.322957i	−0.884780	+	0.466009i	$0.845691\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.251225	+	0.773190i	−0.0121862	+	0.0375052i
$426$		0			0
$427$	−33.1796	+	24.1064i	−1.60568	+	1.16659i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−23.1281	+	16.8036i	−1.11404	+	0.809400i	−0.983296	−	0.182016i	$-0.941738\pi$
$431$	−23.1281	+	16.8036i	−1.11404	+	0.809400i	−0.130748	+	0.991416i	$0.541738\pi$
$432$		0			0
$433$	−8.12653	+	25.0109i	−0.390536	+	1.20195i	0.541848	+	0.840476i	$0.317725\pi$
$433$	−8.12653	+	25.0109i	−0.390536	+	1.20195i	−0.932384	+	0.361469i	$0.882275\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	18.0376	+	55.5140i	0.862855	+	2.65559i
$438$		0			0
$439$	21.9320			1.04676			0.523379	−	0.852100i	$-0.324671\pi$
$439$	21.9320			1.04676			0.523379	+	0.852100i	$0.324671\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.16992	+	28.2221i	0.435676	+	1.34087i	0.892392	+	0.451260i	$0.149025\pi$
$443$	9.16992	+	28.2221i	0.435676	+	1.34087i	−0.456717	+	0.889612i	$0.650975\pi$
$444$		0			0
$445$	0.647339	+	0.470319i	0.0306868	+	0.0222953i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−0.727553	+	0.528598i	−0.0343353	+	0.0249461i	−0.604821	−	0.796362i	$-0.706755\pi$
$449$	−0.727553	+	0.528598i	−0.0343353	+	0.0249461i	0.570485	+	0.821308i	$0.306755\pi$
$450$		0			0
$451$	3.78059	−	20.7855i	0.178021	−	0.978750i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−8.93179	+	27.4892i	−0.418729	+	1.28872i
$456$		0			0
$457$	18.9351	+	13.7571i	0.885745	+	0.643531i	0.934765	−	0.355267i	$-0.115610\pi$
$457$	18.9351	+	13.7571i	0.885745	+	0.643531i	−0.0490204	+	0.998798i	$0.515610\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	32.0061			1.49067			0.745337	−	0.666687i	$-0.232288\pi$
$461$	32.0061			1.49067			0.745337	+	0.666687i	$0.232288\pi$
$462$		0			0
$463$	−5.75259			−0.267345			−0.133673	−	0.991026i	$-0.542677\pi$
$463$	−5.75259			−0.267345			−0.133673	+	0.991026i	$0.542677\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	0.112883	+	0.0820139i	0.00522358	+	0.00379515i	0.590394	−	0.807115i	$-0.298972\pi$
$467$	0.112883	+	0.0820139i	0.00522358	+	0.00379515i	−0.585170	+	0.810910i	$0.698972\pi$
$468$		0			0
$469$	4.11881	−	12.6764i	0.190189	−	0.585342i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	3.94532	+	2.12510i	0.181406	+	0.0977122i
$474$		0			0
$475$	6.72025	−	4.88255i	0.308346	−	0.224027i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−22.5825	−	16.4072i	−1.03182	−	0.749662i	−0.0631490	−	0.998004i	$-0.520114\pi$
$479$	−22.5825	−	16.4072i	−1.03182	−	0.749662i	−0.968672	+	0.248342i	$0.920114\pi$
$480$		0			0
$481$	−6.87155	−	21.1485i	−0.313316	−	0.964287i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.82631			0.219151
$486$		0			0
$487$	3.44524	+	10.6033i	0.156119	+	0.480483i	0.998273	−	0.0587537i	$-0.0187127\pi$
$487$	3.44524	+	10.6033i	0.156119	+	0.480483i	−0.842154	+	0.539237i	$0.818713\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	1.10397	−	3.39767i	0.0498214	−	0.153335i	−0.923051	−	0.384679i	$-0.874312\pi$
$491$	1.10397	−	3.39767i	0.0498214	−	0.153335i	0.972872	+	0.231344i	$0.0743123\pi$
$492$		0			0
$493$	4.67427	−	3.39606i	0.210519	−	0.152951i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	29.4930	−	21.4279i	1.32294	−	0.961174i
$498$		0			0
$499$	10.0212	−	30.8421i	0.448610	−	1.38068i	−0.429865	−	0.902893i	$-0.641439\pi$
$499$	10.0212	−	30.8421i	0.448610	−	1.38068i	0.878475	−	0.477788i	$-0.158561\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−12.8361	−	39.5053i	−0.572332	−	1.76146i	−0.645090	−	0.764106i	$-0.723180\pi$
$503$	−12.8361	−	39.5053i	−0.572332	−	1.76146i	0.0727583	−	0.997350i	$-0.476820\pi$
$504$		0			0
$505$	13.7606			0.612338
$506$		0			0
$507$		0			0
$508$		0			0
$509$	4.32221	+	13.3024i	0.191578	+	0.589618i	0.999999	+	0.00101314i	$0.000322491\pi$
$509$	4.32221	+	13.3024i	0.191578	+	0.589618i	−0.808421	+	0.588605i	$0.799678\pi$
$510$		0			0
$511$	6.94450	+	5.04548i	0.307207	+	0.223199i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−5.06732	+	3.68162i	−0.223293	+	0.162232i
$516$		0			0
$517$	1.64833	−	9.06245i	0.0724936	−	0.398566i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−2.45696	+	7.56173i	−0.107641	+	0.331285i	−0.990341	−	0.138651i	$-0.955723\pi$
$521$	−2.45696	+	7.56173i	−0.107641	+	0.331285i	0.882700	+	0.469937i	$0.155723\pi$
$522$		0			0
$523$	−5.58951	−	4.06102i	−0.244412	−	0.177576i	0.458835	−	0.888522i	$-0.348267\pi$
$523$	−5.58951	−	4.06102i	−0.244412	−	0.177576i	−0.703247	+	0.710946i	$0.748267\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	3.71383			0.161777
$528$		0			0
$529$	26.3784			1.14689
$530$		0			0
$531$		0			0
$532$		0			0
$533$	36.4652	+	26.4935i	1.57948	+	1.14756i
$534$		0			0
$535$	0.523263	−	1.61044i	0.0226226	−	0.0696253i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−13.9259	−	28.9470i	−0.599830	−	1.24683i
$540$		0			0
$541$	−0.791276	+	0.574896i	−0.0340196	+	0.0247167i	−0.604665	−	0.796480i	$-0.706693\pi$
$541$	−0.791276	+	0.574896i	−0.0340196	+	0.0247167i	0.570646	+	0.821197i	$0.306693\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.82276	+	4.23048i	0.249419	+	0.181214i
$546$		0			0
$547$	5.66615	+	17.4386i	0.242267	+	0.745621i	0.996074	+	0.0885251i	$0.0282153\pi$
$547$	5.66615	+	17.4386i	0.242267	+	0.745621i	−0.753807	+	0.657096i	$0.771785\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−59.0343			−2.51495
$552$		0			0
$553$	−15.8569	−	48.8026i	−0.674305	−	2.07530i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−8.29716	+	25.5360i	−0.351562	+	1.08200i	0.606414	+	0.795149i	$0.292607\pi$
$557$	−8.29716	+	25.5360i	−0.351562	+	1.08200i	−0.957976	+	0.286848i	$0.907393\pi$
$558$		0			0
$559$	−7.73481	+	5.61967i	−0.327147	+	0.237687i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−5.60247	+	4.07043i	−0.236116	+	0.171548i	−0.699551	−	0.714583i	$-0.746617\pi$
$563$	−5.60247	+	4.07043i	−0.236116	+	0.171548i	0.463435	+	0.886131i	$0.346617\pi$
$564$		0			0
$565$	−4.98521	+	15.3429i	−0.209730	+	0.645481i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	1.49757	+	4.60903i	0.0627812	+	0.193221i	0.977527	−	0.210808i	$-0.0676095\pi$
$569$	1.49757	+	4.60903i	0.0627812	+	0.193221i	−0.914746	+	0.404029i	$0.867610\pi$
$570$		0			0
$571$	30.2269			1.26496			0.632479	−	0.774578i	$-0.282037\pi$
$571$	30.2269			1.26496			0.632479	+	0.774578i	$0.282037\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−2.17145	−	6.68305i	−0.0905559	−	0.278702i
$576$		0			0
$577$	−21.6416	−	15.7236i	−0.900953	−	0.654581i	0.0377577	−	0.999287i	$-0.487978\pi$
$577$	−21.6416	−	15.7236i	−0.900953	−	0.654581i	−0.938711	+	0.344706i	$0.887978\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	46.1783	−	33.5505i	1.91580	−	1.39191i
$582$		0			0
$583$	22.8487	−	3.08578i	0.946298	−	0.127800i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.72899	+	14.5543i	−0.195186	+	0.600722i	0.804788	+	0.593562i	$0.202279\pi$
$587$	−4.72899	+	14.5543i	−0.195186	+	0.600722i	−0.999974	+	0.00715968i	$0.997721\pi$
$588$		0			0
$589$	−30.6992	−	22.3043i	−1.26494	−	0.919033i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	2.68279			0.110169			0.0550845	−	0.998482i	$-0.482457\pi$
$593$	2.68279			0.110169			0.0550845	+	0.998482i	$0.482457\pi$
$594$		0			0
$595$	3.32083			0.136141
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−23.5560	−	17.1144i	−0.962473	−	0.699277i	−0.00874886	−	0.999962i	$-0.502785\pi$
$599$	−23.5560	−	17.1144i	−0.962473	−	0.699277i	−0.953724	+	0.300685i	$0.902785\pi$
$600$		0			0
$601$	8.69000	−	26.7451i	0.354472	−	1.09095i	−0.601842	−	0.798615i	$-0.705566\pi$
$601$	8.69000	−	26.7451i	0.354472	−	1.09095i	0.956315	−	0.292339i	$-0.0944335\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.502293	−	10.9885i	0.0204211	−	0.446747i
$606$		0			0
$607$	−15.9624	+	11.5974i	−0.647895	+	0.470724i	−0.862554	−	0.505966i	$-0.831136\pi$
$607$	−15.9624	+	11.5974i	−0.647895	+	0.470724i	0.214658	+	0.976689i	$0.431136\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	15.8988	+	11.5511i	0.643196	+	0.467309i
$612$		0			0
$613$	1.73888	+	5.35173i	0.0702327	+	0.216154i	0.980012	−	0.198938i	$-0.0637493\pi$
$613$	1.73888	+	5.35173i	0.0702327	+	0.216154i	−0.909779	+	0.415092i	$0.863749\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	1.97540			0.0795267			0.0397634	−	0.999209i	$-0.487340\pi$
$617$	1.97540			0.0795267			0.0397634	+	0.999209i	$0.487340\pi$
$618$		0			0
$619$	10.3591	+	31.8821i	0.416368	+	1.28145i	0.911021	+	0.412359i	$0.135295\pi$
$619$	10.3591	+	31.8821i	0.416368	+	1.28145i	−0.494653	+	0.869090i	$0.664705\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.01001	−	3.10848i	0.0404650	−	0.124538i
$624$		0			0
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.06691	+	1.50170i	−0.0824130	+	0.0598765i
$630$		0			0
$631$	0.335151	−	1.03149i	0.0133422	−	0.0410630i	−0.944164	−	0.329476i	$-0.893128\pi$
$631$	0.335151	−	1.03149i	0.0133422	−	0.0410630i	0.957506	+	0.288413i	$0.0931278\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.327908	−	1.00920i	−0.0130126	−	0.0400488i
$636$		0			0
$637$	68.5335			2.71540
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−4.62814	−	14.2439i	−0.182800	−	0.562602i	0.817103	−	0.576491i	$-0.195579\pi$
$641$	−4.62814	−	14.2439i	−0.182800	−	0.562602i	−0.999904	+	0.0138898i	$0.995579\pi$
$642$		0			0
$643$	−30.8436	−	22.4092i	−1.21635	−	0.883733i	−0.220563	−	0.975373i	$-0.570789\pi$
$643$	−30.8436	−	22.4092i	−1.21635	−	0.883733i	−0.995792	+	0.0916393i	$0.970789\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−14.9038	+	10.8283i	−0.585929	+	0.425703i	−0.840857	−	0.541258i	$-0.817948\pi$
$647$	−14.9038	+	10.8283i	−0.585929	+	0.425703i	0.254928	+	0.966960i	$0.417948\pi$
$648$		0			0
$649$	10.4020	−	9.93739i	0.408314	−	0.390077i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	9.36436	−	28.8205i	0.366456	−	1.12783i	−0.582609	−	0.812753i	$-0.697968\pi$
$653$	9.36436	−	28.8205i	0.366456	−	1.12783i	0.949064	−	0.315082i	$-0.102032\pi$
$654$		0			0
$655$	1.15064	+	0.835989i	0.0449593	+	0.0326648i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−14.2869			−0.556539			−0.278269	−	0.960503i	$-0.589761\pi$
$659$	−14.2869			−0.556539			−0.278269	+	0.960503i	$0.589761\pi$
$660$		0			0
$661$	33.1552			1.28959			0.644793	−	0.764357i	$-0.276944\pi$
$661$	33.1552			1.28959			0.644793	+	0.764357i	$0.276944\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−27.4506	−	19.9441i	−1.06449	−	0.773398i
$666$		0			0
$667$	−15.4322	+	47.4954i	−0.597536	+	1.83903i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	14.4363	+	30.0080i	0.557307	+	1.15844i
$672$		0			0
$673$	2.01601	−	1.46472i	0.0777114	−	0.0564607i	−0.548251	−	0.836314i	$-0.684706\pi$
$673$	2.01601	−	1.46472i	0.0777114	−	0.0564607i	0.625963	+	0.779853i	$0.284706\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−29.0098	−	21.0769i	−1.11494	−	0.810050i	−0.131504	−	0.991316i	$-0.541981\pi$
$677$	−29.0098	−	21.0769i	−1.11494	−	0.810050i	−0.983434	+	0.181266i	$0.941981\pi$
$678$		0			0
$679$	−6.09207	−	18.7495i	−0.233792	−	0.719538i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	27.7565			1.06207			0.531036	−	0.847349i	$-0.321803\pi$
$683$	27.7565			1.06207			0.531036	+	0.847349i	$0.321803\pi$
$684$		0			0
$685$	1.86244	+	5.73199i	0.0711601	+	0.219008i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−15.2006	+	46.7828i	−0.579099	+	1.78228i
$690$		0			0
$691$	8.42264	−	6.11941i	0.320412	−	0.232793i	−0.415939	−	0.909392i	$-0.636547\pi$
$691$	8.42264	−	6.11941i	0.320412	−	0.232793i	0.736351	+	0.676599i	$0.236547\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.2855	−	8.92596i	0.466017	−	0.338581i
$696$		0			0
$697$	1.60027	−	4.92513i	0.0606146	−	0.186553i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−2.71358	−	8.35155i	−0.102491	−	0.315434i	0.886643	−	0.462455i	$-0.153031\pi$
$701$	−2.71358	−	8.35155i	−0.102491	−	0.315434i	−0.989133	+	0.147021i	$0.953031\pi$
$702$		0			0
$703$	26.1042			0.984540
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−17.3695	−	53.4577i	−0.653246	−	2.01049i
$708$		0			0
$709$	32.4128	+	23.5492i	1.21729	+	0.884410i	0.995872	−	0.0907694i	$-0.0289326\pi$
$709$	32.4128	+	23.5492i	1.21729	+	0.884410i	0.221415	+	0.975180i	$0.428933\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−25.9698	+	18.8681i	−0.972575	+	0.706617i
$714$		0			0
$715$	20.6618	+	11.1292i	0.772708	+	0.416210i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	4.39821	−	13.5363i	0.164026	−	0.504819i	−0.834937	−	0.550345i	$-0.814496\pi$
$719$	4.39821	−	13.5363i	0.164026	−	0.504819i	0.998963	+	0.0455257i	$0.0144963\pi$
$720$		0			0
$721$	20.6988	+	15.0386i	0.770864	+	0.560065i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	7.10684			0.263941
$726$		0			0
$727$	19.2900			0.715427			0.357714	−	0.933831i	$-0.383556\pi$
$727$	19.2900			0.715427			0.357714	+	0.933831i	$0.383556\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	0.888670	+	0.645656i	0.0328686	+	0.0238805i
$732$		0			0
$733$	−4.33900	+	13.3541i	−0.160265	+	0.493244i	−0.998656	−	0.0518243i	$-0.983496\pi$
$733$	−4.33900	+	13.3541i	−0.160265	+	0.493244i	0.838391	+	0.545069i	$0.183496\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−9.52801	−	5.13215i	−0.350969	−	0.189045i
$738$		0			0
$739$	−24.9927	+	18.1583i	−0.919372	+	0.667963i	−0.943368	−	0.331749i	$-0.892361\pi$
$739$	−24.9927	+	18.1583i	−0.919372	+	0.667963i	0.0239956	+	0.999712i	$0.492361\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	20.1696	+	14.6541i	0.739951	+	0.537606i	0.892696	−	0.450660i	$-0.148811\pi$
$743$	20.1696	+	14.6541i	0.739951	+	0.537606i	−0.152745	+	0.988266i	$0.548811\pi$
$744$		0			0
$745$	−1.76290	−	5.42565i	−0.0645877	−	0.198780i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−6.91679			−0.252734
$750$		0			0
$751$	−14.0835	−	43.3445i	−0.513913	−	1.58166i	−0.785251	−	0.619177i	$-0.787466\pi$
$751$	−14.0835	−	43.3445i	−0.513913	−	1.58166i	0.271338	−	0.962484i	$-0.412534\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−0.254179	+	0.782284i	−0.00925054	+	0.0284702i
$756$		0			0
$757$	−39.2692	+	28.5307i	−1.42726	+	1.03697i	−0.436745	+	0.899586i	$0.643869\pi$
$757$	−39.2692	+	28.5307i	−1.42726	+	1.03697i	−0.990518	+	0.137382i	$0.956131\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−18.6226	+	13.5301i	−0.675068	+	0.490466i	−0.871718	−	0.490008i	$-0.836994\pi$
$761$	−18.6226	+	13.5301i	−0.675068	+	0.490466i	0.196650	+	0.980474i	$0.436994\pi$
$762$		0			0
$763$	9.08491	−	27.9605i	0.328896	−	1.01224i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	9.48443	+	29.1901i	0.342463	+	1.05399i
$768$		0			0
$769$	29.2841			1.05601			0.528006	−	0.849241i	$-0.322940\pi$
$769$	29.2841			1.05601			0.528006	+	0.849241i	$0.322940\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−1.84208	−	5.66933i	−0.0662549	−	0.203912i	0.912448	−	0.409192i	$-0.134189\pi$
$773$	−1.84208	−	5.66933i	−0.0662549	−	0.203912i	−0.978703	+	0.205280i	$0.934189\pi$
$774$		0			0
$775$	3.69573	+	2.68510i	0.132754	+	0.0964517i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−42.8072	+	31.1012i	−1.53373	+	1.11432i
$780$		0			0
$781$	−12.8323	−	26.6738i	−0.459175	−	0.954462i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−1.52905	+	4.70594i	−0.0545742	+	0.167962i
$786$		0			0
$787$	−34.0807	−	24.7611i	−1.21485	−	0.882637i	−0.219184	−	0.975684i	$-0.570339\pi$
$787$	−34.0807	−	24.7611i	−1.21485	−	0.882637i	−0.995662	+	0.0930468i	$0.970339\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	65.8974			2.34304
$792$		0			0
$793$	−71.0454			−2.52290
$794$		0			0
$795$		0			0
$796$		0			0
$797$	21.3588	+	15.5181i	0.756567	+	0.549678i	0.897855	−	0.440291i	$-0.145125\pi$
$797$	21.3588	+	15.5181i	0.756567	+	0.549678i	−0.141289	+	0.989968i	$0.545125\pi$
$798$		0			0
$799$	0.697717	−	2.14735i	0.0246835	−	0.0759679i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	5.03957	−	4.81447i	0.177843	−	0.169899i
$804$		0			0
$805$	−23.2217	+	16.8715i	−0.818456	+	0.594643i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	37.2659	+	27.0753i	1.31020	+	0.951915i	0.999999	+	0.00124363i	$0.000395861\pi$
$809$	37.2659	+	27.0753i	1.31020	+	0.951915i	0.310200	+	0.950671i	$0.399604\pi$
$810$		0			0
$811$	−2.11433	−	6.50724i	−0.0742442	−	0.228500i	0.907047	−	0.421029i	$-0.138331\pi$
$811$	−2.11433	−	6.50724i	−0.0742442	−	0.228500i	−0.981291	+	0.192529i	$0.938331\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−9.58974			−0.335914
$816$		0			0
$817$	−3.46827	−	10.6742i	−0.121339	−	0.373444i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−3.63254	+	11.1798i	−0.126777	+	0.390178i	−0.994221	−	0.107357i	$-0.965761\pi$
$821$	−3.63254	+	11.1798i	−0.126777	+	0.390178i	0.867444	+	0.497535i	$0.165761\pi$
$822$		0			0
$823$	−16.5272	+	12.0077i	−0.576103	+	0.418563i	−0.837317	−	0.546718i	$-0.815877\pi$
$823$	−16.5272	+	12.0077i	−0.576103	+	0.418563i	0.261214	+	0.965281i	$0.415877\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−15.6584	+	11.3765i	−0.544497	+	0.395600i	−0.825752	−	0.564033i	$-0.809249\pi$
$827$	−15.6584	+	11.3765i	−0.544497	+	0.395600i	0.281256	+	0.959633i	$0.409249\pi$
$828$		0			0
$829$	0.313545	−	0.964993i	0.0108899	−	0.0335156i	−0.945464	−	0.325727i	$-0.894391\pi$
$829$	0.313545	−	0.964993i	0.0108899	−	0.0335156i	0.956354	+	0.292211i	$0.0943910\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.43319	−	7.48859i	−0.0843050	−	0.259464i
$834$		0			0
$835$	22.4438			0.776701
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−2.80354	−	8.62841i	−0.0967889	−	0.297886i	0.890927	−	0.454147i	$-0.150056\pi$
$839$	−2.80354	−	8.62841i	−0.0967889	−	0.297886i	−0.987716	+	0.156261i	$0.950056\pi$
$840$		0			0
$841$	−17.3997	−	12.6416i	−0.599989	−	0.435917i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−29.9903	+	21.7892i	−1.03170	+	0.749573i
$846$		0			0
$847$	−43.3227	+	11.9191i	−1.48859	+	0.409544i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	6.82392	−	21.0019i	0.233921	−	0.719935i
$852$		0			0
$853$	−12.3625	−	8.98189i	−0.423285	−	0.307534i	0.355674	−	0.934610i	$-0.384252\pi$
$853$	−12.3625	−	8.98189i	−0.423285	−	0.307534i	−0.778958	+	0.627076i	$0.784252\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−41.0382			−1.40184			−0.700919	−	0.713241i	$-0.747227\pi$
$857$	−41.0382			−1.40184			−0.700919	+	0.713241i	$0.747227\pi$
$858$		0			0
$859$	−21.9500			−0.748923			−0.374461	−	0.927242i	$-0.622172\pi$
$859$	−21.9500			−0.748923			−0.374461	+	0.927242i	$0.622172\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−39.0547	−	28.3749i	−1.32944	−	0.965894i	−0.999762	−	0.0218001i	$-0.993060\pi$
$863$	−39.0547	−	28.3749i	−1.32944	−	0.965894i	−0.329677	−	0.944094i	$-0.606940\pi$
$864$		0			0
$865$	2.14359	−	6.59729i	0.0728843	−	0.224315i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−41.2896	+	5.57626i	−1.40065	+	0.189162i
$870$		0			0
$871$	18.6797	−	13.5716i	0.632937	−	0.459855i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	3.30464	+	2.40097i	0.111717	+	0.0811674i
$876$		0			0
$877$	14.1874	+	43.6643i	0.479074	+	1.47444i	0.840383	+	0.541993i	$0.182330\pi$
$877$	14.1874	+	43.6643i	0.479074	+	1.47444i	−0.361309	+	0.932446i	$0.617670\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	33.1091			1.11547			0.557737	−	0.830018i	$-0.311670\pi$
$881$	33.1091			1.11547			0.557737	+	0.830018i	$0.311670\pi$
$882$		0			0
$883$	0.0529664	+	0.163014i	0.00178246	+	0.00548585i	0.951944	−	0.306273i	$-0.0990820\pi$
$883$	0.0529664	+	0.163014i	0.00178246	+	0.00548585i	−0.950161	+	0.311759i	$0.899082\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	12.2589	−	37.7290i	0.411614	−	1.26682i	−0.503631	−	0.863919i	$-0.668003\pi$
$887$	12.2589	−	37.7290i	0.411614	−	1.26682i	0.915245	−	0.402898i	$-0.131997\pi$
$888$		0			0
$889$	−3.50667	+	2.54774i	−0.117610	+	0.0854485i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−18.6639	+	13.5601i	−0.624564	+	0.453772i
$894$		0			0
$895$	5.33574	−	16.4217i	0.178354	−	0.548917i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−10.0323	−	30.8763i	−0.334596	−	1.02978i
$900$		0			0
$901$	5.65159			0.188282
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−1.62653	−	5.00593i	−0.0540675	−	0.166403i
$906$		0			0
$907$	−25.3463	−	18.4152i	−0.841610	−	0.611465i	0.0812101	−	0.996697i	$-0.474122\pi$
$907$	−25.3463	−	18.4152i	−0.841610	−	0.611465i	−0.922820	+	0.385232i	$0.874122\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−23.2850	+	16.9176i	−0.771468	+	0.560504i	−0.902406	−	0.430886i	$-0.858201\pi$
$911$	−23.2850	+	16.9176i	−0.771468	+	0.560504i	0.130938	+	0.991391i	$0.458201\pi$
$912$		0			0
$913$	−20.0920	−	41.7641i	−0.664948	−	1.38219i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	1.79528	−	5.52530i	0.0592853	−	0.182461i
$918$		0			0
$919$	−21.3619	−	15.5203i	−0.704665	−	0.511969i	0.176783	−	0.984250i	$-0.443431\pi$
$919$	−21.3619	−	15.5203i	−0.704665	−	0.511969i	−0.881448	+	0.472281i	$0.843431\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	63.1515			2.07866
$924$		0			0
$925$	−3.14256			−0.103327
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−44.9423	−	32.6525i	−1.47451	−	1.07129i	−0.979275	−	0.202535i	$-0.935082\pi$
$929$	−44.9423	−	32.6525i	−1.47451	−	1.07129i	−0.495235	−	0.868759i	$-0.664918\pi$
$930$		0			0
$931$	−24.8613	+	76.5152i	−0.814796	+	2.50768i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.482512	−	2.65283i	0.0157798	−	0.0867567i
$936$		0			0
$937$	11.8835	−	8.63389i	0.388218	−	0.282057i	−0.376507	−	0.926414i	$-0.622875\pi$
$937$	11.8835	−	8.63389i	0.388218	−	0.282057i	0.764725	+	0.644357i	$0.222875\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−46.0740	−	33.4748i	−1.50197	−	1.09125i	−0.969588	−	0.244742i	$-0.921297\pi$
$941$	−46.0740	−	33.4748i	−1.50197	−	1.09125i	−0.532383	−	0.846504i	$-0.678703\pi$
$942$		0			0
$943$	13.8319	+	42.5702i	0.450429	+	1.38628i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	33.1235			1.07637			0.538184	−	0.842827i	$-0.319110\pi$
$947$	33.1235			1.07637			0.538184	+	0.842827i	$0.319110\pi$
$948$		0			0
$949$	4.59502	+	14.1420i	0.149161	+	0.459070i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	1.99812	−	6.14959i	0.0647255	−	0.199205i	−0.913464	−	0.406920i	$-0.866603\pi$
$953$	1.99812	−	6.14959i	0.0647255	−	0.199205i	0.978189	+	0.207715i	$0.0666028\pi$
$954$		0			0
$955$	12.9856	−	9.43461i	0.420205	−	0.305297i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	19.9170	−	14.4706i	0.643154	−	0.467279i
$960$		0			0
$961$	−3.13091	+	9.63595i	−0.100997	+	0.310837i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	1.98484	+	6.10872i	0.0638944	+	0.196647i
$966$		0			0
$967$	−15.6961			−0.504752			−0.252376	−	0.967629i	$-0.581212\pi$
$967$	−15.6961			−0.504752			−0.252376	+	0.967629i	$0.581212\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	2.09603	+	6.45092i	0.0672649	+	0.207020i	0.979039	−	0.203671i	$-0.0652874\pi$
$971$	2.09603	+	6.45092i	0.0672649	+	0.207020i	−0.911774	+	0.410691i	$0.865287\pi$
$972$		0			0
$973$	−50.1835	−	36.4604i	−1.60881	−	1.16887i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	15.5147	−	11.2721i	0.496358	−	0.360625i	−0.311266	−	0.950323i	$-0.600753\pi$
$977$	15.5147	−	11.2721i	0.496358	−	0.360625i	0.807624	+	0.589697i	$0.200753\pi$
$978$		0			0
$979$	−2.33643	−	1.25849i	−0.0746728	−	0.0402216i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	10.0003	−	30.7777i	0.318959	−	0.981656i	−0.655135	−	0.755512i	$-0.727388\pi$
$983$	10.0003	−	30.7777i	0.318959	−	0.981656i	0.974094	−	0.226143i	$-0.0726118\pi$
$984$		0			0
$985$	−11.6151	−	8.43887i	−0.370088	−	0.268885i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.49448			−0.301907
$990$		0			0
$991$	−40.4694			−1.28555			−0.642776	−	0.766054i	$-0.722218\pi$
$991$	−40.4694			−1.28555			−0.642776	+	0.766054i	$0.722218\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	12.2496	+	8.89982i	0.388337	+	0.282143i
$996$		0			0
$997$	−11.6639	+	35.8978i	−0.369399	+	1.13689i	0.577781	+	0.816192i	$0.303919\pi$
$997$	−11.6639	+	35.8978i	−0.369399	+	1.13689i	−0.947180	+	0.320702i	$0.896081\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1980.2.z.b.1081.1		8
3.2	odd	2		660.2.y.b.421.1	yes	8
11.4	even	5	inner	1980.2.z.b.1621.1		8
33.2	even	10		7260.2.a.bg.1.4		4
33.20	odd	10		7260.2.a.be.1.1		4
33.26	odd	10		660.2.y.b.301.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
660.2.y.b.301.1	✓	8	33.26	odd	10
660.2.y.b.421.1	yes	8	3.2	odd	2
1980.2.z.b.1081.1		8	1.1	even	1	trivial
1980.2.z.b.1621.1		8	11.4	even	5	inner
7260.2.a.be.1.1		4	33.20	odd	10
7260.2.a.bg.1.4		4	33.2	even	10

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:	\( N \)	\(=\)	\( 1980 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1980.z (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 - 0.587785i) q^{5} +(-1.26226 + 3.88484i) q^{7} +(2.91998 + 1.57281i) q^{11} +(-5.72462 + 4.15918i) q^{13} +(0.657715 + 0.477858i) q^{17} +(-2.56691 - 7.90013i) q^{19} -7.02697 q^{23} +(0.309017 + 0.951057i) q^{25} +(2.19613 - 6.75901i) q^{29} +(3.69573 - 2.68510i) q^{31} +(3.30464 - 2.40097i) q^{35} +(-0.971104 + 2.98875i) q^{37} +(-1.96840 - 6.05812i) q^{41} +1.35115 q^{43} +(-0.858221 - 2.64133i) q^{47} +(-7.83558 - 5.69288i) q^{49} +(5.62404 - 4.08610i) q^{53} +(-1.43784 - 2.98875i) q^{55} +(1.34036 - 4.12521i) q^{59} +(8.12278 + 5.90154i) q^{61} +7.07602 q^{65} -3.26304 q^{67} +(-7.22025 - 5.24582i) q^{71} +(0.649380 - 1.99858i) q^{73} +(-9.79590 + 9.35835i) q^{77} +(-10.1631 + 7.38394i) q^{79} +(-11.3050 - 8.21357i) q^{83} +(-0.251225 - 0.773190i) q^{85} -0.800155 q^{89} +(-8.93179 - 27.4892i) q^{91} +(-2.56691 + 7.90013i) q^{95} +(-3.90457 + 2.83683i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{5} - 3 q^{7} + 5 q^{11} - 8 q^{13} - 6 q^{17} + 6 q^{19} - 30 q^{23} - 2 q^{25} - 9 q^{31} + 7 q^{35} - 7 q^{37} - 25 q^{41} - 8 q^{43} + 7 q^{47} - 11 q^{49} - 3 q^{53} + 5 q^{55} - 5 q^{59}+ \cdots + q^{97}+O(q^{100}) \) 8 * q - 2 * q^5 - 3 * q^7 + 5 * q^11 - 8 * q^13 - 6 * q^17 + 6 * q^19 - 30 * q^23 - 2 * q^25 - 9 * q^31 + 7 * q^35 - 7 * q^37 - 25 * q^41 - 8 * q^43 + 7 * q^47 - 11 * q^49 - 3 * q^53 + 5 * q^55 - 5 * q^59 + 13 * q^61 + 2 * q^65 + 18 * q^67 - 5 * q^71 - 15 * q^73 - 29 * q^77 - 50 * q^79 - 13 * q^83 + 4 * q^85 - 32 * q^89 - 15 * q^91 + 6 * q^95 + q^97

Introduction

L-functions

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Database

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