LMFDB - Embedded newform 660.2.y.b.421.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [660,2,Mod(181,660)] 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("660.181"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(660, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	660.y (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,-2,0,2] 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:	$5.27012653340$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			421.1
Root			$0.453245 + 1.39494i$ of defining polynomial
Character	$\chi$	$=$	660.421
Dual form			660.2.y.b.301.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.309017 + 0.951057i) q^{3} +(0.809017 + 0.587785i) q^{5} +(-1.26226 + 3.88484i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-2.91998 - 1.57281i) q^{11} +(-5.72462 + 4.15918i) q^{13} +(-0.309017 + 0.951057i) q^{15} +(-0.657715 - 0.477858i) q^{17} +(-2.56691 - 7.90013i) q^{19} -4.08477 q^{21} +7.02697 q^{23} +(0.309017 + 0.951057i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(-2.19613 + 6.75901i) q^{29} +(3.69573 - 2.68510i) q^{31} +(0.593510 - 3.26309i) q^{33} +(-3.30464 + 2.40097i) q^{35} +(-0.971104 + 2.98875i) q^{37} +(-5.72462 - 4.15918i) q^{39} +(1.96840 + 6.05812i) q^{41} +1.35115 q^{43} -1.00000 q^{45} +(0.858221 + 2.64133i) q^{47} +(-7.83558 - 5.69288i) q^{49} +(0.251225 - 0.773190i) q^{51} +(-5.62404 + 4.08610i) q^{53} +(-1.43784 - 2.98875i) q^{55} +(6.72025 - 4.88255i) q^{57} +(-1.34036 + 4.12521i) q^{59} +(8.12278 + 5.90154i) q^{61} +(-1.26226 - 3.88484i) q^{63} -7.07602 q^{65} -3.26304 q^{67} +(2.17145 + 6.68305i) q^{69} +(7.22025 + 5.24582i) q^{71} +(0.649380 - 1.99858i) q^{73} +(-0.809017 + 0.587785i) q^{75} +(9.79590 - 9.35835i) q^{77} +(-10.1631 + 7.38394i) q^{79} +(0.309017 - 0.951057i) q^{81} +(11.3050 + 8.21357i) q^{83} +(-0.251225 - 0.773190i) q^{85} -7.10684 q^{87} +0.800155 q^{89} +(-8.93179 - 27.4892i) q^{91} +(3.69573 + 2.68510i) q^{93} +(2.56691 - 7.90013i) q^{95} +(-3.90457 + 2.83683i) q^{97} +(3.28679 - 0.443888i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{3} + 2 q^{5} - 3 q^{7} - 2 q^{9} - 5 q^{11} - 8 q^{13} + 2 q^{15} + 6 q^{17} + 6 q^{19} - 8 q^{21} + 30 q^{23} - 2 q^{25} - 2 q^{27} - 9 q^{31} + 10 q^{33} - 7 q^{35} - 7 q^{37} - 8 q^{39} + 25 q^{41}+ \cdots + 5 q^{99}+O(q^{100}) $ 8 * q - 2 * q^3 + 2 * q^5 - 3 * q^7 - 2 * q^9 - 5 * q^11 - 8 * q^13 + 2 * q^15 + 6 * q^17 + 6 * q^19 - 8 * q^21 + 30 * q^23 - 2 * q^25 - 2 * q^27 - 9 * q^31 + 10 * q^33 - 7 * q^35 - 7 * q^37 - 8 * q^39 + 25 * q^41 - 8 * q^43 - 8 * q^45 - 7 * q^47 - 11 * q^49 - 4 * q^51 + 3 * q^53 + 5 * q^55 + q^57 + 5 * q^59 + 13 * q^61 - 3 * q^63 - 2 * q^65 + 18 * q^67 - 5 * q^69 + 5 * q^71 - 15 * q^73 - 2 * q^75 + 29 * q^77 - 50 * q^79 - 2 * q^81 + 13 * q^83 + 4 * q^85 - 30 * q^87 + 32 * q^89 - 15 * q^91 - 9 * q^93 - 6 * q^95 + q^97 + 5 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/660\mathbb{Z}\right)^\times$.

$n$	$221$	$331$	$397$	$541$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$		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
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		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
$15$	−0.309017	+	0.951057i	−0.0797878	+	0.245562i
$16$		0			0
$17$	−0.657715	−	0.477858i	−0.159519	−	0.115898i	0.505162	−	0.863024i	$-0.331433\pi$
$17$	−0.657715	−	0.477858i	−0.159519	−	0.115898i	−0.664681	+	0.747127i	$0.731433\pi$
$18$		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
$21$	−4.08477			−0.891369
$22$		0			0
$23$	7.02697			1.46523			0.732613	−	0.680646i	$-0.238301\pi$
$23$	7.02697			1.46523			0.732613	+	0.680646i	$0.238301\pi$
$24$		0			0
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$		0			0
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$		0			0
$29$	−2.19613	+	6.75901i	−0.407812	+	1.25512i	0.510712	+	0.859752i	$0.329382\pi$
$29$	−2.19613	+	6.75901i	−0.407812	+	1.25512i	−0.918524	+	0.395364i	$0.870618\pi$
$30$		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
$33$	0.593510	−	3.26309i	0.103317	−	0.568031i
$34$		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
$39$	−5.72462	−	4.15918i	−0.916673	−	0.666002i
$40$		0			0
$41$	1.96840	+	6.05812i	0.307413	+	0.946119i	0.978766	+	0.204981i	$0.0657134\pi$
$41$	1.96840	+	6.05812i	0.307413	+	0.946119i	−0.671353	+	0.741138i	$0.734287\pi$
$42$		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
$45$	−1.00000			−0.149071
$46$		0			0
$47$	0.858221	+	2.64133i	0.125184	+	0.385278i	0.993935	−	0.109972i	$-0.0350763\pi$
$47$	0.858221	+	2.64133i	0.125184	+	0.385278i	−0.868750	+	0.495251i	$0.835076\pi$
$48$		0			0
$49$	−7.83558	−	5.69288i	−1.11937	−	0.813269i
$50$		0			0
$51$	0.251225	−	0.773190i	0.0351785	−	0.108268i
$52$		0			0
$53$	−5.62404	+	4.08610i	−0.772521	+	0.561269i	−0.902725	−	0.430218i	$-0.858437\pi$
$53$	−5.62404	+	4.08610i	−0.772521	+	0.561269i	0.130204	+	0.991487i	$0.458437\pi$
$54$		0			0
$55$	−1.43784	−	2.98875i	−0.193878	−	0.403003i
$56$		0			0
$57$	6.72025	−	4.88255i	0.890119	−	0.646709i
$58$		0			0
$59$	−1.34036	+	4.12521i	−0.174500	+	0.537057i	−0.999610	−	0.0279154i	$-0.991113\pi$
$59$	−1.34036	+	4.12521i	−0.174500	+	0.537057i	0.825110	+	0.564972i	$0.191113\pi$
$60$		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
$63$	−1.26226	−	3.88484i	−0.159030	−	0.489444i
$64$		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
$69$	2.17145	+	6.68305i	0.261412	+	0.804545i
$70$		0			0
$71$	7.22025	+	5.24582i	0.856886	+	0.622564i	0.927036	−	0.374972i	$-0.122348\pi$
$71$	7.22025	+	5.24582i	0.856886	+	0.622564i	−0.0701500	+	0.997536i	$0.522348\pi$
$72$		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
$75$	−0.809017	+	0.587785i	−0.0934172	+	0.0678716i
$76$		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
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$		0			0
$83$	11.3050	+	8.21357i	1.24089	+	0.901557i	0.997657	−	0.0684118i	$-0.0217932\pi$
$83$	11.3050	+	8.21357i	1.24089	+	0.901557i	0.243229	+	0.969969i	$0.421793\pi$
$84$		0			0
$85$	−0.251225	−	0.773190i	−0.0272491	−	0.0838642i
$86$		0			0
$87$	−7.10684			−0.761933
$88$		0			0
$89$	0.800155			0.0848163			0.0424081	−	0.999100i	$-0.486497\pi$
$89$	0.800155			0.0848163			0.0424081	+	0.999100i	$0.486497\pi$
$90$		0			0
$91$	−8.93179	−	27.4892i	−0.936306	−	2.88165i
$92$		0			0
$93$	3.69573	+	2.68510i	0.383229	+	0.278432i
$94$		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
$99$	3.28679	−	0.443888i	0.330334	−	0.0446125i
$100$		0			0
$101$	11.1326	−	8.08827i	1.10773	−	0.804813i	0.125426	−	0.992103i	$-0.459970\pi$
$101$	11.1326	−	8.08827i	1.10773	−	0.804813i	0.982305	+	0.187290i	$0.0599703\pi$
$102$		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
$105$	−3.30464	−	2.40097i	−0.322500	−	0.234310i
$106$		0			0
$107$	−0.523263	−	1.61044i	−0.0505857	−	0.155687i	0.922573	−	0.385824i	$-0.126083\pi$
$107$	−0.523263	−	1.61044i	−0.0505857	−	0.155687i	−0.973158	+	0.230137i	$0.926083\pi$
$108$		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
$111$	−3.14256			−0.298278
$112$		0			0
$113$	4.98521	+	15.3429i	0.468969	+	1.44334i	0.853921	+	0.520403i	$0.174218\pi$
$113$	4.98521	+	15.3429i	0.468969	+	1.44334i	−0.384951	+	0.922937i	$0.625782\pi$
$114$		0			0
$115$	5.68494	+	4.13035i	0.530123	+	0.385157i
$116$		0			0
$117$	2.18661	−	6.72970i	0.202152	−	0.622161i
$118$		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
$123$	−5.15334	+	3.74412i	−0.464661	+	0.337596i
$124$		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
$129$	0.417527	+	1.28502i	0.0367612	+	0.113139i
$130$		0			0
$131$	1.42227			0.124264			0.0621322	−	0.998068i	$-0.480210\pi$
$131$	1.42227			0.124264			0.0621322	+	0.998068i	$0.480210\pi$
$132$		0			0
$133$	33.9309			2.94218
$134$		0			0
$135$	−0.309017	−	0.951057i	−0.0265959	−	0.0818539i
$136$		0			0
$137$	4.87592	+	3.54257i	0.416578	+	0.302662i	0.776260	−	0.630413i	$-0.217115\pi$
$137$	4.87592	+	3.54257i	0.416578	+	0.302662i	−0.359681	+	0.933075i	$0.617115\pi$
$138$		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
$141$	−2.24685	+	1.63243i	−0.189219	+	0.137476i
$142$		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
$147$	2.99293	−	9.21128i	0.246852	−	0.759733i
$148$		0			0
$149$	−4.61533	−	3.35323i	−0.378103	−	0.274708i	0.382460	−	0.923972i	$-0.375077\pi$
$149$	−4.61533	−	3.35323i	−0.378103	−	0.274708i	−0.760563	+	0.649264i	$0.775077\pi$
$150$		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
$153$	0.812980			0.0657256
$154$		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
$159$	−5.62404	−	4.08610i	−0.446015	−	0.324049i
$160$		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
$165$	2.39815	−	2.29104i	0.186696	−	0.178357i
$166$		0			0
$167$	18.1574	−	13.1922i	1.40507	−	1.02084i	0.411049	−	0.911613i	$-0.365163\pi$
$167$	18.1574	−	13.1922i	1.40507	−	1.02084i	0.994017	−	0.109226i	$-0.0348373\pi$
$168$		0			0
$169$	11.4553	−	35.2557i	0.881176	−	2.71198i
$170$		0			0
$171$	6.72025	+	4.88255i	0.513910	+	0.373378i
$172$		0			0
$173$	−2.14359	−	6.59729i	−0.162974	−	0.501583i	0.835907	−	0.548871i	$-0.184942\pi$
$173$	−2.14359	−	6.59729i	−0.162974	−	0.501583i	−0.998881	+	0.0472880i	$0.984942\pi$
$174$		0			0
$175$	−4.08477			−0.308779
$176$		0			0
$177$	−4.33750			−0.326027
$178$		0			0
$179$	−5.33574	−	16.4217i	−0.398812	−	1.22742i	−0.925953	−	0.377639i	$-0.876736\pi$
$179$	−5.33574	−	16.4217i	−0.398812	−	1.22742i	0.527141	−	0.849778i	$-0.323264\pi$
$180$		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
$183$	−3.10262	+	9.54890i	−0.229353	+	0.705875i
$184$		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
$189$	3.30464	−	2.40097i	0.240378	−	0.174645i
$190$		0			0
$191$	4.96007	−	15.2655i	0.358898	−	1.10457i	−0.594817	−	0.803861i	$-0.702775\pi$
$191$	4.96007	−	15.2655i	0.358898	−	1.10457i	0.953715	−	0.300713i	$-0.0972245\pi$
$192$		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
$195$	−2.18661	−	6.72970i	−0.156586	−	0.481924i
$196$		0			0
$197$	−14.3571			−1.02290			−0.511449	−	0.859314i	$-0.670891\pi$
$197$	−14.3571			−1.02290			−0.511449	+	0.859314i	$0.670891\pi$
$198$		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
$201$	−1.00834	−	3.10334i	−0.0711225	−	0.218893i
$202$		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
$207$	−5.68494	+	4.13035i	−0.395131	+	0.287079i
$208$		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
$213$	−2.75789	+	8.48791i	−0.188968	+	0.581582i
$214$		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
$219$	2.10144			0.142002
$220$		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
$225$	−0.809017	−	0.587785i	−0.0539345	−	0.0391857i
$226$		0			0
$227$	−3.65630	+	11.2529i	−0.242677	+	0.746883i	0.753333	+	0.657639i	$0.228445\pi$
$227$	−3.65630	+	11.2529i	−0.242677	+	0.746883i	−0.996010	+	0.0892435i	$0.971555\pi$
$228$		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
$231$	11.9274	+	6.42457i	0.784767	+	0.422705i
$232$		0			0
$233$	20.7086	−	15.0457i	1.35666	−	0.985674i	0.358015	−	0.933716i	$-0.383454\pi$
$233$	20.7086	−	15.0457i	1.35666	−	0.985674i	0.998649	−	0.0519580i	$-0.0165462\pi$
$234$		0			0
$235$	−0.858221	+	2.64133i	−0.0559842	+	0.172302i
$236$		0			0
$237$	−10.1631	−	7.38394i	−0.660166	−	0.479638i
$238$		0			0
$239$	−7.26716	−	22.3660i	−0.470074	−	1.44674i	−0.852488	−	0.522747i	$-0.824907\pi$
$239$	−7.26716	−	22.3660i	−0.470074	−	1.44674i	0.382414	−	0.923991i	$-0.375093\pi$
$240$		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
$243$	1.00000			0.0641500
$244$		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
$249$	−4.31813	+	13.2898i	−0.273650	+	0.842210i
$250$		0			0
$251$	11.0134	−	8.00174i	0.695163	−	0.505065i	−0.183191	−	0.983077i	$-0.558643\pi$
$251$	11.0134	−	8.00174i	0.695163	−	0.505065i	0.878353	+	0.478012i	$0.158643\pi$
$252$		0			0
$253$	−20.5186	−	11.0521i	−1.28999	−	0.694840i
$254$		0			0
$255$	0.657715	−	0.477858i	0.0411877	−	0.0299246i
$256$		0			0
$257$	−8.50577	+	26.1781i	−0.530576	+	1.63294i	0.222444	+	0.974946i	$0.428597\pi$
$257$	−8.50577	+	26.1781i	−0.530576	+	1.63294i	−0.753019	+	0.657998i	$0.771403\pi$
$258$		0			0
$259$	−10.3850	−	7.54517i	−0.645295	−	0.468834i
$260$		0			0
$261$	−2.19613	−	6.75901i	−0.135937	−	0.418372i
$262$		0			0
$263$	0.977108			0.0602510			0.0301255	−	0.999546i	$-0.490409\pi$
$263$	0.977108			0.0602510			0.0301255	+	0.999546i	$0.490409\pi$
$264$		0			0
$265$	−6.95169			−0.427039
$266$		0			0
$267$	0.247261	+	0.760993i	0.0151322	+	0.0465720i
$268$		0			0
$269$	10.7562	+	7.81485i	0.655818	+	0.476480i	0.865248	−	0.501344i	$-0.167161\pi$
$269$	10.7562	+	7.81485i	0.655818	+	0.476480i	−0.209430	+	0.977824i	$0.567161\pi$
$270$		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
$273$	23.3837	−	16.9893i	1.41525	−	1.02824i
$274$		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
$279$	−1.41164	+	4.34459i	−0.0845128	+	0.260104i
$280$		0			0
$281$	−20.7021	−	15.0410i	−1.23498	−	0.897268i	−0.237730	−	0.971331i	$-0.576403\pi$
$281$	−20.7021	−	15.0410i	−1.23498	−	0.897268i	−0.997254	+	0.0740630i	$0.976403\pi$
$282$		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
$285$	8.30669			0.492046
$286$		0			0
$287$	−26.0195			−1.53588
$288$		0			0
$289$	−5.04905	−	15.5394i	−0.297003	−	0.914081i
$290$		0			0
$291$	−3.90457	−	2.83683i	−0.228890	−	0.166298i
$292$		0			0
$293$	−7.20757	+	22.1826i	−0.421071	+	1.29592i	0.485637	+	0.874161i	$0.338588\pi$
$293$	−7.20757	+	22.1826i	−0.421071	+	1.29592i	−0.906707	+	0.421761i	$0.861412\pi$
$294$		0			0
$295$	−3.50911	+	2.54952i	−0.204309	+	0.148439i
$296$		0			0
$297$	1.43784	+	2.98875i	0.0834317	+	0.173425i
$298$		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
$303$	11.1326	+	8.08827i	0.639548	+	0.464659i
$304$		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
$309$	6.26355			0.356321
$310$		0			0
$311$	9.34470	+	28.7600i	0.529889	+	1.63083i	0.754440	+	0.656369i	$0.227908\pi$
$311$	9.34470	+	28.7600i	0.529889	+	1.63083i	−0.224551	+	0.974462i	$0.572092\pi$
$312$		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
$315$	1.26226	−	3.88484i	0.0711204	−	0.218886i
$316$		0			0
$317$	10.3686	−	7.53320i	0.582356	−	0.423107i	−0.257217	−	0.966354i	$-0.582805\pi$
$317$	10.3686	−	7.53320i	0.582356	−	0.423107i	0.839573	+	0.543247i	$0.182805\pi$
$318$		0			0
$319$	17.0433	−	16.2820i	0.954242	−	0.911619i
$320$		0			0
$321$	1.36992	−	0.995305i	0.0764615	−	0.0555525i
$322$		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
$327$	−2.22410	−	6.84506i	−0.122993	−	0.378533i
$328$		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
$333$	−0.971104	−	2.98875i	−0.0532162	−	0.163783i
$334$		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
$339$	−13.0515	+	9.48244i	−0.708858	+	0.515015i
$340$		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
$345$	−2.17145	+	6.68305i	−0.116907	+	0.359803i
$346$		0			0
$347$	−0.198657	−	0.144333i	−0.0106645	−	0.00774818i	0.582440	−	0.812874i	$-0.302098\pi$
$347$	−0.198657	−	0.144333i	−0.0106645	−	0.00774818i	−0.593105	+	0.805125i	$0.702098\pi$
$348$		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
$351$	7.07602			0.377690
$352$		0			0
$353$	17.8806			0.951689			0.475845	−	0.879529i	$-0.342142\pi$
$353$	17.8806			0.951689			0.475845	+	0.879529i	$0.342142\pi$
$354$		0			0
$355$	2.75789	+	8.48791i	0.146374	+	0.450492i
$356$		0			0
$357$	2.68661	+	1.95194i	0.142191	+	0.103307i
$358$		0			0
$359$	1.98411	−	6.10646i	0.104717	−	0.322287i	−0.884947	−	0.465692i	$-0.845805\pi$
$359$	1.98411	−	6.10646i	0.104717	−	0.322287i	0.989664	+	0.143406i	$0.0458054\pi$
$360$		0			0
$361$	−40.4517	+	29.3899i	−2.12904	+	1.54683i
$362$		0			0
$363$	−6.86526	+	8.59466i	−0.360333	+	0.451103i
$364$		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
$369$	−5.15334	−	3.74412i	−0.268272	−	0.194911i
$370$		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
$375$	−1.00000			−0.0516398
$376$		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
$381$	−0.327908	+	1.00920i	−0.0167992	+	0.0517027i
$382$		0			0
$383$	−24.6605	+	17.9169i	−1.26009	+	0.915511i	−0.998762	−	0.0497387i	$-0.984161\pi$
$383$	−24.6605	+	17.9169i	−1.26009	+	0.915511i	−0.261330	+	0.965249i	$0.584161\pi$
$384$		0			0
$385$	13.4258	−	1.81318i	0.684240	−	0.0924082i
$386$		0			0
$387$	−1.09310	+	0.794184i	−0.0555654	+	0.0403707i
$388$		0			0
$389$	−1.90292	+	5.85659i	−0.0964819	+	0.296941i	−0.987637	−	0.156758i	$-0.949896\pi$
$389$	−1.90292	+	5.85659i	−0.0964819	+	0.296941i	0.891155	+	0.453699i	$0.149896\pi$
$390$		0			0
$391$	−4.62174	−	3.35789i	−0.233732	−	0.169816i
$392$		0			0
$393$	0.439506	+	1.35266i	0.0221701	+	0.0682326i
$394$		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
$399$	10.4852	+	32.2702i	0.524917	+	1.61553i
$400$		0			0
$401$	−0.00433382	−	0.00314870i	−0.000216421	−	0.000157239i	0.587677	−	0.809096i	$-0.300043\pi$
$401$	−0.00433382	−	0.00314870i	−0.000216421	−	0.000157239i	−0.587893	+	0.808938i	$0.700043\pi$
$402$		0			0
$403$	−9.98881	+	30.7424i	−0.497578	+	1.53139i
$404$		0			0
$405$	0.809017	−	0.587785i	0.0402004	−	0.0292073i
$406$		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
$411$	−1.86244	+	5.73199i	−0.0918673	+	0.282738i
$412$		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
$417$	−15.1857			−0.743649
$418$		0			0
$419$	30.8785			1.50851			0.754256	−	0.656580i	$-0.227998\pi$
$419$	30.8785			1.50851			0.754256	+	0.656580i	$0.227998\pi$
$420$		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
$423$	−2.24685	−	1.63243i	−0.109246	−	0.0793717i
$424$		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
$429$	10.1742	+	21.1485i	0.491213	+	1.02106i
$430$		0			0
$431$	23.1281	−	16.8036i	1.11404	−	0.809400i	0.130748	−	0.991416i	$-0.458262\pi$
$431$	23.1281	−	16.8036i	1.11404	−	0.809400i	0.983296	+	0.182016i	$0.0582622\pi$
$432$		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
$435$	−5.74955	−	4.17730i	−0.275670	−	0.200286i
$436$		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
$441$	9.68531			0.461205
$442$		0			0
$443$	−9.16992	−	28.2221i	−0.435676	−	1.34087i	−0.892392	−	0.451260i	$-0.850975\pi$
$443$	−9.16992	−	28.2221i	−0.435676	−	1.34087i	0.456717	−	0.889612i	$-0.349025\pi$
$444$		0			0
$445$	0.647339	+	0.470319i	0.0306868	+	0.0222953i
$446$		0			0
$447$	1.76290	−	5.42565i	0.0833823	−	0.256624i
$448$		0			0
$449$	0.727553	−	0.528598i	0.0343353	−	0.0249461i	−0.570485	−	0.821308i	$-0.693245\pi$
$449$	0.727553	−	0.528598i	0.0343353	−	0.0249461i	0.604821	+	0.796362i	$0.293245\pi$
$450$		0			0
$451$	3.78059	−	20.7855i	0.178021	−	0.978750i
$452$		0			0
$453$	0.665450	−	0.483478i	0.0312656	−	0.0227158i
$454$		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
$459$	0.251225	+	0.773190i	0.0117262	+	0.0360894i
$460$		0			0
$461$	−32.0061			−1.49067			−0.745337	−	0.666687i	$-0.767712\pi$
$461$	−32.0061			−1.49067			−0.745337	+	0.666687i	$0.767712\pi$
$462$		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
$465$	1.41164	+	4.34459i	0.0654633	+	0.201475i
$466$		0			0
$467$	−0.112883	−	0.0820139i	−0.00522358	−	0.00379515i	0.585170	−	0.810910i	$-0.301028\pi$
$467$	−0.112883	−	0.0820139i	−0.00522358	−	0.00379515i	−0.590394	+	0.807115i	$0.701028\pi$
$468$		0			0
$469$	4.11881	−	12.6764i	0.190189	−	0.585342i
$470$		0			0
$471$	4.00311	−	2.90843i	0.184454	−	0.134013i
$472$		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
$477$	2.14819	−	6.61145i	0.0983589	−	0.302718i
$478$		0			0
$479$	22.5825	+	16.4072i	1.03182	+	0.749662i	0.968672	−	0.248342i	$-0.0798857\pi$
$479$	22.5825	+	16.4072i	1.03182	+	0.749662i	0.0631490	+	0.998004i	$0.479886\pi$
$480$		0			0
$481$	−6.87155	−	21.1485i	−0.313316	−	0.964287i
$482$		0			0
$483$	−28.7035			−1.30606
$484$		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
$489$	7.75826	+	5.63671i	0.350841	+	0.254901i
$490$		0			0
$491$	−1.10397	+	3.39767i	−0.0498214	+	0.153335i	−0.972872	−	0.231344i	$-0.925688\pi$
$491$	−1.10397	+	3.39767i	−0.0498214	+	0.153335i	0.923051	+	0.384679i	$0.125688\pi$
$492$		0			0
$493$	4.67427	−	3.39606i	0.210519	−	0.152951i
$494$		0			0
$495$	2.91998	+	1.57281i	0.131243	+	0.0706926i
$496$		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
$501$	18.1574	+	13.1922i	0.811215	+	0.589382i
$502$		0			0
$503$	12.8361	+	39.5053i	0.572332	+	1.76146i	0.645090	+	0.764106i	$0.276820\pi$
$503$	12.8361	+	39.5053i	0.572332	+	1.76146i	−0.0727583	+	0.997350i	$0.523180\pi$
$504$		0			0
$505$	13.7606			0.612338
$506$		0			0
$507$	37.0701			1.64634
$508$		0			0
$509$	−4.32221	−	13.3024i	−0.191578	−	0.589618i	−0.999999	−	0.00101314i	$-0.999678\pi$
$509$	−4.32221	−	13.3024i	−0.191578	−	0.589618i	0.808421	−	0.588605i	$-0.200322\pi$
$510$		0			0
$511$	6.94450	+	5.04548i	0.307207	+	0.223199i
$512$		0			0
$513$	−2.56691	+	7.90013i	−0.113332	+	0.348799i
$514$		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
$519$	5.61199	−	4.07735i	0.246339	−	0.178976i
$520$		0			0
$521$	2.45696	−	7.56173i	0.107641	−	0.331285i	−0.882700	−	0.469937i	$-0.844277\pi$
$521$	2.45696	−	7.56173i	0.107641	−	0.331285i	0.990341	+	0.138651i	$0.0442767\pi$
$522$		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
$525$	−1.26226	−	3.88484i	−0.0550896	−	0.169548i
$526$		0			0
$527$	−3.71383			−0.161777
$528$		0			0
$529$	26.3784			1.14689
$530$		0			0
$531$	−1.34036	−	4.12521i	−0.0581668	−	0.179019i
$532$		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
$537$	13.9691	−	10.1492i	0.602813	−	0.437969i
$538$		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
$543$	−1.62653	+	5.00593i	−0.0698009	+	0.214825i
$544$		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
$549$	−10.0403			−0.428510
$550$		0			0
$551$	59.0343			2.51495
$552$		0			0
$553$	−15.8569	−	48.8026i	−0.674305	−	2.07530i
$554$		0			0
$555$	−2.54238	−	1.84715i	−0.107918	−	0.0784071i
$556$		0			0
$557$	8.29716	−	25.5360i	0.351562	−	1.08200i	−0.606414	−	0.795149i	$-0.707393\pi$
$557$	8.29716	−	25.5360i	0.351562	−	1.08200i	0.957976	−	0.286848i	$-0.0926074\pi$
$558$		0			0
$559$	−7.73481	+	5.61967i	−0.327147	+	0.237687i
$560$		0			0
$561$	−1.94965	+	1.86257i	−0.0823144	+	0.0786377i
$562$		0			0
$563$	5.60247	−	4.07043i	0.236116	−	0.171548i	−0.463435	−	0.886131i	$-0.653383\pi$
$563$	5.60247	−	4.07043i	0.236116	−	0.171548i	0.699551	+	0.714583i	$0.253383\pi$
$564$		0			0
$565$	−4.98521	+	15.3429i	−0.209730	+	0.645481i
$566$		0			0
$567$	3.30464	+	2.40097i	0.138782	+	0.100831i
$568$		0			0
$569$	−1.49757	−	4.60903i	−0.0627812	−	0.193221i	0.914746	−	0.404029i	$-0.132390\pi$
$569$	−1.49757	−	4.60903i	−0.0627812	−	0.193221i	−0.977527	+	0.210808i	$0.932390\pi$
$570$		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
$573$	16.0511			0.670545
$574$		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
$579$	1.98484	−	6.10872i	0.0824873	−	0.253870i
$580$		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
$585$	5.72462	−	4.15918i	0.236684	−	0.171961i
$586$		0			0
$587$	4.72899	−	14.5543i	0.195186	−	0.600722i	−0.804788	−	0.593562i	$-0.797721\pi$
$587$	4.72899	−	14.5543i	0.195186	−	0.600722i	0.999974	−	0.00715968i	$-0.00227902\pi$
$588$		0			0
$589$	−30.6992	−	22.3043i	−1.26494	−	0.919033i
$590$		0			0
$591$	−4.43657	−	13.6544i	−0.182496	−	0.561666i
$592$		0			0
$593$	−2.68279			−0.110169			−0.0550845	−	0.998482i	$-0.517543\pi$
$593$	−2.68279			−0.110169			−0.0550845	+	0.998482i	$0.517543\pi$
$594$		0			0
$595$	3.32083			0.136141
$596$		0			0
$597$	−4.67891	−	14.4002i	−0.191495	−	0.589362i
$598$		0			0
$599$	23.5560	+	17.1144i	0.962473	+	0.699277i	0.953724	−	0.300685i	$-0.0972151\pi$
$599$	23.5560	+	17.1144i	0.962473	+	0.699277i	0.00874886	+	0.999962i	$0.497215\pi$
$600$		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
$603$	2.63986	−	1.91797i	0.107503	−	0.0781057i
$604$		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
$609$	8.97070	−	27.6090i	0.363511	−	1.11877i
$610$		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
$615$	−6.36988			−0.256858
$616$		0			0
$617$	−1.97540			−0.0795267			−0.0397634	−	0.999209i	$-0.512660\pi$
$617$	−1.97540			−0.0795267			−0.0397634	+	0.999209i	$0.512660\pi$
$618$		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
$621$	−5.68494	−	4.13035i	−0.228129	−	0.165745i
$622$		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
$627$	−27.3023	+	3.68724i	−1.09035	+	0.147254i
$628$		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
$633$	−2.70076	−	1.96222i	−0.107346	−	0.0779911i
$634$		0			0
$635$	0.327908	+	1.00920i	0.0130126	+	0.0400488i
$636$		0			0
$637$	68.5335			2.71540
$638$		0			0
$639$	−8.92472			−0.353056
$640$		0			0
$641$	4.62814	+	14.2439i	0.182800	+	0.562602i	0.999904	−	0.0138898i	$-0.00442140\pi$
$641$	4.62814	+	14.2439i	0.182800	+	0.562602i	−0.817103	+	0.576491i	$0.804421\pi$
$642$		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
$645$	−0.417527	+	1.28502i	−0.0164401	+	0.0505975i
$646$		0			0
$647$	14.9038	−	10.8283i	0.585929	−	0.425703i	−0.254928	−	0.966960i	$-0.582052\pi$
$647$	14.9038	−	10.8283i	0.585929	−	0.425703i	0.840857	+	0.541258i	$0.182052\pi$
$648$		0			0
$649$	10.4020	−	9.93739i	0.408314	−	0.390077i
$650$		0			0
$651$	−15.0962	+	10.9680i	−0.591666	+	0.429870i
$652$		0			0
$653$	−9.36436	+	28.8205i	−0.366456	+	1.12783i	0.582609	+	0.812753i	$0.302032\pi$
$653$	−9.36436	+	28.8205i	−0.366456	+	1.12783i	−0.949064	+	0.315082i	$0.897968\pi$
$654$		0			0
$655$	1.15064	+	0.835989i	0.0449593	+	0.0326648i
$656$		0			0
$657$	0.649380	+	1.99858i	0.0253347	+	0.0779722i
$658$		0			0
$659$	14.2869			0.556539			0.278269	−	0.960503i	$-0.410239\pi$
$659$	14.2869			0.556539			0.278269	+	0.960503i	$0.410239\pi$
$660$		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
$663$	1.77767	+	5.47111i	0.0690390	+	0.212480i
$664$		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
$669$	19.7905	−	14.3787i	0.765146	−	0.555911i
$670$		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
$675$	0.309017	−	0.951057i	0.0118941	−	0.0366062i
$676$		0			0
$677$	29.0098	+	21.0769i	1.11494	+	0.810050i	0.983434	−	0.181266i	$-0.0580195\pi$
$677$	29.0098	+	21.0769i	1.11494	+	0.810050i	0.131504	+	0.991316i	$0.458019\pi$
$678$		0			0
$679$	−6.09207	−	18.7495i	−0.233792	−	0.719538i
$680$		0			0
$681$	−11.8320			−0.453404
$682$		0			0
$683$	−27.7565			−1.06207			−0.531036	−	0.847349i	$-0.678197\pi$
$683$	−27.7565			−1.06207			−0.531036	+	0.847349i	$0.678197\pi$
$684$		0			0
$685$	1.86244	+	5.73199i	0.0711601	+	0.219008i
$686$		0			0
$687$	−3.44953	−	2.50623i	−0.131608	−	0.0956188i
$688$		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
$693$	−2.42435	+	13.3290i	−0.0920934	+	0.506325i
$694$		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
$699$	20.7086	+	15.0457i	0.783270	+	0.569079i
$700$		0			0
$701$	2.71358	+	8.35155i	0.102491	+	0.315434i	0.989133	−	0.147021i	$-0.0469686\pi$
$701$	2.71358	+	8.35155i	0.102491	+	0.315434i	−0.886643	+	0.462455i	$0.846969\pi$
$702$		0			0
$703$	26.1042			0.984540
$704$		0			0
$705$	−2.77726			−0.104598
$706$		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
$711$	3.88197	−	11.9475i	0.145585	−	0.448065i
$712$		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
$717$	19.0257	−	13.8230i	0.710527	−	0.516228i
$718$		0			0
$719$	−4.39821	+	13.5363i	−0.164026	+	0.504819i	−0.998963	−	0.0455257i	$-0.985504\pi$
$719$	−4.39821	+	13.5363i	−0.164026	+	0.504819i	0.834937	+	0.550345i	$0.185504\pi$
$720$		0			0
$721$	20.6988	+	15.0386i	0.770864	+	0.560065i
$722$		0			0
$723$	4.11710	+	12.6711i	0.153117	+	0.471244i
$724$		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
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		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
$735$	7.83558	−	5.69288i	0.289020	−	0.209985i
$736$		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
$741$	−18.1635	+	55.9015i	−0.667252	+	2.05359i
$742$		0			0
$743$	−20.1696	−	14.6541i	−0.739951	−	0.537606i	0.152745	−	0.988266i	$-0.451189\pi$
$743$	−20.1696	−	14.6541i	−0.739951	−	0.537606i	−0.892696	+	0.450660i	$0.851189\pi$
$744$		0			0
$745$	−1.76290	−	5.42565i	−0.0645877	−	0.198780i
$746$		0			0
$747$	−13.9738			−0.511273
$748$		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
$753$	11.0134	+	8.00174i	0.401352	+	0.291600i
$754$		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
$759$	4.17058	−	22.9296i	0.151382	−	0.832293i
$760$		0			0
$761$	18.6226	−	13.5301i	0.675068	−	0.490466i	−0.196650	−	0.980474i	$-0.563006\pi$
$761$	18.6226	−	13.5301i	0.675068	−	0.490466i	0.871718	+	0.490008i	$0.163006\pi$
$762$		0			0
$763$	9.08491	−	27.9605i	0.328896	−	1.01224i
$764$		0			0
$765$	0.657715	+	0.477858i	0.0237797	+	0.0172770i
$766$		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
$771$	−27.5253			−0.991298
$772$		0			0
$773$	1.84208	+	5.66933i	0.0662549	+	0.203912i	0.978703	−	0.205280i	$-0.0658106\pi$
$773$	1.84208	+	5.66933i	0.0662549	+	0.203912i	−0.912448	+	0.409192i	$0.865811\pi$
$774$		0			0
$775$	3.69573	+	2.68510i	0.132754	+	0.0964517i
$776$		0			0
$777$	3.96673	−	12.2083i	0.142306	−	0.437972i
$778$		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
$783$	5.74955	−	4.17730i	0.205472	−	0.149284i
$784$		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
$789$	0.301943	+	0.929285i	0.0107495	+	0.0330834i
$790$		0			0
$791$	−65.8974			−2.34304
$792$		0			0
$793$	−71.0454			−2.52290
$794$		0			0
$795$	−2.14819	−	6.61145i	−0.0761885	−	0.234484i
$796$		0			0
$797$	−21.3588	−	15.5181i	−0.756567	−	0.549678i	0.141289	−	0.989968i	$-0.454875\pi$
$797$	−21.3588	−	15.5181i	−0.756567	−	0.549678i	−0.897855	+	0.440291i	$0.854875\pi$
$798$		0			0
$799$	0.697717	−	2.14735i	0.0246835	−	0.0759679i
$800$		0			0
$801$	−0.647339	+	0.470319i	−0.0228726	+	0.0166179i
$802$		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
$807$	−4.10851	+	12.6447i	−0.144626	+	0.445114i
$808$		0			0
$809$	−37.2659	−	27.0753i	−1.31020	−	0.951915i	−0.999999	−	0.00124363i	$-0.999604\pi$
$809$	−37.2659	−	27.0753i	−1.31020	−	0.951915i	−0.310200	−	0.950671i	$-0.600396\pi$
$810$		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
$813$	−15.7714			−0.553127
$814$		0			0
$815$	9.58974			0.335914
$816$		0			0
$817$	−3.46827	−	10.6742i	−0.121339	−	0.373444i
$818$		0			0
$819$	23.3837	+	16.9893i	0.817094	+	0.593654i
$820$		0			0
$821$	3.63254	−	11.1798i	0.126777	−	0.390178i	−0.867444	−	0.497535i	$-0.834239\pi$
$821$	3.63254	−	11.1798i	0.126777	−	0.390178i	0.994221	+	0.107357i	$0.0342386\pi$
$822$		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
$825$	3.28679	−	0.443888i	0.114431	−	0.0154542i
$826$		0			0
$827$	15.6584	−	11.3765i	0.544497	−	0.395600i	−0.281256	−	0.959633i	$-0.590751\pi$
$827$	15.6584	−	11.3765i	0.544497	−	0.395600i	0.825752	+	0.564033i	$0.190751\pi$
$828$		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
$831$	4.25189	+	3.08918i	0.147496	+	0.107162i
$832$		0			0
$833$	2.43319	+	7.48859i	0.0843050	+	0.259464i
$834$		0			0
$835$	22.4438			0.776701
$836$		0			0
$837$	−4.56817			−0.157899
$838$		0			0
$839$	2.80354	+	8.62841i	0.0967889	+	0.297886i	0.987716	−	0.156261i	$-0.0499441\pi$
$839$	2.80354	+	8.62841i	0.0967889	+	0.297886i	−0.890927	+	0.454147i	$0.849944\pi$
$840$		0			0
$841$	−17.3997	−	12.6416i	−0.599989	−	0.435917i
$842$		0			0
$843$	7.90750	−	24.3368i	0.272349	−	0.838203i
$844$		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
$849$	−6.66916	+	4.84543i	−0.228885	+	0.166295i
$850$		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
$855$	2.56691	+	7.90013i	0.0877864	+	0.270179i
$856$		0			0
$857$	41.0382			1.40184			0.700919	−	0.713241i	$-0.252773\pi$
$857$	41.0382			1.40184			0.700919	+	0.713241i	$0.252773\pi$
$858$		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
$861$	−8.04046	−	24.7460i	−0.274018	−	0.843341i
$862$		0			0
$863$	39.0547	+	28.3749i	1.32944	+	0.965894i	0.999762	+	0.0218001i	$0.00693974\pi$
$863$	39.0547	+	28.3749i	1.32944	+	0.965894i	0.329677	+	0.944094i	$0.393060\pi$
$864$		0			0
$865$	2.14359	−	6.59729i	0.0728843	−	0.224315i
$866$		0			0
$867$	13.2186	−	9.60386i	0.448927	−	0.326164i
$868$		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
$873$	1.49141	−	4.59009i	0.0504767	−	0.155351i
$874$		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
$879$	−23.3242			−0.786705
$880$		0			0
$881$	−33.1091			−1.11547			−0.557737	−	0.830018i	$-0.688330\pi$
$881$	−33.1091			−1.11547			−0.557737	+	0.830018i	$0.688330\pi$
$882$		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
$885$	−3.50911	−	2.54952i	−0.117958	−	0.0857012i
$886$		0			0
$887$	−12.2589	+	37.7290i	−0.411614	+	1.26682i	0.503631	+	0.863919i	$0.331997\pi$
$887$	−12.2589	+	37.7290i	−0.411614	+	1.26682i	−0.915245	+	0.402898i	$0.868003\pi$
$888$		0			0
$889$	−3.50667	+	2.54774i	−0.117610	+	0.0854485i
$890$		0			0
$891$	−2.39815	+	2.29104i	−0.0803412	+	0.0767526i
$892$		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
$897$	−40.2268	−	29.2265i	−1.34313	−	0.975843i
$898$		0			0
$899$	10.0323	+	30.8763i	0.334596	+	1.02978i
$900$		0			0
$901$	5.65159			0.188282
$902$		0			0
$903$	−5.51912			−0.183665
$904$		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
$909$	−4.25226	+	13.0871i	−0.141038	+	0.434072i
$910$		0			0
$911$	23.2850	−	16.9176i	0.771468	−	0.560504i	−0.130938	−	0.991391i	$-0.541799\pi$
$911$	23.2850	−	16.9176i	0.771468	−	0.560504i	0.902406	+	0.430886i	$0.141799\pi$
$912$		0			0
$913$	−20.0920	−	41.7641i	−0.664948	−	1.38219i
$914$		0			0
$915$	−8.12278	+	5.90154i	−0.268531	+	0.195099i
$916$		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
$921$	−7.82860	−	24.0940i	−0.257961	−	0.793923i
$922$		0			0
$923$	−63.1515			−2.07866
$924$		0			0
$925$	−3.14256			−0.103327
$926$		0			0
$927$	1.93554	+	5.95699i	0.0635716	+	0.195653i
$928$		0			0
$929$	44.9423	+	32.6525i	1.47451	+	1.07129i	0.979275	+	0.202535i	$0.0649181\pi$
$929$	44.9423	+	32.6525i	1.47451	+	1.07129i	0.495235	+	0.868759i	$0.335082\pi$
$930$		0			0
$931$	−24.8613	+	76.5152i	−0.814796	+	2.50768i
$932$		0			0
$933$	−24.4647	+	17.7747i	−0.800939	+	0.581917i
$934$		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
$939$	−4.21407	+	12.9696i	−0.137521	+	0.423246i
$940$		0			0
$941$	46.0740	+	33.4748i	1.50197	+	1.09125i	0.969588	+	0.244742i	$0.0787033\pi$
$941$	46.0740	+	33.4748i	1.50197	+	1.09125i	0.532383	+	0.846504i	$0.321297\pi$
$942$		0			0
$943$	13.8319	+	42.5702i	0.450429	+	1.38628i
$944$		0			0
$945$	4.08477			0.132877
$946$		0			0
$947$	−33.1235			−1.07637			−0.538184	−	0.842827i	$-0.680890\pi$
$947$	−33.1235			−1.07637			−0.538184	+	0.842827i	$0.680890\pi$
$948$		0			0
$949$	4.59502	+	14.1420i	0.149161	+	0.459070i
$950$		0			0
$951$	10.3686	+	7.53320i	0.336224	+	0.244281i
$952$		0			0
$953$	−1.99812	+	6.14959i	−0.0647255	+	0.199205i	−0.978189	−	0.207715i	$-0.933397\pi$
$953$	−1.99812	+	6.14959i	−0.0647255	+	0.199205i	0.913464	+	0.406920i	$0.133397\pi$
$954$		0			0
$955$	12.9856	−	9.43461i	0.420205	−	0.305297i
$956$		0			0
$957$	20.7518	+	11.1777i	0.670811	+	0.361324i
$958$		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
$963$	1.36992	+	0.995305i	0.0441451	+	0.0320733i
$964$		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
$969$	−6.75317			−0.216943
$970$		0			0
$971$	−2.09603	−	6.45092i	−0.0672649	−	0.207020i	0.911774	−	0.410691i	$-0.134713\pi$
$971$	−2.09603	−	6.45092i	−0.0672649	−	0.207020i	−0.979039	+	0.203671i	$0.934713\pi$
$972$		0			0
$973$	−50.1835	−	36.4604i	−1.60881	−	1.16887i
$974$		0			0
$975$	2.18661	−	6.72970i	0.0700276	−	0.215523i
$976$		0			0
$977$	−15.5147	+	11.2721i	−0.496358	+	0.360625i	−0.807624	−	0.589697i	$-0.799247\pi$
$977$	−15.5147	+	11.2721i	−0.496358	+	0.360625i	0.311266	+	0.950323i	$0.399247\pi$
$978$		0			0
$979$	−2.33643	−	1.25849i	−0.0746728	−	0.0402216i
$980$		0			0
$981$	5.82276	−	4.23048i	0.185906	−	0.135069i
$982$		0			0
$983$	−10.0003	+	30.7777i	−0.318959	+	0.981656i	0.655135	+	0.755512i	$0.272612\pi$
$983$	−10.0003	+	30.7777i	−0.318959	+	0.981656i	−0.974094	+	0.226143i	$0.927388\pi$
$984$		0			0
$985$	−11.6151	−	8.43887i	−0.370088	−	0.268885i
$986$		0			0
$987$	−3.50563	−	10.7892i	−0.111586	−	0.343425i
$988$		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
$993$	−4.59770	−	14.1503i	−0.145904	−	0.449045i
$994$		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
$999$	2.54238	−	1.84715i	0.0804374	−	0.0584412i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
660.2.y.b.301.1	✓	8	11.4	even	5	inner
660.2.y.b.421.1	yes	8	1.1	even	1	trivial
1980.2.z.b.1081.1		8	3.2	odd	2
1980.2.z.b.1621.1		8	33.26	odd	10
7260.2.a.be.1.1		4	11.9	even	5
7260.2.a.bg.1.4		4	11.2	odd	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:	\( N \)	\(=\)	\( 660 = 2^{2} \cdot 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	660.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{3} +(0.809017 + 0.587785i) q^{5} +(-1.26226 + 3.88484i) q^{7} +(-0.809017 + 0.587785i) q^{9} +(-2.91998 - 1.57281i) q^{11} +(-5.72462 + 4.15918i) q^{13} +(-0.309017 + 0.951057i) q^{15} +(-0.657715 - 0.477858i) q^{17} +(-2.56691 - 7.90013i) q^{19} -4.08477 q^{21} +7.02697 q^{23} +(0.309017 + 0.951057i) q^{25} +(-0.809017 - 0.587785i) q^{27} +(-2.19613 + 6.75901i) q^{29} +(3.69573 - 2.68510i) q^{31} +(0.593510 - 3.26309i) q^{33} +(-3.30464 + 2.40097i) q^{35} +(-0.971104 + 2.98875i) q^{37} +(-5.72462 - 4.15918i) q^{39} +(1.96840 + 6.05812i) q^{41} +1.35115 q^{43} -1.00000 q^{45} +(0.858221 + 2.64133i) q^{47} +(-7.83558 - 5.69288i) q^{49} +(0.251225 - 0.773190i) q^{51} +(-5.62404 + 4.08610i) q^{53} +(-1.43784 - 2.98875i) q^{55} +(6.72025 - 4.88255i) q^{57} +(-1.34036 + 4.12521i) q^{59} +(8.12278 + 5.90154i) q^{61} +(-1.26226 - 3.88484i) q^{63} -7.07602 q^{65} -3.26304 q^{67} +(2.17145 + 6.68305i) q^{69} +(7.22025 + 5.24582i) q^{71} +(0.649380 - 1.99858i) q^{73} +(-0.809017 + 0.587785i) q^{75} +(9.79590 - 9.35835i) q^{77} +(-10.1631 + 7.38394i) q^{79} +(0.309017 - 0.951057i) q^{81} +(11.3050 + 8.21357i) q^{83} +(-0.251225 - 0.773190i) q^{85} -7.10684 q^{87} +0.800155 q^{89} +(-8.93179 - 27.4892i) q^{91} +(3.69573 + 2.68510i) q^{93} +(2.56691 - 7.90013i) q^{95} +(-3.90457 + 2.83683i) q^{97} +(3.28679 - 0.443888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{3} + 2 q^{5} - 3 q^{7} - 2 q^{9} - 5 q^{11} - 8 q^{13} + 2 q^{15} + 6 q^{17} + 6 q^{19} - 8 q^{21} + 30 q^{23} - 2 q^{25} - 2 q^{27} - 9 q^{31} + 10 q^{33} - 7 q^{35} - 7 q^{37} - 8 q^{39} + 25 q^{41}+ \cdots + 5 q^{99}+O(q^{100}) \) 8 * q - 2 * q^3 + 2 * q^5 - 3 * q^7 - 2 * q^9 - 5 * q^11 - 8 * q^13 + 2 * q^15 + 6 * q^17 + 6 * q^19 - 8 * q^21 + 30 * q^23 - 2 * q^25 - 2 * q^27 - 9 * q^31 + 10 * q^33 - 7 * q^35 - 7 * q^37 - 8 * q^39 + 25 * q^41 - 8 * q^43 - 8 * q^45 - 7 * q^47 - 11 * q^49 - 4 * q^51 + 3 * q^53 + 5 * q^55 + q^57 + 5 * q^59 + 13 * q^61 - 3 * q^63 - 2 * q^65 + 18 * q^67 - 5 * q^69 + 5 * q^71 - 15 * q^73 - 2 * q^75 + 29 * q^77 - 50 * q^79 - 2 * q^81 + 13 * q^83 + 4 * q^85 - 30 * q^87 + 32 * q^89 - 15 * q^91 - 9 * q^93 - 6 * q^95 + q^97 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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