LMFDB - Embedded newform 220.2.u.a.73.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(13,220)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("220.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.u (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.5
Character	$\chi$	$=$	220.73
Dual form			220.2.u.a.217.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.46894 - 0.748461i) q^{3} +(-1.69901 - 1.45374i) q^{5} +(1.23911 - 2.43189i) q^{7} +(-0.165773 + 0.228167i) q^{9} +O(q^{10})$	\(q+(1.46894 - 0.748461i) q^{3} +(-1.69901 - 1.45374i) q^{5} +(1.23911 - 2.43189i) q^{7} +(-0.165773 + 0.228167i) q^{9} +(1.97907 - 2.66145i) q^{11} +(0.653168 - 0.103452i) q^{13} +(-3.58381 - 0.863812i) q^{15} +(2.93654 + 0.465103i) q^{17} +(-2.21346 + 6.81233i) q^{19} -4.49972i q^{21} +(-0.404388 - 0.404388i) q^{23} +(0.773271 + 4.93984i) q^{25} +(-0.846442 + 5.34423i) q^{27} +(-2.22290 - 6.84138i) q^{29} +(4.39431 + 3.19265i) q^{31} +(0.915135 - 5.39075i) q^{33} +(-5.64060 + 2.33046i) q^{35} +(3.59315 + 1.83080i) q^{37} +(0.882034 - 0.640835i) q^{39} +(-7.20357 - 2.34058i) q^{41} +(-0.687486 + 0.687486i) q^{43} +(0.613346 - 0.146667i) q^{45} +(4.59203 + 9.01236i) q^{47} +(-0.264199 - 0.363639i) q^{49} +(4.66171 - 1.51468i) q^{51} +(0.271614 + 1.71491i) q^{53} +(-7.23151 + 1.64477i) q^{55} +(1.84733 + 11.6636i) q^{57} +(-2.76174 + 0.897345i) q^{59} +(-6.28978 - 8.65715i) q^{61} +(0.349466 + 0.685866i) q^{63} +(-1.26013 - 0.773772i) q^{65} +(-8.32148 + 8.32148i) q^{67} +(-0.896689 - 0.291352i) q^{69} +(-8.26577 + 6.00543i) q^{71} +(10.3483 + 5.27272i) q^{73} +(4.83317 + 6.67756i) q^{75} +(-4.02007 - 8.11070i) q^{77} +(-1.56236 - 1.13512i) q^{79} +(2.49512 + 7.67918i) q^{81} +(1.37080 - 8.65490i) q^{83} +(-4.31308 - 5.05919i) q^{85} +(-8.38581 - 8.38581i) q^{87} -10.8016i q^{89} +(0.557764 - 1.71662i) q^{91} +(8.84454 + 1.40084i) q^{93} +(13.6641 - 8.35642i) q^{95} +(17.2194 - 2.72728i) q^{97} +(0.279179 + 0.892754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7}+O(q^{10}) $ 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7	$ 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7} - 16 q^{15} + 10 q^{17} + 16 q^{23} - 26 q^{25} - 10 q^{27} + 16 q^{31} + 28 q^{33} - 34 q^{37} - 20 q^{41} - 56 q^{45} - 2 q^{47} - 80 q^{51} + 6 q^{53} - 18 q^{55} - 120 q^{57} - 40 q^{61} - 50 q^{63} - 72 q^{67} + 4 q^{71} - 20 q^{73} + 20 q^{75} - 36 q^{77} + 100 q^{81} + 40 q^{85} - 8 q^{91} - 14 q^{93} + 50 q^{95} + 6 q^{97}+O(q^{100}) $ 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7 - 16 * q^15 + 10 * q^17 + 16 * q^23 - 26 * q^25 - 10 * q^27 + 16 * q^31 + 28 * q^33 - 34 * q^37 - 20 * q^41 - 56 * q^45 - 2 * q^47 - 80 * q^51 + 6 * q^53 - 18 * q^55 - 120 * q^57 - 40 * q^61 - 50 * q^63 - 72 * q^67 + 4 * q^71 - 20 * q^73 + 20 * q^75 - 36 * q^77 + 100 * q^81 + 40 * q^85 - 8 * q^91 - 14 * q^93 + 50 * q^95 + 6 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	1.46894	−	0.748461i	0.848091	−	0.432124i	0.0247656	−	0.999693i	$-0.492116\pi$
$3$	1.46894	−	0.748461i	0.848091	−	0.432124i	0.823326	+	0.567569i	$0.192116\pi$
$4$		0			0
$5$	−1.69901	−	1.45374i	−0.759820	−	0.650133i
$5$	−1.69901	−	1.45374i	−0.759820	−	0.650133i
$6$		0			0
$7$	1.23911	−	2.43189i	0.468340	−	0.919168i	−0.529162	−	0.848521i	$-0.677494\pi$
$7$	1.23911	−	2.43189i	0.468340	−	0.919168i	0.997501	−	0.0706471i	$-0.0225064\pi$
$8$		0			0
$9$	−0.165773	+	0.228167i	−0.0552577	+	0.0760557i
$10$		0			0
$11$	1.97907	−	2.66145i	0.596711	−	0.802456i
$11$	1.97907	−	2.66145i	0.596711	−	0.802456i
$12$		0			0
$13$	0.653168	−	0.103452i	0.181156	−	0.0286923i	−0.0651971	−	0.997872i	$-0.520768\pi$
$13$	0.653168	−	0.103452i	0.181156	−	0.0286923i	0.246353	+	0.969180i	$0.420768\pi$
$14$		0			0
$15$	−3.58381	−	0.863812i	−0.925335	−	0.223035i
$16$		0			0
$17$	2.93654	+	0.465103i	0.712216	+	0.112804i	0.502021	−	0.864855i	$-0.332590\pi$
$17$	2.93654	+	0.465103i	0.712216	+	0.112804i	0.210195	+	0.977659i	$0.432590\pi$
$18$		0			0
$19$	−2.21346	+	6.81233i	−0.507803	+	1.56286i	0.288205	+	0.957569i	$0.406942\pi$
$19$	−2.21346	+	6.81233i	−0.507803	+	1.56286i	−0.796007	+	0.605287i	$0.793058\pi$
$20$		0			0
$21$		−	4.49972i		−	0.981919i
$22$		0			0
$23$	−0.404388	−	0.404388i	−0.0843207	−	0.0843207i	0.663688	−	0.748009i	$-0.268990\pi$
$23$	−0.404388	−	0.404388i	−0.0843207	−	0.0843207i	−0.748009	+	0.663688i	$0.768990\pi$
$24$		0			0
$25$	0.773271	+	4.93984i	0.154654	+	0.987969i
$26$		0			0
$27$	−0.846442	+	5.34423i	−0.162898	+	1.02850i
$28$		0			0
$29$	−2.22290	−	6.84138i	−0.412782	−	1.27041i	−0.914220	−	0.405219i	$-0.867195\pi$
$29$	−2.22290	−	6.84138i	−0.412782	−	1.27041i	0.501437	−	0.865194i	$-0.332805\pi$
$30$		0			0
$31$	4.39431	+	3.19265i	0.789241	+	0.573417i	0.907738	−	0.419537i	$-0.137808\pi$
$31$	4.39431	+	3.19265i	0.789241	+	0.573417i	−0.118497	+	0.992954i	$0.537808\pi$
$32$		0			0
$33$	0.915135	−	5.39075i	0.159305	−	0.938409i
$34$		0			0
$35$	−5.64060	+	2.33046i	−0.953435	+	0.393920i
$36$		0			0
$37$	3.59315	+	1.83080i	0.590710	+	0.300982i	0.723677	−	0.690139i	$-0.242450\pi$
$37$	3.59315	+	1.83080i	0.590710	+	0.300982i	−0.132967	+	0.991120i	$0.542450\pi$
$38$		0			0
$39$	0.882034	−	0.640835i	0.141238	−	0.102616i
$40$		0			0
$41$	−7.20357	−	2.34058i	−1.12501	−	0.365537i	−0.313331	−	0.949644i	$-0.601445\pi$
$41$	−7.20357	−	2.34058i	−1.12501	−	0.365537i	−0.811677	+	0.584107i	$0.801445\pi$
$42$		0			0
$43$	−0.687486	+	0.687486i	−0.104841	+	0.104841i	−0.757581	−	0.652741i	$-0.773619\pi$
$43$	−0.687486	+	0.687486i	−0.104841	+	0.104841i	0.652741	+	0.757581i	$0.273619\pi$
$44$		0			0
$45$	0.613346	−	0.146667i	0.0914323	−	0.0218638i
$46$		0			0
$47$	4.59203	+	9.01236i	0.669816	+	1.31459i	0.936454	+	0.350791i	$0.114087\pi$
$47$	4.59203	+	9.01236i	0.669816	+	1.31459i	−0.266638	+	0.963797i	$0.585913\pi$
$48$		0			0
$49$	−0.264199	−	0.363639i	−0.0377428	−	0.0519485i
$50$		0			0
$51$	4.66171	−	1.51468i	0.652770	−	0.212098i
$52$		0			0
$53$	0.271614	+	1.71491i	0.0373091	+	0.235560i	0.999295	−	0.0375380i	$-0.0119515\pi$
$53$	0.271614	+	1.71491i	0.0373091	+	0.235560i	−0.961986	+	0.273098i	$0.911952\pi$
$54$		0			0
$55$	−7.23151	+	1.64477i	−0.975096	+	0.221781i
$56$		0			0
$57$	1.84733	+	11.6636i	0.244685	+	1.54488i
$58$		0			0
$59$	−2.76174	+	0.897345i	−0.359548	+	0.116824i	−0.483220	−	0.875499i	$-0.660533\pi$
$59$	−2.76174	+	0.897345i	−0.359548	+	0.116824i	0.123672	+	0.992323i	$0.460533\pi$
$60$		0			0
$61$	−6.28978	−	8.65715i	−0.805324	−	1.10843i	−0.992028	−	0.126018i	$-0.959780\pi$
$61$	−6.28978	−	8.65715i	−0.805324	−	1.10843i	0.186704	−	0.982416i	$-0.440220\pi$
$62$		0			0
$63$	0.349466	+	0.685866i	0.0440286	+	0.0864110i
$64$		0			0
$65$	−1.26013	−	0.773772i	−0.156300	−	0.0959747i
$66$		0			0
$67$	−8.32148	+	8.32148i	−1.01663	+	1.01663i	−0.0167718	+	0.999859i	$0.505339\pi$
$67$	−8.32148	+	8.32148i	−1.01663	+	1.01663i	−0.999859	+	0.0167718i	$0.994661\pi$
$68$		0			0
$69$	−0.896689	−	0.291352i	−0.107949	−	0.0350746i
$70$		0			0
$71$	−8.26577	+	6.00543i	−0.980966	+	0.712714i	−0.957924	−	0.287021i	$-0.907335\pi$
$71$	−8.26577	+	6.00543i	−0.980966	+	0.712714i	−0.0230418	+	0.999735i	$0.507335\pi$
$72$		0			0
$73$	10.3483	+	5.27272i	1.21118	+	0.617125i	0.938599	−	0.345009i	$-0.112124\pi$
$73$	10.3483	+	5.27272i	1.21118	+	0.617125i	0.272576	+	0.962134i	$0.412124\pi$
$74$		0			0
$75$	4.83317	+	6.67756i	0.558086	+	0.771058i
$76$		0			0
$77$	−4.02007	−	8.11070i	−0.458129	−	0.924300i
$78$		0			0
$79$	−1.56236	−	1.13512i	−0.175780	−	0.127711i	0.496417	−	0.868084i	$-0.334649\pi$
$79$	−1.56236	−	1.13512i	−0.175780	−	0.127711i	−0.672196	+	0.740373i	$0.734649\pi$
$80$		0			0
$81$	2.49512	+	7.67918i	0.277235	+	0.853242i
$82$		0			0
$83$	1.37080	−	8.65490i	0.150465	−	0.949998i	−0.790738	−	0.612155i	$-0.790303\pi$
$83$	1.37080	−	8.65490i	0.150465	−	0.949998i	0.941202	−	0.337843i	$-0.109697\pi$
$84$		0			0
$85$	−4.31308	−	5.05919i	−0.467819	−	0.548746i
$86$		0			0
$87$	−8.38581	−	8.38581i	−0.899053	−	0.899053i
$88$		0			0
$89$		−	10.8016i		−	1.14497i	−0.819916	−	0.572484i	$-0.805980\pi$
$89$		−	10.8016i		−	1.14497i	0.819916	−	0.572484i	$-0.194020\pi$
$90$		0			0
$91$	0.557764	−	1.71662i	0.0584696	−	0.179951i
$92$		0			0
$93$	8.84454	+	1.40084i	0.917136	+	0.145260i
$94$		0			0
$95$	13.6641	−	8.35642i	1.40190	−	0.857350i
$96$		0			0
$97$	17.2194	−	2.72728i	1.74836	−	0.276913i	0.801369	−	0.598170i	$-0.204105\pi$
$97$	17.2194	−	2.72728i	1.74836	−	0.276913i	0.946992	+	0.321257i	$0.104105\pi$
$98$		0			0
$99$	0.279179	+	0.892754i	0.0280585	+	0.0897252i
$100$		0			0
$101$	4.43283	−	6.10127i	0.441083	−	0.607099i	−0.529369	−	0.848392i	$-0.677571\pi$
$101$	4.43283	−	6.10127i	0.441083	−	0.607099i	0.970452	+	0.241293i	$0.0775713\pi$
$102$		0			0
$103$	5.96029	−	11.6977i	0.587284	−	1.15261i	−0.385891	−	0.922545i	$-0.626106\pi$
$103$	5.96029	−	11.6977i	0.587284	−	1.15261i	0.973175	−	0.230066i	$-0.0738942\pi$
$104$		0			0
$105$	−6.54143	+	7.64507i	−0.638378	+	0.746082i
$106$		0			0
$107$	9.43436	−	4.80705i	0.912054	−	0.464715i	0.0660047	−	0.997819i	$-0.478975\pi$
$107$	9.43436	−	4.80705i	0.912054	−	0.464715i	0.846049	+	0.533105i	$0.178975\pi$
$108$		0			0
$109$	−0.499098			−0.0478049			−0.0239025	−	0.999714i	$-0.507609\pi$
$109$	−0.499098			−0.0478049			−0.0239025	+	0.999714i	$0.507609\pi$
$110$		0			0
$111$	6.64839			0.631038
$112$		0			0
$113$	−16.1398	+	8.22363i	−1.51830	+	0.773614i	−0.996823	−	0.0796494i	$-0.974620\pi$
$113$	−16.1398	+	8.22363i	−1.51830	+	0.773614i	−0.521480	+	0.853263i	$0.674620\pi$
$114$		0			0
$115$	0.0991837	+	1.27493i	0.00924893	+	0.118888i
$116$		0			0
$117$	−0.0846735	+	0.166181i	−0.00782807	+	0.0153634i
$118$		0			0
$119$	4.76978	−	6.56504i	0.437245	−	0.601816i
$120$		0			0
$121$	−3.16660	−	10.5344i	−0.287872	−	0.957669i
$122$		0			0
$123$	−12.3334	+	1.95342i	−1.11207	+	0.176134i
$124$		0			0
$125$	5.86746	−	9.51698i	0.524801	−	0.851225i
$126$		0			0
$127$	−11.5065	−	1.82245i	−1.02104	−	0.161716i	−0.376602	−	0.926375i	$-0.622907\pi$
$127$	−11.5065	−	1.82245i	−1.02104	−	0.161716i	−0.644435	+	0.764659i	$0.722907\pi$
$128$		0			0
$129$	−0.495317	+	1.52443i	−0.0436102	+	0.134219i
$130$		0			0
$131$		−	8.79946i		−	0.768812i	−0.923164	−	0.384406i	$-0.874406\pi$
$131$		−	8.79946i		−	0.768812i	0.923164	−	0.384406i	$-0.125594\pi$
$132$		0			0
$133$	13.8241	+	13.8241i	1.19870	+	1.19870i
$134$		0			0
$135$	9.20724	−	7.84939i	0.792433	−	0.675568i
$136$		0			0
$137$	−0.448233	+	2.83003i	−0.0382951	+	0.241786i	−0.999409	−	0.0343653i	$-0.989059\pi$
$137$	−0.448233	+	2.83003i	−0.0382951	+	0.241786i	0.961114	+	0.276151i	$0.0890590\pi$
$138$		0			0
$139$	1.49638	+	4.60538i	0.126921	+	0.390623i	0.994246	−	0.107119i	$-0.0341626\pi$
$139$	1.49638	+	4.60538i	0.126921	+	0.390623i	−0.867325	+	0.497742i	$0.834163\pi$
$140$		0			0
$141$	13.4908	+	9.80164i	1.13613	+	0.825447i
$142$		0			0
$143$	1.01733	−	1.94311i	0.0850736	−	0.162491i
$144$		0			0
$145$	−6.16887	+	14.8551i	−0.512297	+	1.23365i
$146$		0			0
$147$	−0.660262	−	0.336420i	−0.0544575	−	0.0277475i
$148$		0			0
$149$	−8.42069	+	6.11799i	−0.689850	+	0.501205i	−0.876611	−	0.481200i	$-0.840201\pi$
$149$	−8.42069	+	6.11799i	−0.689850	+	0.501205i	0.186761	+	0.982405i	$0.440201\pi$
$150$		0			0
$151$	3.31672	+	1.07767i	0.269911	+	0.0876994i	0.440846	−	0.897583i	$-0.354679\pi$
$151$	3.31672	+	1.07767i	0.269911	+	0.0876994i	−0.170934	+	0.985282i	$0.554679\pi$
$152$		0			0
$153$	−0.592921	+	0.592921i	−0.0479348	+	0.0479348i
$154$		0			0
$155$	−2.82468	−	11.8125i	−0.226884	−	0.948806i
$156$		0			0
$157$	−9.45835	−	18.5631i	−0.754858	−	1.48149i	−0.872593	−	0.488448i	$-0.837563\pi$
$157$	−9.45835	−	18.5631i	−0.754858	−	1.48149i	0.117735	−	0.993045i	$-0.462437\pi$
$158$		0			0
$159$	1.68252	+	2.31580i	0.133433	+	0.183655i
$160$		0			0
$161$	−1.48451	+	0.482346i	−0.116996	+	0.0380142i
$162$		0			0
$163$	0.697283	+	4.40247i	0.0546154	+	0.344828i	0.999831	+	0.0183815i	$0.00585136\pi$
$163$	0.697283	+	4.40247i	0.0546154	+	0.344828i	−0.945216	+	0.326447i	$0.894149\pi$
$164$		0			0
$165$	−9.39158	+	7.82857i	−0.731134	+	0.609454i
$166$		0			0
$167$	2.07813	+	13.1208i	0.160810	+	1.01532i	0.927643	+	0.373469i	$0.121832\pi$
$167$	2.07813	+	13.1208i	0.160810	+	1.01532i	−0.766832	+	0.641848i	$0.778168\pi$
$168$		0			0
$169$	−11.9478	+	3.88208i	−0.919062	+	0.298621i
$170$		0			0
$171$	−1.18742	−	1.63434i	−0.0908041	−	0.124981i
$172$		0			0
$173$	−8.03251	−	15.7647i	−0.610700	−	1.19857i	−0.964707	−	0.263324i	$-0.915181\pi$
$173$	−8.03251	−	15.7647i	−0.610700	−	1.19857i	0.354007	−	0.935243i	$-0.384819\pi$
$174$		0			0
$175$	12.9713	+	4.24050i	0.980540	+	0.320551i
$176$		0			0
$177$	−3.38520	+	3.38520i	−0.254447	+	0.254447i
$178$		0			0
$179$	8.16791	+	2.65391i	0.610498	+	0.198363i	0.597917	−	0.801558i	$-0.295995\pi$
$179$	8.16791	+	2.65391i	0.610498	+	0.198363i	0.0125810	+	0.999921i	$0.495995\pi$
$180$		0			0
$181$	−12.6600	+	9.19801i	−0.941009	+	0.683683i	−0.948663	−	0.316288i	$-0.897564\pi$
$181$	−12.6600	+	9.19801i	−0.941009	+	0.683683i	0.00765439	+	0.999971i	$0.497564\pi$
$182$		0			0
$183$	−15.7188	−	8.00915i	−1.16197	−	0.592053i
$184$		0			0
$185$	−3.44329	−	8.33406i	−0.253155	−	0.612732i
$186$		0			0
$187$	7.04946	−	6.89498i	0.515507	−	0.504211i
$188$		0			0
$189$	11.9477	+	8.68054i	0.869070	+	0.631416i
$190$		0			0
$191$	4.00219	+	12.3175i	0.289588	+	0.891261i	0.984986	+	0.172636i	$0.0552283\pi$
$191$	4.00219	+	12.3175i	0.289588	+	0.891261i	−0.695398	+	0.718625i	$0.744772\pi$
$192$		0			0
$193$	−1.37079	+	8.65484i	−0.0986718	+	0.622989i	0.887947	+	0.459946i	$0.152131\pi$
$193$	−1.37079	+	8.65484i	−0.0986718	+	0.622989i	−0.986619	+	0.163044i	$0.947869\pi$
$194$		0			0
$195$	−2.43019	−	0.193464i	−0.174030	−	0.0138542i
$196$		0			0
$197$	−11.9910	−	11.9910i	−0.854324	−	0.854324i	0.136338	−	0.990662i	$-0.456467\pi$
$197$	−11.9910	−	11.9910i	−0.854324	−	0.854324i	−0.990662	+	0.136338i	$0.956467\pi$
$198$		0			0
$199$		−	8.98487i		−	0.636921i	−0.947936	−	0.318460i	$-0.896834\pi$
$199$		−	8.98487i		−	0.636921i	0.947936	−	0.318460i	$-0.103166\pi$
$200$		0			0
$201$	−5.99543	+	18.4520i	−0.422885	+	1.30151i
$202$		0			0
$203$	−19.3919	−	3.07138i	−1.36105	−	0.215568i
$204$		0			0
$205$	8.83634	+	14.4488i	0.617156	+	1.00915i
$206$		0			0
$207$	0.159305	−	0.0252314i	0.0110724	−	0.00175370i
$208$		0			0
$209$	13.7501	+	19.3731i	0.951112	+	1.34006i
$210$		0			0
$211$	−6.10685	+	8.40536i	−0.420413	+	0.578649i	−0.965719	−	0.259588i	$-0.916413\pi$
$211$	−6.10685	+	8.40536i	−0.420413	+	0.578649i	0.545306	+	0.838237i	$0.316413\pi$
$212$		0			0
$213$	−7.64706	+	15.0082i	−0.523968	+	1.02835i
$214$		0			0
$215$	2.16747	−	0.168619i	0.147820	−	0.0114997i
$216$		0			0
$217$	13.2092	−	6.73043i	0.896699	−	0.456891i
$218$		0			0
$219$	19.1474			1.29386
$220$		0			0
$221$	1.96617			0.132259
$222$		0			0
$223$	3.64864	−	1.85907i	0.244331	−	0.124493i	−0.327537	−	0.944838i	$-0.606219\pi$
$223$	3.64864	−	1.85907i	0.244331	−	0.124493i	0.571868	+	0.820345i	$0.306219\pi$
$224$		0			0
$225$	−1.25530	−	0.642458i	−0.0836865	−	0.0428305i
$226$		0			0
$227$	3.53093	−	6.92984i	0.234356	−	0.459949i	−0.743638	−	0.668582i	$-0.766901\pi$
$227$	3.53093	−	6.92984i	0.234356	−	0.459949i	0.977994	+	0.208633i	$0.0669014\pi$
$228$		0			0
$229$	4.91469	−	6.76448i	0.324772	−	0.447010i	−0.615145	−	0.788414i	$-0.710903\pi$
$229$	4.91469	−	6.76448i	0.324772	−	0.447010i	0.939917	+	0.341404i	$0.110903\pi$
$230$		0			0
$231$	−11.9758	−	8.90524i	−0.787947	−	0.585922i
$232$		0			0
$233$	16.3775	−	2.59393i	1.07292	−	0.169934i	0.405113	−	0.914266i	$-0.367232\pi$
$233$	16.3775	−	2.59393i	1.07292	−	0.169934i	0.667810	+	0.744332i	$0.267232\pi$
$234$		0			0
$235$	5.29974	−	21.9877i	0.345717	−	1.43432i
$236$		0			0
$237$	−3.14461	−	0.498057i	−0.204264	−	0.0323523i
$238$		0			0
$239$	−9.38570	+	28.8862i	−0.607110	+	1.86849i	−0.125534	+	0.992089i	$0.540064\pi$
$239$	−9.38570	+	28.8862i	−0.607110	+	1.86849i	−0.481576	+	0.876404i	$0.659936\pi$
$240$		0			0
$241$			28.0900i			1.80944i	0.426011	+	0.904718i	$0.359918\pi$
$241$			28.0900i			1.80944i	−0.426011	+	0.904718i	$0.640082\pi$
$242$		0			0
$243$	−2.06539	−	2.06539i	−0.132495	−	0.132495i
$244$		0			0
$245$	−0.0797600	+	1.00190i	−0.00509568	+	0.0640093i
$246$		0			0
$247$	−0.741015	+	4.67858i	−0.0471497	+	0.297691i
$248$		0			0
$249$	−4.46423	−	13.7395i	−0.282909	−	0.870705i
$250$		0			0
$251$	2.23967	+	1.62722i	0.141367	+	0.102709i	0.656221	−	0.754569i	$-0.272154\pi$
$251$	2.23967	+	1.62722i	0.141367	+	0.102709i	−0.514854	+	0.857278i	$0.672154\pi$
$252$		0			0
$253$	−1.87657	+	0.275947i	−0.117979	+	0.0173486i
$254$		0			0
$255$	−10.1222	−	4.20346i	−0.633880	−	0.263231i
$256$		0			0
$257$	−13.0917	−	6.67056i	−0.816638	−	0.416098i	−0.00480567	−	0.999988i	$-0.501530\pi$
$257$	−13.0917	−	6.67056i	−0.816638	−	0.416098i	−0.811832	+	0.583891i	$0.801530\pi$
$258$		0			0
$259$	8.90461	−	6.46958i	0.553306	−	0.402000i
$260$		0			0
$261$	1.92948	+	0.626925i	0.119432	+	0.0388057i
$262$		0			0
$263$	−14.9775	+	14.9775i	−0.923555	+	0.923555i	−0.997279	−	0.0737237i	$-0.976512\pi$
$263$	−14.9775	+	14.9775i	−0.923555	+	0.923555i	0.0737237	+	0.997279i	$0.476512\pi$
$264$		0			0
$265$	2.03155	−	3.30850i	0.124797	−	0.203240i
$266$		0			0
$267$	−8.08458	−	15.8669i	−0.494768	−	0.971037i
$268$		0			0
$269$	−2.07765	−	2.85964i	−0.126676	−	0.174355i	0.740968	−	0.671540i	$-0.234367\pi$
$269$	−2.07765	−	2.85964i	−0.126676	−	0.174355i	−0.867644	+	0.497185i	$0.834367\pi$
$270$		0			0
$271$	−13.2794	+	4.31475i	−0.806669	+	0.262103i	−0.683186	−	0.730244i	$-0.739406\pi$
$271$	−13.2794	+	4.31475i	−0.806669	+	0.262103i	−0.123482	+	0.992347i	$0.539406\pi$
$272$		0			0
$273$	−0.465504	−	2.93907i	−0.0281736	−	0.177881i
$274$		0			0
$275$	14.6775	+	7.71825i	0.885086	+	0.465428i
$276$		0			0
$277$	−1.81474	−	11.4578i	−0.109037	−	0.688432i	−0.980285	−	0.197589i	$-0.936689\pi$
$277$	−1.81474	−	11.4578i	−0.109037	−	0.688432i	0.871248	−	0.490843i	$-0.163311\pi$
$278$		0			0
$279$	−1.45692	+	0.473381i	−0.0872233	+	0.0283406i
$280$		0			0
$281$	−6.42669	−	8.84557i	−0.383384	−	0.527683i	0.573093	−	0.819490i	$-0.305743\pi$
$281$	−6.42669	−	8.84557i	−0.383384	−	0.527683i	−0.956477	+	0.291808i	$0.905743\pi$
$282$		0			0
$283$	−0.239681	−	0.470400i	−0.0142476	−	0.0279624i	0.883773	−	0.467916i	$-0.154995\pi$
$283$	−0.239681	−	0.470400i	−0.0142476	−	0.0279624i	−0.898021	+	0.439953i	$0.854995\pi$
$284$		0			0
$285$	13.8172	−	22.5021i	0.818460	−	1.33291i
$286$		0			0
$287$	−14.6180	+	14.6180i	−0.862876	+	0.862876i
$288$		0			0
$289$	−7.76100	−	2.52170i	−0.456529	−	0.148335i
$290$		0			0
$291$	23.2529	−	16.8942i	1.36311	−	0.990357i
$292$		0			0
$293$	13.1454	+	6.69792i	0.767963	+	0.391297i	0.793651	−	0.608373i	$-0.208178\pi$
$293$	13.1454	+	6.69792i	0.767963	+	0.391297i	−0.0256880	+	0.999670i	$0.508178\pi$
$294$		0			0
$295$	5.99674	+	2.49026i	0.349144	+	0.144989i
$296$		0			0
$297$	12.5482	+	12.8293i	0.728121	+	0.744434i
$298$		0			0
$299$	−0.305968	−	0.222299i	−0.0176946	−	0.0128559i
$300$		0			0
$301$	0.820019	+	2.52376i	0.0472651	+	0.145467i
$302$		0			0
$303$	1.94499	−	12.2802i	0.111737	−	0.705478i
$304$		0			0
$305$	−1.89884	+	23.8523i	−0.108727	+	1.36578i
$306$		0			0
$307$	−21.0899	−	21.0899i	−1.20366	−	1.20366i	−0.973044	−	0.230620i	$-0.925925\pi$
$307$	−21.0899	−	21.0899i	−1.20366	−	1.20366i	−0.230620	−	0.973044i	$-0.574075\pi$
$308$		0			0
$309$		−	21.6443i		−	1.23130i
$310$		0			0
$311$	−2.47776	+	7.62577i	−0.140501	+	0.432418i	−0.996405	−	0.0847168i	$-0.973001\pi$
$311$	−2.47776	+	7.62577i	−0.140501	+	0.432418i	0.855904	+	0.517135i	$0.173001\pi$
$312$		0			0
$313$	11.8471	+	1.87639i	0.669636	+	0.106060i	0.481990	−	0.876177i	$-0.339914\pi$
$313$	11.8471	+	1.87639i	0.669636	+	0.106060i	0.187646	+	0.982237i	$0.439914\pi$
$314$		0			0
$315$	0.403325	−	1.67333i	0.0227248	−	0.0942813i
$316$		0			0
$317$	−15.3779	+	2.43562i	−0.863707	+	0.136798i	−0.572542	−	0.819875i	$-0.694043\pi$
$317$	−15.3779	+	2.43562i	−0.863707	+	0.136798i	−0.291165	+	0.956673i	$0.594043\pi$
$318$		0			0
$319$	−22.6072	−	7.62342i	−1.26576	−	0.426829i
$320$		0			0
$321$	10.2606	−	14.1225i	0.572691	−	0.788241i
$322$		0			0
$323$	−9.66835	+	18.9752i	−0.537962	+	1.05581i
$324$		0			0
$325$	1.01611	+	3.14655i	0.0563637	+	0.174539i
$326$		0			0
$327$	−0.733144	+	0.373555i	−0.0405429	+	0.0206577i
$328$		0			0
$329$	27.6071			1.52203
$330$		0			0
$331$	8.93255			0.490977			0.245489	−	0.969399i	$-0.421052\pi$
$331$	8.93255			0.490977			0.245489	+	0.969399i	$0.421052\pi$
$332$		0			0
$333$	−1.01338	+	0.516341i	−0.0555327	+	0.0282953i
$334$		0			0
$335$	26.2356	−	2.04100i	1.43340	−	0.111512i
$336$		0			0
$337$	3.88737	−	7.62939i	0.211759	−	0.415600i	−0.760557	−	0.649271i	$-0.775074\pi$
$337$	3.88737	−	7.62939i	0.211759	−	0.415600i	0.972316	+	0.233672i	$0.0750741\pi$
$338$		0			0
$339$	−17.5533	+	24.1600i	−0.953362	+	1.31219i
$340$		0			0
$341$	17.1937	−	5.37675i	0.931091	−	0.291167i
$342$		0			0
$343$	17.6587	−	2.79686i	0.953480	−	0.151016i
$344$		0			0
$345$	1.09993	+	1.79856i	0.0592184	+	0.0968314i
$346$		0			0
$347$	31.8581	+	5.04583i	1.71023	+	0.270874i	0.933402	−	0.358833i	$-0.116825\pi$
$347$	31.8581	+	5.04583i	1.71023	+	0.270874i	0.776832	+	0.629708i	$0.216825\pi$
$348$		0			0
$349$	10.6888	−	32.8969i	0.572160	−	1.76093i	−0.0734902	−	0.997296i	$-0.523414\pi$
$349$	10.6888	−	32.8969i	0.572160	−	1.76093i	0.645651	−	0.763633i	$-0.276586\pi$
$350$		0			0
$351$			3.57825i			0.190993i
$352$		0			0
$353$	3.39118	+	3.39118i	0.180494	+	0.180494i	0.791571	−	0.611077i	$-0.209263\pi$
$353$	3.39118	+	3.39118i	0.180494	+	0.180494i	−0.611077	+	0.791571i	$0.709263\pi$
$354$		0			0
$355$	22.7740	+	1.81300i	1.20872	+	0.0962240i
$356$		0			0
$357$	2.09283	−	13.2136i	0.110764	−	0.699339i
$358$		0			0
$359$	−2.79571	−	8.60432i	−0.147552	−	0.454118i	0.849778	−	0.527140i	$-0.176736\pi$
$359$	−2.79571	−	8.60432i	−0.147552	−	0.454118i	−0.997330	+	0.0730218i	$0.976736\pi$
$360$		0			0
$361$	−26.1371	−	18.9897i	−1.37564	−	0.999459i
$362$		0			0
$363$	−12.5361	−	13.1042i	−0.657974	−	0.687794i
$364$		0			0
$365$	−9.91668	−	24.0021i	−0.519063	−	1.25633i
$366$		0			0
$367$	13.0845	+	6.66686i	0.683003	+	0.348007i	0.760823	−	0.648960i	$-0.224796\pi$
$367$	13.0845	+	6.66686i	0.683003	+	0.348007i	−0.0778194	+	0.996967i	$0.524796\pi$
$368$		0			0
$369$	1.72820	−	1.25561i	0.0899666	−	0.0653646i
$370$		0			0
$371$	4.50702	+	1.46442i	0.233993	+	0.0760289i
$372$		0			0
$373$	−13.3954	+	13.3954i	−0.693587	+	0.693587i	−0.963019	−	0.269433i	$-0.913164\pi$
$373$	−13.3954	+	13.3954i	−0.693587	+	0.693587i	0.269433	+	0.963019i	$0.413164\pi$
$374$		0			0
$375$	1.49584	−	18.3714i	0.0772449	−	0.948696i
$376$		0			0
$377$	−2.15968	−	4.23861i	−0.111229	−	0.218300i
$378$		0			0
$379$	−13.1427	−	18.0893i	−0.675094	−	0.929187i	0.324768	−	0.945794i	$-0.394714\pi$
$379$	−13.1427	−	18.0893i	−0.675094	−	0.929187i	−0.999862	+	0.0166063i	$0.994714\pi$
$380$		0			0
$381$	−18.2664	+	5.93510i	−0.935814	+	0.304064i
$382$		0			0
$383$	1.04128	+	6.57440i	0.0532071	+	0.335936i	0.999905	+	0.0138125i	$0.00439678\pi$
$383$	1.04128	+	6.57440i	0.0532071	+	0.335936i	−0.946698	+	0.322124i	$0.895603\pi$
$384$		0			0
$385$	−4.96072	+	19.6243i	−0.252822	+	1.00015i
$386$		0			0
$387$	−0.0428950	−	0.270828i	−0.00218047	−	0.0137670i
$388$		0			0
$389$	2.93098	−	0.952333i	0.148607	−	0.0482852i	−0.233769	−	0.972292i	$-0.575106\pi$
$389$	2.93098	−	0.952333i	0.148607	−	0.0482852i	0.382376	+	0.924007i	$0.375106\pi$
$390$		0			0
$391$	−0.999421	−	1.37558i	−0.0505429	−	0.0695663i
$392$		0			0
$393$	−6.58605	−	12.9259i	−0.332222	−	0.652023i
$394$		0			0
$395$	1.00430	+	4.19986i	0.0505316	+	0.211318i
$396$		0			0
$397$	−21.9943	+	21.9943i	−1.10386	+	1.10386i	−0.109921	+	0.993940i	$0.535060\pi$
$397$	−21.9943	+	21.9943i	−1.10386	+	1.10386i	−0.993940	+	0.109921i	$0.964940\pi$
$398$		0			0
$399$	30.6536	+	9.95995i	1.53460	+	0.498621i
$400$		0			0
$401$	2.90003	−	2.10700i	0.144821	−	0.105218i	−0.513016	−	0.858379i	$-0.671472\pi$
$401$	2.90003	−	2.10700i	0.144821	−	0.105218i	0.657836	+	0.753161i	$0.271472\pi$
$402$		0			0
$403$	3.20051	+	1.63074i	0.159429	+	0.0812330i
$404$		0			0
$405$	6.92431	−	16.6743i	0.344072	−	0.828551i
$406$		0			0
$407$	11.9837	−	5.93970i	0.594008	−	0.294420i
$408$		0			0
$409$	−20.0092	−	14.5375i	−0.989392	−	0.718835i	−0.0296038	−	0.999562i	$-0.509425\pi$
$409$	−20.0092	−	14.5375i	−0.989392	−	0.718835i	−0.959788	+	0.280727i	$0.909425\pi$
$410$		0			0
$411$	1.45974	+	4.49262i	0.0720037	+	0.221605i
$412$		0			0
$413$	−1.23986	+	7.82817i	−0.0610095	+	0.385199i
$414$		0			0
$415$	−14.9110	+	12.7120i	−0.731952	+	0.624006i
$416$		0			0
$417$	5.64503	+	5.64503i	0.276438	+	0.276438i
$418$		0			0
$419$			32.1254i			1.56943i	0.619857	+	0.784715i	$0.287191\pi$
$419$			32.1254i			1.56943i	−0.619857	+	0.784715i	$0.712809\pi$
$420$		0			0
$421$	−4.16343	+	12.8137i	−0.202913	+	0.624503i	0.796879	+	0.604138i	$0.206483\pi$
$421$	−4.16343	+	12.8137i	−0.202913	+	0.624503i	−0.999793	+	0.0203643i	$0.993517\pi$
$422$		0			0
$423$	−2.81756	−	0.446257i	−0.136994	−	0.0216978i
$424$		0			0
$425$	−0.0267896	+	14.8657i	−0.00129949	+	0.721093i
$426$		0			0
$427$	−28.8470	+	4.56891i	−1.39600	+	0.221105i
$428$		0			0
$429$	0.0400546	−	3.61574i	0.00193386	−	0.174570i
$430$		0			0
$431$	16.8253	−	23.1581i	0.810447	−	1.11548i	−0.180808	−	0.983519i	$-0.557871\pi$
$431$	16.8253	−	23.1581i	0.810447	−	1.11548i	0.991254	−	0.131966i	$-0.0421289\pi$
$432$		0			0
$433$	17.9433	−	35.2157i	0.862301	−	1.69236i	0.152095	−	0.988366i	$-0.451398\pi$
$433$	17.9433	−	35.2157i	0.862301	−	1.69236i	0.710206	−	0.703994i	$-0.248602\pi$
$434$		0			0
$435$	2.05678	+	26.4384i	0.0986149	+	1.26762i
$436$		0			0
$437$	3.64992	−	1.85973i	0.174599	−	0.0889628i
$438$		0			0
$439$	−20.6650			−0.986286			−0.493143	−	0.869948i	$-0.664152\pi$
$439$	−20.6650			−0.986286			−0.493143	+	0.869948i	$0.664152\pi$
$440$		0			0
$441$	0.126768			0.00603656
$442$		0			0
$443$	8.09934	−	4.12682i	0.384811	−	0.196071i	−0.250873	−	0.968020i	$-0.580718\pi$
$443$	8.09934	−	4.12682i	0.384811	−	0.196071i	0.635685	+	0.771949i	$0.280718\pi$
$444$		0			0
$445$	−15.7027	+	18.3520i	−0.744381	+	0.869970i
$446$		0			0
$447$	−7.79039	+	15.2895i	−0.368473	+	0.723169i
$448$		0			0
$449$	−6.17770	+	8.50288i	−0.291544	+	0.401276i	−0.929515	−	0.368785i	$-0.879774\pi$
$449$	−6.17770	+	8.50288i	−0.291544	+	0.401276i	0.637971	+	0.770060i	$0.279774\pi$
$450$		0			0
$451$	−20.4857	+	14.5397i	−0.964632	+	0.684650i
$452$		0			0
$453$	5.67865	−	0.899410i	0.266806	−	0.0422580i
$454$		0			0
$455$	−3.44317	+	2.10571i	−0.161418	+	0.0987173i
$456$		0			0
$457$	31.4602	+	4.98281i	1.47165	+	0.233086i	0.840176	−	0.542314i	$-0.182452\pi$
$457$	31.4602	+	4.98281i	1.47165	+	0.233086i	0.631471	+	0.775400i	$0.282452\pi$
$458$		0			0
$459$	−4.97123	+	15.2999i	−0.232037	+	0.714137i
$460$		0			0
$461$			31.1938i			1.45284i	0.687250	+	0.726421i	$0.258817\pi$
$461$			31.1938i			1.45284i	−0.687250	+	0.726421i	$0.741183\pi$
$462$		0			0
$463$	23.0136	+	23.0136i	1.06953	+	1.06953i	0.997395	+	0.0721400i	$0.0229828\pi$
$463$	23.0136	+	23.0136i	1.06953	+	1.06953i	0.0721400	+	0.997395i	$0.477017\pi$
$464$		0			0
$465$	−12.9905	−	15.2377i	−0.602420	−	0.706632i
$466$		0			0
$467$	−3.34260	+	21.1044i	−0.154677	+	0.976593i	0.781204	+	0.624276i	$0.214606\pi$
$467$	−3.34260	+	21.1044i	−0.154677	+	0.976593i	−0.935881	+	0.352317i	$0.885394\pi$
$468$		0			0
$469$	9.92570	+	30.5482i	0.458326	+	1.41058i
$470$		0			0
$471$	−27.7874	−	20.1888i	−1.28038	−	0.930249i
$472$		0			0
$473$	0.469127	+	3.19029i	0.0215705	+	0.146690i
$474$		0			0
$475$	−35.3634	−	5.66637i	−1.62259	−	0.259991i
$476$		0			0
$477$	−0.436312	−	0.222312i	−0.0199773	−	0.0101790i
$478$		0			0
$479$	−0.590214	+	0.428815i	−0.0269676	+	0.0195931i	−0.601187	−	0.799108i	$-0.705305\pi$
$479$	−0.590214	+	0.428815i	−0.0269676	+	0.0195931i	0.574220	+	0.818701i	$0.305305\pi$
$480$		0			0
$481$	2.53633	+	0.824104i	0.115647	+	0.0375759i
$482$		0			0
$483$	−1.81963	+	1.81963i	−0.0827961	+	0.0827961i
$484$		0			0
$485$	−33.2206	−	20.3988i	−1.50847	−	0.926263i
$486$		0			0
$487$	0.491290	+	0.964210i	0.0222625	+	0.0436925i	0.901870	−	0.432008i	$-0.142195\pi$
$487$	0.491290	+	0.964210i	0.0222625	+	0.0436925i	−0.879607	+	0.475700i	$0.842195\pi$
$488$		0			0
$489$	4.31934	+	5.94507i	0.195327	+	0.268845i
$490$		0			0
$491$	−20.1190	+	6.53706i	−0.907958	+	0.295013i	−0.725518	−	0.688203i	$-0.758400\pi$
$491$	−20.1190	+	6.53706i	−0.907958	+	0.295013i	−0.182440	+	0.983217i	$0.558400\pi$
$492$		0			0
$493$	−3.34570	−	21.1239i	−0.150683	−	0.951372i
$494$		0			0
$495$	0.823506	−	1.92265i	0.0370139	−	0.0864168i
$496$		0			0
$497$	4.36236	+	27.5428i	0.195678	+	1.23546i
$498$		0			0
$499$	30.9627	−	10.0604i	1.38608	−	0.450365i	0.481418	−	0.876491i	$-0.340122\pi$
$499$	30.9627	−	10.0604i	1.38608	−	0.450365i	0.904664	+	0.426126i	$0.140122\pi$
$500$		0			0
$501$	12.8730	+	17.7182i	0.575125	+	0.791591i
$502$		0			0
$503$	4.67011	+	9.16560i	0.208230	+	0.408674i	0.971374	−	0.237554i	$-0.0763456\pi$
$503$	4.67011	+	9.16560i	0.208230	+	0.408674i	−0.763145	+	0.646228i	$0.776346\pi$
$504$		0			0
$505$	−16.4011	+	3.92193i	−0.729839	+	0.174524i
$506$		0			0
$507$	−14.6450	+	14.6450i	−0.650407	+	0.650407i
$508$		0			0
$509$	5.03977	+	1.63752i	0.223384	+	0.0725818i	0.418570	−	0.908184i	$-0.362531\pi$
$509$	5.03977	+	1.63752i	0.223384	+	0.0725818i	−0.195187	+	0.980766i	$0.562531\pi$
$510$		0			0
$511$	25.6453	−	18.6324i	1.13448	−	0.824250i
$512$		0			0
$513$	−34.5331	−	17.5955i	−1.52467	−	0.776859i
$514$		0			0
$515$	−27.1320	+	11.2098i	−1.19558	+	0.493964i
$516$		0			0
$517$	33.0738	+	5.61462i	1.45459	+	0.246931i
$518$		0			0
$519$	−23.5985	−	17.1453i	−1.03586	−	0.752596i
$520$		0			0
$521$	−6.32349	−	19.4617i	−0.277037	−	0.852633i	−0.988673	−	0.150084i	$-0.952045\pi$
$521$	−6.32349	−	19.4617i	−0.277037	−	0.852633i	0.711636	−	0.702548i	$-0.247955\pi$
$522$		0			0
$523$	3.83000	−	24.1816i	0.167474	−	1.05739i	−0.750535	−	0.660830i	$-0.770204\pi$
$523$	3.83000	−	24.1816i	0.167474	−	1.05739i	0.918009	−	0.396559i	$-0.129796\pi$
$524$		0			0
$525$	22.2279	−	3.47950i	0.970105	−	0.151858i
$526$		0			0
$527$	11.4192	+	11.4192i	0.497427	+	0.497427i
$528$		0			0
$529$		−	22.6729i		−	0.985780i
$530$		0			0
$531$	0.253078	−	0.778895i	0.0109827	−	0.0338012i
$532$		0			0
$533$	−4.94728	−	0.783572i	−0.214290	−	0.0339403i
$534$		0			0
$535$	−23.0173	−	5.54790i	−0.995124	−	0.239857i
$536$		0			0
$537$	13.9845	−	2.21493i	0.603475	−	0.0955811i
$538$		0			0
$539$	−1.49067	−	0.0165135i	−0.0642079	−	0.000711285i
$540$		0			0
$541$	14.6521	−	20.1669i	0.629943	−	0.867042i	−0.368086	−	0.929792i	$-0.619987\pi$
$541$	14.6521	−	20.1669i	0.629943	−	0.867042i	0.998029	+	0.0627495i	$0.0199869\pi$
$542$		0			0
$543$	−11.7124	+	22.9868i	−0.502626	+	0.986458i
$544$		0			0
$545$	0.847973	+	0.725560i	0.0363232	+	0.0310796i
$546$		0			0
$547$	21.8311	−	11.1235i	0.933432	−	0.475607i	0.0799903	−	0.996796i	$-0.474511\pi$
$547$	21.8311	−	11.1235i	0.933432	−	0.475607i	0.853442	+	0.521188i	$0.174511\pi$
$548$		0			0
$549$	3.01795			0.128803
$550$		0			0
$551$	51.5261			2.19508
$552$		0			0
$553$	−4.69644	+	2.39295i	−0.199713	+	0.101759i
$554$		0			0
$555$	−11.2957	−	9.66505i	−0.479475	−	0.410258i
$556$		0			0
$557$	−9.47486	+	18.5955i	−0.401463	+	0.787915i	−0.999912	−	0.0132455i	$-0.995784\pi$
$557$	−9.47486	+	18.5955i	−0.401463	+	0.787915i	0.598449	+	0.801161i	$0.295784\pi$
$558$		0			0
$559$	−0.377922	+	0.520166i	−0.0159844	+	0.0220007i
$560$		0			0
$561$	5.19459	−	15.4045i	0.219316	−	0.650380i
$562$		0			0
$563$	27.4985	−	4.35533i	1.15892	−	0.183555i	0.452779	−	0.891623i	$-0.350433\pi$
$563$	27.4985	−	4.35533i	1.15892	−	0.183555i	0.706145	+	0.708068i	$0.250433\pi$
$564$		0			0
$565$	39.3767	+	9.49104i	1.65659	+	0.399291i
$566$		0			0
$567$	21.7666	+	3.44750i	0.914113	+	0.144781i
$568$		0			0
$569$	−4.26019	+	13.1115i	−0.178596	+	0.549663i	−0.999779	−	0.0210019i	$-0.993314\pi$
$569$	−4.26019	+	13.1115i	−0.178596	+	0.549663i	0.821183	+	0.570665i	$0.193314\pi$
$570$		0			0
$571$			6.81131i			0.285045i	0.989792	+	0.142522i	$0.0455213\pi$
$571$			6.81131i			0.285045i	−0.989792	+	0.142522i	$0.954479\pi$
$572$		0			0
$573$	15.0981	+	15.0981i	0.630733	+	0.630733i
$574$		0			0
$575$	1.68491	−	2.31031i	0.0702657	−	0.0963468i
$576$		0			0
$577$	3.30988	−	20.8978i	0.137792	−	0.869986i	−0.817845	−	0.575439i	$-0.804831\pi$
$577$	3.30988	−	20.8978i	0.137792	−	0.869986i	0.955637	−	0.294547i	$-0.0951688\pi$
$578$		0			0
$579$	4.46420	+	13.7394i	0.185526	+	0.570990i
$580$		0			0
$581$	−19.3492	−	14.0580i	−0.802739	−	0.583224i
$582$		0			0
$583$	5.10167	+	2.67102i	0.211290	+	0.110623i
$584$		0			0
$585$	0.385445	−	0.159250i	0.0159362	−	0.00658418i
$586$		0			0
$587$	−21.8792	−	11.1480i	−0.903050	−	0.460127i	−0.0601452	−	0.998190i	$-0.519156\pi$
$587$	−21.8792	−	11.1480i	−0.903050	−	0.460127i	−0.842905	+	0.538063i	$0.819156\pi$
$588$		0			0
$589$	−31.4760	+	22.8687i	−1.29695	+	0.942287i
$590$		0			0
$591$	−26.5889	−	8.63924i	−1.09372	−	0.355371i
$592$		0			0
$593$	27.1378	−	27.1378i	1.11442	−	1.11442i	0.121869	−	0.992546i	$-0.461111\pi$
$593$	27.1378	−	27.1378i	1.11442	−	1.11442i	0.992546	−	0.121869i	$-0.0388887\pi$
$594$		0			0
$595$	−17.6478	+	4.22004i	−0.723488	+	0.173005i
$596$		0			0
$597$	−6.72482	−	13.1982i	−0.275229	−	0.540167i
$598$		0			0
$599$	−8.05679	−	11.0892i	−0.329191	−	0.453093i	0.612054	−	0.790816i	$-0.290343\pi$
$599$	−8.05679	−	11.0892i	−0.329191	−	0.453093i	−0.941246	+	0.337723i	$0.890343\pi$
$600$		0			0
$601$	28.8515	−	9.37441i	1.17688	−	0.382390i	0.345671	−	0.938356i	$-0.387651\pi$
$601$	28.8515	−	9.37441i	1.17688	−	0.382390i	0.831205	+	0.555966i	$0.187651\pi$
$602$		0			0
$603$	−0.519211	−	3.27817i	−0.0211439	−	0.133497i
$604$		0			0
$605$	−9.93415	+	22.5014i	−0.403881	+	0.914812i
$606$		0			0
$607$	−2.26233	−	14.2838i	−0.0918253	−	0.579762i	−0.990104	−	0.140336i	$-0.955182\pi$
$607$	−2.26233	−	14.2838i	−0.0918253	−	0.579762i	0.898279	−	0.439426i	$-0.144818\pi$
$608$		0			0
$609$	−30.7843	+	10.0024i	−1.24744	+	0.405319i
$610$		0			0
$611$	3.93171	+	5.41153i	0.159060	+	0.218927i
$612$		0			0
$613$	−15.7878	−	30.9853i	−0.637664	−	1.25149i	−0.953134	−	0.302550i	$-0.902162\pi$
$613$	−15.7878	−	30.9853i	−0.637664	−	1.25149i	0.315470	−	0.948936i	$-0.397838\pi$
$614$		0			0
$615$	23.7944	+	14.6107i	0.959482	+	0.589161i
$616$		0			0
$617$	−0.800590	+	0.800590i	−0.0322306	+	0.0322306i	−0.723038	−	0.690808i	$-0.757255\pi$
$617$	−0.800590	+	0.800590i	−0.0322306	+	0.0322306i	0.690808	+	0.723038i	$0.257255\pi$
$618$		0			0
$619$	−9.45441	−	3.07192i	−0.380005	−	0.123471i	0.112785	−	0.993619i	$-0.464023\pi$
$619$	−9.45441	−	3.07192i	−0.380005	−	0.123471i	−0.492790	+	0.870148i	$0.664023\pi$
$620$		0			0
$621$	2.50343	−	1.81885i	0.100459	−	0.0729879i
$622$		0			0
$623$	−26.2683	−	13.3844i	−1.05242	−	0.536234i
$624$		0			0
$625$	−23.8041	+	7.63968i	−0.952164	+	0.305587i
$626$		0			0
$627$	34.6980	+	18.1664i	1.38570	+	0.725497i
$628$		0			0
$629$	9.69993	+	7.04741i	0.386761	+	0.280999i
$630$		0			0
$631$	−0.103041	−	0.317127i	−0.00410199	−	0.0126246i	0.948985	−	0.315322i	$-0.102113\pi$
$631$	−0.103041	−	0.317127i	−0.00410199	−	0.0126246i	−0.953087	+	0.302698i	$0.902113\pi$
$632$		0			0
$633$	−2.67950	+	16.9177i	−0.106500	+	0.672418i
$634$		0			0
$635$	16.9003	+	19.8238i	0.670668	+	0.786685i
$636$		0			0
$637$	−0.210186	−	0.210186i	−0.00832786	−	0.00832786i
$638$		0			0
$639$		−	2.88152i		−	0.113991i
$640$		0			0
$641$	14.3766	−	44.2465i	0.567840	−	1.74763i	−0.0915201	−	0.995803i	$-0.529173\pi$
$641$	14.3766	−	44.2465i	0.567840	−	1.74763i	0.659360	−	0.751828i	$-0.270827\pi$
$642$		0			0
$643$	37.0947	+	5.87523i	1.46287	+	0.231696i	0.836560	−	0.547875i	$-0.184563\pi$
$643$	37.0947	+	5.87523i	1.46287	+	0.231696i	0.626313	+	0.779572i	$0.284563\pi$
$644$		0			0
$645$	3.05768	−	1.86996i	0.120396	−	0.0736295i
$646$		0			0
$647$	2.97563	−	0.471294i	0.116984	−	0.0185285i	−0.0976678	−	0.995219i	$-0.531138\pi$
$647$	2.97563	−	0.471294i	0.116984	−	0.0185285i	0.214652	+	0.976691i	$0.431138\pi$
$648$		0			0
$649$	−3.07744	+	9.12614i	−0.120800	+	0.358232i
$650$		0			0
$651$	14.3660	−	19.7731i	0.563049	−	0.774971i
$652$		0			0
$653$	−7.49862	+	14.7169i	−0.293444	+	0.575916i	−0.989914	−	0.141670i	$-0.954753\pi$
$653$	−7.49862	+	14.7169i	−0.293444	+	0.575916i	0.696470	+	0.717586i	$0.254753\pi$
$654$		0			0
$655$	−12.7921	+	14.9504i	−0.499830	+	0.584159i
$656$		0			0
$657$	−2.91853	+	1.48706i	−0.113863	+	0.0580159i
$658$		0			0
$659$	−15.0069			−0.584587			−0.292294	−	0.956329i	$-0.594418\pi$
$659$	−15.0069			−0.584587			−0.292294	+	0.956329i	$0.594418\pi$
$660$		0			0
$661$	3.50307			0.136254			0.0681268	−	0.997677i	$-0.478298\pi$
$661$	3.50307			0.136254			0.0681268	+	0.997677i	$0.478298\pi$
$662$		0			0
$663$	2.88818	−	1.47160i	0.112168	−	0.0571523i
$664$		0			0
$665$	−3.39062	−	43.5840i	−0.131483	−	1.69012i
$666$		0			0
$667$	−1.86766	+	3.66549i	−0.0723160	+	0.141928i
$668$		0			0
$669$	3.96818	−	5.46173i	0.153419	−	0.211163i
$670$		0			0
$671$	−35.4884	−	0.393136i	−1.37002	−	0.0151768i
$672$		0			0
$673$	19.7146	−	3.12248i	0.759941	−	0.120363i	0.235576	−	0.971856i	$-0.424302\pi$
$673$	19.7146	−	3.12248i	0.759941	−	0.120363i	0.524366	+	0.851493i	$0.324302\pi$
$674$		0			0
$675$	−27.0542	−	0.0487544i	−1.04132	−	0.00187656i
$676$		0			0
$677$	−4.15962	−	0.658819i	−0.159867	−	0.0253205i	0.0759877	−	0.997109i	$-0.475789\pi$
$677$	−4.15962	−	0.658819i	−0.159867	−	0.0253205i	−0.235855	+	0.971788i	$0.575789\pi$
$678$		0			0
$679$	14.7042	−	45.2550i	0.564297	−	1.73673i
$680$		0			0
$681$		−	12.8223i		−	0.491350i
$682$		0			0
$683$	−11.4089	−	11.4089i	−0.436550	−	0.436550i	0.454299	−	0.890849i	$-0.349890\pi$
$683$	−11.4089	−	11.4089i	−0.436550	−	0.436550i	−0.890849	+	0.454299i	$0.849890\pi$
$684$		0			0
$685$	4.87569	−	4.15664i	0.186290	−	0.158817i
$686$		0			0
$687$	2.15641	−	13.6151i	0.0822723	−	0.519447i
$688$		0			0
$689$	0.354820	+	1.09202i	0.0135176	+	0.0416028i
$690$		0			0
$691$	29.2679	+	21.2644i	1.11340	+	0.808934i	0.983196	−	0.182553i	$-0.0584360\pi$
$691$	29.2679	+	21.2644i	1.11340	+	0.808934i	0.130207	+	0.991487i	$0.458436\pi$
$692$		0			0
$693$	2.51701	+	0.427288i	0.0956134	+	0.0162313i
$694$		0			0
$695$	4.15267	−	9.99993i	0.157520	−	0.379319i
$696$		0			0
$697$	−20.0650	−	10.2236i	−0.760015	−	0.387247i
$698$		0			0
$699$	22.1160	−	16.0682i	0.836504	−	0.607756i
$700$		0			0
$701$	29.6610	+	9.63745i	1.12028	+	0.364002i	0.809875	−	0.586602i	$-0.199535\pi$
$701$	29.6610	+	9.63745i	1.12028	+	0.364002i	0.310407	+	0.950604i	$0.399535\pi$
$702$		0			0
$703$	−20.4253	+	20.4253i	−0.770355	+	0.770355i
$704$		0			0
$705$	−8.67195	−	36.2652i	−0.326605	−	1.36583i
$706$		0			0
$707$	−9.34485	−	18.3403i	−0.351449	−	0.689758i
$708$		0			0
$709$	17.5377	+	24.1385i	0.658641	+	0.906542i	0.999435	−	0.0335959i	$-0.0106959\pi$
$709$	17.5377	+	24.1385i	0.658641	+	0.906542i	−0.340794	+	0.940138i	$0.610696\pi$
$710$		0			0
$711$	0.517996	−	0.168307i	0.0194264	−	0.00631201i
$712$		0			0
$713$	−0.485935	−	3.06807i	−0.0181984	−	0.114900i
$714$		0			0
$715$	−4.55324	+	1.82243i	−0.170281	+	0.0681549i
$716$		0			0
$717$	7.83320	+	49.4569i	0.292536	+	1.84700i
$718$		0			0
$719$	12.2810	−	3.99034i	0.458004	−	0.148815i	−0.0709230	−	0.997482i	$-0.522594\pi$
$719$	12.2810	−	3.99034i	0.458004	−	0.148815i	0.528927	+	0.848667i	$0.322594\pi$
$720$		0			0
$721$	−21.0621	−	28.9895i	−0.784394	−	1.07963i
$722$		0			0
$723$	21.0243	+	41.2624i	0.781901	+	1.53457i
$724$		0			0
$725$	32.0765	−	16.2710i	1.19129	−	0.604291i
$726$		0			0
$727$	10.3834	−	10.3834i	0.385099	−	0.385099i	−0.487836	−	0.872935i	$-0.662214\pi$
$727$	10.3834	−	10.3834i	0.385099	−	0.385099i	0.872935	+	0.487836i	$0.162214\pi$
$728$		0			0
$729$	−27.6173	−	8.97342i	−1.02286	−	0.332349i
$730$		0			0
$731$	−2.33858	+	1.69908i	−0.0864956	+	0.0628427i
$732$		0			0
$733$	24.5219	+	12.4945i	0.905738	+	0.461497i	0.843846	−	0.536586i	$-0.180286\pi$
$733$	24.5219	+	12.4945i	0.905738	+	0.461497i	0.0618926	+	0.998083i	$0.480286\pi$
$734$		0			0
$735$	0.632724	+	1.53143i	0.0233384	+	0.0564877i
$736$		0			0
$737$	5.67842	+	38.6160i	0.209167	+	1.42244i
$738$		0			0
$739$	−28.1908	−	20.4818i	−1.03701	−	0.753435i	−0.0673143	−	0.997732i	$-0.521443\pi$
$739$	−28.1908	−	20.4818i	−1.03701	−	0.753435i	−0.969701	+	0.244296i	$0.921443\pi$
$740$		0			0
$741$	2.41323	+	7.42717i	0.0886523	+	0.272844i
$742$		0			0
$743$	7.83995	−	49.4995i	0.287620	−	1.81596i	−0.244906	−	0.969547i	$-0.578757\pi$
$743$	7.83995	−	49.4995i	0.287620	−	1.81596i	0.532526	−	0.846414i	$-0.321243\pi$
$744$		0			0
$745$	23.2008	+	1.84698i	0.850012	+	0.0676681i
$746$		0			0
$747$	1.74752	+	1.74752i	0.0639384	+	0.0639384i
$748$		0			0
$749$		−	28.8998i		−	1.05598i
$750$		0			0
$751$	−4.99712	+	15.3795i	−0.182347	+	0.561208i	−0.999893	−	0.0146569i	$-0.995334\pi$
$751$	−4.99712	+	15.3795i	−0.182347	+	0.561208i	0.817545	+	0.575864i	$0.195334\pi$
$752$		0			0
$753$	4.50784	+	0.713972i	0.164275	+	0.0260186i
$754$		0			0
$755$	−4.06849	−	6.65263i	−0.148068	−	0.242114i
$756$		0			0
$757$	−24.1962	+	3.83230i	−0.879426	+	0.139287i	−0.579790	−	0.814766i	$-0.696865\pi$
$757$	−24.1962	+	3.83230i	−0.879426	+	0.139287i	−0.299636	+	0.954054i	$0.596865\pi$
$758$		0			0
$759$	−2.55002	+	1.80989i	−0.0925600	+	0.0656947i
$760$		0			0
$761$	0.852430	−	1.17327i	0.0309006	−	0.0425310i	−0.793287	−	0.608848i	$-0.791632\pi$
$761$	0.852430	−	1.17327i	0.0309006	−	0.0425310i	0.824188	+	0.566317i	$0.191632\pi$
$762$		0			0
$763$	−0.618437	+	1.21375i	−0.0223889	+	0.0439408i
$764$		0			0
$765$	1.86933	−	0.145425i	0.0675859	−	0.00525785i
$766$		0			0
$767$	−1.71105	+	0.871825i	−0.0617825	+	0.0314798i
$768$		0			0
$769$	10.2732			0.370462			0.185231	−	0.982695i	$-0.440697\pi$
$769$	10.2732			0.370462			0.185231	+	0.982695i	$0.440697\pi$
$770$		0			0
$771$	−24.2235			−0.872389
$772$		0			0
$773$	−36.4996	+	18.5975i	−1.31280	+	0.668904i	−0.963400	−	0.268070i	$-0.913614\pi$
$773$	−36.4996	+	18.5975i	−1.31280	+	0.668904i	−0.349399	+	0.936974i	$0.613614\pi$
$774$		0			0
$775$	−12.3732	+	24.1760i	−0.444459	+	0.868427i
$776$		0			0
$777$	8.23809	−	16.1682i	0.295540	−	0.580030i
$778$		0			0
$779$	31.8896	−	43.8923i	1.14256	−	1.57260i
$780$		0			0
$781$	−0.375362	+	33.8840i	−0.0134315	+	1.21247i
$782$		0			0
$783$	38.4435	−	6.08884i	1.37386	−	0.217598i
$784$		0			0
$785$	−10.9160	+	45.2888i	−0.389611	+	1.61643i
$786$		0			0
$787$	2.32824	+	0.368757i	0.0829927	+	0.0131448i	0.197793	−	0.980244i	$-0.436623\pi$
$787$	2.32824	+	0.368757i	0.0829927	+	0.0131448i	−0.114800	+	0.993389i	$0.536623\pi$
$788$		0			0
$789$	−10.7910	+	33.2112i	−0.384169	+	1.18235i
$790$		0			0
$791$			49.4402i			1.75789i
$792$		0			0
$793$	−5.00388	−	5.00388i	−0.177693	−	0.177693i
$794$		0			0
$795$	0.507943	−	6.38052i	0.0180149	−	0.226294i
$796$		0			0
$797$	1.20284	−	7.59442i	0.0426067	−	0.269008i	−0.957184	−	0.289481i	$-0.906517\pi$
$797$	1.20284	−	7.59442i	0.0426067	−	0.269008i	0.999790	+	0.0204731i	$0.00651723\pi$
$798$		0			0
$799$	9.29301	+	28.6009i	0.328763	+	1.01183i
$800$		0			0
$801$	2.46457	+	1.79062i	0.0870813	+	0.0632683i
$802$		0			0
$803$	34.5130	−	17.1064i	1.21794	−	0.603670i
$804$		0			0
$805$	3.22340	+	1.33858i	0.113610	+	0.0471788i
$806$		0			0
$807$	−5.19226	−	2.64559i	−0.182776	−	0.0931291i
$808$		0			0
$809$	−27.0136	+	19.6265i	−0.949747	+	0.690032i	−0.950747	−	0.309968i	$-0.899682\pi$
$809$	−27.0136	+	19.6265i	−0.949747	+	0.690032i	0.000999838		1.00000i	$0.499682\pi$
$810$		0			0
$811$	−51.0085	−	16.5737i	−1.79115	−	0.581980i	−0.791573	−	0.611074i	$-0.790738\pi$
$811$	−51.0085	−	16.5737i	−1.79115	−	0.581980i	−0.999577	+	0.0290941i	$0.990738\pi$
$812$		0			0
$813$	−16.2772	+	16.2772i	−0.570868	+	0.570868i
$814$		0			0
$815$	5.21537	−	8.49351i	0.182686	−	0.297515i
$816$		0			0
$817$	−3.16166	−	6.20510i	−0.110612	−	0.217089i
$818$		0			0
$819$	0.299214	+	0.411833i	0.0104554	+	0.0143906i
$820$		0			0
$821$	−37.9455	+	12.3292i	−1.32431	+	0.430294i	−0.883972	−	0.467539i	$-0.845141\pi$
$821$	−37.9455	+	12.3292i	−1.32431	+	0.430294i	−0.440336	+	0.897833i	$0.645141\pi$
$822$		0			0
$823$	−2.77159	−	17.4991i	−0.0966115	−	0.609981i	−0.987725	−	0.156201i	$-0.950075\pi$
$823$	−2.77159	−	17.4991i	−0.0966115	−	0.609981i	0.891114	−	0.453780i	$-0.149925\pi$
$824$		0			0
$825$	27.3371	+	0.352108i	0.951756	+	0.0122588i
$826$		0			0
$827$	5.75031	+	36.3060i	0.199958	+	1.26248i	0.859625	+	0.510926i	$0.170697\pi$
$827$	5.75031	+	36.3060i	0.199958	+	1.26248i	−0.659667	+	0.751558i	$0.729303\pi$
$828$		0			0
$829$	46.4693	−	15.0988i	1.61395	−	0.524403i	0.643444	−	0.765493i	$-0.277505\pi$
$829$	46.4693	−	15.0988i	1.61395	−	0.524403i	0.970503	+	0.241090i	$0.0775049\pi$
$830$		0			0
$831$	−11.2414	−	15.4725i	−0.389961	−	0.536736i
$832$		0			0
$833$	−0.606703	−	1.19072i	−0.0210210	−	0.0412561i
$834$		0			0
$835$	15.5435	−	25.3134i	0.537904	−	0.876007i
$836$		0			0
$837$	−20.7818	+	20.7818i	−0.718323	+	0.718323i
$838$		0			0
$839$	−3.92426	−	1.27507i	−0.135480	−	0.0440203i	0.240492	−	0.970651i	$-0.422691\pi$
$839$	−3.92426	−	1.27507i	−0.135480	−	0.0440203i	−0.375972	+	0.926631i	$0.622691\pi$
$840$		0			0
$841$	−18.4017	+	13.3696i	−0.634543	+	0.461022i
$842$		0			0
$843$	−16.0610	−	8.18347i	−0.553169	−	0.281854i
$844$		0			0
$845$	25.9430	+	10.7733i	0.892466	+	0.370614i
$846$		0			0
$847$	−29.5422	−	5.35241i	−1.01508	−	0.183911i
$848$		0			0
$849$	−0.704153	−	0.511597i	−0.0241665	−	0.0175580i
$850$		0			0
$851$	−0.712672	−	2.19338i	−0.0244301	−	0.0751881i
$852$		0			0
$853$	−6.52352	+	41.1879i	−0.223361	+	1.41025i	0.579934	+	0.814664i	$0.303078\pi$
$853$	−6.52352	+	41.1879i	−0.223361	+	1.41025i	−0.803295	+	0.595582i	$0.796922\pi$
$854$		0			0
$855$	−0.358473	+	4.50296i	−0.0122595	+	0.153998i
$856$		0			0
$857$	−10.0809	−	10.0809i	−0.344355	−	0.344355i	0.513647	−	0.858002i	$-0.328294\pi$
$857$	−10.0809	−	10.0809i	−0.344355	−	0.344355i	−0.858002	+	0.513647i	$0.828294\pi$
$858$		0			0
$859$			12.0021i			0.409508i	0.978813	+	0.204754i	$0.0656394\pi$
$859$			12.0021i			0.409508i	−0.978813	+	0.204754i	$0.934361\pi$
$860$		0			0
$861$	−10.5320	+	32.4140i	−0.358928	+	1.10467i
$862$		0			0
$863$	−22.4644	−	3.55801i	−0.764696	−	0.121116i	−0.238110	−	0.971238i	$-0.576528\pi$
$863$	−22.4644	−	3.55801i	−0.764696	−	0.121116i	−0.526586	+	0.850122i	$0.676528\pi$
$864$		0			0
$865$	−9.27046	+	38.4616i	−0.315205	+	1.30773i
$866$		0			0
$867$	−13.2878	+	2.10458i	−0.451278	+	0.0714754i
$868$		0			0
$869$	−6.11309	+	1.91166i	−0.207372	+	0.0648487i
$870$		0			0
$871$	−4.57446	+	6.29620i	−0.155000	+	0.213339i
$872$		0			0
$873$	−2.23223	+	4.38100i	−0.0755496	+	0.148274i
$874$		0			0
$875$	−15.8738	−	26.0616i	−0.536633	−	0.881043i
$876$		0			0
$877$	7.03297	−	3.58348i	0.237487	−	0.121005i	−0.331198	−	0.943561i	$-0.607453\pi$
$877$	7.03297	−	3.58348i	0.237487	−	0.121005i	0.568684	+	0.822556i	$0.307453\pi$
$878$		0			0
$879$	24.3229			0.820391
$880$		0			0
$881$	27.7099			0.933570			0.466785	−	0.884371i	$-0.345412\pi$
$881$	27.7099			0.933570			0.466785	+	0.884371i	$0.345412\pi$
$882$		0			0
$883$	−6.31538	+	3.21785i	−0.212529	+	0.108289i	−0.557015	−	0.830502i	$-0.688053\pi$
$883$	−6.31538	+	3.21785i	−0.212529	+	0.108289i	0.344485	+	0.938792i	$0.388053\pi$
$884$		0			0
$885$	10.6727	−	0.830284i	0.358759	−	0.0279097i
$886$		0			0
$887$	20.0430	−	39.3366i	0.672978	−	1.32079i	−0.261649	−	0.965163i	$-0.584266\pi$
$887$	20.0430	−	39.3366i	0.672978	−	1.32079i	0.934627	−	0.355630i	$-0.115734\pi$
$888$		0			0
$889$	−18.6898	+	25.7243i	−0.626837	+	0.862766i
$890$		0			0
$891$	25.3757	+	8.55698i	0.850119	+	0.286670i
$892$		0			0
$893$	−71.5594	+	11.3339i	−2.39464	+	0.379274i
$894$		0			0
$895$	−10.0193	−	16.3830i	−0.334907	−	0.547625i
$896$		0			0
$897$	−0.615830	−	0.0975378i	−0.0205620	−	0.00325669i
$898$		0			0
$899$	12.0740	−	37.1601i	0.402692	−	1.23936i
$900$		0			0
$901$			5.16222i			0.171979i
$902$		0			0
$903$	3.09349	+	3.09349i	0.102945	+	0.102945i
$904$		0			0
$905$	34.8810	+	2.77682i	1.15948	+	0.0923046i
$906$		0			0
$907$	−0.717563	+	4.53051i	−0.0238263	+	0.150433i	−0.996733	−	0.0807636i	$-0.974264\pi$
$907$	−0.717563	+	4.53051i	−0.0238263	+	0.150433i	0.972907	+	0.231197i	$0.0742641\pi$
$908$		0			0
$909$	0.657265	+	2.02285i	0.0218001	+	0.0670938i
$910$		0			0
$911$	16.0774	+	11.6809i	0.532668	+	0.387006i	0.821355	−	0.570418i	$-0.193219\pi$
$911$	16.0774	+	11.6809i	0.532668	+	0.387006i	−0.288687	+	0.957424i	$0.593219\pi$
$912$		0			0
$913$	−20.3216	−	20.7769i	−0.672548	−	0.687616i
$914$		0			0
$915$	15.0632	+	36.4587i	0.497975	+	1.20529i
$916$		0			0
$917$	−21.3993	−	10.9035i	−0.706668	−	0.360065i
$918$		0			0
$919$	−4.99757	+	3.63095i	−0.164855	+	0.119774i	−0.667154	−	0.744920i	$-0.732488\pi$
$919$	−4.99757	+	3.63095i	−0.164855	+	0.119774i	0.502299	+	0.864694i	$0.332488\pi$
$920$		0			0
$921$	−46.7647	−	15.1948i	−1.54095	−	0.500685i
$922$		0			0
$923$	−4.77767	+	4.77767i	−0.157259	+	0.157259i
$924$		0			0
$925$	−6.26539	+	19.1653i	−0.206005	+	0.630151i
$926$		0			0
$927$	1.68098	+	3.29911i	0.0552106	+	0.108357i
$928$		0			0
$929$	−2.73706	−	3.76724i	−0.0898000	−	0.123599i	0.761753	−	0.647867i	$-0.224339\pi$
$929$	−2.73706	−	3.76724i	−0.0898000	−	0.123599i	−0.851553	+	0.524268i	$0.824339\pi$
$930$		0			0
$931$	3.06202	−	0.994912i	0.100354	−	0.0326069i
$932$		0			0
$933$	2.06791	+	13.0563i	0.0677005	+	0.427444i
$934$		0			0
$935$	−22.0006	+	1.46656i	−0.719497	+	0.0479616i
$936$		0			0
$937$	3.65875	+	23.1004i	0.119526	+	0.754658i	0.972534	+	0.232760i	$0.0747757\pi$
$937$	3.65875	+	23.1004i	0.119526	+	0.754658i	−0.853008	+	0.521898i	$0.825224\pi$
$938$		0			0
$939$	18.8070	−	6.11077i	0.613743	−	0.199417i
$940$		0			0
$941$	6.83496	+	9.40752i	0.222813	+	0.306676i	0.905759	−	0.423793i	$-0.139302\pi$
$941$	6.83496	+	9.40752i	0.222813	+	0.306676i	−0.682946	+	0.730469i	$0.739302\pi$
$942$		0			0
$943$	1.96653	+	3.85954i	0.0640391	+	0.125684i
$944$		0			0
$945$	−7.68007	−	32.1172i	−0.249833	−	1.04477i
$946$		0			0
$947$	−6.63605	+	6.63605i	−0.215643	+	0.215643i	−0.806659	−	0.591017i	$-0.798727\pi$
$947$	−6.63605	+	6.63605i	−0.215643	+	0.215643i	0.591017	+	0.806659i	$0.298727\pi$
$948$		0			0
$949$	7.30465	+	2.37342i	0.237119	+	0.0770446i
$950$		0			0
$951$	−20.7662	+	15.0875i	−0.673389	+	0.489246i
$952$		0			0
$953$	7.03220	+	3.58309i	0.227795	+	0.116068i	0.564164	−	0.825663i	$-0.309199\pi$
$953$	7.03220	+	3.58309i	0.227795	+	0.116068i	−0.336368	+	0.941731i	$0.609199\pi$
$954$		0			0
$955$	11.1067	−	26.7457i	0.359403	−	0.865469i
$956$		0			0
$957$	−38.9144	+	5.72231i	−1.25793	+	0.184976i
$958$		0			0
$959$	6.32691	+	4.59677i	0.204307	+	0.148438i
$960$		0			0
$961$	−0.462610	−	1.42377i	−0.0149229	−	0.0459279i
$962$		0			0
$963$	−0.467153	+	2.94949i	−0.0150538	+	0.0950460i
$964$		0			0
$965$	14.9109	−	12.7119i	0.479999	−	0.409210i
$966$		0			0
$967$	−23.5445	−	23.5445i	−0.757141	−	0.757141i	0.218660	−	0.975801i	$-0.429831\pi$
$967$	−23.5445	−	23.5445i	−0.757141	−	0.757141i	−0.975801	+	0.218660i	$0.929831\pi$
$968$		0			0
$969$			35.1098i			1.12789i
$970$		0			0
$971$	7.03544	−	21.6529i	0.225778	−	0.694873i	−0.772434	−	0.635095i	$-0.780961\pi$
$971$	7.03544	−	21.6529i	0.225778	−	0.694873i	0.998212	−	0.0597777i	$-0.0190392\pi$
$972$		0			0
$973$	13.0539	+	2.06754i	0.418490	+	0.0662823i
$974$		0			0
$975$	3.84768	+	3.86157i	0.123224	+	0.123669i
$976$		0			0
$977$	30.6715	−	4.85790i	0.981270	−	0.155418i	0.354866	−	0.934917i	$-0.384526\pi$
$977$	30.6715	−	4.85790i	0.981270	−	0.155418i	0.626403	+	0.779499i	$0.284526\pi$
$978$		0			0
$979$	−28.7479	−	21.3771i	−0.918786	−	0.683214i
$980$		0			0
$981$	0.0827371	−	0.113878i	0.00264159	−	0.00363584i
$982$		0			0
$983$	−9.85367	+	19.3389i	−0.314283	+	0.616816i	−0.993071	−	0.117519i	$-0.962506\pi$
$983$	−9.85367	+	19.3389i	−0.314283	+	0.616816i	0.678787	+	0.734335i	$0.262506\pi$
$984$		0			0
$985$	2.94102	+	37.8047i	0.0937087	+	1.20456i
$986$		0			0
$987$	40.5531	−	20.6628i	1.29082	−	0.657705i
$988$		0			0
$989$	0.556022			0.0176805
$990$		0			0
$991$	53.4629			1.69830			0.849152	−	0.528148i	$-0.177113\pi$
$991$	53.4629			1.69830			0.849152	+	0.528148i	$0.177113\pi$
$992$		0			0
$993$	13.1214	−	6.68566i	0.416394	−	0.212163i
$994$		0			0
$995$	−13.0617	+	15.2654i	−0.414083	+	0.483945i
$996$		0			0
$997$	10.9849	−	21.5590i	0.347894	−	0.682780i	−0.649063	−	0.760735i	$-0.724839\pi$
$997$	10.9849	−	21.5590i	0.347894	−	0.682780i	0.996957	+	0.0779545i	$0.0248389\pi$
$998$		0			0
$999$	−12.8256	+	17.6529i	−0.405784	+	0.558514i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.u.a.73.5	✓	48
4.3	odd	2		880.2.cm.b.513.2		48
5.2	odd	4	inner	220.2.u.a.117.2	yes	48
11.8	odd	10	inner	220.2.u.a.173.2	yes	48
20.7	even	4		880.2.cm.b.337.5		48
44.19	even	10		880.2.cm.b.833.5		48
55.52	even	20	inner	220.2.u.a.217.5	yes	48
220.107	odd	20		880.2.cm.b.657.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.u.a.73.5	✓	48	1.1	even	1	trivial
220.2.u.a.117.2	yes	48	5.2	odd	4	inner
220.2.u.a.173.2	yes	48	11.8	odd	10	inner
220.2.u.a.217.5	yes	48	55.52	even	20	inner
880.2.cm.b.337.5		48	20.7	even	4
880.2.cm.b.513.2		48	4.3	odd	2
880.2.cm.b.657.2		48	220.107	odd	20
880.2.cm.b.833.5		48	44.19	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.46894 - 0.748461i) q^{3} +(-1.69901 - 1.45374i) q^{5} +(1.23911 - 2.43189i) q^{7} +(-0.165773 + 0.228167i) q^{9} +O(q^{10})\)	\(q+(1.46894 - 0.748461i) q^{3} +(-1.69901 - 1.45374i) q^{5} +(1.23911 - 2.43189i) q^{7} +(-0.165773 + 0.228167i) q^{9} +(1.97907 - 2.66145i) q^{11} +(0.653168 - 0.103452i) q^{13} +(-3.58381 - 0.863812i) q^{15} +(2.93654 + 0.465103i) q^{17} +(-2.21346 + 6.81233i) q^{19} -4.49972i q^{21} +(-0.404388 - 0.404388i) q^{23} +(0.773271 + 4.93984i) q^{25} +(-0.846442 + 5.34423i) q^{27} +(-2.22290 - 6.84138i) q^{29} +(4.39431 + 3.19265i) q^{31} +(0.915135 - 5.39075i) q^{33} +(-5.64060 + 2.33046i) q^{35} +(3.59315 + 1.83080i) q^{37} +(0.882034 - 0.640835i) q^{39} +(-7.20357 - 2.34058i) q^{41} +(-0.687486 + 0.687486i) q^{43} +(0.613346 - 0.146667i) q^{45} +(4.59203 + 9.01236i) q^{47} +(-0.264199 - 0.363639i) q^{49} +(4.66171 - 1.51468i) q^{51} +(0.271614 + 1.71491i) q^{53} +(-7.23151 + 1.64477i) q^{55} +(1.84733 + 11.6636i) q^{57} +(-2.76174 + 0.897345i) q^{59} +(-6.28978 - 8.65715i) q^{61} +(0.349466 + 0.685866i) q^{63} +(-1.26013 - 0.773772i) q^{65} +(-8.32148 + 8.32148i) q^{67} +(-0.896689 - 0.291352i) q^{69} +(-8.26577 + 6.00543i) q^{71} +(10.3483 + 5.27272i) q^{73} +(4.83317 + 6.67756i) q^{75} +(-4.02007 - 8.11070i) q^{77} +(-1.56236 - 1.13512i) q^{79} +(2.49512 + 7.67918i) q^{81} +(1.37080 - 8.65490i) q^{83} +(-4.31308 - 5.05919i) q^{85} +(-8.38581 - 8.38581i) q^{87} -10.8016i q^{89} +(0.557764 - 1.71662i) q^{91} +(8.84454 + 1.40084i) q^{93} +(13.6641 - 8.35642i) q^{95} +(17.2194 - 2.72728i) q^{97} +(0.279179 + 0.892754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7}+O(q^{10}) \) 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7	\( 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7} - 16 q^{15} + 10 q^{17} + 16 q^{23} - 26 q^{25} - 10 q^{27} + 16 q^{31} + 28 q^{33} - 34 q^{37} - 20 q^{41} - 56 q^{45} - 2 q^{47} - 80 q^{51} + 6 q^{53} - 18 q^{55} - 120 q^{57} - 40 q^{61} - 50 q^{63} - 72 q^{67} + 4 q^{71} - 20 q^{73} + 20 q^{75} - 36 q^{77} + 100 q^{81} + 40 q^{85} - 8 q^{91} - 14 q^{93} + 50 q^{95} + 6 q^{97}+O(q^{100}) \) 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7 - 16 * q^15 + 10 * q^17 + 16 * q^23 - 26 * q^25 - 10 * q^27 + 16 * q^31 + 28 * q^33 - 34 * q^37 - 20 * q^41 - 56 * q^45 - 2 * q^47 - 80 * q^51 + 6 * q^53 - 18 * q^55 - 120 * q^57 - 40 * q^61 - 50 * q^63 - 72 * q^67 + 4 * q^71 - 20 * q^73 + 20 * q^75 - 36 * q^77 + 100 * q^81 + 40 * q^85 - 8 * q^91 - 14 * q^93 + 50 * q^95 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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