LMFDB - Embedded newform 880.2.cm.b.337.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(17,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 5, 18]))

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

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

chi := DirichletCharacter("880.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.cm (of order $20$, degree $8$, not 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:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 220)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			337.5
Character	$\chi$	$=$	880.337
Dual form			880.2.cm.b.833.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.748461 + 1.46894i) q^{3} +(0.857567 + 2.06509i) q^{5} +(-2.43189 - 1.23911i) q^{7} +(0.165773 - 0.228167i) q^{9} +O(q^{10})$	\(q+(0.748461 + 1.46894i) q^{3} +(0.857567 + 2.06509i) q^{5} +(-2.43189 - 1.23911i) q^{7} +(0.165773 - 0.228167i) q^{9} +(-1.97907 + 2.66145i) q^{11} +(-0.103452 - 0.653168i) q^{13} +(-2.39163 + 2.80535i) q^{15} +(-0.465103 + 2.93654i) q^{17} +(-2.21346 + 6.81233i) q^{19} -4.49972i q^{21} +(0.404388 - 0.404388i) q^{23} +(-3.52916 + 3.54190i) q^{25} +(5.34423 + 0.846442i) q^{27} +(2.22290 + 6.84138i) q^{29} +(-4.39431 - 3.19265i) q^{31} +(-5.39075 - 0.915135i) q^{33} +(0.473359 - 6.08468i) q^{35} +(-1.83080 + 3.59315i) q^{37} +(0.882034 - 0.640835i) q^{39} +(-7.20357 - 2.34058i) q^{41} +(-0.687486 - 0.687486i) q^{43} +(0.613346 + 0.146667i) q^{45} +(9.01236 - 4.59203i) q^{47} +(0.264199 + 0.363639i) q^{49} +(-4.66171 + 1.51468i) q^{51} +(1.71491 - 0.271614i) q^{53} +(-7.19330 - 1.80457i) q^{55} +(-11.6636 + 1.84733i) q^{57} +(-2.76174 + 0.897345i) q^{59} +(-6.28978 - 8.65715i) q^{61} +(-0.685866 + 0.349466i) q^{63} +(1.26013 - 0.773772i) q^{65} +(8.32148 + 8.32148i) q^{67} +(0.896689 + 0.291352i) q^{69} +(8.26577 - 6.00543i) q^{71} +(5.27272 - 10.3483i) q^{73} +(-7.84426 - 2.53314i) q^{75} +(8.11070 - 4.02007i) q^{77} +(-1.56236 - 1.13512i) q^{79} +(2.49512 + 7.67918i) q^{81} +(8.65490 + 1.37080i) q^{83} +(-6.46307 + 1.55781i) q^{85} +(-8.38581 + 8.38581i) q^{87} +10.8016i q^{89} +(-0.557764 + 1.71662i) q^{91} +(1.40084 - 8.84454i) q^{93} +(-15.9662 + 1.27105i) q^{95} +(2.72728 + 17.2194i) q^{97} +(0.279179 + 0.892754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.748461	+	1.46894i	0.432124	+	0.848091i	0.999693	+	0.0247656i	$0.00788393\pi$
$3$	0.748461	+	1.46894i	0.432124	+	0.848091i	−0.567569	+	0.823326i	$0.692116\pi$
$4$		0			0
$5$	0.857567	+	2.06509i	0.383516	+	0.923534i
$5$	0.857567	+	2.06509i	0.383516	+	0.923534i
$6$		0			0
$7$	−2.43189	−	1.23911i	−0.919168	−	0.468340i	−0.0706471	−	0.997501i	$-0.522506\pi$
$7$	−2.43189	−	1.23911i	−0.919168	−	0.468340i	−0.848521	+	0.529162i	$0.822506\pi$
$8$		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
$13$	−0.103452	−	0.653168i	−0.0286923	−	0.181156i	0.969180	−	0.246353i	$-0.0792324\pi$
$13$	−0.103452	−	0.653168i	−0.0286923	−	0.181156i	−0.997872	+	0.0651971i	$0.979232\pi$
$14$		0			0
$15$	−2.39163	+	2.80535i	−0.617515	+	0.724338i
$16$		0			0
$17$	−0.465103	+	2.93654i	−0.112804	+	0.712216i	0.864855	+	0.502021i	$0.167410\pi$
$17$	−0.465103	+	2.93654i	−0.112804	+	0.712216i	−0.977659	+	0.210195i	$0.932590\pi$
$18$		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	$-0.731010\pi$
$23$	0.404388	−	0.404388i	0.0843207	−	0.0843207i	0.748009	+	0.663688i	$0.231010\pi$
$24$		0			0
$25$	−3.52916	+	3.54190i	−0.705831	+	0.708380i
$26$		0			0
$27$	5.34423	+	0.846442i	1.02850	+	0.162898i
$28$		0			0
$29$	2.22290	+	6.84138i	0.412782	+	1.27041i	0.914220	+	0.405219i	$0.132805\pi$
$29$	2.22290	+	6.84138i	0.412782	+	1.27041i	−0.501437	+	0.865194i	$0.667195\pi$
$30$		0			0
$31$	−4.39431	−	3.19265i	−0.789241	−	0.573417i	0.118497	−	0.992954i	$-0.462192\pi$
$31$	−4.39431	−	3.19265i	−0.789241	−	0.573417i	−0.907738	+	0.419537i	$0.862192\pi$
$32$		0			0
$33$	−5.39075	−	0.915135i	−0.938409	−	0.159305i
$34$		0			0
$35$	0.473359	−	6.08468i	0.0800122	−	1.02850i
$36$		0			0
$37$	−1.83080	+	3.59315i	−0.300982	+	0.590710i	−0.991120	−	0.132967i	$-0.957550\pi$
$37$	−1.83080	+	3.59315i	−0.300982	+	0.590710i	0.690139	+	0.723677i	$0.257550\pi$
$38$		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	0.652741	−	0.757581i	$-0.273619\pi$
$43$	−0.687486	−	0.687486i	−0.104841	−	0.104841i	−0.757581	+	0.652741i	$0.773619\pi$
$44$		0			0
$45$	0.613346	+	0.146667i	0.0914323	+	0.0218638i
$46$		0			0
$47$	9.01236	−	4.59203i	1.31459	−	0.669816i	0.350791	−	0.936454i	$-0.385913\pi$
$47$	9.01236	−	4.59203i	1.31459	−	0.669816i	0.963797	+	0.266638i	$0.0859129\pi$
$48$		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
$53$	1.71491	−	0.271614i	0.235560	−	0.0373091i	−0.0375380	−	0.999295i	$-0.511952\pi$
$53$	1.71491	−	0.271614i	0.235560	−	0.0373091i	0.273098	+	0.961986i	$0.411952\pi$
$54$		0			0
$55$	−7.19330	−	1.80457i	−0.969944	−	0.243328i
$56$		0			0
$57$	−11.6636	+	1.84733i	−1.54488	+	0.244685i
$58$		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
$63$	−0.685866	+	0.349466i	−0.0864110	+	0.0440286i
$64$		0			0
$65$	1.26013	−	0.773772i	0.156300	−	0.0959747i
$66$		0			0
$67$	8.32148	+	8.32148i	1.01663	+	1.01663i	0.999859	+	0.0167718i	$0.00533889\pi$
$67$	8.32148	+	8.32148i	1.01663	+	1.01663i	0.0167718	+	0.999859i	$0.494661\pi$
$68$		0			0
$69$	0.896689	+	0.291352i	0.107949	+	0.0350746i
$70$		0			0
$71$	8.26577	−	6.00543i	0.980966	−	0.712714i	0.0230418	−	0.999735i	$-0.492665\pi$
$71$	8.26577	−	6.00543i	0.980966	−	0.712714i	0.957924	+	0.287021i	$0.0926649\pi$
$72$		0			0
$73$	5.27272	−	10.3483i	0.617125	−	1.21118i	−0.345009	−	0.938599i	$-0.612124\pi$
$73$	5.27272	−	10.3483i	0.617125	−	1.21118i	0.962134	−	0.272576i	$-0.0878757\pi$
$74$		0			0
$75$	−7.84426	−	2.53314i	−0.905778	−	0.292501i
$76$		0			0
$77$	8.11070	−	4.02007i	0.924300	−	0.458129i
$78$		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
$83$	8.65490	+	1.37080i	0.949998	+	0.150465i	0.612155	−	0.790738i	$-0.290303\pi$
$83$	8.65490	+	1.37080i	0.949998	+	0.150465i	0.337843	+	0.941202i	$0.390303\pi$
$84$		0			0
$85$	−6.46307	+	1.55781i	−0.701018	+	0.168968i
$86$		0			0
$87$	−8.38581	+	8.38581i	−0.899053	+	0.899053i
$88$		0			0
$89$			10.8016i			1.14497i	0.819916	+	0.572484i	$0.194020\pi$
$89$			10.8016i			1.14497i	−0.819916	+	0.572484i	$0.805980\pi$
$90$		0			0
$91$	−0.557764	+	1.71662i	−0.0584696	+	0.179951i
$92$		0			0
$93$	1.40084	−	8.84454i	0.145260	−	0.917136i
$94$		0			0
$95$	−15.9662	+	1.27105i	−1.63810	+	0.130407i
$96$		0			0
$97$	2.72728	+	17.2194i	0.276913	+	1.74836i	0.598170	+	0.801369i	$0.295895\pi$
$97$	2.72728	+	17.2194i	0.276913	+	1.74836i	−0.321257	+	0.946992i	$0.604105\pi$
$98$		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
$103$	11.6977	+	5.96029i	1.15261	+	0.587284i	0.922545	−	0.385891i	$-0.126106\pi$
$103$	11.6977	+	5.96029i	1.15261	+	0.587284i	0.230066	+	0.973175i	$0.426106\pi$
$104$		0			0
$105$	9.29230	−	3.85881i	0.906836	−	0.376581i
$106$		0			0
$107$	−4.80705	−	9.43436i	−0.464715	−	0.912054i	−0.997819	−	0.0660047i	$-0.978975\pi$
$107$	−4.80705	−	9.43436i	−0.464715	−	0.912054i	0.533105	−	0.846049i	$-0.321025\pi$
$108$		0			0
$109$	0.499098			0.0478049			0.0239025	−	0.999714i	$-0.492391\pi$
$109$	0.499098			0.0478049			0.0239025	+	0.999714i	$0.492391\pi$
$110$		0			0
$111$	−6.64839			−0.631038
$112$		0			0
$113$	8.22363	+	16.1398i	0.773614	+	1.51830i	0.853263	+	0.521480i	$0.174620\pi$
$113$	8.22363	+	16.1398i	0.773614	+	1.51830i	−0.0796494	+	0.996823i	$0.525380\pi$
$114$		0			0
$115$	1.18189	+	0.488306i	0.110211	+	0.0455347i
$116$		0			0
$117$	−0.166181	−	0.0846735i	−0.0153634	−	0.00782807i
$118$		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
$123$	−1.95342	−	12.3334i	−0.176134	−	1.11207i
$124$		0			0
$125$	−10.3408	−	4.25059i	−0.924911	−	0.380185i
$126$		0			0
$127$	−1.82245	+	11.5065i	−0.161716	+	1.02104i	0.764659	+	0.644435i	$0.222907\pi$
$127$	−1.82245	+	11.5065i	−0.161716	+	1.02104i	−0.926375	+	0.376602i	$0.877093\pi$
$128$		0			0
$129$	0.495317	−	1.52443i	0.0436102	−	0.134219i
$130$		0			0
$131$			8.79946i			0.768812i	0.923164	+	0.384406i	$0.125594\pi$
$131$			8.79946i			0.768812i	−0.923164	+	0.384406i	$0.874406\pi$
$132$		0			0
$133$	13.8241	−	13.8241i	1.19870	−	1.19870i
$134$		0			0
$135$	2.83506	+	11.7622i	0.244003	+	1.01233i
$136$		0			0
$137$	−2.83003	−	0.448233i	−0.241786	−	0.0382951i	0.0343653	−	0.999409i	$-0.489059\pi$
$137$	−2.83003	−	0.448233i	−0.241786	−	0.0382951i	−0.276151	+	0.961114i	$0.589059\pi$
$138$		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
$143$	1.94311	+	1.01733i	0.162491	+	0.0850736i
$144$		0			0
$145$	−12.2218	+	10.4574i	−1.01496	+	0.868442i
$146$		0			0
$147$	−0.336420	+	0.660262i	−0.0277475	+	0.0544575i
$148$		0			0
$149$	8.42069	−	6.11799i	0.689850	−	0.501205i	−0.186761	−	0.982405i	$-0.559799\pi$
$149$	8.42069	−	6.11799i	0.689850	−	0.501205i	0.876611	+	0.481200i	$0.159799\pi$
$150$		0			0
$151$	−3.31672	−	1.07767i	−0.269911	−	0.0876994i	0.170934	−	0.985282i	$-0.445321\pi$
$151$	−3.31672	−	1.07767i	−0.269911	−	0.0876994i	−0.440846	+	0.897583i	$0.645321\pi$
$152$		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
$157$	18.5631	−	9.45835i	1.48149	−	0.754858i	0.488448	−	0.872593i	$-0.337563\pi$
$157$	18.5631	−	9.45835i	1.48149	−	0.754858i	0.993045	+	0.117735i	$0.0375633\pi$
$158$		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
$163$	−4.40247	+	0.697283i	−0.344828	+	0.0546154i	−0.326447	−	0.945216i	$-0.605851\pi$
$163$	−4.40247	+	0.697283i	−0.344828	+	0.0546154i	−0.0183815	+	0.999831i	$0.505851\pi$
$164$		0			0
$165$	−2.73310	−	11.9172i	−0.212772	−	0.927749i
$166$		0			0
$167$	13.1208	−	2.07813i	1.01532	−	0.160810i	0.373469	−	0.927643i	$-0.378168\pi$
$167$	13.1208	−	2.07813i	1.01532	−	0.160810i	0.641848	+	0.766832i	$0.278168\pi$
$168$		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
$173$	−15.7647	+	8.03251i	−1.19857	+	0.610700i	−0.935243	−	0.354007i	$-0.884819\pi$
$173$	−15.7647	+	8.03251i	−1.19857	+	0.610700i	−0.263324	+	0.964707i	$0.584819\pi$
$174$		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
$183$	8.00915	−	15.7188i	0.592053	−	1.16197i
$184$		0			0
$185$	−8.99020	−	0.699394i	−0.660972	−	0.0514204i
$186$		0			0
$187$	−6.89498	−	7.04946i	−0.504211	−	0.515507i
$188$		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	$-0.944772\pi$
$191$	−4.00219	−	12.3175i	−0.289588	−	0.891261i	0.695398	−	0.718625i	$-0.255228\pi$
$192$		0			0
$193$	8.65484	+	1.37079i	0.622989	+	0.0986718i	0.459946	−	0.887947i	$-0.347869\pi$
$193$	8.65484	+	1.37079i	0.622989	+	0.0986718i	0.163044	+	0.986619i	$0.447869\pi$
$194$		0			0
$195$	2.07978	+	1.27192i	0.148936	+	0.0910838i
$196$		0			0
$197$	11.9910	−	11.9910i	0.854324	−	0.854324i	−0.136338	−	0.990662i	$-0.543533\pi$
$197$	11.9910	−	11.9910i	0.854324	−	0.854324i	0.990662	+	0.136338i	$0.0435333\pi$
$198$		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
$203$	3.07138	−	19.3919i	0.215568	−	1.36105i
$204$		0			0
$205$	−1.34404	−	16.8832i	−0.0938721	−	1.17917i
$206$		0			0
$207$	−0.0252314	−	0.159305i	−0.00175370	−	0.0110724i
$208$		0			0
$209$	−13.7501	−	19.3731i	−0.951112	−	1.34006i
$210$		0			0
$211$	6.10685	−	8.40536i	0.420413	−	0.578649i	−0.545306	−	0.838237i	$-0.683587\pi$
$211$	6.10685	−	8.40536i	0.420413	−	0.578649i	0.965719	+	0.259588i	$0.0835867\pi$
$212$		0			0
$213$	15.0082	+	7.64706i	1.02835	+	0.523968i
$214$		0			0
$215$	0.830152	−	2.00928i	0.0566159	−	0.137032i
$216$		0			0
$217$	6.73043	+	13.2092i	0.456891	+	0.896699i
$218$		0			0
$219$	19.1474			1.29386
$220$		0			0
$221$	1.96617			0.132259
$222$		0			0
$223$	1.85907	+	3.64864i	0.124493	+	0.244331i	0.944838	−	0.327537i	$-0.106219\pi$
$223$	1.85907	+	3.64864i	0.124493	+	0.244331i	−0.820345	+	0.571868i	$0.806219\pi$
$224$		0			0
$225$	0.223106	+	1.39239i	0.0148737	+	0.0928260i
$226$		0			0
$227$	−6.92984	−	3.53093i	−0.459949	−	0.234356i	0.208633	−	0.977994i	$-0.433099\pi$
$227$	−6.92984	−	3.53093i	−0.459949	−	0.234356i	−0.668582	+	0.743638i	$0.733099\pi$
$228$		0			0
$229$	−4.91469	+	6.76448i	−0.324772	+	0.447010i	−0.939917	−	0.341404i	$-0.889097\pi$
$229$	−4.91469	+	6.76448i	−0.324772	+	0.447010i	0.615145	+	0.788414i	$0.289097\pi$
$230$		0			0
$231$	11.9758	+	8.90524i	0.787947	+	0.585922i
$232$		0			0
$233$	−2.59393	−	16.3775i	−0.169934	−	1.07292i	−0.914266	−	0.405113i	$-0.867232\pi$
$233$	−2.59393	−	16.3775i	−0.169934	−	1.07292i	0.744332	−	0.667810i	$-0.232768\pi$
$234$		0			0
$235$	17.2116	+	14.6733i	1.12276	+	0.957182i
$236$		0			0
$237$	0.498057	−	3.14461i	0.0323523	−	0.204264i
$238$		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
$245$	−0.524377	+	0.857439i	−0.0335012	+	0.0547798i
$246$		0			0
$247$	4.67858	+	0.741015i	0.297691	+	0.0471497i
$248$		0			0
$249$	4.46423	+	13.7395i	0.282909	+	0.870705i
$250$		0			0
$251$	−2.23967	−	1.62722i	−0.141367	−	0.102709i	0.514854	−	0.857278i	$-0.327846\pi$
$251$	−2.23967	−	1.62722i	−0.141367	−	0.102709i	−0.656221	+	0.754569i	$0.727846\pi$
$252$		0			0
$253$	0.275947	+	1.87657i	0.0173486	+	0.117979i
$254$		0			0
$255$	−7.12567	−	8.32789i	−0.446227	−	0.521512i
$256$		0			0
$257$	6.67056	−	13.0917i	0.416098	−	0.816638i	−0.583891	−	0.811832i	$-0.698470\pi$
$257$	6.67056	−	13.0917i	0.416098	−	0.816638i	0.999988	−	0.00480567i	$-0.00152970\pi$
$258$		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	0.0737237	−	0.997279i	$-0.476512\pi$
$263$	−14.9775	−	14.9775i	−0.923555	−	0.923555i	−0.997279	+	0.0737237i	$0.976512\pi$
$264$		0			0
$265$	2.03155	+	3.30850i	0.124797	+	0.203240i
$266$		0			0
$267$	−15.8669	+	8.08458i	−0.971037	+	0.494768i
$268$		0			0
$269$	2.07765	+	2.85964i	0.126676	+	0.174355i	0.867644	−	0.497185i	$-0.165633\pi$
$269$	2.07765	+	2.85964i	0.126676	+	0.174355i	−0.740968	+	0.671540i	$0.765633\pi$
$270$		0			0
$271$	13.2794	−	4.31475i	0.806669	−	0.262103i	0.123482	−	0.992347i	$-0.460594\pi$
$271$	13.2794	−	4.31475i	0.806669	−	0.262103i	0.683186	+	0.730244i	$0.260594\pi$
$272$		0			0
$273$	−2.93907	+	0.465504i	−0.177881	+	0.0281736i
$274$		0			0
$275$	−2.44214	−	16.4023i	−0.147267	−	0.989097i
$276$		0			0
$277$	11.4578	−	1.81474i	0.688432	−	0.109037i	0.197589	−	0.980285i	$-0.436689\pi$
$277$	11.4578	−	1.81474i	0.688432	−	0.109037i	0.490843	+	0.871248i	$0.336689\pi$
$278$		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
$283$	0.470400	−	0.239681i	0.0279624	−	0.0142476i	−0.439953	−	0.898021i	$-0.645005\pi$
$283$	0.470400	−	0.239681i	0.0279624	−	0.0142476i	0.467916	+	0.883773i	$0.345005\pi$
$284$		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
$293$	6.69792	−	13.1454i	0.391297	−	0.767963i	−0.608373	−	0.793651i	$-0.708178\pi$
$293$	6.69792	−	13.1454i	0.391297	−	0.767963i	0.999670	+	0.0256880i	$0.00817763\pi$
$294$		0			0
$295$	−4.22148	−	4.93370i	−0.245784	−	0.287251i
$296$		0			0
$297$	−12.8293	+	12.5482i	−0.744434	+	0.728121i
$298$		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
$303$	12.2802	+	1.94499i	0.705478	+	0.111737i
$304$		0			0
$305$	12.4838	−	20.4130i	0.714822	−	1.16885i
$306$		0			0
$307$	−21.0899	+	21.0899i	−1.20366	+	1.20366i	−0.230620	+	0.973044i	$0.574075\pi$
$307$	−21.0899	+	21.0899i	−1.20366	+	1.20366i	−0.973044	+	0.230620i	$0.925925\pi$
$308$		0			0
$309$			21.6443i			1.23130i
$310$		0			0
$311$	2.47776	−	7.62577i	0.140501	−	0.432418i	−0.855904	−	0.517135i	$-0.826999\pi$
$311$	2.47776	−	7.62577i	0.140501	−	0.432418i	0.996405	+	0.0847168i	$0.0269986\pi$
$312$		0			0
$313$	1.87639	−	11.8471i	0.106060	−	0.669636i	−0.876177	−	0.481990i	$-0.839914\pi$
$313$	1.87639	−	11.8471i	0.106060	−	0.669636i	0.982237	−	0.187646i	$-0.0600858\pi$
$314$		0			0
$315$	−1.30985	−	1.11668i	−0.0738019	−	0.0629179i
$316$		0			0
$317$	−2.43562	−	15.3779i	−0.136798	−	0.863707i	−0.956673	−	0.291165i	$-0.905957\pi$
$317$	−2.43562	−	15.3779i	−0.136798	−	0.863707i	0.819875	−	0.572542i	$-0.194043\pi$
$318$		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
$323$	−18.9752	−	9.66835i	−1.05581	−	0.537962i
$324$		0			0
$325$	2.67855	+	1.93872i	0.148579	+	0.107541i
$326$		0			0
$327$	0.373555	+	0.733144i	0.0206577	+	0.0405429i
$328$		0			0
$329$	−27.6071			−1.52203
$330$		0			0
$331$	−8.93255			−0.490977			−0.245489	−	0.969399i	$-0.578948\pi$
$331$	−8.93255			−0.490977			−0.245489	+	0.969399i	$0.578948\pi$
$332$		0			0
$333$	0.516341	+	1.01338i	0.0282953	+	0.0555327i
$334$		0			0
$335$	−10.0483	+	24.3208i	−0.549000	+	1.32879i
$336$		0			0
$337$	7.62939	+	3.88737i	0.415600	+	0.211759i	0.649271	−	0.760557i	$-0.275074\pi$
$337$	7.62939	+	3.88737i	0.415600	+	0.211759i	−0.233672	+	0.972316i	$0.575074\pi$
$338$		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
$343$	2.79686	+	17.6587i	0.151016	+	0.953480i
$344$		0			0
$345$	0.167304	+	2.10159i	0.00900737	+	0.113146i
$346$		0			0
$347$	5.04583	−	31.8581i	0.270874	−	1.71023i	−0.358833	−	0.933402i	$-0.616825\pi$
$347$	5.04583	−	31.8581i	0.270874	−	1.71023i	0.629708	−	0.776832i	$-0.283175\pi$
$348$		0			0
$349$	−10.6888	+	32.8969i	−0.572160	+	1.76093i	0.0734902	+	0.997296i	$0.476586\pi$
$349$	−10.6888	+	32.8969i	−0.572160	+	1.76093i	−0.645651	+	0.763633i	$0.723414\pi$
$350$		0			0
$351$		−	3.57825i		−	0.190993i
$352$		0			0
$353$	3.39118	−	3.39118i	0.180494	−	0.180494i	−0.611077	−	0.791571i	$-0.709263\pi$
$353$	3.39118	−	3.39118i	0.180494	−	0.180494i	0.791571	+	0.611077i	$0.209263\pi$
$354$		0			0
$355$	19.4902	+	11.9195i	1.03443	+	0.632619i
$356$		0			0
$357$	13.2136	+	2.09283i	0.699339	+	0.110764i
$358$		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
$363$	13.1042	−	12.5361i	0.687794	−	0.657974i
$364$		0			0
$365$	25.8918	+	2.01426i	1.35524	+	0.105431i
$366$		0			0
$367$	6.66686	−	13.0845i	0.348007	−	0.683003i	−0.648960	−	0.760823i	$-0.724796\pi$
$367$	6.66686	−	13.0845i	0.348007	−	0.683003i	0.996967	+	0.0778194i	$0.0247958\pi$
$368$		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	$-0.0868361\pi$
$373$	13.3954	+	13.3954i	0.693587	+	0.693587i	−0.269433	+	0.963019i	$0.586836\pi$
$374$		0			0
$375$	−1.49584	−	18.3714i	−0.0772449	−	0.948696i
$376$		0			0
$377$	4.23861	−	2.15968i	0.218300	−	0.111229i
$378$		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
$383$	−6.57440	+	1.04128i	−0.335936	+	0.0532071i	−0.322124	−	0.946698i	$-0.604397\pi$
$383$	−6.57440	+	1.04128i	−0.335936	+	0.0532071i	−0.0138125	+	0.999905i	$0.504397\pi$
$384$		0			0
$385$	15.2572	+	13.3018i	0.777581	+	0.677923i
$386$		0			0
$387$	−0.270828	+	0.0428950i	−0.0137670	+	0.00218047i
$388$		0			0
$389$	−2.93098	+	0.952333i	−0.148607	+	0.0482852i	−0.382376	−	0.924007i	$-0.624894\pi$
$389$	−2.93098	+	0.952333i	−0.148607	+	0.0482852i	0.233769	+	0.972292i	$0.424894\pi$
$390$		0			0
$391$	0.999421	+	1.37558i	0.0505429	+	0.0695663i
$392$		0			0
$393$	−12.9259	+	6.58605i	−0.652023	+	0.332222i
$394$		0			0
$395$	1.00430	−	4.19986i	0.0505316	−	0.211318i
$396$		0			0
$397$	−21.9943	−	21.9943i	−1.10386	−	1.10386i	−0.993940	−	0.109921i	$-0.964940\pi$
$397$	−21.9943	−	21.9943i	−1.10386	−	1.10386i	−0.109921	−	0.993940i	$-0.535060\pi$
$398$		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
$403$	−1.63074	+	3.20051i	−0.0812330	+	0.159429i
$404$		0			0
$405$	−13.7184	+	11.7380i	−0.681675	+	0.583268i
$406$		0			0
$407$	−5.93970	−	11.9837i	−0.294420	−	0.594008i
$408$		0			0
$409$	20.0092	+	14.5375i	0.989392	+	0.718835i	0.959788	−	0.280727i	$-0.0905754\pi$
$409$	20.0092	+	14.5375i	0.989392	+	0.718835i	0.0296038	+	0.999562i	$0.490575\pi$
$410$		0			0
$411$	−1.45974	−	4.49262i	−0.0720037	−	0.221605i
$412$		0			0
$413$	7.82817	+	1.23986i	0.385199	+	0.0610095i
$414$		0			0
$415$	4.59133	+	19.0487i	0.225380	+	0.935062i
$416$		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
$423$	0.446257	−	2.81756i	0.0216978	−	0.136994i
$424$		0			0
$425$	−8.75952	−	12.0109i	−0.424899	−	0.582613i
$426$		0			0
$427$	4.56891	+	28.8470i	0.221105	+	1.39600i
$428$		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	$0.442129\pi$
$431$	−16.8253	+	23.1581i	−0.810447	+	1.11548i	−0.991254	+	0.131966i	$0.957871\pi$
$432$		0			0
$433$	−35.2157	−	17.9433i	−1.69236	−	0.862301i	−0.988366	−	0.152095i	$-0.951398\pi$
$433$	−35.2157	−	17.9433i	−1.69236	−	0.862301i	−0.703994	−	0.710206i	$-0.748602\pi$
$434$		0			0
$435$	−24.5088	−	10.1260i	−1.17511	−	0.485505i
$436$		0			0
$437$	1.85973	+	3.64992i	0.0889628	+	0.174599i
$438$		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
$443$	4.12682	+	8.09934i	0.196071	+	0.384811i	0.968020	−	0.250873i	$-0.0807178\pi$
$443$	4.12682	+	8.09934i	0.196071	+	0.384811i	−0.771949	+	0.635685i	$0.780718\pi$
$444$		0			0
$445$	−22.3062	+	9.26310i	−1.05742	+	0.439113i
$446$		0			0
$447$	15.2895	+	7.79039i	0.723169	+	0.368473i
$448$		0			0
$449$	6.17770	−	8.50288i	0.291544	−	0.401276i	−0.637971	−	0.770060i	$-0.720226\pi$
$449$	6.17770	−	8.50288i	0.291544	−	0.401276i	0.929515	+	0.368785i	$0.120226\pi$
$450$		0			0
$451$	20.4857	−	14.5397i	0.964632	−	0.684650i
$452$		0			0
$453$	−0.899410	−	5.67865i	−0.0422580	−	0.266806i
$454$		0			0
$455$	−4.02329	+	0.320288i	−0.188615	+	0.0150153i
$456$		0			0
$457$	−4.98281	+	31.4602i	−0.233086	+	1.47165i	0.542314	+	0.840176i	$0.317548\pi$
$457$	−4.98281	+	31.4602i	−0.233086	+	1.47165i	−0.775400	+	0.631471i	$0.782452\pi$
$458$		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	−0.0721400	+	0.997395i	$0.522983\pi$
$463$	−23.0136	+	23.0136i	−1.06953	+	1.06953i	−0.997395	+	0.0721400i	$0.977017\pi$
$464$		0			0
$465$	19.4660	−	4.69194i	0.902716	−	0.217583i
$466$		0			0
$467$	21.1044	+	3.34260i	0.976593	+	0.154677i	0.624276	−	0.781204i	$-0.285394\pi$
$467$	21.1044	+	3.34260i	0.976593	+	0.154677i	0.352317	+	0.935881i	$0.385394\pi$
$468$		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
$473$	3.19029	−	0.469127i	0.146690	−	0.0215705i
$474$		0			0
$475$	−16.3169	−	31.8816i	−0.748672	−	1.46283i
$476$		0			0
$477$	0.222312	−	0.436312i	0.0101790	−	0.0199773i
$478$		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
$487$	0.964210	−	0.491290i	0.0436925	−	0.0222625i	−0.432008	−	0.901870i	$-0.642195\pi$
$487$	0.964210	−	0.491290i	0.0436925	−	0.0222625i	0.475700	+	0.879607i	$0.342195\pi$
$488$		0			0
$489$	−4.31934	−	5.94507i	−0.195327	−	0.268845i
$490$		0			0
$491$	20.1190	−	6.53706i	0.907958	−	0.295013i	0.182440	−	0.983217i	$-0.441600\pi$
$491$	20.1190	−	6.53706i	0.907958	−	0.295013i	0.725518	+	0.688203i	$0.241600\pi$
$492$		0			0
$493$	−21.1239	+	3.34570i	−0.951372	+	0.150683i
$494$		0			0
$495$	−1.60420	+	1.34212i	−0.0721034	+	0.0603240i
$496$		0			0
$497$	−27.5428	+	4.36236i	−1.23546	+	0.195678i
$498$		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
$503$	−9.16560	+	4.67011i	−0.408674	+	0.208230i	−0.646228	−	0.763145i	$-0.723654\pi$
$503$	−9.16560	+	4.67011i	−0.408674	+	0.208230i	0.237554	+	0.971374i	$0.423654\pi$
$504$		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	0.195187	−	0.980766i	$-0.437469\pi$
$509$	−5.03977	−	1.63752i	−0.223384	−	0.0725818i	−0.418570	+	0.908184i	$0.637469\pi$
$510$		0			0
$511$	−25.6453	+	18.6324i	−1.13448	+	0.824250i
$512$		0			0
$513$	−17.5955	+	34.5331i	−0.776859	+	1.52467i
$514$		0			0
$515$	−2.27692	+	29.2681i	−0.100333	+	1.28971i
$516$		0			0
$517$	−5.61462	+	33.0738i	−0.246931	+	1.45459i
$518$		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
$523$	24.1816	+	3.83000i	1.05739	+	0.167474i	0.660830	−	0.750535i	$-0.270204\pi$
$523$	24.1816	+	3.83000i	1.05739	+	0.167474i	0.396559	+	0.918009i	$0.370204\pi$
$524$		0			0
$525$	15.9376	+	15.8802i	0.695572	+	0.693069i
$526$		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
$533$	−0.783572	+	4.94728i	−0.0339403	+	0.214290i
$534$		0			0
$535$	15.3604	−	18.0176i	0.664088	−	0.778967i
$536$		0			0
$537$	2.21493	+	13.9845i	0.0955811	+	0.603475i
$538$		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
$543$	−22.9868	−	11.7124i	−0.986458	−	0.502626i
$544$		0			0
$545$	0.428010	+	1.03068i	0.0183339	+	0.0441495i
$546$		0			0
$547$	−11.1235	−	21.8311i	−0.475607	−	0.933432i	−0.996796	−	0.0799903i	$-0.974511\pi$
$547$	−11.1235	−	21.8311i	−0.475607	−	0.933432i	0.521188	−	0.853442i	$-0.325489\pi$
$548$		0			0
$549$	−3.01795			−0.128803
$550$		0			0
$551$	−51.5261			−2.19508
$552$		0			0
$553$	2.39295	+	4.69644i	0.101759	+	0.199713i
$554$		0			0
$555$	−5.70144	−	13.7295i	−0.242013	−	0.582785i
$556$		0			0
$557$	−18.5955	−	9.47486i	−0.787915	−	0.401463i	0.0132455	−	0.999912i	$-0.495784\pi$
$557$	−18.5955	−	9.47486i	−0.787915	−	0.401463i	−0.801161	+	0.598449i	$0.795784\pi$
$558$		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
$563$	4.35533	+	27.4985i	0.183555	+	1.15892i	0.891623	+	0.452779i	$0.149567\pi$
$563$	4.35533	+	27.4985i	0.183555	+	1.15892i	−0.708068	+	0.706145i	$0.750433\pi$
$564$		0			0
$565$	−26.2777	+	30.8234i	−1.10551	+	1.29675i
$566$		0			0
$567$	3.44750	−	21.7666i	0.144781	−	0.914113i
$568$		0			0
$569$	4.26019	−	13.1115i	0.178596	−	0.549663i	−0.821183	−	0.570665i	$-0.806686\pi$
$569$	4.26019	−	13.1115i	0.178596	−	0.549663i	0.999779	+	0.0210019i	$0.00668560\pi$
$570$		0			0
$571$		−	6.81131i		−	0.285045i	−0.989792	−	0.142522i	$-0.954479\pi$
$571$		−	6.81131i		−	0.285045i	0.989792	−	0.142522i	$-0.0455213\pi$
$572$		0			0
$573$	15.0981	−	15.0981i	0.630733	−	0.630733i
$574$		0			0
$575$	0.00515303	+	2.85945i	0.000214896	+	0.119247i
$576$		0			0
$577$	20.8978	+	3.30988i	0.869986	+	0.137792i	0.575439	−	0.817845i	$-0.304831\pi$
$577$	20.8978	+	3.30988i	0.869986	+	0.137792i	0.294547	+	0.955637i	$0.404831\pi$
$578$		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
$583$	−2.67102	+	5.10167i	−0.110623	+	0.211290i
$584$		0			0
$585$	0.0323465	−	0.415791i	0.00133737	−	0.0171909i
$586$		0			0
$587$	−11.1480	+	21.8792i	−0.460127	+	0.903050i	0.538063	+	0.842905i	$0.319156\pi$
$587$	−11.1480	+	21.8792i	−0.460127	+	0.903050i	−0.998190	+	0.0601452i	$0.980844\pi$
$588$		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	−0.992546	−	0.121869i	$-0.961111\pi$
$593$	−27.1378	−	27.1378i	−1.11442	−	1.11442i	−0.121869	−	0.992546i	$-0.538889\pi$
$594$		0			0
$595$	17.6478	+	4.22004i	0.723488	+	0.173005i
$596$		0			0
$597$	13.1982	−	6.72482i	0.540167	−	0.275229i
$598$		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
$603$	3.27817	−	0.519211i	0.133497	−	0.0211439i
$604$		0			0
$605$	19.0388	−	15.5732i	0.774036	−	0.633141i
$606$		0			0
$607$	−14.2838	+	2.26233i	−0.579762	+	0.0918253i	−0.439426	−	0.898279i	$-0.644818\pi$
$607$	−14.2838	+	2.26233i	−0.579762	+	0.0918253i	−0.140336	+	0.990104i	$0.544818\pi$
$608$		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
$613$	−30.9853	+	15.7878i	−1.25149	+	0.637664i	−0.948936	−	0.315470i	$-0.897838\pi$
$613$	−30.9853	+	15.7878i	−1.25149	+	0.637664i	−0.302550	+	0.953134i	$0.597838\pi$
$614$		0			0
$615$	23.7944	−	14.6107i	0.959482	−	0.589161i
$616$		0			0
$617$	−0.800590	−	0.800590i	−0.0322306	−	0.0322306i	0.690808	−	0.723038i	$-0.257255\pi$
$617$	−0.800590	−	0.800590i	−0.0322306	−	0.0322306i	−0.723038	+	0.690808i	$0.757255\pi$
$618$		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
$623$	13.3844	−	26.2683i	0.536234	−	1.05242i
$624$		0			0
$625$	−0.0901049	−	24.9998i	−0.00360420	−	0.999994i
$626$		0			0
$627$	18.1664	−	34.6980i	0.725497	−	1.38570i
$628$		0			0
$629$	−9.69993	−	7.04741i	−0.386761	−	0.280999i
$630$		0			0
$631$	0.103041	+	0.317127i	0.00410199	+	0.0126246i	0.953087	−	0.302698i	$-0.0978873\pi$
$631$	0.103041	+	0.317127i	0.00410199	+	0.0126246i	−0.948985	+	0.315322i	$0.897887\pi$
$632$		0			0
$633$	16.9177	+	2.67950i	0.672418	+	0.106500i
$634$		0			0
$635$	−25.3248	+	6.10408i	−1.00498	+	0.242233i
$636$		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
$643$	−5.87523	+	37.0947i	−0.231696	+	1.46287i	0.547875	+	0.836560i	$0.315437\pi$
$643$	−5.87523	+	37.0947i	−0.231696	+	1.46287i	−0.779572	+	0.626313i	$0.784563\pi$
$644$		0			0
$645$	3.57285	−	0.284428i	0.140681	−	0.0111994i
$646$		0			0
$647$	−0.471294	−	2.97563i	−0.0185285	−	0.116984i	0.976691	−	0.214652i	$-0.0688617\pi$
$647$	−0.471294	−	2.97563i	−0.0185285	−	0.116984i	−0.995219	+	0.0976678i	$0.968862\pi$
$648$		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
$653$	14.7169	+	7.49862i	0.575916	+	0.293444i	0.717586	−	0.696470i	$-0.245247\pi$
$653$	14.7169	+	7.49862i	0.575916	+	0.293444i	−0.141670	+	0.989914i	$0.545247\pi$
$654$		0			0
$655$	−18.1716	+	7.54613i	−0.710025	+	0.294852i
$656$		0			0
$657$	−1.48706	−	2.91853i	−0.0580159	−	0.113863i
$658$		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
$663$	1.47160	+	2.88818i	0.0571523	+	0.112168i
$664$		0			0
$665$	40.4031	+	16.6929i	1.56676	+	0.647322i
$666$		0			0
$667$	3.66549	+	1.86766i	0.141928	+	0.0723160i
$668$		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
$673$	−3.12248	−	19.7146i	−0.120363	−	0.759941i	−0.971856	−	0.235576i	$-0.924302\pi$
$673$	−3.12248	−	19.7146i	−0.120363	−	0.759941i	0.851493	−	0.524366i	$-0.175698\pi$
$674$		0			0
$675$	−21.8586	+	15.9415i	−0.841339	+	0.613588i
$676$		0			0
$677$	0.658819	−	4.15962i	0.0253205	−	0.159867i	−0.971788	−	0.235855i	$-0.924211\pi$
$677$	0.658819	−	4.15962i	0.0253205	−	0.159867i	0.997109	+	0.0759877i	$0.0242110\pi$
$678$		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	$-0.650110\pi$
$683$	11.4089	−	11.4089i	0.436550	−	0.436550i	0.890849	+	0.454299i	$0.150110\pi$
$684$		0			0
$685$	−1.50130	−	6.22865i	−0.0573618	−	0.237984i
$686$		0			0
$687$	−13.6151	−	2.15641i	−0.519447	−	0.0822723i
$688$		0			0
$689$	−0.354820	−	1.09202i	−0.0135176	−	0.0416028i
$690$		0			0
$691$	−29.2679	−	21.2644i	−1.11340	−	0.808934i	−0.130207	−	0.991487i	$-0.541564\pi$
$691$	−29.2679	−	21.2644i	−1.11340	−	0.808934i	−0.983196	+	0.182553i	$0.941564\pi$
$692$		0			0
$693$	0.427288	−	2.51701i	0.0162313	−	0.0956134i
$694$		0			0
$695$	−8.22725	+	7.03957i	−0.312077	+	0.267026i
$696$		0			0
$697$	10.2236	−	20.0650i	0.387247	−	0.760015i
$698$		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
$707$	−18.3403	+	9.34485i	−0.689758	+	0.351449i
$708$		0			0
$709$	−17.5377	−	24.1385i	−0.658641	−	0.906542i	0.340794	−	0.940138i	$-0.389304\pi$
$709$	−17.5377	−	24.1385i	−0.658641	−	0.906542i	−0.999435	+	0.0335959i	$0.989304\pi$
$710$		0			0
$711$	−0.517996	+	0.168307i	−0.0194264	+	0.00631201i
$712$		0			0
$713$	−3.06807	+	0.485935i	−0.114900	+	0.0181984i
$714$		0			0
$715$	−0.434530	+	4.88512i	−0.0162505	+	0.182693i
$716$		0			0
$717$	−49.4569	+	7.83320i	−1.84700	+	0.292536i
$718$		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
$723$	−41.2624	+	21.0243i	−1.53457	+	0.781901i
$724$		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	$-0.337786\pi$
$727$	−10.3834	−	10.3834i	−0.385099	−	0.385099i	−0.872935	+	0.487836i	$0.837786\pi$
$728$		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
$733$	12.4945	−	24.5219i	0.461497	−	0.905738i	−0.536586	−	0.843846i	$-0.680286\pi$
$733$	12.4945	−	24.5219i	0.461497	−	0.905738i	0.998083	−	0.0618926i	$-0.0197136\pi$
$734$		0			0
$735$	−1.65200	−	0.128518i	−0.0609350	−	0.00474044i
$736$		0			0
$737$	−38.6160	+	5.67842i	−1.42244	+	0.209167i
$738$		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
$743$	49.4995	+	7.83995i	1.81596	+	0.287620i	0.969547	−	0.244906i	$-0.0787572\pi$
$743$	49.4995	+	7.83995i	1.81596	+	0.287620i	0.846414	+	0.532526i	$0.178757\pi$
$744$		0			0
$745$	19.8555	+	12.1429i	0.727449	+	0.444880i
$746$		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	−0.817545	−	0.575864i	$-0.804666\pi$
$751$	4.99712	−	15.3795i	0.182347	−	0.561208i	0.999893	+	0.0146569i	$0.00466559\pi$
$752$		0			0
$753$	0.713972	−	4.50784i	0.0260186	−	0.164275i
$754$		0			0
$755$	−0.618835	−	7.77349i	−0.0225217	−	0.282906i
$756$		0			0
$757$	−3.83230	−	24.1962i	−0.139287	−	0.879426i	−0.954054	−	0.299636i	$-0.903135\pi$
$757$	−3.83230	−	24.1962i	−0.139287	−	0.879426i	0.814766	−	0.579790i	$-0.196865\pi$
$758$		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
$763$	−1.21375	−	0.618437i	−0.0439408	−	0.0223889i
$764$		0			0
$765$	−0.715963	+	1.73290i	−0.0258857	+	0.0626532i
$766$		0			0
$767$	0.871825	+	1.71105i	0.0314798	+	0.0617825i
$768$		0			0
$769$	−10.2732			−0.370462			−0.185231	−	0.982695i	$-0.559303\pi$
$769$	−10.2732			−0.370462			−0.185231	+	0.982695i	$0.559303\pi$
$770$		0			0
$771$	24.2235			0.872389
$772$		0			0
$773$	18.5975	+	36.4996i	0.668904	+	1.31280i	0.936974	+	0.349399i	$0.113614\pi$
$773$	18.5975	+	36.4996i	0.668904	+	1.31280i	−0.268070	+	0.963400i	$0.586386\pi$
$774$		0			0
$775$	26.8163	−	4.29683i	0.963268	−	0.154347i
$776$		0			0
$777$	16.1682	+	8.23809i	0.580030	+	0.295540i
$778$		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
$783$	6.08884	+	38.4435i	0.217598	+	1.37386i
$784$		0			0
$785$	35.4514	+	30.2231i	1.26531	+	1.07871i
$786$		0			0
$787$	0.368757	−	2.32824i	0.0131448	−	0.0829927i	−0.980244	−	0.197793i	$-0.936623\pi$
$787$	0.368757	−	2.32824i	0.0131448	−	0.0829927i	0.993389	+	0.114800i	$0.0366227\pi$
$788$		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
$795$	−3.33944	+	5.46051i	−0.118438	+	0.193664i
$796$		0			0
$797$	7.59442	+	1.20284i	0.269008	+	0.0426067i	0.289481	−	0.957184i	$-0.406517\pi$
$797$	7.59442	+	1.20284i	0.269008	+	0.0426067i	−0.0204731	+	0.999790i	$0.506517\pi$
$798$		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
$803$	17.1064	+	34.5130i	0.603670	+	1.21794i
$804$		0			0
$805$	−2.26915	−	2.65199i	−0.0799771	−	0.0934704i
$806$		0			0
$807$	−2.64559	+	5.19226i	−0.0931291	+	0.182776i
$808$		0			0
$809$	27.0136	−	19.6265i	0.949747	−	0.690032i	−0.000999838	−	1.00000i	$-0.500318\pi$
$809$	27.0136	−	19.6265i	0.949747	−	0.690032i	0.950747	+	0.309968i	$0.100318\pi$
$810$		0			0
$811$	51.0085	+	16.5737i	1.79115	+	0.581980i	0.999577	−	0.0290941i	$-0.00926225\pi$
$811$	51.0085	+	16.5737i	1.79115	+	0.581980i	0.791573	+	0.611074i	$0.209262\pi$
$812$		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
$817$	6.20510	−	3.16166i	0.217089	−	0.110612i
$818$		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
$823$	17.4991	−	2.77159i	0.609981	−	0.0966115i	0.156201	−	0.987725i	$-0.450075\pi$
$823$	17.4991	−	2.77159i	0.609981	−	0.0966115i	0.453780	+	0.891114i	$0.350075\pi$
$824$		0			0
$825$	22.2661	−	15.8638i	0.775207	−	0.552308i
$826$		0			0
$827$	36.3060	−	5.75031i	1.26248	−	0.199958i	0.510926	−	0.859625i	$-0.329303\pi$
$827$	36.3060	−	5.75031i	1.26248	−	0.199958i	0.751558	+	0.659667i	$0.229303\pi$
$828$		0			0
$829$	−46.4693	+	15.0988i	−1.61395	+	0.524403i	−0.970503	−	0.241090i	$-0.922495\pi$
$829$	−46.4693	+	15.0988i	−1.61395	+	0.524403i	−0.643444	+	0.765493i	$0.722495\pi$
$830$		0			0
$831$	11.2414	+	15.4725i	0.389961	+	0.536736i
$832$		0			0
$833$	−1.19072	+	0.606703i	−0.0412561	+	0.0210210i
$834$		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
$843$	8.18347	−	16.0610i	0.281854	−	0.553169i
$844$		0			0
$845$	18.2629	+	21.3441i	0.628262	+	0.734259i
$846$		0			0
$847$	−5.35241	+	29.5422i	−0.183911	+	1.01508i
$848$		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
$853$	41.1879	+	6.52352i	1.41025	+	0.223361i	0.814664	−	0.579934i	$-0.196922\pi$
$853$	41.1879	+	6.52352i	1.41025	+	0.223361i	0.595582	+	0.803295i	$0.296922\pi$
$854$		0			0
$855$	−2.35676	+	3.85368i	−0.0805995	+	0.131793i
$856$		0			0
$857$	10.0809	−	10.0809i	0.344355	−	0.344355i	−0.513647	−	0.858002i	$-0.671706\pi$
$857$	10.0809	−	10.0809i	0.344355	−	0.344355i	0.858002	+	0.513647i	$0.171706\pi$
$858$		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
$863$	3.55801	−	22.4644i	0.121116	−	0.764696i	−0.850122	−	0.526586i	$-0.823472\pi$
$863$	3.55801	−	22.4644i	0.121116	−	0.764696i	0.971238	−	0.238110i	$-0.0765280\pi$
$864$		0			0
$865$	−30.1071	−	25.6670i	−1.02367	−	0.872704i
$866$		0			0
$867$	2.10458	+	13.2878i	0.0714754	+	0.451278i
$868$		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
$873$	4.38100	+	2.23223i	0.148274	+	0.0755496i
$874$		0			0
$875$	19.8808	+	23.1504i	0.672093	+	0.782626i
$876$		0			0
$877$	3.58348	+	7.03297i	0.121005	+	0.237487i	0.943561	−	0.331198i	$-0.107453\pi$
$877$	3.58348	+	7.03297i	0.121005	+	0.237487i	−0.822556	+	0.568684i	$0.807453\pi$
$878$		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
$883$	−3.21785	−	6.31538i	−0.108289	−	0.212529i	0.830502	−	0.557015i	$-0.188053\pi$
$883$	−3.21785	−	6.31538i	−0.108289	−	0.212529i	−0.938792	+	0.344485i	$0.888053\pi$
$884$		0			0
$885$	4.08769	−	9.89377i	0.137406	−	0.332575i
$886$		0			0
$887$	−39.3366	−	20.0430i	−1.32079	−	0.672978i	−0.355630	−	0.934627i	$-0.615734\pi$
$887$	−39.3366	−	20.0430i	−1.32079	−	0.672978i	−0.965163	+	0.261649i	$0.915734\pi$
$888$		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
$893$	11.3339	+	71.5594i	0.379274	+	2.39464i
$894$		0			0
$895$	1.52397	+	19.1433i	0.0509407	+	0.639891i
$896$		0			0
$897$	0.0975378	−	0.615830i	0.00325669	−	0.0205620i
$898$		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
$905$	−29.8515	−	18.2560i	−0.992296	−	0.606851i
$906$		0			0
$907$	4.53051	+	0.717563i	0.150433	+	0.0238263i	0.231197	−	0.972907i	$-0.425736\pi$
$907$	4.53051	+	0.717563i	0.150433	+	0.0238263i	−0.0807636	+	0.996733i	$0.525736\pi$
$908$		0			0
$909$	−0.657265	−	2.02285i	−0.0218001	−	0.0670938i
$910$		0			0
$911$	−16.0774	−	11.6809i	−0.532668	−	0.387006i	0.288687	−	0.957424i	$-0.406781\pi$
$911$	−16.0774	−	11.6809i	−0.532668	−	0.387006i	−0.821355	+	0.570418i	$0.806781\pi$
$912$		0			0
$913$	−20.7769	+	20.3216i	−0.687616	+	0.672548i
$914$		0			0
$915$	39.3291	+	3.05961i	1.30018	+	0.101148i
$916$		0			0
$917$	10.9035	−	21.3993i	0.360065	−	0.706668i
$918$		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
$927$	3.29911	−	1.68098i	0.108357	−	0.0552106i
$928$		0			0
$929$	2.73706	+	3.76724i	0.0898000	+	0.123599i	0.851553	−	0.524268i	$-0.175661\pi$
$929$	2.73706	+	3.76724i	0.0898000	+	0.123599i	−0.761753	+	0.647867i	$0.775661\pi$
$930$		0			0
$931$	−3.06202	+	0.994912i	−0.100354	+	0.0326069i
$932$		0			0
$933$	13.0563	−	2.06791i	0.427444	−	0.0677005i
$934$		0			0
$935$	8.64482	−	20.2841i	0.282716	−	0.663362i
$936$		0			0
$937$	−23.1004	+	3.65875i	−0.754658	+	0.119526i	−0.521898	−	0.853008i	$-0.674776\pi$
$937$	−23.1004	+	3.65875i	−0.754658	+	0.119526i	−0.232760	+	0.972534i	$0.574776\pi$
$938$		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
$943$	−3.85954	+	1.96653i	−0.125684	+	0.0640391i
$944$		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	$-0.201273\pi$
$947$	6.63605	+	6.63605i	0.215643	+	0.215643i	−0.591017	+	0.806659i	$0.701273\pi$
$948$		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
$953$	3.58309	−	7.03220i	0.116068	−	0.227795i	−0.825663	−	0.564164i	$-0.809199\pi$
$953$	3.58309	−	7.03220i	0.116068	−	0.227795i	0.941731	+	0.336368i	$0.109199\pi$
$954$		0			0
$955$	22.0045	−	18.8279i	0.712048	−	0.609257i
$956$		0			0
$957$	−5.72231	−	38.9144i	−0.184976	−	1.25793i
$958$		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
$963$	−2.94949	−	0.467153i	−0.0950460	−	0.0150538i
$964$		0			0
$965$	4.59131	+	19.0485i	0.147799	+	0.613194i
$966$		0			0
$967$	−23.5445	+	23.5445i	−0.757141	+	0.757141i	−0.975801	−	0.218660i	$-0.929831\pi$
$967$	−23.5445	+	23.5445i	−0.757141	+	0.757141i	0.218660	+	0.975801i	$0.429831\pi$
$968$		0			0
$969$		−	35.1098i		−	1.12789i
$970$		0			0
$971$	−7.03544	+	21.6529i	−0.225778	+	0.694873i	0.772434	+	0.635095i	$0.219039\pi$
$971$	−7.03544	+	21.6529i	−0.225778	+	0.694873i	−0.998212	+	0.0597777i	$0.980961\pi$
$972$		0			0
$973$	2.06754	−	13.0539i	0.0662823	−	0.418490i
$974$		0			0
$975$	−0.843062	+	5.38568i	−0.0269996	+	0.172480i
$976$		0			0
$977$	4.85790	+	30.6715i	0.155418	+	0.981270i	0.934917	+	0.354866i	$0.115474\pi$
$977$	4.85790	+	30.6715i	0.155418	+	0.981270i	−0.779499	+	0.626403i	$0.784526\pi$
$978$		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
$983$	−19.3389	−	9.85367i	−0.616816	−	0.314283i	0.117519	−	0.993071i	$-0.462506\pi$
$983$	−19.3389	−	9.85367i	−0.616816	−	0.314283i	−0.734335	+	0.678787i	$0.762506\pi$
$984$		0			0
$985$	35.0456	+	14.4794i	1.11664	+	0.461351i
$986$		0			0
$987$	−20.6628	−	40.5531i	−0.657705	−	1.29082i
$988$		0			0
$989$	−0.556022			−0.0176805
$990$		0			0
$991$	−53.4629			−1.69830			−0.849152	−	0.528148i	$-0.822887\pi$
$991$	−53.4629			−1.69830			−0.849152	+	0.528148i	$0.822887\pi$
$992$		0			0
$993$	−6.68566	−	13.1214i	−0.212163	−	0.416394i
$994$		0			0
$995$	18.5545	−	7.70513i	0.588218	−	0.244269i
$996$		0			0
$997$	21.5590	+	10.9849i	0.682780	+	0.347894i	0.760735	−	0.649063i	$-0.224839\pi$
$997$	21.5590	+	10.9849i	0.682780	+	0.347894i	−0.0779545	+	0.996957i	$0.524839\pi$
$998$		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	880.2.cm.b.337.5		48
4.3	odd	2		220.2.u.a.117.2	yes	48
5.3	odd	4	inner	880.2.cm.b.513.2		48
11.8	odd	10	inner	880.2.cm.b.657.2		48
20.3	even	4		220.2.u.a.73.5	✓	48
44.19	even	10		220.2.u.a.217.5	yes	48
55.8	even	20	inner	880.2.cm.b.833.5		48
220.63	odd	20		220.2.u.a.173.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.u.a.73.5	✓	48	20.3	even	4
220.2.u.a.117.2	yes	48	4.3	odd	2
220.2.u.a.173.2	yes	48	220.63	odd	20
220.2.u.a.217.5	yes	48	44.19	even	10
880.2.cm.b.337.5		48	1.1	even	1	trivial
880.2.cm.b.513.2		48	5.3	odd	4	inner
880.2.cm.b.657.2		48	11.8	odd	10	inner
880.2.cm.b.833.5		48	55.8	even	20	inner

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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cm (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.748461 + 1.46894i) q^{3} +(0.857567 + 2.06509i) q^{5} +(-2.43189 - 1.23911i) q^{7} +(0.165773 - 0.228167i) q^{9} +O(q^{10})\)	\(q+(0.748461 + 1.46894i) q^{3} +(0.857567 + 2.06509i) q^{5} +(-2.43189 - 1.23911i) q^{7} +(0.165773 - 0.228167i) q^{9} +(-1.97907 + 2.66145i) q^{11} +(-0.103452 - 0.653168i) q^{13} +(-2.39163 + 2.80535i) q^{15} +(-0.465103 + 2.93654i) q^{17} +(-2.21346 + 6.81233i) q^{19} -4.49972i q^{21} +(0.404388 - 0.404388i) q^{23} +(-3.52916 + 3.54190i) q^{25} +(5.34423 + 0.846442i) q^{27} +(2.22290 + 6.84138i) q^{29} +(-4.39431 - 3.19265i) q^{31} +(-5.39075 - 0.915135i) q^{33} +(0.473359 - 6.08468i) q^{35} +(-1.83080 + 3.59315i) q^{37} +(0.882034 - 0.640835i) q^{39} +(-7.20357 - 2.34058i) q^{41} +(-0.687486 - 0.687486i) q^{43} +(0.613346 + 0.146667i) q^{45} +(9.01236 - 4.59203i) q^{47} +(0.264199 + 0.363639i) q^{49} +(-4.66171 + 1.51468i) q^{51} +(1.71491 - 0.271614i) q^{53} +(-7.19330 - 1.80457i) q^{55} +(-11.6636 + 1.84733i) q^{57} +(-2.76174 + 0.897345i) q^{59} +(-6.28978 - 8.65715i) q^{61} +(-0.685866 + 0.349466i) q^{63} +(1.26013 - 0.773772i) q^{65} +(8.32148 + 8.32148i) q^{67} +(0.896689 + 0.291352i) q^{69} +(8.26577 - 6.00543i) q^{71} +(5.27272 - 10.3483i) q^{73} +(-7.84426 - 2.53314i) q^{75} +(8.11070 - 4.02007i) q^{77} +(-1.56236 - 1.13512i) q^{79} +(2.49512 + 7.67918i) q^{81} +(8.65490 + 1.37080i) q^{83} +(-6.46307 + 1.55781i) q^{85} +(-8.38581 + 8.38581i) q^{87} +10.8016i q^{89} +(-0.557764 + 1.71662i) q^{91} +(1.40084 - 8.84454i) q^{93} +(-15.9662 + 1.27105i) q^{95} +(2.72728 + 17.2194i) q^{97} +(0.279179 + 0.892754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{3} + 4 q^{5} - 10 q^{7}+O(q^{10}) \) 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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