LMFDB - Embedded newform 880.2.cm.a.193.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [880,2,Mod(17,880)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [32,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 55)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			193.3
Character	$\chi$	$=$	880.193
Dual form			880.2.cm.a.497.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.130227 + 0.822224i) q^{3} +(-1.11862 + 1.93615i) q^{5} +(4.16343 + 0.659422i) q^{7} +(2.19408 - 0.712899i) q^{9} +(0.920480 - 3.18633i) q^{11} +(-0.824787 - 0.420250i) q^{13} +(-1.73763 - 0.667616i) q^{15} +(1.71765 - 0.875188i) q^{17} +(4.39439 + 3.19271i) q^{19} +3.50915i q^{21} +(-1.95998 - 1.95998i) q^{23} +(-2.49738 - 4.33164i) q^{25} +(2.00570 + 3.93640i) q^{27} +(0.810497 - 0.588860i) q^{29} +(-0.131006 - 0.403196i) q^{31} +(2.73975 + 0.341892i) q^{33} +(-5.93404 + 7.32339i) q^{35} +(-0.771690 + 4.87226i) q^{37} +(0.238130 - 0.732888i) q^{39} +(0.339428 - 0.467182i) q^{41} +(-5.05373 + 5.05373i) q^{43} +(-1.07406 + 5.04553i) q^{45} +(1.17495 - 0.186094i) q^{47} +(10.2419 + 3.32780i) q^{49} +(0.943286 + 1.29832i) q^{51} +(-4.12294 + 8.09173i) q^{53} +(5.13956 + 5.34649i) q^{55} +(-2.05285 + 4.02895i) q^{57} +(-5.47214 - 7.53175i) q^{59} +(7.40093 + 2.40471i) q^{61} +(9.60498 - 1.52128i) q^{63} +(1.73629 - 1.12681i) q^{65} +(3.05526 - 3.05526i) q^{67} +(1.35630 - 1.86679i) q^{69} +(-2.65487 + 8.17086i) q^{71} +(-0.854195 + 5.39318i) q^{73} +(3.23635 - 2.61750i) q^{75} +(5.93349 - 12.6591i) q^{77} +(0.705861 + 2.17242i) q^{79} +(2.62377 - 1.90628i) q^{81} +(-0.902846 - 1.77193i) q^{83} +(-0.226904 + 4.30464i) q^{85} +(0.589724 + 0.589724i) q^{87} -13.9313i q^{89} +(-3.15682 - 2.29356i) q^{91} +(0.314457 - 0.160224i) q^{93} +(-11.0972 + 4.93678i) q^{95} +(-2.96200 - 1.50922i) q^{97} +(-0.251929 - 7.64727i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} - 2 q^{5} + 24 q^{11} - 10 q^{13} - 14 q^{15} + 24 q^{23} + 16 q^{25} + 16 q^{27} + 28 q^{31} + 66 q^{33} + 10 q^{35} - 8 q^{37} + 40 q^{41} - 28 q^{45} + 28 q^{47} - 20 q^{51} - 24 q^{53}+ \cdots - 8 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 - 2 * q^5 + 24 * q^11 - 10 * q^13 - 14 * q^15 + 24 * q^23 + 16 * q^25 + 16 * q^27 + 28 * q^31 + 66 * q^33 + 10 * q^35 - 8 * q^37 + 40 * q^41 - 28 * q^45 + 28 * q^47 - 20 * q^51 - 24 * q^53 + 64 * q^55 + 30 * q^57 - 60 * q^61 + 30 * q^63 + 8 * q^67 - 24 * q^71 + 50 * q^73 - 34 * q^75 + 70 * q^77 - 12 * q^81 - 90 * q^83 + 30 * q^85 - 20 * q^91 - 8 * q^93 + 40 * q^95 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{9}{10}\right)$	$1$

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
$3$	0.130227	+	0.822224i	0.0751869	+	0.474711i	0.996338	+	0.0855054i	$0.0272505\pi$
$3$	0.130227	+	0.822224i	0.0751869	+	0.474711i	−0.921151	+	0.389206i	$0.872750\pi$
$4$		0			0
$5$	−1.11862	+	1.93615i	−0.500262	+	0.865874i
$5$	−1.11862	+	1.93615i	−0.500262	+	0.865874i
$6$		0			0
$7$	4.16343	+	0.659422i	1.57363	+	0.249238i	0.881375	−	0.472417i	$-0.156618\pi$
$7$	4.16343	+	0.659422i	1.57363	+	0.249238i	0.692253	+	0.721655i	$0.256618\pi$
$8$		0			0
$9$	2.19408	−	0.712899i	0.731359	−	0.237633i
$10$		0			0
$11$	0.920480	−	3.18633i	0.277535	−	0.960716i
$11$	0.920480	−	3.18633i	0.277535	−	0.960716i
$12$		0			0
$13$	−0.824787	−	0.420250i	−0.228755	−	0.116556i	0.335857	−	0.941913i	$-0.390974\pi$
$13$	−0.824787	−	0.420250i	−0.228755	−	0.116556i	−0.564612	+	0.825357i	$0.690974\pi$
$14$		0			0
$15$	−1.73763	−	0.667616i	−0.448653	−	0.172378i
$16$		0			0
$17$	1.71765	−	0.875188i	0.416592	−	0.212264i	−0.233115	−	0.972449i	$-0.574892\pi$
$17$	1.71765	−	0.875188i	0.416592	−	0.212264i	0.649707	+	0.760185i	$0.274892\pi$
$18$		0			0
$19$	4.39439	+	3.19271i	1.00814	+	0.732458i	0.963818	−	0.266560i	$-0.0858869\pi$
$19$	4.39439	+	3.19271i	1.00814	+	0.732458i	0.0443230	+	0.999017i	$0.485887\pi$
$20$		0			0
$21$			3.50915i			0.765758i
$22$		0			0
$23$	−1.95998	−	1.95998i	−0.408685	−	0.408685i	0.472595	−	0.881280i	$-0.343317\pi$
$23$	−1.95998	−	1.95998i	−0.408685	−	0.408685i	−0.881280	+	0.472595i	$0.843317\pi$
$24$		0			0
$25$	−2.49738	−	4.33164i	−0.499475	−	0.866328i
$26$		0			0
$27$	2.00570	+	3.93640i	0.385996	+	0.757561i
$28$		0			0
$29$	0.810497	−	0.588860i	0.150505	−	0.109349i	−0.509984	−	0.860184i	$-0.670349\pi$
$29$	0.810497	−	0.588860i	0.150505	−	0.109349i	0.660490	+	0.750835i	$0.270349\pi$
$30$		0			0
$31$	−0.131006	−	0.403196i	−0.0235294	−	0.0724161i	0.938602	−	0.345001i	$-0.112121\pi$
$31$	−0.131006	−	0.403196i	−0.0235294	−	0.0724161i	−0.962132	+	0.272585i	$0.912121\pi$
$32$		0			0
$33$	2.73975	+	0.341892i	0.476929	+	0.0595158i
$34$		0			0
$35$	−5.93404	+	7.32339i	−1.00304	+	1.23788i
$36$		0			0
$37$	−0.771690	+	4.87226i	−0.126865	+	0.800995i	0.839413	+	0.543494i	$0.182899\pi$
$37$	−0.771690	+	4.87226i	−0.126865	+	0.800995i	−0.966278	+	0.257501i	$0.917101\pi$
$38$		0			0
$39$	0.238130	−	0.732888i	0.0381313	−	0.117356i
$40$		0			0
$41$	0.339428	−	0.467182i	0.0530097	−	0.0729616i	−0.781689	−	0.623668i	$-0.785642\pi$
$41$	0.339428	−	0.467182i	0.0530097	−	0.0729616i	0.834699	+	0.550707i	$0.185642\pi$
$42$		0			0
$43$	−5.05373	+	5.05373i	−0.770687	+	0.770687i	−0.978227	−	0.207540i	$-0.933454\pi$
$43$	−5.05373	+	5.05373i	−0.770687	+	0.770687i	0.207540	+	0.978227i	$0.433454\pi$
$44$		0			0
$45$	−1.07406	+	5.04553i	−0.160111	+	0.752143i
$46$		0			0
$47$	1.17495	−	0.186094i	0.171384	−	0.0271446i	−0.0701524	−	0.997536i	$-0.522349\pi$
$47$	1.17495	−	0.186094i	0.171384	−	0.0271446i	0.241537	+	0.970392i	$0.422349\pi$
$48$		0			0
$49$	10.2419	+	3.32780i	1.46313	+	0.475400i
$50$		0			0
$51$	0.943286	+	1.29832i	0.132086	+	0.181801i
$52$		0			0
$53$	−4.12294	+	8.09173i	−0.566330	+	1.11149i	0.413285	+	0.910602i	$0.364381\pi$
$53$	−4.12294	+	8.09173i	−0.566330	+	1.11149i	−0.979615	+	0.200883i	$0.935619\pi$
$54$		0			0
$55$	5.13956	+	5.34649i	0.693018	+	0.720920i
$56$		0			0
$57$	−2.05285	+	4.02895i	−0.271907	+	0.533647i
$58$		0			0
$59$	−5.47214	−	7.53175i	−0.712411	−	0.980550i	−0.999742	−	0.0227186i	$-0.992768\pi$
$59$	−5.47214	−	7.53175i	−0.712411	−	0.980550i	0.287331	−	0.957831i	$-0.407232\pi$
$60$		0			0
$61$	7.40093	+	2.40471i	0.947591	+	0.307891i	0.741737	−	0.670691i	$-0.234002\pi$
$61$	7.40093	+	2.40471i	0.947591	+	0.307891i	0.205855	+	0.978583i	$0.434002\pi$
$62$		0			0
$63$	9.60498	−	1.52128i	1.21011	−	0.191663i
$64$		0			0
$65$	1.73629	−	1.12681i	0.215361	−	0.139764i
$66$		0			0
$67$	3.05526	−	3.05526i	0.373259	−	0.373259i	−0.495404	−	0.868663i	$-0.664980\pi$
$67$	3.05526	−	3.05526i	0.373259	−	0.373259i	0.868663	+	0.495404i	$0.164980\pi$
$68$		0			0
$69$	1.35630	−	1.86679i	0.163280	−	0.224735i
$70$		0			0
$71$	−2.65487	+	8.17086i	−0.315075	+	0.969702i	0.660648	+	0.750696i	$0.270282\pi$
$71$	−2.65487	+	8.17086i	−0.315075	+	0.969702i	−0.975723	+	0.219006i	$0.929718\pi$
$72$		0			0
$73$	−0.854195	+	5.39318i	−0.0999760	+	0.631224i	0.885917	+	0.463844i	$0.153530\pi$
$73$	−0.854195	+	5.39318i	−0.0999760	+	0.631224i	−0.985893	+	0.167379i	$0.946470\pi$
$74$		0			0
$75$	3.23635	−	2.61750i	0.373702	−	0.302243i
$76$		0			0
$77$	5.93349	−	12.6591i	0.676184	−	1.44264i
$78$		0			0
$79$	0.705861	+	2.17242i	0.0794156	+	0.244416i	0.982880	−	0.184247i	$-0.0589847\pi$
$79$	0.705861	+	2.17242i	0.0794156	+	0.244416i	−0.903464	+	0.428663i	$0.858985\pi$
$80$		0			0
$81$	2.62377	−	1.90628i	0.291530	−	0.211809i
$82$		0			0
$83$	−0.902846	−	1.77193i	−0.0991002	−	0.194495i	0.836134	−	0.548526i	$-0.184811\pi$
$83$	−0.902846	−	1.77193i	−0.0991002	−	0.194495i	−0.935234	+	0.354031i	$0.884811\pi$
$84$		0			0
$85$	−0.226904	+	4.30464i	−0.0246112	+	0.466904i
$86$		0			0
$87$	0.589724	+	0.589724i	0.0632250	+	0.0632250i
$88$		0			0
$89$		−	13.9313i		−	1.47671i	−0.674410	−	0.738357i	$-0.735602\pi$
$89$		−	13.9313i		−	1.47671i	0.674410	−	0.738357i	$-0.264398\pi$
$90$		0			0
$91$	−3.15682	−	2.29356i	−0.330925	−	0.240431i
$92$		0			0
$93$	0.314457	−	0.160224i	0.0326076	−	0.0166144i
$94$		0			0
$95$	−11.0972	+	4.93678i	−1.13855	+	0.506502i
$96$		0			0
$97$	−2.96200	−	1.50922i	−0.300746	−	0.153238i	0.297105	−	0.954845i	$-0.403979\pi$
$97$	−2.96200	−	1.50922i	−0.300746	−	0.153238i	−0.597851	+	0.801607i	$0.703979\pi$
$98$		0			0
$99$	−0.251929	−	7.64727i	−0.0253199	−	0.768579i
$100$		0			0
$101$	−12.6404	+	4.10712i	−1.25777	+	0.408673i	−0.860698	−	0.509116i	$-0.829973\pi$
$101$	−12.6404	+	4.10712i	−1.25777	+	0.408673i	−0.397069	+	0.917789i	$0.629973\pi$
$102$		0			0
$103$	9.95825	+	1.57723i	0.981215	+	0.155409i	0.626378	−	0.779519i	$-0.284536\pi$
$103$	9.95825	+	1.57723i	0.981215	+	0.155409i	0.354837	+	0.934928i	$0.384536\pi$
$104$		0			0
$105$	−6.79424	−	3.92540i	−0.663050	−	0.383080i
$106$		0			0
$107$	−0.964682	−	6.09076i	−0.0932593	−	0.588816i	−0.989419	−	0.145085i	$-0.953654\pi$
$107$	−0.964682	−	6.09076i	−0.0932593	−	0.588816i	0.896160	−	0.443731i	$-0.146346\pi$
$108$		0			0
$109$	−19.9193			−1.90793			−0.953964	−	0.299922i	$-0.903039\pi$
$109$	−19.9193			−1.90793			−0.953964	+	0.299922i	$0.903039\pi$
$110$		0			0
$111$	−4.10659			−0.389780
$112$		0			0
$113$	−1.89632	−	11.9729i	−0.178391	−	1.12632i	−0.900602	−	0.434644i	$-0.856874\pi$
$113$	−1.89632	−	11.9729i	−0.178391	−	1.12632i	0.722211	−	0.691673i	$-0.243126\pi$
$114$		0			0
$115$	5.98731	−	1.60235i	0.558319	−	0.149420i
$116$		0			0
$117$	−2.10924	−	0.334071i	−0.194999	−	0.0308849i
$118$		0			0
$119$	7.72845	−	2.51112i	0.708465	−	0.230194i
$120$		0			0
$121$	−9.30543	−	5.86591i	−0.845949	−	0.533265i
$122$		0			0
$123$	0.428331	+	0.218246i	0.0386213	+	0.0196785i
$124$		0			0
$125$	11.1803	+	0.0101588i	1.00000	+	0.000908633i
$126$		0			0
$127$	1.03315	−	0.526416i	0.0916772	−	0.0467119i	−0.407551	−	0.913183i	$-0.633617\pi$
$127$	1.03315	−	0.526416i	0.0916772	−	0.0467119i	0.499228	+	0.866471i	$0.333617\pi$
$128$		0			0
$129$	−4.81343	−	3.49716i	−0.423799	−	0.307908i
$130$		0			0
$131$		−	14.4532i		−	1.26278i	−0.775465	−	0.631390i	$-0.782485\pi$
$131$		−	14.4532i		−	1.26278i	0.775465	−	0.631390i	$-0.217515\pi$
$132$		0			0
$133$	16.1904	+	16.1904i	1.40388	+	1.40388i
$134$		0			0
$135$	−9.86509	−	0.520003i	−0.849051	−	0.0447548i
$136$		0			0
$137$	5.61663	+	11.0232i	0.479861	+	0.941780i	0.996340	+	0.0854799i	$0.0272423\pi$
$137$	5.61663	+	11.0232i	0.479861	+	0.941780i	−0.516479	+	0.856300i	$0.672758\pi$
$138$		0			0
$139$	0.816606	−	0.593299i	0.0692636	−	0.0503229i	−0.552615	−	0.833437i	$-0.686370\pi$
$139$	0.816606	−	0.593299i	0.0692636	−	0.0503229i	0.621878	+	0.783114i	$0.286370\pi$
$140$		0			0
$141$	0.306022	+	0.941839i	0.0257717	+	0.0793172i
$142$		0			0
$143$	−2.09826	+	2.24121i	−0.175465	+	0.187420i
$144$		0			0
$145$	0.233485	+	2.22796i	0.0193899	+	0.185022i
$146$		0			0
$147$	−1.40242	+	8.85451i	−0.115669	+	0.730308i
$148$		0			0
$149$	0.377177	−	1.16083i	0.0308996	−	0.0950990i	−0.934417	−	0.356180i	$-0.884079\pi$
$149$	0.377177	−	1.16083i	0.0308996	−	0.0950990i	0.965317	+	0.261081i	$0.0840790\pi$
$150$		0			0
$151$	−0.932668	+	1.28371i	−0.0758995	+	0.104467i	−0.845279	−	0.534326i	$-0.820566\pi$
$151$	−0.932668	+	1.28371i	−0.0758995	+	0.104467i	0.769379	+	0.638792i	$0.220566\pi$
$152$		0			0
$153$	3.14474	−	3.14474i	0.254237	−	0.254237i
$154$		0			0
$155$	0.927195	+	0.197375i	0.0744741	+	0.0158535i
$156$		0			0
$157$	7.32783	−	1.16061i	0.584824	−	0.0926271i	0.142991	−	0.989724i	$-0.454328\pi$
$157$	7.32783	−	1.16061i	0.584824	−	0.0926271i	0.441834	+	0.897097i	$0.354328\pi$
$158$		0			0
$159$	−7.19014	−	2.33622i	−0.570215	−	0.185274i
$160$		0			0
$161$	−6.86780	−	9.45272i	−0.541258	−	0.744978i
$162$		0			0
$163$	−6.99546	+	13.7294i	−0.547927	+	1.07537i	0.436522	+	0.899694i	$0.356210\pi$
$163$	−6.99546	+	13.7294i	−0.547927	+	1.07537i	−0.984449	+	0.175673i	$0.943790\pi$
$164$		0			0
$165$	−3.72670	+	4.92213i	−0.290123	+	0.383187i
$166$		0			0
$167$	1.88413	−	3.69782i	0.145799	−	0.286146i	−0.806545	−	0.591172i	$-0.798665\pi$
$167$	1.88413	−	3.69782i	0.145799	−	0.286146i	0.952344	+	0.305026i	$0.0986653\pi$
$168$		0			0
$169$	−7.13754	−	9.82399i	−0.549042	−	0.755691i
$170$		0			0
$171$	11.9177	+	3.87229i	0.911369	+	0.296122i
$172$		0			0
$173$	−4.27643	+	0.677320i	−0.325131	+	0.0514957i	−0.316867	−	0.948470i	$-0.602631\pi$
$173$	−4.27643	+	0.677320i	−0.325131	+	0.0514957i	−0.00826456	+	0.999966i	$0.502631\pi$
$174$		0			0
$175$	−7.54127	−	19.6813i	−0.570066	−	1.48777i
$176$		0			0
$177$	5.48016	−	5.48016i	0.411914	−	0.411914i
$178$		0			0
$179$	2.18633	−	3.00922i	0.163414	−	0.224920i	−0.719456	−	0.694538i	$-0.755609\pi$
$179$	2.18633	−	3.00922i	0.163414	−	0.224920i	0.882869	+	0.469619i	$0.155609\pi$
$180$		0			0
$181$	1.86849	−	5.75062i	0.138884	−	0.427440i	−0.857290	−	0.514834i	$-0.827854\pi$
$181$	1.86849	−	5.75062i	0.138884	−	0.427440i	0.996174	+	0.0873933i	$0.0278537\pi$
$182$		0			0
$183$	−1.01340	+	6.39838i	−0.0749129	+	0.472982i
$184$		0			0
$185$	−8.57022	−	6.94432i	−0.630095	−	0.510557i
$186$		0			0
$187$	−1.20758	−	6.27861i	−0.0883066	−	0.459137i
$188$		0			0
$189$	5.75482	+	17.7115i	0.418602	+	1.28832i
$190$		0			0
$191$	−13.3930	+	9.73057i	−0.969082	+	0.704079i	−0.955242	−	0.295825i	$-0.904405\pi$
$191$	−13.3930	+	9.73057i	−0.969082	+	0.704079i	−0.0138398	+	0.999904i	$0.504405\pi$
$192$		0			0
$193$	7.70155	+	15.1151i	0.554370	+	1.08801i	0.982841	+	0.184456i	$0.0590524\pi$
$193$	7.70155	+	15.1151i	0.554370	+	1.08801i	−0.428471	+	0.903556i	$0.640948\pi$
$194$		0			0
$195$	1.15261	+	1.28088i	0.0825398	+	0.0917256i
$196$		0			0
$197$	−9.63624	−	9.63624i	−0.686554	−	0.686554i	0.274915	−	0.961469i	$-0.411350\pi$
$197$	−9.63624	−	9.63624i	−0.686554	−	0.686554i	−0.961469	+	0.274915i	$0.911350\pi$
$198$		0			0
$199$		−	19.4166i		−	1.37640i	−0.725519	−	0.688202i	$-0.758400\pi$
$199$		−	19.4166i		−	1.37640i	0.725519	−	0.688202i	$-0.241600\pi$
$200$		0			0
$201$	2.90999	+	2.11423i	0.205255	+	0.149126i
$202$		0			0
$203$	3.76275	−	1.91722i	0.264093	−	0.134562i
$204$		0			0
$205$	0.524845	+	1.17978i	0.0366568	+	0.0823996i
$206$		0			0
$207$	−5.69763	−	2.90309i	−0.396012	−	0.201778i
$208$		0			0
$209$	14.2180	−	11.0632i	0.983478	−	0.765254i
$210$		0			0
$211$	−6.07815	+	1.97491i	−0.418437	+	0.135959i	−0.510666	−	0.859779i	$-0.670601\pi$
$211$	−6.07815	+	1.97491i	−0.418437	+	0.135959i	0.0922284	+	0.995738i	$0.470601\pi$
$212$		0			0
$213$	−7.06401	−	1.11883i	−0.484018	−	0.0766609i
$214$		0			0
$215$	−4.13159	−	15.4380i	−0.281772	−	1.05286i
$216$		0			0
$217$	−0.279559	−	1.76507i	−0.0189777	−	0.119820i
$218$		0			0
$219$	−4.54564			−0.307166
$220$		0			0
$221$	−1.78450			−0.120038
$222$		0			0
$223$	2.22058	+	14.0202i	0.148701	+	0.938860i	0.943352	+	0.331794i	$0.107654\pi$
$223$	2.22058	+	14.0202i	0.148701	+	0.938860i	−0.794651	+	0.607066i	$0.792346\pi$
$224$		0			0
$225$	−8.56746	−	7.72357i	−0.571164	−	0.514905i
$226$		0			0
$227$	−8.17622	−	1.29499i	−0.542675	−	0.0859512i	−0.120922	−	0.992662i	$-0.538585\pi$
$227$	−8.17622	−	1.29499i	−0.542675	−	0.0859512i	−0.421753	+	0.906711i	$0.638585\pi$
$228$		0			0
$229$	18.6401	−	6.05655i	1.23178	−	0.400228i	0.380418	−	0.924815i	$-0.375780\pi$
$229$	18.6401	−	6.05655i	1.23178	−	0.400228i	0.851357	+	0.524587i	$0.175780\pi$
$230$		0			0
$231$	11.1813	+	3.23010i	0.735676	+	0.212525i
$232$		0			0
$233$	3.30844	+	1.68573i	0.216743	+	0.110436i	0.558991	−	0.829173i	$-0.311188\pi$
$233$	3.30844	+	1.68573i	0.216743	+	0.110436i	−0.342249	+	0.939609i	$0.611188\pi$
$234$		0			0
$235$	−0.954019	+	2.48306i	−0.0622333	+	0.161977i
$236$		0			0
$237$	−1.69429	+	0.863285i	−0.110056	+	0.0560764i
$238$		0			0
$239$	2.59930	+	1.88850i	0.168135	+	0.122157i	0.668671	−	0.743559i	$-0.266864\pi$
$239$	2.59930	+	1.88850i	0.168135	+	0.122157i	−0.500536	+	0.865716i	$0.666864\pi$
$240$		0			0
$241$		−	25.4119i		−	1.63693i	−0.574559	−	0.818463i	$-0.694826\pi$
$241$		−	25.4119i		−	1.63693i	0.574559	−	0.818463i	$-0.305174\pi$
$242$		0			0
$243$	11.2809	+	11.2809i	0.723671	+	0.723671i
$244$		0			0
$245$	−17.8999	+	16.1074i	−1.14359	+	1.02906i
$246$		0			0
$247$	−2.28270	−	4.48005i	−0.145245	−	0.285059i
$248$		0			0
$249$	1.33935	−	0.973096i	0.0848780	−	0.0616674i
$250$		0			0
$251$	−5.03867	−	15.5074i	−0.318038	−	0.978820i	−0.974486	−	0.224448i	$-0.927942\pi$
$251$	−5.03867	−	15.5074i	−0.318038	−	0.978820i	0.656448	−	0.754371i	$-0.272058\pi$
$252$		0			0
$253$	−8.04929	+	4.44104i	−0.506055	+	0.279206i
$254$		0			0
$255$	−3.56893	+	0.374017i	−0.223495	+	0.0234218i
$256$		0			0
$257$	−2.53487	+	16.0045i	−0.158121	+	0.998335i	0.773207	+	0.634154i	$0.218651\pi$
$257$	−2.53487	+	16.0045i	−0.158121	+	0.998335i	−0.931328	+	0.364182i	$0.881349\pi$
$258$		0			0
$259$	−6.42576	+	19.7764i	−0.399277	+	1.22885i
$260$		0			0
$261$	1.35849	−	1.86981i	0.0840887	−	0.115738i
$262$		0			0
$263$	0.677874	−	0.677874i	0.0417995	−	0.0417995i	−0.685898	−	0.727698i	$-0.740590\pi$
$263$	0.677874	−	0.677874i	0.0417995	−	0.0417995i	0.727698	+	0.685898i	$0.240590\pi$
$264$		0			0
$265$	−11.0548	−	17.0342i	−0.679092	−	1.04640i
$266$		0			0
$267$	11.4546	−	1.81424i	0.701013	−	0.111030i
$268$		0			0
$269$	−27.0327	−	8.78345i	−1.64821	−	0.535536i	−0.669860	−	0.742487i	$-0.733646\pi$
$269$	−27.0327	−	8.78345i	−1.64821	−	0.535536i	−0.978351	+	0.206951i	$0.933646\pi$
$270$		0			0
$271$	−18.0744	−	24.8772i	−1.09794	−	1.51118i	−0.838087	−	0.545536i	$-0.816326\pi$
$271$	−18.0744	−	24.8772i	−1.09794	−	1.51118i	−0.259853	−	0.965648i	$-0.583674\pi$
$272$		0			0
$273$	1.47472	−	2.89430i	0.0892540	−	0.175171i
$274$		0			0
$275$	−16.1008	+	3.97029i	−0.970917	+	0.239417i
$276$		0			0
$277$	13.6871	−	26.8625i	0.822379	−	1.61401i	0.0335176	−	0.999438i	$-0.489329\pi$
$277$	13.6871	−	26.8625i	0.822379	−	1.61401i	0.788861	−	0.614571i	$-0.210671\pi$
$278$		0			0
$279$	−0.574875	−	0.791248i	−0.0344169	−	0.0473708i
$280$		0			0
$281$	8.10210	+	2.63253i	0.483331	+	0.157044i	0.540540	−	0.841319i	$-0.318220\pi$
$281$	8.10210	+	2.63253i	0.483331	+	0.157044i	−0.0572089	+	0.998362i	$0.518220\pi$
$282$		0			0
$283$	−9.42432	+	1.49267i	−0.560218	+	0.0887297i	−0.430120	−	0.902772i	$-0.641529\pi$
$283$	−9.42432	+	1.49267i	−0.560218	+	0.0887297i	−0.130097	+	0.991501i	$0.541529\pi$
$284$		0			0
$285$	−5.50430	−	8.48150i	−0.326046	−	0.502401i
$286$		0			0
$287$	1.72125	−	1.72125i	0.101602	−	0.101602i
$288$		0			0
$289$	−7.80797	+	10.7468i	−0.459292	+	0.632162i
$290$		0			0
$291$	0.855180	−	2.63197i	0.0501315	−	0.154289i
$292$		0			0
$293$	−0.360965	+	2.27904i	−0.0210878	+	0.133143i	−0.995986	−	0.0895072i	$-0.971471\pi$
$293$	−0.360965	+	2.27904i	−0.0210878	+	0.133143i	0.974898	+	0.222650i	$0.0714708\pi$
$294$		0			0
$295$	20.7039	−	2.16972i	1.20543	−	0.126326i
$296$		0			0
$297$	14.3889	−	2.76744i	0.834928	−	0.160583i
$298$		0			0
$299$	0.792887	+	2.44025i	0.0458538	+	0.141124i
$300$		0			0
$301$	−24.3734	+	17.7083i	−1.40486	+	1.02069i
$302$		0			0
$303$	−5.02310	−	9.85838i	−0.288569	−	0.566349i
$304$		0			0
$305$	−12.9347	+	11.6394i	−0.740639	+	0.666468i
$306$		0			0
$307$	−12.4635	−	12.4635i	−0.711327	−	0.711327i	0.255486	−	0.966813i	$-0.417765\pi$
$307$	−12.4635	−	12.4635i	−0.711327	−	0.711327i	−0.966813	+	0.255486i	$0.917765\pi$
$308$		0			0
$309$			8.39331i			0.477479i
$310$		0			0
$311$	12.2271	+	8.88353i	0.693337	+	0.503739i	0.877755	−	0.479109i	$-0.159040\pi$
$311$	12.2271	+	8.88353i	0.693337	+	0.503739i	−0.184419	+	0.982848i	$0.559040\pi$
$312$		0			0
$313$	23.2697	−	11.8565i	1.31528	−	0.670169i	0.351331	−	0.936251i	$-0.385729\pi$
$313$	23.2697	−	11.8565i	1.31528	−	0.670169i	0.963950	+	0.266082i	$0.0857293\pi$
$314$		0			0
$315$	−7.79890	+	20.2985i	−0.439418	+	1.14369i
$316$		0			0
$317$	25.2398	+	12.8603i	1.41761	+	0.722307i	0.983896	−	0.178744i	$-0.0572035\pi$
$317$	25.2398	+	12.8603i	1.41761	+	0.722307i	0.433712	+	0.901051i	$0.357203\pi$
$318$		0			0
$319$	−1.13026	−	3.12455i	−0.0632824	−	0.174941i
$320$		0			0
$321$	4.88234	−	1.58637i	0.272506	−	0.0885425i
$322$		0			0
$323$	10.3423	+	1.63805i	0.575458	+	0.0911436i
$324$		0			0
$325$	0.239432	+	4.62220i	0.0132813	+	0.256394i
$326$		0			0
$327$	−2.59405	−	16.3782i	−0.143451	−	0.905714i
$328$		0			0
$329$	5.01454			0.276461
$330$		0			0
$331$	24.6455			1.35464			0.677319	−	0.735690i	$-0.263142\pi$
$331$	24.6455			1.35464			0.677319	+	0.735690i	$0.263142\pi$
$332$		0			0
$333$	1.78028	+	11.2403i	0.0975588	+	0.615962i
$334$		0			0
$335$	2.49777	+	9.33313i	0.136468	+	0.509923i
$336$		0			0
$337$	−30.6340	−	4.85195i	−1.66874	−	0.264302i	−0.750657	−	0.660692i	$-0.770263\pi$
$337$	−30.6340	−	4.85195i	−1.66874	−	0.264302i	−0.918082	+	0.396390i	$0.870263\pi$
$338$		0			0
$339$	9.59746	−	3.11840i	0.521263	−	0.169369i
$340$		0			0
$341$	−1.40530	+	0.0462960i	−0.0761015	+	0.00250707i
$342$		0			0
$343$	14.1559	+	7.21277i	0.764345	+	0.389453i
$344$		0			0
$345$	2.09720	+	4.71424i	0.112910	+	0.253806i
$346$		0			0
$347$	26.8957	−	13.7041i	1.44384	−	0.735672i	0.455829	−	0.890068i	$-0.349343\pi$
$347$	26.8957	−	13.7041i	1.44384	−	0.735672i	0.988009	+	0.154395i	$0.0493430\pi$
$348$		0			0
$349$	17.2865	+	12.5594i	0.925323	+	0.672287i	0.944843	−	0.327523i	$-0.106214\pi$
$349$	17.2865	+	12.5594i	0.925323	+	0.672287i	−0.0195201	+	0.999809i	$0.506214\pi$
$350$		0			0
$351$		−	4.08959i		−	0.218286i
$352$		0			0
$353$	−2.82626	−	2.82626i	−0.150427	−	0.150427i	0.627882	−	0.778309i	$-0.283922\pi$
$353$	−2.82626	−	2.82626i	−0.150427	−	0.150427i	−0.778309	+	0.627882i	$0.783922\pi$
$354$		0			0
$355$	−12.8502	−	14.2803i	−0.682019	−	0.757921i
$356$		0			0
$357$	3.07116	+	6.02750i	0.162543	+	0.319009i
$358$		0			0
$359$	8.68908	−	6.31298i	0.458592	−	0.333187i	−0.334387	−	0.942436i	$-0.608529\pi$
$359$	8.68908	−	6.31298i	0.458592	−	0.333187i	0.792979	+	0.609249i	$0.208529\pi$
$360$		0			0
$361$	3.24592	+	9.98992i	0.170838	+	0.525785i
$362$		0			0
$363$	3.61127	−	8.41505i	0.189542	−	0.441676i
$364$		0			0
$365$	−9.48649	−	7.68677i	−0.496546	−	0.402344i
$366$		0			0
$367$	−5.41331	+	34.1783i	−0.282572	+	1.78409i	0.282721	+	0.959202i	$0.408763\pi$
$367$	−5.41331	+	34.1783i	−0.282572	+	1.78409i	−0.565293	+	0.824890i	$0.691237\pi$
$368$		0			0
$369$	0.411677	−	1.26701i	0.0214310	−	0.0659579i
$370$		0			0
$371$	−22.5015	+	30.9706i	−1.16822	+	1.60791i
$372$		0			0
$373$	−9.90454	+	9.90454i	−0.512838	+	0.512838i	−0.915395	−	0.402557i	$-0.868121\pi$
$373$	−9.90454	+	9.90454i	−0.512838	+	0.512838i	0.402557	+	0.915395i	$0.368121\pi$
$374$		0			0
$375$	1.44763	+	9.19406i	0.0747555	+	0.474779i
$376$		0			0
$377$	−0.915956	+	0.145073i	−0.0471741	+	0.00747165i
$378$		0			0
$379$	25.2037	+	8.18919i	1.29463	+	0.420651i	0.873710	−	0.486447i	$-0.161708\pi$
$379$	25.2037	+	8.18919i	1.29463	+	0.420651i	0.420919	+	0.907098i	$0.361708\pi$
$380$		0			0
$381$	0.567376	+	0.780926i	0.0290676	+	0.0400081i
$382$		0			0
$383$	−10.9129	+	21.4177i	−0.557622	+	1.09439i	0.424373	+	0.905487i	$0.360495\pi$
$383$	−10.9129	+	21.4177i	−0.557622	+	1.09439i	−0.981995	+	0.188907i	$0.939505\pi$
$384$		0			0
$385$	17.8726	+	25.6489i	0.910872	+	1.30719i
$386$		0			0
$387$	−7.48548	+	14.6911i	−0.380508	+	0.746789i
$388$		0			0
$389$	4.43509	+	6.10438i	0.224868	+	0.309505i	0.906512	−	0.422179i	$-0.138735\pi$
$389$	4.43509	+	6.10438i	0.224868	+	0.309505i	−0.681644	+	0.731684i	$0.738735\pi$
$390$		0			0
$391$	−5.08193	−	1.65122i	−0.257004	−	0.0835057i
$392$		0			0
$393$	11.8838	−	1.88220i	0.599456	−	0.0949445i
$394$		0			0
$395$	−4.99573	−	1.06346i	−0.251362	−	0.0535083i
$396$		0			0
$397$	16.0995	−	16.0995i	0.808008	−	0.808008i	−0.176324	−	0.984332i	$-0.556421\pi$
$397$	16.0995	−	16.0995i	0.808008	−	0.808008i	0.984332	+	0.176324i	$0.0564206\pi$
$398$		0			0
$399$	−11.2037	+	15.4205i	−0.560886	+	0.771993i
$400$		0			0
$401$	−7.46030	+	22.9604i	−0.372550	+	1.14659i	0.572568	+	0.819858i	$0.305947\pi$
$401$	−7.46030	+	22.9604i	−0.372550	+	1.14659i	−0.945117	+	0.326732i	$0.894053\pi$
$402$		0			0
$403$	−0.0613908	+	0.387606i	−0.00305809	+	0.0193080i
$404$		0			0
$405$	0.755849	+	7.21243i	0.0375584	+	0.358389i
$406$		0			0
$407$	14.8143	+	6.94368i	0.734319	+	0.344185i
$408$		0			0
$409$	1.80956	+	5.56925i	0.0894769	+	0.275382i	0.985775	−	0.168070i	$-0.0537536\pi$
$409$	1.80956	+	5.56925i	0.0894769	+	0.275382i	−0.896298	+	0.443452i	$0.853754\pi$
$410$		0			0
$411$	−8.33214	+	6.05365i	−0.410994	+	0.298605i
$412$		0			0
$413$	−17.8162	−	34.9663i	−0.876680	−	1.72058i
$414$		0			0
$415$	4.44068	+	0.234075i	0.217984	+	0.0114903i
$416$		0			0
$417$	0.594169	+	0.594169i	0.0290966	+	0.0290966i
$418$		0			0
$419$		−	11.0599i		−	0.540311i	−0.962817	−	0.270155i	$-0.912925\pi$
$419$		−	11.0599i		−	0.540311i	0.962817	−	0.270155i	$-0.0870751\pi$
$420$		0			0
$421$	−6.36944	−	4.62767i	−0.310428	−	0.225539i	0.421652	−	0.906758i	$-0.361450\pi$
$421$	−6.36944	−	4.62767i	−0.310428	−	0.225539i	−0.732080	+	0.681219i	$0.761450\pi$
$422$		0			0
$423$	2.44527	−	1.24593i	0.118893	−	0.0605790i
$424$		0			0
$425$	−8.08063	−	5.25458i	−0.391968	−	0.254885i
$426$		0			0
$427$	29.2275	+	14.8922i	1.41442	+	0.720682i
$428$		0			0
$429$	−2.11603	−	1.43337i	−0.102163	−	0.0692037i
$430$		0			0
$431$	6.94552	−	2.25674i	0.334554	−	0.108703i	−0.136923	−	0.990582i	$-0.543721\pi$
$431$	6.94552	−	2.25674i	0.334554	−	0.108703i	0.471477	+	0.881879i	$0.343721\pi$
$432$		0			0
$433$	4.98536	+	0.789604i	0.239581	+	0.0379460i	0.275070	−	0.961424i	$-0.411299\pi$
$433$	4.98536	+	0.789604i	0.239581	+	0.0379460i	−0.0354890	+	0.999370i	$0.511299\pi$
$434$		0			0
$435$	−1.80147	+	0.482118i	−0.0863740	+	0.0231158i
$436$		0			0
$437$	−2.35527	−	14.8706i	−0.112668	−	0.711357i
$438$		0			0
$439$	−1.29778			−0.0619394			−0.0309697	−	0.999520i	$-0.509860\pi$
$439$	−1.29778			−0.0619394			−0.0309697	+	0.999520i	$0.509860\pi$
$440$		0			0
$441$	24.8439			1.18304
$442$		0			0
$443$	−2.40922	−	15.2112i	−0.114466	−	0.722707i	−0.976445	−	0.215764i	$-0.930776\pi$
$443$	−2.40922	−	15.2112i	−0.114466	−	0.722707i	0.861980	−	0.506942i	$-0.169224\pi$
$444$		0			0
$445$	26.9731	+	15.5838i	1.27865	+	0.738744i
$446$		0			0
$447$	1.00358	+	0.158952i	0.0474678	+	0.00751816i
$448$		0			0
$449$	11.5295	−	3.74615i	0.544109	−	0.176792i	−0.0240497	−	0.999711i	$-0.507656\pi$
$449$	11.5295	−	3.74615i	0.544109	−	0.176792i	0.568159	+	0.822919i	$0.307656\pi$
$450$		0			0
$451$	−1.17616	−	1.51156i	−0.0553833	−	0.0711766i
$452$		0			0
$453$	−1.17695	−	0.599688i	−0.0552981	−	0.0281758i
$454$		0			0
$455$	7.97198	−	3.54646i	0.373732	−	0.166261i
$456$		0			0
$457$	3.12807	−	1.59383i	0.146325	−	0.0745563i	−0.379295	−	0.925276i	$-0.623833\pi$
$457$	3.12807	−	1.59383i	0.146325	−	0.0745563i	0.525620	+	0.850720i	$0.323833\pi$
$458$		0			0
$459$	6.89018	+	5.00601i	0.321606	+	0.233660i
$460$		0			0
$461$		−	5.45336i		−	0.253988i	−0.991903	−	0.126994i	$-0.959467\pi$
$461$		−	5.45336i		−	0.253988i	0.991903	−	0.126994i	$-0.0405329\pi$
$462$		0			0
$463$	−15.3996	−	15.3996i	−0.715681	−	0.715681i	0.252037	−	0.967718i	$-0.418900\pi$
$463$	−15.3996	−	15.3996i	−0.715681	−	0.715681i	−0.967718	+	0.252037i	$0.918900\pi$
$464$		0			0
$465$	−0.0415401	+	0.788065i	−0.00192638	+	0.0365457i
$466$		0			0
$467$	−6.66632	−	13.0834i	−0.308481	−	0.605427i	0.683768	−	0.729700i	$-0.260340\pi$
$467$	−6.66632	−	13.0834i	−0.308481	−	0.605427i	−0.992248	+	0.124273i	$0.960340\pi$
$468$		0			0
$469$	14.7351	−	10.7057i	0.680402	−	0.494341i
$470$		0			0
$471$	1.90857	+	5.87397i	0.0879422	+	0.270658i
$472$		0			0
$473$	11.4510	+	20.7547i	0.526518	+	0.954303i
$474$		0			0
$475$	2.85523	−	27.0083i	0.131007	−	1.23923i
$476$		0			0
$477$	−3.27747	+	20.6931i	−0.150065	+	0.947473i
$478$		0			0
$479$	−1.51842	+	4.67321i	−0.0693783	+	0.213524i	−0.979734	−	0.200302i	$-0.935808\pi$
$479$	−1.51842	+	4.67321i	−0.0693783	+	0.213524i	0.910356	+	0.413826i	$0.135808\pi$
$480$		0			0
$481$	2.68405	−	3.69428i	0.122382	−	0.168444i
$482$		0			0
$483$	6.87787	−	6.87787i	0.312954	−	0.312954i
$484$		0			0
$485$	6.23543	−	4.04665i	0.283136	−	0.183749i
$486$		0			0
$487$	−10.6054	+	1.67972i	−0.480574	+	0.0761155i	−0.392022	−	0.919956i	$-0.628224\pi$
$487$	−10.6054	+	1.67972i	−0.480574	+	0.0761155i	−0.0885527	+	0.996071i	$0.528224\pi$
$488$		0			0
$489$	−12.1996	−	3.96390i	−0.551686	−	0.179254i
$490$		0			0
$491$	−1.91387	−	2.63421i	−0.0863715	−	0.118880i	0.763645	−	0.645637i	$-0.223408\pi$
$491$	−1.91387	−	2.63421i	−0.0863715	−	0.118880i	−0.850016	+	0.526757i	$0.823408\pi$
$492$		0			0
$493$	0.876788	−	1.72079i	0.0394886	−	0.0775007i
$494$		0			0
$495$	15.0881	+	8.06662i	0.678159	+	0.362567i
$496$		0			0
$497$	−16.4414	+	32.2681i	−0.737498	+	1.44742i
$498$		0			0
$499$	5.25588	+	7.23410i	0.235285	+	0.323843i	0.910290	−	0.413971i	$-0.135858\pi$
$499$	5.25588	+	7.23410i	0.235285	+	0.323843i	−0.675005	+	0.737813i	$0.735858\pi$
$500$		0			0
$501$	3.28580	+	1.06762i	0.146799	+	0.0476978i
$502$		0			0
$503$	−19.0954	+	3.02441i	−0.851421	+	0.134852i	−0.566868	−	0.823808i	$-0.691845\pi$
$503$	−19.0954	+	3.02441i	−0.851421	+	0.134852i	−0.284553	+	0.958660i	$0.591845\pi$
$504$		0			0
$505$	6.18781	−	29.0681i	0.275354	−	1.29351i
$506$		0			0
$507$	7.14801	−	7.14801i	0.317454	−	0.317454i
$508$		0			0
$509$	−1.65845	+	2.28267i	−0.0735097	+	0.101177i	−0.844189	−	0.536046i	$-0.819917\pi$
$509$	−1.65845	+	2.28267i	−0.0735097	+	0.101177i	0.770679	+	0.637224i	$0.219917\pi$
$510$		0			0
$511$	−7.11276	+	21.8908i	−0.314650	+	0.968393i
$512$		0			0
$513$	−3.75398	+	23.7017i	−0.165742	+	1.04645i
$514$		0			0
$515$	−14.1933	+	17.5164i	−0.625430	+	0.771863i
$516$		0			0
$517$	0.488562	−	3.91508i	0.0214869	−	0.172185i
$518$		0			0
$519$	−1.11382	−	3.42798i	−0.0488912	−	0.150472i
$520$		0			0
$521$	−7.68839	+	5.58594i	−0.336835	+	0.244725i	−0.743325	−	0.668930i	$-0.766752\pi$
$521$	−7.68839	+	5.58594i	−0.336835	+	0.244725i	0.406491	+	0.913655i	$0.366752\pi$
$522$		0			0
$523$	6.73563	+	13.2194i	0.294528	+	0.578045i	0.990092	−	0.140420i	$-0.0448453\pi$
$523$	6.73563	+	13.2194i	0.294528	+	0.578045i	−0.695564	+	0.718465i	$0.744845\pi$
$524$		0			0
$525$	15.2004	−	8.76366i	0.663398	−	0.382477i
$526$		0			0
$527$	−0.577895	−	0.577895i	−0.0251735	−	0.0251735i
$528$		0			0
$529$		−	15.3169i		−	0.665953i
$530$		0			0
$531$	−17.3757	−	12.6242i	−0.754039	−	0.547842i
$532$		0			0
$533$	−0.476289	+	0.242681i	−0.0206304	+	0.0105117i
$534$		0			0
$535$	12.8718	+	4.94548i	0.556495	+	0.213812i
$536$		0			0
$537$	2.75897	+	1.40577i	0.119058	+	0.0606633i
$538$		0			0
$539$	20.0309	−	29.5710i	0.862794	−	1.27371i
$540$		0			0
$541$	−29.7351	+	9.66153i	−1.27841	+	0.415381i	−0.868021	−	0.496528i	$-0.834608\pi$
$541$	−29.7351	+	9.66153i	−1.27841	+	0.415381i	−0.410392	+	0.911909i	$0.634608\pi$
$542$		0			0
$543$	4.97163	+	0.787429i	0.213353	+	0.0337918i
$544$		0			0
$545$	22.2822	−	38.5669i	0.954464	−	1.65202i
$546$		0			0
$547$	−4.93799	−	31.1772i	−0.211133	−	1.33304i	−0.834455	−	0.551076i	$-0.814217\pi$
$547$	−4.93799	−	31.1772i	−0.211133	−	1.33304i	0.623322	−	0.781966i	$-0.285783\pi$
$548$		0			0
$549$	17.9525			0.766194
$550$		0			0
$551$	5.44169			0.231824
$552$		0			0
$553$	1.50626	+	9.51017i	0.0640528	+	0.404414i
$554$		0			0
$555$	4.59371	−	7.95098i	0.194992	−	0.337500i
$556$		0			0
$557$	−13.0992	−	2.07471i	−0.555030	−	0.0879082i	−0.127383	−	0.991854i	$-0.540658\pi$
$557$	−13.0992	−	2.07471i	−0.555030	−	0.0879082i	−0.427648	+	0.903945i	$0.640658\pi$
$558$		0			0
$559$	6.29208	−	2.04442i	0.266127	−	0.0864698i
$560$		0			0
$561$	5.00516	−	1.81054i	0.211318	−	0.0764412i
$562$		0			0
$563$	−26.1698	−	13.3342i	−1.10292	−	0.561968i	−0.194874	−	0.980828i	$-0.562430\pi$
$563$	−26.1698	−	13.3342i	−1.10292	−	0.561968i	−0.908051	+	0.418860i	$0.862430\pi$
$564$		0			0
$565$	25.3027	+	9.72158i	1.06449	+	0.408990i
$566$		0			0
$567$	12.1809	−	6.20650i	0.511551	−	0.260648i
$568$		0			0
$569$	−17.3540	−	12.6084i	−0.727518	−	0.528573i	0.161259	−	0.986912i	$-0.448445\pi$
$569$	−17.3540	−	12.6084i	−0.727518	−	0.528573i	−0.888777	+	0.458339i	$0.848445\pi$
$570$		0			0
$571$			28.7176i			1.20179i	0.799326	+	0.600897i	$0.205190\pi$
$571$			28.7176i			1.20179i	−0.799326	+	0.600897i	$0.794810\pi$
$572$		0			0
$573$	−9.74484	−	9.74484i	−0.407097	−	0.407097i
$574$		0			0
$575$	−3.59513	+	13.3848i	−0.149927	+	0.558183i
$576$		0			0
$577$	3.03825	+	5.96290i	0.126484	+	0.248239i	0.945561	−	0.325445i	$-0.105514\pi$
$577$	3.03825	+	5.96290i	0.126484	+	0.248239i	−0.819077	+	0.573683i	$0.805514\pi$
$578$		0			0
$579$	−11.4251	+	8.30081i	−0.474810	+	0.344970i
$580$		0			0
$581$	−2.59048	−	7.97268i	−0.107471	−	0.330763i
$582$		0			0
$583$	21.9879	+	20.5853i	0.910644	+	0.852558i
$584$		0			0
$585$	3.00625	−	3.71012i	0.124293	−	0.153394i
$586$		0			0
$587$	−5.70952	+	36.0485i	−0.235657	+	1.48788i	0.531849	+	0.846839i	$0.321497\pi$
$587$	−5.70952	+	36.0485i	−0.235657	+	1.48788i	−0.767506	+	0.641041i	$0.778503\pi$
$588$		0			0
$589$	0.711594	−	2.19006i	0.0293207	−	0.0902400i
$590$		0			0
$591$	6.66825	−	9.17805i	0.274295	−	0.377535i
$592$		0			0
$593$	−26.6656	+	26.6656i	−1.09502	+	1.09502i	−0.100040	+	0.994983i	$0.531897\pi$
$593$	−26.6656	+	26.6656i	−1.09502	+	1.09502i	−0.994983	+	0.100040i	$0.968103\pi$
$594$		0			0
$595$	−3.78328	+	17.7724i	−0.155099	+	0.728599i
$596$		0			0
$597$	15.9648	−	2.52857i	0.653394	−	0.103487i
$598$		0			0
$599$	−36.7124	−	11.9286i	−1.50003	−	0.487388i	−0.560002	−	0.828492i	$-0.689199\pi$
$599$	−36.7124	−	11.9286i	−1.50003	−	0.487388i	−0.940026	+	0.341103i	$0.889199\pi$
$600$		0			0
$601$	22.4050	+	30.8379i	0.913920	+	1.25790i	0.965810	+	0.259250i	$0.0834753\pi$
$601$	22.4050	+	30.8379i	0.913920	+	1.25790i	−0.0518905	+	0.998653i	$0.516525\pi$
$602$		0			0
$603$	4.52538	−	8.88156i	0.184288	−	0.361685i
$604$		0			0
$605$	21.7665	−	11.4550i	0.884936	−	0.465713i
$606$		0			0
$607$	−16.4492	+	32.2834i	−0.667653	+	1.31034i	0.270031	+	0.962852i	$0.412966\pi$
$607$	−16.4492	+	32.2834i	−0.667653	+	1.31034i	−0.937683	+	0.347491i	$0.887034\pi$
$608$		0			0
$609$	2.06640	+	2.84415i	0.0837346	+	0.115251i
$610$		0			0
$611$	−1.04729	−	0.340286i	−0.0423689	−	0.0137665i
$612$		0			0
$613$	2.37960	−	0.376892i	0.0961113	−	0.0152225i	−0.108194	−	0.994130i	$-0.534507\pi$
$613$	2.37960	−	0.376892i	0.0961113	−	0.0152225i	0.204305	+	0.978907i	$0.434507\pi$
$614$		0			0
$615$	−0.901696	+	0.585180i	−0.0363599	+	0.0235967i
$616$		0			0
$617$	−25.5598	+	25.5598i	−1.02900	+	1.02900i	−0.0294325	+	0.999567i	$0.509370\pi$
$617$	−25.5598	+	25.5598i	−1.02900	+	1.02900i	−0.999567	+	0.0294325i	$0.990630\pi$
$618$		0			0
$619$	0.537145	−	0.739317i	0.0215897	−	0.0297157i	−0.798086	−	0.602544i	$-0.794154\pi$
$619$	0.537145	−	0.739317i	0.0215897	−	0.0297157i	0.819675	+	0.572828i	$0.194154\pi$
$620$		0			0
$621$	3.78415	−	11.6464i	0.151853	−	0.467355i
$622$		0			0
$623$	9.18661	−	58.0020i	0.368054	−	2.32380i
$624$		0			0
$625$	−12.5262	+	21.6355i	−0.501049	+	0.865419i
$626$		0			0
$627$	10.9480	+	10.2496i	0.437219	+	0.409331i
$628$		0			0
$629$	2.93865	+	9.04423i	0.117172	+	0.360617i
$630$		0			0
$631$	18.6941	−	13.5820i	0.744199	−	0.540692i	−0.149824	−	0.988713i	$-0.547871\pi$
$631$	18.6941	−	13.5820i	0.744199	−	0.540692i	0.894023	+	0.448020i	$0.147871\pi$
$632$		0			0
$633$	−2.41536	−	4.74042i	−0.0960020	−	0.188415i
$634$		0			0
$635$	−0.136480	+	2.58920i	−0.00541606	+	0.102749i
$636$		0			0
$637$	−7.04889	−	7.04889i	−0.279287	−	0.279287i
$638$		0			0
$639$			19.8201i			0.784072i
$640$		0			0
$641$	−7.06172	−	5.13064i	−0.278921	−	0.202648i	0.439525	−	0.898230i	$-0.355147\pi$
$641$	−7.06172	−	5.13064i	−0.278921	−	0.202648i	−0.718447	+	0.695582i	$0.755147\pi$
$642$		0			0
$643$	28.1018	−	14.3186i	1.10823	−	0.564670i	0.198594	−	0.980082i	$-0.436362\pi$
$643$	28.1018	−	14.3186i	1.10823	−	0.564670i	0.909634	+	0.415412i	$0.136362\pi$
$644$		0			0
$645$	12.1555	−	5.40754i	0.478620	−	0.212922i
$646$		0			0
$647$	12.2437	+	6.23845i	0.481348	+	0.245259i	0.677789	−	0.735257i	$-0.262938\pi$
$647$	12.2437	+	6.23845i	0.481348	+	0.245259i	−0.196441	+	0.980516i	$0.562938\pi$
$648$		0			0
$649$	−29.0356	+	10.5032i	−1.13975	+	0.412288i
$650$		0			0
$651$	1.41487	−	0.459720i	0.0554532	−	0.0180178i
$652$		0			0
$653$	−5.37414	−	0.851181i	−0.210307	−	0.0333093i	0.0503921	−	0.998730i	$-0.483953\pi$
$653$	−5.37414	−	0.851181i	−0.210307	−	0.0333093i	−0.260699	+	0.965420i	$0.583953\pi$
$654$		0			0
$655$	27.9836	+	16.1676i	1.09341	+	0.631721i
$656$		0			0
$657$	1.97062	+	12.4420i	0.0768812	+	0.485408i
$658$		0			0
$659$	−42.1160			−1.64061			−0.820304	−	0.571928i	$-0.806195\pi$
$659$	−42.1160			−1.64061			−0.820304	+	0.571928i	$0.806195\pi$
$660$		0			0
$661$	−19.5844			−0.761745			−0.380872	−	0.924628i	$-0.624376\pi$
$661$	−19.5844			−0.761745			−0.380872	+	0.924628i	$0.624376\pi$
$662$		0			0
$663$	−0.232390	−	1.46726i	−0.00902529	−	0.0569835i
$664$		0			0
$665$	−49.4579	+	13.2362i	−1.91790	+	0.513276i
$666$		0			0
$667$	−2.74272	−	0.434404i	−0.106198	−	0.0168202i
$668$		0			0
$669$	−11.2385	+	3.65162i	−0.434507	+	0.141180i
$670$		0			0
$671$	14.4746	−	21.3683i	0.558786	−	0.824915i
$672$		0			0
$673$	−4.94179	−	2.51797i	−0.190492	−	0.0970605i	0.356143	−	0.934431i	$-0.384092\pi$
$673$	−4.94179	−	2.51797i	−0.190492	−	0.0970605i	−0.546635	+	0.837371i	$0.684092\pi$
$674$		0			0
$675$	12.0421	−	18.5186i	0.463500	−	0.712782i
$676$		0			0
$677$	−2.07893	+	1.05927i	−0.0798999	+	0.0407110i	−0.493484	−	0.869755i	$-0.664277\pi$
$677$	−2.07893	+	1.05927i	−0.0798999	+	0.0407110i	0.413584	+	0.910466i	$0.364277\pi$
$678$		0			0
$679$	−11.3369	−	8.23673i	−0.435070	−	0.316097i
$680$		0			0
$681$		−	6.89132i		−	0.264076i
$682$		0			0
$683$	25.0400	+	25.0400i	0.958127	+	0.958127i	0.999158	−	0.0410307i	$-0.0130641\pi$
$683$	25.0400	+	25.0400i	0.958127	+	0.958127i	−0.0410307	+	0.999158i	$0.513064\pi$
$684$		0			0
$685$	−27.6256	−	1.45618i	−1.05552	−	0.0556380i
$686$		0			0
$687$	7.40730	+	14.5376i	0.282606	+	0.554646i
$688$		0			0
$689$	6.80110	−	4.94129i	0.259101	−	0.188248i
$690$		0			0
$691$	0.556172	+	1.71172i	0.0211578	+	0.0651170i	0.961078	−	0.276277i	$-0.0891008\pi$
$691$	0.556172	+	1.71172i	0.0211578	+	0.0651170i	−0.939920	+	0.341394i	$0.889101\pi$
$692$		0			0
$693$	3.99389	−	32.0050i	0.151715	−	1.21577i
$694$		0			0
$695$	0.235245	+	2.24475i	0.00892336	+	0.0851482i
$696$		0			0
$697$	0.174147	−	1.09952i	0.00659628	−	0.0416473i
$698$		0			0
$699$	−0.955200	+	2.93980i	−0.0361290	+	0.111194i
$700$		0			0
$701$	10.4715	−	14.4128i	0.395502	−	0.544362i	−0.564106	−	0.825703i	$-0.690779\pi$
$701$	10.4715	−	14.4128i	0.395502	−	0.544362i	0.959608	+	0.281340i	$0.0907790\pi$
$702$		0			0
$703$	−18.9468	+	18.9468i	−0.714593	+	0.714593i
$704$		0			0
$705$	−2.16587	−	0.461055i	−0.0815713	−	0.0173643i
$706$		0			0
$707$	−55.3357	+	8.76432i	−2.08111	+	0.329616i
$708$		0			0
$709$	9.55567	+	3.10483i	0.358871	+	0.116604i	0.482903	−	0.875674i	$-0.339583\pi$
$709$	9.55567	+	3.10483i	0.358871	+	0.116604i	−0.124032	+	0.992278i	$0.539583\pi$
$710$		0			0
$711$	3.09743	+	4.26324i	0.116163	+	0.159884i
$712$		0			0
$713$	−0.533487	+	1.04703i	−0.0199793	+	0.0392115i
$714$		0			0
$715$	−1.99218	−	6.56961i	−0.0745034	−	0.245690i
$716$		0			0
$717$	−1.21427	+	2.38314i	−0.0453478	+	0.0890001i
$718$		0			0
$719$	4.03181	+	5.54931i	0.150361	+	0.206954i	0.877553	−	0.479480i	$-0.159175\pi$
$719$	4.03181	+	5.54931i	0.150361	+	0.206954i	−0.727191	+	0.686435i	$0.759175\pi$
$720$		0			0
$721$	40.4204	+	13.1334i	1.50533	+	0.489113i
$722$		0			0
$723$	20.8943	−	3.30933i	0.777067	−	0.123075i
$724$		0			0
$725$	−4.57485	−	2.04017i	−0.169906	−	0.0757702i
$726$		0			0
$727$	25.2212	−	25.2212i	0.935401	−	0.935401i	−0.0626351	−	0.998036i	$-0.519950\pi$
$727$	25.2212	−	25.2212i	0.935401	−	0.935401i	0.998036	+	0.0626351i	$0.0199504\pi$
$728$		0			0
$729$	−2.08750	+	2.87320i	−0.0773149	+	0.106415i
$730$		0			0
$731$	−4.25759	+	13.1035i	−0.157473	+	0.484651i
$732$		0			0
$733$	1.20620	−	7.61562i	0.0445519	−	0.281289i	−0.955347	−	0.295485i	$-0.904519\pi$
$733$	1.20620	−	7.61562i	0.0445519	−	0.281289i	0.999899	+	0.0141956i	$0.00451876\pi$
$734$		0			0
$735$	−15.5749	−	12.6201i	−0.574490	−	0.465501i
$736$		0			0
$737$	−6.92277	−	12.5474i	−0.255004	−	0.462189i
$738$		0			0
$739$	12.6089	+	38.8062i	0.463825	+	1.42751i	0.860454	+	0.509528i	$0.170180\pi$
$739$	12.6089	+	38.8062i	0.463825	+	1.42751i	−0.396629	+	0.917979i	$0.629820\pi$
$740$		0			0
$741$	3.38633	−	2.46031i	0.124400	−	0.0903819i
$742$		0			0
$743$	−20.1411	−	39.5290i	−0.738904	−	1.45018i	−0.887271	−	0.461248i	$-0.847402\pi$
$743$	−20.1411	−	39.5290i	−0.738904	−	1.45018i	0.148368	−	0.988932i	$-0.452598\pi$
$744$		0			0
$745$	1.82563	+	2.02880i	0.0668859	+	0.0743296i
$746$		0			0
$747$	−3.24412	−	3.24412i	−0.118696	−	0.118696i
$748$		0			0
$749$		−	25.9946i		−	0.949821i
$750$		0			0
$751$	−10.6518	−	7.73896i	−0.388688	−	0.282399i	0.376229	−	0.926527i	$-0.377220\pi$
$751$	−10.6518	−	7.73896i	−0.388688	−	0.282399i	−0.764918	+	0.644128i	$0.777220\pi$
$752$		0			0
$753$	12.0944	−	6.16240i	0.440744	−	0.224570i
$754$		0			0
$755$	−1.44215	−	3.24177i	−0.0524853	−	0.117980i
$756$		0			0
$757$	−17.7060	−	9.02166i	−0.643535	−	0.327898i	0.101586	−	0.994827i	$-0.467608\pi$
$757$	−17.7060	−	9.02166i	−0.643535	−	0.327898i	−0.745121	+	0.666929i	$0.767608\pi$
$758$		0			0
$759$	−4.69977	−	6.03997i	−0.170591	−	0.219237i
$760$		0			0
$761$	16.8706	−	5.48158i	0.611558	−	0.198707i	0.0131694	−	0.999913i	$-0.495808\pi$
$761$	16.8706	−	5.48158i	0.611558	−	0.198707i	0.598389	+	0.801206i	$0.295808\pi$
$762$		0			0
$763$	−82.9328	−	13.1353i	−3.00237	−	0.475528i
$764$		0			0
$765$	2.57093	+	9.60647i	0.0929521	+	0.347323i
$766$		0			0
$767$	1.34813	+	8.51175i	0.0486781	+	0.307342i
$768$		0			0
$769$	−33.4001			−1.20444			−0.602218	−	0.798331i	$-0.705716\pi$
$769$	−33.4001			−1.20444			−0.602218	+	0.798331i	$0.705716\pi$
$770$		0			0
$771$	−13.4894			−0.485810
$772$		0			0
$773$	−5.96974	−	37.6915i	−0.214717	−	1.35567i	−0.825738	−	0.564054i	$-0.809241\pi$
$773$	−5.96974	−	37.6915i	−0.214717	−	1.35567i	0.611021	−	0.791614i	$-0.290759\pi$
$774$		0			0
$775$	−1.41933	+	1.57440i	−0.0509837	+	0.0565542i
$776$		0			0
$777$	−17.0975	−	2.70797i	−0.613369	−	0.0971480i
$778$		0			0
$779$	2.98315	−	0.969285i	0.106882	−	0.0347282i
$780$		0			0
$781$	23.5913	+	15.9804i	0.844163	+	0.571824i
$782$		0			0
$783$	3.94360	+	2.00936i	0.140933	+	0.0718088i
$784$		0			0
$785$	−5.94993	+	15.4861i	−0.212362	+	0.552722i
$786$		0			0
$787$	−32.7403	+	16.6820i	−1.16706	+	0.594649i	−0.926614	−	0.376013i	$-0.877295\pi$
$787$	−32.7403	+	16.6820i	−1.16706	+	0.594649i	−0.240450	+	0.970662i	$0.577295\pi$
$788$		0			0
$789$	0.645642	+	0.469086i	0.0229855	+	0.0166999i
$790$		0			0
$791$		−	51.0989i		−	1.81687i
$792$		0			0
$793$	−5.09361	−	5.09361i	−0.180879	−	0.180879i
$794$		0			0
$795$	12.5663	−	11.3079i	0.445681	−	0.401049i
$796$		0			0
$797$	−9.14395	−	17.9460i	−0.323895	−	0.635680i	0.670441	−	0.741963i	$-0.266105\pi$
$797$	−9.14395	−	17.9460i	−0.323895	−	0.635680i	−0.994336	+	0.106283i	$0.966105\pi$
$798$		0			0
$799$	1.85529	−	1.34795i	0.0656355	−	0.0476870i
$800$		0			0
$801$	−9.93160	−	30.5663i	−0.350916	−	1.08001i
$802$		0			0
$803$	16.3982	+	7.68606i	0.578679	+	0.271235i
$804$		0			0
$805$	25.9844	−	2.72311i	0.915829	−	0.0959770i
$806$		0			0
$807$	3.70156	−	23.3708i	0.130301	−	0.822690i
$808$		0			0
$809$	−16.0484	+	49.3920i	−0.564233	+	1.73653i	0.105987	+	0.994367i	$0.466200\pi$
$809$	−16.0484	+	49.3920i	−0.564233	+	1.73653i	−0.670220	+	0.742162i	$0.733800\pi$
$810$		0			0
$811$	23.0252	−	31.6914i	0.808523	−	1.11284i	−0.183027	−	0.983108i	$-0.558590\pi$
$811$	23.0252	−	31.6914i	0.808523	−	1.11284i	0.991550	−	0.129728i	$-0.0414104\pi$
$812$		0			0
$813$	18.1009	−	18.1009i	0.634826	−	0.634826i
$814$		0			0
$815$	−18.7569	−	28.9022i	−0.657025	−	1.01240i
$816$		0			0
$817$	−38.3431	+	6.07296i	−1.34146	+	0.212466i
$818$		0			0
$819$	−8.56139	−	2.78176i	−0.299159	−	0.0972027i
$820$		0			0
$821$	−14.6926	−	20.2226i	−0.512775	−	0.705774i	0.471609	−	0.881808i	$-0.343673\pi$
$821$	−14.6926	−	20.2226i	−0.512775	−	0.705774i	−0.984384	+	0.176034i	$0.943673\pi$
$822$		0			0
$823$	−10.4310	+	20.4719i	−0.363600	+	0.713606i	−0.998246	−	0.0591972i	$-0.981146\pi$
$823$	−10.4310	+	20.4719i	−0.363600	+	0.713606i	0.634646	+	0.772803i	$0.281146\pi$
$824$		0			0
$825$	−5.36123	−	12.7215i	−0.186654	−	0.442904i
$826$		0			0
$827$	2.51391	−	4.93382i	0.0874171	−	0.171566i	−0.843159	−	0.537664i	$-0.819307\pi$
$827$	2.51391	−	4.93382i	0.0874171	−	0.171566i	0.930576	+	0.366099i	$0.119307\pi$
$828$		0			0
$829$	8.80126	+	12.1139i	0.305680	+	0.420733i	0.934028	−	0.357200i	$-0.116268\pi$
$829$	8.80126	+	12.1139i	0.305680	+	0.420733i	−0.628348	+	0.777933i	$0.716268\pi$
$830$		0			0
$831$	23.8694	+	7.75564i	0.828020	+	0.269040i
$832$		0			0
$833$	20.5045	−	3.24759i	0.710439	−	0.112522i
$834$		0			0
$835$	5.05192	+	7.78443i	0.174829	+	0.269391i
$836$		0			0
$837$	1.32438	−	1.32438i	0.0457773	−	0.0457773i
$838$		0			0
$839$	7.40356	−	10.1901i	0.255599	−	0.351802i	−0.661863	−	0.749625i	$-0.730234\pi$
$839$	7.40356	−	10.1901i	0.255599	−	0.351802i	0.917462	+	0.397823i	$0.130234\pi$
$840$		0			0
$841$	−8.65134	+	26.6261i	−0.298322	+	0.918141i
$842$		0			0
$843$	−1.10941	+	7.00457i	−0.0382103	+	0.241250i
$844$		0			0
$845$	27.0049	−	2.83006i	0.928998	−	0.0973572i
$846$		0			0
$847$	−34.8744	−	30.5585i	−1.19830	−	1.05000i
$848$		0			0
$849$	−2.45461	−	7.55451i	−0.0842420	−	0.259270i
$850$		0			0
$851$	11.0621	−	8.03706i	0.379203	−	0.275507i
$852$		0			0
$853$	−22.5965	−	44.3481i	−0.773689	−	1.51845i	−0.853181	−	0.521614i	$-0.825330\pi$
$853$	−22.5965	−	44.3481i	−0.773689	−	1.51845i	0.0794926	−	0.996835i	$-0.474670\pi$
$854$		0			0
$855$	−20.8287	+	18.7429i	−0.712328	+	0.640992i
$856$		0			0
$857$	21.2860	+	21.2860i	0.727117	+	0.727117i	0.970044	−	0.242927i	$-0.0781077\pi$
$857$	21.2860	+	21.2860i	0.727117	+	0.727117i	−0.242927	+	0.970044i	$0.578108\pi$
$858$		0			0
$859$		−	9.31402i		−	0.317790i	−0.987295	−	0.158895i	$-0.949207\pi$
$859$		−	9.31402i		−	0.317790i	0.987295	−	0.158895i	$-0.0507932\pi$
$860$		0			0
$861$	1.63941	+	1.19110i	0.0558709	+	0.0405926i
$862$		0			0
$863$	−31.5320	+	16.0664i	−1.07336	+	0.546905i	−0.899077	−	0.437790i	$-0.855761\pi$
$863$	−31.5320	+	16.0664i	−1.07336	+	0.546905i	−0.174285	+	0.984695i	$0.555761\pi$
$864$		0			0
$865$	3.47231	−	9.03749i	0.118062	−	0.307284i
$866$		0			0
$867$	−9.85305	−	5.02038i	−0.334627	−	0.170501i
$868$		0			0
$869$	7.57178	−	0.249443i	0.256855	−	0.00846176i
$870$		0			0
$871$	−3.80391	+	1.23597i	−0.128891	+	0.0418791i
$872$		0			0
$873$	−7.57478	−	1.19973i	−0.256368	−	0.0406046i
$874$		0			0
$875$	46.5418	+	7.41486i	1.57340	+	0.250668i
$876$		0			0
$877$	−3.41955	−	21.5902i	−0.115470	−	0.729048i	−0.975695	−	0.219133i	$-0.929677\pi$
$877$	−3.41955	−	21.5902i	−0.115470	−	0.729048i	0.860225	−	0.509915i	$-0.170323\pi$
$878$		0			0
$879$	−1.92089			−0.0647901
$880$		0			0
$881$	46.4810			1.56599			0.782993	−	0.622031i	$-0.213692\pi$
$881$	46.4810			1.56599			0.782993	+	0.622031i	$0.213692\pi$
$882$		0			0
$883$	−4.36822	−	27.5798i	−0.147002	−	0.928135i	−0.945378	−	0.325976i	$-0.894307\pi$
$883$	−4.36822	−	27.5798i	−0.147002	−	0.928135i	0.798376	−	0.602159i	$-0.205693\pi$
$884$		0			0
$885$	4.48021	+	16.7407i	0.150601	+	0.562731i
$886$		0			0
$887$	6.95351	+	1.10133i	0.233476	+	0.0369790i	0.272076	−	0.962276i	$-0.412290\pi$
$887$	6.95351	+	1.10133i	0.233476	+	0.0369790i	−0.0385999	+	0.999255i	$0.512290\pi$
$888$		0			0
$889$	4.64858	−	1.51041i	0.155908	−	0.0506577i
$890$		0			0
$891$	−3.65892	−	10.1149i	−0.122578	−	0.338862i
$892$		0			0
$893$	5.75734	+	2.93351i	0.192662	+	0.0981662i
$894$		0			0
$895$	3.38064	+	7.59923i	0.113002	+	0.254014i
$896$		0			0
$897$	−1.90318	+	0.969718i	−0.0635453	+	0.0323780i
$898$		0			0
$899$	−0.343606	−	0.249644i	−0.0114599	−	0.00832611i
$900$		0			0
$901$			17.5071i			0.583247i
$902$		0			0
$903$	−17.7343	−	17.7343i	−0.590160	−	0.590160i
$904$		0			0
$905$	9.04395	+	10.0504i	0.300631	+	0.334088i
$906$		0			0
$907$	−13.4148	−	26.3281i	−0.445433	−	0.874211i	−0.999139	−	0.0414984i	$-0.986787\pi$
$907$	−13.4148	−	26.3281i	−0.445433	−	0.874211i	0.553706	−	0.832712i	$-0.313213\pi$
$908$		0			0
$909$	−24.8061	+	18.0227i	−0.822765	+	0.597774i
$910$		0			0
$911$	−5.23886	−	16.1236i	−0.173571	−	0.534198i	0.825994	−	0.563679i	$-0.190614\pi$
$911$	−5.23886	−	16.1236i	−0.173571	−	0.534198i	−0.999565	+	0.0294813i	$0.990614\pi$
$912$		0			0
$913$	−6.47702	+	1.24574i	−0.214358	+	0.0412279i
$914$		0			0
$915$	−11.2546	−	9.11946i	−0.372066	−	0.301480i
$916$		0			0
$917$	9.53075	−	60.1748i	0.314733	−	1.98715i
$918$		0			0
$919$	1.55222	−	4.77725i	0.0512030	−	0.157587i	−0.922185	−	0.386748i	$-0.873598\pi$
$919$	1.55222	−	4.77725i	0.0512030	−	0.157587i	0.973388	+	0.229161i	$0.0735983\pi$
$920$		0			0
$921$	8.62467	−	11.8708i	0.284193	−	0.391158i
$922$		0			0
$923$	5.62351	−	5.62351i	0.185100	−	0.185100i
$924$		0			0
$925$	23.0321	−	8.82519i	0.757290	−	0.290170i
$926$		0			0
$927$	22.9736	−	3.63865i	0.754551	−	0.119509i
$928$		0			0
$929$	11.2348	+	3.65041i	0.368602	+	0.119766i	0.487460	−	0.873145i	$-0.337923\pi$
$929$	11.2348	+	3.65041i	0.368602	+	0.119766i	−0.118858	+	0.992911i	$0.537923\pi$
$930$		0			0
$931$	34.3822	+	47.3231i	1.12683	+	1.55095i
$932$		0			0
$933$	−5.71194	+	11.2103i	−0.187001	+	0.367009i
$934$		0			0
$935$	13.5072	+	4.68533i	0.441731	+	0.153227i
$936$		0			0
$937$	−1.04060	+	2.04229i	−0.0339949	+	0.0667187i	−0.907379	−	0.420313i	$-0.861920\pi$
$937$	−1.04060	+	2.04229i	−0.0339949	+	0.0667187i	0.873384	+	0.487032i	$0.161920\pi$
$938$		0			0
$939$	12.7791	+	17.5889i	0.417029	+	0.573991i
$940$		0			0
$941$	1.68653	+	0.547988i	0.0549794	+	0.0178639i	0.336378	−	0.941727i	$-0.390798\pi$
$941$	1.68653	+	0.547988i	0.0549794	+	0.0178639i	−0.281398	+	0.959591i	$0.590798\pi$
$942$		0			0
$943$	−1.58094	+	0.250397i	−0.0514826	+	0.00815404i
$944$		0			0
$945$	−40.7297	−	8.67026i	−1.32494	−	0.282043i
$946$		0			0
$947$	8.63289	−	8.63289i	0.280531	−	0.280531i	−0.552790	−	0.833321i	$-0.686437\pi$
$947$	8.63289	−	8.63289i	0.280531	−	0.280531i	0.833321	+	0.552790i	$0.186437\pi$
$948$		0			0
$949$	2.97101	−	4.08925i	0.0964431	−	0.132743i
$950$		0			0
$951$	−7.28714	+	22.4275i	−0.236302	+	0.727262i
$952$		0			0
$953$	2.88376	−	18.2074i	0.0934143	−	0.589794i	−0.895930	−	0.444196i	$-0.853489\pi$
$953$	2.88376	−	18.2074i	0.0934143	−	0.589794i	0.989344	−	0.145598i	$-0.0465107\pi$
$954$		0			0
$955$	−3.85821	−	36.8157i	−0.124849	−	1.19133i
$956$		0			0
$957$	2.42189	−	1.33623i	0.0782884	−	0.0431941i
$958$		0			0
$959$	16.1154	+	49.5982i	0.520395	+	1.60161i
$960$		0			0
$961$	24.9341	−	18.1157i	0.804327	−	0.584377i
$962$		0			0
$963$	−6.45868	−	12.6759i	−0.208128	−	0.408474i
$964$		0			0
$965$	−37.8803	−	1.99673i	−1.21941	−	0.0642770i
$966$		0			0
$967$	−9.49113	−	9.49113i	−0.305214	−	0.305214i	0.537836	−	0.843050i	$-0.319242\pi$
$967$	−9.49113	−	9.49113i	−0.305214	−	0.305214i	−0.843050	+	0.537836i	$0.819242\pi$
$968$		0			0
$969$			8.71697i			0.280029i
$970$		0			0
$971$	41.4379	+	30.1064i	1.32981	+	0.966161i	0.999754	+	0.0221983i	$0.00706650\pi$
$971$	41.4379	+	30.1064i	1.32981	+	0.966161i	0.330053	+	0.943963i	$0.392933\pi$
$972$		0			0
$973$	3.79111	−	1.93167i	0.121538	−	0.0619265i
$974$		0			0
$975$	−3.76931	+	0.798805i	−0.120714	+	0.0255822i
$976$		0			0
$977$	12.9020	+	6.57391i	0.412772	+	0.210318i	0.648030	−	0.761615i	$-0.275593\pi$
$977$	12.9020	+	6.57391i	0.412772	+	0.210318i	−0.235257	+	0.971933i	$0.575593\pi$
$978$		0			0
$979$	−44.3897	−	12.8235i	−1.41870	−	0.409840i
$980$		0			0
$981$	−43.7046	+	14.2005i	−1.39538	+	0.453386i
$982$		0			0
$983$	56.8388	+	9.00238i	1.81288	+	0.287131i	0.968572	−	0.248734i	$-0.0800143\pi$
$983$	56.8388	+	9.00238i	1.81288	+	0.287131i	0.844304	+	0.535865i	$0.180014\pi$
$984$		0			0
$985$	29.4365	−	7.87794i	0.937926	−	0.251012i
$986$		0			0
$987$	0.653031	+	4.12308i	0.0207862	+	0.131239i
$988$		0			0
$989$	19.8105			0.629936
$990$		0			0
$991$	−13.1102			−0.416458			−0.208229	−	0.978080i	$-0.566770\pi$
$991$	−13.1102			−0.416458			−0.208229	+	0.978080i	$0.566770\pi$
$992$		0			0
$993$	3.20952	+	20.2641i	0.101851	+	0.643062i
$994$		0			0
$995$	37.5934	+	21.7198i	1.19179	+	0.688563i
$996$		0			0
$997$	2.22714	+	0.352744i	0.0705343	+	0.0111715i	0.191602	−	0.981473i	$-0.438632\pi$
$997$	2.22714	+	0.352744i	0.0705343	+	0.0111715i	−0.121068	+	0.992644i	$0.538632\pi$
$998$		0			0
$999$	−20.7269	+	6.73459i	−0.655772	+	0.213073i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.cm.a.193.3		32
4.3	odd	2		55.2.l.a.28.4	yes	32
5.2	odd	4	inner	880.2.cm.a.17.3		32
11.2	odd	10	inner	880.2.cm.a.673.3		32
12.11	even	2		495.2.bj.a.28.1		32
20.3	even	4		275.2.bm.b.182.1		32
20.7	even	4		55.2.l.a.17.4	yes	32
20.19	odd	2		275.2.bm.b.193.1		32
44.3	odd	10		605.2.e.b.483.4		32
44.7	even	10		605.2.m.c.118.1		32
44.15	odd	10		605.2.m.d.118.4		32
44.19	even	10		605.2.e.b.483.13		32
44.27	odd	10		605.2.m.c.403.4		32
44.31	odd	10		605.2.m.e.233.1		32
44.35	even	10		55.2.l.a.13.4	yes	32
44.39	even	10		605.2.m.d.403.1		32
44.43	even	2		605.2.m.e.578.1		32
55.2	even	20	inner	880.2.cm.a.497.3		32
60.47	odd	4		495.2.bj.a.127.1		32
132.35	odd	10		495.2.bj.a.343.1		32
220.7	odd	20		605.2.m.c.602.4		32
220.27	even	20		605.2.m.c.282.1		32
220.47	even	20		605.2.e.b.362.13		32
220.79	even	10		275.2.bm.b.68.1		32
220.87	odd	4		605.2.m.e.457.1		32
220.107	odd	20		605.2.e.b.362.4		32
220.123	odd	20		275.2.bm.b.57.1		32
220.127	odd	20		605.2.m.d.282.4		32
220.147	even	20		605.2.m.d.602.1		32
220.167	odd	20		55.2.l.a.2.4	✓	32
220.207	even	20		605.2.m.e.112.1		32
660.167	even	20		495.2.bj.a.442.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.4	✓	32	220.167	odd	20
55.2.l.a.13.4	yes	32	44.35	even	10
55.2.l.a.17.4	yes	32	20.7	even	4
55.2.l.a.28.4	yes	32	4.3	odd	2
275.2.bm.b.57.1		32	220.123	odd	20
275.2.bm.b.68.1		32	220.79	even	10
275.2.bm.b.182.1		32	20.3	even	4
275.2.bm.b.193.1		32	20.19	odd	2
495.2.bj.a.28.1		32	12.11	even	2
495.2.bj.a.127.1		32	60.47	odd	4
495.2.bj.a.343.1		32	132.35	odd	10
495.2.bj.a.442.1		32	660.167	even	20
605.2.e.b.362.4		32	220.107	odd	20
605.2.e.b.362.13		32	220.47	even	20
605.2.e.b.483.4		32	44.3	odd	10
605.2.e.b.483.13		32	44.19	even	10
605.2.m.c.118.1		32	44.7	even	10
605.2.m.c.282.1		32	220.27	even	20
605.2.m.c.403.4		32	44.27	odd	10
605.2.m.c.602.4		32	220.7	odd	20
605.2.m.d.118.4		32	44.15	odd	10
605.2.m.d.282.4		32	220.127	odd	20
605.2.m.d.403.1		32	44.39	even	10
605.2.m.d.602.1		32	220.147	even	20
605.2.m.e.112.1		32	220.207	even	20
605.2.m.e.233.1		32	44.31	odd	10
605.2.m.e.457.1		32	220.87	odd	4
605.2.m.e.578.1		32	44.43	even	2
880.2.cm.a.17.3		32	5.2	odd	4	inner
880.2.cm.a.193.3		32	1.1	even	1	trivial
880.2.cm.a.497.3		32	55.2	even	20	inner
880.2.cm.a.673.3		32	11.2	odd	10	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.130227 + 0.822224i) q^{3} +(-1.11862 + 1.93615i) q^{5} +(4.16343 + 0.659422i) q^{7} +(2.19408 - 0.712899i) q^{9} +(0.920480 - 3.18633i) q^{11} +(-0.824787 - 0.420250i) q^{13} +(-1.73763 - 0.667616i) q^{15} +(1.71765 - 0.875188i) q^{17} +(4.39439 + 3.19271i) q^{19} +3.50915i q^{21} +(-1.95998 - 1.95998i) q^{23} +(-2.49738 - 4.33164i) q^{25} +(2.00570 + 3.93640i) q^{27} +(0.810497 - 0.588860i) q^{29} +(-0.131006 - 0.403196i) q^{31} +(2.73975 + 0.341892i) q^{33} +(-5.93404 + 7.32339i) q^{35} +(-0.771690 + 4.87226i) q^{37} +(0.238130 - 0.732888i) q^{39} +(0.339428 - 0.467182i) q^{41} +(-5.05373 + 5.05373i) q^{43} +(-1.07406 + 5.04553i) q^{45} +(1.17495 - 0.186094i) q^{47} +(10.2419 + 3.32780i) q^{49} +(0.943286 + 1.29832i) q^{51} +(-4.12294 + 8.09173i) q^{53} +(5.13956 + 5.34649i) q^{55} +(-2.05285 + 4.02895i) q^{57} +(-5.47214 - 7.53175i) q^{59} +(7.40093 + 2.40471i) q^{61} +(9.60498 - 1.52128i) q^{63} +(1.73629 - 1.12681i) q^{65} +(3.05526 - 3.05526i) q^{67} +(1.35630 - 1.86679i) q^{69} +(-2.65487 + 8.17086i) q^{71} +(-0.854195 + 5.39318i) q^{73} +(3.23635 - 2.61750i) q^{75} +(5.93349 - 12.6591i) q^{77} +(0.705861 + 2.17242i) q^{79} +(2.62377 - 1.90628i) q^{81} +(-0.902846 - 1.77193i) q^{83} +(-0.226904 + 4.30464i) q^{85} +(0.589724 + 0.589724i) q^{87} -13.9313i q^{89} +(-3.15682 - 2.29356i) q^{91} +(0.314457 - 0.160224i) q^{93} +(-11.0972 + 4.93678i) q^{95} +(-2.96200 - 1.50922i) q^{97} +(-0.251929 - 7.64727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} - 2 q^{5} + 24 q^{11} - 10 q^{13} - 14 q^{15} + 24 q^{23} + 16 q^{25} + 16 q^{27} + 28 q^{31} + 66 q^{33} + 10 q^{35} - 8 q^{37} + 40 q^{41} - 28 q^{45} + 28 q^{47} - 20 q^{51} - 24 q^{53}+ \cdots - 8 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 - 2 * q^5 + 24 * q^11 - 10 * q^13 - 14 * q^15 + 24 * q^23 + 16 * q^25 + 16 * q^27 + 28 * q^31 + 66 * q^33 + 10 * q^35 - 8 * q^37 + 40 * q^41 - 28 * q^45 + 28 * q^47 - 20 * q^51 - 24 * q^53 + 64 * q^55 + 30 * q^57 - 60 * q^61 + 30 * q^63 + 8 * q^67 - 24 * q^71 + 50 * q^73 - 34 * q^75 + 70 * q^77 - 12 * q^81 - 90 * q^83 + 30 * q^85 - 20 * q^91 - 8 * q^93 + 40 * q^95 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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