LMFDB - Embedded newform 880.2.cm.a.17.3

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			17.3
Character	$\chi$	$=$	880.17
Dual form			880.2.cm.a.673.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.822224 - 0.130227i) q^{3} +(-0.233059 + 2.22389i) q^{5} +(-0.659422 + 4.16343i) q^{7} +(-2.19408 + 0.712899i) q^{9} +(0.920480 - 3.18633i) q^{11} +(-0.420250 + 0.824787i) q^{13} +(0.0979846 + 1.85889i) q^{15} +(0.875188 + 1.71765i) q^{17} +(-4.39439 - 3.19271i) q^{19} +3.50915i q^{21} +(-1.95998 + 1.95998i) q^{23} +(-4.89137 - 1.03660i) q^{25} +(-3.93640 + 2.00570i) q^{27} +(-0.810497 + 0.588860i) q^{29} +(-0.131006 - 0.403196i) q^{31} +(0.341892 - 2.73975i) q^{33} +(-9.10532 - 2.43681i) q^{35} +(-4.87226 - 0.771690i) q^{37} +(-0.238130 + 0.732888i) q^{39} +(0.339428 - 0.467182i) q^{41} +(5.05373 + 5.05373i) q^{43} +(-1.07406 - 5.04553i) q^{45} +(0.186094 + 1.17495i) q^{47} +(-10.2419 - 3.32780i) q^{49} +(0.943286 + 1.29832i) q^{51} +(8.09173 + 4.12294i) q^{53} +(6.87153 + 2.78965i) q^{55} +(-4.02895 - 2.05285i) q^{57} +(5.47214 + 7.53175i) q^{59} +(7.40093 + 2.40471i) q^{61} +(-1.52128 - 9.60498i) q^{63} +(-1.73629 - 1.12681i) q^{65} +(3.05526 + 3.05526i) q^{67} +(-1.35630 + 1.86679i) q^{69} +(-2.65487 + 8.17086i) q^{71} +(5.39318 + 0.854195i) q^{73} +(-4.15679 - 0.215323i) q^{75} +(12.6591 + 5.93349i) q^{77} +(-0.705861 - 2.17242i) q^{79} +(2.62377 - 1.90628i) q^{81} +(-1.77193 + 0.902846i) q^{83} +(-4.02384 + 1.54601i) q^{85} +(-0.589724 + 0.589724i) q^{87} +13.9313i q^{89} +(-3.15682 - 2.29356i) q^{91} +(-0.160224 - 0.314457i) q^{93} +(8.12438 - 9.02854i) q^{95} +(1.50922 - 2.96200i) q^{97} +(0.251929 + 7.64727i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

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

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
$3$	0.822224	−	0.130227i	0.474711	−	0.0751869i	0.0855054	−	0.996338i	$-0.472750\pi$
$3$	0.822224	−	0.130227i	0.474711	−	0.0751869i	0.389206	+	0.921151i	$0.372750\pi$
$4$		0			0
$5$	−0.233059	+	2.22389i	−0.104227	+	0.994554i
$5$	−0.233059	+	2.22389i	−0.104227	+	0.994554i
$6$		0			0
$7$	−0.659422	+	4.16343i	−0.249238	+	1.57363i	0.472417	+	0.881375i	$0.343382\pi$
$7$	−0.659422	+	4.16343i	−0.249238	+	1.57363i	−0.721655	+	0.692253i	$0.756618\pi$
$8$		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
$13$	−0.420250	+	0.824787i	−0.116556	+	0.228755i	−0.941913	−	0.335857i	$-0.890974\pi$
$13$	−0.420250	+	0.824787i	−0.116556	+	0.228755i	0.825357	+	0.564612i	$0.190974\pi$
$14$		0			0
$15$	0.0979846	+	1.85889i	0.0252995	+	0.479962i
$16$		0			0
$17$	0.875188	+	1.71765i	0.212264	+	0.416592i	0.972449	−	0.233115i	$-0.0748917\pi$
$17$	0.875188	+	1.71765i	0.212264	+	0.416592i	−0.760185	+	0.649707i	$0.774892\pi$
$18$		0			0
$19$	−4.39439	−	3.19271i	−1.00814	−	0.732458i	−0.0443230	−	0.999017i	$-0.514113\pi$
$19$	−4.39439	−	3.19271i	−1.00814	−	0.732458i	−0.963818	+	0.266560i	$0.914113\pi$
$20$		0			0
$21$			3.50915i			0.765758i
$22$		0			0
$23$	−1.95998	+	1.95998i	−0.408685	+	0.408685i	−0.881280	−	0.472595i	$-0.843317\pi$
$23$	−1.95998	+	1.95998i	−0.408685	+	0.408685i	0.472595	+	0.881280i	$0.343317\pi$
$24$		0			0
$25$	−4.89137	−	1.03660i	−0.978273	−	0.207319i
$26$		0			0
$27$	−3.93640	+	2.00570i	−0.757561	+	0.385996i
$28$		0			0
$29$	−0.810497	+	0.588860i	−0.150505	+	0.109349i	−0.660490	−	0.750835i	$-0.729651\pi$
$29$	−0.810497	+	0.588860i	−0.150505	+	0.109349i	0.509984	+	0.860184i	$0.329651\pi$
$30$		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
$33$	0.341892	−	2.73975i	0.0595158	−	0.476929i
$34$		0			0
$35$	−9.10532	−	2.43681i	−1.53908	−	0.411896i
$36$		0			0
$37$	−4.87226	−	0.771690i	−0.800995	−	0.126865i	−0.257501	−	0.966278i	$-0.582899\pi$
$37$	−4.87226	−	0.771690i	−0.800995	−	0.126865i	−0.543494	+	0.839413i	$0.682899\pi$
$38$		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	$-0.0665456\pi$
$43$	5.05373	+	5.05373i	0.770687	+	0.770687i	−0.207540	+	0.978227i	$0.566546\pi$
$44$		0			0
$45$	−1.07406	−	5.04553i	−0.160111	−	0.752143i
$46$		0			0
$47$	0.186094	+	1.17495i	0.0271446	+	0.171384i	0.997536	−	0.0701524i	$-0.0223486\pi$
$47$	0.186094	+	1.17495i	0.0271446	+	0.171384i	−0.970392	+	0.241537i	$0.922349\pi$
$48$		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
$53$	8.09173	+	4.12294i	1.11149	+	0.566330i	0.910602	−	0.413285i	$-0.135619\pi$
$53$	8.09173	+	4.12294i	1.11149	+	0.566330i	0.200883	+	0.979615i	$0.435619\pi$
$54$		0			0
$55$	6.87153	+	2.78965i	0.926556	+	0.376156i
$56$		0			0
$57$	−4.02895	−	2.05285i	−0.533647	−	0.271907i
$58$		0			0
$59$	5.47214	+	7.53175i	0.712411	+	0.980550i	0.999742	+	0.0227186i	$0.00723217\pi$
$59$	5.47214	+	7.53175i	0.712411	+	0.980550i	−0.287331	+	0.957831i	$0.592768\pi$
$60$		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
$63$	−1.52128	−	9.60498i	−0.191663	−	1.21011i
$64$		0			0
$65$	−1.73629	−	1.12681i	−0.215361	−	0.139764i
$66$		0			0
$67$	3.05526	+	3.05526i	0.373259	+	0.373259i	0.868663	−	0.495404i	$-0.164980\pi$
$67$	3.05526	+	3.05526i	0.373259	+	0.373259i	−0.495404	+	0.868663i	$0.664980\pi$
$68$		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
$73$	5.39318	+	0.854195i	0.631224	+	0.0999760i	0.463844	−	0.885917i	$-0.346470\pi$
$73$	5.39318	+	0.854195i	0.631224	+	0.0999760i	0.167379	+	0.985893i	$0.446470\pi$
$74$		0			0
$75$	−4.15679	−	0.215323i	−0.479985	−	0.0248634i
$76$		0			0
$77$	12.6591	+	5.93349i	1.44264	+	0.676184i
$78$		0			0
$79$	−0.705861	−	2.17242i	−0.0794156	−	0.244416i	0.903464	−	0.428663i	$-0.141015\pi$
$79$	−0.705861	−	2.17242i	−0.0794156	−	0.244416i	−0.982880	+	0.184247i	$0.941015\pi$
$80$		0			0
$81$	2.62377	−	1.90628i	0.291530	−	0.211809i
$82$		0			0
$83$	−1.77193	+	0.902846i	−0.194495	+	0.0991002i	−0.548526	−	0.836134i	$-0.684811\pi$
$83$	−1.77193	+	0.902846i	−0.194495	+	0.0991002i	0.354031	+	0.935234i	$0.384811\pi$
$84$		0			0
$85$	−4.02384	+	1.54601i	−0.436447	+	0.167688i
$86$		0			0
$87$	−0.589724	+	0.589724i	−0.0632250	+	0.0632250i
$88$		0			0
$89$			13.9313i			1.47671i	0.674410	+	0.738357i	$0.264398\pi$
$89$			13.9313i			1.47671i	−0.674410	+	0.738357i	$0.735602\pi$
$90$		0			0
$91$	−3.15682	−	2.29356i	−0.330925	−	0.240431i
$92$		0			0
$93$	−0.160224	−	0.314457i	−0.0166144	−	0.0326076i
$94$		0			0
$95$	8.12438	−	9.02854i	0.833544	−	0.926309i
$96$		0			0
$97$	1.50922	−	2.96200i	0.153238	−	0.300746i	−0.801607	−	0.597851i	$-0.796021\pi$
$97$	1.50922	−	2.96200i	0.153238	−	0.300746i	0.954845	+	0.297105i	$0.0960213\pi$
$98$		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
$103$	1.57723	−	9.95825i	0.155409	−	0.981215i	−0.779519	−	0.626378i	$-0.784536\pi$
$103$	1.57723	−	9.95825i	0.155409	−	0.981215i	0.934928	−	0.354837i	$-0.115464\pi$
$104$		0			0
$105$	−7.80395	−	0.817839i	−0.761588	−	0.0798129i
$106$		0			0
$107$	6.09076	−	0.964682i	0.588816	−	0.0932593i	0.145085	−	0.989419i	$-0.453654\pi$
$107$	6.09076	−	0.964682i	0.588816	−	0.0932593i	0.443731	+	0.896160i	$0.353654\pi$
$108$		0			0
$109$	19.9193			1.90793			0.953964	−	0.299922i	$-0.0969607\pi$
$109$	19.9193			1.90793			0.953964	+	0.299922i	$0.0969607\pi$
$110$		0			0
$111$	−4.10659			−0.389780
$112$		0			0
$113$	−11.9729	+	1.89632i	−1.12632	+	0.178391i	−0.691673	−	0.722211i	$-0.743126\pi$
$113$	−11.9729	+	1.89632i	−1.12632	+	0.178391i	−0.434644	+	0.900602i	$0.643126\pi$
$114$		0			0
$115$	−3.90200	−	4.81558i	−0.363863	−	0.449055i
$116$		0			0
$117$	0.334071	−	2.10924i	0.0308849	−	0.194999i
$118$		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
$123$	0.218246	−	0.428331i	0.0196785	−	0.0386213i
$124$		0			0
$125$	3.44525	−	10.6363i	0.308153	−	0.951337i
$126$		0			0
$127$	0.526416	+	1.03315i	0.0467119	+	0.0916772i	0.913183	−	0.407551i	$-0.133617\pi$
$127$	0.526416	+	1.03315i	0.0467119	+	0.0916772i	−0.866471	+	0.499228i	$0.833617\pi$
$128$		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
$135$	−3.54303	−	9.22156i	−0.304936	−	0.793666i
$136$		0			0
$137$	−11.0232	+	5.61663i	−0.941780	+	0.479861i	−0.856300	−	0.516479i	$-0.827242\pi$
$137$	−11.0232	+	5.61663i	−0.941780	+	0.479861i	−0.0854799	+	0.996340i	$0.527242\pi$
$138$		0			0
$139$	−0.816606	+	0.593299i	−0.0692636	+	0.0503229i	−0.621878	−	0.783114i	$-0.713630\pi$
$139$	−0.816606	+	0.593299i	−0.0692636	+	0.0503229i	0.552615	+	0.833437i	$0.313630\pi$
$140$		0			0
$141$	0.306022	+	0.941839i	0.0257717	+	0.0793172i
$142$		0			0
$143$	2.24121	+	2.09826i	0.187420	+	0.175465i
$144$		0			0
$145$	−1.12067	−	1.93969i	−0.0930663	−	0.161083i
$146$		0			0
$147$	−8.85451	−	1.40242i	−0.730308	−	0.115669i
$148$		0			0
$149$	−0.377177	+	1.16083i	−0.0308996	+	0.0950990i	−0.965317	−	0.261081i	$-0.915921\pi$
$149$	−0.377177	+	1.16083i	−0.0308996	+	0.0950990i	0.934417	+	0.356180i	$0.115921\pi$
$150$		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
$157$	1.16061	+	7.32783i	0.0926271	+	0.584824i	0.989724	+	0.142991i	$0.0456719\pi$
$157$	1.16061	+	7.32783i	0.0926271	+	0.584824i	−0.897097	+	0.441834i	$0.854328\pi$
$158$		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
$163$	13.7294	+	6.99546i	1.07537	+	0.547927i	0.899694	−	0.436522i	$-0.143790\pi$
$163$	13.7294	+	6.99546i	1.07537	+	0.547927i	0.175673	+	0.984449i	$0.443790\pi$
$164$		0			0
$165$	6.01322	+	1.39885i	0.468129	+	0.108901i
$166$		0			0
$167$	3.69782	+	1.88413i	0.286146	+	0.145799i	0.591172	−	0.806545i	$-0.298665\pi$
$167$	3.69782	+	1.88413i	0.286146	+	0.145799i	−0.305026	+	0.952344i	$0.598665\pi$
$168$		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
$173$	0.677320	+	4.27643i	0.0514957	+	0.325131i	0.999966	+	0.00826456i	$0.00263072\pi$
$173$	0.677320	+	4.27643i	0.0514957	+	0.325131i	−0.948470	+	0.316867i	$0.897369\pi$
$174$		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	−0.882869	−	0.469619i	$-0.844391\pi$
$179$	−2.18633	+	3.00922i	−0.163414	+	0.224920i	0.719456	+	0.694538i	$0.244391\pi$
$180$		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
$183$	6.39838	+	1.01340i	0.472982	+	0.0749129i
$184$		0			0
$185$	2.85168	−	10.6555i	0.209660	−	0.783409i
$186$		0			0
$187$	6.27861	−	1.20758i	0.459137	−	0.0883066i
$188$		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
$193$	15.1151	−	7.70155i	1.08801	−	0.554370i	0.184456	−	0.982841i	$-0.440948\pi$
$193$	15.1151	−	7.70155i	1.08801	−	0.554370i	0.903556	+	0.428471i	$0.140948\pi$
$194$		0			0
$195$	−1.57436	−	0.700380i	−0.112742	−	0.0501553i
$196$		0			0
$197$	9.63624	−	9.63624i	0.686554	−	0.686554i	−0.274915	−	0.961469i	$-0.588650\pi$
$197$	9.63624	−	9.63624i	0.686554	−	0.686554i	0.961469	+	0.274915i	$0.0886496\pi$
$198$		0			0
$199$			19.4166i			1.37640i	0.725519	+	0.688202i	$0.241600\pi$
$199$			19.4166i			1.37640i	−0.725519	+	0.688202i	$0.758400\pi$
$200$		0			0
$201$	2.90999	+	2.11423i	0.205255	+	0.149126i
$202$		0			0
$203$	−1.91722	−	3.76275i	−0.134562	−	0.264093i
$204$		0			0
$205$	0.959854	+	0.863730i	0.0670391	+	0.0603255i
$206$		0			0
$207$	2.90309	−	5.69763i	0.201778	−	0.396012i
$208$		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
$213$	−1.11883	+	7.06401i	−0.0766609	+	0.484018i
$214$		0			0
$215$	−12.4168	+	10.0611i	−0.846816	+	0.686163i
$216$		0			0
$217$	1.76507	−	0.279559i	0.119820	−	0.0189777i
$218$		0			0
$219$	4.54564			0.307166
$220$		0			0
$221$	−1.78450			−0.120038
$222$		0			0
$223$	14.0202	−	2.22058i	0.938860	−	0.148701i	0.331794	−	0.943352i	$-0.392346\pi$
$223$	14.0202	−	2.22058i	0.938860	−	0.148701i	0.607066	+	0.794651i	$0.292346\pi$
$224$		0			0
$225$	11.4710	−	1.21268i	0.764735	−	0.0808452i
$226$		0			0
$227$	1.29499	−	8.17622i	0.0859512	−	0.542675i	−0.906711	−	0.421753i	$-0.861415\pi$
$227$	1.29499	−	8.17622i	0.0859512	−	0.542675i	0.992662	−	0.120922i	$-0.0385850\pi$
$228$		0			0
$229$	−18.6401	+	6.05655i	−1.23178	+	0.400228i	−0.851357	−	0.524587i	$-0.824220\pi$
$229$	−18.6401	+	6.05655i	−1.23178	+	0.400228i	−0.380418	+	0.924815i	$0.624220\pi$
$230$		0			0
$231$	11.1813	+	3.23010i	0.735676	+	0.212525i
$232$		0			0
$233$	1.68573	−	3.30844i	0.110436	−	0.216743i	−0.829173	−	0.558991i	$-0.811188\pi$
$233$	1.68573	−	3.30844i	0.110436	−	0.216743i	0.939609	+	0.342249i	$0.111188\pi$
$234$		0			0
$235$	−2.65633	+	0.140019i	−0.173280	+	0.00913385i
$236$		0			0
$237$	−0.863285	−	1.69429i	−0.0560764	−	0.110056i
$238$		0			0
$239$	−2.59930	−	1.88850i	−0.168135	−	0.122157i	0.500536	−	0.865716i	$-0.333136\pi$
$239$	−2.59930	−	1.88850i	−0.168135	−	0.122157i	−0.668671	+	0.743559i	$0.733136\pi$
$240$		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
$245$	9.78763	−	22.0013i	0.625309	−	1.40561i
$246$		0			0
$247$	4.48005	−	2.28270i	0.285059	−	0.145245i
$248$		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
$253$	4.44104	+	8.04929i	0.279206	+	0.506055i
$254$		0			0
$255$	−3.10717	+	1.79518i	−0.194578	+	0.112418i
$256$		0			0
$257$	−16.0045	−	2.53487i	−0.998335	−	0.158121i	−0.364182	−	0.931328i	$-0.618651\pi$
$257$	−16.0045	−	2.53487i	−0.998335	−	0.158121i	−0.634154	+	0.773207i	$0.718651\pi$
$258$		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	$-0.259410\pi$
$263$	−0.677874	−	0.677874i	−0.0417995	−	0.0417995i	−0.727698	+	0.685898i	$0.759410\pi$
$264$		0			0
$265$	−11.0548	+	17.0342i	−0.679092	+	1.04640i
$266$		0			0
$267$	1.81424	+	11.4546i	0.111030	+	0.701013i
$268$		0			0
$269$	27.0327	+	8.78345i	1.64821	+	0.535536i	0.978351	−	0.206951i	$-0.0663541\pi$
$269$	27.0327	+	8.78345i	1.64821	+	0.535536i	0.669860	+	0.742487i	$0.266354\pi$
$270$		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
$273$	−2.89430	−	1.47472i	−0.175171	−	0.0892540i
$274$		0			0
$275$	−7.80534	+	14.6314i	−0.470680	+	0.882304i
$276$		0			0
$277$	26.8625	+	13.6871i	1.61401	+	0.822379i	0.999438	+	0.0335176i	$0.0106710\pi$
$277$	26.8625	+	13.6871i	1.61401	+	0.822379i	0.614571	+	0.788861i	$0.289329\pi$
$278$		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
$283$	1.49267	+	9.42432i	0.0887297	+	0.560218i	0.991501	+	0.130097i	$0.0415289\pi$
$283$	1.49267	+	9.42432i	0.0887297	+	0.560218i	−0.902772	+	0.430120i	$0.858471\pi$
$284$		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
$293$	2.27904	+	0.360965i	0.133143	+	0.0210878i	0.222650	−	0.974898i	$-0.428529\pi$
$293$	2.27904	+	0.360965i	0.133143	+	0.0210878i	−0.0895072	+	0.995986i	$0.528529\pi$
$294$		0			0
$295$	−18.0251	+	10.4141i	−1.04946	+	0.606331i
$296$		0			0
$297$	2.76744	+	14.3889i	0.160583	+	0.834928i
$298$		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
$303$	−9.85838	+	5.02310i	−0.566349	+	0.288569i
$304$		0			0
$305$	−7.07265	+	15.8984i	−0.404979	+	0.910340i
$306$		0			0
$307$	12.4635	−	12.4635i	0.711327	−	0.711327i	−0.255486	−	0.966813i	$-0.582235\pi$
$307$	12.4635	−	12.4635i	0.711327	−	0.711327i	0.966813	+	0.255486i	$0.0822353\pi$
$308$		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
$313$	−11.8565	−	23.2697i	−0.670169	−	1.31528i	−0.936251	−	0.351331i	$-0.885729\pi$
$313$	−11.8565	−	23.2697i	−0.670169	−	1.31528i	0.266082	−	0.963950i	$-0.414271\pi$
$314$		0			0
$315$	21.7150	−	1.14463i	1.22350	−	0.0644925i
$316$		0			0
$317$	−12.8603	+	25.2398i	−0.722307	+	1.41761i	0.178744	+	0.983896i	$0.442797\pi$
$317$	−12.8603	+	25.2398i	−0.722307	+	1.41761i	−0.901051	+	0.433712i	$0.857203\pi$
$318$		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
$323$	1.63805	−	10.3423i	0.0911436	−	0.575458i
$324$		0			0
$325$	2.91057	−	3.59871i	0.161449	−	0.199620i
$326$		0			0
$327$	16.3782	−	2.59405i	0.905714	−	0.143451i
$328$		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
$333$	11.2403	−	1.78028i	0.615962	−	0.0975588i
$334$		0			0
$335$	−7.50662	+	6.08250i	−0.410130	+	0.332323i
$336$		0			0
$337$	4.85195	−	30.6340i	0.264302	−	1.66874i	−0.396390	−	0.918082i	$-0.629737\pi$
$337$	4.85195	−	30.6340i	0.264302	−	1.66874i	0.660692	−	0.750657i	$-0.270263\pi$
$338$		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
$343$	7.21277	−	14.1559i	0.389453	−	0.764345i
$344$		0			0
$345$	−3.83544	−	3.45134i	−0.206493	−	0.185814i
$346$		0			0
$347$	13.7041	+	26.8957i	0.735672	+	1.44384i	0.890068	+	0.455829i	$0.150657\pi$
$347$	13.7041	+	26.8957i	0.735672	+	1.44384i	−0.154395	+	0.988009i	$0.549343\pi$
$348$		0			0
$349$	−17.2865	−	12.5594i	−0.925323	−	0.672287i	0.0195201	−	0.999809i	$-0.493786\pi$
$349$	−17.2865	−	12.5594i	−0.925323	−	0.672287i	−0.944843	+	0.327523i	$0.893786\pi$
$350$		0			0
$351$		−	4.08959i		−	0.218286i
$352$		0			0
$353$	−2.82626	+	2.82626i	−0.150427	+	0.150427i	−0.778309	−	0.627882i	$-0.783922\pi$
$353$	−2.82626	+	2.82626i	−0.150427	+	0.150427i	0.627882	+	0.778309i	$0.283922\pi$
$354$		0			0
$355$	−17.5523	−	7.80843i	−0.931581	−	0.414429i
$356$		0			0
$357$	−6.02750	+	3.07116i	−0.319009	+	0.162543i
$358$		0			0
$359$	−8.68908	+	6.31298i	−0.458592	+	0.333187i	−0.792979	−	0.609249i	$-0.791471\pi$
$359$	−8.68908	+	6.31298i	−0.458592	+	0.333187i	0.334387	+	0.942436i	$0.391471\pi$
$360$		0			0
$361$	3.24592	+	9.98992i	0.170838	+	0.525785i
$362$		0			0
$363$	−8.41505	−	3.61127i	−0.441676	−	0.189542i
$364$		0			0
$365$	−3.15656	+	11.7947i	−0.165222	+	0.617365i
$366$		0			0
$367$	−34.1783	−	5.41331i	−1.78409	−	0.282572i	−0.824890	−	0.565293i	$-0.808763\pi$
$367$	−34.1783	−	5.41331i	−1.78409	−	0.282572i	−0.959202	+	0.282721i	$0.908763\pi$
$368$		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	$-0.131879\pi$
$373$	9.90454	+	9.90454i	0.512838	+	0.512838i	−0.402557	+	0.915395i	$0.631879\pi$
$374$		0			0
$375$	1.44763	−	9.19406i	0.0747555	−	0.474779i
$376$		0			0
$377$	−0.145073	−	0.915956i	−0.00747165	−	0.0471741i
$378$		0			0
$379$	−25.2037	−	8.18919i	−1.29463	−	0.420651i	−0.420919	−	0.907098i	$-0.638292\pi$
$379$	−25.2037	−	8.18919i	−1.29463	−	0.420651i	−0.873710	+	0.486447i	$0.838292\pi$
$380$		0			0
$381$	0.567376	+	0.780926i	0.0290676	+	0.0400081i
$382$		0			0
$383$	21.4177	+	10.9129i	1.09439	+	0.557622i	0.905487	−	0.424373i	$-0.139505\pi$
$383$	21.4177	+	10.9129i	1.09439	+	0.557622i	0.188907	+	0.981995i	$0.439505\pi$
$384$		0			0
$385$	−16.1457	+	26.7696i	−0.822863	+	1.36430i
$386$		0			0
$387$	−14.6911	−	7.48548i	−0.746789	−	0.380508i
$388$		0			0
$389$	−4.43509	−	6.10438i	−0.224868	−	0.309505i	0.681644	−	0.731684i	$-0.261265\pi$
$389$	−4.43509	−	6.10438i	−0.224868	−	0.309505i	−0.906512	+	0.422179i	$0.861265\pi$
$390$		0			0
$391$	−5.08193	−	1.65122i	−0.257004	−	0.0835057i
$392$		0			0
$393$	−1.88220	−	11.8838i	−0.0949445	−	0.599456i
$394$		0			0
$395$	4.99573	−	1.06346i	0.251362	−	0.0535083i
$396$		0			0
$397$	16.0995	+	16.0995i	0.808008	+	0.808008i	0.984332	−	0.176324i	$-0.0564206\pi$
$397$	16.0995	+	16.0995i	0.808008	+	0.808008i	−0.176324	+	0.984332i	$0.556421\pi$
$398$		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
$403$	0.387606	+	0.0613908i	0.0193080	+	0.00305809i
$404$		0			0
$405$	3.62787	+	6.27926i	0.180270	+	0.312019i
$406$		0			0
$407$	−6.94368	+	14.8143i	−0.344185	+	0.734319i
$408$		0			0
$409$	−1.80956	−	5.56925i	−0.0894769	−	0.275382i	0.896298	−	0.443452i	$-0.146246\pi$
$409$	−1.80956	−	5.56925i	−0.0894769	−	0.275382i	−0.985775	+	0.168070i	$0.946246\pi$
$410$		0			0
$411$	−8.33214	+	6.05365i	−0.410994	+	0.298605i
$412$		0			0
$413$	−34.9663	+	17.8162i	−1.72058	+	0.876680i
$414$		0			0
$415$	−1.59486	−	4.15100i	−0.0782888	−	0.203765i
$416$		0			0
$417$	−0.594169	+	0.594169i	−0.0290966	+	0.0290966i
$418$		0			0
$419$			11.0599i			0.540311i	0.962817	+	0.270155i	$0.0870751\pi$
$419$			11.0599i			0.540311i	−0.962817	+	0.270155i	$0.912925\pi$
$420$		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
$423$	−1.24593	−	2.44527i	−0.0605790	−	0.118893i
$424$		0			0
$425$	−2.50035	−	9.30889i	−0.121285	−	0.451547i
$426$		0			0
$427$	−14.8922	+	29.2275i	−0.720682	+	1.41442i
$428$		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
$433$	0.789604	−	4.98536i	0.0379460	−	0.239581i	−0.961424	−	0.275070i	$-0.911299\pi$
$433$	0.789604	−	4.98536i	0.0379460	−	0.239581i	0.999370	+	0.0354890i	$0.0112989\pi$
$434$		0			0
$435$	−1.17404	−	1.44892i	−0.0562909	−	0.0694705i
$436$		0			0
$437$	14.8706	−	2.35527i	0.711357	−	0.112668i
$438$		0			0
$439$	1.29778			0.0619394			0.0309697	−	0.999520i	$-0.490140\pi$
$439$	1.29778			0.0619394			0.0309697	+	0.999520i	$0.490140\pi$
$440$		0			0
$441$	24.8439			1.18304
$442$		0			0
$443$	−15.2112	+	2.40922i	−0.722707	+	0.114466i	−0.506942	−	0.861980i	$-0.669224\pi$
$443$	−15.2112	+	2.40922i	−0.722707	+	0.114466i	−0.215764	+	0.976445i	$0.569224\pi$
$444$		0			0
$445$	−30.9817	−	3.24682i	−1.46867	−	0.153914i
$446$		0			0
$447$	−0.158952	+	1.00358i	−0.00751816	+	0.0474678i
$448$		0			0
$449$	−11.5295	+	3.74615i	−0.544109	+	0.176792i	−0.568159	−	0.822919i	$-0.692344\pi$
$449$	−11.5295	+	3.74615i	−0.544109	+	0.176792i	0.0240497	+	0.999711i	$0.492344\pi$
$450$		0			0
$451$	−1.17616	−	1.51156i	−0.0553833	−	0.0711766i
$452$		0			0
$453$	−0.599688	+	1.17695i	−0.0281758	+	0.0552981i
$454$		0			0
$455$	5.83636	−	6.48588i	0.273613	−	0.304063i
$456$		0			0
$457$	1.59383	+	3.12807i	0.0745563	+	0.146325i	0.925276	−	0.379295i	$-0.123833\pi$
$457$	1.59383	+	3.12807i	0.0745563	+	0.146325i	−0.850720	+	0.525620i	$0.823833\pi$
$458$		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	−0.967718	−	0.252037i	$-0.918900\pi$
$463$	−15.3996	+	15.3996i	−0.715681	+	0.715681i	0.252037	+	0.967718i	$0.418900\pi$
$464$		0			0
$465$	0.736658	−	0.283033i	0.0341617	−	0.0131253i
$466$		0			0
$467$	13.0834	−	6.66632i	0.605427	−	0.308481i	−0.124273	−	0.992248i	$-0.539660\pi$
$467$	13.0834	−	6.66632i	0.605427	−	0.308481i	0.729700	+	0.683768i	$0.239660\pi$
$468$		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
$473$	20.7547	−	11.4510i	0.954303	−	0.526518i
$474$		0			0
$475$	18.1850	+	20.1719i	0.834385	+	0.925551i
$476$		0			0
$477$	−20.6931	−	3.27747i	−0.947473	−	0.150065i
$478$		0			0
$479$	1.51842	−	4.67321i	0.0693783	−	0.213524i	−0.910356	−	0.413826i	$-0.864192\pi$
$479$	1.51842	−	4.67321i	0.0693783	−	0.213524i	0.979734	+	0.200302i	$0.0641922\pi$
$480$		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
$487$	−1.67972	−	10.6054i	−0.0761155	−	0.480574i	−0.996071	−	0.0885527i	$-0.971776\pi$
$487$	−1.67972	−	10.6054i	−0.0761155	−	0.480574i	0.919956	−	0.392022i	$-0.128224\pi$
$488$		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
$493$	−1.72079	−	0.876788i	−0.0775007	−	0.0394886i
$494$		0			0
$495$	−17.0654	−	1.22200i	−0.767032	−	0.0549249i
$496$		0			0
$497$	−32.2681	−	16.4414i	−1.44742	−	0.737498i
$498$		0			0
$499$	−5.25588	−	7.23410i	−0.235285	−	0.323843i	0.675005	−	0.737813i	$-0.264142\pi$
$499$	−5.25588	−	7.23410i	−0.235285	−	0.323843i	−0.910290	+	0.413971i	$0.864142\pi$
$500$		0			0
$501$	3.28580	+	1.06762i	0.146799	+	0.0476978i
$502$		0			0
$503$	3.02441	+	19.0954i	0.134852	+	0.851421i	0.958660	+	0.284553i	$0.0918451\pi$
$503$	3.02441	+	19.0954i	0.134852	+	0.851421i	−0.823808	+	0.566868i	$0.808155\pi$
$504$		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	−0.770679	−	0.637224i	$-0.780083\pi$
$509$	1.65845	−	2.28267i	0.0735097	−	0.101177i	0.844189	+	0.536046i	$0.180083\pi$
$510$		0			0
$511$	−7.11276	+	21.8908i	−0.314650	+	0.968393i
$512$		0			0
$513$	23.7017	+	3.75398i	1.04645	+	0.165742i
$514$		0			0
$515$	21.7784	+	5.82845i	0.959673	+	0.256832i
$516$		0			0
$517$	3.91508	+	0.488562i	0.172185	+	0.0214869i
$518$		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
$523$	13.2194	−	6.73563i	0.578045	−	0.294528i	−0.140420	−	0.990092i	$-0.544845\pi$
$523$	13.2194	−	6.73563i	0.578045	−	0.294528i	0.718465	+	0.695564i	$0.244845\pi$
$524$		0			0
$525$	3.63757	−	17.1645i	0.158756	−	0.749121i
$526$		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
$533$	0.242681	+	0.476289i	0.0105117	+	0.0206304i
$534$		0			0
$535$	0.725838	+	13.7700i	0.0313807	+	0.595329i
$536$		0			0
$537$	−1.40577	+	2.75897i	−0.0606633	+	0.119058i
$538$		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
$543$	0.787429	−	4.97163i	0.0337918	−	0.213353i
$544$		0			0
$545$	−4.64239	+	44.2984i	−0.198858	+	1.89754i
$546$		0			0
$547$	31.1772	−	4.93799i	1.33304	−	0.211133i	0.551076	−	0.834455i	$-0.314217\pi$
$547$	31.1772	−	4.93799i	1.33304	−	0.211133i	0.781966	+	0.623322i	$0.214217\pi$
$548$		0			0
$549$	−17.9525			−0.766194
$550$		0			0
$551$	5.44169			0.231824
$552$		0			0
$553$	9.51017	−	1.50626i	0.404414	−	0.0640528i
$554$		0			0
$555$	0.957078	−	9.13259i	0.0406257	−	0.387657i
$556$		0			0
$557$	2.07471	−	13.0992i	0.0879082	−	0.555030i	−0.903945	−	0.427648i	$-0.859342\pi$
$557$	2.07471	−	13.0992i	0.0879082	−	0.555030i	0.991854	−	0.127383i	$-0.0406576\pi$
$558$		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
$563$	−13.3342	+	26.1698i	−0.561968	+	1.10292i	0.418860	+	0.908051i	$0.362430\pi$
$563$	−13.3342	+	26.1698i	−0.561968	+	1.10292i	−0.980828	+	0.194874i	$0.937570\pi$
$564$		0			0
$565$	−1.42682	−	27.0684i	−0.0600266	−	1.13878i
$566$		0			0
$567$	6.20650	+	12.1809i	0.260648	+	0.511551i
$568$		0			0
$569$	17.3540	+	12.6084i	0.727518	+	0.528573i	0.888777	−	0.458339i	$-0.151555\pi$
$569$	17.3540	+	12.6084i	0.727518	+	0.528573i	−0.161259	+	0.986912i	$0.551555\pi$
$570$		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
$575$	11.6187	−	7.55529i	0.484534	−	0.315077i
$576$		0			0
$577$	−5.96290	+	3.03825i	−0.248239	+	0.126484i	−0.573683	−	0.819077i	$-0.694486\pi$
$577$	−5.96290	+	3.03825i	−0.248239	+	0.126484i	0.325445	+	0.945561i	$0.394486\pi$
$578$		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
$583$	20.5853	−	21.9879i	0.852558	−	0.910644i
$584$		0			0
$585$	4.61286	+	1.23452i	0.190718	+	0.0510409i
$586$		0			0
$587$	−36.0485	−	5.70952i	−1.48788	−	0.235657i	−0.641041	−	0.767506i	$-0.721497\pi$
$587$	−36.0485	−	5.70952i	−1.48788	−	0.235657i	−0.846839	+	0.531849i	$0.821497\pi$
$588$		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	0.994983	+	0.100040i	$0.0318971\pi$
$593$	26.6656	+	26.6656i	1.09502	+	1.09502i	0.100040	+	0.994983i	$0.468103\pi$
$594$		0			0
$595$	−3.78328	−	17.7724i	−0.155099	−	0.728599i
$596$		0			0
$597$	2.52857	+	15.9648i	0.103487	+	0.653394i
$598$		0			0
$599$	36.7124	+	11.9286i	1.50003	+	0.487388i	0.940026	−	0.341103i	$-0.110801\pi$
$599$	36.7124	+	11.9286i	1.50003	+	0.487388i	0.560002	+	0.828492i	$0.310801\pi$
$600$		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
$603$	−8.88156	−	4.52538i	−0.361685	−	0.184288i
$604$		0			0
$605$	15.2139	−	19.3272i	0.618531	−	0.785760i
$606$		0			0
$607$	−32.2834	−	16.4492i	−1.31034	−	0.667653i	−0.347491	−	0.937683i	$-0.612966\pi$
$607$	−32.2834	−	16.4492i	−1.31034	−	0.667653i	−0.962852	+	0.270031i	$0.912966\pi$
$608$		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
$613$	−0.376892	−	2.37960i	−0.0152225	−	0.0961113i	0.978907	−	0.204305i	$-0.0654934\pi$
$613$	−0.376892	−	2.37960i	−0.0152225	−	0.0961113i	−0.994130	+	0.108194i	$0.965493\pi$
$614$		0			0
$615$	0.901696	+	0.585180i	0.0363599	+	0.0235967i
$616$		0			0
$617$	−25.5598	−	25.5598i	−1.02900	−	1.02900i	−0.999567	−	0.0294325i	$-0.990630\pi$
$617$	−25.5598	−	25.5598i	−1.02900	−	1.02900i	−0.0294325	−	0.999567i	$-0.509370\pi$
$618$		0			0
$619$	−0.537145	+	0.739317i	−0.0215897	+	0.0297157i	−0.819675	−	0.572828i	$-0.805846\pi$
$619$	−0.537145	+	0.739317i	−0.0215897	+	0.0297157i	0.798086	+	0.602544i	$0.205846\pi$
$620$		0			0
$621$	3.78415	−	11.6464i	0.151853	−	0.467355i
$622$		0			0
$623$	−58.0020	−	9.18661i	−2.32380	−	0.368054i
$624$		0			0
$625$	22.8509	+	10.1407i	0.914038	+	0.405630i
$626$		0			0
$627$	−10.2496	+	10.9480i	−0.409331	+	0.437219i
$628$		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
$633$	−4.74042	+	2.41536i	−0.188415	+	0.0960020i
$634$		0			0
$635$	−2.42030	+	0.929906i	−0.0960465	+	0.0369022i
$636$		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
$643$	−14.3186	−	28.1018i	−0.564670	−	1.10823i	−0.980082	−	0.198594i	$-0.936362\pi$
$643$	−14.3186	−	28.1018i	−0.564670	−	1.10823i	0.415412	−	0.909634i	$-0.363638\pi$
$644$		0			0
$645$	−8.89912	+	9.88950i	−0.350403	+	0.389399i
$646$		0			0
$647$	−6.23845	+	12.2437i	−0.245259	+	0.481348i	−0.980516	−	0.196441i	$-0.937062\pi$
$647$	−6.23845	+	12.2437i	−0.245259	+	0.481348i	0.735257	+	0.677789i	$0.237062\pi$
$648$		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
$653$	−0.851181	+	5.37414i	−0.0333093	+	0.210307i	−0.998730	−	0.0503921i	$-0.983953\pi$
$653$	−0.851181	+	5.37414i	−0.0333093	+	0.210307i	0.965420	+	0.260699i	$0.0839529\pi$
$654$		0			0
$655$	32.1423	+	3.36845i	1.25590	+	0.131616i
$656$		0			0
$657$	−12.4420	+	1.97062i	−0.485408	+	0.0768812i
$658$		0			0
$659$	42.1160			1.64061			0.820304	−	0.571928i	$-0.193805\pi$
$659$	42.1160			1.64061			0.820304	+	0.571928i	$0.193805\pi$
$660$		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
$663$	−1.46726	+	0.232390i	−0.0569835	+	0.00902529i
$664$		0			0
$665$	32.2323	+	39.7789i	1.24991	+	1.54256i
$666$		0			0
$667$	0.434404	−	2.74272i	0.0168202	−	0.106198i
$668$		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
$673$	−2.51797	+	4.94179i	−0.0970605	+	0.190492i	−0.934431	−	0.356143i	$-0.884092\pi$
$673$	−2.51797	+	4.94179i	−0.0970605	+	0.190492i	0.837371	+	0.546635i	$0.184092\pi$
$674$		0			0
$675$	21.3335	−	5.73014i	0.821126	−	0.220553i
$676$		0			0
$677$	−1.05927	−	2.07893i	−0.0407110	−	0.0798999i	0.869755	−	0.493484i	$-0.164277\pi$
$677$	−1.05927	−	2.07893i	−0.0407110	−	0.0798999i	−0.910466	+	0.413584i	$0.864277\pi$
$678$		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	−0.0410307	−	0.999158i	$-0.513064\pi$
$683$	25.0400	−	25.0400i	0.958127	−	0.958127i	0.999158	+	0.0410307i	$0.0130641\pi$
$684$		0			0
$685$	−9.92168	−	25.8235i	−0.379088	−	0.986665i
$686$		0			0
$687$	−14.5376	+	7.40730i	−0.554646	+	0.282606i
$688$		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
$693$	−32.0050	−	3.99389i	−1.21577	−	0.151715i
$694$		0			0
$695$	−1.12911	−	1.95431i	−0.0428297	−	0.0741314i
$696$		0			0
$697$	1.09952	+	0.174147i	0.0416473	+	0.00659628i
$698$		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
$707$	−8.76432	−	55.3357i	−0.329616	−	2.08111i
$708$		0			0
$709$	−9.55567	−	3.10483i	−0.358871	−	0.116604i	0.124032	−	0.992278i	$-0.460417\pi$
$709$	−9.55567	−	3.10483i	−0.358871	−	0.116604i	−0.482903	+	0.875674i	$0.660417\pi$
$710$		0			0
$711$	3.09743	+	4.26324i	0.116163	+	0.159884i
$712$		0			0
$713$	1.04703	+	0.533487i	0.0392115	+	0.0199793i
$714$		0			0
$715$	−5.18863	+	4.49520i	−0.194044	+	0.168111i
$716$		0			0
$717$	−2.38314	−	1.21427i	−0.0890001	−	0.0453478i
$718$		0			0
$719$	−4.03181	−	5.54931i	−0.150361	−	0.206954i	0.727191	−	0.686435i	$-0.240825\pi$
$719$	−4.03181	−	5.54931i	−0.150361	−	0.206954i	−0.877553	+	0.479480i	$0.840825\pi$
$720$		0			0
$721$	40.4204	+	13.1334i	1.50533	+	0.489113i
$722$		0			0
$723$	−3.30933	−	20.8943i	−0.123075	−	0.777067i
$724$		0			0
$725$	4.57485	−	2.04017i	0.169906	−	0.0757702i
$726$		0			0
$727$	25.2212	+	25.2212i	0.935401	+	0.935401i	0.998036	−	0.0626351i	$-0.0199504\pi$
$727$	25.2212	+	25.2212i	0.935401	+	0.935401i	−0.0626351	+	0.998036i	$0.519950\pi$
$728$		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
$733$	−7.61562	−	1.20620i	−0.281289	−	0.0445519i	0.0141956	−	0.999899i	$-0.495481\pi$
$733$	−7.61562	−	1.20620i	−0.281289	−	0.0445519i	−0.295485	+	0.955347i	$0.595481\pi$
$734$		0			0
$735$	5.18245	−	19.3646i	0.191157	−	0.714275i
$736$		0			0
$737$	12.5474	−	6.92277i	0.462189	−	0.255004i
$738$		0			0
$739$	−12.6089	−	38.8062i	−0.463825	−	1.42751i	−0.860454	−	0.509528i	$-0.829820\pi$
$739$	−12.6089	−	38.8062i	−0.463825	−	1.42751i	0.396629	−	0.917979i	$-0.370180\pi$
$740$		0			0
$741$	3.38633	−	2.46031i	0.124400	−	0.0903819i
$742$		0			0
$743$	−39.5290	+	20.1411i	−1.45018	+	0.738904i	−0.988932	−	0.148368i	$-0.952598\pi$
$743$	−39.5290	+	20.1411i	−1.45018	+	0.738904i	−0.461248	+	0.887271i	$0.652598\pi$
$744$		0			0
$745$	−2.49366	−	1.10934i	−0.0913605	−	0.0406432i
$746$		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
$753$	−6.16240	−	12.0944i	−0.224570	−	0.440744i
$754$		0			0
$755$	−2.63746	−	2.37333i	−0.0959869	−	0.0863743i
$756$		0			0
$757$	9.02166	−	17.7060i	0.327898	−	0.643535i	−0.666929	−	0.745121i	$-0.732392\pi$
$757$	9.02166	−	17.7060i	0.327898	−	0.643535i	0.994827	+	0.101586i	$0.0323916\pi$
$758$		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
$763$	−13.1353	+	82.9328i	−0.475528	+	3.00237i
$764$		0			0
$765$	7.72647	−	6.26065i	0.279351	−	0.226354i
$766$		0			0
$767$	−8.51175	+	1.34813i	−0.307342	+	0.0486781i
$768$		0			0
$769$	33.4001			1.20444			0.602218	−	0.798331i	$-0.294284\pi$
$769$	33.4001			1.20444			0.602218	+	0.798331i	$0.294284\pi$
$770$		0			0
$771$	−13.4894			−0.485810
$772$		0			0
$773$	−37.6915	+	5.96974i	−1.35567	+	0.214717i	−0.791614	−	0.611021i	$-0.790759\pi$
$773$	−37.6915	+	5.96974i	−1.35567	+	0.214717i	−0.564054	+	0.825738i	$0.690759\pi$
$774$		0			0
$775$	0.222849	+	2.10798i	0.00800496	+	0.0757208i
$776$		0			0
$777$	2.70797	−	17.0975i	0.0971480	−	0.613369i
$778$		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
$783$	2.00936	−	3.94360i	0.0718088	−	0.140933i
$784$		0			0
$785$	−16.5668	+	0.873259i	−0.591293	+	0.0311680i
$786$		0			0
$787$	−16.6820	−	32.7403i	−0.594649	−	1.16706i	−0.970662	−	0.240450i	$-0.922705\pi$
$787$	−16.6820	−	32.7403i	−0.594649	−	1.16706i	0.376013	−	0.926614i	$-0.377295\pi$
$788$		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
$795$	−6.87122	+	15.4456i	−0.243697	+	0.547799i
$796$		0			0
$797$	17.9460	−	9.14395i	0.635680	−	0.323895i	−0.106283	−	0.994336i	$-0.533895\pi$
$797$	17.9460	−	9.14395i	0.635680	−	0.323895i	0.741963	+	0.670441i	$0.233895\pi$
$798$		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
$803$	7.68606	−	16.3982i	0.271235	−	0.578679i
$804$		0			0
$805$	22.6224	−	13.0702i	0.797335	−	0.460663i
$806$		0			0
$807$	23.3708	+	3.70156i	0.822690	+	0.130301i
$808$		0			0
$809$	16.0484	−	49.3920i	0.564233	−	1.73653i	−0.105987	−	0.994367i	$-0.533800\pi$
$809$	16.0484	−	49.3920i	0.564233	−	1.73653i	0.670220	−	0.742162i	$-0.266200\pi$
$810$		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
$817$	−6.07296	−	38.3431i	−0.212466	−	1.34146i
$818$		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
$823$	20.4719	+	10.4310i	0.713606	+	0.363600i	0.772803	−	0.634646i	$-0.218854\pi$
$823$	20.4719	+	10.4310i	0.713606	+	0.363600i	−0.0591972	+	0.998246i	$0.518854\pi$
$824$		0			0
$825$	−4.51233	+	13.0467i	−0.157099	+	0.454229i
$826$		0			0
$827$	4.93382	+	2.51391i	0.171566	+	0.0874171i	0.537664	−	0.843159i	$-0.319307\pi$
$827$	4.93382	+	2.51391i	0.171566	+	0.0874171i	−0.366099	+	0.930576i	$0.619307\pi$
$828$		0			0
$829$	−8.80126	−	12.1139i	−0.305680	−	0.420733i	0.628348	−	0.777933i	$-0.283732\pi$
$829$	−8.80126	−	12.1139i	−0.305680	−	0.420733i	−0.934028	+	0.357200i	$0.883732\pi$
$830$		0			0
$831$	23.8694	+	7.75564i	0.828020	+	0.269040i
$832$		0			0
$833$	−3.24759	−	20.5045i	−0.112522	−	0.710439i
$834$		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	−0.917462	−	0.397823i	$-0.869766\pi$
$839$	−7.40356	+	10.1901i	−0.255599	+	0.351802i	0.661863	+	0.749625i	$0.269766\pi$
$840$		0			0
$841$	−8.65134	+	26.6261i	−0.298322	+	0.918141i
$842$		0			0
$843$	7.00457	+	1.10941i	0.241250	+	0.0382103i
$844$		0			0
$845$	−23.5109	+	13.5835i	−0.808801	+	0.467288i
$846$		0			0
$847$	30.5585	−	34.8744i	1.05000	−	1.19830i
$848$		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
$853$	−44.3481	+	22.5965i	−1.51845	+	0.773689i	−0.996835	−	0.0794926i	$-0.974670\pi$
$853$	−44.3481	+	22.5965i	−1.51845	+	0.773689i	−0.521614	+	0.853181i	$0.674670\pi$
$854$		0			0
$855$	−11.3891	+	25.6012i	−0.389498	+	0.875541i
$856$		0			0
$857$	−21.2860	+	21.2860i	−0.727117	+	0.727117i	−0.970044	−	0.242927i	$-0.921892\pi$
$857$	−21.2860	+	21.2860i	−0.727117	+	0.727117i	0.242927	+	0.970044i	$0.421892\pi$
$858$		0			0
$859$			9.31402i			0.317790i	0.987295	+	0.158895i	$0.0507932\pi$
$859$			9.31402i			0.317790i	−0.987295	+	0.158895i	$0.949207\pi$
$860$		0			0
$861$	1.63941	+	1.19110i	0.0558709	+	0.0405926i
$862$		0			0
$863$	16.0664	+	31.5320i	0.546905	+	1.07336i	0.984695	+	0.174285i	$0.0557613\pi$
$863$	16.0664	+	31.5320i	0.546905	+	1.07336i	−0.437790	+	0.899077i	$0.644239\pi$
$864$		0			0
$865$	−9.66817	+	0.509623i	−0.328727	+	0.0173277i
$866$		0			0
$867$	5.02038	−	9.85305i	0.170501	−	0.334627i
$868$		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
$873$	−1.19973	+	7.57478i	−0.0406046	+	0.256368i
$874$		0			0
$875$	42.0115	+	21.3579i	1.42025	+	0.722027i
$876$		0			0
$877$	21.5902	−	3.41955i	0.729048	−	0.115470i	0.219133	−	0.975695i	$-0.429677\pi$
$877$	21.5902	−	3.41955i	0.729048	−	0.115470i	0.509915	+	0.860225i	$0.329677\pi$
$878$		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
$883$	−27.5798	+	4.36822i	−0.928135	+	0.147002i	−0.602159	−	0.798376i	$-0.705693\pi$
$883$	−27.5798	+	4.36822i	−0.928135	+	0.147002i	−0.325976	+	0.945378i	$0.605693\pi$
$884$		0			0
$885$	−13.4645	+	10.9101i	−0.452603	+	0.366738i
$886$		0			0
$887$	−1.10133	+	6.95351i	−0.0369790	+	0.233476i	−0.999255	−	0.0385999i	$-0.987710\pi$
$887$	−1.10133	+	6.95351i	−0.0369790	+	0.233476i	0.962276	+	0.272076i	$0.0877102\pi$
$888$		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
$893$	2.93351	−	5.75734i	0.0981662	−	0.192662i
$894$		0			0
$895$	−6.18263	−	5.56347i	−0.206662	−	0.185966i
$896$		0			0
$897$	−0.969718	−	1.90318i	−0.0323780	−	0.0635453i
$898$		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
$905$	12.3533	+	5.49555i	0.410637	+	0.182678i
$906$		0			0
$907$	26.3281	−	13.4148i	0.874211	−	0.445433i	0.0414984	−	0.999139i	$-0.486787\pi$
$907$	26.3281	−	13.4148i	0.874211	−	0.445433i	0.832712	+	0.553706i	$0.186787\pi$
$908$		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
$913$	1.24574	+	6.47702i	0.0412279	+	0.214358i
$914$		0			0
$915$	−3.74490	+	13.9931i	−0.123802	+	0.462598i
$916$		0			0
$917$	60.1748	+	9.53075i	1.98715	+	0.314733i
$918$		0			0
$919$	−1.55222	+	4.77725i	−0.0512030	+	0.157587i	−0.973388	−	0.229161i	$-0.926402\pi$
$919$	−1.55222	+	4.77725i	−0.0512030	+	0.157587i	0.922185	+	0.386748i	$0.126402\pi$
$920$		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
$927$	3.63865	+	22.9736i	0.119509	+	0.754551i
$928$		0			0
$929$	−11.2348	−	3.65041i	−0.368602	−	0.119766i	0.118858	−	0.992911i	$-0.462077\pi$
$929$	−11.2348	−	3.65041i	−0.368602	−	0.119766i	−0.487460	+	0.873145i	$0.662077\pi$
$930$		0			0
$931$	34.3822	+	47.3231i	1.12683	+	1.55095i
$932$		0			0
$933$	11.2103	+	5.71194i	0.367009	+	0.187001i
$934$		0			0
$935$	1.22223	+	14.2444i	0.0399711	+	0.465840i
$936$		0			0
$937$	−2.04229	−	1.04060i	−0.0667187	−	0.0339949i	0.420313	−	0.907379i	$-0.361920\pi$
$937$	−2.04229	−	1.04060i	−0.0667187	−	0.0339949i	−0.487032	+	0.873384i	$0.661920\pi$
$938$		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
$943$	0.250397	+	1.58094i	0.00815404	+	0.0514826i
$944$		0			0
$945$	40.7297	−	8.67026i	1.32494	−	0.282043i
$946$		0			0
$947$	8.63289	+	8.63289i	0.280531	+	0.280531i	0.833321	−	0.552790i	$-0.186437\pi$
$947$	8.63289	+	8.63289i	0.280531	+	0.280531i	−0.552790	+	0.833321i	$0.686437\pi$
$948$		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
$953$	−18.2074	−	2.88376i	−0.589794	−	0.0934143i	−0.145598	−	0.989344i	$-0.546511\pi$
$953$	−18.2074	−	2.88376i	−0.589794	−	0.0934143i	−0.444196	+	0.895930i	$0.646511\pi$
$954$		0			0
$955$	−18.5184	−	32.0523i	−0.599240	−	1.03719i
$956$		0			0
$957$	1.33623	+	2.42189i	0.0431941	+	0.0782884i
$958$		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
$963$	−12.6759	+	6.45868i	−0.408474	+	0.208128i
$964$		0			0
$965$	13.6047	+	35.4093i	0.437950	+	1.13987i
$966$		0			0
$967$	9.49113	−	9.49113i	0.305214	−	0.305214i	−0.537836	−	0.843050i	$-0.680758\pi$
$967$	9.49113	−	9.49113i	0.305214	−	0.305214i	0.843050	+	0.537836i	$0.180758\pi$
$968$		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
$973$	−1.93167	−	3.79111i	−0.0619265	−	0.121538i
$974$		0			0
$975$	1.92449	−	3.33798i	0.0616329	−	0.106901i
$976$		0			0
$977$	−6.57391	+	12.9020i	−0.210318	+	0.412772i	−0.971933	−	0.235257i	$-0.924407\pi$
$977$	−6.57391	+	12.9020i	−0.210318	+	0.412772i	0.761615	+	0.648030i	$0.224407\pi$
$978$		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
$983$	9.00238	−	56.8388i	0.287131	−	1.81288i	−0.248734	−	0.968572i	$-0.580014\pi$
$983$	9.00238	−	56.8388i	0.287131	−	1.81288i	0.535865	−	0.844304i	$-0.319986\pi$
$984$		0			0
$985$	19.1841	+	23.6758i	0.611257	+	0.754372i
$986$		0			0
$987$	−4.12308	+	0.653031i	−0.131239	+	0.0207862i
$988$		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
$993$	20.2641	−	3.20952i	0.643062	−	0.101851i
$994$		0			0
$995$	−43.1803	−	4.52521i	−1.36891	−	0.143459i
$996$		0			0
$997$	−0.352744	+	2.22714i	−0.0111715	+	0.0705343i	−0.992644	−	0.121068i	$-0.961368\pi$
$997$	−0.352744	+	2.22714i	−0.0111715	+	0.0705343i	0.981473	+	0.191602i	$0.0613682\pi$
$998$		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.17.3		32
4.3	odd	2		55.2.l.a.17.4	yes	32
5.3	odd	4	inner	880.2.cm.a.193.3		32
11.2	odd	10	inner	880.2.cm.a.497.3		32
12.11	even	2		495.2.bj.a.127.1		32
20.3	even	4		55.2.l.a.28.4	yes	32
20.7	even	4		275.2.bm.b.193.1		32
20.19	odd	2		275.2.bm.b.182.1		32
44.3	odd	10		605.2.e.b.362.13		32
44.7	even	10		605.2.m.c.602.4		32
44.15	odd	10		605.2.m.d.602.1		32
44.19	even	10		605.2.e.b.362.4		32
44.27	odd	10		605.2.m.c.282.1		32
44.31	odd	10		605.2.m.e.112.1		32
44.35	even	10		55.2.l.a.2.4	✓	32
44.39	even	10		605.2.m.d.282.4		32
44.43	even	2		605.2.m.e.457.1		32
55.13	even	20	inner	880.2.cm.a.673.3		32
60.23	odd	4		495.2.bj.a.28.1		32
132.35	odd	10		495.2.bj.a.442.1		32
220.3	even	20		605.2.e.b.483.4		32
220.43	odd	4		605.2.m.e.578.1		32
220.63	odd	20		605.2.e.b.483.13		32
220.79	even	10		275.2.bm.b.57.1		32
220.83	odd	20		605.2.m.d.403.1		32
220.103	even	20		605.2.m.d.118.4		32
220.123	odd	20		55.2.l.a.13.4	yes	32
220.163	even	20		605.2.m.e.233.1		32
220.167	odd	20		275.2.bm.b.68.1		32
220.183	odd	20		605.2.m.c.118.1		32
220.203	even	20		605.2.m.c.403.4		32
660.563	even	20		495.2.bj.a.343.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.l.a.2.4	✓	32	44.35	even	10
55.2.l.a.13.4	yes	32	220.123	odd	20
55.2.l.a.17.4	yes	32	4.3	odd	2
55.2.l.a.28.4	yes	32	20.3	even	4
275.2.bm.b.57.1		32	220.79	even	10
275.2.bm.b.68.1		32	220.167	odd	20
275.2.bm.b.182.1		32	20.19	odd	2
275.2.bm.b.193.1		32	20.7	even	4
495.2.bj.a.28.1		32	60.23	odd	4
495.2.bj.a.127.1		32	12.11	even	2
495.2.bj.a.343.1		32	660.563	even	20
495.2.bj.a.442.1		32	132.35	odd	10
605.2.e.b.362.4		32	44.19	even	10
605.2.e.b.362.13		32	44.3	odd	10
605.2.e.b.483.4		32	220.3	even	20
605.2.e.b.483.13		32	220.63	odd	20
605.2.m.c.118.1		32	220.183	odd	20
605.2.m.c.282.1		32	44.27	odd	10
605.2.m.c.403.4		32	220.203	even	20
605.2.m.c.602.4		32	44.7	even	10
605.2.m.d.118.4		32	220.103	even	20
605.2.m.d.282.4		32	44.39	even	10
605.2.m.d.403.1		32	220.83	odd	20
605.2.m.d.602.1		32	44.15	odd	10
605.2.m.e.112.1		32	44.31	odd	10
605.2.m.e.233.1		32	220.163	even	20
605.2.m.e.457.1		32	44.43	even	2
605.2.m.e.578.1		32	220.43	odd	4
880.2.cm.a.17.3		32	1.1	even	1	trivial
880.2.cm.a.193.3		32	5.3	odd	4	inner
880.2.cm.a.497.3		32	11.2	odd	10	inner
880.2.cm.a.673.3		32	55.13	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 $\F_{q}$
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)

\(f(q)\)	\(=\)	\(q+(0.822224 - 0.130227i) q^{3} +(-0.233059 + 2.22389i) q^{5} +(-0.659422 + 4.16343i) q^{7} +(-2.19408 + 0.712899i) q^{9} +(0.920480 - 3.18633i) q^{11} +(-0.420250 + 0.824787i) q^{13} +(0.0979846 + 1.85889i) q^{15} +(0.875188 + 1.71765i) q^{17} +(-4.39439 - 3.19271i) q^{19} +3.50915i q^{21} +(-1.95998 + 1.95998i) q^{23} +(-4.89137 - 1.03660i) q^{25} +(-3.93640 + 2.00570i) q^{27} +(-0.810497 + 0.588860i) q^{29} +(-0.131006 - 0.403196i) q^{31} +(0.341892 - 2.73975i) q^{33} +(-9.10532 - 2.43681i) q^{35} +(-4.87226 - 0.771690i) q^{37} +(-0.238130 + 0.732888i) q^{39} +(0.339428 - 0.467182i) q^{41} +(5.05373 + 5.05373i) q^{43} +(-1.07406 - 5.04553i) q^{45} +(0.186094 + 1.17495i) q^{47} +(-10.2419 - 3.32780i) q^{49} +(0.943286 + 1.29832i) q^{51} +(8.09173 + 4.12294i) q^{53} +(6.87153 + 2.78965i) q^{55} +(-4.02895 - 2.05285i) q^{57} +(5.47214 + 7.53175i) q^{59} +(7.40093 + 2.40471i) q^{61} +(-1.52128 - 9.60498i) q^{63} +(-1.73629 - 1.12681i) q^{65} +(3.05526 + 3.05526i) q^{67} +(-1.35630 + 1.86679i) q^{69} +(-2.65487 + 8.17086i) q^{71} +(5.39318 + 0.854195i) q^{73} +(-4.15679 - 0.215323i) q^{75} +(12.6591 + 5.93349i) q^{77} +(-0.705861 - 2.17242i) q^{79} +(2.62377 - 1.90628i) q^{81} +(-1.77193 + 0.902846i) q^{83} +(-4.02384 + 1.54601i) q^{85} +(-0.589724 + 0.589724i) q^{87} +13.9313i q^{89} +(-3.15682 - 2.29356i) q^{91} +(-0.160224 - 0.314457i) q^{93} +(8.12438 - 9.02854i) q^{95} +(1.50922 - 2.96200i) q^{97} +(0.251929 + 7.64727i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} - 2 q^{5} + 24 q^{11} - 10 q^{13} - 14 q^{15} + 24 q^{23} + 16 q^{25} + 16 q^{27} + 28 q^{31} + 66 q^{33} + 10 q^{35} - 8 q^{37} + 40 q^{41} - 28 q^{45} + 28 q^{47} - 20 q^{51} - 24 q^{53}+ \cdots - 8 q^{97}+O(q^{100}) \) 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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