LMFDB - Embedded newform 820.2.u.a.461.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(141,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.141"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.u (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			461.5
Character	$\chi$	$=$	820.461
Dual form			820.2.u.a.201.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.53712 q^{3} +(0.309017 + 0.951057i) q^{5} +(2.92498 - 2.12513i) q^{7} +3.43699 q^{9} +(0.677943 - 2.08649i) q^{11} +(-0.433091 - 0.314659i) q^{13} +(0.784014 + 2.41295i) q^{15} +(0.573486 - 1.76501i) q^{17} +(-3.44732 + 2.50462i) q^{19} +(7.42104 - 5.39170i) q^{21} +(-0.406431 - 0.295290i) q^{23} +(-0.809017 + 0.587785i) q^{25} +1.10869 q^{27} +(-1.25236 - 3.85436i) q^{29} +(-2.97174 + 9.14608i) q^{31} +(1.72002 - 5.29369i) q^{33} +(2.92498 + 2.12513i) q^{35} +(-1.08138 - 3.32814i) q^{37} +(-1.09880 - 0.798328i) q^{39} +(4.26527 + 4.77572i) q^{41} +(0.275341 + 0.200047i) q^{43} +(1.06209 + 3.26877i) q^{45} +(0.751982 + 0.546347i) q^{47} +(1.87626 - 5.77452i) q^{49} +(1.45500 - 4.47804i) q^{51} +(2.97238 + 9.14804i) q^{53} +2.19387 q^{55} +(-8.74627 + 6.35454i) q^{57} +(8.01859 + 5.82585i) q^{59} +(-3.28790 + 2.38880i) q^{61} +(10.0531 - 7.30403i) q^{63} +(0.165426 - 0.509129i) q^{65} +(-4.46312 - 13.7361i) q^{67} +(-1.03117 - 0.749186i) q^{69} +(-3.10998 + 9.57152i) q^{71} -1.59943 q^{73} +(-2.05257 + 1.49128i) q^{75} +(-2.45109 - 7.54368i) q^{77} -14.3814 q^{79} -7.49808 q^{81} +7.14716 q^{83} +1.85584 q^{85} +(-3.17738 - 9.77897i) q^{87} +(3.09025 - 2.24520i) q^{89} -1.93547 q^{91} +(-7.53967 + 23.2047i) q^{93} +(-3.44732 - 2.50462i) q^{95} +(-2.83266 - 8.71803i) q^{97} +(2.33008 - 7.17125i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{3} - 6 q^{5} + 5 q^{7} + 18 q^{9} - 7 q^{11} - 5 q^{13} + 2 q^{15} + 3 q^{17} - q^{19} + 2 q^{21} + 20 q^{23} - 6 q^{25} + 20 q^{27} - 15 q^{29} - q^{31} - 6 q^{33} + 5 q^{35} + q^{37} + 28 q^{41}+ \cdots + 34 q^{99}+O(q^{100}) $ 24 * q + 2 * q^3 - 6 * q^5 + 5 * q^7 + 18 * q^9 - 7 * q^11 - 5 * q^13 + 2 * q^15 + 3 * q^17 - q^19 + 2 * q^21 + 20 * q^23 - 6 * q^25 + 20 * q^27 - 15 * q^29 - q^31 - 6 * q^33 + 5 * q^35 + q^37 + 28 * q^41 - 4 * q^43 + 3 * q^45 + 3 * q^47 + 3 * q^49 + 37 * q^51 + 29 * q^53 - 12 * q^55 + 17 * q^57 - 4 * q^59 - 14 * q^61 - 10 * q^63 + 5 * q^65 - 14 * q^67 - 26 * q^69 + q^71 - 84 * q^73 - 3 * q^75 + 24 * q^77 + 18 * q^79 - 40 * q^81 - 6 * q^83 - 12 * q^85 + 39 * q^87 + 12 * q^89 - 2 * q^91 - 58 * q^93 - q^95 - 20 * q^97 + 34 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$	$1$

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
$3$	2.53712			1.46481			0.732404	−	0.680870i	$-0.238398\pi$
$3$	2.53712			1.46481			0.732404	+	0.680870i	$0.238398\pi$
$4$		0			0
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$5$	0.309017	+	0.951057i	0.138197	+	0.425325i
$6$		0			0
$7$	2.92498	−	2.12513i	1.10554	−	0.803222i	0.123585	−	0.992334i	$-0.460561\pi$
$7$	2.92498	−	2.12513i	1.10554	−	0.803222i	0.981955	+	0.189112i	$0.0605610\pi$
$8$		0			0
$9$	3.43699			1.14566
$10$		0			0
$11$	0.677943	−	2.08649i	0.204408	−	0.629102i	−0.795330	−	0.606177i	$-0.792702\pi$
$11$	0.677943	−	2.08649i	0.204408	−	0.629102i	0.999737	−	0.0229245i	$-0.00729774\pi$
$12$		0			0
$13$	−0.433091	−	0.314659i	−0.120118	−	0.0872706i	0.526104	−	0.850420i	$-0.323652\pi$
$13$	−0.433091	−	0.314659i	−0.120118	−	0.0872706i	−0.646222	+	0.763149i	$0.723652\pi$
$14$		0			0
$15$	0.784014	+	2.41295i	0.202431	+	0.623020i
$16$		0			0
$17$	0.573486	−	1.76501i	0.139091	−	0.428077i	−0.857113	−	0.515128i	$-0.827744\pi$
$17$	0.573486	−	1.76501i	0.139091	−	0.428077i	0.996204	+	0.0870509i	$0.0277443\pi$
$18$		0			0
$19$	−3.44732	+	2.50462i	−0.790870	+	0.574600i	−0.908221	−	0.418490i	$-0.862559\pi$
$19$	−3.44732	+	2.50462i	−0.790870	+	0.574600i	0.117352	+	0.993090i	$0.462559\pi$
$20$		0			0
$21$	7.42104	−	5.39170i	1.61940	−	1.17657i
$22$		0			0
$23$	−0.406431	−	0.295290i	−0.0847468	−	0.0615722i	0.544605	−	0.838693i	$-0.316680\pi$
$23$	−0.406431	−	0.295290i	−0.0847468	−	0.0615722i	−0.629352	+	0.777120i	$0.716680\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$		0			0
$27$	1.10869			0.213368
$28$		0			0
$29$	−1.25236	−	3.85436i	−0.232557	−	0.715736i	−0.997436	−	0.0715626i	$-0.977201\pi$
$29$	−1.25236	−	3.85436i	−0.232557	−	0.715736i	0.764879	−	0.644174i	$-0.222799\pi$
$30$		0			0
$31$	−2.97174	+	9.14608i	−0.533741	+	1.64268i	0.212614	+	0.977136i	$0.431802\pi$
$31$	−2.97174	+	9.14608i	−0.533741	+	1.64268i	−0.746355	+	0.665548i	$0.768198\pi$
$32$		0			0
$33$	1.72002	−	5.29369i	0.299418	−	0.921513i
$34$		0			0
$35$	2.92498	+	2.12513i	0.494413	+	0.359212i
$36$		0			0
$37$	−1.08138	−	3.32814i	−0.177778	−	0.547143i	0.821972	−	0.569528i	$-0.192874\pi$
$37$	−1.08138	−	3.32814i	−0.177778	−	0.547143i	−0.999749	+	0.0223851i	$0.992874\pi$
$38$		0			0
$39$	−1.09880	−	0.798328i	−0.175949	−	0.127835i
$40$		0			0
$41$	4.26527	+	4.77572i	0.666123	+	0.745842i
$41$	4.26527	+	4.77572i	0.666123	+	0.745842i
$42$		0			0
$43$	0.275341	+	0.200047i	0.0419891	+	0.0305069i	0.608582	−	0.793491i	$-0.291739\pi$
$43$	0.275341	+	0.200047i	0.0419891	+	0.0305069i	−0.566593	+	0.823998i	$0.691739\pi$
$44$		0			0
$45$	1.06209	+	3.26877i	0.158327	+	0.487279i
$46$		0			0
$47$	0.751982	+	0.546347i	0.109688	+	0.0796929i	0.641277	−	0.767309i	$-0.278405\pi$
$47$	0.751982	+	0.546347i	0.109688	+	0.0796929i	−0.531589	+	0.847002i	$0.678405\pi$
$48$		0			0
$49$	1.87626	−	5.77452i	0.268036	−	0.824931i
$50$		0			0
$51$	1.45500	−	4.47804i	0.203741	−	0.627051i
$52$		0			0
$53$	2.97238	+	9.14804i	0.408287	+	1.25658i	0.918119	+	0.396305i	$0.129708\pi$
$53$	2.97238	+	9.14804i	0.408287	+	1.25658i	−0.509831	+	0.860274i	$0.670292\pi$
$54$		0			0
$55$	2.19387			0.295821
$56$		0			0
$57$	−8.74627	+	6.35454i	−1.15847	+	0.841679i
$58$		0			0
$59$	8.01859	+	5.82585i	1.04393	+	0.758460i	0.971049	−	0.238880i	$-0.0767803\pi$
$59$	8.01859	+	5.82585i	1.04393	+	0.758460i	0.0728822	+	0.997341i	$0.476780\pi$
$60$		0			0
$61$	−3.28790	+	2.38880i	−0.420972	+	0.305854i	−0.778029	−	0.628228i	$-0.783780\pi$
$61$	−3.28790	+	2.38880i	−0.420972	+	0.305854i	0.357057	+	0.934083i	$0.383780\pi$
$62$		0			0
$63$	10.0531	−	7.30403i	1.26658	−	0.920221i
$64$		0			0
$65$	0.165426	−	0.509129i	0.0205186	−	0.0631496i
$66$		0			0
$67$	−4.46312	−	13.7361i	−0.545257	−	1.67813i	−0.720378	−	0.693582i	$-0.756032\pi$
$67$	−4.46312	−	13.7361i	−0.545257	−	1.67813i	0.175121	−	0.984547i	$-0.443968\pi$
$68$		0			0
$69$	−1.03117	−	0.749186i	−0.124138	−	0.0901914i
$70$		0			0
$71$	−3.10998	+	9.57152i	−0.369086	+	1.13593i	0.578296	+	0.815827i	$0.303718\pi$
$71$	−3.10998	+	9.57152i	−0.369086	+	1.13593i	−0.947382	+	0.320104i	$0.896282\pi$
$72$		0			0
$73$	−1.59943			−0.187199			−0.0935994	−	0.995610i	$-0.529837\pi$
$73$	−1.59943			−0.187199			−0.0935994	+	0.995610i	$0.529837\pi$
$74$		0			0
$75$	−2.05257	+	1.49128i	−0.237011	+	0.172199i
$76$		0			0
$77$	−2.45109	−	7.54368i	−0.279327	−	0.859682i
$78$		0			0
$79$	−14.3814			−1.61803			−0.809016	−	0.587786i	$-0.800000\pi$
$79$	−14.3814			−1.61803			−0.809016	+	0.587786i	$0.800000\pi$
$80$		0			0
$81$	−7.49808			−0.833120
$82$		0			0
$83$	7.14716			0.784502			0.392251	−	0.919858i	$-0.371696\pi$
$83$	7.14716			0.784502			0.392251	+	0.919858i	$0.371696\pi$
$84$		0			0
$85$	1.85584			0.201294
$86$		0			0
$87$	−3.17738	−	9.77897i	−0.340651	−	1.04842i
$88$		0			0
$89$	3.09025	−	2.24520i	0.327566	−	0.237990i	−0.411831	−	0.911260i	$-0.635111\pi$
$89$	3.09025	−	2.24520i	0.327566	−	0.237990i	0.739397	+	0.673270i	$0.235111\pi$
$90$		0			0
$91$	−1.93547			−0.202893
$92$		0			0
$93$	−7.53967	+	23.2047i	−0.781827	+	2.40622i
$94$		0			0
$95$	−3.44732	−	2.50462i	−0.353688	−	0.256969i
$96$		0			0
$97$	−2.83266	−	8.71803i	−0.287613	−	0.885182i	−0.985603	−	0.169074i	$-0.945922\pi$
$97$	−2.83266	−	8.71803i	−0.287613	−	0.885182i	0.697990	−	0.716107i	$-0.254078\pi$
$98$		0			0
$99$	2.33008	−	7.17125i	0.234182	−	0.720738i
$100$		0			0
$101$	7.60779	−	5.52738i	0.757003	−	0.549995i	−0.140986	−	0.990012i	$-0.545027\pi$
$101$	7.60779	−	5.52738i	0.757003	−	0.549995i	0.897990	+	0.440016i	$0.145027\pi$
$102$		0			0
$103$	−5.02443	+	3.65046i	−0.495072	+	0.359691i	−0.807131	−	0.590372i	$-0.798981\pi$
$103$	−5.02443	+	3.65046i	−0.495072	+	0.359691i	0.312060	+	0.950063i	$0.398981\pi$
$104$		0			0
$105$	7.42104	+	5.39170i	0.724219	+	0.526176i
$106$		0			0
$107$	−1.17938	+	0.856868i	−0.114015	+	0.0828366i	−0.643332	−	0.765588i	$-0.722448\pi$
$107$	−1.17938	+	0.856868i	−0.114015	+	0.0828366i	0.529317	+	0.848424i	$0.322448\pi$
$108$		0			0
$109$	1.85738			0.177905			0.0889526	−	0.996036i	$-0.471648\pi$
$109$	1.85738			0.177905			0.0889526	+	0.996036i	$0.471648\pi$
$110$		0			0
$111$	−2.74359	−	8.44390i	−0.260410	−	0.801459i
$112$		0			0
$113$	−3.88004	+	11.9415i	−0.365003	+	1.12337i	0.584975	+	0.811051i	$0.301104\pi$
$113$	−3.88004	+	11.9415i	−0.365003	+	1.12337i	−0.949979	+	0.312314i	$0.898896\pi$
$114$		0			0
$115$	0.155243	−	0.477789i	0.0144765	−	0.0445540i
$116$		0			0
$117$	−1.48853	−	1.08148i	−0.137614	−	0.0999827i
$118$		0			0
$119$	−2.07343	−	6.38135i	−0.190071	−	0.584977i
$120$		0			0
$121$	5.00534	+	3.63659i	0.455031	+	0.330599i
$122$		0			0
$123$	10.8215	+	12.1166i	0.975742	+	1.09252i
$124$		0			0
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$		0			0
$127$	0.328149	+	1.00994i	0.0291185	+	0.0896177i	0.964560	−	0.263865i	$-0.0849973\pi$
$127$	0.328149	+	1.00994i	0.0291185	+	0.0896177i	−0.935441	+	0.353483i	$0.884997\pi$
$128$		0			0
$129$	0.698574	+	0.507544i	0.0615060	+	0.0446867i
$130$		0			0
$131$	5.68600	−	17.4997i	0.496788	−	1.52896i	−0.317363	−	0.948304i	$-0.602797\pi$
$131$	5.68600	−	17.4997i	0.496788	−	1.52896i	0.814151	−	0.580653i	$-0.197203\pi$
$132$		0			0
$133$	−4.76072	+	14.6520i	−0.412806	+	1.27049i
$134$		0			0
$135$	0.342604	+	1.05443i	0.0294867	+	0.0907507i
$136$		0			0
$137$	0.176433			0.0150737			0.00753686	−	0.999972i	$-0.497601\pi$
$137$	0.176433			0.0150737			0.00753686	+	0.999972i	$0.497601\pi$
$138$		0			0
$139$	−0.395098	+	0.287055i	−0.0335118	+	0.0243477i	−0.604415	−	0.796670i	$-0.706593\pi$
$139$	−0.395098	+	0.287055i	−0.0335118	+	0.0243477i	0.570903	+	0.821017i	$0.306593\pi$
$140$		0			0
$141$	1.90787	+	1.38615i	0.160672	+	0.116735i
$142$		0			0
$143$	−0.950144	+	0.690320i	−0.0794551	+	0.0577275i
$144$		0			0
$145$	3.27871	−	2.38212i	0.272282	−	0.197825i
$146$		0			0
$147$	4.76029	−	14.6507i	0.392622	−	1.20837i
$148$		0			0
$149$	−1.71762	−	5.28629i	−0.140713	−	0.433070i	0.855722	−	0.517436i	$-0.173113\pi$
$149$	−1.71762	−	5.28629i	−0.140713	−	0.433070i	−0.996435	+	0.0843663i	$0.973113\pi$
$150$		0			0
$151$	−12.6654	−	9.20195i	−1.03070	−	0.748844i	−0.0622475	−	0.998061i	$-0.519827\pi$
$151$	−12.6654	−	9.20195i	−1.03070	−	0.748844i	−0.968448	+	0.249217i	$0.919827\pi$
$152$		0			0
$153$	1.97106	−	6.06631i	0.159351	−	0.490432i
$154$		0			0
$155$	−9.61676			−0.772437
$156$		0			0
$157$	−9.69086	+	7.04082i	−0.773415	+	0.561919i	−0.902996	−	0.429650i	$-0.858637\pi$
$157$	−9.69086	+	7.04082i	−0.773415	+	0.561919i	0.129580	+	0.991569i	$0.458637\pi$
$158$		0			0
$159$	7.54128	+	23.2097i	0.598063	+	1.84065i
$160$		0			0
$161$	−1.81633			−0.143147
$162$		0			0
$163$	19.3352			1.51445			0.757227	−	0.653152i	$-0.226554\pi$
$163$	19.3352			1.51445			0.757227	+	0.653152i	$0.226554\pi$
$164$		0			0
$165$	5.56611			0.433321
$166$		0			0
$167$	−3.92621			−0.303819			−0.151910	−	0.988394i	$-0.548542\pi$
$167$	−3.92621			−0.303819			−0.151910	+	0.988394i	$0.548542\pi$
$168$		0			0
$169$	−3.92866	−	12.0912i	−0.302205	−	0.930091i
$170$		0			0
$171$	−11.8484	+	8.60836i	−0.906070	+	0.658298i
$172$		0			0
$173$	14.8987			1.13273			0.566363	−	0.824156i	$-0.308350\pi$
$173$	14.8987			1.13273			0.566363	+	0.824156i	$0.308350\pi$
$174$		0			0
$175$	−1.11724	+	3.43852i	−0.0844557	+	0.259928i
$176$		0			0
$177$	20.3441	+	14.7809i	1.52916	+	1.11100i
$178$		0			0
$179$	−2.29407	−	7.06041i	−0.171466	−	0.527720i	0.827988	−	0.560746i	$-0.189486\pi$
$179$	−2.29407	−	7.06041i	−0.171466	−	0.527720i	−0.999454	+	0.0330262i	$0.989486\pi$
$180$		0			0
$181$	−8.25055	+	25.3926i	−0.613259	+	1.88742i	−0.188629	+	0.982048i	$0.560404\pi$
$181$	−8.25055	+	25.3926i	−0.613259	+	1.88742i	−0.424630	+	0.905367i	$0.639596\pi$
$182$		0			0
$183$	−8.34180	+	6.06067i	−0.616644	+	0.448018i
$184$		0			0
$185$	2.83109	−	2.05690i	0.208146	−	0.151227i
$186$		0			0
$187$	−3.29389	−	2.39315i	−0.240873	−	0.175004i
$188$		0			0
$189$	3.24290	−	2.35611i	0.235886	−	0.171382i
$190$		0			0
$191$	−7.60989			−0.550632			−0.275316	−	0.961354i	$-0.588783\pi$
$191$	−7.60989			−0.550632			−0.275316	+	0.961354i	$0.588783\pi$
$192$		0			0
$193$	−2.76062	−	8.49632i	−0.198714	−	0.611579i	−0.999913	−	0.0131809i	$-0.995804\pi$
$193$	−2.76062	−	8.49632i	−0.198714	−	0.611579i	0.801199	−	0.598398i	$-0.204196\pi$
$194$		0			0
$195$	0.419706	−	1.29172i	0.0300557	−	0.0925021i
$196$		0			0
$197$	−4.25105	+	13.0834i	−0.302875	+	0.932152i	0.677587	+	0.735442i	$0.263026\pi$
$197$	−4.25105	+	13.0834i	−0.302875	+	0.932152i	−0.980462	+	0.196710i	$0.936974\pi$
$198$		0			0
$199$	−19.4776	−	14.1513i	−1.38073	−	1.00316i	−0.996812	−	0.0797888i	$-0.974575\pi$
$199$	−19.4776	−	14.1513i	−1.38073	−	1.00316i	−0.383915	−	0.923368i	$-0.625425\pi$
$200$		0			0
$201$	−11.3235	−	34.8501i	−0.798697	−	2.45814i
$202$		0			0
$203$	−11.8541	−	8.61252i	−0.831996	−	0.604480i
$204$		0			0
$205$	−3.22394	+	5.53229i	−0.225170	+	0.386392i
$206$		0			0
$207$	−1.39690	−	1.01491i	−0.0970912	−	0.0705409i
$208$		0			0
$209$	2.88880	+	8.89081i	0.199822	+	0.614990i
$210$		0			0
$211$	−2.13503	−	1.55119i	−0.146981	−	0.106788i	0.511864	−	0.859066i	$-0.328955\pi$
$211$	−2.13503	−	1.55119i	−0.146981	−	0.106788i	−0.658846	+	0.752278i	$0.728955\pi$
$212$		0			0
$213$	−7.89039	+	24.2841i	−0.540641	+	1.66392i
$214$		0			0
$215$	−0.105171	+	0.323683i	−0.00717260	+	0.0220750i
$216$		0			0
$217$	10.7443	+	33.0675i	0.729369	+	2.24477i
$218$		0			0
$219$	−4.05794			−0.274210
$220$		0			0
$221$	−0.803747	+	0.583956i	−0.0540659	+	0.0392811i
$222$		0			0
$223$	−12.6550	−	9.19442i	−0.847443	−	0.615704i	0.0769966	−	0.997031i	$-0.475467\pi$
$223$	−12.6550	−	9.19442i	−0.847443	−	0.615704i	−0.924440	+	0.381328i	$0.875467\pi$
$224$		0			0
$225$	−2.78058	+	2.02021i	−0.185372	+	0.134681i
$226$		0			0
$227$	−8.98553	+	6.52837i	−0.596391	+	0.433303i	−0.844596	−	0.535404i	$-0.820159\pi$
$227$	−8.98553	+	6.52837i	−0.596391	+	0.433303i	0.248205	+	0.968707i	$0.420159\pi$
$228$		0			0
$229$	1.56297	−	4.81032i	0.103284	−	0.317875i	−0.886040	−	0.463609i	$-0.846554\pi$
$229$	1.56297	−	4.81032i	0.103284	−	0.317875i	0.989324	+	0.145734i	$0.0465543\pi$
$230$		0			0
$231$	−6.21871	−	19.1392i	−0.409161	−	1.25927i
$232$		0			0
$233$	13.3693	+	9.71339i	0.875854	+	0.636345i	0.932151	−	0.362069i	$-0.117929\pi$
$233$	13.3693	+	9.71339i	0.875854	+	0.636345i	−0.0562972	+	0.998414i	$0.517929\pi$
$234$		0			0
$235$	−0.287232	+	0.884008i	−0.0187369	+	0.0576663i
$236$		0			0
$237$	−36.4873			−2.37011
$238$		0			0
$239$	−12.3319	+	8.95964i	−0.797684	+	0.579551i	−0.910234	−	0.414095i	$-0.864098\pi$
$239$	−12.3319	+	8.95964i	−0.797684	+	0.579551i	0.112550	+	0.993646i	$0.464098\pi$
$240$		0			0
$241$	−0.751896	−	2.31410i	−0.0484339	−	0.149064i	0.923915	−	0.382599i	$-0.124971\pi$
$241$	−0.751896	−	2.31410i	−0.0484339	−	0.149064i	−0.972349	+	0.233535i	$0.924971\pi$
$242$		0			0
$243$	−22.3496			−1.43373
$244$		0			0
$245$	6.07169			0.387906
$246$		0			0
$247$	2.28110			0.145143
$248$		0			0
$249$	18.1332			1.14915
$250$		0			0
$251$	−7.80770	−	24.0296i	−0.492818	−	1.51674i	−0.820330	−	0.571890i	$-0.806210\pi$
$251$	−7.80770	−	24.0296i	−0.492818	−	1.51674i	0.327512	−	0.944847i	$-0.393790\pi$
$252$		0			0
$253$	−0.891658	+	0.647827i	−0.0560580	+	0.0407285i
$254$		0			0
$255$	4.70849			0.294857
$256$		0			0
$257$	5.50947	−	16.9564i	0.343671	−	1.05771i	−0.618620	−	0.785690i	$-0.712308\pi$
$257$	5.50947	−	16.9564i	0.343671	−	1.05771i	0.962291	−	0.272021i	$-0.0876919\pi$
$258$		0			0
$259$	−10.2357	−	7.43669i	−0.636017	−	0.462094i
$260$		0			0
$261$	−4.30433	−	13.2474i	−0.266432	−	0.819992i
$262$		0			0
$263$	0.655038	−	2.01600i	0.0403914	−	0.124312i	−0.928828	−	0.370512i	$-0.879182\pi$
$263$	0.655038	−	2.01600i	0.0403914	−	0.124312i	0.969219	+	0.246200i	$0.0791821\pi$
$264$		0			0
$265$	−7.78178	+	5.65380i	−0.478031	+	0.347310i
$266$		0			0
$267$	7.84033	−	5.69634i	0.479821	−	0.348610i
$268$		0			0
$269$	1.83226	+	1.33122i	0.111715	+	0.0811658i	0.642240	−	0.766503i	$-0.278005\pi$
$269$	1.83226	+	1.33122i	0.111715	+	0.0811658i	−0.530525	+	0.847669i	$0.678005\pi$
$270$		0			0
$271$	12.5363	−	9.10815i	0.761526	−	0.553281i	−0.137852	−	0.990453i	$-0.544020\pi$
$271$	12.5363	−	9.10815i	0.761526	−	0.553281i	0.899378	+	0.437172i	$0.144020\pi$
$272$		0			0
$273$	−4.91053			−0.297199
$274$		0			0
$275$	0.677943	+	2.08649i	0.0408815	+	0.125820i
$276$		0			0
$277$	−1.19417	+	3.67529i	−0.0717509	+	0.220827i	−0.980501	−	0.196514i	$-0.937038\pi$
$277$	−1.19417	+	3.67529i	−0.0717509	+	0.220827i	0.908750	+	0.417341i	$0.137038\pi$
$278$		0			0
$279$	−10.2138	+	31.4350i	−0.611487	+	1.88196i
$280$		0			0
$281$	−25.3144	−	18.3920i	−1.51013	−	1.09717i	−0.966119	−	0.258098i	$-0.916904\pi$
$281$	−25.3144	−	18.3920i	−1.51013	−	1.09717i	−0.544013	−	0.839077i	$-0.683096\pi$
$282$		0			0
$283$	4.52960	+	13.9407i	0.269257	+	0.828687i	0.990682	+	0.136195i	$0.0434873\pi$
$283$	4.52960	+	13.9407i	0.269257	+	0.828687i	−0.721425	+	0.692492i	$0.756513\pi$
$284$		0			0
$285$	−8.74627	−	6.35454i	−0.518084	−	0.376410i
$286$		0			0
$287$	22.6248	+	4.90468i	1.33550	+	0.289514i
$288$		0			0
$289$	10.9669	+	7.96793i	0.645113	+	0.468702i
$290$		0			0
$291$	−7.18680	−	22.1187i	−0.421298	−	1.29662i
$292$		0			0
$293$	15.6439	+	11.3660i	0.913928	+	0.664007i	0.942005	−	0.335599i	$-0.108939\pi$
$293$	15.6439	+	11.3660i	0.913928	+	0.664007i	−0.0280776	+	0.999606i	$0.508939\pi$
$294$		0			0
$295$	−3.06283	+	9.42642i	−0.178325	+	0.548827i
$296$		0			0
$297$	0.751629	−	2.31328i	0.0436139	−	0.134230i
$298$		0			0
$299$	0.0831061	+	0.255774i	0.00480615	+	0.0147918i
$300$		0			0
$301$	1.23049			0.0709245
$302$		0			0
$303$	19.3019	−	14.0236i	1.10886	−	0.805637i
$304$		0			0
$305$	−3.28790	−	2.38880i	−0.188265	−	0.136782i
$306$		0			0
$307$	8.58330	−	6.23613i	0.489875	−	0.355915i	−0.315261	−	0.949005i	$-0.602092\pi$
$307$	8.58330	−	6.23613i	0.489875	−	0.355915i	0.805136	+	0.593090i	$0.202092\pi$
$308$		0			0
$309$	−12.7476	+	9.26167i	−0.725185	+	0.526878i
$310$		0			0
$311$	5.06107	−	15.5764i	0.286987	−	0.883255i	−0.698809	−	0.715308i	$-0.746286\pi$
$311$	5.06107	−	15.5764i	0.286987	−	0.883255i	0.985796	−	0.167947i	$-0.0537136\pi$
$312$		0			0
$313$	3.35529	+	10.3265i	0.189652	+	0.583690i	0.999997	−	0.00226293i	$-0.000720312\pi$
$313$	3.35529	+	10.3265i	0.189652	+	0.583690i	−0.810345	+	0.585953i	$0.800720\pi$
$314$		0			0
$315$	10.0531	+	7.30403i	0.566430	+	0.411535i
$316$		0			0
$317$	−5.06558	+	15.5903i	−0.284511	+	0.875636i	0.702033	+	0.712144i	$0.252276\pi$
$317$	−5.06558	+	15.5903i	−0.284511	+	0.875636i	−0.986545	+	0.163492i	$0.947724\pi$
$318$		0			0
$319$	−8.89112			−0.497807
$320$		0			0
$321$	−2.99223	+	2.17398i	−0.167010	+	0.121340i
$322$		0			0
$323$	2.44369	+	7.52092i	0.135971	+	0.418475i
$324$		0			0
$325$	0.535329			0.0296947
$326$		0			0
$327$	4.71241			0.260597
$328$		0			0
$329$	3.36059			0.185275
$330$		0			0
$331$	−14.8906			−0.818461			−0.409231	−	0.912431i	$-0.634203\pi$
$331$	−14.8906			−0.818461			−0.409231	+	0.912431i	$0.634203\pi$
$332$		0			0
$333$	−3.71668	−	11.4388i	−0.203673	−	0.626841i
$334$		0			0
$335$	11.6846	−	8.48936i	0.638398	−	0.463823i
$336$		0			0
$337$	−2.13348			−0.116218			−0.0581090	−	0.998310i	$-0.518507\pi$
$337$	−2.13348			−0.116218			−0.0581090	+	0.998310i	$0.518507\pi$
$338$		0			0
$339$	−9.84413	+	30.2971i	−0.534660	+	1.64551i
$340$		0			0
$341$	17.0686	+	12.4010i	0.924315	+	0.671554i
$342$		0			0
$343$	1.03715	+	3.19202i	0.0560009	+	0.172353i
$344$		0			0
$345$	0.393870	−	1.21221i	0.0212053	−	0.0652631i
$346$		0			0
$347$	15.4352	−	11.2143i	0.828602	−	0.602015i	−0.0905612	−	0.995891i	$-0.528866\pi$
$347$	15.4352	−	11.2143i	0.828602	−	0.602015i	0.919164	+	0.393876i	$0.128866\pi$
$348$		0			0
$349$	20.6733	−	15.0200i	1.10662	−	0.804004i	0.124489	−	0.992221i	$-0.460271\pi$
$349$	20.6733	−	15.0200i	1.10662	−	0.804004i	0.982127	+	0.188217i	$0.0602709\pi$
$350$		0			0
$351$	−0.480164	−	0.348859i	−0.0256292	−	0.0186207i
$352$		0			0
$353$	10.6071	−	7.70653i	0.564561	−	0.410177i	−0.268565	−	0.963262i	$-0.586549\pi$
$353$	10.6071	−	7.70653i	0.564561	−	0.410177i	0.833125	+	0.553084i	$0.186549\pi$
$354$		0			0
$355$	−10.0641			−0.534147
$356$		0			0
$357$	−5.26054	−	16.1903i	−0.278417	−	0.856880i
$358$		0			0
$359$	1.06195	−	3.26836i	0.0560478	−	0.172497i	−0.919114	−	0.393992i	$-0.871094\pi$
$359$	1.06195	−	3.26836i	0.0560478	−	0.172497i	0.975162	+	0.221495i	$0.0710936\pi$
$360$		0			0
$361$	−0.260451	+	0.801585i	−0.0137079	+	0.0421887i
$362$		0			0
$363$	12.6991	+	9.22647i	0.666532	+	0.484264i
$364$		0			0
$365$	−0.494250	−	1.52115i	−0.0258702	−	0.0796204i
$366$		0			0
$367$	26.0083	+	18.8962i	1.35762	+	0.986372i	0.998592	+	0.0530468i	$0.0168932\pi$
$367$	26.0083	+	18.8962i	1.35762	+	0.986372i	0.359032	+	0.933325i	$0.383107\pi$
$368$		0			0
$369$	14.6597	+	16.4141i	0.763152	+	0.854483i
$370$		0			0
$371$	28.1349	+	20.4412i	1.46069	+	1.06125i
$372$		0			0
$373$	1.37882	+	4.24358i	0.0713927	+	0.219724i	0.980386	−	0.197086i	$-0.0631479\pi$
$373$	1.37882	+	4.24358i	0.0713927	+	0.219724i	−0.908993	+	0.416810i	$0.863148\pi$
$374$		0			0
$375$	−2.05257	−	1.49128i	−0.105995	−	0.0770095i
$376$		0			0
$377$	−0.670423	+	2.06335i	−0.0345286	+	0.106268i
$378$		0			0
$379$	−1.83360	+	5.64324i	−0.0941856	+	0.289874i	−0.987041	−	0.160471i	$-0.948699\pi$
$379$	−1.83360	+	5.64324i	−0.0941856	+	0.289874i	0.892855	+	0.450344i	$0.148699\pi$
$380$		0			0
$381$	0.832555	+	2.56234i	0.0426531	+	0.131273i
$382$		0			0
$383$	0.379598			0.0193965			0.00969827	−	0.999953i	$-0.496913\pi$
$383$	0.379598			0.0193965			0.00969827	+	0.999953i	$0.496913\pi$
$384$		0			0
$385$	6.41703	−	4.66225i	0.327042	−	0.237610i
$386$		0			0
$387$	0.946344	+	0.687559i	0.0481054	+	0.0349506i
$388$		0			0
$389$	27.7760	−	20.1804i	1.40830	−	1.02319i	0.414732	−	0.909943i	$-0.363875\pi$
$389$	27.7760	−	20.1804i	1.40830	−	1.02319i	0.993567	−	0.113246i	$-0.0361248\pi$
$390$		0			0
$391$	−0.754271	+	0.548010i	−0.0381451	+	0.0277141i
$392$		0			0
$393$	14.4261	−	44.3989i	0.727700	−	2.23963i
$394$		0			0
$395$	−4.44409	−	13.6775i	−0.223607	−	0.688190i
$396$		0			0
$397$	5.67126	+	4.12041i	0.284633	+	0.206798i	0.720935	−	0.693002i	$-0.243712\pi$
$397$	5.67126	+	4.12041i	0.284633	+	0.206798i	−0.436303	+	0.899800i	$0.643712\pi$
$398$		0			0
$399$	−12.0785	+	37.1738i	−0.604682	+	1.86102i
$400$		0			0
$401$	−11.6297			−0.580758			−0.290379	−	0.956912i	$-0.593781\pi$
$401$	−11.6297			−0.580758			−0.290379	+	0.956912i	$0.593781\pi$
$402$		0			0
$403$	4.16493	−	3.02600i	0.207470	−	0.150736i
$404$		0			0
$405$	−2.31703	−	7.13110i	−0.115134	−	0.354347i
$406$		0			0
$407$	−7.67726			−0.380548
$408$		0			0
$409$	37.5506			1.85676			0.928380	−	0.371632i	$-0.121202\pi$
$409$	37.5506			1.85676			0.928380	+	0.371632i	$0.121202\pi$
$410$		0			0
$411$	0.447633			0.0220801
$412$		0			0
$413$	35.8349			1.76332
$414$		0			0
$415$	2.20859	+	6.79735i	0.108416	+	0.333669i
$416$		0			0
$417$	−1.00241	+	0.728295i	−0.0490883	+	0.0356647i
$418$		0			0
$419$	39.6119			1.93517			0.967583	−	0.252553i	$-0.0812702\pi$
$419$	39.6119			1.93517			0.967583	+	0.252553i	$0.0812702\pi$
$420$		0			0
$421$	−0.408577	+	1.25747i	−0.0199128	+	0.0612854i	−0.960519	−	0.278214i	$-0.910258\pi$
$421$	−0.408577	+	1.25747i	−0.0199128	+	0.0612854i	0.940606	+	0.339499i	$0.110258\pi$
$422$		0			0
$423$	2.58455	+	1.87779i	0.125665	+	0.0913012i
$424$		0			0
$425$	0.573486	+	1.76501i	0.0278182	+	0.0856155i
$426$		0			0
$427$	−4.54056	+	13.9744i	−0.219733	+	0.676268i
$428$		0			0
$429$	−2.41063	+	1.75143i	−0.116386	+	0.0845597i
$430$		0			0
$431$	25.9679	−	18.8668i	1.25083	−	0.908782i	0.252561	−	0.967581i	$-0.418727\pi$
$431$	25.9679	−	18.8668i	1.25083	−	0.908782i	0.998270	+	0.0587994i	$0.0187272\pi$
$432$		0			0
$433$	6.79174	+	4.93449i	0.326390	+	0.237136i	0.738897	−	0.673818i	$-0.235347\pi$
$433$	6.79174	+	4.93449i	0.326390	+	0.237136i	−0.412507	+	0.910954i	$0.635347\pi$
$434$		0			0
$435$	8.31849	−	6.04374i	0.398841	−	0.289775i
$436$		0			0
$437$	2.14069			0.102403
$438$		0			0
$439$	−9.92997	−	30.5613i	−0.473932	−	1.45861i	−0.847393	−	0.530966i	$-0.821829\pi$
$439$	−9.92997	−	30.5613i	−0.473932	−	1.45861i	0.373461	−	0.927646i	$-0.378171\pi$
$440$		0			0
$441$	6.44867	−	19.8470i	0.307079	−	0.945093i
$442$		0			0
$443$	10.1433	−	31.2179i	0.481923	−	1.48321i	−0.354466	−	0.935069i	$-0.615337\pi$
$443$	10.1433	−	31.2179i	0.481923	−	1.48321i	0.836389	−	0.548136i	$-0.184663\pi$
$444$		0			0
$445$	3.09025	+	2.24520i	0.146492	+	0.106432i
$446$		0			0
$447$	−4.35781	−	13.4120i	−0.206117	−	0.634364i
$448$		0			0
$449$	3.53441	+	2.56790i	0.166799	+	0.121187i	0.668053	−	0.744114i	$-0.267128\pi$
$449$	3.53441	+	2.56790i	0.166799	+	0.121187i	−0.501254	+	0.865300i	$0.667128\pi$
$450$		0			0
$451$	12.8561	−	5.66179i	0.605371	−	0.266603i
$452$		0			0
$453$	−32.1337	−	23.3465i	−1.50977	−	1.09691i
$454$		0			0
$455$	−0.598094	−	1.84074i	−0.0280391	−	0.0862954i
$456$		0			0
$457$	−18.6958	−	13.5833i	−0.874554	−	0.635401i	0.0572512	−	0.998360i	$-0.481766\pi$
$457$	−18.6958	−	13.5833i	−0.874554	−	0.635401i	−0.931805	+	0.362959i	$0.881766\pi$
$458$		0			0
$459$	0.635818	−	1.95685i	0.0296775	−	0.0913378i
$460$		0			0
$461$	−8.22882	+	25.3257i	−0.383254	+	1.17954i	0.554484	+	0.832194i	$0.312916\pi$
$461$	−8.22882	+	25.3257i	−0.383254	+	1.17954i	−0.937739	+	0.347342i	$0.887084\pi$
$462$		0			0
$463$	8.02375	+	24.6946i	0.372895	+	1.14765i	0.944888	+	0.327395i	$0.106171\pi$
$463$	8.02375	+	24.6946i	0.372895	+	1.14765i	−0.571992	+	0.820259i	$0.693829\pi$
$464$		0			0
$465$	−24.3989			−1.13147
$466$		0			0
$467$	18.9958	−	13.8012i	0.879019	−	0.638645i	−0.0539726	−	0.998542i	$-0.517188\pi$
$467$	18.9958	−	13.8012i	0.879019	−	0.638645i	0.932992	+	0.359898i	$0.117188\pi$
$468$		0			0
$469$	−42.2454	−	30.6931i	−1.95071	−	1.41728i
$470$		0			0
$471$	−24.5869	+	17.8634i	−1.13290	+	0.823103i
$472$		0			0
$473$	0.604062	−	0.438877i	0.0277748	−	0.0201796i
$474$		0			0
$475$	1.31676	−	4.05257i	0.0604171	−	0.185945i
$476$		0			0
$477$	10.2160	+	31.4417i	0.467760	+	1.43962i
$478$		0			0
$479$	−17.3871	−	12.6325i	−0.794436	−	0.577192i	0.114840	−	0.993384i	$-0.463364\pi$
$479$	−17.3871	−	12.6325i	−0.794436	−	0.577192i	−0.909277	+	0.416192i	$0.863364\pi$
$480$		0			0
$481$	−0.578894	+	1.78165i	−0.0263953	+	0.0812363i
$482$		0			0
$483$	−4.60826			−0.209683
$484$		0			0
$485$	7.41600	−	5.38804i	0.336743	−	0.244658i
$486$		0			0
$487$	−10.0033	−	30.7871i	−0.453294	−	1.39510i	−0.873126	−	0.487494i	$-0.837911\pi$
$487$	−10.0033	−	30.7871i	−0.453294	−	1.39510i	0.419832	−	0.907602i	$-0.362089\pi$
$488$		0			0
$489$	49.0559			2.21838
$490$		0			0
$491$	27.8124			1.25516			0.627578	−	0.778554i	$-0.284046\pi$
$491$	27.8124			1.25516			0.627578	+	0.778554i	$0.284046\pi$
$492$		0			0
$493$	−7.52118			−0.338737
$494$		0			0
$495$	7.54030			0.338911
$496$		0			0
$497$	11.2441	+	34.6056i	0.504365	+	1.55228i
$498$		0			0
$499$	−19.1387	+	13.9051i	−0.856767	+	0.622478i	−0.927003	−	0.375053i	$-0.877625\pi$
$499$	−19.1387	+	13.9051i	−0.856767	+	0.622478i	0.0702366	+	0.997530i	$0.477625\pi$
$500$		0			0
$501$	−9.96128			−0.445037
$502$		0			0
$503$	−12.5575	+	38.6480i	−0.559911	+	1.72323i	0.122698	+	0.992444i	$0.460845\pi$
$503$	−12.5575	+	38.6480i	−0.559911	+	1.72323i	−0.682609	+	0.730784i	$0.739155\pi$
$504$		0			0
$505$	7.60779	+	5.52738i	0.338542	+	0.245965i
$506$		0			0
$507$	−9.96750	−	30.6768i	−0.442672	−	1.36240i
$508$		0			0
$509$	2.79181	−	8.59232i	0.123745	−	0.380848i	−0.869925	−	0.493183i	$-0.835833\pi$
$509$	2.79181	−	8.59232i	0.123745	−	0.380848i	0.993670	+	0.112336i	$0.0358332\pi$
$510$		0			0
$511$	−4.67830	+	3.39898i	−0.206956	+	0.150362i
$512$		0			0
$513$	−3.82201	+	2.77685i	−0.168746	+	0.122601i
$514$		0			0
$515$	−5.02443	−	3.65046i	−0.221403	−	0.160859i
$516$		0			0
$517$	1.64975	−	1.19861i	0.0725560	−	0.0527150i
$518$		0			0
$519$	37.7998			1.65923
$520$		0			0
$521$	2.93025	+	9.01839i	0.128377	+	0.395103i	0.994501	−	0.104726i	$-0.0333964\pi$
$521$	2.93025	+	9.01839i	0.128377	+	0.395103i	−0.866124	+	0.499828i	$0.833396\pi$
$522$		0			0
$523$	9.80674	−	30.1820i	0.428819	−	1.31977i	−0.470471	−	0.882415i	$-0.655916\pi$
$523$	9.80674	−	30.1820i	0.428819	−	1.31977i	0.899290	−	0.437353i	$-0.144084\pi$
$524$		0			0
$525$	−2.83459	+	8.72396i	−0.123711	+	0.380745i
$526$		0			0
$527$	14.4387	+	10.4903i	0.628958	+	0.456965i
$528$		0			0
$529$	−7.02940	−	21.6343i	−0.305626	−	0.940620i
$530$		0			0
$531$	27.5598	+	20.0234i	1.19599	+	0.868940i
$532$		0			0
$533$	−0.344525	−	3.41042i	−0.0149230	−	0.147722i
$534$		0			0
$535$	−1.17938	−	0.856868i	−0.0509889	−	0.0370456i
$536$		0			0
$537$	−5.82032	−	17.9131i	−0.251165	−	0.773008i
$538$		0			0
$539$	−10.7765	−	7.82959i	−0.464177	−	0.337244i
$540$		0			0
$541$	1.01877	−	3.13544i	0.0438002	−	0.134803i	−0.926765	−	0.375642i	$-0.877422\pi$
$541$	1.01877	−	3.13544i	0.0438002	−	0.134803i	0.970565	+	0.240838i	$0.0774224\pi$
$542$		0			0
$543$	−20.9326	+	64.4241i	−0.898306	+	2.76470i
$544$		0			0
$545$	0.573963	+	1.76648i	0.0245859	+	0.0756676i
$546$		0			0
$547$	29.9344			1.27990			0.639952	−	0.768415i	$-0.278954\pi$
$547$	29.9344			1.27990			0.639952	+	0.768415i	$0.278954\pi$
$548$		0			0
$549$	−11.3005	+	8.21027i	−0.482292	+	0.350406i
$550$		0			0
$551$	13.9710	+	10.1505i	0.595184	+	0.432427i
$552$		0			0
$553$	−42.0653	+	30.5623i	−1.78880	+	1.29964i
$554$		0			0
$555$	7.18281	−	5.21862i	0.304893	−	0.221518i
$556$		0			0
$557$	1.99808	−	6.14945i	0.0846612	−	0.260560i	−0.899760	−	0.436384i	$-0.856259\pi$
$557$	1.99808	−	6.14945i	0.0846612	−	0.260560i	0.984422	+	0.175824i	$0.0562589\pi$
$558$		0			0
$559$	−0.0563011	−	0.173277i	−0.00238128	−	0.00732884i
$560$		0			0
$561$	−8.35700	−	6.07171i	−0.352833	−	0.256348i
$562$		0			0
$563$	−10.1327	+	31.1853i	−0.427043	+	1.31430i	0.473981	+	0.880535i	$0.342816\pi$
$563$	−10.1327	+	31.1853i	−0.427043	+	1.31430i	−0.901024	+	0.433768i	$0.857184\pi$
$564$		0			0
$565$	−12.5561			−0.528238
$566$		0			0
$567$	−21.9318	+	15.9344i	−0.921047	+	0.669180i
$568$		0			0
$569$	0.197639	+	0.608270i	0.00828546	+	0.0255000i	0.955114	−	0.296239i	$-0.0957326\pi$
$569$	0.197639	+	0.608270i	0.00828546	+	0.0255000i	−0.946828	+	0.321739i	$0.895733\pi$
$570$		0			0
$571$	18.2396			0.763304			0.381652	−	0.924306i	$-0.375355\pi$
$571$	18.2396			0.763304			0.381652	+	0.924306i	$0.375355\pi$
$572$		0			0
$573$	−19.3072			−0.806570
$574$		0			0
$575$	0.502377			0.0209506
$576$		0			0
$577$	25.2450			1.05096			0.525481	−	0.850806i	$-0.323886\pi$
$577$	25.2450			1.05096			0.525481	+	0.850806i	$0.323886\pi$
$578$		0			0
$579$	−7.00404	−	21.5562i	−0.291078	−	0.895845i
$580$		0			0
$581$	20.9053	−	15.1886i	0.867299	−	0.630129i
$582$		0			0
$583$	21.1024			0.873973
$584$		0			0
$585$	0.568567	−	1.74987i	0.0235073	−	0.0723482i
$586$		0			0
$587$	−29.4109	−	21.3683i	−1.21392	−	0.881963i	−0.218338	−	0.975873i	$-0.570063\pi$
$587$	−29.4109	−	21.3683i	−1.21392	−	0.881963i	−0.995581	+	0.0939098i	$0.970063\pi$
$588$		0			0
$589$	−12.6630	−	38.9726i	−0.521768	−	1.60584i
$590$		0			0
$591$	−10.7854	+	33.1941i	−0.443653	+	1.36542i
$592$		0			0
$593$	0.954133	−	0.693218i	0.0391815	−	0.0284670i	−0.568022	−	0.823013i	$-0.692291\pi$
$593$	0.954133	−	0.693218i	0.0391815	−	0.0284670i	0.607204	+	0.794546i	$0.292291\pi$
$594$		0			0
$595$	5.42830	−	3.94389i	0.222539	−	0.161684i
$596$		0			0
$597$	−49.4169	−	35.9035i	−2.02250	−	1.46943i
$598$		0			0
$599$	−18.9500	+	13.7680i	−0.774276	+	0.562544i	−0.903256	−	0.429103i	$-0.858830\pi$
$599$	−18.9500	+	13.7680i	−0.774276	+	0.562544i	0.128980	+	0.991647i	$0.458830\pi$
$600$		0			0
$601$	−33.2290			−1.35544			−0.677720	−	0.735321i	$-0.737032\pi$
$601$	−33.2290			−1.35544			−0.677720	+	0.735321i	$0.737032\pi$
$602$		0			0
$603$	−15.3397	−	47.2107i	−0.624681	−	1.92257i
$604$		0			0
$605$	−1.91187	+	5.88413i	−0.0777285	+	0.239224i
$606$		0			0
$607$	−11.5963	+	35.6896i	−0.470678	+	1.44860i	0.381022	+	0.924566i	$0.375572\pi$
$607$	−11.5963	+	35.6896i	−0.470678	+	1.44860i	−0.851699	+	0.524031i	$0.824428\pi$
$608$		0			0
$609$	−30.0753	−	21.8510i	−1.21871	−	0.885448i
$610$		0			0
$611$	−0.153764	−	0.473236i	−0.00622061	−	0.0191451i
$612$		0			0
$613$	−5.44651	−	3.95712i	−0.219982	−	0.159827i	0.472336	−	0.881418i	$-0.343411\pi$
$613$	−5.44651	−	3.95712i	−0.219982	−	0.159827i	−0.692319	+	0.721592i	$0.743411\pi$
$614$		0			0
$615$	−8.17953	+	14.0361i	−0.329830	+	0.565990i
$616$		0			0
$617$	9.97024	+	7.24381i	0.401387	+	0.291625i	0.770106	−	0.637916i	$-0.220203\pi$
$617$	9.97024	+	7.24381i	0.401387	+	0.291625i	−0.368719	+	0.929541i	$0.620203\pi$
$618$		0			0
$619$	11.5468	+	35.5375i	0.464106	+	1.42837i	0.860103	+	0.510120i	$0.170399\pi$
$619$	11.5468	+	35.5375i	0.464106	+	1.42837i	−0.395997	+	0.918252i	$0.629601\pi$
$620$		0			0
$621$	−0.450607	−	0.327385i	−0.0180822	−	0.0131375i
$622$		0			0
$623$	4.26760	−	13.1343i	0.170978	−	0.526216i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$		0			0
$627$	7.32923	+	22.5571i	0.292701	+	0.900842i
$628$		0			0
$629$	−6.49435			−0.258947
$630$		0			0
$631$	−7.32822	+	5.32427i	−0.291732	+	0.211956i	−0.724018	−	0.689781i	$-0.757707\pi$
$631$	−7.32822	+	5.32427i	−0.291732	+	0.211956i	0.432286	+	0.901736i	$0.357707\pi$
$632$		0			0
$633$	−5.41683	−	3.93556i	−0.215300	−	0.156424i
$634$		0			0
$635$	−0.859106	+	0.624177i	−0.0340926	+	0.0247697i
$636$		0			0
$637$	−2.62959	+	1.91051i	−0.104188	+	0.0756972i
$638$		0			0
$639$	−10.6890	+	32.8972i	−0.422848	+	1.30139i
$640$		0			0
$641$	4.69280	+	14.4430i	0.185355	+	0.570463i	0.999954	−	0.00956071i	$-0.00304332\pi$
$641$	4.69280	+	14.4430i	0.185355	+	0.570463i	−0.814600	+	0.580024i	$0.803043\pi$
$642$		0			0
$643$	−25.7728	−	18.7250i	−1.01638	−	0.738444i	−0.0508429	−	0.998707i	$-0.516191\pi$
$643$	−25.7728	−	18.7250i	−1.01638	−	0.738444i	−0.965538	+	0.260263i	$0.916191\pi$
$644$		0			0
$645$	−0.266832	+	0.821223i	−0.0105065	+	0.0323356i
$646$		0			0
$647$	−23.1108			−0.908581			−0.454290	−	0.890854i	$-0.650107\pi$
$647$	−23.1108			−0.908581			−0.454290	+	0.890854i	$0.650107\pi$
$648$		0			0
$649$	17.5917	−	12.7811i	0.690536	−	0.501704i
$650$		0			0
$651$	27.2595	+	83.8962i	1.06838	+	3.28815i
$652$		0			0
$653$	21.5774			0.844388			0.422194	−	0.906505i	$-0.361260\pi$
$653$	21.5774			0.844388			0.422194	+	0.906505i	$0.361260\pi$
$654$		0			0
$655$	18.4003			0.718959
$656$		0			0
$657$	−5.49721			−0.214467
$658$		0			0
$659$	23.6901			0.922835			0.461418	−	0.887183i	$-0.347341\pi$
$659$	23.6901			0.922835			0.461418	+	0.887183i	$0.347341\pi$
$660$		0			0
$661$	−2.28489	−	7.03216i	−0.0888718	−	0.273519i	0.896736	−	0.442565i	$-0.145931\pi$
$661$	−2.28489	−	7.03216i	−0.0888718	−	0.273519i	−0.985608	+	0.169046i	$0.945931\pi$
$662$		0			0
$663$	−2.03920	+	1.48157i	−0.0791961	+	0.0575393i
$664$		0			0
$665$	−15.4060			−0.597419
$666$		0			0
$667$	−0.629155	+	1.93634i	−0.0243610	+	0.0749754i
$668$		0			0
$669$	−32.1073	−	23.3274i	−1.24134	−	0.901888i
$670$		0			0
$671$	2.75521	+	8.47965i	0.106364	+	0.327353i
$672$		0			0
$673$	7.25169	−	22.3184i	0.279532	−	0.860311i	−0.708452	−	0.705759i	$-0.750606\pi$
$673$	7.25169	−	22.3184i	0.279532	−	0.860311i	0.987985	−	0.154553i	$-0.0493936\pi$
$674$		0			0
$675$	−0.896950	+	0.651672i	−0.0345236	+	0.0250829i
$676$		0			0
$677$	37.9434	−	27.5675i	1.45828	−	1.05950i	0.474476	−	0.880268i	$-0.342637\pi$
$677$	37.9434	−	27.5675i	1.45828	−	1.05950i	0.983806	−	0.179236i	$-0.0573626\pi$
$678$		0			0
$679$	−26.8124	−	19.4803i	−1.02896	−	0.747587i
$680$		0			0
$681$	−22.7974	+	16.5633i	−0.873598	+	0.634706i
$682$		0			0
$683$	−34.9728			−1.33820			−0.669098	−	0.743174i	$-0.733319\pi$
$683$	−34.9728			−1.33820			−0.669098	+	0.743174i	$0.733319\pi$
$684$		0			0
$685$	0.0545209	+	0.167798i	0.00208314	+	0.00641124i
$686$		0			0
$687$	3.96544	−	12.2044i	0.151291	−	0.465626i
$688$		0			0
$689$	1.59120	−	4.89721i	0.0606199	−	0.186569i
$690$		0			0
$691$	36.5285	+	26.5395i	1.38961	+	1.00961i	0.995908	+	0.0903723i	$0.0288057\pi$
$691$	36.5285	+	26.5395i	1.38961	+	1.00961i	0.393702	+	0.919238i	$0.371194\pi$
$692$		0			0
$693$	−8.42436	−	25.9275i	−0.320015	−	0.984905i
$694$		0			0
$695$	−0.395098	−	0.287055i	−0.0149869	−	0.0108886i
$696$		0			0
$697$	10.8753	−	4.78942i	0.411930	−	0.181412i
$698$		0			0
$699$	33.9196	+	24.6441i	1.28296	+	0.932124i
$700$		0			0
$701$	8.89671	+	27.3813i	0.336024	+	1.03418i	0.966215	+	0.257736i	$0.0829766\pi$
$701$	8.89671	+	27.3813i	0.336024	+	1.03418i	−0.630191	+	0.776440i	$0.717023\pi$
$702$		0			0
$703$	12.0636	+	8.76472i	0.454987	+	0.330568i
$704$		0			0
$705$	−0.728742	+	2.24284i	−0.0274460	+	0.0844701i
$706$		0			0
$707$	10.5063	−	32.3350i	0.395129	−	1.21608i
$708$		0			0
$709$	−7.52917	−	23.1724i	−0.282764	−	0.870258i	−0.987060	−	0.160352i	$-0.948737\pi$
$709$	−7.52917	−	23.1724i	−0.282764	−	0.870258i	0.704296	−	0.709906i	$-0.251263\pi$
$710$		0			0
$711$	−49.4287			−1.85372
$712$		0			0
$713$	3.90855	−	2.83973i	0.146376	−	0.106349i
$714$		0			0
$715$	−0.950144	−	0.690320i	−0.0355334	−	0.0258165i
$716$		0			0
$717$	−31.2875	+	22.7317i	−1.16845	+	0.848931i
$718$		0			0
$719$	−2.07294	+	1.50608i	−0.0773075	+	0.0561672i	−0.625768	−	0.780009i	$-0.715214\pi$
$719$	−2.07294	+	1.50608i	−0.0773075	+	0.0561672i	0.548460	+	0.836177i	$0.315214\pi$
$720$		0			0
$721$	−6.93869	+	21.3551i	−0.258410	+	0.795305i
$722$		0			0
$723$	−1.90765	−	5.87115i	−0.0709463	−	0.218350i
$724$		0			0
$725$	3.27871	+	2.38212i	0.121768	+	0.0884699i
$726$		0			0
$727$	−7.95870	+	24.4944i	−0.295172	+	0.908446i	0.687992	+	0.725718i	$0.258492\pi$
$727$	−7.95870	+	24.4944i	−0.295172	+	0.908446i	−0.983164	+	0.182727i	$0.941508\pi$
$728$		0			0
$729$	−34.2095			−1.26702
$730$		0			0
$731$	0.510989	−	0.371255i	0.0188996	−	0.0137314i
$732$		0			0
$733$	−14.8221	−	45.6178i	−0.547468	−	1.68493i	−0.715050	−	0.699074i	$-0.753596\pi$
$733$	−14.8221	−	45.6178i	−0.547468	−	1.68493i	0.167582	−	0.985858i	$-0.446404\pi$
$734$		0			0
$735$	15.4046			0.568208
$736$		0			0
$737$	−31.6860			−1.16717
$738$		0			0
$739$	7.73375			0.284491			0.142245	−	0.989831i	$-0.454568\pi$
$739$	7.73375			0.284491			0.142245	+	0.989831i	$0.454568\pi$
$740$		0			0
$741$	5.78744			0.212607
$742$		0			0
$743$	−6.59654	−	20.3021i	−0.242003	−	0.744810i	−0.996115	−	0.0880636i	$-0.971932\pi$
$743$	−6.59654	−	20.3021i	−0.242003	−	0.744810i	0.754111	−	0.656747i	$-0.228068\pi$
$744$		0			0
$745$	4.49679	−	3.26711i	0.164749	−	0.119697i
$746$		0			0
$747$	24.5647			0.898775
$748$		0			0
$749$	−1.62871	+	5.01265i	−0.0595117	+	0.183158i
$750$		0			0
$751$	4.33998	+	3.15318i	0.158368	+	0.115061i	0.664147	−	0.747602i	$-0.268795\pi$
$751$	4.33998	+	3.15318i	0.158368	+	0.115061i	−0.505779	+	0.862663i	$0.668795\pi$
$752$		0			0
$753$	−19.8091	−	60.9661i	−0.721883	−	2.22173i
$754$		0			0
$755$	4.83775	−	14.8891i	0.176064	−	0.541869i
$756$		0			0
$757$	−29.8701	+	21.7019i	−1.08565	+	0.788768i	−0.978659	−	0.205492i	$-0.934120\pi$
$757$	−29.8701	+	21.7019i	−1.08565	+	0.788768i	−0.106987	+	0.994260i	$0.534120\pi$
$758$		0			0
$759$	−2.26224	+	1.64362i	−0.0821142	+	0.0596595i
$760$		0			0
$761$	0.0565426	+	0.0410806i	0.00204967	+	0.00148917i	0.588810	−	0.808272i	$-0.299597\pi$
$761$	0.0565426	+	0.0410806i	0.00204967	+	0.00148917i	−0.586760	+	0.809761i	$0.699597\pi$
$762$		0			0
$763$	5.43282	−	3.94718i	0.196681	−	0.142897i
$764$		0			0
$765$	6.37850			0.230615
$766$		0			0
$767$	−1.63962	−	5.04624i	−0.0592033	−	0.182209i
$768$		0			0
$769$	−7.75381	+	23.8638i	−0.279609	+	0.860549i	0.708353	+	0.705858i	$0.249438\pi$
$769$	−7.75381	+	23.8638i	−0.279609	+	0.860549i	−0.987963	+	0.154691i	$0.950562\pi$
$770$		0			0
$771$	13.9782	−	43.0204i	0.503412	−	1.54934i
$772$		0			0
$773$	7.36232	+	5.34904i	0.264804	+	0.192391i	0.712262	−	0.701913i	$-0.247671\pi$
$773$	7.36232	+	5.34904i	0.264804	+	0.192391i	−0.447458	+	0.894305i	$0.647671\pi$
$774$		0			0
$775$	−2.97174	−	9.14608i	−0.106748	−	0.328537i
$776$		0			0
$777$	−25.9693	−	18.8678i	−0.931643	−	0.676879i
$778$		0			0
$779$	−26.6651	−	5.78054i	−0.955377	−	0.207109i
$780$		0			0
$781$	17.8625	+	12.9779i	0.639172	+	0.464386i
$782$		0			0
$783$	−1.38848	−	4.27329i	−0.0496201	−	0.152715i
$784$		0			0
$785$	−9.69086	−	7.04082i	−0.345882	−	0.251298i
$786$		0			0
$787$	−12.7495	+	39.2389i	−0.454470	+	1.39871i	0.417286	+	0.908775i	$0.362981\pi$
$787$	−12.7495	+	39.2389i	−0.454470	+	1.39871i	−0.871756	+	0.489940i	$0.837019\pi$
$788$		0			0
$789$	1.66191	−	5.11484i	0.0591656	−	0.182093i
$790$		0			0
$791$	14.0282	+	43.1744i	0.498785	+	1.53510i
$792$		0			0
$793$	2.17562			0.0772584
$794$		0			0
$795$	−19.7433	+	14.3444i	−0.700224	+	0.508742i
$796$		0			0
$797$	0.153469	+	0.111502i	0.00543616	+	0.00394960i	0.590500	−	0.807038i	$-0.298931\pi$
$797$	0.153469	+	0.111502i	0.00543616	+	0.00394960i	−0.585064	+	0.810987i	$0.698931\pi$
$798$		0			0
$799$	1.39556	−	1.01393i	0.0493713	−	0.0358703i
$800$		0			0
$801$	10.6211	−	7.71671i	0.375280	−	0.272657i
$802$		0			0
$803$	−1.08432	+	3.33720i	−0.0382648	+	0.117767i
$804$		0			0
$805$	−0.561278	−	1.72744i	−0.0197824	−	0.0608841i
$806$		0			0
$807$	4.64868	+	3.37746i	0.163641	+	0.118892i
$808$		0			0
$809$	−5.71105	+	17.5768i	−0.200790	+	0.617968i	0.799070	+	0.601238i	$0.205326\pi$
$809$	−5.71105	+	17.5768i	−0.200790	+	0.617968i	−0.999860	+	0.0167299i	$0.994674\pi$
$810$		0			0
$811$	1.74792			0.0613777			0.0306889	−	0.999529i	$-0.490230\pi$
$811$	1.74792			0.0613777			0.0306889	+	0.999529i	$0.490230\pi$
$812$		0			0
$813$	31.8061	−	23.1085i	1.11549	−	0.810450i
$814$		0			0
$815$	5.97492	+	18.3889i	0.209292	+	0.644135i
$816$		0			0
$817$	−1.45023			−0.0507372
$818$		0			0
$819$	−6.65219			−0.232446
$820$		0			0
$821$	23.8076			0.830891			0.415445	−	0.909618i	$-0.363626\pi$
$821$	23.8076			0.830891			0.415445	+	0.909618i	$0.363626\pi$
$822$		0			0
$823$	−4.94235			−0.172280			−0.0861398	−	0.996283i	$-0.527453\pi$
$823$	−4.94235			−0.172280			−0.0861398	+	0.996283i	$0.527453\pi$
$824$		0			0
$825$	1.72002	+	5.29369i	0.0598836	+	0.184303i
$826$		0			0
$827$	14.7503	−	10.7167i	0.512919	−	0.372657i	−0.301011	−	0.953621i	$-0.597324\pi$
$827$	14.7503	−	10.7167i	0.512919	−	0.372657i	0.813930	+	0.580963i	$0.197324\pi$
$828$		0			0
$829$	19.2878			0.669892			0.334946	−	0.942237i	$-0.391282\pi$
$829$	19.2878			0.669892			0.334946	+	0.942237i	$0.391282\pi$
$830$		0			0
$831$	−3.02976	+	9.32465i	−0.105101	+	0.323469i
$832$		0			0
$833$	−9.11607	−	6.62321i	−0.315853	−	0.229481i
$834$		0			0
$835$	−1.21327	−	3.73405i	−0.0419868	−	0.129222i
$836$		0			0
$837$	−3.29474	+	10.1402i	−0.113883	+	0.350496i
$838$		0			0
$839$	5.57283	−	4.04890i	0.192395	−	0.139783i	−0.487417	−	0.873169i	$-0.662061\pi$
$839$	5.57283	−	4.04890i	0.192395	−	0.139783i	0.679813	+	0.733386i	$0.262061\pi$
$840$		0			0
$841$	10.1738	−	7.39171i	0.350821	−	0.254887i
$842$		0			0
$843$	−64.2258	−	46.6627i	−2.21205	−	1.60715i
$844$		0			0
$845$	10.2854	−	7.47276i	0.353828	−	0.257071i
$846$		0			0
$847$	22.3687			0.768599
$848$		0			0
$849$	11.4921	+	35.3692i	0.394409	+	1.21387i
$850$		0			0
$851$	−0.543260	+	1.67198i	−0.0186227	+	0.0573148i
$852$		0			0
$853$	−0.457554	+	1.40821i	−0.0156663	+	0.0482160i	−0.958584	−	0.284810i	$-0.908070\pi$
$853$	−0.457554	+	1.40821i	−0.0156663	+	0.0482160i	0.942918	+	0.333026i	$0.108070\pi$
$854$		0			0
$855$	−11.8484	−	8.60836i	−0.405207	−	0.294400i
$856$		0			0
$857$	10.4075	+	32.0309i	0.355513	+	1.09416i	0.955712	+	0.294305i	$0.0950880\pi$
$857$	10.4075	+	32.0309i	0.355513	+	1.09416i	−0.600199	+	0.799851i	$0.704912\pi$
$858$		0			0
$859$	−41.0998	−	29.8607i	−1.40231	−	1.01883i	−0.994386	−	0.105818i	$-0.966254\pi$
$859$	−41.0998	−	29.8607i	−1.40231	−	1.01883i	−0.407921	−	0.913017i	$-0.633746\pi$
$860$		0			0
$861$	57.4020	+	12.4438i	1.95625	+	0.424082i
$862$		0			0
$863$	41.8167	+	30.3816i	1.42346	+	1.03420i	0.991189	+	0.132456i	$0.0422864\pi$
$863$	41.8167	+	30.3816i	1.42346	+	1.03420i	0.432268	+	0.901745i	$0.357714\pi$
$864$		0			0
$865$	4.60394	+	14.1695i	0.156539	+	0.481777i
$866$		0			0
$867$	27.8244	+	20.2156i	0.944967	+	0.686558i
$868$		0			0
$869$	−9.74976	+	30.0067i	−0.330738	+	1.01791i
$870$		0			0
$871$	−2.38924	+	7.35333i	−0.0809563	+	0.249158i
$872$		0			0
$873$	−9.73581	−	29.9638i	−0.329507	−	1.01412i
$874$		0			0
$875$	−3.61548			−0.122226
$876$		0			0
$877$	36.8906	−	26.8026i	1.24571	−	0.905058i	0.247741	−	0.968826i	$-0.420312\pi$
$877$	36.8906	−	26.8026i	1.24571	−	0.905058i	0.997965	+	0.0637680i	$0.0203118\pi$
$878$		0			0
$879$	39.6905	+	28.8369i	1.33873	+	0.972643i
$880$		0			0
$881$	−34.9651	+	25.4036i	−1.17800	+	0.855869i	−0.991945	−	0.126670i	$-0.959571\pi$
$881$	−34.9651	+	25.4036i	−1.17800	+	0.855869i	−0.186058	+	0.982539i	$0.559571\pi$
$882$		0			0
$883$	1.85543	−	1.34805i	0.0624402	−	0.0453655i	−0.556127	−	0.831097i	$-0.687713\pi$
$883$	1.85543	−	1.34805i	0.0624402	−	0.0453655i	0.618568	+	0.785732i	$0.287713\pi$
$884$		0			0
$885$	−7.77077	+	23.9160i	−0.261212	+	0.803926i
$886$		0			0
$887$	−16.6623	−	51.2814i	−0.559466	−	1.72186i	−0.683847	−	0.729625i	$-0.739694\pi$
$887$	−16.6623	−	51.2814i	−0.559466	−	1.72186i	0.124381	−	0.992235i	$-0.460306\pi$
$888$		0			0
$889$	3.10608	+	2.25670i	0.104175	+	0.0756873i
$890$		0			0
$891$	−5.08327	+	15.6447i	−0.170296	+	0.524117i
$892$		0			0
$893$	−3.96072			−0.132540
$894$		0			0
$895$	6.00594	−	4.36357i	0.200756	−	0.145858i
$896$		0			0
$897$	0.210850	+	0.648931i	0.00704009	+	0.0216672i
$898$		0			0
$899$	38.9739			1.29985
$900$		0			0
$901$	17.8510			0.594702
$902$		0			0
$903$	3.12191			0.103891
$904$		0			0
$905$	−26.6993			−0.887516
$906$		0			0
$907$	−3.37815	−	10.3969i	−0.112170	−	0.345222i	0.879177	−	0.476496i	$-0.158093\pi$
$907$	−3.37815	−	10.3969i	−0.112170	−	0.345222i	−0.991346	+	0.131274i	$0.958093\pi$
$908$		0			0
$909$	26.1479	−	18.9975i	0.867271	−	0.630109i
$910$		0			0
$911$	−41.2157			−1.36554			−0.682769	−	0.730634i	$-0.739225\pi$
$911$	−41.2157			−1.36554			−0.682769	+	0.730634i	$0.739225\pi$
$912$		0			0
$913$	4.84537	−	14.9125i	0.160358	−	0.493532i
$914$		0			0
$915$	−8.34180	−	6.06067i	−0.275771	−	0.200360i
$916$		0			0
$917$	−20.5576	−	63.2699i	−0.678873	−	2.08935i
$918$		0			0
$919$	1.69649	−	5.22127i	0.0559621	−	0.172234i	−0.919169	−	0.393864i	$-0.871138\pi$
$919$	1.69649	−	5.22127i	0.0559621	−	0.172234i	0.975131	+	0.221631i	$0.0711379\pi$
$920$		0			0
$921$	21.7769	−	15.8218i	0.717573	−	0.521347i
$922$		0			0
$923$	4.35867	−	3.16676i	0.143467	−	0.104235i
$924$		0			0
$925$	2.83109	+	2.05690i	0.0930855	+	0.0676306i
$926$		0			0
$927$	−17.2689	+	12.5466i	−0.567185	+	0.412084i
$928$		0			0
$929$	−27.4414			−0.900323			−0.450161	−	0.892947i	$-0.648634\pi$
$929$	−27.4414			−0.900323			−0.450161	+	0.892947i	$0.648634\pi$
$930$		0			0
$931$	7.99495	+	24.6059i	0.262024	+	0.806427i
$932$		0			0
$933$	12.8405	−	39.5191i	0.420381	−	1.29380i
$934$		0			0
$935$	1.25815	−	3.87220i	0.0411460	−	0.126634i
$936$		0			0
$937$	41.2232	+	29.9504i	1.34670	+	0.978438i	0.999169	+	0.0407712i	$0.0129815\pi$
$937$	41.2232	+	29.9504i	1.34670	+	0.978438i	0.347536	+	0.937667i	$0.387019\pi$
$938$		0			0
$939$	8.51279	+	26.1997i	0.277804	+	0.854994i
$940$		0			0
$941$	23.3431	+	16.9598i	0.760964	+	0.552872i	0.899206	−	0.437526i	$-0.144145\pi$
$941$	23.3431	+	16.9598i	0.760964	+	0.552872i	−0.138242	+	0.990398i	$0.544145\pi$
$942$		0			0
$943$	−0.323318	−	3.20049i	−0.0105287	−	0.104222i
$944$		0			0
$945$	3.24290	+	2.35611i	0.105492	+	0.0766442i
$946$		0			0
$947$	−4.45864	−	13.7223i	−0.144886	−	0.445915i	0.852110	−	0.523363i	$-0.175323\pi$
$947$	−4.45864	−	13.7223i	−0.144886	−	0.445915i	−0.996996	+	0.0774482i	$0.975323\pi$
$948$		0			0
$949$	0.692697	+	0.503274i	0.0224859	+	0.0163370i
$950$		0			0
$951$	−12.8520	+	39.5544i	−0.416755	+	1.28264i
$952$		0			0
$953$	−13.8129	+	42.5117i	−0.447443	+	1.37709i	0.432338	+	0.901711i	$0.357689\pi$
$953$	−13.8129	+	42.5117i	−0.447443	+	1.37709i	−0.879782	+	0.475378i	$0.842311\pi$
$954$		0			0
$955$	−2.35158	−	7.23743i	−0.0760955	−	0.234198i
$956$		0			0
$957$	−22.5579			−0.729192
$958$		0			0
$959$	0.516065	−	0.374943i	0.0166646	−	0.0121075i
$960$		0			0
$961$	−49.7400	−	36.1382i	−1.60452	−	1.16575i
$962$		0			0
$963$	−4.05351	+	2.94505i	−0.130622	+	0.0949028i
$964$		0			0
$965$	7.22740	−	5.25102i	0.232658	−	0.169036i
$966$		0			0
$967$	−0.659955	+	2.03113i	−0.0212227	+	0.0653168i	−0.961107	−	0.276176i	$-0.910933\pi$
$967$	−0.659955	+	2.03113i	−0.0212227	+	0.0653168i	0.939884	+	0.341493i	$0.110933\pi$
$968$		0			0
$969$	6.19995	+	19.0815i	0.199171	+	0.612985i
$970$		0			0
$971$	−42.1793	−	30.6451i	−1.35360	−	0.983447i	−0.998823	−	0.0484958i	$-0.984557\pi$
$971$	−42.1793	−	30.6451i	−1.35360	−	0.983447i	−0.354776	−	0.934951i	$-0.615443\pi$
$972$		0			0
$973$	−0.545626	+	1.67927i	−0.0174920	+	0.0538348i
$974$		0			0
$975$	1.35820			0.0434971
$976$		0			0
$977$	−23.0909	+	16.7766i	−0.738745	+	0.536729i	−0.892318	−	0.451408i	$-0.850922\pi$
$977$	−23.0909	+	16.7766i	−0.738745	+	0.536729i	0.153573	+	0.988137i	$0.450922\pi$
$978$		0			0
$979$	−2.58958	−	7.96990i	−0.0827632	−	0.254719i
$980$		0			0
$981$	6.38381			0.203819
$982$		0			0
$983$	−55.9425			−1.78429			−0.892144	−	0.451751i	$-0.850799\pi$
$983$	−55.9425			−1.78429			−0.892144	+	0.451751i	$0.850799\pi$
$984$		0			0
$985$	−13.7567			−0.438324
$986$		0			0
$987$	8.52623			0.271393
$988$		0			0
$989$	−0.0528354	−	0.162611i	−0.00168007	−	0.00517072i
$990$		0			0
$991$	15.6321	−	11.3574i	0.496569	−	0.360779i	−0.311136	−	0.950365i	$-0.600709\pi$
$991$	15.6321	−	11.3574i	0.496569	−	0.360779i	0.807705	+	0.589587i	$0.200709\pi$
$992$		0			0
$993$	−37.7793			−1.19889
$994$		0			0
$995$	7.43976	−	22.8972i	0.235856	−	0.725891i
$996$		0			0
$997$	34.8449	+	25.3163i	1.10355	+	0.801776i	0.981636	−	0.190764i	$-0.0610966\pi$
$997$	34.8449	+	25.3163i	1.10355	+	0.801776i	0.121915	+	0.992541i	$0.461097\pi$
$998$		0			0
$999$	−1.19891	−	3.68988i	−0.0379320	−	0.116743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.u.a.461.5	yes	24
41.37	even	5	inner	820.2.u.a.201.5	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.u.a.201.5	✓	24	41.37	even	5	inner
820.2.u.a.461.5	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.u (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+2.53712 q^{3} +(0.309017 + 0.951057i) q^{5} +(2.92498 - 2.12513i) q^{7} +3.43699 q^{9} +(0.677943 - 2.08649i) q^{11} +(-0.433091 - 0.314659i) q^{13} +(0.784014 + 2.41295i) q^{15} +(0.573486 - 1.76501i) q^{17} +(-3.44732 + 2.50462i) q^{19} +(7.42104 - 5.39170i) q^{21} +(-0.406431 - 0.295290i) q^{23} +(-0.809017 + 0.587785i) q^{25} +1.10869 q^{27} +(-1.25236 - 3.85436i) q^{29} +(-2.97174 + 9.14608i) q^{31} +(1.72002 - 5.29369i) q^{33} +(2.92498 + 2.12513i) q^{35} +(-1.08138 - 3.32814i) q^{37} +(-1.09880 - 0.798328i) q^{39} +(4.26527 + 4.77572i) q^{41} +(0.275341 + 0.200047i) q^{43} +(1.06209 + 3.26877i) q^{45} +(0.751982 + 0.546347i) q^{47} +(1.87626 - 5.77452i) q^{49} +(1.45500 - 4.47804i) q^{51} +(2.97238 + 9.14804i) q^{53} +2.19387 q^{55} +(-8.74627 + 6.35454i) q^{57} +(8.01859 + 5.82585i) q^{59} +(-3.28790 + 2.38880i) q^{61} +(10.0531 - 7.30403i) q^{63} +(0.165426 - 0.509129i) q^{65} +(-4.46312 - 13.7361i) q^{67} +(-1.03117 - 0.749186i) q^{69} +(-3.10998 + 9.57152i) q^{71} -1.59943 q^{73} +(-2.05257 + 1.49128i) q^{75} +(-2.45109 - 7.54368i) q^{77} -14.3814 q^{79} -7.49808 q^{81} +7.14716 q^{83} +1.85584 q^{85} +(-3.17738 - 9.77897i) q^{87} +(3.09025 - 2.24520i) q^{89} -1.93547 q^{91} +(-7.53967 + 23.2047i) q^{93} +(-3.44732 - 2.50462i) q^{95} +(-2.83266 - 8.71803i) q^{97} +(2.33008 - 7.17125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{3} - 6 q^{5} + 5 q^{7} + 18 q^{9} - 7 q^{11} - 5 q^{13} + 2 q^{15} + 3 q^{17} - q^{19} + 2 q^{21} + 20 q^{23} - 6 q^{25} + 20 q^{27} - 15 q^{29} - q^{31} - 6 q^{33} + 5 q^{35} + q^{37} + 28 q^{41}+ \cdots + 34 q^{99}+O(q^{100}) \) 24 * q + 2 * q^3 - 6 * q^5 + 5 * q^7 + 18 * q^9 - 7 * q^11 - 5 * q^13 + 2 * q^15 + 3 * q^17 - q^19 + 2 * q^21 + 20 * q^23 - 6 * q^25 + 20 * q^27 - 15 * q^29 - q^31 - 6 * q^33 + 5 * q^35 + q^37 + 28 * q^41 - 4 * q^43 + 3 * q^45 + 3 * q^47 + 3 * q^49 + 37 * q^51 + 29 * q^53 - 12 * q^55 + 17 * q^57 - 4 * q^59 - 14 * q^61 - 10 * q^63 + 5 * q^65 - 14 * q^67 - 26 * q^69 + q^71 - 84 * q^73 - 3 * q^75 + 24 * q^77 + 18 * q^79 - 40 * q^81 - 6 * q^83 - 12 * q^85 + 39 * q^87 + 12 * q^89 - 2 * q^91 - 58 * q^93 - q^95 - 20 * q^97 + 34 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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