LMFDB - Embedded newform 867.2.i.h.131.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(65,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 9])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("867.65"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.i (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,8,-16,0,8,16,0,-8,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{16})$
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			131.4
Character	$\chi$	$=$	867.131
Dual form			867.2.i.h.503.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.34436 - 0.556851i) q^{2} +(0.961322 - 1.44078i) q^{3} +(0.0830021 - 0.0830021i) q^{4} +(-0.595296 + 2.99276i) q^{5} +(0.490059 - 2.47224i) q^{6} +(2.11533 - 0.420765i) q^{7} +(-1.04834 + 2.53091i) q^{8} +(-1.15172 - 2.77012i) q^{9} +(0.866229 + 4.35483i) q^{10} +(1.37013 + 0.915491i) q^{11} +(-0.0397964 - 0.199380i) q^{12} +(3.12551 + 3.12551i) q^{13} +(2.60946 - 1.74358i) q^{14} +(3.73965 + 3.73470i) q^{15} +4.22099i q^{16} +(-3.09087 - 3.08269i) q^{18} +(-0.330416 - 0.797694i) q^{19} +(0.198994 + 0.297816i) q^{20} +(1.42728 - 3.45222i) q^{21} +(2.35174 + 0.467790i) q^{22} +(-0.425893 + 0.637394i) q^{23} +(2.63871 + 3.94345i) q^{24} +(-3.98282 - 1.64974i) q^{25} +(5.94226 + 2.46136i) q^{26} +(-5.09831 - 1.00359i) q^{27} +(0.140652 - 0.210501i) q^{28} +(7.83789 + 1.55905i) q^{29} +(7.10709 + 2.93834i) q^{30} +(-1.60475 - 2.40167i) q^{31} +(0.253786 + 0.612694i) q^{32} +(2.63616 - 1.09398i) q^{33} +6.58114i q^{35} +(-0.325520 - 0.134330i) q^{36} +(1.98027 - 1.32318i) q^{37} +(-0.888394 - 0.888394i) q^{38} +(7.50782 - 1.49857i) q^{39} +(-6.95033 - 4.64406i) q^{40} +(-0.600791 - 3.02038i) q^{41} +(-0.00359897 - 5.43581i) q^{42} +(4.38037 - 10.5751i) q^{43} +(0.189711 - 0.0377359i) q^{44} +(8.97590 - 1.79778i) q^{45} +(-0.217619 + 1.09405i) q^{46} +(-2.21238 + 2.21238i) q^{47} +(6.08153 + 4.05773i) q^{48} +(-2.16958 + 0.898671i) q^{49} -6.27299 q^{50} +0.518848 q^{52} +(-5.88369 + 2.43710i) q^{53} +(-7.41281 + 1.48981i) q^{54} +(-3.55548 + 3.55548i) q^{55} +(-1.15266 + 5.79482i) q^{56} +(-1.46694 - 0.290783i) q^{57} +(11.4051 - 2.26861i) q^{58} +(2.33146 - 5.62864i) q^{59} +(0.620386 - 0.000410749i) q^{60} +(1.14061 + 5.73423i) q^{61} +(-3.49473 - 2.33510i) q^{62} +(-3.60183 - 5.37510i) q^{63} +(-5.28702 - 5.28702i) q^{64} +(-11.2145 + 7.49329i) q^{65} +(2.93476 - 2.93865i) q^{66} +7.19481i q^{67} +(0.508927 + 1.22636i) q^{69} +(3.66472 + 8.84742i) q^{70} +(-1.20808 - 1.80802i) q^{71} +(8.21831 - 0.0108825i) q^{72} +(-12.3377 - 2.45412i) q^{73} +(1.92538 - 2.88154i) q^{74} +(-6.20569 + 4.15245i) q^{75} +(-0.0936354 - 0.0387851i) q^{76} +(3.28348 + 1.36006i) q^{77} +(9.25872 - 6.19535i) q^{78} +(3.31013 - 4.95397i) q^{79} +(-12.6324 - 2.51274i) q^{80} +(-6.34708 + 6.38079i) q^{81} +(-2.48958 - 3.72592i) q^{82} +(-4.96993 - 11.9985i) q^{83} +(-0.168074 - 0.405009i) q^{84} -16.6560i q^{86} +(9.78099 - 9.79395i) q^{87} +(-3.75339 + 2.50793i) q^{88} +(3.42023 + 3.42023i) q^{89} +(11.0657 - 7.41510i) q^{90} +(7.92660 + 5.29638i) q^{91} +(0.0175550 + 0.0882551i) q^{92} +(-5.00297 + 0.00331239i) q^{93} +(-1.74226 + 4.20619i) q^{94} +(2.58400 - 0.513989i) q^{95} +(1.12673 + 0.223345i) q^{96} +(0.692072 - 3.47928i) q^{97} +(-2.41627 + 2.41627i) q^{98} +(0.958012 - 4.84981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{3} - 16 q^{4} + 8 q^{6} + 16 q^{7} - 8 q^{9} + 16 q^{10} - 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} + 16 q^{22} - 16 q^{24} + 16 q^{25} + 8 q^{27} - 32 q^{28} - 8 q^{30}+ \cdots + 64 q^{99}+O(q^{100}) $ 32 * q + 8 * q^3 - 16 * q^4 + 8 * q^6 + 16 * q^7 - 8 * q^9 + 16 * q^10 - 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 + 16 * q^22 - 16 * q^24 + 16 * q^25 + 8 * q^27 - 32 * q^28 - 8 * q^30 - 16 * q^31 + 8 * q^36 - 16 * q^37 + 24 * q^39 - 16 * q^40 - 56 * q^42 + 16 * q^43 + 40 * q^45 + 32 * q^46 + 64 * q^48 - 48 * q^49 - 96 * q^52 + 24 * q^54 - 48 * q^55 - 8 * q^57 + 48 * q^58 + 32 * q^60 + 32 * q^61 - 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 - 48 * q^73 - 88 * q^75 + 48 * q^76 - 96 * q^78 - 16 * q^79 + 48 * q^81 - 112 * q^82 - 56 * q^87 - 16 * q^88 + 88 * q^90 - 16 * q^91 - 72 * q^93 - 48 * q^94 + 112 * q^96 + 16 * q^97 + 64 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$-1$	$e\left(\frac{13}{16}\right)$

Coefficient data

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

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

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

$2$	1.34436	−	0.556851i	0.950605	−	0.393753i	0.147147	−	0.989115i	$-0.452991\pi$
$2$	1.34436	−	0.556851i	0.950605	−	0.393753i	0.803458	+	0.595361i	$0.202991\pi$
$3$	0.961322	−	1.44078i	0.555020	−	0.831837i
$3$	0.961322	−	1.44078i	0.555020	−	0.831837i
$4$	0.0830021	−	0.0830021i	0.0415010	−	0.0415010i
$5$	−0.595296	+	2.99276i	−0.266225	+	1.33840i	0.583902	+	0.811824i	$0.301525\pi$
$5$	−0.595296	+	2.99276i	−0.266225	+	1.33840i	−0.850127	+	0.526578i	$0.823475\pi$
$6$	0.490059	−	2.47224i	0.200066	−	1.00929i
$7$	2.11533	−	0.420765i	0.799519	−	0.159034i	0.221610	−	0.975135i	$-0.428869\pi$
$7$	2.11533	−	0.420765i	0.799519	−	0.159034i	0.577909	+	0.816101i	$0.303869\pi$
$8$	−1.04834	+	2.53091i	−0.370644	+	0.894813i
$9$	−1.15172	−	2.77012i	−0.383906	−	0.923372i
$10$	0.866229	+	4.35483i	0.273926	+	1.37712i
$11$	1.37013	+	0.915491i	0.413110	+	0.276031i	0.744709	−	0.667389i	$-0.232588\pi$
$11$	1.37013	+	0.915491i	0.413110	+	0.276031i	−0.331599	+	0.943420i	$0.607588\pi$
$12$	−0.0397964	−	0.199380i	−0.0114882	−	0.0575560i
$13$	3.12551	+	3.12551i	0.866861	+	0.866861i	0.992124	−	0.125262i	$-0.0399772\pi$
$13$	3.12551	+	3.12551i	0.866861	+	0.866861i	−0.125262	+	0.992124i	$0.539977\pi$
$14$	2.60946	−	1.74358i	0.697407	−	0.465992i
$15$	3.73965	+	3.73470i	0.965572	+	0.964295i
$16$			4.22099i			1.05525i
$17$		0			0
$17$		0			0
$18$	−3.09087	−	3.08269i	−0.728524	−	0.726597i
$19$	−0.330416	−	0.797694i	−0.0758025	−	0.183004i	0.881436	−	0.472304i	$-0.156577\pi$
$19$	−0.330416	−	0.797694i	−0.0758025	−	0.183004i	−0.957238	+	0.289300i	$0.906577\pi$
$20$	0.198994	+	0.297816i	0.0444964	+	0.0665936i
$21$	1.42728	−	3.45222i	0.311458	−	0.753337i
$22$	2.35174	+	0.467790i	0.501392	+	0.0997331i
$23$	−0.425893	+	0.637394i	−0.0888049	+	0.132906i	−0.873212	−	0.487340i	$-0.837967\pi$
$23$	−0.425893	+	0.637394i	−0.0888049	+	0.132906i	0.784407	+	0.620246i	$0.212967\pi$
$24$	2.63871	+	3.94345i	0.538624	+	0.804954i
$25$	−3.98282	−	1.64974i	−0.796563	−	0.329947i
$26$	5.94226	+	2.46136i	1.16537	+	0.482713i
$27$	−5.09831	−	1.00359i	−0.981171	−	0.193142i
$28$	0.140652	−	0.210501i	0.0265808	−	0.0397810i
$29$	7.83789	+	1.55905i	1.45546	+	0.289509i	0.858521	−	0.512778i	$-0.171384\pi$
$29$	7.83789	+	1.55905i	1.45546	+	0.289509i	0.596938	+	0.802287i	$0.296384\pi$
$30$	7.10709	+	2.93834i	1.29757	+	0.536466i
$31$	−1.60475	−	2.40167i	−0.288221	−	0.431353i	0.658900	−	0.752231i	$-0.271022\pi$
$31$	−1.60475	−	2.40167i	−0.288221	−	0.431353i	−0.947121	+	0.320878i	$0.896022\pi$
$32$	0.253786	+	0.612694i	0.0448635	+	0.108310i
$33$	2.63616	−	1.09398i	0.458897	−	0.190437i
$34$		0			0
$35$			6.58114i			1.11242i
$36$	−0.325520	−	0.134330i	−0.0542534	−	0.0223884i
$37$	1.98027	−	1.32318i	0.325555	−	0.217529i	−0.382042	−	0.924145i	$-0.624779\pi$
$37$	1.98027	−	1.32318i	0.325555	−	0.217529i	0.707597	+	0.706616i	$0.249779\pi$
$38$	−0.888394	−	0.888394i	−0.144117	−	0.144117i
$39$	7.50782	−	1.49857i	1.20221	−	0.239963i
$40$	−6.95033	−	4.64406i	−1.09894	−	0.734291i
$41$	−0.600791	−	3.02038i	−0.0938278	−	0.471704i	−0.998919	−	0.0464865i	$-0.985198\pi$
$41$	−0.600791	−	3.02038i	−0.0938278	−	0.471704i	0.905091	−	0.425218i	$-0.139802\pi$
$42$	−0.00359897	−	5.43581i	−0.000555333	−	0.838764i
$43$	4.38037	−	10.5751i	0.668000	−	1.61269i	−0.116952	−	0.993138i	$-0.537312\pi$
$43$	4.38037	−	10.5751i	0.668000	−	1.61269i	0.784952	−	0.619557i	$-0.212688\pi$
$44$	0.189711	−	0.0377359i	0.0286000	−	0.00568890i
$45$	8.97590	−	1.79778i	1.33805	−	0.267997i
$46$	−0.217619	+	1.09405i	−0.0320862	+	0.161308i
$47$	−2.21238	+	2.21238i	−0.322708	+	0.322708i	−0.849805	−	0.527097i	$-0.823281\pi$
$47$	−2.21238	+	2.21238i	−0.322708	+	0.322708i	0.527097	+	0.849805i	$0.323281\pi$
$48$	6.08153	+	4.05773i	0.877793	+	0.585683i
$49$	−2.16958	+	0.898671i	−0.309940	+	0.128382i
$50$	−6.27299			−0.887135
$51$		0			0
$52$	0.518848			0.0719513
$53$	−5.88369	+	2.43710i	−0.808187	+	0.334762i	−0.748230	−	0.663439i	$-0.769096\pi$
$53$	−5.88369	+	2.43710i	−0.808187	+	0.334762i	−0.0599567	+	0.998201i	$0.519096\pi$
$54$	−7.41281	+	1.48981i	−1.00876	+	0.202738i
$55$	−3.55548	+	3.55548i	−0.479420	+	0.479420i
$56$	−1.15266	+	5.79482i	−0.154031	+	0.774365i
$57$	−1.46694	−	0.290783i	−0.194301	−	0.0385152i
$58$	11.4051	−	2.26861i	1.49756	−	0.297884i
$59$	2.33146	−	5.62864i	0.303530	−	0.732786i	−0.696356	−	0.717696i	$-0.745197\pi$
$59$	2.33146	−	5.62864i	0.303530	−	0.732786i	0.999886	−	0.0150898i	$-0.00480343\pi$
$60$	0.620386		0.000410749i	0.0800915		5.30274e-5i
$61$	1.14061	+	5.73423i	0.146040	+	0.734193i	0.982514	+	0.186187i	$0.0596130\pi$
$61$	1.14061	+	5.73423i	0.146040	+	0.734193i	−0.836474	+	0.548006i	$0.815387\pi$
$62$	−3.49473	−	2.33510i	−0.443831	−	0.296558i
$63$	−3.60183	−	5.37510i	−0.453788	−	0.677199i
$64$	−5.28702	−	5.28702i	−0.660877	−	0.660877i
$65$	−11.2145	+	7.49329i	−1.39099	+	0.929429i
$66$	2.93476	−	2.93865i	0.361244	−	0.361723i
$67$			7.19481i			0.878985i	0.898246	+	0.439493i	$0.144842\pi$
$67$			7.19481i			0.878985i	−0.898246	+	0.439493i	$0.855158\pi$
$68$		0			0
$69$	0.508927	+	1.22636i	0.0612676	+	0.147637i
$70$	3.66472	+	8.84742i	0.438018	+	1.05747i
$71$	−1.20808	−	1.80802i	−0.143373	−	0.214573i	0.752832	−	0.658212i	$-0.228687\pi$
$71$	−1.20808	−	1.80802i	−0.143373	−	0.214573i	−0.896205	+	0.443639i	$0.853687\pi$
$72$	8.21831	−	0.0108825i	0.968537	−	0.00128251i
$73$	−12.3377	−	2.45412i	−1.44402	−	0.287233i	−0.589969	−	0.807426i	$-0.700860\pi$
$73$	−12.3377	−	2.45412i	−1.44402	−	0.287233i	−0.854049	+	0.520193i	$0.825860\pi$
$74$	1.92538	−	2.88154i	0.223821	−	0.334972i
$75$	−6.20569	+	4.15245i	−0.716571	+	0.479484i
$76$	−0.0936354	−	0.0387851i	−0.0107407	−	0.00444895i
$77$	3.28348	+	1.36006i	0.374187	+	0.154994i
$78$	9.25872	−	6.19535i	1.04834	−	0.701485i
$79$	3.31013	−	4.95397i	0.372419	−	0.557365i	−0.597166	−	0.802117i	$-0.703707\pi$
$79$	3.31013	−	4.95397i	0.372419	−	0.557365i	0.969586	+	0.244753i	$0.0787068\pi$
$80$	−12.6324	−	2.51274i	−1.41234	−	0.280933i
$81$	−6.34708	+	6.38079i	−0.705232	+	0.708977i
$82$	−2.48958	−	3.72592i	−0.274928	−	0.411459i
$83$	−4.96993	−	11.9985i	−0.545521	−	1.31700i	−0.920779	−	0.390084i	$-0.872446\pi$
$83$	−4.96993	−	11.9985i	−0.545521	−	1.31700i	0.375258	−	0.926920i	$-0.377554\pi$
$84$	−0.168074	−	0.405009i	−0.0183384	−	0.0441901i
$85$		0			0
$86$		−	16.6560i		−	1.79606i
$87$	9.78099	−	9.79395i	1.04863	−	1.05002i
$88$	−3.75339	+	2.50793i	−0.400112	+	0.267347i
$89$	3.42023	+	3.42023i	0.362544	+	0.362544i	0.864749	−	0.502205i	$-0.167478\pi$
$89$	3.42023	+	3.42023i	0.362544	+	0.362544i	−0.502205	+	0.864749i	$0.667478\pi$
$90$	11.0657	−	7.41510i	1.16643	−	0.781620i
$91$	7.92660	+	5.29638i	0.830933	+	0.555212i
$92$	0.0175550	+	0.0882551i	0.00183024	+	0.00920123i
$93$	−5.00297	+	0.00331239i	−0.518783	+	0.000343479i
$94$	−1.74226	+	4.20619i	−0.179701	+	0.433836i
$95$	2.58400	−	0.513989i	0.265113	−	0.0527342i
$96$	1.12673	+	0.223345i	0.114996	+	0.0227951i
$97$	0.692072	−	3.47928i	0.0702692	−	0.353267i	−0.929614	−	0.368534i	$-0.879860\pi$
$97$	0.692072	−	3.47928i	0.0702692	−	0.353267i	0.999883	+	0.0152668i	$0.00485977\pi$
$98$	−2.41627	+	2.41627i	−0.244080	+	0.244080i
$99$	0.958012	−	4.84981i	0.0962839	−	0.487424i
$100$	−0.467514	+	0.193650i	−0.0467514	+	0.0193650i
$101$	−3.73948			−0.372092			−0.186046	−	0.982541i	$-0.559567\pi$
$101$	−3.73948			−0.372092			−0.186046	+	0.982541i	$0.559567\pi$
$102$		0			0
$103$	9.33404			0.919710			0.459855	−	0.887994i	$-0.347901\pi$
$103$	9.33404			0.919710			0.459855	+	0.887994i	$0.347901\pi$
$104$	−11.1870	+	4.63380i	−1.09698	+	0.454382i
$105$	9.48201	+	6.32660i	0.925350	+	0.617413i
$106$	−6.55268	+	6.55268i	−0.636453	+	0.636453i
$107$	0.368714	−	1.85365i	0.0356449	−	0.179199i	−0.958862	−	0.283874i	$-0.908380\pi$
$107$	0.368714	−	1.85365i	0.0356449	−	0.179199i	0.994506	+	0.104675i	$0.0333802\pi$
$108$	−0.506471	+	0.339870i	−0.0487352	+	0.0327040i
$109$	−4.12226	+	0.819969i	−0.394841	+	0.0785388i	−0.388518	−	0.921441i	$-0.627013\pi$
$109$	−4.12226	+	0.819969i	−0.394841	+	0.0785388i	−0.00632347	+	0.999980i	$0.502013\pi$
$110$	−2.79996	+	6.75970i	−0.266966	+	0.644513i
$111$	−0.00273120	−	4.12515i	−0.000259234	−	0.391542i
$112$	1.77604	+	8.92878i	0.167820	+	0.843690i
$113$	−13.7072	−	9.15888i	−1.28947	−	0.861595i	−0.293917	−	0.955831i	$-0.594959\pi$
$113$	−13.7072	−	9.15888i	−1.28947	−	0.861595i	−0.995550	+	0.0942363i	$0.969959\pi$
$114$	−2.13402	+	0.425951i	−0.199869	+	0.0398940i
$115$	−1.65403	−	1.65403i	−0.154239	−	0.154239i
$116$	0.779965	−	0.521156i	0.0724180	−	0.0483881i
$117$	5.05832	−	12.2577i	0.467642	−	1.13323i
$118$		−	8.86518i		−	0.816106i
$119$		0			0
$120$	−13.3726	+	5.54949i	−1.22075	+	0.506597i
$121$	−3.17039	−	7.65399i	−0.288217	−	0.695817i
$122$	4.72650	+	7.07371i	0.427917	+	0.640424i
$123$	−4.92927	−	2.03795i	−0.444457	−	0.183756i
$124$	−0.332541	−	0.0661465i	−0.0298630	−	0.00594013i
$125$	−1.16808	+	1.74816i	−0.104477	+	0.156360i
$126$	−7.83529	−	5.22038i	−0.698023	−	0.465068i
$127$	11.3753	+	4.71179i	1.00939	+	0.418104i	0.825233	−	0.564792i	$-0.191044\pi$
$127$	11.3753	+	4.71179i	1.00939	+	0.418104i	0.184159	+	0.982896i	$0.441044\pi$
$128$	−11.2771	−	4.67113i	−0.996766	−	0.412874i
$129$	−11.0256	−	16.4773i	−0.970746	−	1.45074i
$130$	−10.9037	+	16.3185i	−0.956315	+	1.43123i
$131$	3.45873	+	0.687984i	0.302191	+	0.0601094i	0.343857	−	0.939022i	$-0.388267\pi$
$131$	3.45873	+	0.687984i	0.302191	+	0.0601094i	−0.0416661	+	0.999132i	$0.513267\pi$
$132$	0.128004	−	0.309609i	0.0111413	−	0.0269480i
$133$	−1.03458	−	1.54836i	−0.0897094	−	0.134260i
$134$	4.00644	+	9.67240i	0.346103	+	0.835568i
$135$	6.03852	−	14.6606i	0.519713	−	1.26178i
$136$		0			0
$137$			14.6484i			1.25150i	0.780025	+	0.625748i	$0.215206\pi$
$137$			14.6484i			1.25150i	−0.780025	+	0.625748i	$0.784794\pi$
$138$	1.36708	+	1.36527i	0.116374	+	0.116220i
$139$	4.19445	−	2.80264i	0.355768	−	0.237717i	−0.364823	−	0.931077i	$-0.618870\pi$
$139$	4.19445	−	2.80264i	0.355768	−	0.237717i	0.720591	+	0.693360i	$0.243870\pi$
$140$	0.546249	+	0.546249i	0.0461664	+	0.0461664i
$141$	1.06075	+	5.31437i	0.0893314	+	0.447550i
$142$	−2.63090	−	1.75791i	−0.220780	−	0.147520i
$143$	1.42098	+	7.14374i	0.118828	+	0.597389i
$144$	11.6926	−	4.86139i	0.974385	−	0.405116i
$145$	−9.33173	+	22.5288i	−0.774958	+	1.87091i
$146$	−17.9529	+	3.57105i	−1.48579	+	0.295542i
$147$	−0.790878	+	3.98981i	−0.0652305	+	0.329074i
$148$	0.0545404	−	0.274193i	0.00448319	−	0.0225385i
$149$	4.44785	−	4.44785i	0.364382	−	0.364382i	−0.501041	−	0.865423i	$-0.667050\pi$
$149$	4.44785	−	4.44785i	0.364382	−	0.364382i	0.865423	+	0.501041i	$0.167050\pi$
$150$	−6.03037	+	9.03803i	−0.492377	+	0.737952i
$151$	−14.0551	+	5.82179i	−1.14378	+	0.473771i	−0.872445	−	0.488713i	$-0.837467\pi$
$151$	−14.0551	+	5.82179i	−1.14378	+	0.473771i	−0.271339	+	0.962484i	$0.587467\pi$
$152$	2.36528			0.191850
$153$		0			0
$154$	5.17153			0.416734
$155$	8.14291	−	3.37291i	0.654055	−	0.270918i
$156$	0.498780	−	0.747548i	0.0399344	−	0.0598518i
$157$	1.74527	−	1.74527i	0.139287	−	0.139287i	−0.634025	−	0.773312i	$-0.718598\pi$
$157$	1.74527	−	1.74527i	0.139287	−	0.139287i	0.773312	+	0.634025i	$0.218598\pi$
$158$	1.69138	−	8.50316i	0.134559	−	0.676475i
$159$	−2.14478	+	10.8200i	−0.170092	+	0.858080i
$160$	−1.98472	+	0.394786i	−0.156906	+	0.0312105i
$161$	−0.632711	+	1.52750i	−0.0498646	+	0.120384i
$162$	−4.97960	+	12.1125i	−0.391235	+	0.951644i
$163$	0.216722	+	1.08953i	0.0169749	+	0.0853388i	0.988344	−	0.152236i	$-0.0486474\pi$
$163$	0.216722	+	1.08953i	0.0169749	+	0.0853388i	−0.971369	+	0.237575i	$0.923647\pi$
$164$	−0.300565	−	0.200831i	−0.0234702	−	0.0156823i
$165$	1.70472	+	8.54063i	0.132712	+	0.664887i
$166$	−13.3627	−	13.3627i	−1.03715	−	1.03715i
$167$	16.5131	−	11.0337i	1.27782	−	0.853815i	0.283373	−	0.959010i	$-0.408547\pi$
$167$	16.5131	−	11.0337i	1.27782	−	0.853815i	0.994452	+	0.105195i	$0.0335466\pi$
$168$	7.24100	+	7.23142i	0.558655	+	0.557916i
$169$			6.53766i			0.502897i
$170$		0			0
$171$	−1.82916	+	1.83401i	−0.139879	+	0.140250i
$172$	−0.514179	−	1.24134i	−0.0392058	−	0.0946511i
$173$	−6.46476	−	9.67520i	−0.491507	−	0.735591i	0.499946	−	0.866056i	$-0.333353\pi$
$173$	−6.46476	−	9.67520i	−0.491507	−	0.735591i	−0.991453	+	0.130465i	$0.958353\pi$
$174$	7.69538	−	18.6131i	0.583385	−	1.41106i
$175$	−9.11912	−	1.81391i	−0.689341	−	0.137118i
$176$	−3.86428	+	5.78330i	−0.291281	+	0.435933i
$177$	−5.86837	−	8.77006i	−0.441094	−	0.659198i
$178$	6.50257	+	2.69345i	0.487389	+	0.201883i
$179$	−0.782216	−	0.324004i	−0.0584656	−	0.0242172i	0.353259	−	0.935526i	$-0.385073\pi$
$179$	−0.782216	−	0.324004i	−0.0584656	−	0.0242172i	−0.411725	+	0.911308i	$0.635073\pi$
$180$	0.595799	−	0.894237i	0.0444082	−	0.0666525i
$181$	0.796600	−	1.19220i	0.0592108	−	0.0886152i	−0.800683	−	0.599088i	$-0.795530\pi$
$181$	0.796600	−	1.19220i	0.0592108	−	0.0886152i	0.859894	+	0.510473i	$0.170530\pi$
$182$	13.6055	+	2.70630i	1.00851	+	0.200604i
$183$	9.35828	+	3.86907i	0.691784	+	0.286010i
$184$	−1.16671	−	1.74610i	−0.0860109	−	0.128724i
$185$	2.78110	+	6.71416i	0.204470	+	0.493635i
$186$	−6.72393	+	2.79036i	−0.493023	+	0.204599i
$187$		0			0
$188$			0.367264i			0.0267855i
$189$	−11.2069	+	0.0222598i	−0.815181	+	0.00161916i
$190$	3.18760	−	2.12989i	0.231253	−	0.154518i
$191$	0.509849	+	0.509849i	0.0368914	+	0.0368914i	0.725312	−	0.688420i	$-0.241696\pi$
$191$	0.509849	+	0.509849i	0.0368914	+	0.0368914i	−0.688420	+	0.725312i	$0.741696\pi$
$192$	−12.7000	+	2.53493i	−0.916542	+	0.182942i
$193$	9.66292	+	6.45656i	0.695552	+	0.464753i	0.852414	−	0.522867i	$-0.175138\pi$
$193$	9.66292	+	6.45656i	0.695552	+	0.464753i	−0.156862	+	0.987621i	$0.550138\pi$
$194$	−1.00705	−	5.06278i	−0.0723019	−	0.363486i
$195$	0.0154671	+	23.3612i	0.00110762	+	1.67293i
$196$	−0.105488	+	0.254671i	−0.00753488	+	0.0181908i
$197$	22.8170	−	4.53858i	1.62564	−	0.323360i	0.703643	−	0.710553i	$-0.251555\pi$
$197$	22.8170	−	4.53858i	1.62564	−	0.323360i	0.921999	+	0.387193i	$0.126555\pi$
$198$	−1.41271	−	7.05335i	−0.100397	−	0.501260i
$199$	−4.70456	+	23.6514i	−0.333497	+	1.67661i	0.342357	+	0.939570i	$0.388775\pi$
$199$	−4.70456	+	23.6514i	−0.333497	+	1.67661i	−0.675854	+	0.737035i	$0.736225\pi$
$200$	8.35068	−	8.35068i	0.590482	−	0.590482i
$201$	10.3662	+	6.91653i	0.731173	+	0.487854i
$202$	−5.02720	+	2.08233i	−0.353712	+	0.146512i
$203$	17.2357			1.20971
$204$		0			0
$205$	9.39691			0.656309
$206$	12.5483	−	5.19767i	0.874281	−	0.362139i
$207$	2.25617	+	0.445674i	0.156814	+	0.0309765i
$208$	−13.1927	+	13.1927i	−0.914753	+	0.914753i
$209$	0.277570	−	1.39544i	0.0191999	−	0.0965244i
$210$	16.2702	+	3.22515i	1.12275	+	0.222556i
$211$	−15.3100	+	3.04535i	−1.05398	+	0.209651i	−0.691528	−	0.722350i	$-0.743062\pi$
$211$	−15.3100	+	3.04535i	−1.05398	+	0.209651i	−0.362457	+	0.932000i	$0.618062\pi$
$212$	−0.286074	+	0.690643i	−0.0196476	+	0.0474336i
$213$	−3.76633	+	0.00249363i	−0.258065	+	0.000170861i
$214$	−0.536524	−	2.69729i	−0.0366760	−	0.184383i
$215$	29.0412	+	19.4047i	1.98059	+	1.32339i
$216$	7.88477	−	11.8513i	0.536490	−	0.806377i
$217$	−4.40510	−	4.40510i	−0.299038	−	0.299038i
$218$	−5.08520	+	3.39782i	−0.344413	+	0.230130i
$219$	−15.3964	+	15.4168i	−1.04039	+	1.04177i
$220$			0.590224i			0.0397929i
$221$		0			0
$222$	−2.30077	−	5.54415i	−0.154417	−	0.372099i
$223$	0.930718	+	2.24695i	0.0623255	+	0.150467i	0.951974	−	0.306179i	$-0.0990506\pi$
$223$	0.930718	+	2.24695i	0.0623255	+	0.150467i	−0.889648	+	0.456646i	$0.849051\pi$
$224$	0.794641	+	1.18926i	0.0530942	+	0.0794611i
$225$	0.0171254	+	12.9329i	0.00114169	+	0.862193i
$226$	−23.5276	−	4.67992i	−1.56503	−	0.311304i
$227$	0.780250	−	1.16773i	0.0517870	−	0.0775048i	−0.804673	−	0.593719i	$-0.797659\pi$
$227$	0.780250	−	1.16773i	0.0517870	−	0.0775048i	0.856460	+	0.516214i	$0.172659\pi$
$228$	−0.145895	+	0.0976235i	−0.00966211	+	0.00646527i
$229$	−10.0488	−	4.16234i	−0.664043	−	0.275055i	0.0250960	−	0.999685i	$-0.492011\pi$
$229$	−10.0488	−	4.16234i	−0.664043	−	0.275055i	−0.689139	+	0.724630i	$0.742011\pi$
$230$	−3.14466	−	1.30256i	−0.207353	−	0.0858884i
$231$	5.11604	−	3.42333i	0.336611	−	0.225239i
$232$	−12.1626	+	18.2026i	−0.798513	+	1.19506i
$233$	−14.0608	−	2.79686i	−0.921151	−	0.183228i	−0.288334	−	0.957530i	$-0.593101\pi$
$233$	−14.0608	−	2.79686i	−0.921151	−	0.183228i	−0.632817	+	0.774302i	$0.718101\pi$
$234$	−0.0255506	−	19.2955i	−0.00167030	−	1.26139i
$235$	−5.30409	−	7.93813i	−0.346000	−	0.517826i
$236$	−0.273673	−	0.660704i	−0.0178146	−	0.0430082i
$237$	−3.95549	−	9.53155i	−0.256937	−	0.619140i
$238$		0			0
$239$		−	23.7093i		−	1.53362i	−0.641872	−	0.766812i	$-0.721842\pi$
$239$		−	23.7093i		−	1.53362i	0.641872	−	0.766812i	$-0.278158\pi$
$240$	−15.7641	+	15.7850i	−1.01757	+	1.01892i
$241$	−2.34007	+	1.56359i	−0.150737	+	0.100719i	−0.628652	−	0.777687i	$-0.716393\pi$
$241$	−2.34007	+	1.56359i	−0.150737	+	0.100719i	0.477914	+	0.878406i	$0.341393\pi$
$242$	−8.52427	−	8.52427i	−0.547961	−	0.547961i
$243$	3.09175	+	15.2788i	0.198336	+	0.980134i
$244$	0.570626	+	0.381280i	0.0365306	+	0.0244090i
$245$	−1.39796	−	7.02801i	−0.0893123	−	0.449003i
$246$	−7.76154	+	0.00513881i	−0.494858	+	0.000327638i
$247$	1.46048	−	3.52592i	0.0929284	−	0.224349i
$248$	7.76073	−	1.54371i	0.492807	−	0.0980254i
$249$	−22.0649	−	4.37380i	−1.39831	−	0.277178i
$250$	−0.596858	+	3.00061i	−0.0377486	+	0.189775i
$251$	10.7058	−	10.7058i	0.675745	−	0.675745i	−0.283289	−	0.959034i	$-0.591426\pi$
$251$	10.7058	−	10.7058i	0.675745	−	0.675745i	0.959034	+	0.283289i	$0.0914257\pi$
$252$	−0.745104	−	0.147185i	−0.0469372	−	0.00927179i
$253$	−1.16706	+	0.483411i	−0.0733723	+	0.0303918i
$254$	17.9162			1.12416
$255$		0			0
$256$	−2.80767			−0.175479
$257$	18.3799	−	7.61319i	1.14650	−	0.474898i	0.273145	−	0.961973i	$-0.411936\pi$
$257$	18.3799	−	7.61319i	1.14650	−	0.474898i	0.873360	+	0.487075i	$0.161936\pi$
$258$	−23.9977	−	16.0118i	−1.49403	−	0.996850i
$259$	3.63218	−	3.63218i	0.225693	−	0.225693i
$260$	−0.308868	+	1.55279i	−0.0191552	+	0.0962997i
$261$	−4.70829	−	23.5074i	−0.291436	−	1.45507i
$262$	5.03288	−	1.00110i	0.310932	−	0.0618482i
$263$	−0.0501727	+	0.121128i	−0.00309378	+	0.00746905i	−0.925419	−	0.378946i	$-0.876287\pi$
$263$	−0.0501727	+	0.121128i	−0.00309378	+	0.00746905i	0.922325	+	0.386415i	$0.126287\pi$
$264$	0.00517669	+	7.81875i	0.000318603	+	0.481211i
$265$	−3.79112	−	19.0593i	−0.232887	−	1.17080i
$266$	−2.25305	−	1.50544i	−0.138143	−	0.0923045i
$267$	8.21576	−	1.63987i	0.502796	−	0.100358i
$268$	0.597184	+	0.597184i	0.0364788	+	0.0364788i
$269$	−4.94355	+	3.30317i	−0.301413	+	0.201398i	−0.697075	−	0.716999i	$-0.745515\pi$
$269$	−4.94355	+	3.30317i	−0.301413	+	0.201398i	0.395661	+	0.918396i	$0.370515\pi$
$270$	−0.0458262	−	23.0716i	−0.00278890	−	1.40409i
$271$		−	6.87483i		−	0.417616i	−0.977957	−	0.208808i	$-0.933042\pi$
$271$		−	6.87483i		−	0.417616i	0.977957	−	0.208808i	$-0.0669584\pi$
$272$		0			0
$273$	15.2510	−	6.32899i	0.923030	−	0.383048i
$274$	8.15697	+	19.6927i	0.492781	+	1.18968i
$275$	−3.94666	−	5.90659i	−0.237992	−	0.356181i
$276$	0.144033	+	0.0595485i	0.00866974	+	0.00358440i
$277$	8.13797	+	1.61874i	0.488963	+	0.0972608i	0.433414	−	0.901195i	$-0.357309\pi$
$277$	8.13797	+	1.61874i	0.488963	+	0.0972608i	0.0555495	+	0.998456i	$0.482309\pi$
$278$	4.07818	−	6.10344i	0.244593	−	0.366060i
$279$	−4.80469	+	7.21138i	−0.287649	+	0.431734i
$280$	−16.6563	−	6.89927i	−0.995404	−	0.412310i
$281$	−12.2411	−	5.07041i	−0.730240	−	0.302475i	−0.0135893	−	0.999908i	$-0.504326\pi$
$281$	−12.2411	−	5.07041i	−0.730240	−	0.302475i	−0.716651	+	0.697432i	$0.754326\pi$
$282$	4.38534	+	6.55373i	0.261143	+	0.390269i
$283$	7.79633	−	11.6680i	0.463444	−	0.693593i	−0.523972	−	0.851735i	$-0.675550\pi$
$283$	7.79633	−	11.6680i	0.463444	−	0.693593i	0.987416	+	0.158142i	$0.0505505\pi$
$284$	−0.250343	−	0.0497963i	−0.0148551	−	0.00295487i
$285$	1.74351	−	4.21709i	0.103276	−	0.249799i
$286$	5.88830	+	8.81247i	0.348183	+	0.521092i
$287$	−2.54174	−	6.13631i	−0.150034	−	0.362215i
$288$	1.40494	−	1.40867i	0.0827870	−	0.0830066i
$289$		0			0
$290$			35.4832i			2.08364i
$291$	−4.34759	−	4.34183i	−0.254860	−	0.254523i
$292$	−1.22775	+	0.820357i	−0.0718487	+	0.0480078i
$293$	−18.6721	−	18.6721i	−1.09083	−	1.09083i	−0.995440	−	0.0953949i	$-0.969589\pi$
$293$	−18.6721	−	18.6721i	−1.09083	−	1.09083i	−0.0953949	−	0.995440i	$-0.530411\pi$
$294$	1.15851	+	5.80414i	0.0675657	+	0.338504i
$295$	15.4572	+	10.3282i	0.899955	+	0.601331i
$296$	1.27285	+	6.39904i	0.0739827	+	0.371936i
$297$	−6.06657	−	6.04252i	−0.352018	−	0.350622i
$298$	3.50271	−	8.45629i	0.202907	−	0.489860i
$299$	−3.32332	+	0.661049i	−0.192193	+	0.0382295i
$300$	−0.170423	+	0.859747i	−0.00983935	+	0.0496375i
$301$	4.81627	−	24.2130i	0.277605	−	1.39561i
$302$	−15.6531	+	15.6531i	−0.900738	+	0.900738i
$303$	−3.59484	+	5.38778i	−0.206518	+	0.309520i
$304$	3.36705	−	1.39468i	0.193114	−	0.0799904i
$305$	−17.8402			−1.02152
$306$		0			0
$307$	−24.4315			−1.39438			−0.697189	−	0.716887i	$-0.745566\pi$
$307$	−24.4315			−1.39438			−0.697189	+	0.716887i	$0.745566\pi$
$308$	0.385424	−	0.159648i	0.0219616	−	0.00909677i
$309$	8.97302	−	13.4483i	0.510457	−	0.765049i
$310$	9.06879	−	9.06879i	0.515073	−	0.515073i
$311$	4.55265	−	22.8877i	0.258157	−	1.29784i	−0.606340	−	0.795206i	$-0.707363\pi$
$311$	4.55265	−	22.8877i	0.258157	−	1.29784i	0.864497	−	0.502638i	$-0.167637\pi$
$312$	−4.07799	+	20.5726i	−0.230871	+	1.16470i
$313$	−1.58360	+	0.314998i	−0.0895106	+	0.0178048i	−0.239642	−	0.970861i	$-0.577030\pi$
$313$	−1.58360	+	0.314998i	−0.0895106	+	0.0178048i	0.150132	+	0.988666i	$0.452030\pi$
$314$	1.37441	−	3.31812i	0.0775624	−	0.187252i
$315$	18.2305	−	7.57963i	1.02717	−	0.427064i
$316$	−0.136441	−	0.685937i	−0.00767543	−	0.0385870i
$317$	20.2754	+	13.5476i	1.13878	+	0.760908i	0.974251	−	0.225464i	$-0.0723900\pi$
$317$	20.2754	+	13.5476i	1.13878	+	0.760908i	0.164528	+	0.986372i	$0.447390\pi$
$318$	3.14176	+	15.7402i	0.176181	+	0.882669i
$319$	9.31162	+	9.31162i	0.521351	+	0.521351i
$320$	18.9701	−	12.6754i	1.06046	−	0.708577i
$321$	−2.31626	−	2.31319i	−0.129281	−	0.129110i
$322$			2.40583i			0.134072i
$323$		0			0
$324$	0.00279782	+	1.05644i	0.000155435	+	0.0586911i
$325$	−7.29207	−	17.6046i	−0.404491	−	0.976529i
$326$	0.898060	+	1.34404i	0.0497389	+	0.0744396i
$327$	−2.78143	+	6.72755i	−0.153813	+	0.372034i
$328$	8.27415	+	1.64583i	0.456863	+	0.0908758i
$329$	−3.74901	+	5.61080i	−0.206690	+	0.309333i
$330$	7.04761	+	10.5324i	0.387958	+	0.579789i
$331$	28.1459	+	11.6584i	1.54704	+	0.640804i	0.982777	−	0.184793i	$-0.0591614\pi$
$331$	28.1459	+	11.6584i	1.54704	+	0.640804i	0.564260	+	0.825597i	$0.309161\pi$
$332$	−1.40841	−	0.583384i	−0.0772967	−	0.0320173i
$333$	−5.94607	−	3.96166i	−0.325843	−	0.217098i
$334$	16.0554	−	24.0286i	0.878514	−	1.31479i
$335$	−21.5323	−	4.28304i	−1.17644	−	0.234008i
$336$	14.5718	+	6.02453i	0.794956	+	0.328665i
$337$	9.57025	+	14.3229i	0.521325	+	0.780218i	0.994935	−	0.100517i	$-0.0320496\pi$
$337$	9.57025	+	14.3229i	0.521325	+	0.780218i	−0.473611	+	0.880734i	$0.657050\pi$
$338$	3.64051	+	8.78896i	0.198018	+	0.478057i
$339$	−26.3730	+	10.9445i	−1.43239	+	0.594425i
$340$		0			0
$341$		−	4.75973i		−	0.257754i
$342$	−1.43777	+	3.48413i	−0.0777459	+	0.188400i
$343$	−16.7643	+	11.2015i	−0.905186	+	0.604826i
$344$	22.1727	+	22.1727i	1.19547	+	1.19547i
$345$	−3.97317	+	0.793047i	−0.213908	+	0.0426962i
$346$	−14.0786	−	9.40702i	−0.756870	−	0.505724i
$347$	−3.94759	−	19.8459i	−0.211918	−	1.06538i	−0.929476	−	0.368884i	$-0.879740\pi$
$347$	−3.94759	−	19.8459i	−0.211918	−	1.06538i	0.717558	−	0.696499i	$-0.245260\pi$
$348$	−0.00107573	−	1.62476i	−5.76652e−5	−	0.0870963i
$349$	−2.90948	+	7.02410i	−0.155741	+	0.375992i	−0.982421	−	0.186681i	$-0.940227\pi$
$349$	−2.90948	+	7.02410i	−0.155741	+	0.375992i	0.826680	+	0.562673i	$0.190227\pi$
$350$	−13.2694	+	2.63946i	−0.709281	+	0.141085i
$351$	−12.7981	−	19.0716i	−0.683112	−	1.01797i
$352$	−0.213196	+	1.07181i	−0.0113634	+	0.0571276i
$353$	−8.44344	+	8.44344i	−0.449399	+	0.449399i	−0.895155	−	0.445756i	$-0.852935\pi$
$353$	−8.44344	+	8.44344i	−0.449399	+	0.449399i	0.445756	+	0.895155i	$0.352935\pi$
$354$	−12.7728	−	8.52230i	−0.678867	−	0.452955i
$355$	6.13014	−	2.53919i	0.325354	−	0.134766i
$356$	0.567772			0.0300919
$357$		0			0
$358$	−1.23200			−0.0651133
$359$	−21.2469	+	8.80076i	−1.12137	+	0.464487i	−0.864839	−	0.502049i	$-0.832580\pi$
$359$	−21.2469	+	8.80076i	−1.12137	+	0.464487i	−0.256531	+	0.966536i	$0.582580\pi$
$360$	−4.85976	+	24.6019i	−0.256132	+	1.29663i
$361$	12.9079	−	12.9079i	0.679363	−	0.679363i
$362$	0.407040	−	2.04633i	0.0213935	−	0.107553i
$363$	−14.0755	−	2.79011i	−0.738773	−	0.146443i
$364$	1.09753	−	0.218313i	0.0575264	−	0.0114427i
$365$	14.6892	−	35.4628i	0.768866	−	1.85621i
$366$	14.7354	−	0.00975609i	0.770231	−	0.000509959i
$367$	3.20154	+	16.0952i	0.167119	+	0.840163i	0.969828	+	0.243792i	$0.0783914\pi$
$367$	3.20154	+	16.0952i	0.167119	+	0.840163i	−0.802709	+	0.596371i	$0.796609\pi$
$368$	−2.69043	−	1.79769i	−0.140249	−	0.0937111i
$369$	−7.67486	+	5.14289i	−0.399537	+	0.267728i
$370$	7.47758	+	7.47758i	0.388741	+	0.388741i
$371$	−11.4205	+	7.63093i	−0.592923	+	0.396178i
$372$	−0.414982	+	0.415531i	−0.0215158	+	0.0215443i
$373$			1.61824i			0.0837894i	0.999122	+	0.0418947i	$0.0133394\pi$
$373$			1.61824i			0.0837894i	−0.999122	+	0.0418947i	$0.986661\pi$
$374$		0			0
$375$	1.39582	+	3.36351i	0.0720798	+	0.173691i
$376$	−3.28001	−	7.91865i	−0.169154	−	0.408373i
$377$	19.6246	+	29.3703i	1.01072	+	1.51265i
$378$	−15.0537	+	6.27050i	−0.774278	+	0.322520i
$379$	15.2311	+	3.02965i	0.782368	+	0.155623i	0.570085	−	0.821586i	$-0.306910\pi$
$379$	15.2311	+	3.02965i	0.782368	+	0.155623i	0.212283	+	0.977208i	$0.431910\pi$
$380$	0.171815	−	0.257139i	0.00881393	−	0.0131910i
$381$	17.7240	−	11.8598i	0.908027	−	0.607594i
$382$	0.969330	+	0.401510i	0.0495952	+	0.0205430i
$383$	20.4588	+	8.47433i	1.04540	+	0.433018i	0.838247	−	0.545291i	$-0.183581\pi$
$383$	20.4588	+	8.47433i	1.04540	+	0.433018i	0.207151	+	0.978309i	$0.433581\pi$
$384$	−17.5710	+	11.7574i	−0.896668	+	0.599994i
$385$	−6.02498	+	9.01702i	−0.307061	+	0.459550i
$386$	16.5858	+	3.29912i	0.844194	+	0.167921i
$387$	−34.3393	+	0.0454712i	−1.74557	+	0.00231143i
$388$	−0.231344	−	0.346231i	−0.0117447	−	0.0175772i
$389$	5.80572	+	14.0162i	0.294362	+	0.710652i	0.999998	+	0.00207747i	$0.000661280\pi$
$389$	5.80572	+	14.0162i	0.294362	+	0.710652i	−0.705636	+	0.708574i	$0.749339\pi$
$390$	13.0295	+	31.3972i	0.659774	+	1.58986i
$391$		0			0
$392$		−	6.43314i		−	0.324922i
$393$	4.31619	−	4.32191i	0.217723	−	0.218011i
$394$	28.1469	−	18.8071i	1.41802	−	0.947490i
$395$	12.8555	+	12.8555i	0.646831	+	0.646831i
$396$	−0.323027	−	0.482061i	−0.0162327	−	0.0242245i
$397$	−31.2942	−	20.9101i	−1.57061	−	1.04945i	−0.967850	−	0.251526i	$-0.919068\pi$
$397$	−31.2942	−	20.9101i	−1.57061	−	1.04945i	−0.602760	−	0.797922i	$-0.705932\pi$
$398$	6.84571	+	34.4157i	0.343145	+	1.72510i
$399$	−3.22541	+	0.00213550i	−0.161473	+	0.000106909i
$400$	6.96352	−	16.8114i	0.348176	−	0.840571i
$401$	−3.46595	+	0.689420i	−0.173081	+	0.0344280i	−0.280870	−	0.959746i	$-0.590623\pi$
$401$	−3.46595	+	0.689420i	−0.173081	+	0.0344280i	0.107789	+	0.994174i	$0.465623\pi$
$402$	17.7873	+	3.52588i	0.887151	+	0.175855i
$403$	2.49080	−	12.5221i	0.124076	−	0.623770i
$404$	−0.310384	+	0.310384i	−0.0154422	+	0.0154422i
$405$	−15.3178	−	22.7937i	−0.761146	−	1.13263i
$406$	23.1710	−	9.59773i	1.14996	−	0.476327i
$407$	3.92459			0.194535
$408$		0			0
$409$	12.2079			0.603641			0.301820	−	0.953365i	$-0.402406\pi$
$409$	12.2079			0.603641			0.301820	+	0.953365i	$0.402406\pi$
$410$	12.6328	−	5.23268i	0.623890	−	0.258424i
$411$	21.1052	+	14.0818i	1.04104	+	0.694605i
$412$	0.774744	−	0.774744i	0.0381689	−	0.0381689i
$413$	2.56347	−	12.8874i	0.126140	−	0.634148i
$414$	3.28127	−	0.657203i	0.161266	−	0.0322998i
$415$	38.8671	−	7.73115i	1.90791	−	0.379507i
$416$	−1.12177	+	2.70819i	−0.0549993	+	0.132780i
$417$	−0.00578500	−	8.73753i	−0.000283293	−	0.427879i
$418$	−0.403898	−	2.03053i	−0.0197553	−	0.0993165i
$419$	−26.1021	−	17.4409i	−1.27517	−	0.852042i	−0.280985	−	0.959712i	$-0.590661\pi$
$419$	−26.1021	−	17.4409i	−1.27517	−	0.852042i	−0.994187	+	0.107670i	$0.965661\pi$
$420$	1.31215	−	0.261906i	0.0640262	−	0.0127797i
$421$	10.7245	+	10.7245i	0.522682	+	0.522682i	0.918380	−	0.395699i	$-0.129498\pi$
$421$	10.7245	+	10.7245i	0.522682	+	0.522682i	−0.395699	+	0.918380i	$0.629498\pi$
$422$	−18.8863	+	12.6194i	−0.919373	+	0.614305i
$423$	8.67658	+	3.58050i	0.421870	+	0.174090i
$424$		−	17.4460i		−	0.847253i
$425$		0			0
$426$	−5.06191	+	2.10064i	−0.245250	+	0.101776i
$427$	4.82553	+	11.6499i	0.233524	+	0.563776i
$428$	−0.123253	−	0.184461i	−0.00595764	−	0.00891625i
$429$	11.6586	+	4.82011i	0.562883	+	0.232717i
$430$	49.8473	+	9.91525i	2.40385	+	0.478156i
$431$	6.36331	−	9.52337i	0.306510	−	0.458724i	−0.645954	−	0.763376i	$-0.723540\pi$
$431$	6.36331	−	9.52337i	0.306510	−	0.458724i	0.952464	+	0.304652i	$0.0985402\pi$
$432$	4.23616	−	21.5199i	0.203812	−	1.03538i
$433$	−24.7526	−	10.2528i	−1.18953	−	0.492720i	−0.301930	−	0.953330i	$-0.597631\pi$
$433$	−24.7526	−	10.2528i	−1.18953	−	0.492720i	−0.887603	+	0.460610i	$0.847631\pi$
$434$	−8.37502	−	3.46905i	−0.402014	−	0.166520i
$435$	23.4883	+	35.1024i	1.12618	+	1.68303i
$436$	−0.274097	+	0.410216i	−0.0131269	+	0.0196458i
$437$	0.649167	+	0.129127i	0.0310539	+	0.00617700i
$438$	−12.1134	+	29.2991i	−0.578799	+	1.39997i
$439$	−4.73699	−	7.08940i	−0.226084	−	0.338359i	0.701034	−	0.713128i	$-0.252722\pi$
$439$	−4.73699	−	7.08940i	−0.226084	−	0.338359i	−0.927118	+	0.374769i	$0.877722\pi$
$440$	−5.27126	−	12.7259i	−0.251297	−	0.606685i
$441$	4.98817	+	4.97498i	0.237532	+	0.236904i
$442$		0			0
$443$		−	18.8773i		−	0.896886i	−0.893811	−	0.448443i	$-0.851979\pi$
$443$		−	18.8773i		−	0.896886i	0.893811	−	0.448443i	$-0.148021\pi$
$444$	−0.342622	−	0.342169i	−0.0162601	−	0.0162386i
$445$	−12.2720	+	8.19987i	−0.581747	+	0.388711i
$446$	2.50244	+	2.50244i	0.118494	+	0.118494i
$447$	−2.13257	−	10.6842i	−0.100867	−	0.505345i
$448$	−13.4084	−	8.95919i	−0.633486	−	0.423282i
$449$	5.31908	+	26.7408i	0.251023	+	1.26198i	0.876373	+	0.481633i	$0.159956\pi$
$449$	5.31908	+	26.7408i	0.251023	+	1.26198i	−0.625350	+	0.780345i	$0.715044\pi$
$450$	7.22473	+	17.3769i	0.340577	+	0.819156i
$451$	1.94197	−	4.68833i	0.0914438	−	0.220765i
$452$	−1.89793	+	0.377522i	−0.0892713	+	0.0177572i
$453$	−5.12348	+	25.8469i	−0.240722	+	1.21439i
$454$	0.398685	−	2.00433i	0.0187112	−	0.0940677i
$455$	−20.5695	+	20.5695i	−0.964311	+	0.964311i
$456$	2.27380	−	3.40786i	0.106480	−	0.159588i
$457$	9.73907	−	4.03405i	0.455574	−	0.188705i	−0.143082	−	0.989711i	$-0.545701\pi$
$457$	9.73907	−	4.03405i	0.455574	−	0.188705i	0.598657	+	0.801006i	$0.295701\pi$
$458$	−15.8270			−0.739546
$459$		0			0
$460$	−0.274576			−0.0128022
$461$	−9.13414	+	3.78349i	−0.425419	+	0.176215i	−0.585112	−	0.810952i	$-0.698950\pi$
$461$	−9.13414	+	3.78349i	−0.425419	+	0.176215i	0.159693	+	0.987167i	$0.448950\pi$
$462$	4.97150	−	7.45106i	0.231295	−	0.346655i
$463$	−16.2123	+	16.2123i	−0.753448	+	0.753448i	−0.975121	−	0.221673i	$-0.928848\pi$
$463$	−16.2123	+	16.2123i	−0.753448	+	0.753448i	0.221673	+	0.975121i	$0.428848\pi$
$464$	−6.58074	+	33.0836i	−0.305503	+	1.53587i
$465$	2.96833	−	14.9746i	0.137653	−	0.694432i
$466$	−20.4601	+	4.06977i	−0.947797	+	0.188529i
$467$	−9.89105	+	23.8791i	−0.457703	+	1.10499i	0.511621	+	0.859211i	$0.329045\pi$
$467$	−9.89105	+	23.8791i	−0.457703	+	1.10499i	−0.969325	+	0.245783i	$0.920955\pi$
$468$	−0.597567	−	1.43727i	−0.0276226	−	0.0664378i
$469$	3.02732	+	15.2194i	0.139789	+	0.702766i
$470$	−11.5509	−	7.71810i	−0.532806	−	0.356009i
$471$	−0.836789	−	4.19231i	−0.0385572	−	0.193172i
$472$	11.8014	+	11.8014i	0.543205	+	0.543205i
$473$	15.6831	−	10.4791i	0.721111	−	0.481831i
$474$	−10.6253	−	10.6112i	−0.488034	−	0.487388i
$475$			3.72217i			0.170785i
$476$		0			0
$477$	13.5274	+	13.4916i	0.619378	+	0.617740i
$478$	−13.2025	−	31.8737i	−0.603870	−	1.45787i
$479$	−4.81385	−	7.20443i	−0.219950	−	0.329179i	0.705041	−	0.709166i	$-0.250928\pi$
$479$	−4.81385	−	7.20443i	−0.219950	−	0.329179i	−0.924992	+	0.379987i	$0.875928\pi$
$480$	−1.33916	+	3.23907i	−0.0611238	+	0.147843i
$481$	10.3250	+	2.05377i	0.470778	+	0.0936437i
$482$	−2.27521	+	3.40509i	−0.103633	+	0.155098i
$483$	1.59256	+	2.38002i	0.0724639	+	0.108295i
$484$	−0.898446	−	0.372148i	−0.0408384	−	0.0169158i
$485$	10.0006	+	4.14240i	0.454106	+	0.188097i
$486$	12.6644	+	18.8185i	0.574470	+	0.853625i
$487$	21.5656	−	32.2752i	0.977229	−	1.46253i	0.0928931	−	0.995676i	$-0.470389\pi$
$487$	21.5656	−	32.2752i	0.977229	−	1.46253i	0.884336	−	0.466851i	$-0.154611\pi$
$488$	−15.7086	−	3.12463i	−0.711094	−	0.141445i
$489$	1.77812	+	0.735143i	0.0804094	+	0.0332443i
$490$	−5.79291	−	8.66971i	−0.261697	−	0.391658i
$491$	−4.84934	−	11.7073i	−0.218848	−	0.528345i	0.775882	−	0.630878i	$-0.217305\pi$
$491$	−4.84934	−	11.7073i	−0.218848	−	0.528345i	−0.994730	+	0.102533i	$0.967305\pi$
$492$	−0.578293	+	0.239986i	−0.0260715	+	0.0108194i
$493$		0			0
$494$		−	5.55337i		−	0.249858i
$495$	13.9440	+	5.75417i	0.626736	+	0.258631i
$496$	10.1374	−	6.77361i	0.455184	−	0.304144i
$497$	−3.31625	−	3.31625i	−0.148754	−	0.148754i
$498$	−32.0987	+	6.40693i	−1.43838	+	0.287101i
$499$	30.8610	+	20.6206i	1.38153	+	0.923106i	0.999999	−	0.00125143i	$-0.000398342\pi$
$499$	30.8610	+	20.6206i	1.38153	+	0.923106i	0.381527	+	0.924358i	$0.375398\pi$
$500$	0.0481476	+	0.242054i	0.00215323	+	0.0108250i
$501$	−0.0227750	−	34.3988i	−0.00101751	−	1.53683i
$502$	8.43090	−	20.3540i	0.376290	−	0.908444i
$503$	−31.3353	+	6.23297i	−1.39717	+	0.277914i	−0.835520	−	0.549460i	$-0.814833\pi$
$503$	−31.3353	+	6.23297i	−1.39717	+	0.277914i	−0.561650	+	0.827375i	$0.689833\pi$
$504$	17.3799	−	3.48100i	0.774160	−	0.155056i
$505$	2.22610	−	11.1913i	0.0990600	−	0.498008i
$506$	−1.29976	+	1.29976i	−0.0577812	+	0.0577812i
$507$	9.41937	+	6.28480i	0.418329	+	0.279118i
$508$	1.33526	−	0.553083i	0.0592426	−	0.0245391i
$509$	2.30289			0.102074			0.0510369	−	0.998697i	$-0.483747\pi$
$509$	2.30289			0.102074			0.0510369	+	0.998697i	$0.483747\pi$
$510$		0			0
$511$	−27.1309			−1.20020
$512$	18.7797	−	7.77882i	0.829954	−	0.343778i
$513$	0.884001	+	4.39850i	0.0390296	+	0.194198i
$514$	20.4697	−	20.4697i	0.902880	−	0.902880i
$515$	−5.55652	+	27.9345i	−0.244849	+	1.23094i
$516$	−2.28279	−	0.452505i	−0.100494	−	0.0199204i
$517$	−5.05666	+	1.00583i	−0.222391	+	0.0442364i
$518$	2.86037	−	6.90554i	0.125677	−	0.303412i
$519$	−20.1546	+	0.0133441i	−0.884688	+	0.000585740i
$520$	−7.20827	−	36.2384i	−0.316104	−	1.58916i
$521$	−2.28875	−	1.52929i	−0.100272	−	0.0669995i	0.504423	−	0.863456i	$-0.331705\pi$
$521$	−2.28875	−	1.52929i	−0.100272	−	0.0669995i	−0.604695	+	0.796457i	$0.706705\pi$
$522$	−19.4198	−	28.9806i	−0.849981	−	1.26845i
$523$	29.8001	+	29.8001i	1.30307	+	1.30307i	0.926313	+	0.376755i	$0.122960\pi$
$523$	29.8001	+	29.8001i	1.30307	+	1.30307i	0.376755	+	0.926313i	$0.377040\pi$
$524$	0.344186	−	0.229978i	0.0150358	−	0.0100466i
$525$	−11.3799	+	11.3949i	−0.496658	+	0.497316i
$526$			0.190778i			0.00831830i
$527$		0			0
$528$	4.61767	+	11.1272i	0.200958	+	0.484249i
$529$	8.57683	+	20.7063i	0.372906	+	0.900274i
$530$	−15.7098	−	23.5114i	−0.682390	−	1.02127i
$531$	−18.2772	+	0.0242021i	−0.793161	+	0.00105028i
$532$	−0.214389	−	0.0426446i	−0.00929494	−	0.00184888i
$533$	7.56246	−	11.3180i	0.327566	−	0.490238i
$534$	10.1318	−	6.77953i	0.438444	−	0.293379i
$535$	5.32803	+	2.20694i	0.230351	+	0.0954144i
$536$	−18.2094	−	7.54259i	−0.786527	−	0.325790i
$537$	−1.21878	+	0.815532i	−0.0525943	+	0.0351928i
$538$	−4.80652	+	7.19347i	−0.207224	+	0.310132i
$539$	−3.79534	−	0.754939i	−0.163477	−	0.0325175i
$540$	−0.715648	−	1.71807i	−0.0307966	−	0.0739339i
$541$	8.13164	+	12.1699i	0.349606	+	0.523223i	0.964044	−	0.265742i	$-0.0856171\pi$
$541$	8.13164	+	12.1699i	0.349606	+	0.523223i	−0.614438	+	0.788965i	$0.710617\pi$
$542$	−3.82826	−	9.24223i	−0.164438	−	0.396988i
$543$	−0.951908	−	2.29381i	−0.0408503	−	0.0984369i
$544$		0			0
$545$		−	12.8251i		−	0.549365i
$546$	16.9784	−	17.0009i	0.726610	−	0.727573i
$547$	−22.8049	+	15.2378i	−0.975068	+	0.651520i	−0.937577	−	0.347777i	$-0.886937\pi$
$547$	−22.8049	+	15.2378i	−0.975068	+	0.651520i	−0.0374912	+	0.999297i	$0.511937\pi$
$548$	1.21585	+	1.21585i	0.0519384	+	0.0519384i
$549$	14.5708	−	9.76385i	0.621868	−	0.416711i
$550$	−8.59481	−	5.74287i	−0.366484	−	0.244877i
$551$	−1.34611	−	6.76737i	−0.0573464	−	0.288300i
$552$	−3.63734	+	0.00240823i	−0.154816	+	0.000102501i
$553$	4.91757	−	11.8721i	0.209116	−	0.504851i
$554$	11.8417	−	2.35547i	0.503107	−	0.100074i
$555$	12.3472	+	2.44751i	0.524109	+	0.103891i
$556$	0.115523	−	0.580773i	0.00489926	−	0.0246302i
$557$	31.0707	−	31.0707i	1.31651	−	1.31651i	0.399984	−	0.916522i	$-0.369016\pi$
$557$	31.0707	−	31.0707i	1.31651	−	1.31651i	0.916522	−	0.399984i	$-0.130984\pi$
$558$	−2.44356	+	12.3702i	−0.103444	+	0.523671i
$559$	46.7436	−	19.3619i	1.97705	−	0.818919i
$560$	−27.7789			−1.17387
$561$		0			0
$562$	−19.2798			−0.813270
$563$	−33.9044	+	14.0437i	−1.42890	+	0.591870i	−0.957080	−	0.289825i	$-0.906403\pi$
$563$	−33.9044	+	14.0437i	−1.42890	+	0.591870i	−0.471821	+	0.881695i	$0.656403\pi$
$564$	0.529148	+	0.353059i	0.0222811	+	0.0148665i
$565$	35.5701	−	35.5701i	1.49645	−	1.49645i
$566$	3.98370	−	20.0274i	0.167448	−	0.841815i
$567$	−10.7414	+	16.1681i	−0.451095	+	0.678997i
$568$	5.84243	−	1.16213i	0.245143	−	0.0487620i
$569$	−9.46803	+	22.8578i	−0.396920	+	0.958251i	0.591472	+	0.806326i	$0.298547\pi$
$569$	−9.46803	+	22.8578i	−0.396920	+	0.958251i	−0.988392	+	0.151925i	$0.951453\pi$
$570$	−0.00439636	−	6.64016i	−0.000184143	−	0.278126i
$571$	−0.384503	−	1.93303i	−0.0160910	−	0.0808947i	0.971905	−	0.235372i	$-0.0756307\pi$
$571$	−0.384503	−	1.93303i	−0.0160910	−	0.0808947i	−0.987996	+	0.154477i	$0.950631\pi$
$572$	0.710889	+	0.475001i	0.0297238	+	0.0198608i
$573$	1.22471	−	0.244453i	0.0511631	−	0.0102122i
$574$	−6.83402	−	6.83402i	−0.285247	−	0.285247i
$575$	2.74779	−	1.83601i	0.114591	−	0.0765671i
$576$	−8.55649	+	20.7348i	−0.356520	+	0.863951i
$577$			26.8179i			1.11645i	0.829691	+	0.558223i	$0.188517\pi$
$577$			26.8179i			1.11645i	−0.829691	+	0.558223i	$0.811483\pi$
$578$		0			0
$579$	18.5917	−	7.71536i	0.772644	−	0.320639i
$580$	1.09538	+	2.64449i	0.0454833	+	0.109806i
$581$	−15.5616	−	23.2896i	−0.645603	−	0.966214i
$582$	−8.26247	−	3.41602i	−0.342490	−	0.141599i
$583$	−10.2926	−	2.04732i	−0.426275	−	0.0847913i
$584$	19.1452	−	28.6529i	0.792235	−	1.18566i
$585$	33.6733	+	22.4353i	1.39222	+	0.927586i
$586$	−35.4995	−	14.7044i	−1.46647	−	0.607433i
$587$	41.3023	+	17.1080i	1.70473	+	0.706122i	0.999994	−	0.00334911i	$-0.00106606\pi$
$587$	41.3023	+	17.1080i	1.70473	+	0.706122i	0.704735	+	0.709471i	$0.251066\pi$
$588$	0.265518	+	0.396807i	0.0109498	+	0.0163641i
$589$	−1.38557	+	2.07364i	−0.0570912	+	0.0854430i
$590$	26.5313	+	5.27741i	1.09228	+	0.217268i
$591$	15.3953	−	37.2374i	0.633280	−	1.53174i
$592$	5.58511	+	8.35871i	0.229547	+	0.343541i
$593$	8.44534	+	20.3889i	0.346809	+	0.837270i	0.996993	+	0.0774935i	$0.0246917\pi$
$593$	8.44534	+	20.3889i	0.346809	+	0.837270i	−0.650184	+	0.759777i	$0.725308\pi$
$594$	−11.5204	−	4.74513i	−0.472689	−	0.194695i
$595$		0			0
$596$		−	0.738361i		−	0.0302444i
$597$	29.5540	+	29.5149i	1.20956	+	1.20796i
$598$	−4.09963	+	2.73928i	−0.167646	+	0.112018i
$599$	−16.9345	−	16.9345i	−0.691926	−	0.691926i	0.270729	−	0.962655i	$-0.412735\pi$
$599$	−16.9345	−	16.9345i	−0.691926	−	0.691926i	−0.962655	+	0.270729i	$0.912735\pi$
$600$	−4.00384	−	20.0592i	−0.163456	−	0.818914i
$601$	−2.19329	−	1.46551i	−0.0894662	−	0.0597794i	0.510033	−	0.860155i	$-0.329633\pi$
$601$	−2.19329	−	1.46551i	−0.0894662	−	0.0597794i	−0.599499	+	0.800376i	$0.704633\pi$
$602$	−7.00826	−	35.2329i	−0.285635	−	1.43599i
$603$	19.9304	−	8.28640i	0.811630	−	0.337448i
$604$	−0.683377	+	1.64982i	−0.0278062	+	0.0671302i
$605$	24.7939	−	4.93180i	1.00801	−	0.200506i
$606$	−1.83256	+	9.24490i	−0.0744428	+	0.375548i
$607$	−7.07635	+	35.5752i	−0.287220	+	1.44395i	0.520234	+	0.854024i	$0.325845\pi$
$607$	−7.07635	+	35.5752i	−0.287220	+	1.44395i	−0.807454	+	0.589930i	$0.799155\pi$
$608$	0.404887	−	0.404887i	0.0164203	−	0.0164203i
$609$	16.5691	−	24.8329i	0.671412	−	1.00628i
$610$	−23.9836	+	9.93432i	−0.971066	+	0.402229i
$611$	−13.8296			−0.559487
$612$		0			0
$613$	−25.0887			−1.01333			−0.506663	−	0.862144i	$-0.669121\pi$
$613$	−25.0887			−1.01333			−0.506663	+	0.862144i	$0.669121\pi$
$614$	−32.8447	+	13.6047i	−1.32550	+	0.549041i
$615$	9.03346	−	13.5389i	0.364264	−	0.545942i
$616$	−6.88440	+	6.88440i	−0.277380	+	0.277380i
$617$	−1.92552	+	9.68025i	−0.0775186	+	0.389712i	0.922475	+	0.386057i	$0.126163\pi$
$617$	−1.92552	+	9.68025i	−0.0775186	+	0.389712i	−0.999993	+	0.00365472i	$0.998837\pi$
$618$	4.57422	−	23.0760i	0.184002	−	0.928253i
$619$	−31.6886	+	6.30326i	−1.27367	+	0.253349i	−0.785207	−	0.619233i	$-0.787443\pi$
$619$	−31.6886	+	6.30326i	−1.27367	+	0.253349i	−0.488466	+	0.872583i	$0.662443\pi$
$620$	0.395921	−	0.955837i	0.0159006	−	0.0383873i
$621$	2.81102	−	2.82221i	0.112802	−	0.113251i
$622$	−6.62467	−	33.3044i	−0.265625	−	1.33539i
$623$	8.67402	+	5.79580i	0.347517	+	0.232204i
$624$	6.32543	+	31.6904i	0.253220	+	1.26863i
$625$	−19.7780	−	19.7780i	−0.791122	−	0.791122i
$626$	−1.95352	+	1.30530i	−0.0780785	+	0.0521704i
$627$	−1.74369	−	1.74138i	−0.0696362	−	0.0695441i
$628$		−	0.289721i		−	0.0115611i
$629$		0			0
$630$	20.2876	−	20.3414i	0.808279	−	0.810422i
$631$	−1.47845	−	3.56930i	−0.0588563	−	0.142092i	0.891716	−	0.452596i	$-0.149502\pi$
$631$	−1.47845	−	3.56930i	−0.0588563	−	0.142092i	−0.950572	+	0.310504i	$0.899502\pi$
$632$	9.06791	+	13.5711i	0.360702	+	0.539829i
$633$	−10.3302	+	24.9860i	−0.410587	+	0.993104i
$634$	34.8014	+	6.92242i	1.38214	+	0.274925i
$635$	−20.8729	+	31.2385i	−0.828316	+	1.23966i
$636$	0.720059	+	1.07610i	0.0285522	+	0.0426702i
$637$	−9.58987	−	3.97225i	−0.379964	−	0.157386i
$638$	17.7033	+	7.33297i	0.700882	+	0.290315i
$639$	−3.61706	+	5.42887i	−0.143089	+	0.214763i
$640$	20.6928	−	30.9690i	0.817955	−	1.22416i
$641$	36.7015	+	7.30038i	1.44962	+	0.288348i	0.856242	−	0.516575i	$-0.172793\pi$
$641$	36.7015	+	7.30038i	1.44962	+	0.288348i	0.593380	+	0.804922i	$0.297793\pi$
$642$	−4.40198	−	1.81995i	−0.173732	−	0.0718276i
$643$	23.5997	+	35.3195i	0.930682	+	1.39286i	0.919570	+	0.392925i	$0.128537\pi$
$643$	23.5997	+	35.3195i	0.930682	+	1.39286i	0.0111111	+	0.999938i	$0.496463\pi$
$644$	0.0742693	+	0.179302i	0.00292662	+	0.00706549i
$645$	55.8760	−	23.1879i	2.20011	−	0.913024i
$646$		0			0
$647$			48.3331i			1.90017i	0.311989	+	0.950086i	$0.399005\pi$
$647$			48.3331i			1.90017i	−0.311989	+	0.950086i	$0.600995\pi$
$648$	−9.49533	−	22.7531i	−0.373012	−	0.893828i
$649$	8.34737	−	5.57753i	0.327663	−	0.218937i
$650$	−19.6063	−	19.6063i	−0.769023	−	0.769023i
$651$	−10.5815	+	2.11208i	−0.414723	+	0.0827790i
$652$	0.108422	+	0.0724451i	0.00424613	+	0.00283717i
$653$	1.26227	+	6.34586i	0.0493965	+	0.248333i	0.997592	−	0.0693542i	$-0.0220939\pi$
$653$	1.26227	+	6.34586i	0.0493965	+	0.248333i	−0.948196	+	0.317687i	$0.897094\pi$
$654$	0.00701353	+	10.5931i	0.000274251	+	0.414222i
$655$	−4.11794	+	9.94158i	−0.160901	+	0.388450i
$656$	12.7490	−	2.53593i	0.497764	−	0.0990114i
$657$	7.41136	+	37.0033i	0.289145	+	1.44364i
$658$	−1.91564	+	9.63056i	−0.0746794	+	0.375439i
$659$	17.7005	−	17.7005i	0.689515	−	0.689515i	−0.272610	−	0.962125i	$-0.587887\pi$
$659$	17.7005	−	17.7005i	0.689515	−	0.689515i	0.962125	+	0.272610i	$0.0878869\pi$
$660$	0.850385	+	0.567395i	0.0331012	+	0.0220858i
$661$	−23.0223	+	9.53615i	−0.895464	+	0.370913i	−0.782474	−	0.622683i	$-0.786043\pi$
$661$	−23.0223	+	9.53615i	−0.895464	+	0.370913i	−0.112990	+	0.993596i	$0.536043\pi$
$662$	44.3302			1.72294
$663$		0			0
$664$	35.5773			1.38067
$665$	5.24974	−	2.17451i	0.203576	−	0.0843240i
$666$	−10.1997	−	2.01481i	−0.395231	−	0.0780723i
$667$	−4.33184	+	4.33184i	−0.167729	+	0.167729i
$668$	0.454802	−	2.28645i	0.0175968	−	0.0884652i
$669$	4.13210	+	0.819081i	0.159756	+	0.0316675i
$670$	−31.3321	+	6.23235i	−1.21047	+	0.240777i
$671$	−3.68686	+	8.90086i	−0.142329	+	0.343614i
$672$	2.47738	−	0.00164024i	0.0955670	−	6.32736e-5i
$673$	−3.66436	−	18.4220i	−0.141251	−	0.710115i	−0.984887	−	0.173200i	$-0.944589\pi$
$673$	−3.66436	−	18.4220i	−0.141251	−	0.710115i	0.843636	−	0.536915i	$-0.180411\pi$
$674$	20.8416	+	13.9259i	0.802787	+	0.536405i
$675$	18.6500	+	12.4080i	0.717838	+	0.477584i
$676$	0.542640	+	0.542640i	0.0208708	+	0.0208708i
$677$	−8.24041	+	5.50607i	−0.316705	+	0.211615i	−0.703754	−	0.710444i	$-0.748494\pi$
$677$	−8.24041	+	5.50607i	−0.316705	+	0.211615i	0.387049	+	0.922059i	$0.373494\pi$
$678$	−29.3603	+	29.3992i	−1.12758	+	1.12907i
$679$		−	7.65102i		−	0.293619i
$680$		0			0
$681$	−0.932371	−	2.24673i	−0.0357285	−	0.0860950i
$682$	−2.65046	−	6.39878i	−0.101491	−	0.245022i
$683$	−1.32660	−	1.98540i	−0.0507610	−	0.0759692i	0.805221	−	0.592975i	$-0.202047\pi$
$683$	−1.32660	−	1.98540i	−0.0507610	−	0.0759692i	−0.855982	+	0.517006i	$0.827047\pi$
$684$	0.000402615		0.304050i	1.53944e−5		0.0116257i
$685$	−43.8391	−	8.72013i	−1.67500	−	0.333179i
$686$	−16.2996	+	24.3941i	−0.622322	+	0.931370i
$687$	−15.6572	+	10.4768i	−0.597358	+	0.399714i
$688$	44.6375	+	18.4895i	1.70179	+	0.704905i
$689$	−26.0068	−	10.7724i	−0.990779	−	0.410394i
$690$	−4.89975	+	3.27860i	−0.186530	+	0.124814i
$691$	−18.1140	+	27.1095i	−0.689088	+	1.03129i	0.307722	+	0.951476i	$0.400433\pi$
$691$	−18.1140	+	27.1095i	−0.689088	+	1.03129i	−0.996810	+	0.0798165i	$0.974567\pi$
$692$	−1.33965	−	0.266473i	−0.0509258	−	0.0101298i
$693$	−0.0141184	−	10.6620i	−0.000536313	−	0.405017i
$694$	−16.3582	−	24.4818i	−0.620948	−	0.929315i
$695$	5.89068	+	14.2214i	0.223446	+	0.539447i
$696$	14.5338	+	35.0222i	0.550904	+	1.32751i
$697$		0			0
$698$			11.0631i			0.418743i
$699$	−17.5466	+	17.5698i	−0.663673	+	0.664552i
$700$	−0.907464	+	0.606348i	−0.0342989	+	0.0229178i
$701$	31.7150	+	31.7150i	1.19786	+	1.19786i	0.974807	+	0.223051i	$0.0716016\pi$
$701$	31.7150	+	31.7150i	1.19786	+	1.19786i	0.223051	+	0.974807i	$0.428398\pi$
$702$	−27.8253	−	18.5124i	−1.05020	−	0.698706i
$703$	−1.70980	−	1.14245i	−0.0644864	−	0.0430885i
$704$	−2.40368	−	12.0841i	−0.0905921	−	0.455437i
$705$	−16.5361	+	0.0109483i	−0.622784	+	0.000412337i
$706$	−6.64926	+	16.0527i	−0.250248	+	0.604153i
$707$	−7.91022	+	1.57344i	−0.297495	+	0.0591753i
$708$	−1.21502	−	0.240846i	−0.0456633	−	0.00905156i
$709$	7.70314	−	38.7263i	0.289297	−	1.45440i	−0.513472	−	0.858106i	$-0.671641\pi$
$709$	7.70314	−	38.7263i	0.289297	−	1.45440i	0.802769	−	0.596290i	$-0.203359\pi$
$710$	6.82716	−	6.82716i	0.256219	−	0.256219i
$711$	−17.5354	−	3.46388i	−0.657629	−	0.129906i
$712$	−12.2419	+	5.07074i	−0.458783	+	0.190034i
$713$	2.21426			0.0829248
$714$		0			0
$715$	−22.2254			−0.831182
$716$	−0.0918186	+	0.0380325i	−0.00343142	+	0.00142134i
$717$	−34.1599	−	22.7922i	−1.27573	−	0.851191i
$718$	−23.6628	+	23.6628i	−0.883086	+	0.883086i
$719$	−8.57373	+	43.1030i	−0.319746	+	1.60747i	0.402220	+	0.915543i	$0.368239\pi$
$719$	−8.57373	+	43.1030i	−0.319746	+	1.60747i	−0.721966	+	0.691929i	$0.756761\pi$
$720$	7.58839	+	37.8871i	0.282803	+	1.41197i
$721$	19.7446	−	3.92744i	0.735326	−	0.146265i
$722$	10.1650	−	24.5406i	0.378304	−	0.913307i
$723$	0.00322743	+	4.87465i	0.000120030	+	0.181290i
$724$	−0.0328353	−	0.165074i	−0.00122031	−	0.00613493i
$725$	−28.6448	−	19.1399i	−1.06384	−	0.710837i
$726$	−20.4762	+	4.08707i	−0.759943	+	0.151685i
$727$	−0.0802760	−	0.0802760i	−0.00297727	−	0.00297727i	0.705617	−	0.708594i	$-0.250670\pi$
$727$	−0.0802760	−	0.0802760i	−0.00297727	−	0.00297727i	−0.708594	+	0.705617i	$0.750670\pi$
$728$	−21.7144	+	14.5091i	−0.804790	+	0.537744i
$729$	24.9856	+	10.2333i	0.925392	+	0.379010i
$730$		−	55.8544i		−	2.06726i
$731$		0			0
$732$	1.09790	−	0.455616i	0.0405795	−	0.0168400i
$733$	−3.12587	−	7.54651i	−0.115457	−	0.278737i	0.855579	−	0.517673i	$-0.173201\pi$
$733$	−3.12587	−	7.54651i	−0.115457	−	0.278737i	−0.971035	+	0.238936i	$0.923201\pi$
$734$	13.2667	+	19.8549i	0.489681	+	0.732860i
$735$	−11.4697	−	4.74203i	−0.423068	−	0.174912i
$736$	−0.498613	−	0.0991804i	−0.0183791	−	0.00365584i
$737$	−6.58678	+	9.85781i	−0.242627	+	0.363117i
$738$	−7.45394	+	11.1876i	−0.274383	+	0.411823i
$739$	−10.8531	−	4.49550i	−0.399237	−	0.165370i	0.174025	−	0.984741i	$-0.444323\pi$
$739$	−10.8531	−	4.49550i	−0.399237	−	0.165370i	−0.573263	+	0.819372i	$0.694323\pi$
$740$	0.788126	+	0.326452i	0.0289721	+	0.0120006i
$741$	−3.67610	−	5.49379i	−0.135045	−	0.201819i
$742$	−11.1039	+	16.6182i	−0.407639	+	0.610074i
$743$	40.2557	+	8.00737i	1.47684	+	0.293762i	0.866819	−	0.498623i	$-0.166161\pi$
$743$	40.2557	+	8.00737i	1.47684	+	0.293762i	0.610021	+	0.792385i	$0.291161\pi$
$744$	5.23642	−	12.6655i	0.191976	−	0.464341i
$745$	10.6635	+	15.9591i	0.390682	+	0.584697i
$746$	0.901121	+	2.17550i	0.0329924	+	0.0796507i
$747$	−27.5132	+	27.5862i	−1.00666	+	1.00933i
$748$		0			0
$749$		−	4.07622i		−	0.148942i
$750$	3.74945	+	3.74449i	0.136911	+	0.136730i
$751$	1.40436	−	0.938366i	0.0512460	−	0.0342414i	−0.529683	−	0.848195i	$-0.677689\pi$
$751$	1.40436	−	0.938366i	0.0512460	−	0.0342414i	0.580929	+	0.813954i	$0.302689\pi$
$752$	−9.33841	−	9.33841i	−0.340537	−	0.340537i
$753$	−5.13303	−	25.7165i	−0.187058	−	0.937162i
$754$	42.7373	+	28.5562i	1.55640	+	1.03995i
$755$	−9.05629	−	45.5290i	−0.329592	−	1.65697i
$756$	−0.928347	+	0.932042i	−0.0337637	+	0.0338980i
$757$	−20.8300	+	50.2881i	−0.757080	+	1.82775i	−0.242954	+	0.970038i	$0.578116\pi$
$757$	−20.8300	+	50.2881i	−0.757080	+	1.82775i	−0.514126	+	0.857715i	$0.671884\pi$
$758$	22.1631	−	4.40851i	0.805000	−	0.160124i
$759$	−0.425427	+	2.14619i	−0.0154420	+	0.0779019i
$760$	−1.40804	+	7.07871i	−0.0510751	+	0.256772i
$761$	−24.1395	+	24.1395i	−0.875055	+	0.875055i	−0.993018	−	0.117963i	$-0.962364\pi$
$761$	−24.1395	+	24.1395i	−0.875055	+	0.875055i	0.117963	+	0.993018i	$0.462364\pi$
$762$	17.2233	−	25.8134i	0.623933	−	0.935121i
$763$	−8.37493	+	3.46901i	−0.303193	+	0.125587i
$764$	0.0846370			0.00306206
$765$		0			0
$766$	32.2229			1.16426
$767$	24.8794	−	10.3054i	0.898343	−	0.372106i
$768$	−2.69907	+	4.04525i	−0.0973944	+	0.145970i
$769$	31.3211	−	31.3211i	1.12947	−	1.12947i	0.139204	−	0.990264i	$-0.455546\pi$
$769$	31.3211	−	31.3211i	1.12947	−	1.12947i	0.990264	−	0.139204i	$-0.0444544\pi$
$770$	−3.07859	+	15.4771i	−0.110945	+	0.557757i
$771$	6.70001	−	33.8002i	0.241295	−	1.21728i
$772$	1.33795	−	0.266135i	0.0481539	−	0.00957840i
$773$	−5.31114	+	12.8222i	−0.191028	+	0.461184i	−0.990154	−	0.139980i	$-0.955296\pi$
$773$	−5.31114	+	12.8222i	−0.191028	+	0.461184i	0.799126	+	0.601164i	$0.205296\pi$
$774$	−46.1390	+	19.1830i	−1.65843	+	0.689520i
$775$	2.42928	+	12.2128i	0.0872624	+	0.438698i
$776$	8.08023	+	5.39903i	0.290063	+	0.193814i
$777$	−1.74150	−	8.72489i	−0.0624758	−	0.313004i
$778$	15.6099	+	15.6099i	0.559643	+	0.559643i
$779$	−2.21083	+	1.47723i	−0.0792111	+	0.0529272i
$780$	1.94031	+	1.93774i	0.0694742	+	0.0693822i
$781$		−	3.58322i		−	0.128218i
$782$		0			0
$783$	−38.3954	−	15.8146i	−1.37214	−	0.565168i
$784$	−3.79328	−	9.15778i	−0.135474	−	0.327064i
$785$	4.18421	+	6.26211i	0.149341	+	0.223504i
$786$	3.39584	−	8.21367i	0.121126	−	0.292972i
$787$	23.4782	+	4.67010i	0.836907	+	0.166471i	0.594896	−	0.803802i	$-0.297193\pi$
$787$	23.4782	+	4.67010i	0.836907	+	0.166471i	0.242011	+	0.970274i	$0.422193\pi$
$788$	1.51714	−	2.27057i	0.0540460	−	0.0808856i
$789$	0.126287	+	0.188731i	0.00449593	+	0.00671899i
$790$	24.4410	+	10.1238i	0.869572	+	0.360189i
$791$	−32.8490	−	13.6065i	−1.16798	−	0.483792i
$792$	11.2701	+	7.50888i	0.400466	+	0.266817i
$793$	−14.3574	+	21.4874i	−0.509847	+	0.763040i
$794$	−53.7144	−	10.6845i	−1.90625	−	0.379178i
$795$	−31.1048	−	12.8599i	−1.10317	−	0.456094i
$796$	1.57263	+	2.35361i	0.0557403	+	0.0834213i
$797$	−17.9210	−	43.2651i	−0.634795	−	1.53253i	−0.833529	−	0.552476i	$-0.813683\pi$
$797$	−17.9210	−	43.2651i	−0.634795	−	1.53253i	0.198734	−	0.980053i	$-0.436317\pi$
$798$	−4.33492	+	1.79895i	−0.153455	+	0.0636820i
$799$		0			0
$800$		−	2.85893i		−	0.101078i
$801$	5.53529	−	13.4136i	0.195580	−	0.473945i
$802$	−4.27557	+	2.85685i	−0.150976	+	0.100879i
$803$	−14.6575	−	14.6575i	−0.517252	−	0.517252i
$804$	1.43450	−	0.286327i	0.0505909	−	0.0100980i
$805$	−4.19478	−	2.80287i	−0.147847	−	0.0987880i
$806$	−3.62442	−	18.2212i	−0.127665	−	0.641814i
$807$	0.00681816	+	10.2980i	0.000240011	+	0.362507i
$808$	3.92024	−	9.46429i	0.137913	−	0.332952i
$809$	−11.4907	+	2.28565i	−0.403993	+	0.0803592i	−0.392904	−	0.919579i	$-0.628530\pi$
$809$	−11.4907	+	2.28565i	−0.403993	+	0.0803592i	−0.0110886	+	0.999939i	$0.503530\pi$
$810$	−33.2853	−	22.1132i	−1.16953	−	0.776980i
$811$	−3.67314	+	18.4661i	−0.128982	+	0.648434i	0.861157	+	0.508340i	$0.169741\pi$
$811$	−3.67314	+	18.4661i	−0.128982	+	0.648434i	−0.990138	+	0.140094i	$0.955259\pi$
$812$	1.43060	−	1.43060i	0.0502042	−	0.0502042i
$813$	−9.90514	−	6.60892i	−0.347389	−	0.231785i
$814$	5.27605	−	2.18541i	0.184926	−	0.0765987i
$815$	−3.38972			−0.118737
$816$		0			0
$817$	−9.88307			−0.345765
$818$	16.4118	−	6.79797i	0.573824	−	0.237686i
$819$	5.54238	−	28.0575i	0.193666	−	0.980410i
$820$	0.779963	−	0.779963i	0.0272375	−	0.0272375i
$821$	5.91006	−	29.7119i	0.206263	−	1.03695i	−0.729408	−	0.684079i	$-0.760205\pi$
$821$	5.91006	−	29.7119i	0.206263	−	1.03695i	0.935671	−	0.352874i	$-0.114795\pi$
$822$	36.2144	+	7.17857i	1.26312	+	0.250381i
$823$	−22.5083	+	4.47717i	−0.784589	+	0.156064i	−0.571099	−	0.820881i	$-0.693483\pi$
$823$	−22.5083	+	4.47717i	−0.784589	+	0.156064i	−0.213489	+	0.976945i	$0.568483\pi$
$824$	−9.78523	+	23.6236i	−0.340884	+	0.822968i
$825$	−12.3041	+	0.00814639i	−0.428375	+	0.000283621i
$826$	−3.73016	−	18.7528i	−0.129789	−	0.652493i
$827$	−14.5585	−	9.72768i	−0.506249	−	0.338265i	0.276076	−	0.961136i	$-0.410966\pi$
$827$	−14.5585	−	9.72768i	−0.506249	−	0.338265i	−0.782324	+	0.622871i	$0.785966\pi$
$828$	0.224258	−	0.150275i	0.00779351	−	0.00522240i
$829$	−31.1358	−	31.1358i	−1.08139	−	1.08139i	−0.996380	−	0.0850121i	$-0.972907\pi$
$829$	−31.1358	−	31.1358i	−1.08139	−	1.08139i	−0.0850121	−	0.996380i	$-0.527093\pi$
$830$	47.9462	−	32.0366i	1.66424	−	1.11201i
$831$	10.1555	−	10.1689i	0.352289	−	0.352756i
$832$		−	33.0493i		−	1.14578i
$833$		0			0
$834$	−4.87328	−	11.7432i	−0.168748	−	0.406632i
$835$	23.1910	+	55.9881i	0.802559	+	1.93755i
$836$	−0.0927852	−	0.138863i	−0.00320904	−	0.00480267i
$837$	5.77119	+	13.8550i	0.199481	+	0.478898i
$838$	−44.8026	−	8.91178i	−1.54768	−	0.307852i
$839$	10.9879	−	16.4446i	0.379346	−	0.567731i	−0.591840	−	0.806056i	$-0.701598\pi$
$839$	10.9879	−	16.4446i	0.379346	−	0.567731i	0.971186	+	0.238325i	$0.0765982\pi$
$840$	−25.9524	+	17.3657i	−0.895444	+	0.599174i
$841$	32.2093	+	13.3415i	1.11067	+	0.460053i
$842$	20.3896	+	8.44564i	0.702671	+	0.291056i
$843$	−19.0730	+	12.7624i	−0.656908	+	0.439561i
$844$	−1.01799	+	1.52353i	−0.0350407	+	0.0524422i
$845$	−19.5656	−	3.89185i	−0.673078	−	0.133884i
$846$	13.6582	−	0.0180859i	0.469580	−	0.000621805i
$847$	−9.92694	−	14.8567i	−0.341094	−	0.510483i
$848$	−10.2870	−	24.8350i	−0.353257	−	0.852837i
$849$	−9.31634	−	22.4496i	−0.319736	−	0.770468i
$850$		0			0
$851$			1.82575i			0.0625858i
$852$	−0.312406	+	0.312820i	−0.0107029	+	0.0107170i
$853$	5.13456	−	3.43080i	0.175804	−	0.117469i	−0.464555	−	0.885544i	$-0.653786\pi$
$853$	5.13456	−	3.43080i	0.175804	−	0.117469i	0.640359	+	0.768076i	$0.278786\pi$
$854$	12.9745	+	12.9745i	0.443977	+	0.443977i
$855$	−4.39985	−	6.56600i	−0.150472	−	0.224553i
$856$	4.30489	+	2.87643i	0.147138	+	0.0983145i
$857$	5.07296	+	25.5035i	0.173289	+	0.871184i	0.965393	+	0.260798i	$0.0839856\pi$
$857$	5.07296	+	25.5035i	0.173289	+	0.871184i	−0.792104	+	0.610386i	$0.791014\pi$
$858$	18.3574	−	0.0121542i	0.626712	−	0.000414937i
$859$	−1.25664	+	3.03380i	−0.0428761	+	0.103512i	−0.943867	−	0.330326i	$-0.892841\pi$
$859$	−1.25664	+	3.03380i	−0.0428761	+	0.103512i	0.900991	+	0.433838i	$0.142841\pi$
$860$	4.02111	−	0.799849i	0.137119	−	0.0272746i
$861$	−11.2845	−	2.23687i	−0.384576	−	0.0762322i
$862$	3.25147	−	16.3462i	0.110745	−	0.556755i
$863$	−10.3922	+	10.3922i	−0.353754	+	0.353754i	−0.861504	−	0.507750i	$-0.830477\pi$
$863$	−10.3922	+	10.3922i	−0.353754	+	0.353754i	0.507750	+	0.861504i	$0.330477\pi$
$864$	−0.678985	−	3.37840i	−0.0230995	−	0.114936i
$865$	32.8040	−	13.5878i	1.11537	−	0.462000i
$866$	−38.9856			−1.32479
$867$		0			0
$868$	−0.731265			−0.0248208
$869$	9.07062	−	3.75718i	0.307700	−	0.127453i
$870$	51.1236	+	34.1107i	1.73325	+	1.15646i
$871$	−22.4875	+	22.4875i	−0.761958	+	0.761958i
$872$	2.24626	−	11.2927i	0.0760679	−	0.382419i
$873$	−10.4351	+	2.09003i	−0.353174	+	0.0707370i
$874$	0.944618	−	0.187896i	0.0319522	−	0.00635569i
$875$	−1.73532	+	4.18943i	−0.0586644	+	0.141629i
$876$	0.00169332	+	2.55755i	5.72119e−5	+	0.0864117i
$877$	−2.60180	−	13.0801i	−0.0878565	−	0.441684i	−0.999527	−	0.0307618i	$-0.990207\pi$
$877$	−2.60180	−	13.0801i	−0.0878565	−	0.441684i	0.911670	−	0.410923i	$-0.134793\pi$
$878$	−10.3160	−	6.89290i	−0.348146	−	0.232624i
$879$	−44.8523	+	8.95256i	−1.51283	+	0.301962i
$880$	−15.0076	−	15.0076i	−0.505907	−	0.505907i
$881$	−16.3958	+	10.9553i	−0.552389	+	0.369094i	−0.800218	−	0.599709i	$-0.795283\pi$
$881$	−16.3958	+	10.9553i	−0.552389	+	0.369094i	0.247829	+	0.968804i	$0.420283\pi$
$882$	9.47622	+	3.91048i	0.319081	+	0.131673i
$883$		−	44.5932i		−	1.50068i	−0.661051	−	0.750341i	$-0.729889\pi$
$883$		−	44.5932i		−	1.50068i	0.661051	−	0.750341i	$-0.270111\pi$
$884$		0			0
$885$	29.7401	−	12.3418i	0.999702	−	0.414866i
$886$	−10.5118	−	25.3778i	−0.353152	−	0.852584i
$887$	9.28722	+	13.8993i	0.311834	+	0.466693i	0.953972	−	0.299896i	$-0.0969521\pi$
$887$	9.28722	+	13.8993i	0.311834	+	0.466693i	−0.642137	+	0.766590i	$0.721952\pi$
$888$	10.4432	+	4.31764i	0.350452	+	0.144890i
$889$	26.0450	+	5.18067i	0.873522	+	0.173754i
$890$	−11.9318	+	17.8572i	−0.399955	+	0.598575i
$891$	−14.5379	+	2.93181i	−0.487038	+	0.0982194i
$892$	0.263753	+	0.109250i	0.00883111	+	0.00365797i
$893$	2.49580	+	1.03380i	0.0835189	+	0.0345947i
$894$	−8.81646	−	13.1759i	−0.294866	−	0.440667i
$895$	1.43532	−	2.14810i	0.0479773	−	0.0718032i
$896$	−25.8203	−	5.13597i	−0.862594	−	0.171581i
$897$	−2.24235	+	5.42367i	−0.0748699	+	0.181091i
$898$	22.0414	+	32.9873i	0.735532	+	1.10080i
$899$	−8.83348	−	21.3259i	−0.294613	−	0.711259i
$900$	1.07488	+	1.07204i	0.0358293	+	0.0357345i
$901$		0			0
$902$		−	7.38418i		−	0.245866i
$903$	−30.2557	−	30.2157i	−1.00685	−	1.00552i
$904$	37.5501	−	25.0902i	1.24890	−	0.834487i
$905$	3.09374	+	3.09374i	0.102839	+	0.102839i
$906$	7.50509	+	37.6005i	0.249340	+	1.24919i
$907$	−7.66078	−	5.11877i	−0.254372	−	0.169966i	0.421846	−	0.906668i	$-0.361382\pi$
$907$	−7.66078	−	5.11877i	−0.254372	−	0.169966i	−0.676218	+	0.736702i	$0.736382\pi$
$908$	−0.0321614	−	0.161686i	−0.00106731	−	0.00536574i
$909$	4.30683	+	10.3588i	0.142848	+	0.343579i
$910$	−16.1986	+	39.1068i	−0.536978	+	1.29638i
$911$	1.96677	−	0.391215i	0.0651621	−	0.0129615i	−0.162402	−	0.986725i	$-0.551924\pi$
$911$	1.96677	−	0.391215i	0.0651621	−	0.0129615i	0.227564	+	0.973763i	$0.426924\pi$
$912$	1.22739	−	6.19194i	0.0406430	−	0.205036i
$913$	4.17505	−	20.9894i	0.138174	−	0.694648i
$914$	10.8464	−	10.8464i	0.358768	−	0.358768i
$915$	−17.1501	+	25.7038i	−0.566966	+	0.849742i
$916$	−1.17955	+	0.488587i	−0.0389735	+	0.0161434i
$917$	7.60583			0.251167
$918$		0			0
$919$	4.18774			0.138141			0.0690703	−	0.997612i	$-0.477997\pi$
$919$	4.18774			0.138141			0.0690703	+	0.997612i	$0.477997\pi$
$920$	5.92020	−	2.45223i	0.195183	−	0.0808475i
$921$	−23.4865	+	35.2005i	−0.773907	+	1.15990i
$922$	−10.1727	+	10.1727i	−0.335021	+	0.335021i
$923$	1.87512	−	9.42688i	0.0617204	−	0.310290i
$924$	0.140498	−	0.708785i	0.00462206	−	0.0233173i
$925$	−10.0700	+	2.00304i	−0.331098	+	0.0658595i
$926$	−12.7673	+	30.8229i	−0.419558	+	1.01290i
$927$	−10.7502	−	25.8564i	−0.353083	−	0.849234i
$928$	1.03392	+	5.19789i	0.0339402	+	0.170629i
$929$	−20.3321	−	13.5854i	−0.667073	−	0.445724i	0.175375	−	0.984502i	$-0.443886\pi$
$929$	−20.3321	−	13.5854i	−0.667073	−	0.445724i	−0.842448	+	0.538778i	$0.818886\pi$
$930$	−4.34814	−	21.7842i	−0.142581	−	0.714332i
$931$	1.43373	+	1.43373i	0.0469885	+	0.0469885i
$932$	−1.39922	+	0.934927i	−0.0458329	+	0.0306245i
$933$	−28.5997	−	28.5619i	−0.936312	−	0.935073i
$934$			37.6099i			1.23063i
$935$		0			0
$936$	25.7205	+	25.6524i	0.840699	+	0.838476i
$937$	−19.3663	−	46.7545i	−0.632671	−	1.52740i	−0.836252	−	0.548345i	$-0.815258\pi$
$937$	−19.3663	−	46.7545i	−0.632671	−	1.52740i	0.203582	−	0.979058i	$-0.434742\pi$
$938$	12.5447	+	18.7745i	0.409600	+	0.613010i
$939$	−1.06851	+	2.58445i	−0.0348695	+	0.0843403i
$940$	−1.09913	−	0.218631i	−0.0358497	−	0.00713095i
$941$	−2.00221	+	2.99651i	−0.0652701	+	0.0976836i	−0.862669	−	0.505769i	$-0.831209\pi$
$941$	−2.00221	+	2.99651i	−0.0652701	+	0.0976836i	0.797399	+	0.603453i	$0.206209\pi$
$942$	−3.45944	−	5.17001i	−0.112715	−	0.168448i
$943$	2.18105	+	0.903419i	0.0710246	+	0.0294194i
$944$	23.7584	+	9.84105i	0.773270	+	0.320299i
$945$	6.60480	−	33.5527i	0.214854	−	1.09147i
$946$	15.2484	−	22.8209i	0.495769	−	0.741970i
$947$	−26.2908	−	5.22957i	−0.854336	−	0.169938i	−0.251554	−	0.967843i	$-0.580941\pi$
$947$	−26.2908	−	5.22957i	−0.854336	−	0.169938i	−0.602783	+	0.797905i	$0.705941\pi$
$948$	−1.11945	−	0.462824i	−0.0363581	−	0.0150318i
$949$	−30.8912	−	46.2320i	−1.00277	−	1.50075i
$950$	2.07269	+	5.00393i	0.0672471	+	0.162349i
$951$	39.0103	−	16.1889i	1.26500	−	0.524960i
$952$		0			0
$953$			24.2594i			0.785838i	0.919573	+	0.392919i	$0.128535\pi$
$953$			24.2594i			0.785838i	−0.919573	+	0.392919i	$0.871465\pi$
$954$	25.6985	+	10.6048i	0.832021	+	0.343344i
$955$	−1.82937	+	1.22234i	−0.0591969	+	0.0395541i
$956$	−1.96792	−	1.96792i	−0.0636470	−	0.0636470i
$957$	22.3675	−	4.46457i	0.723039	−	0.144319i
$958$	−10.4833	−	7.00474i	−0.338701	−	0.226313i
$959$	6.16353	+	30.9862i	0.199031	+	1.00060i
$960$	−0.0261636	−	39.5170i	−0.000844428	−	1.27541i
$961$	8.67037	−	20.9321i	0.279689	−	0.675230i
$962$	15.0241	−	2.98848i	0.484397	−	0.0963525i
$963$	−5.55948	+	1.11350i	−0.179152	+	0.0358822i
$964$	−0.0644499	+	0.324012i	−0.00207579	+	0.0104357i
$965$	−25.0752	+	25.0752i	−0.807200	+	0.807200i
$966$	3.46629	+	2.31278i	0.111526	+	0.0744125i
$967$	−12.2636	+	5.07976i	−0.394372	+	0.163354i	−0.571051	−	0.820914i	$-0.693464\pi$
$967$	−12.2636	+	5.07976i	−0.394372	+	0.163354i	0.176680	+	0.984268i	$0.443464\pi$
$968$	22.6952			0.729452
$969$		0			0
$970$	15.7512			0.505739
$971$	−14.2905	+	5.91933i	−0.458605	+	0.189960i	−0.600012	−	0.799991i	$-0.704837\pi$
$971$	−14.2905	+	5.91933i	−0.458605	+	0.189960i	0.141407	+	0.989952i	$0.454837\pi$
$972$	1.52479	+	1.01155i	0.0489077	+	0.0324454i
$973$	7.69338	−	7.69338i	0.246638	−	0.246638i
$974$	11.0194	−	55.3982i	0.353084	−	1.77507i
$975$	−32.3745	−	6.41741i	−1.03681	−	0.205522i
$976$	−24.2041	+	4.81450i	−0.774755	+	0.154108i
$977$	7.72995	−	18.6618i	0.247303	−	0.597042i	−0.750670	−	0.660677i	$-0.770269\pi$
$977$	7.72995	−	18.6618i	0.247303	−	0.597042i	0.997973	+	0.0636347i	$0.0202693\pi$
$978$	2.79980	−	0.00185371i	0.0895277	−	5.92750e-5i
$979$	1.55497	+	7.81735i	0.0496970	+	0.249844i
$980$	−0.699373	−	0.467306i	−0.0223406	−	0.0149275i
$981$	7.01910	+	10.4748i	0.224103	+	0.334434i
$982$	−13.0385	−	13.0385i	−0.416075	−	0.416075i
$983$	−21.6898	+	14.4927i	−0.691797	+	0.462244i	−0.851112	−	0.524984i	$-0.824071\pi$
$983$	−21.6898	+	14.4927i	−0.691797	+	0.462244i	0.159315	+	0.987228i	$0.449071\pi$
$984$	10.3254	−	10.3391i	0.329162	−	0.329598i
$985$			70.9874i			2.26185i
$986$		0			0
$987$	4.47994	+	10.7953i	0.142598	+	0.343618i
$988$	−0.171435	−	0.413882i	−0.00545409	−	0.0131673i
$989$	4.87497	+	7.29590i	0.155015	+	0.231996i
$990$	21.9499	−	0.0290655i	0.697615	−	0.000923762i
$991$	−35.4161	−	7.04470i	−1.12503	−	0.223782i	−0.402701	−	0.915332i	$-0.631928\pi$
$991$	−35.4161	−	7.04470i	−1.12503	−	0.223782i	−0.722329	+	0.691549i	$0.756928\pi$
$992$	1.06423	−	1.59273i	0.0337892	−	0.0505692i
$993$	43.8545	−	29.3447i	1.39168	−	0.931225i
$994$	−6.30488	−	2.61157i	−0.199979	−	0.0828339i
$995$	−67.9824	−	28.1592i	−2.15519	−	0.892707i
$996$	−2.19447	+	1.46840i	−0.0695344	+	0.0465280i
$997$	−8.20777	+	12.2838i	−0.259943	+	0.389032i	−0.938368	−	0.345638i	$-0.887663\pi$
$997$	−8.20777	+	12.2838i	−0.259943	+	0.389032i	0.678425	+	0.734669i	$0.262663\pi$
$998$	52.9708	+	10.5365i	1.67676	+	0.333529i
$999$	−11.4240	+	4.75858i	−0.361439	+	0.150555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.i.h.131.4		32
3.2	odd	2	inner	867.2.i.h.131.1		32
17.2	even	8		867.2.i.b.65.4		32
17.3	odd	16		867.2.i.f.329.4		32
17.4	even	4		867.2.i.c.158.1		32
17.5	odd	16		867.2.i.b.827.1		32
17.6	odd	16		867.2.i.d.653.4		32
17.7	odd	16		51.2.i.a.44.1	yes	32
17.8	even	8		867.2.i.g.224.1		32
17.9	even	8		867.2.i.f.224.1		32
17.10	odd	16	inner	867.2.i.h.503.1		32
17.11	odd	16		867.2.i.c.653.4		32
17.12	odd	16		867.2.i.i.827.1		32
17.13	even	4		867.2.i.d.158.1		32
17.14	odd	16		867.2.i.g.329.4		32
17.15	even	8		867.2.i.i.65.4		32
17.16	even	2		51.2.i.a.29.4	yes	32
51.2	odd	8		867.2.i.b.65.1		32
51.5	even	16		867.2.i.b.827.4		32
51.8	odd	8		867.2.i.g.224.4		32
51.11	even	16		867.2.i.c.653.1		32
51.14	even	16		867.2.i.g.329.1		32
51.20	even	16		867.2.i.f.329.1		32
51.23	even	16		867.2.i.d.653.1		32
51.26	odd	8		867.2.i.f.224.4		32
51.29	even	16		867.2.i.i.827.4		32
51.32	odd	8		867.2.i.i.65.1		32
51.38	odd	4		867.2.i.c.158.4		32
51.41	even	16		51.2.i.a.44.4	yes	32
51.44	even	16	inner	867.2.i.h.503.4		32
51.47	odd	4		867.2.i.d.158.4		32
51.50	odd	2		51.2.i.a.29.1	✓	32
68.7	even	16		816.2.cj.c.401.4		32
68.67	odd	2		816.2.cj.c.641.3		32
204.143	odd	16		816.2.cj.c.401.3		32
204.203	even	2		816.2.cj.c.641.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.29.1	✓	32	51.50	odd	2
51.2.i.a.29.4	yes	32	17.16	even	2
51.2.i.a.44.1	yes	32	17.7	odd	16
51.2.i.a.44.4	yes	32	51.41	even	16
816.2.cj.c.401.3		32	204.143	odd	16
816.2.cj.c.401.4		32	68.7	even	16
816.2.cj.c.641.3		32	68.67	odd	2
816.2.cj.c.641.4		32	204.203	even	2
867.2.i.b.65.1		32	51.2	odd	8
867.2.i.b.65.4		32	17.2	even	8
867.2.i.b.827.1		32	17.5	odd	16
867.2.i.b.827.4		32	51.5	even	16
867.2.i.c.158.1		32	17.4	even	4
867.2.i.c.158.4		32	51.38	odd	4
867.2.i.c.653.1		32	51.11	even	16
867.2.i.c.653.4		32	17.11	odd	16
867.2.i.d.158.1		32	17.13	even	4
867.2.i.d.158.4		32	51.47	odd	4
867.2.i.d.653.1		32	51.23	even	16
867.2.i.d.653.4		32	17.6	odd	16
867.2.i.f.224.1		32	17.9	even	8
867.2.i.f.224.4		32	51.26	odd	8
867.2.i.f.329.1		32	51.20	even	16
867.2.i.f.329.4		32	17.3	odd	16
867.2.i.g.224.1		32	17.8	even	8
867.2.i.g.224.4		32	51.8	odd	8
867.2.i.g.329.1		32	51.14	even	16
867.2.i.g.329.4		32	17.14	odd	16
867.2.i.h.131.1		32	3.2	odd	2	inner
867.2.i.h.131.4		32	1.1	even	1	trivial
867.2.i.h.503.1		32	17.10	odd	16	inner
867.2.i.h.503.4		32	51.44	even	16	inner
867.2.i.i.65.1		32	51.32	odd	8
867.2.i.i.65.4		32	17.15	even	8
867.2.i.i.827.1		32	17.12	odd	16
867.2.i.i.827.4		32	51.29	even	16

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.i (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.34436 - 0.556851i) q^{2} +(0.961322 - 1.44078i) q^{3} +(0.0830021 - 0.0830021i) q^{4} +(-0.595296 + 2.99276i) q^{5} +(0.490059 - 2.47224i) q^{6} +(2.11533 - 0.420765i) q^{7} +(-1.04834 + 2.53091i) q^{8} +(-1.15172 - 2.77012i) q^{9} +(0.866229 + 4.35483i) q^{10} +(1.37013 + 0.915491i) q^{11} +(-0.0397964 - 0.199380i) q^{12} +(3.12551 + 3.12551i) q^{13} +(2.60946 - 1.74358i) q^{14} +(3.73965 + 3.73470i) q^{15} +4.22099i q^{16} +(-3.09087 - 3.08269i) q^{18} +(-0.330416 - 0.797694i) q^{19} +(0.198994 + 0.297816i) q^{20} +(1.42728 - 3.45222i) q^{21} +(2.35174 + 0.467790i) q^{22} +(-0.425893 + 0.637394i) q^{23} +(2.63871 + 3.94345i) q^{24} +(-3.98282 - 1.64974i) q^{25} +(5.94226 + 2.46136i) q^{26} +(-5.09831 - 1.00359i) q^{27} +(0.140652 - 0.210501i) q^{28} +(7.83789 + 1.55905i) q^{29} +(7.10709 + 2.93834i) q^{30} +(-1.60475 - 2.40167i) q^{31} +(0.253786 + 0.612694i) q^{32} +(2.63616 - 1.09398i) q^{33} +6.58114i q^{35} +(-0.325520 - 0.134330i) q^{36} +(1.98027 - 1.32318i) q^{37} +(-0.888394 - 0.888394i) q^{38} +(7.50782 - 1.49857i) q^{39} +(-6.95033 - 4.64406i) q^{40} +(-0.600791 - 3.02038i) q^{41} +(-0.00359897 - 5.43581i) q^{42} +(4.38037 - 10.5751i) q^{43} +(0.189711 - 0.0377359i) q^{44} +(8.97590 - 1.79778i) q^{45} +(-0.217619 + 1.09405i) q^{46} +(-2.21238 + 2.21238i) q^{47} +(6.08153 + 4.05773i) q^{48} +(-2.16958 + 0.898671i) q^{49} -6.27299 q^{50} +0.518848 q^{52} +(-5.88369 + 2.43710i) q^{53} +(-7.41281 + 1.48981i) q^{54} +(-3.55548 + 3.55548i) q^{55} +(-1.15266 + 5.79482i) q^{56} +(-1.46694 - 0.290783i) q^{57} +(11.4051 - 2.26861i) q^{58} +(2.33146 - 5.62864i) q^{59} +(0.620386 - 0.000410749i) q^{60} +(1.14061 + 5.73423i) q^{61} +(-3.49473 - 2.33510i) q^{62} +(-3.60183 - 5.37510i) q^{63} +(-5.28702 - 5.28702i) q^{64} +(-11.2145 + 7.49329i) q^{65} +(2.93476 - 2.93865i) q^{66} +7.19481i q^{67} +(0.508927 + 1.22636i) q^{69} +(3.66472 + 8.84742i) q^{70} +(-1.20808 - 1.80802i) q^{71} +(8.21831 - 0.0108825i) q^{72} +(-12.3377 - 2.45412i) q^{73} +(1.92538 - 2.88154i) q^{74} +(-6.20569 + 4.15245i) q^{75} +(-0.0936354 - 0.0387851i) q^{76} +(3.28348 + 1.36006i) q^{77} +(9.25872 - 6.19535i) q^{78} +(3.31013 - 4.95397i) q^{79} +(-12.6324 - 2.51274i) q^{80} +(-6.34708 + 6.38079i) q^{81} +(-2.48958 - 3.72592i) q^{82} +(-4.96993 - 11.9985i) q^{83} +(-0.168074 - 0.405009i) q^{84} -16.6560i q^{86} +(9.78099 - 9.79395i) q^{87} +(-3.75339 + 2.50793i) q^{88} +(3.42023 + 3.42023i) q^{89} +(11.0657 - 7.41510i) q^{90} +(7.92660 + 5.29638i) q^{91} +(0.0175550 + 0.0882551i) q^{92} +(-5.00297 + 0.00331239i) q^{93} +(-1.74226 + 4.20619i) q^{94} +(2.58400 - 0.513989i) q^{95} +(1.12673 + 0.223345i) q^{96} +(0.692072 - 3.47928i) q^{97} +(-2.41627 + 2.41627i) q^{98} +(0.958012 - 4.84981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{3} - 16 q^{4} + 8 q^{6} + 16 q^{7} - 8 q^{9} + 16 q^{10} - 16 q^{12} - 16 q^{13} + 16 q^{15} + 16 q^{18} - 16 q^{19} + 16 q^{21} + 16 q^{22} - 16 q^{24} + 16 q^{25} + 8 q^{27} - 32 q^{28} - 8 q^{30}+ \cdots + 64 q^{99}+O(q^{100}) \) 32 * q + 8 * q^3 - 16 * q^4 + 8 * q^6 + 16 * q^7 - 8 * q^9 + 16 * q^10 - 16 * q^12 - 16 * q^13 + 16 * q^15 + 16 * q^18 - 16 * q^19 + 16 * q^21 + 16 * q^22 - 16 * q^24 + 16 * q^25 + 8 * q^27 - 32 * q^28 - 8 * q^30 - 16 * q^31 + 8 * q^36 - 16 * q^37 + 24 * q^39 - 16 * q^40 - 56 * q^42 + 16 * q^43 + 40 * q^45 + 32 * q^46 + 64 * q^48 - 48 * q^49 - 96 * q^52 + 24 * q^54 - 48 * q^55 - 8 * q^57 + 48 * q^58 + 32 * q^60 + 32 * q^61 - 64 * q^63 + 16 * q^64 + 72 * q^66 + 80 * q^69 + 48 * q^70 + 64 * q^72 - 48 * q^73 - 88 * q^75 + 48 * q^76 - 96 * q^78 - 16 * q^79 + 48 * q^81 - 112 * q^82 - 56 * q^87 - 16 * q^88 + 88 * q^90 - 16 * q^91 - 72 * q^93 - 48 * q^94 + 112 * q^96 + 16 * q^97 + 64 * q^99

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