LMFDB - Embedded newform 867.2.i.h.131.1

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			131.1
Character	$\chi$	$=$	867.131
Dual form			867.2.i.h.503.1

$q$-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} +(1.69899 - 0.336782i) q^{3} +(0.0830021 - 0.0830021i) q^{4} +(0.595296 - 2.99276i) q^{5} +(-2.09652 + 1.39884i) q^{6} +(2.11533 - 0.420765i) q^{7} +(1.04834 - 2.53091i) q^{8} +(2.77316 - 1.14438i) q^{9} +(0.866229 + 4.35483i) q^{10} +(-1.37013 - 0.915491i) q^{11} +(0.113066 - 0.168973i) q^{12} +(3.12551 + 3.12551i) q^{13} +(-2.60946 + 1.74358i) q^{14} +(0.00349923 - 5.28516i) q^{15} +4.22099i q^{16} +(-3.09087 + 3.08269i) q^{18} +(-0.330416 - 0.797694i) q^{19} +(-0.198994 - 0.297816i) q^{20} +(3.45222 - 1.42728i) q^{21} +(2.35174 + 0.467790i) q^{22} +(0.425893 - 0.637394i) q^{23} +(0.928755 - 4.65306i) q^{24} +(-3.98282 - 1.64974i) q^{25} +(-5.94226 - 2.46136i) q^{26} +(4.32617 - 2.87824i) q^{27} +(0.140652 - 0.210501i) q^{28} +(-7.83789 - 1.55905i) q^{29} +(2.93834 + 7.10709i) q^{30} +(-1.60475 - 2.40167i) q^{31} +(-0.253786 - 0.612694i) q^{32} +(-2.63616 - 1.09398i) q^{33} -6.58114i q^{35} +(0.135192 - 0.325163i) q^{36} +(1.98027 - 1.32318i) q^{37} +(0.888394 + 0.888394i) q^{38} +(6.36284 + 4.25761i) q^{39} +(-6.95033 - 4.64406i) q^{40} +(0.600791 + 3.02038i) q^{41} +(-3.84624 + 3.84115i) q^{42} +(4.38037 - 10.5751i) q^{43} +(-0.189711 + 0.0377359i) q^{44} +(-1.77400 - 8.98063i) q^{45} +(-0.217619 + 1.09405i) q^{46} +(2.21238 - 2.21238i) q^{47} +(1.42155 + 7.17143i) q^{48} +(-2.16958 + 0.898671i) q^{49} +6.27299 q^{50} +0.518848 q^{52} +(5.88369 - 2.43710i) q^{53} +(-4.21317 + 6.27842i) q^{54} +(-3.55548 + 3.55548i) q^{55} +(1.15266 - 5.79482i) q^{56} +(-0.830022 - 1.24400i) q^{57} +(11.4051 - 2.26861i) q^{58} +(-2.33146 + 5.62864i) q^{59} +(-0.438389 - 0.438969i) q^{60} +(1.14061 + 5.73423i) q^{61} +(3.49473 + 2.33510i) q^{62} +(5.38462 - 3.58759i) q^{63} +(-5.28702 - 5.28702i) q^{64} +(11.2145 - 7.49329i) q^{65} +(4.15313 + 0.00274973i) q^{66} +7.19481i q^{67} +(0.508927 - 1.22636i) q^{69} +(3.66472 + 8.84742i) q^{70} +(1.20808 + 1.80802i) q^{71} +(0.0108825 - 8.21831i) q^{72} +(-12.3377 - 2.45412i) q^{73} +(-1.92538 + 2.88154i) q^{74} +(-7.32238 - 1.46155i) q^{75} +(-0.0936354 - 0.0387851i) q^{76} +(-3.28348 - 1.36006i) q^{77} +(-10.9248 - 2.18060i) q^{78} +(3.31013 - 4.95397i) q^{79} +(12.6324 + 2.51274i) q^{80} +(6.38079 - 6.34708i) q^{81} +(-2.48958 - 3.72592i) q^{82} +(4.96993 + 11.9985i) q^{83} +(0.168074 - 0.405009i) q^{84} +16.6560i q^{86} +(-13.8416 - 0.00916431i) q^{87} +(-3.75339 + 2.50793i) q^{88} +(-3.42023 - 3.42023i) q^{89} +(7.38576 + 11.0853i) q^{90} +(7.92660 + 5.29638i) q^{91} +(-0.0175550 - 0.0882551i) q^{92} +(-3.53529 - 3.53997i) q^{93} +(-1.74226 + 4.20619i) q^{94} +(-2.58400 + 0.513989i) q^{95} +(-0.637525 - 0.955492i) q^{96} +(0.692072 - 3.47928i) q^{97} +(2.41627 - 2.41627i) q^{98} +(-4.84725 - 0.970853i) 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	−0.803458	−	0.595361i	$-0.797009\pi$
$2$	−1.34436	+	0.556851i	−0.950605	+	0.393753i	−0.147147	+	0.989115i	$0.547009\pi$
$3$	1.69899	−	0.336782i	0.980914	−	0.194441i
$3$	1.69899	−	0.336782i	0.980914	−	0.194441i
$4$	0.0830021	−	0.0830021i	0.0415010	−	0.0415010i
$5$	0.595296	−	2.99276i	0.266225	−	1.33840i	−0.583902	−	0.811824i	$-0.698475\pi$
$5$	0.595296	−	2.99276i	0.266225	−	1.33840i	0.850127	−	0.526578i	$-0.176525\pi$
$6$	−2.09652	+	1.39884i	−0.855900	+	0.571075i
$7$	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
$9$	2.77316	−	1.14438i	0.924385	−	0.381460i
$10$	0.866229	+	4.35483i	0.273926	+	1.37712i
$11$	−1.37013	−	0.915491i	−0.413110	−	0.276031i	0.331599	−	0.943420i	$-0.392412\pi$
$11$	−1.37013	−	0.915491i	−0.413110	−	0.276031i	−0.744709	+	0.667389i	$0.767412\pi$
$12$	0.113066	−	0.168973i	0.0326395	−	0.0487784i
$13$	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
$15$	0.00349923	−	5.28516i	0.000903497	−	1.36462i
$16$			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
$21$	3.45222	−	1.42728i	0.753337	−	0.311458i
$22$	2.35174	+	0.467790i	0.501392	+	0.0997331i
$23$	0.425893	−	0.637394i	0.0888049	−	0.132906i	−0.784407	−	0.620246i	$-0.787033\pi$
$23$	0.425893	−	0.637394i	0.0888049	−	0.132906i	0.873212	+	0.487340i	$0.162033\pi$
$24$	0.928755	−	4.65306i	0.189581	−	0.949803i
$25$	−3.98282	−	1.64974i	−0.796563	−	0.329947i
$26$	−5.94226	−	2.46136i	−1.16537	−	0.482713i
$27$	4.32617	−	2.87824i	0.832571	−	0.553918i
$28$	0.140652	−	0.210501i	0.0265808	−	0.0397810i
$29$	−7.83789	−	1.55905i	−1.45546	−	0.289509i	−0.596938	−	0.802287i	$-0.703616\pi$
$29$	−7.83789	−	1.55905i	−1.45546	−	0.289509i	−0.858521	+	0.512778i	$0.828616\pi$
$30$	2.93834	+	7.10709i	0.536466	+	1.29757i
$31$	−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
$36$	0.135192	−	0.325163i	0.0225320	−	0.0541939i
$37$	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
$39$	6.36284	+	4.25761i	1.01887	+	0.681763i
$40$	−6.95033	−	4.64406i	−1.09894	−	0.734291i
$41$	0.600791	+	3.02038i	0.0938278	+	0.471704i	0.998919	+	0.0464865i	$0.0148024\pi$
$41$	0.600791	+	3.02038i	0.0938278	+	0.471704i	−0.905091	+	0.425218i	$0.860198\pi$
$42$	−3.84624	+	3.84115i	−0.593488	+	0.592703i
$43$	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
$45$	−1.77400	−	8.98063i	−0.264452	−	1.33875i
$46$	−0.217619	+	1.09405i	−0.0320862	+	0.161308i
$47$	2.21238	−	2.21238i	0.322708	−	0.322708i	−0.527097	−	0.849805i	$-0.676719\pi$
$47$	2.21238	−	2.21238i	0.322708	−	0.322708i	0.849805	+	0.527097i	$0.176719\pi$
$48$	1.42155	+	7.17143i	0.205183	+	1.03511i
$49$	−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	0.0599567	−	0.998201i	$-0.480904\pi$
$53$	5.88369	−	2.43710i	0.808187	−	0.334762i	0.748230	+	0.663439i	$0.230904\pi$
$54$	−4.21317	+	6.27842i	−0.573340	+	0.854385i
$55$	−3.55548	+	3.55548i	−0.479420	+	0.479420i
$56$	1.15266	−	5.79482i	0.154031	−	0.774365i
$57$	−0.830022	−	1.24400i	−0.109939	−	0.164772i
$58$	11.4051	−	2.26861i	1.49756	−	0.297884i
$59$	−2.33146	+	5.62864i	−0.303530	+	0.732786i	0.696356	+	0.717696i	$0.254803\pi$
$59$	−2.33146	+	5.62864i	−0.303530	+	0.732786i	−0.999886	+	0.0150898i	$0.995197\pi$
$60$	−0.438389	−	0.438969i	−0.0565957	−	0.0566707i
$61$	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
$63$	5.38462	−	3.58759i	0.678399	−	0.451993i
$64$	−5.28702	−	5.28702i	−0.660877	−	0.660877i
$65$	11.2145	−	7.49329i	1.39099	−	0.929429i
$66$	4.15313	+	0.00274973i	0.511215	+	0.000338468i
$67$			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	0.896205	−	0.443639i	$-0.146313\pi$
$71$	1.20808	+	1.80802i	0.143373	+	0.214573i	−0.752832	+	0.658212i	$0.771313\pi$
$72$	0.0108825	−	8.21831i	0.00128251	−	0.968537i
$73$	−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
$75$	−7.32238	−	1.46155i	−0.845516	−	0.168766i
$76$	−0.0936354	−	0.0387851i	−0.0107407	−	0.00444895i
$77$	−3.28348	−	1.36006i	−0.374187	−	0.154994i
$78$	−10.9248	−	2.18060i	−1.23699	−	0.246904i
$79$	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
$81$	6.38079	−	6.34708i	0.708977	−	0.705232i
$82$	−2.48958	−	3.72592i	−0.274928	−	0.411459i
$83$	4.96993	+	11.9985i	0.545521	+	1.31700i	0.920779	+	0.390084i	$0.127554\pi$
$83$	4.96993	+	11.9985i	0.545521	+	1.31700i	−0.375258	+	0.926920i	$0.622446\pi$
$84$	0.168074	−	0.405009i	0.0183384	−	0.0441901i
$85$		0			0
$86$			16.6560i			1.79606i
$87$	−13.8416	−	0.00916431i	−1.48397	−	0.000982518i
$88$	−3.75339	+	2.50793i	−0.400112	+	0.267347i
$89$	−3.42023	−	3.42023i	−0.362544	−	0.362544i	0.502205	−	0.864749i	$-0.332522\pi$
$89$	−3.42023	−	3.42023i	−0.362544	−	0.362544i	−0.864749	+	0.502205i	$0.832522\pi$
$90$	7.38576	+	11.0853i	0.778528	+	1.16850i
$91$	7.92660	+	5.29638i	0.830933	+	0.555212i
$92$	−0.0175550	−	0.0882551i	−0.00183024	−	0.00920123i
$93$	−3.53529	−	3.53997i	−0.366592	−	0.367078i
$94$	−1.74226	+	4.20619i	−0.179701	+	0.433836i
$95$	−2.58400	+	0.513989i	−0.265113	+	0.0527342i
$96$	−0.637525	−	0.955492i	−0.0650671	−	0.0975195i
$97$	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
$99$	−4.84725	−	0.970853i	−0.487167	−	0.0975744i
$100$	−0.467514	+	0.193650i	−0.0467514	+	0.0193650i
$101$	3.73948			0.372092			0.186046	−	0.982541i	$-0.440433\pi$
$101$	3.73948			0.372092			0.186046	+	0.982541i	$0.440433\pi$
$102$		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
$105$	−2.21641	−	11.1813i	−0.216299	−	1.09119i
$106$	−6.55268	+	6.55268i	−0.636453	+	0.636453i
$107$	−0.368714	+	1.85365i	−0.0356449	+	0.179199i	−0.994506	−	0.104675i	$-0.966620\pi$
$107$	−0.368714	+	1.85365i	−0.0356449	+	0.179199i	0.958862	+	0.283874i	$0.0916198\pi$
$108$	0.120181	−	0.597981i	0.0115644	−	0.0575407i
$109$	−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
$111$	2.91885	−	2.91499i	0.277045	−	0.276678i
$112$	1.77604	+	8.92878i	0.167820	+	0.843690i
$113$	13.7072	+	9.15888i	1.28947	+	0.861595i	0.995550	−	0.0942363i	$-0.0300409\pi$
$113$	13.7072	+	9.15888i	1.28947	+	0.861595i	0.293917	+	0.955831i	$0.405041\pi$
$114$	1.80857	+	1.21018i	0.169388	+	0.113344i
$115$	−1.65403	−	1.65403i	−0.154239	−	0.154239i
$116$	−0.779965	+	0.521156i	−0.0724180	+	0.0483881i
$117$	12.2443	+	5.09076i	1.13199	+	0.470641i
$118$		−	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
$123$	2.03795	+	4.92927i	0.183756	+	0.444457i
$124$	−0.332541	−	0.0661465i	−0.0298630	−	0.00594013i
$125$	1.16808	−	1.74816i	0.104477	−	0.156360i
$126$	−5.24111	+	7.82144i	−0.466915	+	0.696789i
$127$	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
$129$	3.88070	−	19.4423i	0.341677	−	1.71180i
$130$	−10.9037	+	16.3185i	−0.956315	+	1.43123i
$131$	−3.45873	−	0.687984i	−0.302191	−	0.0601094i	0.0416661	−	0.999132i	$-0.486733\pi$
$131$	−3.45873	−	0.687984i	−0.302191	−	0.0601094i	−0.343857	+	0.939022i	$0.611733\pi$
$132$	−0.309609	+	0.128004i	−0.0269480	+	0.0111413i
$133$	−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	$-0.784794\pi$
$137$		−	14.6484i		−	1.25150i	0.780025	−	0.625748i	$-0.215206\pi$
$138$	−0.00127919	+	1.93207i	−0.000108892	+	0.164468i
$139$	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
$141$	3.01373	−	4.50390i	0.253802	−	0.379297i
$142$	−2.63090	−	1.75791i	−0.220780	−	0.147520i
$143$	−1.42098	−	7.14374i	−0.118828	−	0.597389i
$144$	4.83041	+	11.7055i	0.402534	+	0.975455i
$145$	−9.33173	+	22.5288i	−0.774958	+	1.87091i
$146$	17.9529	−	3.57105i	1.48579	−	0.295542i
$147$	−3.38345	+	2.25751i	−0.279062	+	0.186196i
$148$	0.0545404	−	0.274193i	0.00448319	−	0.0225385i
$149$	−4.44785	+	4.44785i	−0.364382	+	0.364382i	−0.865423	−	0.501041i	$-0.832950\pi$
$149$	−4.44785	+	4.44785i	−0.364382	+	0.364382i	0.501041	+	0.865423i	$0.332950\pi$
$150$	10.6578	−	2.11263i	0.870203	−	0.172495i
$151$	−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
$156$	0.881519	−	0.174738i	0.0705780	−	0.0139903i
$157$	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
$159$	9.17558	−	6.12214i	0.727671	−	0.485518i
$160$	−1.98472	+	0.394786i	−0.156906	+	0.0312105i
$161$	0.632711	−	1.52750i	0.0498646	−	0.120384i
$162$	−5.04369	+	12.0859i	−0.396270	+	0.949559i
$163$	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
$165$	−4.84331	+	7.23815i	−0.377051	+	0.563489i
$166$	−13.3627	−	13.3627i	−1.03715	−	1.03715i
$167$	−16.5131	+	11.0337i	−1.27782	+	0.853815i	−0.994452	−	0.105195i	$-0.966453\pi$
$167$	−16.5131	+	11.0337i	−1.27782	+	0.853815i	−0.283373	+	0.959010i	$0.591453\pi$
$168$	0.00677549	−	10.2335i	0.000522740	−	0.789535i
$169$			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	0.991453	−	0.130465i	$-0.0416470\pi$
$173$	6.46476	+	9.67520i	0.491507	+	0.735591i	−0.499946	+	0.866056i	$0.666647\pi$
$174$	18.6131	−	7.69538i	1.41106	−	0.583385i
$175$	−9.11912	−	1.81391i	−0.689341	−	0.137118i
$176$	3.86428	−	5.78330i	0.291281	−	0.435933i
$177$	−2.06551	+	10.3482i	−0.155253	+	0.777819i
$178$	6.50257	+	2.69345i	0.487389	+	0.201883i
$179$	0.782216	+	0.324004i	0.0584656	+	0.0242172i	0.411725	−	0.911308i	$-0.364927\pi$
$179$	0.782216	+	0.324004i	0.0584656	+	0.0242172i	−0.353259	+	0.935526i	$0.614927\pi$
$180$	−0.892656	−	0.598165i	−0.0665347	−	0.0445846i
$181$	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
$183$	3.86907	+	9.35828i	0.286010	+	0.691784i
$184$	−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
$189$	7.94021	−	7.90873i	0.577565	−	0.575275i
$190$	3.18760	−	2.12989i	0.231253	−	0.154518i
$191$	−0.509849	−	0.509849i	−0.0368914	−	0.0368914i	0.688420	−	0.725312i	$-0.258304\pi$
$191$	−0.509849	−	0.509849i	−0.0368914	−	0.0368914i	−0.725312	+	0.688420i	$0.758304\pi$
$192$	−10.7632	−	7.20204i	−0.776765	−	0.519762i
$193$	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
$195$	16.5298	−	16.5079i	1.18372	−	1.18215i
$196$	−0.105488	+	0.254671i	−0.00753488	+	0.0181908i
$197$	−22.8170	+	4.53858i	−1.62564	+	0.323360i	−0.921999	−	0.387193i	$-0.873445\pi$
$197$	−22.8170	+	4.53858i	−1.62564	+	0.323360i	−0.703643	+	0.710553i	$0.748445\pi$
$198$	7.05706	−	1.39403i	0.501524	−	0.0990691i
$199$	−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
$201$	2.42308	+	12.2239i	0.170911	+	0.862209i
$202$	−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
$207$	0.451648	−	2.25498i	0.0313917	−	0.156732i
$208$	−13.1927	+	13.1927i	−0.914753	+	0.914753i
$209$	−0.277570	+	1.39544i	−0.0191999	+	0.0965244i
$210$	9.20598	+	13.7975i	0.635273	+	0.952117i
$211$	−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
$213$	2.66143	+	2.66496i	0.182358	+	0.182600i
$214$	−0.536524	−	2.69729i	−0.0366760	−	0.184383i
$215$	−29.0412	−	19.4047i	−1.98059	−	1.32339i
$216$	−2.74929	−	13.9665i	−0.187065	−	0.950301i
$217$	−4.40510	−	4.40510i	−0.299038	−	0.299038i
$218$	5.08520	−	3.39782i	0.344413	−	0.230130i
$219$	−21.7882	−	0.0144256i	−1.47231	−	0.000974794i
$220$			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
$225$	−12.9329	−	0.0171254i	−0.862193	−	0.00114169i
$226$	−23.5276	−	4.67992i	−1.56503	−	0.311304i
$227$	−0.780250	+	1.16773i	−0.0517870	+	0.0775048i	−0.856460	−	0.516214i	$-0.827341\pi$
$227$	−0.780250	+	1.16773i	−0.0517870	+	0.0775048i	0.804673	+	0.593719i	$0.202341\pi$
$228$	−0.172148	−	0.0343609i	−0.0114008	−	0.00227560i
$229$	−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
$231$	−6.03666	−	1.20492i	−0.397183	−	0.0792780i
$232$	−12.1626	+	18.2026i	−0.798513	+	1.19506i
$233$	14.0608	+	2.79686i	0.921151	+	0.183228i	0.632817	−	0.774302i	$-0.281899\pi$
$233$	14.0608	+	2.79686i	0.921151	+	0.183228i	0.288334	+	0.957530i	$0.406899\pi$
$234$	−19.2955	−	0.0255506i	−1.26139	−	0.00167030i
$235$	−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	$0.278158\pi$
$239$			23.7093i			1.53362i	−0.641872	+	0.766812i	$0.721842\pi$
$240$	22.3086	+	0.0147702i	1.44001	+	0.000953412i
$241$	−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
$243$	8.70334	−	12.9326i	0.558320	−	0.829626i
$244$	0.570626	+	0.381280i	0.0365306	+	0.0244090i
$245$	1.39796	+	7.02801i	0.0893123	+	0.449003i
$246$	−5.48460	−	5.49187i	−0.349686	−	0.350149i
$247$	1.46048	−	3.52592i	0.0929284	−	0.224349i
$248$	−7.76073	+	1.54371i	−0.492807	+	0.0980254i
$249$	12.4847	+	18.7116i	0.791189	+	1.18580i
$250$	−0.596858	+	3.00061i	−0.0377486	+	0.189775i
$251$	−10.7058	+	10.7058i	−0.675745	+	0.675745i	−0.959034	−	0.283289i	$-0.908574\pi$
$251$	−10.7058	+	10.7058i	−0.675745	+	0.675745i	0.283289	+	0.959034i	$0.408574\pi$
$252$	0.149158	−	0.744712i	0.00939606	−	0.0469124i
$253$	−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	−0.873360	−	0.487075i	$-0.838064\pi$
$257$	−18.3799	+	7.61319i	−1.14650	+	0.474898i	−0.273145	+	0.961973i	$0.588064\pi$
$258$	5.60943	+	28.2984i	0.349228	+	1.76178i
$259$	3.63218	−	3.63218i	0.225693	−	0.225693i
$260$	0.308868	−	1.55279i	0.0191552	−	0.0962997i
$261$	−23.5198	+	4.64602i	−1.45584	+	0.287581i
$262$	5.03288	−	1.00110i	0.310932	−	0.0618482i
$263$	0.0501727	−	0.121128i	0.00309378	−	0.00746905i	−0.922325	−	0.386415i	$-0.873713\pi$
$263$	0.0501727	−	0.121128i	0.00309378	−	0.00746905i	0.925419	+	0.378946i	$0.123713\pi$
$264$	−5.53235	+	5.52503i	−0.340493	+	0.340042i
$265$	−3.79112	−	19.0593i	−0.232887	−	1.17080i
$266$	2.25305	+	1.50544i	0.138143	+	0.0923045i
$267$	−6.96282	−	4.65908i	−0.426118	−	0.285131i
$268$	0.597184	+	0.597184i	0.0364788	+	0.0364788i
$269$	4.94355	−	3.30317i	0.301413	−	0.201398i	−0.395661	−	0.918396i	$-0.629485\pi$
$269$	4.94355	−	3.30317i	0.301413	−	0.201398i	0.697075	+	0.716999i	$0.254485\pi$
$270$	16.2817	+	16.3465i	0.990873	+	0.994817i
$271$		−	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
$276$	−0.0595485	−	0.144033i	−0.00358440	−	0.00866974i
$277$	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
$279$	−7.19863	−	4.82377i	−0.430971	−	0.288792i
$280$	−16.6563	−	6.89927i	−0.995404	−	0.412310i
$281$	12.2411	+	5.07041i	0.730240	+	0.302475i	0.716651	−	0.697432i	$-0.245674\pi$
$281$	12.2411	+	5.07041i	0.730240	+	0.302475i	0.0135893	+	0.999908i	$0.495674\pi$
$282$	−1.54352	+	7.73306i	−0.0919155	+	0.460497i
$283$	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
$285$	−4.21709	+	1.74351i	−0.249799	+	0.103276i
$286$	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
$291$	0.00406809	−	6.14435i	0.000238475	−	0.360188i
$292$	−1.22775	+	0.820357i	−0.0718487	+	0.0480078i
$293$	18.6721	+	18.6721i	1.09083	+	1.09083i	0.995440	+	0.0953949i	$0.0304114\pi$
$293$	18.6721	+	18.6721i	1.09083	+	1.09083i	0.0953949	+	0.995440i	$0.469589\pi$
$294$	3.29147	−	4.91898i	0.191963	−	0.286881i
$295$	15.4572	+	10.3282i	0.899955	+	0.601331i
$296$	−1.27285	−	6.39904i	−0.0739827	−	0.371936i
$297$	−8.56241	−	0.0170072i	−0.496842	−	0.000986857i
$298$	3.50271	−	8.45629i	0.202907	−	0.489860i
$299$	3.32332	−	0.661049i	0.192193	−	0.0382295i
$300$	−0.729085	+	0.486461i	−0.0420937	+	0.0280858i
$301$	4.81627	−	24.2130i	0.277605	−	1.39561i
$302$	15.6531	−	15.6531i	0.900738	−	0.900738i
$303$	6.35335	−	1.25939i	0.364990	−	0.0723499i
$304$	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
$309$	15.8585	−	3.14353i	0.902157	−	0.178829i
$310$	9.06879	−	9.06879i	0.515073	−	0.515073i
$311$	−4.55265	+	22.8877i	−0.258157	+	1.29784i	0.606340	+	0.795206i	$0.292637\pi$
$311$	−4.55265	+	22.8877i	−0.258157	+	1.29784i	−0.864497	+	0.502638i	$0.832363\pi$
$312$	17.4460	−	11.6404i	0.987688	−	0.659007i
$313$	−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
$315$	−7.53133	−	18.2505i	−0.424342	−	1.02830i
$316$	−0.136441	−	0.685937i	−0.00767543	−	0.0385870i
$317$	−20.2754	−	13.5476i	−1.13878	−	0.760908i	−0.164528	−	0.986372i	$-0.552610\pi$
$317$	−20.2754	−	13.5476i	−1.13878	−	0.760908i	−0.974251	+	0.225464i	$0.927610\pi$
$318$	−8.92614	+	13.3398i	−0.500553	+	0.748058i
$319$	9.31162	+	9.31162i	0.521351	+	0.521351i
$320$	−18.9701	+	12.6754i	−1.06046	+	0.708577i
$321$	−0.00216735	+	3.27351i	−0.000120970	+	0.182710i
$322$			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
$327$	−6.72755	+	2.78143i	−0.372034	+	0.153813i
$328$	8.27415	+	1.64583i	0.456863	+	0.0908758i
$329$	3.74901	−	5.61080i	0.206690	−	0.309333i
$330$	2.48057	−	12.4277i	0.136551	−	0.684121i
$331$	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
$333$	3.97739	−	5.93556i	0.217960	−	0.325267i
$334$	16.0554	−	24.0286i	0.878514	−	1.31479i
$335$	21.5323	+	4.28304i	1.17644	+	0.234008i
$336$	6.02453	+	14.5718i	0.328665	+	0.794956i
$337$	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
$342$	3.48031	+	1.44700i	0.188194	+	0.0782446i
$343$	−16.7643	+	11.2015i	−0.905186	+	0.604826i
$344$	−22.1727	−	22.1727i	−1.19547	−	1.19547i
$345$	−3.36724	−	2.25314i	−0.181286	−	0.121305i
$346$	−14.0786	−	9.40702i	−0.756870	−	0.505724i
$347$	3.94759	+	19.8459i	0.211918	+	1.06538i	0.929476	+	0.368884i	$0.120260\pi$
$347$	3.94759	+	19.8459i	0.211918	+	1.06538i	−0.717558	+	0.696499i	$0.754740\pi$
$348$	−1.14964	+	1.14812i	−0.0616272	+	0.0615456i
$349$	−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
$351$	22.5175	+	4.52552i	1.20189	+	0.241554i
$352$	−0.213196	+	1.07181i	−0.0113634	+	0.0571276i
$353$	8.44344	−	8.44344i	0.449399	−	0.449399i	−0.445756	−	0.895155i	$-0.647065\pi$
$353$	8.44344	−	8.44344i	0.449399	−	0.449399i	0.895155	+	0.445756i	$0.147065\pi$
$354$	−2.98563	−	15.0619i	−0.158684	−	0.800530i
$355$	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	0.256531	−	0.966536i	$-0.417420\pi$
$359$	21.2469	−	8.80076i	1.12137	−	0.464487i	0.864839	+	0.502049i	$0.167420\pi$
$360$	−24.5889	−	4.92490i	−1.29595	−	0.259565i
$361$	12.9079	−	12.9079i	0.679363	−	0.679363i
$362$	−0.407040	+	2.04633i	−0.0213935	+	0.107553i
$363$	−7.96419	−	11.9364i	−0.418012	−	0.626496i
$364$	1.09753	−	0.218313i	0.0575264	−	0.0114427i
$365$	−14.6892	+	35.4628i	−0.768866	+	1.85621i
$366$	−10.4126	−	10.4264i	−0.544275	−	0.544996i
$367$	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
$369$	5.12255	+	7.68845i	0.266669	+	0.400245i
$370$	7.47758	+	7.47758i	0.388741	+	0.388741i
$371$	11.4205	−	7.63093i	0.592923	−	0.396178i
$372$	−0.587261		0.000388817i	−0.0304481		2.01592e-5i
$373$			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
$378$	−6.27050	+	15.0537i	−0.322520	+	0.774278i
$379$	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
$381$	20.9134	+	4.17432i	1.07142	+	0.213857i
$382$	0.969330	+	0.401510i	0.0495952	+	0.0205430i
$383$	−20.4588	−	8.47433i	−1.04540	−	0.433018i	−0.207151	−	0.978309i	$-0.566419\pi$
$383$	−20.4588	−	8.47433i	−1.04540	−	0.433018i	−0.838247	+	0.545291i	$0.816419\pi$
$384$	20.7329	+	4.13830i	1.05802	+	0.211182i
$385$	−6.02498	+	9.01702i	−0.307061	+	0.459550i
$386$	−16.5858	−	3.29912i	−0.844194	−	0.167921i
$387$	0.0454712	−	34.3393i	0.00231143	−	1.74557i
$388$	−0.231344	−	0.346231i	−0.0117447	−	0.0175772i
$389$	−5.80572	−	14.0162i	−0.294362	−	0.710652i	−0.999998	−	0.00207747i	$-0.999339\pi$
$389$	−5.80572	−	14.0162i	−0.294362	−	0.710652i	0.705636	−	0.708574i	$-0.250661\pi$
$390$	−13.0295	+	31.3972i	−0.659774	+	1.58986i
$391$		0			0
$392$			6.43314i			0.324922i
$393$	−6.10806	−	0.00404406i	−0.308111	−	0.000203996i
$394$	28.1469	−	18.8071i	1.41802	−	0.947490i
$395$	−12.8555	−	12.8555i	−0.646831	−	0.646831i
$396$	−0.482915	+	0.321749i	−0.0242674	+	0.0161685i
$397$	−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
$399$	−2.27920	−	2.28222i	−0.114103	−	0.114254i
$400$	6.96352	−	16.8114i	0.348176	−	0.840571i
$401$	3.46595	−	0.689420i	0.173081	−	0.0344280i	−0.107789	−	0.994174i	$-0.534377\pi$
$401$	3.46595	−	0.689420i	0.173081	−	0.0344280i	0.280870	+	0.959746i	$0.409377\pi$
$402$	−10.0644	−	15.0840i	−0.501966	−	0.752324i
$403$	2.49080	−	12.5221i	0.124076	−	0.623770i
$404$	0.310384	−	0.310384i	0.0154422	−	0.0154422i
$405$	−15.1968	−	22.8746i	−0.755136	−	1.13665i
$406$	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
$411$	−4.93331	−	24.8875i	−0.243342	−	1.22761i
$412$	0.774744	−	0.774744i	0.0381689	−	0.0381689i
$413$	−2.56347	+	12.8874i	−0.126140	+	0.634148i
$414$	0.648511	+	3.28300i	0.0318726	+	0.161351i
$415$	38.8671	−	7.73115i	1.90791	−	0.379507i
$416$	1.12177	−	2.70819i	0.0549993	−	0.132780i
$417$	6.18246	−	6.17428i	0.302756	−	0.302356i
$418$	−0.403898	−	2.03053i	−0.0197553	−	0.0993165i
$419$	26.1021	+	17.4409i	1.27517	+	0.852042i	0.994187	−	0.107670i	$-0.0343389\pi$
$419$	26.1021	+	17.4409i	1.27517	+	0.852042i	0.280985	+	0.959712i	$0.409339\pi$
$420$	−1.11204	−	0.744106i	−0.0542619	−	0.0363087i
$421$	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
$423$	3.60347	−	8.66707i	0.175207	−	0.421407i
$424$		−	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
$429$	−4.82011	−	11.6586i	−0.232717	−	0.562883i
$430$	49.8473	+	9.91525i	2.40385	+	0.478156i
$431$	−6.36331	+	9.52337i	−0.306510	+	0.458724i	−0.952464	−	0.304652i	$-0.901460\pi$
$431$	−6.36331	+	9.52337i	−0.306510	+	0.458724i	0.645954	+	0.763376i	$0.276460\pi$
$432$	12.1490	+	18.2607i	0.584520	+	0.878568i
$433$	−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
$435$	−8.26727	+	41.4190i	−0.396385	+	1.98589i
$436$	−0.274097	+	0.410216i	−0.0131269	+	0.0196458i
$437$	−0.649167	−	0.129127i	−0.0310539	−	0.00617700i
$438$	29.2991	−	12.1134i	1.39997	−	0.578799i
$439$	−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	$0.148021\pi$
$443$			18.8773i			0.896886i	−0.893811	+	0.448443i	$0.851979\pi$
$444$	0.000320596	−	0.484221i	1.52148e−5	−	0.0229801i
$445$	−12.2720	+	8.19987i	−0.581747	+	0.388711i
$446$	−2.50244	−	2.50244i	−0.118494	−	0.118494i
$447$	−6.05891	+	9.05482i	−0.286577	+	0.428278i
$448$	−13.4084	−	8.95919i	−0.633486	−	0.423282i
$449$	−5.31908	−	26.7408i	−0.251023	−	1.26198i	−0.876373	−	0.481633i	$-0.840044\pi$
$449$	−5.31908	−	26.7408i	−0.251023	−	1.26198i	0.625350	−	0.780345i	$-0.284956\pi$
$450$	17.3960	−	7.17868i	0.820055	−	0.338406i
$451$	1.94197	−	4.68833i	0.0914438	−	0.220765i
$452$	1.89793	−	0.377522i	0.0892713	−	0.0177572i
$453$	−21.9188	+	14.6247i	−1.02983	+	0.687127i
$454$	0.398685	−	2.00433i	0.0187112	−	0.0940677i
$455$	20.5695	−	20.5695i	0.964311	−	0.964311i
$456$	−4.01860	+	0.796583i	−0.188188	+	0.0373034i
$457$	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	−0.159693	−	0.987167i	$-0.551050\pi$
$461$	9.13414	−	3.78349i	0.425419	−	0.176215i	0.585112	+	0.810952i	$0.301050\pi$
$462$	8.78639	−	1.74168i	0.408780	−	0.0810301i
$463$	−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
$465$	−12.6988	+	8.47293i	−0.588894	+	0.392923i
$466$	−20.4601	+	4.06977i	−0.947797	+	0.188529i
$467$	9.89105	−	23.8791i	0.457703	−	1.10499i	−0.511621	−	0.859211i	$-0.670955\pi$
$467$	9.89105	−	23.8791i	0.457703	−	1.10499i	0.969325	−	0.245783i	$-0.0790450\pi$
$468$	1.43885	−	0.593759i	0.0665107	−	0.0274465i
$469$	3.02732	+	15.2194i	0.139789	+	0.702766i
$470$	11.5509	+	7.71810i	0.532806	+	0.356009i
$471$	2.37742	−	3.55297i	0.109546	−	0.163712i
$472$	11.8014	+	11.8014i	0.543205	+	0.543205i
$473$	−15.6831	+	10.4791i	−0.721111	+	0.481831i
$474$	−0.00994217	+	15.0164i	−0.000456659	+	0.689728i
$475$			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	0.924992	−	0.379987i	$-0.124072\pi$
$479$	4.81385	+	7.20443i	0.219950	+	0.329179i	−0.705041	+	0.709166i	$0.749072\pi$
$480$	−3.23907	+	1.33916i	−0.147843	+	0.0611238i
$481$	10.3250	+	2.05377i	0.470778	+	0.0936437i
$482$	2.27521	−	3.40509i	0.103633	−	0.155098i
$483$	0.560538	−	2.80830i	0.0255054	−	0.127782i
$484$	−0.898446	−	0.372148i	−0.0408384	−	0.0169158i
$485$	−10.0006	−	4.14240i	−0.454106	−	0.188097i
$486$	−4.49888	+	22.2325i	−0.204073	+	1.00849i
$487$	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
$489$	0.735143	+	1.77812i	0.0332443	+	0.0804094i
$490$	−5.79291	−	8.66971i	−0.261697	−	0.391658i
$491$	4.84934	+	11.7073i	0.218848	+	0.528345i	0.994730	−	0.102533i	$-0.0326948\pi$
$491$	4.84934	+	11.7073i	0.218848	+	0.528345i	−0.775882	+	0.630878i	$0.782695\pi$
$492$	0.578293	+	0.239986i	0.0260715	+	0.0108194i
$493$		0			0
$494$			5.55337i			0.249858i
$495$	−5.79108	+	13.9287i	−0.260290	+	0.626049i
$496$	10.1374	−	6.77361i	0.455184	−	0.304144i
$497$	3.31625	+	3.31625i	0.148754	+	0.148754i
$498$	−27.2035	−	18.2029i	−1.21902	−	0.815691i
$499$	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
$501$	−24.3397	+	24.3075i	−1.08742	+	1.08598i
$502$	8.43090	−	20.3540i	0.376290	−	0.908444i
$503$	31.3353	−	6.23297i	1.39717	−	0.277914i	0.561650	−	0.827375i	$-0.310167\pi$
$503$	31.3353	−	6.23297i	1.39717	−	0.277914i	0.835520	+	0.549460i	$0.185167\pi$
$504$	−3.43496	−	17.3890i	−0.153005	−	0.774568i
$505$	2.22610	−	11.1913i	0.0990600	−	0.498008i
$506$	1.29976	−	1.29976i	0.0577812	−	0.0577812i
$507$	2.20176	+	11.1074i	0.0977838	+	0.493299i
$508$	1.33526	−	0.553083i	0.0592426	−	0.0245391i
$509$	−2.30289			−0.102074			−0.0510369	−	0.998697i	$-0.516253\pi$
$509$	−2.30289			−0.102074			−0.0510369	+	0.998697i	$0.516253\pi$
$510$		0			0
$511$	−27.1309			−1.20020
$512$	−18.7797	+	7.77882i	−0.829954	+	0.343778i
$513$	−3.72539	−	2.49994i	−0.164480	−	0.110375i
$514$	20.4697	−	20.4697i	0.902880	−	0.902880i
$515$	5.55652	−	27.9345i	0.244849	−	1.23094i
$516$	−1.29165	−	1.93586i	−0.0568616	−	0.0852214i
$517$	−5.05666	+	1.00583i	−0.222391	+	0.0442364i
$518$	−2.86037	+	6.90554i	−0.125677	+	0.303412i
$519$	14.2420	+	14.2609i	0.625155	+	0.625983i
$520$	−7.20827	−	36.2384i	−0.316104	−	1.58916i
$521$	2.28875	+	1.52929i	0.100272	+	0.0669995i	0.604695	−	0.796457i	$-0.293295\pi$
$521$	2.28875	+	1.52929i	0.100272	+	0.0669995i	−0.504423	+	0.863456i	$0.668295\pi$
$522$	29.0319	−	19.3430i	1.27069	−	0.846619i
$523$	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
$525$	−16.1042	−	0.0106624i	−0.702846	−	0.000465344i
$526$			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
$531$	−0.0242021	+	18.2772i	−0.00105028	+	0.793161i
$532$	−0.214389	−	0.0426446i	−0.00929494	−	0.00184888i
$533$	−7.56246	+	11.3180i	−0.327566	+	0.490238i
$534$	11.9549	+	2.38621i	0.517341	+	0.103262i
$535$	5.32803	+	2.20694i	0.230351	+	0.0954144i
$536$	18.2094	+	7.54259i	0.786527	+	0.325790i
$537$	1.43810	+	0.287045i	0.0620585	+	0.0123869i
$538$	−4.80652	+	7.19347i	−0.207224	+	0.310132i
$539$	3.79534	+	0.754939i	0.163477	+	0.0325175i
$540$	−1.71807	−	0.715648i	−0.0739339	−	0.0307966i
$541$	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
$546$	−24.0271	−	0.0159080i	−1.02826	−	0.000680798i
$547$	−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
$549$	9.72522	+	14.5966i	0.415062	+	0.622969i
$550$	−8.59481	−	5.74287i	−0.366484	−	0.244877i
$551$	1.34611	+	6.76737i	0.0573464	+	0.288300i
$552$	−2.57029	−	2.57369i	−0.109399	−	0.109544i
$553$	4.91757	−	11.8721i	0.209116	−	0.504851i
$554$	−11.8417	+	2.35547i	−0.503107	+	0.100074i
$555$	−6.98627	−	10.4707i	−0.296551	−	0.444456i
$556$	0.115523	−	0.580773i	0.00489926	−	0.0246302i
$557$	−31.0707	+	31.0707i	−1.31651	+	1.31651i	−0.399984	+	0.916522i	$0.630984\pi$
$557$	−31.0707	+	31.0707i	−1.31651	+	1.31651i	−0.916522	+	0.399984i	$0.869016\pi$
$558$	12.3637	+	2.47631i	0.523396	+	0.104831i
$559$	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	0.471821	−	0.881695i	$-0.343597\pi$
$563$	33.9044	−	14.0437i	1.42890	−	0.591870i	0.957080	+	0.289825i	$0.0935970\pi$
$564$	−0.123688	−	0.623979i	−0.00520819	−	0.0262742i
$565$	35.5701	−	35.5701i	1.49645	−	1.49645i
$566$	−3.98370	+	20.0274i	−0.167448	+	0.841815i
$567$	10.8268	−	16.1110i	0.454685	−	0.676598i
$568$	5.84243	−	1.16213i	0.245143	−	0.0487620i
$569$	9.46803	−	22.8578i	0.396920	−	0.958251i	−0.591472	−	0.806326i	$-0.701453\pi$
$569$	9.46803	−	22.8578i	0.396920	−	0.958251i	0.988392	−	0.151925i	$-0.0485472\pi$
$570$	4.69841	−	4.69219i	0.196795	−	0.196534i
$571$	−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
$573$	−1.03794	−	0.694522i	−0.0433605	−	0.0290141i
$574$	−6.83402	−	6.83402i	−0.285247	−	0.285247i
$575$	−2.74779	+	1.83601i	−0.114591	+	0.0765671i
$576$	−20.7121	−	8.61137i	−0.863003	−	0.358807i
$577$			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
$582$	3.41602	+	8.26247i	0.141599	+	0.342490i
$583$	−10.2926	−	2.04732i	−0.426275	−	0.0847913i
$584$	−19.1452	+	28.6529i	−0.792235	+	1.18566i
$585$	22.5244	−	33.6137i	0.931270	−	1.38976i
$586$	−35.4995	−	14.7044i	−1.46647	−	0.607433i
$587$	−41.3023	−	17.1080i	−1.70473	−	0.706122i	−0.704735	−	0.709471i	$-0.748934\pi$
$587$	−41.3023	−	17.1080i	−1.70473	−	0.706122i	−0.999994	+	0.00334911i	$0.998934\pi$
$588$	−0.0934554	+	0.468212i	−0.00385403	+	0.0193087i
$589$	−1.38557	+	2.07364i	−0.0570912	+	0.0854430i
$590$	−26.5313	−	5.27741i	−1.09228	−	0.217268i
$591$	−37.2374	+	15.3953i	−1.53174	+	0.633280i
$592$	5.58511	+	8.35871i	0.229547	+	0.343541i
$593$	−8.44534	−	20.3889i	−0.346809	−	0.837270i	−0.996993	−	0.0774935i	$-0.975308\pi$
$593$	−8.44534	−	20.3889i	−0.346809	−	0.837270i	0.650184	−	0.759777i	$-0.274692\pi$
$594$	11.5204	−	4.74513i	0.472689	−	0.194695i
$595$		0			0
$596$			0.738361i			0.0302444i
$597$	−0.0276540	+	41.7680i	−0.00113180	+	1.70945i
$598$	−4.09963	+	2.73928i	−0.167646	+	0.112018i
$599$	16.9345	+	16.9345i	0.691926	+	0.691926i	0.962655	−	0.270729i	$-0.0872649\pi$
$599$	16.9345	+	16.9345i	0.691926	+	0.691926i	−0.270729	+	0.962655i	$0.587265\pi$
$600$	−11.3754	+	17.0001i	−0.464398	+	0.694026i
$601$	−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
$603$	8.23359	+	19.9523i	0.335298	+	0.812521i
$604$	−0.683377	+	1.64982i	−0.0278062	+	0.0671302i
$605$	−24.7939	+	4.93180i	−1.00801	+	0.200506i
$606$	−7.83988	+	5.23094i	−0.318473	+	0.212492i
$607$	−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
$609$	−29.2833	+	5.80467i	−1.18662	+	0.235217i
$610$	−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
$615$	15.9653	−	3.16471i	0.643783	−	0.127613i
$616$	−6.88440	+	6.88440i	−0.277380	+	0.277380i
$617$	1.92552	−	9.68025i	0.0775186	−	0.389712i	−0.922475	−	0.386057i	$-0.873837\pi$
$617$	1.92552	−	9.68025i	0.0775186	−	0.389712i	0.999993	−	0.00365472i	$-0.00116334\pi$
$618$	−19.5690	+	13.0568i	−0.787180	+	0.525223i
$619$	−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
$621$	0.00791187	−	3.98330i	0.000317492	−	0.159844i
$622$	−6.62467	−	33.3044i	−0.265625	−	1.33539i
$623$	−8.67402	−	5.79580i	−0.347517	−	0.232204i
$624$	−17.9713	+	26.8575i	−0.719428	+	1.07516i
$625$	−19.7780	−	19.7780i	−0.791122	−	0.791122i
$626$	1.95352	−	1.30530i	0.0780785	−	0.0521704i
$627$	−0.00163159	+	2.46432i	−6.51594e−5	+	0.0984154i
$628$		−	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
$633$	−24.9860	+	10.3302i	−0.993104	+	0.410587i
$634$	34.8014	+	6.92242i	1.38214	+	0.274925i
$635$	20.8729	−	31.2385i	0.828316	−	1.23966i
$636$	0.253442	−	1.26974i	0.0100496	−	0.0503486i
$637$	−9.58987	−	3.97225i	−0.379964	−	0.157386i
$638$	−17.7033	−	7.33297i	−0.700882	−	0.290315i
$639$	5.41927	+	3.63143i	0.214383	+	0.143657i
$640$	20.6928	−	30.9690i	0.817955	−	1.22416i
$641$	−36.7015	−	7.30038i	−1.44962	−	0.288348i	−0.593380	−	0.804922i	$-0.702207\pi$
$641$	−36.7015	−	7.30038i	−1.44962	−	0.288348i	−0.856242	+	0.516575i	$0.827207\pi$
$642$	−1.81995	−	4.40198i	−0.0718276	−	0.173732i
$643$	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	$-0.600995\pi$
$647$		−	48.3331i		−	1.90017i	0.311989	−	0.950086i	$-0.399005\pi$
$648$	−9.37469	−	22.8031i	−0.368272	−	0.895791i
$649$	8.34737	−	5.57753i	0.327663	−	0.218937i
$650$	19.6063	+	19.6063i	0.769023	+	0.769023i
$651$	−8.96780	−	6.00068i	−0.351476	−	0.235185i
$652$	0.108422	+	0.0724451i	0.00424613	+	0.00283717i
$653$	−1.26227	−	6.34586i	−0.0493965	−	0.248333i	0.948196	−	0.317687i	$-0.102906\pi$
$653$	−1.26227	−	6.34586i	−0.0493965	−	0.248333i	−0.997592	+	0.0693542i	$0.977906\pi$
$654$	7.49540	−	7.48548i	0.293093	−	0.292705i
$655$	−4.11794	+	9.94158i	−0.160901	+	0.388450i
$656$	−12.7490	+	2.53593i	−0.497764	+	0.0990114i
$657$	−37.0228	+	7.31334i	−1.44440	+	0.285321i
$658$	−1.91564	+	9.63056i	−0.0746794	+	0.375439i
$659$	−17.7005	+	17.7005i	−0.689515	+	0.689515i	−0.962125	−	0.272610i	$-0.912113\pi$
$659$	−17.7005	+	17.7005i	−0.689515	+	0.689515i	0.272610	+	0.962125i	$0.412113\pi$
$660$	0.198776	+	1.00279i	0.00773736	+	0.0390334i
$661$	−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
$666$	−2.04182	+	10.1943i	−0.0791188	+	0.395022i
$667$	−4.33184	+	4.33184i	−0.167729	+	0.167729i
$668$	−0.454802	+	2.28645i	−0.0175968	+	0.0884652i
$669$	2.33802	+	3.50411i	0.0903929	+	0.135477i
$670$	−31.3321	+	6.23235i	−1.21047	+	0.240777i
$671$	3.68686	−	8.90086i	0.142329	−	0.343614i
$672$	−1.75061	−	1.75293i	−0.0675313	−	0.0676208i
$673$	−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
$675$	−21.9787	+	4.32647i	−0.845960	+	0.166526i
$676$	0.542640	+	0.542640i	0.0208708	+	0.0208708i
$677$	8.24041	−	5.50607i	0.316705	−	0.211615i	−0.387049	−	0.922059i	$-0.626506\pi$
$677$	8.24041	−	5.50607i	0.316705	−	0.211615i	0.703754	+	0.710444i	$0.251506\pi$
$678$	−41.5493	−	0.0275092i	−1.59569	−	0.00105648i
$679$		−	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	0.855982	−	0.517006i	$-0.172953\pi$
$683$	1.32660	+	1.98540i	0.0507610	+	0.0759692i	−0.805221	+	0.592975i	$0.797953\pi$
$684$	−0.304050		0.000402615i	−0.0116257		1.53944e-5i
$685$	−43.8391	−	8.72013i	−1.67500	−	0.333179i
$686$	16.2996	−	24.3941i	0.622322	−	0.931370i
$687$	−18.4746	−	3.68755i	−0.704851	−	0.140689i
$688$	44.6375	+	18.4895i	1.70179	+	0.704905i
$689$	26.0068	+	10.7724i	0.990779	+	0.410394i
$690$	5.78144	+	1.15398i	0.220096	+	0.0439313i
$691$	−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
$693$	−10.6620	−	0.0141184i	−0.405017	−	0.000536313i
$694$	−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
$699$	24.8311	+	0.0164403i	0.939197	+	0.000621829i
$700$	−0.907464	+	0.606348i	−0.0342989	+	0.0229178i
$701$	−31.7150	−	31.7150i	−1.19786	−	1.19786i	−0.974807	−	0.223051i	$-0.928398\pi$
$701$	−31.7150	−	31.7150i	−1.19786	−	1.19786i	−0.223051	−	0.974807i	$-0.571602\pi$
$702$	−32.7916	+	6.45497i	−1.23764	+	0.243627i
$703$	−1.70980	−	1.14245i	−0.0644864	−	0.0430885i
$704$	2.40368	+	12.0841i	0.0905921	+	0.455437i
$705$	−11.6850	−	11.7005i	−0.440083	−	0.440667i
$706$	−6.64926	+	16.0527i	−0.250248	+	0.604153i
$707$	7.91022	−	1.57344i	0.297495	−	0.0591753i
$708$	0.687481	+	1.03036i	0.0258371	+	0.0387235i
$709$	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
$711$	3.51030	−	17.5262i	0.131647	−	0.657283i
$712$	−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
$717$	7.98484	+	40.2819i	0.298199	+	1.50435i
$718$	−23.6628	+	23.6628i	−0.883086	+	0.883086i
$719$	8.57373	−	43.1030i	0.319746	−	1.60747i	−0.402220	−	0.915543i	$-0.631761\pi$
$719$	8.57373	−	43.1030i	0.319746	−	1.60747i	0.721966	−	0.691929i	$-0.243239\pi$
$720$	37.9071	−	7.48802i	1.41271	−	0.279062i
$721$	19.7446	−	3.92744i	0.735326	−	0.146265i
$722$	−10.1650	+	24.5406i	−0.378304	+	0.913307i
$723$	−3.44918	+	3.44461i	−0.128276	+	0.128107i
$724$	−0.0328353	−	0.165074i	−0.00122031	−	0.00613493i
$725$	28.6448	+	19.1399i	1.06384	+	0.710837i
$726$	17.3535	+	11.6119i	0.644049	+	0.430957i
$727$	−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
$729$	10.4315	−	24.9035i	0.386351	−	0.922352i
$730$		−	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
$735$	4.74203	+	11.4697i	0.174912	+	0.423068i
$736$	−0.498613	−	0.0991804i	−0.0183791	−	0.00365584i
$737$	6.58678	−	9.85781i	0.242627	−	0.363117i
$738$	−11.1679	−	7.48354i	−0.411095	−	0.275473i
$739$	−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
$741$	1.29389	−	6.48238i	0.0475322	−	0.238136i
$742$	−11.1039	+	16.6182i	−0.407639	+	0.610074i
$743$	−40.2557	−	8.00737i	−1.47684	−	0.293762i	−0.610021	−	0.792385i	$-0.708839\pi$
$743$	−40.2557	−	8.00737i	−1.47684	−	0.293762i	−0.866819	+	0.498623i	$0.833839\pi$
$744$	−12.6655	+	5.23642i	−0.464341	+	0.191976i
$745$	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
$750$	−0.00350841	+	5.29902i	−0.000128109	+	0.193493i
$751$	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
$753$	−14.5836	+	21.7946i	−0.531456	+	0.794241i
$754$	42.7373	+	28.5562i	1.55640	+	1.03995i
$755$	9.05629	+	45.5290i	0.329592	+	1.65697i
$756$	0.00261291	−	1.31549i	9.50307e−5	−	0.0478441i
$757$	−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
$759$	−1.82002	+	1.21436i	−0.0660625	+	0.0440783i
$760$	−1.40804	+	7.07871i	−0.0510751	+	0.256772i
$761$	24.1395	−	24.1395i	0.875055	−	0.875055i	−0.117963	−	0.993018i	$-0.537636\pi$
$761$	24.1395	−	24.1395i	0.875055	−	0.875055i	0.993018	+	0.117963i	$0.0376365\pi$
$762$	−30.4395	+	6.03385i	−1.10271	+	0.218583i
$763$	−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
$768$	−4.77021	+	0.945571i	−0.172130	+	0.0341204i
$769$	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
$771$	−28.6633	+	19.1248i	−1.03228	+	0.688761i
$772$	1.33795	−	0.266135i	0.0481539	−	0.00957840i
$773$	5.31114	−	12.8222i	0.191028	−	0.461184i	−0.799126	−	0.601164i	$-0.794704\pi$
$773$	5.31114	−	12.8222i	0.191028	−	0.461184i	0.990154	+	0.139980i	$0.0447039\pi$
$774$	19.0608	+	46.1897i	0.685125	+	1.66025i
$775$	2.42928	+	12.2128i	0.0872624	+	0.438698i
$776$	−8.08023	−	5.39903i	−0.290063	−	0.193814i
$777$	4.94780	−	7.39431i	0.177501	−	0.265269i
$778$	15.6099	+	15.6099i	0.559643	+	0.559643i
$779$	2.21083	−	1.47723i	0.0792111	−	0.0529272i
$780$	0.00181557	−	2.74219i	6.50078e−5	−	0.0981863i
$781$		−	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
$786$	8.21367	−	3.39584i	0.292972	−	0.121126i
$787$	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
$789$	0.0444496	−	0.222692i	0.00158245	−	0.00792806i
$790$	24.4410	+	10.1238i	0.869572	+	0.360189i
$791$	32.8490	+	13.6065i	1.16798	+	0.483792i
$792$	−7.53870	+	11.2502i	−0.267876	+	0.399758i
$793$	−14.3574	+	21.4874i	−0.509847	+	0.763040i
$794$	53.7144	+	10.6845i	1.90625	+	0.379178i
$795$	−12.8599	−	31.1048i	−0.456094	−	1.10317i
$796$	1.57263	+	2.35361i	0.0557403	+	0.0834213i
$797$	17.9210	+	43.2651i	0.634795	+	1.53253i	0.833529	+	0.552476i	$0.186317\pi$
$797$	17.9210	+	43.2651i	0.634795	+	1.53253i	−0.198734	+	0.980053i	$0.563683\pi$
$798$	4.33492	+	1.79895i	0.153455	+	0.0636820i
$799$		0			0
$800$			2.85893i			0.101078i
$801$	−13.3989	−	5.57079i	−0.473426	−	0.196834i
$802$	−4.27557	+	2.85685i	−0.150976	+	0.100879i
$803$	14.6575	+	14.6575i	0.517252	+	0.517252i
$804$	1.21573	+	0.813491i	0.0428755	+	0.0286896i
$805$	−4.19478	−	2.80287i	−0.147847	−	0.0987880i
$806$	3.62442	+	18.2212i	0.127665	+	0.641814i
$807$	7.28661	−	7.27696i	0.256501	−	0.256161i
$808$	3.92024	−	9.46429i	0.137913	−	0.332952i
$809$	11.4907	−	2.28565i	0.403993	−	0.0803592i	0.0110886	−	0.999939i	$-0.496470\pi$
$809$	11.4907	−	2.28565i	0.403993	−	0.0803592i	0.392904	+	0.919579i	$0.371470\pi$
$810$	33.1677	+	22.2892i	1.16539	+	0.783164i
$811$	−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
$813$	−2.31531	−	11.6803i	−0.0812016	−	0.409645i
$814$	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
$819$	28.0428	+	5.61666i	0.979893	+	0.196262i
$820$	0.779963	−	0.779963i	0.0272375	−	0.0272375i
$821$	−5.91006	+	29.7119i	−0.206263	+	1.03695i	0.729408	+	0.684079i	$0.239795\pi$
$821$	−5.91006	+	29.7119i	−0.206263	+	1.03695i	−0.935671	+	0.352874i	$0.885205\pi$
$822$	20.4908	+	30.7106i	0.714698	+	1.07116i
$823$	−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
$825$	8.69457	+	8.70609i	0.302706	+	0.303107i
$826$	−3.73016	−	18.7528i	−0.129789	−	0.652493i
$827$	14.5585	+	9.72768i	0.506249	+	0.338265i	0.782324	−	0.622871i	$-0.214034\pi$
$827$	14.5585	+	9.72768i	0.506249	+	0.338265i	−0.276076	+	0.961136i	$0.589034\pi$
$828$	−0.149680	−	0.224655i	−0.00520174	−	0.00780732i
$829$	−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
$831$	14.3715	+	0.00951518i	0.498542	+	0.000330078i
$832$		−	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
$837$	−13.8550	−	5.77119i	−0.478898	−	0.199481i
$838$	−44.8026	−	8.91178i	−1.54768	−	0.307852i
$839$	−10.9879	+	16.4446i	−0.379346	+	0.567731i	−0.971186	−	0.238325i	$-0.923402\pi$
$839$	−10.9879	+	16.4446i	−0.379346	+	0.567731i	0.591840	+	0.806056i	$0.298402\pi$
$840$	−30.6225	−	6.11227i	−1.05658	−	0.210893i
$841$	32.2093	+	13.3415i	1.11067	+	0.460053i
$842$	−20.3896	−	8.44564i	−0.702671	−	0.291056i
$843$	22.5051	+	4.49203i	0.775116	+	0.154714i
$844$	−1.01799	+	1.52353i	−0.0350407	+	0.0524422i
$845$	19.5656	+	3.89185i	0.673078	+	0.133884i
$846$	−0.0180859	+	13.6582i	−0.000621805	+	0.469580i
$847$	−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
$852$	0.442102		0.000292709i	0.0151462		1.00281e-5i
$853$	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
$855$	−6.57763	+	4.38245i	−0.224950	+	0.149877i
$856$	4.30489	+	2.87643i	0.147138	+	0.0983145i
$857$	−5.07296	−	25.5035i	−0.173289	−	0.871184i	−0.965393	−	0.260798i	$-0.916014\pi$
$857$	−5.07296	−	25.5035i	−0.173289	−	0.871184i	0.792104	−	0.610386i	$-0.208986\pi$
$858$	12.9721	+	12.9893i	0.442859	+	0.443446i
$859$	−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
$861$	6.38500	+	9.56953i	0.217600	+	0.326129i
$862$	3.25147	−	16.3462i	0.110745	−	0.556755i
$863$	10.3922	−	10.3922i	0.353754	−	0.353754i	−0.507750	−	0.861504i	$-0.669523\pi$
$863$	10.3922	−	10.3922i	0.353754	−	0.353754i	0.861504	+	0.507750i	$0.169523\pi$
$864$	−2.86140	−	1.92016i	−0.0973468	−	0.0653251i
$865$	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
$870$	−11.9501	−	60.2856i	−0.405145	−	2.04387i
$871$	−22.4875	+	22.4875i	−0.761958	+	0.761958i
$872$	−2.24626	+	11.2927i	−0.0760679	+	0.382419i
$873$	−2.06239	−	10.4406i	−0.0698014	−	0.353360i
$874$	0.944618	−	0.187896i	0.0319522	−	0.00635569i
$875$	1.73532	−	4.18943i	0.0586644	−	0.141629i
$876$	−1.80966	+	1.80726i	−0.0611427	+	0.0610618i
$877$	−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
$879$	38.0121	+	25.4353i	1.28212	+	0.857912i
$880$	−15.0076	−	15.0076i	−0.505907	−	0.505907i
$881$	16.3958	−	10.9553i	0.552389	−	0.369094i	−0.247829	−	0.968804i	$-0.579717\pi$
$881$	16.3958	−	10.9553i	0.552389	−	0.369094i	0.800218	+	0.599709i	$0.204717\pi$
$882$	3.93557	−	9.46583i	0.132517	−	0.318731i
$883$		−	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	0.642137	−	0.766590i	$-0.278048\pi$
$887$	−9.28722	−	13.8993i	−0.311834	−	0.466693i	−0.953972	+	0.299896i	$0.903048\pi$
$888$	−4.31764	−	10.4432i	−0.144890	−	0.350452i
$889$	26.0450	+	5.18067i	0.873522	+	0.173754i
$890$	11.9318	−	17.8572i	0.399955	−	0.598575i
$891$	−14.5532	+	2.85477i	−0.487551	+	0.0956383i
$892$	0.263753	+	0.109250i	0.00883111	+	0.00365797i
$893$	−2.49580	−	1.03380i	−0.0835189	−	0.0345947i
$894$	3.10316	−	15.5468i	0.103785	−	0.519964i
$895$	1.43532	−	2.14810i	0.0479773	−	0.0718032i
$896$	25.8203	+	5.13597i	0.862594	+	0.171581i
$897$	5.42367	−	2.24235i	0.181091	−	0.0748699i
$898$	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
$903$	0.0283106	−	42.7598i	0.000942119	−	1.42296i
$904$	37.5501	−	25.0902i	1.24890	−	0.834487i
$905$	−3.09374	−	3.09374i	−0.102839	−	0.102839i
$906$	21.3229	−	31.8663i	0.708406	−	1.05869i
$907$	−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
$909$	10.3702	−	4.27938i	0.343956	−	0.141938i
$910$	−16.1986	+	39.1068i	−0.536978	+	1.29638i
$911$	−1.96677	+	0.391215i	−0.0651621	+	0.0129615i	−0.227564	−	0.973763i	$-0.573076\pi$
$911$	−1.96677	+	0.391215i	−0.0651621	+	0.0129615i	0.162402	+	0.986725i	$0.448076\pi$
$912$	5.25090	−	3.50351i	0.173875	−	0.116013i
$913$	4.17505	−	20.9894i	0.138174	−	0.694648i
$914$	−10.8464	+	10.8464i	−0.358768	+	0.358768i
$915$	30.3103	−	6.00824i	1.00203	−	0.198626i
$916$	−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
$921$	−41.5089	+	8.22807i	−1.36777	+	0.271124i
$922$	−10.1727	+	10.1727i	−0.335021	+	0.335021i
$923$	−1.87512	+	9.42688i	−0.0617204	+	0.310290i
$924$	−0.601066	+	0.401044i	−0.0197736	+	0.0131934i
$925$	−10.0700	+	2.00304i	−0.331098	+	0.0658595i
$926$	12.7673	−	30.8229i	0.419558	−	1.01290i
$927$	25.8847	−	10.6817i	0.850166	−	0.350832i
$928$	1.03392	+	5.19789i	0.0339402	+	0.170629i
$929$	20.3321	+	13.5854i	0.667073	+	0.445724i	0.842448	−	0.538778i	$-0.181114\pi$
$929$	20.3321	+	13.5854i	0.667073	+	0.445724i	−0.175375	+	0.984502i	$0.556114\pi$
$930$	12.3536	−	18.4620i	0.405091	−	0.605393i
$931$	1.43373	+	1.43373i	0.0469885	+	0.0469885i
$932$	1.39922	−	0.934927i	0.0458329	−	0.0306245i
$933$	−0.0267611	+	40.4193i	−0.000876118	+	1.32327i
$934$			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
$939$	−2.58445	+	1.06851i	−0.0843403	+	0.0348695i
$940$	−1.09913	−	0.218631i	−0.0358497	−	0.00713095i
$941$	2.00221	−	2.99651i	0.0652701	−	0.0976836i	−0.797399	−	0.603453i	$-0.793791\pi$
$941$	2.00221	−	2.99651i	0.0652701	−	0.0976836i	0.862669	+	0.505769i	$0.168791\pi$
$942$	−1.21763	+	6.10033i	−0.0396726	+	0.198760i
$943$	2.18105	+	0.903419i	0.0710246	+	0.0294194i
$944$	−23.7584	−	9.84105i	−0.773270	−	0.320299i
$945$	−18.9421	−	28.4711i	−0.616187	−	0.926166i
$946$	15.2484	−	22.8209i	0.495769	−	0.741970i
$947$	26.2908	+	5.22957i	0.854336	+	0.169938i	0.602783	−	0.797905i	$-0.294059\pi$
$947$	26.2908	+	5.22957i	0.854336	+	0.169938i	0.251554	+	0.967843i	$0.419059\pi$
$948$	−0.462824	−	1.11945i	−0.0150318	−	0.0363581i
$949$	−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	$-0.871465\pi$
$953$		−	24.2594i		−	0.785838i	0.919573	−	0.392919i	$-0.128535\pi$
$954$	−10.6729	+	25.6704i	−0.345547	+	0.831109i
$955$	−1.82937	+	1.22234i	−0.0591969	+	0.0395541i
$956$	1.96792	+	1.96792i	0.0636470	+	0.0636470i
$957$	18.9564	+	12.6844i	0.612772	+	0.410028i
$958$	−10.4833	−	7.00474i	−0.338701	−	0.226313i
$959$	−6.16353	−	30.9862i	−0.199031	−	1.00060i
$960$	−27.9612	+	27.9242i	−0.902445	+	0.901250i
$961$	8.67037	−	20.9321i	0.279689	−	0.675230i
$962$	−15.0241	+	2.98848i	−0.484397	+	0.0963525i
$963$	1.09878	+	5.56241i	0.0354076	+	0.179246i
$964$	−0.0644499	+	0.324012i	−0.00207579	+	0.0104357i
$965$	25.0752	−	25.0752i	0.807200	−	0.807200i
$966$	0.810240	+	4.08749i	0.0260691	+	0.131513i
$967$	−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	−0.141407	−	0.989952i	$-0.545163\pi$
$971$	14.2905	−	5.91933i	0.458605	−	0.189960i	0.600012	+	0.799991i	$0.295163\pi$
$972$	−0.351036	−	1.79583i	−0.0112595	−	0.0576012i
$973$	7.69338	−	7.69338i	0.246638	−	0.246638i
$974$	−11.0194	+	55.3982i	−0.353084	+	1.77507i
$975$	−18.3181	−	27.4543i	−0.586649	−	0.879241i
$976$	−24.2041	+	4.81450i	−0.774755	+	0.154108i
$977$	−7.72995	+	18.6618i	−0.247303	+	0.597042i	−0.997973	−	0.0636347i	$-0.979731\pi$
$977$	−7.72995	+	18.6618i	−0.247303	+	0.597042i	0.750670	+	0.660677i	$0.229731\pi$
$978$	−1.97845	−	1.98107i	−0.0632637	−	0.0633475i
$979$	1.55497	+	7.81735i	0.0496970	+	0.249844i
$980$	0.699373	+	0.467306i	0.0223406	+	0.0149275i
$981$	−10.4933	+	6.99134i	−0.335026	+	0.223216i
$982$	−13.0385	−	13.0385i	−0.416075	−	0.416075i
$983$	21.6898	−	14.4927i	0.691797	−	0.462244i	−0.159315	−	0.987228i	$-0.550929\pi$
$983$	21.6898	−	14.4927i	0.691797	−	0.462244i	0.851112	+	0.524984i	$0.175929\pi$
$984$	14.6120	+	0.00967440i	0.465814	+	0.000308409i
$985$			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
$990$	0.0290655	−	21.9499i	0.000923762	−	0.697615i
$991$	−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
$993$	51.7460	+	10.3285i	1.64211	+	0.327766i
$994$	−6.30488	−	2.61157i	−0.199979	−	0.0828339i
$995$	67.9824	+	28.1592i	2.15519	+	0.892707i
$996$	2.58936	+	0.516838i	0.0820469	+	0.0163766i
$997$	−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
$999$	4.75858	−	11.4240i	0.150555	−	0.361439i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.i.a.29.1	✓	32	17.16	even	2
51.2.i.a.29.4	yes	32	51.50	odd	2
51.2.i.a.44.1	yes	32	51.41	even	16
51.2.i.a.44.4	yes	32	17.7	odd	16
816.2.cj.c.401.3		32	68.7	even	16
816.2.cj.c.401.4		32	204.143	odd	16
816.2.cj.c.641.3		32	204.203	even	2
816.2.cj.c.641.4		32	68.67	odd	2
867.2.i.b.65.1		32	17.2	even	8
867.2.i.b.65.4		32	51.2	odd	8
867.2.i.b.827.1		32	51.5	even	16
867.2.i.b.827.4		32	17.5	odd	16
867.2.i.c.158.1		32	51.38	odd	4
867.2.i.c.158.4		32	17.4	even	4
867.2.i.c.653.1		32	17.11	odd	16
867.2.i.c.653.4		32	51.11	even	16
867.2.i.d.158.1		32	51.47	odd	4
867.2.i.d.158.4		32	17.13	even	4
867.2.i.d.653.1		32	17.6	odd	16
867.2.i.d.653.4		32	51.23	even	16
867.2.i.f.224.1		32	51.26	odd	8
867.2.i.f.224.4		32	17.9	even	8
867.2.i.f.329.1		32	17.3	odd	16
867.2.i.f.329.4		32	51.20	even	16
867.2.i.g.224.1		32	51.8	odd	8
867.2.i.g.224.4		32	17.8	even	8
867.2.i.g.329.1		32	17.14	odd	16
867.2.i.g.329.4		32	51.14	even	16
867.2.i.h.131.1		32	1.1	even	1	trivial
867.2.i.h.131.4		32	3.2	odd	2	inner
867.2.i.h.503.1		32	51.44	even	16	inner
867.2.i.h.503.4		32	17.10	odd	16	inner
867.2.i.i.65.1		32	17.15	even	8
867.2.i.i.65.4		32	51.32	odd	8
867.2.i.i.827.1		32	51.29	even	16
867.2.i.i.827.4		32	17.12	odd	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} +(1.69899 - 0.336782i) q^{3} +(0.0830021 - 0.0830021i) q^{4} +(0.595296 - 2.99276i) q^{5} +(-2.09652 + 1.39884i) q^{6} +(2.11533 - 0.420765i) q^{7} +(1.04834 - 2.53091i) q^{8} +(2.77316 - 1.14438i) q^{9} +(0.866229 + 4.35483i) q^{10} +(-1.37013 - 0.915491i) q^{11} +(0.113066 - 0.168973i) q^{12} +(3.12551 + 3.12551i) q^{13} +(-2.60946 + 1.74358i) q^{14} +(0.00349923 - 5.28516i) q^{15} +4.22099i q^{16} +(-3.09087 + 3.08269i) q^{18} +(-0.330416 - 0.797694i) q^{19} +(-0.198994 - 0.297816i) q^{20} +(3.45222 - 1.42728i) q^{21} +(2.35174 + 0.467790i) q^{22} +(0.425893 - 0.637394i) q^{23} +(0.928755 - 4.65306i) q^{24} +(-3.98282 - 1.64974i) q^{25} +(-5.94226 - 2.46136i) q^{26} +(4.32617 - 2.87824i) q^{27} +(0.140652 - 0.210501i) q^{28} +(-7.83789 - 1.55905i) q^{29} +(2.93834 + 7.10709i) q^{30} +(-1.60475 - 2.40167i) q^{31} +(-0.253786 - 0.612694i) q^{32} +(-2.63616 - 1.09398i) q^{33} -6.58114i q^{35} +(0.135192 - 0.325163i) q^{36} +(1.98027 - 1.32318i) q^{37} +(0.888394 + 0.888394i) q^{38} +(6.36284 + 4.25761i) q^{39} +(-6.95033 - 4.64406i) q^{40} +(0.600791 + 3.02038i) q^{41} +(-3.84624 + 3.84115i) q^{42} +(4.38037 - 10.5751i) q^{43} +(-0.189711 + 0.0377359i) q^{44} +(-1.77400 - 8.98063i) q^{45} +(-0.217619 + 1.09405i) q^{46} +(2.21238 - 2.21238i) q^{47} +(1.42155 + 7.17143i) q^{48} +(-2.16958 + 0.898671i) q^{49} +6.27299 q^{50} +0.518848 q^{52} +(5.88369 - 2.43710i) q^{53} +(-4.21317 + 6.27842i) q^{54} +(-3.55548 + 3.55548i) q^{55} +(1.15266 - 5.79482i) q^{56} +(-0.830022 - 1.24400i) q^{57} +(11.4051 - 2.26861i) q^{58} +(-2.33146 + 5.62864i) q^{59} +(-0.438389 - 0.438969i) q^{60} +(1.14061 + 5.73423i) q^{61} +(3.49473 + 2.33510i) q^{62} +(5.38462 - 3.58759i) q^{63} +(-5.28702 - 5.28702i) q^{64} +(11.2145 - 7.49329i) q^{65} +(4.15313 + 0.00274973i) q^{66} +7.19481i q^{67} +(0.508927 - 1.22636i) q^{69} +(3.66472 + 8.84742i) q^{70} +(1.20808 + 1.80802i) q^{71} +(0.0108825 - 8.21831i) q^{72} +(-12.3377 - 2.45412i) q^{73} +(-1.92538 + 2.88154i) q^{74} +(-7.32238 - 1.46155i) q^{75} +(-0.0936354 - 0.0387851i) q^{76} +(-3.28348 - 1.36006i) q^{77} +(-10.9248 - 2.18060i) q^{78} +(3.31013 - 4.95397i) q^{79} +(12.6324 + 2.51274i) q^{80} +(6.38079 - 6.34708i) q^{81} +(-2.48958 - 3.72592i) q^{82} +(4.96993 + 11.9985i) q^{83} +(0.168074 - 0.405009i) q^{84} +16.6560i q^{86} +(-13.8416 - 0.00916431i) q^{87} +(-3.75339 + 2.50793i) q^{88} +(-3.42023 - 3.42023i) q^{89} +(7.38576 + 11.0853i) q^{90} +(7.92660 + 5.29638i) q^{91} +(-0.0175550 - 0.0882551i) q^{92} +(-3.53529 - 3.53997i) q^{93} +(-1.74226 + 4.20619i) q^{94} +(-2.58400 + 0.513989i) q^{95} +(-0.637525 - 0.955492i) q^{96} +(0.692072 - 3.47928i) q^{97} +(2.41627 - 2.41627i) q^{98} +(-4.84725 - 0.970853i) 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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