LMFDB - Embedded newform 833.2.bc.c.558.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [833,2,Mod(31,833)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("833.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(833, base_ring=CyclotomicField(48)) chi = DirichletCharacter(H, H._module([8, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.bc (of order $48$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [144,0,0,0,0,0,0,0,24,0,8,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$9$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			558.9
Character	$\chi$	$=$	833.558
Dual form			833.2.bc.c.521.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.303182 - 2.30290i) q^{2} +(0.0950234 + 0.279930i) q^{3} +(-3.27956 - 0.878756i) q^{4} +(-1.21758 + 0.0798047i) q^{5} +(0.673459 - 0.133959i) q^{6} +(-1.24022 + 2.99415i) q^{8} +(2.31073 - 1.77308i) q^{9} +(-0.185368 + 2.82817i) q^{10} +(-1.91064 - 2.17866i) q^{11} +(-0.0656450 - 1.00155i) q^{12} +(-0.992715 + 0.992715i) q^{13} +(-0.138039 - 0.333255i) q^{15} +(0.638463 + 0.368617i) q^{16} +(-4.03287 + 0.857859i) q^{17} +(-3.38266 - 5.85894i) q^{18} +(-3.24860 - 0.427687i) q^{19} +(4.06327 + 0.808235i) q^{20} +(-5.59651 + 3.73947i) q^{22} +(-1.71584 - 0.582449i) q^{23} +(-0.956003 - 0.0626597i) q^{24} +(-3.48108 + 0.458293i) q^{25} +(1.98515 + 2.58709i) q^{26} +(1.45331 + 0.971068i) q^{27} +(-1.94103 - 2.90495i) q^{29} +(-0.809303 + 0.216852i) q^{30} +(1.64377 - 0.557985i) q^{31} +(-2.90335 + 3.78372i) q^{32} +(0.428318 - 0.741868i) q^{33} +(0.752866 + 9.54738i) q^{34} +(-9.13629 + 3.78437i) q^{36} +(0.462299 + 0.405425i) q^{37} +(-1.96984 + 7.35153i) q^{38} +(-0.372222 - 0.183559i) q^{39} +(1.27112 - 3.74461i) q^{40} +(4.22160 - 6.31807i) q^{41} +(-2.34069 - 0.969547i) q^{43} +(4.35154 + 8.82405i) q^{44} +(-2.67201 + 2.34329i) q^{45} +(-1.86153 + 3.77481i) q^{46} +(2.98629 + 11.1450i) q^{47} +(-0.0425179 + 0.213752i) q^{48} +8.15551i q^{50} +(-0.623358 - 1.04741i) q^{51} +(4.12803 - 2.38332i) q^{52} +(6.32467 + 4.85309i) q^{53} +(2.67688 - 3.05240i) q^{54} +(2.50023 + 2.50023i) q^{55} +(-0.188971 - 0.950022i) q^{57} +(-7.27829 + 3.58925i) q^{58} +(-1.10526 - 8.39529i) q^{59} +(0.159857 + 1.21423i) q^{60} +(-8.68507 + 4.28300i) q^{61} +(-0.786620 - 3.95460i) q^{62} +(8.87587 + 8.87587i) q^{64} +(1.12949 - 1.28794i) q^{65} +(-1.57859 - 1.21129i) q^{66} +(-3.61306 + 2.08600i) q^{67} +(13.9799 + 0.730510i) q^{68} -0.535661i q^{69} +(3.14489 - 15.8104i) q^{71} +(2.44308 + 9.11769i) q^{72} +(6.08326 - 12.3356i) q^{73} +(1.07381 - 0.941708i) q^{74} +(-0.459074 - 0.930910i) q^{75} +(10.2782 + 4.25736i) q^{76} +(-0.535570 + 0.801536i) q^{78} +(-3.83540 + 11.2987i) q^{79} +(-0.806800 - 0.397870i) q^{80} +(2.12778 - 7.94100i) q^{81} +(-13.2700 - 11.6374i) q^{82} +(-7.64634 + 3.16722i) q^{83} +(4.84191 - 1.36636i) q^{85} +(-2.94242 + 5.09643i) q^{86} +(0.628740 - 0.819390i) q^{87} +(8.89286 - 3.01872i) q^{88} +(-8.31460 + 2.22789i) q^{89} +(4.58624 + 6.86380i) q^{90} +(5.11537 + 3.41798i) q^{92} +(0.312393 + 0.407119i) q^{93} +(26.5711 - 3.49815i) q^{94} +(3.98958 + 0.261491i) q^{95} +(-1.33506 - 0.453192i) q^{96} +(-3.34327 + 2.23390i) q^{97} +(-8.27792 - 1.64658i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 24 q^{9} + 8 q^{11} + 24 q^{12} - 64 q^{13} - 32 q^{17} - 40 q^{18} + 40 q^{19} + 80 q^{20} - 48 q^{22} + 8 q^{23} - 16 q^{24} + 8 q^{25} - 48 q^{27} - 8 q^{31} - 40 q^{32} - 48 q^{34} - 240 q^{36}+ \cdots - 80 q^{99}+O(q^{100}) $ 144 * q + 24 * q^9 + 8 * q^11 + 24 * q^12 - 64 * q^13 - 32 * q^17 - 40 * q^18 + 40 * q^19 + 80 * q^20 - 48 * q^22 + 8 * q^23 - 16 * q^24 + 8 * q^25 - 48 * q^27 - 8 * q^31 - 40 * q^32 - 48 * q^34 - 240 * q^36 + 48 * q^37 + 56 * q^38 + 16 * q^39 + 48 * q^40 + 112 * q^41 - 48 * q^43 - 96 * q^44 - 40 * q^45 + 64 * q^46 - 24 * q^47 - 448 * q^48 - 104 * q^51 + 40 * q^53 - 48 * q^54 + 96 * q^57 - 32 * q^58 - 8 * q^59 + 48 * q^60 + 128 * q^61 + 96 * q^62 - 56 * q^65 - 120 * q^66 - 32 * q^68 + 120 * q^73 - 48 * q^74 - 32 * q^75 + 16 * q^76 + 96 * q^78 - 32 * q^79 + 32 * q^80 - 80 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^85 + 80 * q^86 + 64 * q^87 - 136 * q^88 + 16 * q^89 + 64 * q^90 - 16 * q^92 + 96 * q^93 - 32 * q^94 - 32 * q^95 - 40 * q^96 - 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{9}{16}\right)$

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 $

$2$	0.303182	−	2.30290i	0.214382	−	1.62839i	−0.458535	−	0.888676i	$-0.651626\pi$
$2$	0.303182	−	2.30290i	0.214382	−	1.62839i	0.672917	−	0.739718i	$-0.265041\pi$
$3$	0.0950234	+	0.279930i	0.0548618	+	0.161618i	0.970907	−	0.239458i	$-0.0769698\pi$
$3$	0.0950234	+	0.279930i	0.0548618	+	0.161618i	−0.916045	+	0.401076i	$0.868636\pi$
$4$	−3.27956	−	0.878756i	−1.63978	−	0.439378i
$5$	−1.21758	+	0.0798047i	−0.544520	+	0.0356898i	−0.335182	−	0.942153i	$-0.608798\pi$
$5$	−1.21758	+	0.0798047i	−0.544520	+	0.0356898i	−0.209339	+	0.977843i	$0.567131\pi$
$6$	0.673459	−	0.133959i	0.274938	−	0.0546887i
$7$		0			0
$7$		0			0
$8$	−1.24022	+	2.99415i	−0.438484	+	1.05859i
$9$	2.31073	−	1.77308i	0.770243	−	0.591028i
$10$	−0.185368	+	2.82817i	−0.0586185	+	0.894345i
$11$	−1.91064	−	2.17866i	−0.576079	−	0.656892i	0.388264	−	0.921548i	$-0.373075\pi$
$11$	−1.91064	−	2.17866i	−0.576079	−	0.656892i	−0.964343	+	0.264656i	$0.914742\pi$
$12$	−0.0656450	−	1.00155i	−0.0189501	−	0.289122i
$13$	−0.992715	+	0.992715i	−0.275330	+	0.275330i	−0.831241	−	0.555912i	$-0.812369\pi$
$13$	−0.992715	+	0.992715i	−0.275330	+	0.275330i	0.555912	+	0.831241i	$0.312369\pi$
$14$		0			0
$15$	−0.138039	−	0.333255i	−0.0356414	−	0.0860461i
$16$	0.638463	+	0.368617i	0.159616	+	0.0921542i
$17$	−4.03287	+	0.857859i	−0.978116	+	0.208061i
$17$	−4.03287	+	0.857859i	−0.978116	+	0.208061i
$18$	−3.38266	−	5.85894i	−0.797300	−	1.38096i
$19$	−3.24860	−	0.427687i	−0.745281	−	0.0981181i	−0.251685	−	0.967809i	$-0.580985\pi$
$19$	−3.24860	−	0.427687i	−0.745281	−	0.0981181i	−0.493596	+	0.869691i	$0.664318\pi$
$20$	4.06327	+	0.808235i	0.908576	+	0.180727i
$21$		0			0
$22$	−5.59651	+	3.73947i	−1.19318	+	0.797257i
$23$	−1.71584	−	0.582449i	−0.357777	−	0.121449i	0.136763	−	0.990604i	$-0.456330\pi$
$23$	−1.71584	−	0.582449i	−0.357777	−	0.121449i	−0.494540	+	0.869155i	$0.664663\pi$
$24$	−0.956003	−	0.0626597i	−0.195143	−	0.0127904i
$25$	−3.48108	+	0.458293i	−0.696216	+	0.0916586i
$26$	1.98515	+	2.58709i	0.389319	+	0.507371i
$27$	1.45331	+	0.971068i	0.279689	+	0.186882i
$28$		0			0
$29$	−1.94103	−	2.90495i	−0.360440	−	0.539436i	0.606288	−	0.795245i	$-0.292658\pi$
$29$	−1.94103	−	2.90495i	−0.360440	−	0.539436i	−0.966727	+	0.255809i	$0.917658\pi$
$30$	−0.809303	+	0.216852i	−0.147758	+	0.0395916i
$31$	1.64377	−	0.557985i	0.295230	−	0.100217i	−0.169895	−	0.985462i	$-0.554343\pi$
$31$	1.64377	−	0.557985i	0.295230	−	0.100217i	0.465125	+	0.885245i	$0.346009\pi$
$32$	−2.90335	+	3.78372i	−0.513245	+	0.668873i
$33$	0.428318	−	0.741868i	0.0745606	−	0.129143i
$34$	0.752866	+	9.54738i	0.129115	+	1.63736i
$35$		0			0
$36$	−9.13629	+	3.78437i	−1.52271	+	0.630729i
$37$	0.462299	+	0.405425i	0.0760014	+	0.0666515i	0.696504	−	0.717553i	$-0.254738\pi$
$37$	0.462299	+	0.405425i	0.0760014	+	0.0666515i	−0.620502	+	0.784205i	$0.713071\pi$
$38$	−1.96984	+	7.35153i	−0.319550	+	1.19258i
$39$	−0.372222	−	0.183559i	−0.0596032	−	0.0293930i
$40$	1.27112	−	3.74461i	0.200982	−	0.592075i
$41$	4.22160	−	6.31807i	0.659303	−	0.986717i	−0.339631	−	0.940559i	$-0.610302\pi$
$41$	4.22160	−	6.31807i	0.659303	−	0.986717i	0.998934	−	0.0461582i	$-0.0146978\pi$
$42$		0			0
$43$	−2.34069	−	0.969547i	−0.356952	−	0.147855i	0.196999	−	0.980404i	$-0.436881\pi$
$43$	−2.34069	−	0.969547i	−0.356952	−	0.147855i	−0.553951	+	0.832549i	$0.686881\pi$
$44$	4.35154	+	8.82405i	0.656019	+	1.33028i
$45$	−2.67201	+	2.34329i	−0.398319	+	0.349317i
$46$	−1.86153	+	3.77481i	−0.274468	+	0.556566i
$47$	2.98629	+	11.1450i	0.435595	+	1.62566i	0.739639	+	0.673003i	$0.234996\pi$
$47$	2.98629	+	11.1450i	0.435595	+	1.62566i	−0.304045	+	0.952658i	$0.598337\pi$
$48$	−0.0425179	+	0.213752i	−0.00613693	+	0.0308524i
$49$		0			0
$50$			8.15551i			1.15336i
$51$	−0.623358	−	1.04741i	−0.0872876	−	0.146666i
$52$	4.12803	−	2.38332i	0.572454	−	0.330507i
$53$	6.32467	+	4.85309i	0.868760	+	0.666623i	0.943786	−	0.330558i	$-0.107237\pi$
$53$	6.32467	+	4.85309i	0.868760	+	0.666623i	−0.0750251	+	0.997182i	$0.523904\pi$
$54$	2.67688	−	3.05240i	0.364278	−	0.415379i
$55$	2.50023	+	2.50023i	0.337131	+	0.337131i
$56$		0			0
$57$	−0.188971	−	0.950022i	−0.0250298	−	0.125833i
$58$	−7.27829	+	3.58925i	−0.955686	+	0.471292i
$59$	−1.10526	−	8.39529i	−0.143893	−	1.09297i	−0.899180	−	0.437580i	$-0.855836\pi$
$59$	−1.10526	−	8.39529i	−0.143893	−	1.09297i	0.755287	−	0.655394i	$-0.227497\pi$
$60$	0.159857	+	1.21423i	0.0206374	+	0.156757i
$61$	−8.68507	+	4.28300i	−1.11201	+	0.548382i	−0.903047	−	0.429541i	$-0.858675\pi$
$61$	−8.68507	+	4.28300i	−1.11201	+	0.548382i	−0.208962	+	0.977924i	$0.567009\pi$
$62$	−0.786620	−	3.95460i	−0.0999008	−	0.502235i
$63$		0			0
$64$	8.87587	+	8.87587i	1.10948	+	1.10948i
$65$	1.12949	−	1.28794i	0.140096	−	0.159749i
$66$	−1.57859	−	1.21129i	−0.194311	−	0.149100i
$67$	−3.61306	+	2.08600i	−0.441406	+	0.254846i	−0.704194	−	0.710008i	$-0.748691\pi$
$67$	−3.61306	+	2.08600i	−0.441406	+	0.254846i	0.262788	+	0.964854i	$0.415358\pi$
$68$	13.9799	+	0.730510i	1.69531	+	0.0885873i
$69$		−	0.535661i		−	0.0644860i
$70$		0			0
$71$	3.14489	−	15.8104i	0.373230	−	1.87635i	−0.0993292	−	0.995055i	$-0.531670\pi$
$71$	3.14489	−	15.8104i	0.373230	−	1.87635i	0.472559	−	0.881299i	$-0.343330\pi$
$72$	2.44308	+	9.11769i	0.287919	+	1.07453i
$73$	6.08326	−	12.3356i	0.711992	−	1.44378i	−0.176224	−	0.984350i	$-0.556388\pi$
$73$	6.08326	−	12.3356i	0.711992	−	1.44378i	0.888216	−	0.459427i	$-0.151945\pi$
$74$	1.07381	−	0.941708i	0.124828	−	0.109471i
$75$	−0.459074	−	0.930910i	−0.0530093	−	0.107492i
$76$	10.2782	+	4.25736i	1.17899	+	0.488352i
$77$		0			0
$78$	−0.535570	+	0.801536i	−0.0606413	+	0.0907561i
$79$	−3.83540	+	11.2987i	−0.431516	+	1.27120i	0.486158	+	0.873871i	$0.338398\pi$
$79$	−3.83540	+	11.2987i	−0.431516	+	1.27120i	−0.917674	+	0.397334i	$0.869935\pi$
$80$	−0.806800	−	0.397870i	−0.0902030	−	0.0444832i
$81$	2.12778	−	7.94100i	0.236420	−	0.882333i
$82$	−13.2700	−	11.6374i	−1.46542	−	1.28514i
$83$	−7.64634	+	3.16722i	−0.839295	+	0.347647i	−0.760575	−	0.649250i	$-0.775083\pi$
$83$	−7.64634	+	3.16722i	−0.839295	+	0.347647i	−0.0787193	+	0.996897i	$0.525083\pi$
$84$		0			0
$85$	4.84191	−	1.36636i	0.525178	−	0.148202i
$86$	−2.94242	+	5.09643i	−0.317290	+	0.549562i
$87$	0.628740	−	0.819390i	0.0674080	−	0.0878478i
$88$	8.89286	−	3.01872i	0.947982	−	0.321797i
$89$	−8.31460	+	2.22789i	−0.881346	+	0.236156i	−0.670988	−	0.741469i	$-0.734130\pi$
$89$	−8.31460	+	2.22789i	−0.881346	+	0.236156i	−0.210358	+	0.977624i	$0.567463\pi$
$90$	4.58624	+	6.86380i	0.483433	+	0.723508i
$91$		0			0
$92$	5.11537	+	3.41798i	0.533314	+	0.356349i
$93$	0.312393	+	0.407119i	0.0323937	+	0.0422163i
$94$	26.5711	−	3.49815i	2.74060	−	0.360807i
$95$	3.98958	+	0.261491i	0.409323	+	0.0268284i
$96$	−1.33506	−	0.453192i	−0.136259	−	0.0462538i
$97$	−3.34327	+	2.23390i	−0.339458	+	0.226818i	−0.713601	−	0.700553i	$-0.752937\pi$
$97$	−3.34327	+	2.23390i	−0.339458	+	0.226818i	0.374143	+	0.927371i	$0.377937\pi$
$98$		0			0
$99$	−8.27792	−	1.64658i	−0.831962	−	0.165488i
$100$	11.8191	+	1.55602i	1.18191	+	0.155602i
$101$	−9.40032	−	16.2818i	−0.935367	−	1.62010i	−0.773978	−	0.633212i	$-0.781736\pi$
$101$	−9.40032	−	16.2818i	−0.935367	−	1.62010i	−0.161389	−	0.986891i	$-0.551597\pi$
$102$	−2.60106	+	1.11797i	−0.257543	+	0.110696i
$103$	−6.71239	−	3.87540i	−0.661392	−	0.381855i	0.131415	−	0.991327i	$-0.458048\pi$
$103$	−6.71239	−	3.87540i	−0.661392	−	0.381855i	−0.792807	+	0.609473i	$0.791381\pi$
$104$	−1.74116	−	4.20353i	−0.170735	−	0.412190i
$105$		0			0
$106$	13.0937	−	13.0937i	1.27177	−	1.27177i
$107$	−0.761512	−	11.6184i	−0.0736181	−	1.12320i	−0.861630	−	0.507536i	$-0.830556\pi$
$107$	−0.761512	−	11.6184i	−0.0736181	−	1.12320i	0.788012	−	0.615659i	$-0.211110\pi$
$108$	−3.91287	−	4.46178i	−0.376516	−	0.429335i
$109$	0.325225	−	4.96197i	0.0311509	−	0.475271i	−0.953575	−	0.301157i	$-0.902627\pi$
$109$	0.325225	−	4.96197i	0.0311509	−	0.475271i	0.984726	−	0.174114i	$-0.0557061\pi$
$110$	6.51580	−	4.99975i	0.621257	−	0.476707i
$111$	−0.0695614	+	0.167936i	−0.00660248	+	0.0159398i
$112$		0			0
$113$	17.7143	−	3.52360i	1.66643	−	0.331473i	0.730297	−	0.683130i	$-0.239382\pi$
$113$	17.7143	−	3.52360i	1.66643	−	0.331473i	0.936129	+	0.351657i	$0.114382\pi$
$114$	−2.24509	+	0.147151i	−0.210272	+	0.0137820i
$115$	2.13566	+	0.572249i	0.199151	+	0.0533625i
$116$	3.81297	+	11.2327i	0.354026	+	1.04293i
$117$	−0.533728	+	4.05406i	−0.0493431	+	0.374798i
$118$	−19.6686			−1.81064
$119$		0			0
$120$	1.16901			0.106716
$121$	0.339745	−	2.58062i	0.0308859	−	0.234602i
$122$	7.23016	+	21.2994i	0.654588	+	1.92835i
$123$	2.16977	+	0.581387i	0.195641	+	0.0524219i
$124$	−5.88118	+	0.385473i	−0.528145	+	0.0346165i
$125$	10.1857	−	2.02606i	0.911036	−	0.181216i
$126$		0			0
$127$	3.10433	−	7.49451i	0.275465	−	0.665030i	−0.724235	−	0.689554i	$-0.757807\pi$
$127$	3.10433	−	7.49451i	0.275465	−	0.665030i	0.999699	+	0.0245232i	$0.00780675\pi$
$128$	15.5638	−	11.9425i	1.37566	−	1.05558i
$129$	0.0489845	−	0.747360i	0.00431285	−	0.0658013i
$130$	−2.62355	−	2.99158i	−0.230100	−	0.262379i
$131$	0.0722947	+	1.10300i	0.00631642	+	0.0963699i	0.999853	−	0.0171419i	$-0.00545669\pi$
$131$	0.0722947	+	1.10300i	0.00631642	+	0.0963699i	−0.993537	+	0.113512i	$0.963790\pi$
$132$	−2.05662	+	2.05662i	−0.179005	+	0.179005i
$133$		0			0
$134$	3.70843	+	8.95295i	0.320360	+	0.773417i
$135$	−1.84702	−	1.06638i	−0.158966	−	0.0917791i
$136$	2.43308	−	13.1390i	0.208635	−	1.12666i
$137$	−1.13032	−	1.95778i	−0.0965701	−	0.167264i	0.813693	−	0.581295i	$-0.197454\pi$
$137$	−1.13032	−	1.95778i	−0.0965701	−	0.167264i	−0.910263	+	0.414031i	$0.864121\pi$
$138$	−1.23357	−	0.162403i	−0.105009	−	0.0138246i
$139$	17.9220	+	3.56491i	1.52012	+	0.302372i	0.883363	−	0.468689i	$-0.155274\pi$
$139$	17.9220	+	3.56491i	1.52012	+	0.302372i	0.636762	+	0.771061i	$0.280274\pi$
$140$		0			0
$141$	−2.83604	+	1.89498i	−0.238838	+	0.159586i
$142$	−35.4563	−	12.0358i	−2.97543	−	1.01002i
$143$	4.05951	+	0.266074i	0.339473	+	0.0222503i
$144$	2.12890	−	0.280275i	0.177409	−	0.0233563i
$145$	2.59519	+	3.38212i	0.215519	+	0.280870i
$146$	−26.5634	−	17.7491i	−2.19840	−	1.46892i
$147$		0			0
$148$	−1.15987	−	1.73586i	−0.0953405	−	0.142687i
$149$	14.4949	−	3.88389i	1.18747	−	0.318181i	0.389582	−	0.920992i	$-0.372619\pi$
$149$	14.4949	−	3.88389i	1.18747	−	0.318181i	0.797884	+	0.602811i	$0.205953\pi$
$150$	−2.28297	+	0.774965i	−0.186404	+	0.0632756i
$151$	−3.63168	+	4.73289i	−0.295542	+	0.385157i	−0.917396	−	0.397975i	$-0.869713\pi$
$151$	−3.63168	+	4.73289i	−0.295542	+	0.385157i	0.621854	+	0.783133i	$0.286380\pi$
$152$	5.30954	−	9.19639i	0.430661	−	0.745926i
$153$	−7.79782	+	9.13291i	−0.630417	+	0.738352i
$154$		0			0
$155$	−1.95690	+	0.810574i	−0.157182	+	0.0651069i
$156$	1.05942	+	0.929087i	0.0848215	+	0.0743865i
$157$	−2.63211	+	9.82316i	−0.210065	+	0.783973i	0.777781	+	0.628536i	$0.216345\pi$
$157$	−2.63211	+	9.82316i	−0.210065	+	0.783973i	−0.987846	+	0.155437i	$0.950321\pi$
$158$	24.8570	+	12.2581i	1.97751	+	0.975201i
$159$	−0.757533	+	2.23162i	−0.0600763	+	0.176979i
$160$	3.23312	−	4.83870i	0.255600	−	0.382533i
$161$		0			0
$162$	−17.6422	−	7.30763i	−1.38610	−	0.574142i
$163$	2.34548	+	4.75616i	0.183712	+	0.372531i	0.969173	−	0.246379i	$-0.0792409\pi$
$163$	2.34548	+	4.75616i	0.183712	+	0.372531i	−0.785461	+	0.618911i	$0.787574\pi$
$164$	−19.3970	+	17.0107i	−1.51465	+	1.32832i
$165$	−0.462309	+	0.937469i	−0.0359907	+	0.0729819i
$166$	4.97554	+	18.5690i	0.386177	+	1.44123i
$167$	4.01155	−	20.1674i	0.310423	−	1.56060i	−0.438987	−	0.898494i	$-0.644663\pi$
$167$	4.01155	−	20.1674i	0.310423	−	1.56060i	0.749409	−	0.662107i	$-0.230337\pi$
$168$		0			0
$169$			11.0290i			0.848387i
$170$	−1.67860	−	11.5647i	−0.128743	−	0.886969i
$171$	−8.26497	+	4.77178i	−0.632038	+	0.364907i
$172$	6.82445	+	5.23659i	0.520360	+	0.399286i
$173$	14.4679	−	16.4974i	1.09997	−	1.25428i	0.135304	−	0.990804i	$-0.456799\pi$
$173$	14.4679	−	16.4974i	1.09997	−	1.25428i	0.964667	−	0.263472i	$-0.0848677\pi$
$174$	−1.69635	−	1.69635i	−0.128600	−	0.128600i
$175$		0			0
$176$	−0.416779	−	2.09529i	−0.0314159	−	0.157938i
$177$	2.24507	−	1.10714i	0.168750	−	0.0832181i
$178$	2.60976	+	19.8231i	0.195610	+	1.48581i
$179$	0.793559	+	6.02768i	0.0593134	+	0.450530i	0.995171	+	0.0981524i	$0.0312933\pi$
$179$	0.793559	+	6.02768i	0.0593134	+	0.450530i	−0.935858	+	0.352377i	$0.885373\pi$
$180$	10.8222	−	5.33691i	0.806639	−	0.397790i
$181$	0.178749	+	0.898634i	0.0132863	+	0.0667949i	0.986860	−	0.161580i	$-0.0516589\pi$
$181$	0.178749	+	0.898634i	0.0132863	+	0.0667949i	−0.973573	+	0.228375i	$0.926659\pi$
$182$		0			0
$183$	−2.02423	−	2.02423i	−0.149635	−	0.149635i
$184$	3.87196	−	4.41512i	0.285444	−	0.325487i
$185$	−0.595243	−	0.456746i	−0.0437631	−	0.0335806i
$186$	1.03226	−	0.595978i	0.0756893	−	0.0436992i
$187$	9.57435	+	7.14722i	0.700146	+	0.522657i
$188$		−	39.1748i		−	2.85712i
$189$		0			0
$190$	1.81176	−	9.10832i	0.131439	−	0.660787i
$191$	2.10455	+	7.85429i	0.152280	+	0.568317i	0.999323	+	0.0367922i	$0.0117140\pi$
$191$	2.10455	+	7.85429i	0.152280	+	0.568317i	−0.847043	+	0.531524i	$0.821619\pi$
$192$	−1.64121	+	3.32804i	−0.118444	+	0.240180i
$193$	10.2711	−	9.00755i	0.739333	−	0.648378i	−0.204475	−	0.978872i	$-0.565549\pi$
$193$	10.2711	−	9.00755i	0.739333	−	0.648378i	0.943808	+	0.330494i	$0.107215\pi$
$194$	4.13082	+	8.37648i	0.296576	+	0.601396i
$195$	0.467861	+	0.193794i	0.0335042	+	0.0138779i
$196$		0			0
$197$	−1.91933	+	2.87248i	−0.136747	+	0.204656i	−0.893522	−	0.449019i	$-0.851774\pi$
$197$	−1.91933	+	2.87248i	−0.136747	+	0.204656i	0.756775	+	0.653675i	$0.226774\pi$
$198$	−6.30162	+	18.5640i	−0.447837	+	1.31928i
$199$	−19.4141	−	9.57400i	−1.37623	−	0.678683i	−0.404450	−	0.914560i	$-0.632537\pi$
$199$	−19.4141	−	9.57400i	−1.37623	−	0.678683i	−0.971783	+	0.235878i	$0.924204\pi$
$200$	2.94510	−	10.9913i	0.208250	−	0.777200i
$201$	−0.927260	−	0.813185i	−0.0654039	−	0.0573577i
$202$	−40.3454	+	16.7116i	−2.83869	+	1.17582i
$203$		0			0
$204$	1.12393	+	3.98281i	0.0786906	+	0.278852i
$205$	−4.63594	+	8.02969i	−0.323788	+	0.560818i
$206$	−10.9597	+	14.2830i	−0.763601	+	0.995144i
$207$	−4.99757	+	1.69645i	−0.347355	+	0.117911i
$208$	−0.999743	+	0.267880i	−0.0693197	+	0.0185742i
$209$	5.27512	+	7.89477i	0.364888	+	0.546093i
$210$		0			0
$211$	−19.6995	−	13.1628i	−1.35617	−	0.906165i	−0.356566	−	0.934270i	$-0.616053\pi$
$211$	−19.6995	−	13.1628i	−1.35617	−	0.906165i	−0.999605	+	0.0281055i	$0.991053\pi$
$212$	−16.4775	−	21.4739i	−1.13168	−	1.47483i
$213$	4.72465	−	0.622012i	0.323728	−	0.0426196i
$214$	−26.9869	−	1.76882i	−1.84479	−	0.120914i
$215$	2.92737	+	0.993707i	0.199645	+	0.0677703i
$216$	−4.70994	+	3.14708i	−0.320471	+	0.214132i
$217$		0			0
$218$	−11.3283	−	2.25334i	−0.767249	−	0.152615i
$219$	4.03116	+	0.530713i	0.272401	+	0.0358623i
$220$	−6.00257	−	10.3968i	−0.404693	−	0.700949i
$221$	3.15189	−	4.85511i	0.212019	−	0.326590i
$222$	0.365650	+	0.211108i	0.0245408	+	0.0141686i
$223$	−1.69064	−	4.08158i	−0.113214	−	0.273323i	0.857109	−	0.515135i	$-0.172258\pi$
$223$	−1.69064	−	4.08158i	−0.113214	−	0.273323i	−0.970323	+	0.241812i	$0.922258\pi$
$224$		0			0
$225$	−7.23124	+	7.23124i	−0.482083	+	0.482083i
$226$	−2.74382	−	41.8626i	−0.182516	−	2.78466i
$227$	−4.43707	−	5.05951i	−0.294499	−	0.335811i	0.585602	−	0.810599i	$-0.300858\pi$
$227$	−4.43707	−	5.05951i	−0.294499	−	0.335811i	−0.880100	+	0.474788i	$0.842525\pi$
$228$	−0.215095	+	3.28171i	−0.0142450	+	0.217337i
$229$	4.71706	−	3.61953i	0.311712	−	0.239185i	−0.441043	−	0.897486i	$-0.645391\pi$
$229$	4.71706	−	3.61953i	0.311712	−	0.239185i	0.752755	+	0.658301i	$0.228725\pi$
$230$	1.96532	−	4.74471i	0.129590	−	0.312857i
$231$		0			0
$232$	11.1052	−	2.20895i	0.729090	−	0.145025i
$233$	6.45807	−	0.423284i	0.423082	−	0.0277303i	0.147625	−	0.989043i	$-0.452837\pi$
$233$	6.45807	−	0.423284i	0.423082	−	0.0277303i	0.275458	+	0.961313i	$0.411171\pi$
$234$	9.17427	+	2.45824i	0.599741	+	0.160700i
$235$	−4.52548	−	13.3316i	−0.295210	−	0.869659i
$236$	−3.75264	+	28.5041i	−0.244276	+	1.85546i
$237$	−3.52730			−0.229123
$238$		0			0
$239$	9.05783			0.585902			0.292951	−	0.956127i	$-0.405363\pi$
$239$	9.05783			0.585902			0.292951	+	0.956127i	$0.405363\pi$
$240$	0.0347108	−	0.263654i	0.00224057	−	0.0170188i
$241$	6.68888	+	19.7048i	0.430869	+	1.26930i	0.918212	+	0.396088i	$0.129633\pi$
$241$	6.68888	+	19.7048i	0.430869	+	1.26930i	−0.487344	+	0.873210i	$0.662034\pi$
$242$	−5.83990	−	1.56480i	−0.375403	−	0.100589i
$243$	7.65751	−	0.501900i	0.491230	−	0.0321969i
$244$	32.2469	−	6.41432i	2.06440	−	0.410635i
$245$		0			0
$246$	1.99671	−	4.82048i	0.127306	−	0.307343i
$247$	3.64951	−	2.80037i	0.232213	−	0.178183i
$248$	−0.367943	+	5.61372i	−0.0233644	+	0.356472i
$249$	−1.61318	−	1.83948i	−0.102231	−	0.116572i
$250$	−1.57769	−	24.0709i	−0.0997817	−	1.52238i
$251$	−14.0153	+	14.0153i	−0.884635	+	0.884635i	−0.994001	−	0.109367i	$-0.965118\pi$
$251$	−14.0153	+	14.0153i	−0.884635	+	0.884635i	0.109367	+	0.994001i	$0.465118\pi$
$252$		0			0
$253$	2.00939	+	4.85109i	0.126329	+	0.304985i
$254$	−16.3179	−	9.42115i	−1.02388	−	0.591136i
$255$	0.842579	+	1.22556i	0.0527643	+	0.0767474i
$256$	−10.2313	−	17.7212i	−0.639459	−	1.10757i
$257$	−9.37853	−	1.23471i	−0.585017	−	0.0770189i	−0.167792	−	0.985822i	$-0.553664\pi$
$257$	−9.37853	−	1.23471i	−0.585017	−	0.0770189i	−0.417224	+	0.908803i	$0.636997\pi$
$258$	−1.70624	−	0.339392i	−0.106226	−	0.0211296i
$259$		0			0
$260$	−4.83602	+	3.23133i	−0.299917	+	0.200398i
$261$	−9.63591	−	3.27095i	−0.596448	−	0.202467i
$262$	2.56202	+	0.167924i	0.158282	+	0.0103744i
$263$	28.6728	−	3.77484i	1.76804	−	0.232767i	0.824927	−	0.565240i	$-0.191216\pi$
$263$	28.6728	−	3.77484i	1.76804	−	0.232767i	0.943113	+	0.332473i	$0.107883\pi$
$264$	1.69006	+	2.20253i	0.104016	+	0.135556i
$265$	−8.08812	−	5.40431i	−0.496849	−	0.331984i
$266$		0			0
$267$	−1.41373	−	2.11580i	−0.0865191	−	0.129485i
$268$	13.6824	−	3.66618i	0.835783	−	0.223947i
$269$	7.09593	−	2.40874i	0.432647	−	0.146864i	−0.0966161	−	0.995322i	$-0.530802\pi$
$269$	7.09593	−	2.40874i	0.432647	−	0.146864i	0.529263	+	0.848458i	$0.322469\pi$
$270$	−3.01574	+	3.93019i	−0.183532	+	0.239183i
$271$	0.609518	−	1.05572i	0.0370256	−	0.0641302i	−0.846919	−	0.531722i	$-0.821545\pi$
$271$	0.609518	−	1.05572i	0.0370256	−	0.0641302i	0.883944	+	0.467592i	$0.154878\pi$
$272$	−2.89106	−	0.938874i	−0.175296	−	0.0569276i
$273$		0			0
$274$	−4.85126	+	2.00946i	−0.293075	+	0.121396i
$275$	7.64955	+	6.70847i	0.461285	+	0.404536i
$276$	−0.470715	+	1.75673i	−0.0283337	+	0.105743i
$277$	−0.838923	−	0.413711i	−0.0504060	−	0.0248575i	0.416911	−	0.908947i	$-0.363113\pi$
$277$	−0.838923	−	0.413711i	−0.0504060	−	0.0248575i	−0.467317	+	0.884090i	$0.654779\pi$
$278$	13.6432	−	40.1917i	0.818268	−	2.41054i
$279$	2.80895	−	4.20390i	0.168168	−	0.251681i
$280$		0			0
$281$	5.59849	+	2.31897i	0.333978	+	0.138338i	0.543369	−	0.839494i	$-0.317148\pi$
$281$	5.59849	+	2.31897i	0.333978	+	0.138338i	−0.209391	+	0.977832i	$0.567148\pi$
$282$	3.50411	+	7.10564i	0.208667	+	0.423135i
$283$	−16.8877	+	14.8101i	−1.00387	+	0.880369i	−0.992826	−	0.119570i	$-0.961848\pi$
$283$	−16.8877	+	14.8101i	−1.00387	+	0.880369i	−0.0110427	+	0.999939i	$0.503515\pi$
$284$	−24.2074	+	49.0877i	−1.43644	+	2.91282i
$285$	0.305904	+	1.14165i	0.0181202	+	0.0676256i
$286$	1.84351	−	9.26797i	0.109009	−	0.548026i
$287$		0			0
$288$			13.8910i			0.818537i
$289$	15.5282	−	6.91928i	0.913421	−	0.407016i
$290$	8.57549	−	4.95106i	0.503570	−	0.290736i
$291$	−0.943024	−	0.723608i	−0.0552811	−	0.0424187i
$292$	−30.7904	+	35.1098i	−1.80187	+	2.05464i
$293$	−11.6686	−	11.6686i	−0.681688	−	0.681688i	0.278692	−	0.960380i	$-0.410099\pi$
$293$	−11.6686	−	11.6686i	−0.681688	−	0.681688i	−0.960380	+	0.278692i	$0.910099\pi$
$294$		0			0
$295$	2.01573	+	10.1338i	0.117360	+	0.590011i
$296$	−1.78726	+	0.881377i	−0.103882	+	0.0512290i
$297$	−0.661109	−	5.02162i	−0.0383614	−	0.291384i
$298$	−4.54961	−	34.5577i	−0.263552	−	2.00187i
$299$	2.28155	−	1.12513i	0.131945	−	0.0650682i
$300$	0.687519	+	3.45639i	0.0396939	+	0.199555i
$301$		0			0
$302$	9.79831	+	9.79831i	0.563829	+	0.563829i
$303$	3.66452	−	4.17859i	0.210521	−	0.240054i
$304$	−1.91646	−	1.47055i	−0.109917	−	0.0843419i
$305$	10.2330	−	5.90803i	0.585940	−	0.338293i
$306$	18.6680	+	20.7265i	1.06718	+	1.18486i
$307$		−	11.4234i		−	0.651969i	−0.945375	−	0.325985i	$-0.894304\pi$
$307$		−	11.4234i		−	0.651969i	0.945375	−	0.325985i	$-0.105696\pi$
$308$		0			0
$309$	0.447007	−	2.24725i	0.0254293	−	0.127842i
$310$	1.27337	+	4.75229i	0.0723227	+	0.269912i
$311$	4.98404	−	10.1066i	0.282619	−	0.573095i	−0.708556	−	0.705655i	$-0.750653\pi$
$311$	4.98404	−	10.1066i	0.282619	−	0.573095i	0.991175	+	0.132560i	$0.0423197\pi$
$312$	1.01124	−	0.886835i	0.0572503	−	0.0502072i
$313$	−12.3688	−	25.0814i	−0.699125	−	1.41768i	−0.899038	−	0.437871i	$-0.855733\pi$
$313$	−12.3688	−	25.0814i	−0.699125	−	1.41768i	0.199913	−	0.979814i	$-0.435934\pi$
$314$	21.8237	+	9.03967i	1.23158	+	0.510138i
$315$		0			0
$316$	22.5072	−	33.6845i	1.26613	−	1.89490i
$317$	−2.75066	+	8.10319i	−0.154493	+	0.455120i	−0.996427	−	0.0844596i	$-0.973084\pi$
$317$	−2.75066	+	8.10319i	−0.154493	+	0.455120i	0.841934	+	0.539580i	$0.181417\pi$
$318$	4.90952	+	2.42111i	0.275312	+	0.135769i
$319$	−2.62032	+	9.77915i	−0.146710	+	0.547527i
$320$	−11.5155	−	10.0988i	−0.643734	−	0.564540i
$321$	3.17998	−	1.31719i	0.177489	−	0.0735185i
$322$		0			0
$323$	13.4681	−	1.06204i	0.749386	−	0.0590934i
$324$	−13.9564	+	24.1732i	−0.775355	+	1.34295i
$325$	3.00077	−	3.91068i	0.166453	−	0.216925i
$326$	11.6641	−	3.95941i	0.646012	−	0.219292i
$327$	1.41991	−	0.380463i	0.0785211	−	0.0210397i
$328$	13.6816	+	20.4759i	0.755438	+	1.13059i
$329$		0			0
$330$	2.01873	+	1.34887i	0.111128	+	0.0742530i
$331$	−9.90100	−	12.9032i	−0.544208	−	0.709226i	0.437585	−	0.899177i	$-0.355834\pi$
$331$	−9.90100	−	12.9032i	−0.544208	−	0.709226i	−0.981794	+	0.189951i	$0.939167\pi$
$332$	27.8599	−	3.66782i	1.52901	−	0.201298i
$333$	1.78710	+	0.117133i	0.0979325	+	0.00641883i
$334$	−45.2272	−	15.3526i	−2.47472	−	0.840055i
$335$	4.23274	−	2.82823i	0.231259	−	0.154522i
$336$		0			0
$337$	5.14392	+	1.02319i	0.280207	+	0.0557366i	0.333193	−	0.942859i	$-0.391874\pi$
$337$	5.14392	+	1.02319i	0.280207	+	0.0557366i	−0.0529861	+	0.998595i	$0.516874\pi$
$338$	25.3987	+	3.34381i	1.38151	+	0.181879i
$339$	2.66964	+	4.62395i	0.144995	+	0.251139i
$340$	−17.0800	+	0.226206i	−0.926294	+	0.0122677i
$341$	−4.35631	−	2.51512i	−0.235907	−	0.136201i
$342$	8.48313	+	20.4801i	0.458715	+	1.10744i
$343$		0			0
$344$	5.80594	−	5.80594i	0.313035	−	0.313035i
$345$	0.0427483	+	0.652212i	0.00230149	+	0.0351139i
$346$	−33.6055	−	38.3197i	−1.80664	−	2.06008i
$347$	−1.30154	+	19.8577i	−0.0698705	+	1.06602i	0.808643	+	0.588300i	$0.200203\pi$
$347$	−1.30154	+	19.8577i	−0.0698705	+	1.06602i	−0.878513	+	0.477718i	$0.841464\pi$
$348$	−2.78203	+	2.13473i	−0.149133	+	0.114434i
$349$	−9.16782	+	22.1331i	−0.490742	+	1.18476i	0.463601	+	0.886044i	$0.346557\pi$
$349$	−9.16782	+	22.1331i	−0.490742	+	1.18476i	−0.954343	+	0.298712i	$0.903443\pi$
$350$		0			0
$351$	−2.40671	+	0.478725i	−0.128461	+	0.0255524i
$352$	13.7907	−	0.903890i	0.735047	−	0.0481775i
$353$	13.8475	+	3.71043i	0.737029	+	0.197486i	0.607757	−	0.794123i	$-0.292069\pi$
$353$	13.8475	+	3.71043i	0.737029	+	0.197486i	0.129272	+	0.991609i	$0.458736\pi$
$354$	−1.86898	−	5.50582i	−0.0993349	−	0.292631i
$355$	−2.56742	+	19.5015i	−0.136265	+	1.03503i
$356$	29.2260			1.54898
$357$		0			0
$358$	14.1217			0.746355
$359$	−4.18927	+	31.8207i	−0.221101	+	1.67943i	0.416556	+	0.909110i	$0.363237\pi$
$359$	−4.18927	+	31.8207i	−0.221101	+	1.67943i	−0.637657	+	0.770320i	$0.720096\pi$
$360$	−3.70229	−	10.9066i	−0.195128	−	0.574828i
$361$	−7.98208	−	2.13879i	−0.420109	−	0.112568i
$362$	2.12365	−	0.139192i	0.111617	−	0.00731575i
$363$	0.754676	−	0.150114i	0.0396102	−	0.00787897i
$364$		0			0
$365$	−6.42244	+	15.5052i	−0.336166	+	0.811577i
$366$	−5.27529	+	4.04787i	−0.275744	+	0.211586i
$367$	1.38895	−	21.1914i	0.0725028	−	1.10618i	−0.794299	−	0.607527i	$-0.792162\pi$
$367$	1.38895	−	21.1914i	0.0725028	−	1.10618i	0.866802	−	0.498653i	$-0.166172\pi$
$368$	−0.880799	−	1.00436i	−0.0459148	−	0.0523558i
$369$	−1.44750	−	22.0846i	−0.0753539	−	1.14968i
$370$	−1.23231	+	1.23231i	−0.0640645	+	0.0640645i
$371$		0			0
$372$	−0.666755	−	1.60969i	−0.0345696	−	0.0834585i
$373$	8.57779	+	4.95239i	0.444141	+	0.256425i	0.705353	−	0.708857i	$-0.250789\pi$
$373$	8.57779	+	4.95239i	0.444141	+	0.256425i	−0.261212	+	0.965282i	$0.584122\pi$
$374$	19.3621	−	19.8818i	1.00119	−	1.02806i
$375$	1.53503	+	2.65876i	0.0792688	+	0.137298i
$376$	−37.0734	−	4.88080i	−1.91191	−	0.251708i
$377$	4.81068	+	0.956903i	0.247762	+	0.0492830i
$378$		0			0
$379$	−22.3558	+	14.9376i	−1.14834	+	0.767295i	−0.976006	−	0.217744i	$-0.930130\pi$
$379$	−22.3558	+	14.9376i	−1.14834	+	0.767295i	−0.172332	+	0.985039i	$0.555130\pi$
$380$	−12.8543	−	4.36345i	−0.659411	−	0.223840i
$381$	2.39292	+	0.156840i	0.122593	+	0.00803518i
$382$	18.7257	−	2.46528i	0.958089	−	0.126135i
$383$	13.8238	+	18.0155i	0.706361	+	0.920548i	0.999367	−	0.0355624i	$-0.0113223\pi$
$383$	13.8238	+	18.0155i	0.706361	+	0.920548i	−0.293006	+	0.956111i	$0.594656\pi$
$384$	4.82199	+	3.22195i	0.246071	+	0.164420i
$385$		0			0
$386$	−17.6294	−	26.3843i	−0.897315	−	1.34293i
$387$	−7.12780	+	1.90989i	−0.362326	+	0.0970850i
$388$	12.9275	−	4.38830i	0.656295	−	0.222782i
$389$	2.95523	−	3.85133i	0.149836	−	0.195270i	−0.712405	−	0.701769i	$-0.752394\pi$
$389$	2.95523	−	3.85133i	0.149836	−	0.195270i	0.862241	+	0.506499i	$0.169061\pi$
$390$	0.588135	−	1.01868i	0.0297814	−	0.0515828i
$391$	7.41942	+	0.876995i	0.375216	+	0.0443515i
$392$		0			0
$393$	−0.301894	+	0.125049i	−0.0152285	+	0.00630787i
$394$	6.03313	+	5.29091i	0.303945	+	0.266552i
$395$	3.76823	−	14.0632i	0.189600	−	0.707598i
$396$	25.7010	+	12.6743i	1.29152	+	0.636909i
$397$	6.59001	−	19.4136i	0.330743	−	0.974338i	−0.646628	−	0.762806i	$-0.723821\pi$
$397$	6.59001	−	19.4136i	0.330743	−	0.974338i	0.977371	−	0.211533i	$-0.0678454\pi$
$398$	−27.9339	+	41.8061i	−1.40020	+	2.09555i
$399$		0			0
$400$	−2.39148	−	0.990581i	−0.119574	−	0.0495291i
$401$	13.6354	+	27.6498i	0.680917	+	1.38076i	0.912956	+	0.408057i	$0.133794\pi$
$401$	13.6354	+	27.6498i	0.680917	+	1.38076i	−0.232039	+	0.972707i	$0.574540\pi$
$402$	−2.15381	+	1.88884i	−0.107422	+	0.0942068i
$403$	−1.07788	+	2.18572i	−0.0536928	+	0.108878i
$404$	16.5212	+	61.6579i	0.821959	+	3.06759i
$405$	−1.95703	+	9.83864i	−0.0972455	+	0.488886i
$406$		0			0
$407$		−	1.78181i		−	0.0883212i
$408$	3.90919	−	0.567417i	0.193534	−	0.0280913i
$409$	−17.7734	+	10.2615i	−0.878837	+	0.507397i	−0.870275	−	0.492566i	$-0.836059\pi$
$409$	−17.7734	+	10.2615i	−0.878837	+	0.507397i	−0.00856243	+	0.999963i	$0.502726\pi$
$410$	17.0860	+	13.1106i	0.843818	+	0.647484i
$411$	0.440633	−	0.502446i	0.0217348	−	0.0247838i
$412$	18.6082	+	18.6082i	0.916759	+	0.916759i
$413$		0			0
$414$	2.39157	+	12.0232i	0.117539	+	0.590909i
$415$	9.05731	−	4.46657i	0.444606	−	0.219255i
$416$	−0.873956	−	6.63835i	−0.0428492	−	0.325472i
$417$	0.705085	+	5.35565i	0.0345282	+	0.262268i
$418$	19.7802	−	9.75450i	0.967480	−	0.477108i
$419$	−0.549943	−	2.76475i	−0.0268665	−	0.135067i	0.965024	−	0.262161i	$-0.0844351\pi$
$419$	−0.549943	−	2.76475i	−0.0268665	−	0.135067i	−0.991891	+	0.127094i	$0.959435\pi$
$420$		0			0
$421$	−1.40311	−	1.40311i	−0.0683836	−	0.0683836i	0.672088	−	0.740471i	$-0.265398\pi$
$421$	−1.40311	−	1.40311i	−0.0683836	−	0.0683836i	−0.740471	+	0.672088i	$0.765398\pi$
$422$	−36.2851	+	41.3752i	−1.76633	+	2.01412i
$423$	26.6615	+	20.4581i	1.29633	+	0.994705i
$424$	−22.3749	+	12.9181i	−1.08662	+	0.627360i
$425$	13.6456	−	4.83452i	0.661909	−	0.234508i
$426$		−	11.0690i		−	0.536293i
$427$		0			0
$428$	−7.71234	+	38.7725i	−0.372790	+	1.87414i
$429$	0.311266	+	1.16166i	0.0150281	+	0.0560856i
$430$	3.17593	−	6.44015i	0.153157	−	0.310572i
$431$	−2.13119	+	1.86901i	−0.102656	+	0.0900268i	−0.709135	−	0.705072i	$-0.750915\pi$
$431$	−2.13119	+	1.86901i	−0.102656	+	0.0900268i	0.606480	+	0.795099i	$0.292581\pi$
$432$	0.569930	+	1.15570i	0.0274208	+	0.0556038i
$433$	14.5043	+	6.00788i	0.697032	+	0.288720i	0.702926	−	0.711262i	$-0.251876\pi$
$433$	14.5043	+	6.00788i	0.697032	+	0.288720i	−0.00589445	+	0.999983i	$0.501876\pi$
$434$		0			0
$435$	−0.700153	+	1.04785i	−0.0335698	+	0.0502407i
$436$	−5.42696	+	15.9873i	−0.259904	+	0.765653i
$437$	5.32498	+	2.62599i	0.254728	+	0.125618i
$438$	2.44435	−	9.12245i	0.116796	−	0.435888i
$439$	25.1601	+	22.0648i	1.20082	+	1.05309i	0.997256	+	0.0740343i	$0.0235874\pi$
$439$	25.1601	+	22.0648i	1.20082	+	1.05309i	0.203569	+	0.979061i	$0.434746\pi$
$440$	−10.5869	+	4.38524i	−0.504711	+	0.209058i
$441$		0			0
$442$	−10.2252	−	8.73045i	−0.486364	−	0.415265i
$443$	−16.5468	+	28.6599i	−0.786162	+	1.36167i	0.142141	+	0.989846i	$0.454602\pi$
$443$	−16.5468	+	28.6599i	−0.786162	+	1.36167i	−0.928302	+	0.371826i	$0.878732\pi$
$444$	0.375706	−	0.489629i	0.0178302	−	0.0232368i
$445$	9.94593	−	3.37619i	0.471482	−	0.160047i
$446$	−9.91202	+	2.65592i	−0.469348	+	0.125761i
$447$	2.46457	+	3.68849i	0.116570	+	0.174459i
$448$		0			0
$449$	−9.67076	−	6.46180i	−0.456392	−	0.304951i	0.306042	−	0.952018i	$-0.400995\pi$
$449$	−9.67076	−	6.46180i	−0.456392	−	0.304951i	−0.762433	+	0.647067i	$0.775995\pi$
$450$	14.4604	+	18.8452i	0.681671	+	0.888370i
$451$	−21.8309	+	2.87409i	−1.02798	+	0.135336i
$452$	−61.1917	−	4.01072i	−2.87822	−	0.188648i
$453$	−1.66997	−	0.566879i	−0.0784622	−	0.0266343i
$454$	−12.9968	+	8.68416i	−0.609968	+	0.407568i
$455$		0			0
$456$	3.07888	+	0.612426i	0.144182	+	0.0286795i
$457$	16.3444	+	2.15178i	0.764559	+	0.100656i	0.502713	−	0.864453i	$-0.332335\pi$
$457$	16.3444	+	2.15178i	0.764559	+	0.100656i	0.261846	+	0.965110i	$0.415669\pi$
$458$	−6.90527	−	11.9603i	−0.322662	−	0.558867i
$459$	−6.69404	−	2.66946i	−0.312451	−	0.124600i
$460$	−6.50117	−	3.75345i	−0.303118	−	0.175006i
$461$	3.58512	+	8.65524i	0.166976	+	0.403115i	0.985113	−	0.171908i	$-0.0549932\pi$
$461$	3.58512	+	8.65524i	0.166976	+	0.403115i	−0.818137	+	0.575023i	$0.804993\pi$
$462$		0			0
$463$	−16.4176	+	16.4176i	−0.762990	+	0.762990i	−0.976862	−	0.213872i	$-0.931392\pi$
$463$	−16.4176	+	16.4176i	−0.762990	+	0.762990i	0.213872	+	0.976862i	$0.431392\pi$
$464$	−0.168460	−	2.57020i	−0.00782055	−	0.119318i
$465$	−0.412855	−	0.470771i	−0.0191457	−	0.0218315i
$466$	0.983192	−	15.0006i	0.0455455	−	0.694890i
$467$	−3.00325	+	2.30448i	−0.138974	+	0.106638i	−0.675909	−	0.736985i	$-0.736249\pi$
$467$	−3.00325	+	2.30448i	−0.138974	+	0.106638i	0.536935	+	0.843624i	$0.319582\pi$
$468$	5.31293	−	12.8265i	0.245590	−	0.592907i
$469$		0			0
$470$	−32.0734	+	6.37980i	−1.47944	+	0.294278i
$471$	−2.99991	+	0.196624i	−0.138228	+	0.00905997i
$472$	26.5075	+	7.10268i	1.22011	+	0.326927i
$473$	2.35990	+	6.95204i	0.108508	+	0.319655i
$474$	−1.06941	+	8.12301i	−0.0491198	+	0.373102i
$475$	11.5047			0.527870
$476$		0			0
$477$	23.2195			1.06315
$478$	2.74617	−	20.8592i	0.125607	−	0.954080i
$479$	0.726690	+	2.14076i	0.0332033	+	0.0978138i	0.962268	−	0.272104i	$-0.0877193\pi$
$479$	0.726690	+	2.14076i	0.0332033	+	0.0978138i	−0.929065	+	0.369917i	$0.879386\pi$
$480$	1.66172	+	0.445256i	0.0758467	+	0.0203231i
$481$	−0.861403	+	0.0564593i	−0.0392766	+	0.00257432i
$482$	47.4061	−	9.42966i	2.15929	−	0.429509i
$483$		0			0
$484$	−3.38195	+	8.16475i	−0.153725	+	0.371125i
$485$	3.89244	−	2.98677i	0.176746	−	0.135622i
$486$	1.16580	−	17.7866i	0.0528816	−	0.806818i
$487$	11.2034	+	12.7750i	0.507675	+	0.578893i	0.947728	−	0.319079i	$-0.103374\pi$
$487$	11.2034	+	12.7750i	0.507675	+	0.578893i	−0.440053	+	0.897972i	$0.645040\pi$
$488$	−2.05258	−	31.3163i	−0.0929159	−	1.41762i
$489$	−1.10852	+	1.10852i	−0.0501288	+	0.0501288i
$490$		0			0
$491$	−8.10418	−	19.5652i	−0.365737	−	0.882966i	−0.994438	−	0.105320i	$-0.966413\pi$
$491$	−8.10418	−	19.5652i	−0.365737	−	0.882966i	0.628702	−	0.777647i	$-0.283587\pi$
$492$	−6.60499	−	3.81339i	−0.297776	−	0.171921i
$493$	10.3200	+	10.0502i	0.464787	+	0.452637i
$494$	−5.34249	−	9.25347i	−0.240370	−	0.416333i
$495$	10.2105	+	1.34423i	0.458927	+	0.0604188i
$496$	1.25517	+	0.249669i	0.0563587	+	0.0112105i
$497$		0			0
$498$	−4.72522	+	3.15729i	−0.211742	+	0.141482i
$499$	−18.6758	−	6.33957i	−0.836043	−	0.283798i	−0.129598	−	0.991567i	$-0.541369\pi$
$499$	−18.6758	−	6.33957i	−0.836043	−	0.283798i	−0.706445	+	0.707768i	$0.749702\pi$
$500$	−35.1850	−	2.30615i	−1.57352	−	0.103134i
$501$	6.02665	−	0.793423i	0.269251	−	0.0354475i
$502$	28.0265	+	36.5248i	1.25088	+	1.63018i
$503$	−26.9483	−	18.0063i	−1.20157	−	0.802862i	−0.216711	−	0.976236i	$-0.569533\pi$
$503$	−26.9483	−	18.0063i	−1.20157	−	0.802862i	−0.984856	+	0.173374i	$0.944533\pi$
$504$		0			0
$505$	12.7451	+	19.0743i	0.567148	+	0.848796i
$506$	11.7808	−	3.15664i	0.523719	−	0.140330i
$507$	−3.08736	+	1.04802i	−0.137114	+	0.0465440i
$508$	−16.7667	+	21.8508i	−0.743901	+	0.969471i
$509$	5.61445	−	9.72451i	0.248856	−	0.431031i	−0.714353	−	0.699786i	$-0.753279\pi$
$509$	5.61445	−	9.72451i	0.248856	−	0.431031i	0.963209	+	0.268755i	$0.0866121\pi$
$510$	3.07779	−	1.56880i	0.136287	−	0.0694678i
$511$		0			0
$512$	−7.66320	+	3.17420i	−0.338669	+	0.140281i
$513$	−4.30590	−	3.77617i	−0.190110	−	0.166722i
$514$	−5.68681	+	21.2234i	−0.250834	+	0.936126i
$515$	8.48218	+	4.18295i	0.373770	+	0.184323i
$516$	−0.817394	+	2.40797i	−0.0359838	+	0.106005i
$517$	18.5754	−	27.8001i	0.816947	−	1.22265i
$518$		0			0
$519$	5.99291	+	2.48234i	0.263059	+	0.108963i
$520$	2.45547	+	4.97920i	0.107679	+	0.218352i
$521$	24.0953	−	21.1310i	1.05564	−	0.925768i	0.0582696	−	0.998301i	$-0.481442\pi$
$521$	24.0953	−	21.1310i	1.05564	−	0.925768i	0.997366	+	0.0725333i	$0.0231084\pi$
$522$	−10.4541	+	21.1988i	−0.457563	+	0.927847i
$523$	−7.97819	−	29.7750i	−0.348862	−	1.30197i	−0.888035	−	0.459775i	$-0.847930\pi$
$523$	−7.97819	−	29.7750i	−0.348862	−	1.30197i	0.539174	−	0.842195i	$-0.318737\pi$
$524$	0.732177	−	3.68090i	0.0319853	−	0.160801i
$525$		0			0
$526$		−	67.1749i		−	2.92897i
$527$	−6.15045	+	3.66041i	−0.267918	+	0.159450i
$528$	0.546930	−	0.315770i	0.0238021	−	0.0137421i
$529$	−15.6423	−	12.0027i	−0.680099	−	0.521858i
$530$	−14.8977	+	16.9876i	−0.647117	+	0.737895i
$531$	−17.4395	−	17.4395i	−0.756811	−	0.756811i
$532$		0			0
$533$	2.08120	+	10.4629i	0.0901467	+	0.453198i
$534$	−5.30109	+	2.61421i	−0.229401	+	0.113128i
$535$	1.85441	+	14.0856i	0.0801732	+	0.608976i
$536$	−1.76482	−	13.4052i	−0.0762288	−	0.579015i
$537$	−1.61192	+	0.794911i	−0.0695595	+	0.0343029i
$538$	−3.39573	−	17.0715i	−0.146400	−	0.736004i
$539$		0			0
$540$	5.12033	+	5.12033i	0.220344	+	0.220344i
$541$	17.0016	−	19.3866i	0.730957	−	0.833496i	−0.260288	−	0.965531i	$-0.583818\pi$
$541$	17.0016	−	19.3866i	0.730957	−	0.833496i	0.991245	+	0.132035i	$0.0421510\pi$
$542$	−2.24641	−	1.72373i	−0.0964916	−	0.0740406i
$543$	−0.234569	+	0.135429i	−0.0100663	+	0.00581179i
$544$	8.46295	−	17.7499i	0.362846	−	0.761022i
$545$			6.06757i			0.259906i
$546$		0			0
$547$	−4.11814	+	20.7033i	−0.176079	+	0.885208i	0.787198	+	0.616700i	$0.211531\pi$
$547$	−4.11814	+	20.7033i	−0.176079	+	0.885208i	−0.963277	+	0.268509i	$0.913469\pi$
$548$	1.98656	+	7.41394i	0.0848615	+	0.316708i
$549$	−12.4747	+	25.2962i	−0.532408	+	1.07962i
$550$	17.7681	−	15.5822i	0.757636	−	0.664429i
$551$	5.06322	+	10.2672i	0.215700	+	0.437397i
$552$	1.60385	+	0.664337i	0.0682644	+	0.0282760i
$553$		0			0
$554$	−1.20708	+	1.80652i	−0.0512839	+	0.0767518i
$555$	0.0712948	−	0.210028i	0.00302630	−	0.00891518i
$556$	−55.6436	−	27.4404i	−2.35982	−	1.16373i
$557$	−0.332208	+	1.23982i	−0.0140761	+	0.0525327i	−0.972607	−	0.232457i	$-0.925324\pi$
$557$	−0.332208	+	1.23982i	−0.0140761	+	0.0525327i	0.958531	+	0.284990i	$0.0919902\pi$
$558$	−8.82951	−	7.74327i	−0.373783	−	0.327799i
$559$	3.28613	−	1.36116i	0.138988	−	0.0575709i
$560$		0			0
$561$	−1.09093	+	3.35930i	−0.0460593	+	0.141830i
$562$	7.03771	−	12.1897i	0.296868	−	0.514191i
$563$	−14.1398	+	18.4274i	−0.595922	+	0.776621i	−0.989788	−	0.142547i	$-0.954471\pi$
$563$	−14.1398	+	18.4274i	−0.595922	+	0.776621i	0.393866	+	0.919168i	$0.371137\pi$
$564$	10.9662	−	3.72253i	0.461761	−	0.156747i
$565$	−21.2875	+	5.70397i	−0.895573	+	0.239968i
$566$	28.9861	+	43.3807i	1.21838	+	1.82343i
$567$		0			0
$568$	43.4385	+	29.0247i	1.82264	+	1.21785i
$569$	−20.8099	−	27.1200i	−0.872397	−	1.13693i	−0.989604	−	0.143822i	$-0.954061\pi$
$569$	−20.8099	−	27.1200i	−0.872397	−	1.13693i	0.117207	−	0.993108i	$-0.462606\pi$
$570$	2.72185	−	0.358338i	0.114006	−	0.0150091i
$571$	−29.4285	−	1.92885i	−1.23155	−	0.0807198i	−0.564308	−	0.825564i	$-0.690857\pi$
$571$	−29.4285	−	1.92885i	−1.23155	−	0.0807198i	−0.667238	+	0.744844i	$0.732524\pi$
$572$	−13.0796	−	4.43993i	−0.546886	−	0.185643i
$573$	−1.99867	+	1.33547i	−0.0834956	+	0.0557900i
$574$		0			0
$575$	6.23991	+	1.24119i	0.260222	+	0.0517614i
$576$	36.2474	+	4.77206i	1.51031	+	0.198836i
$577$	3.70599	+	6.41896i	0.154282	+	0.267225i	0.932797	−	0.360401i	$-0.117360\pi$
$577$	3.70599	+	6.41896i	0.154282	+	0.267225i	−0.778515	+	0.627626i	$0.784027\pi$
$578$	−11.2265	−	37.8575i	−0.466962	−	1.57467i
$579$	3.49748	+	2.01927i	0.145350	+	0.0839181i
$580$	−5.53904	−	13.3724i	−0.229996	−	0.555259i
$581$		0			0
$582$	−1.95230	+	1.95230i	−0.0809255	+	0.0809255i
$583$	−1.51090	−	23.0518i	−0.0625750	−	0.954709i
$584$	29.3902	+	33.5131i	1.21618	+	1.38678i
$585$	0.326325	−	4.97876i	0.0134919	−	0.205846i
$586$	−30.4093	+	23.3339i	−1.25620	+	0.963915i
$587$	−13.7594	+	33.2180i	−0.567909	+	1.37105i	0.335405	+	0.942074i	$0.391127\pi$
$587$	−13.7594	+	33.2180i	−0.567909	+	1.37105i	−0.903314	+	0.428980i	$0.858873\pi$
$588$		0			0
$589$	−5.57860	+	1.10965i	−0.229862	+	0.0457225i
$590$	23.9482	−	1.56965i	0.985930	−	0.0646213i
$591$	−0.986476	−	0.264325i	−0.0405782	−	0.0108729i
$592$	0.145714	+	0.429260i	0.00598881	+	0.0176425i
$593$	5.64494	−	42.8776i	0.231810	−	1.76077i	−0.340038	−	0.940412i	$-0.610440\pi$
$593$	5.64494	−	42.8776i	0.231810	−	1.76077i	0.571848	−	0.820360i	$-0.306227\pi$
$594$	−11.7647			−0.482712
$595$		0			0
$596$	−50.9498			−2.08699
$597$	0.835250	−	6.34435i	0.0341845	−	0.259657i
$598$	−1.89934	−	5.59528i	−0.0776699	−	0.228808i
$599$	−19.6235	−	5.25810i	−0.801794	−	0.214840i	−0.165423	−	0.986223i	$-0.552899\pi$
$599$	−19.6235	−	5.25810i	−0.801794	−	0.214840i	−0.636372	+	0.771383i	$0.719565\pi$
$600$	3.35664	−	0.220006i	0.137034	−	0.00898170i
$601$	−23.9093	+	4.75585i	−0.975280	+	0.193995i	−0.656908	−	0.753971i	$-0.728136\pi$
$601$	−23.9093	+	4.75585i	−0.975280	+	0.193995i	−0.318372	+	0.947966i	$0.603136\pi$
$602$		0			0
$603$	−4.65015	+	11.2265i	−0.189369	+	0.457177i
$604$	16.0694	−	12.3305i	0.653853	−	0.501719i
$605$	−0.207723	+	3.16924i	−0.00844513	+	0.128848i
$606$	−8.51183	−	9.70589i	−0.345770	−	0.394275i
$607$	1.08024	+	16.4813i	0.0438456	+	0.668954i	0.962054	+	0.272858i	$0.0879688\pi$
$607$	1.08024	+	16.4813i	0.0438456	+	0.668954i	−0.918209	+	0.396097i	$0.870365\pi$
$608$	11.0501	−	11.0501i	0.448140	−	0.448140i
$609$		0			0
$610$	−10.5031	−	25.3568i	−0.425259	−	1.02667i
$611$	−14.0283	−	8.09925i	−0.567525	−	0.327661i
$612$	33.5990	−	23.0996i	1.35816	−	0.933744i
$613$	−24.0567	−	41.6674i	−0.971639	−	1.68293i	−0.690607	−	0.723231i	$-0.742656\pi$
$613$	−24.0567	−	41.6674i	−0.971639	−	1.68293i	−0.281033	−	0.959698i	$-0.590677\pi$
$614$	−26.3070	−	3.46338i	−1.06166	−	0.139771i
$615$	−2.68827	−	0.534731i	−0.108402	−	0.0215624i
$616$		0			0
$617$	22.3116	−	14.9081i	0.898230	−	0.600178i	−0.0184371	−	0.999830i	$-0.505869\pi$
$617$	22.3116	−	14.9081i	0.898230	−	0.600178i	0.916667	+	0.399652i	$0.130869\pi$
$618$	−5.03967	−	1.71074i	−0.202725	−	0.0688159i
$619$	32.8473	+	2.15293i	1.32024	+	0.0865334i	0.709169	−	0.705039i	$-0.249070\pi$
$619$	32.8473	+	2.15293i	1.32024	+	0.0865334i	0.611076	+	0.791572i	$0.290737\pi$
$620$	7.13007	−	0.938692i	0.286351	−	0.0376988i
$621$	−1.92804	−	2.51267i	−0.0773696	−	0.100830i
$622$	−21.7635	−	14.5419i	−0.872635	−	0.583076i
$623$		0			0
$624$	−0.169987	−	0.254403i	−0.00680491	−	0.0101843i
$625$	4.71714	−	1.26396i	0.188686	−	0.0505582i
$626$	−61.5099	+	20.8798i	−2.45843	+	0.834524i
$627$	−1.70872	+	2.22685i	−0.0682398	+	0.0889319i
$628$	17.2643	−	29.9027i	0.688921	−	1.19325i
$629$	−2.21219	−	1.23844i	−0.0882058	−	0.0493799i
$630$		0			0
$631$	24.2265	−	10.0349i	0.964441	−	0.399485i	0.155801	−	0.987788i	$-0.450204\pi$
$631$	24.2265	−	10.0349i	0.964441	−	0.399485i	0.808640	+	0.588304i	$0.200204\pi$
$632$	−29.0734	−	25.4966i	−1.15648	−	1.01420i
$633$	1.81275	−	6.76526i	0.0720502	−	0.268895i
$634$	17.8268	+	8.79123i	0.707995	+	0.349144i
$635$	−3.18169	+	9.37294i	−0.126261	+	0.371954i
$636$	4.44543	−	6.65305i	0.176273	−	0.263811i
$637$		0			0
$638$	21.7259	+	8.99918i	0.860138	+	0.356281i
$639$	−20.7662	−	42.1098i	−0.821500	−	1.66584i
$640$	−17.9972	+	15.7831i	−0.711400	+	0.623881i
$641$	5.52731	−	11.2083i	0.218316	−	0.442700i	−0.759971	−	0.649957i	$-0.774787\pi$
$641$	5.52731	−	11.2083i	0.218316	−	0.442700i	0.978287	+	0.207257i	$0.0664536\pi$
$642$	−2.06924	−	7.72252i	−0.0816665	−	0.304784i
$643$	−7.45861	+	37.4970i	−0.294139	+	1.47874i	0.497349	+	0.867551i	$0.334307\pi$
$643$	−7.45861	+	37.4970i	−0.294139	+	1.47874i	−0.791488	+	0.611185i	$0.790693\pi$
$644$		0			0
$645$			0.913883i			0.0359841i
$646$	1.63753	−	31.3377i	0.0644276	−	1.23296i
$647$	−5.15132	+	2.97412i	−0.202519	+	0.116925i	−0.597830	−	0.801623i	$-0.703970\pi$
$647$	−5.15132	+	2.97412i	−0.202519	+	0.116925i	0.395311	+	0.918547i	$0.370637\pi$
$648$	21.1376	+	16.2195i	0.830365	+	0.637161i
$649$	−16.1788	+	18.4483i	−0.635072	+	0.724161i
$650$	−8.09610	−	8.09610i	−0.317555	−	0.317555i
$651$		0			0
$652$	−3.51264	−	17.6592i	−0.137566	−	0.691589i
$653$	20.4628	−	10.0911i	0.800771	−	0.394896i	0.00461580	−	0.999989i	$-0.498531\pi$
$653$	20.4628	−	10.0911i	0.800771	−	0.394896i	0.796155	+	0.605093i	$0.206864\pi$
$654$	−0.445677	−	3.38525i	−0.0174273	−	0.132374i
$655$	−0.176050	−	1.33723i	−0.00687884	−	0.0522500i
$656$	5.02428	−	2.47770i	0.196165	−	0.0967380i
$657$	−7.81535	−	39.2904i	−0.304906	−	1.53287i
$658$		0			0
$659$	−32.6310	−	32.6310i	−1.27112	−	1.27112i	−0.945500	−	0.325623i	$-0.894426\pi$
$659$	−32.6310	−	32.6310i	−1.27112	−	1.27112i	−0.325623	−	0.945500i	$-0.605574\pi$
$660$	2.33998	−	2.66823i	0.0910835	−	0.103861i
$661$	9.40361	+	7.21564i	0.365758	+	0.280656i	0.775246	−	0.631660i	$-0.217626\pi$
$661$	9.40361	+	7.21564i	0.365758	+	0.280656i	−0.409488	+	0.912316i	$0.634293\pi$
$662$	−32.7166	+	18.8890i	−1.27157	+	0.734140i
$663$	1.65859	+	0.420958i	0.0644144	+	0.0163487i
$664$		−	26.8224i		−	1.04091i
$665$		0			0
$666$	0.811561	−	4.07999i	0.0314474	−	0.158097i
$667$	1.63850	+	6.11498i	0.0634431	+	0.236773i
$668$	−30.8783	+	62.6151i	−1.19472	+	2.42265i
$669$	0.981904	−	0.861107i	0.0379626	−	0.0332923i
$670$	−5.22982	−	10.6050i	−0.202046	−	0.409708i
$671$	25.9252	+	10.7386i	1.00083	+	0.414559i
$672$		0			0
$673$	−15.4252	+	23.0854i	−0.594596	+	0.889876i	−0.999702	−	0.0243938i	$-0.992234\pi$
$673$	−15.4252	+	23.0854i	−0.594596	+	0.889876i	0.405106	+	0.914270i	$0.367234\pi$
$674$	3.91584	−	11.5357i	0.150833	−	0.444338i
$675$	−5.50411	−	2.71432i	−0.211853	−	0.104474i
$676$	9.69183	−	36.1704i	0.372763	−	1.39117i
$677$	−16.9781	−	14.8894i	−0.652523	−	0.572247i	0.267767	−	0.963484i	$-0.413714\pi$
$677$	−16.9781	−	14.8894i	−0.652523	−	0.572247i	−0.920290	+	0.391236i	$0.872047\pi$
$678$	11.4579	−	4.74600i	0.440037	−	0.182269i
$679$		0			0
$680$	−1.91393	+	16.1920i	−0.0733960	+	0.620934i
$681$	0.994682	−	1.72284i	0.0381163	−	0.0660194i
$682$	−7.11281	+	9.26959i	−0.272364	+	0.354951i
$683$	−8.87966	+	3.01424i	−0.339771	+	0.115337i	−0.486109	−	0.873898i	$-0.661584\pi$
$683$	−8.87966	+	3.01424i	−0.339771	+	0.115337i	0.146339	+	0.989235i	$0.453251\pi$
$684$	31.2987	−	8.38646i	1.19674	−	0.320664i
$685$	1.53251	+	2.29356i	0.0585540	+	0.0876323i
$686$		0			0
$687$	1.46145	+	0.976506i	0.0557576	+	0.0372560i
$688$	−1.13705	−	1.48184i	−0.0433498	−	0.0564946i
$689$	−11.0963	+	1.46086i	−0.422737	+	0.0556543i
$690$	1.51494	+	0.0992943i	0.0576727	+	0.00378007i
$691$	−14.8713	−	5.04812i	−0.565730	−	0.192040i	0.0238978	−	0.999714i	$-0.492392\pi$
$691$	−14.8713	−	5.04812i	−0.565730	−	0.192040i	−0.589628	+	0.807675i	$0.700726\pi$
$692$	−61.9454	+	41.3906i	−2.35481	+	1.57344i
$693$		0			0
$694$	45.3357	+	9.01782i	1.72092	+	0.342312i
$695$	−22.1061	−	2.91032i	−0.838531	−	0.110395i
$696$	1.67360	+	2.89877i	0.0634378	+	0.109877i
$697$	−11.6052	+	29.1015i	−0.439577	+	1.10230i
$698$	48.1907	+	27.8229i	1.82404	+	1.05311i
$699$	0.732158	+	1.76759i	0.0276928	+	0.0668562i
$700$		0			0
$701$	−15.0328	+	15.0328i	−0.567780	+	0.567780i	−0.931506	−	0.363726i	$-0.881505\pi$
$701$	−15.0328	+	15.0328i	−0.567780	+	0.567780i	0.363726	+	0.931506i	$0.381505\pi$
$702$	0.372782	+	5.68755i	0.0140697	+	0.214663i
$703$	−1.32843	−	1.51478i	−0.0501027	−	0.0571312i
$704$	2.37897	−	36.2961i	0.0896609	−	1.36796i
$705$	3.30189	−	2.53363i	0.124357	−	0.0954221i
$706$	12.7431	−	30.7645i	0.479591	−	1.15784i
$707$		0			0
$708$	−8.33575	+	1.65808i	−0.313277	+	0.0623146i
$709$	−38.2364	+	2.50615i	−1.43600	+	0.0941203i	−0.763419	−	0.645904i	$-0.776481\pi$
$709$	−38.2364	+	2.50615i	−1.43600	+	0.0941203i	−0.672580	+	0.740024i	$0.734814\pi$
$710$	44.1316	+	11.8250i	1.65623	+	0.443785i
$711$	11.1710	+	32.9088i	0.418946	+	1.23417i
$712$	3.64128	−	27.6583i	0.136463	−	1.03654i
$713$	−3.14544			−0.117798
$714$		0			0
$715$	−4.96403			−0.185644
$716$	2.69433	−	20.4655i	0.100692	−	0.764831i
$717$	0.860706	+	2.53556i	0.0321436	+	0.0946921i
$718$	72.0096	+	19.2949i	2.68737	+	0.720080i
$719$	−6.78893	+	0.444970i	−0.253184	+	0.0165946i	−0.191467	−	0.981499i	$-0.561324\pi$
$719$	−6.78893	+	0.444970i	−0.253184	+	0.0165946i	−0.0617175	+	0.998094i	$0.519658\pi$
$720$	−2.56975	+	0.511156i	−0.0957690	+	0.0190496i
$721$		0			0
$722$	−7.34544	+	17.7335i	−0.273369	+	0.659971i
$723$	−4.88036	+	3.74484i	−0.181503	+	0.139272i
$724$	0.203460	−	3.10420i	0.00756154	−	0.115367i
$725$	8.08819	+	9.22281i	0.300388	+	0.342527i
$726$	−0.116894	−	1.78345i	−0.00433833	−	0.0661902i
$727$	24.9994	−	24.9994i	0.927178	−	0.927178i	−0.0703449	−	0.997523i	$-0.522410\pi$
$727$	24.9994	−	24.9994i	0.927178	−	0.927178i	0.997523	+	0.0703449i	$0.0224100\pi$
$728$		0			0
$729$	−8.57013	−	20.6901i	−0.317412	−	0.766301i
$730$	33.7596	+	19.4911i	1.24950	+	0.721398i
$731$	10.2715	+	1.90208i	0.379904	+	0.0703508i
$732$	4.85977	+	8.41737i	0.179622	+	0.311115i
$733$	26.6178	+	3.50430i	0.983152	+	0.129434i	0.604928	−	0.796280i	$-0.293202\pi$
$733$	26.6178	+	3.50430i	0.983152	+	0.129434i	0.378224	+	0.925714i	$0.376535\pi$
$734$	−48.3804	−	9.62346i	−1.78575	−	0.355208i
$735$		0			0
$736$	7.18550	−	4.80120i	0.264861	−	0.176975i
$737$	11.4480	+	3.88606i	0.421691	+	0.143145i
$738$	−51.2974	−	3.36221i	−1.88828	−	0.123765i
$739$	−12.7577	+	1.67958i	−0.469300	+	0.0617845i	−0.361468	−	0.932385i	$-0.617724\pi$
$739$	−12.7577	+	1.67958i	−0.469300	+	0.0617845i	−0.107832	+	0.994169i	$0.534391\pi$
$740$	1.55077	+	2.02100i	0.0570073	+	0.0742934i
$741$	1.13070	+	0.755507i	0.0415371	+	0.0277542i
$742$		0			0
$743$	4.99320	+	7.47285i	0.183183	+	0.274152i	0.911684	−	0.410892i	$-0.134783\pi$
$743$	4.99320	+	7.47285i	0.183183	+	0.274152i	−0.728501	+	0.685044i	$0.759783\pi$
$744$	−1.60641	+	0.430437i	−0.0588939	+	0.0157806i
$745$	−17.3388	+	5.88572i	−0.635244	+	0.215636i
$746$	14.0055	−	18.2523i	0.512777	−	0.668264i
$747$	−12.0529	+	20.8762i	−0.440992	+	0.763820i
$748$	−25.1190	−	31.8533i	−0.918442	−	1.16467i
$749$		0			0
$750$	6.58824	−	2.72894i	0.240568	−	0.0996467i
$751$	−24.4675	−	21.4574i	−0.892831	−	0.782992i	0.0841200	−	0.996456i	$-0.473192\pi$
$751$	−24.4675	−	21.4574i	−0.892831	−	0.782992i	−0.976951	+	0.213464i	$0.931525\pi$
$752$	−2.20159	+	8.21644i	−0.0802837	+	0.299623i
$753$	−5.25506	−	2.59151i	−0.191505	−	0.0944399i
$754$	3.66216	−	10.7884i	0.133368	−	0.392889i
$755$	4.04417	−	6.05252i	0.147182	−	0.220274i
$756$		0			0
$757$	48.4770	+	20.0798i	1.76193	+	0.729815i	0.996243	+	0.0865985i	$0.0275997\pi$
$757$	48.4770	+	20.0798i	1.76193	+	0.729815i	0.765685	+	0.643216i	$0.222400\pi$
$758$	27.6220	+	56.0118i	1.00328	+	2.03444i
$759$	−1.16702	+	1.02345i	−0.0423603	+	0.0371490i
$760$	−5.73090	+	11.6211i	−0.207882	+	0.421542i
$761$	7.21163	+	26.9142i	0.261422	+	0.975638i	0.964404	+	0.264432i	$0.0851844\pi$
$761$	7.21163	+	26.9142i	0.261422	+	0.975638i	−0.702983	+	0.711207i	$0.748149\pi$
$762$	1.08668	−	5.46310i	0.0393662	−	0.197907i
$763$		0			0
$764$		−	27.6080i		−	0.998823i
$765$	8.76566	−	11.7424i	0.316923	−	0.424547i
$766$	45.6789	−	26.3727i	1.65045	−	0.952886i
$767$	9.43134	+	7.23692i	0.340546	+	0.261310i
$768$	3.98848	−	4.54798i	0.143922	−	0.164111i
$769$	−15.7390	−	15.7390i	−0.567562	−	0.567562i	0.363883	−	0.931445i	$-0.381451\pi$
$769$	−15.7390	−	15.7390i	−0.567562	−	0.567562i	−0.931445	+	0.363883i	$0.881451\pi$
$770$		0			0
$771$	−0.545548	−	2.74266i	−0.0196474	−	0.0987744i
$772$	−41.6003	+	20.5150i	−1.49723	+	0.738351i
$773$	−4.38064	−	33.2742i	−0.157561	−	1.19679i	−0.869277	−	0.494325i	$-0.835415\pi$
$773$	−4.38064	−	33.2742i	−0.157561	−	1.19679i	0.711717	−	0.702466i	$-0.247918\pi$
$774$	2.23725	+	16.9936i	0.0804164	+	0.610823i
$775$	−5.46638	+	2.69572i	−0.196358	+	0.0968331i
$776$	−2.54226	−	12.7808i	−0.0912617	−	0.458803i
$777$		0			0
$778$	−7.97324	−	7.97324i	−0.285854	−	0.285854i
$779$	−16.4165	+	18.7194i	−0.588181	+	0.670692i
$780$	−1.36408	−	1.04670i	−0.0488419	−	0.0374777i
$781$	−40.4544	+	23.3563i	−1.44757	+	0.835756i
$782$	4.26906	−	16.8203i	0.152661	−	0.601492i
$783$		−	6.10665i		−	0.218234i
$784$		0			0
$785$	2.42088	−	12.1706i	0.0864049	−	0.434387i
$786$	0.196445	+	0.733144i	0.00700697	+	0.0261504i
$787$	5.29514	−	10.7375i	0.188751	−	0.382750i	−0.781841	−	0.623477i	$-0.785719\pi$
$787$	5.29514	−	10.7375i	0.188751	−	0.382750i	0.970593	+	0.240728i	$0.0773860\pi$
$788$	8.81878	−	7.73387i	0.314156	−	0.275508i
$789$	3.78128	+	7.66767i	0.134617	+	0.272976i
$790$	−31.2437	−	12.9416i	−1.11160	−	0.460440i
$791$		0			0
$792$	15.1965	−	22.7432i	0.539986	−	0.808146i
$793$	4.37000	−	12.8736i	0.155183	−	0.457155i
$794$	−42.7094	−	21.0620i	−1.51570	−	0.747461i
$795$	0.744267	−	2.77764i	0.0263964	−	0.0985128i
$796$	55.2567	+	48.4588i	1.95852	+	1.71758i
$797$	39.2612	−	16.2625i	1.39070	−	0.576049i	0.443383	−	0.896332i	$-0.353778\pi$
$797$	39.2612	−	16.2625i	1.39070	−	0.576049i	0.947322	+	0.320284i	$0.103778\pi$
$798$		0			0
$799$	−21.6041	−	42.3845i	−0.764299	−	1.49945i
$800$	8.37274	−	14.5020i	0.296021	−	0.512724i
$801$	−15.2625	+	19.8905i	−0.539276	+	0.702798i
$802$	67.8086	−	23.0179i	2.39440	−	0.812791i
$803$	−38.4981	+	10.3155i	−1.35857	+	0.364027i
$804$	2.32642	+	3.48173i	0.0820463	+	0.122791i
$805$		0			0
$806$	4.70669	+	3.14491i	0.165786	+	0.110775i
$807$	1.34856	+	1.75748i	0.0474715	+	0.0618661i
$808$	60.4088	−	7.95296i	2.12517	−	0.279784i
$809$	35.0183	+	2.29522i	1.23118	+	0.0806958i	0.667064	−	0.745000i	$-0.267551\pi$
$809$	35.0183	+	2.29522i	1.23118	+	0.0806958i	0.564115	+	0.825696i	$0.309217\pi$
$810$	22.0640	+	7.48973i	0.775252	+	0.263162i
$811$	−9.53464	+	6.37084i	−0.334806	+	0.223711i	−0.711597	−	0.702588i	$-0.752028\pi$
$811$	−9.53464	+	6.37084i	−0.334806	+	0.223711i	0.376790	+	0.926299i	$0.377028\pi$
$812$		0			0
$813$	0.353445	+	0.0703045i	0.0123959	+	0.00246569i
$814$	−4.10333	−	0.540214i	−0.143822	−	0.0189345i
$815$	−3.23538	−	5.60385i	−0.113331	−	0.196294i
$816$	−0.0118997	−	0.898510i	−0.000416574	−	0.0314541i
$817$	7.18932	+	4.15076i	0.251523	+	0.145217i
$818$	18.2425	+	44.0414i	0.637835	+	1.53987i
$819$		0			0
$820$	22.2600	−	22.2600i	0.777353	−	0.777353i
$821$	1.35835	+	20.7244i	0.0474068	+	0.723287i	0.953723	+	0.300687i	$0.0972159\pi$
$821$	1.35835	+	20.7244i	0.0474068	+	0.723287i	−0.906316	+	0.422600i	$0.861117\pi$
$822$	−1.02349	−	1.16707i	−0.0356983	−	0.0407061i
$823$	−2.27461	+	34.7039i	−0.0792880	+	1.20970i	0.754005	+	0.656869i	$0.228120\pi$
$823$	−2.27461	+	34.7039i	−0.0792880	+	1.20970i	−0.833293	+	0.552832i	$0.813547\pi$
$824$	19.9284	−	15.2916i	0.694238	−	0.532708i
$825$	−1.15102	+	2.77880i	−0.0400732	+	0.0967454i
$826$		0			0
$827$	−36.3331	+	7.22711i	−1.26343	+	0.251311i	−0.780948	−	0.624596i	$-0.785264\pi$
$827$	−36.3331	+	7.22711i	−1.26343	+	0.251311i	−0.482479	+	0.875907i	$0.660264\pi$
$828$	17.8806	−	1.17196i	0.621394	−	0.0407283i
$829$	36.0530	+	9.66037i	1.25217	+	0.335518i	0.823175	−	0.567788i	$-0.192200\pi$
$829$	36.0530	+	9.66037i	1.25217	+	0.335518i	0.428997	+	0.903306i	$0.358867\pi$
$830$	−7.54004	−	22.2122i	−0.261718	−	0.770998i
$831$	0.0360928	−	0.274152i	0.00125204	−	0.00951022i
$832$	−17.6224			−0.610948
$833$		0			0
$834$	12.5473			0.434477
$835$	−3.27494	+	24.8757i	−0.113334	+	0.860858i
$836$	−10.3625	−	30.5269i	−0.358394	−	1.05580i
$837$	2.93074	+	0.785290i	0.101301	+	0.0271436i
$838$	−6.53367	+	0.428239i	−0.225702	+	0.0147933i
$839$	−50.8081	+	10.1064i	−1.75409	+	0.348910i	−0.964370	−	0.264557i	$-0.914774\pi$
$839$	−50.8081	+	10.1064i	−1.75409	+	0.348910i	−0.789720	+	0.613468i	$0.789774\pi$
$840$		0			0
$841$	6.42666	−	15.5153i	0.221609	−	0.535011i
$842$	−3.65663	+	2.80583i	−0.126016	+	0.0966952i
$843$	−0.117162	+	1.78754i	−0.00403526	+	0.0615662i
$844$	53.0389	+	60.4793i	1.82567	+	2.08178i
$845$	−0.880169	−	13.4288i	−0.0302787	−	0.461964i
$846$	55.1961	−	55.1961i	1.89768	−	1.89768i
$847$		0			0
$848$	2.24914	+	5.42990i	0.0772357	+	0.186463i
$849$	−5.75051	−	3.32006i	−0.197357	−	0.113944i
$850$	−6.99629	−	32.8902i	−0.239971	−	1.12812i
$851$	−0.557091	−	0.964909i	−0.0190968	−	0.0330767i
$852$	−16.0414	−	2.11189i	−0.549569	−	0.0723521i
$853$	26.6210	+	5.29524i	0.911484	+	0.181305i	0.628491	−	0.777817i	$-0.283673\pi$
$853$	26.6210	+	5.29524i	0.911484	+	0.181305i	0.282993	+	0.959122i	$0.408673\pi$
$854$		0			0
$855$	9.68249	−	6.46963i	0.331134	−	0.221257i
$856$	35.7318	+	12.1293i	1.22129	+	0.414571i
$857$	36.7224	+	2.40692i	1.25441	+	0.0822187i	0.678076	−	0.734992i	$-0.262814\pi$
$857$	36.7224	+	2.40692i	1.25441	+	0.0822187i	0.576339	+	0.817211i	$0.304481\pi$
$858$	2.76956	−	0.364619i	0.0945511	−	0.0124479i
$859$	29.5157	+	38.4656i	1.00706	+	1.31243i	0.949392	+	0.314095i	$0.101701\pi$
$859$	29.5157	+	38.4656i	1.00706	+	1.31243i	0.0576715	+	0.998336i	$0.481632\pi$
$860$	−8.72725	−	5.83137i	−0.297597	−	0.198848i
$861$		0			0
$862$	3.65799	+	5.47457i	0.124592	+	0.186464i
$863$	2.66360	−	0.713709i	0.0906699	−	0.0242949i	−0.213199	−	0.977009i	$-0.568388\pi$
$863$	2.66360	−	0.713709i	0.0906699	−	0.0242949i	0.303869	+	0.952714i	$0.401722\pi$
$864$	−7.89370	+	2.67955i	−0.268549	+	0.0911601i
$865$	−16.2993	+	21.2416i	−0.554192	+	0.722237i
$866$	18.2330	−	31.5804i	0.619581	−	1.07315i
$867$	3.41245	+	3.68930i	0.115893	+	0.125295i
$868$		0			0
$869$	31.9442	−	13.2317i	1.08363	−	0.448855i
$870$	2.20082	+	1.93007i	0.0746149	+	0.0654355i
$871$	1.51594	−	5.65755i	0.0513655	−	0.191699i
$872$	14.4535	+	7.12770i	0.489459	+	0.241374i
$873$	−3.76449	+	11.0898i	−0.127409	+	0.375334i
$874$	7.66182	−	11.4667i	0.259165	−	0.387867i
$875$		0			0
$876$	−12.7541	−	5.28292i	−0.430921	−	0.178493i
$877$	−15.7823	−	32.0033i	−0.532929	−	1.08067i	−0.982298	−	0.187327i	$-0.940018\pi$
$877$	−15.7823	−	32.0033i	−0.532929	−	1.08067i	0.449368	−	0.893347i	$-0.351649\pi$
$878$	58.4410	−	51.2514i	1.97229	−	1.72965i
$879$	2.15760	−	4.37519i	0.0727742	−	0.147571i
$880$	0.674678	+	2.51793i	0.0227434	+	0.0848794i
$881$	−6.27071	+	31.5250i	−0.211266	+	1.06210i	0.718942	+	0.695070i	$0.244627\pi$
$881$	−6.27071	+	31.5250i	−0.211266	+	1.06210i	−0.930208	+	0.367034i	$0.880373\pi$
$882$		0			0
$883$		−	21.3713i		−	0.719203i	−0.933106	−	0.359601i	$-0.882913\pi$
$883$		−	21.3713i		−	0.719203i	0.933106	−	0.359601i	$-0.117087\pi$
$884$	−14.6033	+	13.1529i	−0.491161	+	0.442379i
$885$	−2.64520	+	1.52721i	−0.0889176	+	0.0513366i
$886$	60.9841	+	46.7947i	2.04880	+	1.57210i
$887$	7.33542	−	8.36444i	0.246299	−	0.280850i	−0.615460	−	0.788168i	$-0.711030\pi$
$887$	7.33542	−	8.36444i	0.246299	−	0.280850i	0.861759	+	0.507318i	$0.169363\pi$
$888$	−0.416555	−	0.416555i	−0.0139787	−	0.0139787i
$889$		0			0
$890$	−4.75959	−	23.9281i	−0.159542	−	0.802070i
$891$	−21.3662	+	10.5366i	−0.715794	+	0.352991i
$892$	1.95786	+	14.8714i	0.0655541	+	0.497933i
$893$	−4.93470	−	37.4828i	−0.165134	−	1.25431i
$894$	9.24142	−	4.55736i	0.309079	−	0.152421i
$895$	−1.44726	−	7.27588i	−0.0483766	−	0.243206i
$896$		0			0
$897$	0.531759	+	0.531759i	0.0177549	+	0.0177549i
$898$	−17.8129	+	20.3117i	−0.594423	+	0.677809i
$899$	−4.81152	−	3.69201i	−0.160473	−	0.123135i
$900$	30.0698	−	17.3608i	1.00233	−	0.578694i
$901$	−29.6699	−	14.1462i	−0.988447	−	0.471279i
$902$			51.1457i			1.70296i
$903$		0			0
$904$	−11.4195	+	57.4095i	−0.379806	+	1.90941i
$905$	−0.289358	−	1.07990i	−0.00961858	−	0.0358970i
$906$	−1.81177	+	3.67391i	−0.0601920	+	0.122057i
$907$	−19.1231	+	16.7705i	−0.634971	+	0.556855i	−0.915160	−	0.403090i	$-0.867936\pi$
$907$	−19.1231	+	16.7705i	−0.634971	+	0.556855i	0.280189	+	0.959945i	$0.409603\pi$
$908$	10.1056	+	20.4921i	0.335365	+	0.680053i
$909$	−50.5907	−	20.9553i	−1.67799	−	0.695045i
$910$		0			0
$911$	−6.83991	+	10.2367i	−0.226616	+	0.339155i	−0.927302	−	0.374315i	$-0.877878\pi$
$911$	−6.83991	+	10.2367i	−0.226616	+	0.339155i	0.700685	+	0.713471i	$0.252878\pi$
$912$	0.229543	−	0.676211i	0.00760092	−	0.0223916i
$913$	21.5097	+	10.6074i	0.711867	+	0.351054i
$914$	9.91067	−	36.9871i	0.327816	−	1.22343i
$915$	2.62621	+	2.30312i	0.0868198	+	0.0761389i
$916$	−18.6506	+	7.72532i	−0.616232	+	0.255252i
$917$		0			0
$918$	−8.17701	+	14.6063i	−0.269881	+	0.482081i
$919$	−6.73257	+	11.6612i	−0.222087	+	0.384666i	−0.955442	−	0.295180i	$-0.904620\pi$
$919$	−6.73257	+	11.6612i	−0.222087	+	0.384666i	0.733355	+	0.679846i	$0.237954\pi$
$920$	−4.36209	+	5.68478i	−0.143814	+	0.187422i
$921$	3.19776	−	1.08549i	0.105370	−	0.0357682i
$922$	21.0191	−	5.63204i	0.692226	−	0.185482i
$923$	12.5733	+	18.8172i	0.413855	+	0.619377i
$924$		0			0
$925$	−1.79510	−	1.19945i	−0.0590226	−	0.0394376i
$926$	32.8305	+	42.7855i	1.07888	+	1.40602i
$927$	−22.3819	+	2.94664i	−0.735119	+	0.0967803i
$928$	16.6270	+	1.08979i	0.545808	+	0.0357741i
$929$	−8.90456	−	3.02269i	−0.292149	−	0.0991713i	0.171517	−	0.985181i	$-0.445133\pi$
$929$	−8.90456	−	3.02269i	−0.292149	−	0.0991713i	−0.463666	+	0.886010i	$0.653466\pi$
$930$	−1.20931	+	0.808033i	−0.0396548	+	0.0264965i
$931$		0			0
$932$	−21.5516	−	4.28688i	−0.705947	−	0.140422i
$933$	3.30275	+	0.434815i	0.108127	+	0.0142352i
$934$	4.39644	+	7.61486i	0.143856	+	0.249166i
$935$	−12.2280	−	7.93827i	−0.399897	−	0.259609i
$936$	−11.4765	−	6.62599i	−0.375123	−	0.216577i
$937$	16.1388	+	38.9625i	0.527232	+	1.27285i	0.933330	+	0.359021i	$0.116889\pi$
$937$	16.1388	+	38.9625i	0.527232	+	1.27285i	−0.406098	+	0.913830i	$0.633111\pi$
$938$		0			0
$939$	5.84571	−	5.84571i	0.190768	−	0.190768i
$940$	3.12634	+	47.6987i	0.101970	+	1.55576i
$941$	−9.03219	−	10.2992i	−0.294441	−	0.335746i	0.585638	−	0.810573i	$-0.300844\pi$
$941$	−9.03219	−	10.2992i	−0.294441	−	0.335746i	−0.880079	+	0.474827i	$0.842511\pi$
$942$	−0.456713	+	6.96809i	−0.0148805	+	0.227033i
$943$	−10.9235	+	8.38193i	−0.355719	+	0.272953i
$944$	2.38898	−	5.76750i	0.0777546	−	0.187716i
$945$		0			0
$946$	16.7253	−	3.32687i	0.543786	−	0.108166i
$947$	−20.3618	+	1.33458i	−0.661670	+	0.0433681i	−0.392539	−	0.919736i	$-0.628403\pi$
$947$	−20.3618	+	1.33458i	−0.661670	+	0.0433681i	−0.269131	+	0.963104i	$0.586736\pi$
$948$	11.5680	+	3.09964i	0.375711	+	0.100672i
$949$	6.20683	+	18.2847i	0.201482	+	0.593547i
$950$	3.48801	−	26.4940i	0.113166	−	0.859580i
$951$	−2.52970			−0.0820312
$952$		0			0
$953$	32.5616			1.05477			0.527387	−	0.849625i	$-0.323172\pi$
$953$	32.5616			1.05477			0.527387	+	0.849625i	$0.323172\pi$
$954$	7.03975	−	53.4722i	0.227920	−	1.73123i
$955$	−3.18928	−	9.39531i	−0.103203	−	0.304025i
$956$	−29.7057	−	7.95962i	−0.960751	−	0.257433i
$957$	−2.98647	+	0.195743i	−0.0965388	+	0.00632749i
$958$	5.15027	−	1.02445i	0.166398	−	0.0330985i
$959$		0			0
$960$	1.73272	−	4.18314i	0.0559231	−	0.135010i
$961$	−22.2033	+	17.0372i	−0.716236	+	0.549587i
$962$	−0.131142	+	2.00084i	−0.00422818	+	0.0645096i
$963$	−22.3601	−	25.4968i	−0.720544	−	0.821623i
$964$	−4.62088	−	70.5010i	−0.148829	−	2.27069i
$965$	−11.7871	+	11.7871i	−0.379442	+	0.379442i
$966$		0			0
$967$	0.545323	+	1.31653i	0.0175364	+	0.0423366i	0.932405	−	0.361415i	$-0.117706\pi$
$967$	0.545323	+	1.31653i	0.0175364	+	0.0423366i	−0.914869	+	0.403751i	$0.867706\pi$
$968$	7.30541	+	4.21778i	0.234805	+	0.135565i
$969$	1.57708	+	3.66921i	0.0506632	+	0.117872i
$970$	−5.69811	−	9.86942i	−0.182955	−	0.316888i
$971$	−26.5743	−	3.49857i	−0.852810	−	0.112275i	−0.308567	−	0.951203i	$-0.599849\pi$
$971$	−26.5743	−	3.49857i	−0.852810	−	0.112275i	−0.544242	+	0.838928i	$0.683183\pi$
$972$	−25.5543	−	5.08307i	−0.819655	−	0.163040i
$973$		0			0
$974$	32.8163	−	21.9271i	1.05150	−	0.702591i
$975$	1.37986	+	0.468399i	0.0441908	+	0.0150008i
$976$	−7.12388	−	0.466924i	−0.228030	−	0.0149459i
$977$	−19.6703	+	2.58965i	−0.629309	+	0.0828502i	−0.438433	−	0.898764i	$-0.644466\pi$
$977$	−19.6703	+	2.58965i	−0.629309	+	0.0828502i	−0.190876	+	0.981614i	$0.561133\pi$
$978$	2.21672	+	2.88888i	0.0708828	+	0.0923762i
$979$	20.7400	+	13.8580i	0.662853	+	0.442905i
$980$		0			0
$981$	−8.04649	−	12.0424i	−0.256905	−	0.384485i
$982$	−47.5137	+	12.7313i	−1.51622	+	0.406271i
$983$	−4.54487	+	1.54277i	−0.144959	+	0.0492069i	−0.392976	−	0.919549i	$-0.628554\pi$
$983$	−4.54487	+	1.54277i	−0.144959	+	0.0492069i	0.248017	+	0.968756i	$0.420221\pi$
$984$	−4.43175	+	5.77557i	−0.141279	+	0.184118i
$985$	2.10771	−	3.65067i	0.0671573	−	0.116320i
$986$	26.2733	−	20.7188i	0.836714	−	0.659820i
$987$		0			0
$988$	−14.4296	+	5.97695i	−0.459068	+	0.190152i
$989$	3.45154	+	3.02692i	0.109753	+	0.0962505i
$990$	6.19127	−	23.1061i	0.196771	−	0.734361i
$991$	−3.93125	−	1.93868i	−0.124880	−	0.0615841i	0.378775	−	0.925489i	$-0.376345\pi$
$991$	−3.93125	−	1.93868i	−0.124880	−	0.0615841i	−0.503656	+	0.863905i	$0.668012\pi$
$992$	−2.66118	+	7.83959i	−0.0844926	+	0.248907i
$993$	2.67117	−	3.99769i	0.0847672	−	0.126863i
$994$		0			0
$995$	24.4024	+	10.1078i	0.773609	+	0.320439i
$996$	3.67407	+	7.45028i	0.116417	+	0.236071i
$997$	16.5505	−	14.5144i	0.524161	−	0.459677i	−0.355909	−	0.934521i	$-0.615829\pi$
$997$	16.5505	−	14.5144i	0.524161	−	0.459677i	0.880070	+	0.474844i	$0.157495\pi$
$998$	−20.2615	+	41.0863i	−0.641368	+	1.30057i
$999$	0.278166	+	1.03813i	0.00880078	+	0.0328450i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.bc.c.558.9		144
7.2	even	3		833.2.t.b.48.1	✓	72
7.3	odd	6		833.2.bc.b.31.9		144
7.4	even	3	inner	833.2.bc.c.31.9		144
7.5	odd	6		833.2.t.c.48.1	yes	72
7.6	odd	2		833.2.bc.b.558.9		144
17.11	odd	16		833.2.bc.b.215.9		144
119.11	odd	48		833.2.bc.b.521.9		144
119.45	even	48	inner	833.2.bc.c.521.9		144
119.62	even	16	inner	833.2.bc.c.215.9		144
119.79	odd	48		833.2.t.c.538.1	yes	72
119.96	even	48		833.2.t.b.538.1	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
833.2.t.b.48.1	✓	72	7.2	even	3
833.2.t.b.538.1	yes	72	119.96	even	48
833.2.t.c.48.1	yes	72	7.5	odd	6
833.2.t.c.538.1	yes	72	119.79	odd	48
833.2.bc.b.31.9		144	7.3	odd	6
833.2.bc.b.215.9		144	17.11	odd	16
833.2.bc.b.521.9		144	119.11	odd	48
833.2.bc.b.558.9		144	7.6	odd	2
833.2.bc.c.31.9		144	7.4	even	3	inner
833.2.bc.c.215.9		144	119.62	even	16	inner
833.2.bc.c.521.9		144	119.45	even	48	inner
833.2.bc.c.558.9		144	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.bc (of order \(48\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.303182 - 2.30290i) q^{2} +(0.0950234 + 0.279930i) q^{3} +(-3.27956 - 0.878756i) q^{4} +(-1.21758 + 0.0798047i) q^{5} +(0.673459 - 0.133959i) q^{6} +(-1.24022 + 2.99415i) q^{8} +(2.31073 - 1.77308i) q^{9} +(-0.185368 + 2.82817i) q^{10} +(-1.91064 - 2.17866i) q^{11} +(-0.0656450 - 1.00155i) q^{12} +(-0.992715 + 0.992715i) q^{13} +(-0.138039 - 0.333255i) q^{15} +(0.638463 + 0.368617i) q^{16} +(-4.03287 + 0.857859i) q^{17} +(-3.38266 - 5.85894i) q^{18} +(-3.24860 - 0.427687i) q^{19} +(4.06327 + 0.808235i) q^{20} +(-5.59651 + 3.73947i) q^{22} +(-1.71584 - 0.582449i) q^{23} +(-0.956003 - 0.0626597i) q^{24} +(-3.48108 + 0.458293i) q^{25} +(1.98515 + 2.58709i) q^{26} +(1.45331 + 0.971068i) q^{27} +(-1.94103 - 2.90495i) q^{29} +(-0.809303 + 0.216852i) q^{30} +(1.64377 - 0.557985i) q^{31} +(-2.90335 + 3.78372i) q^{32} +(0.428318 - 0.741868i) q^{33} +(0.752866 + 9.54738i) q^{34} +(-9.13629 + 3.78437i) q^{36} +(0.462299 + 0.405425i) q^{37} +(-1.96984 + 7.35153i) q^{38} +(-0.372222 - 0.183559i) q^{39} +(1.27112 - 3.74461i) q^{40} +(4.22160 - 6.31807i) q^{41} +(-2.34069 - 0.969547i) q^{43} +(4.35154 + 8.82405i) q^{44} +(-2.67201 + 2.34329i) q^{45} +(-1.86153 + 3.77481i) q^{46} +(2.98629 + 11.1450i) q^{47} +(-0.0425179 + 0.213752i) q^{48} +8.15551i q^{50} +(-0.623358 - 1.04741i) q^{51} +(4.12803 - 2.38332i) q^{52} +(6.32467 + 4.85309i) q^{53} +(2.67688 - 3.05240i) q^{54} +(2.50023 + 2.50023i) q^{55} +(-0.188971 - 0.950022i) q^{57} +(-7.27829 + 3.58925i) q^{58} +(-1.10526 - 8.39529i) q^{59} +(0.159857 + 1.21423i) q^{60} +(-8.68507 + 4.28300i) q^{61} +(-0.786620 - 3.95460i) q^{62} +(8.87587 + 8.87587i) q^{64} +(1.12949 - 1.28794i) q^{65} +(-1.57859 - 1.21129i) q^{66} +(-3.61306 + 2.08600i) q^{67} +(13.9799 + 0.730510i) q^{68} -0.535661i q^{69} +(3.14489 - 15.8104i) q^{71} +(2.44308 + 9.11769i) q^{72} +(6.08326 - 12.3356i) q^{73} +(1.07381 - 0.941708i) q^{74} +(-0.459074 - 0.930910i) q^{75} +(10.2782 + 4.25736i) q^{76} +(-0.535570 + 0.801536i) q^{78} +(-3.83540 + 11.2987i) q^{79} +(-0.806800 - 0.397870i) q^{80} +(2.12778 - 7.94100i) q^{81} +(-13.2700 - 11.6374i) q^{82} +(-7.64634 + 3.16722i) q^{83} +(4.84191 - 1.36636i) q^{85} +(-2.94242 + 5.09643i) q^{86} +(0.628740 - 0.819390i) q^{87} +(8.89286 - 3.01872i) q^{88} +(-8.31460 + 2.22789i) q^{89} +(4.58624 + 6.86380i) q^{90} +(5.11537 + 3.41798i) q^{92} +(0.312393 + 0.407119i) q^{93} +(26.5711 - 3.49815i) q^{94} +(3.98958 + 0.261491i) q^{95} +(-1.33506 - 0.453192i) q^{96} +(-3.34327 + 2.23390i) q^{97} +(-8.27792 - 1.64658i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 24 q^{9} + 8 q^{11} + 24 q^{12} - 64 q^{13} - 32 q^{17} - 40 q^{18} + 40 q^{19} + 80 q^{20} - 48 q^{22} + 8 q^{23} - 16 q^{24} + 8 q^{25} - 48 q^{27} - 8 q^{31} - 40 q^{32} - 48 q^{34} - 240 q^{36}+ \cdots - 80 q^{99}+O(q^{100}) \) 144 * q + 24 * q^9 + 8 * q^11 + 24 * q^12 - 64 * q^13 - 32 * q^17 - 40 * q^18 + 40 * q^19 + 80 * q^20 - 48 * q^22 + 8 * q^23 - 16 * q^24 + 8 * q^25 - 48 * q^27 - 8 * q^31 - 40 * q^32 - 48 * q^34 - 240 * q^36 + 48 * q^37 + 56 * q^38 + 16 * q^39 + 48 * q^40 + 112 * q^41 - 48 * q^43 - 96 * q^44 - 40 * q^45 + 64 * q^46 - 24 * q^47 - 448 * q^48 - 104 * q^51 + 40 * q^53 - 48 * q^54 + 96 * q^57 - 32 * q^58 - 8 * q^59 + 48 * q^60 + 128 * q^61 + 96 * q^62 - 56 * q^65 - 120 * q^66 - 32 * q^68 + 120 * q^73 - 48 * q^74 - 32 * q^75 + 16 * q^76 + 96 * q^78 - 32 * q^79 + 32 * q^80 - 80 * q^81 - 64 * q^82 - 64 * q^83 - 64 * q^85 + 80 * q^86 + 64 * q^87 - 136 * q^88 + 16 * q^89 + 64 * q^90 - 16 * q^92 + 96 * q^93 - 32 * q^94 - 32 * q^95 - 40 * q^96 - 80 * q^99

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