LMFDB - Embedded newform 192.2.s.a.131.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [192,2,Mod(11,192)] 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("192.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(192, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([8, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 192 = 2^{6} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	192.s (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.53312771881$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			131.13
Character	$\chi$	$=$	192.131
Dual form			192.2.s.a.107.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.385637 - 1.36062i) q^{2} +(-1.36847 - 1.06173i) q^{3} +(-1.70257 + 1.04941i) q^{4} +(1.45822 - 2.18239i) q^{5} +(-0.916881 + 2.27142i) q^{6} +(-1.27779 - 3.08486i) q^{7} +(2.08442 + 1.91186i) q^{8} +(0.745444 + 2.90591i) q^{9} +(-3.53174 - 1.14248i) q^{10} +(-2.31748 + 0.460975i) q^{11} +(3.44411 + 0.371585i) q^{12} +(-5.55652 + 3.71275i) q^{13} +(-3.70456 + 2.92822i) q^{14} +(-4.31265 + 1.43829i) q^{15} +(1.79748 - 3.57338i) q^{16} +(3.42067 - 3.42067i) q^{17} +(3.66637 - 2.13489i) q^{18} +(-1.23054 + 0.822221i) q^{19} +(-0.192511 + 5.24594i) q^{20} +(-1.52668 + 5.57823i) q^{21} +(1.52092 + 2.97544i) q^{22} +(1.87568 - 4.52828i) q^{23} +(-0.822590 - 4.82942i) q^{24} +(-0.722975 - 1.74542i) q^{25} +(7.19443 + 6.12853i) q^{26} +(2.06518 - 4.76813i) q^{27} +(5.41281 + 3.91127i) q^{28} +(0.760797 - 3.82478i) q^{29} +(3.62009 + 5.31322i) q^{30} -0.0497279 q^{31} +(-5.55519 - 1.06766i) q^{32} +(3.66084 + 1.82971i) q^{33} +(-5.97336 - 3.33509i) q^{34} +(-8.59567 - 1.70978i) q^{35} +(-4.31866 - 4.16524i) q^{36} +(5.53510 - 8.28386i) q^{37} +(1.59327 + 1.35722i) q^{38} +(11.5459 + 0.818742i) q^{39} +(7.21196 - 1.76109i) q^{40} +(-2.28385 - 0.946002i) q^{41} +(8.17859 - 0.0739441i) q^{42} +(-0.522190 + 0.103870i) q^{43} +(3.46191 - 3.21682i) q^{44} +(7.42884 + 2.61062i) q^{45} +(-6.88460 - 0.805810i) q^{46} +(2.51930 + 2.51930i) q^{47} +(-6.25379 + 2.98163i) q^{48} +(-2.93388 + 2.93388i) q^{49} +(-2.09604 + 1.65679i) q^{50} +(-8.31294 + 1.04926i) q^{51} +(5.56417 - 12.1523i) q^{52} +(-1.79038 - 9.00087i) q^{53} +(-7.28401 - 0.971161i) q^{54} +(-2.37338 + 5.72983i) q^{55} +(3.23436 - 8.87310i) q^{56} +(2.55694 + 0.181318i) q^{57} +(-5.49747 + 0.439822i) q^{58} +(-2.56739 - 1.71547i) q^{59} +(5.83323 - 6.97453i) q^{60} +(-0.935842 + 4.70479i) q^{61} +(0.0191769 + 0.0676607i) q^{62} +(8.01181 - 6.01274i) q^{63} +(0.689602 + 7.97022i) q^{64} +17.5405i q^{65} +(1.07779 - 5.68661i) q^{66} +(-3.65093 - 0.726215i) q^{67} +(-2.23425 + 9.41361i) q^{68} +(-7.37464 + 4.20537i) q^{69} +(0.988438 + 12.3548i) q^{70} +(12.6483 - 5.23910i) q^{71} +(-4.00187 + 7.48232i) q^{72} +(13.6168 + 5.64025i) q^{73} +(-13.4057 - 4.33660i) q^{74} +(-0.863794 + 3.15617i) q^{75} +(1.23223 - 2.69123i) q^{76} +(4.38330 + 6.56007i) q^{77} +(-3.33852 - 16.0253i) q^{78} +(-1.69637 - 1.69637i) q^{79} +(-5.17737 - 9.13359i) q^{80} +(-7.88863 + 4.33239i) q^{81} +(-0.406412 + 3.47226i) q^{82} +(5.63016 + 8.42612i) q^{83} +(-3.25457 - 11.0994i) q^{84} +(-2.47712 - 12.4533i) q^{85} +(0.342703 + 0.670446i) q^{86} +(-5.10203 + 4.42636i) q^{87} +(-5.71191 - 3.46982i) q^{88} +(-8.26075 + 3.42172i) q^{89} +(0.687227 - 11.1146i) q^{90} +(18.5534 + 12.3970i) q^{91} +(1.55855 + 9.67806i) q^{92} +(0.0680513 + 0.0527977i) q^{93} +(2.45627 - 4.39934i) q^{94} +3.88450i q^{95} +(6.46856 + 7.35920i) q^{96} -3.93119i q^{97} +(5.12330 + 2.86048i) q^{98} +(-3.06710 - 6.39075i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) $ 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{16}\right)$

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 $

$2$	−0.385637	−	1.36062i	−0.272686	−	0.962103i
$2$	−0.385637	−	1.36062i	−0.272686	−	0.962103i
$3$	−1.36847	−	1.06173i	−0.790089	−	0.612992i
$3$	−1.36847	−	1.06173i	−0.790089	−	0.612992i
$4$	−1.70257	+	1.04941i	−0.851284	+	0.524704i
$5$	1.45822	−	2.18239i	0.652138	−	0.975993i	−0.347133	−	0.937816i	$-0.612845\pi$
$5$	1.45822	−	2.18239i	0.652138	−	0.975993i	0.999271	−	0.0381770i	$-0.0121551\pi$
$6$	−0.916881	+	2.27142i	−0.374315	+	0.927302i
$7$	−1.27779	−	3.08486i	−0.482960	−	1.16597i	−0.958197	−	0.286111i	$-0.907638\pi$
$7$	−1.27779	−	3.08486i	−0.482960	−	1.16597i	0.475237	−	0.879858i	$-0.342362\pi$
$8$	2.08442	+	1.91186i	0.736953	+	0.675944i
$9$	0.745444	+	2.90591i	0.248481	+	0.968637i
$10$	−3.53174	−	1.14248i	−1.11683	−	0.361284i
$11$	−2.31748	+	0.460975i	−0.698746	+	0.138989i	−0.531666	−	0.846954i	$-0.678434\pi$
$11$	−2.31748	+	0.460975i	−0.698746	+	0.138989i	−0.167080	+	0.985943i	$0.553434\pi$
$12$	3.44411	+	0.371585i	0.994230	+	0.107267i
$13$	−5.55652	+	3.71275i	−1.54110	+	1.02973i	−0.561811	+	0.827266i	$0.689895\pi$
$13$	−5.55652	+	3.71275i	−1.54110	+	1.02973i	−0.979289	+	0.202465i	$0.935105\pi$
$14$	−3.70456	+	2.92822i	−0.990085	+	0.782601i
$15$	−4.31265	+	1.43829i	−1.11352	+	0.371366i
$16$	1.79748	−	3.57338i	0.449370	−	0.893345i
$17$	3.42067	−	3.42067i	0.829634	−	0.829634i	−0.157832	−	0.987466i	$-0.550450\pi$
$17$	3.42067	−	3.42067i	0.829634	−	0.829634i	0.987466	+	0.157832i	$0.0504503\pi$
$18$	3.66637	−	2.13489i	0.864171	−	0.503199i
$19$	−1.23054	+	0.822221i	−0.282305	+	0.188630i	−0.688659	−	0.725086i	$-0.741800\pi$
$19$	−1.23054	+	0.822221i	−0.282305	+	0.188630i	0.406353	+	0.913716i	$0.366800\pi$
$20$	−0.192511	+	5.24594i	−0.0430468	+	1.17303i
$21$	−1.52668	+	5.57823i	−0.333148	+	1.21727i
$22$	1.52092	+	2.97544i	0.324260	+	0.634365i
$23$	1.87568	−	4.52828i	0.391105	−	0.944212i	−0.598594	−	0.801052i	$-0.704274\pi$
$23$	1.87568	−	4.52828i	0.391105	−	0.944212i	0.989700	−	0.143160i	$-0.0457263\pi$
$24$	−0.822590	−	4.82942i	−0.167911	−	0.985802i
$25$	−0.722975	−	1.74542i	−0.144595	−	0.349083i
$26$	7.19443	+	6.12853i	1.41094	+	1.20190i
$27$	2.06518	−	4.76813i	0.397444	−	0.917626i
$28$	5.41281	+	3.91127i	1.02293	+	0.739160i
$29$	0.760797	−	3.82478i	0.141276	−	0.710245i	−0.843598	−	0.536975i	$-0.819567\pi$
$29$	0.760797	−	3.82478i	0.141276	−	0.710245i	0.984874	−	0.173269i	$-0.0554331\pi$
$30$	3.62009	+	5.31322i	0.660935	+	0.970057i
$31$	−0.0497279			−0.00893139			−0.00446569	−	0.999990i	$-0.501421\pi$
$31$	−0.0497279			−0.00893139			−0.00446569	+	0.999990i	$0.501421\pi$
$32$	−5.55519	−	1.06766i	−0.982028	−	0.188738i
$33$	3.66084	+	1.82971i	0.637271	+	0.318512i
$34$	−5.97336	−	3.33509i	−1.02442	−	0.571964i
$35$	−8.59567	−	1.70978i	−1.45293	−	0.289006i
$36$	−4.31866	−	4.16524i	−0.719776	−	0.694206i
$37$	5.53510	−	8.28386i	0.909965	−	1.36186i	−0.0221727	−	0.999754i	$-0.507058\pi$
$37$	5.53510	−	8.28386i	0.909965	−	1.36186i	0.932138	−	0.362104i	$-0.117942\pi$
$38$	1.59327	+	1.35722i	0.258463	+	0.220170i
$39$	11.5459	+	0.818742i	1.84882	+	0.131104i
$40$	7.21196	−	1.76109i	1.14031	−	0.278453i
$41$	−2.28385	−	0.946002i	−0.356678	−	0.147741i	0.197147	−	0.980374i	$-0.436832\pi$
$41$	−2.28385	−	0.946002i	−0.356678	−	0.147741i	−0.553825	+	0.832633i	$0.686832\pi$
$42$	8.17859	−	0.0739441i	1.26198	−	0.0114098i
$43$	−0.522190	+	0.103870i	−0.0796333	+	0.0158400i	−0.234746	−	0.972057i	$-0.575426\pi$
$43$	−0.522190	+	0.103870i	−0.0796333	+	0.0158400i	0.155113	+	0.987897i	$0.450426\pi$
$44$	3.46191	−	3.21682i	0.521903	−	0.484954i
$45$	7.42884	+	2.61062i	1.10743	+	0.389168i
$46$	−6.88460	−	0.805810i	−1.01508	−	0.118810i
$47$	2.51930	+	2.51930i	0.367477	+	0.367477i	0.866556	−	0.499079i	$-0.166328\pi$
$47$	2.51930	+	2.51930i	0.367477	+	0.367477i	−0.499079	+	0.866556i	$0.666328\pi$
$48$	−6.25379	+	2.98163i	−0.902656	+	0.430362i
$49$	−2.93388	+	2.93388i	−0.419126	+	0.419126i
$50$	−2.09604	+	1.65679i	−0.296425	+	0.234306i
$51$	−8.31294	+	1.04926i	−1.16404	+	0.146926i
$52$	5.56417	−	12.1523i	0.771611	−	1.68522i
$53$	−1.79038	−	9.00087i	−0.245928	−	1.23636i	−0.884404	−	0.466722i	$-0.845435\pi$
$53$	−1.79038	−	9.00087i	−0.245928	−	1.23636i	0.638476	−	0.769642i	$-0.279565\pi$
$54$	−7.28401	−	0.971161i	−0.991229	−	0.132158i
$55$	−2.37338	+	5.72983i	−0.320026	+	0.772611i
$56$	3.23436	−	8.87310i	0.432210	−	1.18572i
$57$	2.55694	+	0.181318i	0.338675	+	0.0240161i
$58$	−5.49747	+	0.439822i	−0.721853	+	0.0577514i
$59$	−2.56739	−	1.71547i	−0.334245	−	0.223336i	0.377109	−	0.926169i	$-0.376918\pi$
$59$	−2.56739	−	1.71547i	−0.334245	−	0.223336i	−0.711355	+	0.702833i	$0.751918\pi$
$60$	5.83323	−	6.97453i	0.753067	−	0.900408i
$61$	−0.935842	+	4.70479i	−0.119822	+	0.602387i	0.873482	+	0.486857i	$0.161857\pi$
$61$	−0.935842	+	4.70479i	−0.119822	+	0.602387i	−0.993304	+	0.115530i	$0.963143\pi$
$62$	0.0191769	+	0.0676607i	0.00243547	+	0.00859292i
$63$	8.01181	−	6.01274i	1.00939	−	0.757534i
$64$	0.689602	+	7.97022i	0.0862002	+	0.996278i
$65$			17.5405i			2.17563i
$66$	1.07779	−	5.68661i	0.132666	−	0.699974i
$67$	−3.65093	−	0.726215i	−0.446032	−	0.0887213i	−0.0330361	−	0.999454i	$-0.510518\pi$
$67$	−3.65093	−	0.726215i	−0.446032	−	0.0887213i	−0.412996	+	0.910733i	$0.635518\pi$
$68$	−2.23425	+	9.41361i	−0.270942	+	1.14157i
$69$	−7.37464	+	4.20537i	−0.887803	+	0.506267i
$70$	0.988438	+	12.3548i	0.118141	+	1.47668i
$71$	12.6483	−	5.23910i	1.50108	−	0.621767i	0.527384	−	0.849627i	$-0.323173\pi$
$71$	12.6483	−	5.23910i	1.50108	−	0.621767i	0.973694	+	0.227860i	$0.0731728\pi$
$72$	−4.00187	+	7.48232i	−0.471625	+	0.881799i
$73$	13.6168	+	5.64025i	1.59372	+	0.660142i	0.990510	−	0.137439i	$-0.0438870\pi$
$73$	13.6168	+	5.64025i	1.59372	+	0.660142i	0.603213	+	0.797580i	$0.293887\pi$
$74$	−13.4057	−	4.33660i	−1.55838	−	0.504120i
$75$	−0.863794	+	3.15617i	−0.0997424	+	0.364443i
$76$	1.23223	−	2.69123i	0.141347	−	0.308705i
$77$	4.38330	+	6.56007i	0.499523	+	0.747589i
$78$	−3.33852	−	16.0253i	−0.378013	−	1.81451i
$79$	−1.69637	−	1.69637i	−0.190856	−	0.190856i	0.605210	−	0.796066i	$-0.293089\pi$
$79$	−1.69637	−	1.69637i	−0.190856	−	0.190856i	−0.796066	+	0.605210i	$0.793089\pi$
$80$	−5.17737	−	9.13359i	−0.578847	−	1.02117i
$81$	−7.88863	+	4.33239i	−0.876514	+	0.481376i
$82$	−0.406412	+	3.47226i	−0.0448807	+	0.383447i
$83$	5.63016	+	8.42612i	0.617990	+	0.924887i	1.00000		0.000728896i	$0.000232015\pi$
$83$	5.63016	+	8.42612i	0.617990	+	0.924887i	−0.382010	+	0.924158i	$0.624768\pi$
$84$	−3.25457	−	11.0994i	−0.355103	−	1.21105i
$85$	−2.47712	−	12.4533i	−0.268681	−	1.35075i
$86$	0.342703	+	0.670446i	0.0369546	+	0.0722960i
$87$	−5.10203	+	4.42636i	−0.546995	+	0.474555i
$88$	−5.71191	−	3.46982i	−0.608892	−	0.369884i
$89$	−8.26075	+	3.42172i	−0.875638	+	0.362701i	−0.774804	−	0.632202i	$-0.782151\pi$
$89$	−8.26075	+	3.42172i	−0.875638	+	0.362701i	−0.100834	+	0.994903i	$0.532151\pi$
$90$	0.687227	−	11.1146i	0.0724401	−	1.17158i
$91$	18.5534	+	12.3970i	1.94492	+	1.29956i
$92$	1.55855	+	9.67806i	0.162490	+	1.00901i
$93$	0.0680513	+	0.0527977i	0.00705659	+	0.00547487i
$94$	2.45627	−	4.39934i	0.253345	−	0.453757i
$95$			3.88450i			0.398541i
$96$	6.46856	+	7.35920i	0.660194	+	0.751095i
$97$		−	3.93119i		−	0.399152i	−0.979882	−	0.199576i	$-0.936044\pi$
$97$		−	3.93119i		−	0.399152i	0.979882	−	0.199576i	$-0.0639565\pi$
$98$	5.12330	+	2.86048i	0.517532	+	0.288952i
$99$	−3.06710	−	6.39075i	−0.308255	−	0.642294i
$100$	3.06257	+	2.21300i	0.306257	+	0.221300i
$101$	1.14688	+	0.766317i	0.114118	+	0.0762514i	0.611320	−	0.791384i	$-0.290639\pi$
$101$	1.14688	+	0.766317i	0.114118	+	0.0762514i	−0.497201	+	0.867635i	$0.665639\pi$
$102$	4.63342	+	10.9061i	0.458776	+	1.07987i
$103$	3.42308	−	1.41789i	0.337286	−	0.139708i	−0.207611	−	0.978212i	$-0.566569\pi$
$103$	3.42308	−	1.41789i	0.337286	−	0.139708i	0.544897	+	0.838503i	$0.316569\pi$
$104$	−18.6804	−	2.88435i	−1.83176	−	0.282834i
$105$	9.94762	+	11.4661i	0.970788	+	1.11898i
$106$	−11.5563	+	5.90709i	−1.12245	+	0.573748i
$107$	−0.353820	−	1.77877i	−0.0342051	−	0.171960i	0.959907	−	0.280319i	$-0.0904404\pi$
$107$	−0.353820	−	1.77877i	−0.0342051	−	0.171960i	−0.994112	+	0.108359i	$0.965440\pi$
$108$	1.48760	+	10.2853i	0.143145	+	0.989702i
$109$	−4.27438	−	6.39706i	−0.409411	−	0.612728i	0.568264	−	0.822846i	$-0.307615\pi$
$109$	−4.27438	−	6.39706i	−0.409411	−	0.612728i	−0.977676	+	0.210118i	$0.932615\pi$
$110$	8.71138	+	1.01963i	0.830598	+	0.0972175i
$111$	−16.3699	+	5.45945i	−1.55376	+	0.518188i
$112$	−13.3202	−	0.978946i	−1.25864	−	0.0925017i
$113$	−7.68145	−	7.68145i	−0.722610	−	0.722610i	0.246526	−	0.969136i	$-0.420711\pi$
$113$	−7.68145	−	7.68145i	−0.722610	−	0.722610i	−0.969136	+	0.246526i	$0.920711\pi$
$114$	−0.739346	−	3.54895i	−0.0692461	−	0.332389i
$115$	−7.14731	−	10.6967i	−0.666490	−	0.997472i
$116$	2.71845	+	7.31035i	0.252402	+	0.678749i
$117$	−14.9310	−	13.3791i	−1.38037	−	1.23690i
$118$	−1.34403	+	4.15478i	−0.123728	+	0.382479i
$119$	−14.9232	−	6.18139i	−1.36801	−	0.566647i
$120$	−11.7392	−	5.24717i	−1.07164	−	0.478999i
$121$	−5.00447	+	2.07292i	−0.454952	+	0.188447i
$122$	6.76233	−	0.541016i	0.612232	−	0.0489813i
$123$	2.12099	+	3.71942i	0.191243	+	0.335369i
$124$	0.0846651	−	0.0521849i	0.00760315	−	0.00468634i
$125$	8.00807	+	1.59290i	0.716263	+	0.142474i
$126$	−11.2707	−	8.58229i	−1.00407	−	0.764571i
$127$			2.11042i			0.187270i	0.995607	+	0.0936348i	$0.0298486\pi$
$127$			2.11042i			0.187270i	−0.995607	+	0.0936348i	$0.970151\pi$
$128$	10.5785	−	4.01189i	0.935016	−	0.354605i
$129$	0.824886	+	0.412283i	0.0726272	+	0.0362995i
$130$	23.8659	−	6.76425i	2.09318	−	0.593264i
$131$	−2.13696	+	10.7432i	−0.186707	+	0.938640i	0.767854	+	0.640625i	$0.221325\pi$
$131$	−2.13696	+	10.7432i	−0.186707	+	0.938640i	−0.954561	+	0.298015i	$0.903675\pi$
$132$	−8.15295	+	0.726510i	−0.709623	+	0.0632346i
$133$	4.10881	+	2.74542i	0.356279	+	0.238058i
$134$	0.419830	+	5.24758i	0.0362678	+	0.453322i
$135$	−7.39440	−	11.4600i	−0.636408	−	0.986321i
$136$	13.6699	−	0.590275i	1.17219	−	0.0506156i
$137$	1.35133	−	3.26240i	0.115452	−	0.278726i	−0.855582	−	0.517667i	$-0.826800\pi$
$137$	1.35133	−	3.26240i	0.115452	−	0.278726i	0.971034	+	0.238942i	$0.0768005\pi$
$138$	8.56584	+	8.41234i	0.729173	+	0.716106i
$139$	2.25479	+	11.3356i	0.191249	+	0.961475i	0.950511	+	0.310690i	$0.100560\pi$
$139$	2.25479	+	11.3356i	0.191249	+	0.961475i	−0.759262	+	0.650785i	$0.774440\pi$
$140$	16.4290	−	6.10934i	1.38850	−	0.516334i
$141$	−0.772771	−	6.12242i	−0.0650791	−	0.515600i
$142$	−12.0061	−	15.1891i	−1.00753	−	1.27464i
$143$	11.1656	−	11.1656i	0.933716	−	0.933716i
$144$	11.7238	+	2.55956i	0.976987	+	0.213297i
$145$	−7.23774	−	7.23774i	−0.601062	−	0.601062i
$146$	2.42311	−	20.7023i	0.200538	−	1.71334i
$147$	7.12994	−	0.899941i	0.588067	−	0.0742259i
$148$	−0.730730	+	19.9124i	−0.0600657	+	1.63679i
$149$	9.41669	−	1.87310i	0.771445	−	0.153450i	0.206353	−	0.978478i	$-0.433841\pi$
$149$	9.41669	−	1.87310i	0.771445	−	0.153450i	0.565092	+	0.825028i	$0.308841\pi$
$150$	4.62745	−	0.0418376i	0.377830	−	0.00341603i
$151$	15.4374	+	6.39437i	1.25628	+	0.520367i	0.908765	−	0.417309i	$-0.137027\pi$
$151$	15.4374	+	6.39437i	1.25628	+	0.520367i	0.347511	+	0.937676i	$0.387027\pi$
$152$	−4.13693	−	0.638765i	−0.335549	−	0.0518107i
$153$	12.4901	+	7.39024i	1.00976	+	0.597466i
$154$	7.23540	−	8.49380i	0.583045	−	0.684450i
$155$	−0.0725144	+	0.108525i	−0.00582449	+	0.00871697i
$156$	−20.5169	+	10.7224i	−1.64267	+	0.858479i
$157$	−1.10477	−	0.219752i	−0.0881699	−	0.0175381i	0.150808	−	0.988563i	$-0.451812\pi$
$157$	−1.10477	−	0.219752i	−0.0881699	−	0.0175381i	−0.238978	+	0.971025i	$0.576812\pi$
$158$	−1.65393	+	2.96229i	−0.131579	+	0.235667i
$159$	−7.10643	+	14.2184i	−0.563576	+	1.12759i
$160$	−10.4308	+	10.5667i	−0.824624	+	0.835369i
$161$	−16.3659			−1.28981
$162$	8.93687	+	9.06269i	0.702147	+	0.712032i
$163$	−3.95820	+	19.8992i	−0.310030	+	1.55863i	0.440477	+	0.897764i	$0.354809\pi$
$163$	−3.95820	+	19.8992i	−0.310030	+	1.55863i	−0.750507	+	0.660862i	$0.770191\pi$
$164$	4.88116	−	0.786060i	0.381154	−	0.0613810i
$165$	9.33146	−	5.32124i	0.726453	−	0.414258i
$166$	9.29355	−	10.9099i	0.721319	−	0.846774i
$167$	0.109882	+	0.265279i	0.00850292	+	0.0205279i	0.928074	−	0.372396i	$-0.121464\pi$
$167$	0.109882	+	0.265279i	0.00850292	+	0.0205279i	−0.919571	+	0.392924i	$0.871464\pi$
$168$	−13.8470	+	8.70858i	−1.06832	+	0.671881i
$169$	12.1155	−	29.2494i	0.931963	−	2.24996i
$170$	−15.9890	+	8.17287i	−1.22630	+	0.626831i
$171$	−3.30660	−	2.96292i	−0.252862	−	0.226580i
$172$	0.780063	−	0.724837i	0.0594792	−	0.0552683i
$173$	11.1530	−	7.45221i	0.847948	−	0.566581i	−0.0539429	−	0.998544i	$-0.517179\pi$
$173$	11.1530	−	7.45221i	0.847948	−	0.566581i	0.901891	+	0.431963i	$0.142179\pi$
$174$	7.99011	+	5.23496i	0.605729	+	0.396861i
$175$	−4.46056	+	4.46056i	−0.337187	+	0.337187i
$176$	−2.51838	+	9.10983i	−0.189830	+	0.686679i
$177$	1.69203	+	5.07346i	0.127181	+	0.381345i
$178$	7.84130	+	9.92020i	0.587730	+	0.743550i
$179$	13.7986	−	9.21991i	1.03135	−	0.689128i	0.0798628	−	0.996806i	$-0.474552\pi$
$179$	13.7986	−	9.21991i	1.03135	−	0.689128i	0.951491	+	0.307677i	$0.0995518\pi$
$180$	−15.3877	+	3.35113i	−1.14693	+	0.249779i
$181$	−0.368628	+	0.0733247i	−0.0273999	+	0.00545018i	−0.208771	−	0.977965i	$-0.566946\pi$
$181$	−0.368628	+	0.0733247i	−0.0273999	+	0.00545018i	0.181371	+	0.983415i	$0.441946\pi$
$182$	9.71270	−	30.0248i	0.719953	−	2.22559i
$183$	6.27591	−	5.44478i	0.463929	−	0.402489i
$184$	12.5671	−	5.85281i	0.926461	−	0.431475i
$185$	−10.0072	−	24.1595i	−0.735742	−	1.77624i
$186$	0.0455945	−	0.112953i	0.00334315	−	0.00828209i
$187$	−6.35048	+	9.50417i	−0.464393	+	0.695014i
$188$	−6.93305	−	1.64550i	−0.505645	−	0.120011i
$189$	−17.3479	−	0.278125i	−1.26187	−	0.0202306i
$190$	5.28532	−	1.49800i	0.383437	−	0.108677i
$191$	4.88024			0.353122			0.176561	−	0.984290i	$-0.443503\pi$
$191$	4.88024			0.353122			0.176561	+	0.984290i	$0.443503\pi$
$192$	7.51855	−	11.6392i	0.542605	−	0.839988i
$193$	−7.52929			−0.541970			−0.270985	−	0.962584i	$-0.587349\pi$
$193$	−7.52929			−0.541970			−0.270985	+	0.962584i	$0.587349\pi$
$194$	−5.34885	+	1.51601i	−0.384025	+	0.108843i
$195$	18.6233	−	24.0037i	1.33364	−	1.71894i
$196$	1.91629	−	8.07397i	0.136878	−	0.576712i
$197$	−8.61841	+	12.8984i	−0.614036	+	0.918970i	−0.999994	−	0.00354629i	$-0.998871\pi$
$197$	−8.61841	+	12.8984i	−0.614036	+	0.918970i	0.385957	+	0.922517i	$0.373871\pi$
$198$	−7.51259	+	6.63766i	−0.533896	+	0.471718i
$199$	4.43073	+	10.6967i	0.314086	+	0.758271i	0.999545	+	0.0301595i	$0.00960151\pi$
$199$	4.43073	+	10.6967i	0.314086	+	0.758271i	−0.685459	+	0.728111i	$0.740398\pi$
$200$	1.83001	−	5.02041i	0.129401	−	0.354996i
$201$	4.22516	+	4.87012i	0.298020	+	0.343512i
$202$	0.600389	−	1.85598i	0.0422432	−	0.130586i
$203$	−12.7711	+	2.54032i	−0.896354	+	0.178296i
$204$	13.0522	−	10.5101i	0.913840	−	0.735855i
$205$	−5.39491	+	3.60476i	−0.376797	+	0.251768i
$206$	−3.24927	−	4.11072i	−0.226387	−	0.286407i
$207$	14.5570	+	2.07496i	1.01178	+	0.144220i
$208$	3.27932	+	26.5292i	0.227380	+	1.83947i
$209$	2.47273	−	2.47273i	0.171042	−	0.171042i
$210$	11.7648	−	17.9567i	0.811851	−	1.23913i
$211$	17.8899	−	11.9536i	1.23159	−	0.822923i	0.242489	−	0.970154i	$-0.422036\pi$
$211$	17.8899	−	11.9536i	1.23159	−	0.822923i	0.989102	+	0.147232i	$0.0470363\pi$
$212$	12.4938	+	13.4458i	0.858081	+	0.923458i
$213$	−22.8714	−	6.25956i	−1.56712	−	0.428898i
$214$	−2.28379	+	1.16737i	−0.156116	+	0.0798000i
$215$	−0.534786	+	1.29109i	−0.0364721	+	0.0880514i
$216$	13.4207	−	5.99044i	0.913162	−	0.407598i
$217$	0.0635419	+	0.153404i	0.00431350	+	0.0104137i
$218$	−7.05561	+	8.28275i	−0.477866	+	0.560978i
$219$	−12.6458	−	22.1759i	−0.854521	−	1.49851i
$220$	−1.97210	−	12.2461i	−0.132959	−	0.825631i
$221$	−6.30693	+	31.7071i	−0.424250	+	2.13285i
$222$	13.7411	+	20.1678i	0.922240	+	1.35358i
$223$	−1.45744			−0.0975977			−0.0487989	−	0.998809i	$-0.515539\pi$
$223$	−1.45744			−0.0975977			−0.0487989	+	0.998809i	$0.515539\pi$
$224$	3.80478	+	18.5012i	0.254218	+	1.23617i
$225$	4.53309	−	3.40201i	0.302206	−	0.226801i
$226$	−7.48928	+	13.4138i	−0.498180	+	0.892271i
$227$	−19.3684	−	3.85261i	−1.28552	−	0.255707i	−0.495406	−	0.868662i	$-0.664981\pi$
$227$	−19.3684	−	3.85261i	−1.28552	−	0.255707i	−0.790118	+	0.612955i	$0.789981\pi$
$228$	−4.54365	+	2.37457i	−0.300910	+	0.157260i
$229$	0.936069	−	1.40093i	0.0618572	−	0.0925758i	−0.799252	−	0.600997i	$-0.794771\pi$
$229$	0.936069	−	1.40093i	0.0618572	−	0.0925758i	0.861109	+	0.508421i	$0.169771\pi$
$230$	−11.7979	+	13.8498i	−0.777929	+	0.913229i
$231$	0.966614	−	13.6312i	0.0635985	−	0.896866i
$232$	8.89826	−	6.51792i	0.584200	−	0.427922i
$233$	14.4154	+	5.97104i	0.944382	+	0.391176i	0.801117	−	0.598508i	$-0.204240\pi$
$233$	14.4154	+	5.97104i	0.944382	+	0.391176i	0.143266	+	0.989684i	$0.454240\pi$
$234$	−12.4459	+	25.4748i	−0.813615	+	1.66534i
$235$	9.17178	−	1.82438i	0.598301	−	0.119009i
$236$	6.17139	+	0.226473i	0.401723	+	0.0147421i
$237$	0.520345	+	4.12252i	0.0338000	+	0.267787i
$238$	−2.65559	+	22.6886i	−0.172136	+	1.47068i
$239$	−0.690266	−	0.690266i	−0.0446496	−	0.0446496i	0.684429	−	0.729079i	$-0.260051\pi$
$239$	−0.690266	−	0.690266i	−0.0446496	−	0.0446496i	−0.729079	+	0.684429i	$0.760051\pi$
$240$	−2.61234	+	17.9961i	−0.168626	+	1.16164i
$241$	−10.6103	+	10.6103i	−0.683472	+	0.683472i	−0.960781	−	0.277309i	$-0.910558\pi$
$241$	−10.6103	+	10.6103i	−0.683472	+	0.683472i	0.277309	+	0.960781i	$0.410558\pi$
$242$	4.75036	+	6.00979i	0.305365	+	0.386324i
$243$	15.3952	+	2.44686i	0.987604	+	0.156966i
$244$	−3.34392	−	8.99232i	−0.214072	−	0.575674i
$245$	2.12461	+	10.6811i	0.135736	+	0.682391i
$246$	4.24278	−	4.32020i	0.270510	−	0.275446i
$247$	3.78482	−	9.13737i	0.240822	−	0.581397i
$248$	−0.103654	−	0.0950726i	−0.00658202	−	0.00603712i
$249$	1.24157	−	17.5087i	0.0786815	−	1.10957i
$250$	−0.920868	−	11.5102i	−0.0582408	−	0.727970i
$251$	22.7440	+	15.1971i	1.43559	+	0.959232i	0.998201	+	0.0599600i	$0.0190973\pi$
$251$	22.7440	+	15.1971i	1.43559	+	0.959232i	0.437391	+	0.899272i	$0.355903\pi$
$252$	−7.33084	+	18.6448i	−0.461799	+	1.17451i
$253$	−2.25941	+	11.3588i	−0.142048	+	0.714124i
$254$	2.87148	−	0.813855i	0.180173	−	0.0510658i
$255$	−9.83224	+	19.6721i	−0.615719	+	1.23191i
$256$	−9.53812	−	12.8462i	−0.596132	−	0.802886i
$257$			4.51818i			0.281836i	0.990021	+	0.140918i	$0.0450054\pi$
$257$			4.51818i			0.281836i	−0.990021	+	0.140918i	$0.954995\pi$
$258$	0.242854	−	1.28135i	0.0151194	−	0.0797732i
$259$	−32.6273	−	6.48997i	−2.02736	−	0.403267i
$260$	−18.4071	−	29.8639i	−1.14156	−	1.85208i
$261$	11.6816	−	0.640356i	0.723074	−	0.0396370i
$262$	15.4415	−	1.23539i	0.953981	−	0.0763227i
$263$	2.04943	−	0.848904i	0.126374	−	0.0523456i	−0.318601	−	0.947889i	$-0.603213\pi$
$263$	2.04943	−	0.848904i	0.126374	−	0.0523456i	0.444974	+	0.895543i	$0.353213\pi$
$264$	4.13258	+	10.8129i	0.254343	+	0.665487i
$265$	−22.2541	−	9.21797i	−1.36706	−	0.566255i
$266$	2.15096	−	6.64926i	0.131884	−	0.407692i
$267$	14.9376	+	4.08819i	0.914165	+	0.250193i
$268$	6.97805	−	2.59489i	0.426253	−	0.158508i
$269$	−12.8156	−	19.1799i	−0.781379	−	1.16942i	−0.981839	−	0.189715i	$-0.939244\pi$
$269$	−12.8156	−	19.1799i	−0.781379	−	1.16942i	0.200460	−	0.979702i	$-0.435756\pi$
$270$	−12.7412	+	14.4804i	−0.775403	+	0.881247i
$271$	−4.68156	−	4.68156i	−0.284384	−	0.284384i	0.550470	−	0.834855i	$-0.314448\pi$
$271$	−4.68156	−	4.68156i	−0.284384	−	0.284384i	−0.834855	+	0.550470i	$0.814448\pi$
$272$	−6.07477	−	18.3720i	−0.368337	−	1.11396i
$273$	−12.2275	−	36.6637i	−0.740045	−	2.21899i
$274$	−4.96001	−	0.580545i	−0.299645	−	0.0350720i
$275$	2.48007	+	3.71169i	0.149554	+	0.223823i
$276$	8.14269	−	14.8989i	0.490132	−	0.896811i
$277$	0.351539	+	1.76730i	0.0211219	+	0.106187i	0.989908	−	0.141711i	$-0.0452603\pi$
$277$	0.351539	+	1.76730i	0.0211219	+	0.106187i	−0.968786	+	0.247898i	$0.920260\pi$
$278$	14.5539	−	7.43935i	0.872887	−	0.446182i
$279$	−0.0370693	−	0.144505i	−0.00221928	−	0.00865127i
$280$	−14.6481	−	19.9976i	−0.875392	−	1.19509i
$281$	−6.33662	+	2.62472i	−0.378011	+	0.156577i	−0.563595	−	0.826051i	$-0.690582\pi$
$281$	−6.33662	+	2.62472i	−0.378011	+	0.156577i	0.185584	+	0.982628i	$0.440582\pi$
$282$	−8.03227	+	3.41247i	−0.478315	+	0.203210i
$283$	−19.0458	−	12.7260i	−1.13215	−	0.756481i	−0.159146	−	0.987255i	$-0.550874\pi$
$283$	−19.0458	−	12.7260i	−1.13215	−	0.756481i	−0.973007	+	0.230774i	$0.925874\pi$
$284$	−16.0367	+	22.1932i	−0.951601	+	1.31692i
$285$	4.12430	−	5.31583i	0.244302	−	0.314883i
$286$	−19.4980	−	10.8863i	−1.15294	−	0.643720i
$287$			8.25416i			0.487228i
$288$	−1.03855	−	16.9388i	−0.0611973	−	0.998126i
$289$		−	6.40197i		−	0.376586i
$290$	−7.05667	+	12.6390i	−0.414382	+	0.742185i
$291$	−4.17388	+	5.37973i	−0.244677	+	0.315366i
$292$	−29.1024	+	4.68665i	−1.70309	+	0.274265i
$293$	10.4198	+	6.96228i	0.608731	+	0.406741i	0.821375	−	0.570389i	$-0.193207\pi$
$293$	10.4198	+	6.96228i	0.608731	+	0.406741i	−0.212644	+	0.977130i	$0.568207\pi$
$294$	−3.97404	−	9.35408i	−0.231771	−	0.545541i
$295$	−7.48765	+	3.10149i	−0.435948	+	0.180575i
$296$	27.3750	−	6.68471i	1.59114	−	0.388541i
$297$	−2.58802	+	12.0020i	−0.150172	+	0.696428i
$298$	−6.17999	−	12.0902i	−0.357997	−	0.700366i
$299$	6.39014	+	32.1254i	0.369551	+	1.85786i
$300$	−1.84144	−	6.28006i	−0.106316	−	0.362580i
$301$	0.987675	+	1.47816i	0.0569287	+	0.0851998i
$302$	2.74709	−	23.4703i	0.158077	−	1.35056i
$303$	−0.755844	−	2.26636i	−0.0434221	−	0.130199i
$304$	0.726235	+	5.87512i	0.0416524	+	0.336961i
$305$	8.90301	+	8.90301i	0.509785	+	0.509785i
$306$	5.23867	−	19.8442i	0.299475	−	1.13442i
$307$	−7.76821	−	11.6259i	−0.443355	−	0.663528i	0.540736	−	0.841192i	$-0.318146\pi$
$307$	−7.76821	−	11.6259i	−0.443355	−	0.663528i	−0.984091	+	0.177665i	$0.943146\pi$
$308$	−14.3471	−	6.56910i	−0.817500	−	0.374309i
$309$	−6.18982	−	1.69406i	−0.352126	−	0.0963716i
$310$	0.175626	+	0.0568131i	0.00997488	+	0.00322677i
$311$	−30.5106	−	12.6379i	−1.73010	−	0.716630i	−0.999425	−	0.0339024i	$-0.989206\pi$
$311$	−30.5106	−	12.6379i	−1.73010	−	0.716630i	−0.730673	−	0.682728i	$-0.760794\pi$
$312$	22.5012	+	23.7807i	1.27388	+	1.34632i
$313$	−0.773283	+	0.320305i	−0.0437086	+	0.0181047i	−0.404431	−	0.914569i	$-0.632530\pi$
$313$	−0.773283	+	0.320305i	−0.0437086	+	0.0181047i	0.360722	+	0.932673i	$0.382530\pi$
$314$	0.127040	+	1.58791i	0.00716927	+	0.0896109i
$315$	−1.43911	−	26.2528i	−0.0810847	−	1.47918i
$316$	4.66836	+	1.10800i	0.262616	+	0.0623298i
$317$	−13.4190	−	2.66920i	−0.753685	−	0.149917i	−0.196728	−	0.980458i	$-0.563031\pi$
$317$	−13.4190	−	2.66920i	−0.753685	−	0.149917i	−0.556958	+	0.830541i	$0.688031\pi$
$318$	22.0863	+	4.18602i	1.23854	+	0.234740i
$319$			9.21456i			0.515916i
$320$	18.3997	+	10.1174i	1.02857	+	0.565579i
$321$	−1.40439	+	2.80987i	−0.0783853	+	0.156831i
$322$	6.31127	+	22.2677i	0.351713	+	1.24093i
$323$	−1.39673	+	7.02182i	−0.0777159	+	0.390704i
$324$	8.88448	−	15.6546i	0.493582	−	0.869699i
$325$	10.4975	+	7.01422i	0.582297	+	0.389079i
$326$	28.6017	−	2.28826i	1.58410	−	0.126735i
$327$	−0.942595	+	13.2925i	−0.0521256	+	0.735075i
$328$	−2.95188	−	6.33826i	−0.162990	−	0.349972i
$329$	4.55255	−	10.9908i	0.250990	−	0.605944i
$330$	−10.8387	−	10.6445i	−0.596653	−	0.585960i
$331$	2.41877	+	12.1600i	0.132947	+	0.668372i	0.988569	+	0.150770i	$0.0481753\pi$
$331$	2.41877	+	12.1600i	0.132947	+	0.668372i	−0.855621	+	0.517602i	$0.826825\pi$
$332$	−18.4282	−	8.43772i	−1.01138	−	0.463080i
$333$	28.1983	+	9.90935i	1.54526	+	0.543029i
$334$	0.318569	−	0.251809i	0.0174313	−	0.0137784i
$335$	−6.90875	+	6.90875i	−0.377466	+	0.377466i
$336$	17.1890	+	15.4822i	0.937735	+	0.844621i
$337$	22.7974	+	22.7974i	1.24185	+	1.24185i	0.959231	+	0.282622i	$0.0912041\pi$
$337$	22.7974	+	22.7974i	1.24185	+	1.24185i	0.282622	+	0.959231i	$0.408796\pi$
$338$	−44.4695	−	5.20495i	−2.41882	−	0.283112i
$339$	2.35622	+	18.6675i	0.127972	+	1.01388i
$340$	17.2861	+	18.6031i	0.937470	+	1.00890i
$341$	0.115243	−	0.0229233i	0.00624077	−	0.00124137i
$342$	−2.75626	+	5.64163i	−0.149041	+	0.305064i
$343$	−8.79454	−	3.64282i	−0.474860	−	0.196694i
$344$	−1.28705	−	0.781844i	−0.0693930	−	0.0421542i
$345$	−1.57614	+	22.2267i	−0.0848564	+	1.19664i
$346$	−14.4406	−	12.3012i	−0.776333	−	0.661315i
$347$	15.3279	−	22.9398i	0.822843	−	1.23147i	−0.147338	−	0.989086i	$-0.547070\pi$
$347$	15.3279	−	22.9398i	0.822843	−	1.23147i	0.970180	−	0.242385i	$-0.0779296\pi$
$348$	4.04151	−	12.8903i	0.216647	−	0.690992i
$349$	8.15254	+	1.62164i	0.436395	+	0.0868044i	0.408399	−	0.912804i	$-0.366087\pi$
$349$	8.15254	+	1.62164i	0.436395	+	0.0868044i	0.0279965	+	0.999608i	$0.491087\pi$
$350$	7.78928	+	4.34897i	0.416354	+	0.232462i
$351$	6.22763	+	34.1617i	0.332406	+	1.82341i
$352$	13.3662	−	0.0865196i	0.712420	−	0.00461151i
$353$	−12.2210			−0.650460			−0.325230	−	0.945635i	$-0.605442\pi$
$353$	−12.2210			−0.650460			−0.325230	+	0.945635i	$0.605442\pi$
$354$	6.25054	−	4.25872i	0.332212	−	0.226348i
$355$	7.01032	−	35.2433i	0.372069	−	1.87052i
$356$	10.4737	−	14.4946i	0.555106	−	0.768213i
$357$	13.8590	+	24.3035i	0.733498	+	1.28628i
$358$	−17.8660	−	15.2191i	−0.944248	−	0.804353i
$359$	3.41180	+	8.23682i	0.180068	+	0.434723i	0.987980	−	0.154580i	$-0.0494025\pi$
$359$	3.41180	+	8.23682i	0.180068	+	0.434723i	−0.807912	+	0.589303i	$0.799402\pi$
$360$	10.4937	+	19.6445i	0.553066	+	1.03536i
$361$	−6.43280	+	15.5302i	−0.338569	+	0.817377i
$362$	0.241923	+	0.473286i	0.0127152	+	0.0248753i
$363$	9.04938	+	2.47668i	0.474969	+	0.129992i
$364$	−44.5979	−	1.63662i	−2.33757	−	0.0857821i
$365$	32.1655	−	21.4923i	1.68362	−	1.12496i
$366$	−9.82849	−	6.43942i	−0.513743	−	0.336594i
$367$	11.6703	−	11.6703i	0.609183	−	0.609183i	−0.333550	−	0.942733i	$-0.608246\pi$
$367$	11.6703	−	11.6703i	0.609183	−	0.609183i	0.942733	+	0.333550i	$0.108246\pi$
$368$	−12.8098	−	14.8420i	−0.667756	−	0.773693i
$369$	1.04651	−	7.34186i	0.0544793	−	0.382202i
$370$	−29.0127	+	22.9327i	−1.50830	+	1.19222i
$371$	−25.4787	+	17.0243i	−1.32279	+	0.883859i
$372$	−0.171268	−	0.0184781i	−0.00887986	−	0.000958047i
$373$	30.2561	−	6.01831i	1.56660	−	0.311616i	0.665894	−	0.746046i	$-0.268050\pi$
$373$	30.2561	−	6.01831i	1.56660	−	0.311616i	0.900706	+	0.434430i	$0.143050\pi$
$374$	15.3805	+	4.97543i	0.795308	+	0.257274i
$375$	−9.26759	−	10.6823i	−0.478576	−	0.551630i
$376$	0.434733	+	10.0678i	0.0224196	+	0.519208i
$377$	9.97307	+	24.0771i	0.513639	+	1.24004i
$378$	6.31156	+	23.7111i	0.324631	+	1.21957i
$379$	12.8100	−	19.1715i	0.658005	−	0.984774i	−0.340995	−	0.940065i	$-0.610764\pi$
$379$	12.8100	−	19.1715i	0.658005	−	0.984774i	0.999000	−	0.0447089i	$-0.0142360\pi$
$380$	−4.07642	−	6.61362i	−0.209116	−	0.339272i
$381$	2.24070	−	2.88806i	0.114795	−	0.147960i
$382$	−1.88200	−	6.64015i	−0.0962914	−	0.339739i
$383$	−11.5359			−0.589459			−0.294729	−	0.955581i	$-0.595230\pi$
$383$	−11.5359			−0.589459			−0.294729	+	0.955581i	$0.595230\pi$
$384$	−18.7360	−	5.74137i	−0.956116	−	0.292988i
$385$	20.7084			1.05540
$386$	2.90357	+	10.2445i	0.147788	+	0.521431i
$387$	−0.691101	−	1.44001i	−0.0351306	−	0.0731997i
$388$	4.12543	+	6.69312i	0.209437	+	0.339792i
$389$	−12.8942	+	19.2976i	−0.653764	+	0.978427i	0.345436	+	0.938442i	$0.387731\pi$
$389$	−12.8942	+	19.2976i	−0.653764	+	0.978427i	−0.999200	+	0.0399850i	$0.987269\pi$
$390$	−39.8417	−	16.0825i	−2.01746	−	0.814371i
$391$	−9.07369	−	21.9058i	−0.458876	−	1.10783i
$392$	−11.7246	+	0.506273i	−0.592181	+	0.0255707i
$393$	14.3308	−	12.4329i	0.722894	−	0.627159i
$394$	20.8733	+	6.75229i	1.05158	+	0.340176i
$395$	−6.17581	+	1.22844i	−0.310739	+	0.0618097i
$396$	11.9285	+	7.66205i	0.599428	+	0.385032i
$397$	2.60492	−	1.74055i	0.130737	−	0.0873557i	−0.488482	−	0.872574i	$-0.662449\pi$
$397$	2.60492	−	1.74055i	0.130737	−	0.0873557i	0.619219	+	0.785218i	$0.287449\pi$
$398$	12.8455	−	10.1536i	0.643887	−	0.508953i
$399$	−2.70790	−	8.11950i	−0.135565	−	0.406483i
$400$	−7.53658	−	0.553888i	−0.376829	−	0.0276944i
$401$	24.3210	−	24.3210i	1.21453	−	1.21453i	0.245012	−	0.969520i	$-0.421208\pi$
$401$	24.3210	−	24.3210i	1.21453	−	1.21453i	0.969520	−	0.245012i	$-0.0787918\pi$
$402$	4.99700	−	7.62692i	0.249228	−	0.380396i
$403$	0.276314	−	0.184627i	0.0137642	−	0.00919692i
$404$	−2.75681	−	0.101167i	−0.137157	−	0.00503326i
$405$	−2.04844	+	23.5336i	−0.101788	+	1.16939i
$406$	8.38141	+	16.3969i	0.415962	+	0.813766i
$407$	−9.00882	+	21.7492i	−0.446550	+	1.07807i
$408$	−19.3337	−	13.7061i	−0.957160	−	0.678551i
$409$	3.24175	+	7.82629i	0.160294	+	0.386985i	0.983538	−	0.180704i	$-0.0578376\pi$
$409$	3.24175	+	7.82629i	0.160294	+	0.386985i	−0.823243	+	0.567689i	$0.807838\pi$
$410$	6.98518	+	5.95029i	0.344974	+	0.293864i
$411$	−5.31306	+	3.02976i	−0.262074	+	0.149447i
$412$	−4.34009	+	6.00626i	−0.213821	+	0.295907i
$413$	−2.01141	+	10.1121i	−0.0989751	+	0.497582i
$414$	−2.79047	−	20.6067i	−0.137144	−	1.01276i
$415$	26.5991			1.30570
$416$	34.8314	−	14.6925i	1.70775	−	0.720360i
$417$	8.94978	−	17.9065i	0.438272	−	0.876885i
$418$	−4.31801	−	2.41086i	−0.211201	−	0.117919i
$419$	30.5931	+	6.08535i	1.49457	+	0.297289i	0.873639	−	0.486575i	$-0.161754\pi$
$419$	30.5931	+	6.08535i	1.49457	+	0.297289i	0.620933	+	0.783864i	$0.286754\pi$
$420$	−28.9691	−	9.08272i	−1.41355	−	0.443191i
$421$	−3.52363	+	5.27349i	−0.171731	+	0.257014i	−0.907345	−	0.420388i	$-0.861894\pi$
$421$	−3.52363	+	5.27349i	−0.171731	+	0.257014i	0.735613	+	0.677402i	$0.236894\pi$
$422$	−23.1633	−	19.7316i	−1.12757	−	0.960518i
$423$	−5.44286	+	9.19885i	−0.264641	+	0.447263i
$424$	13.4765	−	22.1845i	0.654475	−	1.07738i
$425$	−8.44356	−	3.49744i	−0.409573	−	0.169651i
$426$	0.303180	+	33.5332i	0.0146891	+	1.62469i
$427$	15.7095	−	3.12481i	0.760234	−	0.151220i
$428$	2.46906	+	2.65718i	0.119347	+	0.128440i
$429$	−27.1348	+	3.42495i	−1.31008	+	0.165358i
$430$	1.96291	+	0.229749i	0.0946599	+	0.0110795i
$431$	−25.0198	−	25.0198i	−1.20516	−	1.20516i	−0.972576	−	0.232586i	$-0.925281\pi$
$431$	−25.0198	−	25.0198i	−1.20516	−	1.20516i	−0.232586	−	0.972576i	$-0.574719\pi$
$432$	−13.3262	−	15.9503i	−0.641158	−	0.767409i
$433$	−0.182313	+	0.182313i	−0.00876139	+	0.00876139i	−0.711474	−	0.702713i	$-0.751972\pi$
$433$	−0.182313	+	0.182313i	−0.00876139	+	0.00876139i	0.702713	+	0.711474i	$0.251972\pi$
$434$	0.184220	−	0.145614i	0.00884284	−	0.00698971i
$435$	2.22011	+	17.5892i	0.106446	+	0.843339i
$436$	13.9906	+	6.40587i	0.670026	+	0.306785i
$437$	1.41515	+	7.11445i	0.0676959	+	0.340330i
$438$	−25.2963	+	25.7579i	−1.20871	+	1.23076i
$439$	−15.4119	+	37.2076i	−0.735570	+	1.77582i	−0.112508	+	0.993651i	$0.535888\pi$
$439$	−15.4119	+	37.2076i	−0.735570	+	1.77582i	−0.623062	+	0.782172i	$0.714112\pi$
$440$	−15.9017	+	7.40582i	−0.758085	+	0.353059i
$441$	−10.7126	−	6.33855i	−0.510125	−	0.301836i
$442$	45.5735	−	3.64608i	2.16771	−	0.173426i
$443$	5.50223	+	3.67647i	0.261419	+	0.174674i	0.679372	−	0.733794i	$-0.262252\pi$
$443$	5.50223	+	3.67647i	0.261419	+	0.174674i	−0.417953	+	0.908469i	$0.637252\pi$
$444$	22.1417	−	26.4738i	1.05080	−	1.25639i
$445$	−4.57852	+	23.0178i	−0.217043	+	1.09115i
$446$	0.562044	+	1.98303i	0.0266135	+	0.0938991i
$447$	−14.8752	−	7.43473i	−0.703574	−	0.351651i
$448$	23.7059	−	12.3116i	1.12000	−	0.581669i
$449$		−	13.3291i		−	0.629041i	−0.949251	−	0.314520i	$-0.898156\pi$
$449$		−	13.3291i		−	0.629041i	0.949251	−	0.314520i	$-0.101844\pi$
$450$	−6.37697	−	4.85587i	−0.300613	−	0.228908i
$451$	5.72886	+	1.13954i	0.269761	+	0.0536589i
$452$	21.1392	+	5.01722i	0.994303	+	0.235990i
$453$	−14.3365	−	25.1409i	−0.673589	−	1.18122i
$454$	2.22722	+	27.8387i	0.104529	+	1.30653i
$455$	54.1100	−	22.4131i	2.53672	−	1.05074i
$456$	4.98308	+	5.26645i	0.233354	+	0.246624i
$457$	−18.5018	−	7.66368i	−0.865476	−	0.358492i	−0.0946295	−	0.995513i	$-0.530167\pi$
$457$	−18.5018	−	7.66368i	−0.865476	−	0.358492i	−0.770847	+	0.637020i	$0.780167\pi$
$458$	−2.26711	−	0.733385i	−0.105935	−	0.0342688i
$459$	−9.24589	−	23.3745i	−0.431561	−	1.09103i
$460$	23.3940	+	10.7114i	1.09075	+	0.499423i
$461$	19.4038	+	29.0398i	0.903724	+	1.35252i	0.935613	+	0.353027i	$0.114848\pi$
$461$	19.4038	+	29.0398i	0.903724	+	1.35252i	−0.0318892	+	0.999491i	$0.510152\pi$
$462$	−18.9196	+	3.94149i	−0.880220	+	0.183375i
$463$	−26.4304	−	26.4304i	−1.22833	−	1.22833i	−0.964597	−	0.263728i	$-0.915048\pi$
$463$	−26.4304	−	26.4304i	−1.22833	−	1.22833i	−0.263728	−	0.964597i	$-0.584952\pi$
$464$	−12.2999	−	9.59360i	−0.571008	−	0.445372i
$465$	0.214459	−	0.0715233i	0.00994530	−	0.00331681i
$466$	2.56522	−	21.9165i	0.118832	−	1.01526i
$467$	−6.62269	−	9.91156i	−0.306462	−	0.458652i	0.645988	−	0.763347i	$-0.276445\pi$
$467$	−6.62269	−	9.91156i	−0.306462	−	0.458652i	−0.952450	+	0.304695i	$0.901445\pi$
$468$	39.4612	+	7.11013i	1.82409	+	0.328666i
$469$	2.42485	+	12.1906i	0.111969	+	0.562908i
$470$	−6.01926	−	11.7757i	−0.277648	−	0.543175i
$471$	1.27853	+	1.47369i	0.0589114	+	0.0679041i
$472$	−2.07177	−	8.48424i	−0.0953609	−	0.390519i
$473$	1.16228	−	0.481433i	0.0534418	−	0.0221363i
$474$	5.40852	−	2.29779i	0.248421	−	0.105541i
$475$	2.32477	+	1.55336i	0.106668	+	0.0712731i
$476$	31.8946	−	5.13629i	1.46189	−	0.235422i
$477$	24.8211	−	11.9123i	1.13648	−	0.545428i
$478$	−0.672997	+	1.20538i	−0.0307822	+	0.0551329i
$479$		−	37.9382i		−	1.73344i	−0.498795	−	0.866720i	$-0.666224\pi$
$479$		−	37.9382i		−	1.73344i	0.498795	−	0.866720i	$-0.333776\pi$
$480$	25.4932	−	3.38554i	1.16360	−	0.154528i
$481$			66.5798i			3.03578i
$482$	18.5284	+	10.3449i	0.843944	+	0.471197i
$483$	22.3963	+	17.3762i	1.01906	+	0.790643i
$484$	6.34512	−	8.78103i	0.288414	−	0.399138i
$485$	−8.57938	−	5.73256i	−0.389569	−	0.260302i
$486$	−2.60772	−	21.8906i	−0.118289	−	0.992979i
$487$	−20.1298	+	8.33804i	−0.912168	+	0.377833i	−0.788886	−	0.614539i	$-0.789342\pi$
$487$	−20.1298	+	8.33804i	−0.912168	+	0.377833i	−0.123282	+	0.992372i	$0.539342\pi$
$488$	−10.9456	+	8.01756i	−0.495483	+	0.362938i
$489$	26.5443	−	23.0290i	1.20038	−	1.04141i
$490$	13.7136	−	7.00981i	0.619517	−	0.316671i
$491$	−3.99742	−	20.0964i	−0.180401	−	0.906936i	−0.959859	−	0.280482i	$-0.909506\pi$
$491$	−3.99742	−	20.0964i	−0.180401	−	0.906936i	0.779458	−	0.626454i	$-0.215494\pi$
$492$	−7.51432	−	4.10678i	−0.338772	−	0.185148i
$493$	−10.4809	−	15.6858i	−0.472036	−	0.706451i
$494$	−13.8920	−	1.62600i	−0.625032	−	0.0731571i
$495$	−18.4196	−	2.62554i	−0.827900	−	0.118009i
$496$	−0.0893849	+	0.177697i	−0.00401350	+	0.00797882i
$497$	−32.3238	−	32.3238i	−1.44992	−	1.44992i
$498$	−24.3014	+	5.06267i	−1.08897	+	0.226864i
$499$	10.8139	+	16.1841i	0.484095	+	0.724500i	0.990457	−	0.137821i	$-0.0440099\pi$
$499$	10.8139	+	16.1841i	0.484095	+	0.724500i	−0.506362	+	0.862321i	$0.669010\pi$
$500$	−15.3059	+	5.69171i	−0.684500	+	0.254541i
$501$	0.131284	−	0.479692i	0.00586536	−	0.0214311i
$502$	11.9065	−	36.8065i	0.531414	−	1.64276i
$503$	13.0766	+	5.41650i	0.583056	+	0.241510i	0.654660	−	0.755923i	$-0.272812\pi$
$503$	13.0766	+	5.41650i	0.583056	+	0.241510i	−0.0716041	+	0.997433i	$0.522812\pi$
$504$	28.1955	+	2.78437i	1.25593	+	0.124026i
$505$	3.34480	−	1.38546i	0.148842	−	0.0616522i
$506$	16.3264	−	1.30618i	0.725795	−	0.0580668i
$507$	−47.6349	+	27.1637i	−2.11554	+	1.20638i
$508$	−2.21469	−	3.59314i	−0.0982612	−	0.159420i
$509$	−21.9603	−	4.36817i	−0.973371	−	0.193616i	−0.317309	−	0.948322i	$-0.602779\pi$
$509$	−21.9603	−	4.36817i	−0.973371	−	0.193616i	−0.656062	+	0.754707i	$0.727779\pi$
$510$	30.5579	+	5.79165i	1.35313	+	0.256459i
$511$		−	49.2130i		−	2.17705i
$512$	−13.8005	+	17.9317i	−0.609902	+	0.792477i
$513$	1.37916	+	7.56540i	0.0608916	+	0.334021i
$514$	6.14752	−	1.74237i	0.271155	−	0.0768528i
$515$	1.89724	−	9.53808i	0.0836025	−	0.420298i
$516$	−1.83708	+	0.163702i	−0.0808729	+	0.00720659i
$517$	−6.99975	−	4.67708i	−0.307848	−	0.205698i
$518$	3.75190	+	46.8961i	0.164849	+	2.06050i
$519$	−23.1749	−	1.64338i	−1.01726	−	0.0721362i
$520$	−33.5349	+	36.5617i	−1.47060	+	1.60334i
$521$	0.213242	−	0.514813i	0.00934232	−	0.0225544i	−0.919140	−	0.393932i	$-0.871115\pi$
$521$	0.213242	−	0.514813i	0.00934232	−	0.0225544i	0.928482	+	0.371378i	$0.121115\pi$
$522$	−5.37614	−	15.6473i	−0.235307	−	0.684863i
$523$	−0.636430	−	3.19955i	−0.0278291	−	0.139907i	0.964373	−	0.264547i	$-0.0852223\pi$
$523$	−0.636430	−	3.19955i	−0.0278291	−	0.139907i	−0.992202	+	0.124640i	$0.960222\pi$
$524$	−7.63572	−	20.5336i	−0.333568	−	0.897016i
$525$	10.8401	−	1.36824i	0.473100	−	0.0597147i
$526$	−1.94537	−	2.46113i	−0.0848222	−	0.107310i
$527$	−0.170103	+	0.170103i	−0.00740979	+	0.00740979i
$528$	13.1186	−	9.79271i	0.570912	−	0.426173i
$529$	−0.723726	−	0.723726i	−0.0314664	−	0.0314664i
$530$	−3.96013	+	33.8342i	−0.172017	+	1.46966i
$531$	3.07117	−	8.73938i	0.133277	−	0.379257i
$532$	−9.87660	−	0.362444i	−0.428205	−	0.0157139i
$533$	16.2025	−	3.22288i	0.701809	−	0.139599i
$534$	−0.198010	−	21.9009i	−0.00856873	−	0.947745i
$535$	−4.39792	−	1.82168i	−0.190139	−	0.0787580i
$536$	−6.22164	−	8.49379i	−0.268734	−	0.366876i
$537$	−28.6721	−	2.03319i	−1.23729	−	0.0877388i
$538$	−21.1543	+	24.8336i	−0.912028	+	1.07065i
$539$	5.44675	−	8.15164i	0.234608	−	0.351116i
$540$	24.6157	+	11.7517i	1.05929	+	0.505714i
$541$	−18.6138	−	3.70251i	−0.800270	−	0.159184i	−0.222019	−	0.975042i	$-0.571265\pi$
$541$	−18.6138	−	3.70251i	−0.800270	−	0.159184i	−0.578251	+	0.815859i	$0.696265\pi$
$542$	−4.56444	+	8.17520i	−0.196059	+	0.351155i
$543$	0.582309	+	0.291042i	0.0249893	+	0.0124898i
$544$	−22.6546	+	15.3503i	−0.971307	+	0.658140i
$545$	−20.1939			−0.865010
$546$	−45.1699	+	30.7759i	−1.93309	+	1.31709i
$547$	0.321617	−	1.61688i	0.0137513	−	0.0691327i	−0.973300	−	0.229535i	$-0.926279\pi$
$547$	0.321617	−	1.61688i	0.0137513	−	0.0691327i	0.987052	+	0.160403i	$0.0512793\pi$
$548$	1.12286	+	6.97256i	0.0479661	+	0.297853i
$549$	−14.3693	+	0.787689i	−0.613268	+	0.0336178i
$550$	4.09379	−	4.80580i	0.174560	−	0.204920i
$551$	2.20863	+	5.33209i	0.0940906	+	0.227155i
$552$	−23.4119	−	5.33352i	−0.996477	−	0.227009i
$553$	−3.06545	+	7.40066i	−0.130356	+	0.314708i
$554$	2.26906	−	1.15985i	0.0964032	−	0.0492772i
$555$	−11.9563	+	43.6865i	−0.507518	+	1.85439i
$556$	−15.7346	−	16.9335i	−0.667297	−	0.718139i
$557$	7.81765	−	5.22359i	0.331245	−	0.221330i	−0.378815	−	0.925473i	$-0.623668\pi$
$557$	7.81765	−	5.22359i	0.331245	−	0.221330i	0.710059	+	0.704142i	$0.248668\pi$
$558$	−0.182321	+	0.106164i	−0.00771825	+	0.00449426i
$559$	2.51592	−	2.51592i	0.106412	−	0.106412i
$560$	−21.5603	+	27.6423i	−0.911088	+	1.16810i
$561$	18.7814	−	6.26369i	0.792950	−	0.264453i
$562$	6.01487	+	7.60954i	0.253722	+	0.320989i
$563$	25.4030	−	16.9737i	1.07061	−	0.715357i	0.110186	−	0.993911i	$-0.464855\pi$
$563$	25.4030	−	16.9737i	1.07061	−	0.715357i	0.960420	+	0.278554i	$0.0898552\pi$
$564$	7.74061	+	9.61288i	0.325939	+	0.404775i
$565$	−27.9652	+	5.56262i	−1.17650	+	0.234021i
$566$	−9.97046	+	30.8216i	−0.419090	+	1.29553i
$567$	23.4448	+	18.7994i	0.984591	+	0.789502i
$568$	36.3808	+	13.2613i	1.52650	+	0.556431i
$569$	11.5727	+	27.9391i	0.485154	+	1.17127i	0.957131	+	0.289655i	$0.0935407\pi$
$569$	11.5727	+	27.9391i	0.485154	+	1.17127i	−0.471977	+	0.881611i	$0.656459\pi$
$570$	−8.82330	−	3.56162i	−0.369567	−	0.149180i
$571$	7.03644	−	10.5308i	0.294466	−	0.440700i	−0.654507	−	0.756056i	$-0.727124\pi$
$571$	7.03644	−	10.5308i	0.294466	−	0.440700i	0.948973	+	0.315356i	$0.102124\pi$
$572$	−7.29294	+	30.7275i	−0.304933	+	1.28478i
$573$	−6.67848	−	5.18151i	−0.278998	−	0.216461i
$574$	11.2308	−	3.18311i	0.468763	−	0.132860i
$575$	−9.25981			−0.386161
$576$	−22.6467	+	7.94528i	−0.943612	+	0.331053i
$577$	9.10864			0.379198			0.189599	−	0.981862i	$-0.439281\pi$
$577$	9.10864			0.379198			0.189599	+	0.981862i	$0.439281\pi$
$578$	−8.71064	+	2.46883i	−0.362315	+	0.102690i
$579$	10.3036	+	7.99410i	0.428205	+	0.332223i
$580$	19.9181	+	4.72741i	0.827055	+	0.196295i
$581$	18.7993	−	28.1351i	0.779925	−	1.16724i
$582$	8.92937	+	3.60443i	0.370134	+	0.149409i
$583$	8.29835	+	20.0340i	0.343682	+	0.829723i
$584$	17.5997	+	37.7900i	0.728281	+	1.56376i
$585$	−50.9711	+	13.0754i	−2.10739	+	0.540603i
$586$	5.45476	−	16.8623i	0.225334	−	0.696574i
$587$	−43.4391	+	8.64058i	−1.79292	+	0.356635i	−0.975602	−	0.219546i	$-0.929543\pi$
$587$	−43.4391	+	8.64058i	−1.79292	+	0.356635i	−0.817322	+	0.576180i	$0.804543\pi$
$588$	−11.1948	+	9.01443i	−0.461666	+	0.371749i
$589$	0.0611921	−	0.0408873i	0.00252138	−	0.00168473i
$590$	7.10745	+	8.99179i	0.292609	+	0.370186i
$591$	25.4887	−	8.50062i	1.04846	−	0.349669i
$592$	−19.6522	−	34.6691i	−0.807699	−	1.42489i
$593$	12.4091	−	12.4091i	0.509580	−	0.509580i	−0.404817	−	0.914398i	$-0.632665\pi$
$593$	12.4091	−	12.4091i	0.509580	−	0.509580i	0.914398	+	0.404817i	$0.132665\pi$
$594$	17.3282	−	1.10710i	0.710985	−	0.0454250i
$595$	−35.2516	+	23.5543i	−1.44517	+	0.965634i
$596$	−14.0669	+	13.0710i	−0.576203	+	0.535410i
$597$	5.29373	−	19.3424i	0.216658	−	0.791633i
$598$	41.2462	−	21.0833i	1.68668	−	0.862159i
$599$	−5.32882	+	12.8649i	−0.217730	+	0.525646i	−0.994572	−	0.104049i	$-0.966820\pi$
$599$	−5.32882	+	12.8649i	−0.217730	+	0.525646i	0.776843	+	0.629695i	$0.216820\pi$
$600$	−7.83465	+	4.92732i	−0.319848	+	0.201157i
$601$	−9.61422	−	23.2108i	−0.392172	−	0.946788i	−0.989466	−	0.144765i	$-0.953757\pi$
$601$	−9.61422	−	23.2108i	−0.392172	−	0.946788i	0.597294	−	0.802023i	$-0.296243\pi$
$602$	1.63033	−	1.91388i	0.0664473	−	0.0780040i
$603$	−0.611248	−	11.1506i	−0.0248920	−	0.454089i
$604$	−32.9935	+	5.31326i	−1.34249	+	0.216194i
$605$	−2.77373	+	13.9445i	−0.112768	+	0.566923i
$606$	−2.79217	+	1.90241i	−0.113424	+	0.0772800i
$607$	7.83446			0.317991			0.158995	−	0.987279i	$-0.449175\pi$
$607$	7.83446			0.317991			0.158995	+	0.987279i	$0.449175\pi$
$608$	7.71373	−	3.25379i	0.312833	−	0.131959i
$609$	20.1740	+	10.0831i	0.817493	+	0.408588i
$610$	8.68028	−	15.5469i	0.351454	−	0.629477i
$611$	−23.3520	−	4.64501i	−0.944722	−	0.187917i
$612$	−29.0206	+	0.524804i	−1.17309	+	0.0212139i
$613$	16.6418	−	24.9062i	0.672154	−	1.00595i	−0.326009	−	0.945367i	$-0.605704\pi$
$613$	16.6418	−	24.9062i	0.672154	−	1.00595i	0.998163	−	0.0605835i	$-0.0192961\pi$
$614$	−12.8228	+	15.0530i	−0.517485	+	0.607488i
$615$	11.2101	+	0.794930i	0.452034	+	0.0320547i
$616$	−3.40529	+	22.0542i	−0.137203	+	0.888588i
$617$	−34.0519	−	14.1048i	−1.37088	−	0.567836i	−0.428852	−	0.903375i	$-0.641082\pi$
$617$	−34.0519	−	14.1048i	−1.37088	−	0.567836i	−0.942027	+	0.335538i	$0.891082\pi$
$618$	0.0820512	+	9.07527i	0.00330058	+	0.365061i
$619$	29.7566	−	5.91895i	1.19602	−	0.237903i	0.443377	−	0.896335i	$-0.353780\pi$
$619$	29.7566	−	5.91895i	1.19602	−	0.237903i	0.752640	+	0.658433i	$0.228780\pi$
$620$	0.00957317	−	0.260869i	0.000384468	−	0.0104768i
$621$	−17.7178	−	18.2952i	−0.710991	−	0.734160i
$622$	−5.42937	+	46.3870i	−0.217698	+	1.85995i
$623$	21.1110	+	21.1110i	0.845796	+	0.845796i
$624$	23.6792	−	39.7862i	0.947928	−	1.59272i
$625$	21.8333	−	21.8333i	0.873332	−	0.873332i
$626$	0.734019	+	0.928623i	0.0293373	+	0.0371152i
$627$	−6.00924	+	0.758486i	−0.239986	+	0.0302910i
$628$	2.11155	−	0.785209i	0.0842600	−	0.0313332i
$629$	−9.40261	−	47.2701i	−0.374907	−	1.88478i
$630$	−35.1651	+	12.0821i	−1.40101	+	0.481363i
$631$	−5.45257	+	13.1637i	−0.217063	+	0.524037i	−0.994477	−	0.104952i	$-0.966531\pi$
$631$	−5.45257	+	13.1637i	−0.217063	+	0.524037i	0.777414	+	0.628989i	$0.216531\pi$
$632$	−0.292727	−	6.77915i	−0.0116440	−	0.269660i
$633$	−37.1734	−	2.63604i	−1.47751	−	0.104773i
$634$	1.54308	+	19.2875i	0.0612837	+	0.766003i
$635$	4.60575	+	3.07747i	0.182774	+	0.122126i
$636$	−2.82170	−	31.6653i	−0.111888	−	1.25561i
$637$	5.40940	−	27.1949i	0.214328	−	1.07750i
$638$	12.5375	−	3.55347i	0.496365	−	0.140683i
$639$	24.6530	+	32.8494i	0.975256	+	1.29950i
$640$	6.67032	−	28.9366i	0.263668	−	1.14382i
$641$			7.05243i			0.278554i	0.990253	+	0.139277i	$0.0444779\pi$
$641$			7.05243i			0.278554i	−0.990253	+	0.139277i	$0.955522\pi$
$642$	4.36474	+	0.827251i	0.172263	+	0.0326490i
$643$	29.0442	+	5.77725i	1.14539	+	0.227832i	0.731072	−	0.682300i	$-0.239020\pi$
$643$	29.0442	+	5.77725i	1.14539	+	0.227832i	0.414318	+	0.910132i	$0.364020\pi$
$644$	27.8640	−	17.1745i	1.09800	−	0.676769i
$645$	2.10263	−	1.19902i	0.0827910	−	0.0472113i
$646$	10.0926	−	0.807457i	0.397090	−	0.0317690i
$647$	−43.7051	+	18.1032i	−1.71822	+	0.711711i	−0.718352	+	0.695680i	$0.755103\pi$
$647$	−43.7051	+	18.1032i	−1.71822	+	0.711711i	−0.999871	+	0.0160315i	$0.994897\pi$
$648$	−24.7261	−	6.05142i	−0.971333	−	0.237722i
$649$	6.74065	+	2.79207i	0.264594	+	0.109598i
$650$	5.49545	−	16.9881i	0.215549	−	0.666327i
$651$	0.0759184	−	0.277394i	0.00297548	−	0.0108719i
$652$	−14.1433	−	38.0335i	−0.553894	−	1.48951i
$653$	−14.1402	−	21.1623i	−0.553348	−	0.828143i	0.444358	−	0.895849i	$-0.353432\pi$
$653$	−14.1402	−	21.1623i	−0.553348	−	0.828143i	−0.997705	+	0.0677063i	$0.978432\pi$
$654$	18.4495	−	3.84355i	0.721432	−	0.150295i
$655$	20.3297	+	20.3297i	0.794347	+	0.794347i
$656$	−7.48561	+	6.46065i	−0.292264	+	0.252246i
$657$	−6.23952	+	43.7736i	−0.243427	+	1.70777i
$658$	−16.7100	−	1.95582i	−0.651422	−	0.0762459i
$659$	18.1263	+	27.1279i	0.706100	+	1.05675i	0.995047	+	0.0994083i	$0.0316950\pi$
$659$	18.1263	+	27.1279i	0.706100	+	1.05675i	−0.288947	+	0.957345i	$0.593305\pi$
$660$	−10.3033	+	18.8523i	−0.401055	+	0.733825i
$661$	5.91065	+	29.7149i	0.229898	+	1.15577i	0.907405	+	0.420258i	$0.138060\pi$
$661$	5.91065	+	29.7149i	0.229898	+	1.15577i	−0.677507	+	0.735516i	$0.736940\pi$
$662$	15.6123	−	7.98035i	0.606790	−	0.310165i
$663$	42.2954	−	36.6941i	1.64262	−	1.42508i
$664$	−4.37395	+	28.3276i	−0.169742	+	1.09932i
$665$	11.9831	−	4.96358i	0.464686	−	0.192479i
$666$	2.60856	−	42.1885i	0.101080	−	1.63477i
$667$	−15.8927	−	10.6192i	−0.615368	−	0.411176i
$668$	−0.465467	−	0.336344i	−0.0180095	−	0.0130135i
$669$	1.99448	+	1.54742i	0.0771109	+	0.0598266i
$670$	12.0644	+	6.73591i	0.466090	+	0.260231i
$671$		−	11.3347i		−	0.437569i
$672$	14.4366	−	29.3581i	0.556905	−	1.13251i
$673$			11.0359i			0.425402i	0.977117	+	0.212701i	$0.0682259\pi$
$673$			11.0359i			0.425402i	−0.977117	+	0.212701i	$0.931774\pi$
$674$	22.2271	−	39.8101i	0.856154	−	1.53343i
$675$	−9.81544	−	0.157363i	−0.377797	−	0.00605692i
$676$	10.0671	+	62.5133i	0.387197	+	2.40436i
$677$	−16.1303	−	10.7779i	−0.619939	−	0.414230i	0.205551	−	0.978646i	$-0.434101\pi$
$677$	−16.1303	−	10.7779i	−0.619939	−	0.414230i	−0.825490	+	0.564416i	$0.809101\pi$
$678$	24.4907	−	10.4048i	0.940561	−	0.399594i
$679$	−12.1272	+	5.02324i	−0.465399	+	0.192774i
$680$	18.6456	−	30.6938i	0.715027	−	1.17706i
$681$	22.4147	+	25.8362i	0.858932	+	0.990047i
$682$	−0.0756319	−	0.147962i	−0.00289609	−	0.00566576i
$683$	−9.44062	−	47.4612i	−0.361235	−	1.81605i	−0.551331	−	0.834287i	$-0.685880\pi$
$683$	−9.44062	−	47.4612i	−0.361235	−	1.81605i	0.190095	−	0.981766i	$-0.439120\pi$
$684$	8.73902	+	1.57460i	0.334145	+	0.0602064i
$685$	−5.14927	−	7.70643i	−0.196744	−	0.294448i
$686$	−1.56499	+	13.3708i	−0.0597516	+	0.510500i
$687$	−2.76840	+	0.923276i	−0.105621	+	0.0352252i
$688$	−0.567460	+	2.05269i	−0.0216342	+	0.0782581i
$689$	43.3662	+	43.3662i	1.65212	+	1.65212i
$690$	30.8499	−	6.42690i	1.17443	−	0.244668i
$691$	−2.62103	−	3.92264i	−0.0997085	−	0.149224i	0.778261	−	0.627941i	$-0.216102\pi$
$691$	−2.62103	−	3.92264i	−0.0997085	−	0.149224i	−0.877969	+	0.478717i	$0.841102\pi$
$692$	−11.1684	+	24.3920i	−0.424558	+	0.927244i
$693$	−15.7955	+	17.6276i	−0.600020	+	0.669619i
$694$	−37.1233	−	12.0090i	−1.40918	−	0.455854i
$695$	28.0267	+	11.6090i	1.06311	+	0.440356i
$696$	−19.0973	−	0.527981i	−0.723883	−	0.0200131i
$697$	−11.0483	+	4.57634i	−0.418483	+	0.173341i
$698$	−0.937481	−	11.7179i	−0.0354842	−	0.443528i
$699$	−13.3874	−	23.4765i	−0.506358	−	0.887963i
$700$	2.91346	−	12.2754i	0.110118	−	0.463965i
$701$	−0.420755	−	0.0836934i	−0.0158917	−	0.00316106i	0.187138	−	0.982334i	$-0.440079\pi$
$701$	−0.420755	−	0.0836934i	−0.0158917	−	0.00316106i	−0.203030	+	0.979173i	$0.565079\pi$
$702$	44.0794	−	21.6474i	1.66367	−	0.817029i
$703$			14.7447i			0.556107i
$704$	−5.27221	−	18.1529i	−0.198704	−	0.684164i
$705$	−14.4883	−	7.24137i	−0.545663	−	0.272726i
$706$	4.71288	+	16.6282i	0.177372	+	0.625810i
$707$	0.898516	−	4.51715i	0.0337922	−	0.169885i
$708$	−8.20493	−	6.86229i	−0.308360	−	0.257901i
$709$	25.3814	+	16.9593i	0.953218	+	0.636920i	0.931847	−	0.362852i	$-0.118197\pi$
$709$	25.3814	+	16.9593i	0.953218	+	0.636920i	0.0213708	+	0.999772i	$0.493197\pi$
$710$	−50.6561	+	4.05271i	−1.90109	+	0.152096i
$711$	3.66494	−	6.19403i	0.137446	−	0.232294i
$712$	−23.7607	−	8.66109i	−0.890470	−	0.324588i
$713$	−0.0932734	+	0.225182i	−0.00349312	+	0.00843313i
$714$	27.7233	−	28.2292i	1.03752	−	1.05645i
$715$	−8.08572	−	40.6497i	−0.302389	−	1.52021i
$716$	−13.8176	+	30.1779i	−0.516387	+	1.12780i
$717$	0.211733	+	1.67749i	0.00790731	+	0.0626470i
$718$	9.89146	−	7.81858i	0.369146	−	0.291787i
$719$	−4.47853	+	4.47853i	−0.167021	+	0.167021i	−0.785669	−	0.618648i	$-0.787681\pi$
$719$	−4.47853	+	4.47853i	−0.167021	+	0.167021i	0.618648	+	0.785669i	$0.287681\pi$
$720$	22.6820	−	21.8535i	0.845306	−	0.814434i
$721$	−8.74797	−	8.74797i	−0.325791	−	0.325791i
$722$	23.6114	+	2.76360i	0.878724	+	0.102850i
$723$	25.7853	−	3.25463i	0.958967	−	0.121041i
$724$	0.550667	−	0.511682i	0.0204654	−	0.0190165i
$725$	−7.22588	+	1.43732i	−0.268363	+	0.0533806i
$726$	−0.119957	−	13.2679i	−0.00445203	−	0.492416i
$727$	−3.41297	−	1.41370i	−0.126580	−	0.0524311i	0.318494	−	0.947925i	$-0.396823\pi$
$727$	−3.41297	−	1.41370i	−0.126580	−	0.0524311i	−0.445074	+	0.895494i	$0.646823\pi$
$728$	14.9718	+	61.3119i	0.554891	+	2.27237i
$729$	−18.4701	−	19.6941i	−0.684076	−	0.729411i
$730$	−41.6470	−	35.4768i	−1.54143	−	1.31306i
$731$	−1.43094	+	2.14155i	−0.0529250	+	0.0792079i
$732$	−4.97138	+	15.8561i	−0.183747	+	0.586058i
$733$	−1.76647	−	0.351374i	−0.0652462	−	0.0129783i	0.162359	−	0.986732i	$-0.448090\pi$
$733$	−1.76647	−	0.351374i	−0.0652462	−	0.0129783i	−0.227605	+	0.973753i	$0.573090\pi$
$734$	−20.3793	−	11.3783i	−0.752213	−	0.419981i
$735$	8.43303	−	16.8726i	0.311057	−	0.622355i
$736$	−15.2544	+	23.1529i	−0.562285	+	0.853426i
$737$	8.79571			0.323994
$738$	−10.3930	+	1.40738i	−0.382573	+	0.0518064i
$739$	−7.50862	+	37.7484i	−0.276209	+	1.38860i	0.554636	+	0.832093i	$0.312857\pi$
$739$	−7.50862	+	37.7484i	−0.276209	+	1.38860i	−0.830845	+	0.556504i	$0.812143\pi$
$740$	42.3910	+	30.6315i	1.55833	+	1.12604i
$741$	−14.8809	+	8.48578i	−0.546663	+	0.311733i
$742$	32.9891	+	28.1016i	1.21107	+	1.03164i
$743$	−13.3142	−	32.1432i	−0.488449	−	1.17922i	−0.955500	−	0.294990i	$-0.904684\pi$
$743$	−13.3142	−	32.1432i	−0.488449	−	1.17922i	0.467051	−	0.884230i	$-0.345316\pi$
$744$	0.0409057	+	0.240157i	0.00149967	+	0.00880458i
$745$	9.64382	−	23.2822i	0.353322	−	0.852995i
$746$	−19.8565	−	38.8461i	−0.726997	−	1.42226i
$747$	−20.2886	+	22.6419i	−0.742321	+	0.828425i
$748$	0.838375	−	22.8458i	0.0306540	−	0.835323i
$749$	−5.03516	+	3.36439i	−0.183981	+	0.122932i
$750$	−10.9606	+	16.7291i	−0.400224	+	0.610862i
$751$	30.0300	−	30.0300i	1.09581	−	1.09581i	0.100914	−	0.994895i	$-0.467823\pi$
$751$	30.0300	−	30.0300i	1.09581	−	1.09581i	0.994895	−	0.100914i	$-0.0321768\pi$
$752$	13.5308	−	4.47402i	0.493418	−	0.163151i
$753$	−14.9894	−	44.9449i	−0.546244	−	1.63788i
$754$	28.9138	−	22.8546i	1.05298	−	0.832314i
$755$	36.4661	−	24.3659i	1.32714	−	0.886766i
$756$	29.8278	−	17.7315i	1.08483	−	0.644888i
$757$	37.4839	−	7.45600i	1.36237	−	0.270993i	0.540827	−	0.841134i	$-0.318111\pi$
$757$	37.4839	−	7.45600i	1.36237	−	0.270993i	0.821547	+	0.570141i	$0.193111\pi$
$758$	−31.0251	−	10.0363i	−1.12688	−	0.364534i
$759$	15.1520	−	13.1454i	0.549983	−	0.477147i
$760$	−7.42660	+	8.09691i	−0.269391	+	0.293706i
$761$	5.61157	+	13.5475i	0.203419	+	0.491097i	0.992361	−	0.123371i	$-0.0393705\pi$
$761$	5.61157	+	13.5475i	0.203419	+	0.491097i	−0.788941	+	0.614468i	$0.789371\pi$
$762$	−4.79364	−	1.93501i	−0.173655	−	0.0700978i
$763$	−14.2723	+	21.3600i	−0.516692	+	0.773284i
$764$	−8.30894	+	5.12137i	−0.300607	+	0.185285i
$765$	34.3417	−	16.4815i	1.24163	−	0.595892i
$766$	4.44868	+	15.6960i	0.160737	+	0.567120i
$767$	20.6348			0.745081
$768$	−0.586550	+	27.7066i	−0.0211653	+	0.999776i
$769$	17.9581			0.647587			0.323793	−	0.946128i	$-0.395042\pi$
$769$	17.9581			0.647587			0.323793	+	0.946128i	$0.395042\pi$
$770$	−7.98593	−	28.1763i	−0.287793	−	1.01540i
$771$	4.79710	−	6.18301i	0.172763	−	0.222676i
$772$	12.8191	−	7.90130i	0.461371	−	0.284374i
$773$	−9.82391	+	14.7025i	−0.353341	+	0.528813i	−0.964980	−	0.262325i	$-0.915511\pi$
$773$	−9.82391	+	14.7025i	−0.353341	+	0.528813i	0.611638	+	0.791138i	$0.290511\pi$
$774$	−1.69279	+	1.49564i	−0.0608461	+	0.0537598i
$775$	0.0359520	+	0.0867959i	0.00129144	+	0.00311780i
$776$	7.51588	−	8.19425i	0.269804	−	0.294156i
$777$	37.7590	+	43.5228i	1.35460	+	1.56137i
$778$	31.2292	+	10.1023i	1.11962	+	0.362185i
$779$	3.58819	−	0.713736i	0.128560	−	0.0255722i
$780$	−6.51778	+	60.4114i	−0.233374	+	2.16308i
$781$	−26.8971	+	17.9721i	−0.962453	+	0.643091i
$782$	−26.3063	+	20.7935i	−0.940713	+	0.743575i
$783$	−16.6659	−	11.5264i	−0.595590	−	0.411922i
$784$	5.21028	+	15.7575i	0.186081	+	0.562767i
$785$	−2.09058	+	2.09058i	−0.0746160	+	0.0746160i
$786$	−22.4430	−	14.7042i	−0.800515	−	0.524481i
$787$	−30.2625	+	20.2207i	−1.07874	+	0.720791i	−0.962186	−	0.272393i	$-0.912185\pi$
$787$	−30.2625	+	20.2207i	−1.07874	+	0.720791i	−0.116554	+	0.993184i	$0.537185\pi$
$788$	1.13778	−	31.0046i	0.0405318	−	1.10449i
$789$	−3.70591	−	1.01425i	−0.131934	−	0.0361083i
$790$	4.05306	+	7.92919i	0.144201	+	0.282108i
$791$	−13.8809	+	33.5115i	−0.493549	+	1.19153i
$792$	5.82508	−	19.1849i	0.206985	−	0.681704i
$793$	−12.2677	−	29.6168i	−0.435638	−	1.05172i
$794$	−3.37278	−	2.87308i	−0.119695	−	0.101962i
$795$	20.6672	+	36.2425i	0.732990	+	1.28539i
$796$	−18.7689	−	13.5623i	−0.665244	−	0.480702i
$797$	4.54990	−	22.8739i	0.161166	−	0.810234i	−0.812625	−	0.582787i	$-0.801962\pi$
$797$	4.54990	−	22.8739i	0.161166	−	0.810234i	0.973790	−	0.227447i	$-0.0730378\pi$
$798$	−10.0033	+	6.81560i	−0.354112	+	0.241269i
$799$	17.2354			0.609744
$800$	2.15275	+	10.4680i	0.0761112	+	0.370100i
$801$	−16.1011	−	21.4543i	−0.568905	−	0.758051i
$802$	−42.4706	−	23.7125i	−1.49969	−	0.837319i
$803$	−34.1566	−	6.79417i	−1.20536	−	0.239761i
$804$	−12.3044	−	3.85780i	−0.433942	−	0.136054i
$805$	−23.8651	+	35.7166i	−0.841134	+	1.25885i
$806$	−0.357764	−	0.304759i	−0.0126017	−	0.0107347i
$807$	−2.82612	+	39.8539i	−0.0994840	+	1.40292i
$808$	0.925478	+	3.78999i	0.0325582	+	0.133331i
$809$	18.3664	+	7.60762i	0.645729	+	0.267470i	0.681419	−	0.731893i	$-0.261363\pi$
$809$	18.3664	+	7.60762i	0.645729	+	0.267470i	−0.0356905	+	0.999363i	$0.511363\pi$
$810$	32.8102	−	6.28828i	1.15283	−	0.220947i
$811$	−46.0682	+	9.16353i	−1.61767	+	0.321775i	−0.919179	−	0.393840i	$-0.871146\pi$
$811$	−46.0682	+	9.16353i	−1.61767	+	0.321775i	−0.698494	+	0.715616i	$0.746146\pi$
$812$	19.0778	−	17.7272i	0.669499	−	0.622101i
$813$	1.43603	+	11.3772i	0.0503636	+	0.399014i
$814$	33.0665	+	3.87028i	1.15898	+	0.135653i
$815$	37.6558	+	37.6558i	1.31903	+	1.31903i
$816$	−11.1930	+	31.5913i	−0.391832	+	1.10592i
$817$	0.557172	−	0.557172i	0.0194930	−	0.0194930i
$818$	9.39846	−	7.42890i	0.328609	−	0.259745i
$819$	−22.1940	+	63.1557i	−0.775521	+	2.20684i
$820$	5.40233	−	11.7988i	0.188658	−	0.412033i
$821$	7.82812	+	39.3546i	0.273203	+	1.37349i	0.836833	+	0.547458i	$0.184404\pi$
$821$	7.82812	+	39.3546i	0.273203	+	1.37349i	−0.563630	+	0.826028i	$0.690596\pi$
$822$	6.17126	+	6.06067i	0.215247	+	0.211390i
$823$	10.4572	−	25.2460i	0.364516	−	0.880019i	−0.630112	−	0.776504i	$-0.716991\pi$
$823$	10.4572	−	25.2460i	0.364516	−	0.880019i	0.994628	−	0.103515i	$-0.0330090\pi$
$824$	9.84593	+	3.58897i	0.342999	+	0.125028i
$825$	0.546911	−	7.71253i	0.0190410	−	0.268516i
$826$	14.5343	−	1.16281i	0.505714	−	0.0404594i
$827$	13.3380	+	8.91218i	0.463809	+	0.309907i	0.765428	−	0.643521i	$-0.222527\pi$
$827$	13.3380	+	8.91218i	0.463809	+	0.309907i	−0.301620	+	0.953428i	$0.597527\pi$
$828$	−26.9618	+	11.7435i	−0.936986	+	0.408114i
$829$	4.63371	−	23.2952i	0.160935	−	0.809077i	−0.813002	−	0.582261i	$-0.802168\pi$
$829$	4.63371	−	23.2952i	0.160935	−	0.809077i	0.973938	−	0.226816i	$-0.0728317\pi$
$830$	−10.2576	−	36.1912i	−0.356046	−	1.25622i
$831$	1.39533	−	2.79175i	0.0484036	−	0.0968448i
$832$	−33.4232	−	41.7264i	−1.15874	−	1.44660i
$833$			20.0717i			0.695442i
$834$	−27.8153	−	5.27184i	−0.963164	−	0.182549i
$835$	0.739173	+	0.147031i	0.0255801	+	0.00508820i
$836$	−1.61509	+	6.80489i	−0.0558589	+	0.235352i
$837$	−0.102697	+	0.237109i	−0.00354973	+	0.00819568i
$838$	−3.51798	−	43.9723i	−0.121527	−	1.51900i
$839$	27.5815	−	11.4246i	0.952220	−	0.394423i	0.148155	−	0.988964i	$-0.452666\pi$
$839$	27.5815	−	11.4246i	0.952220	−	0.394423i	0.804065	+	0.594542i	$0.202666\pi$
$840$	−1.18656	+	42.9186i	−0.0409403	+	1.48083i
$841$	12.7423	+	5.27805i	0.439391	+	0.182002i
$842$	8.53405	+	2.76067i	0.294103	+	0.0951390i
$843$	11.4583	+	3.13595i	0.394643	+	0.108008i
$844$	−17.9145	+	39.1257i	−0.616643	+	1.34676i
$845$	−46.1664	−	69.0930i	−1.58817	−	2.37687i
$846$	14.6151	+	3.85824i	0.502477	+	0.132649i
$847$	12.7894	+	12.7894i	0.439447	+	0.439447i
$848$	−35.3817	−	9.78117i	−1.21501	−	0.335887i
$849$	12.5521	+	37.6367i	0.430785	+	1.29169i
$850$	−1.50253	+	12.8372i	−0.0515365	+	0.440312i
$851$	−27.1296	−	40.6023i	−0.929991	−	1.39183i
$852$	45.5090	−	13.3441i	1.55911	−	0.457163i
$853$	0.300445	+	1.51044i	0.0102870	+	0.0517164i	0.985588	−	0.169164i	$-0.0541068\pi$
$853$	0.300445	+	1.51044i	0.0102870	+	0.0517164i	−0.975301	+	0.220881i	$0.929107\pi$
$854$	−10.3098	−	20.1695i	−0.352794	−	0.690188i
$855$	−11.2880	+	2.89567i	−0.386041	+	0.0990300i
$856$	2.66325	−	4.38416i	0.0910280	−	0.149847i
$857$	−6.92900	+	2.87008i	−0.236690	+	0.0980402i	−0.497876	−	0.867248i	$-0.665886\pi$
$857$	−6.92900	+	2.87008i	−0.236690	+	0.0980402i	0.261186	+	0.965289i	$0.415886\pi$
$858$	15.1242	+	35.5993i	0.516332	+	1.21534i
$859$	12.3876	+	8.27714i	0.422660	+	0.282412i	0.748656	−	0.662959i	$-0.230700\pi$
$859$	12.3876	+	8.27714i	0.422660	+	0.282412i	−0.325996	+	0.945371i	$0.605700\pi$
$860$	−0.444368	−	2.75937i	−0.0151528	−	0.0940938i
$861$	8.76372	−	11.2956i	0.298667	−	0.384953i
$862$	−24.3939	+	43.6910i	−0.830859	+	1.48812i
$863$			31.0444i			1.05676i	0.849007	+	0.528382i	$0.177201\pi$
$863$			31.0444i			1.05676i	−0.849007	+	0.528382i	$0.822799\pi$
$864$	−16.5632	+	24.2829i	−0.563492	+	0.826122i
$865$		−	35.2072i		−	1.19708i
$866$	0.318365	+	0.177752i	0.0108185	+	0.00604025i
$867$	−6.79718	+	8.76093i	−0.230844	+	0.297537i
$868$	−0.269168	−	0.194499i	−0.00913614	−	0.00660172i
$869$	4.71327	+	3.14931i	0.159887	+	0.106833i
$870$	23.0761	−	9.80377i	0.782352	−	0.332379i
$871$	22.9827	−	9.51975i	0.778739	−	0.322564i
$872$	3.32067	−	21.5062i	0.112452	−	0.728291i
$873$	11.4237	−	2.93048i	0.386633	−	0.0991818i
$874$	9.13433	−	4.66908i	0.308973	−	0.157934i
$875$	−5.31875	−	26.7392i	−0.179807	−	0.903949i
$876$	44.8019	+	24.4855i	1.51372	+	0.827287i
$877$	13.8663	+	20.7524i	0.468232	+	0.700759i	0.988156	−	0.153454i	$-0.0490397\pi$
$877$	13.8663	+	20.7524i	0.468232	+	0.700759i	−0.519924	+	0.854213i	$0.674040\pi$
$878$	56.5688	+	6.62111i	1.90910	+	0.223452i
$879$	−6.86713	−	20.5907i	−0.231623	−	0.694509i
$880$	16.2088	+	18.7803i	0.546398	+	0.633082i
$881$	22.9018	+	22.9018i	0.771582	+	0.771582i	0.978383	−	0.206801i	$-0.0663052\pi$
$881$	22.9018	+	22.9018i	0.771582	+	0.771582i	−0.206801	+	0.978383i	$0.566305\pi$
$882$	−4.49317	+	17.0202i	−0.151293	+	0.573100i
$883$	10.2732	+	15.3750i	0.345722	+	0.517409i	0.963059	−	0.269289i	$-0.0867888\pi$
$883$	10.2732	+	15.3750i	0.345722	+	0.517409i	−0.617338	+	0.786698i	$0.711789\pi$
$884$	−22.5357	−	60.6021i	−0.757958	−	2.03827i
$885$	13.5396	+	3.70558i	0.455129	+	0.124562i
$886$	2.88042	−	8.90422i	0.0967695	−	0.299143i
$887$	9.52810	+	3.94667i	0.319922	+	0.132516i	0.536865	−	0.843668i	$-0.319608\pi$
$887$	9.52810	+	3.94667i	0.319922	+	0.132516i	−0.216943	+	0.976184i	$0.569608\pi$
$888$	−44.5594	−	19.9171i	−1.49532	−	0.668375i
$889$	6.51036	−	2.69668i	0.218350	−	0.0904437i
$890$	33.0841	−	2.64687i	1.10898	−	0.0887234i
$891$	16.2846	−	13.6767i	0.545554	−	0.458186i
$892$	2.48140	−	1.52946i	0.0830834	−	0.0512100i
$893$	−5.17151	−	1.02868i	−0.173058	−	0.0344234i
$894$	−4.37940	+	23.1066i	−0.146469	+	0.772801i
$895$		−	43.5585i		−	1.45600i
$896$	−25.8933	−	27.5069i	−0.865033	−	0.918940i
$897$	25.3639	−	50.7474i	0.846875	−	1.69441i
$898$	−18.1359	+	5.14020i	−0.605202	+	0.171531i
$899$	−0.0378328	+	0.190198i	−0.00126179	+	0.00634347i
$900$	−4.14779	+	10.5492i	−0.138260	+	0.351641i
$901$	−36.9133	−	24.6647i	−1.22976	−	0.821700i
$902$	−0.658776	−	8.23424i	−0.0219348	−	0.274170i
$903$	0.217804	−	3.07147i	0.00724807	−	0.102212i
$904$	−1.32552	−	30.6972i	−0.0440861	−	1.02097i
$905$	−0.377519	+	0.911413i	−0.0125492	+	0.0302964i
$906$	−28.6785	+	29.2018i	−0.952780	+	0.970166i
$907$	6.38322	+	32.0906i	0.211951	+	1.06555i	0.929438	+	0.368979i	$0.120292\pi$
$907$	6.38322	+	32.0906i	0.211951	+	1.06555i	−0.717487	+	0.696572i	$0.754708\pi$
$908$	37.0189	−	13.7660i	1.22852	−	0.456841i
$909$	−1.37192	+	3.90396i	−0.0455037	+	0.129486i
$910$	−51.3625	−	64.9798i	−1.70265	−	2.15406i
$911$	−20.1753	+	20.1753i	−0.668438	+	0.668438i	−0.957354	−	0.288916i	$-0.906705\pi$
$911$	−20.1753	+	20.1753i	−0.668438	+	0.668438i	0.288916	+	0.957354i	$0.406705\pi$
$912$	5.24397	−	8.81101i	0.173645	−	0.291762i
$913$	−16.9320	−	16.9320i	−0.560367	−	0.560367i
$914$	−3.29240	+	28.1293i	−0.108903	+	0.930433i
$915$	−2.73092	−	21.6362i	−0.0902813	−	0.715270i
$916$	−0.123577	+	3.36749i	−0.00408312	+	0.111265i
$917$	35.8720	−	7.13538i	1.18460	−	0.235631i
$918$	−28.2382	+	21.5942i	−0.932000	+	0.712714i
$919$	−44.0591	−	18.2499i	−1.45338	−	0.602008i	−0.490377	−	0.871510i	$-0.663141\pi$
$919$	−44.0591	−	18.2499i	−1.45338	−	0.602008i	−0.963000	+	0.269502i	$0.913141\pi$
$920$	5.55259	−	35.9610i	0.183063	−	1.18560i
$921$	−1.71306	+	24.1576i	−0.0564473	+	0.796019i
$922$	32.0293	−	37.6000i	1.05483	−	1.23829i
$923$	−50.8291	+	76.0711i	−1.67306	+	2.50391i
$924$	12.6590	+	24.2224i	0.416449	+	0.796858i
$925$	−18.4605	−	3.67203i	−0.606979	−	0.120736i
$926$	−25.7692	+	46.1543i	−0.846828	+	1.51672i
$927$	6.67197	+	8.89021i	0.219136	+	0.291993i
$928$	−8.30994	+	20.4351i	−0.272787	+	0.670816i
$929$	28.1038			0.922057			0.461028	−	0.887385i	$-0.347481\pi$
$929$	28.1038			0.922057			0.461028	+	0.887385i	$0.347481\pi$
$930$	−0.180019	−	0.264215i	−0.00590306	−	0.00866396i
$931$	1.19796	−	6.02255i	0.0392616	−	0.197381i
$932$	−30.8092	+	4.96151i	−1.00919	+	0.162520i
$933$	28.3349	+	49.6888i	0.927643	+	1.62674i
$934$	−10.9319	+	12.8332i	−0.357703	+	0.419916i
$935$	11.4813	+	27.7184i	0.375480	+	0.906489i
$936$	−5.54349	−	56.4335i	−0.181195	−	1.84459i
$937$	−7.86396	+	18.9853i	−0.256904	+	0.620222i	−0.998731	−	0.0503700i	$-0.983960\pi$
$937$	−7.86396	+	18.9853i	−0.256904	+	0.620222i	0.741826	+	0.670592i	$0.233960\pi$
$938$	15.6516	−	8.00043i	0.511043	−	0.261223i
$939$	1.39830	+	0.382692i	0.0456317	+	0.0124887i
$940$	−13.7011	+	12.7311i	−0.446879	+	0.415242i
$941$	−43.2971	+	28.9302i	−1.41145	+	0.943098i	−0.411955	+	0.911204i	$0.635154\pi$
$941$	−43.2971	+	28.9302i	−1.41145	+	0.943098i	−0.999491	+	0.0318944i	$0.989846\pi$
$942$	1.51209	−	2.30790i	0.0492664	−	0.0751953i
$943$	−8.56753	+	8.56753i	−0.278997	+	0.278997i
$944$	−10.7449	+	6.09072i	−0.349716	+	0.198236i
$945$	−25.9041	+	37.4542i	−0.842660	+	1.21839i
$946$	−1.10327	−	1.39577i	−0.0358703	−	0.0453802i
$947$	13.0677	−	8.73155i	0.424643	−	0.283737i	−0.324830	−	0.945772i	$-0.605307\pi$
$947$	13.0677	−	8.73155i	0.424643	−	0.283737i	0.749473	+	0.662035i	$0.230307\pi$
$948$	−5.21213	−	6.47282i	−0.169282	−	0.210228i
$949$	−96.6027	+	19.2155i	−3.13586	+	0.623760i
$950$	1.21702	−	3.76216i	0.0394852	−	0.122060i
$951$	15.5296	+	17.9001i	0.503580	+	0.580451i
$952$	−19.2883	−	41.4157i	−0.625136	−	1.34229i
$953$	18.0842	+	43.6591i	0.585804	+	1.41426i	0.887480	+	0.460846i	$0.152454\pi$
$953$	18.0842	+	43.6591i	0.585804	+	1.41426i	−0.301676	+	0.953411i	$0.597546\pi$
$954$	−25.7801	−	29.1782i	−0.834661	−	0.944679i
$955$	7.11648	−	10.6506i	0.230284	−	0.344644i
$956$	1.89960	+	0.450854i	0.0614374	+	0.0145817i
$957$	9.78341	−	12.6099i	0.316253	−	0.407620i
$958$	−51.6194	+	14.6304i	−1.66775	+	0.472685i
$959$	−11.7908			−0.380744
$960$	−14.4375	−	33.3810i	−0.465970	−	1.07737i
$961$	−30.9975			−0.999920
$962$	90.5898	−	25.6756i	2.92073	−	0.827815i
$963$	4.90520	−	2.35414i	0.158068	−	0.0758612i
$964$	6.93025	−	29.1994i	0.223208	−	0.940450i
$965$	−10.9794	+	16.4318i	−0.353439	+	0.528959i
$966$	15.0055	−	37.1737i	0.482795	−	1.19604i
$967$	7.60618	+	18.3629i	0.244598	+	0.590512i	0.997729	−	0.0673588i	$-0.0214572\pi$
$967$	7.60618	+	18.3629i	0.244598	+	0.590512i	−0.753131	+	0.657871i	$0.771457\pi$
$968$	−14.3945	−	5.24700i	−0.462658	−	0.168645i
$969$	9.36668	−	8.12623i	0.300901	−	0.261052i
$970$	−4.49130	+	13.8839i	−0.144207	+	0.445787i
$971$	23.2362	−	4.62196i	0.745685	−	0.148326i	0.192398	−	0.981317i	$-0.438373\pi$
$971$	23.2362	−	4.62196i	0.745685	−	0.148326i	0.553286	+	0.832991i	$0.313373\pi$
$972$	−28.7792	+	11.9899i	−0.923093	+	0.384578i
$973$	32.0877	−	21.4403i	1.02868	−	0.687344i
$974$	19.1077	+	24.1735i	0.612250	+	0.774570i
$975$	−6.91835	−	20.7443i	−0.221565	−	0.664351i
$976$	15.1299	+	11.8009i	0.484295	+	0.377738i
$977$	−18.8219	+	18.8219i	−0.602164	+	0.602164i	−0.940886	−	0.338722i	$-0.890005\pi$
$977$	−18.8219	+	18.8219i	−0.602164	+	0.602164i	0.338722	+	0.940886i	$0.390005\pi$
$978$	−41.5702	−	27.2359i	−1.32927	−	0.870909i
$979$	17.5668	−	11.7377i	0.561437	−	0.375140i
$980$	−14.8261	−	15.9557i	−0.473604	−	0.509688i
$981$	15.4030	−	17.1896i	0.491779	−	0.548822i
$982$	−25.8020	+	13.1889i	−0.823373	+	0.420873i
$983$	13.8501	−	33.4371i	0.441750	−	1.06648i	−0.533585	−	0.845746i	$-0.679156\pi$
$983$	13.8501	−	33.4371i	0.441750	−	1.06648i	0.975335	−	0.220731i	$-0.0708444\pi$
$984$	−2.68997	+	11.8079i	−0.0857532	+	0.376421i
$985$	15.5816	+	37.6174i	0.496472	+	1.19859i
$986$	−17.3005	+	20.3095i	−0.550961	+	0.646786i
$987$	−17.8994	+	10.2071i	−0.569743	+	0.324895i
$988$	3.14491	+	19.5288i	0.100053	+	0.621295i
$989$	−0.509107	+	2.55945i	−0.0161886	+	0.0813858i
$990$	3.53091	+	26.0746i	0.112220	+	0.828704i
$991$	3.20062			0.101671			0.0508356	−	0.998707i	$-0.483812\pi$
$991$	3.20062			0.101671			0.0508356	+	0.998707i	$0.483812\pi$
$992$	0.276248	+	0.0530925i	0.00877087	+	0.00168569i
$993$	9.60062	−	19.2087i	0.304667	−	0.609569i
$994$	−31.5152	+	56.4457i	−0.999600	+	1.79035i
$995$	29.8054	+	5.92866i	0.944894	+	0.187951i
$996$	16.2599	+	31.1126i	0.515214	+	0.985841i
$997$	25.8757	−	38.7257i	0.819492	−	1.22646i	−0.151764	−	0.988417i	$-0.548495\pi$
$997$	25.8757	−	38.7257i	0.819492	−	1.22646i	0.971256	−	0.238039i	$-0.0765047\pi$
$998$	17.8502	−	20.9547i	0.565038	−	0.663311i
$999$	−28.0675	−	43.4997i	−0.888017	−	1.37627i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	192.2.s.a.131.13	yes	240
3.2	odd	2	inner	192.2.s.a.131.18	yes	240
4.3	odd	2		768.2.s.a.431.24		240
12.11	even	2		768.2.s.a.431.28		240
64.21	even	16		768.2.s.a.335.28		240
64.43	odd	16	inner	192.2.s.a.107.18	yes	240
192.107	even	16	inner	192.2.s.a.107.13	✓	240
192.149	odd	16		768.2.s.a.335.24		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.13	✓	240	192.107	even	16	inner
192.2.s.a.107.18	yes	240	64.43	odd	16	inner
192.2.s.a.131.13	yes	240	1.1	even	1	trivial
192.2.s.a.131.18	yes	240	3.2	odd	2	inner
768.2.s.a.335.24		240	192.149	odd	16
768.2.s.a.335.28		240	64.21	even	16
768.2.s.a.431.24		240	4.3	odd	2
768.2.s.a.431.28		240	12.11	even	2

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:	\( N \)	\(=\)	\( 192 = 2^{6} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	192.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.385637 - 1.36062i) q^{2} +(-1.36847 - 1.06173i) q^{3} +(-1.70257 + 1.04941i) q^{4} +(1.45822 - 2.18239i) q^{5} +(-0.916881 + 2.27142i) q^{6} +(-1.27779 - 3.08486i) q^{7} +(2.08442 + 1.91186i) q^{8} +(0.745444 + 2.90591i) q^{9} +(-3.53174 - 1.14248i) q^{10} +(-2.31748 + 0.460975i) q^{11} +(3.44411 + 0.371585i) q^{12} +(-5.55652 + 3.71275i) q^{13} +(-3.70456 + 2.92822i) q^{14} +(-4.31265 + 1.43829i) q^{15} +(1.79748 - 3.57338i) q^{16} +(3.42067 - 3.42067i) q^{17} +(3.66637 - 2.13489i) q^{18} +(-1.23054 + 0.822221i) q^{19} +(-0.192511 + 5.24594i) q^{20} +(-1.52668 + 5.57823i) q^{21} +(1.52092 + 2.97544i) q^{22} +(1.87568 - 4.52828i) q^{23} +(-0.822590 - 4.82942i) q^{24} +(-0.722975 - 1.74542i) q^{25} +(7.19443 + 6.12853i) q^{26} +(2.06518 - 4.76813i) q^{27} +(5.41281 + 3.91127i) q^{28} +(0.760797 - 3.82478i) q^{29} +(3.62009 + 5.31322i) q^{30} -0.0497279 q^{31} +(-5.55519 - 1.06766i) q^{32} +(3.66084 + 1.82971i) q^{33} +(-5.97336 - 3.33509i) q^{34} +(-8.59567 - 1.70978i) q^{35} +(-4.31866 - 4.16524i) q^{36} +(5.53510 - 8.28386i) q^{37} +(1.59327 + 1.35722i) q^{38} +(11.5459 + 0.818742i) q^{39} +(7.21196 - 1.76109i) q^{40} +(-2.28385 - 0.946002i) q^{41} +(8.17859 - 0.0739441i) q^{42} +(-0.522190 + 0.103870i) q^{43} +(3.46191 - 3.21682i) q^{44} +(7.42884 + 2.61062i) q^{45} +(-6.88460 - 0.805810i) q^{46} +(2.51930 + 2.51930i) q^{47} +(-6.25379 + 2.98163i) q^{48} +(-2.93388 + 2.93388i) q^{49} +(-2.09604 + 1.65679i) q^{50} +(-8.31294 + 1.04926i) q^{51} +(5.56417 - 12.1523i) q^{52} +(-1.79038 - 9.00087i) q^{53} +(-7.28401 - 0.971161i) q^{54} +(-2.37338 + 5.72983i) q^{55} +(3.23436 - 8.87310i) q^{56} +(2.55694 + 0.181318i) q^{57} +(-5.49747 + 0.439822i) q^{58} +(-2.56739 - 1.71547i) q^{59} +(5.83323 - 6.97453i) q^{60} +(-0.935842 + 4.70479i) q^{61} +(0.0191769 + 0.0676607i) q^{62} +(8.01181 - 6.01274i) q^{63} +(0.689602 + 7.97022i) q^{64} +17.5405i q^{65} +(1.07779 - 5.68661i) q^{66} +(-3.65093 - 0.726215i) q^{67} +(-2.23425 + 9.41361i) q^{68} +(-7.37464 + 4.20537i) q^{69} +(0.988438 + 12.3548i) q^{70} +(12.6483 - 5.23910i) q^{71} +(-4.00187 + 7.48232i) q^{72} +(13.6168 + 5.64025i) q^{73} +(-13.4057 - 4.33660i) q^{74} +(-0.863794 + 3.15617i) q^{75} +(1.23223 - 2.69123i) q^{76} +(4.38330 + 6.56007i) q^{77} +(-3.33852 - 16.0253i) q^{78} +(-1.69637 - 1.69637i) q^{79} +(-5.17737 - 9.13359i) q^{80} +(-7.88863 + 4.33239i) q^{81} +(-0.406412 + 3.47226i) q^{82} +(5.63016 + 8.42612i) q^{83} +(-3.25457 - 11.0994i) q^{84} +(-2.47712 - 12.4533i) q^{85} +(0.342703 + 0.670446i) q^{86} +(-5.10203 + 4.42636i) q^{87} +(-5.71191 - 3.46982i) q^{88} +(-8.26075 + 3.42172i) q^{89} +(0.687227 - 11.1146i) q^{90} +(18.5534 + 12.3970i) q^{91} +(1.55855 + 9.67806i) q^{92} +(0.0680513 + 0.0527977i) q^{93} +(2.45627 - 4.39934i) q^{94} +3.88450i q^{95} +(6.46856 + 7.35920i) q^{96} -3.93119i q^{97} +(5.12330 + 2.86048i) q^{98} +(-3.06710 - 6.39075i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 8 q^{3} - 16 q^{4} - 8 q^{6} - 16 q^{7} - 8 q^{9} - 16 q^{10} - 8 q^{12} - 16 q^{13} - 8 q^{15} - 16 q^{16} - 8 q^{18} - 16 q^{19} - 8 q^{21} - 16 q^{22} - 48 q^{24} - 16 q^{25} - 8 q^{27} - 16 q^{28}+ \cdots - 8 q^{99}+O(q^{100}) \) 240 * q - 8 * q^3 - 16 * q^4 - 8 * q^6 - 16 * q^7 - 8 * q^9 - 16 * q^10 - 8 * q^12 - 16 * q^13 - 8 * q^15 - 16 * q^16 - 8 * q^18 - 16 * q^19 - 8 * q^21 - 16 * q^22 - 48 * q^24 - 16 * q^25 - 8 * q^27 - 16 * q^28 - 88 * q^30 - 32 * q^31 - 16 * q^34 - 88 * q^36 - 16 * q^37 - 8 * q^39 - 16 * q^40 - 48 * q^42 - 16 * q^43 - 8 * q^45 - 16 * q^46 - 8 * q^48 - 16 * q^49 - 8 * q^51 + 32 * q^52 - 8 * q^54 - 80 * q^55 - 8 * q^57 + 128 * q^58 - 8 * q^60 - 16 * q^61 + 80 * q^64 - 24 * q^66 - 144 * q^67 - 8 * q^69 + 80 * q^70 - 8 * q^72 - 16 * q^73 - 8 * q^75 + 96 * q^76 + 16 * q^78 - 48 * q^79 - 8 * q^81 + 64 * q^82 + 104 * q^84 - 16 * q^85 - 8 * q^87 + 64 * q^88 + 136 * q^90 - 16 * q^91 - 32 * q^93 + 80 * q^94 + 128 * q^96 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more