LMFDB - Embedded newform 192.2.s.a.107.18

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			107.18
Character	$\chi$	$=$	192.107
Dual form			192.2.s.a.131.18

$q$-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} +(-1.67061 - 0.457221i) q^{3} +(-1.70257 - 1.04941i) q^{4} +(-1.45822 - 2.18239i) q^{5} +(-1.26635 + 2.09675i) q^{6} +(-1.27779 + 3.08486i) q^{7} +(-2.08442 + 1.91186i) q^{8} +(2.58190 + 1.52768i) q^{9} +(-3.53174 + 1.14248i) q^{10} +(2.31748 + 0.460975i) q^{11} +(2.36452 + 2.53161i) q^{12} +(-5.55652 - 3.71275i) q^{13} +(3.70456 + 2.92822i) q^{14} +(1.43829 + 4.31265i) q^{15} +(1.79748 + 3.57338i) q^{16} +(-3.42067 - 3.42067i) q^{17} +(3.07426 - 2.92385i) q^{18} +(-1.23054 - 0.822221i) q^{19} +(0.192511 + 5.24594i) q^{20} +(3.54516 - 4.56938i) q^{21} +(1.52092 - 2.97544i) q^{22} +(-1.87568 - 4.52828i) q^{23} +(4.35640 - 2.24093i) q^{24} +(-0.722975 + 1.74542i) q^{25} +(-7.19443 + 6.12853i) q^{26} +(-3.61486 - 3.73266i) q^{27} +(5.41281 - 3.91127i) q^{28} +(-0.760797 - 3.82478i) q^{29} +(6.42254 - 0.293854i) 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} +(-2.79270 - 5.31045i) q^{36} +(5.53510 + 8.28386i) q^{37} +(-1.59327 + 1.35722i) q^{38} +(7.58524 + 8.74312i) q^{39} +(7.21196 + 1.76109i) q^{40} +(2.28385 - 0.946002i) q^{41} +(-4.85004 - 6.58573i) q^{42} +(-0.522190 - 0.103870i) q^{43} +(-3.46191 - 3.21682i) q^{44} +(-0.430996 - 7.86240i) q^{45} +(-6.88460 + 0.805810i) q^{46} +(-2.51930 + 2.51930i) q^{47} +(-1.36907 - 6.79159i) q^{48} +(-2.93388 - 2.93388i) q^{49} +(2.09604 + 1.65679i) q^{50} +(4.15061 + 7.27862i) q^{51} +(5.56417 + 12.1523i) q^{52} +(1.79038 - 9.00087i) q^{53} +(-6.47275 + 3.47900i) q^{54} +(-2.37338 - 5.72983i) q^{55} +(-3.23436 - 8.87310i) q^{56} +(1.67982 + 1.93624i) q^{57} +(-5.49747 - 0.439822i) q^{58} +(2.56739 - 1.71547i) q^{59} +(2.07694 - 8.85195i) 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} +(-3.90129 + 4.27541i) q^{66} +(-3.65093 + 0.726215i) q^{67} +(2.23425 + 9.41361i) q^{68} +(1.06310 + 8.42261i) q^{69} +(0.988438 - 12.3548i) q^{70} +(-12.6483 - 5.23910i) q^{71} +(-8.30246 + 1.75189i) q^{72} +(13.6168 - 5.64025i) q^{73} +(13.4057 - 4.33660i) q^{74} +(2.00585 - 2.58536i) q^{75} +(1.23223 + 2.69123i) q^{76} +(-4.38330 + 6.56007i) q^{77} +(14.8212 - 6.94896i) q^{78} +(-1.69637 + 1.69637i) q^{79} +(5.17737 - 9.13359i) q^{80} +(4.33239 + 7.88863i) q^{81} +(-0.406412 - 3.47226i) q^{82} +(-5.63016 + 8.42612i) q^{83} +(-10.8310 + 4.05936i) q^{84} +(-2.47712 + 12.4533i) q^{85} +(-0.342703 + 0.670446i) q^{86} +(-0.477776 + 6.73759i) q^{87} +(-5.71191 + 3.46982i) q^{88} +(8.26075 + 3.42172i) q^{89} +(-10.8639 - 2.44561i) q^{90} +(18.5534 - 12.3970i) q^{91} +(-1.55855 + 9.67806i) q^{92} +(0.0830760 + 0.0227366i) q^{93} +(2.45627 + 4.39934i) q^{94} +3.88450i q^{95} +(-9.76873 - 0.756300i) q^{96} +3.93119i q^{97} +(-5.12330 + 2.86048i) q^{98} +(5.27927 + 4.73055i) 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 $\left(\mathbb{Z}/192\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$133$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{16}\right)$

Coefficient data

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

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

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

$2$	0.385637	−	1.36062i	0.272686	−	0.962103i
$2$	0.385637	−	1.36062i	0.272686	−	0.962103i
$3$	−1.67061	−	0.457221i	−0.964529	−	0.263977i
$3$	−1.67061	−	0.457221i	−0.964529	−	0.263977i
$4$	−1.70257	−	1.04941i	−0.851284	−	0.524704i
$5$	−1.45822	−	2.18239i	−0.652138	−	0.975993i	−0.999271	−	0.0381770i	$-0.987845\pi$
$5$	−1.45822	−	2.18239i	−0.652138	−	0.975993i	0.347133	−	0.937816i	$-0.387155\pi$
$6$	−1.26635	+	2.09675i	−0.516987	+	0.855993i
$7$	−1.27779	+	3.08486i	−0.482960	+	1.16597i	0.475237	+	0.879858i	$0.342362\pi$
$7$	−1.27779	+	3.08486i	−0.482960	+	1.16597i	−0.958197	+	0.286111i	$0.907638\pi$
$8$	−2.08442	+	1.91186i	−0.736953	+	0.675944i
$9$	2.58190	+	1.52768i	0.860632	+	0.509227i
$10$	−3.53174	+	1.14248i	−1.11683	+	0.361284i
$11$	2.31748	+	0.460975i	0.698746	+	0.138989i	0.531666	−	0.846954i	$-0.321566\pi$
$11$	2.31748	+	0.460975i	0.698746	+	0.138989i	0.167080	+	0.985943i	$0.446566\pi$
$12$	2.36452	+	2.53161i	0.682579	+	0.730812i
$13$	−5.55652	−	3.71275i	−1.54110	−	1.02973i	−0.979289	−	0.202465i	$-0.935105\pi$
$13$	−5.55652	−	3.71275i	−1.54110	−	1.02973i	−0.561811	−	0.827266i	$-0.689895\pi$
$14$	3.70456	+	2.92822i	0.990085	+	0.782601i
$15$	1.43829	+	4.31265i	0.371366	+	1.11352i
$16$	1.79748	+	3.57338i	0.449370	+	0.893345i
$17$	−3.42067	−	3.42067i	−0.829634	−	0.829634i	0.157832	−	0.987466i	$-0.449550\pi$
$17$	−3.42067	−	3.42067i	−0.829634	−	0.829634i	−0.987466	+	0.157832i	$0.949550\pi$
$18$	3.07426	−	2.92385i	0.724611	−	0.689158i
$19$	−1.23054	−	0.822221i	−0.282305	−	0.188630i	0.406353	−	0.913716i	$-0.366800\pi$
$19$	−1.23054	−	0.822221i	−0.282305	−	0.188630i	−0.688659	+	0.725086i	$0.741800\pi$
$20$	0.192511	+	5.24594i	0.0430468	+	1.17303i
$21$	3.54516	−	4.56938i	0.773618	−	0.997120i
$22$	1.52092	−	2.97544i	0.324260	−	0.634365i
$23$	−1.87568	−	4.52828i	−0.391105	−	0.944212i	−0.989700	−	0.143160i	$-0.954274\pi$
$23$	−1.87568	−	4.52828i	−0.391105	−	0.944212i	0.598594	−	0.801052i	$-0.295726\pi$
$24$	4.35640	−	2.24093i	0.889246	−	0.457429i
$25$	−0.722975	+	1.74542i	−0.144595	+	0.349083i
$26$	−7.19443	+	6.12853i	−1.41094	+	1.20190i
$27$	−3.61486	−	3.73266i	−0.695681	−	0.718351i
$28$	5.41281	−	3.91127i	1.02293	−	0.739160i
$29$	−0.760797	−	3.82478i	−0.141276	−	0.710245i	−0.984874	−	0.173269i	$-0.944567\pi$
$29$	−0.760797	−	3.82478i	−0.141276	−	0.710245i	0.843598	−	0.536975i	$-0.180433\pi$
$30$	6.42254	−	0.293854i	1.17259	−	0.0536502i
$31$	−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
$36$	−2.79270	−	5.31045i	−0.465450	−	0.885074i
$37$	5.53510	+	8.28386i	0.909965	+	1.36186i	0.932138	+	0.362104i	$0.117942\pi$
$37$	5.53510	+	8.28386i	0.909965	+	1.36186i	−0.0221727	+	0.999754i	$0.507058\pi$
$38$	−1.59327	+	1.35722i	−0.258463	+	0.220170i
$39$	7.58524	+	8.74312i	1.21461	+	1.40002i
$40$	7.21196	+	1.76109i	1.14031	+	0.278453i
$41$	2.28385	−	0.946002i	0.356678	−	0.147741i	−0.197147	−	0.980374i	$-0.563168\pi$
$41$	2.28385	−	0.946002i	0.356678	−	0.147741i	0.553825	+	0.832633i	$0.313168\pi$
$42$	−4.85004	−	6.58573i	−0.748378	−	1.01620i
$43$	−0.522190	−	0.103870i	−0.0796333	−	0.0158400i	0.155113	−	0.987897i	$-0.450426\pi$
$43$	−0.522190	−	0.103870i	−0.0796333	−	0.0158400i	−0.234746	+	0.972057i	$0.575426\pi$
$44$	−3.46191	−	3.21682i	−0.521903	−	0.484954i
$45$	−0.430996	−	7.86240i	−0.0642491	−	1.17206i
$46$	−6.88460	+	0.805810i	−1.01508	+	0.118810i
$47$	−2.51930	+	2.51930i	−0.367477	+	0.367477i	−0.866556	−	0.499079i	$-0.833672\pi$
$47$	−2.51930	+	2.51930i	−0.367477	+	0.367477i	0.499079	+	0.866556i	$0.333672\pi$
$48$	−1.36907	−	6.79159i	−0.197608	−	0.980281i
$49$	−2.93388	−	2.93388i	−0.419126	−	0.419126i
$50$	2.09604	+	1.65679i	0.296425	+	0.234306i
$51$	4.15061	+	7.27862i	0.581202	+	1.01921i
$52$	5.56417	+	12.1523i	0.771611	+	1.68522i
$53$	1.79038	−	9.00087i	0.245928	−	1.23636i	−0.638476	−	0.769642i	$-0.720435\pi$
$53$	1.79038	−	9.00087i	0.245928	−	1.23636i	0.884404	−	0.466722i	$-0.154565\pi$
$54$	−6.47275	+	3.47900i	−0.880830	+	0.473432i
$55$	−2.37338	−	5.72983i	−0.320026	−	0.772611i
$56$	−3.23436	−	8.87310i	−0.432210	−	1.18572i
$57$	1.67982	+	1.93624i	0.222498	+	0.256461i
$58$	−5.49747	−	0.439822i	−0.721853	−	0.0577514i
$59$	2.56739	−	1.71547i	0.334245	−	0.223336i	−0.377109	−	0.926169i	$-0.623082\pi$
$59$	2.56739	−	1.71547i	0.334245	−	0.223336i	0.711355	+	0.702833i	$0.248082\pi$
$60$	2.07694	−	8.85195i	0.268132	−	1.14278i
$61$	−0.935842	−	4.70479i	−0.119822	−	0.602387i	−0.993304	−	0.115530i	$-0.963143\pi$
$61$	−0.935842	−	4.70479i	−0.119822	−	0.602387i	0.873482	−	0.486857i	$-0.161857\pi$
$62$	−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
$66$	−3.90129	+	4.27541i	−0.480216	+	0.526266i
$67$	−3.65093	+	0.726215i	−0.446032	+	0.0887213i	−0.412996	−	0.910733i	$-0.635518\pi$
$67$	−3.65093	+	0.726215i	−0.446032	+	0.0887213i	−0.0330361	+	0.999454i	$0.510518\pi$
$68$	2.23425	+	9.41361i	0.270942	+	1.14157i
$69$	1.06310	+	8.42261i	0.127982	+	1.01396i
$70$	0.988438	−	12.3548i	0.118141	−	1.47668i
$71$	−12.6483	−	5.23910i	−1.50108	−	0.621767i	−0.527384	−	0.849627i	$-0.676827\pi$
$71$	−12.6483	−	5.23910i	−1.50108	−	0.621767i	−0.973694	+	0.227860i	$0.926827\pi$
$72$	−8.30246	+	1.75189i	−0.978454	+	0.206463i
$73$	13.6168	−	5.64025i	1.59372	−	0.660142i	0.603213	−	0.797580i	$-0.293887\pi$
$73$	13.6168	−	5.64025i	1.59372	−	0.660142i	0.990510	+	0.137439i	$0.0438870\pi$
$74$	13.4057	−	4.33660i	1.55838	−	0.504120i
$75$	2.00585	−	2.58536i	0.231616	−	0.298531i
$76$	1.23223	+	2.69123i	0.141347	+	0.308705i
$77$	−4.38330	+	6.56007i	−0.499523	+	0.747589i
$78$	14.8212	−	6.94896i	1.67817	−	0.786815i
$79$	−1.69637	+	1.69637i	−0.190856	+	0.190856i	−0.796066	−	0.605210i	$-0.793089\pi$
$79$	−1.69637	+	1.69637i	−0.190856	+	0.190856i	0.605210	+	0.796066i	$0.293089\pi$
$80$	5.17737	−	9.13359i	0.578847	−	1.02117i
$81$	4.33239	+	7.88863i	0.481376	+	0.876514i
$82$	−0.406412	−	3.47226i	−0.0448807	−	0.383447i
$83$	−5.63016	+	8.42612i	−0.617990	+	0.924887i	0.382010	+	0.924158i	$0.375232\pi$
$83$	−5.63016	+	8.42612i	−0.617990	+	0.924887i	−1.00000		0.000728896i	$0.999768\pi$
$84$	−10.8310	+	4.05936i	−1.18176	+	0.442912i
$85$	−2.47712	+	12.4533i	−0.268681	+	1.35075i
$86$	−0.342703	+	0.670446i	−0.0369546	+	0.0722960i
$87$	−0.477776	+	6.73759i	−0.0512229	+	0.722345i
$88$	−5.71191	+	3.46982i	−0.608892	+	0.369884i
$89$	8.26075	+	3.42172i	0.875638	+	0.362701i	0.774804	−	0.632202i	$-0.217849\pi$
$89$	8.26075	+	3.42172i	0.875638	+	0.362701i	0.100834	+	0.994903i	$0.467849\pi$
$90$	−10.8639	−	2.44561i	−1.14516	−	0.257789i
$91$	18.5534	−	12.3970i	1.94492	−	1.29956i
$92$	−1.55855	+	9.67806i	−0.162490	+	1.00901i
$93$	0.0830760	+	0.0227366i	0.00861458	+	0.00235768i
$94$	2.45627	+	4.39934i	0.253345	+	0.453757i
$95$			3.88450i			0.398541i
$96$	−9.76873	−	0.756300i	−0.997016	−	0.0771895i
$97$			3.93119i			0.399152i	0.979882	+	0.199576i	$0.0639565\pi$
$97$			3.93119i			0.399152i	−0.979882	+	0.199576i	$0.936044\pi$
$98$	−5.12330	+	2.86048i	−0.517532	+	0.288952i
$99$	5.27927	+	4.73055i	0.530586	+	0.475439i
$100$	3.06257	−	2.21300i	0.306257	−	0.221300i
$101$	−1.14688	+	0.766317i	−0.114118	+	0.0762514i	−0.611320	−	0.791384i	$-0.709361\pi$
$101$	−1.14688	+	0.766317i	−0.114118	+	0.0762514i	0.497201	+	0.867635i	$0.334361\pi$
$102$	11.5041	−	2.84050i	1.13907	−	0.281252i
$103$	3.42308	+	1.41789i	0.337286	+	0.139708i	0.544897	−	0.838503i	$-0.316569\pi$
$103$	3.42308	+	1.41789i	0.337286	+	0.139708i	−0.207611	+	0.978212i	$0.566569\pi$
$104$	18.6804	−	2.88435i	1.83176	−	0.282834i
$105$	−15.1418	−	1.07373i	−1.47769	−	0.104786i
$106$	−11.5563	−	5.90709i	−1.12245	−	0.573748i
$107$	0.353820	−	1.77877i	0.0342051	−	0.171960i	−0.959907	−	0.280319i	$-0.909560\pi$
$107$	0.353820	−	1.77877i	0.0342051	−	0.171960i	0.994112	+	0.108359i	$0.0345596\pi$
$108$	2.23747	+	10.1486i	0.215300	+	0.976548i
$109$	−4.27438	+	6.39706i	−0.409411	+	0.612728i	−0.977676	−	0.210118i	$-0.932615\pi$
$109$	−4.27438	+	6.39706i	−0.409411	+	0.612728i	0.568264	+	0.822846i	$0.307615\pi$
$110$	−8.71138	+	1.01963i	−0.830598	+	0.0972175i
$111$	−5.45945	−	16.3699i	−0.518188	−	1.55376i
$112$	−13.3202	+	0.978946i	−1.25864	+	0.0925017i
$113$	7.68145	−	7.68145i	0.722610	−	0.722610i	−0.246526	−	0.969136i	$-0.579289\pi$
$113$	7.68145	−	7.68145i	0.722610	−	0.722610i	0.969136	+	0.246526i	$0.0792891\pi$
$114$	3.28229	−	1.53891i	0.307414	−	0.144132i
$115$	−7.14731	+	10.6967i	−0.666490	+	0.997472i
$116$	−2.71845	+	7.31035i	−0.252402	+	0.678749i
$117$	−8.67447	−	18.0745i	−0.801955	−	1.67099i
$118$	−1.34403	−	4.15478i	−0.123728	−	0.382479i
$119$	14.9232	−	6.18139i	1.36801	−	0.566647i
$120$	−11.2432	−	6.23956i	−1.02636	−	0.569592i
$121$	−5.00447	−	2.07292i	−0.454952	−	0.188447i
$122$	−6.76233	−	0.541016i	−0.612232	−	0.0489813i
$123$	−4.24796	+	0.536178i	−0.383026	+	0.0483456i
$124$	0.0846651	+	0.0521849i	0.00760315	+	0.00468634i
$125$	−8.00807	+	1.59290i	−0.716263	+	0.142474i
$126$	5.09140	+	13.2198i	0.453578	+	1.17771i
$127$		−	2.11042i		−	0.187270i	−0.995607	−	0.0936348i	$-0.970151\pi$
$127$		−	2.11042i		−	0.187270i	0.995607	−	0.0936348i	$-0.0298486\pi$
$128$	−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	0.954561	+	0.298015i	$0.0963246\pi$
$131$	2.13696	+	10.7432i	0.186707	+	0.938640i	−0.767854	+	0.640625i	$0.778675\pi$
$132$	4.31272	+	6.95693i	0.375374	+	0.605523i
$133$	4.10881	−	2.74542i	0.356279	−	0.238058i
$134$	−0.419830	+	5.24758i	−0.0362678	+	0.453322i
$135$	−2.87483	+	13.3321i	−0.247426	+	1.14744i
$136$	13.6699	+	0.590275i	1.17219	+	0.0506156i
$137$	−1.35133	−	3.26240i	−0.115452	−	0.278726i	0.855582	−	0.517667i	$-0.173200\pi$
$137$	−1.35133	−	3.26240i	−0.115452	−	0.278726i	−0.971034	+	0.238942i	$0.923200\pi$
$138$	11.8699	+	1.80159i	1.01044	+	0.153361i
$139$	2.25479	−	11.3356i	0.191249	−	0.961475i	−0.759262	−	0.650785i	$-0.774440\pi$
$139$	2.25479	−	11.3356i	0.191249	−	0.961475i	0.950511	−	0.310690i	$-0.100560\pi$
$140$	−16.4290	−	6.10934i	−1.38850	−	0.516334i
$141$	5.36065	−	3.05689i	0.451448	−	0.257437i
$142$	−12.0061	+	15.1891i	−1.00753	+	1.27464i
$143$	−11.1656	−	11.1656i	−0.933716	−	0.933716i
$144$	−0.818071	+	11.9721i	−0.0681725	+	0.997674i
$145$	−7.23774	+	7.23774i	−0.601062	+	0.601062i
$146$	−2.42311	−	20.7023i	−0.200538	−	1.71334i
$147$	3.55995	+	6.24281i	0.293619	+	0.514898i
$148$	−0.730730	−	19.9124i	−0.0600657	−	1.63679i
$149$	−9.41669	−	1.87310i	−0.771445	−	0.153450i	−0.206353	−	0.978478i	$-0.566159\pi$
$149$	−9.41669	−	1.87310i	−0.771445	−	0.153450i	−0.565092	+	0.825028i	$0.691159\pi$
$150$	−2.74416	−	3.72621i	−0.224059	−	0.304244i
$151$	15.4374	−	6.39437i	1.25628	−	0.520367i	0.347511	−	0.937676i	$-0.387027\pi$
$151$	15.4374	−	6.39437i	1.25628	−	0.520367i	0.908765	+	0.417309i	$0.137027\pi$
$152$	4.13693	−	0.638765i	0.335549	−	0.0518107i
$153$	−3.60613	−	14.0575i	−0.291538	−	1.13648i
$154$	7.23540	+	8.49380i	0.583045	+	0.684450i
$155$	0.0725144	+	0.108525i	0.00582449	+	0.00871697i
$156$	−3.73929	−	22.8458i	−0.299383	−	1.82913i
$157$	−1.10477	+	0.219752i	−0.0881699	+	0.0175381i	−0.238978	−	0.971025i	$-0.576812\pi$
$157$	−1.10477	+	0.219752i	−0.0881699	+	0.0175381i	0.150808	+	0.988563i	$0.451812\pi$
$158$	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
$162$	12.4041	−	2.85259i	0.974561	−	0.224120i
$163$	−3.95820	−	19.8992i	−0.310030	−	1.55863i	−0.750507	−	0.660862i	$-0.770191\pi$
$163$	−3.95820	−	19.8992i	−0.310030	−	1.55863i	0.440477	−	0.897764i	$-0.354809\pi$
$164$	−4.88116	−	0.786060i	−0.381154	−	0.0613810i
$165$	1.34519	+	10.6575i	0.104723	+	0.829685i
$166$	9.29355	+	10.9099i	0.721319	+	0.846774i
$167$	−0.109882	+	0.265279i	−0.00850292	+	0.0205279i	−0.928074	−	0.372396i	$-0.878536\pi$
$167$	−0.109882	+	0.265279i	−0.00850292	+	0.0205279i	0.919571	+	0.392924i	$0.128536\pi$
$168$	1.34640	+	16.3023i	0.103877	+	1.25775i
$169$	12.1155	+	29.2494i	0.931963	+	2.24996i
$170$	15.9890	+	8.17287i	1.22630	+	0.626831i
$171$	−1.92104	−	4.00276i	−0.146905	−	0.306099i
$172$	0.780063	+	0.724837i	0.0594792	+	0.0552683i
$173$	−11.1530	−	7.45221i	−0.847948	−	0.566581i	0.0539429	−	0.998544i	$-0.482821\pi$
$173$	−11.1530	−	7.45221i	−0.847948	−	0.566581i	−0.901891	+	0.431963i	$0.857821\pi$
$174$	8.98304	+	3.24833i	0.681003	+	0.246255i
$175$	−4.46056	−	4.46056i	−0.337187	−	0.337187i
$176$	2.51838	+	9.10983i	0.189830	+	0.686679i
$177$	−5.07346	+	1.69203i	−0.381345	+	0.127181i
$178$	7.84130	−	9.92020i	0.587730	−	0.743550i
$179$	−13.7986	−	9.21991i	−1.03135	−	0.689128i	−0.0798628	−	0.996806i	$-0.525448\pi$
$179$	−13.7986	−	9.21991i	−1.03135	−	0.689128i	−0.951491	+	0.307677i	$0.900448\pi$
$180$	−7.51707	+	13.8386i	−0.560289	+	1.03147i
$181$	−0.368628	−	0.0733247i	−0.0273999	−	0.00545018i	0.181371	−	0.983415i	$-0.441946\pi$
$181$	−0.368628	−	0.0733247i	−0.0273999	−	0.00545018i	−0.208771	+	0.977965i	$0.566946\pi$
$182$	−9.71270	−	30.0248i	−0.719953	−	2.22559i
$183$	−0.587703	+	8.28778i	−0.0434442	+	0.612650i
$184$	12.5671	+	5.85281i	0.926461	+	0.431475i
$185$	10.0072	−	24.1595i	0.735742	−	1.77624i
$186$	0.0629731	−	0.104267i	0.00461741	−	0.00764521i
$187$	−6.35048	−	9.50417i	−0.464393	−	0.695014i
$188$	6.93305	−	1.64550i	0.505645	−	0.120011i
$189$	16.1338	−	6.38180i	1.17356	−	0.464207i
$190$	5.28532	+	1.49800i	0.383437	+	0.108677i
$191$	−4.88024			−0.353122			−0.176561	−	0.984290i	$-0.556497\pi$
$191$	−4.88024			−0.353122			−0.176561	+	0.984290i	$0.556497\pi$
$192$	−4.79621	+	12.9999i	−0.346137	+	0.938184i
$193$	−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
$195$	8.01988	−	29.3034i	0.574316	−	2.09846i
$196$	1.91629	+	8.07397i	0.136878	+	0.576712i
$197$	8.61841	+	12.8984i	0.614036	+	0.918970i	0.999994	−	0.00354629i	$-0.00112882\pi$
$197$	8.61841	+	12.8984i	0.614036	+	0.918970i	−0.385957	+	0.922517i	$0.626129\pi$
$198$	8.47236	−	5.35880i	0.602104	−	0.380833i
$199$	4.43073	−	10.6967i	0.314086	−	0.758271i	−0.685459	−	0.728111i	$-0.740398\pi$
$199$	4.43073	−	10.6967i	0.314086	−	0.758271i	0.999545	−	0.0301595i	$-0.00960151\pi$
$200$	−1.83001	−	5.02041i	−0.129401	−	0.354996i
$201$	6.43133	+	0.456058i	0.453631	+	0.0321679i
$202$	0.600389	+	1.85598i	0.0422432	+	0.130586i
$203$	12.7711	+	2.54032i	0.896354	+	0.178296i
$204$	0.571543	−	16.7480i	0.0400160	−	1.17260i
$205$	−5.39491	−	3.60476i	−0.376797	−	0.251768i
$206$	3.24927	−	4.11072i	0.226387	−	0.286407i
$207$	2.07496	−	14.5570i	0.144220	−	1.01178i
$208$	3.27932	−	26.5292i	0.227380	−	1.83947i
$209$	−2.47273	−	2.47273i	−0.171042	−	0.171042i
$210$	−7.30017	+	20.1881i	−0.503760	+	1.39311i
$211$	17.8899	+	11.9536i	1.23159	+	0.822923i	0.989102	−	0.147232i	$-0.0470363\pi$
$211$	17.8899	+	11.9536i	1.23159	+	0.822923i	0.242489	+	0.970154i	$0.422036\pi$
$212$	−12.4938	+	13.4458i	−0.858081	+	0.923458i
$213$	18.7350	+	14.5356i	1.28370	+	0.995962i
$214$	−2.28379	−	1.16737i	−0.156116	−	0.0798000i
$215$	0.534786	+	1.29109i	0.0364721	+	0.0880514i
$216$	14.6712	+	0.869324i	0.998249	+	0.0591500i
$217$	0.0635419	−	0.153404i	0.00431350	−	0.0104137i
$218$	7.05561	+	8.28275i	0.477866	+	0.560978i
$219$	−25.3272	+	3.19680i	−1.71145	+	0.216020i
$220$	−1.97210	+	12.2461i	−0.132959	+	0.825631i
$221$	6.30693	+	31.7071i	0.424250	+	2.13285i
$222$	−24.3786	+	1.11541i	−1.63618	+	0.0748611i
$223$	−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	$-0.335019\pi$
$227$	19.3684	−	3.85261i	1.28552	−	0.255707i	0.790118	+	0.612955i	$0.210019\pi$
$228$	−0.828100	−	5.05940i	−0.0548422	−	0.335067i
$229$	0.936069	+	1.40093i	0.0618572	+	0.0925758i	0.861109	−	0.508421i	$-0.169771\pi$
$229$	0.936069	+	1.40093i	0.0618572	+	0.0925758i	−0.799252	+	0.600997i	$0.794771\pi$
$230$	11.7979	+	13.8498i	0.777929	+	0.913229i
$231$	10.3222	−	8.95520i	0.679151	−	0.589209i
$232$	8.89826	+	6.51792i	0.584200	+	0.427922i
$233$	−14.4154	+	5.97104i	−0.944382	+	0.391176i	−0.801117	−	0.598508i	$-0.795760\pi$
$233$	−14.4154	+	5.97104i	−0.944382	+	0.391176i	−0.143266	+	0.989684i	$0.545760\pi$
$234$	−27.9377	+	4.83246i	−1.82635	+	0.315908i
$235$	9.17178	+	1.82438i	0.598301	+	0.119009i
$236$	−6.17139	+	0.226473i	−0.401723	+	0.0147421i
$237$	3.60959	−	2.05836i	0.234468	−	0.133705i
$238$	−2.65559	−	22.6886i	−0.172136	−	1.47068i
$239$	0.690266	−	0.690266i	0.0446496	−	0.0446496i	−0.684429	−	0.729079i	$-0.739949\pi$
$239$	0.690266	−	0.690266i	0.0446496	−	0.0446496i	0.729079	+	0.684429i	$0.239949\pi$
$240$	−12.8255	+	12.8915i	−0.827879	+	0.832142i
$241$	−10.6103	−	10.6103i	−0.683472	−	0.683472i	0.277309	−	0.960781i	$-0.410558\pi$
$241$	−10.6103	−	10.6103i	−0.683472	−	0.683472i	−0.960781	+	0.277309i	$0.910558\pi$
$242$	−4.75036	+	6.00979i	−0.305365	+	0.386324i
$243$	−3.63090	−	15.1597i	−0.232922	−	0.972495i
$244$	−3.34392	+	8.99232i	−0.214072	+	0.575674i
$245$	−2.12461	+	10.6811i	−0.135736	+	0.682391i
$246$	−0.908636	+	5.98663i	−0.0579325	+	0.381694i
$247$	3.78482	+	9.13737i	0.240822	+	0.581397i
$248$	0.103654	−	0.0950726i	0.00658202	−	0.00603712i
$249$	13.2584	−	11.5026i	0.840218	−	0.728945i
$250$	−0.920868	+	11.5102i	−0.0582408	+	0.727970i
$251$	−22.7440	+	15.1971i	−1.43559	+	0.959232i	−0.437391	+	0.899272i	$0.644097\pi$
$251$	−22.7440	+	15.1971i	−1.43559	+	0.959232i	−0.998201	+	0.0599600i	$0.980903\pi$
$252$	19.9505	−	1.82944i	1.25676	−	0.115244i
$253$	−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	$0.954995\pi$
$258$	0.879067	−	0.963365i	0.0547283	−	0.0599765i
$259$	−32.6273	+	6.48997i	−2.02736	+	0.403267i
$260$	18.4071	−	29.8639i	1.14156	−	1.85208i
$261$	3.87875	−	11.0375i	0.240088	−	0.683201i
$262$	15.4415	+	1.23539i	0.953981	+	0.0763227i
$263$	−2.04943	−	0.848904i	−0.126374	−	0.0523456i	0.318601	−	0.947889i	$-0.396787\pi$
$263$	−2.04943	−	0.848904i	−0.126374	−	0.0523456i	−0.444974	+	0.895543i	$0.646787\pi$
$264$	11.1289	−	3.18512i	0.684935	−	0.196031i
$265$	−22.2541	+	9.21797i	−1.36706	+	0.566255i
$266$	−2.15096	−	6.64926i	−0.131884	−	0.407692i
$267$	−12.2360	−	9.49335i	−0.748833	−	0.580984i
$268$	6.97805	+	2.59489i	0.426253	+	0.158508i
$269$	12.8156	−	19.1799i	0.781379	−	1.16942i	−0.200460	−	0.979702i	$-0.564244\pi$
$269$	12.8156	−	19.1799i	0.781379	−	1.16942i	0.981839	−	0.189715i	$-0.0607564\pi$
$270$	17.0313	+	9.05288i	1.03649	+	0.550941i
$271$	−4.68156	+	4.68156i	−0.284384	+	0.284384i	−0.834855	−	0.550470i	$-0.814448\pi$
$271$	−4.68156	+	4.68156i	−0.284384	+	0.284384i	0.550470	+	0.834855i	$0.314448\pi$
$272$	6.07477	−	18.3720i	0.368337	−	1.11396i
$273$	−36.6637	+	12.2275i	−2.21899	+	0.740045i
$274$	−4.96001	+	0.580545i	−0.299645	+	0.0350720i
$275$	−2.48007	+	3.71169i	−0.149554	+	0.223823i
$276$	7.02876	−	15.4557i	0.423081	−	0.930324i
$277$	0.351539	−	1.76730i	0.0211219	−	0.106187i	−0.968786	−	0.247898i	$-0.920260\pi$
$277$	0.351539	−	1.76730i	0.0211219	−	0.106187i	0.989908	+	0.141711i	$0.0452603\pi$
$278$	−14.5539	−	7.43935i	−0.872887	−	0.446182i
$279$	−0.128392	−	0.0759683i	−0.00768664	−	0.00454810i
$280$	−14.6481	+	19.9976i	−0.875392	+	1.19509i
$281$	6.33662	+	2.62472i	0.378011	+	0.156577i	0.563595	−	0.826051i	$-0.309418\pi$
$281$	6.33662	+	2.62472i	0.378011	+	0.156577i	−0.185584	+	0.982628i	$0.559418\pi$
$282$	−2.09201	−	8.47265i	−0.124577	−	0.504539i
$283$	−19.0458	+	12.7260i	−1.13215	+	0.756481i	−0.973007	−	0.230774i	$-0.925874\pi$
$283$	−19.0458	+	12.7260i	−1.13215	+	0.756481i	−0.159146	+	0.987255i	$0.550874\pi$
$284$	16.0367	+	22.1932i	0.951601	+	1.31692i
$285$	1.77607	−	6.48949i	0.105206	−	0.384404i
$286$	−19.4980	+	10.8863i	−1.15294	+	0.643720i
$287$			8.25416i			0.487228i
$288$	15.9740	+	5.72995i	0.941275	+	0.337641i
$289$			6.40197i			0.376586i
$290$	7.05667	+	12.6390i	0.414382	+	0.742185i
$291$	1.79742	−	6.56750i	0.105367	−	0.384994i
$292$	−29.1024	−	4.68665i	−1.70309	−	0.274265i
$293$	−10.4198	+	6.96228i	−0.608731	+	0.406741i	−0.821375	−	0.570389i	$-0.806793\pi$
$293$	−10.4198	+	6.96228i	−0.608731	+	0.406741i	0.212644	+	0.977130i	$0.431793\pi$
$294$	9.86693	−	2.43627i	0.575451	−	0.142086i
$295$	−7.48765	−	3.10149i	−0.435948	−	0.180575i
$296$	−27.3750	−	6.68471i	−1.59114	−	0.388541i
$297$	−6.65670	−	10.3167i	−0.386261	−	0.598637i
$298$	−6.17999	+	12.0902i	−0.357997	+	0.700366i
$299$	−6.39014	+	32.1254i	−0.369551	+	1.85786i
$300$	−6.12820	+	2.29679i	−0.353812	+	0.132605i
$301$	0.987675	−	1.47816i	0.0569287	−	0.0851998i
$302$	−2.74709	−	23.4703i	−0.158077	−	1.35056i
$303$	2.26636	−	0.755844i	0.130199	−	0.0434221i
$304$	0.726235	−	5.87512i	0.0416524	−	0.336961i
$305$	−8.90301	+	8.90301i	−0.509785	+	0.509785i
$306$	−20.5176	−	0.514520i	−1.17291	−	0.0294132i
$307$	−7.76821	+	11.6259i	−0.443355	+	0.663528i	−0.984091	−	0.177665i	$-0.943146\pi$
$307$	−7.76821	+	11.6259i	−0.443355	+	0.663528i	0.540736	+	0.841192i	$0.318146\pi$
$308$	14.3471	−	6.56910i	0.817500	−	0.374309i
$309$	−5.07036	−	3.93385i	−0.288442	−	0.223789i
$310$	0.175626	−	0.0568131i	0.00997488	−	0.00322677i
$311$	30.5106	−	12.6379i	1.73010	−	0.716630i	0.730673	−	0.682728i	$-0.239206\pi$
$311$	30.5106	−	12.6379i	1.73010	−	0.716630i	0.999425	−	0.0339024i	$-0.0107935\pi$
$312$	−32.5264	−	3.72242i	−1.84145	−	0.210740i
$313$	−0.773283	−	0.320305i	−0.0437086	−	0.0181047i	0.360722	−	0.932673i	$-0.382530\pi$
$313$	−0.773283	−	0.320305i	−0.0437086	−	0.0181047i	−0.404431	+	0.914569i	$0.632530\pi$
$314$	−0.127040	+	1.58791i	−0.00716927	+	0.0896109i
$315$	24.8051	+	8.71694i	1.39761	+	0.491144i
$316$	4.66836	−	1.10800i	0.262616	−	0.0623298i
$317$	13.4190	−	2.66920i	0.753685	−	0.149917i	0.196728	−	0.980458i	$-0.436969\pi$
$317$	13.4190	−	2.66920i	0.753685	−	0.149917i	0.556958	+	0.830541i	$0.311969\pi$
$318$	16.6053	+	15.1523i	0.931178	+	0.849697i
$319$		−	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
$324$	0.902206	−	17.9774i	0.0501226	−	0.998743i
$325$	10.4975	−	7.01422i	0.582297	−	0.389079i
$326$	−28.6017	−	2.28826i	−1.58410	−	0.126735i
$327$	10.0657	−	8.73268i	0.556635	−	0.482918i
$328$	−2.95188	+	6.33826i	−0.162990	+	0.349972i
$329$	−4.55255	−	10.9908i	−0.250990	−	0.605944i
$330$	15.0195	+	2.27963i	0.826799	+	0.125489i
$331$	2.41877	−	12.1600i	0.132947	−	0.668372i	−0.855621	−	0.517602i	$-0.826825\pi$
$331$	2.41877	−	12.1600i	0.132947	−	0.668372i	0.988569	−	0.150770i	$-0.0481753\pi$
$332$	18.4282	−	8.43772i	1.01138	−	0.463080i
$333$	1.63597	+	29.8439i	0.0896505	+	1.63544i
$334$	0.318569	+	0.251809i	0.0174313	+	0.0137784i
$335$	6.90875	+	6.90875i	0.377466	+	0.377466i
$336$	22.7005	+	4.45484i	1.23841	+	0.243031i
$337$	22.7974	−	22.7974i	1.24185	−	1.24185i	0.282622	−	0.959231i	$-0.408796\pi$
$337$	22.7974	−	22.7974i	1.24185	−	1.24185i	0.959231	−	0.282622i	$-0.0912041\pi$
$338$	44.4695	−	5.20495i	2.41882	−	0.283112i
$339$	−16.3449	+	9.32061i	−0.887731	+	0.506226i
$340$	17.2861	−	18.6031i	0.937470	−	1.00890i
$341$	−0.115243	−	0.0229233i	−0.00624077	−	0.00124137i
$342$	−6.18706	+	1.07019i	−0.334558	+	0.0578693i
$343$	−8.79454	+	3.64282i	−0.474860	+	0.196694i
$344$	1.28705	−	0.781844i	0.0693930	−	0.0421542i
$345$	16.8311	−	14.6021i	0.906158	−	0.786153i
$346$	−14.4406	+	12.3012i	−0.776333	+	0.661315i
$347$	−15.3279	−	22.9398i	−0.822843	−	1.23147i	−0.970180	−	0.242385i	$-0.922070\pi$
$347$	−15.3279	−	22.9398i	−0.822843	−	1.23147i	0.147338	−	0.989086i	$-0.452930\pi$
$348$	7.88393	−	10.9698i	0.422623	−	0.588044i
$349$	8.15254	−	1.62164i	0.436395	−	0.0868044i	0.0279965	−	0.999608i	$-0.491087\pi$
$349$	8.15254	−	1.62164i	0.436395	−	0.0868044i	0.408399	+	0.912804i	$0.366087\pi$
$350$	−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	$-0.394558\pi$
$353$	12.2210			0.650460			0.325230	+	0.945635i	$0.394558\pi$
$354$	0.345694	+	7.55556i	0.0183734	+	0.401573i
$355$	7.01032	+	35.2433i	0.372069	+	1.87052i
$356$	−10.4737	−	14.4946i	−0.555106	−	0.768213i
$357$	−27.7572	+	3.50351i	−1.46907	+	0.185425i
$358$	−17.8660	+	15.2191i	−0.944248	+	0.804353i
$359$	−3.41180	+	8.23682i	−0.180068	+	0.434723i	−0.987980	−	0.154580i	$-0.950598\pi$
$359$	−3.41180	+	8.23682i	−0.180068	+	0.434723i	0.807912	+	0.589303i	$0.200598\pi$
$360$	15.9302	+	15.5645i	0.839593	+	0.820322i
$361$	−6.43280	−	15.5302i	−0.338569	−	0.817377i
$362$	−0.241923	+	0.473286i	−0.0127152	+	0.0248753i
$363$	7.41275	+	5.75120i	0.389069	+	0.301860i
$364$	−44.5979	+	1.63662i	−2.33757	+	0.0857821i
$365$	−32.1655	−	21.4923i	−1.68362	−	1.12496i
$366$	11.0499	+	3.99571i	0.577586	+	0.208859i
$367$	11.6703	+	11.6703i	0.609183	+	0.609183i	0.942733	−	0.333550i	$-0.108246\pi$
$367$	11.6703	+	11.6703i	0.609183	+	0.609183i	−0.333550	+	0.942733i	$0.608246\pi$
$368$	12.8098	−	14.8420i	0.667756	−	0.773693i
$369$	7.34186	+	1.04651i	0.382202	+	0.0544793i
$370$	−29.0127	−	22.9327i	−1.50830	−	1.19222i
$371$	25.4787	+	17.0243i	1.32279	+	0.883859i
$372$	−0.117583	−	0.125891i	−0.00609638	−	0.00652717i
$373$	30.2561	+	6.01831i	1.56660	+	0.311616i	0.900706	−	0.434430i	$-0.143050\pi$
$373$	30.2561	+	6.01831i	1.56660	+	0.311616i	0.665894	+	0.746046i	$0.268050\pi$
$374$	−15.3805	+	4.97543i	−0.795308	+	0.257274i
$375$	14.1067	+	1.00033i	0.728466	+	0.0516570i
$376$	0.434733	−	10.0678i	0.0224196	−	0.519208i
$377$	−9.97307	+	24.0771i	−0.513639	+	1.24004i
$378$	−2.46141	−	24.4130i	−0.126601	−	1.25567i
$379$	12.8100	+	19.1715i	0.658005	+	0.984774i	0.999000	+	0.0447089i	$0.0142360\pi$
$379$	12.8100	+	19.1715i	0.658005	+	0.984774i	−0.340995	+	0.940065i	$0.610764\pi$
$380$	4.07642	−	6.61362i	0.209116	−	0.339272i
$381$	−0.964929	+	3.52570i	−0.0494348	+	0.180627i
$382$	−1.88200	+	6.64015i	−0.0962914	+	0.339739i
$383$	11.5359			0.589459			0.294729	−	0.955581i	$-0.404770\pi$
$383$	11.5359			0.589459			0.294729	+	0.955581i	$0.404770\pi$
$384$	15.8383	+	11.5390i	0.808243	+	0.588849i
$385$	20.7084			1.05540
$386$	−2.90357	+	10.2445i	−0.147788	+	0.521431i
$387$	−1.18956	−	1.06592i	−0.0604688	−	0.0541838i
$388$	4.12543	−	6.69312i	0.209437	−	0.339792i
$389$	12.8942	+	19.2976i	0.653764	+	0.978427i	0.999200	+	0.0399850i	$0.0127310\pi$
$389$	12.8942	+	19.2976i	0.653764	+	0.978427i	−0.345436	+	0.938442i	$0.612269\pi$
$390$	−36.7780	−	22.2125i	−1.86232	−	1.12477i
$391$	−9.07369	+	21.9058i	−0.458876	+	1.10783i
$392$	11.7246	+	0.506273i	0.592181	+	0.0255707i
$393$	1.34200	−	18.9248i	0.0676948	−	0.954632i
$394$	20.8733	−	6.75229i	1.05158	−	0.340176i
$395$	6.17581	+	1.22844i	0.310739	+	0.0618097i
$396$	−4.02403	−	13.5942i	−0.202215	−	0.683134i
$397$	2.60492	+	1.74055i	0.130737	+	0.0873557i	0.619219	−	0.785218i	$-0.287449\pi$
$397$	2.60492	+	1.74055i	0.130737	+	0.0873557i	−0.488482	+	0.872574i	$0.662449\pi$
$398$	−12.8455	−	10.1536i	−0.643887	−	0.508953i
$399$	−8.11950	+	2.70790i	−0.406483	+	0.135565i
$400$	−7.53658	+	0.553888i	−0.376829	+	0.0276944i
$401$	−24.3210	−	24.3210i	−1.21453	−	1.21453i	−0.969520	−	0.245012i	$-0.921208\pi$
$401$	−24.3210	−	24.3210i	−1.21453	−	1.21453i	−0.245012	−	0.969520i	$-0.578792\pi$
$402$	3.10068	−	8.57472i	0.154648	−	0.427668i
$403$	0.276314	+	0.184627i	0.0137642	+	0.00919692i
$404$	2.75681	−	0.101167i	0.137157	−	0.00503326i
$405$	10.8984	−	20.9583i	0.541548	−	1.04143i
$406$	8.38141	−	16.3969i	0.415962	−	0.813766i
$407$	9.00882	+	21.7492i	0.446550	+	1.07807i
$408$	−22.5673	−	7.23631i	−1.11725	−	0.358251i
$409$	3.24175	−	7.82629i	0.160294	−	0.386985i	−0.823243	−	0.567689i	$-0.807838\pi$
$409$	3.24175	−	7.82629i	0.160294	−	0.386985i	0.983538	+	0.180704i	$0.0578376\pi$
$410$	−6.98518	+	5.95029i	−0.344974	+	0.293864i
$411$	0.765911	+	6.06807i	0.0377796	+	0.299316i
$412$	−4.34009	−	6.00626i	−0.213821	−	0.295907i
$413$	2.01141	+	10.1121i	0.0989751	+	0.497582i
$414$	−19.0063	−	8.43694i	−0.934111	−	0.414653i
$415$	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	$-0.838246\pi$
$419$	−30.5931	+	6.08535i	−1.49457	+	0.297289i	−0.620933	+	0.783864i	$0.713246\pi$
$420$	24.6532	+	17.7180i	1.20295	+	0.864552i
$421$	−3.52363	−	5.27349i	−0.171731	−	0.257014i	0.735613	−	0.677402i	$-0.236894\pi$
$421$	−3.52363	−	5.27349i	−0.171731	−	0.257014i	−0.907345	+	0.420388i	$0.861894\pi$
$422$	23.1633	−	19.7316i	1.12757	−	0.960518i
$423$	−10.3532	+	2.65589i	−0.503392	+	0.129134i
$424$	13.4765	+	22.1845i	0.654475	+	1.07738i
$425$	8.44356	−	3.49744i	0.409573	−	0.169651i
$426$	27.0023	−	19.8858i	1.30827	−	0.963468i
$427$	15.7095	+	3.12481i	0.760234	+	0.151220i
$428$	−2.46906	+	2.65718i	−0.119347	+	0.128440i
$429$	13.5483	+	23.7586i	0.654117	+	1.14708i
$430$	1.96291	−	0.229749i	0.0946599	−	0.0110795i
$431$	25.0198	−	25.0198i	1.20516	−	1.20516i	0.232586	−	0.972576i	$-0.425281\pi$
$431$	25.0198	−	25.0198i	1.20516	−	1.20516i	0.972576	−	0.232586i	$-0.0747186\pi$
$432$	6.84057	−	19.6267i	0.329117	−	0.944289i
$433$	−0.182313	−	0.182313i	−0.00876139	−	0.00876139i	0.702713	−	0.711474i	$-0.251972\pi$
$433$	−0.182313	−	0.182313i	−0.00876139	−	0.00876139i	−0.711474	+	0.702713i	$0.751972\pi$
$434$	−0.184220	−	0.145614i	−0.00884284	−	0.00698971i
$435$	15.4007	−	8.78222i	0.738408	−	0.421075i
$436$	13.9906	−	6.40587i	0.670026	−	0.306785i
$437$	−1.41515	+	7.11445i	−0.0676959	+	0.340330i
$438$	−5.41747	+	35.6935i	−0.258857	+	1.70550i
$439$	−15.4119	−	37.2076i	−0.735570	−	1.77582i	−0.623062	−	0.782172i	$-0.714112\pi$
$439$	−15.4119	−	37.2076i	−0.735570	−	1.77582i	−0.112508	−	0.993651i	$-0.535888\pi$
$440$	15.9017	+	7.40582i	0.758085	+	0.353059i
$441$	−3.09295	−	12.0570i	−0.147283	−	0.574143i
$442$	45.5735	+	3.64608i	2.16771	+	0.173426i
$443$	−5.50223	+	3.67647i	−0.261419	+	0.174674i	−0.679372	−	0.733794i	$-0.737748\pi$
$443$	−5.50223	+	3.67647i	−0.261419	+	0.174674i	0.417953	+	0.908469i	$0.362748\pi$
$444$	−7.88362	+	33.6001i	−0.374140	+	1.59459i
$445$	−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	$-0.101844\pi$
$450$	2.88072	+	7.47975i	0.135798	+	0.352599i
$451$	5.72886	−	1.13954i	0.269761	−	0.0536589i
$452$	−21.1392	+	5.01722i	−0.994303	+	0.235990i
$453$	−28.7135	+	3.62422i	−1.34908	+	0.170281i
$454$	2.22722	−	27.8387i	0.104529	−	1.30653i
$455$	−54.1100	−	22.4131i	−2.53672	−	1.05074i
$456$	−7.20327	−	0.824362i	−0.337324	−	0.0386043i
$457$	−18.5018	+	7.66368i	−0.865476	+	0.358492i	−0.770847	−	0.637020i	$-0.780167\pi$
$457$	−18.5018	+	7.66368i	−0.865476	+	0.358492i	−0.0946295	+	0.995513i	$0.530167\pi$
$458$	2.26711	−	0.733385i	0.105935	−	0.0342688i
$459$	−0.402945	+	25.1335i	−0.0188079	+	1.17313i
$460$	23.3940	−	10.7114i	1.09075	−	0.499423i
$461$	−19.4038	+	29.0398i	−0.903724	+	1.35252i	0.0318892	+	0.999491i	$0.489848\pi$
$461$	−19.4038	+	29.0398i	−0.903724	+	1.35252i	−0.935613	+	0.353027i	$0.885152\pi$
$462$	−8.20400	−	17.4980i	−0.381685	−	0.814082i
$463$	−26.4304	+	26.4304i	−1.22833	+	1.22833i	−0.263728	+	0.964597i	$0.584952\pi$
$463$	−26.4304	+	26.4304i	−1.22833	+	1.22833i	−0.964597	+	0.263728i	$0.915048\pi$
$464$	12.2999	−	9.59360i	0.571008	−	0.445372i
$465$	−0.0715233	−	0.214459i	−0.00331681	−	0.00994530i
$466$	2.56522	+	21.9165i	0.118832	+	1.01526i
$467$	6.62269	−	9.91156i	0.306462	−	0.458652i	−0.645988	−	0.763347i	$-0.723555\pi$
$467$	6.62269	−	9.91156i	0.306462	−	0.458652i	0.952450	+	0.304695i	$0.0985545\pi$
$468$	−4.19867	+	39.8762i	−0.194084	+	1.84328i
$469$	2.42485	−	12.1906i	0.111969	−	0.562908i
$470$	6.01926	−	11.7757i	0.277648	−	0.543175i
$471$	1.94611	+	0.138003i	0.0896721	+	0.00635882i
$472$	−2.07177	+	8.48424i	−0.0953609	+	0.390519i
$473$	−1.16228	−	0.481433i	−0.0534418	−	0.0221363i
$474$	−1.40865	−	5.70505i	−0.0647015	−	0.262042i
$475$	2.32477	−	1.55336i	0.106668	−	0.0712731i
$476$	−31.8946	−	5.13629i	−1.46189	−	0.235422i
$477$	18.3730	−	20.5042i	0.841243	−	0.938822i
$478$	−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	$-0.333776\pi$
$480$	12.5945	+	22.4220i	0.574855	+	1.02342i
$481$		−	66.5798i		−	3.03578i
$482$	−18.5284	+	10.3449i	−0.843944	+	0.471197i
$483$	−27.3410	−	7.48282i	−1.24406	−	0.340480i
$484$	6.34512	+	8.78103i	0.288414	+	0.399138i
$485$	8.57938	−	5.73256i	0.389569	−	0.260302i
$486$	−22.0268	−	0.905870i	−0.999155	−	0.0410911i
$487$	−20.1298	−	8.33804i	−0.912168	−	0.377833i	−0.123282	−	0.992372i	$-0.539342\pi$
$487$	−20.1298	−	8.33804i	−0.912168	−	0.377833i	−0.788886	+	0.614539i	$0.789342\pi$
$488$	10.9456	+	8.01756i	0.495483	+	0.362938i
$489$	−2.48572	+	35.0536i	−0.112408	+	1.58518i
$490$	13.7136	+	7.00981i	0.619517	+	0.316671i
$491$	3.99742	−	20.0964i	0.180401	−	0.906936i	−0.779458	−	0.626454i	$-0.784506\pi$
$491$	3.99742	−	20.0964i	0.180401	−	0.906936i	0.959859	−	0.280482i	$-0.0904944\pi$
$492$	7.79512	+	3.54497i	0.351431	+	0.159820i
$493$	−10.4809	+	15.6858i	−0.472036	+	0.706451i
$494$	13.8920	−	1.62600i	0.625032	−	0.0731571i
$495$	2.62554	−	18.4196i	0.118009	−	0.827900i
$496$	−0.0893849	−	0.177697i	−0.00401350	−	0.00797882i
$497$	32.3238	−	32.3238i	1.44992	−	1.44992i
$498$	−10.5377	−	22.4755i	−0.472205	−	1.00715i
$499$	10.8139	−	16.1841i	0.484095	−	0.724500i	−0.506362	−	0.862321i	$-0.669010\pi$
$499$	10.8139	−	16.1841i	0.484095	−	0.724500i	0.990457	+	0.137821i	$0.0440099\pi$
$500$	15.3059	+	5.69171i	0.684500	+	0.254541i
$501$	0.304861	−	0.392937i	0.0136202	−	0.0175551i
$502$	11.9065	+	36.8065i	0.531414	+	1.64276i
$503$	−13.0766	+	5.41650i	−0.583056	+	0.241510i	−0.654660	−	0.755923i	$-0.727188\pi$
$503$	−13.0766	+	5.41650i	−0.583056	+	0.241510i	0.0716041	+	0.997433i	$0.477188\pi$
$504$	5.20446	−	27.8505i	0.231825	−	1.24056i
$505$	3.34480	+	1.38546i	0.148842	+	0.0616522i
$506$	−16.3264	−	1.30618i	−0.725795	−	0.0580668i
$507$	−6.86687	−	54.4040i	−0.304969	−	2.41617i
$508$	−2.21469	+	3.59314i	−0.0982612	+	0.159420i
$509$	21.9603	−	4.36817i	0.973371	−	0.193616i	0.317309	−	0.948322i	$-0.397221\pi$
$509$	21.9603	−	4.36817i	0.973371	−	0.193616i	0.656062	+	0.754707i	$0.272221\pi$
$510$	−22.9746	−	20.9642i	−1.01733	−	0.928311i
$511$			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
$516$	−0.971772	−	1.56758i	−0.0427799	−	0.0690090i
$517$	−6.99975	+	4.67708i	−0.307848	+	0.205698i
$518$	−3.75190	+	46.8961i	−0.164849	+	2.06050i
$519$	15.2251	+	17.5492i	0.668307	+	0.770323i
$520$	−33.5349	−	36.5617i	−1.47060	−	1.60334i
$521$	−0.213242	−	0.514813i	−0.00934232	−	0.0225544i	0.919140	−	0.393932i	$-0.128885\pi$
$521$	−0.213242	−	0.514813i	−0.00934232	−	0.0225544i	−0.928482	+	0.371378i	$0.878885\pi$
$522$	−13.5220	−	9.53394i	−0.591841	−	0.417289i
$523$	−0.636430	+	3.19955i	−0.0278291	+	0.139907i	−0.992202	−	0.124640i	$-0.960222\pi$
$523$	−0.636430	+	3.19955i	−0.0278291	+	0.139907i	0.964373	+	0.264547i	$0.0852223\pi$
$524$	7.63572	−	20.5336i	0.333568	−	0.897016i
$525$	5.41241	+	9.49134i	0.236217	+	0.414236i
$526$	−1.94537	+	2.46113i	−0.0848222	+	0.107310i
$527$	0.170103	+	0.170103i	0.00740979	+	0.00740979i
$528$	−0.0420395	−	16.3705i	−0.00182954	−	0.712433i
$529$	−0.723726	+	0.723726i	−0.0314664	+	0.0314664i
$530$	3.96013	+	33.8342i	0.172017	+	1.46966i
$531$	9.24942	−	0.507029i	0.401391	−	0.0220032i
$532$	−9.87660	+	0.362444i	−0.428205	+	0.0157139i
$533$	−16.2025	−	3.22288i	−0.701809	−	0.139599i
$534$	−17.6355	+	12.9876i	−0.763163	+	0.562029i
$535$	−4.39792	+	1.82168i	−0.190139	+	0.0787580i
$536$	6.22164	−	8.49379i	0.268734	−	0.366876i
$537$	18.8365	+	21.7119i	0.812856	+	0.936938i
$538$	−21.1543	−	24.8336i	−0.912028	−	1.07065i
$539$	−5.44675	−	8.15164i	−0.234608	−	0.351116i
$540$	18.8854	−	19.6819i	0.812698	−	0.846975i
$541$	−18.6138	+	3.70251i	−0.800270	+	0.159184i	−0.578251	−	0.815859i	$-0.696265\pi$
$541$	−18.6138	+	3.70251i	−0.800270	+	0.159184i	−0.222019	+	0.975042i	$0.571265\pi$
$542$	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
$546$	2.49818	+	54.6007i	0.106912	+	2.33670i
$547$	0.321617	+	1.61688i	0.0137513	+	0.0691327i	0.987052	−	0.160403i	$-0.0512793\pi$
$547$	0.321617	+	1.61688i	0.0137513	+	0.0691327i	−0.973300	+	0.229535i	$0.926279\pi$
$548$	−1.12286	+	6.97256i	−0.0479661	+	0.297853i
$549$	4.77117	−	13.5770i	0.203629	−	0.579451i
$550$	4.09379	+	4.80580i	0.174560	+	0.204920i
$551$	−2.20863	+	5.33209i	−0.0940906	+	0.227155i
$552$	−18.3188	−	15.5237i	−0.779699	−	0.660734i
$553$	−3.06545	−	7.40066i	−0.130356	−	0.314708i
$554$	−2.26906	−	1.15985i	−0.0964032	−	0.0492772i
$555$	−27.7643	+	35.7856i	−1.17853	+	1.51901i
$556$	−15.7346	+	16.9335i	−0.667297	+	0.718139i
$557$	−7.81765	−	5.22359i	−0.331245	−	0.221330i	0.378815	−	0.925473i	$-0.376332\pi$
$557$	−7.81765	−	5.22359i	−0.331245	−	0.221330i	−0.710059	+	0.704142i	$0.751332\pi$
$558$	−0.152877	+	0.145397i	−0.00647178	+	0.00615514i
$559$	2.51592	+	2.51592i	0.106412	+	0.106412i
$560$	21.5603	+	27.6423i	0.911088	+	1.16810i
$561$	6.26369	+	18.7814i	0.264453	+	0.792950i
$562$	6.01487	−	7.60954i	0.253722	−	0.320989i
$563$	−25.4030	−	16.9737i	−1.07061	−	0.715357i	−0.110186	−	0.993911i	$-0.535145\pi$
$563$	−25.4030	−	16.9737i	−1.07061	−	0.715357i	−0.960420	+	0.278554i	$0.910145\pi$
$564$	−12.3348	−	0.420937i	−0.519389	−	0.0177247i
$565$	−27.9652	−	5.56262i	−1.17650	−	0.234021i
$566$	9.97046	+	30.8216i	0.419090	+	1.29553i
$567$	−29.8712	+	3.28480i	−1.25447	+	0.137949i
$568$	36.3808	−	13.2613i	1.52650	−	0.556431i
$569$	−11.5727	+	27.9391i	−0.485154	+	1.17127i	0.471977	+	0.881611i	$0.343541\pi$
$569$	−11.5727	+	27.9391i	−0.485154	+	1.17127i	−0.957131	+	0.289655i	$0.906459\pi$
$570$	−8.14480	−	4.91914i	−0.341148	−	0.206040i
$571$	7.03644	+	10.5308i	0.294466	+	0.440700i	0.948973	−	0.315356i	$-0.102124\pi$
$571$	7.03644	+	10.5308i	0.294466	+	0.440700i	−0.654507	+	0.756056i	$0.727124\pi$
$572$	7.29294	+	30.7275i	0.304933	+	1.28478i
$573$	8.15299	+	2.23135i	0.340596	+	0.0932160i
$574$	11.2308	+	3.18311i	0.468763	+	0.132860i
$575$	9.25981			0.386161
$576$	13.9564	−	19.5248i	0.581518	−	0.813534i
$577$	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
$579$	12.5785	+	3.44255i	0.522746	+	0.143068i
$580$	19.9181	−	4.72741i	0.827055	−	0.196295i
$581$	−18.7993	−	28.1351i	−0.779925	−	1.16724i
$582$	−8.24271	−	4.97828i	−0.341671	−	0.206356i
$583$	8.29835	−	20.0340i	0.343682	−	0.829723i
$584$	−17.5997	+	37.7900i	−0.728281	+	1.56376i
$585$	−26.7962	+	45.2877i	−1.10789	+	1.87242i
$586$	5.45476	+	16.8623i	0.225334	+	0.696574i
$587$	43.4391	+	8.64058i	1.79292	+	0.356635i	0.975602	−	0.219546i	$-0.0704575\pi$
$587$	43.4391	+	8.64058i	1.79292	+	0.356635i	0.817322	+	0.576180i	$0.195457\pi$
$588$	0.490208	−	14.3647i	0.0202158	−	0.592388i
$589$	0.0611921	+	0.0408873i	0.00252138	+	0.00168473i
$590$	−7.10745	+	8.99179i	−0.292609	+	0.370186i
$591$	−8.50062	−	25.4887i	−0.349669	−	1.04846i
$592$	−19.6522	+	34.6691i	−0.807699	+	1.42489i
$593$	−12.4091	−	12.4091i	−0.509580	−	0.509580i	0.404817	−	0.914398i	$-0.367335\pi$
$593$	−12.4091	−	12.4091i	−0.509580	−	0.509580i	−0.914398	+	0.404817i	$0.867335\pi$
$594$	−16.6042	+	5.07873i	−0.681278	+	0.208383i
$595$	−35.2516	−	23.5543i	−1.44517	−	0.965634i
$596$	14.0669	+	13.0710i	0.576203	+	0.535410i
$597$	−12.2928	+	15.8443i	−0.503111	+	0.648463i
$598$	41.2462	+	21.0833i	1.68668	+	0.862159i
$599$	5.32882	+	12.8649i	0.217730	+	0.525646i	0.994572	−	0.104049i	$-0.0331799\pi$
$599$	5.32882	+	12.8649i	0.217730	+	0.525646i	−0.776843	+	0.629695i	$0.783180\pi$
$600$	0.761795	+	9.22387i	0.0311001	+	0.376563i
$601$	−9.61422	+	23.2108i	−0.392172	+	0.946788i	0.597294	+	0.802023i	$0.296243\pi$
$601$	−9.61422	+	23.2108i	−0.392172	+	0.946788i	−0.989466	+	0.144765i	$0.953757\pi$
$602$	−1.63033	−	1.91388i	−0.0664473	−	0.0780040i
$603$	−10.5357	−	3.70244i	−0.429049	−	0.150775i
$604$	−32.9935	−	5.31326i	−1.34249	−	0.216194i
$605$	2.77373	+	13.9445i	0.112768	+	0.566923i
$606$	−0.154424	−	3.37514i	−0.00627307	−	0.137106i
$607$	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
$612$	−8.61239	+	27.7182i	−0.348135	+	1.12044i
$613$	16.6418	+	24.9062i	0.672154	+	1.00595i	0.998163	+	0.0605835i	$0.0192961\pi$
$613$	16.6418	+	24.9062i	0.672154	+	1.00595i	−0.326009	+	0.945367i	$0.605704\pi$
$614$	12.8228	+	15.0530i	0.517485	+	0.607488i
$615$	7.36463	+	8.48883i	0.296971	+	0.342303i
$616$	−3.40529	−	22.0542i	−0.137203	−	0.888588i
$617$	34.0519	−	14.1048i	1.37088	−	0.567836i	0.428852	−	0.903375i	$-0.358918\pi$
$617$	34.0519	−	14.1048i	1.37088	−	0.567836i	0.942027	+	0.335538i	$0.108918\pi$
$618$	−7.30778	+	5.38179i	−0.293962	+	0.216487i
$619$	29.7566	+	5.91895i	1.19602	+	0.237903i	0.752640	−	0.658433i	$-0.228780\pi$
$619$	29.7566	+	5.91895i	1.19602	+	0.237903i	0.443377	+	0.896335i	$0.353780\pi$
$620$	−0.00957317	−	0.260869i	−0.000384468	−	0.0104768i
$621$	−10.1222	+	23.3704i	−0.406191	+	0.937821i
$622$	−5.42937	−	46.3870i	−0.217698	−	1.85995i
$623$	−21.1110	+	21.1110i	−0.845796	+	0.845796i
$624$	−17.6082	+	42.8206i	−0.704891	+	1.71420i
$625$	21.8333	+	21.8333i	0.873332	+	0.873332i
$626$	−0.734019	+	0.928623i	−0.0293373	+	0.0371152i
$627$	3.00038	+	5.26155i	0.119824	+	0.210126i
$628$	2.11155	+	0.785209i	0.0842600	+	0.0313332i
$629$	9.40261	−	47.2701i	0.374907	−	1.88478i
$630$	21.4262	−	30.3888i	0.853641	−	1.21072i
$631$	−5.45257	−	13.1637i	−0.217063	−	0.524037i	0.777414	−	0.628989i	$-0.216531\pi$
$631$	−5.45257	−	13.1637i	−0.217063	−	0.524037i	−0.994477	+	0.104952i	$0.966531\pi$
$632$	0.292727	−	6.77915i	0.0116440	−	0.269660i
$633$	−24.4216	−	28.1496i	−0.970672	−	1.11884i
$634$	1.54308	−	19.2875i	0.0612837	−	0.766003i
$635$	−4.60575	+	3.07747i	−0.182774	+	0.122126i
$636$	27.0201	−	16.7502i	1.07142	−	0.664189i
$637$	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	$0.955522\pi$
$642$	3.28158	+	2.99443i	0.129513	+	0.118181i
$643$	29.0442	−	5.77725i	1.14539	−	0.227832i	0.414318	−	0.910132i	$-0.364020\pi$
$643$	29.0442	−	5.77725i	1.14539	−	0.227832i	0.731072	+	0.682300i	$0.239020\pi$
$644$	−27.8640	−	17.1745i	−1.09800	−	0.676769i
$645$	−0.303107	−	2.40142i	−0.0119348	−	0.0945559i
$646$	10.0926	+	0.807457i	0.397090	+	0.0317690i
$647$	43.7051	+	18.1032i	1.71822	+	0.711711i	0.999871	+	0.0160315i	$0.00510319\pi$
$647$	43.7051	+	18.1032i	1.71822	+	0.711711i	0.718352	+	0.695680i	$0.244897\pi$
$648$	−24.1124	−	8.16029i	−0.947226	−	0.320567i
$649$	6.74065	−	2.79207i	0.264594	−	0.109598i
$650$	−5.49545	−	16.9881i	−0.215549	−	0.666327i
$651$	−0.176293	+	0.227225i	−0.00690948	+	0.00890567i
$652$	−14.1433	+	38.0335i	−0.553894	+	1.48951i
$653$	14.1402	−	21.1623i	0.553348	−	0.828143i	−0.444358	−	0.895849i	$-0.646568\pi$
$653$	14.1402	−	21.1623i	0.553348	−	0.828143i	0.997705	+	0.0677063i	$0.0215681\pi$
$654$	−8.00015	−	17.0632i	−0.312830	−	0.667226i
$655$	20.3297	−	20.3297i	0.794347	−	0.794347i
$656$	7.48561	+	6.46065i	0.292264	+	0.252246i
$657$	43.7736	+	6.23952i	1.70777	+	0.243427i
$658$	−16.7100	+	1.95582i	−0.651422	+	0.0762459i
$659$	−18.1263	+	27.1279i	−0.706100	+	1.05675i	0.288947	+	0.957345i	$0.406695\pi$
$659$	−18.1263	+	27.1279i	−0.706100	+	1.05675i	−0.995047	+	0.0994083i	$0.968305\pi$
$660$	8.89379	−	19.5568i	0.346190	−	0.761246i
$661$	5.91065	−	29.7149i	0.229898	−	1.15577i	−0.677507	−	0.735516i	$-0.736940\pi$
$661$	5.91065	−	29.7149i	0.229898	−	1.15577i	0.907405	−	0.420258i	$-0.138060\pi$
$662$	−15.6123	−	7.98035i	−0.606790	−	0.310165i
$663$	3.96071	−	55.8540i	0.153821	−	2.16919i
$664$	−4.37395	−	28.3276i	−0.169742	−	1.09932i
$665$	−11.9831	−	4.96358i	−0.464686	−	0.192479i
$666$	41.2371	+	9.28299i	1.59791	+	0.359708i
$667$	−15.8927	+	10.6192i	−0.615368	+	0.411176i
$668$	0.465467	−	0.336344i	0.0180095	−	0.0130135i
$669$	2.43483	+	0.666375i	0.0941358	+	0.0257635i
$670$	12.0644	−	6.73591i	0.466090	−	0.260231i
$671$		−	11.3347i		−	0.437569i
$672$	14.8155	−	29.1688i	0.571520	−	1.12521i
$673$		−	11.0359i		−	0.425402i	−0.977117	−	0.212701i	$-0.931774\pi$
$673$		−	11.0359i		−	0.425402i	0.977117	−	0.212701i	$-0.0682259\pi$
$674$	−22.2271	−	39.8101i	−0.856154	−	1.53343i
$675$	9.12851	−	3.61082i	0.351356	−	0.138981i
$676$	10.0671	−	62.5133i	0.387197	−	2.40436i
$677$	16.1303	−	10.7779i	0.619939	−	0.414230i	−0.205551	−	0.978646i	$-0.565899\pi$
$677$	16.1303	−	10.7779i	0.619939	−	0.414230i	0.825490	+	0.564416i	$0.190899\pi$
$678$	6.37863	+	25.8335i	0.244970	+	0.992129i
$679$	−12.1272	−	5.02324i	−0.465399	−	0.192774i
$680$	−18.6456	−	30.6938i	−0.715027	−	1.17706i
$681$	−34.1185	−	2.41941i	−1.30743	−	0.0927121i
$682$	−0.0756319	+	0.147962i	−0.00289609	+	0.00566576i
$683$	9.44062	−	47.4612i	0.361235	−	1.81605i	−0.190095	−	0.981766i	$-0.560880\pi$
$683$	9.44062	−	47.4612i	0.361235	−	1.81605i	0.551331	−	0.834287i	$-0.314120\pi$
$684$	−0.929833	+	8.83093i	−0.0355530	+	0.337659i
$685$	−5.14927	+	7.70643i	−0.196744	+	0.294448i
$686$	1.56499	+	13.3708i	0.0597516	+	0.510500i
$687$	−0.923276	−	2.76840i	−0.0352252	−	0.105621i
$688$	−0.567460	−	2.05269i	−0.0216342	−	0.0782581i
$689$	−43.3662	+	43.3662i	−1.65212	+	1.65212i
$690$	−13.3773	−	28.5319i	−0.509263	−	1.08619i
$691$	−2.62103	+	3.92264i	−0.0997085	+	0.149224i	−0.877969	−	0.478717i	$-0.841102\pi$
$691$	−2.62103	+	3.92264i	−0.0997085	+	0.149224i	0.778261	+	0.627941i	$0.216102\pi$
$692$	11.1684	+	24.3920i	0.424558	+	0.927244i
$693$	−21.3389	+	10.2411i	−0.810598	+	0.389029i
$694$	−37.1233	+	12.0090i	−1.40918	+	0.455854i
$695$	−28.0267	+	11.6090i	−1.06311	+	0.440356i
$696$	−11.8854	−	14.9574i	−0.450516	−	0.566958i
$697$	−11.0483	−	4.57634i	−0.418483	−	0.173341i
$698$	0.937481	−	11.7179i	0.0354842	−	0.443528i
$699$	26.8126	−	3.38429i	1.01415	−	0.128005i
$700$	2.91346	+	12.2754i	0.110118	+	0.463965i
$701$	0.420755	−	0.0836934i	0.0158917	−	0.00316106i	−0.187138	−	0.982334i	$-0.559921\pi$
$701$	0.420755	−	0.0836934i	0.0158917	−	0.00316106i	0.203030	+	0.979173i	$0.434921\pi$
$702$	48.8826	+	4.70055i	1.84496	+	0.177411i
$703$		−	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
$708$	10.4135	+	2.44334i	0.391365	+	0.0918264i
$709$	25.3814	−	16.9593i	0.953218	−	0.636920i	0.0213708	−	0.999772i	$-0.493197\pi$
$709$	25.3814	−	16.9593i	0.953218	−	0.636920i	0.931847	+	0.362852i	$0.118197\pi$
$710$	50.6561	+	4.05271i	1.90109	+	0.152096i
$711$	−6.97135	+	1.78834i	−0.261446	+	0.0670679i
$712$	−23.7607	+	8.66109i	−0.890470	+	0.324588i
$713$	0.0932734	+	0.225182i	0.00349312	+	0.00843313i
$714$	−5.93723	+	39.1180i	−0.222195	+	1.46395i
$715$	−8.08572	+	40.6497i	−0.302389	+	1.52021i
$716$	13.8176	+	30.1779i	0.516387	+	1.12780i
$717$	−1.46877	+	0.837563i	−0.0548523	+	0.0312794i
$718$	9.89146	+	7.81858i	0.369146	+	0.291787i
$719$	4.47853	+	4.47853i	0.167021	+	0.167021i	0.785669	−	0.618648i	$-0.212319\pi$
$719$	4.47853	+	4.47853i	0.167021	+	0.167021i	−0.618648	+	0.785669i	$0.712319\pi$
$720$	27.3206	−	15.6726i	1.01818	−	0.584084i
$721$	−8.74797	+	8.74797i	−0.325791	+	0.325791i
$722$	−23.6114	+	2.76360i	−0.878724	+	0.102850i
$723$	12.8745	+	22.5770i	0.478808	+	0.839649i
$724$	0.550667	+	0.511682i	0.0204654	+	0.0190165i
$725$	7.22588	+	1.43732i	0.268363	+	0.0533806i
$726$	10.6838	−	7.86806i	0.396514	−	0.292011i
$727$	−3.41297	+	1.41370i	−0.126580	+	0.0524311i	−0.445074	−	0.895494i	$-0.646823\pi$
$727$	−3.41297	+	1.41370i	−0.126580	+	0.0524311i	0.318494	+	0.947925i	$0.396823\pi$
$728$	−14.9718	+	61.3119i	−0.554891	+	2.27237i
$729$	−0.865518	+	26.9861i	−0.0320562	+	0.999486i
$730$	−41.6470	+	35.4768i	−1.54143	+	1.31306i
$731$	1.43094	+	2.14155i	0.0529250	+	0.0792079i
$732$	9.69787	−	13.4938i	0.358444	−	0.498744i
$733$	−1.76647	+	0.351374i	−0.0652462	+	0.0129783i	−0.227605	−	0.973753i	$-0.573090\pi$
$733$	−1.76647	+	0.351374i	−0.0652462	+	0.0129783i	0.162359	+	0.986732i	$0.448090\pi$
$734$	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
$738$	4.25519	−	9.58590i	0.156636	−	0.352862i
$739$	−7.50862	−	37.7484i	−0.276209	−	1.38860i	−0.830845	−	0.556504i	$-0.812143\pi$
$739$	−7.50862	−	37.7484i	−0.276209	−	1.38860i	0.554636	−	0.832093i	$-0.312857\pi$
$740$	−42.3910	+	30.6315i	−1.55833	+	1.12604i
$741$	−2.14517	−	16.9955i	−0.0788049	−	0.624345i
$742$	32.9891	−	28.1016i	1.21107	−	1.03164i
$743$	13.3142	−	32.1432i	0.488449	−	1.17922i	−0.467051	−	0.884230i	$-0.654684\pi$
$743$	13.3142	−	32.1432i	0.488449	−	1.17922i	0.955500	−	0.294990i	$-0.0953165\pi$
$744$	−0.216634	+	0.111437i	−0.00794220	+	0.00408547i
$745$	9.64382	+	23.2822i	0.353322	+	0.852995i
$746$	19.8565	−	38.8461i	0.726997	−	1.42226i
$747$	−27.4089	+	13.1543i	−1.00284	+	0.481291i
$748$	0.838375	+	22.8458i	0.0306540	+	0.835323i
$749$	5.03516	+	3.36439i	0.183981	+	0.122932i
$750$	6.80113	−	18.8081i	0.248342	−	0.686774i
$751$	30.0300	+	30.0300i	1.09581	+	1.09581i	0.994895	+	0.100914i	$0.0321768\pi$
$751$	30.0300	+	30.0300i	1.09581	+	1.09581i	0.100914	+	0.994895i	$0.467823\pi$
$752$	−13.5308	−	4.47402i	−0.493418	−	0.163151i
$753$	44.9449	−	14.9894i	1.63788	−	0.546244i
$754$	28.9138	+	22.8546i	1.05298	+	0.832314i
$755$	−36.4661	−	24.3659i	−1.32714	−	0.886766i
$756$	−34.1660	−	6.06550i	−1.24261	−	0.220600i
$757$	37.4839	+	7.45600i	1.36237	+	0.270993i	0.821547	−	0.570141i	$-0.193111\pi$
$757$	37.4839	+	7.45600i	1.36237	+	0.270993i	0.540827	+	0.841134i	$0.318111\pi$
$758$	31.0251	−	10.0363i	1.12688	−	0.364534i
$759$	−1.41890	+	20.0093i	−0.0515027	+	0.726290i
$760$	−7.42660	−	8.09691i	−0.269391	−	0.293706i
$761$	−5.61157	+	13.5475i	−0.203419	+	0.491097i	−0.992361	−	0.123371i	$-0.960629\pi$
$761$	−5.61157	+	13.5475i	−0.203419	+	0.491097i	0.788941	+	0.614468i	$0.210629\pi$
$762$	4.42502	+	2.67254i	0.160302	+	0.0968159i
$763$	−14.2723	−	21.3600i	−0.516692	−	0.773284i
$764$	8.30894	+	5.12137i	0.300607	+	0.185285i
$765$	−25.4204	+	28.3690i	−0.919075	+	1.02568i
$766$	4.44868	−	15.6960i	0.160737	−	0.567120i
$767$	−20.6348			−0.745081
$768$	21.8081	−	17.1000i	0.786930	−	0.617042i
$769$	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
$771$	2.06581	−	7.54813i	0.0743982	−	0.271839i
$772$	12.8191	+	7.90130i	0.461371	+	0.284374i
$773$	9.82391	+	14.7025i	0.353341	+	0.528813i	0.964980	−	0.262325i	$-0.0844892\pi$
$773$	9.82391	+	14.7025i	0.353341	+	0.528813i	−0.611638	+	0.791138i	$0.709489\pi$
$774$	−1.90905	+	1.20748i	−0.0686194	+	0.0434020i
$775$	0.0359520	−	0.0867959i	0.00129144	−	0.00311780i
$776$	−7.51588	−	8.19425i	−0.269804	−	0.294156i
$777$	57.4749	+	4.07566i	2.06190	+	0.146214i
$778$	31.2292	−	10.1023i	1.11962	−	0.362185i
$779$	−3.58819	−	0.713736i	−0.128560	−	0.0255722i
$780$	−44.4056	+	41.4749i	−1.58998	+	1.48504i
$781$	−26.8971	−	17.9721i	−0.962453	−	0.643091i
$782$	26.3063	+	20.7935i	0.940713	+	0.743575i
$783$	−11.5264	+	16.6659i	−0.411922	+	0.595590i
$784$	5.21028	−	15.7575i	0.186081	−	0.562767i
$785$	2.09058	+	2.09058i	0.0746160	+	0.0746160i
$786$	−25.2320	−	9.12406i	−0.899995	−	0.325444i
$787$	−30.2625	−	20.2207i	−1.07874	−	0.720791i	−0.116554	−	0.993184i	$-0.537185\pi$
$787$	−30.2625	−	20.2207i	−1.07874	−	0.720791i	−0.962186	+	0.272393i	$0.912185\pi$
$788$	−1.13778	−	31.0046i	−0.0405318	−	1.10449i
$789$	3.03568	+	2.35523i	0.108073	+	0.0838486i
$790$	4.05306	−	7.92919i	0.144201	−	0.282108i
$791$	13.8809	+	33.5115i	0.493549	+	1.19153i
$792$	−20.0483	+	0.232751i	−0.712387	+	0.00827043i
$793$	−12.2677	+	29.6168i	−0.435638	+	1.05172i
$794$	3.37278	−	2.87308i	0.119695	−	0.101962i
$795$	41.3927	−	5.22459i	1.46805	−	0.185297i
$796$	−18.7689	+	13.5623i	−0.665244	+	0.480702i
$797$	−4.54990	−	22.8739i	−0.161166	−	0.810234i	−0.973790	−	0.227447i	$-0.926962\pi$
$797$	−4.54990	−	22.8739i	−0.161166	−	0.810234i	0.812625	−	0.582787i	$-0.198038\pi$
$798$	0.553243	+	12.0918i	0.0195846	+	0.428046i
$799$	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
$804$	−10.4712	−	7.52557i	−0.369291	−	0.265406i
$805$	−23.8651	−	35.7166i	−0.841134	−	1.25885i
$806$	0.357764	−	0.304759i	0.0126017	−	0.0107347i
$807$	−30.1793	+	26.1826i	−1.06236	+	0.921671i
$808$	0.925478	−	3.78999i	0.0325582	−	0.133331i
$809$	−18.3664	+	7.60762i	−0.645729	+	0.267470i	−0.681419	−	0.731893i	$-0.738637\pi$
$809$	−18.3664	+	7.60762i	−0.645729	+	0.267470i	0.0356905	+	0.999363i	$0.488637\pi$
$810$	−24.3135	−	22.9109i	−0.854288	−	0.805008i
$811$	−46.0682	−	9.16353i	−1.61767	−	0.321775i	−0.698494	−	0.715616i	$-0.746146\pi$
$811$	−46.0682	−	9.16353i	−1.61767	−	0.321775i	−0.919179	+	0.393840i	$0.871146\pi$
$812$	−19.0778	−	17.7272i	−0.669499	−	0.622101i
$813$	9.96158	−	5.68056i	0.349368	−	0.199226i
$814$	33.0665	−	3.87028i	1.15898	−	0.135653i
$815$	−37.6558	+	37.6558i	−1.31903	+	1.31903i
$816$	−18.5486	+	27.9149i	−0.649332	+	0.977218i
$817$	0.557172	+	0.557172i	0.0194930	+	0.0194930i
$818$	−9.39846	−	7.42890i	−0.328609	−	0.259745i
$819$	66.8416	−	3.66408i	2.33563	−	0.128033i
$820$	5.40233	+	11.7988i	0.188658	+	0.412033i
$821$	−7.82812	+	39.3546i	−0.273203	+	1.37349i	0.563630	+	0.826028i	$0.309404\pi$
$821$	−7.82812	+	39.3546i	−0.273203	+	1.37349i	−0.836833	+	0.547458i	$0.815596\pi$
$822$	8.55169	+	1.29795i	0.298274	+	0.0452713i
$823$	10.4572	+	25.2460i	0.364516	+	0.880019i	0.994628	+	0.103515i	$0.0330090\pi$
$823$	10.4572	+	25.2460i	0.364516	+	0.880019i	−0.630112	+	0.776504i	$0.716991\pi$
$824$	−9.84593	+	3.58897i	−0.342999	+	0.125028i
$825$	5.84031	−	5.06686i	0.203333	−	0.176405i
$826$	14.5343	+	1.16281i	0.505714	+	0.0404594i
$827$	−13.3380	+	8.91218i	−0.463809	+	0.309907i	−0.765428	−	0.643521i	$-0.777473\pi$
$827$	−13.3380	+	8.91218i	−0.463809	+	0.309907i	0.301620	+	0.953428i	$0.402473\pi$
$828$	−18.8090	+	22.6068i	−0.653658	+	0.785641i
$829$	4.63371	+	23.2952i	0.160935	+	0.809077i	0.973938	+	0.226816i	$0.0728317\pi$
$829$	4.63371	+	23.2952i	0.160935	+	0.809077i	−0.813002	+	0.582261i	$0.802168\pi$
$830$	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
$834$	20.9126	+	19.0826i	0.724143	+	0.660778i
$835$	0.739173	−	0.147031i	0.0255801	−	0.00508820i
$836$	1.61509	+	6.80489i	0.0558589	+	0.235352i
$837$	0.179759	+	0.185617i	0.00621340	+	0.00641587i
$838$	−3.51798	+	43.9723i	−0.121527	+	1.51900i
$839$	−27.5815	−	11.4246i	−0.952220	−	0.394423i	−0.148155	−	0.988964i	$-0.547334\pi$
$839$	−27.5815	−	11.4246i	−0.952220	−	0.394423i	−0.804065	+	0.594542i	$0.797334\pi$
$840$	33.6147	−	26.7108i	1.15982	−	0.921611i
$841$	12.7423	−	5.27805i	0.439391	−	0.182002i
$842$	−8.53405	+	2.76067i	−0.294103	+	0.0951390i
$843$	−9.38597	−	7.28212i	−0.323270	−	0.250810i
$844$	−17.9145	−	39.1257i	−0.616643	−	1.34676i
$845$	46.1664	−	69.0930i	1.58817	−	2.37687i
$846$	−0.378940	+	15.1110i	−0.0130282	+	0.519528i
$847$	12.7894	−	12.7894i	0.439447	−	0.439447i
$848$	35.3817	−	9.78117i	1.21501	−	0.335887i
$849$	37.6367	−	12.5521i	1.29169	−	0.430785i
$850$	−1.50253	−	12.8372i	−0.0515365	−	0.440312i
$851$	27.1296	−	40.6023i	0.929991	−	1.39183i
$852$	−16.6439	−	44.4085i	−0.570209	−	1.52141i
$853$	0.300445	−	1.51044i	0.0102870	−	0.0517164i	−0.975301	−	0.220881i	$-0.929107\pi$
$853$	0.300445	−	1.51044i	0.0102870	−	0.0517164i	0.985588	+	0.169164i	$0.0541068\pi$
$854$	10.3098	−	20.1695i	0.352794	−	0.690188i
$855$	−5.93427	+	10.0294i	−0.202948	+	0.342997i
$856$	2.66325	+	4.38416i	0.0910280	+	0.149847i
$857$	6.92900	+	2.87008i	0.236690	+	0.0980402i	0.497876	−	0.867248i	$-0.334114\pi$
$857$	6.92900	+	2.87008i	0.236690	+	0.0980402i	−0.261186	+	0.965289i	$0.584114\pi$
$858$	37.5511	−	9.27186i	1.28197	−	0.316536i
$859$	12.3876	−	8.27714i	0.422660	−	0.282412i	−0.325996	−	0.945371i	$-0.605700\pi$
$859$	12.3876	−	8.27714i	0.422660	−	0.282412i	0.748656	+	0.662959i	$0.230700\pi$
$860$	0.444368	−	2.75937i	0.0151528	−	0.0940938i
$861$	3.77398	−	13.7895i	0.128617	−	0.469945i
$862$	−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	$0.822799\pi$
$864$	−24.0665	−	16.8762i	−0.818758	−	0.574139i
$865$			35.2072i			1.19708i
$866$	−0.318365	+	0.177752i	−0.0108185	+	0.00604025i
$867$	2.92712	−	10.6952i	0.0994101	−	0.363228i
$868$	−0.269168	+	0.194499i	−0.00913614	+	0.00660172i
$869$	−4.71327	+	3.14931i	−0.159887	+	0.106833i
$870$	−6.01018	−	24.3413i	−0.203764	−	0.825246i
$871$	22.9827	+	9.51975i	0.778739	+	0.322564i
$872$	−3.32067	−	21.5062i	−0.112452	−	0.728291i
$873$	−6.00560	+	10.1499i	−0.203259	+	0.343523i
$874$	9.13433	+	4.66908i	0.308973	+	0.157934i
$875$	5.31875	−	26.7392i	0.179807	−	0.903949i
$876$	46.4761	+	21.1358i	1.57028	+	0.714113i
$877$	13.8663	−	20.7524i	0.468232	−	0.700759i	−0.519924	−	0.854213i	$-0.674040\pi$
$877$	13.8663	−	20.7524i	0.468232	−	0.700759i	0.988156	+	0.153454i	$0.0490397\pi$
$878$	−56.5688	+	6.62111i	−1.90910	+	0.223452i
$879$	20.5907	−	6.86713i	0.694509	−	0.231623i
$880$	16.2088	−	18.7803i	0.546398	−	0.633082i
$881$	−22.9018	+	22.9018i	−0.771582	+	0.771582i	−0.978383	−	0.206801i	$-0.933695\pi$
$881$	−22.9018	+	22.9018i	−0.771582	+	0.771582i	0.206801	+	0.978383i	$0.433695\pi$
$882$	−17.5977	−	0.441299i	−0.592547	−	0.0148593i
$883$	10.2732	−	15.3750i	0.345722	−	0.517409i	−0.617338	−	0.786698i	$-0.711789\pi$
$883$	10.2732	−	15.3750i	0.345722	−	0.517409i	0.963059	+	0.269289i	$0.0867888\pi$
$884$	22.5357	−	60.6021i	0.757958	−	2.03827i
$885$	11.0909	+	8.60490i	0.372817	+	0.289250i
$886$	2.88042	+	8.90422i	0.0967695	+	0.299143i
$887$	−9.52810	+	3.94667i	−0.319922	+	0.132516i	−0.536865	−	0.843668i	$-0.680392\pi$
$887$	−9.52810	+	3.94667i	−0.319922	+	0.132516i	0.216943	+	0.976184i	$0.430392\pi$
$888$	42.6767	+	23.6840i	1.43214	+	0.794784i
$889$	6.51036	+	2.69668i	0.218350	+	0.0904437i
$890$	−33.0841	−	2.64687i	−1.10898	−	0.0887234i
$891$	6.40375	+	20.2788i	0.214534	+	0.679366i
$892$	2.48140	+	1.52946i	0.0830834	+	0.0512100i
$893$	5.17151	−	1.02868i	0.173058	−	0.0344234i
$894$	15.8523	−	17.3724i	0.530179	−	0.581020i
$895$			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
$900$	11.2880	−	1.03510i	0.376267	−	0.0345033i
$901$	−36.9133	+	24.6647i	−1.22976	+	0.821700i
$902$	0.658776	−	8.23424i	0.0219348	−	0.274170i
$903$	−2.32587	+	2.01785i	−0.0774001	+	0.0671498i
$904$	−1.32552	+	30.6972i	−0.0440861	+	1.02097i
$905$	0.377519	+	0.911413i	0.0125492	+	0.0302964i
$906$	−6.14180	+	40.4658i	−0.204048	+	1.34439i
$907$	6.38322	−	32.0906i	0.211951	−	1.06555i	−0.717487	−	0.696572i	$-0.754708\pi$
$907$	6.38322	−	32.0906i	0.211951	−	1.06555i	0.929438	−	0.368979i	$-0.120292\pi$
$908$	−37.0189	−	13.7660i	−1.22852	−	0.456841i
$909$	−4.13180	+	0.226495i	−0.137043	+	0.00751235i
$910$	−51.3625	+	64.9798i	−1.70265	+	2.15406i
$911$	20.1753	+	20.1753i	0.668438	+	0.668438i	0.957354	−	0.288916i	$-0.0932950\pi$
$911$	20.1753	+	20.1753i	0.668438	+	0.668438i	−0.288916	+	0.957354i	$0.593295\pi$
$912$	−3.89949	+	9.48300i	−0.129125	+	0.314013i
$913$	−16.9320	+	16.9320i	−0.560367	+	0.560367i
$914$	3.29240	+	28.1293i	0.108903	+	0.930433i
$915$	18.9441	−	10.8028i	0.626274	−	0.357131i
$916$	−0.123577	−	3.36749i	−0.00408312	−	0.111265i
$917$	−35.8720	−	7.13538i	−1.18460	−	0.235631i
$918$	34.0417	+	10.2406i	1.12354	+	0.337991i
$919$	−44.0591	+	18.2499i	−1.45338	+	0.602008i	−0.963000	−	0.269502i	$-0.913141\pi$
$919$	−44.0591	+	18.2499i	−1.45338	+	0.602008i	−0.490377	+	0.871510i	$0.663141\pi$
$920$	−5.55259	−	35.9610i	−0.183063	−	1.18560i
$921$	18.2933	−	15.8707i	0.602785	−	0.522956i
$922$	32.0293	+	37.6000i	1.05483	+	1.23829i
$923$	50.8291	+	76.0711i	1.67306	+	2.50391i
$924$	−26.9719	+	4.41464i	−0.887311	+	0.145231i
$925$	−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	$-0.652519\pi$
$929$	−28.1038			−0.922057			−0.461028	+	0.887385i	$0.652519\pi$
$930$	−0.319379	+	0.0146127i	−0.0104729	+	0.000479170i
$931$	1.19796	+	6.02255i	0.0392616	+	0.197381i
$932$	30.8092	+	4.96151i	1.00919	+	0.162520i
$933$	−56.7498	+	7.16296i	−1.85790	+	0.234505i
$934$	−10.9319	−	12.8332i	−0.357703	−	0.419916i
$935$	−11.4813	+	27.7184i	−0.375480	+	0.906489i
$936$	52.6371	+	21.0905i	1.72050	+	0.689364i
$937$	−7.86396	−	18.9853i	−0.256904	−	0.620222i	0.741826	−	0.670592i	$-0.233960\pi$
$937$	−7.86396	−	18.9853i	−0.256904	−	0.620222i	−0.998731	+	0.0503700i	$0.983960\pi$
$938$	−15.6516	−	8.00043i	−0.511043	−	0.261223i
$939$	1.14541	+	0.888667i	0.0373790	+	0.0290005i
$940$	−13.7011	−	12.7311i	−0.446879	−	0.415242i
$941$	43.2971	+	28.9302i	1.41145	+	0.943098i	0.999491	+	0.0318944i	$0.0101540\pi$
$941$	43.2971	+	28.9302i	1.41145	+	0.943098i	0.411955	+	0.911204i	$0.364846\pi$
$942$	0.938261	−	2.59470i	0.0305702	−	0.0845398i
$943$	−8.56753	−	8.56753i	−0.278997	−	0.278997i
$944$	10.7449	+	6.09072i	0.349716	+	0.198236i
$945$	−37.4542	−	25.9041i	−1.21839	−	0.842660i
$946$	−1.10327	+	1.39577i	−0.0358703	+	0.0453802i
$947$	−13.0677	−	8.73155i	−0.424643	−	0.283737i	0.324830	−	0.945772i	$-0.394693\pi$
$947$	−13.0677	−	8.73155i	−0.424643	−	0.283737i	−0.749473	+	0.662035i	$0.769693\pi$
$948$	−8.30563	−	0.283438i	−0.269754	−	0.00920562i
$949$	−96.6027	−	19.2155i	−3.13586	−	0.623760i
$950$	−1.21702	−	3.76216i	−0.0394852	−	0.122060i
$951$	−23.6384	−	1.67624i	−0.766526	−	0.0543559i
$952$	−19.2883	+	41.4157i	−0.625136	+	1.34229i
$953$	−18.0842	+	43.6591i	−0.585804	+	1.41426i	0.301676	+	0.953411i	$0.402454\pi$
$953$	−18.0842	+	43.6591i	−0.585804	+	1.41426i	−0.887480	+	0.460846i	$0.847546\pi$
$954$	−20.8131	−	32.9059i	−0.673848	−	1.06537i
$955$	7.11648	+	10.6506i	0.230284	+	0.344644i
$956$	−1.89960	+	0.450854i	−0.0614374	+	0.0145817i
$957$	−4.21309	+	15.3940i	−0.136190	+	0.497616i
$958$	−51.6194	−	14.6304i	−1.66775	−	0.472685i
$959$	11.7908			0.380744
$960$	35.3647	−	8.48951i	1.14139	−	0.273998i
$961$	−30.9975			−0.999920
$962$	−90.5898	−	25.6756i	−2.92073	−	0.827815i
$963$	3.63092	−	4.05208i	0.117005	−	0.130577i
$964$	6.93025	+	29.1994i	0.223208	+	0.940450i
$965$	10.9794	+	16.4318i	0.353439	+	0.528959i
$966$	−20.7250	+	34.3151i	−0.666815	+	1.10407i
$967$	7.60618	−	18.3629i	0.244598	−	0.590512i	−0.753131	−	0.657871i	$-0.771457\pi$
$967$	7.60618	−	18.3629i	0.244598	−	0.590512i	0.997729	+	0.0673588i	$0.0214572\pi$
$968$	14.3945	−	5.24700i	0.462658	−	0.168645i
$969$	0.877135	−	12.3694i	0.0281776	−	0.397361i
$970$	−4.49130	−	13.8839i	−0.144207	−	0.445787i
$971$	−23.2362	−	4.62196i	−0.745685	−	0.148326i	−0.192398	−	0.981317i	$-0.561627\pi$
$971$	−23.2362	−	4.62196i	−0.745685	−	0.148326i	−0.553286	+	0.832991i	$0.686627\pi$
$972$	−9.72688	+	29.6207i	−0.311990	+	0.950085i
$973$	32.0877	+	21.4403i	1.02868	+	0.687344i
$974$	−19.1077	+	24.1735i	−0.612250	+	0.774570i
$975$	−20.7443	+	6.91835i	−0.664351	+	0.221565i
$976$	15.1299	−	11.8009i	0.484295	−	0.377738i
$977$	18.8219	+	18.8219i	0.602164	+	0.602164i	0.940886	−	0.338722i	$-0.109995\pi$
$977$	18.8219	+	18.8219i	0.602164	+	0.602164i	−0.338722	+	0.940886i	$0.609995\pi$
$978$	46.7361	+	16.9001i	1.49446	+	0.540405i
$979$	17.5668	+	11.7377i	0.561437	+	0.375140i
$980$	14.8261	−	15.9557i	0.473604	−	0.509688i
$981$	−20.8087	+	9.98667i	−0.664370	+	0.318850i
$982$	−25.8020	−	13.1889i	−0.823373	−	0.420873i
$983$	−13.8501	−	33.4371i	−0.441750	−	1.06648i	−0.975335	−	0.220731i	$-0.929156\pi$
$983$	−13.8501	−	33.4371i	−0.441750	−	1.06648i	0.533585	−	0.845746i	$-0.320844\pi$
$984$	7.82944	−	9.23912i	0.249593	−	0.294532i
$985$	15.5816	−	37.6174i	0.496472	−	1.19859i
$986$	17.3005	+	20.3095i	0.550961	+	0.646786i
$987$	2.58031	+	20.4429i	0.0821321	+	0.650706i
$988$	3.14491	−	19.5288i	0.100053	−	0.621295i
$989$	0.509107	+	2.55945i	0.0161886	+	0.0813858i
$990$	−24.0496	−	10.6756i	−0.764345	−	0.339294i
$991$	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
$996$	−34.6443	+	5.67041i	−1.09775	+	0.179674i
$997$	25.8757	+	38.7257i	0.819492	+	1.22646i	0.971256	+	0.238039i	$0.0765047\pi$
$997$	25.8757	+	38.7257i	0.819492	+	1.22646i	−0.151764	+	0.988417i	$0.548495\pi$
$998$	−17.8502	−	20.9547i	−0.565038	−	0.663311i
$999$	10.9122	−	50.6057i	0.345247	−	1.60109i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
192.2.s.a.107.13	✓	240	3.2	odd	2	inner
192.2.s.a.107.18	yes	240	1.1	even	1	trivial
192.2.s.a.131.13	yes	240	64.3	odd	16	inner
192.2.s.a.131.18	yes	240	192.131	even	16	inner
768.2.s.a.335.24		240	12.11	even	2
768.2.s.a.335.28		240	4.3	odd	2
768.2.s.a.431.24		240	64.61	even	16
768.2.s.a.431.28		240	192.125	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.385637 - 1.36062i) q^{2} +(-1.67061 - 0.457221i) q^{3} +(-1.70257 - 1.04941i) q^{4} +(-1.45822 - 2.18239i) q^{5} +(-1.26635 + 2.09675i) q^{6} +(-1.27779 + 3.08486i) q^{7} +(-2.08442 + 1.91186i) q^{8} +(2.58190 + 1.52768i) q^{9} +(-3.53174 + 1.14248i) q^{10} +(2.31748 + 0.460975i) q^{11} +(2.36452 + 2.53161i) q^{12} +(-5.55652 - 3.71275i) q^{13} +(3.70456 + 2.92822i) q^{14} +(1.43829 + 4.31265i) q^{15} +(1.79748 + 3.57338i) q^{16} +(-3.42067 - 3.42067i) q^{17} +(3.07426 - 2.92385i) q^{18} +(-1.23054 - 0.822221i) q^{19} +(0.192511 + 5.24594i) q^{20} +(3.54516 - 4.56938i) q^{21} +(1.52092 - 2.97544i) q^{22} +(-1.87568 - 4.52828i) q^{23} +(4.35640 - 2.24093i) q^{24} +(-0.722975 + 1.74542i) q^{25} +(-7.19443 + 6.12853i) q^{26} +(-3.61486 - 3.73266i) q^{27} +(5.41281 - 3.91127i) q^{28} +(-0.760797 - 3.82478i) q^{29} +(6.42254 - 0.293854i) 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} +(-2.79270 - 5.31045i) q^{36} +(5.53510 + 8.28386i) q^{37} +(-1.59327 + 1.35722i) q^{38} +(7.58524 + 8.74312i) q^{39} +(7.21196 + 1.76109i) q^{40} +(2.28385 - 0.946002i) q^{41} +(-4.85004 - 6.58573i) q^{42} +(-0.522190 - 0.103870i) q^{43} +(-3.46191 - 3.21682i) q^{44} +(-0.430996 - 7.86240i) q^{45} +(-6.88460 + 0.805810i) q^{46} +(-2.51930 + 2.51930i) q^{47} +(-1.36907 - 6.79159i) q^{48} +(-2.93388 - 2.93388i) q^{49} +(2.09604 + 1.65679i) q^{50} +(4.15061 + 7.27862i) q^{51} +(5.56417 + 12.1523i) q^{52} +(1.79038 - 9.00087i) q^{53} +(-6.47275 + 3.47900i) q^{54} +(-2.37338 - 5.72983i) q^{55} +(-3.23436 - 8.87310i) q^{56} +(1.67982 + 1.93624i) q^{57} +(-5.49747 - 0.439822i) q^{58} +(2.56739 - 1.71547i) q^{59} +(2.07694 - 8.85195i) 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} +(-3.90129 + 4.27541i) q^{66} +(-3.65093 + 0.726215i) q^{67} +(2.23425 + 9.41361i) q^{68} +(1.06310 + 8.42261i) q^{69} +(0.988438 - 12.3548i) q^{70} +(-12.6483 - 5.23910i) q^{71} +(-8.30246 + 1.75189i) q^{72} +(13.6168 - 5.64025i) q^{73} +(13.4057 - 4.33660i) q^{74} +(2.00585 - 2.58536i) q^{75} +(1.23223 + 2.69123i) q^{76} +(-4.38330 + 6.56007i) q^{77} +(14.8212 - 6.94896i) q^{78} +(-1.69637 + 1.69637i) q^{79} +(5.17737 - 9.13359i) q^{80} +(4.33239 + 7.88863i) q^{81} +(-0.406412 - 3.47226i) q^{82} +(-5.63016 + 8.42612i) q^{83} +(-10.8310 + 4.05936i) q^{84} +(-2.47712 + 12.4533i) q^{85} +(-0.342703 + 0.670446i) q^{86} +(-0.477776 + 6.73759i) q^{87} +(-5.71191 + 3.46982i) q^{88} +(8.26075 + 3.42172i) q^{89} +(-10.8639 - 2.44561i) q^{90} +(18.5534 - 12.3970i) q^{91} +(-1.55855 + 9.67806i) q^{92} +(0.0830760 + 0.0227366i) q^{93} +(2.45627 + 4.39934i) q^{94} +3.88450i q^{95} +(-9.76873 - 0.756300i) q^{96} +3.93119i q^{97} +(-5.12330 + 2.86048i) q^{98} +(5.27927 + 4.73055i) 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

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