LMFDB - Embedded newform 650.2.p.a.181.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(181,650)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([4, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("650.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.p (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$34$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			181.4
Character	$\chi$	$=$	650.181
Dual form			650.2.p.a.571.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.951057 + 0.309017i) q^{2} +(-1.63416 + 1.18728i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.970013 - 2.01471i) q^{5} +(1.18728 - 1.63416i) q^{6} +1.37615i q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.333771 - 1.02724i) q^{9} +O(q^{10})$	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.63416 + 1.18728i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.970013 - 2.01471i) q^{5} +(1.18728 - 1.63416i) q^{6} +1.37615i q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.333771 - 1.02724i) q^{9} +(1.54512 + 1.61636i) q^{10} +(-2.30628 + 0.749357i) q^{11} +(-0.624192 + 1.92106i) q^{12} +(-2.58923 - 2.50916i) q^{13} +(-0.425253 - 1.30880i) q^{14} +(3.97719 + 2.14068i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.57930 + 1.14743i) q^{17} +1.08010i q^{18} +(4.48315 - 6.17053i) q^{19} +(-1.96898 - 1.05978i) q^{20} +(-1.63388 - 2.24884i) q^{21} +(1.96184 - 1.42536i) q^{22} +(2.14375 + 6.59778i) q^{23} -2.01993i q^{24} +(-3.11815 + 3.90860i) q^{25} +(3.23788 + 1.58624i) q^{26} +(-1.19838 - 3.68824i) q^{27} +(0.808880 + 1.11333i) q^{28} +(0.639025 - 0.464279i) q^{29} +(-4.44404 - 0.806886i) q^{30} +(4.81874 - 6.63243i) q^{31} +1.00000i q^{32} +(2.87913 - 3.96278i) q^{33} +(-1.85658 - 0.603238i) q^{34} +(2.77255 - 1.33488i) q^{35} +(-0.333771 - 1.02724i) q^{36} +(-3.19595 - 1.03843i) q^{37} +(-2.35693 + 7.25389i) q^{38} +(7.21029 + 1.02621i) q^{39} +(2.20010 + 0.399463i) q^{40} +(-0.349537 - 0.113572i) q^{41} +(2.24884 + 1.63388i) q^{42} +9.70699 q^{43} +(-1.42536 + 1.96184i) q^{44} +(-2.39336 + 0.323983i) q^{45} +(-4.07765 - 5.61241i) q^{46} +(7.44276 + 10.2441i) q^{47} +(0.624192 + 1.92106i) q^{48} +5.10621 q^{49} +(1.75772 - 4.68086i) q^{50} -3.94314 q^{51} +(-3.56958 - 0.508042i) q^{52} +(3.74493 - 2.72085i) q^{53} +(2.27946 + 3.13741i) q^{54} +(3.74686 + 3.91962i) q^{55} +(-1.11333 - 0.808880i) q^{56} +15.4064i q^{57} +(-0.464279 + 0.639025i) q^{58} +(12.3998 + 4.02894i) q^{59} +(4.47587 - 0.605889i) q^{60} +(0.197382 + 0.607479i) q^{61} +(-2.53336 + 7.79689i) q^{62} +(1.41364 + 0.459318i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-2.54366 + 7.65048i) q^{65} +(-1.51365 + 4.65852i) q^{66} +(-4.12347 + 5.67547i) q^{67} +1.95212 q^{68} +(-11.3367 - 8.23656i) q^{69} +(-2.22435 + 2.12631i) q^{70} +(-2.46629 - 3.39455i) q^{71} +(0.634869 + 0.873823i) q^{72} +(1.76821 - 0.574528i) q^{73} +3.36042 q^{74} +(0.454931 - 10.0894i) q^{75} -7.62719i q^{76} +(-1.03123 - 3.17379i) q^{77} +(-7.17451 + 1.25212i) q^{78} +(7.68212 - 5.58139i) q^{79} +(-2.21586 + 0.299956i) q^{80} +(8.95880 + 6.50895i) q^{81} +0.367525 q^{82} +(0.802101 - 1.10400i) q^{83} +(-2.64367 - 0.858981i) q^{84} +(0.779799 - 4.29485i) q^{85} +(-9.23189 + 2.99962i) q^{86} +(-0.493035 + 1.51741i) q^{87} +(0.749357 - 2.30628i) q^{88} +(-6.88009 + 2.23548i) q^{89} +(2.17610 - 1.04771i) q^{90} +(3.45298 - 3.56317i) q^{91} +(5.61241 + 4.07765i) q^{92} +16.5596i q^{93} +(-10.2441 - 7.44276i) q^{94} +(-16.7806 - 3.04678i) q^{95} +(-1.18728 - 1.63416i) q^{96} +(-6.60321 - 9.08854i) q^{97} +(-4.85630 + 1.57791i) q^{98} +2.61922i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q + 34 q^{4} - 30 q^{9}+O(q^{10}) $ 136 * q + 34 * q^4 - 30 * q^9	$ 136 q + 34 q^{4} - 30 q^{9} - 4 q^{10} - 12 q^{13} + 8 q^{14} - 34 q^{16} + 4 q^{23} + 40 q^{25} + 4 q^{26} - 12 q^{27} + 16 q^{29} + 10 q^{30} - 18 q^{35} + 30 q^{36} - 24 q^{38} + 32 q^{39} + 4 q^{40} - 12 q^{42} + 24 q^{43} - 104 q^{49} + 84 q^{51} + 12 q^{52} + 4 q^{53} - 60 q^{55} - 8 q^{56} + 12 q^{61} + 18 q^{62} + 34 q^{64} + 26 q^{65} + 16 q^{66} + 84 q^{69} - 88 q^{74} - 214 q^{75} + 56 q^{78} - 8 q^{79} - 74 q^{81} + 160 q^{82} - 164 q^{87} - 16 q^{90} - 40 q^{91} + 16 q^{92} + 48 q^{94} - 4 q^{95}+O(q^{100}) $ 136 * q + 34 * q^4 - 30 * q^9 - 4 * q^10 - 12 * q^13 + 8 * q^14 - 34 * q^16 + 4 * q^23 + 40 * q^25 + 4 * q^26 - 12 * q^27 + 16 * q^29 + 10 * q^30 - 18 * q^35 + 30 * q^36 - 24 * q^38 + 32 * q^39 + 4 * q^40 - 12 * q^42 + 24 * q^43 - 104 * q^49 + 84 * q^51 + 12 * q^52 + 4 * q^53 - 60 * q^55 - 8 * q^56 + 12 * q^61 + 18 * q^62 + 34 * q^64 + 26 * q^65 + 16 * q^66 + 84 * q^69 - 88 * q^74 - 214 * q^75 + 56 * q^78 - 8 * q^79 - 74 * q^81 + 160 * q^82 - 164 * q^87 - 16 * q^90 - 40 * q^91 + 16 * q^92 + 48 * q^94 - 4 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$-1$

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 $

$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$2$	−0.951057	+	0.309017i	−0.672499	+	0.218508i
$3$	−1.63416	+	1.18728i	−0.943480	+	0.685478i	−0.949256	−	0.314505i	$-0.898161\pi$
$3$	−1.63416	+	1.18728i	−0.943480	+	0.685478i	0.00577592	+	0.999983i	$0.498161\pi$
$4$	0.809017	−	0.587785i	0.404508	−	0.293893i
$5$	−0.970013	−	2.01471i	−0.433803	−	0.901008i
$5$	−0.970013	−	2.01471i	−0.433803	−	0.901008i
$6$	1.18728	−	1.63416i	0.484706	−	0.667141i
$7$			1.37615i			0.520135i	0.965590	+	0.260068i	$0.0837449\pi$
$7$			1.37615i			0.520135i	−0.965590	+	0.260068i	$0.916255\pi$
$8$	−0.587785	+	0.809017i	−0.207813	+	0.286031i
$9$	0.333771	−	1.02724i	0.111257	−	0.342413i
$10$	1.54512	+	1.61636i	0.488609	+	0.511137i
$11$	−2.30628	+	0.749357i	−0.695371	+	0.225940i	−0.635312	−	0.772255i	$-0.719129\pi$
$11$	−2.30628	+	0.749357i	−0.695371	+	0.225940i	−0.0600583	+	0.998195i	$0.519129\pi$
$12$	−0.624192	+	1.92106i	−0.180189	+	0.554564i
$13$	−2.58923	−	2.50916i	−0.718123	−	0.695916i
$13$	−2.58923	−	2.50916i	−0.718123	−	0.695916i
$14$	−0.425253	−	1.30880i	−0.113654	−	0.349790i
$15$	3.97719	+	2.14068i	1.02691	+	0.552720i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	1.57930	+	1.14743i	0.383036	+	0.278292i	0.762596	−	0.646875i	$-0.223925\pi$
$17$	1.57930	+	1.14743i	0.383036	+	0.278292i	−0.379560	+	0.925167i	$0.623925\pi$
$18$			1.08010i			0.254583i
$19$	4.48315	−	6.17053i	1.02851	−	1.41562i	0.122441	−	0.992476i	$-0.460928\pi$
$19$	4.48315	−	6.17053i	1.02851	−	1.41562i	0.906064	−	0.423140i	$-0.139072\pi$
$20$	−1.96898	−	1.05978i	−0.440276	−	0.236974i
$21$	−1.63388	−	2.24884i	−0.356541	−	0.490737i
$22$	1.96184	−	1.42536i	0.418266	−	0.303888i
$23$	2.14375	+	6.59778i	0.447003	+	1.37573i	0.880272	+	0.474469i	$0.157360\pi$
$23$	2.14375	+	6.59778i	0.447003	+	1.37573i	−0.433270	+	0.901264i	$0.642640\pi$
$24$		−	2.01993i		−	0.412316i
$25$	−3.11815	+	3.90860i	−0.623630	+	0.781719i
$26$	3.23788	+	1.58624i	0.635000	+	0.311087i
$27$	−1.19838	−	3.68824i	−0.230629	−	0.709803i
$28$	0.808880	+	1.11333i	0.152864	+	0.210399i
$29$	0.639025	−	0.464279i	0.118664	−	0.0862144i	−0.526870	−	0.849946i	$-0.676635\pi$
$29$	0.639025	−	0.464279i	0.118664	−	0.0862144i	0.645534	+	0.763731i	$0.276635\pi$
$30$	−4.44404	−	0.806886i	−0.811366	−	0.147317i
$31$	4.81874	−	6.63243i	0.865471	−	1.19122i	−0.114766	−	0.993393i	$-0.536612\pi$
$31$	4.81874	−	6.63243i	0.865471	−	1.19122i	0.980237	−	0.197827i	$-0.0633883\pi$
$32$			1.00000i			0.176777i
$33$	2.87913	−	3.96278i	0.501192	−	0.689831i
$34$	−1.85658	−	0.603238i	−0.318400	−	0.103454i
$35$	2.77255	−	1.33488i	0.468646	−	0.225636i
$36$	−0.333771	−	1.02724i	−0.0556284	−	0.171207i
$37$	−3.19595	−	1.03843i	−0.525411	−	0.170716i	0.0342886	−	0.999412i	$-0.489083\pi$
$37$	−3.19595	−	1.03843i	−0.525411	−	0.170716i	−0.559700	+	0.828696i	$0.689083\pi$
$38$	−2.35693	+	7.25389i	−0.382345	+	1.17674i
$39$	7.21029	+	1.02621i	1.15457	+	0.164325i
$40$	2.20010	+	0.399463i	0.347866	+	0.0631606i
$41$	−0.349537	−	0.113572i	−0.0545885	−	0.0177369i	0.281595	−	0.959533i	$-0.409136\pi$
$41$	−0.349537	−	0.113572i	−0.0545885	−	0.0177369i	−0.336184	+	0.941796i	$0.609136\pi$
$42$	2.24884	+	1.63388i	0.347004	+	0.252113i
$43$	9.70699			1.48030			0.740151	−	0.672441i	$-0.234754\pi$
$43$	9.70699			1.48030			0.740151	+	0.672441i	$0.234754\pi$
$44$	−1.42536	+	1.96184i	−0.214881	+	0.295759i
$45$	−2.39336	+	0.323983i	−0.356781	+	0.0482966i
$46$	−4.07765	−	5.61241i	−0.601217	−	0.827505i
$47$	7.44276	+	10.2441i	1.08564	+	1.49425i	0.853158	+	0.521653i	$0.174684\pi$
$47$	7.44276	+	10.2441i	1.08564	+	1.49425i	0.232481	+	0.972601i	$0.425316\pi$
$48$	0.624192	+	1.92106i	0.0900943	+	0.277282i
$49$	5.10621			0.729459
$50$	1.75772	−	4.68086i	0.248578	−	0.661973i
$51$	−3.94314			−0.552150
$52$	−3.56958	−	0.508042i	−0.495012	−	0.0704527i
$53$	3.74493	−	2.72085i	0.514406	−	0.373738i	−0.300087	−	0.953912i	$-0.597016\pi$
$53$	3.74493	−	2.72085i	0.514406	−	0.373738i	0.814492	+	0.580174i	$0.197016\pi$
$54$	2.27946	+	3.13741i	0.310195	+	0.426947i
$55$	3.74686	+	3.91962i	0.505227	+	0.528521i
$56$	−1.11333	−	0.808880i	−0.148775	−	0.108091i
$57$			15.4064i			2.04062i
$58$	−0.464279	+	0.639025i	−0.0609628	+	0.0839081i
$59$	12.3998	+	4.02894i	1.61432	+	0.524523i	0.970591	−	0.240734i	$-0.0773882\pi$
$59$	12.3998	+	4.02894i	1.61432	+	0.524523i	0.643725	+	0.765257i	$0.277388\pi$
$60$	4.47587	−	0.605889i	0.577832	−	0.0782199i
$61$	0.197382	+	0.607479i	0.0252722	+	0.0777797i	0.962897	−	0.269869i	$-0.0869803\pi$
$61$	0.197382	+	0.607479i	0.0252722	+	0.0777797i	−0.937625	+	0.347648i	$0.886980\pi$
$62$	−2.53336	+	7.79689i	−0.321737	+	0.990206i
$63$	1.41364	+	0.459318i	0.178101	+	0.0578686i
$64$	−0.309017	−	0.951057i	−0.0386271	−	0.118882i
$65$	−2.54366	+	7.65048i	−0.315502	+	0.948925i
$66$	−1.51365	+	4.65852i	−0.186317	+	0.573425i
$67$	−4.12347	+	5.67547i	−0.503762	+	0.693369i	−0.982852	−	0.184397i	$-0.940967\pi$
$67$	−4.12347	+	5.67547i	−0.503762	+	0.693369i	0.479090	+	0.877766i	$0.340967\pi$
$68$	1.95212			0.236729
$69$	−11.3367	−	8.23656i	−1.36477	−	0.991566i
$70$	−2.22435	+	2.12631i	−0.265860	+	0.254143i
$71$	−2.46629	−	3.39455i	−0.292694	−	0.402859i	0.637193	−	0.770705i	$-0.280096\pi$
$71$	−2.46629	−	3.39455i	−0.292694	−	0.402859i	−0.929887	+	0.367845i	$0.880096\pi$
$72$	0.634869	+	0.873823i	0.0748201	+	0.102981i
$73$	1.76821	−	0.574528i	0.206954	−	0.0672434i	−0.203706	−	0.979032i	$-0.565299\pi$
$73$	1.76821	−	0.574528i	0.206954	−	0.0672434i	0.410659	+	0.911789i	$0.365299\pi$
$74$	3.36042			0.390641
$75$	0.454931	−	10.0894i	0.0525309	−	1.16502i
$76$		−	7.62719i		−	0.874899i
$77$	−1.03123	−	3.17379i	−0.117519	−	0.361687i
$78$	−7.17451	+	1.25212i	−0.812353	+	0.141775i
$79$	7.68212	−	5.58139i	0.864306	−	0.627955i	−0.0647467	−	0.997902i	$-0.520624\pi$
$79$	7.68212	−	5.58139i	0.864306	−	0.627955i	0.929053	+	0.369946i	$0.120624\pi$
$80$	−2.21586	+	0.299956i	−0.247740	+	0.0335361i
$81$	8.95880	+	6.50895i	0.995422	+	0.723217i
$82$	0.367525			0.0405864
$83$	0.802101	−	1.10400i	0.0880420	−	0.121179i	−0.762724	−	0.646724i	$-0.776138\pi$
$83$	0.802101	−	1.10400i	0.0880420	−	0.121179i	0.850766	+	0.525545i	$0.176138\pi$
$84$	−2.64367	−	0.858981i	−0.288448	−	0.0937225i
$85$	0.779799	−	4.29485i	0.0845811	−	0.465842i
$86$	−9.23189	+	2.99962i	−0.995501	+	0.323458i
$87$	−0.493035	+	1.51741i	−0.0528590	+	0.162683i
$88$	0.749357	−	2.30628i	0.0798817	−	0.245851i
$89$	−6.88009	+	2.23548i	−0.729288	+	0.236960i	−0.650045	−	0.759895i	$-0.725250\pi$
$89$	−6.88009	+	2.23548i	−0.729288	+	0.236960i	−0.0792426	+	0.996855i	$0.525250\pi$
$90$	2.17610	−	1.04771i	0.229381	−	0.110439i
$91$	3.45298	−	3.56317i	0.361970	−	0.373521i
$92$	5.61241	+	4.07765i	0.585134	+	0.425125i
$93$			16.5596i			1.71715i
$94$	−10.2441	−	7.44276i	−1.05660	−	0.767663i
$95$	−16.7806	−	3.04678i	−1.72165	−	0.312593i
$96$	−1.18728	−	1.63416i	−0.121177	−	0.166785i
$97$	−6.60321	−	9.08854i	−0.670454	−	0.922801i	0.329316	−	0.944220i	$-0.393182\pi$
$97$	−6.60321	−	9.08854i	−0.670454	−	0.922801i	−0.999771	+	0.0214186i	$0.993182\pi$
$98$	−4.85630	+	1.57791i	−0.490560	+	0.159393i
$99$			2.61922i			0.263242i
$100$	−0.225221	+	4.99492i	−0.0225221	+	0.499492i
$101$	−2.88680			−0.287247			−0.143623	−	0.989632i	$-0.545875\pi$
$101$	−2.88680			−0.287247			−0.143623	+	0.989632i	$0.545875\pi$
$102$	3.75015	−	1.21850i	0.371320	−	0.120649i
$103$	5.06477	−	3.67977i	0.499046	−	0.362578i	−0.309606	−	0.950865i	$-0.600197\pi$
$103$	5.06477	−	3.67977i	0.499046	−	0.362578i	0.808653	+	0.588286i	$0.200197\pi$
$104$	3.55186	−	0.619884i	0.348289	−	0.0607846i
$105$	−2.94589	+	5.47320i	−0.287489	+	0.534130i
$106$	−2.72085	+	3.74493i	−0.264272	+	0.363740i
$107$	−0.671945			−0.0649593			−0.0324797	−	0.999472i	$-0.510340\pi$
$107$	−0.671945			−0.0649593			−0.0324797	+	0.999472i	$0.510340\pi$
$108$	−3.13741	−	2.27946i	−0.301897	−	0.219341i
$109$	14.6871	+	4.77214i	1.40677	+	0.457088i	0.911374	−	0.411579i	$-0.135023\pi$
$109$	14.6871	+	4.77214i	1.40677	+	0.457088i	0.495397	+	0.868667i	$0.335023\pi$
$110$	−4.77471	−	2.56993i	−0.455251	−	0.245034i
$111$	6.45559	−	2.09755i	0.612737	−	0.199090i
$112$	1.30880	+	0.425253i	0.123670	+	0.0401827i
$113$	6.23561	−	19.1912i	0.586597	−	1.80536i	−0.00616489	−	0.999981i	$-0.501962\pi$
$113$	6.23561	−	19.1912i	0.586597	−	1.80536i	0.592762	−	0.805378i	$-0.298038\pi$
$114$	−4.76083	−	14.6523i	−0.445893	−	1.37232i
$115$	11.2132	−	10.7190i	1.04564	−	0.999550i
$116$	0.244086	−	0.751219i	0.0226628	−	0.0697489i
$117$	−3.44172	+	1.82228i	−0.318187	+	0.168470i
$118$	−13.0379			−1.20024
$119$	−1.57903	+	2.17335i	−0.144749	+	0.199231i
$120$	−4.06958	+	1.95935i	−0.371500	+	0.178864i
$121$	−4.14178	+	3.00918i	−0.376525	+	0.273562i
$122$	−0.375443	−	0.516753i	−0.0339910	−	0.0467846i
$123$	0.706040	−	0.229406i	0.0636614	−	0.0206849i
$124$		−	8.19813i		−	0.736214i
$125$	10.8994	+	2.49080i	0.974868	+	0.222784i
$126$	−1.48638			−0.132418
$127$	−4.96227	−	15.2723i	−0.440330	−	1.35520i	−0.887525	−	0.460760i	$-0.847577\pi$
$127$	−4.96227	−	15.2723i	−0.440330	−	1.35520i	0.447194	−	0.894437i	$-0.352423\pi$
$128$	0.587785	+	0.809017i	0.0519534	+	0.0715077i
$129$	−15.8627	+	11.5249i	−1.39663	+	1.01471i
$130$	0.0550330	−	8.06207i	0.00482672	−	0.707090i
$131$	−13.1246	−	9.53559i	−1.14670	−	0.833128i	−0.158664	−	0.987333i	$-0.550719\pi$
$131$	−13.1246	−	9.53559i	−1.14670	−	0.833128i	−0.988039	+	0.154204i	$0.950719\pi$
$132$		−	4.89826i		−	0.426339i
$133$	8.49156	+	6.16948i	0.736312	+	0.534962i
$134$	2.16784	−	6.67192i	0.187273	−	0.576366i
$135$	−6.26831	+	5.99204i	−0.539490	+	0.515713i
$136$	−1.85658	+	0.603238i	−0.159200	+	0.0517272i
$137$	−10.6966	−	3.47553i	−0.913870	−	0.296934i	−0.185920	−	0.982565i	$-0.559527\pi$
$137$	−10.6966	−	3.47553i	−0.913870	−	0.296934i	−0.727950	+	0.685631i	$0.759527\pi$
$138$	13.3270	+	4.33022i	1.13447	+	0.368613i
$139$	−6.38467	−	19.6500i	−0.541541	−	1.66669i	−0.729076	−	0.684433i	$-0.760050\pi$
$139$	−6.38467	−	19.6500i	−0.541541	−	1.66669i	0.187535	−	0.982258i	$-0.439950\pi$
$140$	1.45841	−	2.70960i	0.123258	−	0.229003i
$141$	−24.3253	−	7.90376i	−2.04856	−	0.665616i
$142$	3.39455	+	2.46629i	0.284865	+	0.206966i
$143$	7.85176	+	3.84658i	0.656597	+	0.321667i
$144$	−0.873823	−	0.634869i	−0.0728186	−	0.0529058i
$145$	−1.55525	−	0.837097i	−0.129157	−	0.0695171i
$146$	−1.50413	+	1.09282i	−0.124483	+	0.0904421i
$147$	−8.34435	+	6.06252i	−0.688230	+	0.500028i
$148$	−3.19595	+	1.03843i	−0.262706	+	0.0853582i
$149$		−	11.0501i		−	0.905263i	−0.891698	−	0.452632i	$-0.850485\pi$
$149$		−	11.0501i		−	0.905263i	0.891698	−	0.452632i	$-0.149515\pi$
$150$	2.68513	+	9.73615i	0.219240	+	0.794954i
$151$			20.4092i			1.66087i	0.557112	+	0.830437i	$0.311909\pi$
$151$			20.4092i			1.66087i	−0.557112	+	0.830437i	$0.688091\pi$
$152$	2.35693	+	7.25389i	0.191172	+	0.588368i
$153$	1.70581	−	1.23934i	0.137906	−	0.100195i
$154$	1.96151	+	2.69979i	0.158063	+	0.217555i
$155$	−18.0367	−	3.27485i	−1.44874	−	0.263042i
$156$	6.43644	−	3.40788i	0.515327	−	0.272849i
$157$	−1.32289			−0.105578			−0.0527892	−	0.998606i	$-0.516811\pi$
$157$	−1.32289			−0.105578			−0.0527892	+	0.998606i	$0.516811\pi$
$158$	−5.58139	+	7.68212i	−0.444032	+	0.611157i
$159$	−2.88938	+	8.89259i	−0.229142	+	0.705228i
$160$	2.01471	−	0.970013i	0.159277	−	0.0766862i
$161$	−9.07953	+	2.95012i	−0.715567	+	0.232502i
$162$	−10.5317	−	3.42196i	−0.827449	−	0.268854i
$163$	7.07377	+	2.29841i	0.554061	+	0.180025i	0.572647	−	0.819802i	$-0.305917\pi$
$163$	7.07377	+	2.29841i	0.554061	+	0.180025i	−0.0185864	+	0.999827i	$0.505917\pi$
$164$	−0.349537	+	0.113572i	−0.0272943	+	0.00886845i
$165$	−10.7767	−	1.95667i	−0.838961	−	0.152327i
$166$	−0.421689	+	1.29783i	−0.0327294	+	0.100731i
$167$	6.48603	−	8.92726i	0.501904	−	0.690812i	−0.480624	−	0.876927i	$-0.659590\pi$
$167$	6.48603	−	8.92726i	0.501904	−	0.690812i	0.982528	+	0.186115i	$0.0595896\pi$
$168$	2.77972			0.214460
$169$	0.408229	+	12.9936i	0.0314022	+	0.999507i
$170$	0.585549	+	4.32562i	0.0449096	+	0.331760i
$171$	−4.84227	−	6.66481i	−0.370298	−	0.509671i
$172$	7.85312	−	5.70562i	0.598795	−	0.435050i
$173$	−1.58131	−	4.86678i	−0.120225	−	0.370014i	0.872776	−	0.488121i	$-0.162317\pi$
$173$	−1.58131	−	4.86678i	−0.120225	−	0.370014i	−0.993001	+	0.118107i	$0.962317\pi$
$174$		−	1.59550i		−	0.120954i
$175$	−5.37881	−	4.29104i	−0.406600	−	0.324372i
$176$			2.42497i			0.182789i
$177$	−25.0467	+	8.13816i	−1.88262	+	0.611701i
$178$	5.85255	−	4.25213i	0.438667	−	0.318711i
$179$	−2.87878	+	2.09155i	−0.215170	+	0.156330i	−0.690150	−	0.723667i	$-0.742455\pi$
$179$	−2.87878	+	2.09155i	−0.215170	+	0.156330i	0.474980	+	0.879997i	$0.342455\pi$
$180$	−1.74583	+	1.66889i	−0.130127	+	0.124392i
$181$	8.19188	+	5.95175i	0.608898	+	0.442390i	0.849026	−	0.528351i	$-0.177189\pi$
$181$	8.19188	+	5.95175i	0.608898	+	0.442390i	−0.240128	+	0.970741i	$0.577189\pi$
$182$	−2.18290	+	4.45580i	−0.161807	+	0.330286i
$183$	−1.04380	−	0.758367i	−0.0771601	−	0.0560601i
$184$	−6.59778	−	2.14375i	−0.486395	−	0.158039i
$185$	1.00798	+	7.44622i	0.0741080	+	0.547457i
$186$	−5.11721	−	15.7491i	−0.375212	−	1.15478i
$187$	−4.50214	−	1.46283i	−0.329229	−	0.106973i
$188$	12.0426	+	3.91289i	0.878300	+	0.285377i
$189$	5.07557	−	1.64915i	0.369194	−	0.119958i
$190$	16.9008	−	2.28782i	1.22611	−	0.165976i
$191$	−8.36458	+	25.7435i	−0.605240	+	1.86274i	−0.110106	+	0.993920i	$0.535119\pi$
$191$	−8.36458	+	25.7435i	−0.605240	+	1.86274i	−0.495133	+	0.868817i	$0.664881\pi$
$192$	1.63416	+	1.18728i	0.117935	+	0.0856848i
$193$		−	5.19967i		−	0.374280i	−0.982333	−	0.187140i	$-0.940078\pi$
$193$		−	5.19967i		−	0.374280i	0.982333	−	0.187140i	$-0.0599219\pi$
$194$	9.08854	+	6.60321i	0.652519	+	0.474083i
$195$	−4.92656	−	15.5221i	−0.352798	−	1.11156i
$196$	4.13101	−	3.00136i	0.295072	−	0.214383i
$197$	6.57795	+	9.05377i	0.468659	+	0.645054i	0.976276	−	0.216529i	$-0.0694735\pi$
$197$	6.57795	+	9.05377i	0.468659	+	0.645054i	−0.507617	+	0.861583i	$0.669473\pi$
$198$	−0.809384	−	2.49103i	−0.0575204	−	0.177030i
$199$	21.4026			1.51719			0.758595	−	0.651563i	$-0.225886\pi$
$199$	21.4026			1.51719			0.758595	+	0.651563i	$0.225886\pi$
$200$	−1.32932	−	4.82005i	−0.0939970	−	0.340829i
$201$		−	14.1703i		−	0.999498i
$202$	2.74551	−	0.892069i	0.193173	−	0.0627657i
$203$	0.638917	+	0.879393i	0.0448432	+	0.0617213i
$204$	−3.19007	+	2.31772i	−0.223349	+	0.162273i
$205$	0.110241	+	0.814384i	0.00769958	+	0.0568790i
$206$	−3.67977	+	5.06477i	−0.256382	+	0.352879i
$207$	7.49303			0.520801
$208$	−3.18647	+	1.68713i	−0.220942	+	0.116982i
$209$	−5.71549	+	17.5905i	−0.395349	+	1.21676i
$210$	1.11040	−	6.11565i	0.0766245	−	0.422020i
$211$	4.87273	+	14.9967i	0.335453	+	1.03242i	0.966499	+	0.256672i	$0.0826260\pi$
$211$	4.87273	+	14.9967i	0.335453	+	1.03242i	−0.631046	+	0.775746i	$0.717374\pi$
$212$	1.43044	−	4.40243i	0.0982428	−	0.302360i
$213$	8.06059	+	2.61904i	0.552303	+	0.179454i
$214$	0.639057	−	0.207642i	0.0436851	−	0.0141941i
$215$	−9.41590	−	19.5568i	−0.642159	−	1.33376i
$216$	3.68824	+	1.19838i	0.250953	+	0.0815396i
$217$	9.12721	+	6.63130i	0.619595	+	0.450162i
$218$	−15.4430			−1.04593
$219$	−2.20741	+	3.03824i	−0.149163	+	0.205305i
$220$	5.33517	+	0.968686i	0.359697	+	0.0653088i
$221$	−1.21009	−	6.93366i	−0.0813993	−	0.466409i
$222$	−5.49145	+	3.98977i	−0.368562	+	0.267776i
$223$	2.73218	−	0.887740i	0.182960	−	0.0594475i	−0.216104	−	0.976370i	$-0.569335\pi$
$223$	2.73218	−	0.887740i	0.182960	−	0.0594475i	0.399064	+	0.916923i	$0.369335\pi$
$224$	−1.37615			−0.0919478
$225$	2.97432	+	4.50766i	0.198288	+	0.300511i
$226$			20.1789i			1.34228i
$227$	−8.06882	+	2.62172i	−0.535546	+	0.174010i	−0.564289	−	0.825577i	$-0.690850\pi$
$227$	−8.06882	+	2.62172i	−0.535546	+	0.174010i	0.0287427	+	0.999587i	$0.490850\pi$
$228$	9.05564	+	12.4640i	0.599724	+	0.825450i
$229$	5.18868	+	7.14160i	0.342877	+	0.471930i	0.945279	−	0.326263i	$-0.105789\pi$
$229$	5.18868	+	7.14160i	0.342877	+	0.471930i	−0.602402	+	0.798193i	$0.705789\pi$
$230$	−7.35203	+	13.6594i	−0.484778	+	0.900675i
$231$	5.45337	+	3.96211i	0.358805	+	0.260687i
$232$			0.789878i			0.0518581i
$233$	−3.65751	−	2.65733i	−0.239611	−	0.174088i	0.461499	−	0.887141i	$-0.347312\pi$
$233$	−3.65751	−	2.65733i	−0.239611	−	0.174088i	−0.701110	+	0.713053i	$0.747312\pi$
$234$	2.71015	−	2.79664i	0.177168	−	0.182822i
$235$	13.4193	−	24.9319i	0.875381	−	1.62638i
$236$	12.3998	−	4.02894i	0.807158	−	0.262261i
$237$	−5.92709	+	18.2417i	−0.385006	+	1.18493i
$238$	0.830145	−	2.55492i	0.0538103	−	0.165611i
$239$	5.34043	−	1.73521i	0.345444	−	0.112242i	−0.131156	−	0.991362i	$-0.541869\pi$
$239$	5.34043	−	1.73521i	0.345444	−	0.112242i	0.476600	+	0.879120i	$0.341869\pi$
$240$	3.26492	−	3.12102i	0.210750	−	0.201461i
$241$	−0.303502	−	0.0986137i	−0.0195503	−	0.00635227i	0.299226	−	0.954182i	$-0.403272\pi$
$241$	−0.303502	−	0.0986137i	−0.0195503	−	0.00635227i	−0.318776	+	0.947830i	$0.603272\pi$
$242$	3.00918	−	4.14178i	0.193437	−	0.266244i
$243$	−10.7339			−0.688579
$244$	0.516753	+	0.375443i	0.0330817	+	0.0240353i
$245$	−4.95309	−	10.2876i	−0.316441	−	0.657248i
$246$	−0.600593	+	0.436356i	−0.0382924	+	0.0278211i
$247$	−27.0908	+	4.72797i	−1.72374	+	0.300834i
$248$	2.53336	+	7.79689i	0.160869	+	0.495103i
$249$			2.75642i			0.174681i
$250$	−11.1356	+	0.999197i	−0.704277	+	0.0631948i
$251$	19.8579			1.25342			0.626711	−	0.779252i	$-0.284401\pi$
$251$	19.8579			1.25342			0.626711	+	0.779252i	$0.284401\pi$
$252$	1.41364	−	0.459318i	0.0890506	−	0.0289343i
$253$	−9.88819	−	13.6099i	−0.621665	−	0.855649i
$254$	9.43880	+	12.9914i	0.592243	+	0.815152i
$255$	3.82489	+	7.94430i	0.239524	+	0.497491i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−16.2474			−1.01348			−0.506742	−	0.862098i	$-0.669150\pi$
$257$	−16.2474			−1.01348			−0.506742	+	0.862098i	$0.669150\pi$
$258$	11.5249	−	15.8627i	0.717512	−	0.987570i
$259$	1.42903	−	4.39810i	0.0887956	−	0.273285i
$260$	2.43898	+	7.68449i	0.151259	+	0.476572i
$261$	−0.263638	−	0.811395i	−0.0163188	−	0.0502241i
$262$	15.4289	+	5.01316i	0.953201	+	0.309714i
$263$	3.74954	−	11.5399i	0.231207	−	0.711581i	−0.766395	−	0.642369i	$-0.777952\pi$
$263$	3.74954	−	11.5399i	0.231207	−	0.711581i	0.997602	−	0.0692120i	$-0.0220485\pi$
$264$	1.51365	+	4.65852i	0.0931585	+	0.286712i
$265$	−9.11437	−	4.90571i	−0.559891	−	0.301355i
$266$	−9.98243	−	3.24349i	−0.612062	−	0.198871i
$267$	8.58899	−	11.8217i	0.525638	−	0.723478i
$268$			7.01527i			0.428526i
$269$	7.10301	+	5.16064i	0.433078	+	0.314650i	0.782879	−	0.622175i	$-0.213751\pi$
$269$	7.10301	+	5.16064i	0.433078	+	0.314650i	−0.349800	+	0.936824i	$0.613751\pi$
$270$	4.10988	−	7.63579i	0.250119	−	0.464699i
$271$	−10.2042	−	14.0449i	−0.619861	−	0.853165i	0.377482	−	0.926017i	$-0.376790\pi$
$271$	−10.2042	−	14.0449i	−0.619861	−	0.853165i	−0.997343	+	0.0728520i	$0.976790\pi$
$272$	1.57930	−	1.14743i	0.0957590	−	0.0695730i
$273$	−1.41221	+	9.92243i	−0.0854711	+	0.600533i
$274$	11.2470			0.679459
$275$	4.26241	−	11.3509i	0.257033	−	0.684488i
$276$	−14.0129			−0.843476
$277$	−4.42468	−	13.6178i	−0.265853	−	0.818212i	−0.991496	−	0.130140i	$-0.958457\pi$
$277$	−4.42468	−	13.6178i	−0.265853	−	0.818212i	0.725642	−	0.688072i	$-0.241543\pi$
$278$	12.1444	+	16.7153i	0.728371	+	1.00252i
$279$	−5.20474	−	7.16371i	−0.311600	−	0.428880i
$280$	−0.549720	+	3.02766i	−0.0328521	+	0.180937i
$281$	0.985217	−	1.35603i	0.0587731	−	0.0808942i	−0.778619	−	0.627497i	$-0.784079\pi$
$281$	0.985217	−	1.35603i	0.0587731	−	0.0808942i	0.837392	+	0.546603i	$0.184079\pi$
$282$	25.5771			1.52309
$283$	9.84425	+	7.15227i	0.585180	+	0.425158i	0.840588	−	0.541675i	$-0.182210\pi$
$283$	9.84425	+	7.15227i	0.585180	+	0.425158i	−0.255408	+	0.966833i	$0.582210\pi$
$284$	−3.99054	−	1.29660i	−0.236795	−	0.0769393i
$285$	31.0394	−	14.9444i	1.83862	−	0.885228i
$286$	−8.65612	−	1.23199i	−0.511847	−	0.0728489i
$287$	0.156291	−	0.481015i	0.00922559	−	0.0283934i
$288$	1.02724	+	0.333771i	0.0605307	+	0.0196676i
$289$	−4.07570	−	12.5437i	−0.239747	−	0.737865i
$290$	1.73781	+	0.315527i	0.102048	+	0.0185284i
$291$	21.5813	+	7.01220i	1.26512	+	0.411062i
$292$	1.09282	−	1.50413i	0.0639522	−	0.0880227i
$293$			30.5854i			1.78682i	0.449241	+	0.893410i	$0.351694\pi$
$293$			30.5854i			1.78682i	−0.449241	+	0.893410i	$0.648306\pi$
$294$	6.06252	−	8.34435i	0.353574	−	0.486652i
$295$	−3.91080	−	28.8902i	−0.227695	−	1.68205i
$296$	2.71864	−	1.97521i	0.158018	−	0.114807i
$297$	5.52762	+	7.60812i	0.320745	+	0.441468i
$298$	3.41468	+	10.5093i	0.197807	+	0.608788i
$299$	11.0042	−	22.4622i	0.636391	−	1.29902i
$300$	−5.56234	−	8.42988i	−0.321142	−	0.486700i
$301$			13.3583i			0.769957i
$302$	−6.30678	−	19.4103i	−0.362914	−	1.11694i
$303$	4.71747	−	3.42744i	0.271012	−	0.196901i
$304$	−4.48315	−	6.17053i	−0.257126	−	0.353904i
$305$	1.03243	−	0.986931i	0.0591170	−	0.0565115i
$306$	−1.23934	+	1.70581i	−0.0708484	+	0.0975144i
$307$			8.66983i			0.494813i	0.968912	+	0.247407i	$0.0795784\pi$
$307$			8.66983i			0.494813i	−0.968912	+	0.247407i	$0.920422\pi$
$308$	−2.69979	−	1.96151i	−0.153835	−	0.111767i
$309$	−3.90769	+	12.0266i	−0.222301	+	0.684171i
$310$	18.1659	−	2.45908i	1.03175	−	0.139666i
$311$	−1.56570	−	4.81873i	−0.0887827	−	0.273245i	0.896801	−	0.442434i	$-0.145885\pi$
$311$	−1.56570	−	4.81873i	−0.0887827	−	0.273245i	−0.985584	+	0.169189i	$0.945885\pi$
$312$	−5.06832	+	5.23006i	−0.286937	+	0.296094i
$313$	−3.27759	+	10.0874i	−0.185260	+	0.570172i	−0.999953	−	0.00972080i	$-0.996906\pi$
$313$	−3.27759	+	10.0874i	−0.185260	+	0.570172i	0.814693	+	0.579893i	$0.196906\pi$
$314$	1.25815	−	0.408797i	0.0710014	−	0.0230697i
$315$	−0.445849	−	3.29362i	−0.0251208	−	0.185574i
$316$	2.93431	−	9.03088i	0.165068	−	0.508027i
$317$	13.3810	−	18.4174i	0.751553	−	1.03442i	−0.246316	−	0.969189i	$-0.579220\pi$
$317$	13.3810	−	18.4174i	0.751553	−	1.03442i	0.997870	−	0.0652351i	$-0.0207797\pi$
$318$		−	9.35022i		−	0.524334i
$319$	−1.12586	+	1.54962i	−0.0630362	+	0.0867619i
$320$	−1.61636	+	1.54512i	−0.0903571	+	0.0863747i
$321$	1.09806	−	0.797789i	0.0612878	−	0.0445282i
$322$	7.72351	−	5.61146i	0.430414	−	0.312714i
$323$	14.1605	−	4.60101i	0.787909	−	0.256007i
$324$	11.0737			0.615205
$325$	17.8809	−	2.29632i	0.991854	−	0.127377i
$326$	−7.43780			−0.411942
$327$	−29.6669	+	9.63936i	−1.64058	+	0.533058i
$328$	0.297334	−	0.216026i	0.0164175	−	0.0119280i
$329$	−14.0974	+	10.2424i	−0.777214	+	0.564679i
$330$	10.8539	−	1.46926i	0.597485	−	0.0808802i
$331$	−11.4619	+	15.7759i	−0.630002	+	0.867123i	−0.998033	−	0.0626906i	$-0.980032\pi$
$331$	−11.4619	+	15.7759i	−0.630002	+	0.867123i	0.368031	+	0.929813i	$0.380032\pi$
$332$		−	1.36462i		−	0.0748930i
$333$	−2.13343	+	2.93641i	−0.116911	+	0.160914i
$334$	−3.40991	+	10.4946i	−0.186582	+	0.574240i
$335$	15.4343	+	2.80234i	0.843265	+	0.153108i
$336$	−2.64367	+	0.858981i	−0.144224	+	0.0468612i
$337$	3.29567	−	10.1430i	0.179527	−	0.552526i	−0.820285	−	0.571956i	$-0.806185\pi$
$337$	3.29567	−	10.1430i	0.179527	−	0.552526i	0.999811	+	0.0194294i	$0.00618497\pi$
$338$	−4.40349	−	12.2315i	−0.239518	−	0.665305i
$339$	12.5955	+	38.7649i	0.684092	+	2.10542i
$340$	−1.89358	−	3.93296i	−0.102694	−	0.213295i
$341$	−6.14333	+	18.9072i	−0.332680	+	1.02388i
$342$	6.66481	+	4.84227i	0.360392	+	0.261840i
$343$			16.6600i			0.899553i
$344$	−5.70562	+	7.85312i	−0.307627	+	0.423412i
$345$	−5.59763	+	30.8297i	−0.301366	+	1.65982i
$346$	3.00783	+	4.13993i	0.161702	+	0.222564i
$347$	−3.32691	+	2.41714i	−0.178598	+	0.129759i	−0.673493	−	0.739194i	$-0.735207\pi$
$347$	−3.32691	+	2.41714i	−0.178598	+	0.129759i	0.494895	+	0.868953i	$0.335207\pi$
$348$	0.493035	+	1.51741i	0.0264295	+	0.0813416i
$349$			14.3623i			0.768796i	0.923167	+	0.384398i	$0.125591\pi$
$349$			14.3623i			0.768796i	−0.923167	+	0.384398i	$0.874409\pi$
$350$	6.44156	+	2.41888i	0.344316	+	0.129294i
$351$	−6.15150	+	12.5566i	−0.328343	+	0.670224i
$352$	−0.749357	−	2.30628i	−0.0399409	−	0.122925i
$353$	−2.48017	−	3.41366i	−0.132006	−	0.181691i	0.737897	−	0.674913i	$-0.235819\pi$
$353$	−2.48017	−	3.41366i	−0.132006	−	0.181691i	−0.869903	+	0.493222i	$0.835819\pi$
$354$	21.3060	−	15.4797i	1.13240	−	0.822737i
$355$	−4.44673	+	8.26162i	−0.236008	+	0.438481i
$356$	−4.25213	+	5.85255i	−0.225362	+	0.310185i
$357$		−	5.42634i		−	0.287193i
$358$	2.09155	−	2.87878i	0.110542	−	0.152148i
$359$	17.6248	+	5.72663i	0.930199	+	0.302240i	0.734644	−	0.678453i	$-0.237349\pi$
$359$	17.6248	+	5.72663i	0.930199	+	0.302240i	0.195555	+	0.980693i	$0.437349\pi$
$360$	1.14467	−	2.12670i	0.0603295	−	0.112087i
$361$	−12.1054	−	37.2567i	−0.637129	−	1.96088i
$362$	−9.63013	−	3.12902i	−0.506149	−	0.164458i
$363$	3.19556	−	9.83493i	0.167723	−	0.516200i
$364$	0.699141	−	4.91227i	0.0366450	−	0.257473i
$365$	−2.87270	−	3.00515i	−0.150364	−	0.157297i
$366$	1.22706	+	0.398697i	0.0641396	+	0.0208402i
$367$	28.5610	+	20.7508i	1.49087	+	1.08318i	0.973846	+	0.227211i	$0.0729605\pi$
$367$	28.5610	+	20.7508i	1.49087	+	1.08318i	0.517025	+	0.855970i	$0.327039\pi$
$368$	6.93732			0.361633
$369$	−0.233330	+	0.321152i	−0.0121467	+	0.0167185i
$370$	−3.25965	−	6.77029i	−0.169461	−	0.351971i
$371$	3.74430	+	5.15358i	0.194394	+	0.267561i
$372$	9.73350	+	13.3970i	0.504659	+	0.694603i
$373$	−8.90794	−	27.4158i	−0.461236	−	1.41954i	−0.863656	−	0.504082i	$-0.831831\pi$
$373$	−8.90794	−	27.4158i	−0.461236	−	1.41954i	0.402420	−	0.915455i	$-0.368169\pi$
$374$	4.73383			0.244781
$375$	−20.7685	+	8.87027i	−1.07248	+	0.458059i
$376$	−12.6624			−0.653013
$377$	−2.81953	−	0.401291i	−0.145213	−	0.0206675i
$378$	−4.31754	+	3.13688i	−0.222070	+	0.161343i
$379$	−17.9064	−	24.6461i	−0.919791	−	1.26598i	−0.963711	−	0.266949i	$-0.913985\pi$
$379$	−17.9064	−	24.6461i	−0.919791	−	1.26598i	0.0439196	−	0.999035i	$-0.486015\pi$
$380$	−15.3666	+	7.39847i	−0.788291	+	0.379534i
$381$	26.2417	+	19.0657i	1.34440	+	0.976764i
$382$		−	27.0684i		−	1.38494i
$383$	−0.887061	+	1.22094i	−0.0453267	+	0.0623869i	−0.831079	−	0.556155i	$-0.812276\pi$
$383$	−0.887061	+	1.22094i	−0.0453267	+	0.0623869i	0.785752	+	0.618542i	$0.212276\pi$
$384$	−1.92106	−	0.624192i	−0.0980339	−	0.0318531i
$385$	−5.39398	+	5.15624i	−0.274903	+	0.262786i
$386$	1.60679	+	4.94518i	0.0817833	+	0.251703i
$387$	3.23991	−	9.97141i	0.164694	−	0.506875i
$388$	−10.6842	−	3.47151i	−0.542409	−	0.176239i
$389$	−1.30967	−	4.03075i	−0.0664029	−	0.204367i	0.912350	−	0.409412i	$-0.134266\pi$
$389$	−1.30967	−	4.03075i	−0.0664029	−	0.204367i	−0.978753	+	0.205045i	$0.934266\pi$
$390$	9.48203	+	13.2400i	0.480141	+	0.670434i
$391$	−4.18485	+	12.8797i	−0.211637	+	0.651352i
$392$	−3.00136	+	4.13101i	−0.151591	+	0.208648i
$393$	32.7691			1.65298
$394$	−9.05377	−	6.57795i	−0.456122	−	0.331392i
$395$	−18.6967	−	10.0633i	−0.940731	−	0.506338i
$396$	1.53954	+	2.11899i	0.0773647	+	0.106483i
$397$	−7.14649	−	9.83630i	−0.358672	−	0.493670i	0.591106	−	0.806594i	$-0.298691\pi$
$397$	−7.14649	−	9.83630i	−0.358672	−	0.493670i	−0.949778	+	0.312924i	$0.898691\pi$
$398$	−20.3551	+	6.61376i	−1.02031	+	0.331518i
$399$	−21.2015			−1.06140
$400$	2.75374	+	4.17336i	0.137687	+	0.208668i
$401$		−	10.8534i		−	0.541994i	−0.962580	−	0.270997i	$-0.912647\pi$
$401$		−	10.8534i		−	0.541994i	0.962580	−	0.270997i	$-0.0873534\pi$
$402$	4.37887	+	13.4768i	0.218398	+	0.672161i
$403$	−29.1187	+	5.08189i	−1.45050	+	0.253147i
$404$	−2.33547	+	1.69682i	−0.116194	+	0.0844197i
$405$	4.42353	−	24.3632i	0.219807	−	1.21062i
$406$	−0.879393	−	0.638917i	−0.0436436	−	0.0317089i
$407$	8.14892			0.403927
$408$	2.31772	−	3.19007i	0.114744	−	0.157932i
$409$	15.7568	+	5.11968i	0.779121	+	0.253152i	0.671465	−	0.741036i	$-0.265665\pi$
$409$	15.7568	+	5.11968i	0.779121	+	0.253152i	0.107656	+	0.994188i	$0.465665\pi$
$410$	−0.356504	−	0.740458i	−0.0176065	−	0.0365686i
$411$	21.6063	−	7.02031i	1.06576	−	0.346286i
$412$	1.93457	−	5.95399i	0.0953094	−	0.293332i
$413$	−5.54442	+	17.0640i	−0.272823	+	0.839663i
$414$	−7.12629	+	2.31547i	−0.350238	+	0.113799i
$415$	−3.00229	−	0.545113i	−0.147376	−	0.0267586i
$416$	2.50916	−	2.58923i	0.123022	−	0.126947i
$417$	33.7637	+	24.5307i	1.65341	+	1.20128i
$418$		−	18.4957i		−	0.904655i
$419$	−26.7057	−	19.4028i	−1.30466	−	0.947889i	−0.304667	−	0.952459i	$-0.598545\pi$
$419$	−26.7057	−	19.4028i	−1.30466	−	0.947889i	−0.999990	+	0.00457029i	$0.998545\pi$
$420$	0.833793	+	6.15946i	0.0406849	+	0.300551i
$421$	−4.63579	−	6.38062i	−0.225935	−	0.310973i	0.680967	−	0.732314i	$-0.261560\pi$
$421$	−4.63579	−	6.38062i	−0.225935	−	0.310973i	−0.906902	+	0.421341i	$0.861560\pi$
$422$	−9.26849	−	12.7570i	−0.451183	−	0.621000i
$423$	13.0073	−	4.22633i	0.632437	−	0.205491i
$424$			4.62899i			0.224804i
$425$	−9.40932	+	2.59499i	−0.456419	+	0.125875i
$426$	−8.47541			−0.410635
$427$	−0.835981	+	0.271627i	−0.0404560	+	0.0131449i
$428$	−0.543615	+	0.394959i	−0.0262766	+	0.0190911i
$429$	−17.3980	+	3.03635i	−0.839982	+	0.146597i
$430$	14.9984	+	15.6900i	0.723289	+	0.756637i
$431$	15.6911	−	21.5969i	0.755812	−	1.04029i	−0.241739	−	0.970341i	$-0.577718\pi$
$431$	15.6911	−	21.5969i	0.755812	−	1.04029i	0.997551	−	0.0699442i	$-0.0222821\pi$
$432$	−3.87805			−0.186583
$433$	−5.54724	−	4.03031i	−0.266583	−	0.193684i	0.446461	−	0.894803i	$-0.352684\pi$
$433$	−5.54724	−	4.03031i	−0.266583	−	0.193684i	−0.713044	+	0.701119i	$0.752684\pi$
$434$	−10.7297	−	3.48628i	−0.515041	−	0.167347i
$435$	3.53539	−	0.478578i	0.169509	−	0.0229461i
$436$	14.6871	−	4.77214i	0.703386	−	0.228544i
$437$	50.3226	+	16.3508i	2.40725	+	0.782164i
$438$	1.16050	−	3.57166i	0.0554510	−	0.170661i
$439$	7.96699	+	24.5199i	0.380244	+	1.17027i	0.939872	+	0.341526i	$0.110944\pi$
$439$	7.96699	+	24.5199i	0.380244	+	1.17027i	−0.559629	+	0.828743i	$0.689056\pi$
$440$	−5.37339	+	0.727384i	−0.256166	+	0.0346767i
$441$	1.70430	−	5.24531i	0.0811573	−	0.249777i
$442$	3.29348	+	6.22037i	0.156655	+	0.295873i
$443$	−9.74445			−0.462973			−0.231487	−	0.972838i	$-0.574359\pi$
$443$	−9.74445			−0.462973			−0.231487	+	0.972838i	$0.574359\pi$
$444$	3.98977	−	5.49145i	0.189346	−	0.260613i
$445$	11.1776	+	11.6930i	0.529870	+	0.554300i
$446$	−2.32413	+	1.68858i	−0.110051	+	0.0799567i
$447$	13.1197	+	18.0577i	0.620538	+	0.854098i
$448$	1.30880	−	0.425253i	0.0618348	−	0.0200913i
$449$			34.2539i			1.61654i	0.588811	+	0.808270i	$0.299596\pi$
$449$			34.2539i			1.61654i	−0.588811	+	0.808270i	$0.700404\pi$
$450$	−4.22169	−	3.36793i	−0.199012	−	0.158766i
$451$	0.891238			0.0419667
$452$	−6.23561	−	19.1912i	−0.293298	−	0.902679i
$453$	−24.2315	−	33.3517i	−1.13849	−	1.56700i
$454$	6.86375	−	4.98680i	0.322132	−	0.234042i
$455$	−10.5282	−	3.50045i	−0.493569	−	0.164104i
$456$	−12.4640	−	9.05564i	−0.583681	−	0.424069i
$457$		−	14.2258i		−	0.665453i	−0.943023	−	0.332726i	$-0.892031\pi$
$457$		−	14.2258i		−	0.665453i	0.943023	−	0.332726i	$-0.107969\pi$
$458$	−7.14160	−	5.18868i	−0.333705	−	0.242451i
$459$	2.33939	−	7.19989i	0.109193	−	0.336062i
$460$	2.77120	−	15.2628i	0.129208	−	0.711631i
$461$	22.9138	−	7.44516i	1.06720	−	0.346756i	0.277806	−	0.960637i	$-0.410393\pi$
$461$	22.9138	−	7.44516i	1.06720	−	0.346756i	0.789398	+	0.613882i	$0.210393\pi$
$462$	−6.41082	−	2.08300i	−0.298258	−	0.0969100i
$463$	−13.7754	−	4.47591i	−0.640198	−	0.208013i	−0.0291108	−	0.999576i	$-0.509268\pi$
$463$	−13.7754	−	4.47591i	−0.640198	−	0.208013i	−0.611087	+	0.791563i	$0.709268\pi$
$464$	−0.244086	−	0.751219i	−0.0113314	−	0.0348745i
$465$	33.3629	−	16.0630i	1.54717	−	0.744906i
$466$	4.29966	+	1.39704i	0.199178	+	0.0647168i
$467$	−1.45025	−	1.05367i	−0.0671097	−	0.0487580i	0.553725	−	0.832700i	$-0.313206\pi$
$467$	−1.45025	−	1.05367i	−0.0671097	−	0.0487580i	−0.620834	+	0.783942i	$0.713206\pi$
$468$	−1.71330	+	3.49725i	−0.0791974	+	0.161660i
$469$	−7.81029	−	5.67451i	−0.360646	−	0.262025i
$470$	−5.05815	+	27.8585i	−0.233315	+	1.28502i
$471$	2.16181	−	1.57065i	0.0996112	−	0.0723717i
$472$	−10.5479	+	7.66349i	−0.485506	+	0.352741i
$473$	−22.3871	+	7.27400i	−1.02936	+	0.334459i
$474$		−	19.1805i		−	0.880988i
$475$	10.1390	+	36.7635i	0.465208	+	1.68682i
$476$			2.68641i			0.123131i
$477$	−1.54502	−	4.75508i	−0.0707416	−	0.217720i
$478$	−4.54284	+	3.30057i	−0.207785	+	0.150965i
$479$	6.69626	+	9.21661i	0.305960	+	0.421118i	0.934116	−	0.356970i	$-0.116190\pi$
$479$	6.69626	+	9.21661i	0.305960	+	0.421118i	−0.628156	+	0.778087i	$0.716190\pi$
$480$	−2.14068	+	3.97719i	−0.0977081	+	0.181533i
$481$	5.66947	+	10.7079i	0.258506	+	0.488237i
$482$	0.319121			0.0145355
$483$	11.3347	−	15.6009i	0.515748	−	0.709867i
$484$	−1.58202	+	4.86895i	−0.0719099	+	0.221316i
$485$	−11.9056	+	22.1196i	−0.540606	+	1.00440i
$486$	10.2085	−	3.31695i	0.463069	−	0.150460i
$487$	24.8282	+	8.06718i	1.12507	+	0.365559i	0.811702	−	0.584072i	$-0.198541\pi$
$487$	24.8282	+	8.06718i	1.12507	+	0.365559i	0.313372	+	0.949630i	$0.398541\pi$
$488$	−0.607479	−	0.197382i	−0.0274993	−	0.00893506i
$489$	−14.2885	+	4.64262i	−0.646148	+	0.209946i
$490$	7.88970	+	8.25347i	0.356420	+	0.372854i
$491$	−7.76690	+	23.9041i	−0.350515	+	1.07877i	0.608049	+	0.793899i	$0.291952\pi$
$491$	−7.76690	+	23.9041i	−0.350515	+	1.07877i	−0.958565	+	0.284876i	$0.908048\pi$
$492$	0.436356	−	0.600593i	0.0196725	−	0.0270768i
$493$	1.54194			0.0694453
$494$	24.3038	−	12.8681i	1.09348	−	0.578962i
$495$	5.27698	−	2.54068i	0.237183	−	0.114195i
$496$	−4.81874	−	6.63243i	−0.216368	−	0.297805i
$497$	4.67141	−	3.39398i	0.209541	−	0.152241i
$498$	−0.851782	−	2.62151i	−0.0381692	−	0.117473i
$499$		−	17.0816i		−	0.764678i	−0.924022	−	0.382339i	$-0.875119\pi$
$499$		−	17.0816i		−	0.764678i	0.924022	−	0.382339i	$-0.124881\pi$
$500$	10.2818	−	4.39138i	0.459817	−	0.196389i
$501$			22.2893i			0.995812i
$502$	−18.8860	+	6.13644i	−0.842925	+	0.273883i
$503$	0.296490	−	0.215412i	0.0132198	−	0.00960476i	−0.581156	−	0.813792i	$-0.697399\pi$
$503$	0.296490	−	0.215412i	0.0132198	−	0.00960476i	0.594376	+	0.804188i	$0.297399\pi$
$504$	−1.20251	+	0.873675i	−0.0535640	+	0.0389166i
$505$	2.80023	+	5.81607i	0.124608	+	0.258812i
$506$	13.6099	+	9.88819i	0.605035	+	0.439584i
$507$	−16.0942	−	20.7489i	−0.714768	−	0.921489i
$508$	−12.9914	−	9.43880i	−0.576400	−	0.418779i
$509$	6.70894	+	2.17987i	0.297369	+	0.0966209i	0.453902	−	0.891052i	$-0.350032\pi$
$509$	6.70894	+	2.17987i	0.297369	+	0.0966209i	−0.156533	+	0.987673i	$0.550032\pi$
$510$	−6.09261	−	6.37352i	−0.269785	−	0.282224i
$511$	0.790635	+	2.43333i	0.0349756	+	0.107644i
$512$	0.951057	+	0.309017i	0.0420312	+	0.0136568i
$513$	−28.1309	−	9.14030i	−1.24201	−	0.403554i
$514$	15.4522	−	5.02072i	0.681566	−	0.221454i
$515$	−12.3266	−	6.63464i	−0.543174	−	0.292357i
$516$	−6.05902	+	18.6477i	−0.266734	+	0.820921i
$517$	−24.8416	−	18.0485i	−1.09253	−	0.793771i
$518$			4.62444i			0.203186i
$519$	8.36235	+	6.07560i	0.367066	+	0.266689i
$520$	−4.69424	−	6.55470i	−0.205856	−	0.287443i
$521$	25.2773	−	18.3651i	1.10742	−	0.804588i	0.125165	−	0.992136i	$-0.460054\pi$
$521$	25.2773	−	18.3651i	1.10742	−	0.804588i	0.982255	+	0.187548i	$0.0600541\pi$
$522$	0.501469	+	0.690214i	0.0219487	+	0.0302098i
$523$	5.87964	+	18.0957i	0.257099	+	0.791268i	0.993409	+	0.114624i	$0.0365664\pi$
$523$	5.87964	+	18.0957i	0.257099	+	0.791268i	−0.736310	+	0.676644i	$0.763434\pi$
$524$	−16.2229			−0.708701
$525$	13.8845	+	0.626052i	0.605969	+	0.0273232i
$526$			12.1338i			0.529058i
$527$	15.2205	−	4.94542i	0.663013	−	0.215426i
$528$	−2.87913	−	3.96278i	−0.125298	−	0.172458i
$529$	−20.3277	+	14.7689i	−0.883812	+	0.642127i
$530$	10.1842	+	1.84911i	0.442375	+	0.0803202i
$531$	8.27737	−	11.3928i	0.359207	−	0.494406i
$532$	10.4962			0.455066
$533$	0.620063	+	1.17111i	0.0268579	+	0.0507263i
$534$	−4.51550	+	13.8973i	−0.195405	+	0.601394i
$535$	0.651795	+	1.35378i	0.0281795	+	0.0585289i
$536$	−2.16784	−	6.67192i	−0.0936363	−	0.288183i
$537$	2.22110	−	6.83585i	0.0958476	−	0.294989i
$538$	−8.35009	−	2.71311i	−0.359998	−	0.116970i
$539$	−11.7764	+	3.82638i	−0.507245	+	0.164814i
$540$	−1.54914	+	8.53209i	−0.0666642	+	0.367163i
$541$	24.1772	+	7.85564i	1.03946	+	0.337740i	0.778523	−	0.627616i	$-0.215969\pi$
$541$	24.1772	+	7.85564i	1.03946	+	0.337740i	0.260935	+	0.965356i	$0.415969\pi$
$542$	14.0449	+	10.2042i	0.603279	+	0.438308i
$543$	−20.4532			−0.877732
$544$	−1.14743	+	1.57930i	−0.0491955	+	0.0677118i
$545$	−4.63220	−	34.2194i	−0.198422	−	1.46580i
$546$	−1.72310	−	9.87319i	−0.0737420	−	0.422533i
$547$	3.64790	−	2.65036i	0.155973	−	0.113321i	−0.507061	−	0.861910i	$-0.669268\pi$
$547$	3.64790	−	2.65036i	0.155973	−	0.113321i	0.663034	+	0.748589i	$0.269268\pi$
$548$	−10.6966	+	3.47553i	−0.456935	+	0.148467i
$549$	0.689907			0.0294445
$550$	−0.546155	+	12.1125i	−0.0232881	+	0.516481i
$551$		−	6.02455i		−	0.256655i
$552$	13.3270	−	4.33022i	0.567236	−	0.184306i
$553$	7.68082	+	10.5717i	0.326622	+	0.449556i
$554$	8.41624	+	11.5840i	0.357572	+	0.492156i
$555$	−10.4880	−	10.9715i	−0.445189	−	0.465715i
$556$	−16.7153	−	12.1444i	−0.708886	−	0.515036i
$557$			23.8540i			1.01073i	0.862907	+	0.505363i	$0.168641\pi$
$557$			23.8540i			1.01073i	−0.862907	+	0.505363i	$0.831359\pi$
$558$	7.16371	+	5.20474i	0.303264	+	0.220334i
$559$	−25.1336	−	24.3564i	−1.06304	−	1.03017i
$560$	−0.412784	−	3.04935i	−0.0174433	−	0.128859i
$561$	9.09399	−	2.95482i	0.383949	−	0.124753i
$562$	−0.517959	+	1.59411i	−0.0218488	+	0.0672436i
$563$	−5.88619	+	18.1158i	−0.248073	+	0.763491i	0.747042	+	0.664776i	$0.231473\pi$
$563$	−5.88619	+	18.1158i	−0.248073	+	0.763491i	−0.995116	+	0.0987148i	$0.968527\pi$
$564$	−24.3253	+	7.90376i	−1.02428	+	0.332808i
$565$	−44.7135	+	6.05276i	−1.88111	+	0.254642i
$566$	−11.5726	−	3.76017i	−0.486433	−	0.158052i
$567$	−8.95728	+	12.3286i	−0.376171	+	0.517754i
$568$	4.19590			0.176056
$569$	3.15935	+	2.29540i	0.132447	+	0.0962281i	0.652036	−	0.758188i	$-0.273915\pi$
$569$	3.15935	+	2.29540i	0.132447	+	0.0962281i	−0.519589	+	0.854416i	$0.673915\pi$
$570$	−24.9022	+	23.8047i	−1.04304	+	0.997067i
$571$	−21.1173	+	15.3426i	−0.883731	+	0.642068i	−0.934236	−	0.356656i	$-0.883917\pi$
$571$	−21.1173	+	15.3426i	−0.883731	+	0.642068i	0.0505052	+	0.998724i	$0.483917\pi$
$572$	8.61317	−	1.50320i	0.360135	−	0.0628520i
$573$	−16.8958	−	52.0001i	−0.705834	−	2.17233i
$574$			0.505769i			0.0211104i
$575$	−32.4726	−	12.1938i	−1.35420	−	0.508518i
$576$	−1.08010			−0.0450043
$577$	6.31334	−	2.05133i	0.262828	−	0.0853979i	−0.174639	−	0.984633i	$-0.555876\pi$
$577$	6.31334	−	2.05133i	0.262828	−	0.0853979i	0.437467	+	0.899235i	$0.355876\pi$
$578$	7.75244	+	10.6703i	0.322459	+	0.443826i
$579$	6.17348	+	8.49707i	0.256561	+	0.353126i
$580$	−1.75026	+	0.236928i	−0.0726755	+	0.00983792i
$581$	1.51926	+	1.10381i	0.0630297	+	0.0457938i
$582$	−22.6920			−0.940612
$583$	−6.59798	+	9.08135i	−0.273261	+	0.376111i
$584$	−0.574528	+	1.76821i	−0.0237741	+	0.0731692i
$585$	7.00988	+	5.16645i	0.289823	+	0.213606i
$586$	−9.45142	−	29.0885i	−0.390435	−	1.20163i
$587$	24.8434	+	8.07213i	1.02540	+	0.333172i	0.772970	−	0.634443i	$-0.218770\pi$
$587$	24.8434	+	8.07213i	1.02540	+	0.333172i	0.252429	+	0.967615i	$0.418770\pi$
$588$	−3.18726	+	9.80937i	−0.131440	+	0.404532i
$589$	−19.3224	−	59.4684i	−0.796167	−	2.45035i
$590$	12.6469	+	26.2677i	0.520666	+	1.08142i
$591$	−21.4988	−	6.98537i	−0.884341	−	0.287340i
$592$	−1.97521	+	2.71864i	−0.0811805	+	0.111735i
$593$		−	43.5839i		−	1.78978i	−0.446289	−	0.894889i	$-0.647255\pi$
$593$		−	43.5839i		−	1.78978i	0.446289	−	0.894889i	$-0.352745\pi$
$594$	−7.60812	−	5.52762i	−0.312165	−	0.226801i
$595$	5.91036	+	1.07312i	0.242301	+	0.0439936i
$596$	−6.49511	−	8.93976i	−0.266050	−	0.366187i
$597$	−34.9752	+	25.4109i	−1.43144	+	1.04000i
$598$	−3.52445	+	24.7633i	−0.144125	+	1.01265i
$599$	39.2720			1.60461			0.802304	−	0.596915i	$-0.203607\pi$
$599$	39.2720			1.60461			0.802304	+	0.596915i	$0.203607\pi$
$600$	7.89508	+	6.29844i	0.322315	+	0.257133i
$601$	16.5577			0.675403			0.337701	−	0.941253i	$-0.390351\pi$
$601$	16.5577			0.675403			0.337701	+	0.941253i	$0.390351\pi$
$602$	−4.12793	−	12.7045i	−0.168242	−	0.517795i
$603$	4.45378	+	6.13010i	0.181372	+	0.249637i
$604$	11.9962	+	16.5114i	0.488119	+	0.671838i
$605$	10.0802	+	5.42556i	0.409819	+	0.220580i
$606$	−3.42744	+	4.71747i	−0.139230	+	0.191634i
$607$	38.0478			1.54431			0.772156	−	0.635433i	$-0.219178\pi$
$607$	38.0478			1.54431			0.772156	+	0.635433i	$0.219178\pi$
$608$	6.17053	+	4.48315i	0.250248	+	0.181816i
$609$	−2.08818	−	0.678490i	−0.0846172	−	0.0274938i
$610$	−0.676925	+	1.25767i	−0.0274079	+	0.0509214i
$611$	6.43302	−	45.1994i	0.260252	−	1.82857i
$612$	0.651560	−	2.00530i	0.0263377	−	0.0810593i
$613$	−36.9197	−	11.9960i	−1.49117	−	0.484512i	−0.553745	−	0.832687i	$-0.686802\pi$
$613$	−36.9197	−	11.9960i	−1.49117	−	0.484512i	−0.937430	+	0.348175i	$0.886802\pi$
$614$	−2.67912	−	8.24550i	−0.108121	−	0.332761i
$615$	−1.14706	−	1.19994i	−0.0462537	−	0.0483863i
$616$	3.17379	+	1.03123i	0.127876	+	0.0415493i
$617$	0.523234	−	0.720170i	0.0210646	−	0.0289930i	−0.798355	−	0.602187i	$-0.794296\pi$
$617$	0.523234	−	0.720170i	0.0210646	−	0.0289930i	0.819419	+	0.573194i	$0.194296\pi$
$618$		−	12.6455i		−	0.508678i
$619$	−4.43918	+	6.11001i	−0.178426	+	0.245582i	−0.888857	−	0.458184i	$-0.848500\pi$
$619$	−4.43918	+	6.11001i	−0.178426	+	0.245582i	0.710431	+	0.703767i	$0.248500\pi$
$620$	−16.5169	+	7.95229i	−0.663335	+	0.319372i
$621$	21.7652	−	15.8133i	0.873407	−	0.634568i
$622$	2.97814	+	4.09906i	0.119412	+	0.164357i
$623$	−3.07635	−	9.46803i	−0.123251	−	0.379328i
$624$	3.20408	−	6.54028i	0.128266	−	0.261821i
$625$	−5.55427	−	24.3752i	−0.222171	−	0.975008i
$626$		−	10.6065i		−	0.423921i
$627$	−11.5449	−	35.5315i	−0.461058	−	1.41899i
$628$	−1.07024	+	0.777578i	−0.0427074	+	0.0310287i
$629$	−3.85584	−	5.30711i	−0.153742	−	0.211608i
$630$	1.44181	+	2.99464i	0.0574431	+	0.119309i
$631$	−16.2187	+	22.3231i	−0.645654	+	0.888667i	−0.998901	−	0.0468631i	$-0.985078\pi$
$631$	−16.2187	+	22.3231i	−0.645654	+	0.888667i	0.353247	+	0.935530i	$0.385078\pi$
$632$			9.49563i			0.377716i
$633$	−25.7682	−	18.7217i	−1.02419	−	0.744120i
$634$	−7.03482	+	21.6510i	−0.279389	+	0.859869i
$635$	−25.9559	+	24.8119i	−1.03003	+	0.984629i
$636$	2.88938	+	8.89259i	0.114571	+	0.352614i
$637$	−13.2212	−	12.8123i	−0.523842	−	0.507642i
$638$	0.591901	−	1.82168i	0.0234336	−	0.0721211i
$639$	−4.31019	+	1.40047i	−0.170509	+	0.0554016i
$640$	1.05978	−	1.96898i	0.0418915	−	0.0778306i
$641$	4.12561	−	12.6973i	0.162952	−	0.501514i	−0.835928	−	0.548839i	$-0.815070\pi$
$641$	4.12561	−	12.6973i	0.162952	−	0.501514i	0.998880	+	0.0473255i	$0.0150698\pi$
$642$	−0.797789	+	1.09806i	−0.0314862	+	0.0433370i
$643$		−	24.0874i		−	0.949914i	−0.880009	−	0.474957i	$-0.842464\pi$
$643$		−	24.0874i		−	0.949914i	0.880009	−	0.474957i	$-0.157536\pi$
$644$	−5.61146	+	7.72351i	−0.221122	+	0.304349i
$645$	38.6065	+	20.7795i	1.52013	+	0.818193i
$646$	−12.0456	+	8.75164i	−0.473928	+	0.344329i
$647$	−33.9108	+	24.6376i	−1.33317	+	0.968604i	−0.333504	+	0.942749i	$0.608231\pi$
$647$	−33.9108	+	24.6376i	−1.33317	+	0.968604i	−0.999666	+	0.0258553i	$0.991769\pi$
$648$	−10.5317	+	3.42196i	−0.413724	+	0.134427i
$649$	−31.6166			−1.24106
$650$	−16.2962	+	7.70943i	−0.639188	+	0.302389i
$651$	−22.7885			−0.893152
$652$	7.07377	−	2.29841i	0.277030	−	0.0900126i
$653$	20.8712	−	15.1638i	0.816752	−	0.593405i	−0.0990284	−	0.995085i	$-0.531573\pi$
$653$	20.8712	−	15.1638i	0.816752	−	0.593405i	0.915780	+	0.401680i	$0.131573\pi$
$654$	25.2362	−	18.3352i	0.986813	−	0.716961i
$655$	−6.48045	+	35.6920i	−0.253212	+	1.39460i
$656$	−0.216026	+	0.297334i	−0.00843439	+	0.0116089i
$657$		−	2.00814i		−	0.0783450i
$658$	10.2424	−	14.0974i	0.399288	−	0.549573i
$659$	5.04745	−	15.5345i	0.196621	−	0.605137i	−0.803333	−	0.595530i	$-0.796942\pi$
$659$	5.04745	−	15.5345i	0.196621	−	0.605137i	0.999954	−	0.00960664i	$-0.00305794\pi$
$660$	−9.86860	+	4.75138i	−0.384135	+	0.184947i
$661$	2.37871	−	0.772890i	0.0925211	−	0.0300619i	−0.262391	−	0.964962i	$-0.584511\pi$
$661$	2.37871	−	0.772890i	0.0925211	−	0.0300619i	0.354912	+	0.934900i	$0.384511\pi$
$662$	6.02586	−	18.5457i	0.234202	−	0.720799i
$663$	10.2097	+	9.89396i	0.396512	+	0.384250i
$664$	0.421689	+	1.29783i	0.0163647	+	0.0503654i
$665$	4.19282	−	23.0926i	0.162591	−	0.895491i
$666$	1.12161	−	3.45196i	0.0434615	−	0.133761i
$667$	4.43312	+	3.22085i	0.171651	+	0.124712i
$668$		−	11.0347i		−	0.426945i
$669$	−3.41081	+	4.69458i	−0.131870	+	0.181503i
$670$	−15.5448	+	2.10427i	−0.600550	+	0.0812950i
$671$	−0.910437	−	1.25311i	−0.0351470	−	0.0483758i
$672$	2.24884	−	1.63388i	0.0867509	−	0.0630282i
$673$	15.6723	+	48.2343i	0.604122	+	1.85930i	0.502715	+	0.864452i	$0.332335\pi$
$673$	15.6723	+	48.2343i	0.604122	+	1.85930i	0.101407	+	0.994845i	$0.467665\pi$
$674$			10.6650i			0.410801i
$675$	18.1526	+	6.81650i	0.698694	+	0.262367i
$676$	7.96770	+	10.2721i	0.306450	+	0.395080i
$677$	−4.90812	−	15.1056i	−0.188634	−	0.580557i	0.811358	−	0.584550i	$-0.198729\pi$
$677$	−4.90812	−	15.1056i	−0.188634	−	0.580557i	−0.999992	+	0.00399333i	$0.998729\pi$
$678$	−23.9580	−	32.9754i	−0.920102	−	1.26641i
$679$	12.5072	−	9.08700i	0.479981	−	0.348727i
$680$	3.01625	+	3.15532i	0.115668	+	0.121001i
$681$	10.0730	−	13.8643i	0.385997	−	0.531280i
$682$		−	19.8802i		−	0.761253i
$683$	10.6361	−	14.6394i	0.406980	−	0.560160i	−0.555499	−	0.831517i	$-0.687473\pi$
$683$	10.6361	−	14.6394i	0.406980	−	0.560160i	0.962479	+	0.271358i	$0.0874727\pi$
$684$	−7.83496	−	2.54573i	−0.299577	−	0.0973385i
$685$	3.37361	+	24.9218i	0.128899	+	0.952215i
$686$	−5.14821	−	15.8446i	−0.196560	−	0.604948i
$687$	−16.9582	−	5.51005i	−0.646996	−	0.210222i
$688$	2.99962	−	9.23189i	0.114360	−	0.351963i
$689$	−16.5235	−	2.35172i	−0.629497	−	0.0895934i
$690$	−4.20324	−	31.0505i	−0.160015	−	1.18207i
$691$	9.14951	+	2.97285i	0.348064	+	0.113093i	0.477831	−	0.878452i	$-0.341423\pi$
$691$	9.14951	+	2.97285i	0.348064	+	0.113093i	−0.129767	+	0.991544i	$0.541423\pi$
$692$	−4.13993	−	3.00783i	−0.157376	−	0.114341i
$693$	−3.60444			−0.136921
$694$	2.41714	−	3.32691i	0.0917535	−	0.126288i
$695$	−33.3959	+	31.9240i	−1.26678	+	1.21095i
$696$	−0.937809	−	1.29078i	−0.0355476	−	0.0489270i
$697$	−0.421708	−	0.580432i	−0.0159733	−	0.0219854i
$698$	−4.43819	−	13.6594i	−0.167988	−	0.517014i
$699$	9.13194			0.345402
$700$	−6.87376	−	0.309938i	−0.259804	−	0.0117146i
$701$	−49.9843			−1.88788			−0.943941	−	0.330116i	$-0.892912\pi$
$701$	−49.9843			−1.88788			−0.943941	+	0.330116i	$0.892912\pi$
$702$	1.97021	−	13.8430i	0.0743608	−	0.522470i
$703$	−20.7356	+	15.0653i	−0.782057	+	0.568198i
$704$	1.42536	+	1.96184i	0.0537203	+	0.0739397i
$705$	7.67199	+	56.6752i	0.288944	+	2.13451i
$706$	3.41366	+	2.48017i	0.128475	+	0.0933425i
$707$		−	3.97266i		−	0.149407i
$708$	−15.4797	+	21.3060i	−0.581763	+	0.800728i
$709$	−14.9074	−	4.84370i	−0.559859	−	0.181909i	0.0153989	−	0.999881i	$-0.495098\pi$
$709$	−14.9074	−	4.84370i	−0.559859	−	0.181909i	−0.575258	+	0.817972i	$0.695098\pi$
$710$	1.67611	−	9.23138i	0.0629031	−	0.346448i
$711$	−3.16936	−	9.75429i	−0.118860	−	0.365814i
$712$	2.23548	−	6.88009i	0.0837780	−	0.257842i
$713$	54.0895	+	17.5747i	2.02567	+	0.658179i
$714$	1.67683	+	5.16076i	0.0627539	+	0.193137i
$715$	0.133453	−	19.5503i	0.00499088	−	0.731139i
$716$	−1.09960	+	3.38421i	−0.0410938	+	0.126474i
$717$	−6.66691	+	9.17621i	−0.248980	+	0.342692i
$718$	−18.5318			−0.691599
$719$	25.4588	+	18.4969i	0.949452	+	0.689817i	0.950677	−	0.310182i	$-0.100390\pi$
$719$	25.4588	+	18.4969i	0.949452	+	0.689817i	−0.00122520	+	0.999999i	$0.500390\pi$
$720$	−0.431462	+	2.37633i	−0.0160796	+	0.0885608i
$721$	5.06391	+	6.96987i	0.188590	+	0.259572i
$722$	23.0259	+	31.6925i	0.856936	+	1.17947i
$723$	0.613051	−	0.199192i	0.0227996	−	0.00740805i
$724$	10.1257			0.376320
$725$	−0.177898	+	3.94538i	−0.00660695	+	0.146528i
$726$			10.3411i			0.383793i
$727$	−11.4809	−	35.3345i	−0.425802	−	1.31048i	−0.902225	−	0.431267i	$-0.858067\pi$
$727$	−11.4809	−	35.3345i	−0.425802	−	1.31048i	0.476423	−	0.879216i	$-0.341933\pi$
$728$	0.853053	+	4.88789i	0.0316162	+	0.181157i
$729$	−9.33556	+	6.78268i	−0.345762	+	0.251210i
$730$	3.66074	+	1.97035i	0.135490	+	0.0729260i
$731$	15.3302	+	11.1381i	0.567009	+	0.411956i
$732$	−1.29021			−0.0476876
$733$	−4.53918	+	6.24764i	−0.167658	+	0.230762i	−0.884576	−	0.466396i	$-0.845552\pi$
$733$	−4.53918	+	6.24764i	−0.167658	+	0.230762i	0.716918	+	0.697158i	$0.245552\pi$
$734$	−33.5754	−	10.9093i	−1.23929	−	0.402670i
$735$	20.3084	+	10.9308i	0.749086	+	0.403187i
$736$	−6.59778	+	2.14375i	−0.243198	+	0.0790197i
$737$	5.25694	−	16.1792i	0.193642	−	0.595969i
$738$	0.122669	−	0.377537i	0.00451551	−	0.0138973i
$739$	29.3579	−	9.53895i	1.07995	−	0.350896i	0.285593	−	0.958351i	$-0.407809\pi$
$739$	29.3579	−	9.53895i	1.07995	−	0.350896i	0.794354	+	0.607455i	$0.207809\pi$
$740$	5.19225	+	5.43164i	0.190871	+	0.199671i
$741$	38.6570	−	39.8906i	1.42010	−	1.46542i
$742$	−5.15358	−	3.74430i	−0.189194	−	0.137457i
$743$			12.9030i			0.473364i	0.971587	+	0.236682i	$0.0760600\pi$
$743$			12.9030i			0.473364i	−0.971587	+	0.236682i	$0.923940\pi$
$744$	−13.3970	−	9.73350i	−0.491159	−	0.356848i
$745$	−22.2629	+	10.7188i	−0.815649	+	0.392706i
$746$	16.9439	+	23.3213i	0.620361	+	0.853853i
$747$	−0.866352	−	1.19243i	−0.0316982	−	0.0436288i
$748$	−4.50214	+	1.46283i	−0.164615	+	0.0534865i
$749$		−	0.924696i		−	0.0337876i
$750$	17.0110	−	14.8540i	0.621153	−	0.542390i
$751$	21.8032			0.795610			0.397805	−	0.917470i	$-0.369772\pi$
$751$	21.8032			0.795610			0.397805	+	0.917470i	$0.369772\pi$
$752$	12.0426	−	3.91289i	0.439150	−	0.142689i
$753$	−32.4510	+	23.5770i	−1.18258	+	0.859194i
$754$	2.80554	−	0.489633i	0.102172	−	0.0178314i
$755$	41.1186	−	19.7971i	1.49646	−	0.720492i
$756$	3.13688	−	4.31754i	0.114087	−	0.157027i
$757$	13.3451			0.485037			0.242518	−	0.970147i	$-0.422027\pi$
$757$	13.3451			0.485037			0.242518	+	0.970147i	$0.422027\pi$
$758$	24.6461	+	17.9064i	0.895186	+	0.650391i
$759$	32.3177	+	10.5006i	1.17306	+	0.381149i
$760$	12.3283	−	11.7849i	0.447193	−	0.427484i
$761$	−13.6961	+	4.45014i	−0.496485	+	0.161318i	−0.546547	−	0.837428i	$-0.684058\pi$
$761$	−13.6961	+	4.45014i	−0.496485	+	0.161318i	0.0500624	+	0.998746i	$0.484058\pi$
$762$	−30.8489	−	10.0234i	−1.11754	−	0.363110i
$763$	−6.56717	+	20.2117i	−0.237747	+	0.731711i
$764$	8.36458	+	25.7435i	0.302620	+	0.931368i
$765$	−4.15157	−	2.23454i	−0.150100	−	0.0807898i
$766$	0.466356	−	1.43530i	0.0168501	−	0.0518593i
$767$	−21.9967	−	41.5449i	−0.794254	−	1.50010i
$768$	2.01993			0.0728878
$769$	0.945426	−	1.30127i	0.0340929	−	0.0469249i	−0.791630	−	0.611000i	$-0.790767\pi$
$769$	0.945426	−	1.30127i	0.0340929	−	0.0469249i	0.825723	+	0.564076i	$0.190767\pi$
$770$	3.53661	−	6.57071i	0.127451	−	0.236792i
$771$	26.5507	−	19.2902i	0.956201	−	0.694721i
$772$	−3.05629	−	4.20662i	−0.109998	−	0.151400i
$773$	22.1880	−	7.20932i	0.798047	−	0.259301i	0.118520	−	0.992952i	$-0.462185\pi$
$773$	22.1880	−	7.20932i	0.798047	−	0.259301i	0.679527	+	0.733650i	$0.262185\pi$
$774$			10.4846i			0.376860i
$775$	10.8979	+	39.5154i	0.391465	+	1.41944i
$776$	11.2340			0.403279
$777$	2.88654	+	8.88385i	0.103554	+	0.318706i
$778$	2.49114	+	3.42876i	0.0893117	+	0.122927i
$779$	−2.26782	+	1.64767i	−0.0812532	+	0.0590339i
$780$	−13.1093	−	9.66189i	−0.469389	−	0.345951i
$781$	8.23169	+	5.98067i	0.294553	+	0.214005i
$782$		−	13.5425i		−	0.484278i
$783$	−2.47817	−	1.80050i	−0.0885626	−	0.0643445i
$784$	1.57791	−	4.85630i	0.0563538	−	0.173439i
$785$	1.28322	+	2.66525i	0.0458002	+	0.0951270i
$786$	−31.1653	+	10.1262i	−1.11163	+	0.361190i
$787$	12.6913	+	4.12366i	0.452396	+	0.146993i	0.526348	−	0.850269i	$-0.323561\pi$
$787$	12.6913	+	4.12366i	0.452396	+	0.146993i	−0.0739514	+	0.997262i	$0.523561\pi$
$788$	10.6433	+	3.45823i	0.379153	+	0.123194i
$789$	7.57380	+	23.3098i	0.269635	+	0.829850i
$790$	20.8913	+	3.79315i	0.743279	+	0.134954i
$791$	26.4100	+	8.58112i	0.939031	+	0.305110i
$792$	−2.11899	−	1.53954i	−0.0752952	−	0.0547051i
$793$	1.01319	−	2.06817i	0.0359796	−	0.0734427i
$794$	9.83630	+	7.14649i	0.349077	+	0.253619i
$795$	20.7188	−	2.80465i	0.734819	−	0.0994707i
$796$	17.3151	−	12.5801i	0.613716	−	0.445891i
$797$	−41.1053	+	29.8647i	−1.45602	+	1.05786i	−0.471647	+	0.881787i	$0.656340\pi$
$797$	−41.1053	+	29.8647i	−1.45602	+	1.05786i	−0.984377	+	0.176076i	$0.943660\pi$
$798$	20.1638	−	6.55161i	0.713790	−	0.231924i
$799$			24.7185i			0.874477i
$800$	−3.90860	−	3.11815i	−0.138190	−	0.110243i
$801$			7.81364i			0.276081i
$802$	3.35389	+	10.3222i	0.118430	+	0.364490i
$803$	−3.64748	+	2.65005i	−0.128717	+	0.0935181i
$804$	−8.32911	−	11.4640i	−0.293745	−	0.404305i
$805$	14.7509	+	15.4310i	0.519901	+	0.543872i
$806$	26.1231	−	13.8313i	0.920147	−	0.487188i
$807$	−17.7346			−0.624286
$808$	1.69682	−	2.33547i	0.0596938	−	0.0821614i
$809$	0.851764	−	2.62146i	0.0299464	−	0.0921656i	−0.934966	−	0.354737i	$-0.884570\pi$
$809$	0.851764	−	2.62146i	0.0299464	−	0.0921656i	0.964913	+	0.262571i	$0.0845705\pi$
$810$	3.32162	+	24.5377i	0.116710	+	0.862168i
$811$	−17.7479	+	5.76665i	−0.623213	+	0.202494i	−0.603567	−	0.797313i	$-0.706254\pi$
$811$	−17.7479	+	5.76665i	−0.623213	+	0.202494i	−0.0196469	+	0.999807i	$0.506254\pi$
$812$	1.03379	+	0.335898i	0.0362789	+	0.0117877i
$813$	33.3505	+	10.8362i	1.16965	+	0.380043i
$814$	−7.75008	+	2.51816i	−0.271640	+	0.0882613i
$815$	−2.23101	−	16.4811i	−0.0781489	−	0.577308i
$816$	−1.21850	+	3.75015i	−0.0426559	+	0.131281i
$817$	43.5179	−	59.8972i	1.52250	−	2.09554i
$818$	−16.5676			−0.579274
$819$	−2.50773	−	4.73632i	−0.0876270	−	0.165500i
$820$	0.567870	+	0.594052i	0.0198309	+	0.0207452i
$821$	0.228834	+	0.314963i	0.00798635	+	0.0109923i	0.812992	−	0.582276i	$-0.197838\pi$
$821$	0.228834	+	0.314963i	0.00798635	+	0.0109923i	−0.805005	+	0.593268i	$0.797838\pi$
$822$	−18.3794	+	13.3534i	−0.641056	+	0.465754i
$823$	7.54024	+	23.2065i	0.262836	+	0.808927i	0.992184	+	0.124784i	$0.0398237\pi$
$823$	7.54024	+	23.2065i	0.262836	+	0.808927i	−0.729348	+	0.684143i	$0.760176\pi$
$824$			6.26040i			0.218091i
$825$	6.51135	+	23.6099i	0.226696	+	0.821991i
$826$		−	17.9421i		−	0.624286i
$827$	41.3642	−	13.4400i	1.43837	−	0.467356i	0.516983	−	0.855996i	$-0.327055\pi$
$827$	41.3642	−	13.4400i	1.43837	−	0.467356i	0.921390	+	0.388640i	$0.127055\pi$
$828$	6.06199	−	4.40429i	0.210669	−	0.153060i
$829$	25.4506	−	18.4910i	0.883937	−	0.642218i	−0.0503530	−	0.998731i	$-0.516035\pi$
$829$	25.4506	−	18.4910i	0.883937	−	0.642218i	0.934290	+	0.356514i	$0.116035\pi$
$830$	3.02379	−	0.409324i	0.104957	−	0.0142078i
$831$	23.3988	+	17.0002i	0.811694	+	0.589730i
$832$	−1.58624	+	3.23788i	−0.0549929	+	0.112253i
$833$	8.06423	+	5.85901i	0.279409	+	0.203003i
$834$	−39.6916	−	12.8966i	−1.37441	−	0.446572i
$835$	−24.2774	−	4.40795i	−0.840155	−	0.152544i
$836$	5.71549	+	17.5905i	0.197674	+	0.608379i
$837$	−30.2367	−	9.82450i	−1.04513	−	0.339584i
$838$	31.3944	+	10.2007i	1.08450	+	0.352376i
$839$	−39.4258	+	12.8102i	−1.36113	+	0.442258i	−0.896420	−	0.443205i	$-0.853841\pi$
$839$	−39.4258	+	12.8102i	−1.36113	+	0.442258i	−0.464710	+	0.885463i	$0.653841\pi$
$840$	−2.69636	−	5.60034i	−0.0930334	−	0.193230i
$841$	−8.76869	+	26.9873i	−0.302369	+	0.930595i
$842$	6.38062	+	4.63579i	0.219891	+	0.159760i
$843$			3.38570i			0.116610i
$844$	12.7570	+	9.26849i	0.439113	+	0.319035i
$845$	25.7824	−	13.4264i	0.886941	−	0.461883i
$846$	−11.0647	+	8.03896i	−0.380412	+	0.276385i
$847$	−4.14108	−	5.69970i	−0.142289	−	0.195844i
$848$	−1.43044	−	4.40243i	−0.0491214	−	0.151180i
$849$	−24.5788			−0.843542
$850$	8.14690	−	5.37562i	0.279436	−	0.184382i
$851$		−	23.3123i		−	0.799136i
$852$	8.06059	−	2.61904i	0.276151	−	0.0897270i
$853$	−2.93336	−	4.03742i	−0.100436	−	0.138239i	0.755841	−	0.654755i	$-0.227228\pi$
$853$	−2.93336	−	4.03742i	−0.100436	−	0.138239i	−0.856277	+	0.516517i	$0.827228\pi$
$854$	0.711128	−	0.516665i	0.0243343	−	0.0176799i
$855$	−8.73063	+	16.2207i	−0.298581	+	0.554738i
$856$	0.394959	−	0.543615i	0.0134994	−	0.0185804i
$857$	0.797459			0.0272407			0.0136203	−	0.999907i	$-0.495664\pi$
$857$	0.797459			0.0272407			0.0136203	+	0.999907i	$0.495664\pi$
$858$	15.6082	−	8.26401i	0.532854	−	0.282129i
$859$	−2.62404	+	8.07596i	−0.0895310	+	0.275548i	−0.985790	−	0.167983i	$-0.946275\pi$
$859$	−2.62404	+	8.07596i	−0.0895310	+	0.275548i	0.896259	+	0.443531i	$0.146275\pi$
$860$	−19.1128	−	10.2873i	−0.651742	−	0.350793i
$861$	0.315697	+	0.971616i	0.0107589	+	0.0331126i
$862$	−8.24928	+	25.3887i	−0.280971	+	0.864741i
$863$	−28.7869	−	9.35342i	−0.979916	−	0.318394i	−0.225104	−	0.974335i	$-0.572272\pi$
$863$	−28.7869	−	9.35342i	−0.979916	−	0.318394i	−0.754812	+	0.655941i	$0.772272\pi$
$864$	3.68824	−	1.19838i	0.125477	−	0.0407698i
$865$	−8.27127	+	7.90672i	−0.281232	+	0.268837i
$866$	6.52117	+	2.11886i	0.221599	+	0.0720017i
$867$	21.5532	+	15.6594i	0.731987	+	0.531819i
$868$	11.2818			0.382931
$869$	−13.5347	+	18.6289i	−0.459133	+	0.631943i
$870$	−3.21447	+	1.54765i	−0.108981	+	0.0524703i
$871$	24.9173	−	4.34865i	0.844290	−	0.147349i
$872$	−12.4936	+	9.07714i	−0.423087	+	0.307391i
$873$	−11.5401	+	3.74959i	−0.390572	+	0.126905i
$874$	−52.9123			−1.78978
$875$	−3.42771	+	14.9991i	−0.115878	+	0.507063i
$876$			3.75547i			0.126886i
$877$	−20.4922	+	6.65833i	−0.691974	+	0.224836i	−0.633830	−	0.773472i	$-0.718518\pi$
$877$	−20.4922	+	6.65833i	−0.691974	+	0.224836i	−0.0581437	+	0.998308i	$0.518518\pi$
$878$	−15.1541	−	20.8578i	−0.511426	−	0.703918i
$879$	−36.3136	−	49.9814i	−1.22483	−	1.68583i
$880$	4.88562	−	2.35225i	0.164694	−	0.0792944i
$881$	−11.4445	−	8.31492i	−0.385575	−	0.280137i	0.378065	−	0.925779i	$-0.376590\pi$
$881$	−11.4445	−	8.31492i	−0.385575	−	0.280137i	−0.763640	+	0.645642i	$0.776590\pi$
$882$			5.51524i			0.185708i
$883$	−28.8025	−	20.9262i	−0.969280	−	0.704223i	−0.0139924	−	0.999902i	$-0.504454\pi$
$883$	−28.8025	−	20.9262i	−0.969280	−	0.704223i	−0.955287	+	0.295679i	$0.904454\pi$
$884$	−5.05449	−	4.89818i	−0.170001	−	0.164744i
$885$	40.6917	+	42.5678i	1.36784	+	1.43090i
$886$	9.26753	−	3.01120i	0.311349	−	0.101163i
$887$	7.76326	−	23.8929i	0.260665	−	0.802244i	−0.731996	−	0.681309i	$-0.761411\pi$
$887$	7.76326	−	23.8929i	0.260665	−	0.802244i	0.992660	−	0.120935i	$-0.0385891\pi$
$888$	−2.09755	+	6.45559i	−0.0703891	+	0.216635i
$889$	21.0170	−	6.82882i	0.704886	−	0.229031i
$890$	−14.2439	−	7.66661i	−0.477456	−	0.256985i
$891$	−25.5391	−	8.29815i	−0.855591	−	0.277998i
$892$	1.68858	−	2.32413i	0.0565379	−	0.0778177i
$893$	96.5785			3.23187
$894$	−18.0577	−	13.1197i	−0.603938	−	0.438787i
$895$	7.00634	+	3.77108i	0.234196	+	0.126053i
$896$	−1.11333	+	0.808880i	−0.0371937	+	0.0270228i
$897$	8.68636	+	49.7718i	0.290029	+	1.66183i
$898$	−10.5850	−	32.5774i	−0.353227	−	1.08712i
$899$		−	6.47553i		−	0.215971i
$900$	5.05581	+	1.89852i	0.168527	+	0.0632838i
$901$	9.03634			0.301044
$902$	−0.847617	+	0.275408i	−0.0282226	+	0.00917007i
$903$	−15.8600	−	21.8295i	−0.527789	−	0.726439i
$904$	11.8608	+	16.3250i	0.394485	+	0.542963i
$905$	4.04485	−	22.2776i	0.134455	−	0.740532i
$906$	33.3517	+	24.2315i	1.10804	+	0.805036i
$907$	43.4857			1.44392			0.721960	−	0.691935i	$-0.243241\pi$
$907$	43.4857			1.44392			0.721960	+	0.691935i	$0.243241\pi$
$908$	−4.98680	+	6.86375i	−0.165493	+	0.227781i
$909$	−0.963527	+	2.96543i	−0.0319582	+	0.0983572i
$910$	11.0946	+	0.0757336i	0.367783	+	0.00251055i
$911$	3.52852	+	10.8597i	0.116905	+	0.359797i	0.992340	−	0.123540i	$-0.0394247\pi$
$911$	3.52852	+	10.8597i	0.116905	+	0.359797i	−0.875435	+	0.483337i	$0.839425\pi$
$912$	14.6523	+	4.76083i	0.485187	+	0.157647i
$913$	−1.02258	+	3.14719i	−0.0338426	+	0.104157i
$914$	4.39600	+	13.5295i	0.145407	+	0.447516i
$915$	−0.515391	+	2.83859i	−0.0170383	+	0.0938409i
$916$	8.39545	+	2.72785i	0.277394	+	0.0901306i
$917$	13.1224	−	18.0614i	0.433340	−	0.596441i
$918$			7.57041i			0.249861i
$919$	33.1773	+	24.1047i	1.09442	+	0.795141i	0.980140	−	0.198308i	$-0.0635447\pi$
$919$	33.1773	+	24.1047i	1.09442	+	0.795141i	0.114278	+	0.993449i	$0.463545\pi$
$920$	2.08089	+	15.3721i	0.0686049	+	0.506804i
$921$	−10.2935	−	14.1678i	−0.339184	−	0.466846i
$922$	−19.4917	+	14.1615i	−0.641924	+	0.466385i
$923$	−2.13169	+	14.9776i	−0.0701655	+	0.492993i
$924$	6.74074			0.221754
$925$	14.0243	−	9.25371i	0.461115	−	0.304260i
$926$	14.4843			0.475985
$927$	−2.08954	−	6.43093i	−0.0686294	−	0.211219i
$928$	0.464279	+	0.639025i	0.0152407	+	0.0209770i
$929$	−1.67156	−	2.30070i	−0.0548420	−	0.0754836i	0.780715	−	0.624887i	$-0.214855\pi$
$929$	−1.67156	−	2.30070i	−0.0548420	−	0.0754836i	−0.835557	+	0.549403i	$0.814855\pi$
$930$	−26.7663	+	25.5866i	−0.877701	+	0.839017i
$931$	22.8919	−	31.5080i	0.750253	−	1.03263i
$932$	−4.52093			−0.148088
$933$	8.27979	+	6.01562i	0.271068	+	0.196943i
$934$	1.70487	+	0.553947i	0.0557852	+	0.0181257i
$935$	1.41994	+	10.4895i	0.0464370	+	0.343043i
$936$	0.548738	−	3.85552i	0.0179361	−	0.126022i
$937$	−13.0449	+	40.1481i	−0.426159	+	1.31158i	0.475721	+	0.879596i	$0.342187\pi$
$937$	−13.0449	+	40.1481i	−0.426159	+	1.31158i	−0.901880	+	0.431987i	$0.857813\pi$
$938$	9.18155	+	2.98327i	0.299788	+	0.0974071i
$939$	−6.62049	−	20.3758i	−0.216051	−	0.664938i
$940$	−3.79815	−	28.0581i	−0.123882	−	0.915153i
$941$	−0.311358	−	0.101166i	−0.0101500	−	0.00329793i	0.303938	−	0.952692i	$-0.401699\pi$
$941$	−0.311358	−	0.101166i	−0.0101500	−	0.00329793i	−0.314088	+	0.949394i	$0.601699\pi$
$942$	−1.57065	+	2.16181i	−0.0511746	+	0.0704357i
$943$		−	2.54964i		−	0.0830277i
$944$	7.66349	−	10.5479i	0.249425	−	0.343305i
$945$	−8.24594	−	8.62613i	−0.268241	−	0.280608i
$946$	19.0436	−	13.8360i	0.619160	−	0.449846i
$947$	−24.6991	−	33.9954i	−0.802613	−	1.10470i	−0.992421	−	0.122881i	$-0.960787\pi$
$947$	−24.6991	−	33.9954i	−0.802613	−	1.10470i	0.189809	−	0.981821i	$-0.439213\pi$
$948$	5.92709	+	18.2417i	0.192503	+	0.592463i
$949$	−6.01989	−	2.94915i	−0.195414	−	0.0957334i
$950$	−21.0033	−	31.8310i	−0.681436	−	1.03273i
$951$			45.9840i			1.49113i
$952$	−0.830145	−	2.55492i	−0.0269052	−	0.0828056i
$953$	13.9157	−	10.1104i	0.450775	−	0.327507i	−0.339127	−	0.940741i	$-0.610132\pi$
$953$	13.9157	−	10.1104i	0.450775	−	0.327507i	0.789902	+	0.613233i	$0.210132\pi$
$954$	2.93880	+	4.04492i	0.0951473	+	0.130959i
$955$	59.9796	−	8.11931i	1.94090	−	0.262735i
$956$	3.30057	−	4.54284i	0.106748	−	0.146926i
$957$		−	3.86903i		−	0.125068i
$958$	−9.21661	−	6.69626i	−0.297775	−	0.216346i
$959$	4.78284	−	14.7201i	0.154446	−	0.475336i
$960$	0.806886	−	4.44404i	0.0260421	−	0.143431i
$961$	−11.1893	−	34.4372i	−0.360945	−	1.11088i
$962$	−8.70091	−	8.43184i	−0.280528	−	0.271853i
$963$	−0.224275	+	0.690248i	−0.00722717	+	0.0222429i
$964$	−0.303502	+	0.0986137i	−0.00977514	+	0.00317613i
$965$	−10.4758	+	5.04374i	−0.337230	+	0.162364i
$966$	−5.95902	+	18.3400i	−0.191728	+	0.590079i
$967$	−21.9315	+	30.1862i	−0.705270	+	0.970721i	0.294616	+	0.955616i	$0.404808\pi$
$967$	−21.9315	+	30.1862i	−0.705270	+	0.970721i	−0.999886	+	0.0151055i	$0.995192\pi$
$968$		−	5.11952i		−	0.164548i
$969$	−17.6777	+	24.3312i	−0.567889	+	0.781632i
$970$	4.48759	−	24.7160i	0.144088	−	0.793583i
$971$	−31.1565	+	22.6365i	−0.999859	+	0.726440i	−0.962058	−	0.272845i	$-0.912035\pi$
$971$	−31.1565	+	22.6365i	−0.999859	+	0.726440i	−0.0378011	+	0.999285i	$0.512035\pi$
$972$	−8.68390	+	6.30922i	−0.278536	+	0.202368i
$973$	27.0413	−	8.78626i	0.866905	−	0.281674i
$974$	−26.1059			−0.836488
$975$	−26.4938	+	24.9822i	−0.848481	+	0.800072i
$976$	0.638741			0.0204456
$977$	9.81876	−	3.19031i	0.314130	−	0.102067i	−0.147709	−	0.989031i	$-0.547190\pi$
$977$	9.81876	−	3.19031i	0.314130	−	0.102067i	0.461839	+	0.886964i	$0.347190\pi$
$978$	12.1545	−	8.83078i	0.388659	−	0.282377i
$979$	14.1923	−	10.3113i	0.453587	−	0.329550i
$980$	−10.0540	−	5.41146i	−0.321164	−	0.172863i
$981$	9.80426	−	13.4944i	0.313026	−	0.430843i
$982$		−	25.1342i		−	0.802065i
$983$	−18.8847	+	25.9925i	−0.602327	+	0.829032i	−0.995919	−	0.0902532i	$-0.971232\pi$
$983$	−18.8847	+	25.9925i	−0.602327	+	0.829032i	0.393592	+	0.919285i	$0.371232\pi$
$984$	−0.229406	+	0.706040i	−0.00731320	+	0.0225077i
$985$	11.8601	−	22.0350i	0.377893	−	0.702092i
$986$	−1.46647	+	0.476485i	−0.0467019	+	0.0151744i
$987$	10.8767	−	33.4752i	0.346211	−	1.06553i
$988$	−19.1378	+	19.7486i	−0.608856	+	0.628285i
$989$	20.8094	+	64.0446i	0.661699	+	2.03650i
$990$	−4.23360	+	4.04700i	−0.134553	+	0.128622i
$991$	−0.573226	+	1.76421i	−0.0182091	+	0.0560420i	−0.959748	−	0.280862i	$-0.909380\pi$
$991$	−0.573226	+	1.76421i	−0.0182091	+	0.0560420i	0.941539	+	0.336904i	$0.109380\pi$
$992$	6.63243	+	4.81874i	0.210580	+	0.152995i
$993$		−	39.3888i		−	1.24997i
$994$	−3.39398	+	4.67141i	−0.107650	+	0.148168i
$995$	−20.7608	−	43.1201i	−0.658161	−	1.36700i
$996$	1.62018	+	2.22999i	0.0513375	+	0.0706600i
$997$	32.0764	−	23.3049i	1.01587	−	0.738073i	0.0504381	−	0.998727i	$-0.483938\pi$
$997$	32.0764	−	23.3049i	1.01587	−	0.738073i	0.965432	+	0.260654i	$0.0839382\pi$
$998$	5.27851	+	16.2456i	0.167088	+	0.514245i
$999$			13.0319i			0.412310i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.p.a.181.4	✓	136
13.12	even	2	inner	650.2.p.a.181.21	yes	136
25.21	even	5	inner	650.2.p.a.571.21	yes	136
325.246	even	10	inner	650.2.p.a.571.4	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.p.a.181.4	✓	136	1.1	even	1	trivial
650.2.p.a.181.21	yes	136	13.12	even	2	inner
650.2.p.a.571.4	yes	136	325.246	even	10	inner
650.2.p.a.571.21	yes	136	25.21	even	5	inner

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.p (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.63416 + 1.18728i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.970013 - 2.01471i) q^{5} +(1.18728 - 1.63416i) q^{6} +1.37615i q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.333771 - 1.02724i) q^{9} +O(q^{10})\)	\(q+(-0.951057 + 0.309017i) q^{2} +(-1.63416 + 1.18728i) q^{3} +(0.809017 - 0.587785i) q^{4} +(-0.970013 - 2.01471i) q^{5} +(1.18728 - 1.63416i) q^{6} +1.37615i q^{7} +(-0.587785 + 0.809017i) q^{8} +(0.333771 - 1.02724i) q^{9} +(1.54512 + 1.61636i) q^{10} +(-2.30628 + 0.749357i) q^{11} +(-0.624192 + 1.92106i) q^{12} +(-2.58923 - 2.50916i) q^{13} +(-0.425253 - 1.30880i) q^{14} +(3.97719 + 2.14068i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.57930 + 1.14743i) q^{17} +1.08010i q^{18} +(4.48315 - 6.17053i) q^{19} +(-1.96898 - 1.05978i) q^{20} +(-1.63388 - 2.24884i) q^{21} +(1.96184 - 1.42536i) q^{22} +(2.14375 + 6.59778i) q^{23} -2.01993i q^{24} +(-3.11815 + 3.90860i) q^{25} +(3.23788 + 1.58624i) q^{26} +(-1.19838 - 3.68824i) q^{27} +(0.808880 + 1.11333i) q^{28} +(0.639025 - 0.464279i) q^{29} +(-4.44404 - 0.806886i) q^{30} +(4.81874 - 6.63243i) q^{31} +1.00000i q^{32} +(2.87913 - 3.96278i) q^{33} +(-1.85658 - 0.603238i) q^{34} +(2.77255 - 1.33488i) q^{35} +(-0.333771 - 1.02724i) q^{36} +(-3.19595 - 1.03843i) q^{37} +(-2.35693 + 7.25389i) q^{38} +(7.21029 + 1.02621i) q^{39} +(2.20010 + 0.399463i) q^{40} +(-0.349537 - 0.113572i) q^{41} +(2.24884 + 1.63388i) q^{42} +9.70699 q^{43} +(-1.42536 + 1.96184i) q^{44} +(-2.39336 + 0.323983i) q^{45} +(-4.07765 - 5.61241i) q^{46} +(7.44276 + 10.2441i) q^{47} +(0.624192 + 1.92106i) q^{48} +5.10621 q^{49} +(1.75772 - 4.68086i) q^{50} -3.94314 q^{51} +(-3.56958 - 0.508042i) q^{52} +(3.74493 - 2.72085i) q^{53} +(2.27946 + 3.13741i) q^{54} +(3.74686 + 3.91962i) q^{55} +(-1.11333 - 0.808880i) q^{56} +15.4064i q^{57} +(-0.464279 + 0.639025i) q^{58} +(12.3998 + 4.02894i) q^{59} +(4.47587 - 0.605889i) q^{60} +(0.197382 + 0.607479i) q^{61} +(-2.53336 + 7.79689i) q^{62} +(1.41364 + 0.459318i) q^{63} +(-0.309017 - 0.951057i) q^{64} +(-2.54366 + 7.65048i) q^{65} +(-1.51365 + 4.65852i) q^{66} +(-4.12347 + 5.67547i) q^{67} +1.95212 q^{68} +(-11.3367 - 8.23656i) q^{69} +(-2.22435 + 2.12631i) q^{70} +(-2.46629 - 3.39455i) q^{71} +(0.634869 + 0.873823i) q^{72} +(1.76821 - 0.574528i) q^{73} +3.36042 q^{74} +(0.454931 - 10.0894i) q^{75} -7.62719i q^{76} +(-1.03123 - 3.17379i) q^{77} +(-7.17451 + 1.25212i) q^{78} +(7.68212 - 5.58139i) q^{79} +(-2.21586 + 0.299956i) q^{80} +(8.95880 + 6.50895i) q^{81} +0.367525 q^{82} +(0.802101 - 1.10400i) q^{83} +(-2.64367 - 0.858981i) q^{84} +(0.779799 - 4.29485i) q^{85} +(-9.23189 + 2.99962i) q^{86} +(-0.493035 + 1.51741i) q^{87} +(0.749357 - 2.30628i) q^{88} +(-6.88009 + 2.23548i) q^{89} +(2.17610 - 1.04771i) q^{90} +(3.45298 - 3.56317i) q^{91} +(5.61241 + 4.07765i) q^{92} +16.5596i q^{93} +(-10.2441 - 7.44276i) q^{94} +(-16.7806 - 3.04678i) q^{95} +(-1.18728 - 1.63416i) q^{96} +(-6.60321 - 9.08854i) q^{97} +(-4.85630 + 1.57791i) q^{98} +2.61922i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q + 34 q^{4} - 30 q^{9}+O(q^{10}) \) 136 * q + 34 * q^4 - 30 * q^9	\( 136 q + 34 q^{4} - 30 q^{9} - 4 q^{10} - 12 q^{13} + 8 q^{14} - 34 q^{16} + 4 q^{23} + 40 q^{25} + 4 q^{26} - 12 q^{27} + 16 q^{29} + 10 q^{30} - 18 q^{35} + 30 q^{36} - 24 q^{38} + 32 q^{39} + 4 q^{40} - 12 q^{42} + 24 q^{43} - 104 q^{49} + 84 q^{51} + 12 q^{52} + 4 q^{53} - 60 q^{55} - 8 q^{56} + 12 q^{61} + 18 q^{62} + 34 q^{64} + 26 q^{65} + 16 q^{66} + 84 q^{69} - 88 q^{74} - 214 q^{75} + 56 q^{78} - 8 q^{79} - 74 q^{81} + 160 q^{82} - 164 q^{87} - 16 q^{90} - 40 q^{91} + 16 q^{92} + 48 q^{94} - 4 q^{95}+O(q^{100}) \) 136 * q + 34 * q^4 - 30 * q^9 - 4 * q^10 - 12 * q^13 + 8 * q^14 - 34 * q^16 + 4 * q^23 + 40 * q^25 + 4 * q^26 - 12 * q^27 + 16 * q^29 + 10 * q^30 - 18 * q^35 + 30 * q^36 - 24 * q^38 + 32 * q^39 + 4 * q^40 - 12 * q^42 + 24 * q^43 - 104 * q^49 + 84 * q^51 + 12 * q^52 + 4 * q^53 - 60 * q^55 - 8 * q^56 + 12 * q^61 + 18 * q^62 + 34 * q^64 + 26 * q^65 + 16 * q^66 + 84 * q^69 - 88 * q^74 - 214 * q^75 + 56 * q^78 - 8 * q^79 - 74 * q^81 + 160 * q^82 - 164 * q^87 - 16 * q^90 - 40 * q^91 + 16 * q^92 + 48 * q^94 - 4 * q^95

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