LMFDB - Embedded newform 143.2.h.b.53.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [143,2,Mod(14,143)] 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("143.14"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(143, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.h (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	16.0.273503893564697265625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 3 x^{15} + 7 x^{14} - 9 x^{13} + 19 x^{12} - 16 x^{11} + 49 x^{10} - 32 x^{9} + 98 x^{8} + \cdots + 1 $ x^16 - 3x^15 + 7x^14 - 9x^13 + 19x^12 - 16x^11 + 49x^10 - 32x^9 + 98x^8 - 110x^7 + 145x^6 - 40x^5 + 52x^4 + 24x^3 + 19x^2 + 6*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			53.1
Root			$-0.208288 + 0.151330i$ of defining polynomial
Character	$\chi$	$=$	143.53
Dual form			143.2.h.b.27.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.620702 + 1.91032i) q^{2} +(1.77587 - 1.29025i) q^{3} +(-1.64603 - 1.19591i) q^{4} +(-0.772191 - 2.37656i) q^{5} +(1.36250 + 4.19336i) q^{6} +(3.01248 + 2.18870i) q^{7} +(0.0562420 - 0.0408622i) q^{8} +(0.561939 - 1.72947i) q^{9} +5.01930 q^{10} +(3.29749 + 0.355767i) q^{11} -4.46618 q^{12} +(-0.309017 + 0.951057i) q^{13} +(-6.05098 + 4.39629i) q^{14} +(-4.43767 - 3.22415i) q^{15} +(-1.21431 - 3.73725i) q^{16} +(-1.47843 - 4.55015i) q^{17} +(2.95505 + 2.14697i) q^{18} +(-5.41545 + 3.93455i) q^{19} +(-1.57111 + 4.83537i) q^{20} +8.17376 q^{21} +(-2.72639 + 6.07845i) q^{22} -3.70084 q^{23} +(0.0471564 - 0.145132i) q^{24} +(-1.00667 + 0.731388i) q^{25} +(-1.62502 - 1.18065i) q^{26} +(0.801459 + 2.46664i) q^{27} +(-2.34116 - 7.20534i) q^{28} +(-7.25458 - 5.27076i) q^{29} +(8.91365 - 6.47614i) q^{30} +(-0.439024 + 1.35118i) q^{31} +8.03213 q^{32} +(6.31495 - 3.62278i) q^{33} +9.60994 q^{34} +(2.87536 - 8.84944i) q^{35} +(-2.99327 + 2.17474i) q^{36} +(-1.63048 - 1.18461i) q^{37} +(-4.15489 - 12.7874i) q^{38} +(0.678324 + 2.08767i) q^{39} +(-0.140541 - 0.102109i) q^{40} +(-3.08783 + 2.24344i) q^{41} +(-5.07347 + 15.6145i) q^{42} +4.32275 q^{43} +(-5.00231 - 4.52912i) q^{44} -4.54411 q^{45} +(2.29712 - 7.06981i) q^{46} +(-1.69194 + 1.22927i) q^{47} +(-6.97845 - 5.07014i) q^{48} +(2.12154 + 6.52943i) q^{49} +(-0.772347 - 2.37704i) q^{50} +(-8.49634 - 6.17295i) q^{51} +(1.64603 - 1.19591i) q^{52} +(-0.660210 + 2.03192i) q^{53} -5.20954 q^{54} +(-1.70079 - 8.11140i) q^{55} +0.258863 q^{56} +(-4.54060 + 13.9745i) q^{57} +(14.5718 - 10.5870i) q^{58} +(5.98775 + 4.35035i) q^{59} +(3.44874 + 10.6141i) q^{60} +(3.30982 + 10.1866i) q^{61} +(-2.30868 - 1.67736i) q^{62} +(5.47812 - 3.98008i) q^{63} +(-2.55694 + 7.86946i) q^{64} +2.49886 q^{65} +(3.00098 + 14.3123i) q^{66} +1.03598 q^{67} +(-3.00804 + 9.25779i) q^{68} +(-6.57223 + 4.77501i) q^{69} +(15.1206 + 10.9857i) q^{70} +(-1.56941 - 4.83014i) q^{71} +(-0.0390654 - 0.120231i) q^{72} +(-4.73341 - 3.43903i) q^{73} +(3.27503 - 2.37945i) q^{74} +(-0.844047 + 2.59771i) q^{75} +13.6194 q^{76} +(9.15496 + 8.28895i) q^{77} -4.40916 q^{78} +(3.55898 - 10.9534i) q^{79} +(-7.94413 + 5.77175i) q^{80} +(9.01939 + 6.55297i) q^{81} +(-2.36907 - 7.29125i) q^{82} +(0.539768 + 1.66123i) q^{83} +(-13.4543 - 9.77511i) q^{84} +(-9.67208 + 7.02717i) q^{85} +(-2.68314 + 8.25786i) q^{86} -19.6838 q^{87} +(0.199995 - 0.114734i) q^{88} -4.32737 q^{89} +(2.82054 - 8.68072i) q^{90} +(-3.01248 + 2.18870i) q^{91} +(6.09171 + 4.42589i) q^{92} +(0.963703 + 2.96597i) q^{93} +(-1.29811 - 3.99516i) q^{94} +(13.5325 + 9.83191i) q^{95} +(14.2641 - 10.3634i) q^{96} +(4.24142 - 13.0537i) q^{97} -13.7902 q^{98} +(2.46827 - 5.50299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{2} + 5 q^{3} - 8 q^{4} + 5 q^{5} - 4 q^{6} + 9 q^{7} - 4 q^{8} - 7 q^{9} - 12 q^{10} + 6 q^{11} - 14 q^{12} + 4 q^{13} - q^{14} - 10 q^{15} + 10 q^{16} - 6 q^{17} + 20 q^{18} + 2 q^{19} - 21 q^{20}+ \cdots - 7 q^{99}+O(q^{100}) $ 16 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 + 5 * q^5 - 4 * q^6 + 9 * q^7 - 4 * q^8 - 7 * q^9 - 12 * q^10 + 6 * q^11 - 14 * q^12 + 4 * q^13 - q^14 - 10 * q^15 + 10 * q^16 - 6 * q^17 + 20 * q^18 + 2 * q^19 - 21 * q^20 - 8 * q^21 + 2 * q^22 - 46 * q^23 + 3 * q^24 + 23 * q^25 + 3 * q^26 + 17 * q^27 - 9 * q^28 - 25 * q^29 + 22 * q^30 + 3 * q^31 + 24 * q^32 - 10 * q^33 + 4 * q^34 + 26 * q^35 - 2 * q^36 - 7 * q^37 + 5 * q^38 + 25 * q^40 - 3 * q^41 - 12 * q^42 - 16 * q^43 + 32 * q^44 - 46 * q^45 - 11 * q^46 + 13 * q^47 - 24 * q^48 + 19 * q^49 - 19 * q^50 - 23 * q^51 + 8 * q^52 - 14 * q^53 + 6 * q^54 - 5 * q^55 - 68 * q^56 + 23 * q^57 + 20 * q^58 + 16 * q^59 + 34 * q^60 - 13 * q^61 + 28 * q^62 + 18 * q^63 - 40 * q^64 + 10 * q^65 + 41 * q^66 - 62 * q^67 + 13 * q^68 + 4 * q^69 - 2 * q^70 + 54 * q^71 + 21 * q^72 - 42 * q^73 + 42 * q^74 + 51 * q^75 - 4 * q^76 + 14 * q^77 - 6 * q^78 - 15 * q^79 - 19 * q^80 + q^81 - 7 * q^82 - 43 * q^83 - 35 * q^84 - 3 * q^85 - 32 * q^86 + 4 * q^87 + 41 * q^88 - 30 * q^89 + 26 * q^90 - 9 * q^91 + 3 * q^92 + 49 * q^93 + 4 * q^94 + 23 * q^95 + 23 * q^96 - 12 * q^97 + 24 * q^98 - 7 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.620702	+	1.91032i	−0.438903	+	1.35080i	0.450131	+	0.892962i	$0.351377\pi$
$2$	−0.620702	+	1.91032i	−0.438903	+	1.35080i	−0.889034	+	0.457841i	$0.848623\pi$
$3$	1.77587	−	1.29025i	1.02530	−	0.744925i	0.0579388	−	0.998320i	$-0.481547\pi$
$3$	1.77587	−	1.29025i	1.02530	−	0.744925i	0.967363	+	0.253395i	$0.0815472\pi$
$4$	−1.64603	−	1.19591i	−0.823017	−	0.597957i
$5$	−0.772191	−	2.37656i	−0.345334	−	1.06283i	−0.961405	−	0.275138i	$-0.911276\pi$
$5$	−0.772191	−	2.37656i	−0.345334	−	1.06283i	0.616070	−	0.787691i	$-0.288724\pi$
$6$	1.36250	+	4.19336i	0.556240	+	1.71193i
$7$	3.01248	+	2.18870i	1.13861	+	0.827250i	0.986925	−	0.161179i	$-0.0515296\pi$
$7$	3.01248	+	2.18870i	1.13861	+	0.827250i	0.151687	+	0.988429i	$0.451530\pi$
$8$	0.0562420	−	0.0408622i	0.0198846	−	0.0144470i
$9$	0.561939	−	1.72947i	0.187313	−	0.576490i
$10$	5.01930			1.58724
$11$	3.29749	+	0.355767i	0.994230	+	0.107268i
$11$	3.29749	+	0.355767i	0.994230	+	0.107268i
$12$	−4.46618			−1.28927
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i
$14$	−6.05098	+	4.39629i	−1.61719	+	1.17496i
$15$	−4.43767	−	3.22415i	−1.14580	−	0.832473i
$16$	−1.21431	−	3.73725i	−0.303577	−	0.934314i
$17$	−1.47843	−	4.55015i	−0.358573	−	1.10357i	−0.953909	−	0.300097i	$-0.902981\pi$
$17$	−1.47843	−	4.55015i	−0.358573	−	1.10357i	0.595336	−	0.803477i	$-0.297019\pi$
$18$	2.95505	+	2.14697i	0.696512	+	0.506046i
$19$	−5.41545	+	3.93455i	−1.24239	+	0.902648i	−0.997755	−	0.0669673i	$-0.978668\pi$
$19$	−5.41545	+	3.93455i	−1.24239	+	0.902648i	−0.244634	+	0.969616i	$0.578668\pi$
$20$	−1.57111	+	4.83537i	−0.351310	+	1.08122i
$21$	8.17376			1.78366
$22$	−2.72639	+	6.07845i	−0.581268	+	1.29593i
$23$	−3.70084			−0.771679			−0.385840	−	0.922566i	$-0.626088\pi$
$23$	−3.70084			−0.771679			−0.385840	+	0.922566i	$0.626088\pi$
$24$	0.0471564	−	0.145132i	0.00962575	−	0.0296250i
$25$	−1.00667	+	0.731388i	−0.201334	+	0.146278i
$26$	−1.62502	−	1.18065i	−0.318692	−	0.231544i
$27$	0.801459	+	2.46664i	0.154241	+	0.474704i
$28$	−2.34116	−	7.20534i	−0.442437	−	1.36168i
$29$	−7.25458	−	5.27076i	−1.34714	−	0.978755i	−0.999149	−	0.0412582i	$-0.986863\pi$
$29$	−7.25458	−	5.27076i	−1.34714	−	0.978755i	−0.347993	−	0.937497i	$-0.613137\pi$
$30$	8.91365	−	6.47614i	1.62740	−	1.18238i
$31$	−0.439024	+	1.35118i	−0.0788511	+	0.242679i	−0.982710	−	0.185152i	$-0.940722\pi$
$31$	−0.439024	+	1.35118i	−0.0788511	+	0.242679i	0.903859	+	0.427831i	$0.140722\pi$
$32$	8.03213			1.41989
$33$	6.31495	−	3.62278i	1.09929	−	0.630645i
$34$	9.60994			1.64809
$35$	2.87536	−	8.84944i	0.486024	−	1.49583i
$36$	−2.99327	+	2.17474i	−0.498878	+	0.362456i
$37$	−1.63048	−	1.18461i	−0.268049	−	0.194749i	0.445639	−	0.895213i	$-0.352976\pi$
$37$	−1.63048	−	1.18461i	−0.268049	−	0.194749i	−0.713688	+	0.700464i	$0.752976\pi$
$38$	−4.15489	−	12.7874i	−0.674013	−	2.07440i
$39$	0.678324	+	2.08767i	0.108619	+	0.334294i
$40$	−0.140541	−	0.102109i	−0.0222215	−	0.0161449i
$41$	−3.08783	+	2.24344i	−0.482237	+	0.350366i	−0.802191	−	0.597067i	$-0.796333\pi$
$41$	−3.08783	+	2.24344i	−0.482237	+	0.350366i	0.319954	+	0.947433i	$0.396333\pi$
$42$	−5.07347	+	15.6145i	−0.782853	+	2.40937i
$43$	4.32275			0.659214			0.329607	−	0.944118i	$-0.393084\pi$
$43$	4.32275			0.659214			0.329607	+	0.944118i	$0.393084\pi$
$44$	−5.00231	−	4.52912i	−0.754127	−	0.682790i
$45$	−4.54411			−0.677396
$46$	2.29712	−	7.06981i	0.338692	−	1.04239i
$47$	−1.69194	+	1.22927i	−0.246795	+	0.179307i	−0.704305	−	0.709897i	$-0.748741\pi$
$47$	−1.69194	+	1.22927i	−0.246795	+	0.179307i	0.457510	+	0.889204i	$0.348741\pi$
$48$	−6.97845	−	5.07014i	−1.00725	−	0.731811i
$49$	2.12154	+	6.52943i	0.303077	+	0.932776i
$50$	−0.772347	−	2.37704i	−0.109226	−	0.336164i
$51$	−8.49634	−	6.17295i	−1.18973	−	0.864386i
$52$	1.64603	−	1.19591i	0.228264	−	0.165843i
$53$	−0.660210	+	2.03192i	−0.0906868	+	0.279105i	−0.986106	−	0.166120i	$-0.946876\pi$
$53$	−0.660210	+	2.03192i	−0.0906868	+	0.279105i	0.895419	+	0.445225i	$0.146876\pi$
$54$	−5.20954			−0.708929
$55$	−1.70079	−	8.11140i	−0.229334	−	1.09374i
$56$	0.258863			0.0345920
$57$	−4.54060	+	13.9745i	−0.601418	+	1.85097i
$58$	14.5718	−	10.5870i	1.91337	−	1.39014i
$59$	5.98775	+	4.35035i	0.779539	+	0.566368i	0.904840	−	0.425751i	$-0.139990\pi$
$59$	5.98775	+	4.35035i	0.779539	+	0.566368i	−0.125302	+	0.992119i	$0.539990\pi$
$60$	3.44874	+	10.6141i	0.445230	+	1.37028i
$61$	3.30982	+	10.1866i	0.423779	+	1.30426i	0.904159	+	0.427196i	$0.140499\pi$
$61$	3.30982	+	10.1866i	0.423779	+	1.30426i	−0.480380	+	0.877060i	$0.659501\pi$
$62$	−2.30868	−	1.67736i	−0.293203	−	0.213025i
$63$	5.47812	−	3.98008i	0.690178	−	0.501443i
$64$	−2.55694	+	7.86946i	−0.319618	+	0.983683i
$65$	2.49886			0.309946
$66$	3.00098	+	14.3123i	0.369396	+	1.76172i
$67$	1.03598			0.126565			0.0632825	−	0.997996i	$-0.479843\pi$
$67$	1.03598			0.126565			0.0632825	+	0.997996i	$0.479843\pi$
$68$	−3.00804	+	9.25779i	−0.364778	+	1.12267i
$69$	−6.57223	+	4.77501i	−0.791204	+	0.574843i
$70$	15.1206	+	10.9857i	1.80725	+	1.31305i
$71$	−1.56941	−	4.83014i	−0.186255	−	0.573233i	0.813713	−	0.581267i	$-0.197443\pi$
$71$	−1.56941	−	4.83014i	−0.186255	−	0.573233i	−0.999968	+	0.00803398i	$0.997443\pi$
$72$	−0.0390654	−	0.120231i	−0.00460390	−	0.0141693i
$73$	−4.73341	−	3.43903i	−0.554004	−	0.402508i	0.275256	−	0.961371i	$-0.411238\pi$
$73$	−4.73341	−	3.43903i	−0.554004	−	0.402508i	−0.829260	+	0.558864i	$0.811238\pi$
$74$	3.27503	−	2.37945i	0.380714	−	0.276605i
$75$	−0.844047	+	2.59771i	−0.0974621	+	0.299957i
$76$	13.6194			1.56225
$77$	9.15496	+	8.28895i	1.04330	+	0.944613i
$78$	−4.40916			−0.499239
$79$	3.55898	−	10.9534i	0.400416	−	1.23235i	−0.524246	−	0.851567i	$-0.675653\pi$
$79$	3.55898	−	10.9534i	0.400416	−	1.23235i	0.924663	−	0.380787i	$-0.124347\pi$
$80$	−7.94413	+	5.77175i	−0.888181	+	0.645301i
$81$	9.01939	+	6.55297i	1.00215	+	0.728108i
$82$	−2.36907	−	7.29125i	−0.261620	−	0.805184i
$83$	0.539768	+	1.66123i	0.0592472	+	0.182344i	0.976300	−	0.216422i	$-0.0694386\pi$
$83$	0.539768	+	1.66123i	0.0592472	+	0.182344i	−0.917053	+	0.398766i	$0.869439\pi$
$84$	−13.4543	−	9.77511i	−1.46798	−	1.06655i
$85$	−9.67208	+	7.02717i	−1.04908	+	0.762204i
$86$	−2.68314	+	8.25786i	−0.289331	+	0.890468i
$87$	−19.6838			−2.11033
$88$	0.199995	−	0.114734i	0.0213195	−	0.0122306i
$89$	−4.32737			−0.458700			−0.229350	−	0.973344i	$-0.573660\pi$
$89$	−4.32737			−0.458700			−0.229350	+	0.973344i	$0.573660\pi$
$90$	2.82054	−	8.68072i	0.297311	−	0.915029i
$91$	−3.01248	+	2.18870i	−0.315794	+	0.229438i
$92$	6.09171	+	4.42589i	0.635105	+	0.461431i
$93$	0.963703	+	2.96597i	0.0999313	+	0.307557i
$94$	−1.29811	−	3.99516i	−0.133890	−	0.412070i
$95$	13.5325	+	9.83191i	1.38840	+	1.00873i
$96$	14.2641	−	10.3634i	1.45582	−	1.05771i
$97$	4.24142	−	13.0537i	0.430651	−	1.32541i	−0.466827	−	0.884348i	$-0.654603\pi$
$97$	4.24142	−	13.0537i	0.430651	−	1.32541i	0.897478	−	0.441059i	$-0.145397\pi$
$98$	−13.7902			−1.39302
$99$	2.46827	−	5.50299i	0.248071	−	0.553071i
$100$	2.53169			0.253169
$101$	−5.08483	+	15.6495i	−0.505960	+	1.55718i	0.293192	+	0.956054i	$0.405283\pi$
$101$	−5.08483	+	15.6495i	−0.505960	+	1.55718i	−0.799151	+	0.601130i	$0.794717\pi$
$102$	17.0660	−	12.3992i	1.68979	−	1.22770i
$103$	−7.40442	−	5.37962i	−0.729579	−	0.530070i	0.159851	−	0.987141i	$-0.448899\pi$
$103$	−7.40442	−	5.37962i	−0.729579	−	0.530070i	−0.889430	+	0.457071i	$0.848899\pi$
$104$	0.0214825	+	0.0661165i	0.00210654	+	0.00648325i
$105$	−6.31170	−	19.4254i	−0.615959	−	1.89573i
$106$	−3.47183	−	2.52243i	−0.337214	−	0.245000i
$107$	7.59770	−	5.52005i	0.734497	−	0.533644i	−0.156486	−	0.987680i	$-0.550016\pi$
$107$	7.59770	−	5.52005i	0.734497	−	0.533644i	0.890983	+	0.454037i	$0.150016\pi$
$108$	1.63066	−	5.01864i	0.156910	−	0.482919i
$109$	4.22727			0.404899			0.202449	−	0.979293i	$-0.435110\pi$
$109$	4.22727			0.404899			0.202449	+	0.979293i	$0.435110\pi$
$110$	16.5511	+	1.78570i	1.57808	+	0.170260i
$111$	−4.42396			−0.419904
$112$	4.52164	−	13.9162i	0.427255	−	1.31495i
$113$	13.1632	−	9.56364i	1.23829	−	0.899672i	0.240809	−	0.970573i	$-0.422587\pi$
$113$	13.1632	−	9.56364i	1.23829	−	0.899672i	0.997483	+	0.0709007i	$0.0225874\pi$
$114$	−23.8776	−	17.3481i	−2.23634	−	1.62479i
$115$	2.85776	+	8.79527i	0.266487	+	0.820163i
$116$	5.63791	+	17.3517i	0.523467	+	1.61106i
$117$	1.47117	+	1.06887i	0.136010	+	0.0988171i
$118$	−12.0272	+	8.73827i	−1.10719	+	0.804423i
$119$	5.50515	−	16.9431i	0.504656	−	1.55317i
$120$	−0.381329			−0.0348104
$121$	10.7469	+	2.34627i	0.976987	+	0.213298i
$122$	−21.5141			−1.94779
$123$	−2.58900	+	7.96812i	−0.233442	+	0.718461i
$124$	2.33854	−	1.69905i	0.210007	−	0.152579i
$125$	−7.59258	−	5.51633i	−0.679101	−	0.493396i
$126$	4.20297	+	12.9354i	0.374431	+	1.15238i
$127$	−5.64177	−	17.3636i	−0.500626	−	1.54077i	−0.808002	−	0.589180i	$-0.799451\pi$
$127$	−5.64177	−	17.3636i	−0.500626	−	1.54077i	0.307376	−	0.951588i	$-0.400549\pi$
$128$	−0.449869	−	0.326849i	−0.0397632	−	0.0288896i
$129$	7.67667	−	5.57742i	0.675893	−	0.491065i
$130$	−1.55105	+	4.77364i	−0.136036	+	0.418676i
$131$	2.65205			0.231711			0.115855	−	0.993266i	$-0.463039\pi$
$131$	2.65205			0.231711			0.115855	+	0.993266i	$0.463039\pi$
$132$	−14.7272	−	1.58892i	−1.28184	−	0.138298i
$133$	−24.9255			−2.16131
$134$	−0.643034	+	1.97905i	−0.0555497	+	0.170964i
$135$	5.24323	−	3.80943i	0.451265	−	0.327863i
$136$	−0.269079	−	0.195498i	−0.0230734	−	0.0167638i
$137$	2.77703	+	8.54682i	0.237258	+	0.730204i	0.996814	+	0.0797626i	$0.0254162\pi$
$137$	2.77703	+	8.54682i	0.237258	+	0.730204i	−0.759556	+	0.650442i	$0.774584\pi$
$138$	−5.04241	−	15.5190i	−0.429239	−	1.32106i
$139$	16.5432	+	12.0193i	1.40317	+	1.01947i	0.994271	+	0.106888i	$0.0340888\pi$
$139$	16.5432	+	12.0193i	1.40317	+	1.01947i	0.408904	+	0.912578i	$0.365911\pi$
$140$	−15.3161	+	11.1278i	−1.29445	+	0.940471i
$141$	−1.41861	+	4.36605i	−0.119469	+	0.367688i
$142$	10.2013			0.856072
$143$	−1.35733	+	3.02616i	−0.113506	+	0.253060i
$144$	−7.14583			−0.595486
$145$	−6.92435	+	21.3110i	−0.575036	+	1.76978i
$146$	9.50769	−	6.90774i	0.786862	−	0.571689i
$147$	12.1922	+	8.85814i	1.00559	+	0.730607i
$148$	1.26713	+	3.89982i	0.104157	+	0.320563i
$149$	6.19656	+	19.0711i	0.507642	+	1.56236i	0.796283	+	0.604925i	$0.206797\pi$
$149$	6.19656	+	19.0711i	0.507642	+	1.56236i	−0.288640	+	0.957438i	$0.593203\pi$
$150$	−4.43856	−	3.22481i	−0.362407	−	0.263304i
$151$	3.77602	−	2.74344i	0.307288	−	0.223258i	−0.423444	−	0.905922i	$-0.639179\pi$
$151$	3.77602	−	2.74344i	0.307288	−	0.223258i	0.730732	+	0.682664i	$0.239179\pi$
$152$	−0.143801	+	0.442574i	−0.0116638	+	0.0358975i
$153$	−8.70014			−0.703365
$154$	−21.5171	+	12.3440i	−1.73390	+	0.994707i
$155$	3.55016			0.285156
$156$	1.38012	−	4.24759i	0.110498	−	0.340079i
$157$	1.79264	−	1.30243i	0.143068	−	0.103945i	−0.513949	−	0.857821i	$-0.671818\pi$
$157$	1.79264	−	1.30243i	0.143068	−	0.103945i	0.657017	+	0.753876i	$0.271818\pi$
$158$	18.7155	+	13.5976i	1.48892	+	1.08177i
$159$	1.44923	+	4.46026i	0.114931	+	0.353722i
$160$	−6.20234	−	19.0888i	−0.490338	−	1.50910i
$161$	−11.1487	−	8.10003i	−0.878643	−	0.638371i
$162$	−18.1166	+	13.1625i	−1.42338	+	1.03414i
$163$	−2.54510	+	7.83300i	−0.199347	+	0.613528i	0.800551	+	0.599265i	$0.204540\pi$
$163$	−2.54510	+	7.83300i	−0.199347	+	0.613528i	−0.999898	+	0.0142633i	$0.995460\pi$
$164$	7.76562			0.606393
$165$	−13.4861	−	12.2104i	−1.04989	−	0.950577i
$166$	−3.50853			−0.272315
$167$	−1.87514	+	5.77110i	−0.145103	+	0.446581i	−0.997024	−	0.0770888i	$-0.975438\pi$
$167$	−1.87514	+	5.77110i	−0.145103	+	0.446581i	0.851921	+	0.523670i	$0.175438\pi$
$168$	0.459709	−	0.333998i	0.0354673	−	0.0257685i
$169$	−0.809017	−	0.587785i	−0.0622321	−	0.0452143i
$170$	−7.42071	−	22.8386i	−0.569142	−	1.75164i
$171$	3.76154	+	11.5768i	0.287652	+	0.885302i
$172$	−7.11540	−	5.16964i	−0.542544	−	0.394181i
$173$	−2.76776	+	2.01090i	−0.210429	+	0.152886i	−0.688008	−	0.725703i	$-0.741514\pi$
$173$	−2.76776	+	2.01090i	−0.210429	+	0.152886i	0.477579	+	0.878589i	$0.341514\pi$
$174$	12.2178	−	37.6025i	0.926227	−	2.85064i
$175$	−4.63336			−0.350249
$176$	−2.67457	−	12.7556i	−0.201604	−	0.961487i
$177$	16.2465			1.22116
$178$	2.68601	−	8.26668i	0.201325	−	0.619614i
$179$	21.1505	−	15.3667i	1.58086	−	1.14856i	0.665158	−	0.746702i	$-0.268364\pi$
$179$	21.1505	−	15.3667i	1.58086	−	1.14856i	0.915701	−	0.401859i	$-0.131636\pi$
$180$	7.47976	+	5.43436i	0.557508	+	0.405054i
$181$	5.09611	+	15.6842i	0.378791	+	1.16580i	0.940885	+	0.338725i	$0.109996\pi$
$181$	5.09611	+	15.6842i	0.378791	+	1.16580i	−0.562095	+	0.827073i	$0.690004\pi$
$182$	−2.31127	−	7.11335i	−0.171323	−	0.527277i
$183$	19.0210	+	13.8196i	1.40607	+	1.02157i
$184$	−0.208143	+	0.151225i	−0.0153445	+	0.0111484i
$185$	−1.55626	+	4.78967i	−0.114418	+	0.352143i
$186$	−6.26414			−0.459309
$187$	−3.25633	−	15.5301i	−0.238126	−	1.13567i
$188$	4.25509			0.310334
$189$	−2.98434	+	9.18485i	−0.217079	+	0.668100i
$190$	−27.1818	+	19.7487i	−1.97197	+	1.43272i
$191$	9.58360	+	6.96289i	0.693445	+	0.503817i	0.877791	−	0.479044i	$-0.159017\pi$
$191$	9.58360	+	6.96289i	0.693445	+	0.503817i	−0.184346	+	0.982861i	$0.559017\pi$
$192$	5.61275	+	17.2743i	0.405065	+	1.24666i
$193$	−7.45016	−	22.9292i	−0.536274	−	1.65048i	−0.740879	−	0.671638i	$-0.765591\pi$
$193$	−7.45016	−	22.9292i	−0.536274	−	1.65048i	0.204605	−	0.978845i	$-0.434409\pi$
$194$	22.3042	+	16.2050i	1.60135	+	1.16345i
$195$	4.43767	−	3.22415i	0.317788	−	0.230886i
$196$	4.31651	−	13.2849i	0.308322	−	0.948918i
$197$	−7.32955			−0.522209			−0.261104	−	0.965311i	$-0.584087\pi$
$197$	−7.32955			−0.522209			−0.261104	+	0.965311i	$0.584087\pi$
$198$	8.98043	+	8.13092i	0.638211	+	0.577839i
$199$	3.03177			0.214916			0.107458	−	0.994210i	$-0.465729\pi$
$199$	3.03177			0.214916			0.107458	+	0.994210i	$0.465729\pi$
$200$	−0.0267310	+	0.0822695i	−0.00189017	+	0.00581733i
$201$	1.83977	−	1.33667i	0.129767	−	0.0942814i
$202$	−26.7395	−	19.4274i	−1.88138	−	1.36690i
$203$	−10.3182	−	31.7561i	−0.724196	−	2.22884i
$204$	6.60295	+	20.3218i	0.462299	+	1.42281i
$205$	7.71605	+	5.60604i	0.538912	+	0.391543i
$206$	14.8728	−	10.8057i	1.03623	−	0.752868i
$207$	−2.07965	+	6.40050i	−0.144545	+	0.444865i
$208$	3.92958			0.272467
$209$	−19.2572	+	11.0475i	−1.33205	+	0.764172i
$210$	41.0265			2.83110
$211$	−2.40547	+	7.40328i	−0.165600	+	0.509663i	−0.999080	−	0.0428860i	$-0.986345\pi$
$211$	−2.40547	+	7.40328i	−0.165600	+	0.509663i	0.833480	+	0.552549i	$0.186345\pi$
$212$	3.51673	−	2.55505i	0.241530	−	0.175482i
$213$	−9.01916	−	6.55280i	−0.617983	−	0.448991i
$214$	5.82918	+	17.9404i	0.398475	+	1.22638i
$215$	−3.33799	−	10.2733i	−0.227649	−	0.700632i
$216$	0.145868	+	0.105979i	0.00992505	+	0.00721097i
$217$	−4.27987	+	3.10951i	−0.290537	+	0.211087i
$218$	−2.62387	+	8.07545i	−0.177711	+	0.546938i
$219$	−12.8431			−0.867859
$220$	−6.90097	+	15.3856i	−0.465264	+	1.03730i
$221$	4.78431			0.321828
$222$	2.74596	−	8.45120i	0.184297	−	0.567208i
$223$	−7.98218	+	5.79939i	−0.534526	+	0.388356i	−0.822048	−	0.569418i	$-0.807169\pi$
$223$	−7.98218	+	5.79939i	−0.534526	+	0.388356i	0.287522	+	0.957774i	$0.407169\pi$
$224$	24.1967	+	17.5799i	1.61671	+	1.17461i
$225$	0.699227	+	2.15200i	0.0466151	+	0.143467i
$226$	10.0992	+	31.0822i	0.671790	+	2.06756i
$227$	−14.6099	−	10.6147i	−0.969694	−	0.704524i	−0.0143124	−	0.999898i	$-0.504556\pi$
$227$	−14.6099	−	10.6147i	−0.969694	−	0.704524i	−0.955382	+	0.295373i	$0.904556\pi$
$228$	24.1863	−	17.5724i	1.60178	−	1.16376i
$229$	2.74537	−	8.44938i	0.181419	−	0.558351i	−0.818449	−	0.574579i	$-0.805166\pi$
$229$	2.74537	−	8.44938i	0.181419	−	0.558351i	0.999868	+	0.0162282i	$0.00516583\pi$
$230$	−18.5756			−1.22484
$231$	26.9529	+	2.90795i	1.77337	+	0.191329i
$232$	−0.623387			−0.0409274
$233$	2.32449	−	7.15405i	0.152282	−	0.468677i	−0.845593	−	0.533828i	$-0.820753\pi$
$233$	2.32449	−	7.15405i	0.152282	−	0.468677i	0.997875	+	0.0651510i	$0.0207529\pi$
$234$	−2.95505	+	2.14697i	−0.193178	+	0.140352i
$235$	4.22793	+	3.07177i	0.275800	+	0.200380i
$236$	−4.65339	−	14.3217i	−0.302910	−	0.932261i
$237$	−7.81231	−	24.0438i	−0.507464	−	1.56181i
$238$	28.9498	+	21.0332i	1.87654	+	1.36338i
$239$	−16.4100	+	11.9226i	−1.06148	+	0.771208i	−0.974361	−	0.224990i	$-0.927765\pi$
$239$	−16.4100	+	11.9226i	−1.06148	+	0.771208i	−0.0871157	+	0.996198i	$0.527765\pi$
$240$	−6.66079	+	20.4998i	−0.429952	+	1.32326i
$241$	3.18069			0.204886			0.102443	−	0.994739i	$-0.467334\pi$
$241$	3.18069			0.204886			0.102443	+	0.994739i	$0.467334\pi$
$242$	−11.1527	+	19.0737i	−0.716925	+	1.22610i
$243$	16.6915			1.07076
$244$	6.73419	−	20.7257i	0.431112	−	1.32683i
$245$	13.8793	−	10.0839i	0.886719	−	0.644239i
$246$	−13.6147	−	9.89166i	−0.868042	−	0.630669i
$247$	−2.06852	−	6.36624i	−0.131617	−	0.405074i
$248$	0.0305205	+	0.0939324i	0.00193805	+	0.00596472i
$249$	3.10196	+	2.25371i	0.196579	+	0.142823i
$250$	15.2507	−	11.0803i	0.964540	−	0.700779i
$251$	−4.63052	+	14.2513i	−0.292276	+	0.899533i	0.691847	+	0.722044i	$0.256797\pi$
$251$	−4.63052	+	14.2513i	−0.292276	+	0.899533i	−0.984123	+	0.177489i	$0.943203\pi$
$252$	−13.7770			−0.867870
$253$	−12.2035	−	1.31664i	−0.767227	−	0.0827763i
$254$	36.6719			2.30100
$255$	−8.10959	+	24.9588i	−0.507842	+	1.56298i
$256$	−12.4847	+	9.07067i	−0.780294	+	0.566917i
$257$	−5.24407	−	3.81004i	−0.327116	−	0.237664i	0.412090	−	0.911143i	$-0.364799\pi$
$257$	−5.24407	−	3.81004i	−0.327116	−	0.237664i	−0.739206	+	0.673479i	$0.764799\pi$
$258$	5.88977	+	18.1268i	0.366681	+	1.12853i
$259$	−2.31903	−	7.13724i	−0.144097	−	0.443486i
$260$	−4.11321	−	2.98842i	−0.255091	−	0.185334i
$261$	−13.1922	+	9.58473i	−0.816579	+	0.593280i
$262$	−1.64613	+	5.06628i	−0.101698	+	0.312996i
$263$	−7.61604			−0.469625			−0.234813	−	0.972041i	$-0.575448\pi$
$263$	−7.61604			−0.469625			−0.234813	+	0.972041i	$0.575448\pi$
$264$	0.207131	−	0.461796i	0.0127480	−	0.0284216i
$265$	5.33878			0.327959
$266$	15.4713	−	47.6158i	0.948606	−	2.91951i
$267$	−7.68486	+	5.58338i	−0.470306	+	0.341697i
$268$	−1.70526	−	1.23894i	−0.104165	−	0.0756804i
$269$	−4.93817	−	15.1981i	−0.301085	−	0.926646i	−0.981109	−	0.193456i	$-0.938030\pi$
$269$	−4.93817	−	15.1981i	−0.301085	−	0.926646i	0.680024	−	0.733190i	$-0.261970\pi$
$270$	4.02276	+	12.3808i	0.244817	+	0.753471i
$271$	−24.0038	−	17.4398i	−1.45813	−	1.05939i	−0.983846	−	0.179018i	$-0.942708\pi$
$271$	−24.0038	−	17.4398i	−1.45813	−	1.05939i	−0.474282	−	0.880373i	$-0.657292\pi$
$272$	−15.2098	+	11.0506i	−0.922230	+	0.670039i
$273$	−2.52583	+	7.77370i	−0.152870	+	0.470486i
$274$	−18.0509			−1.09050
$275$	−3.57969	+	2.05360i	−0.215863	+	0.123837i
$276$	16.5286			0.994906
$277$	4.24920	−	13.0777i	0.255310	−	0.785762i	−0.738459	−	0.674298i	$-0.764446\pi$
$277$	4.24920	−	13.0777i	0.255310	−	0.785762i	0.993769	−	0.111464i	$-0.0355539\pi$
$278$	−33.2292	+	24.1424i	−1.99296	+	1.44797i
$279$	2.09012	+	1.51856i	0.125132	+	0.0909137i
$280$	−0.199892	−	0.615204i	−0.0119458	−	0.0367654i
$281$	0.642463	+	1.97730i	0.0383261	+	0.117956i	0.968389	−	0.249444i	$-0.0802480\pi$
$281$	0.642463	+	1.97730i	0.0383261	+	0.117956i	−0.930063	+	0.367400i	$0.880248\pi$
$282$	−7.46003	−	5.42003i	−0.444238	−	0.322758i
$283$	1.05800	−	0.768682i	0.0628915	−	0.0456934i	−0.555895	−	0.831252i	$-0.687624\pi$
$283$	1.05800	−	0.768682i	0.0628915	−	0.0456934i	0.618787	+	0.785559i	$0.287624\pi$
$284$	−3.19314	+	9.82746i	−0.189478	+	0.583152i
$285$	36.7175			2.17496
$286$	−4.93845	−	4.47129i	−0.292016	−	0.264393i
$287$	−14.2122			−0.838921
$288$	4.51356	−	13.8913i	0.265964	−	0.818554i
$289$	−4.76484	+	3.46186i	−0.280285	+	0.203639i
$290$	−36.4129	−	26.4555i	−2.13824	−	1.55352i
$291$	−9.31035	−	28.6543i	−0.545782	−	1.67974i
$292$	3.67858	+	11.3215i	0.215273	+	0.662541i
$293$	3.49936	+	2.54243i	0.204435	+	0.148530i	0.685292	−	0.728268i	$-0.259675\pi$
$293$	3.49936	+	2.54243i	0.204435	+	0.148530i	−0.480858	+	0.876799i	$0.659675\pi$
$294$	−24.4896	+	17.7928i	−1.42826	+	1.03769i
$295$	5.71519	−	17.5895i	0.332751	−	1.02410i
$296$	−0.140107			−0.00814356
$297$	1.76525	+	8.41884i	0.102430	+	0.488510i
$298$	−40.2781			−2.33325
$299$	1.14362	−	3.51971i	0.0661374	−	0.203550i
$300$	4.49596	−	3.26651i	0.259575	−	0.188592i
$301$	13.0222	+	9.46120i	0.750588	+	0.545334i
$302$	2.89708	+	8.91629i	0.166708	+	0.513075i
$303$	11.1617	+	34.3523i	0.641224	+	1.97349i
$304$	21.2804	+	15.4611i	1.22052	+	0.886758i
$305$	21.6532	−	15.7320i	1.23986	−	0.900809i
$306$	5.40019	−	16.6201i	0.308709	−	0.950107i
$307$	12.6012			0.719186			0.359593	−	0.933109i	$-0.382915\pi$
$307$	12.6012			0.719186			0.359593	+	0.933109i	$0.382915\pi$
$308$	−5.15652	−	24.5924i	−0.293820	−	1.40128i
$309$	−20.0904			−1.14290
$310$	−2.20359	+	6.78196i	−0.125156	+	0.385190i
$311$	−2.00166	+	1.45429i	−0.113504	+	0.0824655i	−0.643089	−	0.765791i	$-0.722348\pi$
$311$	−2.00166	+	1.45429i	−0.113504	+	0.0824655i	0.529585	+	0.848257i	$0.322348\pi$
$312$	0.123457	+	0.0896967i	0.00698937	+	0.00507808i
$313$	8.82902	+	27.1729i	0.499046	+	1.53591i	0.810555	+	0.585662i	$0.199166\pi$
$313$	8.82902	+	27.1729i	0.499046	+	1.53591i	−0.311509	+	0.950243i	$0.600834\pi$
$314$	1.37537	+	4.23295i	0.0776165	+	0.238879i
$315$	−13.6891	−	9.94568i	−0.771291	−	0.560376i
$316$	−18.9575	+	13.7734i	−1.06644	+	0.774817i
$317$	0.853586	−	2.62707i	0.0479422	−	0.147551i	−0.924220	−	0.381861i	$-0.875283\pi$
$317$	0.853586	−	2.62707i	0.0479422	−	0.147551i	0.972162	+	0.234310i	$0.0752832\pi$
$318$	−9.42009			−0.528252
$319$	−22.0467	−	19.9612i	−1.23438	−	1.11761i
$320$	20.6767			1.15586
$321$	6.37032	−	19.6058i	0.355557	−	1.09429i
$322$	22.3937	−	16.2700i	1.24795	−	0.906691i
$323$	25.9092	+	18.8241i	1.44163	+	1.04740i
$324$	−7.00943	−	21.5728i	−0.389413	−	1.19849i
$325$	−0.384514	−	1.18341i	−0.0213290	−	0.0656438i
$326$	−13.3838	−	9.72392i	−0.741262	−	0.538558i
$327$	7.50710	−	5.45422i	0.415143	−	0.301619i
$328$	−0.0819937	+	0.252351i	−0.00452735	+	0.0139337i
$329$	−7.78744			−0.429335
$330$	31.6966	−	18.1838i	1.74484	−	1.00099i
$331$	−9.21192			−0.506333			−0.253166	−	0.967423i	$-0.581472\pi$
$331$	−9.21192			−0.506333			−0.253166	+	0.967423i	$0.581472\pi$
$332$	1.09822	−	3.37996i	0.0602725	−	0.185500i
$333$	−2.96497	+	2.15418i	−0.162480	+	0.118048i
$334$	−9.86077	−	7.16427i	−0.539557	−	0.392011i
$335$	−0.799973	−	2.46206i	−0.0437072	−	0.134517i
$336$	−9.92545	−	30.5474i	−0.541478	−	1.66650i
$337$	−4.80726	−	3.49268i	−0.261868	−	0.190258i	0.449102	−	0.893480i	$-0.351744\pi$
$337$	−4.80726	−	3.49268i	−0.261868	−	0.190258i	−0.710970	+	0.703222i	$0.751744\pi$
$338$	1.62502	−	1.18065i	0.0883894	−	0.0642186i
$339$	11.0368	−	33.9677i	0.599435	−	1.84487i
$340$	24.3245			1.31918
$341$	−1.92838	+	4.29930i	−0.104428	+	0.232820i
$342$	−24.4503			−1.32212
$343$	0.154819	−	0.476484i	0.00835944	−	0.0257277i
$344$	0.243120	−	0.176637i	0.0131082	−	0.00952364i
$345$	16.4231	+	11.9321i	0.884190	+	0.642402i
$346$	−2.12351	−	6.53548i	−0.114160	−	0.351350i
$347$	3.07132	+	9.45256i	0.164877	+	0.507440i	0.999027	−	0.0440976i	$-0.0140412\pi$
$347$	3.07132	+	9.45256i	0.164877	+	0.507440i	−0.834150	+	0.551538i	$0.814041\pi$
$348$	32.4002	+	23.5401i	1.73683	+	1.26188i
$349$	−10.7060	+	7.77835i	−0.573078	+	0.416366i	−0.836222	−	0.548391i	$-0.815241\pi$
$349$	−10.7060	+	7.77835i	−0.573078	+	0.416366i	0.263144	+	0.964757i	$0.415241\pi$
$350$	2.87594	−	8.85123i	0.153725	−	0.473118i
$351$	−2.59357			−0.138435
$352$	26.4859	+	2.85757i	1.41170	+	0.152309i
$353$	26.8587			1.42955			0.714773	−	0.699357i	$-0.246530\pi$
$353$	26.8587			1.42955			0.714773	+	0.699357i	$0.246530\pi$
$354$	−10.0843	+	31.0361i	−0.535972	+	1.64955i
$355$	−10.2672	+	7.45959i	−0.544929	+	0.395914i
$356$	7.12300	+	5.17516i	0.377518	+	0.274283i
$357$	−12.0844	−	37.1918i	−0.639572	−	1.96840i
$358$	16.2273	+	49.9424i	0.857638	+	2.63954i
$359$	21.3232	+	15.4922i	1.12540	+	0.817649i	0.985018	−	0.172449i	$-0.0551680\pi$
$359$	21.3232	+	15.4922i	1.12540	+	0.817649i	0.140379	+	0.990098i	$0.455168\pi$
$360$	−0.255570	+	0.185682i	−0.0134697	+	0.00978632i
$361$	7.97504	−	24.5447i	0.419739	−	1.29182i
$362$	−33.1251			−1.74102
$363$	22.1124	−	9.69943i	1.16060	−	0.509088i
$364$	7.57614			0.397098
$365$	−4.51795	+	13.9048i	−0.236480	+	0.727812i
$366$	−38.2063	+	27.7585i	−1.99707	+	1.45096i
$367$	−2.30166	−	1.67225i	−0.120146	−	0.0872908i	0.526090	−	0.850429i	$-0.323658\pi$
$367$	−2.30166	−	1.67225i	−0.120146	−	0.0872908i	−0.646235	+	0.763138i	$0.723658\pi$
$368$	4.49396	+	13.8310i	0.234264	+	0.720990i
$369$	2.14479	+	6.60097i	0.111653	+	0.343633i
$370$	−8.18385	−	5.94591i	−0.425458	−	0.309113i
$371$	−6.43612	+	4.67612i	−0.334147	+	0.242772i
$372$	1.96076	−	6.03460i	0.101661	−	0.312879i
$373$	−17.1648			−0.888758			−0.444379	−	0.895839i	$-0.646576\pi$
$373$	−17.1648			−0.888758			−0.444379	+	0.895839i	$0.646576\pi$
$374$	31.6887	+	3.41890i	1.63858	+	0.176787i
$375$	−20.6009			−1.06383
$376$	−0.0449276	+	0.138273i	−0.00231696	+	0.00713088i
$377$	7.25458	−	5.27076i	0.373630	−	0.271458i
$378$	−15.6937	−	11.4021i	−0.807195	−	0.586461i
$379$	0.392027	+	1.20654i	0.0201371	+	0.0619756i	0.960620	−	0.277865i	$-0.0896268\pi$
$379$	0.392027	+	1.20654i	0.0201371	+	0.0619756i	−0.940483	+	0.339841i	$0.889627\pi$
$380$	−10.5168	−	32.3673i	−0.539499	−	1.66041i
$381$	−32.4224	−	23.5562i	−1.66105	−	1.20682i
$382$	−19.2499	+	13.9859i	−0.984913	+	0.715581i
$383$	−4.61002	+	14.1882i	−0.235561	+	0.724982i	0.761486	+	0.648182i	$0.224470\pi$
$383$	−4.61002	+	14.1882i	−0.235561	+	0.724982i	−0.997046	+	0.0768002i	$0.975530\pi$
$384$	−1.22063			−0.0622898
$385$	12.6298	−	28.1580i	0.643674	−	1.43506i
$386$	48.4266			2.46485
$387$	2.42912	−	7.47607i	0.123479	−	0.380030i
$388$	−22.5927	+	16.4145i	−1.14697	+	0.833322i
$389$	−24.6712	−	17.9247i	−1.25088	−	0.908818i	−0.252608	−	0.967569i	$-0.581288\pi$
$389$	−24.6712	−	17.9247i	−1.25088	−	0.908818i	−0.998273	+	0.0587505i	$0.981288\pi$
$390$	3.40471	+	10.4786i	0.172404	+	0.530606i
$391$	5.47145	+	16.8394i	0.276703	+	0.851605i
$392$	0.386127	+	0.280538i	0.0195024	+	0.0141693i
$393$	4.70971	−	3.42181i	0.237574	−	0.172607i
$394$	4.54947	−	14.0018i	0.229199	−	0.705401i
$395$	−28.7796			−1.44806
$396$	−10.6440	+	6.10626i	−0.534879	+	0.306851i
$397$	20.3234			1.02000			0.510002	−	0.860173i	$-0.329645\pi$
$397$	20.3234			1.02000			0.510002	+	0.860173i	$0.329645\pi$
$398$	−1.88182	+	5.79166i	−0.0943273	+	0.290310i
$399$	−44.2645	+	32.1601i	−2.21600	+	1.61002i
$400$	3.95579	+	2.87405i	0.197790	+	0.143703i
$401$	3.68041	+	11.3271i	0.183791	+	0.565650i	0.999925	−	0.0122120i	$-0.00388731\pi$
$401$	3.68041	+	11.3271i	0.183791	+	0.565650i	−0.816135	+	0.577862i	$0.803887\pi$
$402$	1.41152	+	4.34423i	0.0704005	+	0.216670i
$403$	−1.14938	−	0.835074i	−0.0572547	−	0.0415980i
$404$	27.0853	−	19.6786i	1.34754	−	0.979047i
$405$	8.60883	−	26.4952i	0.427776	−	1.31656i
$406$	67.0691			3.32858
$407$	−4.95503	−	4.48631i	−0.245612	−	0.222378i
$408$	−0.730092			−0.0361449
$409$	−4.91465	+	15.1257i	−0.243014	+	0.747919i	0.752943	+	0.658085i	$0.228633\pi$
$409$	−4.91465	+	15.1257i	−0.243014	+	0.747919i	−0.995957	+	0.0898334i	$0.971367\pi$
$410$	−15.4987	+	11.2605i	−0.765427	+	0.556115i
$411$	15.9592	+	11.5950i	0.787209	+	0.571941i
$412$	5.75436	+	17.7101i	0.283497	+	0.872513i
$413$	8.51639	+	26.2107i	0.419064	+	1.28975i
$414$	−10.9362	−	7.94560i	−0.537484	−	0.390505i
$415$	3.53122	−	2.56558i	0.173341	−	0.125939i
$416$	−2.48206	+	7.63901i	−0.121693	+	0.374533i
$417$	44.8865			2.19810
$418$	−9.15136	−	43.6446i	−0.447608	−	2.13473i
$419$	−28.9938			−1.41644			−0.708220	−	0.705992i	$-0.750501\pi$
$419$	−28.9938			−1.41644			−0.708220	+	0.705992i	$0.750501\pi$
$420$	−12.8418	+	39.5231i	−0.626618	+	1.92853i
$421$	−8.08489	+	5.87402i	−0.394033	+	0.286282i	−0.767106	−	0.641520i	$-0.778304\pi$
$421$	−8.08489	+	5.87402i	−0.394033	+	0.286282i	0.373073	+	0.927802i	$0.378304\pi$
$422$	−12.6496	−	9.19047i	−0.615772	−	0.447385i
$423$	1.17521	+	3.61693i	0.0571408	+	0.175861i
$424$	0.0458971	+	0.141257i	0.00222896	+	0.00686003i
$425$	4.81622	+	3.49919i	0.233621	+	0.169736i
$426$	18.1162	−	13.1622i	0.877732	−	0.637710i
$427$	−12.3245	+	37.9311i	−0.596427	+	1.83561i
$428$	−19.1076			−0.923600
$429$	1.49404	+	7.12538i	0.0721330	+	0.344017i
$430$	21.6972			1.04633
$431$	8.81274	−	27.1228i	0.424495	−	1.30646i	−0.478982	−	0.877825i	$-0.658994\pi$
$431$	8.81274	−	27.1228i	0.424495	−	1.30646i	0.903477	−	0.428636i	$-0.141006\pi$
$432$	8.24523	−	5.99051i	0.396699	−	0.288219i
$433$	0.808774	+	0.587609i	0.0388672	+	0.0282387i	0.607049	−	0.794664i	$-0.292353\pi$
$433$	0.808774	+	0.587609i	0.0388672	+	0.0282387i	−0.568182	+	0.822903i	$0.692353\pi$
$434$	−3.28365	−	10.1060i	−0.157620	−	0.485105i
$435$	15.1997	+	46.7797i	0.728768	+	2.24292i
$436$	−6.95822	−	5.05545i	−0.333239	−	0.242112i
$437$	20.0417	−	14.5612i	0.958726	−	0.696555i
$438$	7.97177	−	24.5346i	0.380906	−	1.17231i
$439$	−18.2738			−0.872163			−0.436082	−	0.899907i	$-0.643634\pi$
$439$	−18.2738			−0.872163			−0.436082	+	0.899907i	$0.643634\pi$
$440$	−0.427105	−	0.386703i	−0.0203615	−	0.0184354i
$441$	12.4846			0.594506
$442$	−2.96963	+	9.13959i	−0.141251	+	0.434726i
$443$	24.7637	−	17.9918i	1.17656	−	0.854818i	0.184777	−	0.982780i	$-0.440844\pi$
$443$	24.7637	−	17.9918i	1.17656	−	0.854818i	0.991779	+	0.127962i	$0.0408436\pi$
$444$	7.28199	+	5.29068i	0.345588	+	0.251084i
$445$	3.34155	+	10.2842i	0.158405	+	0.487520i
$446$	−6.12417	−	18.8482i	−0.289988	−	0.892490i
$447$	35.6107	+	25.8727i	1.68433	+	1.22374i
$448$	−24.9266	+	18.1103i	−1.17767	+	0.855629i
$449$	−3.93439	+	12.1088i	−0.185676	+	0.571451i	−0.999959	−	0.00901637i	$-0.997130\pi$
$449$	−3.93439	+	12.1088i	−0.185676	+	0.571451i	0.814284	+	0.580467i	$0.197130\pi$
$450$	−4.54503			−0.214255
$451$	−10.9802	+	6.29916i	−0.517038	+	0.296616i
$452$	−33.1044			−1.55710
$453$	3.16602	−	9.74401i	0.148753	−	0.457814i
$454$	29.3460	−	21.3211i	1.37727	−	1.00065i
$455$	7.52778	+	5.46925i	0.352908	+	0.256403i
$456$	0.315658	+	0.971496i	0.0147820	+	0.0454945i
$457$	1.81411	+	5.58326i	0.0848606	+	0.261174i	0.984479	−	0.175503i	$-0.0561552\pi$
$457$	1.81411	+	5.58326i	0.0848606	+	0.261174i	−0.899618	+	0.436677i	$0.856155\pi$
$458$	14.4370	+	10.4891i	0.674597	+	0.490123i
$459$	10.0387	−	7.29352i	0.468565	−	0.340432i
$460$	5.81442	−	17.8950i	0.271099	−	0.834356i
$461$	21.3679			0.995202			0.497601	−	0.867406i	$-0.334214\pi$
$461$	21.3679			0.995202			0.497601	+	0.867406i	$0.334214\pi$
$462$	−22.2848	+	49.6837i	−1.03678	+	2.31150i
$463$	−36.3173			−1.68781			−0.843905	−	0.536493i	$-0.819749\pi$
$463$	−36.3173			−1.68781			−0.843905	+	0.536493i	$0.819749\pi$
$464$	−10.8889	+	33.5125i	−0.505504	+	1.55578i
$465$	6.30465	−	4.58059i	0.292371	−	0.212420i
$466$	12.2237	+	8.88106i	0.566254	+	0.411407i
$467$	−3.17350	−	9.76702i	−0.146852	−	0.451964i	0.850393	−	0.526149i	$-0.176364\pi$
$467$	−3.17350	−	9.76702i	−0.146852	−	0.451964i	−0.997244	+	0.0741850i	$0.976364\pi$
$468$	−1.14333	−	3.51880i	−0.0528503	−	0.162656i
$469$	3.12087	+	2.26744i	0.144108	+	0.104701i
$470$	−8.49236	+	6.17006i	−0.391723	+	0.284604i
$471$	1.50305	−	4.62591i	0.0692568	−	0.213150i
$472$	0.514528			0.0236831
$473$	14.2542	+	1.53789i	0.655410	+	0.0707124i
$474$	50.7806			2.33243
$475$	2.57388	−	7.92159i	0.118098	−	0.363467i
$476$	−29.3242	+	21.3052i	−1.34407	+	0.976524i
$477$	3.14314	+	2.28363i	0.143915	+	0.104560i
$478$	−12.5903	−	38.7489i	−0.575865	−	1.77233i
$479$	−1.80992	−	5.57036i	−0.0826973	−	0.254516i	0.901155	−	0.433496i	$-0.142720\pi$
$479$	−1.80992	−	5.57036i	−0.0826973	−	0.254516i	−0.983853	+	0.178980i	$0.942720\pi$
$480$	−35.6439	−	25.8968i	−1.62691	−	1.18202i
$481$	1.63048	−	1.18461i	0.0743433	−	0.0540136i
$482$	−1.97426	+	6.07615i	−0.0899251	+	0.276761i
$483$	−30.2498			−1.37641
$484$	−14.8838	−	16.7144i	−0.676534	−	0.759744i
$485$	−34.2982			−1.55740
$486$	−10.3605	+	31.8862i	−0.469960	+	1.44639i
$487$	9.44177	−	6.85985i	0.427848	−	0.310849i	−0.352940	−	0.935646i	$-0.614818\pi$
$487$	9.44177	−	6.85985i	0.427848	−	0.310849i	0.780788	+	0.624796i	$0.214818\pi$
$488$	0.602397	+	0.437667i	0.0272692	+	0.0198122i
$489$	5.58675	+	17.1942i	0.252641	+	0.777550i
$490$	10.6487	+	32.7732i	0.481057	+	1.48054i
$491$	−5.73719	−	4.16832i	−0.258916	−	0.188113i	0.450753	−	0.892649i	$-0.351156\pi$
$491$	−5.73719	−	4.16832i	−0.258916	−	0.188113i	−0.709669	+	0.704535i	$0.751156\pi$
$492$	13.7908	−	10.0196i	0.621736	−	0.451718i
$493$	−13.2573	+	40.8019i	−0.597081	+	1.83763i
$494$	13.4455			0.604942
$495$	−14.9842	−	1.61664i	−0.673488	−	0.0726628i
$496$	5.58280			0.250675
$497$	5.84391	−	17.9857i	0.262135	−	0.806769i
$498$	−6.23071	+	4.52688i	−0.279205	+	0.202854i
$499$	−17.2359	−	12.5226i	−0.771585	−	0.560589i	0.130857	−	0.991401i	$-0.458227\pi$
$499$	−17.2359	−	12.5226i	−0.771585	−	0.560589i	−0.902442	+	0.430812i	$0.858227\pi$
$500$	5.90059	+	18.1601i	0.263882	+	0.812146i
$501$	4.11613	+	12.6682i	0.183895	+	0.565971i
$502$	−24.3504	−	17.6916i	−1.08681	−	0.789615i
$503$	7.83054	−	5.68922i	0.349146	−	0.253670i	−0.399364	−	0.916792i	$-0.630769\pi$
$503$	7.83054	−	5.68922i	0.349146	−	0.253670i	0.748511	+	0.663123i	$0.230769\pi$
$504$	0.145465	−	0.447696i	0.00647954	−	0.0199420i
$505$	41.1184			1.82975
$506$	10.0899	−	22.4954i	0.448552	−	1.00004i
$507$	−2.19510			−0.0974879
$508$	−11.4788	+	35.3281i	−0.509289	+	1.56743i
$509$	8.58768	−	6.23931i	0.380642	−	0.276553i	−0.380968	−	0.924588i	$-0.624409\pi$
$509$	8.58768	−	6.23931i	0.380642	−	0.276553i	0.761610	+	0.648036i	$0.224409\pi$
$510$	−42.6457	−	30.9839i	−1.88838	−	1.37199i
$511$	−6.73234	−	20.7200i	−0.297821	−	0.916600i
$512$	−9.92231	−	30.5377i	−0.438508	−	1.34959i
$513$	−14.0454	−	10.2046i	−0.620118	−	0.450542i
$514$	10.5334	−	7.65298i	0.464609	−	0.337558i
$515$	−7.06737	+	21.7511i	−0.311426	+	0.958469i
$516$	−19.3062			−0.849907
$517$	−6.01649	+	3.45156i	−0.264605	+	0.151799i
$518$	15.0739			0.662308
$519$	−2.32064	+	7.14219i	−0.101865	+	0.313508i
$520$	0.140541	−	0.102109i	0.00616313	−	0.00447778i
$521$	8.19142	+	5.95141i	0.358872	+	0.260736i	0.752582	−	0.658499i	$-0.228808\pi$
$521$	8.19142	+	5.95141i	0.358872	+	0.260736i	−0.393709	+	0.919235i	$0.628808\pi$
$522$	−10.1215	−	31.1507i	−0.443005	−	1.36343i
$523$	0.335960	+	1.03398i	0.0146905	+	0.0452127i	0.958133	−	0.286323i	$-0.0924332\pi$
$523$	0.335960	+	1.03398i	0.0146905	+	0.0452127i	−0.943443	+	0.331536i	$0.892433\pi$
$524$	−4.36537	−	3.17163i	−0.190702	−	0.138553i
$525$	−8.22827	+	5.97819i	−0.359111	+	0.260910i
$526$	4.72729	−	14.5491i	0.206120	−	0.634371i
$527$	6.79713			0.296088
$528$	−21.2076	−	19.2014i	−0.922940	−	0.835634i
$529$	−9.30376			−0.404511
$530$	−3.31379	+	10.1988i	−0.143942	+	0.443008i
$531$	10.8886	−	7.91100i	0.472523	−	0.343308i
$532$	41.0282	+	29.8087i	1.77880	+	1.29237i
$533$	−1.17944	−	3.62996i	−0.0510874	−	0.157231i
$534$	−5.89606	−	18.1462i	−0.255147	−	0.785263i
$535$	−18.9856	−	13.7938i	−0.820819	−	0.596360i
$536$	0.0582655	−	0.0423324i	0.00251669	−	0.00182848i
$537$	17.7337	−	54.5787i	0.765265	−	2.35524i
$538$	32.0985			1.38386
$539$	4.67280	+	22.2855i	0.201272	+	0.959905i
$540$	−13.1863			−0.567447
$541$	−4.47556	+	13.7744i	−0.192420	+	0.592207i	0.807577	+	0.589762i	$0.200778\pi$
$541$	−4.47556	+	13.7744i	−0.192420	+	0.592207i	−0.999997	+	0.00244499i	$0.999222\pi$
$542$	48.2149	−	35.0301i	2.07101	−	1.50467i
$543$	29.2866	+	21.2779i	1.25681	+	0.913124i
$544$	−11.8750	−	36.5474i	−0.509135	−	1.56696i
$545$	−3.26426	−	10.0463i	−0.139825	−	0.430338i
$546$	−13.2825	−	9.65031i	−0.568439	−	0.412995i
$547$	10.6661	−	7.74939i	0.456050	−	0.331340i	−0.335929	−	0.941887i	$-0.609050\pi$
$547$	10.6661	−	7.74939i	0.456050	−	0.331340i	0.791980	+	0.610547i	$0.209050\pi$
$548$	5.65018	−	17.3895i	0.241364	−	0.742841i
$549$	19.4773			0.831270
$550$	−1.70113	−	8.11304i	−0.0725366	−	0.345941i
$551$	60.0249			2.55715
$552$	−0.174518	+	0.537112i	−0.00742799	+	0.0228610i
$553$	34.6950	−	25.2074i	1.47538	−	1.07193i
$554$	22.3451	+	16.2347i	0.949354	+	0.689746i
$555$	3.41614	+	10.5138i	0.145007	+	0.446286i
$556$	−12.8566	−	39.5684i	−0.545240	−	1.67808i
$557$	2.51831	+	1.82966i	0.106704	+	0.0775250i	0.639858	−	0.768493i	$-0.278993\pi$
$557$	2.51831	+	1.82966i	0.106704	+	0.0775250i	−0.533154	+	0.846018i	$0.678993\pi$
$558$	−4.19828	+	3.05023i	−0.177727	+	0.129126i
$559$	−1.33580	+	4.11118i	−0.0564985	+	0.173884i
$560$	−36.5642			−1.54512
$561$	−25.8205	−	23.3780i	−1.09014	−	0.987018i
$562$	−4.17606			−0.176156
$563$	−2.92988	+	9.01726i	−0.123480	+	0.380032i	−0.993621	−	0.112770i	$-0.964028\pi$
$563$	−2.92988	+	9.01726i	−0.123480	+	0.380032i	0.870141	+	0.492803i	$0.164028\pi$
$564$	7.55651	−	5.49012i	0.318186	−	0.231176i
$565$	−32.8931	−	23.8982i	−1.38382	−	1.00541i
$566$	0.811729	+	2.49824i	0.0341195	+	0.105009i
$567$	12.8283	+	39.4814i	0.538738	+	1.65806i
$568$	−0.285637	−	0.207528i	−0.0119851	−	0.00870766i
$569$	−26.9186	+	19.5575i	−1.12849	+	0.819893i	−0.985474	−	0.169827i	$-0.945679\pi$
$569$	−26.9186	+	19.5575i	−1.12849	+	0.819893i	−0.143013	+	0.989721i	$0.545679\pi$
$570$	−22.7907	+	70.1424i	−0.954595	+	2.93794i
$571$	−40.1844			−1.68167			−0.840833	−	0.541295i	$-0.817934\pi$
$571$	−40.1844			−1.68167			−0.840833	+	0.541295i	$0.817934\pi$
$572$	5.85325	−	3.35791i	0.244736	−	0.140401i
$573$	26.0031			1.08630
$574$	8.82156	−	27.1500i	0.368205	−	1.13322i
$575$	3.72553	−	2.70675i	0.155365	−	0.112879i
$576$	12.1732	+	8.84431i	0.507215	+	0.368513i
$577$	1.37412	+	4.22912i	0.0572055	+	0.176061i	0.975576	−	0.219660i	$-0.0704948\pi$
$577$	1.37412	+	4.22912i	0.0572055	+	0.176061i	−0.918371	+	0.395721i	$0.870495\pi$
$578$	−3.65573	−	11.2512i	−0.152058	−	0.467987i
$579$	−42.8150	−	31.1069i	−1.77933	−	1.29276i
$580$	36.8838	−	26.7976i	1.53152	−	1.11271i
$581$	−2.00990	+	6.18583i	−0.0833846	+	0.256631i
$582$	60.5180			2.50855
$583$	−2.89992	+	6.46534i	−0.120103	+	0.267767i
$584$	−0.406743			−0.0168311
$585$	1.40421	−	4.32171i	0.0580568	−	0.178681i
$586$	−7.02892	+	5.10681i	−0.290362	+	0.210960i
$587$	21.6033	+	15.6957i	0.891663	+	0.647831i	0.936311	−	0.351172i	$-0.114217\pi$
$587$	21.6033	+	15.6957i	0.891663	+	0.647831i	−0.0446484	+	0.999003i	$0.514217\pi$
$588$	−9.47518	−	29.1616i	−0.390750	−	1.20260i
$589$	−2.93877	−	9.04459i	−0.121090	−	0.372676i
$590$	30.0543	+	21.8357i	1.23732	+	0.898963i
$591$	−13.0164	+	9.45694i	−0.535422	+	0.389006i
$592$	−2.44729	+	7.53198i	−0.100583	+	0.309563i
$593$	−42.3130			−1.73759			−0.868794	−	0.495174i	$-0.835104\pi$
$593$	−42.3130			−1.73759			−0.868794	+	0.495174i	$0.835104\pi$
$594$	−17.1784	−	1.85338i	−0.704838	−	0.0760452i
$595$	−44.5173			−1.82503
$596$	12.6076	−	38.8022i	0.516427	−	1.58940i
$597$	5.38404	−	3.91173i	0.220354	−	0.160097i
$598$	6.01394	+	4.36938i	0.245928	+	0.178677i
$599$	9.39743	+	28.9223i	0.383969	+	1.18173i	0.937226	+	0.348724i	$0.113385\pi$
$599$	9.39743	+	28.9223i	0.383969	+	1.18173i	−0.553257	+	0.833011i	$0.686615\pi$
$600$	0.0586772	+	0.180590i	0.00239549	+	0.00737255i
$601$	29.5173	+	21.4455i	1.20403	+	0.874782i	0.994675	−	0.103057i	$-0.0328623\pi$
$601$	29.5173	+	21.4455i	1.20403	+	0.874782i	0.209359	+	0.977839i	$0.432862\pi$
$602$	−26.1569	+	19.0041i	−1.06607	+	0.774549i
$603$	0.582156	−	1.79169i	0.0237072	−	0.0729634i
$604$	−9.49638			−0.386402
$605$	−2.72257	−	27.3523i	−0.110688	−	1.11203i
$606$	−72.5520			−2.94723
$607$	13.0077	−	40.0336i	0.527966	−	1.62491i	−0.230409	−	0.973094i	$-0.574006\pi$
$607$	13.0077	−	40.0336i	0.527966	−	1.62491i	0.758375	−	0.651819i	$-0.225994\pi$
$608$	−43.4976	+	31.6028i	−1.76406	+	1.28166i
$609$	−59.2971	−	43.0819i	−2.40284	−	1.74577i
$610$	16.6130	+	51.1294i	0.672639	+	2.07017i
$611$	−0.646264	−	1.98900i	−0.0261450	−	0.0804661i
$612$	14.3207	+	10.4046i	0.578881	+	0.420582i
$613$	10.1316	−	7.36102i	0.409211	−	0.297309i	−0.364072	−	0.931371i	$-0.618614\pi$
$613$	10.1316	−	7.36102i	0.409211	−	0.297309i	0.773282	+	0.634062i	$0.218614\pi$
$614$	−7.82157	+	24.0723i	−0.315653	+	0.971479i
$615$	20.9359			0.844218
$616$	0.853598	+	0.0920949i	0.0343925	+	0.00371061i
$617$	−19.3317			−0.778266			−0.389133	−	0.921182i	$-0.627225\pi$
$617$	−19.3317			−0.778266			−0.389133	+	0.921182i	$0.627225\pi$
$618$	12.4701	−	38.3791i	0.501622	−	1.54383i
$619$	25.2779	−	18.3655i	1.01601	−	0.738171i	0.0505449	−	0.998722i	$-0.483904\pi$
$619$	25.2779	−	18.3655i	1.01601	−	0.738171i	0.965460	+	0.260551i	$0.0839042\pi$
$620$	−5.84369	−	4.24569i	−0.234688	−	0.170511i
$621$	−2.96607	−	9.12863i	−0.119024	−	0.366319i
$622$	−1.53574	−	4.72651i	−0.0615774	−	0.189516i
$623$	−13.0361	−	9.47130i	−0.522281	−	0.379460i
$624$	6.97845	−	5.07014i	0.279361	−	0.202968i
$625$	−9.16954	+	28.2209i	−0.366782	+	1.12884i
$626$	−57.3893			−2.29374
$627$	−19.9443	+	44.4655i	−0.796498	+	1.77578i
$628$	−4.50834			−0.179902
$629$	−2.97961	+	9.17028i	−0.118805	+	0.365643i
$630$	27.4963	−	19.9772i	1.09548	−	0.795912i
$631$	−1.06248	−	0.771934i	−0.0422965	−	0.0307302i	0.566436	−	0.824106i	$-0.308322\pi$
$631$	−1.06248	−	0.771934i	−0.0422965	−	0.0307302i	−0.608733	+	0.793375i	$0.708322\pi$
$632$	−0.247416	−	0.761469i	−0.00984169	−	0.0302896i
$633$	5.28026	+	16.2510i	0.209871	+	0.645918i
$634$	4.48873	+	3.26125i	0.178270	+	0.129521i
$635$	−36.9090	+	26.8160i	−1.46469	+	1.06416i
$636$	2.94861	−	9.07490i	0.116920	−	0.359843i
$637$	−6.86545			−0.272019
$638$	51.8168	−	29.7264i	2.05145	−	1.17688i
$639$	−9.23550			−0.365351
$640$	−0.429391	+	1.32153i	−0.0169732	+	0.0522380i
$641$	−14.1055	+	10.2482i	−0.557133	+	0.404781i	−0.830409	−	0.557155i	$-0.811893\pi$
$641$	−14.1055	+	10.2482i	−0.557133	+	0.404781i	0.273275	+	0.961936i	$0.411893\pi$
$642$	33.4994	+	24.3388i	1.32212	+	0.960575i
$643$	13.5143	+	41.5928i	0.532953	+	1.64026i	0.748031	+	0.663664i	$0.231000\pi$
$643$	13.5143	+	41.5928i	0.532953	+	1.64026i	−0.215078	+	0.976597i	$0.569000\pi$
$644$	8.66426	+	26.6658i	0.341419	+	1.05078i
$645$	−19.1829	−	13.9372i	−0.755327	−	0.548777i
$646$	−52.0421	+	37.8108i	−2.04757	+	1.48765i
$647$	−9.46654	+	29.1350i	−0.372168	+	1.14542i	0.573201	+	0.819415i	$0.305701\pi$
$647$	−9.46654	+	29.1350i	−0.372168	+	1.14542i	−0.945369	+	0.326001i	$0.894299\pi$
$648$	0.775037			0.0304463
$649$	18.1968	+	16.4755i	0.714288	+	0.646719i
$650$	2.49937			0.0980333
$651$	−3.58848	+	11.0442i	−0.140643	+	0.432856i
$652$	13.5569	−	9.84967i	0.530930	−	0.385743i
$653$	−23.2868	−	16.9188i	−0.911282	−	0.662085i	0.0300567	−	0.999548i	$-0.490431\pi$
$653$	−23.2868	−	16.9188i	−0.911282	−	0.662085i	−0.941339	+	0.337463i	$0.890431\pi$
$654$	5.75967	+	17.7264i	0.225221	+	0.693158i
$655$	−2.04789	−	6.30276i	−0.0800177	−	0.246269i
$656$	12.1339	+	8.81577i	0.473748	+	0.344198i
$657$	−8.60758	+	6.25377i	−0.335814	+	0.243983i
$658$	4.83368	−	14.8765i	0.188436	−	0.579947i
$659$	0.456631			0.0177878			0.00889390	−	0.999960i	$-0.497169\pi$
$659$	0.456631			0.0177878			0.00889390	+	0.999960i	$0.497169\pi$
$660$	7.59602	+	36.2269i	0.295675	+	1.41013i
$661$	22.3114			0.867815			0.433907	−	0.900958i	$-0.357135\pi$
$661$	22.3114			0.867815			0.433907	+	0.900958i	$0.357135\pi$
$662$	5.71786	−	17.5977i	0.222231	−	0.683956i
$663$	8.49634	−	6.17295i	0.329971	−	0.239738i
$664$	0.0982393	+	0.0713750i	0.00381243	+	0.00276989i
$665$	19.2472	+	59.2369i	0.746376	+	2.29711i
$666$	−2.27482	−	7.00117i	−0.0881474	−	0.271290i
$667$	26.8481	+	19.5063i	1.03956	+	0.755285i
$668$	9.98829	−	7.25692i	0.386459	−	0.280779i
$669$	−6.69269	+	20.5980i	−0.258754	+	0.796364i
$670$	5.19989			0.200889
$671$	7.29004	+	34.7676i	0.281429	+	1.34219i
$672$	65.6527			2.53261
$673$	5.53169	−	17.0248i	0.213231	−	0.656257i	−0.786044	−	0.618171i	$-0.787874\pi$
$673$	5.53169	−	17.0248i	0.213231	−	0.656257i	0.999274	−	0.0380860i	$-0.0121261\pi$
$674$	9.65603	−	7.01552i	0.371936	−	0.270228i
$675$	−2.61087	−	1.89691i	−0.100493	−	0.0730121i
$676$	0.628729	+	1.93503i	0.0241819	+	0.0744242i
$677$	−2.57836	−	7.93539i	−0.0990946	−	0.304982i	0.889205	−	0.457510i	$-0.151259\pi$
$677$	−2.57836	−	7.93539i	−0.0990946	−	0.304982i	−0.988299	+	0.152528i	$0.951259\pi$
$678$	58.0387	+	42.1676i	2.22896	+	1.61944i
$679$	41.3479	−	30.0410i	1.58679	−	1.15287i
$680$	−0.256831	+	0.790445i	−0.00984902	+	0.0303122i
$681$	−39.6410			−1.51905
$682$	−7.01611	−	6.35242i	−0.268661	−	0.243247i
$683$	2.69359			0.103067			0.0515336	−	0.998671i	$-0.483589\pi$
$683$	2.69359			0.103067			0.0515336	+	0.998671i	$0.483589\pi$
$684$	7.65327	−	23.5543i	0.292630	−	0.900622i
$685$	18.1676	−	13.1996i	0.694150	−	0.504329i
$686$	0.814143	+	0.591509i	0.0310841	+	0.0225839i
$687$	−6.02637	−	18.5472i	−0.229920	−	0.707622i
$688$	−5.24915	−	16.1552i	−0.200122	−	0.615912i
$689$	−1.72845	−	1.25579i	−0.0658488	−	0.0478419i
$690$	−32.9880	+	23.9672i	−1.25583	+	0.912415i
$691$	4.05908	−	12.4926i	0.154415	−	0.475239i	−0.843687	−	0.536836i	$-0.819619\pi$
$691$	4.05908	−	12.4926i	0.154415	−	0.475239i	0.998101	+	0.0615969i	$0.0196193\pi$
$692$	6.96068			0.264605
$693$	19.4800	−	11.1753i	0.739984	−	0.424516i
$694$	−19.9638			−0.757817
$695$	15.7901	−	48.5971i	0.598954	−	1.84339i
$696$	−1.10706	+	0.804324i	−0.0419629	+	0.0304878i
$697$	14.7731	+	10.7333i	0.559572	+	0.406553i
$698$	−8.21395	−	25.2799i	−0.310903	−	0.956860i
$699$	−5.10249	−	15.7039i	−0.192994	−	0.593975i
$700$	7.62667	+	5.54110i	0.288261	+	0.209434i
$701$	−22.2654	+	16.1768i	−0.840954	+	0.610989i	−0.922637	−	0.385669i	$-0.873971\pi$
$701$	−22.2654	+	16.1768i	−0.840954	+	0.610989i	0.0816828	+	0.996658i	$0.473971\pi$
$702$	1.60984	−	4.95457i	0.0607594	−	0.186998i
$703$	13.4907			0.508810
$704$	−11.2312	+	25.0398i	−0.423291	+	0.943723i
$705$	11.4716			0.432046
$706$	−16.6713	+	51.3089i	−0.627431	+	1.93104i
$707$	−49.5700	+	36.0147i	−1.86427	+	1.35447i
$708$	−26.7423	−	19.4294i	−1.00504	−	0.730203i
$709$	−10.9015	−	33.5514i	−0.409414	−	1.26005i	−0.917152	−	0.398536i	$-0.869518\pi$
$709$	−10.9015	−	33.5514i	−0.409414	−	1.26005i	0.507738	−	0.861511i	$-0.330482\pi$
$710$	−7.87733	−	24.2439i	−0.295631	−	0.909859i
$711$	−16.9436	−	12.3103i	−0.635436	−	0.461672i
$712$	−0.243380	+	0.176826i	−0.00912105	+	0.00662683i
$713$	1.62476	−	5.00050i	0.0608477	−	0.187270i
$714$	78.5493			2.93963
$715$	8.23997	+	0.889012i	0.308157	+	0.0332472i
$716$	−53.1916			−1.98786
$717$	−13.7591	+	42.3460i	−0.513842	+	1.58144i
$718$	−42.8306	+	31.1182i	−1.59842	+	1.16132i
$719$	36.4440	+	26.4781i	1.35913	+	0.987467i	0.998500	+	0.0547591i	$0.0174391\pi$
$719$	36.4440	+	26.4781i	1.35913	+	0.987467i	0.360632	+	0.932708i	$0.382561\pi$
$720$	5.51795	+	16.9825i	0.205642	+	0.632900i
$721$	−10.5313	−	32.4121i	−0.392207	−	1.20709i
$722$	41.9381	+	30.4698i	1.56078	+	1.13397i
$723$	5.64850	−	4.10388i	0.210070	−	0.152625i
$724$	10.3686	−	31.9112i	0.385346	−	1.18597i
$725$	11.1579			0.414395
$726$	4.80387	+	48.2622i	0.178289	+	1.79118i
$727$	37.9510			1.40752			0.703762	−	0.710436i	$-0.251502\pi$
$727$	37.9510			1.40752			0.703762	+	0.710436i	$0.251502\pi$
$728$	−0.0799931	+	0.246193i	−0.00296474	+	0.00912454i
$729$	2.58391	−	1.87732i	0.0957004	−	0.0695304i
$730$	−23.7584	−	17.2615i	−0.879338	−	0.638877i
$731$	−6.39091	−	19.6692i	−0.236376	−	0.727491i
$732$	−14.7822	−	45.4950i	−0.546367	−	1.68154i
$733$	8.89969	+	6.46600i	0.328718	+	0.238827i	0.739886	−	0.672732i	$-0.234879\pi$
$733$	8.89969	+	6.46600i	0.328718	+	0.238827i	−0.411169	+	0.911559i	$0.634879\pi$
$734$	4.62319	−	3.35894i	0.170645	−	0.123981i
$735$	11.6372	−	35.8156i	0.429245	−	1.32108i
$736$	−29.7257			−1.09570
$737$	3.41613	+	0.368567i	0.125835	+	0.0135763i
$738$	−13.9413			−0.513185
$739$	9.51924	−	29.2972i	0.350171	−	1.07771i	−0.608586	−	0.793488i	$-0.708263\pi$
$739$	9.51924	−	29.2972i	0.350171	−	1.07771i	0.958757	−	0.284227i	$-0.0917370\pi$
$740$	8.28968	−	6.02281i	0.304735	−	0.221403i
$741$	−11.8875	−	8.63674i	−0.436697	−	0.317279i
$742$	−4.93799	−	15.1976i	−0.181279	−	0.557920i
$743$	1.48222	+	4.56181i	0.0543774	+	0.167356i	0.974557	−	0.224140i	$-0.0719574\pi$
$743$	1.48222	+	4.56181i	0.0543774	+	0.167356i	−0.920179	+	0.391497i	$0.871957\pi$
$744$	0.175397	+	0.127433i	0.00643036	+	0.00467193i
$745$	40.5386	−	29.4530i	1.48522	−	1.07907i
$746$	10.6542	−	32.7903i	0.390078	−	1.20054i
$747$	3.17637			0.116217
$748$	−13.2126	+	29.4573i	−0.483100	+	1.07707i
$749$	34.9697			1.27776
$750$	12.7870	−	39.3544i	0.466916	−	1.43702i
$751$	24.8694	−	18.0687i	0.907498	−	0.659336i	−0.0328825	−	0.999459i	$-0.510469\pi$
$751$	24.8694	−	18.0687i	0.907498	−	0.659336i	0.940381	+	0.340123i	$0.110469\pi$
$752$	6.64862	+	4.83050i	0.242450	+	0.176150i
$753$	10.1645	+	31.2830i	0.370414	+	1.14002i
$754$	5.56593	+	17.1302i	0.202699	+	0.623844i
$755$	−9.43576	−	6.85548i	−0.343402	−	0.249496i
$756$	15.8966	−	11.5496i	0.578154	−	0.420054i
$757$	−13.8013	+	42.4759i	−0.501616	+	1.54381i	0.304771	+	0.952426i	$0.401420\pi$
$757$	−13.8013	+	42.4759i	−0.501616	+	1.54381i	−0.806387	+	0.591389i	$0.798580\pi$
$758$	−2.54821			−0.0925550
$759$	−23.3707	+	13.4073i	−0.848301	+	0.486656i
$760$	1.16285			0.0421809
$761$	−3.69663	+	11.3770i	−0.134003	+	0.412418i	−0.995434	−	0.0954572i	$-0.969569\pi$
$761$	−3.69663	+	11.3770i	−0.134003	+	0.412418i	0.861431	+	0.507875i	$0.169569\pi$
$762$	65.1247	−	47.3159i	2.35922	−	1.71407i
$763$	12.7346	+	9.25221i	0.461022	+	0.334952i
$764$	−7.44791	−	22.9223i	−0.269456	−	0.829300i
$765$	6.71817	+	20.6764i	0.242896	+	0.747557i
$766$	−24.2426	−	17.6133i	−0.875920	−	0.636393i
$767$	−5.98775	+	4.35035i	−0.216205	+	0.157082i
$768$	−10.4679	+	32.2168i	−0.377726	+	1.16252i
$769$	−30.6046			−1.10363			−0.551816	−	0.833966i	$-0.686065\pi$
$769$	−30.6046			−1.10363			−0.551816	+	0.833966i	$0.686065\pi$
$770$	45.9515	+	41.6047i	1.65598	+	1.49933i
$771$	−14.2287			−0.512435
$772$	−15.1582	+	46.6521i	−0.545555	+	1.67904i
$773$	−16.5720	+	12.0402i	−0.596052	+	0.433057i	−0.844475	−	0.535594i	$-0.820088\pi$
$773$	−16.5720	+	12.0402i	−0.596052	+	0.433057i	0.248423	+	0.968652i	$0.420088\pi$
$774$	12.7740	+	9.28082i	0.459150	+	0.333592i
$775$	−0.546283	−	1.68129i	−0.0196231	−	0.0603936i
$776$	−0.294859	−	0.907483i	−0.0105848	−	0.0325767i
$777$	−13.3271	−	9.68271i	−0.478108	−	0.347365i
$778$	49.5555	−	36.0042i	1.77665	−	1.29081i
$779$	7.89504	−	24.2984i	0.282869	−	0.870581i
$780$	−11.1604			−0.399605
$781$	−3.45670	−	16.4857i	−0.123691	−	0.589904i
$782$	−35.5649			−1.27180
$783$	7.18680	−	22.1187i	0.256835	−	0.790458i
$784$	21.8260	−	15.8575i	0.779498	−	0.566339i
$785$	−4.47956	−	3.25459i	−0.159882	−	0.116161i
$786$	3.61343	+	11.1210i	0.128887	+	0.396673i
$787$	−16.6413	−	51.2166i	−0.593198	−	1.82567i	−0.563501	−	0.826116i	$-0.690546\pi$
$787$	−16.6413	−	51.2166i	−0.593198	−	1.82567i	−0.0296971	−	0.999559i	$-0.509454\pi$
$788$	12.0647	+	8.76551i	0.429787	+	0.312258i
$789$	−13.5251	+	9.82659i	−0.481508	+	0.349836i
$790$	17.8636	−	54.9784i	0.635557	−	1.95604i
$791$	60.5859			2.15419
$792$	−0.0860435	−	0.410358i	−0.00305742	−	0.0145814i
$793$	−10.7108			−0.380351
$794$	−12.6148	+	38.8243i	−0.447682	+	1.37782i
$795$	9.48100	−	6.88835i	0.336256	−	0.244305i
$796$	−4.99039	−	3.62573i	−0.176880	−	0.128511i
$797$	−5.42038	−	16.6822i	−0.192000	−	0.590915i	−0.999999	−	0.00173037i	$-0.999449\pi$
$797$	−5.42038	−	16.6822i	−0.192000	−	0.590915i	0.807999	−	0.589184i	$-0.200551\pi$
$798$	−33.9611	−	104.521i	−1.20221	−	3.70002i
$799$	8.09478	+	5.88120i	0.286373	+	0.208062i
$800$	−8.08570	+	5.87461i	−0.285873	+	0.207699i
$801$	−2.43172	+	7.48405i	−0.0859204	+	0.264436i
$802$	−23.9229			−0.844748
$803$	−14.3849	−	13.0241i	−0.507632	−	0.459612i
$804$	−4.62686			−0.163177
$805$	−10.6412	+	32.7504i	−0.375055	+	1.15430i
$806$	2.30868	−	1.67736i	0.0813199	−	0.0590824i
$807$	−28.3789	−	20.6185i	−0.998985	−	0.725805i
$808$	0.353492	+	1.08794i	0.0124358	+	0.0382735i
$809$	−13.6769	−	42.0932i	−0.480855	−	1.47992i	−0.837896	−	0.545830i	$-0.816214\pi$
$809$	−13.6769	−	42.0932i	−0.480855	−	1.47992i	0.357041	−	0.934089i	$-0.383786\pi$
$810$	45.2710	+	32.8913i	1.59066	+	1.15568i
$811$	−3.99395	+	2.90178i	−0.140247	+	0.101895i	−0.655696	−	0.755025i	$-0.727625\pi$
$811$	−3.99395	+	2.90178i	−0.140247	+	0.101895i	0.515450	+	0.856920i	$0.327625\pi$
$812$	−20.9935	+	64.6114i	−0.736728	+	2.26741i
$813$	−65.1294			−2.28419
$814$	11.6459	−	6.68106i	0.408189	−	0.234171i
$815$	20.5809			0.720917
$816$	−12.7527	+	39.2489i	−0.446435	+	1.37398i
$817$	−23.4096	+	17.0081i	−0.819000	+	0.595038i
$818$	−25.8445	−	18.7771i	−0.903632	−	0.656527i
$819$	2.09245	+	6.43991i	0.0731163	+	0.225029i
$820$	−5.99654	−	18.4555i	−0.209408	−	0.644493i
$821$	9.60190	+	6.97619i	0.335109	+	0.243471i	0.742595	−	0.669740i	$-0.233595\pi$
$821$	9.60190	+	6.97619i	0.335109	+	0.243471i	−0.407486	+	0.913211i	$0.633595\pi$
$822$	−32.0562	+	23.2902i	−1.11809	+	0.812338i
$823$	−8.91888	+	27.4495i	−0.310893	+	0.956829i	0.666520	+	0.745487i	$0.267783\pi$
$823$	−8.91888	+	27.4495i	−0.310893	+	0.956829i	−0.977412	+	0.211342i	$0.932217\pi$
$824$	−0.636263			−0.0221653
$825$	−3.70741	+	8.26563i	−0.129076	+	0.287772i
$826$	−55.3572			−1.92612
$827$	−10.0817	+	31.0284i	−0.350576	+	1.07896i	0.607955	+	0.793972i	$0.291990\pi$
$827$	−10.0817	+	31.0284i	−0.350576	+	1.07896i	−0.958531	+	0.284990i	$0.908010\pi$
$828$	11.0776	−	8.04835i	0.384974	−	0.279700i
$829$	19.2155	+	13.9609i	0.667383	+	0.484882i	0.869148	−	0.494552i	$-0.164668\pi$
$829$	19.2155	+	13.9609i	0.667383	+	0.484882i	−0.201765	+	0.979434i	$0.564668\pi$
$830$	2.70926	+	8.33823i	0.0940396	+	0.289424i
$831$	−9.32742	−	28.7069i	−0.323565	−	0.995830i
$832$	−6.69417	−	4.86360i	−0.232078	−	0.168615i
$833$	26.5734	−	19.3067i	0.920712	−	0.668937i
$834$	−27.8612	+	85.7479i	−0.964753	+	2.96921i
$835$	15.1633			0.524749
$836$	44.9098	+	4.84533i	1.55324	+	0.167579i
$837$	−3.68472			−0.127363
$838$	17.9965	−	55.3875i	0.621679	−	1.91333i
$839$	−14.3197	+	10.4039i	−0.494371	+	0.359182i	−0.806863	−	0.590739i	$-0.798836\pi$
$839$	−14.3197	+	10.4039i	−0.494371	+	0.359182i	0.312492	+	0.949920i	$0.398836\pi$
$840$	−1.14875	−	0.834614i	−0.0396356	−	0.0287969i
$841$	15.8865	+	48.8936i	0.547810	+	1.68599i
$842$	−6.20297	−	19.0908i	−0.213768	−	0.657912i
$843$	3.69214	+	2.68250i	0.127164	+	0.0923900i
$844$	12.8132	−	9.30932i	0.441048	−	0.320440i
$845$	−0.772191	+	2.37656i	−0.0265642	+	0.0817561i
$846$	−7.63897			−0.262633
$847$	27.2395	+	30.5897i	0.935959	+	1.05108i
$848$	8.39549			0.288302
$849$	0.887084	−	2.73016i	0.0304447	−	0.0936990i
$850$	−9.67403	+	7.02860i	−0.331817	+	0.241079i
$851$	6.03414	+	4.38406i	0.206848	+	0.150284i
$852$	7.00926	+	21.5723i	0.240133	+	0.739054i
$853$	11.4052	+	35.1015i	0.390506	+	1.20185i	0.932406	+	0.361411i	$0.117705\pi$
$853$	11.4052	+	35.1015i	0.390506	+	1.20185i	−0.541900	+	0.840443i	$0.682295\pi$
$854$	−64.8108	−	47.0878i	−2.21778	−	1.61131i
$855$	24.6084	−	17.8790i	0.841589	−	0.611450i
$856$	0.201748	−	0.620918i	0.00689562	−	0.0212225i
$857$	−5.51696			−0.188456			−0.0942278	−	0.995551i	$-0.530038\pi$
$857$	−5.51696			−0.188456			−0.0942278	+	0.995551i	$0.530038\pi$
$858$	−14.5391	−	1.56863i	−0.496358	−	0.0535522i
$859$	−42.1789			−1.43913			−0.719563	−	0.694427i	$-0.755658\pi$
$859$	−42.1789			−1.43913			−0.719563	+	0.694427i	$0.755658\pi$
$860$	−6.79151	+	20.9021i	−0.231589	+	0.712756i
$861$	−25.2391	+	18.3373i	−0.860147	+	0.624934i
$862$	46.3433	+	33.6704i	1.57846	+	1.14682i
$863$	−5.38361	−	16.5690i	−0.183260	−	0.564016i	0.816654	−	0.577128i	$-0.195826\pi$
$863$	−5.38361	−	16.5690i	−0.183260	−	0.564016i	−0.999914	+	0.0131111i	$0.995826\pi$
$864$	6.43742	+	19.8123i	0.219005	+	0.674030i
$865$	6.91625	+	5.02495i	0.235160	+	0.170853i
$866$	−1.62453	+	1.18029i	−0.0552038	+	0.0401079i
$867$	−3.99510	+	12.2957i	−0.135681	+	0.417582i
$868$	10.7635			0.365338
$869$	15.6325	−	34.8526i	0.530298	−	1.18229i
$870$	−98.7989			−3.34960
$871$	−0.320135	+	0.985274i	−0.0108474	+	0.0333847i
$872$	0.237750	−	0.172735i	0.00805123	−	0.00584956i
$873$	−20.1926	−	14.6708i	−0.683417	−	0.496532i
$874$	15.3766	+	47.3243i	0.520121	+	1.60077i
$875$	−10.7989	−	33.2357i	−0.365071	−	1.12357i
$876$	21.1403	+	15.3593i	0.714263	+	0.518943i
$877$	34.7012	−	25.2119i	1.17178	−	0.851346i	0.180556	−	0.983565i	$-0.442210\pi$
$877$	34.7012	−	25.2119i	1.17178	−	0.851346i	0.991221	+	0.132219i	$0.0422102\pi$
$878$	11.3426	−	34.9090i	0.382795	−	1.17812i
$879$	9.49478			0.320251
$880$	−28.2491	+	16.2060i	−0.952276	+	0.546305i
$881$	4.49892			0.151572			0.0757862	−	0.997124i	$-0.475853\pi$
$881$	4.49892			0.151572			0.0757862	+	0.997124i	$0.475853\pi$
$882$	−7.74924	+	23.8497i	−0.260930	+	0.803061i
$883$	18.0899	−	13.1431i	0.608773	−	0.442299i	−0.240209	−	0.970721i	$-0.577216\pi$
$883$	18.0899	−	13.1431i	0.608773	−	0.442299i	0.848982	+	0.528422i	$0.177216\pi$
$884$	−7.87514	−	5.72163i	−0.264870	−	0.192439i
$885$	−12.5454	−	38.6108i	−0.421710	−	1.29789i
$886$	18.9994	+	58.4742i	0.638298	+	1.96448i
$887$	−14.7374	−	10.7074i	−0.494834	−	0.359518i	0.312206	−	0.950014i	$-0.398932\pi$
$887$	−14.7374	−	10.7074i	−0.494834	−	0.359518i	−0.807040	+	0.590497i	$0.798932\pi$
$888$	−0.248813	+	0.180773i	−0.00834960	+	0.00606634i
$889$	21.0079	−	64.6556i	0.704582	−	2.16848i
$890$	−21.7204			−0.728068
$891$	27.4100	+	24.8171i	0.918269	+	0.831405i
$892$	20.0745			0.672145
$893$	4.32600	−	13.3141i	0.144764	−	0.445538i
$894$	−71.5289	+	51.9688i	−2.39229	+	1.73810i
$895$	−52.8521	−	38.3993i	−1.76665	−	1.28355i
$896$	−0.639849	−	1.96925i	−0.0213759	−	0.0657881i
$897$	−2.51037	−	7.72612i	−0.0838188	−	0.257968i
$898$	−20.6897	−	15.0319i	−0.690424	−	0.501622i
$899$	10.3067	−	7.48823i	0.343747	−	0.249747i
$900$	1.42265	−	4.37848i	0.0474218	−	0.145949i
$901$	10.2216			0.340531
$902$	−5.21800	−	24.8857i	−0.173740	−	0.828602i
$903$	35.3331			1.17581
$904$	0.349535	−	1.07576i	0.0116253	−	0.0357791i
$905$	33.3393	−	24.2224i	1.10823	−	0.805180i
$906$	16.6491	+	12.0963i	0.553128	+	0.401871i
$907$	2.69620	+	8.29806i	0.0895259	+	0.275532i	0.985788	−	0.167991i	$-0.0537281\pi$
$907$	2.69620	+	8.29806i	0.0895259	+	0.275532i	−0.896263	+	0.443524i	$0.853728\pi$
$908$	11.3541	+	34.9444i	0.376800	+	1.15967i
$909$	24.2080	+	17.5881i	0.802928	+	0.583361i
$910$	−15.1206	+	10.9857i	−0.501242	+	0.364173i
$911$	7.72518	−	23.7757i	0.255947	−	0.787723i	−0.737695	−	0.675134i	$-0.764086\pi$
$911$	7.72518	−	23.7757i	0.255947	−	0.787723i	0.993642	−	0.112589i	$-0.0359142\pi$
$912$	57.7401			1.91197
$913$	1.18887	+	5.66993i	0.0393457	+	0.187647i
$914$	−11.7919			−0.390040
$915$	18.1552	−	55.8759i	0.600192	−	1.84720i
$916$	−14.6237	+	10.6247i	−0.483181	+	0.351051i
$917$	7.98926	+	5.80454i	0.263829	+	0.191683i
$918$	7.70197	+	23.7042i	0.254203	+	0.782356i
$919$	8.31023	+	25.5763i	0.274129	+	0.843683i	0.989448	+	0.144885i	$0.0462813\pi$
$919$	8.31023	+	25.5763i	0.274129	+	0.843683i	−0.715319	+	0.698798i	$0.753719\pi$
$920$	0.520120	+	0.377890i	0.0171479	+	0.0124586i
$921$	22.3781	−	16.2586i	0.737383	−	0.535740i
$922$	−13.2631	+	40.8196i	−0.436797	+	1.34432i
$923$	5.07871			0.167168
$924$	−40.8877	−	37.0199i	−1.34511	−	1.21787i
$925$	2.50776			0.0824547
$926$	22.5422	−	69.3779i	0.740784	−	2.27990i
$927$	−13.4647	+	9.78269i	−0.442240	+	0.321306i
$928$	−58.2697	−	42.3354i	−1.91280	−	1.38973i
$929$	−6.51334	−	20.0460i	−0.213696	−	0.657688i	−0.999244	−	0.0388869i	$-0.987619\pi$
$929$	−6.51334	−	20.0460i	−0.213696	−	0.657688i	0.785548	−	0.618801i	$-0.212381\pi$
$930$	4.83711	+	14.8871i	0.158615	+	0.488167i
$931$	−37.1795	−	27.0125i	−1.21851	−	0.885298i
$932$	−12.3818	+	8.99592i	−0.405580	+	0.294671i
$933$	−1.67830	+	5.16529i	−0.0549452	+	0.169104i
$934$	20.6280			0.674968
$935$	−34.3936	+	19.7310i	−1.12479	+	0.645273i
$936$	0.126418			0.00413211
$937$	8.34057	−	25.6696i	0.272475	−	0.838591i	−0.717402	−	0.696659i	$-0.754669\pi$
$937$	8.34057	−	25.6696i	0.272475	−	0.838591i	0.989877	−	0.141931i	$-0.0453311\pi$
$938$	−6.26868	+	4.55446i	−0.204680	+	0.148709i
$939$	50.7391	+	36.8641i	1.65581	+	1.20301i
$940$	−3.28574	−	10.1125i	−0.107169	−	0.329832i
$941$	−12.4874	−	38.4324i	−0.407079	−	1.25286i	−0.919147	−	0.393915i	$-0.871121\pi$
$941$	−12.4874	−	38.4324i	−0.407079	−	1.25286i	0.512068	−	0.858945i	$-0.328879\pi$
$942$	7.90403	+	5.74262i	0.257527	+	0.187105i
$943$	11.4276	−	8.30261i	0.372132	−	0.270370i
$944$	8.98741	−	27.6604i	0.292515	−	0.900270i
$945$	24.1328			0.785041
$946$	−11.7855	+	26.2756i	−0.383180	+	0.854294i
$947$	−16.4284			−0.533851			−0.266926	−	0.963717i	$-0.586008\pi$
$947$	−16.4284			−0.533851			−0.266926	+	0.963717i	$0.586008\pi$
$948$	−15.8950	+	48.9198i	−0.516246	+	1.58884i
$949$	4.73341	−	3.43903i	0.153653	−	0.111636i
$950$	13.5352	+	9.83389i	0.439140	+	0.319054i
$951$	−1.87371	−	5.76668i	−0.0607591	−	0.186997i
$952$	−0.382712	−	1.17787i	−0.0124038	−	0.0381749i
$953$	−27.0151	−	19.6276i	−0.875104	−	0.635800i	0.0568477	−	0.998383i	$-0.481895\pi$
$953$	−27.0151	−	19.6276i	−0.875104	−	0.635800i	−0.931952	+	0.362583i	$0.881895\pi$
$954$	−6.31342	+	4.58697i	−0.204404	+	0.148509i
$955$	9.14736	−	28.1527i	0.296002	−	0.910999i
$956$	41.2699			1.33476
$957$	−64.9071	−	7.00285i	−2.09815	−	0.226370i
$958$	11.7646			0.380097
$959$	−10.3406	+	31.8252i	−0.333917	+	1.02769i
$960$	36.7192	−	26.6781i	1.18511	−	0.861031i
$961$	23.4466	+	17.0349i	0.756342	+	0.549514i
$962$	1.25095	+	3.85003i	0.0403322	+	0.124130i
$963$	−5.27732	−	16.2419i	−0.170059	−	0.523389i
$964$	−5.23552	−	3.80383i	−0.168625	−	0.122513i
$965$	−48.7398	+	35.4115i	−1.56899	+	1.13994i
$966$	18.7761	−	57.7869i	0.604111	−	1.85926i
$967$	27.0812			0.870874			0.435437	−	0.900219i	$-0.356594\pi$
$967$	27.0812			0.870874			0.435437	+	0.900219i	$0.356594\pi$
$968$	0.700299	−	0.307181i	0.0225085	−	0.00987318i
$969$	70.2993			2.25834
$970$	21.2890	−	65.5207i	0.683547	−	2.10374i
$971$	−29.6429	+	21.5368i	−0.951285	+	0.691149i	−0.951110	−	0.308851i	$-0.900056\pi$
$971$	−29.6429	+	21.5368i	−0.951285	+	0.691149i	−0.000174553		1.00000i	$0.500056\pi$
$972$	−27.4748	−	19.9616i	−0.881256	−	0.640270i
$973$	23.5294	+	72.4160i	0.754318	+	2.32155i
$974$	7.24401	+	22.2948i	0.232113	+	0.714371i
$975$	−2.20974	−	1.60547i	−0.0707684	−	0.0514163i
$976$	34.0507	−	24.7393i	1.08994	−	0.791884i
$977$	7.28492	−	22.4207i	0.233065	−	0.717301i	−0.764307	−	0.644853i	$-0.776919\pi$
$977$	7.28492	−	22.4207i	0.233065	−	0.717301i	0.997372	−	0.0724482i	$-0.0230812\pi$
$978$	−36.3143			−1.16120
$979$	−14.2694	−	1.53953i	−0.456053	−	0.0492037i
$980$	−34.9054			−1.11501
$981$	2.37546	−	7.31093i	0.0758427	−	0.233420i
$982$	11.5239	−	8.37262i	0.367743	−	0.267181i
$983$	−15.1803	−	11.0292i	−0.484177	−	0.351776i	0.318763	−	0.947834i	$-0.396732\pi$
$983$	−15.1803	−	11.0292i	−0.484177	−	0.351776i	−0.802941	+	0.596059i	$0.796732\pi$
$984$	0.179985	+	0.553936i	0.00573770	+	0.0176588i
$985$	5.65981	+	17.4191i	0.180337	+	0.555019i
$986$	−69.7160	−	50.6517i	−2.22021	−	1.61308i
$987$	−13.8295	+	10.0477i	−0.440198	+	0.319823i
$988$	−4.20863	+	12.9528i	−0.133894	+	0.412084i
$989$	−15.9978			−0.508701
$990$	12.3890	−	27.6211i	0.393749	−	0.877857i
$991$	25.3916			0.806589			0.403295	−	0.915070i	$-0.367865\pi$
$991$	25.3916			0.806589			0.403295	+	0.915070i	$0.367865\pi$
$992$	−3.52630	+	10.8528i	−0.111960	+	0.344578i
$993$	−16.3592	+	11.8857i	−0.519144	+	0.377180i
$994$	30.7312	+	22.3275i	0.974734	+	0.708186i
$995$	−2.34110	−	7.20518i	−0.0742180	−	0.228419i
$996$	−2.41070	−	7.41936i	−0.0763859	−	0.235092i
$997$	−18.9197	−	13.7460i	−0.599192	−	0.435339i	0.246400	−	0.969168i	$-0.420752\pi$
$997$	−18.9197	−	13.7460i	−0.599192	−	0.435339i	−0.845592	+	0.533830i	$0.820752\pi$
$998$	34.6206	−	25.1533i	1.09590	−	0.796215i
$999$	1.61524	−	4.97121i	0.0511040	−	0.157282i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.h.b.53.1	yes	16
11.4	even	5		1573.2.a.o.1.1		8
11.5	even	5	inner	143.2.h.b.27.1	✓	16
11.7	odd	10		1573.2.a.n.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.b.27.1	✓	16	11.5	even	5	inner
143.2.h.b.53.1	yes	16	1.1	even	1	trivial
1573.2.a.n.1.8		8	11.7	odd	10
1573.2.a.o.1.1		8	11.4	even	5

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.620702 + 1.91032i) q^{2} +(1.77587 - 1.29025i) q^{3} +(-1.64603 - 1.19591i) q^{4} +(-0.772191 - 2.37656i) q^{5} +(1.36250 + 4.19336i) q^{6} +(3.01248 + 2.18870i) q^{7} +(0.0562420 - 0.0408622i) q^{8} +(0.561939 - 1.72947i) q^{9} +5.01930 q^{10} +(3.29749 + 0.355767i) q^{11} -4.46618 q^{12} +(-0.309017 + 0.951057i) q^{13} +(-6.05098 + 4.39629i) q^{14} +(-4.43767 - 3.22415i) q^{15} +(-1.21431 - 3.73725i) q^{16} +(-1.47843 - 4.55015i) q^{17} +(2.95505 + 2.14697i) q^{18} +(-5.41545 + 3.93455i) q^{19} +(-1.57111 + 4.83537i) q^{20} +8.17376 q^{21} +(-2.72639 + 6.07845i) q^{22} -3.70084 q^{23} +(0.0471564 - 0.145132i) q^{24} +(-1.00667 + 0.731388i) q^{25} +(-1.62502 - 1.18065i) q^{26} +(0.801459 + 2.46664i) q^{27} +(-2.34116 - 7.20534i) q^{28} +(-7.25458 - 5.27076i) q^{29} +(8.91365 - 6.47614i) q^{30} +(-0.439024 + 1.35118i) q^{31} +8.03213 q^{32} +(6.31495 - 3.62278i) q^{33} +9.60994 q^{34} +(2.87536 - 8.84944i) q^{35} +(-2.99327 + 2.17474i) q^{36} +(-1.63048 - 1.18461i) q^{37} +(-4.15489 - 12.7874i) q^{38} +(0.678324 + 2.08767i) q^{39} +(-0.140541 - 0.102109i) q^{40} +(-3.08783 + 2.24344i) q^{41} +(-5.07347 + 15.6145i) q^{42} +4.32275 q^{43} +(-5.00231 - 4.52912i) q^{44} -4.54411 q^{45} +(2.29712 - 7.06981i) q^{46} +(-1.69194 + 1.22927i) q^{47} +(-6.97845 - 5.07014i) q^{48} +(2.12154 + 6.52943i) q^{49} +(-0.772347 - 2.37704i) q^{50} +(-8.49634 - 6.17295i) q^{51} +(1.64603 - 1.19591i) q^{52} +(-0.660210 + 2.03192i) q^{53} -5.20954 q^{54} +(-1.70079 - 8.11140i) q^{55} +0.258863 q^{56} +(-4.54060 + 13.9745i) q^{57} +(14.5718 - 10.5870i) q^{58} +(5.98775 + 4.35035i) q^{59} +(3.44874 + 10.6141i) q^{60} +(3.30982 + 10.1866i) q^{61} +(-2.30868 - 1.67736i) q^{62} +(5.47812 - 3.98008i) q^{63} +(-2.55694 + 7.86946i) q^{64} +2.49886 q^{65} +(3.00098 + 14.3123i) q^{66} +1.03598 q^{67} +(-3.00804 + 9.25779i) q^{68} +(-6.57223 + 4.77501i) q^{69} +(15.1206 + 10.9857i) q^{70} +(-1.56941 - 4.83014i) q^{71} +(-0.0390654 - 0.120231i) q^{72} +(-4.73341 - 3.43903i) q^{73} +(3.27503 - 2.37945i) q^{74} +(-0.844047 + 2.59771i) q^{75} +13.6194 q^{76} +(9.15496 + 8.28895i) q^{77} -4.40916 q^{78} +(3.55898 - 10.9534i) q^{79} +(-7.94413 + 5.77175i) q^{80} +(9.01939 + 6.55297i) q^{81} +(-2.36907 - 7.29125i) q^{82} +(0.539768 + 1.66123i) q^{83} +(-13.4543 - 9.77511i) q^{84} +(-9.67208 + 7.02717i) q^{85} +(-2.68314 + 8.25786i) q^{86} -19.6838 q^{87} +(0.199995 - 0.114734i) q^{88} -4.32737 q^{89} +(2.82054 - 8.68072i) q^{90} +(-3.01248 + 2.18870i) q^{91} +(6.09171 + 4.42589i) q^{92} +(0.963703 + 2.96597i) q^{93} +(-1.29811 - 3.99516i) q^{94} +(13.5325 + 9.83191i) q^{95} +(14.2641 - 10.3634i) q^{96} +(4.24142 - 13.0537i) q^{97} -13.7902 q^{98} +(2.46827 - 5.50299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{2} + 5 q^{3} - 8 q^{4} + 5 q^{5} - 4 q^{6} + 9 q^{7} - 4 q^{8} - 7 q^{9} - 12 q^{10} + 6 q^{11} - 14 q^{12} + 4 q^{13} - q^{14} - 10 q^{15} + 10 q^{16} - 6 q^{17} + 20 q^{18} + 2 q^{19} - 21 q^{20}+ \cdots - 7 q^{99}+O(q^{100}) \) 16 * q + 2 * q^2 + 5 * q^3 - 8 * q^4 + 5 * q^5 - 4 * q^6 + 9 * q^7 - 4 * q^8 - 7 * q^9 - 12 * q^10 + 6 * q^11 - 14 * q^12 + 4 * q^13 - q^14 - 10 * q^15 + 10 * q^16 - 6 * q^17 + 20 * q^18 + 2 * q^19 - 21 * q^20 - 8 * q^21 + 2 * q^22 - 46 * q^23 + 3 * q^24 + 23 * q^25 + 3 * q^26 + 17 * q^27 - 9 * q^28 - 25 * q^29 + 22 * q^30 + 3 * q^31 + 24 * q^32 - 10 * q^33 + 4 * q^34 + 26 * q^35 - 2 * q^36 - 7 * q^37 + 5 * q^38 + 25 * q^40 - 3 * q^41 - 12 * q^42 - 16 * q^43 + 32 * q^44 - 46 * q^45 - 11 * q^46 + 13 * q^47 - 24 * q^48 + 19 * q^49 - 19 * q^50 - 23 * q^51 + 8 * q^52 - 14 * q^53 + 6 * q^54 - 5 * q^55 - 68 * q^56 + 23 * q^57 + 20 * q^58 + 16 * q^59 + 34 * q^60 - 13 * q^61 + 28 * q^62 + 18 * q^63 - 40 * q^64 + 10 * q^65 + 41 * q^66 - 62 * q^67 + 13 * q^68 + 4 * q^69 - 2 * q^70 + 54 * q^71 + 21 * q^72 - 42 * q^73 + 42 * q^74 + 51 * q^75 - 4 * q^76 + 14 * q^77 - 6 * q^78 - 15 * q^79 - 19 * q^80 + q^81 - 7 * q^82 - 43 * q^83 - 35 * q^84 - 3 * q^85 - 32 * q^86 + 4 * q^87 + 41 * q^88 - 30 * q^89 + 26 * q^90 - 9 * q^91 + 3 * q^92 + 49 * q^93 + 4 * q^94 + 23 * q^95 + 23 * q^96 - 12 * q^97 + 24 * q^98 - 7 * q^99

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