LMFDB - Embedded newform 153.2.s.a.113.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(5,153)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([40, 15]))

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

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

chi := DirichletCharacter("153.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$153 = 3^{2} \cdot 17$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	153.s (of order $48$ , degree $16$ , 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:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			113.8
Character	$\chi$	$=$	153.113
Dual form			153.2.s.a.65.8

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.801255 + 0.105487i) q^{2} +(1.57560 - 0.719363i) q^{3} +(-1.30097 + 0.348594i) q^{4} +(-1.37710 - 2.79247i) q^{5} +(-1.18657 + 0.742599i) q^{6} +(-4.52563 - 2.23179i) q^{7} +(2.49894 - 1.03509i) q^{8} +(1.96503 - 2.26686i) q^{9} +(1.39797 + 2.09222i) q^{10} +(0.780943 - 0.265095i) q^{11} +(-1.79904 + 1.48511i) q^{12} +(1.16796 + 4.35888i) q^{13} +(3.86161 + 1.31084i) q^{14} +(-4.17855 - 3.40919i) q^{15} +(0.439739 - 0.253884i) q^{16} +(3.78892 - 1.62606i) q^{17} +(-1.33537 + 2.02362i) q^{18} +(-1.95880 - 0.811360i) q^{19} +(2.76500 + 3.15288i) q^{20} +(-8.73606 - 0.260843i) q^{21} +(-0.597770 + 0.294788i) q^{22} +(2.61464 - 2.98142i) q^{23} +(3.19272 - 3.42854i) q^{24} +(-2.85771 + 3.72424i) q^{25} +(-1.39564 - 3.36937i) q^{26} +(1.46541 - 4.98524i) q^{27} +(6.66570 + 1.32589i) q^{28} +(-0.0274451 + 0.418731i) q^{29} +(3.70771 + 2.29085i) q^{30} +(0.426633 - 1.25682i) q^{31} +(-4.61733 + 3.54301i) q^{32} +(1.03976 - 0.979465i) q^{33} +(-2.86436 + 1.70257i) q^{34} +15.7111i q^{35} +(-1.76624 + 3.63411i) q^{36} +(0.0132231 + 0.0664768i) q^{37} +(1.65508 + 0.443478i) q^{38} +(4.97586 + 6.02767i) q^{39} +(-6.33175 - 5.55279i) q^{40} +(-3.37615 + 0.221284i) q^{41} +(7.02732 - 0.712541i) q^{42} +(5.74422 + 4.40769i) q^{43} +(-0.923573 + 0.617112i) q^{44} +(-9.03618 - 2.36562i) q^{45} +(-1.78049 + 2.66469i) q^{46} +(1.39277 - 5.19789i) q^{47} +(0.510219 - 0.716351i) q^{48} +(11.2391 + 14.6471i) q^{49} +(1.89689 - 3.28551i) q^{50} +(4.80009 - 5.28764i) q^{51} +(-3.03896 - 5.26363i) q^{52} +(2.70319 - 6.52608i) q^{53} +(-0.648289 + 4.14903i) q^{54} +(-1.81570 - 1.81570i) q^{55} +(-13.6194 - 0.892662i) q^{56} +(-3.66994 + 0.130707i) q^{57} +(-0.0221803 - 0.338405i) q^{58} +(-0.445276 + 3.38221i) q^{59} +(6.62460 + 2.97863i) q^{60} +(0.762232 - 1.54565i) q^{61} +(-0.209263 + 1.05204i) q^{62} +(-13.9522 + 5.87342i) q^{63} +(2.60783 - 2.60783i) q^{64} +(10.5637 - 9.26409i) q^{65} +(-0.729788 + 0.894482i) q^{66} +(-1.90636 - 1.10063i) q^{67} +(-4.36244 + 3.43625i) q^{68} +(1.97490 - 6.57840i) q^{69} +(-1.65732 - 12.5886i) q^{70} +(-2.14171 + 0.426013i) q^{71} +(2.56408 - 7.69873i) q^{72} +(4.79086 + 3.20115i) q^{73} +(-0.0176075 - 0.0518700i) q^{74} +(-1.82352 + 7.92364i) q^{75} +(2.83117 + 0.372731i) q^{76} +(-4.12590 - 0.543185i) q^{77} +(-4.62277 - 4.30481i) q^{78} +(-4.25979 - 12.5489i) q^{79} +(-1.31453 - 0.878338i) q^{80} +(-1.27729 - 8.90890i) q^{81} +(2.68181 - 0.533446i) q^{82} +(-0.479996 - 3.64594i) q^{83} +(11.4563 - 2.70599i) q^{84} +(-9.75844 - 8.34121i) q^{85} +(-5.06754 - 2.92574i) q^{86} +(0.257977 + 0.679496i) q^{87} +(1.67713 - 1.47080i) q^{88} +(-3.26760 + 3.26760i) q^{89} +(7.48982 + 0.942264i) q^{90} +(4.44238 - 22.3333i) q^{91} +(-2.36226 + 4.79019i) q^{92} +(-0.231907 - 2.28715i) q^{93} +(-0.567653 + 4.31175i) q^{94} +(0.431749 + 6.58721i) q^{95} +(-4.72636 + 8.90390i) q^{96} +(17.3795 + 1.13911i) q^{97} +(-10.5505 - 10.5505i) q^{98} +(0.933647 - 2.29121i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22}+ \cdots + 88 q^{99}+O(q^{100})$ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$ .

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{5}{6}\right)$

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

)

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

$2$	−0.801255	+	0.105487i	−0.566573	+	0.0745907i	−0.408371	−	0.912816i	$-0.633903\pi$
$2$	−0.801255	+	0.105487i	−0.566573	+	0.0745907i	−0.158202	+	0.987407i	$0.550570\pi$
$3$	1.57560	−	0.719363i	0.909673	−	0.415325i
$3$	1.57560	−	0.719363i	0.909673	−	0.415325i
$4$	−1.30097	+	0.348594i	−0.650485	+	0.174297i
$5$	−1.37710	−	2.79247i	−0.615856	−	1.24883i	−0.951733	−	0.306926i	$-0.900700\pi$
$5$	−1.37710	−	2.79247i	−0.615856	−	1.24883i	0.335878	−	0.941906i	$-0.390967\pi$
$6$	−1.18657	+	0.742599i	−0.484417	+	0.303165i
$7$	−4.52563	−	2.23179i	−1.71053	−	0.843539i	−0.988417	−	0.151762i	$-0.951505\pi$
$7$	−4.52563	−	2.23179i	−1.71053	−	0.843539i	−0.722111	−	0.691777i	$-0.756828\pi$
$8$	2.49894	−	1.03509i	0.883508	−	0.365961i
$9$	1.96503	−	2.26686i	0.655011	−	0.755619i
$10$	1.39797	+	2.09222i	0.442078	+	0.661617i
$11$	0.780943	−	0.265095i	0.235463	−	0.0799290i	−0.201214	−	0.979547i	$-0.564489\pi$
$11$	0.780943	−	0.265095i	0.235463	−	0.0799290i	0.436677	+	0.899618i	$0.356155\pi$
$12$	−1.79904	+	1.48511i	−0.519339	+	0.428716i
$13$	1.16796	+	4.35888i	0.323934	+	1.20894i	0.915379	+	0.402592i	$0.131891\pi$
$13$	1.16796	+	4.35888i	0.323934	+	1.20894i	−0.591446	+	0.806345i	$0.701443\pi$
$14$	3.86161	+	1.31084i	1.03206	+	0.350337i
$15$	−4.17855	−	3.40919i	−1.07890	−	0.880249i
$16$	0.439739	−	0.253884i	0.109935	−	0.0634709i
$17$	3.78892	−	1.62606i	0.918948	−	0.394378i
$17$	3.78892	−	1.62606i	0.918948	−	0.394378i
$18$	−1.33537	+	2.02362i	−0.314749	+	0.476971i
$19$	−1.95880	−	0.811360i	−0.449379	−	0.186139i	0.146504	−	0.989210i	$-0.453198\pi$
$19$	−1.95880	−	0.811360i	−0.449379	−	0.186139i	−0.595883	+	0.803071i	$0.703198\pi$
$20$	2.76500	+	3.15288i	0.618272	+	0.705005i
$21$	−8.73606	−	0.260843i	−1.90636	−	0.0569205i
$22$	−0.597770	+	0.294788i	−0.127445	+	0.0628490i
$23$	2.61464	−	2.98142i	0.545189	−	0.621669i	−0.411982	−	0.911192i	$-0.635163\pi$
$23$	2.61464	−	2.98142i	0.545189	−	0.621669i	0.957171	+	0.289523i	$0.0934966\pi$
$24$	3.19272	−	3.42854i	0.651711	−	0.699847i
$25$	−2.85771	+	3.72424i	−0.571541	+	0.744847i
$26$	−1.39564	−	3.36937i	−0.273707	−	0.660788i
$27$	1.46541	−	4.98524i	0.282019	−	0.959409i
$28$	6.66570	+	1.32589i	1.25970	+	0.250570i
$29$	−0.0274451	+	0.418731i	−0.00509643	+	0.0777564i	−0.999649	−	0.0264753i	$-0.991572\pi$
$29$	−0.0274451	+	0.418731i	−0.00509643	+	0.0777564i	0.994553	+	0.104232i	$0.0332383\pi$
$30$	3.70771	+	2.29085i	0.676933	+	0.418249i
$31$	0.426633	−	1.25682i	0.0766256	−	0.225732i	−0.901867	−	0.432014i	$-0.857803\pi$
$31$	0.426633	−	1.25682i	0.0766256	−	0.225732i	0.978493	+	0.206282i	$0.0661365\pi$
$32$	−4.61733	+	3.54301i	−0.816237	+	0.626321i
$33$	1.03976	−	0.979465i	0.180998	−	0.170503i
$34$	−2.86436	+	1.70257i	−0.491234	+	0.291989i
$35$			15.7111i			2.65566i
$36$	−1.76624	+	3.63411i	−0.294373	+	0.605686i
$37$	0.0132231	+	0.0664768i	0.00217386	+	0.0109287i	0.981857	−	0.189623i	$-0.0607266\pi$
$37$	0.0132231	+	0.0664768i	0.00217386	+	0.0109287i	−0.979683	+	0.200552i	$0.935727\pi$
$38$	1.65508	+	0.443478i	0.268490	+	0.0719417i
$39$	4.97586	+	6.02767i	0.796775	+	0.965200i
$40$	−6.33175	−	5.55279i	−1.00114	−	0.877974i
$41$	−3.37615	+	0.221284i	−0.527266	+	0.0345588i	−0.326712	−	0.945124i	$-0.605941\pi$
$41$	−3.37615	+	0.221284i	−0.527266	+	0.0345588i	−0.200554	+	0.979683i	$0.564274\pi$
$42$	7.02732	−	0.712541i	1.08434	−	0.109947i
$43$	5.74422	+	4.40769i	0.875985	+	0.672167i	0.945573	−	0.325409i	$-0.105502\pi$
$43$	5.74422	+	4.40769i	0.875985	+	0.672167i	−0.0695883	+	0.997576i	$0.522169\pi$
$44$	−0.923573	+	0.617112i	−0.139234	+	0.0930331i
$45$	−9.03618	−	2.36562i	−1.34703	−	0.352646i
$46$	−1.78049	+	2.66469i	−0.262519	+	0.392887i
$47$	1.39277	−	5.19789i	0.203156	−	0.758190i	−0.786847	−	0.617148i	$-0.788288\pi$
$47$	1.39277	−	5.19789i	0.203156	−	0.758190i	0.990004	−	0.141042i	$-0.0450453\pi$
$48$	0.510219	−	0.716351i	0.0736437	−	0.103396i
$49$	11.2391	+	14.6471i	1.60559	+	2.09244i
$50$	1.89689	−	3.28551i	0.268261	−	0.464642i
$51$	4.80009	−	5.28764i	0.672148	−	0.740417i
$52$	−3.03896	−	5.26363i	−0.421428	−	0.729935i
$53$	2.70319	−	6.52608i	0.371312	−	0.896426i	−0.622217	−	0.782845i	$-0.713768\pi$
$53$	2.70319	−	6.52608i	0.371312	−	0.896426i	0.993529	−	0.113581i	$-0.0362321\pi$
$54$	−0.648289	+	4.14903i	−0.0882210	+	0.564611i
$55$	−1.81570	−	1.81570i	−0.244829	−	0.244829i
$56$	−13.6194	−	0.892662i	−1.81997	−	0.119287i
$57$	−3.66994	+	0.130707i	−0.486096	+	0.0173126i
$58$	−0.0221803	−	0.338405i	−0.00291241	−	0.0444348i
$59$	−0.445276	+	3.38221i	−0.0579700	+	0.440326i	0.937706	+	0.347430i	$0.112946\pi$
$59$	−0.445276	+	3.38221i	−0.0579700	+	0.440326i	−0.995676	+	0.0928957i	$0.970388\pi$
$60$	6.62460	+	2.97863i	0.855232	+	0.384540i
$61$	0.762232	−	1.54565i	0.0975938	−	0.197901i	−0.842601	−	0.538539i	$-0.818976\pi$
$61$	0.762232	−	1.54565i	0.0975938	−	0.197901i	0.940194	+	0.340638i	$0.110643\pi$
$62$	−0.209263	+	1.05204i	−0.0265765	+	0.133609i
$63$	−13.9522	+	5.87342i	−1.75781	+	0.739981i
$64$	2.60783	−	2.60783i	0.325978	−	0.325978i
$65$	10.5637	−	9.26409i	1.31026	−	1.14907i
$66$	−0.729788	+	0.894482i	−0.0898307	+	0.110103i
$67$	−1.90636	−	1.10063i	−0.232898	−	0.134464i	0.379010	−	0.925393i	$-0.376265\pi$
$67$	−1.90636	−	1.10063i	−0.232898	−	0.134464i	−0.611908	+	0.790929i	$0.709598\pi$
$68$	−4.36244	+	3.43625i	−0.529023	+	0.416707i
$69$	1.97490	−	6.57840i	0.237750	−	0.791947i
$70$	−1.65732	−	12.5886i	−0.198088	−	1.50462i
$71$	−2.14171	+	0.426013i	−0.254174	+	0.0505584i	−0.320533	−	0.947237i	$-0.603862\pi$
$71$	−2.14171	+	0.426013i	−0.254174	+	0.0505584i	0.0663583	+	0.997796i	$0.478862\pi$
$72$	2.56408	−	7.69873i	0.302180	−	0.907304i
$73$	4.79086	+	3.20115i	0.560727	+	0.374666i	0.803398	−	0.595443i	$-0.203023\pi$
$73$	4.79086	+	3.20115i	0.560727	+	0.374666i	−0.242670	+	0.970109i	$0.578023\pi$
$74$	−0.0176075	−	0.0518700i	−0.00204683	−	0.00602976i
$75$	−1.82352	+	7.92364i	−0.210562	+	0.914943i
$76$	2.83117	+	0.372731i	0.324758	+	0.0427552i
$77$	−4.12590	−	0.543185i	−0.470190	−	0.0619017i
$78$	−4.62277	−	4.30481i	−0.523426	−	0.487424i
$79$	−4.25979	−	12.5489i	−0.479263	−	1.41186i	−0.870771	−	0.491689i	$-0.836380\pi$
$79$	−4.25979	−	12.5489i	−0.479263	−	1.41186i	0.391507	−	0.920175i	$-0.371954\pi$
$80$	−1.31453	−	0.878338i	−0.146968	−	0.0982012i
$81$	−1.27729	−	8.90890i	−0.141921	−	0.989878i
$82$	2.68181	−	0.533446i	0.296157	−	0.0589092i
$83$	−0.479996	−	3.64594i	−0.0526865	−	0.400193i	−0.997386	−	0.0722565i	$-0.976980\pi$
$83$	−0.479996	−	3.64594i	−0.0526865	−	0.400193i	0.944700	−	0.327937i	$-0.106353\pi$
$84$	11.4563	−	2.70599i	1.24998	−	0.295247i
$85$	−9.75844	−	8.34121i	−1.05845	−	0.904732i
$86$	−5.06754	−	2.92574i	−0.546447	−	0.315491i
$87$	0.257977	+	0.679496i	0.0276581	+	0.0728496i
$88$	1.67713	−	1.47080i	0.178783	−	0.156788i
$89$	−3.26760	+	3.26760i	−0.346365	+	0.346365i	−0.858754	−	0.512389i	$-0.828761\pi$
$89$	−3.26760	+	3.26760i	−0.346365	+	0.346365i	0.512389	+	0.858754i	$0.328761\pi$
$90$	7.48982	+	0.942264i	0.789497	+	0.0993233i
$91$	4.44238	−	22.3333i	0.465688	−	2.34117i
$92$	−2.36226	+	4.79019i	−0.246282	+	0.499411i
$93$	−0.231907	−	2.28715i	−0.0240477	−	0.237167i
$94$	−0.567653	+	4.31175i	−0.0585489	+	0.444723i
$95$	0.431749	+	6.58721i	0.0442965	+	0.675833i
$96$	−4.72636	+	8.90390i	−0.482383	+	0.908751i
$97$	17.3795	+	1.13911i	1.76462	+	0.115659i	0.912859	−	0.408276i	$-0.133870\pi$
$97$	17.3795	+	1.13911i	1.76462	+	0.115659i	0.851758	+	0.523935i	$0.175537\pi$
$98$	−10.5505	−	10.5505i	−1.06576	−	1.06576i
$99$	0.933647	−	2.29121i	0.0938351	−	0.230275i
$100$	2.41954	−	5.84130i	0.241954	−	0.584130i
$101$	7.22857	+	12.5203i	0.719270	+	1.24581i	0.961289	+	0.275541i	$0.0888568\pi$
$101$	7.22857	+	12.5203i	0.719270	+	1.24581i	−0.242020	+	0.970271i	$0.577810\pi$
$102$	−3.28832	+	4.74309i	−0.325592	+	0.469636i
$103$	−0.972232	+	1.68395i	−0.0957968	+	0.165925i	−0.909941	−	0.414738i	$-0.863873\pi$
$103$	−0.972232	+	1.68395i	−0.0957968	+	0.165925i	0.814144	+	0.580663i	$0.197207\pi$
$104$	7.43051	+	9.68363i	0.728621	+	0.949558i
$105$	11.3020	+	24.7544i	1.10296	+	2.41578i
$106$	−1.47753	+	5.51420i	−0.143510	+	0.535587i
$107$	2.20029	−	3.29297i	0.212710	−	0.318344i	−0.709737	−	0.704467i	$-0.751186\pi$
$107$	2.20029	−	3.29297i	0.212710	−	0.318344i	0.922447	+	0.386123i	$0.126186\pi$
$108$	−0.168634	+	6.99647i	−0.0162268	+	0.673236i
$109$	−12.7255	+	8.50289i	−1.21888	+	0.814430i	−0.987374	−	0.158404i	$-0.949365\pi$
$109$	−12.7255	+	8.50289i	−1.21888	+	0.814430i	−0.231506	+	0.972834i	$0.574365\pi$
$110$	1.64637	+	1.26331i	0.156976	+	0.120452i
$111$	0.0686552	+	0.0952286i	0.00651646	+	0.00903870i
$112$	−2.55671	+	0.167576i	−0.241587	+	0.0158344i
$113$	−0.316254	−	0.277347i	−0.0297506	−	0.0260906i	0.644341	−	0.764738i	$-0.277132\pi$
$113$	−0.316254	−	0.277347i	−0.0297506	−	0.0260906i	−0.674092	+	0.738647i	$0.735465\pi$
$114$	2.92677	−	0.491862i	0.274117	−	0.0460671i
$115$	−11.9261	−	3.19560i	−1.11212	−	0.297991i
$116$	−0.110262	−	0.554324i	−0.0102376	−	0.0514677i
$117$	12.1760	+	5.91775i	1.12568	+	0.547096i
$118$		−	2.75698i		−	0.253801i
$119$	−20.7763	−	1.09713i	−1.90456	−	0.100574i
$120$	−13.9708	−	4.19416i	−1.27535	−	0.382872i
$121$	−8.18729	+	6.28233i	−0.744299	+	0.571121i
$122$	−0.447695	+	1.31887i	−0.0405324	+	0.119405i
$123$	−5.16028	+	2.77733i	−0.465286	+	0.250424i
$124$	−0.116917	+	1.78381i	−0.0104995	+	0.160191i
$125$	−0.933539	−	0.185692i	−0.0834983	−	0.0166088i
$126$	10.5597	−	6.17788i	0.940731	−	0.550369i
$127$	6.87458	+	16.5967i	0.610020	+	1.47272i	0.862978	+	0.505241i	$0.168596\pi$
$127$	6.87458	+	16.5967i	0.610020	+	1.47272i	−0.252958	+	0.967477i	$0.581404\pi$
$128$	5.27157	−	6.87004i	0.465945	−	0.607232i
$129$	12.2213	+	2.81258i	1.07603	+	0.247634i
$130$	−7.48695	+	8.53723i	−0.656649	+	0.748765i
$131$	8.97762	−	4.42727i	0.784378	−	0.386812i	−0.00557139	−	0.999984i	$-0.501773\pi$
$131$	8.97762	−	4.42727i	0.784378	−	0.386812i	0.789949	+	0.613172i	$0.210107\pi$
$132$	−1.01125	+	1.63671i	−0.0880184	+	0.142457i
$133$	7.05401	+	8.04355i	0.611660	+	0.697464i
$134$	1.64358	+	0.680793i	0.141984	+	0.0588115i
$135$	−15.9391	+	2.77302i	−1.37182	+	0.238664i
$136$	7.78515	−	7.98532i	0.667571	−	0.684735i
$137$	−0.180228	+	0.104055i	−0.0153979	+	0.00889001i	−0.507679	−	0.861546i	$-0.669496\pi$
$137$	−0.180228	+	0.104055i	−0.0153979	+	0.00889001i	0.492281	+	0.870436i	$0.336163\pi$
$138$	−0.888458	+	5.47930i	−0.0756306	+	0.466429i
$139$	−4.01066	−	1.36144i	−0.340180	−	0.115475i	0.146122	−	0.989267i	$-0.453321\pi$
$139$	−4.01066	−	1.36144i	−0.340180	−	0.115475i	−0.486301	+	0.873791i	$0.661654\pi$
$140$	−5.47679	−	20.4397i	−0.462873	−	1.72747i
$141$	−1.54472	−	9.19170i	−0.130089	−	0.774081i
$142$	1.67112	−	0.567268i	0.140237	−	0.0476041i
$143$	2.06763	+	3.09442i	0.172904	+	0.258769i
$144$	0.288584	−	1.49572i	0.0240487	−	0.124643i
$145$	1.20709	−	0.499993i	0.100243	−	0.0415222i
$146$	−4.17638	−	2.05956i	−0.345639	−	0.170450i
$147$	28.2449	+	14.9930i	2.32960	+	1.23660i
$148$	−0.0403762	−	0.0818748i	−0.00331890	−	0.00673007i
$149$	22.7638	−	6.09953i	1.86488	−	0.499693i	0.864883	−	0.501973i	$-0.167392\pi$
$149$	22.7638	−	6.09953i	1.86488	−	0.499693i	0.999997	+	0.00227989i	$0.000725712\pi$
$150$	0.625266	−	6.54121i	0.0510527	−	0.534088i
$151$	−12.4407	+	1.63785i	−1.01241	+	0.133287i	−0.618437	−	0.785834i	$-0.712234\pi$
$151$	−12.4407	+	1.63785i	−1.01241	+	0.133287i	−0.393976	+	0.919121i	$0.628901\pi$
$152$	−5.73475			−0.465149
$153$	3.75930	−	11.7842i	0.303921	−	0.952697i
$154$	3.36319			0.271014
$155$	−4.09715	+	0.539400i	−0.329091	+	0.0433257i
$156$	−8.57465	−	6.10727i	−0.686522	−	0.488973i
$157$	9.34317	−	2.50349i	0.745666	−	0.199801i	0.134071	−	0.990972i	$-0.457195\pi$
$157$	9.34317	−	2.50349i	0.745666	−	0.199801i	0.611595	+	0.791171i	$0.290528\pi$
$158$	4.73692	+	9.60553i	0.376849	+	0.764175i
$159$	−0.435474	−	12.2271i	−0.0345354	−	0.969669i
$160$	16.2523	+	8.01473i	1.28485	+	0.633620i
$161$	−18.4868	+	7.65748i	−1.45696	+	0.603494i
$162$	1.96321	+	7.00356i	0.154245	+	0.550252i
$163$	−0.147654	−	0.220979i	−0.0115651	−	0.0173084i	0.825642	−	0.564194i	$-0.190813\pi$
$163$	−0.147654	−	0.220979i	−0.0115651	−	0.0173084i	−0.837207	+	0.546886i	$0.815813\pi$
$164$	4.31513	−	1.46479i	0.336955	−	0.114381i
$165$	−4.16697	−	1.55467i	−0.324398	−	0.121031i
$166$	0.769199	+	2.87069i	0.0597014	+	0.222809i
$167$	−1.69588	−	0.575674i	−0.131231	−	0.0445470i	0.255051	−	0.966928i	$-0.417908\pi$
$167$	−1.69588	−	0.575674i	−0.131231	−	0.0445470i	−0.386282	+	0.922381i	$0.626241\pi$
$168$	−22.1009	+	8.39081i	−1.70512	+	0.647365i
$169$	−6.37741	+	3.68200i	−0.490570	+	0.283231i
$170$	8.69889	+	5.65405i	0.667174	+	0.433646i
$171$	−5.68834	+	2.84597i	−0.434998	+	0.217636i
$172$	−9.00955	−	3.73188i	−0.686972	−	0.284553i
$173$	11.6422	+	13.2754i	0.885143	+	1.00931i	0.999873	+	0.0159158i	$0.00506636\pi$
$173$	11.6422	+	13.2754i	0.885143	+	1.00931i	−0.114730	+	0.993397i	$0.536600\pi$
$174$	−0.278384	−	0.517236i	−0.0211042	−	0.0392116i
$175$	21.2447	−	10.4767i	1.60595	−	0.791964i
$176$	0.276108	−	0.314841i	0.0208124	−	0.0237320i
$177$	1.73146	+	5.64932i	0.130144	+	0.424629i
$178$	2.27349	−	2.96287i	0.170405	−	0.222076i
$179$	−8.88505	−	21.4504i	−0.664100	−	1.60328i	−0.791319	−	0.611403i	$-0.790605\pi$
$179$	−8.88505	−	21.4504i	−0.664100	−	1.60328i	0.127220	−	0.991875i	$-0.459395\pi$
$180$	12.5804	−	0.0723544i	0.937690	−	0.00539298i
$181$	−9.79946	−	1.94923i	−0.728388	−	0.144885i	−0.183052	−	0.983103i	$-0.558598\pi$
$181$	−9.79946	−	1.94923i	−0.728388	−	0.144885i	−0.545336	+	0.838218i	$0.683598\pi$
$182$	−1.20360	+	18.3633i	−0.0892164	+	1.36118i
$183$	0.0890864	−	2.98365i	0.00658545	−	0.220558i
$184$	3.44776	−	10.1568i	0.254172	−	0.748768i
$185$	0.167425	−	0.128470i	0.0123093	−	0.00944529i
$186$	0.427082	+	1.80813i	0.0313152	+	0.132578i
$187$	2.52787	−	2.27429i	0.184856	−	0.166312i
$188$			7.24781i			0.528601i
$189$	−17.7579	+	19.2908i	−1.29170	+	1.40320i
$190$	−1.04081	−	5.23249i	−0.0755081	−	0.379605i
$191$	−7.40789	−	1.98494i	−0.536016	−	0.143625i	−0.0193512	−	0.999813i	$-0.506160\pi$
$191$	−7.40789	−	1.98494i	−0.536016	−	0.143625i	−0.516665	+	0.856188i	$0.672827\pi$
$192$	2.23292	−	5.98487i	0.161147	−	0.431921i
$193$	8.68803	+	7.61919i	0.625378	+	0.548442i	0.912305	−	0.409511i	$-0.134301\pi$
$193$	8.68803	+	7.61919i	0.625378	+	0.548442i	−0.286928	+	0.957952i	$0.592634\pi$
$194$	−14.0455	+	0.920593i	−1.00841	+	0.0660947i
$195$	9.97988	−	22.1956i	0.714674	−	1.58946i
$196$	−19.7276	−	15.1375i	−1.40912	−	1.08125i
$197$	−1.59072	+	1.06288i	−0.113334	+	0.0757274i	−0.610946	−	0.791673i	$-0.709211\pi$
$197$	−1.59072	+	1.06288i	−0.113334	+	0.0757274i	0.497611	+	0.867400i	$0.334211\pi$
$198$	−0.506396	+	1.93433i	−0.0359880	+	0.137467i
$199$	−7.63607	+	11.4282i	−0.541306	+	0.810122i	−0.996785	−	0.0801245i	$-0.974468\pi$
$199$	−7.63607	+	11.4282i	−0.541306	+	0.810122i	0.455478	+	0.890247i	$0.349468\pi$
$200$	−3.28630	+	12.2646i	−0.232376	+	0.867240i
$201$	−3.79541	−	0.362798i	−0.267708	−	0.0255898i
$202$	−7.11265	−	9.26939i	−0.500445	−	0.652192i
$203$	1.05873	−	1.83377i	0.0743082	−	0.128705i
$204$	−4.40154	+	8.55234i	−0.308169	+	0.598784i
$205$	5.26721	+	9.12307i	0.367878	+	0.637183i
$206$	0.601370	−	1.45183i	0.0418994	−	0.101154i
$207$	−1.62061	−	11.7856i	−0.112640	−	0.819156i
$208$	1.62025	+	1.62025i	0.112344	+	0.112344i
$209$	−1.74480	−	0.114360i	−0.120690	−	0.00791045i
$210$	−11.6670	−	18.6424i	−0.805103	−	1.28645i
$211$	−0.528242	−	8.05942i	−0.0363657	−	0.554833i	−0.976704	−	0.214592i	$-0.931158\pi$
$211$	−0.528242	−	8.05942i	−0.0363657	−	0.554833i	0.940338	−	0.340241i	$-0.110509\pi$
$212$	−1.24182	+	9.43255i	−0.0852884	+	0.647830i
$213$	−3.06802	+	2.21190i	−0.210218	+	0.151557i
$214$	−1.41563	+	2.87061i	−0.0967704	+	0.196231i
$215$	4.39803	−	22.1104i	0.299943	−	1.50792i
$216$	−1.49821	−	13.9746i	−0.101941	−	0.950853i
$217$	−4.73575	+	4.73575i	−0.321484	+	0.321484i
$218$	9.29941	−	8.15536i	0.629835	−	0.552351i
$219$	9.85126	+	1.59736i	0.665687	+	0.107940i
$220$	2.99512	+	1.72923i	0.201931	+	0.116585i
$221$	11.5131	+	14.6163i	0.774457	+	0.983198i
$222$	−0.0650557	−	0.0690602i	−0.00436625	−	0.00463501i
$223$	2.37603	+	18.0478i	0.159111	+	1.20857i	0.865561	+	0.500804i	$0.166962\pi$
$223$	2.37603	+	18.0478i	0.159111	+	1.20857i	−0.706450	+	0.707763i	$0.749704\pi$
$224$	28.8036	−	5.72939i	1.92452	−	0.382811i
$225$	2.82683	+	13.7963i	0.188455	+	0.919751i
$226$	0.282656	+	0.188865i	0.0188020	+	0.0125631i
$227$	7.49766	+	22.0874i	0.497637	+	1.46599i	0.848313	+	0.529495i	$0.177618\pi$
$227$	7.49766	+	22.0874i	0.497637	+	1.46599i	−0.350676	+	0.936497i	$0.614048\pi$
$228$	4.72892	−	1.44937i	0.313181	−	0.0959866i
$229$	14.6011	+	1.92227i	0.964866	+	0.127027i	0.596464	−	0.802640i	$-0.296572\pi$
$229$	14.6011	+	1.92227i	0.964866	+	0.127027i	0.368402	+	0.929667i	$0.379905\pi$
$230$	9.89297	+	1.30243i	0.652323	+	0.0858800i
$231$	−6.89151	+	2.11218i	−0.453428	+	0.138971i
$232$	0.364842	+	1.07479i	0.0239531	+	0.0705635i
$233$	20.3987	+	13.6300i	1.33636	+	0.892930i	0.998829	−	0.0483830i	$-0.0154068\pi$
$233$	20.3987	+	13.6300i	1.33636	+	0.892930i	0.337535	+	0.941313i	$0.390407\pi$
$234$	−10.3804	−	3.45721i	−0.678586	−	0.226005i
$235$	−16.4329	+	3.26871i	−1.07197	+	0.213227i
$236$	−0.599726	−	4.55537i	−0.0390388	−	0.296529i
$237$	−15.7390	−	16.7078i	−1.02235	−	1.08529i
$238$	16.7628	−	1.31255i	1.08657	−	0.0850803i
$239$	−23.2883	−	13.4455i	−1.50639	−	0.869717i	−0.999972	−	0.00743049i	$-0.997635\pi$
$239$	−23.2883	−	13.4455i	−1.50639	−	0.869717i	−0.506421	−	0.862286i	$-0.669032\pi$
$240$	−2.70301	−	0.438288i	−0.174479	−	0.0282914i
$241$	−6.95983	+	6.10361i	−0.448322	+	0.393168i	−0.853519	−	0.521061i	$-0.825536\pi$
$241$	−6.95983	+	6.10361i	−0.448322	+	0.393168i	0.405197	+	0.914229i	$0.367203\pi$
$242$	5.89740	−	5.89740i	0.379099	−	0.379099i
$243$	−8.42124	−	13.1180i	−0.540223	−	0.841522i
$244$	−0.452835	+	2.27656i	−0.0289898	+	0.145742i
$245$	25.4243	−	51.5553i	1.62430	−	3.29375i
$246$	3.84172	−	2.76969i	0.244939	−	0.176589i
$247$	1.24883	−	9.48581i	0.0794612	−	0.603567i
$248$	−0.234798	−	3.58232i	−0.0149097	−	0.227478i
$249$	−3.37903	−	5.39924i	−0.214138	−	0.342163i
$250$	0.767591	+	0.0503106i	0.0485467	+	0.00318192i
$251$	12.0194	+	12.0194i	0.758657	+	0.758657i	0.976078	−	0.217421i	$-0.0697644\pi$
$251$	12.0194	+	12.0194i	0.758657	+	0.758657i	−0.217421	+	0.976078i	$0.569764\pi$
$252$	16.1039	−	12.5048i	1.01445	−	0.787727i
$253$	1.25152	−	3.02145i	0.0786827	−	0.189957i
$254$	−7.25902	−	12.5730i	−0.455472	−	0.788900i
$255$	−21.3758	−	6.12255i	−1.33860	−	0.383409i
$256$	−7.18719	+	12.4486i	−0.449200	+	0.778036i
$257$	−10.2997	−	13.4228i	−0.642477	−	0.837292i	0.352664	−	0.935750i	$-0.385276\pi$
$257$	−10.2997	−	13.4228i	−0.642477	−	0.837292i	−0.995141	+	0.0984576i	$0.968609\pi$
$258$	−10.0891	−	0.964403i	−0.628119	−	0.0600411i
$259$	0.0885198	−	0.330360i	0.00550035	−	0.0205276i
$260$	−10.5136	+	15.7347i	−0.652027	+	0.975827i
$261$	0.895274	+	0.885035i	0.0554160	+	0.0547823i
$262$	−6.72634	+	4.49440i	−0.415555	+	0.277665i
$263$	−17.2622	−	13.2458i	−1.06444	−	0.816770i	−0.0807624	−	0.996733i	$-0.525736\pi$
$263$	−17.2622	−	13.2458i	−1.06444	−	0.816770i	−0.983673	+	0.179963i	$0.942402\pi$
$264$	1.58445	−	3.52387i	0.0975159	−	0.216879i
$265$	−21.9464	+	1.43845i	−1.34816	+	0.0883630i
$266$	−6.50055	−	5.70083i	−0.398574	−	0.349540i
$267$	−2.79784	+	7.49902i	−0.171225	+	0.458932i
$268$	2.86379	+	0.767349i	0.174934	+	0.0468733i
$269$	0.232394	+	1.16832i	0.0141693	+	0.0712339i	0.987223	−	0.159345i	$-0.0509381\pi$
$269$	0.232394	+	1.16832i	0.0141693	+	0.0712339i	−0.973054	+	0.230579i	$0.925938\pi$
$270$	12.4788	−	3.90327i	0.759435	−	0.237546i
$271$			18.6384i			1.13220i	0.824336	+	0.566101i	$0.191549\pi$
$271$			18.6384i			1.13220i	−0.824336	+	0.566101i	$0.808451\pi$
$272$	1.25331	−	1.67699i	0.0759929	−	0.101682i
$273$	−9.06638	−	38.3841i	−0.548722	−	2.32311i
$274$	0.133432	−	0.102386i	0.00806094	−	0.00618538i
$275$	−1.24443	+	3.66598i	−0.0750421	+	0.221067i
$276$	−0.276091	+	9.24674i	−0.0166187	+	0.556588i
$277$	−0.716507	+	10.9318i	−0.0430507	+	0.656827i	0.920742	+	0.390173i	$0.127585\pi$
$277$	−0.716507	+	10.9318i	−0.0430507	+	0.656827i	−0.963792	+	0.266654i	$0.914082\pi$
$278$	3.35717	+	0.667784i	0.201350	+	0.0400510i
$279$	−2.01069	−	3.43681i	−0.120377	−	0.205756i
$280$	16.2625	+	39.2610i	0.971868	+	2.34630i
$281$	−16.4155	+	21.3931i	−0.979266	+	1.27620i	−0.0182154	+	0.999834i	$0.505798\pi$
$281$	−16.4155	+	21.3931i	−0.979266	+	1.27620i	−0.961051	+	0.276371i	$0.910868\pi$
$282$	2.20732	+	7.20194i	0.131444	+	0.428870i
$283$	−6.05533	+	6.90478i	−0.359952	+	0.410447i	−0.903265	−	0.429084i	$-0.858836\pi$
$283$	−6.05533	+	6.90478i	−0.359952	+	0.410447i	0.543313	+	0.839530i	$0.317170\pi$
$284$	2.63780	−	1.30082i	0.156525	−	0.0771893i
$285$	5.41886	+	10.0682i	0.320986	+	0.596390i
$286$	−1.98312	−	2.26131i	−0.117264	−	0.133714i
$287$	15.7731	+	6.53342i	0.931054	+	0.385655i
$288$	−1.04172	+	17.4290i	−0.0613841	+	1.02701i
$289$	11.7118	−	12.3220i	0.688931	−	0.724826i
$290$	−0.914444	+	0.527954i	−0.0536980	+	0.0310025i
$291$	28.2025	−	10.7074i	1.65326	−	0.627677i
$292$	−7.34866	−	2.49453i	−0.430048	−	0.145982i
$293$	−1.14029	−	4.25560i	−0.0666162	−	0.248615i	0.924586	−	0.380974i	$-0.124411\pi$
$293$	−1.14029	−	4.25560i	−0.0666162	−	0.248615i	−0.991202	+	0.132359i	$0.957745\pi$
$294$	−24.2129	−	9.03370i	−1.41213	−	0.526856i
$295$	10.0579	−	3.41420i	0.585594	−	0.198782i
$296$	0.101853	+	0.152434i	0.00592010	+	0.00886006i
$297$	−0.177155	−	4.28166i	−0.0102796	−	0.248447i
$298$	−17.5962	+	7.28857i	−1.01932	+	0.422215i
$299$	16.0495	+	7.91472i	0.928164	+	0.457720i
$300$	−0.389780	−	10.9441i	−0.0225040	−	0.631857i
$301$	−16.1592	−	32.7675i	−0.931398	−	1.88869i
$302$	9.79543	−	2.62468i	0.563664	−	0.151033i
$303$	20.3960	+	14.5269i	1.17172	+	0.834551i
$304$	−1.06735	+	0.140519i	−0.0612168	+	0.00805934i
$305$	−5.36586			−0.307248
$306$	−1.76907	+	9.83871i	−0.101131	+	0.562442i
$307$	16.0286			0.914801			0.457400	−	0.889261i	$-0.348781\pi$
$307$	16.0286			0.914801			0.457400	+	0.889261i	$0.348781\pi$
$308$	5.55702	−	0.731596i	0.316641	−	0.0416865i
$309$	−0.320473	+	3.35263i	−0.0182311	+	0.190724i
$310$	3.22596	−	0.864394i	0.183222	−	0.0490943i
$311$	6.02290	+	12.2132i	0.341528	+	0.692549i	0.998094	−	0.0617192i	$-0.0196583\pi$
$311$	6.02290	+	12.2132i	0.341528	+	0.692549i	−0.656566	+	0.754269i	$0.727992\pi$
$312$	18.6736	+	9.91229i	1.05718	+	0.561173i
$313$	−1.94022	−	0.956812i	−0.109668	−	0.0540822i	0.386627	−	0.922236i	$-0.373640\pi$
$313$	−1.94022	−	0.956812i	−0.109668	−	0.0540822i	−0.496295	+	0.868154i	$0.665307\pi$
$314$	−7.22217	+	2.99152i	−0.407571	+	0.168821i
$315$	35.6148	+	30.8728i	2.00667	+	1.73949i
$316$	9.91633	+	14.8408i	0.557837	+	0.834862i
$317$	−8.63970	+	2.93278i	−0.485254	+	0.164722i	−0.553336	−	0.832958i	$-0.686645\pi$
$317$	−8.63970	+	2.93278i	−0.485254	+	0.164722i	0.0680819	+	0.997680i	$0.478312\pi$
$318$	1.63872	+	9.75106i	0.0918951	+	0.546812i
$319$	0.0895703	+	0.334281i	0.00501497	+	0.0187161i
$320$	−10.8735	−	3.69106i	−0.607848	−	0.206337i
$321$	1.09794	−	6.77122i	0.0612810	−	0.377932i
$322$	14.0049	−	8.08572i	0.780461	−	0.450599i
$323$	−8.74105	+	0.110949i	−0.486365	+	0.00617335i
$324$	4.76731	+	11.1450i	0.264850	+	0.619164i
$325$	−19.5712	−	8.10665i	−1.08561	−	0.449676i
$326$	0.141619	+	0.161485i	0.00784353	+	0.00894383i
$327$	−13.9336	+	22.5514i	−0.770530	+	1.24710i
$328$	−8.20773	+	4.04761i	−0.453196	+	0.223492i
$329$	−17.9038	+	20.4153i	−0.987067	+	1.12553i
$330$	3.50280	+	0.806126i	0.192823	+	0.0443758i
$331$	0.826504	−	1.07712i	0.0454288	−	0.0592039i	−0.770087	−	0.637939i	$-0.779787\pi$
$331$	0.826504	−	1.07712i	0.0454288	−	0.0592039i	0.815515	+	0.578736i	$0.196454\pi$
$332$	1.89541	+	4.57593i	0.104024	+	0.251137i
$333$	0.176677	+	0.100654i	0.00968185	+	0.00551582i
$334$	1.41956	+	0.282368i	0.0776747	+	0.0154505i
$335$	−0.448260	+	6.83912i	−0.0244911	+	0.373661i
$336$	−3.90781	+	2.10324i	−0.213189	+	0.114741i
$337$	7.70958	−	22.7117i	0.419968	−	1.23718i	−0.506968	−	0.861965i	$-0.669234\pi$
$337$	7.70958	−	22.7117i	0.419968	−	1.23718i	0.926936	−	0.375220i	$-0.122433\pi$
$338$	4.72152	−	3.62295i	0.256817	−	0.197063i
$339$	−0.697803	−	0.209487i	−0.0378994	−	0.0113778i
$340$	15.6031	+	7.44994i	0.846199	+	0.404029i
$341$		−	1.09460i		−	0.0592761i
$342$	4.25760	−	2.88039i	0.230224	−	0.155754i
$343$	−11.2838	−	56.7273i	−0.609266	−	3.06299i
$344$	18.9168	+	5.06875i	1.01993	+	0.273289i
$345$	−21.0896	+	3.54424i	−1.13543	+	0.190816i
$346$	−10.7288	−	9.40890i	−0.576783	−	0.505825i
$347$	−4.13052	+	0.270728i	−0.221738	+	0.0145335i	−0.175867	−	0.984414i	$-0.556273\pi$
$347$	−4.13052	+	0.270728i	−0.221738	+	0.0145335i	−0.0458707	+	0.998947i	$0.514606\pi$
$348$	−0.572489	−	0.794074i	−0.0306886	−	0.0425669i
$349$	1.34809	+	1.03443i	0.0721618	+	0.0553717i	0.644212	−	0.764847i	$-0.277185\pi$
$349$	1.34809	+	1.03443i	0.0721618	+	0.0553717i	−0.572051	+	0.820218i	$0.693852\pi$
$350$	−15.9172	+	10.6355i	−0.850811	+	0.568494i
$351$	23.4416	+	0.565005i	1.25122	+	0.0301577i
$352$	−2.66664	+	3.99092i	−0.142133	+	0.212717i
$353$	4.91469	−	18.3419i	0.261582	−	0.976238i	−0.702727	−	0.711460i	$-0.748034\pi$
$353$	4.91469	−	18.3419i	0.261582	−	0.976238i	0.964309	−	0.264779i	$-0.0852989\pi$
$354$	−1.98327	−	4.34390i	−0.105410	−	0.230876i
$355$	4.13897	+	5.39401i	0.219674	+	0.286284i
$356$	3.11198	−	5.39011i	0.164935	−	0.285675i
$357$	−33.5244	+	13.2171i	−1.77430	+	0.699522i
$358$	9.38193	+	16.2500i	0.495850	+	0.858838i
$359$	9.63555	−	23.2623i	0.508545	−	1.22774i	−0.436176	−	0.899861i	$-0.643667\pi$
$359$	9.63555	−	23.2623i	0.508545	−	1.22774i	0.944721	−	0.327875i	$-0.106333\pi$
$360$	−25.0295	+	3.44175i	−1.31917	+	0.181396i
$361$	−10.2564	−	10.2564i	−0.539813	−	0.539813i
$362$	8.05748	+	0.528115i	0.423492	+	0.0277571i
$363$	−8.38062	+	15.7881i	−0.439868	+	0.828659i
$364$	2.00587	+	30.6036i	0.105136	+	1.60406i
$365$	2.34165	−	17.7866i	0.122568	−	0.930994i
$366$	0.243356	+	2.40006i	0.0127204	+	0.125453i
$367$	4.54401	−	9.21434i	0.237195	−	0.480985i	−0.745430	−	0.666584i	$-0.767756\pi$
$367$	4.54401	−	9.21434i	0.237195	−	0.480985i	0.982626	+	0.185599i	$0.0594225\pi$
$368$	0.392824	−	1.97486i	0.0204774	−	0.102947i
$369$	−6.13262	+	8.08808i	−0.319251	+	0.421049i
$370$	−0.120598	+	0.120598i	−0.00626961	+	0.00626961i
$371$	−26.7985	+	23.5017i	−1.39131	+	1.22015i
$372$	1.09899	+	2.89467i	0.0569801	+	0.150082i
$373$	5.50433	+	3.17793i	0.285004	+	0.164547i	0.635686	−	0.771947i	$-0.280717\pi$
$373$	5.50433	+	3.17793i	0.285004	+	0.164547i	−0.350683	+	0.936494i	$0.614050\pi$
$374$	−1.78556	+	2.08894i	−0.0923292	+	0.108017i
$375$	−1.60446	+	0.378977i	−0.0828542	+	0.0195703i
$376$	−1.89986	−	14.4308i	−0.0979776	−	0.744214i
$377$	−1.85726	+	0.369431i	−0.0956535	+	0.0190267i
$378$	12.1937	−	17.3301i	0.627176	−	0.891365i
$379$	6.75771	+	4.51536i	0.347120	+	0.231938i	0.716892	−	0.697184i	$-0.245564\pi$
$379$	6.75771	+	4.51536i	0.347120	+	0.231938i	−0.369772	+	0.929123i	$0.620564\pi$
$380$	−2.85795	−	8.41926i	−0.146610	−	0.431899i
$381$	22.7706	+	21.2044i	1.16657	+	1.08634i
$382$	6.14499	+	0.809004i	0.314405	+	0.0413922i
$383$	16.4005	+	2.15916i	0.838026	+	0.110328i	0.537309	−	0.843385i	$-0.319441\pi$
$383$	16.4005	+	2.15916i	0.838026	+	0.110328i	0.300716	+	0.953714i	$0.402774\pi$
$384$	3.36383	−	14.6166i	0.171660	−	0.745901i
$385$	4.16493	+	12.2695i	0.212264	+	0.625310i
$386$	−7.76505	−	5.18844i	−0.395231	−	0.264085i
$387$	21.2792	−	4.36007i	1.08168	−	0.221635i
$388$	−23.0072	+	4.57643i	−1.16802	+	0.232333i
$389$	−0.312441	−	2.37323i	−0.0158414	−	0.120327i	0.981697	−	0.190449i	$-0.0609945\pi$
$389$	−0.312441	−	2.37323i	−0.0158414	−	0.120327i	−0.997538	+	0.0701220i	$0.977661\pi$
$390$	−5.65507	+	18.8371i	−0.286356	+	0.953854i
$391$	5.05867	−	15.5479i	0.255828	−	0.786293i
$392$	43.2469	+	24.9686i	2.18430	+	1.26111i
$393$	10.9603	−	13.4338i	0.552875	−	0.677644i
$394$	1.16245	−	1.01944i	0.0585634	−	0.0513587i
$395$	−29.1764	+	29.1764i	−1.46802	+	1.46802i
$396$	−0.415946	+	3.30626i	−0.0209021	+	0.166146i
$397$	−1.66437	+	8.36734i	−0.0835322	+	0.419945i	0.916280	+	0.400539i	$0.131177\pi$
$397$	−1.66437	+	8.36734i	−0.0835322	+	0.419945i	−0.999812	+	0.0194052i	$0.993823\pi$
$398$	4.91291	−	9.96239i	0.246262	−	0.499370i
$399$	16.9005	+	7.59903i	0.846085	+	0.380427i
$400$	−0.311124	+	2.36322i	−0.0155562	+	0.118161i
$401$	−0.562463	−	8.58153i	−0.0280881	−	0.428541i	−0.988626	−	0.150393i	$-0.951946\pi$
$401$	−0.562463	−	8.58153i	−0.0280881	−	0.428541i	0.960538	−	0.278148i	$-0.0897206\pi$
$402$	3.07936	−	0.109673i	0.153585	−	0.00547001i
$403$	5.97663	+	0.391729i	0.297717	+	0.0195134i
$404$	−13.7686	−	13.7686i	−0.685015	−	0.685015i
$405$	−23.1189	+	15.8352i	−1.14879	+	0.786858i
$406$	−0.654872	+	1.58100i	−0.0325007	+	0.0784637i
$407$	0.0279491	+	0.0484092i	0.00138538	+	0.00239956i
$408$	6.52193	−	18.1820i	0.322884	−	0.900144i
$409$	8.77562	−	15.1998i	0.433926	−	0.751582i	−0.563281	−	0.826265i	$-0.690461\pi$
$409$	8.77562	−	15.1998i	0.433926	−	0.751582i	0.997207	+	0.0746830i	$0.0237945\pi$
$410$	−5.18274	−	6.75428i	−0.255957	−	0.333570i
$411$	−0.209115	+	0.293599i	−0.0103149	+	0.0144822i
$412$	0.677828	−	2.52969i	0.0333942	−	0.124629i
$413$	9.56355	−	14.3129i	0.470591	−	0.704290i
$414$	2.54175	+	9.27232i	0.124920	+	0.455709i
$415$	−9.52017	+	6.36118i	−0.467327	+	0.312258i
$416$	−20.8364	−	15.9883i	−1.02159	−	0.783893i
$417$	−7.29856	+	0.740044i	−0.357412	+	0.0362401i
$418$	1.41009	−	0.0924222i	0.0689698	−	0.00452052i
$419$	2.19918	+	1.92863i	0.107437	+	0.0942197i	0.711379	−	0.702808i	$-0.248071\pi$
$419$	2.19918	+	1.92863i	0.107437	+	0.0942197i	−0.603942	+	0.797028i	$0.706404\pi$
$420$	−23.3328	−	28.2649i	−1.13852	−	1.37919i
$421$	13.5300	+	3.62534i	0.659410	+	0.176688i	0.572980	−	0.819569i	$-0.305787\pi$
$421$	13.5300	+	3.62534i	0.659410	+	0.176688i	0.0864304	+	0.996258i	$0.472454\pi$
$422$	1.27342	+	6.40192i	0.0619892	+	0.311641i
$423$	−9.04604	−	13.3712i	−0.439833	−	0.650131i
$424$		−	19.1063i		−	0.927885i
$425$	−4.77178	+	18.7576i	−0.231465	+	0.909879i
$426$	2.22494	−	2.09593i	0.107799	−	0.101548i
$427$	−6.89916	+	5.29391i	−0.333874	+	0.256190i
$428$	−1.71461	+	5.05107i	−0.0828786	+	0.244152i
$429$	5.48377	+	3.38820i	0.264759	+	0.163584i
$430$	−1.19158	+	18.1800i	−0.0574631	+	0.876717i
$431$	21.7828	+	4.33286i	1.04924	+	0.208707i	0.689455	−	0.724329i	$-0.257850\pi$
$431$	21.7828	+	4.33286i	1.04924	+	0.208707i	0.359785	+	0.933035i	$0.382850\pi$
$432$	−0.621271	−	2.56425i	−0.0298909	−	0.123372i
$433$	−13.5406	−	32.6900i	−0.650721	−	1.57098i	−0.811734	−	0.584027i	$-0.801476\pi$
$433$	−13.5406	−	32.6900i	−0.650721	−	1.57098i	0.161014	−	0.986952i	$-0.448524\pi$
$434$	3.29498	−	4.29410i	0.158164	−	0.206124i
$435$	1.54221	−	1.65613i	0.0739435	−	0.0794051i
$436$	13.5914	−	15.4980i	0.650911	−	0.742221i
$437$	−7.54055	+	3.71859i	−0.360713	+	0.177884i
$438$	−8.06187	−	0.240713i	−0.385211	−	0.0115017i
$439$	9.74245	+	11.1091i	0.464982	+	0.530210i	0.936041	−	0.351892i	$-0.114461\pi$
$439$	9.74245	+	11.1091i	0.464982	+	0.530210i	−0.471059	+	0.882102i	$0.656128\pi$
$440$	−6.41675	−	2.65790i	−0.305907	−	0.126711i
$441$	55.2881	+	3.30455i	2.63277	+	0.157359i
$442$	−10.7668	−	10.4969i	−0.512123	−	0.499286i
$443$	−16.9977	+	9.81360i	−0.807583	+	0.466258i	−0.846116	−	0.532999i	$-0.821065\pi$
$443$	−16.9977	+	9.81360i	−0.807583	+	0.466258i	0.0385327	+	0.999257i	$0.487732\pi$
$444$	−0.122514	−	0.0999568i	−0.00581428	−	0.00474374i
$445$	13.6245	+	4.62488i	0.645862	+	0.219241i
$446$	−3.80762	−	14.2102i	−0.180296	−	0.672873i
$447$	31.4788	−	25.9858i	1.48890	−	1.22909i
$448$	−17.6222	+	5.98193i	−0.832571	+	0.282620i
$449$	−10.8428	−	16.2274i	−0.511703	−	0.765818i	0.482202	−	0.876060i	$-0.339837\pi$
$449$	−10.8428	−	16.2274i	−0.511703	−	0.765818i	−0.993905	+	0.110242i	$0.964837\pi$
$450$	−3.72034	−	10.7561i	−0.175378	−	0.507049i
$451$	−2.57792	+	1.06781i	−0.121389	+	0.0502812i
$452$	0.508118	+	0.250576i	0.0238999	+	0.0117861i
$453$	−18.4234	+	11.5300i	−0.865608	+	0.541727i
$454$	−8.33747	−	16.9067i	−0.391297	−	0.793472i
$455$	−68.4828	+	18.3499i	−3.21053	+	0.860258i
$456$	−9.03567	+	4.12537i	−0.423134	+	0.193188i
$457$	−16.2263	+	2.13623i	−0.759034	+	0.0999287i	−0.500101	−	0.865967i	$-0.666704\pi$
$457$	−16.2263	+	2.13623i	−0.759034	+	0.0999287i	−0.258932	+	0.965896i	$0.583371\pi$
$458$	−11.9019			−0.556142
$459$	−2.55398	−	21.2715i	−0.119210	−	0.992869i
$460$	16.6295			0.775355
$461$	26.1730	−	3.44575i	1.21900	−	0.160484i	0.506552	−	0.862209i	$-0.330920\pi$
$461$	26.1730	−	3.44575i	1.21900	−	0.160484i	0.712448	+	0.701725i	$0.247586\pi$
$462$	5.29905	−	2.41936i	0.246534	−	0.112559i
$463$	29.5309	−	7.91277i	1.37242	−	0.367738i	0.504055	−	0.863671i	$-0.331841\pi$
$463$	29.5309	−	7.91277i	1.37242	−	0.367738i	0.868360	+	0.495934i	$0.165174\pi$
$464$	0.0942403	+	0.191100i	0.00437500	+	0.00887161i
$465$	−6.06745	+	3.79722i	−0.281371	+	0.176092i
$466$	−17.7824	−	8.76929i	−0.823752	−	0.406229i
$467$	−32.3041	+	13.3808i	−1.49486	+	0.619190i	−0.972367	−	0.233456i	$-0.924996\pi$
$467$	−32.3041	+	13.3808i	−1.49486	+	0.619190i	−0.522489	+	0.852646i	$0.674996\pi$
$468$	−17.9036	−	3.45432i	−0.827593	−	0.159676i
$469$	6.17107	+	9.23566i	0.284954	+	0.426463i
$470$	12.8222	−	4.35254i	0.591442	−	0.200768i
$471$	12.9202	−	10.6656i	0.595330	−	0.491447i
$472$	2.38819	+	8.91283i	0.109925	+	0.410246i
$473$	5.65437	+	1.91940i	0.259988	+	0.0882540i
$474$	14.3734	+	11.7269i	0.660191	+	0.538635i
$475$	8.61937	−	4.97639i	0.395484	−	0.228333i
$476$	27.4118	−	5.81516i	1.25642	−	0.266537i
$477$	−9.48184	−	18.9517i	−0.434143	−	0.867739i
$478$	20.0782	+	8.31665i	0.918354	+	0.380395i
$479$	−6.12119	−	6.97988i	−0.279684	−	0.318919i	0.594893	−	0.803805i	$-0.297194\pi$
$479$	−6.12119	−	6.97988i	−0.279684	−	0.318919i	−0.874577	+	0.484886i	$0.838861\pi$
$480$	31.3726	+	0.936727i	1.43195	+	0.0427555i
$481$	−0.274320	+	0.135280i	−0.0125079	+	0.00616823i
$482$	4.93275	−	5.62472i	0.224680	−	0.256199i
$483$	−23.6193	+	25.3639i	−1.07472	+	1.15410i
$484$	8.46144	−	11.0272i	0.384611	−	0.501235i
$485$	−20.7522	−	50.1003i	−0.942311	−	2.27494i
$486$	8.13134	+	9.62255i	0.368845	+	0.436488i
$487$	−4.25328	−	0.846029i	−0.192734	−	0.0383373i	0.0977791	−	0.995208i	$-0.468826\pi$
$487$	−4.25328	−	0.846029i	−0.192734	−	0.0383373i	−0.290514	+	0.956871i	$0.593826\pi$
$488$	0.304874	−	4.65147i	0.0138010	−	0.210562i
$489$	−0.391607	−	0.241958i	−0.0177091	−	0.0109417i
$490$	−14.9329	+	43.9909i	−0.674599	+	1.98731i
$491$	−14.5255	+	11.1458i	−0.655527	+	0.503004i	−0.882144	−	0.470980i	$-0.843900\pi$
$491$	−14.5255	+	11.1458i	−0.655527	+	0.503004i	0.226616	+	0.973984i	$0.427234\pi$
$492$	5.74520	−	5.41207i	0.259014	−	0.243995i
$493$	0.576896	+	1.63117i	0.0259821	+	0.0734640i
$494$			7.73228i			0.347892i
$495$	−7.68386	+	0.548026i	−0.345364	+	0.0246319i
$496$	−0.131479	−	0.660989i	−0.00590357	−	0.0296793i
$497$	10.6434	+	2.85188i	0.477421	+	0.127924i
$498$	3.27702	+	3.96973i	0.146847	+	0.177888i
$499$	−19.5224	−	17.1207i	−0.873942	−	0.766426i	0.0995780	−	0.995030i	$-0.468251\pi$
$499$	−19.5224	−	17.1207i	−0.873942	−	0.766426i	−0.973520	+	0.228604i	$0.926584\pi$
$500$	1.27924	−	0.0838457i	0.0572092	−	0.00374969i
$501$	−3.08615	+	0.312922i	−0.137879	+	0.0139803i
$502$	−10.8985	−	8.36270i	−0.486423	−	0.373246i
$503$	−15.4167	+	10.3011i	−0.687399	+	0.459305i	−0.849583	−	0.527455i	$-0.823146\pi$
$503$	−15.4167	+	10.3011i	−0.687399	+	0.459305i	0.162184	+	0.986761i	$0.448146\pi$
$504$	−28.7861	+	29.1191i	−1.28223	+	1.29707i
$505$	25.0080	−	37.4272i	1.11284	−	1.66549i
$506$	−0.684066	+	2.55297i	−0.0304104	+	0.113493i
$507$	−7.39955	+	10.3890i	−0.328626	+	0.461393i
$508$	−14.7291	−	19.1954i	−0.653499	−	0.851657i
$509$	2.96228	−	5.13082i	0.131301	−	0.227420i	−0.792877	−	0.609381i	$-0.791418\pi$
$509$	2.96228	−	5.13082i	0.131301	−	0.227420i	0.924178	+	0.381961i	$0.124751\pi$
$510$	17.7733	+	2.65085i	0.787014	+	0.117382i
$511$	−14.5373	−	25.1794i	−0.643094	−	1.11387i
$512$	−2.18209	+	5.26802i	−0.0964355	+	0.232816i
$513$	−6.91527	+	8.57609i	−0.305316	+	0.378644i
$514$	9.66861	+	9.66861i	0.426464	+	0.426464i
$515$	6.04125	+	0.395965i	0.266209	+	0.0174483i
$516$	−16.8800	+	0.601193i	−0.743102	+	0.0264660i
$517$	−0.290257	−	4.42847i	−0.0127655	−	0.194764i
$518$	−0.0360781	+	0.274041i	−0.00158518	+	0.0120407i
$519$	27.8934	+	12.5418i	1.22438	+	0.550523i
$520$	16.8088	−	34.0848i	0.737113	−	1.49472i
$521$	−5.18504	+	26.0670i	−0.227161	+	1.14202i	0.683847	+	0.729626i	$0.260306\pi$
$521$	−5.18504	+	26.0670i	−0.227161	+	1.14202i	−0.911008	+	0.412389i	$0.864694\pi$
$522$	−0.810702	−	0.614698i	−0.0354835	−	0.0269046i
$523$	−1.49694	+	1.49694i	−0.0654567	+	0.0654567i	−0.739077	−	0.673621i	$-0.764738\pi$
$523$	−1.49694	+	1.49694i	−0.0654567	+	0.0654567i	0.673621	+	0.739077i	$0.264738\pi$
$524$	−10.1363	+	8.88929i	−0.442806	+	0.388330i
$525$	25.9365	−	31.7897i	1.13196	−	1.38742i
$526$	15.2287	+	8.79231i	0.664004	+	0.383363i
$527$	−0.427191	−	5.45573i	−0.0186087	−	0.237655i
$528$	0.208551	−	0.694686i	0.00907602	−	0.0302323i
$529$	0.949552	+	7.21256i	0.0412849	+	0.313590i
$530$	17.4330	−	3.46763i	0.757239	−	0.150624i
$531$	6.79200	+	7.65553i	0.294748	+	0.332222i
$532$	−11.9810	−	8.00544i	−0.519441	−	0.347080i
$533$	−4.90776	−	14.4578i	−0.212579	−	0.626236i
$534$	1.45073	−	6.30376i	0.0627792	−	0.272790i
$535$	−12.2255	−	1.60952i	−0.528556	−	0.0695858i
$536$	−5.90312	−	0.777161i	−0.254976	−	0.0335682i
$537$	−29.4299	−	27.4057i	−1.26999	−	1.18264i
$538$	−0.309450	−	0.911610i	−0.0133413	−	0.0393023i
$539$	12.6600	+	8.45912i	0.545303	+	0.364360i
$540$	19.7697	−	9.16391i	0.850752	−	0.394352i
$541$	16.6949	−	3.32083i	0.717772	−	0.142774i	0.177325	−	0.984152i	$-0.443255\pi$
$541$	16.6949	−	3.32083i	0.717772	−	0.142774i	0.540446	+	0.841379i	$0.318255\pi$
$542$	−1.96611	−	14.9341i	−0.0844518	−	0.641475i
$543$	−16.8422	+	3.97816i	−0.722770	+	0.170719i
$544$	−11.7336	+	20.9322i	−0.503072	+	0.897462i
$545$	41.2683	+	23.8263i	1.76774	+	1.02061i
$546$	11.3135	+	29.7991i	0.484174	+	1.27528i
$547$	22.8366	−	20.0272i	0.976424	−	0.856301i	−0.0132100	−	0.999913i	$-0.504205\pi$
$547$	22.8366	−	20.0272i	0.976424	−	0.856301i	0.989634	+	0.143612i	$0.0458717\pi$
$548$	0.198199	−	0.198199i	0.00846663	−	0.00846663i
$549$	−2.00597	−	4.76513i	−0.0856125	−	0.203371i
$550$	0.610393	−	3.06866i	0.0260273	−	0.130848i
$551$	0.393501	−	0.797942i	0.0167637	−	0.0339935i
$552$	−1.87412	−	18.4832i	−0.0797679	−	0.786698i
$553$	−8.72840	+	66.2988i	−0.371169	+	2.81931i
$554$	−0.579058	−	8.83472i	−0.0246018	−	0.375351i
$555$	0.171379	−	0.322857i	0.00727462	−	0.0137045i
$556$	5.69234	+	0.373095i	0.241409	+	0.0158228i
$557$	17.8937	+	17.8937i	0.758182	+	0.758182i	0.975991	−	0.217809i	$-0.0698911\pi$
$557$	17.8937	+	17.8937i	0.758182	+	0.758182i	−0.217809	+	0.975991i	$0.569891\pi$
$558$	1.97361	+	2.54166i	0.0835496	+	0.107597i
$559$	−12.5036	+	30.1864i	−0.528846	+	1.27675i
$560$	3.98879	+	6.90879i	0.168557	+	0.291950i
$561$	2.34688	−	5.40182i	0.0990852	−	0.228065i
$562$	10.8963	−	18.8729i	0.459633	−	0.796107i
$563$	16.0519	+	20.9192i	0.676506	+	0.881640i	0.997865	−	0.0653178i	$-0.0208061\pi$
$563$	16.0519	+	20.9192i	0.676506	+	0.881640i	−0.321358	+	0.946958i	$0.604139\pi$
$564$	5.21381	+	11.4196i	0.219541	+	0.480854i
$565$	−0.338973	+	1.26506i	−0.0142607	+	0.0532216i
$566$	4.12350	−	6.17125i	0.173323	−	0.259397i
$567$	−14.1023	+	43.1691i	−0.592240	+	1.81293i
$568$	−4.91104	+	3.28145i	−0.206063	+	0.137687i
$569$	−10.1086	−	7.75657i	−0.423773	−	0.325172i	0.374762	−	0.927121i	$-0.377724\pi$
$569$	−10.1086	−	7.75657i	−0.423773	−	0.325172i	−0.798535	+	0.601949i	$0.794391\pi$
$570$	−5.40396	−	7.49559i	−0.226347	−	0.313956i
$571$	26.0799	−	1.70937i	1.09141	−	0.0715349i	0.490949	−	0.871188i	$-0.336650\pi$
$571$	26.0799	−	1.70937i	1.09141	−	0.0715349i	0.600462	+	0.799653i	$0.294983\pi$
$572$	−3.76862	−	3.30499i	−0.157574	−	0.138188i
$573$	−13.0998	+	2.20150i	−0.547251	+	0.0919688i
$574$	−13.3274	−	3.57107i	−0.556276	−	0.149054i
$575$	3.63165	+	18.2576i	0.151450	+	0.761393i
$576$	−0.787109	−	11.0360i	−0.0327962	−	0.459835i
$577$		−	0.792090i		−	0.0329751i	−0.999864	−	0.0164876i	$-0.994752\pi$
$577$		−	0.792090i		−	0.0329751i	0.999864	−	0.0164876i	$-0.00524839\pi$
$578$	−8.08435	+	11.1085i	−0.336264	+	0.462055i
$579$	19.1698	+	5.75496i	0.796671	+	0.239168i
$580$	−1.39609	+	1.07126i	−0.0579696	+	0.0444817i
$581$	−5.96469	+	17.5714i	−0.247457	+	0.728985i
$582$	−21.4679	+	11.5543i	−0.889874	+	0.478942i
$583$	0.381011	−	5.81310i	0.0157798	−	0.240754i
$584$	15.2855	+	3.04048i	0.632520	+	0.125816i
$585$	−0.242423	−	42.1506i	−0.0100229	−	1.74271i
$586$	1.36257	+	3.28954i	0.0562873	+	0.135890i
$587$	4.71260	−	6.14158i	0.194510	−	0.253490i	−0.685909	−	0.727688i	$-0.740595\pi$
$587$	4.71260	−	6.14158i	0.194510	−	0.253490i	0.880419	+	0.474197i	$0.157262\pi$
$588$	−41.9722	−	9.65938i	−1.73091	−	0.398346i
$589$	−1.85542	+	2.11570i	−0.0764514	+	0.0871761i
$590$	−7.69879	+	3.79663i	−0.316954	+	0.156305i
$591$	−1.74174	+	2.81899i	−0.0716455	+	0.115958i
$592$	0.0226921	+	0.0258753i	0.000932638	+	0.00106347i
$593$	−27.9427	−	11.5742i	−1.14747	−	0.475297i	−0.273784	−	0.961791i	$-0.588275\pi$
$593$	−27.9427	−	11.5742i	−1.14747	−	0.475297i	−0.873684	+	0.486495i	$0.838275\pi$
$594$	0.593607	+	3.41201i	0.0243560	+	0.139997i
$595$	25.5472	+	59.5281i	1.04733	+	2.44041i
$596$	−27.4887	+	15.8706i	−1.12598	+	0.650086i
$597$	−3.81037	+	23.4994i	−0.155948	+	0.961765i
$598$	−13.6946	−	4.64869i	−0.560014	−	0.190099i
$599$	7.63845	+	28.5071i	0.312098	+	1.16477i	0.926661	+	0.375899i	$0.122666\pi$
$599$	7.63845	+	28.5071i	0.312098	+	1.16477i	−0.614562	+	0.788868i	$0.710667\pi$
$600$	3.64483	+	21.6882i	0.148800	+	0.885417i
$601$	−2.10832	+	0.715679i	−0.0860002	+	0.0291931i	−0.364108	−	0.931357i	$-0.618626\pi$
$601$	−2.10832	+	0.715679i	−0.0860002	+	0.0291931i	0.278108	+	0.960550i	$0.410293\pi$
$602$	16.4042	+	24.5505i	0.668583	+	1.00061i
$603$	−6.24103	+	2.15865i	−0.254155	+	0.0879072i
$604$	15.6141	−	6.46757i	0.635328	−	0.263162i
$605$	28.8179	+	14.2114i	1.17161	+	0.577776i
$606$	−17.8748	−	9.48827i	−0.726113	−	0.385435i
$607$	3.93237	+	7.97406i	0.159610	+	0.323657i	0.961957	−	0.273201i	$-0.0880823\pi$
$607$	3.93237	+	7.97406i	0.159610	+	0.323657i	−0.802347	+	0.596858i	$0.796416\pi$
$608$	11.9191	−	3.19371i	0.483382	−	0.129522i
$609$	0.348985	−	3.65090i	0.0141416	−	0.147942i
$610$	4.29942	−	0.566029i	0.174078	−	0.0229179i
$611$	24.2837			0.982413
$612$	−0.782828	+	16.6414i	−0.0316440	+	0.672688i
$613$	45.0558			1.81979			0.909893	−	0.414842i	$-0.136163\pi$
$613$	45.0558			1.81979			0.909893	+	0.414842i	$0.136163\pi$
$614$	−12.8430	+	1.69081i	−0.518301	+	0.0682356i
$615$	14.8618	+	10.5853i	0.599286	+	0.426840i
$616$	−10.8726	+	2.91331i	−0.438070	+	0.117380i
$617$	−17.9929	−	36.4860i	−0.724367	−	1.46887i	−0.876951	−	0.480580i	$-0.840426\pi$
$617$	−17.9929	−	36.4860i	−0.724367	−	1.46887i	0.152584	−	0.988291i	$-0.451241\pi$
$618$	−0.0968785	−	2.72011i	−0.00389703	−	0.109419i
$619$	−10.2190	−	5.03947i	−0.410737	−	0.202553i	0.225169	−	0.974320i	$-0.427707\pi$
$619$	−10.2190	−	5.03947i	−0.410737	−	0.202553i	−0.635906	+	0.771767i	$0.719373\pi$
$620$	5.14224	−	2.12999i	0.206517	−	0.0855423i
$621$	−11.0316	−	17.4036i	−0.442682	−	0.698382i
$622$	−6.11422	−	9.15058i	−0.245158	−	0.366905i
$623$	22.0805	−	7.49534i	0.884638	−	0.300294i
$624$	3.71841	+	1.38732i	0.148855	+	0.0555370i
$625$	6.84190	+	25.5343i	0.273676	+	1.02137i
$626$	1.65554	+	0.561982i	0.0661689	+	0.0224613i
$627$	−2.83137	+	1.07496i	−0.113074	+	0.0429297i
$628$	−11.2825	+	6.51394i	−0.450220	+	0.259935i
$629$	0.158197	+	0.230374i	0.00630771	+	0.00918560i
$630$	−31.7932	−	20.9801i	−1.26667	−	0.835867i
$631$	4.28340	+	1.77424i	0.170520	+	0.0706315i	0.466310	−	0.884621i	$-0.345583\pi$
$631$	4.28340	+	1.77424i	0.170520	+	0.0706315i	−0.295791	+	0.955253i	$0.595583\pi$
$632$	−23.6342	−	26.9497i	−0.940120	−	1.07200i
$633$	−6.62995	−	12.3184i	−0.263517	−	0.489613i
$634$	6.61323	−	3.26128i	0.262645	−	0.129522i
$635$	36.8789	−	42.0523i	1.46349	−	1.66879i
$636$	4.82882	+	15.7552i	0.191475	+	0.624736i
$637$	−50.7181	+	66.0971i	−2.00953	+	2.61886i
$638$	−0.107031	−	0.258396i	−0.00423740	−	0.0102300i
$639$	−3.24282	+	5.69209i	−0.128284	+	0.225176i
$640$	−26.4439	−	5.26001i	−1.04529	−	0.207920i
$641$	0.425807	−	6.49656i	0.0168184	−	0.256599i	−0.981167	−	0.193160i	$-0.938126\pi$
$641$	0.425807	−	6.49656i	0.0168184	−	0.256599i	0.997986	−	0.0634391i	$-0.0202068\pi$
$642$	−0.165453	+	5.54129i	−0.00652989	+	0.218697i
$643$	−8.29150	+	24.4260i	−0.326985	+	0.963266i	0.651803	+	0.758388i	$0.274013\pi$
$643$	−8.29150	+	24.4260i	−0.326985	+	0.963266i	−0.978788	+	0.204877i	$0.934320\pi$
$644$	21.3814	−	16.4065i	0.842546	−	0.646508i
$645$	−8.97587	−	38.0009i	−0.353424	−	1.49628i
$646$	6.99211	−	1.01097i	0.275101	−	0.0397760i
$647$		−	32.6053i		−	1.28185i	−0.767604	−	0.640924i	$-0.778551\pi$
$647$		−	32.6053i		−	1.28185i	0.767604	−	0.640924i	$-0.221449\pi$
$648$	−12.4134	−	20.9407i	−0.487645	−	0.822627i
$649$	0.548869	+	2.75935i	0.0215450	+	0.108314i
$650$	16.5367	+	4.43099i	0.648621	+	0.173798i
$651$	−4.05492	+	10.8684i	−0.158925	+	0.425965i
$652$	0.269125	+	0.236016i	0.0105397	+	0.00924311i
$653$	−39.1805	+	2.56802i	−1.53325	+	0.100495i	−0.808492	−	0.588508i	$-0.799716\pi$
$653$	−39.1805	+	2.56802i	−1.53325	+	0.100495i	−0.724759	+	0.689002i	$0.758049\pi$
$654$	8.78548	−	19.5392i	0.343539	−	0.764045i
$655$	−24.7261	−	18.9730i	−0.966127	−	0.741336i
$656$	−1.42844	+	0.954456i	−0.0557714	+	0.0372652i
$657$	16.6707	−	4.56983i	0.650387	−	0.178286i
$658$	12.1919	−	18.2465i	0.475291	−	0.711323i
$659$	−2.37308	+	8.85644i	−0.0924420	+	0.344998i	−0.996619	−	0.0821594i	$-0.973818\pi$
$659$	−2.37308	+	8.85644i	−0.0924420	+	0.344998i	0.904177	+	0.427157i	$0.140485\pi$
$660$	5.96305	+	0.570000i	0.232112	+	0.0221872i
$661$	9.51560	+	12.4010i	0.370114	+	0.482342i	0.940865	−	0.338781i	$-0.110015\pi$
$661$	9.51560	+	12.4010i	0.370114	+	0.482342i	−0.570751	+	0.821123i	$0.693348\pi$
$662$	−0.548618	+	0.950234i	−0.0213226	+	0.0369319i
$663$	28.6545	+	14.7473i	1.11285	+	0.572738i
$664$	−4.97337	−	8.61412i	−0.193004	−	0.334293i
$665$	12.7474	−	30.7749i	0.494322	−	1.19340i
$666$	−0.152181	−	0.0620125i	−0.00589690	−	0.00240294i
$667$	1.17666	+	1.17666i	0.0455603	+	0.0455603i
$668$	2.40696	+	0.157761i	0.0931283	+	0.00610395i
$669$	16.7266	+	26.7268i	0.646687	+	1.03332i
$670$	−0.362270	−	5.52717i	−0.0139957	−	0.213533i
$671$	0.185516	−	1.40913i	0.00716175	−	0.0543989i
$672$	41.2615	−	29.7475i	1.59170	−	1.14753i
$673$	−14.2403	+	28.8764i	−0.548923	+	1.11311i	0.428838	+	0.903381i	$0.358923\pi$
$673$	−14.2403	+	28.8764i	−0.548923	+	1.11311i	−0.977761	+	0.209724i	$0.932744\pi$
$674$	−3.78154	+	19.0111i	−0.145660	+	0.732281i
$675$	14.3785	+	19.7039i	0.553428	+	0.758403i
$676$	7.01329	−	7.01329i	0.269742	−	0.269742i
$677$	−13.0734	+	11.4650i	−0.502450	+	0.440637i	−0.872672	−	0.488306i	$-0.837615\pi$
$677$	−13.0734	+	11.4650i	−0.502450	+	0.440637i	0.370222	+	0.928943i	$0.379282\pi$
$678$	0.581216	+	0.0942430i	0.0223215	+	0.00361938i
$679$	−76.1108	−	43.9426i	−2.92086	−	1.68636i
$680$	−33.0197	−	10.7433i	−1.26625	−	0.411985i
$681$	27.7022	+	29.4074i	1.06155	+	1.12689i
$682$	0.115467	+	0.877057i	0.00442145	+	0.0335842i
$683$	39.2414	−	7.80559i	1.50153	−	0.298673i	0.625230	−	0.780441i	$-0.285005\pi$
$683$	39.2414	−	7.80559i	1.50153	−	0.298673i	0.876299	+	0.481768i	$0.160005\pi$
$684$	6.40827	−	5.68544i	0.245026	−	0.217388i
$685$	0.538762	+	0.359989i	0.0205850	+	0.0137545i
$686$	15.0252	+	44.2627i	0.573664	+	1.68996i
$687$	24.3883	−	7.47475i	0.930470	−	0.285179i
$688$	3.64500	+	0.479873i	0.138964	+	0.0182950i
$689$	31.6036	+	4.16070i	1.20400	+	0.158510i
$690$	16.5243	−	5.06453i	0.629069	−	0.192803i
$691$	−6.50427	−	19.1610i	−0.247434	−	0.728917i	−0.997700	−	0.0677814i	$-0.978408\pi$
$691$	−6.50427	−	19.1610i	−0.247434	−	0.728917i	0.750266	−	0.661136i	$-0.229925\pi$
$692$	−19.7739	−	13.2125i	−0.751692	−	0.502265i
$693$	−9.33885	+	8.28545i	−0.354753	+	0.314738i
$694$	3.28104	−	0.652639i	0.124547	−	0.0247738i
$695$	1.72129	+	13.0745i	0.0652922	+	0.495944i
$696$	1.34801	+	1.43099i	0.0510962	+	0.0542414i
$697$	−12.4321	+	6.32826i	−0.470901	+	0.239700i
$698$	−1.18928	−	0.686634i	−0.0450151	−	0.0259895i
$699$	41.9451	+	6.80132i	1.58651	+	0.257250i
$700$	−23.9865	+	21.0356i	−0.906606	+	0.795072i
$701$	14.1508	−	14.1508i	0.534469	−	0.534469i	−0.387430	−	0.921899i	$-0.626637\pi$
$701$	14.1508	−	14.1508i	0.534469	−	0.534469i	0.921899	+	0.387430i	$0.126637\pi$
$702$	−18.8423	+	2.02008i	−0.711157	+	0.0762428i
$703$	0.0280353	−	0.140943i	0.00105737	−	0.00531577i
$704$	1.34524	−	2.72789i	0.0507008	−	0.102811i
$705$	−23.5403	+	16.9714i	−0.886581	+	0.639181i
$706$	−2.00308	+	15.2149i	−0.0753871	+	0.572622i
$707$	−4.77122	−	72.7948i	−0.179440	−	2.73773i
$708$	−4.22190	−	6.74602i	−0.158669	−	0.253531i
$709$	17.7197	+	1.16141i	0.665476	+	0.0436176i	0.394398	−	0.918940i	$-0.370953\pi$
$709$	17.7197	+	1.16141i	0.665476	+	0.0436176i	0.271078	+	0.962557i	$0.412620\pi$
$710$	−3.88537	−	3.88537i	−0.145815	−	0.145815i
$711$	−36.8172	−	15.0027i	−1.38075	−	0.562646i
$712$	−4.78325	+	11.5478i	−0.179260	+	0.432772i
$713$	−2.63162	−	4.55810i	−0.0985550	−	0.170702i
$714$	25.4673	−	14.1266i	0.953091	−	0.528676i
$715$	5.79377	−	10.0351i	0.216675	−	0.375292i
$716$	19.0367	+	24.8091i	0.711433	+	0.927158i
$717$	−46.3652	−	4.43199i	−1.73154	−	0.165516i
$718$	−5.26666	+	19.6554i	−0.196550	+	0.733535i
$719$	−27.9359	+	41.8091i	−1.04183	+	1.55922i	−0.231862	+	0.972749i	$0.574482\pi$
$719$	−27.9359	+	41.8091i	−1.04183	+	1.55922i	−0.809973	+	0.586467i	$0.800518\pi$
$720$	−4.57415	+	1.25388i	−0.170469	+	0.0467294i
$721$	8.15820	−	5.45114i	0.303827	−	0.203011i
$722$	9.29995	+	7.13610i	0.346108	+	0.265578i
$723$	−6.57520	+	14.6235i	−0.244534	+	0.543854i
$724$	13.4283	−	0.880137i	0.499059	−	0.0327100i
$725$	−1.48102	−	1.29882i	−0.0550038	−	0.0482371i
$726$	5.04957	−	13.5343i	0.187407	−	0.502306i
$727$	−5.23752	−	1.40339i	−0.194249	−	0.0520488i	0.160383	−	0.987055i	$-0.448727\pi$
$727$	−5.23752	−	1.40339i	−0.194249	−	0.0520488i	−0.354632	+	0.935006i	$0.615394\pi$
$728$	−12.0159	−	60.4079i	−0.445338	−	2.23887i
$729$	−22.7051	−	14.6108i	−0.840931	−	0.541142i
$730$			14.4986i			0.536618i
$731$	28.9316	+	7.35994i	1.07007	+	0.272217i
$732$	0.924184	+	3.91270i	0.0341588	+	0.144617i
$733$	28.5784	−	21.9290i	1.05557	−	0.809966i	0.0732741	−	0.997312i	$-0.476655\pi$
$733$	28.5784	−	21.9290i	1.05557	−	0.809966i	0.982294	+	0.187346i	$0.0599885\pi$
$734$	−2.66891	+	7.86237i	−0.0985115	+	0.290205i
$735$	2.97148	−	99.5199i	0.109605	−	3.67085i
$736$	−1.50946	+	23.0299i	−0.0556394	+	0.848893i
$737$	−1.78053	−	0.354169i	−0.0655866	−	0.0130460i
$738$	4.06060	−	7.12753i	0.149473	−	0.262368i
$739$	−0.924601	−	2.23219i	−0.0340120	−	0.0821123i	0.905961	−	0.423362i	$-0.139150\pi$
$739$	−0.924601	−	2.23219i	−0.0340120	−	0.0821123i	−0.939973	+	0.341249i	$0.889150\pi$
$740$	−0.173031	+	0.225499i	−0.00636076	+	0.00828950i
$741$	−4.85608	−	15.8442i	−0.178393	−	0.582051i
$742$	18.9933	−	21.6577i	0.697266	−	0.795080i
$743$	32.1039	−	15.8319i	1.17778	−	0.580815i	0.255298	−	0.966863i	$-0.417827\pi$
$743$	32.1039	−	15.8319i	1.17778	−	0.580815i	0.922479	+	0.386047i	$0.126160\pi$
$744$	−2.94694	−	5.47540i	−0.108040	−	0.200738i
$745$	−48.3807	−	55.1676i	−1.77253	−	2.02118i
$746$	−4.74561	−	1.96569i	−0.173749	−	0.0719692i
$747$	−9.20803	−	6.07630i	−0.336904	−	0.222320i
$748$	−2.49588	+	3.83998i	−0.0912585	+	0.140403i
$749$	−17.3070	+	9.99217i	−0.632382	+	0.365106i
$750$	1.24561	−	0.472907i	0.0454832	−	0.0172681i
$751$	−1.32298	−	0.449091i	−0.0482762	−	0.0163875i	0.297197	−	0.954816i	$-0.403948\pi$
$751$	−1.32298	−	0.449091i	−0.0482762	−	0.0163875i	−0.345473	+	0.938429i	$0.612282\pi$
$752$	−0.707203	−	2.63932i	−0.0257890	−	0.0962460i
$753$	27.5841	+	10.2914i	1.00522	+	0.375041i
$754$	1.44916	−	0.491925i	0.0527754	−	0.0179149i
$755$	21.7057	+	32.4850i	0.789953	+	1.18225i
$756$	16.3779	−	31.2871i	0.595657	−	1.13790i
$757$	−34.0649	+	14.1101i	−1.23811	+	0.512842i	−0.903123	−	0.429382i	$-0.858732\pi$
$757$	−34.0649	+	14.1101i	−1.23811	+	0.512842i	−0.334986	+	0.942223i	$0.608732\pi$
$758$	−5.89096	−	2.90510i	−0.213969	−	0.105518i
$759$	−0.201616	−	5.66089i	−0.00731820	−	0.205477i
$760$	7.89729	+	16.0141i	0.286465	+	0.580893i
$761$	−24.0278	+	6.43824i	−0.871008	+	0.233386i	−0.666524	−	0.745484i	$-0.732218\pi$
$761$	−24.0278	+	6.43824i	−0.871008	+	0.233386i	−0.204484	+	0.978870i	$0.565552\pi$
$762$	−20.4819	−	14.5881i	−0.741980	−	0.528473i
$763$	76.5676	−	10.0803i	2.77193	−	0.364932i
$764$	10.3294			0.373704
$765$	−38.0840	+	5.73025i	−1.37693	+	0.207178i
$766$	−13.3687			−0.483032
$767$	−15.2627	+	2.00937i	−0.551105	+	0.0725543i
$768$	−2.36909	+	24.7842i	−0.0854871	+	0.894323i
$769$	−39.1986	+	10.5032i	−1.41354	+	0.378757i	−0.883187	−	0.469021i	$-0.844607\pi$
$769$	−39.1986	+	10.5032i	−1.41354	+	0.378757i	−0.530352	+	0.847778i	$0.677940\pi$
$770$	−4.63144	−	9.39163i	−0.166905	−	0.338451i
$771$	−25.8841	−	13.7398i	−0.932192	−	0.494826i
$772$	−13.9589	−	6.88375i	−0.502391	−	0.247752i
$773$	40.1788	−	16.6426i	1.44513	−	0.598593i	0.484096	−	0.875015i	$-0.339149\pi$
$773$	40.1788	−	16.6426i	1.44513	−	0.598593i	0.961036	+	0.276422i	$0.0891487\pi$
$774$	−16.5901	+	5.73821i	−0.596320	+	0.206256i
$775$	3.46150	+	5.18051i	0.124341	+	0.186089i
$776$	44.6093	−	15.1428i	1.60138	−	0.543595i
$777$	−0.0981774	−	0.584194i	−0.00352209	−	0.0209578i
$778$	0.500690	+	1.86860i	0.0179506	+	0.0669925i
$779$	6.79273	+	2.30582i	0.243375	+	0.0826146i
$780$	−5.24626	+	32.3548i	−0.187846	+	1.15849i
$781$	−1.55962	+	0.900448i	−0.0558077	+	0.0322206i
$782$	−2.41317	+	12.9915i	−0.0862950	+	0.464574i
$783$	2.04725	+	0.750434i	0.0731629	+	0.0268183i
$784$	8.66093	+	3.58748i	0.309319	+	0.128124i
$785$	−19.8574	−	22.6430i	−0.708740	−	0.808163i
$786$	−7.36492	+	11.9201i	−0.262698	+	0.425174i
$787$	−13.4590	+	6.63725i	−0.479762	+	0.236592i	−0.666056	−	0.745902i	$-0.732019\pi$
$787$	−13.4590	+	6.63725i	−0.479762	+	0.236592i	0.186294	+	0.982494i	$0.440352\pi$
$788$	1.69896	−	1.93730i	0.0605231	−	0.0690133i
$789$	−36.7269	−	8.45224i	−1.30751	−	0.300908i
$790$	20.3000	−	26.4555i	0.722241	−	0.941243i
$791$	0.812266	+	1.96098i	0.0288809	+	0.0697246i
$792$	−0.0384880	−	6.69200i	−0.00136761	−	0.237790i
$793$	7.62758	+	1.51722i	0.270863	+	0.0538780i
$794$	0.450935	−	6.87994i	0.0160031	−	0.244160i
$795$	−33.5441	+	18.0539i	−1.18969	+	0.640305i
$796$	5.95050	−	17.5296i	0.210910	−	0.621320i
$797$	−7.94728	+	6.09816i	−0.281507	+	0.216008i	−0.739858	−	0.672764i	$-0.765107\pi$
$797$	−7.94728	+	6.09816i	−0.281507	+	0.216008i	0.458350	+	0.888772i	$0.348440\pi$
$798$	−14.3432	−	4.30597i	−0.507745	−	0.152430i
$799$	−3.17500	−	21.9591i	−0.112323	−	0.776858i
$800$		−	27.3209i		−	0.965940i
$801$	0.986245	+	13.8281i	0.0348472	+	0.488592i
$802$	1.35592	+	6.81666i	0.0478791	+	0.240705i
$803$	4.58999	+	1.22988i	0.161977	+	0.0434017i
$804$	5.06418	−	0.851067i	0.178600	−	0.0300148i
$805$	46.8414	+	41.0788i	1.65094	+	1.44784i
$806$	−4.83012	+	0.316583i	−0.170134	+	0.0111512i
$807$	1.20661	+	1.67364i	0.0424747	+	0.0589148i
$808$	31.0234	+	23.8051i	1.09140	+	0.837460i
$809$	−43.7755	+	29.2499i	−1.53907	+	1.02837i	−0.559125	+	0.829084i	$0.688863\pi$
$809$	−43.7755	+	29.2499i	−1.53907	+	1.02837i	−0.979941	+	0.199287i	$0.936137\pi$
$810$	16.8537	−	15.1268i	0.592180	−	0.531501i
$811$	−25.6922	+	38.4511i	−0.902175	+	1.35020i	0.0342802	+	0.999412i	$0.489086\pi$
$811$	−25.6922	+	38.4511i	−0.902175	+	1.35020i	−0.936455	+	0.350788i	$0.885914\pi$
$812$	−0.738132	+	2.75475i	−0.0259034	+	0.0966727i
$813$	13.4078	+	29.3667i	0.470232	+	1.02993i
$814$	−0.0275009	−	0.0358399i	−0.000963906	−	0.00125619i
$815$	−0.413745	+	0.716628i	−0.0144929	+	0.0251024i
$816$	0.768346	−	3.54385i	0.0268975	−	0.124059i
$817$	−7.67553	−	13.2944i	−0.268533	−	0.465113i
$818$	−5.42812	+	13.1046i	−0.189790	+	0.458193i
$819$	−41.8971	−	53.9560i	−1.46400	−	1.88538i
$820$	−10.0327	−	10.0327i	−0.350358	−	0.350358i
$821$	−40.5886	−	2.66032i	−1.41655	−	0.0928457i	−0.662205	−	0.749323i	$-0.730379\pi$
$821$	−40.5886	−	2.66032i	−1.41655	−	0.0928457i	−0.754346	+	0.656477i	$0.772046\pi$
$822$	0.136583	−	0.257306i	0.00476389	−	0.00897458i
$823$	0.457694	+	6.98305i	0.0159542	+	0.243414i	0.998386	+	0.0567922i	$0.0180872\pi$
$823$	0.457694	+	6.98305i	0.0159542	+	0.243414i	−0.982432	+	0.186622i	$0.940246\pi$
$824$	−0.686495	+	5.21445i	−0.0239152	+	0.181654i
$825$	0.676443	+	6.67132i	0.0235507	+	0.232265i
$826$	−6.15302	+	12.4771i	−0.214091	+	0.434133i
$827$	8.31435	−	41.7991i	0.289118	−	1.45350i	−0.514058	−	0.857755i	$-0.671859\pi$
$827$	8.31435	−	41.7991i	0.289118	−	1.45350i	0.803177	−	0.595741i	$-0.203141\pi$
$828$	6.21676	+	14.7678i	0.216047	+	0.513216i
$829$	−13.5908	+	13.5908i	−0.472029	+	0.472029i	−0.902571	−	0.430542i	$-0.858322\pi$
$829$	−13.5908	+	13.5908i	−0.472029	+	0.472029i	0.430542	+	0.902571i	$0.358322\pi$
$830$	6.95706	−	6.10118i	0.241483	−	0.211775i
$831$	6.73499	+	17.7395i	0.233634	+	0.615378i
$832$	14.4131	+	8.32138i	0.499683	+	0.288492i
$833$	66.4012	+	37.2211i	2.30066	+	1.28964i
$834$	5.76994	−	1.36287i	0.199797	−	0.0471923i
$835$	0.727835	+	5.52846i	0.0251878	+	0.191320i
$836$	2.30979	−	0.459447i	0.0798859	−	0.0158903i
$837$	−5.64035	−	3.96863i	−0.194959	−	0.137176i
$838$	−1.96555	−	1.31334i	−0.0678988	−	0.0453685i
$839$	10.0456	+	29.5934i	0.346813	+	1.02168i	0.970727	+	0.240185i	$0.0772082\pi$
$839$	10.0456	+	29.5934i	0.346813	+	1.02168i	−0.623914	+	0.781493i	$0.714458\pi$
$840$	53.8661	+	50.1611i	1.85856	+	1.73072i
$841$	28.5773	+	3.76228i	0.985425	+	0.129734i
$842$	−11.2234	−	1.47759i	−0.386783	−	0.0509210i
$843$	−10.4749	+	45.5157i	−0.360773	+	1.56764i
$844$	3.49669	+	10.3009i	0.120361	+	0.354572i
$845$	19.0642	+	12.7383i	0.655828	+	0.438210i
$846$	8.65867	+	9.75952i	0.297691	+	0.335539i
$847$	51.0735	−	10.1592i	1.75491	−	0.349073i
$848$	−0.468165	−	3.55607i	−0.0160769	−	0.122116i
$849$	−4.57373	+	15.2352i	−0.156970	+	0.522869i
$850$	1.84472	−	15.5330i	0.0632734	−	0.532778i
$851$	0.232769	+	0.134389i	0.00797921	+	0.00460680i
$852$	3.22035	−	3.94710i	0.110328	−	0.135226i
$853$	−13.9130	+	12.2014i	−0.476373	+	0.417768i	−0.863570	−	0.504229i	$-0.831777\pi$
$853$	−13.9130	+	12.2014i	−0.476373	+	0.417768i	0.387197	+	0.921997i	$0.373443\pi$
$854$	4.96954	−	4.96954i	0.170054	−	0.170054i
$855$	15.7807	+	11.9654i	0.539688	+	0.409207i
$856$	2.08986	−	10.5064i	0.0714300	−	0.359103i
$857$	−1.95578	+	3.96593i	−0.0668082	+	0.135474i	−0.927715	−	0.373289i	$-0.878230\pi$
$857$	−1.95578	+	3.96593i	−0.0668082	+	0.135474i	0.860907	+	0.508762i	$0.169897\pi$
$858$	−4.75130	−	2.13634i	−0.162207	−	0.0729335i
$859$	3.86989	−	29.3947i	0.132039	−	1.00294i	−0.789254	−	0.614067i	$-0.789533\pi$
$859$	3.86989	−	29.3947i	0.132039	−	1.00294i	0.921293	−	0.388869i	$-0.127134\pi$
$860$	1.98584	+	30.2981i	0.0677166	+	1.03316i
$861$	29.5519	−	1.05251i	1.00713	−	0.0358695i
$862$	−17.9106	−	1.17392i	−0.610038	−	0.0399840i
$863$	−5.63591	−	5.63591i	−0.191849	−	0.191849i	0.604646	−	0.796494i	$-0.293315\pi$
$863$	−5.63591	−	5.63591i	−0.191849	−	0.191849i	−0.796494	+	0.604646i	$0.793315\pi$
$864$	10.8964	+	28.2105i	0.370704	+	0.959739i
$865$	21.0388	−	50.7922i	0.715341	−	1.72699i
$866$	14.2979	+	24.7646i	0.485861	+	0.841536i
$867$	9.58914	−	27.8397i	0.325664	−	0.945485i
$868$	4.51022	−	7.81192i	0.153087	−	0.265154i
$869$	−6.65330	−	8.67075i	−0.225698	−	0.294135i
$870$	−1.06101	+	1.48966i	−0.0359715	+	0.0505043i
$871$	2.57099	−	9.59508i	0.0871148	−	0.325117i
$872$	−22.9989	+	34.4203i	−0.778841	+	1.16562i
$873$	36.7334	−	37.1584i	1.24324	−	1.25762i
$874$	5.64964	−	3.77497i	0.191102	−	0.127690i
$875$	3.81043	+	2.92384i	0.128816	+	0.0988439i
$876$	−13.3730	+	1.35597i	−0.451833	+	0.0458139i
$877$	−31.7829	+	2.08316i	−1.07323	+	0.0703433i	−0.591756	−	0.806117i	$-0.701565\pi$
$877$	−31.7829	+	2.08316i	−1.07323	+	0.0703433i	−0.481474	+	0.876460i	$0.659899\pi$
$878$	−8.97806	−	7.87354i	−0.302995	−	0.265719i
$879$	−4.85796	−	5.88485i	−0.163855	−	0.198491i
$880$	−1.25941	−	0.337459i	−0.0424548	−	0.0113757i
$881$	2.24207	+	11.2716i	0.0755371	+	0.379751i	0.999999	−	0.00152420i	$-0.000485169\pi$
$881$	2.24207	+	11.2716i	0.0755371	+	0.379751i	−0.924462	+	0.381275i	$0.875485\pi$
$882$	−44.6484	+	3.18440i	−1.50339	+	0.107224i
$883$			20.4281i			0.687460i	0.939068	+	0.343730i	$0.111691\pi$
$883$			20.4281i			0.687460i	−0.939068	+	0.343730i	$0.888309\pi$
$884$	−20.0734	−	15.0019i	−0.675141	−	0.504570i
$885$	13.3912	−	12.6147i	0.450140	−	0.424039i
$886$	12.5842	−	9.65623i	0.422776	−	0.324407i
$887$	−6.81537	+	20.0774i	−0.228838	+	0.674134i	0.770489	+	0.637453i	$0.220012\pi$
$887$	−6.81537	+	20.0774i	−0.228838	+	0.674134i	−0.999327	+	0.0366814i	$0.988321\pi$
$888$	0.270136	+	0.166906i	0.00906516	+	0.00560099i
$889$	5.92861	−	90.4532i	0.198839	−	3.03370i
$890$	−11.4045	−	2.26850i	−0.382281	−	0.0760404i
$891$	−3.35919	−	6.61874i	−0.112537	−	0.221736i
$892$	−9.38249	−	22.6513i	−0.314149	−	0.758422i
$893$	−6.94551	+	9.05157i	−0.232423	+	0.302899i
$894$	−22.4814	+	24.1419i	−0.751890	+	0.807426i
$895$	−47.6641	+	54.3505i	−1.59324	+	1.81674i
$896$	−39.1897	+	19.3262i	−1.30924	+	0.645644i
$897$	30.9811	+	0.925038i	1.03443	+	0.0308861i
$898$	10.3996	+	11.8585i	0.347040	+	0.395723i
$899$	0.514561	+	0.213138i	0.0171616	+	0.00710856i
$900$	−8.48691	−	16.9631i	−0.282897	−	0.565437i
$901$	−0.369645	−	29.1223i	−0.0123147	−	0.970206i
$902$	1.95293	−	1.12752i	0.0650254	−	0.0375425i
$903$	−49.0321	−	40.0042i	−1.63169	−	1.33126i
$904$	−1.07738	−	0.365721i	−0.0358331	−	0.0121637i
$905$	8.05161	+	30.0490i	0.267644	+	0.998863i
$906$	13.5456	−	11.1819i	0.450022	−	0.371494i
$907$	36.8376	−	12.5047i	1.22317	−	0.415212i	0.366183	−	0.930543i	$-0.380664\pi$
$907$	36.8376	−	12.5047i	1.22317	−	0.415212i	0.856991	+	0.515331i	$0.172331\pi$
$908$	−17.4538	−	26.1214i	−0.579223	−	0.866869i
$909$	42.5860	+	8.21656i	1.41249	+	0.272526i
$910$	52.9365	−	21.9270i	1.75483	−	0.726874i
$911$	−16.8905	−	8.32947i	−0.559607	−	0.275968i	0.140410	−	0.990093i	$-0.455158\pi$
$911$	−16.8905	−	8.32947i	−0.559607	−	0.275968i	−0.700017	+	0.714126i	$0.746824\pi$
$912$	−1.58063	+	0.989216i	−0.0523400	+	0.0327562i
$913$	−1.34137	−	2.72002i	−0.0443928	−	0.0900197i
$914$	12.7760	−	3.42333i	0.422594	−	0.113234i
$915$	−8.45445	+	3.86000i	−0.279495	+	0.127608i
$916$	−19.6656	+	2.58903i	−0.649771	+	0.0855440i
$917$	−50.5101			−1.66799
$918$	4.29026	+	16.7745i	0.141600	+	0.553641i
$919$	−1.78397			−0.0588476			−0.0294238	−	0.999567i	$-0.509367\pi$
$919$	−1.78397			−0.0588476			−0.0294238	+	0.999567i	$0.509367\pi$
$920$	−33.1104	+	4.35907i	−1.09162	+	0.143714i
$921$	25.2547	−	11.5304i	0.832170	−	0.379939i
$922$	−20.6078	+	5.52184i	−0.678681	+	0.181852i
$923$	−4.35837	−	8.83791i	−0.143458	−	0.290903i
$924$	8.22936	−	5.15022i	0.270726	−	0.169430i
$925$	−0.285363	−	0.140725i	−0.00938267	−	0.00462702i
$926$	−22.8271	+	9.45527i	−0.750143	+	0.310720i
$927$	1.90682	+	5.51294i	0.0626282	+	0.181069i
$928$	−1.35684	−	2.03066i	−0.0445406	−	0.0666597i
$929$	−21.4783	+	7.29092i	−0.704682	+	0.239207i	−0.650700	−	0.759335i	$-0.725525\pi$
$929$	−21.4783	+	7.29092i	−0.704682	+	0.239207i	−0.0539815	+	0.998542i	$0.517191\pi$
$930$	4.46102	−	3.68258i	0.146282	−	0.120757i
$931$	−10.1311	−	37.8096i	−0.332032	−	1.23916i
$932$	−31.2894	−	10.6213i	−1.02492	−	0.347913i
$933$	18.2754	+	14.9105i	0.598311	+	0.488149i
$934$	24.4723	−	14.1291i	0.800759	−	0.462318i
$935$	−9.83200	−	3.92711i	−0.321541	−	0.128430i
$936$	36.5526	+	2.18473i	1.19476	+	0.0714103i
$937$	−40.8313	−	16.9129i	−1.33390	−	0.552520i	−0.402136	−	0.915580i	$-0.631732\pi$
$937$	−40.8313	−	16.9129i	−1.33390	−	0.552520i	−0.931766	+	0.363060i	$0.881732\pi$
$938$	−5.91884	−	6.74915i	−0.193257	−	0.220367i
$939$	−3.74531	−	0.111828i	−0.122224	−	0.00364937i
$940$	20.2393	−	9.98092i	0.660133	−	0.325542i
$941$	11.3524	−	12.9449i	0.370078	−	0.421993i	−0.536587	−	0.843845i	$-0.680287\pi$
$941$	11.3524	−	12.9449i	0.370078	−	0.421993i	0.906665	+	0.421852i	$0.138620\pi$
$942$	−9.22727	+	9.90881i	−0.300641	+	0.322846i
$943$	−8.16766	+	10.6443i	−0.265976	+	0.346626i
$944$	0.662882	+	1.60034i	0.0215750	+	0.0520866i
$945$	78.3235	+	23.0232i	2.54786	+	0.748945i
$946$	−4.73306	−	0.941464i	−0.153885	−	0.0306096i
$947$	3.72847	−	56.8854i	0.121159	−	1.84853i	−0.315531	−	0.948915i	$-0.602183\pi$
$947$	3.72847	−	56.8854i	0.121159	−	1.84853i	0.436690	−	0.899612i	$-0.356151\pi$
$948$	26.3001	+	16.2498i	0.854188	+	0.527768i
$949$	−8.35790	+	24.6216i	−0.271309	+	0.799251i
$950$	−6.38136	+	4.89659i	−0.207039	+	0.158866i
$951$	−11.5030	+	10.8360i	−0.373010	+	0.351381i
$952$	−53.0543	+	18.7638i	−1.71950	+	0.608137i
$953$		−	26.5831i		−	0.861112i	−0.902564	−	0.430556i	$-0.858318\pi$
$953$		−	26.5831i		−	0.861112i	0.902564	−	0.430556i	$-0.141682\pi$
$954$	9.59653	+	14.1849i	0.310699	+	0.459254i
$955$	4.65849	+	23.4198i	0.150745	+	0.757846i
$956$	34.9844	+	9.37403i	1.13148	+	0.303178i
$957$	0.381596	+	0.462259i	0.0123353	+	0.0149427i
$958$	5.64092	+	4.94695i	0.182250	+	0.159829i
$959$	1.04788	−	0.0686814i	0.0338377	−	0.00221784i
$960$	−19.7875	+	2.00637i	−0.638640	+	0.0647554i
$961$	23.1964	+	17.7992i	0.748270	+	0.574168i
$962$	0.205530	−	0.137331i	0.00662656	−	0.00442773i
$963$	−3.14105	−	11.4585i	−0.101219	−	0.369247i
$964$	6.92685	−	10.3668i	0.223099	−	0.333891i
$965$	9.31215	−	34.7534i	0.299769	−	1.11875i
$966$	16.2495	−	22.8144i	0.522819	−	0.734043i
$967$	3.37951	+	4.40426i	0.108678	+	0.141631i	0.844525	−	0.535516i	$-0.179883\pi$
$967$	3.37951	+	4.40426i	0.108678	+	0.141631i	−0.735848	+	0.677147i	$0.763216\pi$
$968$	−13.9567	+	24.1738i	−0.448586	+	0.776974i
$969$	−13.6926	+	6.46280i	−0.439869	+	0.207615i
$970$	21.9128	+	37.9540i	0.703577	+	1.21863i
$971$	−3.10599	+	7.49852i	−0.0996759	+	0.240639i	−0.965849	−	0.259105i	$-0.916572\pi$
$971$	−3.10599	+	7.49852i	−0.0996759	+	0.240639i	0.866173	+	0.499744i	$0.166572\pi$
$972$	15.5286	+	14.1306i	0.498082	+	0.453238i
$973$	15.1123	+	15.1123i	0.484479	+	0.484479i
$974$	3.49720	+	0.229219i	0.112058	+	0.00734465i
$975$	−36.6680	+	1.30595i	−1.17432	+	0.0418240i
$976$	−0.0572327	−	0.873202i	−0.00183197	−	0.0279505i
$977$	−1.75362	+	13.3200i	−0.0561031	+	0.426146i	0.940227	+	0.340549i	$0.110613\pi$
$977$	−1.75362	+	13.3200i	−0.0561031	+	0.426146i	−0.996330	+	0.0855966i	$0.972720\pi$
$978$	0.339301	+	0.152561i	0.0108496	+	0.00487835i
$979$	−1.68559	+	3.41803i	−0.0538716	+	0.109241i
$980$	−15.1043	+	75.9347i	−0.482491	+	2.42564i
$981$	−5.73113	+	45.5553i	−0.182981	+	1.45447i
$982$	10.4629	−	10.4629i	0.333884	−	0.333884i
$983$	46.0381	−	40.3743i	1.46839	−	1.28774i	0.592181	−	0.805805i	$-0.298267\pi$
$983$	46.0381	−	40.3743i	1.46839	−	1.28774i	0.876206	−	0.481936i	$-0.160066\pi$
$984$	−10.0204	+	12.2817i	−0.319439	+	0.391528i
$985$	5.15865	+	2.97835i	0.164368	+	0.0948980i
$986$	−0.634308	−	1.24612i	−0.0202005	−	0.0396847i
$987$	−13.5231	+	45.0457i	−0.430446	+	1.43382i
$988$	1.68200	+	12.7761i	0.0535117	+	0.406461i
$989$	28.1602	−	5.60142i	0.895444	−	0.178115i
$990$	6.09892	−	1.24966i	0.193836	−	0.0397167i
$991$	7.14926	+	4.77698i	0.227104	+	0.151746i	0.663917	−	0.747806i	$-0.268893\pi$
$991$	7.14926	+	4.77698i	0.227104	+	0.151746i	−0.436813	+	0.899552i	$0.643893\pi$
$992$	2.48301	+	7.31473i	0.0788358	+	0.232243i
$993$	0.527399	−	2.29167i	0.0167365	−	0.0727239i
$994$	−8.82889	−	1.16235i	−0.280035	−	0.0368674i
$995$	42.4285	+	5.58582i	1.34507	+	0.177082i
$996$	6.27817	+	5.84634i	0.198931	+	0.185249i
$997$	15.1502	+	44.6310i	0.479811	+	1.41348i	0.870141	+	0.492802i	$0.164027\pi$
$997$	15.1502	+	44.6310i	0.479811	+	1.41348i	−0.390331	+	0.920675i	$0.627639\pi$
$998$	17.4484	+	11.6587i	0.552320	+	0.369048i
$999$	0.350780	+	0.0314958i	0.0110982	+	0.000996483i

Display

a_p

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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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.s.a.113.8	yes	256
3.2	odd	2		459.2.y.a.368.9		256
9.2	odd	6	inner	153.2.s.a.11.8	✓	256
9.7	even	3		459.2.y.a.62.9		256
17.14	odd	16	inner	153.2.s.a.14.8	yes	256
51.14	even	16		459.2.y.a.422.9		256
153.65	even	48	inner	153.2.s.a.65.8	yes	256
153.133	odd	48		459.2.y.a.116.9		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.8	✓	256	9.2	odd	6	inner
153.2.s.a.14.8	yes	256	17.14	odd	16	inner
153.2.s.a.65.8	yes	256	153.65	even	48	inner
153.2.s.a.113.8	yes	256	1.1	even	1	trivial
459.2.y.a.62.9		256	9.7	even	3
459.2.y.a.116.9		256	153.133	odd	48
459.2.y.a.368.9		256	3.2	odd	2
459.2.y.a.422.9		256	51.14	even	16

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Classical	Maass
Hilbert	Bianchi

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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	153.2.s.a.113.8

Level	$153$
Weight	$2$
Character	153.113
Analytic conductor	$1.222$
Analytic rank	$0$
Dimension	$256$
Inner twists	$4$