LMFDB - Embedded newform 162.2.g.b.157.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$162 = 2 \cdot 3^{4}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	162.g (of order $27$ , degree $18$ , 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			157.5
Character	$\chi$	$=$	162.157
Dual form			162.2.g.b.97.5

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.973045 - 0.230616i) q^{2} +(1.70747 - 0.290767i) q^{3} +(0.893633 - 0.448799i) q^{4} +(0.537372 + 0.721815i) q^{5} +(1.59439 - 0.676699i) q^{6} +(-3.95679 + 2.60242i) q^{7} +(0.766044 - 0.642788i) q^{8} +(2.83091 - 0.992953i) q^{9} +(0.689349 + 0.578432i) q^{10} +(-4.21098 - 0.492194i) q^{11} +(1.39536 - 1.02615i) q^{12} +(-1.75605 - 5.86562i) q^{13} +(-3.24997 + 3.44477i) q^{14} +(1.12743 + 1.07623i) q^{15} +(0.597159 - 0.802123i) q^{16} +(-0.432180 + 2.45101i) q^{17} +(2.52561 - 1.61904i) q^{18} +(-0.284021 - 1.61076i) q^{19} +(0.804163 + 0.403866i) q^{20} +(-5.99940 + 5.59406i) q^{21} +(-4.21098 + 0.492194i) q^{22} +(6.35325 + 4.17860i) q^{23} +(1.12110 - 1.32028i) q^{24} +(1.20177 - 4.01418i) q^{25} +(-3.06142 - 5.30254i) q^{26} +(4.54497 - 2.51857i) q^{27} +(-2.36795 + 4.10141i) q^{28} +(2.09368 + 2.21918i) q^{29} +(1.34523 + 0.787216i) q^{30} +(-0.107618 + 1.84773i) q^{31} +(0.396080 - 0.918216i) q^{32} +(-7.33324 + 0.384010i) q^{33} +(0.144712 + 2.48461i) q^{34} +(-4.00473 - 1.45760i) q^{35} +(2.08416 - 2.15784i) q^{36} +(-8.42259 + 3.06557i) q^{37} +(-0.647833 - 1.50184i) q^{38} +(-4.70394 - 9.50478i) q^{39} +(0.875624 + 0.207527i) q^{40} +(5.04755 + 1.19629i) q^{41} +(-4.54760 + 6.82682i) q^{42} +(1.06337 + 2.46516i) q^{43} +(-3.98397 + 1.45005i) q^{44} +(2.23798 + 1.50981i) q^{45} +(7.14564 + 2.60080i) q^{46} +(0.486795 + 8.35794i) q^{47} +(0.786399 - 1.54324i) q^{48} +(6.11101 - 14.1669i) q^{49} +(0.243639 - 4.18313i) q^{50} +(-0.0252598 + 4.31070i) q^{51} +(-4.20175 - 4.45360i) q^{52} +(-1.11544 + 1.93201i) q^{53} +(3.84164 - 3.49883i) q^{54} +(-1.90759 - 3.30404i) q^{55} +(-1.35827 + 4.53694i) q^{56} +(-0.953314 - 2.66775i) q^{57} +(2.54903 + 1.67652i) q^{58} +(-3.71218 + 0.433892i) q^{59} +(1.49051 + 0.455765i) q^{60} +(2.81018 + 1.41133i) q^{61} +(0.321399 + 1.82275i) q^{62} +(-8.61722 + 11.2961i) q^{63} +(0.173648 - 0.984808i) q^{64} +(3.29024 - 4.41957i) q^{65} +(-7.04702 + 2.06482i) q^{66} +(3.28793 - 3.48500i) q^{67} +(0.713803 + 2.38427i) q^{68} +(12.0630 + 5.28751i) q^{69} +(-4.23293 - 0.494758i) q^{70} +(-3.18551 - 2.67296i) q^{71} +(1.53034 - 2.58032i) q^{72} +(1.09995 - 0.922965i) q^{73} +(-7.48859 + 4.92532i) q^{74} +(0.884789 - 7.20353i) q^{75} +(-0.976720 - 1.31196i) q^{76} +(17.9429 - 9.01124i) q^{77} +(-6.76910 - 8.16377i) q^{78} +(-5.03759 + 1.19393i) q^{79} +0.899881 q^{80} +(7.02809 - 5.62192i) q^{81} +5.18737 q^{82} +(-2.63513 + 0.624537i) q^{83} +(-2.85065 + 7.69155i) q^{84} +(-2.00142 + 1.00515i) q^{85} +(1.60321 + 2.15349i) q^{86} +(4.22017 + 3.18040i) q^{87} +(-3.54218 + 2.32973i) q^{88} +(12.5970 - 10.5701i) q^{89} +(2.52584 + 0.952998i) q^{90} +(22.2131 + 18.6390i) q^{91} +(7.55282 + 0.882798i) q^{92} +(0.353505 + 3.18624i) q^{93} +(2.40115 + 8.02039i) q^{94} +(1.01005 - 1.07059i) q^{95} +(0.409307 - 1.68299i) q^{96} +(2.79423 - 3.75330i) q^{97} +(2.67917 - 15.1943i) q^{98} +(-12.4096 + 2.78795i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38}+ \cdots - 81 q^{99}+O(q^{100})$ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$ .

$n$	$83$
$\chi(n)$	$e\left(\frac{25}{27}\right)$

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

)

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

$2$	0.973045	−	0.230616i	0.688047	−	0.163070i
$2$	0.973045	−	0.230616i	0.688047	−	0.163070i
$3$	1.70747	−	0.290767i	0.985808	−	0.167875i
$3$	1.70747	−	0.290767i	0.985808	−	0.167875i
$4$	0.893633	−	0.448799i	0.446816	−	0.224400i
$5$	0.537372	+	0.721815i	0.240320	+	0.322806i	0.905877	−	0.423542i	$-0.139213\pi$
$5$	0.537372	+	0.721815i	0.240320	+	0.322806i	−0.665557	+	0.746347i	$0.731806\pi$
$6$	1.59439	−	0.676699i	0.650907	−	0.276261i
$7$	−3.95679	+	2.60242i	−1.49552	+	0.983622i	−0.502646	+	0.864493i	$0.667640\pi$
$7$	−3.95679	+	2.60242i	−1.49552	+	0.983622i	−0.992879	+	0.119129i	$0.961990\pi$
$8$	0.766044	−	0.642788i	0.270838	−	0.227260i
$9$	2.83091	−	0.992953i	0.943636	−	0.330984i
$10$	0.689349	+	0.578432i	0.217991	+	0.182916i
$11$	−4.21098	−	0.492194i	−1.26966	−	0.148402i	−0.545545	−	0.838082i	$-0.683677\pi$
$11$	−4.21098	−	0.492194i	−1.26966	−	0.148402i	−0.724115	+	0.689680i	$0.757751\pi$
$12$	1.39536	−	1.02615i	0.402804	−	0.296224i
$13$	−1.75605	−	5.86562i	−0.487041	−	1.62683i	−0.749583	−	0.661911i	$-0.769746\pi$
$13$	−1.75605	−	5.86562i	−0.487041	−	1.62683i	0.262541	−	0.964921i	$-0.415439\pi$
$14$	−3.24997	+	3.44477i	−0.868591	+	0.920653i
$15$	1.12743	+	1.07623i	0.291100	+	0.277881i
$16$	0.597159	−	0.802123i	0.149290	−	0.200531i
$17$	−0.432180	+	2.45101i	−0.104819	+	0.594458i	0.886473	+	0.462780i	$0.153148\pi$
$17$	−0.432180	+	2.45101i	−0.104819	+	0.594458i	−0.991292	+	0.131679i	$0.957963\pi$
$18$	2.52561	−	1.61904i	0.595292	−	0.381611i
$19$	−0.284021	−	1.61076i	−0.0651589	−	0.369534i	−0.999899	−	0.0142026i	$-0.995479\pi$
$19$	−0.284021	−	1.61076i	−0.0651589	−	0.369534i	0.934740	−	0.355332i	$-0.115632\pi$
$20$	0.804163	+	0.403866i	0.179816	+	0.0903071i
$21$	−5.99940	+	5.59406i	−1.30918	+	1.22072i
$22$	−4.21098	+	0.492194i	−0.897785	+	0.104936i
$23$	6.35325	+	4.17860i	1.32474	+	0.871297i	0.997290	−	0.0735700i	$-0.0234392\pi$
$23$	6.35325	+	4.17860i	1.32474	+	0.871297i	0.327453	+	0.944867i	$0.393810\pi$
$24$	1.12110	−	1.32028i	0.228843	−	0.269501i
$25$	1.20177	−	4.01418i	0.240353	−	0.802836i
$26$	−3.06142	−	5.30254i	−0.600395	−	1.03991i
$27$	4.54497	−	2.51857i	0.874681	−	0.484699i
$28$	−2.36795	+	4.10141i	−0.447500	+	0.775093i
$29$	2.09368	+	2.21918i	0.388787	+	0.412091i	0.891974	−	0.452087i	$-0.149321\pi$
$29$	2.09368	+	2.21918i	0.388787	+	0.412091i	−0.503186	+	0.864178i	$0.667839\pi$
$30$	1.34523	+	0.787216i	0.245605	+	0.143725i
$31$	−0.107618	+	1.84773i	−0.0193288	+	0.331863i	0.974757	+	0.223267i	$0.0716723\pi$
$31$	−0.107618	+	1.84773i	−0.0193288	+	0.331863i	−0.994086	+	0.108595i	$0.965365\pi$
$32$	0.396080	−	0.918216i	0.0700177	−	0.162319i
$33$	−7.33324	+	0.384010i	−1.27655	+	0.0668476i
$34$	0.144712	+	2.48461i	0.0248180	+	0.426108i
$35$	−4.00473	−	1.45760i	−0.676923	−	0.246380i
$36$	2.08416	−	2.15784i	0.347359	−	0.359641i
$37$	−8.42259	+	3.06557i	−1.38467	+	0.503977i	−0.923589	−	0.383384i	$-0.874759\pi$
$37$	−8.42259	+	3.06557i	−1.38467	+	0.503977i	−0.461076	+	0.887361i	$0.652537\pi$
$38$	−0.647833	−	1.50184i	−0.105092	−	0.243631i
$39$	−4.70394	−	9.50478i	−0.753233	−	1.52198i
$40$	0.875624	+	0.207527i	0.138448	+	0.0328129i
$41$	5.04755	+	1.19629i	0.788295	+	0.186829i	0.604996	−	0.796228i	$-0.293175\pi$
$41$	5.04755	+	1.19629i	0.788295	+	0.186829i	0.183298	+	0.983057i	$0.441323\pi$
$42$	−4.54760	+	6.82682i	−0.701710	+	1.05340i
$43$	1.06337	+	2.46516i	0.162162	+	0.375934i	0.979852	−	0.199725i	$-0.0640049\pi$
$43$	1.06337	+	2.46516i	0.162162	+	0.375934i	−0.817690	+	0.575659i	$0.804746\pi$
$44$	−3.98397	+	1.45005i	−0.600606	+	0.218603i
$45$	2.23798	+	1.50981i	0.333618	+	0.225069i
$46$	7.14564	+	2.60080i	1.05357	+	0.383467i
$47$	0.486795	+	8.35794i	0.0710063	+	1.21913i	0.826103	+	0.563519i	$0.190553\pi$
$47$	0.486795	+	8.35794i	0.0710063	+	1.21913i	−0.755097	+	0.655613i	$0.772410\pi$
$48$	0.786399	−	1.54324i	0.113507	−	0.222747i
$49$	6.11101	−	14.1669i	0.873002	−	2.02384i
$50$	0.243639	−	4.18313i	0.0344558	−	0.591583i
$51$	−0.0252598	+	4.31070i	−0.00353708	+	0.603618i
$52$	−4.20175	−	4.45360i	−0.582678	−	0.617603i
$53$	−1.11544	+	1.93201i	−0.153218	+	0.265381i	−0.932409	−	0.361406i	$-0.882297\pi$
$53$	−1.11544	+	1.93201i	−0.153218	+	0.265381i	0.779191	+	0.626787i	$0.215630\pi$
$54$	3.84164	−	3.49883i	0.522781	−	0.476130i
$55$	−1.90759	−	3.30404i	−0.257219	−	0.445517i
$56$	−1.35827	+	4.53694i	−0.181507	+	0.606274i
$57$	−0.953314	−	2.66775i	−0.126270	−	0.353352i
$58$	2.54903	+	1.67652i	0.334703	+	0.220138i
$59$	−3.71218	+	0.433892i	−0.483285	+	0.0564879i	−0.354247	−	0.935152i	$-0.615263\pi$
$59$	−3.71218	+	0.433892i	−0.483285	+	0.0564879i	−0.129038	+	0.991640i	$0.541189\pi$
$60$	1.49051	+	0.455765i	0.192425	+	0.0588390i
$61$	2.81018	+	1.41133i	0.359807	+	0.180702i	0.619514	−	0.784986i	$-0.287330\pi$
$61$	2.81018	+	1.41133i	0.359807	+	0.180702i	−0.259707	+	0.965687i	$0.583626\pi$
$62$	0.321399	+	1.82275i	0.0408178	+	0.231489i
$63$	−8.61722	+	11.2961i	−1.08567	+	1.42318i
$64$	0.173648	−	0.984808i	0.0217060	−	0.123101i
$65$	3.29024	−	4.41957i	0.408105	−	0.548180i
$66$	−7.04702	+	2.06482i	−0.867428	+	0.254162i
$67$	3.28793	−	3.48500i	0.401685	−	0.425761i	−0.494682	−	0.869074i	$-0.664716\pi$
$67$	3.28793	−	3.48500i	0.401685	−	0.425761i	0.896367	+	0.443313i	$0.146197\pi$
$68$	0.713803	+	2.38427i	0.0865614	+	0.289135i
$69$	12.0630	+	5.28751i	1.45221	+	0.636542i
$70$	−4.23293	−	0.494758i	−0.505932	−	0.0591349i
$71$	−3.18551	−	2.67296i	−0.378051	−	0.317222i	0.433886	−	0.900968i	$-0.357142\pi$
$71$	−3.18551	−	2.67296i	−0.378051	−	0.317222i	−0.811937	+	0.583746i	$0.801587\pi$
$72$	1.53034	−	2.58032i	0.180353	−	0.304094i
$73$	1.09995	−	0.922965i	0.128739	−	0.108025i	−0.576145	−	0.817348i	$-0.695444\pi$
$73$	1.09995	−	0.922965i	0.128739	−	0.108025i	0.704884	+	0.709323i	$0.250999\pi$
$74$	−7.48859	+	4.92532i	−0.870531	+	0.572557i
$75$	0.884789	−	7.20353i	0.102167	−	0.831792i
$76$	−0.976720	−	1.31196i	−0.112037	−	0.150492i
$77$	17.9429	−	9.01124i	2.04478	−	1.02693i
$78$	−6.76910	−	8.16377i	−0.766449	−	0.924365i
$79$	−5.03759	+	1.19393i	−0.566773	+	0.134328i	−0.504005	−	0.863701i	$-0.668141\pi$
$79$	−5.03759	+	1.19393i	−0.566773	+	0.134328i	−0.0627675	+	0.998028i	$0.519993\pi$
$80$	0.899881			0.100610
$81$	7.02809	−	5.62192i	0.780899	−	0.624657i
$82$	5.18737			0.572850
$83$	−2.63513	+	0.624537i	−0.289243	+	0.0685519i	−0.372676	−	0.927962i	$-0.621560\pi$
$83$	−2.63513	+	0.624537i	−0.289243	+	0.0685519i	0.0834329	+	0.996513i	$0.473412\pi$
$84$	−2.85065	+	7.69155i	−0.311031	+	0.839217i
$85$	−2.00142	+	1.00515i	−0.217085	+	0.109024i
$86$	1.60321	+	2.15349i	0.172879	+	0.232216i
$87$	4.22017	+	3.18040i	0.452449	+	0.340975i
$88$	−3.54218	+	2.32973i	−0.377597	+	0.248350i
$89$	12.5970	−	10.5701i	1.33528	−	1.12043i	0.352463	−	0.935826i	$-0.385344\pi$
$89$	12.5970	−	10.5701i	1.33528	−	1.12043i	0.982813	−	0.184604i	$-0.0591003\pi$
$90$	2.52584	+	0.952998i	0.266247	+	0.100455i
$91$	22.2131	+	18.6390i	2.32857	+	1.95390i
$92$	7.55282	+	0.882798i	0.787436	+	0.0920380i
$93$	0.353505	+	3.18624i	0.0366568	+	0.330398i
$94$	2.40115	+	8.02039i	0.247659	+	0.827240i
$95$	1.01005	−	1.07059i	0.103629	−	0.109840i
$96$	0.409307	−	1.68299i	0.0417747	−	0.171770i
$97$	2.79423	−	3.75330i	0.283711	−	0.381090i	−0.637307	−	0.770610i	$-0.719952\pi$
$97$	2.79423	−	3.75330i	0.283711	−	0.381090i	0.921018	+	0.389520i	$0.127359\pi$
$98$	2.67917	−	15.1943i	0.270637	−	1.53486i
$99$	−12.4096	+	2.78795i	−1.24722	+	0.280200i
$100$	−0.727623	−	4.12656i	−0.0727623	−	0.412656i
$101$	−10.7240	−	5.38577i	−1.06707	−	0.535904i	−0.173506	−	0.984833i	$-0.555510\pi$
$101$	−10.7240	−	5.38577i	−1.06707	−	0.535904i	−0.893568	+	0.448928i	$0.851806\pi$
$102$	0.969536	+	4.20033i	0.0959984	+	0.415894i
$103$	7.07350	−	0.826773i	0.696972	−	0.0814644i	0.239774	−	0.970829i	$-0.422927\pi$
$103$	7.07350	−	0.826773i	0.696972	−	0.0814644i	0.457199	+	0.889364i	$0.348853\pi$
$104$	−5.11557	−	3.36456i	−0.501622	−	0.329922i
$105$	−7.26178	−	1.32437i	−0.708677	−	0.129245i
$106$	−0.639826	+	2.13717i	−0.0621454	+	0.207580i
$107$	−4.54371	−	7.86994i	−0.439257	−	0.760816i	0.558375	−	0.829589i	$-0.311425\pi$
$107$	−4.54371	−	7.86994i	−0.439257	−	0.760816i	−0.997632	+	0.0687727i	$0.978092\pi$
$108$	2.93120	−	4.29046i	0.282055	−	0.412850i
$109$	−4.27740	+	7.40867i	−0.409700	+	0.709622i	−0.994856	−	0.101299i	$-0.967700\pi$
$109$	−4.27740	+	7.40867i	−0.409700	+	0.709622i	0.585156	+	0.810921i	$0.301033\pi$
$110$	−2.61814	−	2.77506i	−0.249629	−	0.264592i
$111$	−13.4900	+	7.68339i	−1.28041	+	0.729275i
$112$	−0.275368	+	4.72789i	−0.0260198	+	0.446743i
$113$	−2.11058	+	4.89288i	−0.198547	+	0.460284i	−0.988180	−	0.153295i	$-0.951011\pi$
$113$	−2.11058	+	4.89288i	−0.198547	+	0.460284i	0.789633	+	0.613579i	$0.210271\pi$
$114$	−1.54284	−	2.37599i	−0.144500	−	0.222532i
$115$	0.397880	+	6.83133i	0.0371025	+	0.637025i
$116$	2.86695	+	1.04348i	0.266189	+	0.0968850i
$117$	−10.7955	−	14.8614i	−0.998046	−	1.37393i
$118$	−3.51206	+	1.27828i	−0.323311	+	0.117676i
$119$	−4.66852	−	10.8229i	−0.427963	−	0.992129i
$120$	1.55544	+	0.0997430i	0.141992	+	0.00910524i
$121$	6.78664	+	1.60846i	0.616968	+	0.146224i
$122$	3.05991	+	0.725211i	0.277031	+	0.0656576i
$123$	8.96638	+	0.574970i	0.808471	+	0.0518433i
$124$	0.733090	+	1.69949i	0.0658334	+	0.152619i
$125$	7.77135	−	2.82854i	0.695091	−	0.252992i
$126$	−5.77988	+	12.9789i	−0.514913	+	1.15625i
$127$	−2.08699	−	0.759602i	−0.185190	−	0.0674038i	0.247760	−	0.968821i	$-0.420305\pi$
$127$	−2.08699	−	0.759602i	−0.185190	−	0.0674038i	−0.432951	+	0.901418i	$0.642528\pi$
$128$	−0.0581448	−	0.998308i	−0.00513933	−	0.0882388i
$129$	2.53246	+	3.90000i	0.222970	+	0.343376i
$130$	2.18233	−	5.05922i	0.191403	−	0.443723i
$131$	0.0633149	−	1.08707i	0.00553185	−	0.0949781i	−0.994412	−	0.105568i	$-0.966334\pi$
$131$	0.0633149	−	1.08707i	0.00553185	−	0.0949781i	0.999944	+	0.0105899i	$0.00337094\pi$
$132$	−6.38088	+	3.63432i	−0.555385	+	0.316327i
$133$	5.31569	+	5.63430i	0.460929	+	0.488556i
$134$	2.39561	−	4.14931i	0.206949	−	0.358446i
$135$	4.26028	+	1.92722i	0.366667	+	0.165869i
$136$	1.24441	+	2.15539i	0.106708	+	0.184823i
$137$	−1.73952	+	5.81040i	−0.148617	+	0.496416i	−0.999585	−	0.0288015i	$-0.990831\pi$
$137$	−1.73952	+	5.81040i	−0.148617	+	0.496416i	0.850968	+	0.525218i	$0.176016\pi$
$138$	12.9572	+	2.36307i	1.10299	+	0.201158i
$139$	−11.7886	−	7.75350i	−0.999898	−	0.657644i	−0.0596807	−	0.998218i	$-0.519008\pi$
$139$	−11.7886	−	7.75350i	−0.999898	−	0.657644i	−0.940218	+	0.340574i	$0.889379\pi$
$140$	−4.23293	+	0.494758i	−0.357748	+	0.0418147i
$141$	3.26140	+	14.1294i	0.274660	+	1.18991i
$142$	−3.71607	−	1.86628i	−0.311846	−	0.156615i
$143$	4.50769	+	25.5644i	0.376952	+	2.13780i
$144$	0.894031	−	2.86369i	0.0745026	−	0.238641i
$145$	−0.476748	+	2.70377i	−0.0395918	+	0.224536i
$146$	0.857447	−	1.15175i	0.0709628	−	0.0953196i
$147$	6.31509	−	25.9665i	0.520860	−	2.14168i
$148$	−6.15088	+	6.51955i	−0.505599	+	0.535903i
$149$	−0.589967	−	1.97063i	−0.0483319	−	0.161440i	0.930417	−	0.366503i	$-0.119445\pi$
$149$	−0.589967	−	1.97063i	−0.0483319	−	0.161440i	−0.978749	+	0.205063i	$0.934260\pi$
$150$	−0.800309	−	7.21340i	−0.0653449	−	0.588972i
$151$	−8.84148	−	1.03342i	−0.719509	−	0.0840986i	−0.251545	−	0.967846i	$-0.580939\pi$
$151$	−8.84148	−	1.03342i	−0.719509	−	0.0840986i	−0.467965	+	0.883747i	$0.655013\pi$
$152$	−1.25295	−	1.05135i	−0.101628	−	0.0852758i
$153$	1.21028	+	7.36773i	0.0978453	+	0.595646i
$154$	15.3811	−	12.9063i	1.23944	−	1.04002i
$155$	−1.39155	+	0.915239i	−0.111772	+	0.0735138i
$156$	−8.46933	−	6.38265i	−0.678089	−	0.511021i
$157$	−2.34792	−	3.15381i	−0.187385	−	0.251701i	0.698496	−	0.715613i	$-0.253853\pi$
$157$	−2.34792	−	3.15381i	−0.187385	−	0.251701i	−0.885881	+	0.463912i	$0.846445\pi$
$158$	−4.62646	+	2.32349i	−0.368061	+	0.184847i
$159$	−1.34282	+	3.62318i	−0.106493	+	0.287337i
$160$	0.875624	−	0.207527i	0.0692242	−	0.0164064i
$161$	−36.0129			−2.83821
$162$	5.54214	−	7.09117i	0.435432	−	0.557135i
$163$	−10.9972			−0.861367			−0.430683	−	0.902503i	$-0.641727\pi$
$163$	−10.9972			−0.861367			−0.430683	+	0.902503i	$0.641727\pi$
$164$	5.04755	−	1.19629i	0.394147	−	0.0934146i
$165$	−4.21786	−	5.08689i	−0.328360	−	0.396014i
$166$	−2.42007	+	1.21541i	−0.187834	+	0.0943338i
$167$	−9.59118	−	12.8832i	−0.742188	−	0.996931i	−0.999531	−	0.0306113i	$-0.990255\pi$
$167$	−9.59118	−	12.8832i	−0.742188	−	0.996931i	0.257343	−	0.966320i	$-0.417153\pi$
$168$	−1.00001	+	8.14163i	−0.0771527	+	0.628141i
$169$	−20.4605	+	13.4571i	−1.57388	+	1.03516i
$170$	−1.71567	+	1.43962i	−0.131586	+	0.110414i
$171$	−2.40345	−	4.27790i	−0.183796	−	0.327139i
$172$	2.05662	+	1.72571i	0.156816	+	0.131584i
$173$	−11.5069	−	1.34497i	−0.874855	−	0.102256i	−0.333199	−	0.942856i	$-0.608128\pi$
$173$	−11.5069	−	1.34497i	−0.874855	−	0.102256i	−0.541655	+	0.840601i	$0.682202\pi$
$174$	4.83986	+	2.12144i	0.366909	+	0.160826i
$175$	5.69145	+	19.0108i	0.430233	+	1.43708i
$176$	−2.90943	+	3.08381i	−0.219306	+	0.232451i
$177$	−6.21228	+	1.82024i	−0.466943	+	0.136817i
$178$	9.81978	−	13.1903i	0.736024	−	0.988651i
$179$	1.19249	−	6.76294i	0.0891308	−	0.505486i	−0.907258	−	0.420575i	$-0.861828\pi$
$179$	1.19249	−	6.76294i	0.0891308	−	0.505486i	0.996389	−	0.0849109i	$-0.0270605\pi$
$180$	2.67753	+	0.344812i	0.199571	+	0.0257007i
$181$	−4.15485	−	23.5633i	−0.308827	−	1.75145i	−0.604919	−	0.796287i	$-0.706795\pi$
$181$	−4.15485	−	23.5633i	−0.308827	−	1.75145i	0.296092	−	0.955159i	$-0.404316\pi$
$182$	25.9128	+	13.0139i	1.92079	+	0.964656i
$183$	5.20867	+	1.59269i	0.385036	+	0.117735i
$184$	7.55282	−	0.882798i	0.556801	−	0.0650807i
$185$	−6.73884	−	4.43220i	−0.495449	−	0.325862i
$186$	1.07877	+	3.01883i	0.0790996	+	0.221352i
$187$	3.02628	−	10.1085i	0.221303	−	0.739204i
$188$	4.18605	+	7.25046i	0.305299	+	0.528794i
$189$	−11.4291	+	21.7934i	−0.831345	+	1.58524i
$190$	0.735928	−	1.27466i	0.0533898	−	0.0924739i
$191$	6.80578	+	7.21370i	0.492449	+	0.521965i	0.925165	−	0.379565i	$-0.123926\pi$
$191$	6.80578	+	7.21370i	0.492449	+	0.521965i	−0.432716	+	0.901530i	$0.642445\pi$
$192$	0.0101493	−	1.73202i	0.000732462	−	0.124998i
$193$	−1.01279	+	17.3890i	−0.0729023	+	1.25168i	0.741328	+	0.671143i	$0.234196\pi$
$193$	−1.01279	+	17.3890i	−0.0729023	+	1.25168i	−0.814231	+	0.580542i	$0.802841\pi$
$194$	1.85334	−	4.29653i	0.133062	−	0.308473i
$195$	4.33293	−	8.50297i	0.310288	−	0.608910i
$196$	−0.897101	−	15.4026i	−0.0640787	−	1.10019i
$197$	19.0553	+	6.93558i	1.35764	+	0.494140i	0.915323	−	0.402720i	$-0.131935\pi$
$197$	19.0553	+	6.93558i	1.35764	+	0.494140i	0.442314	+	0.896860i	$0.354158\pi$
$198$	−11.4322	+	5.57466i	−0.812450	+	0.396174i
$199$	4.91031	−	1.78721i	0.348083	−	0.126692i	−0.162062	−	0.986781i	$-0.551814\pi$
$199$	4.91031	−	1.78721i	0.348083	−	0.126692i	0.510144	+	0.860089i	$0.329592\pi$
$200$	−1.65966	−	3.84752i	−0.117356	−	0.272061i
$201$	4.60072	−	6.90656i	0.324510	−	0.487151i
$202$	−11.6769	−	2.76748i	−0.821586	−	0.194720i
$203$	−14.0595	−	3.33216i	−0.986782	−	0.233872i
$204$	1.91206	+	3.86352i	0.133871	+	0.270500i
$205$	1.84891	+	4.28625i	0.129133	+	0.299365i
$206$	6.69216	−	2.43575i	0.466265	−	0.169707i
$207$	22.1346	+	5.52075i	1.53846	+	0.383719i
$208$	−5.75360	−	2.09414i	−0.398940	−	0.145202i
$209$	0.403201	+	6.92269i	0.0278900	+	0.478853i
$210$	−7.37146	+	0.386012i	−0.508679	+	0.0266373i
$211$	−3.96517	+	9.19229i	−0.272973	+	0.632823i	−0.998464	−	0.0554089i	$-0.982354\pi$
$211$	−3.96517	+	9.19229i	−0.272973	+	0.632823i	0.725490	+	0.688232i	$0.241613\pi$
$212$	−0.129715	+	2.22711i	−0.00890884	+	0.152959i
$213$	−6.21637	−	3.63776i	−0.425939	−	0.249255i
$214$	−6.23617	−	6.60995i	−0.426296	−	0.451847i
$215$	−1.20797	+	2.09226i	−0.0823828	+	0.142691i
$216$	1.86275	−	4.85079i	0.126744	−	0.330055i
$217$	−4.38275	−	7.59115i	−0.297521	−	0.515321i
$218$	−2.45354	+	8.19540i	−0.166175	+	0.555063i
$219$	1.60976	−	1.89576i	0.108777	−	0.128104i
$220$	−3.18754	−	2.09648i	−0.214904	−	0.141344i
$221$	15.1357	−	1.76911i	1.01813	−	0.119003i
$222$	−11.3544	+	10.5873i	−0.762059	+	0.710572i
$223$	20.2555	+	10.1727i	1.35641	+	0.681215i	0.970451	−	0.241300i	$-0.0775738\pi$
$223$	20.2555	+	10.1727i	1.35641	+	0.681215i	0.385961	+	0.922515i	$0.373870\pi$
$224$	0.822380	+	4.66395i	0.0549476	+	0.311623i
$225$	−0.583799	−	12.5571i	−0.0389199	−	0.837139i
$226$	−0.925316	+	5.24773i	−0.0615511	+	0.349074i
$227$	1.72373	−	2.31537i	0.114408	−	0.153677i	−0.741230	−	0.671251i	$-0.765757\pi$
$227$	1.72373	−	2.31537i	0.114408	−	0.153677i	0.855638	+	0.517574i	$0.173165\pi$
$228$	−2.04919	−	1.95614i	−0.135711	−	0.129548i
$229$	13.2406	−	14.0343i	0.874967	−	0.927410i	−0.122918	−	0.992417i	$-0.539225\pi$
$229$	13.2406	−	14.0343i	0.874967	−	0.927410i	0.997885	+	0.0650064i	$0.0207068\pi$
$230$	1.96257	+	6.55543i	0.129408	+	0.432252i
$231$	28.0167	−	20.6036i	1.84336	−	1.35562i
$232$	3.03031	+	0.354193i	0.198950	+	0.0232539i
$233$	20.8609	+	17.5044i	1.36664	+	1.14675i	0.973868	+	0.227117i	$0.0729299\pi$
$233$	20.8609	+	17.5044i	1.36664	+	1.14675i	0.392777	+	0.919634i	$0.371515\pi$
$234$	−13.9318	−	11.9712i	−0.910749	−	0.782580i
$235$	−5.77130	+	4.84270i	−0.376478	+	0.315903i
$236$	−3.12260	+	2.05376i	−0.203264	+	0.133689i
$237$	−8.25437	+	3.50336i	−0.536179	+	0.227568i
$238$	−7.03860	−	9.45449i	−0.456245	−	0.612843i
$239$	7.06865	−	3.55001i	0.457233	−	0.229631i	−0.205248	−	0.978710i	$-0.565800\pi$
$239$	7.06865	−	3.55001i	0.457233	−	0.229631i	0.662481	+	0.749079i	$0.269504\pi$
$240$	1.53652	−	0.261656i	0.0991819	−	0.0168898i
$241$	−0.421799	+	0.0999681i	−0.0271704	+	0.00643951i	−0.244179	−	0.969730i	$-0.578518\pi$
$241$	−0.421799	+	0.0999681i	−0.0271704	+	0.00643951i	0.217008	+	0.976170i	$0.430370\pi$
$242$	6.97465			0.448347
$243$	10.3656	−	11.6428i	0.664953	−	0.746886i
$244$	3.14467			0.201317
$245$	13.5098	−	3.20188i	0.863108	−	0.204560i
$246$	8.85729	−	1.50832i	0.564720	−	0.0961669i
$247$	−8.94938	+	4.49455i	−0.569435	+	0.285981i
$248$	1.10526	+	1.48462i	0.0701841	+	0.0942736i
$249$	−4.31781	+	1.83259i	−0.273630	+	0.116136i
$250$	6.90957	−	4.54449i	0.436999	−	0.287419i
$251$	−4.62180	+	3.87815i	−0.291725	+	0.244787i	−0.776890	−	0.629636i	$-0.783204\pi$
$251$	−4.62180	+	3.87815i	−0.291725	+	0.244787i	0.485165	+	0.874423i	$0.338760\pi$
$252$	−2.63094	+	13.9620i	−0.165734	+	0.879522i
$253$	−24.6967	−	20.7230i	−1.55267	−	1.30285i
$254$	−2.20591	−	0.257834i	−0.138411	−	0.0161780i
$255$	−3.12510	+	2.29821i	−0.195701	+	0.143920i
$256$	−0.286803	−	0.957990i	−0.0179252	−	0.0598743i
$257$	−11.6285	+	12.3254i	−0.725363	+	0.768840i	−0.980171	−	0.198152i	$-0.936506\pi$
$257$	−11.6285	+	12.3254i	−0.725363	+	0.768840i	0.254808	+	0.966992i	$0.417988\pi$
$258$	3.36360	+	3.21085i	0.209408	+	0.199899i
$259$	25.3485	−	34.0489i	1.57508	−	2.11570i
$260$	0.956773	−	5.42613i	0.0593365	−	0.336514i
$261$	8.13056	+	4.20335i	0.503269	+	0.260181i
$262$	−0.189088	−	1.07237i	−0.0116819	−	0.0662515i
$263$	−20.4228	−	10.2567i	−1.25933	−	0.632458i	−0.311198	−	0.950345i	$-0.600730\pi$
$263$	−20.4228	−	10.2567i	−1.25933	−	0.632458i	−0.948128	+	0.317887i	$0.897027\pi$
$264$	−5.37075	+	5.00789i	−0.330547	+	0.308214i
$265$	−1.99396	+	0.233060i	−0.122488	+	0.0143168i
$266$	6.47176	+	4.25655i	0.396809	+	0.260986i
$267$	18.4355	−	21.7109i	1.12823	−	1.32869i
$268$	1.37414	−	4.58993i	0.0839387	−	0.280375i
$269$	11.0727	+	19.1784i	0.675113	+	1.16933i	0.976436	+	0.215808i	$0.0692385\pi$
$269$	11.0727	+	19.1784i	0.675113	+	1.16933i	−0.301323	+	0.953522i	$0.597428\pi$
$270$	4.58990	+	0.892785i	0.279332	+	0.0543332i
$271$	8.46422	−	14.6605i	0.514165	−	0.890559i	−0.485700	−	0.874125i	$-0.661435\pi$
$271$	8.46422	−	14.6605i	0.514165	−	0.890559i	0.999865	−	0.0164339i	$-0.00523130\pi$
$272$	1.70794	+	1.81031i	0.103559	+	0.109766i
$273$	43.3479	+	25.3667i	2.62353	+	1.53527i
$274$	−0.352660	+	6.05494i	−0.0213050	+	0.365793i
$275$	−7.03638	+	16.3122i	−0.424309	+	0.983660i
$276$	13.1529	−	0.688761i	0.791712	−	0.0414585i
$277$	1.38639	+	23.8035i	0.0833004	+	1.43021i	0.738244	+	0.674534i	$0.235655\pi$
$277$	1.38639	+	23.8035i	0.0833004	+	1.43021i	−0.654943	+	0.755678i	$0.727307\pi$
$278$	−13.2589	−	4.82586i	−0.795219	−	0.289436i
$279$	1.53005	+	5.33762i	0.0916020	+	0.319555i
$280$	−4.00473	+	1.45760i	−0.239328	+	0.0871084i
$281$	2.40187	+	5.56816i	0.143284	+	0.332169i	0.974713	−	0.223462i	$-0.0717360\pi$
$281$	2.40187	+	5.56816i	0.143284	+	0.332169i	−0.831429	+	0.555631i	$0.812477\pi$
$282$	6.43196	+	12.9964i	0.383017	+	0.773925i
$283$	6.35030	+	1.50505i	0.377486	+	0.0894659i	0.414979	−	0.909831i	$-0.363789\pi$
$283$	6.35030	+	1.50505i	0.377486	+	0.0894659i	−0.0374926	+	0.999297i	$0.511937\pi$
$284$	−4.04630	−	0.958991i	−0.240104	−	0.0569056i
$285$	1.41334	−	2.12169i	0.0837188	−	0.125678i
$286$	10.2817	+	23.8357i	0.607972	+	1.40944i
$287$	−23.0853	+	8.40237i	−1.36268	+	0.495976i
$288$	0.209521	−	2.99267i	0.0123461	−	0.176345i
$289$	10.1541	+	3.69578i	0.597299	+	0.217399i
$290$	0.159636	+	2.74084i	0.00937413	+	0.160948i
$291$	3.67973	−	7.22112i	0.215709	−	0.423310i
$292$	0.568723	−	1.31845i	0.0332820	−	0.0771563i
$293$	0.343009	−	5.88924i	0.0200388	−	0.344053i	−0.973355	−	0.229302i	$-0.926356\pi$
$293$	0.343009	−	5.88924i	0.0200388	−	0.344053i	0.993394	−	0.114751i	$-0.0366072\pi$
$294$	0.156591	−	26.7229i	0.00913256	−	1.55851i
$295$	−2.30801	−	2.44635i	−0.134378	−	0.142432i
$296$	−4.48157	+	7.76230i	−0.260486	+	0.451175i
$297$	−20.3784	+	8.36866i	−1.18248	+	0.485599i
$298$	−1.02852	−	1.78145i	−0.0595806	−	0.103197i
$299$	13.3534	−	44.6036i	0.772249	−	2.57949i
$300$	−2.44226	−	6.83440i	−0.141004	−	0.394584i
$301$	−10.6229	−	6.98680i	−0.612294	−	0.402712i
$302$	−8.84148	+	1.03342i	−0.508770	+	0.0594667i
$303$	−19.8768	−	6.07787i	−1.14189	−	0.349165i
$304$	−1.46164	−	0.734061i	−0.0838306	−	0.0421013i
$305$	0.491395	+	2.78684i	0.0281372	+	0.159574i
$306$	2.87677	+	6.89003i	0.164454	+	0.393877i
$307$	−2.40217	+	13.6234i	−0.137099	+	0.777527i	0.836276	+	0.548309i	$0.184728\pi$
$307$	−2.40217	+	13.6234i	−0.137099	+	0.777527i	−0.973375	+	0.229219i	$0.926383\pi$
$308$	11.9901	−	16.1055i	0.683199	−	0.917695i
$309$	11.8374	−	3.46843i	0.673405	−	0.197312i
$310$	−1.14297	+	1.21148i	−0.0649166	+	0.0688076i
$311$	6.10565	+	20.3943i	0.346220	+	1.15645i	0.936914	+	0.349559i	$0.113669\pi$
$311$	6.10565	+	20.3943i	0.346220	+	1.15645i	−0.590695	+	0.806895i	$0.701146\pi$
$312$	−9.71298	−	4.25745i	−0.549889	−	0.241031i
$313$	−13.4077	−	1.56714i	−0.757849	−	0.0885799i	−0.271612	−	0.962407i	$-0.587557\pi$
$313$	−13.4077	−	1.56714i	−0.757849	−	0.0885799i	−0.486237	+	0.873827i	$0.661631\pi$
$314$	−3.01195	−	2.52733i	−0.169974	−	0.142625i
$315$	−12.7844	−	0.149833i	−0.720317	−	0.00844211i
$316$	−3.96592	+	3.32780i	−0.223100	+	0.187203i
$317$	−7.36594	+	4.84465i	−0.413712	+	0.272103i	−0.739256	−	0.673424i	$-0.764823\pi$
$317$	−7.36594	+	4.84465i	−0.413712	+	0.272103i	0.325544	+	0.945527i	$0.394452\pi$
$318$	−0.471065	+	3.83519i	−0.0264160	+	0.215067i
$319$	−7.72421	−	10.3754i	−0.432473	−	0.580912i
$320$	0.804163	−	0.403866i	0.0449541	−	0.0225768i
$321$	−10.0466	−	12.1165i	−0.560745	−	0.676279i
$322$	−35.0422	+	8.30514i	−1.95282	+	0.462828i
$323$	4.07075			0.226503
$324$	3.75742	−	8.17813i	0.208746	−	0.454341i
$325$	−25.6560			−1.42314
$326$	−10.7008	+	2.53613i	−0.592660	+	0.140463i
$327$	−5.14933	+	13.8938i	−0.284759	+	0.768329i
$328$	4.63561	−	2.32809i	0.255959	−	0.128547i
$329$	−23.6770	−	31.8038i	−1.30536	−	1.75340i
$330$	−5.27729	−	3.97707i	−0.290505	−	0.218930i
$331$	−2.52570	+	1.66118i	−0.138825	+	0.0913066i	−0.617022	−	0.786946i	$-0.711661\pi$
$331$	−2.52570	+	1.66118i	−0.138825	+	0.0913066i	0.478197	+	0.878253i	$0.341291\pi$
$332$	−2.07455	+	1.74075i	−0.113856	+	0.0955361i
$333$	−20.7996	+	17.0416i	−1.13981	+	0.933873i
$334$	−12.3037	−	10.3240i	−0.673230	−	0.564907i
$335$	4.28237	+	0.500537i	0.233971	+	0.0273473i
$336$	0.904532	+	8.15279i	0.0493462	+	0.444771i
$337$	−0.618666	−	2.06649i	−0.0337009	−	0.112569i	0.939484	−	0.342592i	$-0.111305\pi$
$337$	−0.618666	−	2.06649i	−0.0337009	−	0.112569i	−0.973185	+	0.230023i	$0.926120\pi$
$338$	−16.8056	+	17.8129i	−0.914102	+	0.968891i
$339$	−2.18107	+	8.96814i	−0.118459	+	0.487082i
$340$	−1.33742	+	1.79647i	−0.0725320	+	0.0974274i
$341$	1.36262	−	7.72781i	0.0737901	−	0.418484i
$342$	−3.32522	−	3.60832i	−0.179807	−	0.195116i
$343$	6.93163	+	39.3112i	0.374273	+	2.12261i
$344$	2.39916	+	1.20491i	0.129354	+	0.0649641i
$345$	2.66569	+	11.5486i	0.143516	+	0.621756i
$346$	−11.5069	+	1.34497i	−0.618616	+	0.0723058i
$347$	24.2348	+	15.9395i	1.30099	+	0.855677i	0.995336	−	0.0964641i	$-0.0307533\pi$
$347$	24.2348	+	15.9395i	1.30099	+	0.855677i	0.305658	+	0.952141i	$0.401124\pi$
$348$	5.19864	+	0.948103i	0.278676	+	0.0508237i
$349$	7.51624	−	25.1060i	0.402335	−	1.34389i	−0.481645	−	0.876367i	$-0.659960\pi$
$349$	7.51624	−	25.1060i	0.402335	−	1.34389i	0.883980	−	0.467525i	$-0.154854\pi$
$350$	9.92222	+	17.1858i	0.530365	+	0.918619i
$351$	−22.7542	−	22.2364i	−1.21453	−	1.18689i
$352$	−2.11983	+	3.67165i	−0.112987	+	0.195699i
$353$	10.1452	+	10.7533i	0.539974	+	0.572339i	0.938702	−	0.344731i	$-0.112030\pi$
$353$	10.1452	+	10.7533i	0.539974	+	0.572339i	−0.398728	+	0.917069i	$0.630548\pi$
$354$	−5.62505	+	3.20382i	−0.298968	+	0.170281i
$355$	0.217581	−	3.73572i	0.0115480	−	0.198272i
$356$	6.51321	−	15.0993i	0.345199	−	0.800262i
$357$	−11.1183	−	17.1222i	−0.588443	−	0.906205i
$358$	−0.399296	−	6.85565i	−0.0211035	−	0.362332i
$359$	−22.1228	−	8.05203i	−1.16760	−	0.424970i	−0.315790	−	0.948829i	$-0.602270\pi$
$359$	−22.1228	−	8.05203i	−1.16760	−	0.424970i	−0.851805	+	0.523859i	$0.824492\pi$
$360$	2.68488	−	0.281964i	0.141505	−	0.0148608i
$361$	15.3403	−	5.58340i	0.807383	−	0.293863i
$362$	−9.47692	−	21.9700i	−0.498096	−	1.15472i
$363$	12.0557	+	0.773071i	0.632759	+	0.0405757i
$364$	28.2156	+	6.68721i	1.47890	+	0.350505i
$365$	1.25729	+	0.297983i	0.0658096	+	0.0155972i
$366$	5.43557	+	0.348556i	0.284122	+	0.0182193i
$367$	11.0697	+	25.6624i	0.577833	+	1.33957i	0.917017	+	0.398848i	$0.130590\pi$
$367$	11.0697	+	25.6624i	0.577833	+	1.33957i	−0.339184	+	0.940720i	$0.610151\pi$
$368$	7.14564	−	2.60080i	0.372492	−	0.135576i
$369$	15.4770	−	1.62539i	0.805701	−	0.0846142i
$370$	−7.57933	−	2.75865i	−0.394030	−	0.143415i
$371$	−0.614315	−	10.5474i	−0.0318937	−	0.547593i
$372$	1.74589	+	2.68868i	0.0905200	+	0.139401i
$373$	−5.01904	+	11.6354i	−0.259876	+	0.602460i	−0.997337	−	0.0729295i	$-0.976765\pi$
$373$	−5.01904	+	11.6354i	−0.259876	+	0.602460i	0.737461	+	0.675389i	$0.236024\pi$
$374$	0.613530	−	10.5339i	0.0317249	−	0.544695i
$375$	12.4469	−	7.08930i	0.642755	−	0.366090i
$376$	5.74529	+	6.08965i	0.296291	+	0.314050i
$377$	9.34023	−	16.1778i	0.481046	−	0.833197i
$378$	−6.09514	+	23.8417i	−0.313500	+	1.22628i
$379$	−4.98552	−	8.63517i	−0.256089	−	0.443559i	0.709102	−	0.705106i	$-0.249101\pi$
$379$	−4.98552	−	8.63517i	−0.256089	−	0.443559i	−0.965191	+	0.261547i	$0.915767\pi$
$380$	0.422133	−	1.41002i	0.0216550	−	0.0723326i
$381$	−3.78434	−	0.690170i	−0.193878	−	0.0353585i
$382$	8.28592	+	5.44974i	0.423945	+	0.278833i
$383$	−31.6256	+	3.69650i	−1.61599	+	0.188882i	−0.875512	−	0.483197i	$-0.839476\pi$
$383$	−31.6256	+	3.69650i	−1.61599	+	0.188882i	−0.740479	+	0.672079i	$0.765401\pi$
$384$	−0.389556	−	1.68767i	−0.0198794	−	0.0861238i
$385$	16.1464	+	8.10904i	0.822898	+	0.413275i
$386$	3.02468	+	17.1538i	0.153952	+	0.873105i
$387$	5.45809	+	5.92278i	0.277450	+	0.301072i
$388$	0.812536	−	4.60812i	0.0412503	−	0.233942i
$389$	−12.8269	+	17.2296i	−0.650351	+	0.873573i	−0.997945	−	0.0640717i	$-0.979591\pi$
$389$	−12.8269	+	17.2296i	−0.650351	+	0.873573i	0.347594	+	0.937645i	$0.386999\pi$
$390$	2.25521	−	9.27301i	0.114197	−	0.469557i
$391$	−12.9875	+	13.7660i	−0.656808	+	0.696176i
$392$	−4.42501	−	14.7806i	−0.223497	−	0.746531i
$393$	−0.207977	−	1.87456i	−0.0104911	−	0.0945589i
$394$	20.1412	+	2.35416i	1.01470	+	0.118601i
$395$	−3.56885	−	2.99462i	−0.179568	−	0.150676i
$396$	−9.83843	+	8.06084i	−0.494400	+	0.405073i
$397$	3.00463	−	2.52118i	0.150798	−	0.126535i	−0.564267	−	0.825592i	$-0.690841\pi$
$397$	3.00463	−	2.52118i	0.150798	−	0.126535i	0.715065	+	0.699058i	$0.246397\pi$
$398$	4.36579	−	2.87143i	0.218837	−	0.143932i
$399$	10.7147	+	8.07478i	0.536404	+	0.404244i
$400$	−2.50222	−	3.36107i	−0.125111	−	0.168053i
$401$	−22.9043	+	11.5030i	−1.14378	+	0.574430i	−0.916752	−	0.399457i	$-0.869199\pi$
$401$	−22.9043	+	11.5030i	−1.14378	+	0.574430i	−0.227032	+	0.973887i	$0.572902\pi$
$402$	2.88394	−	7.78139i	0.143838	−	0.388100i
$403$	11.0271	−	2.61347i	0.549299	−	0.130186i
$404$	−12.0004			−0.597043
$405$	7.83468	+	2.05192i	0.389308	+	0.101961i
$406$	−14.4490			−0.717090
$407$	36.9763	−	8.76353i	1.83284	−	0.434392i
$408$	2.75151	+	3.31842i	0.136220	+	0.164286i
$409$	−12.5591	+	6.30740i	−0.621006	+	0.311881i	−0.731339	−	0.682014i	$-0.761104\pi$
$409$	−12.5591	+	6.30740i	−0.621006	+	0.311881i	0.110333	+	0.993895i	$0.464808\pi$
$410$	2.78755	+	3.74433i	0.137667	+	0.184919i
$411$	−1.28070	+	10.4269i	−0.0631725	+	0.514320i
$412$	5.95005	−	3.91341i	0.293138	−	0.192800i
$413$	13.5591	−	11.3775i	0.667202	−	0.559849i
$414$	22.8111	+	0.267347i	1.12111	+	0.0131394i
$415$	−1.86684	−	1.56647i	−0.0916398	−	0.0768949i
$416$	−6.08145	−	0.710819i	−0.298168	−	0.0348508i
$417$	−22.3832	−	9.81113i	−1.09611	−	0.480453i
$418$	1.98882	+	6.64310i	0.0972761	+	0.324925i
$419$	27.6612	−	29.3192i	1.35134	−	1.43234i	0.548485	−	0.836160i	$-0.315205\pi$
$419$	27.6612	−	29.3192i	1.35134	−	1.43234i	0.802854	−	0.596176i	$-0.203314\pi$
$420$	−7.08374	+	2.07558i	−0.345651	+	0.101278i
$421$	10.5011	−	14.1054i	0.511791	−	0.687455i	−0.468848	−	0.883279i	$-0.655331\pi$
$421$	10.5011	−	14.1054i	0.511791	−	0.687455i	0.980639	+	0.195824i	$0.0627382\pi$
$422$	−1.73840	+	9.85894i	−0.0846239	+	0.479926i
$423$	9.67712	+	23.1772i	0.470517	+	1.12691i
$424$	0.387390	+	2.19700i	0.0188133	+	0.106696i
$425$	9.31944	+	4.68040i	0.452059	+	0.227033i
$426$	−6.88774	−	2.10611i	−0.333712	−	0.102041i
$427$	−14.7922	+	1.72895i	−0.715842	+	0.0836700i
$428$	−7.59243	−	4.99362i	−0.366994	−	0.241376i
$429$	15.1300	+	42.3397i	0.730485	+	2.04418i
$430$	−0.692899	+	2.31444i	−0.0334146	+	0.111612i
$431$	−12.3193	−	21.3377i	−0.593402	−	1.02780i	−0.993770	−	0.111448i	$-0.964451\pi$
$431$	−12.3193	−	21.3377i	−0.593402	−	1.02780i	0.400368	−	0.916354i	$-0.368882\pi$
$432$	0.693865	−	5.14962i	0.0333836	−	0.247761i
$433$	7.80606	−	13.5205i	0.375135	−	0.649754i	−0.615212	−	0.788362i	$-0.710930\pi$
$433$	7.80606	−	13.5205i	0.375135	−	0.649754i	0.990347	+	0.138608i	$0.0442629\pi$
$434$	−6.01526	−	6.37580i	−0.288742	−	0.306048i
$435$	−0.0278647	+	4.75524i	−0.00133601	+	0.227996i
$436$	−0.497417	+	8.54032i	−0.0238220	+	0.409007i
$437$	4.92627	−	11.4204i	0.235656	−	0.546311i
$438$	1.12917	−	2.21590i	0.0539540	−	0.105880i
$439$	−1.84393	−	31.6591i	−0.0880062	−	1.51101i	−0.696562	−	0.717497i	$-0.745288\pi$
$439$	−1.84393	−	31.6591i	−0.0880062	−	1.51101i	0.608556	−	0.793511i	$-0.291749\pi$
$440$	−3.58510	−	1.30487i	−0.170913	−	0.0622072i
$441$	3.23264	−	46.1732i	0.153935	−	2.19872i
$442$	14.3197	−	5.21194i	0.681118	−	0.247907i
$443$	6.05206	+	14.0302i	0.287542	+	0.666597i	0.999360	−	0.0357667i	$-0.0113873\pi$
$443$	6.05206	+	14.0302i	0.287542	+	0.666597i	−0.711818	+	0.702364i	$0.752128\pi$
$444$	−8.60677	+	12.9204i	−0.408459	+	0.613175i
$445$	14.3989	+	3.41261i	0.682574	+	0.161773i
$446$	22.0555	+	5.22726i	1.04436	+	0.247518i
$447$	−1.58034	−	3.19324i	−0.0747477	−	0.151035i
$448$	1.87579	+	4.34858i	0.0886229	+	0.205451i
$449$	−6.40822	+	2.33240i	−0.302423	+	0.110073i	−0.488774	−	0.872410i	$-0.662556\pi$
$449$	−6.40822	+	2.33240i	−0.302423	+	0.110073i	0.186352	+	0.982483i	$0.440334\pi$
$450$	−3.46392	−	12.0840i	−0.163291	−	0.569644i
$451$	−20.6663	−	7.52193i	−0.973140	−	0.354194i
$452$	0.309835	+	5.31967i	0.0145734	+	0.250216i
$453$	−15.3970	+	0.806277i	−0.723416	+	0.0378822i
$454$	1.14331	−	2.65048i	0.0536580	−	0.124393i
$455$	−1.51723	+	26.0499i	−0.0711289	+	1.22124i
$456$	−2.44508	−	1.43083i	−0.114501	−	0.0670049i
$457$	4.39074	+	4.65391i	0.205390	+	0.217701i	0.821878	−	0.569664i	$-0.192927\pi$
$457$	4.39074	+	4.65391i	0.205390	+	0.217701i	−0.616488	+	0.787364i	$0.711445\pi$
$458$	9.64722	−	16.7095i	0.450785	−	0.780782i
$459$	4.20881	+	12.2283i	0.196450	+	0.570767i
$460$	3.42145	+	5.92613i	0.159526	+	0.276307i
$461$	−0.513842	+	1.71635i	−0.0239320	+	0.0799385i	−0.969121	−	0.246584i	$-0.920692\pi$
$461$	−0.513842	+	1.71635i	−0.0239320	+	0.0799385i	0.945189	+	0.326523i	$0.105877\pi$
$462$	22.5100	−	26.5093i	1.04726	−	1.23333i
$463$	15.9861	+	10.5142i	0.742936	+	0.488637i	0.863676	−	0.504047i	$-0.168156\pi$
$463$	15.9861	+	10.5142i	0.742936	+	0.488637i	−0.120740	+	0.992684i	$0.538527\pi$
$464$	3.03031	−	0.354193i	0.140679	−	0.0164430i
$465$	−2.10991	+	1.96736i	−0.0978449	+	0.0912342i
$466$	24.3354	+	12.2217i	1.12732	+	0.566159i
$467$	−0.191366	−	1.08529i	−0.00885536	−	0.0502212i	0.980060	−	0.198702i	$-0.0636727\pi$
$467$	−0.191366	−	1.08529i	−0.00885536	−	0.0502212i	−0.988915	+	0.148481i	$0.952562\pi$
$468$	−16.3170	−	8.43559i	−0.754253	−	0.389935i
$469$	−3.94020	+	22.3460i	−0.181941	+	1.03184i
$470$	−4.49893	+	6.04312i	−0.207520	+	0.278748i
$471$	−4.92604	−	4.70234i	−0.226980	−	0.216672i
$472$	−2.56480	+	2.71852i	−0.118054	+	0.125130i
$473$	−3.26449	−	10.9041i	−0.150101	−	0.501373i
$474$	−7.22394	+	5.31252i	−0.331807	+	0.244012i
$475$	−6.80722	−	0.795650i	−0.312337	−	0.0365069i
$476$	−9.02923	−	7.57643i	−0.413854	−	0.347265i
$477$	−1.23933	+	6.57691i	−0.0567450	+	0.301136i
$478$	6.05943	−	5.08446i	0.277152	−	0.232558i
$479$	28.4725	−	18.7266i	1.30094	−	0.855642i	0.305608	−	0.952157i	$-0.401140\pi$
$479$	28.4725	−	18.7266i	1.30094	−	0.855642i	0.995331	+	0.0965158i	$0.0307698\pi$
$480$	1.43476	−	0.608949i	0.0654876	−	0.0277946i
$481$	32.7720	+	44.0204i	1.49428	+	2.00716i
$482$	−0.387375	+	0.194547i	−0.0176444	+	0.00886137i
$483$	−61.4909	+	10.4714i	−2.79793	+	0.476464i
$484$	6.78664	−	1.60846i	0.308484	−	0.0731120i
$485$	4.21073			0.191199
$486$	7.40117	−	13.7194i	0.335724	−	0.622326i
$487$	−6.28526			−0.284812			−0.142406	−	0.989808i	$-0.545484\pi$
$487$	−6.28526			−0.284812			−0.142406	+	0.989808i	$0.545484\pi$
$488$	3.05991	−	0.725211i	0.138515	−	0.0328288i
$489$	−18.7774	+	3.19762i	−0.849142	+	0.144602i
$490$	12.4072	−	6.23114i	0.560501	−	0.281494i
$491$	24.0769	+	32.3409i	1.08658	+	1.45952i	0.876227	+	0.481898i	$0.160052\pi$
$491$	24.0769	+	32.3409i	1.08658	+	1.45952i	0.210348	+	0.977627i	$0.432540\pi$
$492$	8.27070	−	3.51029i	0.372872	−	0.158256i
$493$	−6.34408	+	4.17257i	−0.285723	+	0.187923i
$494$	−7.67163	+	6.43726i	−0.345163	+	0.289626i
$495$	−8.68097	−	7.45930i	−0.390181	−	0.335271i
$496$	1.41784	+	1.18971i	0.0636631	+	0.0534197i
$497$	19.5605	+	2.28630i	0.877411	+	0.102555i
$498$	−3.77880	+	2.77895i	−0.169332	+	0.124528i
$499$	−6.22942	−	20.8077i	−0.278867	−	0.931481i	−0.976589	−	0.215112i	$-0.930988\pi$
$499$	−6.22942	−	20.8077i	−0.278867	−	0.931481i	0.697722	−	0.716368i	$-0.254197\pi$
$500$	5.67529	−	6.01545i	0.253806	−	0.269019i
$501$	−20.1227	−	19.2089i	−0.899014	−	0.858189i
$502$	−3.60285	+	4.83947i	−0.160803	+	0.215996i
$503$	2.83726	−	16.0909i	0.126507	−	0.717457i	−0.853894	−	0.520447i	$-0.825766\pi$
$503$	2.83726	−	16.0909i	0.126507	−	0.717457i	0.980401	−	0.197011i	$-0.0631234\pi$
$504$	0.659826	+	14.1924i	0.0293910	+	0.632178i
$505$	−1.87522	−	10.6349i	−0.0834460	−	0.473246i
$506$	−28.8101	−	14.4690i	−1.28077	−	0.643224i
$507$	−31.0228	+	28.9268i	−1.37777	+	1.28468i
$508$	−2.20591	+	0.257834i	−0.0978715	+	0.0114395i
$509$	−23.8891	−	15.7121i	−1.05887	−	0.696428i	−0.104337	−	0.994542i	$-0.533272\pi$
$509$	−23.8891	−	15.7121i	−1.05887	−	0.696428i	−0.954530	+	0.298115i	$0.903642\pi$
$510$	−2.51086	+	2.95696i	−0.111183	+	0.130937i
$511$	−1.95031	+	6.51450i	−0.0862768	+	0.288184i
$512$	−0.500000	−	0.866025i	−0.0220971	−	0.0382733i
$513$	−5.34769	−	6.60555i	−0.236106	−	0.291642i
$514$	−8.47257	+	14.6749i	−0.373709	+	0.647283i
$515$	4.39787	+	4.66147i	0.193793	+	0.205409i
$516$	4.01340	+	2.34860i	0.176680	+	0.103392i
$517$	2.06384	−	35.4348i	0.0907676	−	1.55842i
$518$	16.8130	−	38.9769i	0.738720	−	1.71255i
$519$	−20.0388	+	1.04935i	−0.879605	+	0.0460611i
$520$	−0.320368	−	5.50051i	−0.0140491	−	0.241213i
$521$	6.35056	+	2.31141i	0.278223	+	0.101265i	0.477363	−	0.878706i	$-0.341593\pi$
$521$	6.35056	+	2.31141i	0.278223	+	0.101265i	−0.199140	+	0.979971i	$0.563815\pi$
$522$	8.88076	+	2.21502i	0.388701	+	0.0969486i
$523$	41.5732	−	15.1314i	1.81787	−	0.661650i	0.822145	−	0.569278i	$-0.192777\pi$
$523$	41.5732	−	15.1314i	1.81787	−	0.661650i	0.995725	−	0.0923727i	$-0.0294451\pi$
$524$	−0.431298	−	0.999861i	−0.0188413	−	0.0436791i
$525$	15.2457	+	30.8054i	0.665376	+	1.34446i
$526$	−22.2377	−	5.27044i	−0.969610	−	0.229802i
$527$	−4.48231	−	1.06233i	−0.195253	−	0.0462757i
$528$	−4.07109	+	6.11148i	−0.177171	+	0.265968i
$529$	13.7932	+	31.9763i	0.599706	+	1.39027i
$530$	−1.88646	+	0.686617i	−0.0819428	+	0.0298247i
$531$	−10.0780	+	4.91433i	−0.437349	+	0.213264i
$532$	7.27894	+	2.64932i	0.315582	+	0.114863i
$533$	−1.84677	−	31.7078i	−0.0799924	−	1.37342i
$534$	12.9317	−	25.3772i	0.559609	−	1.09818i
$535$	3.23898	−	7.50880i	0.140033	−	0.324634i
$536$	0.278584	−	4.78311i	0.0120330	−	0.206599i
$537$	0.0696979	−	11.8943i	0.00300769	−	0.513275i
$538$	15.1971	+	16.1079i	0.655192	+	0.694463i
$539$	−32.7062	+	56.6489i	−1.40876	+	2.44004i
$540$	4.67206	−	0.189783i	0.201054	−	0.00816695i
$541$	2.15840	+	3.73845i	0.0927967	+	0.160729i	0.908687	−	0.417478i	$-0.137086\pi$
$541$	2.15840	+	3.73845i	0.0927967	+	0.160729i	−0.815890	+	0.578207i	$0.803753\pi$
$542$	4.85513	−	16.2173i	0.208546	−	0.696591i
$543$	−13.9457	−	39.0255i	−0.598468	−	1.67475i
$544$	2.07938	+	1.36763i	0.0891528	+	0.0586367i
$545$	−7.64624	+	0.893718i	−0.327529	+	0.0382827i
$546$	48.0294	+	14.6863i	2.05547	+	0.628514i
$547$	−29.0025	−	14.5656i	−1.24006	−	0.622779i	−0.296829	−	0.954931i	$-0.595929\pi$
$547$	−29.0025	−	14.5656i	−1.24006	−	0.622779i	−0.943226	+	0.332151i	$0.892226\pi$
$548$	1.05321	+	5.97306i	0.0449910	+	0.255157i
$549$	9.35675	+	1.20496i	0.399336	+	0.0514264i
$550$	−3.08487	+	17.4952i	−0.131539	+	0.745996i
$551$	2.97992	−	4.00272i	0.126949	−	0.170522i
$552$	12.6395	−	3.70346i	0.537974	−	0.157630i
$553$	16.8255	−	17.8340i	0.715495	−	0.758380i
$554$	6.83848	+	22.8421i	0.290539	+	0.970469i
$555$	−12.7951	−	5.60842i	−0.543122	−	0.238064i
$556$	−14.0145	−	1.63806i	−0.594346	−	0.0694691i
$557$	27.5704	+	23.1343i	1.16820	+	0.980233i	0.999985	−	0.00551749i	$-0.00175628\pi$
$557$	27.5704	+	23.1343i	1.16820	+	0.980233i	0.168212	+	0.985751i	$0.446201\pi$
$558$	2.71975	+	4.84089i	0.115136	+	0.204931i
$559$	12.5924	−	10.5663i	0.532602	−	0.446906i
$560$	−3.56064	+	2.34187i	−0.150464	+	0.0989619i
$561$	2.22807	−	18.1399i	0.0940690	−	0.765865i
$562$	3.62123	+	4.86416i	0.152753	+	0.205182i
$563$	10.7328	−	5.39023i	0.452335	−	0.227171i	−0.208020	−	0.978125i	$-0.566702\pi$
$563$	10.7328	−	5.39023i	0.452335	−	0.227171i	0.660355	+	0.750953i	$0.270406\pi$
$564$	9.25576	+	11.1628i	0.389738	+	0.470038i
$565$	−4.66592	+	1.10584i	−0.196297	+	0.0465232i
$566$	6.52622			0.274317
$567$	−13.1781	+	40.5348i	−0.553427	+	1.70230i
$568$	−4.15839			−0.174482
$569$	−29.2471	+	6.93169i	−1.22610	+	0.290592i	−0.792140	−	0.610339i	$-0.791033\pi$
$569$	−29.2471	+	6.93169i	−1.22610	+	0.290592i	−0.433963	+	0.900931i	$0.642885\pi$
$570$	0.885944	−	2.39043i	0.0371081	−	0.100124i
$571$	−18.7127	+	9.39786i	−0.783101	+	0.393288i	−0.794976	−	0.606641i	$-0.792516\pi$
$571$	−18.7127	+	9.39786i	−0.783101	+	0.393288i	0.0118744	+	0.999929i	$0.496220\pi$
$572$	15.5015	+	20.8221i	0.648150	+	0.870616i
$573$	13.7182	+	10.3383i	0.573085	+	0.431888i
$574$	−20.5253	+	13.4997i	−0.856711	+	0.563467i
$575$	24.4088	−	20.4814i	1.01792	−	0.854133i
$576$	−0.486285	−	2.96033i	−0.0202619	−	0.123347i
$577$	25.8767	+	21.7131i	1.07726	+	0.903928i	0.995690	−	0.0927399i	$-0.0295625\pi$
$577$	25.8767	+	21.7131i	1.07726	+	0.903928i	0.0815689	+	0.996668i	$0.474007\pi$
$578$	10.7327	+	1.25447i	0.446421	+	0.0521791i
$579$	3.32683	+	29.9856i	0.138258	+	1.24616i
$580$	0.787414	+	2.63015i	0.0326956	+	0.109211i
$581$	8.80134	−	9.32887i	0.365141	−	0.387027i
$582$	1.91523	−	7.87508i	0.0793890	−	0.326433i
$583$	5.64804	−	7.58663i	0.233918	−	0.314206i
$584$	0.249338	−	1.41406i	0.0103177	−	0.0585144i
$585$	4.92596	−	15.7784i	0.203664	−	0.652358i
$586$	−1.02439	−	5.80960i	−0.0423171	−	0.239992i
$587$	−5.91286	−	2.96955i	−0.244050	−	0.122567i	0.322570	−	0.946545i	$-0.395453\pi$
$587$	−5.91286	−	2.96955i	−0.244050	−	0.122567i	−0.566620	+	0.823979i	$0.691749\pi$
$588$	−6.01035	−	26.0387i	−0.247863	−	1.07382i
$589$	3.00683	−	0.351448i	0.123894	−	0.0144811i
$590$	−2.80996	−	1.84814i	−0.115684	−	0.0760868i
$591$	34.5531	+	6.30163i	1.42132	+	0.259214i
$592$	−2.57066	+	8.58659i	−0.105653	+	0.352907i
$593$	−0.624047	−	1.08088i	−0.0256266	−	0.0443865i	0.852928	−	0.522029i	$-0.174825\pi$
$593$	−0.624047	−	1.08088i	−0.0256266	−	0.0443865i	−0.878554	+	0.477643i	$0.841491\pi$
$594$	−17.8992	+	12.8427i	−0.734413	+	0.526941i
$595$	5.30337	−	9.18570i	0.217417	−	0.376577i
$596$	−1.41163	−	1.49624i	−0.0578226	−	0.0612883i
$597$	7.86454	−	4.47936i	0.321874	−	0.183328i
$598$	2.70720	−	46.4808i	0.110706	−	1.90074i
$599$	−16.0453	+	37.1971i	−0.655592	+	1.51983i	0.187615	+	0.982243i	$0.439924\pi$
$599$	−16.0453	+	37.1971i	−0.655592	+	1.51983i	−0.843207	+	0.537590i	$0.819335\pi$
$600$	−3.95255	−	6.08696i	−0.161362	−	0.248499i
$601$	−2.24413	−	38.5302i	−0.0915399	−	1.57168i	−0.661461	−	0.749980i	$-0.730063\pi$
$601$	−2.24413	−	38.5302i	−0.0915399	−	1.57168i	0.569921	−	0.821700i	$-0.306974\pi$
$602$	−11.9478	−	4.34866i	−0.486957	−	0.177238i
$603$	5.84739	−	13.1305i	0.238124	−	0.534714i
$604$	−8.36483	+	3.04455i	−0.340360	+	0.123881i
$605$	2.48594	+	5.76305i	0.101068	+	0.234301i
$606$	−20.7427	−	1.33013i	−0.842615	−	0.0540327i
$607$	−27.8613	−	6.60324i	−1.13085	−	0.268017i	−0.377743	−	0.925910i	$-0.623300\pi$
$607$	−27.8613	−	6.60324i	−1.13085	−	0.268017i	−0.753111	+	0.657893i	$0.771448\pi$
$608$	−1.59152	−	0.377198i	−0.0645448	−	0.0152974i
$609$	−24.9750	−	1.60153i	−1.01204	−	0.0648971i
$610$	1.12084	+	2.59840i	0.0453814	+	0.105206i
$611$	48.1697	−	17.5323i	1.94874	−	0.709283i
$612$	4.38818	+	6.04087i	0.177382	+	0.244188i
$613$	−3.45856	−	1.25881i	−0.139690	−	0.0508429i	0.271229	−	0.962515i	$-0.412570\pi$
$613$	−3.45856	−	1.25881i	−0.139690	−	0.0508429i	−0.410919	+	0.911672i	$0.634792\pi$
$614$	0.804349	+	13.8101i	0.0324609	+	0.557332i
$615$	4.40326	+	6.78104i	0.177556	+	0.273438i
$616$	7.95271	−	18.4365i	0.320424	−	0.742826i
$617$	−0.480387	+	8.24792i	−0.0193396	+	0.332049i	0.974736	+	0.223359i	$0.0717024\pi$
$617$	−0.480387	+	8.24792i	−0.0193396	+	0.332049i	−0.994076	+	0.108689i	$0.965335\pi$
$618$	10.7184	−	6.10483i	0.431159	−	0.245572i
$619$	−10.8014	−	11.4488i	−0.434143	−	0.460165i	0.472953	−	0.881087i	$-0.343188\pi$
$619$	−10.8014	−	11.4488i	−0.434143	−	0.460165i	−0.907097	+	0.420923i	$0.861706\pi$
$620$	−0.832779	+	1.44242i	−0.0334452	+	0.0579288i
$621$	39.3994	+	2.99050i	1.58104	+	0.120005i
$622$	10.6443	+	18.4365i	0.426798	+	0.739236i
$623$	−22.3356	+	74.6063i	−0.894859	+	2.98904i
$624$	−10.4330	−	1.90272i	−0.417654	−	0.0761698i
$625$	−11.2866	−	7.42330i	−0.451463	−	0.296932i
$626$	−13.4077	+	1.56714i	−0.535880	+	0.0626354i
$627$	2.70135	+	11.7031i	0.107881	+	0.467375i
$628$	−3.51361	−	1.76460i	−0.140208	−	0.0704152i
$629$	−3.87369	−	21.9688i	−0.154454	−	0.875952i
$630$	−12.4743	+	2.80248i	−0.496988	+	0.111654i
$631$	6.42930	−	36.4624i	0.255947	−	1.45155i	−0.537685	−	0.843146i	$-0.680701\pi$
$631$	6.42930	−	36.4624i	0.255947	−	1.45155i	0.793631	−	0.608399i	$-0.208188\pi$
$632$	−3.09157	+	4.15270i	−0.122976	+	0.165186i
$633$	−4.09759	+	16.8485i	−0.162865	+	0.669668i
$634$	−6.05013	+	6.41277i	−0.240281	+	0.254683i
$635$	−0.573197	−	1.91461i	−0.0227466	−	0.0759790i
$636$	0.426088	+	3.84045i	0.0168955	+	0.152284i
$637$	−93.8291	−	10.9670i	−3.71764	−	0.434530i
$638$	−9.90873	−	8.31442i	−0.392291	−	0.329171i
$639$	−11.6720	−	4.40385i	−0.461738	−	0.174214i
$640$	0.689349	−	0.578432i	0.0272489	−	0.0228645i
$641$	−39.3612	+	25.8883i	−1.55467	+	1.02253i	−0.575916	+	0.817509i	$0.695355\pi$
$641$	−39.3612	+	25.8883i	−1.55467	+	1.02253i	−0.978758	+	0.205017i	$0.934275\pi$
$642$	−12.5700	−	9.47303i	−0.496100	−	0.373871i
$643$	3.24751	+	4.36216i	0.128069	+	0.172027i	0.861533	−	0.507702i	$-0.169505\pi$
$643$	3.24751	+	4.36216i	0.128069	+	0.172027i	−0.733464	+	0.679729i	$0.762097\pi$
$644$	−32.1823	+	16.1626i	−1.26816	+	0.636894i
$645$	−1.45421	+	3.92372i	−0.0572594	+	0.154496i
$646$	3.96102	−	0.938780i	0.155844	−	0.0369358i
$647$	25.2978			0.994557			0.497279	−	0.867591i	$-0.334333\pi$
$647$	25.2978			0.994557			0.497279	+	0.867591i	$0.334333\pi$
$648$	1.77013	−	8.82421i	0.0695373	−	0.346648i
$649$	15.8455			0.621990
$650$	−24.9645	+	5.91669i	−0.979188	+	0.232072i
$651$	−9.69068	−	11.6873i	−0.379808	−	0.458062i
$652$	−9.82745	+	4.93553i	−0.384873	+	0.193290i
$653$	−18.2201	−	24.4739i	−0.713008	−	0.957736i	0.286992	−	0.957933i	$-0.407345\pi$
$653$	−18.2201	−	24.4739i	−0.713008	−	0.957736i	−1.00000		0.000197051i	$0.999937\pi$
$654$	−1.80640	+	14.7068i	−0.0706357	+	0.575082i
$655$	0.818691	−	0.538461i	0.0319889	−	0.0210394i
$656$	3.97376	−	3.33438i	0.155149	−	0.130186i
$657$	2.19739	−	3.70503i	0.0857283	−	0.144547i
$658$	−30.3732	−	25.4862i	−1.18407	−	0.993555i
$659$	−18.6840	−	2.18385i	−0.727826	−	0.0850706i	−0.255893	−	0.966705i	$-0.582369\pi$
$659$	−18.6840	−	2.18385i	−0.727826	−	0.0850706i	−0.471933	+	0.881635i	$0.656443\pi$
$660$	−6.05221	−	2.65284i	−0.235582	−	0.103262i
$661$	−0.384072	−	1.28289i	−0.0149387	−	0.0498987i	0.950195	−	0.311655i	$-0.100883\pi$
$661$	−0.384072	−	1.28289i	−0.0149387	−	0.0498987i	−0.965134	+	0.261757i	$0.915698\pi$
$662$	−2.07452	+	2.19887i	−0.0806286	+	0.0854613i
$663$	25.3293	−	7.42165i	0.983708	−	0.288233i
$664$	−1.61718	+	2.17225i	−0.0627588	+	0.0842997i
$665$	−1.21042	+	6.86466i	−0.0469383	+	0.266200i
$666$	−16.3089	+	21.3790i	−0.631957	+	0.828418i
$667$	4.02865	+	22.8476i	0.155990	+	0.884664i
$668$	−14.3530	−	7.20833i	−0.555333	−	0.278899i
$669$	37.5436	+	11.4800i	1.45152	+	0.443841i
$670$	4.28237	−	0.500537i	0.165442	−	0.0193374i
$671$	−11.1390	−	7.32623i	−0.430016	−	0.282826i
$672$	2.76031	+	7.72443i	0.106481	+	0.297977i
$673$	−8.59506	+	28.7095i	−0.331315	+	1.10667i	0.616368	+	0.787458i	$0.288603\pi$
$673$	−8.59506	+	28.7095i	−0.331315	+	1.10667i	−0.947683	+	0.319212i	$0.896582\pi$
$674$	−1.07856	−	1.86811i	−0.0415444	−	0.0719570i
$675$	−4.64801	−	21.2711i	−0.178902	−	0.818725i
$676$	−12.2446	+	21.2083i	−0.470948	+	0.815705i
$677$	−10.4366	−	11.0621i	−0.401110	−	0.425152i	0.495062	−	0.868857i	$-0.335145\pi$
$677$	−10.4366	−	11.0621i	−0.401110	−	0.425152i	−0.896173	+	0.443705i	$0.853664\pi$
$678$	−0.0540824	+	9.22939i	−0.00207702	+	0.354453i
$679$	−1.28850	+	22.1228i	−0.0494483	+	0.848994i
$680$	−0.887079	+	2.05648i	−0.0340179	+	0.0788624i
$681$	2.26999	−	4.45464i	0.0869861	−	0.170702i
$682$	−0.456264	−	7.83375i	−0.0174712	−	0.299970i
$683$	−32.1031	−	11.6846i	−1.22839	−	0.447098i	−0.355346	−	0.934735i	$-0.615637\pi$
$683$	−32.1031	−	11.6846i	−1.22839	−	0.447098i	−0.873047	+	0.487637i	$0.837859\pi$
$684$	−4.06772	−	2.74421i	−0.155533	−	0.104927i
$685$	−5.12881	+	1.86673i	−0.195962	+	0.0713242i
$686$	15.8106	+	36.6530i	0.603650	+	1.39942i
$687$	18.5273	−	27.8130i	0.706861	−	1.06113i
$688$	2.61236	+	0.619142i	0.0995955	+	0.0236046i
$689$	13.2912	+	3.15007i	0.506354	+	0.120008i
$690$	5.25713	+	10.6226i	0.200135	+	0.404394i
$691$	−3.28549	−	7.61662i	−0.124986	−	0.289750i	0.844222	−	0.535994i	$-0.180063\pi$
$691$	−3.28549	−	7.61662i	−0.124986	−	0.289750i	−0.969208	+	0.246244i	$0.920804\pi$
$692$	−10.8866	+	3.96239i	−0.413845	+	0.150627i
$693$	41.8469	−	43.3264i	1.58963	−	1.64583i
$694$	27.2575	+	9.92091i	1.03468	+	0.376593i
$695$	−0.738277	−	12.6757i	−0.0280044	−	0.480818i
$696$	5.27716	−	0.276342i	0.200030	−	0.0104747i
$697$	−5.11358	+	11.8546i	−0.193690	+	0.449025i
$698$	1.52380	−	26.1626i	0.0576766	−	0.990269i
$699$	40.7091	+	23.8226i	1.53976	+	0.901052i
$700$	13.6181	+	14.4343i	0.514715	+	0.545566i
$701$	20.0087	−	34.6561i	0.755718	−	1.30894i	−0.189298	−	0.981920i	$-0.560621\pi$
$701$	20.0087	−	34.6561i	0.755718	−	1.30894i	0.945016	−	0.327023i	$-0.106045\pi$
$702$	−27.2689	−	16.3895i	−1.02920	−	0.618582i
$703$	7.33010	+	12.6961i	0.276460	+	0.478843i
$704$	−1.21595	+	4.06154i	−0.0458277	+	0.153075i
$705$	−8.44623	+	9.94687i	−0.318103	+	0.374621i
$706$	12.3516	+	8.12377i	0.464858	+	0.305742i
$707$	56.4484	−	6.59788i	2.12296	−	0.248139i
$708$	−4.73457	+	4.41469i	−0.177936	+	0.165914i
$709$	26.9452	+	13.5324i	1.01195	+	0.508219i	0.875905	−	0.482483i	$-0.160265\pi$
$709$	26.9452	+	13.5324i	1.01195	+	0.508219i	0.136043	+	0.990703i	$0.456561\pi$
$710$	−0.649801	−	3.68520i	−0.0243866	−	0.138303i
$711$	−13.0754	+	8.38199i	−0.490367	+	0.314349i
$712$	2.85550	−	16.1944i	0.107014	−	0.606909i
$713$	−8.40466	+	11.2894i	−0.314757	+	0.422792i
$714$	−14.7673	−	14.0967i	−0.552651	−	0.527554i
$715$	−16.0305	+	16.9913i	−0.599505	+	0.635438i
$716$	−1.96956	−	6.57877i	−0.0736057	−	0.245860i
$717$	11.0373	−	8.11687i	0.412195	−	0.303130i
$718$	−23.3834	−	2.73313i	−0.872660	−	0.101999i
$719$	−20.1751	−	16.9289i	−0.752404	−	0.631342i	0.183733	−	0.982976i	$-0.441182\pi$
$719$	−20.1751	−	16.9289i	−0.752404	−	0.631342i	−0.936138	+	0.351634i	$0.885626\pi$
$720$	2.54748	−	0.893539i	0.0949390	−	0.0333002i
$721$	−25.8367	+	21.6796i	−0.962209	+	0.807389i
$722$	13.6392	−	8.97061i	0.507597	−	0.333852i
$723$	−0.691141	+	0.293338i	−0.0257038	+	0.0109094i
$724$	−14.2881	−	19.1922i	−0.531013	−	0.713274i
$725$	11.4243	−	5.73750i	0.424288	−	0.213085i
$726$	11.9090	−	2.02800i	0.441984	−	0.0752661i
$727$	−37.7796	+	8.95394i	−1.40117	+	0.332083i	−0.860628	−	0.509234i	$-0.829929\pi$
$727$	−37.7796	+	8.95394i	−1.40117	+	0.332083i	−0.540542	+	0.841317i	$0.681781\pi$
$728$	28.9972			1.07471
$729$	14.3136	−	22.8937i	0.530133	−	0.847915i
$730$	1.29212			0.0478235
$731$	−6.50172	+	1.54094i	−0.240475	+	0.0569936i
$732$	5.36943	−	0.914368i	0.198460	−	0.0337960i
$733$	23.1712	−	11.6370i	0.855849	−	0.429823i	0.0339274	−	0.999424i	$-0.489198\pi$
$733$	23.1712	−	11.6370i	0.855849	−	0.429823i	0.821921	+	0.569601i	$0.192902\pi$
$734$	16.6895	+	22.4178i	0.616019	+	0.827458i
$735$	22.1365	−	9.39531i	0.816519	−	0.346551i
$736$	6.35325	−	4.17860i	0.234184	−	0.154025i
$737$	−15.5607	+	13.0570i	−0.573186	+	0.480960i
$738$	14.6850	−	5.15082i	0.540562	−	0.189604i
$739$	15.3874	+	12.9116i	0.566034	+	0.474959i	0.880327	−	0.474367i	$-0.157323\pi$
$739$	15.3874	+	12.9116i	0.566034	+	0.474959i	−0.314293	+	0.949326i	$0.601767\pi$
$740$	−8.01121	−	0.936377i	−0.294498	−	0.0344219i
$741$	−13.9739	+	10.2765i	−0.513345	+	0.377516i
$742$	−3.03015	−	10.1214i	−0.111240	−	0.371569i
$743$	10.1530	−	10.7616i	0.372478	−	0.394804i	−0.513836	−	0.857889i	$-0.671776\pi$
$743$	10.1530	−	10.7616i	0.372478	−	0.394804i	0.886314	+	0.463085i	$0.153257\pi$
$744$	2.31888	+	2.21357i	0.0850142	+	0.0811536i
$745$	1.10540	−	1.48480i	0.0404986	−	0.0543990i
$746$	−2.20043	+	12.4793i	−0.0805635	+	0.456899i
$747$	−6.83968	+	4.38457i	−0.250251	+	0.160423i
$748$	−1.83229	−	10.3914i	−0.0669953	−	0.379949i
$749$	38.4594	+	19.3150i	1.40528	+	0.705756i
$750$	10.4765	−	9.76866i	0.382547	−	0.356701i
$751$	16.2830	−	1.90321i	0.594176	−	0.0694492i	0.186310	−	0.982491i	$-0.440347\pi$
$751$	16.2830	−	1.90321i	0.594176	−	0.0694492i	0.407866	+	0.913042i	$0.366273\pi$
$752$	6.99479	+	4.60055i	0.255074	+	0.167765i
$753$	−6.76394	+	7.96569i	−0.246492	+	0.290286i
$754$	5.35762	−	17.8957i	0.195113	−	0.651722i
$755$	−4.00522	−	6.93725i	−0.145765	−	0.252472i
$756$	−0.432575	+	24.6046i	−0.0157326	+	0.894862i
$757$	−0.252679	+	0.437653i	−0.00918377	+	0.0159068i	−0.870581	−	0.492026i	$-0.836257\pi$
$757$	−0.252679	+	0.437653i	−0.00918377	+	0.0159068i	0.861397	+	0.507932i	$0.169590\pi$
$758$	−6.84254	−	7.25267i	−0.248532	−	0.263429i
$759$	−48.1945	−	28.2029i	−1.74935	−	1.02370i
$760$	0.0855808	−	1.46937i	0.00310434	−	0.0532995i
$761$	−7.50717	+	17.4036i	−0.272135	+	0.630879i	−0.998401	−	0.0565345i	$-0.981995\pi$
$761$	−7.50717	+	17.4036i	−0.272135	+	0.630879i	0.726266	+	0.687414i	$0.241254\pi$
$762$	−3.84150	+	0.201163i	−0.139163	+	0.00728736i
$763$	−2.35572	−	40.4461i	−0.0852827	−	1.46425i
$764$	9.31937	+	3.39197i	0.337163	+	0.122717i
$765$	−4.66777	+	4.83281i	−0.168764	+	0.174731i
$766$	−29.9206	+	10.8902i	−1.08108	+	0.393480i
$767$	9.06383	+	21.0123i	0.327276	+	0.758711i
$768$	−0.768260	−	1.55235i	−0.0277222	−	0.0560154i
$769$	25.7141	+	6.09434i	0.927273	+	0.219768i	0.666390	−	0.745603i	$-0.267838\pi$
$769$	25.7141	+	6.09434i	0.927273	+	0.219768i	0.260882	+	0.965371i	$0.415987\pi$
$770$	17.5813	+	4.16684i	0.633585	+	0.150162i
$771$	−16.2714	+	24.4265i	−0.586000	+	0.879699i
$772$	6.89908	+	15.9939i	0.248303	+	0.575632i
$773$	−43.8623	+	15.9646i	−1.57762	+	0.574205i	−0.974684	−	0.223587i	$-0.928223\pi$
$773$	−43.8623	+	15.9646i	−1.57762	+	0.574205i	−0.602932	+	0.797793i	$0.706001\pi$
$774$	6.67685	+	4.50441i	0.239994	+	0.161908i
$775$	7.28781	+	2.65254i	0.261786	+	0.0952822i
$776$	−0.272072	−	4.67129i	−0.00976681	−	0.167690i
$777$	33.3815	−	65.5080i	1.19755	−	2.35009i
$778$	−8.50777	+	19.7232i	−0.305018	+	0.707112i
$779$	0.493332	−	8.47018i	0.0176754	−	0.303476i
$780$	0.0559209	−	9.54315i	0.00200229	−	0.341700i
$781$	12.0985	+	12.8237i	0.432919	+	0.458868i
$782$	−9.46281	+	16.3901i	−0.338389	+	0.586107i
$783$	15.1049	+	4.81300i	0.539805	+	0.172003i
$784$	−7.71437	−	13.3617i	−0.275513	−	0.477203i
$785$	1.01476	−	3.38954i	0.0362183	−	0.120978i
$786$	−0.634674	−	1.77607i	−0.0226381	−	0.0633502i
$787$	15.5522	+	10.2289i	0.554377	+	0.364619i	0.795574	−	0.605857i	$-0.207170\pi$
$787$	15.5522	+	10.2289i	0.554377	+	0.364619i	−0.241197	+	0.970476i	$0.577540\pi$
$788$	20.1412	−	2.35416i	0.717499	−	0.0838636i
$789$	−37.8537	−	11.5748i	−1.34763	−	0.412073i
$790$	−4.16326	−	2.09087i	−0.148122	−	0.0743898i
$791$	−4.38220	−	24.8527i	−0.155813	−	0.883660i
$792$	−7.71427	+	10.1125i	−0.274115	+	0.359331i
$793$	3.34348	−	18.9618i	0.118731	−	0.673355i
$794$	2.34221	−	3.14614i	0.0831221	−	0.111652i
$795$	−3.33686	+	0.977721i	−0.118346	+	0.0346762i
$796$	3.58592	−	3.80085i	0.127099	−	0.134717i
$797$	5.36478	+	17.9196i	0.190030	+	0.634746i	0.998906	+	0.0467657i	$0.0148914\pi$
$797$	5.36478	+	17.9196i	0.190030	+	0.634746i	−0.808876	+	0.587980i	$0.799923\pi$
$798$	12.2880	+	5.38615i	0.434991	+	0.190668i
$799$	−20.6958	−	2.41900i	−0.732166	−	0.0855779i
$800$	−3.20989	−	2.69342i	−0.113487	−	0.0952267i
$801$	25.1653	−	42.4312i	0.889171	−	1.49923i
$802$	−19.6341	+	16.4750i	−0.693305	+	0.581752i
$803$	−5.08614	+	3.34521i	−0.179486	+	0.118050i
$804$	1.01169	−	8.23672i	0.0356797	−	0.290487i
$805$	−19.3523	−	25.9946i	−0.682079	−	0.916191i
$806$	10.1271	−	5.08605i	0.356714	−	0.179148i
$807$	24.4827	+	29.5270i	0.861833	+	1.03940i
$808$	−11.6769	+	2.76748i	−0.410793	+	0.0973598i
$809$	0.742090			0.0260905			0.0130452	−	0.999915i	$-0.495847\pi$
$809$	0.742090			0.0260905			0.0130452	+	0.999915i	$0.495847\pi$
$810$	8.09670	+	0.189813i	0.284489	+	0.00666934i
$811$	54.1951			1.90305			0.951524	−	0.307575i	$-0.0995176\pi$
$811$	54.1951			1.90305			0.951524	+	0.307575i	$0.0995176\pi$
$812$	−14.0595	+	3.33216i	−0.493391	+	0.116936i
$813$	10.1896	−	27.4934i	0.357366	−	0.964236i
$814$	33.9585	−	17.0546i	1.19025	−	0.597764i
$815$	−5.90958	−	7.93794i	−0.207003	−	0.278054i
$816$	3.44263	+	2.59443i	0.120516	+	0.0908233i
$817$	3.66878	−	2.41299i	0.128354	−	0.0844199i
$818$	−10.7659	+	9.03370i	−0.376423	+	0.315856i
$819$	81.3910	+	30.7088i	2.84403	+	1.07305i
$820$	3.57591	+	3.00054i	0.124876	+	0.104784i
$821$	22.7451	+	2.65852i	0.793809	+	0.0927830i	0.503326	−	0.864097i	$-0.332110\pi$
$821$	22.7451	+	2.65852i	0.793809	+	0.0927830i	0.290484	+	0.956880i	$0.406184\pi$
$822$	1.15842	+	10.4412i	0.0404046	+	0.364178i
$823$	−10.4292	−	34.8359i	−0.363539	−	1.21430i	−0.922789	−	0.385306i	$-0.874096\pi$
$823$	−10.4292	−	34.8359i	−0.363539	−	1.21430i	0.559250	−	0.828999i	$-0.311089\pi$
$824$	4.88717	−	5.18010i	0.170253	−	0.180457i
$825$	−7.27136	+	29.8985i	−0.253156	+	1.04093i
$826$	10.5698	−	14.1977i	0.367771	−	0.494002i
$827$	−5.01639	+	28.4493i	−0.174437	+	0.989281i	0.764355	+	0.644796i	$0.223058\pi$
$827$	−5.01639	+	28.4493i	−0.174437	+	0.989281i	−0.938792	+	0.344485i	$0.888054\pi$
$828$	22.2579	−	5.00047i	0.773516	−	0.173778i
$829$	1.94646	+	11.0389i	0.0676032	+	0.383397i	0.999772	+	0.0213718i	$0.00680336\pi$
$829$	1.94646	+	11.0389i	0.0676032	+	0.383397i	−0.932168	+	0.362025i	$0.882086\pi$
$830$	−2.17778	−	1.09372i	−0.0755917	−	0.0379636i
$831$	9.28850	+	40.2406i	0.322214	+	1.39593i
$832$	−6.08145	+	0.710819i	−0.210836	+	0.0246432i
$833$	32.0823	+	21.1008i	1.11158	+	0.731101i
$834$	−24.0425	−	4.38475i	−0.832522	−	0.151831i
$835$	4.14526	−	13.8461i	0.143453	−	0.479165i
$836$	3.46721	+	6.00539i	0.119916	+	0.207701i
$837$	4.16453	+	8.66895i	0.143947	+	0.299643i
$838$	20.1541	−	34.9080i	0.696213	−	1.20588i
$839$	9.69596	+	10.2771i	0.334742	+	0.354806i	0.872779	−	0.488116i	$-0.162316\pi$
$839$	9.69596	+	10.2771i	0.334742	+	0.354806i	−0.538037	+	0.842921i	$0.680834\pi$
$840$	−6.41413	+	3.65326i	−0.221309	+	0.126049i
$841$	1.14497	−	19.6584i	0.0394818	−	0.677877i
$842$	6.96509	−	16.1469i	0.240033	−	0.556459i
$843$	5.72016	+	8.80909i	0.197013	+	0.303401i
$844$	0.582090	+	9.99410i	0.0200364	+	0.344011i
$845$	−20.7084	−	7.53724i	−0.712391	−	0.259289i
$846$	14.7613	+	20.3208i	0.507504	+	0.698643i
$847$	−31.0392	+	11.2973i	−1.06652	+	0.388181i
$848$	0.883610	+	2.04844i	0.0303433	+	0.0703436i
$849$	11.2806	+	0.723367i	0.387148	+	0.0248259i
$850$	10.1476	+	2.40503i	0.348060	+	0.0824917i
$851$	−66.3206	−	15.7183i	−2.27344	−	0.538815i
$852$	−7.18778	−	0.460917i	−0.246249	−	0.0157907i
$853$	1.24036	+	2.87547i	0.0424690	+	0.0984543i	0.938130	−	0.346283i	$-0.112556\pi$
$853$	1.24036	+	2.87547i	0.0424690	+	0.0984543i	−0.895661	+	0.444737i	$0.853297\pi$
$854$	−13.9947	+	5.09365i	−0.478889	+	0.174301i
$855$	1.79631	−	4.03367i	0.0614325	−	0.137949i
$856$	−8.53939	−	3.10808i	−0.291870	−	0.106232i
$857$	1.40729	+	24.1622i	0.0480721	+	0.825365i	0.933053	+	0.359738i	$0.117134\pi$
$857$	1.40729	+	24.1622i	0.0480721	+	0.825365i	−0.884981	+	0.465627i	$0.845829\pi$
$858$	24.4864	+	37.7092i	0.835952	+	1.28737i
$859$	−16.7443	+	38.8176i	−0.571308	+	1.32444i	0.350416	+	0.936594i	$0.386040\pi$
$859$	−16.7443	+	38.8176i	−0.571308	+	1.32444i	−0.921724	+	0.387846i	$0.873219\pi$
$860$	−0.140474	+	2.41185i	−0.00479013	+	0.0822434i
$861$	−36.9744	+	21.0592i	−1.26008	+	0.717697i
$862$	−16.9081	−	17.9215i	−0.575892	−	0.610410i
$863$	26.7136	−	46.2693i	0.909341	−	1.57502i	0.0943581	−	0.995538i	$-0.469920\pi$
$863$	26.7136	−	46.2693i	0.909341	−	1.57502i	0.814982	−	0.579486i	$-0.196747\pi$
$864$	−0.512421	−	5.17082i	−0.0174329	−	0.175915i
$865$	−5.21267	−	9.02861i	−0.177236	−	0.306982i
$866$	4.47761	−	14.9563i	0.152155	−	0.508234i
$867$	18.4124	+	3.35797i	0.625318	+	0.114043i
$868$	−7.32348	−	4.81673i	−0.248575	−	0.163490i
$869$	21.8008	−	2.54815i	0.739543	−	0.0864402i
$870$	1.06952	+	4.63349i	0.0362601	+	0.157090i
$871$	−26.2155	−	13.1659i	−0.888278	−	0.446110i
$872$	1.48552	+	8.42483i	0.0503062	+	0.285301i
$873$	4.18336	−	13.3998i	0.141585	−	0.453514i
$874$	2.15976	−	12.2486i	0.0730550	−	0.414316i
$875$	−23.3885	+	31.4162i	−0.790676	+	1.06206i
$876$	0.587716	−	2.41657i	0.0198571	−	0.0816485i
$877$	4.64672	−	4.92524i	0.156909	−	0.166314i	−0.644150	−	0.764899i	$-0.722789\pi$
$877$	4.64672	−	4.92524i	0.156909	−	0.166314i	0.801059	+	0.598585i	$0.204270\pi$
$878$	−9.09533	−	30.3805i	−0.306952	−	1.02529i
$879$	−1.12672	−	10.1554i	−0.0380033	−	0.342534i
$880$	−3.78938	−	0.442915i	−0.127740	−	0.0149307i
$881$	−30.0377	−	25.2046i	−1.01199	−	0.849164i	−0.0233941	−	0.999726i	$-0.507447\pi$
$881$	−30.0377	−	25.2046i	−1.01199	−	0.849164i	−0.988601	+	0.150562i	$0.951892\pi$
$882$	−7.50277	−	45.6741i	−0.252631	−	1.53793i
$883$	−28.9431	+	24.2861i	−0.974012	+	0.817293i	−0.983175	−	0.182665i	$-0.941528\pi$
$883$	−28.9431	+	24.2861i	−0.974012	+	0.817293i	0.00916322	+	0.999958i	$0.497083\pi$
$884$	12.7317	−	8.37380i	0.428215	−	0.281641i
$885$	−4.65218	−	3.50597i	−0.156381	−	0.117852i
$886$	9.12452	+	12.2564i	0.306544	+	0.411760i
$887$	−19.6726	+	9.87993i	−0.660540	+	0.331736i	−0.747293	−	0.664494i	$-0.768647\pi$
$887$	−19.6726	+	9.87993i	−0.660540	+	0.331736i	0.0867535	+	0.996230i	$0.472351\pi$
$888$	−5.39512	+	14.5570i	−0.181048	+	0.488501i
$889$	10.2346	−	2.42564i	0.343257	−	0.0813533i
$890$	14.7978			0.496023
$891$	−32.3623	+	20.2146i	−1.08418	+	0.677215i
$892$	22.6665			0.758931
$893$	13.3244	−	3.15794i	0.445884	−	0.105677i
$894$	−2.27416	−	2.74271i	−0.0760592	−	0.0917301i
$895$	5.52240	−	2.77346i	0.184594	−	0.0927064i
$896$	2.82808	+	3.79877i	0.0944796	+	0.126908i
$897$	9.83134	−	80.0420i	0.328259	−	2.67253i
$898$	−5.69760	+	3.74737i	−0.190131	+	0.125051i
$899$	−4.32576	+	3.62975i	−0.144272	+	0.121059i
$900$	−6.15731	−	10.9594i	−0.205244	−	0.365314i
$901$	−4.25330	−	3.56894i	−0.141698	−	0.118899i
$902$	−21.8440	−	2.55319i	−0.727324	−	0.0850120i
$903$	−20.1698	−	8.84095i	−0.671210	−	0.294208i
$904$	1.52828	+	5.10482i	0.0508299	+	0.169784i
$905$	14.7757	−	15.6613i	0.491159	−	0.520598i
$906$	−14.7961	+	4.33535i	−0.491567	+	0.144032i
$907$	12.6817	−	17.0345i	0.421089	−	0.565620i	−0.540069	−	0.841621i	$-0.681602\pi$
$907$	12.6817	−	17.0345i	0.421089	−	0.565620i	0.961157	+	0.276001i	$0.0890092\pi$
$908$	0.501245	−	2.84270i	0.0166344	−	0.0943384i
$909$	−35.7064	−	4.59825i	−1.18431	−	0.152514i
$910$	4.53118	+	25.6976i	0.150207	+	0.851867i
$911$	38.1183	+	19.1437i	1.26292	+	0.634260i	0.949025	−	0.315199i	$-0.102071\pi$
$911$	38.1183	+	19.1437i	1.26292	+	0.634260i	0.313890	+	0.949459i	$0.398368\pi$
$912$	−2.70914	−	0.828392i	−0.0897086	−	0.0274308i
$913$	11.4039	−	1.33292i	0.377414	−	0.0441133i
$914$	5.34565	+	3.51589i	0.176818	+	0.116295i
$915$	1.64936	+	4.61556i	0.0545263	+	0.152586i
$916$	5.53371	−	18.4839i	0.182839	−	0.610724i
$917$	2.57850	+	4.46609i	0.0851496	+	0.147483i
$918$	6.91540	+	10.9280i	0.228242	+	0.360679i
$919$	−3.54171	+	6.13441i	−0.116830	+	0.202356i	−0.918510	−	0.395398i	$-0.870607\pi$
$919$	−3.54171	+	6.13441i	−0.116830	+	0.202356i	0.801680	+	0.597754i	$0.203940\pi$
$920$	4.69589	+	4.97735i	0.154819	+	0.164098i
$921$	−0.140401	+	23.9600i	−0.00462636	+	0.789508i
$922$	−0.104173	+	1.78859i	−0.00343077	+	0.0589040i
$923$	−10.0847	+	23.3789i	−0.331941	+	0.769525i
$924$	15.7898	−	30.9859i	0.519445	−	1.01936i
$925$	2.18377	+	37.4939i	0.0718020	+	1.23279i
$926$	17.9799	+	6.54416i	0.590857	+	0.215054i
$927$	19.2035	−	9.36417i	0.630725	−	0.307560i
$928$	2.86695	−	1.04348i	0.0941122	−	0.0342540i
$929$	−0.339206	−	0.786369i	−0.0111290	−	0.0257999i	0.912561	−	0.408941i	$-0.134102\pi$
$929$	−0.339206	−	0.786369i	−0.0111290	−	0.0257999i	−0.923690	+	0.383141i	$0.874842\pi$
$930$	−1.59934	+	2.40091i	−0.0524443	+	0.0787289i
$931$	−24.5552	−	5.81969i	−0.804764	−	0.190733i
$932$	26.4980	+	6.28013i	0.867969	+	0.205713i
$933$	16.3552	+	33.0473i	0.535445	+	1.08192i
$934$	−0.436493	−	1.01190i	−0.0142825	−	0.0331105i
$935$	8.92268	−	3.24759i	0.291803	−	0.106208i
$936$	−17.8225	−	4.44525i	−0.582548	−	0.145298i
$937$	15.4751	+	5.63247i	0.505549	+	0.184005i	0.582188	−	0.813054i	$-0.302197\pi$
$937$	15.4751	+	5.63247i	0.505549	+	0.184005i	−0.0766392	+	0.997059i	$0.524419\pi$
$938$	1.31935	+	22.6523i	0.0430782	+	0.739624i
$939$	−23.3490	+	1.22268i	−0.761965	+	0.0399008i
$940$	−2.98403	+	6.91775i	−0.0973282	+	0.225632i
$941$	−3.32253	+	57.0457i	−0.108312	+	1.85964i	0.309240	+	0.950984i	$0.399925\pi$
$941$	−3.32253	+	57.0457i	−0.108312	+	1.85964i	−0.417551	+	0.908653i	$0.637112\pi$
$942$	−5.87769	−	3.43956i	−0.191505	−	0.112067i
$943$	27.0695	+	28.6920i	0.881504	+	0.934340i
$944$	−1.86873	+	3.23673i	−0.0608219	+	0.105347i
$945$	−21.8725	+	3.46144i	−0.711512	+	0.112601i
$946$	−5.69116	−	9.85738i	−0.185036	−	0.320491i
$947$	8.19001	−	27.3565i	0.266139	−	0.888968i	−0.715563	−	0.698548i	$-0.753830\pi$
$947$	8.19001	−	27.3565i	0.266139	−	0.888968i	0.981703	−	0.190420i	$-0.0609849\pi$
$948$	−5.80407	+	6.83528i	−0.188507	+	0.221999i
$949$	−7.34533	−	4.83110i	−0.238440	−	0.156824i
$950$	−6.80722	+	0.795650i	−0.220855	+	0.0258143i
$951$	−11.1685	+	10.4139i	−0.362162	+	0.337693i
$952$	−10.5331	−	5.28992i	−0.341379	−	0.171447i
$953$	−8.34796	−	47.3436i	−0.270417	−	1.53361i	−0.753154	−	0.657845i	$-0.771468\pi$
$953$	−8.34796	−	47.3436i	−0.270417	−	1.53361i	0.482737	−	0.875766i	$-0.339643\pi$
$954$	0.310817	+	6.68544i	0.0100631	+	0.216449i
$955$	−1.54973	+	8.78895i	−0.0501481	+	0.284404i
$956$	4.72354	−	6.34481i	0.152770	−	0.205206i
$957$	−16.2057	−	15.4698i	−0.523855	−	0.500066i
$958$	23.3863	−	24.7881i	0.755578	−	0.800866i
$959$	−8.23819	−	27.5175i	−0.266025	−	0.888586i
$960$	1.25565	−	0.923413i	0.0405260	−	0.0298030i
$961$	27.3879	+	3.20118i	0.883479	+	0.103264i
$962$	42.0404	+	35.2761i	1.35544	+	1.13735i
$963$	−20.6773	−	17.7674i	−0.666317	−	0.572546i
$964$	−0.332067	+	0.278638i	−0.0106952	+	0.00897432i
$965$	−13.0959	+	8.61328i	−0.421570	+	0.277271i
$966$	−57.4186	+	24.3699i	−1.84741	+	0.784088i
$967$	−3.37172	−	4.52900i	−0.108427	−	0.145643i	0.744597	−	0.667514i	$-0.232642\pi$
$967$	−3.37172	−	4.52900i	−0.108427	−	0.145643i	−0.853024	+	0.521871i	$0.825234\pi$
$968$	6.23277	−	3.13022i	0.200329	−	0.100609i
$969$	6.95069	−	1.18364i	0.223288	−	0.0380240i
$970$	4.09723	−	0.971061i	0.131554	−	0.0311789i
$971$	11.5616			0.371028			0.185514	−	0.982642i	$-0.440605\pi$
$971$	11.5616			0.371028			0.185514	+	0.982642i	$0.440605\pi$
$972$	4.03775	−	15.0564i	0.129511	−	0.482936i
$973$	66.8229			2.14225
$974$	−6.11584	+	1.44948i	−0.195964	+	0.0464443i
$975$	−43.8069	+	7.45994i	−1.40294	+	0.238909i
$976$	2.81018	−	1.41133i	0.0899517	−	0.0451755i
$977$	−8.12127	−	10.9088i	−0.259822	−	0.349002i	0.653001	−	0.757357i	$-0.273510\pi$
$977$	−8.12127	−	10.9088i	−0.259822	−	0.349002i	−0.912823	+	0.408355i	$0.866102\pi$
$978$	−17.5338	+	7.44179i	−0.560669	+	0.237962i
$979$	−58.2482	+	38.3104i	−1.86162	+	1.22441i
$980$	10.6358	−	8.92448i	0.339747	−	0.285082i
$981$	−4.75246	+	25.2205i	−0.151735	+	0.805229i
$982$	30.8862	+	25.9166i	0.985619	+	0.827033i
$983$	−16.7654	−	1.95959i	−0.534732	−	0.0625012i	−0.155558	−	0.987827i	$-0.549718\pi$
$983$	−16.7654	−	1.95959i	−0.534732	−	0.0625012i	−0.379174	+	0.925325i	$0.623792\pi$
$984$	7.23823	−	5.32303i	0.230746	−	0.169692i
$985$	5.23359	+	17.4814i	0.166756	+	0.557004i
$986$	−5.21081	+	5.52314i	−0.165946	+	0.175893i
$987$	−49.6753	−	47.4195i	−1.58118	−	1.50938i
$988$	−5.98031	+	8.03294i	−0.190259	+	0.255562i
$989$	−3.54508	+	20.1052i	−0.112727	+	0.639307i
$990$	−10.1672	−	5.25626i	−0.323135	−	0.167055i
$991$	−5.98687	−	33.9532i	−0.190179	−	1.07856i	−0.919118	−	0.393982i	$-0.871097\pi$
$991$	−5.98687	−	33.9532i	−0.190179	−	1.07856i	0.728939	−	0.684579i	$-0.240014\pi$
$992$	1.65399	+	0.830667i	0.0525143	+	0.0263737i
$993$	−3.82954	+	3.57080i	−0.121527	+	0.113316i
$994$	19.5605	−	2.28630i	0.620423	−	0.0725170i
$995$	3.92869	+	2.58394i	0.124548	+	0.0819165i
$996$	−3.03607	+	3.57549i	−0.0962016	+	0.113294i
$997$	4.82965	−	16.1322i	0.152957	−	0.510910i	−0.846824	−	0.531874i	$-0.821488\pi$
$997$	4.82965	−	16.1322i	0.152957	−	0.510910i	0.999780	+	0.0209632i	$0.00667330\pi$
$998$	−10.8601	−	18.8102i	−0.343770	−	0.595427i
$999$	−30.5596	+	35.1459i	−0.966863	+	1.11197i

Display

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a_n

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a_n

instead) (See

a_n

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a_n

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up to: 50 250 1000 (See only

a_p

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a_p

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a_p

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.b.157.5	yes	90
3.2	odd	2		486.2.g.b.361.2		90
81.16	even	27	inner	162.2.g.b.97.5	✓	90
81.65	odd	54		486.2.g.b.451.2		90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.b.97.5	✓	90	81.16	even	27	inner
162.2.g.b.157.5	yes	90	1.1	even	1	trivial
486.2.g.b.361.2		90	3.2	odd	2
486.2.g.b.451.2		90	81.65	odd	54

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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	162.2.g.b.157.5

Level	$162$
Weight	$2$
Character	162.157
Analytic conductor	$1.294$
Analytic rank	$0$
Dimension	$90$
Inner twists	$2$