LMFDB - Embedded newform 116.2.l.b.11.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [116,2,Mod(3,116)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(116, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([14, 5]))

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

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

chi := DirichletCharacter("116.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$116 = 2^{2} \cdot 29$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	116.l (of order $28$ , degree $12$ , 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:	$0.926264663447$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$12$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	116.11
Dual form			116.2.l.b.95.12

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22822 + 0.701049i) q^{2} +(-2.69956 + 0.304168i) q^{3} +(1.01706 + 1.72209i) q^{4} +(-1.20112 + 2.49416i) q^{5} +(-3.52890 - 1.51894i) q^{6} +(0.625709 + 0.498986i) q^{7} +(0.0419068 + 2.82812i) q^{8} +(4.27033 - 0.974675i) q^{9} +(-3.22378 + 2.22134i) q^{10} +(4.00072 - 2.51382i) q^{11} +(-3.26942 - 4.33953i) q^{12} +(-2.59950 - 0.593318i) q^{13} +(0.418696 + 1.05152i) q^{14} +(2.48387 - 7.09848i) q^{15} +(-1.93118 + 3.50293i) q^{16} +(4.12057 - 4.12057i) q^{17} +(5.92821 + 1.79659i) q^{18} +(-0.647599 + 5.74760i) q^{19} +(-5.51678 + 0.468268i) q^{20} +(-1.84092 - 1.15672i) q^{21} +(6.67608 - 0.282827i) q^{22} +(-1.26320 - 2.62305i) q^{23} +(-0.973351 - 7.62193i) q^{24} +(-1.66069 - 2.08244i) q^{25} +(-2.77681 - 2.55110i) q^{26} +(-3.53897 + 1.23834i) q^{27} +(-0.222915 + 1.58503i) q^{28} +(5.26763 - 1.11894i) q^{29} +(8.02713 - 6.97720i) q^{30} +(-0.0981689 - 0.280550i) q^{31} +(-4.82765 + 2.94853i) q^{32} +(-10.0356 + 8.00309i) q^{33} +(7.94971 - 2.17226i) q^{34} +(-1.99611 + 0.961274i) q^{35} +(6.02166 + 6.36258i) q^{36} +(-1.42715 + 2.27130i) q^{37} +(-4.82474 + 6.60533i) q^{38} +(7.19797 + 0.811016i) q^{39} +(-7.10411 - 3.29240i) q^{40} +(6.66062 + 6.66062i) q^{41} +(-1.45013 - 2.71129i) q^{42} +(-1.02284 - 0.357909i) q^{43} +(8.39799 + 4.33289i) q^{44} +(-2.69820 + 11.8216i) q^{45} +(0.287404 - 4.10725i) q^{46} +(-1.28181 - 2.04000i) q^{47} +(4.14786 - 10.0438i) q^{48} +(-1.41512 - 6.20005i) q^{49} +(-0.579804 - 3.72192i) q^{50} +(-9.87040 + 12.3771i) q^{51} +(-1.62210 - 5.08000i) q^{52} +(-12.1981 - 5.87431i) q^{53} +(-5.21478 - 0.960037i) q^{54} +(1.46451 + 12.9978i) q^{55} +(-1.38497 + 1.79049i) q^{56} -15.7130i q^{57} +(7.25426 + 2.31856i) q^{58} -11.1260i q^{59} +(14.7505 - 2.94214i) q^{60} +(-0.603371 - 5.35507i) q^{61} +(0.0761065 - 0.413400i) q^{62} +(3.15833 + 1.52097i) q^{63} +(-7.99649 + 0.237034i) q^{64} +(4.60215 - 5.77091i) q^{65} +(-17.9365 + 2.79415i) q^{66} +(1.16453 + 5.10215i) q^{67} +(11.2869 + 2.90512i) q^{68} +(4.20792 + 6.69687i) q^{69} +(-3.12556 - 0.218711i) q^{70} +(-1.67029 + 7.31802i) q^{71} +(2.93545 + 12.0361i) q^{72} +(-3.02900 - 1.05989i) q^{73} +(-3.34516 + 1.78916i) q^{74} +(5.11654 + 5.11654i) q^{75} +(-10.5565 + 4.73043i) q^{76} +(3.75765 + 0.423385i) q^{77} +(8.27214 + 6.04224i) q^{78} +(4.66348 - 7.42189i) q^{79} +(-6.41730 - 9.02413i) q^{80} +(-2.66213 + 1.28201i) q^{81} +(3.51130 + 12.8502i) q^{82} +(7.68822 - 6.13115i) q^{83} +(0.119660 - 4.34668i) q^{84} +(5.32805 + 15.2267i) q^{85} +(-1.00537 - 1.15666i) q^{86} +(-13.8800 + 4.62289i) q^{87} +(7.27703 + 11.2092i) q^{88} +(-1.83420 + 0.641815i) q^{89} +(-11.6015 + 12.6280i) q^{90} +(-1.33047 - 1.66836i) q^{91} +(3.23238 - 4.84314i) q^{92} +(0.350347 + 0.727503i) q^{93} +(-0.144215 - 3.40418i) q^{94} +(-13.5576 - 8.51880i) q^{95} +(12.1357 - 9.42815i) q^{96} +(-0.198034 + 1.75760i) q^{97} +(2.60846 - 8.60712i) q^{98} +(14.6342 - 14.6342i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$144 q - 12 q^{2} - 14 q^{4} - 28 q^{5} - 14 q^{6} - 12 q^{8} - 28 q^{9} - 8 q^{10} - 12 q^{12} - 28 q^{13} - 14 q^{14} + 2 q^{16} - 4 q^{17} + 14 q^{18} + 14 q^{20} - 28 q^{21} - 14 q^{22} - 22 q^{24} - 12 q^{25}+ \cdots - 110 q^{98}+O(q^{100})$ 144 * q - 12 * q^2 - 14 * q^4 - 28 * q^5 - 14 * q^6 - 12 * q^8 - 28 * q^9 - 8 * q^10 - 12 * q^12 - 28 * q^13 - 14 * q^14 + 2 * q^16 - 4 * q^17 + 14 * q^18 + 14 * q^20 - 28 * q^21 - 14 * q^22 - 22 * q^24 - 12 * q^25 - 30 * q^26 - 36 * q^29 + 16 * q^30 - 12 * q^32 - 28 * q^33 - 56 * q^34 - 50 * q^36 - 36 * q^37 - 14 * q^38 - 60 * q^40 - 12 * q^41 - 14 * q^42 + 30 * q^44 + 36 * q^46 + 136 * q^48 + 12 * q^49 + 56 * q^50 + 66 * q^52 + 48 * q^53 + 56 * q^54 + 52 * q^56 + 184 * q^58 + 108 * q^60 - 28 * q^61 + 84 * q^62 + 112 * q^64 - 68 * q^65 + 92 * q^66 + 68 * q^68 - 44 * q^69 + 46 * q^70 + 4 * q^72 - 148 * q^73 - 32 * q^74 - 14 * q^76 - 60 * q^77 + 2 * q^78 - 14 * q^80 + 36 * q^81 + 6 * q^82 + 28 * q^84 - 92 * q^85 - 48 * q^88 + 28 * q^89 + 28 * q^90 - 14 * q^92 - 28 * q^93 + 62 * q^94 - 56 * q^96 + 184 * q^97 - 110 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/116\mathbb{Z}\right)^\times$ .

$n$	$59$	$89$
$\chi(n)$	$-1$	$e\left(\frac{25}{28}\right)$

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

)

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

$2$	1.22822	+	0.701049i	0.868484	+	0.495717i
$2$	1.22822	+	0.701049i	0.868484	+	0.495717i
$3$	−2.69956	+	0.304168i	−1.55859	+	0.175611i	−0.848767	−	0.528767i	$-0.822655\pi$
$3$	−2.69956	+	0.304168i	−1.55859	+	0.175611i	−0.709825	+	0.704378i	$0.751226\pi$
$4$	1.01706	+	1.72209i	0.508530	+	0.861044i
$5$	−1.20112	+	2.49416i	−0.537159	+	1.11542i	0.439024	+	0.898475i	$0.355324\pi$
$5$	−1.20112	+	2.49416i	−0.537159	+	1.11542i	−0.976183	+	0.216947i	$0.930390\pi$
$6$	−3.52890	−	1.51894i	−1.44067	−	0.620105i
$7$	0.625709	+	0.498986i	0.236496	+	0.188599i	0.734565	−	0.678538i	$-0.237386\pi$
$7$	0.625709	+	0.498986i	0.236496	+	0.188599i	−0.498070	+	0.867137i	$0.665958\pi$
$8$	0.0419068	+	2.82812i	0.0148163	+	0.999890i
$9$	4.27033	−	0.974675i	1.42344	−	0.324892i
$10$	−3.22378	+	2.22134i	−1.01945	+	0.702448i
$11$	4.00072	−	2.51382i	1.20626	−	0.757945i	0.229717	−	0.973258i	$-0.426220\pi$
$11$	4.00072	−	2.51382i	1.20626	−	0.757945i	0.976545	+	0.215313i	$0.0690771\pi$
$12$	−3.26942	−	4.33953i	−0.943800	−	1.25271i
$13$	−2.59950	−	0.593318i	−0.720971	−	0.164557i	−0.153735	−	0.988112i	$-0.549130\pi$
$13$	−2.59950	−	0.593318i	−0.720971	−	0.164557i	−0.567236	+	0.823555i	$0.691987\pi$
$14$	0.418696	+	1.05152i	0.111901	+	0.281030i
$15$	2.48387	−	7.09848i	0.641332	−	1.83282i
$16$	−1.93118	+	3.50293i	−0.482795	+	0.875734i
$17$	4.12057	−	4.12057i	0.999386	−	0.999386i	−0.000613870	−	1.00000i	$-0.500195\pi$
$17$	4.12057	−	4.12057i	0.999386	−	0.999386i	1.00000		0.000613870i	$0.000195401\pi$
$18$	5.92821	+	1.79659i	1.39729	+	0.423461i
$19$	−0.647599	+	5.74760i	−0.148569	+	1.31859i	0.669217	+	0.743067i	$0.266630\pi$
$19$	−0.647599	+	5.74760i	−0.148569	+	1.31859i	−0.817786	+	0.575522i	$0.804799\pi$
$20$	−5.51678	+	0.468268i	−1.23359	+	0.104708i
$21$	−1.84092	−	1.15672i	−0.401721	−	0.252418i
$22$	6.67608	−	0.282827i	1.42335	−	0.0602988i
$23$	−1.26320	−	2.62305i	−0.263394	−	0.546944i	0.726765	−	0.686886i	$-0.241023\pi$
$23$	−1.26320	−	2.62305i	−0.263394	−	0.546944i	−0.990160	+	0.139942i	$0.955309\pi$
$24$	−0.973351	−	7.62193i	−0.198684	−	1.55582i
$25$	−1.66069	−	2.08244i	−0.332138	−	0.416488i
$26$	−2.77681	−	2.55110i	−0.544578	−	0.500312i
$27$	−3.53897	+	1.23834i	−0.681075	+	0.238319i
$28$	−0.222915	+	1.58503i	−0.0421270	+	0.299542i
$29$	5.26763	−	1.11894i	0.978175	−	0.207782i
$29$	5.26763	−	1.11894i	0.978175	−	0.207782i
$30$	8.02713	−	6.97720i	1.46555	−	1.27386i
$31$	−0.0981689	−	0.280550i	−0.0176316	−	0.0503884i	0.934731	−	0.355356i	$-0.115640\pi$
$31$	−0.0981689	−	0.280550i	−0.0176316	−	0.0503884i	−0.952363	+	0.304967i	$0.901354\pi$
$32$	−4.82765	+	2.94853i	−0.853415	+	0.521232i
$33$	−10.0356	+	8.00309i	−1.74697	+	1.39316i
$34$	7.94971	−	2.17226i	1.36336	−	0.372539i
$35$	−1.99611	+	0.961274i	−0.337404	+	0.162485i
$36$	6.02166	+	6.36258i	1.00361	+	1.06043i
$37$	−1.42715	+	2.27130i	−0.234623	+	0.373400i	−0.943196	−	0.332238i	$-0.892196\pi$
$37$	−1.42715	+	2.27130i	−0.234623	+	0.373400i	0.708573	+	0.705638i	$0.249339\pi$
$38$	−4.82474	+	6.60533i	−0.782677	+	1.07153i
$39$	7.19797	+	0.811016i	1.15260	+	0.129867i
$40$	−7.10411	−	3.29240i	−1.12326	−	0.520574i
$41$	6.66062	+	6.66062i	1.04021	+	1.04021i	0.999157	+	0.0410580i	$0.0130729\pi$
$41$	6.66062	+	6.66062i	1.04021	+	1.04021i	0.0410580	+	0.999157i	$0.486927\pi$
$42$	−1.45013	−	2.71129i	−0.223760	−	0.418361i
$43$	−1.02284	−	0.357909i	−0.155982	−	0.0545806i	0.251158	−	0.967946i	$-0.419188\pi$
$43$	−1.02284	−	0.357909i	−0.155982	−	0.0545806i	−0.407141	+	0.913365i	$0.633474\pi$
$44$	8.39799	+	4.33289i	1.26604	+	0.653207i
$45$	−2.69820	+	11.8216i	−0.402224	+	1.76226i
$46$	0.287404	−	4.10725i	0.0423754	−	0.605582i
$47$	−1.28181	−	2.04000i	−0.186972	−	0.297564i	0.740064	−	0.672536i	$-0.234795\pi$
$47$	−1.28181	−	2.04000i	−0.186972	−	0.297564i	−0.927036	+	0.374972i	$0.877652\pi$
$48$	4.14786	−	10.0438i	0.598691	−	1.44970i
$49$	−1.41512	−	6.20005i	−0.202160	−	0.885722i
$50$	−0.579804	−	3.72192i	−0.0819966	−	0.526359i
$51$	−9.87040	+	12.3771i	−1.38213	+	1.73314i
$52$	−1.62210	−	5.08000i	−0.224944	−	0.704470i
$53$	−12.1981	−	5.87431i	−1.67554	−	0.806899i	−0.997407	−	0.0719623i	$-0.977074\pi$
$53$	−12.1981	−	5.87431i	−1.67554	−	0.806899i	−0.678136	−	0.734937i	$-0.737212\pi$
$54$	−5.21478	−	0.960037i	−0.709642	−	0.130644i
$55$	1.46451	+	12.9978i	0.197474	+	1.75263i
$56$	−1.38497	+	1.79049i	−0.185074	+	0.239264i
$57$		−	15.7130i		−	2.08123i
$58$	7.25426	+	2.31856i	0.952531	+	0.304442i
$59$		−	11.1260i		−	1.44849i	−0.689544	−	0.724244i	$-0.742189\pi$
$59$		−	11.1260i		−	1.44849i	0.689544	−	0.724244i	$-0.257811\pi$
$60$	14.7505	−	2.94214i	1.90428	−	0.379829i
$61$	−0.603371	−	5.35507i	−0.0772538	−	0.685646i	−0.971331	−	0.237733i	$-0.923596\pi$
$61$	−0.603371	−	5.35507i	−0.0772538	−	0.685646i	0.894077	−	0.447914i	$-0.147833\pi$
$62$	0.0761065	−	0.413400i	0.00966554	−	0.0525018i
$63$	3.15833	+	1.52097i	0.397913	+	0.191625i
$64$	−7.99649	+	0.237034i	−0.999561	+	0.0296293i
$65$	4.60215	−	5.77091i	0.570827	−	0.715794i
$66$	−17.9365	+	2.79415i	−2.20783	+	0.343937i
$67$	1.16453	+	5.10215i	0.142270	+	0.623327i	0.994905	+	0.100819i	$0.0321463\pi$
$67$	1.16453	+	5.10215i	0.142270	+	0.623327i	−0.852634	+	0.522508i	$0.824997\pi$
$68$	11.2869	+	2.90512i	1.36873	+	0.352298i
$69$	4.20792	+	6.69687i	0.506574	+	0.806208i
$70$	−3.12556	−	0.218711i	−0.373576	−	0.0261409i
$71$	−1.67029	+	7.31802i	−0.198227	+	0.868489i	0.773765	+	0.633473i	$0.218371\pi$
$71$	−1.67029	+	7.31802i	−0.198227	+	0.868489i	−0.971992	+	0.235016i	$0.924486\pi$
$72$	2.93545	+	12.0361i	0.345946	+	1.41847i
$73$	−3.02900	−	1.05989i	−0.354518	−	0.124051i	0.147144	−	0.989115i	$-0.452992\pi$
$73$	−3.02900	−	1.05989i	−0.354518	−	0.124051i	−0.501662	+	0.865064i	$0.667278\pi$
$74$	−3.34516	+	1.78916i	−0.388867	+	0.207986i
$75$	5.11654	+	5.11654i	0.590808	+	0.590808i
$76$	−10.5565	+	4.73043i	−1.21092	+	0.542617i
$77$	3.75765	+	0.423385i	0.428224	+	0.0482492i
$78$	8.27214	+	6.04224i	0.936636	+	0.684149i
$79$	4.66348	−	7.42189i	0.524683	−	0.835028i	−0.474289	−	0.880369i	$-0.657295\pi$
$79$	4.66348	−	7.42189i	0.524683	−	0.835028i	0.998972	+	0.0453415i	$0.0144376\pi$
$80$	−6.41730	−	9.02413i	−0.717476	−	1.00893i
$81$	−2.66213	+	1.28201i	−0.295792	+	0.142446i
$82$	3.51130	+	12.8502i	0.387758	+	1.41906i
$83$	7.68822	−	6.13115i	0.843891	−	0.672981i	−0.102948	−	0.994687i	$-0.532828\pi$
$83$	7.68822	−	6.13115i	0.843891	−	0.672981i	0.946840	+	0.321706i	$0.104256\pi$
$84$	0.119660	−	4.34668i	0.0130559	−	0.474261i
$85$	5.32805	+	15.2267i	0.577908	+	1.65157i
$86$	−1.00537	−	1.15666i	−0.108412	−	0.124725i
$87$	−13.8800	+	4.62289i	−1.48809	+	0.495626i
$88$	7.27703	+	11.2092i	0.775734	+	1.19490i
$89$	−1.83420	+	0.641815i	−0.194425	+	0.0680322i	−0.425735	−	0.904848i	$-0.639984\pi$
$89$	−1.83420	+	0.641815i	−0.194425	+	0.0680322i	0.231310	+	0.972880i	$0.425699\pi$
$90$	−11.6015	+	12.6280i	−1.22291	+	1.33111i
$91$	−1.33047	−	1.66836i	−0.139471	−	0.174891i
$92$	3.23238	−	4.84314i	0.336999	−	0.504932i
$93$	0.350347	+	0.727503i	0.0363293	+	0.0754386i
$94$	−0.144215	−	3.40418i	−0.0148747	−	0.351115i
$95$	−13.5576	−	8.51880i	−1.39098	−	0.874010i
$96$	12.1357	−	9.42815i	1.23859	−	0.962257i
$97$	−0.198034	+	1.75760i	−0.0201073	+	0.178457i	−0.999752	−	0.0222836i	$-0.992906\pi$
$97$	−0.198034	+	1.75760i	−0.0201073	+	0.178457i	0.979644	+	0.200741i	$0.0643349\pi$
$98$	2.60846	−	8.60712i	0.263494	−	0.869450i
$99$	14.6342	−	14.6342i	1.47080	−	1.47080i
$100$	1.89712	−	4.97782i	0.189712	−	0.497782i
$101$	1.11491	−	3.18624i	0.110938	−	0.317042i	−0.875008	−	0.484109i	$-0.839144\pi$
$101$	1.11491	−	3.18624i	0.110938	−	0.317042i	0.985946	+	0.167067i	$0.0534295\pi$
$102$	−20.8000	+	8.28218i	−2.05951	+	0.820058i
$103$	−0.235266	−	0.0536980i	−0.0231815	−	0.00529102i	0.210914	−	0.977505i	$-0.432356\pi$
$103$	−0.235266	−	0.0536980i	−0.0231815	−	0.00529102i	−0.234096	+	0.972213i	$0.575213\pi$
$104$	1.56904	−	7.37654i	0.153857	−	0.723330i
$105$	5.09622	−	3.20217i	0.497341	−	0.312500i
$106$	−10.8638	−	15.7665i	−1.05519	−	1.53137i
$107$	6.68380	−	1.52553i	0.646147	−	0.147479i	0.113126	−	0.993581i	$-0.463914\pi$
$107$	6.68380	−	1.52553i	0.646147	−	0.147479i	0.533021	+	0.846102i	$0.321057\pi$
$108$	−5.73188	−	4.83496i	−0.551550	−	0.465244i
$109$	6.02055	+	4.80123i	0.576664	+	0.459874i	0.867874	−	0.496785i	$-0.165486\pi$
$109$	6.02055	+	4.80123i	0.576664	+	0.459874i	−0.291210	+	0.956659i	$0.594058\pi$
$110$	−7.31339	+	16.9909i	−0.697304	+	1.62002i
$111$	3.16183	−	6.56562i	0.300108	−	0.623181i
$112$	−2.95627	+	1.22819i	−0.279341	+	0.116053i
$113$	10.2351	−	1.15321i	0.962834	−	0.108485i	0.383469	−	0.923554i	$-0.374729\pi$
$113$	10.2351	−	1.15321i	0.962834	−	0.108485i	0.579365	+	0.815068i	$0.303301\pi$
$114$	11.0156	−	19.2990i	1.03170	−	1.80752i
$115$	8.05957			0.751559
$116$	7.28441	+	7.93330i	0.676341	+	0.736589i
$117$	−11.6790			−1.07972
$118$	7.79991	−	13.6653i	0.718039	−	1.25799i
$119$	4.63439	−	0.522170i	0.424834	−	0.0478673i
$120$	20.1794	+	6.72719i	1.84212	+	0.614106i
$121$	4.91374	−	10.2035i	0.446704	−	0.927591i
$122$	3.01309	−	7.00021i	0.272793	−	0.633769i
$123$	−20.0067	−	15.9548i	−1.80394	−	1.43860i
$124$	0.383289	−	0.454392i	0.0344204	−	0.0408056i
$125$	−6.30588	+	1.43928i	−0.564015	+	0.128733i
$126$	2.81286	+	4.08224i	0.250589	+	0.363675i
$127$	−11.0882	+	6.96721i	−0.983923	+	0.618240i	−0.924978	−	0.380022i	$-0.875917\pi$
$127$	−11.0882	+	6.96721i	−0.983923	+	0.618240i	−0.0589452	+	0.998261i	$0.518774\pi$
$128$	−9.98764	−	5.31480i	−0.882791	−	0.469766i
$129$	2.87010	+	0.655081i	0.252698	+	0.0576767i
$130$	9.69816	−	3.86163i	0.850585	−	0.338687i
$131$	3.97123	−	11.3491i	0.346968	−	0.991579i	−0.629702	−	0.776836i	$-0.716823\pi$
$131$	3.97123	−	11.3491i	0.346968	−	0.991579i	0.976671	−	0.214742i	$-0.0688911\pi$
$132$	−23.9888	−	9.14250i	−2.08796	−	0.795753i
$133$	−3.27318	+	3.27318i	−0.283821	+	0.283821i
$134$	−2.14655	+	7.08297i	−0.185434	+	0.611875i
$135$	1.16213	−	10.3142i	0.100020	−	0.887702i
$136$	11.8261	+	11.4808i	1.01408	+	0.984469i
$137$	0.426004	+	0.267676i	0.0363960	+	0.0228691i	0.550107	−	0.835094i	$-0.314587\pi$
$137$	0.426004	+	0.267676i	0.0363960	+	0.0228691i	−0.513711	+	0.857963i	$0.671730\pi$
$138$	0.473428	+	11.1752i	0.0403009	+	0.951297i
$139$	−1.74101	−	3.61524i	−0.147670	−	0.306641i	0.813992	−	0.580876i	$-0.197290\pi$
$139$	−1.74101	−	3.61524i	−0.147670	−	0.306641i	−0.961663	+	0.274235i	$0.911575\pi$
$140$	−3.68556	−	2.45980i	−0.311487	−	0.207891i
$141$	4.08084	+	5.11721i	0.343669	+	0.430947i
$142$	−7.18178	+	7.81720i	−0.602682	+	0.656005i
$143$	−11.8913	+	4.16096i	−0.994405	+	0.347957i
$144$	−4.83255	+	16.8410i	−0.402712	+	1.40341i
$145$	−3.53627	+	14.4823i	−0.293671	+	1.20269i
$146$	−2.97725	−	3.42527i	−0.246399	−	0.283477i
$147$	5.70606	+	16.3070i	0.470628	+	1.34498i
$148$	−5.36289	−	0.147635i	−0.440827	−	0.0121355i
$149$	−4.78964	+	3.81961i	−0.392383	+	0.312915i	−0.799731	−	0.600358i	$-0.795025\pi$
$149$	−4.78964	+	3.81961i	−0.392383	+	0.312915i	0.407349	+	0.913273i	$0.366453\pi$
$150$	2.69730	+	9.87120i	0.220234	+	0.805980i
$151$	−7.16121	+	3.44866i	−0.582771	+	0.280648i	−0.701951	−	0.712225i	$-0.747688\pi$
$151$	−7.16121	+	3.44866i	−0.582771	+	0.280648i	0.119180	+	0.992873i	$0.461973\pi$
$152$	−16.2820	−	1.59062i	−1.32065	−	0.129016i
$153$	13.5800	−	21.6124i	1.09788	−	1.74726i
$154$	4.31841	+	3.15431i	0.347987	+	0.254181i
$155$	0.817651	+	0.0921272i	0.0656753	+	0.00739983i
$156$	5.92412	+	13.2204i	0.474310	+	1.05848i
$157$	6.61861	+	6.61861i	0.528222	+	0.528222i	0.920042	−	0.391820i	$-0.128154\pi$
$157$	6.61861	+	6.61861i	0.528222	+	0.528222i	−0.391820	+	0.920042i	$0.628154\pi$
$158$	10.9309	−	5.84640i	0.869616	−	0.465115i
$159$	34.7164	+	12.1478i	2.75319	+	0.963383i
$160$	−1.55551	−	15.5825i	−0.122974	−	1.23190i
$161$	0.518474	−	2.27159i	0.0408615	−	0.179026i
$162$	−4.16844	−	0.291686i	−0.327504	−	0.0229170i
$163$	2.22070	+	3.53423i	0.173939	+	0.276822i	0.922304	−	0.386464i	$-0.126304\pi$
$163$	2.22070	+	3.53423i	0.173939	+	0.276822i	−0.748365	+	0.663287i	$0.769161\pi$
$164$	−4.69593	+	18.2444i	−0.366691	+	1.42465i
$165$	−7.90704	−	34.6430i	−0.615562	−	2.69696i
$166$	13.7411	−	2.14059i	1.06651	−	0.166142i
$167$	−2.92946	+	3.67343i	−0.226689	+	0.284259i	−0.882148	−	0.470971i	$-0.843903\pi$
$167$	−2.92946	+	3.67343i	−0.226689	+	0.284259i	0.655460	+	0.755230i	$0.272475\pi$
$168$	3.19420	−	5.25480i	0.246438	−	0.405416i
$169$	−5.30724	−	2.55583i	−0.408249	−	0.196602i
$170$	−4.13063	+	22.4370i	−0.316805	+	1.72084i
$171$	2.83658	+	25.1753i	0.216919	+	1.92521i
$172$	−0.423944	−	2.12544i	−0.0323254	−	0.162064i
$173$			11.7211i			0.891141i	0.895247	+	0.445571i	$0.146999\pi$
$173$			11.7211i			0.891141i	−0.895247	+	0.445571i	$0.853001\pi$
$174$	−20.2885	−	4.05260i	−1.53807	−	0.307226i
$175$		−	2.13166i		−	0.161138i
$176$	1.07964	+	18.8689i	0.0813809	+	1.42230i
$177$	3.38418	+	30.0354i	0.254371	+	2.25760i
$178$	−2.70275	−	0.497574i	−0.202580	−	0.0372948i
$179$	−19.2261	−	9.25880i	−1.43703	−	0.692036i	−0.456737	−	0.889602i	$-0.650982\pi$
$179$	−19.2261	−	9.25880i	−1.43703	−	0.692036i	−0.980290	+	0.197566i	$0.936696\pi$
$180$	−23.1021	+	7.37673i	−1.72193	+	0.549829i
$181$	3.61640	−	4.53482i	0.268805	−	0.337071i	−0.629048	−	0.777367i	$-0.716555\pi$
$181$	3.61640	−	4.53482i	0.268805	−	0.337071i	0.897853	+	0.440296i	$0.145126\pi$
$182$	−0.464513	−	2.98184i	−0.0344320	−	0.221029i
$183$	3.25768	+	14.2728i	0.240814	+	1.05508i
$184$	7.36536	−	3.68239i	0.542982	−	0.271469i
$185$	−3.95081	−	6.28767i	−0.290469	−	0.462279i
$186$	−0.0797115	+	1.13915i	−0.00584473	+	0.0835263i
$187$	6.12688	−	26.8436i	0.448042	−	1.96300i
$188$	2.20937	−	4.28220i	0.161135	−	0.312311i
$189$	−2.83228	−	0.991058i	−0.206018	−	0.0720888i
$190$	−10.6796	−	19.9675i	−0.774782	−	1.44860i
$191$	6.03714	+	6.03714i	0.436832	+	0.436832i	0.890944	−	0.454112i	$-0.150043\pi$
$191$	6.03714	+	6.03714i	0.436832	+	0.436832i	−0.454112	+	0.890944i	$0.650043\pi$
$192$	21.5149	−	3.07216i	1.55270	−	0.221714i
$193$	0.683256	+	0.0769844i	0.0491818	+	0.00554146i	0.136521	−	0.990637i	$-0.456408\pi$
$193$	0.683256	+	0.0769844i	0.0491818	+	0.00554146i	−0.0873393	+	0.996179i	$0.527836\pi$
$194$	−1.47539	+	2.01989i	−0.105927	+	0.145020i
$195$	−10.6685	+	16.9788i	−0.763985	+	1.21587i
$196$	9.23778	−	8.74279i	0.659841	−	0.624485i
$197$	19.0985	−	9.19733i	1.36071	−	0.655283i	0.395914	−	0.918288i	$-0.370428\pi$
$197$	19.0985	−	9.19733i	1.36071	−	0.655283i	0.964795	+	0.263005i	$0.0847135\pi$
$198$	28.2334	−	7.71477i	2.00646	−	0.548265i
$199$	−1.45752	+	1.16234i	−0.103321	+	0.0823958i	−0.673788	−	0.738925i	$-0.735334\pi$
$199$	−1.45752	+	1.16234i	−0.103321	+	0.0823958i	0.570467	+	0.821321i	$0.306762\pi$
$200$	5.81979	−	4.78389i	0.411521	−	0.338272i
$201$	−4.69564	−	13.4194i	−0.331205	−	0.946528i
$202$	3.60307	−	3.13180i	0.253511	−	0.220352i
$203$	3.85434	+	1.92835i	0.270522	+	0.135343i
$204$	−31.3532	−	4.40946i	−2.19516	−	0.308724i
$205$	−24.6129	+	8.61243i	−1.71904	+	0.601518i
$206$	−0.251315	−	0.230886i	−0.0175099	−	0.0160866i
$207$	−7.95089	−	9.97010i	−0.552625	−	0.692970i
$208$	7.09845	−	7.96006i	0.492189	−	0.551931i
$209$	11.8576	+	24.6225i	0.820204	+	1.70317i
$210$	8.50417	−	0.360272i	0.586844	−	0.0248611i
$211$	−1.72008	−	1.08080i	−0.118415	−	0.0744050i	0.471522	−	0.881854i	$-0.343705\pi$
$211$	−1.72008	−	1.08080i	−0.118415	−	0.0744050i	−0.589937	+	0.807449i	$0.700848\pi$
$212$	−2.29015	−	26.9808i	−0.157288	−	1.85305i
$213$	2.28315	−	20.2635i	0.156439	−	1.38843i
$214$	9.27866	+	2.81198i	0.634276	+	0.192223i
$215$	2.12125	−	2.12125i	0.144668	−	0.144668i
$216$	−3.65048	−	9.95673i	−0.248383	−	0.677470i
$217$	0.0785657	−	0.224528i	0.00533339	−	0.0152419i
$218$	4.02868	+	10.1177i	0.272856	+	0.685256i
$219$	8.49936	+	1.93992i	0.574334	+	0.131088i
$220$	−20.8939	+	15.7416i	−1.40867	+	1.06130i
$221$	−13.1562	+	8.26661i	−0.884984	+	0.556072i
$222$	8.48626	−	5.84744i	0.569560	−	0.392454i
$223$	−27.3342	+	6.23886i	−1.83044	+	0.417785i	−0.991896	−	0.127054i	$-0.959448\pi$
$223$	−27.3342	+	6.23886i	−1.83044	+	0.417785i	−0.838541	+	0.544839i	$0.816591\pi$
$224$	−4.49198	−	0.564006i	−0.300133	−	0.0376843i
$225$	−9.12139	−	7.27407i	−0.608093	−	0.484938i
$226$	13.3794	+	5.75888i	0.889984	+	0.383075i
$227$	−10.6377	+	22.0893i	−0.706047	+	1.46612i	0.170777	+	0.985310i	$0.445372\pi$
$227$	−10.6377	+	22.0893i	−0.706047	+	1.46612i	−0.876824	+	0.480812i	$0.840342\pi$
$228$	27.0591	−	15.9810i	1.79203	−	1.05837i
$229$	−13.7160	+	1.54542i	−0.906378	+	0.102124i	−0.552832	−	0.833293i	$-0.686453\pi$
$229$	−13.7160	+	1.54542i	−0.906378	+	0.102124i	−0.353546	+	0.935417i	$0.615024\pi$
$230$	9.89894	+	5.65016i	0.652717	+	0.372560i
$231$	−10.2728			−0.675899
$232$	3.38524	+	14.8506i	0.222252	+	0.974989i
$233$	−14.3888			−0.942640			−0.471320	−	0.881962i	$-0.656222\pi$
$233$	−14.3888			−0.942640			−0.471320	+	0.881962i	$0.656222\pi$
$234$	−14.3444	−	8.18756i	−0.937723	−	0.535237i
$235$	6.62770	−	0.746762i	0.432343	−	0.0487134i
$236$	19.1600	−	11.3159i	1.24721	−	0.736599i
$237$	−10.3319	+	21.4543i	−0.671126	+	1.39361i
$238$	6.05813	+	2.60759i	0.392690	+	0.169025i
$239$	22.1659	+	17.6767i	1.43379	+	1.14341i	0.965678	+	0.259741i	$0.0836373\pi$
$239$	22.1659	+	17.6767i	1.43379	+	1.14341i	0.468113	+	0.883669i	$0.344934\pi$
$240$	20.0687	+	22.4093i	1.29543	+	1.44651i
$241$	−14.8720	+	3.39443i	−0.957988	+	0.218654i	−0.672806	−	0.739819i	$-0.734911\pi$
$241$	−14.8720	+	3.39443i	−0.957988	+	0.218654i	−0.285182	+	0.958473i	$0.592054\pi$
$242$	13.1883	−	9.08738i	0.847778	−	0.584159i
$243$	16.3207	−	10.2550i	1.04697	−	0.657856i
$244$	8.60824	−	6.48549i	0.551086	−	0.415191i
$245$	17.1637	+	3.91750i	1.09655	+	0.250280i
$246$	−13.3876	−	33.6218i	−0.853561	−	2.14364i
$247$	5.09359	−	14.5566i	0.324097	−	0.926216i
$248$	0.789316	−	0.289390i	0.0501216	−	0.0183763i
$249$	−18.8899	+	18.8899i	−1.19710	+	1.19710i
$250$	−8.75403	−	2.65298i	−0.553653	−	0.167789i
$251$	0.601378	−	5.33738i	0.0379586	−	0.336892i	−0.960352	−	0.278790i	$-0.910067\pi$
$251$	0.601378	−	5.33738i	0.0379586	−	0.336892i	0.998311	−	0.0581019i	$-0.0185048\pi$
$252$	0.592964	+	6.98585i	0.0373532	+	0.440067i
$253$	−11.6476	−	7.31865i	−0.732276	−	0.460120i
$254$	−18.5032	+	0.783872i	−1.16099	+	0.0491845i
$255$	−19.0149	−	39.4848i	−1.19076	−	2.47263i
$256$	−8.54110	−	13.5296i	−0.533819	−	0.845599i
$257$	−7.06642	−	8.86101i	−0.440791	−	0.552735i	0.510960	−	0.859604i	$-0.329290\pi$
$257$	−7.06642	−	8.86101i	−0.440791	−	0.552735i	−0.951752	+	0.306870i	$0.900718\pi$
$258$	3.06587	+	2.81666i	0.190873	+	0.175358i
$259$	−2.02633	+	0.709044i	−0.125910	+	0.0440579i
$260$	14.6187	+	2.05595i	0.906613	+	0.127504i
$261$	21.4039	−	9.91248i	1.32487	−	0.613567i
$262$	12.8339	−	11.1552i	0.792879	−	0.689172i
$263$	2.79225	+	7.97980i	0.172178	+	0.492056i	0.997344	−	0.0728341i	$-0.0232044\pi$
$263$	2.79225	+	7.97980i	0.172178	+	0.492056i	−0.825166	+	0.564890i	$0.808919\pi$
$264$	−23.0542	−	28.0464i	−1.41889	−	1.72613i
$265$	29.3030	−	23.3683i	1.80007	−	1.43551i
$266$	−6.31486	+	1.72553i	−0.387189	+	0.105799i
$267$	4.75632	−	2.29052i	0.291082	−	0.140178i
$268$	−7.60196	+	7.19462i	−0.464363	+	0.439481i
$269$	−1.72270	+	2.74167i	−0.105035	+	0.167162i	−0.895106	−	0.445853i	$-0.852901\pi$
$269$	−1.72270	+	2.74167i	−0.105035	+	0.167162i	0.790071	+	0.613015i	$0.210043\pi$
$270$	8.65809	−	11.8534i	0.526914	−	0.721374i
$271$	6.94122	+	0.782088i	0.421649	+	0.0475085i	0.320240	−	0.947336i	$-0.396236\pi$
$271$	6.94122	+	0.782088i	0.421649	+	0.0475085i	0.101409	+	0.994845i	$0.467665\pi$
$272$	6.47654	+	22.3917i	0.392698	+	1.35769i
$273$	4.09915	+	4.09915i	0.248092	+	0.248092i
$274$	0.335573	+	0.627415i	0.0202727	+	0.0379035i
$275$	−11.8788	−	4.15658i	−0.716320	−	0.250651i
$276$	−7.25289	+	14.0575i	−0.436573	+	0.846164i
$277$	4.29722	−	18.8274i	0.258195	−	1.13123i	−0.664984	−	0.746857i	$-0.731562\pi$
$277$	4.29722	−	18.8274i	0.258195	−	1.13123i	0.923179	−	0.384369i	$-0.125581\pi$
$278$	0.396117	−	5.66085i	0.0237575	−	0.339515i
$279$	−0.692659	−	1.10236i	−0.0414684	−	0.0659966i
$280$	−2.80225	−	5.60494i	−0.167466	−	0.334959i
$281$	5.02994	+	22.0376i	0.300061	+	1.31465i	0.870034	+	0.492991i	$0.164097\pi$
$281$	5.02994	+	22.0376i	0.300061	+	1.31465i	−0.569973	+	0.821663i	$0.693046\pi$
$282$	1.42476	+	9.14594i	0.0848433	+	0.544633i
$283$	−1.20870	+	1.51566i	−0.0718497	+	0.0900967i	−0.816457	−	0.577406i	$-0.804065\pi$
$283$	−1.20870	+	1.51566i	−0.0718497	+	0.0900967i	0.744608	+	0.667502i	$0.232637\pi$
$284$	−14.3011	+	4.56648i	−0.848612	+	0.270971i
$285$	39.1907	+	18.8732i	2.32146	+	1.11795i
$286$	−17.5223	−	3.22583i	−1.03611	−	0.190748i
$287$	0.844053	+	7.49117i	0.0498228	+	0.442190i
$288$	−17.7418	+	17.2966i	−1.04544	+	1.01921i
$289$		−	16.9583i		−	0.997545i
$290$	−14.4961	+	15.3084i	−0.851243	+	0.898940i
$291$		−	4.80498i		−	0.281673i
$292$	−1.25545	−	6.29419i	−0.0734694	−	0.368339i
$293$	−2.23154	−	19.8054i	−0.130368	−	1.15705i	−0.873129	−	0.487490i	$-0.837913\pi$
$293$	−2.23154	−	19.8054i	−0.130368	−	1.15705i	0.742761	−	0.669557i	$-0.233516\pi$
$294$	−4.42369	+	24.0288i	−0.257995	+	1.40139i
$295$	27.7501	+	13.3638i	1.61568	+	0.778069i
$296$	−6.48332	−	3.94098i	−0.376835	−	0.229065i
$297$	−11.0455	+	13.8506i	−0.640923	+	0.803692i
$298$	−8.56048	+	1.33356i	−0.495895	+	0.0772509i
$299$	1.72737	+	7.56809i	0.0998963	+	0.437674i
$300$	−3.60731	+	14.0150i	−0.208268	+	0.809155i
$301$	−0.461412	−	0.734332i	−0.0265953	−	0.0423262i
$302$	−11.2132	−	0.784644i	−0.645249	−	0.0451512i
$303$	−2.04062	+	8.94056i	−0.117231	+	0.513622i
$304$	−18.8828	−	13.3681i	−1.08300	−	0.766715i
$305$	14.0811	+	4.92720i	0.806283	+	0.282131i
$306$	31.8306	−	17.0246i	1.81964	−	0.973233i
$307$	−0.315168	−	0.315168i	−0.0179876	−	0.0179876i	0.698056	−	0.716043i	$-0.254049\pi$
$307$	−0.315168	−	0.315168i	−0.0179876	−	0.0179876i	−0.716043	+	0.698056i	$0.754049\pi$
$308$	3.09264	+	6.90161i	0.176220	+	0.393256i
$309$	0.651449	+	0.0734007i	0.0370597	+	0.00417562i
$310$	0.939672	+	0.686366i	0.0533698	+	0.0389830i
$311$	13.1460	−	20.9217i	0.745438	−	1.18636i	−0.231499	−	0.972835i	$-0.574363\pi$
$311$	13.1460	−	20.9217i	0.745438	−	1.18636i	0.976938	−	0.213523i	$-0.0684940\pi$
$312$	−1.99201	+	20.3907i	−0.112775	+	1.15440i
$313$	7.14270	−	3.43974i	0.403729	−	0.194426i	−0.220989	−	0.975276i	$-0.570928\pi$
$313$	7.14270	−	3.43974i	0.403729	−	0.194426i	0.624718	+	0.780851i	$0.285214\pi$
$314$	3.48915	+	12.7691i	0.196904	+	0.720601i
$315$	−7.58710	+	6.05051i	−0.427485	+	0.340908i
$316$	17.5242	+	0.482423i	0.985813	+	0.0271384i
$317$	−8.45951	−	24.1759i	−0.475134	−	1.35785i	−0.893291	−	0.449479i	$-0.851610\pi$
$317$	−8.45951	−	24.1759i	−0.475134	−	1.35785i	0.418157	−	0.908375i	$-0.362676\pi$
$318$	34.1233	+	39.2581i	1.91354	+	2.20148i
$319$	18.2615	−	17.7184i	1.02245	−	0.992042i
$320$	9.01358	−	20.2292i	0.503874	−	1.13085i
$321$	−17.5793	+	6.15126i	−0.981181	+	0.343330i
$322$	2.22929	−	2.42654i	0.124234	−	0.135226i
$323$	21.0149	+	26.3519i	1.16930	+	1.46626i
$324$	−4.91528	−	3.28054i	−0.273071	−	0.182252i
$325$	3.08141	+	6.39861i	0.170926	+	0.354931i
$326$	0.249849	+	5.89764i	0.0138378	+	0.326640i
$327$	−17.7132	−	11.1300i	−0.979543	−	0.615488i
$328$	−18.5579	+	19.1161i	−1.02469	+	1.05551i
$329$	0.215887	−	1.91605i	0.0119022	−	0.105635i
$330$	14.5749	−	48.0926i	0.802319	−	2.64741i
$331$	1.02297	−	1.02297i	0.0562275	−	0.0562275i	−0.678434	−	0.734661i	$-0.737341\pi$
$331$	1.02297	−	1.02297i	0.0562275	−	0.0562275i	0.734661	+	0.678434i	$0.237341\pi$
$332$	18.3778	+	7.00404i	1.00861	+	0.384397i
$333$	−3.88064	+	11.0902i	−0.212658	+	0.607741i
$334$	−6.17329	+	2.45809i	−0.337787	+	0.134501i
$335$	−14.1243	−	3.22379i	−0.771695	−	0.176134i
$336$	7.60706	−	4.21477i	0.414999	−	0.229934i
$337$	11.7762	−	7.39948i	0.641491	−	0.403075i	−0.171637	−	0.985160i	$-0.554906\pi$
$337$	11.7762	−	7.39948i	0.641491	−	0.403075i	0.813128	+	0.582085i	$0.197763\pi$
$338$	−4.72670	−	6.85976i	−0.257099	−	0.373122i
$339$	−27.2794	+	6.22635i	−1.48161	+	0.338169i
$340$	−20.8028	+	24.6618i	−1.12819	+	1.33748i
$341$	−1.09800	−	0.875625i	−0.0594600	−	0.0474177i
$342$	−14.1652	+	32.9095i	−0.765966	+	1.77954i
$343$	4.63898	−	9.63295i	0.250482	−	0.520130i
$344$	0.969344	−	2.90772i	0.0522635	−	0.156774i
$345$	−21.7573	+	2.45146i	−1.17137	+	0.131982i
$346$	−8.21709	+	14.3962i	−0.441753	+	0.773942i
$347$	−30.3501			−1.62928			−0.814639	−	0.579968i	$-0.803065\pi$
$347$	−30.3501			−1.62928			−0.814639	+	0.579968i	$0.803065\pi$
$348$	−22.0778	−	19.2008i	−1.18349	−	1.02927i
$349$	22.9901			1.23063			0.615316	−	0.788280i	$-0.289028\pi$
$349$	22.9901			1.23063			0.615316	+	0.788280i	$0.289028\pi$
$350$	1.49440	−	2.61815i	0.0798790	−	0.139946i
$351$	9.93427	−	1.11932i	0.530252	−	0.0597451i
$352$	−11.9020	+	23.9321i	−0.634378	+	1.27558i
$353$	3.58553	−	7.44544i	0.190839	−	0.396281i	−0.783492	−	0.621402i	$-0.786563\pi$
$353$	3.58553	−	7.44544i	0.190839	−	0.396281i	0.974331	+	0.225121i	$0.0722778\pi$
$354$	−16.8998	+	39.2627i	−0.898214	+	2.08679i
$355$	−16.2461	−	12.9558i	−0.862253	−	0.687624i
$356$	−2.97075	−	2.50589i	−0.157450	−	0.132812i
$357$	−12.3520	+	2.81926i	−0.653737	+	0.149211i
$358$	−17.1231	−	24.8503i	−0.904981	−	1.31338i
$359$	7.38962	−	4.64321i	0.390009	−	0.245059i	−0.322726	−	0.946493i	$-0.604599\pi$
$359$	7.38962	−	4.64321i	0.390009	−	0.245059i	0.712735	+	0.701433i	$0.247456\pi$
$360$	−33.5459	−	7.13543i	−1.76803	−	0.376070i
$361$	−14.0919	−	3.21638i	−0.741678	−	0.169283i
$362$	7.62088	−	3.03450i	0.400544	−	0.159490i
$363$	−10.1614	+	29.0396i	−0.533334	+	1.52418i
$364$	1.51989	−	3.98801i	0.0796640	−	0.209028i
$365$	6.28176	−	6.28176i	0.328802	−	0.328802i
$366$	−6.00479	+	19.8140i	−0.313876	+	1.03569i
$367$	0.0903712	−	0.802066i	0.00471734	−	0.0418675i	−0.991133	−	0.132873i	$-0.957580\pi$
$367$	0.0903712	−	0.802066i	0.00471734	−	0.0418675i	0.995850	+	0.0910059i	$0.0290082\pi$
$368$	11.6278	+	0.640691i	0.606143	+	0.0333983i
$369$	34.9350	+	21.9511i	1.81864	+	1.14273i
$370$	−0.444500	−	10.4924i	−0.0231085	−	0.545472i
$371$	−4.70128	−	9.76231i	−0.244078	−	0.506834i
$372$	−0.896501	+	1.34324i	−0.0464814	+	0.0696439i
$373$	10.0101	+	12.5523i	0.518306	+	0.649935i	0.970248	−	0.242112i	$-0.0778402\pi$
$373$	10.0101	+	12.5523i	0.518306	+	0.649935i	−0.451943	+	0.892047i	$0.649269\pi$
$374$	26.3439	−	28.6747i	1.36221	−	1.48273i
$375$	16.5853	−	5.80346i	0.856463	−	0.299689i
$376$	5.71563	−	3.71061i	0.294761	−	0.191360i
$377$	−14.3571	−	0.216702i	−0.739428	−	0.0111607i
$378$	−2.78389	−	3.20281i	−0.143188	−	0.164735i
$379$	−8.26401	−	23.6172i	−0.424494	−	1.21313i	−0.935429	−	0.353514i	$-0.884987\pi$
$379$	−8.26401	−	23.6172i	−0.424494	−	1.21313i	0.510935	−	0.859619i	$-0.329299\pi$
$380$	0.881244	−	32.0115i	0.0452069	−	1.64216i
$381$	27.8142	−	22.1811i	1.42496	−	1.13637i
$382$	3.18262	+	11.6473i	0.162837	+	0.595927i
$383$	17.4585	−	8.40756i	0.892087	−	0.429606i	0.0690622	−	0.997612i	$-0.477999\pi$
$383$	17.4585	−	8.40756i	0.892087	−	0.429606i	0.823024	+	0.568006i	$0.192285\pi$
$384$	28.5788	+	11.3097i	1.45841	+	0.577147i
$385$	−5.56939	+	8.86364i	−0.283842	+	0.451733i
$386$	0.785220	+	0.573550i	0.0399666	+	0.0291929i
$387$	−4.71673	−	0.531448i	−0.239765	−	0.0270150i
$388$	−3.22815	+	1.44655i	−0.163885	+	0.0734375i
$389$	−8.98370	−	8.98370i	−0.455492	−	0.455492i	0.441681	−	0.897172i	$-0.354382\pi$
$389$	−8.98370	−	8.98370i	−0.455492	−	0.455492i	−0.897172	+	0.441681i	$0.854382\pi$
$390$	−25.0062	+	13.3746i	−1.26624	+	0.677248i
$391$	−16.0136	−	5.60339i	−0.809841	−	0.283376i
$392$	17.4752	−	4.26195i	0.882630	−	0.215261i
$393$	−7.26855	+	31.8456i	−0.366650	+	1.60640i
$394$	29.9049	+	2.09259i	1.50659	+	0.105423i
$395$	12.9100	+	20.5461i	0.649571	+	1.03379i
$396$	40.0853	+	10.3176i	2.01436	+	0.518477i
$397$	5.36927	+	23.5243i	0.269476	+	1.18065i	0.910624	+	0.413235i	$0.135601\pi$
$397$	5.36927	+	23.5243i	0.269476	+	1.18065i	−0.641148	+	0.767417i	$0.721542\pi$
$398$	−2.60502	+	0.405811i	−0.130578	+	0.0203415i
$399$	7.84056	−	9.83175i	0.392519	−	0.492203i
$400$	10.5017	−	1.79573i	0.525087	−	0.0897863i
$401$	−31.6555	−	15.2445i	−1.58080	−	0.761273i	−0.582143	−	0.813086i	$-0.697786\pi$
$401$	−31.6555	−	15.2445i	−1.58080	−	0.761273i	−0.998657	+	0.0518133i	$0.983500\pi$
$402$	3.64034	−	19.7738i	0.181564	−	0.986229i
$403$	0.0887339	+	0.787536i	0.00442015	+	0.0392299i
$404$	6.62091	−	1.32062i	0.329403	−	0.0657031i
$405$		−	8.17963i		−	0.406449i
$406$	3.38212	+	5.07052i	0.167852	+	0.251646i
$407$			12.6745i			0.628249i
$408$	−35.4175	−	27.3960i	−1.75343	−	1.35630i
$409$	1.92234	+	17.0612i	0.0950535	+	0.843623i	0.947271	+	0.320435i	$0.103829\pi$
$409$	1.92234	+	17.0612i	0.0950535	+	0.843623i	−0.852217	+	0.523188i	$0.824742\pi$
$410$	−36.2679	−	6.67688i	−1.79114	−	0.329748i
$411$	−1.23144	−	0.593031i	−0.0607426	−	0.0292521i
$412$	−0.146807	−	0.459764i	−0.00723268	−	0.0226509i
$413$	5.55174	−	6.96167i	0.273183	−	0.342561i
$414$	−2.77593	−	17.8195i	−0.136429	−	0.875778i
$415$	6.05756	+	26.5399i	0.297354	+	1.30279i
$416$	14.2989	−	4.80037i	0.701060	−	0.235357i
$417$	5.79960	+	9.23001i	0.284008	+	0.451996i
$418$	−2.69785	+	38.5546i	−0.131956	+	1.88577i
$419$	0.603129	−	2.64248i	0.0294648	−	0.129094i	−0.958056	−	0.286580i	$-0.907482\pi$
$419$	0.603129	−	2.64248i	0.0294648	−	0.129094i	0.987521	+	0.157486i	$0.0503389\pi$
$420$	10.6976	+	5.51935i	0.521989	+	0.269317i
$421$	13.7055	+	4.79576i	0.667965	+	0.233731i	0.642895	−	0.765955i	$-0.277733\pi$
$421$	13.7055	+	4.79576i	0.667965	+	0.233731i	0.0250706	+	0.999686i	$0.492019\pi$
$422$	−1.35495	−	2.53332i	−0.0659577	−	0.123320i
$423$	−7.46211	−	7.46211i	−0.362820	−	0.362820i
$424$	16.1021	−	34.7439i	0.781985	−	1.68731i
$425$	−15.4238	−	1.73785i	−0.748166	−	0.0842981i
$426$	17.0099	−	23.2875i	0.824133	−	1.12828i
$427$	2.29457	−	3.65179i	0.111042	−	0.176722i
$428$	9.42493	+	9.95853i	0.455571	+	0.481364i
$429$	30.8358	−	14.8497i	1.48877	−	0.716952i
$430$	4.09246	−	1.11826i	0.197356	−	0.0539275i
$431$	−19.5342	+	15.5780i	−0.940931	+	0.750368i	−0.968438	−	0.249254i	$-0.919815\pi$
$431$	−19.5342	+	15.5780i	−0.940931	+	0.750368i	0.0275070	+	0.999622i	$0.491243\pi$
$432$	2.49656	−	14.7882i	0.120116	−	0.711499i
$433$	5.42067	+	15.4914i	0.260501	+	0.744469i	0.997636	+	0.0687232i	$0.0218925\pi$
$433$	5.42067	+	15.4914i	0.260501	+	0.744469i	−0.737135	+	0.675746i	$0.763822\pi$
$434$	0.253901	−	0.220692i	0.0121877	−	0.0105935i
$435$	5.14132	−	40.1715i	0.246508	−	1.92608i
$436$	−2.14488	+	15.2511i	−0.102721	+	0.730393i
$437$	15.8943	−	5.56166i	0.760327	−	0.266050i
$438$	9.07913	+	8.34113i	0.433817	+	0.398555i
$439$	−11.9538	−	14.9896i	−0.570524	−	0.715415i	0.409940	−	0.912113i	$-0.365550\pi$
$439$	−11.9538	−	14.9896i	−0.570524	−	0.715415i	−0.980464	+	0.196698i	$0.936978\pi$
$440$	−36.6980	+	4.68649i	−1.74951	+	0.223420i
$441$	−12.0861	−	25.0970i	−0.575527	−	1.19510i
$442$	−21.9541	+	0.930066i	−1.04425	+	0.0442387i
$443$	5.02648	+	3.15834i	0.238815	+	0.150057i	0.646123	−	0.763234i	$-0.276389\pi$
$443$	5.02648	+	3.15834i	0.238815	+	0.150057i	−0.407308	+	0.913291i	$0.633532\pi$
$444$	14.5223	−	1.23267i	0.689200	−	0.0584998i
$445$	0.602315	−	5.34569i	0.0285525	−	0.253410i
$446$	−37.9463	−	11.4999i	−1.79681	−	0.544538i
$447$	11.7681	−	11.7681i	0.556613	−	0.556613i
$448$	−5.12175	−	3.84182i	−0.241980	−	0.181509i
$449$	−7.03778	+	20.1128i	−0.332133	+	0.949182i	0.649825	+	0.760084i	$0.274842\pi$
$449$	−7.03778	+	20.1128i	−0.332133	+	0.949182i	−0.981958	+	0.189098i	$0.939444\pi$
$450$	−6.10362	−	15.3287i	−0.287727	−	0.722603i
$451$	43.3909	+	9.90369i	2.04320	+	0.466346i
$452$	12.3956	+	16.4528i	0.583040	+	0.773874i
$453$	18.2832	−	11.4881i	0.859018	−	0.539757i
$454$	−28.5511	+	19.6731i	−1.33997	+	0.923304i
$455$	5.75921	−	1.31450i	0.269996	−	0.0616249i
$456$	44.4381	−	0.658480i	2.08101	−	0.0308361i
$457$	−17.0415	−	13.5901i	−0.797166	−	0.635718i	0.137799	−	0.990460i	$-0.455997\pi$
$457$	−17.0415	−	13.5901i	−0.797166	−	0.635718i	−0.934964	+	0.354742i	$0.884569\pi$
$458$	−17.9297	−	7.71746i	−0.837800	−	0.360613i
$459$	−9.47992	+	19.6853i	−0.442485	+	0.918829i
$460$	8.19707	+	13.8793i	0.382190	+	0.647125i
$461$	−36.6266	+	4.12683i	−1.70587	+	0.192206i	−0.910384	−	0.413764i	$-0.864214\pi$
$461$	−36.6266	+	4.12683i	−1.70587	+	0.192206i	−0.795488	+	0.605970i	$0.792785\pi$
$462$	−12.6173	−	7.20172i	−0.587008	−	0.335054i
$463$	−23.8950			−1.11050			−0.555248	−	0.831685i	$-0.687377\pi$
$463$	−23.8950			−1.11050			−0.555248	+	0.831685i	$0.687377\pi$
$464$	−6.25317	+	20.6131i	−0.290296	+	0.956937i
$465$	−2.23532			−0.103661
$466$	−17.6726	−	10.0872i	−0.818668	−	0.467282i
$467$	33.6951	−	3.79652i	1.55922	−	0.175682i	0.710185	−	0.704015i	$-0.248611\pi$
$467$	33.6951	−	3.79652i	1.55922	−	0.175682i	0.849037	+	0.528333i	$0.177183\pi$
$468$	−11.8782	−	20.1123i	−0.549072	−	0.929690i
$469$	−1.81724	+	3.77355i	−0.0839126	+	0.174246i
$470$	8.66380	+	3.72915i	0.399632	+	0.172013i
$471$	−19.8805	−	15.8542i	−0.916045	−	0.730521i
$472$	31.4658	−	0.466257i	1.44833	−	0.0214612i
$473$	−4.99183	+	1.13935i	−0.229525	+	0.0523875i
$474$	−27.7304	+	19.1075i	−1.27370	+	0.877638i
$475$	13.0445	−	8.19639i	0.598522	−	0.376076i
$476$	5.61268	+	7.44975i	0.257257	+	0.341459i
$477$	−57.8156	−	13.1960i	−2.64720	−	0.604205i
$478$	14.8324	+	37.2503i	0.678417	+	1.70379i
$479$	−0.848048	+	2.42358i	−0.0387483	+	0.110736i	−0.961632	−	0.274342i	$-0.911540\pi$
$479$	−0.848048	+	2.42358i	−0.0387483	+	0.110736i	0.922884	+	0.385079i	$0.125826\pi$
$480$	8.93887	+	41.5927i	0.408002	+	1.89844i
$481$	5.05749	−	5.05749i	0.230602	−	0.230602i
$482$	−20.6457	−	6.25687i	−0.940388	−	0.284993i
$483$	−0.708711	+	6.28999i	−0.0322475	+	0.286204i
$484$	22.5689	−	1.91566i	1.02586	−	0.0870756i
$485$	−4.14587	−	2.60502i	−0.188254	−	0.118288i
$486$	27.2347	−	1.15377i	1.23539	−	0.0523363i
$487$	17.3472	+	36.0219i	0.786077	+	1.63231i	0.774666	+	0.632371i	$0.217918\pi$
$487$	17.3472	+	36.0219i	0.786077	+	1.63231i	0.0114114	+	0.999935i	$0.496368\pi$
$488$	15.1195	−	1.93082i	0.684427	−	0.0874041i
$489$	−7.06993	−	8.86541i	−0.319713	−	0.400908i
$490$	18.3344	+	16.8441i	0.828266	+	0.760940i
$491$	−2.18407	+	0.764240i	−0.0985659	+	0.0344897i	−0.379111	−	0.925351i	$-0.623770\pi$
$491$	−2.18407	+	0.764240i	−0.0985659	+	0.0344897i	0.280546	+	0.959841i	$0.409485\pi$
$492$	7.12759	−	50.6803i	0.321337	−	2.28485i
$493$	17.0950	−	26.3164i	0.769920	−	1.18523i
$494$	16.4610	−	14.3079i	0.740614	−	0.643744i
$495$	18.9226	+	54.0777i	0.850507	+	2.43061i
$496$	1.17233	+	0.197914i	0.0526392	+	0.00888660i
$497$	−4.69671	+	3.74550i	−0.210676	+	0.168009i
$498$	−36.4438	+	9.95825i	−1.63308	+	0.446240i
$499$	−13.1956	+	6.35469i	−0.590718	+	0.284475i	−0.705266	−	0.708943i	$-0.749172\pi$
$499$	−13.1956	+	6.35469i	−0.590718	+	0.284475i	0.114548	+	0.993418i	$0.463458\pi$
$500$	−8.89202	−	9.39545i	−0.397663	−	0.420178i
$501$	6.79093	−	10.8077i	0.303396	−	0.482853i
$502$	4.48039	−	6.13389i	0.199970	−	0.273769i
$503$	−26.6736	−	3.00540i	−1.18932	−	0.134004i	−0.504955	−	0.863145i	$-0.668491\pi$
$503$	−26.6736	−	3.00540i	−1.18932	−	0.134004i	−0.684363	+	0.729141i	$0.739920\pi$
$504$	−4.16913	+	8.99587i	−0.185708	+	0.400708i
$505$	6.60784	+	6.60784i	0.294045	+	0.294045i
$506$	−9.17507	−	17.1544i	−0.407881	−	0.762608i
$507$	15.1046	+	5.28533i	0.670819	+	0.234730i
$508$	−23.2756	−	12.0089i	−1.03269	−	0.532808i
$509$	−5.55215	+	24.3256i	−0.246095	+	1.07821i	0.689264	+	0.724510i	$0.257934\pi$
$509$	−5.55215	+	24.3256i	−0.246095	+	1.07821i	−0.935359	+	0.353701i	$0.884923\pi$
$510$	4.32629	−	61.8264i	0.191571	−	2.73772i
$511$	−1.36640	−	2.17462i	−0.0604461	−	0.0961994i
$512$	−1.00547	−	22.6051i	−0.0444358	−	0.999012i
$513$	−4.82564	−	21.1425i	−0.213057	−	0.933466i
$514$	−2.46713	−	15.8372i	−0.108820	−	0.698549i
$515$	0.416516	−	0.522294i	0.0183539	−	0.0230150i
$516$	1.79095	+	5.60882i	0.0788423	+	0.246914i
$517$	−10.2564	−	4.93920i	−0.451074	−	0.217226i
$518$	−2.98586	−	0.549695i	−0.131191	−	0.0241522i
$519$	−3.56519	−	31.6419i	−0.156494	−	1.38893i
$520$	16.5137	+	12.7736i	0.724173	+	0.560159i
$521$			7.12512i			0.312157i	0.987745	+	0.156079i	$0.0498853\pi$
$521$			7.12512i			0.312157i	−0.987745	+	0.156079i	$0.950115\pi$
$522$	33.2379	+	2.83049i	1.45478	+	0.123887i
$523$			38.0156i			1.66231i	0.556042	+	0.831154i	$0.312319\pi$
$523$			38.0156i			1.66231i	−0.556042	+	0.831154i	$0.687681\pi$
$524$	23.5832	−	4.70393i	1.03024	−	0.205492i
$525$	0.648382	+	5.75455i	0.0282977	+	0.251149i
$526$	−2.16473	+	11.7585i	−0.0943866	+	0.512694i
$527$	−1.56054	−	0.751517i	−0.0679782	−	0.0327366i
$528$	−8.65386	−	50.6093i	−0.376611	−	2.20249i
$529$	9.05552	−	11.3553i	0.393718	−	0.493707i
$530$	52.3729	−	8.15869i	2.27493	−	0.354391i
$531$	−10.8443	−	47.5119i	−0.470602	−	2.06184i
$532$	−8.96573	−	2.30769i	−0.388714	−	0.100051i
$533$	−13.3624	−	21.2661i	−0.578790	−	0.921139i
$534$	7.44759	+	0.521143i	0.322289	+	0.0225521i
$535$	−4.22315	+	18.5028i	−0.182583	+	0.799947i
$536$	−14.3807	+	3.50725i	−0.621151	+	0.151490i
$537$	54.7183	+	19.1468i	2.36127	+	0.826243i
$538$	−4.03790	+	2.15968i	−0.174086	+	0.0931102i
$539$	−21.2473	−	21.2473i	−0.915187	−	0.915187i
$540$	18.9439	−	8.48884i	0.815214	−	0.365301i
$541$	−22.4426	−	2.52867i	−0.964882	−	0.108716i	−0.384557	−	0.923101i	$-0.625646\pi$
$541$	−22.4426	−	2.52867i	−0.964882	−	0.108716i	−0.580325	+	0.814385i	$0.697074\pi$
$542$	7.97708	+	5.82672i	0.342645	+	0.250279i
$543$	−8.38335	+	13.3420i	−0.359764	+	0.572561i
$544$	−7.74303	+	32.0423i	−0.331980	+	1.37380i
$545$	−19.2065	+	9.24935i	−0.822715	+	0.396198i
$546$	2.16096	+	7.90837i	0.0924806	+	0.338447i
$547$	17.3138	−	13.8073i	0.740283	−	0.590356i	−0.179048	−	0.983840i	$-0.557302\pi$
$547$	17.3138	−	13.8073i	0.740283	−	0.590356i	0.919331	+	0.393484i	$0.128730\pi$
$548$	−0.0276903	+	1.00586i	−0.00118287	+	0.0429682i
$549$	−7.79605	−	22.2798i	−0.332727	−	0.950880i
$550$	−11.6759	−	13.4328i	−0.497861	−	0.572778i
$551$	3.01991	+	31.0009i	0.128652	+	1.32068i
$552$	−18.7632	+	12.1811i	−0.798614	+	0.518464i
$553$	6.62140	−	2.31693i	0.281571	−	0.0985259i
$554$	18.4769	−	20.1116i	0.785006	−	0.854461i
$555$	12.5779	+	15.7722i	0.533904	+	0.669495i
$556$	4.45506	−	6.67509i	0.188937	−	0.283087i
$557$	7.97886	+	16.5683i	0.338075	+	0.702020i	0.998819	−	0.0485915i	$-0.0154732\pi$
$557$	7.97886	+	16.5683i	0.338075	+	0.702020i	−0.660744	+	0.750612i	$0.729759\pi$
$558$	−0.0779302	−	1.83953i	−0.00329905	−	0.0778736i
$559$	2.44653	+	1.53726i	0.103477	+	0.0650190i
$560$	0.487557	−	8.84862i	0.0206030	−	0.373923i
$561$	−8.37494	+	74.3296i	−0.353590	+	3.13820i
$562$	−9.27157	+	30.5933i	−0.391098	+	1.29050i
$563$	27.2146	−	27.2146i	1.14696	−	1.14696i	0.159814	−	0.987147i	$-0.448911\pi$
$563$	27.2146	−	27.2146i	1.14696	−	1.14696i	0.987147	−	0.159814i	$-0.0510893\pi$
$564$	−4.66183	+	12.2321i	−0.196298	+	0.515063i
$565$	−9.41728	+	26.9130i	−0.396188	+	1.13224i
$566$	−2.54711	+	1.01421i	−0.107063	+	0.0426305i
$567$	−2.30542	−	0.526198i	−0.0968187	−	0.0220982i
$568$	−20.7662	−	4.41710i	−0.871331	−	0.185337i
$569$	−6.77494	+	4.25698i	−0.284020	+	0.178462i	−0.666506	−	0.745500i	$-0.732211\pi$
$569$	−6.77494	+	4.25698i	−0.284020	+	0.178462i	0.382486	+	0.923961i	$0.375068\pi$
$570$	34.9038	+	50.6551i	1.46196	+	2.12171i
$571$	−30.0769	+	6.86486i	−1.25868	+	0.287285i	−0.799288	−	0.600948i	$-0.794790\pi$
$571$	−30.0769	+	6.86486i	−1.25868	+	0.287285i	−0.459392	+	0.888234i	$0.651933\pi$
$572$	−19.2598	−	16.2460i	−0.805291	−	0.679280i
$573$	−18.1339	−	14.4613i	−0.757556	−	0.604131i
$574$	−4.21500	+	9.79255i	−0.175931	+	0.408733i
$575$	−3.36457	+	6.98660i	−0.140312	+	0.291361i
$576$	−33.9166	+	8.80619i	−1.41319	+	0.366925i
$577$	18.6080	−	2.09662i	0.774661	−	0.0872833i	0.284221	−	0.958759i	$-0.408265\pi$
$577$	18.6080	−	2.09662i	0.774661	−	0.0872833i	0.490439	+	0.871475i	$0.336836\pi$
$578$	11.8886	−	20.8285i	0.494499	−	0.866352i
$579$	−1.86791			−0.0776275
$580$	−28.5364	+	8.63961i	−1.18491	+	0.358740i
$581$	7.86994			0.326500
$582$	3.36853	−	5.90158i	0.139630	−	0.244629i
$583$	−63.5683	+	7.16242i	−2.63273	+	0.296637i
$584$	2.87057	−	8.61079i	0.118785	−	0.356317i
$585$	14.0279	−	29.1293i	0.579984	−	1.20435i
$586$	11.1438	−	25.8899i	0.460345	−	1.06950i
$587$	22.9858	+	18.3306i	0.948725	+	0.756583i	0.969978	−	0.243191i	$-0.0781942\pi$
$587$	22.9858	+	18.3306i	0.948725	+	0.756583i	−0.0212533	+	0.999774i	$0.506766\pi$
$588$	−22.2787	+	26.4115i	−0.918757	+	1.08919i
$589$	1.67607	−	0.382551i	0.0690611	−	0.0157627i
$590$	24.7147	+	35.8679i	1.01749	+	1.47666i
$591$	−48.7599	+	30.6379i	−2.00572	+	1.26027i
$592$	−5.20014	−	9.38552i	−0.213724	−	0.385743i
$593$	6.64250	+	1.51611i	0.272775	+	0.0622591i	0.356720	−	0.934211i	$-0.383895\pi$
$593$	6.64250	+	1.51611i	0.272775	+	0.0622591i	−0.0839453	+	0.996470i	$0.526752\pi$
$594$	−23.2762	+	9.26817i	−0.955035	+	0.380278i
$595$	−4.26410	+	12.1861i	−0.174811	+	0.499582i
$596$	−11.4491	−	4.36341i	−0.468972	−	0.178732i
$597$	3.58113	−	3.58113i	0.146566	−	0.146566i
$598$	−3.18401	+	10.5063i	−0.130204	+	0.429633i
$599$	−1.05006	+	9.31958i	−0.0429045	+	0.380788i	0.953850	+	0.300284i	$0.0970815\pi$
$599$	−1.05006	+	9.31958i	−0.0429045	+	0.380788i	−0.996754	+	0.0805037i	$0.974347\pi$
$600$	−14.2558	+	14.6846i	−0.581989	+	0.599496i
$601$	23.0323	+	14.4721i	0.939507	+	0.590331i	0.912399	−	0.409301i	$-0.134228\pi$
$601$	23.0323	+	14.4721i	0.939507	+	0.590331i	0.0271074	+	0.999633i	$0.491370\pi$
$602$	−0.0519129	−	1.22540i	−0.00211581	−	0.0499434i
$603$	9.94588	+	20.6528i	0.405027	+	0.841048i
$604$	−13.2223	−	8.82475i	−0.538007	−	0.359074i
$605$	19.5471	+	24.5113i	0.794704	+	0.996528i
$606$	−8.77411	+	9.55042i	−0.356424	+	0.387959i
$607$	20.5398	−	7.18720i	0.833686	−	0.291719i	0.120517	−	0.992711i	$-0.461545\pi$
$607$	20.5398	−	7.18720i	0.833686	−	0.291719i	0.713169	+	0.700992i	$0.247259\pi$
$608$	−13.8206	−	29.6568i	−0.560499	−	1.20274i
$609$	−10.9916	−	4.03332i	−0.445401	−	0.163439i
$610$	13.8405	+	15.9233i	0.560387	+	0.644714i
$611$	2.12171	+	6.06349i	0.0858351	+	0.245303i
$612$	51.0302	+	1.40481i	2.06277	+	0.0567860i
$613$	−24.5855	+	19.6063i	−0.993000	+	0.791891i	−0.978129	−	0.207999i	$-0.933305\pi$
$613$	−24.5855	+	19.6063i	−0.993000	+	0.791891i	−0.0148705	+	0.999889i	$0.504734\pi$
$614$	−0.166148	−	0.608044i	−0.00670519	−	0.0245387i
$615$	63.8244	−	30.7362i	2.57365	−	1.23940i
$616$	−1.03991	+	10.6448i	−0.0418992	+	0.428891i
$617$	−2.79459	+	4.44756i	−0.112506	+	0.179052i	−0.898231	−	0.439524i	$-0.855147\pi$
$617$	−2.79459	+	4.44756i	−0.112506	+	0.179052i	0.785725	+	0.618576i	$0.212290\pi$
$618$	0.748667	+	0.546851i	0.0301158	+	0.0219976i
$619$	1.76648	+	0.199034i	0.0710008	+	0.00799987i	0.147393	−	0.989078i	$-0.452912\pi$
$619$	1.76648	+	0.199034i	0.0710008	+	0.00799987i	−0.0763926	+	0.997078i	$0.524340\pi$
$620$	0.672949	+	1.50177i	0.0270263	+	0.0603124i
$621$	7.71864	+	7.71864i	0.309738	+	0.309738i
$622$	30.8133	−	16.4805i	1.23550	−	0.660807i
$623$	−1.46793	−	0.513652i	−0.0588115	−	0.0205790i
$624$	−16.7415	+	23.6478i	−0.670196	+	0.946670i
$625$	6.94783	−	30.4404i	0.277913	−	1.21762i
$626$	11.1842	+	0.782615i	0.447012	+	0.0312796i
$627$	−39.4996	−	62.8632i	−1.57746	−	2.51051i
$628$	−4.66631	+	18.1293i	−0.186206	+	0.723440i
$629$	3.47838	+	15.2398i	0.138692	+	0.607649i
$630$	−13.5604	+	2.11244i	−0.540258	+	0.0841617i
$631$	−0.662848	+	0.831185i	−0.0263875	+	0.0330889i	−0.794850	−	0.606806i	$-0.792451\pi$
$631$	−0.662848	+	0.831185i	−0.0263875	+	0.0330889i	0.768463	+	0.639895i	$0.221022\pi$
$632$	21.1854	+	12.8778i	0.842710	+	0.512253i
$633$	4.97219	+	2.39448i	0.197627	+	0.0951721i
$634$	6.55833	−	35.6239i	0.260465	−	1.41481i
$635$	−4.05897	−	36.0244i	−0.161075	−	1.42958i
$636$	14.3891	+	72.1397i	0.570564	+	2.86053i
$637$			16.9566i			0.671847i
$638$	34.8507	−	8.95996i	1.37975	−	0.354728i
$639$			32.8784i			1.30065i
$640$	25.2524	−	18.5270i	0.998187	−	0.732345i
$641$	0.411004	+	3.64777i	0.0162337	+	0.144078i	0.999214	−	0.0396308i	$-0.0126182\pi$
$641$	0.411004	+	3.64777i	0.0162337	+	0.144078i	−0.982981	+	0.183709i	$0.941190\pi$
$642$	−25.9036	−	4.76884i	−1.02233	−	0.188211i
$643$	−27.4351	−	13.2120i	−1.08193	−	0.521031i	−0.193999	−	0.981002i	$-0.562146\pi$
$643$	−27.4351	−	13.2120i	−1.08193	−	0.521031i	−0.887934	+	0.459970i	$0.847860\pi$
$644$	4.43919	−	1.41748i	0.174929	−	0.0558565i
$645$	−5.08122	+	6.37165i	−0.200073	+	0.250883i
$646$	7.33703	+	47.0985i	0.288672	+	1.85306i
$647$	−6.36311	−	27.8786i	−0.250160	−	1.09602i	−0.931410	−	0.363971i	$-0.881421\pi$
$647$	−6.36311	−	27.8786i	−0.250160	−	1.09602i	0.681251	−	0.732050i	$-0.261436\pi$
$648$	−3.73724	−	7.47508i	−0.146813	−	0.293649i
$649$	−27.9689	−	44.5122i	−1.09787	−	1.74726i
$650$	−0.701087	+	10.0191i	−0.0274989	+	0.392983i
$651$	−0.143799	+	0.630024i	−0.00563592	+	0.0246926i
$652$	−3.82767	+	7.41877i	−0.149903	+	0.290542i
$653$	11.4348	+	4.00119i	0.447477	+	0.156579i	0.544604	−	0.838693i	$-0.316680\pi$
$653$	11.4348	+	4.00119i	0.447477	+	0.156579i	−0.0971278	+	0.995272i	$0.530966\pi$
$654$	−13.9531	−	26.0879i	−0.545610	−	1.02012i
$655$	23.5366	+	23.5366i	0.919652	+	0.919652i
$656$	−36.1946	+	10.4689i	−1.41316	+	0.408741i
$657$	−13.9679	−	1.57380i	−0.544939	−	0.0613999i
$658$	1.60840	−	2.20199i	0.0627021	−	0.0858425i
$659$	−15.9790	+	25.4304i	−0.622452	+	0.990627i	0.375510	+	0.926818i	$0.377468\pi$
$659$	−15.9790	+	25.4304i	−0.622452	+	0.990627i	−0.997962	+	0.0638088i	$0.979675\pi$
$660$	51.6164	−	48.8507i	2.00917	−	1.90151i
$661$	−40.9883	+	19.7389i	−1.59426	+	0.767755i	−0.999350	−	0.0360380i	$-0.988526\pi$
$661$	−40.9883	+	19.7389i	−1.59426	+	0.767755i	−0.594909	+	0.803793i	$0.702812\pi$
$662$	1.97358	−	0.539282i	0.0767056	−	0.0209598i
$663$	33.0016	−	26.3179i	1.28168	−	1.02210i
$664$	17.6618	+	21.4862i	0.685410	+	0.833828i
$665$	−4.23234	−	12.0953i	−0.164123	−	0.469037i
$666$	−12.5411	+	10.9007i	−0.485957	+	0.422395i
$667$	−9.58909	−	12.4038i	−0.371291	−	0.480279i
$668$	−9.30542	−	1.30870i	−0.360037	−	0.0506350i
$669$	71.8928	−	25.1564i	2.77954	−	0.972602i
$670$	−15.0878	−	13.8614i	−0.582892	−	0.535512i
$671$	−15.8756	−	19.9074i	−0.612870	−	0.768515i
$672$	12.2979	+	0.156256i	0.474403	+	0.00602771i
$673$	−3.68482	−	7.65161i	−0.142039	−	0.294948i	0.817798	−	0.575506i	$-0.195195\pi$
$673$	−3.68482	−	7.65161i	−0.142039	−	0.294948i	−0.959837	+	0.280558i	$0.909481\pi$
$674$	19.6512	−	0.832507i	0.756936	−	0.0320670i
$675$	8.45590	+	5.31319i	0.325468	+	0.204505i
$676$	−0.996411	−	11.7390i	−0.0383235	−	0.451499i
$677$	5.20686	−	46.2121i	0.200116	−	1.77608i	−0.345871	−	0.938282i	$-0.612416\pi$
$677$	5.20686	−	46.2121i	0.200116	−	1.77608i	0.545986	−	0.837794i	$-0.316155\pi$
$678$	−37.8702	−	11.4769i	−1.45439	−	0.440767i
$679$	−1.00093	+	1.00093i	−0.0384121	+	0.0384121i
$680$	−42.8396	+	15.7065i	−1.64282	+	0.602315i
$681$	21.9982	−	62.8672i	0.842972	−	2.40908i
$682$	−0.734730	−	1.84521i	−0.0281343	−	0.0706569i
$683$	37.1656	+	8.48280i	1.42210	+	0.324585i	0.863290	−	0.504709i	$-0.168400\pi$
$683$	37.1656	+	8.48280i	1.42210	+	0.324585i	0.558812	+	0.829294i	$0.311257\pi$
$684$	−40.4692	+	30.4897i	−1.54738	+	1.16580i
$685$	−1.17931	+	0.741010i	−0.0450591	+	0.0283125i
$686$	12.4509	−	8.57925i	0.475377	−	0.327557i
$687$	36.5571	−	8.34392i	1.39474	−	0.318340i
$688$	3.22903	−	2.89177i	0.123106	−	0.110248i
$689$	28.2237	+	22.5076i	1.07524	+	0.857473i
$690$	−28.4414	−	12.2420i	−1.08275	−	0.466045i
$691$	−5.72748	+	11.8932i	−0.217884	+	0.452440i	−0.981048	−	0.193764i	$-0.937930\pi$
$691$	−5.72748	+	11.8932i	−0.217884	+	0.452440i	0.763165	+	0.646204i	$0.223645\pi$
$692$	−20.1848	+	11.9211i	−0.767312	+	0.453172i
$693$	16.4591	−	1.85449i	0.625228	−	0.0704462i
$694$	−37.2767	−	21.2769i	−1.41500	−	0.807661i
$695$	11.1082			0.421357
$696$	−13.6557	−	39.0604i	−0.517619	−	1.48058i
$697$	54.8912			2.07915
$698$	28.2370	+	16.1172i	1.06878	+	0.610045i
$699$	38.8434	−	4.37660i	1.46919	−	0.165538i
$700$	3.67091	−	2.16803i	0.138747	−	0.0819438i
$701$	7.74530	−	16.0833i	0.292536	−	0.607457i	−0.701962	−	0.712214i	$-0.747692\pi$
$701$	7.74530	−	16.0833i	0.292536	−	0.607457i	0.994498	+	0.104758i	$0.0334067\pi$
$702$	12.9862	+	5.58964i	0.490132	+	0.210967i
$703$	−12.1303	−	9.67360i	−0.457504	−	0.364847i
$704$	−31.3958	+	21.0500i	−1.18327	+	0.793353i
$705$	−17.6647	+	4.03186i	−0.665293	+	0.151849i
$706$	9.62345	−	6.63102i	0.362183	−	0.249562i
$707$	2.28750	−	1.43733i	0.0860302	−	0.0540564i
$708$	−48.2818	+	36.3757i	−1.81454	+	1.36708i
$709$	23.4483	+	5.35192i	0.880618	+	0.200995i	0.638843	−	0.769337i	$-0.279413\pi$
$709$	23.4483	+	5.35192i	0.880618	+	0.200995i	0.241775	+	0.970332i	$0.422270\pi$
$710$	−10.8711	−	27.3019i	−0.407987	−	1.02462i
$711$	12.6807	−	36.2393i	0.475563	−	1.35908i
$712$	−1.89199	−	5.16044i	−0.0709054	−	0.193396i
$713$	−0.611892	+	0.611892i	−0.0229155	+	0.0229155i
$714$	−17.1474	−	5.19668i	−0.641727	−	0.194481i
$715$	3.90488	−	34.6568i	0.146034	−	1.29609i
$716$	−3.60962	−	42.5258i	−0.134898	−	1.58926i
$717$	−65.2148	−	40.9772i	−2.43549	−	1.53032i
$718$	12.3312	−	0.522402i	0.460197	−	0.0194959i
$719$	−10.0745	−	20.9199i	−0.375715	−	0.780181i	0.624284	−	0.781197i	$-0.285391\pi$
$719$	−10.0745	−	20.9199i	−0.375715	−	0.780181i	−0.999999	+	0.00101645i	$0.999676\pi$
$720$	−36.1996	−	32.2812i	−1.34908	−	1.20305i
$721$	−0.120414	−	0.150994i	−0.00448444	−	0.00562331i
$722$	−15.0531	−	13.8295i	−0.560219	−	0.514682i
$723$	39.1153	−	13.6870i	1.45471	−	0.509027i
$724$	11.4875	+	1.61558i	0.426928	+	0.0600424i
$725$	−11.0780	−	9.11131i	−0.411428	−	0.338386i
$726$	−32.8386	+	28.5434i	−1.21875	+	1.05935i
$727$	0.570671	+	1.63088i	0.0211650	+	0.0604861i	0.953981	−	0.299866i	$-0.0969421\pi$
$727$	0.570671	+	1.63088i	0.0211650	+	0.0604861i	−0.932816	+	0.360353i	$0.882656\pi$
$728$	4.66256	−	3.83264i	0.172806	−	0.142047i
$729$	−34.0091	+	27.1214i	−1.25960	+	1.00450i
$730$	12.1192	−	3.31157i	0.448552	−	0.122567i
$731$	−5.68950	+	2.73992i	−0.210434	+	0.101340i
$732$	−21.2658	+	20.1263i	−0.786007	+	0.743890i
$733$	−4.56828	+	7.27038i	−0.168733	+	0.268538i	−0.920377	−	0.391031i	$-0.872118\pi$
$733$	−4.56828	+	7.27038i	−0.168733	+	0.268538i	0.751644	+	0.659569i	$0.229261\pi$
$734$	0.673284	−	0.921761i	0.0248514	−	0.0340228i
$735$	−47.5260	−	5.35489i	−1.75302	−	0.197518i
$736$	13.8324	+	8.93860i	0.509870	+	0.329481i
$737$	17.4848	+	17.4848i	0.644063	+	0.644063i
$738$	27.5191	+	51.4520i	1.01299	+	1.89397i
$739$	−24.1179	−	8.43923i	−0.887193	−	0.310442i	−0.152065	−	0.988371i	$-0.548592\pi$
$739$	−24.1179	−	8.43923i	−0.887193	−	0.310442i	−0.735128	+	0.677928i	$0.762878\pi$
$740$	6.80972	−	13.1986i	0.250330	−	0.485189i
$741$	−9.32279	+	40.8458i	−0.342481	+	1.50051i
$742$	1.06964	−	15.2861i	0.0392678	−	0.561171i
$743$	−4.56805	−	7.27002i	−0.167586	−	0.266711i	0.752364	−	0.658748i	$-0.228914\pi$
$743$	−4.56805	−	7.27002i	−0.167586	−	0.266711i	−0.919950	+	0.392037i	$0.871771\pi$
$744$	−2.04278	+	1.02131i	−0.0748921	+	0.0374430i
$745$	−3.77377	−	16.5340i	−0.138260	−	0.605758i
$746$	3.49489	+	22.4347i	0.127957	+	0.821391i
$747$	26.8553	−	33.6755i	0.982586	−	1.23212i
$748$	52.4585	−	16.7505i	1.91807	−	0.612460i
$749$	4.94333	+	2.38058i	0.180625	+	0.0869846i
$750$	24.4390	+	4.49920i	0.892385	+	0.164287i
$751$	−4.03353	−	35.7985i	−0.147185	−	1.30631i	−0.822495	−	0.568772i	$-0.807418\pi$
$751$	−4.03353	−	35.7985i	−0.147185	−	1.30631i	0.675309	−	0.737534i	$-0.264010\pi$
$752$	9.62139	−	0.550516i	0.350856	−	0.0200753i
$753$			14.5915i			0.531743i
$754$	−17.4818	−	10.3312i	−0.636649	−	0.376240i
$755$		−	22.0035i		−	0.800789i
$756$	−1.17391	−	5.88540i	−0.0426947	−	0.214050i
$757$	−0.576625	−	5.11768i	−0.0209578	−	0.186005i	0.978872	−	0.204476i	$-0.0655489\pi$
$757$	−0.576625	−	5.11768i	−0.0209578	−	0.186005i	−0.999829	+	0.0184703i	$0.994120\pi$
$758$	6.40677	−	34.8006i	0.232704	−	1.26402i
$759$	33.6694	+	16.2143i	1.22212	+	0.588543i
$760$	23.5240	−	38.6994i	0.853305	−	1.40378i
$761$	4.01541	−	5.03517i	0.145559	−	0.182525i	−0.703707	−	0.710490i	$-0.748473\pi$
$761$	4.01541	−	5.03517i	0.145559	−	0.182525i	0.849266	+	0.527965i	$0.177045\pi$
$762$	49.7121	−	7.74418i	1.80088	−	0.280542i
$763$	1.37137	+	6.00834i	0.0496468	+	0.217517i
$764$	−4.25636	+	16.5366i	−0.153990	+	0.598274i
$765$	37.5936	+	59.8299i	1.35920	+	2.16315i
$766$	27.3370	+	1.91290i	0.987726	+	0.0691159i
$767$	−6.60129	+	28.9221i	−0.238359	+	1.04432i
$768$	27.1725	+	33.9260i	0.980503	+	1.22420i
$769$	−27.5228	−	9.63063i	−0.992496	−	0.347289i	−0.215300	−	0.976548i	$-0.569073\pi$
$769$	−27.5228	−	9.63063i	−0.992496	−	0.347289i	−0.777196	+	0.629259i	$0.783359\pi$
$770$	−13.0543	+	6.98210i	−0.470444	+	0.251617i
$771$	21.7715	+	21.7715i	0.784080	+	0.784080i
$772$	0.562338	+	1.25492i	0.0202390	+	0.0451657i
$773$	22.6981	+	2.55746i	0.816393	+	0.0919855i	0.510279	−	0.860009i	$-0.329542\pi$
$773$	22.6981	+	2.55746i	0.816393	+	0.0919855i	0.306115	+	0.951995i	$0.400971\pi$
$774$	−5.42062	−	3.95940i	−0.194840	−	0.142318i
$775$	−0.421201	+	0.670338i	−0.0151300	+	0.0240792i
$776$	−4.97899	−	0.486407i	−0.178735	−	0.0174610i
$777$	5.25454	−	2.53045i	0.188506	−	0.0907795i
$778$	−4.73596	−	17.3320i	−0.169793	−	0.621382i
$779$	−42.5960	+	33.9692i	−1.52616	+	1.21707i
$780$	−40.0894	−	1.10362i	−1.43543	−	0.0395160i
$781$	11.7138	+	33.4761i	0.419153	+	1.19787i
$782$	−15.7400	−	18.1085i	−0.562860	−	0.647559i
$783$	−17.2564	+	10.4830i	−0.616693	+	0.374632i
$784$	24.4512	+	7.01633i	0.873259	+	0.250583i
$785$	−24.4576	+	8.55810i	−0.872931	+	0.305452i
$786$	−31.2527	+	34.0179i	−1.11475	+	1.21338i
$787$	14.4631	+	18.1361i	0.515552	+	0.646482i	0.969658	−	0.244466i	$-0.0786125\pi$
$787$	14.4631	+	18.1361i	0.515552	+	0.646482i	−0.454106	+	0.890948i	$0.650041\pi$
$788$	35.2629	+	23.5350i	1.25619	+	0.838400i
$789$	−9.96506	−	20.6927i	−0.354766	−	0.736678i
$790$	1.45248	+	34.2857i	0.0516771	+	1.21983i
$791$	6.97961	+	4.38558i	0.248166	+	0.155933i
$792$	42.0006	+	40.7740i	1.49243	+	1.44884i
$793$	−1.60880	+	14.2785i	−0.0571301	+	0.507044i
$794$	−9.89705	+	32.6572i	−0.351233	+	1.15896i
$795$	−71.9973	+	71.9973i	−2.55348	+	2.55348i
$796$	−3.48403	−	1.32782i	−0.123488	−	0.0470633i
$797$	−10.2962	+	29.4249i	−0.364711	+	1.04228i	0.604618	+	0.796515i	$0.293326\pi$
$797$	−10.2962	+	29.4249i	−0.364711	+	1.04228i	−0.969329	+	0.245767i	$0.920960\pi$
$798$	16.5225	−	6.57896i	0.584890	−	0.232893i
$799$	−13.6878	−	3.12414i	−0.484238	−	0.110524i
$800$	14.1574	+	5.15668i	0.500538	+	0.182316i
$801$	−7.20708	+	4.52851i	−0.254650	+	0.160007i
$802$	−28.1928	−	40.9157i	−0.995524	−	1.44478i
$803$	−14.7826	+	3.37402i	−0.521666	+	0.119067i
$804$	18.3336	−	21.7346i	0.646575	−	0.766520i
$805$	5.04295	+	4.02162i	0.177741	+	0.141743i
$806$	−0.443116	+	1.02948i	−0.0156081	+	0.0362617i
$807$	3.81662	−	7.92529i	0.134351	−	0.278983i
$808$	9.05777	+	3.01958i	0.318651	+	0.106228i
$809$	−30.6338	+	3.45160i	−1.07703	+	0.121352i	−0.632612	−	0.774469i	$-0.718017\pi$
$809$	−30.6338	+	3.45160i	−1.07703	+	0.121352i	−0.444415	+	0.895821i	$0.646589\pi$
$810$	5.73433	−	10.0464i	0.201484	−	0.352995i
$811$	34.7966			1.22187			0.610937	−	0.791679i	$-0.290793\pi$
$811$	34.7966			1.22187			0.610937	+	0.791679i	$0.290793\pi$
$812$	0.599314	+	8.59876i	0.0210318	+	0.301757i
$813$	−18.9761			−0.665522
$814$	−8.88541	+	15.5670i	−0.311434	+	0.545625i
$815$	−11.4823	+	1.29374i	−0.402207	+	0.0453178i
$816$	−24.2946	−	58.4777i	−0.850482	−	2.04713i
$817$	2.71951	−	5.64712i	0.0951436	−	0.197568i
$818$	−9.59970	+	22.3026i	−0.335646	+	0.779793i
$819$	−7.30766	−	5.82766i	−0.255350	−	0.203635i
$820$	−39.8642	−	33.6263i	−1.39212	−	1.17428i
$821$	49.3852	−	11.2719i	1.72356	−	0.393390i	0.757727	−	0.652571i	$-0.226310\pi$
$821$	49.3852	−	11.2719i	1.72356	−	0.393390i	0.965829	+	0.259181i	$0.0834525\pi$
$822$	−1.09674	−	1.59168i	−0.0382532	−	0.0555161i
$823$	22.7792	−	14.3131i	0.794032	−	0.498923i	−0.0729065	−	0.997339i	$-0.523227\pi$
$823$	22.7792	−	14.3131i	0.794032	−	0.498923i	0.866938	+	0.498416i	$0.166085\pi$
$824$	0.142005	−	0.667611i	0.00494698	−	0.0232573i
$825$	33.3319	+	7.60779i	1.16047	+	0.264869i
$826$	11.6992	−	4.65843i	0.407069	−	0.162087i
$827$	−5.84917	+	16.7160i	−0.203396	+	0.581272i	−0.999722	−	0.0235963i	$-0.992488\pi$
$827$	−5.84917	+	16.7160i	−0.203396	+	0.581272i	0.796326	+	0.604868i	$0.206774\pi$
$828$	9.08286	−	23.8323i	0.315651	−	0.828230i
$829$	−28.8430	+	28.8430i	−1.00176	+	1.00176i	−0.00176066	+	0.999998i	$0.500560\pi$
$829$	−28.8430	+	28.8430i	−1.00176	+	1.00176i	−0.999998	+	0.00176066i	$0.999440\pi$
$830$	−11.1658	+	36.8436i	−0.387569	+	1.27886i
$831$	−5.87394	+	52.1327i	−0.203765	+	1.80846i
$832$	20.9275	+	4.12829i	0.725530	+	0.143123i
$833$	−31.3789	−	19.7167i	−1.08721	−	0.683142i
$834$	0.652506	+	15.4023i	0.0225944	+	0.533338i
$835$	−5.64348	−	11.7188i	−0.195301	−	0.405546i
$836$	−30.3422	+	45.4623i	−1.04941	+	1.57235i
$837$	0.694833	+	0.871294i	0.0240170	+	0.0301163i
$838$	2.59329	−	2.82273i	0.0895836	−	0.0975097i
$839$	−50.1924	+	17.5631i	−1.73283	+	0.606345i	−0.997454	−	0.0713102i	$-0.977282\pi$
$839$	−50.1924	+	17.5631i	−1.73283	+	0.606345i	−0.735380	+	0.677655i	$0.762996\pi$
$840$	9.26968	+	14.2785i	0.319834	+	0.492656i
$841$	26.4959	−	11.7883i	0.913653	−	0.406494i
$842$	13.4713	+	15.4985i	0.464253	+	0.534113i
$843$	−20.2818	−	57.9620i	−0.698541	−	1.99632i
$844$	0.111805	−	4.06136i	0.00384849	−	0.139798i
$845$	12.7493	−	10.1672i	0.438589	−	0.349763i
$846$	−3.93382	−	14.3964i	−0.135248	−	0.494959i
$847$	8.16598	−	3.93253i	0.280586	−	0.135123i
$848$	44.1341	−	31.3849i	1.51557	−	1.07776i
$849$	2.80194	−	4.45927i	0.0961625	−	0.153042i
$850$	−17.7256	−	12.9473i	−0.607982	−	0.444090i
$851$	7.76052	+	0.874401i	0.266027	+	0.0299741i
$852$	37.2176	−	16.6774i	1.27506	−	0.571359i
$853$	16.2813	+	16.2813i	0.557460	+	0.557460i	0.928583	−	0.371124i	$-0.121027\pi$
$853$	16.2813	+	16.2813i	0.557460	+	0.557460i	−0.371124	+	0.928583i	$0.621027\pi$
$854$	5.37833	−	2.87660i	0.184043	−	0.0984353i
$855$	−66.1984	−	23.1638i	−2.26394	−	0.792186i
$856$	4.59448	+	18.8386i	0.157036	+	0.643891i
$857$	5.24907	−	22.9977i	0.179305	−	0.785586i	−0.802647	−	0.596454i	$-0.796576\pi$
$857$	5.24907	−	22.9977i	0.179305	−	0.785586i	0.981952	−	0.189131i	$-0.0605672\pi$
$858$	48.2836	+	3.37863i	1.64838	+	0.115345i
$859$	20.0097	+	31.8453i	0.682723	+	1.08655i	0.990819	+	0.135192i	$0.0431651\pi$
$859$	20.0097	+	31.8453i	0.682723	+	1.08655i	−0.308097	+	0.951355i	$0.599692\pi$
$860$	5.81041	+	1.49554i	0.198133	+	0.0509975i
$861$	−4.55714	−	19.9661i	−0.155307	−	0.680445i
$862$	−34.9134	+	5.43883i	−1.18915	+	0.185247i
$863$	4.37904	−	5.49114i	0.149064	−	0.186921i	−0.701693	−	0.712479i	$-0.747572\pi$
$863$	4.37904	−	5.49114i	0.149064	−	0.186921i	0.850757	+	0.525559i	$0.176144\pi$
$864$	13.4336	−	16.4130i	0.457021	−	0.558383i
$865$	−29.2344	−	14.0785i	−0.993999	−	0.478685i
$866$	−4.20244	+	22.8270i	−0.142805	+	0.775694i
$867$	5.15815	+	45.7799i	0.175180	+	1.55477i
$868$	0.466563	−	0.0930612i	0.0158362	−	0.00315870i
$869$		−	41.4160i		−	1.40494i
$870$	34.4769	−	45.7352i	1.16888	−	1.55057i
$871$		−	13.9540i		−	0.472812i
$872$	−13.3261	+	17.2280i	−0.451280	+	0.583414i
$873$	0.867418	+	7.69854i	0.0293576	+	0.260556i
$874$	23.4207	+	4.31174i	0.792218	+	0.145847i
$875$	−4.66383	−	2.24598i	−0.157666	−	0.0759280i
$876$	5.30364	+	16.6097i	0.179193	+	0.561189i
$877$	16.1732	−	20.2805i	0.546129	−	0.684824i	−0.429797	−	0.902926i	$-0.641415\pi$
$877$	16.1732	−	20.2805i	0.546129	−	0.684824i	0.975926	+	0.218101i	$0.0699863\pi$
$878$	−4.17349	−	26.7908i	−0.140848	−	0.904145i
$879$	12.0483	+	52.7873i	0.406381	+	1.78047i
$880$	−48.3588	−	19.9711i	−1.63018	−	0.673225i
$881$	20.1862	+	32.1261i	0.680089	+	1.08236i	0.991250	+	0.131998i	$0.0421392\pi$
$881$	20.1862	+	32.1261i	0.680089	+	1.08236i	−0.311161	+	0.950357i	$0.600718\pi$
$882$	2.74984	−	39.2976i	0.0925920	−	1.32322i
$883$	−11.1907	+	49.0296i	−0.376597	+	1.64998i	0.331200	+	0.943561i	$0.392547\pi$
$883$	−11.1907	+	49.0296i	−0.376597	+	1.64998i	−0.707796	+	0.706417i	$0.750311\pi$
$884$	−27.6165	−	14.2486i	−0.928844	−	0.479231i
$885$	−78.9780	−	27.6356i	−2.65482	−	0.928961i
$886$	3.95948	+	7.40296i	0.133021	+	0.248707i
$887$	13.2494	+	13.2494i	0.444870	+	0.444870i	0.893645	−	0.448775i	$-0.148140\pi$
$887$	13.2494	+	13.2494i	0.444870	+	0.444870i	−0.448775	+	0.893645i	$0.648140\pi$
$888$	18.7008	+	8.66689i	0.627559	+	0.290842i
$889$	−10.4146	−	1.17344i	−0.349293	−	0.0393559i
$890$	4.48737	−	6.14345i	0.150417	−	0.205929i
$891$	−7.42768	+	11.8211i	−0.248837	+	0.396021i
$892$	−38.5444	−	40.7267i	−1.29056	−	1.36363i
$893$	12.5552	−	6.04626i	0.420143	−	0.202330i
$894$	22.7039	−	6.20384i	0.759333	−	0.207487i
$895$	46.1859	−	36.8320i	1.54382	−	1.23116i
$896$	−3.59734	−	8.30921i	−0.120179	−	0.277591i
$897$	−6.96511	−	19.9051i	−0.232558	−	0.664613i
$898$	−22.7440	+	19.7692i	−0.758978	+	0.659706i
$899$	−0.831037	−	1.36799i	−0.0277166	−	0.0456251i
$900$	3.24959	−	23.1060i	0.108320	−	0.770200i
$901$	−74.4689	+	26.0578i	−2.48092	+	0.868111i
$902$	46.3507	+	42.5831i	1.54331	+	1.41786i
$903$	1.46897	+	1.84203i	0.0488842	+	0.0612989i
$904$	3.69034	+	28.8976i	0.122739	+	0.961121i
$905$	6.96683	+	14.4668i	0.231585	+	0.480892i
$906$	30.5095	−	1.29251i	1.01361	−	0.0429407i
$907$	18.1008	+	11.3735i	0.601028	+	0.377651i	0.797910	−	0.602776i	$-0.205939\pi$
$907$	18.1008	+	11.3735i	0.601028	+	0.377651i	−0.196882	+	0.980427i	$0.563082\pi$
$908$	−48.8590	+	4.14718i	−1.62144	+	0.137629i
$909$	1.65550	−	14.6930i	0.0549094	−	0.487335i
$910$	7.99513	+	2.42299i	0.265036	+	0.0803214i
$911$	38.7092	−	38.7092i	1.28249	−	1.28249i	0.343250	−	0.939244i	$-0.388472\pi$
$911$	38.7092	−	38.7092i	1.28249	−	1.28249i	0.939244	−	0.343250i	$-0.111528\pi$
$912$	55.0415	+	30.3446i	1.82261	+	1.00481i
$913$	15.3458	−	43.8558i	0.507872	−	1.45141i
$914$	−11.4034	−	28.6386i	−0.377190	−	0.947280i
$915$	−39.5116	−	9.01826i	−1.30621	−	0.298134i
$916$	−16.6113	−	22.0484i	−0.548854	−	0.728498i
$917$	8.14790	−	5.11967i	0.269067	−	0.169066i
$918$	−25.4438	+	17.5320i	−0.839770	+	0.578642i
$919$	31.4718	−	7.18322i	1.03816	−	0.236953i	0.330720	−	0.943729i	$-0.392708\pi$
$919$	31.4718	−	7.18322i	1.03816	−	0.236953i	0.707437	+	0.706776i	$0.249851\pi$
$920$	0.337751	+	22.7934i	0.0111353	+	0.751476i
$921$	0.946679	+	0.754951i	0.0311941	+	0.0248765i
$922$	−47.8787	−	20.6084i	−1.57680	−	0.678701i
$923$	8.68383	−	18.0322i	0.285832	−	0.593536i
$924$	−10.4480	−	17.6906i	−0.343715	−	0.581979i
$925$	7.09991	−	0.799968i	0.233444	−	0.0263028i
$926$	−29.3484	−	16.7516i	−0.964449	−	0.550492i
$927$	−1.05700			−0.0347165
$928$	−22.1310	+	20.9336i	−0.726487	+	0.687180i
$929$	−17.3669			−0.569790			−0.284895	−	0.958559i	$-0.591959\pi$
$929$	−17.3669			−0.569790			−0.284895	+	0.958559i	$0.591959\pi$
$930$	−2.74547	−	1.56707i	−0.0900276	−	0.0513863i
$931$	36.5519	−	4.11841i	1.19794	−	0.134975i
$932$	−14.6342	−	24.7787i	−0.479361	−	0.811654i
$933$	−29.1246	+	60.4779i	−0.953497	+	1.97996i
$934$	44.0466	+	18.9589i	1.44125	+	0.620355i
$935$	59.5932	+	47.5240i	1.94891	+	1.55420i
$936$	−0.489429	−	33.0296i	−0.0159975	−	1.07961i
$937$	27.1976	−	6.20768i	0.888508	−	0.202796i	0.246178	−	0.969225i	$-0.420825\pi$
$937$	27.1976	−	6.20768i	0.888508	−	0.202796i	0.642330	+	0.766428i	$0.277968\pi$
$938$	−4.87742	+	3.36078i	−0.159254	+	0.109733i
$939$	−18.2359	+	11.4584i	−0.595106	+	0.373930i
$940$	8.02676	+	10.6540i	0.261804	+	0.347495i
$941$	17.3640	+	3.96322i	0.566050	+	0.129197i	0.495963	−	0.868344i	$-0.334815\pi$
$941$	17.3640	+	3.96322i	0.566050	+	0.129197i	0.0700871	+	0.997541i	$0.477672\pi$
$942$	−13.3031	−	33.4096i	−0.433439	−	1.08855i
$943$	9.05750	−	25.8848i	0.294953	−	0.842926i
$944$	38.9738	+	21.4864i	1.26849	+	0.699322i
$945$	5.87378	−	5.87378i	0.191074	−	0.191074i
$946$	−6.92982	−	2.10014i	−0.225308	−	0.0682815i
$947$	−5.11859	+	45.4287i	−0.166332	+	1.47624i	0.582150	+	0.813081i	$0.302211\pi$
$947$	−5.11859	+	45.4287i	−0.166332	+	1.47624i	−0.748482	+	0.663155i	$0.769217\pi$
$948$	−47.4544	+	4.02796i	−1.54125	+	0.130822i
$949$	7.24503	+	4.55235i	0.235184	+	0.147776i
$950$	21.7676	−	0.922166i	0.706234	−	0.0299190i
$951$	30.1905	+	62.6912i	0.978994	+	2.03290i
$952$	1.67097	+	13.0847i	0.0541565	+	0.424078i
$953$	−4.45264	−	5.58344i	−0.144235	−	0.180865i	0.704466	−	0.709738i	$-0.251186\pi$
$953$	−4.45264	−	5.58344i	−0.144235	−	0.180865i	−0.848701	+	0.528872i	$0.822615\pi$
$954$	−61.7594	−	56.7393i	−1.99953	−	1.83700i
$955$	−22.3090	+	7.80624i	−0.721901	+	0.252604i
$956$	−7.89681	+	56.1498i	−0.255401	+	1.81602i
$957$	−43.9087	+	53.3866i	−1.41937	+	1.72574i
$958$	−2.74064	+	2.38218i	−0.0885462	+	0.0769646i
$959$	0.132988	+	0.380057i	0.00429440	+	0.0122727i
$960$	−18.1796	+	57.3517i	−0.586745	+	1.85102i
$961$	24.1677	−	19.2731i	0.779603	−	0.621713i
$962$	9.75727	−	2.66617i	0.314587	−	0.0859608i
$963$	27.0551	−	13.0291i	0.871839	−	0.419856i
$964$	−20.9712	−	22.1585i	−0.675437	−	0.713678i
$965$	−1.01269	+	1.61168i	−0.0325995	+	0.0518819i
$966$	−5.28005	+	7.22866i	−0.169883	+	0.232578i
$967$	−16.3159	−	1.83836i	−0.524685	−	0.0591178i	−0.154350	−	0.988016i	$-0.549328\pi$
$967$	−16.3159	−	1.83836i	−0.524685	−	0.0591178i	−0.370335	+	0.928898i	$0.620757\pi$
$968$	29.0626	+	13.4690i	0.934107	+	0.432912i
$969$	−64.7465	−	64.7465i	−2.07996	−	2.07996i
$970$	−3.26580	−	6.10601i	−0.104859	−	0.196052i
$971$	−16.4925	−	5.77099i	−0.529271	−	0.185200i	0.0523971	−	0.998626i	$-0.483314\pi$
$971$	−16.4925	−	5.77099i	−0.529271	−	0.185200i	−0.581668	+	0.813427i	$0.697600\pi$
$972$	34.2591	+	17.6758i	1.09886	+	0.566950i
$973$	0.714591	−	3.13083i	0.0229087	−	0.100370i
$974$	−3.94686	+	56.4041i	−0.126466	+	1.80730i
$975$	−10.2647	−	16.3362i	−0.328733	−	0.523176i
$976$	19.9237	+	8.22802i	0.637741	+	0.263373i
$977$	−2.49822	−	10.9454i	−0.0799251	−	0.350175i	0.919115	−	0.393990i	$-0.128906\pi$
$977$	−2.49822	−	10.9454i	−0.0799251	−	0.350175i	−0.999040	+	0.0438158i	$0.986049\pi$
$978$	−2.46835	−	15.8451i	−0.0789293	−	0.506669i
$979$	−5.72472	+	7.17857i	−0.182963	+	0.229428i
$980$	10.7102	+	33.5417i	0.342125	+	1.07145i
$981$	30.3894	+	14.6348i	0.970258	+	0.467252i
$982$	−3.21830	−	0.592486i	−0.102700	−	0.0189070i
$983$	−4.63022	−	41.0944i	−0.147681	−	1.31071i	−0.820818	−	0.571189i	$-0.806482\pi$
$983$	−4.63022	−	41.0944i	−0.147681	−	1.31071i	0.673137	−	0.739518i	$-0.264946\pi$
$984$	44.2837	−	57.2499i	1.41171	−	1.82506i
$985$			58.6818i			1.86976i
$986$	39.4455	−	20.3379i	1.25620	−	0.647690i
$987$			5.23817i			0.166733i
$988$	30.2483	−	6.03336i	0.962326	−	0.191947i
$989$	0.353239	+	3.13509i	0.0112324	+	0.0996899i
$990$	−14.6700	+	79.6851i	−0.466242	+	2.53256i
$991$	2.26102	+	1.08885i	0.0718235	+	0.0345884i	0.469451	−	0.882959i	$-0.344452\pi$
$991$	2.26102	+	1.08885i	0.0718235	+	0.0345884i	−0.397627	+	0.917547i	$0.630166\pi$
$992$	1.30114	+	1.06494i	0.0413111	+	0.0338120i
$993$	−2.45041	+	3.07272i	−0.0777615	+	0.0975099i
$994$	−8.39438	+	1.30768i	−0.266254	+	0.0414772i
$995$	−1.14839	−	5.03141i	−0.0364063	−	0.159506i
$996$	−51.7423	−	13.3179i	−1.63952	−	0.421995i
$997$	6.01422	+	9.57158i	0.190472	+	0.303135i	0.928284	−	0.371871i	$-0.121284\pi$
$997$	6.01422	+	9.57158i	0.190472	+	0.303135i	−0.737812	+	0.675006i	$0.764141\pi$
$998$	−20.6621	−	1.44583i	−0.654048	−	0.0457669i
$999$	2.23801	−	9.80538i	0.0708076	−	0.310228i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	116.2.l.b.11.12	yes	144
4.3	odd	2	inner	116.2.l.b.11.10	✓	144
29.8	odd	28	inner	116.2.l.b.95.10	yes	144
116.95	even	28	inner	116.2.l.b.95.12	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
116.2.l.b.11.10	✓	144	4.3	odd	2	inner
116.2.l.b.11.12	yes	144	1.1	even	1	trivial
116.2.l.b.95.10	yes	144	29.8	odd	28	inner
116.2.l.b.95.12	yes	144	116.95	even	28	inner

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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	116.2.l.b.11.12

Level	$116$
Weight	$2$
Character	116.11
Analytic conductor	$0.926$
Analytic rank	$0$
Dimension	$144$
Inner twists	$4$