LMFDB - Embedded newform 90.2.l.a.47.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [90,2,Mod(23,90)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(90, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("90.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$90 = 2 \cdot 3^{2} \cdot 5$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	90.l (of order $12$ , degree $4$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.718653618192$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - x^{4} + 1$ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	90.47
Dual form			90.2.l.a.23.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.258819 + 0.965926i) q^{2} +(1.10721 + 1.33195i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(0.792893 - 2.09077i) q^{5} +(-1.00000 + 1.41421i) q^{6} +(-1.05902 + 0.283763i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.548188 + 2.94949i) q^{9} +(2.22474 + 0.224745i) q^{10} +(-5.44949 - 3.14626i) q^{11} +(-1.62484 - 0.599900i) q^{12} +(3.34607 + 0.896575i) q^{13} +(-0.548188 - 0.949490i) q^{14} +(3.66270 - 1.25882i) q^{15} +(0.500000 - 0.866025i) q^{16} +(3.14626 - 3.14626i) q^{17} +(-2.99087 + 0.233875i) q^{18} +1.55051i q^{19} +(0.358719 + 2.20711i) q^{20} +(-1.55051 - 1.09638i) q^{21} +(1.62863 - 6.07812i) q^{22} +(0.258819 - 0.965926i) q^{23} +(0.158919 - 1.72474i) q^{24} +(-3.74264 - 3.31552i) q^{25} +3.46410i q^{26} +(-4.53553 + 2.53553i) q^{27} +(0.775255 - 0.775255i) q^{28} +(-1.57313 + 2.72474i) q^{29} +(2.16390 + 3.21209i) q^{30} +(2.22474 + 3.85337i) q^{31} +(0.965926 + 0.258819i) q^{32} +(-1.84304 - 10.7420i) q^{33} +(3.85337 + 2.22474i) q^{34} +(-0.246405 + 2.43916i) q^{35} +(-1.00000 - 2.82843i) q^{36} +(-3.00000 - 3.00000i) q^{37} +(-1.49768 + 0.401302i) q^{38} +(2.51059 + 5.44949i) q^{39} +(-2.03906 + 0.917738i) q^{40} +(-3.39898 + 1.96240i) q^{41} +(0.657717 - 1.78144i) q^{42} +(0.896575 + 3.34607i) q^{43} +6.29253 q^{44} +(5.73205 + 3.48477i) q^{45} +1.00000 q^{46} +(2.32937 + 8.69333i) q^{47} +(1.70711 - 0.292893i) q^{48} +(-5.02118 + 2.89898i) q^{49} +(2.23388 - 4.47323i) q^{50} +(7.67423 + 0.707107i) q^{51} +(-3.34607 + 0.896575i) q^{52} +(6.61037 + 6.61037i) q^{53} +(-3.62302 - 3.72474i) q^{54} +(-10.8990 + 8.89898i) q^{55} +(0.949490 + 0.548188i) q^{56} +(-2.06520 + 1.71673i) q^{57} +(-3.03906 - 0.814313i) q^{58} +(-5.90326 - 10.2247i) q^{59} +(-2.54258 + 2.92152i) q^{60} +(2.72474 - 4.71940i) q^{61} +(-3.14626 + 3.14626i) q^{62} +(-0.256415 - 3.27912i) q^{63} +1.00000i q^{64} +(4.52761 - 6.28497i) q^{65} +(9.89898 - 4.56048i) q^{66} +(0.978838 - 3.65307i) q^{67} +(-1.15161 + 4.29788i) q^{68} +(1.57313 - 0.724745i) q^{69} +(-2.41982 + 0.393292i) q^{70} +0.635674i q^{71} +(2.47323 - 1.69798i) q^{72} +(2.89898 - 2.89898i) q^{73} +(2.12132 - 3.67423i) q^{74} +(0.272229 - 8.65597i) q^{75} +(-0.775255 - 1.34278i) q^{76} +(6.66390 + 1.78559i) q^{77} +(-4.61401 + 3.83548i) q^{78} +(2.12132 + 1.22474i) q^{79} +(-1.41421 - 1.73205i) q^{80} +(-8.39898 - 3.23375i) q^{81} +(-2.77526 - 2.77526i) q^{82} +(-0.531752 + 0.142483i) q^{83} +(1.89097 + 0.174235i) q^{84} +(-4.08346 - 9.07277i) q^{85} +(-3.00000 + 1.73205i) q^{86} +(-5.37101 + 0.921519i) q^{87} +(1.62863 + 6.07812i) q^{88} -2.36773 q^{89} +(-1.88246 + 6.43866i) q^{90} -3.79796 q^{91} +(0.258819 + 0.965926i) q^{92} +(-2.66925 + 7.22973i) q^{93} +(-7.79423 + 4.50000i) q^{94} +(3.24176 + 1.22939i) q^{95} +(0.724745 + 1.57313i) q^{96} +(10.7902 - 2.89123i) q^{97} +(-4.09978 - 4.09978i) q^{98} +(12.2672 - 14.3485i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 4 q^{3} + 12 q^{5} - 8 q^{6} - 8 q^{7} + 8 q^{10} - 24 q^{11} - 4 q^{12} + 16 q^{15} + 4 q^{16} - 8 q^{18} - 32 q^{21} - 8 q^{22} + 4 q^{25} - 8 q^{27} + 16 q^{28} - 12 q^{30} + 8 q^{31} + 16 q^{33}+ \cdots + 12 q^{97}+O(q^{100})$ 8 * q + 4 * q^3 + 12 * q^5 - 8 * q^6 - 8 * q^7 + 8 * q^10 - 24 * q^11 - 4 * q^12 + 16 * q^15 + 4 * q^16 - 8 * q^18 - 32 * q^21 - 8 * q^22 + 4 * q^25 - 8 * q^27 + 16 * q^28 - 12 * q^30 + 8 * q^31 + 16 * q^33 - 8 * q^36 - 24 * q^37 + 12 * q^38 + 4 * q^40 + 12 * q^41 + 20 * q^42 + 32 * q^45 + 8 * q^46 + 8 * q^48 + 24 * q^50 + 32 * q^51 - 48 * q^55 - 12 * q^56 + 28 * q^57 - 4 * q^58 - 8 * q^60 + 12 * q^61 - 32 * q^63 - 24 * q^65 + 40 * q^66 + 4 * q^67 - 12 * q^68 - 16 * q^70 + 8 * q^72 - 16 * q^73 + 8 * q^75 - 16 * q^76 + 24 * q^77 - 24 * q^78 - 28 * q^81 - 32 * q^82 + 12 * q^83 - 20 * q^85 - 24 * q^86 - 8 * q^87 - 8 * q^88 - 20 * q^90 + 48 * q^91 - 20 * q^93 - 24 * q^95 - 4 * q^96 + 12 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/90\mathbb{Z}\right)^\times$ .

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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

)

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

$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$2$	0.258819	+	0.965926i	0.183013	+	0.683013i
$3$	1.10721	+	1.33195i	0.639246	+	0.769002i
$3$	1.10721	+	1.33195i	0.639246	+	0.769002i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	0.792893	−	2.09077i	0.354593	−	0.935021i
$5$	0.792893	−	2.09077i	0.354593	−	0.935021i
$6$	−1.00000	+	1.41421i	−0.408248	+	0.577350i
$7$	−1.05902	+	0.283763i	−0.400271	+	0.107252i	−0.453338	−	0.891339i	$-0.649767\pi$
$7$	−1.05902	+	0.283763i	−0.400271	+	0.107252i	0.0530669	+	0.998591i	$0.483100\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$	−0.548188	+	2.94949i	−0.182729	+	0.983163i
$10$	2.22474	+	0.224745i	0.703526	+	0.0710706i
$11$	−5.44949	−	3.14626i	−1.64308	−	0.948634i	−0.979729	−	0.200329i	$-0.935799\pi$
$11$	−5.44949	−	3.14626i	−1.64308	−	0.948634i	−0.663354	−	0.748305i	$-0.730868\pi$
$12$	−1.62484	−	0.599900i	−0.469052	−	0.173176i
$13$	3.34607	+	0.896575i	0.928032	+	0.248665i	0.691015	−	0.722840i	$-0.257164\pi$
$13$	3.34607	+	0.896575i	0.928032	+	0.248665i	0.237016	+	0.971506i	$0.423830\pi$
$14$	−0.548188	−	0.949490i	−0.146509	−	0.253762i
$15$	3.66270	−	1.25882i	0.945705	−	0.325026i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	3.14626	−	3.14626i	0.763081	−	0.763081i	−0.213797	−	0.976878i	$-0.568583\pi$
$17$	3.14626	−	3.14626i	0.763081	−	0.763081i	0.976878	+	0.213797i	$0.0685831\pi$
$18$	−2.99087	+	0.233875i	−0.704955	+	0.0551249i
$19$			1.55051i			0.355711i	0.984057	+	0.177856i	$0.0569160\pi$
$19$			1.55051i			0.355711i	−0.984057	+	0.177856i	$0.943084\pi$
$20$	0.358719	+	2.20711i	0.0802121	+	0.493524i
$21$	−1.55051	−	1.09638i	−0.338349	−	0.239249i
$22$	1.62863	−	6.07812i	0.347224	−	1.29586i
$23$	0.258819	−	0.965926i	0.0539675	−	0.201409i	−0.933678	−	0.358113i	$-0.883420\pi$
$23$	0.258819	−	0.965926i	0.0539675	−	0.201409i	0.987646	+	0.156704i	$0.0500868\pi$
$24$	0.158919	−	1.72474i	0.0324391	−	0.352062i
$25$	−3.74264	−	3.31552i	−0.748528	−	0.663103i
$26$			3.46410i			0.679366i
$27$	−4.53553	+	2.53553i	−0.872864	+	0.487964i
$28$	0.775255	−	0.775255i	0.146509	−	0.146509i
$29$	−1.57313	+	2.72474i	−0.292123	+	0.505972i	−0.974312	−	0.225204i	$-0.927695\pi$
$29$	−1.57313	+	2.72474i	−0.292123	+	0.505972i	0.682188	+	0.731177i	$0.261028\pi$
$30$	2.16390	+	3.21209i	0.395073	+	0.586445i
$31$	2.22474	+	3.85337i	0.399576	+	0.692086i	0.993674	−	0.112307i	$-0.0358240\pi$
$31$	2.22474	+	3.85337i	0.399576	+	0.692086i	−0.594098	+	0.804393i	$0.702491\pi$
$32$	0.965926	+	0.258819i	0.170753	+	0.0457532i
$33$	−1.84304	−	10.7420i	−0.320832	−	1.86995i
$34$	3.85337	+	2.22474i	0.660848	+	0.381541i
$35$	−0.246405	+	2.43916i	−0.0416500	+	0.412293i
$36$	−1.00000	−	2.82843i	−0.166667	−	0.471405i
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	0.416115	−	0.909312i	$-0.363391\pi$
$37$	−3.00000	−	3.00000i	−0.493197	−	0.493197i	−0.909312	+	0.416115i	$0.863391\pi$
$38$	−1.49768	+	0.401302i	−0.242955	+	0.0650997i
$39$	2.51059	+	5.44949i	0.402016	+	0.872617i
$40$	−2.03906	+	0.917738i	−0.322403	+	0.145107i
$41$	−3.39898	+	1.96240i	−0.530831	+	0.306476i	−0.741355	−	0.671113i	$-0.765816\pi$
$41$	−3.39898	+	1.96240i	−0.530831	+	0.306476i	0.210524	+	0.977589i	$0.432483\pi$
$42$	0.657717	−	1.78144i	0.101488	−	0.274882i
$43$	0.896575	+	3.34607i	0.136726	+	0.510270i	0.999985	+	0.00550783i	$0.00175320\pi$
$43$	0.896575	+	3.34607i	0.136726	+	0.510270i	−0.863258	+	0.504762i	$0.831580\pi$
$44$	6.29253			0.948634
$45$	5.73205	+	3.48477i	0.854484	+	0.519478i
$46$	1.00000			0.147442
$47$	2.32937	+	8.69333i	0.339774	+	1.26805i	0.898600	+	0.438768i	$0.144585\pi$
$47$	2.32937	+	8.69333i	0.339774	+	1.26805i	−0.558827	+	0.829285i	$0.688748\pi$
$48$	1.70711	−	0.292893i	0.246400	−	0.0422755i
$49$	−5.02118	+	2.89898i	−0.717311	+	0.414140i
$50$	2.23388	−	4.47323i	0.315918	−	0.632611i
$51$	7.67423	+	0.707107i	1.07461	+	0.0990148i
$52$	−3.34607	+	0.896575i	−0.464016	+	0.124333i
$53$	6.61037	+	6.61037i	0.908004	+	0.908004i	0.996111	−	0.0881074i	$-0.0280819\pi$
$53$	6.61037	+	6.61037i	0.908004	+	0.908004i	−0.0881074	+	0.996111i	$0.528082\pi$
$54$	−3.62302	−	3.72474i	−0.493031	−	0.506874i
$55$	−10.8990	+	8.89898i	−1.46962	+	1.19994i
$56$	0.949490	+	0.548188i	0.126881	+	0.0732547i
$57$	−2.06520	+	1.71673i	−0.273543	+	0.227387i
$58$	−3.03906	−	0.814313i	−0.399048	−	0.106925i
$59$	−5.90326	−	10.2247i	−0.768539	−	1.33115i	−0.938355	−	0.345673i	$-0.887651\pi$
$59$	−5.90326	−	10.2247i	−0.768539	−	1.33115i	0.169816	−	0.985476i	$-0.445683\pi$
$60$	−2.54258	+	2.92152i	−0.328246	+	0.377167i
$61$	2.72474	−	4.71940i	0.348868	−	0.604257i	−0.637181	−	0.770714i	$-0.719900\pi$
$61$	2.72474	−	4.71940i	0.348868	−	0.604257i	0.986049	+	0.166458i	$0.0532329\pi$
$62$	−3.14626	+	3.14626i	−0.399576	+	0.399576i
$63$	−0.256415	−	3.27912i	−0.0323053	−	0.413130i
$64$			1.00000i			0.125000i
$65$	4.52761	−	6.28497i	0.561580	−	0.779554i
$66$	9.89898	−	4.56048i	1.21848	−	0.561356i
$67$	0.978838	−	3.65307i	0.119584	−	0.446294i	−0.880005	−	0.474965i	$-0.842461\pi$
$67$	0.978838	−	3.65307i	0.119584	−	0.446294i	0.999589	+	0.0286709i	$0.00912748\pi$
$68$	−1.15161	+	4.29788i	−0.139654	+	0.521194i
$69$	1.57313	−	0.724745i	0.189383	−	0.0872490i
$70$	−2.41982	+	0.393292i	−0.289224	+	0.0470073i
$71$			0.635674i			0.0754407i	0.999288	+	0.0377203i	$0.0120096\pi$
$71$			0.635674i			0.0754407i	−0.999288	+	0.0377203i	$0.987990\pi$
$72$	2.47323	−	1.69798i	0.291473	−	0.200108i
$73$	2.89898	−	2.89898i	0.339300	−	0.339300i	−0.516804	−	0.856104i	$-0.672878\pi$
$73$	2.89898	−	2.89898i	0.339300	−	0.339300i	0.856104	+	0.516804i	$0.172878\pi$
$74$	2.12132	−	3.67423i	0.246598	−	0.427121i
$75$	0.272229	−	8.65597i	0.0314343	−	0.999506i
$76$	−0.775255	−	1.34278i	−0.0889279	−	0.154028i
$77$	6.66390	+	1.78559i	0.759422	+	0.203487i
$78$	−4.61401	+	3.83548i	−0.522434	+	0.434282i
$79$	2.12132	+	1.22474i	0.238667	+	0.137795i	0.614564	−	0.788867i	$-0.289332\pi$
$79$	2.12132	+	1.22474i	0.238667	+	0.137795i	−0.375897	+	0.926662i	$0.622665\pi$
$80$	−1.41421	−	1.73205i	−0.158114	−	0.193649i
$81$	−8.39898	−	3.23375i	−0.933220	−	0.359306i
$82$	−2.77526	−	2.77526i	−0.306476	−	0.306476i
$83$	−0.531752	+	0.142483i	−0.0583674	+	0.0156395i	−0.287885	−	0.957665i	$-0.592952\pi$
$83$	−0.531752	+	0.142483i	−0.0583674	+	0.0156395i	0.229517	+	0.973305i	$0.426285\pi$
$84$	1.89097	+	0.174235i	0.206322	+	0.0190106i
$85$	−4.08346	−	9.07277i	−0.442914	−	0.984080i
$86$	−3.00000	+	1.73205i	−0.323498	+	0.186772i
$87$	−5.37101	+	0.921519i	−0.575833	+	0.0987973i
$88$	1.62863	+	6.07812i	0.173612	+	0.647929i
$89$	−2.36773			−0.250978			−0.125489	−	0.992095i	$-0.540050\pi$
$89$	−2.36773			−0.250978			−0.125489	+	0.992095i	$0.540050\pi$
$90$	−1.88246	+	6.43866i	−0.198429	+	0.678694i
$91$	−3.79796			−0.398134
$92$	0.258819	+	0.965926i	0.0269838	+	0.100705i
$93$	−2.66925	+	7.22973i	−0.276788	+	0.749688i
$94$	−7.79423	+	4.50000i	−0.803913	+	0.464140i
$95$	3.24176	+	1.22939i	0.332598	+	0.126133i
$96$	0.724745	+	1.57313i	0.0739690	+	0.160557i
$97$	10.7902	−	2.89123i	1.09558	−	0.293560i	0.334616	−	0.942355i	$-0.391393\pi$
$97$	10.7902	−	2.89123i	1.09558	−	0.293560i	0.760963	+	0.648795i	$0.224727\pi$
$98$	−4.09978	−	4.09978i	−0.414140	−	0.414140i
$99$	12.2672	−	14.3485i	1.23290	−	1.44208i
$100$	4.89898	+	1.00000i	0.489898	+	0.100000i
$101$	1.10102	+	0.635674i	0.109556	+	0.0632520i	0.553777	−	0.832665i	$-0.313186\pi$
$101$	1.10102	+	0.635674i	0.109556	+	0.0632520i	−0.444221	+	0.895917i	$0.646519\pi$
$102$	1.30323	+	7.59575i	0.129039	+	0.752092i
$103$	−3.96008	−	1.06110i	−0.390198	−	0.104553i	0.0583855	−	0.998294i	$-0.481405\pi$
$103$	−3.96008	−	1.06110i	−0.390198	−	0.104553i	−0.448584	+	0.893741i	$0.648071\pi$
$104$	−1.73205	−	3.00000i	−0.169842	−	0.294174i
$105$	−3.52166	+	2.37245i	−0.343679	+	0.231528i
$106$	−4.67423	+	8.09601i	−0.454002	+	0.786354i
$107$	3.71051	−	3.71051i	0.358708	−	0.358708i	−0.504628	−	0.863337i	$-0.668370\pi$
$107$	3.71051	−	3.71051i	0.358708	−	0.358708i	0.863337	+	0.504628i	$0.168370\pi$
$108$	2.66012	−	4.46360i	0.255970	−	0.429510i
$109$		−	20.3485i		−	1.94903i	−0.224323	−	0.974515i	$-0.572017\pi$
$109$		−	20.3485i		−	1.94903i	0.224323	−	0.974515i	$-0.427983\pi$
$110$	−11.4166	−	8.22438i	−1.08853	−	0.784164i
$111$	0.674235	−	7.31747i	0.0639955	−	0.694544i
$112$	−0.283763	+	1.05902i	−0.0268131	+	0.100068i
$113$	−3.57117	+	13.3278i	−0.335948	+	1.25377i	0.566890	+	0.823793i	$0.308146\pi$
$113$	−3.57117	+	13.3278i	−0.335948	+	1.25377i	−0.902838	+	0.429981i	$0.858520\pi$
$114$	−2.19275	−	1.55051i	−0.205370	−	0.145219i
$115$	−1.81431	−	1.30701i	−0.169186	−	0.121879i
$116$		−	3.14626i		−	0.292123i
$117$	−4.47871	+	9.37769i	−0.414057	+	0.866968i
$118$	8.34847	−	8.34847i	0.768539	−	0.768539i
$119$	−2.43916	+	4.22474i	−0.223597	+	0.387282i
$120$	−3.48004	−	1.69980i	−0.317683	−	0.155170i
$121$	14.2980	+	24.7648i	1.29981	+	2.25134i
$122$	5.26380	+	1.41043i	0.476562	+	0.127694i
$123$	−6.37720	−	2.35449i	−0.575012	−	0.212297i
$124$	−3.85337	−	2.22474i	−0.346043	−	0.199788i
$125$	−9.89949	+	5.19615i	−0.885438	+	0.464758i
$126$	3.10102	−	1.09638i	0.276261	−	0.0976730i
$127$	14.1237	+	14.1237i	1.25328	+	1.25328i	0.954242	+	0.299036i	$0.0966651\pi$
$127$	14.1237	+	14.1237i	1.25328	+	1.25328i	0.299036	+	0.954242i	$0.403335\pi$
$128$	−0.965926	+	0.258819i	−0.0853766	+	0.0228766i
$129$	−3.46410	+	4.89898i	−0.304997	+	0.431331i
$130$	7.24264	+	2.74666i	0.635222	+	0.240898i
$131$	9.12372	−	5.26758i	0.797143	−	0.460231i	−0.0453278	−	0.998972i	$-0.514433\pi$
$131$	9.12372	−	5.26758i	0.797143	−	0.460231i	0.842471	+	0.538741i	$0.181100\pi$
$132$	6.96713	+	8.38134i	0.606411	+	0.729502i
$133$	−0.439978	−	1.64202i	−0.0381509	−	0.142381i
$134$	3.78194			0.326710
$135$	1.70502	+	11.4932i	0.146745	+	0.989174i
$136$	−4.44949			−0.381541
$137$	−0.569930	−	2.12701i	−0.0486924	−	0.181723i	0.937297	−	0.348533i	$-0.113320\pi$
$137$	−0.569930	−	2.12701i	−0.0486924	−	0.181723i	−0.985989	+	0.166810i	$0.946653\pi$
$138$	1.10721	+	1.33195i	0.0942517	+	0.113383i
$139$	11.1708	−	6.44949i	0.947499	−	0.547039i	0.0551956	−	0.998476i	$-0.482422\pi$
$139$	11.1708	−	6.44949i	0.947499	−	0.547039i	0.892303	+	0.451437i	$0.149088\pi$
$140$	−1.00619	−	2.23557i	−0.0850382	−	0.188941i
$141$	−9.00000	+	12.7279i	−0.757937	+	1.07188i
$142$	−0.614014	+	0.164525i	−0.0515269	+	0.0138066i
$143$	−15.4135	−	15.4135i	−1.28894	−	1.28894i
$144$	2.28024	+	1.94949i	0.190020	+	0.162457i
$145$	4.44949	+	5.44949i	0.369510	+	0.452555i
$146$	3.55051	+	2.04989i	0.293842	+	0.169650i
$147$	−9.42078	−	3.47820i	−0.777013	−	0.286877i
$148$	4.09808	+	1.09808i	0.336860	+	0.0902613i
$149$	6.45145	+	11.1742i	0.528523	+	0.915429i	0.999447	+	0.0332550i	$0.0105874\pi$
$149$	6.45145	+	11.1742i	0.528523	+	0.915429i	−0.470924	+	0.882174i	$0.656079\pi$
$150$	8.43149	−	1.97738i	0.688428	−	0.161452i
$151$	10.7980	−	18.7026i	0.878725	−	1.52200i	0.0259849	−	0.999662i	$-0.491728\pi$
$151$	10.7980	−	18.7026i	0.878725	−	1.52200i	0.852741	−	0.522335i	$-0.174939\pi$
$152$	1.09638	−	1.09638i	0.0889279	−	0.0889279i
$153$	7.55513	+	11.0046i	0.610796	+	0.889671i
$154$			6.89898i			0.555936i
$155$	9.82050	−	1.59612i	0.788801	−	0.128203i
$156$	−4.89898	−	3.46410i	−0.392232	−	0.277350i
$157$	1.59165	−	5.94012i	0.127028	−	0.474073i	−0.872876	−	0.487942i	$-0.837748\pi$
$157$	1.59165	−	5.94012i	0.127028	−	0.474073i	0.999904	+	0.0138684i	$0.00441459\pi$
$158$	−0.633975	+	2.36603i	−0.0504363	+	0.188231i
$159$	−1.48565	+	16.1237i	−0.117819	+	1.27869i
$160$	1.30701	−	1.81431i	0.103328	−	0.143434i
$161$			1.09638i			0.0864066i
$162$	0.949747	−	8.94975i	0.0746192	−	0.703159i
$163$	−0.449490	+	0.449490i	−0.0352068	+	0.0352068i	−0.724491	−	0.689284i	$-0.757925\pi$
$163$	−0.449490	+	0.449490i	−0.0352068	+	0.0352068i	0.689284	+	0.724491i	$0.257925\pi$
$164$	1.96240	−	3.39898i	0.153238	−	0.265416i
$165$	−23.9204	−	4.66390i	−1.86220	−	0.363084i
$166$	−0.275255	−	0.476756i	−0.0213639	−	0.0370034i
$167$	−10.4300	−	2.79472i	−0.807100	−	0.216262i	−0.168401	−	0.985719i	$-0.553860\pi$
$167$	−10.4300	−	2.79472i	−0.807100	−	0.216262i	−0.638699	+	0.769457i	$0.720527\pi$
$168$	0.321121	+	1.87163i	0.0247750	+	0.144400i
$169$	−0.866025	−	0.500000i	−0.0666173	−	0.0384615i
$170$	7.70674	−	6.29253i	0.591080	−	0.482615i
$171$	−4.57321	−	0.849971i	−0.349722	−	0.0649989i
$172$	−2.44949	−	2.44949i	−0.186772	−	0.186772i
$173$	2.99536	−	0.802603i	0.227733	−	0.0610208i	−0.143148	−	0.989701i	$-0.545723\pi$
$173$	2.99536	−	0.802603i	0.227733	−	0.0610208i	0.370881	+	0.928680i	$0.379056\pi$
$174$	−2.28024	−	4.94949i	−0.172864	−	0.375220i
$175$	4.90435	+	2.44917i	0.370734	+	0.185140i
$176$	−5.44949	+	3.14626i	−0.410771	+	0.237159i
$177$	7.08274	−	19.1838i	0.532371	−	1.44194i
$178$	−0.612812	−	2.28705i	−0.0459322	−	0.171421i
$179$	−17.6062			−1.31595			−0.657976	−	0.753039i	$-0.728587\pi$
$179$	−17.6062			−1.31595			−0.657976	+	0.753039i	$0.728587\pi$
$180$	−6.70648	−	0.151870i	−0.499872	−	0.0113198i
$181$	−10.5505			−0.784213			−0.392107	−	0.919920i	$-0.628254\pi$
$181$	−10.5505			−0.784213			−0.392107	+	0.919920i	$0.628254\pi$
$182$	−0.982984	−	3.66855i	−0.0728636	−	0.271931i
$183$	9.30286	−	1.59612i	0.687687	−	0.117988i
$184$	−0.866025	+	0.500000i	−0.0638442	+	0.0368605i
$185$	−8.65099	+	3.89363i	−0.636033	+	0.286265i
$186$	−7.67423	−	0.707107i	−0.562702	−	0.0518476i
$187$	−27.0445	+	7.24656i	−1.97769	+	0.529921i
$188$	−6.36396	−	6.36396i	−0.464140	−	0.464140i
$189$	4.08372	−	3.97219i	0.297047	−	0.288935i
$190$	−0.348469	+	3.44949i	−0.0252806	+	0.250252i
$191$	−2.87628	−	1.66062i	−0.208120	−	0.120158i	0.392317	−	0.919830i	$-0.371673\pi$
$191$	−2.87628	−	1.66062i	−0.208120	−	0.120158i	−0.600437	+	0.799672i	$0.705007\pi$
$192$	−1.33195	+	1.10721i	−0.0961253	+	0.0799057i
$193$	−16.7303	−	4.48288i	−1.20428	−	0.322685i	−0.399762	−	0.916619i	$-0.630907\pi$
$193$	−16.7303	−	4.48288i	−1.20428	−	0.322685i	−0.804513	+	0.593934i	$0.797574\pi$
$194$	5.58542	+	9.67423i	0.401010	+	0.694570i
$195$	13.3843	−	0.928203i	0.958467	−	0.0664700i
$196$	2.89898	−	5.02118i	0.207070	−	0.358656i
$197$	6.92820	−	6.92820i	0.493614	−	0.493614i	−0.415829	−	0.909443i	$-0.636508\pi$
$197$	6.92820	−	6.92820i	0.493614	−	0.493614i	0.909443	+	0.415829i	$0.136508\pi$
$198$	17.0345	+	8.13557i	1.21059	+	0.578170i
$199$			3.55051i			0.251689i	0.992050	+	0.125844i	$0.0401640\pi$
$199$			3.55051i			0.251689i	−0.992050	+	0.125844i	$0.959836\pi$
$200$	0.302023	+	4.99087i	0.0213563	+	0.352908i
$201$	5.94949	−	2.74094i	0.419645	−	0.193331i
$202$	−0.329049	+	1.22803i	−0.0231518	+	0.0864038i
$203$	0.892794	−	3.33195i	0.0626618	−	0.233857i
$204$	−6.99964	+	3.22474i	−0.490073	+	0.225777i
$205$	1.40790	+	8.66246i	0.0983322	+	0.605012i
$206$		−	4.09978i		−	0.285645i
$207$	2.70711	+	1.29289i	0.188157	+	0.0898623i
$208$	2.44949	−	2.44949i	0.169842	−	0.169842i
$209$	4.87832	−	8.44949i	0.337440	−	0.584463i
$210$	−3.20308	−	2.78763i	−0.221034	−	0.192365i
$211$	−9.44949	−	16.3670i	−0.650530	−	1.12675i	−0.982995	−	0.183635i	$-0.941214\pi$
$211$	−9.44949	−	16.3670i	−0.650530	−	1.12675i	0.332465	−	0.943116i	$-0.392120\pi$
$212$	−9.02993	−	2.41956i	−0.620178	−	0.166176i
$213$	−0.846687	+	0.703823i	−0.0580141	+	0.0482251i
$214$	4.54442	+	2.62372i	0.310650	+	0.179354i
$215$	7.70674	+	0.778539i	0.525595	+	0.0530959i
$216$	5.00000	+	1.41421i	0.340207	+	0.0962250i
$217$	−3.44949	−	3.44949i	−0.234167	−	0.234167i
$218$	19.6551	−	5.26657i	1.33121	−	0.356697i
$219$	7.07107	+	0.651531i	0.477818	+	0.0440264i
$220$	4.98930	−	13.1562i	0.336379	−	0.886993i
$221$	13.3485	−	7.70674i	0.897915	−	0.518412i
$222$	7.24264	−	1.24264i	0.486094	−	0.0834006i
$223$	2.15087	+	8.02714i	0.144033	+	0.537537i	0.999797	+	0.0201706i	$0.00642094\pi$
$223$	2.15087	+	8.02714i	0.144033	+	0.537537i	−0.855764	+	0.517367i	$0.826912\pi$
$224$	−1.09638			−0.0732547
$225$	11.8307	−	9.22135i	0.788717	−	0.614757i
$226$	−13.7980			−0.917827
$227$	−3.90843	−	14.5865i	−0.259412	−	0.968138i	−0.965583	−	0.260096i	$-0.916246\pi$
$227$	−3.90843	−	14.5865i	−0.259412	−	0.968138i	0.706171	−	0.708041i	$-0.250421\pi$
$228$	0.930152	−	2.51934i	0.0616008	−	0.166847i
$229$	−14.1582	+	8.17423i	−0.935600	+	0.540169i	−0.888578	−	0.458725i	$-0.848306\pi$
$229$	−14.1582	+	8.17423i	−0.935600	+	0.540169i	−0.0470214	+	0.998894i	$0.514973\pi$
$230$	0.792893	−	2.09077i	0.0522818	−	0.137861i
$231$	5.00000	+	10.8530i	0.328976	+	0.714075i
$232$	3.03906	−	0.814313i	0.199524	−	0.0534623i
$233$	10.9959	+	10.9959i	0.720363	+	0.720363i	0.968679	−	0.248316i	$-0.0798770\pi$
$233$	10.9959	+	10.9959i	0.720363	+	0.720363i	−0.248316	+	0.968679i	$0.579877\pi$
$234$	−10.2173	−	1.89898i	−0.667928	−	0.124140i
$235$	20.0227	+	2.02270i	1.30614	+	0.131947i
$236$	10.2247	+	5.90326i	0.665574	+	0.384269i
$237$	0.717439	+	4.18154i	0.0466027	+	0.271620i
$238$	−4.71209	−	1.26260i	−0.305439	−	0.0818423i
$239$	8.48528	+	14.6969i	0.548867	+	0.950666i	0.998353	+	0.0573782i	$0.0182741\pi$
$239$	8.48528	+	14.6969i	0.548867	+	0.950666i	−0.449485	+	0.893288i	$0.648393\pi$
$240$	0.741181	−	3.80140i	0.0478430	−	0.245379i
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	0.378963	+	0.925412i	$0.376281\pi$
$241$	−9.50000	+	16.4545i	−0.611949	+	1.05993i	−0.990912	+	0.134515i	$0.957053\pi$
$242$	−20.2204	+	20.2204i	−1.29981	+	1.29981i
$243$	−4.99221	−	14.7675i	−0.320250	−	0.947333i
$244$			5.44949i			0.348868i
$245$	2.07984	+	12.7967i	0.132876	+	0.817552i
$246$	0.623724	−	6.76928i	0.0397672	−	0.431594i
$247$	−1.39015	+	5.18811i	−0.0884531	+	0.330111i
$248$	1.15161	−	4.29788i	0.0731275	−	0.272915i
$249$	−0.778539	−	0.550510i	−0.0493379	−	0.0348872i
$250$	−7.58128	−	8.21731i	−0.479482	−	0.519709i
$251$			11.1708i			0.705097i	0.935793	+	0.352549i	$0.114685\pi$
$251$			11.1708i			0.705097i	−0.935793	+	0.352549i	$0.885315\pi$
$252$	1.86162	+	2.71159i	0.117271	+	0.170814i
$253$	−4.44949	+	4.44949i	−0.279737	+	0.279737i
$254$	−9.98698	+	17.2980i	−0.626639	+	1.08537i
$255$	7.56325	−	15.4844i	0.473629	−	0.969671i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−25.1579	−	6.74105i	−1.56931	−	0.420495i	−0.633713	−	0.773568i	$-0.718470\pi$
$257$	−25.1579	−	6.74105i	−1.56931	−	0.420495i	−0.935596	+	0.353073i	$0.885137\pi$
$258$	−5.62863	−	2.07812i	−0.350423	−	0.129378i
$259$	4.02834	+	2.32577i	0.250309	+	0.144516i
$260$	−0.778539	+	7.70674i	−0.0482829	+	0.477952i
$261$	−7.17423	−	6.13361i	−0.444074	−	0.379661i
$262$	7.44949	+	7.44949i	0.460231	+	0.460231i
$263$	12.2643	−	3.28621i	0.756249	−	0.202636i	0.139961	−	0.990157i	$-0.455302\pi$
$263$	12.2643	−	3.28621i	0.756249	−	0.202636i	0.616288	+	0.787521i	$0.288636\pi$
$264$	−6.29253	+	8.89898i	−0.387278	+	0.547694i
$265$	19.0621	−	8.57944i	1.17097	−	0.527031i
$266$	1.47219	−	0.849971i	0.0902660	−	0.0521151i
$267$	−2.62156	−	3.15369i	−0.160437	−	0.193003i
$268$	0.978838	+	3.65307i	0.0597920	+	0.223147i
$269$	4.70334			0.286768			0.143384	−	0.989667i	$-0.454202\pi$
$269$	4.70334			0.286768			0.143384	+	0.989667i	$0.454202\pi$
$270$	−10.6603	+	4.62158i	−0.648762	+	0.281260i
$271$	−16.0454			−0.974689			−0.487345	−	0.873210i	$-0.662034\pi$
$271$	−16.0454			−0.974689			−0.487345	+	0.873210i	$0.662034\pi$
$272$	−1.15161	−	4.29788i	−0.0698268	−	0.260597i
$273$	−4.20512	−	5.05870i	−0.254506	−	0.306166i
$274$	1.90702	−	1.10102i	0.115208	−	0.0665151i
$275$	9.96399	+	29.8432i	0.600851	+	1.79961i
$276$	−1.00000	+	1.41421i	−0.0601929	+	0.0851257i
$277$	13.7983	−	3.69723i	0.829057	−	0.222145i	0.180754	−	0.983528i	$-0.442146\pi$
$277$	13.7983	−	3.69723i	0.829057	−	0.222145i	0.648302	+	0.761383i	$0.275479\pi$
$278$	9.12096	+	9.12096i	0.547039	+	0.547039i
$279$	−12.5851	+	4.44949i	−0.753448	+	0.266384i
$280$	1.89898	−	1.55051i	0.113486	−	0.0926607i
$281$	−0.151531	−	0.0874863i	−0.00903957	−	0.00521900i	0.495473	−	0.868623i	$-0.334995\pi$
$281$	−0.151531	−	0.0874863i	−0.00903957	−	0.00521900i	−0.504513	+	0.863404i	$0.668328\pi$
$282$	−14.6236	−	5.39910i	−0.870823	−	0.321512i
$283$	−6.66112	−	1.78484i	−0.395962	−	0.106098i	0.0553430	−	0.998467i	$-0.482375\pi$
$283$	−6.66112	−	1.78484i	−0.395962	−	0.106098i	−0.451305	+	0.892370i	$0.649041\pi$
$284$	−0.317837	−	0.550510i	−0.0188602	−	0.0326668i
$285$	1.95181	+	5.67905i	0.115615	+	0.336398i
$286$	10.8990	−	18.8776i	0.644470	−	1.11626i
$287$	3.04272	−	3.04272i	0.179606	−	0.179606i
$288$	−1.29289	+	2.70711i	−0.0761845	+	0.159518i
$289$		−	2.79796i		−	0.164586i
$290$	−4.11219	+	5.70831i	−0.241476	+	0.335203i
$291$	15.7980	+	11.1708i	0.926093	+	0.654846i
$292$	−1.06110	+	3.96008i	−0.0620962	+	0.231746i
$293$	5.70577	−	21.2942i	0.333335	−	1.24402i	−0.572329	−	0.820024i	$-0.693960\pi$
$293$	5.70577	−	21.2942i	0.333335	−	1.24402i	0.905663	−	0.423998i	$-0.139374\pi$
$294$	0.921404	−	10.0000i	0.0537374	−	0.583212i
$295$	−26.0582	+	4.23523i	−1.51717	+	0.246585i
$296$			4.24264i			0.246598i
$297$	32.6938	+	0.452623i	1.89709	+	0.0262638i
$298$	−9.12372	+	9.12372i	−0.528523	+	0.528523i
$299$	1.73205	−	3.00000i	0.100167	−	0.173494i
$300$	4.09223	+	7.63241i	0.236265	+	0.440657i
$301$	−1.89898	−	3.28913i	−0.109455	−	0.189582i
$302$	20.8601	+	5.58943i	1.20036	+	0.321636i
$303$	0.372369	+	2.17033i	0.0213921	+	0.124682i
$304$	1.34278	+	0.775255i	0.0770138	+	0.0444639i
$305$	−7.70674	−	9.43879i	−0.441287	−	0.540464i
$306$	−8.67423	+	10.1459i	−0.495873	+	0.580002i
$307$	0.674235	+	0.674235i	0.0384806	+	0.0384806i	0.726085	−	0.687605i	$-0.241338\pi$
$307$	0.674235	+	0.674235i	0.0384806	+	0.0384806i	−0.687605	+	0.726085i	$0.741338\pi$
$308$	−6.66390	+	1.78559i	−0.379711	+	0.101743i
$309$	−2.97129	−	6.44949i	−0.169031	−	0.366899i
$310$	4.08346	+	9.07277i	0.231925	+	0.515299i
$311$	−17.8207	+	10.2888i	−1.01052	+	0.583422i	−0.911343	−	0.411648i	$-0.864953\pi$
$311$	−17.8207	+	10.2888i	−1.01052	+	0.583422i	−0.0991741	+	0.995070i	$0.531620\pi$
$312$	2.07812	−	5.62863i	0.117650	−	0.318658i
$313$	1.29958	+	4.85009i	0.0734564	+	0.274143i	0.992879	−	0.119128i	$-0.0380100\pi$
$313$	1.29958	+	4.85009i	0.0734564	+	0.274143i	−0.919422	+	0.393271i	$0.871343\pi$
$314$	6.14966			0.347046
$315$	−7.05919	−	2.06389i	−0.397741	−	0.116287i
$316$	−2.44949			−0.137795
$317$	0.284965	+	1.06350i	0.0160052	+	0.0597323i	0.973467	−	0.228829i	$-0.0734897\pi$
$317$	0.284965	+	1.06350i	0.0160052	+	0.0597323i	−0.957461	+	0.288561i	$0.906823\pi$
$318$	−15.9588	+	2.73810i	−0.894927	+	0.153545i
$319$	17.1455	−	9.89898i	0.959966	−	0.554236i
$320$	2.09077	+	0.792893i	0.116878	+	0.0443241i
$321$	9.05051	+	0.833917i	0.505150	+	0.0465447i
$322$	−1.05902	+	0.283763i	−0.0590168	+	0.0158135i
$323$	4.87832	+	4.87832i	0.271437	+	0.271437i
$324$	8.89060	−	1.39898i	0.493922	−	0.0777211i
$325$	−9.55051	−	14.4495i	−0.529767	−	0.801513i
$326$	−0.550510	−	0.317837i	−0.0304899	−	0.0176034i
$327$	27.1032	−	22.5300i	1.49881	−	1.24591i
$328$	3.79107	+	1.01581i	0.209327	+	0.0560889i
$329$	−4.93369	−	8.54541i	−0.272003	−	0.471124i
$330$	−1.68608	−	24.3125i	−0.0928155	−	1.33836i
$331$	2.22474	−	3.85337i	0.122283	−	0.211800i	−0.798385	−	0.602148i	$-0.794312\pi$
$331$	2.22474	−	3.85337i	0.122283	−	0.211800i	0.920668	+	0.390347i	$0.127645\pi$
$332$	0.389270	−	0.389270i	0.0213639	−	0.0213639i
$333$	10.4930	−	7.20390i	0.575015	−	0.394772i
$334$		−	10.7980i		−	0.590838i
$335$	−6.86162	−	4.94302i	−0.374890	−	0.270066i
$336$	−1.72474	+	0.794593i	−0.0940925	+	0.0433486i
$337$	−7.97861	+	29.7766i	−0.434622	+	1.62203i	0.307346	+	0.951598i	$0.400559\pi$
$337$	−7.97861	+	29.7766i	−0.434622	+	1.62203i	−0.741968	+	0.670435i	$0.766108\pi$
$338$	0.258819	−	0.965926i	0.0140779	−	0.0525394i
$339$	−21.7060	+	10.0000i	−1.17891	+	0.543125i
$340$	8.07277	+	5.81552i	0.437807	+	0.315391i
$341$		−	27.9985i		−	1.51621i
$342$	−0.362626	−	4.63737i	−0.0196085	−	0.250760i
$343$	9.92168	−	9.92168i	0.535721	−	0.535721i
$344$	1.73205	−	3.00000i	0.0933859	−	0.161749i
$345$	−0.267949	−	3.86370i	−0.0144259	−	0.208015i
$346$	1.55051	+	2.68556i	0.0833559	+	0.144377i
$347$	−4.05886	−	1.08757i	−0.217891	−	0.0583837i	0.148222	−	0.988954i	$-0.452645\pi$
$347$	−4.05886	−	1.08757i	−0.217891	−	0.0583837i	−0.366113	+	0.930570i	$0.619312\pi$
$348$	4.19067	−	3.48356i	0.224644	−	0.186739i
$349$	13.0297	+	7.52270i	0.697464	+	0.402681i	0.806402	−	0.591367i	$-0.201412\pi$
$349$	13.0297	+	7.52270i	0.697464	+	0.402681i	−0.108938	+	0.994049i	$0.534745\pi$
$350$	−1.09638	+	5.37113i	−0.0586038	+	0.287099i
$351$	−17.4495	+	4.41761i	−0.931385	+	0.235795i
$352$	−4.44949	−	4.44949i	−0.237159	−	0.237159i
$353$	−33.1244	+	8.87564i	−1.76303	+	0.472403i	−0.987328	−	0.158694i	$-0.949272\pi$
$353$	−33.1244	+	8.87564i	−1.76303	+	0.472403i	−0.775704	+	0.631097i	$0.782605\pi$
$354$	20.3632	+	1.87628i	1.08229	+	0.0997229i
$355$	1.32905	+	0.504022i	0.0705386	+	0.0267507i
$356$	2.05051	−	1.18386i	0.108677	−	0.0627446i
$357$	−8.32780	+	1.42883i	−0.440754	+	0.0756215i
$358$	−4.55683	−	17.0063i	−0.240836	−	0.898812i
$359$	17.4634			0.921682			0.460841	−	0.887483i	$-0.347548\pi$
$359$	17.4634			0.921682			0.460841	+	0.887483i	$0.347548\pi$
$360$	−1.58907	−	6.51727i	−0.0837514	−	0.343490i
$361$	16.5959			0.873469
$362$	−2.73067	−	10.1910i	−0.143521	−	0.535628i
$363$	−17.1547	+	46.4639i	−0.900388	+	2.43872i
$364$	3.28913	−	1.89898i	0.172397	−	0.0995336i
$365$	−3.76252	−	8.35968i	−0.196939	−	0.437566i
$366$	3.94949	+	8.57277i	0.206443	+	0.448106i
$367$	−9.42418	+	2.52520i	−0.491938	+	0.131814i	−0.496256	−	0.868176i	$-0.665292\pi$
$367$	−9.42418	+	2.52520i	−0.491938	+	0.131814i	0.00431778	+	0.999991i	$0.498626\pi$
$368$	−0.707107	−	0.707107i	−0.0368605	−	0.0368605i
$369$	−3.92480	−	11.1010i	−0.204317	−	0.577896i
$370$	−6.00000	−	7.34847i	−0.311925	−	0.382029i
$371$	−8.87628	−	5.12472i	−0.460833	−	0.266062i
$372$	−1.30323	−	7.59575i	−0.0675691	−	0.393822i
$373$	−19.6004	−	5.25190i	−1.01487	−	0.271933i	−0.287206	−	0.957869i	$-0.592727\pi$
$373$	−19.6004	−	5.25190i	−1.01487	−	0.271933i	−0.727662	+	0.685935i	$0.759393\pi$
$374$	−13.9993	−	24.2474i	−0.723885	−	1.25381i
$375$	−17.8818	−	7.43243i	−0.923412	−	0.383809i
$376$	4.50000	−	7.79423i	0.232070	−	0.401957i
$377$	−7.70674	+	7.70674i	−0.396917	+	0.396917i
$378$	4.89379	+	2.91649i	0.251709	+	0.150008i
$379$		−	6.65153i		−	0.341666i	−0.985300	−	0.170833i	$-0.945354\pi$
$379$		−	6.65153i		−	0.341666i	0.985300	−	0.170833i	$-0.0546459\pi$
$380$	−3.42214	+	0.556198i	−0.175552	+	0.0285324i
$381$	−3.17423	+	34.4500i	−0.162621	+	1.76493i
$382$	0.859599	−	3.20807i	0.0439809	−	0.164139i
$383$	7.19464	−	26.8508i	0.367629	−	1.37201i	−0.496193	−	0.868212i	$-0.665269\pi$
$383$	7.19464	−	26.8508i	0.367629	−	1.37201i	0.863822	−	0.503798i	$-0.168064\pi$
$384$	−1.41421	−	1.00000i	−0.0721688	−	0.0510310i
$385$	9.01702	−	12.5169i	0.459550	−	0.637921i
$386$		−	17.3205i		−	0.881591i
$387$	−10.3607	+	0.810167i	−0.526663	+	0.0411831i
$388$	−7.89898	+	7.89898i	−0.401010	+	0.401010i
$389$	−2.81237	+	4.87117i	−0.142593	+	0.246978i	−0.928472	−	0.371402i	$-0.878877\pi$
$389$	−2.81237	+	4.87117i	−0.142593	+	0.246978i	0.785879	+	0.618380i	$0.212211\pi$
$390$	4.36068	+	12.6880i	0.220811	+	0.642480i
$391$	−2.22474	−	3.85337i	−0.112510	−	0.194873i
$392$	5.60040	+	1.50062i	0.282863	+	0.0757929i
$393$	17.1180	+	6.32005i	0.863489	+	0.318804i
$394$	8.48528	+	4.89898i	0.427482	+	0.246807i
$395$	4.24264	−	3.46410i	0.213470	−	0.174298i
$396$	−3.44949	+	18.5597i	−0.173343	+	0.932662i
$397$	15.4495	+	15.4495i	0.775388	+	0.775388i	0.979043	−	0.203655i	$-0.0652821\pi$
$397$	15.4495	+	15.4495i	0.775388	+	0.775388i	−0.203655	+	0.979043i	$0.565282\pi$
$398$	−3.42953	+	0.918940i	−0.171907	+	0.0460623i
$399$	1.69994	−	2.40408i	0.0851036	−	0.120355i
$400$	−4.74264	+	1.58346i	−0.237132	+	0.0791732i
$401$	22.3485	−	12.9029i	1.11603	−	0.644340i	0.175645	−	0.984454i	$-0.443799\pi$
$401$	22.3485	−	12.9029i	1.11603	−	0.644340i	0.940384	+	0.340114i	$0.110466\pi$
$402$	4.18739	+	5.03736i	0.208848	+	0.251241i
$403$	3.98930	+	14.8883i	0.198721	+	0.741638i
$404$	−1.27135			−0.0632520
$405$	−13.4205	+	14.9963i	−0.666871	+	0.745173i
$406$	3.44949			0.171195
$407$	6.90968	+	25.7873i	0.342500	+	1.27823i
$408$	−4.92650	−	5.92650i	−0.243898	−	0.293406i
$409$	−16.5420	+	9.55051i	−0.817948	+	0.472242i	−0.849708	−	0.527253i	$-0.823222\pi$
$409$	−16.5420	+	9.55051i	−0.817948	+	0.472242i	0.0317605	+	0.999496i	$0.489889\pi$
$410$	−8.00290	+	3.60194i	−0.395235	+	0.177887i
$411$	2.20204	−	3.11416i	0.108619	−	0.153610i
$412$	3.96008	−	1.06110i	0.195099	−	0.0522767i
$413$	9.15306	+	9.15306i	0.450393	+	0.450393i
$414$	−0.548188	+	2.94949i	−0.0269420	+	0.144960i
$415$	−0.123724	+	1.22474i	−0.00607339	+	0.0601204i
$416$	3.00000	+	1.73205i	0.147087	+	0.0849208i
$417$	20.9588	+	7.73810i	1.02636	+	0.378937i
$418$	9.42418	+	2.52520i	0.460952	+	0.123512i
$419$	−5.97469	−	10.3485i	−0.291883	−	0.505556i	0.682372	−	0.731005i	$-0.260948\pi$
$419$	−5.97469	−	10.3485i	−0.291883	−	0.505556i	−0.974255	+	0.225449i	$0.927615\pi$
$420$	1.86362	−	3.81543i	0.0909354	−	0.186174i
$421$	7.44949	−	12.9029i	0.363066	−	0.628849i	−0.625398	−	0.780306i	$-0.715063\pi$
$421$	7.44949	−	12.9029i	0.363066	−	0.628849i	0.988464	+	0.151457i	$0.0483966\pi$
$422$	13.3636	−	13.3636i	0.650530	−	0.650530i
$423$	−26.9178	+	2.10488i	−1.30879	+	0.102343i
$424$		−	9.34847i		−	0.454002i
$425$	−22.2068	+	1.34385i	−1.07719	+	0.0651863i
$426$	−0.898979	−	0.635674i	−0.0435557	−	0.0307985i
$427$	−1.54636	+	5.77111i	−0.0748338	+	0.279284i
$428$	−1.35814	+	5.06865i	−0.0656482	+	0.245002i
$429$	3.46410	−	37.5959i	0.167248	−	1.81515i
$430$	1.24264	+	7.64564i	0.0599255	+	0.368706i
$431$			15.5563i			0.749323i	0.927162	+	0.374661i	$0.122241\pi$
$431$			15.5563i			0.749323i	−0.927162	+	0.374661i	$0.877759\pi$
$432$	−0.0719302	+	5.19565i	−0.00346074	+	0.249976i
$433$	8.55051	−	8.55051i	0.410911	−	0.410911i	−0.471145	−	0.882056i	$-0.656159\pi$
$433$	8.55051	−	8.55051i	0.410911	−	0.410911i	0.882056	+	0.471145i	$0.156159\pi$
$434$	2.43916	−	4.22474i	0.117083	−	0.202794i
$435$	−2.33195	+	11.9602i	−0.111809	+	0.573448i
$436$	10.1742	+	17.6223i	0.487257	+	0.843955i
$437$	1.49768	+	0.401302i	0.0716436	+	0.0191969i
$438$	1.20080	+	6.99876i	0.0573763	+	0.334413i
$439$	−8.83523	−	5.10102i	−0.421682	−	0.243458i	0.274114	−	0.961697i	$-0.411615\pi$
$439$	−8.83523	−	5.10102i	−0.421682	−	0.243458i	−0.695797	+	0.718239i	$0.744949\pi$
$440$	13.9993	+	1.41421i	0.667389	+	0.0674200i
$441$	−5.79796	−	16.3991i	−0.276093	−	0.780910i
$442$	10.8990	+	10.8990i	0.518412	+	0.518412i
$443$	0.531752	−	0.142483i	0.0252643	−	0.00676955i	−0.246165	−	0.969228i	$-0.579170\pi$
$443$	0.531752	−	0.142483i	0.0252643	−	0.00676955i	0.271429	+	0.962458i	$0.412504\pi$
$444$	3.07483	+	6.67423i	0.145925	+	0.316745i
$445$	−1.87735	+	4.95037i	−0.0889951	+	0.234670i
$446$	−7.19694	+	4.15515i	−0.340785	+	0.196752i
$447$	−7.74045	+	20.9652i	−0.366111	+	0.991620i
$448$	−0.283763	−	1.05902i	−0.0134065	−	0.0500339i
$449$	−21.7060			−1.02437			−0.512185	−	0.858875i	$-0.671164\pi$
$449$	−21.7060			−1.02437			−0.512185	+	0.858875i	$0.671164\pi$
$450$	11.9692	+	9.04096i	0.564232	+	0.426195i
$451$	24.6969			1.16293
$452$	−3.57117	−	13.3278i	−0.167974	−	0.626887i
$453$	36.8665	−	6.32530i	1.73214	−	0.297188i
$454$	13.0779	−	7.55051i	0.613775	−	0.354363i
$455$	−3.01138	+	7.94066i	−0.141175	+	0.372264i
$456$	2.67423	+	0.246405i	0.125233	+	0.0115390i
$457$	−5.94012	+	1.59165i	−0.277867	+	0.0744543i	−0.395061	−	0.918655i	$-0.629277\pi$
$457$	−5.94012	+	1.59165i	−0.277867	+	0.0744543i	0.117194	+	0.993109i	$0.462610\pi$
$458$	−11.5601	−	11.5601i	−0.540169	−	0.540169i
$459$	−6.29253	+	22.2474i	−0.293710	+	1.03842i
$460$	2.22474	+	0.224745i	0.103729	+	0.0104788i
$461$	16.3763	+	9.45485i	0.762719	+	0.440356i	0.830271	−	0.557360i	$-0.188186\pi$
$461$	16.3763	+	9.45485i	0.762719	+	0.440356i	−0.0675520	+	0.997716i	$0.521519\pi$
$462$	−9.18910	+	7.63859i	−0.427516	+	0.355380i
$463$	31.8946	+	8.54613i	1.48227	+	0.397172i	0.907118	−	0.420876i	$-0.138277\pi$
$463$	31.8946	+	8.54613i	1.48227	+	0.397172i	0.575150	+	0.818048i	$0.304944\pi$
$464$	1.57313	+	2.72474i	0.0730308	+	0.126493i
$465$	12.9993	+	11.3132i	0.602827	+	0.524637i
$466$	−7.77526	+	13.4671i	−0.360182	+	0.623853i
$467$	−2.82843	+	2.82843i	−0.130884	+	0.130884i	−0.769514	−	0.638630i	$-0.779501\pi$
$467$	−2.82843	+	2.82843i	−0.130884	+	0.130884i	0.638630	+	0.769514i	$0.279501\pi$
$468$	−0.810167	−	10.3607i	−0.0374500	−	0.478922i
$469$			4.14643i			0.191464i
$470$	3.22848	+	19.8640i	0.148918	+	0.916256i
$471$	9.67423	−	4.45694i	0.445765	−	0.205365i
$472$	−3.05575	+	11.4042i	−0.140652	+	0.524922i
$473$	5.64173	−	21.0552i	0.259407	−	0.968120i
$474$	−3.85337	+	1.77526i	−0.176991	+	0.0815402i
$475$	5.14074	−	5.80300i	0.235873	−	0.266260i
$476$		−	4.87832i		−	0.223597i
$477$	−23.1209	+	15.8735i	−1.05863	+	0.726797i
$478$	−12.0000	+	12.0000i	−0.548867	+	0.548867i
$479$	3.53553	−	6.12372i	0.161543	−	0.279800i	−0.773879	−	0.633333i	$-0.781686\pi$
$479$	3.53553	−	6.12372i	0.161543	−	0.279800i	0.935422	+	0.353533i	$0.115020\pi$
$480$	3.86370	−	0.267949i	0.176353	−	0.0122302i
$481$	−7.34847	−	12.7279i	−0.335061	−	0.580343i
$482$	−18.3526	−	4.91756i	−0.835938	−	0.223989i
$483$	−1.46032	+	1.21391i	−0.0664469	+	0.0552350i
$484$	−24.7648	−	14.2980i	−1.12567	−	0.649907i
$485$	2.51059	−	24.8523i	0.114000	−	1.12848i
$486$	12.9722	−	8.64420i	0.588431	−	0.392109i
$487$	−12.0000	−	12.0000i	−0.543772	−	0.543772i	0.380861	−	0.924632i	$-0.375628\pi$
$487$	−12.0000	−	12.0000i	−0.543772	−	0.543772i	−0.924632	+	0.380861i	$0.875628\pi$
$488$	−5.26380	+	1.41043i	−0.238281	+	0.0638472i
$489$	−1.09638	−	0.101021i	−0.0495799	−	0.00456831i
$490$	−11.8224	+	5.32101i	−0.534080	+	0.240379i
$491$	0.247449	−	0.142865i	0.0111672	−	0.00644739i	−0.494406	−	0.869231i	$-0.664614\pi$
$491$	0.247449	−	0.142865i	0.0111672	−	0.00644739i	0.505573	+	0.862784i	$0.331281\pi$
$492$	6.70006	−	1.14955i	0.302062	−	0.0518256i
$493$	3.62328	+	13.5223i	0.163184	+	0.609012i
$494$	−5.37113			−0.241658
$495$	−20.2728	−	37.0247i	−0.911193	−	1.66414i
$496$	4.44949			0.199788
$497$	−0.180381	−	0.673191i	−0.00809119	−	0.0301967i
$498$	0.330251	−	0.894494i	0.0147989	−	0.0400832i
$499$	−7.70674	+	4.44949i	−0.345001	+	0.199187i	−0.662481	−	0.749078i	$-0.730497\pi$
$499$	−7.70674	+	4.44949i	−0.345001	+	0.199187i	0.317480	+	0.948265i	$0.397163\pi$
$500$	5.97514	−	9.44975i	0.267216	−	0.422606i
$501$	−7.82577	−	16.9866i	−0.349629	−	0.758906i
$502$	−10.7902	+	2.89123i	−0.481590	+	0.129042i
$503$	16.7563	+	16.7563i	0.747125	+	0.747125i	0.973938	−	0.226813i	$-0.0728307\pi$
$503$	16.7563	+	16.7563i	0.747125	+	0.747125i	−0.226813	+	0.973938i	$0.572831\pi$
$504$	−2.13737	+	2.50000i	−0.0952062	+	0.111359i
$505$	2.20204	−	1.79796i	0.0979895	−	0.0800081i
$506$	−5.44949	−	3.14626i	−0.242259	−	0.139869i
$507$	−0.292893	−	1.70711i	−0.0130078	−	0.0758153i
$508$	−19.2934	−	5.16964i	−0.856005	−	0.229366i
$509$	19.8150	+	34.3207i	0.878286	+	1.52124i	0.853220	+	0.521551i	$0.174646\pi$
$509$	19.8150	+	34.3207i	0.878286	+	1.52124i	0.0250662	+	0.999686i	$0.492020\pi$
$510$	16.9143	+	3.29788i	0.748978	+	0.146032i
$511$	−2.24745	+	3.89270i	−0.0994213	+	0.172203i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−3.93137	−	7.03239i	−0.173574	−	0.310488i
$514$		−	26.0454i		−	1.14881i
$515$	−5.35844	+	7.43828i	−0.236121	+	0.327770i
$516$	0.550510	−	5.97469i	0.0242349	−	0.263021i
$517$	14.6576	−	54.7030i	0.644642	−	2.40584i
$518$	−1.20390	+	4.49303i	−0.0528965	+	0.197413i
$519$	4.38551	+	3.10102i	0.192502	+	0.136120i
$520$	−7.64564	+	1.24264i	−0.335284	+	0.0544934i
$521$			29.4449i			1.29000i	0.764181	+	0.645001i	$0.223143\pi$
$521$			29.4449i			1.29000i	−0.764181	+	0.645001i	$0.776857\pi$
$522$	4.06778	−	8.51727i	0.178042	−	0.372791i
$523$	1.77526	−	1.77526i	0.0776265	−	0.0776265i	−0.667228	−	0.744854i	$-0.732519\pi$
$523$	1.77526	−	1.77526i	0.0776265	−	0.0776265i	0.744854	+	0.667228i	$0.232519\pi$
$524$	−5.26758	+	9.12372i	−0.230116	+	0.398572i
$525$	2.16795	+	9.24408i	0.0946171	+	0.403445i
$526$	6.34847	+	10.9959i	0.276806	+	0.479443i
$527$	19.1234	+	5.12409i	0.833027	+	0.223209i
$528$	−10.2244	−	3.77489i	−0.444959	−	0.164281i
$529$	19.0526	+	11.0000i	0.828372	+	0.478261i
$530$	13.2207	+	16.1920i	0.574272	+	0.703337i
$531$	33.3939	−	11.8065i	1.44917	−	0.512359i
$532$	1.20204	+	1.20204i	0.0521151	+	0.0521151i
$533$	−13.1326	+	3.51888i	−0.568838	+	0.152420i
$534$	2.36773	−	3.34847i	0.102461	−	0.144902i
$535$	−4.81578	−	10.6999i	−0.208204	−	0.462595i
$536$	−3.27526	+	1.89097i	−0.141469	+	0.0816774i
$537$	−19.4937	−	23.4506i	−0.841217	−	1.01197i
$538$	1.21731	+	4.54308i	0.0524822	+	0.195866i
$539$	36.4838			1.57147
$540$	−7.22318	−	9.10086i	−0.310836	−	0.391639i
$541$	−25.9444			−1.11544			−0.557718	−	0.830030i	$-0.688323\pi$
$541$	−25.9444			−1.11544			−0.557718	+	0.830030i	$0.688323\pi$
$542$	−4.15286	−	15.4987i	−0.178380	−	0.665725i
$543$	−11.6816	−	14.0528i	−0.501305	−	0.603062i
$544$	3.85337	−	2.22474i	0.165212	−	0.0953851i
$545$	−42.5440	−	16.1342i	−1.82238	−	0.691112i
$546$	3.79796	−	5.37113i	0.162538	−	0.229863i
$547$	20.6594	−	5.53567i	0.883332	−	0.236688i	0.211488	−	0.977381i	$-0.432169\pi$
$547$	20.6594	−	5.53567i	0.883332	−	0.236688i	0.671844	+	0.740693i	$0.265502\pi$
$548$	1.55708	+	1.55708i	0.0665151	+	0.0665151i
$549$	12.4261	+	10.6237i	0.530335	+	0.453410i
$550$	−26.2474	+	17.3485i	−1.11919	+	0.739741i
$551$	−4.22474	−	2.43916i	−0.179980	−	0.103912i
$552$	−1.62484	−	0.599900i	−0.0691580	−	0.0255335i
$553$	−2.59405	−	0.695075i	−0.110310	−	0.0295576i
$554$	7.14250	+	12.3712i	0.303456	+	0.525601i
$555$	−14.7646	−	7.21164i	−0.626721	−	0.306117i
$556$	−6.44949	+	11.1708i	−0.273519	+	0.473749i
$557$	−16.3670	+	16.3670i	−0.693492	+	0.693492i	−0.962999	−	0.269507i	$-0.913139\pi$
$557$	−16.3670	+	16.3670i	−0.693492	+	0.693492i	0.269507	+	0.962999i	$0.413139\pi$
$558$	−7.55513	−	11.0046i	−0.319834	−	0.465863i
$559$			12.0000i			0.507546i
$560$	1.98917	+	1.43297i	0.0840578	+	0.0605541i
$561$	−39.5959	−	27.9985i	−1.67174	−	1.18210i
$562$	0.0452863	−	0.169011i	0.00191029	−	0.00712928i
$563$	−8.89004	+	33.1781i	−0.374670	+	1.39829i	0.479155	+	0.877730i	$0.340943\pi$
$563$	−8.89004	+	33.1781i	−0.374670	+	1.39829i	−0.853826	+	0.520559i	$0.825724\pi$
$564$	1.43027	−	15.5227i	0.0602251	−	0.653624i
$565$	25.0338	+	18.0340i	1.05318	+	0.758697i
$566$		−	6.89610i		−	0.289864i
$567$	9.81229	+	1.04128i	0.412077	+	0.0437297i
$568$	0.449490	−	0.449490i	0.0188602	−	0.0188602i
$569$	13.0458	−	22.5959i	0.546907	−	0.947270i	−0.451578	−	0.892232i	$-0.649139\pi$
$569$	13.0458	−	22.5959i	0.546907	−	0.947270i	0.998484	−	0.0550383i	$-0.0175281\pi$
$570$	−4.98038	+	3.35515i	−0.208605	+	0.140532i
$571$	−13.5505	−	23.4702i	−0.567071	−	0.982196i	−0.996854	−	0.0792637i	$-0.974743\pi$
$571$	−13.5505	−	23.4702i	−0.567071	−	0.982196i	0.429782	−	0.902932i	$-0.358590\pi$
$572$	21.0552	+	5.64173i	0.880363	+	0.235892i
$573$	−0.972768	−	5.66971i	−0.0406380	−	0.236855i
$574$	3.72656	+	2.15153i	0.155544	+	0.0898032i
$575$	−4.17121	+	2.75699i	−0.173951	+	0.114975i
$576$	−2.94949	−	0.548188i	−0.122895	−	0.0228412i
$577$	−17.0000	−	17.0000i	−0.707719	−	0.707719i	0.258336	−	0.966055i	$-0.416826\pi$
$577$	−17.0000	−	17.0000i	−0.707719	−	0.707719i	−0.966055	+	0.258336i	$0.916826\pi$
$578$	2.70262	−	0.724165i	0.112414	−	0.0301213i
$579$	−12.5529	−	27.2474i	−0.521683	−	1.13237i
$580$	−6.57812	−	2.49465i	−0.273141	−	0.103585i
$581$	0.522704	−	0.301783i	0.0216854	−	0.0125201i
$582$	−6.70139	+	18.1509i	−0.277782	+	0.752378i
$583$	−15.2252	−	56.8211i	−0.630562	−	2.35329i
$584$	−4.09978			−0.169650
$585$	16.0555	+	16.7995i	0.663812	+	0.694573i
$586$	22.0454			0.910687
$587$	8.03514	+	29.9876i	0.331646	+	1.23772i	0.907460	+	0.420138i	$0.138019\pi$
$587$	8.03514	+	29.9876i	0.331646	+	1.23772i	−0.575814	+	0.817581i	$0.695315\pi$
$588$	9.89774	−	1.69818i	0.408176	−	0.0700319i
$589$	−5.97469	+	3.44949i	−0.246183	+	0.142134i
$590$	−10.8353	−	24.0742i	−0.446082	−	0.991118i
$591$	16.8990	+	1.55708i	0.695131	+	0.0640496i
$592$	−4.09808	+	1.09808i	−0.168430	+	0.0451307i
$593$	−10.0745	−	10.0745i	−0.413709	−	0.413709i	0.469320	−	0.883028i	$-0.344499\pi$
$593$	−10.0745	−	10.0745i	−0.413709	−	0.413709i	−0.883028	+	0.469320i	$0.844499\pi$
$594$	8.02458	+	31.6969i	0.329252	+	1.30054i
$595$	6.89898	+	8.44949i	0.282831	+	0.346395i
$596$	−11.1742	−	6.45145i	−0.457714	−	0.264262i
$597$	−4.72911	+	3.93115i	−0.193549	+	0.160891i
$598$	3.34607	+	0.896575i	0.136831	+	0.0366637i
$599$	−16.8991	−	29.2702i	−0.690480	−	1.19595i	−0.971681	−	0.236297i	$-0.924066\pi$
$599$	−16.8991	−	29.2702i	−0.690480	−	1.19595i	0.281201	−	0.959649i	$-0.409267\pi$
$600$	−6.31319	+	5.92820i	−0.257735	+	0.242018i
$601$	−17.3485	+	30.0484i	−0.707659	+	1.22570i	0.258065	+	0.966128i	$0.416915\pi$
$601$	−17.3485	+	30.0484i	−0.707659	+	1.22570i	−0.965723	+	0.259573i	$0.916418\pi$
$602$	2.68556	−	2.68556i	0.109455	−	0.109455i
$603$	10.2381	+	4.88964i	0.416928	+	0.199122i
$604$			21.5959i			0.878725i
$605$	63.1142	−	10.2579i	2.56596	−	0.417043i
$606$	−2.00000	+	0.921404i	−0.0812444	+	0.0374295i
$607$	5.73717	−	21.4114i	0.232864	−	0.869062i	−0.746235	−	0.665682i	$-0.768141\pi$
$607$	5.73717	−	21.4114i	0.232864	−	0.869062i	0.979100	−	0.203380i	$-0.0651926\pi$
$608$	−0.401302	+	1.49768i	−0.0162749	+	0.0607389i
$609$	5.42650	−	2.50000i	0.219893	−	0.101305i
$610$	7.12252	−	9.88708i	0.288383	−	0.400316i
$611$			31.1769i			1.26128i
$612$	−12.0452	−	5.75272i	−0.486900	−	0.232540i
$613$	−12.7980	+	12.7980i	−0.516905	+	0.516905i	−0.916633	−	0.399729i	$-0.869104\pi$
$613$	−12.7980	+	12.7980i	−0.516905	+	0.516905i	0.399729	+	0.916633i	$0.369104\pi$
$614$	−0.476756	+	0.825765i	−0.0192403	+	0.0333252i
$615$	−9.97914	+	11.4664i	−0.402398	+	0.462369i
$616$	−3.44949	−	5.97469i	−0.138984	−	0.240727i
$617$	6.85906	+	1.83788i	0.276135	+	0.0739902i	0.394229	−	0.919012i	$-0.371012\pi$
$617$	6.85906	+	1.83788i	0.276135	+	0.0739902i	−0.118094	+	0.993002i	$0.537678\pi$
$618$	5.46070	−	4.53930i	0.219662	−	0.182597i
$619$	−21.4275	−	12.3712i	−0.861244	−	0.497239i	0.00318471	−	0.999995i	$-0.498986\pi$
$619$	−21.4275	−	12.3712i	−0.861244	−	0.497239i	−0.864429	+	0.502756i	$0.832320\pi$
$620$	−7.70674	+	6.29253i	−0.309510	+	0.252714i
$621$	1.27526	+	5.03723i	0.0511742	+	0.202137i
$622$	−14.5505	−	14.5505i	−0.583422	−	0.583422i
$623$	2.50746	−	0.671873i	0.100459	−	0.0269180i
$624$	5.97469	+	0.550510i	0.239179	+	0.0220380i
$625$	3.01472	+	24.8176i	0.120589	+	0.992703i
$626$	−4.34847	+	2.51059i	−0.173800	+	0.100343i
$627$	16.6556	−	2.85765i	0.665161	−	0.114124i
$628$	1.59165	+	5.94012i	0.0635138	+	0.237037i
$629$	−18.8776			−0.752699
$630$	0.166507	−	7.35283i	0.00663380	−	0.292944i
$631$	−12.8990			−0.513500			−0.256750	−	0.966478i	$-0.582652\pi$
$631$	−12.8990			−0.513500			−0.256750	+	0.966478i	$0.582652\pi$
$632$	−0.633975	−	2.36603i	−0.0252182	−	0.0941154i
$633$	11.3375	−	30.7079i	0.450625	−	1.22053i
$634$	−0.953512	+	0.550510i	−0.0378688	+	0.0218636i
$635$	40.7281	−	18.3309i	1.61624	−	0.727438i
$636$	−6.77526	−	14.7064i	−0.268656	−	0.583146i
$637$	−19.4003	+	5.19831i	−0.768670	+	0.205964i
$638$	13.9993	+	13.9993i	0.554236	+	0.554236i
$639$	−1.87492	−	0.348469i	−0.0741705	−	0.0137852i
$640$	−0.224745	+	2.22474i	−0.00888382	+	0.0879408i
$641$	−7.74745	−	4.47299i	−0.306006	−	0.176673i	0.339132	−	0.940739i	$-0.389867\pi$
$641$	−7.74745	−	4.47299i	−0.306006	−	0.176673i	−0.645138	+	0.764066i	$0.723200\pi$
$642$	1.53694	+	8.95796i	0.0606583	+	0.353542i
$643$	30.6976	+	8.22539i	1.21059	+	0.324378i	0.806995	−	0.590558i	$-0.201092\pi$
$643$	30.6976	+	8.22539i	1.21059	+	0.324378i	0.403599	+	0.914936i	$0.367759\pi$
$644$	−0.548188	−	0.949490i	−0.0216016	−	0.0374151i
$645$	7.49598	+	11.1270i	0.295154	+	0.438126i
$646$	−3.44949	+	5.97469i	−0.135718	+	0.235071i
$647$	24.9558	−	24.9558i	0.981114	−	0.981114i	−0.0187105	−	0.999825i	$-0.505956\pi$
$647$	24.9558	−	24.9558i	0.981114	−	0.981114i	0.999825	+	0.0187105i	$0.00595608\pi$
$648$	3.65237	+	8.22558i	0.143479	+	0.323131i
$649$			74.2929i			2.91625i
$650$	11.4853	−	12.9649i	0.450490	−	0.508525i
$651$	0.775255	−	8.41385i	0.0303846	−	0.329765i
$652$	0.164525	−	0.614014i	0.00644328	−	0.0240467i
$653$	−5.57768	+	20.8162i	−0.218272	+	0.814601i	0.766718	+	0.641985i	$0.221889\pi$
$653$	−5.57768	+	20.8162i	−0.218272	+	0.814601i	−0.984989	+	0.172616i	$0.944778\pi$
$654$	28.7771	+	20.3485i	1.12527	+	0.795688i
$655$	−3.77917	−	23.2522i	−0.147664	−	0.908540i
$656$			3.92480i			0.153238i
$657$	6.96132	+	10.1397i	0.271587	+	0.395587i
$658$	6.97730	−	6.97730i	0.272003	−	0.272003i
$659$	−5.65685	+	9.79796i	−0.220360	+	0.381674i	−0.954917	−	0.296872i	$-0.904056\pi$
$659$	−5.65685	+	9.79796i	−0.220360	+	0.381674i	0.734557	+	0.678546i	$0.237390\pi$
$660$	23.0476	−	7.92116i	0.897128	−	0.308331i
$661$	15.3485	+	26.5843i	0.596986	+	1.03401i	0.993263	+	0.115880i	$0.0369687\pi$
$661$	15.3485	+	26.5843i	0.596986	+	1.03401i	−0.396277	+	0.918131i	$0.629698\pi$
$662$	4.29788	+	1.15161i	0.167042	+	0.0447587i
$663$	25.0445	+	9.24656i	0.972648	+	0.359106i
$664$	0.476756	+	0.275255i	0.0185017	+	0.0106820i
$665$	−3.78194	−	0.382053i	−0.146657	−	0.0148154i
$666$	9.67423	+	8.27098i	0.374869	+	0.320494i
$667$	2.22474	+	2.22474i	0.0861425	+	0.0861425i
$668$	10.4300	−	2.79472i	0.403550	−	0.108131i
$669$	−8.31031	+	11.7526i	−0.321295	+	0.454380i
$670$	2.99867	−	7.90717i	0.115849	−	0.305480i
$671$	−29.6969	+	17.1455i	−1.14644	+	0.661896i
$672$	−1.21391	−	1.46032i	−0.0468278	−	0.0563331i
$673$	−4.22778	−	15.7783i	−0.162969	−	0.608208i	−0.998291	−	0.0584468i	$-0.981385\pi$
$673$	−4.22778	−	15.7783i	−0.162969	−	0.608208i	0.835322	−	0.549762i	$-0.185281\pi$
$674$	−30.8270			−1.18741
$675$	25.3815	+	5.54804i	0.976933	+	0.213544i
$676$	1.00000			0.0384615
$677$	1.65750	+	6.18587i	0.0637028	+	0.237742i	0.990435	−	0.137981i	$-0.0440612\pi$
$677$	1.65750	+	6.18587i	0.0637028	+	0.237742i	−0.926732	+	0.375723i	$0.877394\pi$
$678$	−15.2772	−	18.3782i	−0.586717	−	0.705811i
$679$	−10.6066	+	6.12372i	−0.407044	+	0.235007i
$680$	−3.52797	+	9.30286i	−0.135291	+	0.356748i
$681$	15.1010	−	21.3561i	0.578672	−	0.818366i
$682$	27.0445	−	7.24656i	1.03559	−	0.277485i
$683$	−13.8564	−	13.8564i	−0.530201	−	0.530201i	0.390431	−	0.920632i	$-0.372326\pi$
$683$	−13.8564	−	13.8564i	−0.530201	−	0.530201i	−0.920632	+	0.390431i	$0.872326\pi$
$684$	4.38551	−	1.55051i	0.167684	−	0.0592852i
$685$	−4.89898	−	0.494897i	−0.187180	−	0.0189091i
$686$	12.1515	+	7.01569i	0.463948	+	0.267860i
$687$	−26.5637	−	9.80745i	−1.01347	−	0.374178i
$688$	3.34607	+	0.896575i	0.127568	+	0.0341816i
$689$	16.1920	+	28.0454i	0.616867	+	1.06844i
$690$	3.66270	−	1.25882i	0.139437	−	0.0479224i
$691$	−16.4722	+	28.5307i	−0.626632	+	1.08536i	0.361591	+	0.932337i	$0.382234\pi$
$691$	−16.4722	+	28.5307i	−0.626632	+	1.08536i	−0.988223	+	0.153021i	$0.951100\pi$
$692$	−2.19275	+	2.19275i	−0.0833559	+	0.0833559i
$693$	−8.91964	+	18.6763i	−0.338829	+	0.709453i
$694$		−	4.20204i		−	0.159507i
$695$	−4.62712	−	28.4694i	−0.175516	−	1.07991i
$696$	4.44949	+	3.14626i	0.168657	+	0.119259i
$697$	−4.51985	+	16.8683i	−0.171202	+	0.638933i
$698$	−3.89404	+	14.5327i	−0.147392	+	0.550073i
$699$	−2.47127	+	26.8207i	−0.0934719	+	1.01445i
$700$	−5.47187	+	0.331131i	−0.206817	+	0.0125156i
$701$		−	23.9309i		−	0.903857i	−0.892054	−	0.451928i	$-0.850736\pi$
$701$		−	23.9309i		−	0.903857i	0.892054	−	0.451928i	$-0.149264\pi$
$702$	−8.78335	−	15.7116i	−0.331506	−	0.592994i
$703$	4.65153	−	4.65153i	0.175436	−	0.175436i
$704$	3.14626	−	5.44949i	0.118579	−	0.205385i
$705$	19.4751	+	28.9088i	0.733476	+	1.08877i
$706$	−17.1464	−	29.6985i	−0.645314	−	1.11772i
$707$	−1.34638	−	0.360762i	−0.0506359	−	0.0135678i
$708$	3.45805	+	20.1550i	0.129961	+	0.757471i
$709$	−38.4069	−	22.1742i	−1.44240	−	0.832771i	−0.444392	−	0.895833i	$-0.646580\pi$
$709$	−38.4069	−	22.1742i	−1.44240	−	0.832771i	−0.998010	+	0.0630617i	$0.979914\pi$
$710$	−0.142865	+	1.41421i	−0.00536161	+	0.0530745i
$711$	−4.77526	+	5.58542i	−0.179086	+	0.209470i
$712$	1.67423	+	1.67423i	0.0627446	+	0.0627446i
$713$	4.29788	−	1.15161i	0.160957	−	0.0431282i
$714$	−3.53553	−	7.67423i	−0.132314	−	0.287201i
$715$	−44.4473	+	20.0048i	−1.66223	+	0.748137i
$716$	15.2474	−	8.80312i	0.569824	−	0.328988i
$717$	−10.1806	+	27.5745i	−0.380203	+	1.02979i
$718$	4.51985	+	16.8683i	0.168679	+	0.629520i
$719$	−32.5269			−1.21305			−0.606525	−	0.795065i	$-0.707437\pi$
$719$	−32.5269			−1.21305			−0.606525	+	0.795065i	$0.707437\pi$
$720$	5.88392	−	3.22172i	0.219281	−	0.120066i
$721$	4.49490			0.167399
$722$	4.29534	+	16.0304i	0.159856	+	0.596591i
$723$	−32.4350	+	5.56497i	−1.20627	+	0.206964i
$724$	9.13701	−	5.27526i	0.339574	−	0.196053i
$725$	14.9216	−	4.98200i	0.554174	−	0.185027i
$726$	−49.3207	−	4.54442i	−1.83046	−	0.168659i
$727$	30.2836	−	8.11447i	1.12316	−	0.300949i	0.350996	−	0.936377i	$-0.385843\pi$
$727$	30.2836	−	8.11447i	1.12316	−	0.300949i	0.772160	+	0.635428i	$0.219176\pi$
$728$	2.68556	+	2.68556i	0.0995336	+	0.0995336i
$729$	14.1421	−	23.0000i	0.523783	−	0.851852i
$730$	7.10102	−	5.79796i	0.262821	−	0.214592i
$731$	13.3485	+	7.70674i	0.493711	+	0.285044i
$732$	−7.25845	+	6.03371i	−0.268280	+	0.223012i
$733$	13.8603	+	3.71385i	0.511941	+	0.137174i	0.505536	−	0.862805i	$-0.331295\pi$
$733$	13.8603	+	3.71385i	0.511941	+	0.137174i	0.00640470	+	0.999979i	$0.497961\pi$
$734$	−4.87832	−	8.44949i	−0.180062	−	0.311876i
$735$	−14.7418	+	16.9389i	−0.543759	+	0.624799i
$736$	0.500000	−	0.866025i	0.0184302	−	0.0319221i
$737$	−16.8277	+	16.8277i	−0.619856	+	0.619856i
$738$	9.70695	−	6.66422i	0.357318	−	0.245313i
$739$		−	24.9444i		−	0.917594i	−0.888541	−	0.458797i	$-0.848280\pi$
$739$		−	24.9444i		−	0.917594i	0.888541	−	0.458797i	$-0.151720\pi$
$740$	5.54516	−	7.69748i	0.203844	−	0.282965i
$741$	−8.44949	+	3.89270i	−0.310400	+	0.143002i
$742$	2.65275	−	9.90020i	0.0973855	−	0.363448i
$743$	0.0261460	−	0.0975783i	0.000959205	−	0.00357980i	−0.965445	−	0.260609i	$-0.916077\pi$
$743$	0.0261460	−	0.0975783i	0.000959205	−	0.00357980i	0.966404	+	0.257029i	$0.0827435\pi$
$744$	6.99964	−	3.22474i	0.256619	−	0.118225i
$745$	28.4781	−	4.62852i	1.04336	−	0.169576i
$746$		−	20.2918i		−	0.742936i
$747$	−0.128751	−	1.64650i	−0.00471074	−	0.0602425i
$748$	19.7980	−	19.7980i	0.723885	−	0.723885i
$749$	−2.87659	+	4.98240i	−0.105108	+	0.182053i
$750$	2.55103	−	19.1962i	0.0931503	−	0.700944i
$751$	4.34847	+	7.53177i	0.158678	+	0.274838i	0.934392	−	0.356246i	$-0.115944\pi$
$751$	4.34847	+	7.53177i	0.158678	+	0.274838i	−0.775714	+	0.631084i	$0.782610\pi$
$752$	8.69333	+	2.32937i	0.317013	+	0.0849434i
$753$	−14.8790	+	12.3684i	−0.542222	+	0.450731i
$754$	−9.43879	−	5.44949i	−0.343741	−	0.198459i
$755$	−30.5412	−	37.4052i	−1.11151	−	1.36132i
$756$	−1.55051	+	5.48188i	−0.0563915	+	0.199374i
$757$	−22.0454	−	22.0454i	−0.801254	−	0.801254i	0.182038	−	0.983292i	$-0.441731\pi$
$757$	−22.0454	−	22.0454i	−0.801254	−	0.801254i	−0.983292	+	0.182038i	$0.941731\pi$
$758$	6.42489	−	1.72154i	0.233362	−	0.0625293i
$759$	−10.8530	−	1.00000i	−0.393939	−	0.0362977i
$760$	−1.42296	−	3.16158i	−0.0516162	−	0.114683i
$761$	−15.3990	+	8.89060i	−0.558213	+	0.322284i	−0.752428	−	0.658675i	$-0.771117\pi$
$761$	−15.3990	+	8.89060i	−0.558213	+	0.322284i	0.194215	+	0.980959i	$0.437784\pi$
$762$	−34.0977	+	5.85024i	−1.23523	+	0.211932i
$763$	5.77414	+	21.5494i	0.209038	+	0.780141i
$764$	3.32124			0.120158
$765$	28.9985	−	7.07055i	1.04844	−	0.255636i
$766$	27.7980			1.00438
$767$	−10.5854	−	39.5054i	−0.382218	−	1.42646i
$768$	0.599900	−	1.62484i	0.0216470	−	0.0586315i
$769$	17.0580	−	9.84847i	0.615129	−	0.355145i	−0.159841	−	0.987143i	$-0.551098\pi$
$769$	17.0580	−	9.84847i	0.615129	−	0.355145i	0.774970	+	0.631998i	$0.217765\pi$
$770$	14.4242	+	5.47015i	0.519811	+	0.197131i
$771$	−18.8763	−	40.9729i	−0.679812	−	1.47560i
$772$	16.7303	−	4.48288i	0.602138	−	0.161342i
$773$	−3.11416	−	3.11416i	−0.112008	−	0.112008i	0.648881	−	0.760890i	$-0.275237\pi$
$773$	−3.11416	−	3.11416i	−0.112008	−	0.112008i	−0.760890	+	0.648881i	$0.775237\pi$
$774$	−3.46410	−	9.79796i	−0.124515	−	0.352180i
$775$	4.44949	−	21.7980i	0.159830	−	0.783006i
$776$	−9.67423	−	5.58542i	−0.347285	−	0.200505i
$777$	1.36240	+	7.94066i	0.0488759	+	0.284870i
$778$	−5.43309	−	1.45579i	−0.194786	−	0.0521927i
$779$	−3.04272	−	5.27015i	−0.109017	−	0.188823i
$780$	−11.1270	+	7.49598i	−0.398411	+	0.268399i
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$	3.14626	−	3.14626i	0.112510	−	0.112510i
$783$	0.226311	−	16.3469i	0.00808771	−	0.584191i
$784$			5.79796i			0.207070i
$785$	−11.1574	−	8.03766i	−0.398225	−	0.286876i
$786$	−1.67423	+	18.1705i	−0.0597180	+	0.648120i
$787$	1.06110	−	3.96008i	0.0378241	−	0.141162i	−0.944432	−	0.328708i	$-0.893387\pi$
$787$	1.06110	−	3.96008i	0.0378241	−	0.141162i	0.982256	+	0.187546i	$0.0600535\pi$
$788$	−2.53590	+	9.46410i	−0.0903376	+	0.337145i
$789$	17.9562	+	12.6969i	0.639257	+	0.452023i
$790$	4.44414	+	3.20150i	0.158115	+	0.113904i
$791$		−	15.1278i		−	0.537881i
$792$	−18.8201	+	1.47167i	−0.668744	+	0.0522933i
$793$	13.3485	−	13.3485i	0.474018	−	0.474018i
$794$	−10.9244	+	18.9217i	−0.387694	+	0.671505i
$795$	32.5330	+	15.8905i	1.15383	+	0.563579i
$796$	−1.77526	−	3.07483i	−0.0629222	−	0.108985i
$797$	−19.5137	−	5.22867i	−0.691210	−	0.185209i	−0.103920	−	0.994586i	$-0.533139\pi$
$797$	−19.5137	−	5.22867i	−0.691210	−	0.185209i	−0.587290	+	0.809377i	$0.699805\pi$
$798$	2.76214	+	1.01980i	0.0977788	+	0.0361004i
$799$	34.6803	+	20.0227i	1.22690	+	0.708352i
$800$	−2.75699	−	4.17121i	−0.0974745	−	0.147474i
$801$	1.29796	−	6.98358i	0.0458611	−	0.246753i
$802$	18.2474	+	18.2474i	0.644340	+	0.644340i
$803$	−24.9189	+	6.67700i	−0.879369	+	0.235626i
$804$	−3.78194	+	5.34847i	−0.133379	+	0.188626i
$805$	2.29227	+	0.869309i	0.0807919	+	0.0306391i
$806$	−13.3485	+	7.70674i	−0.470180	+	0.271458i
$807$	5.20757	+	6.26462i	0.183315	+	0.220525i
$808$	−0.329049	−	1.22803i	−0.0115759	−	0.0432019i
$809$	54.0901			1.90171			0.950853	−	0.309644i	$-0.100210\pi$
$809$	54.0901			1.90171			0.950853	+	0.309644i	$0.100210\pi$
$810$	−17.9588	−	9.08190i	−0.631009	−	0.319105i
$811$	43.6413			1.53245			0.766227	−	0.642570i	$-0.222132\pi$
$811$	43.6413			1.53245			0.766227	+	0.642570i	$0.222132\pi$
$812$	0.892794	+	3.33195i	0.0313309	+	0.116929i
$813$	−17.7656	−	21.3717i	−0.623066	−	0.749538i
$814$	−23.1202	+	13.3485i	−0.810364	+	0.467864i
$815$	0.583382	+	1.29618i	0.0204350	+	0.0454031i
$816$	4.44949	−	6.29253i	0.155763	−	0.220283i
$817$	−5.18811	+	1.39015i	−0.181509	+	0.0486352i
$818$	−13.5065	−	13.5065i	−0.472242	−	0.472242i
$819$	2.08200	−	11.2020i	0.0727508	−	0.391431i
$820$	−5.55051	−	6.79796i	−0.193832	−	0.237395i
$821$	−22.3207	−	12.8868i	−0.778997	−	0.449754i	0.0570780	−	0.998370i	$-0.481822\pi$
$821$	−22.3207	−	12.8868i	−0.778997	−	0.449754i	−0.836075	+	0.548616i	$0.815155\pi$
$822$	3.57797	+	1.32101i	0.124796	+	0.0460754i
$823$	46.9519	+	12.5807i	1.63664	+	0.438536i	0.955829	−	0.293923i	$-0.0949608\pi$
$823$	46.9519	+	12.5807i	1.63664	+	0.438536i	0.680811	+	0.732459i	$0.261627\pi$
$824$	2.04989	+	3.55051i	0.0714112	+	0.123688i
$825$	−28.7175	+	46.3141i	−0.999815	+	1.61245i
$826$	−6.47219	+	11.2102i	−0.225196	+	0.390052i
$827$	27.3235	−	27.3235i	0.950133	−	0.950133i	−0.0486816	−	0.998814i	$-0.515502\pi$
$827$	27.3235	−	27.3235i	0.950133	−	0.950133i	0.998814	+	0.0486816i	$0.0155020\pi$
$828$	−2.99087	+	0.233875i	−0.103940	+	0.00812772i
$829$		−	15.4495i		−	0.536583i	−0.963338	−	0.268291i	$-0.913541\pi$
$829$		−	15.4495i		−	0.536583i	0.963338	−	0.268291i	$-0.0864590\pi$
$830$	−1.21503	+	0.197479i	−0.0421745	+	0.00685459i
$831$	20.2020	+	14.2850i	0.700801	+	0.495541i
$832$	−0.896575	+	3.34607i	−0.0310832	+	0.116004i
$833$	−6.67700	+	24.9189i	−0.231344	+	0.863389i
$834$	−2.04989	+	22.2474i	−0.0709818	+	0.770366i
$835$	−14.1130	+	19.5909i	−0.488401	+	0.677970i
$836$			9.75663i			0.337440i
$837$	−19.8608	−	11.8362i	−0.686488	−	0.409118i
$838$	8.44949	−	8.44949i	0.291883	−	0.291883i
$839$	10.1459	−	17.5732i	0.350275	−	0.606695i	−0.636022	−	0.771671i	$-0.719421\pi$
$839$	10.1459	−	17.5732i	0.350275	−	0.606695i	0.986298	+	0.164976i	$0.0527547\pi$
$840$	4.16777	+	0.812613i	0.143802	+	0.0280378i
$841$	9.55051	+	16.5420i	0.329328	+	0.570413i
$842$	14.3913	+	3.85614i	0.495957	+	0.132891i
$843$	−0.0512483	−	0.298697i	−0.00176509	−	0.0102877i
$844$	16.3670	+	9.44949i	0.563375	+	0.325265i
$845$	−1.73205	+	1.41421i	−0.0595844	+	0.0486504i
$846$	−9.00000	−	25.4558i	−0.309426	−	0.875190i
$847$	−22.1691	−	22.1691i	−0.761740	−	0.761740i
$848$	9.02993	−	2.41956i	0.310089	−	0.0830881i
$849$	−4.99791	−	10.8485i	−0.171528	−	0.372319i
$850$	−7.04561	−	21.1023i	−0.241662	−	0.723804i
$851$	−3.67423	+	2.12132i	−0.125951	+	0.0727179i
$852$	0.381341	−	1.03287i	0.0130645	−	0.0353856i
$853$	−9.60723	−	35.8547i	−0.328945	−	1.22764i	−0.910286	−	0.413980i	$-0.864138\pi$
$853$	−9.60723	−	35.8547i	−0.328945	−	1.22764i	0.581340	−	0.813660i	$-0.302528\pi$
$854$	−5.97469			−0.204450
$855$	−5.40317	+	8.88760i	−0.184784	+	0.303950i
$856$	−5.24745			−0.179354
$857$	0.982984	+	3.66855i	0.0335781	+	0.125315i	0.980680	−	0.195616i	$-0.0626707\pi$
$857$	0.982984	+	3.66855i	0.0335781	+	0.125315i	−0.947102	+	0.320932i	$0.896004\pi$
$858$	37.2114	−	6.38447i	1.27038	−	0.217962i
$859$	2.16064	−	1.24745i	0.0737202	−	0.0425624i	−0.462687	−	0.886522i	$-0.653115\pi$
$859$	2.16064	−	1.24745i	0.0737202	−	0.0425624i	0.536407	+	0.843959i	$0.319781\pi$
$860$	−7.06350	+	3.17914i	−0.240863	+	0.108408i
$861$	7.42168	+	0.683837i	0.252930	+	0.0233051i
$862$	−15.0263	+	4.02628i	−0.511797	+	0.137136i
$863$	−27.7842	−	27.7842i	−0.945787	−	0.945787i	0.0528175	−	0.998604i	$-0.483180\pi$
$863$	−27.7842	−	27.7842i	−0.945787	−	0.945787i	−0.998604	+	0.0528175i	$0.983180\pi$
$864$	−5.03723	+	1.27526i	−0.171370	+	0.0433851i
$865$	0.696938	−	6.89898i	0.0236966	−	0.234572i
$866$	10.4722	+	6.04612i	0.355860	+	0.205456i
$867$	3.72674	−	3.09792i	0.126567	−	0.105211i
$868$	4.71209	+	1.26260i	0.159939	+	0.0428555i
$869$	−7.70674	−	13.3485i	−0.261433	−	0.452816i
$870$	−12.1562	+	0.843039i	−0.412135	+	0.0285817i
$871$	6.55051	−	11.3458i	0.221956	−	0.384438i
$872$	−14.3885	+	14.3885i	−0.487257	+	0.487257i
$873$	2.61258	+	33.4105i	0.0884225	+	1.13078i
$874$			1.55051i			0.0524468i
$875$	9.00927	−	8.31193i	0.304569	−	0.280995i
$876$	−6.44949	+	2.97129i	−0.217908	+	0.100391i
$877$	2.10558	−	7.85813i	0.0711004	−	0.265350i	−0.921220	−	0.389041i	$-0.872806\pi$
$877$	2.10558	−	7.85813i	0.0711004	−	0.265350i	0.992321	+	0.123691i	$0.0394731\pi$
$878$	2.64048	−	9.85441i	0.0891120	−	0.332570i
$879$	34.6803	−	15.9773i	1.16974	−	0.538901i
$880$	2.25725	+	13.8883i	0.0760920	+	0.468174i
$881$		−	58.3006i		−	1.96420i	−0.188368	−	0.982098i	$-0.560320\pi$
$881$		−	58.3006i		−	1.96420i	0.188368	−	0.982098i	$-0.439680\pi$
$882$	14.3397	−	9.84480i	0.482843	−	0.331492i
$883$	−40.2702	+	40.2702i	−1.35520	+	1.35520i	−0.475463	+	0.879736i	$0.657719\pi$
$883$	−40.2702	+	40.2702i	−1.35520	+	1.35520i	−0.879736	+	0.475463i	$0.842281\pi$
$884$	−7.70674	+	13.3485i	−0.259206	+	0.448958i
$885$	−34.4930	−	30.0190i	−1.15947	−	1.00908i
$886$	0.275255	+	0.476756i	0.00924738	+	0.0160169i
$887$	26.8508	+	7.19464i	0.901561	+	0.241572i	0.679686	−	0.733503i	$-0.262116\pi$
$887$	26.8508	+	7.19464i	0.901561	+	0.241572i	0.221874	+	0.975075i	$0.428783\pi$
$888$	−5.65099	+	4.69748i	−0.189635	+	0.157637i
$889$	−18.9651	−	10.9495i	−0.636068	−	0.367234i
$890$	−5.26758	−	0.532134i	−0.176570	−	0.0178372i
$891$	35.5959	+	44.0477i	1.19251	+	1.47565i
$892$	−5.87628	−	5.87628i	−0.196752	−	0.196752i
$893$	−13.4791	+	3.61171i	−0.451061	+	0.120861i
$894$	−22.2542	−	2.05051i	−0.744292	−	0.0685793i
$895$	−13.9599	+	36.8106i	−0.466627	+	1.23044i
$896$	0.949490	−	0.548188i	0.0317202	−	0.0183137i
$897$	5.91359	−	1.01461i	0.197449	−	0.0338769i
$898$	−5.61793	−	20.9664i	−0.187473	−	0.699658i
$899$	−13.9993			−0.466902
$900$	−5.63505	+	13.9013i	−0.187835	+	0.463377i
$901$	41.5959			1.38576
$902$	6.39204	+	23.8554i	0.212832	+	0.794298i
$903$	2.27840	−	6.17109i	0.0758203	−	0.205361i
$904$	11.9494	−	6.89898i	0.397431	−	0.229457i
$905$	−8.36543	+	22.0587i	−0.278076	+	0.733256i
$906$	15.6515	+	33.9732i	0.519987	+	1.12869i
$907$	−6.38512	+	1.71089i	−0.212015	+	0.0568091i	−0.363263	−	0.931687i	$-0.618337\pi$
$907$	−6.38512	+	1.71089i	−0.212015	+	0.0568091i	0.151248	+	0.988496i	$0.451671\pi$
$908$	10.6780	+	10.6780i	0.354363	+	0.354363i
$909$	−2.47848	+	2.89898i	−0.0822061	+	0.0961531i
$910$	−8.44949	−	0.853572i	−0.280098	−	0.0282956i
$911$	6.12372	+	3.53553i	0.202888	+	0.117137i	0.598002	−	0.801495i	$-0.295962\pi$
$911$	6.12372	+	3.53553i	0.202888	+	0.117137i	−0.395114	+	0.918632i	$0.629295\pi$
$912$	0.454134	+	2.64689i	0.0150379	+	0.0876472i
$913$	3.34607	+	0.896575i	0.110739	+	0.0296723i
$914$	−3.07483	−	5.32577i	−0.101706	−	0.176161i
$915$	4.03906	−	20.7157i	0.133527	−	0.684840i
$916$	8.17423	−	14.1582i	0.270084	−	0.467800i
$917$	−8.16744	+	8.16744i	−0.269713	+	0.269713i
$918$	−23.1180	−	0.320053i	−0.763008	−	0.0105633i
$919$			27.3485i			0.902143i	0.892488	+	0.451071i	$0.148958\pi$
$919$			27.3485i			0.902143i	−0.892488	+	0.451071i	$0.851042\pi$
$920$	0.358719	+	2.20711i	0.0118266	+	0.0727662i
$921$	−0.151531	+	1.64456i	−0.00499311	+	0.0541902i
$922$	−4.89419	+	18.2654i	−0.161182	+	0.601538i
$923$	−0.569930	+	2.12701i	−0.0187595	+	0.0700113i
$924$	−9.75663	−	6.89898i	−0.320970	−	0.226960i
$925$	1.28138	+	21.1745i	0.0421314	+	0.696212i
$926$			33.0197i			1.08510i
$927$	5.30057	−	11.0985i	0.174094	−	0.364524i
$928$	−2.22474	+	2.22474i	−0.0730308	+	0.0730308i
$929$	23.9309	−	41.4495i	0.785147	−	1.35991i	−0.143765	−	0.989612i	$-0.545921\pi$
$929$	23.9309	−	41.4495i	0.785147	−	1.35991i	0.928912	−	0.370302i	$-0.120746\pi$
$930$	−7.56325	+	15.4844i	−0.248009	+	0.507754i
$931$	−4.49490	−	7.78539i	−0.147314	−	0.255156i
$932$	−15.0206	−	4.02477i	−0.492017	−	0.131836i
$933$	−33.4353	−	12.3445i	−1.09462	−	0.404140i
$934$	−3.46410	−	2.00000i	−0.113349	−	0.0654420i
$935$	−6.29253	+	62.2896i	−0.205788	+	2.03709i
$936$	9.79796	−	3.46410i	0.320256	−	0.113228i
$937$	−12.8990	−	12.8990i	−0.421391	−	0.421391i	0.464291	−	0.885683i	$-0.346309\pi$
$937$	−12.8990	−	12.8990i	−0.421391	−	0.421391i	−0.885683	+	0.464291i	$0.846309\pi$
$938$	−4.00514	+	1.07317i	−0.130773	+	0.0350404i
$939$	−5.02118	+	7.10102i	−0.163860	+	0.231733i
$940$	−18.3515	+	8.25964i	−0.598561	+	0.269400i
$941$	5.47730	−	3.16232i	0.178555	−	0.103089i	−0.408059	−	0.912956i	$-0.633794\pi$
$941$	5.47730	−	3.16232i	0.178555	−	0.103089i	0.586613	+	0.809867i	$0.300461\pi$
$942$	6.80895	+	8.19105i	0.221847	+	0.266879i
$943$	1.01581	+	3.79107i	0.0330795	+	0.123454i
$944$	−11.8065			−0.384269
$945$	−5.06699	−	11.6877i	−0.164829	−	0.380199i
$946$	21.7980			0.708713
$947$	10.6233	+	39.6468i	0.345212	+	1.28835i	0.892364	+	0.451316i	$0.149045\pi$
$947$	10.6233	+	39.6468i	0.345212	+	1.28835i	−0.547152	+	0.837033i	$0.684288\pi$
$948$	−2.71209	−	3.26260i	−0.0880846	−	0.105964i
$949$	12.2993	−	7.10102i	0.399253	−	0.230509i
$950$	6.93579	+	3.46365i	0.225027	+	0.112376i
$951$	−1.10102	+	1.55708i	−0.0357030	+	0.0504917i
$952$	4.71209	−	1.26260i	0.152720	−	0.0409211i
$953$	19.6561	+	19.6561i	0.636724	+	0.636724i	0.949746	−	0.313022i	$-0.101341\pi$
$953$	19.6561	+	19.6561i	0.636724	+	0.636724i	−0.313022	+	0.949746i	$0.601341\pi$
$954$	−21.3167	−	18.2247i	−0.690155	−	0.590048i
$955$	−5.75255	+	4.69694i	−0.186148	+	0.151989i
$956$	−14.6969	−	8.48528i	−0.475333	−	0.274434i
$957$	32.1686	+	11.8768i	1.03986	+	0.383923i
$958$	6.83013	+	1.83013i	0.220671	+	0.0591287i
$959$	1.20713	+	2.09082i	0.0389804	+	0.0675159i
$960$	1.25882	+	3.66270i	0.0406282	+	0.118213i
$961$	5.60102	−	9.70125i	0.180678	−	0.312944i
$962$	10.3923	−	10.3923i	0.335061	−	0.335061i
$963$	8.91005	+	12.9782i	0.287122	+	0.418215i
$964$		−	19.0000i		−	0.611949i
$965$	−22.6380	+	31.4248i	−0.728744	+	1.01160i
$966$	−1.55051	−	1.09638i	−0.0498868	−	0.0352753i
$967$	−13.0577	+	48.7319i	−0.419907	+	1.56711i	0.354894	+	0.934907i	$0.384517\pi$
$967$	−13.0577	+	48.7319i	−0.419907	+	1.56711i	−0.774800	+	0.632206i	$0.782150\pi$
$968$	7.40117	−	27.6215i	0.237883	−	0.887790i
$969$	−1.09638	+	11.8990i	−0.0352207	+	0.382250i
$970$	24.6552	−	4.00720i	0.791632	−	0.128663i
$971$			49.2117i			1.57928i	0.613570	+	0.789640i	$0.289733\pi$
$971$			49.2117i			1.57928i	−0.613570	+	0.789640i	$0.710267\pi$
$972$	11.7071	+	10.2929i	0.375506	+	0.330145i
$973$	−10.0000	+	10.0000i	−0.320585	+	0.320585i
$974$	8.48528	−	14.6969i	0.271886	−	0.470920i
$975$	8.67163	−	28.7194i	0.277714	−	0.919756i
$976$	−2.72474	−	4.71940i	−0.0872170	−	0.151064i
$977$	41.0469	+	10.9985i	1.31321	+	0.351873i	0.846429	−	0.532502i	$-0.178748\pi$
$977$	41.0469	+	10.9985i	1.31321	+	0.351873i	0.466778	+	0.884374i	$0.345415\pi$
$978$	−0.186185	−	1.08516i	−0.00595353	−	0.0346997i
$979$	12.9029	+	7.44949i	0.412378	+	0.238087i
$980$	−8.19955	−	10.0424i	−0.261925	−	0.320791i
$981$	60.0176	+	11.1548i	1.91621	+	0.356145i
$982$	0.202041	+	0.202041i	0.00644739	+	0.00644739i
$983$	45.2034	−	12.1122i	1.44176	−	0.386319i	0.548612	−	0.836077i	$-0.315156\pi$
$983$	45.2034	−	12.1122i	1.44176	−	0.386319i	0.893151	+	0.449757i	$0.148490\pi$
$984$	2.84448	+	6.17423i	0.0906787	+	0.196827i
$985$	−8.99196	−	19.9786i	−0.286508	−	0.636571i
$986$	−12.1237	+	6.99964i	−0.386098	+	0.222914i
$987$	5.91945	−	16.0330i	0.188418	−	0.510335i
$988$	−1.39015	−	5.18811i	−0.0442265	−	0.165056i
$989$	3.46410			0.110152
$990$	30.5162	−	29.1647i	0.969868	−	0.926915i
$991$	−56.7423			−1.80248			−0.901240	−	0.433320i	$-0.857342\pi$
$991$	−56.7423			−1.80248			−0.901240	+	0.433320i	$0.857342\pi$
$992$	1.15161	+	4.29788i	0.0365637	+	0.136458i
$993$	7.59575	−	1.30323i	0.241044	−	0.0413566i
$994$	0.603566	−	0.348469i	0.0191440	−	0.0110528i
$995$	7.42330	+	2.81518i	0.235334	+	0.0892471i
$996$	0.949490	+	0.0874863i	0.0300857	+	0.00277211i
$997$	39.9528	−	10.7053i	1.26532	−	0.339041i	0.437082	−	0.899422i	$-0.356012\pi$
$997$	39.9528	−	10.7053i	1.26532	−	0.339041i	0.828235	+	0.560381i	$0.189345\pi$
$998$	−6.29253	−	6.29253i	−0.199187	−	0.199187i
$999$	21.2132	+	6.00000i	0.671156	+	0.189832i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	90.2.l.a.47.2	yes	8
3.2	odd	2		270.2.m.a.197.1		8
4.3	odd	2		720.2.cu.a.497.2		8
5.2	odd	4		450.2.p.a.443.1		8
5.3	odd	4	inner	90.2.l.a.83.2	yes	8
5.4	even	2		450.2.p.a.407.1		8
9.2	odd	6		810.2.f.b.647.1		8
9.4	even	3		270.2.m.a.17.1		8
9.5	odd	6	inner	90.2.l.a.77.2	yes	8
9.7	even	3		810.2.f.b.647.4		8
15.2	even	4		1350.2.q.g.143.2		8
15.8	even	4		270.2.m.a.143.1		8
15.14	odd	2		1350.2.q.g.1007.2		8
20.3	even	4		720.2.cu.a.353.2		8
36.23	even	6		720.2.cu.a.257.2		8
45.4	even	6		1350.2.q.g.557.2		8
45.13	odd	12		270.2.m.a.233.1		8
45.14	odd	6		450.2.p.a.257.1		8
45.22	odd	12		1350.2.q.g.1043.2		8
45.23	even	12	inner	90.2.l.a.23.2	✓	8
45.32	even	12		450.2.p.a.293.1		8
45.38	even	12		810.2.f.b.323.3		8
45.43	odd	12		810.2.f.b.323.2		8
180.23	odd	12		720.2.cu.a.113.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.a.23.2	✓	8	45.23	even	12	inner
90.2.l.a.47.2	yes	8	1.1	even	1	trivial
90.2.l.a.77.2	yes	8	9.5	odd	6	inner
90.2.l.a.83.2	yes	8	5.3	odd	4	inner
270.2.m.a.17.1		8	9.4	even	3
270.2.m.a.143.1		8	15.8	even	4
270.2.m.a.197.1		8	3.2	odd	2
270.2.m.a.233.1		8	45.13	odd	12
450.2.p.a.257.1		8	45.14	odd	6
450.2.p.a.293.1		8	45.32	even	12
450.2.p.a.407.1		8	5.4	even	2
450.2.p.a.443.1		8	5.2	odd	4
720.2.cu.a.113.2		8	180.23	odd	12
720.2.cu.a.257.2		8	36.23	even	6
720.2.cu.a.353.2		8	20.3	even	4
720.2.cu.a.497.2		8	4.3	odd	2
810.2.f.b.323.2		8	45.43	odd	12
810.2.f.b.323.3		8	45.38	even	12
810.2.f.b.647.1		8	9.2	odd	6
810.2.f.b.647.4		8	9.7	even	3
1350.2.q.g.143.2		8	15.2	even	4
1350.2.q.g.557.2		8	45.4	even	6
1350.2.q.g.1007.2		8	15.14	odd	2
1350.2.q.g.1043.2		8	45.22	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

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Representations

Groups

Database

Properties

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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	90.2.l.a.47.2

Level	$90$
Weight	$2$
Character	90.47
Analytic conductor	$0.719$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$