LMFDB - Embedded newform 539.2.f.i.344.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [539,2,Mod(148,539)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("539.148"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(539, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.f (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			344.3
Character	$\chi$	$=$	539.344
Dual form			539.2.f.i.246.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.922272 + 0.670070i) q^{2} +(-0.305751 - 0.941006i) q^{3} +(-0.216442 + 0.666140i) q^{4} +(2.21755 + 1.61115i) q^{5} +(0.912526 + 0.662989i) q^{6} +(-0.951295 - 2.92778i) q^{8} +(1.63504 - 1.18793i) q^{9} -3.12477 q^{10} +(2.87804 - 1.64829i) q^{11} +0.693019 q^{12} +(1.08473 - 0.788105i) q^{13} +(0.838079 - 2.57934i) q^{15} +(1.70587 + 1.23939i) q^{16} +(-4.67841 - 3.39907i) q^{17} +(-0.711959 + 2.19119i) q^{18} +(1.55729 + 4.79284i) q^{19} +(-1.55322 + 1.12848i) q^{20} +(-1.54987 + 3.44866i) q^{22} +6.33984 q^{23} +(-2.46420 + 1.79035i) q^{24} +(0.776666 + 2.39033i) q^{25} +(-0.472334 + 1.45369i) q^{26} +(-4.01917 - 2.92010i) q^{27} +(-1.62024 + 4.98658i) q^{29} +(0.955403 + 2.94043i) q^{30} +(3.85054 - 2.79758i) q^{31} +3.75316 q^{32} +(-2.43102 - 2.20429i) q^{33} +6.59238 q^{34} +(0.437434 + 1.34628i) q^{36} +(0.156446 - 0.481493i) q^{37} +(-4.64778 - 3.37681i) q^{38} +(-1.07327 - 0.779776i) q^{39} +(2.60755 - 8.02520i) q^{40} +(1.96943 + 6.06129i) q^{41} +4.30610 q^{43} +(0.475064 + 2.27394i) q^{44} +5.53972 q^{45} +(-5.84705 + 4.24813i) q^{46} +(1.78056 + 5.47999i) q^{47} +(0.644698 - 1.98418i) q^{48} +(-2.31799 - 1.68412i) q^{50} +(-1.76811 + 5.44168i) q^{51} +(0.290206 + 0.893163i) q^{52} +(9.89592 - 7.18981i) q^{53} +5.66343 q^{54} +(9.03786 + 0.981775i) q^{55} +(4.03395 - 2.93083i) q^{57} +(-1.84706 - 5.68466i) q^{58} +(-1.07992 + 3.32366i) q^{59} +(1.53681 + 1.11656i) q^{60} +(-8.18051 - 5.94349i) q^{61} +(-1.67667 + 5.16026i) q^{62} +(-6.87317 + 4.99365i) q^{64} +3.67521 q^{65} +(3.71909 + 0.404001i) q^{66} -2.93728 q^{67} +(3.27686 - 2.38078i) q^{68} +(-1.93841 - 5.96582i) q^{69} +(12.1644 + 8.83796i) q^{71} +(-5.03341 - 3.65698i) q^{72} +(-2.12093 + 6.52756i) q^{73} +(0.178348 + 0.548897i) q^{74} +(2.01185 - 1.46169i) q^{75} -3.52976 q^{76} +1.51235 q^{78} +(-2.61077 + 1.89684i) q^{79} +(1.78602 + 5.49681i) q^{80} +(0.354631 - 1.09144i) q^{81} +(-5.87784 - 4.27050i) q^{82} +(-3.31587 - 2.40912i) q^{83} +(-4.89824 - 15.0752i) q^{85} +(-3.97139 + 2.88539i) q^{86} +5.18779 q^{87} +(-7.56371 - 6.85828i) q^{88} -13.2243 q^{89} +(-5.10913 + 3.71200i) q^{90} +(-1.37221 + 4.22322i) q^{92} +(-3.80984 - 2.76801i) q^{93} +(-5.31413 - 3.86094i) q^{94} +(-4.26860 + 13.1374i) q^{95} +(-1.14753 - 3.53175i) q^{96} +(-10.6270 + 7.72097i) q^{97} +(2.74767 - 6.11394i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 16 q^{4} + 20 q^{8} - 8 q^{11} + 16 q^{15} - 20 q^{16} + 42 q^{18} - 4 q^{22} - 12 q^{25} - 80 q^{32} - 160 q^{36} + 20 q^{37} + 36 q^{39} - 56 q^{43} + 50 q^{44} + 22 q^{46} - 84 q^{50} + 60 q^{51}+ \cdots + 76 q^{99}+O(q^{100}) $ 48 * q - 16 * q^4 + 20 * q^8 - 8 * q^11 + 16 * q^15 - 20 * q^16 + 42 * q^18 - 4 * q^22 - 12 * q^25 - 80 * q^32 - 160 * q^36 + 20 * q^37 + 36 * q^39 - 56 * q^43 + 50 * q^44 + 22 * q^46 - 84 * q^50 + 60 * q^51 + 24 * q^53 - 36 * q^57 - 134 * q^58 - 40 * q^60 - 80 * q^64 - 128 * q^65 + 12 * q^71 - 154 * q^72 + 8 * q^74 + 312 * q^78 + 28 * q^79 + 36 * q^81 + 72 * q^85 - 38 * q^86 + 112 * q^88 + 98 * q^92 + 64 * q^93 + 48 * q^95 + 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−0.922272	+	0.670070i	−0.652145	+	0.473811i	−0.864001	−	0.503490i	$-0.832049\pi$
$2$	−0.922272	+	0.670070i	−0.652145	+	0.473811i	0.211856	+	0.977301i	$0.432049\pi$
$3$	−0.305751	−	0.941006i	−0.176526	−	0.543290i	0.823174	−	0.567789i	$-0.192201\pi$
$3$	−0.305751	−	0.941006i	−0.176526	−	0.543290i	−0.999700	+	0.0244988i	$0.992201\pi$
$4$	−0.216442	+	0.666140i	−0.108221	+	0.333070i
$5$	2.21755	+	1.61115i	0.991721	+	0.720527i	0.960297	−	0.278979i	$-0.0899960\pi$
$5$	2.21755	+	1.61115i	0.991721	+	0.720527i	0.0314233	+	0.999506i	$0.489996\pi$
$6$	0.912526	+	0.662989i	0.372537	+	0.270664i
$7$		0			0
$7$		0			0
$8$	−0.951295	−	2.92778i	−0.336334	−	1.03513i
$9$	1.63504	−	1.18793i	0.545014	−	0.395976i
$10$	−3.12477			−0.988139
$11$	2.87804	−	1.64829i	0.867763	−	0.496979i
$11$	2.87804	−	1.64829i	0.867763	−	0.496979i
$12$	0.693019			0.200057
$13$	1.08473	−	0.788105i	0.300851	−	0.218581i	−0.427110	−	0.904200i	$-0.640468\pi$
$13$	1.08473	−	0.788105i	0.300851	−	0.218581i	0.727961	+	0.685619i	$0.240468\pi$
$14$		0			0
$15$	0.838079	−	2.57934i	0.216391	−	0.665983i
$16$	1.70587	+	1.23939i	0.426467	+	0.309847i
$17$	−4.67841	−	3.39907i	−1.13468	−	0.824394i	−0.148312	−	0.988941i	$-0.547384\pi$
$17$	−4.67841	−	3.39907i	−1.13468	−	0.824394i	−0.986369	+	0.164546i	$0.947384\pi$
$18$	−0.711959	+	2.19119i	−0.167810	+	0.516467i
$19$	1.55729	+	4.79284i	0.357266	+	1.09955i	0.954684	+	0.297622i	$0.0961935\pi$
$19$	1.55729	+	4.79284i	0.357266	+	1.09955i	−0.597417	+	0.801930i	$0.703806\pi$
$20$	−1.55322	+	1.12848i	−0.347311	+	0.252336i
$21$		0			0
$22$	−1.54987	+	3.44866i	−0.330433	+	0.735258i
$23$	6.33984			1.32195			0.660974	−	0.750409i	$-0.270143\pi$
$23$	6.33984			1.32195			0.660974	+	0.750409i	$0.270143\pi$
$24$	−2.46420	+	1.79035i	−0.503003	+	0.365453i
$25$	0.776666	+	2.39033i	0.155333	+	0.478067i
$26$	−0.472334	+	1.45369i	−0.0926323	+	0.285093i
$27$	−4.01917	−	2.92010i	−0.773489	−	0.561973i
$28$		0			0
$29$	−1.62024	+	4.98658i	−0.300871	+	0.925985i	0.680315	+	0.732920i	$0.261843\pi$
$29$	−1.62024	+	4.98658i	−0.300871	+	0.925985i	−0.981186	+	0.193065i	$0.938157\pi$
$30$	0.955403	+	2.94043i	0.174432	+	0.536846i
$31$	3.85054	−	2.79758i	0.691577	−	0.502460i	−0.185601	−	0.982625i	$-0.559423\pi$
$31$	3.85054	−	2.79758i	0.691577	−	0.502460i	0.877178	+	0.480165i	$0.159423\pi$
$32$	3.75316			0.663471
$33$	−2.43102	−	2.20429i	−0.423186	−	0.383717i
$34$	6.59238			1.13058
$35$		0			0
$36$	0.437434	+	1.34628i	0.0729057	+	0.224381i
$37$	0.156446	−	0.481493i	0.0257196	−	0.0791569i	−0.937373	−	0.348328i	$-0.886750\pi$
$37$	0.156446	−	0.481493i	0.0257196	−	0.0791569i	0.963092	+	0.269171i	$0.0867496\pi$
$38$	−4.64778	−	3.37681i	−0.753969	−	0.547791i
$39$	−1.07327	−	0.779776i	−0.171861	−	0.124864i
$40$	2.60755	−	8.02520i	0.412289	−	1.26890i
$41$	1.96943	+	6.06129i	0.307574	+	0.946615i	0.978704	+	0.205276i	$0.0658090\pi$
$41$	1.96943	+	6.06129i	0.307574	+	0.946615i	−0.671130	+	0.741339i	$0.734191\pi$
$42$		0			0
$43$	4.30610			0.656674			0.328337	−	0.944561i	$-0.393512\pi$
$43$	4.30610			0.656674			0.328337	+	0.944561i	$0.393512\pi$
$44$	0.475064	+	2.27394i	0.0716185	+	0.342809i
$45$	5.53972			0.825813
$46$	−5.84705	+	4.24813i	−0.862101	+	0.626353i
$47$	1.78056	+	5.47999i	0.259721	+	0.799338i	0.992863	+	0.119263i	$0.0380531\pi$
$47$	1.78056	+	5.47999i	0.259721	+	0.799338i	−0.733142	+	0.680076i	$0.761947\pi$
$48$	0.644698	−	1.98418i	0.0930541	−	0.286391i
$49$		0			0
$50$	−2.31799	−	1.68412i	−0.327813	−	0.238170i
$51$	−1.76811	+	5.44168i	−0.247585	+	0.761988i
$52$	0.290206	+	0.893163i	0.0402444	+	0.123859i
$53$	9.89592	−	7.18981i	1.35931	−	0.987596i	0.360821	−	0.932635i	$-0.382497\pi$
$53$	9.89592	−	7.18981i	1.35931	−	0.987596i	0.998489	−	0.0549607i	$-0.0175033\pi$
$54$	5.66343			0.770696
$55$	9.03786	+	0.981775i	1.21866	+	0.132382i
$56$		0			0
$57$	4.03395	−	2.93083i	0.534309	−	0.388198i
$58$	−1.84706	−	5.68466i	−0.242530	−	0.746432i
$59$	−1.07992	+	3.32366i	−0.140594	+	0.432704i	−0.996418	−	0.0845629i	$-0.973051\pi$
$59$	−1.07992	+	3.32366i	−0.140594	+	0.432704i	0.855824	+	0.517267i	$0.173051\pi$
$60$	1.53681	+	1.11656i	0.198401	+	0.144147i
$61$	−8.18051	−	5.94349i	−1.04741	−	0.760986i	−0.0756897	−	0.997131i	$-0.524116\pi$
$61$	−8.18051	−	5.94349i	−1.04741	−	0.760986i	−0.971718	+	0.236145i	$0.924116\pi$
$62$	−1.67667	+	5.16026i	−0.212937	+	0.655353i
$63$		0			0
$64$	−6.87317	+	4.99365i	−0.859146	+	0.624206i
$65$	3.67521			0.455854
$66$	3.71909	+	0.404001i	0.457788	+	0.0497291i
$67$	−2.93728			−0.358846			−0.179423	−	0.983772i	$-0.557423\pi$
$67$	−2.93728			−0.358846			−0.179423	+	0.983772i	$0.557423\pi$
$68$	3.27686	−	2.38078i	0.397377	−	0.288711i
$69$	−1.93841	−	5.96582i	−0.233358	−	0.718201i
$70$		0			0
$71$	12.1644	+	8.83796i	1.44365	+	1.04887i	0.987264	+	0.159091i	$0.0508563\pi$
$71$	12.1644	+	8.83796i	1.44365	+	1.04887i	0.456386	+	0.889782i	$0.349144\pi$
$72$	−5.03341	−	3.65698i	−0.593193	−	0.430980i
$73$	−2.12093	+	6.52756i	−0.248236	+	0.763993i	0.746851	+	0.664992i	$0.231565\pi$
$73$	−2.12093	+	6.52756i	−0.248236	+	0.763993i	−0.995087	+	0.0990016i	$0.968435\pi$
$74$	0.178348	+	0.548897i	0.0207325	+	0.0638080i
$75$	2.01185	−	1.46169i	0.232308	−	0.168782i
$76$	−3.52976			−0.404891
$77$		0			0
$78$	1.51235			0.171240
$79$	−2.61077	+	1.89684i	−0.293735	+	0.213411i	−0.724886	−	0.688869i	$-0.758108\pi$
$79$	−2.61077	+	1.89684i	−0.293735	+	0.213411i	0.431151	+	0.902280i	$0.358108\pi$
$80$	1.78602	+	5.49681i	0.199683	+	0.614562i
$81$	0.354631	−	1.09144i	0.0394034	−	0.121271i
$82$	−5.87784	−	4.27050i	−0.649099	−	0.471598i
$83$	−3.31587	−	2.40912i	−0.363964	−	0.264435i	0.390739	−	0.920501i	$-0.372219\pi$
$83$	−3.31587	−	2.40912i	−0.363964	−	0.264435i	−0.754704	+	0.656066i	$0.772219\pi$
$84$		0			0
$85$	−4.89824	−	15.0752i	−0.531288	−	1.63514i
$86$	−3.97139	+	2.88539i	−0.428246	+	0.311139i
$87$	5.18779			0.556190
$88$	−7.56371	−	6.85828i	−0.806294	−	0.731095i
$89$	−13.2243			−1.40177			−0.700885	−	0.713274i	$-0.747211\pi$
$89$	−13.2243			−1.40177			−0.700885	+	0.713274i	$0.747211\pi$
$90$	−5.10913	+	3.71200i	−0.538550	+	0.391279i
$91$		0			0
$92$	−1.37221	+	4.22322i	−0.143062	+	0.440301i
$93$	−3.80984	−	2.76801i	−0.395062	−	0.287030i
$94$	−5.31413	−	3.86094i	−0.548111	−	0.398226i
$95$	−4.26860	+	13.1374i	−0.437949	+	1.34787i
$96$	−1.14753	−	3.53175i	−0.117120	−	0.360457i
$97$	−10.6270	+	7.72097i	−1.07901	+	0.783945i	−0.977510	−	0.210890i	$-0.932364\pi$
$97$	−10.6270	+	7.72097i	−1.07901	+	0.783945i	−0.101498	+	0.994836i	$0.532364\pi$
$98$		0			0
$99$	2.74767	−	6.11394i	0.276151	−	0.614474i
$100$	−1.76040			−0.176040
$101$	1.97135	−	1.43227i	0.196157	−	0.142516i	−0.485371	−	0.874308i	$-0.661316\pi$
$101$	1.97135	−	1.43227i	0.196157	−	0.142516i	0.681528	+	0.731792i	$0.261316\pi$
$102$	−2.01563	−	6.20347i	−0.199577	−	0.614235i
$103$	−3.06817	+	9.44285i	−0.302316	+	0.930432i	0.678350	+	0.734739i	$0.262696\pi$
$103$	−3.06817	+	9.44285i	−0.302316	+	0.930432i	−0.980665	+	0.195693i	$0.937304\pi$
$104$	−3.33930	−	2.42615i	−0.327446	−	0.237903i
$105$		0			0
$106$	−4.30906	+	13.2619i	−0.418533	+	1.28811i
$107$	−1.37382	−	4.22818i	−0.132812	−	0.408754i	0.862431	−	0.506175i	$-0.168941\pi$
$107$	−1.37382	−	4.22818i	−0.132812	−	0.408754i	−0.995243	+	0.0974205i	$0.968941\pi$
$108$	2.81511	−	2.04529i	0.270884	−	0.196809i
$109$	−12.8340			−1.22928			−0.614639	−	0.788808i	$-0.710698\pi$
$109$	−12.8340			−1.22928			−0.614639	+	0.788808i	$0.710698\pi$
$110$	−8.99322	+	5.15053i	−0.857470	+	0.491084i
$111$	−0.500921			−0.0475453
$112$		0			0
$113$	−4.36750	−	13.4418i	−0.410860	−	1.26450i	−0.915902	−	0.401403i	$-0.868523\pi$
$113$	−4.36750	−	13.4418i	−0.410860	−	1.26450i	0.505041	−	0.863095i	$-0.331477\pi$
$114$	−1.75653	+	5.40605i	−0.164514	+	0.506323i
$115$	14.0589	+	10.2144i	1.31100	+	0.952499i
$116$	−2.97107	−	2.15861i	−0.275857	−	0.200422i
$117$	0.837374	−	2.57717i	0.0774152	−	0.238260i
$118$	−1.23110	−	3.78895i	−0.113332	−	0.348801i
$119$		0			0
$120$	−8.34902			−0.762158
$121$	5.56627	−	9.48771i	0.506024	−	0.862519i
$122$	11.5272			1.04362
$123$	5.10155	−	3.70650i	0.459992	−	0.334204i
$124$	1.03016	+	3.17051i	0.0925111	+	0.284720i
$125$	2.10627	−	6.48244i	0.188391	−	0.579807i
$126$		0			0
$127$	−8.76900	−	6.37105i	−0.778123	−	0.565340i	0.126292	−	0.991993i	$-0.459692\pi$
$127$	−8.76900	−	6.37105i	−0.778123	−	0.565340i	−0.904415	+	0.426654i	$0.859692\pi$
$128$	0.673258	−	2.07208i	0.0595082	−	0.183147i
$129$	−1.31660	−	4.05206i	−0.115920	−	0.356764i
$130$	−3.38954	+	2.46265i	−0.297283	+	0.215988i
$131$	20.4185			1.78398			0.891988	−	0.452058i	$-0.149310\pi$
$131$	20.4185			1.78398			0.891988	+	0.452058i	$0.149310\pi$
$132$	1.99454	−	1.14230i	0.173602	−	0.0994242i
$133$		0			0
$134$	2.70897	−	1.96818i	0.234020	−	0.170025i
$135$	−4.20802	−	12.9509i	−0.362168	−	1.11464i
$136$	−5.50118	+	16.9309i	−0.471722	+	1.45181i
$137$	4.33476	+	3.14939i	0.370344	+	0.269070i	0.757353	−	0.653005i	$-0.226492\pi$
$137$	4.33476	+	3.14939i	0.370344	+	0.269070i	−0.387010	+	0.922076i	$0.626492\pi$
$138$	5.78526	+	4.20324i	0.492474	+	0.357804i
$139$	5.59295	−	17.2133i	0.474388	−	1.46002i	−0.372393	−	0.928075i	$-0.621463\pi$
$139$	5.59295	−	17.2133i	0.474388	−	1.46002i	0.846781	−	0.531941i	$-0.178537\pi$
$140$		0			0
$141$	4.61229	−	3.35103i	0.388425	−	0.282207i
$142$	−17.1409			−1.43844
$143$	1.82288	−	4.05616i	0.152437	−	0.339193i
$144$	4.26147			0.355122
$145$	−11.6271	+	8.44757i	−0.965577	+	0.701532i
$146$	−2.41784	−	7.44136i	−0.200102	−	0.615851i
$147$		0			0
$148$	0.286880	+	0.208430i	0.0235814	+	0.0171329i
$149$	−10.0367	−	7.29209i	−0.822239	−	0.597392i	0.0951140	−	0.995466i	$-0.469678\pi$
$149$	−10.0367	−	7.29209i	−0.822239	−	0.597392i	−0.917353	+	0.398075i	$0.869678\pi$
$150$	−0.876036	+	2.69616i	−0.0715280	+	0.220141i
$151$	−3.12938	−	9.63125i	−0.254666	−	0.783780i	−0.993895	−	0.110327i	$-0.964810\pi$
$151$	−3.12938	−	9.63125i	−0.254666	−	0.783780i	0.739230	−	0.673453i	$-0.235190\pi$
$152$	12.5510	−	9.11881i	1.01802	−	0.739633i
$153$	−11.6872			−0.944858
$154$		0			0
$155$	13.0461			1.04789
$156$	0.751741	−	0.546171i	0.0601874	−	0.0437287i
$157$	−5.82668	−	17.9327i	−0.465020	−	1.43118i	−0.858957	−	0.512047i	$-0.828887\pi$
$157$	−5.82668	−	17.9327i	−0.465020	−	1.43118i	0.393937	−	0.919137i	$-0.371113\pi$
$158$	1.13683	−	3.49880i	0.0904412	−	0.278349i
$159$	−9.79134	−	7.11383i	−0.776504	−	0.564163i
$160$	8.32284	+	6.04689i	0.657978	+	0.478049i
$161$		0			0
$162$	0.404276	+	1.24423i	0.0317629	+	0.0977563i
$163$	−6.13990	+	4.46090i	−0.480914	+	0.349405i	−0.801680	−	0.597754i	$-0.796060\pi$
$163$	−6.13990	+	4.46090i	−0.480914	+	0.349405i	0.320765	+	0.947159i	$0.396060\pi$
$164$	−4.46393			−0.348575
$165$	−1.83948	−	8.80486i	−0.143203	−	0.685457i
$166$	4.67242			0.362650
$167$	5.72768	−	4.16140i	0.443221	−	0.322019i	−0.343693	−	0.939082i	$-0.611678\pi$
$167$	5.72768	−	4.16140i	0.443221	−	0.322019i	0.786913	+	0.617063i	$0.211678\pi$
$168$		0			0
$169$	−3.46168	+	10.6540i	−0.266283	+	0.819536i
$170$	14.6190	+	10.6213i	1.12122	+	0.814616i
$171$	8.23978	+	5.98655i	0.630112	+	0.457803i
$172$	−0.932020	+	2.86846i	−0.0710659	+	0.218718i
$173$	2.45744	+	7.56322i	0.186836	+	0.575021i	0.999975	−	0.00704769i	$-0.00224337\pi$
$173$	2.45744	+	7.56322i	0.186836	+	0.575021i	−0.813139	+	0.582069i	$0.802243\pi$
$174$	−4.78455	+	3.47618i	−0.362716	+	0.263529i
$175$		0			0
$176$	6.95243	+	0.755237i	0.524059	+	0.0569281i
$177$	3.45778			0.259902
$178$	12.1964	−	8.86119i	0.914157	−	0.664174i
$179$	4.95756	+	15.2578i	0.370545	+	1.14042i	0.946435	+	0.322894i	$0.104656\pi$
$179$	4.95756	+	15.2578i	0.370545	+	1.14042i	−0.575890	+	0.817527i	$0.695344\pi$
$180$	−1.19903	+	3.69023i	−0.0893703	+	0.275053i
$181$	15.5552	+	11.3015i	1.15621	+	0.840034i	0.989294	−	0.145938i	$-0.0466199\pi$
$181$	15.5552	+	11.3015i	1.15621	+	0.840034i	0.166914	+	0.985972i	$0.446620\pi$
$182$		0			0
$183$	−3.09166	+	9.51514i	−0.228542	+	0.703380i
$184$	−6.03106	−	18.5617i	−0.444615	−	1.36839i
$185$	1.12268	−	0.815678i	0.0825414	−	0.0599698i
$186$	5.36848			0.393636
$187$	−19.0673	−	2.07127i	−1.39434	−	0.151466i
$188$	−4.03582			−0.294343
$189$		0			0
$190$	−4.86617	−	14.9765i	−0.353029	−	1.08651i
$191$	−0.553001	+	1.70196i	−0.0400137	+	0.123150i	−0.969068	−	0.246794i	$-0.920623\pi$
$191$	−0.553001	+	1.70196i	−0.0400137	+	0.123150i	0.929054	+	0.369943i	$0.120623\pi$
$192$	6.80054	+	4.94088i	0.490786	+	0.356577i
$193$	−7.56042	−	5.49297i	−0.544211	−	0.395392i	0.281436	−	0.959580i	$-0.409189\pi$
$193$	−7.56042	−	5.49297i	−0.544211	−	0.395392i	−0.825647	+	0.564188i	$0.809189\pi$
$194$	4.62740	−	14.2417i	0.332228	−	1.02249i
$195$	−1.12370	−	3.45839i	−0.0804698	−	0.247661i
$196$		0			0
$197$	−19.1079			−1.36138			−0.680691	−	0.732571i	$-0.738320\pi$
$197$	−19.1079			−1.36138			−0.680691	+	0.732571i	$0.738320\pi$
$198$	1.56266	+	7.47984i	0.111054	+	0.531569i
$199$	−15.9885			−1.13339			−0.566696	−	0.823927i	$-0.691779\pi$
$199$	−15.9885			−1.13339			−0.566696	+	0.823927i	$0.691779\pi$
$200$	6.25954	−	4.54782i	0.442616	−	0.321580i
$201$	0.898078	+	2.76400i	0.0633455	+	0.194957i
$202$	−0.858401	+	2.64189i	−0.0603969	+	0.185882i
$203$		0			0
$204$	−3.24223	−	2.35562i	−0.227001	−	0.164926i
$205$	−5.39831	+	16.6143i	−0.377034	+	1.16039i
$206$	−3.49769	−	10.7648i	−0.243695	−	0.750017i
$207$	10.3659	−	7.53127i	0.720480	−	0.523460i
$208$	2.82718			0.196030
$209$	12.3819	+	11.2271i	0.856477	+	0.776597i
$210$		0			0
$211$	−12.0619	+	8.76345i	−0.830372	+	0.603301i	−0.919665	−	0.392705i	$-0.871539\pi$
$211$	−12.0619	+	8.76345i	−0.830372	+	0.603301i	0.0892925	+	0.996005i	$0.471539\pi$
$212$	2.64752	+	8.14824i	0.181833	+	0.559623i
$213$	4.59729	−	14.1490i	0.315001	−	0.969473i
$214$	4.10022	+	2.97898i	0.280285	+	0.203639i
$215$	9.54901	+	6.93776i	0.651237	+	0.473151i
$216$	−4.72600	+	14.5451i	−0.321563	+	0.989670i
$217$		0			0
$218$	11.8365	−	8.59971i	0.801668	−	0.582446i
$219$	6.79095			0.458890
$220$	−2.61017	+	5.80798i	−0.175978	+	0.391574i
$221$	−7.75365			−0.521567
$222$	0.461986	−	0.335652i	0.0310064	−	0.0225275i
$223$	−3.69975	−	11.3867i	−0.247753	−	0.762507i	−0.995171	−	0.0981526i	$-0.968707\pi$
$223$	−3.69975	−	11.3867i	−0.247753	−	0.762507i	0.747418	−	0.664354i	$-0.231293\pi$
$224$		0			0
$225$	4.10943	+	2.98567i	0.273962	+	0.199045i
$226$	13.0350	+	9.47046i	0.867073	+	0.629966i
$227$	−3.81394	+	11.7381i	−0.253140	+	0.779086i	0.741050	+	0.671450i	$0.234328\pi$
$227$	−3.81394	+	11.7381i	−0.253140	+	0.779086i	−0.994190	+	0.107636i	$0.965672\pi$
$228$	1.07923	+	3.32153i	0.0714737	+	0.219973i
$229$	0.00910860	−	0.00661778i	0.000601913	−	0.000437316i	−0.587484	−	0.809236i	$-0.699882\pi$
$229$	0.00910860	−	0.00661778i	0.000601913	−	0.000437316i	0.588086	+	0.808798i	$0.299882\pi$
$230$	−19.8105			−1.30627
$231$		0			0
$232$	16.1410			1.05971
$233$	21.0717	−	15.3095i	1.38045	−	1.00296i	0.383613	−	0.923494i	$-0.374680\pi$
$233$	21.0717	−	15.3095i	1.38045	−	1.00296i	0.996838	−	0.0794628i	$-0.0253205\pi$
$234$	0.954598	+	2.93795i	0.0624040	+	0.192060i
$235$	−4.88059	+	15.0209i	−0.318375	+	0.979856i
$236$	−1.98028	−	1.43876i	−0.128905	−	0.0936553i
$237$	2.58318	+	1.87679i	0.167796	+	0.121911i
$238$		0			0
$239$	4.48659	+	13.8083i	0.290213	+	0.893184i	0.984787	+	0.173763i	$0.0555928\pi$
$239$	4.48659	+	13.8083i	0.290213	+	0.893184i	−0.694574	+	0.719421i	$0.744407\pi$
$240$	4.62645	−	3.36132i	0.298636	−	0.216972i
$241$	−13.6430			−0.878823			−0.439411	−	0.898286i	$-0.644813\pi$
$241$	−13.6430			−0.878823			−0.439411	+	0.898286i	$0.644813\pi$
$242$	1.22382	+	12.4800i	0.0786701	+	0.802247i
$243$	−16.0394			−1.02893
$244$	5.72980	−	4.16294i	0.366813	−	0.266505i
$245$		0			0
$246$	−2.22141	+	6.83680i	−0.141632	+	0.435898i
$247$	5.46650	+	3.97165i	0.347825	+	0.252710i
$248$	−11.8537	−	8.61222i	−0.752711	−	0.546876i
$249$	−1.25317	+	3.85685i	−0.0794161	+	0.244418i
$250$	2.40113	+	7.38992i	0.151861	+	0.467380i
$251$	−17.5003	+	12.7147i	−1.10461	+	0.802547i	−0.981806	−	0.189884i	$-0.939189\pi$
$251$	−17.5003	+	12.7147i	−1.10461	+	0.802547i	−0.122804	+	0.992431i	$0.539189\pi$
$252$		0			0
$253$	18.2463	−	10.4499i	1.14714	−	0.656980i
$254$	12.3565			0.775313
$255$	−12.6882	+	9.21854i	−0.794568	+	0.577287i
$256$	−4.48313	−	13.7976i	−0.280195	−	0.862353i
$257$	6.22444	−	19.1568i	0.388270	−	1.19497i	−0.545811	−	0.837909i	$-0.683778\pi$
$257$	6.22444	−	19.1568i	0.388270	−	1.19497i	0.934080	−	0.357063i	$-0.116222\pi$
$258$	3.92942	+	2.85489i	0.244635	+	0.177738i
$259$		0			0
$260$	−0.795469	+	2.44820i	−0.0493329	+	0.151831i
$261$	3.27454	+	10.0780i	0.202689	+	0.623812i
$262$	−18.8315	+	13.6819i	−1.16341	+	0.845268i
$263$	8.33982			0.514255			0.257128	−	0.966377i	$-0.417224\pi$
$263$	8.33982			0.514255			0.257128	+	0.966377i	$0.417224\pi$
$264$	−4.14107	+	9.21443i	−0.254865	+	0.567109i
$265$	33.5286			2.05964
$266$		0			0
$267$	4.04334	+	12.4441i	0.247448	+	0.761568i
$268$	0.635751	−	1.95664i	0.0388346	−	0.119521i
$269$	3.50825	+	2.54889i	0.213902	+	0.155409i	0.689577	−	0.724212i	$-0.257796\pi$
$269$	3.50825	+	2.54889i	0.213902	+	0.155409i	−0.475676	+	0.879621i	$0.657796\pi$
$270$	12.5590	+	9.12463i	0.764315	+	0.555307i
$271$	7.34807	−	22.6150i	0.446364	−	1.37377i	−0.434617	−	0.900615i	$-0.643116\pi$
$271$	7.34807	−	22.6150i	0.446364	−	1.37377i	0.880981	−	0.473151i	$-0.156884\pi$
$272$	−3.76800	−	11.5967i	−0.228469	−	0.703154i
$273$		0			0
$274$	−6.10814			−0.369006
$275$	6.17525	+	5.59931i	0.372381	+	0.337651i
$276$	4.39363			0.264465
$277$	−5.65126	+	4.10588i	−0.339551	+	0.246698i	−0.744472	−	0.667653i	$-0.767299\pi$
$277$	−5.65126	+	4.10588i	−0.339551	+	0.246698i	0.404921	+	0.914352i	$0.367299\pi$
$278$	6.37591	+	19.6230i	0.382402	+	1.17691i
$279$	2.97247	−	9.14832i	0.177957	−	0.547696i
$280$		0			0
$281$	−2.15044	−	1.56239i	−0.128284	−	0.0932041i	0.521793	−	0.853072i	$-0.325263\pi$
$281$	−2.15044	−	1.56239i	−0.128284	−	0.0932041i	−0.650077	+	0.759868i	$0.725263\pi$
$282$	−2.00837	+	6.18112i	−0.119597	+	0.368080i
$283$	−5.51963	−	16.9877i	−0.328108	−	1.00981i	−0.970018	−	0.243033i	$-0.921858\pi$
$283$	−5.51963	−	16.9877i	−0.328108	−	1.00981i	0.641910	−	0.766780i	$-0.278142\pi$
$284$	−8.52020	+	6.19029i	−0.505581	+	0.367326i
$285$	13.6675			0.809593
$286$	1.03672	+	4.96234i	0.0613023	+	0.293429i
$287$		0			0
$288$	6.13658	−	4.45848i	0.361601	−	0.262719i
$289$	5.08061	+	15.6365i	0.298859	+	0.919794i
$290$	5.06287	−	15.5819i	0.297302	−	0.915002i
$291$	10.5147	+	7.63937i	0.616382	+	0.447828i
$292$	−3.88921	−	2.82568i	−0.227599	−	0.165360i
$293$	−7.25799	+	22.3378i	−0.424016	+	1.30499i	0.479917	+	0.877314i	$0.340667\pi$
$293$	−7.25799	+	22.3378i	−0.424016	+	1.30499i	−0.903933	+	0.427674i	$0.859333\pi$
$294$		0			0
$295$	−7.74970	+	5.63049i	−0.451205	+	0.327820i
$296$	−1.55853			−0.0905879
$297$	−16.3805	−	1.77940i	−0.950493	−	0.103251i
$298$	14.1428			0.819269
$299$	6.87703	−	4.99646i	0.397709	−	0.288953i
$300$	0.538244	+	1.65655i	0.0310755	+	0.0956407i
$301$		0			0
$302$	9.33975	+	6.78573i	0.537443	+	0.390475i
$303$	−1.95052	−	1.41713i	−0.112054	−	0.0814123i
$304$	−3.28365	+	10.1060i	−0.188330	+	0.579621i
$305$	−8.56489	−	26.3600i	−0.490424	−	1.50937i
$306$	10.7788	−	7.83127i	0.616184	−	0.447684i
$307$	21.3128			1.21639			0.608193	−	0.793789i	$-0.291894\pi$
$307$	21.3128			1.21639			0.608193	+	0.793789i	$0.291894\pi$
$308$		0			0
$309$	9.82388			0.558861
$310$	−12.0320	+	8.74179i	−0.683374	+	0.496500i
$311$	−0.116349	−	0.358085i	−0.00659754	−	0.0203051i	0.947704	−	0.319152i	$-0.103398\pi$
$311$	−0.116349	−	0.358085i	−0.00659754	−	0.0203051i	−0.954301	+	0.298847i	$0.903398\pi$
$312$	−1.26202	+	3.88410i	−0.0714479	+	0.219894i
$313$	6.45048	+	4.68655i	0.364603	+	0.264899i	0.754969	−	0.655760i	$-0.227652\pi$
$313$	6.45048	+	4.68655i	0.364603	+	0.264899i	−0.390367	+	0.920660i	$0.627652\pi$
$314$	17.3899	+	12.6345i	0.981371	+	0.713008i
$315$		0			0
$316$	−0.698478	−	2.14969i	−0.0392924	−	0.120930i
$317$	−11.1159	+	8.07617i	−0.624331	+	0.453603i	−0.854432	−	0.519564i	$-0.826094\pi$
$317$	−11.1159	+	8.07617i	−0.624331	+	0.453603i	0.230101	+	0.973167i	$0.426094\pi$
$318$	13.7970			0.773700
$319$	3.55623	+	17.0222i	0.199110	+	0.953061i
$320$	−23.2871			−1.30179
$321$	−3.55870	+	2.58555i	−0.198627	+	0.144311i
$322$		0			0
$323$	9.00554	−	27.7162i	0.501082	−	1.54217i
$324$	0.650296	+	0.472468i	0.0361275	+	0.0262482i
$325$	2.72631	+	1.98078i	0.151228	+	0.109874i
$326$	2.67355	−	8.22833i	0.148074	−	0.455725i
$327$	3.92403	+	12.0769i	0.216999	+	0.667855i
$328$	15.8726	−	11.5322i	0.876420	−	0.636757i
$329$		0			0
$330$	7.59637	+	6.88789i	0.418167	+	0.379166i
$331$	2.75208			0.151268			0.0756340	−	0.997136i	$-0.475902\pi$
$331$	2.75208			0.151268			0.0756340	+	0.997136i	$0.475902\pi$
$332$	2.32250	−	1.68740i	0.127464	−	0.0926080i
$333$	−0.316182	−	0.973108i	−0.0173267	−	0.0533260i
$334$	−2.49405	+	7.67589i	−0.136468	+	0.420006i
$335$	−6.51358	−	4.73239i	−0.355875	−	0.258558i
$336$		0			0
$337$	−7.96492	+	24.5135i	−0.433877	+	1.33534i	0.460356	+	0.887734i	$0.347722\pi$
$337$	−7.96492	+	24.5135i	−0.433877	+	1.33534i	−0.894233	+	0.447602i	$0.852278\pi$
$338$	−3.94629	−	12.1454i	−0.214650	−	0.660624i
$339$	−11.3134	+	8.21970i	−0.614462	+	0.446433i
$340$	11.1024			0.602112
$341$	6.47078	−	14.3984i	0.350413	−	0.779715i
$342$	−11.6107			−0.627836
$343$		0			0
$344$	−4.09637	−	12.6073i	−0.220861	−	0.679742i
$345$	5.31329	−	16.3526i	0.286058	−	0.880395i
$346$	−7.33432	−	5.32869i	−0.394295	−	0.286472i
$347$	9.72133	+	7.06296i	0.521868	+	0.379159i	0.817307	−	0.576202i	$-0.195466\pi$
$347$	9.72133	+	7.06296i	0.521868	+	0.379159i	−0.295439	+	0.955362i	$0.595466\pi$
$348$	−1.12286	+	3.45579i	−0.0601914	+	0.185250i
$349$	−2.94427	−	9.06152i	−0.157603	−	0.485052i	0.840812	−	0.541327i	$-0.182078\pi$
$349$	−2.94427	−	9.06152i	−0.157603	−	0.485052i	−0.998415	+	0.0562747i	$0.982078\pi$
$350$		0			0
$351$	−6.66107			−0.355541
$352$	10.8018	−	6.18630i	0.575736	−	0.329731i
$353$	11.8390			0.630124			0.315062	−	0.949071i	$-0.397975\pi$
$353$	11.8390			0.630124			0.315062	+	0.949071i	$0.397975\pi$
$354$	−3.18901	+	2.31695i	−0.169494	+	0.123145i
$355$	12.7360	+	39.1973i	0.675956	+	2.08038i
$356$	2.86229	−	8.80921i	0.151701	−	0.466887i
$357$		0			0
$358$	−14.7960	−	10.7499i	−0.781993	−	0.568151i
$359$	−9.30118	+	28.6261i	−0.490897	+	1.51083i	0.332357	+	0.943154i	$0.392156\pi$
$359$	−9.30118	+	28.6261i	−0.490897	+	1.51083i	−0.823254	+	0.567673i	$0.807844\pi$
$360$	−5.26991	−	16.2191i	−0.277749	−	0.854823i
$361$	−5.17483	+	3.75974i	−0.272360	+	0.197881i
$362$	−21.9189			−1.15203
$363$	−10.6299	−	2.33701i	−0.557924	−	0.122661i
$364$		0			0
$365$	−15.2201	+	11.0581i	−0.796659	+	0.578807i
$366$	−3.52446	−	10.8472i	−0.184227	−	0.566991i
$367$	5.00976	−	15.4184i	0.261507	−	0.804836i	−0.730970	−	0.682409i	$-0.760932\pi$
$367$	5.00976	−	15.4184i	0.261507	−	0.804836i	0.992477	−	0.122427i	$-0.0390678\pi$
$368$	10.8149	+	7.85751i	0.563767	+	0.409601i
$369$	10.4205	+	7.57093i	0.542469	+	0.394127i
$370$	−0.488859	+	1.50455i	−0.0254146	+	0.0782180i
$371$		0			0
$372$	2.66849	−	1.93877i	0.138355	−	0.100521i
$373$	−13.2269			−0.684862			−0.342431	−	0.939543i	$-0.611250\pi$
$373$	−13.2269			−0.684862			−0.342431	+	0.939543i	$0.611250\pi$
$374$	18.9732	−	10.8662i	0.981079	−	0.561876i
$375$	−6.74401			−0.348259
$376$	14.3504	−	10.4262i	0.740065	−	0.537689i
$377$	2.17242	+	6.68603i	0.111885	+	0.344348i
$378$		0			0
$379$	−13.0593	−	9.48810i	−0.670809	−	0.487371i	0.199487	−	0.979900i	$-0.436072\pi$
$379$	−13.0593	−	9.48810i	−0.670809	−	0.487371i	−0.870296	+	0.492529i	$0.836072\pi$
$380$	−7.82744	−	5.68697i	−0.401539	−	0.291735i
$381$	−3.31406	+	10.1996i	−0.169785	+	0.522543i
$382$	−0.630416	−	1.94022i	−0.0322549	−	0.0992703i
$383$	1.37466	−	0.998749i	0.0702419	−	0.0510337i	−0.552110	−	0.833771i	$-0.686177\pi$
$383$	1.37466	−	0.998749i	0.0702419	−	0.0510337i	0.622352	+	0.782737i	$0.286177\pi$
$384$	−2.15569			−0.110007
$385$		0			0
$386$	10.6534			0.542246
$387$	7.04065	−	5.11534i	0.357897	−	0.260027i
$388$	−2.84311	−	8.75020i	−0.144337	−	0.444224i
$389$	7.51943	−	23.1424i	0.381250	−	1.17337i	−0.557914	−	0.829899i	$-0.688398\pi$
$389$	7.51943	−	23.1424i	0.381250	−	1.17337i	0.939164	−	0.343469i	$-0.111602\pi$
$390$	3.35372	+	2.43662i	0.169822	+	0.123383i
$391$	−29.6604	−	21.5495i	−1.49999	−	1.08981i
$392$		0			0
$393$	−6.24300	−	19.2140i	−0.314918	−	0.969217i
$394$	17.6227	−	12.8036i	0.887818	−	0.645038i
$395$	−8.84561			−0.445071
$396$	3.47802	+	3.15364i	0.174777	+	0.158477i
$397$	−6.64819			−0.333663			−0.166831	−	0.985985i	$-0.553354\pi$
$397$	−6.64819			−0.333663			−0.166831	+	0.985985i	$0.553354\pi$
$398$	14.7457	−	10.7134i	0.739136	−	0.537014i
$399$		0			0
$400$	−1.63765	+	5.04018i	−0.0818827	+	0.252009i
$401$	−2.42037	−	1.75850i	−0.120867	−	0.0878153i	0.525709	−	0.850664i	$-0.323800\pi$
$401$	−2.42037	−	1.75850i	−0.120867	−	0.0878153i	−0.646577	+	0.762849i	$0.723800\pi$
$402$	−2.68034	−	1.94738i	−0.133683	−	0.0971267i
$403$	1.97202	−	6.06925i	0.0982333	−	0.302331i
$404$	0.527409	+	1.62320i	0.0262396	+	0.0807572i
$405$	2.54489	−	1.84897i	0.126456	−	0.0918760i
$406$		0			0
$407$	−0.343381	−	1.64363i	−0.0170208	−	0.0814715i
$408$	17.6141			0.872026
$409$	−3.32022	+	2.41228i	−0.164174	+	0.119280i	−0.666839	−	0.745202i	$-0.732353\pi$
$409$	−3.32022	+	2.41228i	−0.164174	+	0.119280i	0.502665	+	0.864482i	$0.332353\pi$
$410$	−6.15403	−	18.9401i	−0.303926	−	0.935387i
$411$	1.63823	−	5.04197i	0.0808081	−	0.248702i
$412$	−5.62618	−	4.08766i	−0.277182	−	0.201384i
$413$		0			0
$414$	−4.51371	+	13.8918i	−0.221837	+	0.682743i
$415$	−3.47168	−	10.6847i	−0.170418	−	0.524492i
$416$	4.07118	−	2.95788i	0.199606	−	0.145022i
$417$	−17.9079			−0.876954
$418$	−18.9425	−	2.05770i	−0.926507	−	0.100646i
$419$	−6.26224			−0.305930			−0.152965	−	0.988232i	$-0.548882\pi$
$419$	−6.26224			−0.305930			−0.152965	+	0.988232i	$0.548882\pi$
$420$		0			0
$421$	−4.19821	−	12.9208i	−0.204608	−	0.629719i	−0.999729	−	0.0232684i	$-0.992593\pi$
$421$	−4.19821	−	12.9208i	−0.204608	−	0.629719i	0.795121	−	0.606451i	$-0.207407\pi$
$422$	5.25219	−	16.1646i	0.255672	−	0.786879i
$423$	9.42112	+	6.84484i	0.458070	+	0.332808i
$424$	−30.4641	−	22.1335i	−1.47947	−	1.07490i
$425$	4.49133	−	13.8229i	0.217862	−	0.670509i
$426$	5.24087	+	16.1297i	0.253921	+	0.781488i
$427$		0			0
$428$	3.11391			0.150517
$429$	−4.37422	−	0.475167i	−0.211189	−	0.0229413i
$430$	−13.4556			−0.648885
$431$	5.45076	−	3.96021i	0.262554	−	0.190757i	−0.448718	−	0.893673i	$-0.648119\pi$
$431$	5.45076	−	3.96021i	0.262554	−	0.190757i	0.711272	+	0.702917i	$0.248119\pi$
$432$	−3.23704	−	9.96260i	−0.155742	−	0.479326i
$433$	−10.9239	+	33.6202i	−0.524967	+	1.61568i	0.239413	+	0.970918i	$0.423045\pi$
$433$	−10.9239	+	33.6202i	−0.524967	+	1.61568i	−0.764380	+	0.644765i	$0.776955\pi$
$434$		0			0
$435$	11.5042	+	8.35830i	0.551585	+	0.400750i
$436$	2.77782	−	8.54926i	0.133034	−	0.409436i
$437$	9.87295	+	30.3858i	0.472287	+	1.45355i
$438$	−6.26310	+	4.55041i	−0.299263	+	0.217427i
$439$	−4.95162			−0.236328			−0.118164	−	0.992994i	$-0.537701\pi$
$439$	−4.95162			−0.236328			−0.118164	+	0.992994i	$0.537701\pi$
$440$	−5.72324	−	27.3949i	−0.272845	−	1.30600i
$441$		0			0
$442$	7.15098	−	5.19549i	0.340137	−	0.247124i
$443$	−7.45141	−	22.9331i	−0.354027	−	1.08958i	−0.956571	−	0.291499i	$-0.905846\pi$
$443$	−7.45141	−	22.9331i	−0.354027	−	1.08958i	0.602544	−	0.798086i	$-0.294154\pi$
$444$	0.108420	−	0.333683i	0.00514540	−	0.0158359i
$445$	−29.3255	−	21.3063i	−1.39016	−	1.01001i
$446$	11.0420	+	8.02250i	0.522855	+	0.379877i
$447$	−3.79317	+	11.6742i	−0.179411	+	0.552169i
$448$		0			0
$449$	−15.4520	+	11.2265i	−0.729224	+	0.529812i	−0.889318	−	0.457290i	$-0.848820\pi$
$449$	−15.4520	+	11.2265i	−0.729224	+	0.529812i	0.160094	+	0.987102i	$0.448820\pi$
$450$	−5.79062			−0.272972
$451$	15.6589	+	14.1985i	0.737349	+	0.668579i
$452$	9.89943			0.465630
$453$	−8.10625	+	5.88954i	−0.380865	+	0.276715i
$454$	−4.34786	−	13.3813i	−0.204055	−	0.628018i
$455$		0			0
$456$	−12.4183	−	9.02244i	−0.581541	−	0.422514i
$457$	20.8262	+	15.1311i	0.974210	+	0.707805i	0.956407	−	0.292037i	$-0.0943329\pi$
$457$	20.8262	+	15.1311i	0.974210	+	0.707805i	0.0178027	+	0.999842i	$0.494333\pi$
$458$	−0.00396623	+	0.0122068i	−0.000185330	+	0.000570386i
$459$	8.87772	+	27.3228i	0.414377	+	1.27532i
$460$	−9.84717	+	7.15439i	−0.459127	+	0.333575i
$461$	−10.6216			−0.494699			−0.247349	−	0.968926i	$-0.579560\pi$
$461$	−10.6216			−0.494699			−0.247349	+	0.968926i	$0.579560\pi$
$462$		0			0
$463$	−7.71447			−0.358522			−0.179261	−	0.983802i	$-0.557371\pi$
$463$	−7.71447			−0.358522			−0.179261	+	0.983802i	$0.557371\pi$
$464$	−8.94421	+	6.49835i	−0.415225	+	0.301678i
$465$	−3.98886	−	12.2764i	−0.184979	−	0.569306i
$466$	−9.17540	+	28.2390i	−0.425042	+	1.30815i
$467$	−11.7575	−	8.54236i	−0.544074	−	0.395293i	0.281522	−	0.959555i	$-0.409161\pi$
$467$	−11.7575	−	8.54236i	−0.544074	−	0.395293i	−0.825596	+	0.564262i	$0.809161\pi$
$468$	1.53551	+	1.11562i	0.0709791	+	0.0515693i
$469$		0			0
$470$	−5.56383	−	17.1237i	−0.256640	−	0.789857i
$471$	−15.0933	+	10.9659i	−0.695460	+	0.505282i
$472$	10.7583			0.495191
$473$	12.3931	−	7.09771i	0.569837	−	0.326353i
$474$	−3.63998			−0.167190
$475$	−10.2470	+	7.44487i	−0.470164	+	0.341594i
$476$		0			0
$477$	7.63928	−	23.5113i	0.349779	−	1.07651i
$478$	−13.3904	−	9.72868i	−0.612462	−	0.444979i
$479$	23.2246	+	16.8737i	1.06116	+	0.770977i	0.974302	−	0.225244i	$-0.0723178\pi$
$479$	23.2246	+	16.8737i	1.06116	+	0.770977i	0.0868566	+	0.996221i	$0.472318\pi$
$480$	3.14545	−	9.68068i	0.143569	−	0.441861i
$481$	−0.209764	−	0.645587i	−0.00956442	−	0.0294363i
$482$	12.5826	−	9.14176i	0.573120	−	0.416396i
$483$		0			0
$484$	5.11537	+	5.76145i	0.232517	+	0.261884i
$485$	−36.0056			−1.63493
$486$	14.7927	−	10.7475i	0.671009	−	0.487516i
$487$	6.62304	+	20.3836i	0.300119	+	0.923670i	0.981454	+	0.191699i	$0.0613996\pi$
$487$	6.62304	+	20.3836i	0.300119	+	0.923670i	−0.681335	+	0.731972i	$0.738600\pi$
$488$	−9.61918	+	29.6048i	−0.435440	+	1.34015i
$489$	6.07502	+	4.41376i	0.274722	+	0.199597i
$490$		0			0
$491$	−7.32338	+	22.5390i	−0.330499	+	1.01717i	0.638397	+	0.769707i	$0.279598\pi$
$491$	−7.32338	+	22.5390i	−0.330499	+	1.01717i	−0.968897	+	0.247466i	$0.920402\pi$
$492$	1.36485	+	4.20059i	0.0615324	+	0.189377i
$493$	24.5299	−	17.8220i	1.10477	−	0.802662i
$494$	−7.70288			−0.346569
$495$	15.9436	−	9.13108i	0.716610	−	0.410412i
$496$	10.0358			0.450620
$497$		0			0
$498$	−1.42860	−	4.39677i	−0.0640170	−	0.197024i
$499$	−5.68063	+	17.4832i	−0.254300	+	0.782655i	0.739667	+	0.672973i	$0.234983\pi$
$499$	−5.68063	+	17.4832i	−0.254300	+	0.782655i	−0.993967	+	0.109682i	$0.965017\pi$
$500$	3.86233	+	2.80614i	0.172728	+	0.125495i
$501$	−5.66715	−	4.11742i	−0.253189	−	0.183953i
$502$	7.62030	−	23.4529i	0.340111	−	1.04675i
$503$	−9.21070	−	28.3476i	−0.410685	−	1.26396i	−0.916054	−	0.401055i	$-0.868644\pi$
$503$	−9.21070	−	28.3476i	−0.410685	−	1.26396i	0.505369	−	0.862903i	$-0.331356\pi$
$504$		0			0
$505$	6.67918			0.297220
$506$	−9.82591	+	21.8640i	−0.436815	+	0.971972i
$507$	11.0839			0.492252
$508$	6.14199	−	4.46242i	0.272507	−	0.197988i
$509$	−5.00299	−	15.3976i	−0.221754	−	0.682487i	−0.998605	−	0.0528032i	$-0.983184\pi$
$509$	−5.00299	−	15.3976i	−0.221754	−	0.682487i	0.776851	−	0.629684i	$-0.216816\pi$
$510$	5.52494	−	17.0040i	0.244648	−	0.752950i
$511$		0			0
$512$	16.9053	+	12.2824i	0.747115	+	0.542811i
$513$	7.73655	−	23.8106i	0.341577	−	1.05127i
$514$	7.09580	+	21.8386i	0.312982	+	0.963261i
$515$	−22.0177	+	15.9968i	−0.970214	+	0.704902i
$516$	2.98421			0.131372
$517$	14.1571	+	12.8368i	0.622630	+	0.564560i
$518$		0			0
$519$	6.36567	−	4.62493i	0.279422	−	0.203012i
$520$	−3.49621	−	10.7602i	−0.153319	−	0.471867i
$521$	−7.61072	+	23.4234i	−0.333432	+	1.02620i	0.634058	+	0.773286i	$0.281388\pi$
$521$	−7.61072	+	23.4234i	−0.333432	+	1.02620i	−0.967489	+	0.252912i	$0.918612\pi$
$522$	−9.77298	−	7.10049i	−0.427752	−	0.310780i
$523$	6.23674	+	4.53126i	0.272714	+	0.198138i	0.715733	−	0.698374i	$-0.246093\pi$
$523$	6.23674	+	4.53126i	0.272714	+	0.198138i	−0.443019	+	0.896512i	$0.646093\pi$
$524$	−4.41943	+	13.6016i	−0.193064	+	0.594189i
$525$		0			0
$526$	−7.69158	+	5.58826i	−0.335369	+	0.243660i
$527$	−27.5235			−1.19894
$528$	−1.41503	−	6.77320i	−0.0615814	−	0.294766i
$529$	17.1935			0.747545
$530$	−30.9225	+	22.4665i	−1.34319	+	0.975882i
$531$	2.18255	+	6.71720i	0.0947147	+	0.291502i
$532$		0			0
$533$	6.91324	+	5.02277i	0.299446	+	0.217560i
$534$	−12.0675	−	8.76754i	−0.522211	−	0.379409i
$535$	3.76571	−	11.5897i	0.162806	−	0.501065i
$536$	2.79422	+	8.59973i	0.120692	+	0.371452i
$537$	12.8419	−	9.33018i	0.554169	−	0.402627i
$538$	−4.94349			−0.213129
$539$		0			0
$540$	9.53792			0.410447
$541$	−27.5270	+	19.9995i	−1.18348	+	0.859846i	−0.992560	−	0.121760i	$-0.961146\pi$
$541$	−27.5270	+	19.9995i	−1.18348	+	0.859846i	−0.190917	+	0.981606i	$0.561146\pi$
$542$	8.37674	+	25.7810i	0.359812	+	1.10739i
$543$	5.87876	−	18.0930i	0.252282	−	0.776443i
$544$	−17.5588	−	12.7572i	−0.752829	−	0.546962i
$545$	−28.4602	−	20.6775i	−1.21910	−	0.885728i
$546$		0			0
$547$	1.85372	+	5.70516i	0.0792593	+	0.243935i	0.982833	−	0.184498i	$-0.0590659\pi$
$547$	1.85372	+	5.70516i	0.0792593	+	0.243935i	−0.903574	+	0.428433i	$0.859066\pi$
$548$	−3.03616	+	2.20590i	−0.129698	+	0.0942312i
$549$	−20.4359			−0.872184
$550$	−9.44718	−	1.02624i	−0.402829	−	0.0437590i
$551$	−26.4230			−1.12566
$552$	−15.6226	+	11.3505i	−0.664944	+	0.483110i
$553$		0			0
$554$	2.46077	−	7.57348i	0.104548	−	0.321766i
$555$	−1.11082	−	0.807058i	−0.0471517	−	0.0342577i
$556$	10.2559	+	7.45137i	0.434949	+	0.316009i
$557$	1.17507	−	3.61651i	0.0497895	−	0.153236i	−0.923071	−	0.384631i	$-0.874329\pi$
$557$	1.17507	−	3.61651i	0.0497895	−	0.153236i	0.972860	+	0.231394i	$0.0743288\pi$
$558$	3.38859	+	10.4290i	0.143450	+	0.441495i
$559$	4.67097	−	3.39366i	0.197561	−	0.143536i
$560$		0			0
$561$	3.88079	+	18.5758i	0.163847	+	0.784269i
$562$	3.03020			0.127821
$563$	−29.7321	+	21.6017i	−1.25306	+	0.910402i	−0.998395	−	0.0566275i	$-0.981965\pi$
$563$	−29.7321	+	21.6017i	−1.25306	+	0.910402i	−0.254665	+	0.967029i	$0.581965\pi$
$564$	1.23396	+	3.79773i	0.0519590	+	0.159913i
$565$	11.9715	−	36.8446i	0.503647	−	1.55006i
$566$	16.4735	+	11.9687i	0.692434	+	0.503083i
$567$		0			0
$568$	14.3037	−	44.0223i	0.600170	−	1.84713i
$569$	−1.98050	−	6.09534i	−0.0830268	−	0.255530i	0.900922	−	0.433981i	$-0.142891\pi$
$569$	−1.98050	−	6.09534i	−0.0830268	−	0.255530i	−0.983949	+	0.178451i	$0.942891\pi$
$570$	−12.6052	+	9.15818i	−0.527972	+	0.383594i
$571$	−1.58858			−0.0664798			−0.0332399	−	0.999447i	$-0.510583\pi$
$571$	−1.58858			−0.0664798			−0.0332399	+	0.999447i	$0.510583\pi$
$572$	2.30742	+	2.09222i	0.0964780	+	0.0874800i
$573$	1.77064			0.0739694
$574$		0			0
$575$	4.92394	+	15.1543i	0.205342	+	0.631979i
$576$	−5.30583	+	16.3297i	−0.221076	+	0.680403i
$577$	−24.0551	−	17.4771i	−1.00143	−	0.727580i	−0.0390341	−	0.999238i	$-0.512428\pi$
$577$	−24.0551	−	17.4771i	−1.00143	−	0.727580i	−0.962394	+	0.271658i	$0.912428\pi$
$578$	−15.1632	−	11.0167i	−0.630708	−	0.458236i
$579$	−2.85730	+	8.79388i	−0.118746	+	0.365461i
$580$	−3.11067	−	9.57367i	−0.129164	−	0.397525i
$581$		0			0
$582$	−14.8163			−0.614156
$583$	16.6300	−	37.0039i	0.688744	−	1.53255i
$584$	21.1289			0.874321
$585$	6.00912	−	4.36588i	0.248447	−	0.180507i
$586$	−8.27404	−	25.4649i	−0.341798	−	1.05194i
$587$	−4.64164	+	14.2855i	−0.191581	+	0.589626i	0.808418	+	0.588608i	$0.200324\pi$
$587$	−4.64164	+	14.2855i	−0.191581	+	0.589626i	−0.999999	+	0.00101767i	$0.999676\pi$
$588$		0			0
$589$	19.4047	+	14.0984i	0.799558	+	0.580913i
$590$	3.37451	−	10.3857i	0.138927	−	0.427572i
$591$	5.84227	+	17.9807i	0.240319	+	0.739625i
$592$	0.863632	−	0.627466i	0.0354951	−	0.0257887i
$593$	16.1882			0.664770			0.332385	−	0.943144i	$-0.392147\pi$
$593$	16.1882			0.664770			0.332385	+	0.943144i	$0.392147\pi$
$594$	16.2996	−	9.33499i	0.668781	−	0.383019i
$595$		0			0
$596$	7.02992	−	5.10753i	0.287957	−	0.209213i
$597$	4.88850	+	15.0453i	0.200073	+	0.615761i
$598$	−2.99452	+	9.21619i	−0.122455	+	0.376878i
$599$	−19.7924	−	14.3801i	−0.808697	−	0.587553i	0.104755	−	0.994498i	$-0.466594\pi$
$599$	−19.7924	−	14.3801i	−0.808697	−	0.587553i	−0.913453	+	0.406945i	$0.866594\pi$
$600$	−6.19339	−	4.49976i	−0.252844	−	0.183702i
$601$	−4.17870	+	12.8607i	−0.170453	+	0.524599i	−0.999397	−	0.0347323i	$-0.988942\pi$
$601$	−4.17870	+	12.8607i	−0.170453	+	0.524599i	0.828944	+	0.559332i	$0.188942\pi$
$602$		0			0
$603$	−4.80258	+	3.48928i	−0.195576	+	0.142094i
$604$	7.09309			0.288614
$605$	27.6296	−	12.0714i	1.12330	−	0.490774i
$606$	2.74849			0.111650
$607$	13.1973	−	9.58843i	0.535664	−	0.389182i	−0.286808	−	0.957988i	$-0.592594\pi$
$607$	13.1973	−	9.58843i	0.535664	−	0.389182i	0.822472	+	0.568806i	$0.192594\pi$
$608$	5.84475	+	17.9883i	0.237036	+	0.729521i
$609$		0			0
$610$	25.5622	+	18.5720i	1.03498	+	0.751960i
$611$	6.25023	+	4.54106i	0.252857	+	0.183712i
$612$	2.52961	−	7.78534i	0.102253	−	0.314704i
$613$	7.14788	+	21.9989i	0.288700	+	0.888528i	0.985265	+	0.171034i	$0.0547108\pi$
$613$	7.14788	+	21.9989i	0.288700	+	0.888528i	−0.696565	+	0.717494i	$0.745289\pi$
$614$	−19.6562	+	14.2811i	−0.793260	+	0.576337i
$615$	17.2847			0.696986
$616$		0			0
$617$	−37.2793			−1.50081			−0.750405	−	0.660979i	$-0.770141\pi$
$617$	−37.2793			−1.50081			−0.750405	+	0.660979i	$0.770141\pi$
$618$	−9.06029	+	6.58269i	−0.364458	+	0.264794i
$619$	−0.512946	−	1.57869i	−0.0206170	−	0.0634527i	0.940219	−	0.340571i	$-0.110620\pi$
$619$	−0.512946	−	1.57869i	−0.0206170	−	0.0634527i	−0.960836	+	0.277119i	$0.910620\pi$
$620$	−2.82372	+	8.69051i	−0.113403	+	0.349019i
$621$	−25.4809	−	18.5129i	−1.02251	−	0.742898i
$622$	0.347247	+	0.252290i	0.0139233	+	0.0101159i
$623$		0			0
$624$	−0.864414	−	2.66039i	−0.0346042	−	0.106501i
$625$	25.2816	−	18.3682i	1.01127	−	0.734727i
$626$	−9.08941			−0.363286
$627$	6.77900	−	15.0842i	0.270727	−	0.602404i
$628$	13.2068			0.527009
$629$	−2.36855	+	1.72085i	−0.0944401	+	0.0686148i
$630$		0			0
$631$	−14.1437	+	43.5298i	−0.563051	+	1.73289i	0.110620	+	0.993863i	$0.464716\pi$
$631$	−14.1437	+	43.5298i	−0.563051	+	1.73289i	−0.673671	+	0.739031i	$0.735284\pi$
$632$	8.03714	+	5.83933i	0.319700	+	0.232276i
$633$	11.9344	+	8.67084i	0.474349	+	0.344635i
$634$	4.84028	−	14.8969i	0.192232	−	0.591630i
$635$	−9.18103	−	28.2563i	−0.364338	−	1.12132i
$636$	6.85806	−	4.98267i	0.271940	−	0.197576i
$637$		0			0
$638$	−14.6859	−	13.3162i	−0.581420	−	0.527193i
$639$	30.3882			1.20214
$640$	4.83141	−	3.51022i	0.190978	−	0.138754i
$641$	−0.389769	−	1.19959i	−0.0153950	−	0.0473808i	0.943064	−	0.332612i	$-0.107930\pi$
$641$	−0.389769	−	1.19959i	−0.0153950	−	0.0473808i	−0.958459	+	0.285231i	$0.907930\pi$
$642$	1.54959	−	4.76915i	0.0611575	−	0.188224i
$643$	−2.81664	−	2.04641i	−0.111078	−	0.0807026i	0.530860	−	0.847460i	$-0.321869\pi$
$643$	−2.81664	−	2.04641i	−0.111078	−	0.0807026i	−0.641937	+	0.766757i	$0.721869\pi$
$644$		0			0
$645$	3.60885	−	11.1069i	0.142098	−	0.437334i
$646$	10.2662	+	31.5962i	0.403919	+	1.24314i
$647$	14.0729	−	10.2245i	0.553261	−	0.401968i	−0.275725	−	0.961237i	$-0.588918\pi$
$647$	14.0729	−	10.2245i	0.553261	−	0.401968i	0.828987	+	0.559269i	$0.188918\pi$
$648$	−3.53287			−0.138784
$649$	2.37030	+	11.3457i	0.0930425	+	0.445357i
$650$	−3.84166			−0.150682
$651$		0			0
$652$	−1.64265	−	5.05556i	−0.0643311	−	0.197991i
$653$	−3.19877	+	9.84481i	−0.125178	+	0.385257i	−0.993933	−	0.109984i	$-0.964920\pi$
$653$	−3.19877	+	9.84481i	−0.125178	+	0.385257i	0.868756	+	0.495241i	$0.164920\pi$
$654$	−11.7114	−	8.50883i	−0.457952	−	0.332721i
$655$	45.2792	+	32.8973i	1.76921	+	1.28540i
$656$	−4.15269	+	12.7807i	−0.162135	+	0.499001i
$657$	4.28646	+	13.1924i	0.167231	+	0.514683i
$658$		0			0
$659$	−12.5897			−0.490427			−0.245213	−	0.969469i	$-0.578858\pi$
$659$	−12.5897			−0.490427			−0.245213	+	0.969469i	$0.578858\pi$
$660$	6.26341	+	0.680388i	0.243803	+	0.0264841i
$661$	4.77924			0.185891			0.0929454	−	0.995671i	$-0.470372\pi$
$661$	4.77924			0.185891			0.0929454	+	0.995671i	$0.470372\pi$
$662$	−2.53817	+	1.84409i	−0.0986486	+	0.0716724i
$663$	2.37069	+	7.29623i	0.0920699	+	0.283362i
$664$	−3.89902	+	11.9999i	−0.151311	+	0.465688i
$665$		0			0
$666$	0.943656	+	0.685606i	0.0365659	+	0.0265667i
$667$	−10.2720	+	31.6141i	−0.397735	+	1.22410i
$668$	1.53236	+	4.71613i	0.0592890	+	0.182473i
$669$	−9.58371	+	6.96297i	−0.370527	+	0.269204i
$670$	9.17833			0.354590
$671$	−33.3405	−	3.62175i	−1.28710	−	0.139816i
$672$		0			0
$673$	28.7700	−	20.9026i	1.10900	−	0.805736i	0.126495	−	0.991967i	$-0.459627\pi$
$673$	28.7700	−	20.9026i	1.10900	−	0.805736i	0.982506	+	0.186231i	$0.0596274\pi$
$674$	−9.07994	−	27.9452i	−0.349746	−	1.07641i
$675$	3.85845	−	11.8751i	0.148512	−	0.457072i
$676$	−6.34778	−	4.61193i	−0.244145	−	0.177382i
$677$	8.74175	+	6.35125i	0.335973	+	0.244098i	0.742961	−	0.669335i	$-0.233421\pi$
$677$	8.74175	+	6.35125i	0.335973	+	0.244098i	−0.406988	+	0.913434i	$0.633421\pi$
$678$	4.92630	−	15.1616i	0.189193	−	0.582277i
$679$		0			0
$680$	−39.4773	+	28.6820i	−1.51389	+	1.09990i
$681$	12.2118			0.467955
$682$	3.68008	+	17.6151i	0.140918	+	0.674516i
$683$	−17.2892			−0.661555			−0.330777	−	0.943709i	$-0.607311\pi$
$683$	−17.2892			−0.661555			−0.330777	+	0.943709i	$0.607311\pi$
$684$	−5.77131	+	4.19310i	−0.220672	+	0.160327i
$685$	4.53844	+	13.9679i	0.173405	+	0.533685i
$686$		0			0
$687$	−0.00901234	−	0.00654785i	−0.000343842	−	0.000249816i
$688$	7.34564	+	5.33692i	0.280050	+	0.203468i
$689$	5.06811	−	15.5980i	0.193080	−	0.594238i
$690$	6.05710	+	18.6418i	0.230590	+	0.709682i
$691$	4.55799	−	3.31157i	0.173394	−	0.125978i	−0.497703	−	0.867347i	$-0.665823\pi$
$691$	4.55799	−	3.31157i	0.173394	−	0.125978i	0.671098	+	0.741369i	$0.265823\pi$
$692$	−5.57006			−0.211742
$693$		0			0
$694$	−13.6984			−0.519983
$695$	40.1359	−	29.1604i	1.52244	−	1.10612i
$696$	−4.93512	−	15.1887i	−0.187065	−	0.575728i
$697$	11.3889	−	35.0515i	0.431386	−	1.32767i
$698$	8.78726	+	6.38432i	0.332603	+	0.241650i
$699$	−20.8490	−	15.1477i	−0.788581	−	0.572938i
$700$		0			0
$701$	−5.50103	−	16.9304i	−0.207771	−	0.639454i	−0.999588	−	0.0286955i	$-0.990865\pi$
$701$	−5.50103	−	16.9304i	−0.207771	−	0.639454i	0.791817	−	0.610758i	$-0.209135\pi$
$702$	6.14331	−	4.46338i	0.231864	−	0.168459i
$703$	2.55135			0.0962259
$704$	−11.5503	+	25.7009i	−0.435318	+	0.968641i
$705$	15.6270			0.588547
$706$	−10.9187	+	7.93293i	−0.410932	+	0.298560i
$707$		0			0
$708$	−0.748407	+	2.30336i	−0.0281269	+	0.0865656i
$709$	−17.1604	−	12.4677i	−0.644471	−	0.468236i	0.216912	−	0.976191i	$-0.430402\pi$
$709$	−17.1604	−	12.4677i	−0.644471	−	0.468236i	−0.861383	+	0.507955i	$0.830402\pi$
$710$	−38.0110	−	27.6166i	−1.42653	−	1.03643i
$711$	−2.01542	+	6.20282i	−0.0755841	+	0.232624i
$712$	12.5802	+	38.7178i	0.471462	+	1.45101i
$713$	24.4118	−	17.7362i	0.914228	−	0.664226i
$714$		0			0
$715$	10.5774	−	6.05782i	0.395573	−	0.226550i
$716$	−11.2368			−0.419941
$717$	11.6219	−	8.44381i	0.434028	−	0.315340i
$718$	−10.6033	−	32.6335i	−0.395710	−	1.21787i
$719$	1.40481	−	4.32355i	0.0523905	−	0.161241i	−0.921438	−	0.388525i	$-0.872985\pi$
$719$	1.40481	−	4.32355i	0.0523905	−	0.161241i	0.973829	+	0.227284i	$0.0729846\pi$
$720$	9.45004	+	6.86586i	0.352182	+	0.255875i
$721$		0			0
$722$	2.25332	−	6.93500i	0.0838598	−	0.258094i
$723$	4.17136	+	12.8381i	0.155135	+	0.477456i
$724$	−10.8952	+	7.91580i	−0.404916	+	0.294189i
$725$	−13.1780			−0.489417
$726$	11.3696	−	4.96741i	0.421966	−	0.184358i
$727$	−27.7173			−1.02798			−0.513989	−	0.857796i	$-0.671833\pi$
$727$	−27.7173			−1.02798			−0.513989	+	0.857796i	$0.671833\pi$
$728$		0			0
$729$	3.84017	+	11.8188i	0.142228	+	0.437734i
$730$	6.62743	−	20.3971i	0.245292	−	0.754932i
$731$	−20.1457	−	14.6367i	−0.745116	−	0.541358i
$732$	−5.66925	−	4.11895i	−0.209541	−	0.152241i
$733$	−13.7609	+	42.3516i	−0.508270	+	1.56429i	0.286933	+	0.957951i	$0.407364\pi$
$733$	−13.7609	+	42.3516i	−0.508270	+	1.56429i	−0.795203	+	0.606343i	$0.792636\pi$
$734$	5.71108	+	17.5769i	0.210800	+	0.648775i
$735$		0			0
$736$	23.7944			0.877074
$737$	−8.45362	+	4.84150i	−0.311393	+	0.178339i
$738$	−14.6836			−0.540510
$739$	−7.85549	+	5.70735i	−0.288969	+	0.209948i	−0.722820	−	0.691036i	$-0.757154\pi$
$739$	−7.85549	+	5.70735i	−0.288969	+	0.209948i	0.433851	+	0.900985i	$0.357154\pi$
$740$	0.300359	+	0.924411i	0.0110414	+	0.0339820i
$741$	2.06595	−	6.35835i	0.0758946	−	0.233580i
$742$		0			0
$743$	11.7326	+	8.52421i	0.430426	+	0.312723i	0.781819	−	0.623505i	$-0.214292\pi$
$743$	11.7326	+	8.52421i	0.430426	+	0.312723i	−0.351393	+	0.936228i	$0.614292\pi$
$744$	−4.47986	+	13.7876i	−0.164240	+	0.505478i
$745$	−10.5083	−	32.3412i	−0.384994	−	1.18489i
$746$	12.1988	−	8.86294i	0.446629	−	0.324495i
$747$	−8.28346			−0.303076
$748$	5.50672	−	12.2532i	0.201346	−	0.448021i
$749$		0			0
$750$	6.21981	−	4.51896i	0.227115	−	0.165009i
$751$	8.71413	+	26.8193i	0.317983	+	0.978651i	0.974509	+	0.224348i	$0.0720252\pi$
$751$	8.71413	+	26.8193i	0.317983	+	0.978651i	−0.656526	+	0.754303i	$0.727975\pi$
$752$	−3.75443	+	11.5549i	−0.136910	+	0.421365i
$753$	17.3154	+	12.5804i	0.631008	+	0.458454i
$754$	−6.48367	−	4.71066i	−0.236121	−	0.171552i
$755$	8.57779	−	26.3997i	0.312178	−	0.960784i
$756$		0			0
$757$	−7.21211	+	5.23991i	−0.262129	+	0.190448i	−0.711085	−	0.703106i	$-0.751796\pi$
$757$	−7.21211	+	5.23991i	−0.262129	+	0.190448i	0.448956	+	0.893554i	$0.351796\pi$
$758$	18.4019			0.668386
$759$	−15.4123	−	13.9748i	−0.559430	−	0.507254i
$760$	42.5242			1.54251
$761$	21.7105	−	15.7736i	0.787006	−	0.571793i	−0.120067	−	0.992766i	$-0.538311\pi$
$761$	21.7105	−	15.7736i	0.787006	−	0.571793i	0.907073	+	0.420972i	$0.138311\pi$
$762$	−3.77800	−	11.6275i	−0.136863	−	0.421220i
$763$		0			0
$764$	−1.01405	−	0.736751i	−0.0366871	−	0.0266547i
$765$	−25.9171	−	18.8299i	−0.937035	−	0.680796i
$766$	−0.598579	+	1.84224i	−0.0216275	+	0.0665627i
$767$	1.44797	+	4.45638i	0.0522830	+	0.160911i
$768$	−11.6129	+	8.43730i	−0.419046	+	0.304455i
$769$	34.8673			1.25735			0.628674	−	0.777669i	$-0.283598\pi$
$769$	34.8673			1.25735			0.628674	+	0.777669i	$0.283598\pi$
$770$		0			0
$771$	−19.9298			−0.717756
$772$	5.29547	−	3.84739i	0.190588	−	0.138470i
$773$	−3.34141	−	10.2838i	−0.120182	−	0.369883i	0.872810	−	0.488059i	$-0.162295\pi$
$773$	−3.34141	−	10.2838i	−0.120182	−	0.369883i	−0.992993	+	0.118177i	$0.962295\pi$
$774$	−3.06577	+	9.43546i	−0.110197	+	0.339151i
$775$	9.67772	+	7.03128i	0.347634	+	0.252571i
$776$	32.7147	+	23.7686i	1.17439	+	0.853245i
$777$		0			0
$778$	8.57208	+	26.3822i	0.307324	+	0.945846i
$779$	−25.9838	+	18.8784i	−0.930967	+	0.676387i
$780$	2.54699			0.0911968
$781$	49.5772	+	5.38553i	1.77401	+	0.192709i
$782$	41.7946			1.49457
$783$	21.0733	−	15.3106i	0.753098	−	0.547158i
$784$		0			0
$785$	15.9712	−	49.1544i	0.570037	−	1.75439i
$786$	18.6324	+	13.5373i	0.664597	+	0.482858i
$787$	−3.76240	−	2.73354i	−0.134115	−	0.0974403i	0.518705	−	0.854953i	$-0.326414\pi$
$787$	−3.76240	−	2.73354i	−0.134115	−	0.0974403i	−0.652820	+	0.757513i	$0.726414\pi$
$788$	4.13575	−	12.7285i	0.147330	−	0.453435i
$789$	−2.54991	−	7.84782i	−0.0907792	−	0.279390i
$790$	8.15806	−	5.92718i	0.290251	−	0.210880i
$791$		0			0
$792$	−20.5141	−	2.22843i	−0.728938	−	0.0791839i
$793$	−13.5578			−0.481451
$794$	6.13144	−	4.45475i	0.217597	−	0.158093i
$795$	−10.2514	−	31.5506i	−0.363580	−	1.11898i
$796$	3.46058	−	10.6506i	0.122657	−	0.377499i
$797$	18.2057	+	13.2272i	0.644878	+	0.468531i	0.861523	−	0.507719i	$-0.169511\pi$
$797$	18.2057	+	13.2272i	0.644878	+	0.468531i	−0.216645	+	0.976251i	$0.569511\pi$
$798$		0			0
$799$	10.2967	−	31.6899i	0.364270	−	1.12111i
$800$	2.91495	+	8.97130i	0.103059	+	0.317183i
$801$	−21.6222	+	15.7095i	−0.763985	+	0.555067i
$802$	3.41055			0.120431
$803$	4.65519	+	22.2825i	0.164278	+	0.786333i
$804$	−2.03559			−0.0717897
$805$		0			0
$806$	2.24809	+	6.91889i	0.0791854	+	0.243708i
$807$	1.32587	−	4.08061i	0.0466728	−	0.143644i
$808$	−6.06872	−	4.40918i	−0.213497	−	0.155114i
$809$	30.4965	+	22.1570i	1.07220	+	0.778998i	0.976306	−	0.216394i	$-0.0694296\pi$
$809$	30.4965	+	22.1570i	1.07220	+	0.778998i	0.0958921	+	0.995392i	$0.469430\pi$
$810$	−1.10814	+	3.41051i	−0.0389361	+	0.119833i
$811$	8.90145	+	27.3959i	0.312572	+	0.961998i	0.976742	+	0.214417i	$0.0687851\pi$
$811$	8.90145	+	27.3959i	0.312572	+	0.961998i	−0.664170	+	0.747582i	$0.731215\pi$
$812$		0			0
$813$	−23.5276			−0.825148
$814$	1.41804	+	1.28578i	0.0497021	+	0.0450666i
$815$	−20.8027			−0.728688
$816$	−9.76051	+	7.09142i	−0.341686	+	0.248250i
$817$	6.70583	+	20.6384i	0.234607	+	0.722047i
$818$	1.44575	−	4.44956i	0.0505495	−	0.155575i
$819$		0			0
$820$	−9.89902	−	7.19206i	−0.345689	−	0.251158i
$821$	17.2425	−	53.0671i	0.601769	−	1.85205i	0.0841285	−	0.996455i	$-0.473189\pi$
$821$	17.2425	−	53.0671i	0.601769	−	1.85205i	0.517640	−	0.855598i	$-0.326811\pi$
$822$	1.86757	+	5.74779i	0.0651390	+	0.200477i
$823$	−5.07223	+	3.68519i	−0.176807	+	0.128458i	−0.672669	−	0.739944i	$-0.734852\pi$
$823$	−5.07223	+	3.68519i	−0.176807	+	0.128458i	0.495862	+	0.868401i	$0.334852\pi$
$824$	30.5654			1.06480
$825$	3.38089	−	7.52294i	0.117708	−	0.261915i
$826$		0			0
$827$	2.01329	−	1.46274i	0.0700090	−	0.0508645i	−0.552230	−	0.833692i	$-0.686223\pi$
$827$	2.01329	−	1.46274i	0.0700090	−	0.0508645i	0.622239	+	0.782827i	$0.286223\pi$
$828$	2.77326	+	8.53522i	0.0963775	+	0.296619i
$829$	1.24365	−	3.82758i	0.0431939	−	0.132937i	−0.927134	−	0.374730i	$-0.877735\pi$
$829$	1.24365	−	3.82758i	0.0431939	−	0.132937i	0.970328	+	0.241793i	$0.0777354\pi$
$830$	10.3613	+	7.52795i	0.359647	+	0.261299i
$831$	5.59154	+	4.06249i	0.193968	+	0.140926i
$832$	−3.52004	+	10.8336i	−0.122035	+	0.375586i
$833$		0			0
$834$	16.5160	−	11.9995i	0.571901	−	0.415510i
$835$	19.4061			0.671575
$836$	−10.1588	+	5.81808i	−0.351350	+	0.201222i
$837$	−23.6451			−0.817296
$838$	5.77549	−	4.19614i	0.199511	−	0.144953i
$839$	−0.549555	−	1.69136i	−0.0189727	−	0.0583921i	0.941122	−	0.338067i	$-0.109773\pi$
$839$	−0.549555	−	1.69136i	−0.0189727	−	0.0583921i	−0.960095	+	0.279675i	$0.909773\pi$
$840$		0			0
$841$	1.22069	+	0.886880i	0.0420926	+	0.0305821i
$842$	12.5297	+	9.10336i	0.431802	+	0.313722i
$843$	−0.812714	+	2.50128i	−0.0279914	+	0.0861486i
$844$	−3.22699	−	9.93165i	−0.111078	−	0.341862i
$845$	−24.8416	+	18.0485i	−0.854577	+	0.620886i
$846$	−13.2754			−0.456416
$847$		0			0
$848$	25.7921			0.885704
$849$	−14.2979	+	10.3880i	−0.490702	+	0.356516i
$850$	5.12008	+	15.7580i	0.175617	+	0.540494i
$851$	0.991845	−	3.05259i	0.0340000	−	0.104641i
$852$	8.43016	+	6.12487i	0.288813	+	0.209835i
$853$	−37.9437	−	27.5677i	−1.29917	−	0.943901i	−0.299222	−	0.954184i	$-0.596727\pi$
$853$	−37.9437	−	27.5677i	−1.29917	−	0.943901i	−0.999947	+	0.0102821i	$0.996727\pi$
$854$		0			0
$855$	8.62694	+	26.5510i	0.295035	+	0.908025i
$856$	−11.0723	+	8.04450i	−0.378444	+	0.274955i
$857$	−57.2798			−1.95664			−0.978320	−	0.207101i	$-0.933597\pi$
$857$	−57.2798			−1.95664			−0.978320	+	0.207101i	$0.933597\pi$
$858$	4.35261	−	2.49280i	0.148596	−	0.0851027i
$859$	53.9917			1.84217			0.921087	−	0.389358i	$-0.127303\pi$
$859$	53.9917			1.84217			0.921087	+	0.389358i	$0.127303\pi$
$860$	−6.68832	+	4.85935i	−0.228070	+	0.165702i
$861$		0			0
$862$	−2.37347	+	7.30478i	−0.0808406	+	0.248802i
$863$	21.2043	+	15.4058i	0.721804	+	0.524421i	0.886960	−	0.461846i	$-0.152813\pi$
$863$	21.2043	+	15.4058i	0.721804	+	0.524421i	−0.165156	+	0.986267i	$0.552813\pi$
$864$	−15.0846	−	10.9596i	−0.513188	−	0.372853i
$865$	−6.73596	+	20.7312i	−0.229030	+	0.704881i
$866$	−12.4531	−	38.3267i	−0.423174	−	1.30239i
$867$	13.1606	−	9.56176i	0.446959	−	0.324734i
$868$		0			0
$869$	−4.38737	+	9.76249i	−0.148831	+	0.331170i
$870$	−16.2107			−0.549593
$871$	−3.18617	+	2.31489i	−0.107959	+	0.0784369i
$872$	12.2090	+	37.5753i	0.413448	+	1.27246i
$873$	−8.20364	+	25.2482i	−0.277651	+	0.854523i
$874$	−29.4662	−	21.4084i	−0.996708	−	0.724151i
$875$		0			0
$876$	−1.46985	+	4.52372i	−0.0496615	+	0.152842i
$877$	0.151880	+	0.467438i	0.00512862	+	0.0157843i	0.953588	−	0.301114i	$-0.0973585\pi$
$877$	0.151880	+	0.467438i	0.00512862	+	0.0157843i	−0.948459	+	0.316898i	$0.897359\pi$
$878$	4.56674	−	3.31793i	0.154120	−	0.111975i
$879$	23.2391			0.783837
$880$	14.2006	+	12.8762i	0.478702	+	0.434056i
$881$	38.3713			1.29276			0.646381	−	0.763015i	$-0.276282\pi$
$881$	38.3713			1.29276			0.646381	+	0.763015i	$0.276282\pi$
$882$		0			0
$883$	−11.2952	−	34.7631i	−0.380114	−	1.16987i	−0.939963	−	0.341276i	$-0.889141\pi$
$883$	−11.2952	−	34.7631i	−0.380114	−	1.16987i	0.559849	−	0.828594i	$-0.310859\pi$
$884$	1.67821	−	5.16501i	0.0564445	−	0.173718i
$885$	7.66780	+	5.57099i	0.257750	+	0.187267i
$886$	22.2390	+	16.1576i	0.747134	+	0.542825i
$887$	−1.40059	+	4.31059i	−0.0470274	+	0.144735i	−0.971813	−	0.235753i	$-0.924244\pi$
$887$	−1.40059	+	4.31059i	−0.0470274	+	0.144735i	0.924786	+	0.380489i	$0.124244\pi$
$888$	0.476524	+	1.46659i	0.0159911	+	0.0492155i
$889$		0			0
$890$	41.3228			1.38514
$891$	−0.778372	−	3.72575i	−0.0260764	−	0.124817i
$892$	8.38588			0.280780
$893$	−23.4919	+	17.0678i	−0.786125	+	0.571153i
$894$	−4.32418	−	13.3084i	−0.144622	−	0.445101i
$895$	−13.5889	+	41.8224i	−0.454227	+	1.39797i
$896$		0			0
$897$	−6.80436	−	4.94366i	−0.227191	−	0.165064i
$898$	6.72837	−	20.7078i	0.224529	−	0.691029i
$899$	7.71156	+	23.7338i	0.257195	+	0.791565i
$900$	−2.87833	+	2.09123i	−0.0959442	+	0.0697076i
$901$	−70.7358			−2.35655
$902$	−23.9557	−	2.60229i	−0.797638	−	0.0866467i
$903$		0			0
$904$	−35.1999	+	25.5742i	−1.17073	+	0.850586i
$905$	16.2861	+	50.1234i	0.541367	+	1.66616i
$906$	3.52977	−	10.8635i	0.117269	−	0.360916i
$907$	1.70377	+	1.23786i	0.0565728	+	0.0411025i	0.615712	−	0.787971i	$-0.288868\pi$
$907$	1.70377	+	1.23786i	0.0565728	+	0.0411025i	−0.559139	+	0.829074i	$0.688868\pi$
$908$	−6.99373	−	5.08124i	−0.232095	−	0.168627i
$909$	1.52181	−	4.68365i	0.0504752	−	0.155347i
$910$		0			0
$911$	32.2324	−	23.4182i	1.06791	−	0.775879i	0.0923709	−	0.995725i	$-0.470555\pi$
$911$	32.2324	−	23.4182i	1.06791	−	0.775879i	0.975535	+	0.219846i	$0.0705554\pi$
$912$	10.5138			0.348147
$913$	−13.5142	−	1.46803i	−0.447253	−	0.0485847i
$914$	−29.3464			−0.970692
$915$	−22.1862	+	16.1192i	−0.733454	+	0.532885i
$916$	0.00243689	+	0.00749996i	8.05170e−5	+	0.000247806i
$917$		0			0
$918$	−26.4959	−	19.2504i	−0.874494	−	0.635357i
$919$	5.11174	+	3.71390i	0.168621	+	0.122510i	0.668895	−	0.743357i	$-0.266768\pi$
$919$	5.11174	+	3.71390i	0.168621	+	0.122510i	−0.500274	+	0.865867i	$0.666768\pi$
$920$	16.5314	−	50.8785i	0.545025	−	1.67741i
$921$	−6.51642	−	20.0555i	−0.214723	−	0.660851i
$922$	9.79604	−	7.11724i	0.322615	−	0.234394i
$923$	20.1604			0.663587
$924$		0			0
$925$	1.27243			0.0418374
$926$	7.11484	−	5.16923i	0.233808	−	0.169871i
$927$	6.20084	+	19.0842i	0.203662	+	0.626809i
$928$	−6.08101	+	18.7154i	−0.199619	+	0.614364i
$929$	26.9217	+	19.5598i	0.883274	+	0.641736i	0.934116	−	0.356971i	$-0.116190\pi$
$929$	26.9217	+	19.5598i	0.883274	+	0.641736i	−0.0508418	+	0.998707i	$0.516190\pi$
$930$	11.9049	+	8.64941i	0.390377	+	0.283625i
$931$		0			0
$932$	5.63745	+	17.3503i	0.184661	+	0.568328i
$933$	−0.301386	+	0.218970i	−0.00986694	+	0.00716875i
$934$	16.5676			0.542110
$935$	−38.9457	−	35.3134i	−1.27366	−	1.15487i
$936$	−8.34199			−0.272666
$937$	−3.06895	+	2.22972i	−0.100258	+	0.0728419i	−0.636785	−	0.771041i	$-0.719736\pi$
$937$	−3.06895	+	2.22972i	−0.100258	+	0.0728419i	0.536527	+	0.843883i	$0.319736\pi$
$938$		0			0
$939$	2.43783	−	7.50286i	0.0795555	−	0.244847i
$940$	−8.94966	−	6.50231i	−0.291906	−	0.212082i
$941$	19.2071	+	13.9548i	0.626135	+	0.454913i	0.855059	−	0.518531i	$-0.173521\pi$
$941$	19.2071	+	13.9548i	0.626135	+	0.454913i	−0.228924	+	0.973444i	$0.573521\pi$
$942$	6.57217	−	20.2271i	0.214133	−	0.659033i
$943$	12.4859	+	38.4276i	0.406596	+	1.25138i
$944$	−5.96151	+	4.33129i	−0.194031	+	0.140972i
$945$		0			0
$946$	−6.67388	+	14.8503i	−0.216987	+	0.482824i
$947$	23.0611			0.749385			0.374692	−	0.927149i	$-0.377748\pi$
$947$	23.0611			0.749385			0.374692	+	0.927149i	$0.377748\pi$
$948$	−1.80931	+	1.31454i	−0.0587638	+	0.0426944i
$949$	2.84376	+	8.75218i	0.0923122	+	0.284108i
$950$	4.46192	−	13.7324i	0.144764	−	0.445538i
$951$	10.9984	+	7.99083i	0.356648	+	0.259120i
$952$		0			0
$953$	4.50052	−	13.8512i	0.145786	−	0.448684i	−0.851325	−	0.524639i	$-0.824200\pi$
$953$	4.50052	−	13.8512i	0.145786	−	0.448684i	0.997111	+	0.0759548i	$0.0242005\pi$
$954$	8.70871	+	26.8026i	0.281955	+	0.867768i
$955$	−3.96842	+	2.88323i	−0.128415	+	0.0932990i
$956$	−10.1693			−0.328900
$957$	14.9307	−	8.55100i	0.482641	−	0.276414i
$958$	−32.7259			−1.05733
$959$		0			0
$960$	7.12008	+	21.9133i	0.229799	+	0.707250i
$961$	−2.57934	+	7.93840i	−0.0832046	+	0.256077i
$962$	0.626048	+	0.454851i	0.0201846	+	0.0146650i
$963$	−7.26903	−	5.28126i	−0.234241	−	0.170186i
$964$	2.95292	−	9.08814i	0.0951070	−	0.292709i
$965$	−7.91566	−	24.3619i	−0.254814	−	0.784237i
$966$		0			0
$967$	41.4551			1.33311			0.666553	−	0.745458i	$-0.267769\pi$
$967$	41.4551			1.33311			0.666553	+	0.745458i	$0.267769\pi$
$968$	−33.0731	−	7.27122i	−1.06301	−	0.233706i
$969$	−28.8346			−0.926300
$970$	33.2069	−	24.1262i	1.06621	−	0.774647i
$971$	−12.4559	−	38.3352i	−0.399727	−	1.23023i	−0.925218	−	0.379435i	$-0.876118\pi$
$971$	−12.4559	−	38.3352i	−0.399727	−	1.23023i	0.525491	−	0.850799i	$-0.323882\pi$
$972$	3.47159	−	10.6845i	0.111351	−	0.342704i
$973$		0			0
$974$	−19.7667	−	14.3613i	−0.633366	−	0.460167i
$975$	1.03035	−	3.17110i	0.0329977	−	0.101556i
$976$	−6.58860	−	20.2776i	−0.210896	−	0.649071i
$977$	−8.06552	+	5.85995i	−0.258039	+	0.187476i	−0.709282	−	0.704925i	$-0.750981\pi$
$977$	−8.06552	+	5.85995i	−0.258039	+	0.187476i	0.451243	+	0.892401i	$0.350981\pi$
$978$	−8.56034			−0.273730
$979$	−38.0600	+	21.7975i	−1.21640	+	0.696650i
$980$		0			0
$981$	−20.9842	+	15.2459i	−0.669974	+	0.486765i
$982$	−8.34859	−	25.6943i	−0.266414	−	0.819938i
$983$	9.43624	−	29.0418i	0.300969	−	0.926289i	−0.680181	−	0.733044i	$-0.738099\pi$
$983$	9.43624	−	29.0418i	0.300969	−	0.926289i	0.981151	−	0.193245i	$-0.0619011\pi$
$984$	−15.7049	−	11.4103i	−0.500654	−	0.363747i
$985$	−42.3728	−	30.7857i	−1.35011	−	0.980913i
$986$	−10.6812	+	32.8734i	−0.340160	+	1.04690i
$987$		0			0
$988$	−3.82885	+	2.78182i	−0.121812	+	0.0885016i
$989$	27.3000			0.868088
$990$	−8.58584	+	19.1046i	−0.272876	+	0.607186i
$991$	−43.0156			−1.36644			−0.683218	−	0.730214i	$-0.739420\pi$
$991$	−43.0156			−1.36644			−0.683218	+	0.730214i	$0.739420\pi$
$992$	14.4517	−	10.4998i	0.458841	−	0.333368i
$993$	−0.841452	−	2.58972i	−0.0267027	−	0.0821824i
$994$		0			0
$995$	−35.4553	−	25.7598i	−1.12401	−	0.816640i
$996$	−2.29796	−	1.66957i	−0.0728137	−	0.0529022i
$997$	6.55760	−	20.1822i	0.207681	−	0.639177i	−0.791911	−	0.610636i	$-0.790914\pi$
$997$	6.55760	−	20.1822i	0.207681	−	0.639177i	0.999593	−	0.0285413i	$-0.00908621\pi$
$998$	−6.47587	−	19.9307i	−0.204990	−	0.630894i
$999$	−2.03479	+	1.47836i	−0.0643779	+	0.0467733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.f.i.344.3	yes	48
7.2	even	3		539.2.q.i.410.10		96
7.3	odd	6		539.2.q.i.520.4		96
7.4	even	3		539.2.q.i.520.3		96
7.5	odd	6		539.2.q.i.410.9		96
7.6	odd	2	inner	539.2.f.i.344.4	yes	48
11.2	odd	10		5929.2.a.ch.1.5		24
11.4	even	5	inner	539.2.f.i.246.3	✓	48
11.9	even	5		5929.2.a.cg.1.19		24
77.4	even	15		539.2.q.i.422.10		96
77.13	even	10		5929.2.a.ch.1.6		24
77.20	odd	10		5929.2.a.cg.1.20		24
77.26	odd	30		539.2.q.i.312.4		96
77.37	even	15		539.2.q.i.312.3		96
77.48	odd	10	inner	539.2.f.i.246.4	yes	48
77.59	odd	30		539.2.q.i.422.9		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
539.2.f.i.246.3	✓	48	11.4	even	5	inner
539.2.f.i.246.4	yes	48	77.48	odd	10	inner
539.2.f.i.344.3	yes	48	1.1	even	1	trivial
539.2.f.i.344.4	yes	48	7.6	odd	2	inner
539.2.q.i.312.3		96	77.37	even	15
539.2.q.i.312.4		96	77.26	odd	30
539.2.q.i.410.9		96	7.5	odd	6
539.2.q.i.410.10		96	7.2	even	3
539.2.q.i.422.9		96	77.59	odd	30
539.2.q.i.422.10		96	77.4	even	15
539.2.q.i.520.3		96	7.4	even	3
539.2.q.i.520.4		96	7.3	odd	6
5929.2.a.cg.1.19		24	11.9	even	5
5929.2.a.cg.1.20		24	77.20	odd	10
5929.2.a.ch.1.5		24	11.2	odd	10
5929.2.a.ch.1.6		24	77.13	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.922272 + 0.670070i) q^{2} +(-0.305751 - 0.941006i) q^{3} +(-0.216442 + 0.666140i) q^{4} +(2.21755 + 1.61115i) q^{5} +(0.912526 + 0.662989i) q^{6} +(-0.951295 - 2.92778i) q^{8} +(1.63504 - 1.18793i) q^{9} -3.12477 q^{10} +(2.87804 - 1.64829i) q^{11} +0.693019 q^{12} +(1.08473 - 0.788105i) q^{13} +(0.838079 - 2.57934i) q^{15} +(1.70587 + 1.23939i) q^{16} +(-4.67841 - 3.39907i) q^{17} +(-0.711959 + 2.19119i) q^{18} +(1.55729 + 4.79284i) q^{19} +(-1.55322 + 1.12848i) q^{20} +(-1.54987 + 3.44866i) q^{22} +6.33984 q^{23} +(-2.46420 + 1.79035i) q^{24} +(0.776666 + 2.39033i) q^{25} +(-0.472334 + 1.45369i) q^{26} +(-4.01917 - 2.92010i) q^{27} +(-1.62024 + 4.98658i) q^{29} +(0.955403 + 2.94043i) q^{30} +(3.85054 - 2.79758i) q^{31} +3.75316 q^{32} +(-2.43102 - 2.20429i) q^{33} +6.59238 q^{34} +(0.437434 + 1.34628i) q^{36} +(0.156446 - 0.481493i) q^{37} +(-4.64778 - 3.37681i) q^{38} +(-1.07327 - 0.779776i) q^{39} +(2.60755 - 8.02520i) q^{40} +(1.96943 + 6.06129i) q^{41} +4.30610 q^{43} +(0.475064 + 2.27394i) q^{44} +5.53972 q^{45} +(-5.84705 + 4.24813i) q^{46} +(1.78056 + 5.47999i) q^{47} +(0.644698 - 1.98418i) q^{48} +(-2.31799 - 1.68412i) q^{50} +(-1.76811 + 5.44168i) q^{51} +(0.290206 + 0.893163i) q^{52} +(9.89592 - 7.18981i) q^{53} +5.66343 q^{54} +(9.03786 + 0.981775i) q^{55} +(4.03395 - 2.93083i) q^{57} +(-1.84706 - 5.68466i) q^{58} +(-1.07992 + 3.32366i) q^{59} +(1.53681 + 1.11656i) q^{60} +(-8.18051 - 5.94349i) q^{61} +(-1.67667 + 5.16026i) q^{62} +(-6.87317 + 4.99365i) q^{64} +3.67521 q^{65} +(3.71909 + 0.404001i) q^{66} -2.93728 q^{67} +(3.27686 - 2.38078i) q^{68} +(-1.93841 - 5.96582i) q^{69} +(12.1644 + 8.83796i) q^{71} +(-5.03341 - 3.65698i) q^{72} +(-2.12093 + 6.52756i) q^{73} +(0.178348 + 0.548897i) q^{74} +(2.01185 - 1.46169i) q^{75} -3.52976 q^{76} +1.51235 q^{78} +(-2.61077 + 1.89684i) q^{79} +(1.78602 + 5.49681i) q^{80} +(0.354631 - 1.09144i) q^{81} +(-5.87784 - 4.27050i) q^{82} +(-3.31587 - 2.40912i) q^{83} +(-4.89824 - 15.0752i) q^{85} +(-3.97139 + 2.88539i) q^{86} +5.18779 q^{87} +(-7.56371 - 6.85828i) q^{88} -13.2243 q^{89} +(-5.10913 + 3.71200i) q^{90} +(-1.37221 + 4.22322i) q^{92} +(-3.80984 - 2.76801i) q^{93} +(-5.31413 - 3.86094i) q^{94} +(-4.26860 + 13.1374i) q^{95} +(-1.14753 - 3.53175i) q^{96} +(-10.6270 + 7.72097i) q^{97} +(2.74767 - 6.11394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 16 q^{4} + 20 q^{8} - 8 q^{11} + 16 q^{15} - 20 q^{16} + 42 q^{18} - 4 q^{22} - 12 q^{25} - 80 q^{32} - 160 q^{36} + 20 q^{37} + 36 q^{39} - 56 q^{43} + 50 q^{44} + 22 q^{46} - 84 q^{50} + 60 q^{51}+ \cdots + 76 q^{99}+O(q^{100}) \) 48 * q - 16 * q^4 + 20 * q^8 - 8 * q^11 + 16 * q^15 - 20 * q^16 + 42 * q^18 - 4 * q^22 - 12 * q^25 - 80 * q^32 - 160 * q^36 + 20 * q^37 + 36 * q^39 - 56 * q^43 + 50 * q^44 + 22 * q^46 - 84 * q^50 + 60 * q^51 + 24 * q^53 - 36 * q^57 - 134 * q^58 - 40 * q^60 - 80 * q^64 - 128 * q^65 + 12 * q^71 - 154 * q^72 + 8 * q^74 + 312 * q^78 + 28 * q^79 + 36 * q^81 + 72 * q^85 - 38 * q^86 + 112 * q^88 + 98 * q^92 + 64 * q^93 + 48 * q^95 + 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more