LMFDB - Embedded newform 735.2.p.f.509.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [735,2,Mod(374,735)] 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("735.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(735, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.p (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [24,0,0] 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:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			509.6
Character	$\chi$	$=$	735.509
Dual form			735.2.p.f.374.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.322403 + 0.558418i) q^{2} +(-1.15761 + 1.28838i) q^{3} +(0.792113 + 1.37198i) q^{4} +(1.60193 - 1.56008i) q^{5} +(-0.346239 - 1.06181i) q^{6} -2.31113 q^{8} +(-0.319861 - 2.98290i) q^{9} +(0.354709 + 1.39752i) q^{10} +(3.51044 - 2.02675i) q^{11} +(-2.68460 - 0.567678i) q^{12} +4.21339 q^{13} +(0.155565 + 3.86986i) q^{15} +(-0.839111 + 1.45338i) q^{16} +(1.88498 - 1.08830i) q^{17} +(1.76883 + 0.783079i) q^{18} +(3.87634 + 2.23800i) q^{19} +(3.40930 + 0.962052i) q^{20} +2.61372i q^{22} +(0.322403 - 0.558418i) q^{23} +(2.67540 - 2.97762i) q^{24} +(0.132327 - 4.99825i) q^{25} +(-1.35841 + 2.35284i) q^{26} +(4.21339 + 3.04094i) q^{27} +1.16875i q^{29} +(-2.21115 - 1.16078i) q^{30} +(0.339111 - 0.195786i) q^{31} +(-2.85219 - 4.94014i) q^{32} +(-1.45250 + 6.86898i) q^{33} +1.40348i q^{34} +(3.83911 - 2.80164i) q^{36} +(-3.69236 - 2.13178i) q^{37} +(-2.49949 + 1.44308i) q^{38} +(-4.87748 + 5.42846i) q^{39} +(-3.70226 + 3.60554i) q^{40} -2.27971 q^{41} +6.54419i q^{43} +(5.56132 + 3.21083i) q^{44} +(-5.16594 - 4.27937i) q^{45} +(0.207887 + 0.360071i) q^{46} +(-6.75621 - 3.90070i) q^{47} +(-0.901147 - 2.76355i) q^{48} +(2.74845 + 1.68534i) q^{50} +(-0.779941 + 3.68841i) q^{51} +(3.33748 + 5.78069i) q^{52} +(3.60074 + 6.23667i) q^{53} +(-3.05653 + 1.37243i) q^{54} +(2.46157 - 8.72325i) q^{55} +(-7.37071 + 2.40346i) q^{57} +(-0.652654 - 0.376810i) q^{58} +(5.66247 + 9.80768i) q^{59} +(-5.18614 + 3.27880i) q^{60} +(-6.05456 - 3.49560i) q^{61} +0.252487i q^{62} +0.321779 q^{64} +(6.74954 - 6.57321i) q^{65} +(-3.36748 - 3.02568i) q^{66} +(7.56680 - 4.36870i) q^{67} +(2.98624 + 1.72411i) q^{68} +(0.346239 + 1.06181i) q^{69} +8.13766i q^{71} +(0.739241 + 6.89387i) q^{72} +(-2.61843 - 4.53525i) q^{73} +(2.38085 - 1.37459i) q^{74} +(6.28647 + 5.95653i) q^{75} +7.09101i q^{76} +(-1.45884 - 4.47383i) q^{78} +(-1.87634 + 3.24991i) q^{79} +(0.923194 + 3.63729i) q^{80} +(-8.79538 + 1.90823i) q^{81} +(0.734986 - 1.27303i) q^{82} +5.27461i q^{83} +(1.32178 - 4.68409i) q^{85} +(-3.65439 - 2.10987i) q^{86} +(-1.50580 - 1.35297i) q^{87} +(-8.11308 + 4.68409i) q^{88} +(0.447379 - 0.774883i) q^{89} +(4.05520 - 1.50507i) q^{90} +1.02152 q^{92} +(-0.140312 + 0.663548i) q^{93} +(4.35644 - 2.51519i) q^{94} +(9.70106 - 2.46227i) q^{95} +(9.66653 + 2.04406i) q^{96} -3.89968 q^{97} +(-7.16845 - 9.82300i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 6 q^{9} - 24 q^{15} - 12 q^{16} - 18 q^{24} - 12 q^{25} + 18 q^{30} + 84 q^{36} - 12 q^{39} + 72 q^{40} + 18 q^{45} + 36 q^{46} - 12 q^{51} + 36 q^{54} + 12 q^{60} - 36 q^{61} + 24 q^{64}+ \cdots - 48 q^{99}+O(q^{100}) $ 24 * q - 12 * q^4 - 6 * q^9 - 24 * q^15 - 12 * q^16 - 18 * q^24 - 12 * q^25 + 18 * q^30 + 84 * q^36 - 12 * q^39 + 72 * q^40 + 18 * q^45 + 36 * q^46 - 12 * q^51 + 36 * q^54 + 12 * q^60 - 36 * q^61 + 24 * q^64 + 72 * q^66 - 72 * q^75 + 48 * q^79 - 6 * q^81 + 48 * q^85 + 72 * q^94 + 90 * q^96 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$

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 $

$2$	−0.322403	+	0.558418i	−0.227973	+	0.394861i	−0.957207	−	0.289403i	$-0.906543\pi$
$2$	−0.322403	+	0.558418i	−0.227973	+	0.394861i	0.729234	+	0.684264i	$0.239877\pi$
$3$	−1.15761	+	1.28838i	−0.668349	+	0.743848i
$3$	−1.15761	+	1.28838i	−0.668349	+	0.743848i
$4$	0.792113	+	1.37198i	0.396056	+	0.685990i
$5$	1.60193	−	1.56008i	0.716403	−	0.697687i
$5$	1.60193	−	1.56008i	0.716403	−	0.697687i
$6$	−0.346239	−	1.06181i	−0.141351	−	0.433483i
$7$		0			0
$7$		0			0
$8$	−2.31113			−0.817108
$9$	−0.319861	−	2.98290i	−0.106620	−	0.994300i
$10$	0.354709	+	1.39752i	0.112169	+	0.441934i
$11$	3.51044	−	2.02675i	1.05844	−	0.611089i	0.133437	−	0.991057i	$-0.457398\pi$
$11$	3.51044	−	2.02675i	1.05844	−	0.611089i	0.924999	+	0.379968i	$0.124065\pi$
$12$	−2.68460	−	0.567678i	−0.774976	−	0.163874i
$13$	4.21339			1.16858			0.584292	−	0.811543i	$-0.301372\pi$
$13$	4.21339			1.16858			0.584292	+	0.811543i	$0.301372\pi$
$14$		0			0
$15$	0.155565	+	3.86986i	0.0401666	+	0.999193i
$16$	−0.839111	+	1.45338i	−0.209778	+	0.363346i
$17$	1.88498	−	1.08830i	0.457176	−	0.263951i	−0.253680	−	0.967288i	$-0.581641\pi$
$17$	1.88498	−	1.08830i	0.457176	−	0.263951i	0.710856	+	0.703338i	$0.248308\pi$
$18$	1.76883	+	0.783079i	0.416917	+	0.184574i
$19$	3.87634	+	2.23800i	0.889293	+	0.513434i	0.873711	−	0.486445i	$-0.161707\pi$
$19$	3.87634	+	2.23800i	0.889293	+	0.513434i	0.0155818	+	0.999879i	$0.495040\pi$
$20$	3.40930	+	0.962052i	0.762342	+	0.215121i
$21$		0			0
$22$			2.61372i			0.557248i
$23$	0.322403	−	0.558418i	0.0672257	−	0.116438i	−0.830453	−	0.557088i	$-0.811919\pi$
$23$	0.322403	−	0.558418i	0.0672257	−	0.116438i	0.897679	+	0.440650i	$0.145252\pi$
$24$	2.67540	−	2.97762i	0.546113	−	0.607804i
$25$	0.132327	−	4.99825i	0.0264655	−	0.999650i
$26$	−1.35841	+	2.35284i	−0.266406	+	0.461429i
$27$	4.21339	+	3.04094i	0.810868	+	0.585229i
$28$		0			0
$29$			1.16875i			0.217032i	0.994095	+	0.108516i	$0.0346099\pi$
$29$			1.16875i			0.217032i	−0.994095	+	0.108516i	$0.965390\pi$
$30$	−2.21115	−	1.16078i	−0.403700	−	0.211929i
$31$	0.339111	−	0.195786i	0.0609061	−	0.0351641i	−0.469238	−	0.883072i	$-0.655471\pi$
$31$	0.339111	−	0.195786i	0.0609061	−	0.0351641i	0.530144	+	0.847908i	$0.322138\pi$
$32$	−2.85219	−	4.94014i	−0.504201	−	0.873302i
$33$	−1.45250	+	6.86898i	−0.252847	+	1.19574i
$34$			1.40348i			0.240695i
$35$		0			0
$36$	3.83911	−	2.80164i	0.639852	−	0.466939i
$37$	−3.69236	−	2.13178i	−0.607020	−	0.350463i	0.164778	−	0.986331i	$-0.447309\pi$
$37$	−3.69236	−	2.13178i	−0.607020	−	0.350463i	−0.771798	+	0.635868i	$0.780642\pi$
$38$	−2.49949	+	1.44308i	−0.405470	+	0.234098i
$39$	−4.87748	+	5.42846i	−0.781022	+	0.869250i
$40$	−3.70226	+	3.60554i	−0.585378	+	0.570085i
$41$	−2.27971			−0.356031			−0.178016	−	0.984028i	$-0.556968\pi$
$41$	−2.27971			−0.356031			−0.178016	+	0.984028i	$0.556968\pi$
$42$		0			0
$43$			6.54419i			0.997980i	0.866608	+	0.498990i	$0.166295\pi$
$43$			6.54419i			0.997980i	−0.866608	+	0.498990i	$0.833705\pi$
$44$	5.56132	+	3.21083i	0.838401	+	0.484051i
$45$	−5.16594	−	4.27937i	−0.770093	−	0.637931i
$46$	0.207887	+	0.360071i	0.0306513	+	0.0530896i
$47$	−6.75621	−	3.90070i	−0.985494	−	0.568975i	−0.0815698	−	0.996668i	$-0.525993\pi$
$47$	−6.75621	−	3.90070i	−0.985494	−	0.568975i	−0.903924	+	0.427692i	$0.859327\pi$
$48$	−0.901147	−	2.76355i	−0.130069	−	0.398884i
$49$		0			0
$50$	2.74845	+	1.68534i	0.388690	+	0.238344i
$51$	−0.779941	+	3.68841i	−0.109214	+	0.516480i
$52$	3.33748	+	5.78069i	0.462825	+	0.801637i
$53$	3.60074	+	6.23667i	0.494600	+	0.856672i	0.999981	−	0.00622439i	$-0.00198130\pi$
$53$	3.60074	+	6.23667i	0.494600	+	0.856672i	−0.505381	+	0.862896i	$0.668648\pi$
$54$	−3.05653	+	1.37243i	−0.415941	+	0.186764i
$55$	2.46157	−	8.72325i	0.331918	−	1.17624i
$56$		0			0
$57$	−7.37071	+	2.40346i	−0.976274	+	0.318346i
$58$	−0.652654	−	0.376810i	−0.0856977	−	0.0494776i
$59$	5.66247	+	9.80768i	0.737190	+	1.27685i	0.953756	+	0.300583i	$0.0971812\pi$
$59$	5.66247	+	9.80768i	0.737190	+	1.27685i	−0.216566	+	0.976268i	$0.569485\pi$
$60$	−5.18614	+	3.27880i	−0.669528	+	0.423291i
$61$	−6.05456	−	3.49560i	−0.775207	−	0.447566i	0.0595220	−	0.998227i	$-0.481042\pi$
$61$	−6.05456	−	3.49560i	−0.775207	−	0.447566i	−0.834729	+	0.550661i	$0.814376\pi$
$62$			0.252487i			0.0320659i
$63$		0			0
$64$	0.321779			0.0402224
$65$	6.74954	−	6.57321i	0.837177	−	0.815307i
$66$	−3.36748	−	3.02568i	−0.414508	−	0.372436i
$67$	7.56680	−	4.36870i	0.924432	−	0.533721i	0.0393859	−	0.999224i	$-0.487460\pi$
$67$	7.56680	−	4.36870i	0.924432	−	0.533721i	0.885046	+	0.465503i	$0.154127\pi$
$68$	2.98624	+	1.72411i	0.362135	+	0.209079i
$69$	0.346239	+	1.06181i	0.0416822	+	0.127827i
$70$		0			0
$71$			8.13766i			0.965762i	0.875686	+	0.482881i	$0.160410\pi$
$71$			8.13766i			0.965762i	−0.875686	+	0.482881i	$0.839590\pi$
$72$	0.739241	+	6.89387i	0.0871204	+	0.812450i
$73$	−2.61843	−	4.53525i	−0.306464	−	0.530810i	0.671123	−	0.741346i	$-0.265812\pi$
$73$	−2.61843	−	4.53525i	−0.306464	−	0.530810i	−0.977586	+	0.210536i	$0.932479\pi$
$74$	2.38085	−	1.37459i	0.276769	−	0.159792i
$75$	6.28647	+	5.95653i	0.725900	+	0.687801i
$76$			7.09101i			0.813394i
$77$		0			0
$78$	−1.45884	−	4.47383i	−0.165181	−	0.506561i
$79$	−1.87634	+	3.24991i	−0.211105	+	0.365644i	−0.952060	−	0.305910i	$-0.901039\pi$
$79$	−1.87634	+	3.24991i	−0.211105	+	0.365644i	0.740956	+	0.671554i	$0.234373\pi$
$80$	0.923194	+	3.63729i	0.103216	+	0.406661i
$81$	−8.79538	+	1.90823i	−0.977264	+	0.212025i
$82$	0.734986	−	1.27303i	0.0811656	−	0.140583i
$83$			5.27461i			0.578964i	0.957183	+	0.289482i	$0.0934831\pi$
$83$			5.27461i			0.578964i	−0.957183	+	0.289482i	$0.906517\pi$
$84$		0			0
$85$	1.32178	−	4.68409i	0.143367	−	0.508061i
$86$	−3.65439	−	2.10987i	−0.394064	−	0.227513i
$87$	−1.50580	−	1.35297i	−0.161439	−	0.145053i
$88$	−8.11308	+	4.68409i	−0.864857	+	0.499325i
$89$	0.447379	−	0.774883i	0.0474221	−	0.0821375i	−0.841340	−	0.540506i	$-0.818233\pi$
$89$	0.447379	−	0.774883i	0.0474221	−	0.0821375i	0.888762	+	0.458369i	$0.151566\pi$
$90$	4.05520	−	1.50507i	0.427455	−	0.158649i
$91$		0			0
$92$	1.02152			0.106501
$93$	−0.140312	+	0.663548i	−0.0145497	+	0.0688068i
$94$	4.35644	−	2.51519i	0.449333	−	0.259422i
$95$	9.70106	−	2.46227i	0.995308	−	0.252623i
$96$	9.66653	+	2.04406i	0.986586	+	0.208621i
$97$	−3.89968			−0.395953			−0.197976	−	0.980207i	$-0.563437\pi$
$97$	−3.89968			−0.395953			−0.197976	+	0.980207i	$0.563437\pi$
$98$		0			0
$99$	−7.16845	−	9.82300i	−0.720456	−	0.987249i
$100$	6.96231	−	3.77763i	0.696231	−	0.377763i
$101$	3.29188	+	5.70171i	0.327555	+	0.567341i	0.982026	−	0.188745i	$-0.0604421\pi$
$101$	3.29188	+	5.70171i	0.327555	+	0.567341i	−0.654471	+	0.756087i	$0.727109\pi$
$102$	−1.80822	−	1.62469i	−0.179040	−	0.160868i
$103$	4.90721	−	8.49954i	0.483522	−	0.837485i	−0.516299	−	0.856408i	$-0.672691\pi$
$103$	4.90721	−	8.49954i	0.483522	−	0.837485i	0.999821	+	0.0189238i	$0.00602398\pi$
$104$	−9.73770			−0.954860
$105$		0			0
$106$	−4.64356			−0.451022
$107$	−9.38974	+	16.2635i	−0.907740	+	1.57225i	−0.0905447	+	0.995892i	$0.528861\pi$
$107$	−9.38974	+	16.2635i	−0.907740	+	1.57225i	−0.817196	+	0.576360i	$0.804473\pi$
$108$	−0.834627	+	8.18946i	−0.0803120	+	0.788031i
$109$	−0.453002	−	0.784623i	−0.0433897	−	0.0751532i	0.843515	−	0.537106i	$-0.180482\pi$
$109$	−0.453002	−	0.784623i	−0.0433897	−	0.0751532i	−0.886905	+	0.461952i	$0.847149\pi$
$110$	4.07761	+	4.18699i	0.388784	+	0.399214i
$111$	7.02088	−	2.28939i	0.666392	−	0.217299i
$112$		0			0
$113$	8.82955			0.830614			0.415307	−	0.909681i	$-0.363674\pi$
$113$	8.82955			0.830614			0.415307	+	0.909681i	$0.363674\pi$
$114$	1.03420	−	4.89082i	0.0968618	−	0.458067i
$115$	−0.354709	−	1.39752i	−0.0330768	−	0.130319i
$116$	−1.60351	+	0.925786i	−0.148882	+	0.0859570i
$117$	−1.34770	−	12.5681i	−0.124595	−	1.16192i
$118$	−7.30238			−0.672239
$119$		0			0
$120$	−0.359530	−	8.94374i	−0.0328205	−	0.816448i
$121$	2.71545	−	4.70330i	0.246859	−	0.427572i
$122$	3.90402	−	2.25398i	0.353453	−	0.204066i
$123$	2.63903	−	2.93714i	0.237953	−	0.264833i
$124$	0.537228	+	0.310168i	0.0482445	+	0.0278540i
$125$	−7.58567	−	8.21326i	−0.678483	−	0.734616i
$126$		0			0
$127$		−	15.8249i		−	1.40424i	−0.712060	−	0.702118i	$-0.752238\pi$
$127$		−	15.8249i		−	1.40424i	0.712060	−	0.702118i	$-0.247762\pi$
$128$	5.60064	−	9.70060i	0.495032	−	0.857420i
$129$	−8.43142	−	7.57564i	−0.742345	−	0.666998i
$130$	1.49453	+	5.88829i	0.131079	+	0.516437i
$131$	8.27814	−	14.3382i	0.723265	−	1.25273i	−0.236419	−	0.971651i	$-0.575974\pi$
$131$	8.27814	−	14.3382i	0.723265	−	1.25273i	0.959684	−	0.281080i	$-0.0906928\pi$
$132$	−10.5746	+	3.44821i	−0.920405	+	0.300128i
$133$		0			0
$134$			5.63392i			0.486697i
$135$	11.4936	−	1.70185i	0.989215	−	0.146472i
$136$	−4.35644	+	2.51519i	−0.373562	+	0.215676i
$137$	−9.93080	−	17.2007i	−0.848446	−	1.46955i	−0.882595	−	0.470135i	$-0.844205\pi$
$137$	−9.93080	−	17.2007i	−0.848446	−	1.46955i	0.0341490	−	0.999417i	$-0.489128\pi$
$138$	−0.704563	−	0.148985i	−0.0599764	−	0.0126825i
$139$			0.228766i			0.0194037i	0.999953	+	0.00970183i	$0.00308824\pi$
$139$			0.228766i			0.0194037i	−0.999953	+	0.00970183i	$0.996912\pi$
$140$		0			0
$141$	12.8467	−	4.18908i	1.08188	−	0.352784i
$142$	−4.54422	−	2.62361i	−0.381342	−	0.220168i
$143$	14.7909	−	8.53950i	1.23687	−	0.714109i
$144$	4.60369	+	2.03810i	0.383641	+	0.169842i
$145$	1.82335	+	1.87226i	0.151421	+	0.155483i
$146$	3.37675			0.279462
$147$		0			0
$148$		−	6.75445i		−	0.555212i
$149$	−8.62438	−	4.97929i	−0.706537	−	0.407919i	0.103240	−	0.994656i	$-0.467079\pi$
$149$	−8.62438	−	4.97929i	−0.706537	−	0.407919i	−0.809777	+	0.586737i	$0.800412\pi$
$150$	−5.35301	+	1.59008i	−0.437072	+	0.129829i
$151$	2.53723	+	4.39461i	0.206477	+	0.357628i	0.950602	−	0.310412i	$-0.100467\pi$
$151$	2.53723	+	4.39461i	0.206477	+	0.357628i	−0.744126	+	0.668040i	$0.767134\pi$
$152$	−8.95872	−	5.17232i	−0.726648	−	0.419530i
$153$	−3.84921	−	5.27461i	−0.311190	−	0.426427i
$154$		0			0
$155$	0.237789	−	0.842672i	0.0190997	−	0.0676850i
$156$	−11.3113	−	2.39185i	−0.905625	−	0.191501i
$157$	−8.42678	−	14.5956i	−0.672531	−	1.16486i	−0.977184	−	0.212394i	$-0.931874\pi$
$157$	−8.42678	−	14.5956i	−0.672531	−	1.16486i	0.304653	−	0.952463i	$-0.401459\pi$
$158$	−1.20987	−	2.09556i	−0.0962524	−	0.166714i
$159$	−12.2035	−	2.58052i	−0.967799	−	0.204648i
$160$	−12.2760	−	3.46410i	−0.970503	−	0.273861i
$161$		0			0
$162$	1.77007	−	5.52672i	0.139070	−	0.434220i
$163$	4.16292	+	2.40346i	0.326065	+	0.188254i	0.654093	−	0.756414i	$-0.273051\pi$
$163$	4.16292	+	2.40346i	0.326065	+	0.188254i	−0.328028	+	0.944668i	$0.606384\pi$
$164$	−1.80579	−	3.12772i	−0.141008	−	0.244234i
$165$	8.38934	+	13.2696i	0.653109	+	1.03304i
$166$	−2.94544	−	1.70055i	−0.228611	−	0.131988i
$167$			4.45089i			0.344420i	0.985060	+	0.172210i	$0.0550908\pi$
$167$			4.45089i			0.344420i	−0.985060	+	0.172210i	$0.944909\pi$
$168$		0			0
$169$	4.75268			0.365590
$170$	2.18953	+	2.24827i	0.167930	+	0.172434i
$171$	5.43585	−	12.2786i	0.415690	−	0.938966i
$172$	−8.97849	+	5.18374i	−0.684604	+	0.395256i
$173$	9.91963	+	5.72710i	0.754175	+	0.435423i	0.827201	−	0.561907i	$-0.189932\pi$
$173$	9.91963	+	5.72710i	0.754175	+	0.435423i	−0.0730252	+	0.997330i	$0.523265\pi$
$174$	1.24100	−	0.404668i	0.0940797	−	0.0306778i
$175$		0			0
$176$			6.80268i			0.512771i
$177$	−19.1910	−	4.05808i	−1.44248	−	0.305024i
$178$	0.288473	+	0.499649i	0.0216219	+	0.0374503i
$179$	9.04522	−	5.22226i	0.676071	−	0.390330i	−0.122302	−	0.992493i	$-0.539028\pi$
$179$	9.04522	−	5.22226i	0.676071	−	0.390330i	0.798373	+	0.602163i	$0.205694\pi$
$180$	1.77920	−	10.4773i	0.132614	−	0.780933i
$181$			11.9616i			0.889095i	0.895755	+	0.444548i	$0.146636\pi$
$181$			11.9616i			0.889095i	−0.895755	+	0.444548i	$0.853364\pi$
$182$		0			0
$183$	11.5125	−	3.75404i	0.851030	−	0.277506i
$184$	−0.745115	+	1.29058i	−0.0549306	+	0.0951426i
$185$	−9.24062	+	2.34540i	−0.679384	+	0.172437i
$186$	−0.325300	−	0.292283i	−0.0238522	−	0.0214312i
$187$	4.41141	−	7.64079i	0.322594	−	0.558750i
$188$		−	12.3592i		−	0.901385i
$189$		0			0
$190$	−1.75268	+	6.21109i	−0.127153	+	0.450600i
$191$	12.2522	+	7.07383i	0.886541	+	0.511844i	0.872809	−	0.488061i	$-0.162296\pi$
$191$	12.2522	+	7.07383i	0.886541	+	0.511844i	0.0137312	+	0.999906i	$0.495629\pi$
$192$	−0.372496	+	0.414574i	−0.0268826	+	0.0299193i
$193$	5.36185	−	3.09566i	0.385954	−	0.222831i	−0.294452	−	0.955666i	$-0.595137\pi$
$193$	5.36185	−	3.09566i	0.385954	−	0.222831i	0.680406	+	0.732836i	$0.261804\pi$
$194$	1.25727	−	2.17765i	0.0902667	−	0.156346i
$195$	0.655455	+	16.3052i	0.0469381	+	1.16764i
$196$		0			0
$197$	−13.0751			−0.931562			−0.465781	−	0.884900i	$-0.654227\pi$
$197$	−13.0751			−0.931562			−0.465781	+	0.884900i	$0.654227\pi$
$198$	7.79647	−	0.836029i	0.554071	−	0.0594140i
$199$	−14.6810	+	8.47608i	−1.04071	+	0.600854i	−0.920034	−	0.391838i	$-0.871839\pi$
$199$	−14.6810	+	8.47608i	−1.04071	+	0.600854i	−0.120675	+	0.992692i	$0.538506\pi$
$200$	−0.305826	+	11.5516i	−0.0216251	+	0.816821i
$201$	−3.13088	+	14.8062i	−0.220835	+	1.04435i
$202$	−4.24525			−0.298695
$203$		0			0
$204$	−5.67822	+	1.85157i	−0.397555	+	0.129636i
$205$	−3.65193	+	3.55652i	−0.255062	+	0.248398i
$206$	3.16420	+	5.48055i	0.220460	+	0.381848i
$207$	−1.76883	−	0.783079i	−0.122942	−	0.0544278i
$208$	−3.53550	+	6.12367i	−0.245143	+	0.424600i
$209$	18.1435			1.25501
$210$		0			0
$211$	−18.4309			−1.26884			−0.634418	−	0.772990i	$-0.718760\pi$
$211$	−18.4309			−1.26884			−0.634418	+	0.772990i	$0.718760\pi$
$212$	−5.70439	+	9.88029i	−0.391779	+	0.678581i
$213$	−10.4844	−	9.42027i	−0.718381	−	0.645466i
$214$	−6.05456	−	10.4868i	−0.413881	−	0.716863i
$215$	10.2094	+	10.4833i	0.696277	+	0.714955i
$216$	−9.73770	−	7.02801i	−0.662566	−	0.478195i
$217$		0			0
$218$	0.584197			0.0395668
$219$	8.87426	+	1.87653i	0.599667	+	0.126804i
$220$	13.9180	−	3.53258i	0.938349	−	0.238166i
$221$	7.94218	−	4.58542i	0.534249	−	0.308449i
$222$	−0.985115	+	4.65869i	−0.0661166	+	0.312671i
$223$	0.627418			0.0420150			0.0210075	−	0.999779i	$-0.493313\pi$
$223$	0.627418			0.0420150			0.0210075	+	0.999779i	$0.493313\pi$
$224$		0			0
$225$	−14.9516	+	1.20403i	−0.996773	+	0.0802685i
$226$	−2.84667	+	4.93058i	−0.189358	+	0.327977i
$227$	−4.70200	+	2.71470i	−0.312082	+	0.180181i	−0.647858	−	0.761761i	$-0.724335\pi$
$227$	−4.70200	+	2.71470i	−0.312082	+	0.180181i	0.335776	+	0.941942i	$0.391002\pi$
$228$	−9.13593	−	8.20865i	−0.605042	−	0.543631i
$229$	12.4482	+	7.18699i	0.822602	+	0.474930i	0.851313	−	0.524658i	$-0.175807\pi$
$229$	12.4482	+	7.18699i	0.822602	+	0.474930i	−0.0287108	+	0.999588i	$0.509140\pi$
$230$	0.894758	+	0.252487i	0.0589986	+	0.0166485i
$231$		0			0
$232$		−	2.70114i		−	0.177339i
$233$	4.21524	−	7.30101i	0.276150	−	0.478305i	−0.694275	−	0.719710i	$-0.744275\pi$
$233$	4.21524	−	7.30101i	0.276150	−	0.478305i	0.970425	+	0.241405i	$0.0776081\pi$
$234$	7.45277	+	3.29942i	0.487203	+	0.215690i
$235$	−16.9083	+	4.29157i	−1.10298	+	0.279951i
$236$	−8.97062	+	15.5376i	−0.583938	+	1.01141i
$237$	−2.01506	−	6.17959i	−0.130892	−	0.401407i
$238$		0			0
$239$			2.71852i			0.175847i	0.996127	+	0.0879233i	$0.0280230\pi$
$239$			2.71852i			0.175847i	−0.996127	+	0.0879233i	$0.971977\pi$
$240$	−5.75492	−	3.02114i	−0.371478	−	0.195014i
$241$	1.32457	−	0.764739i	0.0853229	−	0.0492612i	−0.456732	−	0.889605i	$-0.650980\pi$
$241$	1.32457	−	0.764739i	0.0853229	−	0.0492612i	0.542054	+	0.840343i	$0.317647\pi$
$242$	1.75094	+	3.03271i	0.112555	+	0.194950i
$243$	7.72312	−	13.5408i	0.495438	−	0.868643i
$244$		−	11.0756i		−	0.709045i
$245$		0			0
$246$	0.789324	+	2.42062i	0.0503255	+	0.154333i
$247$	16.3325	+	9.42959i	1.03921	+	0.599991i
$248$	−0.783728	+	0.452486i	−0.0497668	+	0.0287329i
$249$	−6.79572	−	6.10597i	−0.430661	−	0.386950i
$250$	7.03208	−	1.58800i	0.444748	−	0.100434i
$251$	−8.81039			−0.556107			−0.278054	−	0.960566i	$-0.589689\pi$
$251$	−8.81039			−0.556107			−0.278054	+	0.960566i	$0.589689\pi$
$252$		0			0
$253$		−	2.61372i		−	0.164323i
$254$	8.83694	+	5.10201i	0.554479	+	0.320128i
$255$	4.50479	+	7.12532i	0.282101	+	0.446205i
$256$	3.93311	+	6.81234i	0.245819	+	0.425771i
$257$	−17.4101	−	10.0517i	−1.08601	−	0.627011i	−0.153502	−	0.988148i	$-0.549055\pi$
$257$	−17.4101	−	10.0517i	−1.08601	−	0.627011i	−0.932512	+	0.361138i	$0.882388\pi$
$258$	6.94869	−	2.26585i	0.432607	−	0.141066i
$259$		0			0
$260$	14.3647	+	4.05350i	0.890861	+	0.251388i
$261$	3.48628	−	0.373839i	0.215795	−	0.0231401i
$262$	5.33780	+	9.24533i	0.329770	+	0.571179i
$263$	4.37959	+	7.58568i	0.270057	+	0.467753i	0.968876	−	0.247546i	$-0.0796240\pi$
$263$	4.37959	+	7.58568i	0.270057	+	0.467753i	−0.698819	+	0.715299i	$0.746291\pi$
$264$	3.35691	−	15.8751i	0.206604	−	0.977046i
$265$	15.4978	+	4.37324i	0.952022	+	0.268646i
$266$		0			0
$267$	0.480454	+	1.47341i	0.0294033	+	0.0901713i
$268$	11.9875	+	6.92100i	0.732255	+	0.422767i
$269$	−8.62438	−	14.9379i	−0.525838	−	0.910778i	−0.999547	−	0.0300966i	$-0.990419\pi$
$269$	−8.62438	−	14.9379i	−0.525838	−	0.910778i	0.473709	−	0.880681i	$-0.342915\pi$
$270$	−2.75524	+	6.96694i	−0.167678	+	0.423994i
$271$	−19.6117	−	11.3228i	−1.19132	−	0.687812i	−0.232718	−	0.972544i	$-0.574762\pi$
$271$	−19.6117	−	11.3228i	−1.19132	−	0.687812i	−0.958607	+	0.284733i	$0.908095\pi$
$272$			3.65280i			0.221484i
$273$		0			0
$274$	12.8069			0.773692
$275$	−9.66568	−	17.8142i	−0.582863	−	1.07424i
$276$	−1.18252	+	1.31611i	−0.0711795	+	0.0792203i
$277$	11.4413	−	6.60561i	0.687438	−	0.396893i	−0.115213	−	0.993341i	$-0.536755\pi$
$277$	11.4413	−	6.60561i	0.687438	−	0.396893i	0.802652	+	0.596448i	$0.203422\pi$
$278$	−0.127747	−	0.0737548i	−0.00766176	−	0.00442352i
$279$	−0.692477	−	0.948908i	−0.0414575	−	0.0568097i
$280$		0			0
$281$		−	32.8703i		−	1.96088i	−0.196817	−	0.980440i	$-0.563060\pi$
$281$		−	32.8703i		−	1.96088i	0.196817	−	0.980440i	$-0.436940\pi$
$282$	−1.80255	+	8.52439i	−0.107340	+	0.507620i
$283$	7.90575	+	13.6932i	0.469948	+	0.813974i	0.999410	−	0.0343601i	$-0.0109393\pi$
$283$	7.90575	+	13.6932i	0.469948	+	0.813974i	−0.529462	+	0.848334i	$0.677606\pi$
$284$	−11.1647	+	6.44594i	−0.662503	+	0.382496i
$285$	−8.05774	+	15.3490i	−0.477299	+	0.909198i
$286$			11.0126i			0.651191i
$287$		0			0
$288$	−13.8236	+	10.0880i	−0.814566	+	0.594439i
$289$	−6.13122	+	10.6196i	−0.360660	+	0.624682i
$290$	−1.63336	+	0.414568i	−0.0959139	+	0.0243443i
$291$	4.51433	−	5.02429i	0.264635	−	0.294529i
$292$	4.14818	−	7.18485i	0.242754	−	0.420462i
$293$			20.7797i			1.21396i	0.794716	+	0.606982i	$0.207620\pi$
$293$			20.7797i			1.21396i	−0.794716	+	0.606982i	$0.792380\pi$
$294$		0			0
$295$	24.3716	+	6.87729i	1.41897	+	0.400411i
$296$	8.53351	+	4.92683i	0.496000	+	0.286366i
$297$	20.9541	+	2.13553i	1.21588	+	0.123916i
$298$	5.56105	−	3.21068i	0.322143	−	0.185989i
$299$	1.35841	−	2.35284i	0.0785589	−	0.136068i
$300$	−3.19264	+	13.3432i	−0.184327	+	0.770367i
$301$		0			0
$302$	−3.27204			−0.188285
$303$	−11.1567	−	2.35917i	−0.640937	−	0.135531i
$304$	−6.50535	+	3.75587i	−0.373108	+	0.215414i
$305$	−15.1524	+	3.84588i	−0.867621	+	0.220214i
$306$	4.18644	−	0.448919i	0.239323	−	0.0256630i
$307$	12.9857			0.741136			0.370568	−	0.928805i	$-0.379163\pi$
$307$	12.9857			0.741136			0.370568	+	0.928805i	$0.379163\pi$
$308$		0			0
$309$	5.27001	+	16.1616i	0.299800	+	0.919399i
$310$	0.393899	+	0.404466i	0.0223720	+	0.0229721i
$311$	−0.228825	−	0.396337i	−0.0129755	−	0.0224742i	0.859465	−	0.511195i	$-0.170797\pi$
$311$	−0.228825	−	0.396337i	−0.0129755	−	0.0224742i	−0.872440	+	0.488721i	$0.837464\pi$
$312$	11.2725	−	12.5459i	0.638179	−	0.710271i
$313$	−13.8710	+	24.0252i	−0.784033	+	1.35799i	0.145542	+	0.989352i	$0.453507\pi$
$313$	−13.8710	+	24.0252i	−0.784033	+	1.35799i	−0.929575	+	0.368633i	$0.879826\pi$
$314$	10.8673			0.613276
$315$		0			0
$316$	−5.94509			−0.334437
$317$	2.26170	−	3.91737i	0.127030	−	0.220022i	−0.795495	−	0.605960i	$-0.792789\pi$
$317$	2.26170	−	3.91737i	0.127030	−	0.220022i	0.922524	+	0.385939i	$0.126122\pi$
$318$	5.37545	−	5.98268i	0.301440	−	0.335492i
$319$	2.36878	+	4.10284i	0.132626	+	0.229715i
$320$	0.515466	−	0.501999i	0.0288154	−	0.0280626i
$321$	−10.0839	−	30.9244i	−0.562830	−	1.72603i
$322$		0			0
$323$	9.74245			0.542084
$324$	−9.58498	−	10.5555i	−0.532499	−	0.586419i
$325$	0.557547	−	21.0596i	0.0309272	−	1.16818i
$326$	−2.68428	+	1.54977i	−0.148668	+	0.0858337i
$327$	1.53530	+	0.324650i	0.0849021	+	0.0179532i
$328$	5.26871			0.290916
$329$		0			0
$330$	−10.1147	+	0.406603i	−0.556798	+	0.0223828i
$331$	11.4482	−	19.8289i	0.629252	−	1.08990i	−0.358451	−	0.933549i	$-0.616695\pi$
$331$	11.4482	−	19.8289i	0.629252	−	1.08990i	0.987702	−	0.156347i	$-0.0499718\pi$
$332$	−7.23666	+	4.17809i	−0.397163	+	0.229302i
$333$	−5.17785	+	11.6958i	−0.283745	+	0.640926i
$334$	−2.48546	−	1.43498i	−0.135998	−	0.0785186i
$335$	5.30596	−	18.8031i	0.289895	−	1.02732i
$336$		0			0
$337$			31.2616i			1.70293i	0.524413	+	0.851464i	$0.324285\pi$
$337$			31.2616i			1.70293i	−0.524413	+	0.851464i	$0.675715\pi$
$338$	−1.53228	+	2.65398i	−0.0833449	+	0.144358i
$339$	−10.2212	+	11.3758i	−0.555140	+	0.617851i
$340$	7.47347	−	1.89687i	0.405306	−	0.102872i
$341$	0.793618	−	1.37459i	0.0429768	−	0.0744380i
$342$	5.10405	+	6.99413i	0.275995	+	0.378199i
$343$		0			0
$344$		−	15.1245i		−	0.815457i
$345$	2.21115	+	1.16078i	0.119045	+	0.0624945i
$346$	−6.39623	+	3.69287i	−0.343864	+	0.198530i
$347$	−1.39335	−	2.41336i	−0.0747992	−	0.129556i	0.826200	−	0.563377i	$-0.190498\pi$
$347$	−1.39335	−	2.41336i	−0.0747992	−	0.129556i	−0.900999	+	0.433821i	$0.857165\pi$
$348$	0.663476	−	3.13763i	0.0355661	−	0.168195i
$349$		−	16.5636i		−	0.886627i	−0.896367	−	0.443314i	$-0.853803\pi$
$349$		−	16.5636i		−	0.886627i	0.896367	−	0.443314i	$-0.146197\pi$
$350$		0			0
$351$	17.7527	+	12.8127i	0.947568	+	0.683890i
$352$	−20.0249	−	11.5614i	−1.06733	−	0.616223i
$353$	−2.83794	+	1.63849i	−0.151048	+	0.0872078i	−0.573619	−	0.819122i	$-0.694461\pi$
$353$	−2.83794	+	1.63849i	−0.151048	+	0.0872078i	0.422571	+	0.906330i	$0.361128\pi$
$354$	8.45334	−	9.40826i	0.449290	−	0.500044i
$355$	12.6954	+	13.0359i	0.673800	+	0.691875i
$356$	1.41750			0.0751273
$357$		0			0
$358$			6.73469i			0.355939i
$359$	−14.7282	−	8.50335i	−0.777326	−	0.448789i	0.0581557	−	0.998308i	$-0.481478\pi$
$359$	−14.7282	−	8.50335i	−0.777326	−	0.448789i	−0.835482	+	0.549518i	$0.814811\pi$
$360$	11.9392	+	9.89019i	0.629249	+	0.521259i
$361$	0.517332	+	0.896045i	0.0272280	+	0.0471603i
$362$	−6.67955	−	3.85644i	−0.351069	−	0.202690i
$363$	2.91620	+	8.94314i	0.153061	+	0.469393i
$364$		0			0
$365$	−11.2698	−	3.18018i	−0.589891	−	0.166458i
$366$	−1.61535	+	7.63911i	−0.0844355	+	0.399303i
$367$	8.55840	+	14.8236i	0.446745	+	0.773785i	0.998172	−	0.0604381i	$-0.0192498\pi$
$367$	8.55840	+	14.8236i	0.446745	+	0.773785i	−0.551427	+	0.834223i	$0.685916\pi$
$368$	0.541063	+	0.937149i	0.0282049	+	0.0488523i
$369$	0.729192	+	6.80015i	0.0379602	+	0.354002i
$370$	1.66949	−	5.91630i	0.0867926	−	0.307574i
$371$		0			0
$372$	−1.02152	+	0.333100i	−0.0529632	+	0.0172704i
$373$	−25.0397	−	14.4567i	−1.29651	−	0.748538i	−0.316706	−	0.948524i	$-0.602577\pi$
$373$	−25.0397	−	14.4567i	−1.29651	−	0.748538i	−0.979799	+	0.199986i	$0.935910\pi$
$374$	2.84450	+	4.92683i	0.147086	+	0.254760i
$375$	19.3631	−	0.265463i	0.999906	−	0.0137084i
$376$	15.6145	+	9.01502i	0.805255	+	0.464914i
$377$			4.92442i			0.253621i
$378$		0			0
$379$	−0.559557			−0.0287425			−0.0143712	−	0.999897i	$-0.504575\pi$
$379$	−0.559557			−0.0287425			−0.0143712	+	0.999897i	$0.504575\pi$
$380$	11.0625	+	11.3593i	0.567495	+	0.582718i
$381$	20.3886	+	18.3192i	1.04454	+	0.938519i
$382$	−7.90031	+	4.56125i	−0.404215	+	0.233374i
$383$	−3.28951	−	1.89920i	−0.168086	−	0.0970447i	0.413597	−	0.910460i	$-0.364272\pi$
$383$	−3.28951	−	1.89920i	−0.168086	−	0.0970447i	−0.581683	+	0.813415i	$0.697606\pi$
$384$	6.01470	+	18.4453i	0.306937	+	0.941284i
$385$		0			0
$386$			3.99220i			0.203198i
$387$	19.5207	−	2.09323i	0.992291	−	0.106405i
$388$	−3.08899	−	5.35029i	−0.156820	−	0.271620i
$389$	7.88909	−	4.55477i	0.399993	−	0.230936i	−0.286488	−	0.958084i	$-0.592488\pi$
$389$	7.88909	−	4.55477i	0.399993	−	0.230936i	0.686481	+	0.727148i	$0.259155\pi$
$390$	−9.31646	−	4.89084i	−0.471757	−	0.247657i
$391$		−	1.40348i		−	0.0709770i
$392$		0			0
$393$	8.89016	+	27.2635i	0.448449	+	1.37526i
$394$	4.21545	−	7.30137i	0.212371	−	0.367838i
$395$	2.06436	+	8.13335i	0.103869	+	0.409233i
$396$	7.79874	−	17.6159i	0.391901	−	0.885232i
$397$	−12.1191	+	20.9910i	−0.608242	+	1.05351i	0.383288	+	0.923629i	$0.374792\pi$
$397$	−12.1191	+	20.9910i	−0.608242	+	1.05351i	−0.991530	+	0.129878i	$0.958542\pi$
$398$		−	10.9309i		−	0.547914i
$399$		0			0
$400$	7.15333	+	4.38641i	0.357666	+	0.219320i
$401$	−26.1500	−	15.0977i	−1.30587	−	0.753944i	−0.324466	−	0.945897i	$-0.605185\pi$
$401$	−26.1500	−	15.0977i	−1.30587	−	0.753944i	−0.981404	+	0.191953i	$0.938518\pi$
$402$	−7.25865	−	6.52190i	−0.362028	−	0.325283i
$403$	1.42881	−	0.824921i	0.0711739	−	0.0410923i
$404$	−5.21509	+	9.03279i	−0.259460	+	0.449398i
$405$	−11.1126	+	16.7783i	−0.552187	+	0.833720i
$406$		0			0
$407$	−17.2824			−0.856656
$408$	1.80255	−	8.52439i	0.0892393	−	0.422020i
$409$	21.3618	−	12.3332i	1.05627	−	0.609839i	0.131874	−	0.991267i	$-0.457901\pi$
$409$	21.3618	−	12.3332i	1.05627	−	0.609839i	0.924399	+	0.381427i	$0.124567\pi$
$410$	−0.808636	−	3.18594i	−0.0399357	−	0.157342i
$411$	33.6571	+	7.11704i	1.66018	+	0.351058i
$412$	15.5483			0.766008
$413$		0			0
$414$	1.00756	−	0.735280i	0.0495189	−	0.0361370i
$415$	8.22880	+	8.44954i	0.403936	+	0.414771i
$416$	−12.0174	−	20.8148i	−0.589202	−	1.02053i
$417$	−0.294738	−	0.264822i	−0.0144334	−	0.0129684i
$418$	−5.84953	+	10.1317i	−0.286110	+	0.495556i
$419$	−39.4615			−1.92782			−0.963911	−	0.266226i	$-0.914223\pi$
$419$	−39.4615			−1.92782			−0.963911	+	0.266226i	$0.914223\pi$
$420$		0			0
$421$	−30.9363			−1.50774			−0.753870	−	0.657023i	$-0.771815\pi$
$421$	−30.9363			−1.50774			−0.753870	+	0.657023i	$0.771815\pi$
$422$	5.94218	−	10.2921i	0.289261	−	0.501014i
$423$	−9.47434	+	21.4008i	−0.460658	+	1.04054i
$424$	−8.32178	−	14.4137i	−0.404141	−	0.699993i
$425$	−5.19014	−	9.56563i	−0.251759	−	0.464001i
$426$	8.64066	−	2.81757i	0.418641	−	0.136512i
$427$		0			0
$428$	−29.7509			−1.43807
$429$	−6.11994	+	28.9417i	−0.295474	+	1.39732i
$430$	−9.14562	+	2.32129i	−0.441041	+	0.111942i
$431$	−26.6240	+	15.3713i	−1.28243	+	0.740412i	−0.977292	−	0.211896i	$-0.932036\pi$
$431$	−26.6240	+	15.3713i	−1.28243	+	0.740412i	−0.305138	+	0.952308i	$0.598703\pi$
$432$	−7.95515	+	3.57198i	−0.382742	+	0.171857i
$433$	−2.95856			−0.142179			−0.0710896	−	0.997470i	$-0.522648\pi$
$433$	−2.95856			−0.142179			−0.0710896	+	0.997470i	$0.522648\pi$
$434$		0			0
$435$	−4.52292	+	0.181817i	−0.216857	+	0.00871746i
$436$	0.717658	−	1.24302i	0.0343696	−	0.0595298i
$437$	2.49949	−	1.44308i	0.119567	−	0.0690318i
$438$	−3.90897	+	4.35055i	−0.186778	+	0.207877i
$439$	−15.0772	−	8.70485i	−0.719598	−	0.415460i	0.0950070	−	0.995477i	$-0.469713\pi$
$439$	−15.0772	−	8.70485i	−0.719598	−	0.415460i	−0.814605	+	0.580017i	$0.803046\pi$
$440$	−5.68901	+	20.1606i	−0.271213	+	0.961117i
$441$		0			0
$442$			5.91341i			0.281272i
$443$	−15.8970	+	27.5344i	−0.755288	+	1.30820i	0.189942	+	0.981795i	$0.439170\pi$
$443$	−15.8970	+	27.5344i	−0.755288	+	1.30820i	−0.945231	+	0.326403i	$0.894163\pi$
$444$	8.70232	+	7.81904i	0.412994	+	0.371075i
$445$	−0.492209	−	1.93925i	−0.0233329	−	0.0919293i
$446$	−0.202281	+	0.350362i	−0.00957830	+	0.0165901i
$447$	16.3989	−	5.34741i	0.775643	−	0.252924i
$448$		0			0
$449$		−	2.99461i		−	0.141324i	−0.997500	−	0.0706621i	$-0.977489\pi$
$449$		−	2.99461i		−	0.141324i	0.997500	−	0.0706621i	$-0.0225112\pi$
$450$	4.14809	−	8.73743i	0.195543	−	0.411886i
$451$	−8.00279	+	4.62041i	−0.376837	+	0.217567i
$452$	6.99400	+	12.1140i	0.328970	+	0.569793i
$453$	−8.59907	−	1.81834i	−0.404019	−	0.0854329i
$454$		−	3.50091i		−	0.164306i
$455$		0			0
$456$	17.0347	−	5.55471i	0.797721	−	0.260123i
$457$	−7.62540	−	4.40252i	−0.356701	−	0.205941i	0.310932	−	0.950432i	$-0.399359\pi$
$457$	−7.62540	−	4.40252i	−0.356701	−	0.205941i	−0.667633	+	0.744491i	$0.732692\pi$
$458$	−8.02669	+	4.63421i	−0.375063	+	0.216543i
$459$	11.2516	+	1.14671i	0.525181	+	0.0535237i
$460$	1.63639	−	1.59365i	0.0762973	−	0.0743041i
$461$	31.9710			1.48904			0.744519	−	0.667602i	$-0.232679\pi$
$461$	31.9710			1.48904			0.744519	+	0.667602i	$0.232679\pi$
$462$		0			0
$463$		−	6.94495i		−	0.322759i	−0.986892	−	0.161380i	$-0.948406\pi$
$463$		−	6.94495i		−	0.322759i	0.986892	−	0.161380i	$-0.0515943\pi$
$464$	−1.69865	−	0.980715i	−0.0788577	−	0.0455285i
$465$	0.810416	+	1.28185i	0.0375821	+	0.0594445i
$466$	2.71801	+	4.70774i	0.125910	+	0.218082i
$467$	21.1944	+	12.2366i	0.980758	+	0.566241i	0.902499	−	0.430692i	$-0.141731\pi$
$467$	21.1944	+	12.2366i	0.980758	+	0.566241i	0.0782589	+	0.996933i	$0.475064\pi$
$468$	16.1757	−	11.8044i	0.747721	−	0.545658i
$469$		0			0
$470$	3.05480	−	10.8255i	0.140908	−	0.499344i
$471$	28.5597	+	6.03916i	1.31596	+	0.278270i
$472$	−13.0867	−	22.6668i	−0.602364	−	1.04332i
$473$	13.2635	+	22.9730i	0.609854	+	1.05630i
$474$	4.10045	+	0.867071i	0.188340	+	0.0398259i
$475$	11.6991	−	19.0788i	0.536789	−	0.875393i
$476$		0			0
$477$	17.4516	−	12.7355i	0.799054	−	0.583119i
$478$	−1.51807	−	0.876459i	−0.0694350	−	0.0400883i
$479$	−12.1451	−	21.0359i	−0.554923	−	0.961156i	−0.997909	−	0.0646271i	$-0.979414\pi$
$479$	−12.1451	−	21.0359i	−0.554923	−	0.961156i	0.442986	−	0.896529i	$-0.353919\pi$
$480$	18.6740	−	11.8061i	0.852345	−	0.538872i
$481$	−15.5573	−	8.98204i	−0.709354	−	0.409546i
$482$			0.986217i			0.0449209i
$483$		0			0
$484$	8.60377			0.391080
$485$	−6.24700	+	6.08380i	−0.283662	+	0.276251i
$486$	5.07148	+	8.67833i	0.230047	+	0.393657i
$487$	−8.44934	+	4.87823i	−0.382876	+	0.221054i	−0.679069	−	0.734075i	$-0.737616\pi$
$487$	−8.44934	+	4.87823i	−0.382876	+	0.221054i	0.296193	+	0.955128i	$0.404283\pi$
$488$	13.9929	+	8.07879i	0.633427	+	0.365710i
$489$	−7.91563	+	2.58115i	−0.357957	+	0.116724i
$490$		0			0
$491$			23.6689i			1.06816i	0.845434	+	0.534080i	$0.179342\pi$
$491$			23.6689i			1.06816i	−0.845434	+	0.534080i	$0.820658\pi$
$492$	6.12011	+	1.29414i	0.275916	+	0.0583444i
$493$	1.27195	+	2.20308i	0.0572858	+	0.0992219i
$494$	−10.5313	+	6.08026i	−0.473826	+	0.273564i
$495$	−26.8079	−	4.55239i	−1.20493	−	0.204615i
$496$			0.657143i			0.0295066i
$497$		0			0
$498$	5.60064	−	1.82627i	0.250971	−	0.0818373i
$499$	5.73534	−	9.93391i	0.256749	−	0.444703i	−0.708620	−	0.705590i	$-0.750682\pi$
$499$	5.73534	−	9.93391i	0.256749	−	0.444703i	0.965369	+	0.260888i	$0.0840152\pi$
$500$	5.25972	−	16.9132i	0.235222	−	0.756382i
$501$	−5.73445	−	5.15241i	−0.256196	−	0.230193i
$502$	2.84050	−	4.91988i	0.126778	−	0.219585i
$503$			16.8580i			0.751659i	0.926689	+	0.375830i	$0.122642\pi$
$503$			16.8580i			0.751659i	−0.926689	+	0.375830i	$0.877358\pi$
$504$		0			0
$505$	14.1685	+	3.99812i	0.630488	+	0.177914i
$506$	1.45955	+	0.842672i	0.0648849	+	0.0374613i
$507$	−5.50176	+	6.12327i	−0.244342	+	0.271944i
$508$	21.7115	−	12.5351i	0.963292	−	0.556157i
$509$	−1.47582	+	2.55620i	−0.0654147	+	0.113302i	−0.896878	−	0.442278i	$-0.854170\pi$
$509$	−1.47582	+	2.55620i	−0.0654147	+	0.113302i	0.831463	+	0.555580i	$0.187504\pi$
$510$	−5.43127	+	0.218332i	−0.240500	+	0.00966790i
$511$		0			0
$512$	17.3304			0.765902
$513$	9.52689	+	21.2173i	0.420623	+	0.936767i
$514$	11.2262	−	6.48142i	0.495164	−	0.285883i
$515$	−5.39894	−	21.2713i	−0.237906	−	0.937323i
$516$	3.71499	−	17.5685i	0.163543	−	0.773410i
$517$	−31.6230			−1.39078
$518$		0			0
$519$	−18.8618	+	6.15051i	−0.827941	+	0.269977i
$520$	−15.5991	+	15.1915i	−0.684064	+	0.666193i
$521$	−7.91563	−	13.7103i	−0.346790	−	0.600658i	0.638887	−	0.769300i	$-0.279395\pi$
$521$	−7.91563	−	13.7103i	−0.346790	−	0.600658i	−0.985677	+	0.168642i	$0.946062\pi$
$522$	−0.915228	+	2.06733i	−0.0400584	+	0.0904845i
$523$	10.9800	−	19.0179i	0.480122	−	0.831595i	−0.519618	−	0.854398i	$-0.673926\pi$
$523$	10.9800	−	19.0179i	0.480122	−	0.831595i	0.999740	+	0.0228034i	$0.00725919\pi$
$524$	26.2289			1.14581
$525$		0			0
$526$	−5.64798			−0.246263
$527$	0.426145	−	0.738105i	0.0185632	−	0.0321524i
$528$	−8.76445	−	7.87487i	−0.381424	−	0.342710i
$529$	11.2921	+	19.5585i	0.490961	+	0.850370i
$530$	−7.43863	+	7.24430i	−0.323113	+	0.314672i
$531$	27.4441	−	20.0277i	1.19097	−	0.869126i
$532$		0			0
$533$	−9.60532			−0.416053
$534$	−0.977680	−	0.206738i	−0.0423083	−	0.00894641i
$535$	10.3306	+	40.7016i	0.446633	+	1.75968i
$536$	−17.4879	+	10.0966i	−0.755361	+	0.436108i
$537$	−3.74260	+	17.6991i	−0.161505	+	0.763771i
$538$	11.1221			0.479508
$539$		0			0
$540$	11.4392	+	14.4210i	0.492263	+	0.620580i
$541$	−2.34667	+	4.06456i	−0.100891	+	0.174749i	−0.912052	−	0.410074i	$-0.865503\pi$
$541$	−2.34667	+	4.06456i	−0.100891	+	0.174749i	0.811161	+	0.584823i	$0.198836\pi$
$542$	12.6457	−	7.30101i	0.543181	−	0.313605i
$543$	−15.4111	−	13.8469i	−0.661352	−	0.594225i
$544$	−10.7527	−	6.20806i	−0.461017	−	0.266168i
$545$	−1.94975	−	0.550189i	−0.0835180	−	0.0235675i
$546$		0			0
$547$		−	14.9485i		−	0.639151i	−0.947561	−	0.319575i	$-0.896460\pi$
$547$		−	14.9485i		−	0.639151i	0.947561	−	0.319575i	$-0.103540\pi$
$548$	15.7326	−	27.2497i	0.672065	−	1.16405i
$549$	−8.49041	+	19.1782i	−0.362362	+	0.818508i
$550$	13.0640	+	0.345867i	0.557052	+	0.0147478i
$551$	−2.61568	+	4.53049i	−0.111432	+	0.193005i
$552$	−0.800202	−	2.45398i	−0.0340589	−	0.104448i
$553$		0			0
$554$			8.51867i			0.361924i
$555$	7.67530	−	14.6205i	0.325798	−	0.620607i
$556$	−0.313862	+	0.181208i	−0.0133107	+	0.00768494i
$557$	−0.614501	−	1.06435i	−0.0260373	−	0.0450979i	0.852713	−	0.522379i	$-0.174956\pi$
$557$	−0.614501	−	1.06435i	−0.0260373	−	0.0450979i	−0.878750	+	0.477282i	$0.841622\pi$
$558$	0.753144	−	0.0807609i	0.0318831	−	0.00341888i
$559$			27.5732i			1.16622i
$560$		0			0
$561$	4.73755	+	14.5287i	0.200020	+	0.613401i
$562$	18.3554	+	10.5975i	0.774276	+	0.447028i
$563$	−3.64387	+	2.10379i	−0.153571	+	0.0886643i	−0.574816	−	0.818282i	$-0.694926\pi$
$563$	−3.64387	+	2.10379i	−0.153571	+	0.0886643i	0.421245	+	0.906947i	$0.361593\pi$
$564$	15.9233	+	14.3071i	0.670494	+	0.602440i
$565$	14.1443	−	13.7748i	0.595054	−	0.579509i
$566$	−10.1953			−0.428542
$567$		0			0
$568$		−	18.8072i		−	0.789132i
$569$	22.3139	+	12.8829i	0.935447	+	0.540081i	0.888530	−	0.458818i	$-0.151727\pi$
$569$	22.3139	+	12.8829i	0.935447	+	0.540081i	0.0469169	+	0.998899i	$0.485060\pi$
$570$	−5.97334	−	9.44816i	−0.250196	−	0.395740i
$571$	−12.3419	−	21.3768i	−0.516492	−	0.894591i	−0.999817	−	0.0191497i	$-0.993904\pi$
$571$	−12.3419	−	21.3768i	−0.516492	−	0.894591i	0.483324	−	0.875441i	$-0.339429\pi$
$572$	23.4320	+	13.5285i	0.979743	+	0.565655i
$573$	−23.2972	+	7.59681i	−0.973253	+	0.317361i
$574$		0			0
$575$	−2.74845	−	1.68534i	−0.114618	−	0.0702837i
$576$	−0.102925	−	0.959834i	−0.00428852	−	0.0399931i
$577$	2.86692	+	4.96565i	0.119351	+	0.206723i	0.919511	−	0.393065i	$-0.128585\pi$
$577$	2.86692	+	4.96565i	0.119351	+	0.206723i	−0.800159	+	0.599787i	$0.795252\pi$
$578$	−3.95345	−	6.84757i	−0.164442	−	0.284822i
$579$	−2.21855	+	10.4917i	−0.0921996	+	0.436020i
$580$	−1.12440	+	3.98463i	−0.0466883	+	0.165453i
$581$		0			0
$582$	1.35022	+	4.14073i	0.0559684	+	0.171639i
$583$	25.2804	+	14.5956i	1.04701	+	0.604489i
$584$	6.05152	+	10.4815i	0.250414	+	0.433729i
$585$	−21.7661	−	18.0307i	−0.899919	−	0.745477i
$586$	−11.6038	−	6.69944i	−0.479347	−	0.276751i
$587$		−	31.0435i		−	1.28130i	−0.767832	−	0.640652i	$-0.778664\pi$
$587$		−	31.0435i		−	1.28130i	0.767832	−	0.640652i	$-0.221336\pi$
$588$		0			0
$589$	1.75268			0.0722178
$590$	−11.6979	+	11.3923i	−0.481594	+	0.469012i
$591$	15.1359	−	16.8457i	0.622608	−	0.692941i
$592$	6.19659	−	3.57760i	0.254678	−	0.147039i
$593$	−28.2124	−	16.2884i	−1.15854	−	0.668885i	−0.207588	−	0.978216i	$-0.566561\pi$
$593$	−28.2124	−	16.2884i	−1.15854	−	0.668885i	−0.950954	+	0.309331i	$0.899895\pi$
$594$	−7.94818	+	11.0126i	−0.326118	+	0.451854i
$595$		0			0
$596$		−	15.7766i		−	0.646236i
$597$	6.07449	−	28.7268i	0.248612	−	1.17571i
$598$	0.875911	+	1.51712i	0.0358187	+	0.0620397i
$599$	−31.8553	+	18.3917i	−1.30157	+	0.751463i	−0.980674	−	0.195650i	$-0.937318\pi$
$599$	−31.8553	+	18.3917i	−1.30157	+	0.751463i	−0.320899	+	0.947113i	$0.603985\pi$
$600$	−14.5289	−	13.7663i	−0.593138	−	0.562007i
$601$			42.5075i			1.73392i	0.498380	+	0.866959i	$0.333929\pi$
$601$			42.5075i			1.73392i	−0.498380	+	0.866959i	$0.666071\pi$
$602$		0			0
$603$	−15.4517	−	21.1736i	−0.629242	−	0.862257i
$604$	−4.01954	+	6.96205i	−0.163553	+	0.283282i
$605$	−2.98755	−	11.7706i	−0.121461	−	0.478544i
$606$	4.91436	−	5.46951i	0.199632	−	0.222184i
$607$	8.47607	−	14.6810i	0.344033	−	0.595883i	−0.641144	−	0.767420i	$-0.721540\pi$
$607$	8.47607	−	14.6810i	0.344033	−	0.595883i	0.985178	+	0.171537i	$0.0548734\pi$
$608$		−	25.5329i		−	1.03550i
$609$		0			0
$610$	2.73755	−	9.70127i	0.110840	−	0.392793i
$611$	−28.4666	−	16.4352i	−1.15163	−	0.664896i
$612$	4.18765	−	9.45913i	0.169276	−	0.382363i
$613$	−30.0373	+	17.3421i	−1.21320	+	0.700439i	−0.963454	−	0.267873i	$-0.913679\pi$
$613$	−30.0373	+	17.3421i	−1.21320	+	0.700439i	−0.249742	+	0.968312i	$0.580346\pi$
$614$	−4.18664	+	7.25148i	−0.168959	+	0.292646i
$615$	−0.354643	−	8.82216i	−0.0143006	−	0.355744i
$616$		0			0
$617$	45.7116			1.84028			0.920140	−	0.391590i	$-0.128075\pi$
$617$	45.7116			1.84028			0.920140	+	0.391590i	$0.128075\pi$
$618$	−10.7240	−	2.26766i	−0.431381	−	0.0912188i
$619$	34.2356	−	19.7659i	1.37604	−	0.794459i	0.384363	−	0.923182i	$-0.374421\pi$
$619$	34.2356	−	19.7659i	1.37604	−	0.794459i	0.991681	+	0.128723i	$0.0410877\pi$
$620$	1.34448	−	0.341249i	0.0539958	−	0.0137049i
$621$	3.05653	−	1.37243i	0.122654	−	0.0550736i
$622$	0.295096			0.0118323
$623$		0			0
$624$	−3.79689	−	11.6439i	−0.151997	−	0.466130i
$625$	−24.9650	−	1.32281i	−0.998599	−	0.0529124i
$626$	−8.94408	−	15.4916i	−0.357477	−	0.619169i
$627$	−21.0032	+	23.3758i	−0.838787	+	0.933540i
$628$	13.3499	−	23.1228i	0.532720	−	0.922698i
$629$	−9.28004			−0.370020
$630$		0			0
$631$	−21.1685			−0.842703			−0.421351	−	0.906897i	$-0.638444\pi$
$631$	−21.1685			−0.842703			−0.421351	+	0.906897i	$0.638444\pi$
$632$	4.33646	−	7.51097i	0.172495	−	0.298770i
$633$	21.3359	−	23.7461i	0.848024	−	0.943821i
$634$	1.45835	+	2.52594i	0.0579187	+	0.100318i
$635$	−24.6881	−	25.3504i	−0.979718	−	1.00600i
$636$	−6.12612	−	18.7870i	−0.242916	−	0.744952i
$637$		0			0
$638$	−3.05480			−0.120941
$639$	24.2738	−	2.60292i	0.960257	−	0.102970i
$640$	−6.16186	−	24.2771i	−0.243569	−	0.959635i
$641$	30.6083	−	17.6717i	1.20896	−	0.697991i	0.246424	−	0.969162i	$-0.420744\pi$
$641$	30.6083	−	17.6717i	1.20896	−	0.697991i	0.962531	+	0.271171i	$0.0874109\pi$
$642$	20.5199	+	4.33908i	0.809854	+	0.171250i
$643$	−26.0538			−1.02746			−0.513731	−	0.857951i	$-0.671737\pi$
$643$	−26.0538			−1.02746			−0.513731	+	0.857951i	$0.671737\pi$
$644$		0			0
$645$	−25.3251	+	1.01805i	−0.997174	+	0.0400855i
$646$	−3.14099	+	5.44036i	−0.123581	+	0.214048i
$647$	−35.3707	+	20.4213i	−1.39057	+	0.802844i	−0.993378	−	0.114894i	$-0.963347\pi$
$647$	−35.3707	+	20.4213i	−1.39057	+	0.802844i	−0.397188	+	0.917737i	$0.630014\pi$
$648$	20.3273	−	4.41016i	0.798530	−	0.173248i
$649$	39.7555	+	22.9528i	1.56054	+	0.900977i
$650$	11.5803	+	7.10102i	0.454217	+	0.278525i
$651$		0			0
$652$			7.61525i			0.298236i
$653$	−12.0041	+	20.7918i	−0.469758	+	0.813645i	−0.999402	−	0.0345747i	$-0.988992\pi$
$653$	−12.0041	+	20.7918i	−0.469758	+	0.813645i	0.529644	+	0.848220i	$0.322326\pi$
$654$	−0.676274	+	0.752669i	−0.0264444	+	0.0294317i
$655$	−9.10766	−	35.8832i	−0.355866	−	1.40207i
$656$	1.91293	−	3.31329i	0.0746874	−	0.129362i
$657$	−12.6906	+	9.26115i	−0.495109	+	0.361312i
$658$		0			0
$659$		−	38.7398i		−	1.50909i	−0.656248	−	0.754545i	$-0.727858\pi$
$659$		−	38.7398i		−	1.50909i	0.656248	−	0.754545i	$-0.272142\pi$
$660$	−11.5603	+	22.0210i	−0.449985	+	0.857167i
$661$	−44.0826	+	25.4511i	−1.71461	+	0.989933i	−0.786539	+	0.617541i	$0.788129\pi$
$661$	−44.0826	+	25.4511i	−1.71461	+	0.989933i	−0.928075	+	0.372392i	$0.878538\pi$
$662$	7.38188	+	12.7858i	0.286905	+	0.496934i
$663$	−3.28620	+	15.5407i	−0.127625	+	0.603551i
$664$		−	12.1903i		−	0.473076i
$665$		0			0
$666$	−4.86179	−	6.66217i	−0.188391	−	0.258154i
$667$	0.652654	+	0.376810i	0.0252709	+	0.0145901i
$668$	−6.10653	+	3.52560i	−0.236269	+	0.136410i
$669$	−0.726307	+	0.808354i	−0.0280807	+	0.0312528i
$670$	8.78934	+	9.02512i	0.339562	+	0.348671i
$671$	−28.3389			−1.09401
$672$		0			0
$673$		−	3.33192i		−	0.128436i	−0.997936	−	0.0642181i	$-0.979545\pi$
$673$		−	3.33192i		−	0.128436i	0.997936	−	0.0642181i	$-0.0204553\pi$
$674$	−17.4570	−	10.0788i	−0.672420	−	0.388222i
$675$	15.7569	−	20.6572i	0.606484	−	0.795095i
$676$	3.76466	+	6.52057i	0.144794	+	0.250791i
$677$	28.0352	+	16.1861i	1.07748	+	0.622083i	0.930215	−	0.367014i	$-0.119620\pi$
$677$	28.0352	+	16.1861i	1.07748	+	0.622083i	0.147264	+	0.989097i	$0.452953\pi$
$678$	−3.05713	−	9.37531i	−0.117408	−	0.360057i
$679$		0			0
$680$	−3.05480	+	10.8255i	−0.117146	+	0.415140i
$681$	1.94552	−	9.20055i	0.0745526	−	0.352566i
$682$	0.511729	+	0.886341i	0.0195951	+	0.0339398i
$683$	−10.8868	−	18.8566i	−0.416573	−	0.721526i	0.579019	−	0.815314i	$-0.303436\pi$
$683$	−10.8868	−	18.8566i	−0.416573	−	0.721526i	−0.995592	+	0.0937881i	$0.970102\pi$
$684$	21.1518	−	2.26814i	0.808758	−	0.0867245i
$685$	−42.7427	−	12.0614i	−1.63312	−	0.460841i
$686$		0			0
$687$	−23.6698	+	7.71833i	−0.903060	+	0.294473i
$688$	−9.51121	−	5.49130i	−0.362611	−	0.209354i
$689$	15.1713	+	26.2775i	0.577982	+	1.00109i
$690$	−1.36108	+	0.860509i	−0.0518156	+	0.0327590i
$691$	−5.15554	−	2.97655i	−0.196126	−	0.113233i	0.398721	−	0.917072i	$-0.369454\pi$
$691$	−5.15554	−	2.97655i	−0.196126	−	0.113233i	−0.594847	+	0.803839i	$0.702787\pi$
$692$			18.1460i			0.689809i
$693$		0			0
$694$	1.79689			0.0682088
$695$	0.356892	+	0.366466i	0.0135377	+	0.0139008i
$696$	3.48011	+	3.12688i	0.131913	+	0.118524i
$697$	−4.29722	+	2.48100i	−0.162769	+	0.0939747i
$698$	9.24939	+	5.34014i	0.350095	+	0.202127i
$699$	4.52688	+	13.8826i	0.171222	+	0.525088i
$700$		0			0
$701$		−	19.3393i		−	0.730434i	−0.930922	−	0.365217i	$-0.880995\pi$
$701$		−	19.3393i		−	0.730434i	0.930922	−	0.365217i	$-0.119005\pi$
$702$	−12.8783	+	5.78257i	−0.486062	+	0.218249i
$703$	−9.54188	−	16.5270i	−0.359879	−	0.623329i
$704$	1.12958	−	0.652166i	0.0425728	−	0.0245794i
$705$	14.0441	−	26.7524i	0.528932	−	1.00755i
$706$		−	2.11301i		−	0.0795242i
$707$		0			0
$708$	−9.63383	−	29.5441i	−0.362061	−	1.11034i
$709$	16.9012	−	29.2738i	0.634739	−	1.09940i	−0.351831	−	0.936063i	$-0.614441\pi$
$709$	16.9012	−	29.2738i	0.634739	−	1.09940i	0.986570	−	0.163337i	$-0.0522257\pi$
$710$	−11.3725	+	2.88650i	−0.426803	+	0.108329i
$711$	10.2943	+	4.55741i	0.386068	+	0.170916i
$712$	−1.03395	+	1.79086i	−0.0387490	+	0.0671152i
$713$		−	0.252487i		−	0.00945573i
$714$		0			0
$715$	10.3716	−	36.7545i	0.387875	−	1.37454i
$716$	14.3297	+	8.27324i	0.535525	+	0.309185i
$717$	−3.50250	−	3.14700i	−0.130803	−	0.117527i
$718$	9.49685	−	5.48301i	0.354419	−	0.204624i
$719$	13.7118	−	23.7495i	0.511363	−	0.885707i	−0.488550	−	0.872536i	$-0.662474\pi$
$719$	13.7118	−	23.7495i	0.511363	−	0.885707i	0.999913	−	0.0131713i	$-0.00419267\pi$
$720$	10.5544	−	3.91722i	0.393338	−	0.145986i
$721$		0			0
$722$	−0.667157			−0.0248290
$723$	−0.548060	+	2.59182i	−0.0203826	+	0.0963909i
$724$	−16.4110	+	9.47490i	−0.609910	+	0.352132i
$725$	5.84173	+	0.154658i	0.216956	+	0.00574387i
$726$	−5.93420	−	1.25483i	−0.220239	−	0.0465712i
$727$	−6.14612			−0.227947			−0.113973	−	0.993484i	$-0.536358\pi$
$727$	−6.14612			−0.227947			−0.113973	+	0.993484i	$0.536358\pi$
$728$		0			0
$729$	8.50535	+	25.6254i	0.315013	+	0.949087i
$730$	5.40930	−	5.26799i	0.200207	−	0.194977i
$731$	7.12202	+	12.3357i	0.263417	+	0.456252i
$732$	14.2697	+	12.8213i	0.527422	+	0.473889i
$733$	8.41748	−	14.5795i	0.310907	−	0.538506i	−0.667652	−	0.744473i	$-0.732701\pi$
$733$	8.41748	−	14.5795i	0.310907	−	0.538506i	0.978559	+	0.205967i	$0.0660340\pi$
$734$	−11.0370			−0.407384
$735$		0			0
$736$	−3.67822			−0.135581
$737$	17.7085	−	30.6721i	0.652302	−	1.12982i
$738$	−4.03242	−	1.78520i	−0.148436	−	0.0657139i
$739$	19.3419	+	33.5012i	0.711503	+	1.23236i	0.964293	+	0.264838i	$0.0853186\pi$
$739$	19.3419	+	33.5012i	0.711503	+	1.23236i	−0.252790	+	0.967521i	$0.581348\pi$
$740$	−10.5375	−	10.8201i	−0.387364	−	0.397756i
$741$	−31.0557	+	10.1267i	−1.14086	+	0.372015i
$742$		0			0
$743$	39.3563			1.44384			0.721920	−	0.691976i	$-0.243260\pi$
$743$	39.3563			1.44384			0.721920	+	0.691976i	$0.243260\pi$
$744$	0.324280	−	1.53355i	0.0118887	−	0.0562225i
$745$	−21.5837	+	5.47824i	−0.790765	+	0.200707i
$746$	16.1457	−	9.32174i	0.591137	−	0.341293i
$747$	15.7336	−	1.68714i	0.575664	−	0.0617294i
$748$	13.9773			0.511062
$749$		0			0
$750$	−6.09448	+	10.8983i	−0.222539	+	0.397949i
$751$	−16.1416	+	27.9580i	−0.589014	+	1.02020i	0.405347	+	0.914163i	$0.367151\pi$
$751$	−16.1416	+	27.9580i	−0.589014	+	1.02020i	−0.994362	+	0.106040i	$0.966183\pi$
$752$	11.3384	−	6.54623i	0.413469	−	0.238717i
$753$	10.1990	−	11.3512i	0.371673	−	0.413659i
$754$	−2.74989	−	1.58765i	−0.100145	−	0.0578187i
$755$	10.9204	+	3.08156i	0.397433	+	0.112150i
$756$		0			0
$757$		−	40.0667i		−	1.45625i	−0.685446	−	0.728124i	$-0.740393\pi$
$757$		−	40.0667i		−	1.45625i	0.685446	−	0.728124i	$-0.259607\pi$
$758$	0.180403	−	0.312467i	0.00655252	−	0.0113493i
$759$	3.36748	+	3.02568i	0.122232	+	0.109825i
$760$	−22.4204	+	5.69061i	−0.813274	+	0.206420i
$761$	−6.58977	+	11.4138i	−0.238879	+	0.413750i	−0.960393	−	0.278649i	$-0.910113\pi$
$761$	−6.58977	+	11.4138i	−0.238879	+	0.413750i	0.721514	+	0.692400i	$0.243447\pi$
$762$	−16.8031	+	5.47920i	−0.608712	+	0.198491i
$763$		0			0
$764$			22.4131i			0.810877i
$765$	−14.3949	−	2.44448i	−0.520450	−	0.0883802i
$766$	2.12110	−	1.22462i	0.0766384	−	0.0442472i
$767$	23.8582	+	41.3236i	0.861469	+	1.49211i
$768$	−13.3299	−	2.81871i	−0.481002	−	0.101711i
$769$		−	12.7709i		−	0.460530i	−0.973128	−	0.230265i	$-0.926041\pi$
$769$		−	12.7709i		−	0.460530i	0.973128	−	0.230265i	$-0.0739593\pi$
$770$		0			0
$771$	33.1047	−	10.7949i	1.19224	−	0.388768i
$772$	8.49437	+	4.90423i	0.305719	+	0.176507i
$773$	15.7518	−	9.09428i	0.566551	−	0.327099i	−0.189219	−	0.981935i	$-0.560596\pi$
$773$	15.7518	−	9.09428i	0.566551	−	0.327099i	0.755771	+	0.654836i	$0.227262\pi$
$774$	−5.12462	+	11.5756i	−0.184201	+	0.416075i
$775$	−0.933711	−	1.72087i	−0.0335399	−	0.0618154i
$776$	9.01267			0.323536
$777$		0			0
$778$			5.87388i			0.210589i
$779$	−8.83694	−	5.10201i	−0.316616	−	0.182798i
$780$	−21.8512	+	13.8149i	−0.782400	+	0.494651i
$781$	16.4930	+	28.5667i	0.590167	+	1.02220i
$782$	0.783728	+	0.452486i	0.0280261	+	0.0161809i
$783$	−3.55412	+	4.92442i	−0.127014	+	0.175985i
$784$		0			0
$785$	−36.2693	−	10.2347i	−1.29451	−	0.365291i
$786$	−18.0906	−	3.82540i	−0.645272	−	0.136447i
$787$	−0.619297	−	1.07265i	−0.0220756	−	0.0382360i	0.854777	−	0.518996i	$-0.173694\pi$
$787$	−0.619297	−	1.07265i	−0.0220756	−	0.0382360i	−0.876852	+	0.480760i	$0.840361\pi$
$788$	−10.3569	−	17.9388i	−0.368951	−	0.639042i
$789$	−14.8431	−	3.13869i	−0.528430	−	0.111740i
$790$	−5.20736	−	1.46944i	−0.185270	−	0.0522803i
$791$		0			0
$792$	16.5672	+	22.7022i	0.588690	+	0.806689i
$793$	−25.5102	−	14.7283i	−0.905895	−	0.523019i
$794$	−7.81449	−	13.5351i	−0.277326	−	0.480343i
$795$	−23.5749	+	14.9046i	−0.836114	+	0.528610i
$796$	−23.2580	−	13.4280i	−0.824359	−	0.475944i
$797$		−	51.4416i		−	1.82216i	−0.412235	−	0.911078i	$-0.635252\pi$
$797$		−	51.4416i		−	1.82216i	0.412235	−	0.911078i	$-0.364748\pi$
$798$		0			0
$799$	−16.9805			−0.600725
$800$	−25.0695	+	13.6023i	−0.886340	+	0.480912i
$801$	−2.45450	−	1.08663i	−0.0867254	−	0.0383942i
$802$	16.8617	−	9.73510i	0.595407	−	0.343758i
$803$	−18.3836	−	10.6138i	−0.648745	−	0.374553i
$804$	−22.7938	+	7.43268i	−0.803876	+	0.262130i
$805$		0			0
$806$			1.06383i			0.0374718i
$807$	29.2294	+	6.18077i	1.02892	+	0.217574i
$808$	−7.60797	−	13.1774i	−0.267647	−	0.463579i
$809$	−2.44518	+	1.41172i	−0.0859679	+	0.0496336i	−0.542368	−	0.840141i	$-0.682472\pi$
$809$	−2.44518	+	1.41172i	−0.0859679	+	0.0496336i	0.456400	+	0.889775i	$0.349139\pi$
$810$	−5.78658	−	11.6148i	−0.203320	−	0.408103i
$811$			0.162805i			0.00571687i	0.999996	+	0.00285843i	$0.000909869\pi$
$811$			0.162805i			0.00571687i	−0.999996	+	0.00285843i	$0.999090\pi$
$812$		0			0
$813$	37.2909	−	12.1599i	1.30785	−	0.426467i
$814$	5.57189	−	9.65080i	0.195295	−	0.338260i
$815$	10.4183	−	2.64430i	0.364936	−	0.0926259i
$816$	−4.70621	−	4.22853i	−0.164750	−	0.148028i
$817$	−14.6459	+	25.3675i	−0.512396	+	0.887496i
$818$			15.9051i			0.556108i
$819$		0			0
$820$	−7.77222	−	2.19320i	−0.271418	−	0.0765900i
$821$	43.3765	+	25.0434i	1.51385	+	0.874022i	0.999868	+	0.0162217i	$0.00516375\pi$
$821$	43.3765	+	25.0434i	1.51385	+	0.874022i	0.513983	+	0.857801i	$0.328170\pi$
$822$	−14.8254	+	16.5002i	−0.517096	+	0.575509i
$823$	−33.1050	+	19.1132i	−1.15397	+	0.666243i	−0.949851	−	0.312704i	$-0.898765\pi$
$823$	−33.1050	+	19.1132i	−1.15397	+	0.666243i	−0.204116	+	0.978947i	$0.565432\pi$
$824$	−11.3412	+	19.6435i	−0.395090	+	0.684315i
$825$	34.1407	+	8.16890i	1.18863	+	0.284405i
$826$		0			0
$827$	−7.13112			−0.247973			−0.123987	−	0.992284i	$-0.539568\pi$
$827$	−7.13112			−0.247973			−0.123987	+	0.992284i	$0.539568\pi$
$828$	−0.326744	−	3.04708i	−0.0113551	−	0.105894i
$829$	−0.876338	+	0.505954i	−0.0304365	+	0.0175725i	−0.515141	−	0.857105i	$-0.672260\pi$
$829$	−0.876338	+	0.505954i	−0.0304365	+	0.0175725i	0.484705	+	0.874678i	$0.338927\pi$
$830$	−7.37136	+	1.87096i	−0.255864	+	0.0649418i
$831$	−4.73399	+	22.3875i	−0.164220	+	0.776612i
$832$	1.35578			0.0470032
$833$		0			0
$834$	0.242906	−	0.0792075i	0.00841115	−	0.00274273i
$835$	6.94372	+	7.12999i	0.240297	+	0.246743i
$836$	14.3717	+	24.8925i	0.497056	+	0.860927i
$837$	2.02418	+	0.206294i	0.0699658	+	0.00713056i
$838$	12.7225	−	22.0360i	0.439492	−	0.761222i
$839$	29.5215			1.01920			0.509598	−	0.860412i	$-0.329794\pi$
$839$	29.5215			1.01920			0.509598	+	0.860412i	$0.329794\pi$
$840$		0			0
$841$	27.6340			0.952897
$842$	9.97394	−	17.2754i	0.343725	−	0.595348i
$843$	42.3496	+	38.0512i	1.45860	+	1.31055i
$844$	−14.5993	−	25.2868i	−0.502530	−	0.870408i
$845$	7.61343	−	7.41454i	0.261910	−	0.255068i
$846$	−8.89603	−	12.1903i	−0.305852	−	0.419112i
$847$		0			0
$848$	−12.0857			−0.415024
$849$	−26.7938	−	5.66576i	−0.919562	−	0.194448i
$850$	7.01494	+	0.185719i	0.240610	+	0.00637010i
$851$	−2.38085	+	1.37459i	−0.0816146	+	0.0471202i
$852$	4.61957	−	21.8463i	0.158264	−	0.748443i
$853$	−22.0904			−0.756362			−0.378181	−	0.925732i	$-0.623450\pi$
$853$	−22.0904			−0.756362			−0.378181	+	0.925732i	$0.623450\pi$
$854$		0			0
$855$	−10.4477	−	28.1497i	−0.357303	−	0.962700i
$856$	21.7009	−	37.5871i	0.741722	−	1.28470i
$857$	12.4112	−	7.16559i	0.423957	−	0.244772i	−0.272812	−	0.962067i	$-0.587954\pi$
$857$	12.4112	−	7.16559i	0.423957	−	0.244772i	0.696769	+	0.717296i	$0.254620\pi$
$858$	−14.1885	−	12.7484i	−0.484387	−	0.435223i
$859$	−23.7901	−	13.7352i	−0.811709	−	0.468640i	0.0358402	−	0.999358i	$-0.488589\pi$
$859$	−23.7901	−	13.7352i	−0.811709	−	0.468640i	−0.847549	+	0.530717i	$0.821923\pi$
$860$	−6.29585	+	22.3111i	−0.214687	+	0.760802i
$861$		0			0
$862$		−	19.8231i		−	0.675176i
$863$	−8.11130	+	14.0492i	−0.276112	+	0.478240i	−0.970415	−	0.241443i	$-0.922379\pi$
$863$	−8.11130	+	14.0492i	−0.276112	+	0.478240i	0.694303	+	0.719683i	$0.255713\pi$
$864$	3.00528	−	29.4881i	0.102242	−	1.00321i
$865$	24.8252	−	6.30099i	0.844082	−	0.214240i
$866$	0.953847	−	1.65211i	0.0324131	−	0.0561411i
$867$	−6.58451	−	20.1927i	−0.223622	−	0.685782i
$868$		0			0
$869$			15.2115i			0.516014i
$870$	1.35667	−	2.58430i	0.0459955	−	0.0876159i
$871$	31.8819	−	18.4070i	1.08028	−	0.623698i
$872$	1.04695	+	1.81336i	0.0354541	+	0.0614083i
$873$	1.24736	+	11.6324i	0.0422167	+	0.393696i
$874$			1.86101i			0.0629496i
$875$		0			0
$876$	4.45486	+	13.6617i	0.150516	+	0.461587i
$877$	38.5317	+	22.2463i	1.30112	+	0.751204i	0.980597	−	0.196036i	$-0.0628068\pi$
$877$	38.5317	+	22.2463i	1.30112	+	0.751204i	0.320527	+	0.947240i	$0.396140\pi$
$878$	9.72189	−	5.61294i	0.328098	−	0.189427i
$879$	−26.7722	−	24.0549i	−0.903004	−	0.811351i
$880$	10.6127	+	10.8974i	0.357754	+	0.367351i
$881$	0.841670			0.0283566			0.0141783	−	0.999899i	$-0.495487\pi$
$881$	0.841670			0.0283566			0.0141783	+	0.999899i	$0.495487\pi$
$882$		0			0
$883$			51.7706i			1.74222i	0.491088	+	0.871110i	$0.336600\pi$
$883$			51.7706i			1.74222i	−0.491088	+	0.871110i	$0.663400\pi$
$884$	12.5822	+	7.26434i	0.423185	+	0.244326i
$885$	−37.0734	+	23.4387i	−1.24621	+	0.787882i
$886$	−10.2505	−	17.7543i	−0.344371	−	0.596468i
$887$	48.4743	+	27.9867i	1.62761	+	0.939700i	0.984804	+	0.173669i	$0.0555623\pi$
$887$	48.4743	+	27.9867i	1.62761	+	0.939700i	0.642804	+	0.766031i	$0.277771\pi$
$888$	−16.2262	+	5.29107i	−0.544514	+	0.177557i
$889$		0			0
$890$	1.24160	+	0.350362i	0.0416186	+	0.0117441i
$891$	−27.0081	+	24.5248i	−0.904806	+	0.821611i
$892$	0.496986	+	0.860804i	0.0166403	+	0.0288219i
$893$	−17.4596	−	30.2409i	−0.584262	−	1.01197i
$894$	−2.30097	+	10.8815i	−0.0769560	+	0.363931i
$895$	6.34264	−	22.4769i	0.212011	−	0.751320i
$896$		0			0
$897$	1.45884	+	4.47383i	0.0487092	+	0.149377i
$898$	1.67224	+	0.965470i	0.0558035	+	0.0322182i
$899$	0.228825	+	0.396337i	0.00763175	+	0.0132186i
$900$	−13.4953	−	19.5596i	−0.449842	−	0.651985i
$901$	13.5747	+	7.83734i	0.452238	+	0.261100i
$902$		−	5.95854i		−	0.198398i
$903$		0			0
$904$	−20.4062			−0.678701
$905$	18.6609	+	19.1615i	0.620310	+	0.636950i
$906$	3.78776	−	4.21564i	0.125840	−	0.140055i
$907$	−31.4075	+	18.1332i	−1.04287	+	0.602102i	−0.920645	−	0.390401i	$-0.872336\pi$
$907$	−31.4075	+	18.1332i	−1.04287	+	0.602102i	−0.122226	+	0.992502i	$0.539003\pi$
$908$	−7.44902	−	4.30070i	−0.247205	−	0.142724i
$909$	15.9547	−	11.6431i	0.529183	−	0.386178i
$910$		0			0
$911$		−	5.35784i		−	0.177513i	−0.996053	−	0.0887565i	$-0.971711\pi$
$911$		−	5.35784i		−	0.177513i	0.996053	−	0.0887565i	$-0.0282893\pi$
$912$	2.69169	−	12.7292i	0.0891308	−	0.421507i
$913$	10.6903	+	18.5162i	0.353798	+	0.612797i
$914$	4.91690	−	2.83877i	0.162637	−	0.0938983i
$915$	12.5856	−	23.9741i	0.416067	−	0.792559i
$916$			22.7716i			0.752396i
$917$		0			0
$918$	−4.26790	+	5.91341i	−0.140862	+	0.195172i
$919$	−10.0571	+	17.4194i	−0.331754	+	0.574615i	−0.982856	−	0.184376i	$-0.940974\pi$
$919$	−10.0571	+	17.4194i	−0.331754	+	0.574615i	0.651102	+	0.758990i	$0.274307\pi$
$920$	0.819779	+	3.22984i	0.0270273	+	0.106485i
$921$	−15.0325	+	16.7306i	−0.495337	+	0.551292i
$922$	−10.3075	+	17.8532i	−0.339461	+	0.587963i
$923$			34.2872i			1.12858i
$924$		0			0
$925$	−11.1438	+	18.1732i	−0.366405	+	0.597532i
$926$	3.87818	+	2.23907i	0.127445	+	0.0735804i
$927$	−26.9229	−	11.9190i	−0.884264	−	0.391473i
$928$	5.77382	−	3.33351i	0.189535	−	0.109428i
$929$	−3.39903	+	5.88728i	−0.111518	+	0.193156i	−0.916383	−	0.400303i	$-0.868905\pi$
$929$	−3.39903	+	5.88728i	−0.111518	+	0.193156i	0.804864	+	0.593459i	$0.202238\pi$
$930$	−0.977090	+	0.0392781i	−0.0320401	+	0.00128798i
$931$		0			0
$932$	13.3558			0.437483
$933$	0.775525	+	0.163991i	0.0253896	+	0.00536881i
$934$	−13.6662	+	7.89021i	−0.447173	+	0.258176i
$935$	−4.85346	−	19.1221i	−0.158725	−	0.625360i
$936$	3.11471	+	29.0466i	0.101808	+	0.949417i
$937$	44.1327			1.44175			0.720877	−	0.693063i	$-0.243739\pi$
$937$	44.1327			1.44175			0.720877	+	0.693063i	$0.243739\pi$
$938$		0			0
$939$	−14.8965	−	45.6830i	−0.486128	−	1.49081i
$940$	−19.2812	−	19.7985i	−0.628885	−	0.645755i
$941$	4.53288	+	7.85118i	0.147768	+	0.255941i	0.930402	−	0.366540i	$-0.119458\pi$
$941$	4.53288	+	7.85118i	0.147768	+	0.255941i	−0.782634	+	0.622482i	$0.786125\pi$
$942$	−12.5801	+	14.0012i	−0.409882	+	0.456184i
$943$	−0.734986	+	1.27303i	−0.0239344	+	0.0414557i
$944$	−19.0057			−0.618584
$945$		0			0
$946$	−17.1047			−0.556122
$947$	17.7437	−	30.7330i	0.576593	−	0.998689i	−0.419273	−	0.907860i	$-0.637715\pi$
$947$	17.7437	−	30.7330i	0.576593	−	0.998689i	0.995867	−	0.0908285i	$-0.0289515\pi$
$948$	6.88211	−	7.65955i	0.223521	−	0.248771i
$949$	−11.0325	−	19.1088i	−0.358129	−	0.620297i
$950$	6.88212	+	12.6840i	0.223285	+	0.411524i
$951$	2.42891	+	7.44873i	0.0787627	+	0.241542i
$952$		0			0
$953$	−10.8726			−0.352198			−0.176099	−	0.984373i	$-0.556348\pi$
$953$	−10.8726			−0.352198			−0.176099	+	0.984373i	$0.556348\pi$
$954$	1.48529	+	13.8513i	0.0480882	+	0.448451i
$955$	30.6629	−	7.78267i	0.992227	−	0.251841i
$956$	−3.72976	+	2.15338i	−0.120629	+	0.0696452i
$957$	−8.02816	−	1.69761i	−0.259514	−	0.0548761i
$958$	15.6625			0.506031
$959$		0			0
$960$	0.0500574	+	1.24524i	0.00161560	+	0.0401899i
$961$	−15.4233	+	26.7140i	−0.497527	+	0.861742i
$962$	10.0315	−	5.79167i	0.323428	−	0.186731i
$963$	51.5158	+	22.8066i	1.66007	+	0.734932i
$964$	2.09841	+	1.21152i	0.0675853	+	0.0390204i
$965$	3.75981	−	13.3239i	0.121032	−	0.428912i
$966$		0			0
$967$			21.3855i			0.687711i	0.939023	+	0.343855i	$0.111733\pi$
$967$			21.3855i			0.687711i	−0.939023	+	0.343855i	$0.888267\pi$
$968$	−6.27575	+	10.8699i	−0.201710	+	0.349373i
$969$	−11.2780	+	12.5520i	−0.362301	+	0.403228i
$970$	−1.38325	−	5.44987i	−0.0444136	−	0.174985i
$971$	4.43174	−	7.67600i	0.142221	−	0.246335i	−0.786112	−	0.618085i	$-0.787909\pi$
$971$	4.43174	−	7.67600i	0.142221	−	0.246335i	0.928333	+	0.371750i	$0.121242\pi$
$972$	24.6953	−	0.129881i	0.792102	−	0.00416593i
$973$		0			0
$974$		−	6.29102i		−	0.201577i
$975$	26.4874	+	25.0972i	0.848275	+	0.803754i
$976$	10.1609	−	5.86639i	0.325242	−	0.187779i
$977$	0.365536	+	0.633128i	0.0116945	+	0.0202555i	0.871813	−	0.489838i	$-0.162944\pi$
$977$	0.365536	+	0.633128i	0.0116945	+	0.0202555i	−0.860119	+	0.510094i	$0.829611\pi$
$978$	1.11066	−	5.25241i	0.0355150	−	0.167953i
$979$		−	3.62691i		−	0.115916i
$980$		0			0
$981$	−2.19555	+	1.60223i	−0.0700986	+	0.0511553i
$982$	−13.2171	−	7.63091i	−0.421775	−	0.243512i
$983$	3.23213	−	1.86607i	0.103089	−	0.0595184i	−0.447569	−	0.894249i	$-0.647710\pi$
$983$	3.23213	−	1.86607i	0.103089	−	0.0595184i	0.550658	+	0.834731i	$0.314377\pi$
$984$	−6.09913	+	6.78812i	−0.194433	+	0.216397i
$985$	−20.9453	+	20.3981i	−0.667373	+	0.649939i
$986$	−1.64032			−0.0522385
$987$		0			0
$988$			29.8772i			0.950520i
$989$	3.65439	+	2.10987i	0.116203	+	0.0670898i
$990$	11.1851	−	13.5023i	0.355486	−	0.429133i
$991$	2.74255	+	4.75024i	0.0871200	+	0.150896i	0.906293	−	0.422651i	$-0.138900\pi$
$991$	2.74255	+	4.75024i	0.0871200	+	0.150896i	−0.819173	+	0.573547i	$0.805567\pi$
$992$	−1.93442	−	1.11684i	−0.0614178	−	0.0354596i
$993$	12.2946	+	37.7039i	0.390158	+	1.19650i
$994$		0			0
$995$	−10.2945	+	36.4815i	−0.326359	+	1.15654i
$996$	2.99428	−	14.1602i	0.0948774	−	0.448683i
$997$	−2.53609	−	4.39264i	−0.0803189	−	0.139116i	0.823068	−	0.567943i	$-0.192261\pi$
$997$	−2.53609	−	4.39264i	−0.0803189	−	0.139116i	−0.903387	+	0.428826i	$0.858927\pi$
$998$	3.69818	+	6.40544i	0.117064	+	0.202761i
$999$	−9.07472	−	20.2103i	−0.287111	−	0.639425i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.p.f.509.6		24
3.2	odd	2	inner	735.2.p.f.509.8		24
5.4	even	2	inner	735.2.p.f.509.7		24
7.2	even	3		735.2.g.b.734.13		24
7.3	odd	6	inner	735.2.p.f.374.5		24
7.4	even	3		105.2.p.a.59.6	yes	24
7.5	odd	6		735.2.g.b.734.16		24
7.6	odd	2		105.2.p.a.89.5	yes	24
15.14	odd	2	inner	735.2.p.f.509.5		24
21.2	odd	6		735.2.g.b.734.10		24
21.5	even	6		735.2.g.b.734.11		24
21.11	odd	6		105.2.p.a.59.8	yes	24
21.17	even	6	inner	735.2.p.f.374.7		24
21.20	even	2		105.2.p.a.89.7	yes	24
35.4	even	6		105.2.p.a.59.7	yes	24
35.9	even	6		735.2.g.b.734.12		24
35.13	even	4		525.2.t.j.26.8		24
35.18	odd	12		525.2.t.j.101.6		24
35.19	odd	6		735.2.g.b.734.9		24
35.24	odd	6	inner	735.2.p.f.374.8		24
35.27	even	4		525.2.t.j.26.5		24
35.32	odd	12		525.2.t.j.101.7		24
35.34	odd	2		105.2.p.a.89.8	yes	24
105.32	even	12		525.2.t.j.101.5		24
105.44	odd	6		735.2.g.b.734.15		24
105.53	even	12		525.2.t.j.101.8		24
105.59	even	6	inner	735.2.p.f.374.6		24
105.62	odd	4		525.2.t.j.26.7		24
105.74	odd	6		105.2.p.a.59.5	✓	24
105.83	odd	4		525.2.t.j.26.6		24
105.89	even	6		735.2.g.b.734.14		24
105.104	even	2		105.2.p.a.89.6	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.p.a.59.5	✓	24	105.74	odd	6
105.2.p.a.59.6	yes	24	7.4	even	3
105.2.p.a.59.7	yes	24	35.4	even	6
105.2.p.a.59.8	yes	24	21.11	odd	6
105.2.p.a.89.5	yes	24	7.6	odd	2
105.2.p.a.89.6	yes	24	105.104	even	2
105.2.p.a.89.7	yes	24	21.20	even	2
105.2.p.a.89.8	yes	24	35.34	odd	2
525.2.t.j.26.5		24	35.27	even	4
525.2.t.j.26.6		24	105.83	odd	4
525.2.t.j.26.7		24	105.62	odd	4
525.2.t.j.26.8		24	35.13	even	4
525.2.t.j.101.5		24	105.32	even	12
525.2.t.j.101.6		24	35.18	odd	12
525.2.t.j.101.7		24	35.32	odd	12
525.2.t.j.101.8		24	105.53	even	12
735.2.g.b.734.9		24	35.19	odd	6
735.2.g.b.734.10		24	21.2	odd	6
735.2.g.b.734.11		24	21.5	even	6
735.2.g.b.734.12		24	35.9	even	6
735.2.g.b.734.13		24	7.2	even	3
735.2.g.b.734.14		24	105.89	even	6
735.2.g.b.734.15		24	105.44	odd	6
735.2.g.b.734.16		24	7.5	odd	6
735.2.p.f.374.5		24	7.3	odd	6	inner
735.2.p.f.374.6		24	105.59	even	6	inner
735.2.p.f.374.7		24	21.17	even	6	inner
735.2.p.f.374.8		24	35.24	odd	6	inner
735.2.p.f.509.5		24	15.14	odd	2	inner
735.2.p.f.509.6		24	1.1	even	1	trivial
735.2.p.f.509.7		24	5.4	even	2	inner
735.2.p.f.509.8		24	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.322403 + 0.558418i) q^{2} +(-1.15761 + 1.28838i) q^{3} +(0.792113 + 1.37198i) q^{4} +(1.60193 - 1.56008i) q^{5} +(-0.346239 - 1.06181i) q^{6} -2.31113 q^{8} +(-0.319861 - 2.98290i) q^{9} +(0.354709 + 1.39752i) q^{10} +(3.51044 - 2.02675i) q^{11} +(-2.68460 - 0.567678i) q^{12} +4.21339 q^{13} +(0.155565 + 3.86986i) q^{15} +(-0.839111 + 1.45338i) q^{16} +(1.88498 - 1.08830i) q^{17} +(1.76883 + 0.783079i) q^{18} +(3.87634 + 2.23800i) q^{19} +(3.40930 + 0.962052i) q^{20} +2.61372i q^{22} +(0.322403 - 0.558418i) q^{23} +(2.67540 - 2.97762i) q^{24} +(0.132327 - 4.99825i) q^{25} +(-1.35841 + 2.35284i) q^{26} +(4.21339 + 3.04094i) q^{27} +1.16875i q^{29} +(-2.21115 - 1.16078i) q^{30} +(0.339111 - 0.195786i) q^{31} +(-2.85219 - 4.94014i) q^{32} +(-1.45250 + 6.86898i) q^{33} +1.40348i q^{34} +(3.83911 - 2.80164i) q^{36} +(-3.69236 - 2.13178i) q^{37} +(-2.49949 + 1.44308i) q^{38} +(-4.87748 + 5.42846i) q^{39} +(-3.70226 + 3.60554i) q^{40} -2.27971 q^{41} +6.54419i q^{43} +(5.56132 + 3.21083i) q^{44} +(-5.16594 - 4.27937i) q^{45} +(0.207887 + 0.360071i) q^{46} +(-6.75621 - 3.90070i) q^{47} +(-0.901147 - 2.76355i) q^{48} +(2.74845 + 1.68534i) q^{50} +(-0.779941 + 3.68841i) q^{51} +(3.33748 + 5.78069i) q^{52} +(3.60074 + 6.23667i) q^{53} +(-3.05653 + 1.37243i) q^{54} +(2.46157 - 8.72325i) q^{55} +(-7.37071 + 2.40346i) q^{57} +(-0.652654 - 0.376810i) q^{58} +(5.66247 + 9.80768i) q^{59} +(-5.18614 + 3.27880i) q^{60} +(-6.05456 - 3.49560i) q^{61} +0.252487i q^{62} +0.321779 q^{64} +(6.74954 - 6.57321i) q^{65} +(-3.36748 - 3.02568i) q^{66} +(7.56680 - 4.36870i) q^{67} +(2.98624 + 1.72411i) q^{68} +(0.346239 + 1.06181i) q^{69} +8.13766i q^{71} +(0.739241 + 6.89387i) q^{72} +(-2.61843 - 4.53525i) q^{73} +(2.38085 - 1.37459i) q^{74} +(6.28647 + 5.95653i) q^{75} +7.09101i q^{76} +(-1.45884 - 4.47383i) q^{78} +(-1.87634 + 3.24991i) q^{79} +(0.923194 + 3.63729i) q^{80} +(-8.79538 + 1.90823i) q^{81} +(0.734986 - 1.27303i) q^{82} +5.27461i q^{83} +(1.32178 - 4.68409i) q^{85} +(-3.65439 - 2.10987i) q^{86} +(-1.50580 - 1.35297i) q^{87} +(-8.11308 + 4.68409i) q^{88} +(0.447379 - 0.774883i) q^{89} +(4.05520 - 1.50507i) q^{90} +1.02152 q^{92} +(-0.140312 + 0.663548i) q^{93} +(4.35644 - 2.51519i) q^{94} +(9.70106 - 2.46227i) q^{95} +(9.66653 + 2.04406i) q^{96} -3.89968 q^{97} +(-7.16845 - 9.82300i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 6 q^{9} - 24 q^{15} - 12 q^{16} - 18 q^{24} - 12 q^{25} + 18 q^{30} + 84 q^{36} - 12 q^{39} + 72 q^{40} + 18 q^{45} + 36 q^{46} - 12 q^{51} + 36 q^{54} + 12 q^{60} - 36 q^{61} + 24 q^{64}+ \cdots - 48 q^{99}+O(q^{100}) \) 24 * q - 12 * q^4 - 6 * q^9 - 24 * q^15 - 12 * q^16 - 18 * q^24 - 12 * q^25 + 18 * q^30 + 84 * q^36 - 12 * q^39 + 72 * q^40 + 18 * q^45 + 36 * q^46 - 12 * q^51 + 36 * q^54 + 12 * q^60 - 36 * q^61 + 24 * q^64 + 72 * q^66 - 72 * q^75 + 48 * q^79 - 6 * q^81 + 48 * q^85 + 72 * q^94 + 90 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

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