LMFDB - Embedded newform 798.2.bu.b.527.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(53,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 12, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.53"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bu (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [162,0,0,0,0,0,0,81] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			527.5
Character	$\chi$	$=$	798.527
Dual form			798.2.bu.b.53.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 + 0.984808i) q^{2} +(-1.50443 - 0.858307i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(1.35069 + 3.71100i) q^{5} +(1.10651 - 1.33253i) q^{6} +(0.939767 - 2.47322i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.52662 + 2.58253i) q^{9} +(-3.88916 + 0.685764i) q^{10} -2.71460i q^{11} +(1.12014 + 1.32109i) q^{12} +(3.46167 - 0.610385i) q^{13} +(2.27246 + 1.35496i) q^{14} +(1.15315 - 6.74224i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.0364524 + 0.0434422i) q^{17} +(-2.80839 + 1.05497i) q^{18} +(1.41333 - 4.12341i) q^{19} -3.94916i q^{20} +(-3.53660 + 2.91418i) q^{21} +(2.67336 + 0.471385i) q^{22} +(-2.76563 + 0.487655i) q^{23} +(-1.49553 + 0.873721i) q^{24} +(-8.11690 + 6.81089i) q^{25} +3.51507i q^{26} +(-0.0800903 - 5.19554i) q^{27} +(-1.72898 + 2.00265i) q^{28} +(0.757331 + 0.275646i) q^{29} +(6.43957 + 2.30641i) q^{30} +(8.15495 + 4.70826i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-2.32996 + 4.08392i) q^{33} +(-0.0364524 - 0.0434422i) q^{34} +(10.4475 + 0.146906i) q^{35} +(-0.551276 - 2.94891i) q^{36} +(5.82959 + 3.36571i) q^{37} +(3.81534 + 2.10788i) q^{38} +(-5.73173 - 2.05289i) q^{39} +(3.88916 + 0.685764i) q^{40} +(0.280452 - 1.59052i) q^{41} +(-2.25579 - 3.98891i) q^{42} +(6.84678 + 5.74513i) q^{43} +(-0.928448 + 2.55089i) q^{44} +(-7.52175 + 9.15347i) q^{45} -2.80829i q^{46} +(-2.85011 - 3.39663i) q^{47} +(-0.600751 - 1.62453i) q^{48} +(-5.23368 - 4.64851i) q^{49} +(-5.29793 - 9.17628i) q^{50} +(0.0921268 - 0.0340685i) q^{51} +(-3.46167 - 0.610385i) q^{52} +(8.67661 + 3.15803i) q^{53} +(5.13051 + 0.823322i) q^{54} +(10.0739 - 3.66659i) q^{55} +(-1.67199 - 2.05047i) q^{56} +(-5.66540 + 4.99031i) q^{57} +(-0.402967 + 0.697960i) q^{58} +(5.03918 + 4.22838i) q^{59} +(-3.38959 + 5.94123i) q^{60} +(-0.0164697 - 0.0934044i) q^{61} +(-6.05282 + 7.21347i) q^{62} +(7.82183 - 1.34870i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(6.94078 + 12.0218i) q^{65} +(-3.61729 - 3.00373i) q^{66} +(-11.8003 + 2.08072i) q^{67} +(0.0491121 - 0.0283549i) q^{68} +(4.57925 + 1.64012i) q^{69} +(-1.95886 + 10.2632i) q^{70} +(9.86443 + 8.27724i) q^{71} +(2.99984 - 0.0308274i) q^{72} +(8.25330 - 3.00395i) q^{73} +(-4.32688 + 5.15657i) q^{74} +(18.0571 - 3.27971i) q^{75} +(-2.73838 + 3.39135i) q^{76} +(-6.71381 - 2.55109i) q^{77} +(3.01701 - 5.28817i) q^{78} +(-0.766708 + 0.913727i) q^{79} +(-1.35069 + 3.71100i) q^{80} +(-4.33887 + 7.88506i) q^{81} +(1.51766 + 0.552382i) q^{82} +(-7.35714 + 4.24765i) q^{83} +(4.32003 - 1.52885i) q^{84} +(-0.210450 - 0.0765975i) q^{85} +(-6.84678 + 5.74513i) q^{86} +(-0.902763 - 1.06471i) q^{87} +(-2.35091 - 1.35730i) q^{88} +(5.32221 + 1.93713i) q^{89} +(-7.70827 - 8.99696i) q^{90} +(1.74354 - 9.13510i) q^{91} +(2.76563 + 0.487655i) q^{92} +(-8.22741 - 14.0827i) q^{93} +(3.83995 - 2.21699i) q^{94} +(17.2109 - 0.324613i) q^{95} +(1.70417 - 0.309528i) q^{96} +(-3.03805 - 8.34698i) q^{97} +(5.48671 - 4.34696i) q^{98} +(7.01052 - 4.14416i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 81 q^{8} + 15 q^{13} - 6 q^{14} + 3 q^{15} + 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} + 9 q^{27} + 9 q^{28} - 6 q^{29} + 24 q^{33} + 6 q^{34} - 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots + 39 q^{99}+O(q^{100}) $ 162 * q + 81 * q^8 + 15 * q^13 - 6 * q^14 + 3 * q^15 + 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 + 9 * q^27 + 9 * q^28 - 6 * q^29 + 24 * q^33 + 6 * q^34 - 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 + 12 * q^44 + 45 * q^45 - 12 * q^47 - 48 * q^49 - 87 * q^50 + 24 * q^51 - 15 * q^52 + 18 * q^54 - 18 * q^57 + 48 * q^59 + 18 * q^60 + 45 * q^61 - 36 * q^62 - 21 * q^63 - 81 * q^64 - 36 * q^65 + 12 * q^66 + 9 * q^67 - 9 * q^69 - 24 * q^70 - 12 * q^71 + 102 * q^73 - 39 * q^74 - 18 * q^78 - 42 * q^79 - 12 * q^81 + 57 * q^84 - 6 * q^85 + 9 * q^86 + 60 * q^87 - 54 * q^89 + 12 * q^90 - 18 * q^91 + 105 * q^93 - 72 * q^94 - 12 * q^97 + 27 * q^98 + 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{18}\right)$	$-1$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	−1.50443	−	0.858307i	−0.868583	−	0.495544i
$3$	−1.50443	−	0.858307i	−0.868583	−	0.495544i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	1.35069	+	3.71100i	0.604048	+	1.65961i	0.742986	+	0.669307i	$0.233409\pi$
$5$	1.35069	+	3.71100i	0.604048	+	1.65961i	−0.138938	+	0.990301i	$0.544369\pi$
$6$	1.10651	−	1.33253i	0.451730	−	0.544003i
$7$	0.939767	−	2.47322i	0.355198	−	0.934791i
$7$	0.939767	−	2.47322i	0.355198	−	0.934791i
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	1.52662	+	2.58253i	0.508873	+	0.860842i
$10$	−3.88916	+	0.685764i	−1.22986	+	0.216858i
$11$		−	2.71460i		−	0.818482i	−0.912426	−	0.409241i	$-0.865793\pi$
$11$		−	2.71460i		−	0.818482i	0.912426	−	0.409241i	$-0.134207\pi$
$12$	1.12014	+	1.32109i	0.323358	+	0.381366i
$13$	3.46167	−	0.610385i	0.960094	−	0.169290i	0.328426	−	0.944530i	$-0.393482\pi$
$13$	3.46167	−	0.610385i	0.960094	−	0.169290i	0.631668	+	0.775239i	$0.282371\pi$
$14$	2.27246	+	1.35496i	0.607341	+	0.362128i
$15$	1.15315	−	6.74224i	0.297743	−	1.74084i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−0.0364524	+	0.0434422i	−0.00884100	+	0.0105363i	−0.770447	−	0.637504i	$-0.779967\pi$
$17$	−0.0364524	+	0.0434422i	−0.00884100	+	0.0105363i	0.761606	+	0.648041i	$0.224411\pi$
$18$	−2.80839	+	1.05497i	−0.661943	+	0.248660i
$19$	1.41333	−	4.12341i	0.324239	−	0.945975i
$19$	1.41333	−	4.12341i	0.324239	−	0.945975i
$20$		−	3.94916i		−	0.883059i
$21$	−3.53660	+	2.91418i	−0.771749	+	0.635927i
$22$	2.67336	+	0.471385i	0.569962	+	0.100500i
$23$	−2.76563	+	0.487655i	−0.576674	+	0.101683i	−0.454376	−	0.890810i	$-0.650138\pi$
$23$	−2.76563	+	0.487655i	−0.576674	+	0.101683i	−0.122298	+	0.992493i	$0.539026\pi$
$24$	−1.49553	+	0.873721i	−0.305274	+	0.178348i
$25$	−8.11690	+	6.81089i	−1.62338	+	1.36218i
$26$			3.51507i			0.689362i
$27$	−0.0800903	−	5.19554i	−0.0154134	−	0.999881i
$28$	−1.72898	+	2.00265i	−0.326747	+	0.378466i
$29$	0.757331	+	0.275646i	0.140633	+	0.0511862i	0.411378	−	0.911465i	$-0.365048\pi$
$29$	0.757331	+	0.275646i	0.140633	+	0.0511862i	−0.270745	+	0.962651i	$0.587270\pi$
$30$	6.43957	+	2.30641i	1.17570	+	0.421091i
$31$	8.15495	+	4.70826i	1.46467	+	0.845629i	0.999222	−	0.0394454i	$-0.0125591\pi$
$31$	8.15495	+	4.70826i	1.46467	+	0.845629i	0.465450	+	0.885074i	$0.345892\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	−2.32996	+	4.08392i	−0.405594	+	0.710920i
$34$	−0.0364524	−	0.0434422i	−0.00625153	−	0.00745028i
$35$	10.4475	+	0.146906i	1.76594	+	0.0248317i
$36$	−0.551276	−	2.94891i	−0.0918794	−	0.491486i
$37$	5.82959	+	3.36571i	0.958378	+	0.553320i	0.895674	−	0.444712i	$-0.146694\pi$
$37$	5.82959	+	3.36571i	0.958378	+	0.553320i	0.0627049	+	0.998032i	$0.480027\pi$
$38$	3.81534	+	2.10788i	0.618931	+	0.341943i
$39$	−5.73173	−	2.05289i	−0.917812	−	0.328726i
$40$	3.88916	+	0.685764i	0.614931	+	0.108429i
$41$	0.280452	−	1.59052i	0.0437992	−	0.248398i	−0.955045	−	0.296461i	$-0.904194\pi$
$41$	0.280452	−	1.59052i	0.0437992	−	0.248398i	0.998844	+	0.0480629i	$0.0153048\pi$
$42$	−2.25579	−	3.98891i	−0.348075	−	0.615503i
$43$	6.84678	+	5.74513i	1.04412	+	0.876125i	0.992464	−	0.122540i	$-0.0391040\pi$
$43$	6.84678	+	5.74513i	1.04412	+	0.876125i	0.0516611	+	0.998665i	$0.483548\pi$
$44$	−0.928448	+	2.55089i	−0.139969	+	0.384561i
$45$	−7.52175	+	9.15347i	−1.12128	+	1.36452i
$46$		−	2.80829i		−	0.414060i
$47$	−2.85011	−	3.39663i	−0.415732	−	0.495450i	0.517018	−	0.855974i	$-0.327042\pi$
$47$	−2.85011	−	3.39663i	−0.415732	−	0.495450i	−0.932750	+	0.360525i	$0.882598\pi$
$48$	−0.600751	−	1.62453i	−0.0867109	−	0.234481i
$49$	−5.23368	−	4.64851i	−0.747668	−	0.664073i
$50$	−5.29793	−	9.17628i	−0.749240	−	1.29772i
$51$	0.0921268	−	0.0340685i	0.0129003	−	0.00477054i
$52$	−3.46167	−	0.610385i	−0.480047	−	0.0846452i
$53$	8.67661	+	3.15803i	1.19182	+	0.433788i	0.860364	−	0.509681i	$-0.170237\pi$
$53$	8.67661	+	3.15803i	1.19182	+	0.433788i	0.331460	+	0.943469i	$0.392459\pi$
$54$	5.13051	+	0.823322i	0.698174	+	0.112040i
$55$	10.0739	−	3.66659i	1.35836	−	0.494403i
$56$	−1.67199	−	2.05047i	−0.223429	−	0.274006i
$57$	−5.66540	+	4.99031i	−0.750401	+	0.660983i
$58$	−0.402967	+	0.697960i	−0.0529122	+	0.0916467i
$59$	5.03918	+	4.22838i	0.656046	+	0.550488i	0.908899	−	0.417017i	$-0.136924\pi$
$59$	5.03918	+	4.22838i	0.656046	+	0.550488i	−0.252853	+	0.967505i	$0.581369\pi$
$60$	−3.38959	+	5.94123i	−0.437594	+	0.767010i
$61$	−0.0164697	−	0.0934044i	−0.00210873	−	0.0119592i	0.983735	−	0.179625i	$-0.0574883\pi$
$61$	−0.0164697	−	0.0934044i	−0.00210873	−	0.0119592i	−0.985844	+	0.167665i	$0.946377\pi$
$62$	−6.05282	+	7.21347i	−0.768709	+	0.916112i
$63$	7.82183	−	1.34870i	0.985458	−	0.169920i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	6.94078	+	12.0218i	0.860898	+	1.49112i
$66$	−3.61729	−	3.00373i	−0.445257	−	0.369733i
$67$	−11.8003	+	2.08072i	−1.44164	+	0.254200i	−0.839139	−	0.543917i	$-0.816941\pi$
$67$	−11.8003	+	2.08072i	−1.44164	+	0.254200i	−0.602502	+	0.798117i	$0.705830\pi$
$68$	0.0491121	−	0.0283549i	0.00595572	−	0.00343854i
$69$	4.57925	+	1.64012i	0.551277	+	0.197447i
$70$	−1.95886	+	10.2632i	−0.234128	+	1.22669i
$71$	9.86443	+	8.27724i	1.17069	+	0.982327i	0.999996	−	0.00299625i	$-0.000953739\pi$
$71$	9.86443	+	8.27724i	1.17069	+	0.982327i	0.170697	+	0.985324i	$0.445398\pi$
$72$	2.99984	−	0.0308274i	0.353535	−	0.00363305i
$73$	8.25330	−	3.00395i	0.965975	−	0.351586i	0.189603	−	0.981861i	$-0.439280\pi$
$73$	8.25330	−	3.00395i	0.965975	−	0.351586i	0.776372	+	0.630275i	$0.217058\pi$
$74$	−4.32688	+	5.15657i	−0.502990	+	0.599440i
$75$	18.0571	−	3.27971i	2.08506	−	0.378708i
$76$	−2.73838	+	3.39135i	−0.314114	+	0.389015i
$77$	−6.71381	−	2.55109i	−0.765110	−	0.290724i
$78$	3.01701	−	5.28817i	0.341609	−	0.598768i
$79$	−0.766708	+	0.913727i	−0.0862614	+	0.102802i	−0.807449	−	0.589938i	$-0.799152\pi$
$79$	−0.766708	+	0.913727i	−0.0862614	+	0.102802i	0.721187	+	0.692740i	$0.243597\pi$
$80$	−1.35069	+	3.71100i	−0.151012	+	0.414902i
$81$	−4.33887	+	7.88506i	−0.482097	+	0.876118i
$82$	1.51766	+	0.552382i	0.167597	+	0.0610004i
$83$	−7.35714	+	4.24765i	−0.807551	+	0.466240i	−0.846105	−	0.533017i	$-0.821058\pi$
$83$	−7.35714	+	4.24765i	−0.807551	+	0.466240i	0.0385538	+	0.999257i	$0.487725\pi$
$84$	4.32003	−	1.52885i	0.471353	−	0.166811i
$85$	−0.210450	−	0.0765975i	−0.0228265	−	0.00830817i
$86$	−6.84678	+	5.74513i	−0.738308	+	0.619514i
$87$	−0.902763	−	1.06471i	−0.0967863	−	0.114149i
$88$	−2.35091	−	1.35730i	−0.250608	−	0.144689i
$89$	5.32221	+	1.93713i	0.564154	+	0.205335i	0.608324	−	0.793689i	$-0.291842\pi$
$89$	5.32221	+	1.93713i	0.564154	+	0.205335i	−0.0441702	+	0.999024i	$0.514064\pi$
$90$	−7.70827	−	8.99696i	−0.812523	−	0.948363i
$91$	1.74354	−	9.13510i	0.182773	−	0.957618i
$92$	2.76563	+	0.487655i	0.288337	+	0.0508416i
$93$	−8.22741	−	14.0827i	−0.853143	−	1.46031i
$94$	3.83995	−	2.21699i	0.396060	−	0.228665i
$95$	17.2109	−	0.324613i	1.76580	−	0.0333046i
$96$	1.70417	−	0.309528i	0.173931	−	0.0315910i
$97$	−3.03805	−	8.34698i	−0.308467	−	0.847507i	−0.992956	−	0.118484i	$-0.962197\pi$
$97$	−3.03805	−	8.34698i	−0.308467	−	0.847507i	0.684489	−	0.729024i	$-0.260026\pi$
$98$	5.48671	−	4.34696i	0.554241	−	0.439109i
$99$	7.01052	−	4.14416i	0.704584	−	0.416503i
$100$	9.95685	−	3.62400i	0.995685	−	0.362400i
$101$	−6.80491	−	8.10978i	−0.677114	−	0.806953i	0.312619	−	0.949879i	$-0.398794\pi$
$101$	−6.80491	−	8.10978i	−0.677114	−	0.806953i	−0.989734	+	0.142925i	$0.954349\pi$
$102$	0.0175533	+	0.0966431i	0.00173803	+	0.00956910i
$103$	−16.9721	+	9.79883i	−1.67231	+	0.965507i	−0.705965	+	0.708247i	$0.749486\pi$
$103$	−16.9721	+	9.79883i	−1.67231	+	0.965507i	−0.966342	+	0.257260i	$0.917180\pi$
$104$	1.20222	−	3.30308i	0.117888	−	0.323894i
$105$	−15.5914	−	9.18814i	−1.52156	−	0.896670i
$106$	−4.61673	+	7.99640i	−0.448416	+	0.776680i
$107$	−14.0234			−1.35570			−0.677848	−	0.735202i	$-0.737087\pi$
$107$	−14.0234			−1.35570			−0.677848	+	0.735202i	$0.737087\pi$
$108$	−1.70172	+	4.90960i	−0.163748	+	0.472426i
$109$	14.6037	+	2.57502i	1.39878	+	0.246642i	0.821641	−	0.570006i	$-0.193059\pi$
$109$	14.6037	+	2.57502i	1.39878	+	0.246642i	0.577136	+	0.816648i	$0.304170\pi$
$110$	1.86158	+	10.5575i	0.177494	+	1.00662i
$111$	−5.88139	−	10.0671i	−0.558237	−	0.955523i
$112$	2.30966	−	1.29053i	0.218242	−	0.121944i
$113$	8.08573			0.760641			0.380321	−	0.924855i	$-0.375814\pi$
$113$	8.08573			0.760641			0.380321	+	0.924855i	$0.375814\pi$
$114$	−3.93071	−	6.44589i	−0.368145	−	0.603713i
$115$	−5.54520	−	9.60457i	−0.517093	−	0.895631i
$116$	−0.617382	−	0.518045i	−0.0573225	−	0.0480993i
$117$	6.86098	+	8.00802i	0.634298	+	0.740341i
$118$	−5.03918	+	4.22838i	−0.463894	+	0.389254i
$119$	0.0731857	+	0.130980i	0.00670892	+	0.0120070i
$120$	−5.26238	−	4.36978i	−0.480387	−	0.398904i
$121$	3.63095			0.330087
$122$	0.0948453			0.00858689
$123$	−1.78707	+	2.15211i	−0.161135	+	0.194049i
$124$	−6.05282	−	7.21347i	−0.543560	−	0.647789i
$125$	−19.1382	−	11.0495i	−1.71178	−	0.988294i
$126$	−0.0300386	+	7.93720i	−0.00267605	+	0.707102i
$127$	0.681510	−	0.120169i	0.0604742	−	0.0106632i	−0.143329	−	0.989675i	$-0.545781\pi$
$127$	0.681510	−	0.120169i	0.0604742	−	0.0106632i	0.203803	+	0.979012i	$0.434670\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	−5.36942	−	14.5198i	−0.472751	−	1.27840i
$130$	−13.0444	+	4.74777i	−1.14407	+	0.416407i
$131$	−8.61472	−	1.51901i	−0.752671	−	0.132716i	−0.215867	−	0.976423i	$-0.569258\pi$
$131$	−8.61472	−	1.51901i	−0.752671	−	0.132716i	−0.536805	+	0.843707i	$0.680369\pi$
$132$	3.58623	−	3.04074i	0.312141	−	0.264662i
$133$	−8.86992	−	7.37051i	−0.769120	−	0.639105i
$134$		−	11.9824i		−	1.03512i
$135$	19.1724	−	7.31478i	1.65010	−	0.629556i
$136$	0.0193959	+	0.0532898i	0.00166318	+	0.00456956i
$137$	1.03767	−	2.85096i	0.0886538	−	0.243574i	−0.887440	−	0.460923i	$-0.847519\pi$
$137$	1.03767	−	2.85096i	0.0886538	−	0.243574i	0.976094	+	0.217348i	$0.0697408\pi$
$138$	−2.41038	+	4.22488i	−0.205185	+	0.359646i
$139$	−3.92412	−	22.2548i	−0.332839	−	1.88763i	−0.447601	−	0.894233i	$-0.647722\pi$
$139$	−3.92412	−	22.2548i	−0.332839	−	1.88763i	0.114762	−	0.993393i	$-0.463390\pi$
$140$	−9.76716	−	3.71129i	−0.825475	−	0.313661i
$141$	1.37244	+	7.55626i	0.115580	+	0.636352i
$142$	−9.86443	+	8.27724i	−0.827804	+	0.694610i
$143$	−1.65695	−	9.39704i	−0.138561	−	0.785820i
$144$	−0.490558	+	2.95962i	−0.0408798	+	0.246635i
$145$			3.18277i			0.264314i
$146$	1.52515	+	8.64954i	0.126222	+	0.715841i
$147$	3.88385	+	11.4855i	0.320335	+	0.947304i
$148$	−4.32688	−	5.15657i	−0.355667	−	0.423868i
$149$	−1.80498	+	2.15109i	−0.147869	+	0.176224i	−0.834895	−	0.550409i	$-0.814472\pi$
$149$	−1.80498	+	2.15109i	−0.147869	+	0.176224i	0.687025	+	0.726633i	$0.258916\pi$
$150$	0.0942950	+	18.3523i	0.00769915	+	1.49846i
$151$	7.97690	−	4.60546i	0.649151	−	0.374787i	−0.138980	−	0.990295i	$-0.544382\pi$
$151$	7.97690	−	4.60546i	0.649151	−	0.374787i	0.788131	+	0.615508i	$0.211049\pi$
$152$	−2.86432	−	3.28568i	−0.232327	−	0.266504i
$153$	−0.167840	−	0.0278195i	−0.0135690	−	0.00224907i
$154$	3.67817	−	6.16882i	0.296396	−	0.497098i
$155$	−6.45751	+	36.6224i	−0.518680	+	2.94158i
$156$	4.68394	+	3.88945i	0.375015	+	0.311406i
$157$	−1.04174	+	5.90799i	−0.0831397	+	0.471509i	0.914603	+	0.404353i	$0.132503\pi$
$157$	−1.04174	+	5.90799i	−0.0831397	+	0.471509i	−0.997743	+	0.0671552i	$0.978608\pi$
$158$	−0.766708	−	0.913727i	−0.0609960	−	0.0726922i
$159$	−10.3428	−	12.1982i	−0.820237	−	0.967382i
$160$	−3.42007	−	1.97458i	−0.270380	−	0.156104i
$161$	−1.39297	+	7.29831i	−0.109781	+	0.575187i
$162$	−7.01183	−	5.64218i	−0.550901	−	0.443292i
$163$	−8.47949	−	14.6869i	−0.664165	−	1.15037i	−0.979511	−	0.201391i	$-0.935454\pi$
$163$	−8.47949	−	14.6869i	−0.664165	−	1.15037i	0.315346	−	0.948977i	$-0.397879\pi$
$164$	−0.807529	+	1.39868i	−0.0630574	+	0.109219i
$165$	−18.3025	−	3.13035i	−1.42485	−	0.243697i
$166$	−2.90556	−	7.98296i	−0.225515	−	0.619598i
$167$	5.17415	−	4.34163i	0.400388	−	0.335965i	−0.420256	−	0.907406i	$-0.638060\pi$
$167$	5.17415	−	4.34163i	0.400388	−	0.335965i	0.820644	+	0.571440i	$0.193615\pi$
$168$	0.755458	+	4.51988i	0.0582848	+	0.348716i
$169$	−0.605437	+	0.220361i	−0.0465721	+	0.0169509i
$170$	0.111978	−	0.193952i	0.00858832	−	0.0148754i
$171$	12.8064	−	2.64492i	0.979331	−	0.202262i
$172$	−4.46892	−	7.74040i	−0.340752	−	0.590200i
$173$	4.12394	−	23.3880i	0.313537	−	1.77816i	−0.266769	−	0.963760i	$-0.585956\pi$
$173$	4.12394	−	23.3880i	0.313537	−	1.77816i	0.580307	−	0.814398i	$-0.302933\pi$
$174$	1.20530	−	0.704162i	0.0913736	−	0.0533824i
$175$	9.21686	+	26.4756i	0.696729	+	2.00136i
$176$	1.74491	−	2.07950i	0.131528	−	0.156748i
$177$	−3.95185	−	10.6865i	−0.297039	−	0.803244i
$178$	−2.83189	+	4.90498i	−0.212259	+	0.367644i
$179$	−11.8079			−0.882563			−0.441282	−	0.897369i	$-0.645476\pi$
$179$	−11.8079			−0.882563			−0.441282	+	0.897369i	$0.645476\pi$
$180$	10.1988	−	6.02886i	0.760174	−	0.449365i
$181$	−2.12488	+	5.83807i	−0.157941	+	0.433940i	−0.993272	−	0.115808i	$-0.963054\pi$
$181$	−2.12488	+	5.83807i	−0.157941	+	0.433940i	0.835330	+	0.549748i	$0.185276\pi$
$182$	8.69355	+	3.30334i	0.644409	+	0.244860i
$183$	−0.0553921	+	0.154656i	−0.00409470	+	0.0114325i
$184$	−0.960493	+	2.63893i	−0.0708085	+	0.194545i
$185$	−4.61617	+	26.1796i	−0.339388	+	1.92476i
$186$	15.2974	−	5.65699i	1.12166	−	0.414790i
$187$	0.117928	+	0.0989536i	0.00862377	+	0.00723620i
$188$	1.51651	+	4.16658i	0.110603	+	0.303879i
$189$	−12.9250	−	4.68451i	−0.940155	−	0.340748i
$190$	−2.66896	+	17.0058i	−0.193627	+	1.23373i
$191$	16.8166	+	9.70905i	1.21680	+	0.702522i	0.964233	−	0.265056i	$-0.0853904\pi$
$191$	16.8166	+	9.70905i	1.21680	+	0.702522i	0.252572	+	0.967578i	$0.418724\pi$
$192$	0.00889923	+	1.73203i	0.000642247	+	0.124998i
$193$	−0.741872	−	2.03828i	−0.0534011	−	0.146718i	0.910124	−	0.414336i	$-0.135986\pi$
$193$	−0.741872	−	2.03828i	−0.0534011	−	0.146718i	−0.963525	+	0.267617i	$0.913764\pi$
$194$	8.74772	−	1.54246i	0.628050	−	0.110742i
$195$	−0.123535	−	24.0433i	−0.00884654	−	1.72177i
$196$	3.32816	+	6.15819i	0.237726	+	0.439871i
$197$	−8.27774	+	4.77915i	−0.589764	+	0.340501i	−0.765004	−	0.644025i	$-0.777263\pi$
$197$	−8.27774	+	4.77915i	−0.589764	+	0.340501i	0.175240	+	0.984526i	$0.443930\pi$
$198$	2.86383	+	7.62364i	0.203524	+	0.541789i
$199$	−0.187794	−	1.06504i	−0.0133124	−	0.0754984i	0.977428	−	0.211270i	$-0.0677598\pi$
$199$	−0.187794	−	1.06504i	−0.0133124	−	0.0754984i	−0.990740	+	0.135771i	$0.956649\pi$
$200$	1.83995	+	10.4349i	0.130104	+	0.737858i
$201$	19.5387	+	6.99802i	1.37815	+	0.493602i
$202$	9.16824	−	5.29328i	0.645075	−	0.372434i
$203$	1.39345	−	1.61401i	0.0978009	−	0.113281i
$204$	−0.0982230		0.000504674i	−0.00687699		3.53342e-5i
$205$	6.28122	−	1.10755i	0.438699	−	0.0773545i
$206$	−6.70279	−	18.4158i	−0.467006	−	1.28309i
$207$	−5.48144	−	6.39785i	−0.380987	−	0.444681i
$208$	3.04414	+	1.75753i	0.211073	+	0.121863i
$209$	−11.1934	−	3.83661i	−0.774264	−	0.265384i
$210$	11.7560	−	13.7590i	0.811239	−	0.949462i
$211$	3.70231	+	10.1720i	0.254878	+	0.700271i	0.999464	+	0.0327445i	$0.0104247\pi$
$211$	3.70231	+	10.1720i	0.254878	+	0.700271i	−0.744586	+	0.667527i	$0.767353\pi$
$212$	−7.07324	−	5.93515i	−0.485792	−	0.407628i
$213$	−7.73593	−	20.9192i	−0.530057	−	1.43336i
$214$	2.43514	−	13.8104i	0.166463	−	0.944058i
$215$	−12.0723	+	33.1683i	−0.823322	+	2.26206i
$216$	−4.53951	−	2.52841i	−0.308875	−	0.172036i
$217$	19.3083	−	15.7443i	1.31074	−	1.06880i
$218$	−5.07180	+	13.9347i	−0.343506	+	0.943774i
$219$	−14.9948	−	2.56462i	−1.01326	−	0.173301i
$220$	−10.7204			−0.722768
$221$	−0.0996695	+	0.172633i	−0.00670449	+	0.0116125i
$222$	10.9354	−	4.04391i	0.733937	−	0.271410i
$223$	16.2821	−	19.4043i	1.09033	−	1.29941i	0.139321	−	0.990247i	$-0.455508\pi$
$223$	16.2821	−	19.4043i	1.09033	−	1.29941i	0.951010	−	0.309159i	$-0.100048\pi$
$224$	0.869855	+	2.49867i	0.0581196	+	0.166949i
$225$	−29.9807	−	10.5645i	−1.99871	−	0.704298i
$226$	−1.40407	+	7.96289i	−0.0933975	+	0.529683i
$227$	3.13145	+	5.42382i	0.207841	+	0.359992i	0.951034	−	0.309085i	$-0.100023\pi$
$227$	3.13145	+	5.42382i	0.207841	+	0.359992i	−0.743193	+	0.669077i	$0.766690\pi$
$228$	7.03052	−	2.75168i	0.465608	−	0.182234i
$229$	0.439100	−	0.760544i	0.0290166	−	0.0502582i	−0.851152	−	0.524919i	$-0.824096\pi$
$229$	0.439100	−	0.760544i	0.0290166	−	0.0502582i	0.880169	+	0.474660i	$0.157429\pi$
$230$	10.4216	−	3.79314i	0.687178	−	0.250112i
$231$	7.91084	+	9.60045i	0.520495	+	0.631663i
$232$	0.617382	−	0.518045i	0.0405331	−	0.0340113i
$233$	−7.83720	−	21.5325i	−0.513432	−	1.41064i	−0.877638	−	0.479324i	$-0.840882\pi$
$233$	−7.83720	−	21.5325i	−0.513432	−	1.41064i	0.364206	−	0.931318i	$-0.381340\pi$
$234$	−9.07775	+	5.36617i	−0.593431	+	0.350797i
$235$	8.75526	−	15.1646i	0.571130	−	0.989226i
$236$	−3.28909	−	5.69688i	−0.214102	−	0.370835i
$237$	1.93772	−	0.716567i	0.125868	−	0.0465460i
$238$	−0.141699	+	0.0493293i	−0.00918499	+	0.00319754i
$239$	7.76940	+	4.48567i	0.502561	+	0.290154i	0.729771	−	0.683692i	$-0.239627\pi$
$239$	7.76940	+	4.48567i	0.502561	+	0.290154i	−0.227210	+	0.973846i	$0.572960\pi$
$240$	5.21719	−	4.42362i	0.336768	−	0.285544i
$241$	4.46593	+	5.32229i	0.287676	+	0.342839i	0.890457	−	0.455068i	$-0.150385\pi$
$241$	4.46593	+	5.32229i	0.287676	+	0.342839i	−0.602781	+	0.797907i	$0.705941\pi$
$242$	−0.630508	+	3.57579i	−0.0405306	+	0.229860i
$243$	13.2953	−	8.13843i	0.852896	−	0.522081i
$244$	−0.0164697	+	0.0934044i	−0.00105437	+	0.00597961i
$245$	10.1815	−	25.7009i	0.650473	−	1.64197i
$246$	−1.80910	−	2.13364i	−0.115344	−	0.136036i
$247$	2.37559	−	15.1365i	0.151155	−	0.963115i
$248$	8.15495	−	4.70826i	0.517840	−	0.298975i
$249$	14.7141	−	0.0756016i	0.932467	−	0.00479105i
$250$	14.2049	−	16.9288i	0.898398	−	1.07067i
$251$	−13.6987	−	16.3254i	−0.864652	−	1.03045i	−0.999218	−	0.0395474i	$-0.987408\pi$
$251$	−13.6987	−	16.3254i	−0.864652	−	1.03045i	0.134566	−	0.990905i	$-0.457036\pi$
$252$	−7.81140	−	1.40786i	−0.492072	−	0.0886870i
$253$	1.32379	+	7.50758i	0.0832259	+	0.471997i
$254$			0.692023i			0.0434214i
$255$	0.250863	+	0.295866i	0.0157096	+	0.0185279i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	6.41442	−	5.38234i	0.400121	−	0.335741i	−0.420420	−	0.907330i	$-0.638117\pi$
$257$	6.41442	−	5.38234i	0.400121	−	0.335741i	0.820540	+	0.571589i	$0.193673\pi$
$258$	15.2316	−	2.76651i	0.948278	−	0.172235i
$259$	13.8026	−	11.2549i	0.857653	−	0.699345i
$260$	−2.41051	−	13.6707i	−0.149493	−	0.847819i
$261$	0.444293	+	2.37663i	0.0275010	+	0.147110i
$262$	2.99186	−	8.22007i	0.184838	−	0.507838i
$263$	8.92114	+	24.5106i	0.550101	+	1.51139i	0.833573	+	0.552410i	$0.186292\pi$
$263$	8.92114	+	24.5106i	0.550101	+	1.51139i	−0.283471	+	0.958981i	$0.591486\pi$
$264$	2.37180	+	4.05977i	0.145974	+	0.249861i
$265$			36.4644i			2.23999i
$266$	8.79879	−	7.45529i	0.539488	−	0.457113i
$267$	−6.34425	−	7.48237i	−0.388262	−	0.457913i
$268$	11.8003	+	2.08072i	0.720821	+	0.127100i
$269$	−7.45831	+	2.71460i	−0.454741	+	0.165512i	−0.559228	−	0.829014i	$-0.688902\pi$
$269$	−7.45831	+	2.71460i	−0.454741	+	0.165512i	0.104486	+	0.994526i	$0.466680\pi$
$270$	3.87440	+	20.1514i	0.235788	+	1.22637i
$271$	13.1680	−	4.79275i	0.799897	−	0.291139i	0.0904533	−	0.995901i	$-0.471168\pi$
$271$	13.1680	−	4.79275i	0.799897	−	0.291139i	0.709444	+	0.704762i	$0.248946\pi$
$272$	−0.0558483	+	0.00984756i	−0.00338630	+	0.000597096i
$273$	−10.4638	+	12.2466i	−0.633295	+	0.741199i
$274$	2.62746	+	1.51697i	0.158731	+	0.0916432i
$275$	18.4888	+	22.0341i	1.11492	+	1.32871i
$276$	−3.74214	−	3.10740i	−0.225250	−	0.187044i
$277$	−16.4670			−0.989404			−0.494702	−	0.869063i	$-0.664723\pi$
$277$	−16.4670			−0.989404			−0.494702	+	0.869063i	$0.664723\pi$
$278$	22.5981			1.35534
$279$	0.290287	+	28.2481i	0.0173790	+	1.69117i
$280$	5.35095	−	8.97431i	0.319781	−	0.536318i
$281$	−10.6359	+	8.92456i	−0.634484	+	0.532395i	−0.902319	−	0.431070i	$-0.858136\pi$
$281$	−10.6359	+	8.92456i	−0.634484	+	0.532395i	0.267835	+	0.963465i	$0.413692\pi$
$282$	−7.67979	+	0.0394591i	−0.457325	+	0.00234975i
$283$	5.21625	+	4.37695i	0.310074	+	0.260183i	0.784523	−	0.620100i	$-0.212908\pi$
$283$	5.21625	+	4.37695i	0.310074	+	0.260183i	−0.474449	+	0.880283i	$0.657353\pi$
$284$	−6.43855	−	11.1519i	−0.382058	−	0.661743i
$285$	−26.1712	−	14.2839i	−1.55025	−	0.846105i
$286$	9.54200			0.564230
$287$	−3.67016	−	2.18834i	−0.216642	−	0.129174i
$288$	−2.82947	−	0.997038i	−0.166728	−	0.0587510i
$289$	2.95146	+	16.7386i	0.173615	+	0.984621i
$290$	−3.13441	−	0.552681i	−0.184059	−	0.0324546i
$291$	−2.59373	+	15.1650i	−0.152047	+	0.888989i
$292$	−8.78297			−0.513985
$293$	12.8852	−	22.3179i	0.752764	−	1.30383i	−0.193714	−	0.981058i	$-0.562053\pi$
$293$	12.8852	−	22.3179i	0.752764	−	1.30383i	0.946478	−	0.322768i	$-0.104613\pi$
$294$	−11.9854	+	1.83042i	−0.699002	+	0.106752i
$295$	−8.88510	+	24.4116i	−0.517311	+	1.42130i
$296$	5.82959	−	3.36571i	0.338838	−	0.195628i
$297$	−14.1038	+	0.217413i	−0.818385	+	0.0126156i
$298$	−1.80498	−	2.15109i	−0.104559	−	0.124609i
$299$	−9.27603	+	3.37620i	−0.536447	+	0.195251i
$300$	−18.0899	−	3.09398i	−1.04442	−	0.178631i
$301$	20.6434	−	11.5345i	1.18986	−	0.664840i
$302$	3.15032	+	8.65544i	0.181281	+	0.498065i
$303$	3.27683	+	18.0413i	0.188249	+	1.03645i
$304$	3.73315	−	2.25025i	0.214111	−	0.129061i
$305$	0.324378	−	0.187280i	0.0185738	−	0.0107236i
$306$	0.0565418	−	0.160459i	0.00323228	−	0.00917282i
$307$	2.20450	+	0.388713i	0.125818	+	0.0221850i	0.236202	−	0.971704i	$-0.424097\pi$
$307$	2.20450	+	0.388713i	0.125818	+	0.0221850i	−0.110385	+	0.993889i	$0.535208\pi$
$308$	5.43640	+	4.69350i	0.309767	+	0.267437i
$309$	33.9437	−	0.174404i	1.93099	−	0.00992150i
$310$	−34.9447	−	12.7188i	−1.98472	−	0.722380i
$311$	17.6612	+	10.1967i	1.00148	+	0.578203i	0.908685	−	0.417483i	$-0.137088\pi$
$311$	17.6612	+	10.1967i	1.00148	+	0.578203i	0.0927914	+	0.995686i	$0.470421\pi$
$312$	−4.64372	+	3.93738i	−0.262899	+	0.222910i
$313$	−16.0356	+	13.4555i	−0.906385	+	0.760547i	−0.971428	−	0.237335i	$-0.923726\pi$
$313$	−16.0356	+	13.4555i	−0.906385	+	0.760547i	0.0650427	+	0.997882i	$0.479282\pi$
$314$	−5.63733	−	2.05182i	−0.318133	−	0.115791i
$315$	15.5699	+	27.2051i	0.877264	+	1.53283i
$316$	1.03298	−	0.596393i	0.0581098	−	0.0335497i
$317$	−26.6961	−	9.71659i	−1.49940	−	0.545738i	−0.543497	−	0.839411i	$-0.682900\pi$
$317$	−26.6961	−	9.71659i	−1.49940	−	0.545738i	−0.955906	+	0.293673i	$0.905122\pi$
$318$	13.8089	−	8.06746i	0.774365	−	0.452401i
$319$	0.748268	−	2.05585i	0.0418950	−	0.115106i
$320$	2.53847	−	3.02523i	0.141905	−	0.169116i
$321$	21.0973	+	12.0364i	1.17753	+	0.671807i
$322$	−6.94554	−	2.63914i	−0.387060	−	0.147074i
$323$	0.127611	+	0.211706i	0.00710047	+	0.0117796i
$324$	6.77406	−	5.92555i	0.376337	−	0.329197i
$325$	−23.9407	+	28.5314i	−1.32799	+	1.58264i
$326$	15.9362	−	5.80031i	0.882626	−	0.321250i
$327$	−19.7600	−	16.4084i	−1.09273	−	0.907384i
$328$	−1.23721	−	1.03814i	−0.0683132	−	0.0573216i
$329$	−11.0791	+	3.85692i	−0.610809	+	0.212639i
$330$	6.26098	−	17.4808i	0.344656	−	0.962289i
$331$	−22.1601	+	12.7942i	−1.21803	+	0.703230i	−0.964496	−	0.264096i	$-0.914926\pi$
$331$	−22.1601	+	12.7942i	−1.21803	+	0.703230i	−0.253534	+	0.967326i	$0.581593\pi$
$332$	8.36623	−	1.47519i	0.459156	−	0.0809617i
$333$	0.207513	+	20.1932i	0.0113716	+	1.10658i
$334$	3.37719	+	5.84946i	0.184791	+	0.320068i
$335$	−23.6602	−	40.9806i	−1.29269	−	2.23901i
$336$	−4.58239	−	0.0408875i	−0.249990	−	0.00223060i
$337$	−13.6435	+	16.2597i	−0.743211	+	0.885724i	−0.996663	−	0.0816240i	$-0.973989\pi$
$337$	−13.6435	+	16.2597i	−0.743211	+	0.885724i	0.253453	+	0.967348i	$0.418434\pi$
$338$	−0.111880	−	0.634505i	−0.00608549	−	0.0345125i
$339$	−12.1644	−	6.94004i	−0.660680	−	0.376931i
$340$	0.171560	+	0.143956i	0.00930417	+	0.00780712i
$341$	12.7810	−	22.1374i	0.692132	−	1.19881i
$342$	0.380931	+	13.0711i	0.0205984	+	0.706807i
$343$	−16.4152	+	8.57554i	−0.886340	+	0.463036i
$344$	8.39882	−	3.05692i	0.452834	−	0.164818i
$345$	0.0986960	+	19.2089i	0.00531362	+	1.03417i
$346$	22.3166	+	8.12257i	1.19975	+	0.436672i
$347$	−8.74957	−	1.54278i	−0.469701	−	0.0828210i	−0.0662124	−	0.997806i	$-0.521091\pi$
$347$	−8.74957	−	1.54278i	−0.469701	−	0.0828210i	−0.403489	+	0.914985i	$0.632203\pi$
$348$	0.484166	+	1.30927i	0.0259540	+	0.0701840i
$349$	−2.20752	−	3.82353i	−0.118166	−	0.204669i	0.800875	−	0.598831i	$-0.204368\pi$
$349$	−2.20752	−	3.82353i	−0.118166	−	0.204669i	−0.919041	+	0.394162i	$0.871035\pi$
$350$	−27.6738	+	4.47940i	−1.47923	+	0.239434i
$351$	−3.44852	−	17.9363i	−0.184069	−	0.957370i
$352$	1.74491	+	2.07950i	0.0930041	+	0.110838i
$353$			3.02335i			0.160917i	0.996758	+	0.0804583i	$0.0256384\pi$
$353$			3.02335i			0.160917i	−0.996758	+	0.0804583i	$0.974362\pi$
$354$	11.2103	−	2.03613i	0.595823	−	0.108219i
$355$	−17.3930	+	47.7868i	−0.923124	+	2.53626i
$356$	−4.33871	−	3.64061i	−0.229951	−	0.192952i
$357$	0.00231872	−	0.259867i	0.000122720	−	0.0137536i
$358$	2.05042	−	11.6285i	0.108368	−	0.614585i
$359$	−9.27371	−	1.63521i	−0.489448	−	0.0863028i	−0.0765227	−	0.997068i	$-0.524382\pi$
$359$	−9.27371	−	1.63521i	−0.489448	−	0.0863028i	−0.412925	+	0.910765i	$0.635493\pi$
$360$	4.16626	+	11.0908i	0.219581	+	0.584534i
$361$	−15.0050	−	11.6554i	−0.789738	−	0.613444i
$362$	−5.38039	−	3.10637i	−0.282787	−	0.163267i
$363$	−5.46251	−	3.11647i	−0.286708	−	0.163572i
$364$	−4.76278	+	7.98786i	−0.249637	+	0.418678i
$365$	22.2953	+	26.5705i	1.16699	+	1.39076i
$366$	−0.142688	−	0.0814064i	−0.00745843	−	0.00425518i
$367$	−17.9555	+	15.0664i	−0.937268	+	0.786461i	−0.977108	−	0.212745i	$-0.931760\pi$
$367$	−17.9555	+	15.0664i	−0.937268	+	0.786461i	0.0398401	+	0.999206i	$0.487315\pi$
$368$	−2.43205	−	1.40415i	−0.126780	−	0.0731962i
$369$	4.53570	−	1.70384i	0.236119	−	0.0886986i
$370$	−24.9803	−	9.09209i	−1.29866	−	0.472675i
$371$	15.9645	−	18.4914i	0.828835	−	0.960025i
$372$	2.91467	+	16.0473i	0.151119	+	0.832016i
$373$		−	9.69793i		−	0.502140i	−0.967969	−	0.251070i	$-0.919218\pi$
$373$		−	9.69793i		−	0.502140i	0.967969	−	0.251070i	$-0.0807824\pi$
$374$	−0.117928	+	0.0989536i	−0.00609793	+	0.00511677i
$375$	19.3083	+	33.0496i	0.997076	+	1.70668i
$376$	−4.36662	+	0.769954i	−0.225191	+	0.0397073i
$377$	2.78988	+	0.491931i	0.143686	+	0.0253357i
$378$	6.85774	−	11.9152i	0.352724	−	0.612850i
$379$			3.05210i			0.156776i	0.996923	+	0.0783880i	$0.0249773\pi$
$379$			3.05210i			0.156776i	−0.996923	+	0.0783880i	$0.975023\pi$
$380$	−16.2840	−	5.58145i	−0.835352	−	0.286322i
$381$	−1.12843	−	0.404160i	−0.0578110	−	0.0207057i
$382$	−12.4817	+	14.8751i	−0.638620	+	0.761078i
$383$	−18.0806	−	15.1715i	−0.923877	−	0.775225i	0.0508306	−	0.998707i	$-0.483813\pi$
$383$	−18.0806	−	15.1715i	−0.923877	−	0.775225i	−0.974708	+	0.223482i	$0.928258\pi$
$384$	−1.70726	−	0.291999i	−0.0871232	−	0.0149010i
$385$	0.398791	−	28.3607i	0.0203243	−	1.44539i
$386$	2.13614	−	0.376658i	0.108726	−	0.0191714i
$387$	−4.38453	+	26.4526i	−0.222878	+	1.34466i
$388$			8.88267i			0.450949i
$389$	−18.6061	+	3.28075i	−0.943366	+	0.166341i	−0.624118	−	0.781330i	$-0.714541\pi$
$389$	−18.6061	+	3.28075i	−0.943366	+	0.166341i	−0.319248	+	0.947671i	$0.603430\pi$
$390$	23.6994	+	4.05341i	1.20007	+	0.205252i
$391$	0.0796289	−	0.137921i	0.00402701	−	0.00697498i
$392$	−6.64256	+	2.20824i	−0.335500	+	0.111533i
$393$	11.6565	+	9.67931i	0.587991	+	0.488257i
$394$	−3.26913	−	8.98187i	−0.164697	−	0.452500i
$395$	−4.42642	−	1.61109i	−0.222718	−	0.0810625i
$396$	−8.00512	+	1.49649i	−0.402272	+	0.0752016i
$397$	2.22604	−	12.6245i	0.111722	−	0.633605i	−0.876600	−	0.481220i	$-0.840194\pi$
$397$	2.22604	−	12.6245i	0.111722	−	0.633605i	0.988321	−	0.152384i	$-0.0486951\pi$
$398$	1.08147			0.0542090
$399$	7.01801	+	18.7015i	0.351340	+	0.936248i
$400$	−10.5959			−0.529793
$401$	−4.38468	+	24.8667i	−0.218960	+	1.24179i	0.654940	+	0.755681i	$0.272694\pi$
$401$	−4.38468	+	24.8667i	−0.218960	+	1.24179i	−0.873900	+	0.486105i	$0.838417\pi$
$402$	−10.2846	+	18.0267i	−0.512947	+	0.899088i
$403$	31.1036	+	11.3208i	1.54938	+	0.563928i
$404$	3.62082	+	9.94812i	0.180142	+	0.494937i
$405$	−35.1219	−	5.45126i	−1.74522	−	0.270875i
$406$	1.34752	+	1.65255i	0.0668761	+	0.0820146i
$407$	9.13657	−	15.8250i	0.452883	−	0.784416i
$408$	0.0165592	−	0.0968184i	0.000819804	−	0.00479323i
$409$	19.9392	−	3.51581i	0.985929	−	0.173846i	0.342638	−	0.939468i	$-0.388680\pi$
$409$	19.9392	−	3.51581i	0.985929	−	0.173846i	0.643291	+	0.765622i	$0.277569\pi$
$410$			6.37812i			0.314993i
$411$	−4.00810	+	3.39844i	−0.197705	+	0.167633i
$412$	19.2999	−	3.40310i	0.950839	−	0.167659i
$413$	15.1934	−	8.48934i	0.747617	−	0.417733i
$414$	7.25249	−	4.28719i	0.356441	−	0.210704i
$415$	−25.7002	−	21.5650i	−1.26157	−	1.05859i
$416$	−2.25944	+	2.69270i	−0.110778	+	0.132020i
$417$	−13.1979	+	36.8489i	−0.646303	+	1.80450i
$418$	5.72204	−	10.3571i	0.279874	−	0.506584i
$419$			17.4967i			0.854770i	0.904070	+	0.427385i	$0.140565\pi$
$419$			17.4967i			0.854770i	−0.904070	+	0.427385i	$0.859435\pi$
$420$	11.5086	+	13.9666i	0.561561	+	0.681500i
$421$	4.69881	+	0.828527i	0.229006	+	0.0403799i	0.286973	−	0.957939i	$-0.407351\pi$
$421$	4.69881	+	0.828527i	0.229006	+	0.0403799i	−0.0579675	+	0.998318i	$0.518462\pi$
$422$	−10.6604	+	1.87971i	−0.518940	+	0.0915031i
$423$	4.42085	−	12.5458i	0.214949	−	0.610000i
$424$	7.07324	−	5.93515i	0.343507	−	0.288236i
$425$		−	0.600889i		−	0.0291474i
$426$	21.9448	−	3.98582i	1.06323	−	0.193113i
$427$	−0.246488	−	0.0470451i	−0.0119284	−	0.00227667i
$428$	13.1777	+	4.79629i	0.636969	+	0.231838i
$429$	−5.57278	+	15.5594i	−0.269056	+	0.751213i
$430$	−30.5681	−	17.6485i	−1.47412	−	0.851085i
$431$	28.2998	−	23.7464i	1.36315	−	1.14382i	0.388159	−	0.921592i	$-0.373111\pi$
$431$	28.2998	−	23.7464i	1.36315	−	1.14382i	0.974994	−	0.222229i	$-0.0713334\pi$
$432$	3.27827	−	4.03149i	0.157726	−	0.193965i
$433$	4.88546	+	5.82226i	0.234780	+	0.279800i	0.870551	−	0.492077i	$-0.163762\pi$
$433$	4.88546	+	5.82226i	0.234780	+	0.279800i	−0.635771	+	0.771877i	$0.719318\pi$
$434$	12.1523	+	21.7490i	0.583329	+	1.04398i
$435$	2.73179	−	4.78825i	0.130979	−	0.229579i
$436$	−12.8422	−	7.41447i	−0.615032	−	0.355089i
$437$	−1.89793	+	12.0930i	−0.0907904	+	0.578489i
$438$	5.12948	−	14.3217i	0.245096	−	0.684316i
$439$	16.4817	+	2.90616i	0.786626	+	0.138703i	0.552511	−	0.833505i	$-0.313670\pi$
$439$	16.4817	+	2.90616i	0.786626	+	0.138703i	0.234115	+	0.972209i	$0.424781\pi$
$440$	1.86158	−	10.5575i	0.0887471	−	0.503310i
$441$	4.01506	−	20.6126i	0.191194	−	0.981552i
$442$	−0.152702	−	0.128133i	−0.00726332	−	0.00609465i
$443$	10.2544	−	28.1736i	0.487199	−	1.33857i	−0.416006	−	0.909362i	$-0.636571\pi$
$443$	10.2544	−	28.1736i	0.487199	−	1.33857i	0.903206	−	0.429208i	$-0.141207\pi$
$444$	2.08356	+	11.4715i	0.0988815	+	0.544413i
$445$			22.3672i			1.06031i
$446$	16.2821	+	19.4043i	0.770981	+	0.918819i
$447$	4.56175	−	1.68694i	0.215764	−	0.0797893i
$448$	−2.61176	+	0.422750i	−0.123394	+	0.0199731i
$449$	−10.9552	−	18.9750i	−0.517008	−	0.895484i	−0.999805	−	0.0197518i	$-0.993712\pi$
$449$	−10.9552	−	18.9750i	−0.517008	−	0.895484i	0.482797	−	0.875732i	$-0.339621\pi$
$450$	15.6101	−	27.6907i	0.735865	−	1.30535i
$451$	−4.31763	−	0.761314i	−0.203309	−	0.0358489i
$452$	−7.59810	−	2.76548i	−0.357385	−	0.130077i
$453$	−15.9536	+	0.0819702i	−0.749565	+	0.00385129i
$454$	−5.88519	+	2.14203i	−0.276206	+	0.100531i
$455$	36.2553	−	5.86843i	1.69967	−	0.275116i
$456$	1.48904	+	7.40154i	0.0697306	+	0.346609i
$457$	4.68200	−	8.10945i	0.219015	−	0.379344i	−0.735492	−	0.677533i	$-0.763049\pi$
$457$	4.68200	−	8.10945i	0.219015	−	0.379344i	0.954507	+	0.298189i	$0.0963825\pi$
$458$	0.672741	+	0.564497i	0.0314351	+	0.0263772i
$459$	0.228625	+	0.185910i	0.0106713	+	0.00867755i
$460$	1.92583	+	10.9219i	0.0897922	+	0.509237i
$461$	9.39299	−	11.1941i	0.437475	−	0.521363i	−0.501588	−	0.865106i	$-0.667251\pi$
$461$	9.39299	−	11.1941i	0.437475	−	0.521363i	0.939063	+	0.343744i	$0.111695\pi$
$462$	−10.8283	+	6.12356i	−0.503778	+	0.284894i
$463$	−15.3184	−	26.5322i	−0.711906	−	1.23306i	−0.964141	−	0.265392i	$-0.914499\pi$
$463$	−15.3184	−	26.5322i	−0.711906	−	1.23306i	0.252234	−	0.967666i	$-0.418835\pi$
$464$	0.402967	+	0.697960i	0.0187073	+	0.0324020i
$465$	41.1481	−	49.5533i	1.90820	−	2.29798i
$466$	22.5663	−	3.97905i	1.04536	−	0.184326i
$467$	−29.2046	+	16.8613i	−1.35143	+	0.780246i	−0.988449	−	0.151552i	$-0.951573\pi$
$467$	−29.2046	+	16.8613i	−1.35143	+	0.780246i	−0.362976	+	0.931798i	$0.618239\pi$
$468$	−3.70831	−	9.87167i	−0.171417	−	0.456318i
$469$	−5.94349	+	31.1403i	−0.274445	+	1.43793i
$470$	13.4138	+	11.2555i	0.618734	+	0.519180i
$471$	6.63809	−	7.99402i	0.305867	−	0.368345i
$472$	6.18147	−	2.24987i	0.284525	−	0.103559i
$473$	15.5957	−	18.5863i	0.717093	−	0.854598i
$474$	0.369200	+	2.03271i	0.0169579	+	0.0933654i
$475$	16.6123	+	43.0953i	0.762223	+	1.97735i
$476$	−0.0239741	−	0.148112i	−0.00109885	−	0.00678872i
$477$	5.09018	+	27.2287i	0.233063	+	1.24671i
$478$	−5.76666	+	6.87244i	−0.263761	+	0.314338i
$479$	8.38294	−	23.0319i	0.383026	−	1.05236i	−0.587049	−	0.809552i	$-0.699710\pi$
$479$	8.38294	−	23.0319i	0.383026	−	1.05236i	0.970075	−	0.242805i	$-0.0780674\pi$
$480$	3.45046	+	5.90609i	0.157491	+	0.269575i
$481$	22.2345	+	8.09269i	1.01380	+	0.368995i
$482$	−6.01693	+	3.47388i	−0.274064	+	0.158231i
$483$	8.35981	−	9.78420i	0.380384	−	0.445196i
$484$	−3.41198	−	1.24186i	−0.155090	−	0.0564481i
$485$	26.8721	−	22.5484i	1.22020	−	1.02387i
$486$	5.70608	+	14.5066i	0.258833	+	0.658031i
$487$	−7.25707	−	4.18987i	−0.328849	−	0.189861i	0.326481	−	0.945204i	$-0.394137\pi$
$487$	−7.25707	−	4.18987i	−0.328849	−	0.189861i	−0.655330	+	0.755343i	$0.727470\pi$
$488$	−0.0891255	−	0.0324390i	−0.00403452	−	0.00146845i
$489$	0.150922	+	29.3734i	0.00682493	+	1.32831i
$490$	23.5424	+	14.4897i	1.06354	+	0.654579i
$491$	29.6456	+	5.22731i	1.33789	+	0.235905i	0.796382	−	0.604794i	$-0.206744\pi$
$491$	29.6456	+	5.22731i	1.33789	+	0.235905i	0.541503	+	0.840699i	$0.317856\pi$
$492$	2.41537	−	1.41111i	0.108893	−	0.0636177i
$493$	−0.0395812	+	0.0228522i	−0.00178265	+	0.00102921i
$494$	14.4941	+	4.96794i	0.652119	+	0.223518i
$495$	24.8480	+	20.4185i	1.11683	+	0.917745i
$496$	3.22064	+	8.84864i	0.144611	+	0.397316i
$497$	29.7417	−	16.6183i	1.33410	−	0.745431i
$498$	−2.48062	+	14.5037i	−0.111159	+	0.649925i
$499$	−2.29126	+	0.833949i	−0.102571	+	0.0373327i	−0.392796	−	0.919626i	$-0.628492\pi$
$499$	−2.29126	+	0.833949i	−0.102571	+	0.0373327i	0.290225	+	0.956958i	$0.406270\pi$
$500$	14.2049	+	16.9288i	0.635263	+	0.757077i
$501$	−11.5106	+	2.09067i	−0.514256	+	0.0934040i
$502$	18.4562	−	10.6557i	0.823739	−	0.475586i
$503$	−11.4196	+	31.3751i	−0.509174	+	1.39894i	0.372916	+	0.927865i	$0.378358\pi$
$503$	−11.4196	+	31.3751i	−0.509174	+	1.39894i	−0.882091	+	0.471080i	$0.843864\pi$
$504$	2.74291	−	7.44825i	0.122179	−	0.331772i
$505$	20.9040	−	36.2068i	0.930217	−	1.61118i
$506$	−7.62339			−0.338901
$507$	1.09998	+	0.188133i	0.0488516	+	0.00835529i
$508$	−0.681510	−	0.120169i	−0.0302371	−	0.00533162i
$509$	−3.03273	−	17.1995i	−0.134423	−	0.762353i	−0.975260	−	0.221063i	$-0.929047\pi$
$509$	−3.03273	−	17.1995i	−0.134423	−	0.762353i	0.840836	−	0.541290i	$-0.182064\pi$
$510$	−0.334933	+	0.195675i	−0.0148311	+	0.00866464i
$511$	0.326721	−	23.2353i	0.0144533	−	1.02787i
$512$	−1.00000			−0.0441942
$513$	−21.5365	−	7.01274i	−0.950860	−	0.309620i
$514$	4.18672	+	7.25161i	0.184668	+	0.319855i
$515$	−59.2874	−	49.7481i	−2.61252	−	2.19216i
$516$	0.0795399	+	15.4806i	0.00350155	+	0.681495i
$517$	−9.22049	+	7.73691i	−0.405517	+	0.340269i
$518$	8.68711	+	15.5473i	0.381690	+	0.683110i
$519$	−26.2783	+	31.6460i	−1.15349	+	1.38911i
$520$	13.8816			0.608747
$521$	−22.5063			−0.986019			−0.493010	−	0.870024i	$-0.664103\pi$
$521$	−22.5063			−0.986019			−0.493010	+	0.870024i	$0.664103\pi$
$522$	−2.41768	+	0.0248449i	−0.105819	+	0.00108743i
$523$	−9.38051	−	11.1793i	−0.410181	−	0.488835i	0.520915	−	0.853608i	$-0.325591\pi$
$523$	−9.38051	−	11.1793i	−0.410181	−	0.488835i	−0.931096	+	0.364774i	$0.881146\pi$
$524$	7.57566	+	4.37381i	0.330944	+	0.191071i
$525$	8.85804	−	47.7415i	0.386596	−	2.08361i
$526$	−25.6874	+	4.52938i	−1.12002	+	0.197490i
$527$	−0.501805	+	0.182642i	−0.0218590	+	0.00795601i
$528$	−4.40995	+	1.63080i	−0.191918	+	0.0709714i
$529$	−14.2020	+	5.16912i	−0.617479	+	0.224744i
$530$	−35.9104	−	6.33197i	−1.55985	−	0.275043i
$531$	−3.22698	+	19.4689i	−0.140039	+	0.844880i
$532$	5.81414	+	9.95971i	0.252075	+	0.431808i
$533$		−	5.67704i		−	0.245900i
$534$	8.47036	−	4.94857i	0.366548	−	0.214145i
$535$	−18.9413	−	52.0409i	−0.818905	−	2.24992i
$536$	−4.09822	+	11.2598i	−0.177016	+	0.486348i
$537$	17.7641	+	10.1348i	0.766579	+	0.437349i
$538$	−1.37824	−	7.81639i	−0.0594202	−	0.336989i
$539$	−12.6188	+	14.2073i	−0.543532	+	0.611953i
$540$	−20.5180	+	0.316289i	−0.882954	+	0.0136109i
$541$	−20.0819	+	16.8507i	−0.863387	+	0.724468i	−0.962695	−	0.270589i	$-0.912782\pi$
$541$	−20.0819	+	16.8507i	−0.863387	+	0.724468i	0.0993077	+	0.995057i	$0.468337\pi$
$542$	2.43334	+	13.8002i	0.104521	+	0.592768i
$543$	8.20759	−	6.95916i	0.352222	−	0.298646i
$544$		−	0.0567098i		−	0.00243141i
$545$	10.1692	+	57.6722i	0.435599	+	2.47040i
$546$	−10.2436	−	12.4314i	−0.438384	−	0.532014i
$547$	−16.5263	−	19.6952i	−0.706611	−	0.842107i	0.286646	−	0.958037i	$-0.407460\pi$
$547$	−16.5263	−	19.6952i	−0.706611	−	0.842107i	−0.993257	+	0.115930i	$0.963015\pi$
$548$	−1.95017	+	2.32413i	−0.0833073	+	0.0992818i
$549$	0.216076	−	0.185126i	0.00922191	−	0.00790100i
$550$	−24.9099	+	14.3818i	−1.06216	+	0.613240i
$551$	2.20696	−	2.73321i	0.0940195	−	0.116439i
$552$	3.71001	−	3.14569i	0.157909	−	0.133890i
$553$	1.53933	+	2.75493i	0.0654588	+	0.117152i
$554$	2.85946	−	16.2168i	0.121487	−	0.688986i
$555$	29.4149	−	35.4233i	1.24859	−	1.50364i
$556$	−3.92412	+	22.2548i	−0.166420	+	0.943813i
$557$	−25.9253	−	30.8965i	−1.09849	−	1.30913i	−0.947202	−	0.320637i	$-0.896103\pi$
$557$	−25.9253	−	30.8965i	−1.09849	−	1.30913i	−0.151286	−	0.988490i	$-0.548342\pi$
$558$	−27.8693	−	4.61935i	−1.17980	−	0.195553i
$559$	27.2080	+	15.7086i	1.15078	+	0.664401i
$560$	7.90879	+	6.82803i	0.334207	+	0.288537i
$561$	−0.0924823	−	0.250087i	−0.00390460	−	0.0105587i
$562$	−6.94208	−	12.0240i	−0.292834	−	0.507203i
$563$	−16.3900	+	28.3883i	−0.690757	+	1.19643i	0.280833	+	0.959757i	$0.409389\pi$
$563$	−16.3900	+	28.3883i	−0.690757	+	1.19643i	−0.971590	+	0.236670i	$0.923944\pi$
$564$	1.29472	−	7.56997i	0.0545176	−	0.318753i
$565$	10.9213	+	30.0061i	0.459464	+	1.26237i
$566$	−5.21625	+	4.37695i	−0.219255	+	0.183977i
$567$	15.4240	+	18.1411i	0.647747	+	0.761856i
$568$	12.1005	−	4.40423i	0.507726	−	0.184797i
$569$	−13.9452	+	24.1538i	−0.584614	+	1.01258i	0.410310	+	0.911946i	$0.365421\pi$
$569$	−13.9452	+	24.1538i	−0.584614	+	1.01258i	−0.994923	+	0.100635i	$0.967913\pi$
$570$	18.6115	−	23.2933i	0.779549	−	0.975648i
$571$	8.02580	+	13.9011i	0.335869	+	0.581743i	0.983651	−	0.180083i	$-0.0576366\pi$
$571$	8.02580	+	13.9011i	0.335869	+	0.581743i	−0.647782	+	0.761826i	$0.724303\pi$
$572$	−1.65695	+	9.39704i	−0.0692806	+	0.392910i
$573$	−16.9660	−	29.0404i	−0.708765	−	1.21318i
$574$	2.79241	−	3.23440i	0.116553	−	0.135001i
$575$	19.1270	−	22.7946i	0.797650	−	0.950602i
$576$	1.47322	−	2.61335i	0.0613843	−	0.108890i
$577$	15.3186	−	26.5326i	0.637722	−	1.10457i	−0.348209	−	0.937417i	$-0.613210\pi$
$577$	15.3186	−	26.5326i	0.637722	−	1.10457i	0.985931	−	0.167150i	$-0.0534565\pi$
$578$	−16.9968			−0.706973
$579$	−0.633373	+	3.70320i	−0.0263221	+	0.153900i
$580$	1.08857	−	2.99082i	0.0452004	−	0.124187i
$581$	3.59139	+	22.1876i	0.148996	+	0.920499i
$582$	−14.4842	−	5.18771i	−0.600391	−	0.215037i
$583$	8.57278	−	23.5535i	0.355048	−	0.975487i
$584$	1.52515	−	8.64954i	0.0631110	−	0.357921i
$585$	−20.4506	+	36.2774i	−0.845530	+	1.49989i
$586$	19.7413	+	16.5650i	0.815507	+	0.684292i
$587$	−7.83194	−	21.5181i	−0.323259	−	0.888147i	−0.989773	−	0.142654i	$-0.954436\pi$
$587$	−7.83194	−	21.5181i	−0.323259	−	0.888147i	0.666514	−	0.745493i	$-0.267786\pi$
$588$	0.278630	−	12.1212i	0.0114905	−	0.499868i
$589$	30.9397	−	26.9719i	1.27485	−	1.11136i
$590$	−22.4979	−	12.9892i	−0.926223	−	0.534755i
$591$	16.5553	−	0.0850616i	0.680992	−	0.00349897i
$592$	2.30228	+	6.32547i	0.0946233	+	0.259975i
$593$	10.9378	−	1.92862i	0.449160	−	0.0791991i	0.0555076	−	0.998458i	$-0.482322\pi$
$593$	10.9378	−	1.92862i	0.449160	−	0.0791991i	0.393653	+	0.919259i	$0.371211\pi$
$594$	2.23499	−	13.9273i	0.0917027	−	0.571443i
$595$	−0.387217	+	0.448506i	−0.0158743	+	0.0183870i
$596$	2.43184	−	1.40402i	0.0996120	−	0.0575110i
$597$	−0.631604	+	1.76346i	−0.0258498	+	0.0721735i
$598$	−1.71414	−	9.72138i	−0.0700965	−	0.397537i
$599$	4.03693	+	22.8945i	0.164944	+	0.935446i	0.949122	+	0.314909i	$0.101974\pi$
$599$	4.03693	+	22.8945i	0.164944	+	0.935446i	−0.784178	+	0.620537i	$0.786915\pi$
$600$	6.18825	−	17.2778i	0.252634	−	0.705363i
$601$	3.06815	−	1.77140i	0.125152	−	0.0722568i	−0.436117	−	0.899890i	$-0.643647\pi$
$601$	3.06815	−	1.77140i	0.125152	−	0.0722568i	0.561269	+	0.827633i	$0.310313\pi$
$602$	7.77462	+	22.3327i	0.316870	+	0.910214i
$603$	−23.3881	−	27.2982i	−0.952438	−	1.11167i
$604$	−9.07099	+	1.59946i	−0.369093	+	0.0650811i
$605$	4.90430	+	13.4744i	0.199388	+	0.547814i
$606$	−18.3362	+	0.0942123i	−0.744858	+	0.00382711i
$607$	−6.19835	−	3.57862i	−0.251583	−	0.145252i	0.368906	−	0.929467i	$-0.379733\pi$
$607$	−6.19835	−	3.57862i	−0.251583	−	0.145252i	−0.620489	+	0.784215i	$0.713066\pi$
$608$	1.56781	+	4.06718i	0.0635830	+	0.164946i
$609$	−3.48166	+	1.23215i	−0.141084	+	0.0499294i
$610$	0.128107	+	0.351971i	0.00518689	+	0.0142509i
$611$	−11.9394	−	10.0183i	−0.483016	−	0.405299i
$612$	0.148203	+	0.0835462i	0.00599074	+	0.00337716i
$613$	−7.29444	+	41.3688i	−0.294620	+	1.67087i	0.374125	+	0.927378i	$0.377943\pi$
$613$	−7.29444	+	41.3688i	−0.294620	+	1.67087i	−0.668745	+	0.743492i	$0.733168\pi$
$614$	−0.765616	+	2.10351i	−0.0308977	+	0.0848909i
$615$	−10.4003	−	3.72499i	−0.419379	−	0.150206i
$616$	−5.56622	+	4.53879i	−0.224269	+	0.182873i
$617$	−1.55915	+	4.28372i	−0.0627689	+	0.172456i	−0.967112	−	0.254349i	$-0.918139\pi$
$617$	−1.55915	+	4.28372i	−0.0627689	+	0.172456i	0.904344	+	0.426805i	$0.140361\pi$
$618$	−5.72250	+	33.4583i	−0.230193	+	1.34589i
$619$	−8.63313			−0.346995			−0.173497	−	0.984834i	$-0.555507\pi$
$619$	−8.63313			−0.346995			−0.173497	+	0.984834i	$0.555507\pi$
$620$	18.5937	−	32.2052i	0.746740	−	1.29339i
$621$	2.75513	+	14.3299i	0.110560	+	0.575038i
$622$	−13.1086	+	15.6223i	−0.525609	+	0.626396i
$623$	9.79259	−	11.3426i	0.392332	−	0.454431i
$624$	−3.07119	−	5.25689i	−0.122946	−	0.210444i
$625$	5.95490	−	33.7719i	0.238196	−	1.35088i
$626$	−10.4665	−	18.1285i	−0.418325	−	0.724560i
$627$	13.5467	+	15.3793i	0.541003	+	0.614190i
$628$	2.99956	−	5.19539i	0.119696	−	0.207319i
$629$	−0.358717	+	0.130562i	−0.0143030	+	0.00520585i
$630$	−29.4955	+	10.6092i	−1.17513	+	0.422682i
$631$	13.1486	−	11.0330i	0.523438	−	0.439217i	−0.342390	−	0.939558i	$-0.611236\pi$
$631$	13.1486	−	11.0330i	0.523438	−	0.439217i	0.865828	+	0.500341i	$0.166792\pi$
$632$	0.407957	+	1.12085i	0.0162277	+	0.0445851i
$633$	3.16085	−	18.4808i	0.125632	−	0.734547i
$634$	14.2047	−	24.6033i	0.564141	−	0.977121i
$635$	1.36646	+	2.36677i	0.0542261	+	0.0939224i
$636$	5.54701	+	15.0000i	0.219953	+	0.594790i
$637$	−20.9546	−	12.8970i	−0.830253	−	0.510999i
$638$	1.89468	+	1.09390i	0.0750112	+	0.0433077i
$639$	−6.31696	+	38.1113i	−0.249895	+	1.50766i
$640$	2.53847	+	3.02523i	0.100342	+	0.119583i
$641$	2.65089	−	15.0339i	0.104704	−	0.593805i	−0.886634	−	0.462471i	$-0.846963\pi$
$641$	2.65089	−	15.0339i	0.104704	−	0.593805i	0.991338	−	0.131334i	$-0.0419259\pi$
$642$	−15.5170	+	18.6866i	−0.612409	+	0.737503i
$643$	−0.713294	+	4.04529i	−0.0281296	+	0.159531i	−0.995637	−	0.0933123i	$-0.970255\pi$
$643$	−0.713294	+	4.04529i	−0.0281296	+	0.159531i	0.967507	+	0.252843i	$0.0813656\pi$
$644$	3.80513	−	6.38174i	0.149943	−	0.251476i
$645$	46.6305	−	39.5376i	1.83607	−	1.55679i
$646$	−0.230649	+	0.0889101i	−0.00907477	+	0.00349812i
$647$	−16.0839	+	9.28605i	−0.632324	+	0.365072i	−0.781651	−	0.623716i	$-0.785622\pi$
$647$	−16.0839	+	9.28605i	−0.632324	+	0.365072i	0.149328	+	0.988788i	$0.452289\pi$
$648$	4.65923	+	7.70011i	0.183032	+	0.302489i
$649$	11.4783	−	13.6794i	0.450565	−	0.536962i
$650$	−23.9407	−	28.5314i	−0.939033	−	1.11910i
$651$	−42.5615	+	7.11379i	−1.66812	+	0.278811i
$652$	2.94490	+	16.7013i	0.115331	+	0.654075i
$653$			10.2435i			0.400859i	0.979708	+	0.200429i	$0.0642337\pi$
$653$			10.2435i			0.400859i	−0.979708	+	0.200429i	$0.935766\pi$
$654$	19.5904	−	16.6105i	0.766044	−	0.649524i
$655$	−5.99880	−	34.0209i	−0.234393	−	1.32931i
$656$	1.23721	−	1.03814i	0.0483048	−	0.0405325i
$657$	20.3574	+	16.7285i	0.794218	+	0.652639i
$658$	−1.87447	−	11.5805i	−0.0730744	−	0.451455i
$659$	2.02243	+	11.4698i	0.0787828	+	0.446800i	0.998526	+	0.0542785i	$0.0172859\pi$
$659$	2.02243	+	11.4698i	0.0787828	+	0.446800i	−0.919743	+	0.392521i	$0.871603\pi$
$660$	16.1281	+	9.20138i	0.627784	+	0.358163i
$661$	−10.5576	+	29.0067i	−0.410642	+	1.12823i	0.546209	+	0.837649i	$0.316070\pi$
$661$	−10.5576	+	29.0067i	−0.410642	+	1.12823i	−0.956851	+	0.290580i	$0.906152\pi$
$662$	−8.75172	−	24.0451i	−0.340145	−	0.934541i
$663$	0.298117	−	0.174167i	0.0115779	−	0.00676407i
$664$			8.49529i			0.329681i
$665$	15.3714	−	42.8715i	0.596078	−	1.66249i
$666$	−19.9225	−	3.30216i	−0.771980	−	0.127956i
$667$	−2.22892	−	0.393018i	−0.0863040	−	0.0152177i
$668$	−6.34704	+	2.31013i	−0.245574	+	0.0893817i
$669$	−41.1501	+	15.2173i	−1.59096	+	0.588335i
$670$	44.4666	−	16.1845i	1.71789	−	0.625262i
$671$	−0.253556	+	0.0447087i	−0.00978840	+	0.00172596i
$672$	0.835991	−	4.50568i	0.0322490	−	0.173810i
$673$	8.44172	+	4.87383i	0.325405	+	0.187872i	0.653799	−	0.756668i	$-0.273174\pi$
$673$	8.44172	+	4.87383i	0.325405	+	0.187872i	−0.328394	+	0.944541i	$0.606508\pi$
$674$	−13.6435	−	16.2597i	−0.525529	−	0.626301i
$675$	36.0363	+	41.6261i	1.38704	+	1.60219i
$676$	0.644293			0.0247805
$677$	3.49778			0.134430			0.0672152	−	0.997738i	$-0.478589\pi$
$677$	3.49778			0.134430			0.0672152	+	0.997738i	$0.478589\pi$
$678$	8.94693	−	10.7745i	0.343605	−	0.413791i
$679$	−23.4990	−	0.330430i	−0.901809	−	0.0126807i
$680$	−0.171560	+	0.143956i	−0.00657904	+	0.00552047i
$681$	−0.0557349	−	10.8475i	−0.00213577	−	0.415677i
$682$	19.5817	+	16.4310i	0.749822	+	0.629175i
$683$	−9.13165	−	15.8165i	−0.349413	−	0.605201i	0.636732	−	0.771085i	$-0.280286\pi$
$683$	−9.13165	−	15.8165i	−0.349413	−	0.605201i	−0.986145	+	0.165884i	$0.946952\pi$
$684$	−12.9387	−	1.89464i	−0.494724	−	0.0724433i
$685$	11.9815			0.457789
$686$	−5.59479	−	17.6550i	−0.213610	−	0.674070i
$687$	−1.31338	+	0.767303i	−0.0501084	+	0.0292744i
$688$	1.55204	+	8.80205i	0.0591710	+	0.335575i
$689$	31.9631	+	5.63596i	1.21770	+	0.214713i
$690$	−18.9342	−	3.23839i	−0.720813	−	0.123283i
$691$	41.9682			1.59655			0.798273	−	0.602296i	$-0.205747\pi$
$691$	41.9682			1.59655			0.798273	+	0.602296i	$0.205747\pi$
$692$	−11.8744	+	20.5671i	−0.451397	+	0.781843i
$693$	−3.66117	−	21.2331i	−0.139076	−	0.806580i
$694$	3.03869	−	8.34874i	0.115347	−	0.316914i
$695$	77.2871	−	44.6217i	2.93167	−	1.69260i
$696$	−1.37345	+	0.249459i	−0.0520605	+	0.00945572i
$697$	0.0588727	+	0.0701617i	0.00222996	+	0.00265756i
$698$	4.14877	−	1.51003i	0.157033	−	0.0571555i
$699$	−6.69100	+	39.1209i	−0.253077	+	1.47969i
$700$	0.394159	−	28.0312i	0.0148978	−	1.05948i
$701$	−9.91497	−	27.2412i	−0.374483	−	1.02888i	−0.973608	−	0.228228i	$-0.926707\pi$
$701$	−9.91497	−	27.2412i	−0.374483	−	1.02888i	0.599124	−	0.800656i	$-0.295516\pi$
$702$	18.2627	−	0.281523i	0.689280	−	0.0106254i
$703$	22.1173	−	19.2809i	0.834171	−	0.727194i
$704$	−2.35091	+	1.35730i	−0.0886033	+	0.0511552i
$705$	−26.1875	+	15.2993i	−0.986279	+	0.576205i
$706$	−2.97742	−	0.524999i	−0.112057	−	0.0197586i
$707$	−26.4523	+	9.20878i	−0.994843	+	0.346332i
$708$	0.0585408	+	11.3936i	0.00220010	+	0.428198i
$709$	−0.361449	−	0.131557i	−0.0135745	−	0.00494072i	0.335224	−	0.942138i	$-0.391188\pi$
$709$	−0.361449	−	0.131557i	−0.0135745	−	0.00494072i	−0.348798	+	0.937198i	$0.613410\pi$
$710$	−44.0406	−	25.4268i	−1.65281	−	0.954253i
$711$	−3.53019	−	0.585131i	−0.132393	−	0.0219441i
$712$	4.33871	−	3.64061i	0.162600	−	0.136438i
$713$	−24.8496	−	9.04451i	−0.930624	−	0.338719i
$714$	0.255516	+	0.0474089i	0.00956245	+	0.00177423i
$715$	32.6343	−	18.8414i	1.22045	−	0.704630i
$716$	11.0958	+	4.03854i	0.414669	+	0.150927i
$717$	−7.83844	−	13.4169i	−0.292732	−	0.501064i
$718$	3.22073	−	8.84887i	0.120196	−	0.330237i
$719$	−26.3481	+	31.4005i	−0.982620	+	1.17104i	0.00264390	+	0.999997i	$0.499158\pi$
$719$	−26.3481	+	31.4005i	−0.982620	+	1.17104i	−0.985263	+	0.171044i	$0.945286\pi$
$720$	−11.6457	+	2.17708i	−0.434011	+	0.0811349i
$721$	8.28491	+	51.1843i	0.308546	+	1.90620i
$722$	14.0840	−	12.7531i	0.524151	−	0.474622i
$723$	−2.15052	−	11.8402i	−0.0799788	−	0.440340i
$724$	3.99347	−	4.75924i	0.148416	−	0.176876i
$725$	−8.02457	+	2.92071i	−0.298025	+	0.108472i
$726$	4.01768	−	4.83835i	0.149110	−	0.179568i
$727$	−24.1070	−	20.2282i	−0.894081	−	0.750223i	0.0749438	−	0.997188i	$-0.476122\pi$
$727$	−24.1070	−	20.2282i	−0.894081	−	0.750223i	−0.969024	+	0.246965i	$0.920567\pi$
$728$	−7.03946	−	6.07750i	−0.260900	−	0.225247i
$729$	−26.9872	+	0.832223i	−0.999525	+	0.0308231i
$730$	−30.0384	+	17.3427i	−1.11177	+	0.641881i
$731$	−0.499163	+	0.0880159i	−0.0184622	+	0.00325539i
$732$	0.104947	−	0.126384i	0.00387896	−	0.00467130i
$733$	20.0357	+	34.7028i	0.740034	+	1.28178i	0.952479	+	0.304603i	$0.0985239\pi$
$733$	20.0357	+	34.7028i	0.740034	+	1.28178i	−0.212445	+	0.977173i	$0.568143\pi$
$734$	−11.7196	−	20.2989i	−0.432578	−	0.749247i
$735$	−37.3766	+	29.9263i	−1.37866	+	1.10385i
$736$	1.80514	−	2.15128i	0.0665382	−	0.0792972i
$737$	5.64832	+	32.0332i	0.208058	+	1.17996i
$738$	0.890342	+	4.76266i	0.0327740	+	0.175316i
$739$	−19.9919	−	16.7752i	−0.735414	−	0.617086i	0.196188	−	0.980566i	$-0.437144\pi$
$739$	−19.9919	−	16.7752i	−0.735414	−	0.617086i	−0.931602	+	0.363481i	$0.881588\pi$
$740$	13.2917	−	23.0220i	0.488614	−	0.846305i
$741$	−16.5657	+	20.7329i	−0.608557	+	0.761641i
$742$	15.4383	+	18.9330i	0.566756	+	0.695051i
$743$	5.88810	−	2.14309i	0.216013	−	0.0786224i	−0.231747	−	0.972776i	$-0.574444\pi$
$743$	5.88810	−	2.14309i	0.216013	−	0.0786224i	0.447760	+	0.894154i	$0.352222\pi$
$744$	−16.3097	+	0.0837998i	−0.597942	+	0.00307225i
$745$	−10.4206	−	3.79280i	−0.381783	−	0.138958i
$746$	9.55060	+	1.68403i	0.349672	+	0.0616567i
$747$	−22.2012	−	12.5155i	−0.812299	−	0.457917i
$748$	−0.0769722	−	0.133320i	−0.00281438	−	0.00487465i
$749$	−13.1787	+	34.6831i	−0.481541	+	1.26729i
$750$	−35.9004	+	13.2760i	−1.31090	+	0.484769i
$751$	22.8770	+	27.2638i	0.834794	+	0.994869i	0.999963	+	0.00860374i	$0.00273869\pi$
$751$	22.8770	+	27.2638i	0.834794	+	0.994869i	−0.165169	+	0.986265i	$0.552817\pi$
$752$		−	4.43399i		−	0.161691i
$753$	6.59645	+	36.3181i	0.240388	+	1.32351i
$754$	−0.968914	+	2.66207i	−0.0352858	+	0.0969469i
$755$	27.8652	+	23.3817i	1.01412	+	0.850946i
$756$	10.5433	+	8.82261i	0.383457	+	0.320875i
$757$	2.43070	−	13.7852i	0.0883455	−	0.501032i	−0.908239	−	0.418452i	$-0.862573\pi$
$757$	2.43070	−	13.7852i	0.0883455	−	0.501032i	0.996584	−	0.0825801i	$-0.0263160\pi$
$758$	−3.00573	−	0.529992i	−0.109173	−	0.0192502i
$759$	4.45226	−	12.4308i	0.161607	−	0.451211i
$760$	8.32434	−	15.0674i	0.301956	−	0.546552i
$761$	−13.1047	−	7.56601i	−0.475046	−	0.274268i	0.243304	−	0.969950i	$-0.421769\pi$
$761$	−13.1047	−	7.56601i	−0.475046	−	0.274268i	−0.718350	+	0.695682i	$0.755102\pi$
$762$	0.593969	−	1.04110i	0.0215172	−	0.0377151i
$763$	20.0926	−	33.6982i	0.727402	−	1.21996i
$764$	−12.4817	−	14.8751i	−0.451573	−	0.538163i
$765$	−0.123462	−	0.660427i	−0.00446377	−	0.0238778i
$766$	18.0806	−	15.1715i	0.653280	−	0.548167i
$767$	20.0249	+	11.5614i	0.723058	+	0.417458i
$768$	0.584026	−	1.63062i	0.0210742	−	0.0588398i
$769$	5.76951	+	2.09993i	0.208054	+	0.0757254i	0.443945	−	0.896054i	$-0.353579\pi$
$769$	5.76951	+	2.09993i	0.208054	+	0.0757254i	−0.235891	+	0.971780i	$0.575801\pi$
$770$	27.8606	+	5.31751i	1.00402	+	0.191630i
$771$	−14.2697	+	2.59181i	−0.513912	+	0.0933417i
$772$			2.16909i			0.0780672i
$773$	−3.64406	+	3.05773i	−0.131068	+	0.109979i	−0.705965	−	0.708247i	$-0.749486\pi$
$773$	−3.64406	+	3.05773i	−0.131068	+	0.109979i	0.574897	+	0.818226i	$0.305042\pi$
$774$	−25.2894	−	8.91137i	−0.909008	−	0.320312i
$775$	−98.2603	+	17.3259i	−3.52961	+	0.622366i
$776$	−8.74772	−	1.54246i	−0.314025	−	0.0553710i
$777$	−30.4252	+	5.08531i	−1.09150	+	0.182435i
$778$		−	18.8931i		−	0.677351i
$779$	−6.16200	−	3.40434i	−0.220777	−	0.121973i
$780$	−8.10719	+	22.6355i	−0.290284	+	0.810482i
$781$	22.4694	−	26.7780i	0.804018	−	0.958191i
$782$	0.121999	+	0.102369i	0.00436266	+	0.00366071i
$783$	1.37147	−	3.95682i	0.0490125	−	0.141405i
$784$	−1.02123	−	6.92511i	−0.0364723	−	0.247325i
$785$	−23.3316	+	4.11399i	−0.832740	+	0.146834i
$786$	−11.5564	+	9.79858i	−0.412203	+	0.349504i
$787$		−	26.8963i		−	0.958751i	−0.877610	−	0.479376i	$-0.840863\pi$
$787$		−	26.8963i		−	0.958751i	0.877610	−	0.479376i	$-0.159137\pi$
$788$	9.41309	−	1.65978i	0.335328	−	0.0591273i
$789$	7.61642	−	44.5316i	0.271152	−	1.58537i
$790$	2.35525	−	4.07941i	0.0837961	−	0.145139i
$791$	7.59870	−	19.9978i	0.270179	−	0.711041i
$792$	−0.0836841	−	8.14337i	−0.00297359	−	0.289362i
$793$	−0.114025	−	0.313282i	−0.00404916	−	0.0111250i
$794$	12.0461	+	4.38444i	0.427501	+	0.155598i
$795$	31.2976	−	54.8581i	1.11001	−	1.94562i
$796$	−0.187794	+	1.06504i	−0.00665620	+	0.0377492i
$797$	−19.1520			−0.678400			−0.339200	−	0.940714i	$-0.610156\pi$
$797$	−19.1520			−0.678400			−0.339200	+	0.940714i	$0.610156\pi$
$798$	−19.6361	+	3.66390i	−0.695110	+	0.129701i
$799$	0.251451			0.00889568
$800$	1.83995	−	10.4349i	0.0650521	−	0.368929i
$801$	3.12231	+	16.7020i	0.110321	+	0.590136i
$802$	−23.7276	−	8.63613i	−0.837850	−	0.304952i
$803$	−8.15453	−	22.4044i	−0.287767	−	0.790634i
$804$	−15.9669	−	13.2586i	−0.563109	−	0.467595i
$805$	−28.9655	+	4.68847i	−1.02090	+	0.165247i
$806$	−16.5499	+	28.6652i	−0.582944	+	1.00969i
$807$	13.5505	+	2.31759i	0.476999	+	0.0815831i
$808$	−10.4257	+	1.83834i	−0.366776	+	0.0646725i
$809$			34.8843i			1.22647i	0.789902	+	0.613233i	$0.210131\pi$
$809$			34.8843i			1.22647i	−0.789902	+	0.613233i	$0.789869\pi$
$810$	11.4673	−	33.6417i	0.402920	−	1.18205i
$811$	32.1924	−	5.67639i	1.13043	−	0.199325i	0.423013	−	0.906124i	$-0.360973\pi$
$811$	32.1924	−	5.67639i	1.13043	−	0.199325i	0.707415	+	0.706799i	$0.249861\pi$
$812$	−1.86144	+	1.04008i	−0.0653236	+	0.0364997i
$813$	−23.9239	−	4.09181i	−0.839049	−	0.143506i
$814$	13.9980	+	11.7457i	0.490631	+	0.411688i
$815$	43.0499	−	51.3049i	1.50797	−	1.79713i
$816$	0.0924720	+	0.0331200i	0.00323717	+	0.00115943i
$817$	33.3663	−	20.1124i	1.16734	−	0.703642i
$818$			20.2468i			0.707912i
$819$	26.2533	−	9.44307i	0.917366	−	0.329968i
$820$	−6.28122	−	1.10755i	−0.219350	−	0.0386773i
$821$	−23.9286	+	4.21925i	−0.835112	+	0.147253i	−0.574823	−	0.818278i	$-0.694929\pi$
$821$	−23.9286	+	4.21925i	−0.835112	+	0.147253i	−0.260289	+	0.965531i	$0.583818\pi$
$822$	−2.65081	−	4.53734i	−0.0924576	−	0.158258i
$823$	−28.0227	+	23.5138i	−0.976810	+	0.819641i	−0.983605	−	0.180336i	$-0.942281\pi$
$823$	−28.0227	+	23.5138i	−0.976810	+	0.819641i	0.00679507	+	0.999977i	$0.497837\pi$
$824$			19.5977i			0.682717i
$825$	−8.90310	−	49.0179i	−0.309966	−	1.70658i
$826$	5.72207	+	16.4367i	0.199096	+	0.571907i
$827$	10.3816	+	3.77860i	0.361004	+	0.131395i	0.516153	−	0.856496i	$-0.327364\pi$
$827$	10.3816	+	3.77860i	0.361004	+	0.131395i	−0.155149	+	0.987891i	$0.549586\pi$
$828$	2.96268	+	7.88677i	0.102960	+	0.274084i
$829$	−8.32118	−	4.80423i	−0.289006	−	0.166858i	0.348487	−	0.937314i	$-0.386695\pi$
$829$	−8.32118	−	4.80423i	−0.289006	−	0.166858i	−0.637494	+	0.770456i	$0.720029\pi$
$830$	25.7002	−	21.5650i	0.892068	−	0.748534i
$831$	24.7734	+	14.1337i	0.859380	+	0.490293i
$832$	−2.25944	−	2.69270i	−0.0783321	−	0.0933525i
$833$	0.392722	−	0.0579135i	0.0136070	−	0.00200658i
$834$	−33.9973	−	19.3961i	−1.17723	−	0.671632i
$835$	23.1005	+	13.3371i	0.799424	+	0.461548i
$836$	9.20616	+	7.43361i	0.318402	+	0.257097i
$837$	23.8088	−	42.7464i	0.822953	−	1.47753i
$838$	−17.2309	−	3.03827i	−0.595232	−	0.104955i
$839$	−4.39099	+	24.9025i	−0.151594	+	0.859731i	0.810240	+	0.586098i	$0.199336\pi$
$839$	−4.39099	+	24.9025i	−0.151594	+	0.859731i	−0.961834	+	0.273633i	$0.911775\pi$
$840$	−15.7529	+	8.90846i	−0.543525	+	0.307371i
$841$	−21.7177	−	18.2233i	−0.748887	−	0.628391i
$842$	−1.63188	+	4.48355i	−0.0562383	+	0.154513i
$843$	23.6610	−	4.29753i	0.814927	−	0.148015i
$844$		−	10.8248i		−	0.372606i
$845$	−1.63552	−	1.94914i	−0.0562636	−	0.0670523i
$846$	11.5876	+	6.53225i	0.398389	+	0.224583i
$847$	3.41225	−	8.98016i	0.117246	−	0.308562i
$848$	4.61673	+	7.99640i	0.158539	+	0.274598i
$849$	−4.09071	−	11.0620i	−0.140393	−	0.379645i
$850$	0.591760	+	0.104343i	0.0202972	+	0.00357895i
$851$	−17.7638	−	6.46549i	−0.608935	−	0.221634i
$852$	0.114596	+	22.3035i	0.00392600	+	0.764105i
$853$	2.71440	−	0.987961i	0.0929393	−	0.0338271i	−0.295132	−	0.955456i	$-0.595364\pi$
$853$	2.71440	−	0.987961i	0.0929393	−	0.0338271i	0.388071	+	0.921629i	$0.373141\pi$
$854$	0.0891325	−	0.234574i	0.00305005	−	0.00802695i
$855$	27.1128	+	43.9521i	0.927239	+	1.50313i
$856$	−7.01171	+	12.1446i	−0.239655	+	0.415095i
$857$	14.4174	+	12.0977i	0.492490	+	0.413248i	0.854918	−	0.518764i	$-0.173608\pi$
$857$	14.4174	+	12.0977i	0.492490	+	0.413248i	−0.362428	+	0.932012i	$0.618052\pi$
$858$	−14.3553	−	8.18997i	−0.490081	−	0.279601i
$859$	−7.68975	−	43.6108i	−0.262371	−	1.48798i	−0.776418	−	0.630218i	$-0.782966\pi$
$859$	−7.68975	−	43.6108i	−0.262371	−	1.48798i	0.514047	−	0.857762i	$-0.328146\pi$
$860$	22.6884	−	27.0390i	0.773670	−	0.922023i
$861$	3.64322	+	6.44232i	0.124161	+	0.219554i
$862$	18.4714	+	31.9934i	0.629138	+	1.08970i
$863$	4.62762	+	8.01527i	0.157526	+	0.272843i	0.933976	−	0.357336i	$-0.116315\pi$
$863$	4.62762	+	8.01527i	0.157526	+	0.272843i	−0.776450	+	0.630179i	$0.782982\pi$
$864$	3.40098	+	3.92853i	0.115704	+	0.133651i
$865$	92.3630	−	16.2861i	3.14044	−	0.553744i
$866$	−6.58216	+	3.80021i	−0.223671	+	0.129136i
$867$	9.92656	−	27.7153i	0.337124	−	0.941259i
$868$	−23.5288	+	8.19101i	−0.798619	+	0.278021i
$869$	2.48040	+	2.08130i	0.0841419	+	0.0706034i
$870$	4.24113	+	3.52176i	0.143788	+	0.119399i
$871$	−39.5788	+	14.4055i	−1.34108	+	0.488112i
$872$	9.53186	−	11.3596i	0.322790	−	0.384686i
$873$	16.9183	−	20.5885i	0.572599	−	0.696815i
$874$	−11.5798	−	3.96903i	−0.391691	−	0.134255i
$875$	−45.3133	+	36.9492i	−1.53187	+	1.24911i
$876$	13.2134	+	7.53849i	0.446438	+	0.254702i
$877$	−25.6156	+	30.5274i	−0.864976	+	1.03084i	0.134228	+	0.990950i	$0.457145\pi$
$877$	−25.6156	+	30.5274i	−0.864976	+	1.03084i	−0.999204	+	0.0398879i	$0.987300\pi$
$878$	−5.72402	+	15.7266i	−0.193176	+	0.530747i
$879$	−38.5406	+	22.5162i	−1.29994	+	0.759453i
$880$	10.0739	+	3.66659i	0.339590	+	0.123601i
$881$	−7.45301	+	4.30300i	−0.251098	+	0.144972i	−0.620267	−	0.784391i	$-0.712976\pi$
$881$	−7.45301	+	4.30300i	−0.251098	+	0.144972i	0.369169	+	0.929362i	$0.379642\pi$
$882$	19.6022	+	7.53341i	0.660042	+	0.253663i
$883$	−29.5785	−	10.7657i	−0.995396	−	0.362294i	−0.207589	−	0.978216i	$-0.566562\pi$
$883$	−29.5785	−	10.7657i	−0.995396	−	0.362294i	−0.787807	+	0.615922i	$0.788784\pi$
$884$	0.152702	−	0.128133i	0.00513594	−	0.00430957i
$885$	34.3197	−	29.0994i	1.15364	−	0.978167i
$886$	25.9650	+	14.9909i	0.872310	+	0.503628i
$887$	−43.8939	−	15.9761i	−1.47381	−	0.536423i	−0.524679	−	0.851300i	$-0.675815\pi$
$887$	−43.8939	−	15.9761i	−1.47381	−	0.536423i	−0.949133	+	0.314877i	$0.898037\pi$
$888$	−11.6590	+	0.0599045i	−0.391251	+	0.00201026i
$889$	0.343257	−	1.79846i	0.0115125	−	0.0603183i
$890$	−22.0274	−	3.88402i	−0.738359	−	0.130193i
$891$	21.4048	+	11.7783i	0.717087	+	0.394588i
$892$	−21.9368	+	12.6652i	−0.734500	+	0.424064i
$893$	−18.0338	+	6.95164i	−0.603479	+	0.232628i
$894$	0.869167	+	4.78538i	0.0290693	+	0.160047i
$895$	−15.9488	−	43.8190i	−0.533110	−	1.46471i
$896$	0.0371994	−	2.64549i	0.00124274	−	0.0883796i
$897$	16.8530	+	2.88243i	0.562704	+	0.0962415i
$898$	20.5890	−	7.49380i	0.687065	−	0.250071i
$899$	4.87818	+	5.81359i	0.162696	+	0.193894i
$900$	24.5594	+	20.1814i	0.818646	+	0.672712i
$901$	−0.453475	+	0.261814i	−0.0151074	+	0.00872228i
$902$	1.49950	−	4.11983i	0.0499277	−	0.137175i
$903$	−40.9567	−	0.365446i	−1.36295	−	0.0121613i
$904$	4.04286	−	7.00245i	0.134464	−	0.232898i
$905$	−24.5351			−0.815575
$906$	2.68959	−	15.7254i	0.0893555	−	0.522443i
$907$	7.35615	+	1.29709i	0.244257	+	0.0430691i	0.294436	−	0.955671i	$-0.404868\pi$
$907$	7.35615	+	1.29709i	0.244257	+	0.0430691i	−0.0501792	+	0.998740i	$0.515979\pi$
$908$	−1.08754	−	6.16774i	−0.0360913	−	0.204684i
$909$	10.5552	−	29.9544i	0.350094	−	0.993525i
$910$	−0.516385	+	36.7235i	−0.0171180	+	1.21737i
$911$	−15.7199			−0.520825			−0.260412	−	0.965498i	$-0.583858\pi$
$911$	−15.7199			−0.520825			−0.260412	+	0.965498i	$0.583858\pi$
$912$	−7.54766	+	0.181153i	−0.249928	+	0.00599858i
$913$	11.5307	+	19.9717i	0.381609	+	0.660966i
$914$	7.17323	+	6.01906i	0.237269	+	0.199093i
$915$	−0.648747	+	0.00333329i	−0.0214469	+	0.000110195i
$916$	−0.672741	+	0.564497i	−0.0222280	+	0.0186515i
$917$	−11.8527	+	19.8786i	−0.391410	+	0.656450i
$918$	−0.222786	+	0.192869i	−0.00735304	+	0.00636562i
$919$	−2.74665			−0.0906035			−0.0453018	−	0.998973i	$-0.514425\pi$
$919$	−2.74665			−0.0906035			−0.0453018	+	0.998973i	$0.514425\pi$
$920$	−11.0904			−0.365640
$921$	−2.98289	−	2.47693i	−0.0982894	−	0.0816177i
$922$	9.39299	+	11.1941i	0.309342	+	0.368659i
$923$	39.1997	+	22.6319i	1.29027	+	0.744939i
$924$	−4.15021	−	11.7271i	−0.136532	−	0.385794i
$925$	−70.2417	+	12.3855i	−2.30953	+	0.407233i
$926$	28.7892	−	10.4784i	0.946071	−	0.344342i
$927$	−51.2156	−	28.8717i	−1.68214	−	0.948272i
$928$	−0.757331	+	0.275646i	−0.0248606	+	0.00904852i
$929$	20.7347	+	3.65609i	0.680285	+	0.119953i	0.503104	−	0.864226i	$-0.332191\pi$
$929$	20.7347	+	3.65609i	0.680285	+	0.119953i	0.177181	+	0.984178i	$0.443302\pi$
$930$	41.6552	+	49.1278i	1.36593	+	1.61097i
$931$	−26.5646	+	15.0107i	−0.870619	+	0.491957i
$932$			22.9144i			0.750587i
$933$	−17.8182	−	30.4990i	−0.583340	−	0.998492i
$934$	−11.5338	−	31.6888i	−0.377397	−	1.03689i
$935$	−0.207932	+	0.571287i	−0.00680009	+	0.0186831i
$936$	10.3656	−	1.93777i	0.338811	−	0.0633381i
$937$	−7.71966	−	43.7804i	−0.252190	−	1.43024i	−0.803183	−	0.595733i	$-0.796862\pi$
$937$	−7.71966	−	43.7804i	−0.252190	−	1.43024i	0.550993	−	0.834510i	$-0.314249\pi$
$938$	−29.6351	−	11.2606i	−0.967621	−	0.367673i
$939$	35.6733	−	6.47933i	1.16416	−	0.211445i
$940$	−13.4138	+	11.2555i	−0.437511	+	0.367115i
$941$	−6.63111	−	37.6069i	−0.216168	−	1.22595i	−0.878868	−	0.477065i	$-0.841701\pi$
$941$	−6.63111	−	37.6069i	−0.216168	−	1.22595i	0.662700	−	0.748885i	$-0.269411\pi$
$942$	6.71988	+	7.92538i	0.218946	+	0.258223i
$943$			4.53556i			0.147698i
$944$	1.14229	+	6.47825i	0.0371784	+	0.210849i
$945$	−0.0734833	−	54.2919i	−0.00239041	−	1.76612i
$946$	15.5957	+	18.5863i	0.507061	+	0.604292i
$947$	−36.6966	+	43.7333i	−1.19248	+	1.42114i	−0.310036	+	0.950725i	$0.600341\pi$
$947$	−36.6966	+	43.7333i	−1.19248	+	1.42114i	−0.882444	+	0.470418i	$0.844103\pi$
$948$	−2.06594	+	0.0106149i	−0.0670986	+	0.000344755i
$949$	26.7366	−	15.4364i	0.867906	−	0.501086i
$950$	−45.3253	+	8.87646i	−1.47055	+	0.287990i
$951$	31.8226	+	37.5314i	1.03192	+	1.21704i
$952$	0.150025	+	0.00210957i	0.00486235	+	6.83715e-5i
$953$	−5.94345	+	33.7070i	−0.192527	+	1.09188i	0.723369	+	0.690462i	$0.242593\pi$
$953$	−5.94345	+	33.7070i	−0.192527	+	1.09188i	−0.915896	+	0.401415i	$0.868519\pi$
$954$	−27.6989	+	0.284644i	−0.896785	+	0.00921568i
$955$	−13.3162	+	75.5202i	−0.430904	+	2.44378i
$956$	−5.76666	−	6.87244i	−0.186507	−	0.222271i
$957$	−2.89027	+	2.45064i	−0.0934291	+	0.0792179i
$958$	21.2264	+	12.2550i	0.685792	+	0.395942i
$959$	−6.07591	−	5.24562i	−0.196201	−	0.169390i
$960$	−6.41553	+	2.37246i	−0.207060	+	0.0765709i
$961$	28.8354	+	49.9445i	0.930176	+	1.61111i
$962$	−11.8307	+	20.4914i	−0.381438	+	0.660669i
$963$	−21.4084	−	36.2159i	−0.689877	−	1.16704i
$964$	−2.37627	−	6.52875i	−0.0765346	−	0.210277i
$965$	6.56200	−	5.50617i	0.211238	−	0.177250i
$966$	8.18389	+	9.93181i	0.263312	+	0.319551i
$967$	8.48095	−	3.08681i	0.272729	−	0.0992652i	−0.202035	−	0.979378i	$-0.564756\pi$
$967$	8.48095	−	3.08681i	0.272729	−	0.0992652i	0.474764	+	0.880113i	$0.342533\pi$
$968$	1.81548	−	3.14450i	0.0583516	−	0.101068i
$969$	−0.0102732	−	0.428027i	−0.000330022	−	0.0137502i
$970$	17.5395	+	30.3794i	0.563160	+	0.975422i
$971$	2.15527	−	12.2231i	0.0691659	−	0.392259i	−0.930497	−	0.366299i	$-0.880625\pi$
$971$	2.15527	−	12.2231i	0.0691659	−	0.392259i	0.999663	−	0.0259599i	$-0.00826422\pi$
$972$	−15.2770	+	3.10035i	−0.490011	+	0.0994439i
$973$	−58.7288	−	11.2091i	−1.88276	−	0.359347i
$974$	5.38639	−	6.41925i	0.172591	−	0.205686i
$975$	60.5059	−	22.3751i	1.93774	−	0.716576i
$976$	0.0474227	−	0.0821385i	0.00151796	−	0.00262919i
$977$	38.2065			1.22233			0.611167	−	0.791501i	$-0.290700\pi$
$977$	38.2065			1.22233			0.611167	+	0.791501i	$0.290700\pi$
$978$	−28.9534	−	4.95201i	−0.925828	−	0.158348i
$979$	5.25853	−	14.4477i	0.168063	−	0.461750i
$980$	−18.3577	+	20.6686i	−0.586415	+	0.660235i
$981$	15.6442	+	41.6454i	0.499480	+	1.32964i
$982$	−10.2958	+	28.2875i	−0.328552	+	0.902689i
$983$	3.47377	−	19.7008i	0.110796	−	0.628356i	−0.877950	−	0.478753i	$-0.841089\pi$
$983$	3.47377	−	19.7008i	0.110796	−	0.628356i	0.988746	−	0.149604i	$-0.0477998\pi$
$984$	0.970247	+	2.62371i	0.0309303	+	0.0836408i
$985$	−28.9161	−	24.2635i	−0.921343	−	0.773099i
$986$	−0.0156318	−	0.0429481i	−0.000497819	−	0.00136775i
$987$	19.9781	+	3.70677i	0.635910	+	0.117988i
$988$	−7.40933	+	13.4112i	−0.235722	+	0.426667i
$989$	−21.7373	−	12.5500i	−0.691206	−	0.399068i
$990$	−24.4231	+	20.9249i	−0.776218	+	0.665036i
$991$	19.1400	+	52.5866i	0.608001	+	1.67047i	0.734589	+	0.678513i	$0.237375\pi$
$991$	19.1400	+	52.5866i	0.608001	+	1.67047i	−0.126588	+	0.991955i	$0.540403\pi$
$992$	−9.27346	+	1.63516i	−0.294433	+	0.0519164i
$993$	44.3197	−	0.227716i	1.40644	−	0.00722636i
$994$	11.2012	+	32.1756i	0.355281	+	1.02055i
$995$	3.69869	−	2.13544i	0.117256	−	0.0676980i
$996$	−13.8526	−	4.96147i	−0.438936	−	0.157210i
$997$	−8.04188	−	45.6078i	−0.254689	−	1.44441i	−0.796870	−	0.604151i	$-0.793512\pi$
$997$	−8.04188	−	45.6078i	−0.254689	−	1.44441i	0.542181	−	0.840262i	$-0.317599\pi$
$998$	−0.423407	−	2.40126i	−0.0134027	−	0.0760106i
$999$	17.0198	−	30.5574i	0.538482	−	0.966793i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bu.b.527.5	yes	162
3.2	odd	2		798.2.bu.a.527.17	yes	162
7.4	even	3		798.2.cc.b.641.14	yes	162
19.15	odd	18		798.2.cc.a.737.3	yes	162
21.11	odd	6		798.2.cc.a.641.3	yes	162
57.53	even	18		798.2.cc.b.737.14	yes	162
133.53	odd	18		798.2.bu.a.53.17	✓	162
399.53	even	18	inner	798.2.bu.b.53.5	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.53.17	✓	162	133.53	odd	18
798.2.bu.a.527.17	yes	162	3.2	odd	2
798.2.bu.b.53.5	yes	162	399.53	even	18	inner
798.2.bu.b.527.5	yes	162	1.1	even	1	trivial
798.2.cc.a.641.3	yes	162	21.11	odd	6
798.2.cc.a.737.3	yes	162	19.15	odd	18
798.2.cc.b.641.14	yes	162	7.4	even	3
798.2.cc.b.737.14	yes	162	57.53	even	18

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bu (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-1.50443 - 0.858307i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(1.35069 + 3.71100i) q^{5} +(1.10651 - 1.33253i) q^{6} +(0.939767 - 2.47322i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.52662 + 2.58253i) q^{9} +(-3.88916 + 0.685764i) q^{10} -2.71460i q^{11} +(1.12014 + 1.32109i) q^{12} +(3.46167 - 0.610385i) q^{13} +(2.27246 + 1.35496i) q^{14} +(1.15315 - 6.74224i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-0.0364524 + 0.0434422i) q^{17} +(-2.80839 + 1.05497i) q^{18} +(1.41333 - 4.12341i) q^{19} -3.94916i q^{20} +(-3.53660 + 2.91418i) q^{21} +(2.67336 + 0.471385i) q^{22} +(-2.76563 + 0.487655i) q^{23} +(-1.49553 + 0.873721i) q^{24} +(-8.11690 + 6.81089i) q^{25} +3.51507i q^{26} +(-0.0800903 - 5.19554i) q^{27} +(-1.72898 + 2.00265i) q^{28} +(0.757331 + 0.275646i) q^{29} +(6.43957 + 2.30641i) q^{30} +(8.15495 + 4.70826i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-2.32996 + 4.08392i) q^{33} +(-0.0364524 - 0.0434422i) q^{34} +(10.4475 + 0.146906i) q^{35} +(-0.551276 - 2.94891i) q^{36} +(5.82959 + 3.36571i) q^{37} +(3.81534 + 2.10788i) q^{38} +(-5.73173 - 2.05289i) q^{39} +(3.88916 + 0.685764i) q^{40} +(0.280452 - 1.59052i) q^{41} +(-2.25579 - 3.98891i) q^{42} +(6.84678 + 5.74513i) q^{43} +(-0.928448 + 2.55089i) q^{44} +(-7.52175 + 9.15347i) q^{45} -2.80829i q^{46} +(-2.85011 - 3.39663i) q^{47} +(-0.600751 - 1.62453i) q^{48} +(-5.23368 - 4.64851i) q^{49} +(-5.29793 - 9.17628i) q^{50} +(0.0921268 - 0.0340685i) q^{51} +(-3.46167 - 0.610385i) q^{52} +(8.67661 + 3.15803i) q^{53} +(5.13051 + 0.823322i) q^{54} +(10.0739 - 3.66659i) q^{55} +(-1.67199 - 2.05047i) q^{56} +(-5.66540 + 4.99031i) q^{57} +(-0.402967 + 0.697960i) q^{58} +(5.03918 + 4.22838i) q^{59} +(-3.38959 + 5.94123i) q^{60} +(-0.0164697 - 0.0934044i) q^{61} +(-6.05282 + 7.21347i) q^{62} +(7.82183 - 1.34870i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(6.94078 + 12.0218i) q^{65} +(-3.61729 - 3.00373i) q^{66} +(-11.8003 + 2.08072i) q^{67} +(0.0491121 - 0.0283549i) q^{68} +(4.57925 + 1.64012i) q^{69} +(-1.95886 + 10.2632i) q^{70} +(9.86443 + 8.27724i) q^{71} +(2.99984 - 0.0308274i) q^{72} +(8.25330 - 3.00395i) q^{73} +(-4.32688 + 5.15657i) q^{74} +(18.0571 - 3.27971i) q^{75} +(-2.73838 + 3.39135i) q^{76} +(-6.71381 - 2.55109i) q^{77} +(3.01701 - 5.28817i) q^{78} +(-0.766708 + 0.913727i) q^{79} +(-1.35069 + 3.71100i) q^{80} +(-4.33887 + 7.88506i) q^{81} +(1.51766 + 0.552382i) q^{82} +(-7.35714 + 4.24765i) q^{83} +(4.32003 - 1.52885i) q^{84} +(-0.210450 - 0.0765975i) q^{85} +(-6.84678 + 5.74513i) q^{86} +(-0.902763 - 1.06471i) q^{87} +(-2.35091 - 1.35730i) q^{88} +(5.32221 + 1.93713i) q^{89} +(-7.70827 - 8.99696i) q^{90} +(1.74354 - 9.13510i) q^{91} +(2.76563 + 0.487655i) q^{92} +(-8.22741 - 14.0827i) q^{93} +(3.83995 - 2.21699i) q^{94} +(17.2109 - 0.324613i) q^{95} +(1.70417 - 0.309528i) q^{96} +(-3.03805 - 8.34698i) q^{97} +(5.48671 - 4.34696i) q^{98} +(7.01052 - 4.14416i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 81 q^{8} + 15 q^{13} - 6 q^{14} + 3 q^{15} + 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} + 9 q^{27} + 9 q^{28} - 6 q^{29} + 24 q^{33} + 6 q^{34} - 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots + 39 q^{99}+O(q^{100}) \) 162 * q + 81 * q^8 + 15 * q^13 - 6 * q^14 + 3 * q^15 + 6 * q^17 - 18 * q^18 + 9 * q^19 - 6 * q^22 - 6 * q^25 + 9 * q^27 + 9 * q^28 - 6 * q^29 + 24 * q^33 + 6 * q^34 - 24 * q^35 + 18 * q^37 - 9 * q^39 - 9 * q^43 + 12 * q^44 + 45 * q^45 - 12 * q^47 - 48 * q^49 - 87 * q^50 + 24 * q^51 - 15 * q^52 + 18 * q^54 - 18 * q^57 + 48 * q^59 + 18 * q^60 + 45 * q^61 - 36 * q^62 - 21 * q^63 - 81 * q^64 - 36 * q^65 + 12 * q^66 + 9 * q^67 - 9 * q^69 - 24 * q^70 - 12 * q^71 + 102 * q^73 - 39 * q^74 - 18 * q^78 - 42 * q^79 - 12 * q^81 + 57 * q^84 - 6 * q^85 + 9 * q^86 + 60 * q^87 - 54 * q^89 + 12 * q^90 - 18 * q^91 + 105 * q^93 - 72 * q^94 - 12 * q^97 + 27 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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