LMFDB - Embedded newform 798.2.bu.a.53.17

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			53.17
Character	$\chi$	$=$	798.53
Dual form			798.2.bu.a.527.17

$q$-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} +(0.600751 + 1.62453i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.35069 + 3.71100i) q^{5} +(-1.49553 + 0.873721i) q^{6} +(0.939767 + 2.47322i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.27820 + 1.95188i) 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} +(-6.84005 + 0.0351445i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.0364524 + 0.0434422i) q^{17} +(-2.31783 - 1.90465i) q^{18} +(1.41333 + 4.12341i) q^{19} -3.94916i q^{20} +(-3.45326 + 3.01247i) q^{21} +(2.67336 - 0.471385i) q^{22} +(2.76563 + 0.487655i) q^{23} +(1.10651 - 1.33253i) q^{24} +(-8.11690 - 6.81089i) q^{25} +3.51507i q^{26} +(-4.53951 - 2.52841i) q^{27} +(-1.72898 - 2.00265i) q^{28} +(-0.757331 + 0.275646i) q^{29} +(-1.22237 - 6.73004i) q^{30} +(8.15495 - 4.70826i) q^{31} +(0.766044 + 0.642788i) q^{32} +(4.40995 - 1.63080i) q^{33} +(-0.0364524 + 0.0434422i) q^{34} +(-10.4475 + 0.146906i) q^{35} +(1.47322 - 2.61335i) q^{36} +(5.82959 - 3.36571i) q^{37} +(-3.81534 + 2.10788i) q^{38} +(1.08801 + 5.99027i) q^{39} +(3.88916 - 0.685764i) q^{40} +(-0.280452 - 1.59052i) q^{41} +(-3.56636 - 2.87769i) q^{42} +(6.84678 - 5.74513i) q^{43} +(0.928448 + 2.55089i) q^{44} +(-4.16626 - 11.0908i) q^{45} +2.80829i q^{46} +(2.85011 - 3.39663i) q^{47} +(1.50443 + 0.858307i) q^{48} +(-5.23368 + 4.64851i) q^{49} +(5.29793 - 9.17628i) q^{50} +(-0.0486744 + 0.0853160i) q^{51} +(-3.46167 + 0.610385i) q^{52} +(-8.67661 + 3.15803i) q^{53} +(1.70172 - 4.90960i) q^{54} +(10.0739 + 3.66659i) q^{55} +(1.67199 - 2.05047i) q^{56} +(-5.84955 + 4.77313i) q^{57} +(-0.402967 - 0.697960i) q^{58} +(-5.03918 + 4.22838i) q^{59} +(6.41553 - 2.37246i) q^{60} +(-0.0164697 + 0.0934044i) q^{61} +(6.05282 + 7.21347i) q^{62} +(-6.96840 - 3.80018i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-6.94078 + 12.0218i) q^{65} +(2.37180 + 4.05977i) q^{66} +(-11.8003 - 2.08072i) q^{67} +(-0.0491121 - 0.0283549i) q^{68} +(0.869244 + 4.78581i) q^{69} +(-1.95886 - 10.2632i) q^{70} +(-9.86443 + 8.27724i) q^{71} +(2.82947 + 0.997038i) q^{72} +(8.25330 + 3.00395i) q^{73} +(4.32688 + 5.15657i) q^{74} +(6.18825 - 17.2778i) q^{75} +(-2.73838 - 3.39135i) q^{76} +(6.71381 - 2.55109i) q^{77} +(-5.71033 + 2.11168i) q^{78} +(-0.766708 - 0.913727i) q^{79} +(1.35069 + 3.71100i) q^{80} +(1.38036 - 8.89352i) q^{81} +(1.51766 - 0.552382i) q^{82} +(7.35714 + 4.24765i) q^{83} +(2.21468 - 4.01188i) 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} +(10.1988 - 6.02886i) q^{90} +(1.74354 + 9.13510i) q^{91} +(-2.76563 + 0.487655i) q^{92} +(12.5478 + 10.4195i) q^{93} +(3.83995 + 2.21699i) q^{94} +(-17.2109 - 0.324613i) q^{95} +(-0.584026 + 1.63062i) q^{96} +(-3.03805 + 8.34698i) q^{97} +(-5.48671 - 4.34696i) q^{98} +(5.29856 + 6.18439i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q - 81 q^{8} + 15 q^{13} + 6 q^{14} + 27 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 - 57 q^{99}+O(q^{100}) $ 162 * q - 81 * q^8 + 15 * q^13 + 6 * q^14 + 27 * 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 - 63 * 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 + 6 * q^60 + 45 * q^61 + 36 * q^62 - 15 * 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 - 6 * q^78 - 42 * q^79 + 84 * q^81 - 3 * q^84 - 6 * q^85 - 9 * q^86 + 60 * q^87 + 54 * q^89 + 36 * q^90 - 18 * q^91 - 21 * q^93 - 72 * q^94 - 12 * q^97 - 27 * q^98 - 57 * q^99

Character values

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

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{18}\right)$	$-1$

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
$3$	0.600751	+	1.62453i	0.346844	+	0.937923i
$3$	0.600751	+	1.62453i	0.346844	+	0.937923i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−1.35069	+	3.71100i	−0.604048	+	1.65961i	0.138938	+	0.990301i	$0.455631\pi$
$5$	−1.35069	+	3.71100i	−0.604048	+	1.65961i	−0.742986	+	0.669307i	$0.766591\pi$
$6$	−1.49553	+	0.873721i	−0.610548	+	0.356695i
$7$	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
$9$	−2.27820	+	1.95188i	−0.759399	+	0.650625i
$10$	−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	0.631668	−	0.775239i	$-0.282371\pi$
$13$	3.46167	+	0.610385i	0.960094	+	0.169290i	0.328426	+	0.944530i	$0.393482\pi$
$14$	−2.27246	+	1.35496i	−0.607341	+	0.362128i
$15$	−6.84005	+	0.0351445i	−1.76609	+	0.00907426i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.0364524	+	0.0434422i	0.00884100	+	0.0105363i	0.770447	−	0.637504i	$-0.220033\pi$
$17$	0.0364524	+	0.0434422i	0.00884100	+	0.0105363i	−0.761606	+	0.648041i	$0.775589\pi$
$18$	−2.31783	−	1.90465i	−0.546317	−	0.448929i
$19$	1.41333	+	4.12341i	0.324239	+	0.945975i
$19$	1.41333	+	4.12341i	0.324239	+	0.945975i
$20$		−	3.94916i		−	0.883059i
$21$	−3.45326	+	3.01247i	−0.753563	+	0.657375i
$22$	2.67336	−	0.471385i	0.569962	−	0.100500i
$23$	2.76563	+	0.487655i	0.576674	+	0.101683i	0.454376	−	0.890810i	$-0.349862\pi$
$23$	2.76563	+	0.487655i	0.576674	+	0.101683i	0.122298	+	0.992493i	$0.460974\pi$
$24$	1.10651	−	1.33253i	0.225865	−	0.272002i
$25$	−8.11690	−	6.81089i	−1.62338	−	1.36218i
$26$			3.51507i			0.689362i
$27$	−4.53951	−	2.52841i	−0.873629	−	0.486592i
$28$	−1.72898	−	2.00265i	−0.326747	−	0.378466i
$29$	−0.757331	+	0.275646i	−0.140633	+	0.0511862i	−0.411378	−	0.911465i	$-0.634952\pi$
$29$	−0.757331	+	0.275646i	−0.140633	+	0.0511862i	0.270745	+	0.962651i	$0.412730\pi$
$30$	−1.22237	−	6.73004i	−0.223174	−	1.22873i
$31$	8.15495	−	4.70826i	1.46467	−	0.845629i	0.465450	−	0.885074i	$-0.345892\pi$
$31$	8.15495	−	4.70826i	1.46467	−	0.845629i	0.999222	+	0.0394454i	$0.0125591\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	4.40995	−	1.63080i	0.767673	−	0.283886i
$34$	−0.0364524	+	0.0434422i	−0.00625153	+	0.00745028i
$35$	−10.4475	+	0.146906i	−1.76594	+	0.0248317i
$36$	1.47322	−	2.61335i	0.245537	−	0.435559i
$37$	5.82959	−	3.36571i	0.958378	−	0.553320i	0.0627049	−	0.998032i	$-0.480027\pi$
$37$	5.82959	−	3.36571i	0.958378	−	0.553320i	0.895674	+	0.444712i	$0.146694\pi$
$38$	−3.81534	+	2.10788i	−0.618931	+	0.341943i
$39$	1.08801	+	5.99027i	0.174221	+	0.959211i
$40$	3.88916	−	0.685764i	0.614931	−	0.108429i
$41$	−0.280452	−	1.59052i	−0.0437992	−	0.248398i	0.955045	−	0.296461i	$-0.0958063\pi$
$41$	−0.280452	−	1.59052i	−0.0437992	−	0.248398i	−0.998844	+	0.0480629i	$0.984695\pi$
$42$	−3.56636	−	2.87769i	−0.550301	−	0.444037i
$43$	6.84678	−	5.74513i	1.04412	−	0.876125i	0.0516611	−	0.998665i	$-0.483548\pi$
$43$	6.84678	−	5.74513i	1.04412	−	0.876125i	0.992464	+	0.122540i	$0.0391040\pi$
$44$	0.928448	+	2.55089i	0.139969	+	0.384561i
$45$	−4.16626	−	11.0908i	−0.621070	−	1.65331i
$46$			2.80829i			0.414060i
$47$	2.85011	−	3.39663i	0.415732	−	0.495450i	−0.517018	−	0.855974i	$-0.672958\pi$
$47$	2.85011	−	3.39663i	0.415732	−	0.495450i	0.932750	+	0.360525i	$0.117402\pi$
$48$	1.50443	+	0.858307i	0.217146	+	0.123886i
$49$	−5.23368	+	4.64851i	−0.747668	+	0.664073i
$50$	5.29793	−	9.17628i	0.749240	−	1.29772i
$51$	−0.0486744	+	0.0853160i	−0.00681578	+	0.0119466i
$52$	−3.46167	+	0.610385i	−0.480047	+	0.0846452i
$53$	−8.67661	+	3.15803i	−1.19182	+	0.433788i	−0.860364	−	0.509681i	$-0.829763\pi$
$53$	−8.67661	+	3.15803i	−1.19182	+	0.433788i	−0.331460	+	0.943469i	$0.607541\pi$
$54$	1.70172	−	4.90960i	0.231574	−	0.668112i
$55$	10.0739	+	3.66659i	1.35836	+	0.494403i
$56$	1.67199	−	2.05047i	0.223429	−	0.274006i
$57$	−5.84955	+	4.77313i	−0.774792	+	0.632217i
$58$	−0.402967	−	0.697960i	−0.0529122	−	0.0916467i
$59$	−5.03918	+	4.22838i	−0.656046	+	0.550488i	−0.908899	−	0.417017i	$-0.863076\pi$
$59$	−5.03918	+	4.22838i	−0.656046	+	0.550488i	0.252853	+	0.967505i	$0.418631\pi$
$60$	6.41553	−	2.37246i	0.828241	−	0.306283i
$61$	−0.0164697	+	0.0934044i	−0.00210873	+	0.0119592i	−0.985844	−	0.167665i	$-0.946377\pi$
$61$	−0.0164697	+	0.0934044i	−0.00210873	+	0.0119592i	0.983735	+	0.179625i	$0.0574883\pi$
$62$	6.05282	+	7.21347i	0.768709	+	0.916112i
$63$	−6.96840	−	3.80018i	−0.877936	−	0.478778i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−6.94078	+	12.0218i	−0.860898	+	1.49112i
$66$	2.37180	+	4.05977i	0.291949	+	0.499723i
$67$	−11.8003	−	2.08072i	−1.44164	−	0.254200i	−0.602502	−	0.798117i	$-0.705830\pi$
$67$	−11.8003	−	2.08072i	−1.44164	−	0.254200i	−0.839139	+	0.543917i	$0.816941\pi$
$68$	−0.0491121	−	0.0283549i	−0.00595572	−	0.00343854i
$69$	0.869244	+	4.78581i	0.104645	+	0.576144i
$70$	−1.95886	−	10.2632i	−0.234128	−	1.22669i
$71$	−9.86443	+	8.27724i	−1.17069	+	0.982327i	−0.999996	−	0.00299625i	$-0.999046\pi$
$71$	−9.86443	+	8.27724i	−1.17069	+	0.982327i	−0.170697	+	0.985324i	$0.554602\pi$
$72$	2.82947	+	0.997038i	0.333457	+	0.117502i
$73$	8.25330	+	3.00395i	0.965975	+	0.351586i	0.776372	−	0.630275i	$-0.217058\pi$
$73$	8.25330	+	3.00395i	0.965975	+	0.351586i	0.189603	+	0.981861i	$0.439280\pi$
$74$	4.32688	+	5.15657i	0.502990	+	0.599440i
$75$	6.18825	−	17.2778i	0.714558	−	1.99507i
$76$	−2.73838	−	3.39135i	−0.314114	−	0.389015i
$77$	6.71381	−	2.55109i	0.765110	−	0.290724i
$78$	−5.71033	+	2.11168i	−0.646568	+	0.239101i
$79$	−0.766708	−	0.913727i	−0.0862614	−	0.102802i	0.721187	−	0.692740i	$-0.243597\pi$
$79$	−0.766708	−	0.913727i	−0.0862614	−	0.102802i	−0.807449	+	0.589938i	$0.799152\pi$
$80$	1.35069	+	3.71100i	0.151012	+	0.414902i
$81$	1.38036	−	8.89352i	0.153373	−	0.988168i
$82$	1.51766	−	0.552382i	0.167597	−	0.0610004i
$83$	7.35714	+	4.24765i	0.807551	+	0.466240i	0.846105	−	0.533017i	$-0.178942\pi$
$83$	7.35714	+	4.24765i	0.807551	+	0.466240i	−0.0385538	+	0.999257i	$0.512275\pi$
$84$	2.21468	−	4.01188i	0.241641	−	0.437732i
$85$	−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	$-0.708158\pi$
$89$	−5.32221	+	1.93713i	−0.564154	+	0.205335i	0.0441702	+	0.999024i	$0.485936\pi$
$90$	10.1988	−	6.02886i	1.07505	−	0.635497i
$91$	1.74354	+	9.13510i	0.182773	+	0.957618i
$92$	−2.76563	+	0.487655i	−0.288337	+	0.0508416i
$93$	12.5478	+	10.4195i	1.30115	+	1.08045i
$94$	3.83995	+	2.21699i	0.396060	+	0.228665i
$95$	−17.2109	−	0.324613i	−1.76580	−	0.0333046i
$96$	−0.584026	+	1.63062i	−0.0596069	+	0.166424i
$97$	−3.03805	+	8.34698i	−0.308467	+	0.847507i	0.684489	+	0.729024i	$0.260026\pi$
$97$	−3.03805	+	8.34698i	−0.308467	+	0.847507i	−0.992956	+	0.118484i	$0.962197\pi$
$98$	−5.48671	−	4.34696i	−0.554241	−	0.439109i
$99$	5.29856	+	6.18439i	0.532525	+	0.621555i
$100$	9.95685	+	3.62400i	0.995685	+	0.362400i
$101$	6.80491	−	8.10978i	0.677114	−	0.806953i	−0.312619	−	0.949879i	$-0.601206\pi$
$101$	6.80491	−	8.10978i	0.677114	−	0.806953i	0.989734	+	0.142925i	$0.0456508\pi$
$102$	−0.0924720	−	0.0331200i	−0.00915610	−	0.00327937i
$103$	−16.9721	−	9.79883i	−1.67231	−	0.965507i	−0.966342	−	0.257260i	$-0.917180\pi$
$103$	−16.9721	−	9.79883i	−1.67231	−	0.965507i	−0.705965	−	0.708247i	$-0.749486\pi$
$104$	−1.20222	−	3.30308i	−0.117888	−	0.323894i
$105$	−6.51498	−	16.8840i	−0.635796	−	1.64771i
$106$	−4.61673	−	7.99640i	−0.448416	−	0.776680i
$107$	14.0234			1.35570			0.677848	−	0.735202i	$-0.262913\pi$
$107$	14.0234			1.35570			0.677848	+	0.735202i	$0.262913\pi$
$108$	5.13051	+	0.823322i	0.493684	+	0.0792242i
$109$	14.6037	−	2.57502i	1.39878	−	0.246642i	0.577136	−	0.816648i	$-0.304170\pi$
$109$	14.6037	−	2.57502i	1.39878	−	0.246642i	0.821641	+	0.570006i	$0.193059\pi$
$110$	−1.86158	+	10.5575i	−0.177494	+	1.00662i
$111$	8.96984	+	7.44839i	0.851379	+	0.706970i
$112$	2.30966	+	1.29053i	0.218242	+	0.121944i
$113$	−8.08573			−0.760641			−0.380321	−	0.924855i	$-0.624186\pi$
$113$	−8.08573			−0.760641			−0.380321	+	0.924855i	$0.624186\pi$
$114$	−5.71638	−	4.93183i	−0.535388	−	0.461909i
$115$	−5.54520	+	9.60457i	−0.517093	+	0.895631i
$116$	0.617382	−	0.518045i	0.0573225	−	0.0480993i
$117$	−9.07775	+	5.36617i	−0.839239	+	0.496102i
$118$	−5.03918	−	4.22838i	−0.463894	−	0.389254i
$119$	−0.0731857	+	0.130980i	−0.00670892	+	0.0120070i
$120$	3.45046	+	5.90609i	0.314983	+	0.539150i
$121$	3.63095			0.330087
$122$	−0.0948453			−0.00858689
$123$	2.41537	−	1.41111i	0.217786	−	0.127235i
$124$	−6.05282	+	7.21347i	−0.543560	+	0.647789i
$125$	19.1382	−	11.0495i	1.71178	−	0.988294i
$126$	2.53240	−	7.52243i	0.225604	−	0.670151i
$127$	0.681510	+	0.120169i	0.0604742	+	0.0106632i	0.203803	−	0.979012i	$-0.434670\pi$
$127$	0.681510	+	0.120169i	0.0604742	+	0.0106632i	−0.143329	+	0.989675i	$0.545781\pi$
$128$	−0.939693	−	0.342020i	−0.0830579	−	0.0302306i
$129$	13.4464	+	7.67141i	1.18389	+	0.675430i
$130$	−13.0444	−	4.74777i	−1.14407	−	0.416407i
$131$	8.61472	−	1.51901i	0.752671	−	0.132716i	0.215867	−	0.976423i	$-0.430742\pi$
$131$	8.61472	−	1.51901i	0.752671	−	0.132716i	0.536805	+	0.843707i	$0.319631\pi$
$132$	−3.58623	+	3.04074i	−0.312141	+	0.264662i
$133$	−8.86992	+	7.37051i	−0.769120	+	0.639105i
$134$		−	11.9824i		−	1.03512i
$135$	15.5144	−	13.4310i	1.33527	−	1.15596i
$136$	0.0193959	−	0.0532898i	0.00166318	−	0.00456956i
$137$	−1.03767	−	2.85096i	−0.0886538	−	0.243574i	0.887440	−	0.460923i	$-0.152481\pi$
$137$	−1.03767	−	2.85096i	−0.0886538	−	0.243574i	−0.976094	+	0.217348i	$0.930259\pi$
$138$	−4.56216	+	1.68709i	−0.388357	+	0.143614i
$139$	−3.92412	+	22.2548i	−0.332839	+	1.88763i	0.114762	+	0.993393i	$0.463390\pi$
$139$	−3.92412	+	22.2548i	−0.332839	+	1.88763i	−0.447601	+	0.894233i	$0.647722\pi$
$140$	9.76716	−	3.71129i	0.825475	−	0.313661i
$141$	7.23014	+	2.58956i	0.608887	+	0.218081i
$142$	−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
$147$	−10.6958	−	5.70967i	−0.882173	−	0.470926i
$148$	−4.32688	+	5.15657i	−0.355667	+	0.423868i
$149$	1.80498	+	2.15109i	0.147869	+	0.176224i	0.834895	−	0.550409i	$-0.185528\pi$
$149$	1.80498	+	2.15109i	0.147869	+	0.176224i	−0.687025	+	0.726633i	$0.741084\pi$
$150$	18.0899	+	3.09398i	1.47703	+	0.252623i
$151$	7.97690	+	4.60546i	0.649151	+	0.374787i	0.788131	−	0.615508i	$-0.211049\pi$
$151$	7.97690	+	4.60546i	0.649151	+	0.374787i	−0.138980	+	0.990295i	$0.544382\pi$
$152$	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
$156$	−3.07119	−	5.25689i	−0.245892	−	0.420888i
$157$	−1.04174	−	5.90799i	−0.0831397	−	0.471509i	−0.997743	−	0.0671552i	$-0.978608\pi$
$157$	−1.04174	−	5.90799i	−0.0831397	−	0.471509i	0.914603	−	0.404353i	$-0.132503\pi$
$158$	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
$162$	8.99810	−	0.184955i	0.706957	−	0.0145314i
$163$	−8.47949	+	14.6869i	−0.664165	+	1.15037i	0.315346	+	0.948977i	$0.397879\pi$
$163$	−8.47949	+	14.6869i	−0.664165	+	1.15037i	−0.979511	+	0.201391i	$0.935454\pi$
$164$	0.807529	+	1.39868i	0.0630574	+	0.109219i
$165$	0.0954032	+	18.5680i	0.00742713	+	1.44552i
$166$	−2.90556	+	7.98296i	−0.225515	+	0.619598i
$167$	−5.17415	−	4.34163i	−0.400388	−	0.335965i	0.420256	−	0.907406i	$-0.361940\pi$
$167$	−5.17415	−	4.34163i	−0.400388	−	0.335965i	−0.820644	+	0.571440i	$0.806385\pi$
$168$	4.33551	+	1.48438i	0.334492	+	0.114522i
$169$	−0.605437	−	0.220361i	−0.0465721	−	0.0169509i
$170$	−0.111978	−	0.193952i	−0.00858832	−	0.0148754i
$171$	−11.2682	−	6.63530i	−0.861702	−	0.507414i
$172$	−4.46892	+	7.74040i	−0.340752	+	0.590200i
$173$	−4.12394	−	23.3880i	−0.313537	−	1.77816i	−0.580307	−	0.814398i	$-0.697067\pi$
$173$	−4.12394	−	23.3880i	−0.313537	−	1.77816i	0.266769	−	0.963760i	$-0.414044\pi$
$174$	0.891774	−	1.07393i	0.0676052	−	0.0814146i
$175$	9.21686	−	26.4756i	0.696729	−	2.00136i
$176$	−1.74491	−	2.07950i	−0.131528	−	0.156748i
$177$	−9.89642	−	5.64610i	−0.743861	−	0.424387i
$178$	−2.83189	−	4.90498i	−0.212259	−	0.367644i
$179$	11.8079			0.882563			0.441282	−	0.897369i	$-0.354524\pi$
$179$	11.8079			0.882563			0.441282	+	0.897369i	$0.354524\pi$
$180$	7.70827	+	8.99696i	0.574540	+	0.670594i
$181$	−2.12488	−	5.83807i	−0.157941	−	0.433940i	0.835330	−	0.549748i	$-0.185276\pi$
$181$	−2.12488	−	5.83807i	−0.157941	−	0.433940i	−0.993272	+	0.115808i	$0.963054\pi$
$182$	−8.69355	+	3.30334i	−0.644409	+	0.244860i
$183$	−0.161632	+	0.0293572i	−0.0119482	+	0.00217015i
$184$	−0.960493	−	2.63893i	−0.0708085	−	0.194545i
$185$	4.61617	+	26.1796i	0.339388	+	1.92476i
$186$	−8.08227	+	14.1665i	−0.592621	+	1.03874i
$187$	0.117928	−	0.0989536i	0.00862377	−	0.00723620i
$188$	−1.51651	+	4.16658i	−0.110603	+	0.303879i
$189$	1.98724	−	13.6033i	0.144550	−	0.989497i
$190$	−2.66896	−	17.0058i	−0.193627	−	1.23373i
$191$	−16.8166	+	9.70905i	−1.21680	+	0.702522i	−0.964233	−	0.265056i	$-0.914610\pi$
$191$	−16.8166	+	9.70905i	−1.21680	+	0.702522i	−0.252572	+	0.967578i	$0.581276\pi$
$192$	−1.70726	−	0.291999i	−0.123211	−	0.0210732i
$193$	−0.741872	+	2.03828i	−0.0534011	+	0.146718i	−0.963525	−	0.267617i	$-0.913764\pi$
$193$	−0.741872	+	2.03828i	−0.0534011	+	0.146718i	0.910124	+	0.414336i	$0.135986\pi$
$194$	−8.74772	−	1.54246i	−0.628050	−	0.110742i
$195$	−23.6994	−	4.05341i	−1.69715	−	0.290271i
$196$	3.32816	−	6.15819i	0.237726	−	0.439871i
$197$	8.27774	+	4.77915i	0.589764	+	0.340501i	0.765004	−	0.644025i	$-0.222737\pi$
$197$	8.27774	+	4.77915i	0.589764	+	0.340501i	−0.175240	+	0.984526i	$0.556070\pi$
$198$	−5.17035	+	6.29197i	−0.367441	+	0.447151i
$199$	−0.187794	+	1.06504i	−0.0133124	+	0.0754984i	−0.990740	−	0.135771i	$-0.956649\pi$
$199$	−0.187794	+	1.06504i	−0.0133124	+	0.0754984i	0.977428	+	0.211270i	$0.0677598\pi$
$200$	−1.83995	+	10.4349i	−0.130104	+	0.737858i
$201$	−3.70888	−	20.4200i	−0.261604	−	1.44032i
$202$	9.16824	+	5.29328i	0.645075	+	0.372434i
$203$	−1.39345	−	1.61401i	−0.0978009	−	0.113281i
$204$	0.0165592	−	0.0968184i	0.00115938	−	0.00677864i
$205$	6.28122	+	1.10755i	0.438699	+	0.0773545i
$206$	6.70279	−	18.4158i	0.467006	−	1.28309i
$207$	−7.25249	+	4.28719i	−0.504083	+	0.297981i
$208$	3.04414	−	1.75753i	0.211073	−	0.121863i
$209$	11.1934	−	3.83661i	0.774264	−	0.265384i
$210$	15.4961	−	9.34787i	1.06934	−	0.645064i
$211$	3.70231	−	10.1720i	0.254878	−	0.700271i	−0.744586	−	0.667527i	$-0.767353\pi$
$211$	3.70231	−	10.1720i	0.254878	−	0.700271i	0.999464	−	0.0327445i	$-0.0104247\pi$
$212$	7.07324	−	5.93515i	0.485792	−	0.407628i
$213$	−19.3727	−	11.0525i	−1.32739	−	0.757305i
$214$	2.43514	+	13.8104i	0.166463	+	0.944058i
$215$	12.0723	+	33.1683i	0.823322	+	2.26206i
$216$	0.0800903	+	5.19554i	0.00544945	+	0.353511i
$217$	19.3083	+	15.7443i	1.31074	+	1.06880i
$218$	5.07180	+	13.9347i	0.343506	+	0.943774i
$219$	0.0781617	+	15.2124i	0.00528168	+	1.02796i
$220$	−10.7204			−0.722768
$221$	0.0996695	+	0.172633i	0.00670449	+	0.0116125i
$222$	−5.77763	+	10.1270i	−0.387769	+	0.679677i
$223$	16.2821	+	19.4043i	1.09033	+	1.29941i	0.951010	+	0.309159i	$0.100048\pi$
$223$	16.2821	+	19.4043i	1.09033	+	1.29941i	0.139321	+	0.990247i	$0.455508\pi$
$224$	−0.869855	+	2.49867i	−0.0581196	+	0.166949i
$225$	31.7859	−	0.326643i	2.11906	−	0.0217762i
$226$	−1.40407	−	7.96289i	−0.0933975	−	0.529683i
$227$	−3.13145	+	5.42382i	−0.207841	+	0.359992i	−0.951034	−	0.309085i	$-0.899977\pi$
$227$	−3.13145	+	5.42382i	−0.207841	+	0.359992i	0.743193	+	0.669077i	$0.233310\pi$
$228$	3.86427	−	6.48594i	0.255917	−	0.429542i
$229$	0.439100	+	0.760544i	0.0290166	+	0.0502582i	0.880169	−	0.474660i	$-0.157429\pi$
$229$	0.439100	+	0.760544i	0.0290166	+	0.0502582i	−0.851152	+	0.524919i	$0.824096\pi$
$230$	−10.4216	−	3.79314i	−0.687178	−	0.250112i
$231$	8.17765	+	9.37422i	0.538050	+	0.616778i
$232$	0.617382	+	0.518045i	0.0405331	+	0.0340113i
$233$	7.83720	−	21.5325i	0.513432	−	1.41064i	−0.364206	−	0.931318i	$-0.618660\pi$
$233$	7.83720	−	21.5325i	0.513432	−	1.41064i	0.877638	−	0.479324i	$-0.159118\pi$
$234$	−6.86098	−	8.00802i	−0.448516	−	0.523500i
$235$	8.75526	+	15.1646i	0.571130	+	0.989226i
$236$	3.28909	−	5.69688i	0.214102	−	0.370835i
$237$	1.02378	−	1.79446i	0.0665014	−	0.116563i
$238$	−0.141699	−	0.0493293i	−0.00918499	−	0.00319754i
$239$	−7.76940	+	4.48567i	−0.502561	+	0.290154i	−0.729771	−	0.683692i	$-0.760373\pi$
$239$	−7.76940	+	4.48567i	−0.502561	+	0.290154i	0.227210	+	0.973846i	$0.427040\pi$
$240$	−5.21719	+	4.42362i	−0.336768	+	0.285544i
$241$	4.46593	−	5.32229i	0.287676	−	0.342839i	−0.602781	−	0.797907i	$-0.705941\pi$
$241$	4.46593	−	5.32229i	0.287676	−	0.342839i	0.890457	+	0.455068i	$0.150385\pi$
$242$	0.630508	+	3.57579i	0.0405306	+	0.229860i
$243$	15.2770	−	3.10035i	0.980022	−	0.198888i
$244$	−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
$249$	−2.48062	+	14.5037i	−0.157203	+	0.919133i
$250$	14.2049	+	16.9288i	0.898398	+	1.07067i
$251$	13.6987	−	16.3254i	0.864652	−	1.03045i	−0.134566	−	0.990905i	$-0.542964\pi$
$251$	13.6987	−	16.3254i	0.864652	−	1.03045i	0.999218	−	0.0395474i	$-0.0125916\pi$
$252$	7.84789	+	1.18767i	0.494371	+	0.0748162i
$253$	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	$-0.361883\pi$
$257$	−6.41442	−	5.38234i	−0.400121	−	0.335741i	−0.820540	+	0.571589i	$0.806327\pi$
$258$	−5.21993	+	14.5742i	−0.324979	+	0.907350i
$259$	13.8026	+	11.2549i	0.857653	+	0.699345i
$260$	2.41051	−	13.6707i	0.149493	−	0.847819i
$261$	1.18732	−	2.10619i	0.0734934	−	0.130370i
$262$	2.99186	+	8.22007i	0.184838	+	0.507838i
$263$	−8.92114	+	24.5106i	−0.550101	+	1.51139i	0.283471	+	0.958981i	$0.408514\pi$
$263$	−8.92114	+	24.5106i	−0.550101	+	1.51139i	−0.833573	+	0.552410i	$0.813708\pi$
$264$	−3.61729	−	3.00373i	−0.222629	−	0.184867i
$265$		−	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	$-0.311098\pi$
$269$	7.45831	+	2.71460i	0.454741	+	0.165512i	−0.104486	+	0.994526i	$0.533320\pi$
$270$	15.9210	+	12.9464i	0.968921	+	0.787894i
$271$	13.1680	+	4.79275i	0.799897	+	0.291139i	0.709444	−	0.704762i	$-0.248946\pi$
$271$	13.1680	+	4.79275i	0.799897	+	0.291139i	0.0904533	+	0.995901i	$0.471168\pi$
$272$	0.0558483	+	0.00984756i	0.00338630	+	0.000597096i
$273$	−13.7928	+	8.32035i	−0.834779	+	0.503571i
$274$	2.62746	−	1.51697i	0.158731	−	0.0916432i
$275$	−18.4888	+	22.0341i	−1.11492	+	1.32871i
$276$	−2.45367	−	4.19989i	−0.147693	−	0.252804i
$277$	−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
$279$	−9.38863	+	26.6438i	−0.562083	+	1.59512i
$280$	5.35095	+	8.97431i	0.319781	+	0.536318i
$281$	10.6359	+	8.92456i	0.634484	+	0.532395i	0.902319	−	0.431070i	$-0.141864\pi$
$281$	10.6359	+	8.92456i	0.634484	+	0.532395i	−0.267835	+	0.963465i	$0.586308\pi$
$282$	−1.29472	+	7.56997i	−0.0770996	+	0.450785i
$283$	5.21625	−	4.37695i	0.310074	−	0.260183i	−0.474449	−	0.880283i	$-0.657353\pi$
$283$	5.21625	−	4.37695i	0.310074	−	0.260183i	0.784523	+	0.620100i	$0.212908\pi$
$284$	6.43855	−	11.1519i	0.382058	−	0.661743i
$285$	−9.81214	−	28.1547i	−0.581221	−	1.66774i
$286$	9.54200			0.564230
$287$	3.67016	−	2.18834i	0.216642	−	0.129174i
$288$	−2.99984	+	0.0308274i	−0.176767	+	0.00181652i
$289$	2.95146	−	16.7386i	0.173615	−	0.984621i
$290$	3.13441	−	0.552681i	0.184059	−	0.0324546i
$291$	−15.3850	+	0.0790489i	−0.901886	+	0.00463393i
$292$	−8.78297			−0.513985
$293$	−12.8852	−	22.3179i	−0.752764	−	1.30383i	−0.946478	−	0.322768i	$-0.895387\pi$
$293$	−12.8852	−	22.3179i	−0.752764	−	1.30383i	0.193714	−	0.981058i	$-0.437947\pi$
$294$	3.76563	−	11.5248i	0.219616	−	0.672138i
$295$	−8.88510	−	24.4116i	−0.517311	−	1.42130i
$296$	−5.82959	−	3.36571i	−0.338838	−	0.195628i
$297$	−6.86361	+	12.3230i	−0.398267	+	0.715050i
$298$	−1.80498	+	2.15109i	−0.104559	+	0.124609i
$299$	9.27603	+	3.37620i	0.536447	+	0.195251i
$300$	0.0942950	+	18.3523i	0.00544412	+	1.05957i
$301$	20.6434	+	11.5345i	1.18986	+	0.664840i
$302$	−3.15032	+	8.65544i	−0.181281	+	0.498065i
$303$	17.2626	+	6.18283i	0.991713	+	0.355194i
$304$	3.73315	+	2.25025i	0.214111	+	0.129061i
$305$	−0.324378	−	0.187280i	−0.0185738	−	0.0107236i
$306$	−0.00174822	−	0.170120i	−9.99390e−5	−	0.00972514i
$307$	2.20450	−	0.388713i	0.125818	−	0.0221850i	−0.110385	−	0.993889i	$-0.535208\pi$
$307$	2.20450	−	0.388713i	0.125818	−	0.0221850i	0.236202	+	0.971704i	$0.424097\pi$
$308$	−5.43640	+	4.69350i	−0.309767	+	0.267437i
$309$	5.72250	−	33.4583i	0.325542	−	1.90338i
$310$	−34.9447	+	12.7188i	−1.98472	+	0.722380i
$311$	−17.6612	+	10.1967i	−1.00148	+	0.578203i	−0.908685	−	0.417483i	$-0.862912\pi$
$311$	−17.6612	+	10.1967i	−1.00148	+	0.578203i	−0.0927914	+	0.995686i	$0.529579\pi$
$312$	4.64372	−	3.93738i	0.262899	−	0.222910i
$313$	−16.0356	−	13.4555i	−0.906385	−	0.760547i	0.0650427	−	0.997882i	$-0.479282\pi$
$313$	−16.0356	−	13.4555i	−0.906385	−	0.760547i	−0.971428	+	0.237335i	$0.923726\pi$
$314$	5.63733	−	2.05182i	0.318133	−	0.115791i
$315$	23.5146	−	20.7268i	1.32490	−	1.16782i
$316$	1.03298	+	0.596393i	0.0581098	+	0.0335497i
$317$	26.6961	−	9.71659i	1.49940	−	0.545738i	0.543497	−	0.839411i	$-0.317100\pi$
$317$	26.6961	−	9.71659i	1.49940	−	0.545738i	0.955906	+	0.293673i	$0.0948776\pi$
$318$	10.2169	−	12.3039i	0.572935	−	0.689966i
$319$	0.748268	+	2.05585i	0.0418950	+	0.115106i
$320$	−2.53847	−	3.02523i	−0.141905	−	0.169116i
$321$	8.42459	+	22.7815i	0.470215	+	1.27154i
$322$	−6.94554	+	2.63914i	−0.387060	+	0.147074i
$323$	−0.127611	+	0.211706i	−0.00710047	+	0.0117796i
$324$	1.74465	+	8.82928i	0.0969249	+	0.490516i
$325$	−23.9407	−	28.5314i	−1.32799	−	1.58264i
$326$	−15.9362	−	5.80031i	−0.882626	−	0.321250i
$327$	12.9564	+	22.1771i	0.716488	+	1.22640i
$328$	−1.23721	+	1.03814i	−0.0683132	+	0.0573216i
$329$	11.0791	+	3.85692i	0.610809	+	0.212639i
$330$	−18.2693	+	3.31825i	−1.00569	+	0.182664i
$331$	−22.1601	−	12.7942i	−1.21803	−	0.703230i	−0.253534	−	0.967326i	$-0.581593\pi$
$331$	−22.1601	−	12.7942i	−1.21803	−	0.703230i	−0.964496	+	0.264096i	$0.914926\pi$
$332$	−8.36623	−	1.47519i	−0.459156	−	0.0809617i
$333$	−6.71149	+	19.0464i	−0.367787	+	1.04374i
$334$	3.37719	−	5.84946i	0.184791	−	0.320068i
$335$	23.6602	−	40.9806i	1.29269	−	2.23901i
$336$	−0.708973	+	4.52740i	−0.0386776	+	0.246990i
$337$	−13.6435	−	16.2597i	−0.743211	−	0.885724i	0.253453	−	0.967348i	$-0.418434\pi$
$337$	−13.6435	−	16.2597i	−0.743211	−	0.885724i	−0.996663	+	0.0816240i	$0.973989\pi$
$338$	0.111880	−	0.634505i	0.00608549	−	0.0345125i
$339$	−4.85751	−	13.1355i	−0.263824	−	0.713423i
$340$	0.171560	−	0.143956i	0.00930417	−	0.00780712i
$341$	−12.7810	−	22.1374i	−0.692132	−	1.19881i
$342$	4.57779	−	12.2492i	0.247539	−	0.662363i
$343$	−16.4152	−	8.57554i	−0.886340	−	0.463036i
$344$	−8.39882	−	3.05692i	−0.452834	−	0.164818i
$345$	−18.9342	−	3.23839i	−1.01938	−	0.174349i
$346$	22.3166	−	8.12257i	1.19975	−	0.436672i
$347$	8.74957	−	1.54278i	0.469701	−	0.0828210i	0.0662124	−	0.997806i	$-0.478909\pi$
$347$	8.74957	−	1.54278i	0.469701	−	0.0828210i	0.403489	+	0.914985i	$0.367797\pi$
$348$	1.21247	+	0.691740i	0.0649953	+	0.0370811i
$349$	−2.20752	+	3.82353i	−0.118166	+	0.204669i	−0.919041	−	0.394162i	$-0.871035\pi$
$349$	−2.20752	+	3.82353i	−0.118166	+	0.204669i	0.800875	+	0.598831i	$0.204368\pi$
$350$	27.6738	+	4.47940i	1.47923	+	0.239434i
$351$	−14.1710	−	11.5234i	−0.756390	−	0.615071i
$352$	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	$0.974362\pi$
$354$	3.84183	−	10.7265i	0.204191	−	0.570107i
$355$	−17.3930	−	47.7868i	−0.923124	−	2.53626i
$356$	4.33871	−	3.64061i	0.229951	−	0.192952i
$357$	−0.256748	−	0.0402057i	−0.0135886	−	0.00212791i
$358$	2.05042	+	11.6285i	0.108368	+	0.614585i
$359$	9.27371	−	1.63521i	0.489448	−	0.0863028i	0.0765227	−	0.997068i	$-0.475618\pi$
$359$	9.27371	−	1.63521i	0.489448	−	0.0863028i	0.412925	+	0.910765i	$0.364507\pi$
$360$	−7.52175	+	9.15347i	−0.396431	+	0.482430i
$361$	−15.0050	+	11.6554i	−0.789738	+	0.613444i
$362$	5.38039	−	3.10637i	0.282787	−	0.163267i
$363$	2.18130	+	5.89859i	0.114488	+	0.309596i
$364$	−4.76278	−	7.98786i	−0.249637	−	0.418678i
$365$	−22.2953	+	26.5705i	−1.16699	+	1.39076i
$366$	−0.0569784	−	0.154079i	−0.00297831	−	0.00805384i
$367$	−17.9555	−	15.0664i	−0.937268	−	0.786461i	0.0398401	−	0.999206i	$-0.487315\pi$
$367$	−17.9555	−	15.0664i	−0.937268	−	0.786461i	−0.977108	+	0.212745i	$0.931760\pi$
$368$	2.43205	−	1.40415i	0.126780	−	0.0731962i
$369$	3.74342	+	3.07611i	0.194875	+	0.160136i
$370$	−24.9803	+	9.09209i	−1.29866	+	0.472675i
$371$	−15.9645	−	18.4914i	−0.828835	−	0.960025i
$372$	−15.3547	−	5.49949i	−0.796107	−	0.285135i
$373$			9.69793i			0.502140i	0.967969	+	0.251070i	$0.0807824\pi$
$373$			9.69793i			0.502140i	−0.967969	+	0.251070i	$0.919218\pi$
$374$	0.117928	+	0.0989536i	0.00609793	+	0.00511677i
$375$	29.4475	+	24.4527i	1.52066	+	1.26273i
$376$	−4.36662	−	0.769954i	−0.225191	−	0.0397073i
$377$	−2.78988	+	0.491931i	−0.143686	+	0.0253357i
$378$	13.7418	−	0.405149i	0.706800	−	0.0208386i
$379$		−	3.05210i		−	0.156776i	−0.996923	−	0.0783880i	$-0.975023\pi$
$379$		−	3.05210i		−	0.156776i	0.996923	−	0.0783880i	$-0.0249773\pi$
$380$	16.2840	−	5.58145i	0.835352	−	0.286322i
$381$	0.214200	+	1.17933i	0.0109738	+	0.0604187i
$382$	−12.4817	−	14.8751i	−0.638620	−	0.761078i
$383$	18.0806	−	15.1715i	0.923877	−	0.775225i	−0.0508306	−	0.998707i	$-0.516187\pi$
$383$	18.0806	−	15.1715i	0.923877	−	0.775225i	0.974708	+	0.223482i	$0.0717424\pi$
$384$	−0.00889923	−	1.73203i	−0.000454137	−	0.0883872i
$385$	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	$-0.285459\pi$
$389$	18.6061	+	3.28075i	0.943366	+	0.166341i	0.319248	+	0.947671i	$0.396570\pi$
$390$	−0.123535	−	24.0433i	−0.00625545	−	1.21748i
$391$	0.0796289	+	0.137921i	0.00402701	+	0.00697498i
$392$	6.64256	+	2.20824i	0.335500	+	0.111533i
$393$	7.64297	+	13.0823i	0.385537	+	0.659916i
$394$	−3.26913	+	8.98187i	−0.164697	+	0.452500i
$395$	4.42642	−	1.61109i	0.222718	−	0.0810625i
$396$	−7.09421	−	3.99921i	−0.356497	−	0.200968i
$397$	2.22604	+	12.6245i	0.111722	+	0.633605i	0.988321	+	0.152384i	$0.0486951\pi$
$397$	2.22604	+	12.6245i	0.111722	+	0.633605i	−0.876600	+	0.481220i	$0.840194\pi$
$398$	−1.08147			−0.0542090
$399$	−17.3022	−	9.98161i	−0.866195	−	0.499706i
$400$	−10.5959			−0.529793
$401$	4.38468	+	24.8667i	0.218960	+	1.24179i	0.873900	+	0.486105i	$0.161583\pi$
$401$	4.38468	+	24.8667i	0.218960	+	1.24179i	−0.654940	+	0.755681i	$0.727306\pi$
$402$	19.4657	−	7.19843i	0.970863	−	0.359025i
$403$	31.1036	−	11.3208i	1.54938	−	0.563928i
$404$	−3.62082	+	9.94812i	−0.180142	+	0.494937i
$405$	31.1394	+	17.1349i	1.54733	+	0.851440i
$406$	1.34752	−	1.65255i	0.0668761	−	0.0820146i
$407$	−9.13657	−	15.8250i	−0.452883	−	0.784416i
$408$	0.0982230		0.000504674i	0.00486276		2.49851e-5i
$409$	19.9392	+	3.51581i	0.985929	+	0.173846i	0.643291	−	0.765622i	$-0.277569\pi$
$409$	19.9392	+	3.51581i	0.985929	+	0.173846i	0.342638	+	0.939468i	$0.388680\pi$
$410$			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
$414$	−5.48144	−	6.39785i	−0.269398	−	0.314437i
$415$	−25.7002	+	21.5650i	−1.26157	+	1.05859i
$416$	2.25944	+	2.69270i	0.110778	+	0.132020i
$417$	−38.5110	+	6.99473i	−1.88589	+	0.342534i
$418$	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	$0.859435\pi$
$420$	11.8967	+	13.6375i	0.580501	+	0.665441i
$421$	4.69881	−	0.828527i	0.229006	−	0.0403799i	−0.0579675	−	0.998318i	$-0.518462\pi$
$421$	4.69881	−	0.828527i	0.229006	−	0.0403799i	0.286973	+	0.957939i	$0.407351\pi$
$422$	10.6604	+	1.87971i	0.518940	+	0.0915031i
$423$	0.136688	+	13.3013i	0.00664602	+	0.646729i
$424$	7.07324	+	5.93515i	0.343507	+	0.288236i
$425$		−	0.600889i		−	0.0291474i
$426$	7.52056	−	20.9976i	0.364372	−	1.01734i
$427$	−0.246488	+	0.0470451i	−0.0119284	+	0.00227667i
$428$	−13.1777	+	4.79629i	−0.636969	+	0.231838i
$429$	16.2612	−	2.95351i	0.785097	−	0.142597i
$430$	−30.5681	+	17.6485i	−1.47412	+	0.851085i
$431$	−28.2998	−	23.7464i	−1.36315	−	1.14382i	−0.974994	−	0.222229i	$-0.928667\pi$
$431$	−28.2998	−	23.7464i	−1.36315	−	1.14382i	−0.388159	−	0.921592i	$-0.626889\pi$
$432$	−5.10270	+	0.981069i	−0.245504	+	0.0472017i
$433$	4.88546	−	5.82226i	0.234780	−	0.279800i	−0.635771	−	0.771877i	$-0.719318\pi$
$433$	4.88546	−	5.82226i	0.234780	−	0.279800i	0.870551	+	0.492077i	$0.163762\pi$
$434$	−12.1523	+	21.7490i	−0.583329	+	1.04398i
$435$	5.17050	−	1.91205i	0.247906	−	0.0916757i
$436$	−12.8422	+	7.41447i	−0.615032	+	0.355089i
$437$	1.89793	+	12.0930i	0.0907904	+	0.578489i
$438$	−14.9677	+	2.71857i	−0.715183	+	0.129898i
$439$	16.4817	−	2.90616i	0.786626	−	0.138703i	0.234115	−	0.972209i	$-0.424781\pi$
$439$	16.4817	−	2.90616i	0.786626	−	0.138703i	0.552511	+	0.833505i	$0.313670\pi$
$440$	−1.86158	−	10.5575i	−0.0887471	−	0.503310i
$441$	2.85003	−	20.8057i	0.135716	−	0.990748i
$442$	−0.152702	+	0.128133i	−0.00726332	+	0.00609465i
$443$	−10.2544	−	28.1736i	−0.487199	−	1.33857i	−0.903206	−	0.429208i	$-0.858793\pi$
$443$	−10.2544	−	28.1736i	−0.487199	−	1.33857i	0.416006	−	0.909362i	$-0.363429\pi$
$444$	−10.9764	−	3.93133i	−0.520916	−	0.186573i
$445$		−	22.3672i		−	1.06031i
$446$	−16.2821	+	19.4043i	−0.770981	+	0.918819i
$447$	−2.41016	+	4.22451i	−0.113997	+	0.199812i
$448$	−2.61176	−	0.422750i	−0.123394	−	0.0199731i
$449$	10.9552	−	18.9750i	0.517008	−	0.895484i	−0.482797	−	0.875732i	$-0.660379\pi$
$449$	10.9552	−	18.9750i	0.517008	−	0.895484i	0.999805	−	0.0197518i	$-0.00628761\pi$
$450$	5.84124	+	31.2463i	0.275359	+	1.47296i
$451$	−4.31763	+	0.761314i	−0.203309	+	0.0358489i
$452$	7.59810	−	2.76548i	0.357385	−	0.130077i
$453$	−2.68959	+	15.7254i	−0.126368	+	0.738846i
$454$	−5.88519	−	2.14203i	−0.276206	−	0.100531i
$455$	−36.2553	−	5.86843i	−1.69967	−	0.275116i
$456$	7.05843	+	2.67929i	0.330541	+	0.125469i
$457$	4.68200	+	8.10945i	0.219015	+	0.379344i	0.954507	−	0.298189i	$-0.0963825\pi$
$457$	4.68200	+	8.10945i	0.219015	+	0.379344i	−0.735492	+	0.677533i	$0.763049\pi$
$458$	−0.672741	+	0.564497i	−0.0314351	+	0.0263772i
$459$	−0.0556362	−	0.289373i	−0.00259688	−	0.0135068i
$460$	1.92583	−	10.9219i	0.0897922	−	0.509237i
$461$	−9.39299	−	11.1941i	−0.437475	−	0.521363i	0.501588	−	0.865106i	$-0.332749\pi$
$461$	−9.39299	−	11.1941i	−0.437475	−	0.521363i	−0.939063	+	0.343744i	$0.888305\pi$
$462$	−7.81177	+	9.68123i	−0.363436	+	0.450412i
$463$	−15.3184	+	26.5322i	−0.711906	+	1.23306i	0.252234	+	0.967666i	$0.418835\pi$
$463$	−15.3184	+	26.5322i	−0.711906	+	1.23306i	−0.964141	+	0.265392i	$0.914499\pi$
$464$	−0.402967	+	0.697960i	−0.0187073	+	0.0324020i
$465$	−55.6148	+	32.4914i	−2.57908	+	1.50675i
$466$	22.5663	+	3.97905i	1.04536	+	0.184326i
$467$	29.2046	+	16.8613i	1.35143	+	0.780246i	0.988449	−	0.151552i	$-0.0484273\pi$
$467$	29.2046	+	16.8613i	1.35143	+	0.780246i	0.362976	+	0.931798i	$0.381761\pi$
$468$	6.69496	−	8.14732i	0.309475	−	0.376610i
$469$	−5.94349	−	31.1403i	−0.274445	−	1.43793i
$470$	−13.4138	+	11.2555i	−0.618734	+	0.519180i
$471$	8.97188	−	5.24156i	0.413402	−	0.241518i
$472$	6.18147	+	2.24987i	0.284525	+	0.103559i
$473$	−15.5957	−	18.5863i	−0.717093	−	0.854598i
$474$	1.94498	+	0.696618i	0.0893358	+	0.0319967i
$475$	16.6123	−	43.0953i	0.762223	−	1.97735i
$476$	0.0239741	−	0.148112i	0.00109885	−	0.00678872i
$477$	13.6029	−	24.1303i	0.622836	−	1.10485i
$478$	−5.76666	−	6.87244i	−0.263761	−	0.314338i
$479$	−8.38294	−	23.0319i	−0.383026	−	1.05236i	−0.970075	−	0.242805i	$-0.921933\pi$
$479$	−8.38294	−	23.0319i	−0.383026	−	1.05236i	0.587049	−	0.809552i	$-0.300290\pi$
$480$	−5.26238	−	4.36978i	−0.240193	−	0.199452i
$481$	22.2345	−	8.09269i	1.01380	−	0.368995i
$482$	6.01693	+	3.47388i	0.274064	+	0.158231i
$483$	−11.0195	+	6.64738i	−0.501404	+	0.302466i
$484$	−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	−0.655330	−	0.755343i	$-0.727470\pi$
$487$	−7.25707	+	4.18987i	−0.328849	+	0.189861i	0.326481	+	0.945204i	$0.394137\pi$
$488$	0.0891255	−	0.0324390i	0.00403452	−	0.00146845i
$489$	−28.9534	−	4.95201i	−1.30932	−	0.223938i
$490$	23.5424	−	14.4897i	1.06354	−	0.654579i
$491$	−29.6456	+	5.22731i	−1.33789	+	0.235905i	−0.796382	−	0.604794i	$-0.793256\pi$
$491$	−29.6456	+	5.22731i	−1.33789	+	0.235905i	−0.541503	+	0.840699i	$0.682144\pi$
$492$	−1.78707	+	2.15211i	−0.0805676	+	0.0970247i
$493$	−0.0395812	−	0.0228522i	−0.00178265	−	0.00102921i
$494$	−14.4941	+	4.96794i	−0.652119	+	0.223518i
$495$	−30.1070	+	11.3097i	−1.35321	+	0.508335i
$496$	3.22064	−	8.84864i	0.144611	−	0.397316i
$497$	−29.7417	−	16.6183i	−1.33410	−	0.745431i
$498$	−14.7141	+	0.0756016i	−0.659354	+	0.00338779i
$499$	−2.29126	−	0.833949i	−0.102571	−	0.0373327i	0.290225	−	0.956958i	$-0.406270\pi$
$499$	−2.29126	−	0.833949i	−0.102571	−	0.0373327i	−0.392796	+	0.919626i	$0.628492\pi$
$500$	−14.2049	+	16.9288i	−0.635263	+	0.757077i
$501$	3.94473	−	11.0138i	0.176238	−	0.492060i
$502$	18.4562	+	10.6557i	0.823739	+	0.475586i
$503$	11.4196	+	31.3751i	0.509174	+	1.39894i	0.882091	+	0.471080i	$0.156136\pi$
$503$	11.4196	+	31.3751i	0.509174	+	1.39894i	−0.372916	+	0.927865i	$0.621642\pi$
$504$	0.193146	+	7.93490i	0.00860340	+	0.353449i
$505$	20.9040	+	36.2068i	0.930217	+	1.61118i
$506$	7.62339			0.338901
$507$	−0.00573371	−	1.11593i	−0.000254643	−	0.0495604i
$508$	−0.681510	+	0.120169i	−0.0302371	+	0.00533162i
$509$	3.03273	−	17.1995i	0.134423	−	0.762353i	−0.840836	−	0.541290i	$-0.817936\pi$
$509$	3.03273	−	17.1995i	0.134423	−	0.762353i	0.975260	−	0.221063i	$-0.0709526\pi$
$510$	0.247809	−	0.298428i	0.0109732	−	0.0132146i
$511$	0.326721	+	23.2353i	0.0144533	+	1.02787i
$512$	1.00000			0.0441942
$513$	4.00986	−	22.2917i	0.177039	−	0.984204i
$514$	4.18672	−	7.25161i	0.184668	−	0.319855i
$515$	59.2874	−	49.7481i	2.61252	−	2.19216i
$516$	−15.2592	−	2.60984i	−0.671750	−	0.114892i
$517$	−9.22049	−	7.73691i	−0.405517	−	0.340269i
$518$	−8.68711	+	15.5473i	−0.381690	+	0.683110i
$519$	35.5171	−	20.7498i	1.55903	−	0.910817i
$520$	13.8816			0.608747
$521$	22.5063			0.986019			0.493010	−	0.870024i	$-0.335897\pi$
$521$	22.5063			0.986019			0.493010	+	0.870024i	$0.335897\pi$
$522$	2.28037	+	0.803548i	0.0998091	+	0.0351703i
$523$	−9.38051	+	11.1793i	−0.410181	+	0.488835i	−0.931096	−	0.364774i	$-0.881146\pi$
$523$	−9.38051	+	11.1793i	−0.410181	+	0.488835i	0.520915	+	0.853608i	$0.325591\pi$
$524$	−7.57566	+	4.37381i	−0.330944	+	0.191071i
$525$	48.5474	−	0.932151i	2.11878	−	0.0406824i
$526$	−25.6874	−	4.52938i	−1.12002	−	0.197490i
$527$	0.501805	+	0.182642i	0.0218590	+	0.00795601i
$528$	2.32996	−	4.08392i	0.101398	−	0.177730i
$529$	−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
$534$	6.26703	−	7.54716i	0.271201	−	0.326598i
$535$	−18.9413	+	52.0409i	−0.818905	+	2.24992i
$536$	4.09822	+	11.2598i	0.177016	+	0.486348i
$537$	7.09360	+	19.1823i	0.306112	+	0.827776i
$538$	−1.37824	+	7.81639i	−0.0594202	+	0.336989i
$539$	12.6188	+	14.2073i	0.543532	+	0.611953i
$540$	−9.98508	+	17.9272i	−0.429690	+	0.771466i
$541$	−20.0819	−	16.8507i	−0.863387	−	0.724468i	0.0993077	−	0.995057i	$-0.468337\pi$
$541$	−20.0819	−	16.8507i	−0.863387	−	0.724468i	−0.962695	+	0.270589i	$0.912782\pi$
$542$	−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
$546$	−10.5890	−	12.1385i	−0.453169	−	0.519478i
$547$	−16.5263	+	19.6952i	−0.706611	+	0.842107i	−0.993257	−	0.115930i	$-0.963015\pi$
$547$	−16.5263	+	19.6952i	−0.706611	+	0.842107i	0.286646	+	0.958037i	$0.407460\pi$
$548$	1.95017	+	2.32413i	0.0833073	+	0.0992818i
$549$	−0.144793	−	0.244940i	−0.00617960	−	0.0104538i
$550$	−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
$555$	−39.7564	+	23.2265i	−1.68757	+	0.985912i
$556$	−3.92412	−	22.2548i	−0.166420	−	0.943813i
$557$	25.9253	−	30.8965i	1.09849	−	1.30913i	0.151286	−	0.988490i	$-0.451658\pi$
$557$	25.9253	−	30.8965i	1.09849	−	1.30913i	0.947202	−	0.320637i	$-0.103897\pi$
$558$	−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
$561$	0.231599	+	0.132132i	0.00977810	+	0.00557860i
$562$	−6.94208	+	12.0240i	−0.292834	+	0.507203i
$563$	16.3900	+	28.3883i	0.690757	+	1.19643i	0.971590	+	0.236670i	$0.0760559\pi$
$563$	16.3900	+	28.3883i	0.690757	+	1.19643i	−0.280833	+	0.959757i	$0.590611\pi$
$564$	−7.67979	+	0.0394591i	−0.323377	+	0.00166153i
$565$	10.9213	−	30.0061i	0.459464	−	1.26237i
$566$	5.21625	+	4.37695i	0.219255	+	0.183977i
$567$	23.2929	−	4.94389i	0.978209	−	0.207624i
$568$	12.1005	+	4.40423i	0.507726	+	0.184797i
$569$	13.9452	+	24.1538i	0.584614	+	1.01258i	0.994923	+	0.100635i	$0.0320873\pi$
$569$	13.9452	+	24.1538i	0.584614	+	1.01258i	−0.410310	+	0.911946i	$0.634579\pi$
$570$	26.0231	−	14.5521i	1.08999	−	0.609519i
$571$	8.02580	−	13.9011i	0.335869	−	0.581743i	−0.647782	−	0.761826i	$-0.724303\pi$
$571$	8.02580	−	13.9011i	0.335869	−	0.581743i	0.983651	+	0.180083i	$0.0576366\pi$
$572$	1.65695	+	9.39704i	0.0692806	+	0.392910i
$573$	−25.8752	−	21.4863i	−1.08095	−	0.897603i
$574$	2.79241	+	3.23440i	0.116553	+	0.135001i
$575$	−19.1270	−	22.7946i	−0.797650	−	0.950602i
$576$	−0.551276	−	2.94891i	−0.0229698	−	0.122871i
$577$	15.3186	+	26.5326i	0.637722	+	1.10457i	0.985931	+	0.167150i	$0.0534565\pi$
$577$	15.3186	+	26.5326i	0.637722	+	1.10457i	−0.348209	+	0.937417i	$0.613210\pi$
$578$	16.9968			0.706973
$579$	−3.75692	+	0.0193032i	−0.156132	+	0.000802215i
$580$	1.08857	+	2.99082i	0.0452004	+	0.124187i
$581$	−3.59139	+	22.1876i	−0.148996	+	0.920499i
$582$	−2.74943	−	15.1376i	−0.113968	−	0.627472i
$583$	8.57278	+	23.5535i	0.355048	+	0.975487i
$584$	−1.52515	−	8.64954i	−0.0631110	−	0.357921i
$585$	−7.65258	−	40.9355i	−0.316395	−	1.69248i
$586$	19.7413	−	16.5650i	0.815507	−	0.684292i
$587$	7.83194	−	21.5181i	0.323259	−	0.888147i	−0.666514	−	0.745493i	$-0.732214\pi$
$587$	7.83194	−	21.5181i	0.323259	−	0.888147i	0.989773	−	0.142654i	$-0.0455635\pi$
$588$	12.0036	+	1.70716i	0.495019	+	0.0704022i
$589$	30.9397	+	26.9719i	1.27485	+	1.11136i
$590$	22.4979	−	12.9892i	0.926223	−	0.534755i
$591$	−2.79102	+	16.3185i	−0.114807	+	0.671254i
$592$	2.30228	−	6.32547i	0.0946233	−	0.259975i
$593$	−10.9378	−	1.92862i	−0.449160	−	0.0791991i	−0.0555076	−	0.998458i	$-0.517678\pi$
$593$	−10.9378	−	1.92862i	−0.449160	−	0.0791991i	−0.393653	+	0.919259i	$0.628789\pi$
$594$	−13.3276	−	4.61948i	−0.546838	−	0.189540i
$595$	−0.387217	−	0.448506i	−0.0158743	−	0.0183870i
$596$	−2.43184	−	1.40402i	−0.0996120	−	0.0575110i
$597$	−1.84300	+	0.334743i	−0.0754290	+	0.0137001i
$598$	−1.71414	+	9.72138i	−0.0700965	+	0.397537i
$599$	−4.03693	+	22.8945i	−0.164944	+	0.935446i	0.784178	+	0.620537i	$0.213085\pi$
$599$	−4.03693	+	22.8945i	−0.164944	+	0.935446i	−0.949122	+	0.314909i	$0.898026\pi$
$600$	−18.0571	+	3.27971i	−0.737179	+	0.133894i
$601$	3.06815	+	1.77140i	0.125152	+	0.0722568i	0.561269	−	0.827633i	$-0.310313\pi$
$601$	3.06815	+	1.77140i	0.125152	+	0.0722568i	−0.436117	+	0.899890i	$0.643647\pi$
$602$	−7.77462	+	22.3327i	−0.316870	+	0.910214i
$603$	30.9448	−	18.2925i	1.26017	−	0.744929i
$604$	−9.07099	−	1.59946i	−0.369093	−	0.0650811i
$605$	−4.90430	+	13.4744i	−0.199388	+	0.547814i
$606$	−3.09127	+	18.0740i	−0.125574	+	0.734207i
$607$	−6.19835	+	3.57862i	−0.251583	+	0.145252i	−0.620489	−	0.784215i	$-0.713066\pi$
$607$	−6.19835	+	3.57862i	−0.251583	+	0.145252i	0.368906	+	0.929467i	$0.379733\pi$
$608$	−1.56781	+	4.06718i	−0.0635830	+	0.164946i
$609$	1.78489	−	3.23332i	0.0723273	−	0.131021i
$610$	0.128107	−	0.351971i	0.00518689	−	0.0142509i
$611$	11.9394	−	10.0183i	0.483016	−	0.405299i
$612$	0.167232	−	0.0312628i	0.00675997	−	0.00126372i
$613$	−7.29444	−	41.3688i	−0.294620	−	1.67087i	−0.668745	−	0.743492i	$-0.733168\pi$
$613$	−7.29444	−	41.3688i	−0.294620	−	1.67087i	0.374125	−	0.927378i	$-0.377943\pi$
$614$	0.765616	+	2.10351i	0.0308977	+	0.0848909i
$615$	1.97420	+	10.8694i	0.0796075	+	0.438296i
$616$	−5.56622	−	4.53879i	−0.224269	−	0.182873i
$617$	1.55915	+	4.28372i	0.0627689	+	0.172456i	0.967112	−	0.254349i	$-0.0818612\pi$
$617$	1.55915	+	4.28372i	0.0627689	+	0.172456i	−0.904344	+	0.426805i	$0.859639\pi$
$618$	33.9437	−	0.174404i	1.36542	−	0.00701556i
$619$	−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
$621$	−11.3216	−	9.20636i	−0.454321	−	0.369438i
$622$	−13.1086	−	15.6223i	−0.525609	−	0.626396i
$623$	−9.79259	−	11.3426i	−0.392332	−	0.454431i
$624$	4.68394	+	3.88945i	0.187508	+	0.155703i
$625$	5.95490	+	33.7719i	0.238196	+	1.35088i
$626$	10.4665	−	18.1285i	0.418325	−	0.724560i
$627$	12.9571	+	15.8792i	0.517458	+	0.634153i
$628$	2.99956	+	5.19539i	0.119696	+	0.207319i
$629$	0.358717	+	0.130562i	0.0143030	+	0.00520585i
$630$	24.4952	+	19.5582i	0.975913	+	0.779218i
$631$	13.1486	+	11.0330i	0.523438	+	0.439217i	0.865828	−	0.500341i	$-0.166792\pi$
$631$	13.1486	+	11.0330i	0.523438	+	0.439217i	−0.342390	+	0.939558i	$0.611236\pi$
$632$	−0.407957	+	1.12085i	−0.0162277	+	0.0445851i
$633$	18.7489	−	0.0963328i	0.745203	−	0.00382888i
$634$	14.2047	+	24.6033i	0.564141	+	0.977121i
$635$	−1.36646	+	2.36677i	−0.0542261	+	0.0939224i
$636$	13.8911	+	7.92514i	0.550817	+	0.314252i
$637$	−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	−0.991338	−	0.131334i	$-0.958074\pi$
$641$	−2.65089	−	15.0339i	−0.104704	−	0.593805i	0.886634	−	0.462471i	$-0.153037\pi$
$642$	−20.9725	+	12.2526i	−0.827717	+	0.483570i
$643$	−0.713294	−	4.04529i	−0.0281296	−	0.159531i	0.967507	−	0.252843i	$-0.0813656\pi$
$643$	−0.713294	−	4.04529i	−0.0281296	−	0.159531i	−0.995637	+	0.0933123i	$0.970255\pi$
$644$	−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	$-0.214378\pi$
$647$	16.0839	+	9.28605i	0.632324	+	0.365072i	−0.149328	+	0.988788i	$0.547711\pi$
$648$	−8.39219	+	3.25133i	−0.329676	+	0.127724i
$649$	11.4783	+	13.6794i	0.450565	+	0.536962i
$650$	23.9407	−	28.5314i	0.939033	−	1.11910i
$651$	−13.9777	+	40.8254i	−0.547828	+	1.60007i
$652$	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
$657$	−24.6660	+	9.26581i	−0.962311	+	0.361494i
$658$	−1.87447	+	11.5805i	−0.0730744	+	0.451455i
$659$	−2.02243	+	11.4698i	−0.0787828	+	0.446800i	0.919743	+	0.392521i	$0.128397\pi$
$659$	−2.02243	+	11.4698i	−0.0787828	+	0.446800i	−0.998526	+	0.0542785i	$0.982714\pi$
$660$	−6.44028	−	17.4156i	−0.250688	−	0.677901i
$661$	−10.5576	−	29.0067i	−0.410642	−	1.12823i	−0.956851	−	0.290580i	$-0.906152\pi$
$661$	−10.5576	−	29.0067i	−0.410642	−	1.12823i	0.546209	−	0.837649i	$-0.316070\pi$
$662$	8.75172	−	24.0451i	0.340145	−	0.934541i
$663$	−0.220570	+	0.265625i	−0.00856624	+	0.0103160i
$664$		−	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
$669$	−21.7413	+	38.1079i	−0.840568	+	1.47334i
$670$	44.4666	+	16.1845i	1.71789	+	0.625262i
$671$	0.253556	+	0.0447087i	0.00978840	+	0.00172596i
$672$	−4.58173	+	0.0879732i	−0.176744	+	0.00339364i
$673$	8.44172	−	4.87383i	0.325405	−	0.187872i	−0.328394	−	0.944541i	$-0.606508\pi$
$673$	8.44172	−	4.87383i	0.325405	−	0.187872i	0.653799	+	0.756668i	$0.273174\pi$
$674$	13.6435	−	16.2597i	0.525529	−	0.626301i
$675$	19.6260	+	51.4409i	0.755407	+	1.97996i
$676$	0.644293			0.0247805
$677$	−3.49778			−0.134430			−0.0672152	−	0.997738i	$-0.521411\pi$
$677$	−3.49778			−0.134430			−0.0672152	+	0.997738i	$0.521411\pi$
$678$	12.0925	−	7.06467i	0.464408	−	0.271317i
$679$	−23.4990	+	0.330430i	−0.901809	+	0.0126807i
$680$	0.171560	+	0.143956i	0.00657904	+	0.00552047i
$681$	−10.6924	−	1.82876i	−0.409733	−	0.0700783i
$682$	19.5817	−	16.4310i	0.749822	−	0.629175i
$683$	9.13165	−	15.8165i	0.349413	−	0.605201i	−0.636732	−	0.771085i	$-0.719714\pi$
$683$	9.13165	−	15.8165i	0.349413	−	0.605201i	0.986145	+	0.165884i	$0.0530477\pi$
$684$	12.8581	+	2.38119i	0.491641	+	0.0910470i
$685$	11.9815			0.457789
$686$	5.59479	−	17.6550i	0.213610	−	0.674070i
$687$	−0.971737	+	1.17023i	−0.0370741	+	0.0446470i
$688$	1.55204	−	8.80205i	0.0591710	−	0.335575i
$689$	−31.9631	+	5.63596i	−1.21770	+	0.214713i
$690$	−0.0986960	−	19.2089i	−0.00375729	−	0.731270i
$691$	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
$693$	−10.3160	+	18.9164i	−0.391871	+	0.718575i
$694$	3.03869	+	8.34874i	0.115347	+	0.316914i
$695$	−77.2871	−	44.6217i	−2.93167	−	1.69260i
$696$	−0.470687	+	1.31417i	−0.0178413	+	0.0498135i
$697$	0.0588727	−	0.0701617i	0.00222996	−	0.00265756i
$698$	−4.14877	−	1.51003i	−0.157033	−	0.0571555i
$699$	39.6884	−	0.203921i	1.50115	−	0.00771299i
$700$	0.394159	+	28.0312i	0.0148978	+	1.05948i
$701$	9.91497	−	27.2412i	0.374483	−	1.02888i	−0.599124	−	0.800656i	$-0.704484\pi$
$701$	9.91497	−	27.2412i	0.374483	−	1.02888i	0.973608	−	0.228228i	$-0.0732933\pi$
$702$	8.88753	−	15.9567i	0.335438	−	0.602246i
$703$	22.1173	+	19.2809i	0.834171	+	0.727194i
$704$	2.35091	+	1.35730i	0.0886033	+	0.0511552i
$705$	−19.3755	+	23.3333i	−0.729725	+	0.878783i
$706$	−2.97742	+	0.524999i	−0.112057	+	0.0197586i
$707$	26.4523	+	9.20878i	0.994843	+	0.346332i
$708$	11.2307	+	1.92083i	0.422075	+	0.0721891i
$709$	−0.361449	+	0.131557i	−0.0135745	+	0.00494072i	−0.348798	−	0.937198i	$-0.613410\pi$
$709$	−0.361449	+	0.131557i	−0.0135745	+	0.00494072i	0.335224	+	0.942138i	$0.391188\pi$
$710$	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
$714$	−0.00498894	−	0.259829i	−0.000186706	−	0.00972386i
$715$	32.6343	+	18.8414i	1.22045	+	0.704630i
$716$	−11.0958	+	4.03854i	−0.414669	+	0.150927i
$717$	−11.9546	−	9.92686i	−0.446452	−	0.370725i
$718$	3.22073	+	8.84887i	0.120196	+	0.330237i
$719$	26.3481	+	31.4005i	0.982620	+	1.17104i	0.985263	+	0.171044i	$0.0547140\pi$
$719$	26.3481	+	31.4005i	0.982620	+	1.17104i	−0.00264390	+	0.999997i	$0.500842\pi$
$720$	−10.3205	−	5.81799i	−0.384624	−	0.216824i
$721$	8.28491	−	51.1843i	0.308546	−	1.90620i
$722$	−14.0840	−	12.7531i	−0.524151	−	0.474622i
$723$	11.3291	+	4.05767i	0.421335	+	0.150906i
$724$	3.99347	+	4.75924i	0.148416	+	0.176876i
$725$	8.02457	+	2.92071i	0.298025	+	0.108472i
$726$	−5.43020	+	3.17244i	−0.201534	+	0.117740i
$727$	−24.1070	+	20.2282i	−0.894081	+	0.750223i	−0.969024	−	0.246965i	$-0.920567\pi$
$727$	−24.1070	+	20.2282i	−0.894081	+	0.750223i	0.0749438	+	0.997188i	$0.476122\pi$
$728$	7.03946	−	6.07750i	0.260900	−	0.225247i
$729$	14.2143	+	22.9555i	0.526456	+	0.850202i
$730$	−30.0384	−	17.3427i	−1.11177	−	0.641881i
$731$	0.499163	+	0.0880159i	0.0184622	+	0.00325539i
$732$	0.141844	−	0.0828684i	0.00524271	−	0.00306290i
$733$	20.0357	−	34.7028i	0.740034	−	1.28178i	−0.212445	−	0.977173i	$-0.568143\pi$
$733$	20.0357	−	34.7028i	0.740034	−	1.28178i	0.952479	−	0.304603i	$-0.0985239\pi$
$734$	11.7196	−	20.2989i	0.432578	−	0.749247i
$735$	35.6353	−	31.9800i	1.31443	−	1.17960i
$736$	1.80514	+	2.15128i	0.0665382	+	0.0792972i
$737$	−5.64832	+	32.0332i	−0.208058	+	1.17996i
$738$	−2.37934	+	4.22071i	−0.0875847	+	0.155367i
$739$	−19.9919	+	16.7752i	−0.735414	+	0.617086i	−0.931602	−	0.363481i	$-0.881588\pi$
$739$	−19.9919	+	16.7752i	−0.735414	+	0.617086i	0.196188	+	0.980566i	$0.437144\pi$
$740$	−13.2917	−	23.0220i	−0.488614	−	0.846305i
$741$	−23.1626	+	12.9525i	−0.850901	+	0.475823i
$742$	15.4383	−	18.9330i	0.566756	−	0.695051i
$743$	−5.88810	−	2.14309i	−0.216013	−	0.0786224i	0.231747	−	0.972776i	$-0.425556\pi$
$743$	−5.88810	−	2.14309i	−0.216013	−	0.0786224i	−0.447760	+	0.894154i	$0.647778\pi$
$744$	2.74962	−	16.0765i	0.100806	−	0.589391i
$745$	−10.4206	+	3.79280i	−0.381783	+	0.138958i
$746$	−9.55060	+	1.68403i	−0.349672	+	0.0616567i
$747$	−25.0519	+	4.68325i	−0.916601	+	0.171351i
$748$	−0.0769722	+	0.133320i	−0.00281438	+	0.00487465i
$749$	13.1787	+	34.6831i	0.481541	+	1.26729i
$750$	−18.9677	+	33.2463i	−0.692601	+	1.21398i
$751$	22.8770	−	27.2638i	0.834794	−	0.994869i	−0.165169	−	0.986265i	$-0.552817\pi$
$751$	22.8770	−	27.2638i	0.834794	−	0.994869i	0.999963	−	0.00860374i	$-0.00273869\pi$
$752$		−	4.43399i		−	0.161691i
$753$	34.7506	+	12.4464i	1.26638	+	0.453571i
$754$	−0.968914	−	2.66207i	−0.0352858	−	0.0969469i
$755$	−27.8652	+	23.3817i	−1.01412	+	0.850946i
$756$	2.78522	+	13.4626i	0.101298	+	0.489631i
$757$	2.43070	+	13.7852i	0.0883455	+	0.501032i	0.996584	+	0.0825801i	$0.0263160\pi$
$757$	2.43070	+	13.7852i	0.0883455	+	0.501032i	−0.908239	+	0.418452i	$0.862573\pi$
$758$	3.00573	−	0.529992i	0.109173	−	0.0192502i
$759$	12.9916	−	2.35965i	0.471564	−	0.0856499i
$760$	8.32434	+	15.0674i	0.301956	+	0.546552i
$761$	13.1047	−	7.56601i	0.475046	−	0.274268i	−0.243304	−	0.969950i	$-0.578231\pi$
$761$	13.1047	−	7.56601i	0.475046	−	0.274268i	0.718350	+	0.695682i	$0.244898\pi$
$762$	−1.12421	+	0.415734i	−0.0407259	+	0.0150604i
$763$	20.0926	+	33.6982i	0.727402	+	1.21996i
$764$	12.4817	−	14.8751i	0.451573	−	0.538163i
$765$	0.329937	−	0.585276i	0.0119289	−	0.0211607i
$766$	18.0806	+	15.1715i	0.653280	+	0.548167i
$767$	−20.0249	+	11.5614i	−0.723058	+	0.417458i
$768$	1.70417	−	0.309528i	0.0614939	−	0.0111691i
$769$	5.76951	−	2.09993i	0.208054	−	0.0757254i	−0.235891	−	0.971780i	$-0.575801\pi$
$769$	5.76951	−	2.09993i	0.208054	−	0.0757254i	0.443945	+	0.896054i	$0.353579\pi$
$770$	−27.8606	+	5.31751i	−1.00402	+	0.191630i
$771$	4.89030	−	13.6539i	0.176120	−	0.491732i
$772$		−	2.16909i		−	0.0780672i
$773$	3.64406	+	3.05773i	0.131068	+	0.109979i	0.705965	−	0.708247i	$-0.250514\pi$
$773$	3.64406	+	3.05773i	0.131068	+	0.109979i	−0.574897	+	0.818226i	$0.694958\pi$
$774$	−26.8121	+	0.275531i	−0.963741	+	0.00990375i
$775$	−98.2603	−	17.3259i	−3.52961	−	0.622366i
$776$	8.74772	−	1.54246i	0.314025	−	0.0553710i
$777$	−9.99198	+	29.1842i	−0.358460	+	1.04698i
$778$			18.8931i			0.677351i
$779$	6.16200	−	3.40434i	0.220777	−	0.121973i
$780$	23.6565	−	4.29673i	0.847040	−	0.153847i
$781$	22.4694	+	26.7780i	0.804018	+	0.958191i
$782$	−0.121999	+	0.102369i	−0.00436266	+	0.00366071i
$783$	4.13486	+	0.663544i	0.147768	+	0.0237131i
$784$	−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	$0.159137\pi$
$787$			26.8963i			0.958751i	−0.877610	+	0.479376i	$0.840863\pi$
$788$	−9.41309	−	1.65978i	−0.335328	−	0.0591273i
$789$	−45.1777	+	0.232125i	−1.60837	+	0.00826386i
$790$	2.35525	+	4.07941i	0.0837961	+	0.145139i
$791$	−7.59870	−	19.9978i	−0.270179	−	0.711041i
$792$	2.70656	−	7.68088i	0.0961734	−	0.272928i
$793$	−0.114025	+	0.313282i	−0.00404916	+	0.0111250i
$794$	−12.0461	+	4.38444i	−0.427501	+	0.155598i
$795$	59.2375	−	21.9060i	2.10094	−	0.776926i
$796$	−0.187794	−	1.06504i	−0.00665620	−	0.0377492i
$797$	19.1520			0.678400			0.339200	−	0.940714i	$-0.389844\pi$
$797$	19.1520			0.678400			0.339200	+	0.940714i	$0.389844\pi$
$798$	6.82547	−	18.7727i	0.241619	−	0.664545i
$799$	0.251451			0.00889568
$800$	−1.83995	−	10.4349i	−0.0650521	−	0.368929i
$801$	8.34402	−	14.8015i	0.294821	−	0.522984i
$802$	−23.7276	+	8.63613i	−0.837850	+	0.304952i
$803$	8.15453	−	22.4044i	0.287767	−	0.790634i
$804$	10.4693	+	17.9200i	0.369222	+	0.631990i
$805$	−28.9655	−	4.68847i	−1.02090	−	0.165247i
$806$	16.5499	+	28.6652i	0.582944	+	1.00969i
$807$	0.0706329	+	13.7471i	0.00248640	+	0.483919i
$808$	−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	0.707415	−	0.706799i	$-0.249861\pi$
$811$	32.1924	+	5.67639i	1.13043	+	0.199325i	0.423013	+	0.906124i	$0.360973\pi$
$812$	1.86144	+	1.04008i	0.0653236	+	0.0364997i
$813$	0.124705	+	24.2710i	0.00437361	+	0.851222i
$814$	13.9980	−	11.7457i	0.490631	−	0.411688i
$815$	−43.0499	−	51.3049i	−1.50797	−	1.79713i
$816$	0.0175533	+	0.0966431i	0.000614487	+	0.00338319i
$817$	33.3663	+	20.1124i	1.16734	+	0.703642i
$818$			20.2468i			0.707912i
$819$	−21.8027	−	17.4084i	−0.761848	−	0.608298i
$820$	−6.28122	+	1.10755i	−0.219350	+	0.0386773i
$821$	23.9286	+	4.21925i	0.835112	+	0.147253i	0.574823	−	0.818278i	$-0.305071\pi$
$821$	23.9286	+	4.21925i	0.835112	+	0.147253i	0.260289	+	0.965531i	$0.416182\pi$
$822$	4.04281	+	3.35707i	0.141009	+	0.117091i
$823$	−28.0227	−	23.5138i	−0.976810	−	0.819641i	0.00679507	−	0.999977i	$-0.497837\pi$
$823$	−28.0227	−	23.5138i	−0.976810	−	0.819641i	−0.983605	+	0.180336i	$0.942281\pi$
$824$			19.5977i			0.682717i
$825$	−46.9023	−	16.7986i	−1.63293	−	0.584853i
$826$	5.72207	−	16.4367i	0.199096	−	0.571907i
$827$	−10.3816	+	3.77860i	−0.361004	+	0.131395i	−0.516153	−	0.856496i	$-0.672636\pi$
$827$	−10.3816	+	3.77860i	−0.361004	+	0.131395i	0.155149	+	0.987891i	$0.450414\pi$
$828$	5.34881	−	6.50914i	0.185884	−	0.226208i
$829$	−8.32118	+	4.80423i	−0.289006	+	0.166858i	−0.637494	−	0.770456i	$-0.720029\pi$
$829$	−8.32118	+	4.80423i	−0.289006	+	0.166858i	0.348487	+	0.937314i	$0.386695\pi$
$830$	−25.7002	−	21.5650i	−0.892068	−	0.748534i
$831$	−9.89255	−	26.7511i	−0.343169	−	0.927985i
$832$	−2.25944	+	2.69270i	−0.0783321	+	0.0933525i
$833$	−0.392722	−	0.0579135i	−0.0136070	−	0.00200658i
$834$	−13.5758	−	36.7113i	−0.470093	−	1.27121i
$835$	23.1005	−	13.3371i	0.799424	−	0.461548i
$836$	−9.20616	+	7.43361i	−0.318402	+	0.257097i
$837$	−48.9239	+	0.754172i	−1.69106	+	0.0260680i
$838$	−17.2309	+	3.03827i	−0.595232	+	0.104955i
$839$	4.39099	+	24.9025i	0.151594	+	0.859731i	0.961834	+	0.273633i	$0.0882254\pi$
$839$	4.39099	+	24.9025i	0.151594	+	0.859731i	−0.810240	+	0.586098i	$0.800664\pi$
$840$	−11.3645	+	14.0841i	−0.392111	+	0.485948i
$841$	−21.7177	+	18.2233i	−0.748887	+	0.628391i
$842$	1.63188	+	4.48355i	0.0562383	+	0.154513i
$843$	−8.10871	+	22.6398i	−0.279279	+	0.779754i
$844$			10.8248i			0.372606i
$845$	1.63552	−	1.94914i	0.0562636	−	0.0670523i
$846$	−13.0754	+	2.44435i	−0.449543	+	0.0840385i
$847$	3.41225	+	8.98016i	0.117246	+	0.308562i
$848$	−4.61673	+	7.99640i	−0.158539	+	0.274598i
$849$	10.2442	+	5.84449i	0.351579	+	0.200583i
$850$	0.591760	−	0.104343i	0.0202972	−	0.00357895i
$851$	17.7638	−	6.46549i	0.608935	−	0.221634i
$852$	21.9845	+	3.76011i	0.753178	+	0.128819i
$853$	2.71440	+	0.987961i	0.0929393	+	0.0338271i	0.388071	−	0.921629i	$-0.373141\pi$
$853$	2.71440	+	0.987961i	0.0929393	+	0.0338271i	−0.295132	+	0.955456i	$0.595364\pi$
$854$	−0.0891325	−	0.234574i	−0.00305005	−	0.00802695i
$855$	39.8435	−	32.8541i	1.36262	−	1.12359i
$856$	−7.01171	−	12.1446i	−0.239655	−	0.415095i
$857$	−14.4174	+	12.0977i	−0.492490	+	0.413248i	−0.854918	−	0.518764i	$-0.826392\pi$
$857$	−14.4174	+	12.0977i	−0.492490	+	0.413248i	0.362428	+	0.932012i	$0.381948\pi$
$858$	5.73237	+	15.5013i	0.195700	+	0.529205i
$859$	−7.68975	+	43.6108i	−0.262371	+	1.48798i	0.514047	+	0.857762i	$0.328146\pi$
$859$	−7.68975	+	43.6108i	−0.262371	+	1.48798i	−0.776418	+	0.630218i	$0.782966\pi$
$860$	−22.6884	−	27.0390i	−0.773670	−	0.922023i
$861$	5.75987	+	4.64763i	0.196296	+	0.158391i
$862$	18.4714	−	31.9934i	0.629138	−	1.08970i
$863$	−4.62762	+	8.01527i	−0.157526	+	0.272843i	−0.933976	−	0.357336i	$-0.883685\pi$
$863$	−4.62762	+	8.01527i	−0.157526	+	0.272843i	0.776450	+	0.630179i	$0.217018\pi$
$864$	−1.85224	−	4.85481i	−0.0630144	−	0.165164i
$865$	92.3630	+	16.2861i	3.14044	+	0.553744i
$866$	6.58216	+	3.80021i	0.223671	+	0.129136i
$867$	28.9654	−	5.26097i	0.983716	−	0.178672i
$868$	−23.5288	−	8.19101i	−0.798619	−	0.278021i
$869$	−2.48040	+	2.08130i	−0.0841419	+	0.0706034i
$870$	2.78085	+	4.75992i	0.0942796	+	0.161376i
$871$	−39.5788	−	14.4055i	−1.34108	−	0.488112i
$872$	−9.53186	−	11.3596i	−0.322790	−	0.384686i
$873$	−9.37099	−	24.9460i	−0.317160	−	0.844293i
$874$	−11.5798	+	3.96903i	−0.391691	+	0.134255i
$875$	45.3133	+	36.9492i	1.53187	+	1.24911i
$876$	−5.27638	−	14.2682i	−0.178272	−	0.482078i
$877$	−25.6156	−	30.5274i	−0.864976	−	1.03084i	−0.999204	−	0.0398879i	$-0.987300\pi$
$877$	−25.6156	−	30.5274i	−0.864976	−	1.03084i	0.134228	−	0.990950i	$-0.457145\pi$
$878$	5.72402	+	15.7266i	0.193176	+	0.530747i
$879$	28.5153	−	34.3400i	0.961796	−	1.15826i
$880$	10.0739	−	3.66659i	0.339590	−	0.123601i
$881$	7.45301	+	4.30300i	0.251098	+	0.144972i	0.620267	−	0.784391i	$-0.287024\pi$
$881$	7.45301	+	4.30300i	0.251098	+	0.144972i	−0.369169	+	0.929362i	$0.620358\pi$
$882$	20.9845	−	0.806139i	0.706586	−	0.0271441i
$883$	−29.5785	+	10.7657i	−0.995396	+	0.362294i	−0.787807	−	0.615922i	$-0.788784\pi$
$883$	−29.5785	+	10.7657i	−0.995396	+	0.362294i	−0.207589	+	0.978216i	$0.566562\pi$
$884$	−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	$-0.324185\pi$
$887$	43.8939	−	15.9761i	1.47381	−	0.536423i	0.949133	+	0.314877i	$0.101963\pi$
$888$	1.96557	−	11.4923i	0.0659603	−	0.385656i
$889$	0.343257	+	1.79846i	0.0115125	+	0.0603183i
$890$	22.0274	−	3.88402i	0.738359	−	0.130193i
$891$	−24.1423	−	3.74712i	−0.808798	−	0.125533i
$892$	−21.9368	−	12.6652i	−0.734500	−	0.424064i
$893$	18.0338	+	6.95164i	0.603479	+	0.232628i
$894$	−4.57885	−	1.63997i	−0.153140	−	0.0548488i
$895$	−15.9488	+	43.8190i	−0.533110	+	1.46471i
$896$	−0.0371994	−	2.64549i	−0.00124274	−	0.0883796i
$897$	0.0878474	+	17.0975i	0.00293314	+	0.570867i
$898$	20.5890	+	7.49380i	0.687065	+	0.250071i
$899$	−4.87818	+	5.81359i	−0.162696	+	0.193894i
$900$	−29.7572	+	11.1784i	−0.991908	+	0.372612i
$901$	−0.453475	−	0.261814i	−0.0151074	−	0.00872228i
$902$	−1.49950	−	4.11983i	−0.0499277	−	0.137175i
$903$	−6.33668	+	40.4652i	−0.210872	+	1.34660i
$904$	4.04286	+	7.00245i	0.134464	+	0.232898i
$905$	24.5351			0.815575
$906$	−15.9536	+	0.0819702i	−0.530022	+	0.00272328i
$907$	7.35615	−	1.29709i	0.244257	−	0.0430691i	−0.0501792	−	0.998740i	$-0.515979\pi$
$907$	7.35615	−	1.29709i	0.244257	−	0.0430691i	0.294436	+	0.955671i	$0.404868\pi$
$908$	1.08754	−	6.16774i	0.0360913	−	0.204684i
$909$	0.326357	+	31.7580i	0.0108246	+	1.05335i
$910$	−0.516385	−	36.7235i	−0.0171180	−	1.21737i
$911$	15.7199			0.520825			0.260412	−	0.965498i	$-0.416142\pi$
$911$	15.7199			0.520825			0.260412	+	0.965498i	$0.416142\pi$
$912$	−1.41290	+	7.41645i	−0.0467859	+	0.245583i
$913$	11.5307	−	19.9717i	0.381609	−	0.660966i
$914$	−7.17323	+	6.01906i	−0.237269	+	0.199093i
$915$	0.109371	−	0.639470i	0.00361570	−	0.0211402i
$916$	−0.672741	−	0.564497i	−0.0222280	−	0.0186515i
$917$	11.8527	+	19.8786i	0.391410	+	0.656450i
$918$	0.275316	−	0.105040i	0.00908677	−	0.00346684i
$919$	−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
$921$	1.95583	+	3.34776i	0.0644469	+	0.110313i
$922$	9.39299	−	11.1941i	0.309342	−	0.368659i
$923$	−39.1997	+	22.6319i	−1.29027	+	0.744939i
$924$	−10.8907	−	6.01196i	−0.358276	−	0.197779i
$925$	−70.2417	−	12.3855i	−2.30953	−	0.407233i
$926$	−28.7892	−	10.4784i	−0.946071	−	0.344342i
$927$	57.7918	−	10.8037i	1.89813	−	0.354841i
$928$	−0.757331	−	0.275646i	−0.0248606	−	0.00904852i
$929$	−20.7347	+	3.65609i	−0.680285	+	0.119953i	−0.503104	−	0.864226i	$-0.667809\pi$
$929$	−20.7347	+	3.65609i	−0.680285	+	0.119953i	−0.177181	+	0.984178i	$0.556698\pi$
$930$	−41.6552	−	49.1278i	−1.36593	−	1.61097i
$931$	−26.5646	−	15.0107i	−0.870619	−	0.491957i
$932$			22.9144i			0.750587i
$933$	−27.1749	−	22.5655i	−0.889665	−	0.738762i
$934$	−11.5338	+	31.6888i	−0.377397	+	1.03689i
$935$	0.207932	+	0.571287i	0.00680009	+	0.0186831i
$936$	9.18611	+	5.17848i	0.300258	+	0.169264i
$937$	−7.71966	+	43.7804i	−0.252190	+	1.43024i	0.550993	+	0.834510i	$0.314249\pi$
$937$	−7.71966	+	43.7804i	−0.252190	+	1.43024i	−0.803183	+	0.595733i	$0.796862\pi$
$938$	29.6351	−	11.2606i	0.967621	−	0.367673i
$939$	12.2254	−	34.1337i	0.398961	−	1.11391i
$940$	−13.4138	−	11.2555i	−0.437511	−	0.367115i
$941$	6.63111	−	37.6069i	0.216168	−	1.22595i	−0.662700	−	0.748885i	$-0.730589\pi$
$941$	6.63111	−	37.6069i	0.216168	−	1.22595i	0.878868	−	0.477065i	$-0.158299\pi$
$942$	6.71988	+	7.92538i	0.218946	+	0.258223i
$943$		−	4.53556i		−	0.147698i
$944$	−1.14229	+	6.47825i	−0.0371784	+	0.210849i
$945$	47.7978	+	25.7486i	1.55486	+	0.837600i
$946$	15.5957	−	18.5863i	0.507061	−	0.604292i
$947$	36.6966	+	43.7333i	1.19248	+	1.42114i	0.882444	+	0.470418i	$0.155897\pi$
$947$	36.6966	+	43.7333i	1.19248	+	1.42114i	0.310036	+	0.950725i	$0.399659\pi$
$948$	−0.348293	+	2.03640i	−0.0113120	+	0.0661391i
$949$	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	0.915896	+	0.401415i	$0.131481\pi$
$953$	5.94345	+	33.7070i	0.192527	+	1.09188i	−0.723369	+	0.690462i	$0.757407\pi$
$954$	26.1258	+	9.20610i	0.845854	+	0.298059i
$955$	−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
$960$	3.38959	−	5.94123i	0.109399	−	0.191752i
$961$	28.8354	−	49.9445i	0.930176	−	1.61111i
$962$	11.8307	+	20.4914i	0.381438	+	0.660669i
$963$	−31.9481	+	27.3720i	−1.02951	+	0.882050i
$964$	−2.37627	+	6.52875i	−0.0765346	+	0.210277i
$965$	−6.56200	−	5.50617i	−0.211238	−	0.177250i
$966$	−8.45991	−	9.69778i	−0.272193	−	0.312021i
$967$	8.48095	+	3.08681i	0.272729	+	0.0992652i	0.474764	−	0.880113i	$-0.342533\pi$
$967$	8.48095	+	3.08681i	0.272729	+	0.0992652i	−0.202035	+	0.979378i	$0.564756\pi$
$968$	−1.81548	−	3.14450i	−0.0583516	−	0.101068i
$969$	−0.420585	−	0.0801255i	−0.0135112	−	0.00257400i
$970$	17.5395	−	30.3794i	0.563160	−	0.975422i
$971$	−2.15527	−	12.2231i	−0.0691659	−	0.392259i	−0.999663	−	0.0259599i	$-0.991736\pi$
$971$	−2.15527	−	12.2231i	−0.0691659	−	0.392259i	0.930497	−	0.366299i	$-0.119375\pi$
$972$	−13.2953	+	8.13843i	−0.426448	+	0.261040i
$973$	−58.7288	+	11.2091i	−1.88276	+	0.359347i
$974$	−5.38639	−	6.41925i	−0.172591	−	0.205686i
$975$	31.9678	−	56.0327i	1.02379	−	1.79448i
$976$	0.0474227	+	0.0821385i	0.00151796	+	0.00262919i
$977$	−38.2065			−1.22233			−0.611167	−	0.791501i	$-0.709300\pi$
$977$	−38.2065			−1.22233			−0.611167	+	0.791501i	$0.709300\pi$
$978$	−0.150922	−	29.3734i	−0.00482595	−	0.939259i
$979$	5.25853	+	14.4477i	0.168063	+	0.461750i
$980$	18.3577	+	20.6686i	0.586415	+	0.660235i
$981$	−28.2439	+	34.3709i	−0.901758	+	1.09738i
$982$	−10.2958	−	28.2875i	−0.328552	−	0.902689i
$983$	−3.47377	−	19.7008i	−0.110796	−	0.628356i	−0.988746	−	0.149604i	$-0.952200\pi$
$983$	−3.47377	−	19.7008i	−0.110796	−	0.628356i	0.877950	−	0.478753i	$-0.158911\pi$
$984$	−2.42974	−	1.38621i	−0.0774573	−	0.0441909i
$985$	−28.9161	+	24.2635i	−0.921343	+	0.773099i
$986$	0.0156318	−	0.0429481i	0.000497819	−	0.00136775i
$987$	0.390072	+	20.3153i	0.0124161	+	0.646644i
$988$	−7.40933	−	13.4112i	−0.235722	−	0.426667i
$989$	21.7373	−	12.5500i	0.691206	−	0.399068i
$990$	−16.3659	−	27.6857i	−0.520143	−	0.879908i
$991$	19.1400	−	52.5866i	0.608001	−	1.67047i	−0.126588	−	0.991955i	$-0.540403\pi$
$991$	19.1400	−	52.5866i	0.608001	−	1.67047i	0.734589	−	0.678513i	$-0.237375\pi$
$992$	9.27346	+	1.63516i	0.294433	+	0.0519164i
$993$	7.47177	−	43.6859i	0.237110	−	1.38633i
$994$	11.2012	−	32.1756i	0.355281	−	1.02055i
$995$	−3.69869	−	2.13544i	−0.117256	−	0.0676980i
$996$	−2.62953	−	14.4774i	−0.0833197	−	0.458734i
$997$	−8.04188	+	45.6078i	−0.254689	+	1.44441i	0.542181	+	0.840262i	$0.317599\pi$
$997$	−8.04188	+	45.6078i	−0.254689	+	1.44441i	−0.796870	+	0.604151i	$0.793512\pi$
$998$	0.423407	−	2.40126i	0.0134027	−	0.0760106i
$999$	−34.9734	+	0.539122i	−1.10651	+	0.0170571i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bu.a.53.17	✓	162
3.2	odd	2		798.2.bu.b.53.5	yes	162
7.2	even	3		798.2.cc.a.737.3	yes	162
19.14	odd	18		798.2.cc.b.641.14	yes	162
21.2	odd	6		798.2.cc.b.737.14	yes	162
57.14	even	18		798.2.cc.a.641.3	yes	162
133.128	odd	18		798.2.bu.b.527.5	yes	162
399.128	even	18	inner	798.2.bu.a.527.17	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.53.17	✓	162	1.1	even	1	trivial
798.2.bu.a.527.17	yes	162	399.128	even	18	inner
798.2.bu.b.53.5	yes	162	3.2	odd	2
798.2.bu.b.527.5	yes	162	133.128	odd	18
798.2.cc.a.641.3	yes	162	57.14	even	18
798.2.cc.a.737.3	yes	162	7.2	even	3
798.2.cc.b.641.14	yes	162	19.14	odd	18
798.2.cc.b.737.14	yes	162	21.2	odd	6

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} +(0.600751 + 1.62453i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-1.35069 + 3.71100i) q^{5} +(-1.49553 + 0.873721i) q^{6} +(0.939767 + 2.47322i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.27820 + 1.95188i) 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} +(-6.84005 + 0.0351445i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.0364524 + 0.0434422i) q^{17} +(-2.31783 - 1.90465i) q^{18} +(1.41333 + 4.12341i) q^{19} -3.94916i q^{20} +(-3.45326 + 3.01247i) q^{21} +(2.67336 - 0.471385i) q^{22} +(2.76563 + 0.487655i) q^{23} +(1.10651 - 1.33253i) q^{24} +(-8.11690 - 6.81089i) q^{25} +3.51507i q^{26} +(-4.53951 - 2.52841i) q^{27} +(-1.72898 - 2.00265i) q^{28} +(-0.757331 + 0.275646i) q^{29} +(-1.22237 - 6.73004i) q^{30} +(8.15495 - 4.70826i) q^{31} +(0.766044 + 0.642788i) q^{32} +(4.40995 - 1.63080i) q^{33} +(-0.0364524 + 0.0434422i) q^{34} +(-10.4475 + 0.146906i) q^{35} +(1.47322 - 2.61335i) q^{36} +(5.82959 - 3.36571i) q^{37} +(-3.81534 + 2.10788i) q^{38} +(1.08801 + 5.99027i) q^{39} +(3.88916 - 0.685764i) q^{40} +(-0.280452 - 1.59052i) q^{41} +(-3.56636 - 2.87769i) q^{42} +(6.84678 - 5.74513i) q^{43} +(0.928448 + 2.55089i) q^{44} +(-4.16626 - 11.0908i) q^{45} +2.80829i q^{46} +(2.85011 - 3.39663i) q^{47} +(1.50443 + 0.858307i) q^{48} +(-5.23368 + 4.64851i) q^{49} +(5.29793 - 9.17628i) q^{50} +(-0.0486744 + 0.0853160i) q^{51} +(-3.46167 + 0.610385i) q^{52} +(-8.67661 + 3.15803i) q^{53} +(1.70172 - 4.90960i) q^{54} +(10.0739 + 3.66659i) q^{55} +(1.67199 - 2.05047i) q^{56} +(-5.84955 + 4.77313i) q^{57} +(-0.402967 - 0.697960i) q^{58} +(-5.03918 + 4.22838i) q^{59} +(6.41553 - 2.37246i) q^{60} +(-0.0164697 + 0.0934044i) q^{61} +(6.05282 + 7.21347i) q^{62} +(-6.96840 - 3.80018i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-6.94078 + 12.0218i) q^{65} +(2.37180 + 4.05977i) q^{66} +(-11.8003 - 2.08072i) q^{67} +(-0.0491121 - 0.0283549i) q^{68} +(0.869244 + 4.78581i) q^{69} +(-1.95886 - 10.2632i) q^{70} +(-9.86443 + 8.27724i) q^{71} +(2.82947 + 0.997038i) q^{72} +(8.25330 + 3.00395i) q^{73} +(4.32688 + 5.15657i) q^{74} +(6.18825 - 17.2778i) q^{75} +(-2.73838 - 3.39135i) q^{76} +(6.71381 - 2.55109i) q^{77} +(-5.71033 + 2.11168i) q^{78} +(-0.766708 - 0.913727i) q^{79} +(1.35069 + 3.71100i) q^{80} +(1.38036 - 8.89352i) q^{81} +(1.51766 - 0.552382i) q^{82} +(7.35714 + 4.24765i) q^{83} +(2.21468 - 4.01188i) 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} +(10.1988 - 6.02886i) q^{90} +(1.74354 + 9.13510i) q^{91} +(-2.76563 + 0.487655i) q^{92} +(12.5478 + 10.4195i) q^{93} +(3.83995 + 2.21699i) q^{94} +(-17.2109 - 0.324613i) q^{95} +(-0.584026 + 1.63062i) q^{96} +(-3.03805 + 8.34698i) q^{97} +(-5.48671 - 4.34696i) q^{98} +(5.29856 + 6.18439i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q - 81 q^{8} + 15 q^{13} + 6 q^{14} + 27 q^{15} - 6 q^{17} - 18 q^{18} + 9 q^{19} - 6 q^{22} - 6 q^{25} - 9 q^{27} + 9 q^{28} + 6 q^{29} - 24 q^{33} + 6 q^{34} + 24 q^{35} + 18 q^{37} - 9 q^{39} - 9 q^{43}+ \cdots - 57 q^{99}+O(q^{100}) \) 162 * q - 81 * q^8 + 15 * q^13 + 6 * q^14 + 27 * 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 - 63 * 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 + 6 * q^60 + 45 * q^61 + 36 * q^62 - 15 * 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 - 6 * q^78 - 42 * q^79 + 84 * q^81 - 3 * q^84 - 6 * q^85 - 9 * q^86 + 60 * q^87 + 54 * q^89 + 36 * q^90 - 18 * q^91 - 21 * q^93 - 72 * q^94 - 12 * q^97 - 27 * q^98 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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