LMFDB - Embedded newform 117.2.x.a.2.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(2,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.x (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			2.5
Character	$\chi$	$=$	117.2
Dual form			117.2.x.a.59.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.754009 - 0.754009i) q^{2} +(0.861374 - 1.50268i) q^{3} -0.862941i q^{4} +(0.595426 - 2.22216i) q^{5} +(-1.78251 + 0.483547i) q^{6} +(-1.34030 + 5.00206i) q^{7} +(-2.15868 + 2.15868i) q^{8} +(-1.51607 - 2.58873i) q^{9} +(-2.12448 + 1.22657i) q^{10} +(1.93671 - 1.93671i) q^{11} +(-1.29672 - 0.743315i) q^{12} +(3.42168 - 1.13671i) q^{13} +(4.78220 - 2.76100i) q^{14} +(-2.82630 - 2.80884i) q^{15} +1.52945 q^{16} +(0.0716242 - 0.124057i) q^{17} +(-0.808798 + 3.09506i) q^{18} +(0.552200 + 2.06084i) q^{19} +(-1.91759 - 0.513817i) q^{20} +(6.36198 + 6.32269i) q^{21} -2.92060 q^{22} +(0.421808 - 0.730594i) q^{23} +(1.38437 + 5.10323i) q^{24} +(-0.253329 - 0.146260i) q^{25} +(-3.43707 - 1.72289i) q^{26} +(-5.19593 + 0.0482913i) q^{27} +(4.31649 + 1.15660i) q^{28} +0.605036i q^{29} +(0.0131630 + 4.24895i) q^{30} +(3.38018 + 0.905716i) q^{31} +(3.16415 + 3.16415i) q^{32} +(-1.24202 - 4.57849i) q^{33} +(-0.147545 + 0.0395346i) q^{34} +(10.3173 + 5.95671i) q^{35} +(-2.23392 + 1.30828i) q^{36} +(0.973046 - 3.63146i) q^{37} +(1.13753 - 1.97025i) q^{38} +(1.23924 - 6.12081i) q^{39} +(3.51160 + 6.08227i) q^{40} +(-7.55452 + 2.02423i) q^{41} +(-0.0296298 - 9.56435i) q^{42} +(0.187567 - 0.108292i) q^{43} +(-1.67127 - 1.67127i) q^{44} +(-6.65528 + 1.82755i) q^{45} +(-0.868921 + 0.232827i) q^{46} +(2.72952 + 10.1867i) q^{47} +(1.31743 - 2.29827i) q^{48} +(-17.1621 - 9.90853i) q^{49} +(0.0807314 + 0.301294i) q^{50} +(-0.124722 - 0.214487i) q^{51} +(-0.980914 - 2.95271i) q^{52} +8.00631i q^{53} +(3.95419 + 3.88136i) q^{54} +(-3.15052 - 5.45686i) q^{55} +(-7.90459 - 13.6912i) q^{56} +(3.57242 + 0.945376i) q^{57} +(0.456203 - 0.456203i) q^{58} +(5.26532 - 5.26532i) q^{59} +(-2.42386 + 2.43893i) q^{60} +(0.675442 + 1.16990i) q^{61} +(-1.86577 - 3.23160i) q^{62} +(14.9810 - 4.11380i) q^{63} -7.83049i q^{64} +(-0.488596 - 8.28034i) q^{65} +(-2.51573 + 4.38871i) q^{66} +(1.98346 + 7.40238i) q^{67} +(-0.107054 - 0.0618075i) q^{68} +(-0.734510 - 1.26316i) q^{69} +(-3.28794 - 12.2708i) q^{70} +(-7.04646 + 1.88809i) q^{71} +(8.86096 + 2.31554i) q^{72} +(-3.76736 - 3.76736i) q^{73} +(-3.47184 + 2.00447i) q^{74} +(-0.437992 + 0.254687i) q^{75} +(1.77838 - 0.476516i) q^{76} +(7.09179 + 12.2833i) q^{77} +(-5.54954 + 3.68075i) q^{78} +(1.62641 - 2.81703i) q^{79} +(0.910674 - 3.39868i) q^{80} +(-4.40307 + 7.84939i) q^{81} +(7.22246 + 4.16989i) q^{82} +(-14.7099 + 3.94150i) q^{83} +(5.45610 - 5.49002i) q^{84} +(-0.233027 - 0.233027i) q^{85} +(-0.223081 - 0.0597743i) q^{86} +(0.909174 + 0.521163i) q^{87} +8.36151i q^{88} +(-14.2431 - 3.81643i) q^{89} +(6.39613 + 3.64015i) q^{90} +(1.09983 + 18.6390i) q^{91} +(-0.630459 - 0.363996i) q^{92} +(4.27260 - 4.29915i) q^{93} +(5.62279 - 9.73895i) q^{94} +4.90830 q^{95} +(7.48020 - 2.02917i) q^{96} +(0.525725 + 0.140868i) q^{97} +(5.46924 + 20.4115i) q^{98} +(-7.94983 - 2.07744i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) $ 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.754009	−	0.754009i	−0.533165	−	0.533165i	0.388348	−	0.921513i	$-0.373046\pi$
$2$	−0.754009	−	0.754009i	−0.533165	−	0.533165i	−0.921513	+	0.388348i	$0.873046\pi$
$3$	0.861374	−	1.50268i	0.497315	−	0.867570i
$3$	0.861374	−	1.50268i	0.497315	−	0.867570i
$4$		−	0.862941i		−	0.431471i
$5$	0.595426	−	2.22216i	0.266282	−	0.993779i	−0.695178	−	0.718837i	$-0.744675\pi$
$5$	0.595426	−	2.22216i	0.266282	−	0.993779i	0.961461	−	0.274942i	$-0.0886587\pi$
$6$	−1.78251	+	0.483547i	−0.727709	+	0.197407i
$7$	−1.34030	+	5.00206i	−0.506585	+	1.89060i	−0.0547531	+	0.998500i	$0.517437\pi$
$7$	−1.34030	+	5.00206i	−0.506585	+	1.89060i	−0.451832	+	0.892103i	$0.649229\pi$
$8$	−2.15868	+	2.15868i	−0.763210	+	0.763210i
$9$	−1.51607	−	2.58873i	−0.505356	−	0.862911i
$10$	−2.12448	+	1.22657i	−0.671821	+	0.387876i
$11$	1.93671	−	1.93671i	0.583941	−	0.583941i	−0.352043	−	0.935984i	$-0.614513\pi$
$11$	1.93671	−	1.93671i	0.583941	−	0.583941i	0.935984	+	0.352043i	$0.114513\pi$
$12$	−1.29672	−	0.743315i	−0.374331	−	0.214577i
$13$	3.42168	−	1.13671i	0.949003	−	0.315267i
$13$	3.42168	−	1.13671i	0.949003	−	0.315267i
$14$	4.78220	−	2.76100i	1.27810	−	0.737909i
$15$	−2.82630	−	2.80884i	−0.729747	−	0.725240i
$16$	1.52945			0.382363
$17$	0.0716242	−	0.124057i	0.0173714	−	0.0300882i	−0.857209	−	0.514969i	$-0.827804\pi$
$17$	0.0716242	−	0.124057i	0.0173714	−	0.0300882i	0.874580	+	0.484880i	$0.161137\pi$
$18$	−0.808798	+	3.09506i	−0.190636	+	0.729512i
$19$	0.552200	+	2.06084i	0.126683	+	0.472789i	0.999894	−	0.0145541i	$-0.00463288\pi$
$19$	0.552200	+	2.06084i	0.126683	+	0.472789i	−0.873211	+	0.487343i	$0.837966\pi$
$20$	−1.91759	−	0.513817i	−0.428787	−	0.114893i
$21$	6.36198	+	6.32269i	1.38830	+	1.37972i
$22$	−2.92060			−0.622674
$23$	0.421808	−	0.730594i	0.0879531	−	0.152339i	−0.818693	−	0.574232i	$-0.805301\pi$
$23$	0.421808	−	0.730594i	0.0879531	−	0.152339i	0.906646	+	0.421893i	$0.138634\pi$
$24$	1.38437	+	5.10323i	0.282583	+	1.04169i
$25$	−0.253329	−	0.146260i	−0.0506658	−	0.0292519i
$26$	−3.43707	−	1.72289i	−0.674064	−	0.337886i
$27$	−5.19593	+	0.0482913i	−0.999957	+	0.00929366i
$28$	4.31649	+	1.15660i	0.815739	+	0.218577i
$29$			0.605036i			0.112352i	0.998421	+	0.0561762i	$0.0178909\pi$
$29$			0.605036i			0.112352i	−0.998421	+	0.0561762i	$0.982109\pi$
$30$	0.0131630	+	4.24895i	0.00240322	+	0.775748i
$31$	3.38018	+	0.905716i	0.607098	+	0.162671i	0.549256	−	0.835654i	$-0.314911\pi$
$31$	3.38018	+	0.905716i	0.607098	+	0.162671i	0.0578423	+	0.998326i	$0.481578\pi$
$32$	3.16415	+	3.16415i	0.559347	+	0.559347i
$33$	−1.24202	−	4.57849i	−0.216208	−	0.797013i
$34$	−0.147545	+	0.0395346i	−0.0253038	+	0.00678013i
$35$	10.3173	+	5.95671i	1.74395	+	1.00687i
$36$	−2.23392	+	1.30828i	−0.372321	+	0.218046i
$37$	0.973046	−	3.63146i	0.159968	−	0.597008i	−0.838661	−	0.544654i	$-0.816661\pi$
$37$	0.973046	−	3.63146i	0.159968	−	0.597008i	0.998629	−	0.0523539i	$-0.0166724\pi$
$38$	1.13753	−	1.97025i	0.184531	−	0.319617i
$39$	1.23924	−	6.12081i	0.198437	−	0.980114i
$40$	3.51160	+	6.08227i	0.555233	+	0.961691i
$41$	−7.55452	+	2.02423i	−1.17982	+	0.316131i	−0.794854	−	0.606801i	$-0.792453\pi$
$41$	−7.55452	+	2.02423i	−1.17982	+	0.316131i	−0.384963	+	0.922932i	$0.625786\pi$
$42$	−0.0296298	−	9.56435i	−0.00457198	−	1.47581i
$43$	0.187567	−	0.108292i	0.0286038	−	0.0165144i	−0.485630	−	0.874164i	$-0.661410\pi$
$43$	0.187567	−	0.108292i	0.0286038	−	0.0165144i	0.514234	+	0.857650i	$0.328076\pi$
$44$	−1.67127	−	1.67127i	−0.251953	−	0.251953i
$45$	−6.65528	+	1.82755i	−0.992111	+	0.272435i
$46$	−0.868921	+	0.232827i	−0.128115	+	0.0343284i
$47$	2.72952	+	10.1867i	0.398141	+	1.48588i	0.816363	+	0.577539i	$0.195987\pi$
$47$	2.72952	+	10.1867i	0.398141	+	1.48588i	−0.418222	+	0.908345i	$0.637347\pi$
$48$	1.31743	−	2.29827i	0.190155	−	0.331726i
$49$	−17.1621	−	9.90853i	−2.45172	−	1.41550i
$50$	0.0807314	+	0.301294i	0.0114171	+	0.0426093i
$51$	−0.124722	−	0.214487i	−0.0174645	−	0.0300342i
$52$	−0.980914	−	2.95271i	−0.136028	−	0.409467i
$53$			8.00631i			1.09975i	0.835246	+	0.549876i	$0.185325\pi$
$53$			8.00631i			1.09975i	−0.835246	+	0.549876i	$0.814675\pi$
$54$	3.95419	+	3.88136i	0.538097	+	0.528187i
$55$	−3.15052	−	5.45686i	−0.424816	−	0.735802i
$56$	−7.90459	−	13.6912i	−1.05630	−	1.82956i
$57$	3.57242	+	0.945376i	0.473179	+	0.125218i
$58$	0.456203	−	0.456203i	0.0599024	−	0.0599024i
$59$	5.26532	−	5.26532i	0.685487	−	0.685487i	−0.275744	−	0.961231i	$-0.588924\pi$
$59$	5.26532	−	5.26532i	0.685487	−	0.685487i	0.961231	+	0.275744i	$0.0889243\pi$
$60$	−2.42386	+	2.43893i	−0.312920	+	0.314864i
$61$	0.675442	+	1.16990i	0.0864815	+	0.149790i	0.906022	−	0.423232i	$-0.139104\pi$
$61$	0.675442	+	1.16990i	0.0864815	+	0.149790i	−0.819540	+	0.573022i	$0.805771\pi$
$62$	−1.86577	−	3.23160i	−0.236953	−	0.410414i
$63$	14.9810	−	4.11380i	1.88743	−	0.518290i
$64$		−	7.83049i		−	0.978811i
$65$	−0.488596	−	8.28034i	−0.0606028	−	1.02705i
$66$	−2.51573	+	4.38871i	−0.309665	+	0.540213i
$67$	1.98346	+	7.40238i	0.242318	+	0.904345i	0.974712	+	0.223464i	$0.0717364\pi$
$67$	1.98346	+	7.40238i	0.242318	+	0.904345i	−0.732394	+	0.680881i	$0.761597\pi$
$68$	−0.107054	−	0.0618075i	−0.0129822	−	0.00749526i
$69$	−0.734510	−	1.26316i	−0.0884246	−	0.152066i
$70$	−3.28794	−	12.2708i	−0.392985	−	1.46664i
$71$	−7.04646	+	1.88809i	−0.836261	+	0.224075i	−0.651443	−	0.758697i	$-0.725836\pi$
$71$	−7.04646	+	1.88809i	−0.836261	+	0.224075i	−0.184818	+	0.982773i	$0.559169\pi$
$72$	8.86096	+	2.31554i	1.04427	+	0.272889i
$73$	−3.76736	−	3.76736i	−0.440936	−	0.440936i	0.451391	−	0.892326i	$-0.350928\pi$
$73$	−3.76736	−	3.76736i	−0.440936	−	0.440936i	−0.892326	+	0.451391i	$0.850928\pi$
$74$	−3.47184	+	2.00447i	−0.403593	+	0.233014i
$75$	−0.437992	+	0.254687i	−0.0505750	+	0.0294088i
$76$	1.77838	−	0.476516i	0.203994	−	0.0546601i
$77$	7.09179	+	12.2833i	0.808185	+	1.39982i
$78$	−5.54954	+	3.68075i	−0.628362	+	0.416762i
$79$	1.62641	−	2.81703i	0.182986	−	0.316941i	−0.759910	−	0.650028i	$-0.774757\pi$
$79$	1.62641	−	2.81703i	0.182986	−	0.316941i	0.942896	+	0.333087i	$0.108090\pi$
$80$	0.910674	−	3.39868i	0.101816	−	0.379984i
$81$	−4.40307	+	7.84939i	−0.489230	+	0.872155i
$82$	7.22246	+	4.16989i	0.797587	+	0.460487i
$83$	−14.7099	+	3.94150i	−1.61462	+	0.432636i	−0.949415	−	0.314025i	$-0.898323\pi$
$83$	−14.7099	+	3.94150i	−1.61462	+	0.432636i	−0.665205	+	0.746661i	$0.731656\pi$
$84$	5.45610	−	5.49002i	0.595310	−	0.599010i
$85$	−0.233027	−	0.233027i	−0.0252753	−	0.0252753i
$86$	−0.223081	−	0.0597743i	−0.0240554	−	0.00644563i
$87$	0.909174	+	0.521163i	0.0974736	+	0.0558745i
$88$			8.36151i			0.891340i
$89$	−14.2431	−	3.81643i	−1.50977	−	0.404541i	−0.593409	−	0.804901i	$-0.702218\pi$
$89$	−14.2431	−	3.81643i	−1.50977	−	0.404541i	−0.916358	+	0.400361i	$0.868885\pi$
$90$	6.39613	+	3.64015i	0.674211	+	0.383706i
$91$	1.09983	+	18.6390i	0.115293	+	1.95390i
$92$	−0.630459	−	0.363996i	−0.0657299	−	0.0379492i
$93$	4.27260	−	4.29915i	0.443048	−	0.445801i
$94$	5.62279	−	9.73895i	0.579946	−	1.00450i
$95$	4.90830			0.503581
$96$	7.48020	−	2.02917i	0.763445	−	0.207101i
$97$	0.525725	+	0.140868i	0.0533793	+	0.0143029i	0.285410	−	0.958406i	$-0.407870\pi$
$97$	0.525725	+	0.140868i	0.0533793	+	0.0143029i	−0.232031	+	0.972708i	$0.574537\pi$
$98$	5.46924	+	20.4115i	0.552476	+	2.06187i
$99$	−7.94983	−	2.07744i	−0.798988	−	0.208791i
$100$	−0.126213	+	0.218608i	−0.0126213	+	0.0218608i
$101$	3.51090			0.349347			0.174674	−	0.984626i	$-0.444113\pi$
$101$	3.51090			0.349347			0.174674	+	0.984626i	$0.444113\pi$
$102$	−0.0676839	+	0.255767i	−0.00670171	+	0.0253247i
$103$	0.661851	−	0.382120i	0.0652141	−	0.0376514i	−0.467038	−	0.884237i	$-0.654679\pi$
$103$	0.661851	−	0.382120i	0.0652141	−	0.0376514i	0.532253	+	0.846586i	$0.321346\pi$
$104$	−4.93252	+	9.84012i	−0.483674	+	0.964903i
$105$	17.8381	−	10.3726i	1.74082	−	1.01227i
$106$	6.03683	−	6.03683i	0.586349	−	0.586349i
$107$	5.29840	−	3.05903i	0.512216	−	0.295728i	−0.221528	−	0.975154i	$-0.571104\pi$
$107$	5.29840	−	3.05903i	0.512216	−	0.295728i	0.733744	+	0.679426i	$0.237771\pi$
$108$	0.0416725	+	4.48378i	0.00400994	+	0.431452i
$109$	−3.64352	+	3.64352i	−0.348986	+	0.348986i	−0.859732	−	0.510746i	$-0.829369\pi$
$109$	−3.64352	+	3.64352i	−0.348986	+	0.348986i	0.510746	+	0.859732i	$0.329369\pi$
$110$	−1.73900	+	6.49004i	−0.165807	+	0.618801i
$111$	−4.61875	−	4.59022i	−0.438392	−	0.435684i
$112$	−2.04992	+	7.65041i	−0.193699	+	0.722896i
$113$		−	9.31035i		−	0.875844i	−0.899013	−	0.437922i	$-0.855715\pi$
$113$		−	9.31035i		−	0.875844i	0.899013	−	0.437922i	$-0.144285\pi$
$114$	−1.98082	−	3.40646i	−0.185520	−	0.319044i
$115$	−1.37234	−	1.37234i	−0.127971	−	0.127971i
$116$	0.522111			0.0484768
$117$	−8.13014	−	7.13448i	−0.751632	−	0.659583i
$118$	−7.94020			−0.730955
$119$	0.524542	+	0.524542i	0.0480847	+	0.0480847i
$120$	12.1645	−	0.0376848i	1.11046	−	0.00344014i
$121$			3.49827i			0.318025i
$122$	0.372826	−	1.39140i	0.0337541	−	0.125972i
$123$	−3.46551	+	13.0956i	−0.312475	+	1.18079i
$124$	0.781580	−	2.91690i	0.0701879	−	0.261945i
$125$	7.65781	−	7.65781i	0.684936	−	0.684936i
$126$	−14.3976	−	8.19396i	−1.28264	−	0.729976i
$127$	0.310458	−	0.179243i	0.0275487	−	0.0159052i	−0.486162	−	0.873868i	$-0.661604\pi$
$127$	0.310458	−	0.179243i	0.0275487	−	0.0159052i	0.513711	+	0.857963i	$0.328270\pi$
$128$	0.424033	−	0.424033i	0.0374796	−	0.0374796i
$129$	−0.00116214	−	0.375133i	−0.000102321	−	0.0330286i
$130$	−5.87504	+	6.61186i	−0.515276	+	0.579898i
$131$	−10.1169	+	5.84101i	−0.883920	+	0.510331i	−0.871949	−	0.489597i	$-0.837144\pi$
$131$	−10.1169	+	5.84101i	−0.883920	+	0.510331i	−0.0119710	+	0.999928i	$0.503811\pi$
$132$	−3.95097	+	1.07179i	−0.343888	+	0.0932872i
$133$	−11.0486			−0.958032
$134$	4.08591	−	7.07701i	0.352969	−	0.611361i
$135$	−2.98648	+	11.5749i	−0.257035	+	0.996211i
$136$	0.113185	+	0.422413i	0.00970556	+	0.0362216i
$137$	15.1873	+	4.06943i	1.29754	+	0.347675i	0.840520	−	0.541781i	$-0.182250\pi$
$137$	15.1873	+	4.06943i	1.29754	+	0.347675i	0.457021	+	0.889456i	$0.348916\pi$
$138$	−0.398603	+	1.50626i	−0.0339314	+	0.128221i
$139$	13.7650			1.16753			0.583767	−	0.811922i	$-0.301578\pi$
$139$	13.7650			1.16753			0.583767	+	0.811922i	$0.301578\pi$
$140$	5.14029	−	8.90325i	0.434434	−	0.752462i
$141$	17.6585	+	4.67298i	1.48711	+	0.393536i
$142$	6.73673	+	3.88945i	0.565334	+	0.326396i
$143$	4.42533	−	8.82830i	0.370065	−	0.738260i
$144$	−2.31875	−	3.95934i	−0.193229	−	0.329945i
$145$	1.34449	+	0.360254i	0.111654	+	0.0299175i
$146$			5.68124i			0.470183i
$147$	−29.6723	+	17.2541i	−2.44733	+	1.42309i
$148$	−3.13373	−	0.839681i	−0.257591	−	0.0690214i
$149$	−9.35362	−	9.35362i	−0.766278	−	0.766278i	0.211171	−	0.977449i	$-0.432272\pi$
$149$	−9.35362	−	9.35362i	−0.766278	−	0.766278i	−0.977449	+	0.211171i	$0.932272\pi$
$150$	0.522286	+	0.138213i	0.0426445	+	0.0112851i
$151$	−11.1072	+	2.97615i	−0.903888	+	0.242196i	−0.680685	−	0.732576i	$-0.738318\pi$
$151$	−11.1072	+	2.97615i	−0.903888	+	0.242196i	−0.223203	+	0.974772i	$0.571651\pi$
$152$	−5.64072	−	3.25667i	−0.457523	−	0.264151i
$153$	−0.429737	+	0.00266262i	−0.0347422	+	0.000215260i
$154$	3.91448	−	14.6090i	0.315438	−	1.17723i
$155$	4.02529	−	6.97201i	0.323319	−	0.560005i
$156$	−5.28190	−	1.06939i	−0.422890	−	0.0856198i
$157$	−4.68972	−	8.12283i	−0.374280	−	0.648272i	0.615939	−	0.787794i	$-0.288777\pi$
$157$	−4.68972	−	8.12283i	−0.374280	−	0.648272i	−0.990219	+	0.139522i	$0.955443\pi$
$158$	−3.35040	+	0.897737i	−0.266543	+	0.0714201i
$159$	12.0309	+	6.89643i	0.954112	+	0.546923i
$160$	8.91525	−	5.14722i	0.704812	−	0.406924i
$161$	3.08913	+	3.08913i	0.243457	+	0.243457i
$162$	9.23847	−	2.59855i	0.725843	−	0.204162i
$163$	−14.3617	+	3.84819i	−1.12489	+	0.301414i	−0.772861	−	0.634575i	$-0.781175\pi$
$163$	−14.3617	+	3.84819i	−1.12489	+	0.301414i	−0.352030	+	0.935989i	$0.614508\pi$
$164$	1.74679	+	6.51910i	0.136401	+	0.509056i
$165$	−10.9137	+	0.0338099i	−0.849627	+	0.00263209i
$166$	14.0633	+	8.11946i	1.09152	+	0.630192i
$167$	−0.558665	−	2.08497i	−0.0432308	−	0.161339i	0.940936	−	0.338585i	$-0.109948\pi$
$167$	−0.558665	−	2.08497i	−0.0432308	−	0.161339i	−0.984167	+	0.177245i	$0.943281\pi$
$168$	−27.3822	+	0.0848284i	−2.11258	+	0.00654465i
$169$	10.4158	−	7.77892i	0.801214	−	0.598378i
$170$			0.351409i			0.0269518i
$171$	4.49779	−	4.55387i	0.343954	−	0.348243i
$172$	−0.0934497	−	0.161860i	−0.00712547	−	0.0123417i
$173$	6.04205	+	10.4651i	0.459369	+	0.795650i	0.998928	−	0.0462976i	$-0.0147423\pi$
$173$	6.04205	+	10.4651i	0.459369	+	0.795650i	−0.539559	+	0.841948i	$0.681409\pi$
$174$	−0.292564	−	1.07849i	−0.0221792	−	0.0817598i
$175$	1.07114	−	1.07114i	0.0809704	−	0.0809704i
$176$	2.96211	−	2.96211i	0.223277	−	0.223277i
$177$	−3.37666	−	12.4475i	−0.253805	−	0.935610i
$178$	7.86181	+	13.6171i	0.589267	+	1.02064i
$179$	−1.54606	−	2.67786i	−0.115558	−	0.200152i	0.802445	−	0.596727i	$-0.203532\pi$
$179$	−1.54606	−	2.67786i	−0.115558	−	0.200152i	−0.918003	+	0.396574i	$0.870199\pi$
$180$	1.57706	+	5.74311i	0.117547	+	0.428066i
$181$		−	20.3888i		−	1.51549i	−0.652550	−	0.757745i	$-0.726301\pi$
$181$		−	20.3888i		−	1.51549i	0.652550	−	0.757745i	$-0.273699\pi$
$182$	13.2247	−	14.8832i	0.980279	−	1.10322i
$183$	2.33979	−	0.00724853i	0.172962	−	0.000535827i
$184$	0.666569	+	2.48767i	0.0491401	+	0.183394i
$185$	−7.49030	−	4.32453i	−0.550698	−	0.317945i
$186$	−6.46318	+	0.0200225i	−0.473903	+	0.00146812i
$187$	−0.101547	−	0.378978i	−0.00742584	−	0.0277136i
$188$	8.79053	−	2.35541i	0.641115	−	0.171786i
$189$	6.72254	−	26.0551i	0.488993	−	1.89523i
$190$	−3.70090	−	3.70090i	−0.268492	−	0.268492i
$191$	8.18928	−	4.72808i	0.592555	−	0.342112i	−0.173552	−	0.984825i	$-0.555524\pi$
$191$	8.18928	−	4.72808i	0.592555	−	0.342112i	0.766107	+	0.642713i	$0.222191\pi$
$192$	−11.7667	−	6.74498i	−0.849188	−	0.486777i
$193$	0.383474	−	0.102752i	0.0276031	−	0.00739622i	−0.244991	−	0.969525i	$-0.578785\pi$
$193$	0.383474	−	0.102752i	0.0276031	−	0.00739622i	0.272594	+	0.962129i	$0.412118\pi$
$194$	−0.290186	−	0.502617i	−0.0208341	−	0.0360858i
$195$	−12.8635	−	6.39827i	−0.921176	−	0.458190i
$196$	−8.55047	+	14.8099i	−0.610748	+	1.05785i
$197$	0.713601	−	2.66320i	0.0508420	−	0.189745i	−0.935834	−	0.352440i	$-0.885352\pi$
$197$	0.713601	−	2.66320i	0.0508420	−	0.189745i	0.986676	+	0.162695i	$0.0520187\pi$
$198$	4.42783	+	7.56065i	0.314672	+	0.537312i
$199$	13.4785	+	7.78181i	0.955465	+	0.551638i	0.894774	−	0.446519i	$-0.147336\pi$
$199$	13.4785	+	7.78181i	0.955465	+	0.551638i	0.0606908	+	0.998157i	$0.480670\pi$
$200$	0.862586	−	0.231129i	0.0609940	−	0.0163433i
$201$	12.8319	+	3.39572i	0.905091	+	0.239516i
$202$	−2.64725	−	2.64725i	−0.186260	−	0.186260i
$203$	−3.02643	−	0.810930i	−0.212414	−	0.0569161i
$204$	−0.185090	+	0.107628i	−0.0129589	+	0.00753544i
$205$			17.9926i			1.25666i
$206$	−0.787163	−	0.210920i	−0.0548443	−	0.0146955i
$207$	−2.53080	+	0.0156807i	−0.175903	+	0.00108988i
$208$	5.23329	−	1.73854i	0.362863	−	0.120546i
$209$	5.06071	+	2.92180i	0.350057	+	0.202105i
$210$	−21.2711	−	5.62902i	−1.46785	−	0.388439i
$211$	−4.61191	+	7.98807i	−0.317497	+	0.549921i	−0.979965	−	0.199169i	$-0.936176\pi$
$211$	−4.61191	+	7.98807i	−0.317497	+	0.549921i	0.662468	+	0.749090i	$0.269509\pi$
$212$	6.90898			0.474510
$213$	−3.23245	+	12.2149i	−0.221484	+	0.836951i
$214$	−6.30158	−	1.68850i	−0.430767	−	0.115424i
$215$	−0.128960	−	0.481284i	−0.00879498	−	0.0328233i
$216$	11.1121	−	11.3206i	0.756084	−	0.770270i
$217$	−9.06090	+	15.6939i	−0.615094	+	1.06537i
$218$	5.49449			0.372134
$219$	−8.90622	+	2.41601i	−0.601827	+	0.163259i
$220$	−4.70894	+	2.71871i	−0.317477	+	0.183295i
$221$	0.104058	−	0.505898i	0.00699973	−	0.0340304i
$222$	0.0215110	+	6.94364i	0.00144372	+	0.466027i
$223$	1.36740	−	1.36740i	0.0915676	−	0.0915676i	−0.659839	−	0.751407i	$-0.729376\pi$
$223$	1.36740	−	1.36740i	0.0915676	−	0.0915676i	0.751407	+	0.659839i	$0.229376\pi$
$224$	−20.0682	+	11.5864i	−1.34086	+	0.774146i
$225$	0.00543719	+	0.877541i	0.000362480	+	0.0585027i
$226$	−7.02009	+	7.02009i	−0.466969	+	0.466969i
$227$	4.96201	−	18.5185i	0.329340	−	1.22912i	−0.580536	−	0.814235i	$-0.697157\pi$
$227$	4.96201	−	18.5185i	0.329340	−	1.22912i	0.909876	−	0.414880i	$-0.136177\pi$
$228$	0.815804	−	3.08279i	0.0540279	−	0.204163i
$229$	4.89219	−	18.2579i	0.323285	−	1.20652i	−0.592739	−	0.805394i	$-0.701954\pi$
$229$	4.89219	−	18.2579i	0.323285	−	1.20652i	0.916025	−	0.401122i	$-0.131380\pi$
$230$			2.06951i			0.136460i
$231$	24.5666	−	0.0761058i	1.61636	−	0.00500739i
$232$	−1.30608	−	1.30608i	−0.0857485	−	0.0857485i
$233$	−15.0092			−0.983286			−0.491643	−	0.870797i	$-0.663603\pi$
$233$	−15.0092			−0.983286			−0.491643	+	0.870797i	$0.663603\pi$
$234$	0.750735	+	11.5097i	0.0490771	+	0.752410i
$235$	24.2617			1.58266
$236$	−4.54366	−	4.54366i	−0.295767	−	0.295767i
$237$	−2.83213	−	4.87049i	−0.183967	−	0.316373i
$238$		−	0.791019i		−	0.0512741i
$239$	1.78174	−	6.64956i	0.115251	−	0.430124i	−0.884054	−	0.467384i	$-0.845196\pi$
$239$	1.78174	−	6.64956i	0.115251	−	0.430124i	0.999306	+	0.0372603i	$0.0118631\pi$
$240$	−4.32268	−	4.29598i	−0.279028	−	0.277305i
$241$	0.264008	−	0.985292i	0.0170063	−	0.0634683i	−0.956901	−	0.290413i	$-0.906207\pi$
$241$	0.264008	−	0.985292i	0.0170063	−	0.0634683i	0.973908	+	0.226945i	$0.0728738\pi$
$242$	2.63773	−	2.63773i	0.169560	−	0.169560i
$243$	8.00240	+	13.3777i	0.513354	+	0.858177i
$244$	1.00956	−	0.582867i	0.0646301	−	0.0373142i
$245$	−32.2371	+	32.2371i	−2.05955	+	2.05955i
$246$	12.4872	−	7.26118i	0.796157	−	0.462956i
$247$	4.23203	+	6.42384i	0.269277	+	0.408739i
$248$	−9.25189	+	5.34158i	−0.587496	+	0.339191i
$249$	−6.74792	+	25.4993i	−0.427632	+	1.61595i
$250$	−11.5481			−0.730367
$251$	14.6482	−	25.3714i	0.924586	−	1.60143i	0.132359	−	0.991202i	$-0.457745\pi$
$251$	14.6482	−	25.3714i	0.924586	−	1.60143i	0.792226	−	0.610228i	$-0.208922\pi$
$252$	−3.54996	−	12.9277i	−0.223627	−	0.814369i
$253$	−0.598029	−	2.23187i	−0.0375977	−	0.140317i
$254$	−0.369239	−	0.0989372i	−0.0231681	−	0.00620787i
$255$	−0.550887	+	0.149440i	−0.0344979	+	0.00935832i
$256$	−16.3004			−1.01878
$257$	−9.09224	+	15.7482i	−0.567159	+	0.982347i	0.429687	+	0.902978i	$0.358624\pi$
$257$	−9.09224	+	15.7482i	−0.567159	+	0.982347i	−0.996845	+	0.0793694i	$0.974709\pi$
$258$	−0.281977	+	0.283730i	−0.0175551	+	0.0176642i
$259$	16.8606	+	9.73448i	1.04767	+	0.604871i
$260$	−7.14545	+	0.421629i	−0.443142	+	0.0261483i
$261$	1.56628	−	0.917277i	0.0969501	−	0.0567780i
$262$	12.0324	+	3.22408i	0.743366	+	0.199184i
$263$			19.5534i			1.20572i	0.797848	+	0.602858i	$0.205971\pi$
$263$			19.5534i			1.20572i	−0.797848	+	0.602858i	$0.794029\pi$
$264$	12.5646	+	7.20239i	0.773300	+	0.443276i
$265$	17.7913	+	4.76716i	1.09291	+	0.292845i
$266$	8.33071	+	8.33071i	0.510789	+	0.510789i
$267$	−18.0035	+	18.1154i	−1.10180	+	1.10864i
$268$	6.38782	−	1.71161i	0.390198	−	0.104553i
$269$	23.9955	+	13.8538i	1.46303	+	0.844683i	0.999150	−	0.0412138i	$-0.0131225\pi$
$269$	23.9955	+	13.8538i	1.46303	+	0.844683i	0.463883	+	0.885896i	$0.346456\pi$
$270$	10.9794	−	6.47577i	0.668187	−	0.394103i
$271$	2.16310	−	8.07278i	0.131399	−	0.490387i	−0.868588	−	0.495535i	$-0.834972\pi$
$271$	2.16310	−	8.07278i	0.131399	−	0.490387i	0.999987	+	0.00514827i	$0.00163875\pi$
$272$	0.109546	−	0.189739i	0.00664218	−	0.0115046i
$273$	28.9557	+	14.4025i	1.75248	+	0.871677i
$274$	−8.38299	−	14.5198i	−0.506435	−	0.877171i
$275$	−0.773889	+	0.207363i	−0.0466673	+	0.0125045i
$276$	−1.09003	+	0.633839i	−0.0656120	+	0.0381526i
$277$	13.6565	−	7.88460i	0.820541	−	0.473740i	−0.0300620	−	0.999548i	$-0.509570\pi$
$277$	13.6565	−	7.88460i	0.820541	−	0.473740i	0.850603	+	0.525808i	$0.176237\pi$
$278$	−10.3789	−	10.3789i	−0.622488	−	0.622488i
$279$	−2.77993	−	10.1235i	−0.166430	−	0.606079i
$280$	−35.1305	+	9.41319i	−2.09945	+	0.562546i
$281$	3.53952	+	13.2097i	0.211150	+	0.788022i	0.987486	+	0.157704i	$0.0504091\pi$
$281$	3.53952	+	13.2097i	0.211150	+	0.788022i	−0.776337	+	0.630319i	$0.782924\pi$
$282$	−9.79116	−	16.8381i	−0.583055	−	1.00269i
$283$	−11.6559	−	6.72951i	−0.692869	−	0.400028i	0.111817	−	0.993729i	$-0.464333\pi$
$283$	−11.6559	−	6.72951i	−0.692869	−	0.400028i	−0.804686	+	0.593701i	$0.797666\pi$
$284$	1.62931	+	6.08068i	0.0966820	+	0.360822i
$285$	4.22789	−	7.37559i	0.250438	−	0.436892i
$286$	−9.99336	+	3.31988i	−0.590920	+	0.196308i
$287$		−	40.5013i		−	2.39071i
$288$	3.39407	−	12.9882i	0.199997	−	0.765337i
$289$	8.48974	+	14.7047i	0.499396	+	0.864980i
$290$	−0.742120	−	1.28539i	−0.0435788	−	0.0754807i
$291$	0.664525	−	0.668655i	0.0389551	−	0.0391972i
$292$	−3.25101	+	3.25101i	−0.190251	+	0.190251i
$293$	5.04007	−	5.04007i	0.294444	−	0.294444i	−0.544389	−	0.838833i	$-0.683238\pi$
$293$	5.04007	−	5.04007i	0.294444	−	0.294444i	0.838833	+	0.544389i	$0.183238\pi$
$294$	35.3829	+	9.36343i	2.06357	+	0.546086i
$295$	−8.56527	−	14.8355i	−0.498689	−	0.863756i
$296$	5.73867	+	9.93966i	0.333553	+	0.577731i
$297$	−9.96950	+	10.1566i	−0.578489	+	0.589343i
$298$			14.1054i			0.817105i
$299$	0.612820	−	2.97933i	0.0354403	−	0.172299i
$300$	0.219780	+	0.377961i	0.0126890	+	0.0218216i
$301$	0.290288	+	1.08337i	0.0167319	+	0.0624443i
$302$	10.6189	+	6.13085i	0.611051	+	0.352791i
$303$	3.02420	−	5.27574i	0.173736	−	0.303083i
$304$	0.844562	+	3.15195i	0.0484390	+	0.180777i
$305$	3.00188	−	0.804351i	0.171887	−	0.0460570i
$306$	0.326033	+	0.322018i	0.0186381	+	0.0184085i
$307$	−8.37481	−	8.37481i	−0.477976	−	0.477976i	0.426508	−	0.904484i	$-0.359744\pi$
$307$	−8.37481	−	8.37481i	−0.477976	−	0.477976i	−0.904484	+	0.426508i	$0.859744\pi$
$308$	10.5998	−	6.11980i	0.603980	−	0.348708i
$309$	−0.00410073	−	1.32370i	−0.000233282	−	0.0753024i
$310$	−8.29206	+	2.22185i	−0.470957	+	0.126193i
$311$	1.34766	+	2.33421i	0.0764186	+	0.132361i	0.901702	−	0.432357i	$-0.142318\pi$
$311$	1.34766	+	2.33421i	0.0764186	+	0.132361i	−0.825284	+	0.564718i	$0.808985\pi$
$312$	10.5378	+	15.8880i	0.596583	+	0.899481i
$313$	1.67357	−	2.89871i	0.0945958	−	0.163845i	−0.814844	−	0.579680i	$-0.803177\pi$
$313$	1.67357	−	2.89871i	0.0945958	−	0.163845i	0.909440	+	0.415836i	$0.136511\pi$
$314$	−2.58860	+	9.66077i	−0.146083	+	0.545189i
$315$	−0.221440	−	35.7396i	−0.0124768	−	2.01370i
$316$	−2.43093	−	1.40350i	−0.136751	−	0.0789530i
$317$	−3.08107	+	0.825569i	−0.173050	+	0.0463686i	−0.344304	−	0.938858i	$-0.611885\pi$
$317$	−3.08107	+	0.825569i	−0.173050	+	0.0463686i	0.171254	+	0.985227i	$0.445218\pi$
$318$	−3.87143	−	14.2714i	−0.217099	−	0.800299i
$319$	1.17178	+	1.17178i	0.0656072	+	0.0656072i
$320$	−17.4006	−	4.66247i	−0.972723	−	0.260640i
$321$	−0.0328281	−	10.5968i	−0.00183229	−	0.591453i
$322$		−	4.65846i		−	0.259606i
$323$	0.295212	+	0.0791017i	0.0164260	+	0.00440134i
$324$	6.77356	+	3.79959i	0.376309	+	0.211088i
$325$	−1.03307	−	0.212492i	−0.0573042	−	0.0117869i
$326$	13.7304	+	7.92724i	0.760456	+	0.439049i
$327$	2.33659	+	8.61346i	0.129214	+	0.476325i
$328$	11.9381	−	20.6775i	0.659174	−	1.14172i
$329$	−54.6129			−3.01091
$330$	8.25449	+	8.20350i	0.454395	+	0.451588i
$331$	−29.7907	−	7.98241i	−1.63745	−	0.438753i	−0.681387	−	0.731923i	$-0.738623\pi$
$331$	−29.7907	−	7.98241i	−1.63745	−	0.438753i	−0.956060	+	0.293170i	$0.905290\pi$
$332$	3.40128	+	12.6938i	0.186670	+	0.696661i
$333$	−10.8761	+	2.98658i	−0.596005	+	0.163664i
$334$	−1.15084	+	1.99332i	−0.0629714	+	0.109070i
$335$	17.6303			0.963244
$336$	9.73034	+	9.67024i	0.530833	+	0.527555i
$337$	−4.37979	+	2.52867i	−0.238582	+	0.137745i	−0.614525	−	0.788897i	$-0.710652\pi$
$337$	−4.37979	+	2.52867i	−0.238582	+	0.137745i	0.375943	+	0.926643i	$0.377319\pi$
$338$	−13.7190	−	1.98822i	−0.746213	−	0.108145i
$339$	−13.9904	−	8.01969i	−0.759856	−	0.435570i
$340$	−0.201088	+	0.201088i	−0.0109056	+	0.0109056i
$341$	8.30056	−	4.79233i	0.449500	−	0.259519i
$342$	−6.82503	+	0.0422875i	−0.369055	+	0.00228664i
$343$	46.9330	−	46.9330i	2.53415	−	2.53415i
$344$	−0.171130	+	0.638667i	−0.00922672	+	0.0344346i
$345$	−3.24428	+	0.880083i	−0.174666	+	0.0473821i
$346$	3.33505	−	12.4466i	0.179293	−	0.669132i
$347$			9.93186i			0.533170i	0.963811	+	0.266585i	$0.0858954\pi$
$347$			9.93186i			0.533170i	−0.963811	+	0.266585i	$0.914105\pi$
$348$	0.449733	−	0.784563i	0.0241082	−	0.0420570i
$349$	−16.7774	−	16.7774i	−0.898073	−	0.898073i	0.0971927	−	0.995266i	$-0.469014\pi$
$349$	−16.7774	−	16.7774i	−0.898073	−	0.898073i	−0.995266	+	0.0971927i	$0.969014\pi$
$350$	−1.61529			−0.0863411
$351$	−17.7239	+	6.07150i	−0.946032	+	0.324073i
$352$	12.2561			0.653252
$353$	−14.8488	−	14.8488i	−0.790322	−	0.790322i	0.191225	−	0.981546i	$-0.438754\pi$
$353$	−14.8488	−	14.8488i	−0.790322	−	0.790322i	−0.981546	+	0.191225i	$0.938754\pi$
$354$	−6.83949	+	11.9315i	−0.363515	+	0.634155i
$355$			16.7826i			0.890726i
$356$	−3.29335	+	12.2910i	−0.174547	+	0.651420i
$357$	1.24004	−	0.336389i	0.0656301	−	0.0178036i
$358$	−0.853384	+	3.18487i	−0.0451027	+	0.168326i
$359$	−8.32119	+	8.32119i	−0.439175	+	0.439175i	−0.891734	−	0.452559i	$-0.850511\pi$
$359$	−8.32119	+	8.32119i	−0.439175	+	0.439175i	0.452559	+	0.891734i	$0.350511\pi$
$360$	10.4215	−	18.3117i	0.549264	−	0.965113i
$361$	12.5124	−	7.22401i	0.658545	−	0.380211i
$362$	−15.3734	+	15.3734i	−0.808006	+	0.808006i
$363$	5.25677	+	3.01332i	0.275909	+	0.158158i
$364$	16.0844	−	0.949085i	0.843049	−	0.0497456i
$365$	−10.6148	+	6.12849i	−0.555607	+	0.320780i
$366$	−1.76969	−	1.75876i	−0.0925031	−	0.0919317i
$367$	−5.67060			−0.296003			−0.148001	−	0.988987i	$-0.547284\pi$
$367$	−5.67060			−0.296003			−0.148001	+	0.988987i	$0.547284\pi$
$368$	0.645135	−	1.11741i	0.0336300	−	0.0582489i
$369$	16.6933	+	16.4878i	0.869021	+	0.858318i
$370$	2.38702	+	8.90848i	0.124095	+	0.463130i
$371$	−40.0481	−	10.7309i	−2.07919	−	0.557118i
$372$	−3.70992	−	3.68700i	−0.192350	−	0.191162i
$373$	−26.9106			−1.39338			−0.696690	−	0.717373i	$-0.745345\pi$
$373$	−26.9106			−1.39338			−0.696690	+	0.717373i	$0.745345\pi$
$374$	−0.209186	+	0.362320i	−0.0108167	+	0.0187351i
$375$	−4.91097	−	18.1035i	−0.253601	−	0.934858i
$376$	−27.8820	−	16.0977i	−1.43791	−	0.830176i
$377$	0.687751	+	2.07024i	0.0354210	+	0.106623i
$378$	−24.7146	+	14.5769i	−1.27118	+	0.749756i
$379$	−26.3773	−	7.06778i	−1.35491	−	0.363047i	−0.492966	−	0.870049i	$-0.664087\pi$
$379$	−26.3773	−	7.06778i	−1.35491	−	0.363047i	−0.861945	+	0.507001i	$0.830754\pi$
$380$		−	4.23558i		−	0.217280i
$381$	−0.00192355	−	0.620913i	−9.85465e−5	−	0.0318103i
$382$	−9.73981	−	2.60977i	−0.498332	−	0.133528i
$383$	11.8575	+	11.8575i	0.605891	+	0.605891i	0.941870	−	0.335978i	$-0.109067\pi$
$383$	11.8575	+	11.8575i	0.605891	+	0.605891i	−0.335978	+	0.941870i	$0.609067\pi$
$384$	−0.271933	−	1.00244i	−0.0138770	−	0.0511553i
$385$	31.5182	−	8.44527i	1.60632	−	0.430411i
$386$	−0.366619	−	0.211667i	−0.0186604	−	0.0107736i
$387$	−0.564704	−	0.321384i	−0.0287055	−	0.0163368i
$388$	0.121560	−	0.453670i	0.00617130	−	0.0230316i
$389$	0.566623	−	0.981420i	0.0287289	−	0.0497600i	−0.851303	−	0.524674i	$-0.824187\pi$
$389$	0.566623	−	0.981420i	0.0287289	−	0.0497600i	0.880032	+	0.474914i	$0.157521\pi$
$390$	4.87486	+	14.5236i	0.246848	+	0.735430i
$391$	−0.0604234	−	0.104656i	−0.00305574	−	0.00529270i
$392$	58.4368	−	15.6581i	2.95151	−	0.790854i
$393$	0.0626830	+	20.2338i	0.00316194	+	1.02066i
$394$	−2.54613	+	1.47001i	−0.128272	+	0.0740581i
$395$	−5.29148	−	5.29148i	−0.266243	−	0.266243i
$396$	−1.79271	+	6.86023i	−0.0900872	+	0.344740i
$397$	17.9346	−	4.80557i	0.900114	−	0.241185i	0.221049	−	0.975263i	$-0.429052\pi$
$397$	17.9346	−	4.80557i	0.900114	−	0.241185i	0.679065	+	0.734078i	$0.262385\pi$
$398$	−4.29535	−	16.0305i	−0.215306	−	0.803534i
$399$	−9.51695	+	16.6024i	−0.476443	+	0.831160i
$400$	−0.387454	−	0.223697i	−0.0193727	−	0.0111848i
$401$	−4.50864	−	16.8265i	−0.225151	−	0.840274i	−0.982344	−	0.187083i	$-0.940097\pi$
$401$	−4.50864	−	16.8265i	−0.225151	−	0.840274i	0.757193	−	0.653191i	$-0.226570\pi$
$402$	−7.11495	−	12.2358i	−0.354861	−	0.610264i
$403$	12.5954	−	0.743215i	0.627423	−	0.0370222i
$404$		−	3.02970i		−	0.150733i
$405$	14.8209	+	14.4581i	0.736456	+	0.718426i
$406$	1.67051	+	2.89340i	0.0829059	+	0.143597i
$407$	−5.14858	−	8.91761i	−0.255206	−	0.442029i
$408$	0.732245	+	0.193775i	0.0362515	+	0.00959330i
$409$	21.9023	−	21.9023i	1.08300	−	1.08300i	0.0867723	−	0.996228i	$-0.472345\pi$
$409$	21.9023	−	21.9023i	1.08300	−	1.08300i	0.996228	−	0.0867723i	$-0.0276553\pi$
$410$	13.5666	−	13.5666i	0.670006	−	0.670006i
$411$	19.1970	−	19.3163i	0.946918	−	0.952804i
$412$	−0.329747	−	0.571138i	−0.0162455	−	0.0281380i
$413$	19.2804	+	33.3946i	0.948725	+	1.64324i
$414$	1.92007	+	1.89642i	0.0943663	+	0.0932041i
$415$			35.0346i			1.71978i
$416$	14.4234	+	7.22998i	0.707166	+	0.354479i
$417$	11.8568	−	20.6843i	0.580631	−	1.01292i
$418$	−1.61276	−	6.01888i	−0.0788824	−	0.294393i
$419$	18.5952	+	10.7360i	0.908436	+	0.524486i	0.879928	−	0.475108i	$-0.157591\pi$
$419$	18.5952	+	10.7360i	0.908436	+	0.524486i	0.0285086	+	0.999594i	$0.490924\pi$
$420$	−8.95098	−	15.3932i	−0.436763	−	0.751112i
$421$	6.14101	+	22.9186i	0.299295	+	1.11698i	0.937746	+	0.347321i	$0.112908\pi$
$421$	6.14101	+	22.9186i	0.299295	+	1.11698i	−0.638452	+	0.769662i	$0.720425\pi$
$422$	9.50050	−	2.54565i	0.462477	−	0.123920i
$423$	22.2325	−	22.5097i	1.08098	−	1.09446i
$424$	−17.2831	−	17.2831i	−0.839341	−	0.839341i
$425$	−0.0362890	+	0.0209515i	−0.00176027	+	0.00101630i
$426$	11.6474	−	6.77285i	0.564320	−	0.328146i
$427$	−6.75721	+	1.81059i	−0.327004	+	0.0876206i
$428$	−2.63977	−	4.57221i	−0.127598	−	0.221006i
$429$	−9.45420	−	14.2543i	−0.456453	−	0.688205i
$430$	−0.265656	+	0.460129i	−0.0128111	+	0.0221894i
$431$	−6.05706	+	22.6052i	−0.291758	+	1.08886i	0.652000	+	0.758219i	$0.273930\pi$
$431$	−6.05706	+	22.6052i	−0.291758	+	1.08886i	−0.943758	+	0.330637i	$0.892736\pi$
$432$	−7.94692	+	0.0738591i	−0.382346	+	0.00355355i
$433$	−23.0080	−	13.2837i	−1.10569	−	0.638372i	−0.167982	−	0.985790i	$-0.553725\pi$
$433$	−23.0080	−	13.2837i	−1.10569	−	0.638372i	−0.937710	+	0.347418i	$0.887058\pi$
$434$	18.6654	−	5.00137i	0.895967	−	0.240074i
$435$	1.69945	−	1.71001i	0.0814825	−	0.0819889i
$436$	3.14414	+	3.14414i	0.150577	+	0.150577i
$437$	1.73856	+	0.465845i	0.0831665	+	0.0222844i
$438$	8.53707	+	4.89368i	0.407917	+	0.233829i
$439$		−	0.426976i		−	0.0203784i	−0.999948	−	0.0101892i	$-0.996757\pi$
$439$		−	0.426976i		−	0.0203784i	0.999948	−	0.0101892i	$-0.00324338\pi$
$440$	18.5806	+	4.97865i	0.885795	+	0.237348i
$441$	0.368349	+	59.4500i	0.0175404	+	2.83095i
$442$	−0.459913	+	0.302991i	−0.0218758	+	0.0144118i
$443$	9.92611	+	5.73084i	0.471604	+	0.272281i	0.716911	−	0.697165i	$-0.245555\pi$
$443$	9.92611	+	5.73084i	0.471604	+	0.272281i	−0.245307	+	0.969445i	$0.578889\pi$
$444$	−3.96109	+	3.98571i	−0.187985	+	0.189153i
$445$	−16.9614	+	29.3780i	−0.804048	+	1.39265i
$446$	−2.06206			−0.0976412
$447$	−22.1124	+	5.99849i	−1.04588	+	0.283719i
$448$	39.1686	+	10.4952i	1.85054	+	0.495852i
$449$	1.66954	+	6.23079i	0.0787903	+	0.294049i	0.994066	−	0.108779i	$-0.0346940\pi$
$449$	1.66954	+	6.23079i	0.0787903	+	0.294049i	−0.915276	+	0.402828i	$0.868027\pi$
$450$	0.657574	−	0.665774i	0.0309983	−	0.0313849i
$451$	−10.7106	+	18.5513i	−0.504342	+	0.873546i
$452$	−8.03428			−0.377901
$453$	−5.09523	+	19.2540i	−0.239395	+	0.904634i
$454$	−17.7045	+	10.2217i	−0.830914	+	0.479728i
$455$	42.0737	+	8.65415i	1.97244	+	0.405713i
$456$	−9.75249	+	5.67096i	−0.456702	+	0.265567i
$457$	7.68615	−	7.68615i	0.359543	−	0.359543i	−0.504101	−	0.863644i	$-0.668176\pi$
$457$	7.68615	−	7.68615i	0.359543	−	0.359543i	0.863644	+	0.504101i	$0.168176\pi$
$458$	−17.4554	+	10.0779i	−0.815636	+	0.470908i
$459$	−0.366163	+	0.648049i	−0.0170910	+	0.0302483i
$460$	−1.18425	+	1.18425i	−0.0552158	+	0.0552158i
$461$	−4.40054	+	16.4230i	−0.204953	+	0.764896i	0.784510	+	0.620116i	$0.212914\pi$
$461$	−4.40054	+	16.4230i	−0.204953	+	0.764896i	−0.989464	+	0.144781i	$0.953752\pi$
$462$	−18.5808	−	18.4660i	−0.864457	−	0.859118i
$463$	−10.0407	+	37.4724i	−0.466630	+	1.74149i	0.184796	+	0.982777i	$0.440838\pi$
$463$	−10.0407	+	37.4724i	−0.466630	+	1.74149i	−0.651427	+	0.758712i	$0.725829\pi$
$464$			0.925373i			0.0429594i
$465$	−7.00938	−	12.0542i	−0.325052	−	0.559001i
$466$	11.3171	+	11.3171i	0.524253	+	0.524253i
$467$	−37.7239			−1.74566			−0.872828	−	0.488028i	$-0.837716\pi$
$467$	−37.7239			−1.74566			−0.872828	+	0.488028i	$0.837716\pi$
$468$	−6.15664	+	7.01583i	−0.284591	+	0.324307i
$469$	−39.6856			−1.83251
$470$	−18.2935	−	18.2935i	−0.843818	−	0.843818i
$471$	−16.2456	+	0.0503278i	−0.748557	+	0.00231898i
$472$			22.7323i			1.04634i
$473$	0.153534	−	0.572995i	0.00705948	−	0.0263463i
$474$	−1.53694	+	5.80785i	−0.0705940	+	0.266763i
$475$	0.161529	−	0.602835i	0.00741147	−	0.0276600i
$476$	0.452649	−	0.452649i	0.0207471	−	0.0207471i
$477$	20.7262	−	12.1381i	0.948988	−	0.555766i
$478$	−6.35728	+	3.67037i	−0.290775	+	0.167879i
$479$	14.7645	−	14.7645i	0.674607	−	0.674607i	−0.284167	−	0.958775i	$-0.591717\pi$
$479$	14.7645	−	14.7645i	0.674607	−	0.674607i	0.958775	+	0.284167i	$0.0917171\pi$
$480$	−0.0552376	−	17.8304i	−0.00252124	−	0.813843i
$481$	−0.798464	−	13.5318i	−0.0364068	−	0.616995i
$482$	−0.941984	+	0.543855i	−0.0429062	+	0.0247719i
$483$	7.30285	−	1.98106i	0.332291	−	0.0901414i
$484$	3.01880			0.137218
$485$	0.626060	−	1.08437i	0.0284279	−	0.0492386i
$486$	4.05299	−	16.1207i	0.183848	−	0.731252i
$487$	4.59917	+	17.1643i	0.208408	+	0.777791i	0.988384	+	0.151980i	$0.0485650\pi$
$487$	4.59917	+	17.1643i	0.208408	+	0.777791i	−0.779975	+	0.625811i	$0.784768\pi$
$488$	−3.98351	−	1.06738i	−0.180325	−	0.0483180i
$489$	−6.58817	+	24.8956i	−0.297927	+	1.12582i
$490$	48.6141			2.19616
$491$	7.29594	−	12.6369i	0.329261	−	0.570297i	−0.653104	−	0.757268i	$-0.726534\pi$
$491$	7.29594	−	12.6369i	0.329261	−	0.570297i	0.982365	+	0.186971i	$0.0598670\pi$
$492$	11.3007	+	2.99053i	0.509477	+	0.134824i
$493$	0.0750588	+	0.0433352i	0.00338048	+	0.00195172i
$494$	1.65264	−	8.03462i	0.0743559	−	0.361494i
$495$	−9.34994	+	16.4288i	−0.420249	+	0.738420i
$496$	5.16982	+	1.38525i	0.232132	+	0.0621995i
$497$		−	37.7775i		−	1.69455i
$498$	24.3147	−	14.1387i	1.08957	−	0.633571i
$499$	11.5561	+	3.09645i	0.517323	+	0.138616i	0.508028	−	0.861341i	$-0.330375\pi$
$499$	11.5561	+	3.09645i	0.517323	+	0.138616i	0.00929473	+	0.999957i	$0.497041\pi$
$500$	−6.60824	−	6.60824i	−0.295530	−	0.295530i
$501$	−3.61425	−	0.956444i	−0.161473	−	0.0427308i
$502$	−30.1751	+	8.08540i	−1.34678	+	0.360869i
$503$	−24.4849	−	14.1364i	−1.09173	−	0.630310i	−0.157693	−	0.987488i	$-0.550406\pi$
$503$	−24.4849	−	14.1364i	−1.09173	−	0.630310i	−0.934036	+	0.357178i	$0.883739\pi$
$504$	−23.4588	+	41.2196i	−1.04494	+	1.83607i
$505$	2.09048	−	7.80177i	0.0930250	−	0.347174i
$506$	−1.23193	+	2.13377i	−0.0547661	+	0.0948577i
$507$	−2.71731	−	22.3521i	−0.120680	−	0.992691i
$508$	−0.154676	−	0.267907i	−0.00686264	−	0.0118864i
$509$	8.79489	−	2.35658i	0.389827	−	0.104454i	−0.0585816	−	0.998283i	$-0.518658\pi$
$509$	8.79489	−	2.35658i	0.389827	−	0.104454i	0.448408	+	0.893829i	$0.351991\pi$
$510$	0.528053	+	0.302694i	0.0233826	+	0.0134035i
$511$	23.8940	−	13.7952i	1.05701	−	0.610263i
$512$	11.4426	+	11.4426i	0.505696	+	0.505696i
$513$	−2.96871	−	10.6813i	−0.131072	−	0.471591i
$514$	18.7299	−	5.01867i	0.826142	−	0.221364i
$515$	−0.455048	−	1.69826i	−0.0200518	−	0.0748344i
$516$	−0.323718	+	0.00100286i	−0.0142509	+	4.41484e-5i
$517$	25.0150	+	14.4424i	1.10016	+	0.635178i
$518$	−5.37317	−	20.0529i	−0.236083	−	0.881075i
$519$	20.9302	−	0.0648405i	0.918733	−	0.00284618i
$520$	18.9294	+	16.8199i	0.830107	+	0.737602i
$521$		−	10.8148i		−	0.473806i	−0.971533	−	0.236903i	$-0.923868\pi$
$521$		−	10.8148i		−	0.473806i	0.971533	−	0.236903i	$-0.0761324\pi$
$522$	−1.87262	−	0.489352i	−0.0819624	−	0.0214184i
$523$	−16.8346	−	29.1584i	−0.736125	−	1.27501i	−0.954228	−	0.299080i	$-0.903320\pi$
$523$	−16.8346	−	29.1584i	−0.736125	−	1.27501i	0.218103	−	0.975926i	$-0.430013\pi$
$524$	5.04045	+	8.73031i	0.220193	+	0.381385i
$525$	−0.686922	−	2.53222i	−0.0299797	−	0.110515i
$526$	14.7435	−	14.7435i	0.642845	−	0.642845i
$527$	0.354463	−	0.354463i	0.0154406	−	0.0154406i
$528$	−1.89960	−	7.00257i	−0.0826697	−	0.304748i
$529$	11.1442	+	19.3022i	0.484528	+	0.839228i
$530$	−9.82031	−	17.0093i	−0.426567	−	0.738836i
$531$	−21.6131	−	5.64792i	−0.937929	−	0.245099i
$532$			9.53425i			0.413362i
$533$	−23.5482	+	15.5136i	−1.01998	+	0.671967i
$534$	27.2340	−	0.0843692i	1.17853	−	0.00365101i
$535$	−3.64285	−	13.5953i	−0.157494	−	0.587777i
$536$	−20.2611	−	11.6977i	−0.875145	−	0.505265i
$537$	−5.35569	+	0.0165916i	−0.231115	+	0.000715980i
$538$	−7.64694	−	28.5388i	−0.329683	−	1.23039i
$539$	−52.4280	+	14.0480i	−2.25823	+	0.605092i
$540$	9.98848	+	2.57715i	0.429836	+	0.110903i
$541$	19.2044	+	19.2044i	0.825663	+	0.825663i	0.986914	−	0.161250i	$-0.0515526\pi$
$541$	19.2044	+	19.2044i	0.825663	+	0.825663i	−0.161250	+	0.986914i	$0.551553\pi$
$542$	−7.71794	+	4.45596i	−0.331514	+	0.191400i
$543$	−30.6378	−	17.5624i	−1.31479	−	0.753676i
$544$	0.619163	−	0.165904i	0.0265464	−	0.00711309i
$545$	5.92703	+	10.2659i	0.253886	+	0.439744i
$546$	−10.9733	−	32.6925i	−0.469613	−	1.39911i
$547$	−12.0347	+	20.8447i	−0.514565	+	0.891253i	0.485292	+	0.874352i	$0.338713\pi$
$547$	−12.0347	+	20.8447i	−0.514565	+	0.891253i	−0.999857	+	0.0169009i	$0.994620\pi$
$548$	3.51168	−	13.1058i	0.150011	−	0.559850i
$549$	2.00454	−	3.52219i	0.0855518	−	0.150323i
$550$	0.739873	+	0.427166i	0.0315483	+	0.0182144i
$551$	−1.24688	+	0.334101i	−0.0531190	+	0.0142332i
$552$	4.31233	+	1.14118i	0.183545	+	0.0485718i
$553$	11.9111	+	11.9111i	0.506511	+	0.506511i
$554$	−16.2422	−	4.35208i	−0.690065	−	0.184902i
$555$	−12.9503	+	7.53045i	−0.549710	+	0.319650i
$556$		−	11.8784i		−	0.503756i
$557$	25.0352	+	6.70816i	1.06078	+	0.284234i	0.746698	−	0.665163i	$-0.231638\pi$
$557$	25.0352	+	6.70816i	1.06078	+	0.284234i	0.314078	+	0.949397i	$0.398305\pi$
$558$	−5.53713	+	9.72930i	−0.234405	+	0.411874i
$559$	0.518699	−	0.583750i	0.0219386	−	0.0246900i
$560$	15.7798	+	9.11050i	0.666820	+	0.384989i
$561$	−0.656951	−	0.173850i	−0.0277365	−	0.00733995i
$562$	7.29137	−	12.6290i	0.307568	−	0.532723i
$563$	16.4516			0.693352			0.346676	−	0.937985i	$-0.387310\pi$
$563$	16.4516			0.693352			0.346676	+	0.937985i	$0.387310\pi$
$564$	4.03251	−	15.2382i	0.169799	−	0.641644i
$565$	−20.6891	−	5.54362i	−0.870396	−	0.233222i
$566$	3.71451	+	13.8627i	0.156132	+	0.582694i
$567$	−33.3617	−	32.5450i	−1.40106	−	1.36676i
$568$	11.1353	−	19.2869i	0.467226	−	0.809259i
$569$	14.2291			0.596516			0.298258	−	0.954485i	$-0.403594\pi$
$569$	14.2291			0.596516			0.298258	+	0.954485i	$0.403594\pi$
$570$	−8.74912	+	2.37339i	−0.366460	+	0.0994106i
$571$	18.0451	−	10.4184i	0.755164	−	0.435994i	−0.0723925	−	0.997376i	$-0.523063\pi$
$571$	18.0451	−	10.4184i	0.755164	−	0.435994i	0.827557	+	0.561382i	$0.189730\pi$
$572$	−7.61830	−	3.81880i	−0.318537	−	0.159672i
$573$	−0.0507396	−	16.3785i	−0.00211968	−	0.684221i
$574$	−30.5383	+	30.5383i	−1.27464	+	1.27464i
$575$	−0.213713	+	0.123387i	−0.00891244	+	0.00514560i
$576$	−20.2710	+	11.8716i	−0.844627	+	0.494648i
$577$	−32.0720	+	32.0720i	−1.33517	+	1.33517i	−0.434505	+	0.900670i	$0.643076\pi$
$577$	−32.0720	+	32.0720i	−1.33517	+	1.33517i	−0.900670	+	0.434505i	$0.856924\pi$
$578$	4.68611	−	17.4888i	0.194916	−	0.727438i
$579$	0.175913	−	0.664745i	0.00731068	−	0.0276259i
$580$	0.310878	−	1.16021i	0.0129085	−	0.0481752i
$581$		−	78.8626i		−	3.27177i
$582$	−1.00523	+	0.00311414i	−0.0416681	+	0.000129085i
$583$	15.5059	+	15.5059i	0.642191	+	0.642191i
$584$	16.2651			0.673053
$585$	−20.6948	+	13.8184i	−0.855626	+	0.571321i
$586$	−7.60051			−0.313974
$587$	11.1721	+	11.1721i	0.461121	+	0.461121i	0.899023	−	0.437902i	$-0.144278\pi$
$587$	11.1721	+	11.1721i	0.461121	+	0.461121i	−0.437902	+	0.899023i	$0.644278\pi$
$588$	14.8893	+	25.6054i	0.614022	+	1.05595i
$589$			7.46614i			0.307637i
$590$	−4.72780	+	17.6444i	−0.194640	+	0.726408i
$591$	−3.38724	−	3.36632i	−0.139332	−	0.138472i
$592$	1.48823	−	5.55414i	0.0611657	−	0.228274i
$593$	25.1695	−	25.1695i	1.03359	−	1.03359i	0.0341707	−	0.999416i	$-0.489121\pi$
$593$	25.1695	−	25.1695i	1.03359	−	1.03359i	0.999416	−	0.0341707i	$-0.0108790\pi$
$594$	15.1752	−	0.141039i	0.622647	−	0.00578692i
$595$	1.47794	−	0.853290i	0.0605897	−	0.0349815i
$596$	−8.07162	+	8.07162i	−0.330626	+	0.330626i
$597$	23.3036	−	13.5508i	0.953752	−	0.554595i
$598$	−2.70851	+	1.78437i	−0.110759	+	0.0729683i
$599$	−1.33423	+	0.770320i	−0.0545153	+	0.0314744i	−0.527010	−	0.849859i	$-0.676687\pi$
$599$	−1.33423	+	0.770320i	−0.0545153	+	0.0314744i	0.472495	+	0.881334i	$0.343354\pi$
$600$	0.395697	−	1.49528i	0.0161543	−	0.0610444i
$601$	29.3874			1.19874			0.599369	−	0.800473i	$-0.295418\pi$
$601$	29.3874			1.19874			0.599369	+	0.800473i	$0.295418\pi$
$602$	0.597990	−	1.03575i	0.0243722	−	0.0422140i
$603$	16.1557	−	16.3572i	0.657912	−	0.666115i
$604$	2.56825	+	9.58482i	0.104500	+	0.390001i
$605$	7.77372	+	2.08296i	0.316047	+	0.0846844i
$606$	−6.25823	+	1.69768i	−0.254223	+	0.0689637i
$607$	−20.8526			−0.846382			−0.423191	−	0.906041i	$-0.639090\pi$
$607$	−20.8526			−0.846382			−0.423191	+	0.906041i	$0.639090\pi$
$608$	−4.77355	+	8.26804i	−0.193593	+	0.335313i
$609$	−3.82546	+	3.84923i	−0.155015	+	0.155979i
$610$	−2.86993	−	1.65696i	−0.116200	−	0.0670882i
$611$	20.9189	+	31.7530i	0.846287	+	1.28459i
$612$	0.00229769	+	0.370838i	9.28785e−5	+	0.0149902i
$613$	−21.4484	−	5.74708i	−0.866292	−	0.232122i	−0.201809	−	0.979425i	$-0.564682\pi$
$613$	−21.4484	−	5.74708i	−0.866292	−	0.232122i	−0.664484	+	0.747303i	$0.731349\pi$
$614$			12.6294i			0.509680i
$615$	27.0371	+	15.4984i	1.09024	+	0.624955i
$616$	−41.8248	−	11.2069i	−1.68517	−	0.451540i
$617$	8.58385	+	8.58385i	0.345573	+	0.345573i	0.858457	−	0.512885i	$-0.171423\pi$
$617$	8.58385	+	8.58385i	0.345573	+	0.345573i	−0.512885	+	0.858457i	$0.671423\pi$
$618$	−0.994986	+	1.00117i	−0.0400242	+	0.0402730i
$619$	−5.57125	+	1.49281i	−0.223928	+	0.0600012i	−0.369038	−	0.929414i	$-0.620313\pi$
$619$	−5.57125	+	1.49281i	−0.223928	+	0.0600012i	0.145111	+	0.989415i	$0.453646\pi$
$620$	−6.01643	−	3.47359i	−0.241626	−	0.139503i
$621$	−2.15640	+	3.81648i	−0.0865335	+	0.153150i
$622$	0.743870	−	2.77616i	0.0298265	−	0.111314i
$623$	38.1800	−	66.1298i	1.52965	−	2.64943i
$624$	1.89536	−	9.36147i	0.0758749	−	0.374759i
$625$	−13.1885	−	22.8432i	−0.527541	−	0.913727i
$626$	−3.44754	+	0.923765i	−0.137791	+	0.0369211i
$627$	8.74968	−	5.08784i	0.349429	−	0.203189i
$628$	−7.00952	+	4.04695i	−0.279710	+	0.161491i
$629$	−0.380813	−	0.380813i	−0.0151840	−	0.0151840i
$630$	−26.7810	+	27.1149i	−1.06698	+	1.08029i
$631$	−0.701230	+	0.187894i	−0.0279155	+	0.00747994i	−0.272750	−	0.962085i	$-0.587933\pi$
$631$	−0.701230	+	0.187894i	−0.0279155	+	0.00747994i	0.244834	+	0.969565i	$0.421266\pi$
$632$	2.57017	+	9.59200i	0.102236	+	0.381549i
$633$	8.03089	+	13.8109i	0.319199	+	0.548935i
$634$	2.94564	+	1.70066i	0.116986	+	0.0675420i
$635$	−0.213452	−	0.796612i	−0.00847057	−	0.0316126i
$636$	5.95122	−	10.3820i	0.235981	−	0.411671i
$637$	−69.9862	−	14.3955i	−2.77296	−	0.570370i
$638$		−	1.76707i		−	0.0699589i
$639$	15.5707	+	15.3789i	0.615967	+	0.608381i
$640$	−0.689789	−	1.19475i	−0.0272663	−	0.0472266i
$641$	−0.968362	−	1.67725i	−0.0382480	−	0.0662475i	0.846268	−	0.532758i	$-0.178844\pi$
$641$	−0.968362	−	1.67725i	−0.0382480	−	0.0662475i	−0.884516	+	0.466510i	$0.845511\pi$
$642$	−7.96529	+	8.01480i	−0.314365	+	0.316319i
$643$	3.83575	−	3.83575i	0.151267	−	0.151267i	−0.627417	−	0.778684i	$-0.715888\pi$
$643$	3.83575	−	3.83575i	0.151267	−	0.151267i	0.778684	+	0.627417i	$0.215888\pi$
$644$	2.66573	−	2.66573i	0.105045	−	0.105045i
$645$	−0.834297	−	0.220781i	−0.0328504	−	0.00869325i
$646$	−0.162949	−	0.282236i	−0.00641114	−	0.0111044i
$647$	−5.52455	−	9.56880i	−0.217192	−	0.376188i	0.736756	−	0.676159i	$-0.236357\pi$
$647$	−5.52455	−	9.56880i	−0.217192	−	0.376188i	−0.953949	+	0.299970i	$0.903023\pi$
$648$	−7.43951	−	26.4492i	−0.292252	−	1.03902i
$649$		−	20.3949i		−	0.800568i
$650$	0.618720	+	0.939162i	0.0242682	+	0.0368370i
$651$	15.7781	+	27.1340i	0.618392	+	1.06346i
$652$	3.32076	+	12.3933i	0.130051	+	0.485357i
$653$	22.9231	+	13.2346i	0.897049	+	0.517912i	0.876242	−	0.481872i	$-0.160043\pi$
$653$	22.9231	+	13.2346i	0.897049	+	0.517912i	0.0208076	+	0.999783i	$0.493376\pi$
$654$	4.73281	−	8.25644i	0.185068	−	0.322852i
$655$	6.95577	+	25.9593i	0.271784	+	1.01431i
$656$	−11.5543	+	3.09595i	−0.451118	+	0.120877i
$657$	−4.04111	+	15.4643i	−0.157659	+	0.603318i
$658$	41.1786	+	41.1786i	1.60531	+	1.60531i
$659$	−38.2912	+	22.1074i	−1.49161	+	0.861184i	−0.999954	−	0.00960334i	$-0.996943\pi$
$659$	−38.2912	+	22.1074i	−1.49161	+	0.861184i	−0.491660	+	0.870787i	$0.663610\pi$
$660$	0.0291759	+	9.41784i	0.00113567	+	0.366589i
$661$	30.5589	−	8.18823i	1.18860	−	0.318485i	0.390270	−	0.920701i	$-0.372382\pi$
$661$	30.5589	−	8.18823i	1.18860	−	0.318485i	0.798334	+	0.602215i	$0.205715\pi$
$662$	16.4437	+	28.4813i	0.639102	+	1.10696i
$663$	−0.670568	−	0.592134i	−0.0260427	−	0.0229966i
$664$	23.2455	−	40.2624i	0.902102	−	1.56249i
$665$	−6.57859	+	24.5516i	−0.255107	+	0.952072i
$666$	10.4526	+	5.94875i	0.405029	+	0.230509i
$667$	0.442036	+	0.255209i	0.0171157	+	0.00988175i
$668$	−1.79920	+	0.482095i	−0.0696132	+	0.0186528i
$669$	−0.876913	−	3.23259i	−0.0339034	−	0.124979i
$670$	−13.2934	−	13.2934i	−0.513568	−	0.513568i
$671$	3.57390	+	0.957624i	0.137969	+	0.0369687i
$672$	0.124339	+	40.1361i	0.00479650	+	1.54829i
$673$		−	18.3367i		−	0.706829i	−0.935467	−	0.353414i	$-0.885021\pi$
$673$		−	18.3367i		−	0.706829i	0.935467	−	0.353414i	$-0.114979\pi$
$674$	5.20904	+	1.39576i	0.200645	+	0.0537626i
$675$	1.32334	+	0.747721i	0.0509355	+	0.0287798i
$676$	−6.71275	−	8.98820i	−0.258183	−	0.345700i
$677$	16.0817	+	9.28475i	0.618068	+	0.356842i	0.776116	−	0.630590i	$-0.217187\pi$
$677$	16.0817	+	9.28475i	0.618068	+	0.356842i	−0.158048	+	0.987431i	$0.550520\pi$
$678$	4.50199	+	16.5958i	0.172898	+	0.637359i
$679$	−1.40926	+	2.44091i	−0.0540824	+	0.0936734i
$680$	1.00606			0.0385807
$681$	−23.5531	−	23.4076i	−0.902558	−	0.896983i
$682$	−9.87215	−	2.64524i	−0.378024	−	0.101291i
$683$	6.10105	+	22.7694i	0.233450	+	0.871249i	0.978841	+	0.204621i	$0.0655962\pi$
$683$	6.10105	+	22.7694i	0.233450	+	0.871249i	−0.745391	+	0.666628i	$0.767737\pi$
$684$	−3.92972	−	3.88132i	−0.150257	−	0.148406i
$685$	18.0858	−	31.3256i	0.691024	−	1.19689i
$686$	−70.7759			−2.70224
$687$	−23.2217	−	23.0783i	−0.885963	−	0.880491i
$688$	0.286875	−	0.165627i	0.0109370	−	0.00631448i
$689$	9.10086	+	27.3950i	0.346715	+	1.04367i
$690$	3.10981	+	1.78262i	0.118388	+	0.0678634i
$691$	30.5011	−	30.5011i	1.16032	−	1.16032i	0.175910	−	0.984406i	$-0.443713\pi$
$691$	30.5011	−	30.5011i	1.16032	−	1.16032i	0.984406	−	0.175910i	$-0.0562867\pi$
$692$	9.03080	−	5.21394i	0.343300	−	0.198204i
$693$	21.0467	−	36.9812i	0.799496	−	1.40480i
$694$	7.48871	−	7.48871i	0.284268	−	0.284268i
$695$	8.19604	−	30.5880i	0.310893	−	1.16027i
$696$	−3.08764	+	0.837592i	−0.117037	+	0.0317488i
$697$	−0.289967	+	1.08217i	−0.0109833	+	0.0409902i
$698$			25.3006i			0.957642i
$699$	−12.9285	+	22.5540i	−0.489003	+	0.853070i
$700$	−0.924328	−	0.924328i	−0.0349363	−	0.0349363i
$701$	−16.2764			−0.614753			−0.307376	−	0.951588i	$-0.599451\pi$
$701$	−16.2764			−0.614753			−0.307376	+	0.951588i	$0.599451\pi$
$702$	17.9420	+	8.78602i	0.677175	+	0.331607i
$703$	8.02116			0.302524
$704$	−15.1654	−	15.1654i	−0.571568	−	0.571568i
$705$	20.8984	−	36.4575i	0.787080	−	1.37307i
$706$			22.3923i			0.842744i
$707$	−4.70565	+	17.5617i	−0.176974	+	0.660477i
$708$	−10.7414	+	2.91386i	−0.403688	+	0.109509i
$709$	−1.26752	+	4.73044i	−0.0476026	+	0.177655i	−0.985634	−	0.168895i	$-0.945980\pi$
$709$	−1.26752	+	4.73044i	−0.0476026	+	0.177655i	0.938032	+	0.346550i	$0.112647\pi$
$710$	12.6542	−	12.6542i	0.474904	−	0.474904i
$711$	−9.75830	+	0.0604619i	−0.365965	+	0.00226750i
$712$	38.9848	−	22.5079i	1.46102	−	0.843519i
$713$	2.08750	−	2.08750i	0.0781774	−	0.0781774i
$714$	−1.18864	−	0.681363i	−0.0444839	−	0.0254994i
$715$	−16.9829	−	15.0904i	−0.635125	−	0.564348i
$716$	−2.31083	+	1.33416i	−0.0863599	+	0.0498599i
$717$	−8.45738	−	8.40514i	−0.315847	−	0.313896i
$718$	12.5485			0.468306
$719$	−17.2570	+	29.8900i	−0.643577	+	1.11471i	0.341052	+	0.940045i	$0.389217\pi$
$719$	−17.2570	+	29.8900i	−0.643577	+	1.11471i	−0.984628	+	0.174663i	$0.944116\pi$
$720$	−10.1789	+	2.79514i	−0.379346	+	0.104169i
$721$	1.02431	+	3.82278i	0.0381473	+	0.142368i
$722$	−14.8814	−	3.98746i	−0.553828	−	0.148398i
$723$	−1.25316	−	1.24542i	−0.0466057	−	0.0463178i
$724$	−17.5944			−0.653890
$725$	0.0884924	−	0.153273i	0.00328653	−	0.00569243i
$726$	−1.69158	−	6.23573i	−0.0627804	−	0.231429i
$727$	6.05240	+	3.49435i	0.224471	+	0.129598i	0.608019	−	0.793923i	$-0.291965\pi$
$727$	6.05240	+	3.49435i	0.224471	+	0.129598i	−0.383548	+	0.923521i	$0.625298\pi$
$728$	−42.6099	−	37.8615i	−1.57923	−	1.40324i
$729$	26.9953	−	0.501836i	0.999827	−	0.0185865i
$730$	12.6246	+	3.38276i	0.467258	+	0.125201i
$731$		−	0.0310253i		−	0.00114751i
$732$	−0.00625505	−	2.01910i	−0.000231193	−	0.0746281i
$733$	−22.0147	−	5.89883i	−0.813133	−	0.217878i	−0.171791	−	0.985133i	$-0.554955\pi$
$733$	−22.0147	−	5.89883i	−0.813133	−	0.217878i	−0.641342	+	0.767255i	$0.721622\pi$
$734$	4.27568	+	4.27568i	0.157818	+	0.157818i
$735$	20.6737	+	76.2100i	0.762560	+	2.81105i
$736$	3.64637	−	0.977042i	0.134407	−	0.0360142i
$737$	18.1777	+	10.4949i	0.669584	+	0.386585i
$738$	−0.155015	−	25.0189i	−0.00570619	−	0.920957i
$739$	−3.70607	+	13.8313i	−0.136330	+	0.508791i	0.863659	+	0.504077i	$0.168167\pi$
$739$	−3.70607	+	13.8313i	−0.136330	+	0.508791i	−0.999989	+	0.00471409i	$0.998499\pi$
$740$	−3.73181	+	6.46368i	−0.137184	+	0.237610i
$741$	13.2983	−	0.826037i	0.488525	−	0.0303452i
$742$	22.1055	+	38.2878i	0.811517	+	1.40559i
$743$	−6.00805	+	1.60985i	−0.220414	+	0.0590598i	−0.367336	−	0.930088i	$-0.619730\pi$
$743$	−6.00805	+	1.60985i	−0.220414	+	0.0590598i	0.146922	+	0.989148i	$0.453063\pi$
$744$	0.0573233	+	18.5037i	0.00210158	+	0.678378i
$745$	−26.3546	+	15.2158i	−0.965558	+	0.557465i
$746$	20.2909	+	20.2909i	0.742901	+	0.742901i
$747$	32.5047	+	32.1044i	1.18928	+	1.17464i
$748$	−0.327036	+	0.0876290i	−0.0119576	+	0.00320403i
$749$	8.20004	+	30.6030i	0.299623	+	1.11821i
$750$	−9.94725	+	17.3531i	−0.363222	+	0.633645i
$751$	−37.8087	−	21.8289i	−1.37966	−	0.796547i	−0.387542	−	0.921852i	$-0.626676\pi$
$751$	−37.8087	−	21.8289i	−1.37966	−	0.796547i	−0.992118	+	0.125304i	$0.960009\pi$
$752$	4.17467	+	15.5801i	0.152234	+	0.568146i
$753$	−25.5074	−	43.8658i	−0.929542	−	1.59856i
$754$	1.04241	−	2.07955i	0.0379623	−	0.0757328i
$755$			26.4539i			0.962757i
$756$	−22.4840	−	5.80116i	−0.817736	−	0.210986i
$757$	9.84349	+	17.0494i	0.357768	+	0.619672i	0.987588	−	0.157069i	$-0.0502046\pi$
$757$	9.84349	+	17.0494i	0.357768	+	0.619672i	−0.629820	+	0.776741i	$0.716871\pi$
$758$	14.5596	+	25.2179i	0.528827	+	0.915955i
$759$	−3.86891	−	1.02384i	−0.140432	−	0.0371629i
$760$	−10.5955	+	10.5955i	−0.384338	+	0.384338i
$761$	6.11282	−	6.11282i	0.221590	−	0.221590i	−0.587578	−	0.809168i	$-0.699918\pi$
$761$	6.11282	−	6.11282i	0.221590	−	0.221590i	0.809168	+	0.587578i	$0.199918\pi$
$762$	−0.466723	+	0.469624i	−0.0169076	+	0.0170127i
$763$	−13.3417	−	23.1085i	−0.483002	−	0.836585i
$764$	−4.08006	−	7.06686i	−0.147611	−	0.255670i
$765$	−0.249960	+	0.956529i	−0.00903731	+	0.0345834i
$766$		−	17.8814i		−	0.646080i
$767$	12.0311	−	24.0014i	0.434418	−	0.866640i
$768$	−14.0408	+	24.4943i	−0.506653	+	0.883861i
$769$	−2.26984	−	8.47115i	−0.0818524	−	0.305477i	0.912847	−	0.408301i	$-0.133879\pi$
$769$	−2.26984	−	8.47115i	−0.0818524	−	0.305477i	−0.994700	+	0.102824i	$0.967212\pi$
$770$	−30.1328	−	17.3972i	−1.08591	−	0.626951i
$771$	15.8327	+	27.2278i	0.570199	+	0.980586i
$772$	−0.0886686	−	0.330916i	−0.00319125	−	0.0119099i
$773$	3.74962	−	1.00471i	0.134865	−	0.0361368i	−0.190755	−	0.981638i	$-0.561094\pi$
$773$	3.74962	−	1.00471i	0.134865	−	0.0361368i	0.325620	+	0.945501i	$0.394427\pi$
$774$	0.183466	+	0.668118i	0.00659455	+	0.0240150i
$775$	−0.723828	−	0.723828i	−0.0260007	−	0.0260007i
$776$	−1.43896	+	0.830785i	−0.0516558	+	0.0298235i
$777$	29.1511	−	16.9510i	1.04579	−	0.608114i
$778$	−1.16724	+	0.312761i	−0.0418475	+	0.0112130i
$779$	−8.34321	−	14.4509i	−0.298926	−	0.517756i
$780$	−5.52133	+	11.1005i	−0.197695	+	0.397460i
$781$	−9.99028	+	17.3037i	−0.357480	+	0.619174i
$782$	−0.0333521	+	0.124472i	−0.00119267	+	0.00445109i
$783$	−0.0292180	−	3.14373i	−0.00104417	−	0.112348i
$784$	−26.2485	−	15.1546i	−0.937448	−	0.541236i
$785$	−20.8426	+	5.58475i	−0.743904	+	0.199328i
$786$	15.2092	−	15.3037i	0.542493	−	0.545865i
$787$	3.03191	+	3.03191i	0.108076	+	0.108076i	0.759077	−	0.651001i	$-0.225651\pi$
$787$	3.03191	+	3.03191i	0.108076	+	0.108076i	−0.651001	+	0.759077i	$0.725651\pi$
$788$	−2.29818	−	0.615796i	−0.0818693	−	0.0219368i
$789$	29.3825	+	16.8428i	1.04604	+	0.599620i
$790$			7.97965i			0.283903i
$791$	46.5710	+	12.4787i	1.65587	+	0.443690i
$792$	21.6457	−	12.6766i	0.769147	−	0.450444i
$793$	3.64099	+	3.23524i	0.129295	+	0.114887i
$794$	−17.1463	−	9.89944i	−0.608501	−	0.351318i
$795$	22.4885	−	22.6282i	0.797584	−	0.802541i
$796$	6.71525	−	11.6311i	0.238016	−	0.412255i
$797$	10.9142			0.386603			0.193301	−	0.981139i	$-0.438081\pi$
$797$	10.9142			0.386603			0.193301	+	0.981139i	$0.438081\pi$
$798$	19.6942	−	5.34250i	0.697168	−	0.189122i
$799$	1.45923	+	0.390999i	0.0516238	+	0.0138326i
$800$	−0.338784	−	1.26436i	−0.0119778	−	0.0447018i
$801$	11.7138	+	42.6576i	0.413887	+	1.50723i
$802$	−9.28776	+	16.0869i	−0.327962	+	0.568047i
$803$	−14.5926			−0.514962
$804$	2.93031	−	11.0732i	0.103344	−	0.390520i
$805$	8.70387	−	5.02518i	0.306771	−	0.177114i
$806$	−10.0575	−	8.93667i	−0.354259	−	0.314781i
$807$	41.4869	−	24.1242i	1.46041	−	0.849211i
$808$	−7.57891	+	7.57891i	−0.266625	+	0.266625i
$809$	24.7010	−	14.2611i	0.868439	−	0.501394i	0.00160994	−	0.999999i	$-0.499488\pi$
$809$	24.7010	−	14.2611i	0.868439	−	0.501394i	0.866829	+	0.498605i	$0.166154\pi$
$810$	−0.273581	−	22.0766i	−0.00961265	−	0.775692i
$811$	−14.4345	+	14.4345i	−0.506862	+	0.506862i	−0.913562	−	0.406700i	$-0.866680\pi$
$811$	−14.4345	+	14.4345i	−0.506862	+	0.506862i	0.406700	+	0.913562i	$0.366680\pi$
$812$	−0.699785	+	2.61163i	−0.0245576	+	0.0916503i
$813$	−10.2675	−	10.2041i	−0.360098	−	0.357874i
$814$	−2.84188	+	10.6060i	−0.0996078	+	0.371741i
$815$			34.2052i			1.19815i
$816$	−0.190756	−	0.328048i	−0.00667779	−	0.0114840i
$817$	0.326747	+	0.326747i	0.0114314	+	0.0114314i
$818$	−33.0291			−1.15484
$819$	46.5840	−	31.1051i	1.62778	−	1.08690i
$820$	15.5266			0.542211
$821$	15.7089	+	15.7089i	0.548243	+	0.548243i	0.925932	−	0.377689i	$-0.123281\pi$
$821$	15.7089	+	15.7089i	0.548243	+	0.548243i	−0.377689	+	0.925932i	$0.623281\pi$
$822$	−29.0394	+	0.0899623i	−1.01286	+	0.00313780i
$823$		−	56.1423i		−	1.95700i	−0.206255	−	0.978498i	$-0.566128\pi$
$823$		−	56.1423i		−	1.95700i	0.206255	−	0.978498i	$-0.433872\pi$
$824$	−0.603851	+	2.25360i	−0.0210361	+	0.0785080i
$825$	−0.355009	+	1.34152i	−0.0123598	+	0.0467058i
$826$	10.6422	−	39.7174i	0.370291	−	1.38195i
$827$	−7.73555	+	7.73555i	−0.268991	+	0.268991i	−0.828694	−	0.559702i	$-0.810915\pi$
$827$	−7.73555	+	7.73555i	−0.268991	+	0.268991i	0.559702	+	0.828694i	$0.310915\pi$
$828$	0.0135315	+	2.18393i	0.000470253	+	0.0758969i
$829$	−22.3717	+	12.9163i	−0.777001	+	0.448602i	−0.835366	−	0.549693i	$-0.814745\pi$
$829$	−22.3717	+	12.9163i	−0.777001	+	0.448602i	0.0583652	+	0.998295i	$0.481411\pi$
$830$	26.4164	−	26.4164i	0.916926	−	0.916926i
$831$	−0.0846138	−	27.3129i	−0.00293522	−	0.947475i
$832$	−8.90100	−	26.7934i	−0.308587	−	0.928895i
$833$	−2.45844	+	1.41938i	−0.0851799	+	0.0491786i
$834$	−24.5363	+	6.65603i	−0.849624	+	0.230479i
$835$	−4.96577			−0.171847
$836$	2.52134	−	4.36709i	0.0872024	−	0.151039i
$837$	−17.6069	−	4.54280i	−0.608584	−	0.157022i
$838$	−5.92596	−	22.1160i	−0.204709	−	0.763984i
$839$	−34.3643	−	9.20790i	−1.18639	−	0.317892i	−0.388931	−	0.921267i	$-0.627156\pi$
$839$	−34.3643	−	9.20790i	−1.18639	−	0.317892i	−0.797458	+	0.603375i	$0.793822\pi$
$840$	−16.1155	+	60.8980i	−0.556039	+	2.10118i
$841$	28.6339			0.987377
$842$	12.6504	−	21.9112i	0.435962	−	0.755109i
$843$	22.8987	+	6.05971i	0.788673	+	0.208708i
$844$	6.89323	+	3.97981i	0.237275	+	0.136991i
$845$	−11.0842	−	27.7773i	−0.381307	−	0.955567i
$846$	−33.7361	+	0.209027i	−1.15987	+	0.00718648i
$847$	−17.4986	−	4.68873i	−0.601259	−	0.161107i
$848$			12.2453i			0.420504i
$849$	−20.1523	+	11.7183i	−0.691626	+	0.402172i
$850$	0.0431598	+	0.0115646i	0.00148037	+	0.000396664i
$851$	−2.24268	−	2.24268i	−0.0768781	−	0.0768781i
$852$	10.5407	+	2.78941i	0.361120	+	0.0955637i
$853$	−11.9527	+	3.20271i	−0.409252	+	0.109659i	−0.457571	−	0.889173i	$-0.651280\pi$
$853$	−11.9527	+	3.20271i	−0.409252	+	0.109659i	0.0483186	+	0.998832i	$0.484614\pi$
$854$	6.46020	+	3.72980i	0.221063	+	0.127631i
$855$	−7.44132	−	12.7063i	−0.254488	−	0.434546i
$856$	−4.83409	+	18.0411i	−0.165226	+	0.616630i
$857$	−1.46053	+	2.52971i	−0.0498907	+	0.0864132i	−0.889892	−	0.456171i	$-0.849221\pi$
$857$	−1.46053	+	2.52971i	−0.0498907	+	0.0864132i	0.840002	+	0.542584i	$0.182554\pi$
$858$	−3.61932	+	17.8764i	−0.123562	+	0.610291i
$859$	14.1298	+	24.4734i	0.482101	+	0.835023i	0.999789	−	0.0205462i	$-0.00654052\pi$
$859$	14.1298	+	24.4734i	0.482101	+	0.835023i	−0.517688	+	0.855569i	$0.673207\pi$
$860$	−0.415320	+	0.111285i	−0.0141623	+	0.00379477i
$861$	−60.8602	−	34.8867i	−2.07411	−	1.18894i
$862$	21.6116	−	12.4775i	0.736095	−	0.424985i
$863$	−32.6894	−	32.6894i	−1.11276	−	1.11276i	−0.992776	−	0.119986i	$-0.961715\pi$
$863$	−32.6894	−	32.6894i	−1.11276	−	1.11276i	−0.119986	−	0.992776i	$-0.538285\pi$
$864$	−16.5935	−	16.2879i	−0.564522	−	0.554125i
$865$	26.8528	−	7.19519i	0.913023	−	0.244644i
$866$	7.33222	+	27.3642i	0.249159	+	0.929874i
$867$	29.4092	−	0.0911079i	0.998788	−	0.00309419i
$868$	13.5429	+	7.81903i	0.459678	+	0.265395i
$869$	−2.30589	−	8.60569i	−0.0782219	−	0.291928i
$870$	−2.57077	+	0.00796408i	−0.0871572	+	0.000270008i
$871$	15.2011	+	23.0740i	0.515071	+	0.781831i
$872$		−	15.7304i		−	0.532699i
$873$	−0.432367	−	1.57453i	−0.0146334	−	0.0532897i
$874$	−0.959637	−	1.66214i	−0.0324602	−	0.0562227i
$875$	28.0411	+	48.5686i	0.947963	+	1.64192i
$876$	2.08488	+	7.68555i	0.0704414	+	0.259671i
$877$	−39.9952	+	39.9952i	−1.35054	+	1.35054i	−0.465486	+	0.885055i	$0.654120\pi$
$877$	−39.9952	+	39.9952i	−1.35054	+	1.35054i	−0.885055	+	0.465486i	$0.845880\pi$
$878$	−0.321943	+	0.321943i	−0.0108651	+	0.0108651i
$879$	−3.23220	−	11.9150i	−0.109019	−	0.401882i
$880$	−4.81856	−	8.34599i	−0.162434	−	0.281343i
$881$	−14.1084	−	24.4364i	−0.475323	−	0.823284i	0.524278	−	0.851547i	$-0.324335\pi$
$881$	−14.1084	−	24.4364i	−0.475323	−	0.823284i	−0.999600	+	0.0282639i	$0.991002\pi$
$882$	44.5481	−	45.1036i	1.50001	−	1.51872i
$883$		−	7.20265i		−	0.242388i	−0.992629	−	0.121194i	$-0.961328\pi$
$883$		−	7.20265i		−	0.242388i	0.992629	−	0.121194i	$-0.0386724\pi$
$884$	−0.436560	−	0.0897963i	−0.0146831	−	0.00302018i
$885$	−29.6708	+	0.0919185i	−0.997374	+	0.00308981i
$886$	−3.16327	−	11.8055i	−0.106272	−	0.396613i
$887$	−27.3550	−	15.7934i	−0.918490	−	0.530291i	−0.0353373	−	0.999375i	$-0.511251\pi$
$887$	−27.3550	−	15.7934i	−0.918490	−	0.530291i	−0.883153	+	0.469085i	$0.844584\pi$
$888$	19.8792	−	0.0615847i	0.667103	−	0.00206665i
$889$	0.480478	+	1.79317i	0.0161147	+	0.0601410i
$890$	34.9404	−	9.36224i	1.17120	−	0.313823i
$891$	6.67453	+	23.7295i	0.223605	+	0.794969i
$892$	−1.17998	−	1.17998i	−0.0395087	−	0.0395087i
$893$	−19.4859	+	11.2502i	−0.652071	+	0.376473i
$894$	21.1959	+	12.1501i	0.708896	+	0.406358i
$895$	−6.87119	+	1.84113i	−0.229678	+	0.0615421i
$896$	1.55271	+	2.68937i	0.0518724	+	0.0898456i
$897$	−3.94910	−	3.48719i	−0.131857	−	0.116434i
$898$	3.43923	−	5.95692i	0.114769	−	0.198785i
$899$	−0.547991	+	2.04513i	−0.0182765	+	0.0682090i
$900$	0.757266	−	0.00469198i	0.0252422	−	0.000156399i
$901$	0.993237	+	0.573446i	0.0330895	+	0.0191042i
$902$	22.0637	−	5.91196i	0.734642	−	0.196847i
$903$	1.87800	+	0.496977i	0.0624958	+	0.0165384i
$904$	20.0981	+	20.0981i	0.668453	+	0.668453i
$905$	−45.3072	−	12.1400i	−1.50606	−	0.403549i
$906$	18.3596	−	10.6759i	0.609956	−	0.354682i
$907$			22.6161i			0.750954i	0.926832	+	0.375477i	$0.122521\pi$
$907$			22.6161i			0.750954i	−0.926832	+	0.375477i	$0.877479\pi$
$908$	−15.9804	−	4.28192i	−0.530327	−	0.142101i
$909$	−5.32276	−	9.08877i	−0.176545	−	0.301456i
$910$	−25.1986	−	38.2492i	−0.835326	−	1.26795i
$911$	−20.2816	−	11.7096i	−0.671958	−	0.387955i	0.124860	−	0.992174i	$-0.460152\pi$
$911$	−20.2816	−	11.7096i	−0.671958	−	0.387955i	−0.796818	+	0.604219i	$0.793485\pi$
$912$	5.46384	+	1.44591i	0.180926	+	0.0478787i
$913$	−20.8553	+	36.1224i	−0.690209	+	1.19548i
$914$	−11.5909			−0.383391
$915$	1.37706	−	5.20370i	0.0455243	−	0.172029i
$916$	−15.7555	−	4.22167i	−0.520576	−	0.139488i
$917$	−15.6574	−	58.4342i	−0.517053	−	1.92967i
$918$	0.764725	−	0.212544i	0.0252397	−	0.00701500i
$919$	13.0969	−	22.6845i	0.432027	−	0.748293i	−0.565020	−	0.825077i	$-0.691132\pi$
$919$	13.0969	−	22.6845i	0.432027	−	0.748293i	0.997048	+	0.0767835i	$0.0244650\pi$
$920$	5.92489			0.195338
$921$	−19.7985	+	5.37078i	−0.652382	+	0.176973i
$922$	15.7012	−	9.06506i	0.517090	−	0.298542i
$923$	−21.9645	+	14.4702i	−0.722971	+	0.476294i
$924$	−0.0656748	−	21.1995i	−0.00216054	−	0.697413i
$925$	−0.777637	+	0.777637i	−0.0255685	+	0.0255685i
$926$	35.8253	−	20.6837i	1.17729	−	0.679710i
$927$	−1.99262	−	1.13404i	−0.0654462	−	0.0372466i
$928$	−1.91442	+	1.91442i	−0.0628440	+	0.0628440i
$929$	2.52294	−	9.41573i	0.0827749	−	0.308920i	−0.912109	−	0.409949i	$-0.865547\pi$
$929$	2.52294	−	9.41573i	0.0827749	−	0.308920i	0.994884	+	0.101028i	$0.0322133\pi$
$930$	−3.80385	+	14.3741i	−0.124733	+	0.471346i
$931$	10.9430	−	40.8397i	0.358642	−	1.33847i
$932$			12.9521i			0.424259i
$933$	4.66840	−	0.0144624i	0.152836	−	0.000473478i
$934$	28.4442	+	28.4442i	0.930722	+	0.930722i
$935$	−0.902613			−0.0295186
$936$	32.9515	−	2.14931i	1.07705	−	0.0702524i
$937$	38.7284			1.26520			0.632601	−	0.774478i	$-0.281987\pi$
$937$	38.7284			1.26520			0.632601	+	0.774478i	$0.281987\pi$
$938$	29.9233	+	29.9233i	0.977031	+	0.977031i
$939$	−2.91425	−	5.01171i	−0.0951029	−	0.163551i
$940$		−	20.9364i		−	0.682871i
$941$	13.5986	−	50.7507i	0.443302	−	1.65442i	−0.277080	−	0.960847i	$-0.589367\pi$
$941$	13.5986	−	50.7507i	0.443302	−	1.65442i	0.720382	−	0.693578i	$-0.243967\pi$
$942$	12.2873	+	12.2114i	0.400341	+	0.397868i
$943$	−1.70767	+	6.37312i	−0.0556094	+	0.207537i
$944$	8.05305	−	8.05305i	0.262104	−	0.262104i
$945$	−53.8958	−	30.4524i	−1.75323	−	0.990617i
$946$	−0.547809	+	0.316278i	−0.0178108	+	0.0102831i
$947$	33.3193	−	33.3193i	1.08273	−	1.08273i	0.0864783	−	0.996254i	$-0.472439\pi$
$947$	33.3193	−	33.3193i	1.08273	−	1.08273i	0.996254	−	0.0864783i	$-0.0275613\pi$
$948$	−4.20295	+	2.44397i	−0.136505	+	0.0793763i
$949$	−17.1731	−	8.60830i	−0.557462	−	0.279437i
$950$	−0.576337	+	0.332749i	−0.0186989	+	0.0107958i
$951$	−1.41339	+	5.34097i	−0.0458323	+	0.173193i
$952$	−2.26464			−0.0733974
$953$	−24.8010	+	42.9566i	−0.803383	+	1.39150i	0.113994	+	0.993481i	$0.463636\pi$
$953$	−24.8010	+	42.9566i	−0.803383	+	1.39150i	−0.917377	+	0.398019i	$0.869698\pi$
$954$	−24.7800	−	6.47549i	−0.802282	−	0.209652i
$955$	−5.63044	−	21.0131i	−0.182197	−	0.679968i
$956$	−5.73818	−	1.53754i	−0.185586	−	0.0497276i
$957$	2.77015	−	0.751466i	0.0895463	−	0.0242914i
$958$	−22.2651			−0.719354
$959$	−40.7111	+	70.5137i	−1.31463	+	2.27701i
$960$	−21.9946	+	22.1313i	−0.709873	+	0.714285i
$961$	−16.2415	−	9.37703i	−0.523919	−	0.302485i
$962$	−9.60101	+	10.8051i	−0.309549	+	0.348371i
$963$	−15.9518	−	9.07844i	−0.514038	−	0.292549i
$964$	−0.850249	−	0.227824i	−0.0273847	−	0.00733770i
$965$		−	0.913321i		−	0.0294009i
$966$	−7.00015	−	4.01268i	−0.225226	−	0.129106i
$967$	57.2307	+	15.3349i	1.84042	+	0.493138i	0.998891	−	0.0470805i	$-0.0149917\pi$
$967$	57.2307	+	15.3349i	1.84042	+	0.493138i	0.841525	+	0.540218i	$0.181658\pi$
$968$	−7.55166	−	7.55166i	−0.242720	−	0.242720i
$969$	0.373152	−	0.375471i	0.0119874	−	0.0120619i
$970$	−1.28968	+	0.345568i	−0.0414091	+	0.0110955i
$971$	19.4119	+	11.2075i	0.622957	+	0.359665i	0.778019	−	0.628240i	$-0.216224\pi$
$971$	19.4119	+	11.2075i	0.622957	+	0.359665i	−0.155062	+	0.987905i	$0.549558\pi$
$972$	11.5441	−	6.90560i	0.370278	−	0.221497i
$973$	−18.4492	+	68.8535i	−0.591455	+	2.20734i
$974$	9.47425	−	16.4099i	0.303575	−	0.525807i
$975$	−1.20916	+	1.36933i	−0.0387242	+	0.0438536i
$976$	1.03306	+	1.78931i	0.0330673	+	0.0572743i
$977$	−14.9916	+	4.01699i	−0.479624	+	0.128515i	−0.490528	−	0.871426i	$-0.663196\pi$
$977$	−14.9916	+	4.01699i	−0.479624	+	0.128515i	0.0109035	+	0.999941i	$0.496529\pi$
$978$	23.7391	−	13.8040i	0.759092	−	0.441403i
$979$	−34.9762	+	20.1935i	−1.11784	+	0.645387i
$980$	27.8187	+	27.8187i	0.888635	+	0.888635i
$981$	14.9559	+	3.90827i	0.477506	+	0.124782i
$982$	−15.0296	+	4.02716i	−0.479613	+	0.128512i
$983$	0.650655	+	2.42828i	0.0207527	+	0.0774500i	0.975526	−	0.219886i	$-0.0705685\pi$
$983$	0.650655	+	2.42828i	0.0207527	+	0.0774500i	−0.954773	+	0.297336i	$0.903902\pi$
$984$	−20.7883	−	35.7502i	−0.662708	−	1.13967i
$985$	−5.49315	−	3.17147i	−0.175026	−	0.101051i
$986$	−0.0239199	−	0.0892702i	−0.000761764	−	0.00284294i
$987$	−47.0422	+	82.0655i	−1.49737	+	2.61217i
$988$	5.54339	−	3.65199i	0.176359	−	0.116185i
$989$		−	0.182714i		−	0.00580997i
$990$	19.4374	−	5.33753i	0.617761	−	0.169638i
$991$	15.2437	+	26.4028i	0.484231	+	0.838713i	0.999836	−	0.0181139i	$-0.00576614\pi$
$991$	15.2437	+	26.4028i	0.484231	+	0.838713i	−0.515605	+	0.856826i	$0.672433\pi$
$992$	7.82956	+	13.5612i	0.248589	+	0.430569i
$993$	−37.6560	+	37.8900i	−1.19498	+	1.20240i
$994$	−28.4845	+	28.4845i	−0.903475	+	0.903475i
$995$	25.3179	−	25.3179i	0.802630	−	0.802630i
$996$	22.0044	+	5.82306i	0.697236	+	0.184511i
$997$	3.99304	+	6.91615i	0.126461	+	0.219037i	0.922303	−	0.386467i	$-0.126305\pi$
$997$	3.99304	+	6.91615i	0.126461	+	0.219037i	−0.795842	+	0.605504i	$0.792972\pi$
$998$	−6.37866	−	11.0482i	−0.201913	−	0.349723i
$999$	−4.88051	+	18.9158i	−0.154412	+	0.598469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.x.a.2.5	✓	48
3.2	odd	2		351.2.ba.a.197.8		48
9.4	even	3		351.2.bf.a.314.8		48
9.5	odd	6		117.2.bc.a.41.5	yes	48
13.7	odd	12		117.2.bc.a.20.5	yes	48
39.20	even	12		351.2.bf.a.332.8		48
117.59	even	12	inner	117.2.x.a.59.5	yes	48
117.85	odd	12		351.2.ba.a.98.8		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.x.a.2.5	✓	48	1.1	even	1	trivial
117.2.x.a.59.5	yes	48	117.59	even	12	inner
117.2.bc.a.20.5	yes	48	13.7	odd	12
117.2.bc.a.41.5	yes	48	9.5	odd	6
351.2.ba.a.98.8		48	117.85	odd	12
351.2.ba.a.197.8		48	3.2	odd	2
351.2.bf.a.314.8		48	9.4	even	3
351.2.bf.a.332.8		48	39.20	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.754009 - 0.754009i) q^{2} +(0.861374 - 1.50268i) q^{3} -0.862941i q^{4} +(0.595426 - 2.22216i) q^{5} +(-1.78251 + 0.483547i) q^{6} +(-1.34030 + 5.00206i) q^{7} +(-2.15868 + 2.15868i) q^{8} +(-1.51607 - 2.58873i) q^{9} +(-2.12448 + 1.22657i) q^{10} +(1.93671 - 1.93671i) q^{11} +(-1.29672 - 0.743315i) q^{12} +(3.42168 - 1.13671i) q^{13} +(4.78220 - 2.76100i) q^{14} +(-2.82630 - 2.80884i) q^{15} +1.52945 q^{16} +(0.0716242 - 0.124057i) q^{17} +(-0.808798 + 3.09506i) q^{18} +(0.552200 + 2.06084i) q^{19} +(-1.91759 - 0.513817i) q^{20} +(6.36198 + 6.32269i) q^{21} -2.92060 q^{22} +(0.421808 - 0.730594i) q^{23} +(1.38437 + 5.10323i) q^{24} +(-0.253329 - 0.146260i) q^{25} +(-3.43707 - 1.72289i) q^{26} +(-5.19593 + 0.0482913i) q^{27} +(4.31649 + 1.15660i) q^{28} +0.605036i q^{29} +(0.0131630 + 4.24895i) q^{30} +(3.38018 + 0.905716i) q^{31} +(3.16415 + 3.16415i) q^{32} +(-1.24202 - 4.57849i) q^{33} +(-0.147545 + 0.0395346i) q^{34} +(10.3173 + 5.95671i) q^{35} +(-2.23392 + 1.30828i) q^{36} +(0.973046 - 3.63146i) q^{37} +(1.13753 - 1.97025i) q^{38} +(1.23924 - 6.12081i) q^{39} +(3.51160 + 6.08227i) q^{40} +(-7.55452 + 2.02423i) q^{41} +(-0.0296298 - 9.56435i) q^{42} +(0.187567 - 0.108292i) q^{43} +(-1.67127 - 1.67127i) q^{44} +(-6.65528 + 1.82755i) q^{45} +(-0.868921 + 0.232827i) q^{46} +(2.72952 + 10.1867i) q^{47} +(1.31743 - 2.29827i) q^{48} +(-17.1621 - 9.90853i) q^{49} +(0.0807314 + 0.301294i) q^{50} +(-0.124722 - 0.214487i) q^{51} +(-0.980914 - 2.95271i) q^{52} +8.00631i q^{53} +(3.95419 + 3.88136i) q^{54} +(-3.15052 - 5.45686i) q^{55} +(-7.90459 - 13.6912i) q^{56} +(3.57242 + 0.945376i) q^{57} +(0.456203 - 0.456203i) q^{58} +(5.26532 - 5.26532i) q^{59} +(-2.42386 + 2.43893i) q^{60} +(0.675442 + 1.16990i) q^{61} +(-1.86577 - 3.23160i) q^{62} +(14.9810 - 4.11380i) q^{63} -7.83049i q^{64} +(-0.488596 - 8.28034i) q^{65} +(-2.51573 + 4.38871i) q^{66} +(1.98346 + 7.40238i) q^{67} +(-0.107054 - 0.0618075i) q^{68} +(-0.734510 - 1.26316i) q^{69} +(-3.28794 - 12.2708i) q^{70} +(-7.04646 + 1.88809i) q^{71} +(8.86096 + 2.31554i) q^{72} +(-3.76736 - 3.76736i) q^{73} +(-3.47184 + 2.00447i) q^{74} +(-0.437992 + 0.254687i) q^{75} +(1.77838 - 0.476516i) q^{76} +(7.09179 + 12.2833i) q^{77} +(-5.54954 + 3.68075i) q^{78} +(1.62641 - 2.81703i) q^{79} +(0.910674 - 3.39868i) q^{80} +(-4.40307 + 7.84939i) q^{81} +(7.22246 + 4.16989i) q^{82} +(-14.7099 + 3.94150i) q^{83} +(5.45610 - 5.49002i) q^{84} +(-0.233027 - 0.233027i) q^{85} +(-0.223081 - 0.0597743i) q^{86} +(0.909174 + 0.521163i) q^{87} +8.36151i q^{88} +(-14.2431 - 3.81643i) q^{89} +(6.39613 + 3.64015i) q^{90} +(1.09983 + 18.6390i) q^{91} +(-0.630459 - 0.363996i) q^{92} +(4.27260 - 4.29915i) q^{93} +(5.62279 - 9.73895i) q^{94} +4.90830 q^{95} +(7.48020 - 2.02917i) q^{96} +(0.525725 + 0.140868i) q^{97} +(5.46924 + 20.4115i) q^{98} +(-7.94983 - 2.07744i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 2 q^{3} - 6 q^{5} - 8 q^{6} - 4 q^{7} + 30 q^{8} - 2 q^{9} - 12 q^{10} - 6 q^{11} + 18 q^{12} - 2 q^{13} - 12 q^{14} - 26 q^{15} - 28 q^{16} - 14 q^{18} - 4 q^{19} - 18 q^{20} - 8 q^{21}+ \cdots - 8 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 2 * q^3 - 6 * q^5 - 8 * q^6 - 4 * q^7 + 30 * q^8 - 2 * q^9 - 12 * q^10 - 6 * q^11 + 18 * q^12 - 2 * q^13 - 12 * q^14 - 26 * q^15 - 28 * q^16 - 14 * q^18 - 4 * q^19 - 18 * q^20 - 8 * q^21 - 4 * q^22 - 6 * q^23 + 6 * q^24 - 48 * q^26 - 32 * q^27 + 42 * q^30 - 18 * q^31 + 54 * q^32 + 28 * q^33 + 6 * q^34 + 6 * q^35 + 24 * q^36 - 6 * q^37 + 36 * q^38 + 10 * q^39 - 12 * q^40 + 18 * q^41 - 70 * q^42 - 30 * q^43 + 12 * q^44 + 40 * q^45 - 12 * q^46 - 36 * q^47 - 14 * q^48 - 6 * q^49 - 60 * q^50 + 56 * q^52 + 34 * q^54 - 4 * q^55 - 6 * q^56 - 56 * q^57 + 50 * q^58 - 6 * q^59 + 44 * q^60 + 2 * q^61 + 18 * q^62 + 22 * q^63 + 72 * q^65 + 32 * q^66 + 26 * q^67 + 42 * q^68 + 30 * q^69 - 16 * q^70 - 48 * q^71 + 30 * q^72 - 22 * q^73 + 30 * q^74 - 24 * q^75 + 6 * q^76 + 72 * q^77 - 20 * q^78 + 8 * q^79 - 54 * q^80 + 82 * q^81 - 12 * q^82 + 54 * q^83 - 38 * q^84 - 24 * q^85 - 54 * q^86 + 2 * q^87 - 114 * q^90 - 16 * q^91 + 120 * q^92 + 52 * q^93 + 26 * q^94 - 12 * q^95 + 94 * q^96 - 24 * q^97 + 36 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more