LMFDB - Embedded newform 798.2.cc.b.317.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(317,798)] 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, 6, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.317"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cc (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			317.12
Character	$\chi$	$=$	798.317
Dual form			798.2.cc.b.725.12

$q$-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} +(-0.560498 - 1.63885i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.0666847 + 0.183215i) q^{5} +(-1.51663 + 0.836567i) q^{6} +(1.64561 + 2.07170i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.37168 + 1.83715i) q^{9} +(0.192011 + 0.0338567i) q^{10} +(4.42934 + 2.55728i) q^{11} +(1.08722 + 1.34832i) q^{12} +(-1.65749 - 4.55391i) q^{13} +(1.75447 - 1.98036i) q^{14} +(0.337639 + 0.00659504i) q^{15} +(0.766044 - 0.642788i) q^{16} +(2.40829 - 6.61672i) q^{17} +(2.22108 + 2.01664i) q^{18} +(-4.34664 - 0.326711i) q^{19} -0.194973i q^{20} +(2.47285 - 3.85811i) q^{21} +(1.74928 - 4.80612i) q^{22} +(5.56812 - 6.63582i) q^{23} +(1.13904 - 1.30483i) q^{24} +(3.80110 + 3.18950i) q^{25} +(-4.19691 + 2.42308i) q^{26} +(4.34014 + 2.85713i) q^{27} +(-2.25494 - 1.38393i) q^{28} +(1.51822 + 1.27394i) q^{29} +(-0.0521355 - 0.333655i) q^{30} -0.481848i q^{31} +(-0.766044 - 0.642788i) q^{32} +(1.70837 - 8.69239i) q^{33} +(-6.93439 - 1.22272i) q^{34} +(-0.489304 + 0.163350i) q^{35} +(1.60031 - 2.53752i) q^{36} +(0.661000 + 0.381628i) q^{37} +(0.433039 + 4.33734i) q^{38} +(-6.53417 + 5.26884i) q^{39} +(-0.192011 + 0.0338567i) q^{40} +(-8.40841 - 3.06041i) q^{41} +(-4.22890 - 1.76533i) q^{42} +(-1.13707 - 6.44867i) q^{43} +(-5.03686 - 0.888134i) q^{44} +(-0.178438 - 0.557037i) q^{45} +(-7.50190 - 4.33123i) q^{46} +(-0.279048 - 0.766678i) q^{47} +(-1.48280 - 0.895154i) q^{48} +(-1.58391 + 6.81845i) q^{49} +(2.48099 - 4.29721i) q^{50} +(-12.1937 - 0.238177i) q^{51} +(3.11506 + 3.71238i) q^{52} +(2.36708 - 0.861546i) q^{53} +(2.06006 - 4.77034i) q^{54} +(-0.763901 + 0.640989i) q^{55} +(-0.971340 + 2.46100i) q^{56} +(1.90085 + 7.30663i) q^{57} +(0.990946 - 1.71637i) q^{58} +(6.01532 + 2.18940i) q^{59} +(-0.319532 + 0.109282i) q^{60} +(7.82041 + 6.56210i) q^{61} +(-0.474528 + 0.0836721i) q^{62} +(-7.70890 - 1.89019i) q^{63} +(-0.500000 + 0.866025i) q^{64} +0.944872 q^{65} +(-8.85699 - 0.173002i) q^{66} +(-1.32595 - 0.233802i) q^{67} +7.04136i q^{68} +(-13.9961 - 5.40597i) q^{69} +(0.245835 + 0.453505i) q^{70} +(-2.09330 - 11.8717i) q^{71} +(-2.77686 - 1.13536i) q^{72} +(-0.527858 - 2.99363i) q^{73} +(0.261049 - 0.717227i) q^{74} +(3.09662 - 8.01716i) q^{75} +(4.19625 - 1.17963i) q^{76} +(1.99106 + 13.3846i) q^{77} +(6.32344 + 5.51998i) q^{78} +(2.73497 + 3.25941i) q^{79} +(0.0666847 + 0.183215i) q^{80} +(2.24977 - 8.71427i) q^{81} +(-1.55381 + 8.81210i) q^{82} +(5.01312 + 2.89433i) q^{83} +(-1.00417 + 4.47120i) q^{84} +(1.05168 + 0.882468i) q^{85} +(-6.15325 + 2.23960i) q^{86} +(1.23684 - 3.20218i) q^{87} +5.11456i q^{88} +(0.163655 - 0.928132i) q^{89} +(-0.517589 + 0.272455i) q^{90} +(6.70676 - 10.9278i) q^{91} +(-2.96273 + 8.14004i) q^{92} +(-0.789679 + 0.270075i) q^{93} +(-0.706575 + 0.407941i) q^{94} +(0.349712 - 0.774582i) q^{95} +(-0.624069 + 1.61572i) q^{96} +(-2.63474 - 3.13996i) q^{97} +(6.98990 + 0.375831i) q^{98} +(-15.2031 + 2.07229i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 81 q^{8} + 15 q^{13} - 9 q^{14} + 3 q^{15} - 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} + 9 q^{27} - 12 q^{28} - 6 q^{29} - 12 q^{33} + 6 q^{34} + 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots + 39 q^{99}+O(q^{100}) $ 162 * q + 81 * q^8 + 15 * q^13 - 9 * q^14 + 3 * q^15 - 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 + 9 * q^27 - 12 * q^28 - 6 * q^29 - 12 * q^33 + 6 * q^34 + 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 - 6 * q^44 + 18 * q^45 - 18 * q^46 - 12 * q^47 + 24 * q^49 - 87 * q^50 + 24 * q^51 + 12 * q^52 + 36 * q^53 + 18 * q^54 - 18 * q^57 - 24 * q^59 - 27 * q^60 - 9 * q^61 - 36 * q^62 + 6 * q^63 - 81 * q^64 + 72 * q^65 + 12 * q^66 - 63 * q^67 - 9 * q^69 + 12 * q^70 - 12 * q^71 - 51 * q^73 + 42 * q^74 - 18 * q^78 + 21 * q^79 - 12 * q^81 + 3 * q^84 - 6 * q^85 - 36 * q^86 - 84 * q^87 + 54 * q^89 + 12 * q^90 + 75 * q^91 - 66 * q^93 + 72 * q^94 - 12 * q^97 - 12 * q^98 + 39 * q^99

Character values

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

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$	$-1$

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
$3$	−0.560498	−	1.63885i	−0.323604	−	0.946193i
$3$	−0.560498	−	1.63885i	−0.323604	−	0.946193i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	−0.0666847	+	0.183215i	−0.0298223	+	0.0819361i	−0.953710	−	0.300727i	$-0.902771\pi$
$5$	−0.0666847	+	0.183215i	−0.0298223	+	0.0819361i	0.923888	+	0.382663i	$0.124993\pi$
$6$	−1.51663	+	0.836567i	−0.619160	+	0.341527i
$7$	1.64561	+	2.07170i	0.621984	+	0.783030i
$7$	1.64561	+	2.07170i	0.621984	+	0.783030i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−2.37168	+	1.83715i	−0.790561	+	0.612383i
$10$	0.192011	+	0.0338567i	0.0607192	+	0.0107064i
$11$	4.42934	+	2.55728i	1.33550	+	0.771049i	0.986136	−	0.165939i	$-0.0530656\pi$
$11$	4.42934	+	2.55728i	1.33550	+	0.771049i	0.349360	+	0.936988i	$0.386399\pi$
$12$	1.08722	+	1.34832i	0.313852	+	0.389226i
$13$	−1.65749	−	4.55391i	−0.459704	−	1.26303i	−0.925706	−	0.378243i	$-0.876528\pi$
$13$	−1.65749	−	4.55391i	−0.459704	−	1.26303i	0.466002	−	0.884784i	$-0.345694\pi$
$14$	1.75447	−	1.98036i	0.468902	−	0.529274i
$15$	0.337639	+	0.00659504i	0.0871780	+	0.00170283i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	2.40829	−	6.61672i	0.584096	−	1.60479i	−0.197017	−	0.980400i	$-0.563125\pi$
$17$	2.40829	−	6.61672i	0.584096	−	1.60479i	0.781113	−	0.624390i	$-0.214652\pi$
$18$	2.22108	+	2.01664i	0.523513	+	0.475326i
$19$	−4.34664	−	0.326711i	−0.997187	−	0.0749525i
$19$	−4.34664	−	0.326711i	−0.997187	−	0.0749525i
$20$		−	0.194973i		−	0.0435973i
$21$	2.47285	−	3.85811i	0.539621	−	0.841908i
$22$	1.74928	−	4.80612i	0.372948	−	1.02467i
$23$	5.56812	−	6.63582i	1.16103	−	1.38366i	0.251591	−	0.967834i	$-0.419046\pi$
$23$	5.56812	−	6.63582i	1.16103	−	1.38366i	0.909442	−	0.415831i	$-0.136509\pi$
$24$	1.13904	−	1.30483i	0.232506	−	0.266348i
$25$	3.80110	+	3.18950i	0.760220	+	0.637901i
$26$	−4.19691	+	2.42308i	−0.823081	+	0.475206i
$27$	4.34014	+	2.85713i	0.835261	+	0.549854i
$28$	−2.25494	−	1.38393i	−0.426143	−	0.261538i
$29$	1.51822	+	1.27394i	0.281926	+	0.236564i	0.772774	−	0.634681i	$-0.218869\pi$
$29$	1.51822	+	1.27394i	0.281926	+	0.236564i	−0.490848	+	0.871245i	$0.663313\pi$
$30$	−0.0521355	−	0.333655i	−0.00951860	−	0.0609167i
$31$		−	0.481848i		−	0.0865425i	−0.999063	−	0.0432713i	$-0.986222\pi$
$31$		−	0.481848i		−	0.0865425i	0.999063	−	0.0432713i	$-0.0137780\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	1.70837	−	8.69239i	0.297390	−	1.51315i
$34$	−6.93439	−	1.22272i	−1.18924	−	0.209695i
$35$	−0.489304	+	0.163350i	−0.0827074	+	0.0276112i
$36$	1.60031	−	2.53752i	0.266719	−	0.422920i
$37$	0.661000	+	0.381628i	0.108668	+	0.0627393i	0.553349	−	0.832950i	$-0.313350\pi$
$37$	0.661000	+	0.381628i	0.108668	+	0.0627393i	−0.444681	+	0.895689i	$0.646683\pi$
$38$	0.433039	+	4.33734i	0.0702481	+	0.703609i
$39$	−6.53417	+	5.26884i	−1.04631	+	0.843689i
$40$	−0.192011	+	0.0338567i	−0.0303596	+	0.00535322i
$41$	−8.40841	−	3.06041i	−1.31317	−	0.477956i	−0.411909	−	0.911225i	$-0.635138\pi$
$41$	−8.40841	−	3.06041i	−1.31317	−	0.477956i	−0.901265	+	0.433269i	$0.857360\pi$
$42$	−4.22890	−	1.76533i	−0.652533	−	0.272397i
$43$	−1.13707	−	6.44867i	−0.173402	−	0.983412i	−0.939972	−	0.341251i	$-0.889149\pi$
$43$	−1.13707	−	6.44867i	−0.173402	−	0.983412i	0.766570	−	0.642161i	$-0.221962\pi$
$44$	−5.03686	−	0.888134i	−0.759335	−	0.133891i
$45$	−0.178438	−	0.557037i	−0.0265999	−	0.0830382i
$46$	−7.50190	−	4.33123i	−1.10610	−	0.638604i
$47$	−0.279048	−	0.766678i	−0.0407034	−	0.111832i	0.917676	−	0.397330i	$-0.130063\pi$
$47$	−0.279048	−	0.766678i	−0.0407034	−	0.111832i	−0.958379	+	0.285498i	$0.907841\pi$
$48$	−1.48280	−	0.895154i	−0.214024	−	0.129204i
$49$	−1.58391	+	6.81845i	−0.226272	+	0.974064i
$50$	2.48099	−	4.29721i	0.350865	−	0.607717i
$51$	−12.1937	−	0.238177i	−1.70746	−	0.0333515i
$52$	3.11506	+	3.71238i	0.431981	+	0.514815i
$53$	2.36708	−	0.861546i	0.325143	−	0.118342i	−0.174291	−	0.984694i	$-0.555763\pi$
$53$	2.36708	−	0.861546i	0.325143	−	0.118342i	0.499434	+	0.866352i	$0.333541\pi$
$54$	2.06006	−	4.77034i	0.280339	−	0.649161i
$55$	−0.763901	+	0.640989i	−0.103004	+	0.0864309i
$56$	−0.971340	+	2.46100i	−0.129801	+	0.328864i
$57$	1.90085	+	7.30663i	0.251774	+	0.967786i
$58$	0.990946	−	1.71637i	0.130118	−	0.225370i
$59$	6.01532	+	2.18940i	0.783129	+	0.285035i	0.702477	−	0.711707i	$-0.252078\pi$
$59$	6.01532	+	2.18940i	0.783129	+	0.285035i	0.0806520	+	0.996742i	$0.474300\pi$
$60$	−0.319532	+	0.109282i	−0.0412514	+	0.0141082i
$61$	7.82041	+	6.56210i	1.00130	+	0.840191i	0.987164	−	0.159709i	$-0.0510556\pi$
$61$	7.82041	+	6.56210i	1.00130	+	0.840191i	0.0141365	+	0.999900i	$0.495500\pi$
$62$	−0.474528	+	0.0836721i	−0.0602651	+	0.0106264i
$63$	−7.70890	−	1.89019i	−0.971231	−	0.238141i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.944872			0.117197
$66$	−8.85699	−	0.173002i	−1.09022	−	0.0212951i
$67$	−1.32595	−	0.233802i	−0.161991	−	0.0285634i	0.0920643	−	0.995753i	$-0.470653\pi$
$67$	−1.32595	−	0.233802i	−0.161991	−	0.0285634i	−0.254055	+	0.967190i	$0.581765\pi$
$68$			7.04136i			0.853891i
$69$	−13.9961	−	5.40597i	−1.68493	−	0.650802i
$70$	0.245835	+	0.453505i	0.0293829	+	0.0542042i
$71$	−2.09330	−	11.8717i	−0.248429	−	1.40891i	−0.812392	−	0.583112i	$-0.801835\pi$
$71$	−2.09330	−	11.8717i	−0.248429	−	1.40891i	0.563963	−	0.825800i	$-0.309276\pi$
$72$	−2.77686	−	1.13536i	−0.327256	−	0.133804i
$73$	−0.527858	−	2.99363i	−0.0617811	−	0.350378i	−0.999991	−	0.00431062i	$-0.998628\pi$
$73$	−0.527858	−	2.99363i	−0.0617811	−	0.350378i	0.938210	−	0.346068i	$-0.112483\pi$
$74$	0.261049	−	0.717227i	0.0303464	−	0.0833759i
$75$	3.09662	−	8.01716i	0.357567	−	0.925742i
$76$	4.19625	−	1.17963i	0.481342	−	0.135313i
$77$	1.99106	+	13.3846i	0.226902	+	1.52531i
$78$	6.32344	+	5.51998i	0.715988	+	0.625015i
$79$	2.73497	+	3.25941i	0.307708	+	0.366712i	0.897631	−	0.440747i	$-0.145286\pi$
$79$	2.73497	+	3.25941i	0.307708	+	0.366712i	−0.589923	+	0.807459i	$0.700842\pi$
$80$	0.0666847	+	0.183215i	0.00745558	+	0.0204840i
$81$	2.24977	−	8.71427i	0.249975	−	0.968252i
$82$	−1.55381	+	8.81210i	−0.171590	+	0.973134i
$83$	5.01312	+	2.89433i	0.550261	+	0.317694i	0.749227	−	0.662313i	$-0.230425\pi$
$83$	5.01312	+	2.89433i	0.550261	+	0.317694i	−0.198966	+	0.980006i	$0.563758\pi$
$84$	−1.00417	+	4.47120i	−0.109564	+	0.487848i
$85$	1.05168	+	0.882468i	0.114071	+	0.0957171i
$86$	−6.15325	+	2.23960i	−0.663521	+	0.241502i
$87$	1.23684	−	3.20218i	0.132603	−	0.343309i
$88$			5.11456i			0.545214i
$89$	0.163655	−	0.928132i	0.0173474	−	0.0983818i	−0.974905	−	0.222622i	$-0.928538\pi$
$89$	0.163655	−	0.928132i	0.0173474	−	0.0983818i	0.992252	+	0.124241i	$0.0396494\pi$
$90$	−0.517589	+	0.272455i	−0.0545587	+	0.0287193i
$91$	6.70676	−	10.9278i	0.703060	−	1.14554i
$92$	−2.96273	+	8.14004i	−0.308886	+	0.848658i
$93$	−0.789679	+	0.270075i	−0.0818859	+	0.0280055i
$94$	−0.706575	+	0.407941i	−0.0728776	+	0.0420759i
$95$	0.349712	−	0.774582i	0.0358797	−	0.0794704i
$96$	−0.624069	+	1.61572i	−0.0636938	+	0.164903i
$97$	−2.63474	−	3.13996i	−0.267517	−	0.318815i	0.615516	−	0.788124i	$-0.288947\pi$
$97$	−2.63474	−	3.13996i	−0.267517	−	0.318815i	−0.883034	+	0.469309i	$0.844503\pi$
$98$	6.98990	+	0.375831i	0.706087	+	0.0379646i
$99$	−15.2031	+	2.07229i	−1.52797	+	0.208273i
$100$	−4.66274	−	1.69710i	−0.466274	−	0.169710i
$101$	2.23281	−	2.66096i	0.222173	−	0.264776i	−0.643432	−	0.765504i	$-0.722490\pi$
$101$	2.23281	−	2.66096i	0.222173	−	0.264776i	0.865605	+	0.500728i	$0.166934\pi$
$102$	1.88285	+	12.0498i	0.186430	+	1.19311i
$103$		−	14.0202i		−	1.38145i	−0.723119	−	0.690723i	$-0.757292\pi$
$103$		−	14.0202i		−	1.38145i	0.723119	−	0.690723i	$-0.242708\pi$
$104$	3.11506	−	3.71238i	0.305456	−	0.364029i
$105$	0.541960	+	0.710340i	0.0528899	+	0.0693221i
$106$	−1.25950	−	2.18151i	−0.122333	−	0.211887i
$107$	−5.65395	−	9.79293i	−0.546588	−	0.946719i	−0.998505	−	0.0546586i	$-0.982593\pi$
$107$	−5.65395	−	9.79293i	−0.546588	−	0.946719i	0.451917	−	0.892060i	$-0.350740\pi$
$108$	−5.05559	−	1.20041i	−0.486475	−	0.115509i
$109$	12.8669	+	15.3342i	1.23243	+	1.46875i	0.834201	+	0.551460i	$0.185929\pi$
$109$	12.8669	+	15.3342i	1.23243	+	1.46875i	0.398224	+	0.917288i	$0.369627\pi$
$110$	0.763901	+	0.640989i	0.0728351	+	0.0611159i
$111$	0.254944	−	1.29718i	0.0241982	−	0.123123i
$112$	2.59228	+	0.529236i	0.244947	+	0.0500081i
$113$	−12.0260			−1.13131			−0.565656	−	0.824642i	$-0.691377\pi$
$113$	−12.0260			−1.13131			−0.565656	+	0.824642i	$0.691377\pi$
$114$	6.86554	−	3.14075i	0.643017	−	0.294159i
$115$	0.844472	+	1.46267i	0.0787475	+	0.136395i
$116$	−1.86237	−	0.677847i	−0.172917	−	0.0629365i
$117$	12.2972	+	7.75539i	1.13688	+	0.716986i
$118$	1.11159	−	6.30412i	0.102330	−	0.580342i
$119$	17.6710	−	5.89931i	1.61990	−	0.540789i
$120$	0.163108	+	0.295701i	0.0148896	+	0.0269937i
$121$	7.57937	+	13.1279i	0.689034	+	1.19344i
$122$	5.10441	−	8.84110i	0.462131	−	0.800435i
$123$	−0.302671	+	15.4955i	−0.0272910	+	1.39718i
$124$	0.164802	+	0.452789i	0.0147996	+	0.0406617i
$125$	−1.68210	+	0.971159i	−0.150451	+	0.0868631i
$126$	−0.522835	+	7.92002i	−0.0465778	+	0.705571i
$127$	1.96992	+	5.41231i	0.174802	+	0.480265i	0.995894	−	0.0905318i	$-0.0288567\pi$
$127$	1.96992	+	5.41231i	0.174802	+	0.480265i	−0.821091	+	0.570797i	$0.806634\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	−9.93109	+	5.47796i	−0.874384	+	0.482308i
$130$	−0.164075	−	0.930518i	−0.0143904	−	0.0816118i
$131$	6.36106	−	1.12163i	0.555768	−	0.0979969i	0.111292	−	0.993788i	$-0.464501\pi$
$131$	6.36106	−	1.12163i	0.555768	−	0.0979969i	0.444476	+	0.895791i	$0.353390\pi$
$132$	1.36763	+	8.75247i	0.119037	+	0.761805i
$133$	−6.47604	−	9.54258i	−0.561544	−	0.827447i
$134$			1.34641i			0.116312i
$135$	−0.812889	+	0.604651i	−0.0699623	+	0.0520401i
$136$	6.93439	−	1.22272i	0.594619	−	0.104847i
$137$	2.79722	+	7.68530i	0.238983	+	0.656599i	0.999969	+	0.00783182i	$0.00249297\pi$
$137$	2.79722	+	7.68530i	0.238983	+	0.656599i	−0.760987	+	0.648767i	$0.775285\pi$
$138$	−2.89345	+	14.7222i	−0.246307	+	1.25323i
$139$	−8.17595	+	2.97580i	−0.693475	+	0.252404i	−0.664622	−	0.747180i	$-0.731407\pi$
$139$	−8.17595	+	2.97580i	−0.693475	+	0.252404i	−0.0288524	+	0.999584i	$0.509185\pi$
$140$	0.403926	−	0.320850i	0.0341380	−	0.0271168i
$141$	−1.10007	+	0.887041i	−0.0926424	+	0.0747023i
$142$	−11.3279	+	4.12300i	−0.950612	+	0.345995i
$143$	4.30405	−	24.4095i	0.359923	−	2.04122i
$144$	−0.635920	+	2.93183i	−0.0529933	+	0.244319i
$145$	−0.334646	+	0.193208i	−0.0277908	+	0.0160450i
$146$	−2.85649	+	1.03968i	−0.236405	+	0.0860444i
$147$	12.0622	−	1.22594i	0.994875	−	0.101114i
$148$	−0.751661	−	0.132538i	−0.0617862	−	0.0108946i
$149$	0.949315	+	1.13135i	0.0777709	+	0.0926838i	0.803527	−	0.595268i	$-0.202954\pi$
$149$	0.949315	+	1.13135i	0.0777709	+	0.0926838i	−0.725756	+	0.687952i	$0.758510\pi$
$150$	−8.43308	−	1.65741i	−0.688558	−	0.135327i
$151$	−8.85631	+	5.11319i	−0.720716	+	0.416106i	−0.815016	−	0.579438i	$-0.803272\pi$
$151$	−8.85631	+	5.11319i	−0.720716	+	0.416106i	0.0943001	+	0.995544i	$0.469939\pi$
$152$	−1.89038	−	3.92765i	−0.153330	−	0.318575i
$153$	6.44419	+	20.1171i	0.520982	+	1.62638i
$154$	12.8355	−	4.28502i	1.03431	−	0.345297i
$155$	0.0882817	+	0.0321319i	0.00709096	+	0.00258090i
$156$	4.33807	−	7.18590i	0.347323	−	0.575333i
$157$	−11.3046	+	9.48570i	−0.902207	+	0.757042i	−0.970621	−	0.240615i	$-0.922651\pi$
$157$	−11.3046	+	9.48570i	−0.902207	+	0.757042i	0.0684135	+	0.997657i	$0.478206\pi$
$158$	2.73497	−	3.25941i	0.217583	−	0.259305i
$159$	−2.73869	−	3.39640i	−0.217192	−	0.269352i
$160$	0.168852	−	0.0974865i	0.0133489	−	0.00770699i
$161$	22.9104	+	0.615476i	1.80559	+	0.0485063i
$162$	−8.97255	−	0.702378i	−0.704950	−	0.0551840i
$163$	9.03487			0.707665			0.353833	−	0.935309i	$-0.384878\pi$
$163$	9.03487			0.707665			0.353833	+	0.935309i	$0.384878\pi$
$164$	8.94804			0.698725
$165$	1.47865	+	0.892649i	0.115113	+	0.0694926i
$166$	1.97984	−	5.43955i	0.153665	−	0.422191i
$167$	0.900701	−	5.10813i	0.0696983	−	0.395279i	−0.929923	−	0.367755i	$-0.880127\pi$
$167$	0.900701	−	5.10813i	0.0696983	−	0.395279i	0.999621	−	0.0275240i	$-0.00876228\pi$
$168$	4.57765	+	0.212502i	0.353173	+	0.0163949i
$169$	−8.03224	+	6.73985i	−0.617865	+	0.518450i
$170$	0.686438	−	1.18895i	0.0526474	−	0.0911880i
$171$	10.9091	−	7.21056i	0.834237	−	0.551406i
$172$	3.27407	+	5.67086i	0.249646	+	0.432399i
$173$	2.05219	+	11.6385i	0.156025	+	0.884862i	0.957843	+	0.287293i	$0.0927554\pi$
$173$	2.05219	+	11.6385i	0.156025	+	0.884862i	−0.801818	+	0.597569i	$0.796134\pi$
$174$	−3.36830	−	0.661995i	−0.255350	−	0.0501857i
$175$	−0.352554	+	13.1234i	−0.0266506	+	0.992039i
$176$	5.03686	−	0.888134i	0.379668	−	0.0669456i
$177$	0.216529	−	11.0854i	0.0162753	−	0.833229i
$178$	−0.942450			−0.0706396
$179$	10.6531	−	18.4516i	0.796247	−	1.37914i	−0.125798	−	0.992056i	$-0.540149\pi$
$179$	10.6531	−	18.4516i	0.796247	−	1.37914i	0.922044	−	0.387084i	$-0.126518\pi$
$180$	0.358194	+	0.462415i	0.0266982	+	0.0344663i
$181$	−6.62937	+	7.90058i	−0.492758	+	0.587246i	−0.953917	−	0.300072i	$-0.902989\pi$
$181$	−6.62937	+	7.90058i	−0.492758	+	0.587246i	0.461159	+	0.887317i	$0.347434\pi$
$182$	−11.9264	−	4.70728i	−0.884043	−	0.348927i
$183$	6.37100	−	16.4946i	0.470958	−	1.21931i
$184$	8.53085	+	1.50422i	0.628903	+	0.110892i
$185$	−0.113999	+	0.0956561i	−0.00838134	+	0.00703278i
$186$	0.403098	+	0.730784i	0.0295566	+	0.0535837i
$187$	27.5879	−	23.1490i	2.01743	−	1.69282i
$188$	0.524439	+	0.625002i	0.0382486	+	0.0455830i
$189$	1.22308	+	13.6932i	0.0889661	+	0.996035i
$190$	−0.823541	−	0.209895i	−0.0597459	−	0.0152274i
$191$	−14.0932	−	8.13673i	−1.01975	−	0.588753i	−0.105719	−	0.994396i	$-0.533714\pi$
$191$	−14.0932	−	8.13673i	−1.01975	−	0.588753i	−0.914032	+	0.405643i	$0.867048\pi$
$192$	1.69954	+	0.334022i	0.122654	+	0.0241059i
$193$	1.24503	−	0.219532i	0.0896189	−	0.0158022i	−0.128659	−	0.991689i	$-0.541067\pi$
$193$	1.24503	−	0.219532i	0.0896189	−	0.0158022i	0.218278	+	0.975887i	$0.429956\pi$
$194$	−2.63474	+	3.13996i	−0.189163	+	0.225436i
$195$	−0.529599	−	1.54851i	−0.0379254	−	0.110891i
$196$	−0.843663	−	6.94897i	−0.0602616	−	0.496355i
$197$	16.9368	+	9.77847i	1.20670	+	0.696687i	0.962036	−	0.272922i	$-0.0879900\pi$
$197$	16.9368	+	9.77847i	1.20670	+	0.696687i	0.244661	+	0.969609i	$0.421323\pi$
$198$	4.68080	+	14.6123i	0.332650	+	1.03845i
$199$	−1.56159	+	8.85621i	−0.110698	+	0.627800i	0.878092	+	0.478491i	$0.158816\pi$
$199$	−1.56159	+	8.85621i	−0.110698	+	0.627800i	−0.988791	+	0.149309i	$0.952295\pi$
$200$	−0.861640	+	4.88660i	−0.0609271	+	0.345535i
$201$	0.360028	+	2.30409i	0.0253944	+	0.162518i
$202$	−3.00826	−	1.73682i	−0.211660	−	0.122202i
$203$	−0.140815	+	5.24170i	−0.00988330	+	0.367895i
$204$	11.5398	−	3.94667i	0.807945	−	0.276322i
$205$	1.12142	−	1.33646i	0.0783237	−	0.0933426i
$206$	−13.8072	+	2.43457i	−0.961990	+	0.169625i
$207$	−1.01483	+	25.9675i	−0.0705353	+	1.80487i
$208$	−4.19691	−	2.42308i	−0.291003	−	0.168011i
$209$	−18.4172	−	12.5627i	−1.27395	−	0.868979i
$210$	0.605438	−	0.657076i	0.0417792	−	0.0453426i
$211$	12.2821	+	14.6373i	0.845537	+	1.00767i	0.999807	+	0.0196427i	$0.00625286\pi$
$211$	12.2821	+	14.6373i	0.845537	+	1.00767i	−0.154270	+	0.988029i	$0.549303\pi$
$212$	−1.92966	+	1.61918i	−0.132530	+	0.111206i
$213$	−18.2827	+	10.0847i	−1.25271	+	0.690991i
$214$	−8.66236	+	7.26858i	−0.592147	+	0.496870i
$215$	1.25732	+	0.221699i	0.0857482	+	0.0151197i
$216$	−0.304274	+	5.18724i	−0.0207032	+	0.352947i
$217$	0.998247	−	0.792937i	0.0677654	−	0.0538280i
$218$	12.8669	−	15.3342i	0.871457	−	1.03856i
$219$	−4.61026	+	2.54301i	−0.311533	+	0.171841i
$220$	0.498601	−	0.863602i	0.0336157	−	0.0582240i
$221$	−34.1236			−2.29540
$222$	−1.32175	−	0.0258175i	−0.0887099	−	0.00173276i
$223$	−18.7661	+	3.30896i	−1.25667	+	0.221585i	−0.762046	−	0.647523i	$-0.775805\pi$
$223$	−18.7661	+	3.30896i	−1.25667	+	0.221585i	−0.494623	+	0.869108i	$0.664694\pi$
$224$	0.0710510	−	2.64480i	0.00474729	−	0.176713i
$225$	−14.8746	−	0.581308i	−0.991640	−	0.0387539i
$226$	2.08829	+	11.8433i	0.138911	+	0.787805i
$227$	8.79449	+	15.2325i	0.583711	+	1.01102i	0.995035	+	0.0995275i	$0.0317331\pi$
$227$	8.79449	+	15.2325i	0.583711	+	1.01102i	−0.411324	+	0.911489i	$0.634934\pi$
$228$	−4.28523	−	6.21585i	−0.283796	−	0.411655i
$229$	2.24551	−	3.88934i	0.148388	−	0.257015i	−0.782244	−	0.622972i	$-0.785925\pi$
$229$	2.24551	−	3.88934i	0.148388	−	0.257015i	0.930632	+	0.365957i	$0.119258\pi$
$230$	1.29381	−	1.08563i	0.0853111	−	0.0715845i
$231$	20.8194	−	10.7651i	1.36981	−	0.708290i
$232$	−0.344152	+	1.95178i	−0.0225947	+	0.128141i
$233$	−3.50328	+	9.62517i	−0.229507	+	0.630566i	−0.999976	−	0.00691155i	$-0.997800\pi$
$233$	−3.50328	+	9.62517i	−0.229507	+	0.630566i	0.770469	+	0.637478i	$0.220022\pi$
$234$	5.50217	−	13.4571i	0.359688	−	0.879720i
$235$	0.159075			0.0103769
$236$	−6.40137			−0.416694
$237$	3.80875	−	6.30911i	0.247405	−	0.409821i
$238$	−8.87822	−	16.3781i	−0.575490	−	1.06164i
$239$	−18.7146	+	10.8049i	−1.21055	+	0.698911i	−0.962879	−	0.269933i	$-0.912998\pi$
$239$	−18.7146	+	10.8049i	−1.21055	+	0.698911i	−0.247671	+	0.968844i	$0.579665\pi$
$240$	0.262886	−	0.211978i	0.0169692	−	0.0136831i
$241$	0.133124	−	0.158651i	0.00857529	−	0.0102196i	−0.761740	−	0.647883i	$-0.775655\pi$
$241$	0.133124	−	0.158651i	0.00857529	−	0.0102196i	0.770315	+	0.637663i	$0.220099\pi$
$242$	11.6123	−	9.74385i	0.746465	−	0.626358i
$243$	−15.5424	+	1.19728i	−0.997046	+	0.0768054i
$244$	−9.59315	−	3.49162i	−0.614139	−	0.223528i
$245$	−1.14362	−	0.744881i	−0.0730631	−	0.0475887i
$246$	15.3127	−	2.39269i	0.976299	−	0.152553i
$247$	5.71669	+	20.3357i	0.363744	+	1.29393i
$248$	0.417293	−	0.240924i	0.0264981	−	0.0152987i
$249$	1.93354	−	9.83803i	0.122533	−	0.623460i
$250$	1.24850	+	1.48790i	0.0789620	+	0.0941032i
$251$	26.2787	+	4.63365i	1.65870	+	0.292474i	0.922990	−	0.384824i	$-0.125738\pi$
$251$	26.2787	+	4.63365i	1.65870	+	0.292474i	0.735710	+	0.677297i	$0.236849\pi$
$252$	7.89048	−	0.860405i	0.497054	−	0.0542004i
$253$	41.6327	−	15.1531i	2.61743	−	0.952666i
$254$	4.98801	−	2.87983i	0.312976	−	0.180697i
$255$	0.856769	−	2.21818i	0.0536530	−	0.138908i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−1.56385	+	0.569195i	−0.0975504	+	0.0355054i	−0.390334	−	0.920673i	$-0.627641\pi$
$257$	−1.56385	+	0.569195i	−0.0975504	+	0.0355054i	0.292784	+	0.956179i	$0.405418\pi$
$258$	7.11925	+	8.82898i	0.443225	+	0.549668i
$259$	0.297130	+	1.99741i	0.0184628	+	0.124113i
$260$	−0.887889	+	0.323165i	−0.0550646	+	0.0200419i
$261$	−5.94114	−	0.232183i	−0.367747	−	0.0143718i
$262$	−2.20917	−	6.06965i	−0.136483	−	0.374984i
$263$	9.70551	−	1.71134i	0.598467	−	0.105526i	0.133796	−	0.991009i	$-0.457283\pi$
$263$	9.70551	−	1.71134i	0.598467	−	0.105526i	0.464672	+	0.885483i	$0.346172\pi$
$264$	8.38202	−	2.86670i	0.515878	−	0.176433i
$265$			0.491136i			0.0301702i
$266$	−8.27305	+	8.03471i	−0.507254	+	0.492640i
$267$	−1.61280	+	0.252010i	−0.0987018	+	0.0154228i
$268$	1.32595	−	0.233802i	0.0809956	−	0.0142817i
$269$	1.22271	+	6.93433i	0.0745499	+	0.422794i	0.999126	+	0.0417965i	$0.0133081\pi$
$269$	1.22271	+	6.93433i	0.0745499	+	0.422794i	−0.924576	+	0.380997i	$0.875581\pi$
$270$	0.736622	+	0.695543i	0.0448294	+	0.0423294i
$271$	−26.1634	−	9.52269i	−1.58931	−	0.578462i	−0.612110	−	0.790773i	$-0.709679\pi$
$271$	−26.1634	−	9.52269i	−1.58931	−	0.578462i	−0.977202	+	0.212311i	$0.931901\pi$
$272$	−2.40829	−	6.61672i	−0.146024	−	0.401197i
$273$	−21.6682	−	4.86639i	−1.31142	−	0.294528i
$274$	7.08281	−	4.08926i	0.427888	−	0.247041i
$275$	8.67992	+	23.8479i	0.523419	+	1.43808i
$276$	15.0009	+	0.293011i	0.902951	+	0.0176372i
$277$	−9.33252	+	16.1644i	−0.560737	+	0.971224i	0.436696	+	0.899609i	$0.356149\pi$
$277$	−9.33252	+	16.1644i	−0.560737	+	0.971224i	−0.997432	+	0.0716151i	$0.977185\pi$
$278$	4.35033	+	7.53499i	0.260915	+	0.451919i
$279$	0.885227	+	1.14279i	0.0529971	+	0.0684172i
$280$	−0.386117	−	0.342075i	−0.0230749	−	0.0204429i
$281$	−0.399945	+	2.26820i	−0.0238587	+	0.135309i	−0.994410	−	0.105583i	$-0.966329\pi$
$281$	−0.399945	+	2.26820i	−0.0238587	+	0.135309i	0.970552	+	0.240893i	$0.0774402\pi$
$282$	1.06459	+	0.929323i	0.0633954	+	0.0553404i
$283$	27.8384	+	10.1324i	1.65482	+	0.602307i	0.989537	−	0.144281i	$-0.0460870\pi$
$283$	27.8384	+	10.1324i	1.65482	+	0.602307i	0.665287	+	0.746588i	$0.268309\pi$
$284$	6.02742	+	10.4398i	0.357662	+	0.619488i
$285$	−1.46544	−	0.138976i	−0.0868051	−	0.00823225i
$286$	−24.7860			−1.46563
$287$	−7.49674	−	22.4560i	−0.442519	−	1.32554i
$288$	2.99771	+	0.117152i	0.176642	+	0.00690327i
$289$	−24.9583	−	20.9425i	−1.46814	−	1.23191i
$290$	0.248383	+	0.296012i	0.0145856	+	0.0173824i
$291$	−3.66917	+	6.07790i	−0.215091	+	0.356293i
$292$	1.51991	+	2.63256i	0.0889459	+	0.154059i
$293$	−2.93758	−	5.08804i	−0.171615	−	0.297246i	0.767369	−	0.641205i	$-0.221565\pi$
$293$	−2.93758	−	5.08804i	−0.171615	−	0.297246i	−0.938985	+	0.343959i	$0.888232\pi$
$294$	−3.30189	−	11.6661i	−0.192570	−	0.680380i
$295$	−0.802260	+	0.956097i	−0.0467094	+	0.0556661i
$296$			0.763257i			0.0443634i
$297$	11.9175	+	23.7541i	0.691523	+	1.37836i
$298$	0.949315	−	1.13135i	0.0549923	−	0.0655373i
$299$	−39.4480	−	14.3579i	−2.28134	−	0.830339i
$300$	−0.167841	+	8.59277i	−0.00969032	+	0.496104i
$301$	11.4885	−	12.9677i	0.662188	−	0.747446i
$302$	6.57339	+	7.83386i	0.378256	+	0.450788i
$303$	−5.61241	−	2.16779i	−0.322425	−	0.124536i
$304$	−3.53972	+	2.54369i	−0.203017	+	0.145891i
$305$	−1.72378	+	0.995222i	−0.0987031	+	0.0569863i
$306$	18.6925	−	9.83959i	1.06858	−	0.562492i
$307$	−0.890063	+	2.44543i	−0.0507986	+	0.139568i	−0.962497	−	0.271292i	$-0.912549\pi$
$307$	−0.890063	+	2.44543i	−0.0507986	+	0.139568i	0.911699	+	0.410860i	$0.134771\pi$
$308$	−6.44878	−	11.8964i	−0.367453	−	0.677860i
$309$	−22.9770	+	7.85827i	−1.30711	+	0.447041i
$310$	0.0163138	−	0.0925202i	0.000926562	−	0.00525479i
$311$			26.8455i			1.52227i	0.648595	+	0.761134i	$0.275357\pi$
$311$			26.8455i			1.52227i	−0.648595	+	0.761134i	$0.724643\pi$
$312$	−7.83003	−	3.02434i	−0.443288	−	0.171220i
$313$	7.64628	−	2.78302i	0.432193	−	0.157305i	−0.116757	−	0.993161i	$-0.537250\pi$
$313$	7.64628	−	2.78302i	0.432193	−	0.157305i	0.548950	+	0.835855i	$0.315028\pi$
$314$	11.3046	+	9.48570i	0.637957	+	0.535309i
$315$	0.860376	−	1.28634i	0.0484767	−	0.0724769i
$316$	−3.68482	−	2.12743i	−0.207287	−	0.119677i
$317$	−2.26824	+	12.8638i	−0.127397	+	0.722504i	0.852458	+	0.522795i	$0.175111\pi$
$317$	−2.26824	+	12.8638i	−0.127397	+	0.722504i	−0.979855	+	0.199709i	$0.936000\pi$
$318$	−2.86923	+	3.28686i	−0.160899	+	0.184318i
$319$	3.46689	+	9.52520i	0.194109	+	0.533309i
$320$	−0.125326	−	0.149358i	−0.00700595	−	0.00834937i
$321$	−12.8802	+	14.7549i	−0.718901	+	0.823539i
$322$	−3.37223	−	22.6692i	−0.187927	−	1.26331i
$323$	−12.6297	+	27.9737i	−0.702736	+	1.55650i
$324$	0.866360	+	8.95820i	0.0481311	+	0.497678i
$325$	8.22443	−	22.5964i	0.456209	−	1.25342i
$326$	−1.56889	−	8.89761i	−0.0868927	−	0.492793i
$327$	17.9186	−	29.6817i	0.990901	−	1.64140i
$328$	−1.55381	−	8.81210i	−0.0857949	−	0.486567i
$329$	1.12912	−	1.83976i	0.0622506	−	0.101429i
$330$	0.622322	−	1.61119i	0.0342577	−	0.0886933i
$331$		−	27.6162i		−	1.51793i	−0.651134	−	0.758963i	$-0.725707\pi$
$331$		−	27.6162i		−	1.51793i	0.651134	−	0.758963i	$-0.274293\pi$
$332$	−5.70071	−	1.00519i	−0.312867	−	0.0551669i
$333$	−2.26879	+	0.309252i	−0.124329	+	0.0169469i
$334$	−5.18693			−0.283816
$335$	0.131257	−	0.227343i	0.00717133	−	0.0124211i
$336$	−0.585626	−	4.54500i	−0.0319485	−	0.247950i
$337$	−17.3056	+	3.05145i	−0.942697	+	0.166223i	−0.623816	−	0.781572i	$-0.714418\pi$
$337$	−17.3056	+	3.05145i	−0.942697	+	0.166223i	−0.318882	+	0.947795i	$0.603307\pi$
$338$	8.03224	+	6.73985i	0.436896	+	0.366600i
$339$	6.74055	+	19.7089i	0.366096	+	1.07044i
$340$	−1.29008	−	0.469551i	−0.0699645	−	0.0254650i
$341$	1.23222	−	2.13427i	0.0667285	−	0.115577i
$342$	−8.99536	−	9.49123i	−0.486413	−	0.513227i
$343$	−16.7323	+	7.93916i	−0.903459	+	0.428674i
$344$	5.01617	−	4.20907i	0.270454	−	0.226938i
$345$	1.92378	−	2.20379i	0.103573	−	0.118648i
$346$	11.1054	−	4.04202i	0.597028	−	0.217300i
$347$	−14.9781	−	17.8502i	−0.804065	−	0.958248i	0.195683	−	0.980667i	$-0.437308\pi$
$347$	−14.9781	−	17.8502i	−0.804065	−	0.958248i	−0.999749	+	0.0224194i	$0.992863\pi$
$348$	−0.0670383	+	3.43208i	−0.00359363	+	0.183979i
$349$	7.84067	−	13.5804i	0.419701	−	0.726944i	−0.576208	−	0.817303i	$-0.695468\pi$
$349$	7.84067	−	13.5804i	0.419701	−	0.726944i	0.995909	+	0.0903591i	$0.0288015\pi$
$350$	12.9853	−	1.93166i	0.694093	−	0.103252i
$351$	5.81737	−	24.5003i	0.310508	−	1.30773i
$352$	−1.74928	−	4.80612i	−0.0932371	−	0.256167i
$353$	2.02486	+	1.16905i	0.107773	+	0.0622225i	0.552917	−	0.833236i	$-0.313514\pi$
$353$	2.02486	+	1.16905i	0.107773	+	0.0622225i	−0.445145	+	0.895459i	$0.646848\pi$
$354$	−10.9546	+	1.71172i	−0.582229	+	0.0909768i
$355$	2.31466	+	0.408138i	0.122850	+	0.0216617i
$356$	0.163655	+	0.928132i	0.00867368	+	0.0491909i
$357$	−19.5727	−	25.6536i	−1.03589	−	1.35773i
$358$	−20.0212	−	7.28712i	−1.05815	−	0.385136i
$359$	−19.6887	+	3.47165i	−1.03913	+	0.183227i	−0.667080	−	0.744986i	$-0.732456\pi$
$359$	−19.6887	+	3.47165i	−1.03913	+	0.183227i	−0.372050	+	0.928213i	$0.621345\pi$
$360$	0.393190	−	0.433050i	0.0207229	−	0.0228237i
$361$	18.7865	+	2.84018i	0.988764	+	0.149483i
$362$	8.93173	+	5.15674i	0.469441	+	0.271032i
$363$	17.2664	−	19.7796i	0.906252	−	1.03816i
$364$	−2.56477	+	12.5626i	−0.134430	+	0.658460i
$365$	0.583678	+	0.102918i	0.0305511	+	0.00538698i
$366$	−17.3503	−	3.40997i	−0.906913	−	0.178242i
$367$	−18.4790	−	15.5057i	−0.964594	−	0.809390i	0.0171005	−	0.999854i	$-0.494556\pi$
$367$	−18.4790	−	15.5057i	−0.964594	−	0.809390i	−0.981694	+	0.190464i	$0.939001\pi$
$368$		−	8.66245i		−	0.451562i
$369$	25.5645	−	8.18917i	1.33084	−	0.426311i
$370$	0.113999	+	0.0956561i	0.00592650	+	0.00497292i
$371$	5.68017	+	3.48611i	0.294900	+	0.180990i
$372$	0.649684	−	0.523874i	0.0336846	−	0.0271616i
$373$	−8.63225	+	4.98383i	−0.446961	+	0.258053i	−0.706546	−	0.707667i	$-0.749748\pi$
$373$	−8.63225	+	4.98383i	−0.446961	+	0.258053i	0.259585	+	0.965720i	$0.416414\pi$
$374$	−27.5879	−	23.1490i	−1.42654	−	1.19701i
$375$	2.53440	+	2.21238i	0.130876	+	0.114247i
$376$	0.524439	−	0.625002i	0.0270459	−	0.0322320i
$377$	3.28496	−	9.02536i	0.169184	−	0.464830i
$378$	13.2728	−	3.58230i	0.682679	−	0.184254i
$379$			37.5428i			1.92844i	0.265098	+	0.964222i	$0.414596\pi$
$379$			37.5428i			1.92844i	−0.265098	+	0.964222i	$0.585404\pi$
$380$	−0.0636997	+	0.847477i	−0.00326773	+	0.0434747i
$381$	7.76585	−	6.26200i	0.397857	−	0.320812i
$382$	−5.56585	+	15.2920i	−0.284774	+	0.782409i
$383$	−18.0478	+	15.1439i	−0.922198	+	0.773816i	−0.974400	−	0.224820i	$-0.927820\pi$
$383$	−18.0478	+	15.1439i	−0.922198	+	0.773816i	0.0522020	+	0.998637i	$0.483376\pi$
$384$	0.0338254	−	1.73172i	0.00172615	−	0.0883715i
$385$	−2.58502	−	0.527755i	−0.131745	−	0.0268969i
$386$	−0.432393	−	1.18799i	−0.0220082	−	0.0604671i
$387$	14.5439	+	13.2052i	0.739310	+	0.671259i
$388$	3.54978	+	2.04947i	0.180213	+	0.104046i
$389$	−12.7507	−	2.24829i	−0.646484	−	0.113993i	−0.159214	−	0.987244i	$-0.550896\pi$
$389$	−12.7507	−	2.24829i	−0.646484	−	0.113993i	−0.487270	+	0.873251i	$0.662007\pi$
$390$	−1.43302	+	0.790449i	−0.0725637	+	0.0400259i
$391$	−30.4977	−	52.8236i	−1.54234	−	2.67141i
$392$	−6.69690	+	2.03752i	−0.338245	+	0.102910i
$393$	−5.40354	−	9.79618i	−0.272573	−	0.494152i
$394$	6.68887	−	18.3775i	0.336980	−	0.925846i
$395$	−0.779553	+	0.283734i	−0.0392236	+	0.0142762i
$396$	13.5775	−	7.14708i	0.682294	−	0.359154i
$397$	−2.11992	−	12.0227i	−0.106396	−	0.603400i	−0.990654	−	0.136401i	$-0.956446\pi$
$397$	−2.11992	−	12.0227i	−0.106396	−	0.603400i	0.884258	−	0.466999i	$-0.154665\pi$
$398$	8.99283			0.450770
$399$	−12.0091	+	15.9619i	−0.601206	+	0.799094i
$400$	4.96199			0.248099
$401$	3.24315	+	18.3928i	0.161955	+	0.918494i	0.952148	+	0.305636i	$0.0988691\pi$
$401$	3.24315	+	18.3928i	0.161955	+	0.918494i	−0.790193	+	0.612858i	$0.790020\pi$
$402$	2.20657	−	0.754660i	0.110054	−	0.0376390i
$403$	−2.19429	+	0.798657i	−0.109306	+	0.0397840i
$404$	−1.18805	+	3.26415i	−0.0591079	+	0.162398i
$405$	1.44656	+	0.993300i	0.0718800	+	0.0493575i
$406$	5.18652	−	0.771536i	0.257403	−	0.0382907i
$407$	1.95186	+	3.38072i	0.0967502	+	0.167576i
$408$	−5.89057	−	10.6791i	−0.291627	−	0.528695i
$409$	24.7190	+	4.35862i	1.22227	+	0.215520i	0.747304	−	0.664482i	$-0.231348\pi$
$409$	24.7190	+	4.35862i	1.22227	+	0.215520i	0.474970	+	0.880002i	$0.342459\pi$
$410$	−1.51089	−	0.872314i	−0.0746176	−	0.0430805i
$411$	11.0272	−	8.89183i	0.543934	−	0.438601i
$412$	4.79517	+	13.1746i	0.236241	+	0.649068i
$413$	5.36312	+	16.0649i	0.263902	+	0.790501i
$414$	25.7493	−	3.50981i	1.26551	−	0.172498i
$415$	−0.864582	+	0.725470i	−0.0424406	+	0.0356119i
$416$	−1.65749	+	4.55391i	−0.0812650	+	0.223274i
$417$	9.45950	+	11.7313i	0.463234	+	0.574482i
$418$	−9.17371	+	20.3189i	−0.448701	+	0.993832i
$419$			5.69757i			0.278345i	0.990268	+	0.139172i	$0.0444442\pi$
$419$			5.69757i			0.278345i	−0.990268	+	0.139172i	$0.955556\pi$
$420$	−0.752227	−	0.482140i	−0.0367049	−	0.0235260i
$421$	0.419139	−	1.15157i	0.0204276	−	0.0561243i	−0.929060	−	0.369930i	$-0.879382\pi$
$421$	0.419139	−	1.15157i	0.0204276	−	0.0561243i	0.949487	+	0.313805i	$0.101604\pi$
$422$	12.2821	−	14.6373i	0.597885	−	0.712531i
$423$	2.07032	+	1.30567i	0.100662	+	0.0634837i
$424$	1.92966	+	1.61918i	0.0937126	+	0.0786342i
$425$	30.2582	−	17.4696i	1.46774	−	0.847399i
$426$	13.1062	+	16.2538i	0.634999	+	0.787497i
$427$	−0.725346	+	27.0003i	−0.0351020	+	1.30663i
$428$	8.66236	+	7.26858i	0.418711	+	0.351340i
$429$	−42.4160	+	6.62775i	−2.04786	+	0.319991i
$430$		−	1.27671i		−	0.0615685i
$431$	−9.69965	−	8.13897i	−0.467216	−	0.392040i	0.378562	−	0.925576i	$-0.376419\pi$
$431$	−9.69965	−	8.13897i	−0.467216	−	0.392040i	−0.845778	+	0.533535i	$0.820863\pi$
$432$	5.16127	−	0.601103i	0.248322	−	0.0289206i
$433$	16.0890	+	2.83692i	0.773186	+	0.136333i	0.546302	−	0.837588i	$-0.316035\pi$
$433$	16.0890	+	2.83692i	0.773186	+	0.136333i	0.226884	+	0.973922i	$0.427146\pi$
$434$	−0.954234	−	0.845389i	−0.0458047	−	0.0405800i
$435$	0.504208	+	0.440143i	0.0241749	+	0.0211032i
$436$	−17.3355	−	10.0087i	−0.830221	−	0.479329i
$437$	−26.3706	+	27.0244i	−1.26148	+	1.29275i
$438$	3.30494	+	4.09864i	0.157916	+	0.195840i
$439$	8.40498	−	1.48203i	0.401148	−	0.0707332i	0.0305655	−	0.999533i	$-0.490269\pi$
$439$	8.40498	−	1.48203i	0.401148	−	0.0707332i	0.370583	+	0.928800i	$0.379158\pi$
$440$	−0.937063	−	0.341063i	−0.0446727	−	0.0162595i
$441$	−8.76998	−	19.0811i	−0.417618	−	0.908623i
$442$	5.92551	+	33.6052i	0.281848	+	1.59844i
$443$	−2.94751	−	0.519726i	−0.140041	−	0.0246929i	0.103188	−	0.994662i	$-0.467096\pi$
$443$	−2.94751	−	0.519726i	−0.140041	−	0.0246929i	−0.243229	+	0.969969i	$0.578207\pi$
$444$	0.204094	+	1.30615i	0.00968586	+	0.0619871i
$445$	0.159134	+	0.0918762i	0.00754369	+	0.00435535i
$446$	6.51739	+	17.9064i	0.308607	+	0.847891i
$447$	1.32203	−	2.18991i	0.0625298	−	0.103579i
$448$	−2.61695	+	0.389293i	−0.123639	+	0.0183923i
$449$	6.74168	−	11.6769i	0.318160	−	0.551069i	−0.661944	−	0.749553i	$-0.730269\pi$
$449$	6.74168	−	11.6769i	0.318160	−	0.551069i	0.980104	+	0.198484i	$0.0636019\pi$
$450$	2.01047	+	14.7496i	0.0947745	+	0.695301i
$451$	−29.4174	−	35.0583i	−1.38521	−	1.65083i
$452$	11.3007	−	4.11314i	0.531542	−	0.193466i
$453$	13.3437	+	11.6483i	0.626942	+	0.547283i
$454$	13.4739	−	11.3060i	0.632363	−	0.530616i
$455$	1.55490	+	1.95749i	0.0728946	+	0.0917688i
$456$	−5.37730	+	5.29950i	−0.251815	+	0.248172i
$457$	−12.1969	+	21.1256i	−0.570546	+	0.988215i	0.425963	+	0.904740i	$0.359935\pi$
$457$	−12.1969	+	21.1256i	−0.570546	+	0.988215i	−0.996510	+	0.0834751i	$0.973398\pi$
$458$	−4.22018	−	1.53602i	−0.197196	−	0.0717735i
$459$	29.3571	−	21.8367i	1.37027	−	1.01925i
$460$	−1.29381	−	1.08563i	−0.0603240	−	0.0506179i
$461$	−25.9455	+	4.57490i	−1.20840	+	0.213074i	−0.741328	−	0.671143i	$-0.765804\pi$
$461$	−25.9455	+	4.57490i	−1.20840	+	0.213074i	−0.467076	+	0.884217i	$0.654692\pi$
$462$	−14.2168	−	18.6337i	−0.661425	−	0.866920i
$463$	15.2156	−	26.3542i	0.707128	−	1.22478i	−0.258790	−	0.965934i	$-0.583324\pi$
$463$	15.2156	−	26.3542i	0.707128	−	1.22478i	0.965918	−	0.258848i	$-0.0833428\pi$
$464$	1.98189			0.0920070
$465$	0.00317781	−	0.162691i	0.000147367	−	0.00754460i
$466$	10.0873	+	1.77866i	0.467284	+	0.0823949i
$467$		−	24.6742i		−	1.14179i	−0.821024	−	0.570893i	$-0.806597\pi$
$467$		−	24.6742i		−	1.14179i	0.821024	−	0.570893i	$-0.193403\pi$
$468$	−14.2081	−	3.08177i	−0.656771	−	0.142455i
$469$	−1.69764	−	3.13173i	−0.0783899	−	0.144610i
$470$	−0.0276231	−	0.156658i	−0.00127416	−	0.00722611i
$471$	21.8819	+	13.2099i	1.00826	+	0.608680i
$472$	1.11159	+	6.30412i	0.0511649	+	0.290171i
$473$	11.4546	−	31.4711i	0.526681	−	1.44704i
$474$	−6.87464	−	2.65532i	−0.315763	−	0.121963i
$475$	−15.4800	−	15.1055i	−0.710270	−	0.693087i
$476$	−14.5876	+	11.5874i	−0.668622	+	0.531106i
$477$	−4.03118	+	6.39199i	−0.184575	+	0.292669i
$478$	13.8905	+	16.5541i	0.635338	+	0.757166i
$479$	6.45769	+	17.7424i	0.295059	+	0.810669i	0.995307	+	0.0967686i	$0.0308507\pi$
$479$	6.45769	+	17.7424i	0.295059	+	0.810669i	−0.700248	+	0.713900i	$0.746927\pi$
$480$	−0.254407	−	0.222082i	−0.0116120	−	0.0101366i
$481$	0.642302	−	3.64268i	0.0292865	−	0.166092i
$482$	−0.179358	−	0.103552i	−0.00816953	−	0.00471668i
$483$	−11.8326	−	37.8918i	−0.538401	−	1.72414i
$484$	−11.6123	−	9.74385i	−0.527830	−	0.442902i
$485$	0.750984	−	0.273336i	0.0341004	−	0.0124115i
$486$	3.87800	+	15.0984i	0.175910	+	0.684876i
$487$			24.5953i			1.11452i	0.830338	+	0.557260i	$0.188147\pi$
$487$			24.5953i			1.11452i	−0.830338	+	0.557260i	$0.811853\pi$
$488$	−1.77274	+	10.0537i	−0.0802483	+	0.455111i
$489$	−5.06402	−	14.8068i	−0.229003	−	0.669588i
$490$	−0.534977	+	1.25559i	−0.0241678	+	0.0567218i
$491$	2.34057	−	6.43066i	0.105628	−	0.290212i	−0.875607	−	0.483024i	$-0.839539\pi$
$491$	2.34057	−	6.43066i	0.105628	−	0.290212i	0.981236	+	0.192812i	$0.0617607\pi$
$492$	−5.01536	−	14.6645i	−0.226110	−	0.661128i
$493$	12.0856	−	6.97761i	0.544307	−	0.314256i
$494$	19.0341	−	9.16110i	0.856383	−	0.412177i
$495$	0.634140	−	2.92362i	0.0285025	−	0.131407i
$496$	−0.309726	−	0.369117i	−0.0139071	−	0.0165739i
$497$	21.1499	−	23.8730i	0.948702	−	1.07085i
$498$	−10.0243	−	0.195804i	−0.449201	−	0.00877417i
$499$	25.7234	+	9.36256i	1.15154	+	0.419126i	0.846068	−	0.533075i	$-0.178964\pi$
$499$	25.7234	+	9.36256i	1.15154	+	0.419126i	0.305471	+	0.952201i	$0.401186\pi$
$500$	1.24850	−	1.48790i	0.0558345	−	0.0665410i
$501$	−8.87631	+	1.38698i	−0.396565	+	0.0619656i
$502$		−	26.6841i		−	1.19097i
$503$	3.32057	−	3.95730i	0.148057	−	0.176447i	−0.686919	−	0.726734i	$-0.741037\pi$
$503$	3.32057	−	3.95730i	0.148057	−	0.176447i	0.834976	+	0.550287i	$0.185482\pi$
$504$	−2.21750	−	7.62120i	−0.0987753	−	0.339475i
$505$	0.338633	+	0.586530i	0.0150690	+	0.0261002i
$506$	−22.1523	−	38.3689i	−0.984791	−	1.70571i
$507$	15.5477	+	9.38600i	0.690497	+	0.416847i
$508$	−3.70224	−	4.41216i	−0.164260	−	0.195758i
$509$	−19.6844	−	16.5172i	−0.872497	−	0.732112i	0.0921258	−	0.995747i	$-0.470634\pi$
$509$	−19.6844	−	16.5172i	−0.872497	−	0.732112i	−0.964622	+	0.263636i	$0.915078\pi$
$510$	−2.33326	−	0.458570i	−0.103318	−	0.0203058i
$511$	5.33327	−	6.01993i	0.235930	−	0.266306i
$512$	−1.00000			−0.0441942
$513$	−17.9316	−	13.8369i	−0.791698	−	0.610913i
$514$	0.832108	+	1.44125i	0.0367027	+	0.0635710i
$515$	2.56870	+	0.934930i	0.113190	+	0.0411979i
$516$	7.45860	−	8.54423i	0.328347	−	0.376139i
$517$	0.724613	−	4.10948i	0.0318684	−	0.180735i
$518$	1.91547	−	0.639462i	0.0841608	−	0.0280964i
$519$	17.9236	−	9.88661i	0.786760	−	0.433974i
$520$	0.472436	+	0.818283i	0.0207177	+	0.0358841i
$521$	−14.6985	+	25.4585i	−0.643953	+	1.11536i	0.340590	+	0.940212i	$0.389373\pi$
$521$	−14.6985	+	25.4585i	−0.643953	+	1.11536i	−0.984542	+	0.175147i	$0.943960\pi$
$522$	0.803013	+	5.89120i	0.0351469	+	0.257851i
$523$	11.5727	+	31.7957i	0.506038	+	1.39033i	0.885292	+	0.465036i	$0.153958\pi$
$523$	11.5727	+	31.7957i	0.506038	+	1.39033i	−0.379254	+	0.925293i	$0.623819\pi$
$524$	−5.59382	+	3.22959i	−0.244367	+	0.141085i
$525$	21.7050	−	6.77788i	0.947285	−	0.295811i
$526$	−3.37069	−	9.26089i	−0.146969	−	0.403794i
$527$	−3.18825	−	1.16043i	−0.138883	−	0.0505491i
$528$	−4.27867	−	7.75688i	−0.186205	−	0.337575i
$529$	−9.03632	−	51.2475i	−0.392883	−	2.22815i
$530$	0.483674	−	0.0852848i	0.0210095	−	0.00370454i
$531$	−18.2887	+	5.85848i	−0.793662	+	0.254236i
$532$	9.34925	+	6.75216i	0.405341	+	0.292743i
$533$			43.3637i			1.87829i
$534$	0.528241	+	1.54454i	0.0228592	+	0.0668387i
$535$	2.17124	−	0.382849i	0.0938710	−	0.0165520i
$536$	−0.460499	−	1.26521i	−0.0198905	−	0.0546488i
$537$	−36.2105	−	7.11670i	−1.56260	−	0.307108i
$538$	6.61666	−	2.40827i	0.285265	−	0.103828i
$539$	−24.4523	+	26.1507i	−1.05324	+	1.12639i
$540$	0.557063	−	0.846211i	0.0239722	−	0.0364151i
$541$	−40.3229	+	14.6763i	−1.73362	+	0.630985i	−0.998878	−	0.0473653i	$-0.984918\pi$
$541$	−40.3229	+	14.6763i	−1.73362	+	0.630985i	−0.734739	+	0.678350i	$0.762695\pi$
$542$	−4.83480	+	27.4195i	−0.207672	+	1.17777i
$543$	16.6636	+	6.43632i	0.715106	+	0.276209i
$544$	−6.09800	+	3.52068i	−0.261450	+	0.150948i
$545$	−3.66747	+	1.33485i	−0.157097	+	0.0571787i
$546$	−1.02982	+	22.1840i	−0.0440722	+	0.949389i
$547$	−23.9409	−	4.22143i	−1.02364	−	0.180496i	−0.363466	−	0.931607i	$-0.618407\pi$
$547$	−23.9409	−	4.22143i	−1.02364	−	0.180496i	−0.660175	+	0.751112i	$0.729518\pi$
$548$	−5.25705	−	6.26511i	−0.224570	−	0.267632i
$549$	−30.6031	−	1.19599i	−1.30611	−	0.0510435i
$550$	21.9783	−	12.6892i	0.937159	−	0.541069i
$551$	−6.18293	−	6.03336i	−0.263402	−	0.257030i
$552$	−2.31633	−	14.8239i	−0.0985894	−	0.630948i
$553$	−2.25182	+	11.0298i	−0.0957573	+	0.469034i
$554$	17.5394	+	6.38382i	0.745178	+	0.271222i
$555$	0.220662	+	0.133212i	0.00936659	+	0.00565453i
$556$	6.66509	−	5.59268i	0.282663	−	0.237182i
$557$	−24.6479	+	29.3742i	−1.04436	+	1.24462i	−0.0754706	+	0.997148i	$0.524046\pi$
$557$	−24.6479	+	29.3742i	−1.04436	+	1.24462i	−0.968894	+	0.247477i	$0.920399\pi$
$558$	0.971713	−	1.07022i	0.0411359	−	0.0453061i
$559$	−27.4819	+	15.8667i	−1.16236	+	0.671090i
$560$	−0.269829	+	0.439652i	−0.0114024	+	0.0185787i
$561$	−53.4008	−	32.2376i	−2.25459	−	1.36107i
$562$	2.30319			0.0971542
$563$	34.5738			1.45711			0.728555	−	0.684987i	$-0.240192\pi$
$563$	34.5738			1.45711			0.728555	+	0.684987i	$0.240192\pi$
$564$	0.730340	−	1.20979i	0.0307529	−	0.0509414i
$565$	0.801951	−	2.20334i	0.0337383	−	0.0926953i
$566$	5.14434	−	29.1750i	0.216233	−	1.22632i
$567$	21.7556	−	9.67947i	0.913651	−	0.406499i
$568$	9.23455	−	7.74871i	0.387473	−	0.325128i
$569$	5.85842	−	10.1471i	0.245598	−	0.425388i	−0.716702	−	0.697380i	$-0.754349\pi$
$569$	5.85842	−	10.1471i	0.245598	−	0.425388i	0.962299	+	0.271992i	$0.0876825\pi$
$570$	0.117606	+	1.46731i	0.00492596	+	0.0614588i
$571$	−6.21536	−	10.7653i	−0.260105	−	0.450514i	0.706165	−	0.708047i	$-0.250424\pi$
$571$	−6.21536	−	10.7653i	−0.260105	−	0.450514i	−0.966269	+	0.257533i	$0.917090\pi$
$572$	4.30405	+	24.4095i	0.179961	+	1.02061i
$573$	−5.43569	+	27.6574i	−0.227079	+	1.15540i
$574$	−20.8130	+	11.2823i	−0.868719	+	0.470914i
$575$	42.3300	−	7.46391i	1.76528	−	0.311267i
$576$	−0.405175	−	2.97251i	−0.0168823	−	0.123855i
$577$	−22.1549			−0.922320			−0.461160	−	0.887317i	$-0.652567\pi$
$577$	−22.1549			−0.922320			−0.461160	+	0.887317i	$0.652567\pi$
$578$	−16.2904	+	28.2158i	−0.677591	+	1.17362i
$579$	−1.05761	−	1.91737i	−0.0439530	−	0.0796831i
$580$	0.248383	−	0.296012i	0.0103135	−	0.0122912i
$581$	2.25348	+	15.1486i	0.0934901	+	0.628471i
$582$	6.62271	+	2.55801i	0.274520	+	0.106033i
$583$	12.6878	+	2.23720i	0.525476	+	0.0926555i
$584$	2.32863	−	1.95396i	0.0963595	−	0.0808552i
$585$	−2.24094	+	1.73587i	−0.0926514	+	0.0717694i
$586$	−4.50063	+	3.77648i	−0.185919	+	0.156005i
$587$	−10.8724	−	12.9572i	−0.448752	−	0.534802i	0.493482	−	0.869756i	$-0.335724\pi$
$587$	−10.8724	−	12.9572i	−0.448752	−	0.534802i	−0.942235	+	0.334954i	$0.891279\pi$
$588$	−10.9155	+	5.27752i	−0.450147	+	0.217641i
$589$	−0.157425	+	2.09442i	−0.00648658	+	0.0862991i
$590$	1.08088	+	0.624048i	0.0444992	+	0.0256916i
$591$	6.53244	−	33.2378i	0.268709	−	1.36722i
$592$	0.751661	−	0.132538i	0.0308931	−	0.00544728i
$593$	−3.16395	+	3.77065i	−0.129928	+	0.154842i	−0.827086	−	0.562075i	$-0.810003\pi$
$593$	−3.16395	+	3.77065i	−0.129928	+	0.154842i	0.697158	+	0.716917i	$0.254448\pi$
$594$	21.3238	−	15.8613i	0.874927	−	0.650797i
$595$	−0.0975442	+	3.63098i	−0.00399892	+	0.148856i
$596$	−1.27901	−	0.738436i	−0.0523902	−	0.0302475i
$597$	15.3893	−	2.40467i	0.629842	−	0.0984166i
$598$	−7.28970	+	41.3419i	−0.298098	+	1.69060i
$599$	3.89890	−	22.1118i	0.159305	−	0.903462i	−0.795439	−	0.606033i	$-0.792760\pi$
$599$	3.89890	−	22.1118i	0.159305	−	0.903462i	0.954744	−	0.297429i	$-0.0961291\pi$
$600$	8.49137	−	1.32683i	0.346659	−	0.0541675i
$601$	37.3662	+	21.5734i	1.52420	+	0.879996i	0.999589	+	0.0286522i	$0.00912152\pi$
$601$	37.3662	+	21.5734i	1.52420	+	0.879996i	0.524608	+	0.851344i	$0.324212\pi$
$602$	−14.7657	−	9.06218i	−0.601803	−	0.369347i
$603$	3.57427	−	1.88147i	0.145556	−	0.0766195i
$604$	6.57339	−	7.83386i	0.267468	−	0.318755i
$605$	−2.91064	+	0.513225i	−0.118335	+	0.0208656i
$606$	−1.16027	+	5.90358i	−0.0471328	+	0.239817i
$607$	−6.31932	−	3.64846i	−0.256493	−	0.148086i	0.366241	−	0.930520i	$-0.380645\pi$
$607$	−6.31932	−	3.64846i	−0.256493	−	0.148086i	−0.622734	+	0.782434i	$0.713978\pi$
$608$	3.11971	+	3.04424i	0.126521	+	0.123460i
$609$	8.66931	−	2.70719i	0.351298	−	0.109701i
$610$	1.27943	+	1.52477i	0.0518027	+	0.0617361i
$611$	−3.02886	+	2.54152i	−0.122535	+	0.102819i
$612$	−12.9360	−	16.6999i	−0.522908	−	0.675053i
$613$	−19.9154	+	16.7110i	−0.804377	+	0.674953i	−0.949259	−	0.314496i	$-0.898164\pi$
$613$	−19.9154	+	16.7110i	−0.804377	+	0.674953i	0.144882	+	0.989449i	$0.453720\pi$
$614$	2.56283	+	0.451897i	0.103428	+	0.0182371i
$615$	−2.81882	−	1.08877i	−0.113666	−	0.0439033i
$616$	−10.5959	+	8.41660i	−0.426919	+	0.339114i
$617$	−14.7794	+	17.6134i	−0.594997	+	0.709090i	−0.976558	−	0.215254i	$-0.930942\pi$
$617$	−14.7794	+	17.6134i	−0.594997	+	0.709090i	0.381561	+	0.924344i	$0.375387\pi$
$618$	11.7288	+	21.2633i	0.471801	+	0.855337i
$619$	−19.6515	+	34.0374i	−0.789860	+	1.36808i	0.136192	+	0.990682i	$0.456514\pi$
$619$	−19.6515	+	34.0374i	−0.789860	+	1.36808i	−0.926052	+	0.377395i	$0.876820\pi$
$620$	−0.0939474			−0.00377302
$621$	43.1258	−	12.8916i	1.73058	−	0.517322i
$622$	26.4376	−	4.66167i	1.06005	−	0.186916i
$623$	2.19213	−	1.18830i	0.0878257	−	0.0476084i
$624$	−1.61873	+	8.23625i	−0.0648009	+	0.329714i
$625$	4.24244	+	24.0601i	0.169698	+	0.962402i
$626$	−4.06850	−	7.04685i	−0.162610	−	0.281649i
$627$	−10.2656	+	37.2245i	−0.409968	+	1.48660i
$628$	7.37857	−	12.7801i	0.294437	−	0.509980i
$629$	4.11701	−	3.45458i	0.164156	−	0.137743i
$630$	−1.41620	−	0.623935i	−0.0564227	−	0.0248582i
$631$	6.58941	−	37.3704i	0.262320	−	1.48769i	−0.514238	−	0.857647i	$-0.671925\pi$
$631$	6.58941	−	37.3704i	0.262320	−	1.48769i	0.776559	−	0.630045i	$-0.216964\pi$
$632$	−1.45525	+	3.99826i	−0.0578866	+	0.159042i
$633$	17.1042	−	28.3328i	0.679833	−	1.12613i
$634$	13.0623			0.518769
$635$	−1.12298			−0.0445640
$636$	3.73517	+	2.25489i	0.148109	+	0.0894121i
$637$	33.6759	−	4.08853i	1.33429	−	0.161994i
$638$	8.77848	−	5.06825i	0.347543	−	0.200654i
$639$	26.7747	+	24.3102i	1.05919	+	0.961698i
$640$	−0.125326	+	0.149358i	−0.00495396	+	0.00590389i
$641$	30.4935	−	25.5871i	1.20442	−	1.01063i	0.204929	−	0.978777i	$-0.434304\pi$
$641$	30.4935	−	25.5871i	1.20442	−	1.01063i	0.999493	−	0.0318525i	$-0.0101407\pi$
$642$	16.7674	+	10.1223i	0.661756	+	0.399496i
$643$	27.9950	+	10.1893i	1.10401	+	0.401828i	0.828794	−	0.559554i	$-0.189027\pi$
$643$	27.9950	+	10.1893i	1.10401	+	0.401828i	0.275219	+	0.961382i	$0.411250\pi$
$644$	−21.7393	+	7.25747i	−0.856647	+	0.285984i
$645$	−0.341391	−	2.18482i	−0.0134423	−	0.0860272i
$646$	29.7418	+	7.58026i	1.17018	+	0.298241i
$647$	22.3907	−	12.9273i	0.880269	−	0.508224i	0.00952191	−	0.999955i	$-0.496969\pi$
$647$	22.3907	−	12.9273i	0.880269	−	0.508224i	0.870747	+	0.491731i	$0.163636\pi$
$648$	8.67167	−	2.40877i	0.340655	−	0.0946256i
$649$	21.0450	+	25.0805i	0.826089	+	0.984494i
$650$	−23.6813	−	4.17565i	−0.928857	−	0.163783i
$651$	−1.85902	−	1.19154i	−0.0728608	−	0.0467002i
$652$	−8.49000	+	3.09011i	−0.332494	+	0.121018i
$653$	−3.29309	+	1.90127i	−0.128869	+	0.0744024i	−0.563049	−	0.826424i	$-0.690372\pi$
$653$	−3.29309	+	1.90127i	−0.128869	+	0.0744024i	0.434180	+	0.900826i	$0.357038\pi$
$654$	−32.3423	−	12.4922i	−1.26469	−	0.488484i
$655$	−0.218687	+	1.24023i	−0.00854480	+	0.0484600i
$656$	−8.40841	+	3.06041i	−0.328293	+	0.119489i
$657$	6.75166	+	6.13020i	0.263407	+	0.239162i
$658$	−2.00788	−	0.792499i	−0.0782754	−	0.0308948i
$659$	3.76099	−	1.36889i	0.146508	−	0.0533244i	−0.267726	−	0.963495i	$-0.586272\pi$
$659$	3.76099	−	1.36889i	0.146508	−	0.0533244i	0.414233	+	0.910171i	$0.364050\pi$
$660$	−1.69478	−	0.333087i	−0.0659693	−	0.0129654i
$661$	−5.80025	−	15.9361i	−0.225604	−	0.619841i	0.774312	−	0.632804i	$-0.218096\pi$
$661$	−5.80025	−	15.9361i	−0.225604	−	0.619841i	−0.999916	+	0.0129626i	$0.995874\pi$
$662$	−27.1967	+	4.79551i	−1.05703	+	0.186383i
$663$	19.1262	+	55.9237i	0.742801	+	2.17189i
$664$			5.78865i			0.224643i
$665$	2.18019	−	0.550162i	0.0845443	−	0.0213344i
$666$	0.698525	+	2.18062i	0.0270673	+	0.0844974i
$667$	16.9072	−	2.98120i	0.654650	−	0.115433i
$668$	0.900701	+	5.10813i	0.0348492	+	0.197639i
$669$	15.9413	+	28.9002i	0.616324	+	1.11735i
$670$	−0.246682	−	0.0897850i	−0.00953016	−	0.00346870i
$671$	17.8581	+	49.0648i	0.689405	+	1.89412i
$672$	−4.37426	+	1.36596i	−0.168741	+	0.0526931i
$673$	10.7054	−	6.18077i	0.412663	−	0.238251i	−0.279270	−	0.960213i	$-0.590093\pi$
$673$	10.7054	−	6.18077i	0.412663	−	0.238251i	0.691933	+	0.721961i	$0.256759\pi$
$674$	6.01018	+	16.5128i	0.231503	+	0.636051i
$675$	7.38450	+	24.7031i	0.284230	+	0.950824i
$676$	5.24267	−	9.08058i	0.201641	−	0.349253i
$677$	−1.17065	−	2.02763i	−0.0449919	−	0.0779282i	0.842652	−	0.538458i	$-0.180993\pi$
$677$	−1.17065	−	2.02763i	−0.0449919	−	0.0779282i	−0.887644	+	0.460530i	$0.847660\pi$
$678$	18.2390	−	10.0606i	0.700463	−	0.386373i
$679$	2.16930	−	10.6256i	0.0832501	−	0.407772i
$680$	−0.238397	+	1.35202i	−0.00914213	+	0.0518476i
$681$	20.0346	−	22.9507i	0.767726	−	0.879471i
$682$	−2.31582	−	0.842889i	−0.0886773	−	0.0322759i
$683$	−18.4048	−	31.8780i	−0.704239	−	1.21978i	−0.966965	−	0.254908i	$-0.917955\pi$
$683$	−18.4048	−	31.8780i	−0.704239	−	1.21978i	0.262726	−	0.964870i	$-0.415378\pi$
$684$	−7.78501	+	10.5068i	−0.297667	+	0.401739i
$685$	−1.59459			−0.0609262
$686$	10.7241	+	15.0995i	0.409447	+	0.576501i
$687$	−7.63266	−	1.50010i	−0.291204	−	0.0572323i
$688$	−5.01617	−	4.20907i	−0.191240	−	0.160469i
$689$	−7.84681	−	9.35146i	−0.298940	−	0.356262i
$690$	−2.50437	−	1.51187i	−0.0953397	−	0.0575557i
$691$	7.30758	+	12.6571i	0.277993	+	0.481499i	0.970886	−	0.239542i	$-0.0769973\pi$
$691$	7.30758	+	12.6571i	0.277993	+	0.481499i	−0.692893	+	0.721041i	$0.743664\pi$
$692$	−5.90904	−	10.2348i	−0.224628	−	0.389067i
$693$	−29.3116	−	28.0861i	−1.11346	−	1.06690i
$694$	−14.9781	+	17.8502i	−0.568560	+	0.677583i
$695$		−	1.69639i		−	0.0643479i
$696$	3.39158	−	0.529955i	0.128558	−	0.0200879i
$697$	−40.4998	+	48.2657i	−1.53404	+	1.82819i
$698$	−14.7356	−	5.36333i	−0.557752	−	0.203005i
$699$	17.7378	+	0.346470i	0.670907	+	0.0131047i
$700$	−4.15719	−	12.4526i	−0.157127	−	0.470663i
$701$	−4.32171	−	5.15042i	−0.163229	−	0.194529i	0.678230	−	0.734850i	$-0.262747\pi$
$701$	−4.32171	−	5.15042i	−0.163229	−	0.194529i	−0.841459	+	0.540321i	$0.818303\pi$
$702$	−25.1382	−	1.47456i	−0.948781	−	0.0556538i
$703$	−2.74844	−	1.87476i	−0.103660	−	0.0707078i
$704$	−4.42934	+	2.55728i	−0.166937	+	0.0963811i
$705$	−0.0891612	−	0.260701i	−0.00335801	−	0.00981856i
$706$	0.799680	−	2.19710i	0.0300964	−	0.0826891i
$707$	9.18707	+	0.246805i	0.345515	+	0.00928208i
$708$	3.58796	+	10.4909i	0.134844	+	0.394273i
$709$	−3.64894	+	20.6942i	−0.137039	+	0.777186i	0.836379	+	0.548151i	$0.184668\pi$
$709$	−3.64894	+	20.6942i	−0.137039	+	0.777186i	−0.973418	+	0.229035i	$0.926443\pi$
$710$		−	2.35037i		−	0.0882078i
$711$	−12.4745	−	2.70575i	−0.467831	−	0.101474i
$712$	0.885613	−	0.322337i	0.0331898	−	0.0120801i
$713$	−3.19746	−	2.68299i	−0.119746	−	0.100479i
$714$	−21.8651	+	23.7300i	−0.818282	+	0.888073i
$715$	4.18516	+	2.41630i	0.156516	+	0.0903646i
$716$	−3.69977	+	20.9824i	−0.138267	+	0.784150i
$717$	28.1972	+	24.6144i	1.05304	+	0.919243i
$718$	6.83782	+	18.7868i	0.255185	+	0.701116i
$719$	2.28401	+	2.72198i	0.0851792	+	0.101513i	0.806951	−	0.590619i	$-0.201116\pi$
$719$	2.28401	+	2.72198i	0.0851792	+	0.101513i	−0.721772	+	0.692131i	$0.756672\pi$
$720$	−0.494748	−	0.312018i	−0.0184382	−	0.0116282i
$721$	29.0456	−	23.0718i	1.08171	−	0.859238i
$722$	−0.465209	−	18.9943i	−0.0173133	−	0.706895i
$723$	−0.334622	−	0.129248i	−0.0124447	−	0.00480677i
$724$	3.52742	−	9.69150i	0.131095	−	0.360182i
$725$	1.70768	+	9.68472i	0.0634215	+	0.359681i
$726$	−22.4774	−	13.5694i	−0.834214	−	0.503608i
$727$	1.77798	+	10.0835i	0.0659418	+	0.373974i	0.999864	+	0.0164979i	$0.00525169\pi$
$727$	1.77798	+	10.0835i	0.0659418	+	0.373974i	−0.933922	+	0.357477i	$0.883637\pi$
$728$	12.8171	+	0.344325i	0.475035	+	0.0127615i
$729$	10.6737	+	24.8007i	0.395320	+	0.918543i
$730$		−	0.592682i		−	0.0219361i
$731$	−45.4074	−	8.00655i	−1.67945	−	0.296133i
$732$	−0.345318	+	17.6788i	−0.0127633	+	0.653428i
$733$	7.64977			0.282551			0.141275	−	0.989970i	$-0.454880\pi$
$733$	7.64977			0.282551			0.141275	+	0.989970i	$0.454880\pi$
$734$	−12.0613	+	20.8908i	−0.445190	+	0.771092i
$735$	−0.579756	+	2.29173i	−0.0213846	+	0.0845316i
$736$	−8.53085	+	1.50422i	−0.314451	+	0.0554462i
$737$	−5.27521	−	4.42643i	−0.194315	−	0.163049i
$738$	−12.5040	−	23.7541i	−0.460278	−	0.874401i
$739$	14.7562	+	5.37083i	0.542817	+	0.197569i	0.598852	−	0.800860i	$-0.295624\pi$
$739$	14.7562	+	5.37083i	0.542817	+	0.197569i	−0.0560351	+	0.998429i	$0.517846\pi$
$740$	0.0744072	−	0.128877i	0.00273526	−	0.00473762i
$741$	30.1231	−	20.7669i	1.10660	−	0.762892i
$742$	2.44680	−	6.19923i	0.0898248	−	0.227581i
$743$	−8.27067	+	6.93992i	−0.303422	+	0.254601i	−0.781767	−	0.623571i	$-0.785681\pi$
$743$	−8.27067	+	6.93992i	−0.303422	+	0.254601i	0.478345	+	0.878172i	$0.341237\pi$
$744$	−0.628731	−	0.548845i	−0.0230504	−	0.0201216i
$745$	−0.270585	+	0.0984848i	−0.00991346	+	0.00360820i
$746$	6.40709	+	7.63567i	0.234580	+	0.279562i
$747$	−17.2068	+	2.34542i	−0.629565	+	0.0858142i
$748$	−18.0067	+	31.1886i	−0.658392	+	1.14037i
$749$	10.9838	−	27.8287i	0.401340	−	1.01684i
$750$	1.73867	−	2.88007i	0.0634874	−	0.105165i
$751$	4.84159	+	13.3022i	0.176672	+	0.485403i	0.996146	−	0.0877144i	$-0.0279563\pi$
$751$	4.84159	+	13.3022i	0.176672	+	0.485403i	−0.819474	+	0.573117i	$0.805734\pi$
$752$	−0.706575	−	0.407941i	−0.0257661	−	0.0148761i
$753$	−7.13530	−	45.6642i	−0.260025	−	1.66410i
$754$	−9.45867	−	1.66782i	−0.344464	−	0.0607384i
$755$	−0.346232	−	1.96358i	−0.0126007	−	0.0714619i
$756$	−5.83268	−	12.4491i	−0.212132	−	0.452769i
$757$	28.5696	+	10.3985i	1.03838	+	0.377939i	0.804266	−	0.594270i	$-0.202559\pi$
$757$	28.5696	+	10.3985i	1.03838	+	0.377939i	0.234114	+	0.972209i	$0.424781\pi$
$758$	36.9724	−	6.51924i	1.34290	−	0.236789i
$759$	−48.1687	−	59.7367i	−1.74841	−	2.16831i
$760$	0.845663	−	0.0844309i	0.0306754	−	0.00306263i
$761$	5.92182	+	3.41897i	0.214666	+	0.123937i	0.603478	−	0.797380i	$-0.293781\pi$
$761$	5.92182	+	3.41897i	0.214666	+	0.123937i	−0.388812	+	0.921317i	$0.627114\pi$
$762$	−7.51539	−	6.56048i	−0.272254	−	0.237661i
$763$	−10.5939	+	51.8905i	−0.383525	+	1.87856i
$764$	16.0262	+	2.82586i	0.579808	+	0.102236i
$765$	−4.11549	−	0.160836i	−0.148796	−	0.00581503i
$766$	18.0478	+	15.1439i	0.652093	+	0.547171i
$767$		−	31.0221i		−	1.12014i
$768$	−1.71129	+	0.267399i	−0.0617507	+	0.00964891i
$769$	15.3743	+	12.9006i	0.554412	+	0.465207i	0.876432	−	0.481526i	$-0.159917\pi$
$769$	15.3743	+	12.9006i	0.554412	+	0.465207i	−0.322020	+	0.946733i	$0.604362\pi$
$770$	−0.0708522	+	2.63740i	−0.00255333	+	0.0950452i
$771$	1.80936	+	2.24389i	0.0651626	+	0.0808118i
$772$	−1.09486	+	0.632116i	−0.0394048	+	0.0227504i
$773$	41.2058	+	34.5758i	1.48207	+	1.24360i	0.903940	+	0.427658i	$0.140661\pi$
$773$	41.2058	+	34.5758i	1.48207	+	1.24360i	0.578129	+	0.815945i	$0.303783\pi$
$774$	10.4791	−	16.6160i	0.376663	−	0.597251i
$775$	1.53686	−	1.83155i	0.0552055	−	0.0657914i
$776$	1.40192	−	3.85173i	0.0503259	−	0.138269i
$777$	3.10692	−	1.60650i	0.111460	−	0.0576327i
$778$			12.9474i			0.464185i
$779$	35.5485	+	16.0496i	1.27366	+	0.575037i
$780$	1.02728	+	1.27399i	0.0367826	+	0.0456161i
$781$	21.0873	−	57.9370i	0.754564	−	2.07315i
$782$	−46.7252	+	39.2071i	−1.67089	+	1.40204i
$783$	2.94948	+	9.86680i	0.105406	+	0.352611i
$784$	3.16947	+	6.24135i	0.113195	+	0.222905i
$785$	−0.984075	−	2.70372i	−0.0351232	−	0.0965001i
$786$	−8.70904	+	7.02254i	−0.310641	+	0.250486i
$787$	−4.97715	−	2.87356i	−0.177416	−	0.102431i	0.408662	−	0.912686i	$-0.365996\pi$
$787$	−4.97715	−	2.87356i	−0.177416	−	0.102431i	−0.586078	+	0.810255i	$0.699329\pi$
$788$	−19.2598	−	3.39603i	−0.686103	−	0.120978i
$789$	−8.24456	−	14.9467i	−0.293514	−	0.532117i
$790$	0.414791	+	0.718440i	0.0147576	+	0.0255609i
$791$	−19.7902	−	24.9143i	−0.703657	−	0.885851i
$792$	−9.39621	−	12.1301i	−0.333880	−	0.431025i
$793$	16.9210	−	46.4900i	0.600882	−	1.65091i
$794$	−11.4719	+	4.17543i	−0.407122	+	0.148180i
$795$	0.804900	−	0.275280i	0.0285468	−	0.00976319i
$796$	−1.56159	−	8.85621i	−0.0553491	−	0.313900i
$797$	−15.0697			−0.533797			−0.266899	−	0.963725i	$-0.585999\pi$
$797$	−15.0697			−0.533797			−0.266899	+	0.963725i	$0.585999\pi$
$798$	17.8047	+	9.05489i	0.630281	+	0.320540i
$799$	−5.74492			−0.203241
$800$	−0.861640	−	4.88660i	−0.0304636	−	0.172767i
$801$	1.31698	+	2.50189i	0.0465332	+	0.0884001i
$802$	17.5502	−	6.38776i	0.619720	−	0.225560i
$803$	5.31750	−	14.6097i	0.187650	−	0.515565i
$804$	−1.12636	−	2.04200i	−0.0397237	−	0.0720158i
$805$	−1.64054	+	4.15649i	−0.0578214	+	0.146497i
$806$	1.16756	+	2.02227i	0.0411255	+	0.0712315i
$807$	10.6790	−	5.89052i	0.375920	−	0.207356i
$808$	3.42087	+	0.603191i	0.120346	+	0.0212202i
$809$	−18.5598	−	10.7155i	−0.652528	−	0.376737i	0.136896	−	0.990585i	$-0.456287\pi$
$809$	−18.5598	−	10.7155i	−0.652528	−	0.376737i	−0.789424	+	0.613848i	$0.789621\pi$
$810$	0.727018	−	1.59707i	0.0255448	−	0.0561152i
$811$	−16.0110	−	43.9898i	−0.562222	−	1.54469i	−0.816372	−	0.577526i	$-0.804018\pi$
$811$	−16.0110	−	43.9898i	−0.562222	−	1.54469i	0.254151	−	0.967165i	$-0.418204\pi$
$812$	−1.66044	−	4.97375i	−0.0582702	−	0.174544i
$813$	−0.941784	+	48.2154i	−0.0330298	+	1.69099i
$814$	2.99043	−	2.50927i	0.104814	−	0.0879497i
$815$	−0.602487	+	1.65532i	−0.0211042	+	0.0579833i
$816$	−9.49399	+	7.65549i	−0.332356	+	0.267996i
$817$	2.83560	+	28.4015i	0.0992051	+	0.993643i
$818$		−	25.1003i		−	0.877611i
$819$	4.16967	+	38.2386i	0.145700	+	1.33616i
$820$	−0.596698	+	1.63941i	−0.0208376	+	0.0572508i
$821$	4.73409	−	5.64187i	0.165221	−	0.196903i	−0.677081	−	0.735908i	$-0.736755\pi$
$821$	4.73409	−	5.64187i	0.165221	−	0.196903i	0.842302	+	0.539006i	$0.181200\pi$
$822$	−10.6716	−	9.31567i	−0.372215	−	0.324921i
$823$	−38.6600	−	32.4396i	−1.34760	−	1.13077i	−0.979602	−	0.200945i	$-0.935599\pi$
$823$	−38.6600	−	32.4396i	−1.34760	−	1.13077i	−0.367999	−	0.929826i	$-0.619957\pi$
$824$	12.1418	−	7.01008i	0.422980	−	0.244208i
$825$	34.2181	−	27.5918i	1.19132	−	0.960623i
$826$	14.8895	−	8.07128i	0.518072	−	0.280836i
$827$	20.5119	+	17.2115i	0.713267	+	0.598502i	0.925514	−	0.378714i	$-0.123634\pi$
$827$	20.5119	+	17.2115i	0.713267	+	0.598502i	−0.212247	+	0.977216i	$0.568078\pi$
$828$	−7.92779	−	24.7486i	−0.275510	−	0.860073i
$829$			43.2007i			1.50042i	0.661198	+	0.750212i	$0.270048\pi$
$829$			43.2007i			1.50042i	−0.661198	+	0.750212i	$0.729952\pi$
$830$	0.864582	+	0.725470i	0.0300101	+	0.0251814i
$831$	31.7219	+	6.23453i	1.10042	+	0.216273i
$832$	4.77254	+	0.841528i	0.165458	+	0.0291747i
$833$	41.3013	+	26.9010i	1.43100	+	0.932066i
$834$	9.91040	−	11.3529i	0.343169	−	0.393119i
$835$	0.875821	+	0.505656i	0.0303090	+	0.0174989i
$836$	21.6032	+	5.50599i	0.747164	+	0.190429i
$837$	1.37670	−	2.09129i	0.0475858	−	0.0722855i
$838$	5.61101	−	0.989373i	0.193829	−	0.0341773i
$839$	−0.550877	−	0.200503i	−0.0190184	−	0.00692213i	0.332493	−	0.943106i	$-0.392110\pi$
$839$	−0.550877	−	0.200503i	−0.0190184	−	0.00692213i	−0.351512	+	0.936183i	$0.614332\pi$
$840$	−0.344192	+	0.824522i	−0.0118758	+	0.0284487i
$841$	−4.35372	−	24.6912i	−0.150128	−	0.851421i
$842$	−1.20686	−	0.212802i	−0.0415912	−	0.00733365i
$843$	3.94142	−	0.615870i	0.135750	−	0.0212117i
$844$	−16.5477	−	9.55380i	−0.569594	−	0.328855i
$845$	−0.699213	−	1.92107i	−0.0240536	−	0.0660868i
$846$	0.926324	−	2.26559i	0.0318477	−	0.0778926i
$847$	−14.7243	+	37.3056i	−0.505933	+	1.28184i
$848$	1.25950	−	2.18151i	0.0432513	−	0.0749134i
$849$	1.00208	−	51.3023i	0.0343913	−	1.76069i
$850$	−22.4585	−	26.7649i	−0.770318	−	0.918030i
$851$	6.21294	−	2.26133i	0.212977	−	0.0775173i
$852$	13.7310	−	15.7296i	0.470415	−	0.538886i
$853$	−34.4754	+	28.9283i	−1.18042	+	0.990487i	−0.180440	+	0.983586i	$0.557752\pi$
$853$	−34.4754	+	28.9283i	−1.18042	+	0.990487i	−0.999976	+	0.00690099i	$0.997803\pi$
$854$	26.7160	−	3.97422i	0.914203	−	0.135995i
$855$	0.593613	+	2.47954i	0.0203011	+	0.0847984i
$856$	5.65395	−	9.79293i	0.193248	−	0.334716i
$857$	−24.8776	−	9.05469i	−0.849801	−	0.309302i	−0.119842	−	0.992793i	$-0.538239\pi$
$857$	−24.8776	−	9.05469i	−0.849801	−	0.309302i	−0.729959	+	0.683491i	$0.760461\pi$
$858$	13.8925	+	40.6207i	0.474283	+	1.38677i
$859$	−9.93432	−	8.33589i	−0.338955	−	0.284417i	0.457382	−	0.889270i	$-0.348787\pi$
$859$	−9.93432	−	8.33589i	−0.338955	−	0.284417i	−0.796337	+	0.604854i	$0.793232\pi$
$860$	−1.25732	+	0.221699i	−0.0428741	+	0.00755986i
$861$	−32.6002	+	24.8726i	−1.11101	+	0.847656i
$862$	−6.33100	+	10.9656i	−0.215635	+	0.373490i
$863$	47.2007			1.60673			0.803365	−	0.595487i	$-0.203041\pi$
$863$	47.2007			1.60673			0.803365	+	0.595487i	$0.203041\pi$
$864$	−1.48822	−	4.97848i	−0.0506301	−	0.169371i
$865$	−2.26920	−	0.400122i	−0.0771552	−	0.0136045i
$866$		−	16.3371i		−	0.555159i
$867$	−20.3327	+	52.6413i	−0.690533	+	1.78779i
$868$	−0.666845	+	1.08654i	−0.0226342	+	0.0368795i
$869$	3.77889	+	21.4311i	0.128190	+	0.727001i
$870$	0.345901	−	0.572978i	0.0117272	−	0.0194258i
$871$	1.13304	+	6.42580i	0.0383917	+	0.217730i
$872$	−6.84634	+	18.8102i	−0.231846	+	0.636992i
$873$	12.0174	+	2.60659i	0.406726	+	0.0882197i
$874$	31.1930	+	21.2772i	1.05512	+	0.719713i
$875$	−4.78004	−	1.88665i	−0.161595	−	0.0637805i
$876$	3.46247	−	3.96645i	0.116986	−	0.134014i
$877$	14.8664	+	17.7170i	0.502001	+	0.598262i	0.956227	−	0.292625i	$-0.0945287\pi$
$877$	14.8664	+	17.7170i	0.502001	+	0.598262i	−0.454226	+	0.890886i	$0.650084\pi$
$878$	−2.91902	−	8.01994i	−0.0985122	−	0.270660i
$879$	−6.69204	+	7.66610i	−0.225717	+	0.258571i
$880$	−0.173162	+	0.982052i	−0.00583730	+	0.0331050i
$881$	−36.7210	−	21.2009i	−1.23716	−	0.714275i	−0.268648	−	0.963239i	$-0.586577\pi$
$881$	−36.7210	−	21.2009i	−1.23716	−	0.714275i	−0.968513	+	0.248964i	$0.919910\pi$
$882$	−17.2683	+	11.9501i	−0.581454	+	0.402382i
$883$	−27.9401	−	23.4445i	−0.940259	−	0.788971i	0.0373716	−	0.999301i	$-0.488101\pi$
$883$	−27.9401	−	23.4445i	−0.940259	−	0.788971i	−0.977630	+	0.210331i	$0.932546\pi$
$884$	32.0657	−	11.6710i	1.07849	−	0.392537i
$885$	2.01657	+	0.778897i	0.0677862	+	0.0261824i
$886$			2.99298i			0.100551i
$887$	−7.84524	+	44.4926i	−0.263417	+	1.49391i	0.510087	+	0.860123i	$0.329613\pi$
$887$	−7.84524	+	44.4926i	−0.263417	+	1.49391i	−0.773504	+	0.633791i	$0.781498\pi$
$888$	1.25087	−	0.427804i	0.0419763	−	0.0143562i
$889$	−7.97097	+	12.9877i	−0.267338	+	0.435592i
$890$	0.0628470	−	0.172671i	0.00210664	−	0.00578794i
$891$	32.2499	−	32.8452i	1.08041	−	1.10035i
$892$	16.5026	−	9.52778i	0.552548	−	0.319014i
$893$	0.962439	+	3.42364i	0.0322068	+	0.114568i
$894$	−2.38621	−	0.921670i	−0.0798067	−	0.0308252i
$895$	2.67022	+	3.18224i	0.0892555	+	0.106371i
$896$	0.837808	+	2.50960i	0.0279892	+	0.0838398i
$897$	−1.41998	+	72.6971i	−0.0474118	+	2.42729i
$898$	−12.6702	−	4.61158i	−0.422811	−	0.153890i
$899$	0.613844	−	0.731551i	0.0204728	−	0.0243986i
$900$	14.1764	−	4.54116i	0.472546	−	0.151372i
$901$		−	17.7371i		−	0.590910i
$902$	−29.4174	+	35.0583i	−0.979492	+	1.16731i
$903$	−27.6915	−	11.5597i	−0.921514	−	0.384681i
$904$	−6.01300	−	10.4148i	−0.199989	−	0.346392i
$905$	−1.00542	−	1.74145i	−0.0334215	−	0.0578877i
$906$	9.15419	−	15.1637i	0.304127	−	0.503780i
$907$	6.91326	+	8.23891i	0.229551	+	0.273568i	0.868509	−	0.495673i	$-0.165079\pi$
$907$	6.91326	+	8.23891i	0.229551	+	0.273568i	−0.638958	+	0.769242i	$0.720634\pi$
$908$	−13.4739	−	11.3060i	−0.447148	−	0.375202i
$909$	−0.406945	+	10.4130i	−0.0134975	+	0.345376i
$910$	1.65775	−	1.87119i	0.0549539	−	0.0620293i
$911$	−13.5003			−0.447286			−0.223643	−	0.974671i	$-0.571795\pi$
$911$	−13.5003			−0.447286			−0.223643	+	0.974671i	$0.571795\pi$
$912$	6.15274	+	4.37536i	0.203738	+	0.144883i
$913$	14.8032	+	25.6399i	0.489915	+	0.848557i
$914$	22.9227	+	8.34316i	0.758214	+	0.275967i
$915$	2.59720	+	2.26720i	0.0858607	+	0.0749512i
$916$	−0.779858	+	4.42279i	−0.0257672	+	0.146133i
$917$	12.7915	+	11.3325i	0.422413	+	0.374231i
$918$	−26.6028	−	25.1192i	−0.878022	−	0.829057i
$919$	−2.62032	−	4.53852i	−0.0864362	−	0.149712i	0.819566	−	0.572985i	$-0.194215\pi$
$919$	−2.62032	−	4.53852i	−0.0864362	−	0.149712i	−0.906002	+	0.423273i	$0.860881\pi$
$920$	−0.844472	+	1.46267i	−0.0278414	+	0.0482228i
$921$	4.50658	+	0.0880262i	0.148497	+	0.00290056i
$922$	9.01079	+	24.7569i	0.296754	+	0.815326i
$923$	−50.5930	+	29.2099i	−1.66529	+	0.961456i
$924$	−15.8819	+	17.2365i	−0.522477	+	0.567040i
$925$	1.29532	+	3.55887i	0.0425899	+	0.117015i
$926$	−28.5959	−	10.4081i	−0.939721	−	0.342030i
$927$	25.7571	+	33.2514i	0.845974	+	1.09212i
$928$	−0.344152	−	1.95178i	−0.0112973	−	0.0640704i
$929$	−26.9669	+	4.75499i	−0.884754	+	0.156006i	−0.597520	−	0.801854i	$-0.703847\pi$
$929$	−26.9669	+	4.75499i	−0.884754	+	0.156006i	−0.287235	+	0.957860i	$0.592736\pi$
$930$	−0.160771	+	0.0251214i	−0.00527189	+	0.000823764i
$931$	9.11232	−	29.1198i	0.298644	−	0.954365i
$932$		−	10.2429i		−	0.335517i
$933$	43.9958	−	15.0468i	1.44036	−	0.492611i
$934$	−24.2994	+	4.28463i	−0.795100	+	0.140198i
$935$	2.40155	+	6.59820i	0.0785391	+	0.215784i
$936$	−0.567740	+	14.5274i	−0.0185572	+	0.474843i
$937$	33.0612	−	12.0333i	1.08006	−	0.393111i	0.260132	−	0.965573i	$-0.416234\pi$
$937$	33.0612	−	12.0333i	1.08006	−	0.393111i	0.819931	+	0.572462i	$0.194012\pi$
$938$	−2.78936	+	2.21567i	−0.0910759	+	0.0723442i
$939$	−8.84668	−	10.9713i	−0.288701	−	0.358033i
$940$	−0.149482	+	0.0544069i	−0.00487555	+	0.00177456i
$941$	−9.02065	+	51.1586i	−0.294065	+	1.66772i	0.376915	+	0.926248i	$0.376985\pi$
$941$	−9.02065	+	51.1586i	−0.294065	+	1.66772i	−0.670979	+	0.741476i	$0.734126\pi$
$942$	9.20947	−	23.8433i	0.300061	−	0.776858i
$943$	−67.1274	+	38.7560i	−2.18597	+	1.26207i
$944$	6.01532	−	2.18940i	0.195782	−	0.0712589i
$945$	−2.59036	−	0.689041i	−0.0842644	−	0.0224145i
$946$	−32.9821	−	5.81563i	−1.07234	−	0.189083i
$947$	−17.4768	−	20.8281i	−0.567921	−	0.676821i	0.403282	−	0.915076i	$-0.367869\pi$
$947$	−17.4768	−	20.8281i	−0.567921	−	0.676821i	−0.971203	+	0.238254i	$0.923425\pi$
$948$	−1.42122	+	7.23130i	−0.0461589	+	0.234862i
$949$	−12.7578	+	7.36573i	−0.414136	+	0.239102i
$950$	−12.1879	+	17.8678i	−0.395428	+	0.579709i
$951$	22.3533	−	3.49283i	0.724854	−	0.113263i
$952$	13.9444	+	12.3539i	0.451942	+	0.400391i
$953$	−19.0368	−	6.92884i	−0.616663	−	0.224447i	0.0147530	−	0.999891i	$-0.495304\pi$
$953$	−19.0368	−	6.92884i	−0.616663	−	0.224447i	−0.631416	+	0.775444i	$0.717526\pi$
$954$	6.99489	+	2.85998i	0.226468	+	0.0925951i
$955$	2.43057	−	2.03949i	0.0786514	−	0.0659964i
$956$	13.8905	−	16.5541i	0.449252	−	0.535397i
$957$	13.6672	−	11.0206i	0.441799	−	0.356245i
$958$	16.3514	−	9.44051i	0.528291	−	0.305009i
$959$	−11.3185	+	18.4420i	−0.365494	+	0.595525i
$960$	−0.174531	+	0.289106i	−0.00563296	+	0.00933087i
$961$	30.7678			0.992510
$962$	−3.69887			−0.119256
$963$	31.4005	+	12.8386i	1.01187	+	0.413718i
$964$	−0.0708340	+	0.194615i	−0.00228141	+	0.00626812i
$965$	−0.0428028	+	0.242747i	−0.00137787	+	0.00781429i
$966$	−35.2615	+	18.2327i	−1.13452	+	0.586626i
$967$	−6.19324	+	5.19675i	−0.199161	+	0.167116i	−0.736914	−	0.675986i	$-0.763718\pi$
$967$	−6.19324	+	5.19675i	−0.199161	+	0.167116i	0.537753	+	0.843103i	$0.319273\pi$
$968$	−7.57937	+	13.1279i	−0.243610	+	0.421945i
$969$	52.9237	+	5.01907i	1.70015	+	0.161236i
$970$	−0.399590	−	0.692111i	−0.0128301	−	0.0222223i
$971$	−8.69707	−	49.3235i	−0.279102	−	1.58287i	−0.725622	−	0.688093i	$-0.758448\pi$
$971$	−8.69707	−	49.3235i	−0.279102	−	1.58287i	0.446520	−	0.894774i	$-0.352663\pi$
$972$	14.1956	−	6.44089i	0.455324	−	0.206592i
$973$	−19.6194	−	12.0411i	−0.628970	−	0.386020i
$974$	24.2217	−	4.27093i	0.776112	−	0.136850i
$975$	−41.6420	−	0.813387i	−1.33361	−	0.0260492i
$976$	10.2088			0.326776
$977$	0.555129	−	0.961511i	0.0177601	−	0.0307615i	−0.857009	−	0.515302i	$-0.827680\pi$
$977$	0.555129	−	0.961511i	0.0177601	−	0.0307615i	0.874769	+	0.484540i	$0.161013\pi$
$978$	−13.7025	+	7.55827i	−0.438158	+	0.241687i
$979$	3.09838	−	3.69250i	0.0990246	−	0.118013i
$980$	1.32941	+	0.308819i	0.0424666	+	0.00986486i
$981$	−58.6874	−	12.7294i	−1.87374	−	0.406419i
$982$	−6.73940	−	1.18834i	−0.215063	−	0.0379214i
$983$	−23.1865	+	19.4558i	−0.739534	+	0.620542i	−0.932712	−	0.360621i	$-0.882565\pi$
$983$	−23.1865	+	19.4558i	−0.739534	+	0.620542i	0.193179	+	0.981164i	$0.438120\pi$
$984$	−13.5708	+	7.48563i	−0.432623	+	0.238633i
$985$	−2.92099	+	2.45100i	−0.0930703	+	0.0780953i
$986$	−8.97025	−	10.6903i	−0.285671	−	0.340449i
$987$	−3.64797	−	0.819287i	−0.116116	−	0.0260782i
$988$	−12.3272	−	17.1541i	−0.392179	−	0.545744i
$989$	−49.1236	−	28.3615i	−1.56204	−	0.901843i
$990$	−2.98932	−	0.116824i	−0.0950069	−	0.00371293i
$991$	21.9496	−	3.87031i	0.697253	−	0.122944i	0.186223	−	0.982507i	$-0.440375\pi$
$991$	21.9496	−	3.87031i	0.697253	−	0.122944i	0.511030	+	0.859563i	$0.329264\pi$
$992$	−0.309726	+	0.369117i	−0.00983381	+	0.0117195i
$993$	−45.2590	+	15.4788i	−1.43625	+	0.491206i
$994$	−27.1829	−	16.6831i	−0.862189	−	0.529155i
$995$	−1.51845	−	0.876680i	−0.0481382	−	0.0277926i
$996$	1.54788	+	9.90604i	0.0490464	+	0.313885i
$997$	2.67556	−	15.1738i	0.0847358	−	0.480560i	−0.912678	−	0.408680i	$-0.865989\pi$
$997$	2.67556	−	15.1738i	0.0847358	−	0.480560i	0.997413	−	0.0718799i	$-0.0228998\pi$
$998$	4.75350	−	26.9584i	0.150469	−	0.853354i
$999$	1.77847	+	3.54488i	0.0562683	+	0.112155i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.cc.b.317.12	yes	162
3.2	odd	2		798.2.cc.a.317.15	yes	162
7.4	even	3		798.2.bu.b.431.7	yes	162
19.3	odd	18		798.2.bu.a.611.21	yes	162
21.11	odd	6		798.2.bu.a.431.21	✓	162
57.41	even	18		798.2.bu.b.611.7	yes	162
133.60	odd	18		798.2.cc.a.725.15	yes	162
399.326	even	18	inner	798.2.cc.b.725.12	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.431.21	✓	162	21.11	odd	6
798.2.bu.a.611.21	yes	162	19.3	odd	18
798.2.bu.b.431.7	yes	162	7.4	even	3
798.2.bu.b.611.7	yes	162	57.41	even	18
798.2.cc.a.317.15	yes	162	3.2	odd	2
798.2.cc.a.725.15	yes	162	133.60	odd	18
798.2.cc.b.317.12	yes	162	1.1	even	1	trivial
798.2.cc.b.725.12	yes	162	399.326	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-0.560498 - 1.63885i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(-0.0666847 + 0.183215i) q^{5} +(-1.51663 + 0.836567i) q^{6} +(1.64561 + 2.07170i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.37168 + 1.83715i) q^{9} +(0.192011 + 0.0338567i) q^{10} +(4.42934 + 2.55728i) q^{11} +(1.08722 + 1.34832i) q^{12} +(-1.65749 - 4.55391i) q^{13} +(1.75447 - 1.98036i) q^{14} +(0.337639 + 0.00659504i) q^{15} +(0.766044 - 0.642788i) q^{16} +(2.40829 - 6.61672i) q^{17} +(2.22108 + 2.01664i) q^{18} +(-4.34664 - 0.326711i) q^{19} -0.194973i q^{20} +(2.47285 - 3.85811i) q^{21} +(1.74928 - 4.80612i) q^{22} +(5.56812 - 6.63582i) q^{23} +(1.13904 - 1.30483i) q^{24} +(3.80110 + 3.18950i) q^{25} +(-4.19691 + 2.42308i) q^{26} +(4.34014 + 2.85713i) q^{27} +(-2.25494 - 1.38393i) q^{28} +(1.51822 + 1.27394i) q^{29} +(-0.0521355 - 0.333655i) q^{30} -0.481848i q^{31} +(-0.766044 - 0.642788i) q^{32} +(1.70837 - 8.69239i) q^{33} +(-6.93439 - 1.22272i) q^{34} +(-0.489304 + 0.163350i) q^{35} +(1.60031 - 2.53752i) q^{36} +(0.661000 + 0.381628i) q^{37} +(0.433039 + 4.33734i) q^{38} +(-6.53417 + 5.26884i) q^{39} +(-0.192011 + 0.0338567i) q^{40} +(-8.40841 - 3.06041i) q^{41} +(-4.22890 - 1.76533i) q^{42} +(-1.13707 - 6.44867i) q^{43} +(-5.03686 - 0.888134i) q^{44} +(-0.178438 - 0.557037i) q^{45} +(-7.50190 - 4.33123i) q^{46} +(-0.279048 - 0.766678i) q^{47} +(-1.48280 - 0.895154i) q^{48} +(-1.58391 + 6.81845i) q^{49} +(2.48099 - 4.29721i) q^{50} +(-12.1937 - 0.238177i) q^{51} +(3.11506 + 3.71238i) q^{52} +(2.36708 - 0.861546i) q^{53} +(2.06006 - 4.77034i) q^{54} +(-0.763901 + 0.640989i) q^{55} +(-0.971340 + 2.46100i) q^{56} +(1.90085 + 7.30663i) q^{57} +(0.990946 - 1.71637i) q^{58} +(6.01532 + 2.18940i) q^{59} +(-0.319532 + 0.109282i) q^{60} +(7.82041 + 6.56210i) q^{61} +(-0.474528 + 0.0836721i) q^{62} +(-7.70890 - 1.89019i) q^{63} +(-0.500000 + 0.866025i) q^{64} +0.944872 q^{65} +(-8.85699 - 0.173002i) q^{66} +(-1.32595 - 0.233802i) q^{67} +7.04136i q^{68} +(-13.9961 - 5.40597i) q^{69} +(0.245835 + 0.453505i) q^{70} +(-2.09330 - 11.8717i) q^{71} +(-2.77686 - 1.13536i) q^{72} +(-0.527858 - 2.99363i) q^{73} +(0.261049 - 0.717227i) q^{74} +(3.09662 - 8.01716i) q^{75} +(4.19625 - 1.17963i) q^{76} +(1.99106 + 13.3846i) q^{77} +(6.32344 + 5.51998i) q^{78} +(2.73497 + 3.25941i) q^{79} +(0.0666847 + 0.183215i) q^{80} +(2.24977 - 8.71427i) q^{81} +(-1.55381 + 8.81210i) q^{82} +(5.01312 + 2.89433i) q^{83} +(-1.00417 + 4.47120i) q^{84} +(1.05168 + 0.882468i) q^{85} +(-6.15325 + 2.23960i) q^{86} +(1.23684 - 3.20218i) q^{87} +5.11456i q^{88} +(0.163655 - 0.928132i) q^{89} +(-0.517589 + 0.272455i) q^{90} +(6.70676 - 10.9278i) q^{91} +(-2.96273 + 8.14004i) q^{92} +(-0.789679 + 0.270075i) q^{93} +(-0.706575 + 0.407941i) q^{94} +(0.349712 - 0.774582i) q^{95} +(-0.624069 + 1.61572i) q^{96} +(-2.63474 - 3.13996i) q^{97} +(6.98990 + 0.375831i) q^{98} +(-15.2031 + 2.07229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 81 q^{8} + 15 q^{13} - 9 q^{14} + 3 q^{15} - 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} + 9 q^{27} - 12 q^{28} - 6 q^{29} - 12 q^{33} + 6 q^{34} + 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots + 39 q^{99}+O(q^{100}) \) 162 * q + 81 * q^8 + 15 * q^13 - 9 * q^14 + 3 * q^15 - 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 + 9 * q^27 - 12 * q^28 - 6 * q^29 - 12 * q^33 + 6 * q^34 + 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 - 6 * q^44 + 18 * q^45 - 18 * q^46 - 12 * q^47 + 24 * q^49 - 87 * q^50 + 24 * q^51 + 12 * q^52 + 36 * q^53 + 18 * q^54 - 18 * q^57 - 24 * q^59 - 27 * q^60 - 9 * q^61 - 36 * q^62 + 6 * q^63 - 81 * q^64 + 72 * q^65 + 12 * q^66 - 63 * q^67 - 9 * q^69 + 12 * q^70 - 12 * q^71 - 51 * q^73 + 42 * q^74 - 18 * q^78 + 21 * q^79 - 12 * q^81 + 3 * q^84 - 6 * q^85 - 36 * q^86 - 84 * q^87 + 54 * q^89 + 12 * q^90 + 75 * q^91 - 66 * q^93 + 72 * q^94 - 12 * q^97 - 12 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more