LMFDB - Embedded newform 798.2.cc.a.317.15

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			317.15
Character	$\chi$	$=$	798.317
Dual form			798.2.cc.a.725.15

$q$-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} +(0.0338254 + 1.73172i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.0666847 - 0.183215i) q^{5} +(-1.69954 + 0.334022i) q^{6} +(1.64561 + 2.07170i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.99771 + 0.117152i) q^{9} +(0.192011 + 0.0338567i) q^{10} +(-4.42934 - 2.55728i) q^{11} +(-0.624069 - 1.61572i) q^{12} +(-1.65749 - 4.55391i) q^{13} +(-1.75447 + 1.98036i) q^{14} +(0.319532 + 0.109282i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-2.40829 + 6.61672i) q^{17} +(-0.635920 - 2.93183i) q^{18} +(-4.34664 - 0.326711i) q^{19} +0.194973i q^{20} +(-3.53195 + 2.91982i) q^{21} +(1.74928 - 4.80612i) q^{22} +(-5.56812 + 6.63582i) q^{23} +(1.48280 - 0.895154i) q^{24} +(3.80110 + 3.18950i) q^{25} +(4.19691 - 2.42308i) q^{26} +(-0.304274 - 5.18724i) 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} +(4.27867 - 7.75688i) q^{33} +(-6.93439 - 1.22272i) q^{34} +(0.489304 - 0.163350i) q^{35} +(2.77686 - 1.13536i) q^{36} +(0.661000 + 0.381628i) q^{37} +(-0.433039 - 4.33734i) q^{38} +(7.83003 - 3.02434i) q^{39} +(-0.192011 + 0.0338567i) q^{40} +(8.40841 + 3.06041i) q^{41} +(-3.48878 - 2.97127i) 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} +(1.13904 + 1.30483i) q^{48} +(-1.58391 + 6.81845i) q^{49} +(-2.48099 + 4.29721i) q^{50} +(-11.5398 - 3.94667i) q^{51} +(3.11506 + 3.71238i) q^{52} +(-2.36708 + 0.861546i) q^{53} +(5.05559 - 1.20041i) q^{54} +(-0.763901 + 0.640989i) q^{55} +(0.971340 - 2.46100i) q^{56} +(0.418744 - 7.53821i) q^{57} +(0.990946 - 1.71637i) q^{58} +(-6.01532 - 2.18940i) q^{59} +(-0.337639 + 0.00659504i) q^{60} +(7.82041 + 6.56210i) q^{61} +(0.474528 - 0.0836721i) q^{62} +(-5.17578 - 6.01758i) q^{63} +(-0.500000 + 0.866025i) q^{64} -0.944872 q^{65} +(8.38202 + 2.86670i) q^{66} +(-1.32595 - 0.233802i) q^{67} -7.04136i q^{68} +(-11.6797 - 9.41796i) q^{69} +(0.245835 + 0.453505i) q^{70} +(2.09330 + 11.8717i) q^{71} +(1.60031 + 2.53752i) q^{72} +(-0.527858 - 2.99363i) q^{73} +(-0.261049 + 0.717227i) q^{74} +(-5.39475 + 6.69033i) q^{75} +(4.19625 - 1.17963i) q^{76} +(-1.99106 - 13.3846i) q^{77} +(4.33807 + 7.18590i) q^{78} +(2.73497 + 3.25941i) q^{79} +(-0.0666847 - 0.183215i) q^{80} +(8.97255 - 0.702378i) q^{81} +(-1.55381 + 8.81210i) q^{82} +(-5.01312 - 2.89433i) q^{83} +(2.32031 - 3.95173i) q^{84} +(1.05168 + 0.882468i) q^{85} +(6.15325 - 2.23960i) q^{86} +(2.15475 - 2.67222i) q^{87} +5.11456i q^{88} +(-0.163655 + 0.928132i) q^{89} +(-0.579560 - 0.0789981i) q^{90} +(6.70676 - 10.9278i) q^{91} +(2.96273 - 8.14004i) q^{92} +(0.834427 - 0.0162987i) q^{93} +(-0.706575 + 0.407941i) q^{94} +(-0.349712 + 0.774582i) q^{95} +(-1.08722 + 1.34832i) q^{96} +(-2.63474 - 3.13996i) q^{97} +(-6.98990 - 0.375831i) q^{98} +(13.5775 + 7.14708i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q - 81 q^{8} + 15 q^{13} + 9 q^{14} + 27 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 - 57 q^{99}+O(q^{100}) $ 162 * q - 81 * q^8 + 15 * q^13 + 9 * q^14 + 27 * 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 - 3 * q^60 - 9 * q^61 + 36 * q^62 + 12 * 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 - 6 * q^78 + 21 * q^79 + 12 * q^81 - 3 * q^84 - 6 * q^85 + 36 * q^86 + 24 * q^87 - 54 * q^89 + 36 * q^90 + 75 * q^91 + 42 * q^93 + 72 * q^94 - 12 * q^97 + 12 * q^98 - 57 * q^99

Character values

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

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

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
$3$	0.0338254	+	1.73172i	0.0195291	+	0.999809i
$3$	0.0338254	+	1.73172i	0.0195291	+	0.999809i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	0.0666847	−	0.183215i	0.0298223	−	0.0819361i	−0.923888	−	0.382663i	$-0.875007\pi$
$5$	0.0666847	−	0.183215i	0.0298223	−	0.0819361i	0.953710	+	0.300727i	$0.0972293\pi$
$6$	−1.69954	+	0.334022i	−0.693833	+	0.136364i
$7$	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
$9$	−2.99771	+	0.117152i	−0.999237	+	0.0390508i
$10$	0.192011	+	0.0338567i	0.0607192	+	0.0107064i
$11$	−4.42934	−	2.55728i	−1.33550	−	0.771049i	−0.349360	−	0.936988i	$-0.613601\pi$
$11$	−4.42934	−	2.55728i	−1.33550	−	0.771049i	−0.986136	+	0.165939i	$0.946934\pi$
$12$	−0.624069	−	1.61572i	−0.180153	−	0.466417i
$13$	−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
$15$	0.319532	+	0.109282i	0.0825029	+	0.0282165i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	−2.40829	+	6.61672i	−0.584096	+	1.60479i	0.197017	+	0.980400i	$0.436875\pi$
$17$	−2.40829	+	6.61672i	−0.584096	+	1.60479i	−0.781113	+	0.624390i	$0.785348\pi$
$18$	−0.635920	−	2.93183i	−0.149888	−	0.691038i
$19$	−4.34664	−	0.326711i	−0.997187	−	0.0749525i
$19$	−4.34664	−	0.326711i	−0.997187	−	0.0749525i
$20$			0.194973i			0.0435973i
$21$	−3.53195	+	2.91982i	−0.770734	+	0.637157i
$22$	1.74928	−	4.80612i	0.372948	−	1.02467i
$23$	−5.56812	+	6.63582i	−1.16103	+	1.38366i	−0.251591	+	0.967834i	$0.580954\pi$
$23$	−5.56812	+	6.63582i	−1.16103	+	1.38366i	−0.909442	+	0.415831i	$0.863491\pi$
$24$	1.48280	−	0.895154i	0.302676	−	0.182723i
$25$	3.80110	+	3.18950i	0.760220	+	0.637901i
$26$	4.19691	−	2.42308i	0.823081	−	0.475206i
$27$	−0.304274	−	5.18724i	−0.0585575	−	0.998284i
$28$	−2.25494	−	1.38393i	−0.426143	−	0.261538i
$29$	−1.51822	−	1.27394i	−0.281926	−	0.236564i	0.490848	−	0.871245i	$-0.336687\pi$
$29$	−1.51822	−	1.27394i	−0.281926	−	0.236564i	−0.772774	+	0.634681i	$0.781131\pi$
$30$	−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
$33$	4.27867	−	7.75688i	0.744821	−	1.35030i
$34$	−6.93439	−	1.22272i	−1.18924	−	0.209695i
$35$	0.489304	−	0.163350i	0.0827074	−	0.0276112i
$36$	2.77686	−	1.13536i	0.462810	−	0.189227i
$37$	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
$39$	7.83003	−	3.02434i	1.25381	−	0.484282i
$40$	−0.192011	+	0.0338567i	−0.0303596	+	0.00535322i
$41$	8.40841	+	3.06041i	1.31317	+	0.477956i	0.901265	−	0.433269i	$-0.142640\pi$
$41$	8.40841	+	3.06041i	1.31317	+	0.477956i	0.411909	+	0.911225i	$0.364862\pi$
$42$	−3.48878	−	2.97127i	−0.538330	−	0.458476i
$43$	−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	0.958379	−	0.285498i	$-0.0921591\pi$
$47$	0.279048	+	0.766678i	0.0407034	+	0.111832i	−0.917676	+	0.397330i	$0.869937\pi$
$48$	1.13904	+	1.30483i	0.164406	+	0.188336i
$49$	−1.58391	+	6.81845i	−0.226272	+	0.974064i
$50$	−2.48099	+	4.29721i	−0.350865	+	0.607717i
$51$	−11.5398	−	3.94667i	−1.61589	−	0.552644i
$52$	3.11506	+	3.71238i	0.431981	+	0.514815i
$53$	−2.36708	+	0.861546i	−0.325143	+	0.118342i	−0.499434	−	0.866352i	$-0.666459\pi$
$53$	−2.36708	+	0.861546i	−0.325143	+	0.118342i	0.174291	+	0.984694i	$0.444237\pi$
$54$	5.05559	−	1.20041i	0.687979	−	0.163354i
$55$	−0.763901	+	0.640989i	−0.103004	+	0.0864309i
$56$	0.971340	−	2.46100i	0.129801	−	0.328864i
$57$	0.418744	−	7.53821i	0.0554641	−	0.998461i
$58$	0.990946	−	1.71637i	0.130118	−	0.225370i
$59$	−6.01532	−	2.18940i	−0.783129	−	0.285035i	−0.0806520	−	0.996742i	$-0.525700\pi$
$59$	−6.01532	−	2.18940i	−0.783129	−	0.285035i	−0.702477	+	0.711707i	$0.747922\pi$
$60$	−0.337639	+	0.00659504i	−0.0435890	+	0.000851417i
$61$	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
$63$	−5.17578	−	6.01758i	−0.652087	−	0.758144i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.944872			−0.117197
$66$	8.38202	+	2.86670i	1.03176	+	0.352866i
$67$	−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
$69$	−11.6797	−	9.41796i	−1.40607	−	1.13379i
$70$	0.245835	+	0.453505i	0.0293829	+	0.0542042i
$71$	2.09330	+	11.8717i	0.248429	+	1.40891i	0.812392	+	0.583112i	$0.198165\pi$
$71$	2.09330	+	11.8717i	0.248429	+	1.40891i	−0.563963	+	0.825800i	$0.690724\pi$
$72$	1.60031	+	2.53752i	0.188599	+	0.299049i
$73$	−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
$75$	−5.39475	+	6.69033i	−0.622932	+	0.772533i
$76$	4.19625	−	1.17963i	0.481342	−	0.135313i
$77$	−1.99106	−	13.3846i	−0.226902	−	1.52531i
$78$	4.33807	+	7.18590i	0.491189	+	0.813643i
$79$	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
$81$	8.97255	−	0.702378i	0.996950	−	0.0780420i
$82$	−1.55381	+	8.81210i	−0.171590	+	0.973134i
$83$	−5.01312	−	2.89433i	−0.550261	−	0.317694i	0.198966	−	0.980006i	$-0.436242\pi$
$83$	−5.01312	−	2.89433i	−0.550261	−	0.317694i	−0.749227	+	0.662313i	$0.769575\pi$
$84$	2.32031	−	3.95173i	0.253166	−	0.431169i
$85$	1.05168	+	0.882468i	0.114071	+	0.0957171i
$86$	6.15325	−	2.23960i	0.663521	−	0.241502i
$87$	2.15475	−	2.67222i	0.231013	−	0.286492i
$88$			5.11456i			0.545214i
$89$	−0.163655	+	0.928132i	−0.0173474	+	0.0983818i	−0.992252	−	0.124241i	$-0.960351\pi$
$89$	−0.163655	+	0.928132i	−0.0173474	+	0.0983818i	0.974905	+	0.222622i	$0.0714617\pi$
$90$	−0.579560	−	0.0789981i	−0.0610910	−	0.00832713i
$91$	6.70676	−	10.9278i	0.703060	−	1.14554i
$92$	2.96273	−	8.14004i	0.308886	−	0.848658i
$93$	0.834427	−	0.0162987i	0.0865260	−	0.00169010i
$94$	−0.706575	+	0.407941i	−0.0728776	+	0.0420759i
$95$	−0.349712	+	0.774582i	−0.0358797	+	0.0794704i
$96$	−1.08722	+	1.34832i	−0.110964	+	0.137612i
$97$	−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
$99$	13.5775	+	7.14708i	1.36459	+	0.718309i
$100$	−4.66274	−	1.69710i	−0.466274	−	0.169710i
$101$	−2.23281	+	2.66096i	−0.222173	+	0.264776i	−0.865605	−	0.500728i	$-0.833066\pi$
$101$	−2.23281	+	2.66096i	−0.222173	+	0.264776i	0.643432	+	0.765504i	$0.277510\pi$
$102$	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
$105$	0.299427	+	0.841812i	0.0292211	+	0.0821524i
$106$	−1.25950	−	2.18151i	−0.122333	−	0.211887i
$107$	5.65395	+	9.79293i	0.546588	+	0.946719i	0.998505	+	0.0546586i	$0.0174071\pi$
$107$	5.65395	+	9.79293i	0.546588	+	0.946719i	−0.451917	+	0.892060i	$0.649260\pi$
$108$	2.06006	+	4.77034i	0.198230	+	0.459026i
$109$	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
$111$	−0.638515	+	1.15758i	−0.0606052	+	0.109872i
$112$	2.59228	+	0.529236i	0.244947	+	0.0500081i
$113$	12.0260			1.13131			0.565656	−	0.824642i	$-0.308623\pi$
$113$	12.0260			1.13131			0.565656	+	0.824642i	$0.308623\pi$
$114$	7.49640	−	0.896614i	0.702103	−	0.0839756i
$115$	0.844472	+	1.46267i	0.0787475	+	0.136395i
$116$	1.86237	+	0.677847i	0.172917	+	0.0629365i
$117$	5.50217	+	13.4571i	0.508676	+	1.24411i
$118$	1.11159	−	6.30412i	0.102330	−	0.580342i
$119$	−17.6710	+	5.89931i	−1.61990	+	0.540789i
$120$	−0.0651252	−	0.331364i	−0.00594509	−	0.0302493i
$121$	7.57937	+	13.1279i	0.689034	+	1.19344i
$122$	−5.10441	+	8.84110i	−0.462131	+	0.800435i
$123$	−5.01536	+	14.6645i	−0.452220	+	1.32226i
$124$	0.164802	+	0.452789i	0.0147996	+	0.0406617i
$125$	1.68210	−	0.971159i	0.150451	−	0.0868631i
$126$	5.02739	−	6.14209i	0.447876	−	0.547181i
$127$	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
$129$	11.1288	−	2.18722i	0.979838	−	0.192574i
$130$	−0.164075	−	0.930518i	−0.0143904	−	0.0816118i
$131$	−6.36106	+	1.12163i	−0.555768	+	0.0979969i	−0.444476	−	0.895791i	$-0.646610\pi$
$131$	−6.36106	+	1.12163i	−0.555768	+	0.0979969i	−0.111292	+	0.993788i	$0.535499\pi$
$132$	−1.36763	+	8.75247i	−0.119037	+	0.761805i
$133$	−6.47604	−	9.54258i	−0.561544	−	0.827447i
$134$		−	1.34641i		−	0.116312i
$135$	−0.970668	−	0.290162i	−0.0835418	−	0.0249732i
$136$	6.93439	−	1.22272i	0.594619	−	0.104847i
$137$	−2.79722	−	7.68530i	−0.238983	−	0.656599i	−0.999969	−	0.00783182i	$-0.997507\pi$
$137$	−2.79722	−	7.68530i	−0.238983	−	0.656599i	0.760987	−	0.648767i	$-0.224715\pi$
$138$	7.24672	−	13.1377i	0.616882	−	1.11836i
$139$	−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
$141$	−1.31823	+	0.509167i	−0.111015	+	0.0428796i
$142$	−11.3279	+	4.12300i	−0.950612	+	0.345995i
$143$	−4.30405	+	24.4095i	−0.359923	+	2.04122i
$144$	−2.22108	+	2.01664i	−0.185090	+	0.168053i
$145$	−0.334646	+	0.193208i	−0.0277908	+	0.0160450i
$146$	2.85649	−	1.03968i	0.236405	−	0.0860444i
$147$	−11.8612	−	2.51224i	−0.978297	−	0.207206i
$148$	−0.751661	−	0.132538i	−0.0617862	−	0.0108946i
$149$	−0.949315	−	1.13135i	−0.0777709	−	0.0926838i	0.725756	−	0.687952i	$-0.241490\pi$
$149$	−0.949315	−	1.13135i	−0.0777709	−	0.0926838i	−0.803527	+	0.595268i	$0.797046\pi$
$150$	−7.52548	−	4.15103i	−0.614453	−	0.338930i
$151$	−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
$156$	−6.32344	+	5.51998i	−0.506280	+	0.441952i
$157$	−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
$159$	−1.57202	−	4.06998i	−0.124670	−	0.322770i
$160$	0.168852	−	0.0974865i	0.0133489	−	0.00770699i
$161$	−22.9104	−	0.615476i	−1.80559	−	0.0485063i
$162$	2.24977	+	8.71427i	0.176759	+	0.684658i
$163$	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
$165$	−1.13585	−	1.30118i	−0.0884260	−	0.101297i
$166$	1.97984	−	5.43955i	0.153665	−	0.422191i
$167$	−0.900701	+	5.10813i	−0.0696983	+	0.395279i	0.929923	+	0.367755i	$0.119873\pi$
$167$	−0.900701	+	5.10813i	−0.0696983	+	0.395279i	−0.999621	+	0.0275240i	$0.991238\pi$
$168$	4.29461	+	1.59885i	0.331337	+	0.123354i
$169$	−8.03224	+	6.73985i	−0.617865	+	0.518450i
$170$	−0.686438	+	1.18895i	−0.0526474	+	0.0911880i
$171$	13.0682	+	0.470165i	0.999353	+	0.0359544i
$172$	3.27407	+	5.67086i	0.249646	+	0.432399i
$173$	−2.05219	−	11.6385i	−0.156025	−	0.884862i	−0.957843	−	0.287293i	$-0.907245\pi$
$173$	−2.05219	−	11.6385i	−0.156025	−	0.884862i	0.801818	−	0.597569i	$-0.203866\pi$
$174$	3.00579	+	1.65798i	0.227868	+	0.125692i
$175$	−0.352554	+	13.1234i	−0.0266506	+	0.992039i
$176$	−5.03686	+	0.888134i	−0.379668	+	0.0669456i
$177$	3.58796	−	10.4909i	0.269687	−	0.788546i
$178$	−0.942450			−0.0706396
$179$	−10.6531	+	18.4516i	−0.796247	+	1.37914i	0.125798	+	0.992056i	$0.459851\pi$
$179$	−10.6531	+	18.4516i	−0.796247	+	1.37914i	−0.922044	+	0.387084i	$0.873482\pi$
$180$	−0.0228415	−	0.584473i	−0.00170251	−	0.0435640i
$181$	−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
$183$	−11.0992	+	13.7647i	−0.820476	+	1.01752i
$184$	8.53085	+	1.50422i	0.628903	+	0.110892i
$185$	0.113999	−	0.0956561i	0.00838134	−	0.00703278i
$186$	0.160948	+	0.818920i	0.0118013	+	0.0600461i
$187$	27.5879	−	23.1490i	2.01743	−	1.69282i
$188$	−0.524439	−	0.625002i	−0.0382486	−	0.0455830i
$189$	10.2457	−	9.16656i	0.745265	−	0.666769i
$190$	−0.823541	−	0.209895i	−0.0597459	−	0.0152274i
$191$	14.0932	+	8.13673i	1.01975	+	0.588753i	0.914032	−	0.405643i	$-0.132952\pi$
$191$	14.0932	+	8.13673i	1.01975	+	0.588753i	0.105719	+	0.994396i	$0.466286\pi$
$192$	−1.51663	−	0.836567i	−0.109453	−	0.0603740i
$193$	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
$195$	−0.0319607	−	1.63625i	−0.00228875	−	0.117175i
$196$	−0.843663	−	6.94897i	−0.0602616	−	0.496355i
$197$	−16.9368	−	9.77847i	−1.20670	−	0.696687i	−0.244661	−	0.969609i	$-0.578677\pi$
$197$	−16.9368	−	9.77847i	−1.20670	−	0.696687i	−0.962036	+	0.272922i	$0.912010\pi$
$198$	−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
$204$	12.1937	−	0.238177i	0.853728	−	0.0166757i
$205$	1.12142	−	1.33646i	0.0783237	−	0.0933426i
$206$	13.8072	−	2.43457i	0.961990	−	0.169625i
$207$	15.9142	−	20.5446i	1.10611	−	1.42795i
$208$	−4.19691	−	2.42308i	−0.291003	−	0.168011i
$209$	18.4172	+	12.5627i	1.27395	+	0.868979i
$210$	−0.777028	+	0.441058i	−0.0536200	+	0.0304359i
$211$	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
$213$	−20.4877	+	4.02658i	−1.40379	+	0.275897i
$214$	−8.66236	+	7.26858i	−0.592147	+	0.496870i
$215$	−1.25732	−	0.221699i	−0.0857482	−	0.0151197i
$216$	−4.34014	+	2.85713i	−0.295309	+	0.194403i
$217$	0.998247	−	0.792937i	0.0677654	−	0.0538280i
$218$	−12.8669	+	15.3342i	−0.871457	+	1.03856i
$219$	5.16628	−	1.01536i	0.349105	−	0.0686119i
$220$	0.498601	−	0.863602i	0.0336157	−	0.0582240i
$221$	34.1236			2.29540
$222$	−1.25087	−	0.427804i	−0.0839527	−	0.0287123i
$223$	−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
$225$	−11.7683	−	9.11590i	−0.784551	−	0.607727i
$226$	2.08829	+	11.8433i	0.138911	+	0.787805i
$227$	−8.79449	−	15.2325i	−0.583711	−	1.01102i	−0.995035	−	0.0995275i	$-0.968267\pi$
$227$	−8.79449	−	15.2325i	−0.583711	−	1.01102i	0.411324	−	0.911489i	$-0.365066\pi$
$228$	2.18473	+	7.22682i	0.144687	+	0.478608i
$229$	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
$231$	23.1110	−	3.90070i	1.52059	−	0.256647i
$232$	−0.344152	+	1.95178i	−0.0225947	+	0.128141i
$233$	3.50328	−	9.62517i	0.229507	−	0.630566i	−0.770469	−	0.637478i	$-0.779978\pi$
$233$	3.50328	−	9.62517i	0.229507	−	0.630566i	0.999976	+	0.00691155i	$0.00220003\pi$
$234$	−12.2972	+	7.75539i	−0.803896	+	0.506985i
$235$	0.159075			0.0103769
$236$	6.40137			0.416694
$237$	−5.55188	+	4.84646i	−0.360633	+	0.314811i
$238$	−8.87822	−	16.3781i	−0.575490	−	1.06164i
$239$	18.7146	−	10.8049i	1.21055	−	0.698911i	0.247671	−	0.968844i	$-0.420335\pi$
$239$	18.7146	−	10.8049i	1.21055	−	0.698911i	0.962879	+	0.269933i	$0.0870015\pi$
$240$	0.315021	−	0.121677i	0.0203345	−	0.00785419i
$241$	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
$243$	1.51982	+	15.5142i	0.0974966	+	0.995236i
$244$	−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
$249$	4.84259	−	8.77922i	0.306887	−	0.556361i
$250$	1.24850	+	1.48790i	0.0789620	+	0.0941032i
$251$	−26.2787	−	4.63365i	−1.65870	−	0.292474i	−0.735710	−	0.677297i	$-0.763151\pi$
$251$	−26.2787	−	4.63365i	−1.65870	−	0.292474i	−0.922990	+	0.384824i	$0.874262\pi$
$252$	6.92178	+	3.88445i	0.436031	+	0.244698i
$253$	41.6327	−	15.1531i	2.61743	−	0.952666i
$254$	−4.98801	+	2.87983i	−0.312976	+	0.180697i
$255$	−1.49261	+	1.85107i	−0.0934711	+	0.115919i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	1.56385	−	0.569195i	0.0975504	−	0.0355054i	−0.292784	−	0.956179i	$-0.594582\pi$
$257$	1.56385	−	0.569195i	0.0975504	−	0.0355054i	0.390334	+	0.920673i	$0.372359\pi$
$258$	4.08649	+	10.5799i	0.254414	+	0.658679i
$259$	0.297130	+	1.99741i	0.0184628	+	0.124113i
$260$	0.887889	−	0.323165i	0.0550646	−	0.0200419i
$261$	4.70042	+	3.64103i	0.290949	+	0.225374i
$262$	−2.20917	−	6.06965i	−0.136483	−	0.374984i
$263$	−9.70551	+	1.71134i	−0.598467	+	0.105526i	−0.464672	−	0.885483i	$-0.653828\pi$
$263$	−9.70551	+	1.71134i	−0.598467	+	0.105526i	−0.133796	+	0.991009i	$0.542717\pi$
$264$	−8.85699	+	0.173002i	−0.545110	+	0.0106475i
$265$			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	$-0.986692\pi$
$269$	−1.22271	−	6.93433i	−0.0745499	−	0.422794i	0.924576	−	0.380997i	$-0.124419\pi$
$270$	0.117199	−	1.00631i	0.00713249	−	0.0612420i
$271$	−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
$273$	19.1508	+	11.2446i	1.15906	+	0.680554i
$274$	7.08281	−	4.08926i	0.427888	−	0.247041i
$275$	−8.67992	−	23.8479i	−0.523419	−	1.43808i
$276$	14.1965	+	4.85529i	0.854528	+	0.292254i
$277$	−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
$279$	0.0564497	+	1.44444i	0.00337955	+	0.0864765i
$280$	−0.386117	−	0.342075i	−0.0230749	−	0.0204429i
$281$	0.399945	−	2.26820i	0.0238587	−	0.135309i	−0.970552	−	0.240893i	$-0.922560\pi$
$281$	0.399945	−	2.26820i	0.0238587	−	0.135309i	0.994410	+	0.105583i	$0.0336709\pi$
$282$	−0.730340	−	1.20979i	−0.0434911	−	0.0720420i
$283$	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
$285$	−1.35319	−	0.579404i	−0.0801559	−	0.0343209i
$286$	−24.7860			−1.46563
$287$	7.49674	+	22.4560i	0.442519	+	1.32554i
$288$	−2.37168	−	1.83715i	−0.139753	−	0.108255i
$289$	−24.9583	−	20.9425i	−1.46814	−	1.23191i
$290$	−0.248383	−	0.296012i	−0.0145856	−	0.0173824i
$291$	5.34842	−	4.66885i	0.313530	−	0.273693i
$292$	1.51991	+	2.63256i	0.0889459	+	0.154059i
$293$	2.93758	+	5.08804i	0.171615	+	0.297246i	0.938985	−	0.343959i	$-0.111768\pi$
$293$	2.93758	+	5.08804i	0.171615	+	0.297246i	−0.767369	+	0.641205i	$0.778435\pi$
$294$	0.414398	−	12.1173i	0.0241682	−	0.706694i
$295$	−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
$300$	2.78118	−	8.13197i	0.160572	−	0.469499i
$301$	11.4885	−	12.9677i	0.662188	−	0.747446i
$302$	−6.57339	−	7.83386i	−0.378256	−	0.450788i
$303$	−4.68357	−	3.77660i	−0.269064	−	0.216960i
$304$	−3.53972	+	2.54369i	−0.203017	+	0.145891i
$305$	1.72378	−	0.995222i	0.0987031	−	0.0569863i
$306$	20.9305	+	2.85298i	1.19652	+	0.163094i
$307$	−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
$309$	24.2790	−	0.474238i	1.38118	−	0.0269784i
$310$	0.0163138	−	0.0925202i	0.000926562	−	0.00525479i
$311$		−	26.8455i		−	1.52227i	−0.648595	−	0.761134i	$-0.724643\pi$
$311$		−	26.8455i		−	1.52227i	0.648595	−	0.761134i	$-0.275357\pi$
$312$	−6.53417	−	5.26884i	−0.369925	−	0.298289i
$313$	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
$315$	−1.44765	+	0.546999i	−0.0815661	+	0.0308199i
$316$	−3.68482	−	2.12743i	−0.207287	−	0.119677i
$317$	2.26824	−	12.8638i	0.127397	−	0.722504i	−0.852458	−	0.522795i	$-0.824889\pi$
$317$	2.26824	−	12.8638i	0.127397	−	0.722504i	0.979855	−	0.199709i	$-0.0639997\pi$
$318$	3.73517	−	2.25489i	0.209458	−	0.126448i
$319$	3.46689	+	9.52520i	0.194109	+	0.533309i
$320$	0.125326	+	0.149358i	0.00700595	+	0.00834937i
$321$	−16.7674	+	10.1223i	−0.935864	+	0.564973i
$322$	−3.37223	−	22.6692i	−0.187927	−	1.26331i
$323$	12.6297	−	27.9737i	0.702736	−	1.55650i
$324$	−8.19121	+	3.72881i	−0.455067	+	0.207156i
$325$	8.22443	−	22.5964i	0.456209	−	1.25342i
$326$	1.56889	+	8.89761i	0.0868927	+	0.492793i
$327$	−26.1193	+	22.8006i	−1.44440	+	1.26087i
$328$	−1.55381	−	8.81210i	−0.0857949	−	0.486567i
$329$	−1.12912	+	1.83976i	−0.0622506	+	0.101429i
$330$	1.08417	−	1.34454i	0.0596818	−	0.0740147i
$331$		−	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
$333$	−2.02620	−	1.06657i	−0.111035	−	0.0584479i
$334$	−5.18693			−0.283816
$335$	−0.131257	+	0.227343i	−0.00717133	+	0.0124211i
$336$	−0.828803	+	4.50700i	−0.0452149	+	0.245877i
$337$	−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
$339$	0.406785	+	20.8257i	0.0220935	+	1.13110i
$340$	−1.29008	−	0.469551i	−0.0699645	−	0.0254650i
$341$	−1.23222	+	2.13427i	−0.0667285	+	0.115577i
$342$	1.80625	+	12.9513i	0.0976710	+	0.700329i
$343$	−16.7323	+	7.93916i	−0.903459	+	0.428674i
$344$	−5.01617	+	4.20907i	−0.270454	+	0.226938i
$345$	−2.50437	+	1.51187i	−0.134831	+	0.0813961i
$346$	11.1054	−	4.04202i	0.597028	−	0.217300i
$347$	14.9781	+	17.8502i	0.804065	+	0.958248i	0.999749	−	0.0224194i	$-0.00713692\pi$
$347$	14.9781	+	17.8502i	0.804065	+	0.958248i	−0.195683	+	0.980667i	$0.562692\pi$
$348$	−1.11085	+	3.24803i	−0.0595476	+	0.174113i
$349$	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
$351$	−23.1179	+	9.98341i	−1.23394	+	0.532875i
$352$	−1.74928	−	4.80612i	−0.0932371	−	0.256167i
$353$	−2.02486	−	1.16905i	−0.107773	−	0.0622225i	0.445145	−	0.895459i	$-0.353152\pi$
$353$	−2.02486	−	1.16905i	−0.107773	−	0.0622225i	−0.552917	+	0.833236i	$0.686486\pi$
$354$	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
$357$	−10.8137	−	30.4017i	−0.572321	−	1.60903i
$358$	−20.0212	−	7.28712i	−1.05815	−	0.385136i
$359$	19.6887	−	3.47165i	1.03913	−	0.183227i	0.372050	−	0.928213i	$-0.378655\pi$
$359$	19.6887	−	3.47165i	1.03913	−	0.183227i	0.667080	+	0.744986i	$0.267544\pi$
$360$	0.571627	−	0.123987i	0.0301274	−	0.00653470i
$361$	18.7865	+	2.84018i	0.988764	+	0.149483i
$362$	−8.93173	−	5.15674i	−0.469441	−	0.271032i
$363$	−22.4774	+	13.5694i	−1.17976	+	0.712209i
$364$	−2.56477	+	12.5626i	−0.134430	+	0.658460i
$365$	−0.583678	−	0.102918i	−0.0305511	−	0.00538698i
$366$	−15.4830	−	8.54036i	−0.809308	−	0.446412i
$367$	−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
$372$	−0.778530	+	0.300707i	−0.0403649	+	0.0155909i
$373$	−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
$375$	1.73867	+	2.88007i	0.0897847	+	0.148726i
$376$	0.524439	−	0.625002i	0.0270459	−	0.0322320i
$377$	−3.28496	+	9.02536i	−0.169184	+	0.464830i
$378$	10.8064	+	8.49828i	0.555823	+	0.437105i
$379$			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
$381$	−9.30597	+	3.59442i	−0.476760	+	0.184148i
$382$	−5.56585	+	15.2920i	−0.284774	+	0.782409i
$383$	18.0478	−	15.1439i	0.922198	−	0.773816i	−0.0522020	−	0.998637i	$-0.516624\pi$
$383$	18.0478	−	15.1439i	0.922198	−	0.773816i	0.974400	+	0.224820i	$0.0721795\pi$
$384$	0.560498	−	1.63885i	0.0286028	−	0.0836324i
$385$	−2.58502	−	0.527755i	−0.131745	−	0.0268969i
$386$	0.432393	+	1.18799i	0.0220082	+	0.0604671i
$387$	4.16410	+	19.1980i	0.211673	+	0.975891i
$388$	3.54978	+	2.04947i	0.180213	+	0.104046i
$389$	12.7507	+	2.24829i	0.646484	+	0.113993i	0.487270	−	0.873251i	$-0.337993\pi$
$389$	12.7507	+	2.24829i	0.646484	+	0.113993i	0.159214	+	0.987244i	$0.449104\pi$
$390$	1.60585	−	0.315608i	0.0813152	−	0.0159814i
$391$	−30.4977	−	52.8236i	−1.54234	−	2.67141i
$392$	6.69690	−	2.03752i	0.338245	−	0.102910i
$393$	−2.15751	−	10.9776i	−0.108832	−	0.553748i
$394$	6.68887	−	18.3775i	0.336980	−	0.925846i
$395$	0.779553	−	0.283734i	0.0392236	−	0.0142762i
$396$	−15.2031	−	2.07229i	−0.763985	−	0.104137i
$397$	−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
$399$	16.3060	−	11.5375i	0.816322	−	0.577596i
$400$	4.96199			0.248099
$401$	−3.24315	−	18.3928i	−0.161955	−	0.918494i	−0.952148	−	0.305636i	$-0.901131\pi$
$401$	−3.24315	−	18.3928i	−0.161955	−	0.918494i	0.790193	−	0.612858i	$-0.209980\pi$
$402$	2.33161	−	0.0455429i	0.116290	−	0.00227147i
$403$	−2.19429	+	0.798657i	−0.109306	+	0.0397840i
$404$	1.18805	−	3.26415i	0.0591079	−	0.162398i
$405$	0.469646	−	1.69074i	0.0233369	−	0.0840136i
$406$	5.18652	−	0.771536i	0.257403	−	0.0382907i
$407$	−1.95186	−	3.38072i	−0.0967502	−	0.167576i
$408$	2.35197	+	11.9671i	0.116440	+	0.592458i
$409$	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
$411$	13.2142	−	5.10396i	0.651807	−	0.251760i
$412$	4.79517	+	13.1746i	0.236241	+	0.649068i
$413$	−5.36312	−	16.0649i	−0.263902	−	0.790501i
$414$	22.9960	+	12.1049i	1.13019	+	0.594923i
$415$	−0.864582	+	0.725470i	−0.0424406	+	0.0356119i
$416$	1.65749	−	4.55391i	0.0812650	−	0.223274i
$417$	−5.42981	−	14.0578i	−0.265899	−	0.688413i
$418$	−9.17371	+	20.3189i	−0.448701	+	0.993832i
$419$		−	5.69757i		−	0.278345i	−0.990268	−	0.139172i	$-0.955556\pi$
$419$		−	5.69757i		−	0.278345i	0.990268	−	0.139172i	$-0.0444442\pi$
$420$	−0.569286	−	0.688634i	−0.0277783	−	0.0336019i
$421$	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
$423$	−0.926324	−	2.26559i	−0.0450394	−	0.110157i
$424$	1.92966	+	1.61918i	0.0937126	+	0.0786342i
$425$	−30.2582	+	17.4696i	−1.46774	+	0.847399i
$426$	−7.52305	−	19.4772i	−0.364493	−	0.943674i
$427$	−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	0.845778	−	0.533535i	$-0.179137\pi$
$431$	9.69965	+	8.13897i	0.467216	+	0.392040i	−0.378562	+	0.925576i	$0.623581\pi$
$432$	−3.56738	−	3.77807i	−0.171636	−	0.181772i
$433$	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
$435$	−0.345901	−	0.572978i	−0.0165847	−	0.0274722i
$436$	−17.3355	−	10.0087i	−0.830221	−	0.479329i
$437$	26.3706	−	27.0244i	1.26148	−	1.29275i
$438$	1.89705	+	4.91148i	0.0906447	+	0.234679i
$439$	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
$441$	3.94929	−	20.6253i	0.188062	−	0.982157i
$442$	5.92551	+	33.6052i	0.281848	+	1.59844i
$443$	2.94751	+	0.519726i	0.140041	+	0.0246929i	0.243229	−	0.969969i	$-0.421793\pi$
$443$	2.94751	+	0.519726i	0.140041	+	0.0246929i	−0.103188	+	0.994662i	$0.532904\pi$
$444$	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
$447$	1.92707	−	1.68222i	0.0911473	−	0.0795661i
$448$	−2.61695	+	0.389293i	−0.123639	+	0.0183923i
$449$	−6.74168	+	11.6769i	−0.318160	+	0.551069i	−0.980104	−	0.198484i	$-0.936398\pi$
$449$	−6.74168	+	11.6769i	−0.318160	+	0.551069i	0.661944	+	0.749553i	$0.269731\pi$
$450$	6.93387	−	13.1724i	0.326866	−	0.620955i
$451$	−29.4174	−	35.0583i	−1.38521	−	1.65083i
$452$	−11.3007	+	4.11314i	−0.531542	+	0.193466i
$453$	−9.15419	−	15.1637i	−0.430101	−	0.712452i
$454$	13.4739	−	11.3060i	0.632363	−	0.530616i
$455$	−1.55490	−	1.95749i	−0.0728946	−	0.0917688i
$456$	−6.73766	+	3.40646i	−0.315520	+	0.159522i
$457$	−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
$459$	35.0553	+	10.4791i	1.63624	+	0.489121i
$460$	−1.29381	−	1.08563i	−0.0603240	−	0.0506179i
$461$	25.9455	−	4.57490i	1.20840	−	0.213074i	0.467076	−	0.884217i	$-0.345308\pi$
$461$	25.9455	−	4.57490i	1.20840	−	0.213074i	0.741328	+	0.671143i	$0.234196\pi$
$462$	7.85462	+	22.0825i	0.365430	+	1.02737i
$463$	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
$465$	0.0526573	−	0.153966i	0.00244193	−	0.00714001i
$466$	10.0873	+	1.77866i	0.467284	+	0.0823949i
$467$			24.6742i			1.14179i	0.821024	+	0.570893i	$0.193403\pi$
$467$			24.6742i			1.14179i	−0.821024	+	0.570893i	$0.806597\pi$
$468$	−9.77296	−	10.7637i	−0.451755	−	0.497553i
$469$	−1.69764	−	3.13173i	−0.0783899	−	0.144610i
$470$	0.0276231	+	0.156658i	0.00127416	+	0.00722611i
$471$	−16.8090	−	19.2556i	−0.774517	−	0.887251i
$472$	1.11159	+	6.30412i	0.0511649	+	0.290171i
$473$	−11.4546	+	31.4711i	−0.526681	+	1.44704i
$474$	−5.73690	−	4.62595i	−0.263505	−	0.212477i
$475$	−15.4800	−	15.1055i	−0.710270	−	0.693087i
$476$	14.5876	−	11.5874i	0.668622	−	0.531106i
$477$	6.99489	−	2.85998i	0.320274	−	0.130949i
$478$	13.8905	+	16.5541i	0.635338	+	0.757166i
$479$	−6.45769	−	17.7424i	−0.295059	−	0.810669i	−0.995307	−	0.0967686i	$-0.969149\pi$
$479$	−6.45769	−	17.7424i	−0.295059	−	0.810669i	0.700248	−	0.713900i	$-0.253073\pi$
$480$	0.174531	+	0.289106i	0.00796621	+	0.0131958i
$481$	0.642302	−	3.64268i	0.0292865	−	0.166092i
$482$	0.179358	+	0.103552i	0.00816953	+	0.00471668i
$483$	0.290877	−	39.6953i	0.0132354	−	1.80620i
$484$	−11.6123	−	9.74385i	−0.527830	−	0.442902i
$485$	−0.750984	+	0.273336i	−0.0341004	+	0.0124115i
$486$	−15.0146	+	4.19074i	−0.681075	+	0.190096i
$487$			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
$489$	0.305608	+	15.6459i	0.0138201	+	0.707530i
$490$	−0.534977	+	1.25559i	−0.0241678	+	0.0567218i
$491$	−2.34057	+	6.43066i	−0.105628	+	0.290212i	−0.981236	−	0.192812i	$-0.938239\pi$
$491$	−2.34057	+	6.43066i	−0.105628	+	0.290212i	0.875607	+	0.483024i	$0.160461\pi$
$492$	−0.302671	−	15.4955i	−0.0136455	−	0.698592i
$493$	12.0856	−	6.97761i	0.544307	−	0.314256i
$494$	−19.0341	+	9.16110i	−0.856383	+	0.412177i
$495$	2.21486	−	2.01099i	0.0995506	−	0.0903874i
$496$	−0.309726	−	0.369117i	−0.0139071	−	0.0165739i
$497$	−21.1499	+	23.8730i	−0.948702	+	1.07085i
$498$	9.48676	+	3.24453i	0.425112	+	0.145391i
$499$	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	−0.834976	−	0.550287i	$-0.814518\pi$
$503$	−3.32057	+	3.95730i	−0.148057	+	0.176447i	0.686919	+	0.726734i	$0.258963\pi$
$504$	−2.62349	+	7.49115i	−0.116859	+	0.333682i
$505$	0.338633	+	0.586530i	0.0150690	+	0.0261002i
$506$	22.1523	+	38.3689i	0.984791	+	1.70571i
$507$	−11.9432	−	13.6816i	−0.530418	−	0.607622i
$508$	−3.70224	−	4.41216i	−0.164260	−	0.195758i
$509$	19.6844	+	16.5172i	0.872497	+	0.732112i	0.964622	−	0.263636i	$-0.0849217\pi$
$509$	19.6844	+	16.5172i	0.872497	+	0.732112i	−0.0921258	+	0.995747i	$0.529366\pi$
$510$	−2.08214	−	1.14850i	−0.0921987	−	0.0508565i
$511$	5.33327	−	6.01993i	0.235930	−	0.266306i
$512$	1.00000			0.0441942
$513$	−0.372156	+	22.6464i	−0.0164311	+	0.999865i
$514$	0.832108	+	1.44125i	0.0367027	+	0.0635710i
$515$	−2.56870	−	0.934930i	−0.113190	−	0.0411979i
$516$	−9.70960	+	5.86160i	−0.427441	+	0.258043i
$517$	0.724613	−	4.10948i	0.0318684	−	0.180735i
$518$	−1.91547	+	0.639462i	−0.0841608	+	0.0280964i
$519$	20.0853	−	3.94750i	0.881646	−	0.173276i
$520$	0.472436	+	0.818283i	0.0207177	+	0.0358841i
$521$	14.6985	−	25.4585i	0.643953	−	1.11536i	−0.340590	−	0.940212i	$-0.610627\pi$
$521$	14.6985	−	25.4585i	0.643953	−	1.11536i	0.984542	−	0.175147i	$-0.0560400\pi$
$522$	−2.76949	+	5.26127i	−0.121217	+	0.230280i
$523$	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
$525$	−22.7381	−	0.166619i	−0.992370	−	0.00727184i
$526$	−3.37069	−	9.26089i	−0.146969	−	0.403794i
$527$	3.18825	+	1.16043i	0.138883	+	0.0505491i
$528$	−1.70837	−	8.69239i	−0.0743474	−	0.378288i
$529$	−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
$534$	−0.0318788	−	1.63206i	−0.00137953	−	0.0706262i
$535$	2.17124	−	0.382849i	0.0938710	−	0.0165520i
$536$	0.460499	+	1.26521i	0.0198905	+	0.0546488i
$537$	−32.3134	−	17.8240i	−1.39443	−	0.769162i
$538$	6.61666	−	2.40827i	0.285265	−	0.103828i
$539$	24.4523	−	26.1507i	1.05324	−	1.12639i
$540$	1.01137	−	0.0593252i	0.0435225	−	0.00255295i
$541$	−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
$543$	−13.9058	−	11.2130i	−0.596757	−	0.481195i
$544$	−6.09800	+	3.52068i	−0.261450	+	0.150948i
$545$	3.66747	−	1.33485i	0.157097	−	0.0571787i
$546$	−7.74827	+	20.8124i	−0.331595	+	0.890689i
$547$	−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
$549$	−24.2121	−	18.7551i	−1.03335	−	0.800449i
$550$	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
$555$	0.169506	+	0.194178i	0.00719512	+	0.00824240i
$556$	6.66509	−	5.59268i	0.282663	−	0.237182i
$557$	24.6479	−	29.3742i	1.04436	−	1.24462i	0.0754706	−	0.997148i	$-0.475954\pi$
$557$	24.6479	−	29.3742i	1.04436	−	1.24462i	0.968894	−	0.247477i	$-0.0796014\pi$
$558$	−1.41270	+	0.306417i	−0.0598042	+	0.0129717i
$559$	−27.4819	+	15.8667i	−1.16236	+	0.671090i
$560$	0.269829	−	0.439652i	0.0114024	−	0.0185787i
$561$	41.0208	+	46.9916i	1.73190	+	1.98399i
$562$	2.30319			0.0971542
$563$	−34.5738			−1.45711			−0.728555	−	0.684987i	$-0.759808\pi$
$563$	−34.5738			−1.45711			−0.728555	+	0.684987i	$0.759808\pi$
$564$	1.06459	−	0.929323i	0.0448273	−	0.0391315i
$565$	0.801951	−	2.20334i	0.0337383	−	0.0926953i
$566$	−5.14434	+	29.1750i	−0.216233	+	1.22632i
$567$	16.2205	+	17.4326i	0.681196	+	0.732101i
$568$	9.23455	−	7.74871i	0.387473	−	0.325128i
$569$	−5.85842	+	10.1471i	−0.245598	+	0.425388i	−0.962299	−	0.271992i	$-0.912318\pi$
$569$	−5.85842	+	10.1471i	−0.245598	+	0.425388i	0.716702	+	0.697380i	$0.245651\pi$
$570$	0.335623	−	1.43324i	0.0140577	−	0.0600319i
$571$	−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
$573$	−13.6138	+	24.6808i	−0.568726	+	1.03105i
$574$	−20.8130	+	11.2823i	−0.868719	+	0.470914i
$575$	−42.3300	+	7.46391i	−1.76528	+	0.311267i
$576$	1.39740	−	2.65467i	0.0582250	−	0.110611i
$577$	−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
$579$	0.422281	+	2.14861i	0.0175494	+	0.0892932i
$580$	0.248383	−	0.296012i	0.0103135	−	0.0122912i
$581$	−2.25348	−	15.1486i	−0.0934901	−	0.628471i
$582$	5.52666	+	4.45643i	0.229087	+	0.184725i
$583$	12.6878	+	2.23720i	0.525476	+	0.0926555i
$584$	−2.32863	+	1.95396i	−0.0963595	+	0.0808552i
$585$	2.83245	−	0.110694i	0.117108	−	0.00457663i
$586$	−4.50063	+	3.77648i	−0.185919	+	0.156005i
$587$	10.8724	+	12.9572i	0.448752	+	0.534802i	0.942235	−	0.334954i	$-0.108721\pi$
$587$	10.8724	+	12.9572i	0.448752	+	0.534802i	−0.493482	+	0.869756i	$0.664276\pi$
$588$	12.0051	−	1.69604i	0.495084	−	0.0699435i
$589$	−0.157425	+	2.09442i	−0.00648658	+	0.0862991i
$590$	−1.08088	−	0.624048i	−0.0444992	−	0.0256916i
$591$	16.3607	−	29.6606i	0.672988	−	1.22007i
$592$	0.751661	−	0.132538i	0.0308931	−	0.00544728i
$593$	3.16395	−	3.77065i	0.129928	−	0.154842i	−0.697158	−	0.716917i	$-0.745552\pi$
$593$	3.16395	−	3.77065i	0.129928	−	0.154842i	0.827086	+	0.562075i	$0.189997\pi$
$594$	−25.4627	−	7.61157i	−1.04475	−	0.312306i
$595$	−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	$0.207240\pi$
$599$	−3.89890	+	22.1118i	−0.159305	+	0.903462i	−0.954744	+	0.297429i	$0.903871\pi$
$600$	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
$603$	4.00222	+	0.545531i	0.162983	+	0.0222157i
$604$	6.57339	−	7.83386i	0.267468	−	0.318755i
$605$	2.91064	−	0.513225i	0.118335	−	0.0208656i
$606$	2.90593	−	5.26821i	0.118045	−	0.214007i
$607$	−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
$609$	9.08193	+	0.0665501i	0.368018	+	0.00269675i
$610$	1.27943	+	1.52477i	0.0518027	+	0.0617361i
$611$	3.02886	−	2.54152i	0.122535	−	0.102819i
$612$	0.824912	+	21.1080i	0.0333451	+	0.853239i
$613$	−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
$615$	2.35231	+	1.89679i	0.0948544	+	0.0764859i
$616$	−10.5959	+	8.41660i	−0.426919	+	0.339114i
$617$	14.7794	−	17.6134i	0.594997	−	0.709090i	−0.381561	−	0.924344i	$-0.624613\pi$
$617$	14.7794	−	17.6134i	0.594997	−	0.709090i	0.976558	+	0.215254i	$0.0690578\pi$
$618$	4.68303	+	23.8278i	0.188379	+	0.958494i
$619$	−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
$621$	36.1158	+	26.8640i	1.44928	+	1.07802i
$622$	26.4376	−	4.66167i	1.06005	−	0.186916i
$623$	−2.19213	+	1.18830i	−0.0878257	+	0.0476084i
$624$	4.05414	−	7.34983i	0.162296	−	0.294229i
$625$	4.24244	+	24.0601i	0.169698	+	0.962402i
$626$	4.06850	+	7.04685i	0.162610	+	0.281649i
$627$	−21.1321	+	32.3185i	−0.843934	+	1.29067i
$628$	7.37857	−	12.7801i	0.294437	−	0.509980i
$629$	−4.11701	+	3.45458i	−0.164156	+	0.137743i
$630$	−0.790072	−	1.33068i	−0.0314772	−	0.0530154i
$631$	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
$633$	−24.9322	+	21.7643i	−0.990967	+	0.865054i
$634$	13.0623			0.518769
$635$	1.12298			0.0445640
$636$	2.86923	+	3.28686i	0.113773	+	0.130333i
$637$	33.6759	−	4.08853i	1.33429	−	0.161994i
$638$	−8.77848	+	5.06825i	−0.347543	+	0.200654i
$639$	−7.66591	−	35.3427i	−0.303259	−	1.39814i
$640$	−0.125326	+	0.149358i	−0.00495396	+	0.00590389i
$641$	−30.4935	+	25.5871i	−1.20442	+	1.01063i	−0.204929	+	0.978777i	$0.565696\pi$
$641$	−30.4935	+	25.5871i	−1.20442	+	1.01063i	−0.999493	+	0.0318525i	$0.989859\pi$
$642$	−12.8802	−	14.7549i	−0.508339	−	0.582330i
$643$	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	−0.870747	−	0.491731i	$-0.836364\pi$
$647$	−22.3907	+	12.9273i	−0.880269	+	0.508224i	−0.00952191	+	0.999955i	$0.503031\pi$
$648$	−5.09455	−	7.41927i	−0.200133	−	0.291456i
$649$	21.0450	+	25.0805i	0.826089	+	0.984494i
$650$	23.6813	+	4.17565i	0.928857	+	0.163783i
$651$	1.40691	+	1.70186i	0.0551412	+	0.0667013i
$652$	−8.49000	+	3.09011i	−0.332494	+	0.121018i
$653$	3.29309	−	1.90127i	0.128869	−	0.0744024i	−0.434180	−	0.900826i	$-0.642962\pi$
$653$	3.29309	−	1.90127i	0.128869	−	0.0744024i	0.563049	+	0.826424i	$0.309628\pi$
$654$	−26.9897	−	21.7632i	−1.05538	−	0.851008i
$655$	−0.218687	+	1.24023i	−0.00854480	+	0.0484600i
$656$	8.40841	−	3.06041i	0.328293	−	0.119489i
$657$	1.93308	+	8.91221i	0.0754166	+	0.347698i
$658$	−2.00788	−	0.792499i	−0.0782754	−	0.0308948i
$659$	−3.76099	+	1.36889i	−0.146508	+	0.0533244i	−0.414233	−	0.910171i	$-0.635950\pi$
$659$	−3.76099	+	1.36889i	−0.146508	+	0.0533244i	0.267726	+	0.963495i	$0.413728\pi$
$660$	1.51238	+	0.834226i	0.0588694	+	0.0324722i
$661$	−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
$663$	1.15425	+	59.0926i	0.0448272	+	2.29497i
$664$			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
$669$	−6.36497	−	32.3857i	−0.246084	−	1.25210i
$670$	−0.246682	−	0.0897850i	−0.00953016	−	0.00346870i
$671$	−17.8581	−	49.0648i	−0.689405	−	1.89412i
$672$	−4.58245	−	0.0335791i	−0.176772	−	0.00129534i
$673$	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
$675$	15.3881	−	20.6877i	0.592289	−	0.796270i
$676$	5.24267	−	9.08058i	0.201641	−	0.349253i
$677$	1.17065	+	2.02763i	0.0449919	+	0.0779282i	0.887644	−	0.460530i	$-0.152340\pi$
$677$	1.17065	+	2.02763i	0.0449919	+	0.0779282i	−0.842652	+	0.538458i	$0.819007\pi$
$678$	−20.4387	+	4.01695i	−0.784942	+	0.154270i
$679$	2.16930	−	10.6256i	0.0832501	−	0.407772i
$680$	0.238397	−	1.35202i	0.00914213	−	0.0518476i
$681$	26.0810	−	15.7448i	0.999424	−	0.603344i
$682$	−2.31582	−	0.842889i	−0.0886773	−	0.0322759i
$683$	18.4048	+	31.8780i	0.704239	+	1.21978i	0.966965	+	0.254908i	$0.0820451\pi$
$683$	18.4048	+	31.8780i	0.704239	+	1.21978i	−0.262726	+	0.964870i	$0.584622\pi$
$684$	−12.4409	+	4.02779i	−0.475691	+	0.154006i
$685$	−1.59459			−0.0609262
$686$	−10.7241	−	15.0995i	−0.409447	−	0.576501i
$687$	6.81121	+	3.75704i	0.259864	+	0.143340i
$688$	−5.01617	−	4.20907i	−0.191240	−	0.160469i
$689$	7.84681	+	9.35146i	0.298940	+	0.356262i
$690$	−1.92378	−	2.20379i	−0.0732369	−	0.0838968i
$691$	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
$693$	7.53666	+	39.8898i	0.286294	+	1.51529i
$694$	−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
$699$	16.7866	+	5.74112i	0.634928	+	0.217149i
$700$	−4.15719	−	12.4526i	−0.157127	−	0.470663i
$701$	4.32171	+	5.15042i	0.163229	+	0.194529i	0.841459	−	0.540321i	$-0.181697\pi$
$701$	4.32171	+	5.15042i	0.163229	+	0.194529i	−0.678230	+	0.734850i	$0.737253\pi$
$702$	−13.8461	−	21.0331i	−0.522588	−	0.793842i
$703$	−2.74844	−	1.87476i	−0.103660	−	0.0707078i
$704$	4.42934	−	2.55728i	0.166937	−	0.0963811i
$705$	0.00538078	+	0.275473i	0.000202652	+	0.0103749i
$706$	0.799680	−	2.19710i	0.0300964	−	0.0826891i
$707$	−9.18707	−	0.246805i	−0.345515	−	0.00928208i
$708$	0.216529	+	11.0854i	0.00813766	+	0.416615i
$709$	−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
$711$	−8.58050	−	9.45037i	−0.321794	−	0.354416i
$712$	0.885613	−	0.322337i	0.0331898	−	0.0120801i
$713$	3.19746	+	2.68299i	0.119746	+	0.100479i
$714$	28.0620	−	15.9286i	1.05019	−	0.596113i
$715$	4.18516	+	2.41630i	0.156516	+	0.0903646i
$716$	3.69977	−	20.9824i	0.138267	−	0.784150i
$717$	19.3441	+	32.0431i	0.722419	+	1.19667i
$718$	6.83782	+	18.7868i	0.255185	+	0.701116i
$719$	−2.28401	−	2.72198i	−0.0851792	−	0.101513i	0.721772	−	0.692131i	$-0.243328\pi$
$719$	−2.28401	−	2.72198i	−0.0851792	−	0.101513i	−0.806951	+	0.590619i	$0.798884\pi$
$720$	0.221366	+	0.541413i	0.00824981	+	0.0201773i
$721$	29.0456	−	23.0718i	1.08171	−	0.859238i
$722$	0.465209	+	18.9943i	0.0173133	+	0.706895i
$723$	0.279243	+	0.225168i	0.0103852	+	0.00837408i
$724$	3.52742	−	9.69150i	0.131095	−	0.360182i
$725$	−1.70768	−	9.68472i	−0.0634215	−	0.359681i
$726$	−17.2664	−	19.7796i	−0.640817	−	0.734090i
$727$	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
$729$	−26.8148	+	3.15668i	−0.993142	+	0.116914i
$730$		−	0.592682i		−	0.0219361i
$731$	45.4074	+	8.00655i	1.67945	+	0.296133i
$732$	5.72202	−	16.7308i	0.211492	−	0.618387i
$733$	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
$735$	−1.25124	+	2.00562i	−0.0461528	+	0.0739785i
$736$	−8.53085	+	1.50422i	−0.314451	+	0.0554462i
$737$	5.27521	+	4.42643i	0.194315	+	0.163049i
$738$	3.62552	−	26.5982i	0.133457	−	0.979092i
$739$	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
$741$	−35.0224	+	10.5876i	−1.28658	+	0.388944i
$742$	2.44680	−	6.19923i	0.0898248	−	0.227581i
$743$	8.27067	−	6.93992i	0.303422	−	0.254601i	−0.478345	−	0.878172i	$-0.658763\pi$
$743$	8.27067	−	6.93992i	0.303422	−	0.254601i	0.781767	+	0.623571i	$0.214319\pi$
$744$	−0.431328	−	0.714485i	−0.0158133	−	0.0261943i
$745$	−0.270585	+	0.0984848i	−0.00991346	+	0.00360820i
$746$	−6.40709	−	7.63567i	−0.234580	−	0.279562i
$747$	15.3670	+	8.08906i	0.562248	+	0.295963i
$748$	−18.0067	+	31.1886i	−0.658392	+	1.14037i
$749$	−10.9838	+	27.8287i	−0.401340	+	1.01684i
$750$	−2.53440	+	2.21238i	−0.0925432	+	0.0807847i
$751$	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
$756$	−6.49266	+	12.1180i	−0.236136	+	0.440727i
$757$	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
$759$	27.6491	+	71.5837i	1.00360	+	2.59832i
$760$	0.845663	−	0.0844309i	0.0306754	−	0.00306263i
$761$	−5.92182	−	3.41897i	−0.214666	−	0.123937i	0.388812	−	0.921317i	$-0.372886\pi$
$761$	−5.92182	−	3.41897i	−0.214666	−	0.123937i	−0.603478	+	0.797380i	$0.706219\pi$
$762$	−5.15578	−	8.54043i	−0.186774	−	0.309387i
$763$	−10.5939	+	51.8905i	−0.383525	+	1.87856i
$764$	−16.0262	−	2.82586i	−0.579808	−	0.102236i
$765$	−3.25603	−	2.52218i	−0.117722	−	0.0911895i
$766$	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
$771$	1.03859	+	2.68890i	0.0374037	+	0.0968384i
$772$	−1.09486	+	0.632116i	−0.0394048	+	0.0227504i
$773$	−41.2058	−	34.5758i	−1.48207	−	1.24360i	−0.903940	−	0.427658i	$-0.859339\pi$
$773$	−41.2058	−	34.5758i	−1.48207	−	1.24360i	−0.578129	−	0.815945i	$-0.696217\pi$
$774$	−18.1833	+	7.43454i	−0.653585	+	0.267229i
$775$	1.53686	−	1.83155i	0.0552055	−	0.0657914i
$776$	−1.40192	+	3.85173i	−0.0503259	+	0.138269i
$777$	−3.44890	+	0.582110i	−0.123729	+	0.0208831i
$778$			12.9474i			0.464185i
$779$	−35.5485	−	16.0496i	−1.27366	−	0.575037i
$780$	0.589665	+	1.52665i	0.0211134	+	0.0546627i
$781$	21.0873	−	57.9370i	0.754564	−	2.07315i
$782$	46.7252	−	39.2071i	1.67089	−	1.40204i
$783$	−6.14625	+	8.26298i	−0.219649	+	0.295295i
$784$	3.16947	+	6.24135i	0.113195	+	0.222905i
$785$	0.984075	+	2.70372i	0.0351232	+	0.0965001i
$786$	10.4362	−	4.03098i	0.372247	−	0.143780i
$787$	−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
$789$	−3.29186	−	16.7493i	−0.117193	−	0.596293i
$790$	0.414791	+	0.718440i	0.0147576	+	0.0255609i
$791$	19.7902	+	24.9143i	0.703657	+	0.885851i
$792$	−0.599183	−	15.3320i	−0.0212910	−	0.544798i
$793$	16.9210	−	46.4900i	0.600882	−	1.65091i
$794$	11.4719	−	4.17543i	0.407122	−	0.148180i
$795$	−0.850510	+	0.0166129i	−0.0301645	+	0.000589198i
$796$	−1.56159	−	8.85621i	−0.0553491	−	0.313900i
$797$	15.0697			0.533797			0.266899	−	0.963725i	$-0.414001\pi$
$797$	15.0697			0.533797			0.266899	+	0.963725i	$0.414001\pi$
$798$	14.1937	+	14.0548i	0.502452	+	0.497536i
$799$	−5.74492			−0.203241
$800$	0.861640	+	4.88660i	0.0304636	+	0.172767i
$801$	0.381857	−	2.80145i	0.0134923	−	0.0989842i
$802$	17.5502	−	6.38776i	0.619720	−	0.225560i
$803$	−5.31750	+	14.6097i	−0.187650	+	0.515565i
$804$	0.449730	+	2.28827i	0.0158608	+	0.0807012i
$805$	−1.64054	+	4.15649i	−0.0578214	+	0.146497i
$806$	−1.16756	−	2.02227i	−0.0411255	−	0.0712315i
$807$	11.9670	−	2.35195i	0.421257	−	0.0827925i
$808$	3.42087	+	0.603191i	0.120346	+	0.0212202i
$809$	18.5598	+	10.7155i	0.652528	+	0.376737i	0.789424	−	0.613848i	$-0.210379\pi$
$809$	18.5598	+	10.7155i	0.652528	+	0.376737i	−0.136896	+	0.990585i	$0.543713\pi$
$810$	1.74661	+	0.168917i	0.0613696	+	0.00593513i
$811$	−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
$813$	15.6057	−	45.6298i	0.547314	−	1.60031i
$814$	2.99043	−	2.50927i	0.104814	−	0.0879497i
$815$	0.602487	−	1.65532i	0.0211042	−	0.0579833i
$816$	−11.3768	+	4.39430i	−0.398269	+	0.153831i
$817$	2.83560	+	28.4015i	0.0992051	+	0.993643i
$818$			25.1003i			0.877611i
$819$	−18.8247	+	33.5441i	−0.657789	+	1.17213i
$820$	−0.596698	+	1.63941i	−0.0208376	+	0.0572508i
$821$	−4.73409	+	5.64187i	−0.165221	+	0.196903i	−0.842302	−	0.539006i	$-0.818800\pi$
$821$	−4.73409	+	5.64187i	−0.165221	+	0.196903i	0.677081	+	0.735908i	$0.263245\pi$
$822$	7.32104	+	12.1271i	0.255350	+	0.422982i
$823$	−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
$825$	41.0043	−	15.8379i	1.42758	−	0.551403i
$826$	14.8895	−	8.07128i	0.518072	−	0.280836i
$827$	−20.5119	−	17.2115i	−0.713267	−	0.598502i	0.212247	−	0.977216i	$-0.431922\pi$
$827$	−20.5119	−	17.2115i	−0.713267	−	0.598502i	−0.925514	+	0.378714i	$0.876366\pi$
$828$	−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
$831$	−28.3079	−	15.6145i	−0.981990	−	0.541663i
$832$	4.77254	+	0.841528i	0.165458	+	0.0291747i
$833$	−41.3013	−	26.9010i	−1.43100	−	0.932066i
$834$	12.9013	−	7.78843i	0.446737	−	0.269691i
$835$	0.875821	+	0.505656i	0.0303090	+	0.0174989i
$836$	−21.6032	−	5.50599i	−0.747164	−	0.190429i
$837$	−2.49946	+	0.146614i	−0.0863940	+	0.00506772i
$838$	5.61101	−	0.989373i	0.193829	−	0.0341773i
$839$	0.550877	+	0.200503i	0.0190184	+	0.00692213i	0.351512	−	0.936183i	$-0.385668\pi$
$839$	0.550877	+	0.200503i	0.0190184	+	0.00692213i	−0.332493	+	0.943106i	$0.607890\pi$
$840$	0.579317	−	0.680218i	0.0199883	−	0.0234697i
$841$	−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
$846$	2.07032	−	1.30567i	0.0711789	−	0.0448897i
$847$	−14.7243	+	37.3056i	−0.505933	+	1.28184i
$848$	−1.25950	+	2.18151i	−0.0432513	+	0.0749134i
$849$	−16.6048	+	48.5511i	−0.569874	+	1.66627i
$850$	−22.4585	−	26.7649i	−0.770318	−	0.918030i
$851$	−6.21294	+	2.26133i	−0.212977	+	0.0775173i
$852$	17.8749	−	10.7909i	0.612385	−	0.369692i
$853$	−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
$855$	0.957593	−	2.36294i	0.0327490	−	0.0808109i
$856$	5.65395	−	9.79293i	0.193248	−	0.334716i
$857$	24.8776	+	9.05469i	0.849801	+	0.309302i	0.729959	−	0.683491i	$-0.239539\pi$
$857$	24.8776	+	9.05469i	0.849801	+	0.309302i	0.119842	+	0.992793i	$0.461761\pi$
$858$	−0.838398	−	42.9225i	−0.0286224	−	1.46535i
$859$	−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
$861$	−38.6339	+	13.7418i	−1.31664	+	0.468321i
$862$	−6.33100	+	10.9656i	−0.215635	+	0.373490i
$863$	−47.2007			−1.60673			−0.803365	−	0.595487i	$-0.796959\pi$
$863$	−47.2007			−1.60673			−0.803365	+	0.595487i	$0.796959\pi$
$864$	3.10120	−	4.16924i	0.105505	−	0.141840i
$865$	−2.26920	−	0.400122i	−0.0771552	−	0.0136045i
$866$			16.3371i			0.555159i
$867$	35.4224	−	43.9293i	1.20301	−	1.49192i
$868$	−0.666845	+	1.08654i	−0.0226342	+	0.0368795i
$869$	−3.77889	−	21.4311i	−0.128190	−	0.727001i
$870$	0.504208	−	0.440143i	0.0170942	−	0.0149222i
$871$	1.13304	+	6.42580i	0.0383917	+	0.217730i
$872$	6.84634	−	18.8102i	0.231846	−	0.636992i
$873$	8.26605	+	9.10404i	0.279763	+	0.308125i
$874$	31.1930	+	21.2772i	1.05512	+	0.719713i
$875$	4.78004	+	1.88665i	0.161595	+	0.0637805i
$876$	−4.50744	+	2.72110i	−0.152292	+	0.0919375i
$877$	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
$879$	−8.71170	+	5.25917i	−0.293838	+	0.177388i
$880$	−0.173162	+	0.982052i	−0.00583730	+	0.0331050i
$881$	36.7210	+	21.2009i	1.23716	+	0.714275i	0.968513	−	0.248964i	$-0.0800900\pi$
$881$	36.7210	+	21.2009i	1.23716	+	0.714275i	0.268648	+	0.963239i	$0.413423\pi$
$882$	20.9977	+	0.307749i	0.707031	+	0.0103624i
$883$	−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
$885$	−1.68283	−	1.35695i	−0.0565677	−	0.0456134i
$886$			2.99298i			0.100551i
$887$	7.84524	−	44.4926i	0.263417	−	1.49391i	−0.510087	−	0.860123i	$-0.670387\pi$
$887$	7.84524	−	44.4926i	0.263417	−	1.49391i	0.773504	−	0.633791i	$-0.218502\pi$
$888$	1.32175	−	0.0258175i	0.0443549	−	0.000866378i
$889$	−7.97097	+	12.9877i	−0.267338	+	0.435592i
$890$	−0.0628470	+	0.172671i	−0.00210664	+	0.00578794i
$891$	−41.5387	−	19.8343i	−1.39160	−	0.664473i
$892$	16.5026	−	9.52778i	0.552548	−	0.319014i
$893$	−0.962439	−	3.42364i	−0.0322068	−	0.114568i
$894$	1.99129	+	1.60568i	0.0665988	+	0.0537020i
$895$	2.67022	+	3.18224i	0.0892555	+	0.106371i
$896$	−0.837808	−	2.50960i	−0.0279892	−	0.0838398i
$897$	−23.5295	+	68.7986i	−0.785628	+	2.29712i
$898$	−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
$903$	22.8450	+	19.4563i	0.760235	+	0.647465i
$904$	−6.01300	−	10.4148i	−0.199989	−	0.346392i
$905$	1.00542	+	1.74145i	0.0334215	+	0.0578877i
$906$	13.3437	−	11.6483i	0.443315	−	0.386988i
$907$	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
$909$	6.38159	−	8.23838i	0.211664	−	0.273250i
$910$	1.65775	−	1.87119i	0.0549539	−	0.0620293i
$911$	13.5003			0.447286			0.223643	−	0.974671i	$-0.428205\pi$
$911$	13.5003			0.447286			0.223643	+	0.974671i	$0.428205\pi$
$912$	−4.52469	−	6.04377i	−0.149828	−	0.200129i
$913$	14.8032	+	25.6399i	0.489915	+	0.848557i
$914$	−22.9227	−	8.34316i	−0.758214	−	0.275967i
$915$	1.78175	+	2.95143i	0.0589030	+	0.0975714i
$916$	−0.779858	+	4.42279i	−0.0257672	+	0.146133i
$917$	−12.7915	−	11.3325i	−0.422413	−	0.374231i
$918$	−4.23258	+	36.3424i	−0.139696	+	1.19948i
$919$	−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
$921$	−4.26490	−	1.45862i	−0.140533	−	0.0480632i
$922$	9.01079	+	24.7569i	0.296754	+	0.815326i
$923$	50.5930	−	29.2099i	1.66529	−	0.961456i
$924$	−20.3831	+	11.5699i	−0.670555	+	0.380621i
$925$	1.29532	+	3.55887i	0.0425899	+	0.117015i
$926$	28.5959	+	10.4081i	0.939721	+	0.342030i
$927$	1.64249	+	42.0284i	0.0539466	+	1.38039i
$928$	−0.344152	−	1.95178i	−0.0112973	−	0.0640704i
$929$	26.9669	−	4.75499i	0.884754	−	0.156006i	0.287235	−	0.957860i	$-0.407264\pi$
$929$	26.9669	−	4.75499i	0.884754	−	0.156006i	0.597520	+	0.801854i	$0.296153\pi$
$930$	0.160771	+	0.0251214i	0.00527189	+	0.000823764i
$931$	9.11232	−	29.1198i	0.298644	−	0.954365i
$932$			10.2429i			0.335517i
$933$	46.4889	−	0.908059i	1.52198	−	0.0297285i
$934$	−24.2994	+	4.28463i	−0.795100	+	0.140198i
$935$	−2.40155	−	6.59820i	−0.0785391	−	0.215784i
$936$	8.90313	−	11.4936i	0.291008	−	0.375679i
$937$	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
$939$	5.07805	+	13.1471i	0.165716	+	0.429039i
$940$	−0.149482	+	0.0544069i	−0.00487555	+	0.00177456i
$941$	9.02065	−	51.1586i	0.294065	−	1.66772i	−0.376915	−	0.926248i	$-0.623015\pi$
$941$	9.02065	−	51.1586i	0.294065	−	1.66772i	0.670979	−	0.741476i	$-0.265874\pi$
$942$	16.0442	−	19.8973i	0.522748	−	0.648289i
$943$	−67.1274	+	38.7560i	−2.18597	+	1.26207i
$944$	−6.01532	+	2.18940i	−0.195782	+	0.0712589i
$945$	−0.996217	−	2.48843i	−0.0324069	−	0.0809487i
$946$	−32.9821	−	5.81563i	−1.07234	−	0.189083i
$947$	17.4768	+	20.8281i	0.567921	+	0.676821i	0.971203	−	0.238254i	$-0.0765752\pi$
$947$	17.4768	+	20.8281i	0.567921	+	0.676821i	−0.403282	+	0.915076i	$0.632131\pi$
$948$	3.55947	−	6.45303i	0.115606	−	0.209585i
$949$	−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	0.631416	−	0.775444i	$-0.282474\pi$
$953$	19.0368	+	6.92884i	0.616663	+	0.224447i	−0.0147530	+	0.999891i	$0.504696\pi$
$954$	4.03118	+	6.39199i	0.130514	+	0.206948i
$955$	2.43057	−	2.03949i	0.0786514	−	0.0659964i
$956$	−13.8905	+	16.5541i	−0.449252	+	0.535397i
$957$	−16.3777	+	6.32588i	−0.529417	+	0.204487i
$958$	16.3514	−	9.44051i	0.528291	−	0.305009i
$959$	11.3185	−	18.4420i	0.365494	−	0.595525i
$960$	−0.254407	+	0.222082i	−0.00821095	+	0.00716767i
$961$	30.7678			0.992510
$962$	3.69887			0.119256
$963$	−18.0962	−	28.6940i	−0.583142	−	0.924652i
$964$	−0.0708340	+	0.194615i	−0.00228141	+	0.00626812i
$965$	0.0428028	−	0.242747i	0.00137787	−	0.00781429i
$966$	39.1427	−	6.60655i	1.25940	−	0.212562i
$967$	−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
$969$	48.8698	+	20.9249i	1.56992	+	0.672205i
$970$	−0.399590	−	0.692111i	−0.0128301	−	0.0222223i
$971$	8.69707	+	49.3235i	0.279102	+	1.58287i	0.725622	+	0.688093i	$0.241552\pi$
$971$	8.69707	+	49.3235i	0.279102	+	1.58287i	−0.446520	+	0.894774i	$0.647337\pi$
$972$	−6.73433	−	14.0588i	−0.216004	−	0.450935i
$973$	−19.6194	−	12.0411i	−0.628970	−	0.386020i
$974$	−24.2217	+	4.27093i	−0.776112	+	0.136850i
$975$	39.4089	+	13.4781i	1.26209	+	0.431644i
$976$	10.2088			0.326776
$977$	−0.555129	+	0.961511i	−0.0177601	+	0.0307615i	−0.874769	−	0.484540i	$-0.838987\pi$
$977$	−0.555129	+	0.961511i	−0.0177601	+	0.0307615i	0.857009	+	0.515302i	$0.172320\pi$
$978$	−15.3551	+	3.01784i	−0.491002	+	0.0964999i
$979$	3.09838	−	3.69250i	0.0990246	−	0.118013i
$980$	−1.32941	−	0.308819i	−0.0424666	−	0.00986486i
$981$	−40.3677	−	44.4601i	−1.28884	−	1.41950i
$982$	−6.73940	−	1.18834i	−0.215063	−	0.0379214i
$983$	23.1865	−	19.4558i	0.739534	−	0.620542i	−0.193179	−	0.981164i	$-0.561880\pi$
$983$	23.1865	−	19.4558i	0.739534	−	0.620542i	0.932712	+	0.360621i	$0.117435\pi$
$984$	15.2075	−	2.98884i	0.484799	−	0.0952808i
$985$	−2.92099	+	2.45100i	−0.0930703	+	0.0780953i
$986$	8.97025	+	10.6903i	0.285671	+	0.340449i
$987$	−3.22415	−	1.89310i	−0.102626	−	0.0602579i
$988$	−12.3272	−	17.1541i	−0.392179	−	0.545744i
$989$	49.1236	+	28.3615i	1.56204	+	0.901843i
$990$	2.36505	+	1.83201i	0.0751661	+	0.0582250i
$991$	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
$993$	47.8236	−	0.934130i	1.51764	−	0.0296437i
$994$	−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.a.317.15	yes	162
3.2	odd	2		798.2.cc.b.317.12	yes	162
7.4	even	3		798.2.bu.a.431.21	✓	162
19.3	odd	18		798.2.bu.b.611.7	yes	162
21.11	odd	6		798.2.bu.b.431.7	yes	162
57.41	even	18		798.2.bu.a.611.21	yes	162
133.60	odd	18		798.2.cc.b.725.12	yes	162
399.326	even	18	inner	798.2.cc.a.725.15	yes	162

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.173648 + 0.984808i) q^{2} +(0.0338254 + 1.73172i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.0666847 - 0.183215i) q^{5} +(-1.69954 + 0.334022i) q^{6} +(1.64561 + 2.07170i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-2.99771 + 0.117152i) q^{9} +(0.192011 + 0.0338567i) q^{10} +(-4.42934 - 2.55728i) q^{11} +(-0.624069 - 1.61572i) q^{12} +(-1.65749 - 4.55391i) q^{13} +(-1.75447 + 1.98036i) q^{14} +(0.319532 + 0.109282i) q^{15} +(0.766044 - 0.642788i) q^{16} +(-2.40829 + 6.61672i) q^{17} +(-0.635920 - 2.93183i) q^{18} +(-4.34664 - 0.326711i) q^{19} +0.194973i q^{20} +(-3.53195 + 2.91982i) q^{21} +(1.74928 - 4.80612i) q^{22} +(-5.56812 + 6.63582i) q^{23} +(1.48280 - 0.895154i) q^{24} +(3.80110 + 3.18950i) q^{25} +(4.19691 - 2.42308i) q^{26} +(-0.304274 - 5.18724i) 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} +(4.27867 - 7.75688i) q^{33} +(-6.93439 - 1.22272i) q^{34} +(0.489304 - 0.163350i) q^{35} +(2.77686 - 1.13536i) q^{36} +(0.661000 + 0.381628i) q^{37} +(-0.433039 - 4.33734i) q^{38} +(7.83003 - 3.02434i) q^{39} +(-0.192011 + 0.0338567i) q^{40} +(8.40841 + 3.06041i) q^{41} +(-3.48878 - 2.97127i) 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} +(1.13904 + 1.30483i) q^{48} +(-1.58391 + 6.81845i) q^{49} +(-2.48099 + 4.29721i) q^{50} +(-11.5398 - 3.94667i) q^{51} +(3.11506 + 3.71238i) q^{52} +(-2.36708 + 0.861546i) q^{53} +(5.05559 - 1.20041i) q^{54} +(-0.763901 + 0.640989i) q^{55} +(0.971340 - 2.46100i) q^{56} +(0.418744 - 7.53821i) q^{57} +(0.990946 - 1.71637i) q^{58} +(-6.01532 - 2.18940i) q^{59} +(-0.337639 + 0.00659504i) q^{60} +(7.82041 + 6.56210i) q^{61} +(0.474528 - 0.0836721i) q^{62} +(-5.17578 - 6.01758i) q^{63} +(-0.500000 + 0.866025i) q^{64} -0.944872 q^{65} +(8.38202 + 2.86670i) q^{66} +(-1.32595 - 0.233802i) q^{67} -7.04136i q^{68} +(-11.6797 - 9.41796i) q^{69} +(0.245835 + 0.453505i) q^{70} +(2.09330 + 11.8717i) q^{71} +(1.60031 + 2.53752i) q^{72} +(-0.527858 - 2.99363i) q^{73} +(-0.261049 + 0.717227i) q^{74} +(-5.39475 + 6.69033i) q^{75} +(4.19625 - 1.17963i) q^{76} +(-1.99106 - 13.3846i) q^{77} +(4.33807 + 7.18590i) q^{78} +(2.73497 + 3.25941i) q^{79} +(-0.0666847 - 0.183215i) q^{80} +(8.97255 - 0.702378i) q^{81} +(-1.55381 + 8.81210i) q^{82} +(-5.01312 - 2.89433i) q^{83} +(2.32031 - 3.95173i) q^{84} +(1.05168 + 0.882468i) q^{85} +(6.15325 - 2.23960i) q^{86} +(2.15475 - 2.67222i) q^{87} +5.11456i q^{88} +(-0.163655 + 0.928132i) q^{89} +(-0.579560 - 0.0789981i) q^{90} +(6.70676 - 10.9278i) q^{91} +(2.96273 - 8.14004i) q^{92} +(0.834427 - 0.0162987i) q^{93} +(-0.706575 + 0.407941i) q^{94} +(-0.349712 + 0.774582i) q^{95} +(-1.08722 + 1.34832i) q^{96} +(-2.63474 - 3.13996i) q^{97} +(-6.98990 - 0.375831i) q^{98} +(13.5775 + 7.14708i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q - 81 q^{8} + 15 q^{13} + 9 q^{14} + 27 q^{15} + 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} - 9 q^{27} - 12 q^{28} + 6 q^{29} + 12 q^{33} + 6 q^{34} - 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots - 57 q^{99}+O(q^{100}) \) 162 * q - 81 * q^8 + 15 * q^13 + 9 * q^14 + 27 * 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 - 3 * q^60 - 9 * q^61 + 36 * q^62 + 12 * 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 - 6 * q^78 + 21 * q^79 + 12 * q^81 - 3 * q^84 - 6 * q^85 + 36 * q^86 + 24 * q^87 - 54 * q^89 + 36 * q^90 + 75 * q^91 + 42 * q^93 + 72 * q^94 - 12 * q^97 + 12 * q^98 - 57 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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