LMFDB - Embedded newform 290.2.l.b.109.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [290,2,Mod(9,290)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(290, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 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("290.9"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 290 = 2 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	290.l (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.31566165862$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			109.4
Character	$\chi$	$=$	290.109
Dual form			290.2.l.b.149.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.222521 + 0.974928i) q^{2} +(-0.668503 - 0.321934i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(-2.19009 - 0.451105i) q^{5} +(0.165107 - 0.723379i) q^{6} +(-0.462566 + 0.960527i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-1.52721 - 1.91507i) q^{9} +(-0.0475467 - 2.23556i) q^{10} +(-0.140368 - 0.111939i) q^{11} +0.741982 q^{12} +(-2.63819 - 2.10388i) q^{13} +(-1.03938 - 0.237231i) q^{14} +(1.31886 + 1.00663i) q^{15} +(0.623490 - 0.781831i) q^{16} -3.72757 q^{17} +(1.52721 - 1.91507i) q^{18} +(-2.07358 - 4.30583i) q^{19} +(2.16893 - 0.543814i) q^{20} +(0.618453 - 0.493200i) q^{21} +(0.0778981 - 0.161757i) q^{22} +(-1.38810 - 0.316825i) q^{23} +(0.165107 + 0.723379i) q^{24} +(4.59301 + 1.97592i) q^{25} +(1.46408 - 3.04020i) q^{26} +(0.899742 + 3.94203i) q^{27} -1.06610i q^{28} +(-1.60038 + 5.14187i) q^{29} +(-0.687918 + 1.50979i) q^{30} +(-2.99842 + 0.684369i) q^{31} +(0.900969 + 0.433884i) q^{32} +(0.0577990 + 0.120021i) q^{33} +(-0.829463 - 3.63411i) q^{34} +(1.44636 - 1.89498i) q^{35} +(2.20689 + 1.06278i) q^{36} +(1.71622 + 2.15207i) q^{37} +(3.73646 - 2.97973i) q^{38} +(1.08632 + 2.25577i) q^{39} +(1.01281 + 1.99354i) q^{40} +6.78729i q^{41} +(0.618453 + 0.493200i) q^{42} +(1.84263 - 8.07309i) q^{43} +(0.175035 + 0.0399507i) q^{44} +(2.48085 + 4.88311i) q^{45} -1.42380i q^{46} +(4.48540 - 5.62452i) q^{47} +(-0.668503 + 0.321934i) q^{48} +(3.65578 + 4.58421i) q^{49} +(-0.904341 + 4.91754i) q^{50} +(2.49189 + 1.20003i) q^{51} +(3.28976 + 0.750867i) q^{52} +(-8.65158 + 1.97467i) q^{53} +(-3.64298 + 1.75437i) q^{54} +(0.256921 + 0.308478i) q^{55} +(1.03938 - 0.237231i) q^{56} +3.54601i q^{57} +(-5.36907 - 0.416082i) q^{58} -3.63566 q^{59} +(-1.62501 - 0.334712i) q^{60} +(1.51345 - 3.14272i) q^{61} +(-1.33442 - 2.77095i) q^{62} +(2.54591 - 0.581088i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(4.82880 + 5.79779i) q^{65} +(-0.104150 + 0.0830570i) q^{66} +(-1.04886 + 0.836440i) q^{67} +(3.35843 - 1.61733i) q^{68} +(0.825952 + 0.658675i) q^{69} +(2.16931 + 0.988424i) q^{70} +(-8.01648 + 10.0524i) q^{71} +(-0.545057 + 2.38805i) q^{72} +(0.918317 - 4.02341i) q^{73} +(-1.71622 + 2.15207i) q^{74} +(-2.43432 - 2.79955i) q^{75} +(3.73646 + 2.97973i) q^{76} +(0.172450 - 0.0830475i) q^{77} +(-1.95749 + 1.56104i) q^{78} +(5.76877 - 4.60044i) q^{79} +(-1.71819 + 1.43102i) q^{80} +(-0.967578 + 4.23924i) q^{81} +(-6.61712 + 1.51031i) q^{82} +(-6.91661 - 14.3625i) q^{83} +(-0.343215 + 0.712694i) q^{84} +(8.16373 + 1.68153i) q^{85} +8.28071 q^{86} +(2.72520 - 2.92213i) q^{87} +0.179537i q^{88} +(-3.89123 + 0.888147i) q^{89} +(-4.20864 + 3.50524i) q^{90} +(3.24117 - 1.56087i) q^{91} +(1.38810 - 0.316825i) q^{92} +(2.22477 + 0.507789i) q^{93} +(6.48159 + 3.12137i) q^{94} +(2.59895 + 10.3656i) q^{95} +(-0.462618 - 0.580105i) q^{96} +(-0.639804 + 0.308114i) q^{97} +(-3.65578 + 4.58421i) q^{98} +0.439769i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 8 q^{2} - 4 q^{3} - 8 q^{4} + 8 q^{5} - 3 q^{6} + 7 q^{7} + 8 q^{8} - 8 q^{9} - q^{10} + 10 q^{12} - 10 q^{15} - 8 q^{16} - 30 q^{17} + 8 q^{18} - 13 q^{20} + 7 q^{21} + 7 q^{23} - 3 q^{24} - 12 q^{25}+ \cdots - 27 q^{98}+O(q^{100}) $ 48 * q + 8 * q^2 - 4 * q^3 - 8 * q^4 + 8 * q^5 - 3 * q^6 + 7 * q^7 + 8 * q^8 - 8 * q^9 - q^10 + 10 * q^12 - 10 * q^15 - 8 * q^16 - 30 * q^17 + 8 * q^18 - 13 * q^20 + 7 * q^21 + 7 * q^23 - 3 * q^24 - 12 * q^25 + 21 * q^26 + 11 * q^27 - 10 * q^29 - 18 * q^30 + 14 * q^31 + 8 * q^32 - 14 * q^33 - 33 * q^34 - q^36 - 44 * q^37 - 28 * q^38 - 14 * q^39 - 8 * q^40 + 7 * q^42 - 8 * q^43 + 14 * q^44 + 25 * q^45 - 6 * q^47 - 4 * q^48 + 27 * q^49 + 5 * q^50 + 24 * q^51 + 77 * q^53 + 10 * q^54 - 32 * q^55 + 10 * q^58 - 24 * q^59 + 4 * q^60 + 56 * q^61 - 8 * q^64 - 34 * q^65 + 42 * q^67 - 2 * q^68 + 28 * q^69 - 30 * q^71 + 22 * q^72 - 29 * q^73 + 44 * q^74 - 32 * q^75 - 28 * q^76 - 30 * q^77 + 14 * q^78 + q^80 - 130 * q^81 - 42 * q^82 - 42 * q^84 + 28 * q^85 - 62 * q^86 + 32 * q^87 + 31 * q^90 - 106 * q^91 - 7 * q^92 - 70 * q^93 + 27 * q^94 + 165 * q^95 + 4 * q^96 - 49 * q^97 - 27 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/290\mathbb{Z}\right)^\times$.

$n$	$31$	$117$
$\chi(n)$	$e\left(\frac{13}{14}\right)$	$-1$

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 $

$2$	0.222521	+	0.974928i	0.157346	+	0.689378i
$2$	0.222521	+	0.974928i	0.157346	+	0.689378i
$3$	−0.668503	−	0.321934i	−0.385960	−	0.185869i	0.230834	−	0.972993i	$-0.425855\pi$
$3$	−0.668503	−	0.321934i	−0.385960	−	0.185869i	−0.616794	+	0.787125i	$0.711569\pi$
$4$	−0.900969	+	0.433884i	−0.450484	+	0.216942i
$5$	−2.19009	−	0.451105i	−0.979439	−	0.201740i
$5$	−2.19009	−	0.451105i	−0.979439	−	0.201740i
$6$	0.165107	−	0.723379i	0.0674045	−	0.295318i
$7$	−0.462566	+	0.960527i	−0.174833	+	0.363045i	−0.969910	−	0.243464i	$-0.921716\pi$
$7$	−0.462566	+	0.960527i	−0.174833	+	0.363045i	0.795077	+	0.606509i	$0.207431\pi$
$8$	−0.623490	−	0.781831i	−0.220437	−	0.276419i
$9$	−1.52721	−	1.91507i	−0.509072	−	0.638356i
$10$	−0.0475467	−	2.23556i	−0.0150356	−	0.706947i
$11$	−0.140368	−	0.111939i	−0.0423224	−	0.0337510i	0.602100	−	0.798421i	$-0.294331\pi$
$11$	−0.140368	−	0.111939i	−0.0423224	−	0.0337510i	−0.644423	+	0.764670i	$0.722902\pi$
$12$	0.741982			0.214192
$13$	−2.63819	−	2.10388i	−0.731701	−	0.583512i	0.185165	−	0.982707i	$-0.440718\pi$
$13$	−2.63819	−	2.10388i	−0.731701	−	0.583512i	−0.916866	+	0.399195i	$0.869289\pi$
$14$	−1.03938	−	0.237231i	−0.277785	−	0.0634026i
$15$	1.31886	+	1.00663i	0.340527	+	0.259911i
$16$	0.623490	−	0.781831i	0.155872	−	0.195458i
$17$	−3.72757			−0.904069			−0.452035	−	0.892000i	$-0.649302\pi$
$17$	−3.72757			−0.904069			−0.452035	+	0.892000i	$0.649302\pi$
$18$	1.52721	−	1.91507i	0.359968	−	0.451386i
$19$	−2.07358	−	4.30583i	−0.475711	−	0.987825i	−0.991378	−	0.131035i	$-0.958170\pi$
$19$	−2.07358	−	4.30583i	−0.475711	−	0.987825i	0.515666	−	0.856789i	$-0.327544\pi$
$20$	2.16893	−	0.543814i	0.484988	−	0.121601i
$21$	0.618453	−	0.493200i	0.134957	−	0.107625i
$22$	0.0778981	−	0.161757i	0.0166079	−	0.0344867i
$23$	−1.38810	−	0.316825i	−0.289439	−	0.0660626i	0.0753362	−	0.997158i	$-0.475997\pi$
$23$	−1.38810	−	0.316825i	−0.289439	−	0.0660626i	−0.364775	+	0.931096i	$0.618854\pi$
$24$	0.165107	+	0.723379i	0.0337022	+	0.147659i
$25$	4.59301	+	1.97592i	0.918602	+	0.395184i
$26$	1.46408	−	3.04020i	0.287130	−	0.596232i
$27$	0.899742	+	3.94203i	0.173155	+	0.758643i
$28$		−	1.06610i		−	0.201475i
$29$	−1.60038	+	5.14187i	−0.297183	+	0.954821i
$29$	−1.60038	+	5.14187i	−0.297183	+	0.954821i
$30$	−0.687918	+	1.50979i	−0.125596	+	0.275648i
$31$	−2.99842	+	0.684369i	−0.538531	+	0.122916i	−0.483131	−	0.875548i	$-0.660501\pi$
$31$	−2.99842	+	0.684369i	−0.538531	+	0.122916i	−0.0554001	+	0.998464i	$0.517643\pi$
$32$	0.900969	+	0.433884i	0.159270	+	0.0767005i
$33$	0.0577990	+	0.120021i	0.0100615	+	0.0208929i
$34$	−0.829463	−	3.63411i	−0.142252	−	0.623246i
$35$	1.44636	−	1.89498i	0.244479	−	0.320310i
$36$	2.20689	+	1.06278i	0.367815	+	0.177130i
$37$	1.71622	+	2.15207i	0.282144	+	0.353798i	0.902628	−	0.430422i	$-0.141635\pi$
$37$	1.71622	+	2.15207i	0.282144	+	0.353798i	−0.620484	+	0.784219i	$0.713064\pi$
$38$	3.73646	−	2.97973i	0.606133	−	0.483375i
$39$	1.08632	+	2.25577i	0.173951	+	0.361213i
$40$	1.01281	+	1.99354i	0.160140	+	0.315207i
$41$			6.78729i			1.06000i	0.847999	+	0.529998i	$0.177807\pi$
$41$			6.78729i			1.06000i	−0.847999	+	0.529998i	$0.822193\pi$
$42$	0.618453	+	0.493200i	0.0954293	+	0.0761023i
$43$	1.84263	−	8.07309i	0.280999	−	1.23113i	−0.615517	−	0.788123i	$-0.711053\pi$
$43$	1.84263	−	8.07309i	0.280999	−	1.23113i	0.896516	−	0.443012i	$-0.146090\pi$
$44$	0.175035	+	0.0399507i	0.0263876	+	0.00602279i
$45$	2.48085	+	4.88311i	0.369823	+	0.727931i
$46$		−	1.42380i		−	0.209928i
$47$	4.48540	−	5.62452i	0.654263	−	0.820420i	−0.338442	−	0.940987i	$-0.609900\pi$
$47$	4.48540	−	5.62452i	0.654263	−	0.820420i	0.992705	+	0.120567i	$0.0384714\pi$
$48$	−0.668503	+	0.321934i	−0.0964901	+	0.0464672i
$49$	3.65578	+	4.58421i	0.522255	+	0.654887i
$50$	−0.904341	+	4.91754i	−0.127893	+	0.695445i
$51$	2.49189	+	1.20003i	0.348935	+	0.168038i
$52$	3.28976	+	0.750867i	0.456208	+	0.104127i
$53$	−8.65158	+	1.97467i	−1.18839	+	0.271241i	−0.770609	−	0.637308i	$-0.780048\pi$
$53$	−8.65158	+	1.97467i	−1.18839	+	0.271241i	−0.417777	+	0.908550i	$0.637191\pi$
$54$	−3.64298	+	1.75437i	−0.495747	+	0.238739i
$55$	0.256921	+	0.308478i	0.0346433	+	0.0415952i
$56$	1.03938	−	0.237231i	0.138892	−	0.0317013i
$57$			3.54601i			0.469681i
$58$	−5.36907	−	0.416082i	−0.704993	−	0.0546342i
$59$	−3.63566			−0.473322			−0.236661	−	0.971592i	$-0.576053\pi$
$59$	−3.63566			−0.473322			−0.236661	+	0.971592i	$0.576053\pi$
$60$	−1.62501	−	0.334712i	−0.209788	−	0.0432111i
$61$	1.51345	−	3.14272i	0.193778	−	0.402384i	−0.781329	−	0.624119i	$-0.785458\pi$
$61$	1.51345	−	3.14272i	0.193778	−	0.402384i	0.975107	+	0.221736i	$0.0711722\pi$
$62$	−1.33442	−	2.77095i	−0.169472	−	0.351911i
$63$	2.54591	−	0.581088i	0.320755	−	0.0732102i
$64$	−0.222521	+	0.974928i	−0.0278151	+	0.121866i
$65$	4.82880	+	5.79779i	0.598939	+	0.719128i
$66$	−0.104150	+	0.0830570i	−0.0128200	+	0.0102236i
$67$	−1.04886	+	0.836440i	−0.128139	+	0.102187i	−0.685462	−	0.728108i	$-0.740400\pi$
$67$	−1.04886	+	0.836440i	−0.128139	+	0.102187i	0.557323	+	0.830296i	$0.311828\pi$
$68$	3.35843	−	1.61733i	0.407269	−	0.196130i
$69$	0.825952	+	0.658675i	0.0994330	+	0.0792952i
$70$	2.16931	+	0.988424i	0.259282	+	0.118139i
$71$	−8.01648	+	10.0524i	−0.951382	+	1.19299i	0.0297312	+	0.999558i	$0.490535\pi$
$71$	−8.01648	+	10.0524i	−0.951382	+	1.19299i	−0.981113	+	0.193437i	$0.938037\pi$
$72$	−0.545057	+	2.38805i	−0.0642355	+	0.281434i
$73$	0.918317	−	4.02341i	0.107481	−	0.470905i	−0.892329	−	0.451386i	$-0.850930\pi$
$73$	0.918317	−	4.02341i	0.107481	−	0.470905i	0.999810	−	0.0195182i	$-0.00621322\pi$
$74$	−1.71622	+	2.15207i	−0.199506	+	0.250173i
$75$	−2.43432	−	2.79955i	−0.281091	−	0.323265i
$76$	3.73646	+	2.97973i	0.428601	+	0.341798i
$77$	0.172450	−	0.0830475i	0.0196525	−	0.00946415i
$78$	−1.95749	+	1.56104i	−0.221642	+	0.176753i
$79$	5.76877	−	4.60044i	0.649037	−	0.517590i	−0.242725	−	0.970095i	$-0.578041\pi$
$79$	5.76877	−	4.60044i	0.649037	−	0.517590i	0.891762	+	0.452505i	$0.149470\pi$
$80$	−1.71819	+	1.43102i	−0.192099	+	0.159993i
$81$	−0.967578	+	4.23924i	−0.107509	+	0.471026i
$82$	−6.61712	+	1.51031i	−0.730738	+	0.166786i
$83$	−6.91661	−	14.3625i	−0.759196	−	1.57649i	−0.815966	−	0.578100i	$-0.803794\pi$
$83$	−6.91661	−	14.3625i	−0.759196	−	1.57649i	0.0567700	−	0.998387i	$-0.481920\pi$
$84$	−0.343215	+	0.712694i	−0.0374479	+	0.0777613i
$85$	8.16373	+	1.68153i	0.885481	+	0.182387i
$86$	8.28071			0.892932
$87$	2.72520	−	2.92213i	0.292172	−	0.313286i
$88$			0.179537i			0.0191387i
$89$	−3.89123	+	0.888147i	−0.412469	+	0.0941434i	−0.423720	−	0.905793i	$-0.639276\pi$
$89$	−3.89123	+	0.888147i	−0.412469	+	0.0941434i	0.0112506	+	0.999937i	$0.496419\pi$
$90$	−4.20864	+	3.50524i	−0.443629	+	0.369485i
$91$	3.24117	−	1.56087i	0.339767	−	0.163623i
$92$	1.38810	−	0.316825i	0.144720	−	0.0330313i
$93$	2.22477	+	0.507789i	0.230698	+	0.0526553i
$94$	6.48159	+	3.12137i	0.668525	+	0.321945i
$95$	2.59895	+	10.3656i	0.266646	+	1.06348i
$96$	−0.462618	−	0.580105i	−0.0472158	−	0.0592067i
$97$	−0.639804	+	0.308114i	−0.0649623	+	0.0312842i	−0.466083	−	0.884741i	$-0.654335\pi$
$97$	−0.639804	+	0.308114i	−0.0649623	+	0.0312842i	0.401121	+	0.916025i	$0.368621\pi$
$98$	−3.65578	+	4.58421i	−0.369290	+	0.463075i
$99$			0.439769i			0.0441984i
$100$	−4.99548	+	0.212587i	−0.499548	+	0.0212587i
$101$	−13.8933	−	3.17105i	−1.38243	−	0.315531i	−0.534291	−	0.845300i	$-0.679421\pi$
$101$	−13.8933	−	3.17105i	−1.38243	−	0.315531i	−0.848142	+	0.529769i	$0.822279\pi$
$102$	−0.615447	+	2.69645i	−0.0609383	+	0.266988i
$103$	4.73171	+	3.77341i	0.466229	+	0.371805i	0.828244	−	0.560367i	$-0.189340\pi$
$103$	4.73171	+	3.77341i	0.466229	+	0.371805i	−0.362016	+	0.932172i	$0.617911\pi$
$104$			3.37437i			0.330884i
$105$	−1.57695	+	0.801166i	−0.153895	+	0.0781858i
$106$	−3.85032	−	7.99526i	−0.373976	−	0.776569i
$107$	13.4358	−	10.7147i	1.29889	−	1.03583i	0.302307	−	0.953211i	$-0.402243\pi$
$107$	13.4358	−	10.7147i	1.29889	−	1.03583i	0.996581	−	0.0826185i	$-0.0263283\pi$
$108$	−2.52102	−	3.16126i	−0.242585	−	0.304192i
$109$	5.79246	+	2.78950i	0.554817	+	0.267186i	0.690213	−	0.723606i	$-0.257517\pi$
$109$	5.79246	+	2.78950i	0.554817	+	0.267186i	−0.135397	+	0.990791i	$0.543231\pi$
$110$	−0.243573	+	0.319123i	−0.0232238	+	0.0304272i
$111$	−0.454472	−	1.99117i	−0.0431366	−	0.188994i
$112$	0.462566	+	0.960527i	0.0437083	+	0.0907613i
$113$	−4.31249	−	2.07678i	−0.405685	−	0.195367i	0.219902	−	0.975522i	$-0.429426\pi$
$113$	−4.31249	−	2.07678i	−0.405685	−	0.195367i	−0.625587	+	0.780154i	$0.715140\pi$
$114$	−3.45711	+	0.789062i	−0.323788	+	0.0739024i
$115$	2.89715	+	1.32005i	0.270160	+	0.123096i
$116$	−0.789080	−	5.32704i	−0.0732642	−	0.494603i
$117$			8.26538i			0.764135i
$118$	−0.809010	−	3.54450i	−0.0744754	−	0.326298i
$119$	1.72425	−	3.58044i	0.158061	−	0.328218i
$120$	−0.0352788	−	1.65875i	−0.00322050	−	0.151422i
$121$	−2.44056	−	10.6928i	−0.221869	−	0.972071i
$122$	3.40070	+	0.776187i	0.307885	+	0.0702727i
$123$	2.18506	−	4.53732i	0.197020	−	0.409116i
$124$	2.40454	−	1.91756i	0.215934	−	0.172202i
$125$	−9.16777	−	6.39938i	−0.819990	−	0.572378i
$126$	1.13304	+	2.35278i	0.100939	+	0.209602i
$127$	−3.68804	+	4.62466i	−0.327261	+	0.410372i	−0.918057	−	0.396449i	$-0.870242\pi$
$127$	−3.68804	+	4.62466i	−0.327261	+	0.410372i	0.590796	+	0.806821i	$0.298814\pi$
$128$	−1.00000			−0.0883883
$129$	−3.83081	+	4.80368i	−0.337284	+	0.422940i
$130$	−4.57792	+	5.99786i	−0.401510	+	0.526047i
$131$	−9.27512	−	2.11698i	−0.810371	−	0.184962i	−0.202793	−	0.979222i	$-0.565002\pi$
$131$	−9.27512	−	2.11698i	−0.810371	−	0.184962i	−0.607578	+	0.794260i	$0.707859\pi$
$132$	−0.104150	−	0.0830570i	−0.00906511	−	0.00722918i
$133$	5.09503			0.441795
$134$	−1.04886	−	0.836440i	−0.0906079	−	0.0722574i
$135$	−0.192251	−	9.03928i	−0.0165463	−	0.777977i
$136$	2.32410	+	2.91433i	0.199290	+	0.249902i
$137$	1.60793	+	2.01629i	0.137375	+	0.172263i	0.845760	−	0.533563i	$-0.179147\pi$
$137$	1.60793	+	2.01629i	0.137375	+	0.172263i	−0.708385	+	0.705826i	$0.750576\pi$
$138$	−0.458369	+	0.951813i	−0.0390190	+	0.0810237i
$139$	4.39606	−	19.2604i	0.372869	−	1.63365i	−0.345810	−	0.938305i	$-0.612396\pi$
$139$	4.39606	−	19.2604i	0.372869	−	1.63365i	0.718679	−	0.695342i	$-0.244747\pi$
$140$	−0.480925	+	2.33487i	−0.0406456	+	0.197332i
$141$	−4.80923	+	2.31600i	−0.405010	+	0.195042i
$142$	−11.5842	−	5.57863i	−0.972121	−	0.468149i
$143$	0.134808	+	0.590634i	0.0112732	+	0.0493913i
$144$	−2.44946			−0.204122
$145$	5.82450	−	10.5392i	0.483698	−	0.875235i
$146$	4.12688			0.341543
$147$	−0.968089	−	4.24148i	−0.0798466	−	0.349831i
$148$	−2.48001	−	1.19431i	−0.203855	−	0.0981715i
$149$	15.5867	−	7.50616i	1.27691	−	0.614929i	0.332318	−	0.943168i	$-0.392169\pi$
$149$	15.5867	−	7.50616i	1.27691	−	0.614929i	0.944595	+	0.328239i	$0.106455\pi$
$150$	2.18768	−	2.99625i	0.178623	−	0.244643i
$151$	2.93988	−	12.8805i	0.239244	−	1.04820i	−0.702452	−	0.711732i	$-0.747911\pi$
$151$	2.93988	−	12.8805i	0.239244	−	1.04820i	0.941696	−	0.336466i	$-0.109232\pi$
$152$	−2.07358	+	4.30583i	−0.168189	+	0.349249i
$153$	5.69280	+	7.13855i	0.460236	+	0.577118i
$154$	0.119339	+	0.149646i	0.00961662	+	0.0120589i
$155$	6.87553	−	0.146231i	0.552256	−	0.0117456i
$156$	−1.95749	−	1.56104i	−0.156724	−	0.124983i
$157$	−8.82423			−0.704250			−0.352125	−	0.935953i	$-0.614541\pi$
$157$	−8.82423			−0.704250			−0.352125	+	0.935953i	$0.614541\pi$
$158$	5.76877	+	4.60044i	0.458939	+	0.365991i
$159$	6.41932	+	1.46517i	0.509085	+	0.116195i
$160$	−1.77748	−	1.35668i	−0.140522	−	0.107255i
$161$	0.946407	−	1.18676i	0.0745873	−	0.0935295i
$162$	−4.34826			−0.341631
$163$	7.11997	−	8.92816i	0.557679	−	0.699307i	−0.420448	−	0.907317i	$-0.638127\pi$
$163$	7.11997	−	8.92816i	0.557679	−	0.699307i	0.978127	+	0.208009i	$0.0666984\pi$
$164$	−2.94489	−	6.11514i	−0.229958	−	0.477512i
$165$	−0.0724432	−	0.288930i	−0.00563969	−	0.0224932i
$166$	12.4633	−	9.93914i	0.967339	−	0.771427i
$167$	−3.07062	+	6.37620i	−0.237612	+	0.493406i	−0.985341	−	0.170598i	$-0.945430\pi$
$167$	−3.07062	+	6.37620i	−0.237612	+	0.493406i	0.747729	+	0.664004i	$0.231144\pi$
$168$	−0.771198	−	0.176021i	−0.0594992	−	0.0135803i
$169$	−0.359073	−	1.57320i	−0.0276210	−	0.121015i
$170$	0.177234	+	8.33322i	0.0135932	+	0.639129i
$171$	−5.07915	+	10.5470i	−0.388412	+	0.806547i
$172$	1.84263	+	8.07309i	0.140499	+	0.615567i
$173$			7.97593i			0.606399i	0.952927	+	0.303199i	$0.0980548\pi$
$173$			7.97593i			0.606399i	−0.952927	+	0.303199i	$0.901945\pi$
$174$	3.45528	+	2.00664i	0.261944	+	0.152123i
$175$	−4.02249	+	3.49772i	−0.304072	+	0.264403i
$176$	−0.175035	+	0.0399507i	−0.0131938	+	0.00301140i
$177$	2.43045	+	1.17044i	0.182684	+	0.0879758i
$178$	−1.73176	−	3.59603i	−0.129801	−	0.269534i
$179$	−3.28120	−	14.3759i	−0.245248	−	1.07450i	−0.936163	−	0.351566i	$-0.885649\pi$
$179$	−3.28120	−	14.3759i	−0.245248	−	1.07450i	0.690915	−	0.722936i	$-0.257208\pi$
$180$	−4.35387	−	3.32313i	−0.324518	−	0.247691i
$181$	1.72898	+	0.832631i	0.128514	+	0.0618889i	0.497036	−	0.867730i	$-0.334422\pi$
$181$	1.72898	+	0.832631i	0.128514	+	0.0618889i	−0.368522	+	0.929619i	$0.620136\pi$
$182$	2.24296	+	2.81258i	0.166259	+	0.208482i
$183$	−2.02349	+	1.61368i	−0.149581	+	0.119287i
$184$	0.617763	+	1.28280i	0.0455421	+	0.0945691i
$185$	−2.78787	−	5.48742i	−0.204968	−	0.403443i
$186$			2.28198i			0.167323i
$187$	0.523230	+	0.417262i	0.0382624	+	0.0305132i
$188$	−1.60082	+	7.01366i	−0.116752	+	0.511523i
$189$	−4.20261	−	0.959219i	−0.305695	−	0.0697729i
$190$	−9.52735	+	4.84034i	−0.691187	+	0.351155i
$191$			10.4906i			0.759076i	0.925176	+	0.379538i	$0.123917\pi$
$191$			10.4906i			0.759076i	−0.925176	+	0.379538i	$0.876083\pi$
$192$	0.462618	−	0.580105i	0.0333866	−	0.0418655i
$193$	−16.5481	+	7.96916i	−1.19116	+	0.573633i	−0.921144	−	0.389223i	$-0.872744\pi$
$193$	−16.5481	+	7.96916i	−1.19116	+	0.573633i	−0.270017	+	0.962856i	$0.587029\pi$
$194$	−0.442758	−	0.555201i	−0.0317882	−	0.0398611i
$195$	−1.36156	−	5.43040i	−0.0975032	−	0.388879i
$196$	−5.28276	−	2.54404i	−0.377340	−	0.181717i
$197$	−12.7842	−	2.91792i	−0.910839	−	0.207893i	−0.258669	−	0.965966i	$-0.583284\pi$
$197$	−12.7842	−	2.91792i	−0.910839	−	0.207893i	−0.652170	+	0.758073i	$0.726141\pi$
$198$	−0.428743	+	0.0978577i	−0.0304694	+	0.00695445i
$199$	1.15957	−	0.558418i	0.0821996	−	0.0395852i	−0.392332	−	0.919824i	$-0.628332\pi$
$199$	1.15957	−	0.558418i	0.0821996	−	0.0395852i	0.474532	+	0.880238i	$0.342617\pi$
$200$	−1.31886	−	4.82293i	−0.0932572	−	0.341032i
$201$	0.970446	−	0.221498i	0.0684500	−	0.0156233i
$202$		−	14.2506i		−	1.00267i
$203$	−4.19862	−	3.91566i	−0.294685	−	0.274825i
$204$	−2.76579			−0.193644
$205$	3.06178	−	14.8648i	0.213844	−	1.03820i
$206$	−2.62590	+	5.45274i	−0.182955	+	0.379910i
$207$	1.51319	+	3.14217i	0.105174	+	0.218396i
$208$	−3.28976	+	0.750867i	−0.228104	+	0.0520633i
$209$	−0.190929	+	0.836513i	−0.0132068	+	0.0578628i
$210$	−1.13198	−	1.35914i	−0.0781143	−	0.0937895i
$211$	−21.8656	+	17.4373i	−1.50529	+	1.20043i	−0.583881	+	0.811839i	$0.698467\pi$
$211$	−21.8656	+	17.4373i	−1.50529	+	1.20043i	−0.921410	+	0.388591i	$0.872962\pi$
$212$	6.93803	−	5.53289i	0.476506	−	0.380001i
$213$	8.59523	−	4.13925i	0.588936	−	0.283617i
$214$	13.4358	+	10.7147i	0.918453	+	0.732442i
$215$	−7.67734	+	16.8496i	−0.523590	+	1.14913i
$216$	2.52102	−	3.16126i	0.171534	−	0.215097i
$217$	0.729609	−	3.19662i	0.0495291	−	0.217001i
$218$	−1.43062	+	6.26795i	−0.0968937	+	0.424519i
$219$	−1.90917	+	2.39402i	−0.129010	+	0.161773i
$220$	−0.365322	−	0.166455i	−0.0246300	−	0.0112224i
$221$	9.83403	+	7.84238i	0.661508	+	0.527535i
$222$	1.84012	−	0.886155i	0.123501	−	0.0594748i
$223$	0.551501	−	0.439807i	0.0369312	−	0.0294517i	−0.604850	−	0.796339i	$-0.706767\pi$
$223$	0.551501	−	0.439807i	0.0369312	−	0.0294517i	0.641781	+	0.766888i	$0.278196\pi$
$224$	−0.833514	+	0.664705i	−0.0556915	+	0.0444125i
$225$	−3.23049	−	11.8136i	−0.215366	−	0.787572i
$226$	1.06510	−	4.66649i	0.0708491	−	0.310410i
$227$	9.43403	−	2.15326i	0.626158	−	0.142917i	0.102344	−	0.994749i	$-0.467366\pi$
$227$	9.43403	−	2.15326i	0.626158	−	0.142917i	0.523814	+	0.851832i	$0.324509\pi$
$228$	−1.53856	−	3.19485i	−0.101893	−	0.211584i
$229$	−0.122903	+	0.255210i	−0.00812165	+	0.0168648i	−0.904990	−	0.425432i	$-0.860122\pi$
$229$	−0.122903	+	0.255210i	−0.00812165	+	0.0168648i	0.896869	+	0.442297i	$0.145836\pi$
$230$	−0.642282	+	3.11825i	−0.0423508	+	0.205611i
$231$	−0.142019			−0.00934417
$232$	5.01789	−	1.95467i	0.329441	−	0.128331i
$233$			23.4407i			1.53565i	0.640660	+	0.767825i	$0.278661\pi$
$233$			23.4407i			1.53565i	−0.640660	+	0.767825i	$0.721339\pi$
$234$	−8.05815	+	1.83922i	−0.526778	+	0.120234i
$235$	−12.3607	+	10.2948i	−0.806322	+	0.671560i
$236$	3.27561	−	1.57745i	0.213224	−	0.102683i
$237$	−5.33747	+	1.21824i	−0.346706	+	0.0791334i
$238$	3.87435	+	0.884294i	0.251137	+	0.0573203i
$239$	19.6133	+	9.44529i	1.26868	+	0.610965i	0.942457	−	0.334327i	$-0.108509\pi$
$239$	19.6133	+	9.44529i	1.26868	+	0.610965i	0.326225	+	0.945292i	$0.394223\pi$
$240$	1.60931	−	0.403500i	0.103880	−	0.0260458i
$241$	−3.45263	−	4.32946i	−0.222403	−	0.278885i	0.658094	−	0.752935i	$-0.271363\pi$
$241$	−3.45263	−	4.32946i	−0.222403	−	0.278885i	−0.880498	+	0.474051i	$0.842791\pi$
$242$	9.88162	−	4.75874i	0.635214	−	0.305903i
$243$	9.57464	−	12.0062i	0.614214	−	0.770200i
$244$			3.48815i			0.223306i
$245$	−5.93854	−	11.6890i	−0.379400	−	0.746781i
$246$	4.90978	+	1.12063i	0.313036	+	0.0714485i
$247$	−3.58847	+	15.7221i	−0.228329	+	1.00038i
$248$	2.40454	+	1.91756i	0.152689	+	0.121765i
$249$			11.8280i			0.749572i
$250$	4.19892	−	10.3619i	0.265563	−	0.655345i
$251$	1.87167	+	3.88657i	0.118139	+	0.245318i	0.951650	−	0.307185i	$-0.0993870\pi$
$251$	1.87167	+	3.88657i	0.118139	+	0.245318i	−0.833511	+	0.552503i	$0.813673\pi$
$252$	−2.04166	+	1.62817i	−0.128613	+	0.102565i
$253$	0.159379	+	0.199855i	0.0100201	+	0.0125648i
$254$	−5.32938	−	2.56649i	−0.334395	−	0.161036i
$255$	−4.91613	−	3.75229i	−0.307860	−	0.234977i
$256$	−0.222521	−	0.974928i	−0.0139076	−	0.0609330i
$257$	−7.33971	−	15.2411i	−0.457838	−	0.950711i	−0.994283	−	0.106776i	$-0.965947\pi$
$257$	−7.33971	−	15.2411i	−0.457838	−	0.950711i	0.536445	−	0.843935i	$-0.319767\pi$
$258$	−5.53567	−	2.66584i	−0.344636	−	0.165968i
$259$	−2.86098	+	0.653001i	−0.177773	+	0.0405755i
$260$	−6.86617	−	3.12850i	−0.425821	−	0.194021i
$261$	12.2911	−	4.78790i	0.760803	−	0.296364i
$262$		−	9.51364i		−	0.587755i
$263$	6.65343	+	29.1506i	0.410268	+	1.79750i	0.582933	+	0.812520i	$0.301905\pi$
$263$	6.65343	+	29.1506i	0.410268	+	1.79750i	−0.172665	+	0.984981i	$0.555238\pi$
$264$	0.0577990	−	0.120021i	0.00355728	−	0.00738677i
$265$	19.8385	−	0.421933i	1.21867	−	0.0259191i
$266$	1.13375	+	4.96729i	0.0695147	+	0.304564i
$267$	2.88722	+	0.658989i	0.176695	+	0.0403295i
$268$	0.582075	−	1.20869i	0.0355559	−	0.0738325i
$269$	−23.7720	+	18.9576i	−1.44941	+	1.15586i	−0.490749	+	0.871301i	$0.663277\pi$
$269$	−23.7720	+	18.9576i	−1.44941	+	1.15586i	−0.958657	+	0.284563i	$0.908152\pi$
$270$	8.76987	−	2.19886i	0.533717	−	0.133818i
$271$	−5.10279	−	10.5960i	−0.309972	−	0.643664i	0.686542	−	0.727090i	$-0.259128\pi$
$271$	−5.10279	−	10.5960i	−0.309972	−	0.643664i	−0.996514	+	0.0834266i	$0.973414\pi$
$272$	−2.32410	+	2.91433i	−0.140919	+	0.176707i
$273$	−2.66923			−0.161549
$274$	−1.60793	+	2.01629i	−0.0971389	+	0.121808i
$275$	−0.423526	−	0.791494i	−0.0255396	−	0.0477289i
$276$	−1.02995	−	0.235078i	−0.0619955	−	0.0141501i
$277$	19.4861	+	15.5396i	1.17081	+	0.933686i	0.998679	−	0.0513888i	$-0.0163648\pi$
$277$	19.4861	+	15.5396i	1.17081	+	0.933686i	0.172127	+	0.985075i	$0.444936\pi$
$278$	19.7557			1.18487
$279$	5.88984	+	4.69699i	0.352615	+	0.281201i
$280$	−2.38334	+	0.0506898i	−0.142432	+	0.00302929i
$281$	20.0545	+	25.1475i	1.19635	+	1.50018i	0.818695	+	0.574229i	$0.194698\pi$
$281$	20.0545	+	25.1475i	1.19635	+	1.50018i	0.377655	+	0.925946i	$0.376730\pi$
$282$	−3.32809	−	4.17329i	−0.198185	−	0.248516i
$283$	−2.97387	+	6.17531i	−0.176778	+	0.367084i	−0.970465	−	0.241243i	$-0.922445\pi$
$283$	−2.97387	+	6.17531i	−0.176778	+	0.367084i	0.793686	+	0.608327i	$0.208159\pi$
$284$	2.86105	−	12.5351i	0.169772	−	0.743820i
$285$	1.59962	−	7.76610i	0.0947535	−	0.460024i
$286$	−0.545828	+	0.262857i	−0.0322755	+	0.0155430i
$287$	−6.51938	−	3.13957i	−0.384827	−	0.185323i
$288$	−0.545057	−	2.38805i	−0.0321178	−	0.140717i
$289$	−3.10520			−0.182659
$290$	11.5711	+	3.33327i	0.679476	+	0.195736i
$291$	0.526903			0.0308876
$292$	0.918317	+	4.02341i	0.0537404	+	0.235452i
$293$	−0.768130	−	0.369912i	−0.0448746	−	0.0216105i	0.411312	−	0.911495i	$-0.365071\pi$
$293$	−0.768130	−	0.369912i	−0.0448746	−	0.0216105i	−0.456186	+	0.889884i	$0.650785\pi$
$294$	3.91971	−	1.88763i	0.228602	−	0.110089i
$295$	7.96242	+	1.64006i	0.463590	+	0.0954881i
$296$	0.612511	−	2.68359i	0.0356015	−	0.155980i
$297$	0.314973	−	0.654049i	0.0182766	−	0.0379518i
$298$	10.7863	+	13.5256i	0.624835	+	0.783519i
$299$	2.99550	+	3.75624i	0.173234	+	0.217229i
$300$	3.40793	+	1.46610i	0.196757	+	0.0846453i
$301$	6.90209	+	5.50423i	0.397830	+	0.317259i
$302$	13.2117			0.760248
$303$	8.26683	+	6.59258i	0.474917	+	0.378734i
$304$	−4.65929	−	1.06345i	−0.267228	−	0.0609931i
$305$	−4.73229	+	6.20011i	−0.270970	+	0.355017i
$306$	−5.69280	+	7.13855i	−0.325436	+	0.408084i
$307$	−18.1807			−1.03763			−0.518814	−	0.854887i	$-0.673626\pi$
$307$	−18.1807			−1.03763			−0.518814	+	0.854887i	$0.673626\pi$
$308$	−0.119339	+	0.149646i	−0.00679998	+	0.00852690i
$309$	−1.94837	−	4.04583i	−0.110839	−	0.230159i
$310$	1.67251	+	6.67061i	0.0949924	+	0.378865i
$311$	15.7347	−	12.5480i	0.892232	−	0.711531i	−0.0659095	−	0.997826i	$-0.520995\pi$
$311$	15.7347	−	12.5480i	0.892232	−	0.711531i	0.958142	+	0.286294i	$0.0924234\pi$
$312$	1.08632	−	2.25577i	0.0615009	−	0.127708i
$313$	14.1391	+	3.22716i	0.799189	+	0.182410i	0.602566	−	0.798069i	$-0.294145\pi$
$313$	14.1391	+	3.22716i	0.799189	+	0.182410i	0.196623	+	0.980479i	$0.437002\pi$
$314$	−1.96358	−	8.60299i	−0.110811	−	0.485495i
$315$	−5.83791	+	0.124163i	−0.328929	+	0.00699578i
$316$	−3.20142	+	6.64783i	−0.180094	+	0.373970i
$317$	−5.63999	−	24.7104i	−0.316773	−	1.38787i	−0.843176	−	0.537638i	$-0.819317\pi$
$317$	−5.63999	−	24.7104i	−0.316773	−	1.38787i	0.526402	−	0.850236i	$-0.323541\pi$
$318$			6.58440i			0.369235i
$319$	0.800219	−	0.542606i	0.0448036	−	0.0303801i
$320$	0.927136	−	2.03480i	0.0518285	−	0.113749i
$321$	−12.4313	+	2.83736i	−0.693847	+	0.158366i
$322$	1.36760	+	0.658600i	0.0762132	+	0.0367023i
$323$	7.72941	+	16.0503i	0.430076	+	0.893062i
$324$	−0.967578	−	4.23924i	−0.0537543	−	0.235513i
$325$	−7.96010	−	14.8760i	−0.441547	−	0.825172i
$326$	10.2887	+	4.95475i	0.569836	+	0.274418i
$327$	−2.97424	−	3.72958i	−0.164476	−	0.206246i
$328$	5.30652	−	4.23181i	0.293003	−	0.233662i
$329$	3.32771	+	6.91006i	0.183462	+	0.380964i
$330$	0.265566	−	0.134920i	0.0146189	−	0.00742709i
$331$			11.5740i			0.636165i	0.948063	+	0.318083i	$0.103039\pi$
$331$			11.5740i			0.636165i	−0.948063	+	0.318083i	$0.896961\pi$
$332$	12.4633	+	9.93914i	0.684012	+	0.545481i
$333$	1.50032	−	6.57334i	0.0822172	−	0.360217i
$334$	−6.89962	−	1.57479i	−0.377530	−	0.0861688i
$335$	2.67443	−	1.35873i	0.146120	−	0.0742356i
$336$		−	0.791031i		−	0.0431543i
$337$	11.1013	−	13.9205i	0.604724	−	0.758300i	−0.381382	−	0.924418i	$-0.624552\pi$
$337$	11.1013	−	13.9205i	0.604724	−	0.758300i	0.986106	+	0.166117i	$0.0531230\pi$
$338$	1.45386	−	0.700140i	0.0790793	−	0.0380826i
$339$	2.21432	+	2.77667i	0.120265	+	0.150808i
$340$	−8.08485	+	2.02711i	−0.438463	+	0.109935i
$341$	0.497488	+	0.239578i	0.0269405	+	0.0129739i
$342$	−11.4127	−	2.60489i	−0.617131	−	0.140856i
$343$	−13.3699	+	3.05160i	−0.721908	+	0.164771i
$344$	−7.46066	+	3.59286i	−0.402252	+	0.193714i
$345$	−1.51178	−	1.81515i	−0.0813915	−	0.0977244i
$346$	−7.77596	+	1.77481i	−0.418038	+	0.0954144i
$347$		−	22.6660i		−	1.21678i	−0.793639	−	0.608388i	$-0.791816\pi$
$347$		−	22.6660i		−	1.21678i	0.793639	−	0.608388i	$-0.208184\pi$
$348$	−1.18745	+	3.81517i	−0.0636542	+	0.204515i
$349$	−18.8496			−1.00900			−0.504498	−	0.863413i	$-0.668322\pi$
$349$	−18.8496			−1.00900			−0.504498	+	0.863413i	$0.668322\pi$
$350$	−4.30511	−	3.14333i	−0.230118	−	0.168018i
$351$	5.91988	−	12.2927i	0.315980	−	0.656138i
$352$	−0.0778981	−	0.161757i	−0.00415198	−	0.00862168i
$353$	−5.31543	+	1.21321i	−0.282912	+	0.0645727i	−0.361622	−	0.932325i	$-0.617777\pi$
$353$	−5.31543	+	1.21321i	−0.282912	+	0.0645727i	0.0787104	+	0.996898i	$0.474920\pi$
$354$	−0.600271	+	2.62996i	−0.0319040	+	0.139781i
$355$	22.0915	−	18.3993i	1.17250	−	0.976534i
$356$	3.12052	−	2.48853i	0.165387	−	0.131892i
$357$	−2.30533	+	1.83844i	−0.122011	+	0.0973004i
$358$	13.2853	−	6.39786i	0.702150	−	0.338137i
$359$	−16.0140	−	12.7708i	−0.845189	−	0.674016i	0.101968	−	0.994788i	$-0.467486\pi$
$359$	−16.0140	−	12.7708i	−0.845189	−	0.674016i	−0.947156	+	0.320772i	$0.896058\pi$
$360$	2.27099	−	4.98417i	0.119691	−	0.262689i
$361$	−2.39412	+	3.00214i	−0.126007	+	0.158007i
$362$	−0.427022	+	1.87090i	−0.0224438	+	0.0983325i
$363$	−1.81085	+	7.93385i	−0.0950450	+	0.416419i
$364$	−2.24296	+	2.81258i	−0.117563	+	0.147419i
$365$	−3.82618	+	8.39738i	−0.200271	+	0.439539i
$366$	−2.02349	−	1.61368i	−0.105770	−	0.0843485i
$367$	−17.3902	+	8.37469i	−0.907762	+	0.437155i	−0.828686	−	0.559713i	$-0.810911\pi$
$367$	−17.3902	+	8.37469i	−0.907762	+	0.437155i	−0.0790761	+	0.996869i	$0.525197\pi$
$368$	−1.11317	+	0.887724i	−0.0580280	+	0.0462758i
$369$	12.9981	−	10.3656i	0.676655	−	0.539614i
$370$	4.72948	−	3.93903i	0.245874	−	0.204781i
$371$	2.10520	−	9.22349i	0.109297	−	0.478860i
$372$	−2.22477	+	0.507789i	−0.115349	+	0.0263276i
$373$	11.0683	+	22.9835i	0.573093	+	1.19004i	0.963079	+	0.269220i	$0.0867658\pi$
$373$	11.0683	+	22.9835i	0.573093	+	1.19004i	−0.389985	+	0.920821i	$0.627520\pi$
$374$	−0.290371	+	0.602961i	−0.0150147	+	0.0311784i
$375$	4.06850	+	7.22942i	0.210096	+	0.373326i
$376$	−7.19403			−0.371004
$377$	15.0400	−	10.1982i	0.774598	−	0.525233i
$378$		−	4.31069i		−	0.221718i
$379$	−25.6920	+	5.86403i	−1.31971	+	0.301215i	−0.823662	−	0.567081i	$-0.808073\pi$
$379$	−25.6920	+	5.86403i	−1.31971	+	0.301215i	−0.496047	+	0.868296i	$0.665215\pi$
$380$	−6.83902	−	8.21141i	−0.350834	−	0.421236i
$381$	3.95430	−	1.90429i	0.202585	−	0.0975598i
$382$	−10.2276	+	2.33439i	−0.523290	+	0.119438i
$383$	−23.4858	−	5.36048i	−1.20007	−	0.273908i	−0.424651	−	0.905357i	$-0.639603\pi$
$383$	−23.4858	−	5.36048i	−1.20007	−	0.273908i	−0.775417	+	0.631450i	$0.782460\pi$
$384$	0.668503	+	0.321934i	0.0341144	+	0.0164286i
$385$	−0.415145	+	0.104089i	−0.0211577	+	0.00530485i
$386$	−11.4517	−	14.3599i	−0.582874	−	0.730901i
$387$	−18.2746	+	8.80059i	−0.928950	+	0.447359i
$388$	0.442758	−	0.555201i	0.0224777	−	0.0281861i
$389$			12.9062i			0.654370i	0.944960	+	0.327185i	$0.106100\pi$
$389$			12.9062i			0.654370i	−0.944960	+	0.327185i	$0.893900\pi$
$390$	4.99127	−	2.53580i	0.252743	−	0.128405i
$391$	5.17425	+	1.18099i	0.261673	+	0.0597251i
$392$	1.30473	−	5.71641i	0.0658990	−	0.288722i
$393$	5.51891	+	4.40118i	0.278392	+	0.222010i
$394$		−	13.1130i		−	0.660624i
$395$	−14.7094	+	7.47307i	−0.740111	+	0.376011i
$396$	−0.190808	−	0.396218i	−0.00958849	−	0.0199107i
$397$	11.0244	−	8.79164i	0.553297	−	0.441240i	−0.306504	−	0.951869i	$-0.599159\pi$
$397$	11.0244	−	8.79164i	0.553297	−	0.441240i	0.859801	+	0.510630i	$0.170588\pi$
$398$	0.802446	+	1.00623i	0.0402230	+	0.0504380i
$399$	−3.40604	−	1.64026i	−0.170515	−	0.0821159i
$400$	4.40853	−	2.35899i	0.220427	−	0.117950i
$401$	−6.12914	−	26.8535i	−0.306074	−	1.34100i	−0.860790	−	0.508960i	$-0.830030\pi$
$401$	−6.12914	−	26.8535i	−0.306074	−	1.34100i	0.554716	−	0.832040i	$-0.312827\pi$
$402$	0.431889	+	0.896827i	0.0215407	+	0.0447297i
$403$	9.35021	+	4.50282i	0.465767	+	0.224302i
$404$	13.8933	−	3.17105i	0.691217	−	0.157766i
$405$	4.03142	−	8.84784i	0.200323	−	0.439653i
$406$	2.88320	−	4.96467i	0.143091	−	0.246392i
$407$		−	0.494193i		−	0.0244962i
$408$	−0.615447	−	2.69645i	−0.0304691	−	0.133494i
$409$	−12.7735	+	26.5243i	−0.631606	+	1.31154i	0.302022	+	0.953301i	$0.402338\pi$
$409$	−12.7735	+	26.5243i	−0.631606	+	1.31154i	−0.933628	+	0.358243i	$0.883376\pi$
$410$	15.1734	−	0.322713i	0.749361	−	0.0159377i
$411$	−0.425798	−	1.86554i	−0.0210030	−	0.0920204i
$412$	−5.90034	−	1.34671i	−0.290689	−	0.0663479i
$413$	1.68173	−	3.49215i	0.0827525	−	0.171837i
$414$	−2.72667	+	2.17445i	−0.134008	+	0.106868i
$415$	8.66902	+	34.5753i	0.425546	+	1.69723i
$416$	−1.46408	−	3.04020i	−0.0717825	−	0.149058i
$417$	−9.13936	+	11.4604i	−0.447556	+	0.561218i
$418$	−0.858026			−0.0419674
$419$	23.4488	−	29.4039i	1.14555	−	1.43648i	0.263915	−	0.964546i	$-0.414986\pi$
$419$	23.4488	−	29.4039i	1.14555	−	1.43648i	0.881636	−	0.471929i	$-0.156442\pi$
$420$	1.07317	−	1.40604i	0.0523655	−	0.0686077i
$421$	−22.9160	−	5.23042i	−1.11686	−	0.254915i	−0.376027	−	0.926609i	$-0.622710\pi$
$421$	−22.9160	−	5.23042i	−1.11686	−	0.254915i	−0.740829	+	0.671693i	$0.765567\pi$
$422$	−21.8656	−	17.4373i	−1.06440	−	0.848832i
$423$	−17.6215			−0.856786
$424$	6.93803	+	5.53289i	0.336940	+	0.268701i
$425$	−17.1208	−	7.36539i	−0.830480	−	0.357274i
$426$	5.94809	+	7.45867i	0.288186	+	0.361374i
$427$	2.31859	+	2.90742i	0.112205	+	0.140700i
$428$	−7.45631	+	15.4832i	−0.360414	+	0.748408i
$429$	0.100025	−	0.438240i	0.00482927	−	0.0211584i
$430$	−18.1355	−	3.73547i	−0.874572	−	0.180140i
$431$	−1.59367	+	0.767472i	−0.0767645	+	0.0369678i	−0.471872	−	0.881667i	$-0.656422\pi$
$431$	−1.59367	+	0.767472i	−0.0767645	+	0.0369678i	0.395108	+	0.918635i	$0.370707\pi$
$432$	3.64298	+	1.75437i	0.175273	+	0.0844070i
$433$	−6.21169	−	27.2152i	−0.298515	−	1.30788i	−0.872340	−	0.488900i	$-0.837398\pi$
$433$	−6.21169	−	27.2152i	−0.298515	−	1.30788i	0.573825	−	0.818978i	$-0.305459\pi$
$434$	3.27883			0.157389
$435$	−7.28663	+	5.17039i	−0.349367	+	0.247901i
$436$	−6.42914			−0.307900
$437$	1.51414	+	6.63388i	0.0724312	+	0.317342i
$438$	−2.75883	−	1.32858i	−0.131822	−	0.0634821i
$439$	20.5550	−	9.89876i	0.981036	−	0.472442i	0.126575	−	0.991957i	$-0.459602\pi$
$439$	20.5550	−	9.89876i	0.981036	−	0.472442i	0.854461	+	0.519515i	$0.173887\pi$
$440$	0.0809899	−	0.393202i	0.00386104	−	0.0187452i
$441$	3.19590	−	14.0021i	0.152186	−	0.666768i
$442$	−5.45747	+	11.3326i	−0.259586	+	0.539035i
$443$	1.44914	+	1.81716i	0.0688506	+	0.0863359i	0.815064	−	0.579371i	$-0.196702\pi$
$443$	1.44914	+	1.81716i	0.0688506	+	0.0863359i	−0.746214	+	0.665707i	$0.768130\pi$
$444$	1.27340	+	1.59680i	0.0604330	+	0.0757806i
$445$	8.92279	−	0.189773i	0.422981	−	0.00899611i
$446$	0.551501	+	0.439807i	0.0261143	+	0.0208255i
$447$	−12.8362			−0.607133
$448$	−0.833514	−	0.664705i	−0.0393798	−	0.0314044i
$449$	−28.0564	−	6.40370i	−1.32406	−	0.302209i	−0.498683	−	0.866784i	$-0.666183\pi$
$449$	−28.0564	−	6.40370i	−1.32406	−	0.302209i	−0.825382	+	0.564575i	$0.809040\pi$
$450$	10.7985	−	5.77826i	0.509048	−	0.272390i
$451$	0.759765	−	0.952715i	0.0357759	−	0.0448616i
$452$	4.78650			0.225138
$453$	−6.11198	+	7.66418i	−0.287166	+	0.360094i
$454$	4.19854	+	8.71835i	0.197047	+	0.409173i
$455$	−7.80258	+	1.95633i	−0.365790	+	0.0917142i
$456$	2.77238	−	2.21090i	0.129829	−	0.103535i
$457$	0.620555	−	1.28860i	0.0290283	−	0.0602780i	−0.885950	−	0.463780i	$-0.846493\pi$
$457$	0.620555	−	1.28860i	0.0290283	−	0.0602780i	0.914979	+	0.403502i	$0.132207\pi$
$458$	−0.276160	−	0.0630317i	−0.0129041	−	0.00294528i
$459$	−3.35385	−	14.6942i	−0.156544	−	0.685866i
$460$	−3.18299	+	0.0676970i	−0.148408	+	0.00315639i
$461$	6.94892	−	14.4296i	0.323644	−	0.672053i	−0.674139	−	0.738604i	$-0.735485\pi$
$461$	6.94892	−	14.4296i	0.323644	−	0.672053i	0.997783	+	0.0665512i	$0.0211996\pi$
$462$	−0.0316022	−	0.138458i	−0.00147027	−	0.00644167i
$463$			25.3141i			1.17645i	0.808698	+	0.588224i	$0.200173\pi$
$463$			25.3141i			1.17645i	−0.808698	+	0.588224i	$0.799827\pi$
$464$	3.02225	+	4.45713i	0.140305	+	0.206917i
$465$	−4.64339	−	2.11571i	−0.215332	−	0.0981137i
$466$	−22.8530	+	5.21604i	−1.05864	+	0.241628i
$467$	15.0411	+	7.24344i	0.696021	+	0.335186i	0.748220	−	0.663451i	$-0.230909\pi$
$467$	15.0411	+	7.24344i	0.696021	+	0.335186i	−0.0521988	+	0.998637i	$0.516623\pi$
$468$	−3.58621	−	7.44685i	−0.165773	−	0.344231i
$469$	−0.318256	−	1.39437i	−0.0146957	−	0.0643860i
$470$	−12.7872	−	9.75997i	−0.589831	−	0.450194i
$471$	5.89902	+	2.84082i	0.271813	+	0.130898i
$472$	2.26680	+	2.84247i	0.104338	+	0.130835i
$473$	−1.16234	+	0.926937i	−0.0534446	+	0.0426206i
$474$	−2.37540	−	4.93257i	−0.109106	−	0.226560i
$475$	−1.01598	−	23.8739i	−0.0466163	−	1.09541i
$476$			3.97398i			0.182147i
$477$	16.9944	+	13.5526i	0.778122	+	0.620532i
$478$	−4.84410	+	21.2234i	−0.221564	+	0.970734i
$479$	13.7323	+	3.13431i	0.627445	+	0.143210i	0.524408	−	0.851467i	$-0.324287\pi$
$479$	13.7323	+	3.13431i	0.627445	+	0.143210i	0.103037	+	0.994677i	$0.467144\pi$
$480$	0.751489	+	1.47917i	0.0343006	+	0.0675147i
$481$		−	9.28827i		−	0.423509i
$482$	3.45263	−	4.32946i	0.157263	−	0.197201i
$483$	−1.01473	+	0.488669i	−0.0461719	+	0.0222352i
$484$	6.83829	+	8.57495i	0.310831	+	0.389770i
$485$	1.54022	−	0.386178i	0.0699379	−	0.0175355i
$486$	13.8358	+	6.66295i	0.627603	+	0.302238i
$487$	−4.74245	−	1.08243i	−0.214901	−	0.0490497i	0.113715	−	0.993513i	$-0.463725\pi$
$487$	−4.74245	−	1.08243i	−0.214901	−	0.0490497i	−0.328616	+	0.944464i	$0.606582\pi$
$488$	−3.40070	+	0.776187i	−0.153942	+	0.0351363i
$489$	−7.63400	+	3.67634i	−0.345221	+	0.166250i
$490$	10.0745	−	8.39069i	0.455118	−	0.379053i
$491$	−4.80042	+	1.09566i	−0.216640	+	0.0494467i	−0.329463	−	0.944168i	$-0.606868\pi$
$491$	−4.80042	+	1.09566i	−0.216640	+	0.0494467i	0.112823	+	0.993615i	$0.464011\pi$
$492$			5.03605i			0.227043i
$493$	5.96553	−	19.1667i	0.268674	−	0.863224i
$494$	−16.1265			−0.725564
$495$	0.198382	−	0.963134i	0.00891660	−	0.0432897i
$496$	−1.33442	+	2.77095i	−0.0599172	+	0.124419i
$497$	−5.94741	−	12.3499i	−0.266778	−	0.553970i
$498$	−11.5315	+	2.63199i	−0.516739	+	0.117942i
$499$	6.11428	−	26.7884i	0.273713	−	1.19921i	−0.631880	−	0.775066i	$-0.717717\pi$
$499$	6.11428	−	26.7884i	0.273713	−	1.19921i	0.905593	−	0.424148i	$-0.139426\pi$
$500$	11.0365	+	1.78790i	0.493565	+	0.0799572i
$501$	4.10543	−	3.27397i	0.183417	−	0.146270i
$502$	−3.37264	+	2.68959i	−0.150528	+	0.120042i
$503$	8.82865	−	4.25165i	0.393650	−	0.189572i	−0.226579	−	0.973993i	$-0.572754\pi$
$503$	8.82865	−	4.25165i	0.393650	−	0.189572i	0.620229	+	0.784421i	$0.287040\pi$
$504$	−2.04166	−	1.62817i	−0.0909429	−	0.0725245i
$505$	28.9971	+	13.2122i	1.29035	+	0.587936i
$506$	−0.159379	+	0.199855i	−0.00708526	+	0.00888464i
$507$	−0.266425	+	1.16729i	−0.0118324	+	0.0518410i
$508$	1.31625	−	5.76686i	0.0583990	−	0.255863i
$509$	−4.20478	+	5.27263i	−0.186374	+	0.233705i	−0.866237	−	0.499634i	$-0.833468\pi$
$509$	−4.20478	+	5.27263i	−0.186374	+	0.233705i	0.679863	+	0.733339i	$0.262039\pi$
$510$	2.56427	−	5.62784i	0.113548	−	0.249205i
$511$	3.43981	+	2.74316i	0.152168	+	0.121350i
$512$	0.900969	−	0.433884i	0.0398176	−	0.0191751i
$513$	15.1080	−	12.0482i	0.667035	−	0.531942i
$514$	13.2257	−	10.5471i	0.583360	−	0.465214i
$515$	−8.66067	−	10.3986i	−0.381635	−	0.458218i
$516$	1.36720	−	5.99009i	0.0601876	−	0.263699i
$517$	−1.25921	+	0.287406i	−0.0553800	+	0.0126401i
$518$	−1.27326	−	2.64395i	−0.0559437	−	0.116168i
$519$	2.56772	−	5.33193i	0.112710	−	0.234046i
$520$	1.52219	−	7.39017i	0.0667526	−	0.324080i
$521$	−11.5016			−0.503893			−0.251947	−	0.967741i	$-0.581071\pi$
$521$	−11.5016			−0.503893			−0.251947	+	0.967741i	$0.581071\pi$
$522$	7.40289	+	10.9176i	0.324016	+	0.477849i
$523$		−	3.26484i		−	0.142762i	−0.997449	−	0.0713808i	$-0.977259\pi$
$523$		−	3.26484i		−	0.142762i	0.997449	−	0.0713808i	$-0.0227406\pi$
$524$	9.27512	−	2.11698i	0.405185	−	0.0924809i
$525$	3.81508	−	1.04326i	0.166504	−	0.0455314i
$526$	−26.9392	+	12.9732i	−1.17460	+	0.565659i
$527$	11.1768	−	2.55103i	0.486870	−	0.111125i
$528$	0.129873	+	0.0296427i	0.00565200	+	0.00129003i
$529$	−18.8958	−	9.09976i	−0.821558	−	0.395642i
$530$	4.82585	+	19.2473i	0.209621	+	0.836048i
$531$	5.55243	+	6.96253i	0.240955	+	0.302148i
$532$	−4.59046	+	2.21065i	−0.199022	+	0.0958439i
$533$	14.2797	−	17.9061i	0.618521	−	0.775600i
$534$			2.96147i			0.128155i
$535$	−34.2591	+	17.4052i	−1.48115	+	0.752493i
$536$	1.30791	+	0.298522i	0.0564931	+	0.0128942i
$537$	−2.43459	+	10.6666i	−0.105060	+	0.460299i
$538$	−23.7720	−	18.9576i	−1.02489	−	0.817319i
$539$		−	1.05270i		−	0.0453430i
$540$	4.09521	+	8.06070i	0.176230	+	0.346877i
$541$	−4.22029	−	8.76351i	−0.181444	−	0.376773i	0.790331	−	0.612680i	$-0.209908\pi$
$541$	−4.22029	−	8.76351i	−0.181444	−	0.376773i	−0.971776	+	0.235907i	$0.924194\pi$
$542$	9.19490	−	7.33269i	0.394955	−	0.314966i
$543$	−0.887773	−	1.11323i	−0.0380980	−	0.0477733i
$544$	−3.35843	−	1.61733i	−0.143991	−	0.0693426i
$545$	−11.4277	−	8.72227i	−0.489507	−	0.373621i
$546$	−0.593959	−	2.60230i	−0.0254191	−	0.111368i
$547$	0.965806	+	2.00552i	0.0412949	+	0.0857497i	0.920596	−	0.390517i	$-0.127704\pi$
$547$	0.965806	+	2.00552i	0.0412949	+	0.0857497i	−0.879301	+	0.476267i	$0.841990\pi$
$548$	−2.32353	−	1.11895i	−0.0992564	−	0.0477994i
$549$	−8.32988	+	1.90124i	−0.355511	+	0.0811430i
$550$	0.677406	−	0.589031i	0.0288847	−	0.0251164i
$551$	25.4585	−	3.77110i	1.08457	−	0.160654i
$552$		−	1.05643i		−	0.0449648i
$553$	1.75041	+	7.66906i	0.0744352	+	0.326122i
$554$	−10.8140	+	22.4554i	−0.459441	+	0.954039i
$555$	0.0971084	+	4.56586i	0.00412202	+	0.193810i
$556$	4.39606	+	19.2604i	0.186435	+	0.816823i
$557$	34.7133	+	7.92310i	1.47085	+	0.335712i	0.881508	−	0.472170i	$-0.156529\pi$
$557$	34.7133	+	7.92310i	1.47085	+	0.335712i	0.589344	+	0.807882i	$0.299386\pi$
$558$	−3.26861	+	6.78734i	−0.138371	+	0.287331i
$559$	−21.8460	+	17.4216i	−0.923989	+	0.736857i
$560$	−0.579763	−	2.31231i	−0.0244994	−	0.0977129i
$561$	−0.215450	−	0.447386i	−0.00909630	−	0.0188887i
$562$	−20.0545	+	25.1475i	−0.845947	+	1.06078i
$563$	11.9682			0.504399			0.252199	−	0.967675i	$-0.418846\pi$
$563$	11.9682			0.504399			0.252199	+	0.967675i	$0.418846\pi$
$564$	3.32809	−	4.17329i	0.140138	−	0.175727i
$565$	8.50790	+	6.49373i	0.357930	+	0.273193i
$566$	−6.68223	−	1.52517i	−0.280875	−	0.0641079i
$567$	−3.62433	−	2.89031i	−0.152208	−	0.121382i
$568$	12.8574			0.539486
$569$	26.9416	+	21.4852i	1.12945	+	0.900707i	0.995911	−	0.0903360i	$-0.0287941\pi$
$569$	26.9416	+	21.4852i	1.12945	+	0.900707i	0.133540	+	0.991043i	$0.457366\pi$
$570$	7.92733	−	0.168601i	0.332039	−	0.00706193i
$571$	22.8116	+	28.6048i	0.954635	+	1.19707i	0.980322	+	0.197404i	$0.0632511\pi$
$571$	22.8116	+	28.6048i	0.954635	+	1.19707i	−0.0256876	+	0.999670i	$0.508178\pi$
$572$	−0.377724	−	0.473651i	−0.0157934	−	0.0198044i
$573$	3.37729	−	7.01302i	0.141088	−	0.292973i
$574$	1.61015	−	7.05454i	0.0672065	−	0.294451i
$575$	−5.74954	−	4.19796i	−0.239772	−	0.175067i
$576$	2.20689	−	1.06278i	0.0919537	−	0.0442826i
$577$	18.3827	+	8.85264i	0.765282	+	0.368540i	0.775451	−	0.631408i	$-0.217523\pi$
$577$	18.3827	+	8.85264i	0.765282	+	0.368540i	−0.0101691	+	0.999948i	$0.503237\pi$
$578$	−0.690972	−	3.02735i	−0.0287407	−	0.125921i
$579$	13.6280			0.566361
$580$	−0.674895	+	12.0227i	−0.0280235	+	0.499214i
$581$	16.9949			0.705069
$582$	0.117247	+	0.513693i	0.00486004	+	0.0212932i
$583$	1.43544	+	0.691273i	0.0594500	+	0.0286296i
$584$	−3.71819	+	1.79059i	−0.153860	+	0.0740950i
$585$	3.72855	−	18.1020i	0.154157	−	0.748424i
$586$	0.189713	−	0.831185i	0.00783695	−	0.0343359i
$587$	20.0550	−	41.6446i	0.827758	−	1.71886i	0.143458	−	0.989656i	$-0.454178\pi$
$587$	20.0550	−	41.6446i	0.827758	−	1.71886i	0.684300	−	0.729201i	$-0.260108\pi$
$588$	2.71253	+	3.40140i	0.111863	+	0.140271i
$589$	9.16422	+	11.4916i	0.377605	+	0.473502i
$590$	0.172864	+	8.12774i	0.00711668	+	0.334614i
$591$	7.60692	+	6.06631i	0.312907	+	0.249535i
$592$	2.75260			0.113131
$593$	−30.8789	−	24.6251i	−1.26804	−	1.01123i	−0.998840	−	0.0481479i	$-0.984668\pi$
$593$	−30.8789	−	24.6251i	−1.26804	−	1.01123i	−0.269204	−	0.963083i	$-0.586760\pi$
$594$	0.707739	+	0.161537i	0.0290389	+	0.00662794i
$595$	−5.39141	+	7.06367i	−0.221026	+	0.289582i
$596$	−10.7863	+	13.5256i	−0.441825	+	0.554031i
$597$	−0.954948			−0.0390834
$598$	−2.99550	+	3.75624i	−0.122495	+	0.153604i
$599$	−1.23566	−	2.56587i	−0.0504875	−	0.104838i	0.874199	−	0.485568i	$-0.161387\pi$
$599$	−1.23566	−	2.56587i	−0.0504875	−	0.104838i	−0.924686	+	0.380730i	$0.875673\pi$
$600$	−0.671005	+	3.64872i	−0.0273937	+	0.148959i
$601$	31.4481	−	25.0790i	1.28279	−	1.02299i	0.284871	−	0.958566i	$-0.408049\pi$
$601$	31.4481	−	25.0790i	1.28279	−	1.02299i	0.997922	−	0.0644281i	$-0.0205223\pi$
$602$	−3.83037	+	7.95384i	−0.156114	+	0.324174i
$603$	3.20368	+	0.731218i	0.130464	+	0.0297775i
$604$	2.93988	+	12.8805i	0.119622	+	0.524099i
$605$	0.521481	+	24.5191i	0.0212012	+	0.996844i
$606$	−4.58774	+	9.52655i	−0.186364	+	0.386990i
$607$	8.27129	+	36.2389i	0.335721	+	1.47089i	0.807864	+	0.589369i	$0.200623\pi$
$607$	8.27129	+	36.2389i	0.335721	+	1.47089i	−0.472143	+	0.881522i	$0.656519\pi$
$608$		−	4.77911i		−	0.193818i
$609$	1.54621	+	3.96931i	0.0626555	+	0.160844i
$610$	−7.09770	−	3.23399i	−0.287377	−	0.130940i
$611$	−23.6666	+	5.40176i	−0.957450	+	0.218532i
$612$	−8.22634	−	3.96160i	−0.332530	−	0.160138i
$613$	1.12054	+	2.32683i	0.0452583	+	0.0939799i	0.922372	−	0.386303i	$-0.126248\pi$
$613$	1.12054	+	2.32683i	0.0452583	+	0.0939799i	−0.877113	+	0.480283i	$0.840534\pi$
$614$	−4.04559	−	17.7249i	−0.163267	−	0.715317i
$615$	−6.83229	+	8.95146i	−0.275504	+	0.360958i
$616$	−0.172450	−	0.0830475i	−0.00694821	−	0.00334608i
$617$	−13.8123	−	17.3201i	−0.556063	−	0.697281i	0.421761	−	0.906707i	$-0.361412\pi$
$617$	−13.8123	−	17.3201i	−0.556063	−	0.697281i	−0.977825	+	0.209426i	$0.932841\pi$
$618$	3.51084	−	2.79980i	0.141227	−	0.112625i
$619$	11.8210	+	24.5466i	0.475126	+	0.986610i	0.991483	+	0.130236i	$0.0415736\pi$
$619$	11.8210	+	24.5466i	0.475126	+	0.986610i	−0.516357	+	0.856374i	$0.672712\pi$
$620$	−6.13119	+	3.11493i	−0.246235	+	0.125099i
$621$		−	5.75699i		−	0.231020i
$622$	15.7347	+	12.5480i	0.630903	+	0.503129i
$623$	0.946858	−	4.14845i	0.0379351	−	0.166204i
$624$	2.44095	+	0.557130i	0.0977160	+	0.0223030i
$625$	17.1915	+	18.1509i	0.687658	+	0.726034i
$626$			14.5027i			0.579645i
$627$	0.396938	−	0.497745i	0.0158522	−	0.0198780i
$628$	7.95036	−	3.82869i	0.317254	−	0.152781i
$629$	−6.39732	−	8.02199i	−0.255078	−	0.319858i
$630$	−1.42011	−	5.66391i	−0.0565784	−	0.225656i
$631$	−23.2023	−	11.1737i	−0.923670	−	0.444816i	−0.0892900	−	0.996006i	$-0.528460\pi$
$631$	−23.2023	−	11.1737i	−0.923670	−	0.444816i	−0.834380	+	0.551190i	$0.814174\pi$
$632$	−7.19354	−	1.64188i	−0.286144	−	0.0653104i
$633$	20.2309	−	4.61756i	0.804105	−	0.183532i
$634$	22.8358	−	10.9972i	0.906927	−	0.436753i
$635$	10.1634	−	8.46474i	0.403321	−	0.335913i
$636$	−6.41932	+	1.46517i	−0.254543	+	0.0580977i
$637$		−	19.7853i		−	0.783923i
$638$	0.707067	+	0.659414i	0.0279930	+	0.0261065i
$639$	31.4938			1.24588
$640$	2.19009	+	0.451105i	0.0865710	+	0.0178315i
$641$	9.00370	−	18.6964i	0.355625	−	0.738463i	−0.644023	−	0.765006i	$-0.722736\pi$
$641$	9.00370	−	18.6964i	0.355625	−	0.738463i	0.999648	+	0.0265436i	$0.00845009\pi$
$642$	−5.53245	−	11.4882i	−0.218348	−	0.453405i
$643$	−20.5085	+	4.68094i	−0.808778	+	0.184598i	−0.606865	−	0.794805i	$-0.707573\pi$
$643$	−20.5085	+	4.68094i	−0.808778	+	0.184598i	−0.201913	+	0.979403i	$0.564716\pi$
$644$	−0.337769	+	1.47986i	−0.0133099	+	0.0583147i
$645$	10.5568	−	8.79240i	0.415673	−	0.346201i
$646$	−13.9279	+	11.1071i	−0.547987	+	0.437005i
$647$	−6.09793	+	4.86294i	−0.239734	+	0.191182i	−0.735986	−	0.676997i	$-0.763281\pi$
$647$	−6.09793	+	4.86294i	−0.239734	+	0.191182i	0.496251	+	0.868179i	$0.334709\pi$
$648$	3.91764	−	1.88664i	0.153900	−	0.0741141i
$649$	0.510328	+	0.406973i	0.0200321	+	0.0159751i
$650$	12.7317	−	11.0707i	0.499380	−	0.434230i
$651$	−1.51685	+	1.90207i	−0.0594499	+	0.0745479i
$652$	−2.54109	+	11.1332i	−0.0995167	+	0.436011i
$653$	4.76082	−	20.8585i	0.186305	−	0.816257i	−0.792237	−	0.610213i	$-0.791084\pi$
$653$	4.76082	−	20.8585i	0.186305	−	0.816257i	0.978543	−	0.206044i	$-0.0660590\pi$
$654$	2.97424	−	3.72958i	0.116302	−	0.145838i
$655$	19.3584	+	8.82044i	0.756394	+	0.344643i
$656$	5.30652	+	4.23181i	0.207185	+	0.165224i
$657$	−9.10757	+	4.38597i	−0.355320	+	0.171113i
$658$	−5.99632	+	4.78191i	−0.233761	+	0.186418i
$659$	−27.7060	+	22.0948i	−1.07927	+	0.860691i	−0.990793	−	0.135387i	$-0.956772\pi$
$659$	−27.7060	+	22.0948i	−1.07927	+	0.860691i	−0.0884794	+	0.996078i	$0.528201\pi$
$660$	0.190631	+	0.228885i	0.00742031	+	0.00890934i
$661$	−4.16846	+	18.2632i	−0.162134	+	0.710356i	0.826861	+	0.562407i	$0.190124\pi$
$661$	−4.16846	+	18.2632i	−0.162134	+	0.710356i	−0.988995	+	0.147949i	$0.952733\pi$
$662$	−11.2838	+	2.57546i	−0.438558	+	0.100098i
$663$	−4.04935	−	8.40856i	−0.157264	−	0.326561i
$664$	−6.91661	+	14.3625i	−0.268416	+	0.557372i
$665$	−11.1586	−	2.29839i	−0.432711	−	0.0891278i
$666$	6.74239			0.261262
$667$	3.85056	−	6.63039i	0.149094	−	0.256730i
$668$		−	7.07705i		−	0.273819i
$669$	−0.510269	+	0.116465i	−0.0197281	+	0.00450282i
$670$	1.91978	+	2.30503i	0.0741677	+	0.0890510i
$671$	−0.564233	+	0.271720i	−0.0217820	+	0.0104897i
$672$	0.771198	−	0.176021i	0.0297496	−	0.00679015i
$673$	16.7483	+	3.82270i	0.645601	+	0.147354i	0.532770	−	0.846260i	$-0.321151\pi$
$673$	16.7483	+	3.82270i	0.645601	+	0.147354i	0.112831	+	0.993614i	$0.464008\pi$
$674$	16.0418	+	7.72532i	0.617907	+	0.297568i
$675$	−3.65662	+	19.8836i	−0.140743	+	0.765320i
$676$	1.00610	+	1.26161i	0.0386961	+	0.0485234i
$677$	−43.6606	+	21.0258i	−1.67801	+	0.808088i	−0.680881	+	0.732394i	$0.738403\pi$
$677$	−43.6606	+	21.0258i	−1.67801	+	0.808088i	−0.997131	+	0.0756935i	$0.975883\pi$
$678$	−2.21432	+	2.77667i	−0.0850405	+	0.106637i
$679$		−	0.757072i		−	0.0290538i
$680$	−3.77533	−	7.43107i	−0.144777	−	0.284969i
$681$	−6.99988	−	1.59768i	−0.268236	−	0.0612231i
$682$	−0.122869	+	0.538326i	−0.00470491	+	0.0206136i
$683$	−10.3121	−	8.22366i	−0.394583	−	0.314670i	0.406020	−	0.913864i	$-0.366916\pi$
$683$	−10.3121	−	8.22366i	−0.394583	−	0.314670i	−0.800604	+	0.599194i	$0.795488\pi$
$684$		−	11.7062i		−	0.447600i
$685$	−2.61197	−	5.14120i	−0.0997982	−	0.196435i
$686$	−5.95018	−	12.3557i	−0.227179	−	0.471742i
$687$	0.164322	−	0.131042i	0.00626926	−	0.00499957i
$688$	−5.16294	−	6.47412i	−0.196835	−	0.246823i
$689$	26.9789	+	12.9924i	1.02782	+	0.494970i
$690$	1.43324	−	1.87779i	0.0545624	−	0.0714861i
$691$	5.79816	+	25.4034i	0.220572	+	0.966391i	0.957049	+	0.289927i	$0.0936311\pi$
$691$	5.79816	+	25.4034i	0.220572	+	0.966391i	−0.736476	+	0.676463i	$0.763512\pi$
$692$	−3.46063	−	7.18606i	−0.131553	−	0.273173i
$693$	−0.422410	−	0.203422i	−0.0160460	−	0.00772736i
$694$	22.0978	−	5.04367i	0.838819	−	0.191455i
$695$	−18.3162	+	40.1990i	−0.694775	+	1.52483i
$696$	−3.98375	−	0.308725i	−0.151004	−	0.0117022i
$697$		−	25.3001i		−	0.958310i
$698$	−4.19443	−	18.3770i	−0.158762	−	0.695580i
$699$	7.54635	−	15.6702i	0.285429	−	0.592700i
$700$	2.10654	−	4.89663i	0.0796197	−	0.185075i
$701$	0.197989	+	0.867445i	0.00747793	+	0.0327629i	0.978529	−	0.206108i	$-0.0660798\pi$
$701$	0.197989	+	0.867445i	0.00747793	+	0.0327629i	−0.971051	+	0.238871i	$0.923223\pi$
$702$	13.3018	+	3.03606i	0.502046	+	0.114589i
$703$	5.70773	−	11.8522i	0.215271	−	0.447015i
$704$	0.140368	−	0.111939i	0.00529030	−	0.00421887i
$705$	11.5774	−	2.90279i	0.436030	−	0.109325i
$706$	−2.36559	−	4.91219i	−0.0890300	−	0.184873i
$707$	9.47243	−	11.8781i	0.356248	−	0.446720i
$708$	−2.69759			−0.101382
$709$	−25.8271	+	32.3862i	−0.969957	+	1.21629i	0.00636832	+	0.999980i	$0.497973\pi$
$709$	−25.8271	+	32.3862i	−0.969957	+	1.21629i	−0.976325	+	0.216308i	$0.930599\pi$
$710$	22.8538	+	17.4434i	0.857689	+	0.654639i
$711$	−17.6203	−	4.02172i	−0.660813	−	0.150826i
$712$	3.12052	+	2.48853i	0.116946	+	0.0932617i
$713$	4.37893			0.163992
$714$	−2.30533	−	1.83844i	−0.0862747	−	0.0688018i
$715$	−0.0288049	−	1.35435i	−0.00107724	−	0.0506500i
$716$	9.19371	+	11.5285i	0.343585	+	0.430842i
$717$	−10.0708	−	12.6284i	−0.376101	−	0.471616i
$718$	8.88712	−	18.4543i	0.331664	−	0.688708i
$719$	6.61770	−	28.9940i	0.246799	−	1.08130i	−0.687886	−	0.725818i	$-0.741461\pi$
$719$	6.61770	−	28.9940i	0.246799	−	1.08130i	0.934685	−	0.355477i	$-0.115682\pi$
$720$	5.36455	+	1.10496i	0.199925	+	0.0411796i
$721$	−5.81319	+	2.79948i	−0.216494	+	0.104258i
$722$	−3.45961	−	1.66606i	−0.128753	−	0.0620043i
$723$	0.914291	+	4.00577i	0.0340029	+	0.148976i
$724$	−1.91902			−0.0713197
$725$	−17.5105	+	20.4544i	−0.650323	+	0.759658i
$726$	−8.13789			−0.302025
$727$	11.7779	+	51.6023i	0.436817	+	1.91382i	0.404971	+	0.914330i	$0.367282\pi$
$727$	11.7779	+	51.6023i	0.436817	+	1.91382i	0.0318468	+	0.999493i	$0.489861\pi$
$728$	−3.24117	−	1.56087i	−0.120126	−	0.0578495i
$729$	1.48704	−	0.716121i	0.0550755	−	0.0265230i
$730$	−9.03825	−	1.86166i	−0.334521	−	0.0689029i
$731$	−6.86854	+	30.0930i	−0.254042	+	1.11303i
$732$	1.12295	−	2.33184i	0.0415056	−	0.0861872i
$733$	−32.4415	−	40.6803i	−1.19825	−	1.50256i	−0.815545	−	0.578694i	$-0.803563\pi$
$733$	−32.4415	−	40.6803i	−1.19825	−	1.50256i	−0.382709	−	0.923869i	$-0.625009\pi$
$734$	−12.0344	−	15.0907i	−0.444198	−	0.557007i
$735$	0.206855	+	9.72593i	0.00762995	+	0.358746i
$736$	−1.11317	−	0.887724i	−0.0410320	−	0.0327219i
$737$	0.240857			0.00887207
$738$	12.9981	+	10.3656i	0.478467	+	0.381565i
$739$	−16.2333	−	3.70515i	−0.597152	−	0.136296i	−0.0867471	−	0.996230i	$-0.527647\pi$
$739$	−16.2333	−	3.70515i	−0.597152	−	0.136296i	−0.510405	+	0.859934i	$0.670504\pi$
$740$	4.89268	+	3.73439i	0.179859	+	0.137279i
$741$	7.46039	−	9.35504i	0.274064	−	0.343666i
$742$	9.46069			0.347313
$743$	−7.06382	+	8.85775i	−0.259146	+	0.324959i	−0.894335	−	0.447398i	$-0.852351\pi$
$743$	−7.06382	+	8.85775i	−0.259146	+	0.324959i	0.635189	+	0.772357i	$0.280922\pi$
$744$	−0.990116	−	2.05600i	−0.0362994	−	0.0753765i
$745$	−37.5224	+	9.40795i	−1.37471	+	0.344681i
$746$	−19.9443	+	15.9051i	−0.730214	+	0.582326i
$747$	−16.9420	+	35.1804i	−0.619874	+	1.28718i
$748$	−0.652457	−	0.148919i	−0.0238562	−	0.00544502i
$749$	4.07682	+	17.8617i	0.148964	+	0.652653i
$750$	−6.14284	+	5.57519i	−0.224305	+	0.203577i
$751$	12.7166	−	26.4062i	0.464034	−	0.963576i	−0.529314	−	0.848426i	$-0.677551\pi$
$751$	12.7166	−	26.4062i	0.464034	−	0.963576i	0.993348	−	0.115150i	$-0.0367350\pi$
$752$	−1.60082	−	7.01366i	−0.0583759	−	0.255762i
$753$		−	3.20074i		−	0.116641i
$754$	13.2892	+	12.3936i	0.483964	+	0.451348i
$755$	−12.2491	+	26.8832i	−0.445789	+	0.978380i
$756$	4.20261	−	0.959219i	0.152848	−	0.0348865i
$757$	49.1915	+	23.6894i	1.78789	+	0.861005i	0.948011	+	0.318239i	$0.103091\pi$
$757$	49.1915	+	23.6894i	1.78789	+	0.861005i	0.839884	+	0.542766i	$0.182623\pi$
$758$	−11.4340	−	23.7430i	−0.415302	−	0.862383i
$759$	−0.0422052	−	0.184913i	−0.00153195	−	0.00671192i
$760$	6.48371	−	8.49476i	0.235189	−	0.308137i
$761$	20.4344	+	9.84070i	0.740747	+	0.356725i	0.765901	−	0.642959i	$-0.222293\pi$
$761$	20.4344	+	9.84070i	0.740747	+	0.356725i	−0.0251537	+	0.999684i	$0.508008\pi$
$762$	2.73646	+	3.43141i	0.0991315	+	0.124307i
$763$	−5.35878	+	4.27348i	−0.194001	+	0.154711i
$764$	−4.55171	−	9.45173i	−0.164675	−	0.341952i
$765$	−9.24753	−	18.2021i	−0.334345	−	0.658100i
$766$		−	24.0898i		−	0.870399i
$767$	9.59154	+	7.64900i	0.346330	+	0.276189i
$768$	−0.165107	+	0.723379i	−0.00595777	+	0.0261027i
$769$	−9.37609	−	2.14003i	−0.338110	−	0.0771715i	0.0500948	−	0.998744i	$-0.484048\pi$
$769$	−9.37609	−	2.14003i	−0.338110	−	0.0771715i	−0.388205	+	0.921573i	$0.626905\pi$
$770$	−0.193857	−	0.381574i	−0.00698614	−	0.0137510i
$771$			12.5516i			0.452035i
$772$	11.4517	−	14.3599i	0.412154	−	0.516825i
$773$	−22.2292	+	10.7050i	−0.799527	+	0.385032i	−0.788599	−	0.614908i	$-0.789193\pi$
$773$	−22.2292	+	10.7050i	−0.799527	+	0.385032i	−0.0109286	+	0.999940i	$0.503479\pi$
$774$	−12.6464	−	15.8581i	−0.454566	−	0.570008i
$775$	−15.1240	−	2.78132i	−0.543270	−	0.0999081i
$776$	0.639804	+	0.308114i	0.0229676	+	0.0110606i
$777$	2.12280	+	0.484515i	0.0761550	+	0.0173819i
$778$	−12.5826	+	2.87190i	−0.451108	+	0.102962i
$779$	29.2249	−	14.0740i	1.04709	−	0.504252i
$780$	3.58288	+	4.30186i	0.128288	+	0.154031i
$781$	2.25051	−	0.513664i	0.0805295	−	0.0183803i
$782$			5.30731i			0.189789i
$783$	−21.7093	−	1.68239i	−0.775827	−	0.0601236i
$784$	5.86342			0.209408
$785$	19.3259	+	3.98065i	0.689770	+	0.142076i
$786$	−3.06276	+	6.35990i	−0.109245	+	0.226850i
$787$	−17.4946	−	36.3279i	−0.623616	−	1.29495i	−0.938322	−	0.345762i	$-0.887620\pi$
$787$	−17.4946	−	36.3279i	−0.623616	−	1.29495i	0.314706	−	0.949189i	$-0.398094\pi$
$788$	12.7842	−	2.91792i	0.455419	−	0.103947i
$789$	4.93672	−	21.6292i	0.175752	−	0.770020i
$790$	−10.5589	−	12.6777i	−0.375667	−	0.451053i
$791$	3.98962	−	3.18161i	0.141854	−	0.113125i
$792$	0.343825	−	0.274191i	0.0122173	−	0.00974296i
$793$	−10.6047	+	5.10694i	−0.376583	+	0.181353i
$794$	11.0244	+	8.79164i	0.391240	+	0.312004i
$795$	−13.3980	−	6.10464i	−0.475176	−	0.216509i
$796$	−0.802446	+	1.00623i	−0.0284419	+	0.0356650i
$797$	3.20989	−	14.0634i	0.113700	−	0.498153i	−0.885724	−	0.464213i	$-0.846337\pi$
$797$	3.20989	−	14.0634i	0.113700	−	0.498153i	0.999424	−	0.0339402i	$-0.0108056\pi$
$798$	0.841223	−	3.68564i	0.0297790	−	0.130470i
$799$	−16.7197	+	20.9658i	−0.591499	+	0.741716i
$800$	3.28084	+	3.77308i	0.115995	+	0.133398i
$801$	7.64360	+	6.09557i	0.270073	+	0.215376i
$802$	24.8164	−	11.9509i	0.876296	−	0.422002i
$803$	−0.579280	+	0.461960i	−0.0204423	+	0.0163022i
$804$	−0.778237	+	0.620623i	−0.0274463	+	0.0218877i
$805$	−2.60807	+	2.17218i	−0.0919224	+	0.0765592i
$806$	−2.30931	+	10.1177i	−0.0813420	+	0.356383i
$807$	21.9948	−	5.02016i	0.774252	−	0.176718i
$808$	6.18309	+	12.8393i	0.217520	+	0.451686i
$809$	7.85054	−	16.3018i	0.276010	−	0.573141i	−0.716174	−	0.697922i	$-0.754108\pi$
$809$	7.85054	−	16.3018i	0.276010	−	0.573141i	0.992184	+	0.124781i	$0.0398227\pi$
$810$	9.52308	+	1.96152i	0.334607	+	0.0689207i
$811$	47.4893			1.66758			0.833788	−	0.552085i	$-0.186168\pi$
$811$	47.4893			1.66758			0.833788	+	0.552085i	$0.186168\pi$
$812$	5.48177	+	1.70617i	0.192372	+	0.0598749i
$813$			8.72624i			0.306043i
$814$	0.481802	−	0.109968i	0.0168872	−	0.00385438i
$815$	−19.6209	+	16.3416i	−0.687291	+	0.572423i
$816$	2.49189	−	1.20003i	0.0872337	−	0.0420095i
$817$	−38.5822	+	8.80613i	−1.34982	+	0.308088i
$818$	−28.7017	−	6.55097i	−1.00353	−	0.229049i
$819$	−7.93912	−	3.82328i	−0.277415	−	0.133596i
$820$	3.69102	+	14.7212i	0.128896	+	0.514086i
$821$	−21.8623	−	27.4145i	−0.763000	−	0.956772i	0.236891	−	0.971536i	$-0.423872\pi$
$821$	−21.8623	−	27.4145i	−0.763000	−	0.956772i	−0.999891	+	0.0147642i	$0.995300\pi$
$822$	1.72402	−	0.830244i	0.0601321	−	0.0289581i
$823$	11.1784	−	14.0173i	0.389655	−	0.488611i	−0.547854	−	0.836574i	$-0.684555\pi$
$823$	11.1784	−	14.0173i	0.389655	−	0.488611i	0.937508	+	0.347963i	$0.113126\pi$
$824$		−	6.05208i		−	0.210834i
$825$	0.0283194	+	0.665463i	0.000985956	+	0.0231685i
$826$	3.77881	+	0.862489i	0.131482	+	0.0300098i
$827$	−6.47787	+	28.3814i	−0.225258	+	0.986918i	0.728194	+	0.685371i	$0.240360\pi$
$827$	−6.47787	+	28.3814i	−0.225258	+	0.986918i	−0.953451	+	0.301547i	$0.902497\pi$
$828$	−2.72667	−	2.17445i	−0.0947583	−	0.0755672i
$829$		−	21.0414i		−	0.730798i	−0.930851	−	0.365399i	$-0.880933\pi$
$829$		−	21.0414i		−	0.730798i	0.930851	−	0.365399i	$-0.119067\pi$
$830$	−31.7794	+	16.1454i	−1.10308	+	0.560415i
$831$	−8.02376	−	16.6615i	−0.278341	−	0.577982i
$832$	2.63819	−	2.10388i	0.0914626	−	0.0729390i
$833$	−13.6272	−	17.0880i	−0.472154	−	0.592063i
$834$	−13.2068	−	6.36004i	−0.457313	−	0.220230i
$835$	9.60127	−	12.5793i	0.332266	−	0.435325i
$836$	−0.190929	−	0.836513i	−0.00660341	−	0.0289314i
$837$	−5.39560	−	11.2041i	−0.186499	−	0.387270i
$838$	33.8846	+	16.3179i	1.17052	+	0.563694i
$839$	21.0826	−	4.81197i	0.727852	−	0.166128i	0.157490	−	0.987521i	$-0.449660\pi$
$839$	21.0826	−	4.81197i	0.727852	−	0.166128i	0.570363	+	0.821393i	$0.306803\pi$
$840$	1.60959	+	0.733393i	0.0555362	+	0.0253045i
$841$	−23.8776	−	16.4579i	−0.823365	−	0.567513i
$842$		−	23.5053i		−	0.810046i
$843$	−5.31063	−	23.2674i	−0.182908	−	0.801372i
$844$	12.1345	−	25.1976i	0.417687	−	0.867336i
$845$	0.0767241	+	3.60743i	0.00263939	+	0.124099i
$846$	−3.92115	−	17.1797i	−0.134812	−	0.590650i
$847$	11.3996	+	2.60189i	0.391696	+	0.0894020i
$848$	−3.85032	+	7.99526i	−0.132220	+	0.274558i
$849$	3.97608	−	3.17082i	0.136459	−	0.108822i
$850$	3.37100	−	18.3305i	0.115624	−	0.628730i
$851$	−1.70045	−	3.53103i	−0.0582908	−	0.121042i
$852$	−5.94809	+	7.45867i	−0.203778	+	0.255530i
$853$	19.7268			0.675431			0.337716	−	0.941248i	$-0.390346\pi$
$853$	19.7268			0.675431			0.337716	+	0.941248i	$0.390346\pi$
$854$	−2.31859	+	2.90742i	−0.0793406	+	0.0994900i
$855$	15.8816	−	20.8076i	0.543139	−	0.711605i
$856$	−16.7542	−	3.82403i	−0.572646	−	0.130703i
$857$	13.0247	+	10.3869i	0.444916	+	0.354809i	0.820176	−	0.572111i	$-0.193875\pi$
$857$	13.0247	+	10.3869i	0.444916	+	0.354809i	−0.375260	+	0.926920i	$0.622447\pi$
$858$	0.449510			0.0153460
$859$	−11.0183	−	8.78678i	−0.375939	−	0.299801i	0.417233	−	0.908800i	$-0.363000\pi$
$859$	−11.0183	−	8.78678i	−0.375939	−	0.299801i	−0.793171	+	0.608999i	$0.791571\pi$
$860$	−0.393721	−	18.5120i	−0.0134258	−	0.631255i
$861$	3.34749	+	4.19762i	0.114082	+	0.143054i
$862$	−1.10286	−	1.38294i	−0.0375634	−	0.0471030i
$863$	−0.370411	+	0.769167i	−0.0126090	+	0.0261828i	−0.907178	−	0.420747i	$-0.861768\pi$
$863$	−0.370411	+	0.769167i	−0.0126090	+	0.0261828i	0.894569	+	0.446929i	$0.147482\pi$
$864$	−0.899742	+	3.94203i	−0.0306098	+	0.134110i
$865$	3.59798	−	17.4680i	0.122335	−	0.593931i
$866$	25.1506	−	12.1119i	0.854652	−	0.411579i
$867$	2.07584	+	0.999670i	0.0704991	+	0.0339506i
$868$	0.729609	+	3.19662i	0.0247645	+	0.108501i
$869$	−1.32472			−0.0449380
$870$	−6.66219	−	5.95342i	−0.225869	−	0.201840i
$871$	4.52686			0.153387
$872$	−1.43062	−	6.26795i	−0.0484468	−	0.212260i
$873$	1.56718	+	0.754713i	0.0530409	+	0.0255432i
$874$	−6.13063	+	2.95236i	−0.207372	+	0.0998649i
$875$	10.3875	−	5.84576i	0.351161	−	0.197623i
$876$	0.681375	−	2.98530i	0.0230215	−	0.100864i
$877$	−22.6712	+	47.0773i	−0.765553	+	1.58969i	0.0414500	+	0.999141i	$0.486802\pi$
$877$	−22.6712	+	47.0773i	−0.765553	+	1.58969i	−0.807003	+	0.590547i	$0.798912\pi$
$878$	14.2245	+	17.8369i	0.480053	+	0.601968i
$879$	0.394410	+	0.494574i	0.0133031	+	0.0166816i
$880$	0.401366	−	0.00853639i	0.0135300	−	0.000287762i
$881$	2.81840	+	2.24760i	0.0949542	+	0.0757234i	0.669816	−	0.742527i	$-0.266373\pi$
$881$	2.81840	+	2.24760i	0.0949542	+	0.0757234i	−0.574862	+	0.818250i	$0.694944\pi$
$882$	14.3622			0.483601
$883$	−30.5853	−	24.3909i	−1.02928	−	0.820820i	−0.0452735	−	0.998975i	$-0.514416\pi$
$883$	−30.5853	−	24.3909i	−1.02928	−	0.820820i	−0.984003	+	0.178154i	$0.942987\pi$
$884$	−12.2628	−	2.79891i	−0.412444	−	0.0941376i
$885$	−4.79491	−	3.65976i	−0.161179	−	0.123022i
$886$	−1.44914	+	1.81716i	−0.0486847	+	0.0610487i
$887$	−31.1905			−1.04727			−0.523637	−	0.851941i	$-0.675425\pi$
$887$	−31.1905			−1.04727			−0.523637	+	0.851941i	$0.675425\pi$
$888$	−1.27340	+	1.59680i	−0.0427326	+	0.0535850i
$889$	−2.73615	−	5.68167i	−0.0917675	−	0.190557i
$890$	2.17052	+	8.65685i	0.0727561	+	0.290178i
$891$	0.610354	−	0.486741i	0.0204476	−	0.0163064i
$892$	−0.306060	+	0.635540i	−0.0102476	+	0.0212794i
$893$	−33.5190	−	7.65050i	−1.12167	−	0.256014i
$894$	−2.85633	−	12.5144i	−0.0955300	−	0.418544i
$895$	0.701103	+	32.9646i	0.0234353	+	1.10189i
$896$	0.462566	−	0.960527i	0.0154532	−	0.0320890i
$897$	−0.793240	−	3.47541i	−0.0264855	−	0.116041i
$898$		−	28.7780i		−	0.960333i
$899$	1.27967	−	16.5127i	0.0426794	−	0.550729i
$900$	8.03629	+	9.24201i	0.267876	+	0.308067i
$901$	32.2494	−	7.36071i	1.07438	−	0.245221i
$902$	1.09789	+	0.528717i	0.0365558	+	0.0176043i
$903$	−2.84207	−	5.90161i	−0.0945780	−	0.196393i
$904$	1.06510	+	4.66649i	0.0354246	+	0.155205i
$905$	−3.41101	−	2.60349i	−0.113386	−	0.0865428i
$906$	−8.83206	−	4.25330i	−0.293426	−	0.141306i
$907$	−27.6060	−	34.6168i	−0.916643	−	1.14943i	−0.988379	−	0.152010i	$-0.951425\pi$
$907$	−27.6060	−	34.6168i	−0.916643	−	1.14943i	0.0717362	−	0.997424i	$-0.477146\pi$
$908$	−7.56550	+	6.03329i	−0.251070	+	0.200222i
$909$	15.1453	+	31.4494i	0.502336	+	1.04311i
$910$	−3.64352	−	7.17162i	−0.120781	−	0.237737i
$911$		−	8.57713i		−	0.284173i	−0.989854	−	0.142087i	$-0.954619\pi$
$911$		−	8.57713i		−	0.284173i	0.989854	−	0.142087i	$-0.0453811\pi$
$912$	2.77238	+	2.21090i	0.0918028	+	0.0732103i
$913$	−0.636860	+	2.79027i	−0.0210770	+	0.0923443i
$914$	1.39437	+	0.318257i	0.0461218	+	0.0105270i
$915$	5.15958	−	2.62131i	0.170570	−	0.0866577i
$916$		−	0.283262i		−	0.00935924i
$917$	6.32377	−	7.92976i	0.208829	−	0.261864i
$918$	13.5795	−	6.53953i	0.448189	−	0.215837i
$919$	−10.7696	−	13.5046i	−0.355256	−	0.445476i	0.571804	−	0.820390i	$-0.306244\pi$
$919$	−10.7696	−	13.5046i	−0.355256	−	0.445476i	−0.927060	+	0.374914i	$0.877672\pi$
$920$	−0.774282	−	3.08812i	−0.0255273	−	0.101812i
$921$	12.1538	+	5.85298i	0.400483	+	0.192862i
$922$	15.6141	+	3.56381i	0.514223	+	0.117368i
$923$	42.2979	−	9.65423i	1.39225	−	0.317773i
$924$	0.127955	−	0.0616198i	0.00420940	−	0.00202714i
$925$	3.63028	+	13.2756i	0.119363	+	0.436498i
$926$	−24.6795	+	5.63293i	−0.811018	+	0.185109i
$927$		−	14.8243i		−	0.486895i
$928$	−3.67286	+	3.93828i	−0.120568	+	0.129280i
$929$	−37.5010			−1.23037			−0.615184	−	0.788383i	$-0.710918\pi$
$929$	−37.5010			−1.23037			−0.615184	+	0.788383i	$0.710918\pi$
$930$	1.02941	−	4.99776i	0.0337558	−	0.163883i
$931$	12.1583	−	25.2469i	0.398471	−	0.827433i
$932$	−10.1705	−	21.1193i	−0.333147	−	0.691786i
$933$	−14.5583	+	3.32284i	−0.476618	+	0.108785i
$934$	−3.71486	+	16.2759i	−0.121554	+	0.532562i
$935$	−0.957693	−	1.14987i	−0.0313199	−	0.0376049i
$936$	6.46214	−	5.15338i	0.211222	−	0.168444i
$937$	−42.6535	+	34.0151i	−1.39343	+	1.11122i	−0.413811	+	0.910363i	$0.635802\pi$
$937$	−42.6535	+	34.0151i	−1.39343	+	1.11122i	−0.979620	+	0.200861i	$0.935626\pi$
$938$	1.28859	−	0.620553i	0.0420740	−	0.0202618i
$939$	−8.41309	−	6.70922i	−0.274551	−	0.218947i
$940$	6.66984	−	14.6384i	0.217546	−	0.477453i
$941$	6.68519	−	8.38297i	0.217931	−	0.273277i	−0.660833	−	0.750533i	$-0.729797\pi$
$941$	6.68519	−	8.38297i	0.217931	−	0.273277i	0.878764	+	0.477256i	$0.158368\pi$
$942$	−1.45694	+	6.38326i	−0.0474696	+	0.207978i
$943$	2.15038	−	9.42144i	0.0700261	−	0.306804i
$944$	−2.26680	+	2.84247i	−0.0737779	+	0.0925146i
$945$	8.77140	+	3.99660i	0.285334	+	0.130009i
$946$	−1.16234	−	0.926937i	−0.0377910	−	0.0301373i
$947$	40.2669	−	19.3915i	1.30850	−	0.630140i	0.355944	−	0.934507i	$-0.384160\pi$
$947$	40.2669	−	19.3915i	1.30850	−	0.630140i	0.952555	+	0.304368i	$0.0984452\pi$
$948$	4.28032	−	3.41344i	0.139018	−	0.110863i
$949$	−10.8875	+	8.68247i	−0.353422	+	0.281845i
$950$	23.0493	−	6.30296i	0.747818	−	0.204495i
$951$	−4.18477	+	18.3347i	−0.135700	+	0.594542i
$952$	−3.87435	+	0.884294i	−0.125568	+	0.0286601i
$953$	8.55325	+	17.7610i	0.277067	+	0.575336i	0.992344	−	0.123506i	$-0.0394137\pi$
$953$	8.55325	+	17.7610i	0.277067	+	0.575336i	−0.715277	+	0.698841i	$0.753699\pi$
$954$	−9.43120	+	19.5841i	−0.305347	+	0.634059i
$955$	4.73237	−	22.9755i	0.153136	−	0.743468i
$956$	−21.7692			−0.704065
$957$	−0.709631	+	0.105116i	−0.0229391	+	0.00339791i
$958$			14.0855i			0.455081i
$959$	−2.68047	+	0.611800i	−0.0865570	+	0.0197561i
$960$	−1.27486	+	1.06179i	−0.0411461	+	0.0342693i
$961$	−19.4079	+	9.34635i	−0.626061	+	0.301495i
$962$	9.05540	−	2.06684i	0.291958	−	0.0666374i
$963$	−41.0387	−	9.36682i	−1.32245	−	0.301842i
$964$	4.98919	+	2.40267i	0.160691	+	0.0773847i
$965$	39.8369	−	9.98825i	1.28239	−	0.321533i
$966$	−0.702217	−	0.880552i	−0.0225935	−	0.0283313i
$967$	−13.1512	+	6.33328i	−0.422914	+	0.203665i	−0.633221	−	0.773971i	$-0.718268\pi$
$967$	−13.1512	+	6.33328i	−0.422914	+	0.203665i	0.210308	+	0.977635i	$0.432553\pi$
$968$	−6.83829	+	8.57495i	−0.219791	+	0.275609i
$969$		−	13.2180i		−	0.424624i
$970$	0.719228	+	1.41567i	0.0230930	+	0.0454545i
$971$	−56.2781	−	12.8451i	−1.80605	−	0.412219i	−0.819153	−	0.573576i	$-0.805556\pi$
$971$	−56.2781	−	12.8451i	−1.80605	−	0.412219i	−0.986896	+	0.161357i	$0.948413\pi$
$972$	−3.41715	+	14.9715i	−0.109605	+	0.480212i
$973$	16.4667	+	13.1317i	0.527897	+	0.420984i
$974$		−	4.86441i		−	0.155866i
$975$	0.532259	+	12.5073i	0.0170459	+	0.400553i
$976$	−1.51345	−	3.14272i	−0.0484444	−	0.100596i
$977$	30.0899	−	23.9959i	0.962661	−	0.767696i	−0.00999446	−	0.999950i	$-0.503181\pi$
$977$	30.0899	−	23.9959i	0.962661	−	0.767696i	0.972655	+	0.232254i	$0.0746100\pi$
$978$	−5.28289	−	6.62453i	−0.168928	−	0.211829i
$979$	0.645620	+	0.310914i	0.0206341	+	0.00993687i
$980$	10.4221	+	7.95477i	0.332922	+	0.254106i
$981$	−3.50425	−	15.3531i	−0.111882	−	0.490187i
$982$	−2.13639	−	4.43626i	−0.0681749	−	0.141567i
$983$	12.2293	+	5.88933i	0.390055	+	0.187840i	0.618624	−	0.785687i	$-0.287690\pi$
$983$	12.2293	+	5.88933i	0.390055	+	0.187840i	−0.228569	+	0.973528i	$0.573405\pi$
$984$	−4.90978	+	1.12063i	−0.156518	+	0.0357242i
$985$	26.6824	+	12.1575i	0.850171	+	0.387371i
$986$	20.0136	+	1.55098i	0.637362	+	0.0493931i
$987$		−	5.69069i		−	0.181137i
$988$	−3.58847	−	15.7221i	−0.114165	−	0.500188i
$989$	−5.11551	+	10.6225i	−0.162664	+	0.337775i
$990$	0.983130	−	0.0209096i	0.0312459	−	0.000664550i
$991$	5.25270	+	23.0136i	0.166857	+	0.731050i	0.987241	+	0.159236i	$0.0509030\pi$
$991$	5.25270	+	23.0136i	0.166857	+	0.731050i	−0.820383	+	0.571814i	$0.806240\pi$
$992$	−2.99842	−	0.684369i	−0.0951998	−	0.0217287i
$993$	3.72607	−	7.73726i	0.118243	−	0.245534i
$994$	10.7169	−	8.54641i	0.339918	−	0.271076i
$995$	−2.79146	+	0.699901i	−0.0884954	+	0.0221884i
$996$	−5.13200	−	10.6567i	−0.162614	−	0.337671i
$997$	−23.6890	+	29.7050i	−0.750237	+	0.940767i	−0.999618	−	0.0276381i	$-0.991201\pi$
$997$	−23.6890	+	29.7050i	−0.750237	+	0.940767i	0.249381	+	0.968405i	$0.419773\pi$
$998$	27.4773			0.869779
$999$	−6.93936	+	8.70168i	−0.219552	+	0.275309i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	290.2.l.b.109.4	yes	48
5.4	even	2		290.2.l.a.109.5	✓	48
29.4	even	14		290.2.l.a.149.5	yes	48
145.4	even	14	inner	290.2.l.b.149.4	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.l.a.109.5	✓	48	5.4	even	2
290.2.l.a.149.5	yes	48	29.4	even	14
290.2.l.b.109.4	yes	48	1.1	even	1	trivial
290.2.l.b.149.4	yes	48	145.4	even	14	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:	\( N \)	\(=\)	\( 290 = 2 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	290.l (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.222521 + 0.974928i) q^{2} +(-0.668503 - 0.321934i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(-2.19009 - 0.451105i) q^{5} +(0.165107 - 0.723379i) q^{6} +(-0.462566 + 0.960527i) q^{7} +(-0.623490 - 0.781831i) q^{8} +(-1.52721 - 1.91507i) q^{9} +(-0.0475467 - 2.23556i) q^{10} +(-0.140368 - 0.111939i) q^{11} +0.741982 q^{12} +(-2.63819 - 2.10388i) q^{13} +(-1.03938 - 0.237231i) q^{14} +(1.31886 + 1.00663i) q^{15} +(0.623490 - 0.781831i) q^{16} -3.72757 q^{17} +(1.52721 - 1.91507i) q^{18} +(-2.07358 - 4.30583i) q^{19} +(2.16893 - 0.543814i) q^{20} +(0.618453 - 0.493200i) q^{21} +(0.0778981 - 0.161757i) q^{22} +(-1.38810 - 0.316825i) q^{23} +(0.165107 + 0.723379i) q^{24} +(4.59301 + 1.97592i) q^{25} +(1.46408 - 3.04020i) q^{26} +(0.899742 + 3.94203i) q^{27} -1.06610i q^{28} +(-1.60038 + 5.14187i) q^{29} +(-0.687918 + 1.50979i) q^{30} +(-2.99842 + 0.684369i) q^{31} +(0.900969 + 0.433884i) q^{32} +(0.0577990 + 0.120021i) q^{33} +(-0.829463 - 3.63411i) q^{34} +(1.44636 - 1.89498i) q^{35} +(2.20689 + 1.06278i) q^{36} +(1.71622 + 2.15207i) q^{37} +(3.73646 - 2.97973i) q^{38} +(1.08632 + 2.25577i) q^{39} +(1.01281 + 1.99354i) q^{40} +6.78729i q^{41} +(0.618453 + 0.493200i) q^{42} +(1.84263 - 8.07309i) q^{43} +(0.175035 + 0.0399507i) q^{44} +(2.48085 + 4.88311i) q^{45} -1.42380i q^{46} +(4.48540 - 5.62452i) q^{47} +(-0.668503 + 0.321934i) q^{48} +(3.65578 + 4.58421i) q^{49} +(-0.904341 + 4.91754i) q^{50} +(2.49189 + 1.20003i) q^{51} +(3.28976 + 0.750867i) q^{52} +(-8.65158 + 1.97467i) q^{53} +(-3.64298 + 1.75437i) q^{54} +(0.256921 + 0.308478i) q^{55} +(1.03938 - 0.237231i) q^{56} +3.54601i q^{57} +(-5.36907 - 0.416082i) q^{58} -3.63566 q^{59} +(-1.62501 - 0.334712i) q^{60} +(1.51345 - 3.14272i) q^{61} +(-1.33442 - 2.77095i) q^{62} +(2.54591 - 0.581088i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(4.82880 + 5.79779i) q^{65} +(-0.104150 + 0.0830570i) q^{66} +(-1.04886 + 0.836440i) q^{67} +(3.35843 - 1.61733i) q^{68} +(0.825952 + 0.658675i) q^{69} +(2.16931 + 0.988424i) q^{70} +(-8.01648 + 10.0524i) q^{71} +(-0.545057 + 2.38805i) q^{72} +(0.918317 - 4.02341i) q^{73} +(-1.71622 + 2.15207i) q^{74} +(-2.43432 - 2.79955i) q^{75} +(3.73646 + 2.97973i) q^{76} +(0.172450 - 0.0830475i) q^{77} +(-1.95749 + 1.56104i) q^{78} +(5.76877 - 4.60044i) q^{79} +(-1.71819 + 1.43102i) q^{80} +(-0.967578 + 4.23924i) q^{81} +(-6.61712 + 1.51031i) q^{82} +(-6.91661 - 14.3625i) q^{83} +(-0.343215 + 0.712694i) q^{84} +(8.16373 + 1.68153i) q^{85} +8.28071 q^{86} +(2.72520 - 2.92213i) q^{87} +0.179537i q^{88} +(-3.89123 + 0.888147i) q^{89} +(-4.20864 + 3.50524i) q^{90} +(3.24117 - 1.56087i) q^{91} +(1.38810 - 0.316825i) q^{92} +(2.22477 + 0.507789i) q^{93} +(6.48159 + 3.12137i) q^{94} +(2.59895 + 10.3656i) q^{95} +(-0.462618 - 0.580105i) q^{96} +(-0.639804 + 0.308114i) q^{97} +(-3.65578 + 4.58421i) q^{98} +0.439769i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 8 q^{2} - 4 q^{3} - 8 q^{4} + 8 q^{5} - 3 q^{6} + 7 q^{7} + 8 q^{8} - 8 q^{9} - q^{10} + 10 q^{12} - 10 q^{15} - 8 q^{16} - 30 q^{17} + 8 q^{18} - 13 q^{20} + 7 q^{21} + 7 q^{23} - 3 q^{24} - 12 q^{25}+ \cdots - 27 q^{98}+O(q^{100}) \) 48 * q + 8 * q^2 - 4 * q^3 - 8 * q^4 + 8 * q^5 - 3 * q^6 + 7 * q^7 + 8 * q^8 - 8 * q^9 - q^10 + 10 * q^12 - 10 * q^15 - 8 * q^16 - 30 * q^17 + 8 * q^18 - 13 * q^20 + 7 * q^21 + 7 * q^23 - 3 * q^24 - 12 * q^25 + 21 * q^26 + 11 * q^27 - 10 * q^29 - 18 * q^30 + 14 * q^31 + 8 * q^32 - 14 * q^33 - 33 * q^34 - q^36 - 44 * q^37 - 28 * q^38 - 14 * q^39 - 8 * q^40 + 7 * q^42 - 8 * q^43 + 14 * q^44 + 25 * q^45 - 6 * q^47 - 4 * q^48 + 27 * q^49 + 5 * q^50 + 24 * q^51 + 77 * q^53 + 10 * q^54 - 32 * q^55 + 10 * q^58 - 24 * q^59 + 4 * q^60 + 56 * q^61 - 8 * q^64 - 34 * q^65 + 42 * q^67 - 2 * q^68 + 28 * q^69 - 30 * q^71 + 22 * q^72 - 29 * q^73 + 44 * q^74 - 32 * q^75 - 28 * q^76 - 30 * q^77 + 14 * q^78 + q^80 - 130 * q^81 - 42 * q^82 - 42 * q^84 + 28 * q^85 - 62 * q^86 + 32 * q^87 + 31 * q^90 - 106 * q^91 - 7 * q^92 - 70 * q^93 + 27 * q^94 + 165 * q^95 + 4 * q^96 - 49 * q^97 - 27 * q^98

Introduction

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