LMFDB - Embedded newform 890.2.o.a.271.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [890,2,Mod(91,890)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("890.91"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(890, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 890 = 2 \cdot 5 \cdot 89 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	890.o (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,-6,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.10668577989$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$6$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			271.1
Character	$\chi$	$=$	890.271
Dual form			890.2.o.a.601.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.841254 - 0.540641i) q^{2} +(-0.881612 - 1.93046i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-1.78534 - 1.14737i) q^{6} +(-0.00872159 - 0.0606600i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.984857 + 1.13659i) q^{9} +(-0.654861 - 0.755750i) q^{10} +(-0.0757347 + 0.526747i) q^{11} -2.12224 q^{12} +(-0.666857 - 1.46021i) q^{13} +(-0.0401323 - 0.0463152i) q^{14} +(-1.78534 + 1.14737i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-5.25859 - 3.37949i) q^{17} +(-0.214030 + 1.48861i) q^{18} +(4.15779 - 4.79835i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(-0.109413 + 0.0703153i) q^{21} +(0.221069 + 0.484073i) q^{22} +(-2.75023 + 3.17394i) q^{23} +(-1.78534 + 1.14737i) q^{24} +(-0.959493 + 0.281733i) q^{25} +(-1.35045 - 0.867879i) q^{26} +(-3.04644 - 0.894515i) q^{27} +(-0.0588014 - 0.0172656i) q^{28} +(0.908288 + 6.31728i) q^{29} +(-0.881612 + 1.93046i) q^{30} +(-1.85858 - 2.14491i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(1.08363 - 0.318183i) q^{33} -6.25090 q^{34} +(-0.0588014 + 0.0172656i) q^{35} +(0.624750 + 1.36801i) q^{36} +1.26720 q^{37} +(0.903574 - 6.28450i) q^{38} +(-2.23098 + 2.57468i) q^{39} +(-0.959493 + 0.281733i) q^{40} +(2.01831 - 4.41948i) q^{41} +(-0.0540285 + 0.118306i) q^{42} +(-0.579935 + 4.03354i) q^{43} +(0.447684 + 0.287709i) q^{44} +(1.26518 + 0.813079i) q^{45} +(-0.597683 + 4.15697i) q^{46} +(-3.97671 + 8.70779i) q^{47} +(-0.881612 + 1.93046i) q^{48} +(6.71285 - 1.97107i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(-1.88794 + 13.1309i) q^{51} -1.60528 q^{52} +(5.35190 + 11.7190i) q^{53} +(-3.04644 + 0.894515i) q^{54} +0.532163 q^{55} +(-0.0588014 + 0.0172656i) q^{56} +(-12.9286 - 3.79617i) q^{57} +(4.17948 + 4.82338i) q^{58} +(4.46290 - 9.77239i) q^{59} +(0.302027 + 2.10064i) q^{60} +(-4.00764 - 1.17675i) q^{61} +(-2.72316 - 0.799593i) q^{62} +(0.0775348 + 0.0498286i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-1.35045 + 0.867879i) q^{65} +(0.739587 - 0.853529i) q^{66} +(-3.83827 - 8.40463i) q^{67} +(-5.25859 + 3.37949i) q^{68} +(8.55180 + 2.51103i) q^{69} +(-0.0401323 + 0.0463152i) q^{70} +(1.89065 - 13.1497i) q^{71} +(1.26518 + 0.813079i) q^{72} +(2.01717 + 2.32794i) q^{73} +(1.06604 - 0.685102i) q^{74} +(1.38977 + 1.60388i) q^{75} +(-2.63752 - 5.77536i) q^{76} +0.0326130 q^{77} +(-0.484837 + 3.37212i) q^{78} +(-5.16787 - 5.96404i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(1.60104 + 11.1355i) q^{81} +(-0.691442 - 4.80908i) q^{82} +(1.37929 + 0.886416i) q^{83} +(0.0185093 + 0.128735i) q^{84} +(-2.59672 + 5.68602i) q^{85} +(1.69282 + 3.70677i) q^{86} +(11.3945 - 7.32281i) q^{87} +0.532163 q^{88} +(9.07193 + 2.58845i) q^{89} +1.50392 q^{90} +(-0.0827605 + 0.0531869i) q^{91} +(1.74463 + 3.82020i) q^{92} +(-2.50213 + 5.47890i) q^{93} +(1.36236 + 9.47543i) q^{94} +(-5.34122 - 3.43259i) q^{95} +(0.302027 + 2.10064i) q^{96} +(-2.27478 - 15.8214i) q^{97} +(4.58157 - 5.28741i) q^{98} +(-0.524105 - 0.604849i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 6 q^{2} + 4 q^{3} - 6 q^{4} - 6 q^{5} + 4 q^{6} + 6 q^{7} - 6 q^{8} + 6 q^{9} - 6 q^{10} - 6 q^{11} + 4 q^{12} - 30 q^{13} + 6 q^{14} + 4 q^{15} - 6 q^{16} - 10 q^{17} + 6 q^{18} + 7 q^{19} - 6 q^{20}+ \cdots - 54 q^{99}+O(q^{100}) $ 60 * q - 6 * q^2 + 4 * q^3 - 6 * q^4 - 6 * q^5 + 4 * q^6 + 6 * q^7 - 6 * q^8 + 6 * q^9 - 6 * q^10 - 6 * q^11 + 4 * q^12 - 30 * q^13 + 6 * q^14 + 4 * q^15 - 6 * q^16 - 10 * q^17 + 6 * q^18 + 7 * q^19 - 6 * q^20 - 8 * q^21 + 16 * q^22 - 9 * q^23 + 4 * q^24 - 6 * q^25 + 3 * q^26 + 13 * q^27 - 16 * q^28 + q^29 + 4 * q^30 - 10 * q^31 - 6 * q^32 - 10 * q^33 - 54 * q^34 - 16 * q^35 - 16 * q^36 - 4 * q^37 - 26 * q^38 + 11 * q^39 - 6 * q^40 + 30 * q^41 - 19 * q^42 + 34 * q^43 - 6 * q^44 - 5 * q^45 + 13 * q^46 + 38 * q^47 + 4 * q^48 + 14 * q^49 - 6 * q^50 - 6 * q^51 + 14 * q^52 + 38 * q^53 + 13 * q^54 - 28 * q^55 - 16 * q^56 + 54 * q^57 - 10 * q^58 + 16 * q^59 - 7 * q^60 + 7 * q^61 + 34 * q^62 - 77 * q^63 - 6 * q^64 + 3 * q^65 + 12 * q^66 - 4 * q^67 - 10 * q^68 + 12 * q^69 + 6 * q^70 + 17 * q^71 - 5 * q^72 + 25 * q^73 + 18 * q^74 + 4 * q^75 - 15 * q^76 - 46 * q^77 + 11 * q^78 + 85 * q^79 - 6 * q^80 + 18 * q^81 - 14 * q^82 + 9 * q^83 + 3 * q^84 + 12 * q^85 + 12 * q^86 - 31 * q^87 - 28 * q^88 - 37 * q^89 + 28 * q^90 + 16 * q^91 + 2 * q^92 - 85 * q^93 + 16 * q^94 + 7 * q^95 - 7 * q^96 - 77 * q^97 + 14 * q^98 - 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/890\mathbb{Z}\right)^\times$.

$n$	$181$	$357$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$

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 $

$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$3$	−0.881612	−	1.93046i	−0.508999	−	1.11455i	−0.973439	−	0.228947i	$-0.926472\pi$
$3$	−0.881612	−	1.93046i	−0.508999	−	1.11455i	0.464440	−	0.885605i	$-0.346256\pi$
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	−0.142315	−	0.989821i	−0.0636451	−	0.442662i
$5$	−0.142315	−	0.989821i	−0.0636451	−	0.442662i
$6$	−1.78534	−	1.14737i	−0.728864	−	0.468412i
$7$	−0.00872159	−	0.0606600i	−0.00329645	−	0.0229273i	0.988107	−	0.153769i	$-0.0491411\pi$
$7$	−0.00872159	−	0.0606600i	−0.00329645	−	0.0229273i	−0.991403	+	0.130842i	$0.958232\pi$
$8$	−0.142315	−	0.989821i	−0.0503159	−	0.349955i
$9$	−0.984857	+	1.13659i	−0.328286	+	0.378862i
$10$	−0.654861	−	0.755750i	−0.207085	−	0.238989i
$11$	−0.0757347	+	0.526747i	−0.0228349	+	0.158820i	−0.998048	−	0.0624460i	$-0.980110\pi$
$11$	−0.0757347	+	0.526747i	−0.0228349	+	0.158820i	0.975213	+	0.221266i	$0.0710190\pi$
$12$	−2.12224			−0.612639
$13$	−0.666857	−	1.46021i	−0.184953	−	0.404990i	0.794330	−	0.607486i	$-0.207822\pi$
$13$	−0.666857	−	1.46021i	−0.184953	−	0.404990i	−0.979283	+	0.202496i	$0.935095\pi$
$14$	−0.0401323	−	0.0463152i	−0.0107258	−	0.0123783i
$15$	−1.78534	+	1.14737i	−0.460974	+	0.296250i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−5.25859	−	3.37949i	−1.27540	−	0.819647i	−0.285083	−	0.958503i	$-0.592021\pi$
$17$	−5.25859	−	3.37949i	−1.27540	−	0.819647i	−0.990313	+	0.138856i	$0.955658\pi$
$18$	−0.214030	+	1.48861i	−0.0504473	+	0.350869i
$19$	4.15779	−	4.79835i	0.953863	−	1.10082i	−0.0409571	−	0.999161i	$-0.513041\pi$
$19$	4.15779	−	4.79835i	0.953863	−	1.10082i	0.994820	−	0.101655i	$-0.0324138\pi$
$20$	−0.959493	−	0.281733i	−0.214549	−	0.0629973i
$21$	−0.109413	+	0.0703153i	−0.0238758	+	0.0153440i
$22$	0.221069	+	0.484073i	0.0471320	+	0.103205i
$23$	−2.75023	+	3.17394i	−0.573463	+	0.661812i	−0.966186	−	0.257845i	$-0.916988\pi$
$23$	−2.75023	+	3.17394i	−0.573463	+	0.661812i	0.392723	+	0.919657i	$0.371533\pi$
$24$	−1.78534	+	1.14737i	−0.364432	+	0.234206i
$25$	−0.959493	+	0.281733i	−0.191899	+	0.0563465i
$26$	−1.35045	−	0.867879i	−0.264844	−	0.170205i
$27$	−3.04644	−	0.894515i	−0.586288	−	0.172150i
$28$	−0.0588014	−	0.0172656i	−0.0111124	−	0.00326290i
$29$	0.908288	+	6.31728i	0.168665	+	1.17309i	0.881648	+	0.471908i	$0.156435\pi$
$29$	0.908288	+	6.31728i	0.168665	+	1.17309i	−0.712983	+	0.701182i	$0.752656\pi$
$30$	−0.881612	+	1.93046i	−0.160960	+	0.352452i
$31$	−1.85858	−	2.14491i	−0.333811	−	0.385238i	0.563886	−	0.825853i	$-0.309306\pi$
$31$	−1.85858	−	2.14491i	−0.333811	−	0.385238i	−0.897696	+	0.440615i	$0.854760\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$	1.08363	−	0.318183i	0.188636	−	0.0553886i
$34$	−6.25090			−1.07202
$35$	−0.0588014	+	0.0172656i	−0.00993924	+	0.00291842i
$36$	0.624750	+	1.36801i	0.104125	+	0.228002i
$37$	1.26720			0.208327			0.104163	−	0.994560i	$-0.466783\pi$
$37$	1.26720			0.208327			0.104163	+	0.994560i	$0.466783\pi$
$38$	0.903574	−	6.28450i	0.146579	−	1.01948i
$39$	−2.23098	+	2.57468i	−0.357242	+	0.412279i
$40$	−0.959493	+	0.281733i	−0.151709	+	0.0445458i
$41$	2.01831	−	4.41948i	0.315207	−	0.690207i	−0.684022	−	0.729461i	$-0.739771\pi$
$41$	2.01831	−	4.41948i	0.315207	−	0.690207i	0.999229	+	0.0392544i	$0.0124983\pi$
$42$	−0.0540285	+	0.118306i	−0.00833678	+	0.0182550i
$43$	−0.579935	+	4.03354i	−0.0884393	+	0.615109i	0.896608	+	0.442825i	$0.146024\pi$
$43$	−0.579935	+	4.03354i	−0.0884393	+	0.615109i	−0.985047	+	0.172284i	$0.944885\pi$
$44$	0.447684	+	0.287709i	0.0674910	+	0.0433738i
$45$	1.26518	+	0.813079i	0.188601	+	0.121207i
$46$	−0.597683	+	4.15697i	−0.0881235	+	0.612912i
$47$	−3.97671	+	8.70779i	−0.580063	+	1.27016i	0.361200	+	0.932488i	$0.382367\pi$
$47$	−3.97671	+	8.70779i	−0.580063	+	1.27016i	−0.941263	+	0.337673i	$0.890360\pi$
$48$	−0.881612	+	1.93046i	−0.127250	+	0.278638i
$49$	6.71285	−	1.97107i	0.958978	−	0.281581i
$50$	−0.654861	+	0.755750i	−0.0926113	+	0.106879i
$51$	−1.88794	+	13.1309i	−0.264364	+	1.83869i
$52$	−1.60528			−0.222612
$53$	5.35190	+	11.7190i	0.735140	+	1.60973i	0.791387	+	0.611315i	$0.209359\pi$
$53$	5.35190	+	11.7190i	0.735140	+	1.60973i	−0.0562470	+	0.998417i	$0.517913\pi$
$54$	−3.04644	+	0.894515i	−0.414568	+	0.121728i
$55$	0.532163			0.0717569
$56$	−0.0588014	+	0.0172656i	−0.00785766	+	0.00230722i
$57$	−12.9286	−	3.79617i	−1.71243	−	0.502815i
$58$	4.17948	+	4.82338i	0.548793	+	0.633341i
$59$	4.46290	−	9.77239i	0.581020	−	1.27226i	−0.359698	−	0.933069i	$-0.617120\pi$
$59$	4.46290	−	9.77239i	0.581020	−	1.27226i	0.940719	−	0.339188i	$-0.110152\pi$
$60$	0.302027	+	2.10064i	0.0389915	+	0.271192i
$61$	−4.00764	−	1.17675i	−0.513126	−	0.150667i	0.0149110	−	0.999889i	$-0.495254\pi$
$61$	−4.00764	−	1.17675i	−0.513126	−	0.150667i	−0.528037	+	0.849221i	$0.677072\pi$
$62$	−2.72316	−	0.799593i	−0.345842	−	0.101548i
$63$	0.0775348	+	0.0498286i	0.00976846	+	0.00627781i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	−1.35045	+	0.867879i	−0.167502	+	0.107647i
$66$	0.739587	−	0.853529i	0.0910368	−	0.105062i
$67$	−3.83827	−	8.40463i	−0.468919	−	1.02679i	−0.985363	−	0.170468i	$-0.945472\pi$
$67$	−3.83827	−	8.40463i	−0.468919	−	1.02679i	0.516444	−	0.856321i	$-0.327255\pi$
$68$	−5.25859	+	3.37949i	−0.637698	+	0.409824i
$69$	8.55180	+	2.51103i	1.02952	+	0.302293i
$70$	−0.0401323	+	0.0463152i	−0.00479673	+	0.00553572i
$71$	1.89065	−	13.1497i	0.224378	−	1.56059i	−0.496818	−	0.867855i	$-0.665498\pi$
$71$	1.89065	−	13.1497i	0.224378	−	1.56059i	0.721196	−	0.692731i	$-0.243593\pi$
$72$	1.26518	+	0.813079i	0.149102	+	0.0958223i
$73$	2.01717	+	2.32794i	0.236092	+	0.272465i	0.861415	−	0.507901i	$-0.169578\pi$
$73$	2.01717	+	2.32794i	0.236092	+	0.272465i	−0.625323	+	0.780366i	$0.715033\pi$
$74$	1.06604	−	0.685102i	0.123925	−	0.0796415i
$75$	1.38977	+	1.60388i	0.160477	+	0.185201i
$76$	−2.63752	−	5.77536i	−0.302544	−	0.662480i
$77$	0.0326130			0.00371659
$78$	−0.484837	+	3.37212i	−0.0548970	+	0.381817i
$79$	−5.16787	−	5.96404i	−0.581431	−	0.671007i	0.386481	−	0.922297i	$-0.373690\pi$
$79$	−5.16787	−	5.96404i	−0.581431	−	0.671007i	−0.967912	+	0.251291i	$0.919145\pi$
$80$	−0.654861	+	0.755750i	−0.0732157	+	0.0844954i
$81$	1.60104	+	11.1355i	0.177893	+	1.23728i
$82$	−0.691442	−	4.80908i	−0.0763569	−	0.531074i
$83$	1.37929	+	0.886416i	0.151397	+	0.0972968i	0.614146	−	0.789192i	$-0.289501\pi$
$83$	1.37929	+	0.886416i	0.151397	+	0.0972968i	−0.462749	+	0.886489i	$0.653137\pi$
$84$	0.0185093	+	0.128735i	0.00201953	+	0.0140462i
$85$	−2.59672	+	5.68602i	−0.281654	+	0.616735i
$86$	1.69282	+	3.70677i	0.182542	+	0.399711i
$87$	11.3945	−	7.32281i	1.22162	−	0.785087i
$88$	0.532163			0.0567288
$89$	9.07193	+	2.58845i	0.961623	+	0.274375i
$89$	9.07193	+	2.58845i	0.961623	+	0.274375i
$90$	1.50392			0.158527
$91$	−0.0827605	+	0.0531869i	−0.00867565	+	0.00557550i
$92$	1.74463	+	3.82020i	0.181890	+	0.398283i
$93$	−2.50213	+	5.47890i	−0.259459	+	0.568135i
$94$	1.36236	+	9.47543i	0.140517	+	0.977316i
$95$	−5.34122	−	3.43259i	−0.547998	−	0.352177i
$96$	0.302027	+	2.10064i	0.0308255	+	0.214396i
$97$	−2.27478	−	15.8214i	−0.230969	−	1.60642i	−0.693928	−	0.720044i	$-0.744122\pi$
$97$	−2.27478	−	15.8214i	−0.230969	−	1.60642i	0.462960	−	0.886379i	$-0.346787\pi$
$98$	4.58157	−	5.28741i	0.462808	−	0.534109i
$99$	−0.524105	−	0.604849i	−0.0526745	−	0.0607896i
$100$	−0.142315	+	0.989821i	−0.0142315	+	0.0989821i
$101$	1.01915			0.101410			0.0507048	−	0.998714i	$-0.483853\pi$
$101$	1.01915			0.101410			0.0507048	+	0.998714i	$0.483853\pi$
$102$	5.51087	+	12.0671i	0.545657	+	1.19482i
$103$	−6.14558	−	7.09238i	−0.605542	−	0.698833i	0.367353	−	0.930082i	$-0.380264\pi$
$103$	−6.14558	−	7.09238i	−0.605542	−	0.698833i	−0.972895	+	0.231249i	$0.925719\pi$
$104$	−1.35045	+	0.867879i	−0.132422	+	0.0851026i
$105$	0.0851706	+	0.0982921i	0.00831180	+	0.00959233i
$106$	10.8381	+	6.96522i	1.05269	+	0.676522i
$107$	1.86785	−	12.9912i	0.180572	−	1.25591i	−0.674842	−	0.737963i	$-0.735788\pi$
$107$	1.86785	−	12.9912i	0.180572	−	1.25591i	0.855414	−	0.517945i	$-0.173303\pi$
$108$	−2.07922	+	2.39954i	−0.200073	+	0.230896i
$109$	−3.51150	−	1.03107i	−0.336341	−	0.0987585i	0.109201	−	0.994020i	$-0.465171\pi$
$109$	−3.51150	−	1.03107i	−0.336341	−	0.0987585i	−0.445542	+	0.895261i	$0.646989\pi$
$110$	0.447684	−	0.287709i	0.0426850	−	0.0274320i
$111$	−1.11718	−	2.44629i	−0.106038	−	0.232191i
$112$	−0.0401323	+	0.0463152i	−0.00379215	+	0.00437637i
$113$	13.1407	−	8.44501i	1.23617	−	0.794440i	0.251332	−	0.967901i	$-0.419131\pi$
$113$	13.1407	−	8.44501i	1.23617	−	0.794440i	0.984841	+	0.173461i	$0.0554950\pi$
$114$	−12.9286	+	3.79617i	−1.21087	+	0.355544i
$115$	3.53303	+	2.27054i	0.329457	+	0.211729i
$116$	6.12372	+	1.79809i	0.568573	+	0.166948i
$117$	2.31642	+	0.680161i	0.214153	+	0.0628809i
$118$	−1.52892	−	10.6339i	−0.140749	−	0.978928i
$119$	−0.159137	+	0.348461i	−0.0145880	+	0.0319433i
$120$	1.38977	+	1.60388i	0.126868	+	0.146414i
$121$	10.2827	+	3.01927i	0.934791	+	0.274479i
$122$	−4.00764	+	1.17675i	−0.362835	+	0.106538i
$123$	−10.3110			−0.929711
$124$	−2.72316	+	0.799593i	−0.244547	+	0.0718056i
$125$	0.415415	+	0.909632i	0.0371558	+	0.0813600i
$126$	0.0921657			0.00821078
$127$	0.986938	−	6.86430i	0.0875765	−	0.609108i	−0.898015	−	0.439965i	$-0.854991\pi$
$127$	0.986938	−	6.86430i	0.0875765	−	0.609108i	0.985591	−	0.169143i	$-0.0541001\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$	8.29787	−	2.43647i	0.730586	−	0.214520i
$130$	−0.666857	+	1.46021i	−0.0584872	+	0.128069i
$131$	2.25293	−	4.93323i	0.196840	−	0.431019i	−0.785314	−	0.619097i	$-0.787499\pi$
$131$	2.25293	−	4.93323i	0.196840	−	0.431019i	0.982154	+	0.188079i	$0.0602260\pi$
$132$	0.160728	−	1.11788i	0.0139895	−	0.0972994i
$133$	−0.327330	−	0.210362i	−0.0283831	−	0.0182407i
$134$	−7.77284	−	4.99530i	−0.671471	−	0.431528i
$135$	−0.451857	+	3.14273i	−0.0388897	+	0.270483i
$136$	−2.59672	+	5.68602i	−0.222667	+	0.487572i
$137$	−4.33101	+	9.48360i	−0.370023	+	0.810238i	0.629426	+	0.777060i	$0.283290\pi$
$137$	−4.33101	+	9.48360i	−0.370023	+	0.810238i	−0.999449	+	0.0331779i	$0.989437\pi$
$138$	8.55180	−	2.51103i	0.727977	−	0.213753i
$139$	−12.0406	+	13.8955i	−1.02127	+	1.17861i	−0.0374740	+	0.999298i	$0.511931\pi$
$139$	−12.0406	+	13.8955i	−1.02127	+	1.17861i	−0.983793	+	0.179307i	$0.942614\pi$
$140$	−0.00872159	+	0.0606600i	−0.000737109	+	0.00512671i
$141$	20.3160			1.71091
$142$	−5.51877	−	12.0844i	−0.463125	−	1.01410i
$143$	0.819667	−	0.240676i	0.0685440	−	0.0201263i
$144$	1.50392			0.125326
$145$	6.12372	−	1.79809i	0.508547	−	0.149323i
$146$	2.95553	+	0.867822i	0.244602	+	0.0718215i
$147$	−9.72320	−	11.2212i	−0.801956	−	0.925506i
$148$	0.526415	−	1.15269i	0.0432711	−	0.0947504i
$149$	0.473589	+	3.29389i	0.0387979	+	0.269846i	0.999982	−	0.00606370i	$-0.00193015\pi$
$149$	0.473589	+	3.29389i	0.0387979	+	0.269846i	−0.961184	+	0.275909i	$0.911021\pi$
$150$	2.03628	+	0.597905i	0.166261	+	0.0488187i
$151$	−4.06039	−	1.19224i	−0.330430	−	0.0970230i	0.112310	−	0.993673i	$-0.464175\pi$
$151$	−4.06039	−	1.19224i	−0.330430	−	0.0970230i	−0.442740	+	0.896650i	$0.645993\pi$
$152$	−5.34122	−	3.43259i	−0.433230	−	0.278420i
$153$	9.02004	−	2.64852i	0.729227	−	0.214120i
$154$	0.0274358	−	0.0176319i	0.00221084	−	0.00142082i
$155$	−1.85858	+	2.14491i	−0.149285	+	0.172284i
$156$	1.41523	+	3.09893i	0.113309	+	0.248113i
$157$	17.2990	−	11.1174i	1.38061	−	0.887265i	0.381303	−	0.924450i	$-0.375475\pi$
$157$	17.2990	−	11.1174i	1.38061	−	0.887265i	0.999308	+	0.0371851i	$0.0118391\pi$
$158$	−7.57189	−	2.22331i	−0.602387	−	0.176877i
$159$	17.9048	−	20.6633i	1.41994	−	1.63870i
$160$	−0.142315	+	0.989821i	−0.0112510	+	0.0782523i
$161$	0.216517	+	0.139147i	0.0170640	+	0.0109663i
$162$	7.36717	+	8.50217i	0.578820	+	0.667994i
$163$	−8.86047	+	5.69428i	−0.694006	+	0.446010i	−0.839508	−	0.543348i	$-0.817157\pi$
$163$	−8.86047	+	5.69428i	−0.694006	+	0.446010i	0.145502	+	0.989358i	$0.453520\pi$
$164$	−3.18166	−	3.67184i	−0.248446	−	0.286722i
$165$	−0.469162	−	1.02732i	−0.0365242	−	0.0799768i
$166$	1.63957			0.127255
$167$	1.07060	−	7.44619i	0.0828456	−	0.576204i	−0.905543	−	0.424255i	$-0.860536\pi$
$167$	1.07060	−	7.44619i	0.0828456	−	0.576204i	0.988388	−	0.151949i	$-0.0485549\pi$
$168$	0.0851706	+	0.0982921i	0.00657105	+	0.00758340i
$169$	6.82567	−	7.87724i	0.525051	−	0.605941i
$170$	0.889596	+	6.18728i	0.0682289	+	0.474542i
$171$	1.35890	+	9.45137i	0.103918	+	0.722764i
$172$	3.42812	+	2.20312i	0.261392	+	0.167986i
$173$	0.481655	+	3.34999i	0.0366196	+	0.254695i	0.999905	−	0.0137847i	$-0.00438795\pi$
$173$	0.481655	+	3.34999i	0.0366196	+	0.254695i	−0.963285	+	0.268479i	$0.913479\pi$
$174$	5.62666	−	12.3207i	0.426556	−	0.934028i
$175$	0.0254582	+	0.0557457i	0.00192446	+	0.00421398i
$176$	0.447684	−	0.287709i	0.0337455	−	0.0216869i
$177$	−22.7998			−1.71373
$178$	9.03122	−	2.72711i	0.676918	−	0.204406i
$179$	0.682476			0.0510107			0.0255053	−	0.999675i	$-0.491881\pi$
$179$	0.682476			0.0510107			0.0255053	+	0.999675i	$0.491881\pi$
$180$	1.26518	−	0.813079i	0.0943007	−	0.0606033i
$181$	1.74125	+	3.81280i	0.129426	+	0.283403i	0.963240	−	0.268642i	$-0.0865748\pi$
$181$	1.74125	+	3.81280i	0.129426	+	0.283403i	−0.833814	+	0.552045i	$0.813848\pi$
$182$	−0.0408675	+	0.0894874i	−0.00302930	+	0.00663325i
$183$	1.26151	+	8.77403i	0.0932539	+	0.648595i
$184$	3.53303	+	2.27054i	0.260458	+	0.167386i
$185$	−0.180342	−	1.25430i	−0.0132590	−	0.0922183i
$186$	0.857191	+	5.96189i	0.0628523	+	0.437147i
$187$	2.17839	−	2.51400i	0.159300	−	0.183842i
$188$	6.26890	+	7.23469i	0.457206	+	0.527644i
$189$	−0.0276915	+	0.192599i	−0.00201426	+	0.0140095i
$190$	−6.34912			−0.460614
$191$	7.46677	+	16.3500i	0.540277	+	1.18304i	0.961177	+	0.275934i	$0.0889871\pi$
$191$	7.46677	+	16.3500i	0.540277	+	1.18304i	−0.420900	+	0.907107i	$0.638286\pi$
$192$	1.38977	+	1.60388i	0.100298	+	0.115750i
$193$	12.7578	−	8.19895i	0.918328	−	0.590173i	0.00615562	−	0.999981i	$-0.498041\pi$
$193$	12.7578	−	8.19895i	0.918328	−	0.590173i	0.912172	+	0.409808i	$0.134404\pi$
$194$	−10.4674	−	12.0800i	−0.751514	−	0.867293i
$195$	2.86598	+	1.84185i	0.205237	+	0.131898i
$196$	0.995669	−	6.92503i	0.0711192	−	0.494645i
$197$	5.76355	−	6.65149i	0.410636	−	0.473899i	−0.512326	−	0.858791i	$-0.671216\pi$
$197$	5.76355	−	6.65149i	0.410636	−	0.473899i	0.922962	+	0.384892i	$0.125761\pi$
$198$	−0.767911	−	0.225479i	−0.0545731	−	0.0160241i
$199$	19.2933	−	12.3990i	1.36766	−	0.878945i	0.368941	−	0.929453i	$-0.379720\pi$
$199$	19.2933	−	12.3990i	1.36766	−	0.878945i	0.998724	+	0.0505078i	$0.0160840\pi$
$200$	0.415415	+	0.909632i	0.0293743	+	0.0643207i
$201$	−12.8409	+	14.8192i	−0.905731	+	1.04527i
$202$	0.857367	−	0.550996i	0.0603241	−	0.0387679i
$203$	0.375285	−	0.110194i	0.0263398	−	0.00773407i
$204$	11.1600	+	7.17210i	0.781357	+	0.502148i
$205$	−4.66173	−	1.36881i	−0.325589	−	0.0956017i
$206$	−9.00442	−	2.64394i	−0.627368	−	0.184212i
$207$	−0.898865	−	6.25175i	−0.0624755	−	0.434526i
$208$	−0.666857	+	1.46021i	−0.0462382	+	0.101248i
$209$	2.21262	+	2.55350i	0.153050	+	0.176630i
$210$	0.124791	+	0.0366419i	0.00861138	+	0.00252853i
$211$	12.1357	−	3.56336i	0.835456	−	0.245312i	0.164097	−	0.986444i	$-0.447529\pi$
$211$	12.1357	−	3.56336i	0.835456	−	0.245312i	0.671359	+	0.741132i	$0.265711\pi$
$212$	12.8833			0.884826
$213$	−27.0519	+	7.94314i	−1.85356	+	0.544255i
$214$	−5.45224	−	11.9387i	−0.372707	−	0.816115i
$215$	4.07502			0.277914
$216$	−0.451857	+	3.14273i	−0.0307450	+	0.213836i
$217$	−0.113901	+	0.131448i	−0.00773209	+	0.00892330i
$218$	−3.51150	+	1.03107i	−0.237829	+	0.0698328i
$219$	2.71563	−	5.94641i	0.183506	−	0.401821i
$220$	0.221069	−	0.484073i	0.0149044	−	0.0326362i
$221$	−1.42805	+	9.93230i	−0.0960610	+	0.668119i
$222$	−2.26239	−	1.45395i	−0.151842	−	0.0975829i
$223$	−12.0812	−	7.76414i	−0.809020	−	0.519925i	0.0695281	−	0.997580i	$-0.477851\pi$
$223$	−12.0812	−	7.76414i	−0.809020	−	0.519925i	−0.878548	+	0.477655i	$0.841487\pi$
$224$	−0.00872159	+	0.0606600i	−0.000582736	+	0.00405302i
$225$	0.624750	−	1.36801i	0.0416500	−	0.0912008i
$226$	6.48894	−	14.2088i	0.431638	−	0.945155i
$227$	−10.4872	+	3.07933i	−0.696061	+	0.204382i	−0.610576	−	0.791957i	$-0.709062\pi$
$227$	−10.4872	+	3.07933i	−0.696061	+	0.204382i	−0.0854850	+	0.996339i	$0.527244\pi$
$228$	−8.82384	+	10.1833i	−0.584373	+	0.674403i
$229$	0.683036	−	4.75062i	0.0451363	−	0.313930i	−0.954728	−	0.297479i	$-0.903854\pi$
$229$	0.683036	−	4.75062i	0.0451363	−	0.313930i	0.999865	−	0.0164507i	$-0.00523667\pi$
$230$	4.19972			0.276921
$231$	−0.0287520	−	0.0629581i	−0.00189174	−	0.00414234i
$232$	6.12372	−	1.79809i	0.402042	−	0.118050i
$233$	−3.37283			−0.220962			−0.110481	−	0.993878i	$-0.535239\pi$
$233$	−3.37283			−0.220962			−0.110481	+	0.993878i	$0.535239\pi$
$234$	2.31642	−	0.680161i	0.151429	−	0.0444635i
$235$	9.18510	+	2.69699i	0.599170	+	0.175932i
$236$	−7.03532	−	8.11919i	−0.457960	−	0.528515i
$237$	−6.95729	+	15.2343i	−0.451924	+	0.989576i
$238$	0.0545178	+	0.379180i	0.00353386	+	0.0245786i
$239$	−16.3783	−	4.80909i	−1.05942	−	0.311074i	−0.294804	−	0.955558i	$-0.595254\pi$
$239$	−16.3783	−	4.80909i	−1.05942	−	0.311074i	−0.764618	+	0.644483i	$0.777072\pi$
$240$	2.03628	+	0.597905i	0.131441	+	0.0385946i
$241$	13.7162	+	8.81484i	0.883535	+	0.567814i	0.901865	−	0.432018i	$-0.142198\pi$
$241$	13.7162	+	8.81484i	0.883535	+	0.567814i	−0.0183295	+	0.999832i	$0.505835\pi$
$242$	10.2827	−	3.01927i	0.660997	−	0.194086i
$243$	12.0720	−	7.75822i	0.774421	−	0.497690i
$244$	−2.73524	+	3.15664i	−0.175106	+	0.202083i
$245$	−2.90634	−	6.36401i	−0.185680	−	0.406582i
$246$	−8.67416	+	5.57454i	−0.553044	+	0.355420i
$247$	−9.77926	−	2.87145i	−0.622239	−	0.182706i
$248$	−1.85858	+	2.14491i	−0.118020	+	0.136202i
$249$	0.495193	−	3.44414i	0.0313816	−	0.218263i
$250$	0.841254	+	0.540641i	0.0532055	+	0.0341931i
$251$	13.0111	+	15.0156i	0.821255	+	0.947779i	0.999343	−	0.0362354i	$-0.0115366\pi$
$251$	13.0111	+	15.0156i	0.821255	+	0.947779i	−0.178088	+	0.984015i	$0.556991\pi$
$252$	0.0775348	−	0.0498286i	0.00488423	−	0.00313890i
$253$	−1.46357	−	1.68905i	−0.0920140	−	0.106190i
$254$	−2.88086	−	6.30820i	−0.180761	−	0.395811i
$255$	13.2659			0.830745
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	18.6315	+	21.5019i	1.16220	+	1.34125i	0.929553	+	0.368688i	$0.120193\pi$
$257$	18.6315	+	21.5019i	1.16220	+	1.34125i	0.232647	+	0.972561i	$0.425261\pi$
$258$	5.66335	−	6.53586i	0.352585	−	0.406905i
$259$	−0.0110520	−	0.0768685i	−0.000686740	−	0.00477638i
$260$	0.228455	+	1.58894i	0.0141682	+	0.0985419i
$261$	−8.07466	−	5.18927i	−0.499809	−	0.321208i
$262$	−0.771820	−	5.36813i	−0.0476832	−	0.331644i
$263$	2.99745	−	6.56349i	0.184831	−	0.404722i	−0.794422	−	0.607366i	$-0.792226\pi$
$263$	2.99745	−	6.56349i	0.184831	−	0.404722i	0.979253	+	0.202644i	$0.0649534\pi$
$264$	−0.469162	−	1.02732i	−0.0288749	−	0.0632272i
$265$	10.8381	−	6.96522i	0.665779	−	0.427870i
$266$	−0.389098			−0.0238571
$267$	−3.00102	−	19.7950i	−0.183660	−	1.21144i
$268$	−9.23960			−0.564398
$269$	−17.3194	+	11.1305i	−1.05598	+	0.678639i	−0.948889	−	0.315610i	$-0.897791\pi$
$269$	−17.3194	+	11.1305i	−1.05598	+	0.678639i	−0.107094	+	0.994249i	$0.534155\pi$
$270$	1.31896	+	2.88813i	0.0802696	+	0.175766i
$271$	−2.57650	+	5.64174i	−0.156511	+	0.342711i	−0.971602	−	0.236622i	$-0.923960\pi$
$271$	−2.57650	+	5.64174i	−0.156511	+	0.342711i	0.815091	+	0.579333i	$0.196687\pi$
$272$	0.889596	+	6.18728i	0.0539397	+	0.375159i
$273$	0.175638	+	0.112876i	0.0106301	+	0.00683154i
$274$	1.48374	+	10.3196i	0.0896360	+	0.623432i
$275$	−0.0757347	−	0.526747i	−0.00456698	−	0.0317640i
$276$	5.83666	−	6.73587i	0.351326	−	0.405452i
$277$	−6.67310	−	7.70117i	−0.400948	−	0.462719i	0.518991	−	0.854780i	$-0.326308\pi$
$277$	−6.67310	−	7.70117i	−0.400948	−	0.462719i	−0.919939	+	0.392061i	$0.871762\pi$
$278$	−2.61666	+	18.1993i	−0.156937	+	1.09152i
$279$	4.26831			0.255537
$280$	0.0254582	+	0.0557457i	0.00152142	+	0.00333144i
$281$	−3.05261	−	3.52290i	−0.182104	−	0.210159i	0.657357	−	0.753579i	$-0.271674\pi$
$281$	−3.05261	−	3.52290i	−0.182104	−	0.210159i	−0.839461	+	0.543421i	$0.817129\pi$
$282$	17.0909	−	10.9836i	1.01775	−	0.654066i
$283$	9.52600	+	10.9936i	0.566262	+	0.653501i	0.964594	−	0.263740i	$-0.0849563\pi$
$283$	9.52600	+	10.9936i	0.566262	+	0.653501i	−0.398332	+	0.917241i	$0.630411\pi$
$284$	−11.1760	−	7.18239i	−0.663174	−	0.426196i
$285$	−1.91760	+	13.3372i	−0.113589	+	0.790029i
$286$	0.559428	−	0.645615i	0.0330797	−	0.0381760i
$287$	−0.285688	−	0.0838857i	−0.0168637	−	0.00495162i
$288$	1.26518	−	0.813079i	0.0745512	−	0.0479112i
$289$	9.16977	+	20.0790i	0.539398	+	1.18112i
$290$	4.17948	−	4.82338i	0.245428	−	0.283239i
$291$	−28.5372	+	18.3397i	−1.67288	+	1.07509i
$292$	2.95553	−	0.867822i	0.172959	−	0.0507855i
$293$	14.0210	+	9.01076i	0.819116	+	0.526414i	0.881802	−	0.471619i	$-0.156330\pi$
$293$	14.0210	+	9.01076i	0.819116	+	0.526414i	−0.0626860	+	0.998033i	$0.519967\pi$
$294$	−14.2463	−	4.18309i	−0.830861	−	0.243963i
$295$	−10.3081	−	3.02672i	−0.600158	−	0.176222i
$296$	−0.180342	−	1.25430i	−0.0104822	−	0.0729050i
$297$	0.701904	−	1.53696i	0.0407286	−	0.0891832i
$298$	2.17922	+	2.51495i	0.126239	+	0.145687i
$299$	6.46864	+	1.89936i	0.374091	+	0.109843i
$300$	2.03628	−	0.597905i	0.117565	−	0.0345201i
$301$	0.249732			0.0143943
$302$	−4.06039	+	1.19224i	−0.233649	+	0.0686056i
$303$	−0.898498	−	1.96744i	−0.0516174	−	0.113026i
$304$	−6.34912			−0.364147
$305$	−0.594425	+	4.13432i	−0.0340367	+	0.236730i
$306$	6.15624	−	7.10468i	0.351929	−	0.406148i
$307$	−7.09544	+	2.08341i	−0.404958	+	0.118906i	−0.477867	−	0.878432i	$-0.658590\pi$
$307$	−7.09544	+	2.08341i	−0.404958	+	0.118906i	0.0729089	+	0.997339i	$0.476772\pi$
$308$	0.0135479	−	0.0296658i	0.000771965	−	0.00169037i
$309$	−8.27354	+	18.1165i	−0.470665	+	1.03061i
$310$	−0.403908	+	2.80924i	−0.0229404	+	0.159554i
$311$	13.9335	+	8.95454i	0.790098	+	0.507765i	0.872371	−	0.488845i	$-0.162581\pi$
$311$	13.9335	+	8.95454i	0.790098	+	0.507765i	−0.0822727	+	0.996610i	$0.526218\pi$
$312$	2.86598	+	1.84185i	0.162254	+	0.104274i
$313$	−1.42115	+	9.88434i	−0.0803283	+	0.558696i	0.909421	+	0.415878i	$0.136526\pi$
$313$	−1.42115	+	9.88434i	−0.0803283	+	0.558696i	−0.989749	+	0.142818i	$0.954384\pi$
$314$	8.54233	−	18.7051i	0.482072	−	1.05559i
$315$	0.0382870	−	0.0838369i	0.00215723	−	0.00472367i
$316$	−7.57189	+	2.22331i	−0.425952	+	0.125071i
$317$	−1.22117	+	1.40931i	−0.0685878	+	0.0791545i	−0.789006	−	0.614385i	$-0.789404\pi$
$317$	−1.22117	+	1.40931i	−0.0685878	+	0.0791545i	0.720419	+	0.693539i	$0.243950\pi$
$318$	3.89109	−	27.0631i	0.218201	−	1.51762i
$319$	−3.39640			−0.190162
$320$	0.415415	+	0.909632i	0.0232224	+	0.0508500i
$321$	−26.7257	+	7.84739i	−1.49169	+	0.437998i
$322$	0.257375			0.0143429
$323$	−38.0801	+	11.1813i	−2.11883	+	0.622146i
$324$	10.7943	+	3.16949i	0.599682	+	0.176083i
$325$	1.05123	+	1.21319i	0.0583120	+	0.0672956i
$326$	−4.37534	+	9.58067i	−0.242328	+	0.530624i
$327$	1.10534	+	7.68781i	0.0611255	+	0.425137i
$328$	−4.66173	−	1.36881i	−0.257401	−	0.0755797i
$329$	0.562898	+	0.165282i	0.0310336	+	0.00911227i
$330$	−0.950095	−	0.610589i	−0.0523010	−	0.0336118i
$331$	−19.4234	+	5.70321i	−1.06760	+	0.313477i	−0.767910	−	0.640558i	$-0.778703\pi$
$331$	−19.4234	+	5.70321i	−1.06760	+	0.313477i	−0.299695	+	0.954035i	$0.596885\pi$
$332$	1.37929	−	0.886416i	0.0756984	−	0.0486484i
$333$	−1.24801	+	1.44028i	−0.0683907	+	0.0789271i
$334$	−3.12507	−	6.84295i	−0.170996	−	0.374429i
$335$	−7.77284	+	4.99530i	−0.424676	+	0.272923i
$336$	0.124791	+	0.0366419i	0.00680790	+	0.00199898i
$337$	−1.12448	+	1.29772i	−0.0612542	+	0.0706911i	−0.785550	−	0.618799i	$-0.787620\pi$
$337$	−1.12448	+	1.29772i	−0.0612542	+	0.0706911i	0.724295	+	0.689490i	$0.242165\pi$
$338$	1.48336	−	10.3170i	0.0806841	−	0.561170i
$339$	−27.8878	−	17.9224i	−1.51466	−	0.973410i
$340$	4.09347	+	4.72412i	0.222000	+	0.256201i
$341$	1.27059	−	0.816556i	0.0688061	−	0.0442190i
$342$	6.25297	+	7.21632i	0.338122	+	0.390214i
$343$	−0.356319	−	0.780230i	−0.0192394	−	0.0421285i
$344$	4.07502			0.219710
$345$	1.26843	−	8.82211i	0.0682899	−	0.474966i
$346$	2.21633	+	2.55779i	0.119151	+	0.137507i
$347$	17.3301	−	20.0001i	0.930331	−	1.07366i	−0.0667853	−	0.997767i	$-0.521274\pi$
$347$	17.3301	−	20.0001i	0.930331	−	1.07366i	0.997116	−	0.0758916i	$-0.0241803\pi$
$348$	−1.92761	−	13.4068i	−0.103331	−	0.718681i
$349$	−2.12333	−	14.7681i	−0.113659	−	0.790519i	−0.964308	−	0.264784i	$-0.914699\pi$
$349$	−2.12333	−	14.7681i	−0.113659	−	0.790519i	0.850648	−	0.525735i	$-0.176210\pi$
$350$	0.0515552	+	0.0331325i	0.00275574	+	0.00177101i
$351$	0.725356	+	5.04496i	0.0387167	+	0.269280i
$352$	0.221069	−	0.484073i	0.0117830	−	0.0258012i
$353$	3.07649	+	6.73657i	0.163745	+	0.358551i	0.973663	−	0.227991i	$-0.0732158\pi$
$353$	3.07649	+	6.73657i	0.163745	+	0.358551i	−0.809918	+	0.586543i	$0.800489\pi$
$354$	−19.1804	+	12.3265i	−1.01943	+	0.655145i
$355$	−13.2850			−0.705092
$356$	6.12315	−	7.17684i	0.324526	−	0.380372i
$357$	0.812986			0.0430278
$358$	0.574136	−	0.368975i	0.0303440	−	0.0195009i
$359$	12.4994	+	27.3699i	0.659695	+	1.44453i	0.882806	+	0.469738i	$0.155651\pi$
$359$	12.4994	+	27.3699i	0.659695	+	1.44453i	−0.223111	+	0.974793i	$0.571621\pi$
$360$	0.624750	−	1.36801i	0.0329272	−	0.0721005i
$361$	−3.03292	−	21.0944i	−0.159627	−	1.11023i
$362$	3.52619	+	2.26614i	0.185332	+	0.119106i
$363$	−3.23676	−	22.5122i	−0.169886	−	1.18158i
$364$	0.0140006	+	0.0973762i	0.000733830	+	0.00510390i
$365$	2.01717	−	2.32794i	0.105584	−	0.121850i
$366$	5.80485	+	6.69916i	0.303424	+	0.350171i
$367$	1.59484	−	11.0924i	0.0832502	−	0.579018i	−0.904911	−	0.425600i	$-0.860063\pi$
$367$	1.59484	−	11.0924i	0.0832502	−	0.579018i	0.988161	−	0.153418i	$-0.0490280\pi$
$368$	4.19972			0.218926
$369$	3.03537	+	6.64653i	0.158015	+	0.346005i
$370$	−0.829842	−	0.957688i	−0.0431414	−	0.0497878i
$371$	0.664199	−	0.426855i	0.0344835	−	0.0221612i
$372$	3.94436	+	4.55203i	0.204505	+	0.236012i
$373$	17.1271	+	11.0069i	0.886809	+	0.569918i	0.902851	−	0.429954i	$-0.141470\pi$
$373$	17.1271	+	11.0069i	0.886809	+	0.569918i	−0.0160417	+	0.999871i	$0.505106\pi$
$374$	0.473410	−	3.29264i	0.0244795	−	0.170258i
$375$	1.38977	−	1.60388i	0.0717676	−	0.0828242i
$376$	9.18510	+	2.69699i	0.473685	+	0.139087i
$377$	8.61888	−	5.53902i	0.443895	−	0.285274i
$378$	0.0808311	+	0.176995i	0.00415750	+	0.00910366i
$379$	−9.54777	+	11.0187i	−0.490436	+	0.565993i	−0.945982	−	0.324219i	$-0.894899\pi$
$379$	−9.54777	+	11.0187i	−0.490436	+	0.565993i	0.455546	+	0.890212i	$0.349444\pi$
$380$	−5.34122	+	3.43259i	−0.273999	+	0.176088i
$381$	−14.1214	+	4.14641i	−0.723459	+	0.212427i
$382$	15.1209	+	9.71761i	0.773653	+	0.497196i
$383$	2.67870	+	0.786539i	0.136875	+	0.0401902i	0.349453	−	0.936954i	$-0.386368\pi$
$383$	2.67870	+	0.786539i	0.136875	+	0.0401902i	−0.212577	+	0.977144i	$0.568186\pi$
$384$	2.03628	+	0.597905i	0.103913	+	0.0305117i
$385$	−0.00464131	−	0.0322810i	−0.000236543	−	0.00164519i
$386$	6.29987	−	13.7948i	0.320655	−	0.702136i
$387$	−4.01331	−	4.63160i	−0.204008	−	0.235438i
$388$	−15.3367	−	4.50325i	−0.778601	−	0.228618i
$389$	−11.5127	+	3.38044i	−0.583719	+	0.171395i	−0.560242	−	0.828329i	$-0.689292\pi$
$389$	−11.5127	+	3.38044i	−0.583719	+	0.171395i	−0.0234769	+	0.999724i	$0.507474\pi$
$390$	3.40679			0.172510
$391$	25.1886	−	7.39605i	1.27384	−	0.374034i
$392$	−2.90634	−	6.36401i	−0.146793	−	0.321431i
$393$	−11.5096			−0.580584
$394$	1.25254	−	8.71160i	0.0631020	−	0.438884i
$395$	−5.16787	+	5.96404i	−0.260024	+	0.300083i
$396$	−0.767911	+	0.225479i	−0.0385890	+	0.0113307i
$397$	−16.4218	+	35.9586i	−0.824184	+	1.80471i	−0.297271	+	0.954793i	$0.596076\pi$
$397$	−16.4218	+	35.9586i	−0.824184	+	1.80471i	−0.526914	+	0.849919i	$0.676651\pi$
$398$	9.52712	−	20.8615i	0.477551	−	1.04569i
$399$	−0.117518	+	0.817356i	−0.00588326	+	0.0409190i
$400$	0.841254	+	0.540641i	0.0420627	+	0.0270320i
$401$	−8.44124	−	5.42485i	−0.421535	−	0.270904i	0.312630	−	0.949875i	$-0.398790\pi$
$401$	−8.44124	−	5.42485i	−0.421535	−	0.270904i	−0.734165	+	0.678971i	$0.762426\pi$
$402$	−2.79061	+	19.4091i	−0.139183	+	0.968037i
$403$	−1.89263	+	4.14427i	−0.0942784	+	0.206441i
$404$	0.423372	−	0.927055i	0.0210635	−	0.0461227i
$405$	10.7943	−	3.16949i	0.536372	−	0.157493i
$406$	0.256134	−	0.295595i	0.0127117	−	0.0146701i
$407$	−0.0959713	+	0.667495i	−0.00475712	+	0.0330865i
$408$	13.2659			0.656762
$409$	−8.04563	−	17.6175i	−0.397831	−	0.871128i	−0.997486	−	0.0708694i	$-0.977423\pi$
$409$	−8.04563	−	17.6175i	−0.397831	−	0.871128i	0.599655	−	0.800259i	$-0.295305\pi$
$410$	−4.66173	+	1.36881i	−0.230226	+	0.0676006i
$411$	22.1260			1.09139
$412$	−9.00442	+	2.64394i	−0.443616	+	0.130257i
$413$	−0.631717	−	0.185489i	−0.0310847	−	0.00912731i
$414$	−4.13612	−	4.77334i	−0.203279	−	0.234597i
$415$	0.681100	−	1.49140i	0.0334339	−	0.0732100i
$416$	0.228455	+	1.58894i	0.0112009	+	0.0779042i
$417$	37.4399	+	10.9933i	1.83344	+	0.538347i
$418$	3.24191	+	0.951910i	0.158567	+	0.0465594i
$419$	−32.5436	−	20.9145i	−1.58986	−	1.02174i	−0.971860	−	0.235559i	$-0.924308\pi$
$419$	−32.5436	−	20.9145i	−1.58986	−	1.02174i	−0.617997	−	0.786180i	$-0.712056\pi$
$420$	0.124791	−	0.0366419i	0.00608917	−	0.00178794i
$421$	5.30831	−	3.41144i	0.258711	−	0.166264i	−0.404856	−	0.914381i	$-0.632678\pi$
$421$	5.30831	−	3.41144i	0.258711	−	0.166264i	0.663567	+	0.748117i	$0.269042\pi$
$422$	8.28270	−	9.55875i	0.403196	−	0.465313i
$423$	−5.98065	−	13.0958i	−0.290789	−	0.636739i
$424$	10.8381	−	6.96522i	0.526344	−	0.338261i
$425$	5.99769	+	1.76108i	0.290931	+	0.0854250i
$426$	−18.4631	+	21.3075i	−0.894539	+	1.03235i
$427$	−0.0364286	+	0.253367i	−0.00176290	+	0.0122613i
$428$	−11.0413	−	7.09580i	−0.533701	−	0.342989i
$429$	−1.18724	−	1.37015i	−0.0573206	−	0.0661516i
$430$	3.42812	−	2.20312i	0.165319	−	0.106244i
$431$	14.6969	+	16.9611i	0.707924	+	0.816988i	0.989800	−	0.142463i	$-0.0455021\pi$
$431$	14.6969	+	16.9611i	0.707924	+	0.816988i	−0.281876	+	0.959451i	$0.590957\pi$
$432$	1.31896	+	2.88813i	0.0634587	+	0.138955i
$433$	−3.63816			−0.174839			−0.0874193	−	0.996172i	$-0.527862\pi$
$433$	−3.63816			−0.174839			−0.0874193	+	0.996172i	$0.527862\pi$
$434$	−0.0247530	+	0.172161i	−0.00118818	+	0.00826399i
$435$	−8.86988	−	10.2364i	−0.425278	−	0.490797i
$436$	−2.39662	+	2.76585i	−0.114777	+	0.132460i
$437$	3.79476	+	26.3931i	0.181528	+	1.26255i
$438$	−0.930335	−	6.47062i	−0.0444531	−	0.309178i
$439$	30.9545	+	19.8933i	1.47738	+	0.949454i	0.997392	+	0.0721785i	$0.0229951\pi$
$439$	30.9545	+	19.8933i	1.47738	+	0.949454i	0.479987	+	0.877275i	$0.340641\pi$
$440$	−0.0757347	−	0.526747i	−0.00361051	−	0.0251117i
$441$	−4.37090	+	9.57094i	−0.208138	+	0.455759i
$442$	4.16846	+	9.12765i	0.198273	+	0.434158i
$443$	5.09053	−	3.27148i	0.241858	−	0.155433i	−0.414097	−	0.910233i	$-0.635902\pi$
$443$	5.09053	−	3.27148i	0.241858	−	0.155433i	0.655955	+	0.754800i	$0.272266\pi$
$444$	−2.68931			−0.127629
$445$	1.27103	−	9.34797i	0.0602527	−	0.443136i
$446$	−14.3610			−0.680013
$447$	5.94119	−	3.81817i	0.281009	−	0.180593i
$448$	0.0254582	+	0.0557457i	0.00120279	+	0.00263374i
$449$	−6.38291	+	13.9766i	−0.301228	+	0.659597i	−0.998354	−	0.0573513i	$-0.981734\pi$
$449$	−6.38291	+	13.9766i	−0.301228	+	0.659597i	0.697126	+	0.716949i	$0.254462\pi$
$450$	−0.214030	−	1.48861i	−0.0100895	−	0.0701737i
$451$	2.17509	+	1.39785i	0.102421	+	0.0658220i
$452$	−2.22301	−	15.4614i	−0.104562	−	0.727242i
$453$	1.27812	+	8.88952i	0.0600513	+	0.417666i
$454$	−7.15760	+	8.26031i	−0.335923	+	0.387676i
$455$	0.0644236	+	0.0743488i	0.00302023	+	0.00348553i
$456$	−1.91760	+	13.3372i	−0.0898001	+	0.624573i
$457$	−6.85702			−0.320758			−0.160379	−	0.987056i	$-0.551272\pi$
$457$	−6.85702			−0.320758			−0.160379	+	0.987056i	$0.551272\pi$
$458$	−1.99377	−	4.36575i	−0.0931628	−	0.203998i
$459$	12.9970	+	14.9993i	0.606647	+	0.700108i
$460$	3.53303	−	2.27054i	0.164728	−	0.105864i
$461$	−13.3801	−	15.4415i	−0.623174	−	0.719181i	0.353133	−	0.935573i	$-0.385116\pi$
$461$	−13.3801	−	15.4415i	−0.623174	−	0.719181i	−0.976306	+	0.216393i	$0.930571\pi$
$462$	−0.0582254	−	0.0374192i	−0.00270889	−	0.00174090i
$463$	3.80861	−	26.4895i	0.177001	−	1.23107i	−0.686653	−	0.726985i	$-0.740921\pi$
$463$	3.80861	−	26.4895i	0.177001	−	1.23107i	0.863654	−	0.504084i	$-0.168170\pi$
$464$	4.17948	−	4.82338i	0.194028	−	0.223920i
$465$	5.77922	+	1.69693i	0.268005	+	0.0786933i
$466$	−2.83741	+	1.82349i	−0.131440	+	0.0844716i
$467$	−10.9411	−	23.9577i	−0.506295	−	1.10863i	−0.974372	−	0.224944i	$-0.927780\pi$
$467$	−10.9411	−	23.9577i	−0.506295	−	1.10863i	0.468076	−	0.883688i	$-0.344947\pi$
$468$	1.58097	−	1.82454i	0.0730804	−	0.0843392i
$469$	−0.476349	+	0.306131i	−0.0219958	+	0.0141358i
$470$	9.18510	−	2.69699i	0.423677	−	0.124403i
$471$	−36.7127	−	23.5938i	−1.69163	−	1.08715i
$472$	−10.3081	−	3.02672i	−0.474467	−	0.139316i
$473$	−2.08073	−	0.610958i	−0.0956722	−	0.0280919i
$474$	2.38346	+	16.5773i	0.109476	+	0.761422i
$475$	−2.63752	+	5.77536i	−0.121018	+	0.264992i
$476$	0.250863	+	0.289512i	0.0114983	+	0.0132697i
$477$	−18.5905	−	5.45867i	−0.851202	−	0.249935i
$478$	−16.3783	+	4.80909i	−0.749125	+	0.219963i
$479$	−11.2152			−0.512437			−0.256219	−	0.966619i	$-0.582477\pi$
$479$	−11.2152			−0.512437			−0.256219	+	0.966619i	$0.582477\pi$
$480$	2.03628	−	0.597905i	0.0929429	−	0.0272905i
$481$	−0.845043	−	1.85039i	−0.0385307	−	0.0843704i
$482$	16.3044			0.742646
$483$	0.0777340	−	0.540652i	0.00353702	−	0.0246005i
$484$	7.01801	−	8.09922i	0.319001	−	0.368146i
$485$	−15.3367	+	4.50325i	−0.696402	+	0.204482i
$486$	5.96123	−	13.0533i	0.270407	−	0.592108i
$487$	7.91958	−	17.3415i	0.358870	−	0.785817i	−0.640963	−	0.767572i	$-0.721465\pi$
$487$	7.91958	−	17.3415i	0.358870	−	0.785817i	0.999834	−	0.0182450i	$-0.00580788\pi$
$488$	−0.594425	+	4.13432i	−0.0269084	+	0.187152i
$489$	18.8041	+	12.0846i	0.850350	+	0.546487i
$490$	−5.88562	−	3.78246i	−0.265885	−	0.170874i
$491$	0.234176	−	1.62873i	0.0105682	−	0.0735035i	−0.983855	−	0.178968i	$-0.942724\pi$
$491$	0.234176	−	1.62873i	0.0105682	−	0.0735035i	0.994423	+	0.105465i	$0.0336331\pi$
$492$	−4.28334	+	9.37921i	−0.193108	+	0.422847i
$493$	16.5729	−	36.2896i	0.746406	−	1.63440i
$494$	−9.77926	+	2.87145i	−0.439990	+	0.129193i
$495$	−0.524105	+	0.604849i	−0.0235568	+	0.0271859i
$496$	−0.403908	+	2.80924i	−0.0181360	+	0.126139i
$497$	−0.814152			−0.0365197
$498$	−1.44546	−	3.16512i	−0.0647726	−	0.141832i
$499$	12.4554	−	3.65722i	0.557578	−	0.163720i	0.00921135	−	0.999958i	$-0.497068\pi$
$499$	12.4554	−	3.65722i	0.557578	−	0.163720i	0.548367	+	0.836238i	$0.315250\pi$
$500$	1.00000			0.0447214
$501$	−15.3184	+	4.49790i	−0.684377	+	0.200951i
$502$	19.0637	+	5.59762i	0.850856	+	0.249834i
$503$	20.7761	+	23.9768i	0.926358	+	1.06907i	0.997433	+	0.0716036i	$0.0228117\pi$
$503$	20.7761	+	23.9768i	0.926358	+	1.06907i	−0.0710747	+	0.997471i	$0.522643\pi$
$504$	0.0382870	−	0.0838369i	0.00170544	−	0.00373439i
$505$	−0.145041	−	1.00878i	−0.00645423	−	0.0448901i
$506$	−2.14441	−	0.629655i	−0.0953305	−	0.0279916i
$507$	−21.2243	−	6.23201i	−0.942604	−	0.276773i
$508$	−5.83400	−	3.74928i	−0.258842	−	0.166348i
$509$	−16.0122	+	4.70160i	−0.709727	+	0.208395i	−0.616620	−	0.787261i	$-0.711498\pi$
$509$	−16.0122	+	4.70160i	−0.709727	+	0.208395i	−0.0931078	+	0.995656i	$0.529680\pi$
$510$	11.1600	−	7.17210i	0.494174	−	0.317586i
$511$	0.123620	−	0.142665i	0.00546862	−	0.00631113i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$	−16.9587	+	10.8987i	−0.748743	+	0.481188i
$514$	27.2986	+	8.01559i	1.20409	+	0.353552i
$515$	−6.14558	+	7.09238i	−0.270807	+	0.312528i
$516$	1.23076	−	8.56015i	0.0541814	−	0.376840i
$517$	−4.28562	−	2.75420i	−0.188482	−	0.121130i
$518$	−0.0508558	−	0.0586908i	−0.00223448	−	0.00257872i
$519$	6.04238	−	3.88320i	0.265231	−	0.170454i
$520$	1.05123	+	1.21319i	0.0460997	+	0.0532019i
$521$	−9.49443	−	20.7899i	−0.415959	−	0.910823i	−0.995400	−	0.0958084i	$-0.969456\pi$
$521$	−9.49443	−	20.7899i	−0.415959	−	0.910823i	0.579441	−	0.815014i	$-0.303271\pi$
$522$	−9.59837			−0.420109
$523$	2.77930	−	19.3304i	0.121530	−	0.845261i	−0.834294	−	0.551320i	$-0.814124\pi$
$523$	2.77930	−	19.3304i	0.121530	−	0.845261i	0.955824	−	0.293940i	$-0.0949667\pi$
$524$	−3.55153	−	4.09868i	−0.155149	−	0.179052i
$525$	0.0851706	−	0.0982921i	0.00371715	−	0.00428982i
$526$	−1.02688	−	7.14211i	−0.0447741	−	0.311411i
$527$	2.52479	+	17.5603i	0.109981	+	0.764938i
$528$	−0.950095	−	0.610589i	−0.0413476	−	0.0265725i
$529$	0.763142	+	5.30777i	0.0331801	+	0.230773i
$530$	5.35190	−	11.7190i	0.232472	−	0.509042i
$531$	6.71184	+	14.6969i	0.291269	+	0.637790i
$532$	−0.327330	+	0.210362i	−0.0141916	+	0.00912036i
$533$	−7.79930			−0.337825
$534$	−13.2266	−	15.0301i	−0.572371	−	0.650418i
$535$	−13.1248			−0.567435
$536$	−7.77284	+	4.99530i	−0.335736	+	0.215764i
$537$	−0.601679	−	1.31749i	−0.0259644	−	0.0568540i
$538$	−8.55241	+	18.7272i	−0.368721	+	0.807385i
$539$	0.529859	+	3.68525i	0.0228226	+	0.158735i
$540$	2.67102	+	1.71656i	0.114943	+	0.0738691i
$541$	4.35609	+	30.2972i	0.187283	+	1.30258i	0.839005	+	0.544123i	$0.183138\pi$
$541$	4.35609	+	30.2972i	0.187283	+	1.30258i	−0.651723	+	0.758457i	$0.725953\pi$
$542$	0.882669	+	6.13909i	0.0379139	+	0.263697i
$543$	5.82536	−	6.72282i	0.249990	−	0.288504i
$544$	4.09347	+	4.72412i	0.175506	+	0.202545i
$545$	−0.520836	+	3.62249i	−0.0223102	+	0.155171i
$546$	0.208781			0.00893501
$547$	−4.94861	−	10.8359i	−0.211587	−	0.463312i	0.773846	−	0.633374i	$-0.218330\pi$
$547$	−4.94861	−	10.8359i	−0.211587	−	0.463312i	−0.985433	+	0.170062i	$0.945603\pi$
$548$	6.82742	+	7.87926i	0.291653	+	0.336585i
$549$	5.28443	−	3.39610i	0.225534	−	0.144942i
$550$	−0.348493	−	0.402182i	−0.0148598	−	0.0171491i
$551$	34.0890	+	21.9077i	1.45224	+	0.933298i
$552$	1.26843	−	8.82211i	0.0539879	−	0.375494i
$553$	−0.316706	+	0.365499i	−0.0134677	+	0.0155426i
$554$	−9.77734	−	2.87089i	−0.415399	−	0.121972i
$555$	−2.26239	+	1.45395i	−0.0960333	+	0.0617169i
$556$	7.63801	+	16.7249i	0.323924	+	0.709294i
$557$	−28.1279	+	32.4613i	−1.19182	+	1.37543i	−0.282533	+	0.959258i	$0.591175\pi$
$557$	−28.1279	+	32.4613i	−1.19182	+	1.37543i	−0.909285	+	0.416174i	$0.863371\pi$
$558$	3.59073	−	2.30762i	0.152008	−	0.0976895i
$559$	6.27656	−	1.84296i	0.265470	−	0.0779491i
$560$	0.0515552	+	0.0331325i	0.00217860	+	0.00140010i
$561$	−6.77368	−	1.98893i	−0.285985	−	0.0839728i
$562$	−4.47265	−	1.31329i	−0.188667	−	0.0553977i
$563$	5.45516	+	37.9415i	0.229907	+	1.59904i	0.698489	+	0.715621i	$0.253856\pi$
$563$	5.45516	+	37.9415i	0.229907	+	1.59904i	−0.468581	+	0.883420i	$0.655235\pi$
$564$	8.43956	−	18.4801i	0.355369	−	0.778150i
$565$	−10.2292	−	11.8051i	−0.430344	−	0.496644i
$566$	13.9574	+	4.09825i	0.586672	+	0.172262i
$567$	0.661514	−	0.194238i	0.0277810	−	0.00815723i
$568$	−13.2850			−0.557424
$569$	−22.1711	+	6.51002i	−0.929461	+	0.272914i	−0.711211	−	0.702979i	$-0.751853\pi$
$569$	−22.1711	+	6.51002i	−0.929461	+	0.272914i	−0.218250	+	0.975893i	$0.570035\pi$
$570$	5.59746	+	12.2567i	0.234452	+	0.513378i
$571$	−25.4332			−1.06435			−0.532174	−	0.846635i	$-0.678625\pi$
$571$	−25.4332			−1.06435			−0.532174	+	0.846635i	$0.678625\pi$
$572$	0.121575	−	0.845576i	0.00508332	−	0.0353553i
$573$	24.9801	−	28.8286i	1.04356	−	1.20433i
$574$	−0.285688	+	0.0838857i	−0.0119244	+	0.00350132i
$575$	1.74463	−	3.82020i	0.0727560	−	0.159313i
$576$	0.624750	−	1.36801i	0.0260312	−	0.0570005i
$577$	2.86084	−	19.8976i	0.119098	−	0.828347i	−0.839454	−	0.543431i	$-0.817125\pi$
$577$	2.86084	−	19.8976i	0.119098	−	0.828347i	0.958552	−	0.284916i	$-0.0919658\pi$
$578$	18.5696	+	11.9340i	0.772395	+	0.496388i
$579$	−27.0752	−	17.4002i	−1.12521	−	0.723126i
$580$	0.908288	−	6.31728i	0.0377146	−	0.262311i
$581$	0.0417404	−	0.0913987i	0.00173168	−	0.00379186i
$582$	−14.0918	+	30.8567i	−0.584124	+	1.27905i
$583$	−6.57828	+	1.93156i	−0.272445	+	0.0799970i
$584$	2.01717	−	2.32794i	0.0834711	−	0.0963308i
$585$	0.343578	−	2.38963i	0.0142052	−	0.0987992i
$586$	16.6668			0.688500
$587$	17.2357	+	37.7409i	0.711394	+	1.55773i	0.825586	+	0.564276i	$0.190845\pi$
$587$	17.2357	+	37.7409i	0.711394	+	1.55773i	−0.114193	+	0.993459i	$0.536428\pi$
$588$	−14.2463	+	4.18309i	−0.587507	+	0.172508i
$589$	−18.0196			−0.742486
$590$	−10.3081	+	3.02672i	−0.424376	+	0.124608i
$591$	−17.9217	−	5.26227i	−0.737199	−	0.216461i
$592$	−0.829842	−	0.957688i	−0.0341063	−	0.0393607i
$593$	12.6920	−	27.7916i	0.521198	−	1.14127i	−0.447785	−	0.894141i	$-0.647787\pi$
$593$	12.6920	−	27.7916i	0.521198	−	1.14127i	0.968984	−	0.247124i	$-0.0794856\pi$
$594$	−0.240462	−	1.67245i	−0.00986626	−	0.0686214i
$595$	0.367561	+	0.107926i	0.0150685	+	0.00442452i
$596$	3.19296	+	0.937538i	0.130789	+	0.0384030i
$597$	−40.9451	−	26.3138i	−1.67577	−	1.07695i
$598$	6.46864	−	1.89936i	0.264522	−	0.0776707i
$599$	−21.9676	+	14.1178i	−0.897574	+	0.576836i	−0.906070	−	0.423128i	$-0.860932\pi$
$599$	−21.9676	+	14.1178i	−0.897574	+	0.576836i	0.00849600	+	0.999964i	$0.497296\pi$
$600$	1.38977	−	1.60388i	0.0567373	−	0.0654783i
$601$	−18.0020	−	39.4189i	−0.734318	−	1.60793i	−0.792681	−	0.609636i	$-0.791316\pi$
$601$	−18.0020	−	39.4189i	−0.734318	−	1.60793i	0.0583635	−	0.998295i	$-0.481412\pi$
$602$	0.210088	−	0.135016i	0.00856256	−	0.00550282i
$603$	13.3327	+	3.91484i	0.542950	+	0.159425i
$604$	−2.77125	+	3.19819i	−0.112760	+	0.130132i
$605$	1.52516	−	10.6077i	0.0620066	−	0.431265i
$606$	−1.81954	−	1.16935i	−0.0739138	−	0.0475015i
$607$	−11.2361	−	12.9671i	−0.456058	−	0.526319i	0.480423	−	0.877037i	$-0.340483\pi$
$607$	−11.2361	−	12.9671i	−0.456058	−	0.526319i	−0.936481	+	0.350718i	$0.885938\pi$
$608$	−5.34122	+	3.43259i	−0.216615	+	0.139210i
$609$	−0.543580	−	0.627324i	−0.0220270	−	0.0254205i
$610$	1.73512	+	3.79938i	0.0702529	+	0.153832i
$611$	15.3671			0.621688
$612$	1.33788	−	9.30515i	0.0540805	−	0.376138i
$613$	20.7077	+	23.8980i	0.836377	+	0.965230i	0.999772	−	0.0213303i	$-0.00679015\pi$
$613$	20.7077	+	23.8980i	0.836377	+	0.965230i	−0.163396	+	0.986561i	$0.552245\pi$
$614$	−4.84269	+	5.58876i	−0.195435	+	0.225544i
$615$	1.46741	+	10.2060i	0.0591716	+	0.411547i
$616$	−0.00464131	−	0.0322810i	−0.000187004	−	0.00130064i
$617$	−2.76128	−	1.77457i	−0.111165	−	0.0714414i	0.483877	−	0.875136i	$-0.339228\pi$
$617$	−2.76128	−	1.77457i	−0.111165	−	0.0714414i	−0.595042	+	0.803695i	$0.702865\pi$
$618$	2.83439	+	19.7136i	0.114016	+	0.792997i
$619$	−11.3394	+	24.8299i	−0.455771	+	0.997999i	0.532660	+	0.846329i	$0.321192\pi$
$619$	−11.3394	+	24.8299i	−0.455771	+	0.997999i	−0.988431	+	0.151670i	$0.951535\pi$
$620$	1.17900	+	2.58165i	0.0473498	+	0.103682i
$621$	11.2175	−	7.20908i	0.450145	−	0.289290i
$622$	16.5628			0.664109
$623$	0.0778937	−	0.572879i	0.00312074	−	0.0229519i
$624$	3.40679			0.136381
$625$	0.841254	−	0.540641i	0.0336501	−	0.0216256i
$626$	4.14833	+	9.08357i	0.165800	+	0.363052i
$627$	2.97876	−	6.52258i	0.118960	−	0.260487i
$628$	−2.92647	−	20.3541i	−0.116779	−	0.812216i
$629$	−6.66370	−	4.28250i	−0.265699	−	0.170755i
$630$	−0.0131166	−	0.0912276i	−0.000522576	−	0.00363460i
$631$	−4.04744	−	28.1505i	−0.161126	−	1.12065i	−0.896516	−	0.443011i	$-0.853910\pi$
$631$	−4.04744	−	28.1505i	−0.161126	−	1.12065i	0.735390	−	0.677644i	$-0.236999\pi$
$632$	−5.16787	+	5.96404i	−0.205567	+	0.237237i
$633$	−17.5779	−	20.2860i	−0.698659	−	0.806296i
$634$	−0.265386	+	1.84580i	−0.0105398	+	0.0733060i
$635$	−6.93489			−0.275203
$636$	−11.3580	−	24.8706i	−0.450375	−	0.986185i
$637$	−7.35469	−	8.48777i	−0.291403	−	0.336298i
$638$	−2.85723	+	1.83623i	−0.113119	+	0.0726971i
$639$	13.0838	+	15.0995i	0.517586	+	0.597326i
$640$	0.841254	+	0.540641i	0.0332535	+	0.0213707i
$641$	−1.96164	+	13.6435i	−0.0774803	+	0.538887i	0.913702	+	0.406384i	$0.133211\pi$
$641$	−1.96164	+	13.6435i	−0.0774803	+	0.538887i	−0.991183	+	0.132503i	$0.957699\pi$
$642$	−18.2405	+	21.0507i	−0.719895	+	0.830804i
$643$	−11.8908	−	3.49146i	−0.468928	−	0.137690i	0.0387274	−	0.999250i	$-0.487670\pi$
$643$	−11.8908	−	3.49146i	−0.468928	−	0.137690i	−0.507656	+	0.861560i	$0.669488\pi$
$644$	0.216517	−	0.139147i	0.00853198	−	0.00548317i
$645$	−3.59258	−	7.86666i	−0.141458	−	0.309749i
$646$	−25.9899	+	29.9940i	−1.02256	+	1.18010i
$647$	−7.67332	+	4.93134i	−0.301669	+	0.193871i	−0.682714	−	0.730685i	$-0.739201\pi$
$647$	−7.67332	+	4.93134i	−0.301669	+	0.193871i	0.381045	+	0.924556i	$0.375564\pi$
$648$	10.7943	−	3.16949i	0.424039	−	0.124509i
$649$	4.80958	+	3.09093i	0.188792	+	0.121330i
$650$	1.54025	+	0.452259i	0.0604137	+	0.0177391i
$651$	0.354172	+	0.103994i	0.0138811	+	0.00407586i
$652$	1.49893	+	10.4253i	0.0587025	+	0.408285i
$653$	−18.0383	+	39.4984i	−0.705894	+	1.54569i	0.126781	+	0.991931i	$0.459535\pi$
$653$	−18.0383	+	39.4984i	−0.705894	+	1.54569i	−0.832675	+	0.553761i	$0.813192\pi$
$654$	5.08622	+	5.86981i	0.198887	+	0.229528i
$655$	−5.20365	−	1.52793i	−0.203323	−	0.0597011i
$656$	−4.66173	+	1.36881i	−0.182010	+	0.0534429i
$657$	−4.63253			−0.180732
$658$	0.562898	−	0.165282i	0.0219440	−	0.00644335i
$659$	2.74571	+	6.01227i	0.106958	+	0.234205i	0.955542	−	0.294856i	$-0.0952716\pi$
$659$	2.74571	+	6.01227i	0.106958	+	0.234205i	−0.848584	+	0.529061i	$0.822544\pi$
$660$	−1.12938			−0.0439611
$661$	−5.07550	+	35.3009i	−0.197414	+	1.37305i	0.614337	+	0.789043i	$0.289423\pi$
$661$	−5.07550	+	35.3009i	−0.197414	+	1.37305i	−0.811752	+	0.584003i	$0.801486\pi$
$662$	−13.2566	+	15.2989i	−0.515232	+	0.594609i
$663$	20.4329	−	5.99964i	0.793548	−	0.233007i
$664$	0.681100	−	1.49140i	0.0264318	−	0.0578776i
$665$	−0.161637	+	0.353936i	−0.00626802	+	0.0137251i
$666$	−0.271219	+	1.88637i	−0.0105095	+	0.0730954i
$667$	−22.5487	−	14.4911i	−0.873088	−	0.561099i
$668$	−6.32855	−	4.06711i	−0.244859	−	0.157361i
$669$	−4.33741	+	30.1673i	−0.167694	+	1.16634i
$670$	−3.83827	+	8.40463i	−0.148285	+	0.324699i
$671$	0.923367	−	2.02189i	0.0356462	−	0.0780542i
$672$	0.124791	−	0.0366419i	0.00481391	−	0.00141349i
$673$	14.6536	−	16.9112i	0.564855	−	0.651877i	−0.399424	−	0.916766i	$-0.630790\pi$
$673$	14.6536	−	16.9112i	0.564855	−	0.651877i	0.964279	+	0.264889i	$0.0853354\pi$
$674$	−0.244372	+	1.69965i	−0.00941287	+	0.0654680i
$675$	3.17505			0.122208
$676$	−4.32990	−	9.48117i	−0.166535	−	0.364660i
$677$	20.1951	−	5.92982i	0.776162	−	0.227902i	0.130421	−	0.991459i	$-0.458367\pi$
$677$	20.1951	−	5.92982i	0.776162	−	0.227902i	0.645740	+	0.763557i	$0.276549\pi$
$678$	−33.1502			−1.27313
$679$	−0.939888	+	0.275976i	−0.0360696	+	0.0105910i
$680$	5.99769	+	1.76108i	0.230001	+	0.0675344i
$681$	15.1902	+	17.5304i	0.582089	+	0.671766i
$682$	0.627421	−	1.37386i	0.0240252	−	0.0526079i
$683$	−0.776388	−	5.39989i	−0.0297076	−	0.206621i	0.969561	−	0.244848i	$-0.0787381\pi$
$683$	−0.776388	−	5.39989i	−0.0297076	−	0.206621i	−0.999269	+	0.0382269i	$0.987829\pi$
$684$	9.16177	+	2.69014i	0.350309	+	0.102860i
$685$	10.0034	+	2.93727i	0.382212	+	0.112227i
$686$	−0.721579	−	0.463731i	−0.0275500	−	0.0177053i
$687$	−9.77305	+	2.86963i	−0.372865	+	0.109483i
$688$	3.42812	−	2.20312i	0.130696	−	0.0839932i
$689$	13.5433	−	15.6298i	0.515960	−	0.595449i
$690$	−3.70252	−	8.10739i	−0.140953	−	0.308643i
$691$	40.4159	−	25.9737i	1.53749	−	0.988087i	0.549171	−	0.835710i	$-0.314943\pi$
$691$	40.4159	−	25.9737i	1.53749	−	0.988087i	0.988322	−	0.152377i	$-0.0486929\pi$
$692$	3.24734	+	0.953506i	0.123445	+	0.0362468i
$693$	−0.0321191	+	0.0370674i	−0.00122010	+	0.00140808i
$694$	3.76620	−	26.1945i	0.142963	−	0.994329i
$695$	15.4677	+	9.94046i	0.586722	+	0.377063i
$696$	−8.86988	−	10.2364i	−0.336212	−	0.388009i
$697$	−25.5491	+	16.4194i	−0.967739	+	0.621928i
$698$	−9.77050	−	11.2758i	−0.369819	−	0.426794i
$699$	2.97353	+	6.51112i	0.112469	+	0.246273i
$700$	0.0612838			0.00231631
$701$	4.13546	−	28.7628i	0.156194	−	1.08636i	−0.749371	−	0.662150i	$-0.769644\pi$
$701$	4.13546	−	28.7628i	0.156194	−	1.08636i	0.905566	−	0.424206i	$-0.139447\pi$
$702$	3.33772	+	3.85194i	0.125974	+	0.145382i
$703$	5.26877	−	6.08048i	0.198715	−	0.229330i
$704$	−0.0757347	−	0.526747i	−0.00285436	−	0.0198525i
$705$	−2.89126	−	20.1092i	−0.108891	−	0.757355i
$706$	6.23017	+	4.00389i	0.234476	+	0.150688i
$707$	−0.00888864	−	0.0618219i	−0.000334292	−	0.00232505i
$708$	−9.47136	+	20.7394i	−0.355956	+	0.779434i
$709$	12.9603	+	28.3792i	0.486735	+	1.06580i	0.980556	+	0.196238i	$0.0628725\pi$
$709$	12.9603	+	28.3792i	0.486735	+	1.06580i	−0.493821	+	0.869564i	$0.664400\pi$
$710$	−11.1760	+	7.18239i	−0.419428	+	0.269550i
$711$	11.8682			0.445094
$712$	1.27103	−	9.34797i	0.0476340	−	0.350330i
$713$	11.9193			0.446383
$714$	0.683928	−	0.439534i	0.0255954	−	0.0164491i
$715$	−0.354877	−	0.777072i	−0.0132716	−	0.0290608i
$716$	0.283511	−	0.620802i	0.0105953	−	0.0232005i
$717$	5.15551	+	35.8574i	0.192536	+	1.33912i
$718$	25.3125	+	16.2674i	0.944654	+	0.607092i
$719$	1.22166	+	8.49686i	0.0455604	+	0.316879i	0.999839	+	0.0179598i	$0.00571709\pi$
$719$	1.22166	+	8.49686i	0.0455604	+	0.316879i	−0.954278	+	0.298919i	$0.903374\pi$
$720$	−0.214030	−	1.48861i	−0.00797642	−	0.0554772i
$721$	−0.376624	+	0.434648i	−0.0140262	+	0.0161871i
$722$	−13.9560	−	16.1060i	−0.519387	−	0.599405i
$723$	4.92437	−	34.2498i	0.183139	−	1.27376i
$724$	4.19159			0.155779
$725$	−2.65128	−	5.80550i	−0.0984661	−	0.215611i
$726$	−14.8939	−	17.1885i	−0.552766	−	0.637926i
$727$	29.1717	−	18.7475i	1.08192	−	0.695307i	0.126918	−	0.991913i	$-0.459491\pi$
$727$	29.1717	−	18.7475i	1.08192	−	0.695307i	0.955000	+	0.296607i	$0.0958550\pi$
$728$	0.0644236	+	0.0743488i	0.00238770	+	0.00275555i
$729$	2.77247	+	1.78176i	0.102684	+	0.0659911i
$730$	0.438373	−	3.04895i	0.0162249	−	0.112847i
$731$	16.6810	−	19.2508i	0.616967	−	0.712018i
$732$	8.50519	+	2.49735i	0.314361	+	0.0923047i
$733$	7.97624	−	5.12602i	0.294609	−	0.189334i	−0.384983	−	0.922923i	$-0.625793\pi$
$733$	7.97624	−	5.12602i	0.294609	−	0.189334i	0.679593	+	0.733590i	$0.262156\pi$
$734$	−4.65533	−	10.1937i	−0.171831	−	0.376258i
$735$	−9.72320	+	11.2212i	−0.358646	+	0.413899i
$736$	3.53303	−	2.27054i	0.130229	−	0.0836932i
$737$	4.71780	−	1.38527i	0.173782	−	0.0510271i
$738$	6.14690	+	3.95037i	0.226271	+	0.145415i
$739$	42.0153	+	12.3368i	1.54556	+	0.453816i	0.939769	−	0.341811i	$-0.111040\pi$
$739$	42.0153	+	12.3368i	1.54556	+	0.453816i	0.605787	+	0.795627i	$0.292858\pi$
$740$	−1.21587	−	0.357012i	−0.0446964	−	0.0131240i
$741$	3.07829	+	21.4100i	0.113084	+	0.786515i
$742$	0.327985	−	0.718186i	0.0120407	−	0.0263654i
$743$	11.5430	+	13.3213i	0.423471	+	0.488712i	0.926891	−	0.375330i	$-0.122471\pi$
$743$	11.5430	+	13.3213i	0.423471	+	0.488712i	−0.503420	+	0.864042i	$0.667925\pi$
$744$	5.77922	+	1.69693i	0.211876	+	0.0622125i
$745$	3.19296	−	0.937538i	0.116981	−	0.0343487i
$746$	20.3591			0.745398
$747$	−2.36589	+	0.694688i	−0.0865634	+	0.0254173i
$748$	−1.38188	−	3.02589i	−0.0505265	−	0.110638i
$749$	−0.804337			−0.0293899
$750$	0.302027	−	2.10064i	0.0110285	−	0.0767046i
$751$	−7.97506	+	9.20371i	−0.291014	+	0.335848i	−0.882364	−	0.470567i	$-0.844050\pi$
$751$	−7.97506	+	9.20371i	−0.291014	+	0.335848i	0.591350	+	0.806415i	$0.298595\pi$
$752$	9.18510	−	2.69699i	0.334946	−	0.0983491i
$753$	17.5163	−	38.3555i	0.638331	−	1.39775i
$754$	4.25605	−	9.31944i	0.154996	−	0.339394i
$755$	−0.602249	+	4.18874i	−0.0219181	+	0.152444i
$756$	0.163690	+	0.105197i	0.00595336	+	0.00382599i
$757$	12.9199	+	8.30314i	0.469583	+	0.301783i	0.753949	−	0.656933i	$-0.228147\pi$
$757$	12.9199	+	8.30314i	0.469583	+	0.301783i	−0.284366	+	0.958716i	$0.591783\pi$
$758$	−2.07493	+	14.4314i	−0.0753648	+	0.524174i
$759$	−1.97035	+	4.31446i	−0.0715191	+	0.156605i
$760$	−2.63752	+	5.77536i	−0.0956729	+	0.209494i
$761$	9.19598	−	2.70018i	0.333354	−	0.0978815i	−0.110772	−	0.993846i	$-0.535332\pi$
$761$	9.19598	−	2.70018i	0.333354	−	0.0978815i	0.444126	+	0.895964i	$0.353514\pi$
$762$	−9.63793	+	11.1228i	−0.349145	+	0.402935i
$763$	−0.0319188	+	0.222000i	−0.00115554	+	0.00803694i
$764$	17.9742			0.650285
$765$	−3.90525	−	8.55130i	−0.141195	−	0.309173i
$766$	2.67870	−	0.786539i	0.0967855	−	0.0284188i
$767$	−17.2459			−0.622713
$768$	2.03628	−	0.597905i	0.0734778	−	0.0215750i
$769$	2.65927	+	0.780831i	0.0958956	+	0.0281575i	0.329328	−	0.944215i	$-0.393178\pi$
$769$	2.65927	+	0.780831i	0.0958956	+	0.0281575i	−0.233433	+	0.972373i	$0.574996\pi$
$770$	−0.0213570	−	0.0246472i	−0.000769651	−	0.000888225i
$771$	25.0828	−	54.9236i	0.903334	−	1.97803i
$772$	−2.15824	−	15.0109i	−0.0776767	−	0.540253i
$773$	8.73110	+	2.56368i	0.314036	+	0.0922093i	0.434953	−	0.900453i	$-0.356765\pi$
$773$	8.73110	+	2.56368i	0.314036	+	0.0922093i	−0.120917	+	0.992663i	$0.538583\pi$
$774$	−5.88024	−	1.72660i	−0.211361	−	0.0620612i
$775$	2.38759	+	1.53441i	0.0857646	+	0.0551176i
$776$	−15.3367	+	4.50325i	−0.550554	+	0.161657i
$777$	−0.138648	+	0.0891037i	−0.00497397	+	0.00319658i
$778$	−7.85752	+	9.06806i	−0.281706	+	0.325106i
$779$	−12.8145	−	28.0598i	−0.459127	−	1.00535i
$780$	2.86598	−	1.84185i	0.102618	−	0.0659489i
$781$	6.78339	+	1.99178i	0.242729	+	0.0712716i
$782$	17.1914	−	19.8400i	0.614764	−	0.709476i
$783$	2.88386	−	20.0577i	0.103061	−	0.716804i
$784$	−5.88562	−	3.78246i	−0.210201	−	0.135088i
$785$	−13.4661	−	15.5408i	−0.480627	−	0.554674i
$786$	−9.68251	+	6.22257i	−0.345364	+	0.221952i
$787$	−10.6345	−	12.2729i	−0.379079	−	0.437480i	0.533862	−	0.845571i	$-0.320740\pi$
$787$	−10.6345	−	12.2729i	−0.379079	−	0.437480i	−0.912941	+	0.408091i	$0.866195\pi$
$788$	−3.65614	−	8.00584i	−0.130245	−	0.285196i
$789$	−15.3132			−0.545163
$790$	−1.12308	+	7.81123i	−0.0399576	+	0.277911i
$791$	−0.626882	−	0.723461i	−0.0222894	−	0.0257233i
$792$	−0.524105	+	0.604849i	−0.0186232	+	0.0214924i
$793$	0.954218	+	6.63673i	0.0338853	+	0.235677i
$794$	5.62584	+	39.1286i	0.199654	+	1.38862i
$795$	−23.0011	−	14.7819i	−0.815764	−	0.524260i
$796$	−3.26385	−	22.7005i	−0.115684	−	0.804599i
$797$	−11.6709	+	25.5557i	−0.413405	+	0.905230i	0.582329	+	0.812954i	$0.302142\pi$
$797$	−11.6709	+	25.5557i	−0.413405	+	0.905230i	−0.995733	+	0.0922768i	$0.970586\pi$
$798$	0.343034	+	0.751139i	0.0121433	+	0.0265900i
$799$	50.3398	−	32.3514i	1.78089	−	1.14451i
$800$	1.00000			0.0353553
$801$	−11.8765	+	7.76177i	−0.419637	+	0.274249i
$802$	−10.0341			−0.354317
$803$	−1.37900	+	0.886232i	−0.0486640	+	0.0312745i
$804$	8.14574	+	17.8367i	0.287278	+	0.629051i
$805$	0.106917	−	0.234116i	0.00376834	−	0.00825151i
$806$	0.648385	+	4.50962i	0.0228384	+	0.158844i
$807$	36.7560	+	23.6217i	1.29387	+	0.831522i
$808$	−0.145041	−	1.00878i	−0.00510251	−	0.0354888i
$809$	0.361181	+	2.51207i	0.0126984	+	0.0883195i	0.995185	−	0.0980134i	$-0.0312488\pi$
$809$	0.361181	+	2.51207i	0.0126984	+	0.0883195i	−0.982487	+	0.186333i	$0.940340\pi$
$810$	7.36717	−	8.50217i	0.258856	−	0.298736i
$811$	1.23538	+	1.42571i	0.0433802	+	0.0500634i	0.777025	−	0.629470i	$-0.216728\pi$
$811$	1.23538	+	1.42571i	0.0433802	+	0.0500634i	−0.733645	+	0.679533i	$0.762182\pi$
$812$	0.0556633	−	0.387147i	0.00195340	−	0.0135862i
$813$	13.1626			0.461634
$814$	0.280139	+	0.613419i	0.00981886	+	0.0215003i
$815$	6.89730	+	7.95990i	0.241602	+	0.278823i
$816$	11.1600	−	7.17210i	0.390679	−	0.251074i
$817$	16.9431	+	19.5533i	0.592763	+	0.684085i
$818$	−16.2931	−	10.4710i	−0.569677	−	0.366109i
$819$	0.0210557	−	0.146446i	0.000735747	−	0.00511723i
$820$	−3.18166	+	3.67184i	−0.111109	+	0.128226i
$821$	21.3509	+	6.26918i	0.745150	+	0.218796i	0.632200	−	0.774805i	$-0.282152\pi$
$821$	21.3509	+	6.26918i	0.745150	+	0.218796i	0.112950	+	0.993601i	$0.463970\pi$
$822$	18.6136	−	11.9622i	0.649223	−	0.417230i
$823$	16.2878	+	35.6653i	0.567757	+	1.24322i	0.947983	+	0.318321i	$0.103119\pi$
$823$	16.2878	+	35.6653i	0.567757	+	1.24322i	−0.380226	+	0.924894i	$0.624154\pi$
$824$	−6.14558	+	7.09238i	−0.214091	+	0.247075i
$825$	−0.950095	+	0.610589i	−0.0330781	+	0.0212580i
$826$	−0.631717	+	0.185489i	−0.0219802	+	0.00645398i
$827$	5.69484	+	3.65985i	0.198029	+	0.127265i	0.635897	−	0.771774i	$-0.280630\pi$
$827$	5.69484	+	3.65985i	0.198029	+	0.127265i	−0.437869	+	0.899039i	$0.644266\pi$
$828$	−6.06019	−	1.77943i	−0.210606	−	0.0618395i
$829$	36.1469	+	10.6137i	1.25544	+	0.368629i	0.840794	−	0.541356i	$-0.182089\pi$
$829$	36.1469	+	10.6137i	1.25544	+	0.368629i	0.414642	+	0.909985i	$0.363907\pi$
$830$	−0.233334	−	1.62288i	−0.00809916	−	0.0563309i
$831$	−8.98372	+	19.6716i	−0.311642	+	0.682401i
$832$	1.05123	+	1.21319i	0.0364450	+	0.0420598i
$833$	−41.9613	−	12.3210i	−1.45387	−	0.426896i
$834$	37.4399	−	10.9933i	1.29644	−	0.380669i
$835$	−7.52276			−0.260336
$836$	3.24191	−	0.951910i	0.112124	−	0.0329225i
$837$	3.74339	+	8.19688i	0.129390	+	0.283326i
$838$	−38.6846			−1.33634
$839$	5.23712	−	36.4250i	0.180806	−	1.25753i	−0.674059	−	0.738678i	$-0.735450\pi$
$839$	5.23712	−	36.4250i	0.180806	−	1.25753i	0.854864	−	0.518852i	$-0.173640\pi$
$840$	0.0851706	−	0.0982921i	0.00293866	−	0.00339140i
$841$	−11.2578	+	3.30559i	−0.388200	+	0.113986i
$842$	2.62127	−	5.73978i	0.0903349	−	0.197806i
$843$	−4.10960	+	8.99878i	−0.141542	+	0.309934i
$844$	1.80000	−	12.5193i	0.0619587	−	0.430932i
$845$	−8.76845	−	5.63514i	−0.301644	−	0.193855i
$846$	−12.1114	−	7.78350i	−0.416397	−	0.267602i
$847$	0.0934676	−	0.650081i	0.00321158	−	0.0223371i
$848$	5.35190	−	11.7190i	0.183785	−	0.402433i
$849$	12.8245	−	28.0816i	0.440134	−	0.963759i
$850$	5.99769	−	1.76108i	0.205719	−	0.0604046i
$851$	−3.48510	+	4.02202i	−0.119468	+	0.137873i
$852$	−4.01241	+	27.9069i	−0.137463	+	0.956076i
$853$	20.7553			0.710648			0.355324	−	0.934743i	$-0.384371\pi$
$853$	20.7553			0.710648			0.355324	+	0.934743i	$0.384371\pi$
$854$	0.106335	+	0.232840i	0.00363870	+	0.00796763i
$855$	9.16177	−	2.69014i	0.313326	−	0.0920008i
$856$	−13.1248			−0.448597
$857$	−52.6184	+	15.4502i	−1.79741	+	0.527768i	−0.997390	−	0.0722036i	$-0.976997\pi$
$857$	−52.6184	+	15.4502i	−1.79741	+	0.527768i	−0.800022	+	0.599971i	$0.795179\pi$
$858$	−1.73953	−	0.510773i	−0.0593867	−	0.0174375i
$859$	7.97535	+	9.20405i	0.272115	+	0.314038i	0.875316	−	0.483552i	$-0.160653\pi$
$859$	7.97535	+	9.20405i	0.272115	+	0.314038i	−0.603200	+	0.797590i	$0.706108\pi$
$860$	1.69282	−	3.70677i	0.0577248	−	0.126400i
$861$	0.0899283	+	0.625465i	0.00306475	+	0.0213158i
$862$	21.5337	+	6.32286i	0.733440	+	0.215357i
$863$	−29.5040	−	8.66316i	−1.00433	−	0.294897i	−0.262097	−	0.965042i	$-0.584414\pi$
$863$	−29.5040	−	8.66316i	−1.00433	−	0.294897i	−0.742231	+	0.670144i	$0.766232\pi$
$864$	2.67102	+	1.71656i	0.0908700	+	0.0583986i
$865$	3.24734	−	0.953506i	0.110413	−	0.0324202i
$866$	−3.06061	+	1.96694i	−0.104004	+	0.0668392i
$867$	30.6775	−	35.4038i	1.04186	−	1.20237i
$868$	0.0722537	+	0.158213i	0.00245245	+	0.00537011i
$869$	3.53292	−	2.27047i	0.119846	−	0.0770205i
$870$	−12.9960	−	3.81598i	−0.440607	−	0.129374i
$871$	−9.71298	+	11.2094i	−0.329112	+	0.379815i
$872$	−0.520836	+	3.62249i	−0.0176377	+	0.122673i
$873$	20.2227	+	12.9964i	0.684436	+	0.439860i
$874$	17.4616	+	20.1517i	0.590646	+	0.681642i
$875$	0.0515552	−	0.0331325i	0.00174288	−	0.00112008i
$876$	−4.28093	−	4.94045i	−0.144639	−	0.166923i
$877$	−20.3282	−	44.5125i	−0.686434	−	1.50308i	−0.855679	−	0.517507i	$-0.826860\pi$
$877$	−20.3282	−	44.5125i	−0.686434	−	1.50308i	0.169245	−	0.985574i	$-0.445867\pi$
$878$	36.7957			1.24180
$879$	5.03382	−	35.0110i	0.169787	−	1.18089i
$880$	−0.348493	−	0.402182i	−0.0117477	−	0.0135576i
$881$	22.6750	−	26.1684i	0.763942	−	0.881636i	−0.231900	−	0.972740i	$-0.574494\pi$
$881$	22.6750	−	26.1684i	0.763942	−	0.881636i	0.995841	+	0.0911040i	$0.0290396\pi$
$882$	1.49740	+	10.4147i	0.0504202	+	0.350680i
$883$	4.50966	+	31.3654i	0.151762	+	1.05553i	0.913264	+	0.407367i	$0.133553\pi$
$883$	4.50966	+	31.3654i	0.151762	+	1.05553i	−0.761502	+	0.648162i	$0.775538\pi$
$884$	8.44151	+	5.42503i	0.283919	+	0.182463i
$885$	3.24474	+	22.5677i	0.109071	+	0.758605i
$886$	2.51373	−	5.50429i	0.0844503	−	0.184920i
$887$	15.0854	+	33.0325i	0.506519	+	1.10912i	0.974295	+	0.225276i	$0.0723283\pi$
$887$	15.0854	+	33.0325i	0.506519	+	1.10912i	−0.467776	+	0.883847i	$0.654944\pi$
$888$	−2.26239	+	1.45395i	−0.0759210	+	0.0487915i
$889$	−0.424996			−0.0142539
$890$	−3.98463	−	8.55118i	−0.133565	−	0.286636i
$891$	−5.98683			−0.200566
$892$	−12.0812	+	7.76414i	−0.404510	+	0.259963i
$893$	25.2486	+	55.2868i	0.844914	+	1.85010i
$894$	2.93379	−	6.42410i	0.0981206	−	0.214854i
$895$	−0.0971265	−	0.675530i	−0.00324658	−	0.0225805i
$896$	0.0515552	+	0.0331325i	0.00172234	+	0.00110688i
$897$	−2.03618	−	14.1619i	−0.0679861	−	0.472854i
$898$	2.18669	+	15.2087i	0.0729707	+	0.507522i
$899$	11.8619	−	13.6894i	0.395617	−	0.456566i
$900$	−0.984857	−	1.13659i	−0.0328286	−	0.0378862i
$901$	11.4609	−	79.7123i	0.381818	−	2.65560i
$902$	2.58553			0.0860889
$903$	−0.220167	−	0.482099i	−0.00732670	−	0.0160432i
$904$	−10.2292	−	11.8051i	−0.340217	−	0.392632i
$905$	3.52619	−	2.26614i	0.117214	−	0.0753292i
$906$	5.88126	+	6.78734i	0.195392	+	0.225494i
$907$	−3.25468	−	2.09166i	−0.108070	−	0.0694523i	0.485489	−	0.874243i	$-0.338641\pi$
$907$	−3.25468	−	2.09166i	−0.108070	−	0.0694523i	−0.593559	+	0.804790i	$0.702278\pi$
$908$	−1.55550	+	10.8187i	−0.0516209	+	0.359031i
$909$	−1.00372	+	1.15835i	−0.0332913	+	0.0384202i
$910$	0.0943926	+	0.0277162i	0.00312908	+	0.000918782i
$911$	10.7784	−	6.92687i	0.357105	−	0.229497i	−0.349771	−	0.936835i	$-0.613740\pi$
$911$	10.7784	−	6.92687i	0.357105	−	0.229497i	0.706876	+	0.707338i	$0.250104\pi$
$912$	5.59746	+	12.2567i	0.185350	+	0.405861i
$913$	−0.571377	+	0.659404i	−0.0189098	+	0.0218231i
$914$	−5.76849	+	3.70718i	−0.190805	+	0.122623i
$915$	8.50519	−	2.49735i	0.281173	−	0.0825598i
$916$	−4.03757	−	2.59479i	−0.133405	−	0.0857342i
$917$	−0.318899	−	0.0936372i	−0.0105310	−	0.00309217i
$918$	19.0430	+	5.59153i	0.628512	+	0.184548i
$919$	6.51689	+	45.3259i	0.214972	+	1.49517i	0.756229	+	0.654307i	$0.227040\pi$
$919$	6.51689	+	45.3259i	0.214972	+	1.49517i	−0.541256	+	0.840858i	$0.682051\pi$
$920$	1.74463	−	3.82020i	0.0575186	−	0.125948i
$921$	10.2774	+	11.8607i	0.338651	+	0.390824i
$922$	−19.6043	−	5.75636i	−0.645635	−	0.189575i
$923$	−20.4622	+	6.00824i	−0.673522	+	0.197764i
$924$	−0.0692127			−0.00227693
$925$	−1.21587	+	0.357012i	−0.0399776	+	0.0117385i
$926$	−11.1173	−	24.3434i	−0.365336	−	0.799975i
$927$	14.1136			0.463552
$928$	0.908288	−	6.31728i	0.0298160	−	0.207375i
$929$	10.4525	−	12.0628i	0.342934	−	0.395767i	−0.557916	−	0.829897i	$-0.688399\pi$
$929$	10.4525	−	12.0628i	0.342934	−	0.395767i	0.900850	+	0.434130i	$0.142944\pi$
$930$	5.77922	−	1.69693i	0.189508	−	0.0556446i
$931$	18.4527	−	40.4059i	0.604764	−	1.32425i
$932$	−1.40113	+	3.06804i	−0.0458954	+	0.100497i
$933$	5.00242	−	34.7926i	0.163772	−	1.13906i
$934$	−22.1568	−	14.2393i	−0.724993	−	0.465925i
$935$	−2.79843	−	1.79844i	−0.0915185	−	0.0588153i
$936$	0.343578	−	2.38963i	0.0112302	−	0.0781076i
$937$	16.5812	−	36.3078i	0.541685	−	1.18612i	−0.418873	−	0.908045i	$-0.637575\pi$
$937$	16.5812	−	36.3078i	0.541685	−	1.18612i	0.960558	−	0.278080i	$-0.0896981\pi$
$938$	−0.235223	+	0.515068i	−0.00768032	+	0.0168176i
$939$	20.3342	−	5.97067i	0.663582	−	0.194845i
$940$	6.26890	−	7.23469i	0.204469	−	0.235970i
$941$	7.23076	−	50.2910i	0.235716	−	1.63944i	−0.436944	−	0.899489i	$-0.643939\pi$
$941$	7.23076	−	50.2910i	0.235716	−	1.63944i	0.672660	−	0.739952i	$-0.265152\pi$
$942$	−43.6405			−1.42188
$943$	8.47633	+	18.5606i	0.276027	+	0.604415i
$944$	−10.3081	+	3.02672i	−0.335499	+	0.0985113i
$945$	0.194579			0.00632966
$946$	−2.08073	+	0.610958i	−0.0676504	+	0.0198640i
$947$	−19.6160	−	5.75978i	−0.637435	−	0.187168i	−0.0529822	−	0.998595i	$-0.516873\pi$
$947$	−19.6160	−	5.75978i	−0.637435	−	0.187168i	−0.584453	+	0.811428i	$0.698691\pi$
$948$	10.9675	+	12.6571i	0.356207	+	0.411085i
$949$	2.05412	−	4.49790i	0.0666797	−	0.146008i
$950$	0.903574	+	6.28450i	0.0293158	+	0.203896i
$951$	3.79721	+	1.11496i	0.123133	+	0.0361551i
$952$	0.367561	+	0.107926i	0.0119127	+	0.00349789i
$953$	10.6480	+	6.84308i	0.344924	+	0.221669i	0.701620	−	0.712551i	$-0.252460\pi$
$953$	10.6480	+	6.84308i	0.344924	+	0.221669i	−0.356696	+	0.934220i	$0.616097\pi$
$954$	−18.5905	+	5.45867i	−0.601891	+	0.176731i
$955$	15.1209	−	9.71761i	0.489301	−	0.314455i
$956$	−11.1783	+	12.9004i	−0.361532	+	0.417230i
$957$	2.99430	+	6.55661i	0.0967921	+	0.211945i
$958$	−9.43486	+	6.06342i	−0.304827	+	0.195900i
$959$	0.613048	+	0.180007i	0.0197964	+	0.00581274i
$960$	1.38977	−	1.60388i	0.0448548	−	0.0517652i
$961$	3.26542	−	22.7115i	0.105336	−	0.732628i
$962$	−1.71129	−	1.09978i	−0.0551742	−	0.0354583i
$963$	12.9260	+	14.9175i	0.416536	+	0.480708i
$964$	13.7162	−	8.81484i	0.441768	−	0.283907i
$965$	−9.93112	−	11.4611i	−0.319694	−	0.368947i
$966$	−0.226905	−	0.496852i	−0.00730054	−	0.0159859i
$967$	4.96709			0.159731			0.0798654	−	0.996806i	$-0.474551\pi$
$967$	4.96709			0.159731			0.0798654	+	0.996806i	$0.474551\pi$
$968$	1.52516	−	10.6077i	0.0490205	−	0.340945i
$969$	55.1570	+	63.6545i	1.77190	+	2.04488i
$970$	−10.4674	+	12.0800i	−0.336087	+	0.387865i
$971$	6.59598	+	45.8761i	0.211675	+	1.47223i	0.767562	+	0.640975i	$0.221470\pi$
$971$	6.59598	+	45.8761i	0.211675	+	1.47223i	−0.555887	+	0.831258i	$0.687621\pi$
$972$	−2.04223	−	14.2040i	−0.0655044	−	0.455593i
$973$	0.947917	+	0.609189i	0.0303888	+	0.0195297i
$974$	−2.71313	−	18.8702i	−0.0869342	−	0.604641i
$975$	1.41523	−	3.09893i	0.0453237	−	0.0992451i
$976$	1.73512	+	3.79938i	0.0555398	+	0.121615i
$977$	0.714839	−	0.459399i	0.0228697	−	0.0146975i	−0.529156	−	0.848525i	$-0.677491\pi$
$977$	0.714839	−	0.459399i	0.0228697	−	0.0146975i	0.552026	+	0.833827i	$0.313855\pi$
$978$	22.3525			0.714753
$979$	−2.05052	+	4.58257i	−0.0655348	+	0.146460i
$980$	−6.99624			−0.223487
$981$	4.63022	−	2.97566i	0.147832	−	0.0950056i
$982$	−0.683556	−	1.49678i	−0.0218131	−	0.0477641i
$983$	12.0442	−	26.3731i	0.384150	−	0.841172i	−0.614484	−	0.788929i	$-0.710636\pi$
$983$	12.0442	−	26.3731i	0.384150	−	0.841172i	0.998634	−	0.0522427i	$-0.0166369\pi$
$984$	1.46741	+	10.2060i	0.0467792	+	0.325357i
$985$	−7.40403	−	4.75828i	−0.235912	−	0.151611i
$986$	−5.67762	−	39.4887i	−0.180812	−	1.25758i
$987$	−0.177188	−	1.23237i	−0.00563994	−	0.0392266i
$988$	−6.67441	+	7.70268i	−0.212341	+	0.245055i
$989$	−11.2072	−	12.9338i	−0.356370	−	0.411272i
$990$	−0.113899	+	0.792184i	−0.00361994	+	0.0251773i
$991$	8.13883			0.258539			0.129269	−	0.991610i	$-0.458737\pi$
$991$	8.13883			0.258539			0.129269	+	0.991610i	$0.458737\pi$
$992$	1.17900	+	2.58165i	0.0374333	+	0.0819676i
$993$	28.1337	+	32.4680i	0.892796	+	1.03034i
$994$	−0.684908	+	0.440164i	−0.0217240	+	0.0139611i
$995$	−15.0186	−	17.3323i	−0.476120	−	0.549472i
$996$	−2.92719	−	1.88119i	−0.0927515	−	0.0596078i
$997$	−7.25443	+	50.4557i	−0.229750	+	1.59795i	0.469408	+	0.882981i	$0.344467\pi$
$997$	−7.25443	+	50.4557i	−0.229750	+	1.59795i	−0.699158	+	0.714967i	$0.746442\pi$
$998$	8.50087	−	9.81053i	0.269090	−	0.310547i
$999$	−3.86046	−	1.13353i	−0.122139	−	0.0358634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	890.2.o.a.271.1	✓	60
89.67	even	11	inner	890.2.o.a.601.1	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
890.2.o.a.271.1	✓	60	1.1	even	1	trivial
890.2.o.a.601.1	yes	60	89.67	even	11	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:	\( N \)	\(=\)	\( 890 = 2 \cdot 5 \cdot 89 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	890.o (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(-0.881612 - 1.93046i) q^{3} +(0.415415 - 0.909632i) q^{4} +(-0.142315 - 0.989821i) q^{5} +(-1.78534 - 1.14737i) q^{6} +(-0.00872159 - 0.0606600i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(-0.984857 + 1.13659i) q^{9} +(-0.654861 - 0.755750i) q^{10} +(-0.0757347 + 0.526747i) q^{11} -2.12224 q^{12} +(-0.666857 - 1.46021i) q^{13} +(-0.0401323 - 0.0463152i) q^{14} +(-1.78534 + 1.14737i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-5.25859 - 3.37949i) q^{17} +(-0.214030 + 1.48861i) q^{18} +(4.15779 - 4.79835i) q^{19} +(-0.959493 - 0.281733i) q^{20} +(-0.109413 + 0.0703153i) q^{21} +(0.221069 + 0.484073i) q^{22} +(-2.75023 + 3.17394i) q^{23} +(-1.78534 + 1.14737i) q^{24} +(-0.959493 + 0.281733i) q^{25} +(-1.35045 - 0.867879i) q^{26} +(-3.04644 - 0.894515i) q^{27} +(-0.0588014 - 0.0172656i) q^{28} +(0.908288 + 6.31728i) q^{29} +(-0.881612 + 1.93046i) q^{30} +(-1.85858 - 2.14491i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(1.08363 - 0.318183i) q^{33} -6.25090 q^{34} +(-0.0588014 + 0.0172656i) q^{35} +(0.624750 + 1.36801i) q^{36} +1.26720 q^{37} +(0.903574 - 6.28450i) q^{38} +(-2.23098 + 2.57468i) q^{39} +(-0.959493 + 0.281733i) q^{40} +(2.01831 - 4.41948i) q^{41} +(-0.0540285 + 0.118306i) q^{42} +(-0.579935 + 4.03354i) q^{43} +(0.447684 + 0.287709i) q^{44} +(1.26518 + 0.813079i) q^{45} +(-0.597683 + 4.15697i) q^{46} +(-3.97671 + 8.70779i) q^{47} +(-0.881612 + 1.93046i) q^{48} +(6.71285 - 1.97107i) q^{49} +(-0.654861 + 0.755750i) q^{50} +(-1.88794 + 13.1309i) q^{51} -1.60528 q^{52} +(5.35190 + 11.7190i) q^{53} +(-3.04644 + 0.894515i) q^{54} +0.532163 q^{55} +(-0.0588014 + 0.0172656i) q^{56} +(-12.9286 - 3.79617i) q^{57} +(4.17948 + 4.82338i) q^{58} +(4.46290 - 9.77239i) q^{59} +(0.302027 + 2.10064i) q^{60} +(-4.00764 - 1.17675i) q^{61} +(-2.72316 - 0.799593i) q^{62} +(0.0775348 + 0.0498286i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-1.35045 + 0.867879i) q^{65} +(0.739587 - 0.853529i) q^{66} +(-3.83827 - 8.40463i) q^{67} +(-5.25859 + 3.37949i) q^{68} +(8.55180 + 2.51103i) q^{69} +(-0.0401323 + 0.0463152i) q^{70} +(1.89065 - 13.1497i) q^{71} +(1.26518 + 0.813079i) q^{72} +(2.01717 + 2.32794i) q^{73} +(1.06604 - 0.685102i) q^{74} +(1.38977 + 1.60388i) q^{75} +(-2.63752 - 5.77536i) q^{76} +0.0326130 q^{77} +(-0.484837 + 3.37212i) q^{78} +(-5.16787 - 5.96404i) q^{79} +(-0.654861 + 0.755750i) q^{80} +(1.60104 + 11.1355i) q^{81} +(-0.691442 - 4.80908i) q^{82} +(1.37929 + 0.886416i) q^{83} +(0.0185093 + 0.128735i) q^{84} +(-2.59672 + 5.68602i) q^{85} +(1.69282 + 3.70677i) q^{86} +(11.3945 - 7.32281i) q^{87} +0.532163 q^{88} +(9.07193 + 2.58845i) q^{89} +1.50392 q^{90} +(-0.0827605 + 0.0531869i) q^{91} +(1.74463 + 3.82020i) q^{92} +(-2.50213 + 5.47890i) q^{93} +(1.36236 + 9.47543i) q^{94} +(-5.34122 - 3.43259i) q^{95} +(0.302027 + 2.10064i) q^{96} +(-2.27478 - 15.8214i) q^{97} +(4.58157 - 5.28741i) q^{98} +(-0.524105 - 0.604849i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 6 q^{2} + 4 q^{3} - 6 q^{4} - 6 q^{5} + 4 q^{6} + 6 q^{7} - 6 q^{8} + 6 q^{9} - 6 q^{10} - 6 q^{11} + 4 q^{12} - 30 q^{13} + 6 q^{14} + 4 q^{15} - 6 q^{16} - 10 q^{17} + 6 q^{18} + 7 q^{19} - 6 q^{20}+ \cdots - 54 q^{99}+O(q^{100}) \) 60 * q - 6 * q^2 + 4 * q^3 - 6 * q^4 - 6 * q^5 + 4 * q^6 + 6 * q^7 - 6 * q^8 + 6 * q^9 - 6 * q^10 - 6 * q^11 + 4 * q^12 - 30 * q^13 + 6 * q^14 + 4 * q^15 - 6 * q^16 - 10 * q^17 + 6 * q^18 + 7 * q^19 - 6 * q^20 - 8 * q^21 + 16 * q^22 - 9 * q^23 + 4 * q^24 - 6 * q^25 + 3 * q^26 + 13 * q^27 - 16 * q^28 + q^29 + 4 * q^30 - 10 * q^31 - 6 * q^32 - 10 * q^33 - 54 * q^34 - 16 * q^35 - 16 * q^36 - 4 * q^37 - 26 * q^38 + 11 * q^39 - 6 * q^40 + 30 * q^41 - 19 * q^42 + 34 * q^43 - 6 * q^44 - 5 * q^45 + 13 * q^46 + 38 * q^47 + 4 * q^48 + 14 * q^49 - 6 * q^50 - 6 * q^51 + 14 * q^52 + 38 * q^53 + 13 * q^54 - 28 * q^55 - 16 * q^56 + 54 * q^57 - 10 * q^58 + 16 * q^59 - 7 * q^60 + 7 * q^61 + 34 * q^62 - 77 * q^63 - 6 * q^64 + 3 * q^65 + 12 * q^66 - 4 * q^67 - 10 * q^68 + 12 * q^69 + 6 * q^70 + 17 * q^71 - 5 * q^72 + 25 * q^73 + 18 * q^74 + 4 * q^75 - 15 * q^76 - 46 * q^77 + 11 * q^78 + 85 * q^79 - 6 * q^80 + 18 * q^81 - 14 * q^82 + 9 * q^83 + 3 * q^84 + 12 * q^85 + 12 * q^86 - 31 * q^87 - 28 * q^88 - 37 * q^89 + 28 * q^90 + 16 * q^91 + 2 * q^92 - 85 * q^93 + 16 * q^94 + 7 * q^95 - 7 * q^96 - 77 * q^97 + 14 * q^98 - 54 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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