LMFDB - Embedded newform 147.2.k.a.104.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [147,2,Mod(20,147)] 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("147.20"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(147, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	147.k (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$1.17380090971$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			104.15
Character	$\chi$	$=$	147.104
Dual form			147.2.k.a.41.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.78148 + 1.42068i) q^{2} +(-1.38035 + 1.04625i) q^{3} +(0.710285 + 3.11196i) q^{4} +(1.09528 + 0.527460i) q^{5} +(-3.94544 - 0.0971647i) q^{6} +(-2.21851 - 1.44160i) q^{7} +(-1.17846 + 2.44709i) q^{8} +(0.810724 - 2.88838i) q^{9} +(1.20187 + 2.49571i) q^{10} +(3.63827 + 2.90142i) q^{11} +(-4.23633 - 3.55246i) q^{12} +(-2.21274 - 1.76460i) q^{13} +(-1.90416 - 5.71997i) q^{14} +(-2.06373 + 0.417860i) q^{15} +(0.175848 - 0.0846840i) q^{16} +(0.896447 - 3.92759i) q^{17} +(5.54775 - 3.99380i) q^{18} +5.20859i q^{19} +(-0.863474 + 3.78312i) q^{20} +(4.57059 - 0.331197i) q^{21} +(2.35950 + 10.3376i) q^{22} +(3.01360 - 0.687835i) q^{23} +(-0.933585 - 4.61079i) q^{24} +(-2.19602 - 2.75372i) q^{25} +(-1.43501 - 6.28720i) q^{26} +(1.90288 + 4.83519i) q^{27} +(2.91044 - 7.92786i) q^{28} +(-5.02894 - 1.14782i) q^{29} +(-4.27013 - 2.18749i) q^{30} -5.29517i q^{31} +(5.72951 + 1.30772i) q^{32} +(-8.05769 - 0.198437i) q^{33} +(7.17685 - 5.72335i) q^{34} +(-1.66950 - 2.74914i) q^{35} +(9.56436 + 0.471370i) q^{36} +(0.330947 - 1.44998i) q^{37} +(-7.39975 + 9.27899i) q^{38} +(4.90057 + 0.120687i) q^{39} +(-2.58148 + 2.05867i) q^{40} +(-5.32713 - 2.56541i) q^{41} +(8.61293 + 5.90333i) q^{42} +(-9.88760 + 4.76162i) q^{43} +(-6.44491 + 13.3830i) q^{44} +(2.41148 - 2.73597i) q^{45} +(6.34585 + 3.05600i) q^{46} +(0.464613 - 0.582607i) q^{47} +(-0.154131 + 0.300874i) q^{48} +(2.84356 + 6.39642i) q^{49} -8.02553i q^{50} +(2.87183 + 6.35935i) q^{51} +(3.91970 - 8.13934i) q^{52} +(-2.20747 + 0.503841i) q^{53} +(-3.47931 + 11.3172i) q^{54} +(2.45455 + 5.09692i) q^{55} +(6.14215 - 3.73002i) q^{56} +(-5.44949 - 7.18967i) q^{57} +(-7.32825 - 9.18934i) q^{58} +(-6.73222 + 3.24207i) q^{59} +(-2.76620 - 6.12544i) q^{60} +(8.54761 + 1.95094i) q^{61} +(7.52275 - 9.43323i) q^{62} +(-5.96249 + 5.23915i) q^{63} +(8.10575 + 10.1643i) q^{64} +(-1.49282 - 3.09988i) q^{65} +(-14.0727 - 11.8009i) q^{66} -6.55713 q^{67} +12.8592 q^{68} +(-3.44017 + 4.10243i) q^{69} +(0.931464 - 7.26936i) q^{70} +(2.32335 - 0.530289i) q^{71} +(6.11271 + 5.38774i) q^{72} +(2.07358 - 1.65362i) q^{73} +(2.64953 - 2.11293i) q^{74} +(5.91235 + 1.50351i) q^{75} +(-16.2089 + 3.69958i) q^{76} +(-3.88883 - 11.6818i) q^{77} +(8.55880 + 7.17715i) q^{78} -13.7357 q^{79} +0.237271 q^{80} +(-7.68545 - 4.68335i) q^{81} +(-5.84553 - 12.1384i) q^{82} +(-1.42620 - 1.78840i) q^{83} +(4.27709 + 13.9883i) q^{84} +(3.05351 - 3.82898i) q^{85} +(-24.3793 - 5.56441i) q^{86} +(8.14260 - 3.67713i) q^{87} +(-11.3876 + 5.48397i) q^{88} +(11.4774 + 14.3922i) q^{89} +(8.18292 - 1.44812i) q^{90} +(2.36513 + 7.10469i) q^{91} +(4.28103 + 8.88965i) q^{92} +(5.54007 + 7.30918i) q^{93} +(1.65540 - 0.377833i) q^{94} +(-2.74733 + 5.70488i) q^{95} +(-9.27692 + 4.18938i) q^{96} -2.44495i q^{97} +(-4.02154 + 15.4349i) q^{98} +(11.3300 - 8.15644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 7 q^{3} + 2 q^{4} + 7 q^{6} - 14 q^{7} + 5 q^{9} - 14 q^{10} - 42 q^{12} - 14 q^{13} - 5 q^{15} - 22 q^{16} - 18 q^{18} - 7 q^{21} + 4 q^{22} - 7 q^{24} - 26 q^{25} - 28 q^{27} + 28 q^{28} - 20 q^{30}+ \cdots + 100 q^{99}+O(q^{100}) $ 96 * q - 7 * q^3 + 2 * q^4 + 7 * q^6 - 14 * q^7 + 5 * q^9 - 14 * q^10 - 42 * q^12 - 14 * q^13 - 5 * q^15 - 22 * q^16 - 18 * q^18 - 7 * q^21 + 4 * q^22 - 7 * q^24 - 26 * q^25 - 28 * q^27 + 28 * q^28 - 20 * q^30 - 7 * q^33 - 70 * q^34 - 37 * q^36 + 38 * q^37 - 9 * q^39 - 28 * q^40 + 7 * q^42 - 18 * q^43 + 14 * q^45 + 62 * q^46 + 14 * q^49 - q^51 + 112 * q^52 - 7 * q^54 - 56 * q^55 + q^57 - 84 * q^58 + 111 * q^60 + 84 * q^61 - 7 * q^63 - 2 * q^64 + 21 * q^66 - 16 * q^67 - 91 * q^69 - 70 * q^70 - 27 * q^72 - 14 * q^73 + 119 * q^75 + 210 * q^76 - 87 * q^78 - 32 * q^79 - 71 * q^81 - 84 * q^82 + 154 * q^84 + 46 * q^85 + 49 * q^87 - 22 * q^88 + 203 * q^90 - 42 * q^91 + 53 * q^93 - 42 * q^94 - 28 * q^96 + 100 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$e\left(\frac{9}{14}\right)$

Coefficient data

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

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

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

$2$	1.78148	+	1.42068i	1.25969	+	1.00457i	0.999236	+	0.0390875i	$0.0124451\pi$
$2$	1.78148	+	1.42068i	1.25969	+	1.00457i	0.260458	+	0.965485i	$0.416126\pi$
$3$	−1.38035	+	1.04625i	−0.796945	+	0.604052i
$3$	−1.38035	+	1.04625i	−0.796945	+	0.604052i
$4$	0.710285	+	3.11196i	0.355142	+	1.55598i
$5$	1.09528	+	0.527460i	0.489825	+	0.235887i	0.662458	−	0.749099i	$-0.269513\pi$
$5$	1.09528	+	0.527460i	0.489825	+	0.235887i	−0.172633	+	0.984986i	$0.555227\pi$
$6$	−3.94544	−	0.0971647i	−1.61072	−	0.0396673i
$7$	−2.21851	−	1.44160i	−0.838517	−	0.544875i
$7$	−2.21851	−	1.44160i	−0.838517	−	0.544875i
$8$	−1.17846	+	2.44709i	−0.416647	+	0.865176i
$9$	0.810724	−	2.88838i	0.270241	−	0.962793i
$10$	1.20187	+	2.49571i	0.380064	+	0.789211i
$11$	3.63827	+	2.90142i	1.09698	+	0.874812i	0.992804	−	0.119747i	$-0.0382083\pi$
$11$	3.63827	+	2.90142i	1.09698	+	0.874812i	0.104175	+	0.994559i	$0.466780\pi$
$12$	−4.23633	−	3.55246i	−1.22292	−	1.02551i
$13$	−2.21274	−	1.76460i	−0.613705	−	0.489413i	0.266609	−	0.963805i	$-0.414097\pi$
$13$	−2.21274	−	1.76460i	−0.613705	−	0.489413i	−0.880314	+	0.474392i	$0.842668\pi$
$14$	−1.90416	−	5.71997i	−0.508909	−	1.52873i
$15$	−2.06373	+	0.417860i	−0.532852	+	0.107891i
$16$	0.175848	−	0.0846840i	0.0439620	−	0.0211710i
$17$	0.896447	−	3.92759i	0.217420	−	0.952581i	−0.741955	−	0.670449i	$-0.766101\pi$
$17$	0.896447	−	3.92759i	0.217420	−	0.952581i	0.959376	−	0.282132i	$-0.0910415\pi$
$18$	5.54775	−	3.99380i	1.30762	−	0.941347i
$19$			5.20859i			1.19493i	0.801894	+	0.597467i	$0.203826\pi$
$19$			5.20859i			1.19493i	−0.801894	+	0.597467i	$0.796174\pi$
$20$	−0.863474	+	3.78312i	−0.193079	+	0.845932i
$21$	4.57059	−	0.331197i	0.997385	−	0.0722732i
$22$	2.35950	+	10.3376i	0.503047	+	2.20399i
$23$	3.01360	−	0.687835i	0.628379	−	0.143423i	0.103541	−	0.994625i	$-0.466983\pi$
$23$	3.01360	−	0.687835i	0.628379	−	0.143423i	0.524839	+	0.851202i	$0.324126\pi$
$24$	−0.933585	−	4.61079i	−0.190567	−	0.941174i
$25$	−2.19602	−	2.75372i	−0.439204	−	0.550744i
$26$	−1.43501	−	6.28720i	−0.281429	−	1.23302i
$27$	1.90288	+	4.83519i	0.366210	+	0.930532i
$28$	2.91044	−	7.92786i	0.550022	−	1.49822i
$29$	−5.02894	−	1.14782i	−0.933851	−	0.213145i	−0.271585	−	0.962414i	$-0.587548\pi$
$29$	−5.02894	−	1.14782i	−0.933851	−	0.213145i	−0.662266	+	0.749269i	$0.730405\pi$
$30$	−4.27013	−	2.18749i	−0.779615	−	0.399379i
$31$		−	5.29517i		−	0.951041i	−0.879705	−	0.475521i	$-0.842260\pi$
$31$		−	5.29517i		−	0.951041i	0.879705	−	0.475521i	$-0.157740\pi$
$32$	5.72951	+	1.30772i	1.01284	+	0.231175i
$33$	−8.05769	−	0.198437i	−1.40266	−	0.0345435i
$34$	7.17685	−	5.72335i	1.23082	−	0.981546i
$35$	−1.66950	−	2.74914i	−0.282198	−	0.464689i
$36$	9.56436	+	0.471370i	1.59406	+	0.0785617i
$37$	0.330947	−	1.44998i	0.0544074	−	0.238375i	−0.940411	−	0.340039i	$-0.889560\pi$
$37$	0.330947	−	1.44998i	0.0544074	−	0.238375i	0.994819	+	0.101665i	$0.0324168\pi$
$38$	−7.39975	+	9.27899i	−1.20040	+	1.50525i
$39$	4.90057	+	0.120687i	0.784720	+	0.0193254i
$40$	−2.58148	+	2.05867i	−0.408169	+	0.325504i
$41$	−5.32713	−	2.56541i	−0.831958	−	0.400650i	−0.0311086	−	0.999516i	$-0.509904\pi$
$41$	−5.32713	−	2.56541i	−0.831958	−	0.400650i	−0.800849	+	0.598866i	$0.795618\pi$
$42$	8.61293	+	5.90333i	1.32900	+	0.910903i
$43$	−9.88760	+	4.76162i	−1.50784	+	0.726140i	−0.991484	−	0.130232i	$-0.958428\pi$
$43$	−9.88760	+	4.76162i	−1.50784	+	0.726140i	−0.516361	+	0.856371i	$0.672714\pi$
$44$	−6.44491	+	13.3830i	−0.971606	+	2.01756i
$45$	2.41148	−	2.73597i	0.359482	−	0.407854i
$46$	6.34585	+	3.05600i	0.935645	+	0.450583i
$47$	0.464613	−	0.582607i	0.0677708	−	0.0849819i	−0.746791	−	0.665059i	$-0.768406\pi$
$47$	0.464613	−	0.582607i	0.0677708	−	0.0849819i	0.814561	+	0.580077i	$0.196978\pi$
$48$	−0.154131	+	0.300874i	−0.0222469	+	0.0434275i
$49$	2.84356	+	6.39642i	0.406222	+	0.913774i
$50$		−	8.02553i		−	1.13498i
$51$	2.87183	+	6.35935i	0.402137	+	0.890488i
$52$	3.91970	−	8.13934i	0.543565	−	1.12872i
$53$	−2.20747	+	0.503841i	−0.303219	+	0.0692078i	−0.371424	−	0.928464i	$-0.621130\pi$
$53$	−2.20747	+	0.503841i	−0.303219	+	0.0692078i	0.0682042	+	0.997671i	$0.478273\pi$
$54$	−3.47931	+	11.3172i	−0.473475	+	1.54007i
$55$	2.45455	+	5.09692i	0.330971	+	0.687269i
$56$	6.14215	−	3.73002i	0.820779	−	0.498445i
$57$	−5.44949	−	7.18967i	−0.721802	−	0.952296i
$58$	−7.32825	−	9.18934i	−0.962247	−	1.20662i
$59$	−6.73222	+	3.24207i	−0.876461	+	0.422081i	−0.817331	−	0.576169i	$-0.804547\pi$
$59$	−6.73222	+	3.24207i	−0.876461	+	0.422081i	−0.0591303	+	0.998250i	$0.518833\pi$
$60$	−2.76620	−	6.12544i	−0.357115	−	0.790791i
$61$	8.54761	+	1.95094i	1.09441	+	0.249792i	0.731369	−	0.681982i	$-0.238882\pi$
$61$	8.54761	+	1.95094i	1.09441	+	0.249792i	0.363040	+	0.931774i	$0.381739\pi$
$62$	7.52275	−	9.43323i	0.955390	−	1.19802i
$63$	−5.96249	+	5.23915i	−0.751204	+	0.660070i
$64$	8.10575	+	10.1643i	1.01322	+	1.27054i
$65$	−1.49282	−	3.09988i	−0.185162	−	0.384492i
$66$	−14.0727	−	11.8009i	−1.73223	−	1.45259i
$67$	−6.55713			−0.801081			−0.400540	−	0.916279i	$-0.631178\pi$
$67$	−6.55713			−0.801081			−0.400540	+	0.916279i	$0.631178\pi$
$68$	12.8592			1.55941
$69$	−3.44017	+	4.10243i	−0.414148	+	0.493875i
$70$	0.931464	−	7.26936i	0.111331	−	0.868855i
$71$	2.32335	−	0.530289i	0.275730	−	0.0629337i	−0.0824196	−	0.996598i	$-0.526265\pi$
$71$	2.32335	−	0.530289i	0.275730	−	0.0629337i	0.358150	+	0.933664i	$0.383408\pi$
$72$	6.11271	+	5.38774i	0.720390	+	0.634951i
$73$	2.07358	−	1.65362i	0.242694	−	0.193542i	−0.494587	−	0.869128i	$-0.664681\pi$
$73$	2.07358	−	1.65362i	0.242694	−	0.193542i	0.737281	+	0.675586i	$0.236109\pi$
$74$	2.64953	−	2.11293i	0.308001	−	0.245623i
$75$	5.91235	+	1.50351i	0.682699	+	0.173610i
$76$	−16.2089	+	3.69958i	−1.85929	+	0.424371i
$77$	−3.88883	−	11.6818i	−0.443173	−	1.33126i
$78$	8.55880	+	7.17715i	0.969093	+	0.812652i
$79$	−13.7357			−1.54539			−0.772693	−	0.634780i	$-0.781091\pi$
$79$	−13.7357			−1.54539			−0.772693	+	0.634780i	$0.781091\pi$
$80$	0.237271			0.0265277
$81$	−7.68545	−	4.68335i	−0.853939	−	0.520373i
$82$	−5.84553	−	12.1384i	−0.645530	−	1.34046i
$83$	−1.42620	−	1.78840i	−0.156546	−	0.196303i	0.697373	−	0.716708i	$-0.254352\pi$
$83$	−1.42620	−	1.78840i	−0.156546	−	0.196303i	−0.853919	+	0.520406i	$0.825781\pi$
$84$	4.27709	+	13.9883i	0.466669	+	1.52624i
$85$	3.05351	−	3.82898i	0.331200	−	0.415312i
$86$	−24.3793	−	5.56441i	−2.62888	−	0.600025i
$87$	8.14260	−	3.67713i	0.872979	−	0.394230i
$88$	−11.3876	+	5.48397i	−1.21392	+	0.584593i
$89$	11.4774	+	14.3922i	1.21660	+	1.52557i	0.779822	+	0.626001i	$0.215310\pi$
$89$	11.4774	+	14.3922i	1.21660	+	1.52557i	0.436779	+	0.899569i	$0.356119\pi$
$90$	8.18292	−	1.44812i	0.862556	−	0.152645i
$91$	2.36513	+	7.10469i	0.247933	+	0.744774i
$92$	4.28103	+	8.88965i	0.446328	+	0.926810i
$93$	5.54007	+	7.30918i	0.574479	+	0.757927i
$94$	1.65540	−	0.377833i	0.170741	−	0.0389705i
$95$	−2.74733	+	5.70488i	−0.281870	+	0.585309i
$96$	−9.27692	+	4.18938i	−0.946822	+	0.427577i
$97$		−	2.44495i		−	0.248247i	−0.992267	−	0.124124i	$-0.960388\pi$
$97$		−	2.44495i		−	0.248247i	0.992267	−	0.124124i	$-0.0396120\pi$
$98$	−4.02154	+	15.4349i	−0.406237	+	1.55916i
$99$	11.3300	−	8.15644i	1.13871	−	0.819753i
$100$	7.00967	−	8.78985i	0.700967	−	0.878985i
$101$	15.7396	+	7.57979i	1.56615	+	0.754218i	0.997653	−	0.0684684i	$-0.0218112\pi$
$101$	15.7396	+	7.57979i	1.56615	+	0.754218i	0.568496	+	0.822686i	$0.307526\pi$
$102$	−3.91851	+	15.4090i	−0.387990	+	1.52572i
$103$	−0.975386	+	2.02541i	−0.0961077	+	0.199570i	−0.943480	−	0.331430i	$-0.892469\pi$
$103$	−0.975386	+	2.02541i	−0.0961077	+	0.199570i	0.847372	+	0.530999i	$0.178183\pi$
$104$	6.92576	−	3.33527i	0.679127	−	0.327050i
$105$	5.18078	+	2.04805i	0.505593	+	0.199869i
$106$	−4.64835	−	2.23853i	−0.451488	−	0.217425i
$107$	11.9427	−	9.52401i	1.15455	−	0.920721i	0.156788	−	0.987632i	$-0.449886\pi$
$107$	11.9427	−	9.52401i	1.15455	−	0.920721i	0.997759	+	0.0669116i	$0.0213145\pi$
$108$	−13.6953	+	9.35606i	−1.31783	+	0.900287i
$109$	−0.805534	+	1.01011i	−0.0771562	+	0.0967508i	−0.818912	−	0.573920i	$-0.805422\pi$
$109$	−0.805534	+	1.01011i	−0.0771562	+	0.0967508i	0.741755	+	0.670671i	$0.233994\pi$
$110$	−2.86838	+	12.5672i	−0.273489	+	1.19823i
$111$	1.06021	+	2.34773i	0.100631	+	0.222836i
$112$	−0.512201	−	0.0656312i	−0.0483984	−	0.00620156i
$113$	−1.81831	+	1.45006i	−0.171053	+	0.136410i	−0.705274	−	0.708934i	$-0.749176\pi$
$113$	−1.81831	+	1.45006i	−0.171053	+	0.136410i	0.534222	+	0.845344i	$0.320605\pi$
$114$	0.506092	−	20.5502i	0.0473998	−	1.92470i
$115$	3.66355	+	0.836182i	0.341628	+	0.0779744i
$116$		−	16.4652i		−	1.52875i
$117$	−6.89077	+	4.96063i	−0.637052	+	0.458611i
$118$	−16.5992	−	3.78867i	−1.52808	−	0.348775i
$119$	−7.65081	+	7.42107i	−0.701348	+	0.680289i
$120$	1.40947	−	5.54255i	0.128666	−	0.505963i
$121$	2.37102	+	10.3881i	0.215547	+	0.944374i
$122$	12.4557	+	15.6190i	1.12769	+	1.41407i
$123$	10.0374	−	2.03235i	0.905037	−	0.183250i
$124$	16.4784	−	3.76108i	1.47980	−	0.337755i
$125$	−2.30535	−	10.1004i	−0.206196	−	0.903405i
$126$	−18.0652	+	0.862620i	−1.60938	+	0.0768483i
$127$	4.51789	−	19.7942i	0.400898	−	1.75645i	−0.222879	−	0.974846i	$-0.571545\pi$
$127$	4.51789	−	19.7942i	0.400898	−	1.75645i	0.623777	−	0.781603i	$-0.285597\pi$
$128$			17.8694i			1.57945i
$129$	8.66649	−	16.9176i	0.763042	−	1.48951i
$130$	1.74451	−	7.64318i	0.153003	−	0.670351i
$131$	5.72141	−	2.75529i	0.499882	−	0.240731i	−0.166913	−	0.985972i	$-0.553380\pi$
$131$	5.72141	−	2.75529i	0.499882	−	0.240731i	0.666795	+	0.745241i	$0.267666\pi$
$132$	−5.10573	−	25.2162i	−0.444396	−	2.19479i
$133$	7.50873	−	11.5553i	0.651089	−	1.00197i
$134$	−11.6814	−	9.31558i	−1.00912	−	0.804744i
$135$	−0.466176	+	6.29959i	−0.0401220	+	0.542183i
$136$	8.55474	+	6.82218i	0.733563	+	0.584997i
$137$	8.12983	+	16.8818i	0.694578	+	1.44231i	0.887366	+	0.461066i	$0.152533\pi$
$137$	8.12983	+	16.8818i	0.694578	+	1.44231i	−0.192787	+	0.981241i	$0.561753\pi$
$138$	−11.9568	+	2.42100i	−1.01783	+	0.206089i
$139$	−4.95068	+	10.2802i	−0.419911	+	0.871954i	0.578504	+	0.815679i	$0.303637\pi$
$139$	−4.95068	+	10.2802i	−0.419911	+	0.871954i	−0.998415	+	0.0562747i	$0.982078\pi$
$140$	7.36939	−	7.14811i	0.622827	−	0.604125i
$141$	−0.0317764	+	1.29030i	−0.00267605	+	0.108663i
$142$	4.89236	+	2.35604i	0.410558	+	0.197714i
$143$	−2.93069	−	12.8402i	−0.245077	−	1.07375i
$144$	−0.102035	−	0.576571i	−0.00850292	−	0.0480476i
$145$	−4.90268	−	3.90976i	−0.407146	−	0.324688i
$146$	6.04330			0.500147
$147$	−10.6173	−	5.85422i	−0.875704	−	0.482848i
$148$	4.74733			0.390228
$149$	−5.48149	−	4.37134i	−0.449061	−	0.358114i	0.372695	−	0.927954i	$-0.378434\pi$
$149$	−5.48149	−	4.37134i	−0.449061	−	0.358114i	−0.821756	+	0.569840i	$0.807005\pi$
$150$	8.39671	+	11.0780i	0.685588	+	0.904517i
$151$	3.31264	+	14.5136i	0.269579	+	1.18110i	0.910505	+	0.413499i	$0.135694\pi$
$151$	3.31264	+	14.5136i	0.269579	+	1.18110i	−0.640926	+	0.767603i	$0.721449\pi$
$152$	−12.7459	−	6.13810i	−1.03383	−	0.497865i
$153$	−10.6176	−	5.77347i	−0.858382	−	0.466757i
$154$	9.66821	−	26.3356i	0.779087	−	2.12218i
$155$	2.79299	−	5.79971i	0.224339	−	0.465844i
$156$	3.10523	+	15.3361i	0.248617	+	1.22787i
$157$	3.62466	+	7.52669i	0.289279	+	0.600695i	0.994073	−	0.108718i	$-0.0346745\pi$
$157$	3.62466	+	7.52669i	0.289279	+	0.600695i	−0.704793	+	0.709413i	$0.748960\pi$
$158$	−24.4698	−	19.5140i	−1.94671	−	1.55245i
$159$	2.51993	−	3.00504i	0.199844	−	0.238315i
$160$	5.58566	+	4.45442i	0.441585	+	0.352153i
$161$	−7.67728	−	2.81845i	−0.605055	−	0.222125i
$162$	−7.03791	−	19.2619i	−0.552950	−	1.51335i
$163$	−5.85121	+	2.81779i	−0.458302	+	0.220707i	−0.648767	−	0.760987i	$-0.724715\pi$
$163$	−5.85121	+	2.81779i	−0.458302	+	0.220707i	0.190464	+	0.981694i	$0.439001\pi$
$164$	4.19968	−	18.4000i	0.327940	−	1.43680i
$165$	−8.72078	−	4.46746i	−0.678912	−	0.347791i
$166$		−	5.21217i		−	0.404543i
$167$	−0.836868	+	3.66656i	−0.0647588	+	0.283727i	−0.996931	−	0.0782892i	$-0.975054\pi$
$167$	−0.836868	+	3.66656i	−0.0647588	+	0.283727i	0.932172	+	0.362016i	$0.117911\pi$
$168$	−4.57577	+	11.5749i	−0.353028	+	0.893026i
$169$	−1.11037	−	4.86483i	−0.0854127	−	0.374218i
$170$	10.8795	−	2.48318i	0.834421	−	0.190451i
$171$	15.0444	+	4.22273i	1.15047	+	0.322920i
$172$	−21.8410	−	27.3877i	−1.66536	−	2.08829i
$173$	−3.38009	−	14.8091i	−0.256983	−	1.12592i	−0.924457	−	0.381285i	$-0.875482\pi$
$173$	−3.38009	−	14.8091i	−0.256983	−	1.12592i	0.667474	−	0.744633i	$-0.267376\pi$
$174$	19.7299	+	5.01731i	1.49572	+	0.380361i
$175$	0.902111	+	9.27494i	0.0681932	+	0.701120i
$176$	0.885487	+	0.202107i	0.0667461	+	0.0152344i
$177$	5.90080	−	11.5188i	0.443532	−	0.865804i
$178$			41.9451i			3.14392i
$179$	13.9200	+	3.17715i	1.04043	+	0.237471i	0.708409	−	0.705802i	$-0.249413\pi$
$179$	13.9200	+	3.17715i	1.04043	+	0.237471i	0.332019	+	0.943273i	$0.392270\pi$
$180$	10.2271	+	5.56111i	0.762280	+	0.414500i
$181$	4.72811	−	3.77054i	0.351438	−	0.280262i	−0.431819	−	0.901960i	$-0.642128\pi$
$181$	4.72811	−	3.77054i	0.351438	−	0.280262i	0.783257	+	0.621698i	$0.213557\pi$
$182$	−5.88007	+	16.0169i	−0.435860	+	1.18725i
$183$	−13.8398	+	6.24996i	−1.02307	+	0.462010i
$184$	−1.86820	+	8.18513i	−0.137726	+	0.603416i
$185$	1.12729	−	1.41357i	0.0828797	−	0.103928i
$186$	−0.514504	+	20.8918i	−0.0377253	+	1.53186i
$187$	14.6571	−	11.6887i	1.07183	−	0.854760i
$188$	2.14306	+	1.03204i	0.156299	+	0.0752694i
$189$	2.74887	−	13.4701i	0.199951	−	0.979806i
$190$	−12.9991	+	6.26004i	−0.943055	+	0.454151i
$191$	−6.61781	+	13.7420i	−0.478848	+	0.994339i	0.511953	+	0.859013i	$0.328922\pi$
$191$	−6.61781	+	13.7420i	−0.478848	+	0.994339i	−0.990801	+	0.135325i	$0.956792\pi$
$192$	−21.8231	−	5.54962i	−1.57495	−	0.400510i
$193$	−9.71036	−	4.67626i	−0.698967	−	0.336605i	0.0504281	−	0.998728i	$-0.483941\pi$
$193$	−9.71036	−	4.67626i	−0.698967	−	0.336605i	−0.749395	+	0.662123i	$0.769656\pi$
$194$	3.47350	−	4.35563i	0.249383	−	0.312716i
$195$	5.30386	+	2.71705i	0.379817	+	0.194572i
$196$	−17.8857	+	13.3923i	−1.27755	+	0.956594i
$197$			13.8064i			0.983668i	0.870689	+	0.491834i	$0.163673\pi$
$197$			13.8064i			0.983668i	−0.870689	+	0.491834i	$0.836327\pi$
$198$	31.7719	+	1.56585i	2.25793	+	0.111280i
$199$	8.88810	−	18.4563i	0.630061	−	1.30833i	−0.304493	−	0.952514i	$-0.598487\pi$
$199$	8.88810	−	18.4563i	0.630061	−	1.30833i	0.934554	−	0.355821i	$-0.115799\pi$
$200$	9.32651	−	2.12871i	0.659484	−	0.150523i
$201$	9.05112	−	6.86039i	0.638417	−	0.483895i
$202$	17.2713	+	35.8642i	1.21520	+	2.52339i
$203$	9.50204	+	9.79620i	0.666913	+	0.687558i
$204$	−17.7502	+	13.4540i	−1.24277	+	0.941967i
$205$	−4.48156	−	5.61970i	−0.313006	−	0.392497i
$206$	−4.61509	+	2.22251i	−0.321548	+	0.154850i
$207$	0.456472	−	9.26206i	0.0317270	−	0.643758i
$208$	−0.538540	−	0.122918i	−0.0373411	−	0.00852285i
$209$	−15.1123	+	18.9503i	−1.04534	+	1.31082i
$210$	6.31982	+	11.0088i	0.436109	+	0.759679i
$211$	3.18469	+	3.99348i	0.219243	+	0.274922i	0.879274	−	0.476316i	$-0.158028\pi$
$211$	3.18469	+	3.99348i	0.219243	+	0.274922i	−0.660031	+	0.751239i	$0.729457\pi$
$212$	−3.13586	−	6.51169i	−0.215372	−	0.447225i
$213$	−2.65221	+	3.16278i	−0.181727	+	0.216710i
$214$	34.8063			2.37931
$215$	−13.3413			−0.909868
$216$	−14.0746	−	1.04153i	−0.957655	−	0.0708673i
$217$	−7.63354	+	11.7474i	−0.518199	+	0.797464i
$218$	−2.87008	+	0.655077i	−0.194386	+	0.0443674i
$219$	−1.13216	+	4.45206i	−0.0765042	+	0.300842i
$220$	−14.1180	+	11.2587i	−0.951835	+	0.759063i
$221$	−8.91425	+	7.10888i	−0.599638	+	0.478195i
$222$	−1.44662	+	5.68864i	−0.0970909	+	0.381797i
$223$	−6.84308	+	1.56189i	−0.458247	+	0.104592i	−0.445412	−	0.895326i	$-0.646943\pi$
$223$	−6.84308	+	1.56189i	−0.458247	+	0.104592i	−0.0128349	+	0.999918i	$0.504086\pi$
$224$	−10.8257	−	11.1609i	−0.723325	−	0.745717i
$225$	−9.73415	+	4.11043i	−0.648943	+	0.274028i
$226$	−5.29935			−0.352508
$227$	−25.4570			−1.68964			−0.844822	−	0.535048i	$-0.820294\pi$
$227$	−25.4570			−1.68964			−0.844822	+	0.535048i	$0.820294\pi$
$228$	18.5033	−	22.0653i	1.22541	−	1.46131i
$229$	3.45021	+	7.16443i	0.227996	+	0.473439i	0.983313	−	0.181921i	$-0.0582314\pi$
$229$	3.45021	+	7.16443i	0.227996	+	0.473439i	−0.755317	+	0.655359i	$0.772517\pi$
$230$	5.33858	+	6.69437i	0.352016	+	0.441414i
$231$	17.5900	+	12.0562i	1.15734	+	0.793242i
$232$	8.73521	−	10.9536i	0.573495	−	0.719139i
$233$	8.73002	+	1.99257i	0.571923	+	0.130538i	0.498695	−	0.866778i	$-0.333813\pi$
$233$	8.73002	+	1.99257i	0.571923	+	0.130538i	0.0732277	+	0.997315i	$0.476670\pi$
$234$	−19.3232	−	0.952326i	−1.26320	−	0.0622555i
$235$	0.816185	−	0.393054i	0.0532421	−	0.0256400i
$236$	−14.8710	−	18.6476i	−0.968019	−	1.21386i
$237$	18.9600	−	14.3710i	1.23159	−	0.933494i
$238$	−24.1727	+	2.35112i	−1.56688	+	0.152400i
$239$	3.51486	+	7.29868i	0.227357	+	0.472112i	0.983174	−	0.182671i	$-0.0584742\pi$
$239$	3.51486	+	7.29868i	0.227357	+	0.472112i	−0.755817	+	0.654783i	$0.772760\pi$
$240$	−0.327516	+	0.248244i	−0.0211411	+	0.0160241i
$241$	−21.3667	+	4.87681i	−1.37635	+	0.314143i	−0.845795	−	0.533508i	$-0.820873\pi$
$241$	−21.3667	+	4.87681i	−1.37635	+	0.314143i	−0.530554	+	0.847651i	$0.678016\pi$
$242$	−10.5343	+	21.8746i	−0.677169	+	1.40615i
$243$	15.5086	−	1.57624i	0.994875	−	0.101116i
$244$			27.9855i			1.79159i
$245$	−0.259360	+	8.50575i	−0.0165699	+	0.543413i
$246$	20.7686	+	10.6393i	1.32416	+	0.678336i
$247$	9.19111	−	11.5253i	0.584816	−	0.733336i
$248$	12.9578	+	6.24013i	0.822818	+	0.396248i
$249$	3.83977	+	0.976454i	0.243336	+	0.0618802i
$250$	10.2425	−	21.2687i	0.647792	−	1.34515i
$251$	16.2784	−	7.83927i	1.02748	−	0.494810i	0.157307	−	0.987550i	$-0.449719\pi$
$251$	16.2784	−	7.83927i	1.02748	−	0.494810i	0.870177	+	0.492740i	$0.164005\pi$
$252$	−20.5391	−	14.8338i	−1.29384	−	0.934439i
$253$	12.9600	+	6.24120i	0.814788	+	0.392381i
$254$	36.1697	−	28.8444i	2.26949	−	1.80986i
$255$	−0.208839	+	8.48007i	−0.0130780	+	0.531042i
$256$	−9.17522	+	11.5054i	−0.573451	+	0.719085i
$257$	1.62073	−	7.10088i	0.101098	−	0.442941i	−0.898890	−	0.438174i	$-0.855625\pi$
$257$	1.62073	−	7.10088i	0.101098	−	0.442941i	0.999989	−	0.00476704i	$-0.00151740\pi$
$258$	39.4736	−	17.8260i	2.45752	−	1.10980i
$259$	−2.82450	+	2.73969i	−0.175506	+	0.170236i
$260$	8.58636	−	6.84740i	0.532504	−	0.424658i
$261$	−7.39243	+	13.5949i	−0.457580	+	0.841504i
$262$	14.1069	+	3.21982i	0.871530	+	0.198921i
$263$		−	5.80525i		−	0.357967i	−0.983852	−	0.178983i	$-0.942719\pi$
$263$		−	5.80525i		−	0.357967i	0.983852	−	0.178983i	$-0.0572808\pi$
$264$	9.98123	−	19.4840i	0.614302	−	1.19916i
$265$	−2.68356	−	0.612505i	−0.164850	−	0.0376259i
$266$	29.7930	−	9.91801i	1.82673	−	0.608112i
$267$	−30.9006	−	7.85803i	−1.89109	−	0.480904i
$268$	−4.65743	−	20.4055i	−0.284498	−	1.24647i
$269$	−8.96584	−	11.2428i	−0.546657	−	0.685486i	0.429372	−	0.903128i	$-0.358735\pi$
$269$	−8.96584	−	11.2428i	−0.546657	−	0.685486i	−0.976029	+	0.217642i	$0.930164\pi$
$270$	−9.78019	+	10.5603i	−0.595203	+	0.642679i
$271$	−13.6960	+	3.12602i	−0.831971	+	0.189892i	−0.617234	−	0.786780i	$-0.711747\pi$
$271$	−13.6960	+	3.12602i	−0.831971	+	0.189892i	−0.214737	+	0.976672i	$0.568890\pi$
$272$	−0.174966	−	0.766574i	−0.0106088	−	0.0464804i
$273$	−10.6980	−	7.33243i	−0.647471	−	0.443779i
$274$	−9.50049	+	41.6244i	−0.573946	+	2.51462i
$275$		−	16.3904i		−	0.988376i
$276$	−15.2101	−	7.79179i	−0.915541	−	0.469011i
$277$	−1.27760	+	5.59755i	−0.0767638	+	0.336324i	−0.998697	−	0.0510237i	$-0.983752\pi$
$277$	−1.27760	+	5.59755i	−0.0767638	+	0.336324i	0.921934	+	0.387348i	$0.126609\pi$
$278$	−23.4244	+	11.2806i	−1.40490	+	0.676564i
$279$	−15.2945	−	4.29292i	−0.915655	−	0.257011i
$280$	8.69482	−	0.845687i	0.519615	−	0.0505395i
$281$	−6.10881	−	4.87161i	−0.364421	−	0.290616i	0.424111	−	0.905610i	$-0.360587\pi$
$281$	−6.10881	−	4.87161i	−0.364421	−	0.290616i	−0.788531	+	0.614994i	$0.789158\pi$
$282$	−1.88972	+	2.25350i	−0.112531	+	0.134194i
$283$	−7.33800	−	5.85186i	−0.436199	−	0.347857i	0.380640	−	0.924723i	$-0.375704\pi$
$283$	−7.33800	−	5.85186i	−0.436199	−	0.347857i	−0.816838	+	0.576867i	$0.804275\pi$
$284$	3.30047	+	6.85351i	0.195847	+	0.406681i
$285$	−2.17646	−	10.7491i	−0.128923	−	0.636723i
$286$	13.0209	−	27.0381i	0.769940	−	1.59880i
$287$	8.11997	+	13.3710i	0.479307	+	0.789265i
$288$	8.42225	−	15.4888i	0.496286	−	0.912685i
$289$	0.694109	+	0.334265i	0.0408300	+	0.0196627i
$290$	−3.17950	−	13.9303i	−0.186707	−	0.818015i
$291$	2.55803	+	3.37489i	0.149954	+	0.197839i
$292$	6.61884	+	5.27835i	0.387339	+	0.308892i
$293$	−12.4703			−0.728525			−0.364263	−	0.931296i	$-0.618679\pi$
$293$	−12.4703			−0.728525			−0.364263	+	0.931296i	$0.618679\pi$
$294$	−10.5976	−	25.5130i	−0.618064	−	1.48795i
$295$	−9.08375			−0.528877
$296$	3.15821	+	2.51859i	0.183567	+	0.146390i
$297$	−7.10573	+	23.1128i	−0.412316	+	1.34114i
$298$	−3.55486	−	15.5749i	−0.205928	−	0.902228i
$299$	−7.88208	−	3.79581i	−0.455833	−	0.219517i
$300$	−0.479413	+	19.4669i	−0.0276789	+	1.12392i
$301$	28.8001	+	3.69032i	1.66001	+	0.212706i
$302$	−14.7178	+	30.5619i	−0.846916	+	1.75864i
$303$	−29.6565	+	6.00480i	−1.70372	+	0.344967i
$304$	0.441084	+	0.915921i	0.0252979	+	0.0525317i
$305$	8.33301	+	6.64535i	0.477147	+	0.380512i
$306$	−10.7127	−	25.3695i	−0.612407	−	1.45028i
$307$	3.41217	+	2.72112i	0.194743	+	0.155302i	0.716007	−	0.698093i	$-0.245968\pi$
$307$	3.41217	+	2.72112i	0.194743	+	0.155302i	−0.521264	+	0.853395i	$0.674539\pi$
$308$	33.5910	−	20.3993i	1.91403	−	1.16236i
$309$	−0.772712	−	3.81627i	−0.0439580	−	0.217100i
$310$	13.2152	−	6.36410i	0.750572	−	0.361457i
$311$	−0.594255	+	2.60360i	−0.0336971	+	0.147637i	−0.988978	−	0.148064i	$-0.952696\pi$
$311$	−0.594255	+	2.60360i	−0.0336971	+	0.147637i	0.955281	+	0.295701i	$0.0955530\pi$
$312$	−6.07044	+	11.8499i	−0.343671	+	0.670869i
$313$			17.3571i			0.981081i	0.871418	+	0.490540i	$0.163201\pi$
$313$			17.3571i			0.981081i	−0.871418	+	0.490540i	$0.836799\pi$
$314$	−4.23576	+	18.5581i	−0.239038	+	1.04729i
$315$	−9.29406	+	2.59337i	−0.523661	+	0.146120i
$316$	−9.75625	−	42.7449i	−0.548832	−	2.40459i
$317$	1.18103	−	0.269562i	0.0663331	−	0.0151401i	−0.189226	−	0.981934i	$-0.560598\pi$
$317$	1.18103	−	0.269562i	0.0663331	−	0.0151401i	0.255559	+	0.966794i	$0.417741\pi$
$318$	8.75841	−	1.77339i	0.491147	−	0.0994466i
$319$	−14.9663	−	18.7672i	−0.837953	−	1.05076i
$320$	3.51683	+	15.4082i	0.196597	+	0.861346i
$321$	−6.52064	+	25.6415i	−0.363947	+	1.43117i
$322$	−9.67278	−	15.9280i	−0.539043	−	0.887631i
$323$	20.4572	+	4.66923i	1.13827	+	0.259803i
$324$	9.11555	−	27.2433i	0.506420	−	1.51352i
$325$			9.96838i			0.552946i
$326$	−14.4270	−	3.29286i	−0.799036	−	0.182375i
$327$	0.0550930	−	2.23709i	0.00304665	−	0.123711i
$328$	12.5556	−	10.0127i	0.693265	−	0.552860i
$329$	−1.87064	+	0.622729i	−0.103132	+	0.0343322i
$330$	−9.18904	−	20.3481i	−0.505840	−	1.12013i
$331$	1.39165	−	6.09724i	0.0764923	−	0.335135i	−0.922173	−	0.386777i	$-0.873588\pi$
$331$	1.39165	−	6.09724i	0.0764923	−	0.335135i	0.998666	+	0.0516422i	$0.0164455\pi$
$332$	4.55243	−	5.70856i	0.249847	−	0.313298i
$333$	−3.91977	−	2.13143i	−0.214802	−	0.116802i
$334$	−6.69987	+	5.34297i	−0.366600	+	0.292354i
$335$	−7.18191	−	3.45863i	−0.392390	−	0.188965i
$336$	0.775682	−	0.445296i	0.0423169	−	0.0242929i
$337$	12.3918	−	5.96755i	0.675022	−	0.325073i	−0.0647787	−	0.997900i	$-0.520634\pi$
$337$	12.3918	−	5.96755i	0.675022	−	0.325073i	0.739801	+	0.672826i	$0.234920\pi$
$338$	4.93328	−	10.2441i	0.268335	−	0.557203i
$339$	0.992786	−	3.90400i	0.0539207	−	0.212036i
$340$	14.0845	+	6.78274i	0.763840	+	0.367846i
$341$	15.3635	−	19.2653i	0.831982	−	1.04327i
$342$	20.8021	+	28.8960i	1.12485	+	1.56251i
$343$	2.91265	−	18.2898i	0.157268	−	0.987556i
$344$		−	29.8072i		−	1.60710i
$345$	−5.93183	+	2.67877i	−0.319359	+	0.144220i
$346$	15.0175	−	31.1842i	0.807346	−	1.67647i
$347$	−16.1224	+	3.67984i	−0.865498	+	0.197544i	−0.632147	−	0.774849i	$-0.717826\pi$
$347$	−16.1224	+	3.67984i	−0.865498	+	0.197544i	−0.233351	+	0.972393i	$0.574969\pi$
$348$	17.2267	+	22.7276i	0.923446	+	1.21833i
$349$	−5.67844	−	11.7914i	−0.303960	−	0.631180i	0.691908	−	0.721985i	$-0.256770\pi$
$349$	−5.67844	−	11.7914i	−0.303960	−	0.631180i	−0.995869	+	0.0908054i	$0.971056\pi$
$350$	−11.5696	+	17.8047i	−0.618423	+	0.951701i
$351$	4.32160	−	14.0569i	0.230670	−	0.750300i
$352$	17.0512	+	21.3816i	0.908834	+	1.13964i
$353$	−17.5552	+	8.45414i	−0.934369	+	0.449969i	−0.838180	−	0.545394i	$-0.816380\pi$
$353$	−17.5552	+	8.45414i	−0.934369	+	0.449969i	−0.0961898	+	0.995363i	$0.530666\pi$
$354$	26.8766	−	12.1373i	1.42848	−	0.645088i
$355$	2.82443	+	0.644657i	0.149905	+	0.0342149i
$356$	−36.6357	+	45.9398i	−1.94169	+	2.43480i
$357$	2.79649	−	18.2483i	0.148006	−	0.965804i
$358$	20.2844	+	25.4359i	1.07206	+	1.34433i
$359$	8.73196	+	18.1321i	0.460855	+	0.956976i	0.993837	+	0.110849i	$0.0353570\pi$
$359$	8.73196	+	18.1321i	0.460855	+	0.956976i	−0.532982	+	0.846127i	$0.678929\pi$
$360$	3.85333	+	9.12531i	0.203088	+	0.480946i
$361$	−8.12945			−0.427866
$362$	13.7798			0.724248
$363$	−14.1414	−	11.8585i	−0.742230	−	0.622412i
$364$	−20.4296	+	12.4065i	−1.07080	+	0.650280i
$365$	3.14338	−	0.717455i	0.164532	−	0.0375533i
$366$	−33.5345	−	8.52783i	−1.75288	−	0.445757i
$367$	2.83003	−	2.25687i	0.147726	−	0.117808i	−0.546838	−	0.837239i	$-0.684169\pi$
$367$	2.83003	−	2.25687i	0.147726	−	0.117808i	0.694564	+	0.719431i	$0.255597\pi$
$368$	0.471687	−	0.376158i	0.0245884	−	0.0196086i
$369$	−11.7287	+	13.3069i	−0.610572	+	0.692730i
$370$	4.01647	−	0.916732i	0.208806	−	0.0476586i
$371$	5.62363	+	2.06452i	0.291964	+	0.107185i
$372$	−18.8109	+	22.4321i	−0.975298	+	1.16305i
$373$	32.2331			1.66896			0.834482	−	0.551035i	$-0.185767\pi$
$373$	32.2331			1.66896			0.834482	+	0.551035i	$0.185767\pi$
$374$	42.7172			2.20885
$375$	13.7497	+	11.5301i	0.710031	+	0.595411i
$376$	0.878164	+	1.82353i	0.0452878	+	0.0940412i
$377$	9.10231	+	11.4139i	0.468793	+	0.587847i
$378$	24.0338	−	20.0914i	1.23616	−	1.03339i
$379$	0.0834977	−	0.104703i	0.00428899	−	0.00537822i	−0.779682	−	0.626175i	$-0.784619\pi$
$379$	0.0834977	−	0.104703i	0.00428899	−	0.00537822i	0.783971	+	0.620797i	$0.213191\pi$
$380$	−19.7048	−	4.49748i	−1.01083	−	0.230716i
$381$	14.4734	+	32.0497i	0.741494	+	1.64196i
$382$	−31.3125	+	15.0793i	−1.60209	+	0.771525i
$383$	10.9837	+	13.7731i	0.561241	+	0.703773i	0.978787	−	0.204882i	$-0.0656812\pi$
$383$	10.9837	+	13.7731i	0.561241	+	0.703773i	−0.417546	+	0.908656i	$0.637110\pi$
$384$	−18.6959	−	24.6660i	−0.954069	−	1.25873i
$385$	1.90231	−	14.8461i	0.0969506	−	0.756625i
$386$	−10.6553	−	22.1260i	−0.542341	−	1.12618i
$387$	5.73723	+	32.4195i	0.291640	+	1.64797i
$388$	7.60860	−	1.73661i	0.386268	−	0.0881632i
$389$	10.9969	−	22.8353i	0.557565	−	1.15780i	−0.411595	−	0.911367i	$-0.635028\pi$
$389$	10.9969	−	22.8353i	0.557565	−	1.15780i	0.969161	−	0.246430i	$-0.0792574\pi$
$390$	5.58865	+	12.3754i	0.282992	+	0.626655i
$391$		−	12.4528i		−	0.629765i
$392$	−19.0036	−	0.579464i	−0.959827	−	0.0292673i
$393$	−5.01482	+	9.78928i	−0.252964	+	0.493804i
$394$	−19.6145	+	24.5959i	−0.988166	+	1.23912i
$395$	−15.0445	−	7.24503i	−0.756969	−	0.364537i
$396$	33.4301	+	29.4652i	1.67993	+	1.48068i
$397$	5.90008	−	12.2516i	0.296116	−	0.614892i	−0.698831	−	0.715287i	$-0.746296\pi$
$397$	5.90008	−	12.2516i	0.296116	−	0.614892i	0.994948	+	0.100394i	$0.0320105\pi$
$398$	42.0545	−	20.2524i	2.10800	−	1.01516i
$399$	1.72507	+	23.8064i	0.0863616	+	1.19181i
$400$	−0.619362	−	0.298269i	−0.0309681	−	0.0149134i
$401$	18.3831	−	14.6601i	0.918010	−	0.732088i	−0.0457240	−	0.998954i	$-0.514559\pi$
$401$	18.3831	−	14.6601i	0.918010	−	0.732088i	0.963734	+	0.266866i	$0.0859881\pi$
$402$	25.8708	+	0.637122i	1.29032	+	0.0317767i
$403$	−9.34388	+	11.7169i	−0.465452	+	0.583658i
$404$	−12.4084	+	54.3648i	−0.617342	+	2.70475i
$405$	−5.94746	−	9.18337i	−0.295532	−	0.456325i
$406$	3.01040	+	30.9511i	0.149404	+	1.53608i
$407$	5.41107	−	4.31518i	0.268217	−	0.213896i
$408$	−18.9462	−	0.466590i	−0.937978	−	0.0230996i
$409$	−2.75644	−	0.629140i	−0.136297	−	0.0311090i	0.153828	−	0.988098i	$-0.450840\pi$
$409$	−2.75644	−	0.629140i	−0.136297	−	0.0311090i	−0.290125	+	0.956989i	$0.593697\pi$
$410$		−	16.3782i		−	0.808863i
$411$	−28.8845	−	14.7969i	−1.42477	−	0.729877i
$412$	−6.99580	−	1.59675i	−0.344658	−	0.0786660i
$413$	19.6093	+	2.51265i	0.964909	+	0.123639i
$414$	13.9716	−	15.8516i	0.686668	−	0.779066i
$415$	−0.618784	−	2.71107i	−0.0303749	−	0.133081i
$416$	−10.3703	−	13.0040i	−0.508447	−	0.637572i
$417$	−3.92198	−	19.3699i	−0.192060	−	0.948547i
$418$	−53.8445	+	12.2897i	−2.63362	+	0.601107i
$419$	0.541529	+	2.37259i	0.0264554	+	0.115909i	0.986432	−	0.164173i	$-0.0524956\pi$
$419$	0.541529	+	2.37259i	0.0264554	+	0.115909i	−0.959976	+	0.280082i	$0.909638\pi$
$420$	−2.69362	+	17.5771i	−0.131435	+	0.857675i
$421$	2.85370	−	12.5029i	0.139081	−	0.609353i	−0.856557	−	0.516052i	$-0.827401\pi$
$421$	2.85370	−	12.5029i	0.139081	−	0.609353i	0.995638	−	0.0933008i	$-0.0297418\pi$
$422$			11.6387i			0.566564i
$423$	−1.30612	−	1.81431i	−0.0635055	−	0.0882149i
$424$	1.36846	−	5.99563i	0.0664584	−	0.291173i
$425$	−12.7841	+	6.15650i	−0.620120	+	0.298634i
$426$	−9.21816	+	1.86648i	−0.446621	+	0.0904311i
$427$	−16.1505	−	16.6504i	−0.781575	−	0.805771i
$428$	38.1211	+	30.4005i	1.84265	+	1.46947i
$429$	17.4794	+	14.6577i	0.843916	+	0.707682i
$430$	−23.7672	−	18.9537i	−1.14616	−	0.914028i
$431$	−7.19350	−	14.9375i	−0.346499	−	0.719512i	0.652777	−	0.757550i	$-0.273604\pi$
$431$	−7.19350	−	14.9375i	−0.346499	−	0.719512i	−0.999276	+	0.0380374i	$0.987889\pi$
$432$	0.744081	+	0.689115i	0.0357996	+	0.0331550i
$433$	−3.85221	+	7.99920i	−0.185125	+	0.384417i	−0.972790	−	0.231687i	$-0.925576\pi$
$433$	−3.85221	+	7.99920i	−0.185125	+	0.384417i	0.787665	+	0.616104i	$0.211290\pi$
$434$	−30.2883	+	10.0829i	−1.45388	+	0.483993i
$435$	10.8580	+	0.267401i	0.520601	+	0.0128209i
$436$	−3.71557	−	1.78933i	−0.177944	−	0.0856932i
$437$	3.58265	+	15.6966i	0.171382	+	0.750871i
$438$	−8.34186	+	6.32280i	−0.398590	+	0.302115i
$439$	6.35498	+	5.06792i	0.303306	+	0.241879i	0.763301	−	0.646043i	$-0.223577\pi$
$439$	6.35498	+	5.06792i	0.303306	+	0.241879i	−0.459995	+	0.887922i	$0.652149\pi$
$440$	−15.3652			−0.732507
$441$	20.7806	−	3.02753i	0.989553	−	0.144168i
$442$	−25.9800			−1.23574
$443$	−15.6379	−	12.4708i	−0.742978	−	0.592506i	0.177122	−	0.984189i	$-0.443321\pi$
$443$	−15.6379	−	12.4708i	−0.742978	−	0.592506i	−0.920100	+	0.391683i	$0.871893\pi$
$444$	−6.55298	+	4.96690i	−0.310990	+	0.235718i
$445$	4.97968	+	21.8174i	0.236059	+	1.03424i
$446$	−14.4097	−	6.93936i	−0.682321	−	0.328588i
$447$	12.1399	+	0.298970i	0.574196	+	0.0141408i
$448$	−3.32979	−	34.2348i	−0.157318	−	1.61744i
$449$	14.4581	−	30.0226i	0.682320	−	1.41685i	−0.215506	−	0.976503i	$-0.569140\pi$
$449$	14.4581	−	30.0226i	0.682320	−	1.41685i	0.897826	−	0.440350i	$-0.145146\pi$
$450$	−23.1808	−	6.50649i	−1.09275	−	0.306719i
$451$	−11.9382	−	24.7899i	−0.562147	−	1.16731i
$452$	−5.80404	−	4.62857i	−0.272999	−	0.217710i
$453$	−19.7575	−	16.5680i	−0.928287	−	0.778433i
$454$	−45.3511	−	36.1663i	−2.12843	−	1.69737i
$455$	−1.15696	+	9.02916i	−0.0542390	+	0.423293i
$456$	24.0157	−	4.86267i	1.12464	−	0.227715i
$457$	−8.98176	+	4.32539i	−0.420149	+	0.202333i	−0.631999	−	0.774969i	$-0.717765\pi$
$457$	−8.98176	+	4.32539i	−0.420149	+	0.202333i	0.211850	+	0.977302i	$0.432051\pi$
$458$	−4.03190	+	17.6649i	−0.188398	+	0.825427i
$459$	20.6965	−	3.13925i	0.966029	−	0.146528i
$460$			11.9948i			0.559258i
$461$	7.17953	−	31.4556i	0.334384	−	1.46503i	−0.476162	−	0.879358i	$-0.657972\pi$
$461$	7.17953	−	31.4556i	0.334384	−	1.46503i	0.810546	−	0.585675i	$-0.199170\pi$
$462$	14.2081	+	46.4676i	0.661020	+	2.16187i
$463$	−1.96464	−	8.60766i	−0.0913047	−	0.400032i	0.908537	−	0.417804i	$-0.137200\pi$
$463$	−1.96464	−	8.60766i	−0.0913047	−	0.400032i	−0.999842	+	0.0177716i	$0.994343\pi$
$464$	−0.981532	+	0.224028i	−0.0455665	+	0.0104002i
$465$	2.21264	+	10.9278i	0.102609	+	0.506764i
$466$	12.7215	+	15.9523i	0.589313	+	0.738975i
$467$	−0.834693	−	3.65703i	−0.0386250	−	0.169227i	0.951937	−	0.306295i	$-0.0990893\pi$
$467$	−0.834693	−	3.65703i	−0.0386250	−	0.169227i	−0.990562	+	0.137068i	$0.956232\pi$
$468$	−20.3317	−	17.9203i	−0.939833	−	0.828368i
$469$	14.5470	+	9.45278i	0.671720	+	0.436489i
$470$	2.01242	+	0.459321i	0.0928260	+	0.0211869i
$471$	−12.8781	−	6.59715i	−0.593391	−	0.303981i
$472$		−	20.2950i		−	0.934152i
$473$	−49.7892	−	11.3641i	−2.28931	−	0.522520i
$474$	54.1934	+	1.33462i	2.48919	+	0.0613013i
$475$	14.3430	−	11.4382i	0.658103	−	0.524819i
$476$	−28.5283	−	18.5379i	−1.30759	−	0.849685i
$477$	−0.334367	+	6.78448i	−0.0153096	+	0.310640i
$478$	−4.10745	+	17.9959i	−0.187870	+	0.823114i
$479$	23.3602	−	29.2928i	1.06736	−	1.33842i	0.129430	−	0.991589i	$-0.458685\pi$
$479$	23.3602	−	29.2928i	1.06736	−	1.33842i	0.937926	−	0.346834i	$-0.112743\pi$
$480$	−12.3706	−	0.304651i	−0.564638	−	0.0139054i
$481$	−3.29094	+	2.62443i	−0.150054	+	0.119664i
$482$	−44.9926	−	21.6673i	−2.04936	−	0.986919i
$483$	13.5461	−	4.14191i	0.616370	−	0.188463i
$484$	−30.6433	+	14.7570i	−1.39288	+	0.670774i
$485$	1.28962	−	2.67792i	0.0585585	−	0.121598i
$486$	29.8675	+	19.2247i	1.35482	+	0.872049i
$487$	11.5467	+	5.56059i	0.523231	+	0.251975i	0.676805	−	0.736163i	$-0.263364\pi$
$487$	11.5467	+	5.56059i	0.523231	+	0.251975i	−0.153574	+	0.988137i	$0.549078\pi$
$488$	−14.8471	+	18.6177i	−0.672096	+	0.842782i
$489$	5.12859	−	10.0114i	0.231923	−	0.452730i
$490$	−12.5460	+	14.7843i	−0.566770	+	0.667888i
$491$			36.2126i			1.63425i	0.576458	+	0.817127i	$0.304434\pi$
$491$			36.2126i			1.63425i	−0.576458	+	0.817127i	$0.695566\pi$
$492$	13.4540	+	29.7923i	0.606551	+	1.34314i
$493$	−9.01636	+	18.7227i	−0.406077	+	0.843227i
$494$	32.7475	−	7.47440i	1.47338	−	0.336289i
$495$	16.7118	−	2.95747i	0.751139	−	0.132928i
$496$	−0.448416	−	0.931146i	−0.0201345	−	0.0418097i
$497$	−5.91883	−	2.17290i	−0.265496	−	0.0974677i
$498$	5.45324	+	7.19462i	0.244365	+	0.322399i
$499$	−10.0815	−	12.6419i	−0.451312	−	0.565927i	0.503173	−	0.864185i	$-0.332166\pi$
$499$	−10.0815	−	12.6419i	−0.451312	−	0.565927i	−0.954485	+	0.298258i	$0.903594\pi$
$500$	29.7945	−	14.3483i	1.33245	−	0.641675i
$501$	−2.68096	−	5.93670i	−0.119777	−	0.265232i
$502$	40.1367	+	9.16094i	1.79139	+	0.408873i
$503$	20.5935	−	25.8234i	0.918219	−	1.15141i	−0.0698751	−	0.997556i	$-0.522260\pi$
$503$	20.5935	−	25.8234i	0.918219	−	1.15141i	0.988094	−	0.153854i	$-0.0491685\pi$
$504$	−5.79412	−	20.7649i	−0.258091	−	0.924940i
$505$	13.2413	+	16.6040i	0.589229	+	0.738870i
$506$	14.2212	+	29.5306i	0.632208	+	1.31279i
$507$	6.62252	+	5.55344i	0.294116	+	0.246637i
$508$	64.8077			2.87538
$509$	13.6921			0.606891			0.303445	−	0.952849i	$-0.401863\pi$
$509$	13.6921			0.606891			0.303445	+	0.952849i	$0.401863\pi$
$510$	−12.4195	+	14.8103i	−0.549945	+	0.655813i
$511$	−6.98412	+	0.679299i	−0.308959	+	0.0300504i
$512$	2.15191	−	0.491159i	0.0951018	−	0.0217064i
$513$	−25.1845	+	9.91134i	−1.11192	+	0.437596i
$514$	12.9754	−	10.3475i	0.572319	−	0.456409i
$515$	−2.13665	+	1.70392i	−0.0941520	+	0.0750837i
$516$	58.8025	+	14.9535i	2.58864	+	0.658290i
$517$	3.38078	−	0.771640i	0.148686	−	0.0339367i
$518$	−8.92400	+	0.867978i	−0.392098	+	0.0381367i
$519$	20.1598	+	16.9054i	0.884915	+	0.742063i
$520$	9.34489			0.409801
$521$	2.52812			0.110759			0.0553795	−	0.998465i	$-0.482363\pi$
$521$	2.52812			0.110759			0.0553795	+	0.998465i	$0.482363\pi$
$522$	−32.4835	+	13.7167i	−1.42176	+	0.600366i
$523$	11.7402	+	24.3788i	0.513364	+	1.06601i	0.983077	+	0.183192i	$0.0586429\pi$
$523$	11.7402	+	24.3788i	0.513364	+	1.06601i	−0.469714	+	0.882819i	$0.655643\pi$
$524$	12.6382	+	15.8478i	0.552101	+	0.692313i
$525$	−10.9491	−	11.8588i	−0.477859	−	0.517561i
$526$	8.24740	−	10.3419i	0.359604	−	0.450929i
$527$	−20.7973	−	4.74684i	−0.905944	−	0.206776i
$528$	−1.43373	+	0.647462i	−0.0623953	+	0.0281772i
$529$	−12.1136	+	5.83361i	−0.526679	+	0.253635i
$530$	−3.91053	−	4.90364i	−0.169862	−	0.213001i
$531$	3.90634	+	22.0736i	0.169521	+	0.957914i
$532$	41.2930	+	15.1593i	1.79028	+	0.657240i
$533$	7.26064	+	15.0769i	0.314493	+	0.653052i
$534$	−43.8850	−	57.8988i	−1.89909	−	2.50553i
$535$	18.1042	−	4.13217i	0.782713	−	0.178649i
$536$	7.72728	−	16.0459i	0.333768	−	0.693076i
$537$	−22.5385	+	10.1782i	−0.972609	+	0.439222i
$538$		−	32.7664i		−	1.41266i
$539$	−8.21310	+	31.5223i	−0.353763	+	1.35776i
$540$	−19.9352	+	3.02378i	−0.857875	+	0.130123i
$541$	−0.558082	+	0.699813i	−0.0239938	+	0.0300873i	−0.793684	−	0.608331i	$-0.791839\pi$
$541$	−0.558082	+	0.699813i	−0.0239938	+	0.0300873i	0.769690	+	0.638418i	$0.220411\pi$
$542$	−28.8401	−	13.8887i	−1.23879	−	0.596569i
$543$	−2.58151	+	10.1514i	−0.110783	+	0.435640i
$544$	10.2724	−	21.3309i	0.440426	−	0.914554i
$545$	−1.41508	+	0.681466i	−0.0606153	+	0.0291908i
$546$	−8.64116	−	28.2610i	−0.369808	−	1.20946i
$547$	−22.3315	−	10.7543i	−0.954825	−	0.459819i	−0.109450	−	0.993992i	$-0.534909\pi$
$547$	−22.3315	−	10.7543i	−0.954825	−	0.459819i	−0.845375	+	0.534173i	$0.820623\pi$
$548$	−46.7609	+	37.2906i	−1.99753	+	1.59297i
$549$	12.5648	−	23.1070i	0.536252	−	0.986185i
$550$	23.2855	−	29.1990i	0.992895	−	1.24505i
$551$	5.97855	−	26.1937i	0.254695	−	1.11589i
$552$	−5.98492	−	13.2529i	−0.254735	−	0.564083i
$553$	30.4727	+	19.8014i	1.29583	+	0.842042i
$554$	−10.2283	+	8.15684i	−0.434561	+	0.346551i
$555$	−0.0770986	+	3.13064i	−0.00327265	+	0.132888i
$556$	−35.5079	−	8.10445i	−1.50587	−	0.343705i
$557$			17.9057i			0.758691i	0.925255	+	0.379345i	$0.123851\pi$
$557$			17.9057i			0.758691i	−0.925255	+	0.379345i	$0.876149\pi$
$558$	−21.1479	−	29.3763i	−0.895260	−	1.24360i
$559$	30.2811	+	6.91146i	1.28075	+	0.292324i
$560$	−0.526387	−	0.342050i	−0.0222439	−	0.0144543i
$561$	−8.00268	+	31.4694i	−0.337873	+	1.32864i
$562$	−3.96170	−	17.3573i	−0.167114	−	0.732174i
$563$	−2.65452	−	3.32867i	−0.111875	−	0.140287i	0.722741	−	0.691119i	$-0.242882\pi$
$563$	−2.65452	−	3.32867i	−0.111875	−	0.140287i	−0.834616	+	0.550832i	$0.814310\pi$
$564$	−4.03794	+	0.817595i	−0.170028	+	0.0344270i
$565$	−2.75642	+	0.629134i	−0.115963	+	0.0264679i
$566$	−4.75885	−	20.8499i	−0.200030	−	0.876387i
$567$	10.2987	+	21.4694i	0.432505	+	0.901632i
$568$	−1.44030	+	6.31035i	−0.0604335	+	0.264777i
$569$			23.4816i			0.984401i	0.870482	+	0.492201i	$0.163807\pi$
$569$			23.4816i			0.984401i	−0.870482	+	0.492201i	$0.836193\pi$
$570$	11.3937	−	22.2414i	0.477231	−	0.931588i
$571$	4.62246	−	20.2523i	0.193444	−	0.847533i	−0.781291	−	0.624167i	$-0.785438\pi$
$571$	4.62246	−	20.2523i	0.193444	−	0.847533i	0.974735	−	0.223366i	$-0.0717045\pi$
$572$	37.8766	−	18.2404i	1.58370	−	0.762670i
$573$	−5.24270	−	25.8927i	−0.219017	−	1.08168i
$574$	−4.53036	+	35.3560i	−0.189094	+	1.47573i
$575$	−8.51203	−	6.78812i	−0.354976	−	0.283084i
$576$	35.9298	−	15.1720i	1.49708	−	0.632168i
$577$	17.1343	+	13.6641i	0.713309	+	0.568845i	0.911491	−	0.411321i	$-0.134932\pi$
$577$	17.1343	+	13.6641i	0.713309	+	0.568845i	−0.198182	+	0.980165i	$0.563504\pi$
$578$	0.761655	+	1.58159i	0.0316807	+	0.0657856i
$579$	18.2962	−	3.70459i	0.760365	−	0.153957i
$580$	8.68472	−	18.0340i	0.360613	−	0.748821i
$581$	0.585876	+	6.02360i	0.0243062	+	0.249901i
$582$	−0.237563	+	9.64643i	−0.00984732	+	0.399857i
$583$	−9.49323	−	4.57170i	−0.393169	−	0.189340i
$584$	1.60294	+	7.02295i	0.0663303	+	0.290612i
$585$	−10.1639	+	1.79869i	−0.420225	+	0.0743666i
$586$	−22.2156	−	17.7164i	−0.917719	−	0.731856i
$587$	−7.23980			−0.298818			−0.149409	−	0.988775i	$-0.547737\pi$
$587$	−7.23980			−0.298818			−0.149409	+	0.988775i	$0.547737\pi$
$588$	10.6768	−	37.1989i	0.440302	−	1.53406i
$589$	27.5804			1.13643
$590$	−16.1825	−	12.9051i	−0.666223	−	0.531295i
$591$	−14.4450	−	19.0577i	−0.594187	−	0.783929i
$592$	−0.0645932	−	0.283001i	−0.00265476	−	0.0116313i
$593$	0.442394	+	0.213046i	0.0181669	+	0.00874874i	0.442945	−	0.896549i	$-0.353934\pi$
$593$	0.442394	+	0.213046i	0.0181669	+	0.00874874i	−0.424778	+	0.905297i	$0.639648\pi$
$594$	−45.4946	+	31.0799i	−1.86666	+	1.27522i
$595$	−12.2941	+	4.09268i	−0.504010	+	0.167783i
$596$	9.71002	−	20.1631i	0.397738	−	0.825911i
$597$	7.04125	+	34.7753i	0.288179	+	1.42326i
$598$	−8.64911	−	17.9601i	−0.353689	−	0.734442i
$599$	−5.72338	−	4.56424i	−0.233851	−	0.186490i	0.499552	−	0.866284i	$-0.333498\pi$
$599$	−5.72338	−	4.56424i	−0.233851	−	0.186490i	−0.733403	+	0.679794i	$0.762069\pi$
$600$	−10.6467	+	12.6962i	−0.434648	+	0.518321i
$601$	−10.8364	−	8.64175i	−0.442026	−	0.352504i	0.377046	−	0.926195i	$-0.376940\pi$
$601$	−10.8364	−	8.64175i	−0.442026	−	0.352504i	−0.819072	+	0.573690i	$0.805511\pi$
$602$	46.0639	+	47.4899i	1.87742	+	1.93554i
$603$	−5.31602	+	18.9395i	−0.216485	+	0.771275i
$604$	−42.8129	+	20.6176i	−1.74203	+	0.838919i
$605$	−2.88238	+	12.6285i	−0.117185	+	0.513423i
$606$	−61.3632	−	31.4350i	−2.49271	−	1.27696i
$607$			1.23435i			0.0501005i	0.999686	+	0.0250503i	$0.00797458\pi$
$607$			1.23435i			0.0501005i	−0.999686	+	0.0250503i	$0.992025\pi$
$608$	−6.81140	+	29.8427i	−0.276239	+	1.21028i
$609$	−23.3654	−	3.58066i	−0.946814	−	0.145096i
$610$	5.40414	+	23.6771i	0.218807	+	0.958657i
$611$	−2.05614	+	0.469301i	−0.0831826	+	0.0189859i
$612$	10.4253	−	37.1424i	0.421418	−	1.50139i
$613$	12.1625	+	15.2513i	0.491238	+	0.615993i	0.964228	−	0.265075i	$-0.0853966\pi$
$613$	12.1625	+	15.2513i	0.491238	+	0.615993i	−0.472990	+	0.881068i	$0.656825\pi$
$614$	2.21287	+	9.69521i	0.0893041	+	0.391267i
$615$	12.0657	+	3.06831i	0.486537	+	0.123726i
$616$	33.1691	+	4.25015i	1.33642	+	0.171243i
$617$	35.6212	+	8.13032i	1.43406	+	0.327314i	0.867800	−	0.496914i	$-0.165534\pi$
$617$	35.6212	+	8.13032i	1.43406	+	0.327314i	0.566258	+	0.824228i	$0.308391\pi$
$618$	4.04513	−	7.89637i	0.162719	−	0.317639i
$619$		−	29.0609i		−	1.16806i	−0.811734	−	0.584028i	$-0.801476\pi$
$619$		−	29.0609i		−	1.16806i	0.811734	−	0.584028i	$-0.198524\pi$
$620$	20.0323	+	4.57224i	0.804516	+	0.183626i
$621$	9.06034	+	13.2625i	0.363579	+	0.532204i
$622$	−4.75754	+	3.79401i	−0.190760	+	0.152126i
$623$	−4.71484	−	48.4751i	−0.188896	−	1.94211i
$624$	0.871977	−	0.393777i	0.0349070	−	0.0157637i
$625$	−1.11621	+	4.89041i	−0.0446482	+	0.195617i
$626$	−24.6589	+	30.9213i	−0.985567	+	1.23586i
$627$	1.03358	−	41.9692i	0.0412772	−	1.67609i
$628$	−20.8482	+	16.6259i	−0.831934	+	0.663445i
$629$	−5.39824	−	2.59965i	−0.215242	−	0.103655i
$630$	−20.2415	−	8.58386i	−0.806441	−	0.341989i
$631$	−7.98181	+	3.84384i	−0.317751	+	0.153021i	−0.585960	−	0.810340i	$-0.699282\pi$
$631$	−7.98181	+	3.84384i	−0.317751	+	0.153021i	0.268209	+	0.963361i	$0.413568\pi$
$632$	16.1869	−	33.6124i	0.643880	−	1.33703i
$633$	−8.57416	−	2.18041i	−0.340792	−	0.0866635i
$634$	2.48693	+	1.19764i	0.0987687	+	0.0475645i
$635$	15.3890	−	19.2972i	0.610694	−	0.765786i
$636$	11.1414	+	5.70750i	0.441787	+	0.226317i
$637$	4.99509	−	19.1714i	0.197913	−	0.759598i
$638$		−	54.6957i		−	2.16542i
$639$	0.351919	−	7.14062i	0.0139217	−	0.282479i
$640$	−9.42541	+	19.5721i	−0.372572	+	0.773653i
$641$	25.8181	−	5.89282i	1.01975	−	0.232752i	0.320214	−	0.947345i	$-0.396245\pi$
$641$	25.8181	−	5.89282i	1.01975	−	0.232752i	0.699541	+	0.714593i	$0.253388\pi$
$642$	−48.0448	+	36.4160i	−1.89618	+	1.43723i
$643$	21.6463	+	44.9489i	0.853645	+	1.77261i	0.588704	+	0.808349i	$0.299638\pi$
$643$	21.6463	+	44.9489i	0.853645	+	1.77261i	0.264941	+	0.964265i	$0.414647\pi$
$644$	3.31786	−	25.8933i	0.130742	−	1.02034i
$645$	18.4156	−	13.9583i	0.725114	−	0.549608i
$646$	29.8106	+	37.3813i	1.17288	+	1.47075i
$647$	−18.9786	+	9.13962i	−0.746127	+	0.359316i	−0.768004	−	0.640445i	$-0.778750\pi$
$647$	−18.9786	+	9.13962i	−0.746127	+	0.359316i	0.0218773	+	0.999761i	$0.493036\pi$
$648$	20.5175	−	13.2879i	0.806005	−	0.521996i
$649$	−33.9003	−	7.73751i	−1.33070	−	0.303724i
$650$	−14.1619	+	17.7584i	−0.555475	+	0.696543i
$651$	−1.75375	−	24.2021i	−0.0687347	−	0.948554i
$652$	−12.9249	−	16.2073i	−0.506178	−	0.634727i
$653$	2.53277	+	5.25935i	0.0991149	+	0.205814i	0.944630	−	0.328137i	$-0.106421\pi$
$653$	2.53277	+	5.25935i	0.0991149	+	0.205814i	−0.845515	+	0.533951i	$0.820707\pi$
$654$	3.27634	−	3.90705i	0.128115	−	0.152778i
$655$	7.71987			0.301640
$656$	−1.15401			−0.0450567
$657$	−3.09519	−	7.32991i	−0.120755	−	0.285967i
$658$	−4.21720	−	1.54820i	−0.164403	−	0.0603551i
$659$	−42.8287	+	9.77536i	−1.66837	+	0.380794i	−0.949356	−	0.314204i	$-0.898263\pi$
$659$	−42.8287	+	9.77536i	−1.66837	+	0.380794i	−0.719012	+	0.694998i	$0.755405\pi$
$660$	7.70832	−	30.3119i	0.300046	−	1.17989i
$661$	−31.7489	+	25.3189i	−1.23489	+	0.984790i	−0.234969	+	0.972003i	$0.575499\pi$
$661$	−31.7489	+	25.3189i	−1.23489	+	0.984790i	−0.999918	+	0.0127871i	$0.995930\pi$
$662$	11.1414	−	8.88499i	0.433024	−	0.345325i
$663$	4.86711	−	19.1393i	0.189023	−	0.743307i
$664$	6.05709	−	1.38249i	0.235061	−	0.0536511i
$665$	14.3192	−	8.69577i	0.555273	−	0.337208i
$666$	−3.95490	−	9.36583i	−0.153249	−	0.362919i
$667$	−15.9447			−0.617383
$668$	−12.0046			−0.464472
$669$	7.81171	−	9.31552i	0.302018	−	0.360159i
$670$	−7.88080	−	16.3647i	−0.304462	−	0.632222i
$671$	25.4380	+	31.8983i	0.982023	+	1.23142i
$672$	26.6204	+	4.07947i	1.02690	+	0.157369i
$673$	11.0736	−	13.8859i	0.426858	−	0.535262i	−0.521169	−	0.853453i	$-0.674504\pi$
$673$	11.0736	−	13.8859i	0.426858	−	0.535262i	0.948027	+	0.318191i	$0.103075\pi$
$674$	30.5536	+	6.97366i	1.17688	+	0.268615i
$675$	9.13599	−	15.8582i	0.351644	−	0.610381i
$676$	14.3505	−	6.91083i	0.551942	−	0.265801i
$677$	18.1821	+	22.7996i	0.698794	+	0.876260i	0.996933	−	0.0782627i	$-0.0249373\pi$
$677$	18.1821	+	22.7996i	0.698794	+	0.876260i	−0.298139	+	0.954522i	$0.596366\pi$
$678$	7.31495	−	5.54444i	0.280929	−	0.212933i
$679$	−3.52465	+	5.42415i	−0.135264	+	0.208160i
$680$	5.77143	+	11.9845i	0.221324	+	0.459585i
$681$	35.1396	−	26.6344i	1.34655	−	1.02063i
$682$	54.7396	−	12.4939i	2.09609	−	0.478418i
$683$	8.75104	−	18.1717i	0.334849	−	0.695321i	−0.663766	−	0.747941i	$-0.731043\pi$
$683$	8.75104	−	18.1717i	0.334849	−	0.695321i	0.998615	+	0.0526194i	$0.0167570\pi$
$684$	−2.45518	+	49.8169i	−0.0938760	+	1.90480i
$685$			22.7785i			0.870321i
$686$	31.1728	−	28.4449i	1.19018	−	1.08603i
$687$	−12.2583	−	6.27963i	−0.467682	−	0.239583i
$688$	−1.33548	+	1.67464i	−0.0509148	+	0.0638451i
$689$	5.77365	+	2.78044i	0.219958	+	0.105926i
$690$	−14.3731	−	3.65508i	−0.547174	−	0.139146i
$691$	−17.2226	+	35.7630i	−0.655177	+	1.36049i	0.263184	+	0.964746i	$0.415227\pi$
$691$	−17.2226	+	35.7630i	−0.655177	+	1.36049i	−0.918361	+	0.395744i	$0.870487\pi$
$692$	43.6846	−	21.0374i	1.66064	−	0.799723i
$693$	−36.8941	+	1.76171i	−1.40149	+	0.0669218i
$694$	−33.9496	−	16.3493i	−1.28871	−	0.620610i
$695$	−10.8448	+	8.64842i	−0.411366	+	0.328053i
$696$	−0.597428	+	24.2590i	−0.0226455	+	0.919535i
$697$	−14.8514	+	18.6230i	−0.562536	+	0.705398i
$698$	6.63581	−	29.0734i	0.251169	−	1.10044i
$699$	−14.1352	+	6.38334i	−0.534642	+	0.241440i
$700$	−28.2225	+	9.39518i	−1.06671	+	0.355105i
$701$	−11.0796	+	8.83568i	−0.418471	+	0.333719i	−0.809983	−	0.586454i	$-0.800524\pi$
$701$	−11.0796	+	8.83568i	−0.418471	+	0.333719i	0.391512	+	0.920173i	$0.371952\pi$
$702$	27.6691	−	18.9024i	1.04430	−	0.713424i
$703$	7.55233	+	1.72377i	0.284842	+	0.0650133i
$704$			60.4986i			2.28013i
$705$	−0.715387	+	1.39648i	−0.0269430	+	0.0525947i
$706$	−43.2848	−	9.87948i	−1.62905	−	0.371819i
$707$	−23.9914	−	39.5061i	−0.902289	−	1.48578i
$708$	40.0372	+	10.1815i	1.50469	+	0.382643i
$709$	4.04622	+	17.7277i	0.151959	+	0.665776i	0.992315	+	0.123741i	$0.0394890\pi$
$709$	4.04622	+	17.7277i	0.151959	+	0.665776i	−0.840356	+	0.542036i	$0.817654\pi$
$710$	4.11580	+	5.16105i	0.154463	+	0.193691i
$711$	−11.1359	+	39.6739i	−0.417627	+	1.48789i
$712$	−48.7446	+	11.1256i	−1.82678	+	0.416951i
$713$	−3.64220	−	15.9575i	−0.136402	−	0.597615i
$714$	30.9069	−	28.5360i	1.15666	−	1.06793i
$715$	3.56276	−	15.6095i	0.133240	−	0.583762i
$716$			45.5751i			1.70322i
$717$	−12.4880	−	6.39730i	−0.466372	−	0.238912i
$718$	−10.2041	+	44.7072i	−0.380815	+	1.66846i
$719$	−26.4016	+	12.7143i	−0.984614	+	0.474165i	−0.855690	−	0.517489i	$-0.826867\pi$
$719$	−26.4016	+	12.7143i	−0.984614	+	0.474165i	−0.128924	+	0.991654i	$0.541152\pi$
$720$	0.192361	−	0.685328i	0.00716888	−	0.0255407i
$721$	5.08374	−	3.08727i	0.189328	−	0.114976i
$722$	−14.4824	−	11.5493i	−0.538980	−	0.429822i
$723$	24.3911	−	29.0866i	0.907115	−	1.08174i
$724$	15.0921	+	12.0355i	0.560893	+	0.447297i
$725$	7.88287	+	16.3689i	0.292762	+	0.607927i
$726$	−8.34536	−	41.2161i	−0.309726	−	1.52967i
$727$	8.72737	−	18.1226i	0.323680	−	0.672129i	−0.674106	−	0.738635i	$-0.735471\pi$
$727$	8.72737	−	18.1226i	0.323680	−	0.672129i	0.997786	+	0.0665058i	$0.0211851\pi$
$728$	−20.1730	−	2.58488i	−0.747661	−	0.0958020i
$729$	−19.7581	+	18.4016i	−0.731781	+	0.681540i
$730$	6.61913	+	3.18760i	0.244985	+	0.117978i
$731$	9.83797	+	43.1030i	0.363871	+	1.59422i
$732$	−29.2799	−	38.6298i	−1.08221	−	1.42780i
$733$	−31.8590	−	25.4067i	−1.17674	−	0.938417i	−0.177780	−	0.984070i	$-0.556892\pi$
$733$	−31.8590	−	25.4067i	−1.17674	−	0.938417i	−0.998957	+	0.0456536i	$0.985463\pi$
$734$	8.24793			0.304437
$735$	−8.54113	−	12.0123i	−0.315044	−	0.443079i
$736$	18.1660			0.669606
$737$	−23.8566	−	19.0250i	−0.878769	−	0.700795i
$738$	−39.7993	+	7.04323i	−1.46503	+	0.259265i
$739$	−6.45473	−	28.2800i	−0.237441	−	1.04030i	−0.943299	−	0.331944i	$-0.892296\pi$
$739$	−6.45473	−	28.2800i	−0.237441	−	1.04030i	0.705858	−	0.708353i	$-0.250562\pi$
$740$	5.19967	+	2.50403i	0.191144	+	0.0920500i
$741$	−0.628608	+	25.5251i	−0.0230925	+	0.937688i
$742$	7.08534	+	11.6673i	0.260111	+	0.428319i
$743$	−13.3919	+	27.8086i	−0.491301	+	1.02020i	0.497010	+	0.867745i	$0.334431\pi$
$743$	−13.3919	+	27.8086i	−0.491301	+	1.02020i	−0.988311	+	0.152453i	$0.951283\pi$
$744$	−24.4149	+	4.94350i	−0.895095	+	0.181237i
$745$	−3.69807	−	7.67912i	−0.135487	−	0.281341i
$746$	57.4224	+	45.7929i	2.10238	+	1.67660i
$747$	−6.32184	+	2.66951i	−0.231304	+	0.0976724i
$748$	46.7854	+	37.3101i	1.71064	+	1.36419i
$749$	−40.2249	+	3.91241i	−1.46979	+	0.142956i
$750$	8.11421	+	40.0745i	0.296289	+	1.46331i
$751$	30.1918	−	14.5396i	1.10172	−	0.530558i	0.207518	−	0.978231i	$-0.433461\pi$
$751$	30.1918	−	14.5396i	1.10172	−	0.530558i	0.894197	+	0.447673i	$0.147747\pi$
$752$	0.0323639	−	0.141796i	0.00118019	−	0.00517075i
$753$	−14.2680	+	27.8522i	−0.519956	+	1.01499i
$754$			33.2651i			1.21144i
$755$	−4.02708	+	17.6438i	−0.146561	+	0.642124i
$756$	43.8709	−	1.01325i	1.59557	−	0.0368515i
$757$	2.95644	+	12.9530i	0.107454	+	0.470785i	0.999811	+	0.0194552i	$0.00619317\pi$
$757$	2.95644	+	12.9530i	0.107454	+	0.470785i	−0.892357	+	0.451330i	$0.850950\pi$
$758$	0.297498	−	0.0679020i	0.0108056	−	0.00246631i
$759$	−24.4192	+	4.94435i	−0.886360	+	0.179469i
$760$	−10.7228	−	13.4459i	−0.388955	−	0.487734i
$761$	2.99957	+	13.1420i	0.108734	+	0.476396i	0.999749	+	0.0224208i	$0.00713735\pi$
$761$	2.99957	+	13.1420i	0.108734	+	0.476396i	−0.891014	+	0.453975i	$0.850006\pi$
$762$	−19.7484	+	77.6578i	−0.715408	+	2.81325i
$763$	3.24326	−	1.07967i	0.117414	−	0.0390867i
$764$	−47.4652	−	10.8336i	−1.71723	−	0.391947i
$765$	−8.58400	−	11.9239i	−0.310355	−	0.431111i
$766$			40.1408i			1.45035i
$767$	20.6177	+	4.70585i	0.744460	+	0.169918i
$768$	0.627522	−	25.4810i	0.0226437	−	0.919465i
$769$	−1.20617	+	0.961889i	−0.0434956	+	0.0346866i	−0.644996	−	0.764186i	$-0.723141\pi$
$769$	−1.20617	+	0.961889i	−0.0434956	+	0.0346866i	0.601501	+	0.798872i	$0.294570\pi$
$770$	24.4804	−	23.7453i	0.882213	−	0.855722i
$771$	5.19212	+	11.4974i	0.186990	+	0.414068i
$772$	7.65523	−	33.5398i	0.275518	−	1.20712i
$773$	9.57734	−	12.0096i	0.344473	−	0.431956i	−0.579172	−	0.815206i	$-0.696624\pi$
$773$	9.57734	−	12.0096i	0.344473	−	0.431956i	0.923645	+	0.383250i	$0.125195\pi$
$774$	−35.8370	+	65.9053i	−1.28813	+	2.36892i
$775$	−14.5814	+	11.6283i	−0.523780	+	0.417701i
$776$	5.98302	+	2.88127i	0.214778	+	0.103432i
$777$	1.03240	−	6.73686i	0.0370371	−	0.241683i
$778$	52.0324	−	25.0575i	1.86545	−	0.898354i
$779$	13.3622	−	27.7468i	0.478750	−	0.994134i
$780$	−4.68809	+	18.4353i	−0.167861	+	0.660089i
$781$	9.99155	+	4.81168i	0.357526	+	0.172175i
$782$	17.6915	−	22.1844i	0.632645	−	0.793312i
$783$	−4.01954	−	26.5001i	−0.143647	−	0.947035i
$784$	1.04171	+	0.883994i	0.0372039	+	0.0315712i
$785$			10.1557i			0.362473i
$786$	−22.8412	+	10.3149i	−0.814720	+	0.367921i
$787$	−13.9060	+	28.8762i	−0.495697	+	1.02932i	0.491657	+	0.870789i	$0.336392\pi$
$787$	−13.9060	+	28.8762i	−0.495697	+	1.02932i	−0.987353	+	0.158535i	$0.949323\pi$
$788$	−42.9651	+	9.80651i	−1.53057	+	0.349342i
$789$	6.07374	+	8.01326i	0.216231	+	0.285280i
$790$	−16.5085	−	34.2802i	−0.587346	−	1.21964i
$791$	6.12435	−	0.595675i	0.217757	−	0.0211798i
$792$	6.60759	+	37.3376i	0.234791	+	1.32673i
$793$	−15.4710	−	19.4001i	−0.549393	−	0.688916i
$794$	27.9165	−	13.4439i	0.990720	−	0.477106i
$795$	4.34508	−	1.96220i	0.154104	−	0.0695922i
$796$	63.7485	+	14.5502i	2.25950	+	0.515717i
$797$	−7.45030	+	9.34238i	−0.263903	+	0.330924i	−0.896074	−	0.443905i	$-0.853593\pi$
$797$	−7.45030	+	9.34238i	−0.263903	+	0.330924i	0.632171	+	0.774829i	$0.282164\pi$
$798$	−30.7480	+	44.8612i	−1.08847	+	1.58807i
$799$	−1.87174	−	2.34709i	−0.0662174	−	0.0830340i
$800$	−8.98101	−	18.6493i	−0.317527	−	0.659351i
$801$	50.8751	−	21.4830i	1.79758	−	0.759063i
$802$	53.5764			1.89185
$803$	12.3421			0.435543
$804$	27.7781	+	23.2939i	0.979660	+	0.821513i
$805$	−6.92218	−	7.13647i	−0.243975	−	0.251527i
$806$	−33.2918	+	7.59864i	−1.17265	+	0.267651i
$807$	24.1388	+	6.13849i	0.849725	+	0.216085i
$808$	−37.0968	+	29.5838i	−1.30506	+	1.04075i
$809$	−25.5321	+	20.3612i	−0.897660	+	0.715860i	−0.959345	−	0.282236i	$-0.908924\pi$
$809$	−25.5321	+	20.3612i	−0.897660	+	0.715860i	0.0616850	+	0.998096i	$0.480353\pi$
$810$	2.45137	−	24.8094i	0.0861323	−	0.871713i
$811$	−25.4001	+	5.79742i	−0.891919	+	0.203575i	−0.643836	−	0.765164i	$-0.722658\pi$
$811$	−25.4001	+	5.79742i	−0.891919	+	0.203575i	−0.248084	+	0.968739i	$0.579801\pi$
$812$	−23.7362	+	36.5281i	−0.832978	+	1.28188i
$813$	15.6346	−	18.6444i	0.548330	−	0.653887i
$814$	15.7702			0.552745
$815$	−7.89501			−0.276550
$816$	1.04354	+	0.875082i	0.0365312	+	0.0306340i
$817$	−24.8013	−	51.5005i	−0.867688	−	1.80177i
$818$	−4.01673	−	5.03682i	−0.140442	−	0.176108i
$819$	22.4385	−	1.07145i	0.784064	−	0.0374394i
$820$	14.3051	−	17.9380i	0.499556	−	0.626423i
$821$	29.4349	+	6.71833i	1.02729	+	0.234471i	0.702776	−	0.711411i	$-0.251943\pi$
$821$	29.4349	+	6.71833i	1.02729	+	0.234471i	0.324510	+	0.945882i	$0.394801\pi$
$822$	−30.4355	−	67.3960i	−1.06156	−	2.35071i
$823$	39.4542	−	19.0001i	1.37529	−	0.662303i	0.407298	−	0.913295i	$-0.366471\pi$
$823$	39.4542	−	19.0001i	1.37529	−	0.662303i	0.967989	+	0.250992i	$0.0807568\pi$
$824$	−3.80691	−	4.77371i	−0.132620	−	0.166300i
$825$	17.1484	+	22.6244i	0.597031	+	0.787681i
$826$	31.3638	+	32.3347i	1.09129	+	1.12507i
$827$	−14.4237	−	29.9512i	−0.501562	−	1.04150i	−0.986010	−	0.166684i	$-0.946694\pi$
$827$	−14.4237	−	29.9512i	−0.501562	−	1.04150i	0.484448	−	0.874820i	$-0.339020\pi$
$828$	29.1474	−	5.15818i	1.01294	−	0.179259i
$829$	−19.2613	+	4.39627i	−0.668973	+	0.152689i	−0.543501	−	0.839408i	$-0.682902\pi$
$829$	−19.2613	+	4.39627i	−0.668973	+	0.152689i	−0.125472	+	0.992097i	$0.540044\pi$
$830$	2.74922	−	5.70881i	0.0954267	−	0.198156i
$831$	−4.09289	−	9.06326i	−0.141981	−	0.314401i
$832$		−	36.7944i		−	1.27562i
$833$	27.6716	−	5.43428i	0.958765	−	0.188287i
$834$	20.5315	−	40.0789i	0.710947	−	1.38782i
$835$	−2.85057	+	3.57450i	−0.0986481	+	0.123701i
$836$	−69.7066	−	33.5689i	−2.41085	−	1.16100i
$837$	25.6032	−	10.0761i	0.884974	−	0.348281i
$838$	−2.40597	+	4.99606i	−0.0831130	+	0.172586i
$839$	0.947402	−	0.456245i	0.0327079	−	0.0157513i	−0.417458	−	0.908696i	$-0.637079\pi$
$839$	0.947402	−	0.456245i	0.0327079	−	0.0157513i	0.450166	+	0.892945i	$0.351365\pi$
$840$	−11.1171	+	10.2643i	−0.383576	+	0.354152i
$841$	−2.15534	−	1.03795i	−0.0743219	−	0.0357915i
$842$	22.8464	−	18.2194i	0.787339	−	0.627882i
$843$	13.5292	+	0.333185i	0.465971	+	0.0114755i
$844$	−10.1655	+	12.7471i	−0.349911	+	0.438775i
$845$	1.34984	−	5.91404i	0.0464359	−	0.203449i
$846$	0.250744	−	5.08773i	0.00862075	−	0.174920i
$847$	9.71542	−	26.4642i	0.333826	−	0.909320i
$848$	−0.345512	+	0.275537i	−0.0118649	+	0.00946197i
$849$	16.2515	+	0.400227i	0.557750	+	0.0137357i
$850$	−31.5210	−	7.19446i	−1.08116	−	0.246768i
$851$		−	4.59729i		−	0.157593i
$852$	−11.7263	−	6.00711i	−0.401736	−	0.205800i
$853$	12.4496	+	2.84153i	0.426265	+	0.0972921i	0.430271	−	0.902700i	$-0.358418\pi$
$853$	12.4496	+	2.84153i	0.426265	+	0.0972921i	−0.00400617	+	0.999992i	$0.501275\pi$
$854$	−5.11673	−	52.6070i	−0.175091	−	1.80017i
$855$	14.2505	+	12.5604i	0.487358	+	0.429557i
$856$	9.23211	+	40.4485i	0.315547	+	1.38250i
$857$	−11.7847	−	14.7775i	−0.402557	−	0.504790i	0.538693	−	0.842502i	$-0.318918\pi$
$857$	−11.7847	−	14.7775i	−0.402557	−	0.504790i	−0.941249	+	0.337712i	$0.890347\pi$
$858$	10.3153	+	50.9451i	0.352158	+	1.73924i
$859$	18.8033	−	4.29173i	0.641560	−	0.146432i	0.110649	−	0.993860i	$-0.464707\pi$
$859$	18.8033	−	4.29173i	0.641560	−	0.146432i	0.530911	+	0.847428i	$0.321850\pi$
$860$	−9.47611	−	41.5175i	−0.323133	−	1.41574i
$861$	−25.1978	−	9.96111i	−0.858738	−	0.339474i
$862$	8.40630	−	36.8304i	0.286320	−	1.25445i
$863$			26.8824i			0.915087i	0.889187	+	0.457543i	$0.151271\pi$
$863$			26.8824i			0.915087i	−0.889187	+	0.457543i	$0.848729\pi$
$864$	4.57950	+	30.1917i	0.155798	+	1.02714i
$865$	4.10908	−	18.0031i	0.139713	−	0.612123i
$866$	−18.2269	+	8.77763i	−0.619376	+	0.298276i
$867$	−1.30784	+	0.264809i	−0.0444165	+	0.00899338i
$868$	−41.9794	−	15.4113i	−1.42487	−	0.523093i
$869$	−49.9741	−	39.8530i	−1.69526	−	1.35192i
$870$	18.9634	+	15.9021i	0.642919	+	0.539132i
$871$	14.5092	+	11.5707i	0.491627	+	0.392059i
$872$	−1.52254	−	3.16158i	−0.0515596	−	0.107065i
$873$	−7.06195	−	1.98218i	−0.239011	−	0.0670867i
$874$	−15.9175	+	33.0530i	−0.538417	+	1.11803i
$875$	−9.44632	+	25.7312i	−0.319344	+	0.869872i
$876$	−14.6588	−	0.361003i	−0.495274	−	0.0121972i
$877$	−13.5239	−	6.51277i	−0.456670	−	0.219921i	0.191384	−	0.981515i	$-0.438703\pi$
$877$	−13.5239	−	6.51277i	−0.456670	−	0.219921i	−0.648054	+	0.761595i	$0.724417\pi$
$878$	4.12134	+	18.0568i	0.139089	+	0.609387i
$879$	17.2134	−	13.0471i	0.580594	−	0.440067i
$880$	0.863255	+	0.688423i	0.0291003	+	0.0232067i
$881$	16.2425			0.547225			0.273613	−	0.961840i	$-0.411781\pi$
$881$	16.2425			0.547225			0.273613	+	0.961840i	$0.411781\pi$
$882$	41.3213	+	24.1291i	1.39136	+	0.812470i
$883$	3.25846			0.109656			0.0548280	−	0.998496i	$-0.482539\pi$
$883$	3.25846			0.109656			0.0548280	+	0.998496i	$0.482539\pi$
$884$	−28.4542	−	22.6915i	−0.957019	−	0.763197i
$885$	12.5387	−	9.50387i	0.421485	−	0.319469i
$886$	−10.1415	−	44.4329i	−0.340711	−	1.49275i
$887$	34.3334	+	16.5341i	1.15280	+	0.555160i	0.909874	−	0.414884i	$-0.136178\pi$
$887$	34.3334	+	16.5341i	1.15280	+	0.555160i	0.242928	+	0.970044i	$0.421892\pi$
$888$	−6.99451	−	0.172254i	−0.234720	−	0.00578047i
$889$	−38.5583	+	37.4005i	−1.29320	+	1.25437i
$890$	−22.1244	+	45.9417i	−0.741610	+	1.53997i
$891$	−14.3734	−	39.3381i	−0.481526	−	1.31787i
$892$	−9.72108	−	20.1860i	−0.325486	−	0.675878i
$893$	3.03456	+	2.41998i	0.101548	+	0.0809816i
$894$	21.2022	+	17.7795i	0.709106	+	0.594635i
$895$	13.5705	+	10.8221i	0.453612	+	0.361743i
$896$	25.7606	−	39.6434i	0.860602	−	1.32439i
$897$	14.8514	−	3.00708i	0.495873	−	0.100404i
$898$	68.4093	−	32.9442i	2.28285	−	1.09936i
$899$	−6.07792	+	26.6291i	−0.202710	+	0.888131i
$900$	−19.7055	−	27.3727i	−0.656850	−	0.912424i
$901$			9.12171i			0.303888i
$902$	13.9509	−	61.1230i	0.464515	−	2.03517i
$903$	−43.6151	+	25.0381i	−1.45142	+	0.833217i
$904$	−1.40562	−	6.15840i	−0.0467501	−	0.204825i
$905$	7.16743	−	1.63592i	0.238254	−	0.0543798i
$906$	−11.6596	−	57.5846i	−0.387365	−	1.91312i
$907$	−21.0969	−	26.4547i	−0.700512	−	0.878414i	0.296550	−	0.955017i	$-0.404164\pi$
$907$	−21.0969	−	26.4547i	−0.700512	−	0.878414i	−0.997062	+	0.0766036i	$0.975592\pi$
$908$	−18.0818	−	79.2213i	−0.600064	−	2.62905i
$909$	34.6538	−	39.3168i	1.14939	−	1.30406i
$910$	−14.8886	+	14.4416i	−0.493553	+	0.478733i
$911$	−13.7758	−	3.14424i	−0.456413	−	0.104173i	−0.0118676	−	0.999930i	$-0.503778\pi$
$911$	−13.7758	−	3.14424i	−0.456413	−	0.104173i	−0.444546	+	0.895756i	$0.646635\pi$
$912$	−1.56713	−	0.802806i	−0.0518929	−	0.0265836i
$913$		−	10.6447i		−	0.352288i
$914$	−22.1458	−	5.05463i	−0.732517	−	0.167192i
$915$	−18.4551	−	0.454496i	−0.610108	−	0.0150252i
$916$	−19.8448	+	15.8257i	−0.655690	+	0.522896i
$917$	−16.6650	−	2.13538i	−0.550328	−	0.0705166i
$918$	41.3302	+	23.8106i	1.36410	+	0.785866i
$919$	10.1887	−	44.6394i	0.336093	−	1.47252i	−0.471020	−	0.882122i	$-0.656114\pi$
$919$	10.1887	−	44.6394i	0.336093	−	1.47252i	0.807113	−	0.590397i	$-0.201029\pi$
$920$	−6.36354	+	7.97963i	−0.209800	+	0.263081i
$921$	−7.55695	−	0.186106i	−0.249010	−	0.00613239i
$922$	57.4785	−	45.8376i	1.89295	−	1.50958i
$923$	−6.07672	−	2.92639i	−0.200018	−	0.0963234i
$924$	−25.0246	+	63.3027i	−0.823250	+	2.08251i
$925$	−4.71959	+	2.27284i	−0.155179	+	0.0747304i
$926$	8.72877	−	18.1255i	0.286845	−	0.595640i
$927$	5.05938	+	4.45933i	0.166172	+	0.146464i
$928$	−27.3123	−	13.1529i	−0.896571	−	0.431766i
$929$	−33.2796	+	41.7314i	−1.09187	+	1.36916i	−0.168298	+	0.985736i	$0.553827\pi$
$929$	−33.2796	+	41.7314i	−1.09187	+	1.36916i	−0.923572	+	0.383425i	$0.874744\pi$
$930$	−11.5831	+	22.6111i	−0.379826	+	0.741446i
$931$	−33.3164	+	14.8109i	−1.09190	+	0.485409i
$932$			28.5828i			0.936260i
$933$	−1.90374	−	4.21562i	−0.0623256	−	0.138013i
$934$	3.70848	−	7.70074i	0.121345	−	0.251976i
$935$	22.2190	−	5.07134i	0.726639	−	0.165851i
$936$	−4.01864	−	22.7082i	−0.131353	−	0.742241i
$937$	−9.34352	−	19.4020i	−0.305239	−	0.633836i	0.690771	−	0.723074i	$-0.257271\pi$
$937$	−9.34352	−	19.4020i	−0.305239	−	0.633836i	−0.996010	+	0.0892374i	$0.971557\pi$
$938$	12.4858	+	37.5066i	0.407677	+	1.22463i
$939$	−18.1598	−	23.9588i	−0.592624	−	0.781867i
$940$	1.80289	+	2.26076i	0.0588039	+	0.0737377i
$941$	45.6320	−	21.9752i	1.48756	−	0.716371i	0.498916	−	0.866650i	$-0.333732\pi$
$941$	45.6320	−	21.9752i	1.48756	−	0.716371i	0.988644	+	0.150279i	$0.0480173\pi$
$942$	−13.5696	−	30.0483i	−0.442120	−	0.979027i
$943$	−17.8184	−	4.06694i	−0.580247	−	0.132438i
$944$	−0.909297	+	1.14022i	−0.0295951	+	0.0371111i
$945$	10.1157	−	13.3037i	0.329065	−	0.432768i
$946$	−72.5536	−	90.9793i	−2.35892	−	2.95799i
$947$	24.9201	+	51.7471i	0.809793	+	1.68155i	0.728686	+	0.684848i	$0.240131\pi$
$947$	24.9201	+	51.7471i	0.809793	+	1.68155i	0.0811073	+	0.996705i	$0.474154\pi$
$948$	58.1889	+	48.7954i	1.88989	+	1.58480i
$949$	−7.50629			−0.243664
$950$	41.8017			1.35623
$951$	−1.34820	+	1.60774i	−0.0437184	+	0.0521345i
$952$	−9.14388	−	27.4676i	−0.296355	−	0.890230i
$953$	47.7629	−	10.9016i	1.54719	−	0.353136i	0.638173	−	0.769893i	$-0.279690\pi$
$953$	47.7629	−	10.9016i	1.54719	−	0.353136i	0.909018	+	0.416757i	$0.136833\pi$
$954$	−10.2342	+	11.6114i	−0.331346	+	0.375932i
$955$	−14.4968	+	11.5608i	−0.469104	+	0.374098i
$956$	−20.2167	+	16.1222i	−0.653853	+	0.521431i
$957$	40.2939	+	10.2467i	1.30252	+	0.331230i
$958$	83.2314	−	18.9970i	2.68909	−	0.613766i
$959$	6.30073	−	49.1723i	0.203461	−	1.58786i
$960$	−20.9753	−	17.5892i	−0.676975	−	0.567691i
$961$	2.96114			0.0955208
$962$	−9.59120			−0.309233
$963$	−17.8267	−	42.2165i	−0.574457	−	1.36041i
$964$	−30.3529	−	63.0284i	−0.977600	−	2.03001i
$965$	−8.16905	−	10.2437i	−0.262971	−	0.329755i
$966$	30.0164	+	11.8660i	0.965763	+	0.381783i
$967$	−38.0675	+	47.7351i	−1.22417	+	1.53506i	−0.463224	+	0.886241i	$0.653307\pi$
$967$	−38.0675	+	47.7351i	−1.22417	+	1.53506i	−0.760944	+	0.648817i	$0.775264\pi$
$968$	−28.2148	−	6.43984i	−0.906857	−	0.206984i
$969$	−33.1233	+	14.9582i	−1.06407	+	0.480527i
$970$	6.10188	−	2.93851i	0.195920	−	0.0943499i
$971$	−9.26106	−	11.6130i	−0.297202	−	0.372679i	0.610700	−	0.791862i	$-0.290888\pi$
$971$	−9.26106	−	11.6130i	−0.297202	−	0.372679i	−0.907902	+	0.419183i	$0.862317\pi$
$972$	15.9207	+	47.1425i	0.510657	+	1.51209i
$973$	25.8031	−	15.6698i	0.827208	−	0.502349i
$974$	12.6703	+	26.3102i	0.405984	+	0.843034i
$975$	−10.4294	−	13.7598i	−0.334009	−	0.440668i
$976$	1.66829	−	0.380777i	0.0534007	−	0.0121884i
$977$	−6.36068	+	13.2081i	−0.203496	+	0.422564i	−0.977593	−	0.210503i	$-0.932490\pi$
$977$	−6.36068	+	13.2081i	−0.203496	+	0.422564i	0.774097	+	0.633067i	$0.218204\pi$
$978$	23.3594	−	10.5489i	0.746952	−	0.337317i
$979$			85.6635i			2.73782i
$980$	−26.6538	+	5.23439i	−0.851424	+	0.167206i
$981$	2.26451	+	3.14561i	0.0723001	+	0.100431i
$982$	−51.4466	+	64.5120i	−1.64173	+	2.05866i
$983$	52.1166	+	25.0980i	1.66226	+	0.800503i	0.998624	+	0.0524492i	$0.0167028\pi$
$983$	52.1166	+	25.0980i	1.66226	+	0.800503i	0.663638	+	0.748054i	$0.269012\pi$
$984$	−6.85524	+	26.9573i	−0.218537	+	0.859368i
$985$	−7.28235	+	15.1220i	−0.232035	+	0.481826i
$986$	−42.6614	+	20.5446i	−1.35861	+	0.654274i
$987$	1.93060	−	2.81674i	0.0614517	−	0.0896577i
$988$	42.3945	+	20.4161i	1.34875	+	0.649524i
$989$	−26.5221	+	21.1506i	−0.843353	+	0.672551i
$990$	33.9733	+	18.4735i	1.07974	+	0.587125i
$991$	−9.54219	+	11.9655i	−0.303118	+	0.380097i	−0.909940	−	0.414740i	$-0.863873\pi$
$991$	−9.54219	+	11.9655i	−0.303118	+	0.380097i	0.606822	+	0.794838i	$0.292444\pi$
$992$	6.92462	−	30.3387i	0.219857	−	0.963256i
$993$	4.45826	+	9.87233i	0.141479	+	0.313289i
$994$	−7.45727	−	12.2797i	−0.236530	−	0.389489i
$995$	19.4700	−	15.5268i	0.617240	−	0.492232i
$996$	−0.311355	+	12.6428i	−0.00986565	+	0.400602i
$997$	−22.9953	−	5.24852i	−0.728268	−	0.166222i	−0.157717	−	0.987484i	$-0.550413\pi$
$997$	−22.9953	−	5.24852i	−0.728268	−	0.166222i	−0.570551	+	0.821262i	$0.693270\pi$
$998$		−	36.8438i		−	1.16627i
$999$	7.64066	−	1.15894i	0.241740	−	0.0366672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.2.k.a.104.15	yes	96
3.2	odd	2	inner	147.2.k.a.104.2	yes	96
49.41	odd	14	inner	147.2.k.a.41.2	✓	96
147.41	even	14	inner	147.2.k.a.41.15	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.2.k.a.41.2	✓	96	49.41	odd	14	inner
147.2.k.a.41.15	yes	96	147.41	even	14	inner
147.2.k.a.104.2	yes	96	3.2	odd	2	inner
147.2.k.a.104.15	yes	96	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	147.k (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.78148 + 1.42068i) q^{2} +(-1.38035 + 1.04625i) q^{3} +(0.710285 + 3.11196i) q^{4} +(1.09528 + 0.527460i) q^{5} +(-3.94544 - 0.0971647i) q^{6} +(-2.21851 - 1.44160i) q^{7} +(-1.17846 + 2.44709i) q^{8} +(0.810724 - 2.88838i) q^{9} +(1.20187 + 2.49571i) q^{10} +(3.63827 + 2.90142i) q^{11} +(-4.23633 - 3.55246i) q^{12} +(-2.21274 - 1.76460i) q^{13} +(-1.90416 - 5.71997i) q^{14} +(-2.06373 + 0.417860i) q^{15} +(0.175848 - 0.0846840i) q^{16} +(0.896447 - 3.92759i) q^{17} +(5.54775 - 3.99380i) q^{18} +5.20859i q^{19} +(-0.863474 + 3.78312i) q^{20} +(4.57059 - 0.331197i) q^{21} +(2.35950 + 10.3376i) q^{22} +(3.01360 - 0.687835i) q^{23} +(-0.933585 - 4.61079i) q^{24} +(-2.19602 - 2.75372i) q^{25} +(-1.43501 - 6.28720i) q^{26} +(1.90288 + 4.83519i) q^{27} +(2.91044 - 7.92786i) q^{28} +(-5.02894 - 1.14782i) q^{29} +(-4.27013 - 2.18749i) q^{30} -5.29517i q^{31} +(5.72951 + 1.30772i) q^{32} +(-8.05769 - 0.198437i) q^{33} +(7.17685 - 5.72335i) q^{34} +(-1.66950 - 2.74914i) q^{35} +(9.56436 + 0.471370i) q^{36} +(0.330947 - 1.44998i) q^{37} +(-7.39975 + 9.27899i) q^{38} +(4.90057 + 0.120687i) q^{39} +(-2.58148 + 2.05867i) q^{40} +(-5.32713 - 2.56541i) q^{41} +(8.61293 + 5.90333i) q^{42} +(-9.88760 + 4.76162i) q^{43} +(-6.44491 + 13.3830i) q^{44} +(2.41148 - 2.73597i) q^{45} +(6.34585 + 3.05600i) q^{46} +(0.464613 - 0.582607i) q^{47} +(-0.154131 + 0.300874i) q^{48} +(2.84356 + 6.39642i) q^{49} -8.02553i q^{50} +(2.87183 + 6.35935i) q^{51} +(3.91970 - 8.13934i) q^{52} +(-2.20747 + 0.503841i) q^{53} +(-3.47931 + 11.3172i) q^{54} +(2.45455 + 5.09692i) q^{55} +(6.14215 - 3.73002i) q^{56} +(-5.44949 - 7.18967i) q^{57} +(-7.32825 - 9.18934i) q^{58} +(-6.73222 + 3.24207i) q^{59} +(-2.76620 - 6.12544i) q^{60} +(8.54761 + 1.95094i) q^{61} +(7.52275 - 9.43323i) q^{62} +(-5.96249 + 5.23915i) q^{63} +(8.10575 + 10.1643i) q^{64} +(-1.49282 - 3.09988i) q^{65} +(-14.0727 - 11.8009i) q^{66} -6.55713 q^{67} +12.8592 q^{68} +(-3.44017 + 4.10243i) q^{69} +(0.931464 - 7.26936i) q^{70} +(2.32335 - 0.530289i) q^{71} +(6.11271 + 5.38774i) q^{72} +(2.07358 - 1.65362i) q^{73} +(2.64953 - 2.11293i) q^{74} +(5.91235 + 1.50351i) q^{75} +(-16.2089 + 3.69958i) q^{76} +(-3.88883 - 11.6818i) q^{77} +(8.55880 + 7.17715i) q^{78} -13.7357 q^{79} +0.237271 q^{80} +(-7.68545 - 4.68335i) q^{81} +(-5.84553 - 12.1384i) q^{82} +(-1.42620 - 1.78840i) q^{83} +(4.27709 + 13.9883i) q^{84} +(3.05351 - 3.82898i) q^{85} +(-24.3793 - 5.56441i) q^{86} +(8.14260 - 3.67713i) q^{87} +(-11.3876 + 5.48397i) q^{88} +(11.4774 + 14.3922i) q^{89} +(8.18292 - 1.44812i) q^{90} +(2.36513 + 7.10469i) q^{91} +(4.28103 + 8.88965i) q^{92} +(5.54007 + 7.30918i) q^{93} +(1.65540 - 0.377833i) q^{94} +(-2.74733 + 5.70488i) q^{95} +(-9.27692 + 4.18938i) q^{96} -2.44495i q^{97} +(-4.02154 + 15.4349i) q^{98} +(11.3300 - 8.15644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 7 q^{3} + 2 q^{4} + 7 q^{6} - 14 q^{7} + 5 q^{9} - 14 q^{10} - 42 q^{12} - 14 q^{13} - 5 q^{15} - 22 q^{16} - 18 q^{18} - 7 q^{21} + 4 q^{22} - 7 q^{24} - 26 q^{25} - 28 q^{27} + 28 q^{28} - 20 q^{30}+ \cdots + 100 q^{99}+O(q^{100}) \) 96 * q - 7 * q^3 + 2 * q^4 + 7 * q^6 - 14 * q^7 + 5 * q^9 - 14 * q^10 - 42 * q^12 - 14 * q^13 - 5 * q^15 - 22 * q^16 - 18 * q^18 - 7 * q^21 + 4 * q^22 - 7 * q^24 - 26 * q^25 - 28 * q^27 + 28 * q^28 - 20 * q^30 - 7 * q^33 - 70 * q^34 - 37 * q^36 + 38 * q^37 - 9 * q^39 - 28 * q^40 + 7 * q^42 - 18 * q^43 + 14 * q^45 + 62 * q^46 + 14 * q^49 - q^51 + 112 * q^52 - 7 * q^54 - 56 * q^55 + q^57 - 84 * q^58 + 111 * q^60 + 84 * q^61 - 7 * q^63 - 2 * q^64 + 21 * q^66 - 16 * q^67 - 91 * q^69 - 70 * q^70 - 27 * q^72 - 14 * q^73 + 119 * q^75 + 210 * q^76 - 87 * q^78 - 32 * q^79 - 71 * q^81 - 84 * q^82 + 154 * q^84 + 46 * q^85 + 49 * q^87 - 22 * q^88 + 203 * q^90 - 42 * q^91 + 53 * q^93 - 42 * q^94 - 28 * q^96 + 100 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more