LMFDB - Embedded newform 200.2.o.a.189.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [200,2,Mod(29,200)] 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("200.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(200, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.o (of order $10$, degree $4$, 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:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			189.10
Character	$\chi$	$=$	200.189
Dual form			200.2.o.a.109.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.729227 - 1.21170i) q^{2} +(-0.305611 + 0.940574i) q^{3} +(-0.936457 + 1.76721i) q^{4} +(1.04427 - 1.97724i) q^{5} +(1.36256 - 0.315581i) q^{6} +3.68114i q^{7} +(2.82423 - 0.153991i) q^{8} +(1.63577 + 1.18846i) q^{9} +(-3.15735 + 0.176505i) q^{10} +(-2.38116 - 3.27739i) q^{11} +(-1.37601 - 1.42089i) q^{12} +(4.97551 + 3.61492i) q^{13} +(4.46045 - 2.68438i) q^{14} +(1.54060 + 1.58649i) q^{15} +(-2.24610 - 3.30984i) q^{16} +(3.70129 - 1.20262i) q^{17} +(0.247211 - 2.84872i) q^{18} +(3.35127 - 1.08889i) q^{19} +(2.51629 + 3.69706i) q^{20} +(-3.46238 - 1.12500i) q^{21} +(-2.23482 + 5.27522i) q^{22} +(1.50362 + 2.06955i) q^{23} +(-0.718277 + 2.70346i) q^{24} +(-2.81898 - 4.12957i) q^{25} +(0.751941 - 8.66495i) q^{26} +(-4.01804 + 2.91928i) q^{27} +(-6.50536 - 3.44723i) q^{28} +(-5.85554 - 1.90258i) q^{29} +(0.798904 - 3.02366i) q^{30} +(1.35546 + 4.17167i) q^{31} +(-2.37264 + 5.13523i) q^{32} +(3.81033 - 1.23805i) q^{33} +(-4.15630 - 3.60789i) q^{34} +(7.27850 + 3.84412i) q^{35} +(-3.63208 + 1.77782i) q^{36} +(-2.99215 - 2.17392i) q^{37} +(-3.76325 - 3.26670i) q^{38} +(-4.92068 + 3.57508i) q^{39} +(2.64480 - 5.74500i) q^{40} +(-3.35481 - 2.43741i) q^{41} +(1.16170 + 5.01577i) q^{42} +1.74279 q^{43} +(8.02170 - 1.13889i) q^{44} +(4.05806 - 1.99324i) q^{45} +(1.41121 - 3.33111i) q^{46} +(-4.86486 - 1.58069i) q^{47} +(3.79958 - 1.10110i) q^{48} -6.55078 q^{49} +(-2.94815 + 6.42716i) q^{50} +3.84887i q^{51} +(-11.0477 + 5.40758i) q^{52} +(-3.95398 + 12.1691i) q^{53} +(6.46737 + 2.73986i) q^{54} +(-8.96677 + 1.28564i) q^{55} +(0.566862 + 10.3964i) q^{56} +3.48489i q^{57} +(1.96465 + 8.48260i) q^{58} +(0.784512 - 1.07979i) q^{59} +(-4.24637 + 1.23690i) q^{60} +(0.998070 + 1.37373i) q^{61} +(4.06640 - 4.68451i) q^{62} +(-4.37487 + 6.02149i) q^{63} +(7.95257 - 0.869812i) q^{64} +(12.3434 - 6.06283i) q^{65} +(-4.27875 - 3.71418i) q^{66} +(-4.50052 - 13.8512i) q^{67} +(-1.34081 + 7.66718i) q^{68} +(-2.40609 + 0.781786i) q^{69} +(-0.649740 - 11.6226i) q^{70} +(1.24027 - 3.81715i) q^{71} +(4.80280 + 3.10458i) q^{72} +(-5.69843 - 7.84322i) q^{73} +(-0.452199 + 5.21089i) q^{74} +(4.74568 - 1.38942i) q^{75} +(-1.21401 + 6.94211i) q^{76} +(12.0645 - 8.76538i) q^{77} +(7.92023 + 3.35536i) q^{78} +(4.76893 - 14.6772i) q^{79} +(-8.88990 + 0.984695i) q^{80} +(0.356584 + 1.09745i) q^{81} +(-0.507007 + 5.84247i) q^{82} +(0.520370 + 1.60153i) q^{83} +(5.23049 - 5.06527i) q^{84} +(1.48729 - 8.57422i) q^{85} +(-1.27089 - 2.11174i) q^{86} +(3.57904 - 4.92612i) q^{87} +(-7.22964 - 8.88942i) q^{88} +(6.61157 - 4.80359i) q^{89} +(-5.37446 - 3.46365i) q^{90} +(-13.3070 + 18.3156i) q^{91} +(-5.06542 + 0.719169i) q^{92} -4.33801 q^{93} +(1.63226 + 7.04745i) q^{94} +(1.34664 - 7.76337i) q^{95} +(-4.10496 - 3.80103i) q^{96} +(-6.90528 - 2.24366i) q^{97} +(4.77700 + 7.93761i) q^{98} -8.19095i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28}+ \cdots + 90 q^{98}+O(q^{100}) $ 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.729227	−	1.21170i	−0.515641	−	0.856805i
$2$	−0.729227	−	1.21170i	−0.515641	−	0.856805i
$3$	−0.305611	+	0.940574i	−0.176445	+	0.543041i	−0.999697	−	0.0246354i	$-0.992158\pi$
$3$	−0.305611	+	0.940574i	−0.176445	+	0.543041i	0.823252	+	0.567676i	$0.192158\pi$
$4$	−0.936457	+	1.76721i	−0.468228	+	0.883607i
$5$	1.04427	−	1.97724i	0.467014	−	0.884250i
$5$	1.04427	−	1.97724i	0.467014	−	0.884250i
$6$	1.36256	−	0.315581i	0.556262	−	0.128836i
$7$			3.68114i			1.39134i	0.718362	+	0.695670i	$0.244892\pi$
$7$			3.68114i			1.39134i	−0.718362	+	0.695670i	$0.755108\pi$
$8$	2.82423	−	0.153991i	0.998517	−	0.0544440i
$9$	1.63577	+	1.18846i	0.545256	+	0.396152i
$10$	−3.15735	+	0.176505i	−0.998441	+	0.0558159i
$11$	−2.38116	−	3.27739i	−0.717947	−	0.988169i	−0.999590	−	0.0286497i	$-0.990879\pi$
$11$	−2.38116	−	3.27739i	−0.717947	−	0.988169i	0.281643	−	0.959519i	$-0.409121\pi$
$12$	−1.37601	−	1.42089i	−0.397219	−	0.410175i
$13$	4.97551	+	3.61492i	1.37996	+	1.00260i	0.996884	+	0.0788822i	$0.0251351\pi$
$13$	4.97551	+	3.61492i	1.37996	+	1.00260i	0.383076	+	0.923717i	$0.374865\pi$
$14$	4.46045	−	2.68438i	1.19211	−	0.717432i
$15$	1.54060	+	1.58649i	0.397782	+	0.409629i
$16$	−2.24610	−	3.30984i	−0.561524	−	0.827460i
$17$	3.70129	−	1.20262i	0.897694	−	0.291679i	0.176409	−	0.984317i	$-0.443552\pi$
$17$	3.70129	−	1.20262i	0.897694	−	0.291679i	0.721285	+	0.692638i	$0.243552\pi$
$18$	0.247211	−	2.84872i	0.0582682	−	0.671450i
$19$	3.35127	−	1.08889i	0.768833	−	0.249809i	0.101768	−	0.994808i	$-0.467550\pi$
$19$	3.35127	−	1.08889i	0.768833	−	0.249809i	0.667065	+	0.744999i	$0.267550\pi$
$20$	2.51629	+	3.69706i	0.562661	+	0.826688i
$21$	−3.46238	−	1.12500i	−0.755554	−	0.245494i
$22$	−2.23482	+	5.27522i	−0.476465	+	1.12468i
$23$	1.50362	+	2.06955i	0.313526	+	0.431531i	0.936477	−	0.350730i	$-0.114066\pi$
$23$	1.50362	+	2.06955i	0.313526	+	0.431531i	−0.622951	+	0.782261i	$0.714066\pi$
$24$	−0.718277	+	2.70346i	−0.146618	+	0.551842i
$25$	−2.81898	−	4.12957i	−0.563796	−	0.825914i
$26$	0.751941	−	8.66495i	0.147468	−	1.69934i
$27$	−4.01804	+	2.91928i	−0.773272	+	0.561815i
$28$	−6.50536	−	3.44723i	−1.22940	−	0.651465i
$29$	−5.85554	−	1.90258i	−1.08735	−	0.353300i	−0.290126	−	0.956988i	$-0.593697\pi$
$29$	−5.85554	−	1.90258i	−1.08735	−	0.353300i	−0.797220	+	0.603688i	$0.793697\pi$
$30$	0.798904	−	3.02366i	0.145859	−	0.552043i
$31$	1.35546	+	4.17167i	0.243448	+	0.749255i	0.995888	+	0.0905941i	$0.0288766\pi$
$31$	1.35546	+	4.17167i	0.243448	+	0.749255i	−0.752440	+	0.658660i	$0.771123\pi$
$32$	−2.37264	+	5.13523i	−0.419427	+	0.907789i
$33$	3.81033	−	1.23805i	0.663294	−	0.215517i
$34$	−4.15630	−	3.60789i	−0.712800	−	0.618747i
$35$	7.27850	+	3.84412i	1.23029	+	0.649775i
$36$	−3.63208	+	1.77782i	−0.605347	+	0.296303i
$37$	−2.99215	−	2.17392i	−0.491906	−	0.357391i	0.314011	−	0.949420i	$-0.398327\pi$
$37$	−2.99215	−	2.17392i	−0.491906	−	0.357391i	−0.805917	+	0.592029i	$0.798327\pi$
$38$	−3.76325	−	3.26670i	−0.610479	−	0.529928i
$39$	−4.92068	+	3.57508i	−0.787939	+	0.572471i
$40$	2.64480	−	5.74500i	0.418179	−	0.908365i
$41$	−3.35481	−	2.43741i	−0.523934	−	0.380660i	0.294150	−	0.955759i	$-0.404963\pi$
$41$	−3.35481	−	2.43741i	−0.523934	−	0.380660i	−0.818084	+	0.575099i	$0.804963\pi$
$42$	1.16170	+	5.01577i	0.179254	+	0.773949i
$43$	1.74279			0.265772			0.132886	−	0.991131i	$-0.457576\pi$
$43$	1.74279			0.265772			0.132886	+	0.991131i	$0.457576\pi$
$44$	8.02170	−	1.13889i	1.20932	−	0.171694i
$45$	4.05806	−	1.99324i	0.604940	−	0.297134i
$46$	1.41121	−	3.33111i	0.208071	−	0.491146i
$47$	−4.86486	−	1.58069i	−0.709612	−	0.230567i	−0.0680985	−	0.997679i	$-0.521693\pi$
$47$	−4.86486	−	1.58069i	−0.709612	−	0.230567i	−0.641514	+	0.767112i	$0.721693\pi$
$48$	3.79958	−	1.10110i	0.548423	−	0.158930i
$49$	−6.55078			−0.935825
$50$	−2.94815	+	6.42716i	−0.416931	+	0.908938i
$51$			3.84887i			0.538950i
$52$	−11.0477	+	5.40758i	−1.53204	+	0.749897i
$53$	−3.95398	+	12.1691i	−0.543121	+	1.67155i	0.182295	+	0.983244i	$0.441647\pi$
$53$	−3.95398	+	12.1691i	−0.543121	+	1.67155i	−0.725416	+	0.688310i	$0.758353\pi$
$54$	6.46737	+	2.73986i	0.880097	+	0.372848i
$55$	−8.96677	+	1.28564i	−1.20908	+	0.173356i
$56$	0.566862	+	10.3964i	0.0757501	+	1.38928i
$57$			3.48489i			0.461585i
$58$	1.96465	+	8.48260i	0.257971	+	1.11382i
$59$	0.784512	−	1.07979i	0.102135	−	0.140576i	−0.754891	−	0.655851i	$-0.772310\pi$
$59$	0.784512	−	1.07979i	0.102135	−	0.140576i	0.857025	+	0.515274i	$0.172310\pi$
$60$	−4.24637	+	1.23690i	−0.548204	+	0.159683i
$61$	0.998070	+	1.37373i	0.127790	+	0.175888i	0.868118	−	0.496358i	$-0.165330\pi$
$61$	0.998070	+	1.37373i	0.127790	+	0.175888i	−0.740328	+	0.672246i	$0.765330\pi$
$62$	4.06640	−	4.68451i	0.516433	−	0.594933i
$63$	−4.37487	+	6.02149i	−0.551182	+	0.758637i
$64$	7.95257	−	0.869812i	0.994072	−	0.108726i
$65$	12.3434	−	6.06283i	1.53101	−	0.752001i
$66$	−4.27875	−	3.71418i	−0.526678	−	0.457184i
$67$	−4.50052	−	13.8512i	−0.549826	−	1.69219i	−0.709230	−	0.704977i	$-0.750957\pi$
$67$	−4.50052	−	13.8512i	−0.549826	−	1.69219i	0.159404	−	0.987213i	$-0.449043\pi$
$68$	−1.34081	+	7.66718i	−0.162597	+	0.929782i
$69$	−2.40609	+	0.781786i	−0.289659	+	0.0941160i
$70$	−0.649740	−	11.6226i	−0.0776588	−	1.38917i
$71$	1.24027	−	3.81715i	0.147193	−	0.453013i	−0.850094	−	0.526631i	$-0.823455\pi$
$71$	1.24027	−	3.81715i	0.147193	−	0.453013i	0.997286	+	0.0736188i	$0.0234548\pi$
$72$	4.80280	+	3.10458i	0.566016	+	0.365878i
$73$	−5.69843	−	7.84322i	−0.666951	−	0.917979i	0.332736	−	0.943020i	$-0.392028\pi$
$73$	−5.69843	−	7.84322i	−0.666951	−	0.917979i	−0.999686	+	0.0250412i	$0.992028\pi$
$74$	−0.452199	+	5.21089i	−0.0525670	+	0.605753i
$75$	4.74568	−	1.38942i	0.547984	−	0.160436i
$76$	−1.21401	+	6.94211i	−0.139256	+	0.796314i
$77$	12.0645	−	8.76538i	1.37488	−	0.998908i
$78$	7.92023	+	3.35536i	0.896790	+	0.379920i
$79$	4.76893	−	14.6772i	0.536546	−	1.65132i	−0.203738	−	0.979025i	$-0.565309\pi$
$79$	4.76893	−	14.6772i	0.536546	−	1.65132i	0.740284	−	0.672294i	$-0.234691\pi$
$80$	−8.88990	+	0.984695i	−0.993921	+	0.110092i
$81$	0.356584	+	1.09745i	0.0396205	+	0.121939i
$82$	−0.507007	+	5.84247i	−0.0559896	+	0.645193i
$83$	0.520370	+	1.60153i	0.0571181	+	0.175791i	0.975545	−	0.219799i	$-0.0705401\pi$
$83$	0.520370	+	1.60153i	0.0571181	+	0.175791i	−0.918427	+	0.395590i	$0.870540\pi$
$84$	5.23049	−	5.06527i	0.570693	−	0.552666i
$85$	1.48729	−	8.57422i	0.161319	−	0.930004i
$86$	−1.27089	−	2.11174i	−0.137043	−	0.227715i
$87$	3.57904	−	4.92612i	0.383713	−	0.528136i
$88$	−7.22964	−	8.88942i	−0.770682	−	0.947616i
$89$	6.61157	−	4.80359i	0.700825	−	0.509179i	−0.179376	−	0.983781i	$-0.557408\pi$
$89$	6.61157	−	4.80359i	0.700825	−	0.509179i	0.880201	+	0.474602i	$0.157408\pi$
$90$	−5.37446	−	3.46365i	−0.566518	−	0.365100i
$91$	−13.3070	+	18.3156i	−1.39496	+	1.91999i
$92$	−5.06542	+	0.719169i	−0.528106	+	0.0749785i
$93$	−4.33801			−0.449831
$94$	1.63226	+	7.04745i	0.168354	+	0.726889i
$95$	1.34664	−	7.76337i	0.138162	−	0.796505i
$96$	−4.10496	−	3.80103i	−0.418961	−	0.387941i
$97$	−6.90528	−	2.24366i	−0.701125	−	0.227809i	−0.0633041	−	0.997994i	$-0.520164\pi$
$97$	−6.90528	−	2.24366i	−0.701125	−	0.227809i	−0.637820	+	0.770185i	$0.720164\pi$
$98$	4.77700	+	7.93761i	0.482550	+	0.801820i
$99$		−	8.19095i		−	0.823221i
$100$	9.93769	−	1.11458i	0.993769	−	0.111458i
$101$		−	9.04213i		−	0.899726i	−0.893098	−	0.449863i	$-0.851473\pi$
$101$		−	9.04213i		−	0.899726i	0.893098	−	0.449863i	$-0.148527\pi$
$102$	4.66370	−	2.80670i	0.461775	−	0.277905i
$103$	10.0754	+	3.27371i	0.992762	+	0.322568i	0.759970	−	0.649959i	$-0.225214\pi$
$103$	10.0754	+	3.27371i	0.992762	+	0.322568i	0.232792	+	0.972527i	$0.425214\pi$
$104$	14.6087	+	9.44320i	1.43250	+	0.925982i
$105$	−5.84007	+	5.67117i	−0.569933	+	0.553449i
$106$	17.6287	−	4.08298i	1.71225	−	0.396574i
$107$	−0.391362			−0.0378344			−0.0189172	−	0.999821i	$-0.506022\pi$
$107$	−0.391362			−0.0378344			−0.0189172	+	0.999821i	$0.506022\pi$
$108$	−1.39627	−	9.83452i	−0.134356	−	0.946327i
$109$	−5.07531	+	6.98557i	−0.486127	+	0.669096i	−0.979668	−	0.200626i	$-0.935702\pi$
$109$	−5.07531	+	6.98557i	−0.486127	+	0.669096i	0.493541	+	0.869723i	$0.335702\pi$
$110$	8.09663	+	9.92756i	0.771983	+	0.946556i
$111$	2.95917	−	2.14996i	0.280872	−	0.204066i
$112$	12.1840	−	8.26819i	1.15128	−	0.781271i
$113$	−1.59983	+	2.20198i	−0.150500	+	0.207145i	−0.877610	−	0.479376i	$-0.840863\pi$
$113$	−1.59983	+	2.20198i	−0.150500	+	0.207145i	0.727110	+	0.686521i	$0.240863\pi$
$114$	4.22266	−	2.54128i	0.395488	−	0.238012i
$115$	5.66220	−	0.811836i	0.528003	−	0.0757041i
$116$	8.84573	−	8.56631i	0.821305	−	0.795362i
$117$	3.84262	+	11.8264i	0.355250	+	1.09335i
$118$	−1.88047	−	0.163187i	−0.173111	−	0.0150225i
$119$	4.42702	+	13.6250i	0.405824	+	1.24900i
$120$	4.59532	+	4.24337i	0.419494	+	0.387365i
$121$	−1.67215	+	5.14634i	−0.152013	+	0.467849i
$122$	0.936731	−	2.21112i	0.0848076	−	0.200186i
$123$	3.31784	−	2.41055i	0.299159	−	0.217352i
$124$	−8.64157	−	1.51121i	−0.776036	−	0.135710i
$125$	−11.1090	+	1.26140i	−0.993615	+	0.112823i
$126$	10.4865	+	0.910018i	0.934215	+	0.0810709i
$127$	−2.19692	−	3.02379i	−0.194945	−	0.268318i	0.700343	−	0.713806i	$-0.253030\pi$
$127$	−2.19692	−	3.02379i	−0.194945	−	0.268318i	−0.895288	+	0.445488i	$0.853030\pi$
$128$	−6.85318	−	9.00188i	−0.605742	−	0.795661i
$129$	−0.532615	+	1.63922i	−0.0468941	+	0.144325i
$130$	−16.3475	−	10.5354i	−1.43377	−	0.924013i
$131$	−14.6559	+	4.76200i	−1.28049	+	0.416058i	−0.868754	−	0.495243i	$-0.835079\pi$
$131$	−14.6559	+	4.76200i	−1.28049	+	0.416058i	−0.411740	+	0.911301i	$0.635079\pi$
$132$	−1.38031	+	7.89306i	−0.120140	+	0.687003i
$133$	4.00836	+	12.3365i	0.347569	+	1.06971i
$134$	−13.5016	+	15.5540i	−1.16636	+	1.34366i
$135$	1.57618	+	10.9932i	0.135656	+	0.946142i
$136$	10.2681	−	3.96645i	0.880483	−	0.340120i
$137$	4.78116	−	6.58071i	0.408482	−	0.562228i	−0.554365	−	0.832274i	$-0.687039\pi$
$137$	4.78116	−	6.58071i	0.408482	−	0.562228i	0.962847	+	0.270046i	$0.0870389\pi$
$138$	2.70188	+	2.34537i	0.229999	+	0.199651i
$139$	−0.476853	−	0.656333i	−0.0404462	−	0.0556694i	0.788315	−	0.615272i	$-0.210954\pi$
$139$	−0.476853	−	0.656333i	−0.0404462	−	0.0556694i	−0.828761	+	0.559603i	$0.810954\pi$
$140$	−13.6094	+	9.26283i	−1.15020	+	0.782852i
$141$	2.97351	−	4.09268i	0.250415	−	0.344666i
$142$	−5.52970	+	1.28073i	−0.464042	+	0.107477i
$143$		−	24.9144i		−	2.08345i
$144$	0.259504	−	8.08352i	0.0216254	−	0.673627i
$145$	−9.87666	+	9.59101i	−0.820212	+	0.796490i
$146$	−5.34821	+	12.6243i	−0.442621	+	1.04479i
$147$	2.00199	−	6.16149i	0.165121	−	0.508192i
$148$	6.64381	−	3.25199i	0.546118	−	0.267312i
$149$			2.79356i			0.228857i	0.993431	+	0.114429i	$0.0365037\pi$
$149$			2.79356i			0.228857i	−0.993431	+	0.114429i	$0.963496\pi$
$150$	−5.14424	−	4.73716i	−0.420025	−	0.386788i
$151$	−4.41781			−0.359516			−0.179758	−	0.983711i	$-0.557531\pi$
$151$	−4.41781			−0.359516			−0.179758	+	0.983711i	$0.557531\pi$
$152$	9.29707	−	3.59135i	0.754092	−	0.291297i
$153$	7.48372	+	2.43161i	0.605023	+	0.196584i
$154$	−19.4188	−	8.22668i	−1.56481	−	0.662924i
$155$	9.66388	+	1.67630i	0.776222	+	0.134644i
$156$	−1.70993	−	12.0438i	−0.136904	−	0.964276i
$157$	13.1399			1.04867			0.524337	−	0.851511i	$-0.324313\pi$
$157$	13.1399			1.04867			0.524337	+	0.851511i	$0.324313\pi$
$158$	−21.2621	+	4.92451i	−1.69152	+	0.391773i
$159$	−10.2376	−	7.43803i	−0.811892	−	0.589874i
$160$	7.67591	+	10.0539i	0.606834	+	0.794828i
$161$	−7.61831	+	5.53502i	−0.600407	+	0.436221i
$162$	1.06976	−	1.23237i	0.0840482	−	0.0968239i
$163$	−0.389815	−	0.283217i	−0.0305327	−	0.0221833i	0.572414	−	0.819965i	$-0.306007\pi$
$163$	−0.389815	−	0.283217i	−0.0305327	−	0.0221833i	−0.602947	+	0.797781i	$0.706007\pi$
$164$	7.44907	−	3.64614i	0.581675	−	0.284716i
$165$	1.53111	−	8.82683i	0.119196	−	0.687167i
$166$	1.56112	−	1.79842i	0.121166	−	0.139584i
$167$	−9.62622	+	3.12775i	−0.744899	+	0.242032i	−0.656785	−	0.754078i	$-0.728084\pi$
$167$	−9.62622	+	3.12775i	−0.744899	+	0.242032i	−0.0881142	+	0.996110i	$0.528084\pi$
$168$	−9.95182	−	2.64408i	−0.767799	−	0.203995i
$169$	7.67086	+	23.6085i	0.590066	+	1.81604i
$170$	−11.4740	+	4.45039i	−0.880015	+	0.341330i
$171$	6.77600	+	2.20165i	0.518173	+	0.168365i
$172$	−1.63204	+	3.07988i	−0.124442	+	0.234838i
$173$	−1.25123	+	0.909073i	−0.0951293	+	0.0691155i	−0.634333	−	0.773060i	$-0.718725\pi$
$173$	−1.25123	+	0.909073i	−0.0951293	+	0.0691155i	0.539204	+	0.842175i	$0.318725\pi$
$174$	−8.57893	−	0.744477i	−0.650367	−	0.0564386i
$175$	15.2015	−	10.3771i	1.14913	−	0.784431i
$176$	−5.49931	+	15.2426i	−0.414526	+	1.14895i
$177$	0.775865	+	1.06789i	0.0583176	+	0.0802673i
$178$	−10.6419	−	4.50837i	−0.797641	−	0.337916i
$179$	−2.90435	−	0.943680i	−0.217081	−	0.0705340i	0.198457	−	0.980110i	$-0.436407\pi$
$179$	−2.90435	−	0.943680i	−0.217081	−	0.0705340i	−0.415539	+	0.909576i	$0.636407\pi$
$180$	−0.277717	+	9.03804i	−0.0206998	+	0.673656i
$181$	−0.859346	+	0.279218i	−0.0638747	+	0.0207541i	−0.340780	−	0.940143i	$-0.610691\pi$
$181$	−0.859346	+	0.279218i	−0.0638747	+	0.0207541i	0.276905	+	0.960897i	$0.410691\pi$
$182$	31.8969	+	2.76800i	2.36435	+	0.205178i
$183$	−1.59711	+	0.518934i	−0.118062	+	0.0383607i
$184$	4.56526	+	5.61335i	0.336555	+	0.413822i
$185$	−7.42300	+	3.64603i	−0.545750	+	0.268062i
$186$	3.16339	+	5.25639i	0.231951	+	0.385417i
$187$	−12.7548	−	9.26692i	−0.932725	−	0.677664i
$188$	7.34914	−	7.11700i	0.535991	−	0.519060i
$189$	−10.7463	−	14.7910i	−0.781676	−	1.07588i
$190$	−10.3889	+	4.02953i	−0.753691	+	0.292333i
$191$	2.13116	+	1.54838i	0.154205	+	0.112037i	0.662212	−	0.749316i	$-0.269618\pi$
$191$	2.13116	+	1.54838i	0.154205	+	0.112037i	−0.508007	+	0.861353i	$0.669618\pi$
$192$	−1.61227	+	7.74581i	−0.116356	+	0.559006i
$193$			22.0562i			1.58764i	0.608154	+	0.793819i	$0.291910\pi$
$193$			22.0562i			1.58764i	−0.608154	+	0.793819i	$0.708090\pi$
$194$	2.31686	+	10.0033i	0.166341	+	0.718195i
$195$	1.93026	+	13.4627i	0.138229	+	0.964087i
$196$	6.13452	−	11.5766i	0.438180	−	0.826902i
$197$	2.80194	−	8.62350i	0.199630	−	0.614399i	−0.800261	−	0.599652i	$-0.795306\pi$
$197$	2.80194	−	8.62350i	0.199630	−	0.614399i	0.999891	−	0.0147469i	$-0.00469424\pi$
$198$	−9.92501	+	5.97306i	−0.705340	+	0.424487i
$199$	6.18489			0.438435			0.219217	−	0.975676i	$-0.429650\pi$
$199$	6.18489			0.438435			0.219217	+	0.975676i	$0.429650\pi$
$200$	−8.59737	−	11.2288i	−0.607926	−	0.793994i
$201$	14.4035			1.01594
$202$	−10.9564	+	6.59376i	−0.770889	+	0.463936i
$203$	7.00366	−	21.5550i	0.491561	−	1.51287i
$204$	−6.80178	−	3.60430i	−0.476220	−	0.252352i
$205$	−8.32270	+	4.08795i	−0.581283	+	0.285515i
$206$	−3.38051	−	14.5957i	−0.235531	−	1.01693i
$207$			5.17229i			0.359499i
$208$	0.789334	−	24.5876i	0.0547304	−	1.70485i
$209$	−11.5486	−	8.39056i	−0.798835	−	0.580387i
$210$	11.1305	+	2.94088i	0.768079	+	0.202940i
$211$	11.9734	+	16.4800i	0.824283	+	1.13453i	0.988960	+	0.148181i	$0.0473418\pi$
$211$	11.9734	+	16.4800i	0.824283	+	1.13453i	−0.164677	+	0.986348i	$0.552658\pi$
$212$	−17.8027	−	18.3834i	−1.22269	−	1.26257i
$213$	3.21128	+	2.33313i	0.220033	+	0.159863i
$214$	0.285391	+	0.474215i	0.0195089	+	0.0324167i
$215$	1.81995	−	3.44591i	0.124119	−	0.235009i
$216$	−10.8983	+	8.86346i	−0.741538	+	0.603082i
$217$	−15.3565	+	4.98963i	−1.04247	+	0.338718i
$218$	12.1655	+	1.05572i	0.823952	+	0.0715022i
$219$	9.11863	−	2.96282i	0.616180	−	0.200209i
$220$	6.12500	−	17.0502i	0.412947	−	1.14952i
$221$	22.7632	+	7.39621i	1.53122	+	0.497523i
$222$	−4.76303	−	2.01783i	−0.319674	−	0.135428i
$223$	−6.21151	−	8.54941i	−0.415953	−	0.572511i	0.548705	−	0.836016i	$-0.315121\pi$
$223$	−6.21151	−	8.54941i	−0.415953	−	0.572511i	−0.964658	+	0.263506i	$0.915121\pi$
$224$	−18.9035	−	8.73400i	−1.26304	−	0.583565i
$225$	0.296613	−	10.1053i	0.0197742	−	0.673684i
$226$	3.83479	+	0.332782i	0.255086	+	0.0221363i
$227$	−7.62995	+	5.54348i	−0.506418	+	0.367934i	−0.811463	−	0.584404i	$-0.801328\pi$
$227$	−7.62995	+	5.54348i	−0.506418	+	0.367934i	0.305045	+	0.952338i	$0.401328\pi$
$228$	−6.15855	−	3.26345i	−0.407860	−	0.216127i
$229$	−9.67686	−	3.14420i	−0.639465	−	0.207775i	−0.0287017	−	0.999588i	$-0.509137\pi$
$229$	−9.67686	−	3.14420i	−0.639465	−	0.207775i	−0.610763	+	0.791813i	$0.709137\pi$
$230$	−5.11273	−	6.26890i	−0.337123	−	0.413359i
$231$	4.55744	+	14.0264i	0.299858	+	0.922867i
$232$	−16.8304	−	4.47163i	−1.10497	−	0.293577i
$233$	4.61735	−	1.50027i	0.302493	−	0.0982858i	−0.153838	−	0.988096i	$-0.549163\pi$
$233$	4.61735	−	1.50027i	0.302493	−	0.0982858i	0.456331	+	0.889810i	$0.349163\pi$
$234$	11.5279	−	13.2802i	0.753603	−	0.868155i
$235$	−8.20565	+	7.96833i	−0.535278	+	0.519796i
$236$	1.17356	+	2.39757i	0.0763919	+	0.156069i
$237$	12.3476	+	8.97106i	0.802063	+	0.582733i
$238$	13.2811	−	15.2999i	0.860888	−	0.991746i
$239$	7.15100	−	5.19551i	0.462560	−	0.336069i	−0.331975	−	0.943288i	$-0.607715\pi$
$239$	7.15100	−	5.19551i	0.462560	−	0.336069i	0.794535	+	0.607219i	$0.207715\pi$
$240$	1.79067	−	8.66255i	0.115588	−	0.559165i
$241$	2.81129	+	2.04252i	0.181091	+	0.131571i	0.674638	−	0.738149i	$-0.264300\pi$
$241$	2.81129	+	2.04252i	0.181091	+	0.131571i	−0.493547	+	0.869719i	$0.664300\pi$
$242$	7.45522	−	1.72670i	0.479240	−	0.110996i
$243$	−16.0409			−1.02903
$244$	−3.36232	+	0.477370i	−0.215250	+	0.0305605i
$245$	−6.84081	+	12.9525i	−0.437044	+	0.827504i
$246$	−5.34033	−	2.26240i	−0.340487	−	0.144245i
$247$	20.6105	+	6.69677i	1.31142	+	0.426105i
$248$	4.47053	+	11.5730i	0.283879	+	0.734889i
$249$	−1.66539			−0.105540
$250$	9.62939	+	12.5409i	0.609016	+	0.793158i
$251$		−	10.6028i		−	0.669245i	−0.942352	−	0.334622i	$-0.891391\pi$
$251$		−	10.6028i		−	0.669245i	0.942352	−	0.334622i	$-0.108609\pi$
$252$	−6.54439	−	13.3702i	−0.412258	−	0.842244i
$253$	3.20237	−	9.85587i	0.201331	−	0.619633i
$254$	−2.06190	+	4.86704i	−0.129375	+	0.305386i
$255$	7.61016	+	4.01928i	0.476566	+	0.251697i
$256$	−5.91010	+	14.8684i	−0.369381	+	0.929278i
$257$			7.56452i			0.471862i	0.971770	+	0.235931i	$0.0758139\pi$
$257$			7.56452i			0.471862i	−0.971770	+	0.235931i	$0.924186\pi$
$258$	2.37465	−	0.549991i	0.147839	−	0.0342409i
$259$	8.00252	−	11.0145i	0.497252	−	0.684409i
$260$	−0.844731	+	27.4910i	−0.0523880	+	1.70492i
$261$	−7.31718	−	10.0712i	−0.452922	−	0.623393i
$262$	16.4576	+	14.2861i	1.01676	+	0.882597i
$263$	−17.5706	+	24.1838i	−1.08345	+	1.49124i	−0.227780	+	0.973713i	$0.573147\pi$
$263$	−17.5706	+	24.1838i	−1.08345	+	1.49124i	−0.855668	+	0.517526i	$0.826853\pi$
$264$	10.5706	−	4.08331i	0.650577	−	0.251310i
$265$	19.9322	+	20.5259i	1.22443	+	1.26089i
$266$	12.0252	−	13.8530i	0.737310	−	0.849384i
$267$	2.49756	+	7.68670i	0.152848	+	0.470419i
$268$	28.6926	+	5.01764i	1.75268	+	0.306501i
$269$	−21.8536	+	7.10065i	−1.33244	+	0.432934i	−0.886748	−	0.462254i	$-0.847041\pi$
$269$	−21.8536	+	7.10065i	−1.33244	+	0.432934i	−0.445688	+	0.895188i	$0.647041\pi$
$270$	12.1711	−	9.92638i	0.740709	−	0.604100i
$271$	7.44078	−	22.9004i	0.451995	−	1.39110i	−0.422632	−	0.906301i	$-0.638894\pi$
$271$	7.44078	−	22.9004i	0.451995	−	1.39110i	0.874627	−	0.484796i	$-0.161106\pi$
$272$	−12.2939	−	9.54947i	−0.745430	−	0.579022i
$273$	−13.1604	−	18.1137i	−0.796502	−	1.09629i
$274$	−11.4604	−	0.994531i	−0.692350	−	0.0600818i
$275$	−6.82176	+	19.0721i	−0.411367	+	1.15009i
$276$	0.871616	−	4.98419i	0.0524651	−	0.300013i
$277$	−2.35420	+	1.71043i	−0.141450	+	0.102770i	−0.656260	−	0.754535i	$-0.727863\pi$
$277$	−2.35420	+	1.71043i	−0.141450	+	0.102770i	0.514810	+	0.857304i	$0.327863\pi$
$278$	−0.447547	+	1.05642i	−0.0268421	+	0.0633599i
$279$	−2.74063	+	8.43480i	−0.164077	+	0.504978i
$280$	21.1481	+	9.73587i	1.26384	+	0.581829i
$281$	−7.31490	−	22.5130i	−0.436371	−	1.34301i	−0.891676	−	0.452675i	$-0.850470\pi$
$281$	−7.31490	−	22.5130i	−0.436371	−	1.34301i	0.455305	−	0.890335i	$-0.349530\pi$
$282$	−7.12748	−	0.618521i	−0.424436	−	0.0368324i
$283$	−8.95835	−	27.5710i	−0.532518	−	1.63892i	−0.748951	−	0.662626i	$-0.769442\pi$
$283$	−8.95835	−	27.5710i	−0.532518	−	1.63892i	0.216432	−	0.976298i	$-0.430558\pi$
$284$	5.58427	+	5.76642i	0.331365	+	0.342174i
$285$	6.89048	+	3.63919i	0.408157	+	0.215567i
$286$	−30.1889	+	18.1682i	−1.78511	+	1.07431i
$287$	8.97245	−	12.3495i	0.529627	−	0.728969i
$288$	−9.98408	+	5.58028i	−0.588318	+	0.328821i
$289$	−1.50005	+	1.08985i	−0.0882381	+	0.0641087i
$290$	18.8238	+	4.97357i	1.10537	+	0.292058i
$291$	4.22066	−	5.80924i	0.247419	−	0.340544i
$292$	19.1970	−	2.72552i	1.12342	−	0.159499i
$293$	13.8184			0.807281			0.403640	−	0.914918i	$-0.367745\pi$
$293$	13.8184			0.807281			0.403640	+	0.914918i	$0.367745\pi$
$294$	−8.92582	+	2.06730i	−0.520564	+	0.120568i
$295$	−1.31576	−	2.67876i	−0.0766063	−	0.155964i
$296$	−8.78529	−	5.67890i	−0.510635	−	0.330080i
$297$	19.1352	+	6.21740i	1.11034	+	0.360770i
$298$	3.38497	−	2.03714i	0.196086	−	0.118008i
$299$			15.7325i			0.909837i
$300$	−1.98873	+	9.68777i	−0.114819	+	0.559323i
$301$			6.41543i			0.369779i
$302$	3.22158	+	5.35308i	0.185381	+	0.308035i
$303$	8.50480	+	2.76338i	0.488588	+	0.158752i
$304$	−11.1313	−	8.64640i	−0.638425	−	0.495905i
$305$	3.75845	−	0.538880i	0.215208	−	0.0308562i
$306$	−2.51094	−	10.8412i	−0.143541	−	0.619753i
$307$	7.71657			0.440408			0.220204	−	0.975454i	$-0.429328\pi$
$307$	7.71657			0.440408			0.220204	+	0.975454i	$0.429328\pi$
$308$	4.19242	+	29.5290i	0.238885	+	1.68257i
$309$	−6.15833	+	8.47621i	−0.350335	+	0.482195i
$310$	−5.01598	−	12.9322i	−0.284888	−	0.734498i
$311$	−8.02122	+	5.82776i	−0.454842	+	0.330462i	−0.791504	−	0.611163i	$-0.790702\pi$
$311$	−8.02122	+	5.82776i	−0.454842	+	0.330462i	0.336663	+	0.941625i	$0.390702\pi$
$312$	−13.3466	+	10.8546i	−0.755603	+	0.614521i
$313$	−1.13921	+	1.56798i	−0.0643917	+	0.0886276i	−0.839998	−	0.542589i	$-0.817444\pi$
$313$	−1.13921	+	1.56798i	−0.0643917	+	0.0886276i	0.775607	+	0.631217i	$0.217444\pi$
$314$	−9.58193	−	15.9216i	−0.540740	−	0.898509i
$315$	7.33738	+	14.9383i	0.413415	+	0.841676i
$316$	21.4720	+	22.1723i	1.20789	+	1.24729i
$317$	−0.587317	−	1.80758i	−0.0329870	−	0.101524i	0.933207	−	0.359338i	$-0.116998\pi$
$317$	−0.587317	−	1.80758i	−0.0329870	−	0.101524i	−0.966194	+	0.257815i	$0.916998\pi$
$318$	−1.54719	+	17.8289i	−0.0867619	+	0.999796i
$319$	7.70749	+	23.7212i	0.431537	+	1.32813i
$320$	6.58484	−	16.6325i	0.368104	−	0.929785i
$321$	0.119604	−	0.368105i	0.00667567	−	0.0205456i
$322$	12.2623	+	5.19485i	0.683350	+	0.289498i
$323$	11.0945	−	8.06061i	0.617313	−	0.448504i
$324$	−2.27336	−	0.397557i	−0.126298	−	0.0220865i
$325$	0.902206	−	30.7371i	0.0500454	−	1.70499i
$326$	−0.0589121	+	0.678870i	−0.00326284	+	0.0375991i
$327$	−5.01938	−	6.90858i	−0.277572	−	0.382045i
$328$	−9.85011	−	6.36721i	−0.543881	−	0.351570i
$329$	5.81873	−	17.9082i	0.320797	−	0.987311i
$330$	−11.8120	+	4.58151i	−0.650231	+	0.252204i
$331$	28.5960	−	9.29140i	1.57178	−	0.510702i	0.611856	−	0.790969i	$-0.290423\pi$
$331$	28.5960	−	9.29140i	1.57178	−	0.510702i	0.959922	+	0.280267i	$0.0904230\pi$
$332$	−3.31756	−	0.580162i	−0.182075	−	0.0318406i
$333$	−2.31085	−	7.11208i	−0.126634	−	0.389739i
$334$	10.8096	+	9.38330i	0.591475	+	0.513431i
$335$	−32.0869	−	5.56582i	−1.75310	−	0.304093i
$336$	4.05329	+	13.9868i	0.221125	+	0.763042i
$337$	2.92944	−	4.03203i	0.159577	−	0.219639i	−0.721740	−	0.692164i	$-0.756658\pi$
$337$	2.92944	−	4.03203i	0.159577	−	0.219639i	0.881317	+	0.472525i	$0.156658\pi$
$338$	23.0127	−	26.5107i	1.25173	−	1.44199i
$339$	−1.58220	−	2.17771i	−0.0859333	−	0.118277i
$340$	13.7597	+	10.6577i	0.746224	+	0.577997i
$341$	10.4446	−	14.3758i	0.565608	−	0.778492i
$342$	−2.27348	−	9.81601i	−0.122936	−	0.530789i
$343$			1.65365i			0.0892886i
$344$	4.92203	−	0.268373i	0.265378	−	0.0144697i
$345$	−0.966839	+	5.57382i	−0.0520528	+	0.300085i
$346$	2.01396	+	0.853203i	0.108271	+	0.0458685i
$347$	−6.67727	+	20.5505i	−0.358455	+	1.10321i	0.595525	+	0.803337i	$0.296944\pi$
$347$	−6.67727	+	20.5505i	−0.358455	+	1.10321i	−0.953979	+	0.299873i	$0.903056\pi$
$348$	5.35390	+	10.9380i	0.286999	+	0.586340i
$349$			3.79138i			0.202948i	0.994838	+	0.101474i	$0.0323558\pi$
$349$			3.79138i			0.202948i	−0.994838	+	0.101474i	$0.967644\pi$
$350$	−23.6593	−	10.8525i	−1.26464	−	0.580092i
$351$	−30.5448			−1.63036
$352$	22.4798	−	4.45176i	1.19818	−	0.237280i
$353$	23.7877	+	7.72909i	1.26609	+	0.411378i	0.863661	−	0.504072i	$-0.168166\pi$
$353$	23.7877	+	7.72909i	1.26609	+	0.411378i	0.402430	+	0.915451i	$0.368166\pi$
$354$	0.728182	−	1.71885i	0.0387024	−	0.0913559i
$355$	−6.25226	−	6.43847i	−0.331835	−	0.341718i
$356$	2.29752	+	16.1824i	0.121768	+	0.857666i
$357$	−14.1682			−0.749862
$358$	0.974467	+	4.20737i	0.0515022	+	0.222366i
$359$	−18.7926	−	13.6536i	−0.991834	−	0.720609i	−0.0315118	−	0.999503i	$-0.510032\pi$
$359$	−18.7926	−	13.6536i	−0.991834	−	0.720609i	−0.960322	+	0.278894i	$0.910032\pi$
$360$	11.1540	−	6.25427i	0.587865	−	0.329629i
$361$	−5.32603	+	3.86959i	−0.280317	+	0.203662i
$362$	0.964988	+	0.837660i	0.0507187	+	0.0440264i
$363$	−4.32949	−	3.14556i	−0.227239	−	0.165099i
$364$	−19.9061	−	40.6681i	−1.04336	−	2.13159i
$365$	−21.4587	+	3.07671i	−1.12320	+	0.161042i
$366$	1.79345	+	1.55681i	0.0937452	+	0.0813757i
$367$	3.79273	−	1.23233i	0.197979	−	0.0643272i	−0.208349	−	0.978054i	$-0.566809\pi$
$367$	3.79273	−	1.23233i	0.197979	−	0.0643272i	0.406328	+	0.913727i	$0.366809\pi$
$368$	3.47262	−	9.62515i	0.181023	−	0.501746i
$369$	−2.59094	−	7.97409i	−0.134879	−	0.415114i
$370$	9.83097	+	6.33571i	0.511088	+	0.329378i
$371$	−44.7961	−	14.5551i	−2.32570	−	0.755666i
$372$	4.06236	−	7.66620i	0.210624	−	0.397474i
$373$	−16.6167	+	12.0728i	−0.860382	+	0.625104i	−0.927989	−	0.372608i	$-0.878464\pi$
$373$	−16.6167	+	12.0728i	−0.860382	+	0.625104i	0.0676065	+	0.997712i	$0.478464\pi$
$374$	−1.92762	+	22.2128i	−0.0996746	+	1.14859i
$375$	2.20858	−	10.8343i	0.114051	−	0.559481i
$376$	−13.9829	−	3.71508i	−0.721113	−	0.191591i
$377$	−22.2566	−	30.6336i	−1.14628	−	1.57771i
$378$	−10.0858	+	23.8073i	−0.518759	+	1.22451i
$379$	27.2341	+	8.84890i	1.39892	+	0.454538i	0.908843	−	0.417139i	$-0.136967\pi$
$379$	27.2341	+	8.84890i	1.39892	+	0.454538i	0.490081	+	0.871677i	$0.336967\pi$
$380$	12.4585	+	9.64986i	0.639106	+	0.495027i
$381$	3.51551	−	1.14226i	0.180105	−	0.0585196i
$382$	0.322079	−	3.71146i	0.0164790	−	0.189895i
$383$	11.6284	−	3.77828i	0.594181	−	0.193061i	0.00353757	−	0.999994i	$-0.498874\pi$
$383$	11.6284	−	3.77828i	0.594181	−	0.193061i	0.590644	+	0.806933i	$0.298874\pi$
$384$	10.5613	−	3.69485i	0.538957	−	0.188552i
$385$	−4.73262	−	33.0079i	−0.241197	−	1.68224i
$386$	26.7256	−	16.0839i	1.36030	−	0.818651i
$387$	2.85079	+	2.07122i	0.144914	+	0.105286i
$388$	10.4315	−	10.1020i	0.529580	−	0.512852i
$389$	16.6269	+	22.8849i	0.843015	+	1.16031i	0.985359	+	0.170494i	$0.0545362\pi$
$389$	16.6269	+	22.8849i	0.843015	+	1.16031i	−0.142344	+	0.989817i	$0.545464\pi$
$390$	14.9053	−	12.1563i	0.754758	−	0.615558i
$391$	8.05421	+	5.85173i	0.407319	+	0.295935i
$392$	−18.5009	+	1.00876i	−0.934437	+	0.0509501i
$393$		−	15.2403i		−	0.768772i
$394$	−12.4924	+	2.89335i	−0.629357	+	0.145765i
$395$	−24.0404	−	24.7564i	−1.20960	−	1.24563i
$396$	14.4752	+	7.67047i	0.727405	+	0.385456i
$397$	−2.11608	+	6.51261i	−0.106203	+	0.326859i	−0.990011	−	0.140991i	$-0.954971\pi$
$397$	−2.11608	+	6.51261i	−0.106203	+	0.326859i	0.883808	+	0.467850i	$0.154971\pi$
$398$	−4.51018	−	7.49426i	−0.226075	−	0.375653i
$399$	−12.8284			−0.642222
$400$	−7.33652	+	18.6058i	−0.366826	+	0.930290i
$401$	34.1131			1.70352			0.851762	−	0.523929i	$-0.175534\pi$
$401$	34.1131			1.70352			0.851762	+	0.523929i	$0.175534\pi$
$402$	−10.5034	−	17.4528i	−0.523862	−	0.870464i
$403$	−8.33617	+	25.6561i	−0.415254	+	1.27802i
$404$	15.9794	+	8.46757i	0.795004	+	0.421277i
$405$	2.54230	+	0.440990i	0.126328	+	0.0219129i
$406$	−31.2256	+	7.23215i	−1.54970	+	0.358925i
$407$			14.9829i			0.742675i
$408$	0.592691	+	10.8701i	0.0293426	+	0.538151i
$409$	−21.8970	−	15.9091i	−1.08274	−	0.786655i	−0.104580	−	0.994516i	$-0.533350\pi$
$409$	−21.8970	−	15.9091i	−1.08274	−	0.786655i	−0.978158	+	0.207861i	$0.933350\pi$
$410$	11.0225	+	7.10362i	0.544364	+	0.350823i
$411$	4.72847	+	6.50818i	0.233238	+	0.321025i
$412$	−15.2205	+	14.7398i	−0.749863	+	0.726176i
$413$	3.97485	+	2.88790i	0.195589	+	0.142104i
$414$	6.26729	−	3.77177i	0.308020	−	0.185373i
$415$	3.71003	+	0.643544i	0.182118	+	0.0315904i
$416$	−30.3686	+	16.9735i	−1.48894	+	0.832195i
$417$	0.763061	−	0.247934i	0.0373673	−	0.0121414i
$418$	−1.74532	+	20.1121i	−0.0853666	+	0.983717i
$419$	19.6287	−	6.37775i	0.958925	−	0.311573i	0.212588	−	0.977142i	$-0.431811\pi$
$419$	19.6287	−	6.37775i	0.958925	−	0.311573i	0.746337	+	0.665568i	$0.231811\pi$
$420$	−4.55320	−	15.6315i	−0.222173	−	0.762738i
$421$	8.92197	+	2.89892i	0.434830	+	0.141285i	0.518249	−	0.855230i	$-0.326584\pi$
$421$	8.92197	+	2.89892i	0.434830	+	0.141285i	−0.0834190	+	0.996515i	$0.526584\pi$
$422$	11.2375	−	26.5259i	0.547035	−	1.29126i
$423$	−6.07920	−	8.36730i	−0.295581	−	0.406832i
$424$	−9.29303	+	34.9772i	−0.451309	+	1.69864i
$425$	−15.4002	−	11.8946i	−0.747018	−	0.576971i
$426$	0.485315	−	5.59250i	0.0235136	−	0.270957i
$427$	−5.05688	+	3.67404i	−0.244719	+	0.177799i
$428$	0.366493	−	0.691620i	0.0177151	−	0.0334307i
$429$	23.4338	+	7.61412i	1.13140	+	0.367613i
$430$	−5.50258	+	0.307611i	−0.265358	+	0.0148343i
$431$	0.317339	+	0.976670i	0.0152857	+	0.0470446i	0.958408	−	0.285400i	$-0.0921265\pi$
$431$	0.317339	+	0.976670i	0.0152857	+	0.0470446i	−0.943123	+	0.332445i	$0.892127\pi$
$432$	18.6873	+	6.74210i	0.899091	+	0.324379i
$433$	−25.6115	+	8.32169i	−1.23081	+	0.399915i	−0.851008	−	0.525152i	$-0.824008\pi$
$433$	−25.6115	+	8.32169i	−1.23081	+	0.399915i	−0.379803	+	0.925067i	$0.624008\pi$
$434$	17.2443	+	14.9690i	0.827754	+	0.718534i
$435$	−6.00264	−	12.2208i	−0.287805	−	0.585945i
$436$	−7.59219	−	15.5109i	−0.363600	−	0.742835i
$437$	7.29254	+	5.29834i	0.348850	+	0.253454i
$438$	−10.2396	−	8.88852i	−0.489268	−	0.424710i
$439$	1.22399	−	0.889282i	0.0584179	−	0.0424431i	−0.558193	−	0.829711i	$-0.688505\pi$
$439$	1.22399	−	0.889282i	0.0584179	−	0.0424431i	0.616611	+	0.787268i	$0.288505\pi$
$440$	−25.1263	+	5.01175i	−1.19785	+	0.238926i
$441$	−10.7156	−	7.78531i	−0.510265	−	0.370729i
$442$	−7.63751	−	32.9758i	−0.363279	−	1.56850i
$443$	15.1085			0.717828			0.358914	−	0.933371i	$-0.383147\pi$
$443$	15.1085			0.717828			0.358914	+	0.933371i	$0.383147\pi$
$444$	1.02831	+	7.24284i	0.0488015	+	0.343730i
$445$	−2.59356	−	18.0889i	−0.122947	−	0.857498i
$446$	−5.82976	+	13.7610i	−0.276047	+	0.651601i
$447$	−2.62755	−	0.853743i	−0.124279	−	0.0403807i
$448$	3.20190	+	29.2745i	0.151275	+	1.38309i
$449$	32.5044			1.53398			0.766988	−	0.641661i	$-0.221755\pi$
$449$	32.5044			1.53398			0.766988	+	0.641661i	$0.221755\pi$
$450$	−12.4609	+	7.00961i	−0.587412	+	0.330436i
$451$			16.7989i			0.791029i
$452$	−2.39320	−	4.88931i	−0.112567	−	0.229974i
$453$	1.35013	−	4.15528i	0.0634347	−	0.195232i
$454$	12.2810	+	5.20279i	0.576377	+	0.244179i
$455$	22.3181	+	45.4377i	1.04629	+	2.13015i
$456$	0.536642	+	9.84215i	0.0251305	+	0.460901i
$457$			0.743713i			0.0347894i	0.999849	+	0.0173947i	$0.00553719\pi$
$457$			0.743713i			0.0347894i	−0.999849	+	0.0173947i	$0.994463\pi$
$458$	3.24678	+	14.0183i	0.151712	+	0.655034i
$459$	−11.3611	+	15.6373i	−0.530293	+	0.729886i
$460$	−3.86772	+	10.7666i	−0.180333	+	0.501994i
$461$	−16.2261	−	22.3333i	−0.755723	−	1.04016i	−0.997558	−	0.0698465i	$-0.977749\pi$
$461$	−16.2261	−	22.3333i	−0.755723	−	1.04016i	0.241834	−	0.970318i	$-0.422251\pi$
$462$	13.6724	−	15.7507i	0.636098	−	0.732788i
$463$	−10.5034	+	14.4567i	−0.488133	+	0.671858i	−0.980042	−	0.198789i	$-0.936299\pi$
$463$	−10.5034	+	14.4567i	−0.488133	+	0.671858i	0.491909	+	0.870646i	$0.336299\pi$
$464$	6.85487	+	23.6543i	0.318229	+	1.09812i
$465$	−4.53008	+	8.57730i	−0.210077	+	0.397763i
$466$	−5.18498	−	4.50083i	−0.240189	−	0.208497i
$467$	2.08094	+	6.40448i	0.0962945	+	0.296364i	0.987589	−	0.157061i	$-0.0502020\pi$
$467$	2.08094	+	6.40448i	0.0962945	+	0.296364i	−0.891294	+	0.453425i	$0.850202\pi$
$468$	−24.4982	−	4.28415i	−1.13243	−	0.198035i
$469$	50.9881	−	16.5670i	2.35441	−	0.764995i
$470$	15.6390	+	4.13211i	0.721375	+	0.190600i
$471$	−4.01569	+	12.3590i	−0.185033	+	0.569473i
$472$	2.04937	−	3.17038i	0.0943297	−	0.145928i
$473$	−4.14985	−	5.71178i	−0.190810	−	0.262628i
$474$	1.86607	−	21.5036i	0.0857116	−	0.987693i
$475$	−13.9438	−	10.7697i	−0.639786	−	0.494149i
$476$	−28.2239	−	4.93570i	−1.29364	−	0.226227i
$477$	−20.9302	+	15.2067i	−0.958329	+	0.696267i
$478$	−11.5101	−	4.87620i	−0.526461	−	0.223032i
$479$	1.53203	−	4.71509i	0.0700001	−	0.215438i	−0.909937	−	0.414748i	$-0.863870\pi$
$479$	1.53203	−	4.71509i	0.0700001	−	0.215438i	0.979937	+	0.199309i	$0.0638699\pi$
$480$	−11.8023	+	4.14719i	−0.538697	+	0.189293i
$481$	−7.02892	−	21.6328i	−0.320491	−	0.986370i
$482$	0.424866	−	4.89592i	0.0193521	−	0.223003i
$483$	−2.87786	−	8.85715i	−0.130947	−	0.403014i
$484$	−7.52880	−	7.77437i	−0.342218	−	0.353381i
$485$	−11.6473	+	11.3104i	−0.528875	+	0.513579i
$486$	11.6975	+	19.4369i	0.530608	+	0.881674i
$487$	−22.3423	+	30.7515i	−1.01243	+	1.39349i	−0.0950461	+	0.995473i	$0.530300\pi$
$487$	−22.3423	+	30.7515i	−1.01243	+	1.39349i	−0.917380	+	0.398012i	$0.869700\pi$
$488$	3.03032	+	3.72603i	0.137176	+	0.168669i
$489$	0.385518	−	0.280096i	0.0174337	−	0.0126664i
$490$	20.6831	−	1.15625i	0.934367	−	0.0522339i
$491$	9.39398	−	12.9297i	0.423944	−	0.583509i	−0.542606	−	0.839988i	$-0.682562\pi$
$491$	9.39398	−	12.9297i	0.423944	−	0.583509i	0.966550	+	0.256478i	$0.0825622\pi$
$492$	1.15295	+	8.12071i	0.0519789	+	0.366110i
$493$	−23.9611			−1.07915
$494$	−6.91524	−	29.8573i	−0.311132	−	1.34335i
$495$	−16.1955	−	8.55360i	−0.727933	−	0.384456i
$496$	10.7631	−	13.8563i	0.483277	−	0.622168i
$497$	14.0515	+	4.56560i	0.630294	+	0.204795i
$498$	1.21445	+	2.01797i	0.0544208	+	0.0904272i
$499$		−	8.08744i		−	0.362044i	−0.983479	−	0.181022i	$-0.942060\pi$
$499$		−	8.08744i		−	0.362044i	0.983479	−	0.181022i	$-0.0579405\pi$
$500$	8.17389	−	20.8132i	0.365548	−	0.930793i
$501$		−	10.0100i		−	0.447216i
$502$	−12.8475	+	7.73187i	−0.573412	+	0.345090i
$503$	−24.0791	−	7.82378i	−1.07364	−	0.348845i	−0.281733	−	0.959493i	$-0.590909\pi$
$503$	−24.0791	−	7.82378i	−1.07364	−	0.348845i	−0.791903	+	0.610648i	$0.790909\pi$
$504$	−11.4284	+	17.6798i	−0.509061	+	0.787520i
$505$	−17.8785	−	9.44247i	−0.795582	−	0.420184i
$506$	−14.2777	+	3.30684i	−0.634719	+	0.147007i
$507$	−24.5498			−1.09030
$508$	7.40101	−	1.05077i	0.328367	−	0.0466203i
$509$	8.31244	−	11.4411i	0.368442	−	0.507117i	−0.584034	−	0.811729i	$-0.698527\pi$
$509$	8.31244	−	11.4411i	0.368442	−	0.507117i	0.952477	+	0.304612i	$0.0985267\pi$
$510$	−0.679346	−	12.1522i	−0.0300820	−	0.538110i
$511$	28.8720	−	20.9767i	1.27722	−	0.927955i
$512$	22.3260	−	3.68117i	0.986678	−	0.162686i
$513$	−10.2867	+	14.1585i	−0.454171	+	0.625113i
$514$	9.16596	−	5.51625i	0.404293	−	0.243311i
$515$	16.9944	−	16.5029i	0.748864	−	0.727206i
$516$	−2.39808	−	2.47630i	−0.105570	−	0.109013i
$517$	6.40348	+	19.7079i	0.281625	+	0.866752i
$518$	−19.1820	−	1.66461i	−0.842808	−	0.0731386i
$519$	−0.472660	−	1.45470i	−0.0207475	−	0.0638542i
$520$	33.9270	−	19.0236i	1.48780	−	0.834240i
$521$	−12.1780	+	37.4801i	−0.533530	+	1.64204i	0.213275	+	0.976992i	$0.431587\pi$
$521$	−12.1780	+	37.4801i	−0.533530	+	1.64204i	−0.746805	+	0.665043i	$0.768413\pi$
$522$	−6.86748	+	16.2105i	−0.300581	+	0.709513i
$523$	−26.6792	+	19.3836i	−1.16660	+	0.847586i	−0.990598	−	0.136804i	$-0.956317\pi$
$523$	−26.6792	+	19.3836i	−1.16660	+	0.847586i	−0.176003	+	0.984390i	$0.556317\pi$
$524$	5.30917	−	30.3596i	0.231932	−	1.32627i
$525$	5.11464	+	17.4695i	0.223221	+	0.762432i
$526$	42.1166	+	3.65486i	1.83637	+	0.159360i
$527$	10.0339	+	13.8105i	0.437083	+	0.601593i
$528$	−12.6561	−	9.83082i	−0.550788	−	0.427831i
$529$	5.08521	−	15.6507i	0.221096	−	0.680464i
$530$	10.3362	−	39.1200i	0.448975	−	1.69926i
$531$	2.56656	−	0.833926i	0.111379	−	0.0361893i
$532$	−25.5549	−	4.46894i	−1.10794	−	0.193753i
$533$	−7.88085	−	24.2548i	−0.341358	−	1.05059i
$534$	7.49273	−	8.63166i	0.324242	−	0.373528i
$535$	−0.408689	+	0.773817i	−0.0176692	+	0.0334550i
$536$	−14.8435	−	38.4259i	−0.641140	−	1.65975i
$537$	1.77520	−	2.44336i	0.0766057	−	0.105439i
$538$	24.5401	+	21.3021i	1.05800	+	0.918398i
$539$	15.5985	+	21.4694i	0.671873	+	0.924754i
$540$	−20.9033	−	7.50918i	−0.899536	−	0.323144i
$541$	−1.48837	+	2.04857i	−0.0639902	+	0.0880749i	−0.839813	−	0.542876i	$-0.817335\pi$
$541$	−1.48837	+	2.04857i	−0.0639902	+	0.0880749i	0.775822	+	0.630951i	$0.217335\pi$
$542$	−33.1745	+	7.68353i	−1.42497	+	0.330036i
$543$		−	0.893611i		−	0.0383485i
$544$	−2.60607	+	21.8604i	−0.111735	+	0.937255i
$545$	8.51215	+	17.3300i	0.364620	+	0.742335i
$546$	−12.3516	+	29.1555i	−0.528598	+	1.24774i
$547$	1.55043	−	4.77172i	0.0662915	−	0.204024i	−0.912424	−	0.409246i	$-0.865792\pi$
$547$	1.55043	−	4.77172i	0.0662915	−	0.204024i	0.978715	+	0.205222i	$0.0657917\pi$
$548$	7.15217	+	14.6119i	0.305525	+	0.624189i
$549$			3.43326i			0.146528i
$550$	28.0843	−	5.64190i	1.19752	−	0.240571i
$551$	−21.6952			−0.924245
$552$	−6.67497	+	2.57846i	−0.284106	+	0.109747i
$553$	54.0290	+	17.5551i	2.29755	+	0.746518i
$554$	3.78928	+	1.60531i	0.160991	+	0.0682030i
$555$	−1.16081	−	8.09616i	−0.0492738	−	0.343663i
$556$	1.60643	−	0.228075i	0.0681279	−	0.00967255i
$557$	−12.1514			−0.514869			−0.257435	−	0.966296i	$-0.582877\pi$
$557$	−12.1514			−0.514869			−0.257435	+	0.966296i	$0.582877\pi$
$558$	12.2190	−	2.83004i	0.517272	−	0.119805i
$559$	8.67125	+	6.30003i	0.366755	+	0.266463i
$560$	−3.62480	−	32.7250i	−0.153176	−	1.38288i
$561$	12.6142	−	9.16478i	0.532574	−	0.386937i
$562$	−21.9448	+	25.2805i	−0.925687	+	1.06640i
$563$	28.4313	+	20.6565i	1.19824	+	0.870569i	0.994110	−	0.108375i	$-0.0345648\pi$
$563$	28.4313	+	20.6565i	1.19824	+	0.870569i	0.204126	+	0.978945i	$0.434565\pi$
$564$	4.44809	+	9.08745i	0.187298	+	0.382651i
$565$	2.68318	+	5.46273i	0.112882	+	0.229819i
$566$	−26.8752	+	30.9604i	−1.12965	+	1.30136i
$567$	−4.03988	+	1.31264i	−0.169659	+	0.0551255i
$568$	2.91500	−	10.9715i	0.122311	−	0.460354i
$569$	11.1973	+	34.4618i	0.469415	+	1.44471i	0.853344	+	0.521349i	$0.174571\pi$
$569$	11.1973	+	34.4618i	0.469415	+	1.44471i	−0.383928	+	0.923363i	$0.625429\pi$
$570$	−0.615102	−	11.0030i	−0.0257638	−	0.460866i
$571$	34.0692	+	11.0697i	1.42575	+	0.463255i	0.917425	−	0.397910i	$-0.130264\pi$
$571$	34.0692	+	11.0697i	1.42575	+	0.463255i	0.508327	+	0.861164i	$0.330264\pi$
$572$	44.0291	+	23.3313i	1.84095	+	0.975529i
$573$	−2.10767	+	1.53131i	−0.0880492	+	0.0639715i
$574$	−21.5069	−	1.86636i	−0.897682	−	0.0779005i
$575$	4.30769	−	12.0433i	0.179643	−	0.502241i
$576$	14.0423	+	8.02847i	0.585096	+	0.334520i
$577$	22.3615	+	30.7780i	0.930922	+	1.28130i	0.959499	+	0.281712i	$0.0909023\pi$
$577$	22.3615	+	30.7780i	0.930922	+	1.28130i	−0.0285774	+	0.999592i	$0.509098\pi$
$578$	2.41445	+	1.02287i	0.100428	+	0.0425457i
$579$	−20.7455	−	6.74061i	−0.862152	−	0.280130i
$580$	−7.70031	−	26.4357i	−0.319738	−	1.09768i
$581$	−5.89547	+	1.91555i	−0.244585	+	0.0794706i
$582$	−10.1169	−	0.877941i	−0.419359	−	0.0363918i
$583$	49.2979	−	16.0179i	2.04171	−	0.663392i
$584$	−17.3015	−	21.2736i	−0.715940	−	0.880306i
$585$	27.3963	+	4.75218i	1.13270	+	0.196479i
$586$	−10.0768	−	16.7438i	−0.416267	−	0.691682i
$587$	12.8092	+	9.30640i	0.528690	+	0.384116i	0.819868	−	0.572553i	$-0.194047\pi$
$587$	12.8092	+	9.30640i	0.528690	+	0.384116i	−0.291177	+	0.956669i	$0.594047\pi$
$588$	9.01391	+	9.30792i	0.371727	+	0.383852i
$589$	9.08500	+	12.5044i	0.374341	+	0.515236i
$590$	−2.28639	+	3.54774i	−0.0941291	+	0.146058i
$591$	7.25474	+	5.27087i	0.298420	+	0.216815i
$592$	−0.474686	+	14.7864i	−0.0195095	+	0.607717i
$593$		−	31.5299i		−	1.29478i	−0.762160	−	0.647389i	$-0.775861\pi$
$593$		−	31.5299i		−	1.29478i	0.762160	−	0.647389i	$-0.224139\pi$
$594$	−6.42024	−	27.7201i	−0.263426	−	1.13737i
$595$	31.5629	+	5.47491i	1.29395	+	0.224450i
$596$	−4.93682	−	2.61605i	−0.202220	−	0.107158i
$597$	−1.89017	+	5.81735i	−0.0773595	+	0.238088i
$598$	19.0632	−	11.4726i	0.779552	−	0.469149i
$599$	28.8872			1.18030			0.590149	−	0.807294i	$-0.299069\pi$
$599$	28.8872			1.18030			0.590149	+	0.807294i	$0.299069\pi$
$600$	13.1889	−	4.65483i	0.538436	−	0.190033i
$601$	−16.6170			−0.677822			−0.338911	−	0.940818i	$-0.610059\pi$
$601$	−16.6170			−0.677822			−0.338911	+	0.940818i	$0.610059\pi$
$602$	7.77361	−	4.67830i	0.316829	−	0.190673i
$603$	9.09970	−	28.0060i	0.370568	−	1.14049i
$604$	4.13709	−	7.80722i	0.168336	−	0.317671i
$605$	8.42939	+	8.68044i	0.342703	+	0.352910i
$606$	−2.85353	−	12.3204i	−0.115917	−	0.500483i
$607$		−	46.4232i		−	1.88426i	−0.335249	−	0.942129i	$-0.608821\pi$
$607$		−	46.4232i		−	1.88426i	0.335249	−	0.942129i	$-0.391179\pi$
$608$	−2.35962	+	19.7931i	−0.0956954	+	0.802715i
$609$	18.1337	+	13.1749i	0.734816	+	0.533875i
$610$	−3.39373	−	4.16117i	−0.137408	−	0.168481i
$611$	−18.4911	−	25.4508i	−0.748070	−	1.02963i
$612$	−11.3053	+	10.9482i	−0.456992	+	0.442556i
$613$	−29.1219	−	21.1583i	−1.17622	−	0.854576i	−0.184483	−	0.982836i	$-0.559061\pi$
$613$	−29.1219	−	21.1583i	−1.17622	−	0.854576i	−0.991741	+	0.128259i	$0.959061\pi$
$614$	−5.62713	−	9.35020i	−0.227092	−	0.377343i
$615$	−1.30151	−	9.07744i	−0.0524819	−	0.366038i
$616$	32.7232	−	26.6133i	1.31845	−	1.07228i
$617$	8.45602	−	2.74753i	0.340427	−	0.110611i	−0.133814	−	0.991006i	$-0.542723\pi$
$617$	8.45602	−	2.74753i	0.340427	−	0.110611i	0.474241	+	0.880395i	$0.342723\pi$
$618$	14.7615	+	1.28100i	0.593794	+	0.0515292i
$619$	−24.2453	+	7.87779i	−0.974503	+	0.316635i	−0.752632	−	0.658441i	$-0.771216\pi$
$619$	−24.2453	+	7.87779i	−0.974503	+	0.316635i	−0.221870	+	0.975076i	$0.571216\pi$
$620$	−12.0122	+	15.5084i	−0.482421	+	0.622831i
$621$	−12.0832	−	3.92607i	−0.484882	−	0.157548i
$622$	12.9108	+	5.46960i	0.517677	+	0.219311i
$623$	17.6827	+	24.3381i	0.708441	+	0.975085i
$624$	22.8853	+	8.25668i	0.916144	+	0.330532i
$625$	−9.10671	+	23.2824i	−0.364268	+	0.931294i
$626$	2.73067	+	0.236967i	0.109140	+	0.00947109i
$627$	11.4213	−	8.29809i	0.456124	−	0.331394i
$628$	−12.3049	+	23.2209i	−0.491019	+	0.926617i
$629$	−13.6892	−	4.44790i	−0.545825	−	0.177349i
$630$	12.7502	−	19.7841i	0.507979	−	0.788219i
$631$	11.0609	+	34.0420i	0.440328	+	1.35519i	0.887527	+	0.460756i	$0.152422\pi$
$631$	11.0609	+	34.0420i	0.440328	+	1.35519i	−0.447199	+	0.894435i	$0.647578\pi$
$632$	11.2084	−	42.1863i	0.445846	−	1.67808i
$633$	−19.1599	+	6.22541i	−0.761536	+	0.247438i
$634$	−1.76196	+	2.02979i	−0.0699764	+	0.0806131i
$635$	−8.27296	+	1.18616i	−0.328302	+	0.0470714i
$636$	22.7316	−	11.1266i	0.901368	−	0.441198i
$637$	−32.5935	−	23.6806i	−1.29140	−	0.938258i
$638$	23.1226	−	26.6373i	0.915432	−	1.05458i
$639$	6.56531	−	4.76997i	0.259720	−	0.188697i
$640$	−24.9555	+	4.14997i	−0.986453	+	0.164042i
$641$	−1.61137	−	1.17073i	−0.0636453	−	0.0462410i	0.555508	−	0.831511i	$-0.312524\pi$
$641$	−1.61137	−	1.17073i	−0.0636453	−	0.0462410i	−0.619153	+	0.785270i	$0.712524\pi$
$642$	−0.533253	+	0.123506i	−0.0210458	+	0.00487441i
$643$	−14.4169			−0.568548			−0.284274	−	0.958743i	$-0.591752\pi$
$643$	−14.4169			−0.568548			−0.284274	+	0.958743i	$0.591752\pi$
$644$	−2.64736	−	18.6465i	−0.104321	−	0.734775i
$645$	2.68494	+	2.76490i	0.105719	+	0.108868i
$646$	−17.8575	−	7.56522i	−0.702593	−	0.297650i
$647$	−3.84494	−	1.24930i	−0.151160	−	0.0491149i	0.232460	−	0.972606i	$-0.425323\pi$
$647$	−3.84494	−	1.24930i	−0.151160	−	0.0491149i	−0.383620	+	0.923491i	$0.625323\pi$
$648$	1.17607	+	3.04455i	0.0462006	+	0.119601i
$649$	−5.40693			−0.212240
$650$	−37.9022	+	21.3211i	−1.48665	+	0.836284i
$651$		−	15.9688i		−	0.625868i
$652$	0.865550	−	0.423666i	0.0338976	−	0.0165920i
$653$	10.5252	−	32.3932i	0.411882	−	1.26764i	−0.503128	−	0.864212i	$-0.667817\pi$
$653$	10.5252	−	32.3932i	0.411882	−	1.26764i	0.915010	−	0.403431i	$-0.132183\pi$
$654$	−4.71089	+	11.1199i	−0.184211	+	0.434823i
$655$	−5.88919	+	33.9512i	−0.230110	+	1.32658i
$656$	−0.532219	+	16.5786i	−0.0207797	+	0.647284i
$657$		−	19.6020i		−	0.764748i
$658$	−25.9426	+	6.00856i	−1.01135	+	0.234238i
$659$	−6.87300	+	9.45988i	−0.267734	+	0.368504i	−0.921623	−	0.388086i	$-0.873136\pi$
$659$	−6.87300	+	9.45988i	−0.267734	+	0.368504i	0.653889	+	0.756591i	$0.273136\pi$
$660$	14.1651	+	10.9717i	0.551375	+	0.427074i
$661$	23.0527	+	31.7294i	0.896647	+	1.23413i	0.971525	+	0.236937i	$0.0761434\pi$
$661$	23.0527	+	31.7294i	0.896647	+	1.23413i	−0.0748777	+	0.997193i	$0.523857\pi$
$662$	−32.1114	−	27.8744i	−1.24805	−	1.08337i
$663$	−13.9134	+	19.1501i	−0.540351	+	0.743729i
$664$	1.71627	+	4.44297i	0.0666041	+	0.172421i
$665$	28.5780	+	4.95716i	1.10821	+	0.192230i
$666$	−6.93260	+	7.98639i	−0.268633	+	0.309466i
$667$	−4.86700	−	14.9791i	−0.188451	−	0.579993i
$668$	3.48714	−	19.9406i	0.134921	−	0.771525i
$669$	9.93966	−	3.22959i	0.384289	−	0.124863i
$670$	16.6545	+	42.9386i	0.643420	+	1.65886i
$671$	2.12567	−	6.54212i	0.0820604	−	0.252556i
$672$	13.9921	−	15.1109i	0.539757	−	0.582917i
$673$	−19.4849	−	26.8187i	−0.751088	−	1.03378i	−0.997903	−	0.0647213i	$-0.979384\pi$
$673$	−19.4849	−	26.8187i	−0.751088	−	1.03378i	0.246816	−	0.969062i	$-0.420616\pi$
$674$	−7.02185	−	0.609354i	−0.270472	−	0.0234714i
$675$	23.3821	+	8.36340i	0.899979	+	0.321907i
$676$	−48.9047	−	8.55226i	−1.88095	−	0.328933i
$677$	11.1735	−	8.11803i	0.429433	−	0.312001i	−0.351989	−	0.936004i	$-0.614495\pi$
$677$	11.1735	−	8.11803i	0.429433	−	0.312001i	0.781422	+	0.624003i	$0.214495\pi$
$678$	−1.48496	+	3.50520i	−0.0570296	+	0.134617i
$679$	8.25922	−	25.4193i	0.316960	−	0.975502i
$680$	2.88010	−	24.4446i	0.110447	−	0.937408i
$681$	−2.88226	−	8.87069i	−0.110448	−	0.339925i
$682$	−25.0357	−	2.17259i	−0.958666	−	0.0831927i
$683$	15.0801	+	46.4117i	0.577023	+	1.77589i	0.629186	+	0.777255i	$0.283389\pi$
$683$	15.0801	+	46.4117i	0.577023	+	1.77589i	−0.0521629	+	0.998639i	$0.516611\pi$
$684$	−10.2362	+	9.91289i	−0.391392	+	0.379029i
$685$	−8.01881	−	16.3256i	−0.306383	−	0.623769i
$686$	2.00373	−	1.20588i	0.0765029	−	0.0460409i
$687$	5.91471	−	8.14090i	0.225660	−	0.310595i
$688$	−3.91446	−	5.76834i	−0.149238	−	0.219916i
$689$	−63.6634	+	46.2542i	−2.42538	+	1.76214i
$690$	7.45887	−	2.89306i	0.283954	−	0.110137i
$691$	18.4219	−	25.3556i	0.700803	−	0.964573i	−0.299143	−	0.954208i	$-0.596701\pi$
$691$	18.4219	−	25.3556i	0.700803	−	0.964573i	0.999946	−	0.0103648i	$-0.00329927\pi$
$692$	−0.434803	−	3.06250i	−0.0165287	−	0.116419i
$693$	30.1520			1.14538
$694$	29.7704	−	6.89511i	1.13007	−	0.261735i
$695$	−1.79570	+	0.257464i	−0.0681146	+	0.00976615i
$696$	9.34945	−	14.4636i	0.354390	−	0.548243i
$697$	−15.3484	−	4.98700i	−0.581363	−	0.188896i
$698$	4.59403	−	2.76477i	0.173887	−	0.104648i
$699$			4.80146i			0.181608i
$700$	4.10291	+	36.5820i	0.155076	+	1.38267i
$701$			10.0510i			0.379622i	0.981821	+	0.189811i	$0.0607875\pi$
$701$			10.0510i			0.379622i	−0.981821	+	0.189811i	$0.939212\pi$
$702$	22.2741	+	37.0113i	0.840681	+	1.39690i
$703$	−12.3947	−	4.02727i	−0.467473	−	0.151891i
$704$	−21.7871	−	23.9925i	−0.821131	−	0.904251i
$705$	−4.98707	−	10.1532i	−0.187824	−	0.382393i
$706$	−7.98125	−	34.4599i	−0.300378	−	1.29692i
$707$	33.2853			1.25182
$708$	−2.61375	+	0.371090i	−0.0982307	+	0.0139464i
$709$	10.3892	−	14.2995i	0.390175	−	0.537030i	−0.568069	−	0.822981i	$-0.692309\pi$
$709$	10.3892	−	14.2995i	0.390175	−	0.537030i	0.958244	+	0.285951i	$0.0923094\pi$
$710$	−3.24221	+	12.2710i	−0.121678	+	0.460522i
$711$	25.2441	−	18.3409i	0.946729	−	0.687839i
$712$	17.9329	−	14.5846i	0.672064	−	0.546580i
$713$	−6.59540	+	9.07779i	−0.247000	+	0.339966i
$714$	10.3319	+	17.1677i	0.386660	+	0.642486i
$715$	−49.2618	−	26.0175i	−1.84229	−	0.972999i
$716$	4.38748	−	4.24889i	0.163968	−	0.158789i
$717$	2.70134	+	8.31386i	0.100883	+	0.310487i
$718$	−2.84009	+	32.7276i	−0.105991	+	1.22138i
$719$	−6.84341	−	21.0618i	−0.255216	−	0.785474i	−0.993787	−	0.111298i	$-0.964499\pi$
$719$	−6.84341	−	21.0618i	−0.255216	−	0.785474i	0.738571	−	0.674176i	$-0.235501\pi$
$720$	−15.7121	−	8.95452i	−0.585555	−	0.333715i
$721$	−12.0510	+	37.0891i	−0.448801	+	1.38127i
$722$	8.57268	+	3.63177i	0.319042	+	0.135160i
$723$	−2.78031	+	2.02001i	−0.103401	+	0.0751251i
$724$	0.311302	−	1.78013i	0.0115694	−	0.0661578i
$725$	8.64981	+	29.5442i	0.321246	+	1.09724i
$726$	−0.654309	+	7.53989i	−0.0242837	+	0.279832i
$727$	−6.64344	−	9.14391i	−0.246392	−	0.339129i	0.667852	−	0.744294i	$-0.267214\pi$
$727$	−6.64344	−	9.14391i	−0.246392	−	0.339129i	−0.914243	+	0.405165i	$0.867214\pi$
$728$	−34.7617	+	53.7765i	−1.28835	+	1.99309i
$729$	3.83253	−	11.7953i	0.141946	−	0.436864i
$730$	19.3763	+	23.7580i	0.717149	+	0.879321i
$731$	6.45055	−	2.09591i	0.238582	−	0.0775201i
$732$	0.578561	−	3.30840i	0.0213842	−	0.122282i
$733$	10.8888	+	33.5122i	0.402186	+	1.23780i	0.923222	+	0.384267i	$0.125546\pi$
$733$	10.8888	+	33.5122i	0.402186	+	1.23780i	−0.521036	+	0.853535i	$0.674454\pi$
$734$	−4.25898	−	3.69702i	−0.157202	−	0.136459i
$735$	−10.0921	−	10.3927i	−0.372254	−	0.383341i
$736$	−14.1952	+	2.81113i	−0.523241	+	0.103620i
$737$	−34.6792	+	47.7318i	−1.27742	+	1.75822i
$738$	−7.77286	+	8.95437i	−0.286123	+	0.329615i
$739$	−11.1878	−	15.3987i	−0.411549	−	0.566449i	0.552046	−	0.833814i	$-0.313847\pi$
$739$	−11.1878	−	15.3987i	−0.411549	−	0.566449i	−0.963595	+	0.267365i	$0.913847\pi$
$740$	0.508000	−	16.5324i	0.0186744	−	0.607743i
$741$	−12.5976	+	17.3391i	−0.462785	+	0.636969i
$742$	15.0300	+	64.8937i	0.551768	+	2.38232i
$743$		−	11.0416i		−	0.405078i	−0.979274	−	0.202539i	$-0.935081\pi$
$743$		−	11.0416i		−	0.405078i	0.979274	−	0.202539i	$-0.0649193\pi$
$744$	−12.2516	+	0.668014i	−0.449164	+	0.0244906i
$745$	5.52355	+	2.91724i	0.202367	+	0.106880i
$746$	26.7460	+	11.3308i	0.979241	+	0.414850i
$747$	−1.05215	+	3.23818i	−0.0384961	+	0.118479i
$748$	28.3210	−	13.8624i	1.03552	−	0.506861i
$749$		−	1.44066i		−	0.0526404i
$750$	−14.7385	+	5.22451i	−0.538175	+	0.190772i
$751$	−40.7628			−1.48746			−0.743728	−	0.668483i	$-0.766944\pi$
$751$	−40.7628			−1.48746			−0.743728	+	0.668483i	$0.766944\pi$
$752$	5.69511	+	19.6523i	0.207679	+	0.716645i
$753$	9.97275	+	3.24034i	0.363427	+	0.118085i
$754$	−20.8888	+	49.3073i	−0.760725	+	1.79567i
$755$	−4.61341	+	8.73508i	−0.167899	+	0.317902i
$756$	36.2022	−	5.13986i	1.31666	−	0.186935i
$757$	−15.9064			−0.578128			−0.289064	−	0.957310i	$-0.593344\pi$
$757$	−15.9064			−0.578128			−0.289064	+	0.957310i	$0.593344\pi$
$758$	−9.13759	−	39.4526i	−0.331892	−	1.43298i
$759$	8.29150	+	6.02413i	0.300962	+	0.218662i
$760$	2.60773	−	22.1329i	0.0945924	−	0.802846i
$761$	−28.7709	+	20.9033i	−1.04294	+	0.757743i	−0.970858	−	0.239656i	$-0.922965\pi$
$761$	−28.7709	+	20.9033i	−1.04294	+	0.757743i	−0.0720855	+	0.997398i	$0.522965\pi$
$762$	−3.94768	−	3.42679i	−0.143009	−	0.124140i
$763$	−25.7148	−	18.6829i	−0.930940	−	0.676368i
$764$	−4.73206	+	2.31623i	−0.171200	+	0.0837982i
$765$	12.6229	−	12.2579i	0.456383	−	0.443184i
$766$	−13.0579	−	11.3349i	−0.471800	−	0.409547i
$767$	7.80670	−	2.53655i	0.281883	−	0.0915895i
$768$	−12.1787	−	10.1029i	−0.439461	−	0.364555i
$769$	−11.6054	−	35.7176i	−0.418500	−	1.28801i	−0.909082	−	0.416616i	$-0.863216\pi$
$769$	−11.6054	−	35.7176i	−0.418500	−	1.28801i	0.490582	−	0.871395i	$-0.336784\pi$
$770$	−36.5447	+	29.8048i	−1.31698	+	1.07409i
$771$	−7.11499	−	2.31180i	−0.256240	−	0.0832575i
$772$	−38.9780	−	20.6547i	−1.40285	−	0.743377i
$773$	32.1938	−	23.3902i	1.15793	−	0.841287i	0.168416	−	0.985716i	$-0.446135\pi$
$773$	32.1938	−	23.3902i	1.15793	−	0.841287i	0.989515	+	0.144429i	$0.0461347\pi$
$774$	0.430836	−	4.96471i	0.0154861	−	0.178453i
$775$	13.4062	−	17.3573i	0.481565	−	0.623493i
$776$	−19.8476	−	5.27327i	−0.712488	−	0.189299i
$777$	7.91432	+	10.8931i	0.283925	+	0.390789i
$778$	15.6050	−	36.8351i	0.559467	−	1.32060i
$779$	−13.8969	−	4.51539i	−0.497910	−	0.161781i
$780$	−25.5992	−	9.19609i	−0.916597	−	0.329273i
$781$	−15.4636	+	5.02441i	−0.553330	+	0.179788i
$782$	1.21722	−	14.0266i	0.0435277	−	0.501589i
$783$	29.0820	−	9.44930i	1.03930	−	0.337690i
$784$	14.7137	+	21.6820i	0.525489	+	0.774358i
$785$	13.7216	−	25.9807i	0.489746	−	0.927290i
$786$	−18.4668	+	11.1136i	−0.658688	+	0.396411i
$787$	37.0424	+	26.9129i	1.32042	+	0.959341i	0.999927	+	0.0120896i	$0.00384833\pi$
$787$	37.0424	+	26.9129i	1.32042	+	0.959341i	0.320492	+	0.947251i	$0.396152\pi$
$788$	12.6157	+	13.0272i	0.449415	+	0.464074i
$789$	−17.3769	−	23.9173i	−0.618635	−	0.851478i
$790$	−12.4665	+	47.1829i	−0.443540	+	1.67869i
$791$	−8.10579	−	5.88920i	−0.288209	−	0.209396i
$792$	−1.26133	−	23.1331i	−0.0448195	−	0.822000i
$793$			10.4429i			0.370840i
$794$	9.43446	−	2.18511i	0.334816	−	0.0775467i
$795$	−25.3976	+	12.4748i	−0.900761	+	0.442436i
$796$	−5.79188	+	10.9300i	−0.205288	+	0.387404i
$797$	1.61885	−	4.98230i	0.0573425	−	0.176482i	−0.918283	−	0.395925i	$-0.870424\pi$
$797$	1.61885	−	4.98230i	0.0573425	−	0.176482i	0.975625	+	0.219443i	$0.0704240\pi$
$798$	9.35479	+	15.5442i	0.331156	+	0.550259i
$799$	−19.9072			−0.704266
$800$	27.8947	−	4.67814i	0.986227	−	0.165397i
$801$	16.5238			0.583841
$802$	−24.8761	−	41.3349i	−0.878407	−	1.45959i
$803$	−12.1364	+	37.3519i	−0.428283	+	1.31812i
$804$	−13.4882	+	25.4540i	−0.475693	+	0.897695i
$805$	2.98848	+	20.8433i	0.105330	+	0.734631i
$806$	37.1666	−	8.60813i	1.30914	−	0.303209i
$807$		−	22.7249i		−	0.799956i
$808$	−1.39241	−	25.5371i	−0.0489847	−	0.898391i
$809$	8.37189	+	6.08254i	0.294340	+	0.213851i	0.725148	−	0.688593i	$-0.241771\pi$
$809$	8.37189	+	6.08254i	0.294340	+	0.213851i	−0.430808	+	0.902444i	$0.641771\pi$
$810$	−1.31957	−	3.40210i	−0.0463649	−	0.119538i
$811$	−7.75245	−	10.6703i	−0.272225	−	0.374686i	0.650914	−	0.759151i	$-0.274386\pi$
$811$	−7.75245	−	10.6703i	−0.272225	−	0.374686i	−0.923139	+	0.384465i	$0.874386\pi$
$812$	31.5338	+	32.5623i	1.10662	+	1.14271i
$813$	19.2655	+	13.9972i	0.675671	+	0.490904i
$814$	18.1548	−	10.9259i	0.636327	−	0.382954i
$815$	−0.967063	+	0.475002i	−0.0338747	+	0.0166386i
$816$	12.7392	−	8.64494i	0.445960	−	0.302633i
$817$	5.84054	−	1.89771i	0.204334	−	0.0663923i
$818$	−3.30926	+	38.1341i	−0.115706	+	1.33333i
$819$	−43.5345	+	14.1452i	−1.52122	+	0.494273i
$820$	0.569572	−	18.5362i	0.0198903	−	0.647312i
$821$	−22.3506	−	7.26213i	−0.780040	−	0.253450i	−0.108183	−	0.994131i	$-0.534503\pi$
$821$	−22.3506	−	7.26213i	−0.780040	−	0.253450i	−0.671857	+	0.740681i	$0.734503\pi$
$822$	4.43786	−	10.4754i	0.154788	−	0.365373i
$823$	−13.8810	−	19.1055i	−0.483861	−	0.665977i	0.495380	−	0.868676i	$-0.335029\pi$
$823$	−13.8810	−	19.1055i	−0.483861	−	0.665977i	−0.979241	+	0.202699i	$0.935029\pi$
$824$	28.9595	+	7.69418i	1.00885	+	0.268040i
$825$	−15.8539	−	12.2450i	−0.551961	−	0.426316i
$826$	0.600712	−	6.92227i	0.0209015	−	0.240857i
$827$	−35.9043	+	26.0860i	−1.24852	+	0.907100i	−0.998135	−	0.0610478i	$-0.980556\pi$
$827$	−35.9043	+	26.0860i	−1.24852	+	0.907100i	−0.250381	+	0.968147i	$0.580556\pi$
$828$	−9.14055	−	4.84363i	−0.317656	−	0.168328i
$829$	19.4026	+	6.30430i	0.673881	+	0.218957i	0.625915	−	0.779892i	$-0.284726\pi$
$829$	19.4026	+	6.30430i	0.673881	+	0.218957i	0.0479668	+	0.998849i	$0.484726\pi$
$830$	−1.92567	−	4.96475i	−0.0668410	−	0.172329i
$831$	−0.889314	−	2.73703i	−0.0308499	−	0.0949464i
$832$	42.7124	+	24.4202i	1.48079	+	0.846617i
$833$	−24.2463	+	7.87811i	−0.840085	+	0.272960i
$834$	−0.856867	−	0.743805i	−0.0296709	−	0.0257559i
$835$	−3.86810	+	22.2996i	−0.133861	+	0.771709i
$836$	25.6427	−	12.5515i	0.886872	−	0.434102i
$837$	−17.6246	−	12.8050i	−0.609194	−	0.442605i
$838$	−22.0417	−	19.1334i	−0.761419	−	0.660951i
$839$	−36.5182	+	26.5320i	−1.26075	+	0.915988i	−0.998794	−	0.0490920i	$-0.984367\pi$
$839$	−36.5182	+	26.5320i	−1.26075	+	0.915988i	−0.261955	+	0.965080i	$0.584367\pi$
$840$	−15.6204	+	16.9160i	−0.538956	+	0.583658i
$841$	7.20604	+	5.23549i	0.248484	+	0.180534i
$842$	−2.99350	−	12.9248i	−0.103163	−	0.445417i
$843$	23.4106			0.806305
$844$	−40.3362	+	5.72679i	−1.38843	+	0.197124i
$845$	54.6902	+	9.48659i	1.88140	+	0.326348i
$846$	−5.70559	+	13.4679i	−0.196162	+	0.463035i
$847$	−18.9444	−	6.15541i	−0.650937	−	0.211502i
$848$	49.1588	−	14.2459i	1.68812	−	0.489207i
$849$	28.6703			0.983963
$850$	−3.18249	+	27.3343i	−0.109159	+	0.937559i
$851$		−	9.46116i		−	0.324324i
$852$	−7.13036	+	3.49014i	−0.244282	+	0.119570i
$853$	−0.692652	+	2.13176i	−0.0237160	+	0.0729902i	−0.962214	−	0.272294i	$-0.912218\pi$
$853$	−0.692652	+	2.13176i	−0.0237160	+	0.0729902i	0.938498	+	0.345285i	$0.112218\pi$
$854$	8.13945	+	3.44824i	0.278526	+	0.117996i
$855$	11.4292	−	11.0987i	0.390871	−	0.379566i
$856$	−1.10530	+	0.0602661i	−0.0377782	+	0.00205985i
$857$		−	2.14330i		−	0.0732138i	−0.999330	−	0.0366069i	$-0.988345\pi$
$857$		−	2.14330i		−	0.0732138i	0.999330	−	0.0366069i	$-0.0116549\pi$
$858$	−7.86252	−	33.9473i	−0.268422	−	1.15894i
$859$	5.15215	−	7.09132i	0.175789	−	0.241953i	−0.712026	−	0.702153i	$-0.752222\pi$
$859$	5.15215	−	7.09132i	0.175789	−	0.241953i	0.887815	+	0.460200i	$0.152222\pi$
$860$	4.38536	+	6.44318i	0.149540	+	0.219711i
$861$	8.87356	+	12.2134i	0.302410	+	0.416232i
$862$	0.952024	−	1.09674i	0.0324261	−	0.0373550i
$863$	−1.54670	+	2.12885i	−0.0526504	+	0.0724670i	−0.834530	−	0.550962i	$-0.814261\pi$
$863$	−1.54670	+	2.12885i	−0.0526504	+	0.0724670i	0.781880	+	0.623429i	$0.214261\pi$
$864$	−5.45781	−	27.5600i	−0.185679	−	0.937609i
$865$	0.490828	+	3.42331i	0.0166887	+	0.116396i
$866$	28.7600	+	24.9652i	0.977306	+	0.848353i
$867$	−0.566652	−	1.74398i	−0.0192445	−	0.0592285i
$868$	5.56296	−	31.8108i	0.188819	−	1.07973i
$869$	−59.4586	+	19.3193i	−2.01699	+	0.655361i
$870$	−10.4308	+	16.1852i	−0.353636	+	0.548730i
$871$	27.6785	−	85.1858i	0.937851	−	2.88641i
$872$	−13.2581	+	20.5104i	−0.448978	+	0.694571i
$873$	−8.62895	−	11.8767i	−0.292046	−	0.401966i
$874$	1.10211	−	12.7001i	0.0372794	−	0.429587i
$875$	−4.64339	−	40.8936i	−0.156975	−	1.38246i
$876$	−3.30326	+	18.8891i	−0.111607	+	0.638205i
$877$	17.1035	−	12.4265i	0.577546	−	0.419611i	−0.260293	−	0.965530i	$-0.583819\pi$
$877$	17.1035	−	12.4265i	0.577546	−	0.419611i	0.837838	+	0.545918i	$0.183819\pi$
$878$	−1.97011	−	0.834628i	−0.0664881	−	0.0281673i
$879$	−4.22306	+	12.9973i	−0.142440	+	0.438387i
$880$	24.3955	+	26.7909i	0.822372	+	0.903122i
$881$	−9.15253	−	28.1686i	−0.308357	−	0.949024i	−0.978403	−	0.206705i	$-0.933726\pi$
$881$	−9.15253	−	28.1686i	−0.308357	−	0.949024i	0.670047	−	0.742319i	$-0.266274\pi$
$882$	−1.61943	+	18.6613i	−0.0545289	+	0.628360i
$883$	9.33779	+	28.7388i	0.314242	+	0.967137i	0.976065	+	0.217477i	$0.0697827\pi$
$883$	9.33779	+	28.7388i	0.314242	+	0.967137i	−0.661824	+	0.749660i	$0.730217\pi$
$884$	−34.3875	+	33.3012i	−1.15658	+	1.12004i
$885$	2.92169	−	0.418906i	0.0982115	−	0.0140814i
$886$	−11.0175	−	18.3071i	−0.370142	−	0.615038i
$887$	0.435322	−	0.599169i	0.0146167	−	0.0201181i	−0.801646	−	0.597799i	$-0.796042\pi$
$887$	0.435322	−	0.599169i	0.0146167	−	0.0201181i	0.816263	+	0.577681i	$0.196042\pi$
$888$	8.02631	−	6.52768i	0.269345	−	0.219055i
$889$	11.1310	−	8.08715i	0.373322	−	0.271234i
$890$	−20.0272	+	16.3336i	−0.671312	+	0.547502i
$891$	2.74769	−	3.78188i	0.0920512	−	0.126698i
$892$	20.9254	−	2.97092i	0.700636	−	0.0994737i
$893$	−18.0246			−0.603171
$894$	0.881596	+	3.80639i	0.0294850	+	0.127305i
$895$	−4.89882	+	4.75714i	−0.163750	+	0.159014i
$896$	33.1372	−	25.2275i	1.10704	−	0.842792i
$897$	−14.7976	−	4.80804i	−0.494079	−	0.160536i
$898$	−23.7031	−	39.3857i	−0.790981	−	1.31432i
$899$		−	27.0063i		−	0.900709i
$900$	17.5804	+	9.98731i	0.586013	+	0.332910i
$901$			49.7965i			1.65896i
$902$	20.3553	−	12.2502i	0.677757	−	0.407887i
$903$	−6.03419	−	1.96063i	−0.200805	−	0.0652456i
$904$	−4.17921	+	6.46526i	−0.138999	+	0.215031i
$905$	−0.345311	+	1.99072i	−0.0114785	+	0.0661737i
$906$	−6.01952	+	1.39418i	−0.199985	+	0.0463185i
$907$	25.0444			0.831586			0.415793	−	0.909459i	$-0.363504\pi$
$907$	25.0444			0.831586			0.415793	+	0.909459i	$0.363504\pi$
$908$	−2.65141	−	18.6750i	−0.0879900	−	0.619751i
$909$	10.7462	−	14.7908i	0.356428	−	0.490581i
$910$	38.7821	−	60.1773i	1.28562	−	1.99486i
$911$	−10.3682	+	7.53297i	−0.343515	+	0.249579i	−0.746144	−	0.665785i	$-0.768097\pi$
$911$	−10.3682	+	7.53297i	−0.343515	+	0.249579i	0.402628	+	0.915364i	$0.368097\pi$
$912$	11.5344	−	7.82741i	0.381944	−	0.259191i
$913$	4.00976	−	5.51897i	0.132704	−	0.182651i
$914$	0.901161	−	0.542335i	0.0298077	−	0.0179389i
$915$	−0.641768	+	3.69979i	−0.0212162	+	0.122311i
$916$	14.6184	−	14.1567i	0.483007	−	0.467750i
$917$	−17.5296	−	53.9505i	−0.578878	−	1.78160i
$918$	27.2326	+	2.36324i	0.898810	+	0.0779984i
$919$	−9.20989	−	28.3451i	−0.303806	−	0.935019i	−0.980120	−	0.198405i	$-0.936424\pi$
$919$	−9.20989	−	28.3451i	−0.303806	−	0.935019i	0.676314	−	0.736613i	$-0.263576\pi$
$920$	15.8663	−	3.16474i	0.523098	−	0.104338i
$921$	−2.35827	+	7.25801i	−0.0777076	+	0.239159i
$922$	−15.2288	+	35.9472i	−0.501535	+	1.18386i
$923$	19.9697	−	14.5088i	0.657310	−	0.477564i
$924$	−29.0555	−	5.08111i	−0.955854	−	0.167156i
$925$	−0.542564	+	18.4845i	−0.0178394	+	0.607768i
$926$	25.1765	+	2.18481i	0.827352	+	0.0717973i
$927$	12.5904	+	17.3292i	0.413524	+	0.569167i
$928$	23.6633	−	25.5554i	0.776784	−	0.838898i
$929$	−1.45324	+	4.47263i	−0.0476794	+	0.146742i	−0.972062	−	0.234725i	$-0.924581\pi$
$929$	−1.45324	+	4.47263i	−0.0476794	+	0.146742i	0.924382	+	0.381467i	$0.124581\pi$
$930$	13.6966	−	0.765682i	0.449130	−	0.0251077i
$931$	−21.9534	+	7.13309i	−0.719494	+	0.233778i
$932$	−1.67265	+	9.56478i	−0.0547896	+	0.313305i
$933$	−3.03007	−	9.32559i	−0.0991999	−	0.305306i
$934$	6.24286	−	7.19180i	0.204273	−	0.235323i
$935$	−31.6425	+	15.5422i	−1.03482	+	0.508283i
$936$	12.6736	+	32.8086i	0.414249	+	1.07238i
$937$	26.5112	−	36.4895i	0.866083	−	1.19206i	−0.114001	−	0.993481i	$-0.536367\pi$
$937$	26.5112	−	36.4895i	0.866083	−	1.19206i	0.980085	−	0.198581i	$-0.0636332\pi$
$938$	−57.2562	−	49.7014i	−1.86948	−	1.62281i
$939$	−1.12665	−	1.55070i	−0.0367668	−	0.0506052i
$940$	−6.39751	−	21.9631i	−0.208664	−	0.716359i
$941$	−19.7024	+	27.1181i	−0.642281	+	0.884024i	−0.998735	−	0.0502890i	$-0.983986\pi$
$941$	−19.7024	+	27.1181i	−0.642281	+	0.884024i	0.356454	+	0.934313i	$0.383986\pi$
$942$	17.9038	−	4.14669i	0.583338	−	0.135107i
$943$		−	10.6079i		−	0.345441i
$944$	−5.33601	−	0.171301i	−0.173672	−	0.00557539i
$945$	−40.4674	+	5.80214i	−1.31640	+	0.188744i
$946$	−3.89481	+	9.19358i	−0.126631	+	0.298909i
$947$	13.5036	−	41.5598i	0.438808	−	1.35051i	−0.450325	−	0.892865i	$-0.648692\pi$
$947$	13.5036	−	41.5598i	0.438808	−	1.35051i	0.889133	−	0.457648i	$-0.151308\pi$
$948$	−27.4168	+	13.4199i	−0.890456	+	0.435857i
$949$		−	59.6234i		−	1.93546i
$950$	−2.88153	+	24.7493i	−0.0934892	+	0.802975i
$951$	1.87965			0.0609518
$952$	14.6010	+	37.7983i	0.473222	+	1.22505i
$953$	−18.8268	−	6.11721i	−0.609861	−	0.198156i	−0.0122276	−	0.999925i	$-0.503892\pi$
$953$	−18.8268	−	6.11721i	−0.609861	−	0.198156i	−0.597634	+	0.801769i	$0.703892\pi$
$954$	33.6889	+	14.2721i	1.09072	+	0.462077i
$955$	5.28704	−	2.59689i	0.171085	−	0.0840333i
$956$	2.48497	+	17.5027i	0.0803697	+	0.566079i
$957$	−24.6671			−0.797373
$958$	−6.83050	+	1.58201i	−0.220683	+	0.0511124i
$959$	24.2245	+	17.6001i	0.782249	+	0.568338i
$960$	13.6317	+	11.2766i	0.439961	+	0.363951i
$961$	9.51394	−	6.91228i	0.306901	−	0.222977i
$962$	−21.0869	+	24.2922i	−0.679868	+	0.783211i
$963$	−0.640177	−	0.465116i	−0.0206294	−	0.0149882i
$964$	−6.24223	+	3.05542i	−0.201049	+	0.0984086i
$965$	43.6104	+	23.0327i	1.40387	+	0.741449i
$966$	−8.63364	+	9.94599i	−0.277783	+	0.320007i
$967$	26.8836	−	8.73502i	0.864519	−	0.280899i	0.157004	−	0.987598i	$-0.449816\pi$
$967$	26.8836	−	8.73502i	0.864519	−	0.280899i	0.707515	+	0.706699i	$0.249816\pi$
$968$	−3.93004	+	14.7920i	−0.126316	+	0.475432i
$969$	4.19101	+	12.8986i	0.134635	+	0.414363i
$970$	22.1984	+	5.86520i	0.712747	+	0.188320i
$971$	43.8882	+	14.2601i	1.40844	+	0.457629i	0.911910	−	0.410391i	$-0.134608\pi$
$971$	43.8882	+	14.2601i	1.40844	+	0.457629i	0.496528	+	0.868021i	$0.334608\pi$
$972$	15.0216	−	28.3478i	0.481819	−	0.909255i
$973$	2.41605	−	1.75536i	0.0774550	−	0.0562744i
$974$	53.5544	+	4.64743i	1.71599	+	0.148913i
$975$	28.6348	+	10.2422i	0.917049	+	0.328013i
$976$	2.30505	−	6.38898i	0.0737829	−	0.204506i
$977$	−2.24013	−	3.08328i	−0.0716682	−	0.0986428i	0.771678	−	0.636013i	$-0.219418\pi$
$977$	−2.24013	−	3.08328i	−0.0716682	−	0.0986428i	−0.843346	+	0.537371i	$0.819418\pi$
$978$	−0.620523	−	0.262881i	−0.0198422	−	0.00840602i
$979$	−31.4864	−	10.2306i	−1.00631	−	0.326970i
$980$	−16.4837	−	24.2186i	−0.526552	−	0.773636i
$981$	−16.6041	+	5.39499i	−0.530127	+	0.172249i
$982$	−22.5173	−	1.95404i	−0.718557	−	0.0623561i
$983$	20.2704	−	6.58625i	0.646525	−	0.210069i	0.0326438	−	0.999467i	$-0.489607\pi$
$983$	20.2704	−	6.58625i	0.646525	−	0.210069i	0.613881	+	0.789398i	$0.289607\pi$
$984$	8.99914	−	7.31887i	0.286882	−	0.233317i
$985$	−14.1247	−	14.5454i	−0.450052	−	0.463456i
$986$	17.4731	+	29.0338i	0.556457	+	0.924625i
$987$	15.0657	+	10.9459i	0.479548	+	0.348412i
$988$	−31.1355	+	30.1520i	−0.990552	+	0.959263i
$989$	2.62048	+	3.60678i	0.0833265	+	0.114689i
$990$	1.44575	+	25.8617i	0.0459488	+	0.821938i
$991$	18.4326	+	13.3921i	0.585532	+	0.425414i	0.840714	−	0.541479i	$-0.182135\pi$
$991$	18.4326	+	13.3921i	0.585532	+	0.425414i	−0.255182	+	0.966893i	$0.582135\pi$
$992$	−24.6385	−	2.93727i	−0.782274	−	0.0932585i
$993$			29.7362i			0.943651i
$994$	−4.71455	−	20.3556i	−0.149536	−	0.645640i
$995$	6.45872	−	12.2290i	0.204755	−	0.387686i
$996$	1.55957	−	2.94311i	0.0494169	−	0.0932560i
$997$	5.01908	−	15.4471i	0.158956	−	0.489216i	−0.839584	−	0.543229i	$-0.817201\pi$
$997$	5.01908	−	15.4471i	0.158956	−	0.489216i	0.998540	+	0.0540134i	$0.0172014\pi$
$998$	−9.79959	+	5.89758i	−0.310201	+	0.186685i
$999$	18.3689			0.581165

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.o.a.189.10	yes	112
4.3	odd	2		800.2.be.a.689.18		112
5.2	odd	4		1000.2.t.b.301.47		224
5.3	odd	4		1000.2.t.b.301.10		224
5.4	even	2		1000.2.o.a.949.19		112
8.3	odd	2		800.2.be.a.689.11		112
8.5	even	2	inner	200.2.o.a.189.9	yes	112
25.9	even	10	inner	200.2.o.a.109.9	✓	112
25.12	odd	20		1000.2.t.b.701.45		224
25.13	odd	20		1000.2.t.b.701.12		224
25.16	even	5		1000.2.o.a.549.20		112
40.13	odd	4		1000.2.t.b.301.12		224
40.29	even	2		1000.2.o.a.949.20		112
40.37	odd	4		1000.2.t.b.301.45		224
100.59	odd	10		800.2.be.a.209.11		112
200.13	odd	20		1000.2.t.b.701.10		224
200.37	odd	20		1000.2.t.b.701.47		224
200.59	odd	10		800.2.be.a.209.18		112
200.109	even	10	inner	200.2.o.a.109.10	yes	112
200.141	even	10		1000.2.o.a.549.19		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.9	✓	112	25.9	even	10	inner
200.2.o.a.109.10	yes	112	200.109	even	10	inner
200.2.o.a.189.9	yes	112	8.5	even	2	inner
200.2.o.a.189.10	yes	112	1.1	even	1	trivial
800.2.be.a.209.11		112	100.59	odd	10
800.2.be.a.209.18		112	200.59	odd	10
800.2.be.a.689.11		112	8.3	odd	2
800.2.be.a.689.18		112	4.3	odd	2
1000.2.o.a.549.19		112	200.141	even	10
1000.2.o.a.549.20		112	25.16	even	5
1000.2.o.a.949.19		112	5.4	even	2
1000.2.o.a.949.20		112	40.29	even	2
1000.2.t.b.301.10		224	5.3	odd	4
1000.2.t.b.301.12		224	40.13	odd	4
1000.2.t.b.301.45		224	40.37	odd	4
1000.2.t.b.301.47		224	5.2	odd	4
1000.2.t.b.701.10		224	200.13	odd	20
1000.2.t.b.701.12		224	25.13	odd	20
1000.2.t.b.701.45		224	25.12	odd	20
1000.2.t.b.701.47		224	200.37	odd	20

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.729227 - 1.21170i) q^{2} +(-0.305611 + 0.940574i) q^{3} +(-0.936457 + 1.76721i) q^{4} +(1.04427 - 1.97724i) q^{5} +(1.36256 - 0.315581i) q^{6} +3.68114i q^{7} +(2.82423 - 0.153991i) q^{8} +(1.63577 + 1.18846i) q^{9} +(-3.15735 + 0.176505i) q^{10} +(-2.38116 - 3.27739i) q^{11} +(-1.37601 - 1.42089i) q^{12} +(4.97551 + 3.61492i) q^{13} +(4.46045 - 2.68438i) q^{14} +(1.54060 + 1.58649i) q^{15} +(-2.24610 - 3.30984i) q^{16} +(3.70129 - 1.20262i) q^{17} +(0.247211 - 2.84872i) q^{18} +(3.35127 - 1.08889i) q^{19} +(2.51629 + 3.69706i) q^{20} +(-3.46238 - 1.12500i) q^{21} +(-2.23482 + 5.27522i) q^{22} +(1.50362 + 2.06955i) q^{23} +(-0.718277 + 2.70346i) q^{24} +(-2.81898 - 4.12957i) q^{25} +(0.751941 - 8.66495i) q^{26} +(-4.01804 + 2.91928i) q^{27} +(-6.50536 - 3.44723i) q^{28} +(-5.85554 - 1.90258i) q^{29} +(0.798904 - 3.02366i) q^{30} +(1.35546 + 4.17167i) q^{31} +(-2.37264 + 5.13523i) q^{32} +(3.81033 - 1.23805i) q^{33} +(-4.15630 - 3.60789i) q^{34} +(7.27850 + 3.84412i) q^{35} +(-3.63208 + 1.77782i) q^{36} +(-2.99215 - 2.17392i) q^{37} +(-3.76325 - 3.26670i) q^{38} +(-4.92068 + 3.57508i) q^{39} +(2.64480 - 5.74500i) q^{40} +(-3.35481 - 2.43741i) q^{41} +(1.16170 + 5.01577i) q^{42} +1.74279 q^{43} +(8.02170 - 1.13889i) q^{44} +(4.05806 - 1.99324i) q^{45} +(1.41121 - 3.33111i) q^{46} +(-4.86486 - 1.58069i) q^{47} +(3.79958 - 1.10110i) q^{48} -6.55078 q^{49} +(-2.94815 + 6.42716i) q^{50} +3.84887i q^{51} +(-11.0477 + 5.40758i) q^{52} +(-3.95398 + 12.1691i) q^{53} +(6.46737 + 2.73986i) q^{54} +(-8.96677 + 1.28564i) q^{55} +(0.566862 + 10.3964i) q^{56} +3.48489i q^{57} +(1.96465 + 8.48260i) q^{58} +(0.784512 - 1.07979i) q^{59} +(-4.24637 + 1.23690i) q^{60} +(0.998070 + 1.37373i) q^{61} +(4.06640 - 4.68451i) q^{62} +(-4.37487 + 6.02149i) q^{63} +(7.95257 - 0.869812i) q^{64} +(12.3434 - 6.06283i) q^{65} +(-4.27875 - 3.71418i) q^{66} +(-4.50052 - 13.8512i) q^{67} +(-1.34081 + 7.66718i) q^{68} +(-2.40609 + 0.781786i) q^{69} +(-0.649740 - 11.6226i) q^{70} +(1.24027 - 3.81715i) q^{71} +(4.80280 + 3.10458i) q^{72} +(-5.69843 - 7.84322i) q^{73} +(-0.452199 + 5.21089i) q^{74} +(4.74568 - 1.38942i) q^{75} +(-1.21401 + 6.94211i) q^{76} +(12.0645 - 8.76538i) q^{77} +(7.92023 + 3.35536i) q^{78} +(4.76893 - 14.6772i) q^{79} +(-8.88990 + 0.984695i) q^{80} +(0.356584 + 1.09745i) q^{81} +(-0.507007 + 5.84247i) q^{82} +(0.520370 + 1.60153i) q^{83} +(5.23049 - 5.06527i) q^{84} +(1.48729 - 8.57422i) q^{85} +(-1.27089 - 2.11174i) q^{86} +(3.57904 - 4.92612i) q^{87} +(-7.22964 - 8.88942i) q^{88} +(6.61157 - 4.80359i) q^{89} +(-5.37446 - 3.46365i) q^{90} +(-13.3070 + 18.3156i) q^{91} +(-5.06542 + 0.719169i) q^{92} -4.33801 q^{93} +(1.63226 + 7.04745i) q^{94} +(1.34664 - 7.76337i) q^{95} +(-4.10496 - 3.80103i) q^{96} +(-6.90528 - 2.24366i) q^{97} +(4.77700 + 7.93761i) q^{98} -8.19095i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28}+ \cdots + 90 q^{98}+O(q^{100}) \) 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

Introduction

L-functions

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