LMFDB - Embedded newform 152.2.o.c.107.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,2,Mod(27,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.27"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.o (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,-3,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			107.14
Character	$\chi$	$=$	152.107
Dual form			152.2.o.c.27.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41219 - 0.0756882i) q^{2} +(-2.65547 + 1.53314i) q^{3} +(1.98854 - 0.213772i) q^{4} +(-2.25688 + 1.30301i) q^{5} +(-3.63398 + 2.36606i) q^{6} +4.30088i q^{7} +(2.79201 - 0.452395i) q^{8} +(3.20101 - 5.54431i) q^{9} +(-3.08851 + 2.01091i) q^{10} -0.349633 q^{11} +(-4.95277 + 3.61637i) q^{12} +(0.839767 - 1.45452i) q^{13} +(0.325526 + 6.07365i) q^{14} +(3.99538 - 6.92020i) q^{15} +(3.90860 - 0.850188i) q^{16} +(0.357047 + 0.618424i) q^{17} +(4.10079 - 8.07189i) q^{18} +(4.35063 - 0.268300i) q^{19} +(-4.20935 + 3.07354i) q^{20} +(-6.59384 - 11.4209i) q^{21} +(-0.493748 + 0.0264631i) q^{22} +(-1.38083 - 0.797223i) q^{23} +(-6.72052 + 5.48186i) q^{24} +(0.895662 - 1.55133i) q^{25} +(1.07582 - 2.11761i) q^{26} +10.4315i q^{27} +(0.919407 + 8.55249i) q^{28} +(0.463655 - 0.803074i) q^{29} +(5.11844 - 10.0750i) q^{30} -2.80517 q^{31} +(5.45533 - 1.49646i) q^{32} +(0.928441 - 0.536035i) q^{33} +(0.551025 + 0.846306i) q^{34} +(-5.60409 - 9.70656i) q^{35} +(5.18013 - 11.7094i) q^{36} +10.2099 q^{37} +(6.12360 - 0.708181i) q^{38} +5.14991i q^{39} +(-5.71176 + 4.65902i) q^{40} +(4.87850 - 2.81660i) q^{41} +(-10.1762 - 15.6293i) q^{42} +(4.32286 + 7.48741i) q^{43} +(-0.695261 + 0.0747417i) q^{44} +16.6838i q^{45} +(-2.01033 - 1.02132i) q^{46} +(-6.26395 - 3.61649i) q^{47} +(-9.07572 + 8.25007i) q^{48} -11.4976 q^{49} +(1.14742 - 2.25856i) q^{50} +(-1.89626 - 1.09480i) q^{51} +(1.35898 - 3.07189i) q^{52} +(-4.73541 + 8.20196i) q^{53} +(0.789543 + 14.7313i) q^{54} +(0.789079 - 0.455575i) q^{55} +(1.94570 + 12.0081i) q^{56} +(-11.1416 + 7.38258i) q^{57} +(0.593984 - 1.16918i) q^{58} +(6.62664 - 3.82589i) q^{59} +(6.46564 - 14.6152i) q^{60} +(-3.46531 - 2.00070i) q^{61} +(-3.96143 + 0.212318i) q^{62} +(23.8454 + 13.7672i) q^{63} +(7.59068 - 2.52618i) q^{64} +4.37690i q^{65} +(1.27056 - 0.827254i) q^{66} +(-10.6067 - 6.12378i) q^{67} +(0.842205 + 1.15344i) q^{68} +4.88901 q^{69} +(-8.64869 - 13.2833i) q^{70} +(-5.09365 - 8.82246i) q^{71} +(6.42905 - 16.9279i) q^{72} +(2.54260 + 4.40392i) q^{73} +(14.4182 - 0.772765i) q^{74} +5.49268i q^{75} +(8.59407 - 1.46357i) q^{76} -1.50373i q^{77} +(0.389787 + 7.27263i) q^{78} +(-1.31170 - 2.27193i) q^{79} +(-7.71343 + 7.01171i) q^{80} +(-6.38991 - 11.0677i) q^{81} +(6.67616 - 4.34681i) q^{82} -4.69293 q^{83} +(-15.5536 - 21.3013i) q^{84} +(-1.61162 - 0.930471i) q^{85} +(6.67139 + 10.2464i) q^{86} +2.84338i q^{87} +(-0.976181 + 0.158172i) q^{88} +(7.37293 + 4.25676i) q^{89} +(1.26276 + 23.5606i) q^{90} +(6.25572 + 3.61174i) q^{91} +(-2.91626 - 1.29013i) q^{92} +(7.44905 - 4.30071i) q^{93} +(-9.11959 - 4.63306i) q^{94} +(-9.46925 + 6.27443i) q^{95} +(-12.1922 + 12.3376i) q^{96} +(6.30190 - 3.63841i) q^{97} +(-16.2368 + 0.870232i) q^{98} +(-1.11918 + 1.93848i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) $ 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.41219	−	0.0756882i	0.998567	−	0.0535196i
$2$	1.41219	−	0.0756882i	0.998567	−	0.0535196i
$3$	−2.65547	+	1.53314i	−1.53314	+	0.885156i	−0.533921	+	0.845534i	$0.679282\pi$
$3$	−2.65547	+	1.53314i	−1.53314	+	0.885156i	−0.999215	+	0.0396221i	$0.987385\pi$
$4$	1.98854	−	0.213772i	0.994271	−	0.106886i
$5$	−2.25688	+	1.30301i	−1.00931	+	0.582723i	−0.910988	−	0.412432i	$-0.864679\pi$
$5$	−2.25688	+	1.30301i	−1.00931	+	0.582723i	−0.0983176	+	0.995155i	$0.531346\pi$
$6$	−3.63398	+	2.36606i	−1.48357	+	0.965941i
$7$			4.30088i			1.62558i	0.582556	+	0.812791i	$0.302053\pi$
$7$			4.30088i			1.62558i	−0.582556	+	0.812791i	$0.697947\pi$
$8$	2.79201	−	0.452395i	0.987126	−	0.159946i
$9$	3.20101	−	5.54431i	1.06700	−	1.84810i
$10$	−3.08851	+	2.01091i	−0.976672	+	0.635906i
$11$	−0.349633			−0.105418			−0.0527092	−	0.998610i	$-0.516786\pi$
$11$	−0.349633			−0.105418			−0.0527092	+	0.998610i	$0.516786\pi$
$12$	−4.95277	+	3.61637i	−1.42974	+	1.04396i
$13$	0.839767	−	1.45452i	0.232910	−	0.403411i	−0.725754	−	0.687955i	$-0.758509\pi$
$13$	0.839767	−	1.45452i	0.232910	−	0.403411i	0.958663	+	0.284544i	$0.0918421\pi$
$14$	0.325526	+	6.07365i	0.0870005	+	1.62325i
$15$	3.99538	−	6.92020i	1.03160	−	1.78679i
$16$	3.90860	−	0.850188i	0.977151	−	0.212547i
$17$	0.357047	+	0.618424i	0.0865967	+	0.149990i	0.906070	−	0.423127i	$-0.139068\pi$
$17$	0.357047	+	0.618424i	0.0865967	+	0.149990i	−0.819474	+	0.573117i	$0.805734\pi$
$18$	4.10079	−	8.07189i	0.966565	−	1.90256i
$19$	4.35063	−	0.268300i	0.998104	−	0.0615522i
$19$	4.35063	−	0.268300i	0.998104	−	0.0615522i
$20$	−4.20935	+	3.07354i	−0.941239	+	0.687265i
$21$	−6.59384	−	11.4209i	−1.43889	−	2.49224i
$22$	−0.493748	+	0.0264631i	−0.105267	+	0.00564195i
$23$	−1.38083	−	0.797223i	−0.287923	−	0.166233i	0.349082	−	0.937092i	$-0.386494\pi$
$23$	−1.38083	−	0.797223i	−0.287923	−	0.166233i	−0.637005	+	0.770860i	$0.719827\pi$
$24$	−6.72052	+	5.48186i	−1.37182	+	1.11898i
$25$	0.895662	−	1.55133i	0.179132	−	0.310266i
$26$	1.07582	−	2.11761i	0.210985	−	0.415298i
$27$			10.4315i			2.00755i
$28$	0.919407	+	8.55249i	0.173752	+	1.61627i
$29$	0.463655	−	0.803074i	0.0860985	−	0.149127i	−0.819760	−	0.572707i	$-0.805893\pi$
$29$	0.463655	−	0.803074i	0.0860985	−	0.149127i	0.905859	+	0.423580i	$0.139227\pi$
$30$	5.11844	−	10.0750i	0.934495	−	1.83944i
$31$	−2.80517			−0.503824			−0.251912	−	0.967750i	$-0.581059\pi$
$31$	−2.80517			−0.503824			−0.251912	+	0.967750i	$0.581059\pi$
$32$	5.45533	−	1.49646i	0.964375	−	0.264539i
$33$	0.928441	−	0.536035i	0.161621	−	0.0933118i
$34$	0.551025	+	0.846306i	0.0945000	+	0.145140i
$35$	−5.60409	−	9.70656i	−0.947264	−	1.64071i
$36$	5.18013	−	11.7094i	0.863355	−	1.95157i
$37$	10.2099			1.67849			0.839245	−	0.543753i	$-0.182997\pi$
$37$	10.2099			1.67849			0.839245	+	0.543753i	$0.182997\pi$
$38$	6.12360	−	0.708181i	0.993379	−	0.114882i
$39$			5.14991i			0.824645i
$40$	−5.71176	+	4.65902i	−0.903108	+	0.736655i
$41$	4.87850	−	2.81660i	0.761893	−	0.439879i	−0.0680819	−	0.997680i	$-0.521688\pi$
$41$	4.87850	−	2.81660i	0.761893	−	0.439879i	0.829975	+	0.557801i	$0.188355\pi$
$42$	−10.1762	−	15.6293i	−1.57021	−	2.41166i
$43$	4.32286	+	7.48741i	0.659230	+	1.14182i	0.980815	+	0.194939i	$0.0624508\pi$
$43$	4.32286	+	7.48741i	0.659230	+	1.14182i	−0.321586	+	0.946880i	$0.604216\pi$
$44$	−0.695261	+	0.0747417i	−0.104815	+	0.0112677i
$45$			16.6838i			2.48707i
$46$	−2.01033	−	1.02132i	−0.296407	−	0.150585i
$47$	−6.26395	−	3.61649i	−0.913691	−	0.527520i	−0.0320740	−	0.999485i	$-0.510211\pi$
$47$	−6.26395	−	3.61649i	−0.913691	−	0.527520i	−0.881617	+	0.471966i	$0.843545\pi$
$48$	−9.07572	+	8.25007i	−1.30997	+	1.19079i
$49$	−11.4976			−1.64251
$50$	1.14742	−	2.25856i	0.162270	−	0.319409i
$51$	−1.89626	−	1.09480i	−0.265529	−	0.153303i
$52$	1.35898	−	3.07189i	0.188456	−	0.425995i
$53$	−4.73541	+	8.20196i	−0.650458	+	1.12663i	0.332554	+	0.943084i	$0.392090\pi$
$53$	−4.73541	+	8.20196i	−0.650458	+	1.12663i	−0.983012	+	0.183542i	$0.941244\pi$
$54$	0.789543	+	14.7313i	0.107443	+	2.00467i
$55$	0.789079	−	0.455575i	0.106399	−	0.0614297i
$56$	1.94570	+	12.0081i	0.260005	+	1.60465i
$57$	−11.1416	+	7.38258i	−1.47575	+	0.977846i
$58$	0.593984	−	1.16918i	0.0779939	−	0.153521i
$59$	6.62664	−	3.82589i	0.862715	−	0.498089i	−0.00220531	−	0.999998i	$-0.500702\pi$
$59$	6.62664	−	3.82589i	0.862715	−	0.498089i	0.864921	+	0.501909i	$0.167369\pi$
$60$	6.46564	−	14.6152i	0.834710	−	1.88681i
$61$	−3.46531	−	2.00070i	−0.443687	−	0.256163i	0.261473	−	0.965211i	$-0.415792\pi$
$61$	−3.46531	−	2.00070i	−0.443687	−	0.256163i	−0.705160	+	0.709048i	$0.749125\pi$
$62$	−3.96143	+	0.212318i	−0.503102	+	0.0269645i
$63$	23.8454	+	13.7672i	3.00424	+	1.73450i
$64$	7.59068	−	2.52618i	0.948835	−	0.315773i
$65$			4.37690i			0.542887i
$66$	1.27056	−	0.827254i	0.156395	−	0.101828i
$67$	−10.6067	−	6.12378i	−1.29581	−	0.748139i	−0.316136	−	0.948714i	$-0.602386\pi$
$67$	−10.6067	−	6.12378i	−1.29581	−	0.748139i	−0.979678	+	0.200575i	$0.935719\pi$
$68$	0.842205	+	1.15344i	0.102132	+	0.139875i
$69$	4.88901			0.588567
$70$	−8.64869	−	13.2833i	−1.03372	−	1.58766i
$71$	−5.09365	−	8.82246i	−0.604505	−	1.04703i	−0.992129	−	0.125216i	$-0.960038\pi$
$71$	−5.09365	−	8.82246i	−0.604505	−	1.04703i	0.387624	−	0.921817i	$-0.373296\pi$
$72$	6.42905	−	16.9279i	0.757671	−	1.99497i
$73$	2.54260	+	4.40392i	0.297589	+	0.515439i	0.975584	−	0.219627i	$-0.0704842\pi$
$73$	2.54260	+	4.40392i	0.297589	+	0.515439i	−0.677995	+	0.735067i	$0.737151\pi$
$74$	14.4182	−	0.772765i	1.67608	−	0.0898321i
$75$			5.49268i			0.634241i
$76$	8.59407	−	1.46357i	0.985807	−	0.167883i
$77$		−	1.50373i		−	0.171366i
$78$	0.389787	+	7.27263i	0.0441347	+	0.823464i
$79$	−1.31170	−	2.27193i	−0.147578	−	0.255612i	0.782754	−	0.622331i	$-0.213814\pi$
$79$	−1.31170	−	2.27193i	−0.147578	−	0.255612i	−0.930332	+	0.366719i	$0.880481\pi$
$80$	−7.71343	+	7.01171i	−0.862388	+	0.783933i
$81$	−6.38991	−	11.0677i	−0.709990	−	1.22974i
$82$	6.67616	−	4.34681i	0.737259	−	0.480025i
$83$	−4.69293			−0.515116			−0.257558	−	0.966263i	$-0.582918\pi$
$83$	−4.69293			−0.515116			−0.257558	+	0.966263i	$0.582918\pi$
$84$	−15.5536	−	21.3013i	−1.69704	−	2.32416i
$85$	−1.61162	−	0.930471i	−0.174805	−	0.100924i
$86$	6.67139	+	10.2464i	0.719395	+	1.10490i
$87$			2.84338i			0.304843i
$88$	−0.976181	+	0.158172i	−0.104061	+	0.0168612i
$89$	7.37293	+	4.25676i	0.781529	+	0.451216i	0.836972	−	0.547246i	$-0.184324\pi$
$89$	7.37293	+	4.25676i	0.781529	+	0.451216i	−0.0554428	+	0.998462i	$0.517657\pi$
$90$	1.26276	+	23.5606i	0.133107	+	2.48351i
$91$	6.25572	+	3.61174i	0.655778	+	0.378613i
$92$	−2.91626	−	1.29013i	−0.304042	−	0.134505i
$93$	7.44905	−	4.30071i	0.772430	−	0.445963i
$94$	−9.11959	−	4.63306i	−0.940614	−	0.477863i
$95$	−9.46925	+	6.27443i	−0.971524	+	0.643743i
$96$	−12.1922	+	12.3376i	−1.24436	+	1.25920i
$97$	6.30190	−	3.63841i	0.639861	−	0.369424i	−0.144700	−	0.989476i	$-0.546222\pi$
$97$	6.30190	−	3.63841i	0.639861	−	0.369424i	0.784561	+	0.620051i	$0.212888\pi$
$98$	−16.2368	+	0.870232i	−1.64016	+	0.0879067i
$99$	−1.11918	+	1.93848i	−0.112482	+	0.194824i
$100$	1.44943	−	3.27636i	0.144943	−	0.327636i
$101$	−3.66074	−	2.11353i	−0.364257	−	0.210304i	0.306689	−	0.951810i	$-0.400779\pi$
$101$	−3.66074	−	2.11353i	−0.364257	−	0.210304i	−0.670947	+	0.741506i	$0.734112\pi$
$102$	−2.76073	−	1.40254i	−0.273353	−	0.138873i
$103$	18.3567			1.80874			0.904370	−	0.426750i	$-0.140341\pi$
$103$	18.3567			1.80874			0.904370	+	0.426750i	$0.140341\pi$
$104$	1.68662	−	4.44094i	0.165387	−	0.435470i
$105$	29.7630	+	17.1837i	2.90457	+	1.67695i
$106$	−6.06648	+	11.9411i	−0.589229	+	1.15982i
$107$		−	11.6010i		−	1.12151i	−0.827982	−	0.560754i	$-0.810511\pi$
$107$		−	11.6010i		−	1.12151i	0.827982	−	0.560754i	$-0.189489\pi$
$108$	2.22996	+	20.7435i	0.214578	+	1.99605i
$109$	−0.253698	−	0.439417i	−0.0242998	−	0.0420886i	0.853620	−	0.520897i	$-0.174402\pi$
$109$	−0.253698	−	0.439417i	−0.0242998	−	0.0420886i	−0.877920	+	0.478808i	$0.841069\pi$
$110$	1.07985	−	0.703081i	0.102959	−	0.0670362i
$111$	−27.1120	+	15.6531i	−2.57335	+	1.48573i
$112$	3.65656	+	16.8104i	0.345512	+	1.58844i
$113$		−	7.70645i		−	0.724961i	−0.931991	−	0.362481i	$-0.881930\pi$
$113$		−	7.70645i		−	0.724961i	0.931991	−	0.362481i	$-0.118070\pi$
$114$	−15.1753	+	11.2689i	−1.42130	+	1.05543i
$115$	4.15515			0.387470
$116$	0.750323	−	1.69606i	0.0696657	−	0.157475i
$117$	−5.37621	−	9.31187i	−0.497031	−	0.860882i
$118$	9.06848	−	5.90443i	0.834821	−	0.543547i
$119$	−2.65977	+	1.53562i	−0.243821	+	0.140770i
$120$	8.02449	−	21.1288i	0.732532	−	1.92878i
$121$	−10.8778			−0.988887
$122$	−5.04509	−	2.56307i	−0.456761	−	0.232050i
$123$	−8.63647	+	14.9588i	−0.778724	+	1.34879i
$124$	−5.57820	+	0.599666i	−0.500938	+	0.0538516i
$125$		−	8.36186i		−	0.747908i
$126$	34.7162	+	17.6370i	3.09277	+	1.57123i
$127$	6.90707	−	11.9634i	0.612903	−	1.06158i	−0.377846	−	0.925869i	$-0.623335\pi$
$127$	6.90707	−	11.9634i	0.612903	−	1.06158i	0.990749	−	0.135710i	$-0.0433317\pi$
$128$	10.5283	−	4.14197i	0.930575	−	0.366102i
$129$	−22.9584	−	13.2551i	−2.02138	−	1.16704i
$130$	0.331279	+	6.18099i	0.0290551	+	0.542109i
$131$	−7.66432	−	13.2750i	−0.669635	−	1.15984i	−0.978006	−	0.208575i	$-0.933117\pi$
$131$	−7.66432	−	13.2750i	−0.669635	−	1.15984i	0.308372	−	0.951266i	$-0.400216\pi$
$132$	1.73165	−	1.26440i	0.150721	−	0.110052i
$133$	1.15393	+	18.7116i	0.100058	+	1.62250i
$134$	−15.4421	−	7.84512i	−1.33400	−	0.677715i
$135$	−13.5924	−	23.5427i	−1.16984	−	2.02623i
$136$	1.27665	+	1.56512i	0.109472	+	0.134208i
$137$	−4.73230	+	8.19659i	−0.404308	+	0.700282i	−0.994241	−	0.107171i	$-0.965821\pi$
$137$	−4.73230	+	8.19659i	−0.404308	+	0.700282i	0.589933	+	0.807452i	$0.299154\pi$
$138$	6.90419	−	0.370040i	0.587724	−	0.0314999i
$139$	−2.16855	+	3.75604i	−0.183934	+	0.318583i	−0.943217	−	0.332178i	$-0.892217\pi$
$139$	−2.16855	+	3.75604i	−0.183934	+	0.318583i	0.759283	+	0.650761i	$0.225550\pi$
$140$	−13.2190	−	18.1039i	−1.11721	−	1.53006i
$141$	22.1783			1.86775
$142$	−7.86094	−	12.0734i	−0.659676	−	1.01318i
$143$	−0.293611	+	0.508549i	−0.0245530	+	0.0425270i
$144$	7.79777	−	24.3920i	0.649815	−	2.03267i
$145$			2.41658i			0.200686i
$146$	3.92395	+	6.02671i	0.324749	+	0.498774i
$147$	30.5315	−	17.6274i	2.51820	−	1.45388i
$148$	20.3027	−	2.18258i	1.66887	−	0.179407i
$149$	4.50515	−	2.60105i	0.369076	−	0.213086i	−0.303978	−	0.952679i	$-0.598315\pi$
$149$	4.50515	−	2.60105i	0.369076	−	0.213086i	0.673055	+	0.739592i	$0.264982\pi$
$150$	0.415731	+	7.75670i	0.0339443	+	0.633332i
$151$	−4.14034			−0.336936			−0.168468	−	0.985707i	$-0.553882\pi$
$151$	−4.14034			−0.336936			−0.168468	+	0.985707i	$0.553882\pi$
$152$	12.0257	−	2.71730i	0.975409	−	0.220402i
$153$	4.57165			0.369596
$154$	−0.113815	−	2.12355i	−0.00917145	−	0.171121i
$155$	6.33093	−	3.65516i	0.508512	−	0.293590i
$156$	1.10090	+	10.2408i	0.0881429	+	0.819921i
$157$	2.57943	−	1.48923i	0.205861	−	0.118854i	−0.393525	−	0.919314i	$-0.628745\pi$
$157$	2.57943	−	1.48923i	0.205861	−	0.118854i	0.599386	+	0.800460i	$0.295411\pi$
$158$	−2.02432	−	3.10911i	−0.161047	−	0.247348i
$159$		−	29.0401i		−	2.30303i
$160$	−10.3621	+	10.4857i	−0.819196	+	0.828964i
$161$	3.42876	−	5.93879i	0.270224	−	0.468042i
$162$	−9.86144	−	15.1460i	−0.774788	−	1.18998i
$163$	−0.299245			−0.0234387			−0.0117194	−	0.999931i	$-0.503730\pi$
$163$	−0.299245			−0.0234387			−0.0117194	+	0.999931i	$0.503730\pi$
$164$	9.09899	−	6.64382i	0.710512	−	0.518795i
$165$	−1.39692	+	2.41953i	−0.108750	+	0.188360i
$166$	−6.62730	+	0.355199i	−0.514378	+	0.0275688i
$167$	−3.94944	+	6.84063i	−0.305617	+	0.529344i	−0.977398	−	0.211405i	$-0.932196\pi$
$167$	−3.94944	+	6.84063i	−0.305617	+	0.529344i	0.671782	+	0.740749i	$0.265529\pi$
$168$	−23.5768	−	28.9042i	−1.81899	−	2.23001i
$169$	5.08958	+	8.81541i	0.391506	+	0.678109i
$170$	−2.34634	−	1.19202i	−0.179956	−	0.0914236i
$171$	12.4389	−	24.9801i	0.951226	−	1.91028i
$172$	10.1968	+	13.9649i	0.777497	+	1.06482i
$173$	−8.01754	−	13.8868i	−0.609562	−	1.05579i	−0.991313	−	0.131527i	$-0.958012\pi$
$173$	−8.01754	−	13.8868i	−0.609562	−	1.05579i	0.381751	−	0.924265i	$-0.375321\pi$
$174$	0.215210	+	4.01539i	0.0163151	+	0.304406i
$175$	6.67210	+	3.85214i	0.504363	+	0.291194i
$176$	−1.36658	+	0.297254i	−0.103010	+	0.0224064i
$177$	−11.7312	+	20.3191i	−0.881773	+	1.52728i
$178$	10.7341	+	5.45330i	0.804558	+	0.408742i
$179$			15.5488i			1.16218i	0.813841	+	0.581088i	$0.197373\pi$
$179$			15.5488i			1.16218i	−0.813841	+	0.581088i	$0.802627\pi$
$180$	3.56652	+	33.1764i	0.265833	+	2.47282i
$181$	−0.129430	+	0.224180i	−0.00962046	+	0.0166631i	−0.870796	−	0.491645i	$-0.836396\pi$
$181$	−0.129430	+	0.224180i	−0.00962046	+	0.0166631i	0.861175	+	0.508308i	$0.169729\pi$
$182$	9.10761	+	4.62697i	0.675101	+	0.342974i
$183$	12.2694			0.906977
$184$	−4.21596	−	1.60118i	−0.310805	−	0.118040i
$185$	−23.0424	+	13.3035i	−1.69411	+	0.978095i
$186$	10.1939	−	6.63721i	0.747456	−	0.486664i
$187$	−0.124836	−	0.216222i	−0.00912889	−	0.0158117i
$188$	−13.2292	−	5.85250i	−0.964841	−	0.426837i
$189$	−44.8648			−3.26343
$190$	−12.8974	+	9.57738i	−0.935679	+	0.694816i
$191$			6.00136i			0.434244i	0.976145	+	0.217122i	$0.0696669\pi$
$191$			6.00136i			0.434244i	−0.976145	+	0.217122i	$0.930333\pi$
$192$	−16.2838	+	18.3457i	−1.17518	+	1.32399i
$193$	−6.63936	+	3.83324i	−0.477912	+	0.275922i	−0.719546	−	0.694445i	$-0.755650\pi$
$193$	−6.63936	+	3.83324i	−0.477912	+	0.275922i	0.241634	+	0.970367i	$0.422317\pi$
$194$	8.62408	−	5.61509i	0.619173	−	0.403140i
$195$	−6.71037	−	11.6227i	−0.480540	−	0.832320i
$196$	−22.8635	+	2.45786i	−1.63310	+	0.175561i
$197$			5.38374i			0.383576i	0.981436	+	0.191788i	$0.0614286\pi$
$197$			5.38374i			0.383576i	−0.981436	+	0.191788i	$0.938571\pi$
$198$	−1.43377	+	2.82220i	−0.101894	+	0.200565i
$199$	16.1469	+	9.32240i	1.14462	+	0.660847i	0.947571	−	0.319546i	$-0.103530\pi$
$199$	16.1469	+	9.32240i	1.14462	+	0.660847i	0.197050	+	0.980393i	$0.436864\pi$
$200$	1.79889	−	4.73653i	0.127200	−	0.334923i
$201$	37.5544			2.64888
$202$	−5.32962	−	2.70762i	−0.374991	−	0.190508i
$203$	3.45393	+	1.99413i	0.242418	+	0.139960i
$204$	−4.00482	−	1.77170i	−0.280394	−	0.124044i
$205$	−7.34011	+	12.7134i	−0.512656	+	0.887945i
$206$	25.9231	−	1.38938i	1.80615	−	0.0968030i
$207$	−8.84011	+	5.10384i	−0.614430	+	0.354741i
$208$	2.04570	−	6.39910i	0.141844	−	0.443698i
$209$	−1.52113	+	0.0938066i	−0.105219	+	0.00648874i
$210$	43.3315	+	22.0138i	2.99015	+	1.51910i
$211$	0.807263	−	0.466073i	0.0555743	−	0.0320858i	−0.471955	−	0.881622i	$-0.656452\pi$
$211$	0.807263	−	0.466073i	0.0555743	−	0.0320858i	0.527530	+	0.849537i	$0.323118\pi$
$212$	−7.66321	+	17.3222i	−0.526311	+	1.18970i
$213$	27.0521	+	15.6185i	1.85358	+	1.07016i
$214$	−0.878056	−	16.3827i	−0.0600227	−	1.11990i
$215$	−19.5123	−	11.2654i	−1.33073	−	0.768297i
$216$	4.71917	+	29.1250i	0.321099	+	1.98170i
$217$		−	12.0647i		−	0.819006i
$218$	−0.391527	−	0.601337i	−0.0265176	−	0.0407277i
$219$	−13.5036	−	7.79631i	−0.912489	−	0.526826i
$220$	1.47173	−	1.07461i	0.0992239	−	0.0724504i
$221$	1.19935			0.0806768
$222$	−37.1024	+	24.1572i	−2.49015	+	1.62132i
$223$	−7.62648	−	13.2095i	−0.510707	−	0.884571i	−0.999923	−	0.0124080i	$-0.996050\pi$
$223$	−7.62648	−	13.2095i	−0.510707	−	0.884571i	0.489216	−	0.872163i	$-0.337283\pi$
$224$	6.43610	+	23.4627i	0.430030	+	1.56767i
$225$	−5.73405	−	9.93166i	−0.382270	−	0.662111i
$226$	−0.583287	−	10.8829i	−0.0387997	−	0.723922i
$227$			5.51895i			0.366306i	0.983084	+	0.183153i	$0.0586303\pi$
$227$			5.51895i			0.366306i	−0.983084	+	0.183153i	$0.941370\pi$
$228$	−20.5774	+	17.0623i	−1.36277	+	1.12998i
$229$		−	12.8139i		−	0.846768i	−0.905950	−	0.423384i	$-0.860842\pi$
$229$		−	12.8139i		−	0.846768i	0.905950	−	0.423384i	$-0.139158\pi$
$230$	5.86785	−	0.314496i	0.386915	−	0.0207372i
$231$	2.30543	+	3.99311i	0.151686	+	0.262728i
$232$	0.931224	−	2.45195i	0.0611379	−	0.160978i
$233$	0.958205	+	1.65966i	0.0627741	+	0.108728i	0.895704	−	0.444650i	$-0.146672\pi$
$233$	0.958205	+	1.65966i	0.0627741	+	0.108728i	−0.832930	+	0.553378i	$0.813339\pi$
$234$	−8.29701	−	12.7432i	−0.542392	−	0.833048i
$235$	18.8493			1.22959
$236$	12.3595	−	9.02454i	0.804534	−	0.587448i
$237$	6.96636	+	4.02203i	0.452514	+	0.261259i
$238$	−3.63986	+	2.36989i	−0.235937	+	0.153617i
$239$			26.1872i			1.69391i	0.531665	+	0.846955i	$0.321566\pi$
$239$			26.1872i			1.69391i	−0.531665	+	0.846955i	$0.678434\pi$
$240$	9.73288	−	30.4451i	0.628255	−	1.96522i
$241$	−13.2053	−	7.62406i	−0.850625	−	0.491109i	0.0102365	−	0.999948i	$-0.496742\pi$
$241$	−13.2053	−	7.62406i	−0.850625	−	0.491109i	−0.860862	+	0.508839i	$0.830075\pi$
$242$	−15.3614	+	0.823317i	−0.987470	+	0.0529248i
$243$	6.83453	+	3.94592i	0.438435	+	0.253131i
$244$	−7.31860	−	3.23769i	−0.468526	−	0.207272i
$245$	25.9487	−	14.9815i	1.65780	−	0.957131i
$246$	−11.0641	+	21.7783i	−0.705421	+	1.38853i
$247$	3.26327	−	6.55339i	0.207637	−	0.416982i
$248$	−7.83208	+	1.26904i	−0.497337	+	0.0805844i
$249$	12.4619	−	7.19490i	0.789743	−	0.455958i
$250$	−0.632894	−	11.8085i	−0.0400277	−	0.746836i
$251$	−3.40850	+	5.90370i	−0.215143	+	0.372638i	−0.953317	−	0.301972i	$-0.902355\pi$
$251$	−3.40850	+	5.90370i	−0.215143	+	0.372638i	0.738174	+	0.674610i	$0.235688\pi$
$252$	50.3607	+	22.2791i	3.17243	+	1.40345i
$253$	0.482785	+	0.278736i	0.0303524	+	0.0175240i
$254$	8.84858	−	17.4173i	0.555209	−	1.09286i
$255$	5.70616			0.357333
$256$	14.5544	−	6.64609i	0.909648	−	0.415381i
$257$	9.99669	+	5.77159i	0.623576	+	0.360022i	0.778260	−	0.627942i	$-0.216103\pi$
$257$	9.99669	+	5.77159i	0.623576	+	0.360022i	−0.154684	+	0.987964i	$0.549436\pi$
$258$	−33.4248	−	16.9809i	−2.08094	−	1.05719i
$259$			43.9114i			2.72852i
$260$	0.935656	+	8.70364i	0.0580269	+	0.539777i
$261$	−2.96833	−	5.14130i	−0.183735	−	0.318238i
$262$	−11.8282	−	18.1667i	−0.730749	−	1.12234i
$263$	11.8061	−	6.81625i	0.727994	−	0.420308i	−0.0896937	−	0.995969i	$-0.528589\pi$
$263$	11.8061	−	6.81625i	0.727994	−	0.420308i	0.817688	+	0.575662i	$0.195255\pi$
$264$	2.34972	−	1.91664i	0.144615	−	0.117961i
$265$		−	24.6811i		−	1.51615i
$266$	3.04580	+	26.3369i	0.186750	+	1.61482i
$267$	−26.1048			−1.59759
$268$	−22.4010	−	9.90999i	−1.36836	−	0.605349i
$269$	14.0715	+	24.3725i	0.857953	+	1.48602i	0.873878	+	0.486144i	$0.161597\pi$
$269$	14.0715	+	24.3725i	0.857953	+	1.48602i	−0.0159257	+	0.999873i	$0.505070\pi$
$270$	−20.9769	−	32.2179i	−1.27661	−	1.96072i
$271$	3.45517	−	1.99485i	0.209887	−	0.121178i	−0.391372	−	0.920233i	$-0.627999\pi$
$271$	3.45517	−	1.99485i	0.209887	−	0.121178i	0.601259	+	0.799054i	$0.294666\pi$
$272$	1.92133	+	2.11362i	0.116498	+	0.128157i
$273$	−22.1492			−1.34053
$274$	−6.06251	+	11.9333i	−0.366250	+	0.720916i
$275$	−0.313153	+	0.542397i	−0.0188838	+	0.0327078i
$276$	9.72200	−	1.04513i	0.585195	−	0.0629095i
$277$			12.1974i			0.732869i	0.930444	+	0.366435i	$0.119422\pi$
$277$			12.1974i			0.732869i	−0.930444	+	0.366435i	$0.880578\pi$
$278$	−2.77811	+	5.46837i	−0.166620	+	0.327971i
$279$	−8.97939	+	15.5528i	−0.537582	+	0.931119i
$280$	−20.0379	−	24.5656i	−1.19749	−	1.46808i
$281$	−0.459532	−	0.265311i	−0.0274134	−	0.0158271i	0.486231	−	0.873830i	$-0.338371\pi$
$281$	−0.459532	−	0.265311i	−0.0274134	−	0.0158271i	−0.513644	+	0.858003i	$0.671705\pi$
$282$	31.3199	−	1.67863i	1.86507	−	0.0999612i
$283$	1.48484	+	2.57181i	0.0882644	+	0.152878i	0.906778	−	0.421609i	$-0.138535\pi$
$283$	1.48484	+	2.57181i	0.0882644	+	0.152878i	−0.818513	+	0.574488i	$0.805201\pi$
$284$	−12.0149	−	16.4550i	−0.712955	−	0.976423i
$285$	15.5257	−	31.1792i	0.919665	−	1.84690i
$286$	−0.376142	+	0.740388i	−0.0222417	+	0.0437801i
$287$	12.1139	+	20.9818i	0.715059	+	1.23852i
$288$	9.16573	−	35.0362i	0.540096	−	2.06453i
$289$	8.24503	−	14.2808i	0.485002	−	0.840048i
$290$	0.182907	+	3.41267i	0.0107407	+	0.200399i
$291$	−11.1563	+	19.3233i	−0.653996	+	1.13275i
$292$	5.99750	+	8.21384i	0.350977	+	0.480678i
$293$	−15.8714			−0.927216			−0.463608	−	0.886040i	$-0.653445\pi$
$293$	−15.8714			−0.927216			−0.463608	+	0.886040i	$0.653445\pi$
$294$	41.7820	−	27.2040i	2.43678	−	1.58657i
$295$	−9.97034	+	17.2691i	−0.580496	+	1.00545i
$296$	28.5061	−	4.61888i	1.65688	−	0.268467i
$297$		−	3.64721i		−	0.211633i
$298$	6.16525	−	4.01416i	0.357143	−	0.232534i
$299$	−2.31915	+	1.33896i	−0.134120	+	0.0774343i
$300$	1.17418	+	10.9224i	0.0677913	+	0.630607i
$301$	−32.2025	+	18.5921i	−1.85612	+	1.07163i
$302$	−5.84693	+	0.313375i	−0.336453	+	0.0180327i
$303$	12.9613			0.744608
$304$	16.7768	−	4.74753i	0.962215	−	0.272290i
$305$	10.4277			0.597088
$306$	6.45602	−	0.346020i	0.369066	−	0.0197806i
$307$	−19.5928	+	11.3119i	−1.11822	+	0.645605i	−0.940946	−	0.338557i	$-0.890061\pi$
$307$	−19.5928	+	11.3119i	−1.11822	+	0.645605i	−0.177274	+	0.984161i	$0.556728\pi$
$308$	−0.321455	−	2.99024i	−0.0183166	−	0.170384i
$309$	−48.7457	+	28.1433i	−2.77304	+	1.60102i
$310$	8.66380	−	5.64095i	0.492071	−	0.320384i
$311$			15.1802i			0.860792i	0.902640	+	0.430396i	$0.141626\pi$
$311$			15.1802i			0.860792i	−0.902640	+	0.430396i	$0.858374\pi$
$312$	2.32979	+	14.3786i	0.131898	+	0.814029i
$313$	2.14838	−	3.72111i	0.121434	−	0.210330i	−0.798899	−	0.601465i	$-0.794584\pi$
$313$	2.14838	−	3.72111i	0.121434	−	0.210330i	0.920333	+	0.391135i	$0.127917\pi$
$314$	3.52992	−	2.29831i	0.199205	−	0.129701i
$315$	−71.7550			−4.04294
$316$	−3.09405	−	4.23743i	−0.174054	−	0.238374i
$317$	0.160202	−	0.277479i	0.00899787	−	0.0155848i	−0.861491	−	0.507772i	$-0.830469\pi$
$317$	0.160202	−	0.277479i	0.00899787	−	0.0155848i	0.870489	+	0.492187i	$0.163803\pi$
$318$	−2.19799	−	41.0100i	−0.123257	−	2.29973i
$319$	−0.162109	+	0.280781i	−0.00907637	+	0.0157207i
$320$	−13.8396	+	15.5920i	−0.773656	+	0.871619i
$321$	17.7859	+	30.8060i	0.992710	+	1.71942i
$322$	4.39256	−	8.64620i	0.244788	−	0.481834i
$323$	1.71931	+	2.59474i	0.0956647	+	0.144375i
$324$	−15.0726	−	20.6425i	−0.837365	−	1.14681i
$325$	−1.50429	−	2.60552i	−0.0834433	−	0.144528i
$326$	−0.422590	+	0.0226493i	−0.0234051	+	0.00125443i
$327$	1.34737	+	0.777906i	0.0745099	+	0.0430183i
$328$	12.3466	−	10.0710i	0.681728	−	0.556078i
$329$	15.5541	−	26.9405i	0.857526	−	1.48528i
$330$	−1.78958	+	3.52256i	−0.0985130	+	0.193911i
$331$		−	15.7503i		−	0.865713i	−0.901463	−	0.432856i	$-0.857506\pi$
$331$		−	15.7503i		−	0.865713i	0.901463	−	0.432856i	$-0.142494\pi$
$332$	−9.33210	+	1.00322i	−0.512165	+	0.0550586i
$333$	32.6819	−	56.6067i	1.79096	−	3.10203i
$334$	−5.05959	+	9.95917i	−0.276848	+	0.544942i
$335$	31.9174			1.74383
$336$	−35.4826	−	39.0336i	−1.93573	−	2.12946i
$337$	−3.84020	+	2.21714i	−0.209189	+	0.120775i	−0.600934	−	0.799298i	$-0.705205\pi$
$337$	−3.84020	+	2.21714i	−0.209189	+	0.120775i	0.391746	+	0.920074i	$0.371871\pi$
$338$	7.85466	+	12.0638i	0.427237	+	0.656184i
$339$	11.8150	+	20.4642i	0.641704	+	1.11146i
$340$	−3.40369	−	1.50576i	−0.184591	−	0.0816614i
$341$	0.980782			0.0531123
$342$	15.6753	−	36.2181i	0.847625	−	1.95845i
$343$		−	19.3436i		−	1.04446i
$344$	15.4567	+	18.9493i	0.833372	+	1.02168i
$345$	−11.0339	+	6.37042i	−0.594044	+	0.342972i
$346$	−12.3733	−	19.0039i	−0.665194	−	1.02166i
$347$	−4.37820	−	7.58327i	−0.235034	−	0.407091i	0.724248	−	0.689539i	$-0.242187\pi$
$347$	−4.37820	−	7.58327i	−0.235034	−	0.407091i	−0.959283	+	0.282448i	$0.908854\pi$
$348$	0.607835	+	5.65419i	0.0325834	+	0.303096i
$349$		−	31.3794i		−	1.67970i	−0.542819	−	0.839850i	$-0.682643\pi$
$349$		−	31.3794i		−	1.67970i	0.542819	−	0.839850i	$-0.317357\pi$
$350$	9.71381	+	4.93494i	0.519225	+	0.263784i
$351$	15.1729	+	8.76005i	0.809867	+	0.467577i
$352$	−1.90736	+	0.523212i	−0.101663	+	0.0278873i
$353$	−3.85737			−0.205307			−0.102653	−	0.994717i	$-0.532733\pi$
$353$	−3.85737			−0.205307			−0.102653	+	0.994717i	$0.532733\pi$
$354$	−15.0288	+	29.5823i	−0.798770	+	1.57228i
$355$	22.9915	+	13.2741i	1.22026	+	0.704518i
$356$	15.5714	+	6.88863i	0.825281	+	0.365097i
$357$	4.70862	−	8.15558i	0.249207	−	0.431639i
$358$	1.17686	+	21.9579i	0.0621992	+	1.16051i
$359$	25.0177	−	14.4440i	1.32039	−	0.762325i	0.336596	−	0.941649i	$-0.390724\pi$
$359$	25.0177	−	14.4440i	1.32039	−	0.762325i	0.983790	+	0.179324i	$0.0573910\pi$
$360$	7.54765	+	46.5813i	0.397796	+	2.45505i
$361$	18.8560	−	2.33455i	0.992423	−	0.122871i
$362$	−0.165812	+	0.326380i	−0.00871487	+	0.0171541i
$363$	28.8855	−	16.6771i	1.51610	−	0.875320i
$364$	13.2119	+	5.84481i	0.692489	+	0.306351i
$365$	−11.4767	−	6.62606i	−0.600717	−	0.346824i
$366$	17.3266	−	0.928645i	0.905677	−	0.0485410i
$367$	−30.0071	−	17.3246i	−1.56636	−	0.904336i	−0.996589	−	0.0825294i	$-0.973700\pi$
$367$	−30.0071	−	17.3246i	−1.56636	−	0.904336i	−0.569767	−	0.821806i	$-0.692966\pi$
$368$	−6.07491	−	1.94206i	−0.316677	−	0.101237i
$369$		−	36.0639i		−	1.87741i
$370$	−31.5332	+	20.5311i	−1.63934	+	1.06736i
$371$	−35.2757	−	20.3664i	−1.83142	−	1.05737i
$372$	13.8934	−	10.1445i	0.720338	−	0.525970i
$373$	−6.50847			−0.336996			−0.168498	−	0.985702i	$-0.553892\pi$
$373$	−6.50847			−0.336996			−0.168498	+	0.985702i	$0.553892\pi$
$374$	−0.192657	−	0.295897i	−0.00996204	−	0.0153005i
$375$	12.8199	+	22.2047i	0.662015	+	1.14664i
$376$	−19.1251	−	7.26352i	−0.986302	−	0.374587i
$377$	−0.778724	−	1.34879i	−0.0401063	−	0.0694662i
$378$	−63.3574	+	3.39573i	−3.25875	+	0.174658i
$379$			22.8576i			1.17412i	0.809544	+	0.587059i	$0.199714\pi$
$379$			22.8576i			1.17412i	−0.809544	+	0.587059i	$0.800286\pi$
$380$	−17.4887	+	14.5012i	−0.897152	+	0.743898i
$381$			42.3579i			2.17006i
$382$	0.454232	+	8.47505i	0.0232405	+	0.433621i
$383$	−3.86012	−	6.68592i	−0.197243	−	0.341634i	0.750391	−	0.660995i	$-0.229865\pi$
$383$	−3.86012	−	6.68592i	−0.197243	−	0.341634i	−0.947633	+	0.319360i	$0.896532\pi$
$384$	−21.6073	+	27.1401i	−1.10264	+	1.38499i
$385$	1.95938	+	3.39374i	0.0998590	+	0.172961i
$386$	−9.08588	+	5.91577i	−0.462459	+	0.301105i
$387$	55.3501			2.81360
$388$	11.7538	−	8.58229i	0.596710	−	0.435700i
$389$	−13.5074	−	7.79852i	−0.684854	−	0.395401i	0.116827	−	0.993152i	$-0.462728\pi$
$389$	−13.5074	−	7.79852i	−0.684854	−	0.395401i	−0.801681	+	0.597752i	$0.796061\pi$
$390$	−10.3560	−	15.9055i	−0.524397	−	0.805408i
$391$		−	1.13859i		−	0.0575807i
$392$	−32.1014	+	5.20145i	−1.62137	+	0.262713i
$393$	40.7047	+	23.5009i	2.05328	+	1.18546i
$394$	0.407486	+	7.60285i	0.0205288	+	0.383026i
$395$	5.92069	+	3.41831i	0.297902	+	0.171994i
$396$	−1.81115	+	4.09399i	−0.0910135	+	0.205731i
$397$	−17.5633	+	10.1402i	−0.881478	+	0.508922i	−0.871146	−	0.491025i	$-0.836622\pi$
$397$	−17.5633	+	10.1402i	−0.881478	+	0.508922i	−0.0103327	+	0.999947i	$0.503289\pi$
$398$	23.5080	+	11.9428i	1.17835	+	0.598640i
$399$	−31.7516	−	47.9189i	−1.58957	−	2.39894i
$400$	2.18186	−	6.82502i	0.109093	−	0.341251i
$401$	−17.7743	+	10.2620i	−0.887608	+	0.512461i	−0.873159	−	0.487435i	$-0.837933\pi$
$401$	−17.7743	+	10.2620i	−0.887608	+	0.512461i	−0.0144489	+	0.999896i	$0.504599\pi$
$402$	53.0338	−	2.84242i	2.64508	−	0.141767i
$403$	−2.35569	+	4.08018i	−0.117345	+	0.203248i
$404$	−7.73135	−	3.42028i	−0.384649	−	0.170165i
$405$	28.8425	+	16.6522i	1.43319	+	0.827455i
$406$	5.02852	+	2.55466i	0.249561	+	0.126785i
$407$	−3.56971			−0.176944
$408$	−5.78966	−	2.19885i	−0.286631	−	0.108859i
$409$	−9.46841	−	5.46659i	−0.468183	−	0.270306i	0.247296	−	0.968940i	$-0.420458\pi$
$409$	−9.46841	−	5.46659i	−0.468183	−	0.270306i	−0.715479	+	0.698634i	$0.753791\pi$
$410$	−9.40335	+	18.5093i	−0.464398	+	0.914110i
$411$		−	29.0210i		−	1.43150i
$412$	36.5031	−	3.92414i	1.79838	−	0.193329i
$413$	16.4547	+	28.5004i	0.809684	+	1.40241i
$414$	−12.0976	+	7.87667i	−0.594564	+	0.387117i
$415$	10.5914	−	6.11493i	0.519910	−	0.300170i
$416$	2.40458	−	9.19156i	0.117894	−	0.450653i
$417$		−	13.2987i		−	0.651242i
$418$	−2.14101	+	0.247604i	−0.104720	+	0.0121107i
$419$	25.2865			1.23532			0.617662	−	0.786443i	$-0.288080\pi$
$419$	25.2865			1.23532			0.617662	+	0.786443i	$0.288080\pi$
$420$	62.8583	+	27.8080i	3.06717	+	1.35689i
$421$	−7.89762	−	13.6791i	−0.384906	−	0.666677i	0.606850	−	0.794816i	$-0.292433\pi$
$421$	−7.89762	−	13.6791i	−0.384906	−	0.666677i	−0.991756	+	0.128139i	$0.959100\pi$
$422$	1.10473	−	0.719283i	0.0537774	−	0.0350141i
$423$	−40.1019	+	23.1529i	−1.94982	+	1.12573i
$424$	−9.51079	+	25.0423i	−0.461885	+	1.21616i
$425$	1.27917			0.0620491
$426$	39.3847	+	20.0087i	1.90820	+	0.969427i
$427$	8.60476	−	14.9039i	0.416414	−	0.721249i
$428$	−2.47996	−	23.0690i	−0.119873	−	1.11508i
$429$		−	1.80058i		−	0.0869328i
$430$	−28.4077	−	14.4321i	−1.36994	−	0.695975i
$431$	18.9346	−	32.7957i	0.912048	−	1.57971i	0.100882	−	0.994898i	$-0.467834\pi$
$431$	18.9346	−	32.7957i	0.912048	−	1.57971i	0.811166	−	0.584816i	$-0.198833\pi$
$432$	8.86876	+	40.7727i	0.426698	+	1.96168i
$433$	−32.1519	−	18.5629i	−1.54512	−	0.892077i	−0.998503	−	0.0546959i	$-0.982581\pi$
$433$	−32.1519	−	18.5629i	−1.54512	−	0.892077i	−0.546620	−	0.837381i	$-0.684086\pi$
$434$	−0.913156	−	17.0376i	−0.0438329	−	0.817833i
$435$	−3.70495	−	6.41717i	−0.177639	−	0.307680i
$436$	−0.598424	−	0.819567i	−0.0286593	−	0.0392501i
$437$	−6.22138	−	3.09795i	−0.297609	−	0.148195i
$438$	−19.6597	−	9.98778i	−0.939377	−	0.477235i
$439$	−8.17633	−	14.1618i	−0.390235	−	0.675907i	0.602245	−	0.798311i	$-0.294273\pi$
$439$	−8.17633	−	14.1618i	−0.390235	−	0.675907i	−0.992480	+	0.122404i	$0.960940\pi$
$440$	1.99702	−	1.62895i	0.0952042	−	0.0776570i
$441$	−36.8039	+	63.7463i	−1.75257	+	3.03554i
$442$	1.69370	−	0.0907763i	0.0805612	−	0.00431779i
$443$	1.30941	−	2.26796i	0.0622119	−	0.107754i	−0.833242	−	0.552909i	$-0.813518\pi$
$443$	1.30941	−	2.26796i	0.0622119	−	0.107754i	0.895454	+	0.445154i	$0.146851\pi$
$444$	−50.5671	+	36.9226i	−2.39981	+	1.75227i
$445$	−22.1864			−1.05174
$446$	−11.7698	−	18.0770i	−0.557317	−	0.855970i
$447$	−7.97553	+	13.8140i	−0.377230	+	0.653381i
$448$	10.8648	+	32.6466i	0.513314	+	1.54241i
$449$		−	17.9548i		−	0.847342i	−0.905816	−	0.423671i	$-0.860741\pi$
$449$		−	17.9548i		−	0.847342i	0.905816	−	0.423671i	$-0.139259\pi$
$450$	−8.84925	−	13.5914i	−0.417158	−	0.640703i
$451$	−1.70569	+	0.984778i	−0.0803176	+	0.0463714i
$452$	−1.64742	−	15.3246i	−0.0774881	−	0.720808i
$453$	10.9945	−	6.34770i	0.516569	−	0.298241i
$454$	0.417719	+	7.79379i	0.0196045	+	0.365781i
$455$	−18.8245			−0.882507
$456$	−27.7678	+	25.6527i	−1.30034	+	1.20130i
$457$	−15.9102			−0.744246			−0.372123	−	0.928183i	$-0.621370\pi$
$457$	−15.9102			−0.744246			−0.372123	+	0.928183i	$0.621370\pi$
$458$	−0.969863	−	18.0957i	−0.0453187	−	0.845555i
$459$	−6.45111	+	3.72455i	−0.301112	+	0.173847i
$460$	8.26270	−	0.888254i	0.385250	−	0.0414151i
$461$	15.3144	−	8.84177i	0.713262	−	0.411802i	−0.0990055	−	0.995087i	$-0.531566\pi$
$461$	15.3144	−	8.84177i	0.713262	−	0.411802i	0.812268	+	0.583285i	$0.198233\pi$
$462$	3.55792	+	5.46453i	0.165530	+	0.254233i
$463$			22.4205i			1.04197i	0.853566	+	0.520985i	$0.174435\pi$
$463$			22.4205i			1.04197i	−0.853566	+	0.520985i	$0.825565\pi$
$464$	1.12948	−	3.53309i	0.0524348	−	0.164020i
$465$	−11.2077	+	19.4123i	−0.519746	+	0.900226i
$466$	1.47878	+	2.27123i	0.0685032	+	0.105212i
$467$	36.8007			1.70293			0.851467	−	0.524408i	$-0.175713\pi$
$467$	36.8007			1.70293			0.851467	+	0.524408i	$0.175713\pi$
$468$	−12.6814	−	17.3678i	−0.586199	−	0.802825i
$469$	26.3377	−	45.6182i	1.21616	−	2.10645i
$470$	26.6187	−	1.42667i	1.22783	−	0.0658073i
$471$	−4.56639	+	7.90923i	−0.210408	+	0.364438i
$472$	16.7709	−	13.6798i	0.771941	−	0.629664i
$473$	−1.51142	−	2.61785i	−0.0694949	−	0.120369i
$474$	10.1422	+	5.15259i	0.465848	+	0.236666i
$475$	3.48047	−	6.98958i	0.159695	−	0.320704i
$476$	−4.96079	+	3.62223i	−0.227378	+	0.166024i
$477$	30.3162	+	52.5091i	1.38808	+	2.40423i
$478$	1.98206	+	36.9812i	0.0906574	+	1.69148i
$479$	1.17380	+	0.677696i	0.0536324	+	0.0309647i	0.526576	−	0.850128i	$-0.323475\pi$
$479$	1.17380	+	0.677696i	0.0536324	+	0.0309647i	−0.472944	+	0.881092i	$0.656809\pi$
$480$	11.4403	−	43.7309i	0.522176	−	1.99603i
$481$	8.57390	−	14.8504i	0.390936	−	0.677122i
$482$	−19.2253	−	9.76711i	−0.875690	−	0.444880i
$483$			21.0270i			0.956764i
$484$	−21.6309	+	2.32536i	−0.983222	+	0.105698i
$485$	−9.48175	+	16.4229i	−0.430544	+	0.745724i
$486$	9.95029	+	5.05508i	0.451354	+	0.229303i
$487$	−16.1529			−0.731957			−0.365979	−	0.930623i	$-0.619266\pi$
$487$	−16.1529			−0.731957			−0.365979	+	0.930623i	$0.619266\pi$
$488$	−10.5803	−	4.01828i	−0.478947	−	0.181899i
$489$	0.794637	−	0.458784i	0.0359347	−	0.0207469i
$490$	35.5104	−	23.1206i	1.60420	−	1.04448i
$491$	−0.839069	−	1.45331i	−0.0378666	−	0.0655870i	0.846471	−	0.532435i	$-0.178723\pi$
$491$	−0.839069	−	1.45331i	−0.0378666	−	0.0655870i	−0.884338	+	0.466848i	$0.845390\pi$
$492$	−13.9762	+	31.5924i	−0.630096	+	1.42430i
$493$	0.662187			0.0298234
$494$	4.11234	−	9.50160i	0.185023	−	0.427497i
$495$		−	5.83321i		−	0.262183i
$496$	−10.9643	+	2.38492i	−0.492312	+	0.107086i
$497$	37.9444	−	21.9072i	1.70204	−	0.982672i
$498$	17.0540	−	11.1038i	0.764209	−	0.497572i
$499$	−11.6119	−	20.1124i	−0.519819	−	0.900354i	−0.999735	−	0.0230387i	$-0.992666\pi$
$499$	−11.6119	−	20.1124i	−0.519819	−	0.900354i	0.479915	−	0.877315i	$-0.340667\pi$
$500$	−1.78753	−	16.6279i	−0.0799407	−	0.743623i
$501$		−	24.2201i		−	1.08207i
$502$	−4.36660	+	8.59511i	−0.194891	+	0.383618i
$503$	−25.5941	−	14.7768i	−1.14118	−	0.658863i	−0.194460	−	0.980910i	$-0.562296\pi$
$503$	−25.5941	−	14.7768i	−1.14118	−	0.658863i	−0.946724	+	0.322047i	$0.895629\pi$
$504$	72.8050	+	27.6506i	3.24299	+	1.23166i
$505$	11.0158			0.490196
$506$	0.702879	+	0.357086i	0.0312468	+	0.0158744i
$507$	−27.0305	−	15.6060i	−1.20046	−	0.693089i
$508$	11.1776	−	25.2662i	0.495924	−	1.12101i
$509$	−1.27450	+	2.20750i	−0.0564913	+	0.0978459i	−0.892888	−	0.450279i	$-0.851325\pi$
$509$	−1.27450	+	2.20750i	−0.0564913	+	0.0978459i	0.836397	+	0.548124i	$0.184658\pi$
$510$	8.05816	−	0.431888i	0.356821	−	0.0191243i
$511$	−18.9407	+	10.9354i	−0.837888	+	0.483755i
$512$	20.0504	−	10.4871i	0.886113	−	0.463470i
$513$	2.79878	+	45.3837i	0.123569	+	2.00374i
$514$	14.5540	+	7.39393i	0.641951	+	0.326132i
$515$	−41.4288	+	23.9189i	−1.82557	+	1.05399i
$516$	−48.4874	−	21.4504i	−2.13454	−	0.944301i
$517$	2.19009	+	1.26445i	0.0963199	+	0.0556103i
$518$	3.32357	+	62.0111i	0.146029	+	2.72461i
$519$	42.5806	+	24.5839i	1.86908	+	1.07912i
$520$	1.98008	+	12.2204i	0.0868324	+	0.535898i
$521$			36.4489i			1.59686i	0.602091	+	0.798428i	$0.294335\pi$
$521$			36.4489i			1.59686i	−0.602091	+	0.798428i	$0.705665\pi$
$522$	−4.58097	−	7.03580i	−0.200504	−	0.307949i
$523$	22.0155	+	12.7107i	0.962673	+	0.555799i	0.896995	−	0.442041i	$-0.145746\pi$
$523$	22.0155	+	12.7107i	0.962673	+	0.555799i	0.0656782	+	0.997841i	$0.479079\pi$
$524$	−18.0786	−	24.7595i	−0.789769	−	1.08162i
$525$	−23.6234			−1.03101
$526$	16.1565	−	10.5194i	0.704456	−	0.458667i
$527$	−1.00158	−	1.73479i	−0.0436295	−	0.0755685i
$528$	3.17318	−	2.88450i	0.138095	−	0.125532i
$529$	−10.2289	−	17.7169i	−0.444734	−	0.770301i
$530$	−1.86807	−	34.8543i	−0.0811436	−	1.51397i
$531$		−	48.9869i		−	2.12585i
$532$	6.29464	+	36.9621i	0.272907	+	1.60251i
$533$		−	9.46116i		−	0.409808i
$534$	−36.8648	+	1.97582i	−1.59530	+	0.0855022i
$535$	15.1162	+	26.1820i	0.653529	+	1.13194i
$536$	−32.3844	−	12.2993i	−1.39879	−	0.531247i
$537$	−23.8385	−	41.2895i	−1.02871	−	1.78177i
$538$	21.7163	+	33.3535i	0.936254	+	1.43797i
$539$	4.01994			0.173151
$540$	−32.0618	−	43.9099i	−1.37972	−	1.88958i
$541$	19.1779	+	11.0724i	0.824524	+	0.476039i	0.851974	−	0.523584i	$-0.175405\pi$
$541$	19.1779	+	11.0724i	0.824524	+	0.476039i	−0.0274503	+	0.999623i	$0.508739\pi$
$542$	4.72836	−	3.07861i	0.203101	−	0.132238i
$543$		−	0.793736i		−	0.0340625i
$544$	2.87326	+	2.83940i	0.123190	+	0.121738i
$545$	1.14513	+	0.661141i	0.0490519	+	0.0283202i
$546$	−31.2787	+	1.67643i	−1.33861	+	0.0717445i
$547$	−7.87144	−	4.54458i	−0.336559	−	0.194312i	0.322191	−	0.946675i	$-0.395581\pi$
$547$	−7.87144	−	4.54458i	−0.336559	−	0.194312i	−0.658749	+	0.752363i	$0.728914\pi$
$548$	−7.65819	+	17.3109i	−0.327142	+	0.739485i
$549$	−22.1850	+	12.8085i	−0.946832	+	0.546654i
$550$	−0.401178	+	0.789668i	−0.0171063	+	0.0336716i
$551$	1.80173	−	3.61828i	0.0767562	−	0.154144i
$552$	13.6502	−	2.21176i	0.580990	−	0.0941387i
$553$	9.77132	−	5.64147i	0.415519	−	0.239900i
$554$	0.923197	+	17.2250i	0.0392229	+	0.731819i
$555$	40.7922	−	70.6542i	1.73153	−	2.99911i
$556$	−3.50932	+	7.93263i	−0.148828	+	0.336418i
$557$	−8.28385	−	4.78268i	−0.350998	−	0.202649i	0.314127	−	0.949381i	$-0.398288\pi$
$557$	−8.28385	−	4.78268i	−0.350998	−	0.202649i	−0.665125	+	0.746732i	$0.731622\pi$
$558$	−11.5034	+	22.6430i	−0.486978	+	0.958556i
$559$	14.5208			0.614163
$560$	−30.1566	−	33.1746i	−1.27435	−	1.40188i
$561$	0.662994	+	0.382780i	0.0279916	+	0.0161610i
$562$	−0.669026	−	0.339888i	−0.0282212	−	0.0143373i
$563$			28.0350i			1.18153i	0.806842	+	0.590767i	$0.201175\pi$
$563$			28.0350i			1.18153i	−0.806842	+	0.590767i	$0.798825\pi$
$564$	44.1025	−	4.74109i	1.85705	−	0.199636i
$565$	10.0416	+	17.3925i	0.422452	+	0.731708i
$566$	2.29152	+	3.51950i	0.0963199	+	0.147935i
$567$	47.6007	−	27.4823i	1.99904	−	1.15415i
$568$	−18.2128	−	22.3281i	−0.764191	−	0.936866i
$569$			37.1158i			1.55597i	0.628280	+	0.777987i	$0.283759\pi$
$569$			37.1158i			1.55597i	−0.628280	+	0.777987i	$0.716241\pi$
$570$	19.5653	−	45.2060i	0.819502	−	1.89347i
$571$	7.10876			0.297492			0.148746	−	0.988875i	$-0.452476\pi$
$571$	7.10876			0.297492			0.148746	+	0.988875i	$0.452476\pi$
$572$	−0.475144	+	1.07404i	−0.0198668	+	0.0449077i
$573$	−9.20091	−	15.9364i	−0.384373	−	0.665754i
$574$	18.6951	+	28.7134i	0.780320	+	1.19847i
$575$	−2.47351	+	1.42808i	−0.103153	+	0.0595552i
$576$	10.2919	−	50.1714i	0.428829	−	2.09048i
$577$	−6.48963			−0.270167			−0.135083	−	0.990834i	$-0.543130\pi$
$577$	−6.48963			−0.270167			−0.135083	+	0.990834i	$0.543130\pi$
$578$	10.5626	−	20.7912i	0.439348	−	0.864801i
$579$	11.7537	−	20.3581i	0.488469	−	0.846053i
$580$	0.516597	+	4.80548i	0.0214505	+	0.199537i
$581$		−	20.1838i		−	0.837363i
$582$	−14.2923	+	28.1326i	−0.592434	+	1.16613i
$583$	1.65566	−	2.86768i	0.0685702	−	0.118767i
$584$	9.09129	+	11.1455i	0.376200	+	0.461205i
$585$	24.2669	+	14.0105i	1.00331	+	0.579262i
$586$	−22.4134	+	1.20128i	−0.925887	+	0.0496242i
$587$	17.8311	+	30.8843i	0.735966	+	1.27473i	0.954298	+	0.298856i	$0.0966052\pi$
$587$	17.8311	+	30.8843i	0.735966	+	1.27473i	−0.218332	+	0.975875i	$0.570061\pi$
$588$	56.9450	−	41.5796i	2.34837	−	1.71471i
$589$	−12.2043	+	0.752628i	−0.502868	+	0.0310115i
$590$	−12.7729	+	25.1419i	−0.525853	+	1.03508i
$591$	−8.25401	−	14.2964i	−0.339525	−	0.588074i
$592$	39.9063	−	8.68030i	1.64014	−	0.356758i
$593$	−11.0443	+	19.1293i	−0.453536	+	0.785547i	−0.998603	−	0.0528454i	$-0.983171\pi$
$593$	−11.0443	+	19.1293i	−0.453536	+	0.785547i	0.545067	+	0.838393i	$0.316504\pi$
$594$	−0.276051	−	5.15054i	−0.0113265	−	0.211329i
$595$	4.00185	−	6.93140i	0.164060	−	0.284160i
$596$	8.40266	−	6.13537i	0.344186	−	0.251315i
$597$	−57.1700			−2.33981
$598$	−3.17373	+	2.06640i	−0.129784	+	0.0845013i
$599$	4.63842	−	8.03398i	0.189521	−	0.328260i	−0.755570	−	0.655068i	$-0.772640\pi$
$599$	4.63842	−	8.03398i	0.189521	−	0.328260i	0.945091	+	0.326809i	$0.105973\pi$
$600$	2.48486	+	15.3356i	0.101444	+	0.626075i
$601$		−	20.5743i		−	0.839245i	−0.907699	−	0.419622i	$-0.862163\pi$
$601$		−	20.5743i		−	0.839245i	0.907699	−	0.419622i	$-0.137837\pi$
$602$	−44.0687	+	28.6929i	−1.79611	+	1.16943i
$603$	−67.9043	+	39.2046i	−2.76528	+	1.59653i
$604$	−8.23324	+	0.885087i	−0.335006	+	0.0360137i
$605$	24.5498	−	14.1738i	0.998090	−	0.576247i
$606$	18.3038	−	0.981017i	0.743541	−	0.0398511i
$607$	0.329758			0.0133845			0.00669223	−	0.999978i	$-0.497870\pi$
$607$	0.329758			0.0133845			0.00669223	+	0.999978i	$0.497870\pi$
$608$	23.3326	−	7.97421i	0.946263	−	0.323397i
$609$	−12.2291			−0.495546
$610$	14.7259	−	0.789253i	0.596232	−	0.0319559i
$611$	−10.5205	+	6.07402i	−0.425615	+	0.245729i
$612$	9.09092	−	0.977289i	0.367479	−	0.0395046i
$613$	22.6430	−	13.0730i	0.914544	−	0.528012i	0.0326533	−	0.999467i	$-0.489604\pi$
$613$	22.6430	−	13.0730i	0.914544	−	0.528012i	0.881890	+	0.471455i	$0.156271\pi$
$614$	−26.8125	+	17.4575i	−1.08207	+	0.704526i
$615$		−	45.0135i		−	1.81512i
$616$	−0.680280	−	4.19844i	−0.0274093	−	0.169160i
$617$	−17.8159	+	30.8580i	−0.717240	+	1.24230i	0.244849	+	0.969561i	$0.421262\pi$
$617$	−17.8159	+	30.8580i	−0.717240	+	1.24230i	−0.962089	+	0.272735i	$0.912072\pi$
$618$	−66.7079	+	43.4331i	−2.68338	+	1.74714i
$619$	9.09549			0.365579			0.182789	−	0.983152i	$-0.441487\pi$
$619$	9.09549			0.365579			0.182789	+	0.983152i	$0.441487\pi$
$620$	11.8079	−	8.62182i	0.474219	−	0.346261i
$621$	8.31625	−	14.4042i	0.333720	−	0.578020i
$622$	1.14896	+	21.4373i	0.0460693	+	0.859559i
$623$	−18.3078	+	31.7101i	−0.733488	+	1.27044i
$624$	4.37839	+	20.1290i	0.175276	+	0.805803i
$625$	15.3739	+	26.6284i	0.614956	+	1.06513i
$626$	2.75228	−	5.41751i	0.110003	−	0.216527i
$627$	3.89549	−	2.58119i	0.155571	−	0.103083i
$628$	4.81095	−	3.51281i	0.191978	−	0.140176i
$629$	3.64540	+	6.31402i	0.145352	+	0.251757i
$630$	−101.331	+	5.43100i	−4.03714	+	0.216376i
$631$	−34.9863	−	20.1993i	−1.39278	−	0.804123i	−0.399160	−	0.916881i	$-0.630698\pi$
$631$	−34.9863	−	20.1993i	−1.39278	−	0.804123i	−0.993622	+	0.112758i	$0.964032\pi$
$632$	−4.69010	−	5.74986i	−0.186562	−	0.228717i
$633$	−1.42911	+	2.47529i	−0.0568019	+	0.0983838i
$634$	0.205234	−	0.403977i	0.00815088	−	0.0160440i
$635$			35.9999i			1.42861i
$636$	−6.20794	−	57.7474i	−0.246161	−	2.28983i
$637$	−9.65530	+	16.7235i	−0.382557	+	0.662608i
$638$	−0.207677	+	0.408785i	−0.00822200	+	0.0161840i
$639$	−65.2193			−2.58004
$640$	−18.3640	+	23.0663i	−0.725899	+	0.911776i
$641$	42.3374	−	24.4435i	1.67223	−	0.965461i	0.705839	−	0.708373i	$-0.250570\pi$
$641$	42.3374	−	24.4435i	1.67223	−	0.965461i	0.966388	−	0.257088i	$-0.0827630\pi$
$642$	27.4486	+	42.1577i	1.08331	+	1.66383i
$643$	−8.70125	−	15.0710i	−0.343144	−	0.594343i	0.641871	−	0.766813i	$-0.278158\pi$
$643$	−8.70125	−	15.0710i	−0.343144	−	0.594343i	−0.985015	+	0.172470i	$0.944825\pi$
$644$	5.54870	−	12.5425i	0.218649	−	0.494244i
$645$	69.0858			2.72025
$646$	2.62437	+	3.53413i	0.103255	+	0.139048i
$647$		−	17.5279i		−	0.689094i	−0.938769	−	0.344547i	$-0.888033\pi$
$647$		−	17.5279i		−	0.689094i	0.938769	−	0.344547i	$-0.111967\pi$
$648$	−22.8477	−	28.0103i	−0.897541	−	1.10035i
$649$	−2.31690	+	1.33766i	−0.0909461	+	0.0525077i
$650$	−2.32155	−	3.56562i	−0.0910588	−	0.139855i
$651$	18.4969	+	32.0375i	0.724949	+	1.25565i
$652$	−0.595062	+	0.0639702i	−0.0233044	+	0.00250526i
$653$			43.4983i			1.70222i	0.524987	+	0.851111i	$0.324070\pi$
$653$			43.4983i			1.70222i	−0.524987	+	0.851111i	$0.675930\pi$
$654$	1.96162	+	0.996569i	0.0767054	+	0.0389689i
$655$	34.5948	+	19.9733i	1.35173	+	0.780423i
$656$	16.6735	−	15.1566i	0.650990	−	0.591766i
$657$	32.5556			1.27011
$658$	19.9262	−	39.2223i	0.776805	−	1.52904i
$659$	−36.1331	−	20.8615i	−1.40755	−	0.812648i	−0.412396	−	0.911005i	$-0.635308\pi$
$659$	−36.1331	−	20.8615i	−1.40755	−	0.812648i	−0.995151	+	0.0983571i	$0.968641\pi$
$660$	−2.26060	+	5.10996i	−0.0879938	+	0.198905i
$661$	−9.52479	+	16.4974i	−0.370471	+	0.641675i	−0.989638	−	0.143584i	$-0.954137\pi$
$661$	−9.52479	+	16.4974i	−0.370471	+	0.641675i	0.619167	+	0.785259i	$0.287470\pi$
$662$	−1.19211	−	22.2423i	−0.0463326	−	0.864472i
$663$	−3.18483	+	1.83876i	−0.123688	+	0.0714116i
$664$	−13.1027	+	2.12306i	−0.508485	+	0.0823906i
$665$	−26.9856	−	40.7261i	−1.04646	−	1.57929i
$666$	41.8685	−	82.4128i	1.62237	−	3.19343i
$667$	−1.28046	+	0.739273i	−0.0495795	+	0.0286248i
$668$	−6.39130	+	14.4472i	−0.247287	+	0.558977i
$669$	40.5038	+	23.3849i	1.56597	+	0.904111i
$670$	45.0733	−	2.41577i	1.74133	−	0.0933292i
$671$	1.21159	+	0.699510i	0.0467728	+	0.0270043i
$672$	−53.0624	−	52.4372i	−2.04693	−	2.02281i
$673$		−	47.4291i		−	1.82826i	−0.405424	−	0.914129i	$-0.632876\pi$
$673$		−	47.4291i		−	1.82826i	0.405424	−	0.914129i	$-0.367124\pi$
$674$	−5.25526	+	3.42167i	−0.202425	+	0.131798i
$675$	16.1828	+	9.34312i	0.622875	+	0.359617i
$676$	12.0053	+	16.4418i	0.461744	+	0.632378i
$677$	−28.6229			−1.10007			−0.550034	−	0.835142i	$-0.685385\pi$
$677$	−28.6229			−1.10007			−0.550034	+	0.835142i	$0.685385\pi$
$678$	18.2339	+	28.0051i	0.700270	+	1.07553i
$679$	15.6484	+	27.1038i	0.600529	+	1.04015i
$680$	−4.92061	−	1.86880i	−0.188697	−	0.0716652i
$681$	−8.46131	−	14.6554i	−0.324238	−	0.561597i
$682$	1.38505	−	0.0742336i	0.0530362	−	0.00284255i
$683$		−	31.8971i		−	1.22051i	−0.792206	−	0.610254i	$-0.791067\pi$
$683$		−	31.8971i		−	1.22051i	0.792206	−	0.610254i	$-0.208933\pi$
$684$	19.3952	−	52.3331i	0.741595	−	2.00101i
$685$		−	24.6649i		−	0.942398i
$686$	−1.46408	−	27.3168i	−0.0558990	−	1.04296i
$687$	19.6455	+	34.0270i	0.749522	+	1.29821i
$688$	23.2620	+	25.5901i	0.886857	+	0.975612i
$689$	7.95328	+	13.7755i	0.302996	+	0.524804i
$690$	−15.0997	+	9.83135i	−0.574837	+	0.374273i
$691$	−37.7829			−1.43733			−0.718664	−	0.695358i	$-0.755246\pi$
$691$	−37.7829			−1.43733			−0.718664	+	0.695358i	$0.755246\pi$
$692$	−18.9118	−	25.9005i	−0.718919	−	0.984591i
$693$	−8.33716	−	4.81346i	−0.316703	−	0.182848i
$694$	−6.75680	−	10.3776i	−0.256485	−	0.393929i
$695$		−	11.3026i		−	0.428731i
$696$	1.28633	+	7.93876i	0.0487583	+	0.300918i
$697$	3.48371	+	2.01132i	0.131955	+	0.0761842i
$698$	−2.37505	−	44.3135i	−0.0898968	−	1.67729i
$699$	−5.08897	−	2.93812i	−0.192483	−	0.111130i
$700$	14.0912	+	6.23383i	0.532598	+	0.235617i
$701$	27.5119	−	15.8840i	1.03911	−	0.599930i	0.119529	−	0.992831i	$-0.461862\pi$
$701$	27.5119	−	15.8840i	1.03911	−	0.599930i	0.919581	+	0.392900i	$0.128528\pi$
$702$	22.0899	+	11.2224i	0.833731	+	0.423563i
$703$	44.4194	−	2.73931i	1.67531	−	0.103315i
$704$	−2.65395	+	0.883238i	−0.100025	+	0.0332883i
$705$	−50.0537	+	28.8985i	−1.88513	+	1.08838i
$706$	−5.44732	+	0.291957i	−0.205013	+	0.0109879i
$707$	9.09004	−	15.7444i	0.341866	−	0.592130i
$708$	−18.9844	+	42.9132i	−0.713478	+	1.61278i
$709$	19.9172	+	11.4992i	0.748007	+	0.431862i	0.824974	−	0.565171i	$-0.191190\pi$
$709$	19.9172	+	11.4992i	0.748007	+	0.431862i	−0.0769660	+	0.997034i	$0.524523\pi$
$710$	33.4730	+	17.0054i	1.25622	+	0.638201i
$711$	−16.7951			−0.629865
$712$	22.5111	+	8.54947i	0.843638	+	0.320405i
$713$	3.87347	+	2.23635i	0.145063	+	0.0837519i
$714$	6.03218	−	11.8736i	0.225749	−	0.444358i
$715$		−	1.53031i		−	0.0572303i
$716$	3.32390	+	30.9195i	0.124220	+	1.15552i
$717$	−40.1485	−	69.5393i	−1.49937	−	2.59699i
$718$	34.2365	−	22.2912i	1.27769	−	0.831899i
$719$	21.7769	−	12.5729i	0.812142	−	0.468890i	−0.0355572	−	0.999368i	$-0.511321\pi$
$719$	21.7769	−	12.5729i	0.812142	−	0.468890i	0.847699	+	0.530477i	$0.177987\pi$
$720$	14.1843	+	65.2103i	0.528619	+	2.43024i
$721$			78.9500i			2.94025i
$722$	26.4515	−	4.72400i	0.984424	−	0.175809i
$723$	46.7549			1.73883
$724$	−0.209454	+	0.473459i	−0.00778430	+	0.0175960i
$725$	−0.830556	−	1.43856i	−0.0308461	−	0.0534270i
$726$	39.5295	−	25.7374i	1.46708	−	0.955206i
$727$	36.5628	−	21.1095i	1.35604	−	0.782909i	0.366951	−	0.930240i	$-0.380402\pi$
$727$	36.5628	−	21.1095i	1.35604	−	0.782909i	0.989087	+	0.147331i	$0.0470684\pi$
$728$	19.1000	+	7.25398i	0.707892	+	0.268850i
$729$	14.1410			0.523739
$730$	−16.7087	−	8.48859i	−0.618418	−	0.314177i
$731$	−3.08693	+	5.34672i	−0.114174	+	0.197756i
$732$	24.3981	−	2.62284i	0.901781	−	0.0969430i
$733$			39.5644i			1.46134i	0.682729	+	0.730671i	$0.260793\pi$
$733$			39.5644i			1.46134i	−0.682729	+	0.730671i	$0.739207\pi$
$734$	−43.6868	−	22.1944i	−1.61251	−	0.819209i
$735$	−45.9372	+	79.5656i	−1.69442	+	2.93482i
$736$	−8.72590	−	2.28276i	−0.321641	−	0.0841435i
$737$	3.70846	+	2.14108i	0.136603	+	0.0788676i
$738$	−2.72961	−	50.9289i	−0.100478	−	1.87472i
$739$	−21.0534	−	36.4655i	−0.774461	−	1.34141i	−0.935097	−	0.354392i	$-0.884688\pi$
$739$	−21.0534	−	36.4655i	−0.774461	−	1.34141i	0.160636	−	0.987014i	$-0.448645\pi$
$740$	−42.9769	+	31.3804i	−1.57986	+	1.15357i
$741$	1.38172	+	22.4054i	0.0507588	+	0.823082i
$742$	−51.3573	−	26.0912i	−1.88539	−	0.957840i
$743$	8.26746	+	14.3197i	0.303304	+	0.525338i	0.976882	−	0.213778i	$-0.0685770\pi$
$743$	8.26746	+	14.3197i	0.303304	+	0.525338i	−0.673578	+	0.739116i	$0.735244\pi$
$744$	18.8522	−	15.3775i	0.691156	−	0.563768i
$745$	−6.77838	+	11.7405i	−0.248341	+	0.430139i
$746$	−9.19118	+	0.492614i	−0.336513	+	0.0180359i
$747$	−15.0221	+	26.0191i	−0.549631	+	0.951989i
$748$	−0.294463	−	0.403280i	−0.0107666	−	0.0147454i
$749$	49.8944			1.82310
$750$	19.7847	+	30.3868i	0.722435	+	1.10957i
$751$	−26.7472	+	46.3274i	−0.976018	+	1.69051i	−0.299483	+	0.954102i	$0.596814\pi$
$751$	−26.7472	+	46.3274i	−0.976018	+	1.69051i	−0.676535	+	0.736411i	$0.736519\pi$
$752$	−27.5580	−	8.80990i	−1.00494	−	0.321264i
$753$		−	20.9028i		−	0.761740i
$754$	−1.20179	−	1.84580i	−0.0437667	−	0.0672202i
$755$	9.34424	−	5.39490i	0.340072	−	0.196340i
$756$	−89.2155	+	9.59081i	−3.24474	+	0.348815i
$757$	−26.9142	+	15.5389i	−0.978212	+	0.564771i	−0.901730	−	0.432300i	$-0.857702\pi$
$757$	−26.9142	+	15.5389i	−0.978212	+	0.564771i	−0.0764821	+	0.997071i	$0.524369\pi$
$758$	1.73005	+	32.2793i	0.0628383	+	1.17244i
$759$	−1.70936			−0.0620458
$760$	−23.5997	+	21.8021i	−0.856053	+	0.790847i
$761$	−24.1446			−0.875242			−0.437621	−	0.899160i	$-0.644179\pi$
$761$	−24.1446			−0.875242			−0.437621	+	0.899160i	$0.644179\pi$
$762$	3.20599	+	59.8172i	0.116141	+	2.16695i
$763$	1.88988	−	1.09112i	0.0684184	−	0.0395014i
$764$	1.28292	+	11.9340i	0.0464145	+	0.431756i
$765$	−10.3177	+	5.95690i	−0.373035	+	0.215372i
$766$	−5.95725	−	9.14960i	−0.215244	−	0.330588i
$767$		−	12.8514i		−	0.464039i
$768$	−28.4593	+	39.9623i	−1.02694	+	1.44202i
$769$	−27.1275	+	46.9862i	−0.978242	+	1.69437i	−0.309450	+	0.950916i	$0.600145\pi$
$769$	−27.1275	+	46.9862i	−0.978242	+	1.69437i	−0.668792	+	0.743450i	$0.733188\pi$
$770$	3.02387	+	4.64429i	0.108973	+	0.167369i
$771$	−35.3945			−1.27470
$772$	−12.3832	+	9.04186i	−0.445682	+	0.325424i
$773$	−12.2153	+	21.1576i	−0.439356	+	0.760986i	−0.997640	−	0.0686636i	$-0.978126\pi$
$773$	−12.2153	+	21.1576i	−0.439356	+	0.760986i	0.558284	+	0.829650i	$0.311460\pi$
$774$	78.1646	−	4.18934i	2.80957	−	0.150583i
$775$	−2.51249	+	4.35175i	−0.0902511	+	0.156320i
$776$	15.9490	−	13.0094i	0.572536	−	0.467011i
$777$	−67.3222	−	116.605i	−2.41517	−	4.18320i
$778$	−19.6653	−	9.99061i	−0.705034	−	0.358181i
$779$	20.4689	−	13.5629i	0.733373	−	0.485941i
$780$	−15.8285	−	21.6778i	−0.566750	−	0.776189i
$781$	1.78091	+	3.08463i	0.0637260	+	0.110377i
$782$	−0.0861774	−	1.60790i	−0.00308170	−	0.0574982i
$783$	8.37728	+	4.83663i	0.299380	+	0.172847i
$784$	−44.9395	+	9.77512i	−1.60498	+	0.349111i
$785$	−3.88097	+	6.72203i	−0.138518	+	0.239920i
$786$	59.2614	+	30.1068i	2.11378	+	1.07387i
$787$			7.34461i			0.261807i	0.991395	+	0.130903i	$0.0417878\pi$
$787$			7.34461i			0.261807i	−0.991395	+	0.130903i	$0.958212\pi$
$788$	1.15089	+	10.7058i	0.0409988	+	0.381378i
$789$	−20.9005	+	36.2007i	−0.744076	+	1.28878i
$790$	8.61985	+	4.37917i	0.306681	+	0.155804i
$791$	33.1445			1.17848
$792$	−2.24781	+	5.91857i	−0.0798724	+	0.210307i
$793$	−5.82010	+	3.36024i	−0.206678	+	0.119326i
$794$	−24.0352	+	15.6492i	−0.852978	+	0.555369i
$795$	37.8395	+	65.5399i	1.34203	+	2.32446i
$796$	34.1016	+	15.0862i	1.20870	+	0.534718i
$797$	−31.5903			−1.11899			−0.559493	−	0.828835i	$-0.689004\pi$
$797$	−31.5903			−1.11899			−0.559493	+	0.828835i	$0.689004\pi$
$798$	−48.4661	−	65.2672i	−1.71568	−	2.31043i
$799$		−	5.16504i		−	0.182726i
$800$	2.56462	−	9.80335i	0.0906732	−	0.346601i
$801$	47.2017	−	27.2519i	1.66779	−	0.962898i
$802$	−24.3240	+	15.8372i	−0.858909	+	0.559231i
$803$	−0.888978	−	1.53976i	−0.0313714	−	0.0543368i
$804$	74.6784	−	8.02806i	2.63371	−	0.283128i
$805$			17.8708i			0.629864i
$806$	−3.01786	+	5.94027i	−0.106299	+	0.209237i
$807$	−74.7327	−	43.1470i	−2.63072	−	1.51884i
$808$	−11.1770	−	4.24490i	−0.393205	−	0.149335i
$809$	−50.1923			−1.76467			−0.882334	−	0.470624i	$-0.844029\pi$
$809$	−50.1923			−1.76467			−0.882334	+	0.470624i	$0.844029\pi$
$810$	41.9914	+	21.3330i	1.47543	+	0.749565i
$811$	19.2290	+	11.1018i	0.675220	+	0.389838i	0.798052	−	0.602589i	$-0.205864\pi$
$811$	19.2290	+	11.1018i	0.675220	+	0.389838i	−0.122832	+	0.992428i	$0.539198\pi$
$812$	7.29457	+	3.22705i	0.255989	+	0.113247i
$813$	−6.11674	+	10.5945i	−0.214523	+	0.371565i
$814$	−5.04109	+	0.270185i	−0.176690	+	0.00946996i
$815$	0.675360	−	0.389919i	0.0236568	−	0.0136583i
$816$	−8.34250	−	2.66698i	−0.292046	−	0.0933630i
$817$	20.8160	+	31.4152i	0.728261	+	1.09908i
$818$	−13.7849	−	7.00320i	−0.481979	−	0.244861i
$819$	40.0493	−	23.1224i	1.39943	−	0.807964i
$820$	−11.8783	+	26.8503i	−0.414810	+	0.937654i
$821$	42.6691	+	24.6350i	1.48916	+	0.859769i	0.999923	−	0.0123810i	$-0.00394108\pi$
$821$	42.6691	+	24.6350i	1.48916	+	0.859769i	0.489239	+	0.872150i	$0.337274\pi$
$822$	−2.19655	−	40.9831i	−0.0766135	−	1.42945i
$823$	−0.331446	−	0.191360i	−0.0115535	−	0.00667040i	0.494212	−	0.869341i	$-0.335457\pi$
$823$	−0.331446	−	0.191360i	−0.0115535	−	0.00667040i	−0.505766	+	0.862671i	$0.668790\pi$
$824$	51.2522	−	8.30447i	1.78545	−	0.289300i
$825$		−	1.92043i		−	0.0668606i
$826$	25.3943	+	39.0025i	0.883580	+	1.35707i
$827$	1.33960	+	0.773418i	0.0465824	+	0.0268944i	0.523110	−	0.852265i	$-0.324772\pi$
$827$	1.33960	+	0.773418i	0.0465824	+	0.0268944i	−0.476528	+	0.879159i	$0.658105\pi$
$828$	−16.4879	+	12.0390i	−0.572993	+	0.418383i
$829$	32.7078			1.13599			0.567994	−	0.823033i	$-0.307720\pi$
$829$	32.7078			1.13599			0.567994	+	0.823033i	$0.307720\pi$
$830$	14.4942	−	9.43707i	0.503100	−	0.327565i
$831$	−18.7002	−	32.3898i	−0.648704	−	1.12359i
$832$	2.70002	−	13.1622i	0.0936064	−	0.456317i
$833$	−4.10519	−	7.11039i	−0.142236	−	0.246360i
$834$	−1.00656	−	18.7803i	−0.0348542	−	0.650309i
$835$		−	20.5846i		−	0.712360i
$836$	−3.00477	+	0.511712i	−0.103922	+	0.0176979i
$837$		−	29.2622i		−	1.01145i
$838$	35.7092	−	1.91389i	1.23355	−	0.0661141i
$839$	3.97923	+	6.89223i	0.137378	+	0.237946i	0.926504	−	0.376286i	$-0.122799\pi$
$839$	3.97923	+	6.89223i	0.137378	+	0.237946i	−0.789125	+	0.614233i	$0.789466\pi$
$840$	90.8724	+	34.5124i	3.13539	+	1.19079i
$841$	14.0700	+	24.3700i	0.485174	+	0.840346i
$842$	−12.1883	−	18.7197i	−0.420035	−	0.645122i
$843$	1.62703			0.0560379
$844$	1.50564	−	1.09938i	0.0518264	−	0.0378421i
$845$	−22.9731	−	13.2635i	−0.790299	−	0.456280i
$846$	−54.8790	+	35.7314i	−1.88678	+	1.22847i
$847$		−	46.7840i		−	1.60752i
$848$	−11.5356	+	36.0842i	−0.396135	+	1.23914i
$849$	−7.88588	−	4.55291i	−0.270643	−	0.156256i
$850$	1.80643	−	0.0968184i	0.0619601	−	0.00332084i
$851$	−14.0981	−	8.13954i	−0.483276	−	0.279020i
$852$	57.1330	+	25.2751i	1.95734	+	0.865912i
$853$	5.06060	−	2.92174i	0.173272	−	0.100039i	−0.410856	−	0.911700i	$-0.634770\pi$
$853$	5.06060	−	2.92174i	0.173272	−	0.100039i	0.584128	+	0.811662i	$0.301437\pi$
$854$	11.0235	−	21.6983i	0.377216	−	0.742502i
$855$	4.47626	+	72.5850i	0.153085	+	2.48235i
$856$	−5.24821	−	32.3901i	−0.179380	−	1.10707i
$857$	26.6433	−	15.3825i	0.910118	−	0.525457i	0.0296491	−	0.999560i	$-0.490561\pi$
$857$	26.6433	−	15.3825i	0.910118	−	0.525457i	0.880469	+	0.474103i	$0.157228\pi$
$858$	−0.136283	−	2.54276i	−0.00465261	−	0.0868082i
$859$	4.27545	−	7.40529i	0.145876	−	0.252665i	−0.783823	−	0.620984i	$-0.786733\pi$
$859$	4.27545	−	7.40529i	0.145876	−	0.252665i	0.929700	+	0.368319i	$0.120067\pi$
$860$	−41.2093	−	18.2306i	−1.40523	−	0.621659i
$861$	−64.3360	−	37.1444i	−2.19257	−	1.26588i
$862$	24.2570	−	47.7468i	0.826196	−	1.62626i
$863$	−14.5152			−0.494103			−0.247052	−	0.969002i	$-0.579462\pi$
$863$	−14.5152			−0.494103			−0.247052	+	0.969002i	$0.579462\pi$
$864$	15.6103	+	56.9074i	0.531075	+	1.93603i
$865$	36.1892	+	20.8938i	1.23047	+	0.710412i
$866$	−46.8095	−	23.7808i	−1.59065	−	0.808104i
$867$			50.5630i			1.71721i
$868$	−2.57909	−	23.9912i	−0.0875402	−	0.814315i
$869$	0.458614	+	0.794343i	0.0155574	+	0.0269463i
$870$	−5.71779	−	8.78181i	−0.193851	−	0.297731i
$871$	−17.8143	+	10.2851i	−0.603615	+	0.348497i
$872$	−0.907118	−	1.11209i	−0.0307189	−	0.0376600i
$873$		−	46.5863i		−	1.57671i
$874$	−9.02024	−	3.90400i	−0.305114	−	0.132055i
$875$	35.9634			1.21578
$876$	−28.5191	−	12.6166i	−0.963572	−	0.426276i
$877$	−10.8262	−	18.7515i	−0.365575	−	0.633194i	0.623294	−	0.781988i	$-0.285794\pi$
$877$	−10.8262	−	18.7515i	−0.365575	−	0.633194i	−0.988868	+	0.148794i	$0.952461\pi$
$878$	−12.6184	−	19.3803i	−0.425850	−	0.654053i
$879$	42.1460	−	24.3330i	1.42155	−	0.820731i
$880$	2.69687	−	2.45153i	0.0909116	−	0.0826410i
$881$	5.75645			0.193940			0.0969698	−	0.995287i	$-0.469085\pi$
$881$	5.75645			0.193940			0.0969698	+	0.995287i	$0.469085\pi$
$882$	−47.1492	+	92.8073i	−1.58760	+	3.12498i
$883$	18.9840	−	32.8813i	0.638863	−	1.10654i	−0.346819	−	0.937932i	$-0.612738\pi$
$883$	18.9840	−	32.8813i	0.638863	−	1.10654i	0.985683	−	0.168612i	$-0.0539284\pi$
$884$	2.38495	−	0.256386i	0.0802146	−	0.00862320i
$885$		−	61.1436i		−	2.05532i
$886$	1.67747	−	3.30190i	0.0563558	−	0.110929i
$887$	−10.8432	+	18.7809i	−0.364078	+	0.630602i	−0.988628	−	0.150383i	$-0.951949\pi$
$887$	−10.8432	+	18.7809i	−0.364078	+	0.630602i	0.624550	+	0.780985i	$0.285283\pi$
$888$	−68.6156	+	55.9690i	−2.30259	+	1.87820i
$889$	51.4531	+	29.7065i	1.72568	+	0.996323i
$890$	−31.3313	+	1.67925i	−1.05023	+	0.0562885i
$891$	2.23413	+	3.86962i	0.0748460	+	0.129637i
$892$	−17.9894	−	24.6372i	−0.602329	−	0.824916i
$893$	−28.2225	−	14.0534i	−0.944428	−	0.470280i
$894$	−10.2174	+	20.1116i	−0.341720	+	0.672634i
$895$	−20.2603	−	35.0918i	−0.677226	−	1.17299i
$896$	17.8141	+	45.2808i	0.595128	+	1.51272i
$897$	4.10563	−	7.11115i	0.137083	−	0.237435i
$898$	−1.35897	−	25.3556i	−0.0453494	−	0.846127i
$899$	−1.30063	+	2.25276i	−0.0433785	+	0.0751337i
$900$	−13.5255	−	18.5238i	−0.450850	−	0.617458i
$901$	−6.76305			−0.225310
$902$	−2.33421	+	1.51979i	−0.0777207	+	0.0506035i
$903$	57.0085	−	98.7415i	1.89712	−	3.28591i
$904$	−3.48635	−	21.5165i	−0.115954	−	0.715628i
$905$		−	0.674594i		−	0.0224243i
$906$	15.0459	−	9.79630i	0.499867	−	0.325460i
$907$	−27.7864	+	16.0425i	−0.922633	+	0.532683i	−0.884474	−	0.466589i	$-0.845483\pi$
$907$	−27.7864	+	16.0425i	−0.922633	+	0.532683i	−0.0381590	+	0.999272i	$0.512149\pi$
$908$	1.17980	+	10.9747i	0.0391529	+	0.364207i
$909$	−23.4361	+	13.5309i	−0.777328	+	0.448790i
$910$	−26.5837	+	1.42479i	−0.881242	+	0.0472314i
$911$	38.7962			1.28538			0.642688	−	0.766128i	$-0.277819\pi$
$911$	38.7962			1.28538			0.642688	+	0.766128i	$0.277819\pi$
$912$	−37.2717	+	38.3280i	−1.23419	+	1.26917i
$913$	1.64081			0.0543027
$914$	−22.4681	+	1.20421i	−0.743179	+	0.0398317i
$915$	−27.6904	+	15.9871i	−0.915417	+	0.528516i
$916$	−2.73925	−	25.4810i	−0.0905075	−	0.841917i
$917$	57.0942	−	32.9633i	1.88542	−	1.08855i
$918$	−8.82826	+	5.74803i	−0.291376	+	0.189713i
$919$		−	4.09055i		−	0.134935i	−0.997721	−	0.0674674i	$-0.978508\pi$
$919$		−	4.09055i		−	0.134935i	0.997721	−	0.0674674i	$-0.0214919\pi$
$920$	11.6012	−	1.87977i	0.382482	−	0.0619741i
$921$	34.6854	−	60.0769i	1.14292	−	1.97960i
$922$	20.9576	−	13.6453i	0.690201	−	0.449385i
$923$	−17.1099			−0.563180
$924$	5.43805	+	7.44764i	0.178899	+	0.245009i
$925$	9.14458	−	15.8389i	0.300672	−	0.520779i
$926$	1.69697	+	31.6620i	0.0557658	+	1.04048i
$927$	58.7600	−	101.775i	1.92993	−	3.34274i
$928$	1.32762	−	5.07487i	0.0435813	−	0.166591i
$929$	14.0628	+	24.3575i	0.461385	+	0.799143i	0.999030	−	0.0440285i	$-0.0140192\pi$
$929$	14.0628	+	24.3575i	0.461385	+	0.799143i	−0.537645	+	0.843171i	$0.680686\pi$
$930$	−14.3581	+	28.2621i	−0.470821	+	0.926752i
$931$	−50.0218	+	3.08481i	−1.63940	+	0.101100i
$932$	2.26022	+	3.09547i	0.0740360	+	0.101395i
$933$	−23.2734	−	40.3107i	−0.761936	−	1.31971i
$934$	51.9695	−	2.78538i	1.70049	−	0.0911404i
$935$	0.563477	+	0.325324i	0.0184277	+	0.0106392i
$936$	−19.2231	−	23.5667i	−0.628326	−	0.770301i
$937$	20.2150	−	35.0135i	0.660397	−	1.14384i	−0.320115	−	0.947379i	$-0.603721\pi$
$937$	20.2150	−	35.0135i	0.660397	−	1.14384i	0.980511	−	0.196462i	$-0.0629452\pi$
$938$	33.7409	−	66.4148i	1.10168	−	2.16852i
$939$			13.1751i			0.429952i
$940$	37.4826	−	4.02944i	1.22255	−	0.131426i
$941$	13.0744	−	22.6456i	0.426215	−	0.738226i	−0.570318	−	0.821424i	$-0.693180\pi$
$941$	13.0744	−	22.6456i	0.426215	−	0.738226i	0.996533	+	0.0831981i	$0.0265134\pi$
$942$	−5.84997	+	11.5149i	−0.190602	+	0.375177i
$943$	−8.98184			−0.292489
$944$	22.6482	−	20.5878i	0.737136	−	0.670076i
$945$	101.254	−	58.4592i	3.29380	−	1.90168i
$946$	−2.33254	−	3.58249i	−0.0758374	−	0.116477i
$947$	16.0421	+	27.7858i	0.521299	+	0.902917i	0.999693	+	0.0247713i	$0.00788576\pi$
$947$	16.0421	+	27.7858i	0.521299	+	0.902917i	−0.478394	+	0.878145i	$0.658781\pi$
$948$	14.7127	+	6.50877i	0.477846	+	0.211395i
$949$	8.54077			0.277245
$950$	4.38605	−	10.1340i	0.142302	−	0.328791i
$951$			0.982449i			0.0318581i
$952$	−6.73141	+	5.49073i	−0.218166	+	0.177956i
$953$	−13.9593	+	8.05939i	−0.452185	+	0.261069i	−0.708753	−	0.705457i	$-0.750742\pi$
$953$	−13.9593	+	8.05939i	−0.452185	+	0.261069i	0.256567	+	0.966526i	$0.417408\pi$
$954$	46.7864	+	71.8581i	1.51477	+	2.32649i
$955$	−7.81983	−	13.5443i	−0.253044	−	0.438285i
$956$	5.59808	+	52.0744i	0.181055	+	1.68421i
$957$		−	0.994142i		−	0.0321360i
$958$	1.70892	+	0.868190i	0.0552128	+	0.0280499i
$959$	−35.2526	−	20.3531i	−1.13836	−	0.657235i
$960$	12.8459	−	62.6220i	0.414601	−	2.02112i
$961$	−23.1310			−0.746162
$962$	10.9840	−	21.6205i	0.354137	−	0.697074i
$963$	−64.3194	−	37.1348i	−2.07266	−	1.19665i
$964$	−27.8890	−	12.3379i	−0.898245	−	0.397376i
$965$	9.98948	−	17.3023i	0.321573	−	0.556980i
$966$	1.59150	+	29.6941i	0.0512056	+	0.955392i
$967$	−33.9035	+	19.5742i	−1.09026	+	0.629464i	−0.933647	−	0.358195i	$-0.883392\pi$
$967$	−33.9035	+	19.5742i	−1.09026	+	0.629464i	−0.156617	+	0.987659i	$0.550059\pi$
$968$	−30.3708	+	4.92104i	−0.976156	+	0.158168i
$969$	−8.54365	−	4.25433i	−0.274462	−	0.136669i
$970$	−12.1470	+	23.9098i	−0.390016	+	0.767698i
$971$	11.3501	−	6.55297i	0.364241	−	0.210295i	−0.306698	−	0.951807i	$-0.599224\pi$
$971$	11.3501	−	6.55297i	0.364241	−	0.210295i	0.670940	+	0.741512i	$0.265891\pi$
$972$	14.4343	+	6.38560i	0.462980	+	0.204818i
$973$	−16.1543	−	9.32669i	−0.517883	−	0.299000i
$974$	−22.8109	+	1.22258i	−0.730908	+	0.0391741i
$975$	7.98922	+	4.61258i	0.255860	+	0.147721i
$976$	−15.2455	−	4.87377i	−0.487996	−	0.156005i
$977$		−	36.1689i		−	1.15715i	−0.815631	−	0.578573i	$-0.803610\pi$
$977$		−	36.1689i		−	1.15715i	0.815631	−	0.578573i	$-0.196390\pi$
$978$	1.08745	−	0.708033i	0.0347728	−	0.0226404i
$979$	−2.57782	−	1.48831i	−0.0823876	−	0.0475665i
$980$	48.3974	−	35.3384i	1.54600	−	1.12884i
$981$	−3.24836			−0.103712
$982$	−1.29492	−	1.98884i	−0.0413226	−	0.0634663i
$983$	12.9126	+	22.3653i	0.411849	+	0.713343i	0.995092	−	0.0989546i	$-0.0315499\pi$
$983$	12.9126	+	22.3653i	0.411849	+	0.713343i	−0.583243	+	0.812298i	$0.698217\pi$
$984$	−17.3458	+	45.6722i	−0.552965	+	1.45598i
$985$	−7.01506	−	12.1504i	−0.223519	−	0.387145i
$986$	0.935131	−	0.0501197i	0.0297806	−	0.00159614i
$987$			95.3863i			3.03618i
$988$	5.08823	−	13.7293i	0.161878	−	0.436787i
$989$		−	13.7851i		−	0.438342i
$990$	−0.441505	−	8.23757i	−0.0140319	−	0.261807i
$991$	13.0397	+	22.5855i	0.414221	+	0.717452i	0.995346	−	0.0963621i	$-0.0307207\pi$
$991$	13.0397	+	22.5855i	0.414221	+	0.717452i	−0.581125	+	0.813814i	$0.697387\pi$
$992$	−15.3031	+	4.19783i	−0.485875	+	0.133281i
$993$	24.1473	+	41.8243i	0.766291	+	1.32726i
$994$	51.9264	−	33.8090i	1.64701	−	1.07236i
$995$	−48.5886			−1.54036
$996$	23.2430	−	16.9714i	0.736484	−	0.537759i
$997$	28.5744	+	16.4974i	0.904961	+	0.522479i	0.878806	−	0.477179i	$-0.158341\pi$
$997$	28.5744	+	16.4974i	0.904961	+	0.522479i	0.0261544	+	0.999658i	$0.491674\pi$
$998$	−17.9204	−	27.5235i	−0.567261	−	0.871243i
$999$			106.504i			3.36965i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.o.c.107.14	yes	28
4.3	odd	2		608.2.s.c.335.13		28
8.3	odd	2	inner	152.2.o.c.107.11	yes	28
8.5	even	2		608.2.s.c.335.14		28
19.8	odd	6	inner	152.2.o.c.27.11	✓	28
76.27	even	6		608.2.s.c.559.14		28
152.27	even	6	inner	152.2.o.c.27.14	yes	28
152.141	odd	6		608.2.s.c.559.13		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.o.c.27.11	✓	28	19.8	odd	6	inner
152.2.o.c.27.14	yes	28	152.27	even	6	inner
152.2.o.c.107.11	yes	28	8.3	odd	2	inner
152.2.o.c.107.14	yes	28	1.1	even	1	trivial
608.2.s.c.335.13		28	4.3	odd	2
608.2.s.c.335.14		28	8.5	even	2
608.2.s.c.559.13		28	152.141	odd	6
608.2.s.c.559.14		28	76.27	even	6

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41219 - 0.0756882i) q^{2} +(-2.65547 + 1.53314i) q^{3} +(1.98854 - 0.213772i) q^{4} +(-2.25688 + 1.30301i) q^{5} +(-3.63398 + 2.36606i) q^{6} +4.30088i q^{7} +(2.79201 - 0.452395i) q^{8} +(3.20101 - 5.54431i) q^{9} +(-3.08851 + 2.01091i) q^{10} -0.349633 q^{11} +(-4.95277 + 3.61637i) q^{12} +(0.839767 - 1.45452i) q^{13} +(0.325526 + 6.07365i) q^{14} +(3.99538 - 6.92020i) q^{15} +(3.90860 - 0.850188i) q^{16} +(0.357047 + 0.618424i) q^{17} +(4.10079 - 8.07189i) q^{18} +(4.35063 - 0.268300i) q^{19} +(-4.20935 + 3.07354i) q^{20} +(-6.59384 - 11.4209i) q^{21} +(-0.493748 + 0.0264631i) q^{22} +(-1.38083 - 0.797223i) q^{23} +(-6.72052 + 5.48186i) q^{24} +(0.895662 - 1.55133i) q^{25} +(1.07582 - 2.11761i) q^{26} +10.4315i q^{27} +(0.919407 + 8.55249i) q^{28} +(0.463655 - 0.803074i) q^{29} +(5.11844 - 10.0750i) q^{30} -2.80517 q^{31} +(5.45533 - 1.49646i) q^{32} +(0.928441 - 0.536035i) q^{33} +(0.551025 + 0.846306i) q^{34} +(-5.60409 - 9.70656i) q^{35} +(5.18013 - 11.7094i) q^{36} +10.2099 q^{37} +(6.12360 - 0.708181i) q^{38} +5.14991i q^{39} +(-5.71176 + 4.65902i) q^{40} +(4.87850 - 2.81660i) q^{41} +(-10.1762 - 15.6293i) q^{42} +(4.32286 + 7.48741i) q^{43} +(-0.695261 + 0.0747417i) q^{44} +16.6838i q^{45} +(-2.01033 - 1.02132i) q^{46} +(-6.26395 - 3.61649i) q^{47} +(-9.07572 + 8.25007i) q^{48} -11.4976 q^{49} +(1.14742 - 2.25856i) q^{50} +(-1.89626 - 1.09480i) q^{51} +(1.35898 - 3.07189i) q^{52} +(-4.73541 + 8.20196i) q^{53} +(0.789543 + 14.7313i) q^{54} +(0.789079 - 0.455575i) q^{55} +(1.94570 + 12.0081i) q^{56} +(-11.1416 + 7.38258i) q^{57} +(0.593984 - 1.16918i) q^{58} +(6.62664 - 3.82589i) q^{59} +(6.46564 - 14.6152i) q^{60} +(-3.46531 - 2.00070i) q^{61} +(-3.96143 + 0.212318i) q^{62} +(23.8454 + 13.7672i) q^{63} +(7.59068 - 2.52618i) q^{64} +4.37690i q^{65} +(1.27056 - 0.827254i) q^{66} +(-10.6067 - 6.12378i) q^{67} +(0.842205 + 1.15344i) q^{68} +4.88901 q^{69} +(-8.64869 - 13.2833i) q^{70} +(-5.09365 - 8.82246i) q^{71} +(6.42905 - 16.9279i) q^{72} +(2.54260 + 4.40392i) q^{73} +(14.4182 - 0.772765i) q^{74} +5.49268i q^{75} +(8.59407 - 1.46357i) q^{76} -1.50373i q^{77} +(0.389787 + 7.27263i) q^{78} +(-1.31170 - 2.27193i) q^{79} +(-7.71343 + 7.01171i) q^{80} +(-6.38991 - 11.0677i) q^{81} +(6.67616 - 4.34681i) q^{82} -4.69293 q^{83} +(-15.5536 - 21.3013i) q^{84} +(-1.61162 - 0.930471i) q^{85} +(6.67139 + 10.2464i) q^{86} +2.84338i q^{87} +(-0.976181 + 0.158172i) q^{88} +(7.37293 + 4.25676i) q^{89} +(1.26276 + 23.5606i) q^{90} +(6.25572 + 3.61174i) q^{91} +(-2.91626 - 1.29013i) q^{92} +(7.44905 - 4.30071i) q^{93} +(-9.11959 - 4.63306i) q^{94} +(-9.46925 + 6.27443i) q^{95} +(-12.1922 + 12.3376i) q^{96} +(6.30190 - 3.63841i) q^{97} +(-16.2368 + 0.870232i) q^{98} +(-1.11918 + 1.93848i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 3 q^{2} - 6 q^{3} + q^{4} - 3 q^{6} + 8 q^{9} + 6 q^{10} - 16 q^{11} + 13 q^{16} - 22 q^{17} + 4 q^{19} - 40 q^{20} - 21 q^{22} - 11 q^{24} + 16 q^{25} + 36 q^{26} - 10 q^{28} + 4 q^{30} - 3 q^{32}+ \cdots - 28 q^{99}+O(q^{100}) \) 28 * q - 3 * q^2 - 6 * q^3 + q^4 - 3 * q^6 + 8 * q^9 + 6 * q^10 - 16 * q^11 + 13 * q^16 - 22 * q^17 + 4 * q^19 - 40 * q^20 - 21 * q^22 - 11 * q^24 + 16 * q^25 + 36 * q^26 - 10 * q^28 + 4 * q^30 - 3 * q^32 + 36 * q^33 - 12 * q^34 - 28 * q^35 - 8 * q^36 + 38 * q^38 - 48 * q^40 + 6 * q^41 + 14 * q^42 + 30 * q^43 + 5 * q^44 - 15 * q^48 - 68 * q^49 - 42 * q^51 + 36 * q^52 + 23 * q^54 - 26 * q^57 + 20 * q^58 - 18 * q^59 - 42 * q^60 + 22 * q^62 + 70 * q^64 - 27 * q^66 + 78 * q^67 + 4 * q^68 + 18 * q^70 - 24 * q^72 + 14 * q^73 + 4 * q^74 + 47 * q^76 - 30 * q^78 - 20 * q^80 + 6 * q^81 + 23 * q^82 - 32 * q^83 + 42 * q^86 - 18 * q^89 - 96 * q^90 - 12 * q^91 + 46 * q^92 + 50 * q^96 + 30 * q^97 + 15 * q^98 - 28 * q^99

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