LMFDB - Embedded newform 220.2.r.d.151.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [220,2,Mod(51,220)] 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("220.51"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(220, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.r (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] 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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			151.5
Character	$\chi$	$=$	220.151
Dual form			220.2.r.d.51.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.631838 - 1.26522i) q^{2} +(-0.115659 + 0.0375799i) q^{3} +(-1.20156 + 1.59883i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.120625 + 0.122590i) q^{6} +(1.38450 - 4.26105i) q^{7} +(2.78206 + 0.510037i) q^{8} +(-2.41509 + 1.75466i) q^{9} +(-0.232509 + 1.39497i) q^{10} +(-2.15687 - 2.51950i) q^{11} +(0.0788876 - 0.230074i) q^{12} +(-1.46184 - 2.01205i) q^{13} +(-6.26594 + 0.940598i) q^{14} +(0.115659 + 0.0375799i) q^{15} +(-1.11250 - 3.84218i) q^{16} +(-0.925394 + 1.27370i) q^{17} +(3.74598 + 1.94695i) q^{18} +(-2.16501 - 6.66320i) q^{19} +(1.91185 - 0.587219i) q^{20} +0.544858i q^{21} +(-1.82493 + 4.32084i) q^{22} +3.51120i q^{23} +(-0.340938 + 0.0455592i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-1.62204 + 3.12084i) q^{26} +(0.427830 - 0.588858i) q^{27} +(5.14912 + 7.33348i) q^{28} +(7.15919 + 2.32616i) q^{29} +(-0.0255310 - 0.170079i) q^{30} +(0.0636833 + 0.0876525i) q^{31} +(-4.15828 + 3.83520i) q^{32} +(0.344145 + 0.210348i) q^{33} +(2.19620 + 0.366057i) q^{34} +(-3.62466 + 2.63347i) q^{35} +(0.0964685 - 5.96964i) q^{36} +(1.69433 - 5.21461i) q^{37} +(-7.06248 + 6.94928i) q^{38} +(0.244688 + 0.177776i) q^{39} +(-1.95094 - 2.04788i) q^{40} +(-2.58719 + 0.840630i) q^{41} +(0.689365 - 0.344262i) q^{42} +9.66919 q^{43} +(6.61987 - 0.421136i) q^{44} +2.98521 q^{45} +(4.44244 - 2.21851i) q^{46} +(6.21868 - 2.02057i) q^{47} +(0.273060 + 0.402575i) q^{48} +(-10.5766 - 7.68432i) q^{49} +(1.00805 - 0.991888i) q^{50} +(0.0591649 - 0.182091i) q^{51} +(4.97341 + 0.0803696i) q^{52} +(2.44632 - 1.77735i) q^{53} +(-1.01535 - 0.169236i) q^{54} +(0.264022 + 3.30610i) q^{55} +(6.02505 - 11.1483i) q^{56} +(0.500805 + 0.689300i) q^{57} +(-1.58034 - 10.5277i) q^{58} +(4.30358 + 1.39832i) q^{59} +(-0.199055 + 0.139764i) q^{60} +(-2.86345 + 3.94119i) q^{61} +(0.0706621 - 0.135956i) q^{62} +(4.13302 + 12.7201i) q^{63} +(7.47972 + 2.83791i) q^{64} +2.48703i q^{65} +(0.0486928 - 0.568325i) q^{66} -5.92809i q^{67} +(-0.924503 - 3.00997i) q^{68} +(-0.131951 - 0.406102i) q^{69} +(5.62212 + 2.92206i) q^{70} +(-8.27369 + 11.3878i) q^{71} +(-7.61386 + 3.64979i) q^{72} +(14.4548 + 4.69663i) q^{73} +(-7.66817 + 1.15109i) q^{74} +(-0.0714813 - 0.0983855i) q^{75} +(13.2547 + 4.54477i) q^{76} +(-13.7219 + 5.70229i) q^{77} +(0.0703227 - 0.421910i) q^{78} +(-1.78591 + 1.29754i) q^{79} +(-1.35834 + 3.76230i) q^{80} +(2.74009 - 8.43313i) q^{81} +(2.69827 + 2.74223i) q^{82} +(-7.55967 - 5.49242i) q^{83} +(-0.871134 - 0.654680i) q^{84} +(1.49732 - 0.486508i) q^{85} +(-6.10936 - 12.2336i) q^{86} -0.915442 q^{87} +(-4.71552 - 8.10950i) q^{88} +3.97318 q^{89} +(-1.88617 - 3.77695i) q^{90} +(-10.5973 + 3.44329i) q^{91} +(-5.61381 - 4.21892i) q^{92} +(-0.0106595 - 0.00774460i) q^{93} +(-6.48567 - 6.59132i) q^{94} +(-2.16501 + 6.66320i) q^{95} +(0.336816 - 0.599843i) q^{96} +(7.04211 - 5.11639i) q^{97} +(-3.03968 + 18.2369i) q^{98} +(9.62992 + 2.30023i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{5} + 20 q^{6} + 16 q^{9} + 14 q^{12} - 10 q^{13} - 21 q^{14} - 4 q^{16} - 25 q^{18} + 5 q^{20} + 15 q^{22} - 30 q^{24} - 12 q^{25} - 4 q^{26} - 60 q^{28} + 20 q^{29} - 10 q^{33} - 18 q^{34}+ \cdots + 38 q^{97}+O(q^{100}) $ 48 * q - 12 * q^5 + 20 * q^6 + 16 * q^9 + 14 * q^12 - 10 * q^13 - 21 * q^14 - 4 * q^16 - 25 * q^18 + 5 * q^20 + 15 * q^22 - 30 * q^24 - 12 * q^25 - 4 * q^26 - 60 * q^28 + 20 * q^29 - 10 * q^33 - 18 * q^34 + 66 * q^36 - 44 * q^37 + 11 * q^38 - 10 * q^41 + 19 * q^42 - 35 * q^44 - 44 * q^45 + 5 * q^46 + 41 * q^48 - 2 * q^49 + 50 * q^52 - 36 * q^53 - 28 * q^56 + 30 * q^57 - 38 * q^58 - 21 * q^60 + 36 * q^64 + 43 * q^66 - 65 * q^68 + 24 * q^69 - 21 * q^70 - 60 * q^72 - 20 * q^73 - 70 * q^74 + 16 * q^77 - 56 * q^78 + q^80 + 50 * q^81 + 35 * q^82 + 60 * q^84 + 10 * q^85 + 38 * q^86 - 101 * q^88 + 64 * q^89 + 70 * q^92 - 28 * q^93 + 130 * q^94 + 105 * q^96 + 38 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.631838	−	1.26522i	−0.446777	−	0.894645i
$2$	−0.631838	−	1.26522i	−0.446777	−	0.894645i
$3$	−0.115659	+	0.0375799i	−0.0667758	+	0.0216968i	−0.342214	−	0.939622i	$-0.611177\pi$
$3$	−0.115659	+	0.0375799i	−0.0667758	+	0.0216968i	0.275439	+	0.961319i	$0.411177\pi$
$4$	−1.20156	+	1.59883i	−0.600780	+	0.799414i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	0.120625	+	0.122590i	0.0492448	+	0.0500471i
$7$	1.38450	−	4.26105i	0.523291	−	1.61052i	−0.244380	−	0.969680i	$-0.578584\pi$
$7$	1.38450	−	4.26105i	0.523291	−	1.61052i	0.767671	−	0.640844i	$-0.221416\pi$
$8$	2.78206	+	0.510037i	0.983607	+	0.180325i
$9$	−2.41509	+	1.75466i	−0.805029	+	0.584888i
$10$	−0.232509	+	1.39497i	−0.0735260	+	0.441128i
$11$	−2.15687	−	2.51950i	−0.650322	−	0.759659i
$11$	−2.15687	−	2.51950i	−0.650322	−	0.759659i
$12$	0.0788876	−	0.230074i	0.0227729	−	0.0664165i
$13$	−1.46184	−	2.01205i	−0.405441	−	0.558042i	0.556658	−	0.830742i	$-0.312083\pi$
$13$	−1.46184	−	2.01205i	−0.405441	−	0.558042i	−0.962099	+	0.272700i	$0.912083\pi$
$14$	−6.26594	+	0.940598i	−1.67464	+	0.251385i
$15$	0.115659	+	0.0375799i	0.0298631	+	0.00970310i
$16$	−1.11250	−	3.84218i	−0.278126	−	0.960545i
$17$	−0.925394	+	1.27370i	−0.224441	+	0.308917i	−0.906356	−	0.422515i	$-0.861147\pi$
$17$	−0.925394	+	1.27370i	−0.224441	+	0.308917i	0.681915	+	0.731431i	$0.261147\pi$
$18$	3.74598	+	1.94695i	0.882935	+	0.458901i
$19$	−2.16501	−	6.66320i	−0.496687	−	1.52864i	−0.814312	−	0.580428i	$-0.802885\pi$
$19$	−2.16501	−	6.66320i	−0.496687	−	1.52864i	0.317625	−	0.948216i	$-0.397115\pi$
$20$	1.91185	−	0.587219i	0.427503	−	0.131306i
$21$			0.544858i			0.118898i
$22$	−1.82493	+	4.32084i	−0.389076	+	0.921206i
$23$			3.51120i			0.732136i	0.930588	+	0.366068i	$0.119296\pi$
$23$			3.51120i			0.732136i	−0.930588	+	0.366068i	$0.880704\pi$
$24$	−0.340938	+	0.0455592i	−0.0695936	+	0.00929973i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−1.62204	+	3.12084i	−0.318108	+	0.612047i
$27$	0.427830	−	0.588858i	0.0823360	−	0.113326i
$28$	5.14912	+	7.33348i	0.973092	+	1.38590i
$29$	7.15919	+	2.32616i	1.32943	+	0.431957i	0.885722	−	0.464216i	$-0.153664\pi$
$29$	7.15919	+	2.32616i	1.32943	+	0.431957i	0.443705	+	0.896173i	$0.353664\pi$
$30$	−0.0255310	−	0.170079i	−0.00466130	−	0.0310520i
$31$	0.0636833	+	0.0876525i	0.0114379	+	0.0157429i	0.814698	−	0.579886i	$-0.196903\pi$
$31$	0.0636833	+	0.0876525i	0.0114379	+	0.0157429i	−0.803260	+	0.595629i	$0.796903\pi$
$32$	−4.15828	+	3.83520i	−0.735087	+	0.677973i
$33$	0.344145	+	0.210348i	0.0599079	+	0.0366169i
$34$	2.19620	+	0.366057i	0.376646	+	0.0627783i
$35$	−3.62466	+	2.63347i	−0.612680	+	0.445138i
$36$	0.0964685	−	5.96964i	0.0160781	−	0.994940i
$37$	1.69433	−	5.21461i	0.278546	−	0.857277i	−0.709713	−	0.704491i	$-0.751175\pi$
$37$	1.69433	−	5.21461i	0.278546	−	0.857277i	0.988259	−	0.152786i	$-0.0488246\pi$
$38$	−7.06248	+	6.94928i	−1.14569	+	1.12732i
$39$	0.244688	+	0.177776i	0.0391814	+	0.0284670i
$40$	−1.95094	−	2.04788i	−0.308471	−	0.323799i
$41$	−2.58719	+	0.840630i	−0.404052	+	0.131284i	−0.503990	−	0.863709i	$-0.668135\pi$
$41$	−2.58719	+	0.840630i	−0.404052	+	0.131284i	0.0999387	+	0.994994i	$0.468135\pi$
$42$	0.689365	−	0.344262i	0.106371	−	0.0531208i
$43$	9.66919			1.47454			0.737269	−	0.675599i	$-0.236115\pi$
$43$	9.66919			1.47454			0.737269	+	0.675599i	$0.236115\pi$
$44$	6.61987	−	0.421136i	0.997983	−	0.0634887i
$45$	2.98521			0.445009
$46$	4.44244	−	2.21851i	0.655002	−	0.327102i
$47$	6.21868	−	2.02057i	0.907088	−	0.294731i	0.181928	−	0.983312i	$-0.441766\pi$
$47$	6.21868	−	2.02057i	0.907088	−	0.294731i	0.725159	+	0.688581i	$0.241766\pi$
$48$	0.273060	+	0.402575i	0.0394128	+	0.0581067i
$49$	−10.5766	−	7.68432i	−1.51094	−	1.09776i
$50$	1.00805	−	0.991888i	0.142559	−	0.140274i
$51$	0.0591649	−	0.182091i	0.00828474	−	0.0254978i
$52$	4.97341	+	0.0803696i	0.689688	+	0.0111453i
$53$	2.44632	−	1.77735i	0.336028	−	0.244138i	−0.406956	−	0.913448i	$-0.633410\pi$
$53$	2.44632	−	1.77735i	0.336028	−	0.244138i	0.742984	+	0.669309i	$0.233410\pi$
$54$	−1.01535	−	0.169236i	−0.138172	−	0.0230302i
$55$	0.264022	+	3.30610i	0.0356007	+	0.445794i
$56$	6.02505	−	11.1483i	0.805131	−	1.48976i
$57$	0.500805	+	0.689300i	0.0663333	+	0.0913000i
$58$	−1.58034	−	10.5277i	−0.207509	−	1.38235i
$59$	4.30358	+	1.39832i	0.560278	+	0.182045i	0.575446	−	0.817840i	$-0.304828\pi$
$59$	4.30358	+	1.39832i	0.560278	+	0.182045i	−0.0151681	+	0.999885i	$0.504828\pi$
$60$	−0.199055	+	0.139764i	−0.0256979	+	0.0180435i
$61$	−2.86345	+	3.94119i	−0.366627	+	0.504618i	−0.951980	−	0.306160i	$-0.900956\pi$
$61$	−2.86345	+	3.94119i	−0.366627	+	0.504618i	0.585353	+	0.810778i	$0.300956\pi$
$62$	0.0706621	−	0.135956i	0.00897410	−	0.0172664i
$63$	4.13302	+	12.7201i	0.520711	+	1.60258i
$64$	7.47972	+	2.83791i	0.934965	+	0.354739i
$65$			2.48703i			0.308478i
$66$	0.0486928	−	0.568325i	0.00599367	−	0.0699560i
$67$		−	5.92809i		−	0.724232i	−0.932133	−	0.362116i	$-0.882054\pi$
$67$		−	5.92809i		−	0.724232i	0.932133	−	0.362116i	$-0.117946\pi$
$68$	−0.924503	−	3.00997i	−0.112113	−	0.365012i
$69$	−0.131951	−	0.406102i	−0.0158850	−	0.0488890i
$70$	5.62212	+	2.92206i	0.671972	+	0.349254i
$71$	−8.27369	+	11.3878i	−0.981906	+	1.35148i	−0.0461094	+	0.998936i	$0.514682\pi$
$71$	−8.27369	+	11.3878i	−0.981906	+	1.35148i	−0.935796	+	0.352541i	$0.885318\pi$
$72$	−7.61386	+	3.64979i	−0.897302	+	0.430132i
$73$	14.4548	+	4.69663i	1.69180	+	0.549699i	0.987142	−	0.159847i	$-0.0511000\pi$
$73$	14.4548	+	4.69663i	1.69180	+	0.549699i	0.704659	+	0.709546i	$0.251100\pi$
$74$	−7.66817	+	1.15109i	−0.891407	+	0.133812i
$75$	−0.0714813	−	0.0983855i	−0.00825395	−	0.0113606i
$76$	13.2547	+	4.54477i	1.52042	+	0.521321i
$77$	−13.7219	+	5.70229i	−1.56376	+	0.649837i
$78$	0.0703227	−	0.421910i	0.00796247	−	0.0477718i
$79$	−1.78591	+	1.29754i	−0.200931	+	0.145985i	−0.683701	−	0.729762i	$-0.739631\pi$
$79$	−1.78591	+	1.29754i	−0.200931	+	0.145985i	0.482770	+	0.875747i	$0.339631\pi$
$80$	−1.35834	+	3.76230i	−0.151867	+	0.420638i
$81$	2.74009	−	8.43313i	0.304454	−	0.937014i
$82$	2.69827	+	2.74223i	0.297974	+	0.302828i
$83$	−7.55967	−	5.49242i	−0.829782	−	0.602872i	0.0897160	−	0.995967i	$-0.471404\pi$
$83$	−7.55967	−	5.49242i	−0.829782	−	0.602872i	−0.919498	+	0.393096i	$0.871404\pi$
$84$	−0.871134	−	0.654680i	−0.0950486	−	0.0714315i
$85$	1.49732	−	0.486508i	0.162407	−	0.0527693i
$86$	−6.10936	−	12.2336i	−0.658790	−	1.31919i
$87$	−0.915442			−0.0981457
$88$	−4.71552	−	8.10950i	−0.502676	−	0.864475i
$89$	3.97318			0.421156			0.210578	−	0.977577i	$-0.432465\pi$
$89$	3.97318			0.421156			0.210578	+	0.977577i	$0.432465\pi$
$90$	−1.88617	−	3.77695i	−0.198820	−	0.398125i
$91$	−10.5973	+	3.44329i	−1.11090	+	0.360955i
$92$	−5.61381	−	4.21892i	−0.585280	−	0.439853i
$93$	−0.0106595	−	0.00774460i	−0.00110534	−	0.000803078i
$94$	−6.48567	−	6.59132i	−0.668945	−	0.679843i
$95$	−2.16501	+	6.66320i	−0.222125	+	0.683630i
$96$	0.336816	−	0.599843i	0.0343762	−	0.0612212i
$97$	7.04211	−	5.11639i	0.715018	−	0.519491i	−0.169771	−	0.985484i	$-0.554303\pi$
$97$	7.04211	−	5.11639i	0.715018	−	0.519491i	0.884789	+	0.465993i	$0.154303\pi$
$98$	−3.03968	+	18.2369i	−0.307054	+	1.84221i
$99$	9.62992	+	2.30023i	0.967843	+	0.231182i
$100$	−1.89188	−	0.648687i	−0.189188	−	0.0648687i
$101$	−2.07072	−	2.85010i	−0.206044	−	0.283595i	0.693471	−	0.720484i	$-0.256080\pi$
$101$	−2.07072	−	2.85010i	−0.206044	−	0.283595i	−0.899516	+	0.436889i	$0.856080\pi$
$102$	−0.267767	+	0.0401954i	−0.0265129	+	0.00397993i
$103$	−12.3545	−	4.01423i	−1.21733	−	0.395534i	−0.371220	−	0.928545i	$-0.621061\pi$
$103$	−12.3545	−	4.01423i	−1.21733	−	0.395534i	−0.846109	+	0.533011i	$0.821061\pi$
$104$	−3.04071	−	6.34324i	−0.298166	−	0.622006i
$105$	0.320260	−	0.440799i	0.0312541	−	0.0430176i
$106$	−3.79442	−	1.97213i	−0.368547	−	0.191550i
$107$	−2.14976	−	6.61628i	−0.207825	−	0.639620i	−0.999586	−	0.0287882i	$-0.990835\pi$
$107$	−2.14976	−	6.61628i	−0.207825	−	0.639620i	0.791760	−	0.610832i	$-0.209165\pi$
$108$	0.427419	+	1.39158i	0.0411284	+	0.133904i
$109$			11.3681i			1.08887i	0.838804	+	0.544433i	$0.183255\pi$
$109$			11.3681i			1.08887i	−0.838804	+	0.544433i	$0.816745\pi$
$110$	4.01612	−	2.42297i	0.382922	−	0.231021i
$111$			0.666791i			0.0632890i
$112$	−17.9120	−	0.579060i	−1.69252	−	0.0547160i
$113$	1.41923	+	4.36795i	0.133510	+	0.410902i	0.995355	−	0.0962694i	$-0.0306910\pi$
$113$	1.41923	+	4.36795i	0.133510	+	0.410902i	−0.861845	+	0.507172i	$0.830691\pi$
$114$	0.555687	−	1.06915i	0.0520449	−	0.100136i
$115$	2.06383	−	2.84062i	0.192453	−	0.264889i
$116$	−12.3213	+	8.65128i	−1.14401	+	0.803252i
$117$	7.06094	+	2.29424i	0.652784	+	0.212102i
$118$	−0.949987	−	6.32848i	−0.0874534	−	0.582584i
$119$	4.14607	+	5.70657i	0.380070	+	0.523121i
$120$	0.302604	+	0.163540i	0.0276238	+	0.0149291i
$121$	−1.69579	+	10.8685i	−0.154162	+	0.988046i
$122$	6.79571	+	1.13269i	0.615255	+	0.102549i
$123$	0.267642	−	0.194453i	0.0241324	−	0.0175332i
$124$	−0.216661	−	0.00350120i	−0.0194567	−	0.000314417i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	13.4823	−	13.2662i	1.20110	−	1.18185i
$127$	8.92935	+	6.48756i	0.792352	+	0.575677i	0.908661	−	0.417536i	$-0.137106\pi$
$127$	8.92935	+	6.48756i	0.792352	+	0.575677i	−0.116308	+	0.993213i	$0.537106\pi$
$128$	−1.13540	−	11.2566i	−0.100356	−	0.994952i
$129$	−1.11833	+	0.363367i	−0.0984635	+	0.0319927i
$130$	3.14664	−	1.57140i	0.275979	−	0.137821i
$131$	−18.2532			−1.59479			−0.797396	−	0.603456i	$-0.793790\pi$
$131$	−18.2532			−1.59479			−0.797396	+	0.603456i	$0.793790\pi$
$132$	−0.749822	+	0.297482i	−0.0652636	+	0.0258925i
$133$	−31.3897			−2.72183
$134$	−7.50034	+	3.74560i	−0.647930	+	0.323570i
$135$	−0.692244	+	0.224924i	−0.0595789	+	0.0193584i
$136$	−3.22414	+	3.07151i	−0.276467	+	0.263380i
$137$	−6.65097	−	4.83221i	−0.568231	−	0.412844i	0.266231	−	0.963909i	$-0.414222\pi$
$137$	−6.65097	−	4.83221i	−0.568231	−	0.412844i	−0.834462	+	0.551065i	$0.814222\pi$
$138$	−0.430437	+	0.423538i	−0.0366412	+	0.0360539i
$139$	3.16377	−	9.73710i	0.268348	−	0.825890i	−0.722555	−	0.691313i	$-0.757033\pi$
$139$	3.16377	−	9.73710i	0.268348	−	0.825890i	0.990903	−	0.134577i	$-0.0429674\pi$
$140$	0.144784	−	8.95949i	0.0122365	−	0.757215i
$141$	−0.643314	+	0.467395i	−0.0541768	+	0.0393618i
$142$	19.6356	+	3.27281i	1.64779	+	0.274648i
$143$	−1.91636	+	8.02285i	−0.160254	+	0.670904i
$144$	9.42852	+	7.32712i	0.785710	+	0.610594i
$145$	−4.42462	−	6.08997i	−0.367445	−	0.505744i
$146$	−3.19079	−	21.2559i	−0.264072	−	1.75915i
$147$	1.51205	+	0.491295i	0.124712	+	0.0405213i
$148$	6.30143	+	8.97462i	0.517974	+	0.737709i
$149$	13.4501	−	18.5124i	1.10187	−	1.51660i	0.268991	−	0.963143i	$-0.413310\pi$
$149$	13.4501	−	18.5124i	1.10187	−	1.51660i	0.832881	−	0.553453i	$-0.186690\pi$
$150$	−0.0793147	+	0.152603i	−0.00647602	+	0.0124600i
$151$	1.41979	+	4.36966i	0.115541	+	0.355598i	0.992059	−	0.125770i	$-0.0401401\pi$
$151$	1.41979	+	4.36966i	0.115541	+	0.355598i	−0.876519	+	0.481368i	$0.840140\pi$
$152$	−2.62470	−	19.6417i	−0.212891	−	1.59315i
$153$		−	4.69984i		−	0.379960i
$154$	15.8847	+	13.7583i	1.28002	+	1.10867i
$155$		−	0.108344i		−	0.00870244i
$156$	−0.578241	+	0.177605i	−0.0462963	+	0.0142198i
$157$	3.12247	+	9.60996i	0.249200	+	0.766959i	0.994917	+	0.100696i	$0.0321070\pi$
$157$	3.12247	+	9.60996i	0.249200	+	0.766959i	−0.745717	+	0.666263i	$0.767893\pi$
$158$	2.77009	+	1.43974i	0.220376	+	0.114539i
$159$	−0.216146	+	0.297500i	−0.0171415	+	0.0235933i
$160$	5.61839	−	0.658565i	0.444173	−	0.0520641i
$161$	14.9614	+	4.86125i	1.17912	+	0.383120i
$162$	−12.4011	+	1.86156i	−0.974319	+	0.146258i
$163$	−7.92005	−	10.9010i	−0.620346	−	0.853833i	0.377032	−	0.926200i	$-0.376945\pi$
$163$	−7.92005	−	10.9010i	−0.620346	−	0.853833i	−0.997378	+	0.0723671i	$0.976945\pi$
$164$	1.76465	−	5.14655i	0.137796	−	0.401878i
$165$	−0.154779	−	0.372459i	−0.0120496	−	0.0289959i
$166$	−2.17263	+	13.0350i	−0.168629	+	1.01171i
$167$	12.1175	−	8.80388i	0.937680	−	0.681264i	−0.0101811	−	0.999948i	$-0.503241\pi$
$167$	12.1175	−	8.80388i	0.937680	−	0.681264i	0.947861	+	0.318684i	$0.103241\pi$
$168$	−0.277898	+	1.51583i	−0.0214403	+	0.116949i
$169$	2.10585	−	6.48114i	0.161989	−	0.498550i
$170$	−1.56160	−	1.58704i	−0.119770	−	0.121721i
$171$	16.9204	+	12.2934i	1.29393	+	0.940097i
$172$	−11.6181	+	15.4594i	−0.885873	+	1.17877i
$173$	3.56847	−	1.15946i	0.271305	−	0.0881525i	−0.170205	−	0.985409i	$-0.554443\pi$
$173$	3.56847	−	1.15946i	0.271305	−	0.0881525i	0.441510	+	0.897256i	$0.354443\pi$
$174$	0.578411	+	1.15824i	0.0438492	+	0.0878056i
$175$	4.48033			0.338681
$176$	−7.28085	+	11.0901i	−0.548815	+	0.835944i
$177$	−0.550297			−0.0413628
$178$	−2.51040	−	5.02694i	−0.188163	−	0.376785i
$179$	−3.37551	+	1.09677i	−0.252298	+	0.0819765i	−0.432435	−	0.901665i	$-0.642346\pi$
$179$	−3.37551	+	1.09677i	−0.252298	+	0.0819765i	0.180138	+	0.983641i	$0.442346\pi$
$180$	−3.58691	+	4.77284i	−0.267353	+	0.355746i
$181$	10.3603	+	7.52720i	0.770075	+	0.559492i	0.901984	−	0.431770i	$-0.142111\pi$
$181$	10.3603	+	7.52720i	0.770075	+	0.559492i	−0.131909	+	0.991262i	$0.542111\pi$
$182$	11.0523	+	11.2324i	0.819253	+	0.832599i
$183$	0.183074	−	0.563443i	0.0135332	−	0.0416509i
$184$	−1.79084	+	9.76837i	−0.132023	+	0.720134i
$185$	−4.43582	+	3.22281i	−0.326128	+	0.236946i
$186$	−0.00306352	+	0.0183800i	−0.000224628	+	0.00134769i
$187$	5.20504	−	0.415669i	0.380630	−	0.0303967i
$188$	−4.24157	+	12.3704i	−0.309349	+	0.902207i
$189$	−1.91682	−	2.63828i	−0.139428	−	0.191906i
$190$	9.79835	−	1.47086i	0.710847	−	0.106707i
$191$	0.680513	+	0.221112i	0.0492402	+	0.0159991i	0.333534	−	0.942738i	$-0.391759\pi$
$191$	0.680513	+	0.221112i	0.0492402	+	0.0159991i	−0.284293	+	0.958737i	$0.591759\pi$
$192$	−0.971747	−	0.0471427i	−0.0701298	−	0.00340223i
$193$	−1.69178	+	2.32854i	−0.121777	+	0.167612i	−0.865553	−	0.500817i	$-0.833033\pi$
$193$	−1.69178	+	2.32854i	−0.121777	+	0.167612i	0.743776	+	0.668429i	$0.233033\pi$
$194$	−10.9228	−	5.67708i	−0.784214	−	0.407591i
$195$	−0.0934624	−	0.287648i	−0.00669298	−	0.0205989i
$196$	24.9943	−	7.67692i	1.78531	−	0.548351i
$197$		−	18.4594i		−	1.31518i	−0.753378	−	0.657588i	$-0.771577\pi$
$197$		−	18.4594i		−	1.31518i	0.753378	−	0.657588i	$-0.228423\pi$
$198$	−3.17426	−	13.6373i	−0.225584	−	0.969163i
$199$		−	9.53878i		−	0.676186i	−0.941113	−	0.338093i	$-0.890218\pi$
$199$		−	9.53878i		−	0.676186i	0.941113	−	0.338093i	$-0.109782\pi$
$200$	0.374630	+	2.80351i	0.0264903	+	0.198238i
$201$	0.222777	+	0.685638i	0.0157135	+	0.0483612i
$202$	−2.29764	+	4.42071i	−0.161661	+	0.311040i
$203$	19.8237	−	27.2851i	1.39135	−	1.91504i
$204$	0.220042	+	0.313388i	0.0154060	+	0.0219415i
$205$	2.58719	+	0.840630i	0.180697	+	0.0587122i
$206$	2.72718	+	18.1675i	0.190012	+	1.26579i
$207$	−6.16097	−	8.47985i	−0.428217	−	0.589390i
$208$	−6.10435	+	7.85506i	−0.423261	+	0.544651i
$209$	−12.1183	+	19.8264i	−0.838241	+	1.37142i
$210$	−0.760060	−	0.126685i	−0.0524491	−	0.00874207i
$211$	−2.62136	+	1.90453i	−0.180462	+	0.131113i	−0.674349	−	0.738413i	$-0.735576\pi$
$211$	−2.62136	+	1.90453i	−0.180462	+	0.131113i	0.493887	+	0.869526i	$0.335576\pi$
$212$	−0.0977160	+	6.04684i	−0.00671116	+	0.415299i
$213$	0.528976	−	1.62802i	0.0362449	−	0.111550i
$214$	−7.01275	+	6.90034i	−0.479382	+	0.471697i
$215$	−7.82254	−	5.68341i	−0.533493	−	0.387605i
$216$	1.49059	−	1.42003i	0.101422	−	0.0966208i
$217$	0.461661	−	0.150003i	0.0313396	−	0.0101828i
$218$	14.3831	−	7.18280i	0.974149	−	0.486481i
$219$	−1.84832			−0.124898
$220$	−5.60312	−	3.55035i	−0.377762	−	0.239365i
$221$	3.91552			0.263386
$222$	0.843636	−	0.421304i	0.0566212	−	0.0282761i
$223$	7.74647	−	2.51698i	0.518742	−	0.168549i	−0.0379325	−	0.999280i	$-0.512077\pi$
$223$	7.74647	−	2.51698i	0.518742	−	0.168549i	0.556674	+	0.830731i	$0.312077\pi$
$224$	10.5848	+	23.0284i	0.707228	+	1.53865i
$225$	−2.41509	−	1.75466i	−0.161006	−	0.116978i
$226$	4.62969	−	4.55548i	0.307962	−	0.303026i
$227$	−0.982420	+	3.02358i	−0.0652055	+	0.200682i	−0.978351	−	0.206951i	$-0.933646\pi$
$227$	−0.982420	+	3.02358i	−0.0652055	+	0.200682i	0.913146	+	0.407633i	$0.133646\pi$
$228$	−1.70382	−	0.0275335i	−0.112838	−	0.00182345i
$229$	−7.15271	+	5.19675i	−0.472665	+	0.343411i	−0.798479	−	0.602023i	$-0.794362\pi$
$229$	−7.15271	+	5.19675i	−0.472665	+	0.343411i	0.325814	+	0.945434i	$0.394362\pi$
$230$	−4.89802	−	0.816387i	−0.322966	−	0.0538310i
$231$	1.37277	−	1.17519i	0.0903217	−	0.0773219i
$232$	18.7309	+	10.1230i	1.22974	+	0.664606i
$233$	−3.54030	−	4.87281i	−0.231933	−	0.319228i	0.677149	−	0.735846i	$-0.263215\pi$
$233$	−3.54030	−	4.87281i	−0.231933	−	0.319228i	−0.909082	+	0.416618i	$0.863215\pi$
$234$	−1.55866	−	10.3832i	−0.101893	−	0.678773i
$235$	−6.21868	−	2.02057i	−0.405662	−	0.131808i
$236$	−7.40668	+	5.20052i	−0.482134	+	0.338525i
$237$	0.157796	−	0.217187i	0.0102499	−	0.0141078i
$238$	4.60042	−	8.85132i	0.298201	−	0.573746i
$239$	5.86606	+	18.0539i	0.379444	+	1.16781i	0.940431	+	0.339984i	$0.110422\pi$
$239$	5.86606	+	18.0539i	0.379444	+	1.16781i	−0.560987	+	0.827824i	$0.689578\pi$
$240$	0.0157176	−	0.486191i	0.00101457	−	0.0313835i
$241$		−	28.7168i		−	1.84981i	−0.380194	−	0.924907i	$-0.624143\pi$
$241$		−	28.7168i		−	1.84981i	0.380194	−	0.924907i	$-0.375857\pi$
$242$	14.8225	−	4.72159i	0.952826	−	0.303516i
$243$			3.26195i			0.209254i
$244$	−2.86069	−	9.31374i	−0.183137	−	0.596251i
$245$	4.03988	+	12.4335i	0.258099	+	0.794346i
$246$	−0.415132	−	0.215763i	−0.0264679	−	0.0137565i
$247$	−10.2418	+	14.0966i	−0.651671	+	0.896948i
$248$	0.132465	+	0.276335i	0.00841152	+	0.0175473i
$249$	1.08075	+	0.351157i	0.0684897	+	0.0222537i
$250$	−1.39854	+	0.209940i	−0.0884517	+	0.0132777i
$251$	7.09600	+	9.76681i	0.447896	+	0.616476i	0.971944	−	0.235213i	$-0.0755788\pi$
$251$	7.09600	+	9.76681i	0.447896	+	0.616476i	−0.524048	+	0.851689i	$0.675579\pi$
$252$	−25.3034	−	8.67601i	−1.59396	−	0.546537i
$253$	8.84648	−	7.57322i	0.556173	−	0.476124i
$254$	2.56627	−	15.3967i	0.161022	−	0.966074i
$255$	−0.154896	+	0.112538i	−0.00969994	+	0.00704742i
$256$	−13.5247	+	8.54887i	−0.845292	+	0.534305i
$257$	−3.93935	+	12.1241i	−0.245730	+	0.756280i	0.749785	+	0.661681i	$0.230157\pi$
$257$	−3.93935	+	12.1241i	−0.245730	+	0.756280i	−0.995516	+	0.0945985i	$0.969843\pi$
$258$	1.16634	+	1.18534i	0.0726134	+	0.0737963i
$259$	−19.8739	−	14.4392i	−1.23490	−	0.897211i
$260$	−3.97633	−	2.98832i	−0.246602	−	0.185328i
$261$	−21.3717	+	6.94408i	−1.32287	+	0.429828i
$262$	11.5331	+	23.0943i	0.712517	+	1.42677i
$263$	4.94683			0.305034			0.152517	−	0.988301i	$-0.451262\pi$
$263$	4.94683			0.305034			0.152517	+	0.988301i	$0.451262\pi$
$264$	0.850147	+	0.760728i	0.0523229	+	0.0468196i
$265$	−3.02381			−0.185751
$266$	19.8332	+	39.7148i	1.21605	+	2.43507i
$267$	−0.459534	+	0.149312i	−0.0281230	+	0.00913773i
$268$	9.47800	+	7.12296i	0.578961	+	0.435104i
$269$	−4.06187	−	2.95112i	−0.247656	−	0.179933i	0.457031	−	0.889451i	$-0.348913\pi$
$269$	−4.06187	−	2.95112i	−0.247656	−	0.179933i	−0.704688	+	0.709518i	$0.748913\pi$
$270$	0.721964	+	0.733725i	0.0439373	+	0.0446531i
$271$	4.08329	−	12.5671i	0.248042	−	0.763395i	−0.747079	−	0.664735i	$-0.768544\pi$
$271$	4.08329	−	12.5671i	0.248042	−	0.763395i	0.995121	−	0.0986599i	$-0.0314556\pi$
$272$	5.92327	+	2.13854i	0.359151	+	0.129668i
$273$	1.09628	−	0.796495i	0.0663500	−	0.0482061i
$274$	−1.91147	+	11.4681i	−0.115476	+	0.692814i
$275$	1.72968	−	2.82988i	0.104304	−	0.170648i
$276$	0.807835	+	0.276990i	0.0486259	+	0.0166729i
$277$	8.66048	+	11.9201i	0.520358	+	0.716211i	0.985623	−	0.168960i	$-0.0540409\pi$
$277$	8.66048	+	11.9201i	0.520358	+	0.716211i	−0.465265	+	0.885172i	$0.654041\pi$
$278$	−14.3186	+	2.14940i	−0.858770	+	0.128912i
$279$	−0.307601	−	0.0999457i	−0.0184156	−	0.00598359i
$280$	−11.4272	+	5.47776i	−0.682906	+	0.327359i
$281$	−12.8826	+	17.7313i	−0.768509	+	1.05776i	0.227949	+	0.973673i	$0.426798\pi$
$281$	−12.8826	+	17.7313i	−0.768509	+	1.05776i	−0.996458	+	0.0840890i	$0.973202\pi$
$282$	0.997828	+	0.518615i	0.0594198	+	0.0308831i
$283$	−7.66102	−	23.5782i	−0.455400	−	1.40158i	−0.870665	−	0.491877i	$-0.836311\pi$
$283$	−7.66102	−	23.5782i	−0.455400	−	1.40158i	0.415265	−	0.909701i	$-0.363689\pi$
$284$	−8.26572	−	26.9113i	−0.490480	−	1.59689i
$285$		−	0.852021i		−	0.0504694i
$286$	11.3615	−	2.64453i	0.671819	−	0.156374i
$287$			12.1880i			0.719435i
$288$	3.31312	−	16.5587i	0.195228	−	0.975731i
$289$	4.48734	+	13.8106i	0.263961	+	0.812389i
$290$	−4.90950	+	9.44599i	−0.288296	+	0.554688i
$291$	−0.622211	+	0.856400i	−0.0364746	+	0.0502030i
$292$	−24.8774	+	17.4674i	−1.45584	+	1.02220i
$293$	14.2666	+	4.63550i	0.833464	+	0.270809i	0.694504	−	0.719489i	$-0.255624\pi$
$293$	14.2666	+	4.63550i	0.833464	+	0.270809i	0.138960	+	0.990298i	$0.455624\pi$
$294$	−0.333775	−	2.22350i	−0.0194662	−	0.129677i
$295$	−2.65976	−	3.66084i	−0.154857	−	0.213143i
$296$	7.37338	−	13.6432i	0.428569	−	0.792995i
$297$	−2.40641	+	0.192173i	−0.139634	+	0.0111510i
$298$	−31.9205	−	5.32042i	−1.84911	−	0.308204i
$299$	7.06471	−	5.13281i	0.408563	−	0.296838i
$300$	0.243191	+	0.00392992i	0.0140406	+	0.000226894i
$301$	13.3870	−	41.2009i	0.771612	−	2.37478i
$302$	4.63150	−	4.55726i	0.266513	−	0.262241i
$303$	0.346604	+	0.251822i	0.0199119	+	0.0144668i
$304$	−23.1926	+	15.7312i	−1.33019	+	0.902245i
$305$	4.63315	−	1.50540i	0.265293	−	0.0861991i
$306$	−5.94633	+	2.96954i	−0.339929	+	0.169757i
$307$	−12.1423			−0.692997			−0.346498	−	0.938051i	$-0.612629\pi$
$307$	−12.1423			−0.692997			−0.346498	+	0.938051i	$0.612629\pi$
$308$	7.37071	−	28.7906i	0.419985	−	1.64050i
$309$	1.57977			0.0898700
$310$	−0.137080	+	0.0684562i	−0.00778559	+	0.00388805i
$311$	20.9169	−	6.79632i	1.18609	−	0.385384i	0.351464	−	0.936201i	$-0.385684\pi$
$311$	20.9169	−	6.79632i	1.18609	−	0.385384i	0.834626	+	0.550817i	$0.185684\pi$
$312$	0.590064	+	0.619384i	0.0334058	+	0.0350657i
$313$	1.19019	+	0.864725i	0.0672736	+	0.0488771i	0.620914	−	0.783879i	$-0.286762\pi$
$313$	1.19019	+	0.864725i	0.0672736	+	0.0488771i	−0.553640	+	0.832756i	$0.686762\pi$
$314$	10.1858	−	10.0225i	0.574819	−	0.565605i
$315$	4.13302	−	12.7201i	0.232869	−	0.716697i
$316$	0.0713368	−	4.41445i	0.00401301	−	0.248332i
$317$	2.97489	−	2.16139i	0.167087	−	0.121396i	−0.501100	−	0.865390i	$-0.667071\pi$
$317$	2.97489	−	2.16139i	0.167087	−	0.121396i	0.668186	+	0.743994i	$0.267071\pi$
$318$	0.512972	+	0.0855006i	0.0287660	+	0.00479464i
$319$	−9.58070	−	23.0548i	−0.536416	−	1.29082i
$320$	−4.38314	−	6.69239i	−0.245025	−	0.374116i
$321$	0.497279	+	0.684445i	0.0277554	+	0.0382020i
$322$	−3.30263	−	22.0010i	−0.184048	−	1.22607i
$323$	10.4904	+	3.40853i	0.583700	+	0.189656i
$324$	10.1907	+	14.5138i	0.566152	+	0.806325i
$325$	1.46184	−	2.01205i	0.0810883	−	0.111608i
$326$	−8.78798	+	16.9083i	−0.486721	+	0.936463i
$327$	−0.427212	−	1.31482i	−0.0236249	−	0.0727100i
$328$	−7.62648	+	1.01912i	−0.421102	+	0.0562714i
$329$		−	29.2955i		−	1.61512i
$330$	−0.373446	+	0.431164i	−0.0205575	+	0.0237348i
$331$			7.23140i			0.397474i	0.980053	+	0.198737i	$0.0636839\pi$
$331$			7.23140i			0.397474i	−0.980053	+	0.198737i	$0.936316\pi$
$332$	17.8648	−	5.48713i	0.980461	−	0.301146i
$333$	5.05793	+	15.5667i	0.277173	+	0.853051i
$334$	−18.7951	−	9.76867i	−1.02842	−	0.534518i
$335$	−3.48444	+	4.79593i	−0.190376	+	0.262029i
$336$	2.09344	−	0.606156i	0.114207	−	0.0330685i
$337$	3.79749	+	1.23388i	0.206862	+	0.0672137i	0.410615	−	0.911809i	$-0.365314\pi$
$337$	3.79749	+	1.23388i	0.206862	+	0.0672137i	−0.203753	+	0.979022i	$0.565314\pi$
$338$	−9.53063	+	1.43067i	−0.518398	+	0.0778182i
$339$	−0.328295	−	0.451859i	−0.0178305	−	0.0245416i
$340$	−1.02128	+	2.97853i	−0.0553865	+	0.161533i
$341$	0.0834839	−	0.349506i	0.00452091	−	0.0189268i
$342$	4.86287	−	29.1754i	0.262954	−	1.57762i
$343$	−22.0138	+	15.9940i	−1.18863	+	0.863593i
$344$	26.9003	+	4.93165i	1.45037	+	0.265897i
$345$	−0.131951	+	0.406102i	−0.00710398	+	0.0218638i
$346$	−3.72167	−	3.78230i	−0.200078	−	0.203338i
$347$	0.628694	+	0.456773i	0.0337501	+	0.0245209i	0.604532	−	0.796581i	$-0.293360\pi$
$347$	0.628694	+	0.456773i	0.0337501	+	0.0245209i	−0.570782	+	0.821101i	$0.693360\pi$
$348$	1.09996	−	1.46363i	0.0589640	−	0.0784590i
$349$	2.32768	−	0.756308i	0.124598	−	0.0404843i	−0.246054	−	0.969256i	$-0.579134\pi$
$349$	2.32768	−	0.756308i	0.124598	−	0.0404843i	0.370652	+	0.928772i	$0.379134\pi$
$350$	−2.83084	−	5.66860i	−0.151315	−	0.302999i
$351$	−1.81023			−0.0966230
$352$	18.6317	+	2.20475i	0.993071	+	0.117514i
$353$	−23.9837			−1.27652			−0.638261	−	0.769820i	$-0.720346\pi$
$353$	−23.9837			−1.27652			−0.638261	+	0.769820i	$0.720346\pi$
$354$	0.347699	+	0.696246i	0.0184800	+	0.0370051i
$355$	13.3871	−	4.34973i	0.710514	−	0.230860i
$356$	−4.77401	+	6.35243i	−0.253022	+	0.336678i
$357$	−0.693983	−	0.504208i	−0.0367295	−	0.0266855i
$358$	3.52044	+	3.57778i	0.186061	+	0.189092i
$359$	−7.91130	+	24.3485i	−0.417542	+	1.28506i	0.492415	+	0.870361i	$0.336114\pi$
$359$	−7.91130	+	24.3485i	−0.417542	+	1.28506i	−0.909957	+	0.414703i	$0.863886\pi$
$360$	8.30504	+	1.52257i	0.437714	+	0.0802464i
$361$	−24.3397	+	17.6838i	−1.28104	+	0.930729i
$362$	2.97752	−	17.8640i	0.156495	−	0.938912i
$363$	−0.212304	−	1.32077i	−0.0111431	−	0.0693224i
$364$	7.22813	−	21.0807i	0.378857	−	1.10493i
$365$	−8.93353	−	12.2959i	−0.467602	−	0.643599i
$366$	−0.828552	+	0.124376i	−0.0433091	+	0.00650126i
$367$	10.5262	+	3.42016i	0.549461	+	0.178531i	0.570574	−	0.821246i	$-0.306721\pi$
$367$	10.5262	+	3.42016i	0.549461	+	0.178531i	−0.0211127	+	0.999777i	$0.506721\pi$
$368$	13.4907	−	3.90622i	0.703249	−	0.203626i
$369$	4.77327	−	6.56985i	0.248487	−	0.342013i
$370$	6.88028	+	3.57599i	0.357689	+	0.185907i
$371$	−4.18646	−	12.8846i	−0.217350	−	0.668936i
$372$	0.0251904	−	0.00773715i	0.00130606	−	0.000401152i
$373$			21.3483i			1.10537i	0.833389	+	0.552687i	$0.186398\pi$
$373$			21.3483i			1.10537i	−0.833389	+	0.552687i	$0.813602\pi$
$374$	−3.81466	−	6.32288i	−0.197251	−	0.326948i
$375$			0.121611i			0.00627998i
$376$	18.3313	−	2.44959i	0.945365	−	0.126328i
$377$	−5.78523	−	17.8051i	−0.297955	−	0.917010i
$378$	−2.12688	+	4.09216i	−0.109395	+	0.210478i
$379$	−15.3462	+	21.1222i	−0.788281	+	1.08498i	0.206039	+	0.978544i	$0.433942\pi$
$379$	−15.3462	+	21.1222i	−0.788281	+	1.08498i	−0.994320	+	0.106432i	$0.966058\pi$
$380$	−8.05193	−	11.4677i	−0.413055	−	0.588282i
$381$	−1.27656	−	0.414780i	−0.0654003	−	0.0212498i
$382$	−0.150219	−	1.00070i	−0.00768586	−	0.0512005i
$383$	5.47232	+	7.53200i	0.279622	+	0.384867i	0.925609	−	0.378482i	$-0.123554\pi$
$383$	5.47232	+	7.53200i	0.279622	+	0.384867i	−0.645986	+	0.763349i	$0.723554\pi$
$384$	0.554341	+	1.25926i	0.0282886	+	0.0642613i
$385$	14.4530	+	3.45228i	0.736592	+	0.175944i
$386$	4.01504	+	0.669216i	0.204360	+	0.0340622i
$387$	−23.3519	+	16.9662i	−1.18705	+	0.862439i
$388$	−0.281291	+	17.4068i	−0.0142804	+	0.883696i
$389$	−8.60379	+	26.4797i	−0.436230	+	1.34258i	0.455592	+	0.890189i	$0.349428\pi$
$389$	−8.60379	+	26.4797i	−0.436230	+	1.34258i	−0.891821	+	0.452388i	$0.850572\pi$
$390$	−0.304884	+	0.299997i	−0.0154384	+	0.0151910i
$391$	−4.47220	−	3.24924i	−0.226169	−	0.164321i
$392$	−25.5053	−	26.7727i	−1.28821	−	1.35222i
$393$	2.11115	−	0.685955i	0.106494	−	0.0346019i
$394$	−23.3551	+	11.6633i	−1.17662	+	0.587590i
$395$	2.20751			0.111072
$396$	−15.2486	+	12.6327i	−0.766271	+	0.634818i
$397$	−21.7027			−1.08923			−0.544613	−	0.838687i	$-0.683323\pi$
$397$	−21.7027			−1.08923			−0.544613	+	0.838687i	$0.683323\pi$
$398$	−12.0687	+	6.02697i	−0.604947	+	0.302105i
$399$	3.63050	−	1.17962i	0.181752	−	0.0590549i
$400$	3.31035	−	2.24535i	0.165517	−	0.112268i
$401$	9.00139	+	6.53989i	0.449508	+	0.326587i	0.789401	−	0.613877i	$-0.210391\pi$
$401$	9.00139	+	6.53989i	0.449508	+	0.326587i	−0.339894	+	0.940464i	$0.610391\pi$
$402$	0.726723	−	0.715074i	0.0362457	−	0.0356647i
$403$	0.0832665	−	0.256268i	0.00414780	−	0.0127656i
$404$	7.04491	+	0.113845i	0.350497	+	0.00566398i
$405$	−7.17365	+	5.21196i	−0.356461	+	0.258984i
$406$	−47.0470	−	7.84166i	−2.33490	−	0.389175i
$407$	−16.7927	+	6.97840i	−0.832383	+	0.345906i
$408$	0.257473	−	0.476411i	0.0127468	−	0.0235859i
$409$	14.5054	+	19.9650i	0.717248	+	0.987207i	0.999611	+	0.0278994i	$0.00888181\pi$
$409$	14.5054	+	19.9650i	0.717248	+	0.987207i	−0.282363	+	0.959308i	$0.591118\pi$
$410$	−0.571106	−	3.80451i	−0.0282049	−	0.187891i
$411$	0.950840	+	0.308947i	0.0469015	+	0.0152392i
$412$	21.2628	−	14.9294i	1.04754	−	0.735521i
$413$	11.9166	−	16.4018i	0.586377	−	0.807079i
$414$	−6.83613	+	13.1529i	−0.335978	+	0.646429i
$415$	2.88754	+	8.88692i	0.141744	+	0.436242i
$416$	13.7953	+	2.76022i	0.676372	+	0.135331i
$417$			1.24508i			0.0609717i
$418$	32.7416	+	2.80523i	1.60144	+	0.137208i
$419$			18.8311i			0.919958i	0.887930	+	0.459979i	$0.152143\pi$
$419$			18.8311i			0.919958i	−0.887930	+	0.459979i	$0.847857\pi$
$420$	0.319951	+	1.04169i	0.0156120	+	0.0508291i
$421$	6.03082	+	18.5610i	0.293924	+	0.904605i	0.983581	+	0.180469i	$0.0577615\pi$
$421$	6.03082	+	18.5610i	0.293924	+	0.904605i	−0.689657	+	0.724137i	$0.742239\pi$
$422$	4.06593	+	2.11324i	0.197926	+	0.102871i
$423$	−11.4732	+	15.7915i	−0.557847	+	0.767811i
$424$	7.71232	−	3.69699i	0.374543	−	0.179542i
$425$	−1.49732	−	0.486508i	−0.0726306	−	0.0235991i
$426$	−2.39403	+	0.359375i	−0.115991	+	0.0174118i
$427$	12.8292	+	17.6578i	0.620847	+	0.854523i
$428$	13.1614	+	4.51277i	0.636179	+	0.218133i
$429$	−0.0798536	−	0.999932i	−0.00385537	−	0.0482772i
$430$	−2.24818	+	13.4882i	−0.108417	+	0.650460i
$431$	17.6347	−	12.8124i	0.849435	−	0.617151i	−0.0755552	−	0.997142i	$-0.524073\pi$
$431$	17.6347	−	12.8124i	0.849435	−	0.617151i	0.924990	+	0.379991i	$0.124073\pi$
$432$	−2.73846	−	0.988694i	−0.131754	−	0.0475686i
$433$	5.42192	−	16.6870i	0.260561	−	0.801924i	−0.732122	−	0.681173i	$-0.761470\pi$
$433$	5.42192	−	16.6870i	0.260561	−	0.801924i	0.992683	−	0.120750i	$-0.0385300\pi$
$434$	−0.481481	−	0.489325i	−0.0231118	−	0.0234883i
$435$	0.740608	+	0.538083i	0.0355094	+	0.0257991i
$436$	−18.1756	−	13.6595i	−0.870455	−	0.654170i
$437$	23.3958	−	7.60177i	1.11918	−	0.363642i
$438$	1.16784	+	2.33853i	0.0558016	+	0.111740i
$439$	13.9299			0.664839			0.332419	−	0.943132i	$-0.392135\pi$
$439$	13.9299			0.664839			0.332419	+	0.943132i	$0.392135\pi$
$440$	−0.951710	+	9.33243i	−0.0453710	+	0.444906i
$441$	39.0267			1.85841
$442$	−2.47397	−	4.95399i	−0.117675	−	0.235637i
$443$	−14.9426	+	4.85516i	−0.709946	+	0.230676i	−0.641659	−	0.766990i	$-0.721754\pi$
$443$	−14.9426	+	4.85516i	−0.709946	+	0.230676i	−0.0682875	+	0.997666i	$0.521754\pi$
$444$	−1.06608	−	0.801189i	−0.0505941	−	0.0380228i
$445$	−3.21437	−	2.33537i	−0.152376	−	0.110707i
$446$	−8.07904	−	8.21066i	−0.382554	−	0.388786i
$447$	−0.859926	+	2.64658i	−0.0406731	+	0.125179i
$448$	22.4481	−	27.9424i	1.06057	−	1.32015i
$449$	12.7789	−	9.28442i	0.603074	−	0.438159i	−0.243895	−	0.969802i	$-0.578425\pi$
$449$	12.7789	−	9.28442i	0.603074	−	0.438159i	0.846969	+	0.531643i	$0.178425\pi$
$450$	−0.694090	+	4.16428i	−0.0327197	+	0.196306i
$451$	7.69822	+	4.70531i	0.362495	+	0.221564i
$452$	−8.68890	−	2.97925i	−0.408691	−	0.140132i
$453$	−0.328423	−	0.452035i	−0.0154307	−	0.0212385i
$454$	4.44622	−	0.667435i	0.208671	−	0.0313243i
$455$	10.5973	+	3.44329i	0.496811	+	0.161424i
$456$	1.04170	+	2.17310i	0.0487822	+	0.101765i
$457$	10.7256	−	14.7626i	0.501724	−	0.690563i	−0.480773	−	0.876845i	$-0.659644\pi$
$457$	10.7256	−	14.7626i	0.501724	−	0.690563i	0.982496	+	0.186282i	$0.0596437\pi$
$458$	11.0944	+	5.76625i	0.518407	+	0.269439i
$459$	0.354114	+	1.08985i	0.0165286	+	0.0508699i
$460$	2.06185	+	6.71289i	0.0961340	+	0.312990i
$461$		−	9.08512i		−	0.423136i	−0.977363	−	0.211568i	$-0.932143\pi$
$461$		−	9.08512i		−	0.423136i	0.977363	−	0.211568i	$-0.0678570\pi$
$462$	−2.35424	−	0.994327i	−0.109529	−	0.0462603i
$463$			40.2474i			1.87046i	0.354045	+	0.935229i	$0.384806\pi$
$463$			40.2474i			1.87046i	−0.354045	+	0.935229i	$0.615194\pi$
$464$	0.972907	−	30.0947i	0.0451661	−	1.39711i
$465$	0.00407158	+	0.0125310i	0.000188815	+	0.000581112i
$466$	−3.92828	+	7.55809i	−0.181974	+	0.350122i
$467$	9.90989	−	13.6398i	0.458575	−	0.631174i	−0.515637	−	0.856807i	$-0.672445\pi$
$467$	9.90989	−	13.6398i	0.458575	−	0.631174i	0.974212	+	0.225632i	$0.0724449\pi$
$468$	−12.1522	+	8.53256i	−0.561737	+	0.394418i
$469$	−25.2599	−	8.20743i	−1.16639	−	0.378984i
$470$	1.37273	+	9.14467i	0.0633195	+	0.421812i
$471$	−0.722283	−	0.994138i	−0.0332811	−	0.0458075i
$472$	11.2596	+	6.08519i	0.518266	+	0.280094i
$473$	−20.8552	−	24.3615i	−0.958924	−	1.12015i
$474$	−0.374491	−	0.0624191i	−0.0172009	−	0.00286700i
$475$	5.66806	−	4.11809i	0.260068	−	0.188951i
$476$	−14.1056	−	0.227944i	−0.646529	−	0.0104478i
$477$	−2.78941	+	8.58492i	−0.127718	+	0.393077i
$478$	19.1357	−	18.8290i	0.875247	−	0.861218i
$479$	17.1183	+	12.4372i	0.782156	+	0.568269i	0.905625	−	0.424079i	$-0.139402\pi$
$479$	17.1183	+	12.4372i	0.782156	+	0.568269i	−0.123470	+	0.992348i	$0.539402\pi$
$480$	−0.625069	+	0.287308i	−0.0285304	+	0.0131137i
$481$	−12.9689	+	4.21385i	−0.591331	+	0.192135i
$482$	−36.3331	+	18.1444i	−1.65493	+	0.826454i
$483$	−1.91311			−0.0870493
$484$	−15.3393	−	15.7704i	−0.697240	−	0.716838i
$485$	−8.70453			−0.395252
$486$	4.12708	−	2.06102i	0.187208	−	0.0934899i
$487$	−24.6508	+	8.00953i	−1.11703	+	0.362947i	−0.808635	−	0.588310i	$-0.799793\pi$
$487$	−24.6508	+	8.00953i	−1.11703	+	0.362947i	−0.308400	+	0.951257i	$0.599793\pi$
$488$	−9.97643	+	9.50418i	−0.451612	+	0.430234i
$489$	1.32569	+	0.963167i	0.0599495	+	0.0435559i
$490$	13.1785	−	12.9673i	0.595345	−	0.585802i
$491$	−0.915445	+	2.81745i	−0.0413134	+	0.127150i	−0.969586	−	0.244751i	$-0.921294\pi$
$491$	−0.915445	+	2.81745i	−0.0413134	+	0.127150i	0.928273	+	0.371901i	$0.121294\pi$
$492$	−0.0106907	+	0.661560i	−0.000481975	+	0.0298254i
$493$	−9.58789	+	6.96601i	−0.431817	+	0.313733i
$494$	24.3065	+	4.05134i	1.09360	+	0.182278i
$495$	−6.43872	−	7.52125i	−0.289399	−	0.338055i
$496$	0.265929	−	0.342196i	0.0119406	−	0.0153651i
$497$	37.0688	+	51.0209i	1.66276	+	2.28860i
$498$	−0.238568	−	1.58926i	−0.0106905	−	0.0712164i
$499$	−13.5983	−	4.41837i	−0.608745	−	0.197793i	−0.0116082	−	0.999933i	$-0.503695\pi$
$499$	−13.5983	−	4.41837i	−0.608745	−	0.197793i	−0.597137	+	0.802139i	$0.703695\pi$
$500$	1.14927	+	1.63682i	0.0513971	+	0.0732007i
$501$	−1.07065	+	1.47362i	−0.0478331	+	0.0658366i
$502$	7.87363	−	15.1490i	0.351417	−	0.676135i
$503$	−1.85269	−	5.70198i	−0.0826072	−	0.254239i	0.901219	−	0.433364i	$-0.142673\pi$
$503$	−1.85269	−	5.70198i	−0.0826072	−	0.254239i	−0.983826	+	0.179125i	$0.942673\pi$
$504$	5.01057	+	37.4961i	0.223188	+	1.67021i
$505$			3.52291i			0.156768i
$506$	−15.1713	−	6.40769i	−0.674448	−	0.284856i
$507$			0.828741i			0.0368057i
$508$	−21.1016	+	6.48131i	−0.936234	+	0.287562i
$509$	−1.73926	−	5.35290i	−0.0770914	−	0.237263i	0.905083	−	0.425235i	$-0.139809\pi$
$509$	−1.73926	−	5.35290i	−0.0770914	−	0.237263i	−0.982174	+	0.187972i	$0.939809\pi$
$510$	0.240255	+	0.124871i	0.0106387	+	0.00552938i
$511$	40.0251	−	55.0899i	1.77061	−	2.43703i
$512$	19.3616	+	11.7102i	0.855670	+	0.517522i
$513$	−4.84994	−	1.57584i	−0.214130	−	0.0695750i
$514$	17.8287	−	2.67631i	0.786389	−	0.118047i
$515$	7.63552	+	10.5094i	0.336461	+	0.463099i
$516$	0.762779	−	2.22463i	0.0335795	−	0.0979337i
$517$	−18.5037	−	11.3099i	−0.813794	−	0.497407i
$518$	−5.71171	+	34.2681i	−0.250958	+	1.50565i
$519$	−0.369153	+	0.268205i	−0.0162040	+	0.0117729i
$520$	−1.26848	+	6.91907i	−0.0556265	+	0.303421i
$521$	5.38618	−	16.5769i	0.235973	−	0.726249i	−0.761018	−	0.648730i	$-0.775300\pi$
$521$	5.38618	−	16.5769i	0.235973	−	0.726249i	0.996991	−	0.0775187i	$-0.0246997\pi$
$522$	22.2892	+	22.6523i	0.975573	+	0.991466i
$523$	14.8461	+	10.7863i	0.649175	+	0.471653i	0.862990	−	0.505221i	$-0.168589\pi$
$523$	14.8461	+	10.7863i	0.649175	+	0.471653i	−0.213815	+	0.976874i	$0.568589\pi$
$524$	21.9324	−	29.1838i	0.958120	−	1.27490i
$525$	−0.518191	+	0.168370i	−0.0226157	+	0.00734829i
$526$	−3.12559	−	6.25882i	−0.136282	−	0.272898i
$527$	−0.170575			−0.00743035
$528$	0.425333	−	1.55628i	0.0185103	−	0.0677284i
$529$	10.6715			0.463977
$530$	1.91056	+	3.82579i	0.0829895	+	0.166182i
$531$	−12.8471	+	4.17427i	−0.557516	+	0.181148i
$532$	37.7166	−	50.1867i	1.63522	−	2.17587i
$533$	5.47345	+	3.97670i	0.237082	+	0.172250i
$534$	0.479263	+	0.487071i	0.0207397	+	0.0210776i
$535$	−2.14976	+	6.61628i	−0.0929422	+	0.286047i
$536$	3.02355	−	16.4923i	0.130597	−	0.712359i
$537$	0.349192	−	0.253703i	0.0150688	−	0.0109481i
$538$	−1.16737	+	7.00378i	−0.0503289	+	0.301955i
$539$	3.45165	+	43.2218i	0.148673	+	1.86169i
$540$	0.472159	−	1.37704i	0.0203185	−	0.0592583i
$541$	−3.95511	−	5.44374i	−0.170044	−	0.234045i	0.715487	−	0.698626i	$-0.246205\pi$
$541$	−3.95511	−	5.44374i	−0.170044	−	0.234045i	−0.885530	+	0.464581i	$0.846205\pi$
$542$	−18.4801	+	2.77410i	−0.793787	+	0.119158i
$543$	−1.48113	−	0.481250i	−0.0635616	−	0.0206524i
$544$	−1.03683	−	8.84545i	−0.0444536	−	0.379245i
$545$	6.68200	−	9.19699i	0.286226	−	0.393956i
$546$	−1.70041	−	0.883781i	−0.0727710	−	0.0378223i
$547$	10.6735	+	32.8498i	0.456368	+	1.40456i	0.869522	+	0.493895i	$0.164427\pi$
$547$	10.6735	+	32.8498i	0.456368	+	1.40456i	−0.413154	+	0.910661i	$0.635573\pi$
$548$	15.7174	−	4.82756i	0.671415	−	0.206223i
$549$		−	14.5427i		−	0.620667i
$550$	−4.67329	−	0.400397i	−0.199270	−	0.0170730i
$551$		−	52.7393i		−	2.24677i
$552$	−0.159967	−	1.19710i	−0.00680866	−	0.0509520i
$553$	3.05630	+	9.40631i	0.129967	+	0.399997i
$554$	9.60956	−	18.4890i	0.408271	−	0.785523i
$555$	0.391930	−	0.539445i	0.0166365	−	0.0228982i
$556$	11.7665	+	16.7580i	0.499010	+	0.710699i
$557$	−12.9381	−	4.20384i	−0.548204	−	0.178122i	0.0218025	−	0.999762i	$-0.493059\pi$
$557$	−12.9381	−	4.20384i	−0.548204	−	0.178122i	−0.570007	+	0.821640i	$0.693059\pi$
$558$	0.0679010	+	0.452333i	0.00287448	+	0.0191488i
$559$	−14.1348	−	19.4549i	−0.597839	−	0.822854i
$560$	14.1507	+	10.9969i	0.597977	+	0.464702i
$561$	−0.586389	+	0.243681i	−0.0247574	+	0.0102882i
$562$	30.5737	+	5.09594i	1.28967	+	0.214959i
$563$	24.0393	−	17.4656i	1.01314	−	0.736086i	0.0482710	−	0.998834i	$-0.484629\pi$
$563$	24.0393	−	17.4656i	1.01314	−	0.736086i	0.964864	+	0.262748i	$0.0846289\pi$
$564$	0.0256966	−	1.59015i	0.00108202	−	0.0669575i
$565$	1.41923	−	4.36795i	0.0597076	−	0.183761i
$566$	−24.9911	+	24.5905i	−1.05045	+	1.03361i
$567$	−32.1403	−	23.3513i	−1.34977	−	0.980662i
$568$	−28.8261	+	27.4615i	−1.20952	+	1.15226i
$569$	10.6998	−	3.47659i	0.448560	−	0.145746i	−0.0760214	−	0.997106i	$-0.524222\pi$
$569$	10.6998	−	3.47659i	0.448560	−	0.145746i	0.524582	+	0.851360i	$0.324222\pi$
$570$	−1.07799	+	0.538340i	−0.0451522	+	0.0225486i
$571$	26.4616			1.10738			0.553692	−	0.832721i	$-0.313218\pi$
$571$	26.4616			1.10738			0.553692	+	0.832721i	$0.313218\pi$
$572$	−10.5245	−	12.7039i	−0.440053	−	0.531176i
$573$	−0.0870168			−0.00363518
$574$	15.4205	−	7.70085i	0.643639	−	0.321427i
$575$	−3.33935	+	1.08502i	−0.139261	+	0.0452485i
$576$	−23.0438	+	6.27060i	−0.960156	+	0.261275i
$577$	−12.8562	−	9.34055i	−0.535209	−	0.388852i	0.287094	−	0.957903i	$-0.407311\pi$
$577$	−12.8562	−	9.34055i	−0.535209	−	0.388852i	−0.822303	+	0.569050i	$0.807311\pi$
$578$	14.6382	−	14.4036i	0.608868	−	0.599109i
$579$	0.108164	−	0.332894i	0.00449513	−	0.0138346i
$580$	15.0533	+	0.243258i	0.625053	+	0.0101008i
$581$	−33.8698	+	24.6078i	−1.40516	+	1.02091i
$582$	1.47667	+	0.246127i	0.0612099	+	0.0102023i
$583$	−9.75445	−	2.32997i	−0.403988	−	0.0964977i
$584$	37.8185	+	20.4388i	1.56494	+	0.845763i
$585$	−4.36390	−	6.00639i	−0.180425	−	0.248334i
$586$	−3.14926	−	20.9793i	−0.130095	−	0.866646i
$587$	−30.3271	−	9.85387i	−1.25173	−	0.406713i	−0.393192	−	0.919456i	$-0.628629\pi$
$587$	−30.3271	−	9.85387i	−1.25173	−	0.406713i	−0.858542	+	0.512744i	$0.828629\pi$
$588$	−2.60232	+	1.82719i	−0.107318	+	0.0753520i
$589$	0.446172	−	0.614103i	0.0183842	−	0.0253037i
$590$	−2.95123	+	5.67824i	−0.121500	+	0.233769i
$591$	0.693701	+	2.13499i	0.0285351	+	0.0878219i
$592$	−21.9204	−	0.708647i	−0.900924	−	0.0291252i
$593$			36.4226i			1.49570i	0.663870	+	0.747848i	$0.268913\pi$
$593$			36.4226i			1.49570i	−0.663870	+	0.747848i	$0.731087\pi$
$594$	1.76360	+	2.92321i	0.0723614	+	0.119941i
$595$		−	7.05371i		−	0.289174i
$596$	13.4371	+	43.7481i	0.550405	+	1.79199i
$597$	0.358467	+	1.10325i	0.0146711	+	0.0451529i
$598$	−10.9579	−	5.69530i	−0.448101	−	0.232898i
$599$	2.96698	−	4.08370i	0.121228	−	0.166856i	−0.744090	−	0.668079i	$-0.767117\pi$
$599$	2.96698	−	4.08370i	0.121228	−	0.166856i	0.865318	+	0.501224i	$0.167117\pi$
$600$	−0.148685	−	0.310173i	−0.00607004	−	0.0126627i
$601$	−35.0117	−	11.3760i	−1.42816	−	0.464036i	−0.509972	−	0.860191i	$-0.670344\pi$
$601$	−35.0117	−	11.3760i	−1.42816	−	0.464036i	−0.918183	+	0.396155i	$0.870344\pi$
$602$	−60.5865	+	9.09482i	−2.46932	+	0.370677i
$603$	10.4018	+	14.3169i	0.423594	+	0.583027i
$604$	−8.69230	−	2.98041i	−0.353685	−	0.121271i
$605$	7.76026	−	7.79604i	0.315500	−	0.316954i
$606$	0.0996131	−	0.597641i	0.00404650	−	0.0242775i
$607$	29.6894	−	21.5706i	1.20506	−	0.875525i	0.210285	−	0.977640i	$-0.432561\pi$
$607$	29.6894	−	21.5706i	1.20506	−	0.875525i	0.994773	+	0.102115i	$0.0325609\pi$
$608$	34.5574	+	19.4042i	1.40149	+	0.786945i
$609$	−1.26743	+	3.90074i	−0.0513587	+	0.158066i
$610$	−4.83207	−	4.91078i	−0.195645	−	0.198832i
$611$	−13.1562	−	9.55854i	−0.532243	−	0.386697i
$612$	7.51424	+	5.64714i	0.303745	+	0.228272i
$613$	40.4082	−	13.1294i	1.63207	−	0.530292i	0.657326	−	0.753607i	$-0.271688\pi$
$613$	40.4082	−	13.1294i	1.63207	−	0.530292i	0.974746	+	0.223314i	$0.0716877\pi$
$614$	7.67196	+	15.3627i	0.309615	+	0.619986i
$615$	−0.330823			−0.0133401
$616$	−41.0835	+	8.86545i	−1.65530	+	0.357199i
$617$	8.90031			0.358313			0.179157	−	0.983821i	$-0.442663\pi$
$617$	8.90031			0.358313			0.179157	+	0.983821i	$0.442663\pi$
$618$	−0.998159	−	1.99876i	−0.0401518	−	0.0804017i
$619$	37.3028	−	12.1204i	1.49933	−	0.487161i	0.559505	−	0.828827i	$-0.310991\pi$
$619$	37.3028	−	12.1204i	1.49933	−	0.487161i	0.939821	+	0.341666i	$0.110991\pi$
$620$	0.173224	+	0.130182i	0.00695685	+	0.00522825i
$621$	2.06760	+	1.50220i	0.0829699	+	0.0602811i
$622$	−21.8150	−	22.1703i	−0.874700	−	0.888949i
$623$	5.50085	−	16.9299i	0.220387	−	0.678281i
$624$	0.410832	−	1.13791i	0.0164464	−	0.0455529i
$625$	−0.809017	+	0.587785i	−0.0323607	+	0.0235114i
$626$	0.342058	−	2.05222i	0.0136714	−	0.0820232i
$627$	0.656518	−	2.74851i	0.0262188	−	0.109765i
$628$	−19.1165	−	6.55467i	−0.762832	−	0.261560i
$629$	5.07391	+	6.98364i	0.202310	+	0.278456i
$630$	−18.7051	+	2.80788i	−0.745231	+	0.111869i
$631$	−38.1771	−	12.4045i	−1.51981	−	0.493815i	−0.574085	−	0.818796i	$-0.694642\pi$
$631$	−38.1771	−	12.4045i	−1.51981	−	0.493815i	−0.945720	+	0.324981i	$0.894642\pi$
$632$	−5.63032	+	2.69896i	−0.223962	+	0.107359i
$633$	0.231612	−	0.318787i	0.00920576	−	0.0126706i
$634$	−4.61428	−	2.39825i	−0.183256	−	0.0952465i
$635$	−3.41071	−	10.4971i	−0.135350	−	0.416564i
$636$	−0.215938	−	0.703044i	−0.00856250	−	0.0278775i
$637$			32.5138i			1.28824i
$638$	−23.1160	+	26.6886i	−0.915170	+	1.05661i
$639$		−	42.0199i		−	1.66228i
$640$	−5.69790	+	9.77414i	−0.225229	+	0.386357i
$641$	−13.3611	−	41.1212i	−0.527731	−	1.62419i	−0.758851	−	0.651265i	$-0.774239\pi$
$641$	−13.3611	−	41.1212i	−0.527731	−	1.62419i	0.231119	−	0.972925i	$-0.425761\pi$
$642$	0.551774	−	1.06163i	0.0217768	−	0.0418990i
$643$	−20.2347	+	27.8507i	−0.797979	+	1.09832i	0.195089	+	0.980785i	$0.437500\pi$
$643$	−20.2347	+	27.8507i	−0.797979	+	1.09832i	−0.993068	+	0.117538i	$0.962500\pi$
$644$	−25.7493	+	18.0796i	−1.01466	+	0.712436i
$645$	1.11833	+	0.363367i	0.0440342	+	0.0143076i
$646$	−2.31568	−	15.4263i	−0.0911093	−	0.606939i
$647$	−10.2966	−	14.1721i	−0.404801	−	0.557161i	0.557140	−	0.830419i	$-0.311899\pi$
$647$	−10.2966	−	14.1721i	−0.404801	−	0.557161i	−0.961941	+	0.273258i	$0.911899\pi$
$648$	11.9243	−	22.0639i	0.468431	−	0.866753i
$649$	−5.75921	−	13.8589i	−0.226069	−	0.544008i
$650$	−3.46933	−	0.578258i	−0.136078	−	0.0226812i
$651$	−0.0477582	+	0.0346983i	−0.00187179	+	0.00135994i
$652$	26.9453	+	0.435431i	1.05526	+	0.0170528i
$653$	−11.8594	+	36.4994i	−0.464093	+	1.42833i	0.396028	+	0.918239i	$0.370388\pi$
$653$	−11.8594	+	36.4994i	−0.464093	+	1.42833i	−0.860120	+	0.510092i	$0.829612\pi$
$654$	−1.39361	+	1.37127i	−0.0544946	+	0.0536211i
$655$	14.7672	+	10.7290i	0.577001	+	0.419216i
$656$	6.10811	+	9.00526i	0.238482	+	0.351596i
$657$	−43.1505	+	14.0204i	−1.68346	+	0.546990i
$658$	−37.0653	+	18.5100i	−1.44496	+	0.721597i
$659$	−40.0343			−1.55951			−0.779757	−	0.626082i	$-0.784657\pi$
$659$	−40.0343			−1.55951			−0.779757	+	0.626082i	$0.784657\pi$
$660$	0.781474	+	0.200066i	0.0304188	+	0.00778755i
$661$	32.7231			1.27278			0.636390	−	0.771368i	$-0.280427\pi$
$661$	32.7231			1.27278			0.636390	+	0.771368i	$0.280427\pi$
$662$	9.14931	−	4.56907i	0.355598	−	0.177582i
$663$	−0.452865	+	0.147145i	−0.0175878	+	0.00571463i
$664$	−18.2301	−	19.1360i	−0.707466	−	0.742619i
$665$	25.3948	+	18.4504i	0.984767	+	0.715475i
$666$	16.4995	−	16.2350i	0.639344	−	0.629095i
$667$	−8.16762	+	25.1373i	−0.316251	+	0.973321i
$668$	−0.484023	+	29.9522i	−0.0187274	+	1.15888i
$669$	−0.801361	+	0.582223i	−0.0309824	+	0.0225100i
$670$	8.26951	+	1.37834i	0.319479	+	0.0532498i
$671$	16.1059	−	1.28620i	0.621763	−	0.0496533i
$672$	−2.08964	−	2.26567i	−0.0806095	−	0.0874001i
$673$	−5.11446	−	7.03945i	−0.197148	−	0.271351i	0.698985	−	0.715136i	$-0.253635\pi$
$673$	−5.11446	−	7.03945i	−0.197148	−	0.271351i	−0.896133	+	0.443785i	$0.853635\pi$
$674$	−0.838271	−	5.58427i	−0.0322890	−	0.215098i
$675$	0.692244	+	0.224924i	0.0266445	+	0.00865732i
$676$	7.83193	+	11.1544i	0.301228	+	0.429015i
$677$	19.3870	−	26.6840i	0.745105	−	1.02555i	−0.253204	−	0.967413i	$-0.581484\pi$
$677$	19.3870	−	26.6840i	0.745105	−	1.02555i	0.998309	−	0.0581357i	$-0.0185156\pi$
$678$	−0.364271	+	0.700866i	−0.0139898	+	0.0269166i
$679$	−12.0514	−	37.0904i	−0.462490	−	1.42340i
$680$	4.41377	−	0.589807i	0.169260	−	0.0226181i
$681$		−	0.386624i		−	0.0148154i
$682$	−0.494950	+	0.115206i	−0.0189526	+	0.00441145i
$683$		−	32.2020i		−	1.23218i	−0.787677	−	0.616088i	$-0.788717\pi$
$683$		−	32.2020i		−	1.23218i	0.787677	−	0.616088i	$-0.211283\pi$
$684$	−39.9858	+	12.2815i	−1.52890	+	0.469596i
$685$	2.54045	+	7.81869i	0.0970654	+	0.298737i
$686$	34.1450	+	17.7467i	1.30366	+	0.677572i
$687$	0.631983	−	0.869850i	0.0241117	−	0.0331868i
$688$	−10.7570	−	37.1508i	−0.410107	−	1.41636i
$689$	−7.15225	−	2.32391i	−0.272479	−	0.0885338i
$690$	0.597180	−	0.0896445i	0.0227343	−	0.00341271i
$691$	−9.77927	−	13.4600i	−0.372021	−	0.512043i	0.581428	−	0.813598i	$-0.302494\pi$
$691$	−9.77927	−	13.4600i	−0.372021	−	0.512043i	−0.953449	+	0.301555i	$0.902494\pi$
$692$	−2.43394	+	7.09853i	−0.0925246	+	0.269846i
$693$	23.1340	−	37.8488i	0.878787	−	1.43776i
$694$	0.180685	−	1.08404i	0.00685872	−	0.0411497i
$695$	−8.28287	+	6.01786i	−0.314187	+	0.228270i
$696$	−2.54682	−	0.466910i	−0.0965368	−	0.0176982i
$697$	1.32347	−	4.07321i	0.0501299	−	0.154284i
$698$	−2.42761	−	2.46716i	−0.0918865	−	0.0933834i
$699$	0.592588	+	0.430541i	0.0224137	+	0.0162845i
$700$	−5.38339	+	7.16327i	−0.203473	+	0.270746i
$701$	2.83741	−	0.921930i	0.107167	−	0.0348208i	−0.254942	−	0.966956i	$-0.582057\pi$
$701$	2.83741	−	0.921930i	0.107167	−	0.0348208i	0.362110	+	0.932135i	$0.382057\pi$
$702$	1.14377	+	2.29034i	0.0431690	+	0.0864433i
$703$	−38.4143			−1.44882
$704$	−8.98270	−	24.9662i	−0.338548	−	0.940949i
$705$	0.795180			0.0299482
$706$	15.1538	+	30.3446i	0.570321	+	1.14203i
$707$	−15.0113	+	4.87747i	−0.564558	+	0.183436i
$708$	0.661215	−	0.879830i	0.0248500	−	0.0330660i
$709$	−3.22718	−	2.34469i	−0.121199	−	0.0880566i	0.525534	−	0.850772i	$-0.323865\pi$
$709$	−3.22718	−	2.34469i	−0.121199	−	0.0880566i	−0.646734	+	0.762716i	$0.723865\pi$
$710$	−13.9619	−	14.1893i	−0.523979	−	0.532515i
$711$	2.03639	−	6.26736i	0.0763705	−	0.235044i
$712$	11.0536	+	2.02647i	0.414252	+	0.0759451i
$713$	−0.307766	+	0.223605i	−0.0115259	+	0.00837406i
$714$	−0.199449	+	1.19662i	−0.00746419	+	0.0447824i
$715$	6.26608	−	5.36421i	0.234338	−	0.200610i
$716$	2.30234	−	6.71470i	0.0860424	−	0.250940i
$717$	−1.35693	−	1.86765i	−0.0506753	−	0.0697486i
$718$	35.8048	−	5.37477i	1.33622	−	0.200585i
$719$	23.6939	+	7.69862i	0.883634	+	0.287110i	0.715465	−	0.698648i	$-0.246215\pi$
$719$	23.6939	+	7.69862i	0.883634	+	0.287110i	0.168169	+	0.985758i	$0.446215\pi$
$720$	−3.32106	−	11.4697i	−0.123768	−	0.427451i
$721$	−34.2097	+	47.0856i	−1.27403	+	1.75356i
$722$	37.7527	+	19.6218i	1.40501	+	0.730246i
$723$	1.07918	+	3.32136i	0.0401350	+	0.123523i
$724$	−24.4832	+	7.51995i	−0.909912	+	0.279477i
$725$			7.52761i			0.279569i
$726$	−1.53692	+	1.10312i	−0.0570405	+	0.0409408i
$727$		−	24.6077i		−	0.912650i	−0.889813	−	0.456325i	$-0.849165\pi$
$727$		−	24.6077i		−	0.912650i	0.889813	−	0.456325i	$-0.150835\pi$
$728$	−31.2387	+	4.17439i	−1.15778	+	0.154713i
$729$	8.09768	+	24.9221i	0.299914	+	0.923041i
$730$	−9.91253	+	19.0719i	−0.366879	+	0.705884i
$731$	−8.94781	+	12.3156i	−0.330947	+	0.455509i
$732$	0.680874	+	0.969715i	0.0251658	+	0.0358417i
$733$	3.80395	+	1.23598i	0.140502	+	0.0456519i	0.378424	−	0.925632i	$-0.376466\pi$
$733$	3.80395	+	1.23598i	0.140502	+	0.0456519i	−0.237922	+	0.971284i	$0.576466\pi$
$734$	−2.32358	−	15.4789i	−0.0857650	−	0.571336i
$735$	−0.934499	−	1.28623i	−0.0344695	−	0.0474432i
$736$	−13.4661	−	14.6005i	−0.496369	−	0.538183i
$737$	−14.9358	+	12.7861i	−0.550169	+	0.470984i
$738$	−11.3282	−	1.88816i	−0.416998	−	0.0695041i
$739$	−9.37909	+	6.81431i	−0.345015	+	0.250668i	−0.746775	−	0.665077i	$-0.768399\pi$
$739$	−9.37909	+	6.81431i	−0.345015	+	0.250668i	0.401760	+	0.915745i	$0.368399\pi$
$740$	0.177185	−	10.9645i	0.00651344	−	0.403063i
$741$	0.654808	−	2.01529i	0.0240550	−	0.0740336i
$742$	−13.6567	+	13.4378i	−0.501353	+	0.493317i
$743$	−0.189782	−	0.137885i	−0.00696244	−	0.00505851i	0.584299	−	0.811539i	$-0.301370\pi$
$743$	−0.189782	−	0.137885i	−0.00696244	−	0.00505851i	−0.591261	+	0.806480i	$0.701370\pi$
$744$	−0.0257054	−	0.0269827i	−0.000942406	−	0.000989234i
$745$	−21.7626	+	7.07111i	−0.797321	+	0.259065i
$746$	27.0103	−	13.4887i	0.988918	−	0.493856i
$747$	27.8946			1.02061
$748$	−5.58959	+	8.82141i	−0.204376	+	0.322543i
$749$	−31.1686			−1.13888
$750$	0.153865	−	0.0768386i	0.00561835	−	0.00280575i
$751$	3.84996	−	1.25093i	0.140487	−	0.0456470i	−0.237930	−	0.971282i	$-0.576469\pi$
$751$	3.84996	−	1.25093i	0.140487	−	0.0456470i	0.378416	+	0.925635i	$0.376469\pi$
$752$	−14.6817	−	21.6454i	−0.535386	−	0.789326i
$753$	−1.18775	−	0.862953i	−0.0432841	−	0.0314478i
$754$	−18.8720	+	18.5695i	−0.687279	+	0.676263i
$755$	1.41979	−	4.36966i	0.0516714	−	0.159028i
$756$	6.52133	+	0.105384i	0.237178	+	0.00383277i
$757$	13.3925	−	9.73020i	0.486758	−	0.353650i	−0.317178	−	0.948366i	$-0.602735\pi$
$757$	13.3925	−	9.73020i	0.486758	−	0.353650i	0.803936	+	0.594716i	$0.202735\pi$
$758$	36.4205	+	6.07047i	1.32285	+	0.220489i
$759$	−0.738575	+	1.20836i	−0.0268086	+	0.0438608i
$760$	−9.42166	+	17.4332i	−0.341760	+	0.632369i
$761$	−18.4462	−	25.3890i	−0.668675	−	0.920352i	0.331055	−	0.943612i	$-0.392596\pi$
$761$	−18.4462	−	25.3890i	−0.668675	−	0.920352i	−0.999729	+	0.0232597i	$0.992596\pi$
$762$	0.281793	+	1.87721i	0.0102083	+	0.0680040i
$763$	48.4400	+	15.7391i	1.75365	+	0.569794i
$764$	−1.17120	+	0.822343i	−0.0423724	+	0.0297513i
$765$	−2.76250	+	3.80225i	−0.0998783	+	0.137471i
$766$	6.07201	−	11.6827i	0.219391	−	0.422113i
$767$	−3.47766	−	10.7031i	−0.125571	−	0.386468i
$768$	1.24299	−	1.49701i	0.0448524	−	0.0540187i
$769$			10.2709i			0.370377i	0.982703	+	0.185189i	$0.0592896\pi$
$769$			10.2709i			0.370377i	−0.982703	+	0.185189i	$0.940710\pi$
$770$	−4.76405	−	20.4675i	−0.171685	−	0.737596i
$771$		−	1.55030i		−	0.0558328i
$772$	−1.69015	−	5.50275i	−0.0608299	−	0.198048i
$773$	−3.52845	−	10.8595i	−0.126910	−	0.390588i	0.867335	−	0.497726i	$-0.165831\pi$
$773$	−3.52845	−	10.8595i	−0.126910	−	0.390588i	−0.994244	+	0.107138i	$0.965831\pi$
$774$	36.2206	+	18.8254i	1.30192	+	0.676666i
$775$	−0.0636833	+	0.0876525i	−0.00228757	+	0.00314857i
$776$	22.2011	−	10.6424i	0.796974	−	0.382039i
$777$	2.84122	+	0.923170i	0.101928	+	0.0331185i
$778$	38.9389	−	5.84523i	1.39603	−	0.209562i
$779$	11.2026	+	15.4190i	0.401374	+	0.552444i
$780$	0.572200	+	0.196196i	0.0204881	+	0.00702494i
$781$	46.5368	−	3.71638i	1.66522	−	0.132982i
$782$	−1.28530	+	7.71131i	−0.0459622	+	0.275756i
$783$	4.43270	−	3.22054i	0.158412	−	0.115093i
$784$	−17.7581	+	49.1858i	−0.634217	+	1.75664i
$785$	3.12247	−	9.60996i	0.111446	−	0.342994i
$786$	−2.20179	−	2.23766i	−0.0785353	−	0.0798146i
$787$	12.7259	+	9.24589i	0.453629	+	0.329580i	0.791027	−	0.611782i	$-0.209547\pi$
$787$	12.7259	+	9.24589i	0.453629	+	0.329580i	−0.337398	+	0.941362i	$0.609547\pi$
$788$	29.5133	+	22.1800i	1.05137	+	0.790131i
$789$	−0.572145	+	0.185901i	−0.0203689	+	0.00661826i
$790$	−1.39479	−	2.79299i	−0.0496244	−	0.0993700i
$791$	20.5770			0.731632
$792$	25.6178	+	11.3110i	0.910289	+	0.401919i
$793$	12.1158			0.430244
$794$	13.7126	+	27.4586i	0.486641	+	0.974471i
$795$	0.349732	−	0.113635i	0.0124037	−	0.00403021i
$796$	15.2509	+	11.4614i	0.540553	+	0.406239i
$797$	4.86101	+	3.53173i	0.172186	+	0.125100i	0.670540	−	0.741873i	$-0.266062\pi$
$797$	4.86101	+	3.53173i	0.172186	+	0.125100i	−0.498355	+	0.866973i	$0.666062\pi$
$798$	−3.78637	−	3.84805i	−0.134036	−	0.136220i
$799$	−3.18114	+	9.79053i	−0.112541	+	0.346364i
$800$	−4.93247	−	2.76962i	−0.174389	−	0.0979207i
$801$	−9.59556	+	6.97159i	−0.339043	+	0.246329i
$802$	2.58698	−	15.5209i	0.0913493	−	0.548061i
$803$	−19.3439	−	46.5488i	−0.682632	−	1.64267i
$804$	−1.36390	−	0.467653i	−0.0481010	−	0.0164929i
$805$	−9.24664	−	12.7269i	−0.325901	−	0.448565i
$806$	−0.376846	+	0.0565695i	−0.0132738	+	0.00199257i
$807$	0.580695	+	0.188679i	0.0204414	+	0.00664182i
$808$	−4.30720	−	8.98529i	−0.151527	−	0.316101i
$809$	−13.9523	+	19.2036i	−0.490535	+	0.675164i	−0.980487	−	0.196586i	$-0.937015\pi$
$809$	−13.9523	+	19.2036i	−0.490535	+	0.675164i	0.489951	+	0.871750i	$0.337015\pi$
$810$	11.1269	+	5.78312i	0.390958	+	0.203198i
$811$	16.7838	+	51.6551i	0.589357	+	1.81386i	0.581018	+	0.813890i	$0.302654\pi$
$811$	16.7838	+	51.6551i	0.589357	+	1.81386i	0.00833908	+	0.999965i	$0.497346\pi$
$812$	19.8047	+	64.4794i	0.695008	+	2.26278i
$813$			1.60695i			0.0563580i
$814$	19.4395	+	16.8372i	0.681353	+	0.590144i
$815$			13.4744i			0.471987i
$816$	−0.765446	−	0.0247455i	−0.0267960	−	0.000866264i
$817$	−20.9339	−	64.4278i	−0.732383	−	2.25404i
$818$	16.0950	−	30.9672i	0.562750	−	1.08274i
$819$	19.5517	−	26.9106i	0.683192	−	0.940333i
$820$	−4.45269	+	3.12641i	−0.155495	+	0.109179i
$821$	−5.50760	−	1.78953i	−0.192216	−	0.0624549i	0.211327	−	0.977415i	$-0.432222\pi$
$821$	−5.50760	−	1.78953i	−0.192216	−	0.0624549i	−0.403543	+	0.914961i	$0.632222\pi$
$822$	−0.209892	−	1.39823i	−0.00732082	−	0.0487687i
$823$	26.5574	+	36.5531i	0.925731	+	1.27416i	0.961501	+	0.274800i	$0.0886116\pi$
$823$	26.5574	+	36.5531i	0.925731	+	1.27416i	−0.0357700	+	0.999360i	$0.511388\pi$
$824$	−32.3237	−	17.4691i	−1.12605	−	0.608565i
$825$	−0.0937064	+	0.392302i	−0.00326244	+	0.0136582i
$826$	−28.2812	−	4.71383i	−0.984029	−	0.164015i
$827$	−1.16367	+	0.845457i	−0.0404648	+	0.0293994i	−0.607834	−	0.794064i	$-0.707961\pi$
$827$	−1.16367	+	0.845457i	−0.0404648	+	0.0293994i	0.567369	+	0.823464i	$0.307961\pi$
$828$	20.9606	+	0.338720i	0.728431	+	0.0117713i
$829$	0.930511	−	2.86382i	0.0323180	−	0.0994645i	−0.933596	−	0.358326i	$-0.883347\pi$
$829$	0.930511	−	2.86382i	0.0323180	−	0.0994645i	0.965914	+	0.258862i	$0.0833475\pi$
$830$	9.41945	−	9.26847i	0.326954	−	0.321713i
$831$	−1.44962	−	1.05321i	−0.0502868	−	0.0365355i
$832$	−5.22414	−	19.1981i	−0.181115	−	0.665576i
$833$	19.5750	−	6.36029i	0.678232	−	0.220371i
$834$	1.57530	−	0.786688i	0.0545481	−	0.0272408i
$835$	−14.9780			−0.518337
$836$	−17.1382	−	43.1978i	−0.592736	−	1.49403i
$837$	0.0788605			0.00272582
$838$	23.8254	−	11.8982i	0.823036	−	0.411016i
$839$	−48.7944	+	15.8542i	−1.68457	+	0.547349i	−0.985789	−	0.167988i	$-0.946273\pi$
$839$	−48.7944	+	15.8542i	−1.68457	+	0.547349i	−0.698779	+	0.715337i	$0.746273\pi$
$840$	1.11581	−	1.06299i	0.0384990	−	0.0366765i
$841$	22.3814	+	16.2611i	0.771773	+	0.560726i
$842$	19.6732	−	19.3578i	0.677982	−	0.667115i
$843$	0.823644	−	2.53491i	0.0283678	−	0.0873071i
$844$	0.104708	−	6.47952i	0.00360420	−	0.223034i
$845$	−5.51319	+	4.00557i	−0.189660	+	0.137796i
$846$	27.2290	+	4.53845i	0.936152	+	0.156035i
$847$	43.9634	+	22.2732i	1.51060	+	0.765317i
$848$	−9.55045	−	7.42188i	−0.327964	−	0.254868i
$849$	1.77213	+	2.43913i	0.0608194	+	0.0837108i
$850$	0.330524	+	2.20183i	0.0113369	+	0.0755222i
$851$	18.3096	+	5.94913i	0.627643	+	0.203934i
$852$	1.96733	+	2.80191i	0.0673996	+	0.0959918i
$853$	2.84735	−	3.91904i	0.0974915	−	0.134186i	−0.757484	−	0.652853i	$-0.773572\pi$
$853$	2.84735	−	3.91904i	0.0974915	−	0.134186i	0.854976	+	0.518668i	$0.173572\pi$
$854$	14.2351	−	27.3886i	0.487115	−	0.937219i
$855$	−6.46300	−	19.8911i	−0.221030	−	0.680260i
$856$	−2.60621	−	19.5034i	−0.0890785	−	0.666611i
$857$		−	34.2852i		−	1.17116i	−0.810614	−	0.585581i	$-0.800867\pi$
$857$		−	34.2852i		−	1.17116i	0.810614	−	0.585581i	$-0.199133\pi$
$858$	−1.21468	+	0.732828i	−0.0414685	+	0.0250183i
$859$			32.9123i			1.12295i	0.827492	+	0.561477i	$0.189767\pi$
$859$			32.9123i			1.12295i	−0.827492	+	0.561477i	$0.810233\pi$
$860$	18.4860	−	5.67794i	0.630369	−	0.193616i
$861$	−0.458024	−	1.40965i	−0.0156094	−	0.0480409i
$862$	−27.3528	−	14.2165i	−0.931639	−	0.484214i
$863$	−23.6324	+	32.5273i	−0.804457	+	1.10724i	0.187698	+	0.982227i	$0.439897\pi$
$863$	−23.6324	+	32.5273i	−0.804457	+	1.10724i	−0.992155	+	0.125014i	$0.960103\pi$
$864$	0.479349	+	4.08945i	0.0163078	+	0.139126i
$865$	−3.56847	−	1.15946i	−0.121331	−	0.0394230i
$866$	−24.5384	+	3.68354i	−0.833850	+	0.125172i
$867$	−1.03800	−	1.42869i	−0.0352525	−	0.0485209i
$868$	−0.314885	+	0.918353i	−0.0106879	+	0.0311709i
$869$	7.12116	+	1.70098i	0.241569	+	0.0577018i
$870$	0.212849	−	1.27701i	0.00721626	−	0.0432948i
$871$	−11.9276	+	8.66592i	−0.404152	+	0.293634i
$872$	−5.79816	+	31.6267i	−0.196350	+	1.07102i
$873$	−8.02976	+	24.7131i	−0.271766	+	0.836410i
$874$	−24.4003	−	24.7978i	−0.825352	−	0.838798i
$875$	−3.62466	−	2.63347i	−0.122536	−	0.0890276i
$876$	2.22087	−	2.95515i	0.0750363	−	0.0998453i
$877$	40.7169	−	13.2297i	1.37491	−	0.446736i	0.473918	−	0.880569i	$-0.342839\pi$
$877$	40.7169	−	13.2297i	1.37491	−	0.446736i	0.900993	+	0.433834i	$0.142839\pi$
$878$	−8.80145	−	17.6244i	−0.297035	−	0.594795i
$879$	−1.82426			−0.0615309
$880$	12.4089	−	4.69246i	0.418304	−	0.158183i
$881$	55.5720			1.87227			0.936134	−	0.351643i	$-0.114377\pi$
$881$	55.5720			1.87227			0.936134	+	0.351643i	$0.114377\pi$
$882$	−24.6585	−	49.3773i	−0.830296	−	1.66262i
$883$	18.8261	−	6.11696i	0.633547	−	0.205852i	0.0254014	−	0.999677i	$-0.491914\pi$
$883$	18.8261	−	6.11696i	0.633547	−	0.205852i	0.608146	+	0.793825i	$0.291914\pi$
$884$	−4.70473	+	6.26024i	−0.158237	+	0.210555i
$885$	0.445199	+	0.323456i	0.0149652	+	0.0108729i
$886$	15.5842	+	15.8381i	0.523561	+	0.532090i
$887$	12.3009	−	37.8582i	0.413023	−	1.27116i	−0.500984	−	0.865457i	$-0.667028\pi$
$887$	12.3009	−	37.8582i	0.413023	−	1.27116i	0.914007	−	0.405699i	$-0.132972\pi$
$888$	−0.340088	+	1.85505i	−0.0114126	+	0.0622515i
$889$	40.0064	−	29.0664i	1.34177	−	0.974855i
$890$	−0.923801	+	5.54246i	−0.0309659	+	0.185784i
$891$	−27.1573	+	11.2855i	−0.909804	+	0.378080i
$892$	−5.28363	+	15.4096i	−0.176909	+	0.515951i
$893$	−26.9270	−	37.0618i	−0.901076	−	1.24023i
$894$	3.89184	−	0.584216i	0.130163	−	0.0195391i
$895$	3.37551	+	1.09677i	0.112831	+	0.0366610i
$896$	−49.5368	−	10.7467i	−1.65491	−	0.359024i
$897$	−0.624207	+	0.859148i	−0.0208417	+	0.0286861i
$898$	−19.8210	−	10.3019i	−0.661436	−	0.343778i
$899$	0.252027	+	0.775658i	0.00840556	+	0.0258696i
$900$	5.70728	−	1.75297i	0.190243	−	0.0584325i
$901$			4.76062i			0.158599i
$902$	1.08922	−	12.7129i	0.0362669	−	0.423294i
$903$			5.26834i			0.175319i
$904$	1.72058	+	12.8758i	0.0572255	+	0.428242i
$905$	−3.95728	−	12.1793i	−0.131545	−	0.404852i
$906$	−0.364414	+	0.701140i	−0.0121068	+	0.0232938i
$907$	−11.0946	+	15.2704i	−0.368389	+	0.507044i	−0.952462	−	0.304657i	$-0.901458\pi$
$907$	−11.0946	+	15.2704i	−0.368389	+	0.507044i	0.584073	+	0.811701i	$0.301458\pi$
$908$	−3.65374	−	5.20373i	−0.121254	−	0.172692i
$909$	10.0019	+	3.24982i	0.331743	+	0.107790i
$910$	−2.33930	−	15.5836i	−0.0775469	−	0.516590i
$911$	2.42801	+	3.34186i	0.0804434	+	0.110721i	0.847342	−	0.531047i	$-0.178201\pi$
$911$	2.42801	+	3.34186i	0.0804434	+	0.110721i	−0.766899	+	0.641768i	$0.778201\pi$
$912$	2.09126	−	2.69103i	0.0692487	−	0.0891090i
$913$	2.46709	+	30.8931i	0.0816487	+	1.02241i
$914$	−25.4547	−	4.24272i	−0.841968	−	0.140337i
$915$	−0.479293	+	0.348227i	−0.0158449	+	0.0115120i
$916$	0.285709	−	17.6802i	0.00944009	−	0.584169i
$917$	−25.2716	+	77.7778i	−0.834540	+	2.56845i
$918$	1.15516	−	1.13664i	0.0381259	−	0.0375148i
$919$	4.84527	+	3.52029i	0.159831	+	0.116124i	0.664826	−	0.746998i	$-0.268506\pi$
$919$	4.84527	+	3.52029i	0.159831	+	0.116124i	−0.504995	+	0.863122i	$0.668506\pi$
$920$	7.19053	−	6.85015i	0.237065	−	0.225843i
$921$	1.40437	−	0.456306i	0.0462754	−	0.0150358i
$922$	−11.4947	+	5.74033i	−0.378557	+	0.189048i
$923$	35.0075			1.15229
$924$	0.229459	+	3.60689i	0.00754866	+	0.118658i
$925$	5.48297			0.180279
$926$	50.9218	−	25.4299i	1.67340	−	0.835677i
$927$	36.8809	−	11.9833i	1.21133	−	0.393584i
$928$	−38.6912	+	17.7841i	−1.27010	+	0.583790i
$929$	6.57619	+	4.77788i	0.215758	+	0.156757i	0.690415	−	0.723414i	$-0.257428\pi$
$929$	6.57619	+	4.77788i	0.215758	+	0.156757i	−0.474657	+	0.880171i	$0.657428\pi$
$930$	0.0132819	−	0.0130690i	0.000435531	−	0.000428550i
$931$	−28.3039	+	87.1103i	−0.927622	+	2.85493i
$932$	12.0447	+	0.194640i	0.394537	+	0.00637565i
$933$	−2.16383	+	1.57211i	−0.0708405	+	0.0514687i
$934$	−23.5188	−	3.92004i	−0.769558	−	0.128268i
$935$	−4.45529	−	2.72316i	−0.145704	−	0.0890569i
$936$	18.4738	+	9.98405i	0.603835	+	0.326339i
$937$	35.2642	+	48.5371i	1.15203	+	1.58564i	0.737098	+	0.675786i	$0.236196\pi$
$937$	35.2642	+	48.5371i	1.15203	+	1.58564i	0.414935	+	0.909851i	$0.363804\pi$
$938$	5.57595	+	37.1450i	0.182061	+	1.21283i
$939$	−0.170153	−	0.0552860i	−0.00555273	−	0.00180419i
$940$	10.7027	−	7.51476i	0.349083	−	0.245104i
$941$	−23.3083	+	32.0811i	−0.759829	+	1.04581i	0.237400	+	0.971412i	$0.423705\pi$
$941$	−23.3083	+	32.0811i	−0.759829	+	1.04581i	−0.997228	+	0.0744022i	$0.976295\pi$
$942$	−0.801436	+	1.54198i	−0.0261122	+	0.0502405i
$943$	−2.95162	−	9.08416i	−0.0961180	−	0.295821i
$944$	0.584840	−	18.0908i	0.0190349	−	0.588804i
$945$			3.26109i			0.106083i
$946$	−17.6456	+	41.7790i	−0.573707	+	1.35835i
$947$			46.8461i			1.52229i	0.648581	+	0.761146i	$0.275363\pi$
$947$			46.8461i			1.52229i	−0.648581	+	0.761146i	$0.724637\pi$
$948$	0.157644	+	0.513252i	0.00512004	+	0.0166697i
$949$	−11.6807	−	35.9494i	−0.379171	−	1.16697i
$950$	−8.79158	−	4.56938i	−0.285237	−	0.148250i
$951$	−0.262849	+	0.361780i	−0.00852345	+	0.0117315i
$952$	8.62405	+	17.9907i	0.279507	+	0.583082i
$953$	−40.2708	−	13.0848i	−1.30450	−	0.423858i	−0.427355	−	0.904084i	$-0.640555\pi$
$953$	−40.2708	−	13.0848i	−1.30450	−	0.423858i	−0.877145	+	0.480226i	$0.840555\pi$
$954$	12.6243	−	1.89507i	0.408726	−	0.0613550i
$955$	−0.420580	−	0.578879i	−0.0136096	−	0.0187321i
$956$	−35.9135	−	12.3140i	−1.16152	−	0.398263i
$957$	1.97449	+	2.30646i	0.0638263	+	0.0745572i
$958$	4.91976	−	29.5167i	0.158950	−	0.953642i
$959$	−29.7985	+	21.6499i	−0.962245	+	0.699112i
$960$	0.758450	+	0.609318i	0.0244789	+	0.0196656i
$961$	9.57590	−	29.4716i	0.308900	−	0.950696i
$962$	13.5257	+	13.7460i	0.436086	+	0.443190i
$963$	16.8012	+	12.2068i	0.541411	+	0.393358i
$964$	45.9133	+	34.5050i	1.47877	+	1.11133i
$965$	2.73736	−	0.889422i	0.0881187	−	0.0286315i
$966$	1.20877	+	2.42050i	0.0388916	+	0.0778783i
$967$	−0.818731			−0.0263286			−0.0131643	−	0.999913i	$-0.504190\pi$
$967$	−0.818731			−0.0263286			−0.0131643	+	0.999913i	$0.504190\pi$
$968$	−10.2611	+	29.3719i	−0.329805	+	0.944049i
$969$	−1.34140			−0.0430920
$970$	5.49985	+	11.0131i	0.176590	+	0.353611i
$971$	−15.1273	+	4.91516i	−0.485458	+	0.157735i	−0.541512	−	0.840693i	$-0.682148\pi$
$971$	−15.1273	+	4.91516i	−0.485458	+	0.157735i	0.0560541	+	0.998428i	$0.482148\pi$
$972$	−5.21529	−	3.91943i	−0.167281	−	0.125716i
$973$	−37.1100	−	26.9620i	−1.18969	−	0.864361i
$974$	25.7091	+	26.1280i	0.823774	+	0.837194i
$975$	−0.0934624	+	0.287648i	−0.00299319	+	0.00921210i
$976$	18.3284	+	6.61728i	0.586677	+	0.211814i
$977$	11.8690	−	8.62334i	0.379723	−	0.275885i	−0.381508	−	0.924365i	$-0.624595\pi$
$977$	11.8690	−	8.62334i	0.379723	−	0.275885i	0.761231	+	0.648480i	$0.224595\pi$
$978$	0.380999	−	2.28585i	0.0121830	−	0.0730934i
$979$	−8.56964	−	10.0104i	−0.273887	−	0.319935i
$980$	−24.7332	−	8.48051i	−0.790072	−	0.270900i
$981$	−19.9472	−	27.4549i	−0.636865	−	0.876569i
$982$	4.14311	−	0.621934i	0.132212	−	0.0198467i
$983$	−21.3149	−	6.92563i	−0.679839	−	0.220893i	−0.0513143	−	0.998683i	$-0.516341\pi$
$983$	−21.3149	−	6.92563i	−0.679839	−	0.220893i	−0.628525	+	0.777789i	$0.716341\pi$
$984$	0.843774	−	0.404473i	0.0268985	−	0.0128941i
$985$	−10.8501	+	14.9339i	−0.345714	+	0.475835i
$986$	14.8715	+	7.72939i	0.473606	+	0.246154i
$987$	1.10092	+	3.38830i	0.0350428	+	0.107851i
$988$	−10.2320	−	33.3129i	−0.325522	−	1.05982i
$989$			33.9505i			1.07956i
$990$	−5.44779	+	12.8986i	−0.173142	+	0.409945i
$991$			48.1472i			1.52945i	0.644359	+	0.764723i	$0.277124\pi$
$991$			48.1472i			1.52945i	−0.644359	+	0.764723i	$0.722876\pi$
$992$	−0.600977	−	0.120246i	−0.0190811	−	0.00381780i
$993$	−0.271755	−	0.836377i	−0.00862390	−	0.0265416i
$994$	41.1311	−	79.1371i	1.30460	−	2.51008i
$995$	−5.60676	+	7.71704i	−0.177746	+	0.244646i
$996$	−1.86003	+	1.30600i	−0.0589372	+	0.0413821i
$997$	−19.4645	−	6.32440i	−0.616447	−	0.200296i	−0.0158850	−	0.999874i	$-0.505057\pi$
$997$	−19.4645	−	6.32440i	−0.616447	−	0.200296i	−0.600562	+	0.799578i	$0.705057\pi$
$998$	3.00174	+	19.9966i	0.0950186	+	0.632980i
$999$	−2.34578	−	3.22869i	−0.0742172	−	0.102151i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.r.d.151.5	yes	48
4.3	odd	2	inner	220.2.r.d.151.4	yes	48
11.7	odd	10	inner	220.2.r.d.51.4	✓	48
44.7	even	10	inner	220.2.r.d.51.5	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.r.d.51.4	✓	48	11.7	odd	10	inner
220.2.r.d.51.5	yes	48	44.7	even	10	inner
220.2.r.d.151.4	yes	48	4.3	odd	2	inner
220.2.r.d.151.5	yes	48	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.631838 - 1.26522i) q^{2} +(-0.115659 + 0.0375799i) q^{3} +(-1.20156 + 1.59883i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(0.120625 + 0.122590i) q^{6} +(1.38450 - 4.26105i) q^{7} +(2.78206 + 0.510037i) q^{8} +(-2.41509 + 1.75466i) q^{9} +(-0.232509 + 1.39497i) q^{10} +(-2.15687 - 2.51950i) q^{11} +(0.0788876 - 0.230074i) q^{12} +(-1.46184 - 2.01205i) q^{13} +(-6.26594 + 0.940598i) q^{14} +(0.115659 + 0.0375799i) q^{15} +(-1.11250 - 3.84218i) q^{16} +(-0.925394 + 1.27370i) q^{17} +(3.74598 + 1.94695i) q^{18} +(-2.16501 - 6.66320i) q^{19} +(1.91185 - 0.587219i) q^{20} +0.544858i q^{21} +(-1.82493 + 4.32084i) q^{22} +3.51120i q^{23} +(-0.340938 + 0.0455592i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-1.62204 + 3.12084i) q^{26} +(0.427830 - 0.588858i) q^{27} +(5.14912 + 7.33348i) q^{28} +(7.15919 + 2.32616i) q^{29} +(-0.0255310 - 0.170079i) q^{30} +(0.0636833 + 0.0876525i) q^{31} +(-4.15828 + 3.83520i) q^{32} +(0.344145 + 0.210348i) q^{33} +(2.19620 + 0.366057i) q^{34} +(-3.62466 + 2.63347i) q^{35} +(0.0964685 - 5.96964i) q^{36} +(1.69433 - 5.21461i) q^{37} +(-7.06248 + 6.94928i) q^{38} +(0.244688 + 0.177776i) q^{39} +(-1.95094 - 2.04788i) q^{40} +(-2.58719 + 0.840630i) q^{41} +(0.689365 - 0.344262i) q^{42} +9.66919 q^{43} +(6.61987 - 0.421136i) q^{44} +2.98521 q^{45} +(4.44244 - 2.21851i) q^{46} +(6.21868 - 2.02057i) q^{47} +(0.273060 + 0.402575i) q^{48} +(-10.5766 - 7.68432i) q^{49} +(1.00805 - 0.991888i) q^{50} +(0.0591649 - 0.182091i) q^{51} +(4.97341 + 0.0803696i) q^{52} +(2.44632 - 1.77735i) q^{53} +(-1.01535 - 0.169236i) q^{54} +(0.264022 + 3.30610i) q^{55} +(6.02505 - 11.1483i) q^{56} +(0.500805 + 0.689300i) q^{57} +(-1.58034 - 10.5277i) q^{58} +(4.30358 + 1.39832i) q^{59} +(-0.199055 + 0.139764i) q^{60} +(-2.86345 + 3.94119i) q^{61} +(0.0706621 - 0.135956i) q^{62} +(4.13302 + 12.7201i) q^{63} +(7.47972 + 2.83791i) q^{64} +2.48703i q^{65} +(0.0486928 - 0.568325i) q^{66} -5.92809i q^{67} +(-0.924503 - 3.00997i) q^{68} +(-0.131951 - 0.406102i) q^{69} +(5.62212 + 2.92206i) q^{70} +(-8.27369 + 11.3878i) q^{71} +(-7.61386 + 3.64979i) q^{72} +(14.4548 + 4.69663i) q^{73} +(-7.66817 + 1.15109i) q^{74} +(-0.0714813 - 0.0983855i) q^{75} +(13.2547 + 4.54477i) q^{76} +(-13.7219 + 5.70229i) q^{77} +(0.0703227 - 0.421910i) q^{78} +(-1.78591 + 1.29754i) q^{79} +(-1.35834 + 3.76230i) q^{80} +(2.74009 - 8.43313i) q^{81} +(2.69827 + 2.74223i) q^{82} +(-7.55967 - 5.49242i) q^{83} +(-0.871134 - 0.654680i) q^{84} +(1.49732 - 0.486508i) q^{85} +(-6.10936 - 12.2336i) q^{86} -0.915442 q^{87} +(-4.71552 - 8.10950i) q^{88} +3.97318 q^{89} +(-1.88617 - 3.77695i) q^{90} +(-10.5973 + 3.44329i) q^{91} +(-5.61381 - 4.21892i) q^{92} +(-0.0106595 - 0.00774460i) q^{93} +(-6.48567 - 6.59132i) q^{94} +(-2.16501 + 6.66320i) q^{95} +(0.336816 - 0.599843i) q^{96} +(7.04211 - 5.11639i) q^{97} +(-3.03968 + 18.2369i) q^{98} +(9.62992 + 2.30023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{5} + 20 q^{6} + 16 q^{9} + 14 q^{12} - 10 q^{13} - 21 q^{14} - 4 q^{16} - 25 q^{18} + 5 q^{20} + 15 q^{22} - 30 q^{24} - 12 q^{25} - 4 q^{26} - 60 q^{28} + 20 q^{29} - 10 q^{33} - 18 q^{34}+ \cdots + 38 q^{97}+O(q^{100}) \) 48 * q - 12 * q^5 + 20 * q^6 + 16 * q^9 + 14 * q^12 - 10 * q^13 - 21 * q^14 - 4 * q^16 - 25 * q^18 + 5 * q^20 + 15 * q^22 - 30 * q^24 - 12 * q^25 - 4 * q^26 - 60 * q^28 + 20 * q^29 - 10 * q^33 - 18 * q^34 + 66 * q^36 - 44 * q^37 + 11 * q^38 - 10 * q^41 + 19 * q^42 - 35 * q^44 - 44 * q^45 + 5 * q^46 + 41 * q^48 - 2 * q^49 + 50 * q^52 - 36 * q^53 - 28 * q^56 + 30 * q^57 - 38 * q^58 - 21 * q^60 + 36 * q^64 + 43 * q^66 - 65 * q^68 + 24 * q^69 - 21 * q^70 - 60 * q^72 - 20 * q^73 - 70 * q^74 + 16 * q^77 - 56 * q^78 + q^80 + 50 * q^81 + 35 * q^82 + 60 * q^84 + 10 * q^85 + 38 * q^86 - 101 * q^88 + 64 * q^89 + 70 * q^92 - 28 * q^93 + 130 * q^94 + 105 * q^96 + 38 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more