LMFDB - Embedded newform 220.2.r.d.151.4

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			151.4
Character	$\chi$	$=$	220.151
Dual form			220.2.r.d.51.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00805 - 0.991888i) q^{2} +(0.115659 - 0.0375799i) q^{3} +(0.0323155 + 1.99974i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.153865 - 0.0768386i) q^{6} +(-1.38450 + 4.26105i) q^{7} +(1.95094 - 2.04788i) 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} +(5.62212 - 2.92206i) q^{14} +(-0.115659 - 0.0375799i) q^{15} +(-3.99791 + 0.129245i) q^{16} +(-0.925394 + 1.27370i) q^{17} +(4.17495 + 0.626714i) q^{18} +(2.16501 + 6.66320i) q^{19} +(1.14927 - 1.63682i) q^{20} +0.544858i q^{21} +(0.324835 - 4.67915i) q^{22} -3.51120i q^{23} +(0.148685 - 0.310173i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.522126 + 3.47822i) q^{26} +(-0.427830 + 0.588858i) q^{27} +(-8.56572 - 2.63094i) q^{28} +(7.15919 + 2.32616i) q^{29} +(0.0793147 + 0.152603i) 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} +(-3.58691 - 4.77284i) q^{36} +(1.69433 - 5.21461i) q^{37} +(4.42673 - 8.86426i) q^{38} +(-0.244688 - 0.177776i) q^{39} +(-2.78206 + 0.510037i) q^{40} +(-2.58719 + 0.840630i) q^{41} +(0.540438 - 0.549242i) q^{42} -9.66919 q^{43} +(-4.96865 + 4.39460i) q^{44} +2.98521 q^{45} +(-3.48272 + 3.53945i) q^{46} +(-6.21868 + 2.02057i) q^{47} +(-0.457538 + 0.165190i) q^{48} +(-10.5766 - 7.68432i) q^{49} +(0.631838 - 1.26522i) q^{50} +(-0.0591649 + 0.182091i) q^{51} +(3.97633 - 2.98832i) 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} +(-4.90950 - 9.44599i) q^{58} +(-4.30358 - 1.39832i) q^{59} +(0.0714125 - 0.232502i) q^{60} +(-2.86345 + 3.94119i) q^{61} +(-0.0227458 + 0.151525i) q^{62} +(-4.13302 - 12.7201i) q^{63} +(-0.387651 - 7.99060i) q^{64} +2.48703i q^{65} +(-0.138272 - 0.553394i) q^{66} +5.92809i q^{67} +(-2.57696 - 1.80939i) q^{68} +(-0.131951 - 0.406102i) q^{69} +(-6.26594 - 0.940598i) q^{70} +(8.27369 - 11.3878i) q^{71} +(-1.11835 + 8.36906i) q^{72} +(14.4548 + 4.69663i) q^{73} +(-6.88028 + 3.57599i) 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} +(3.31035 + 2.24535i) q^{80} +(2.74009 - 8.43313i) q^{81} +(3.44182 + 1.71881i) q^{82} +(7.55967 + 5.49242i) q^{83} +(-1.08957 + 0.0176074i) q^{84} +(1.49732 - 0.486508i) q^{85} +(9.74699 + 9.59076i) q^{86} +0.915442 q^{87} +(9.36758 + 0.498376i) q^{88} +3.97318 q^{89} +(-3.00923 - 2.96100i) q^{90} +(10.5973 - 3.44329i) q^{91} +(7.02148 - 0.113466i) q^{92} +(-0.0106595 - 0.00774460i) q^{93} +(8.27290 + 4.13140i) q^{94} +(2.16501 - 6.66320i) q^{95} +(0.625069 + 0.287308i) 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 $

$2$	−1.00805	−	0.991888i	−0.712797	−	0.701371i
$2$	−1.00805	−	0.991888i	−0.712797	−	0.701371i
$3$	0.115659	−	0.0375799i	0.0667758	−	0.0216968i	−0.275439	−	0.961319i	$-0.588823\pi$
$3$	0.115659	−	0.0375799i	0.0667758	−	0.0216968i	0.342214	+	0.939622i	$0.388823\pi$
$4$	0.0323155	+	1.99974i	0.0161577	+	0.999869i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$5$	−0.809017	−	0.587785i	−0.361803	−	0.262866i
$6$	−0.153865	−	0.0768386i	−0.0628151	−	0.0313692i
$7$	−1.38450	+	4.26105i	−0.523291	+	1.61052i	0.244380	+	0.969680i	$0.421416\pi$
$7$	−1.38450	+	4.26105i	−0.523291	+	1.61052i	−0.767671	+	0.640844i	$0.778584\pi$
$8$	1.95094	−	2.04788i	0.689762	−	0.724036i
$9$	−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	$0.912083\pi$
$14$	5.62212	−	2.92206i	1.50257	−	0.780955i
$15$	−0.115659	−	0.0375799i	−0.0298631	−	0.00970310i
$16$	−3.99791	+	0.129245i	−0.999478	+	0.0323113i
$17$	−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	$0.261147\pi$
$18$	4.17495	+	0.626714i	0.984045	+	0.147718i
$19$	2.16501	+	6.66320i	0.496687	+	1.52864i	0.814312	+	0.580428i	$0.197115\pi$
$19$	2.16501	+	6.66320i	0.496687	+	1.52864i	−0.317625	+	0.948216i	$0.602885\pi$
$20$	1.14927	−	1.63682i	0.256985	−	0.366003i
$21$			0.544858i			0.118898i
$22$	0.324835	−	4.67915i	0.0692551	−	0.997599i
$23$		−	3.51120i		−	0.732136i	−0.930588	−	0.366068i	$-0.880704\pi$
$23$		−	3.51120i		−	0.732136i	0.930588	−	0.366068i	$-0.119296\pi$
$24$	0.148685	−	0.310173i	0.0303502	−	0.0633137i
$25$	0.309017	+	0.951057i	0.0618034	+	0.190211i
$26$	−0.522126	+	3.47822i	−0.102397	+	0.682135i
$27$	−0.427830	+	0.588858i	−0.0823360	+	0.113326i
$28$	−8.56572	−	2.63094i	−1.61877	−	0.497200i
$29$	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	$0.353664\pi$
$30$	0.0793147	+	0.152603i	0.0144808	+	0.0278614i
$31$	−0.0636833	−	0.0876525i	−0.0114379	−	0.0157429i	0.803260	−	0.595629i	$-0.203097\pi$
$31$	−0.0636833	−	0.0876525i	−0.0114379	−	0.0157429i	−0.814698	+	0.579886i	$0.803097\pi$
$32$	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
$36$	−3.58691	−	4.77284i	−0.597819	−	0.795473i
$37$	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	$-0.0488246\pi$
$38$	4.42673	−	8.86426i	0.718110	−	1.43797i
$39$	−0.244688	−	0.177776i	−0.0391814	−	0.0284670i
$40$	−2.78206	+	0.510037i	−0.439882	+	0.0806440i
$41$	−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	$0.468135\pi$
$42$	0.540438	−	0.549242i	0.0833914	−	0.0847499i
$43$	−9.66919			−1.47454			−0.737269	−	0.675599i	$-0.763885\pi$
$43$	−9.66919			−1.47454			−0.737269	+	0.675599i	$0.763885\pi$
$44$	−4.96865	+	4.39460i	−0.749052	+	0.662512i
$45$	2.98521			0.445009
$46$	−3.48272	+	3.53945i	−0.513499	+	0.521864i
$47$	−6.21868	+	2.02057i	−0.907088	+	0.294731i	−0.725159	−	0.688581i	$-0.758234\pi$
$47$	−6.21868	+	2.02057i	−0.907088	+	0.294731i	−0.181928	+	0.983312i	$0.558234\pi$
$48$	−0.457538	+	0.165190i	−0.0660399	+	0.0238431i
$49$	−10.5766	−	7.68432i	−1.51094	−	1.09776i
$50$	0.631838	−	1.26522i	0.0893554	−	0.178929i
$51$	−0.0591649	+	0.182091i	−0.00828474	+	0.0254978i
$52$	3.97633	−	2.98832i	0.551418	−	0.414405i
$53$	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
$58$	−4.90950	−	9.44599i	−0.644649	−	1.24032i
$59$	−4.30358	−	1.39832i	−0.560278	−	0.182045i	0.0151681	−	0.999885i	$-0.495172\pi$
$59$	−4.30358	−	1.39832i	−0.560278	−	0.182045i	−0.575446	+	0.817840i	$0.695172\pi$
$60$	0.0714125	−	0.232502i	0.00921931	−	0.0300159i
$61$	−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	$0.300956\pi$
$62$	−0.0227458	+	0.151525i	−0.00288872	+	0.0192436i
$63$	−4.13302	−	12.7201i	−0.520711	−	1.60258i
$64$	−0.387651	−	7.99060i	−0.0484563	−	0.998825i
$65$			2.48703i			0.308478i
$66$	−0.138272	−	0.553394i	−0.0170201	−	0.0681181i
$67$			5.92809i			0.724232i	0.932133	+	0.362116i	$0.117946\pi$
$67$			5.92809i			0.724232i	−0.932133	+	0.362116i	$0.882054\pi$
$68$	−2.57696	−	1.80939i	−0.312503	−	0.219420i
$69$	−0.131951	−	0.406102i	−0.0158850	−	0.0488890i
$70$	−6.26594	−	0.940598i	−0.748923	−	0.112423i
$71$	8.27369	−	11.3878i	0.981906	−	1.35148i	0.0461094	−	0.998936i	$-0.485318\pi$
$71$	8.27369	−	11.3878i	0.981906	−	1.35148i	0.935796	−	0.352541i	$-0.114682\pi$
$72$	−1.11835	+	8.36906i	−0.131799	+	0.986303i
$73$	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	$0.251100\pi$
$74$	−6.88028	+	3.57599i	−0.799816	+	0.415700i
$75$	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	−0.482770	−	0.875747i	$-0.660369\pi$
$79$	1.78591	−	1.29754i	0.200931	−	0.145985i	0.683701	+	0.729762i	$0.260369\pi$
$80$	3.31035	+	2.24535i	0.370108	+	0.251038i
$81$	2.74009	−	8.43313i	0.304454	−	0.937014i
$82$	3.44182	+	1.71881i	0.380086	+	0.189811i
$83$	7.55967	+	5.49242i	0.829782	+	0.602872i	0.919498	−	0.393096i	$-0.128596\pi$
$83$	7.55967	+	5.49242i	0.829782	+	0.602872i	−0.0897160	+	0.995967i	$0.528596\pi$
$84$	−1.08957	+	0.0176074i	−0.118882	+	0.00192112i
$85$	1.49732	−	0.486508i	0.162407	−	0.0527693i
$86$	9.74699	+	9.59076i	1.05105	+	1.03420i
$87$	0.915442			0.0981457
$88$	9.36758	+	0.498376i	0.998588	+	0.0531271i
$89$	3.97318			0.421156			0.210578	−	0.977577i	$-0.432465\pi$
$89$	3.97318			0.421156			0.210578	+	0.977577i	$0.432465\pi$
$90$	−3.00923	−	2.96100i	−0.317201	−	0.312116i
$91$	10.5973	−	3.44329i	1.11090	−	0.360955i
$92$	7.02148	−	0.113466i	0.732040	−	0.0118297i
$93$	−0.0106595	−	0.00774460i	−0.00110534	−	0.000803078i
$94$	8.27290	+	4.13140i	0.853284	+	0.426122i
$95$	2.16501	−	6.66320i	0.222125	−	0.683630i
$96$	0.625069	+	0.287308i	0.0637958	+	0.0293232i
$97$	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	$0.856080\pi$
$102$	0.240255	−	0.124871i	0.0237888	−	0.0123641i
$103$	12.3545	+	4.01423i	1.21733	+	0.395534i	0.846109	−	0.533011i	$-0.178939\pi$
$103$	12.3545	+	4.01423i	1.21733	+	0.395534i	0.371220	+	0.928545i	$0.378939\pi$
$104$	−6.97241	−	0.931716i	−0.683701	−	0.0913622i
$105$	0.320260	−	0.440799i	0.0312541	−	0.0430176i
$106$	−4.22894	−	0.634818i	−0.410751	−	0.0616590i
$107$	2.14976	+	6.61628i	0.207825	+	0.639620i	0.999586	+	0.0287882i	$0.00916484\pi$
$107$	2.14976	+	6.61628i	0.207825	+	0.639620i	−0.791760	+	0.610832i	$0.790835\pi$
$108$	−1.19139	−	0.836520i	−0.114641	−	0.0804942i
$109$			11.3681i			1.08887i	0.838804	+	0.544433i	$0.183255\pi$
$109$			11.3681i			1.08887i	−0.838804	+	0.544433i	$0.816745\pi$
$110$	−3.01313	+	3.59458i	−0.287291	+	0.342730i
$111$		−	0.666791i		−	0.0632890i
$112$	4.98438	−	17.2142i	0.470980	−	1.62659i
$113$	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	$0.830691\pi$
$114$	0.178873	−	1.19159i	0.0167530	−	0.111603i
$115$	−2.06383	+	2.84062i	−0.192453	+	0.264889i
$116$	−4.42036	+	14.3917i	−0.410420	+	1.33623i
$117$	7.06094	+	2.29424i	0.652784	+	0.212102i
$118$	2.95123	+	5.67824i	0.271683	+	0.522724i
$119$	−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
$124$	0.173224	−	0.130182i	0.0155560	−	0.0116907i
$125$	0.309017	−	0.951057i	0.0276393	−	0.0850651i
$126$	−8.45066	+	16.9220i	−0.752845	+	1.50753i
$127$	−8.92935	−	6.48756i	−0.792352	−	0.575677i	0.116308	−	0.993213i	$-0.462894\pi$
$127$	−8.92935	−	6.48756i	−0.792352	−	0.575677i	−0.908661	+	0.417536i	$0.862894\pi$
$128$	−7.53501	+	8.43941i	−0.666007	+	0.745945i
$129$	−1.11833	+	0.363367i	−0.0984635	+	0.0319927i
$130$	2.46686	−	2.50704i	0.216358	−	0.219882i
$131$	18.2532			1.59479			0.797396	−	0.603456i	$-0.206210\pi$
$131$	18.2532			1.59479			0.797396	+	0.603456i	$0.206210\pi$
$132$	−0.409520	+	0.694997i	−0.0356442	+	0.0604918i
$133$	−31.3897			−2.72183
$134$	5.88000	−	5.97579i	0.507955	−	0.516230i
$135$	0.692244	−	0.224924i	0.0595789	−	0.0193584i
$136$	0.802990	+	4.38001i	0.0688558	+	0.375582i
$137$	−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	$0.814222\pi$
$138$	−0.269796	+	0.540250i	−0.0229665	+	0.0459892i
$139$	−3.16377	+	9.73710i	−0.268348	+	0.825890i	0.722555	+	0.691313i	$0.242967\pi$
$139$	−3.16377	+	9.73710i	−0.268348	+	0.825890i	−0.990903	+	0.134577i	$0.957033\pi$
$140$	5.38339	+	7.16327i	0.454979	+	0.605407i
$141$	−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
$146$	−9.91253	−	19.0719i	−0.820367	−	1.57840i
$147$	−1.51205	−	0.491295i	−0.124712	−	0.0405213i
$148$	10.4826	+	3.21971i	0.861666	+	0.264658i
$149$	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	$-0.186690\pi$
$150$	0.0255310	−	0.170079i	0.00208460	−	0.0138869i
$151$	−1.41979	−	4.36966i	−0.115541	−	0.355598i	0.876519	−	0.481368i	$-0.159860\pi$
$151$	−1.41979	−	4.36966i	−0.115541	−	0.355598i	−0.992059	+	0.125770i	$0.959860\pi$
$152$	17.8693	+	8.56585i	1.44939	+	0.694782i
$153$		−	4.69984i		−	0.379960i
$154$	19.4884	+	7.86241i	1.57042	+	0.633571i
$155$			0.108344i			0.00870244i
$156$	0.347599	−	0.495057i	0.0278302	−	0.0396363i
$157$	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	$0.767893\pi$
$158$	−3.08730	−	0.463444i	−0.245613	−	0.0368696i
$159$	0.216146	−	0.297500i	0.0171415	−	0.0235933i
$160$	−1.10985	−	5.54691i	−0.0877410	−	0.438522i
$161$	14.9614	+	4.86125i	1.17912	+	0.383120i
$162$	−11.1269	+	5.78312i	−0.874208	+	0.454365i
$163$	7.92005	+	10.9010i	0.620346	+	0.853833i	0.997378	−	0.0723671i	$-0.0230553\pi$
$163$	7.92005	+	10.9010i	0.620346	+	0.853833i	−0.377032	+	0.926200i	$0.623055\pi$
$164$	−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	−0.947861	−	0.318684i	$-0.896759\pi$
$167$	−12.1175	+	8.80388i	−0.937680	+	0.681264i	0.0101811	+	0.999948i	$0.496759\pi$
$168$	1.11581	+	1.06299i	0.0860863	+	0.0820112i
$169$	2.10585	−	6.48114i	0.161989	−	0.498550i
$170$	−1.99193	−	0.994750i	−0.152774	−	0.0762938i
$171$	−16.9204	−	12.2934i	−1.29393	−	0.940097i
$172$	−0.312465	−	19.3359i	−0.0238252	−	1.47435i
$173$	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	$0.354443\pi$
$174$	−0.922808	−	0.908016i	−0.0699579	−	0.0688365i
$175$	−4.48033			−0.338681
$176$	−8.94863	−	9.79398i	−0.674528	−	0.738249i
$177$	−0.550297			−0.0413628
$178$	−4.00515	−	3.94095i	−0.300198	−	0.295386i
$179$	3.37551	−	1.09677i	0.252298	−	0.0819765i	−0.180138	−	0.983641i	$-0.557654\pi$
$179$	3.37551	−	1.09677i	0.252298	−	0.0819765i	0.432435	+	0.901665i	$0.357654\pi$
$180$	0.0964685	+	5.96964i	0.00719034	+	0.444951i
$181$	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	$0.542111\pi$
$182$	−14.0980	−	7.04039i	−1.04501	−	0.521869i
$183$	−0.183074	+	0.563443i	−0.0135332	+	0.0416509i
$184$	−7.19053	−	6.85015i	−0.530093	−	0.505000i
$185$	−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
$190$	−8.79158	+	4.56938i	−0.637808	+	0.331497i
$191$	−0.680513	−	0.221112i	−0.0492402	−	0.0159991i	0.284293	−	0.958737i	$-0.408241\pi$
$191$	−0.680513	−	0.221112i	−0.0492402	−	0.0159991i	−0.333534	+	0.942738i	$0.608241\pi$
$192$	−0.345122	−	0.909618i	−0.0249070	−	0.0656460i
$193$	−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	$0.233033\pi$
$194$	−12.1737	−	1.82742i	−0.874018	−	0.131201i
$195$	0.0934624	+	0.287648i	0.00669298	+	0.0205989i
$196$	15.0248	−	21.3987i	1.07320	−	1.52848i
$197$		−	18.4594i		−	1.31518i	−0.753378	−	0.657588i	$-0.771577\pi$
$197$		−	18.4594i		−	1.31518i	0.753378	−	0.657588i	$-0.228423\pi$
$198$	7.42583	+	11.8705i	0.527731	+	0.843602i
$199$			9.53878i			0.676186i	0.941113	+	0.338093i	$0.109782\pi$
$199$			9.53878i			0.676186i	−0.941113	+	0.338093i	$0.890218\pi$
$200$	2.55053	+	1.22263i	0.180349	+	0.0864527i
$201$	0.222777	+	0.685638i	0.0157135	+	0.0483612i
$202$	−0.739599	+	4.92695i	−0.0520380	+	0.346659i
$203$	−19.8237	+	27.2851i	−1.39135	+	1.91504i
$204$	−0.366046	−	0.112430i	−0.0256283	−	0.00787167i
$205$	2.58719	+	0.840630i	0.180697	+	0.0587122i
$206$	−8.47228	−	16.3009i	−0.590292	−	1.13573i
$207$	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	−0.493887	−	0.869526i	$-0.664424\pi$
$211$	2.62136	−	1.90453i	0.180462	−	0.131113i	0.674349	+	0.738413i	$0.264424\pi$
$212$	3.63330	+	4.83456i	0.249536	+	0.332039i
$213$	0.528976	−	1.62802i	0.0362449	−	0.111550i
$214$	4.39555	−	8.80184i	0.300474	−	0.601681i
$215$	7.82254	+	5.68341i	0.533493	+	0.387605i
$216$	0.371240	+	2.02497i	0.0252597	+	0.137782i
$217$	0.461661	−	0.150003i	0.0313396	−	0.0101828i
$218$	11.2759	−	11.4596i	0.763699	−	0.776140i
$219$	1.84832			0.124898
$220$	6.60280	−	0.634813i	0.445161	−	0.0427991i
$221$	3.91552			0.263386
$222$	−0.661382	+	0.672156i	−0.0443890	+	0.0451121i
$223$	−7.74647	+	2.51698i	−0.518742	+	0.168549i	−0.556674	−	0.830731i	$-0.687923\pi$
$223$	−7.74647	+	2.51698i	−0.518742	+	0.168549i	0.0379325	+	0.999280i	$0.487923\pi$
$224$	−22.0991	+	12.4088i	−1.47656	+	0.829097i
$225$	−2.41509	−	1.75466i	−0.161006	−	0.116978i
$226$	2.90187	−	5.81082i	0.193029	−	0.386530i
$227$	0.982420	−	3.02358i	0.0652055	−	0.200682i	−0.913146	−	0.407633i	$-0.866354\pi$
$227$	0.982420	−	3.02358i	0.0652055	−	0.200682i	0.978351	+	0.206951i	$0.0663542\pi$
$228$	−1.36224	+	1.02376i	−0.0902162	+	0.0677998i
$229$	−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	$0.863215\pi$
$234$	−4.84213	−	9.31636i	−0.316540	−	0.609030i
$235$	6.21868	+	2.02057i	0.405662	+	0.131808i
$236$	2.65720	−	8.65122i	0.172969	−	0.563147i
$237$	0.157796	−	0.217187i	0.0102499	−	0.0141078i
$238$	−1.48085	+	9.86493i	−0.0959895	+	0.639448i
$239$	−5.86606	−	18.0539i	−0.379444	−	1.16781i	−0.940431	−	0.339984i	$-0.889578\pi$
$239$	−5.86606	−	18.0539i	−0.379444	−	1.16781i	0.560987	−	0.827824i	$-0.310422\pi$
$240$	0.467252	+	0.135293i	0.0301610	+	0.00873312i
$241$		−	28.7168i		−	1.84981i	−0.380194	−	0.924907i	$-0.624143\pi$
$241$		−	28.7168i		−	1.84981i	0.380194	−	0.924907i	$-0.375857\pi$
$242$	12.4898	−	9.27392i	0.802873	−	0.596150i
$243$		−	3.26195i		−	0.209254i
$244$	−7.97389	−	5.59878i	−0.510476	−	0.358425i
$245$	4.03988	+	12.4335i	0.258099	+	0.794346i
$246$	0.462671	+	0.0694529i	0.0294988	+	0.00442816i
$247$	10.2418	−	14.0966i	0.651671	−	0.896948i
$248$	−0.303745	−	0.0405891i	−0.0192878	−	0.00257741i
$249$	1.08075	+	0.351157i	0.0684897	+	0.0222537i
$250$	−1.25485	+	0.652199i	−0.0793634	+	0.0412487i
$251$	−7.09600	−	9.76681i	−0.447896	−	0.616476i	0.524048	−	0.851689i	$-0.324421\pi$
$251$	−7.09600	−	9.76681i	−0.447896	−	0.616476i	−0.971944	+	0.235213i	$0.924421\pi$
$252$	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
$256$	15.9666	−	1.03342i	0.997912	−	0.0645888i
$257$	−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	$0.969843\pi$
$258$	1.48775	+	0.742967i	0.0926232	+	0.0462551i
$259$	19.8739	+	14.4392i	1.23490	+	0.897211i
$260$	−4.97341	+	0.0803696i	−0.308438	+	0.00498431i
$261$	−21.3717	+	6.94408i	−1.32287	+	0.429828i
$262$	−18.4001	−	18.1052i	−1.13676	−	1.11854i
$263$	−4.94683			−0.305034			−0.152517	−	0.988301i	$-0.548738\pi$
$263$	−4.94683			−0.305034			−0.152517	+	0.988301i	$0.548738\pi$
$264$	1.10218	−	0.294391i	0.0678342	−	0.0181185i
$265$	−3.02381			−0.185751
$266$	31.6422	+	31.1350i	1.94011	+	1.90901i
$267$	0.459534	−	0.149312i	0.0281230	−	0.00913773i
$268$	−11.8546	+	0.191569i	−0.724137	+	0.0117019i
$269$	−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	$0.748913\pi$
$270$	−0.920914	−	0.459895i	−0.0560450	−	0.0279883i
$271$	−4.08329	+	12.5671i	−0.248042	+	0.763395i	0.747079	+	0.664735i	$0.231456\pi$
$271$	−4.08329	+	12.5671i	−0.248042	+	0.763395i	−0.995121	+	0.0986599i	$0.968544\pi$
$272$	3.53502	−	5.21173i	0.214342	−	0.316007i
$273$	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	$0.654041\pi$
$278$	12.8473	−	6.67733i	0.770532	−	0.400480i
$279$	0.307601	+	0.0999457i	0.0184156	+	0.00598359i
$280$	1.67846	−	12.5606i	0.100307	−	0.750641i
$281$	−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	$0.973202\pi$
$282$	1.11209	+	0.166940i	0.0662242	+	0.00994112i
$283$	7.66102	+	23.5782i	0.455400	+	1.40158i	0.870665	+	0.491877i	$0.163689\pi$
$283$	7.66102	+	23.5782i	0.455400	+	1.40158i	−0.415265	+	0.909701i	$0.636311\pi$
$284$	23.0399	+	16.1772i	1.36717	+	0.959941i
$285$		−	0.852021i		−	0.0504694i
$286$	−9.88955	+	6.18659i	−0.584781	+	0.365821i
$287$		−	12.1880i		−	0.719435i
$288$	−16.7721	−	1.96596i	−0.988304	−	0.115845i
$289$	4.48734	+	13.8106i	0.263961	+	0.812389i
$290$	−1.58034	+	10.5277i	−0.0928010	+	0.618208i
$291$	0.622211	−	0.856400i	0.0364746	−	0.0502030i
$292$	−8.92493	+	29.0575i	−0.522292	+	1.70046i
$293$	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	$0.455624\pi$
$294$	1.03691	+	1.99503i	0.0604737	+	0.116353i
$295$	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
$300$	−0.194435	+	0.146123i	−0.0112257	+	0.00843643i
$301$	13.3870	−	41.2009i	0.771612	−	2.37478i
$302$	−2.90300	+	5.81309i	−0.167049	+	0.334506i
$303$	−0.346604	−	0.251822i	−0.0199119	−	0.0144668i
$304$	−9.51669	−	26.3591i	−0.545820	−	1.51180i
$305$	4.63315	−	1.50540i	0.265293	−	0.0861991i
$306$	−4.66172	+	4.73766i	−0.266493	+	0.270834i
$307$	12.1423			0.692997			0.346498	−	0.938051i	$-0.387371\pi$
$307$	12.1423			0.692997			0.346498	+	0.938051i	$0.387371\pi$
$308$	−11.8465	−	27.2559i	−0.675019	−	1.55305i
$309$	1.57977			0.0898700
$310$	0.107466	−	0.109216i	0.00610364	−	0.00620307i
$311$	−20.9169	+	6.79632i	−1.18609	+	0.385384i	−0.834626	−	0.550817i	$-0.814316\pi$
$311$	−20.9169	+	6.79632i	−1.18609	+	0.385384i	−0.351464	+	0.936201i	$0.614316\pi$
$312$	−0.841436	+	0.154261i	−0.0476370	+	0.00873332i
$313$	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	$0.686762\pi$
$314$	6.38442	−	12.7844i	0.360294	−	0.721467i
$315$	−4.13302	+	12.7201i	−0.232869	+	0.716697i
$316$	2.65246	+	3.52943i	0.149213	+	0.198546i
$317$	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
$322$	−10.2600	−	19.7404i	−0.571765	−	1.10009i
$323$	−10.4904	−	3.40853i	−0.583700	−	0.189656i
$324$	16.9526	+	5.20694i	0.941811	+	0.289275i
$325$	1.46184	−	2.01205i	0.0810883	−	0.111608i
$326$	2.82881	−	18.8445i	0.156673	−	1.04370i
$327$	0.427212	+	1.31482i	0.0236249	+	0.0727100i
$328$	−3.32595	+	6.93829i	−0.183645	+	0.383103i
$329$		−	29.2955i		−	1.61512i
$330$	−0.213412	+	0.528980i	−0.0117480	+	0.0291194i
$331$		−	7.23140i		−	0.397474i	−0.980053	−	0.198737i	$-0.936316\pi$
$331$		−	7.23140i		−	0.397474i	0.980053	−	0.198737i	$-0.0636839\pi$
$332$	−10.7391	+	15.2949i	−0.589385	+	0.839414i
$333$	5.05793	+	15.5667i	0.277173	+	0.853051i
$334$	20.9475	+	3.14449i	1.14619	+	0.172059i
$335$	3.48444	−	4.79593i	0.190376	−	0.262029i
$336$	−0.0704202	−	2.17829i	−0.00384174	−	0.118836i
$337$	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	$0.565314\pi$
$338$	−8.55137	+	4.44453i	−0.465133	+	0.241750i
$339$	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
$344$	−18.8640	+	19.8014i	−1.01708	+	1.06762i
$345$	−0.131951	+	0.406102i	−0.00710398	+	0.0218638i
$346$	−4.74724	−	2.37072i	−0.255213	−	0.127451i
$347$	−0.628694	−	0.456773i	−0.0337501	−	0.0245209i	0.570782	−	0.821101i	$-0.306640\pi$
$347$	−0.628694	−	0.456773i	−0.0337501	−	0.0245209i	−0.604532	+	0.796581i	$0.706640\pi$
$348$	0.0295830	+	1.83065i	0.00158581	+	0.0981329i
$349$	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	$0.379134\pi$
$350$	4.51638	+	4.44398i	0.241411	+	0.237541i
$351$	1.81023			0.0966230
$352$	−0.693904	+	18.7488i	−0.0369852	+	0.999316i
$353$	−23.9837			−1.27652			−0.638261	−	0.769820i	$-0.720346\pi$
$353$	−23.9837			−1.27652			−0.638261	+	0.769820i	$0.720346\pi$
$354$	0.554725	+	0.545833i	0.0294833	+	0.0290107i
$355$	−13.3871	+	4.34973i	−0.710514	+	0.230860i
$356$	0.128395	+	7.94532i	0.00680493	+	0.421101i
$357$	−0.693983	−	0.504208i	−0.0367295	−	0.0266855i
$358$	−4.49055	−	2.24254i	−0.237333	−	0.118522i
$359$	7.91130	−	24.3485i	0.417542	−	1.28506i	−0.492415	−	0.870361i	$-0.663886\pi$
$359$	7.91130	−	24.3485i	0.417542	−	1.28506i	0.909957	−	0.414703i	$-0.136114\pi$
$360$	5.82397	−	6.11336i	0.306950	−	0.322203i
$361$	−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
$366$	0.743419	−	0.386388i	0.0388592	−	0.0201968i
$367$	−10.5262	−	3.42016i	−0.549461	−	0.178531i	0.0211127	−	0.999777i	$-0.493279\pi$
$367$	−10.5262	−	3.42016i	−0.549461	−	0.178531i	−0.570574	+	0.821246i	$0.693279\pi$
$368$	0.453805	+	14.0375i	0.0236562	+	0.731754i
$369$	4.77327	−	6.56985i	0.248487	−	0.342013i
$370$	7.66817	+	1.15109i	0.398649	+	0.0598424i
$371$	4.18646	+	12.8846i	0.217350	+	0.668936i
$372$	0.0151427	−	0.0215665i	0.000785113	−	0.00111817i
$373$			21.3483i			1.10537i	0.833389	+	0.552687i	$0.186398\pi$
$373$			21.3483i			1.10537i	−0.833389	+	0.552687i	$0.813602\pi$
$374$	5.65922	+	4.74380i	0.292631	+	0.245296i
$375$		−	0.121611i		−	0.00627998i
$376$	−7.99439	+	16.6771i	−0.412279	+	0.860058i
$377$	−5.78523	−	17.8051i	−0.297955	−	0.917010i
$378$	−0.684632	+	4.56078i	−0.0352137	+	0.234581i
$379$	15.3462	−	21.1222i	0.788281	−	1.08498i	−0.206039	−	0.978544i	$-0.566058\pi$
$379$	15.3462	−	21.1222i	0.788281	−	1.08498i	0.994320	−	0.106432i	$-0.0339425\pi$
$380$	13.3946	+	4.11412i	0.687130	+	0.211050i
$381$	−1.27656	−	0.414780i	−0.0654003	−	0.0212498i
$382$	0.466670	+	0.897883i	0.0238769	+	0.0459397i
$383$	−5.47232	−	7.53200i	−0.279622	−	0.384867i	0.645986	−	0.763349i	$-0.276446\pi$
$383$	−5.47232	−	7.53200i	−0.279622	−	0.384867i	−0.925609	+	0.378482i	$0.876446\pi$
$384$	−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
$388$	10.4590	+	13.9170i	0.530976	+	0.706531i
$389$	−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	$0.850572\pi$
$390$	0.191100	−	0.382667i	0.00967672	−	0.0193771i
$391$	4.47220	+	3.24924i	0.226169	+	0.164321i
$392$	−36.3708	+	6.66789i	−1.83700	+	0.336779i
$393$	2.11115	−	0.685955i	0.106494	−	0.0346019i
$394$	−18.3096	+	18.6079i	−0.922426	+	0.937452i
$395$	−2.20751			−0.111072
$396$	4.28866	−	19.3316i	0.215513	−	0.971452i
$397$	−21.7027			−1.08923			−0.544613	−	0.838687i	$-0.683323\pi$
$397$	−21.7027			−1.08923			−0.544613	+	0.838687i	$0.683323\pi$
$398$	9.46141	−	9.61554i	0.474257	−	0.481983i
$399$	−3.63050	+	1.17962i	−0.181752	+	0.0590549i
$400$	−1.35834	−	3.76230i	−0.0679171	−	0.188115i
$401$	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	$0.610391\pi$
$402$	0.455506	−	0.912125i	0.0227186	−	0.0454927i
$403$	−0.0832665	+	0.256268i	−0.00414780	+	0.0127656i
$404$	5.63253	−	4.23300i	0.280229	−	0.210599i
$405$	−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	$0.591118\pi$
$410$	−1.77420	−	3.41360i	−0.0876215	−	0.168586i
$411$	−0.950840	−	0.308947i	−0.0469015	−	0.0152392i
$412$	−7.62817	+	24.8356i	−0.375813	+	1.22356i
$413$	11.9166	−	16.4018i	0.586377	−	0.807079i
$414$	2.20052	−	14.6591i	0.108150	−	0.720454i
$415$	−2.88754	−	8.88692i	−0.141744	−	0.436242i
$416$	1.63787	−	13.9731i	0.0803032	−	0.685088i
$417$			1.24508i			0.0609717i
$418$	31.8814	−	7.96596i	1.55937	−	0.389628i
$419$		−	18.8311i		−	0.919958i	−0.887930	−	0.459979i	$-0.847857\pi$
$419$		−	18.8311i		−	0.919958i	0.887930	−	0.459979i	$-0.152143\pi$
$420$	0.891833	+	0.626191i	0.0435170	+	0.0305550i
$421$	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	$0.742239\pi$
$422$	−4.53154	−	0.680242i	−0.220592	−	0.0331137i
$423$	11.4732	−	15.7915i	0.557847	−	0.767811i
$424$	1.13281	−	8.47729i	0.0550142	−	0.411693i
$425$	−1.49732	−	0.486508i	−0.0726306	−	0.0235991i
$426$	−2.14805	+	1.11644i	−0.104073	+	0.0540915i
$427$	−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	−0.924990	−	0.379991i	$-0.875927\pi$
$431$	−17.6347	+	12.8124i	−0.849435	+	0.617151i	0.0755552	+	0.997142i	$0.475927\pi$
$432$	1.63432	−	2.40950i	0.0786313	−	0.115927i
$433$	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	$-0.0385300\pi$
$434$	−0.614161	−	0.306706i	−0.0294807	−	0.0147224i
$435$	−0.740608	−	0.538083i	−0.0355094	−	0.0257991i
$436$	−22.7332	+	0.367366i	−1.08872	+	0.0175936i
$437$	23.3958	−	7.60177i	1.11918	−	0.363642i
$438$	−1.86320	−	1.83333i	−0.0890269	−	0.0875999i
$439$	−13.9299			−0.664839			−0.332419	−	0.943132i	$-0.607865\pi$
$439$	−13.9299			−0.664839			−0.332419	+	0.943132i	$0.607865\pi$
$440$	−7.28560	−	5.90932i	−0.347327	−	0.281716i
$441$	39.0267			1.85841
$442$	−3.94702	−	3.88376i	−0.187741	−	0.184731i
$443$	14.9426	−	4.85516i	0.709946	−	0.230676i	0.0682875	−	0.997666i	$-0.478246\pi$
$443$	14.9426	−	4.85516i	0.709946	−	0.230676i	0.641659	+	0.766990i	$0.278246\pi$
$444$	1.33341	−	0.0215477i	0.0632807	−	0.00102261i
$445$	−3.21437	−	2.33537i	−0.152376	−	0.110707i
$446$	10.3054	+	5.14640i	0.487973	+	0.243689i
$447$	0.859926	−	2.64658i	0.0406731	−	0.125179i
$448$	34.5850	+	9.41117i	1.63399	+	0.444636i
$449$	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
$454$	−3.98938	+	2.07346i	−0.187231	+	0.0973121i
$455$	−10.5973	−	3.44329i	−0.496811	−	0.161424i
$456$	2.38865	+	0.319192i	0.111859	+	0.0149476i
$457$	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	$0.0596437\pi$
$458$	12.3649	+	1.85613i	0.577772	+	0.0867311i
$459$	−0.354114	−	1.08985i	−0.0165286	−	0.0508699i
$460$	−5.74719	−	4.03533i	−0.267964	−	0.188148i
$461$		−	9.08512i		−	0.423136i	−0.977363	−	0.211568i	$-0.932143\pi$
$461$		−	9.08512i		−	0.423136i	0.977363	−	0.211568i	$-0.0678570\pi$
$462$	2.54947	+	0.176989i	0.118612	+	0.00823427i
$463$		−	40.2474i		−	1.87046i	−0.354045	−	0.935229i	$-0.615194\pi$
$463$		−	40.2474i		−	1.87046i	0.354045	−	0.935229i	$-0.384806\pi$
$464$	−28.9224	−	8.37449i	−1.34269	−	0.388776i
$465$	0.00407158	+	0.0125310i	0.000188815	+	0.000581112i
$466$	−1.26449	+	8.42361i	−0.0585765	+	0.390216i
$467$	−9.90989	+	13.6398i	−0.458575	+	0.631174i	−0.974212	−	0.225632i	$-0.927555\pi$
$467$	−9.90989	+	13.6398i	−0.458575	+	0.631174i	0.515637	+	0.856807i	$0.327555\pi$
$468$	−4.35970	+	14.1942i	−0.201527	+	0.656126i
$469$	−25.2599	−	8.20743i	−1.16639	−	0.378984i
$470$	−4.26454	−	8.20506i	−0.196708	−	0.378471i
$471$	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
$476$	11.2777	−	8.47547i	0.516911	−	0.388472i
$477$	−2.78941	+	8.58492i	−0.127718	+	0.393077i
$478$	−11.9942	+	24.0176i	−0.548600	+	1.09854i
$479$	−17.1183	−	12.4372i	−0.782156	−	0.568269i	0.123470	−	0.992348i	$-0.460598\pi$
$479$	−17.1183	−	12.4372i	−0.782156	−	0.568269i	−0.905625	+	0.424079i	$0.860598\pi$
$480$	−0.336816	−	0.599843i	−0.0153735	−	0.0273790i
$481$	−12.9689	+	4.21385i	−0.591331	+	0.192135i
$482$	−28.4839	+	28.9479i	−1.29741	+	1.31854i
$483$	1.91311			0.0870493
$484$	−21.7890	−	3.03991i	−0.990407	−	0.138178i
$485$	−8.70453			−0.395252
$486$	−3.23549	+	3.28819i	−0.146765	+	0.149155i
$487$	24.6508	−	8.00953i	1.11703	−	0.362947i	0.308400	−	0.951257i	$-0.400207\pi$
$487$	24.6508	−	8.00953i	1.11703	−	0.362947i	0.808635	+	0.588310i	$0.200207\pi$
$488$	2.48469	+	13.5530i	0.112477	+	0.613517i
$489$	1.32569	+	0.963167i	0.0599495	+	0.0435559i
$490$	8.26024	−	16.5406i	0.373159	−	0.747230i
$491$	0.915445	−	2.81745i	0.0413134	−	0.127150i	−0.928273	−	0.371901i	$-0.878706\pi$
$491$	0.915445	−	2.81745i	0.0413134	−	0.127150i	0.969586	+	0.244751i	$0.0787062\pi$
$492$	−0.397504	−	0.528930i	−0.0179209	−	0.0238460i
$493$	−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
$498$	−0.741137	−	1.42597i	−0.0332112	−	0.0638990i
$499$	13.5983	+	4.41837i	0.608745	+	0.197793i	0.597137	−	0.802139i	$-0.296305\pi$
$499$	13.5983	+	4.41837i	0.608745	+	0.197793i	0.0116082	+	0.999933i	$0.496305\pi$
$500$	1.91185	+	0.587219i	0.0855006	+	0.0262613i
$501$	−1.07065	+	1.47362i	−0.0478331	+	0.0658366i
$502$	−2.53448	+	16.8838i	−0.113120	+	0.753563i
$503$	1.85269	+	5.70198i	0.0826072	+	0.254239i	0.983826	−	0.179125i	$-0.0573266\pi$
$503$	1.85269	+	5.70198i	0.0826072	+	0.254239i	−0.901219	+	0.433364i	$0.857327\pi$
$504$	−34.1126	−	16.3523i	−1.51950	−	0.728388i
$505$			3.52291i			0.156768i
$506$	−16.4294	−	1.14056i	−0.730378	−	0.0507041i
$507$		−	0.828741i		−	0.0368057i
$508$	12.6849	−	18.0660i	0.562800	−	0.801550i
$509$	−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	$0.939809\pi$
$510$	−0.267767	−	0.0401954i	−0.0118569	−	0.00177988i
$511$	−40.0251	+	55.0899i	−1.77061	+	2.43703i
$512$	−17.1201	−	14.7953i	−0.756609	−	0.653868i
$513$	−4.84994	−	1.57584i	−0.214130	−	0.0695750i
$514$	15.9968	−	8.31424i	0.705588	−	0.366726i
$515$	−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
$520$	5.09315	+	4.85205i	0.223349	+	0.212777i
$521$	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	$-0.0246997\pi$
$522$	28.4314	+	14.1984i	1.24441	+	0.621445i
$523$	−14.8461	−	10.7863i	−0.649175	−	0.471653i	0.213815	−	0.976874i	$-0.431411\pi$
$523$	−14.8461	−	10.7863i	−0.649175	−	0.471653i	−0.862990	+	0.505221i	$0.831411\pi$
$524$	0.589862	+	36.5017i	0.0257682	+	1.59458i
$525$	−0.518191	+	0.168370i	−0.0226157	+	0.00734829i
$526$	4.98663	+	4.90670i	0.217427	+	0.213942i
$527$	0.170575			0.00743035
$528$	−1.40305	−	0.796475i	−0.0610598	−	0.0346621i
$529$	10.6715			0.463977
$530$	3.04815	+	2.99929i	0.132403	+	0.130281i
$531$	12.8471	−	4.17427i	0.557516	−	0.181148i
$532$	−1.01437	−	62.7711i	−0.0439786	−	2.72147i
$533$	5.47345	+	3.97670i	0.237082	+	0.172250i
$534$	−0.611332	−	0.305293i	−0.0264549	−	0.0132113i
$535$	2.14976	−	6.61628i	0.0929422	−	0.286047i
$536$	12.1400	+	11.5654i	0.524370	+	0.499548i
$537$	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	$0.846205\pi$
$542$	16.5813	−	8.61802i	0.712227	−	0.370176i
$543$	1.48113	+	0.481250i	0.0635616	+	0.0206524i
$544$	−8.73292	+	1.74731i	−0.374421	+	0.0749154i
$545$	6.68200	−	9.19699i	0.286226	−	0.393956i
$546$	−1.89514	−	0.284485i	−0.0811044	−	0.0121748i
$547$	−10.6735	−	32.8498i	−0.456368	−	1.40456i	−0.869522	−	0.493895i	$-0.835573\pi$
$547$	−10.6735	−	32.8498i	−0.456368	−	1.40456i	0.413154	−	0.910661i	$-0.364427\pi$
$548$	9.44824	−	13.4564i	0.403609	−	0.574827i
$549$		−	14.5427i		−	0.620667i
$550$	4.55052	−	1.13700i	0.194035	−	0.0484819i
$551$			52.7393i			2.24677i
$552$	−1.08908	−	0.522063i	−0.0463542	−	0.0222205i
$553$	3.05630	+	9.40631i	0.129967	+	0.399997i
$554$	3.09327	−	20.6063i	0.131420	−	0.875477i
$555$	−0.391930	+	0.539445i	−0.0166365	+	0.0228982i
$556$	−19.5739	−	6.01206i	−0.830118	−	0.254968i
$557$	−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	$0.693059\pi$
$558$	−0.210941	−	0.405856i	−0.00892986	−	0.0171813i
$559$	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	−0.964864	−	0.262748i	$-0.915371\pi$
$563$	−24.0393	+	17.4656i	−1.01314	+	0.736086i	−0.0482710	+	0.998834i	$0.515371\pi$
$564$	−0.955457	−	1.27136i	−0.0402320	−	0.0535337i
$565$	1.41923	−	4.36795i	0.0597076	−	0.183761i
$566$	15.6643	−	31.3668i	0.658418	−	1.31844i
$567$	32.1403	+	23.3513i	1.34977	+	0.980662i
$568$	−7.17930	−	39.1604i	−0.301237	−	1.64313i
$569$	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	$0.324222\pi$
$570$	−0.845110	+	0.858877i	−0.0353978	+	0.0359744i
$571$	−26.4616			−1.10738			−0.553692	−	0.832721i	$-0.686782\pi$
$571$	−26.4616			−1.10738			−0.553692	+	0.832721i	$0.686782\pi$
$572$	16.1055	+	3.57296i	0.673406	+	0.149393i
$573$	−0.0870168			−0.00363518
$574$	−12.0891	+	12.2861i	−0.504591	+	0.512811i
$575$	3.33935	−	1.08502i	0.139261	−	0.0452485i
$576$	14.9570	+	18.6178i	0.623209	+	0.775742i
$577$	−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	$0.807311\pi$
$578$	9.17514	−	18.3727i	0.381636	−	0.764203i
$579$	−0.108164	+	0.332894i	−0.00449513	+	0.0138346i
$580$	12.0354	−	9.04489i	0.499741	−	0.375568i
$581$	−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
$586$	−9.78350	−	18.8237i	−0.404153	−	0.777599i
$587$	30.3271	+	9.85387i	1.25173	+	0.406713i	0.858542	−	0.512744i	$-0.171371\pi$
$587$	30.3271	+	9.85387i	1.25173	+	0.406713i	0.393192	+	0.919456i	$0.371371\pi$
$588$	0.933599	−	3.03958i	0.0385010	−	0.125350i
$589$	0.446172	−	0.614103i	0.0183842	−	0.0253037i
$590$	0.949987	−	6.32848i	0.0391104	−	0.260539i
$591$	−0.693701	−	2.13499i	−0.0285351	−	0.0878219i
$592$	−6.09982	+	21.0666i	−0.250701	+	0.865830i
$593$			36.4226i			1.49570i	0.663870	+	0.747848i	$0.268913\pi$
$593$			36.4226i			1.49570i	−0.663870	+	0.747848i	$0.731087\pi$
$594$	2.61638	+	2.19317i	0.107352	+	0.0899867i
$595$			7.05371i			0.289174i
$596$	37.4546	+	26.2984i	1.53420	+	1.07722i
$597$	0.358467	+	1.10325i	0.0146711	+	0.0451529i
$598$	12.2127	+	1.83329i	0.499416	+	0.0749688i
$599$	−2.96698	+	4.08370i	−0.121228	+	0.166856i	−0.865318	−	0.501224i	$-0.832883\pi$
$599$	−2.96698	+	4.08370i	−0.121228	+	0.166856i	0.744090	+	0.668079i	$0.232883\pi$
$600$	0.340938	+	0.0455592i	0.0139187	+	0.00185995i
$601$	−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	$0.870344\pi$
$602$	−54.3613	+	28.2540i	−2.21560	+	1.15155i
$603$	−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	−0.994773	−	0.102115i	$-0.967439\pi$
$607$	−29.6894	+	21.5706i	−1.20506	+	0.875525i	−0.210285	+	0.977640i	$0.567439\pi$
$608$	−16.5520	+	36.0107i	−0.671272	+	1.46043i
$609$	−1.26743	+	3.90074i	−0.0513587	+	0.158066i
$610$	−6.16362	−	3.07805i	−0.249558	−	0.124627i
$611$	13.1562	+	9.55854i	0.532243	+	0.386697i
$612$	9.39845	−	0.151878i	0.379910	−	0.00613929i
$613$	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	$0.0716877\pi$
$614$	−12.2400	−	12.0438i	−0.493966	−	0.486048i
$615$	0.330823			0.0133401
$616$	−15.0930	+	39.2257i	−0.608114	+	1.58045i
$617$	8.90031			0.358313			0.179157	−	0.983821i	$-0.442663\pi$
$617$	8.90031			0.358313			0.179157	+	0.983821i	$0.442663\pi$
$618$	−1.59248	−	1.56695i	−0.0640590	−	0.0630322i
$619$	−37.3028	+	12.1204i	−1.49933	+	0.487161i	−0.939821	−	0.341666i	$-0.889009\pi$
$619$	−37.3028	+	12.1204i	−1.49933	+	0.487161i	−0.559505	+	0.828827i	$0.689009\pi$
$620$	−0.216661	+	0.00350120i	−0.00870130	+	0.000140612i
$621$	2.06760	+	1.50220i	0.0829699	+	0.0602811i
$622$	27.8264	+	13.8962i	1.11574	+	0.557189i
$623$	−5.50085	+	16.9299i	−0.220387	+	0.678281i
$624$	1.00122	+	0.679108i	0.0400808	+	0.0271861i
$625$	−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
$630$	16.7832	−	8.72298i	0.668659	−	0.347532i
$631$	38.1771	+	12.4045i	1.51981	+	0.493815i	0.945720	−	0.324981i	$-0.105358\pi$
$631$	38.1771	+	12.4045i	1.51981	+	0.493815i	0.574085	+	0.818796i	$0.305358\pi$
$632$	0.827000	−	6.18878i	0.0328963	−	0.246176i
$633$	0.231612	−	0.318787i	0.00920576	−	0.0126706i
$634$	−5.14268	−	0.771983i	−0.204242	−	0.0306594i
$635$	3.41071	+	10.4971i	0.135350	+	0.416564i
$636$	0.601906	+	0.422622i	0.0238671	+	0.0167580i
$637$			32.5138i			1.28824i
$638$	13.2100	−	32.7433i	0.522990	−	1.29632i
$639$			42.0199i			1.66228i
$640$	11.0565	−	2.39865i	0.437047	−	0.0948150i
$641$	−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	$-0.425761\pi$
$642$	0.177613	−	1.18320i	0.00700984	−	0.0466971i
$643$	20.2347	−	27.8507i	0.797979	−	1.09832i	−0.195089	−	0.980785i	$-0.562500\pi$
$643$	20.2347	−	27.8507i	0.797979	−	1.09832i	0.993068	−	0.117538i	$-0.0375003\pi$
$644$	−9.23774	+	30.0760i	−0.364018	+	1.18516i
$645$	1.11833	+	0.363367i	0.0440342	+	0.0143076i
$646$	7.19391	+	13.8412i	0.283041	+	0.544576i
$647$	10.2966	+	14.1721i	0.404801	+	0.557161i	0.961941	−	0.273258i	$-0.0881012\pi$
$647$	10.2966	+	14.1721i	0.404801	+	0.557161i	−0.557140	+	0.830419i	$0.688101\pi$
$648$	−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
$652$	−21.5432	+	16.1903i	−0.843698	+	0.634061i
$653$	−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	$0.829612\pi$
$654$	0.873509	−	1.74915i	0.0341569	−	0.0683972i
$655$	−14.7672	−	10.7290i	−0.577001	−	0.419216i
$656$	10.2347	−	3.69515i	0.399599	−	0.144271i
$657$	−43.1505	+	14.0204i	−1.68346	+	0.546990i
$658$	−29.0579	+	29.5313i	−1.13280	+	1.15125i
$659$	40.0343			1.55951			0.779757	−	0.626082i	$-0.215343\pi$
$659$	40.0343			1.55951			0.779757	+	0.626082i	$0.215343\pi$
$660$	0.739818	−	0.321555i	0.0287974	−	0.0125165i
$661$	32.7231			1.27278			0.636390	−	0.771368i	$-0.280427\pi$
$661$	32.7231			1.27278			0.636390	+	0.771368i	$0.280427\pi$
$662$	−7.17274	+	7.28959i	−0.278776	+	0.283318i
$663$	0.452865	−	0.147145i	0.0175878	−	0.00571463i
$664$	25.9963	−	4.76592i	1.00885	−	0.184954i
$665$	25.3948	+	18.4504i	0.984767	+	0.715475i
$666$	10.3418	−	20.7089i	0.400737	−	0.802453i
$667$	8.16762	−	25.1373i	0.316251	−	0.973321i
$668$	−17.9970	−	23.9473i	−0.696326	−	0.926550i
$669$	−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	$0.853635\pi$
$674$	−2.60418	−	5.01049i	−0.100309	−	0.192997i
$675$	−0.692244	−	0.224924i	−0.0266445	−	0.00865732i
$676$	13.0286	+	4.00171i	0.501102	+	0.153912i
$677$	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	$-0.0185156\pi$
$678$	0.117257	−	0.781126i	0.00450323	−	0.0299990i
$679$	12.0514	+	37.0904i	0.462490	+	1.42340i
$680$	1.92487	−	4.01548i	0.0738154	−	0.153987i
$681$		−	0.386624i		−	0.0148154i
$682$	−0.430826	+	0.269511i	−0.0164972	+	0.0103201i
$683$			32.2020i			1.23218i	0.787677	+	0.616088i	$0.211283\pi$
$683$			32.2020i			1.23218i	−0.787677	+	0.616088i	$0.788717\pi$
$684$	24.0367	−	34.2336i	0.919067	−	1.30895i
$685$	2.54045	+	7.81869i	0.0970654	+	0.298737i
$686$	−38.0552	−	5.71257i	−1.45295	−	0.218107i
$687$	−0.631983	+	0.869850i	−0.0241117	+	0.0331868i
$688$	38.6566	−	1.24969i	1.47377	−	0.0476442i
$689$	−7.15225	−	2.32391i	−0.272479	−	0.0885338i
$690$	0.535820	−	0.278490i	0.0203983	−	0.0106019i
$691$	9.77927	+	13.4600i	0.372021	+	0.512043i	0.953449	−	0.301555i	$-0.0975057\pi$
$691$	9.77927	+	13.4600i	0.372021	+	0.512043i	−0.581428	+	0.813598i	$0.697506\pi$
$692$	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
$696$	1.78597	−	1.87472i	0.0676972	−	0.0710610i
$697$	1.32347	−	4.07321i	0.0501299	−	0.154284i
$698$	−3.09658	−	1.54640i	−0.117207	−	0.0585322i
$699$	−0.592588	−	0.430541i	−0.0224137	−	0.0162845i
$700$	−0.144784	−	8.95949i	−0.00547232	−	0.338637i
$701$	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	$0.382057\pi$
$702$	−1.82480	−	1.79555i	−0.0688725	−	0.0677686i
$703$	38.4143			1.44882
$704$	19.2962	−	18.2114i	0.727254	−	0.686368i
$705$	0.795180			0.0299482
$706$	24.1767	+	23.7891i	0.909900	+	0.895315i
$707$	15.0113	−	4.87747i	0.564558	−	0.183436i
$708$	−0.0177831	−	1.10045i	−0.000668330	−	0.0413574i
$709$	−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	$0.723865\pi$
$710$	17.8093	+	8.89378i	0.668370	+	0.333777i
$711$	−2.03639	+	6.26736i	−0.0763705	+	0.235044i
$712$	7.75144	−	8.13660i	0.290497	−	0.304932i
$713$	−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
$718$	−32.1259	+	16.6973i	−1.19893	+	0.623137i
$719$	−23.6939	−	7.69862i	−0.883634	−	0.287110i	−0.168169	−	0.985758i	$-0.553785\pi$
$719$	−23.6939	−	7.69862i	−0.883634	−	0.287110i	−0.715465	+	0.698648i	$0.753785\pi$
$720$	−11.9346	+	0.385824i	−0.444777	+	0.0143788i
$721$	−34.2097	+	47.0856i	−1.27403	+	1.75356i
$722$	42.0760	+	6.31615i	1.56591	+	0.235063i
$723$	−1.07918	−	3.32136i	−0.0401350	−	0.123523i
$724$	−14.7176	+	20.9611i	−0.546976	+	0.779015i
$725$			7.52761i			0.279569i
$726$	1.09604	−	1.54198i	0.0406779	−	0.0572282i
$727$			24.6077i			0.912650i	0.889813	+	0.456325i	$0.150835\pi$
$727$			24.6077i			0.912650i	−0.889813	+	0.456325i	$0.849165\pi$
$728$	13.6234	−	28.4198i	0.504915	−	1.05331i
$729$	8.09768	+	24.9221i	0.299914	+	0.923041i
$730$	−3.19079	+	21.2559i	−0.118097	+	0.786718i
$731$	8.94781	−	12.3156i	0.330947	−	0.455509i
$732$	−1.13266	−	0.347892i	−0.0418641	−	0.0128585i
$733$	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	$0.576466\pi$
$734$	7.21845	+	13.8885i	0.266438	+	0.512632i
$735$	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	−0.401760	−	0.915745i	$-0.631601\pi$
$739$	9.37909	−	6.81431i	0.345015	−	0.250668i	0.746775	+	0.665077i	$0.231601\pi$
$740$	−6.58812	−	8.76633i	−0.242184	−	0.322257i
$741$	0.654808	−	2.01529i	0.0240550	−	0.0740336i
$742$	8.55994	−	17.1408i	0.314245	−	0.629258i
$743$	0.189782	+	0.137885i	0.00696244	+	0.00505851i	0.591261	−	0.806480i	$-0.298630\pi$
$743$	0.189782	+	0.137885i	0.00696244	+	0.00505851i	−0.584299	+	0.811539i	$0.698630\pi$
$744$	−0.0366562	+	0.00672020i	−0.00134388	+	0.000246375i
$745$	−21.7626	+	7.07111i	−0.797321	+	0.259065i
$746$	21.1752	−	21.5201i	0.775278	−	0.787907i
$747$	−27.8946			−1.02061
$748$	−0.999433	−	10.3953i	−0.0365429	−	0.380089i
$749$	−31.1686			−1.13888
$750$	−0.120625	+	0.122590i	−0.00440459	+	0.00447634i
$751$	−3.84996	+	1.25093i	−0.140487	+	0.0456470i	−0.378416	−	0.925635i	$-0.623531\pi$
$751$	−3.84996	+	1.25093i	−0.140487	+	0.0456470i	0.237930	+	0.971282i	$0.423531\pi$
$752$	24.6006	−	8.88180i	0.897091	−	0.323886i
$753$	−1.18775	−	0.862953i	−0.0432841	−	0.0314478i
$754$	−11.8289	+	23.6867i	−0.430783	+	0.862618i
$755$	−1.41979	+	4.36966i	−0.0516714	+	0.159028i
$756$	5.21392	−	3.91840i	0.189629	−	0.142511i
$757$	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	$0.992596\pi$
$762$	0.875419	+	1.68433i	0.0317131	+	0.0610167i
$763$	−48.4400	−	15.7391i	−1.75365	−	0.569794i
$764$	0.420175	−	1.36799i	0.0152014	−	0.0494922i
$765$	−2.76250	+	3.80225i	−0.0998783	+	0.137471i
$766$	−1.95455	+	13.0205i	−0.0706208	+	0.470451i
$767$	3.47766	+	10.7031i	0.125571	+	0.386468i
$768$	1.80785	−	0.719548i	0.0652350	−	0.0259644i
$769$			10.2709i			0.370377i	0.982703	+	0.185189i	$0.0592896\pi$
$769$			10.2709i			0.370377i	−0.982703	+	0.185189i	$0.940710\pi$
$770$	−11.1450	−	17.8158i	−0.401638	−	0.642037i
$771$			1.55030i			0.0558328i
$772$	−4.71114	−	3.30787i	−0.169558	−	0.119053i
$773$	−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	$0.965831\pi$
$774$	−40.3684	−	6.05982i	−1.45101	−	0.217816i
$775$	0.0636833	−	0.0876525i	0.00228757	−	0.00314857i
$776$	3.26097	−	24.4032i	0.117062	−	0.876024i
$777$	2.84122	+	0.923170i	0.101928	+	0.0331185i
$778$	34.9380	−	18.1588i	1.25259	−	0.651025i
$779$	−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
$784$	43.2773	+	29.3542i	1.54562	+	1.04837i
$785$	3.12247	−	9.60996i	0.111446	−	0.342994i
$786$	−2.80853	−	1.40255i	−0.100177	−	0.0500274i
$787$	−12.7259	−	9.24589i	−0.453629	−	0.329580i	0.337398	−	0.941362i	$-0.390453\pi$
$787$	−12.7259	−	9.24589i	−0.453629	−	0.329580i	−0.791027	+	0.611782i	$0.790453\pi$
$788$	36.9139	−	0.596523i	1.31500	−	0.0212503i
$789$	−0.572145	+	0.185901i	−0.0203689	+	0.00661826i
$790$	2.22527	+	2.18961i	0.0791717	+	0.0779027i
$791$	−20.5770			−0.731632
$792$	−23.4980	+	15.2333i	−0.834965	+	0.541293i
$793$	12.1158			0.430244
$794$	21.8773	+	21.5266i	0.776396	+	0.763951i
$795$	−0.349732	+	0.113635i	−0.0124037	+	0.00403021i
$796$	−19.0751	+	0.308250i	−0.676098	+	0.0109256i
$797$	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	$0.666062\pi$
$798$	4.82977	+	2.41194i	0.170972	+	0.0853817i
$799$	3.18114	−	9.79053i	0.112541	−	0.346364i
$800$	−2.36251	+	5.13990i	−0.0835273	+	0.181723i
$801$	−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
$806$	0.338126	−	0.175739i	0.0119100	−	0.00619014i
$807$	−0.580695	−	0.188679i	−0.0204414	−	0.00664182i
$808$	−9.87652	−	1.31979i	−0.347455	−	0.0464300i
$809$	−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	$0.337015\pi$
$810$	12.4011	+	1.86156i	0.435729	+	0.0654085i
$811$	−16.7838	−	51.6551i	−0.589357	−	1.81386i	−0.581018	−	0.813890i	$-0.697346\pi$
$811$	−16.7838	−	51.6551i	−0.589357	−	1.81386i	−0.00833908	−	0.999965i	$-0.502654\pi$
$812$	−55.2036	−	38.7606i	−1.93727	−	1.36023i
$813$			1.60695i			0.0563580i
$814$	−23.8496	−	9.62192i	−0.835928	−	0.337248i
$815$		−	13.4744i		−	0.471987i
$816$	0.213002	−	0.735630i	0.00745655	−	0.0257522i
$817$	−20.9339	−	64.4278i	−0.732383	−	2.25404i
$818$	5.18092	−	34.5135i	0.181146	−	1.20673i
$819$	−19.5517	+	26.9106i	−0.683192	+	0.940333i
$820$	−1.59743	+	5.20088i	−0.0557848	+	0.181623i
$821$	−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	$0.632222\pi$
$822$	0.652050	+	1.25456i	0.0227429	+	0.0437578i
$823$	−26.5574	−	36.5531i	−0.925731	−	1.27416i	−0.961501	−	0.274800i	$-0.911388\pi$
$823$	−26.5574	−	36.5531i	−0.925731	−	1.27416i	0.0357700	−	0.999360i	$-0.488612\pi$
$824$	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	−0.567369	−	0.823464i	$-0.692039\pi$
$827$	1.16367	−	0.845457i	0.0404648	−	0.0293994i	0.607834	+	0.794064i	$0.292039\pi$
$828$	−16.7584	+	12.5944i	−0.582394	+	0.437685i
$829$	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	$0.0833475\pi$
$830$	−5.90406	+	11.8225i	−0.204933	+	0.410367i
$831$	1.44962	+	1.05321i	0.0502868	+	0.0365355i
$832$	−15.5108	+	12.4610i	−0.537741	+	0.432006i
$833$	19.5750	−	6.36029i	0.678232	−	0.220371i
$834$	1.23498	−	1.25510i	0.0427638	−	0.0434604i
$835$	14.9780			0.518337
$836$	−40.0393	−	23.5928i	−1.38479	−	0.815973i
$837$	0.0788605			0.00272582
$838$	−18.6783	+	18.9826i	−0.645232	+	0.655743i
$839$	48.7944	−	15.8542i	1.68457	−	0.547349i	0.698779	−	0.715337i	$-0.253727\pi$
$839$	48.7944	−	15.8542i	1.68457	−	0.547349i	0.985789	+	0.167988i	$0.0537270\pi$
$840$	−0.277898	−	1.51583i	−0.00958839	−	0.0523010i
$841$	22.3814	+	16.2611i	0.771773	+	0.560726i
$842$	12.3310	−	24.6922i	0.424956	−	0.850949i
$843$	−0.823644	+	2.53491i	−0.0283678	+	0.0873071i
$844$	3.89327	+	5.18049i	0.134012	+	0.178320i
$845$	−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
$850$	1.02681	+	1.97560i	0.0352191	+	0.0677624i
$851$	−18.3096	−	5.94913i	−0.627643	−	0.203934i
$852$	3.27271	+	1.00520i	0.112121	+	0.0344377i
$853$	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	$0.173572\pi$
$854$	−4.58220	+	30.5250i	−0.156800	+	1.04455i
$855$	6.46300	+	19.8911i	0.221030	+	0.680260i
$856$	17.7434	+	8.50552i	0.606458	+	0.290713i
$857$		−	34.2852i		−	1.17116i	−0.810614	−	0.585581i	$-0.800867\pi$
$857$		−	34.2852i		−	1.17116i	0.810614	−	0.585581i	$-0.199133\pi$
$858$	−0.911325	+	1.08718i	−0.0311121	+	0.0371159i
$859$		−	32.9123i		−	1.12295i	−0.827492	−	0.561477i	$-0.810233\pi$
$859$		−	32.9123i		−	1.12295i	0.827492	−	0.561477i	$-0.189767\pi$
$860$	−11.1125	+	15.8267i	−0.378935	+	0.539686i
$861$	−0.458024	−	1.40965i	−0.0156094	−	0.0480409i
$862$	30.4851	+	4.57620i	1.03833	+	0.155866i
$863$	23.6324	−	32.5273i	0.804457	−	1.10724i	−0.187698	−	0.982227i	$-0.560103\pi$
$863$	23.6324	−	32.5273i	0.804457	−	1.10724i	0.992155	−	0.125014i	$-0.0398975\pi$
$864$	−4.03742	+	0.807821i	−0.137356	+	0.0274826i
$865$	−3.56847	−	1.15946i	−0.121331	−	0.0394230i
$866$	−22.0171	+	11.4433i	−0.748173	+	0.388859i
$867$	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
$872$	23.2805	+	22.1785i	0.788379	+	0.751059i
$873$	−8.02976	+	24.7131i	−0.271766	+	0.836410i
$874$	−31.1242	−	15.5431i	−1.05279	−	0.525754i
$875$	3.62466	+	2.63347i	0.122536	+	0.0890276i
$876$	0.0597295	+	3.69616i	0.00201807	+	0.124882i
$877$	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	$0.142839\pi$
$878$	14.0420	+	13.8169i	0.473895	+	0.466298i
$879$	1.82426			0.0615309
$880$	1.48283	+	13.1834i	0.0499863	+	0.444411i
$881$	55.5720			1.87227			0.936134	−	0.351643i	$-0.114377\pi$
$881$	55.5720			1.87227			0.936134	+	0.351643i	$0.114377\pi$
$882$	−39.3407	−	38.7101i	−1.32467	−	1.30344i
$883$	−18.8261	+	6.11696i	−0.633547	+	0.205852i	−0.608146	−	0.793825i	$-0.708086\pi$
$883$	−18.8261	+	6.11696i	−0.633547	+	0.205852i	−0.0254014	+	0.999677i	$0.508086\pi$
$884$	0.126532	+	7.83001i	0.00425573	+	0.263352i
$885$	0.445199	+	0.323456i	0.0149652	+	0.0108729i
$886$	−19.8787	−	9.92721i	−0.667837	−	0.333511i
$887$	−12.3009	+	37.8582i	−0.413023	+	1.27116i	0.500984	+	0.865457i	$0.332972\pi$
$887$	−12.3009	+	37.8582i	−0.413023	+	1.27116i	−0.914007	+	0.405699i	$0.867028\pi$
$888$	−1.36551	−	1.30087i	−0.0458235	−	0.0436543i
$889$	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
$894$	−3.49196	+	1.81493i	−0.116789	+	0.0607002i
$895$	−3.37551	−	1.09677i	−0.112831	−	0.0366610i
$896$	−25.5285	−	43.7914i	−0.852847	−	1.46297i
$897$	−0.624207	+	0.859148i	−0.0208417	+	0.0286861i
$898$	−22.0908	−	3.31612i	−0.737181	−	0.110660i
$899$	−0.252027	−	0.775658i	−0.00840556	−	0.0258696i
$900$	3.43082	−	4.88624i	0.114361	−	0.162875i
$901$			4.76062i			0.158599i
$902$	3.09303	+	12.3789i	0.102987	+	0.412174i
$903$		−	5.26834i		−	0.175319i
$904$	11.7139	+	5.61519i	0.389598	+	0.186759i
$905$	−3.95728	−	12.1793i	−0.131545	−	0.404852i
$906$	−0.117303	+	0.781432i	−0.00389713	+	0.0259613i
$907$	11.0946	−	15.2704i	0.368389	−	0.507044i	−0.584073	−	0.811701i	$-0.698542\pi$
$907$	11.0946	−	15.2704i	0.368389	−	0.507044i	0.952462	+	0.304657i	$0.0985419\pi$
$908$	6.07811	+	1.86687i	0.201709	+	0.0619544i
$909$	10.0019	+	3.24982i	0.331743	+	0.107790i
$910$	7.26726	+	13.9824i	0.240907	+	0.463511i
$911$	−2.42801	−	3.34186i	−0.0804434	−	0.110721i	0.766899	−	0.641768i	$-0.221799\pi$
$911$	−2.42801	−	3.34186i	−0.0804434	−	0.110721i	−0.847342	+	0.531047i	$0.821799\pi$
$912$	−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
$916$	−10.6233	−	14.1356i	−0.351003	−	0.467054i
$917$	−25.2716	+	77.7778i	−0.834540	+	2.56845i
$918$	−0.724047	+	1.44986i	−0.0238971	+	0.0478526i
$919$	−4.84527	−	3.52029i	−0.159831	−	0.116124i	0.504995	−	0.863122i	$-0.331494\pi$
$919$	−4.84527	−	3.52029i	−0.159831	−	0.116124i	−0.664826	+	0.746998i	$0.731494\pi$
$920$	1.79084	+	9.76837i	0.0590424	+	0.322054i
$921$	1.40437	−	0.456306i	0.0462754	−	0.0150358i
$922$	−9.01143	+	9.15823i	−0.296776	+	0.301610i
$923$	−35.0075			−1.15229
$924$	−2.39444	−	2.70721i	−0.0787712	−	0.0890606i
$925$	5.48297			0.180279
$926$	−39.9210	+	40.5713i	−1.31188	+	1.33326i
$927$	−36.8809	+	11.9833i	−1.21133	+	0.393584i
$928$	20.8486	+	37.1297i	0.684389	+	1.21884i
$929$	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	$0.657428\pi$
$930$	0.00832504	−	0.0166704i	0.000272989	−	0.000546644i
$931$	28.3039	−	87.1103i	0.927622	−	2.85493i
$932$	9.62994	−	7.23715i	0.315439	−	0.237061i
$933$	−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	$0.363804\pi$
$938$	17.3223	+	33.3284i	0.565592	+	1.08821i
$939$	0.170153	+	0.0552860i	0.00555273	+	0.00180419i
$940$	−3.83966	+	12.5010i	−0.125236	+	0.407739i
$941$	−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	$0.976295\pi$
$942$	0.257978	−	1.71856i	0.00840539	−	0.0559938i
$943$	2.95162	+	9.08416i	0.0961180	+	0.295821i
$944$	17.3861	+	5.03413i	0.565868	+	0.163847i
$945$			3.26109i			0.106083i
$946$	−3.14089	+	45.2436i	−0.102119	+	1.47100i
$947$		−	46.8461i		−	1.52229i	−0.648581	−	0.761146i	$-0.724637\pi$
$947$		−	46.8461i		−	1.52229i	0.648581	−	0.761146i	$-0.275363\pi$
$948$	0.439417	+	0.308532i	0.0142716	+	0.0100206i
$949$	−11.6807	−	35.9494i	−0.379171	−	1.16697i
$950$	9.79835	+	1.47086i	0.317900	+	0.0477210i
$951$	0.262849	−	0.361780i	0.00852345	−	0.0117315i
$952$	−19.7751	−	2.64253i	−0.640916	−	0.0856449i
$953$	−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	$0.840555\pi$
$954$	11.3271	−	5.88722i	0.366730	−	0.190606i
$955$	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
$960$	−0.255451	+	0.938754i	−0.00824464	+	0.0302982i
$961$	9.57590	−	29.4716i	0.308900	−	0.950696i
$962$	17.2529	+	8.61595i	0.556257	+	0.277789i
$963$	−16.8012	−	12.2068i	−0.541411	−	0.393358i
$964$	57.4262	−	0.927998i	1.84957	−	0.0298888i
$965$	2.73736	−	0.889422i	0.0881187	−	0.0286315i
$966$	−1.92850	−	1.89759i	−0.0620485	−	0.0610539i
$967$	0.818731			0.0263286			0.0131643	−	0.999913i	$-0.495810\pi$
$967$	0.818731			0.0263286			0.0131643	+	0.999913i	$0.495810\pi$
$968$	18.9490	+	24.6766i	0.609045	+	0.793135i
$969$	−1.34140			−0.0430920
$970$	8.77457	+	8.63392i	0.281734	+	0.277218i
$971$	15.1273	−	4.91516i	0.485458	−	0.157735i	−0.0560541	−	0.998428i	$-0.517852\pi$
$971$	15.1273	−	4.91516i	0.485458	−	0.157735i	0.541512	+	0.840693i	$0.317852\pi$
$972$	6.52304	−	0.105411i	0.209227	−	0.00338107i
$973$	−37.1100	−	26.9620i	−1.18969	−	0.864361i
$974$	−32.7937	−	16.3769i	−1.05078	−	0.524749i
$975$	0.0934624	−	0.287648i	0.00299319	−	0.00921210i
$976$	10.9384	−	16.1266i	0.350130	−	0.516201i
$977$	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
$982$	−3.71741	+	1.93210i	−0.118627	+	0.0616558i
$983$	21.3149	+	6.92563i	0.679839	+	0.220893i	0.628525	−	0.777789i	$-0.283659\pi$
$983$	21.3149	+	6.92563i	0.679839	+	0.220893i	0.0513143	+	0.998683i	$0.483659\pi$
$984$	−0.123936	+	0.927466i	−0.00395094	+	0.0295665i
$985$	−10.8501	+	14.9339i	−0.345714	+	0.475835i
$986$	16.5745	+	2.48805i	0.527841	+	0.0792358i
$987$	−1.10092	−	3.38830i	−0.0350428	−	0.107851i
$988$	28.5206	+	20.0254i	0.907360	+	0.637093i
$989$			33.9505i			1.07956i
$990$	0.969701	−	13.9683i	0.0308191	−	0.443940i
$991$		−	48.1472i		−	1.52945i	−0.644359	−	0.764723i	$-0.722876\pi$
$991$		−	48.1472i		−	1.52945i	0.644359	−	0.764723i	$-0.277124\pi$
$992$	0.0713519	−	0.608721i	0.00226542	−	0.0193269i
$993$	−0.271755	−	0.836377i	−0.00862390	−	0.0265416i
$994$	13.2399	−	88.1995i	0.419944	−	2.79752i
$995$	5.60676	−	7.71704i	0.177746	−	0.244646i
$996$	−0.667297	+	2.17256i	−0.0211441	+	0.0688403i
$997$	−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	$0.705057\pi$
$998$	−9.32523	−	17.9419i	−0.295185	−	0.567942i
$999$	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.151.4	yes	48
4.3	odd	2	inner	220.2.r.d.151.5	yes	48
11.7	odd	10	inner	220.2.r.d.51.5	yes	48
44.7	even	10	inner	220.2.r.d.51.4	✓	48

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.00805 - 0.991888i) q^{2} +(0.115659 - 0.0375799i) q^{3} +(0.0323155 + 1.99974i) q^{4} +(-0.809017 - 0.587785i) q^{5} +(-0.153865 - 0.0768386i) q^{6} +(-1.38450 + 4.26105i) q^{7} +(1.95094 - 2.04788i) 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} +(5.62212 - 2.92206i) q^{14} +(-0.115659 - 0.0375799i) q^{15} +(-3.99791 + 0.129245i) q^{16} +(-0.925394 + 1.27370i) q^{17} +(4.17495 + 0.626714i) q^{18} +(2.16501 + 6.66320i) q^{19} +(1.14927 - 1.63682i) q^{20} +0.544858i q^{21} +(0.324835 - 4.67915i) q^{22} -3.51120i q^{23} +(0.148685 - 0.310173i) q^{24} +(0.309017 + 0.951057i) q^{25} +(-0.522126 + 3.47822i) q^{26} +(-0.427830 + 0.588858i) q^{27} +(-8.56572 - 2.63094i) q^{28} +(7.15919 + 2.32616i) q^{29} +(0.0793147 + 0.152603i) 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} +(-3.58691 - 4.77284i) q^{36} +(1.69433 - 5.21461i) q^{37} +(4.42673 - 8.86426i) q^{38} +(-0.244688 - 0.177776i) q^{39} +(-2.78206 + 0.510037i) q^{40} +(-2.58719 + 0.840630i) q^{41} +(0.540438 - 0.549242i) q^{42} -9.66919 q^{43} +(-4.96865 + 4.39460i) q^{44} +2.98521 q^{45} +(-3.48272 + 3.53945i) q^{46} +(-6.21868 + 2.02057i) q^{47} +(-0.457538 + 0.165190i) q^{48} +(-10.5766 - 7.68432i) q^{49} +(0.631838 - 1.26522i) q^{50} +(-0.0591649 + 0.182091i) q^{51} +(3.97633 - 2.98832i) 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} +(-4.90950 - 9.44599i) q^{58} +(-4.30358 - 1.39832i) q^{59} +(0.0714125 - 0.232502i) q^{60} +(-2.86345 + 3.94119i) q^{61} +(-0.0227458 + 0.151525i) q^{62} +(-4.13302 - 12.7201i) q^{63} +(-0.387651 - 7.99060i) q^{64} +2.48703i q^{65} +(-0.138272 - 0.553394i) q^{66} +5.92809i q^{67} +(-2.57696 - 1.80939i) q^{68} +(-0.131951 - 0.406102i) q^{69} +(-6.26594 - 0.940598i) q^{70} +(8.27369 - 11.3878i) q^{71} +(-1.11835 + 8.36906i) q^{72} +(14.4548 + 4.69663i) q^{73} +(-6.88028 + 3.57599i) 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} +(3.31035 + 2.24535i) q^{80} +(2.74009 - 8.43313i) q^{81} +(3.44182 + 1.71881i) q^{82} +(7.55967 + 5.49242i) q^{83} +(-1.08957 + 0.0176074i) q^{84} +(1.49732 - 0.486508i) q^{85} +(9.74699 + 9.59076i) q^{86} +0.915442 q^{87} +(9.36758 + 0.498376i) q^{88} +3.97318 q^{89} +(-3.00923 - 2.96100i) q^{90} +(10.5973 - 3.44329i) q^{91} +(7.02148 - 0.113466i) q^{92} +(-0.0106595 - 0.00774460i) q^{93} +(8.27290 + 4.13140i) q^{94} +(2.16501 - 6.66320i) q^{95} +(0.625069 + 0.287308i) 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

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