LMFDB - Embedded newform 924.2.bu.b.223.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [924,2,Mod(223,924)] 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("924.223"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(924, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 0, 5, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 924 = 2^{2} \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	924.bu (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [192,2,48] 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:	$7.37817714677$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			223.1
Character	$\chi$	$=$	924.223
Dual form			924.2.bu.b.895.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41179 - 0.0828155i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.98628 + 0.233836i) q^{4} +(1.42882 - 1.96660i) q^{5} +(0.357504 + 1.36828i) q^{6} +(-0.147880 - 2.64162i) q^{7} +(-2.78484 - 0.494621i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-2.18005 + 2.65809i) q^{10} +(3.26775 - 0.567303i) q^{11} +(-0.391404 - 1.96133i) q^{12} +(-2.95465 - 4.06673i) q^{13} +(-0.00999184 + 3.74164i) q^{14} +(-2.31188 - 0.751175i) q^{15} +(3.89064 + 0.928927i) q^{16} +(-2.12962 + 2.93118i) q^{17} +(1.19084 - 0.762828i) q^{18} +(-1.65743 - 5.10105i) q^{19} +(3.29790 - 3.57212i) q^{20} +(-2.46663 + 0.956946i) q^{21} +(-4.66034 + 0.530291i) q^{22} -4.33028i q^{23} +(0.390151 + 2.80139i) q^{24} +(-0.280913 - 0.864561i) q^{25} +(3.83455 + 5.98604i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.323972 - 5.28158i) q^{28} +(-2.73596 + 8.42043i) q^{29} +(3.20167 + 1.25196i) q^{30} +(3.55588 - 2.58350i) q^{31} +(-5.41583 - 1.63365i) q^{32} +(-1.54933 - 2.93251i) q^{33} +(3.24932 - 3.96183i) q^{34} +(-5.40630 - 3.48357i) q^{35} +(-1.74438 + 0.978331i) q^{36} +(-1.74053 + 5.35679i) q^{37} +(1.91749 + 7.33885i) q^{38} +(-2.95465 + 4.06673i) q^{39} +(-4.95176 + 4.76995i) q^{40} +(9.08770 - 2.95277i) q^{41} +(3.56160 - 1.14673i) q^{42} -7.37372i q^{43} +(6.62333 - 0.362709i) q^{44} +2.43085i q^{45} +(-0.358614 + 6.11343i) q^{46} +(3.31147 + 10.1917i) q^{47} +(-0.318812 - 3.98727i) q^{48} +(-6.95626 + 0.781283i) q^{49} +(0.324990 + 1.24384i) q^{50} +(3.44580 + 1.11961i) q^{51} +(-4.91783 - 8.76858i) q^{52} +(-0.613041 + 0.445400i) q^{53} +(-1.09348 - 0.896827i) q^{54} +(3.55336 - 7.23693i) q^{55} +(-0.894776 + 7.42963i) q^{56} +(-4.33921 + 3.15262i) q^{57} +(4.55994 - 11.6613i) q^{58} +(-1.35795 + 4.17933i) q^{59} +(-4.41640 - 2.03265i) q^{60} +(-0.429361 + 0.590964i) q^{61} +(-5.23410 + 3.35287i) q^{62} +(1.67234 + 2.05019i) q^{63} +(7.51070 + 2.75488i) q^{64} -12.2193 q^{65} +(1.94446 + 4.26838i) q^{66} -13.4747i q^{67} +(-4.91545 + 5.32416i) q^{68} +(-4.11834 + 1.33813i) q^{69} +(7.34405 + 5.36579i) q^{70} +(-4.16191 + 5.72838i) q^{71} +(2.54372 - 1.23673i) q^{72} +(3.09250 + 1.00482i) q^{73} +(2.90088 - 7.41851i) q^{74} +(-0.735439 + 0.534328i) q^{75} +(-2.09932 - 10.5197i) q^{76} +(-1.98183 - 8.54824i) q^{77} +(4.50813 - 5.49666i) q^{78} +(2.99590 + 4.12351i) q^{79} +(7.38586 - 6.32408i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-13.0744 + 3.41608i) q^{82} +(-6.72658 - 4.88715i) q^{83} +(-5.12319 + 1.32398i) q^{84} +(2.72161 + 8.37625i) q^{85} +(-0.610658 + 10.4101i) q^{86} +8.85376 q^{87} +(-9.38076 - 0.0364466i) q^{88} -7.82978i q^{89} +(0.201312 - 3.43185i) q^{90} +(-10.3058 + 8.40644i) q^{91} +(1.01257 - 8.60116i) q^{92} +(-3.55588 - 2.58350i) q^{93} +(-3.83106 - 14.6627i) q^{94} +(-12.3999 - 4.02897i) q^{95} +(0.119886 + 5.65558i) q^{96} +(-4.95513 - 6.82014i) q^{97} +(9.88546 - 0.526919i) q^{98} +(-2.31021 + 2.37969i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q + 2 q^{2} + 48 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{8} - 48 q^{9} + 2 q^{12} + 13 q^{14} + 6 q^{16} - 3 q^{18} + 6 q^{20} + 24 q^{22} + 3 q^{24} + 56 q^{25} - 18 q^{26} + 48 q^{27} + 16 q^{29} + 12 q^{31}+ \cdots + 50 q^{98}+O(q^{100}) $ 192 * q + 2 * q^2 + 48 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^8 - 48 * q^9 + 2 * q^12 + 13 * q^14 + 6 * q^16 - 3 * q^18 + 6 * q^20 + 24 * q^22 + 3 * q^24 + 56 * q^25 - 18 * q^26 + 48 * q^27 + 16 * q^29 + 12 * q^31 - 8 * q^32 + 24 * q^34 + 14 * q^35 - 2 * q^36 - 24 * q^37 - 36 * q^38 - 36 * q^40 + 2 * q^42 + 29 * q^44 - 23 * q^46 + 8 * q^47 - 11 * q^48 + 16 * q^49 - 14 * q^50 - 40 * q^52 + 8 * q^53 - 2 * q^54 - 4 * q^55 - 8 * q^56 + 7 * q^58 - 40 * q^59 - 6 * q^60 - 56 * q^64 - 16 * q^65 + 11 * q^66 - 78 * q^68 + 86 * q^70 - 3 * q^72 + 28 * q^74 - 36 * q^75 - 56 * q^76 + 28 * q^77 - 12 * q^78 + 6 * q^80 - 48 * q^81 + 8 * q^83 + 15 * q^84 - 60 * q^85 - 51 * q^86 - 16 * q^87 - 4 * q^88 + 8 * q^91 - 47 * q^92 - 12 * q^93 + 64 * q^94 - 2 * q^96 + 50 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/924\mathbb{Z}\right)^\times$.

$n$	$463$	$617$	$661$	$673$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−1.41179	−	0.0828155i	−0.998284	−	0.0585594i
$2$	−1.41179	−	0.0828155i	−0.998284	−	0.0585594i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	1.98628	+	0.233836i	0.993142	+	0.116918i
$5$	1.42882	−	1.96660i	0.638988	−	0.879491i	−0.359573	−	0.933117i	$-0.617078\pi$
$5$	1.42882	−	1.96660i	0.638988	−	0.879491i	0.998561	+	0.0536255i	$0.0170777\pi$
$6$	0.357504	+	1.36828i	0.145950	+	0.558598i
$7$	−0.147880	−	2.64162i	−0.0558933	−	0.998437i
$7$	−0.147880	−	2.64162i	−0.0558933	−	0.998437i
$8$	−2.78484	−	0.494621i	−0.984591	−	0.174875i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−2.18005	+	2.65809i	−0.689394	+	0.840563i
$11$	3.26775	−	0.567303i	0.985263	−	0.171048i
$11$	3.26775	−	0.567303i	0.985263	−	0.171048i
$12$	−0.391404	−	1.96133i	−0.112989	−	0.566186i
$13$	−2.95465	−	4.06673i	−0.819473	−	1.12791i	−0.989792	−	0.142519i	$-0.954480\pi$
$13$	−2.95465	−	4.06673i	−0.819473	−	1.12791i	0.170319	−	0.985389i	$-0.445520\pi$
$14$	−0.00999184	+	3.74164i	−0.00267043	+	0.999996i
$15$	−2.31188	−	0.751175i	−0.596925	−	0.193953i
$16$	3.89064	+	0.928927i	0.972660	+	0.232232i
$17$	−2.12962	+	2.93118i	−0.516510	+	0.710915i	−0.985000	−	0.172554i	$-0.944798\pi$
$17$	−2.12962	+	2.93118i	−0.516510	+	0.710915i	0.468490	+	0.883469i	$0.344798\pi$
$18$	1.19084	−	0.762828i	0.280683	−	0.179800i
$19$	−1.65743	−	5.10105i	−0.380241	−	1.17026i	−0.939874	−	0.341520i	$-0.889058\pi$
$19$	−1.65743	−	5.10105i	−0.380241	−	1.17026i	0.559634	−	0.828740i	$-0.310942\pi$
$20$	3.29790	−	3.57212i	0.737434	−	0.798750i
$21$	−2.46663	+	0.956946i	−0.538262	+	0.208823i
$22$	−4.66034	+	0.530291i	−0.993588	+	0.113058i
$23$		−	4.33028i		−	0.902925i	−0.892290	−	0.451463i	$-0.850902\pi$
$23$		−	4.33028i		−	0.902925i	0.892290	−	0.451463i	$-0.149098\pi$
$24$	0.390151	+	2.80139i	0.0796393	+	0.571831i
$25$	−0.280913	−	0.864561i	−0.0561826	−	0.172912i
$26$	3.83455	+	5.98604i	0.752017	+	1.17396i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.323972	−	5.28158i	0.0612250	−	0.998124i
$29$	−2.73596	+	8.42043i	−0.508056	+	1.56363i	0.287516	+	0.957776i	$0.407170\pi$
$29$	−2.73596	+	8.42043i	−0.508056	+	1.56363i	−0.795572	+	0.605859i	$0.792830\pi$
$30$	3.20167	+	1.25196i	0.584543	+	0.228575i
$31$	3.55588	−	2.58350i	0.638656	−	0.464010i	−0.220732	−	0.975334i	$-0.570845\pi$
$31$	3.55588	−	2.58350i	0.638656	−	0.464010i	0.859388	+	0.511324i	$0.170845\pi$
$32$	−5.41583	−	1.63365i	−0.957392	−	0.288792i
$33$	−1.54933	−	2.93251i	−0.269703	−	0.510484i
$34$	3.24932	−	3.96183i	0.557254	−	0.679448i
$35$	−5.40630	−	3.48357i	−0.913832	−	0.588831i
$36$	−1.74438	+	0.978331i	−0.290730	+	0.163055i
$37$	−1.74053	+	5.35679i	−0.286141	+	0.880651i	0.699913	+	0.714228i	$0.253222\pi$
$37$	−1.74053	+	5.35679i	−0.286141	+	0.880651i	−0.986054	+	0.166424i	$0.946778\pi$
$38$	1.91749	+	7.33885i	0.311058	+	1.19052i
$39$	−2.95465	+	4.06673i	−0.473123	+	0.651198i
$40$	−4.95176	+	4.76995i	−0.782942	+	0.754196i
$41$	9.08770	−	2.95277i	1.41926	−	0.461146i	0.503893	−	0.863766i	$-0.331900\pi$
$41$	9.08770	−	2.95277i	1.41926	−	0.461146i	0.915367	+	0.402620i	$0.131900\pi$
$42$	3.56160	−	1.14673i	0.549567	−	0.176944i
$43$		−	7.37372i		−	1.12448i	−0.826974	−	0.562241i	$-0.809939\pi$
$43$		−	7.37372i		−	1.12448i	0.826974	−	0.562241i	$-0.190061\pi$
$44$	6.62333	−	0.362709i	0.998504	−	0.0546804i
$45$			2.43085i			0.362370i
$46$	−0.358614	+	6.11343i	−0.0528747	+	0.901376i
$47$	3.31147	+	10.1917i	0.483028	+	1.48661i	0.834817	+	0.550527i	$0.185573\pi$
$47$	3.31147	+	10.1917i	0.483028	+	1.48661i	−0.351790	+	0.936079i	$0.614427\pi$
$48$	−0.318812	−	3.98727i	−0.0460165	−	0.575514i
$49$	−6.95626	+	0.781283i	−0.993752	+	0.111612i
$50$	0.324990	+	1.24384i	0.0459605	+	0.175905i
$51$	3.44580	+	1.11961i	0.482509	+	0.156777i
$52$	−4.91783	−	8.76858i	−0.681980	−	1.21598i
$53$	−0.613041	+	0.445400i	−0.0842076	+	0.0611804i	−0.629093	−	0.777330i	$-0.716573\pi$
$53$	−0.613041	+	0.445400i	−0.0842076	+	0.0611804i	0.544885	+	0.838511i	$0.316573\pi$
$54$	−1.09348	−	0.896827i	−0.148804	−	0.122043i
$55$	3.55336	−	7.23693i	0.479135	−	0.975828i
$56$	−0.894776	+	7.42963i	−0.119569	+	0.992826i
$57$	−4.33921	+	3.15262i	−0.574742	+	0.417575i
$58$	4.55994	−	11.6613i	0.598749	−	1.53120i
$59$	−1.35795	+	4.17933i	−0.176789	+	0.544102i	−0.999711	−	0.0240536i	$-0.992343\pi$
$59$	−1.35795	+	4.17933i	−0.176789	+	0.544102i	0.822921	+	0.568155i	$0.192343\pi$
$60$	−4.41640	−	2.03265i	−0.570154	−	0.262414i
$61$	−0.429361	+	0.590964i	−0.0549740	+	0.0756652i	−0.835619	−	0.549310i	$-0.814891\pi$
$61$	−0.429361	+	0.590964i	−0.0549740	+	0.0756652i	0.780645	+	0.624975i	$0.214891\pi$
$62$	−5.23410	+	3.35287i	−0.664732	+	0.425815i
$63$	1.67234	+	2.05019i	0.210695	+	0.258300i
$64$	7.51070	+	2.75488i	0.938838	+	0.344360i
$65$	−12.2193			−1.51562
$66$	1.94446	+	4.26838i	0.239347	+	0.525401i
$67$		−	13.4747i		−	1.64620i	−0.567898	−	0.823099i	$-0.692243\pi$
$67$		−	13.4747i		−	1.64620i	0.567898	−	0.823099i	$-0.307757\pi$
$68$	−4.91545	+	5.32416i	−0.596086	+	0.645650i
$69$	−4.11834	+	1.33813i	−0.495790	+	0.161092i
$70$	7.34405	+	5.36579i	0.877782	+	0.641334i
$71$	−4.16191	+	5.72838i	−0.493928	+	0.679833i	−0.981106	−	0.193469i	$-0.938026\pi$
$71$	−4.16191	+	5.72838i	−0.493928	+	0.679833i	0.487179	+	0.873302i	$0.338026\pi$
$72$	2.54372	−	1.23673i	0.299780	−	0.145750i
$73$	3.09250	+	1.00482i	0.361950	+	0.117605i	0.484346	−	0.874877i	$-0.339058\pi$
$73$	3.09250	+	1.00482i	0.361950	+	0.117605i	−0.122396	+	0.992481i	$0.539058\pi$
$74$	2.90088	−	7.41851i	0.337220	−	0.862384i
$75$	−0.735439	+	0.534328i	−0.0849212	+	0.0616989i
$76$	−2.09932	−	10.5197i	−0.240809	−	1.20669i
$77$	−1.98183	−	8.54824i	−0.225850	−	0.974162i
$78$	4.50813	−	5.49666i	0.510445	−	0.622374i
$79$	2.99590	+	4.12351i	0.337065	+	0.463931i	0.943581	−	0.331141i	$-0.107433\pi$
$79$	2.99590	+	4.12351i	0.337065	+	0.463931i	−0.606516	+	0.795071i	$0.707433\pi$
$80$	7.38586	−	6.32408i	0.825764	−	0.707053i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−13.0744	+	3.41608i	−1.44383	+	0.377243i
$83$	−6.72658	−	4.88715i	−0.738338	−	0.536434i	0.153852	−	0.988094i	$-0.450832\pi$
$83$	−6.72658	−	4.88715i	−0.738338	−	0.536434i	−0.892190	+	0.451660i	$0.850832\pi$
$84$	−5.12319	+	1.32398i	−0.558986	+	0.144458i
$85$	2.72161	+	8.37625i	0.295200	+	0.908532i
$86$	−0.610658	+	10.4101i	−0.0658490	+	1.12255i
$87$	8.85376			0.949223
$88$	−9.38076	−	0.0364466i	−0.999992	−	0.00388522i
$89$		−	7.82978i		−	0.829955i	−0.909832	−	0.414978i	$-0.863789\pi$
$89$		−	7.82978i		−	0.829955i	0.909832	−	0.414978i	$-0.136211\pi$
$90$	0.201312	−	3.43185i	0.0212202	−	0.361749i
$91$	−10.3058	+	8.40644i	−1.08034	+	0.881234i
$92$	1.01257	−	8.60116i	0.105568	−	0.896732i
$93$	−3.55588	−	2.58350i	−0.368728	−	0.267897i
$94$	−3.83106	−	14.6627i	−0.395144	−	1.51234i
$95$	−12.3999	−	4.02897i	−1.27220	−	0.413364i
$96$	0.119886	+	5.65558i	0.0122359	+	0.577221i
$97$	−4.95513	−	6.82014i	−0.503117	−	0.692481i	0.479623	−	0.877475i	$-0.340773\pi$
$97$	−4.95513	−	6.82014i	−0.503117	−	0.692481i	−0.982740	+	0.184994i	$0.940773\pi$
$98$	9.88546	−	0.526919i	0.998582	−	0.0532269i
$99$	−2.31021	+	2.37969i	−0.232185	+	0.239168i
$100$	−0.355807	−	1.78295i	−0.0355807	−	0.178295i
$101$	−6.46744	−	8.90166i	−0.643534	−	0.885748i	0.355264	−	0.934766i	$-0.384391\pi$
$101$	−6.46744	−	8.90166i	−0.643534	−	0.885748i	−0.998798	+	0.0490176i	$0.984391\pi$
$102$	−4.77202	−	1.86602i	−0.472500	−	0.184763i
$103$	−4.07299	+	12.5354i	−0.401324	+	1.23515i	0.522603	+	0.852576i	$0.324961\pi$
$103$	−4.07299	+	12.5354i	−0.401324	+	1.23515i	−0.923926	+	0.382571i	$0.875039\pi$
$104$	6.21675	+	12.7866i	0.609603	+	1.25383i
$105$	−1.64244	+	6.21818i	−0.160285	+	0.606832i
$106$	0.902369	−	0.578041i	0.0876458	−	0.0561443i
$107$	−16.3310	+	5.30626i	−1.57878	+	0.512975i	−0.961741	−	0.273961i	$-0.911666\pi$
$107$	−16.3310	+	5.30626i	−1.57878	+	0.512975i	−0.617034	+	0.786936i	$0.711666\pi$
$108$	1.46949	+	1.35668i	0.141402	+	0.130547i
$109$	−12.7845			−1.22453			−0.612265	−	0.790653i	$-0.709741\pi$
$109$	−12.7845			−1.22453			−0.612265	+	0.790653i	$0.709741\pi$
$110$	−5.61592	+	9.92273i	−0.535457	+	0.946095i
$111$	5.63247			0.534610
$112$	1.87852	−	10.4149i	0.177504	−	0.984120i
$113$	−5.54105	−	17.0536i	−0.521258	−	1.60427i	−0.771599	−	0.636110i	$-0.780543\pi$
$113$	−5.54105	−	17.0536i	−0.521258	−	1.60427i	0.250341	−	0.968158i	$-0.419457\pi$
$114$	6.38712	−	4.09147i	0.598209	−	0.383202i
$115$	−8.51593	−	6.18719i	−0.794115	−	0.576958i
$116$	−7.40340	+	16.0856i	−0.687388	+	1.49351i
$117$	4.78073	+	1.55335i	0.441978	+	0.143607i
$118$	2.26324	−	5.78786i	0.208348	−	0.532815i
$119$	8.05797	+	5.19218i	0.738673	+	0.475967i
$120$	6.06668	+	3.23541i	0.553809	+	0.295351i
$121$	10.3563	−	3.70760i	0.941485	−	0.337055i
$122$	0.655107	−	0.798758i	0.0593106	−	0.0723161i
$123$	−5.61651	−	7.73046i	−0.506424	−	0.697032i
$124$	7.66711	−	4.30007i	0.688526	−	0.386158i
$125$	9.45778	+	3.07302i	0.845929	+	0.274859i
$126$	−2.19120	−	3.03293i	−0.195208	−	0.270195i
$127$	4.20698	−	5.79041i	0.373309	−	0.513816i	−0.580488	−	0.814269i	$-0.697138\pi$
$127$	4.20698	−	5.79041i	0.373309	−	0.513816i	0.953796	+	0.300454i	$0.0971380\pi$
$128$	−10.3754	−	4.51131i	−0.917061	−	0.398747i
$129$	−7.01282	+	2.27860i	−0.617445	+	0.200620i
$130$	17.2511	+	1.01195i	1.51302	+	0.0887537i
$131$	−1.30532			−0.114047			−0.0570233	−	0.998373i	$-0.518161\pi$
$131$	−1.30532			−0.114047			−0.0570233	+	0.998373i	$0.518161\pi$
$132$	−2.39168	−	6.18707i	−0.208169	−	0.538516i
$133$	−13.2299	+	5.13264i	−1.14718	+	0.445056i
$134$	−1.11591	+	19.0234i	−0.0964004	+	1.64337i
$135$	2.31188	−	0.751175i	0.198975	−	0.0646509i
$136$	7.38049	−	7.10951i	0.632872	−	0.609635i
$137$	13.6709	+	9.93252i	1.16799	+	0.848592i	0.990767	−	0.135579i	$-0.0432894\pi$
$137$	13.6709	+	9.93252i	1.16799	+	0.848592i	0.177220	+	0.984171i	$0.443289\pi$
$138$	5.92503	−	1.54809i	0.504372	−	0.131782i
$139$	6.15415	−	18.9405i	0.521988	−	1.60651i	−0.248208	−	0.968707i	$-0.579842\pi$
$139$	6.15415	−	18.9405i	0.521988	−	1.60651i	0.770196	−	0.637807i	$-0.220158\pi$
$140$	−9.92386	−	8.18355i	−0.838719	−	0.691636i
$141$	8.66954	−	6.29879i	0.730107	−	0.530454i
$142$	6.35013	−	7.74258i	0.532891	−	0.649743i
$143$	−11.9621	−	11.6129i	−1.00032	−	0.971116i
$144$	−3.69361	+	1.53534i	−0.307800	+	0.127945i
$145$	12.6504	+	17.4118i	1.05056	+	1.44597i
$146$	−4.28274	−	1.67469i	−0.354442	−	0.138598i
$147$	2.89265	+	6.37437i	0.238582	+	0.525749i
$148$	−4.70979	+	10.2331i	−0.387142	+	0.841156i
$149$	13.6738	+	9.93457i	1.12020	+	0.813872i	0.984239	−	0.176843i	$-0.0565884\pi$
$149$	13.6738	+	9.93457i	1.12020	+	0.813872i	0.135959	+	0.990714i	$0.456588\pi$
$150$	1.08253	−	0.693451i	0.0883885	−	0.0566201i
$151$	−0.954944	+	0.310280i	−0.0777123	+	0.0252502i	−0.347615	−	0.937637i	$-0.613008\pi$
$151$	−0.954944	+	0.310280i	−0.0777123	+	0.0252502i	0.269903	+	0.962888i	$0.413008\pi$
$152$	2.09260	+	15.0254i	0.169732	+	1.21872i
$153$		−	3.62313i		−	0.292913i
$154$	2.08999	+	12.2324i	0.168417	+	0.985716i
$155$		−	10.6844i		−	0.858189i
$156$	−6.81972	+	7.38677i	−0.546015	+	0.591415i
$157$	−3.61684	+	1.17518i	−0.288656	+	0.0937899i	−0.449766	−	0.893147i	$-0.648493\pi$
$157$	−3.61684	+	1.17518i	−0.288656	+	0.0937899i	0.161110	+	0.986936i	$0.448493\pi$
$158$	−3.88809	−	6.06962i	−0.309319	−	0.482873i
$159$	0.613041	+	0.445400i	0.0486173	+	0.0353225i
$160$	−10.9510	+	8.31658i	−0.865752	+	0.657484i
$161$	−11.4389	+	0.640361i	−0.901514	+	0.0504675i
$162$	−0.515028	+	1.31710i	−0.0404644	+	0.103481i
$163$	6.69180	+	9.21047i	0.524142	+	0.721419i	0.986224	−	0.165418i	$-0.0528973\pi$
$163$	6.69180	+	9.21047i	0.524142	+	0.721419i	−0.462082	+	0.886837i	$0.652897\pi$
$164$	18.7412	−	3.74002i	1.46344	−	0.292046i
$165$	−7.98078	−	1.14311i	−0.621303	−	0.0889913i
$166$	9.09177	+	7.45668i	0.705658	+	0.578750i
$167$	4.85978	−	3.53084i	0.376061	−	0.273225i	−0.383659	−	0.923475i	$-0.625336\pi$
$167$	4.85978	−	3.53084i	0.376061	−	0.273225i	0.759720	+	0.650250i	$0.225336\pi$
$168$	7.34250	−	1.44490i	0.566486	−	0.111476i
$169$	−3.79110	+	11.6678i	−0.291623	+	0.897523i
$170$	−3.14865	−	12.0509i	−0.241490	−	0.924259i
$171$	4.33921	+	3.15262i	0.331828	+	0.241087i
$172$	1.72424	−	14.6463i	0.131472	−	1.11677i
$173$	−6.95725	+	2.26055i	−0.528950	+	0.171866i	−0.561303	−	0.827610i	$-0.689700\pi$
$173$	−6.95725	+	2.26055i	−0.528950	+	0.171866i	0.0323531	+	0.999477i	$0.489700\pi$
$174$	−12.4996	−	0.733229i	−0.947594	−	0.0555859i
$175$	−2.24230	+	0.869915i	−0.169502	+	0.0657594i
$176$	13.2406	+	0.828327i	0.998049	+	0.0624375i
$177$	4.39440			0.330304
$178$	−0.648427	+	11.0540i	−0.0486017	+	0.828531i
$179$	21.7282	−	7.05991i	1.62404	−	0.527682i	0.651149	−	0.758950i	$-0.274287\pi$
$179$	21.7282	−	7.05991i	1.62404	−	0.527682i	0.972890	+	0.231268i	$0.0742873\pi$
$180$	−0.568420	+	4.82837i	−0.0423675	+	0.359885i
$181$	2.32927	−	3.20596i	0.173133	−	0.238297i	−0.713628	−	0.700524i	$-0.752949\pi$
$181$	2.32927	−	3.20596i	0.173133	−	0.238297i	0.886762	+	0.462227i	$0.152949\pi$
$182$	15.2458	−	11.0146i	1.13009	−	0.816458i
$183$	0.694720	+	0.225728i	0.0513552	+	0.0166863i
$184$	−2.14185	+	12.0591i	−0.157899	+	0.889012i
$185$	8.04778	+	11.0768i	0.591685	+	0.814384i
$186$	4.80620	+	3.94183i	0.352407	+	0.289029i
$187$	−5.29621	+	10.7865i	−0.387297	+	0.788786i
$188$	4.19435	+	21.0179i	0.305904	+	1.53289i
$189$	1.43307	−	2.22403i	0.104240	−	0.161775i
$190$	17.1724	+	6.71495i	1.24581	+	0.487154i
$191$	1.52648	+	0.495983i	0.110452	+	0.0358881i	0.363722	−	0.931508i	$-0.381506\pi$
$191$	1.52648	+	0.495983i	0.110452	+	0.0358881i	−0.253269	+	0.967396i	$0.581506\pi$
$192$	0.299116	−	7.99441i	0.0215868	−	0.576947i
$193$	16.0348	+	11.6500i	1.15421	+	0.838582i	0.989035	−	0.147683i	$-0.0471814\pi$
$193$	16.0348	+	11.6500i	1.15421	+	0.838582i	0.165174	+	0.986264i	$0.447181\pi$
$194$	6.43077	+	10.0390i	0.461702	+	0.720755i
$195$	3.77597	+	11.6212i	0.270403	+	0.832215i
$196$	−13.9998	−	0.0747718i	−0.999986	−	0.00534084i
$197$	14.4618			1.03036			0.515179	−	0.857082i	$-0.327725\pi$
$197$	14.4618			1.03036			0.515179	+	0.857082i	$0.327725\pi$
$198$	3.45860	−	3.16829i	0.245792	−	0.225161i
$199$	9.00740			0.638517			0.319259	−	0.947668i	$-0.396566\pi$
$199$	9.00740			0.638517			0.319259	+	0.947668i	$0.396566\pi$
$200$	0.354668	+	2.54661i	0.0250788	+	0.180073i
$201$	−12.8152	+	4.16392i	−0.903916	+	0.293700i
$202$	8.39344	+	13.1028i	0.590561	+	0.921913i
$203$	22.6481	+	5.98215i	1.58959	+	0.419865i
$204$	6.58254	+	3.02961i	0.460870	+	0.212115i
$205$	7.17776	−	22.0909i	0.501317	−	1.54289i
$206$	6.78832	−	17.3600i	0.472964	−	1.20953i
$207$	2.54527	+	3.50327i	0.176909	+	0.243494i
$208$	−7.71779	−	18.5668i	−0.535133	−	1.28738i
$209$	−8.30990	−	15.7287i	−0.574808	−	1.08797i
$210$	2.83373	−	8.64273i	0.195546	−	0.596405i
$211$	−4.33220	−	5.96276i	−0.298241	−	0.410493i	0.633428	−	0.773802i	$-0.281647\pi$
$211$	−4.33220	−	5.96276i	−0.298241	−	0.410493i	−0.931669	+	0.363308i	$0.881647\pi$
$212$	−1.32182	+	0.741340i	−0.0907832	+	0.0509154i
$213$	6.73411	+	2.18805i	0.461414	+	0.149922i
$214$	23.4953	−	6.13884i	1.60611	−	0.419643i
$215$	−14.5012	−	10.5357i	−0.988972	−	0.718530i
$216$	−1.96225	−	2.03705i	−0.133514	−	0.138603i
$217$	−7.35046	−	9.01123i	−0.498982	−	0.611722i
$218$	18.0489	+	1.05875i	1.22243	+	0.0717077i
$219$		−	3.25165i		−	0.219726i
$220$	8.75024	−	13.5437i	0.589941	−	0.913116i
$221$	18.2126			1.22511
$222$	−7.95184	−	0.466455i	−0.533692	−	0.0313064i
$223$	−8.75412	−	26.9424i	−0.586219	−	1.80420i	−0.594318	−	0.804230i	$-0.702578\pi$
$223$	−8.75412	−	26.9424i	−0.586219	−	1.80420i	0.00809868	−	0.999967i	$-0.497422\pi$
$224$	−3.51459	+	14.5481i	−0.234828	+	0.972037i
$225$	0.735439	+	0.534328i	0.0490293	+	0.0356219i
$226$	6.41048	+	24.5349i	0.426419	+	1.63204i
$227$	4.43277	−	13.6427i	0.294213	−	0.905496i	−0.689271	−	0.724503i	$-0.742069\pi$
$227$	4.43277	−	13.6427i	0.294213	−	0.905496i	0.983485	−	0.180992i	$-0.0579309\pi$
$228$	−9.35610	+	5.24734i	−0.619623	+	0.347513i
$229$	0.595386	+	0.819478i	0.0393442	+	0.0541526i	0.828236	−	0.560380i	$-0.189345\pi$
$229$	0.595386	+	0.819478i	0.0393442	+	0.0541526i	−0.788892	+	0.614532i	$0.789345\pi$
$230$	11.5103	+	9.44024i	0.758966	+	0.622471i
$231$	−7.51744	+	4.52638i	−0.494611	+	0.297814i
$232$	11.7842	−	22.0963i	0.773667	−	1.45069i
$233$	2.29897	−	1.67030i	0.150610	−	0.109425i	−0.509928	−	0.860217i	$-0.670328\pi$
$233$	2.29897	−	1.67030i	0.150610	−	0.109425i	0.660539	+	0.750792i	$0.270328\pi$
$234$	−6.62072	−	2.58892i	−0.432810	−	0.169243i
$235$	24.7744	+	8.04970i	1.61611	+	0.525105i
$236$	−3.67454	+	7.98379i	−0.239192	+	0.519700i
$237$	2.99590	−	4.12351i	0.194605	−	0.267851i
$238$	−10.9461	−	7.99758i	−0.709533	−	0.518406i
$239$	−4.11683	+	1.33764i	−0.266296	+	0.0865247i	−0.439121	−	0.898428i	$-0.644710\pi$
$239$	−4.11683	+	1.33764i	−0.266296	+	0.0865247i	0.172826	+	0.984952i	$0.444710\pi$
$240$	−8.29691	−	5.07012i	−0.535563	−	0.327275i
$241$			9.50581i			0.612323i	0.951980	+	0.306161i	$0.0990447\pi$
$241$			9.50581i			0.612323i	−0.951980	+	0.306161i	$0.900955\pi$
$242$	−14.9280	+	4.37668i	−0.959607	+	0.281344i
$243$	−1.00000			−0.0641500
$244$	−0.991021	+	1.07342i	−0.0634436	+	0.0687189i
$245$	−8.40278	+	14.7965i	−0.536834	+	0.945315i
$246$	7.28911	+	11.3789i	0.464737	+	0.725492i
$247$	−15.8474	+	21.8121i	−1.00835	+	1.38787i
$248$	−11.1804	+	5.43583i	−0.709958	+	0.345175i
$249$	−2.56933	+	7.90757i	−0.162824	+	0.501122i
$250$	−13.0979	−	5.12170i	−0.828382	−	0.323925i
$251$	1.54830	−	1.12490i	0.0977276	−	0.0710033i	−0.537848	−	0.843042i	$-0.680763\pi$
$251$	1.54830	−	1.12490i	0.0977276	−	0.0710033i	0.635576	+	0.772038i	$0.280763\pi$
$252$	2.84233	+	4.46331i	0.179050	+	0.281162i
$253$	−2.45658	−	14.1502i	−0.154444	−	0.889618i
$254$	−6.41889	+	7.82642i	−0.402757	+	0.491073i
$255$	7.12526	−	5.17681i	0.446201	−	0.324184i
$256$	14.2742	+	7.22825i	0.892137	+	0.451765i
$257$	3.80915	+	1.23767i	0.237608	+	0.0772035i	0.425400	−	0.905005i	$-0.360133\pi$
$257$	3.80915	+	1.23767i	0.237608	+	0.0772035i	−0.187793	+	0.982209i	$0.560133\pi$
$258$	10.0893	−	2.63613i	0.628133	−	0.164118i
$259$	14.4080	+	3.80564i	0.895268	+	0.236471i
$260$	−24.2710	−	2.85731i	−1.50522	−	0.177203i
$261$	−2.73596	−	8.42043i	−0.169352	−	0.521212i
$262$	1.84284	+	0.108101i	0.113851	+	0.00667849i
$263$			5.88484i			0.362875i	0.983403	+	0.181437i	$0.0580749\pi$
$263$			5.88484i			0.362875i	−0.983403	+	0.181437i	$0.941925\pi$
$264$	2.86415	+	8.93290i	0.176276	+	0.549782i
$265$			1.84200i			0.113153i
$266$	19.1029	−	6.15055i	1.17127	−	0.377114i
$267$	−7.44657	+	2.41954i	−0.455722	+	0.148073i
$268$	3.15087	−	26.7646i	0.192470	−	1.63491i
$269$	1.36061	−	1.87272i	0.0829580	−	0.114182i	−0.765521	−	0.643411i	$-0.777519\pi$
$269$	1.36061	−	1.87272i	0.0829580	−	0.114182i	0.848479	+	0.529229i	$0.177519\pi$
$270$	−3.32609	+	0.869040i	−0.202419	+	0.0528881i
$271$	−6.32230	+	19.4580i	−0.384052	+	1.18199i	0.553113	+	0.833106i	$0.313440\pi$
$271$	−6.32230	+	19.4580i	−0.384052	+	1.18199i	−0.937166	+	0.348885i	$0.886560\pi$
$272$	−11.0085	+	9.42589i	−0.667485	+	0.571528i
$273$	11.1797	+	7.20366i	0.676624	+	0.435986i
$274$	−18.4779	−	15.1548i	−1.11629	−	0.915533i
$275$	−1.40842	−	2.66580i	−0.0849309	−	0.160754i
$276$	−8.49309	+	1.69489i	−0.511224	+	0.102020i
$277$	11.4099	−	8.28981i	0.685557	−	0.498086i	−0.189639	−	0.981854i	$-0.560732\pi$
$277$	11.4099	−	8.28981i	0.685557	−	0.498086i	0.875197	+	0.483767i	$0.160732\pi$
$278$	−10.2569	+	26.2303i	−0.615169	+	1.57319i
$279$	−1.35823	+	4.18019i	−0.0813149	+	0.250262i
$280$	13.3327	+	12.3753i	0.796778	+	0.739564i
$281$	−12.3279	−	8.95677i	−0.735423	−	0.534316i	0.155851	−	0.987781i	$-0.450188\pi$
$281$	−12.3279	−	8.95677i	−0.735423	−	0.534316i	−0.891274	+	0.453464i	$0.850188\pi$
$282$	−12.7612	+	8.17458i	−0.759917	+	0.486789i
$283$	4.62259	+	14.2269i	0.274785	+	0.845700i	0.989276	+	0.146056i	$0.0466580\pi$
$283$	4.62259	+	14.2269i	0.274785	+	0.845700i	−0.714492	+	0.699644i	$0.753342\pi$
$284$	−9.60623	+	10.4050i	−0.570025	+	0.617422i
$285$			13.0380i			0.772306i
$286$	15.9262	+	17.3855i	0.941738	+	1.02803i
$287$	−9.14398	−	23.5696i	−0.539752	−	1.39127i
$288$	5.34173	−	1.86169i	0.314765	−	0.109701i
$289$	1.19680	+	3.68336i	0.0703997	+	0.216668i
$290$	−16.4178	−	25.6295i	−0.964084	−	1.50501i
$291$	−4.95513	+	6.82014i	−0.290475	+	0.399804i
$292$	5.90763	+	2.71899i	0.345718	+	0.159117i
$293$	22.8706	+	7.43111i	1.33611	+	0.434130i	0.887999	−	0.459846i	$-0.152095\pi$
$293$	22.8706	+	7.43111i	1.33611	+	0.434130i	0.448115	+	0.893976i	$0.352095\pi$
$294$	−3.55591	−	9.23881i	−0.207385	−	0.538818i
$295$	6.27881	+	8.64204i	0.365567	+	0.503159i
$296$	7.49668	−	14.0569i	0.435736	−	0.817042i
$297$	2.97711	+	1.46178i	0.172750	+	0.0848208i
$298$	−18.4817	−	15.1579i	−1.07062	−	0.878073i
$299$	−17.6101	+	12.7945i	−1.01842	+	0.739923i
$300$	−1.58574	+	0.889355i	−0.0915525	+	0.0513469i
$301$	−19.4785	+	1.09042i	−1.12272	+	0.0628510i
$302$	1.37387	−	0.358965i	0.0790575	−	0.0206561i
$303$	−6.46744	+	8.90166i	−0.371544	+	0.511387i
$304$	−1.70997	−	21.3860i	−0.0980733	−	1.22657i
$305$	0.548713	+	1.68876i	0.0314192	+	0.0966983i
$306$	−0.300051	+	5.11509i	−0.0171528	+	0.292410i
$307$	−3.17206			−0.181039			−0.0905194	−	0.995895i	$-0.528853\pi$
$307$	−3.17206			−0.181039			−0.0905194	+	0.995895i	$0.528853\pi$
$308$	−1.93759	−	17.4426i	−0.110405	−	0.993887i
$309$	13.1805			0.749811
$310$	−0.884831	+	15.0840i	−0.0502550	+	0.856716i
$311$	−0.334045	−	1.02808i	−0.0189419	−	0.0582973i	0.941139	−	0.338020i	$-0.109757\pi$
$311$	−0.334045	−	1.02808i	−0.0189419	−	0.0582973i	−0.960081	+	0.279723i	$0.909757\pi$
$312$	10.2397	−	9.86377i	0.579710	−	0.558426i
$313$	9.97840	−	13.7341i	0.564012	−	0.776296i	−0.427817	−	0.903865i	$-0.640717\pi$
$313$	9.97840	−	13.7341i	0.564012	−	0.776296i	0.991830	+	0.127569i	$0.0407174\pi$
$314$	5.20354	−	1.35958i	0.293653	−	0.0767255i
$315$	6.42138	−	0.359474i	0.361804	−	0.0202541i
$316$	4.98649	+	8.89100i	0.280512	+	0.500158i
$317$	−0.860382	+	0.625104i	−0.0483239	+	0.0351094i	−0.611685	−	0.791101i	$-0.709508\pi$
$317$	−0.860382	+	0.625104i	−0.0483239	+	0.0351094i	0.563361	+	0.826211i	$0.309508\pi$
$318$	−0.828597	−	0.679579i	−0.0464654	−	0.0381089i
$319$	−4.16350	+	29.0680i	−0.233111	+	1.62749i
$320$	16.1492	−	10.8343i	0.902768	−	0.605657i
$321$	10.0931	+	13.8920i	0.563342	+	0.775374i
$322$	16.2024	+	0.0432674i	0.902922	+	0.00241120i
$323$	18.4818	+	6.00509i	1.02835	+	0.334132i
$324$	0.836186	−	1.81681i	0.0464548	−	0.100934i
$325$	−2.68593	+	3.69687i	−0.148989	+	0.205066i
$326$	−8.68462	−	13.5574i	−0.480997	−	0.750875i
$327$	3.95062	+	12.1587i	0.218470	+	0.672380i
$328$	−26.7683	+	3.72804i	−1.47803	+	0.205847i
$329$	26.4327	−	10.2548i	1.45728	−	0.565364i
$330$	11.1725	+	2.27477i	0.615026	+	0.125222i
$331$		−	22.9535i		−	1.26164i	−0.775930	−	0.630819i	$-0.782719\pi$
$331$		−	22.9535i		−	1.26164i	0.775930	−	0.630819i	$-0.217281\pi$
$332$	−12.2181	−	11.2802i	−0.670556	−	0.619080i
$333$	−1.74053	−	5.35679i	−0.0953803	−	0.293550i
$334$	−7.15339	+	4.58233i	−0.391416	+	0.250734i
$335$	−26.4994	−	19.2529i	−1.44782	−	1.05190i
$336$	−10.4857	+	1.43182i	−0.572042	+	0.0781120i
$337$	−5.45788	+	16.7976i	−0.297310	+	0.915025i	0.685126	+	0.728424i	$0.259747\pi$
$337$	−5.45788	+	16.7976i	−0.297310	+	0.915025i	−0.982436	+	0.186601i	$0.940253\pi$
$338$	6.31849	−	16.1585i	0.343681	−	0.878905i
$339$	−14.5067	+	10.5397i	−0.787893	+	0.572438i
$340$	3.44722	+	17.2740i	0.186952	+	0.936815i
$341$	10.1541	−	10.4595i	0.549875	−	0.566413i
$342$	−5.86495	−	4.81018i	−0.317140	−	0.260105i
$343$	3.09254	+	18.2602i	0.166982	+	0.985960i
$344$	−3.64720	+	20.5346i	−0.196644	+	1.10715i
$345$	−3.25280	+	10.0111i	−0.175125	+	0.538978i
$346$	10.0094	−	2.61524i	0.538107	−	0.140596i
$347$	−2.55406	+	3.51536i	−0.137109	+	0.188714i	−0.872050	−	0.489417i	$-0.837210\pi$
$347$	−2.55406	+	3.51536i	−0.137109	+	0.188714i	0.734941	+	0.678131i	$0.237210\pi$
$348$	17.5861	+	2.07033i	0.942713	+	0.110981i
$349$	−0.0938112	+	0.0304811i	−0.00502160	+	0.00163162i	−0.311527	−	0.950237i	$-0.600840\pi$
$349$	−0.0938112	+	0.0304811i	−0.00502160	+	0.00163162i	0.306505	+	0.951869i	$0.400840\pi$
$350$	3.23769	−	1.04244i	0.173062	−	0.0557206i
$351$		−	5.02675i		−	0.268308i
$352$	−18.6243	−	2.26595i	−0.992680	−	0.120775i
$353$		−	14.9059i		−	0.793359i	−0.917957	−	0.396679i	$-0.870162\pi$
$353$		−	14.9059i		−	0.793359i	0.917957	−	0.396679i	$-0.129838\pi$
$354$	−6.20396	−	0.363925i	−0.329737	−	0.0193424i
$355$	5.31882	+	16.3696i	0.282294	+	0.868811i
$356$	1.83088	−	15.5522i	0.0970365	−	0.824263i
$357$	2.44801	−	9.26806i	0.129563	−	0.490518i
$358$	−31.2602	+	8.16766i	−1.65215	+	0.431674i
$359$	18.4416	+	5.99203i	0.973308	+	0.316247i	0.752151	−	0.658991i	$-0.229016\pi$
$359$	18.4416	+	5.99203i	0.973308	+	0.316247i	0.221158	+	0.975238i	$0.429016\pi$
$360$	1.20235	−	6.76955i	0.0633695	−	0.356786i
$361$	−7.90229	+	5.74135i	−0.415910	+	0.302176i
$362$	−3.55393	+	4.33324i	−0.186791	+	0.227750i
$363$	−6.72642	−	8.70375i	−0.353046	−	0.456828i
$364$	−22.4360	+	14.2877i	−1.17596	+	0.748879i
$365$	6.39470	−	4.64602i	0.334714	−	0.243184i
$366$	−0.962103	−	0.376214i	−0.0502899	−	0.0196650i
$367$	4.70489	−	14.4802i	0.245593	−	0.755858i	−0.749945	−	0.661500i	$-0.769920\pi$
$367$	4.70489	−	14.4802i	0.245593	−	0.755858i	0.995538	−	0.0943582i	$-0.0300799\pi$
$368$	4.02251	−	16.8476i	0.209688	−	0.878240i
$369$	−5.61651	+	7.73046i	−0.292384	+	0.402432i
$370$	−10.4444	−	16.3046i	−0.542979	−	0.847635i
$371$	1.26723	+	1.55355i	0.0657914	+	0.0806564i
$372$	−6.45888	−	5.96306i	−0.334877	−	0.309170i
$373$	10.6360			0.550713			0.275356	−	0.961342i	$-0.411204\pi$
$373$	10.6360			0.550713			0.275356	+	0.961342i	$0.411204\pi$
$374$	8.37040	−	14.7896i	0.432823	−	0.764752i
$375$		−	9.94450i		−	0.513532i
$376$	−4.18092	−	30.0201i	−0.215614	−	1.54817i
$377$	42.3274	−	13.7530i	2.17997	−	0.708316i
$378$	−2.20737	+	3.02118i	−0.113535	+	0.155393i
$379$	10.9855	−	15.1203i	0.564289	−	0.776678i	−0.427575	−	0.903980i	$-0.640632\pi$
$379$	10.9855	−	15.1203i	0.564289	−	0.776678i	0.991864	+	0.127302i	$0.0406318\pi$
$380$	−23.6876	−	10.9022i	−1.21515	−	0.559272i
$381$	−6.80703	−	2.21174i	−0.348735	−	0.113311i
$382$	−2.11399	−	0.826639i	−0.108161	−	0.0422945i
$383$	9.89933	−	7.19228i	0.505832	−	0.367509i	−0.305408	−	0.952222i	$-0.598793\pi$
$383$	9.89933	−	7.19228i	0.505832	−	0.367509i	0.811240	+	0.584713i	$0.198793\pi$
$384$	−1.08435	+	11.2616i	−0.0553354	+	0.574692i
$385$	−19.6427	−	8.31642i	−1.00108	−	0.423844i
$386$	−21.6729	−	17.7752i	−1.10312	−	0.904733i
$387$	4.33416	+	5.96546i	0.220318	+	0.303242i
$388$	−8.24749	−	14.7054i	−0.418703	−	0.746555i
$389$	8.03429	−	24.7270i	0.407355	−	1.25371i	−0.511559	−	0.859248i	$-0.670932\pi$
$389$	8.03429	−	24.7270i	0.407355	−	1.25371i	0.918913	−	0.394460i	$-0.129068\pi$
$390$	−4.36845	−	16.7194i	−0.221205	−	0.846621i
$391$	12.6928	+	9.22186i	0.641903	+	0.466369i
$392$	19.7585	+	1.26496i	0.997957	+	0.0638902i
$393$	0.403367	+	1.24143i	0.0203472	+	0.0626221i
$394$	−20.4169	−	1.19766i	−1.02859	−	0.0603372i
$395$	12.3899			0.623404
$396$	−5.14519	+	4.18653i	−0.258555	+	0.210381i
$397$		−	5.17129i		−	0.259539i	−0.991544	−	0.129770i	$-0.958576\pi$
$397$		−	5.17129i		−	0.259539i	0.991544	−	0.129770i	$-0.0414238\pi$
$398$	−12.7165	−	0.745952i	−0.637422	−	0.0373912i
$399$	8.96969	+	10.9963i	0.449046	+	0.550504i
$400$	−0.289817	−	3.62464i	−0.0144908	−	0.181232i
$401$	−28.4329	−	20.6577i	−1.41987	−	1.03160i	−0.991792	−	0.127858i	$-0.959190\pi$
$401$	−28.4329	−	20.6577i	−1.41987	−	1.03160i	−0.428081	−	0.903740i	$-0.640810\pi$
$402$	18.4372	−	4.81726i	0.919563	−	0.240263i
$403$	−21.0128	−	6.82747i	−1.04672	−	0.340101i
$404$	−10.7646	−	19.1935i	−0.535560	−	0.954914i
$405$	−1.42882	−	1.96660i	−0.0709987	−	0.0977213i
$406$	−31.4789	−	10.3211i	−1.56227	−	0.512229i
$407$	−2.64868	+	18.4920i	−0.131290	+	0.916617i
$408$	−9.04224	−	4.82230i	−0.447658	−	0.238740i
$409$	8.74596	+	12.0378i	0.432460	+	0.595230i	0.968516	−	0.248953i	$-0.0800864\pi$
$409$	8.74596	+	12.0378i	0.432460	+	0.595230i	−0.536056	+	0.844183i	$0.680086\pi$
$410$	−11.9629	+	30.5932i	−0.590807	+	1.51089i
$411$	5.22183	−	16.0712i	0.257574	−	0.792731i
$412$	−11.0213	+	23.9464i	−0.542982	+	1.17975i
$413$	11.2410	+	2.96913i	0.553133	+	0.146101i
$414$	−3.30326	−	5.15665i	−0.162346	−	0.253436i
$415$	−19.2222	+	6.24566i	−0.943578	+	0.306587i
$416$	9.35826	+	26.8516i	0.458826	+	1.31651i
$417$	−19.9152			−0.975254
$418$	10.4292	+	22.8937i	0.510110	+	1.11977i
$419$	−9.63862			−0.470878			−0.235439	−	0.971889i	$-0.575653\pi$
$419$	−9.63862			−0.470878			−0.235439	+	0.971889i	$0.575653\pi$
$420$	−4.71637	+	11.9670i	−0.230136	+	0.583930i
$421$	0.544575	+	1.67603i	0.0265410	+	0.0816847i	0.963450	−	0.267890i	$-0.0863262\pi$
$421$	0.544575	+	1.67603i	0.0265410	+	0.0816847i	−0.936909	+	0.349574i	$0.886326\pi$
$422$	5.62233	+	8.77692i	0.273691	+	0.427254i
$423$	−8.66954	−	6.29879i	−0.421528	−	0.306258i
$424$	1.92753	−	0.937147i	0.0936089	−	0.0455119i
$425$	3.13242	+	1.01778i	0.151945	+	0.0493698i
$426$	−9.32593	−	3.64674i	−0.451843	−	0.176685i
$427$	1.62459	+	1.04681i	0.0786196	+	0.0506589i
$428$	−33.6787	+	6.72096i	−1.62792	+	0.324870i
$429$	−7.34798	+	14.9652i	−0.354764	+	0.722528i
$430$	19.6000	+	16.0751i	0.945198	+	0.775211i
$431$	7.55249	+	10.3951i	0.363791	+	0.500715i	0.951200	−	0.308575i	$-0.0998521\pi$
$431$	7.55249	+	10.3951i	0.363791	+	0.500715i	−0.587409	+	0.809290i	$0.699852\pi$
$432$	2.60159	+	3.03838i	0.125169	+	0.146184i
$433$	21.3749	+	6.94512i	1.02721	+	0.333761i	0.773687	−	0.633568i	$-0.218410\pi$
$433$	21.3749	+	6.94512i	1.02721	+	0.333761i	0.253524	+	0.967329i	$0.418410\pi$
$434$	9.63101	+	13.3307i	0.462303	+	0.639892i
$435$	12.6504	−	17.4118i	0.606542	−	0.834834i
$436$	−25.3936	−	2.98946i	−1.21613	−	0.143169i
$437$	−22.0889	+	7.17713i	−1.05666	+	0.343329i
$438$	−0.269287	+	4.59064i	−0.0128670	+	0.219349i
$439$	−21.7547			−1.03830			−0.519148	−	0.854684i	$-0.673751\pi$
$439$	−21.7547			−1.03830			−0.519148	+	0.854684i	$0.673751\pi$
$440$	−13.4751	+	18.3962i	−0.642400	+	0.877002i
$441$	5.16851	−	4.72086i	0.246119	−	0.224803i
$442$	−25.7123	−	1.50828i	−1.22301	−	0.0717418i
$443$	13.8454	−	4.49863i	0.657813	−	0.213736i	0.0389569	−	0.999241i	$-0.487596\pi$
$443$	13.8454	−	4.49863i	0.657813	−	0.213736i	0.618856	+	0.785505i	$0.287596\pi$
$444$	11.1877	+	1.31707i	0.530943	+	0.0625054i
$445$	−15.3981	−	11.1874i	−0.729939	−	0.530331i
$446$	10.1277	+	38.7619i	0.479561	+	1.83543i
$447$	5.22291	−	16.0745i	0.247035	−	0.760297i
$448$	6.16666	−	20.2478i	0.291347	−	0.956617i
$449$	−11.1370	+	8.09149i	−0.525587	+	0.381861i	−0.818704	−	0.574215i	$-0.805307\pi$
$449$	−11.1370	+	8.09149i	−0.525587	+	0.381861i	0.293118	+	0.956076i	$0.405307\pi$
$450$	−0.994033	−	0.815263i	−0.0468592	−	0.0384319i
$451$	28.0212	−	14.8044i	1.31947	−	0.697112i
$452$	−7.01836	−	35.1690i	−0.330116	−	1.65421i
$453$	0.590188	+	0.812324i	0.0277295	+	0.0381663i
$454$	−7.38795	+	18.8934i	−0.346734	+	0.886713i
$455$	1.80699	+	32.2787i	0.0847130	+	1.51325i
$456$	13.6434	−	6.63329i	0.638909	−	0.310632i
$457$	14.5650	+	10.5821i	0.681323	+	0.495010i	0.873796	−	0.486292i	$-0.161651\pi$
$457$	14.5650	+	10.5821i	0.681323	+	0.495010i	−0.192473	+	0.981302i	$0.561651\pi$
$458$	−0.772692	−	1.20624i	−0.0361055	−	0.0563637i
$459$	−3.44580	+	1.11961i	−0.160836	+	0.0522589i
$460$	−15.4683	−	14.2808i	−0.721212	−	0.665847i
$461$		−	8.70294i		−	0.405336i	−0.979247	−	0.202668i	$-0.935039\pi$
$461$		−	8.70294i		−	0.405336i	0.979247	−	0.202668i	$-0.0649613\pi$
$462$	10.9879	−	5.76773i	0.511202	−	0.268339i
$463$			14.3261i			0.665788i	0.942964	+	0.332894i	$0.108025\pi$
$463$			14.3261i			0.665788i	−0.942964	+	0.332894i	$0.891975\pi$
$464$	−18.4666	+	30.2194i	−0.857292	+	1.40290i
$465$	−10.1614	+	3.30165i	−0.471225	+	0.153110i
$466$	−3.38398	+	2.16771i	−0.156760	+	0.100417i
$467$	−31.9419	−	23.2071i	−1.47809	−	1.07390i	−0.978165	−	0.207831i	$-0.933360\pi$
$467$	−31.9419	−	23.2071i	−1.47809	−	1.07390i	−0.499929	−	0.866067i	$-0.666640\pi$
$468$	9.13265	+	4.20330i	0.422157	+	0.194298i
$469$	−35.5950	+	1.99264i	−1.64362	+	0.0920115i
$470$	−34.3096	−	13.4162i	−1.58258	−	0.618842i
$471$	2.23533	+	3.07667i	0.102999	+	0.141766i
$472$	5.84885	−	10.9671i	0.269215	−	0.504802i
$473$	−4.18313	−	24.0954i	−0.192341	−	1.10791i
$474$	−4.57107	+	5.57340i	−0.209956	+	0.255995i
$475$	−3.94457	+	2.86590i	−0.180989	+	0.131496i
$476$	14.7913	+	12.1974i	0.677958	+	0.559066i
$477$	0.234161	−	0.720673i	0.0107215	−	0.0329973i
$478$	5.92286	−	1.54752i	0.270905	−	0.0707821i
$479$	−4.68903	−	3.40678i	−0.214247	−	0.155660i	0.475486	−	0.879723i	$-0.342272\pi$
$479$	−4.68903	−	3.40678i	−0.214247	−	0.155660i	−0.689733	+	0.724063i	$0.742272\pi$
$480$	11.2936	+	7.84504i	0.515479	+	0.358076i
$481$	26.9273	−	8.74920i	1.22778	−	0.398929i
$482$	0.787228	−	13.4202i	0.0358573	−	0.611272i
$483$	4.14384	+	10.6812i	0.188551	+	0.486011i
$484$	21.4376	−	4.94267i	0.974436	−	0.224667i
$485$	−20.4925			−0.930516
$486$	1.41179	+	0.0828155i	0.0640399	+	0.00375659i
$487$	−13.7419	+	4.46501i	−0.622704	+	0.202329i	−0.603341	−	0.797484i	$-0.706164\pi$
$487$	−13.7419	+	4.46501i	−0.622704	+	0.202329i	−0.0193638	+	0.999813i	$0.506164\pi$
$488$	1.48801	−	1.43337i	0.0673589	−	0.0648857i
$489$	6.69180	−	9.21047i	0.302613	−	0.416512i
$490$	13.0883	−	20.1936i	0.591270	−	0.912256i
$491$	−9.93195	−	3.22709i	−0.448223	−	0.145636i	0.0762035	−	0.997092i	$-0.475720\pi$
$491$	−9.93195	−	3.22709i	−0.448223	−	0.145636i	−0.524426	+	0.851456i	$0.675720\pi$
$492$	−9.34832	−	16.6682i	−0.421455	−	0.751462i
$493$	−18.8552	−	25.9519i	−0.849195	−	1.16882i
$494$	24.1796	−	29.4817i	1.08789	−	1.32644i
$495$	1.37903	+	7.94342i	0.0619828	+	0.357030i
$496$	16.2346	−	6.74832i	0.728953	−	0.303008i
$497$	15.7476	+	10.1471i	0.706378	+	0.455158i
$498$	4.28221	−	10.9510i	0.191890	−	0.490727i
$499$	15.5122	+	5.04022i	0.694422	+	0.225631i	0.634899	−	0.772595i	$-0.281042\pi$
$499$	15.5122	+	5.04022i	0.694422	+	0.225631i	0.0595236	+	0.998227i	$0.481042\pi$
$500$	18.0672	+	8.31545i	0.807992	+	0.371878i
$501$	−4.85978	−	3.53084i	−0.217119	−	0.157746i
$502$	−2.27902	+	1.45990i	−0.101718	+	0.0651586i
$503$	−5.59413	−	17.2170i	−0.249430	−	0.767667i	−0.994876	−	0.101101i	$-0.967763\pi$
$503$	−5.59413	−	17.2170i	−0.249430	−	0.767667i	0.745446	−	0.666566i	$-0.232237\pi$
$504$	−3.64314	−	6.53663i	−0.162278	−	0.291165i
$505$	−26.7468			−1.19022
$506$	2.29631	+	20.1806i	0.102083	+	0.897136i
$507$	12.2682			0.544852
$508$	9.71025	−	10.5176i	0.430823	−	0.466645i
$509$	1.28874	−	0.418738i	0.0571226	−	0.0185603i	−0.280316	−	0.959908i	$-0.590439\pi$
$509$	1.28874	−	0.418738i	0.0571226	−	0.0185603i	0.337439	+	0.941347i	$0.390439\pi$
$510$	−10.4881	+	6.71846i	−0.464419	+	0.297499i
$511$	2.19702	−	8.31780i	0.0971903	−	0.367958i
$512$	−19.5535	−	11.3869i	−0.864151	−	0.503233i
$513$	1.65743	−	5.10105i	0.0731774	−	0.225217i
$514$	−5.27520	−	2.06278i	−0.232679	−	0.0909852i
$515$	18.8325	+	25.9207i	0.829860	+	1.14220i
$516$	−14.4623	+	2.88611i	−0.636666	+	0.127054i
$517$	16.6028	+	31.4252i	0.730191	+	1.38208i
$518$	−20.0258	−	6.56596i	−0.879884	−	0.288492i
$519$	4.29982	+	5.91819i	0.188741	+	0.259780i
$520$	34.0288	+	6.04392i	1.49226	+	0.265044i
$521$	−15.2899	−	4.96799i	−0.669862	−	0.217651i	−0.0457107	−	0.998955i	$-0.514555\pi$
$521$	−15.2899	−	4.96799i	−0.669862	−	0.217651i	−0.624152	+	0.781303i	$0.714555\pi$
$522$	3.16526	+	12.1144i	0.138539	+	0.530234i
$523$	27.4240	+	19.9247i	1.19917	+	0.871248i	0.994203	−	0.107521i	$-0.0342914\pi$
$523$	27.4240	+	19.9247i	1.19917	+	0.871248i	0.204967	+	0.978769i	$0.434291\pi$
$524$	−2.59274	−	0.305231i	−0.113264	−	0.0133341i
$525$	1.52025	+	1.86373i	0.0663490	+	0.0813399i
$526$	0.487356	−	8.30813i	0.0212497	−	0.362252i
$527$			15.9248i			0.693695i
$528$	−3.30379	−	12.8485i	−0.143779	−	0.559161i
$529$	4.24871			0.184726
$530$	0.152546	−	2.60052i	0.00662619	−	0.112959i
$531$	−1.35795	−	4.17933i	−0.0589298	−	0.181367i
$532$	−27.4785	+	7.10125i	−1.19135	+	0.307878i
$533$	−38.8591	−	28.2328i	−1.68318	−	1.22290i
$534$	10.7133	−	2.79918i	0.463611	−	0.121132i
$535$	−12.8987	+	39.6982i	−0.557661	+	1.71630i
$536$	−6.66488	+	37.5250i	−0.287879	+	1.62083i
$537$	−13.4287	−	18.4831i	−0.579493	−	0.797604i
$538$	−2.07599	+	2.53121i	−0.0895021	+	0.109128i
$539$	−22.2881	+	6.49934i	−0.960016	+	0.279947i
$540$	4.76770	−	0.951447i	0.205169	−	0.0409438i
$541$	30.2155	−	21.9528i	1.29906	−	0.943825i	0.299118	−	0.954216i	$-0.403308\pi$
$541$	30.2155	−	21.9528i	1.29906	−	0.943825i	0.999946	+	0.0103906i	$0.00330751\pi$
$542$	10.5372	−	26.9470i	0.452610	−	1.15747i
$543$	−3.76884	−	1.22457i	−0.161736	−	0.0525513i
$544$	16.3222	−	12.3957i	0.699808	−	0.531460i
$545$	−18.2667	+	25.1419i	−0.782459	+	1.07696i
$546$	−15.1867	−	11.0959i	−0.649932	−	0.474860i
$547$	10.4478	−	3.39469i	0.446715	−	0.145146i	−0.0770168	−	0.997030i	$-0.524540\pi$
$547$	10.4478	−	3.39469i	0.446715	−	0.145146i	0.523732	+	0.851883i	$0.324540\pi$
$548$	24.8318	+	22.9255i	1.06076	+	0.979331i
$549$		−	0.730472i		−	0.0311758i
$550$	1.76762	+	3.88018i	0.0753715	+	0.165452i
$551$	47.4877			2.02304
$552$	12.1308	−	1.68946i	0.516321	−	0.0719083i
$553$	10.4497	−	8.52381i	0.444366	−	0.362469i
$554$	−16.7949	+	10.7585i	−0.713548	+	0.457086i
$555$	8.04778	−	11.0768i	0.341609	−	0.470185i
$556$	16.6529	−	36.1822i	0.706238	−	1.53447i
$557$	−4.83645	+	14.8851i	−0.204927	+	0.630700i	0.794789	+	0.606885i	$0.207581\pi$
$557$	−4.83645	+	14.8851i	−0.204927	+	0.630700i	−0.999716	+	0.0238151i	$0.992419\pi$
$558$	2.26371	−	5.78906i	0.0958305	−	0.245070i
$559$	−29.9869	+	21.7868i	−1.26831	+	0.921482i
$560$	−17.7980	−	18.5754i	−0.752103	−	0.784954i
$561$	11.8952	+	1.70379i	0.502214	+	0.0719339i
$562$	16.6627	+	13.6660i	0.702872	+	0.576465i
$563$	18.5194	−	13.4551i	0.780500	−	0.567067i	−0.124629	−	0.992203i	$-0.539774\pi$
$563$	18.5194	−	13.4551i	0.780500	−	0.567067i	0.905129	+	0.425137i	$0.139774\pi$
$564$	18.6930	−	10.4839i	0.787119	−	0.441453i
$565$	−41.4548	−	13.4695i	−1.74402	−	0.566666i
$566$	−5.34791	−	20.4681i	−0.224789	−	0.860340i
$567$	−2.55802	−	0.675662i	−0.107427	−	0.0283751i
$568$	14.4236	−	13.8941i	0.605203	−	0.582982i
$569$	12.4055	+	38.1801i	0.520064	+	1.60059i	0.773876	+	0.633338i	$0.218315\pi$
$569$	12.4055	+	38.1801i	0.520064	+	1.60059i	−0.253812	+	0.967254i	$0.581685\pi$
$570$	1.07975	−	18.4069i	0.0452258	−	0.770981i
$571$		−	36.8226i		−	1.54098i	−0.637453	−	0.770489i	$-0.720012\pi$
$571$		−	36.8226i		−	1.54098i	0.637453	−	0.770489i	$-0.279988\pi$
$572$	−21.0447	−	25.8636i	−0.879921	−	1.08141i
$573$		−	1.60504i		−	0.0670513i
$574$	10.9574	+	34.0324i	0.457354	+	1.42049i
$575$	−3.74379	+	1.21643i	−0.156127	+	0.0507286i
$576$	−7.69556	+	2.18593i	−0.320648	+	0.0910805i
$577$	−24.4828	+	33.6977i	−1.01923	+	1.40285i	−0.106491	+	0.994314i	$0.533962\pi$
$577$	−24.4828	+	33.6977i	−1.01923	+	1.40285i	−0.912741	+	0.408539i	$0.866038\pi$
$578$	−1.38458	−	5.29923i	−0.0575910	−	0.220419i
$579$	6.12474	−	18.8500i	0.254536	−	0.783380i
$580$	21.0558	+	37.5430i	0.874296	+	1.55889i
$581$	−11.9152	+	18.4918i	−0.494327	+	0.767167i
$582$	7.56039	−	9.21823i	0.313388	−	0.382108i
$583$	−1.75058	+	1.80323i	−0.0725018	+	0.0746823i
$584$	−8.11513	−	4.32787i	−0.335807	−	0.179089i
$585$	9.88562	−	7.18233i	0.408720	−	0.296953i
$586$	−31.6730	−	12.3852i	−1.30840	−	0.511627i
$587$	−0.709680	+	2.18417i	−0.0292916	+	0.0901504i	−0.964634	−	0.263595i	$-0.915092\pi$
$587$	−0.709680	+	2.18417i	−0.0292916	+	0.0901504i	0.935342	+	0.353745i	$0.115092\pi$
$588$	4.25506	+	13.3377i	0.175476	+	0.550038i
$589$	−19.0722	−	13.8568i	−0.785856	−	0.570958i
$590$	−8.14865	−	12.7207i	−0.335475	−	0.523703i
$591$	−4.46893	−	13.7540i	−0.183827	−	0.565762i
$592$	−11.7478	+	19.2245i	−0.482833	+	0.790124i
$593$		−	7.11464i		−	0.292163i	−0.989273	−	0.146082i	$-0.953334\pi$
$593$		−	7.11464i		−	0.292163i	0.989273	−	0.146082i	$-0.0466662\pi$
$594$	−4.08199	−	2.31027i	−0.167486	−	0.0947914i
$595$	21.7244	−	8.42812i	0.890612	−	0.345519i
$596$	24.8369	+	22.9303i	1.01736	+	0.939261i
$597$	−2.78344	−	8.56654i	−0.113919	−	0.350605i
$598$	25.9212	−	16.6047i	1.06000	−	0.679015i
$599$	−15.8049	+	21.7536i	−0.645772	+	0.888830i	−0.998907	−	0.0467430i	$-0.985116\pi$
$599$	−15.8049	+	21.7536i	−0.645772	+	0.888830i	0.353134	+	0.935573i	$0.385116\pi$
$600$	2.31237	−	1.12426i	0.0944022	−	0.0458975i
$601$	−14.6791	−	4.76951i	−0.598771	−	0.194553i	−0.00607890	−	0.999982i	$-0.501935\pi$
$601$	−14.6791	−	4.76951i	−0.598771	−	0.194553i	−0.592692	+	0.805429i	$0.701935\pi$
$602$	27.5898	+	0.0736770i	1.12448	+	0.00300285i
$603$	7.92024	+	10.9013i	0.322537	+	0.443934i
$604$	−1.96934	+	0.393004i	−0.0801315	+	0.0159911i
$605$	7.50596	−	25.6643i	0.305161	−	1.04340i
$606$	9.86783	−	12.0316i	0.400853	−	0.488752i
$607$	16.7417	−	12.1635i	0.679524	−	0.493703i	−0.193676	−	0.981066i	$-0.562041\pi$
$607$	16.7417	−	12.1635i	0.679524	−	0.493703i	0.873200	+	0.487363i	$0.162041\pi$
$608$	0.643018	+	30.3341i	0.0260778	+	1.23021i
$609$	−1.30929	−	23.3882i	−0.0530553	−	0.947739i
$610$	−0.634809	−	2.42962i	−0.0257027	−	0.0983723i
$611$	31.6625	−	43.5797i	1.28093	−	1.76304i
$612$	0.847217	−	7.19657i	0.0342467	−	0.290904i
$613$	−11.2389	−	34.5899i	−0.453936	−	1.39707i	−0.872380	−	0.488829i	$-0.837424\pi$
$613$	−11.2389	−	34.5899i	−0.453936	−	1.39707i	0.418443	−	0.908243i	$-0.362576\pi$
$614$	4.47827	+	0.262695i	0.180728	+	0.0106015i
$615$	−23.2277			−0.936632
$616$	1.29095	+	24.7858i	0.0520138	+	0.998646i
$617$	35.8522			1.44335			0.721677	−	0.692230i	$-0.243372\pi$
$617$	35.8522			1.44335			0.721677	+	0.692230i	$0.243372\pi$
$618$	−18.6080	−	1.09155i	−0.748524	−	0.0439085i
$619$	−0.485570	−	1.49443i	−0.0195167	−	0.0600663i	0.940824	−	0.338896i	$-0.110053\pi$
$619$	−0.485570	−	1.49443i	−0.0195167	−	0.0600663i	−0.960341	+	0.278830i	$0.910053\pi$
$620$	2.49839	−	21.2222i	0.100338	−	0.852303i
$621$	2.54527	−	3.50327i	0.102138	−	0.140581i
$622$	0.386459	+	1.47910i	0.0154956	+	0.0593065i
$623$	−20.6833	+	1.15787i	−0.828658	+	0.0463890i
$624$	−15.2732	+	13.0775i	−0.611417	+	0.523520i
$625$	23.2341	−	16.8805i	0.929363	−	0.675222i
$626$	−15.2248	+	18.5632i	−0.608504	+	0.741936i
$627$	−12.3909	+	12.7636i	−0.494847	+	0.509730i
$628$	−7.45888	+	1.48850i	−0.297642	+	0.0593977i
$629$	−11.9950	−	16.5097i	−0.478273	−	0.658287i
$630$	−9.09539	−	0.0242887i	−0.362369	−	0.000967685i
$631$	6.30822	+	2.04967i	0.251126	+	0.0815959i	0.431875	−	0.901933i	$-0.357852\pi$
$631$	6.30822	+	2.04967i	0.251126	+	0.0815959i	−0.180749	+	0.983529i	$0.557852\pi$
$632$	−6.30355	−	12.9652i	−0.250742	−	0.515726i
$633$	−4.33220	+	5.96276i	−0.172189	+	0.236999i
$634$	1.26644	−	0.811261i	0.0502969	−	0.0322193i
$635$	−5.37641	−	16.5469i	−0.213357	−	0.656644i
$636$	1.11352	+	1.02804i	0.0441540	+	0.0407645i
$637$	23.7306	+	25.9808i	0.940241	+	1.02940i
$638$	8.28525	−	40.6929i	0.328016	−	1.61105i
$639$		−	7.08066i		−	0.280107i
$640$	−23.6965	+	13.9584i	−0.936686	+	0.551752i
$641$	2.14991	+	6.61674i	0.0849163	+	0.261345i	0.984495	−	0.175414i	$-0.0561263\pi$
$641$	2.14991	+	6.61674i	0.0849163	+	0.261345i	−0.899579	+	0.436759i	$0.856126\pi$
$642$	−13.0988	−	20.4483i	−0.516970	−	0.807032i
$643$	5.23428	+	3.80293i	0.206420	+	0.149973i	0.686192	−	0.727420i	$-0.259281\pi$
$643$	5.23428	+	3.80293i	0.206420	+	0.149973i	−0.479773	+	0.877393i	$0.659281\pi$
$644$	−22.8707	−	1.40289i	−0.901231	−	0.0552816i
$645$	−5.53896	+	17.0472i	−0.218096	+	0.671231i
$646$	−25.5950	−	10.0085i	−1.00702	−	0.393779i
$647$	−21.7003	+	15.7662i	−0.853126	+	0.619832i	−0.926006	−	0.377508i	$-0.876781\pi$
$647$	−21.7003	+	15.7662i	−0.853126	+	0.619832i	0.0728801	+	0.997341i	$0.476781\pi$
$648$	−1.33098	+	2.49570i	−0.0522857	+	0.0980402i
$649$	−2.06648	+	14.4273i	−0.0811163	+	0.566323i
$650$	4.09812	−	4.99676i	0.160742	−	0.195989i
$651$	−6.29877	+	9.77532i	−0.246868	+	0.383125i
$652$	11.1381	+	19.8594i	0.436200	+	0.777753i
$653$	−11.8098	+	36.3469i	−0.462154	+	1.42237i	0.400372	+	0.916353i	$0.368881\pi$
$653$	−11.8098	+	36.3469i	−0.462154	+	1.42237i	−0.862526	+	0.506012i	$0.831119\pi$
$654$	−4.57049	−	17.4927i	−0.178720	−	0.684020i
$655$	−1.86507	+	2.56705i	−0.0728743	+	0.100303i
$656$	38.0999	−	3.04637i	1.48755	−	0.118941i
$657$	−3.09250	+	1.00482i	−0.120650	+	0.0392016i
$658$	−38.1666	+	12.2885i	−1.48789	+	0.479056i
$659$			47.5989i			1.85419i	0.374828	+	0.927094i	$0.377702\pi$
$659$			47.5989i			1.85419i	−0.374828	+	0.927094i	$0.622298\pi$
$660$	−15.5848	−	4.13674i	−0.606637	−	0.161022i
$661$			37.3250i			1.45177i	0.687815	+	0.725886i	$0.258570\pi$
$661$			37.3250i			1.45177i	−0.687815	+	0.725886i	$0.741430\pi$
$662$	−1.90090	+	32.4054i	−0.0738807	+	1.25947i
$663$	−5.62800	−	17.3212i	−0.218573	−	0.672700i
$664$	16.3152	+	16.9370i	0.633152	+	0.657285i
$665$	−8.80930	+	33.3516i	−0.341610	+	1.29332i
$666$	2.01363	+	7.70679i	0.0780265	+	0.298632i
$667$	36.4628	+	11.8475i	1.41185	+	0.458736i
$668$	10.4785	−	5.87686i	0.405427	−	0.227382i
$669$	−22.9186	+	16.6513i	−0.886084	+	0.643777i
$670$	35.8171	+	29.3756i	1.38373	+	1.13488i
$671$	−1.06779	+	2.17470i	−0.0412214	+	0.0839533i
$672$	14.9221	−	1.15304i	0.575634	−	0.0444795i
$673$	1.76706	−	1.28384i	0.0681151	−	0.0494885i	−0.553207	−	0.833044i	$-0.686596\pi$
$673$	1.76706	−	1.28384i	0.0681151	−	0.0494885i	0.621322	+	0.783556i	$0.286596\pi$
$674$	9.09647	−	23.2627i	0.350383	−	0.896045i
$675$	0.280913	−	0.864561i	0.0108123	−	0.0332770i
$676$	−10.2585	+	22.2891i	−0.394559	+	0.857271i
$677$	−4.43713	+	6.10719i	−0.170533	+	0.234718i	−0.885726	−	0.464209i	$-0.846339\pi$
$677$	−4.43713	+	6.10719i	−0.170533	+	0.234718i	0.715193	+	0.698927i	$0.246339\pi$
$678$	21.3532	−	13.6784i	0.820063	−	0.525317i
$679$	−17.2834	+	14.0981i	−0.663277	+	0.541035i
$680$	−3.43618	−	24.6727i	−0.131772	−	0.946155i
$681$	−14.3448			−0.549692
$682$	−15.2016	+	13.9257i	−0.582100	+	0.533241i
$683$		−	28.1839i		−	1.07843i	−0.842169	−	0.539213i	$-0.818722\pi$
$683$		−	28.1839i		−	1.07843i	0.842169	−	0.539213i	$-0.181278\pi$
$684$	7.88171	+	7.27666i	0.301365	+	0.278230i
$685$	39.0666	−	12.6935i	1.49266	−	0.484994i
$686$	−2.85378	−	26.0357i	−0.108958	−	0.994046i
$687$	0.595386	−	0.819478i	0.0227154	−	0.0312650i
$688$	6.84965	−	28.6885i	0.261140	−	1.09374i
$689$	3.62264	+	1.17707i	0.138012	+	0.0448427i
$690$	5.42133	−	13.8641i	0.206386	−	0.527798i
$691$	20.8800	−	15.1702i	0.794312	−	0.577101i	−0.114928	−	0.993374i	$-0.536664\pi$
$691$	20.8800	−	15.1702i	0.794312	−	0.577101i	0.909240	+	0.416272i	$0.136664\pi$
$692$	−14.3477	+	2.86324i	−0.545417	+	0.108844i
$693$	6.62786	+	5.75078i	0.251772	+	0.218454i
$694$	3.89691	−	4.75142i	0.147925	−	0.180362i
$695$	−28.4553	−	39.1654i	−1.07937	−	1.48563i
$696$	−24.6563	−	4.37926i	−0.934596	−	0.165995i
$697$	−10.6983	+	32.9259i	−0.405227	+	1.24716i
$698$	0.134966	−	0.0352638i	0.00510853	−	0.00133476i
$699$	−2.29897	−	1.67030i	−0.0869550	−	0.0631765i
$700$	−4.65725	+	1.20357i	−0.176028	+	0.0454906i
$701$	6.27902	+	19.3248i	0.237155	+	0.729889i	0.996828	+	0.0795837i	$0.0253591\pi$
$701$	6.27902	+	19.3248i	0.237155	+	0.729889i	−0.759673	+	0.650306i	$0.774641\pi$
$702$	−0.416293	+	7.09670i	−0.0157120	+	0.267848i
$703$	30.2101			1.13939
$704$	26.1059	+	4.74142i	0.983904	+	0.178699i
$705$		−	26.0494i		−	0.981077i
$706$	−1.23444	+	21.0439i	−0.0464586	+	0.791997i
$707$	−22.5584	+	18.4009i	−0.848394	+	0.692035i
$708$	8.72853	+	1.02757i	0.328038	+	0.0386184i
$709$	30.9208	+	22.4652i	1.16125	+	0.843700i	0.989936	−	0.141516i	$-0.0451977\pi$
$709$	30.9208	+	22.4652i	1.16125	+	0.843700i	0.171317	+	0.985216i	$0.445198\pi$
$710$	−6.15338	−	23.5509i	−0.230932	−	0.883851i
$711$	−4.84747	−	1.57504i	−0.181794	−	0.0590686i
$712$	−3.87277	+	21.8047i	−0.145138	+	0.817166i
$713$	−11.1873	−	15.3980i	−0.418967	−	0.576658i
$714$	−4.22361	+	12.8818i	−0.158065	+	0.482089i
$715$	−39.9296	+	6.93205i	−1.49328	+	0.259244i
$716$	44.8091	−	8.94216i	1.67460	−	0.334184i
$717$	2.54434	+	3.50198i	0.0950201	+	0.130784i
$718$	−25.5393	−	9.98671i	−0.953119	−	0.372701i
$719$	−2.02512	+	6.23268i	−0.0755242	+	0.232440i	−0.981691	−	0.190481i	$-0.938995\pi$
$719$	−2.02512	+	6.23268i	−0.0755242	+	0.232440i	0.906167	+	0.422921i	$0.138995\pi$
$720$	−2.25809	+	9.45758i	−0.0841539	+	0.352463i
$721$	33.7159	+	8.90554i	1.25565	+	0.331660i
$722$	11.6318	−	7.45113i	0.432891	−	0.277302i
$723$	9.04056	−	2.93746i	0.336222	−	0.109245i
$724$	5.37626	−	5.82328i	0.199807	−	0.216421i
$725$	8.04854			0.298915
$726$	8.77547	+	12.8449i	0.325688	+	0.476718i
$727$	−14.7510			−0.547086			−0.273543	−	0.961860i	$-0.588196\pi$
$727$	−14.7510			−0.547086			−0.273543	+	0.961860i	$0.588196\pi$
$728$	32.8580	−	18.3131i	1.21780	−	0.678730i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−9.41272	+	6.02961i	−0.348380	+	0.223166i
$731$	21.6137	+	15.7032i	0.799410	+	0.580806i
$732$	1.32713	+	0.610811i	0.0490521	+	0.0225762i
$733$	27.5511	+	8.95188i	1.01762	+	0.330645i	0.769885	−	0.638182i	$-0.220313\pi$
$733$	27.5511	+	8.95188i	1.01762	+	0.330645i	0.247736	+	0.968827i	$0.420313\pi$
$734$	−7.84148	+	20.0533i	−0.289434	+	0.740179i
$735$	16.6689	+	3.41914i	0.614843	+	0.126117i
$736$	−7.07417	+	23.4520i	−0.260757	+	0.864453i
$737$	−7.64424	−	44.0319i	−0.281579	−	1.62194i
$738$	8.56951	−	10.4486i	0.315448	−	0.384619i
$739$	−10.0802	−	13.8742i	−0.370806	−	0.510371i	0.582313	−	0.812964i	$-0.302148\pi$
$739$	−10.0802	−	13.8742i	−0.370806	−	0.510371i	−0.953120	+	0.302593i	$0.902148\pi$
$740$	13.3950	+	23.8836i	0.492411	+	0.877977i
$741$	25.6417	+	8.33150i	0.941972	+	0.306065i
$742$	−1.66040	−	2.29823i	−0.0609553	−	0.0843707i
$743$	6.55975	−	9.02873i	0.240654	−	0.331232i	−0.671557	−	0.740953i	$-0.734374\pi$
$743$	6.55975	−	9.02873i	0.240654	−	0.331232i	0.912211	+	0.409721i	$0.134374\pi$
$744$	8.62472	+	8.95346i	0.316198	+	0.328250i
$745$	39.0747	−	12.6961i	1.43159	−	0.465151i
$746$	−15.0158	−	0.880828i	−0.549768	−	0.0322494i
$747$	8.31451			0.304212
$748$	−13.0420	+	20.1866i	−0.476864	+	0.738094i
$749$	16.4321	+	42.3555i	0.600416	+	1.54764i
$750$	−0.823558	+	14.0395i	−0.0300721	+	0.512650i
$751$	5.51336	−	1.79140i	0.201185	−	0.0653691i	−0.206691	−	0.978406i	$-0.566269\pi$
$751$	5.51336	−	1.79140i	0.201185	−	0.0653691i	0.407876	+	0.913037i	$0.366269\pi$
$752$	3.41644	+	42.7282i	0.124585	+	1.55814i
$753$	−1.54830	−	1.12490i	−0.0564231	−	0.0409938i
$754$	−60.8963	+	15.9110i	−2.21771	+	0.579443i
$755$	−0.754246	+	2.32133i	−0.0274498	+	0.0844819i
$756$	3.36653	−	4.08246i	0.122440	−	0.148478i
$757$	23.0512	−	16.7477i	0.837809	−	0.608704i	−0.0839484	−	0.996470i	$-0.526753\pi$
$757$	23.0512	−	16.7477i	0.837809	−	0.608704i	0.921758	+	0.387766i	$0.126753\pi$
$758$	−16.7614	+	20.4369i	−0.608803	+	0.742301i
$759$	−12.6986	+	6.70901i	−0.460929	+	0.243522i
$760$	32.5390	+	17.3533i	1.18031	+	0.629471i
$761$	−15.3316	−	21.1022i	−0.555771	−	0.764953i	0.435010	−	0.900426i	$-0.356745\pi$
$761$	−15.3316	−	21.1022i	−0.555771	−	0.764953i	−0.990781	+	0.135473i	$0.956745\pi$
$762$	9.42691	+	3.68623i	0.341501	+	0.133538i
$763$	1.89056	+	33.7716i	0.0684430	+	1.22261i
$764$	2.91604	+	1.34211i	0.105499	+	0.0485558i
$765$	−7.12526	−	5.17681i	−0.257614	−	0.187168i
$766$	−14.5714	+	9.33415i	−0.526485	+	0.337257i
$767$	21.0084	−	6.82605i	0.758571	−	0.246475i
$768$	2.46351	−	15.8092i	0.0888941	−	0.570466i
$769$		−	46.2552i		−	1.66801i	−0.551760	−	0.834003i	$-0.686044\pi$
$769$		−	46.2552i		−	1.66801i	0.551760	−	0.834003i	$-0.313956\pi$
$770$	27.0425	+	13.3677i	0.974545	+	0.481740i
$771$		−	4.00517i		−	0.144243i
$772$	29.1254	+	26.8896i	1.04825	+	0.967778i
$773$	19.0785	−	6.19898i	0.686206	−	0.222962i	0.0548954	−	0.998492i	$-0.482517\pi$
$773$	19.0785	−	6.19898i	0.686206	−	0.222962i	0.631310	+	0.775530i	$0.282517\pi$
$774$	−5.62488	−	8.78090i	−0.202182	−	0.315623i
$775$	−3.23249	−	2.34854i	−0.116114	−	0.0843620i
$776$	10.4259	+	21.4439i	0.374267	+	0.769793i
$777$	−0.832928	−	14.8788i	−0.0298811	−	0.533774i
$778$	−13.3905	+	34.2439i	−0.480072	+	1.22770i
$779$	−30.1245	−	41.4628i	−1.07932	−	1.48556i
$780$	4.78269	+	23.9660i	0.171248	+	0.858122i
$781$	−10.3503	+	21.0800i	−0.370364	+	0.754300i
$782$	−17.1558	−	14.0705i	−0.613491	−	0.503159i
$783$	−7.16285	+	5.20411i	−0.255979	+	0.185980i
$784$	−27.7901	−	3.42217i	−0.992503	−	0.122220i
$785$	−2.85670	+	8.79202i	−0.101960	+	0.313801i
$786$	−0.466658	−	1.78605i	−0.0166451	−	0.0637062i
$787$	−11.7760	−	8.55574i	−0.419768	−	0.304979i	0.357777	−	0.933807i	$-0.383535\pi$
$787$	−11.7760	−	8.55574i	−0.419768	−	0.304979i	−0.777544	+	0.628828i	$0.783535\pi$
$788$	28.7252	+	3.38168i	1.02329	+	0.120467i
$789$	5.59681	−	1.81851i	0.199252	−	0.0647408i
$790$	−17.4919	−	1.02608i	−0.622334	−	0.0365061i
$791$	−44.2296	+	17.1592i	−1.57262	+	0.610111i
$792$	7.61062	−	5.48439i	0.270432	−	0.194879i
$793$	3.67190			0.130393
$794$	−0.428263	+	7.30075i	−0.0151985	+	0.259094i
$795$	1.75185	−	0.569211i	0.0621317	−	0.0201878i
$796$	17.8912	+	2.10625i	0.634138	+	0.0746540i
$797$	12.6143	−	17.3621i	0.446822	−	0.614998i	−0.524889	−	0.851171i	$-0.675893\pi$
$797$	12.6143	−	17.3621i	0.446822	−	0.614998i	0.971711	+	0.236173i	$0.0758932\pi$
$798$	−11.7526	−	16.2673i	−0.416039	−	0.575855i
$799$	−36.9257	−	11.9979i	−1.30634	−	0.424455i
$800$	0.108983	+	5.14122i	0.00385313	+	0.181770i
$801$	4.60223	+	6.33443i	0.162612	+	0.223816i
$802$	38.4305	+	31.5190i	1.35703	+	1.11298i
$803$	10.6756	+	1.52910i	0.376732	+	0.0539606i
$804$	−26.4283	+	5.27406i	−0.932055	+	0.186002i
$805$	−15.0848	+	23.4108i	−0.531671	+	0.825122i
$806$	29.1002	+	11.3791i	1.02501	+	0.400812i
$807$	−2.20152	−	0.715317i	−0.0774971	−	0.0251803i
$808$	13.6078	+	27.9887i	0.478722	+	0.984637i
$809$	−0.571345	−	0.415106i	−0.0200874	−	0.0145944i	0.577696	−	0.816252i	$-0.303952\pi$
$809$	−0.571345	−	0.415106i	−0.0200874	−	0.0145944i	−0.597784	+	0.801657i	$0.703952\pi$
$810$	1.85432	+	2.89475i	0.0651543	+	0.101711i
$811$	−4.44699	−	13.6864i	−0.156155	−	0.480595i	0.842121	−	0.539288i	$-0.181307\pi$
$811$	−4.44699	−	13.6864i	−0.156155	−	0.480595i	−0.998276	+	0.0586931i	$0.981307\pi$
$812$	43.5868	+	17.1782i	1.52960	+	0.602836i
$813$	20.4594			0.717542
$814$	5.27080	−	25.8875i	0.184741	−	0.907355i
$815$	27.6747			0.969403
$816$	12.3664	+	7.55690i	0.432909	+	0.264544i
$817$	−37.6137	+	12.2214i	−1.31594	+	0.427574i
$818$	−11.3505	−	17.7191i	−0.396861	−	0.619533i
$819$	3.39639	−	12.8585i	0.118679	−	0.449314i
$820$	19.4227	−	42.2003i	0.678270	−	1.47370i
$821$	−12.9145	+	39.7468i	−0.450720	+	1.38717i	0.425368	+	0.905020i	$0.360145\pi$
$821$	−12.9145	+	39.7468i	−0.450720	+	1.38717i	−0.876088	+	0.482152i	$0.839855\pi$
$822$	−8.70306	+	22.2566i	−0.303554	+	0.776288i
$823$	−2.13504	−	2.93863i	−0.0744229	−	0.102434i	0.770183	−	0.637823i	$-0.220165\pi$
$823$	−2.13504	−	2.93863i	−0.0744229	−	0.102434i	−0.844606	+	0.535389i	$0.820165\pi$
$824$	17.5429	−	32.8945i	0.611136	−	1.14593i
$825$	−2.10010	+	2.16326i	−0.0731162	+	0.0753152i
$826$	−15.6240	−	5.12271i	−0.543628	−	0.178242i
$827$	−10.9330	−	15.0480i	−0.380179	−	0.523271i	0.575453	−	0.817835i	$-0.304826\pi$
$827$	−10.9330	−	15.0480i	−0.380179	−	0.523271i	−0.955632	+	0.294564i	$0.904826\pi$
$828$	4.23644	+	7.55366i	0.147227	+	0.262508i
$829$	−41.3537	−	13.4366i	−1.43627	−	0.466674i	−0.515541	−	0.856865i	$-0.672409\pi$
$829$	−41.3537	−	13.4366i	−1.43627	−	0.466674i	−0.920734	+	0.390191i	$0.872409\pi$
$830$	27.6548	−	7.22564i	0.959913	−	0.250806i
$831$	−11.4099	−	8.28981i	−0.395807	−	0.287570i
$832$	−10.9881	−	38.6837i	−0.380945	−	1.34112i
$833$	12.5241	−	22.0539i	0.433936	−	0.764121i
$834$	28.1161	+	1.64929i	0.973580	+	0.0571103i
$835$		−	14.6022i		−	0.505330i
$836$	−12.8279	−	33.1847i	−0.443662	−	1.14772i
$837$	4.39531			0.151924
$838$	13.6077	+	0.798227i	0.470070	+	0.0275743i
$839$	2.01340	+	6.19662i	0.0695104	+	0.213931i	0.979777	−	0.200091i	$-0.0641237\pi$
$839$	2.01340	+	6.19662i	0.0695104	+	0.213931i	−0.910267	+	0.414022i	$0.864124\pi$
$840$	7.64957	−	16.5043i	0.263935	−	0.569452i
$841$	−39.9567	−	29.0302i	−1.37782	−	1.00104i
$842$	−0.630023	−	2.41130i	−0.0217120	−	0.0830988i
$843$	−4.70885	+	14.4924i	−0.162181	+	0.499143i
$844$	−7.21067	−	12.8568i	−0.248202	−	0.442548i
$845$	17.5291	+	24.1268i	0.603020	+	0.829986i
$846$	11.7179	+	9.61052i	0.402870	+	0.330417i
$847$	−11.3256	−	26.8092i	−0.389151	−	0.921174i
$848$	−2.79887	+	1.16342i	−0.0961135	+	0.0399521i
$849$	12.1021	−	8.79270i	0.415343	−	0.301765i
$850$	−4.33802	−	1.69631i	−0.148793	−	0.0581828i
$851$	23.1964	+	7.53697i	0.795162	+	0.258364i
$852$	12.8642	+	5.92075i	0.440721	+	0.202842i
$853$	18.8732	−	25.9768i	0.646207	−	0.889427i	−0.352721	−	0.935729i	$-0.614744\pi$
$853$	18.8732	−	25.9768i	0.646207	−	0.889427i	0.998928	+	0.0463015i	$0.0147435\pi$
$854$	−2.20689	−	1.61242i	−0.0755182	−	0.0551759i
$855$	12.3999	−	4.02897i	0.424068	−	0.137788i
$856$	48.1038	−	6.69945i	1.64415	−	0.228982i
$857$			39.0454i			1.33377i	0.745163	+	0.666883i	$0.232372\pi$
$857$			39.0454i			1.33377i	−0.745163	+	0.666883i	$0.767628\pi$
$858$	11.6131	−	20.5192i	0.396466	−	0.700513i
$859$	17.0258			0.580914			0.290457	−	0.956888i	$-0.406193\pi$
$859$	17.0258			0.580914			0.290457	+	0.956888i	$0.406193\pi$
$860$	−26.3398	−	24.3178i	−0.898180	−	0.829231i
$861$	−19.5903	+	15.9798i	−0.667637	+	0.544591i
$862$	−9.80163	−	15.3011i	−0.333845	−	0.521159i
$863$	−28.8816	+	39.7521i	−0.983140	+	1.35318i	−0.0480191	+	0.998846i	$0.515291\pi$
$863$	−28.8816	+	39.7521i	−0.983140	+	1.35318i	−0.935121	+	0.354329i	$0.884709\pi$
$864$	−3.42126	−	4.50500i	−0.116394	−	0.153263i
$865$	−5.49507	+	16.9121i	−0.186838	+	0.575028i
$866$	−29.6016	−	11.5752i	−1.00590	−	0.393341i
$867$	3.13325	−	2.27644i	0.106411	−	0.0773120i
$868$	−12.4929	−	19.6177i	−0.424038	−	0.665866i
$869$	12.1291	+	11.7750i	0.411452	+	0.399439i
$870$	−19.3017	+	23.5341i	−0.654389	+	0.797882i
$871$	−54.7980	+	39.8131i	−1.85676	+	1.34901i
$872$	35.6027	+	6.32346i	1.20566	+	0.214139i
$873$	8.01756	+	2.60506i	0.271353	+	0.0881680i
$874$	31.7793	−	8.30327i	1.07495	−	0.280862i
$875$	6.71912	−	25.4382i	0.227148	−	0.859970i
$876$	0.760352	−	6.45870i	0.0256899	−	0.218219i
$877$	8.70342	+	26.7864i	0.293893	+	0.904511i	0.983591	+	0.180413i	$0.0577436\pi$
$877$	8.70342	+	26.7864i	0.293893	+	0.904511i	−0.689697	+	0.724098i	$0.742256\pi$
$878$	30.7130	+	1.80163i	1.03651	+	0.0608020i
$879$		−	24.0476i		−	0.811104i
$880$	20.5474	−	24.8555i	0.692654	−	0.837879i
$881$			2.41820i			0.0814712i	0.999170	+	0.0407356i	$0.0129701\pi$
$881$			2.41820i			0.0814712i	−0.999170	+	0.0407356i	$0.987030\pi$
$882$	−7.68779	+	6.23682i	−0.258861	+	0.210004i
$883$	−0.647884	+	0.210510i	−0.0218030	+	0.00708423i	−0.319898	−	0.947452i	$-0.603649\pi$
$883$	−0.647884	+	0.210510i	−0.0218030	+	0.00708423i	0.298095	+	0.954536i	$0.403649\pi$
$884$	36.1754	+	4.25875i	1.21671	+	0.143237i
$885$	6.27881	−	8.64204i	0.211060	−	0.290499i
$886$	−19.9192	+	5.20450i	−0.669200	+	0.174848i
$887$	1.33664	−	4.11375i	0.0448799	−	0.138126i	−0.926106	−	0.377264i	$-0.876865\pi$
$887$	1.33664	−	4.11375i	0.0448799	−	0.138126i	0.970986	+	0.239138i	$0.0768649\pi$
$888$	−15.6855	−	2.78594i	−0.526372	−	0.0934899i
$889$	−15.9182	−	10.2569i	−0.533878	−	0.344006i
$890$	20.8123	+	17.0694i	0.697630	+	0.572166i
$891$	0.470252	−	3.28312i	0.0157540	−	0.109989i
$892$	−11.0881	−	55.5623i	−0.371256	−	1.86036i
$893$	46.4996	−	33.7839i	1.55605	−	1.13054i
$894$	−8.70485	+	22.2612i	−0.291134	+	0.744526i
$895$	17.1616	−	52.8180i	0.573649	−	1.76551i
$896$	−10.3828	+	28.0748i	−0.346866	+	0.937915i
$897$	17.6101	+	12.7945i	0.587983	+	0.427194i
$898$	16.3931	−	10.5011i	0.547046	−	0.350428i
$899$	12.0254	+	37.0104i	0.401070	+	1.23437i
$900$	1.33585	+	1.23330i	0.0445282	+	0.0411099i
$901$		−	2.74546i		−	0.0914647i
$902$	−40.7860	+	18.5801i	−1.35802	+	0.618648i
$903$	7.05625	+	18.1882i	0.234817	+	0.605266i
$904$	6.99589	+	50.2323i	0.232680	+	1.67070i
$905$	−2.97675	−	9.16149i	−0.0989505	−	0.304538i
$906$	−0.765947	−	1.19571i	−0.0254469	−	0.0397246i
$907$	−21.1169	+	29.0650i	−0.701176	+	0.965086i	0.298766	+	0.954326i	$0.403425\pi$
$907$	−21.1169	+	29.0650i	−0.701176	+	0.965086i	−0.999942	+	0.0107598i	$0.996575\pi$
$908$	11.9949	−	26.0617i	0.398064	−	0.864887i
$909$	10.4645	+	3.40013i	0.347087	+	0.112775i
$910$	0.122093	−	45.7203i	0.00404735	−	1.51561i
$911$	−12.1989	−	16.7904i	−0.404169	−	0.556291i	0.557615	−	0.830100i	$-0.311717\pi$
$911$	−12.1989	−	16.7904i	−0.404169	−	0.556291i	−0.961784	+	0.273809i	$0.911717\pi$
$912$	−19.8109	+	8.23491i	−0.656003	+	0.272685i
$913$	−24.7533	−	12.1540i	−0.819213	−	0.402237i
$914$	−19.6863	−	16.1459i	−0.651167	−	0.534059i
$915$	1.43655	−	1.04371i	0.0474908	−	0.0345041i
$916$	0.990982	+	1.76694i	0.0327430	+	0.0583813i
$917$	0.193031	+	3.44816i	0.00637444	+	0.113868i
$918$	4.95746	−	1.29528i	0.163621	−	0.0427507i
$919$	11.1784	−	15.3857i	0.368741	−	0.507529i	−0.583817	−	0.811885i	$-0.698441\pi$
$919$	11.1784	−	15.3857i	0.368741	−	0.507529i	0.952558	+	0.304356i	$0.0984414\pi$
$920$	20.6552	+	21.4425i	0.680983	+	0.706938i
$921$	0.980219	+	3.01680i	0.0322993	+	0.0994071i
$922$	−0.720738	+	12.2867i	−0.0237362	+	0.404641i
$923$	35.5928			1.17155
$924$	−15.9902	+	7.23283i	−0.526039	+	0.237943i
$925$	5.12021			0.168351
$926$	1.18642	−	20.2253i	0.0389881	−	0.664645i
$927$	−4.07299	−	12.5354i	−0.133775	−	0.411716i
$928$	28.5736	−	41.1340i	0.937973	−	1.35029i
$929$	−0.0641308	+	0.0882685i	−0.00210406	+	0.00289600i	−0.810068	−	0.586336i	$-0.800570\pi$
$929$	−0.0641308	+	0.0882685i	−0.00210406	+	0.00289600i	0.807964	+	0.589232i	$0.200570\pi$
$930$	14.6192	−	3.81970i	0.479383	−	0.125253i
$931$	15.5149	+	34.1893i	0.508480	+	1.12051i
$932$	4.95698	−	2.78010i	0.162371	−	0.0910653i
$933$	−0.874541	+	0.635391i	−0.0286312	+	0.0208018i
$934$	43.1732	+	35.4088i	1.41267	+	1.15861i
$935$	13.6454	+	25.8275i	0.446252	+	0.844649i
$936$	−12.5453	−	6.69049i	−0.410054	−	0.218685i
$937$	18.2348	+	25.0981i	0.595706	+	0.819919i	0.995307	−	0.0967703i	$-0.0308512\pi$
$937$	18.2348	+	25.0981i	0.595706	+	0.819919i	−0.399601	+	0.916689i	$0.630851\pi$
$938$	50.4176	+	0.134637i	1.64619	+	0.00439606i
$939$	−16.1454	−	5.24595i	−0.526885	−	0.171195i
$940$	47.3267	+	21.7821i	1.54363	+	0.710455i
$941$	−34.9659	+	48.1265i	−1.13986	+	1.56888i	−0.372031	+	0.928220i	$0.621338\pi$
$941$	−34.9659	+	48.1265i	−1.13986	+	1.56888i	−0.767826	+	0.640658i	$0.778662\pi$
$942$	−2.90102	−	4.52872i	−0.0945203	−	0.147554i
$943$	−12.7863	−	39.3523i	−0.416380	−	1.28149i
$944$	−9.16557	+	14.9988i	−0.298314	+	0.488170i
$945$	−2.32620	−	5.99601i	−0.0756712	−	0.195050i
$946$	3.91021	+	34.3641i	0.127132	+	1.11727i
$947$		−	4.19558i		−	0.136338i	−0.997674	−	0.0681690i	$-0.978284\pi$
$947$		−	4.19558i		−	0.136338i	0.997674	−	0.0681690i	$-0.0217157\pi$
$948$	6.91493	−	7.48990i	0.224587	−	0.243261i
$949$	−5.05096	−	15.5453i	−0.163961	−	0.504620i
$950$	5.80623	−	3.71937i	0.188379	−	0.120672i
$951$	0.860382	+	0.625104i	0.0278998	+	0.0202704i
$952$	−19.8720	−	18.4451i	−0.644056	−	0.597808i
$953$	9.71876	−	29.9113i	0.314821	−	0.968921i	−0.661007	−	0.750380i	$-0.729870\pi$
$953$	9.71876	−	29.9113i	0.314821	−	0.968921i	0.975828	−	0.218540i	$-0.0701295\pi$
$954$	−0.390268	+	0.998044i	−0.0126354	+	0.0323129i
$955$	3.15647	−	2.29331i	0.102141	−	0.0742097i
$956$	−8.48998	+	1.69427i	−0.274585	+	0.0547966i
$957$	28.9319	−	5.02277i	0.935234	−	0.162363i
$958$	6.33778	+	5.19797i	0.204764	+	0.167939i
$959$	24.2162	−	37.5822i	0.781983	−	1.21359i
$960$	−15.2944	−	12.0108i	−0.493626	−	0.387647i
$961$	−3.60969	+	11.1095i	−0.116442	+	0.358371i
$962$	−38.7401	+	10.1220i	−1.24903	+	0.326347i
$963$	10.0931	−	13.8920i	0.325246	−	0.447662i
$964$	−2.22280	+	18.8812i	−0.0715914	+	0.608123i
$965$	45.8216	−	14.8884i	1.47505	−	0.479273i
$966$	−4.96565	−	15.4227i	−0.159767	−	0.496218i
$967$			14.1749i			0.455833i	0.973681	+	0.227916i	$0.0731913\pi$
$967$			14.1749i			0.455833i	−0.973681	+	0.227916i	$0.926809\pi$
$968$	−30.6746	+	5.20263i	−0.985920	+	0.167219i
$969$		−	19.4329i		−	0.624274i
$970$	28.9310	+	1.69710i	0.928920	+	0.0544905i
$971$	−9.36556	−	28.8242i	−0.300555	−	0.925013i	−0.981299	−	0.192491i	$-0.938343\pi$
$971$	−9.36556	−	28.8242i	−0.300555	−	0.925013i	0.680744	−	0.732522i	$-0.261657\pi$
$972$	−1.98628	−	0.233836i	−0.0637101	−	0.00750028i
$973$	−50.9437	−	13.4560i	−1.63318	−	0.431379i
$974$	19.7704	−	5.16560i	0.633484	−	0.165517i
$975$	4.34593	+	1.41208i	0.139181	+	0.0452227i
$976$	−2.21945	+	1.90039i	−0.0710429	+	0.0608299i
$977$	−19.3644	+	14.0691i	−0.619523	+	0.450110i	−0.852755	−	0.522311i	$-0.825070\pi$
$977$	−19.3644	+	14.0691i	−0.619523	+	0.450110i	0.233232	+	0.972421i	$0.425070\pi$
$978$	−10.2102	+	12.4490i	−0.326485	+	0.398076i
$979$	−4.44186	−	25.5857i	−0.141962	−	0.817724i
$980$	−20.1502	+	27.4252i	−0.643676	+	0.876066i
$981$	10.3428	−	7.51452i	0.330222	−	0.239920i
$982$	13.7545	+	5.37848i	0.438925	+	0.171634i
$983$	−0.461551	+	1.42051i	−0.0147212	+	0.0453071i	−0.958147	−	0.286276i	$-0.907583\pi$
$983$	−0.461551	+	1.42051i	−0.0147212	+	0.0453071i	0.943426	+	0.331583i	$0.107583\pi$
$984$	11.8174	+	24.3062i	0.376726	+	0.774852i
$985$	20.6633	−	28.4406i	0.658387	−	0.906192i
$986$	24.4703	+	38.2001i	0.779292	+	1.21654i
$987$	−17.9210	−	21.9701i	−0.570433	−	0.699317i
$988$	−36.5780	+	39.6194i	−1.16370	+	1.26046i
$989$	−31.9302			−1.01532
$990$	−1.28906	−	11.3286i	−0.0409690	−	0.360047i
$991$		−	5.11896i		−	0.162609i	−0.996689	−	0.0813046i	$-0.974091\pi$
$991$		−	5.11896i		−	0.162609i	0.996689	−	0.0813046i	$-0.0259087\pi$
$992$	−23.4786	+	8.18271i	−0.745446	+	0.259801i
$993$	−21.8301	+	7.09301i	−0.692756	+	0.225090i
$994$	−21.3920	−	15.6296i	−0.678512	−	0.495742i
$995$	12.8700	−	17.7140i	0.408005	−	0.561570i
$996$	−6.95248	+	15.1059i	−0.220298	+	0.478648i
$997$	−50.0651	−	16.2671i	−1.58558	−	0.515185i	−0.622092	−	0.782945i	$-0.713717\pi$
$997$	−50.0651	−	16.2671i	−1.58558	−	0.515185i	−0.963486	+	0.267759i	$0.913717\pi$
$998$	−21.4825	−	8.40037i	−0.680018	−	0.265909i
$999$	−4.55676	+	3.31068i	−0.144170	+	0.104745i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	924.2.bu.b.223.1	yes	192
4.3	odd	2		924.2.bu.a.223.20	yes	192
7.6	odd	2		924.2.bu.a.223.1	✓	192
11.4	even	5	inner	924.2.bu.b.895.20	yes	192
28.27	even	2	inner	924.2.bu.b.223.20	yes	192
44.15	odd	10		924.2.bu.a.895.1	yes	192
77.48	odd	10		924.2.bu.a.895.20	yes	192
308.279	even	10	inner	924.2.bu.b.895.1	yes	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
924.2.bu.a.223.1	✓	192	7.6	odd	2
924.2.bu.a.223.20	yes	192	4.3	odd	2
924.2.bu.a.895.1	yes	192	44.15	odd	10
924.2.bu.a.895.20	yes	192	77.48	odd	10
924.2.bu.b.223.1	yes	192	1.1	even	1	trivial
924.2.bu.b.223.20	yes	192	28.27	even	2	inner
924.2.bu.b.895.1	yes	192	308.279	even	10	inner
924.2.bu.b.895.20	yes	192	11.4	even	5	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:	\( N \)	\(=\)	\( 924 = 2^{2} \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	924.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41179 - 0.0828155i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(1.98628 + 0.233836i) q^{4} +(1.42882 - 1.96660i) q^{5} +(0.357504 + 1.36828i) q^{6} +(-0.147880 - 2.64162i) q^{7} +(-2.78484 - 0.494621i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-2.18005 + 2.65809i) q^{10} +(3.26775 - 0.567303i) q^{11} +(-0.391404 - 1.96133i) q^{12} +(-2.95465 - 4.06673i) q^{13} +(-0.00999184 + 3.74164i) q^{14} +(-2.31188 - 0.751175i) q^{15} +(3.89064 + 0.928927i) q^{16} +(-2.12962 + 2.93118i) q^{17} +(1.19084 - 0.762828i) q^{18} +(-1.65743 - 5.10105i) q^{19} +(3.29790 - 3.57212i) q^{20} +(-2.46663 + 0.956946i) q^{21} +(-4.66034 + 0.530291i) q^{22} -4.33028i q^{23} +(0.390151 + 2.80139i) q^{24} +(-0.280913 - 0.864561i) q^{25} +(3.83455 + 5.98604i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.323972 - 5.28158i) q^{28} +(-2.73596 + 8.42043i) q^{29} +(3.20167 + 1.25196i) q^{30} +(3.55588 - 2.58350i) q^{31} +(-5.41583 - 1.63365i) q^{32} +(-1.54933 - 2.93251i) q^{33} +(3.24932 - 3.96183i) q^{34} +(-5.40630 - 3.48357i) q^{35} +(-1.74438 + 0.978331i) q^{36} +(-1.74053 + 5.35679i) q^{37} +(1.91749 + 7.33885i) q^{38} +(-2.95465 + 4.06673i) q^{39} +(-4.95176 + 4.76995i) q^{40} +(9.08770 - 2.95277i) q^{41} +(3.56160 - 1.14673i) q^{42} -7.37372i q^{43} +(6.62333 - 0.362709i) q^{44} +2.43085i q^{45} +(-0.358614 + 6.11343i) q^{46} +(3.31147 + 10.1917i) q^{47} +(-0.318812 - 3.98727i) q^{48} +(-6.95626 + 0.781283i) q^{49} +(0.324990 + 1.24384i) q^{50} +(3.44580 + 1.11961i) q^{51} +(-4.91783 - 8.76858i) q^{52} +(-0.613041 + 0.445400i) q^{53} +(-1.09348 - 0.896827i) q^{54} +(3.55336 - 7.23693i) q^{55} +(-0.894776 + 7.42963i) q^{56} +(-4.33921 + 3.15262i) q^{57} +(4.55994 - 11.6613i) q^{58} +(-1.35795 + 4.17933i) q^{59} +(-4.41640 - 2.03265i) q^{60} +(-0.429361 + 0.590964i) q^{61} +(-5.23410 + 3.35287i) q^{62} +(1.67234 + 2.05019i) q^{63} +(7.51070 + 2.75488i) q^{64} -12.2193 q^{65} +(1.94446 + 4.26838i) q^{66} -13.4747i q^{67} +(-4.91545 + 5.32416i) q^{68} +(-4.11834 + 1.33813i) q^{69} +(7.34405 + 5.36579i) q^{70} +(-4.16191 + 5.72838i) q^{71} +(2.54372 - 1.23673i) q^{72} +(3.09250 + 1.00482i) q^{73} +(2.90088 - 7.41851i) q^{74} +(-0.735439 + 0.534328i) q^{75} +(-2.09932 - 10.5197i) q^{76} +(-1.98183 - 8.54824i) q^{77} +(4.50813 - 5.49666i) q^{78} +(2.99590 + 4.12351i) q^{79} +(7.38586 - 6.32408i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-13.0744 + 3.41608i) q^{82} +(-6.72658 - 4.88715i) q^{83} +(-5.12319 + 1.32398i) q^{84} +(2.72161 + 8.37625i) q^{85} +(-0.610658 + 10.4101i) q^{86} +8.85376 q^{87} +(-9.38076 - 0.0364466i) q^{88} -7.82978i q^{89} +(0.201312 - 3.43185i) q^{90} +(-10.3058 + 8.40644i) q^{91} +(1.01257 - 8.60116i) q^{92} +(-3.55588 - 2.58350i) q^{93} +(-3.83106 - 14.6627i) q^{94} +(-12.3999 - 4.02897i) q^{95} +(0.119886 + 5.65558i) q^{96} +(-4.95513 - 6.82014i) q^{97} +(9.88546 - 0.526919i) q^{98} +(-2.31021 + 2.37969i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q + 2 q^{2} + 48 q^{3} - 2 q^{4} - 2 q^{6} + 2 q^{8} - 48 q^{9} + 2 q^{12} + 13 q^{14} + 6 q^{16} - 3 q^{18} + 6 q^{20} + 24 q^{22} + 3 q^{24} + 56 q^{25} - 18 q^{26} + 48 q^{27} + 16 q^{29} + 12 q^{31}+ \cdots + 50 q^{98}+O(q^{100}) \) 192 * q + 2 * q^2 + 48 * q^3 - 2 * q^4 - 2 * q^6 + 2 * q^8 - 48 * q^9 + 2 * q^12 + 13 * q^14 + 6 * q^16 - 3 * q^18 + 6 * q^20 + 24 * q^22 + 3 * q^24 + 56 * q^25 - 18 * q^26 + 48 * q^27 + 16 * q^29 + 12 * q^31 - 8 * q^32 + 24 * q^34 + 14 * q^35 - 2 * q^36 - 24 * q^37 - 36 * q^38 - 36 * q^40 + 2 * q^42 + 29 * q^44 - 23 * q^46 + 8 * q^47 - 11 * q^48 + 16 * q^49 - 14 * q^50 - 40 * q^52 + 8 * q^53 - 2 * q^54 - 4 * q^55 - 8 * q^56 + 7 * q^58 - 40 * q^59 - 6 * q^60 - 56 * q^64 - 16 * q^65 + 11 * q^66 - 78 * q^68 + 86 * q^70 - 3 * q^72 + 28 * q^74 - 36 * q^75 - 56 * q^76 + 28 * q^77 - 12 * q^78 + 6 * q^80 - 48 * q^81 + 8 * q^83 + 15 * q^84 - 60 * q^85 - 51 * q^86 - 16 * q^87 - 4 * q^88 + 8 * q^91 - 47 * q^92 - 12 * q^93 + 64 * q^94 - 2 * q^96 + 50 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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