LMFDB - Embedded newform 600.2.bm.a.61.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(61,600)] 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("600.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.bm (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$60$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			61.15
Character	$\chi$	$=$	600.61
Dual form			600.2.bm.a.541.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.967261 - 1.03170i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.128814 + 1.99585i) q^{4} +(1.68421 + 1.47086i) q^{5} +(-0.601106 - 1.28011i) q^{6} +2.08501 q^{7} +(2.18371 - 1.79761i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-0.111588 - 3.16031i) q^{10} +(2.20130 + 3.02983i) q^{11} +(-0.739260 + 1.85836i) q^{12} +(-1.42445 + 1.96059i) q^{13} +(-2.01675 - 2.15110i) q^{14} +(1.14726 + 1.91932i) q^{15} +(-3.96681 - 0.514185i) q^{16} +(-0.784515 - 2.41449i) q^{17} +(-0.176112 - 1.40321i) q^{18} +(-5.97044 + 1.93992i) q^{19} +(-3.15256 + 3.17197i) q^{20} +(1.98296 + 0.644303i) q^{21} +(0.996647 - 5.20172i) q^{22} +(1.49694 - 1.08759i) q^{23} +(2.63233 - 1.03482i) q^{24} +(0.673153 + 4.95448i) q^{25} +(3.40055 - 0.426792i) q^{26} +(0.587785 + 0.809017i) q^{27} +(-0.268578 + 4.16136i) q^{28} +(0.213333 + 0.0693161i) q^{29} +(0.870462 - 3.04011i) q^{30} +(-1.72308 - 5.30308i) q^{31} +(3.30646 + 4.58992i) q^{32} +(1.15729 + 3.56178i) q^{33} +(-1.73220 + 3.14482i) q^{34} +(3.51160 + 3.06675i) q^{35} +(-1.27734 + 1.53896i) q^{36} +(-2.01755 + 2.77692i) q^{37} +(7.77639 + 4.28331i) q^{38} +(-1.96059 + 1.42445i) q^{39} +(6.32187 + 0.184379i) q^{40} +(6.44324 + 4.68129i) q^{41} +(-1.25331 - 2.66903i) q^{42} +1.31176i q^{43} +(-6.33063 + 4.00317i) q^{44} +(0.498009 + 2.17991i) q^{45} +(-2.57000 - 0.492411i) q^{46} +(3.49403 - 10.7535i) q^{47} +(-3.61377 - 1.71483i) q^{48} -2.65274 q^{49} +(4.46043 - 5.48677i) q^{50} -2.53874i q^{51} +(-3.72954 - 3.09553i) q^{52} +(7.13282 + 2.31759i) q^{53} +(0.266122 - 1.38895i) q^{54} +(-0.748989 + 8.34068i) q^{55} +(4.55306 - 3.74803i) q^{56} -6.27770 q^{57} +(-0.134835 - 0.287143i) q^{58} +(1.56491 - 2.15392i) q^{59} +(-3.97845 + 2.04253i) q^{60} +(-3.52395 - 4.85031i) q^{61} +(-3.80453 + 6.90716i) q^{62} +(1.68681 + 1.22554i) q^{63} +(1.53722 - 7.85092i) q^{64} +(-5.28282 + 1.20688i) q^{65} +(2.55529 - 4.63914i) q^{66} +(11.3688 - 3.69394i) q^{67} +(4.92001 - 1.25475i) q^{68} +(1.75976 - 0.571780i) q^{69} +(-0.232662 - 6.58927i) q^{70} +(3.21846 - 9.90540i) q^{71} +(2.82327 - 0.170740i) q^{72} +(-1.02722 + 0.746320i) q^{73} +(4.81645 - 0.604497i) q^{74} +(-0.890812 + 4.92001i) q^{75} +(-3.10270 - 12.1660i) q^{76} +(4.58973 + 6.31722i) q^{77} +(3.36600 + 0.644925i) q^{78} +(0.872015 - 2.68379i) q^{79} +(-5.92467 - 6.70062i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-1.40260 - 11.1755i) q^{82} +(7.94645 - 2.58196i) q^{83} +(-1.54136 + 3.87469i) q^{84} +(2.23008 - 5.22042i) q^{85} +(1.35334 - 1.26881i) q^{86} +(0.181472 + 0.131847i) q^{87} +(10.2534 + 2.65921i) q^{88} +(-13.6365 + 9.90747i) q^{89} +(1.76731 - 2.62233i) q^{90} +(-2.96999 + 4.08784i) q^{91} +(1.97784 + 3.12776i) q^{92} -5.57599i q^{93} +(-14.4741 + 6.79667i) q^{94} +(-12.9088 - 5.51445i) q^{95} +(1.72627 + 5.38702i) q^{96} +(-1.09220 + 3.36144i) q^{97} +(2.56589 + 2.73684i) q^{98} +3.74507i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 18 q^{8} + 60 q^{9} - 2 q^{10} - 8 q^{12} + 12 q^{14} - 12 q^{16} + 8 q^{17} + 16 q^{20} - 38 q^{22} - 4 q^{25} - 20 q^{26} + 28 q^{28} - 36 q^{30} - 24 q^{31} - 20 q^{32} - 16 q^{34} - 46 q^{38}+ \cdots - 140 q^{98}+O(q^{100}) $ 240 * q + 18 * q^8 + 60 * q^9 - 2 * q^10 - 8 * q^12 + 12 * q^14 - 12 * q^16 + 8 * q^17 + 16 * q^20 - 38 * q^22 - 4 * q^25 - 20 * q^26 + 28 * q^28 - 36 * q^30 - 24 * q^31 - 20 * q^32 - 16 * q^34 - 46 * q^38 + 16 * q^39 + 40 * q^40 - 8 * q^41 - 20 * q^42 + 42 * q^44 + 20 * q^46 + 48 * q^47 - 16 * q^48 + 240 * q^49 - 144 * q^50 + 16 * q^52 - 16 * q^55 + 36 * q^56 - 94 * q^58 - 2 * q^60 - 66 * q^62 + 42 * q^64 + 84 * q^65 + 8 * q^66 + 16 * q^68 + 4 * q^70 - 18 * q^72 + 40 * q^73 - 44 * q^74 + 8 * q^76 - 24 * q^78 - 40 * q^79 - 16 * q^80 - 60 * q^81 - 80 * q^82 - 24 * q^84 - 60 * q^86 + 22 * q^88 - 60 * q^89 - 28 * q^90 + 14 * q^92 - 50 * q^94 - 184 * q^95 + 40 * q^96 + 32 * q^97 - 140 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.967261	−	1.03170i	−0.683957	−	0.729523i
$2$	−0.967261	−	1.03170i	−0.683957	−	0.729523i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−0.128814	+	1.99585i	−0.0644069	+	0.997924i
$5$	1.68421	+	1.47086i	0.753203	+	0.657788i
$5$	1.68421	+	1.47086i	0.753203	+	0.657788i
$6$	−0.601106	−	1.28011i	−0.245401	−	0.522601i
$7$	2.08501			0.788059			0.394029	−	0.919098i	$-0.371081\pi$
$7$	2.08501			0.788059			0.394029	+	0.919098i	$0.371081\pi$
$8$	2.18371	−	1.79761i	0.772060	−	0.635550i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$	−0.111588	−	3.16031i	−0.0352872	−	0.999377i
$11$	2.20130	+	3.02983i	0.663717	+	0.913527i	0.999597	−	0.0283771i	$-0.00903391\pi$
$11$	2.20130	+	3.02983i	0.663717	+	0.913527i	−0.335881	+	0.941905i	$0.609034\pi$
$12$	−0.739260	+	1.85836i	−0.213406	+	0.536462i
$13$	−1.42445	+	1.96059i	−0.395071	+	0.543769i	−0.959498	−	0.281714i	$-0.909097\pi$
$13$	−1.42445	+	1.96059i	−0.395071	+	0.543769i	0.564427	+	0.825483i	$0.309097\pi$
$14$	−2.01675	−	2.15110i	−0.538998	−	0.574907i
$15$	1.14726	+	1.91932i	0.296222	+	0.495566i
$16$	−3.96681	−	0.514185i	−0.991704	−	0.128546i
$17$	−0.784515	−	2.41449i	−0.190273	−	0.585599i	0.809726	−	0.586807i	$-0.199615\pi$
$17$	−0.784515	−	2.41449i	−0.190273	−	0.585599i	−0.999999	+	0.00120805i	$0.999615\pi$
$18$	−0.176112	−	1.40321i	−0.0415099	−	0.330739i
$19$	−5.97044	+	1.93992i	−1.36971	+	0.445047i	−0.899274	−	0.437385i	$-0.855905\pi$
$19$	−5.97044	+	1.93992i	−1.36971	+	0.445047i	−0.470440	+	0.882432i	$0.655905\pi$
$20$	−3.15256	+	3.17197i	−0.704933	+	0.709273i
$21$	1.98296	+	0.644303i	0.432717	+	0.140598i
$22$	0.996647	−	5.20172i	0.212486	−	1.10901i
$23$	1.49694	−	1.08759i	0.312134	−	0.226778i	−0.420678	−	0.907210i	$-0.638208\pi$
$23$	1.49694	−	1.08759i	0.312134	−	0.226778i	0.732812	+	0.680432i	$0.238208\pi$
$24$	2.63233	−	1.03482i	0.537321	−	0.211232i
$25$	0.673153	+	4.95448i	0.134631	+	0.990896i
$26$	3.40055	−	0.426792i	0.666903	−	0.0837008i
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	−0.268578	+	4.16136i	−0.0507564	+	0.786423i
$29$	0.213333	+	0.0693161i	0.0396149	+	0.0128717i	0.328757	−	0.944414i	$-0.393370\pi$
$29$	0.213333	+	0.0693161i	0.0396149	+	0.0128717i	−0.289143	+	0.957286i	$0.593370\pi$
$30$	0.870462	−	3.04011i	0.158924	−	0.555046i
$31$	−1.72308	−	5.30308i	−0.309473	−	0.952461i	−0.977970	−	0.208746i	$-0.933062\pi$
$31$	−1.72308	−	5.30308i	−0.309473	−	0.952461i	0.668496	−	0.743715i	$-0.266938\pi$
$32$	3.30646	+	4.58992i	0.584505	+	0.811390i
$33$	1.15729	+	3.56178i	0.201459	+	0.620026i
$34$	−1.73220	+	3.14482i	−0.297070	+	0.539333i
$35$	3.51160	+	3.06675i	0.593569	+	0.518376i
$36$	−1.27734	+	1.53896i	−0.212890	+	0.256493i
$37$	−2.01755	+	2.77692i	−0.331684	+	0.456523i	−0.941989	−	0.335643i	$-0.891047\pi$
$37$	−2.01755	+	2.77692i	−0.331684	+	0.456523i	0.610306	+	0.792166i	$0.291047\pi$
$38$	7.77639	+	4.28331i	1.26150	+	0.694845i
$39$	−1.96059	+	1.42445i	−0.313945	+	0.228094i
$40$	6.32187	+	0.184379i	0.999575	+	0.0291528i
$41$	6.44324	+	4.68129i	1.00627	+	0.731095i	0.963422	−	0.267987i	$-0.0863585\pi$
$41$	6.44324	+	4.68129i	1.00627	+	0.731095i	0.0428429	+	0.999082i	$0.486358\pi$
$42$	−1.25331	−	2.66903i	−0.193390	−	0.411840i
$43$			1.31176i			0.200041i	0.994985	+	0.100021i	$0.0318909\pi$
$43$			1.31176i			0.200041i	−0.994985	+	0.100021i	$0.968109\pi$
$44$	−6.33063	+	4.00317i	−0.954379	+	0.603501i
$45$	0.498009	+	2.17991i	0.0742388	+	0.324961i
$46$	−2.57000	−	0.492411i	−0.378926	−	0.0726021i
$47$	3.49403	−	10.7535i	0.509657	−	1.56856i	−0.283141	−	0.959078i	$-0.591376\pi$
$47$	3.49403	−	10.7535i	0.509657	−	1.56856i	0.792798	−	0.609485i	$-0.208624\pi$
$48$	−3.61377	−	1.71483i	−0.521603	−	0.247515i
$49$	−2.65274			−0.378963
$50$	4.46043	−	5.48677i	0.630800	−	0.775946i
$51$		−	2.53874i		−	0.355495i
$52$	−3.72954	−	3.09553i	−0.517194	−	0.429273i
$53$	7.13282	+	2.31759i	0.979768	+	0.318346i	0.754753	−	0.656009i	$-0.227757\pi$
$53$	7.13282	+	2.31759i	0.979768	+	0.318346i	0.225015	+	0.974355i	$0.427757\pi$
$54$	0.266122	−	1.38895i	0.0362146	−	0.189012i
$55$	−0.748989	+	8.34068i	−0.100994	+	1.12466i
$56$	4.55306	−	3.74803i	0.608428	−	0.500851i
$57$	−6.27770			−0.831501
$58$	−0.134835	−	0.287143i	−0.0177047	−	0.0377037i
$59$	1.56491	−	2.15392i	0.203734	−	0.280416i	−0.694908	−	0.719099i	$-0.744555\pi$
$59$	1.56491	−	2.15392i	0.203734	−	0.280416i	0.898642	+	0.438683i	$0.144555\pi$
$60$	−3.97845	+	2.04253i	−0.513616	+	0.263689i
$61$	−3.52395	−	4.85031i	−0.451196	−	0.621018i	0.521458	−	0.853277i	$-0.325388\pi$
$61$	−3.52395	−	4.85031i	−0.451196	−	0.621018i	−0.972654	+	0.232259i	$0.925388\pi$
$62$	−3.80453	+	6.90716i	−0.483176	+	0.877210i
$63$	1.68681	+	1.22554i	0.212518	+	0.154403i
$64$	1.53722	−	7.85092i	0.192152	−	0.981365i
$65$	−5.28282	+	1.20688i	−0.655253	+	0.149695i
$66$	2.55529	−	4.63914i	0.314534	−	0.571039i
$67$	11.3688	−	3.69394i	1.38892	−	0.451286i	0.483326	−	0.875441i	$-0.339429\pi$
$67$	11.3688	−	3.69394i	1.38892	−	0.451286i	0.905590	+	0.424155i	$0.139429\pi$
$68$	4.92001	−	1.25475i	0.596638	−	0.152161i
$69$	1.75976	−	0.571780i	0.211850	−	0.0688343i
$70$	−0.232662	−	6.58927i	−0.0278084	−	0.787568i
$71$	3.21846	−	9.90540i	0.381961	−	1.17555i	−0.556700	−	0.830713i	$-0.687933\pi$
$71$	3.21846	−	9.90540i	0.381961	−	1.17555i	0.938661	−	0.344841i	$-0.112067\pi$
$72$	2.82327	−	0.170740i	0.332725	−	0.0201219i
$73$	−1.02722	+	0.746320i	−0.120227	+	0.0873502i	−0.646274	−	0.763105i	$-0.723674\pi$
$73$	−1.02722	+	0.746320i	−0.120227	+	0.0873502i	0.526047	+	0.850456i	$0.323674\pi$
$74$	4.81645	−	0.604497i	0.559901	−	0.0702714i
$75$	−0.890812	+	4.92001i	−0.102862	+	0.568113i
$76$	−3.10270	−	12.1660i	−0.355904	−	1.39553i
$77$	4.58973	+	6.31722i	0.523048	+	0.719913i
$78$	3.36600	+	0.644925i	0.381125	+	0.0730234i
$79$	0.872015	−	2.68379i	0.0981094	−	0.301950i	−0.889942	−	0.456073i	$-0.849255\pi$
$79$	0.872015	−	2.68379i	0.0981094	−	0.301950i	0.988052	+	0.154124i	$0.0492555\pi$
$80$	−5.92467	−	6.70062i	−0.662398	−	0.749152i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−1.40260	−	11.1755i	−0.154892	−	1.23413i
$83$	7.94645	−	2.58196i	0.872237	−	0.283407i	0.161506	−	0.986872i	$-0.448365\pi$
$83$	7.94645	−	2.58196i	0.872237	−	0.283407i	0.710730	+	0.703465i	$0.248365\pi$
$84$	−1.54136	+	3.87469i	−0.168176	+	0.422763i
$85$	2.23008	−	5.22042i	0.241886	−	0.566235i
$86$	1.35334	−	1.26881i	0.145935	−	0.136819i
$87$	0.181472	+	0.131847i	0.0194558	+	0.0141355i
$88$	10.2534	+	2.65921i	1.09302	+	0.283472i
$89$	−13.6365	+	9.90747i	−1.44546	+	1.05019i	−0.458596	+	0.888645i	$0.651648\pi$
$89$	−13.6365	+	9.90747i	−1.44546	+	1.05019i	−0.986865	+	0.161545i	$0.948352\pi$
$90$	1.76731	−	2.62233i	0.186290	−	0.276418i
$91$	−2.96999	+	4.08784i	−0.311339	+	0.428522i
$92$	1.97784	+	3.12776i	0.206204	+	0.326092i
$93$		−	5.57599i		−	0.578203i
$94$	−14.4741	+	6.79667i	−1.49289	+	0.701023i
$95$	−12.9088	−	5.51445i	−1.32442	−	0.565770i
$96$	1.72627	+	5.38702i	0.176186	+	0.549811i
$97$	−1.09220	+	3.36144i	−0.110896	+	0.341302i	−0.991069	−	0.133351i	$-0.957426\pi$
$97$	−1.09220	+	3.36144i	−0.110896	+	0.341302i	0.880173	+	0.474653i	$0.157426\pi$
$98$	2.56589	+	2.73684i	0.259194	+	0.276462i
$99$			3.74507i			0.376394i
$100$	−9.97510	+	0.705305i	−0.997510	+	0.0705305i
$101$		−	15.3280i		−	1.52520i	−0.646873	−	0.762598i	$-0.723924\pi$
$101$		−	15.3280i		−	1.52520i	0.646873	−	0.762598i	$-0.276076\pi$
$102$	−2.61922	+	2.45563i	−0.259342	+	0.243143i
$103$	2.69877	−	8.30595i	0.265917	−	0.818409i	−0.725563	−	0.688155i	$-0.758421\pi$
$103$	2.69877	−	8.30595i	0.265917	−	0.818409i	0.991481	−	0.130254i	$-0.0415793\pi$
$104$	0.413774	+	6.84196i	0.0405739	+	0.670909i
$105$	2.39205	+	4.00180i	0.233440	+	0.390535i
$106$	−4.50823	−	9.60065i	−0.437878	−	0.932498i
$107$			19.3452i			1.87017i	0.354417	+	0.935087i	$0.384679\pi$
$107$			19.3452i			1.87017i	−0.354417	+	0.935087i	$0.615321\pi$
$108$	−1.69039	+	1.06892i	−0.162658	+	0.102857i
$109$	−1.44131	+	1.98379i	−0.138052	+	0.190012i	−0.872445	−	0.488712i	$-0.837467\pi$
$109$	−1.44131	+	1.98379i	−0.138052	+	0.190012i	0.734393	+	0.678724i	$0.237467\pi$
$110$	9.32955	−	7.29487i	0.889538	−	0.695539i
$111$	−2.77692	+	2.01755i	−0.263574	+	0.191498i
$112$	−8.27084	−	1.07208i	−0.781521	−	0.101302i
$113$	−3.82213	−	2.77694i	−0.359555	−	0.261232i	0.393311	−	0.919405i	$-0.371329\pi$
$113$	−3.82213	−	2.77694i	−0.359555	−	0.261232i	−0.752867	+	0.658173i	$0.771329\pi$
$114$	6.07217	+	6.47671i	0.568711	+	0.606599i
$115$	4.12086	+	0.370051i	0.384272	+	0.0345075i
$116$	−0.165825	+	0.416851i	−0.0153964	+	0.0387037i
$117$	−2.30481	+	0.748877i	−0.213079	+	0.0692337i
$118$	−3.73588	+	0.468877i	−0.343915	+	0.0431637i
$119$	−1.63572	−	5.03423i	−0.149946	−	0.461487i
$120$	5.95548	+	2.12892i	0.543658	+	0.194343i
$121$	−0.934953	+	2.87749i	−0.0849958	+	0.261590i
$122$	−1.59548	+	8.32718i	−0.144448	+	0.753907i
$123$	4.68129	+	6.44324i	0.422098	+	0.580968i
$124$	10.8061	−	2.75588i	0.970416	−	0.247486i
$125$	−6.15360	+	9.33452i	−0.550395	+	0.834904i
$126$	−0.367194	−	2.92569i	−0.0327123	−	0.260642i
$127$	1.36156	−	0.989235i	0.120819	−	0.0877804i	−0.525735	−	0.850649i	$-0.676210\pi$
$127$	1.36156	−	0.989235i	0.120819	−	0.0877804i	0.646554	+	0.762868i	$0.276210\pi$
$128$	−9.58669	+	6.00794i	−0.847352	+	0.531032i
$129$	−0.405355	+	1.24756i	−0.0356895	+	0.109841i
$130$	6.35501	+	4.28292i	0.557371	+	0.375637i
$131$	−5.29051	+	1.71899i	−0.462234	+	0.150189i	−0.530871	−	0.847453i	$-0.678135\pi$
$131$	−5.29051	+	1.71899i	−0.462234	+	0.150189i	0.0686366	+	0.997642i	$0.478135\pi$
$132$	−7.25784	+	1.85097i	−0.631714	+	0.161106i
$133$	−12.4484	+	4.04474i	−1.07942	+	0.350723i
$134$	−14.8076	−	8.15617i	−1.27918	−	0.704585i
$135$	−0.199993	+	2.22711i	−0.0172127	+	0.191679i
$136$	−6.05346	−	3.86230i	−0.519080	−	0.331190i
$137$	13.5619	+	9.85332i	1.15867	+	0.841826i	0.989610	−	0.143779i	$-0.0459254\pi$
$137$	13.5619	+	9.85332i	1.15867	+	0.841826i	0.169064	+	0.985605i	$0.445925\pi$
$138$	−2.29205	−	1.26248i	−0.195112	−	0.107470i
$139$	−12.3316	−	16.9729i	−1.04595	−	1.43962i	−0.892269	−	0.451504i	$-0.850888\pi$
$139$	−12.3316	−	16.9729i	−1.04595	−	1.43962i	−0.153679	−	0.988121i	$-0.549112\pi$
$140$	−6.57311	+	6.61358i	−0.555529	+	0.558949i
$141$	6.64605	−	9.14750i	0.559698	−	0.770358i
$142$	−13.3325	+	6.26061i	−1.11884	+	0.525379i
$143$	−9.07588			−0.758963
$144$	−2.90699	−	2.74762i	−0.242249	−	0.228968i
$145$	0.257344	+	0.430526i	0.0213713	+	0.0357532i
$146$	1.76357	+	0.337899i	0.145954	+	0.0279648i
$147$	−2.52291	−	0.819742i	−0.208086	−	0.0676112i
$148$	−5.28243	−	4.38443i	−0.434213	−	0.360398i
$149$		−	10.8967i		−	0.892690i	−0.894861	−	0.446345i	$-0.852725\pi$
$149$		−	10.8967i		−	0.892690i	0.894861	−	0.446345i	$-0.147275\pi$
$150$	5.93762	−	3.83988i	0.484805	−	0.313525i
$151$	7.50781			0.610977			0.305488	−	0.952196i	$-0.401180\pi$
$151$	7.50781			0.610977			0.305488	+	0.952196i	$0.401180\pi$
$152$	−9.55054	+	14.9687i	−0.774651	+	1.21412i
$153$	0.784515	−	2.41449i	0.0634243	−	0.195200i
$154$	2.07802	−	10.8456i	0.167451	−	0.873965i
$155$	4.89805	−	11.4659i	0.393421	−	0.920965i
$156$	−2.59043	−	4.09652i	−0.207401	−	0.327984i
$157$			21.0741i			1.68189i	0.541118	+	0.840947i	$0.318001\pi$
$157$			21.0741i			1.68189i	−0.541118	+	0.840947i	$0.681999\pi$
$158$	−3.61233	+	1.69626i	−0.287382	+	0.134947i
$159$	6.06754	+	4.40832i	0.481187	+	0.349603i
$160$	−1.18234	+	12.5937i	−0.0934718	+	0.995622i
$161$	3.12113	−	2.26764i	0.245980	−	0.178715i
$162$	0.682306	−	1.23873i	0.0536070	−	0.0973240i
$163$	5.52872	−	7.60963i	0.433043	−	0.596032i	−0.535605	−	0.844468i	$-0.679917\pi$
$163$	5.52872	−	7.60963i	0.433043	−	0.596032i	0.968648	+	0.248436i	$0.0799165\pi$
$164$	−10.1731	+	12.2567i	−0.794387	+	0.957089i
$165$	−3.28974	+	7.70100i	−0.256106	+	0.599522i
$166$	−10.3501	−	5.70094i	−0.803324	−	0.442478i
$167$	−6.19823	−	19.0762i	−0.479633	−	1.47616i	−0.839605	−	0.543197i	$-0.817214\pi$
$167$	−6.19823	−	19.0762i	−0.479633	−	1.47616i	0.359972	−	0.932963i	$-0.382786\pi$
$168$	5.48842	−	2.15761i	0.423441	−	0.166463i
$169$	2.20238	+	6.77822i	0.169414	+	0.521402i
$170$	−7.54298	+	2.74874i	−0.578521	+	0.210818i
$171$	−5.97044	−	1.93992i	−0.456571	−	0.148349i
$172$	−2.61807	−	0.168972i	−0.199626	−	0.0128840i
$173$	−9.94088	−	13.6824i	−0.755791	−	1.04026i	−0.997552	−	0.0699215i	$-0.977725\pi$
$173$	−9.94088	−	13.6824i	−0.755791	−	1.04026i	0.241761	−	0.970336i	$-0.422275\pi$
$174$	−0.0395039	−	0.314755i	−0.00299478	−	0.0238615i
$175$	1.40353	+	10.3301i	0.106097	+	0.780884i
$176$	−7.17425	−	13.1506i	−0.540779	−	0.991267i
$177$	2.15392	−	1.56491i	0.161898	−	0.117626i
$178$	23.4116	+	4.48564i	1.75477	+	0.336213i
$179$	−13.4428	−	4.36784i	−1.00476	−	0.326468i	−0.239997	−	0.970774i	$-0.577146\pi$
$179$	−13.4428	−	4.36784i	−1.00476	−	0.326468i	−0.764768	+	0.644306i	$0.777146\pi$
$180$	−4.41491	+	0.713148i	−0.329068	+	0.0531549i
$181$	−17.0501	+	5.53991i	−1.26732	+	0.411778i	−0.864098	−	0.503323i	$-0.832111\pi$
$181$	−17.0501	+	5.53991i	−1.26732	+	0.411778i	−0.403225	+	0.915101i	$0.632111\pi$
$182$	7.09018	−	0.889865i	0.525559	−	0.0659612i
$183$	−1.85265	−	5.70188i	−0.136952	−	0.421495i
$184$	1.31383	−	5.06590i	0.0968568	−	0.373463i
$185$	−7.48245	+	1.70940i	−0.550121	+	0.125677i
$186$	−5.75275	+	5.39343i	−0.421812	+	0.395466i
$187$	5.58853	−	7.69195i	0.408674	−	0.562491i
$188$	21.0123	+	8.35876i	1.53248	+	0.609625i
$189$	1.22554	+	1.68681i	0.0891447	+	0.122697i
$190$	6.79696	+	18.6520i	0.493103	+	1.35316i
$191$	10.4058	+	7.56023i	0.752935	+	0.547039i	0.896735	−	0.442568i	$-0.145932\pi$
$191$	10.4058	+	7.56023i	0.752935	+	0.547039i	−0.143800	+	0.989607i	$0.545932\pi$
$192$	3.88805	−	6.99164i	0.280596	−	0.504578i
$193$	−21.6962			−1.56173			−0.780864	−	0.624701i	$-0.785221\pi$
$193$	−21.6962			−1.56173			−0.780864	+	0.624701i	$0.785221\pi$
$194$	4.52444	−	2.12456i	0.324836	−	0.152535i
$195$	−5.39721	−	0.484667i	−0.386502	−	0.0347077i
$196$	0.341710	−	5.29447i	0.0244078	−	0.378176i
$197$	9.76241	+	3.17200i	0.695543	+	0.225996i	0.635387	−	0.772194i	$-0.280840\pi$
$197$	9.76241	+	3.17200i	0.695543	+	0.225996i	0.0601553	+	0.998189i	$0.480840\pi$
$198$	3.86380	−	3.62246i	0.274588	−	0.257437i
$199$	−4.50845			−0.319596			−0.159798	−	0.987150i	$-0.551084\pi$
$199$	−4.50845			−0.319596			−0.159798	+	0.987150i	$0.551084\pi$
$200$	10.3762	+	9.60910i	0.733707	+	0.679466i
$201$	11.9538			0.843158
$202$	−15.8139	+	14.8262i	−1.11266	+	1.04317i
$203$	0.444801	+	0.144525i	0.0312189	+	0.0101436i
$204$	5.06694	+	0.327025i	0.354757	+	0.0228963i
$205$	3.96629	+	17.3614i	0.277017	+	1.21257i
$206$	−11.1797	+	5.24970i	−0.778924	+	0.365764i
$207$	1.85032			0.128606
$208$	6.65863	−	7.04485i	0.461693	−	0.488472i
$209$	−19.0203	−	13.8191i	−1.31566	−	0.955886i
$210$	1.81492	−	6.33866i	0.125241	−	0.437409i
$211$	−1.92607	−	2.65100i	−0.132596	−	0.182502i	0.737556	−	0.675286i	$-0.235980\pi$
$211$	−1.92607	−	2.65100i	−0.132596	−	0.182502i	−0.870152	+	0.492783i	$0.835980\pi$
$212$	−5.54437	+	13.9375i	−0.380789	+	0.957230i
$213$	6.12187	−	8.42604i	0.419464	−	0.577342i
$214$	19.9585	−	18.7119i	1.36434	−	1.27912i
$215$	−1.92941	+	2.20928i	−0.131585	+	0.150672i
$216$	2.73785	+	0.710055i	0.186287	+	0.0483131i
$217$	−3.59263	−	11.0570i	−0.243883	−	0.750596i
$218$	3.44079	−	0.431843i	0.233040	−	0.0292481i
$219$	−1.20757	+	0.392364i	−0.0816001	+	0.0265135i
$220$	−16.5502	−	2.56926i	−1.11582	−	0.173220i
$221$	5.85131	+	1.90121i	0.393602	+	0.127889i
$222$	4.76752	+	0.913455i	0.319975	+	0.0613071i
$223$	14.7346	−	10.7053i	0.986701	−	0.716880i	0.0275046	−	0.999622i	$-0.491244\pi$
$223$	14.7346	−	10.7053i	0.986701	−	0.716880i	0.959196	+	0.282742i	$0.0912439\pi$
$224$	6.89399	+	9.57001i	0.460624	+	0.639423i
$225$	−2.36758	+	4.40393i	−0.157839	+	0.293595i
$226$	0.832023	+	6.62931i	0.0553454	+	0.440975i
$227$	−17.4475	−	24.0144i	−1.15803	−	1.59389i	−0.718251	−	0.695784i	$-0.755057\pi$
$227$	−17.4475	−	24.0144i	−1.15803	−	1.59389i	−0.439778	−	0.898107i	$-0.644943\pi$
$228$	0.808654	−	12.5293i	0.0535544	−	0.829775i
$229$	0.625173	+	0.203131i	0.0413126	+	0.0134233i	0.329600	−	0.944121i	$-0.393086\pi$
$229$	0.625173	+	0.203131i	0.0413126	+	0.0134233i	−0.288288	+	0.957544i	$0.593086\pi$
$230$	−3.60416	−	4.60943i	−0.237652	−	0.303937i
$231$	2.41296	+	7.42633i	0.158761	+	0.488617i
$232$	0.590461	−	0.232122i	0.0387657	−	0.0152396i
$233$	−3.44255	−	10.5951i	−0.225529	−	0.694107i	−0.998237	−	0.0593457i	$-0.981099\pi$
$233$	−3.44255	−	10.5951i	−0.225529	−	0.694107i	0.772709	−	0.634761i	$-0.218901\pi$
$234$	3.00197	+	1.65351i	0.196245	+	0.108093i
$235$	21.7016	−	12.9720i	1.41566	−	0.846201i
$236$	4.09731	+	3.40078i	0.266712	+	0.221372i
$237$	1.65867	−	2.28297i	0.107742	−	0.148295i
$238$	−3.61165	+	6.55698i	−0.234109	+	0.425026i
$239$	−11.8599	+	8.61675i	−0.767156	+	0.557371i	−0.901097	−	0.433618i	$-0.857237\pi$
$239$	−11.8599	+	8.61675i	−0.767156	+	0.557371i	0.133941	+	0.990989i	$0.457237\pi$
$240$	−3.56409	−	8.20349i	−0.230061	−	0.529533i
$241$	14.2919	+	10.3837i	0.920620	+	0.668870i	0.943678	−	0.330864i	$-0.107340\pi$
$241$	14.2919	+	10.3837i	0.920620	+	0.668870i	−0.0230580	+	0.999734i	$0.507340\pi$
$242$	3.87305	−	1.81869i	0.248969	−	0.116910i
$243$			1.00000i			0.0641500i
$244$	10.1344	−	6.40849i	0.648789	−	0.410261i
$245$	−4.46778	−	3.90181i	−0.285436	−	0.249277i
$246$	2.11947	−	11.0620i	0.135133	−	0.705286i
$247$	4.70122	−	14.4689i	0.299132	−	0.920633i
$248$	−13.2956	−	8.48300i	−0.844269	−	0.538671i
$249$	8.35540			0.529502
$250$	15.5826	−	2.68023i	0.985528	−	0.169513i
$251$		−	1.41882i		−	0.0895551i	−0.998997	−	0.0447775i	$-0.985742\pi$
$251$		−	1.41882i		−	0.0895551i	0.998997	−	0.0447775i	$-0.0142579\pi$
$252$	−2.66327	+	3.20874i	−0.167770	+	0.202132i
$253$	6.59043	+	2.14136i	0.414337	+	0.134626i
$254$	−2.33758	−	0.447880i	−0.146673	−	0.0281025i
$255$	3.73413	−	4.27579i	0.233840	−	0.267760i
$256$	15.4712	+	4.07936i	0.966952	+	0.254960i
$257$	15.2364			0.950420			0.475210	−	0.879872i	$-0.342372\pi$
$257$	15.2364			0.950420			0.475210	+	0.879872i	$0.342372\pi$
$258$	1.67919	−	0.788506i	0.104542	−	0.0490902i
$259$	−4.20661	+	5.78991i	−0.261386	+	0.359767i
$260$	−1.72826	−	10.6992i	−0.107182	−	0.663534i
$261$	0.131847	+	0.181472i	0.00816113	+	0.0112328i
$262$	6.89079	+	3.79551i	0.425714	+	0.234488i
$263$	−3.19251	−	2.31949i	−0.196858	−	0.143026i	0.484990	−	0.874520i	$-0.338823\pi$
$263$	−3.19251	−	2.31949i	−0.196858	−	0.143026i	−0.681848	+	0.731494i	$0.738823\pi$
$264$	8.92987	+	5.69755i	0.549595	+	0.350660i
$265$	8.60434	+	14.3947i	0.528560	+	0.884259i
$266$	16.2138	+	8.93074i	0.994134	+	0.547579i
$267$	−16.0306	+	5.20866i	−0.981058	+	0.318765i
$268$	5.90808	+	23.1661i	0.360893	+	1.41510i
$269$	15.5602	−	5.05583i	0.948724	−	0.308259i	0.206527	−	0.978441i	$-0.433784\pi$
$269$	15.5602	−	5.05583i	0.948724	−	0.308259i	0.742197	+	0.670182i	$0.233784\pi$
$270$	2.49115	−	1.94786i	0.151607	−	0.118543i
$271$	−7.99900	+	24.6184i	−0.485905	+	1.49546i	0.344762	+	0.938690i	$0.387960\pi$
$271$	−7.99900	+	24.6184i	−0.485905	+	1.49546i	−0.830666	+	0.556770i	$0.812040\pi$
$272$	1.87053	+	9.98121i	0.113418	+	0.605200i
$273$	−4.08784	+	2.96999i	−0.247407	+	0.179752i
$274$	−2.95224	−	23.5226i	−0.178352	−	1.42105i
$275$	−13.5294	+	12.9458i	−0.815854	+	0.780663i
$276$	0.914505	+	3.58586i	0.0550467	+	0.215844i
$277$	−2.83884	−	3.90733i	−0.170570	−	0.234769i	0.715171	−	0.698950i	$-0.246349\pi$
$277$	−2.83884	−	3.90733i	−0.170570	−	0.234769i	−0.885741	+	0.464181i	$0.846349\pi$
$278$	−5.58316	+	29.1397i	−0.334856	+	1.74768i
$279$	1.72308	−	5.30308i	0.103158	−	0.317487i
$280$	13.1811	+	0.384431i	0.787724	+	0.0229742i
$281$	−1.77020	−	5.44811i	−0.105601	−	0.325007i	0.884270	−	0.466976i	$-0.154657\pi$
$281$	−1.77020	−	5.44811i	−0.105601	−	0.325007i	−0.989871	+	0.141969i	$0.954657\pi$
$282$	−15.8659	+	1.99128i	−0.944803	+	0.118579i
$283$	10.2547	−	3.33195i	0.609579	−	0.198064i	0.0120707	−	0.999927i	$-0.496158\pi$
$283$	10.2547	−	3.33195i	0.609579	−	0.198064i	0.597508	+	0.801863i	$0.296158\pi$
$284$	19.3551	+	7.69951i	1.14851	+	0.456882i
$285$	−10.5730	−	9.23360i	−0.626290	−	0.546951i
$286$	8.77874	+	9.36359i	0.519098	+	0.553681i
$287$	13.4342	+	9.76053i	0.792996	+	0.576146i
$288$	−0.0229055	+	5.65681i	−0.00134972	+	0.333331i
$289$	8.53900	−	6.20395i	0.502294	−	0.364938i
$290$	0.195255	−	0.681933i	0.0114658	−	0.0400445i
$291$	−2.07748	+	2.85941i	−0.121784	+	0.167622i
$292$	−1.35722	−	2.14631i	−0.0794253	−	0.125604i
$293$		−	15.3425i		−	0.896320i	−0.893953	−	0.448160i	$-0.852080\pi$
$293$		−	15.3425i		−	0.896320i	0.893953	−	0.448160i	$-0.147920\pi$
$294$	1.59458	+	3.39579i	0.0929978	+	0.198047i
$295$	5.80375	−	1.32589i	0.337908	−	0.0771965i
$296$	0.586058	+	9.69077i	0.0340640	+	0.563265i
$297$	−1.15729	+	3.56178i	−0.0671528	+	0.206675i
$298$	−11.2421	+	10.5399i	−0.651238	+	0.610561i
$299$			4.48410i			0.259322i
$300$	−9.70483	−	2.41169i	−0.560309	−	0.139239i
$301$			2.73502i			0.157644i
$302$	−7.26201	−	7.74581i	−0.417881	−	0.445721i
$303$	4.73662	−	14.5778i	0.272112	−	0.837474i
$304$	24.6811	−	4.62537i	1.41556	−	0.265283i
$305$	1.19902	−	13.3522i	0.0686557	−	0.764544i
$306$	−3.24986	+	1.52605i	−0.185782	+	0.0872387i
$307$		−	26.0430i		−	1.48635i	−0.669095	−	0.743177i	$-0.733318\pi$
$307$		−	26.0430i		−	1.48635i	0.669095	−	0.743177i	$-0.266682\pi$
$308$	−13.1994	+	8.34665i	−0.752107	+	0.475594i
$309$	5.13336	−	7.06546i	0.292027	−	0.401940i
$310$	−16.5671	+	6.03721i	−0.940948	+	0.342890i
$311$	16.6437	−	12.0923i	0.943775	−	0.685693i	−0.00555132	−	0.999985i	$-0.501767\pi$
$311$	16.6437	−	12.0923i	0.943775	−	0.685693i	0.949326	+	0.314292i	$0.101767\pi$
$312$	−1.72076	+	6.63495i	−0.0974188	+	0.375630i
$313$	14.8096	+	10.7598i	0.837086	+	0.608178i	0.921555	−	0.388248i	$-0.126920\pi$
$313$	14.8096	+	10.7598i	0.837086	+	0.608178i	−0.0844694	+	0.996426i	$0.526920\pi$
$314$	21.7421	−	20.3841i	1.22698	−	1.15034i
$315$	1.03835	+	4.54512i	0.0585045	+	0.256088i
$316$	5.24410	+	2.08612i	0.295004	+	0.117353i
$317$	−20.8324	+	6.76885i	−1.17006	+	0.380176i	−0.828666	−	0.559743i	$-0.810900\pi$
$317$	−20.8324	+	6.76885i	−1.17006	+	0.380176i	−0.341396	+	0.939920i	$0.610900\pi$
$318$	−1.32082	−	10.5239i	−0.0740678	−	0.590150i
$319$	0.259594	+	0.798947i	0.0145345	+	0.0447325i
$320$	14.1366	−	10.9616i	0.790260	−	0.612772i
$321$	−5.97801	+	18.3984i	−0.333660	+	1.02690i
$322$	−5.35847	−	1.02668i	−0.298616	−	0.0572147i
$323$	9.36780	+	12.8937i	0.521239	+	0.717423i
$324$	−1.93797	+	0.494242i	−0.107665	+	0.0274579i
$325$	−10.6726	−	5.73763i	−0.592007	−	0.318266i
$326$	−13.1986	+	1.65651i	−0.731002	+	0.0917456i
$327$	−1.98379	+	1.44131i	−0.109704	+	0.0797044i
$328$	22.4853	−	1.35982i	1.24154	−	0.0750835i
$329$	7.28509	−	22.4212i	0.401640	−	1.23612i
$330$	11.1272	−	4.05485i	0.612531	−	0.223212i
$331$	−18.0617	+	5.86861i	−0.992763	+	0.322568i	−0.759970	−	0.649958i	$-0.774786\pi$
$331$	−18.0617	+	5.86861i	−0.992763	+	0.322568i	−0.232793	+	0.972526i	$0.574786\pi$
$332$	4.12958	+	16.1925i	0.226640	+	0.888679i
$333$	−3.26447	+	1.06069i	−0.178892	+	0.0581255i
$334$	−13.6856	+	24.8464i	−0.748844	+	1.35953i
$335$	24.5807	+	10.5005i	1.34299	+	0.573701i
$336$	−7.53474	−	3.57544i	−0.411054	−	0.195056i
$337$	5.80866	+	4.22024i	0.316418	+	0.229891i	0.734645	−	0.678451i	$-0.237349\pi$
$337$	5.80866	+	4.22024i	0.316418	+	0.229891i	−0.418227	+	0.908342i	$0.637349\pi$
$338$	4.86283	−	8.82851i	0.264503	−	0.480207i
$339$	−2.77694	−	3.82213i	−0.150822	−	0.207589i
$340$	10.1319	+	5.12336i	0.549480	+	0.277853i
$341$	12.2744	−	16.8943i	0.664697	−	0.914877i
$342$	3.77356	+	8.03612i	0.204051	+	0.434543i
$343$	−20.1260			−1.08670
$344$	2.35802	+	2.86450i	0.127136	+	0.154444i
$345$	3.80482	+	1.62536i	0.204845	+	0.0875062i
$346$	−4.50077	+	23.4905i	−0.241963	+	1.26286i
$347$	−3.13530	−	1.01872i	−0.168312	−	0.0546879i	0.223649	−	0.974670i	$-0.428203\pi$
$347$	−3.13530	−	1.01872i	−0.168312	−	0.0546879i	−0.391961	+	0.919982i	$0.628203\pi$
$348$	−0.286523	+	0.345206i	−0.0153592	+	0.0185050i
$349$			31.7638i			1.70028i	0.526560	+	0.850138i	$0.323481\pi$
$349$			31.7638i			1.70028i	−0.526560	+	0.850138i	$0.676519\pi$
$350$	9.30003	−	11.4399i	0.497107	−	0.611491i
$351$	−2.42342			−0.129352
$352$	−6.62816	+	20.1218i	−0.353282	+	1.07249i
$353$	3.57870	−	11.0141i	0.190475	−	0.586222i	−0.809525	−	0.587086i	$-0.800275\pi$
$353$	3.57870	−	11.0141i	0.190475	−	0.586222i	1.00000		0.000864238i	$0.000275095\pi$
$354$	−3.69792	−	0.708520i	−0.196542	−	0.0376574i
$355$	19.9900	−	11.9489i	1.06096	−	0.634182i
$356$	−18.0172	−	28.4925i	−0.954911	−	1.51010i
$357$		−	5.29330i		−	0.280151i
$358$	8.49642	+	18.0938i	0.449050	+	0.956288i
$359$	−6.31756	−	4.58998i	−0.333428	−	0.242250i	0.408456	−	0.912778i	$-0.366067\pi$
$359$	−6.31756	−	4.58998i	−0.333428	−	0.242250i	−0.741884	+	0.670528i	$0.766067\pi$
$360$	5.00612	+	3.86507i	0.263846	+	0.203707i
$361$	16.5116	−	11.9964i	0.869032	−	0.631389i
$362$	22.2074	+	12.2321i	1.16720	+	0.642903i
$363$	−1.77839	+	2.44774i	−0.0933411	+	0.128473i
$364$	−7.77612	−	6.45421i	−0.407580	−	0.338293i
$365$	−2.82779	−	0.253934i	−0.148013	−	0.0132915i
$366$	−4.09064	+	7.42659i	−0.213821	+	0.388194i
$367$	3.89305	+	11.9816i	0.203215	+	0.625433i	0.999782	+	0.0208819i	$0.00664740\pi$
$367$	3.89305	+	11.9816i	0.203215	+	0.625433i	−0.796567	+	0.604551i	$0.793353\pi$
$368$	−6.49731	+	3.54457i	−0.338696	+	0.184773i
$369$	2.46110	+	7.57449i	0.128120	+	0.394312i
$370$	9.00107	+	6.06622i	0.467943	+	0.315368i
$371$	14.8720	+	4.83220i	0.772115	+	0.250875i
$372$	11.1288	+	0.718264i	0.577003	+	0.0372403i
$373$	−19.5346	−	26.8870i	−1.01146	−	1.39216i	−0.918021	−	0.396532i	$-0.870213\pi$
$373$	−19.5346	−	26.8870i	−1.01146	−	1.39216i	−0.0934406	−	0.995625i	$-0.529787\pi$
$374$	−13.3414	+	1.67443i	−0.689866	+	0.0865828i
$375$	−8.73695	+	6.97608i	−0.451174	+	0.360243i
$376$	−11.7006	−	29.7635i	−0.603415	−	1.53494i
$377$	−0.439782	+	0.319520i	−0.0226499	+	0.0164561i
$378$	0.554867	−	2.89597i	0.0285393	−	0.148953i
$379$	4.03977	+	1.31260i	0.207509	+	0.0674238i	0.410927	−	0.911668i	$-0.365205\pi$
$379$	4.03977	+	1.31260i	0.207509	+	0.0674238i	−0.203418	+	0.979092i	$0.565205\pi$
$380$	12.6688	−	25.0537i	0.649897	−	1.28523i
$381$	1.60062	−	0.520072i	0.0820020	−	0.0266441i
$382$	−2.26519	−	18.0484i	−0.115897	−	0.923434i
$383$	7.19526	+	22.1447i	0.367660	+	1.13154i	0.948298	+	0.317380i	$0.102803\pi$
$383$	7.19526	+	22.1447i	0.367660	+	1.13154i	−0.580638	+	0.814162i	$0.697197\pi$
$384$	−10.9740	+	2.75144i	−0.560017	+	0.140409i
$385$	−1.56165	+	17.3904i	−0.0795889	+	0.886296i
$386$	20.9859	+	22.3840i	1.06815	+	1.13932i
$387$	−0.771032	+	1.06123i	−0.0391937	+	0.0539455i
$388$	−6.56823	−	2.61286i	−0.333451	−	0.132648i
$389$	−3.17937	−	4.37603i	−0.161201	−	0.221873i	0.720775	−	0.693170i	$-0.243786\pi$
$389$	−3.17937	−	4.37603i	−0.161201	−	0.221873i	−0.881975	+	0.471296i	$0.843786\pi$
$390$	4.72048	+	6.03710i	0.239031	+	0.305701i
$391$	−3.80035	−	2.76111i	−0.192192	−	0.139636i
$392$	−5.79283	+	4.76859i	−0.292582	+	0.240850i
$393$	−5.56278			−0.280605
$394$	−6.17024	−	13.1400i	−0.310852	−	0.661985i
$395$	5.41613	−	3.23746i	0.272515	−	0.162894i
$396$	−7.47459	−	0.482417i	−0.375613	−	0.0242424i
$397$	22.6301	+	7.35296i	1.13577	+	0.369035i	0.815767	−	0.578381i	$-0.196315\pi$
$397$	22.6301	+	7.35296i	1.13577	+	0.369035i	0.320005	+	0.947416i	$0.396315\pi$
$398$	4.36085	+	4.65137i	0.218589	+	0.233152i
$399$	−13.0890			−0.655272
$400$	−0.122751	−	19.9996i	−0.00613753	−	0.999981i
$401$	17.2207			0.859961			0.429981	−	0.902838i	$-0.358520\pi$
$401$	17.2207			0.859961			0.429981	+	0.902838i	$0.358520\pi$
$402$	−11.5625	−	12.3328i	−0.576683	−	0.615103i
$403$	12.8516	+	4.17573i	0.640183	+	0.208008i
$404$	30.5924	+	1.97446i	1.52203	+	0.0982331i
$405$	−0.878418	+	2.05630i	−0.0436490	+	0.102179i
$406$	−0.281132	−	0.598694i	−0.0139524	−	0.0297127i
$407$	−12.8548			−0.637191
$408$	−4.56366	−	5.54389i	−0.225935	−	0.274463i
$409$	−18.7109	−	13.5942i	−0.925193	−	0.672192i	0.0196184	−	0.999808i	$-0.493755\pi$
$409$	−18.7109	−	13.5942i	−0.925193	−	0.672192i	−0.944811	+	0.327616i	$0.893755\pi$
$410$	14.0753	−	20.8850i	0.695131	−	1.03144i
$411$	9.85332	+	13.5619i	0.486029	+	0.668961i
$412$	16.2298	+	6.45625i	0.799583	+	0.318076i
$413$	3.26285	−	4.49093i	0.160555	−	0.220984i
$414$	−1.78974	−	1.90898i	−0.0879610	−	0.0938211i
$415$	17.1812	+	7.33953i	0.843393	+	0.360284i
$416$	−13.7088	−	0.0555096i	−0.672130	−	0.00272158i
$417$	−6.48308	−	19.9529i	−0.317478	−	0.977096i
$418$	4.14046	+	32.9900i	0.202517	+	1.61359i
$419$	−23.0485	+	7.48891i	−1.12599	+	0.365857i	−0.812052	−	0.583586i	$-0.801649\pi$
$419$	−23.0485	+	7.48891i	−1.12599	+	0.365857i	−0.313940	+	0.949443i	$0.601649\pi$
$420$	−8.29511	+	4.25868i	−0.404760	+	0.207802i
$421$	−4.64433	−	1.50903i	−0.226351	−	0.0735458i	0.193646	−	0.981071i	$-0.437969\pi$
$421$	−4.64433	−	1.50903i	−0.226351	−	0.0735458i	−0.419997	+	0.907526i	$0.637969\pi$
$422$	−0.872034	+	4.55133i	−0.0424499	+	0.221555i
$423$	9.14750	−	6.64605i	0.444767	−	0.323142i
$424$	19.7422	−	7.76104i	0.958764	−	0.376910i
$425$	11.4344	−	5.51218i	0.554652	−	0.267380i
$426$	−14.6146	+	1.83423i	−0.708079	+	0.0888687i
$427$	−7.34747	−	10.1129i	−0.355569	−	0.489399i
$428$	−38.6101	−	2.49193i	−1.86629	−	0.120452i
$429$	−8.63167	−	2.80460i	−0.416741	−	0.135407i
$430$	4.14556	−	0.146376i	0.199917	−	0.00705889i
$431$	−4.91430	−	15.1247i	−0.236714	−	0.728530i	−0.996889	−	0.0788122i	$-0.974887\pi$
$431$	−4.91430	−	15.1247i	−0.236714	−	0.728530i	0.760176	−	0.649717i	$-0.225113\pi$
$432$	−1.91565	−	3.51145i	−0.0921668	−	0.168945i
$433$	−12.3080	−	37.8802i	−0.591486	−	1.82041i	−0.571494	−	0.820606i	$-0.693636\pi$
$433$	−12.3080	−	37.8802i	−0.591486	−	1.82041i	−0.0199915	−	0.999800i	$-0.506364\pi$
$434$	−7.93248	+	14.4015i	−0.380771	+	0.691293i
$435$	0.111709	+	0.488978i	0.00535604	+	0.0234447i
$436$	−3.77368	−	3.13217i	−0.180726	−	0.150004i
$437$	−6.82757	+	9.39734i	−0.326607	+	0.449536i
$438$	1.57284	+	0.866335i	0.0751531	+	0.0413951i
$439$	−7.19438	+	5.22702i	−0.343369	+	0.249472i	−0.746082	−	0.665854i	$-0.768067\pi$
$439$	−7.19438	+	5.22702i	−0.343369	+	0.249472i	0.402713	+	0.915326i	$0.368067\pi$
$440$	13.3577	+	19.5600i	0.636803	+	0.932488i
$441$	−2.14611	−	1.55924i	−0.102196	−	0.0742496i
$442$	−3.69827	−	7.87577i	−0.175909	−	0.374612i
$443$			26.6182i			1.26467i	0.774696	+	0.632334i	$0.217903\pi$
$443$			26.6182i			1.26467i	−0.774696	+	0.632334i	$0.782097\pi$
$444$	−3.66902	−	5.80220i	−0.174124	−	0.275360i
$445$	−37.5392	−	3.37100i	−1.77953	−	0.159801i
$446$	−25.2969	−	4.84687i	−1.19784	−	0.229506i
$447$	3.36726	−	10.3633i	0.159266	−	0.490170i
$448$	3.20511	−	16.3692i	0.151427	−	0.773374i
$449$	−28.3941			−1.34000			−0.670000	−	0.742361i	$-0.733706\pi$
$449$	−28.3941			−1.34000			−0.670000	+	0.742361i	$0.733706\pi$
$450$	6.83360	−	1.81711i	0.322139	−	0.0856595i
$451$			29.8268i			1.40449i
$452$	6.03468	−	7.27067i	0.283848	−	0.341984i
$453$	7.14035	+	2.32004i	0.335483	+	0.109005i
$454$	−7.89941	+	41.2287i	−0.370738	+	1.93496i
$455$	−11.0147	+	2.51636i	−0.516378	+	0.117969i
$456$	−13.7087	+	11.2848i	−0.641969	+	0.528461i
$457$	−26.7539			−1.25149			−0.625747	−	0.780026i	$-0.715206\pi$
$457$	−26.7539			−1.25149			−0.625747	+	0.780026i	$0.715206\pi$
$458$	−0.395135	−	0.841473i	−0.0184634	−	0.0393194i
$459$	1.49224	−	2.05389i	0.0696516	−	0.0958672i
$460$	−1.26939	+	8.17694i	−0.0591856	+	0.381252i
$461$	17.9582	+	24.7174i	0.836398	+	1.15120i	0.986698	+	0.162563i	$0.0519760\pi$
$461$	17.9582	+	24.7174i	0.836398	+	1.15120i	−0.150300	+	0.988640i	$0.548024\pi$
$462$	5.32779	−	9.67265i	0.247871	−	0.450013i
$463$	−23.5876	−	17.1374i	−1.09621	−	0.796444i	−0.115774	−	0.993276i	$-0.536935\pi$
$463$	−23.5876	−	17.1374i	−1.09621	−	0.796444i	−0.980437	+	0.196832i	$0.936935\pi$
$464$	−0.810611	−	0.384657i	−0.0376317	−	0.0178572i
$465$	8.20149	−	9.39116i	0.380335	−	0.435504i
$466$	−7.60111	+	13.7999i	−0.352115	+	0.639267i
$467$	−14.2226	+	4.62122i	−0.658146	+	0.213844i	−0.619002	−	0.785389i	$-0.712463\pi$
$467$	−14.2226	+	4.62122i	−0.658146	+	0.213844i	−0.0391432	+	0.999234i	$0.512463\pi$
$468$	−1.19775	−	4.69651i	−0.0553662	−	0.217096i
$469$	23.7040	−	7.70188i	1.09455	−	0.355640i
$470$	−34.3744	−	9.84226i	−1.58557	−	0.453989i
$471$	−6.51224	+	20.0426i	−0.300068	+	0.923515i
$472$	−0.454575	−	7.51664i	−0.0209235	−	0.345981i
$473$	−3.97440	+	2.88757i	−0.182743	+	0.132771i
$474$	−3.95970	+	0.496969i	−0.181875	+	0.0228266i
$475$	−13.6303	−	28.2746i	−0.625401	−	1.29733i
$476$	10.2583	−	2.61617i	0.470186	−	0.119912i
$477$	4.40832	+	6.06754i	0.201843	+	0.277813i
$478$	20.3616	+	3.90127i	0.931316	+	0.178440i
$479$	−7.70642	+	23.7179i	−0.352115	+	1.08370i	0.605548	+	0.795809i	$0.292954\pi$
$479$	−7.70642	+	23.7179i	−0.352115	+	1.08370i	−0.957663	+	0.287891i	$0.907046\pi$
$480$	−5.01615	+	11.6120i	−0.228955	+	0.530012i
$481$	−2.57050	−	7.91117i	−0.117205	−	0.360718i
$482$	−3.11114	−	24.7886i	−0.141709	−	1.12909i
$483$	3.66911	−	1.19217i	0.166950	−	0.0542455i
$484$	−5.62260	−	2.23668i	−0.255573	−	0.101667i
$485$	−6.78369	+	4.05491i	−0.308032	+	0.184124i
$486$	1.03170	−	0.967261i	0.0467989	−	0.0438758i
$487$	7.65939	+	5.56487i	0.347080	+	0.252168i	0.747643	−	0.664101i	$-0.231185\pi$
$487$	7.65939	+	5.56487i	0.347080	+	0.252168i	−0.400563	+	0.916269i	$0.631185\pi$
$488$	−16.4143	−	4.25700i	−0.743038	−	0.192705i
$489$	7.60963	−	5.52872i	0.344119	−	0.250017i
$490$	0.296014	+	8.38348i	0.0133726	+	0.378727i
$491$	−14.7793	+	20.3420i	−0.666982	+	0.918021i	−0.999687	−	0.0250093i	$-0.992038\pi$
$491$	−14.7793	+	20.3420i	−0.666982	+	0.918021i	0.332706	+	0.943031i	$0.392038\pi$
$492$	−13.4627	+	8.51316i	−0.606947	+	0.383803i
$493$		−	0.569469i		−	0.0256476i
$494$	−19.4749	+	9.14492i	−0.876216	+	0.411449i
$495$	−5.50847	+	6.30750i	−0.247587	+	0.283501i
$496$	4.10835	+	21.9223i	0.184470	+	0.984341i
$497$	6.71051	−	20.6528i	0.301008	−	0.926406i
$498$	−8.08184	−	8.62027i	−0.362156	−	0.386284i
$499$			36.3895i			1.62902i	0.580150	+	0.814510i	$0.302994\pi$
$499$			36.3895i			1.62902i	−0.580150	+	0.814510i	$0.697006\pi$
$500$	−17.8376	−	13.4841i	−0.797722	−	0.603026i
$501$		−	20.0579i		−	0.896121i
$502$	−1.46380	+	1.37237i	−0.0653325	+	0.0612518i
$503$	−11.3184	+	34.8344i	−0.504661	+	1.55319i	0.296678	+	0.954978i	$0.404121\pi$
$503$	−11.3184	+	34.8344i	−0.504661	+	1.55319i	−0.801339	+	0.598210i	$0.795879\pi$
$504$	5.88654	−	0.355994i	0.262207	−	0.0158572i
$505$	22.5454	−	25.8157i	1.00325	−	1.14878i
$506$	−4.16542	−	8.87060i	−0.185175	−	0.394346i
$507$			7.12705i			0.316523i
$508$	1.79897	+	2.84490i	0.0798165	+	0.126222i
$509$	20.2075	−	27.8132i	0.895681	−	1.23280i	−0.0761437	−	0.997097i	$-0.524261\pi$
$509$	20.2075	−	27.8132i	0.895681	−	1.23280i	0.971825	−	0.235703i	$-0.0757392\pi$
$510$	−8.02321	+	0.283293i	−0.355274	+	0.0125444i
$511$	−2.14176	+	1.55608i	−0.0947461	+	0.0688371i
$512$	−10.7560	−	19.9075i	−0.475354	−	0.879795i
$513$	−5.07876	−	3.68994i	−0.224233	−	0.162915i
$514$	−14.7376	−	15.7194i	−0.650046	−	0.693353i
$515$	16.7622	−	10.0195i	0.738630	−	0.441512i
$516$	−2.43771	−	0.969730i	−0.107314	−	0.0426900i
$517$	40.2727	−	13.0854i	1.77119	−	0.575496i
$518$	10.0423	−	1.26038i	0.441235	−	0.0553780i
$519$	−5.22623	−	16.0847i	−0.229406	−	0.706039i
$520$	−9.36667	+	12.1319i	−0.410756	+	0.532020i
$521$	−3.12182	+	9.60796i	−0.136769	+	0.420933i	−0.995861	−	0.0908891i	$-0.971029\pi$
$521$	−3.12182	+	9.60796i	−0.136769	+	0.420933i	0.859092	+	0.511822i	$0.171029\pi$
$522$	0.0596943	−	0.311557i	0.00261275	−	0.0136365i
$523$	−2.56425	−	3.52938i	−0.112127	−	0.154329i	0.749265	−	0.662270i	$-0.230407\pi$
$523$	−2.56425	−	3.52938i	−0.112127	−	0.154329i	−0.861392	+	0.507941i	$0.830407\pi$
$524$	−2.74935	−	10.7805i	−0.120106	−	0.470948i
$525$	−1.85735	+	10.2583i	−0.0810614	+	0.447707i
$526$	0.694964	+	5.53727i	0.0303019	+	0.241436i
$527$	−11.4524	+	8.32069i	−0.498876	+	0.362455i
$528$	−2.75935	−	14.7240i	−0.120085	−	0.640778i
$529$	−6.04941	+	18.6182i	−0.263018	+	0.809486i
$530$	6.52837	−	22.8005i	0.283574	−	0.990391i
$531$	2.53208	−	0.822723i	0.109883	−	0.0357031i
$532$	−6.46915	−	25.3662i	−0.280473	−	1.09976i
$533$	−18.3561	+	5.96427i	−0.795093	+	0.258341i
$534$	20.8796	+	11.5007i	0.903547	+	0.497683i
$535$	−28.4541	+	32.5815i	−1.23018	+	1.40862i
$536$	18.1859	−	28.5031i	0.785511	−	1.23115i
$537$	−11.4352	−	8.30813i	−0.493463	−	0.358522i
$538$	−20.2669	−	11.1632i	−0.873768	−	0.481280i
$539$	−5.83948	−	8.03735i	−0.251524	−	0.346193i
$540$	−4.41920	−	0.686038i	−0.190172	−	0.0295224i
$541$	−12.1307	+	16.6964i	−0.521538	+	0.717836i	−0.985811	−	0.167856i	$-0.946316\pi$
$541$	−12.1307	+	16.6964i	−0.521538	+	0.717836i	0.464273	+	0.885692i	$0.346316\pi$
$542$	33.1359	−	15.5598i	1.42331	−	0.668352i
$543$	−17.9275			−0.769344
$544$	8.48834	−	11.5843i	0.363934	−	0.496671i
$545$	−5.34534	+	1.22117i	−0.228969	+	0.0523090i
$546$	7.01814	+	1.34467i	0.300349	+	0.0575467i
$547$	24.7747	+	8.04979i	1.05929	+	0.344184i	0.786308	−	0.617835i	$-0.211990\pi$
$547$	24.7747	+	8.04979i	1.05929	+	0.344184i	0.272982	+	0.962019i	$0.411990\pi$
$548$	−21.4127	+	25.7983i	−0.914705	+	1.10205i
$549$		−	5.99531i		−	0.255874i
$550$	26.4427	+	1.43632i	1.12752	+	0.0612447i
$551$	−1.40816			−0.0599896
$552$	2.81497	−	4.41196i	0.119813	−	0.187786i
$553$	1.81816	−	5.59572i	0.0773160	−	0.237954i
$554$	−1.28530	+	6.70825i	−0.0546071	+	0.285006i
$555$	−7.64447	−	0.686470i	−0.324490	−	0.0291390i
$556$	35.4638	−	22.4255i	1.50400	−	0.951055i
$557$			29.1661i			1.23581i	0.786254	+	0.617903i	$0.212018\pi$
$557$			29.1661i			1.23581i	−0.786254	+	0.617903i	$0.787982\pi$
$558$	−7.13786	+	3.35176i	−0.302170	+	0.141891i
$559$	−2.57181	−	1.86853i	−0.108776	−	0.0790305i
$560$	−12.3530	−	13.9708i	−0.522009	−	0.590376i
$561$	7.69195	−	5.58853i	0.324755	−	0.235948i
$562$	−3.90857	+	7.09605i	−0.164873	+	0.299329i
$563$	−2.19123	+	3.01597i	−0.0923493	+	0.127108i	−0.852691	−	0.522415i	$-0.825031\pi$
$563$	−2.19123	+	3.01597i	−0.0923493	+	0.127108i	0.760342	+	0.649523i	$0.225031\pi$
$564$	17.4009	+	14.4428i	0.732710	+	0.608152i
$565$	−2.35280	−	10.2988i	−0.0989829	−	0.433272i
$566$	−13.3565	−	7.35691i	−0.561417	−	0.309234i
$567$	0.644303	+	1.98296i	0.0270582	+	0.0832765i
$568$	−10.7778	−	27.4161i	−0.452227	−	1.15035i
$569$	11.2924	+	34.7544i	0.473402	+	1.45698i	0.848101	+	0.529835i	$0.177746\pi$
$569$	11.2924	+	34.7544i	0.473402	+	1.45698i	−0.374699	+	0.927146i	$0.622254\pi$
$570$	0.700516	+	19.8395i	0.0293414	+	0.830983i
$571$	4.19240	+	1.36219i	0.175447	+	0.0570061i	0.395423	−	0.918499i	$-0.370598\pi$
$571$	4.19240	+	1.36219i	0.175447	+	0.0570061i	−0.219976	+	0.975505i	$0.570598\pi$
$572$	1.16910	−	18.1141i	0.0488825	−	0.757387i
$573$	7.56023	+	10.4058i	0.315833	+	0.434707i
$574$	−2.92444	−	23.3011i	−0.122064	−	0.972568i
$575$	6.39612	+	6.68445i	0.266737	+	0.278761i
$576$	5.85829	−	5.44798i	0.244095	−	0.226999i
$577$	3.91411	−	2.84377i	0.162947	−	0.118388i	−0.503324	−	0.864098i	$-0.667890\pi$
$577$	3.91411	−	2.84377i	0.162947	−	0.118388i	0.666270	+	0.745710i	$0.267890\pi$
$578$	−14.6601	−	2.80886i	−0.609778	−	0.116833i
$579$	−20.6343	−	6.70450i	−0.857534	−	0.278630i
$580$	−0.892413	+	0.458162i	−0.0370554	+	0.0190241i
$581$	16.5684	−	5.38341i	0.687374	−	0.223341i
$582$	4.95952	−	0.622453i	0.205579	−	0.0258015i
$583$	8.67956	+	26.7129i	0.359470	+	1.10634i
$584$	−0.901568	+	3.47629i	−0.0373071	+	0.143850i
$585$	−4.98328	−	2.12877i	−0.206033	−	0.0880140i
$586$	−15.8289	+	14.8402i	−0.653886	+	0.613044i
$587$	17.9408	−	24.6934i	0.740495	−	1.01920i	−0.258095	−	0.966119i	$-0.583095\pi$
$587$	17.9408	−	24.6934i	0.740495	−	1.01920i	0.998590	−	0.0530842i	$-0.0169052\pi$
$588$	1.96107	−	4.92974i	0.0808730	−	0.203299i
$589$	20.5750	+	28.3191i	0.847780	+	1.16687i
$590$	−6.98167	−	4.70525i	−0.287431	−	0.193712i
$591$	8.30440	+	6.03350i	0.341597	+	0.248185i
$592$	9.43111	−	9.97814i	0.387616	−	0.410099i
$593$	44.6323			1.83283			0.916415	−	0.400230i	$-0.131070\pi$
$593$	44.6323			1.83283			0.916415	+	0.400230i	$0.131070\pi$
$594$	4.79409	−	2.25119i	0.196704	−	0.0923673i
$595$	4.64973	−	10.8846i	0.190620	−	0.446226i
$596$	21.7481	+	1.40364i	0.890836	+	0.0574954i
$597$	−4.28779	−	1.39319i	−0.175488	−	0.0570194i
$598$	4.62625	−	4.33729i	0.189181	−	0.177365i
$599$	20.1105			0.821691			0.410845	−	0.911705i	$-0.365234\pi$
$599$	20.1105			0.821691			0.410845	+	0.911705i	$0.365234\pi$
$600$	6.89896	+	12.3452i	0.281649	+	0.503991i
$601$	−38.4878			−1.56995			−0.784974	−	0.619528i	$-0.787324\pi$
$601$	−38.4878			−1.56995			−0.784974	+	0.619528i	$0.787324\pi$
$602$	2.82173	−	2.64548i	0.115005	−	0.107822i
$603$	11.3688	+	3.69394i	0.462972	+	0.150429i
$604$	−0.967109	+	14.9844i	−0.0393511	+	0.609708i
$605$	−5.80704	+	3.47113i	−0.236090	+	0.141121i
$606$	−19.6215	+	9.21377i	−0.797069	+	0.374284i
$607$	33.5192			1.36050			0.680252	−	0.732979i	$-0.261871\pi$
$607$	33.5192			1.36050			0.680252	+	0.732979i	$0.261871\pi$
$608$	−28.6451	−	20.9896i	−1.16171	−	0.851241i
$609$	0.378370	+	0.274902i	0.0153323	+	0.0111396i
$610$	−14.9352	+	11.6780i	−0.604710	+	0.472829i
$611$	16.1061	+	22.1682i	0.651585	+	0.896830i
$612$	4.71789	+	1.87679i	0.190710	+	0.0758648i
$613$	7.15098	−	9.84249i	0.288826	−	0.397534i	−0.639807	−	0.768536i	$-0.720986\pi$
$613$	7.15098	−	9.84249i	0.288826	−	0.397534i	0.928632	+	0.371002i	$0.120986\pi$
$614$	−26.8686	+	25.1904i	−1.08433	+	1.01660i
$615$	−1.59280	+	17.7373i	−0.0642280	+	0.715237i
$616$	21.3785	+	5.54447i	0.861365	+	0.223393i
$617$	1.91375	+	5.88993i	0.0770448	+	0.237120i	0.982160	−	0.188047i	$-0.0602156\pi$
$617$	1.91375	+	5.88993i	0.0770448	+	0.237120i	−0.905115	+	0.425166i	$0.860216\pi$
$618$	−12.2547	+	1.53805i	−0.492958	+	0.0618695i
$619$	43.1886	−	14.0328i	1.73590	−	0.564027i	0.741616	−	0.670825i	$-0.234060\pi$
$619$	43.1886	−	14.0328i	1.73590	−	0.564027i	0.994281	+	0.106798i	$0.0340598\pi$
$620$	22.2533	+	11.2527i	0.893714	+	0.451921i
$621$	1.75976	+	0.571780i	0.0706167	+	0.0229448i
$622$	−28.5744	−	5.47485i	−1.14573	−	0.219521i
$623$	−28.4321	+	20.6571i	−1.13911	+	0.827611i
$624$	8.50971	−	4.64242i	0.340661	−	0.185846i
$625$	−24.0937	+	6.67024i	−0.963749	+	0.266810i
$626$	−3.22383	−	25.6865i	−0.128850	−	1.02664i
$627$	−13.8191	−	19.0203i	−0.551881	−	0.759599i
$628$	−42.0606	−	2.71463i	−1.67840	−	0.108326i
$629$	8.28765	+	2.69282i	0.330450	+	0.107370i
$630$	3.68485	−	5.46758i	0.146808	−	0.217834i
$631$	0.770358	+	2.37092i	0.0306675	+	0.0943847i	0.965219	−	0.261444i	$-0.0841987\pi$
$631$	0.770358	+	2.37092i	0.0306675	+	0.0943847i	−0.934551	+	0.355829i	$0.884199\pi$
$632$	−2.92016	−	7.42816i	−0.116158	−	0.295476i
$633$	−1.01259	−	3.11644i	−0.0402469	−	0.123867i
$634$	27.1337	+	14.9455i	1.07762	+	0.593563i
$635$	3.74819	+	0.336586i	0.148742	+	0.0133570i
$636$	−9.57993	+	11.5420i	−0.379869	+	0.457671i
$637$	3.77870	−	5.20093i	0.149717	−	0.206068i
$638$	0.573180	−	1.04061i	0.0226924	−	0.0411983i
$639$	8.42604	−	6.12187i	0.333329	−	0.242178i
$640$	−24.9829	−	3.98201i	−0.987535	−	0.157403i
$641$	17.5189	+	12.7282i	0.691955	+	0.502735i	0.877302	−	0.479938i	$-0.159341\pi$
$641$	17.5189	+	12.7282i	0.691955	+	0.502735i	−0.185347	+	0.982673i	$0.559341\pi$
$642$	24.7640	−	11.6285i	0.977355	−	0.458942i
$643$		−	2.96784i		−	0.117040i	−0.998286	−	0.0585201i	$-0.981362\pi$
$643$		−	2.96784i		−	0.117040i	0.998286	−	0.0585201i	$-0.0186382\pi$
$644$	4.12381	+	6.52141i	0.162501	+	0.256980i
$645$	−2.51768	+	1.50493i	−0.0991336	+	0.0592565i
$646$	4.24131	−	22.1363i	0.166872	−	0.870942i
$647$	1.16732	−	3.59263i	0.0458920	−	0.141241i	−0.925485	−	0.378784i	$-0.876342\pi$
$647$	1.16732	−	3.59263i	0.0458920	−	0.141241i	0.971377	+	0.237543i	$0.0763422\pi$
$648$	2.38443	+	1.52134i	0.0936693	+	0.0597641i
$649$	9.97084			0.391390
$650$	4.40362	+	16.5607i	0.172724	+	0.649563i
$651$		−	11.6260i		−	0.455658i
$652$	14.4755	+	12.0147i	0.566904	+	0.470532i
$653$	−16.1964	−	5.26254i	−0.633815	−	0.205939i	−0.0255508	−	0.999674i	$-0.508134\pi$
$653$	−16.1964	−	5.26254i	−0.633815	−	0.205939i	−0.608264	+	0.793735i	$0.708134\pi$
$654$	3.40584	+	0.652557i	0.133179	+	0.0255170i
$655$	−11.4387	−	4.88644i	−0.446949	−	0.190929i
$656$	−23.1521	−	21.8828i	−0.903937	−	0.854381i
$657$	−1.26972			−0.0495363
$658$	−30.1785	+	14.1711i	−1.17648	+	0.552447i
$659$	8.57651	−	11.8045i	0.334093	−	0.459840i	−0.608611	−	0.793468i	$-0.708273\pi$
$659$	8.57651	−	11.8045i	0.334093	−	0.459840i	0.942705	+	0.333629i	$0.108273\pi$
$660$	−14.9463	−	7.55782i	−0.581783	−	0.294188i
$661$	10.7237	+	14.7599i	0.417104	+	0.574094i	0.964933	−	0.262496i	$-0.0845456\pi$
$661$	10.7237	+	14.7599i	0.417104	+	0.574094i	−0.547829	+	0.836590i	$0.684546\pi$
$662$	23.5251	+	12.9578i	0.914327	+	0.503620i
$663$	4.97742	+	3.61631i	0.193307	+	0.140446i
$664$	12.7114	−	19.9229i	0.493299	−	0.773157i
$665$	−26.9150	−	11.4977i	−1.04372	−	0.445860i
$666$	4.25191	+	2.34199i	0.164758	+	0.0907503i
$667$	0.394734	−	0.128257i	0.0152842	−	0.00496613i
$668$	38.8716	−	9.91344i	1.50399	−	0.383563i
$669$	17.3215	−	5.62811i	0.669690	−	0.217595i
$670$	−12.9426	−	35.5166i	−0.500016	−	1.37213i
$671$	6.93832	−	21.3539i	0.267851	−	0.824360i
$672$	3.59928	+	11.2320i	0.138845	+	0.433283i
$673$	6.86228	−	4.98574i	0.264522	−	0.192186i	−0.447616	−	0.894226i	$-0.647727\pi$
$673$	6.86228	−	4.98574i	0.264522	−	0.192186i	0.712138	+	0.702039i	$0.247727\pi$
$674$	−1.26446	−	10.0749i	−0.0487054	−	0.388070i
$675$	−3.61259	+	3.45676i	−0.139049	+	0.133051i
$676$	−13.8120	+	3.52248i	−0.531231	+	0.135480i
$677$	−15.5730	−	21.4344i	−0.598520	−	0.823792i	0.397052	−	0.917796i	$-0.370033\pi$
$677$	−15.5730	−	21.4344i	−0.598520	−	0.823792i	−0.995572	+	0.0940039i	$0.970033\pi$
$678$	−1.25727	+	6.56196i	−0.0482851	+	0.252011i
$679$	−2.27724	+	7.00862i	−0.0873924	+	0.268966i
$680$	−4.51442	−	15.4087i	−0.173120	−	0.590898i
$681$	−9.17268	−	28.2306i	−0.351498	−	1.08180i
$682$	−29.3024	+	3.67765i	−1.12205	+	0.140824i
$683$	−5.89573	+	1.91564i	−0.225594	+	0.0732998i	−0.419633	−	0.907694i	$-0.637841\pi$
$683$	−5.89573	+	1.91564i	−0.225594	+	0.0732998i	0.194039	+	0.980994i	$0.437841\pi$
$684$	4.64085	−	11.6662i	0.177447	−	0.446069i
$685$	8.34836	+	36.5428i	0.318974	+	1.39623i
$686$	19.4671	+	20.7641i	0.743258	+	0.792775i
$687$	0.531804	+	0.386378i	0.0202896	+	0.0147413i
$688$	0.674486	−	5.20350i	0.0257146	−	0.198381i
$689$	−14.7042	+	10.6832i	−0.560185	+	0.406998i
$690$	−2.00337	−	5.49758i	−0.0762670	−	0.209289i
$691$	−27.1228	+	37.3313i	−1.03180	+	1.42015i	−0.128213	+	0.991747i	$0.540924\pi$
$691$	−27.1228	+	37.3313i	−1.03180	+	1.42015i	−0.903587	+	0.428405i	$0.859076\pi$
$692$	28.5886	−	18.0780i	1.08678	−	0.687222i
$693$			7.80851i			0.296621i
$694$	1.98164	+	4.22006i	0.0752220	+	0.160191i
$695$	4.19579	−	46.7240i	0.159156	−	1.77234i
$696$	0.633292	−	0.0382989i	0.0240049	−	0.00145172i
$697$	6.24810	−	19.2297i	0.236664	−	0.728376i
$698$	32.7707	−	30.7238i	1.24039	−	1.16291i
$699$		−	11.1403i		−	0.421366i
$700$	−20.7982	+	1.47057i	−0.786096	+	0.0555822i
$701$		−	23.1733i		−	0.875244i	−0.899159	−	0.437622i	$-0.855821\pi$
$701$		−	23.1733i		−	0.875244i	0.899159	−	0.437622i	$-0.144179\pi$
$702$	2.34408	+	2.50024i	0.0884715	+	0.0943656i
$703$	6.65869	−	20.4933i	0.251137	−	0.772921i
$704$	27.1708	−	12.6247i	1.02404	−	0.475812i
$705$	24.6480	−	5.63095i	0.928299	−	0.212074i
$706$	−14.8248	+	6.96136i	−0.557939	+	0.261994i
$707$		−	31.9591i		−	1.20194i
$708$	2.84587	+	4.50047i	0.106954	+	0.169138i
$709$	−3.29931	+	4.54111i	−0.123908	+	0.170545i	−0.866465	−	0.499239i	$-0.833613\pi$
$709$	−3.29931	+	4.54111i	−0.123908	+	0.170545i	0.742556	+	0.669784i	$0.233613\pi$
$710$	−31.6633	−	9.06600i	−1.18830	−	0.340241i
$711$	2.28297	−	1.65867i	0.0856179	−	0.0622050i
$712$	−11.9684	+	46.1481i	−0.448535	+	1.72947i
$713$	−8.34692	−	6.06439i	−0.312595	−	0.227113i
$714$	−5.46110	+	5.12000i	−0.204377	+	0.191611i
$715$	−15.2857	−	13.3493i	−0.571653	−	0.499236i
$716$	10.4492	−	26.2672i	0.390504	−	0.981651i
$717$	−13.9422	+	4.53009i	−0.520681	+	0.169179i
$718$	1.37524	+	10.9575i	0.0513237	+	0.408932i
$719$	11.4714	+	35.3053i	0.427810	+	1.31666i	0.900278	+	0.435316i	$0.143363\pi$
$719$	11.4714	+	35.3053i	0.427810	+	1.31666i	−0.472467	+	0.881348i	$0.656637\pi$
$720$	−0.854633	−	8.90335i	−0.0318503	−	0.331808i
$721$	5.62695	−	17.3180i	0.209559	−	0.644955i
$722$	−28.3477	−	5.43141i	−1.05499	−	0.202136i
$723$	10.3837	+	14.2919i	0.386172	+	0.531520i
$724$	−8.86053	−	34.7430i	−0.329299	−	1.29121i
$725$	−0.199819	+	1.10361i	−0.00742111	+	0.0409872i
$726$	4.24550	−	0.532839i	0.157565	−	0.0197755i
$727$	−28.8410	+	20.9542i	−1.06965	+	0.777147i	−0.975850	−	0.218443i	$-0.929902\pi$
$727$	−28.8410	+	20.9542i	−1.06965	+	0.777147i	−0.0938020	+	0.995591i	$0.529902\pi$
$728$	0.862722	+	14.2655i	0.0319746	+	0.528716i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$	2.47323	+	3.16306i	0.0915382	+	0.117070i
$731$	3.16722	−	1.02909i	0.117144	−	0.0380624i
$732$	11.6187	−	2.96313i	0.429440	−	0.109520i
$733$	−33.2319	+	10.7977i	−1.22745	+	0.398822i	−0.849789	−	0.527122i	$-0.823271\pi$
$733$	−33.2319	+	10.7977i	−1.22745	+	0.398822i	−0.377659	+	0.925945i	$0.623271\pi$
$734$	8.59580	−	15.6058i	0.317277	−	0.576019i
$735$	−3.04339	−	5.09146i	−0.112257	−	0.187801i
$736$	9.94152	+	3.27476i	0.366449	+	0.120709i
$737$	36.2180	+	26.3139i	1.33411	+	0.969286i
$738$	5.43408	−	9.86562i	0.200031	−	0.363159i
$739$	15.2495	+	20.9891i	0.560961	+	0.772096i	0.991448	−	0.130500i	$-0.0416584\pi$
$739$	15.2495	+	20.9891i	0.560961	+	0.772096i	−0.430488	+	0.902596i	$0.641658\pi$
$740$	−2.44786	−	15.1540i	−0.0899850	−	0.557073i
$741$	8.94226	−	12.3080i	0.328502	−	0.452144i
$742$	−9.39970	−	20.0174i	−0.345074	−	0.734863i
$743$	−0.888284			−0.0325880			−0.0162940	−	0.999867i	$-0.505187\pi$
$743$	−0.888284			−0.0325880			−0.0162940	+	0.999867i	$0.505187\pi$
$744$	−10.0234	−	12.1764i	−0.367477	−	0.446407i
$745$	16.0275	−	18.3523i	0.587201	−	0.672377i
$746$	−8.84435	+	46.1606i	−0.323815	+	1.69006i
$747$	7.94645	+	2.58196i	0.290746	+	0.0944689i
$748$	14.6321	+	12.1447i	0.535002	+	0.444054i
$749$			40.3350i			1.47381i
$750$	15.6481	+	2.26623i	0.571389	+	0.0827509i
$751$	−11.6196			−0.424007			−0.212003	−	0.977269i	$-0.567999\pi$
$751$	−11.6196			−0.424007			−0.212003	+	0.977269i	$0.567999\pi$
$752$	−19.3895	+	40.8607i	−0.707062	+	1.49004i
$753$	0.438439	−	1.34938i	0.0159776	−	0.0491740i
$754$	0.755033	+	0.144664i	0.0274967	+	0.00526836i
$755$	12.6448	+	11.0429i	0.460190	+	0.401893i
$756$	−3.52448	+	2.22870i	−0.128184	+	0.0810571i
$757$			36.5090i			1.32694i	0.748202	+	0.663471i	$0.230917\pi$
$757$			36.5090i			1.32694i	−0.748202	+	0.663471i	$0.769083\pi$
$758$	−2.55330	−	5.43746i	−0.0927400	−	0.197498i
$759$	5.60615	+	4.07311i	0.203490	+	0.147844i
$760$	−38.1020	+	11.1631i	−1.38211	+	0.404927i
$761$	−20.5103	+	14.9016i	−0.743498	+	0.540183i	−0.893805	−	0.448456i	$-0.851974\pi$
$761$	−20.5103	+	14.9016i	−0.743498	+	0.540183i	0.150306	+	0.988639i	$0.451974\pi$
$762$	−2.08477	−	1.14831i	−0.0755233	−	0.0415990i
$763$	−3.00513	+	4.13621i	−0.108793	+	0.149741i
$764$	−16.4295	+	19.7945i	−0.594398	+	0.716138i
$765$	4.87266	−	2.91260i	0.176171	−	0.105305i
$766$	15.8870	−	28.8431i	0.574022	−	1.04214i
$767$	1.99380	+	6.13629i	0.0719920	+	0.221569i
$768$	13.4534	+	8.66057i	0.485458	+	0.312511i
$769$	8.94922	+	27.5429i	0.322717	+	0.993222i	0.972460	+	0.233068i	$0.0748764\pi$
$769$	8.94922	+	27.5429i	0.322717	+	0.993222i	−0.649743	+	0.760154i	$0.725124\pi$
$770$	19.4522	−	15.2099i	0.701008	−	0.548126i
$771$	14.4907	+	4.70830i	0.521869	+	0.169565i
$772$	2.79477	−	43.3023i	0.100586	−	1.55849i
$773$	8.60165	+	11.8392i	0.309380	+	0.425825i	0.935188	−	0.354152i	$-0.115231\pi$
$773$	8.60165	+	11.8392i	0.309380	+	0.425825i	−0.625808	+	0.779977i	$0.715231\pi$
$774$	1.84066	−	0.231016i	0.0661613	−	0.00830369i
$775$	25.1141	−	12.1067i	0.902125	−	0.434886i
$776$	3.65750	+	9.30376i	0.131297	+	0.333986i
$777$	−5.78991	+	4.20661i	−0.207712	+	0.150911i
$778$	−1.43947	+	7.51292i	−0.0516076	+	0.269351i
$779$	−47.5503	−	15.4500i	−1.70367	−	0.553555i
$780$	1.66256	−	10.7096i	0.0595291	−	0.383464i
$781$	37.0964	−	12.0534i	1.32742	−	0.431303i
$782$	0.827283	+	6.59154i	0.0295836	+	0.235713i
$783$	0.0693161	+	0.213333i	0.00247715	+	0.00762390i
$784$	10.5229	+	1.36400i	0.375819	+	0.0487143i
$785$	−30.9970	+	35.4932i	−1.10633	+	1.26681i
$786$	5.38065	+	5.73912i	0.191922	+	0.204708i
$787$	−2.17585	+	2.99481i	−0.0775608	+	0.106753i	−0.846035	−	0.533128i	$-0.821016\pi$
$787$	−2.17585	+	2.99481i	−0.0775608	+	0.106753i	0.768474	+	0.639881i	$0.221016\pi$
$788$	−7.58836	+	19.0757i	−0.270324	+	0.679543i
$789$	−2.31949	−	3.19251i	−0.0825761	−	0.113656i
$790$	−8.57890	−	2.45636i	−0.305224	−	0.0873933i
$791$	−7.96916	−	5.78993i	−0.283351	−	0.205866i
$792$	6.73217	+	8.17817i	0.239217	+	0.290599i
$793$	14.5291			0.515945
$794$	−14.3031	−	30.4597i	−0.507599	−	1.08097i
$795$	3.73501	+	16.3490i	0.132467	+	0.579841i
$796$	0.580751	−	8.99818i	0.0205842	−	0.318932i
$797$	31.4159	+	10.2076i	1.11281	+	0.361573i	0.807018	−	0.590526i	$-0.201080\pi$
$797$	31.4159	+	10.2076i	1.11281	+	0.361573i	0.305789	+	0.952099i	$0.401080\pi$
$798$	12.6605	+	13.5040i	0.448178	+	0.478036i
$799$	−28.7054			−1.01552
$800$	−20.5149	+	19.4715i	−0.725311	+	0.688421i
$801$	−16.8556			−0.595563
$802$	−16.6569	−	17.7666i	−0.588176	−	0.627361i
$803$	−4.52244	−	1.46943i	−0.159594	−	0.0518551i
$804$	−1.53982	+	23.8580i	−0.0543052	+	0.841407i
$805$	8.59203	+	0.771560i	0.302829	+	0.0271939i
$806$	−8.12272	−	17.2980i	−0.286111	−	0.609296i
$807$	16.3610			0.575934
$808$	−27.5538	−	33.4720i	−0.969338	−	1.17754i
$809$	18.6917	+	13.5803i	0.657164	+	0.477458i	0.865704	−	0.500556i	$-0.166871\pi$
$809$	18.6917	+	13.5803i	0.657164	+	0.477458i	−0.208540	+	0.978014i	$0.566871\pi$
$810$	2.97115	−	1.08272i	0.104396	−	0.0380427i
$811$	−26.6043	−	36.6177i	−0.934204	−	1.28582i	−0.958197	−	0.286109i	$-0.907638\pi$
$811$	−26.6043	−	36.6177i	−0.934204	−	1.28582i	0.0239931	−	0.999712i	$-0.492362\pi$
$812$	−0.345745	+	0.869138i	−0.0121333	+	0.0305008i
$813$	−15.2150	+	20.9417i	−0.533613	+	0.734456i
$814$	12.4340	+	13.2623i	0.435811	+	0.464845i
$815$	20.5042	−	4.68428i	0.718232	−	0.164083i
$816$	−1.30538	+	10.0707i	−0.0456976	+	0.352546i
$817$	−2.54470	−	7.83177i	−0.0890277	−	0.273999i
$818$	4.07309	+	32.4532i	0.142412	+	1.13470i
$819$	−4.80554	+	1.56141i	−0.167919	+	0.0545603i
$820$	−35.1616	+	5.67971i	−1.22790	+	0.198344i
$821$	−16.9494	−	5.50719i	−0.591538	−	0.192202i	−0.00207502	−	0.999998i	$-0.500660\pi$
$821$	−16.9494	−	5.50719i	−0.591538	−	0.192202i	−0.589463	+	0.807796i	$0.700660\pi$
$822$	4.46113	−	23.2836i	0.155600	−	0.812109i
$823$	41.4710	−	30.1304i	1.44559	−	1.05028i	0.458749	−	0.888566i	$-0.348298\pi$
$823$	41.4710	−	30.1304i	1.44559	−	1.05028i	0.986838	−	0.161715i	$-0.0517024\pi$
$824$	−9.03750	−	22.9891i	−0.314836	−	0.800865i
$825$	−16.8677	+	8.13140i	−0.587258	+	0.283099i
$826$	−7.78933	+	0.977613i	−0.271025	+	0.0340155i
$827$	2.73352	+	3.76237i	0.0950539	+	0.130831i	0.853895	−	0.520445i	$-0.174234\pi$
$827$	2.73352	+	3.76237i	0.0950539	+	0.130831i	−0.758841	+	0.651276i	$0.774234\pi$
$828$	−0.238347	+	3.69296i	−0.00828313	+	0.128339i
$829$	22.4434	+	7.29229i	0.779490	+	0.253272i	0.671623	−	0.740893i	$-0.265598\pi$
$829$	22.4434	+	7.29229i	0.779490	+	0.253272i	0.107868	+	0.994165i	$0.465598\pi$
$830$	−9.04652	−	24.8251i	−0.314009	−	0.861693i
$831$	−1.49247	−	4.59335i	−0.0517732	−	0.159341i
$832$	13.2027	+	14.1971i	0.457722	+	0.492195i
$833$	2.08112	+	6.40501i	0.0721064	+	0.221921i
$834$	−14.3146	+	25.9882i	−0.495673	+	0.899899i
$835$	17.6192	−	41.2451i	0.609738	−	1.42735i
$836$	30.0309	−	36.1816i	1.03864	−	1.25137i
$837$	3.27748	−	4.51107i	0.113286	−	0.155925i
$838$	30.0202	+	16.5354i	1.03703	+	0.571206i
$839$	12.8193	−	9.31373i	0.442570	−	0.321546i	−0.344085	−	0.938938i	$-0.611811\pi$
$839$	12.8193	−	9.31373i	0.442570	−	0.321546i	0.786655	+	0.617393i	$0.211811\pi$
$840$	12.4172	+	4.43881i	0.428435	+	0.153154i
$841$	−23.4208	−	17.0162i	−0.807613	−	0.586765i
$842$	2.93540	+	6.25118i	0.101161	+	0.215430i
$843$		−	5.72848i		−	0.197299i
$844$	5.53910	−	3.50265i	0.190664	−	0.120566i
$845$	−6.26053	+	14.6554i	−0.215369	+	0.504160i
$846$	−15.7047	−	3.00902i	−0.539940	−	0.103452i
$847$	−1.94939	+	5.99959i	−0.0669817	+	0.206148i
$848$	−27.1029	−	12.8611i	−0.930717	−	0.441650i
$849$	10.7824			0.370052
$850$	−16.7470	−	6.46520i	−0.574417	−	0.221755i
$851$			6.35116i			0.217715i
$852$	16.0285	+	13.3037i	0.549127	+	0.455778i
$853$	−49.5496	−	16.0996i	−1.69654	−	0.551241i	−0.708541	−	0.705670i	$-0.750646\pi$
$853$	−49.5496	−	16.0996i	−1.69654	−	0.551241i	−0.988004	+	0.154429i	$0.950646\pi$
$854$	−3.32660	+	17.3622i	−0.113834	+	0.594123i
$855$	−7.20217	−	12.0489i	−0.246309	−	0.412064i
$856$	34.7751	+	42.2445i	1.18859	+	1.44389i
$857$	20.1737			0.689119			0.344560	−	0.938764i	$-0.388028\pi$
$857$	20.1737			0.689119			0.344560	+	0.938764i	$0.388028\pi$
$858$	5.45557	+	11.6181i	0.186250	+	0.396635i
$859$	−5.98267	+	8.23444i	−0.204126	+	0.280956i	−0.898790	−	0.438379i	$-0.855553\pi$
$859$	−5.98267	+	8.23444i	−0.204126	+	0.280956i	0.694664	+	0.719334i	$0.255553\pi$
$860$	−4.16085	−	4.13539i	−0.141884	−	0.141016i
$861$	9.76053	+	13.4342i	0.332638	+	0.457837i
$862$	−10.8507	+	19.6996i	−0.369577	+	0.670971i
$863$	−19.8586	−	14.4281i	−0.675993	−	0.491138i	0.196033	−	0.980597i	$-0.437194\pi$
$863$	−19.8586	−	14.4281i	−0.675993	−	0.491138i	−0.872026	+	0.489459i	$0.837194\pi$
$864$	−1.76983	+	5.37287i	−0.0602110	+	0.182789i
$865$	3.38237	−	37.6658i	0.115004	−	1.28068i
$866$	−27.1760	+	49.3382i	−0.923477	+	1.67658i
$867$	10.0382	−	3.26161i	0.340915	−	0.110770i
$868$	22.5308	−	5.74604i	0.764745	−	0.195033i
$869$	10.0510	−	3.26576i	0.340956	−	0.110783i
$870$	0.396427	−	0.588219i	0.0134401	−	0.0199425i
$871$	−8.95195	+	27.5513i	−0.303325	+	0.933539i
$872$	0.418670	+	6.92293i	0.0141780	+	0.234440i
$873$	−2.85941	+	2.07748i	−0.0967763	+	0.0703121i
$874$	16.2993	−	2.04567i	0.551331	−	0.0691958i
$875$	−12.8303	+	19.4625i	−0.433744	+	0.657954i
$876$	−0.627546	−	2.46067i	−0.0212028	−	0.0831383i
$877$	−3.63728	−	5.00629i	−0.122822	−	0.169050i	0.743178	−	0.669094i	$-0.233317\pi$
$877$	−3.63728	−	5.00629i	−0.122822	−	0.169050i	−0.866000	+	0.500043i	$0.833317\pi$
$878$	12.3516	+	2.36656i	0.416845	+	0.0798674i
$879$	4.74110	−	14.5916i	0.159913	−	0.492163i
$880$	7.25975	−	32.7008i	0.244726	−	1.10234i
$881$	8.99720	+	27.6905i	0.303123	+	0.932917i	0.980371	+	0.197162i	$0.0631726\pi$
$881$	8.99720	+	27.6905i	0.303123	+	0.932917i	−0.677248	+	0.735755i	$0.736827\pi$
$882$	0.467179	+	3.72234i	0.0157307	+	0.125338i
$883$	−29.2620	+	9.50779i	−0.984744	+	0.319963i	−0.756753	−	0.653701i	$-0.773216\pi$
$883$	−29.2620	+	9.50779i	−0.984744	+	0.319963i	−0.227991	+	0.973663i	$0.573216\pi$
$884$	−4.54825	+	11.4334i	−0.152974	+	0.384548i
$885$	5.92942	+	0.532459i	0.199315	+	0.0178984i
$886$	27.4620	−	25.7467i	0.922605	−	0.864979i
$887$	29.7350	+	21.6037i	0.998403	+	0.725382i	0.961745	−	0.273946i	$-0.0883289\pi$
$887$	29.7350	+	21.6037i	0.998403	+	0.725382i	0.0366576	+	0.999328i	$0.488329\pi$
$888$	−2.43724	+	9.39758i	−0.0817884	+	0.315362i
$889$	2.83887	−	2.06256i	0.0952128	−	0.0691761i
$890$	32.8323	+	41.9899i	1.10054	+	1.40750i
$891$	−2.20130	+	3.02983i	−0.0737463	+	0.101503i
$892$	19.4681	+	30.7870i	0.651841	+	1.03082i
$893$			70.9815i			2.37530i
$894$	−13.9489	+	6.55006i	−0.466521	+	0.219067i
$895$	−16.2161	−	27.1289i	−0.542045	−	0.906818i
$896$	−19.9883	+	12.5266i	−0.667763	+	0.418484i
$897$	−1.38566	+	4.26463i	−0.0462659	+	0.142392i
$898$	27.4645	+	29.2942i	0.916502	+	0.977560i
$899$		−	1.25076i		−	0.0417151i
$900$	−8.48459	−	5.29261i	−0.282820	−	0.176420i
$901$		−	19.0403i		−	0.634324i
$902$	30.7724	−	28.8503i	1.02461	−	0.960611i
$903$	−0.845169	+	2.60116i	−0.0281255	+	0.0865613i
$904$	−13.3383	+	0.806644i	−0.443624	+	0.0268286i
$905$	−36.8644	−	15.7479i	−1.22541	−	0.523477i
$906$	−4.51299	−	9.61079i	−0.149934	−	0.319297i
$907$		−	18.1209i		−	0.601694i	−0.953672	−	0.300847i	$-0.902731\pi$
$907$		−	18.1209i		−	0.601694i	0.953672	−	0.300847i	$-0.0972693\pi$
$908$	50.1765	−	31.7291i	1.66517	−	1.05297i
$909$	9.00959	−	12.4006i	0.298829	−	0.411303i
$910$	13.2502	+	8.92992i	0.439241	+	0.296024i
$911$	−31.1183	+	22.6088i	−1.03100	+	0.749063i	−0.968508	−	0.248983i	$-0.919904\pi$
$911$	−31.1183	+	22.6088i	−1.03100	+	0.749063i	−0.0624889	+	0.998046i	$0.519904\pi$
$912$	24.9025	+	3.22790i	0.824603	+	0.106886i
$913$	25.3154	+	18.3927i	0.837818	+	0.608710i
$914$	25.8780	+	27.6020i	0.855967	+	0.912993i
$915$	5.26639	−	12.3282i	0.174101	−	0.407557i
$916$	−0.485950	+	1.22158i	−0.0160562	+	0.0403623i
$917$	−11.0308	+	3.58411i	−0.364268	+	0.118358i
$918$	−3.56238	+	0.447102i	−0.117576	+	0.0147566i
$919$	−15.2907	−	47.0600i	−0.504394	−	1.55236i	−0.801787	−	0.597610i	$-0.796117\pi$
$919$	−15.2907	−	47.0600i	−0.504394	−	1.55236i	0.297393	−	0.954755i	$-0.403883\pi$
$920$	9.66399	−	6.59960i	0.318612	−	0.217582i
$921$	8.04774	−	24.7684i	0.265182	−	0.816146i
$922$	8.13066	−	42.4357i	0.267769	−	1.39754i
$923$	14.8359	+	20.4198i	0.488328	+	0.672126i
$924$	−15.1326	+	3.85929i	−0.497828	+	0.126961i
$925$	−15.1163	−	8.12663i	−0.497022	−	0.267202i
$926$	5.13470	+	40.9118i	0.168737	+	1.34444i
$927$	7.06546	−	5.13336i	0.232060	−	0.168602i
$928$	0.387221	+	1.20837i	0.0127112	+	0.0396667i
$929$	18.3395	−	56.4433i	0.601701	−	1.85185i	0.0836505	−	0.996495i	$-0.473342\pi$
$929$	18.3395	−	56.4433i	0.601701	−	1.85185i	0.518050	−	0.855350i	$-0.326658\pi$
$930$	−17.6218	+	0.622213i	−0.577843	+	0.0204032i
$931$	15.8380	−	5.14609i	0.519071	−	0.168656i
$932$	21.5896	−	5.50601i	0.707191	−	0.180355i
$933$	19.5658	−	6.35731i	0.640555	−	0.208129i
$934$	18.5247	+	10.2036i	0.606147	+	0.333872i
$935$	20.7261	−	4.73496i	0.677815	−	0.154850i
$936$	−3.68685	+	5.77847i	−0.120509	+	0.188875i
$937$	−13.1327	−	9.54146i	−0.429026	−	0.311706i	0.352233	−	0.935912i	$-0.385422\pi$
$937$	−13.1327	−	9.54146i	−0.429026	−	0.311706i	−0.781259	+	0.624206i	$0.785422\pi$
$938$	−30.8740	−	17.0057i	−1.00807	−	0.555255i
$939$	10.7598	+	14.8096i	0.351132	+	0.483292i
$940$	23.0947	+	44.9841i	0.753266	+	1.46722i
$941$	16.0795	−	22.1316i	0.524178	−	0.721469i	−0.462052	−	0.886853i	$-0.652887\pi$
$941$	16.0795	−	22.1316i	0.524178	−	0.721469i	0.986229	+	0.165385i	$0.0528865\pi$
$942$	26.9770	−	12.6678i	0.878959	−	0.412738i
$943$	14.7365			0.479886
$944$	−7.31523	+	7.73953i	−0.238090	+	0.251900i
$945$	−0.416987	+	4.64353i	−0.0135646	+	0.151054i
$946$	6.82339	+	1.30736i	0.221847	+	0.0425059i
$947$	5.64055	+	1.83273i	0.183293	+	0.0595556i	0.399226	−	0.916853i	$-0.369279\pi$
$947$	5.64055	+	1.83273i	0.183293	+	0.0595556i	−0.215932	+	0.976408i	$0.569279\pi$
$948$	4.34279	+	3.60453i	0.141047	+	0.117070i
$949$		−	3.07705i		−	0.0998853i
$950$	−15.9869	+	41.4113i	−0.518683	+	1.34356i
$951$	−21.9044			−0.710300
$952$	−12.6215	−	8.05293i	−0.409065	−	0.260997i
$953$	−9.38933	+	28.8974i	−0.304150	+	0.936078i	0.675843	+	0.737046i	$0.263780\pi$
$953$	−9.38933	+	28.8974i	−0.304150	+	0.936078i	−0.979993	+	0.199032i	$0.936220\pi$
$954$	1.99589	−	10.4170i	0.0646192	−	0.337262i
$955$	6.40551	+	28.0385i	0.207277	+	0.907303i
$956$	−15.6700	−	24.7806i	−0.506804	−	0.801461i
$957$			0.840063i			0.0271554i
$958$	31.9239	−	14.9907i	1.03141	−	0.484327i
$959$	28.2767	+	20.5443i	0.913104	+	0.663409i
$960$	16.8320	−	6.05666i	0.543251	−	0.195478i
$961$	−0.0741401	+	0.0538659i	−0.00239162	+	0.00173761i
$962$	−5.67562	+	10.3041i	−0.182989	+	0.332219i
$963$	−11.3708	+	15.6506i	−0.366420	+	0.504334i
$964$	−22.5652	+	27.1868i	−0.726775	+	0.875629i
$965$	−36.5411	−	31.9121i	−1.17630	−	1.02729i
$966$	−4.77895	−	2.63229i	−0.153760	−	0.0846926i
$967$	−4.94374	−	15.2153i	−0.158980	−	0.489290i	0.839562	−	0.543263i	$-0.182811\pi$
$967$	−4.94374	−	15.2153i	−0.158980	−	0.489290i	−0.998542	+	0.0539731i	$0.982811\pi$
$968$	3.13093	+	7.96430i	0.100632	+	0.255982i
$969$	4.92495	+	15.1574i	0.158212	+	0.486927i
$970$	10.7451	+	3.07658i	0.345003	+	0.0987831i
$971$	13.0524	+	4.24098i	0.418871	+	0.136100i	0.510867	−	0.859660i	$-0.329325\pi$
$971$	13.0524	+	4.24098i	0.418871	+	0.136100i	−0.0919954	+	0.995759i	$0.529325\pi$
$972$	−1.99585	−	0.128814i	−0.0640168	−	0.00413171i
$973$	−25.7114	−	35.3887i	−0.824269	−	1.13451i
$974$	−1.66734	−	13.2849i	−0.0534251	−	0.425675i
$975$	−8.37718	−	8.75481i	−0.268284	−	0.280378i
$976$	11.4849	+	21.0522i	0.367623	+	0.673866i
$977$	−12.3021	+	8.93797i	−0.393578	+	0.285951i	−0.766920	−	0.641743i	$-0.778212\pi$
$977$	−12.3021	+	8.93797i	−0.393578	+	0.285951i	0.373342	+	0.927694i	$0.378212\pi$
$978$	−13.0645	−	2.50315i	−0.417756	−	0.0800419i
$979$	−60.0358	−	19.5068i	−1.91875	−	0.623441i
$980$	8.36292	−	8.41441i	0.267144	−	0.268788i
$981$	−2.33208	+	0.757739i	−0.0744577	+	0.0241928i
$982$	35.2823	−	4.42817i	1.12590	−	0.141308i
$983$	5.96093	+	18.3459i	0.190124	+	0.585142i	0.999999	−	0.00146094i	$-0.000465030\pi$
$983$	5.96093	+	18.3459i	0.190124	+	0.585142i	−0.809875	+	0.586603i	$0.800465\pi$
$984$	21.8050	+	5.65508i	0.695119	+	0.180277i
$985$	11.7764	+	19.7014i	0.375228	+	0.627740i
$986$	−0.587522	+	0.550825i	−0.0187105	+	0.0175419i
$987$	13.8571	−	19.0726i	0.441075	−	0.607088i
$988$	28.2721	+	11.2467i	0.899455	+	0.357806i
$989$	1.42666	+	1.96362i	0.0453650	+	0.0624396i
$990$	11.8356	−	0.417905i	0.376160	−	0.0132819i
$991$	8.17278	+	5.93788i	0.259617	+	0.188623i	0.709978	−	0.704224i	$-0.248705\pi$
$991$	8.17278	+	5.93788i	0.259617	+	0.188623i	−0.450361	+	0.892846i	$0.648705\pi$
$992$	18.6434	−	25.4432i	0.591929	−	0.807822i
$993$	−18.9912			−0.602669
$994$	−27.7984	+	13.0534i	−0.881711	+	0.414030i
$995$	−7.59319	−	6.63129i	−0.240720	−	0.210226i
$996$	−1.07629	+	16.6761i	−0.0341036	+	0.528402i
$997$	4.39920	+	1.42939i	0.139324	+	0.0452691i	0.377849	−	0.925867i	$-0.376664\pi$
$997$	4.39920	+	1.42939i	0.139324	+	0.0452691i	−0.238525	+	0.971136i	$0.576664\pi$
$998$	37.5431	−	35.1982i	1.18841	−	1.11418i
$999$	−3.43247			−0.108598

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.bm.a.61.15	✓	240
8.5	even	2	inner	600.2.bm.a.61.40	yes	240
25.16	even	5	inner	600.2.bm.a.541.40	yes	240
200.141	even	10	inner	600.2.bm.a.541.15	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.bm.a.61.15	✓	240	1.1	even	1	trivial
600.2.bm.a.61.40	yes	240	8.5	even	2	inner
600.2.bm.a.541.15	yes	240	200.141	even	10	inner
600.2.bm.a.541.40	yes	240	25.16	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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.bm (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.967261 - 1.03170i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-0.128814 + 1.99585i) q^{4} +(1.68421 + 1.47086i) q^{5} +(-0.601106 - 1.28011i) q^{6} +2.08501 q^{7} +(2.18371 - 1.79761i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-0.111588 - 3.16031i) q^{10} +(2.20130 + 3.02983i) q^{11} +(-0.739260 + 1.85836i) q^{12} +(-1.42445 + 1.96059i) q^{13} +(-2.01675 - 2.15110i) q^{14} +(1.14726 + 1.91932i) q^{15} +(-3.96681 - 0.514185i) q^{16} +(-0.784515 - 2.41449i) q^{17} +(-0.176112 - 1.40321i) q^{18} +(-5.97044 + 1.93992i) q^{19} +(-3.15256 + 3.17197i) q^{20} +(1.98296 + 0.644303i) q^{21} +(0.996647 - 5.20172i) q^{22} +(1.49694 - 1.08759i) q^{23} +(2.63233 - 1.03482i) q^{24} +(0.673153 + 4.95448i) q^{25} +(3.40055 - 0.426792i) q^{26} +(0.587785 + 0.809017i) q^{27} +(-0.268578 + 4.16136i) q^{28} +(0.213333 + 0.0693161i) q^{29} +(0.870462 - 3.04011i) q^{30} +(-1.72308 - 5.30308i) q^{31} +(3.30646 + 4.58992i) q^{32} +(1.15729 + 3.56178i) q^{33} +(-1.73220 + 3.14482i) q^{34} +(3.51160 + 3.06675i) q^{35} +(-1.27734 + 1.53896i) q^{36} +(-2.01755 + 2.77692i) q^{37} +(7.77639 + 4.28331i) q^{38} +(-1.96059 + 1.42445i) q^{39} +(6.32187 + 0.184379i) q^{40} +(6.44324 + 4.68129i) q^{41} +(-1.25331 - 2.66903i) q^{42} +1.31176i q^{43} +(-6.33063 + 4.00317i) q^{44} +(0.498009 + 2.17991i) q^{45} +(-2.57000 - 0.492411i) q^{46} +(3.49403 - 10.7535i) q^{47} +(-3.61377 - 1.71483i) q^{48} -2.65274 q^{49} +(4.46043 - 5.48677i) q^{50} -2.53874i q^{51} +(-3.72954 - 3.09553i) q^{52} +(7.13282 + 2.31759i) q^{53} +(0.266122 - 1.38895i) q^{54} +(-0.748989 + 8.34068i) q^{55} +(4.55306 - 3.74803i) q^{56} -6.27770 q^{57} +(-0.134835 - 0.287143i) q^{58} +(1.56491 - 2.15392i) q^{59} +(-3.97845 + 2.04253i) q^{60} +(-3.52395 - 4.85031i) q^{61} +(-3.80453 + 6.90716i) q^{62} +(1.68681 + 1.22554i) q^{63} +(1.53722 - 7.85092i) q^{64} +(-5.28282 + 1.20688i) q^{65} +(2.55529 - 4.63914i) q^{66} +(11.3688 - 3.69394i) q^{67} +(4.92001 - 1.25475i) q^{68} +(1.75976 - 0.571780i) q^{69} +(-0.232662 - 6.58927i) q^{70} +(3.21846 - 9.90540i) q^{71} +(2.82327 - 0.170740i) q^{72} +(-1.02722 + 0.746320i) q^{73} +(4.81645 - 0.604497i) q^{74} +(-0.890812 + 4.92001i) q^{75} +(-3.10270 - 12.1660i) q^{76} +(4.58973 + 6.31722i) q^{77} +(3.36600 + 0.644925i) q^{78} +(0.872015 - 2.68379i) q^{79} +(-5.92467 - 6.70062i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-1.40260 - 11.1755i) q^{82} +(7.94645 - 2.58196i) q^{83} +(-1.54136 + 3.87469i) q^{84} +(2.23008 - 5.22042i) q^{85} +(1.35334 - 1.26881i) q^{86} +(0.181472 + 0.131847i) q^{87} +(10.2534 + 2.65921i) q^{88} +(-13.6365 + 9.90747i) q^{89} +(1.76731 - 2.62233i) q^{90} +(-2.96999 + 4.08784i) q^{91} +(1.97784 + 3.12776i) q^{92} -5.57599i q^{93} +(-14.4741 + 6.79667i) q^{94} +(-12.9088 - 5.51445i) q^{95} +(1.72627 + 5.38702i) q^{96} +(-1.09220 + 3.36144i) q^{97} +(2.56589 + 2.73684i) q^{98} +3.74507i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 18 q^{8} + 60 q^{9} - 2 q^{10} - 8 q^{12} + 12 q^{14} - 12 q^{16} + 8 q^{17} + 16 q^{20} - 38 q^{22} - 4 q^{25} - 20 q^{26} + 28 q^{28} - 36 q^{30} - 24 q^{31} - 20 q^{32} - 16 q^{34} - 46 q^{38}+ \cdots - 140 q^{98}+O(q^{100}) \) 240 * q + 18 * q^8 + 60 * q^9 - 2 * q^10 - 8 * q^12 + 12 * q^14 - 12 * q^16 + 8 * q^17 + 16 * q^20 - 38 * q^22 - 4 * q^25 - 20 * q^26 + 28 * q^28 - 36 * q^30 - 24 * q^31 - 20 * q^32 - 16 * q^34 - 46 * q^38 + 16 * q^39 + 40 * q^40 - 8 * q^41 - 20 * q^42 + 42 * q^44 + 20 * q^46 + 48 * q^47 - 16 * q^48 + 240 * q^49 - 144 * q^50 + 16 * q^52 - 16 * q^55 + 36 * q^56 - 94 * q^58 - 2 * q^60 - 66 * q^62 + 42 * q^64 + 84 * q^65 + 8 * q^66 + 16 * q^68 + 4 * q^70 - 18 * q^72 + 40 * q^73 - 44 * q^74 + 8 * q^76 - 24 * q^78 - 40 * q^79 - 16 * q^80 - 60 * q^81 - 80 * q^82 - 24 * q^84 - 60 * q^86 + 22 * q^88 - 60 * q^89 - 28 * q^90 + 14 * q^92 - 50 * q^94 - 184 * q^95 + 40 * q^96 + 32 * q^97 - 140 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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