LMFDB - Embedded newform 550.2.l.d.191.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(181,550)] 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("550.181"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(550, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([4, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 550 = 2 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	550.l (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,12,-22] 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:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			191.3
Character	$\chi$	$=$	550.191
Dual form			550.2.l.d.311.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 - 0.951057i) q^{2} -2.20028 q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.31045 + 1.81183i) q^{5} +(0.679923 + 2.09259i) q^{6} +(-1.59332 - 4.90374i) q^{7} +(0.809017 + 0.587785i) q^{8} +1.84122 q^{9} +(2.12810 + 0.686427i) q^{10} +(1.13352 + 3.11691i) q^{11} +(1.78006 - 1.29329i) q^{12} -5.58286 q^{13} +(-4.17137 + 3.03068i) q^{14} +(2.88335 - 3.98652i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.0789633 - 0.243024i) q^{17} +(-0.568969 - 1.75111i) q^{18} +(2.69414 + 1.95741i) q^{19} +(-0.00478894 - 2.23606i) q^{20} +(3.50575 + 10.7896i) q^{21} +(2.61408 - 2.04122i) q^{22} +(5.71967 + 4.15558i) q^{23} +(-1.78006 - 1.29329i) q^{24} +(-1.56544 - 4.74862i) q^{25} +(1.72520 + 5.30961i) q^{26} +2.54963 q^{27} +(4.17137 + 3.03068i) q^{28} +(4.96750 - 3.60910i) q^{29} +(-4.68242 - 1.51033i) q^{30} +(1.47830 - 1.07405i) q^{31} -1.00000 q^{32} +(-2.49405 - 6.85807i) q^{33} +(-0.206729 + 0.150197i) q^{34} +(10.9727 + 3.53928i) q^{35} +(-1.48958 + 1.08224i) q^{36} +(5.75740 + 4.18300i) q^{37} +(1.02907 - 3.16715i) q^{38} +12.2838 q^{39} +(-2.12514 + 0.695536i) q^{40} +(-0.0633259 - 0.194897i) q^{41} +(9.17818 - 6.66834i) q^{42} +7.18246 q^{43} +(-2.74911 - 1.85537i) q^{44} +(-2.41283 + 3.33598i) q^{45} +(2.18472 - 6.72387i) q^{46} -5.50094 q^{47} +(-0.679923 + 2.09259i) q^{48} +(-15.8449 + 11.5120i) q^{49} +(-4.03246 + 2.95623i) q^{50} +(0.173741 + 0.534721i) q^{51} +(4.51663 - 3.28152i) q^{52} +(-1.49926 + 4.61425i) q^{53} +(-0.787880 - 2.42485i) q^{54} +(-7.13272 - 2.03082i) q^{55} +(1.59332 - 4.90374i) q^{56} +(-5.92786 - 4.30684i) q^{57} +(-4.96750 - 3.60910i) q^{58} +(-1.50030 - 1.09004i) q^{59} +(0.0105370 + 4.91996i) q^{60} +3.91717 q^{61} +(-1.47830 - 1.07405i) q^{62} +(-2.93366 - 9.02887i) q^{63} +(0.309017 + 0.951057i) q^{64} +(7.31606 - 10.1152i) q^{65} +(-5.75171 + 4.49124i) q^{66} +(-1.84215 + 5.66956i) q^{67} +(0.206729 + 0.150197i) q^{68} +(-12.5849 - 9.14343i) q^{69} +(-0.0246923 - 11.5294i) q^{70} +(9.44536 + 6.86245i) q^{71} +(1.48958 + 1.08224i) q^{72} +(0.570022 - 1.75435i) q^{73} +(2.19913 - 6.76823i) q^{74} +(3.44440 + 10.4483i) q^{75} -3.33014 q^{76} +(13.4785 - 10.5247i) q^{77} +(-3.79591 - 11.6826i) q^{78} +(1.09597 - 3.37304i) q^{79} +(1.31820 + 1.80620i) q^{80} -11.1336 q^{81} +(-0.165789 + 0.120453i) q^{82} +(-1.07373 - 3.30460i) q^{83} +(-9.17818 - 6.66834i) q^{84} +(0.543795 + 0.175403i) q^{85} +(-2.21950 - 6.83093i) q^{86} +(-10.9299 + 7.94101i) q^{87} +(-0.915041 + 3.18790i) q^{88} +(-4.43693 - 3.22362i) q^{89} +(3.91831 + 1.26386i) q^{90} +(8.89529 + 27.3769i) q^{91} -7.06990 q^{92} +(-3.25267 + 2.36320i) q^{93} +(1.69988 + 5.23170i) q^{94} +(-7.07702 + 2.31623i) q^{95} +2.20028 q^{96} +(-3.29397 + 10.1378i) q^{97} +(15.8449 + 11.5120i) q^{98} +(2.08705 + 5.73893i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{2} - 22 q^{3} - 12 q^{4} - q^{5} - 3 q^{6} + 11 q^{7} + 12 q^{8} + 70 q^{9} + 6 q^{10} + 3 q^{11} + 8 q^{12} - 34 q^{13} - q^{14} + 7 q^{15} - 12 q^{16} - 9 q^{17} + 10 q^{18} - 6 q^{19}+ \cdots - 54 q^{99}+O(q^{100}) $ 48 * q + 12 * q^2 - 22 * q^3 - 12 * q^4 - q^5 - 3 * q^6 + 11 * q^7 + 12 * q^8 + 70 * q^9 + 6 * q^10 + 3 * q^11 + 8 * q^12 - 34 * q^13 - q^14 + 7 * q^15 - 12 * q^16 - 9 * q^17 + 10 * q^18 - 6 * q^19 + 19 * q^20 - 15 * q^21 - 8 * q^22 + 14 * q^23 - 8 * q^24 + 7 * q^25 - 16 * q^26 - 34 * q^27 + q^28 - q^29 - 12 * q^30 + 17 * q^31 - 48 * q^32 + 4 * q^34 - 41 * q^35 - 25 * q^36 - 23 * q^37 + q^38 - 20 * q^39 + 6 * q^40 + 29 * q^41 + 22 * q^43 + 13 * q^44 + 62 * q^45 - 9 * q^46 - 52 * q^47 + 3 * q^48 - 23 * q^49 - 2 * q^50 + 4 * q^51 + q^52 + 44 * q^53 - 11 * q^54 - 7 * q^55 - 11 * q^56 - 5 * q^57 + q^58 - 18 * q^59 + 2 * q^60 + 16 * q^61 - 17 * q^62 - 13 * q^63 - 12 * q^64 - 2 * q^65 + 20 * q^67 - 4 * q^68 - 2 * q^69 - 59 * q^70 + 39 * q^71 + 25 * q^72 - 42 * q^73 - 37 * q^74 + 20 * q^75 + 14 * q^76 - 13 * q^77 - 15 * q^78 + 53 * q^79 - 6 * q^80 + 56 * q^81 + 36 * q^82 + 14 * q^83 + 6 * q^85 + 13 * q^86 - 18 * q^87 + 17 * q^88 - 8 * q^89 + 28 * q^90 - 5 * q^91 - 46 * q^92 + 15 * q^93 - 13 * q^94 - 24 * q^95 + 22 * q^96 - 16 * q^97 + 23 * q^98 - 54 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/550\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	−2.20028			−1.27033			−0.635165	−	0.772376i	$-0.719068\pi$
$3$	−2.20028			−1.27033			−0.635165	+	0.772376i	$0.719068\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	−1.31045	+	1.81183i	−0.586051	+	0.810274i
$5$	−1.31045	+	1.81183i	−0.586051	+	0.810274i
$6$	0.679923	+	2.09259i	0.277577	+	0.854296i
$7$	−1.59332	−	4.90374i	−0.602219	−	1.85344i	−0.514881	−	0.857261i	$-0.672164\pi$
$7$	−1.59332	−	4.90374i	−0.602219	−	1.85344i	−0.0873377	−	0.996179i	$-0.527836\pi$
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	1.84122			0.613741
$10$	2.12810	+	0.686427i	0.672965	+	0.217067i
$11$	1.13352	+	3.11691i	0.341768	+	0.939784i
$11$	1.13352	+	3.11691i	0.341768	+	0.939784i
$12$	1.78006	−	1.29329i	0.513860	−	0.373341i
$13$	−5.58286			−1.54841			−0.774203	−	0.632937i	$-0.781849\pi$
$13$	−5.58286			−1.54841			−0.774203	+	0.632937i	$0.781849\pi$
$14$	−4.17137	+	3.03068i	−1.11485	+	0.809983i
$15$	2.88335	−	3.98652i	0.744479	−	1.02932i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	−0.0789633	−	0.243024i	−0.0191514	−	0.0589420i	0.941024	−	0.338340i	$-0.109865\pi$
$17$	−0.0789633	−	0.243024i	−0.0191514	−	0.0589420i	−0.960175	+	0.279398i	$0.909865\pi$
$18$	−0.568969	−	1.75111i	−0.134107	−	0.412740i
$19$	2.69414	+	1.95741i	0.618078	+	0.449060i	0.852250	−	0.523135i	$-0.175238\pi$
$19$	2.69414	+	1.95741i	0.618078	+	0.449060i	−0.234172	+	0.972195i	$0.575238\pi$
$20$	−0.00478894	−	2.23606i	−0.00107084	−	0.499999i
$21$	3.50575	+	10.7896i	0.765018	+	2.35448i
$22$	2.61408	−	2.04122i	0.557324	−	0.435189i
$23$	5.71967	+	4.15558i	1.19263	+	0.866498i	0.993540	−	0.113482i	$-0.0362005\pi$
$23$	5.71967	+	4.15558i	1.19263	+	0.866498i	0.199093	+	0.979981i	$0.436201\pi$
$24$	−1.78006	−	1.29329i	−0.363354	−	0.263992i
$25$	−1.56544	−	4.74862i	−0.313088	−	0.949724i
$26$	1.72520	+	5.30961i	0.338339	+	1.04130i
$27$	2.54963			0.490677
$28$	4.17137	+	3.03068i	0.788315	+	0.572745i
$29$	4.96750	−	3.60910i	0.922441	−	0.670192i	−0.0216896	−	0.999765i	$-0.506905\pi$
$29$	4.96750	−	3.60910i	0.922441	−	0.670192i	0.944130	+	0.329572i	$0.106905\pi$
$30$	−4.68242	−	1.51033i	−0.854888	−	0.275747i
$31$	1.47830	−	1.07405i	0.265510	−	0.192905i	−0.447062	−	0.894503i	$-0.647530\pi$
$31$	1.47830	−	1.07405i	0.265510	−	0.192905i	0.712573	+	0.701598i	$0.247530\pi$
$32$	−1.00000			−0.176777
$33$	−2.49405	−	6.85807i	−0.434159	−	1.19384i
$34$	−0.206729	+	0.150197i	−0.0354537	+	0.0257586i
$35$	10.9727	+	3.53928i	1.85473	+	0.598248i
$36$	−1.48958	+	1.08224i	−0.248263	+	0.180374i
$37$	5.75740	+	4.18300i	0.946511	+	0.687680i	0.949979	−	0.312314i	$-0.101104\pi$
$37$	5.75740	+	4.18300i	0.946511	+	0.687680i	−0.00346815	+	0.999994i	$0.501104\pi$
$38$	1.02907	−	3.16715i	0.166937	−	0.513780i
$39$	12.2838			1.96699
$40$	−2.12514	+	0.695536i	−0.336014	+	0.109974i
$41$	−0.0633259	−	0.194897i	−0.00988984	−	0.0304378i	0.945990	−	0.324196i	$-0.105094\pi$
$41$	−0.0633259	−	0.194897i	−0.00988984	−	0.0304378i	−0.955880	+	0.293759i	$0.905094\pi$
$42$	9.17818	−	6.66834i	1.41622	−	1.02895i
$43$	7.18246			1.09531			0.547657	−	0.836703i	$-0.315520\pi$
$43$	7.18246			1.09531			0.547657	+	0.836703i	$0.315520\pi$
$44$	−2.74911	−	1.85537i	−0.414444	−	0.279708i
$45$	−2.41283	+	3.33598i	−0.359683	+	0.497298i
$46$	2.18472	−	6.72387i	0.322119	−	0.991381i
$47$	−5.50094			−0.802394			−0.401197	−	0.915992i	$-0.631406\pi$
$47$	−5.50094			−0.802394			−0.401197	+	0.915992i	$0.631406\pi$
$48$	−0.679923	+	2.09259i	−0.0981385	+	0.302039i
$49$	−15.8449	+	11.5120i	−2.26356	+	1.64457i
$50$	−4.03246	+	2.95623i	−0.570276	+	0.418073i
$51$	0.173741	+	0.534721i	0.0243286	+	0.0748759i
$52$	4.51663	−	3.28152i	0.626343	−	0.455065i
$53$	−1.49926	+	4.61425i	−0.205939	+	0.633816i	0.793734	+	0.608265i	$0.208134\pi$
$53$	−1.49926	+	4.61425i	−0.205939	+	0.633816i	−0.999674	+	0.0255510i	$0.991866\pi$
$54$	−0.787880	−	2.42485i	−0.107217	−	0.329980i
$55$	−7.13272	−	2.03082i	−0.961776	−	0.273836i
$56$	1.59332	−	4.90374i	0.212917	−	0.655290i
$57$	−5.92786	−	4.30684i	−0.785164	−	0.570455i
$58$	−4.96750	−	3.60910i	−0.652264	−	0.473898i
$59$	−1.50030	−	1.09004i	−0.195323	−	0.141910i	0.485825	−	0.874056i	$-0.338519\pi$
$59$	−1.50030	−	1.09004i	−0.195323	−	0.141910i	−0.681148	+	0.732145i	$0.738519\pi$
$60$	0.0105370	+	4.91996i	0.00136032	+	0.635164i
$61$	3.91717			0.501542			0.250771	−	0.968046i	$-0.419316\pi$
$61$	3.91717			0.501542			0.250771	+	0.968046i	$0.419316\pi$
$62$	−1.47830	−	1.07405i	−0.187744	−	0.136404i
$63$	−2.93366	−	9.02887i	−0.369606	−	1.13753i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	7.31606	−	10.1152i	0.907445	−	1.25463i
$66$	−5.75171	+	4.49124i	−0.707987	+	0.552834i
$67$	−1.84215	+	5.66956i	−0.225055	+	0.692647i	0.773231	+	0.634124i	$0.218639\pi$
$67$	−1.84215	+	5.66956i	−0.225055	+	0.692647i	−0.998286	+	0.0585232i	$0.981361\pi$
$68$	0.206729	+	0.150197i	0.0250695	+	0.0182141i
$69$	−12.5849	−	9.14343i	−1.51504	−	1.10074i
$70$	−0.0246923	−	11.5294i	−0.00295129	−	1.37802i
$71$	9.44536	+	6.86245i	1.12096	+	0.814423i	0.984354	−	0.176203i	$-0.0563814\pi$
$71$	9.44536	+	6.86245i	1.12096	+	0.814423i	0.136604	+	0.990626i	$0.456381\pi$
$72$	1.48958	+	1.08224i	0.175549	+	0.127544i
$73$	0.570022	−	1.75435i	0.0667160	−	0.205331i	−0.912141	−	0.409877i	$-0.865572\pi$
$73$	0.570022	−	1.75435i	0.0667160	−	0.205331i	0.978857	+	0.204546i	$0.0655718\pi$
$74$	2.19913	−	6.76823i	0.255644	−	0.786791i
$75$	3.44440	+	10.4483i	0.397725	+	1.20646i
$76$	−3.33014			−0.381993
$77$	13.4785	−	10.5247i	1.53601	−	1.19940i
$78$	−3.79591	−	11.6826i	−0.429803	−	1.32280i
$79$	1.09597	−	3.37304i	0.123306	−	0.379497i	−0.870283	−	0.492553i	$-0.836064\pi$
$79$	1.09597	−	3.37304i	0.123306	−	0.379497i	0.993589	+	0.113056i	$0.0360639\pi$
$80$	1.31820	+	1.80620i	0.147379	+	0.201939i
$81$	−11.1336			−1.23706
$82$	−0.165789	+	0.120453i	−0.0183084	+	0.0133018i
$83$	−1.07373	−	3.30460i	−0.117857	−	0.362727i	0.874675	−	0.484710i	$-0.161075\pi$
$83$	−1.07373	−	3.30460i	−0.117857	−	0.362727i	−0.992532	+	0.121983i	$0.961075\pi$
$84$	−9.17818	−	6.66834i	−1.00142	−	0.727575i
$85$	0.543795	+	0.175403i	0.0589829	+	0.0190251i
$86$	−2.21950	−	6.83093i	−0.239335	−	0.736598i
$87$	−10.9299	+	7.94101i	−1.17180	+	0.851366i
$88$	−0.915041	+	3.18790i	−0.0975437	+	0.339831i
$89$	−4.43693	−	3.22362i	−0.470314	−	0.341703i	0.327250	−	0.944938i	$-0.393878\pi$
$89$	−4.43693	−	3.22362i	−0.470314	−	0.341703i	−0.797564	+	0.603235i	$0.793878\pi$
$90$	3.91831	+	1.26386i	0.413026	+	0.133223i
$91$	8.89529	+	27.3769i	0.932480	+	2.86988i
$92$	−7.06990			−0.737088
$93$	−3.25267	+	2.36320i	−0.337286	+	0.245053i
$94$	1.69988	+	5.23170i	0.175329	+	0.539609i
$95$	−7.07702	+	2.31623i	−0.726087	+	0.237640i
$96$	2.20028			0.224565
$97$	−3.29397	+	10.1378i	−0.334452	+	1.02934i	0.632539	+	0.774529i	$0.282013\pi$
$97$	−3.29397	+	10.1378i	−0.334452	+	1.02934i	−0.966991	+	0.254810i	$0.917987\pi$
$98$	15.8449	+	11.5120i	1.60058	+	1.16289i
$99$	2.08705	+	5.73893i	0.209757	+	0.576784i
$100$	4.05764	+	2.92157i	0.405764	+	0.292157i
$101$	5.75306	+	4.17984i	0.572450	+	0.415910i	0.835995	−	0.548738i	$-0.184891\pi$
$101$	5.75306	+	4.17984i	0.572450	+	0.415910i	−0.263544	+	0.964647i	$0.584891\pi$
$102$	0.454860	−	0.330475i	0.0450379	−	0.0327219i
$103$	11.8973	−	8.64387i	1.17227	−	0.851706i	0.180994	−	0.983484i	$-0.442069\pi$
$103$	11.8973	−	8.64387i	1.17227	−	0.851706i	0.991279	+	0.131778i	$0.0420687\pi$
$104$	−4.51663	−	3.28152i	−0.442892	−	0.321780i
$105$	−24.1430	−	7.78741i	−2.35612	−	0.759973i
$106$	4.85171			0.471239
$107$	−1.97569	+	6.08056i	−0.190998	+	0.587830i	0.809002	+	0.587805i	$0.200008\pi$
$107$	−1.97569	+	6.08056i	−0.190998	+	0.587830i	−1.00000		2.47897e-5i	$0.999992\pi$
$108$	−2.06270	+	1.49864i	−0.198483	+	0.144206i
$109$	−5.44681	+	3.95734i	−0.521709	+	0.379044i	−0.817247	−	0.576287i	$-0.804501\pi$
$109$	−5.44681	+	3.95734i	−0.521709	+	0.379044i	0.295538	+	0.955331i	$0.404501\pi$
$110$	0.272707	+	7.41118i	0.0260016	+	0.706629i
$111$	−12.6679	−	9.20375i	−1.20238	−	0.873582i
$112$	−5.15610			−0.487206
$113$	0.226485	+	0.697048i	0.0213059	+	0.0655728i	0.961144	−	0.276047i	$-0.0890245\pi$
$113$	0.226485	+	0.697048i	0.0213059	+	0.0655728i	−0.939838	+	0.341620i	$0.889025\pi$
$114$	−2.26424	+	6.96861i	−0.212065	+	0.652670i
$115$	−15.0245	+	4.91737i	−1.40104	+	0.458547i
$116$	−1.89741	+	5.83964i	−0.176171	+	0.542197i
$117$	−10.2793			−0.950320
$118$	−0.573065	+	1.76371i	−0.0527549	+	0.162363i
$119$	−1.06591	+	0.774432i	−0.0977121	+	0.0709920i
$120$	4.67590	−	1.53037i	0.426850	−	0.139703i
$121$	−8.43028	+	7.06614i	−0.766389	+	0.642377i
$122$	−1.21047	−	3.72545i	−0.109591	−	0.337287i
$123$	0.139335	+	0.428828i	0.0125634	+	0.0386661i
$124$	−0.564660	+	1.73784i	−0.0507080	+	0.156063i
$125$	10.6551	+	3.38653i	0.953022	+	0.302900i
$126$	−7.68042	+	5.58015i	−0.684226	+	0.497119i
$127$	8.03849			0.713301			0.356651	−	0.934238i	$-0.383919\pi$
$127$	8.03849			0.713301			0.356651	+	0.934238i	$0.383919\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−15.8034			−1.39141
$130$	−11.8809	−	3.83222i	−1.04202	−	0.336108i
$131$	5.23687	−	16.1174i	0.457547	−	1.40819i	−0.410571	−	0.911829i	$-0.634670\pi$
$131$	5.23687	−	16.1174i	0.457547	−	1.40819i	0.868118	−	0.496358i	$-0.165330\pi$
$132$	6.04880	+	4.08233i	0.526481	+	0.355321i
$133$	5.30599	−	16.3301i	0.460087	−	1.41600i
$134$	5.96133			0.514981
$135$	−3.34117	+	4.61950i	−0.287562	+	0.397583i
$136$	0.0789633	−	0.243024i	0.00677105	−	0.0208391i
$137$	−3.35140	+	10.3145i	−0.286329	+	0.881231i	0.699668	+	0.714468i	$0.253331\pi$
$137$	−3.35140	+	10.3145i	−0.286329	+	0.881231i	−0.985997	+	0.166763i	$0.946669\pi$
$138$	−4.80699	+	14.7944i	−0.409198	+	1.25938i
$139$	−5.66437	+	17.4331i	−0.480445	+	1.47866i	0.358026	+	0.933712i	$0.383450\pi$
$139$	−5.66437	+	17.4331i	−0.480445	+	1.47866i	−0.838471	+	0.544947i	$0.816550\pi$
$140$	−10.9574	+	3.58625i	−0.926073	+	0.303094i
$141$	12.1036			1.01931
$142$	3.60780	−	11.1037i	0.302760	−	0.931800i
$143$	−6.32826	−	17.4013i	−0.529196	−	1.45517i
$144$	0.568969	−	1.75111i	0.0474141	−	0.145925i
$145$	0.0294049	+	13.7298i	0.00244194	+	1.14020i
$146$	−1.84463			−0.152663
$147$	34.8632	−	25.3296i	2.87546	−	2.08915i
$148$	−7.11654			−0.584976
$149$	18.4015	−	13.3694i	1.50751	−	1.09527i	0.540237	−	0.841513i	$-0.318335\pi$
$149$	18.4015	−	13.3694i	1.50751	−	1.09527i	0.967269	−	0.253754i	$-0.0816653\pi$
$150$	8.87253	−	6.50452i	0.724439	−	0.531092i
$151$	−4.05494	+	12.4798i	−0.329986	+	1.01559i	0.639153	+	0.769080i	$0.279285\pi$
$151$	−4.05494	+	12.4798i	−0.329986	+	1.01559i	−0.969139	+	0.246514i	$0.920715\pi$
$152$	1.02907	+	3.16715i	0.0834686	+	0.256890i
$153$	−0.145389	−	0.447461i	−0.0117540	−	0.0361751i
$154$	−14.1747	−	9.56647i	−1.14223	−	0.770888i
$155$	0.00875073	+	4.08591i	0.000702875	+	0.328188i
$156$	−9.93783	+	7.22026i	−0.795663	+	0.578083i
$157$	0.685859	−	2.11086i	0.0547375	−	0.168465i	−0.919950	−	0.392035i	$-0.871771\pi$
$157$	0.685859	−	2.11086i	0.0547375	−	0.168465i	0.974688	+	0.223570i	$0.0717712\pi$
$158$	−3.54663			−0.282154
$159$	3.29879	−	10.1526i	0.261611	−	0.805155i
$160$	1.31045	−	1.81183i	0.103600	−	0.143238i
$161$	11.2646	−	34.6689i	0.887777	−	2.73230i
$162$	3.44046	+	10.5887i	0.270308	+	0.831923i
$163$	−18.1778			−1.42379			−0.711897	−	0.702284i	$-0.752164\pi$
$163$	−18.1778			−1.42379			−0.711897	+	0.702284i	$0.752164\pi$
$164$	0.165789	+	0.120453i	0.0129460	+	0.00940580i
$165$	15.6940	+	4.46837i	1.22177	+	0.347862i
$166$	−2.81106	+	2.04236i	−0.218181	+	0.158518i
$167$	10.5719	−	7.68092i	0.818076	−	0.594367i	−0.0980845	−	0.995178i	$-0.531272\pi$
$167$	10.5719	−	7.68092i	0.818076	−	0.594367i	0.916161	+	0.400811i	$0.131272\pi$
$168$	−3.50575	+	10.7896i	−0.270475	+	0.832435i
$169$	18.1683			1.39756
$170$	−0.00122372	−	0.571383i	−9.38552e−5	−	0.0438231i
$171$	4.96051	+	3.60402i	0.379340	+	0.275606i
$172$	−5.81073	+	4.22174i	−0.443064	+	0.321905i
$173$	−5.99554	+	4.35601i	−0.455832	+	0.331182i	−0.791894	−	0.610658i	$-0.790905\pi$
$173$	−5.99554	+	4.35601i	−0.455832	+	0.331182i	0.336062	+	0.941840i	$0.390905\pi$
$174$	10.9299	+	7.94101i	0.828591	+	0.602007i
$175$	−20.7918	+	15.2426i	−1.57171	+	1.15223i
$176$	3.31464	−	0.114859i	0.249850	−	0.00865786i
$177$	3.30109	+	2.39838i	0.248125	+	0.180273i
$178$	−1.69476	+	5.21592i	−0.127027	+	0.390950i
$179$	−1.42356			−0.106402			−0.0532008	−	0.998584i	$-0.516942\pi$
$179$	−1.42356			−0.106402			−0.0532008	+	0.998584i	$0.516942\pi$
$180$	−0.00881750	−	4.11709i	−0.000657218	−	0.306870i
$181$	−4.92235	−	15.1494i	−0.365875	−	1.12605i	−0.949431	−	0.313976i	$-0.898339\pi$
$181$	−4.92235	−	15.1494i	−0.365875	−	1.12605i	0.583556	−	0.812073i	$-0.301661\pi$
$182$	23.2882	−	16.9199i	1.72623	−	1.25418i
$183$	−8.61887			−0.637125
$184$	2.18472	+	6.72387i	0.161060	+	0.495690i
$185$	−15.1237	+	4.94981i	−1.11191	+	0.363917i
$186$	3.25267	+	2.36320i	0.238497	+	0.173278i
$187$	0.667979	−	0.521594i	0.0488474	−	0.0381427i
$188$	4.45035	−	3.23337i	0.324575	−	0.235818i
$189$	−4.06239	−	12.5027i	−0.295495	−	0.909441i
$190$	4.38979	+	6.01489i	0.318469	+	0.436366i
$191$	10.6920	+	7.76822i	0.773648	+	0.562088i	0.903066	−	0.429502i	$-0.141311\pi$
$191$	10.6920	+	7.76822i	0.773648	+	0.562088i	−0.129418	+	0.991590i	$0.541311\pi$
$192$	−0.679923	−	2.09259i	−0.0490692	−	0.151020i
$193$	3.44847	−	2.50546i	0.248227	−	0.180347i	−0.456714	−	0.889614i	$-0.650974\pi$
$193$	3.44847	−	2.50546i	0.248227	−	0.180347i	0.704941	+	0.709266i	$0.250974\pi$
$194$	10.6595			0.765309
$195$	−16.0974	+	22.2562i	−1.15276	+	1.59380i
$196$	6.05221	−	18.6268i	0.432301	−	1.33048i
$197$	−1.38745	−	4.27012i	−0.0988515	−	0.304234i	0.889387	−	0.457155i	$-0.151132\pi$
$197$	−1.38745	−	4.27012i	−0.0988515	−	0.304234i	−0.988238	+	0.152922i	$0.951132\pi$
$198$	4.81311	−	3.75833i	0.342053	−	0.267093i
$199$	9.20308			0.652389			0.326194	−	0.945303i	$-0.394234\pi$
$199$	9.20308			0.652389			0.326194	+	0.945303i	$0.394234\pi$
$200$	1.52470	−	4.76186i	0.107813	−	0.336714i
$201$	4.05325	−	12.4746i	0.285894	−	0.879891i
$202$	2.19747	−	6.76312i	0.154614	−	0.475852i
$203$	−25.6129	−	18.6089i	−1.79767	−	1.30609i
$204$	−0.454860	−	0.330475i	−0.0318466	−	0.0231379i
$205$	0.436105	+	0.140667i	0.0304589	+	0.00982463i
$206$	−11.8973	−	8.64387i	−0.828922	−	0.602247i
$207$	10.5312	+	7.65134i	0.731967	+	0.531805i
$208$	−1.72520	+	5.30961i	−0.119621	+	0.368155i
$209$	−3.04721	+	10.6162i	−0.210780	+	0.734335i
$210$	0.0543298	+	25.3678i	0.00374911	+	1.75054i
$211$	1.76982	+	5.44694i	0.121839	+	0.374983i	0.993312	−	0.115461i	$-0.0368346\pi$
$211$	1.76982	+	5.44694i	0.121839	+	0.374983i	−0.871473	+	0.490444i	$0.836835\pi$
$212$	−1.49926	−	4.61425i	−0.102970	−	0.316908i
$213$	−20.7824	−	15.0993i	−1.42399	−	1.03459i
$214$	6.39348			0.437049
$215$	−9.41226	+	13.0134i	−0.641911	+	0.887505i
$216$	2.06270	+	1.49864i	0.140349	+	0.101969i
$217$	−7.62226	−	5.53789i	−0.517432	−	0.375937i
$218$	5.44681	+	3.95734i	0.368904	+	0.268025i
$219$	−1.25421	+	3.86005i	−0.0847514	+	0.260838i
$220$	6.96418	−	2.54954i	0.469525	−	0.171890i
$221$	0.440841	+	1.35677i	0.0296542	+	0.0912662i
$222$	−4.83870	+	14.8920i	−0.324752	+	0.999485i
$223$	14.4525	−	10.5004i	0.967814	−	0.703158i	0.0128617	−	0.999917i	$-0.495906\pi$
$223$	14.4525	−	10.5004i	0.967814	−	0.703158i	0.954952	+	0.296759i	$0.0959059\pi$
$224$	1.59332	+	4.90374i	0.106458	+	0.327645i
$225$	−2.88232	−	8.74326i	−0.192155	−	0.582884i
$226$	0.592945	−	0.430800i	0.0394421	−	0.0286564i
$227$	−2.68774	+	8.27200i	−0.178391	+	0.549032i	−0.999772	−	0.0213483i	$-0.993204\pi$
$227$	−2.68774	+	8.27200i	−0.178391	+	0.549032i	0.821381	+	0.570380i	$0.193204\pi$
$228$	7.32723			0.485258
$229$	−8.45506	+	26.0220i	−0.558726	+	1.71958i	0.127169	+	0.991881i	$0.459411\pi$
$229$	−8.45506	+	26.0220i	−0.558726	+	1.71958i	−0.685895	+	0.727701i	$0.740589\pi$
$230$	9.31953	+	12.7696i	0.614512	+	0.842004i
$231$	−29.6564	+	23.1573i	−1.95125	+	1.52364i
$232$	6.14016			0.403121
$233$	6.64757	−	4.82975i	0.435497	−	0.316407i	−0.348346	−	0.937366i	$-0.613257\pi$
$233$	6.64757	−	4.82975i	0.435497	−	0.316407i	0.783843	+	0.620959i	$0.213257\pi$
$234$	3.17647	+	9.77618i	0.207652	+	0.639089i
$235$	7.20870	−	9.96675i	0.470244	−	0.650159i
$236$	1.85448			0.120716
$237$	−2.41143	+	7.42163i	−0.156639	+	0.482086i
$238$	1.06591	+	0.774432i	0.0690929	+	0.0501989i
$239$	3.81550	−	2.77212i	0.246804	−	0.179314i	−0.457505	−	0.889207i	$-0.651257\pi$
$239$	3.81550	−	2.77212i	0.246804	−	0.179314i	0.704309	+	0.709893i	$0.251257\pi$
$240$	−2.90040	−	3.97414i	−0.187220	−	0.256529i
$241$	2.26880	−	1.64838i	0.146146	−	0.106181i	−0.512310	−	0.858801i	$-0.671210\pi$
$241$	2.26880	−	1.64838i	0.146146	−	0.106181i	0.658456	+	0.752619i	$0.271210\pi$
$242$	9.32540	+	5.83412i	0.599459	+	0.375031i
$243$	16.8480			1.08080
$244$	−3.16906	+	2.30246i	−0.202878	+	0.147400i
$245$	−0.0937932	−	43.7941i	−0.00599223	−	2.79790i
$246$	0.364783	−	0.265030i	0.0232577	−	0.0168977i
$247$	−15.0410	−	10.9279i	−0.957036	−	0.695327i
$248$	1.82728			0.116032
$249$	2.36250	+	7.27104i	0.149718	+	0.460783i
$250$	−0.0718337	−	11.1801i	−0.00454316	−	0.707092i
$251$	23.3553	+	16.9686i	1.47417	+	1.07105i	0.979378	+	0.202039i	$0.0647567\pi$
$251$	23.3553	+	16.9686i	1.47417	+	1.07105i	0.494795	+	0.869010i	$0.335243\pi$
$252$	7.68042	+	5.58015i	0.483821	+	0.351517i
$253$	−6.46924	+	22.5381i	−0.406718	+	1.41696i
$254$	−2.48403	−	7.64506i	−0.155862	−	0.479694i
$255$	−1.19650	−	0.385936i	−0.0749278	−	0.0241682i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	3.44860	+	10.6137i	0.215118	+	0.662064i	0.999145	+	0.0413378i	$0.0131620\pi$
$257$	3.44860	+	10.6137i	0.215118	+	0.662064i	−0.784028	+	0.620726i	$0.786838\pi$
$258$	4.88352	+	15.0299i	0.304035	+	0.935723i
$259$	11.3389	−	34.8977i	0.704567	−	2.16844i
$260$	0.0267360	+	12.4836i	0.00165810	+	0.774201i
$261$	9.14626	−	6.64515i	0.566139	−	0.411324i
$262$	−16.9469			−1.04698
$263$	5.21689	−	3.79029i	0.321687	−	0.233720i	−0.415208	−	0.909727i	$-0.636291\pi$
$263$	5.21689	−	3.79029i	0.321687	−	0.233720i	0.736895	+	0.676007i	$0.236291\pi$
$264$	2.01334	−	7.01426i	0.123913	−	0.431698i
$265$	−6.39551	−	8.76314i	−0.392873	−	0.538315i
$266$	−17.1705			−1.05279
$267$	9.76248	+	7.09286i	0.597454	+	0.434076i
$268$	−1.84215	−	5.66956i	−0.112527	−	0.346324i
$269$	−4.73870	−	14.5842i	−0.288923	−	0.889215i	−0.985195	−	0.171437i	$-0.945159\pi$
$269$	−4.73870	−	14.5842i	−0.288923	−	0.889215i	0.696272	−	0.717778i	$-0.254841\pi$
$270$	5.42588	+	1.75014i	0.330209	+	0.106510i
$271$	16.4521	−	11.9531i	0.999392	−	0.726101i	0.0374342	−	0.999299i	$-0.488082\pi$
$271$	16.4521	−	11.9531i	0.999392	−	0.726101i	0.961958	+	0.273198i	$0.0880815\pi$
$272$	−0.255531			−0.0154938
$273$	−19.5721	−	60.2368i	−1.18456	−	3.64570i
$274$	10.8454			0.655192
$275$	13.0266	−	10.2620i	0.785532	−	0.618820i
$276$	15.5557			0.936345
$277$	6.86503	+	21.1284i	0.412480	+	1.26948i	0.914486	+	0.404618i	$0.132595\pi$
$277$	6.86503	+	21.1284i	0.412480	+	1.26948i	−0.502006	+	0.864864i	$0.667405\pi$
$278$	18.3303			1.09938
$279$	2.72188	−	1.97756i	0.162954	−	0.118393i
$280$	6.79677	+	9.31294i	0.406184	+	0.556554i
$281$	7.06273	+	21.7368i	0.421327	+	1.29671i	0.906468	+	0.422275i	$0.138768\pi$
$281$	7.06273	+	21.7368i	0.421327	+	1.29671i	−0.485141	+	0.874436i	$0.661232\pi$
$282$	−3.74021	−	11.5112i	−0.222726	−	0.685482i
$283$	16.4198	+	11.9297i	0.976057	+	0.709147i	0.956824	−	0.290668i	$-0.0938776\pi$
$283$	16.4198	+	11.9297i	0.976057	+	0.709147i	0.0192328	+	0.999815i	$0.493878\pi$
$284$	−11.6751			−0.692790
$285$	15.5714	−	5.09635i	0.922371	−	0.301882i
$286$	−14.5941	+	11.3958i	−0.862965	+	0.673849i
$287$	−0.854826	+	0.621068i	−0.0504588	+	0.0366605i
$288$	−1.84122			−0.108495
$289$	13.7005	−	9.95397i	0.805910	−	0.585528i
$290$	13.0487	−	4.27070i	0.766247	−	0.250784i
$291$	7.24765	−	22.3060i	0.424865	−	1.30760i
$292$	0.570022	+	1.75435i	0.0333580	+	0.102665i
$293$	8.07498	+	24.8522i	0.471745	+	1.45188i	0.850297	+	0.526303i	$0.176422\pi$
$293$	8.07498	+	24.8522i	0.471745	+	1.45188i	−0.378552	+	0.925580i	$0.623578\pi$
$294$	−34.8632	−	25.3296i	−2.03326	−	1.47725i
$295$	3.94103	−	1.28986i	0.229456	−	0.0750984i
$296$	2.19913	+	6.76823i	0.127822	+	0.393395i
$297$	2.89005	+	7.94699i	0.167698	+	0.461131i
$298$	−18.4015	−	13.3694i	−1.06597	−	0.774471i
$299$	−31.9321	−	23.2000i	−1.84668	−	1.34169i
$300$	−8.92793	−	6.42827i	−0.515454	−	0.371136i
$301$	−11.4440	−	35.2209i	−0.659620	−	2.03010i
$302$	13.1221			0.755090
$303$	−12.6583	−	9.19681i	−0.727201	−	0.528343i
$304$	2.69414	−	1.95741i	0.154520	−	0.112265i
$305$	−5.13326	+	7.09724i	−0.293930	+	0.406387i
$306$	−0.380633	+	0.276546i	−0.0217594	+	0.0158091i
$307$	−11.7856			−0.672640			−0.336320	−	0.941748i	$-0.609182\pi$
$307$	−11.7856			−0.672640			−0.336320	+	0.941748i	$0.609182\pi$
$308$	−4.71804	+	16.4371i	−0.268835	+	0.936592i
$309$	−26.1773	+	19.0189i	−1.48917	+	1.08195i
$310$	3.88323	−	1.27094i	0.220552	−	0.0721844i
$311$	−12.1301	+	8.81304i	−0.687835	+	0.499741i	−0.875948	−	0.482406i	$-0.839763\pi$
$311$	−12.1301	+	8.81304i	−0.687835	+	0.499741i	0.188113	+	0.982147i	$0.439763\pi$
$312$	9.93783	+	7.22026i	0.562619	+	0.408767i
$313$	−2.14929	+	6.61482i	−0.121485	+	0.373892i	−0.993244	−	0.116042i	$-0.962979\pi$
$313$	−2.14929	+	6.61482i	−0.121485	+	0.373892i	0.871759	+	0.489934i	$0.162979\pi$
$314$	−2.21949			−0.125253
$315$	20.2032	+	6.51661i	1.13832	+	0.367169i
$316$	1.09597	+	3.37304i	0.0616530	+	0.189748i
$317$	−9.50102	+	6.90290i	−0.533631	+	0.387705i	−0.821714	−	0.569900i	$-0.806982\pi$
$317$	−9.50102	+	6.90290i	−0.533631	+	0.387705i	0.288083	+	0.957605i	$0.406982\pi$
$318$	−10.6751			−0.598630
$319$	16.8800	+	11.3923i	0.945097	+	0.637845i
$320$	−2.12810	−	0.686427i	−0.118965	−	0.0383724i
$321$	4.34708	−	13.3789i	0.242630	−	0.746739i
$322$	−36.4531			−2.03145
$323$	0.262959	−	0.809305i	0.0146314	−	0.0450309i
$324$	9.00725	−	6.54415i	0.500403	−	0.363564i
$325$	8.73963	+	26.5109i	0.484787	+	1.47056i
$326$	5.61724	+	17.2881i	0.311110	+	0.957499i
$327$	11.9845	−	8.70724i	0.662744	−	0.481511i
$328$	0.0633259	−	0.194897i	0.00349659	−	0.0107614i
$329$	8.76476	+	26.9752i	0.483217	+	1.48719i
$330$	−0.600030	−	16.3067i	−0.0330306	−	0.897652i
$331$	11.1615	−	34.3516i	0.613492	−	1.88813i	0.191650	−	0.981463i	$-0.438616\pi$
$331$	11.1615	−	34.3516i	0.613492	−	1.88813i	0.421842	−	0.906670i	$-0.361384\pi$
$332$	2.81106	+	2.04236i	0.154277	+	0.112089i
$333$	10.6007	+	7.70182i	0.580912	+	0.422057i
$334$	−10.5719	−	7.68092i	−0.578467	−	0.420281i
$335$	−7.85822	−	10.7673i	−0.429340	−	0.588283i
$336$	11.3448			0.618912
$337$	−26.5452	−	19.2862i	−1.44601	−	1.05059i	−0.986744	−	0.162286i	$-0.948113\pi$
$337$	−26.5452	−	19.2862i	−1.44601	−	1.05059i	−0.459264	−	0.888300i	$-0.651887\pi$
$338$	−5.61432	−	17.2791i	−0.305378	−	0.939858i
$339$	−0.498329	−	1.53370i	−0.0270655	−	0.0832991i
$340$	−0.543039	+	0.177731i	−0.0294504	+	0.00963881i
$341$	5.02339	+	3.39028i	0.272032	+	0.183594i
$342$	1.89475	−	5.83143i	0.102456	−	0.315328i
$343$	52.4982	+	38.1422i	2.83464	+	2.05948i
$344$	5.81073	+	4.22174i	0.313294	+	0.227621i
$345$	33.0581	−	10.8196i	1.77979	−	0.582506i
$346$	5.99554	+	4.35601i	0.322322	+	0.234181i
$347$	8.34471	+	6.06279i	0.447968	+	0.325468i	0.788793	−	0.614659i	$-0.210706\pi$
$347$	8.34471	+	6.06279i	0.447968	+	0.325468i	−0.340825	+	0.940127i	$0.610706\pi$
$348$	4.17484	−	12.8488i	0.223795	−	0.688770i
$349$	2.03085	−	6.25030i	0.108709	−	0.334571i	−0.881874	−	0.471485i	$-0.843718\pi$
$349$	2.03085	−	6.25030i	0.108709	−	0.334571i	0.990583	+	0.136914i	$0.0437183\pi$
$350$	20.9216	+	15.0639i	1.11831	+	0.805200i
$351$	−14.2342			−0.759768
$352$	−1.13352	−	3.11691i	−0.0604166	−	0.166132i
$353$	5.56517	+	17.1278i	0.296204	+	0.911623i	0.982814	+	0.184597i	$0.0590980\pi$
$353$	5.56517	+	17.1278i	0.296204	+	0.911623i	−0.686610	+	0.727026i	$0.740902\pi$
$354$	1.26090	−	3.88066i	0.0670162	−	0.206255i
$355$	−24.8113	+	8.12045i	−1.31684	+	0.430989i
$356$	5.48435			0.290670
$357$	2.34531	−	1.70396i	0.124127	−	0.0901834i
$358$	0.439903	+	1.35388i	0.0232496	+	0.0715549i
$359$	5.64528	+	4.10154i	0.297947	+	0.216471i	0.726707	−	0.686947i	$-0.241050\pi$
$359$	5.64528	+	4.10154i	0.297947	+	0.216471i	−0.428761	+	0.903418i	$0.641050\pi$
$360$	−3.91286	+	1.28064i	−0.206226	+	0.0674954i
$361$	−2.44437	−	7.52301i	−0.128651	−	0.395948i
$362$	−12.8869	+	9.36287i	−0.677319	+	0.492101i
$363$	18.5490	−	15.5475i	0.973568	−	0.816031i
$364$	−23.2882	−	16.9199i	−1.22063	−	0.886841i
$365$	2.43159	+	3.33177i	0.127275	+	0.174393i
$366$	2.66338	+	8.19703i	0.139217	+	0.428466i
$367$	−11.8914			−0.620726			−0.310363	−	0.950618i	$-0.600451\pi$
$367$	−11.8914			−0.620726			−0.310363	+	0.950618i	$0.600451\pi$
$368$	5.71967	−	4.15558i	0.298158	−	0.216625i
$369$	−0.116597	−	0.358849i	−0.00606980	−	0.0186809i
$370$	9.38102	+	12.8539i	0.487696	+	0.668241i
$371$	25.0159			1.29876
$372$	1.24241	−	3.82374i	0.0644159	−	0.198252i
$373$	9.56970	+	6.95279i	0.495500	+	0.360002i	0.807296	−	0.590147i	$-0.200930\pi$
$373$	9.56970	+	6.95279i	0.495500	+	0.360002i	−0.311795	+	0.950149i	$0.600930\pi$
$374$	−0.702482	−	0.474104i	−0.0363245	−	0.0245153i
$375$	−23.4442	−	7.45130i	−1.21065	−	0.384783i
$376$	−4.45035	−	3.23337i	−0.229509	−	0.166748i
$377$	−27.7328	+	20.1491i	−1.42831	+	1.03773i
$378$	−10.6355	+	7.72712i	−0.547030	+	0.397440i
$379$	14.3972	+	10.4601i	0.739532	+	0.537302i	0.892565	−	0.450919i	$-0.148904\pi$
$379$	14.3972	+	10.4601i	0.739532	+	0.537302i	−0.153032	+	0.988221i	$0.548904\pi$
$380$	4.36398	−	6.03364i	0.223868	−	0.309519i
$381$	−17.6869			−0.906128
$382$	4.08399	−	12.5692i	0.208955	−	0.643098i
$383$	14.5839	−	10.5958i	0.745200	−	0.541420i	−0.149135	−	0.988817i	$-0.547649\pi$
$383$	14.5839	−	10.5958i	0.745200	−	0.541420i	0.894335	+	0.447397i	$0.147649\pi$
$384$	−1.78006	+	1.29329i	−0.0908384	+	0.0659980i
$385$	1.40610	+	38.2128i	0.0716616	+	1.94750i
$386$	−3.44847	−	2.50546i	−0.175523	−	0.127525i
$387$	13.2245			0.672239
$388$	−3.29397	−	10.1378i	−0.167226	−	0.514669i
$389$	−6.37851	+	19.6310i	−0.323403	+	0.995332i	0.648753	+	0.760999i	$0.275291\pi$
$389$	−6.37851	+	19.6310i	−0.323403	+	0.995332i	−0.972156	+	0.234333i	$0.924709\pi$
$390$	26.1413	+	8.43196i	1.32371	+	0.426969i
$391$	0.558262	−	1.71816i	0.0282325	−	0.0868908i
$392$	−19.5854			−0.989210
$393$	−11.5226	+	35.4628i	−0.581237	+	1.78886i
$394$	−3.63238	+	2.63908i	−0.182997	+	0.132955i
$395$	4.67516	+	6.40591i	0.235233	+	0.322316i
$396$	−5.06172	−	3.41615i	−0.254361	−	0.171668i
$397$	3.94512	+	12.1418i	0.198000	+	0.609381i	0.999928	+	0.0119610i	$0.00380740\pi$
$397$	3.94512	+	12.1418i	0.198000	+	0.609381i	−0.801929	+	0.597420i	$0.796193\pi$
$398$	−2.84391	−	8.75265i	−0.142552	−	0.438731i
$399$	−11.6746	+	35.9309i	−0.584463	+	1.79879i
$400$	−4.99995	+	0.0214168i	−0.249998	+	0.00107084i
$401$	30.2560	−	21.9823i	1.51091	−	1.09774i	0.545140	−	0.838345i	$-0.316476\pi$
$401$	30.2560	−	21.9823i	1.51091	−	1.09774i	0.965771	−	0.259397i	$-0.0835237\pi$
$402$	−13.1166			−0.654196
$403$	−8.25313	+	5.99625i	−0.411118	+	0.298695i
$404$	−7.11117			−0.353794
$405$	14.5900	−	20.1721i	0.724982	−	1.00236i
$406$	−9.78326	+	30.1098i	−0.485535	+	1.49432i
$407$	−6.51192	+	22.6868i	−0.322784	+	1.12454i
$408$	−0.173741	+	0.534721i	−0.00860147	+	0.0264726i
$409$	−23.9067			−1.18211			−0.591054	−	0.806632i	$-0.701288\pi$
$409$	−23.9067			−1.18211			−0.591054	+	0.806632i	$0.701288\pi$
$410$	−0.000981383	−	0.458229i	−4.84671e−5	−	0.0226303i
$411$	7.37401	−	22.6949i	0.363733	−	1.11945i
$412$	−4.54435	+	13.9861i	−0.223884	+	0.689045i
$413$	−2.95478	+	9.09388i	−0.145395	+	0.447481i
$414$	4.02255	−	12.3801i	0.197698	−	0.608450i
$415$	7.39444	+	2.38510i	0.362979	+	0.117080i
$416$	5.58286			0.273722
$417$	12.4632	−	38.3577i	0.610324	−	1.87839i
$418$	11.0382	−	0.382498i	0.539896	−	0.0187086i
$419$	7.12780	−	21.9371i	0.348216	−	1.07170i	−0.611624	−	0.791149i	$-0.709483\pi$
$419$	7.12780	−	21.9371i	0.348216	−	1.07170i	0.959840	−	0.280549i	$-0.0905166\pi$
$420$	24.1094	−	7.89075i	1.17642	−	0.385029i
$421$	−23.9607			−1.16777			−0.583885	−	0.811836i	$-0.698468\pi$
$421$	−23.9607			−1.16777			−0.583885	+	0.811836i	$0.698468\pi$
$422$	4.63344	−	3.36639i	0.225553	−	0.163874i
$423$	−10.1284			−0.492462
$424$	−3.92511	+	2.85176i	−0.190620	+	0.138494i
$425$	−1.03042	+	0.755406i	−0.0499826	+	0.0366426i
$426$	−7.93817	+	24.4312i	−0.384606	+	1.18369i
$427$	−6.24132	−	19.2088i	−0.302039	−	0.929579i
$428$	−1.97569	−	6.08056i	−0.0954988	−	0.293915i
$429$	13.9239	+	38.2876i	0.672254	+	1.84854i
$430$	15.2850	+	4.93023i	0.737109	+	0.237757i
$431$	−14.3380	+	10.4172i	−0.690639	+	0.501779i	−0.876870	−	0.480727i	$-0.840373\pi$
$431$	−14.3380	+	10.4172i	−0.690639	+	0.501779i	0.186231	+	0.982506i	$0.440373\pi$
$432$	0.787880	−	2.42485i	0.0379069	−	0.116665i
$433$	1.43893			0.0691507			0.0345754	−	0.999402i	$-0.488992\pi$
$433$	1.43893			0.0691507			0.0345754	+	0.999402i	$0.488992\pi$
$434$	−2.91144	+	8.96050i	−0.139754	+	0.430118i
$435$	−0.0646989	−	30.2093i	−0.00310208	−	1.44843i
$436$	2.08050	−	6.40311i	0.0996376	−	0.306653i
$437$	7.27542	+	22.3914i	0.348030	+	1.07113i
$438$	4.05870			0.193932
$439$	−18.8875	−	13.7226i	−0.901451	−	0.654942i	0.0373874	−	0.999301i	$-0.488096\pi$
$439$	−18.8875	−	13.7226i	−0.901451	−	0.654942i	−0.938838	+	0.344358i	$0.888096\pi$
$440$	−4.57681	−	5.83548i	−0.218191	−	0.278196i
$441$	−29.1739	+	21.1961i	−1.38924	+	1.00934i
$442$	1.15414	−	0.838530i	0.0548967	−	0.0398848i
$443$	4.36982	−	13.4489i	0.207616	−	0.638977i	−0.791979	−	0.610548i	$-0.790949\pi$
$443$	4.36982	−	13.4489i	0.207616	−	0.638977i	0.999596	−	0.0284297i	$-0.00905066\pi$
$444$	15.6584			0.743113
$445$	11.6550	−	3.81456i	0.552501	−	0.180828i
$446$	−14.4525	−	10.5004i	−0.684348	−	0.497208i
$447$	−40.4883	+	29.4165i	−1.91503	+	1.39135i
$448$	4.17137	−	3.03068i	0.197079	−	0.143186i
$449$	5.85331	+	4.25268i	0.276235	+	0.200696i	0.717273	−	0.696792i	$-0.245390\pi$
$449$	5.85331	+	4.25268i	0.276235	+	0.200696i	−0.441039	+	0.897488i	$0.645390\pi$
$450$	−7.42465	+	5.44307i	−0.350001	+	0.256589i
$451$	0.535696	−	0.418300i	0.0252249	−	0.0196970i
$452$	−0.592945	−	0.430800i	−0.0278898	−	0.0202631i
$453$	8.92199	−	27.4591i	0.419192	−	1.29014i
$454$	8.69770			0.408203
$455$	−61.2591	−	19.7593i	−2.87187	−	0.926332i
$456$	−2.26424	−	6.96861i	−0.106033	−	0.326335i
$457$	−8.08823	+	5.87644i	−0.378351	+	0.274888i	−0.760665	−	0.649144i	$-0.775127\pi$
$457$	−8.08823	+	5.87644i	−0.378351	+	0.274888i	0.382314	+	0.924032i	$0.375127\pi$
$458$	27.3611			1.27850
$459$	−0.201328	−	0.619623i	−0.00939717	−	0.0289215i
$460$	9.26475	−	12.8094i	0.431971	−	0.597243i
$461$	−2.57792	−	1.87297i	−0.120066	−	0.0872327i	0.526132	−	0.850403i	$-0.323642\pi$
$461$	−2.57792	−	1.87297i	−0.120066	−	0.0872327i	−0.646198	+	0.763170i	$0.723642\pi$
$462$	31.1882	+	21.0489i	1.45101	+	0.979283i
$463$	25.8736	−	18.7983i	1.20245	−	0.873629i	0.207924	−	0.978145i	$-0.433329\pi$
$463$	25.8736	−	18.7983i	1.20245	−	0.873629i	0.994523	+	0.104516i	$0.0333293\pi$
$464$	−1.89741	−	5.83964i	−0.0880853	−	0.271099i
$465$	−0.0192540	−	8.99013i	−0.000892884	−	0.416907i
$466$	−6.64757	−	4.82975i	−0.307943	−	0.223734i
$467$	3.85185	+	11.8548i	0.178242	+	0.548573i	0.999767	−	0.0216002i	$-0.00687608\pi$
$467$	3.85185	+	11.8548i	0.178242	+	0.548573i	−0.821524	+	0.570173i	$0.806876\pi$
$468$	8.31611	−	6.04201i	0.384412	−	0.279292i
$469$	30.7372			1.41931
$470$	−11.7066	−	3.77599i	−0.539983	−	0.174173i
$471$	−1.50908	+	4.64447i	−0.0695348	+	0.214006i
$472$	−0.573065	−	1.76371i	−0.0263775	−	0.0811815i
$473$	8.14144	+	22.3871i	0.374344	+	1.02936i
$474$	7.80356			0.358429
$475$	5.07747	−	15.8577i	0.232970	−	0.727599i
$476$	0.407143	−	1.25306i	0.0186614	−	0.0574338i
$477$	−2.76047	+	8.49585i	−0.126393	+	0.388998i
$478$	−3.81550	−	2.77212i	−0.174517	−	0.126794i
$479$	−7.48959	−	5.44150i	−0.342208	−	0.248629i	0.403385	−	0.915030i	$-0.367834\pi$
$479$	−7.48959	−	5.44150i	−0.342208	−	0.248629i	−0.745593	+	0.666402i	$0.767834\pi$
$480$	−2.88335	+	3.98652i	−0.131607	+	0.181959i
$481$	−32.1428	−	23.3531i	−1.46558	−	1.06481i
$482$	−2.26880	−	1.64838i	−0.103341	−	0.0750815i
$483$	−24.7853	+	76.2813i	−1.12777	+	3.47092i
$484$	2.66687	−	10.6718i	0.121221	−	0.485083i
$485$	−14.0514	−	19.2532i	−0.638040	−	0.874243i
$486$	−5.20633	−	16.0234i	−0.236164	−	0.726838i
$487$	−1.63080	−	5.01909i	−0.0738986	−	0.227436i	0.907284	−	0.420518i	$-0.138152\pi$
$487$	−1.63080	−	5.01909i	−0.0738986	−	0.227436i	−0.981183	+	0.193082i	$0.938152\pi$
$488$	3.16906	+	2.30246i	0.143457	+	0.104227i
$489$	39.9962			1.80869
$490$	−41.6217	+	13.6223i	−1.88028	+	0.615394i
$491$	1.89176	+	1.37445i	0.0853742	+	0.0620280i	0.629654	−	0.776876i	$-0.283197\pi$
$491$	1.89176	+	1.37445i	0.0853742	+	0.0620280i	−0.544279	+	0.838904i	$0.683197\pi$
$492$	−0.364783	−	0.265030i	−0.0164457	−	0.0119485i
$493$	−1.26935	−	0.922235i	−0.0571685	−	0.0415354i
$494$	−5.74515	+	17.6818i	−0.258487	+	0.795540i
$495$	−13.1329	−	3.73919i	−0.590281	−	0.168064i
$496$	−0.564660	−	1.73784i	−0.0253540	−	0.0780315i
$497$	18.6022	−	57.2517i	0.834423	−	2.56809i
$498$	6.18512	−	4.49375i	0.277162	−	0.201370i
$499$	−7.82480	−	24.0823i	−0.350286	−	1.07807i	−0.958693	−	0.284444i	$-0.908191\pi$
$499$	−7.82480	−	24.0823i	−0.350286	−	1.07807i	0.608406	−	0.793626i	$-0.291809\pi$
$500$	−10.6107	+	3.52316i	−0.474526	+	0.157561i
$501$	−23.2611	+	16.9001i	−1.03923	+	0.755043i
$502$	8.92092	−	27.4558i	0.398160	−	1.22541i
$503$	18.7252			0.834916			0.417458	−	0.908696i	$-0.362921\pi$
$503$	18.7252			0.834916			0.417458	+	0.908696i	$0.362921\pi$
$504$	2.93366	−	9.02887i	0.130676	−	0.402178i
$505$	−15.1122	+	4.94607i	−0.672486	+	0.220097i
$506$	23.4341	−	0.812044i	1.04177	−	0.0360998i
$507$	−39.9753			−1.77537
$508$	−6.50328	+	4.72491i	−0.288536	+	0.209634i
$509$	11.3233	+	34.8497i	0.501898	+	1.54468i	0.805923	+	0.592020i	$0.201669\pi$
$509$	11.3233	+	34.8497i	0.501898	+	1.54468i	−0.304025	+	0.952664i	$0.598331\pi$
$510$	0.00269253	+	1.25720i	0.000119227	+	0.0556698i
$511$	−9.51109			−0.420746
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	6.86907	+	4.99067i	0.303277	+	0.220344i
$514$	9.02854	−	6.55962i	0.398232	−	0.289332i
$515$	0.0704254	+	32.8832i	0.00310331	+	1.44901i
$516$	12.7852	−	9.28901i	0.562838	−	0.408926i
$517$	−6.23540	−	17.1459i	−0.274233	−	0.754077i
$518$	−36.6936			−1.61222
$519$	13.1918	−	9.58444i	0.579058	−	0.420710i
$520$	11.8644	−	3.88308i	0.520287	−	0.170284i
$521$	−32.4310	+	23.5625i	−1.42083	+	1.03229i	−0.429194	+	0.903212i	$0.641202\pi$
$521$	−32.4310	+	23.5625i	−1.42083	+	1.03229i	−0.991634	+	0.129080i	$0.958798\pi$
$522$	−9.14626	−	6.64515i	−0.400321	−	0.290850i
$523$	17.3762			0.759808			0.379904	−	0.925026i	$-0.375957\pi$
$523$	17.3762			0.759808			0.379904	+	0.925026i	$0.375957\pi$
$524$	5.23687	+	16.1174i	0.228774	+	0.704093i
$525$	45.7476	−	33.5379i	1.99659	−	1.46372i
$526$	−5.21689	−	3.79029i	−0.227467	−	0.165265i
$527$	−0.377751	−	0.274452i	−0.0164551	−	0.0119553i
$528$	−7.29312	+	0.252723i	−0.317392	+	0.0109983i
$529$	8.33833	+	25.6628i	0.362536	+	1.11577i
$530$	−6.35792	+	8.79046i	−0.276170	+	0.381833i
$531$	−2.76239	−	2.00700i	−0.119878	−	0.0870962i
$532$	5.30599	+	16.3301i	0.230044	+	0.708002i
$533$	0.353540	+	1.08808i	0.0153135	+	0.0471301i
$534$	3.72894	−	11.4765i	0.161367	−	0.496636i
$535$	−8.42788	−	11.5479i	−0.364369	−	0.499259i
$536$	−4.82282	+	3.50398i	−0.208314	+	0.151349i
$537$	3.13222			0.135165
$538$	−12.4061	+	9.01354i	−0.534864	+	0.388601i
$539$	−53.8423	−	36.3381i	−2.31915	−	1.56519i
$540$	−0.0122101	−	5.70114i	−0.000525437	−	0.245338i
$541$	−5.50072			−0.236494			−0.118247	−	0.992984i	$-0.537728\pi$
$541$	−5.50072			−0.236494			−0.118247	+	0.992984i	$0.537728\pi$
$542$	−16.4521	−	11.9531i	−0.706677	−	0.513431i
$543$	10.8305	+	33.3330i	0.464783	+	1.43045i
$544$	0.0789633	+	0.243024i	0.00338552	+	0.0104196i
$545$	−0.0322421	−	15.0546i	−0.00138110	−	0.644867i
$546$	−51.2405	+	37.2284i	−2.19289	+	1.59323i
$547$	−16.7425			−0.715858			−0.357929	−	0.933749i	$-0.616517\pi$
$547$	−16.7425			−0.715858			−0.357929	+	0.933749i	$0.616517\pi$
$548$	−3.35140	−	10.3145i	−0.143165	−	0.440615i
$549$	7.21238			0.307817
$550$	−13.7852	−	9.21789i	−0.587801	−	0.393052i
$551$	20.4476			0.871097
$552$	−4.80699	−	14.7944i	−0.204599	−	0.629691i
$553$	−18.2868			−0.777632
$554$	17.9729	−	13.0581i	0.763595	−	0.554784i
$555$	33.2762	−	10.8910i	1.41250	−	0.462295i
$556$	−5.66437	−	17.4331i	−0.240223	−	0.739329i
$557$	12.3723	+	38.0780i	0.524231	+	1.61342i	0.765831	+	0.643042i	$0.222328\pi$
$557$	12.3723	+	38.0780i	0.524231	+	1.61342i	−0.241600	+	0.970376i	$0.577672\pi$
$558$	−2.72188	−	1.97756i	−0.115226	−	0.0837167i
$559$	−40.0987			−1.69599
$560$	6.75681	−	9.34196i	0.285527	−	0.394770i
$561$	−1.46974	+	1.14765i	−0.0620524	+	0.0484539i
$562$	18.4905	−	13.4341i	0.779973	−	0.566683i
$563$	−35.6301			−1.50163			−0.750815	−	0.660513i	$-0.770339\pi$
$563$	−35.6301			−1.50163			−0.750815	+	0.660513i	$0.770339\pi$
$564$	−9.79201	+	7.11431i	−0.412318	+	0.299566i
$565$	−1.55973	−	0.503096i	−0.0656183	−	0.0211654i
$566$	6.27181	−	19.3026i	0.263624	−	0.811351i
$567$	17.7394	+	54.5961i	0.744983	+	2.29282i
$568$	3.60780	+	11.1037i	0.151380	+	0.465900i
$569$	−21.1379	−	15.3576i	−0.886146	−	0.643823i	0.0487245	−	0.998812i	$-0.484484\pi$
$569$	−21.1379	−	15.3576i	−0.886146	−	0.643823i	−0.934870	+	0.354990i	$0.884484\pi$
$570$	−9.65875	−	13.2344i	−0.404561	−	0.554329i
$571$	5.49499	+	16.9118i	0.229958	+	0.707738i	0.997750	+	0.0670392i	$0.0213553\pi$
$571$	5.49499	+	16.9118i	0.229958	+	0.707738i	−0.767792	+	0.640699i	$0.778645\pi$
$572$	15.3479	+	10.3583i	0.641727	+	0.433101i
$573$	−23.5254	−	17.0922i	−0.982789	−	0.714038i
$574$	0.854826	+	0.621068i	0.0356798	+	0.0259229i
$575$	10.7795	−	33.6658i	0.449536	−	1.40396i
$576$	0.568969	+	1.75111i	0.0237070	+	0.0729627i
$577$	−24.0447			−1.00099			−0.500496	−	0.865739i	$-0.666849\pi$
$577$	−24.0447			−1.00099			−0.500496	+	0.865739i	$0.666849\pi$
$578$	−13.7005	−	9.95397i	−0.569864	−	0.414031i
$579$	−7.58760	+	5.51272i	−0.315330	+	0.229101i
$580$	−8.09396	−	11.0903i	−0.336083	−	0.460502i
$581$	−14.4941	+	10.5306i	−0.601317	+	0.436882i
$582$	−23.4539			−0.972196
$583$	−16.0816	+	0.557264i	−0.666033	+	0.0230795i
$584$	1.49234	−	1.08425i	0.0617533	−	0.0448664i
$585$	13.4705	−	18.6243i	0.556936	−	0.770019i
$586$	21.1406	−	15.3595i	0.873309	−	0.634496i
$587$	−30.7289	−	22.3258i	−1.26832	−	0.921485i	−0.269182	−	0.963089i	$-0.586753\pi$
$587$	−30.7289	−	22.3258i	−1.26832	−	0.921485i	−0.999134	+	0.0416040i	$0.986753\pi$
$588$	−13.3165	+	40.9841i	−0.549165	+	1.69016i
$589$	6.08509			0.250732
$590$	−2.44457	−	3.34956i	−0.100641	−	0.137899i
$591$	3.05277	+	9.39545i	0.125574	+	0.386477i
$592$	5.75740	−	4.18300i	0.236628	−	0.171920i
$593$	2.19475			0.0901278			0.0450639	−	0.998984i	$-0.485651\pi$
$593$	2.19475			0.0901278			0.0450639	+	0.998984i	$0.485651\pi$
$594$	6.66496	−	5.20436i	0.273467	−	0.213537i
$595$	−0.00630963	−	2.94611i	−0.000258670	−	0.120779i
$596$	−7.02873	+	21.6322i	−0.287908	+	0.886090i
$597$	−20.2493			−0.828750
$598$	−12.1970	+	37.5384i	−0.498771	+	1.53506i
$599$	−1.86021	+	1.35152i	−0.0760063	+	0.0552218i	−0.625140	−	0.780513i	$-0.714958\pi$
$599$	−1.86021	+	1.35152i	−0.0760063	+	0.0552218i	0.549133	+	0.835735i	$0.314958\pi$
$600$	−3.35477	+	10.4774i	−0.136958	+	0.427738i
$601$	5.09992	+	15.6959i	0.208030	+	0.640250i	0.999575	+	0.0291398i	$0.00927682\pi$
$601$	5.09992	+	15.6959i	0.208030	+	0.640250i	−0.791545	+	0.611110i	$0.790723\pi$
$602$	−29.9607	+	21.7677i	−1.22111	+	0.887187i
$603$	−3.39181	+	10.4389i	−0.138125	+	0.425106i
$604$	−4.05494	−	12.4798i	−0.164993	−	0.507797i
$605$	−1.75517	−	24.5340i	−0.0713577	−	0.997451i
$606$	−4.83505	+	14.8807i	−0.196410	+	0.604489i
$607$	−27.4481	−	19.9422i	−1.11409	−	0.809430i	−0.130783	−	0.991411i	$-0.541749\pi$
$607$	−27.4481	−	19.9422i	−1.11409	−	0.809430i	−0.983302	+	0.181981i	$0.941749\pi$
$608$	−2.69414	−	1.95741i	−0.109262	−	0.0793834i
$609$	56.3555	+	40.9447i	2.28364	+	1.65916i
$610$	8.33614	+	2.68885i	0.337521	+	0.108868i
$611$	30.7109			1.24243
$612$	0.380633	+	0.276546i	0.0153862	+	0.0111787i
$613$	−9.29331	−	28.6019i	−0.375353	−	1.15522i	−0.943240	−	0.332112i	$-0.892239\pi$
$613$	−9.29331	−	28.6019i	−0.375353	−	1.15522i	0.567887	−	0.823107i	$-0.307761\pi$
$614$	3.64195	+	11.2088i	0.146977	+	0.452349i
$615$	−0.959553	−	0.309507i	−0.0386929	−	0.0124805i
$616$	17.0906	−	0.592227i	0.688599	−	0.0238615i
$617$	−7.47035	+	22.9914i	−0.300745	+	0.925598i	0.680486	+	0.732761i	$0.261769\pi$
$617$	−7.47035	+	22.9914i	−0.300745	+	0.925598i	−0.981231	+	0.192837i	$0.938231\pi$
$618$	26.1773	+	19.0189i	1.05301	+	0.765053i
$619$	11.7846	+	8.56202i	0.473663	+	0.344136i	0.798867	−	0.601507i	$-0.205433\pi$
$619$	11.7846	+	8.56202i	0.473663	+	0.344136i	−0.325204	+	0.945644i	$0.605433\pi$
$620$	−2.40872	−	3.30043i	−0.0967364	−	0.132548i
$621$	14.5831	+	10.5952i	0.585198	+	0.425171i
$622$	12.1301	+	8.81304i	0.486373	+	0.353371i
$623$	−8.73833	+	26.8938i	−0.350094	+	1.07748i
$624$	3.79591	−	11.6826i	0.151958	−	0.467679i
$625$	−20.0988	+	14.8674i	−0.803952	+	0.594694i
$626$	6.95524			0.277987
$627$	6.70472	−	23.3585i	0.267761	−	0.932848i
$628$	0.685859	+	2.11086i	0.0273688	+	0.0842324i
$629$	0.561946	−	1.72949i	0.0224062	−	0.0689593i
$630$	−0.0454639	−	21.2281i	−0.00181133	−	0.845748i
$631$	−22.0067			−0.876073			−0.438037	−	0.898957i	$-0.644326\pi$
$631$	−22.0067			−0.876073			−0.438037	+	0.898957i	$0.644326\pi$
$632$	2.86928	−	2.08465i	0.114134	−	0.0829231i
$633$	−3.89409	−	11.9848i	−0.154776	−	0.476352i
$634$	9.50102	+	6.90290i	0.377334	+	0.274149i
$635$	−10.5340	+	14.5644i	−0.418031	+	0.577969i
$636$	3.29879	+	10.1526i	0.130805	+	0.402578i
$637$	88.4598	−	64.2698i	3.50490	−	2.54646i
$638$	5.61850	−	19.5742i	0.222438	−	0.774951i
$639$	17.3910	+	12.6353i	0.687977	+	0.499845i
$640$	0.00478894	+	2.23606i	0.000189300	+	0.0883881i
$641$	4.91894	+	15.1389i	0.194287	+	0.597953i	0.999984	+	0.00562547i	$0.00179065\pi$
$641$	4.91894	+	15.1389i	0.194287	+	0.597953i	−0.805698	+	0.592327i	$0.798209\pi$
$642$	−14.0674			−0.555197
$643$	−37.3659	+	27.1479i	−1.47357	+	1.07061i	−0.494006	+	0.869458i	$0.664468\pi$
$643$	−37.3659	+	27.1479i	−1.47357	+	1.07061i	−0.979560	+	0.201150i	$0.935532\pi$
$644$	11.2646	+	34.6689i	0.443888	+	1.36615i
$645$	20.7096	−	28.6331i	0.815439	−	1.12743i
$646$	−0.850953			−0.0334803
$647$	7.73665	−	23.8110i	0.304159	−	0.936106i	−0.675830	−	0.737057i	$-0.736215\pi$
$647$	7.73665	−	23.8110i	0.304159	−	0.936106i	0.979990	−	0.199049i	$-0.0637852\pi$
$648$	−9.00725	−	6.54415i	−0.353838	−	0.257078i
$649$	1.69692	−	5.91189i	0.0666101	−	0.232062i
$650$	22.5126	−	16.5042i	0.883019	−	0.647348i
$651$	16.7711	+	12.1849i	0.657310	+	0.477564i
$652$	14.7061	−	10.6846i	0.575937	−	0.418443i
$653$	24.8631	−	18.0641i	0.972970	−	0.706904i	0.0168433	−	0.999858i	$-0.494638\pi$
$653$	24.8631	−	18.0641i	0.972970	−	0.706904i	0.956126	+	0.292954i	$0.0946384\pi$
$654$	−11.9845	−	8.70724i	−0.468631	−	0.340480i
$655$	22.3393	+	30.6094i	0.872870	+	1.19601i
$656$	−0.204927			−0.00800105
$657$	1.04954	−	3.23014i	0.0409463	−	0.126020i
$658$	22.9464	−	16.6716i	0.894546	−	0.649925i
$659$	23.9010	−	17.3651i	0.931052	−	0.676449i	−0.0151983	−	0.999884i	$-0.504838\pi$
$659$	23.9010	−	17.3651i	0.931052	−	0.676449i	0.946250	+	0.323436i	$0.104838\pi$
$660$	−15.3231	+	5.60970i	−0.596452	+	0.218357i
$661$	3.66772	+	2.66476i	0.142658	+	0.103647i	0.656825	−	0.754043i	$-0.271899\pi$
$661$	3.66772	+	2.66476i	0.142658	+	0.103647i	−0.514167	+	0.857690i	$0.671899\pi$
$662$	−36.1194			−1.40382
$663$	−0.969973	−	2.98527i	−0.0376706	−	0.115938i
$664$	1.07373	−	3.30460i	0.0416688	−	0.128243i
$665$	22.6342	+	31.0134i	0.877716	+	1.20265i
$666$	4.04909	−	12.4618i	0.156899	−	0.482885i
$667$	43.4103			1.68085
$668$	−4.03810	+	12.4280i	−0.156239	+	0.480853i
$669$	−31.7996	+	23.1038i	−1.22944	+	0.893243i
$670$	−7.81203	+	10.8009i	−0.301805	+	0.417275i
$671$	4.44018	+	12.2095i	0.171411	+	0.471342i
$672$	−3.50575	−	10.7896i	−0.135237	−	0.416218i
$673$	−1.33441	−	4.10691i	−0.0514379	−	0.158310i	0.922038	−	0.387100i	$-0.126523\pi$
$673$	−1.33441	−	4.10691i	−0.0514379	−	0.158310i	−0.973476	+	0.228790i	$0.926523\pi$
$674$	−10.1394	+	31.2057i	−0.390553	+	1.20200i
$675$	−3.99130	−	12.1072i	−0.153625	−	0.466008i
$676$	−14.6985	+	10.6791i	−0.565326	+	0.410733i
$677$	−18.6157			−0.715459			−0.357729	−	0.933825i	$-0.616449\pi$
$677$	−18.6157			−0.715459			−0.357729	+	0.933825i	$0.616449\pi$
$678$	−1.30464	+	0.947879i	−0.0501045	+	0.0364031i
$679$	54.9615			2.10923
$680$	0.336840	+	0.461539i	0.0129172	+	0.0176992i
$681$	5.91376	−	18.2007i	0.226616	−	0.697452i
$682$	1.67203	−	5.82518i	0.0640255	−	0.223058i
$683$	−6.67436	+	20.5416i	−0.255387	+	0.786001i	0.738366	+	0.674400i	$0.235598\pi$
$683$	−6.67436	+	20.5416i	−0.255387	+	0.786001i	−0.993753	+	0.111601i	$0.964402\pi$
$684$	−6.13153			−0.234445
$685$	−14.2963	−	19.5889i	−0.546235	−	0.748452i
$686$	20.0525	−	61.7153i	0.765609	−	2.35630i
$687$	18.6035	−	57.2556i	0.709767	−	2.18444i
$688$	2.21950	−	6.83093i	0.0846177	−	0.260427i
$689$	8.37015	−	25.7607i	0.318877	−	0.981404i
$690$	−20.5056	−	28.0967i	−0.780633	−	1.06962i
$691$	42.0909			1.60121			0.800606	−	0.599191i	$-0.204511\pi$
$691$	42.0909			1.60121			0.800606	+	0.599191i	$0.204511\pi$
$692$	2.29009	−	7.04818i	0.0870562	−	0.267932i
$693$	24.8169	−	19.3783i	0.942714	−	0.736122i
$694$	3.18740	−	9.80980i	0.120992	−	0.372375i
$695$	−24.1629	−	33.1081i	−0.916553	−	1.25586i
$696$	−13.5101			−0.512098
$697$	−0.0423643	+	0.0307794i	−0.00160466	+	0.00116585i
$698$	−6.57196			−0.248752
$699$	−14.6265	+	10.6268i	−0.553225	+	0.401942i
$700$	7.86152	−	24.5526i	0.297137	−	0.928001i
$701$	11.7352	−	36.1172i	0.443232	−	1.36413i	−0.441180	−	0.897419i	$-0.645440\pi$
$701$	11.7352	−	36.1172i	0.443232	−	1.36413i	0.884412	−	0.466708i	$-0.154560\pi$
$702$	4.39862	+	13.5376i	0.166015	+	0.510943i
$703$	7.32342	+	22.5392i	0.276208	+	0.850081i
$704$	−2.61408	+	2.04122i	−0.0985220	+	0.0769313i
$705$	−15.8611	+	21.9296i	−0.597365	+	0.825917i
$706$	14.5698	−	10.5856i	0.548342	−	0.398394i
$707$	11.3304	−	34.8713i	0.426123	−	1.31147i
$708$	−4.08037			−0.153350
$709$	4.30744	−	13.2569i	0.161769	−	0.497874i	−0.837015	−	0.547181i	$-0.815701\pi$
$709$	4.30744	−	13.2569i	0.161769	−	0.497874i	0.998784	+	0.0493063i	$0.0157011\pi$
$710$	15.3901	+	21.0875i	0.577580	+	0.791401i
$711$	2.01792	−	6.21052i	0.0756779	−	0.232913i
$712$	−1.69476	−	5.21592i	−0.0635137	−	0.195475i
$713$	12.9187			0.483808
$714$	−2.34531	−	1.70396i	−0.0877709	−	0.0637693i
$715$	39.8210	+	11.3378i	1.48922	+	0.424009i
$716$	1.15168	−	0.836745i	0.0430403	−	0.0312706i
$717$	−8.39515	+	6.09943i	−0.313523	+	0.227788i
$718$	2.15631	−	6.63643i	0.0804726	−	0.247669i
$719$	−2.65136			−0.0988792			−0.0494396	−	0.998777i	$-0.515744\pi$
$719$	−2.65136			−0.0988792			−0.0494396	+	0.998777i	$0.515744\pi$
$720$	2.42710	+	3.32561i	0.0904526	+	0.123938i
$721$	−61.3435	−	44.5687i	−2.28455	−	1.65982i
$722$	−6.39946	+	4.64948i	−0.238163	+	0.173036i
$723$	−4.99198	+	3.62689i	−0.185654	+	0.134885i
$724$	12.8869	+	9.36287i	0.478937	+	0.347968i
$725$	−24.9145	−	17.9389i	−0.925303	−	0.666235i
$726$	−20.5185	−	12.8367i	−0.761512	−	0.476414i
$727$	5.30484	+	3.85420i	0.196746	+	0.142944i	0.681797	−	0.731542i	$-0.261199\pi$
$727$	5.30484	+	3.85420i	0.196746	+	0.142944i	−0.485051	+	0.874486i	$0.661199\pi$
$728$	−8.89529	+	27.3769i	−0.329681	+	1.01466i
$729$	−3.66966			−0.135913
$730$	2.41730	−	3.34215i	0.0894681	−	0.123699i
$731$	−0.567151	−	1.74551i	−0.0209768	−	0.0645601i
$732$	6.97281	−	5.06604i	0.257722	−	0.187246i
$733$	15.6151			0.576757			0.288378	−	0.957517i	$-0.406884\pi$
$733$	15.6151			0.576757			0.288378	+	0.957517i	$0.406884\pi$
$734$	3.67465	+	11.3094i	0.135634	+	0.417438i
$735$	0.206371	+	96.3592i	0.00761211	+	3.55426i
$736$	−5.71967	−	4.15558i	−0.210830	−	0.153177i
$737$	−19.7596	+	0.684715i	−0.727856	+	0.0252218i
$738$	−0.305255	+	0.221781i	−0.0112366	+	0.00816386i
$739$	16.1404	+	49.6751i	0.593735	+	1.82733i	0.560927	+	0.827865i	$0.310445\pi$
$739$	16.1404	+	49.6751i	0.593735	+	1.82733i	0.0328078	+	0.999462i	$0.489555\pi$
$740$	9.32587	−	12.8939i	0.342826	−	0.473991i
$741$	33.0944	+	24.0445i	1.21575	+	0.883296i
$742$	−7.73033	−	23.7915i	−0.283789	−	0.873414i
$743$	−16.6581	+	12.1028i	−0.611126	+	0.444009i	−0.849811	−	0.527088i	$-0.823284\pi$
$743$	−16.6581	+	12.1028i	−0.611126	+	0.444009i	0.238685	+	0.971097i	$0.423284\pi$
$744$	−4.02052			−0.147399
$745$	0.108927	+	50.8602i	0.00399076	+	1.86338i
$746$	3.65530	−	11.2499i	0.133830	−	0.411886i
$747$	−1.97697	−	6.08450i	−0.0723337	−	0.222620i
$748$	−0.233821	+	0.814606i	−0.00854934	+	0.0297849i
$749$	32.9654			1.20453
$750$	0.158054	+	24.5993i	0.00577132	+	0.898241i
$751$	−2.77211	+	8.53169i	−0.101156	+	0.311326i	−0.988809	−	0.149187i	$-0.952334\pi$
$751$	−2.77211	+	8.53169i	−0.101156	+	0.311326i	0.887653	+	0.460513i	$0.152334\pi$
$752$	−1.69988	+	5.23170i	−0.0619883	+	0.190780i
$753$	−51.3881	−	37.3356i	−1.87269	−	1.36059i
$754$	27.7328	+	20.1491i	1.00997	+	0.733786i
$755$	−17.2975	−	23.7010i	−0.629520	−	0.862569i
$756$	10.6355	+	7.72712i	0.386808	+	0.281033i
$757$	−6.49694	−	4.72030i	−0.236135	−	0.171562i	0.463424	−	0.886136i	$-0.346621\pi$
$757$	−6.49694	−	4.72030i	−0.236135	−	0.171562i	−0.699560	+	0.714574i	$0.746621\pi$
$758$	5.49923	−	16.9249i	0.199741	−	0.614739i
$759$	14.2341	−	49.5901i	0.516666	−	1.80001i
$760$	−7.08688	−	2.28590i	−0.257068	−	0.0829182i
$761$	−7.90978	−	24.3438i	−0.286729	−	0.882462i	−0.985875	−	0.167483i	$-0.946436\pi$
$761$	−7.90978	−	24.3438i	−0.286729	−	0.882462i	0.699146	−	0.714979i	$-0.253564\pi$
$762$	5.46556	+	16.8213i	0.197996	+	0.609370i
$763$	28.0843	+	20.4044i	1.01672	+	0.738690i
$764$	−13.2161			−0.478141
$765$	1.00125	+	0.322956i	0.0362002	+	0.0116765i
$766$	−14.5839	−	10.5958i	−0.526936	−	0.382841i
$767$	8.37599	+	6.08551i	0.302439	+	0.219735i
$768$	1.78006	+	1.29329i	0.0642325	+	0.0466676i
$769$	−3.39948	+	10.4625i	−0.122588	+	0.377288i	−0.993454	−	0.114233i	$-0.963559\pi$
$769$	−3.39948	+	10.4625i	−0.122588	+	0.377288i	0.870866	+	0.491521i	$0.163559\pi$
$770$	35.9080	−	13.1457i	1.29404	−	0.473738i
$771$	−7.58787	−	23.3531i	−0.273270	−	0.841040i
$772$	−1.31720	+	4.05393i	−0.0474071	+	0.145904i
$773$	27.9756	−	20.3254i	1.00621	−	0.731055i	0.0428004	−	0.999084i	$-0.486372\pi$
$773$	27.9756	−	20.3254i	1.00621	−	0.731055i	0.963411	+	0.268028i	$0.0863720\pi$
$774$	−4.08660	−	12.5772i	−0.146890	−	0.452080i
$775$	−7.41443	−	5.33853i	−0.266334	−	0.191765i
$776$	−8.62373	+	6.26551i	−0.309574	+	0.224919i
$777$	−24.9488	+	76.7846i	−0.895034	+	2.75463i
$778$	20.6413			0.740026
$779$	0.210884	−	0.649035i	0.00755571	−	0.0232541i
$780$	−0.0588266	−	27.4674i	−0.00210633	−	0.983492i
$781$	−10.6832	+	37.2190i	−0.382275	+	1.33180i
$782$	−1.80658			−0.0646030
$783$	12.6653	−	9.20188i	0.452621	−	0.328848i
$784$	6.05221	+	18.6268i	0.216150	+	0.665242i
$785$	2.92573	+	4.00883i	0.104424	+	0.143081i
$786$	37.2878			1.33001
$787$	−13.5745	+	41.7779i	−0.483878	+	1.48922i	0.349722	+	0.936853i	$0.386276\pi$
$787$	−13.5745	+	41.7779i	−0.483878	+	1.48922i	−0.833600	+	0.552369i	$0.813724\pi$
$788$	3.63238	+	2.63908i	0.129398	+	0.0940133i
$789$	−11.4786	+	8.33970i	−0.408649	+	0.296901i
$790$	4.64768	−	6.42587i	0.165357	−	0.228622i
$791$	3.05728	−	2.22125i	0.108704	−	0.0789784i
$792$	−1.68479	+	5.86963i	−0.0598665	+	0.208568i
$793$	−21.8690			−0.776592
$794$	10.3285	−	7.50406i	0.366543	−	0.266309i
$795$	14.0719	+	19.2813i	0.499079	+	0.683839i
$796$	−7.44545	+	5.40943i	−0.263897	+	0.191732i
$797$	24.7230	+	17.9623i	0.875733	+	0.636258i	0.932119	−	0.362152i	$-0.117958\pi$
$797$	24.7230	+	17.9623i	0.875733	+	0.636258i	−0.0563859	+	0.998409i	$0.517958\pi$
$798$	37.7799			1.33740
$799$	0.434372	+	1.33686i	0.0153670	+	0.0472947i
$800$	1.56544	+	4.74862i	0.0553466	+	0.167889i
$801$	−8.16937	−	5.93540i	−0.288651	−	0.209717i
$802$	−30.2560	−	21.9823i	−1.06838	−	0.776220i
$803$	6.11427	−	0.211873i	0.215768	−	0.00747684i
$804$	4.05325	+	12.4746i	0.142947	+	0.439946i
$805$	48.0524	+	65.8415i	1.69363	+	2.32061i
$806$	8.25313	+	5.99625i	0.290704	+	0.211209i
$807$	10.4264	+	32.0893i	0.367028	+	1.12960i
$808$	2.19747	+	6.76312i	0.0773068	+	0.237926i
$809$	5.19210	−	15.9796i	0.182544	−	0.561814i	−0.817353	−	0.576137i	$-0.804559\pi$
$809$	5.19210	−	15.9796i	0.182544	−	0.561814i	0.999897	+	0.0143232i	$0.00455939\pi$
$810$	−23.6934	−	7.64238i	−0.832500	−	0.268526i
$811$	−32.3669	+	23.5159i	−1.13656	+	0.825756i	−0.986636	−	0.162942i	$-0.947902\pi$
$811$	−32.3669	+	23.5159i	−1.13656	+	0.825756i	−0.149920	+	0.988698i	$0.547902\pi$
$812$	31.6593			1.11102
$813$	−36.1991	+	26.3002i	−1.26956	+	0.922388i
$814$	23.5887	−	0.817402i	0.826785	−	0.0286499i
$815$	23.8211	−	32.9350i	0.834416	−	1.15366i
$816$	0.562238			0.0196823
$817$	19.3506	+	14.0590i	0.676990	+	0.491862i
$818$	7.38756	+	22.7366i	0.258300	+	0.794966i
$819$	16.3782	+	50.4069i	0.572301	+	1.76136i
$820$	−0.435499	+	0.142534i	−0.0152083	+	0.00497750i
$821$	29.8624	−	21.6963i	1.04220	−	0.757205i	0.0714890	−	0.997441i	$-0.477225\pi$
$821$	29.8624	−	21.6963i	1.04220	−	0.757205i	0.970714	+	0.240236i	$0.0772249\pi$
$822$	−23.8628			−0.832310
$823$	−0.681471	−	2.09735i	−0.0237546	−	0.0731091i	0.938476	−	0.345343i	$-0.112237\pi$
$823$	−0.681471	−	2.09735i	−0.0237546	−	0.0731091i	−0.962231	+	0.272234i	$0.912237\pi$
$824$	14.7058			0.512302
$825$	−28.6621	+	22.5792i	−0.997886	+	0.786107i
$826$	9.56188			0.332700
$827$	6.12248	+	18.8430i	0.212899	+	0.655237i	0.999296	+	0.0375151i	$0.0119442\pi$
$827$	6.12248	+	18.8430i	0.212899	+	0.655237i	−0.786397	+	0.617722i	$0.788056\pi$
$828$	−13.0172			−0.452380
$829$	38.3956	−	27.8961i	1.33354	−	0.968870i	0.333880	−	0.942616i	$-0.391642\pi$
$829$	38.3956	−	27.8961i	1.33354	−	0.968870i	0.999655	−	0.0262542i	$-0.00835794\pi$
$830$	−0.0166400	−	7.76956i	−0.000577582	−	0.269686i
$831$	−15.1050	−	46.4883i	−0.523986	−	1.61266i
$832$	−1.72520	−	5.30961i	−0.0598105	−	0.184078i
$833$	4.04886	+	2.94167i	0.140285	+	0.101923i
$834$	−40.3317			−1.39657
$835$	0.0625798	+	29.2199i	0.00216566	+	1.01120i
$836$	−3.77477	−	10.3798i	−0.130553	−	0.358991i
$837$	3.76912	−	2.73843i	0.130280	−	0.0946539i
$838$	−23.0660			−0.796803
$839$	−18.2360	+	13.2493i	−0.629578	+	0.457415i	−0.856254	−	0.516555i	$-0.827214\pi$
$839$	−18.2360	+	13.2493i	−0.629578	+	0.457415i	0.226676	+	0.973970i	$0.427214\pi$
$840$	−14.9548	−	20.4910i	−0.515989	−	0.707008i
$841$	2.68894	−	8.27570i	0.0927220	−	0.285369i
$842$	7.40425	+	22.7879i	0.255167	+	0.785324i
$843$	−15.5400	−	47.8271i	−0.535225	−	1.64725i
$844$	−4.63344	−	3.36639i	−0.159490	−	0.115876i
$845$	−23.8087	+	32.9178i	−0.819043	+	1.13241i
$846$	3.12986	+	9.63272i	0.107607	+	0.331180i
$847$	48.0827	+	30.0813i	1.65214	+	1.03360i
$848$	3.92511	+	2.85176i	0.134789	+	0.0979299i
$849$	−36.1281	−	26.2486i	−1.23991	−	0.900851i
$850$	1.03685	+	0.746552i	0.0355637	+	0.0256065i
$851$	15.5476	+	47.8507i	0.532966	+	1.64030i
$852$	25.6885			0.880072
$853$	−29.7707	−	21.6297i	−1.01933	−	0.740585i	−0.0531831	−	0.998585i	$-0.516937\pi$
$853$	−29.7707	−	21.6297i	−1.01933	−	0.740585i	−0.966145	+	0.258000i	$0.916937\pi$
$854$	−16.3400	+	11.8717i	−0.559143	+	0.406241i
$855$	−13.0304	+	4.26470i	−0.445629	+	0.145850i
$856$	−5.17243	+	3.75799i	−0.176790	+	0.128446i
$857$	−5.35261			−0.182842			−0.0914208	−	0.995812i	$-0.529141\pi$
$857$	−5.35261			−0.182842			−0.0914208	+	0.995812i	$0.529141\pi$
$858$	32.1110	−	25.0740i	1.09625	−	0.856012i
$859$	−15.6429	+	11.3652i	−0.533729	+	0.387777i	−0.821751	−	0.569847i	$-0.807002\pi$
$859$	−15.6429	+	11.3652i	−0.533729	+	0.387777i	0.288022	+	0.957624i	$0.407002\pi$
$860$	−0.0343964	−	16.0604i	−0.00117291	−	0.547656i
$861$	1.88086	−	1.36652i	0.0640994	−	0.0465709i
$862$	14.3380	+	10.4172i	0.488356	+	0.354811i
$863$	−7.79315	+	23.9849i	−0.265282	+	0.816454i	0.726346	+	0.687329i	$0.241217\pi$
$863$	−7.79315	+	23.9849i	−0.265282	+	0.816454i	−0.991628	+	0.129125i	$0.958783\pi$
$864$	−2.54963			−0.0867403
$865$	−0.0354903	−	16.5712i	−0.00120671	−	0.563438i
$866$	−0.444655	−	1.36851i	−0.0151100	−	0.0465038i
$867$	−30.1448	+	21.9015i	−1.02377	+	0.743814i
$868$	9.42163			0.319791
$869$	11.7558	−	0.407364i	0.398787	−	0.0138189i
$870$	−28.7108	+	9.39673i	−0.973387	+	0.318579i
$871$	10.2845	−	31.6524i	0.348476	−	1.07250i
$872$	−6.73262			−0.227995
$873$	−6.06493	+	18.6659i	−0.205267	+	0.631747i
$874$	19.0473	−	13.8387i	0.644284	−	0.468100i
$875$	−0.370382	−	57.6458i	−0.0125212	−	1.94878i
$876$	−1.25421	−	3.86005i	−0.0423757	−	0.130419i
$877$	13.5956	−	9.87775i	0.459089	−	0.333548i	−0.334085	−	0.942543i	$-0.608427\pi$
$877$	13.5956	−	9.87775i	0.459089	−	0.333548i	0.793174	+	0.608995i	$0.208427\pi$
$878$	−7.21438	+	22.2036i	−0.243474	+	0.749335i
$879$	−17.7672	−	54.6818i	−0.599273	−	1.84437i
$880$	−4.13556	+	6.15607i	−0.139410	+	0.207521i
$881$	−3.42279	+	10.5343i	−0.115317	+	0.354908i	−0.992013	−	0.126136i	$-0.959742\pi$
$881$	−3.42279	+	10.5343i	−0.115317	+	0.354908i	0.876696	+	0.481044i	$0.159742\pi$
$882$	29.1739	+	21.1961i	0.982338	+	0.713710i
$883$	−8.85803	−	6.43573i	−0.298096	−	0.216580i	0.428676	−	0.903458i	$-0.358980\pi$
$883$	−8.85803	−	6.43573i	−0.298096	−	0.216580i	−0.726772	+	0.686879i	$0.758980\pi$
$884$	−1.15414	−	0.838530i	−0.0388178	−	0.0282028i
$885$	−8.67136	+	2.83804i	−0.291485	+	0.0953998i
$886$	−14.1410			−0.475077
$887$	−22.0189	−	15.9977i	−0.739322	−	0.537149i	0.153177	−	0.988199i	$-0.451050\pi$
$887$	−22.0189	−	15.9977i	−0.739322	−	0.537149i	−0.892499	+	0.451050i	$0.851050\pi$
$888$	−4.83870	−	14.8920i	−0.162376	−	0.499742i
$889$	−12.8079	−	39.4187i	−0.429564	−	1.32206i
$890$	−7.22946	−	9.90582i	−0.242332	−	0.332044i
$891$	−12.6201	−	34.7024i	−0.422789	−	1.16257i
$892$	−5.52038	+	16.9900i	−0.184836	+	0.568867i
$893$	−14.8203	−	10.7676i	−0.495942	−	0.360323i
$894$	40.4883	+	29.4165i	1.35413	+	0.983834i
$895$	1.86550	−	2.57924i	0.0623568	−	0.0862144i
$896$	−4.17137	−	3.03068i	−0.139356	−	0.101248i
$897$	70.2594	+	51.0465i	2.34589	+	1.70439i
$898$	2.23576	−	6.88098i	0.0746084	−	0.229621i
$899$	3.46710	−	10.6706i	0.115634	−	0.355886i
$900$	7.47101	+	5.37926i	0.249034	+	0.179309i
$901$	1.23976			0.0413024
$902$	−0.563366	−	0.380215i	−0.0187580	−	0.0126598i
$903$	25.1799	+	77.4958i	0.837935	+	2.57890i
$904$	−0.226485	+	0.697048i	−0.00753277	+	0.0231835i
$905$	33.8987	+	10.9341i	1.12683	+	0.363463i
$906$	−28.8722			−0.959214
$907$	15.3657	−	11.1638i	0.510210	−	0.370689i	−0.302693	−	0.953088i	$-0.597886\pi$
$907$	15.3657	−	11.1638i	0.510210	−	0.370689i	0.812903	+	0.582399i	$0.197886\pi$
$908$	−2.68774	−	8.27200i	−0.0891956	−	0.274516i
$909$	10.5927	+	7.69601i	0.351336	+	0.255261i
$910$	0.137853	+	64.3668i	0.00456980	+	2.13374i
$911$	−7.31295	−	22.5070i	−0.242289	−	0.745689i	−0.996071	−	0.0885637i	$-0.971772\pi$
$911$	−7.31295	−	22.5070i	−0.242289	−	0.745689i	0.753782	−	0.657125i	$-0.228228\pi$
$912$	−5.92786	+	4.30684i	−0.196291	+	0.142614i
$913$	9.08306	−	7.09254i	0.300605	−	0.234729i
$914$	8.08823	+	5.87644i	0.267535	+	0.194375i
$915$	11.2946	−	15.6159i	0.373388	−	0.516246i
$916$	−8.45506	−	26.0220i	−0.279363	−	0.859791i
$917$	−87.3797			−2.88553
$918$	−0.527083	+	0.382948i	−0.0173963	+	0.0126392i
$919$	−14.0385	−	43.2061i	−0.463088	−	1.42524i	−0.861372	−	0.507975i	$-0.830394\pi$
$919$	−14.0385	−	43.2061i	−0.463088	−	1.42524i	0.398284	−	0.917262i	$-0.369606\pi$
$920$	−15.0455	−	4.85297i	−0.496034	−	0.159998i
$921$	25.9316			0.854475
$922$	−0.984676	+	3.03052i	−0.0324286	+	0.0998049i
$923$	−52.7321	−	38.3121i	−1.73570	−	1.26106i
$924$	10.3810	−	36.1662i	0.341510	−	1.18978i
$925$	10.8506	−	33.8879i	0.356766	−	1.11423i
$926$	−25.8736	−	18.7983i	−0.850259	−	0.617749i
$927$	21.9055	−	15.9153i	0.719471	−	0.522726i
$928$	−4.96750	+	3.60910i	−0.163066	+	0.118474i
$929$	−16.6760	−	12.1158i	−0.547121	−	0.397507i	0.279602	−	0.960116i	$-0.409798\pi$
$929$	−16.6760	−	12.1158i	−0.547121	−	0.397507i	−0.826723	+	0.562609i	$0.809798\pi$
$930$	−8.54417	+	2.79642i	−0.280175	+	0.0916981i
$931$	−65.2220			−2.13756
$932$	−2.53915	+	7.81469i	−0.0831725	+	0.255979i
$933$	26.6896	−	19.3911i	0.873778	−	0.634837i
$934$	10.0843	−	7.32665i	0.329967	−	0.239735i
$935$	0.0696849	+	1.89378i	0.00227894	+	0.0619334i
$936$	−8.31611	−	6.04201i	−0.271821	−	0.197489i
$937$	18.3152			0.598333			0.299167	−	0.954201i	$-0.403291\pi$
$937$	18.3152			0.598333			0.299167	+	0.954201i	$0.403291\pi$
$938$	−9.49832	−	29.2328i	−0.310131	−	0.954486i
$939$	4.72903	−	14.5544i	0.154326	−	0.474966i
$940$	0.0263437	+	12.3004i	0.000859236	+	0.401196i
$941$	−3.21889	+	9.90672i	−0.104933	+	0.322950i	−0.989715	−	0.143055i	$-0.954307\pi$
$941$	−3.21889	+	9.90672i	−0.104933	+	0.322950i	0.884782	+	0.466005i	$0.154307\pi$
$942$	4.88349			0.159113
$943$	0.447707	−	1.37790i	0.0145794	−	0.0448707i
$944$	−1.50030	+	1.09004i	−0.0488308	+	0.0354776i
$945$	27.9764	+	9.02388i	0.910072	+	0.293547i
$946$	18.7756	−	14.6610i	0.610446	−	0.476669i
$947$	−9.77364	−	30.0802i	−0.317601	−	0.977475i	−0.974671	−	0.223645i	$-0.928204\pi$
$947$	−9.77364	−	30.0802i	−0.317601	−	0.977475i	0.657070	−	0.753830i	$-0.271796\pi$
$948$	−2.41143	−	7.42163i	−0.0783197	−	0.241043i
$949$	−3.18235	+	9.79427i	−0.103303	+	0.317935i
$950$	−16.6506	+	0.0713208i	−0.540215	+	0.00231395i
$951$	20.9049	−	15.1883i	0.677887	−	0.492514i
$952$	−1.31754			−0.0427018
$953$	−4.16476	+	3.02587i	−0.134910	+	0.0980177i	−0.653193	−	0.757191i	$-0.726571\pi$
$953$	−4.16476	+	3.02587i	−0.134910	+	0.0980177i	0.518284	+	0.855209i	$0.326571\pi$
$954$	8.93307			0.289219
$955$	−28.0860	+	9.19226i	−0.908843	+	0.297455i
$956$	−1.45739	+	4.48538i	−0.0471354	+	0.145068i
$957$	−37.1406	−	25.0662i	−1.20059	−	0.810274i
$958$	−2.86077	+	8.80454i	−0.0924272	+	0.284462i
$959$	55.9197			1.80574
$960$	4.68242	+	1.51033i	0.151124	+	0.0487457i
$961$	−8.54774	+	26.3072i	−0.275733	+	0.848620i
$962$	−12.2774	+	37.7861i	−0.395841	+	1.21827i
$963$	−3.63769	+	11.1957i	−0.117223	+	0.360775i
$964$	−0.866603	+	2.66713i	−0.0279114	+	0.0859025i
$965$	0.0204131	+	9.53133i	0.000657121	+	0.306824i
$966$	80.2069			2.58061
$967$	13.5426	−	41.6800i	0.435502	−	1.34034i	−0.457069	−	0.889431i	$-0.651101\pi$
$967$	13.5426	−	41.6800i	0.435502	−	1.34034i	0.892571	−	0.450907i	$-0.148899\pi$
$968$	−10.9736	+	0.761435i	−0.352705	+	0.0244734i
$969$	−0.578583	+	1.78069i	−0.0185868	+	0.0572042i
$970$	−13.9688	+	19.3132i	−0.448510	+	0.620110i
$971$	37.3159			1.19752			0.598762	−	0.800927i	$-0.295659\pi$
$971$	37.3159			1.19752			0.598762	+	0.800927i	$0.295659\pi$
$972$	−13.6303	+	9.90303i	−0.437194	+	0.317640i
$973$	94.5127			3.02994
$974$	−4.26949	+	3.10197i	−0.136803	+	0.0993934i
$975$	−19.2296	−	58.3313i	−0.615840	−	1.86810i
$976$	1.21047	−	3.72545i	0.0387463	−	0.119249i
$977$	−0.771996	−	2.37596i	−0.0246983	−	0.0760137i	0.937948	−	0.346777i	$-0.112724\pi$
$977$	−0.771996	−	2.37596i	−0.0246983	−	0.0760137i	−0.962646	+	0.270763i	$0.912724\pi$
$978$	−12.3595	−	38.0386i	−0.395213	−	1.21634i
$979$	5.01840	−	17.4835i	0.160389	−	0.558777i
$980$	25.8174	+	35.3750i	0.824707	+	1.13001i
$981$	−10.0288	+	7.28633i	−0.320194	+	0.232635i
$982$	0.722590	−	2.22390i	0.0230588	−	0.0709676i
$983$	26.8608			0.856726			0.428363	−	0.903607i	$-0.359090\pi$
$983$	26.8608			0.856726			0.428363	+	0.903607i	$0.359090\pi$
$984$	−0.139335	+	0.428828i	−0.00444182	+	0.0136705i
$985$	9.55490	+	3.08197i	0.304445	+	0.0981997i
$986$	−0.484848	+	1.49221i	−0.0154407	+	0.0475216i
$987$	−19.2849	−	59.3529i	−0.613845	−	1.88922i
$988$	18.5917			0.591481
$989$	41.0813	+	29.8473i	1.30631	+	0.949089i
$990$	0.502113	+	13.6456i	0.0159582	+	0.433687i
$991$	−16.8238	+	12.2232i	−0.534426	+	0.388283i	−0.822011	−	0.569472i	$-0.807148\pi$
$991$	−16.8238	+	12.2232i	−0.534426	+	0.388283i	0.287585	+	0.957755i	$0.407148\pi$
$992$	−1.47830	+	1.07405i	−0.0469360	+	0.0341010i
$993$	−24.5584	+	75.5830i	−0.779337	+	2.39855i
$994$	−60.1980			−1.90936
$995$	−12.0602	+	16.6744i	−0.382333	+	0.528614i
$996$	−6.18512	−	4.49375i	−0.195983	−	0.142390i
$997$	−1.27293	+	0.924836i	−0.0403140	+	0.0292898i	−0.607760	−	0.794121i	$-0.707932\pi$
$997$	−1.27293	+	0.924836i	−0.0403140	+	0.0292898i	0.567446	+	0.823411i	$0.307932\pi$
$998$	−20.4856	+	14.8837i	−0.648460	+	0.471134i
$999$	14.6793	+	10.6651i	0.464431	+	0.337429i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.l.d.191.3	yes	48
11.3	even	5		550.2.i.d.91.10	✓	48
25.11	even	5		550.2.i.d.411.10	yes	48
275.36	even	5	inner	550.2.l.d.311.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.i.d.91.10	✓	48	11.3	even	5
550.2.i.d.411.10	yes	48	25.11	even	5
550.2.l.d.191.3	yes	48	1.1	even	1	trivial
550.2.l.d.311.3	yes	48	275.36	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:	\( N \)	\(=\)	\( 550 = 2 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	550.l (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} -2.20028 q^{3} +(-0.809017 + 0.587785i) q^{4} +(-1.31045 + 1.81183i) q^{5} +(0.679923 + 2.09259i) q^{6} +(-1.59332 - 4.90374i) q^{7} +(0.809017 + 0.587785i) q^{8} +1.84122 q^{9} +(2.12810 + 0.686427i) q^{10} +(1.13352 + 3.11691i) q^{11} +(1.78006 - 1.29329i) q^{12} -5.58286 q^{13} +(-4.17137 + 3.03068i) q^{14} +(2.88335 - 3.98652i) q^{15} +(0.309017 - 0.951057i) q^{16} +(-0.0789633 - 0.243024i) q^{17} +(-0.568969 - 1.75111i) q^{18} +(2.69414 + 1.95741i) q^{19} +(-0.00478894 - 2.23606i) q^{20} +(3.50575 + 10.7896i) q^{21} +(2.61408 - 2.04122i) q^{22} +(5.71967 + 4.15558i) q^{23} +(-1.78006 - 1.29329i) q^{24} +(-1.56544 - 4.74862i) q^{25} +(1.72520 + 5.30961i) q^{26} +2.54963 q^{27} +(4.17137 + 3.03068i) q^{28} +(4.96750 - 3.60910i) q^{29} +(-4.68242 - 1.51033i) q^{30} +(1.47830 - 1.07405i) q^{31} -1.00000 q^{32} +(-2.49405 - 6.85807i) q^{33} +(-0.206729 + 0.150197i) q^{34} +(10.9727 + 3.53928i) q^{35} +(-1.48958 + 1.08224i) q^{36} +(5.75740 + 4.18300i) q^{37} +(1.02907 - 3.16715i) q^{38} +12.2838 q^{39} +(-2.12514 + 0.695536i) q^{40} +(-0.0633259 - 0.194897i) q^{41} +(9.17818 - 6.66834i) q^{42} +7.18246 q^{43} +(-2.74911 - 1.85537i) q^{44} +(-2.41283 + 3.33598i) q^{45} +(2.18472 - 6.72387i) q^{46} -5.50094 q^{47} +(-0.679923 + 2.09259i) q^{48} +(-15.8449 + 11.5120i) q^{49} +(-4.03246 + 2.95623i) q^{50} +(0.173741 + 0.534721i) q^{51} +(4.51663 - 3.28152i) q^{52} +(-1.49926 + 4.61425i) q^{53} +(-0.787880 - 2.42485i) q^{54} +(-7.13272 - 2.03082i) q^{55} +(1.59332 - 4.90374i) q^{56} +(-5.92786 - 4.30684i) q^{57} +(-4.96750 - 3.60910i) q^{58} +(-1.50030 - 1.09004i) q^{59} +(0.0105370 + 4.91996i) q^{60} +3.91717 q^{61} +(-1.47830 - 1.07405i) q^{62} +(-2.93366 - 9.02887i) q^{63} +(0.309017 + 0.951057i) q^{64} +(7.31606 - 10.1152i) q^{65} +(-5.75171 + 4.49124i) q^{66} +(-1.84215 + 5.66956i) q^{67} +(0.206729 + 0.150197i) q^{68} +(-12.5849 - 9.14343i) q^{69} +(-0.0246923 - 11.5294i) q^{70} +(9.44536 + 6.86245i) q^{71} +(1.48958 + 1.08224i) q^{72} +(0.570022 - 1.75435i) q^{73} +(2.19913 - 6.76823i) q^{74} +(3.44440 + 10.4483i) q^{75} -3.33014 q^{76} +(13.4785 - 10.5247i) q^{77} +(-3.79591 - 11.6826i) q^{78} +(1.09597 - 3.37304i) q^{79} +(1.31820 + 1.80620i) q^{80} -11.1336 q^{81} +(-0.165789 + 0.120453i) q^{82} +(-1.07373 - 3.30460i) q^{83} +(-9.17818 - 6.66834i) q^{84} +(0.543795 + 0.175403i) q^{85} +(-2.21950 - 6.83093i) q^{86} +(-10.9299 + 7.94101i) q^{87} +(-0.915041 + 3.18790i) q^{88} +(-4.43693 - 3.22362i) q^{89} +(3.91831 + 1.26386i) q^{90} +(8.89529 + 27.3769i) q^{91} -7.06990 q^{92} +(-3.25267 + 2.36320i) q^{93} +(1.69988 + 5.23170i) q^{94} +(-7.07702 + 2.31623i) q^{95} +2.20028 q^{96} +(-3.29397 + 10.1378i) q^{97} +(15.8449 + 11.5120i) q^{98} +(2.08705 + 5.73893i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{2} - 22 q^{3} - 12 q^{4} - q^{5} - 3 q^{6} + 11 q^{7} + 12 q^{8} + 70 q^{9} + 6 q^{10} + 3 q^{11} + 8 q^{12} - 34 q^{13} - q^{14} + 7 q^{15} - 12 q^{16} - 9 q^{17} + 10 q^{18} - 6 q^{19}+ \cdots - 54 q^{99}+O(q^{100}) \) 48 * q + 12 * q^2 - 22 * q^3 - 12 * q^4 - q^5 - 3 * q^6 + 11 * q^7 + 12 * q^8 + 70 * q^9 + 6 * q^10 + 3 * q^11 + 8 * q^12 - 34 * q^13 - q^14 + 7 * q^15 - 12 * q^16 - 9 * q^17 + 10 * q^18 - 6 * q^19 + 19 * q^20 - 15 * q^21 - 8 * q^22 + 14 * q^23 - 8 * q^24 + 7 * q^25 - 16 * q^26 - 34 * q^27 + q^28 - q^29 - 12 * q^30 + 17 * q^31 - 48 * q^32 + 4 * q^34 - 41 * q^35 - 25 * q^36 - 23 * q^37 + q^38 - 20 * q^39 + 6 * q^40 + 29 * q^41 + 22 * q^43 + 13 * q^44 + 62 * q^45 - 9 * q^46 - 52 * q^47 + 3 * q^48 - 23 * q^49 - 2 * q^50 + 4 * q^51 + q^52 + 44 * q^53 - 11 * q^54 - 7 * q^55 - 11 * q^56 - 5 * q^57 + q^58 - 18 * q^59 + 2 * q^60 + 16 * q^61 - 17 * q^62 - 13 * q^63 - 12 * q^64 - 2 * q^65 + 20 * q^67 - 4 * q^68 - 2 * q^69 - 59 * q^70 + 39 * q^71 + 25 * q^72 - 42 * q^73 - 37 * q^74 + 20 * q^75 + 14 * q^76 - 13 * q^77 - 15 * q^78 + 53 * q^79 - 6 * q^80 + 56 * q^81 + 36 * q^82 + 14 * q^83 + 6 * q^85 + 13 * q^86 - 18 * q^87 + 17 * q^88 - 8 * q^89 + 28 * q^90 - 5 * q^91 - 46 * q^92 + 15 * q^93 - 13 * q^94 - 24 * q^95 + 22 * q^96 - 16 * q^97 + 23 * q^98 - 54 * q^99

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