LMFDB - Embedded newform 550.2.g.c.361.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [550,2,Mod(291,550)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("550.291"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [60] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.39177211117$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$15$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.3
Character	$\chi$	$=$	550.361
Dual form			550.2.g.c.291.3

$q$-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} +(-0.805027 - 2.47762i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.01112 - 1.99440i) q^{5} +(2.10759 - 1.53125i) q^{6} +(2.12811 + 1.54617i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-3.06348 + 2.22575i) q^{9} +(2.20924 + 0.345330i) q^{10} +(2.91080 - 1.58973i) q^{11} +(2.10759 + 1.53125i) q^{12} +(0.545747 - 0.396508i) q^{13} +(-0.812867 + 2.50175i) q^{14} +(-5.75535 - 0.899627i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.36235 - 0.989803i) q^{17} +(-3.06348 - 2.22575i) q^{18} +(-2.71273 - 1.97092i) q^{19} +(0.354265 + 2.20783i) q^{20} +(2.11762 - 6.51736i) q^{21} +(2.41141 + 2.27708i) q^{22} +(0.178275 - 0.129524i) q^{23} +(-0.805027 + 2.47762i) q^{24} +(-2.95527 - 4.03316i) q^{25} +(0.545747 + 0.396508i) q^{26} +(1.65797 + 1.20459i) q^{27} -2.63049 q^{28} +(1.67940 - 1.22016i) q^{29} +(-0.922904 - 5.75166i) q^{30} -8.09414 q^{31} +1.00000 q^{32} +(-6.28202 - 5.93208i) q^{33} +(1.36235 + 0.989803i) q^{34} +(5.23546 - 2.68095i) q^{35} +(1.17014 - 3.60133i) q^{36} +(-3.01983 - 9.29407i) q^{37} +(1.03617 - 3.18901i) q^{38} +(-1.42174 - 1.03295i) q^{39} +(-1.99029 + 1.01918i) q^{40} -2.05870 q^{41} +6.85276 q^{42} +12.0505 q^{43} +(-1.42047 + 2.99704i) q^{44} +(1.34148 + 8.36030i) q^{45} +(0.178275 + 0.129524i) q^{46} +(3.45347 + 10.6287i) q^{47} -2.60512 q^{48} +(-0.0248762 - 0.0765612i) q^{49} +(2.92254 - 4.05694i) q^{50} +(-3.54908 - 2.57856i) q^{51} +(-0.208457 + 0.641564i) q^{52} +(5.97027 + 4.33765i) q^{53} +(-0.633289 + 1.94906i) q^{54} +(-0.227385 - 7.41271i) q^{55} +(-0.812867 - 2.50175i) q^{56} +(-2.69935 + 8.30776i) q^{57} +(1.67940 + 1.22016i) q^{58} +(0.457738 + 1.40877i) q^{59} +(5.18496 - 2.65509i) q^{60} +(-3.42082 - 2.48537i) q^{61} +(-2.50123 - 7.69799i) q^{62} -9.96081 q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.238980 - 1.48936i) q^{65} +(3.70049 - 7.80767i) q^{66} +(4.09471 + 12.6022i) q^{67} +(-0.520370 + 1.60153i) q^{68} +(-0.464428 - 0.337427i) q^{69} +(4.16758 + 4.15075i) q^{70} +0.279865 q^{71} +3.78667 q^{72} +5.38052 q^{73} +(7.90601 - 5.74405i) q^{74} +(-7.61357 + 10.5688i) q^{75} +3.35312 q^{76} +(8.65250 + 1.11745i) q^{77} +(0.543056 - 1.67135i) q^{78} +(0.942252 + 0.684586i) q^{79} +(-1.58433 - 1.57794i) q^{80} +(-1.86064 + 5.72646i) q^{81} +(-0.636172 - 1.95794i) q^{82} +(-9.72480 + 7.06548i) q^{83} +(2.11762 + 6.51736i) q^{84} +(-0.596566 - 3.71788i) q^{85} +(3.72381 + 11.4607i) q^{86} +(-4.37505 - 3.17866i) q^{87} +(-3.28931 - 0.424807i) q^{88} +(-4.11165 + 2.98729i) q^{89} +(-7.53658 + 3.85930i) q^{90} +1.77448 q^{91} +(-0.0680950 + 0.209575i) q^{92} +(6.51601 + 20.0542i) q^{93} +(-9.04130 + 6.56889i) q^{94} +(-6.67370 + 3.41744i) q^{95} +(-0.805027 - 2.47762i) q^{96} +(7.94824 + 5.77473i) q^{97} +(0.0651268 - 0.0473174i) q^{98} +(-5.37884 + 11.3488i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 15 q^{2} - 4 q^{3} - 15 q^{4} + q^{6} - 3 q^{7} - 15 q^{8} - 17 q^{9} - 5 q^{10} + 7 q^{11} + q^{12} + 12 q^{13} - 3 q^{14} + 12 q^{15} - 15 q^{16} + q^{17} - 17 q^{18} + 3 q^{19} - 5 q^{20} - 4 q^{21}+ \cdots + 21 q^{99}+O(q^{100}) $ 60 * q - 15 * q^2 - 4 * q^3 - 15 * q^4 + q^6 - 3 * q^7 - 15 * q^8 - 17 * q^9 - 5 * q^10 + 7 * q^11 + q^12 + 12 * q^13 - 3 * q^14 + 12 * q^15 - 15 * q^16 + q^17 - 17 * q^18 + 3 * q^19 - 5 * q^20 - 4 * q^21 - 3 * q^22 - 3 * q^23 - 4 * q^24 + 8 * q^25 + 12 * q^26 + 2 * q^27 + 12 * q^28 + 18 * q^29 + 2 * q^30 - 20 * q^31 + 60 * q^32 + 10 * q^33 + q^34 - 19 * q^35 - 12 * q^36 - 36 * q^37 - 22 * q^38 + 13 * q^39 + 64 * q^41 + 46 * q^42 + 40 * q^43 - 8 * q^44 - 20 * q^45 - 3 * q^46 - 9 * q^47 + 6 * q^48 - 30 * q^49 + 18 * q^50 - 48 * q^51 - 8 * q^52 + 31 * q^53 - 8 * q^54 - 42 * q^55 - 3 * q^56 + 30 * q^57 + 18 * q^58 + 23 * q^59 - 8 * q^60 - 41 * q^61 - 5 * q^62 + 6 * q^63 - 15 * q^64 - 7 * q^65 - 30 * q^66 - 40 * q^67 - 4 * q^68 - 22 * q^69 - 4 * q^70 + 4 * q^71 + 58 * q^72 + 74 * q^73 - 11 * q^74 + 35 * q^75 + 38 * q^76 + 22 * q^77 - 12 * q^78 - 45 * q^79 + 10 * q^80 + 24 * q^81 - 11 * q^82 + 16 * q^83 - 4 * q^84 + 9 * q^85 - 20 * q^86 + 68 * q^87 + 7 * q^88 + q^89 + 10 * q^90 + 10 * q^91 + 2 * q^92 - 40 * q^93 - 24 * q^94 + 24 * q^95 - 4 * q^96 + 6 * q^97 - 30 * q^98 + 21 * q^99

Character values

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

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$2$	0.309017	+	0.951057i	0.218508	+	0.672499i
$3$	−0.805027	−	2.47762i	−0.464783	−	1.43045i	−0.859256	−	0.511547i	$-0.829073\pi$
$3$	−0.805027	−	2.47762i	−0.464783	−	1.43045i	0.394473	−	0.918908i	$-0.370927\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	1.01112	−	1.99440i	0.452187	−	0.891923i
$5$	1.01112	−	1.99440i	0.452187	−	0.891923i
$6$	2.10759	−	1.53125i	0.860420	−	0.625131i
$7$	2.12811	+	1.54617i	0.804352	+	0.584396i	0.912188	−	0.409773i	$-0.134392\pi$
$7$	2.12811	+	1.54617i	0.804352	+	0.584396i	−0.107836	+	0.994169i	$0.534392\pi$
$8$	−0.809017	−	0.587785i	−0.286031	−	0.207813i
$9$	−3.06348	+	2.22575i	−1.02116	+	0.741916i
$10$	2.20924	+	0.345330i	0.698623	+	0.109203i
$11$	2.91080	−	1.58973i	0.877639	−	0.479322i
$11$	2.91080	−	1.58973i	0.877639	−	0.479322i
$12$	2.10759	+	1.53125i	0.608409	+	0.442035i
$13$	0.545747	−	0.396508i	0.151363	−	0.109972i	−0.509526	−	0.860455i	$-0.670179\pi$
$13$	0.545747	−	0.396508i	0.151363	−	0.109972i	0.660889	+	0.750483i	$0.270179\pi$
$14$	−0.812867	+	2.50175i	−0.217248	+	0.668620i
$15$	−5.75535	−	0.899627i	−1.48602	−	0.232283i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	1.36235	−	0.989803i	0.330418	−	0.240062i	−0.410190	−	0.912000i	$-0.634538\pi$
$17$	1.36235	−	0.989803i	0.330418	−	0.240062i	0.740608	+	0.671938i	$0.234538\pi$
$18$	−3.06348	−	2.22575i	−0.722069	−	0.524614i
$19$	−2.71273	−	1.97092i	−0.622343	−	0.452159i	0.231396	−	0.972860i	$-0.425671\pi$
$19$	−2.71273	−	1.97092i	−0.622343	−	0.452159i	−0.853739	+	0.520701i	$0.825671\pi$
$20$	0.354265	+	2.20783i	0.0792161	+	0.493685i
$21$	2.11762	−	6.51736i	0.462103	−	1.42221i
$22$	2.41141	+	2.27708i	0.514114	+	0.485476i
$23$	0.178275	−	0.129524i	0.0371729	−	0.0270077i	−0.569044	−	0.822307i	$-0.692686\pi$
$23$	0.178275	−	0.129524i	0.0371729	−	0.0270077i	0.606217	+	0.795300i	$0.292686\pi$
$24$	−0.805027	+	2.47762i	−0.164326	+	0.505742i
$25$	−2.95527	−	4.03316i	−0.591054	−	0.806632i
$26$	0.545747	+	0.396508i	0.107030	+	0.0777617i
$27$	1.65797	+	1.20459i	0.319077	+	0.231823i
$28$	−2.63049			−0.497117
$29$	1.67940	−	1.22016i	0.311857	−	0.226577i	−0.420836	−	0.907137i	$-0.638263\pi$
$29$	1.67940	−	1.22016i	0.311857	−	0.226577i	0.732693	+	0.680559i	$0.238263\pi$
$30$	−0.922904	−	5.75166i	−0.168498	−	1.05010i
$31$	−8.09414			−1.45375			−0.726876	−	0.686769i	$-0.759028\pi$
$31$	−8.09414			−1.45375			−0.726876	+	0.686769i	$0.759028\pi$
$32$	1.00000			0.176777
$33$	−6.28202	−	5.93208i	−1.09356	−	1.03264i
$34$	1.36235	+	0.989803i	0.233641	+	0.169750i
$35$	5.23546	−	2.68095i	0.884953	−	0.453164i
$36$	1.17014	−	3.60133i	0.195024	−	0.600222i
$37$	−3.01983	−	9.29407i	−0.496456	−	1.52794i	−0.814675	−	0.579918i	$-0.803085\pi$
$37$	−3.01983	−	9.29407i	−0.496456	−	1.52794i	0.318219	−	0.948017i	$-0.396915\pi$
$38$	1.03617	−	3.18901i	0.168089	−	0.517325i
$39$	−1.42174	−	1.03295i	−0.227660	−	0.165405i
$40$	−1.99029	+	1.01918i	−0.314693	+	0.161147i
$41$	−2.05870			−0.321514			−0.160757	−	0.986994i	$-0.551394\pi$
$41$	−2.05870			−0.321514			−0.160757	+	0.986994i	$0.551394\pi$
$42$	6.85276			1.05740
$43$	12.0505			1.83769			0.918843	−	0.394623i	$-0.129125\pi$
$43$	12.0505			1.83769			0.918843	+	0.394623i	$0.129125\pi$
$44$	−1.42047	+	2.99704i	−0.214144	+	0.451821i
$45$	1.34148	+	8.36030i	0.199977	+	1.24628i
$46$	0.178275	+	0.129524i	0.0262852	+	0.0190973i
$47$	3.45347	+	10.6287i	0.503740	+	1.55035i	0.802878	+	0.596143i	$0.203301\pi$
$47$	3.45347	+	10.6287i	0.503740	+	1.55035i	−0.299138	+	0.954210i	$0.596699\pi$
$48$	−2.60512			−0.376017
$49$	−0.0248762	−	0.0765612i	−0.00355375	−	0.0109373i
$50$	2.92254	−	4.05694i	0.413309	−	0.573738i
$51$	−3.54908	−	2.57856i	−0.496971	−	0.361070i
$52$	−0.208457	+	0.641564i	−0.0289078	+	0.0889689i
$53$	5.97027	+	4.33765i	0.820079	+	0.595822i	0.916735	−	0.399496i	$-0.130815\pi$
$53$	5.97027	+	4.33765i	0.820079	+	0.595822i	−0.0966561	+	0.995318i	$0.530815\pi$
$54$	−0.633289	+	1.94906i	−0.0861797	+	0.265234i
$55$	−0.227385	−	7.41271i	−0.0306606	−	0.999530i
$56$	−0.812867	−	2.50175i	−0.108624	−	0.334310i
$57$	−2.69935	+	8.30776i	−0.357538	+	1.10039i
$58$	1.67940	+	1.22016i	0.220516	+	0.160214i
$59$	0.457738	+	1.40877i	0.0595925	+	0.183407i	0.976421	−	0.215874i	$-0.0692600\pi$
$59$	0.457738	+	1.40877i	0.0595925	+	0.183407i	−0.916829	+	0.399280i	$0.869260\pi$
$60$	5.18496	−	2.65509i	0.669375	−	0.342771i
$61$	−3.42082	−	2.48537i	−0.437991	−	0.318219i	0.346845	−	0.937922i	$-0.387253\pi$
$61$	−3.42082	−	2.48537i	−0.437991	−	0.318219i	−0.784836	+	0.619703i	$0.787253\pi$
$62$	−2.50123	−	7.69799i	−0.317656	−	0.977645i
$63$	−9.96081			−1.25494
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	−0.238980	−	1.48936i	−0.0296418	−	0.184732i
$66$	3.70049	−	7.80767i	0.455499	−	0.961058i
$67$	4.09471	+	12.6022i	0.500248	+	1.53961i	0.808615	+	0.588338i	$0.200218\pi$
$67$	4.09471	+	12.6022i	0.500248	+	1.53961i	−0.308367	+	0.951268i	$0.599782\pi$
$68$	−0.520370	+	1.60153i	−0.0631041	+	0.194215i
$69$	−0.464428	−	0.337427i	−0.0559106	−	0.0406214i
$70$	4.16758	+	4.15075i	0.498121	+	0.496110i
$71$	0.279865			0.0332139			0.0166069	−	0.999862i	$-0.494714\pi$
$71$	0.279865			0.0332139			0.0166069	+	0.999862i	$0.494714\pi$
$72$	3.78667			0.446263
$73$	5.38052			0.629742			0.314871	−	0.949134i	$-0.398039\pi$
$73$	5.38052			0.629742			0.314871	+	0.949134i	$0.398039\pi$
$74$	7.90601	−	5.74405i	0.919054	−	0.667732i
$75$	−7.61357	+	10.5688i	−0.879139	+	1.22038i
$76$	3.35312			0.384629
$77$	8.65250	+	1.11745i	0.986044	+	0.127346i
$78$	0.543056	−	1.67135i	0.0614889	−	0.189244i
$79$	0.942252	+	0.684586i	0.106012	+	0.0770219i	0.639528	−	0.768768i	$-0.279130\pi$
$79$	0.942252	+	0.684586i	0.106012	+	0.0770219i	−0.533516	+	0.845790i	$0.679130\pi$
$80$	−1.58433	−	1.57794i	−0.177134	−	0.176419i
$81$	−1.86064	+	5.72646i	−0.206738	+	0.636273i
$82$	−0.636172	−	1.95794i	−0.0702535	−	0.216218i
$83$	−9.72480	+	7.06548i	−1.06744	+	0.775537i	−0.975450	−	0.220223i	$-0.929322\pi$
$83$	−9.72480	+	7.06548i	−1.06744	+	0.775537i	−0.0919860	+	0.995760i	$0.529322\pi$
$84$	2.11762	+	6.51736i	0.231051	+	0.711103i
$85$	−0.596566	−	3.71788i	−0.0647066	−	0.403260i
$86$	3.72381	+	11.4607i	0.401549	+	1.23584i
$87$	−4.37505	−	3.17866i	−0.469054	−	0.340788i
$88$	−3.28931	−	0.424807i	−0.350641	−	0.0452846i
$89$	−4.11165	+	2.98729i	−0.435834	+	0.316652i	−0.783978	−	0.620789i	$-0.786812\pi$
$89$	−4.11165	+	2.98729i	−0.435834	+	0.316652i	0.348143	+	0.937441i	$0.386812\pi$
$90$	−7.53658	+	3.85930i	−0.794425	+	0.406806i
$91$	1.77448			0.186016
$92$	−0.0680950	+	0.209575i	−0.00709939	+	0.0218497i
$93$	6.51601	+	20.0542i	0.675678	+	2.07952i
$94$	−9.04130	+	6.56889i	−0.932539	+	0.677529i
$95$	−6.67370	+	3.41744i	−0.684707	+	0.350622i
$96$	−0.805027	−	2.47762i	−0.0821628	−	0.252871i
$97$	7.94824	+	5.77473i	0.807021	+	0.586335i	0.912966	−	0.408037i	$-0.133786\pi$
$97$	7.94824	+	5.77473i	0.807021	+	0.586335i	−0.105944	+	0.994372i	$0.533786\pi$
$98$	0.0651268	−	0.0473174i	0.00657880	−	0.00477978i
$99$	−5.37884	+	11.3488i	−0.540594	+	1.14060i
$100$	4.76149	+	1.52583i	0.476149	+	0.152583i
$101$	4.22475	−	13.0024i	0.420378	−	1.29379i	−0.486973	−	0.873417i	$-0.661899\pi$
$101$	4.22475	−	13.0024i	0.420378	−	1.29379i	0.907351	−	0.420373i	$-0.138101\pi$
$102$	1.35563	−	4.17219i	0.134227	−	0.413109i
$103$	−0.392585	+	0.285230i	−0.0386826	+	0.0281046i	−0.606959	−	0.794733i	$-0.707611\pi$
$103$	−0.392585	+	0.285230i	−0.0386826	+	0.0281046i	0.568276	+	0.822838i	$0.307611\pi$
$104$	−0.674580			−0.0661480
$105$	−10.8571	−	10.8132i	−1.05954	−	1.05526i
$106$	−2.28044	+	7.01847i	−0.221496	+	0.681694i
$107$	−9.60256	+	6.97667i	−0.928315	+	0.674460i	−0.945580	−	0.325391i	$-0.894504\pi$
$107$	−9.60256	+	6.97667i	−0.928315	+	0.674460i	0.0172647	+	0.999851i	$0.494504\pi$
$108$	−2.04937			−0.197200
$109$	9.23100	+	6.70672i	0.884170	+	0.642387i	0.934351	−	0.356353i	$-0.115980\pi$
$109$	9.23100	+	6.70672i	0.884170	+	0.642387i	−0.0501815	+	0.998740i	$0.515980\pi$
$110$	6.97964	−	2.50691i	0.665483	−	0.239025i
$111$	−20.5961	+	14.9640i	−1.95490	+	1.42032i
$112$	2.12811	−	1.54617i	0.201088	−	0.146099i
$113$	11.6209			1.09320			0.546602	−	0.837393i	$-0.315921\pi$
$113$	11.6209			1.09320			0.546602	+	0.837393i	$0.315921\pi$
$114$	−8.73529			−0.818135
$115$	−0.0780658	−	0.486517i	−0.00727968	−	0.0453679i
$116$	−0.641474	+	1.97425i	−0.0595594	+	0.183305i
$117$	−0.789357	+	2.42939i	−0.0729760	+	0.224597i
$118$	−1.19837	+	0.870670i	−0.110319	+	0.0801517i
$119$	4.42963			0.406063
$120$	4.12739	+	4.11072i	0.376777	+	0.375256i
$121$	5.94552	−	9.25477i	0.540502	−	0.841343i
$122$	1.30664	−	4.02141i	0.118297	−	0.364082i
$123$	1.65731	+	5.10067i	0.149434	+	0.459912i
$124$	6.54830	−	4.75762i	0.588055	−	0.427247i
$125$	−11.0319	+	1.81597i	−0.986721	+	0.162425i
$126$	−3.07806	−	9.47329i	−0.274215	−	0.843948i
$127$	−4.04264	−	2.93715i	−0.358726	−	0.260630i	0.393794	−	0.919199i	$-0.371162\pi$
$127$	−4.04264	−	2.93715i	−0.358726	−	0.260630i	−0.752521	+	0.658569i	$0.771162\pi$
$128$	−0.809017	+	0.587785i	−0.0715077	+	0.0519534i
$129$	−9.70099	−	29.8566i	−0.854125	−	2.62873i
$130$	1.34261	−	0.687520i	0.117755	−	0.0602995i
$131$	1.69115	+	5.20482i	0.147756	+	0.454747i	0.997355	−	0.0726823i	$-0.0231559\pi$
$131$	1.69115	+	5.20482i	0.147756	+	0.454747i	−0.849599	+	0.527429i	$0.823156\pi$
$132$	8.56905	+	1.10668i	0.745840	+	0.0963237i
$133$	−2.72564	−	8.38867i	−0.236343	−	0.727390i
$134$	−10.7201	+	7.78860i	−0.926074	+	0.672832i
$135$	4.07884	−	2.08868i	0.351051	−	0.179765i
$136$	−1.68395			−0.144398
$137$	1.91726	−	5.90071i	0.163802	−	0.504132i	−0.835144	−	0.550032i	$-0.814616\pi$
$137$	1.91726	−	5.90071i	0.163802	−	0.504132i	0.998946	+	0.0458999i	$0.0146155\pi$
$138$	0.177396	−	0.545968i	0.0151009	−	0.0464759i
$139$	3.81778			0.323820			0.161910	−	0.986806i	$-0.448235\pi$
$139$	3.81778			0.323820			0.161910	+	0.986806i	$0.448235\pi$
$140$	−2.65975	+	5.24626i	−0.224790	+	0.443390i
$141$	23.5537	−	17.1128i	1.98358	−	1.44115i
$142$	0.0864831	+	0.266167i	0.00725750	+	0.0223363i
$143$	0.958220	−	2.02175i	0.0801303	−	0.169067i
$144$	1.17014	+	3.60133i	0.0975121	+	0.300111i
$145$	−0.735402	−	4.58312i	−0.0610718	−	0.380608i
$146$	1.66267	+	5.11718i	0.137604	+	0.423500i
$147$	−0.169663	+	0.123268i	−0.0139936	+	0.0101669i
$148$	7.90601	+	5.74405i	0.649870	+	0.472158i
$149$	−1.80012	−	5.54019i	−0.147471	−	0.453870i	0.849849	−	0.527026i	$-0.176693\pi$
$149$	−1.80012	−	5.54019i	−0.147471	−	0.453870i	−0.997321	+	0.0731560i	$0.976693\pi$
$150$	−12.4043	−	3.97498i	−1.01281	−	0.324556i
$151$	9.36033	−	6.80068i	0.761733	−	0.553431i	−0.137708	−	0.990473i	$-0.543974\pi$
$151$	9.36033	−	6.80068i	0.761733	−	0.553431i	0.899441	+	0.437041i	$0.143974\pi$
$152$	1.03617	+	3.18901i	0.0840446	+	0.258663i
$153$	−1.97047	+	6.06448i	−0.159303	+	0.490284i
$154$	1.61101	+	8.57433i	0.129819	+	0.690939i
$155$	−8.18416	+	16.1430i	−0.657368	+	1.29663i
$156$	1.75737			0.140702
$157$	16.1936	−	11.7653i	1.29239	−	0.938974i	0.292536	−	0.956254i	$-0.405501\pi$
$157$	16.1936	−	11.7653i	1.29239	−	0.938974i	0.999851	+	0.0172804i	$0.00550081\pi$
$158$	−0.359908	+	1.10768i	−0.0286328	+	0.0881226i
$159$	5.94082	−	18.2840i	0.471138	−	1.45001i
$160$	1.01112	−	1.99440i	0.0799362	−	0.157671i
$161$	0.579656			0.0456833
$162$	−6.02115			−0.473066
$163$	1.26567	−	0.919563i	0.0991350	−	0.0720258i	−0.537113	−	0.843510i	$-0.680485\pi$
$163$	1.26567	−	0.919563i	0.0991350	−	0.0720258i	0.636248	+	0.771484i	$0.280485\pi$
$164$	1.66552	−	1.21007i	0.130055	−	0.0944907i
$165$	−18.1828	+	6.53081i	−1.41553	+	0.508423i
$166$	−9.72480	−	7.06548i	−0.754791	−	0.548388i
$167$	−19.6423			−1.51997			−0.759984	−	0.649941i	$-0.774793\pi$
$167$	−19.6423			−1.51997			−0.759984	+	0.649941i	$0.774793\pi$
$168$	−5.54400	+	4.02795i	−0.427729	+	0.310763i
$169$	−3.87660	+	11.9309i	−0.298200	+	0.917765i
$170$	3.35156	−	1.71625i	0.257053	−	0.131631i
$171$	12.6972			0.970976
$172$	−9.74907	+	7.08311i	−0.743360	+	0.540082i
$173$	−4.78317	+	14.7211i	−0.363658	+	1.11922i	0.587160	+	0.809471i	$0.300246\pi$
$173$	−4.78317	+	14.7211i	−0.363658	+	1.11922i	−0.950817	+	0.309752i	$0.899754\pi$
$174$	1.67112	−	5.14318i	0.126687	−	0.389903i
$175$	−0.0532117	−	13.1524i	−0.00402242	−	0.994225i
$176$	−0.612436	−	3.25959i	−0.0461641	−	0.245701i
$177$	3.12191	−	2.26820i	0.234657	−	0.170489i
$178$	−4.11165	−	2.98729i	−0.308182	−	0.223907i
$179$	2.03207	+	6.25407i	0.151884	+	0.467451i	0.997832	−	0.0658144i	$-0.0209645\pi$
$179$	2.03207	+	6.25407i	0.151884	+	0.467451i	−0.845948	+	0.533266i	$0.820965\pi$
$180$	−5.99935	−	5.97512i	−0.447165	−	0.445359i
$181$	11.6640	−	8.47437i	0.866976	−	0.629895i	−0.0627976	−	0.998026i	$-0.520002\pi$
$181$	11.6640	−	8.47437i	0.866976	−	0.629895i	0.929774	+	0.368131i	$0.120002\pi$
$182$	0.548344	+	1.68763i	0.0406460	+	0.125095i
$183$	−3.40395	+	10.4763i	−0.251627	+	0.774429i
$184$	−0.220360			−0.0162452
$185$	−21.5895	−	3.37469i	−1.58729	−	0.248112i
$186$	−17.0591	+	12.3942i	−1.25084	+	0.908786i
$187$	2.39200	−	5.04688i	0.174920	−	0.369064i
$188$	−9.04130	−	6.56889i	−0.659404	−	0.479085i
$189$	1.66586	+	5.12700i	0.121174	+	0.372934i
$190$	−5.31246	−	5.29101i	−0.385407	−	0.383851i
$191$	6.76349	+	20.8159i	0.489389	+	1.50618i	0.825522	+	0.564369i	$0.190881\pi$
$191$	6.76349	+	20.8159i	0.489389	+	1.50618i	−0.336134	+	0.941814i	$0.609119\pi$
$192$	2.10759	−	1.53125i	0.152102	−	0.110509i
$193$	5.02942	+	15.4790i	0.362026	+	1.11420i	0.951823	+	0.306649i	$0.0992077\pi$
$193$	5.02942	+	15.4790i	0.362026	+	1.11420i	−0.589797	+	0.807551i	$0.700792\pi$
$194$	−3.03596	+	9.34371i	−0.217969	+	0.670840i
$195$	−3.49767	+	1.79107i	−0.250474	+	0.128262i
$196$	0.0651268	+	0.0473174i	0.00465192	+	0.00337982i
$197$	−5.81617	+	17.9003i	−0.414385	+	1.27534i	0.498415	+	0.866938i	$0.333915\pi$
$197$	−5.81617	+	17.9003i	−0.414385	+	1.27534i	−0.912800	+	0.408407i	$0.866085\pi$
$198$	−12.4555	−	1.60860i	−0.885175	−	0.114319i
$199$	−18.6279			−1.32050			−0.660248	−	0.751048i	$-0.729549\pi$
$199$	−18.6279			−1.32050			−0.660248	+	0.751048i	$0.729549\pi$
$200$	0.0202288	+	4.99996i	0.00143039	+	0.353550i
$201$	27.9271	−	20.2903i	1.96983	−	1.43116i
$202$	13.6716			0.961928
$203$	5.46052			0.383253
$204$	4.38691			0.307145
$205$	−2.08159	+	4.10587i	−0.145385	+	0.286766i
$206$	−0.392585	−	0.285230i	−0.0273527	−	0.0198729i
$207$	−0.257853	+	0.793590i	−0.0179220	+	0.0551583i
$208$	−0.208457	−	0.641564i	−0.0144539	−	0.0444845i
$209$	−11.0294	−	1.42443i	−0.762923	−	0.0985299i
$210$	6.92897	−	13.6672i	0.478145	−	0.943123i
$211$	2.37373	+	7.30560i	0.163415	+	0.502938i	0.998916	−	0.0465500i	$-0.0148227\pi$
$211$	2.37373	+	7.30560i	0.163415	+	0.502938i	−0.835501	+	0.549488i	$0.814823\pi$
$212$	−7.37965			−0.506837
$213$	−0.225299	−	0.693399i	−0.0154372	−	0.0475109i
$214$	−9.60256	−	6.97667i	−0.656418	−	0.476915i
$215$	12.1845	−	24.0336i	0.830978	−	1.63907i
$216$	−0.633289	−	1.94906i	−0.0430899	−	0.132617i
$217$	−17.2253	−	12.5149i	−1.16933	−	0.849566i
$218$	−3.52593	+	10.8517i	−0.238806	+	0.734970i
$219$	−4.33146	−	13.3309i	−0.292693	−	0.900817i
$220$	4.54104	+	5.86336i	0.306157	+	0.395307i
$221$	0.351031	−	1.08036i	0.0236129	−	0.0726731i
$222$	−20.5961	−	14.9640i	−1.38232	−	1.00432i
$223$	−7.55913	+	23.2646i	−0.506197	+	1.55791i	0.292553	+	0.956249i	$0.405495\pi$
$223$	−7.55913	+	23.2646i	−0.506197	+	1.55791i	−0.798749	+	0.601664i	$0.794505\pi$
$224$	2.12811	+	1.54617i	0.142191	+	0.103308i
$225$	18.0302	+	5.77782i	1.20201	+	0.385188i
$226$	3.59106	+	11.0521i	0.238874	+	0.735178i
$227$	25.4135			1.68675			0.843375	−	0.537325i	$-0.180565\pi$
$227$	25.4135			1.68675			0.843375	+	0.537325i	$0.180565\pi$
$228$	−2.69935	−	8.30776i	−0.178769	−	0.550195i
$229$	−16.6909	−	12.1266i	−1.10296	−	0.801350i	−0.121422	−	0.992601i	$-0.538745\pi$
$229$	−16.6909	−	12.1266i	−1.10296	−	0.801350i	−0.981541	+	0.191251i	$0.938745\pi$
$230$	0.438581	−	0.224587i	0.0289192	−	0.0148088i
$231$	−4.19688	−	22.3372i	−0.276134	−	1.46968i
$232$	−2.07585			−0.136286
$233$	25.7459			1.68667			0.843337	−	0.537386i	$-0.180588\pi$
$233$	25.7459			1.68667			0.843337	+	0.537386i	$0.180588\pi$
$234$	−2.55441			−0.166987
$235$	24.6897	+	3.85929i	1.61058	+	0.251752i
$236$	−1.19837	−	0.870670i	−0.0780075	−	0.0566758i
$237$	0.937605	−	2.88565i	0.0609040	−	0.187443i
$238$	1.36883	+	4.21283i	0.0887281	+	0.273077i
$239$	3.87632	−	11.9301i	0.250738	−	0.771692i	−0.743901	−	0.668289i	$-0.767027\pi$
$239$	3.87632	−	11.9301i	0.250738	−	0.771692i	0.994640	−	0.103403i	$-0.0329732\pi$
$240$	−2.63410	+	5.19566i	−0.170030	+	0.335378i
$241$	−8.70746	−	6.32634i	−0.560897	−	0.407515i	0.270890	−	0.962610i	$-0.412682\pi$
$241$	−8.70746	−	6.32634i	−0.560897	−	0.407515i	−0.831787	+	0.555095i	$0.812682\pi$
$242$	10.6391	+	2.79464i	0.683906	+	0.179646i
$243$	21.8339			1.40065
$244$	4.22836			0.270693
$245$	−0.177847	−	0.0277995i	−0.0113622	−	0.00177604i
$246$	−4.33889	+	3.15239i	−0.276637	+	0.200989i
$247$	−2.26195			−0.143924
$248$	6.54830	+	4.75762i	0.415817	+	0.302109i
$249$	25.3343	+	18.4065i	1.60550	+	1.16646i
$250$	−5.13613	−	9.93077i	−0.324837	−	0.628077i
$251$	−6.27585	+	19.3151i	−0.396128	+	1.21916i	0.531951	+	0.846775i	$0.321459\pi$
$251$	−6.27585	+	19.3151i	−0.396128	+	1.21916i	−0.928080	+	0.372382i	$0.878541\pi$
$252$	8.05846	−	5.85482i	0.507635	−	0.368819i
$253$	0.313014	−	0.660429i	0.0196790	−	0.0415208i
$254$	1.54415	−	4.75241i	0.0968887	−	0.298193i
$255$	−8.73123	+	4.47105i	−0.546771	+	0.279988i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−11.6373	−	8.45497i	−0.725913	−	0.527407i	0.162355	−	0.986732i	$-0.448091\pi$
$257$	−11.6373	−	8.45497i	−0.725913	−	0.527407i	−0.888268	+	0.459326i	$0.848091\pi$
$258$	25.3975	−	18.4524i	1.58118	−	1.14880i
$259$	7.94363	−	24.4480i	0.493593	−	1.51912i
$260$	1.06876	+	1.06445i	0.0662817	+	0.0660141i
$261$	−2.42905	+	7.47585i	−0.150354	+	0.462743i
$262$	−4.42748	+	3.21676i	−0.273531	+	0.198732i
$263$	−1.94615	−	1.41396i	−0.120005	−	0.0871887i	0.526164	−	0.850383i	$-0.323630\pi$
$263$	−1.94615	−	1.41396i	−0.120005	−	0.0871887i	−0.646169	+	0.763194i	$0.723630\pi$
$264$	1.59547	+	8.49163i	0.0981944	+	0.522624i
$265$	14.6877	−	7.52121i	0.902257	−	0.462024i
$266$	7.13583	−	5.18448i	0.437526	−	0.317881i
$267$	10.7114	+	7.78226i	0.655525	+	0.476267i
$268$	−10.7201	−	7.78860i	−0.654833	−	0.475764i
$269$	−8.13451	+	5.91007i	−0.495970	+	0.360343i	−0.807475	−	0.589901i	$-0.799167\pi$
$269$	−8.13451	+	5.91007i	−0.495970	+	0.360343i	0.311506	+	0.950244i	$0.399167\pi$
$270$	3.24688	+	3.23377i	0.197599	+	0.196801i
$271$	15.0499	−	10.9344i	0.914215	−	0.664216i	−0.0278622	−	0.999612i	$-0.508870\pi$
$271$	15.0499	−	10.9344i	0.914215	−	0.664216i	0.942077	+	0.335396i	$0.108870\pi$
$272$	−0.520370	−	1.60153i	−0.0315521	−	0.0971073i
$273$	−1.42850	−	4.39649i	−0.0864570	−	0.266087i
$274$	6.20438			0.374820
$275$	−15.0138	−	7.04165i	−0.905368	−	0.424628i
$276$	0.574065			0.0345547
$277$	−5.58487	−	17.1885i	−0.335563	−	1.03276i	−0.966444	−	0.256876i	$-0.917307\pi$
$277$	−5.58487	−	17.1885i	−0.335563	−	1.03276i	0.630882	−	0.775879i	$-0.282693\pi$
$278$	1.17976	+	3.63092i	0.0707572	+	0.217768i
$279$	24.7962	−	18.0155i	1.48451	−	1.07856i
$280$	−5.81140	−	0.908388i	−0.347297	−	0.0542866i
$281$	−12.3717	+	8.98855i	−0.738033	+	0.536212i	−0.892094	−	0.451849i	$-0.850765\pi$
$281$	−12.3717	+	8.98855i	−0.738033	+	0.536212i	0.154062	+	0.988061i	$0.450765\pi$
$282$	23.5537	+	17.1128i	1.40260	+	1.01905i
$283$	18.3532	+	13.3344i	1.09098	+	0.792645i	0.979565	−	0.201129i	$-0.0644609\pi$
$283$	18.3532	+	13.3344i	1.09098	+	0.792645i	0.111417	+	0.993774i	$0.464461\pi$
$284$	−0.226416	+	0.164501i	−0.0134353	+	0.00976131i
$285$	13.8396	+	13.7837i	0.819789	+	0.816479i
$286$	2.21890	+	0.286567i	0.131206	+	0.0169450i
$287$	−4.38114	−	3.18309i	−0.258611	−	0.187892i
$288$	−3.06348	+	2.22575i	−0.180517	+	0.131153i
$289$	−4.37701	+	13.4711i	−0.257471	+	0.792415i
$290$	4.13156	−	2.11567i	0.242613	−	0.124237i
$291$	7.90904	−	24.3415i	0.463636	−	1.42693i
$292$	−4.35293	+	3.16259i	−0.254736	+	0.185077i
$293$	7.58007	+	5.50725i	0.442833	+	0.321737i	0.786759	−	0.617260i	$-0.211757\pi$
$293$	7.58007	+	5.50725i	0.442833	+	0.321737i	−0.343927	+	0.938996i	$0.611757\pi$
$294$	−0.169663	−	0.123268i	−0.00989497	−	0.00718912i
$295$	3.27249	+	0.511527i	0.190532	+	0.0297823i
$296$	−3.01983	+	9.29407i	−0.175524	+	0.540207i
$297$	6.74099	+	0.870586i	0.391152	+	0.0505165i
$298$	4.71276	−	3.42402i	0.273003	−	0.198348i
$299$	0.0459355	−	0.141375i	0.00265652	−	0.00817593i
$300$	−0.0526984	−	13.0255i	−0.00304255	−	0.752028i
$301$	25.6449	+	18.6321i	1.47815	+	1.07394i
$302$	9.36033	+	6.80068i	0.538627	+	0.391335i
$303$	−35.6161			−2.04609
$304$	−2.71273	+	1.97092i	−0.155586	+	0.113040i
$305$	−8.41569	+	4.30947i	−0.481881	+	0.246760i
$306$	−6.37657			−0.364524
$307$	−32.1179			−1.83307			−0.916534	−	0.399957i	$-0.869025\pi$
$307$	−32.1179			−1.83307			−0.916534	+	0.399957i	$0.869025\pi$
$308$	−7.65684	+	4.18177i	−0.436289	+	0.238279i
$309$	1.02273	+	0.743059i	0.0581813	+	0.0422712i
$310$	−17.8819	−	2.79515i	−1.01562	−	0.158754i
$311$	−4.54821	+	13.9979i	−0.257905	+	0.793751i	0.735338	+	0.677700i	$0.237023\pi$
$311$	−4.54821	+	13.9979i	−0.257905	+	0.793751i	−0.993243	+	0.116050i	$0.962977\pi$
$312$	0.543056	+	1.67135i	0.0307445	+	0.0946218i
$313$	0.0329147	−	0.101301i	0.00186045	−	0.00572587i	−0.950122	−	0.311879i	$-0.899042\pi$
$313$	0.0329147	−	0.101301i	0.00186045	−	0.00572587i	0.951982	+	0.306153i	$0.0990418\pi$
$314$	16.1936	+	11.7653i	0.913856	+	0.663955i
$315$	−10.0716	+	19.8658i	−0.567469	+	1.11931i
$316$	−1.16469			−0.0655188
$317$	12.8589			0.722225			0.361113	−	0.932522i	$-0.382397\pi$
$317$	12.8589			0.722225			0.361113	+	0.932522i	$0.382397\pi$
$318$	19.2249			1.07808
$319$	2.94868	−	6.22143i	0.165095	−	0.348333i
$320$	2.20924	+	0.345330i	0.123500	+	0.0193045i
$321$	25.0159	+	18.1751i	1.39625	+	1.01443i
$322$	0.179123	+	0.551285i	0.00998216	+	0.0307219i
$323$	−5.64650			−0.314180
$324$	−1.86064	−	5.72646i	−0.103369	−	0.318136i
$325$	−3.21201	−	1.02930i	−0.178170	−	0.0570951i
$326$	1.26567	+	0.919563i	0.0700990	+	0.0509299i
$327$	9.18548	−	28.2700i	0.507958	−	1.56334i
$328$	1.66552	+	1.21007i	0.0919630	+	0.0668150i
$329$	−9.08433	+	27.9587i	−0.500835	+	1.54141i
$330$	−11.8300	−	15.2748i	−0.651219	−	0.840848i
$331$	−4.73828	−	14.5829i	−0.260439	−	0.801550i	−0.992709	−	0.120535i	$-0.961539\pi$
$331$	−4.73828	−	14.5829i	−0.260439	−	0.801550i	0.732270	−	0.681015i	$-0.238461\pi$
$332$	3.71454	−	11.4322i	0.203862	−	0.627423i
$333$	29.9374	+	21.7508i	1.64056	+	1.19194i
$334$	−6.06981	−	18.6810i	−0.332125	−	1.02218i
$335$	29.2741	+	4.57588i	1.59942	+	0.250007i
$336$	−5.54400	−	4.02795i	−0.302450	−	0.219743i
$337$	−8.65627	−	26.6412i	−0.471537	−	1.45124i	−0.850572	−	0.525859i	$-0.823744\pi$
$337$	−8.65627	−	26.6412i	−0.471537	−	1.45124i	0.379035	−	0.925382i	$-0.376256\pi$
$338$	−12.5449			−0.682355
$339$	−9.35516	−	28.7922i	−0.508102	−	1.56378i
$340$	2.66794	+	2.65717i	0.144690	+	0.144105i
$341$	−23.5604	+	12.8675i	−1.27587	+	0.696814i
$342$	3.92364	+	12.0757i	0.212166	+	0.652980i
$343$	5.75551	−	17.7136i	0.310768	−	0.956446i
$344$	−9.74907	−	7.08311i	−0.525635	−	0.381896i
$345$	−1.14256	+	0.585077i	−0.0615133	+	0.0314995i
$346$	−15.4787			−0.832138
$347$	31.6461			1.69885			0.849426	−	0.527708i	$-0.176948\pi$
$347$	31.6461			1.69885			0.849426	+	0.527708i	$0.176948\pi$
$348$	5.40786			0.289891
$349$	−6.72587	+	4.88663i	−0.360028	+	0.261575i	−0.753064	−	0.657948i	$-0.771425\pi$
$349$	−6.72587	+	4.88663i	−0.360028	+	0.261575i	0.393036	+	0.919523i	$0.371425\pi$
$350$	12.4922	−	4.11491i	0.667736	−	0.219951i
$351$	1.38246			0.0737904
$352$	2.91080	−	1.58973i	0.155146	−	0.0847329i
$353$	9.82565	−	30.2402i	0.522966	−	1.60952i	−0.245336	−	0.969438i	$-0.578898\pi$
$353$	9.82565	−	30.2402i	0.522966	−	1.60952i	0.768303	−	0.640087i	$-0.221102\pi$
$354$	3.12191	+	2.26820i	0.165928	+	0.120554i
$355$	0.282977	−	0.558163i	0.0150189	−	0.0296242i
$356$	1.57051	−	4.83354i	0.0832370	−	0.256177i
$357$	−3.56597	−	10.9749i	−0.188731	−	0.580855i
$358$	−5.32003	+	3.86523i	−0.281172	+	0.204284i
$359$	−0.615110	−	1.89311i	−0.0324643	−	0.0999147i	0.933511	−	0.358548i	$-0.116728\pi$
$359$	−0.615110	−	1.89311i	−0.0324643	−	0.0999147i	−0.965976	+	0.258633i	$0.916728\pi$
$360$	3.82878	−	7.55213i	0.201794	−	0.398032i
$361$	−2.39691	−	7.37694i	−0.126153	−	0.388260i
$362$	11.6640	+	8.47437i	0.613045	+	0.445403i
$363$	−27.7161	−	7.28039i	−1.45472	−	0.382121i
$364$	−1.43558	+	1.04301i	−0.0752451	+	0.0546687i
$365$	5.44036	−	10.7309i	0.284761	−	0.561681i
$366$	−11.0154			−0.575785
$367$	6.46086	−	19.8845i	0.337254	−	1.03796i	−0.628347	−	0.777933i	$-0.716268\pi$
$367$	6.46086	−	19.8845i	0.337254	−	1.03796i	0.965601	−	0.260028i	$-0.0837319\pi$
$368$	−0.0680950	−	0.209575i	−0.00354970	−	0.0109248i
$369$	6.30677	−	4.58214i	0.328317	−	0.238537i
$370$	−3.46201	−	21.5757i	−0.179981	−	1.12167i
$371$	5.99868	+	18.4620i	0.311436	+	0.958501i
$372$	−17.0591	−	12.3942i	−0.884475	−	0.642608i
$373$	−17.1151	+	12.4348i	−0.886184	+	0.643850i	−0.934880	−	0.354963i	$-0.884493\pi$
$373$	−17.1151	+	12.4348i	−0.886184	+	0.643850i	0.0486963	+	0.998814i	$0.484493\pi$
$374$	5.53904	+	0.715356i	0.286417	+	0.0369902i
$375$	13.3802	+	25.8709i	0.690953	+	1.33597i
$376$	3.45347	−	10.6287i	0.178099	−	0.548132i
$377$	0.432726	−	1.33179i	0.0222865	−	0.0685908i
$378$	−4.36129	+	3.16866i	−0.224320	+	0.162978i
$379$	−32.4752			−1.66814			−0.834069	−	0.551660i	$-0.813995\pi$
$379$	−32.4752			−1.66814			−0.834069	+	0.551660i	$0.813995\pi$
$380$	3.39041	−	6.68747i	0.173924	−	0.343060i
$381$	−4.02271	+	12.3806i	−0.206089	+	0.634278i
$382$	−17.7070	+	12.8649i	−0.905971	+	0.658226i
$383$	−16.9596			−0.866594			−0.433297	−	0.901251i	$-0.642650\pi$
$383$	−16.9596			−0.866594			−0.433297	+	0.901251i	$0.642650\pi$
$384$	2.10759	+	1.53125i	0.107552	+	0.0781414i
$385$	10.9774	−	16.1267i	0.559459	−	0.821891i
$386$	−13.1672	+	9.56653i	−0.670192	+	0.486923i
$387$	−36.9165	+	26.8214i	−1.87657	+	1.36341i
$388$	−9.82456			−0.498767
$389$	5.65669			0.286806			0.143403	−	0.989664i	$-0.454196\pi$
$389$	5.65669			0.286806			0.143403	+	0.989664i	$0.454196\pi$
$390$	−2.78425	−	2.77301i	−0.140986	−	0.140417i
$391$	0.114669	−	0.352914i	0.00579905	−	0.0178476i
$392$	−0.0248762	+	0.0765612i	−0.00125644	+	0.00386692i
$393$	11.5341	−	8.38004i	0.581820	−	0.422717i
$394$	−18.8215			−0.948214
$395$	2.31807	−	1.18703i	0.116635	−	0.0597259i
$396$	−2.31909	−	12.3430i	−0.116539	−	0.620258i
$397$	−2.47168	+	7.60705i	−0.124050	+	0.381787i	−0.993727	−	0.111835i	$-0.964327\pi$
$397$	−2.47168	+	7.60705i	−0.124050	+	0.381787i	0.869677	+	0.493622i	$0.164327\pi$
$398$	−5.75633	−	17.7162i	−0.288539	−	0.888031i
$399$	−18.5897	+	13.5062i	−0.930649	+	0.676156i
$400$	−4.74899	+	1.56431i	−0.237450	+	0.0782156i
$401$	−1.05979	−	3.26169i	−0.0529232	−	0.162881i	0.921102	−	0.389322i	$-0.127291\pi$
$401$	−1.05979	−	3.26169i	−0.0529232	−	0.162881i	−0.974025	+	0.226441i	$0.927291\pi$
$402$	27.9271	+	20.2903i	1.39288	+	1.01199i
$403$	−4.41735	+	3.20940i	−0.220044	+	0.159871i
$404$	4.22475	+	13.0024i	0.210189	+	0.646895i
$405$	9.53952	+	9.50100i	0.474022	+	0.472108i
$406$	1.68739	+	5.19326i	0.0837440	+	0.257737i
$407$	−23.5652	−	22.2525i	−1.16808	−	1.10301i
$408$	1.35563	+	4.17219i	0.0671136	+	0.206554i
$409$	8.71590	−	6.33247i	0.430973	−	0.313121i	−0.351065	−	0.936351i	$-0.614180\pi$
$409$	8.71590	−	6.33247i	0.430973	−	0.313121i	0.782038	+	0.623231i	$0.214180\pi$
$410$	−4.54816	−	0.710929i	−0.224617	−	0.0351103i
$411$	−16.1632			−0.797270
$412$	0.149954	−	0.461512i	0.00738772	−	0.0227371i
$413$	−1.20408	+	3.70577i	−0.0592488	+	0.182349i
$414$	−0.834430			−0.0410100
$415$	4.25845	+	26.5392i	0.209039	+	1.30276i
$416$	0.545747	−	0.396508i	0.0267574	−	0.0194404i
$417$	−3.07341	−	9.45900i	−0.150506	−	0.463209i
$418$	−2.05357	−	10.9298i	−0.100443	−	0.534594i
$419$	−1.75651	−	5.40599i	−0.0858113	−	0.264100i	0.898939	−	0.438074i	$-0.144339\pi$
$419$	−1.75651	−	5.40599i	−0.0858113	−	0.264100i	−0.984750	+	0.173974i	$0.944339\pi$
$420$	15.1394	+	2.36646i	0.738727	+	0.115472i
$421$	−6.33752	−	19.5049i	−0.308872	−	0.950610i	−0.978204	−	0.207647i	$-0.933420\pi$
$421$	−6.33752	−	19.5049i	−0.308872	−	0.950610i	0.669332	−	0.742964i	$-0.266580\pi$
$422$	−6.21452	+	4.51511i	−0.302518	+	0.219792i
$423$	−34.2364	−	24.8742i	−1.66463	−	1.20942i
$424$	−2.28044	−	7.01847i	−0.110748	−	0.340847i
$425$	−8.01813	−	2.56943i	−0.388937	−	0.124636i
$426$	0.589840	−	0.428544i	0.0285779	−	0.0207630i
$427$	−3.43710	−	10.5783i	−0.166333	−	0.511920i
$428$	3.66785	−	11.2885i	0.177292	−	0.545650i
$429$	−5.78051	−	0.746542i	−0.279086	−	0.0360434i
$430$	26.6225	+	4.16140i	1.28385	+	0.200681i
$431$	−24.0572			−1.15880			−0.579398	−	0.815045i	$-0.696712\pi$
$431$	−24.0572			−1.15880			−0.579398	+	0.815045i	$0.696712\pi$
$432$	1.65797	−	1.20459i	0.0797692	−	0.0579557i
$433$	2.89011	−	8.89484i	0.138890	−	0.427459i	−0.857285	−	0.514842i	$-0.827851\pi$
$433$	2.89011	−	8.89484i	0.138890	−	0.427459i	0.996175	+	0.0873835i	$0.0278505\pi$
$434$	6.57947	−	20.2495i	0.315824	−	0.972008i
$435$	−10.7632	+	5.51159i	−0.516057	+	0.264260i
$436$	−11.4101			−0.546447
$437$	−0.738894			−0.0353461
$438$	11.3399	−	8.23893i	0.541842	−	0.393671i
$439$	−18.4068	+	13.3734i	−0.878511	+	0.638275i	−0.932857	−	0.360247i	$-0.882692\pi$
$439$	−18.4068	+	13.3734i	−0.878511	+	0.638275i	0.0543463	+	0.998522i	$0.482692\pi$
$440$	−4.17312	+	6.13066i	−0.198946	+	0.292268i
$441$	0.246614	+	0.179175i	0.0117435	+	0.00853216i
$442$	1.13596			0.0540322
$443$	14.5983	−	10.6063i	0.693584	−	0.503918i	−0.184252	−	0.982879i	$-0.558986\pi$
$443$	14.5983	−	10.6063i	0.693584	−	0.503918i	0.877836	+	0.478961i	$0.158986\pi$
$444$	7.86702	−	24.2122i	0.373352	−	1.14906i
$445$	1.80048	+	11.2208i	0.0853507	+	0.531917i
$446$	−24.4619			−1.15830
$447$	−12.2773	+	8.92000i	−0.580698	+	0.421902i
$448$	−0.812867	+	2.50175i	−0.0384044	+	0.118197i
$449$	−12.2442	+	37.6839i	−0.577842	+	1.77841i	0.0484506	+	0.998826i	$0.484572\pi$
$449$	−12.2442	+	37.6839i	−0.577842	+	1.77841i	−0.626292	+	0.779588i	$0.715428\pi$
$450$	0.0765996	+	18.9332i	0.00361094	+	0.892519i
$451$	−5.99246	+	3.27277i	−0.282174	+	0.154109i
$452$	−9.40152	+	6.83060i	−0.442210	+	0.321285i
$453$	−24.3848	−	17.7166i	−1.14570	−	0.832399i
$454$	7.85319	+	24.1696i	0.368569	+	1.13434i
$455$	1.79421	−	3.53902i	0.0841141	−	0.165912i
$456$	7.06700	−	5.13448i	0.330943	−	0.240444i
$457$	3.48834	+	10.7360i	0.163177	+	0.502209i	0.998897	−	0.0469474i	$-0.0149493\pi$
$457$	3.48834	+	10.7360i	0.163177	+	0.502209i	−0.835720	+	0.549156i	$0.814949\pi$
$458$	6.37534	−	19.6213i	0.297900	−	0.916842i
$459$	3.45104			0.161081
$460$	0.349124	+	0.347714i	0.0162780	+	0.0162123i
$461$	−10.8723	+	7.89922i	−0.506375	+	0.367903i	−0.811447	−	0.584426i	$-0.801320\pi$
$461$	−10.8723	+	7.89922i	−0.506375	+	0.367903i	0.305071	+	0.952329i	$0.401320\pi$
$462$	19.9470	−	10.8940i	0.928019	−	0.506836i
$463$	−4.09924	−	2.97827i	−0.190508	−	0.138412i	0.488443	−	0.872596i	$-0.337565\pi$
$463$	−4.09924	−	2.97827i	−0.190508	−	0.138412i	−0.678951	+	0.734184i	$0.737565\pi$
$464$	−0.641474	−	1.97425i	−0.0297797	−	0.0916525i
$465$	46.5846	+	7.28171i	2.16031	+	0.337681i
$466$	7.95594	+	24.4859i	0.368552	+	1.13429i
$467$	−16.2952	+	11.8392i	−0.754053	+	0.547851i	−0.897080	−	0.441867i	$-0.854316\pi$
$467$	−16.2952	+	11.8392i	−0.754053	+	0.547851i	0.143028	+	0.989719i	$0.454316\pi$
$468$	−0.789357	−	2.42939i	−0.0364880	−	0.112299i
$469$	−10.7711	+	33.1501i	−0.497363	+	1.53073i
$470$	3.95914	+	24.6739i	0.182622	+	1.13812i
$471$	−42.1862	−	30.6501i	−1.94384	−	1.41228i
$472$	0.457738	−	1.40877i	0.0210691	−	0.0648441i
$473$	35.0766	−	19.1571i	1.61283	−	0.880843i
$474$	3.03415			0.139363
$475$	0.0678295	+	16.7655i	0.00311223	+	0.769253i
$476$	−3.58364	+	2.60367i	−0.164256	+	0.119339i
$477$	−27.9443			−1.27948
$478$	12.5440			0.573750
$479$	38.9711			1.78063			0.890317	−	0.455341i	$-0.150483\pi$
$479$	38.9711			1.78063			0.890317	+	0.455341i	$0.150483\pi$
$480$	−5.75535	−	0.899627i	−0.262694	−	0.0410622i
$481$	−5.33324	−	3.87482i	−0.243175	−	0.176677i
$482$	3.32595	−	10.2362i	0.151493	−	0.466247i
$483$	−0.466639	−	1.43617i	−0.0212328	−	0.0653478i
$484$	0.629792	+	10.9820i	0.0286269	+	0.499180i
$485$	19.5538	−	10.0130i	0.887891	−	0.454668i
$486$	6.74706	+	20.7653i	0.306053	+	0.941934i
$487$	1.38001			0.0625340			0.0312670	−	0.999511i	$-0.490046\pi$
$487$	1.38001			0.0625340			0.0312670	+	0.999511i	$0.490046\pi$
$488$	1.30664	+	4.02141i	0.0591487	+	0.182041i
$489$	−3.29723	−	2.39558i	−0.149106	−	0.108332i
$490$	−0.0285188	−	0.177733i	−0.00128835	−	0.00802914i
$491$	1.17043	+	3.60221i	0.0528207	+	0.162565i	0.973987	−	0.226604i	$-0.0727622\pi$
$491$	1.17043	+	3.60221i	0.0528207	+	0.162565i	−0.921166	+	0.389169i	$0.872762\pi$
$492$	−4.33889	−	3.15239i	−0.195612	−	0.142121i
$493$	1.08021	−	3.32455i	0.0486503	−	0.149730i
$494$	−0.698981	−	2.15124i	−0.0314486	−	0.0967890i
$495$	17.1954	+	22.2026i	0.772876	+	0.997932i
$496$	−2.50123	+	7.69799i	−0.112308	+	0.345650i
$497$	0.595585	+	0.432718i	0.0267156	+	0.0194100i
$498$	−9.67684	+	29.7823i	−0.433630	+	1.33458i
$499$	25.6537	+	18.6385i	1.14842	+	0.834374i	0.988270	−	0.152719i	$-0.0488030\pi$
$499$	25.6537	+	18.6385i	1.14842	+	0.834374i	0.160148	+	0.987093i	$0.448803\pi$
$500$	7.85757	−	7.95353i	0.351401	−	0.355692i
$501$	15.8126	+	48.6662i	0.706455	+	2.17425i
$502$	−20.3091			−0.906438
$503$	2.10045	+	6.46451i	0.0936543	+	0.288238i	0.986901	−	0.161329i	$-0.0515781\pi$
$503$	2.10045	+	6.46451i	0.0936543	+	0.288238i	−0.893246	+	0.449568i	$0.851578\pi$
$504$	8.05846	+	5.85482i	0.358952	+	0.260794i
$505$	−21.6603	−	21.5729i	−0.963872	−	0.959980i
$506$	0.724832	+	0.0936106i	0.0322227	+	0.00416150i
$507$	32.6811			1.45142
$508$	4.99698			0.221705
$509$	−20.2698			−0.898444			−0.449222	−	0.893420i	$-0.648299\pi$
$509$	−20.2698			−0.898444			−0.449222	+	0.893420i	$0.648299\pi$
$510$	−6.95032	−	6.92226i	−0.307765	−	0.306523i
$511$	11.4504	+	8.31917i	0.506534	+	0.368018i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	−2.12349	−	6.53544i	−0.0937546	−	0.288547i
$514$	4.44504	−	13.6804i	0.196062	−	0.603418i
$515$	0.171911	+	1.07137i	0.00757532	+	0.0472104i
$516$	25.3975	+	18.4524i	1.11806	+	0.812321i
$517$	26.9491	+	25.4479i	1.18522	+	1.11920i
$518$	25.7061			1.12946
$519$	40.3238			1.77002
$520$	−0.682083	+	1.34538i	−0.0299113	+	0.0589990i
$521$	−4.00074	+	2.90671i	−0.175276	+	0.127345i	−0.671964	−	0.740584i	$-0.734549\pi$
$521$	−4.00074	+	2.90671i	−0.175276	+	0.127345i	0.496689	+	0.867929i	$0.334549\pi$
$522$	−7.86057			−0.344048
$523$	−20.4498	−	14.8576i	−0.894207	−	0.649679i	0.0427647	−	0.999085i	$-0.486383\pi$
$523$	−20.4498	−	14.8576i	−0.894207	−	0.649679i	−0.936971	+	0.349406i	$0.886383\pi$
$524$	−4.42748	−	3.21676i	−0.193416	−	0.140525i
$525$	−32.5437	+	10.7199i	−1.42032	+	0.467853i
$526$	0.743364	−	2.28784i	0.0324122	−	0.0997546i
$527$	−11.0270	+	8.01161i	−0.480345	+	0.348991i
$528$	−7.58299	+	4.14144i	−0.330007	+	0.180233i
$529$	−7.09239	+	21.8281i	−0.308365	+	0.949049i
$530$	11.6918	+	11.6446i	0.507861	+	0.505810i
$531$	−4.53785	−	3.29694i	−0.196926	−	0.143075i
$532$	7.13583	+	5.18448i	0.309377	+	0.224776i
$533$	−1.12353	+	0.816291i	−0.0486654	+	0.0353575i
$534$	−4.09138	+	12.5920i	−0.177051	+	0.544908i
$535$	4.20492	+	26.2056i	0.181795	+	1.13297i
$536$	4.09471	−	12.6022i	0.176864	−	0.544333i
$537$	13.8593	−	10.0694i	0.598075	−	0.434527i
$538$	−8.13451	−	5.91007i	−0.350704	−	0.254801i
$539$	−0.194121	−	0.183308i	−0.00836140	−	0.00789563i
$540$	−2.07216	+	4.08726i	−0.0891715	+	0.175888i
$541$	−20.4206	+	14.8364i	−0.877948	+	0.637867i	−0.932708	−	0.360633i	$-0.882561\pi$
$541$	−20.4206	+	14.8364i	−0.877948	+	0.637867i	0.0547597	+	0.998500i	$0.482561\pi$
$542$	15.0499	+	10.9344i	0.646448	+	0.469672i
$543$	−30.3861	−	22.0768i	−1.30399	−	0.947406i
$544$	1.36235	−	0.989803i	0.0584101	−	0.0424374i
$545$	22.7095	−	11.6290i	0.972770	−	0.498132i
$546$	3.73987	−	2.71718i	0.160052	−	0.116284i
$547$	−7.11954	−	21.9117i	−0.304410	−	0.936876i	−0.979897	−	0.199505i	$-0.936067\pi$
$547$	−7.11954	−	21.9117i	−0.304410	−	0.936876i	0.675487	−	0.737372i	$-0.263933\pi$
$548$	1.91726	+	5.90071i	0.0819012	+	0.252066i
$549$	16.0114			0.683350
$550$	2.05748	−	16.4550i	0.0877313	−	0.701643i
$551$	−6.96059			−0.296531
$552$	0.177396	+	0.545968i	0.00755047	+	0.0232380i
$553$	0.946736	+	2.91375i	0.0402593	+	0.123905i
$554$	14.6214	−	10.6231i	0.621203	−	0.451331i
$555$	9.01895	+	56.2073i	0.382833	+	2.38587i
$556$	−3.08865	+	2.24403i	−0.130988	+	0.0951682i
$557$	3.60978	+	2.62266i	0.152951	+	0.111125i	0.661629	−	0.749832i	$-0.269865\pi$
$557$	3.60978	+	2.62266i	0.152951	+	0.111125i	−0.508678	+	0.860957i	$0.669865\pi$
$558$	24.7962	+	18.0155i	1.04971	+	0.762658i
$559$	6.57653	−	4.77813i	0.278158	−	0.202093i
$560$	−0.931892	−	5.80767i	−0.0393796	−	0.245419i
$561$	−14.4299	−	1.86359i	−0.609230	−	0.0786808i
$562$	−12.3717	−	8.98855i	−0.521868	−	0.379159i
$563$	27.7638	−	20.1716i	1.17010	−	0.850130i	0.179082	−	0.983834i	$-0.442687\pi$
$563$	27.7638	−	20.1716i	1.17010	−	0.850130i	0.991021	+	0.133705i	$0.0426873\pi$
$564$	−8.99671	+	27.6890i	−0.378830	+	1.16592i
$565$	11.7502	−	23.1768i	0.494333	−	0.975054i
$566$	−7.01028	+	21.5754i	−0.294664	+	0.906883i
$567$	−12.8137	+	9.30970i	−0.538125	+	0.390971i
$568$	−0.226416	−	0.164501i	−0.00950019	−	0.00690229i
$569$	−16.8989	−	12.2778i	−0.708439	−	0.514711i	0.174231	−	0.984705i	$-0.444256\pi$
$569$	−16.8989	−	12.2778i	−0.708439	−	0.514711i	−0.882670	+	0.469994i	$0.844256\pi$
$570$	−8.83244	+	17.4217i	−0.369950	+	0.729714i
$571$	9.62844	−	29.6333i	0.402938	−	1.24011i	−0.519667	−	0.854369i	$-0.673944\pi$
$571$	9.62844	−	29.6333i	0.402938	−	1.24011i	0.922605	−	0.385746i	$-0.126056\pi$
$572$	0.413137	+	2.19886i	0.0172741	+	0.0919387i
$573$	46.1290	−	33.5147i	1.92707	−	1.40010i
$574$	1.67345	−	5.15034i	0.0698483	−	0.214971i
$575$	−1.04924	−	0.336233i	−0.0437565	−	0.0140219i
$576$	−3.06348	−	2.22575i	−0.127645	−	0.0927395i
$577$	−14.4475	−	10.4967i	−0.601456	−	0.436983i	0.244939	−	0.969538i	$-0.421232\pi$
$577$	−14.4475	−	10.4967i	−0.601456	−	0.436983i	−0.846395	+	0.532555i	$0.821232\pi$
$578$	−14.1643			−0.589157
$579$	34.3022	−	24.9220i	1.42555	−	1.03572i
$580$	3.28885	+	3.27557i	0.136562	+	0.136011i
$581$	−31.6199			−1.31181
$582$	25.5942			1.06091
$583$	24.2739	+	3.13493i	1.00532	+	0.129836i
$584$	−4.35293	−	3.16259i	−0.180126	−	0.130869i
$585$	4.04704	+	4.03070i	0.167325	+	0.166649i
$586$	−2.89533	+	8.91091i	−0.119605	+	0.368106i
$587$	12.3847	+	38.1162i	0.511171	+	1.57322i	0.790142	+	0.612923i	$0.210007\pi$
$587$	12.3847	+	38.1162i	0.511171	+	1.57322i	−0.278971	+	0.960299i	$0.589993\pi$
$588$	0.0648057	−	0.199451i	0.00267254	−	0.00822523i
$589$	21.9572	+	15.9529i	0.904733	+	0.657327i
$590$	0.524763	+	3.27039i	0.0216041	+	0.134640i
$591$	49.0324			2.01692
$592$	−9.77236			−0.401642
$593$	2.27244			0.0933179			0.0466589	−	0.998911i	$-0.485143\pi$
$593$	2.27244			0.0933179			0.0466589	+	0.998911i	$0.485143\pi$
$594$	1.25511	+	6.68009i	0.0514976	+	0.274087i
$595$	4.47889	−	8.83445i	0.183617	−	0.362177i
$596$	4.71276	+	3.42402i	0.193042	+	0.140253i
$597$	14.9960	+	46.1528i	0.613743	+	1.88891i
$598$	0.148651			0.00607877
$599$	−1.19630	−	3.68182i	−0.0488794	−	0.150435i	0.923638	−	0.383267i	$-0.125201\pi$
$599$	−1.19630	−	3.68182i	−0.0488794	−	0.150435i	−0.972517	+	0.232831i	$0.925201\pi$
$600$	12.3717	−	4.07522i	0.505073	−	0.166370i
$601$	10.3857	+	7.54562i	0.423640	+	0.307792i	0.779101	−	0.626899i	$-0.215676\pi$
$601$	10.3857	+	7.54562i	0.423640	+	0.307792i	−0.355461	+	0.934691i	$0.615676\pi$
$602$	−9.79547	+	30.1474i	−0.399234	+	1.22871i
$603$	−40.5934	−	29.4928i	−1.65309	−	1.20104i
$604$	−3.57533	+	11.0037i	−0.145478	+	0.447735i
$605$	−12.4461	−	21.2154i	−0.506005	−	0.862530i
$606$	−11.0060	−	33.8729i	−0.447088	−	1.37599i
$607$	−9.96875	+	30.6807i	−0.404619	+	1.24529i	0.516593	+	0.856231i	$0.327200\pi$
$607$	−9.96875	+	30.6807i	−0.404619	+	1.24529i	−0.921213	+	0.389059i	$0.872800\pi$
$608$	−2.71273	−	1.97092i	−0.110016	−	0.0799312i
$609$	−4.39587	−	13.5291i	−0.178130	−	0.548227i
$610$	−6.69914	−	6.67209i	−0.271240	−	0.270145i
$611$	6.09908	+	4.43124i	0.246742	+	0.179269i
$612$	−1.97047	−	6.06448i	−0.0796515	−	0.245142i
$613$	−41.7387			−1.68581			−0.842905	−	0.538062i	$-0.819157\pi$
$613$	−41.7387			−1.68581			−0.842905	+	0.538062i	$0.819157\pi$
$614$	−9.92499	−	30.5460i	−0.400540	−	1.23274i
$615$	11.8485	+	1.85206i	0.477778	+	0.0746822i
$616$	−6.34320	−	5.98985i	−0.255575	−	0.241338i
$617$	−4.48884	−	13.8152i	−0.180714	−	0.556180i	0.819134	−	0.573602i	$-0.194454\pi$
$617$	−4.48884	−	13.8152i	−0.180714	−	0.556180i	−0.999848	+	0.0174215i	$0.994454\pi$
$618$	−0.390649	+	1.20230i	−0.0157142	+	0.0483634i
$619$	−2.63242	−	1.91256i	−0.105806	−	0.0768724i	0.533624	−	0.845722i	$-0.320830\pi$
$619$	−2.63242	−	1.91256i	−0.105806	−	0.0768724i	−0.639430	+	0.768849i	$0.720830\pi$
$620$	−2.86747	−	17.8705i	−0.115160	−	0.717695i
$621$	0.451598			0.0181220
$622$	−14.7183			−0.590150
$623$	−13.3689			−0.535614
$624$	−1.42174	+	1.03295i	−0.0569151	+	0.0413512i
$625$	−7.53279	+	23.8381i	−0.301311	+	0.953526i
$626$	0.106514			0.00425716
$627$	5.34981	+	28.4735i	0.213651	+	1.13712i
$628$	−6.18539	+	19.0367i	−0.246824	+	0.759646i
$629$	−13.3133	−	9.67271i	−0.530838	−	0.385676i
$630$	−22.0058	−	3.43976i	−0.876733	−	0.137043i
$631$	7.14521	−	21.9907i	0.284446	−	0.875436i	−0.702118	−	0.712061i	$-0.747762\pi$
$631$	7.14521	−	21.9907i	0.284446	−	0.875436i	0.986564	−	0.163375i	$-0.0522380\pi$
$632$	−0.359908	−	1.10768i	−0.0143164	−	0.0440613i
$633$	16.1896	−	11.7624i	0.643478	−	0.467514i
$634$	3.97361	+	12.2295i	0.157812	+	0.485695i
$635$	−9.94546	+	5.09283i	−0.394673	+	0.202103i
$636$	5.94082	+	18.2840i	0.235569	+	0.725007i
$637$	−0.0439333	−	0.0319194i	−0.00174070	−	0.00126469i
$638$	6.82812	+	0.881838i	0.270328	+	0.0349123i
$639$	−0.857360	+	0.622909i	−0.0339167	+	0.0246419i
$640$	0.354265	+	2.20783i	0.0140036	+	0.0872720i
$641$	34.7563			1.37279			0.686396	−	0.727228i	$-0.259192\pi$
$641$	34.7563			1.37279			0.686396	+	0.727228i	$0.259192\pi$
$642$	−9.55521	+	29.4079i	−0.377114	+	1.16064i
$643$	−5.64852	−	17.3843i	−0.222756	−	0.685572i	−0.998512	−	0.0545385i	$-0.982631\pi$
$643$	−5.64852	−	17.3843i	−0.222756	−	0.685572i	0.775756	−	0.631033i	$-0.217369\pi$
$644$	−0.468951	+	0.340713i	−0.0184793	+	0.0134260i
$645$	−69.3549	−	10.8410i	−2.73085	−	0.426863i
$646$	−1.74486	−	5.37014i	−0.0686508	−	0.211285i
$647$	−22.4881	−	16.3386i	−0.884099	−	0.642335i	0.0502339	−	0.998737i	$-0.484003\pi$
$647$	−22.4881	−	16.3386i	−0.884099	−	0.642335i	−0.934333	+	0.356402i	$0.884003\pi$
$648$	4.87121	−	3.53914i	0.191359	−	0.139031i
$649$	3.57195	+	3.37298i	0.140211	+	0.132401i
$650$	−0.0136459	−	3.37287i	−0.000535237	−	0.132295i
$651$	−17.1403	+	52.7525i	−0.671782	+	2.06753i
$652$	−0.483443	+	1.48788i	−0.0189331	+	0.0582701i
$653$	−36.7606	+	26.7082i	−1.43855	+	1.04517i	−0.450212	+	0.892922i	$0.648652\pi$
$653$	−36.7606	+	26.7082i	−1.43855	+	1.04517i	−0.988342	+	0.152249i	$0.951348\pi$
$654$	29.7248			1.16233
$655$	12.0905	+	1.88988i	0.472413	+	0.0738436i
$656$	−0.636172	+	1.95794i	−0.0248384	+	0.0764446i
$657$	−16.4831	+	11.9757i	−0.643067	+	0.467215i
$658$	−29.3975			−1.14603
$659$	17.7324	+	12.8834i	0.690758	+	0.501865i	0.876909	−	0.480656i	$-0.159601\pi$
$659$	17.7324	+	12.8834i	0.690758	+	0.501865i	−0.186151	+	0.982521i	$0.559601\pi$
$660$	10.8715	−	15.9711i	0.423173	−	0.621676i
$661$	−19.2952	+	14.0188i	−0.750497	+	0.545268i	−0.895981	−	0.444093i	$-0.853526\pi$
$661$	−19.2952	+	14.0188i	−0.750497	+	0.545268i	0.145484	+	0.989361i	$0.453526\pi$
$662$	12.4050	−	9.01274i	0.482133	−	0.350290i
$663$	−2.95932			−0.114930
$664$	12.0205			0.466486
$665$	−19.4863	−	3.04593i	−0.755647	−	0.118116i
$666$	−11.4351	+	35.1935i	−0.443100	+	1.36372i
$667$	0.141355	−	0.435047i	0.00547330	−	0.0168451i
$668$	15.8910	−	11.5455i	0.614840	−	0.446708i
$669$	63.7261			2.46379
$670$	4.69428	+	29.2554i	0.181356	+	1.13023i
$671$	−13.9084	−	1.79624i	−0.536927	−	0.0693431i
$672$	2.11762	−	6.51736i	0.0816890	−	0.251413i
$673$	3.14494	+	9.67914i	0.121229	+	0.373103i	0.993195	−	0.116462i	$-0.0371554\pi$
$673$	3.14494	+	9.67914i	0.121229	+	0.373103i	−0.871966	+	0.489566i	$0.837155\pi$
$674$	22.6624	−	16.4652i	0.872923	−	0.634216i
$675$	−0.0414562	−	10.2467i	−0.00159565	−	0.394397i
$676$	−3.87660	−	11.9309i	−0.149100	−	0.458883i
$677$	−27.5675	−	20.0290i	−1.05951	−	0.769777i	−0.0855096	−	0.996337i	$-0.527252\pi$
$677$	−27.5675	−	20.0290i	−1.05951	−	0.769777i	−0.973997	+	0.226561i	$0.927252\pi$
$678$	24.4921	−	17.7946i	0.940614	−	0.683396i
$679$	7.98607	+	24.5786i	0.306477	+	0.943240i
$680$	−1.70268	+	3.35848i	−0.0652948	+	0.128792i
$681$	−20.4585	−	62.9649i	−0.783973	−	2.41282i
$682$	−19.5183	−	18.4310i	−0.747394	−	0.705761i
$683$	1.14297	+	3.51769i	0.0437344	+	0.134601i	0.970540	−	0.240942i	$-0.0774564\pi$
$683$	1.14297	+	3.51769i	0.0437344	+	0.134601i	−0.926805	+	0.375543i	$0.877456\pi$
$684$	−10.2722	+	7.46320i	−0.392768	+	0.285363i
$685$	−9.82981	−	9.79012i	−0.375578	−	0.374061i
$686$	18.6252			0.711114
$687$	−16.6086	+	51.1159i	−0.633656	+	1.95019i
$688$	3.72381	−	11.4607i	0.141969	−	0.436936i
$689$	4.97817			0.189653
$690$	−0.909511	−	0.905839i	−0.0346245	−	0.0344847i
$691$	31.3600	−	22.7844i	1.19299	−	0.866759i	0.199415	−	0.979915i	$-0.436096\pi$
$691$	31.3600	−	22.7844i	1.19299	−	0.866759i	0.993577	+	0.113156i	$0.0360959\pi$
$692$	−4.78317	−	14.7211i	−0.181829	−	0.559612i
$693$	−28.9939	+	15.8350i	−1.10139	+	0.601521i
$694$	9.77918	+	30.0972i	0.371213	+	1.14248i
$695$	3.86024	−	7.61418i	0.146427	−	0.288822i
$696$	1.67112	+	5.14318i	0.0633436	+	0.194952i
$697$	−2.80466	+	2.03770i	−0.106234	+	0.0771835i
$698$	−6.72587	−	4.88663i	−0.254578	−	0.184962i
$699$	−20.7262	−	63.7887i	−0.783937	−	2.41271i
$700$	7.77381	+	10.6092i	0.293823	+	0.400990i
$701$	0.0130352	−	0.00947065i	0.000492334	−	0.000357702i	−0.587539	−	0.809196i	$-0.699903\pi$
$701$	0.0130352	−	0.00947065i	0.000492334	−	0.000357702i	0.588031	+	0.808838i	$0.299903\pi$
$702$	0.427204	+	1.31480i	0.0161238	+	0.0496239i
$703$	−10.1258	+	31.1641i	−0.381903	+	1.17538i
$704$	2.41141	+	2.27708i	0.0908834	+	0.0858208i
$705$	−10.3141	−	64.2786i	−0.388450	−	2.42087i
$706$	31.7965			1.19668
$707$	29.0947	−	21.1385i	1.09422	−	0.794995i
$708$	−1.19246	+	3.67003i	−0.0448156	+	0.137928i
$709$	4.06448	−	12.5092i	0.152645	−	0.469792i	−0.845270	−	0.534340i	$-0.820560\pi$
$709$	4.06448	−	12.5092i	0.152645	−	0.469792i	0.997915	+	0.0645473i	$0.0205604\pi$
$710$	0.618289	+	0.0966457i	0.0232040	+	0.00362705i
$711$	−4.41028			−0.165399
$712$	5.08228			0.190467
$713$	−1.44298	+	1.04839i	−0.0540402	+	0.0392625i
$714$	9.33584	−	6.78288i	0.349385	−	0.253843i
$715$	−3.06330	−	3.95530i	−0.114561	−	0.147920i
$716$	−5.32003	−	3.86523i	−0.198819	−	0.144450i
$717$	−32.6787			−1.22041
$718$	1.61038	−	1.17001i	0.0600988	−	0.0436643i
$719$	−0.705584	+	2.17156i	−0.0263138	+	0.0809857i	−0.963351	−	0.268244i	$-0.913557\pi$
$719$	−0.705584	+	2.17156i	−0.0263138	+	0.0809857i	0.937037	+	0.349230i	$0.113557\pi$
$720$	8.36566	+	1.30765i	0.311770	+	0.0487332i
$721$	−1.27648			−0.0475386
$722$	6.27520	−	4.55920i	0.233539	−	0.169676i
$723$	−8.66452	+	26.6666i	−0.322237	+	0.991743i
$724$	−4.45524	+	13.7118i	−0.165578	+	0.509596i
$725$	−9.88417	−	3.16741i	−0.367089	−	0.117635i
$726$	−1.64069	−	28.6094i	−0.0608915	−	1.06179i
$727$	−9.64772	+	7.00948i	−0.357814	+	0.259967i	−0.752140	−	0.659004i	$-0.770978\pi$
$727$	−9.64772	+	7.00948i	−0.357814	+	0.259967i	0.394326	+	0.918971i	$0.370978\pi$
$728$	−1.43558	−	1.04301i	−0.0532063	−	0.0386566i
$729$	−11.9950	−	36.9168i	−0.444259	−	1.36729i
$730$	11.8869	+	1.85805i	0.439952	+	0.0687696i
$731$	16.4170	−	11.9276i	0.607204	−	0.441159i
$732$	−3.40395	−	10.4763i	−0.125814	−	0.387214i
$733$	−0.0745406	+	0.229412i	−0.00275322	+	0.00847353i	−0.952424	−	0.304777i	$-0.901418\pi$
$733$	−0.0745406	+	0.229412i	−0.00275322	+	0.00847353i	0.949670	+	0.313251i	$0.101418\pi$
$734$	20.9078			0.771720
$735$	0.0742949	+	0.463015i	0.00274041	+	0.0170786i
$736$	0.178275	−	0.129524i	0.00657130	−	0.00477433i
$737$	31.9530	+	30.1731i	1.17700	+	1.11144i
$738$	6.30677	+	4.58214i	0.232156	+	0.168671i
$739$	−10.6398	−	32.7460i	−0.391392	−	1.20458i	−0.931736	−	0.363136i	$-0.881706\pi$
$739$	−10.6398	−	32.7460i	−0.391392	−	1.20458i	0.540344	−	0.841444i	$-0.318294\pi$
$740$	19.4499	−	9.95981i	0.714991	−	0.366130i
$741$	1.82093	+	5.60425i	0.0668936	+	0.205877i
$742$	−15.7047	+	11.4102i	−0.576539	+	0.418880i
$743$	2.22082	+	6.83499i	0.0814740	+	0.250751i	0.983493	−	0.180944i	$-0.0579154\pi$
$743$	2.22082	+	6.83499i	0.0814740	+	0.250751i	−0.902019	+	0.431696i	$0.857915\pi$
$744$	6.51601	−	20.0542i	0.238888	−	0.735223i
$745$	−12.8695	−	2.01165i	−0.471502	−	0.0737011i
$746$	−17.1151	−	12.4348i	−0.626627	−	0.455271i
$747$	14.0657	−	43.2899i	0.514639	−	1.58389i
$748$	1.03131	+	5.48899i	0.0377085	+	0.200698i
$749$	−31.2224			−1.14084
$750$	−20.4699	+	20.7199i	−0.747457	+	0.756584i
$751$	19.9673	−	14.5071i	0.728616	−	0.529370i	−0.160510	−	0.987034i	$-0.551314\pi$
$751$	19.9673	−	14.5071i	0.728616	−	0.529370i	0.889125	+	0.457664i	$0.151314\pi$
$752$	11.1757			0.407534
$753$	52.9076			1.92806
$754$	1.40033			0.0509970
$755$	−4.09885	−	25.5446i	−0.149172	−	0.929662i
$756$	−4.36129	−	3.16866i	−0.158618	−	0.115243i
$757$	1.63737	−	5.03929i	0.0595111	−	0.183156i	−0.916882	−	0.399159i	$-0.869302\pi$
$757$	1.63737	−	5.03929i	0.0595111	−	0.183156i	0.976393	+	0.216003i	$0.0693021\pi$
$758$	−10.0354	−	30.8857i	−0.364502	−	1.12182i
$759$	−1.88828	−	0.243867i	−0.0685401	−	0.00885181i
$760$	7.40785	+	1.15793i	0.268711	+	0.0420026i
$761$	−5.27389	−	16.2314i	−0.191179	−	0.588387i	−1.00000		0.000332681i	$-0.999894\pi$
$761$	−5.27389	−	16.2314i	−0.191179	−	0.588387i	0.808821	−	0.588054i	$-0.200106\pi$
$762$	−13.0178			−0.471583
$763$	9.27494	+	28.5453i	0.335775	+	1.03341i
$764$	−17.7070	−	12.8649i	−0.640618	−	0.465436i
$765$	10.1026	+	10.0618i	0.365261	+	0.363786i
$766$	−5.24080	−	16.1295i	−0.189358	−	0.582783i
$767$	0.808400	+	0.587337i	0.0291896	+	0.0212075i
$768$	−0.805027	+	2.47762i	−0.0290489	+	0.0894034i
$769$	0.0149865	+	0.0461238i	0.000540429	+	0.00166327i	0.951326	−	0.308185i	$-0.0997217\pi$
$769$	0.0149865	+	0.0461238i	0.000540429	+	0.00166327i	−0.950786	+	0.309849i	$0.899722\pi$
$770$	18.7296	+	5.45669i	0.674967	+	0.196645i
$771$	−11.5799	+	35.6392i	−0.417039	+	1.28352i
$772$	−13.1672	−	9.56653i	−0.473898	−	0.344307i
$773$	1.44955	−	4.46125i	0.0521366	−	0.160460i	−0.921598	−	0.388145i	$-0.873116\pi$
$773$	1.44955	−	4.46125i	0.0521366	−	0.160460i	0.973735	+	0.227686i	$0.0731158\pi$
$774$	−36.9165	−	26.8214i	−1.32694	−	0.964075i
$775$	23.9204	+	32.6450i	0.859245	+	1.17264i
$776$	−3.03596	−	9.34371i	−0.108985	−	0.335420i
$777$	−66.9677			−2.40245
$778$	1.74801	+	5.37983i	0.0626693	+	0.192876i
$779$	5.58469	+	4.05752i	0.200092	+	0.145376i
$780$	1.77691	−	3.50489i	0.0636236	−	0.125495i
$781$	0.814631	−	0.444910i	0.0291498	−	0.0159201i
$782$	0.371076			0.0132696
$783$	4.25418			0.152032
$784$	−0.0805012			−0.00287504
$785$	−7.09109	−	44.1926i	−0.253092	−	1.57730i
$786$	11.5341	+	8.38004i	0.411409	+	0.298906i
$787$	14.0305	−	43.1815i	0.500134	−	1.53926i	−0.308665	−	0.951171i	$-0.599882\pi$
$787$	14.0305	−	43.1815i	0.500134	−	1.53926i	0.808800	−	0.588084i	$-0.200118\pi$
$788$	−5.81617	−	17.9003i	−0.207192	−	0.637672i
$789$	−1.93656	+	5.96011i	−0.0689432	+	0.212185i
$790$	1.84525	+	1.83780i	0.0656512	+	0.0653861i
$791$	24.7306	+	17.9679i	0.879320	+	0.638864i
$792$	11.0222	−	6.01978i	0.391658	−	0.213903i
$793$	−2.85237			−0.101291
$794$	−7.99853			−0.283857
$795$	−30.4587	−	30.3357i	−1.08026	−	1.07590i
$796$	15.0703	−	10.9492i	0.534152	−	0.388084i
$797$	10.3587			0.366923			0.183461	−	0.983027i	$-0.441270\pi$
$797$	10.3587			0.366923			0.183461	+	0.983027i	$0.441270\pi$
$798$	−18.5897	−	13.5062i	−0.658068	−	0.478115i
$799$	15.2251	+	11.0617i	0.538626	+	0.391335i
$800$	−2.95527	−	4.03316i	−0.104484	−	0.142594i
$801$	5.94701	−	18.3030i	0.210127	−	0.646705i
$802$	2.77456	−	2.01583i	0.0979730	−	0.0711816i
$803$	15.6616	−	8.55357i	0.552686	−	0.301849i
$804$	−10.6672	+	32.8303i	−0.376204	+	1.15784i
$805$	0.586102	−	1.15607i	0.0206574	−	0.0407460i
$806$	−4.41735	−	3.20940i	−0.155595	−	0.113046i
$807$	21.1914	+	15.3964i	0.745972	+	0.541981i
$808$	−11.0605	+	8.03594i	−0.389108	+	0.282704i
$809$	−2.78731	+	8.57845i	−0.0979965	+	0.301602i	−0.988023	−	0.154307i	$-0.950686\pi$
$809$	−2.78731	+	8.57845i	−0.0979965	+	0.301602i	0.890027	+	0.455909i	$0.150686\pi$
$810$	−6.08811	+	12.0086i	−0.213915	+	0.421939i
$811$	8.56017	−	26.3455i	0.300588	−	0.925115i	−0.680699	−	0.732564i	$-0.738324\pi$
$811$	8.56017	−	26.3455i	0.300588	−	0.925115i	0.981287	−	0.192552i	$-0.0616763\pi$
$812$	−4.41765	+	3.20961i	−0.155029	+	0.112635i
$813$	−39.2068	−	28.4854i	−1.37504	−	0.999027i
$814$	13.8813	−	29.2882i	0.486540	−	1.02655i
$815$	−0.554232	−	3.45404i	−0.0194139	−	0.120990i
$816$	−3.54908	+	2.57856i	−0.124243	+	0.0902676i
$817$	−32.6898	−	23.7505i	−1.14367	−	0.830926i
$818$	8.71590	+	6.33247i	0.304744	+	0.221410i
$819$	−5.43608	+	3.94954i	−0.189952	+	0.138008i
$820$	−0.729324	−	4.54524i	−0.0254691	−	0.158727i
$821$	−20.8328	+	15.1359i	−0.727069	+	0.528246i	−0.888635	−	0.458615i	$-0.848346\pi$
$821$	−20.8328	+	15.1359i	−0.727069	+	0.528246i	0.161566	+	0.986862i	$0.448346\pi$
$822$	−4.99469	−	15.3721i	−0.174210	−	0.536163i
$823$	17.1649	+	52.8283i	0.598332	+	1.84148i	0.537386	+	0.843336i	$0.319412\pi$
$823$	17.1649	+	52.8283i	0.598332	+	1.84148i	0.0609463	+	0.998141i	$0.480588\pi$
$824$	0.485262			0.0169049
$825$	−5.35999	+	42.8673i	−0.186611	+	1.49245i
$826$	−3.89648			−0.135576
$827$	−0.711080	−	2.18848i	−0.0247267	−	0.0761009i	0.937932	−	0.346820i	$-0.112739\pi$
$827$	−0.711080	−	2.18848i	−0.0247267	−	0.0761009i	−0.962658	+	0.270719i	$0.912739\pi$
$828$	−0.257853	−	0.793590i	−0.00896101	−	0.0275792i
$829$	20.2310	−	14.6987i	0.702653	−	0.510507i	−0.178142	−	0.984005i	$-0.557009\pi$
$829$	20.2310	−	14.6987i	0.702653	−	0.510507i	0.880795	+	0.473498i	$0.157009\pi$
$830$	−23.9244	+	12.2511i	−0.830426	+	0.425242i
$831$	−38.0905	+	27.6744i	−1.32135	+	0.960014i
$832$	0.545747	+	0.396508i	0.0189204	+	0.0137465i
$833$	−0.109671	−	0.0796803i	−0.00379986	−	0.00276076i
$834$	8.04630	−	5.84598i	0.278621	−	0.202430i
$835$	−19.8608	+	39.1747i	−0.687310	+	1.35570i
$836$	9.76027	−	5.33056i	0.337566	−	0.184361i
$837$	−13.4199	−	9.75010i	−0.463858	−	0.337013i
$838$	4.59861	−	3.34109i	0.158856	−	0.115416i
$839$	−1.18410	+	3.64429i	−0.0408797	+	0.125815i	−0.969414	−	0.245433i	$-0.921070\pi$
$839$	−1.18410	+	3.64429i	−0.0408797	+	0.125815i	0.928534	+	0.371248i	$0.121070\pi$
$840$	2.42769	+	15.1297i	0.0837634	+	0.522024i
$841$	−7.62989	+	23.4824i	−0.263100	+	0.809737i
$842$	16.5919	−	12.0547i	0.571793	−	0.415432i
$843$	32.2298	+	23.4163i	1.11005	+	0.806500i
$844$	−6.21452	−	4.51511i	−0.213912	−	0.155417i
$845$	19.8754	+	19.7951i	0.683734	+	0.680973i
$846$	13.0771	−	40.2473i	0.449601	−	1.38373i
$847$	26.9622	−	10.5025i	0.926431	−	0.360869i
$848$	5.97027	−	4.33765i	0.205020	−	0.148956i
$849$	18.2627	−	56.2067i	0.626773	−	1.92901i
$850$	−0.0340643	−	8.41970i	−0.00116840	−	0.288793i
$851$	−1.74217	−	1.26576i	−0.0597207	−	0.0433897i
$852$	0.589840	+	0.428544i	0.0202076	+	0.0146817i
$853$	16.9320			0.579742			0.289871	−	0.957066i	$-0.406388\pi$
$853$	16.9320			0.579742			0.289871	+	0.957066i	$0.406388\pi$
$854$	8.99844	−	6.53775i	0.307920	−	0.223717i
$855$	12.8384	−	25.3232i	0.439063	−	0.866036i
$856$	11.8694			0.405689
$857$	27.3942			0.935768			0.467884	−	0.883790i	$-0.345017\pi$
$857$	27.3942			0.935768			0.467884	+	0.883790i	$0.345017\pi$
$858$	−1.07627	−	5.72829i	−0.0367434	−	0.195561i
$859$	7.86701	+	5.71572i	0.268419	+	0.195018i	0.713850	−	0.700298i	$-0.246950\pi$
$859$	7.86701	+	5.71572i	0.268419	+	0.195018i	−0.445431	+	0.895316i	$0.646950\pi$
$860$	4.26908	+	26.6054i	0.145574	+	0.907238i
$861$	−4.35954	+	13.4173i	−0.148573	+	0.457259i
$862$	−7.43409	−	22.8798i	−0.253206	−	0.779288i
$863$	−7.84230	+	24.1361i	−0.266955	+	0.821603i	0.724282	+	0.689504i	$0.242172\pi$
$863$	−7.84230	+	24.1361i	−0.266955	+	0.821603i	−0.991237	+	0.132098i	$0.957828\pi$
$864$	1.65797	+	1.20459i	0.0564054	+	0.0409809i
$865$	24.5234	+	24.4244i	0.833820	+	0.830453i
$866$	9.35259			0.317814
$867$	36.8998			1.25318
$868$	21.2916			0.722684
$869$	3.83101	+	0.494768i	0.129958	+	0.0167838i
$870$	−8.56785	−	8.53326i	−0.290477	−	0.289304i
$871$	7.23156	+	5.25404i	0.245032	+	0.178026i
$872$	−3.52593	−	10.8517i	−0.119403	−	0.367485i
$873$	−37.2024			−1.25911
$874$	−0.228331	−	0.702730i	−0.00772340	−	0.0237702i
$875$	−26.2849	−	13.1925i	−0.888591	−	0.445988i
$876$	11.3399	+	8.23893i	0.383140	+	0.278368i
$877$	9.62023	−	29.6080i	0.324852	−	0.999792i	−0.646655	−	0.762782i	$-0.723833\pi$
$877$	9.62023	−	29.6080i	0.324852	−	0.999792i	0.971507	−	0.237010i	$-0.0761673\pi$
$878$	−18.4068	−	13.3734i	−0.621201	−	0.451329i
$879$	7.54269	−	23.2140i	0.254409	−	0.782989i
$880$	−7.12017	−	2.07440i	−0.240021	−	0.0699279i
$881$	5.58827	+	17.1989i	0.188274	+	0.579446i	0.999989	−	0.00460622i	$-0.00146621\pi$
$881$	5.58827	+	17.1989i	0.188274	+	0.579446i	−0.811716	+	0.584053i	$0.801466\pi$
$882$	−0.0941980	+	0.289912i	−0.00317181	+	0.00976184i
$883$	−18.1205	−	13.1653i	−0.609803	−	0.443048i	0.239542	−	0.970886i	$-0.423003\pi$
$883$	−18.1205	−	13.1653i	−0.609803	−	0.443048i	−0.849345	+	0.527838i	$0.823003\pi$
$884$	0.351031	+	1.08036i	0.0118065	+	0.0363366i
$885$	−1.36707	−	8.51977i	−0.0459536	−	0.286389i
$886$	14.5983	+	10.6063i	0.490438	+	0.356324i
$887$	18.1565	+	55.8799i	0.609635	+	1.87626i	0.461079	+	0.887359i	$0.347462\pi$
$887$	18.1565	+	55.8799i	0.609635	+	1.87626i	0.148556	+	0.988904i	$0.452538\pi$
$888$	25.4582			0.854321
$889$	−4.06188	−	12.5012i	−0.136231	−	0.419276i
$890$	−10.1152	+	5.17977i	−0.339064	+	0.173626i
$891$	3.68757	+	19.6265i	0.123538	+	0.657512i
$892$	−7.55913	−	23.2646i	−0.253098	−	0.778957i
$893$	11.5799	−	35.6393i	0.387507	−	1.19262i
$894$	−12.2773	−	8.92000i	−0.410615	−	0.298330i
$895$	14.5278	+	2.27086i	0.485611	+	0.0759065i
$896$	−2.63049			−0.0878786
$897$	−0.387253			−0.0129300
$898$	−39.6232			−1.32224
$899$	−13.5933	+	9.87612i	−0.453362	+	0.329387i
$900$	−17.9829	+	5.92353i	−0.599429	+	0.197451i
$901$	12.4270			0.414003
$902$	−4.96436	−	4.68782i	−0.165295	−	0.156087i
$903$	25.5184	−	78.5376i	0.849199	−	2.61357i
$904$	−9.40152	−	6.83060i	−0.312690	−	0.227182i
$905$	−5.10760	−	31.8313i	−0.169782	−	1.05811i
$906$	9.31417	−	28.6661i	0.309443	−	0.952367i
$907$	−12.7524	−	39.2477i	−0.423435	−	1.30320i	−0.904485	−	0.426506i	$-0.859744\pi$
$907$	−12.7524	−	39.2477i	−0.423435	−	1.30320i	0.481049	−	0.876694i	$-0.340256\pi$
$908$	−20.5599	+	14.9377i	−0.682305	+	0.495724i
$909$	15.9977	+	49.2359i	0.530610	+	1.63305i
$910$	3.92025	+	0.612781i	0.129955	+	0.0203135i
$911$	1.97287	+	6.07188i	0.0653642	+	0.201170i	0.978405	−	0.206699i	$-0.0662720\pi$
$911$	1.97287	+	6.07188i	0.0653642	+	0.201170i	−0.913040	+	0.407869i	$0.866272\pi$
$912$	7.06700	+	5.13448i	0.234012	+	0.170020i
$913$	−17.0748	+	36.0260i	−0.565092	+	1.19229i
$914$	−9.13258	+	6.63521i	−0.302079	+	0.219473i
$915$	17.4521	+	17.3816i	0.576948	+	0.574619i
$916$	20.6310			0.681669
$917$	−4.44856	+	13.6912i	−0.146904	+	0.452125i
$918$	1.06643	+	3.28213i	0.0351974	+	0.108326i
$919$	31.8325	−	23.1277i	1.05006	−	0.762912i	0.0778348	−	0.996966i	$-0.475199\pi$
$919$	31.8325	−	23.1277i	1.05006	−	0.762912i	0.972224	+	0.234054i	$0.0751993\pi$
$920$	−0.222811	+	0.439486i	−0.00734585	+	0.0144894i
$921$	25.8558	+	79.5760i	0.851978	+	2.62212i
$922$	−10.8723	−	7.89922i	−0.358061	−	0.260147i
$923$	0.152736	−	0.110969i	0.00502735	−	0.00365258i
$924$	16.5248	+	15.6043i	0.543626	+	0.513344i
$925$	−28.5601	+	39.6459i	−0.939050	+	1.30355i
$926$	1.56577	−	4.81895i	0.0514544	−	0.158360i
$927$	0.567827	−	1.74759i	0.0186499	−	0.0573985i
$928$	1.67940	−	1.22016i	0.0551290	−	0.0400536i
$929$	23.5935			0.774077			0.387038	−	0.922064i	$-0.373498\pi$
$929$	23.5935			0.774077			0.387038	+	0.922064i	$0.373498\pi$
$930$	7.47012	+	46.5548i	0.244955	+	1.52659i
$931$	−0.0834130	+	0.256719i	−0.00273375	+	0.00841362i
$932$	−20.8289	+	15.1331i	−0.682274	+	0.495701i
$933$	38.3430			1.25529
$934$	−16.2952	−	11.8392i	−0.533196	−	0.387389i
$935$	−7.64690	−	9.87362i	−0.250080	−	0.322902i
$936$	2.06656	−	1.50145i	0.0675477	−	0.0490763i
$937$	−27.4483	+	19.9424i	−0.896697	+	0.651488i	−0.937615	−	0.347674i	$-0.886972\pi$
$937$	−27.4483	+	19.9424i	−0.896697	+	0.651488i	0.0409187	+	0.999162i	$0.486972\pi$
$938$	−34.8560			−1.13809
$939$	−0.277483			−0.00905530
$940$	−22.2428	+	11.3900i	−0.725482	+	0.371502i
$941$	0.181021	−	0.557126i	0.00590113	−	0.0181618i	−0.948063	−	0.318084i	$-0.896961\pi$
$941$	0.181021	−	0.557126i	0.00590113	−	0.0181618i	0.953964	+	0.299922i	$0.0969607\pi$
$942$	16.1137	−	49.5929i	0.525013	−	1.61582i
$943$	−0.367014	+	0.266651i	−0.0119516	+	0.00868336i
$944$	1.48127			0.0482113
$945$	11.9097	+	1.86162i	0.387422	+	0.0605585i
$946$	29.0587	+	27.4400i	0.944781	+	0.892152i
$947$	13.6857	−	42.1201i	0.444724	−	1.36872i	−0.438062	−	0.898945i	$-0.644335\pi$
$947$	13.6857	−	42.1201i	0.444724	−	1.36872i	0.882786	−	0.469776i	$-0.155665\pi$
$948$	0.937605	+	2.88565i	0.0304520	+	0.0937216i
$949$	2.93640	−	2.13342i	0.0953196	−	0.0692538i
$950$	−15.9239	+	5.24532i	−0.516641	+	0.170181i
$951$	−10.3517	−	31.8594i	−0.335678	−	1.03311i
$952$	−3.58364	−	2.60367i	−0.116147	−	0.0843854i
$953$	38.6469	−	28.0786i	1.25190	−	0.909556i	0.253566	−	0.967318i	$-0.418396\pi$
$953$	38.6469	−	28.0786i	1.25190	−	0.909556i	0.998330	+	0.0577620i	$0.0183965\pi$
$954$	−8.63526	−	26.5766i	−0.279577	−	0.860449i
$955$	48.3539	+	7.55827i	1.56470	+	0.244580i
$956$	3.87632	+	11.9301i	0.125369	+	0.385846i
$957$	−17.7881	−	2.29730i	−0.575007	−	0.0742611i
$958$	12.0427	+	37.0637i	0.389083	+	1.19747i
$959$	13.2036	−	9.59300i	0.426367	−	0.309774i
$960$	−0.922904	−	5.75166i	−0.0297866	−	0.185634i
$961$	34.5152			1.11339
$962$	2.03711	−	6.26960i	0.0656792	−	0.202140i
$963$	13.8889	−	42.7458i	0.447565	−	1.37746i
$964$	10.7630			0.346653
$965$	35.9566	+	5.62043i	1.15748	+	0.180928i
$966$	1.22168	−	0.887600i	0.0393068	−	0.0285580i
$967$	−15.9488	−	49.0853i	−0.512878	−	1.57848i	−0.787110	−	0.616813i	$-0.788424\pi$
$967$	−15.9488	−	49.0853i	−0.512878	−	1.57848i	0.274232	−	0.961664i	$-0.411576\pi$
$968$	−10.2498	+	3.99258i	−0.329442	+	0.128326i
$969$	4.54559	+	13.9899i	0.146025	+	0.449420i
$970$	15.5654	+	15.5025i	0.499775	+	0.497757i
$971$	−4.25630	−	13.0996i	−0.136591	−	0.420385i	0.859243	−	0.511568i	$-0.170935\pi$
$971$	−4.25630	−	13.0996i	−0.136591	−	0.420385i	−0.995834	+	0.0911831i	$0.970935\pi$
$972$	−17.6640	+	12.8337i	−0.566574	+	0.411640i
$973$	8.12467	+	5.90291i	0.260465	+	0.189239i
$974$	0.426445	+	1.31246i	0.0136642	+	0.0420540i
$975$	0.0355493	+	8.78675i	0.00113849	+	0.281401i
$976$	−3.42082	+	2.48537i	−0.109498	+	0.0795548i
$977$	7.82539	+	24.0841i	0.250356	+	0.770518i	0.994709	+	0.102731i	$0.0327581\pi$
$977$	7.82539	+	24.0841i	0.250356	+	0.770518i	−0.744353	+	0.667787i	$0.767242\pi$
$978$	1.25943	−	3.87612i	0.0402721	−	0.123945i
$979$	−7.21922	+	15.2318i	−0.230727	+	0.486811i
$980$	0.160221	−	0.0820454i	0.00511807	−	0.00262084i
$981$	−43.2064			−1.37948
$982$	−3.06422	+	2.22629i	−0.0977832	+	0.0710437i
$983$	−10.7178	+	32.9859i	−0.341843	+	1.05209i	0.621409	+	0.783487i	$0.286561\pi$
$983$	−10.7178	+	32.9859i	−0.341843	+	1.05209i	−0.963252	+	0.268599i	$0.913439\pi$
$984$	1.65731	−	5.10067i	0.0528330	−	0.162603i
$985$	29.8196	+	29.6992i	0.950130	+	0.946294i
$986$	3.49564			0.111324
$987$	76.5841			2.43770
$988$	1.82996	−	1.32954i	0.0582187	−	0.0422983i
$989$	2.14831	−	1.56084i	0.0683121	−	0.0496317i
$990$	−15.8022	+	23.2148i	−0.502228	+	0.737814i
$991$	11.1289	+	8.08561i	0.353521	+	0.256848i	0.750345	−	0.661047i	$-0.229888\pi$
$991$	11.1289	+	8.08561i	0.353521	+	0.256848i	−0.396824	+	0.917895i	$0.629888\pi$
$992$	−8.09414			−0.256989
$993$	−32.3165	+	23.4793i	−1.02553	+	0.745093i
$994$	−0.227493	+	0.700152i	−0.00721564	+	0.0222075i
$995$	−18.8350	+	37.1515i	−0.597111	+	1.17778i
$996$	−31.3149			−0.992251
$997$	20.5768	−	14.9499i	0.651675	−	0.473469i	−0.212167	−	0.977234i	$-0.568052\pi$
$997$	20.5768	−	14.9499i	0.651675	−	0.473469i	0.863841	+	0.503764i	$0.168052\pi$
$998$	−9.79884	+	30.1577i	−0.310177	+	0.954626i
$999$	6.18873	−	19.0469i	0.195803	−	0.602619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	550.2.g.c.361.3	yes	60
11.5	even	5		550.2.j.c.511.13	yes	60
25.16	even	5		550.2.j.c.141.13	yes	60
275.16	even	5	inner	550.2.g.c.291.3	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
550.2.g.c.291.3	✓	60	275.16	even	5	inner
550.2.g.c.361.3	yes	60	1.1	even	1	trivial
550.2.j.c.141.13	yes	60	25.16	even	5
550.2.j.c.511.13	yes	60	11.5	even	5

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.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.309017 + 0.951057i) q^{2} +(-0.805027 - 2.47762i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.01112 - 1.99440i) q^{5} +(2.10759 - 1.53125i) q^{6} +(2.12811 + 1.54617i) q^{7} +(-0.809017 - 0.587785i) q^{8} +(-3.06348 + 2.22575i) q^{9} +(2.20924 + 0.345330i) q^{10} +(2.91080 - 1.58973i) q^{11} +(2.10759 + 1.53125i) q^{12} +(0.545747 - 0.396508i) q^{13} +(-0.812867 + 2.50175i) q^{14} +(-5.75535 - 0.899627i) q^{15} +(0.309017 - 0.951057i) q^{16} +(1.36235 - 0.989803i) q^{17} +(-3.06348 - 2.22575i) q^{18} +(-2.71273 - 1.97092i) q^{19} +(0.354265 + 2.20783i) q^{20} +(2.11762 - 6.51736i) q^{21} +(2.41141 + 2.27708i) q^{22} +(0.178275 - 0.129524i) q^{23} +(-0.805027 + 2.47762i) q^{24} +(-2.95527 - 4.03316i) q^{25} +(0.545747 + 0.396508i) q^{26} +(1.65797 + 1.20459i) q^{27} -2.63049 q^{28} +(1.67940 - 1.22016i) q^{29} +(-0.922904 - 5.75166i) q^{30} -8.09414 q^{31} +1.00000 q^{32} +(-6.28202 - 5.93208i) q^{33} +(1.36235 + 0.989803i) q^{34} +(5.23546 - 2.68095i) q^{35} +(1.17014 - 3.60133i) q^{36} +(-3.01983 - 9.29407i) q^{37} +(1.03617 - 3.18901i) q^{38} +(-1.42174 - 1.03295i) q^{39} +(-1.99029 + 1.01918i) q^{40} -2.05870 q^{41} +6.85276 q^{42} +12.0505 q^{43} +(-1.42047 + 2.99704i) q^{44} +(1.34148 + 8.36030i) q^{45} +(0.178275 + 0.129524i) q^{46} +(3.45347 + 10.6287i) q^{47} -2.60512 q^{48} +(-0.0248762 - 0.0765612i) q^{49} +(2.92254 - 4.05694i) q^{50} +(-3.54908 - 2.57856i) q^{51} +(-0.208457 + 0.641564i) q^{52} +(5.97027 + 4.33765i) q^{53} +(-0.633289 + 1.94906i) q^{54} +(-0.227385 - 7.41271i) q^{55} +(-0.812867 - 2.50175i) q^{56} +(-2.69935 + 8.30776i) q^{57} +(1.67940 + 1.22016i) q^{58} +(0.457738 + 1.40877i) q^{59} +(5.18496 - 2.65509i) q^{60} +(-3.42082 - 2.48537i) q^{61} +(-2.50123 - 7.69799i) q^{62} -9.96081 q^{63} +(0.309017 + 0.951057i) q^{64} +(-0.238980 - 1.48936i) q^{65} +(3.70049 - 7.80767i) q^{66} +(4.09471 + 12.6022i) q^{67} +(-0.520370 + 1.60153i) q^{68} +(-0.464428 - 0.337427i) q^{69} +(4.16758 + 4.15075i) q^{70} +0.279865 q^{71} +3.78667 q^{72} +5.38052 q^{73} +(7.90601 - 5.74405i) q^{74} +(-7.61357 + 10.5688i) q^{75} +3.35312 q^{76} +(8.65250 + 1.11745i) q^{77} +(0.543056 - 1.67135i) q^{78} +(0.942252 + 0.684586i) q^{79} +(-1.58433 - 1.57794i) q^{80} +(-1.86064 + 5.72646i) q^{81} +(-0.636172 - 1.95794i) q^{82} +(-9.72480 + 7.06548i) q^{83} +(2.11762 + 6.51736i) q^{84} +(-0.596566 - 3.71788i) q^{85} +(3.72381 + 11.4607i) q^{86} +(-4.37505 - 3.17866i) q^{87} +(-3.28931 - 0.424807i) q^{88} +(-4.11165 + 2.98729i) q^{89} +(-7.53658 + 3.85930i) q^{90} +1.77448 q^{91} +(-0.0680950 + 0.209575i) q^{92} +(6.51601 + 20.0542i) q^{93} +(-9.04130 + 6.56889i) q^{94} +(-6.67370 + 3.41744i) q^{95} +(-0.805027 - 2.47762i) q^{96} +(7.94824 + 5.77473i) q^{97} +(0.0651268 - 0.0473174i) q^{98} +(-5.37884 + 11.3488i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 15 q^{2} - 4 q^{3} - 15 q^{4} + q^{6} - 3 q^{7} - 15 q^{8} - 17 q^{9} - 5 q^{10} + 7 q^{11} + q^{12} + 12 q^{13} - 3 q^{14} + 12 q^{15} - 15 q^{16} + q^{17} - 17 q^{18} + 3 q^{19} - 5 q^{20} - 4 q^{21}+ \cdots + 21 q^{99}+O(q^{100}) \) 60 * q - 15 * q^2 - 4 * q^3 - 15 * q^4 + q^6 - 3 * q^7 - 15 * q^8 - 17 * q^9 - 5 * q^10 + 7 * q^11 + q^12 + 12 * q^13 - 3 * q^14 + 12 * q^15 - 15 * q^16 + q^17 - 17 * q^18 + 3 * q^19 - 5 * q^20 - 4 * q^21 - 3 * q^22 - 3 * q^23 - 4 * q^24 + 8 * q^25 + 12 * q^26 + 2 * q^27 + 12 * q^28 + 18 * q^29 + 2 * q^30 - 20 * q^31 + 60 * q^32 + 10 * q^33 + q^34 - 19 * q^35 - 12 * q^36 - 36 * q^37 - 22 * q^38 + 13 * q^39 + 64 * q^41 + 46 * q^42 + 40 * q^43 - 8 * q^44 - 20 * q^45 - 3 * q^46 - 9 * q^47 + 6 * q^48 - 30 * q^49 + 18 * q^50 - 48 * q^51 - 8 * q^52 + 31 * q^53 - 8 * q^54 - 42 * q^55 - 3 * q^56 + 30 * q^57 + 18 * q^58 + 23 * q^59 - 8 * q^60 - 41 * q^61 - 5 * q^62 + 6 * q^63 - 15 * q^64 - 7 * q^65 - 30 * q^66 - 40 * q^67 - 4 * q^68 - 22 * q^69 - 4 * q^70 + 4 * q^71 + 58 * q^72 + 74 * q^73 - 11 * q^74 + 35 * q^75 + 38 * q^76 + 22 * q^77 - 12 * q^78 - 45 * q^79 + 10 * q^80 + 24 * q^81 - 11 * q^82 + 16 * q^83 - 4 * q^84 + 9 * q^85 - 20 * q^86 + 68 * q^87 + 7 * q^88 + q^89 + 10 * q^90 + 10 * q^91 + 2 * q^92 - 40 * q^93 - 24 * q^94 + 24 * q^95 - 4 * q^96 + 6 * q^97 - 30 * q^98 + 21 * q^99

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