LMFDB - Embedded newform 504.2.w.a.445.65

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [504,2,Mod(205,504)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(504, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("504.205"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$504 = 2^{3} \cdot 3^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	504.w (of order $6$ , degree $2$ , minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			445.65
Character	$\chi$	$=$	504.445
Dual form			504.2.w.a.205.65

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.850020 - 1.13025i) q^{2} +(0.219417 - 1.71810i) q^{3} +(-0.554934 - 1.92147i) q^{4} -0.246812i q^{5} +(-1.75537 - 1.70841i) q^{6} +(-0.204482 - 2.63784i) q^{7} +(-2.64345 - 1.00607i) q^{8} +(-2.90371 - 0.753959i) q^{9} +(-0.278959 - 0.209795i) q^{10} +1.86910i q^{11} +(-3.42303 + 0.531827i) q^{12} +(4.72805 + 2.72974i) q^{13} +(-3.15523 - 2.01110i) q^{14} +(-0.424046 - 0.0541547i) q^{15} +(-3.38410 + 2.13258i) q^{16} +(2.66475 - 4.61548i) q^{17} +(-3.32037 + 2.64104i) q^{18} +(-5.13617 + 2.96537i) q^{19} +(-0.474242 + 0.136964i) q^{20} +(-4.57693 - 0.227466i) q^{21} +(2.11255 + 1.58877i) q^{22} -1.17246 q^{23} +(-2.30855 + 4.32095i) q^{24} +4.93908 q^{25} +(7.10422 - 3.02355i) q^{26} +(-1.93250 + 4.82343i) q^{27} +(-4.95505 + 1.85673i) q^{28} +(-0.0123976 + 0.00715774i) q^{29} +(-0.421656 + 0.433246i) q^{30} +(-3.14612 - 5.44924i) q^{31} +(-0.466202 + 5.63761i) q^{32} +(3.21129 + 0.410111i) q^{33} +(-2.95156 - 6.93509i) q^{34} +(-0.651049 + 0.0504685i) q^{35} +(0.162658 + 5.99779i) q^{36} +(9.20518 - 5.31461i) q^{37} +(-1.01423 + 8.32578i) q^{38} +(5.72737 - 7.52429i) q^{39} +(-0.248311 + 0.652434i) q^{40} +(-5.17669 + 8.96629i) q^{41} +(-4.14757 + 4.97972i) q^{42} +(9.20509 - 5.31456i) q^{43} +(3.59141 - 1.03722i) q^{44} +(-0.186086 + 0.716670i) q^{45} +(-0.996614 + 1.32517i) q^{46} +(4.61006 - 7.98486i) q^{47} +(2.92145 + 6.28213i) q^{48} +(-6.91637 + 1.07878i) q^{49} +(4.19832 - 5.58240i) q^{50} +(-7.34515 - 5.59101i) q^{51} +(2.62136 - 10.5996i) q^{52} +(-5.81764 - 3.35882i) q^{53} +(3.80902 + 6.28421i) q^{54} +0.461315 q^{55} +(-2.11332 + 7.17871i) q^{56} +(3.96783 + 9.47509i) q^{57} +(-0.00244813 + 0.0200966i) q^{58} +(-10.7402 + 6.20086i) q^{59} +(0.131261 + 0.844845i) q^{60} +(2.41510 + 1.39436i) q^{61} +(-8.83328 - 1.07606i) q^{62} +(-1.39506 + 7.81369i) q^{63} +(5.97563 + 5.31900i) q^{64} +(0.673732 - 1.16694i) q^{65} +(3.19319 - 3.28096i) q^{66} +(1.70496 - 0.984357i) q^{67} +(-10.3473 - 2.55895i) q^{68} +(-0.257257 + 2.01440i) q^{69} +(-0.496363 + 0.778748i) q^{70} +8.78800 q^{71} +(6.91727 + 4.91440i) q^{72} +(0.891446 - 1.54403i) q^{73} +(1.81774 - 14.9217i) q^{74} +(1.08372 - 8.48582i) q^{75} +(8.54810 + 8.22342i) q^{76} +(4.93037 - 0.382196i) q^{77} +(-3.63596 - 12.8692i) q^{78} +(2.32610 - 4.02893i) q^{79} +(0.526345 + 0.835235i) q^{80} +(7.86309 + 4.37856i) q^{81} +(5.73387 + 13.4725i) q^{82} +(-3.89087 + 2.24639i) q^{83} +(2.10282 + 8.92066i) q^{84} +(-1.13916 - 0.657692i) q^{85} +(1.81772 - 14.9215i) q^{86} +(0.00957745 + 0.0228707i) q^{87} +(1.88045 - 4.94086i) q^{88} +(6.71334 + 11.6278i) q^{89} +(0.651841 + 0.819508i) q^{90} +(6.23381 - 13.0300i) q^{91} +(0.650637 + 2.25285i) q^{92} +(-10.0526 + 4.20969i) q^{93} +(-5.10625 - 11.9978i) q^{94} +(0.731888 + 1.26767i) q^{95} +(9.58367 + 2.03797i) q^{96} +(-2.06206 - 3.57159i) q^{97} +(-4.65976 + 8.73422i) q^{98} +(1.40922 - 5.42732i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$184 q + q^{2} + q^{4} - 2 q^{6} - 2 q^{7} - 8 q^{8} - 2 q^{9} + 2 q^{10} - 17 q^{12} - 7 q^{14} - 2 q^{15} + q^{16} - 4 q^{17} + 13 q^{18} + 6 q^{20} + 2 q^{22} - 4 q^{23} + 12 q^{24} - 156 q^{25} - 4 q^{26}+ \cdots - 83 q^{98}+O(q^{100})$ 184 * q + q^2 + q^4 - 2 * q^6 - 2 * q^7 - 8 * q^8 - 2 * q^9 + 2 * q^10 - 17 * q^12 - 7 * q^14 - 2 * q^15 + q^16 - 4 * q^17 + 13 * q^18 + 6 * q^20 + 2 * q^22 - 4 * q^23 + 12 * q^24 - 156 * q^25 - 4 * q^26 - 8 * q^28 - 18 * q^30 + 2 * q^31 + q^32 + 22 * q^33 - 18 * q^36 + 10 * q^38 - 14 * q^39 + 8 * q^40 - 4 * q^41 + 3 * q^42 + 17 * q^44 - 6 * q^46 + 42 * q^47 - 3 * q^48 - 2 * q^49 - 31 * q^50 - 18 * q^52 - 58 * q^54 + 4 * q^55 - 34 * q^56 - 20 * q^57 - 10 * q^58 + 26 * q^60 + 32 * q^62 + 50 * q^63 - 8 * q^64 + 22 * q^65 + 79 * q^66 + 24 * q^68 + 8 * q^70 - 16 * q^71 - 27 * q^72 - 4 * q^73 - 38 * q^74 - 6 * q^76 - 47 * q^78 + 2 * q^79 - 11 * q^80 + 6 * q^81 + q^84 + 46 * q^86 + 4 * q^87 + 14 * q^88 + 4 * q^89 - 35 * q^90 - 48 * q^92 + 9 * q^94 + 22 * q^95 - 16 * q^96 - 4 * q^97 - 83 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$ .

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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

)

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

$2$	0.850020	−	1.13025i	0.601055	−	0.799208i
$2$	0.850020	−	1.13025i	0.601055	−	0.799208i
$3$	0.219417	−	1.71810i	0.126680	−	0.991944i
$3$	0.219417	−	1.71810i	0.126680	−	0.991944i
$4$	−0.554934	−	1.92147i	−0.277467	−	0.960735i
$5$		−	0.246812i		−	0.110378i	−0.998476	−	0.0551888i	$-0.982424\pi$
$5$		−	0.246812i		−	0.110378i	0.998476	−	0.0551888i	$-0.0175761\pi$
$6$	−1.75537	−	1.70841i	−0.716627	−	0.697456i
$7$	−0.204482	−	2.63784i	−0.0772869	−	0.997009i
$7$	−0.204482	−	2.63784i	−0.0772869	−	0.997009i
$8$	−2.64345	−	1.00607i	−0.934600	−	0.355701i
$9$	−2.90371	−	0.753959i	−0.967904	−	0.251320i
$10$	−0.278959	−	0.209795i	−0.0882146	−	0.0663429i
$11$			1.86910i			0.563554i	0.959480	+	0.281777i	$0.0909238\pi$
$11$			1.86910i			0.563554i	−0.959480	+	0.281777i	$0.909076\pi$
$12$	−3.42303	+	0.531827i	−0.988145	+	0.153525i
$13$	4.72805	+	2.72974i	1.31132	+	0.757093i	0.982315	−	0.187234i	$-0.0599521\pi$
$13$	4.72805	+	2.72974i	1.31132	+	0.757093i	0.329009	+	0.944327i	$0.393285\pi$
$14$	−3.15523	−	2.01110i	−0.843271	−	0.537488i
$15$	−0.424046	−	0.0541547i	−0.109488	−	0.0139827i
$16$	−3.38410	+	2.13258i	−0.846024	+	0.533144i
$17$	2.66475	−	4.61548i	0.646297	−	1.11942i	−0.337704	−	0.941253i	$-0.609650\pi$
$17$	2.66475	−	4.61548i	0.646297	−	1.11942i	0.984000	−	0.178166i	$-0.0570165\pi$
$18$	−3.32037	+	2.64104i	−0.782620	+	0.622500i
$19$	−5.13617	+	2.96537i	−1.17832	+	0.680302i	−0.955625	−	0.294586i	$-0.904818\pi$
$19$	−5.13617	+	2.96537i	−1.17832	+	0.680302i	−0.222693	+	0.974889i	$0.571485\pi$
$20$	−0.474242	+	0.136964i	−0.106044	+	0.0306261i
$21$	−4.57693	−	0.227466i	−0.998767	−	0.0496372i
$22$	2.11255	+	1.58877i	0.450397	+	0.338726i
$23$	−1.17246			−0.244475			−0.122237	−	0.992501i	$-0.539007\pi$
$23$	−1.17246			−0.244475			−0.122237	+	0.992501i	$0.539007\pi$
$24$	−2.30855	+	4.32095i	−0.471230	+	0.882010i
$25$	4.93908			0.987817
$26$	7.10422	−	3.02355i	1.39325	−	0.592966i
$27$	−1.93250	+	4.82343i	−0.371909	+	0.928269i
$28$	−4.95505	+	1.85673i	−0.936417	+	0.350889i
$29$	−0.0123976	+	0.00715774i	−0.00230217	+	0.00132916i	−0.501151	−	0.865360i	$-0.667090\pi$
$29$	−0.0123976	+	0.00715774i	−0.00230217	+	0.00132916i	0.498848	+	0.866689i	$0.333756\pi$
$30$	−0.421656	+	0.433246i	−0.0769835	+	0.0790996i
$31$	−3.14612	−	5.44924i	−0.565060	−	0.978713i	−0.997044	−	0.0768318i	$-0.975520\pi$
$31$	−3.14612	−	5.44924i	−0.565060	−	0.978713i	0.431984	−	0.901881i	$-0.357814\pi$
$32$	−0.466202	+	5.63761i	−0.0824136	+	0.996598i
$33$	3.21129	+	0.410111i	0.559013	+	0.0713912i
$34$	−2.95156	−	6.93509i	−0.506189	−	1.18936i
$35$	−0.651049	+	0.0504685i	−0.110047	+	0.00853074i
$36$	0.162658	+	5.99779i	0.0271097	+	0.999632i
$37$	9.20518	−	5.31461i	1.51332	−	0.873717i	0.513443	−	0.858124i	$-0.328370\pi$
$37$	9.20518	−	5.31461i	1.51332	−	0.873717i	0.999878	−	0.0155929i	$-0.00496358\pi$
$38$	−1.01423	+	8.32578i	−0.164530	+	1.35062i
$39$	5.72737	−	7.52429i	0.917113	−	1.20485i
$40$	−0.248311	+	0.652434i	−0.0392614	+	0.103159i
$41$	−5.17669	+	8.96629i	−0.808463	+	1.40030i	0.105464	+	0.994423i	$0.466367\pi$
$41$	−5.17669	+	8.96629i	−0.808463	+	1.40030i	−0.913928	+	0.405877i	$0.866966\pi$
$42$	−4.14757	+	4.97972i	−0.639984	+	0.768388i
$43$	9.20509	−	5.31456i	1.40376	−	0.810463i	0.408987	−	0.912540i	$-0.365882\pi$
$43$	9.20509	−	5.31456i	1.40376	−	0.810463i	0.994777	+	0.102077i	$0.0325487\pi$
$44$	3.59141	−	1.03722i	0.541426	−	0.156367i
$45$	−0.186086	+	0.716670i	−0.0277401	+	0.106835i
$46$	−0.996614	+	1.32517i	−0.146943	+	0.195386i
$47$	4.61006	−	7.98486i	0.672446	−	1.16471i	−0.304762	−	0.952428i	$-0.598577\pi$
$47$	4.61006	−	7.98486i	0.672446	−	1.16471i	0.977208	−	0.212282i	$-0.0680897\pi$
$48$	2.92145	+	6.28213i	0.421674	+	0.906747i
$49$	−6.91637	+	1.07878i	−0.988053	+	0.154111i
$50$	4.19832	−	5.58240i	0.593732	−	0.789471i
$51$	−7.34515	−	5.59101i	−1.02853	−	0.782898i
$52$	2.62136	−	10.5996i	0.363517	−	1.46990i
$53$	−5.81764	−	3.35882i	−0.799114	−	0.461369i	0.0440470	−	0.999029i	$-0.485975\pi$
$53$	−5.81764	−	3.35882i	−0.799114	−	0.461369i	−0.843161	+	0.537661i	$0.819308\pi$
$54$	3.80902	+	6.28421i	0.518342	+	0.855173i
$55$	0.461315			0.0622037
$56$	−2.11332	+	7.17871i	−0.282404	+	0.959295i
$57$	3.96783	+	9.47509i	0.525552	+	1.25501i
$58$	−0.00244813	+	0.0200966i	−0.000321456	+	0.00263881i
$59$	−10.7402	+	6.20086i	−1.39825	+	0.807283i	−0.994210	−	0.107457i	$-0.965729\pi$
$59$	−10.7402	+	6.20086i	−1.39825	+	0.807283i	−0.404045	+	0.914739i	$0.632396\pi$
$60$	0.131261	+	0.844845i	0.0169457	+	0.109069i
$61$	2.41510	+	1.39436i	0.309222	+	0.178530i	0.646578	−	0.762847i	$-0.276199\pi$
$61$	2.41510	+	1.39436i	0.309222	+	0.178530i	−0.337356	+	0.941377i	$0.609533\pi$
$62$	−8.83328	−	1.07606i	−1.12183	−	0.136659i
$63$	−1.39506	+	7.81369i	−0.175762	+	0.984433i
$64$	5.97563	+	5.31900i	0.746954	+	0.664875i
$65$	0.673732	−	1.16694i	0.0835661	−	0.144741i
$66$	3.19319	−	3.28096i	0.393054	−	0.403858i
$67$	1.70496	−	0.984357i	0.208294	−	0.120258i	−0.392225	−	0.919870i	$-0.628294\pi$
$67$	1.70496	−	0.984357i	0.208294	−	0.120258i	0.600518	+	0.799611i	$0.294961\pi$
$68$	−10.3473	−	2.55895i	−1.25479	−	0.310319i
$69$	−0.257257	+	2.01440i	−0.0309702	+	0.242505i
$70$	−0.496363	+	0.778748i	−0.0593267	+	0.0930782i
$71$	8.78800			1.04294			0.521472	−	0.853268i	$-0.325383\pi$
$71$	8.78800			1.04294			0.521472	+	0.853268i	$0.325383\pi$
$72$	6.91727	+	4.91440i	0.815209	+	0.579167i
$73$	0.891446	−	1.54403i	0.104336	−	0.180715i	−0.809131	−	0.587629i	$-0.800062\pi$
$73$	0.891446	−	1.54403i	0.104336	−	0.180715i	0.913467	+	0.406914i	$0.133395\pi$
$74$	1.81774	−	14.9217i	0.211308	−	1.73461i
$75$	1.08372	−	8.48582i	0.125137	−	0.979859i
$76$	8.54810	+	8.22342i	0.980535	+	0.943290i
$77$	4.93037	−	0.382196i	0.561868	−	0.0435553i
$78$	−3.63596	−	12.8692i	−0.411691	−	1.45714i
$79$	2.32610	−	4.02893i	0.261707	−	0.453290i	−0.704988	−	0.709219i	$-0.749048\pi$
$79$	2.32610	−	4.02893i	0.261707	−	0.453290i	0.966696	+	0.255929i	$0.0823812\pi$
$80$	0.526345	+	0.835235i	0.0588472	+	0.0933821i
$81$	7.86309	+	4.37856i	0.873677	+	0.486507i
$82$	5.73387	+	13.4725i	0.633200	+	1.48779i
$83$	−3.89087	+	2.24639i	−0.427078	+	0.246574i	−0.698101	−	0.715999i	$-0.745971\pi$
$83$	−3.89087	+	2.24639i	−0.427078	+	0.246574i	0.271023	+	0.962573i	$0.412638\pi$
$84$	2.10282	+	8.92066i	0.229437	+	0.973324i
$85$	−1.13916	−	0.657692i	−0.123559	−	0.0713367i
$86$	1.81772	−	14.9215i	0.196010	−	1.60903i
$87$	0.00957745	+	0.0228707i	0.00102681	+	0.00245200i
$88$	1.88045	−	4.94086i	0.200456	−	0.526697i
$89$	6.71334	+	11.6278i	0.711612	+	1.23255i	0.964252	+	0.264988i	$0.0853680\pi$
$89$	6.71334	+	11.6278i	0.711612	+	1.23255i	−0.252639	+	0.967561i	$0.581299\pi$
$90$	0.651841	+	0.819508i	0.0687100	+	0.0863837i
$91$	6.23381	−	13.0300i	0.653481	−	1.36592i
$92$	0.650637	+	2.25285i	0.0678336	+	0.234875i
$93$	−10.0526	+	4.20969i	−1.04241	+	0.436524i
$94$	−5.10625	−	11.9978i	−0.526669	−	1.23748i
$95$	0.731888	+	1.26767i	0.0750901	+	0.130060i
$96$	9.58367	+	2.03797i	0.978129	+	0.207999i
$97$	−2.06206	−	3.57159i	−0.209370	−	0.362640i	0.742146	−	0.670238i	$-0.233808\pi$
$97$	−2.06206	−	3.57159i	−0.209370	−	0.362640i	−0.951516	+	0.307598i	$0.900475\pi$
$98$	−4.65976	+	8.73422i	−0.470707	+	0.882290i
$99$	1.40922	−	5.42732i	0.141632	−	0.545466i
$100$	−2.74086	−	9.49030i	−0.274086	−	0.949030i
$101$		−	11.6788i		−	1.16209i	−0.813873	−	0.581043i	$-0.802645\pi$
$101$		−	11.6788i		−	1.16209i	0.813873	−	0.581043i	$-0.197355\pi$
$102$	−12.5628	+	3.54940i	−1.24390	+	0.351443i
$103$	11.7555			1.15830			0.579150	−	0.815221i	$-0.303384\pi$
$103$	11.7555			1.15830			0.579150	+	0.815221i	$0.303384\pi$
$104$	−9.75203	−	11.9727i	−0.956265	−	1.17402i
$105$	−0.0561414	+	1.12964i	−0.00547884	+	0.110242i
$106$	−8.74141	+	3.72033i	−0.849041	+	0.361351i
$107$	1.77646	−	1.02564i	0.171737	−	0.0991525i	−0.411668	−	0.911334i	$-0.635053\pi$
$107$	1.77646	−	1.02564i	0.171737	−	0.0991525i	0.583405	+	0.812182i	$0.301720\pi$
$108$	10.3405	+	1.03656i	0.995013	+	0.0997426i
$109$	8.66752	+	5.00420i	0.830198	+	0.479315i	0.853920	−	0.520404i	$-0.174218\pi$
$109$	8.66752	+	5.00420i	0.830198	+	0.479315i	−0.0237225	+	0.999719i	$0.507552\pi$
$110$	0.392127	−	0.521401i	0.0373878	−	0.0497137i
$111$	−7.11124	−	16.9815i	−0.674969	−	1.61181i
$112$	6.31738	+	8.49063i	0.596936	+	0.802289i
$113$	−0.759378	+	1.31528i	−0.0714363	+	0.123731i	−0.899531	−	0.436857i	$-0.856092\pi$
$113$	−0.759378	+	1.31528i	−0.0714363	+	0.123731i	0.828095	+	0.560588i	$0.189425\pi$
$114$	14.0820	+	3.56937i	1.31890	+	0.334302i
$115$			0.289377i			0.0269845i
$116$	0.0206332	+	0.0198495i	0.00191575	+	0.00184298i
$117$	−11.6708	−	11.4911i	−1.07896	−	1.06236i
$118$	−2.12086	+	17.4100i	−0.195241	+	1.60272i
$119$	−12.7198	−	6.08540i	−1.16602	−	0.557847i
$120$	1.06646	+	0.569777i	0.0973541	+	0.0520133i
$121$	7.50648			0.682407
$122$	3.62886	−	1.54444i	0.328542	−	0.139827i
$123$	14.2691	+	10.8614i	1.28660	+	0.979341i
$124$	−8.72467	+	9.06915i	−0.783499	+	0.814434i
$125$		−	2.45308i		−	0.219410i
$126$	7.64560	+	8.21856i	0.681124	+	0.732168i
$127$	−6.26076			−0.555553			−0.277777	−	0.960646i	$-0.589597\pi$
$127$	−6.26076			−0.555553			−0.277777	+	0.960646i	$0.589597\pi$
$128$	11.0912	−	2.23271i	0.980334	−	0.197345i
$129$	−7.11118	−	16.9813i	−0.626105	−	1.49512i
$130$	−0.746247	−	1.75341i	−0.0654502	−	0.153784i
$131$			13.4485i			1.17500i	0.809225	+	0.587499i	$0.199888\pi$
$131$			13.4485i			1.17500i	−0.809225	+	0.587499i	$0.800112\pi$
$132$	−0.994035	−	6.39798i	−0.0865196	−	0.556873i
$133$	8.87242	+	12.9420i	0.769336	+	1.12222i
$134$	0.336676	−	2.76375i	0.0290844	−	0.238752i
$135$	1.19048	+	0.476963i	0.102460	+	0.0410505i
$136$	−11.6876	+	9.51985i	−1.00221	+	0.816321i
$137$	0.771014			0.0658722			0.0329361	−	0.999457i	$-0.489514\pi$
$137$	0.771014			0.0658722			0.0329361	+	0.999457i	$0.489514\pi$
$138$	2.05810	+	2.00304i	0.175197	+	0.170510i
$139$	−0.0270629	−	0.0156248i	−0.00229544	−	0.00132528i	0.498852	−	0.866687i	$-0.333755\pi$
$139$	−0.0270629	−	0.0156248i	−0.00229544	−	0.00132528i	−0.501147	+	0.865362i	$0.667089\pi$
$140$	0.458263	+	1.22297i	0.0387303	+	0.103359i
$141$	−12.7072	−	9.67254i	−1.07014	−	0.814575i
$142$	7.46997	−	9.93265i	0.626866	−	0.833529i
$143$	−5.10214	+	8.83717i	−0.426663	+	0.739001i
$144$	11.4343	−	3.64092i	0.952860	−	0.303410i
$145$	0.00176661	+	0.00305986i	0.000146709	+	0.000254108i
$146$	−0.987395	−	2.32001i	−0.0817174	−	0.192006i
$147$	0.335879	+	12.1197i	0.0277029	+	0.999616i
$148$	−15.3201	−	14.7382i	−1.25931	−	1.21147i
$149$			15.4650i			1.26694i	0.773767	+	0.633470i	$0.218370\pi$
$149$			15.4650i			1.26694i	−0.773767	+	0.633470i	$0.781630\pi$
$150$	−8.66993	−	8.43799i	−0.707897	−	0.688959i
$151$	5.66020			0.460621			0.230310	−	0.973117i	$-0.426026\pi$
$151$	5.66020			0.460621			0.230310	+	0.973117i	$0.426026\pi$
$152$	16.5606	−	2.67144i	1.34324	−	0.216682i
$153$	−11.2176	+	11.3929i	−0.906885	+	0.921063i
$154$	3.75893	−	5.89743i	0.302904	−	0.475229i
$155$	−1.34494	+	0.776500i	−0.108028	+	0.0623700i
$156$	−17.6360	−	6.82949i	−1.41201	−	0.546797i
$157$	−8.00342	+	4.62078i	−0.638743	+	0.368778i	−0.784130	−	0.620596i	$-0.786891\pi$
$157$	−8.00342	+	4.62078i	−0.638743	+	0.368778i	0.145387	+	0.989375i	$0.453557\pi$
$158$	−2.57647	−	6.05375i	−0.204973	−	0.481611i
$159$	−7.04726	+	9.25829i	−0.558884	+	0.734230i
$160$	1.39143	+	0.115064i	0.110002	+	0.00909661i
$161$	0.239747	+	3.09276i	0.0188947	+	0.243743i
$162$	11.6327	−	5.16540i	0.913947	−	0.405832i
$163$	2.08108	−	1.20151i	0.163002	−	0.0941095i	−0.416280	−	0.909237i	$-0.636666\pi$
$163$	2.08108	−	1.20151i	0.163002	−	0.0941095i	0.579282	+	0.815127i	$0.303333\pi$
$164$	20.1012	+	4.97116i	1.56964	+	0.388183i
$165$	0.101220	−	0.792584i	0.00787999	−	0.0617025i
$166$	−0.768326	+	6.30714i	−0.0596336	+	0.489529i
$167$	1.95626	−	3.38835i	0.151380	−	0.262198i	−0.780355	−	0.625337i	$-0.784962\pi$
$167$	1.95626	−	3.38835i	0.151380	−	0.262198i	0.931735	+	0.363139i	$0.118295\pi$
$168$	11.8700	+	5.20602i	0.915792	+	0.401653i
$169$	8.40295	+	14.5543i	0.646381	+	1.11956i
$170$	−1.71166	+	0.728481i	−0.131278	+	0.0558719i
$171$	17.1497	−	4.73812i	1.31147	−	0.362333i
$172$	−15.3200	−	14.7381i	−1.16814	−	1.12377i
$173$	−8.43502	−	4.86996i	−0.641303	−	0.370256i	0.143813	−	0.989605i	$-0.454063\pi$
$173$	−8.43502	−	4.86996i	−0.641303	−	0.370256i	−0.785116	+	0.619348i	$0.787397\pi$
$174$	0.0339907	+	0.00861566i	0.00257683	+	0.000653151i
$175$	−1.00995	−	13.0285i	−0.0763453	−	0.984862i
$176$	−3.98599	−	6.32520i	−0.300455	−	0.476780i
$177$	8.29709	+	19.8133i	0.623647	+	1.48926i
$178$	18.8488	+	2.29614i	1.41278	+	0.172103i
$179$	−16.5335	−	9.54562i	−1.23577	−	0.713473i	−0.267544	−	0.963546i	$-0.586212\pi$
$179$	−16.5335	−	9.54562i	−1.23577	−	0.713473i	−0.968227	+	0.250073i	$0.919546\pi$
$180$	1.48033	−	0.0401459i	0.110337	−	0.00299230i
$181$			11.0363i			0.820324i	0.912013	+	0.410162i	$0.134528\pi$
$181$			11.0363i			0.820324i	−0.912013	+	0.410162i	$0.865472\pi$
$182$	−9.42831	−	18.1215i	−0.698873	−	1.34326i
$183$	2.92556	−	3.84344i	0.216264	−	0.284115i
$184$	3.09934	+	1.17958i	0.228486	+	0.0869598i
$185$	−1.31171	−	2.27195i	−0.0964387	−	0.167037i
$186$	−3.78694	+	14.9403i	−0.277672	+	1.09548i
$187$	8.62678	+	4.98067i	0.630853	+	0.364223i
$188$	−17.9009	−	4.42703i	−1.30556	−	0.322874i
$189$	13.1186	+	4.11131i	0.954236	+	0.299054i
$190$	2.05490	+	0.250325i	0.149078	+	0.0181605i
$191$	1.32381	−	2.29290i	0.0957874	−	0.165909i	−0.814150	−	0.580655i	$-0.802796\pi$
$191$	1.32381	−	2.29290i	0.0957874	−	0.165909i	0.909937	+	0.414747i	$0.136130\pi$
$192$	10.4497	−	9.09964i	0.754143	−	0.656710i
$193$	0.675543	+	1.17007i	0.0486266	+	0.0842238i	0.889314	−	0.457297i	$-0.151182\pi$
$193$	0.675543	+	1.17007i	0.0486266	+	0.0842238i	−0.840688	+	0.541520i	$0.817849\pi$
$194$	−5.78957	−	0.705277i	−0.415667	−	0.0506359i
$195$	−1.85708	−	1.41358i	−0.132988	−	0.101229i
$196$	5.91097	+	12.6910i	0.422212	+	0.906497i
$197$			15.4647i			1.10181i	0.834567	+	0.550907i	$0.185718\pi$
$197$			15.4647i			1.10181i	−0.834567	+	0.550907i	$0.814282\pi$
$198$	−4.93636	−	6.20610i	−0.350812	−	0.441048i
$199$	−8.95285	+	15.5068i	−0.634651	+	1.09925i	0.351938	+	0.936023i	$0.385523\pi$
$199$	−8.95285	+	15.5068i	−0.634651	+	1.09925i	−0.986589	+	0.163224i	$0.947811\pi$
$200$	−13.0562	−	4.96908i	−0.923214	−	0.351367i
$201$	−1.31712	−	3.14526i	−0.0929028	−	0.221850i
$202$	−13.2000	−	9.92723i	−0.928749	−	0.698477i
$203$	0.0214160	+	0.0312391i	0.00150311	+	0.00219256i
$204$	−6.66689	+	17.2161i	−0.466776	+	1.20537i
$205$	2.21299	+	1.27767i	0.154562	+	0.0892362i
$206$	9.99238	−	13.2866i	0.696202	−	0.925723i
$207$	3.40449	+	0.883986i	0.236628	+	0.0614413i
$208$	−21.8215	+	0.845223i	−1.51305	+	0.0586056i
$209$	−5.54256	−	9.59999i	−0.383387	−	0.664046i
$210$	1.22905	+	1.02367i	0.0848128	+	0.0706399i
$211$	3.27095	+	1.88848i	0.225181	+	0.130008i	0.608347	−	0.793671i	$-0.291833\pi$
$211$	3.27095	+	1.88848i	0.225181	+	0.130008i	−0.383166	+	0.923680i	$0.625166\pi$
$212$	−3.22546	+	13.0423i	−0.221526	+	0.895752i
$213$	1.92824	−	15.0986i	0.132121	−	1.03454i
$214$	0.350796	−	2.87966i	0.0239799	−	0.196850i
$215$	−1.31170	−	2.27193i	−0.0894570	−	0.154944i
$216$	9.96118	−	10.8062i	0.677772	−	0.735272i
$217$	−13.7309	+	9.41323i	−0.932114	+	0.639012i
$218$	13.0236	−	5.54281i	0.882067	−	0.375406i
$219$	−2.45719	−	1.87038i	−0.166042	−	0.126388i
$220$	−0.255999	−	0.886403i	−0.0172595	−	0.0597613i
$221$	25.1981	−	14.5481i	1.69501	−	0.978614i
$222$	−25.2380	−	6.39711i	−1.69387	−	0.429346i
$223$	−2.01131	−	3.48369i	−0.134687	−	0.233285i	0.790791	−	0.612087i	$-0.209670\pi$
$223$	−2.01131	−	3.48369i	−0.134687	−	0.233285i	−0.925478	+	0.378802i	$0.876336\pi$
$224$	14.9664	+	0.0769743i	0.999987	+	0.00514306i
$225$	−14.3417	−	3.72387i	−0.956112	−	0.248258i
$226$	0.841112	+	1.97630i	0.0559499	+	0.131462i
$227$			19.8986i			1.32072i	0.750951	+	0.660358i	$0.229596\pi$
$227$			19.8986i			1.32072i	−0.750951	+	0.660358i	$0.770404\pi$
$228$	16.0042	−	12.8821i	1.05991	−	0.853139i
$229$			14.1186i			0.932985i	0.884525	+	0.466492i	$0.154482\pi$
$229$			14.1186i			0.932985i	−0.884525	+	0.466492i	$0.845518\pi$
$230$	0.327068	+	0.245976i	0.0215662	+	0.0162192i
$231$	0.425157	−	8.55472i	0.0279733	−	0.562859i
$232$	0.0399735	−	0.00644825i	0.00262439	−	0.000423348i
$233$	−1.07535	−	1.86256i	−0.0704484	−	0.122020i	0.828650	−	0.559768i	$-0.189110\pi$
$233$	−1.07535	−	1.86256i	−0.0704484	−	0.122020i	−0.899098	+	0.437748i	$0.855776\pi$
$234$	−22.9082	+	3.42322i	−1.49756	+	0.223783i
$235$	−1.97076	−	1.13782i	−0.128558	−	0.0742230i
$236$	17.8749	+	17.1959i	1.16355	+	1.11936i
$237$	−6.41171	−	4.88049i	−0.416485	−	0.317022i
$238$	−17.6901	+	9.20384i	−1.14668	+	0.596597i
$239$	−10.4593	+	18.1161i	−0.676559	+	1.17183i	0.299452	+	0.954111i	$0.403196\pi$
$239$	−10.4593	+	18.1161i	−0.676559	+	1.17183i	−0.976011	+	0.217722i	$0.930137\pi$
$240$	1.55050	−	0.721047i	0.100085	−	0.0465434i
$241$	−3.94215			−0.253937			−0.126968	−	0.991907i	$-0.540525\pi$
$241$	−3.94215			−0.253937			−0.126968	+	0.991907i	$0.540525\pi$
$242$	6.38065	−	8.48421i	0.410164	−	0.545385i
$243$	9.24808	−	12.5488i	0.593265	−	0.805007i
$244$	1.33900	−	5.41433i	0.0857207	−	0.346617i
$245$	0.266256	+	1.70704i	0.0170105	+	0.109059i
$246$	24.4051	−	6.89525i	1.55601	−	0.439625i
$247$	−32.3787			−2.06021
$248$	2.83427	+	17.5700i	0.179977	+	1.11570i
$249$	3.00580	+	7.17779i	0.190485	+	0.454874i
$250$	−2.77260	−	2.08517i	−0.175355	−	0.131878i
$251$			1.53948i			0.0971712i	0.998819	+	0.0485856i	$0.0154714\pi$
$251$			1.53948i			0.0971712i	−0.998819	+	0.0485856i	$0.984529\pi$
$252$	15.7879	−	1.65551i	0.994547	−	0.104287i
$253$		−	2.19144i		−	0.137775i
$254$	−5.32177	+	7.07623i	−0.333918	+	0.444002i
$255$	−1.37993	+	1.81287i	−0.0864144	+	0.113526i
$256$	6.90423	−	14.4337i	0.431514	−	0.902106i
$257$	−2.61369			−0.163038			−0.0815188	−	0.996672i	$-0.525977\pi$
$257$	−2.61369			−0.163038			−0.0815188	+	0.996672i	$0.525977\pi$
$258$	−25.2378	−	6.39706i	−1.57124	−	0.398263i
$259$	−15.9014	−	23.1950i	−0.988063	−	1.44127i
$260$	−2.61611	−	0.646983i	−0.162244	−	0.0401242i
$261$	0.0413956	−	0.0114368i	0.00256232	−	0.000707917i
$262$	15.2001	+	11.4315i	0.939068	+	0.706238i
$263$	−4.78361			−0.294970			−0.147485	−	0.989064i	$-0.547118\pi$
$263$	−4.78361			−0.294970			−0.147485	+	0.989064i	$0.547118\pi$
$264$	−8.07627	−	4.31490i	−0.497060	−	0.265564i
$265$	−0.828995	+	1.43586i	−0.0509248	+	0.0882043i
$266$	22.1695	+	0.972912i	1.35930	+	0.0596531i
$267$	21.4508	−	8.98282i	1.31277	−	0.549739i
$268$	−2.83755	−	2.72977i	−0.173331	−	0.166747i
$269$	−8.92577	−	5.15329i	−0.544214	−	0.314202i	0.202571	−	0.979268i	$-0.435070\pi$
$269$	−8.92577	−	5.15329i	−0.544214	−	0.314202i	−0.746785	+	0.665066i	$0.768404\pi$
$270$	1.55102	−	0.940111i	0.0943920	−	0.0572134i
$271$	3.85789	+	6.68207i	0.234350	+	0.405907i	0.959084	−	0.283123i	$-0.0913704\pi$
$271$	3.85789	+	6.68207i	0.234350	+	0.405907i	−0.724733	+	0.689029i	$0.758037\pi$
$272$	0.825100	+	21.3020i	0.0500290	+	1.29163i
$273$	−21.0190	−	13.5693i	−1.27213	−	0.821251i
$274$	0.655377	−	0.871440i	0.0395928	−	0.0526456i
$275$			9.23162i			0.556688i
$276$	4.01337	−	0.623545i	0.241576	−	0.0375330i
$277$			21.6643i			1.30168i	0.759214	+	0.650842i	$0.225584\pi$
$277$			21.6643i			1.30168i	−0.759214	+	0.650842i	$0.774416\pi$
$278$	−0.0406639	+	0.0173065i	−0.00243886	+	0.00103797i
$279$	5.02693	+	18.1951i	0.300954	+	1.08931i
$280$	1.77179	+	0.521592i	0.105885	+	0.0311711i
$281$	1.09787	+	1.90157i	0.0654936	+	0.113438i	0.896913	−	0.442207i	$-0.145804\pi$
$281$	1.09787	+	1.90157i	0.0654936	+	0.113438i	−0.831419	+	0.555646i	$0.812471\pi$
$282$	−21.7338	+	6.14051i	−1.29423	+	0.365662i
$283$	−18.1264	+	10.4653i	−1.07750	+	0.622097i	−0.930222	−	0.366997i	$-0.880386\pi$
$283$	−18.1264	+	10.4653i	−1.07750	+	0.622097i	−0.147282	+	0.989095i	$0.547053\pi$
$284$	−4.87676	−	16.8859i	−0.289382	−	1.00199i
$285$	2.33856	−	0.979307i	0.138525	−	0.0580091i
$286$	5.65130	+	13.2785i	0.334168	+	0.785172i
$287$	24.7102	+	11.8218i	1.45859	+	0.697820i
$288$	5.60424	−	16.0185i	0.330233	−	0.943899i
$289$	−5.70179	−	9.87578i	−0.335399	−	0.580929i
$290$	0.00496007		0.000604228i	0.000291265		3.54815e-5i
$291$	−6.58878	+	2.75914i	−0.386241	+	0.161744i
$292$	−3.46150	−	0.856053i	−0.202569	−	0.0500967i
$293$	−0.725056	−	0.418611i	−0.0423582	−	0.0244555i	0.478671	−	0.877994i	$-0.341119\pi$
$293$	−0.725056	−	0.418611i	−0.0423582	−	0.0244555i	−0.521030	+	0.853539i	$0.674452\pi$
$294$	13.9838	+	9.92236i	0.815552	+	0.578684i
$295$	1.53044	+	2.65081i	0.0891059	+	0.154336i
$296$	−29.6803	+	4.78782i	−1.72513	+	0.278286i
$297$	−9.01545	−	3.61202i	−0.523129	−	0.209591i
$298$	17.4793	+	13.1455i	1.01255	+	0.761500i
$299$	−5.54344	−	3.20051i	−0.320586	−	0.185090i
$300$	−16.9067	+	2.62674i	−0.976106	+	0.151655i
$301$	−15.9012	−	23.1948i	−0.916532	−	1.33693i
$302$	4.81128	−	6.39745i	0.276858	−	0.368132i
$303$	−20.0653	−	2.56253i	−1.15272	−	0.147214i
$304$	11.0574	−	20.9884i	0.634187	−	1.20377i
$305$	0.344145	−	0.596076i	0.0197057	−	0.0341312i
$306$	3.34172	+	22.3629i	0.191033	+	1.27840i
$307$		−	2.44381i		−	0.139475i	−0.997565	−	0.0697377i	$-0.977784\pi$
$307$		−	2.44381i		−	0.139475i	0.997565	−	0.0697377i	$-0.0222162\pi$
$308$	−3.47041	−	9.26147i	−0.197745	−	0.527721i
$309$	2.57935	−	20.1970i	0.146734	−	1.14897i
$310$	−0.265583	+	2.18016i	−0.0150841	+	0.123825i
$311$	4.38036	+	7.58701i	0.248387	+	0.430220i	0.963079	−	0.269221i	$-0.0867661\pi$
$311$	4.38036	+	7.58701i	0.248387	+	0.430220i	−0.714691	+	0.699440i	$0.753433\pi$
$312$	−22.7100	+	14.1279i	−1.28570	+	0.799836i
$313$	4.31888	−	7.48051i	0.244117	−	0.422824i	−0.717766	−	0.696285i	$-0.754835\pi$
$313$	4.31888	−	7.48051i	0.244117	−	0.422824i	0.961883	+	0.273461i	$0.0881685\pi$
$314$	−1.58043	+	12.9736i	−0.0891887	+	0.732144i
$315$	1.92851	+	0.344318i	0.108659	+	0.0194001i
$316$	−9.03231	−	2.23375i	−0.508107	−	0.125658i
$317$	12.2505	+	7.07282i	0.688056	+	0.397249i	0.802883	−	0.596136i	$-0.203298\pi$
$317$	12.2505	+	7.07282i	0.688056	+	0.397249i	−0.114828	+	0.993385i	$0.536632\pi$
$318$	4.47388	+	15.8349i	0.250883	+	0.887977i
$319$	−0.0133785	−	0.0231722i	−0.000749052	−	0.00129740i
$320$	1.31279	−	1.47486i	0.0733873	−	0.0824470i
$321$	−1.37237	−	3.27718i	−0.0765980	−	0.182914i
$322$	3.69938	+	2.35793i	0.206158	+	0.131402i
$323$			31.6079i			1.75871i
$324$	4.04978	−	17.5385i	0.224988	−	0.974362i
$325$	23.3522	+	13.4824i	1.29535	+	0.747870i
$326$	0.410948	−	3.37344i	0.0227603	−	0.186838i
$327$	10.4995	−	13.7936i	0.580623	−	0.762790i
$328$	22.7051	−	18.4938i	1.25368	−	1.02115i
$329$	−22.0054	−	10.5278i	−1.21320	−	0.580418i
$330$	−0.809779	−	0.788116i	−0.0445769	−	0.0433843i
$331$	−9.83478	−	5.67811i	−0.540568	−	0.312097i	0.204741	−	0.978816i	$-0.434365\pi$
$331$	−9.83478	−	5.67811i	−0.540568	−	0.312097i	−0.745309	+	0.666719i	$0.767698\pi$
$332$	6.47555	+	6.22959i	0.355392	+	0.341893i
$333$	−30.7362	+	8.49178i	−1.68433	+	0.465346i
$334$	−2.16682	−	5.09123i	−0.118563	−	0.278580i
$335$	−0.242951	−	0.420803i	−0.0132738	−	0.0229909i
$336$	15.9739	−	8.99088i	0.871445	−	0.490493i
$337$	7.01019	−	12.1420i	0.381869	−	0.661417i	−0.609460	−	0.792817i	$-0.708614\pi$
$337$	7.01019	−	12.1420i	0.381869	−	0.661417i	0.991329	+	0.131400i	$0.0419472\pi$
$338$	23.5927	+	2.87403i	1.28327	+	0.156327i
$339$	2.09316	+	1.59328i	0.113685	+	0.0865351i
$340$	−0.631579	+	2.55383i	−0.0342522	+	0.138501i
$341$	10.1852	−	5.88041i	0.551557	−	0.318442i
$342$	9.22234	−	23.4110i	0.498687	−	1.26592i
$343$	4.25992	+	18.0237i	0.230014	+	0.973187i
$344$	−29.6800	+	4.78777i	−1.60024	+	0.258139i
$345$	0.497177	+	0.0634942i	0.0267671	+	0.00341841i
$346$	−12.6742	+	5.39413i	−0.681370	+	0.289990i
$347$	−5.50995	+	3.18117i	−0.295790	+	0.170774i	−0.640550	−	0.767917i	$-0.721294\pi$
$347$	−5.50995	+	3.18117i	−0.295790	+	0.170774i	0.344760	+	0.938691i	$0.387960\pi$
$348$	0.0386306	−	0.0310945i	0.00207082	−	0.00166684i
$349$	−4.42346	+	2.55388i	−0.236782	+	0.136706i	−0.613697	−	0.789542i	$-0.710318\pi$
$349$	−4.42346	+	2.55388i	−0.236782	+	0.136706i	0.376915	+	0.926248i	$0.376985\pi$
$350$	−15.5840	−	9.93298i	−0.832997	−	0.530940i
$351$	−22.3036	+	17.5302i	−1.19048	+	0.935691i
$352$	−10.5372	−	0.871375i	−0.561637	−	0.0464445i
$353$	−21.3677			−1.13729			−0.568644	−	0.822584i	$-0.692532\pi$
$353$	−21.3677			−1.13729			−0.568644	+	0.822584i	$0.692532\pi$
$354$	29.4467	+	7.46387i	1.56507	+	0.396700i
$355$		−	2.16898i		−	0.115118i
$356$	18.6171	−	19.3522i	0.986704	−	1.02566i
$357$	−13.2462	+	20.5186i	−0.701065	+	1.08596i
$358$	−24.8427	+	10.5730i	−1.31298	+	0.558802i
$359$	−7.57368	−	13.1180i	−0.399723	−	0.692341i	0.593968	−	0.804489i	$-0.297561\pi$
$359$	−7.57368	−	13.1180i	−0.399723	−	0.692341i	−0.993692	+	0.112147i	$0.964227\pi$
$360$	1.21293	−	1.70726i	0.0639271	−	0.0899808i
$361$	8.08683	−	14.0068i	0.425623	−	0.737200i
$362$	12.4738	+	9.38110i	0.655610	+	0.493060i
$363$	1.64705	−	12.8969i	0.0864476	−	0.676910i
$364$	−28.4961	−	4.74729i	−1.49360	−	0.248826i
$365$	−0.381085	−	0.220019i	−0.0199469	−	0.0115163i
$366$	−1.85726	−	6.57361i	−0.0970806	−	0.343608i
$367$	24.4406			1.27579			0.637895	−	0.770123i	$-0.279805\pi$
$367$	24.4406			1.27579			0.637895	+	0.770123i	$0.279805\pi$
$368$	3.96772	−	2.50036i	0.206832	−	0.130340i
$369$	21.7918	−	22.1325i	1.13444	−	1.15217i
$370$	−3.68285	−	0.448639i	−0.191462	−	0.0233236i
$371$	−7.67041	+	16.0328i	−0.398228	+	0.832382i
$372$	13.6673	+	16.9798i	0.708618	+	0.880359i
$373$		−	30.9464i		−	1.60235i	−0.598433	−	0.801173i	$-0.704210\pi$
$373$		−	30.9464i		−	1.60235i	0.598433	−	0.801173i	$-0.295790\pi$
$374$	12.9623	−	5.51676i	0.670267	−	0.285265i
$375$	−4.21463	−	0.538248i	−0.217643	−	0.0277950i
$376$	−20.2198	+	16.4695i	−1.04276	+	0.849349i
$377$	−0.0781550			−0.00402519
$378$	15.7979	−	11.3326i	0.812554	−	0.582885i
$379$		−	7.96954i		−	0.409368i	−0.978828	−	0.204684i	$-0.934383\pi$
$379$		−	7.96954i		−	0.409368i	0.978828	−	0.204684i	$-0.0656167\pi$
$380$	2.02964	−	2.10977i	0.104118	−	0.108229i
$381$	−1.37372	+	10.7566i	−0.0703777	+	0.551077i
$382$	−1.46629	−	3.44525i	−0.0750221	−	0.176274i
$383$	6.91005			0.353087			0.176544	−	0.984293i	$-0.443508\pi$
$383$	6.91005			0.353087			0.176544	+	0.984293i	$0.443508\pi$
$384$	−1.40241	−	19.5457i	−0.0715663	−	0.997436i
$385$	−0.0943306	−	1.21687i	−0.00480753	−	0.0620176i
$386$	1.89670	+	0.231053i	0.0965396	+	0.0117603i
$387$	−30.7359	+	8.49170i	−1.56239	+	0.431657i
$388$	−5.71839	+	5.94417i	−0.290307	+	0.301770i
$389$		−	37.6666i		−	1.90977i	−0.296972	−	0.954886i	$-0.595977\pi$
$389$		−	37.6666i		−	1.90977i	0.296972	−	0.954886i	$-0.404023\pi$
$390$	−3.17626	+	0.897398i	−0.160836	+	0.0454415i
$391$	−3.12431	+	5.41147i	−0.158003	+	0.273670i
$392$	19.3684	+	4.10668i	0.978252	+	0.207419i
$393$	23.1058	+	2.95082i	1.16553	+	0.148849i
$394$	17.4790	+	13.1453i	0.880579	+	0.662250i
$395$	−0.994388	−	0.574110i	−0.0500331	−	0.0288866i
$396$	−11.2105	+	0.304023i	−0.563347	+	0.0152778i
$397$	2.08436	−	1.20340i	0.104611	−	0.0603971i	−0.446782	−	0.894643i	$-0.647430\pi$
$397$	2.08436	−	1.20340i	0.104611	−	0.0603971i	0.551393	+	0.834246i	$0.314097\pi$
$398$	9.91647	+	23.3000i	0.497068	+	1.16793i
$399$	24.1824	−	12.4040i	1.21063	−	0.620975i
$400$	−16.7143	+	10.5330i	−0.835717	+	0.526649i
$401$	35.3441			1.76500			0.882501	−	0.470311i	$-0.155858\pi$
$401$	35.3441			1.76500			0.882501	+	0.470311i	$0.155858\pi$
$402$	−4.67452	−	1.18486i	−0.233144	−	0.0590952i
$403$		−	34.3524i		−	1.71121i
$404$	−22.4405	+	6.48097i	−1.11646	+	0.322440i
$405$	1.08068	−	1.94070i	0.0536994	−	0.0964343i
$406$	0.0535121	+	0.00234839i	0.00265576	+	0.000116549i
$407$	9.93352	+	17.2054i	0.492386	+	0.852838i
$408$	13.7916	+	22.1693i	0.682784	+	1.09754i
$409$	−12.2518	−	21.2207i	−0.605812	−	1.04930i	−0.991923	−	0.126844i	$-0.959515\pi$
$409$	−12.2518	−	21.2207i	−0.605812	−	1.04930i	0.386111	−	0.922452i	$-0.373818\pi$
$410$	3.32517	−	1.41519i	0.164218	−	0.0698911i
$411$	0.169174	−	1.32468i	0.00834472	−	0.0653415i
$412$	−6.52351	−	22.5878i	−0.321390	−	1.11282i
$413$	18.5530	+	27.0629i	0.912935	+	1.33168i
$414$	3.89301	−	3.09652i	0.191331	−	0.152185i
$415$	0.554436	+	0.960312i	0.0272162	+	0.0471399i
$416$	−17.5934	+	25.3823i	−0.862589	+	1.24447i
$417$	−0.0327829	+	0.0430683i	−0.00160539	+	0.00210906i
$418$	−15.5617	−	1.89570i	−0.761147	−	0.0927217i
$419$	−7.56849	−	4.36967i	−0.369745	−	0.213472i	0.303602	−	0.952799i	$-0.401811\pi$
$419$	−7.56849	−	4.36967i	−0.369745	−	0.213472i	−0.673347	+	0.739327i	$0.735144\pi$
$420$	2.20172	−	0.519001i	0.107433	−	0.0253247i
$421$	−0.976041	+	0.563517i	−0.0475693	+	0.0274642i	−0.523596	−	0.851967i	$-0.675410\pi$
$421$	−0.976041	+	0.563517i	−0.0475693	+	0.0274642i	0.476027	+	0.879431i	$0.342077\pi$
$422$	4.91483	−	2.09174i	0.239250	−	0.101825i
$423$	−19.4065	+	19.7099i	−0.943578	+	0.958330i
$424$	11.9994	+	14.7318i	0.582743	+	0.715441i
$425$	13.1614	−	22.7963i	0.638423	−	1.10578i
$426$	−15.4262	−	15.0135i	−0.747402	−	0.727408i
$427$	3.18425	−	6.65577i	0.154097	−	0.322095i
$428$	−2.95656	−	2.84426i	−0.142911	−	0.137482i
$429$	14.0636	+	10.7050i	0.678998	+	0.516842i
$430$	−3.68281	−	0.448635i	−0.177601	−	0.0216351i
$431$	13.1417	−	22.7620i	0.633011	−	1.09641i	−0.353922	−	0.935275i	$-0.615152\pi$
$431$	13.1417	−	22.7620i	0.633011	−	1.09641i	0.986933	−	0.161132i	$-0.0515146\pi$
$432$	−3.74657	−	20.4441i	−0.180257	−	0.983620i
$433$	−17.8216			−0.856451			−0.428225	−	0.903672i	$-0.640861\pi$
$433$	−17.8216			−0.856451			−0.428225	+	0.903672i	$0.640861\pi$
$434$	−1.03222	+	23.5208i	−0.0495480	+	1.12903i
$435$	0.00564477	−	0.00236383i	0.000270646	−	0.000113337i
$436$	4.80551	−	19.4314i	0.230142	−	0.930594i
$437$	6.02195	−	3.47678i	0.288069	−	0.166317i
$438$	−4.20266	+	1.18739i	−0.200811	+	0.0567357i
$439$	4.54117	−	7.86554i	0.216738	−	0.375402i	−0.737071	−	0.675816i	$-0.763792\pi$
$439$	4.54117	−	7.86554i	0.216738	−	0.375402i	0.953809	+	0.300414i	$0.0971249\pi$
$440$	−1.21946	−	0.464116i	−0.0581356	−	0.0221259i
$441$	20.8965	+	2.08219i	0.995072	+	0.0991521i
$442$	4.97585	−	40.8464i	0.236677	−	1.94287i
$443$	27.8506	+	16.0796i	1.32322	+	0.763964i	0.984242	−	0.176829i	$-0.0565840\pi$
$443$	27.8506	+	16.0796i	1.32322	+	0.763964i	0.338982	+	0.940793i	$0.389917\pi$
$444$	−28.6832	+	23.0876i	−1.36124	+	1.09569i
$445$	2.86989	−	1.65693i	0.136046	−	0.0785460i
$446$	−5.64709	−	0.687920i	−0.267398	−	0.0325740i
$447$	26.5703	+	3.39328i	1.25673	+	0.160496i
$448$	12.8088	−	16.8504i	0.605157	−	0.796106i
$449$	31.5353			1.48824			0.744122	−	0.668044i	$-0.232868\pi$
$449$	31.5353			1.48824			0.744122	+	0.668044i	$0.232868\pi$
$450$	−16.3996	+	13.0443i	−0.773085	+	0.614916i
$451$	−16.7589	−	9.67573i	−0.789144	−	0.455613i
$452$	2.94868	+	0.729229i	0.138694	+	0.0343000i
$453$	1.24194	−	9.72477i	0.0583516	−	0.456910i
$454$	22.4904	+	16.9142i	1.05553	+	0.793823i
$455$	−3.21596	−	1.53858i	−0.150766	−	0.0721296i
$456$	−0.956115	−	29.0388i	−0.0447742	−	1.35987i
$457$	−15.5543	+	26.9409i	−0.727600	+	1.26024i	0.230294	+	0.973121i	$0.426031\pi$
$457$	−15.5543	+	26.9409i	−0.727600	+	1.26024i	−0.957895	+	0.287120i	$0.907302\pi$
$458$	15.9576	+	12.0011i	0.745649	+	0.560775i
$459$	17.1128	+	21.7726i	0.798758	+	1.01626i
$460$	0.556029	−	0.160585i	0.0259250	−	0.00748731i
$461$	19.2187	−	11.0959i	0.895103	−	0.516788i	0.0194945	−	0.999810i	$-0.493794\pi$
$461$	19.2187	−	11.0959i	0.895103	−	0.516788i	0.875608	+	0.483022i	$0.160461\pi$
$462$	−9.30758	−	7.75221i	−0.433028	−	0.360665i
$463$	−18.6891	+	32.3704i	−0.868555	+	1.50438i	−0.00508254	+	0.999987i	$0.501618\pi$
$463$	−18.6891	+	32.3704i	−0.868555	+	1.50438i	−0.863473	+	0.504395i	$0.831716\pi$
$464$	0.0266901	−	0.0506612i	0.00123906	−	0.00235189i
$465$	1.03900	+	2.48111i	0.0481825	+	0.115059i
$466$	−3.01922	−	0.367797i	−0.139863	−	0.0170379i
$467$	18.5047	−	10.6837i	0.856296	−	0.494383i	−0.00647422	−	0.999979i	$-0.502061\pi$
$467$	18.5047	−	10.6837i	0.856296	−	0.494383i	0.862770	+	0.505596i	$0.168727\pi$
$468$	−15.6034	+	28.8019i	−0.721266	+	1.33137i
$469$	−2.94521	−	4.29611i	−0.135997	−	0.198376i
$470$	−2.96120	+	1.26028i	−0.136590	+	0.0581325i
$471$	6.18286	+	14.7645i	0.284891	+	0.680314i
$472$	34.6297	−	5.58622i	1.59396	−	0.257126i
$473$	9.93343	+	17.2052i	0.456740	+	0.791096i
$474$	−10.9663	+	3.09833i	−0.503697	+	0.142311i
$475$	−25.3680	+	14.6462i	−1.16396	+	0.672014i
$476$	−4.63427	+	27.8177i	−0.212411	+	1.27502i
$477$	14.3603	+	14.1393i	0.657515	+	0.647394i
$478$	11.5851	+	27.2207i	0.529890	+	1.24505i
$479$	2.33685			0.106773			0.0533866	−	0.998574i	$-0.482998\pi$
$479$	2.33685			0.106773			0.0533866	+	0.998574i	$0.482998\pi$
$480$	0.502994	−	2.36536i	0.0229584	−	0.107964i
$481$	58.0300			2.64594
$482$	−3.35091	+	4.45562i	−0.152630	+	0.202948i
$483$	5.36626	+	0.266695i	0.244173	+	0.0121351i
$484$	−4.16560	−	14.4235i	−0.189345	−	0.655613i
$485$	−0.881509	+	0.508940i	−0.0400273	+	0.0231098i
$486$	−6.32226	−	21.1194i	−0.286784	−	0.957995i
$487$	3.39056	−	5.87262i	0.153641	−	0.266114i	−0.778922	−	0.627120i	$-0.784233\pi$
$487$	3.39056	−	5.87262i	0.153641	−	0.266114i	0.932563	+	0.361006i	$0.117567\pi$
$488$	−4.98137	−	6.11569i	−0.225496	−	0.276844i
$489$	−1.60769	−	3.83912i	−0.0727021	−	0.173611i
$490$	2.15571	+	1.15008i	0.0973850	+	0.0519555i
$491$	−6.61633	−	3.81994i	−0.298591	−	0.172391i	0.343219	−	0.939255i	$-0.388483\pi$
$491$	−6.61633	−	3.81994i	−0.298591	−	0.172391i	−0.641810	+	0.766864i	$0.721816\pi$
$492$	12.9515	−	33.4450i	0.583898	−	1.50782i
$493$			0.0762943i			0.00343612i
$494$	−27.5226	+	36.5961i	−1.23830	+	1.64654i
$495$	−1.33953	−	0.347812i	−0.0602072	−	0.0156330i
$496$	22.2677	+	11.7314i	0.999850	+	0.526756i
$497$	−1.79699	−	23.1813i	−0.0806059	−	1.03982i
$498$	10.6677	+	2.70395i	0.478030	+	0.121167i
$499$			7.30518i			0.327025i	0.986541	+	0.163512i	$0.0522824\pi$
$499$			7.30518i			0.327025i	−0.986541	+	0.163512i	$0.947718\pi$
$500$	−4.71353	+	1.36130i	−0.210795	+	0.0608791i
$501$	−5.39227	−	4.10451i	−0.240909	−	0.183376i
$502$	1.74000	+	1.30859i	0.0776600	+	0.0584052i
$503$	2.20140			0.0981554			0.0490777	−	0.998795i	$-0.484372\pi$
$503$	2.20140			0.0981554			0.0490777	+	0.998795i	$0.484372\pi$
$504$	11.5489	−	19.2516i	0.514430	−	0.857532i
$505$	−2.88247			−0.128268
$506$	−2.47688	−	1.86277i	−0.110111	−	0.0828101i
$507$	26.8495	−	11.2436i	1.19243	−	0.499346i
$508$	3.47431	+	12.0299i	0.154148	+	0.533739i
$509$		−	20.5799i		−	0.912188i	−0.889932	−	0.456094i	$-0.849248\pi$
$509$		−	20.5799i		−	0.912188i	0.889932	−	0.456094i	$-0.150752\pi$
$510$	0.876033	+	3.10064i	0.0387914	+	0.137299i
$511$	−4.25519	−	2.03576i	−0.188238	−	0.0900569i
$512$	−10.4450	−	20.0724i	−0.461607	−	0.887085i
$513$	−4.37760	−	30.5045i	−0.193276	−	1.34681i
$514$	−2.22169	+	2.95413i	−0.0979945	+	0.130301i
$515$		−	2.90139i		−	0.127850i
$516$	−28.6829	+	23.0874i	−1.26270	+	1.01637i
$517$	14.9245	+	8.61664i	0.656377	+	0.378959i
$518$	−39.7327	−	1.74368i	−1.74575	−	0.0766128i
$519$	−10.2179	+	13.4236i	−0.448514	+	0.589232i
$520$	−2.95500	+	2.40692i	−0.129585	+	0.105550i
$521$	9.03080	−	15.6418i	0.395647	−	0.685280i	−0.597537	−	0.801841i	$-0.703854\pi$
$521$	9.03080	−	15.6418i	0.395647	−	0.685280i	0.993183	+	0.116562i	$0.0371872\pi$
$522$	0.0222607	−	0.0565089i	0.000974323	−	0.00247333i
$523$	−35.0286	+	20.2238i	−1.53169	+	0.884323i	−0.532409	+	0.846487i	$0.678713\pi$
$523$	−35.0286	+	20.2238i	−1.53169	+	0.884323i	−0.999284	+	0.0378360i	$0.987954\pi$
$524$	25.8408	−	7.46301i	1.12886	−	0.326023i
$525$	−22.6058	−	1.12348i	−0.986599	−	0.0490325i
$526$	−4.06616	+	5.40668i	−0.177293	+	0.235743i
$527$	−33.5345			−1.46079
$528$	−11.7419	+	5.46046i	−0.511001	+	0.237636i
$529$	−21.6253			−0.940232
$530$	0.918222	+	2.15748i	0.0398850	+	0.0937151i
$531$	35.8616	−	9.90783i	1.55626	−	0.429963i
$532$	19.9441	−	24.2300i	0.864687	−	1.05051i
$533$	−48.9513	+	28.2620i	−2.12032	+	1.22416i
$534$	8.08074	−	31.8803i	0.349688	−	1.37960i
$535$	−0.253140	−	0.438452i	−0.0109442	−	0.0189559i
$536$	−5.49730	+	0.886786i	−0.237447	+	0.0383033i
$537$	−20.0280	+	26.3117i	−0.864273	+	1.13543i
$538$	−13.4116	+	5.70796i	−0.578215	+	0.246087i
$539$	−2.01634	−	12.9274i	−0.0868501	−	0.556821i
$540$	0.255834	−	2.55215i	0.0110093	−	0.109827i
$541$	−28.5785	+	16.4998i	−1.22869	+	0.709383i	−0.966755	−	0.255703i	$-0.917693\pi$
$541$	−28.5785	+	16.4998i	−1.22869	+	0.709383i	−0.261932	+	0.965086i	$0.584360\pi$
$542$	10.8317	+	1.31950i	0.465261	+	0.0566774i
$543$	18.9615	+	2.42156i	0.813715	+	0.103919i
$544$	24.7780	+	17.1746i	1.06235	+	0.736354i
$545$	1.23509	−	2.13925i	0.0529056	−	0.0916352i
$546$	−33.2033	+	12.2226i	−1.42097	+	0.523078i
$547$	26.3987	−	15.2413i	1.12873	−	0.651672i	0.185114	−	0.982717i	$-0.440735\pi$
$547$	26.3987	−	15.2413i	1.12873	−	0.651672i	0.943615	+	0.331045i	$0.107401\pi$
$548$	−0.427862	−	1.48148i	−0.0182774	−	0.0632857i
$549$	−5.96148	−	5.86971i	−0.254430	−	0.250513i
$550$	10.4340	+	7.84706i	0.444909	+	0.334600i
$551$	0.0424507	−	0.0735267i	0.00180846	−	0.00313234i
$552$	2.70668	−	5.06614i	0.115204	−	0.215629i
$553$	−11.1033	−	5.31204i	−0.472161	−	0.225891i
$554$	24.4861	+	18.4151i	1.04032	+	0.782383i
$555$	−4.19123	+	1.75514i	−0.177908	+	0.0745015i
$556$	−0.0150044	+	0.0606713i	−0.000636329	+	0.00257303i
$557$	−10.3874	−	5.99718i	−0.440129	−	0.254108i	0.263523	−	0.964653i	$-0.415115\pi$
$557$	−10.3874	−	5.99718i	−0.440129	−	0.254108i	−0.703652	+	0.710544i	$0.748449\pi$
$558$	24.8380	+	9.78449i	1.05148	+	0.414210i
$559$	58.0295			2.45439
$560$	2.09559	−	1.55920i	0.0885547	−	0.0658884i
$561$	10.4501	−	13.7288i	0.441205	−	0.579630i
$562$	3.08247	+	0.375501i	0.130026	+	0.0158396i
$563$	31.0563	−	17.9304i	1.30887	−	0.755675i	0.326960	−	0.945038i	$-0.393976\pi$
$563$	31.0563	−	17.9304i	1.30887	−	0.755675i	0.981907	+	0.189363i	$0.0606423\pi$
$564$	−11.5338	+	29.7842i	−0.485662	+	1.25414i
$565$	0.324627	+	0.187423i	0.0136572	+	0.00788496i
$566$	−3.57941	+	29.3831i	−0.150454	+	1.23506i
$567$	9.94207	−	21.6369i	0.417528	−	0.908664i
$568$	−23.2306	−	8.84137i	−0.974736	−	0.370976i
$569$	−11.6802	+	20.2306i	−0.489658	+	0.848112i	−0.999929	−	0.0119015i	$-0.996212\pi$
$569$	−11.6802	+	20.2306i	−0.489658	+	0.848112i	0.510272	+	0.860013i	$0.329545\pi$
$570$	0.880962	−	3.47559i	0.0368995	−	0.145577i
$571$	9.41731	−	5.43709i	0.394102	−	0.227535i	−0.289834	−	0.957077i	$-0.593600\pi$
$571$	9.41731	−	5.43709i	0.394102	−	0.227535i	0.683936	+	0.729542i	$0.260267\pi$
$572$	19.8117	+	4.89957i	0.828369	+	0.204861i
$573$	−3.64896	−	2.77753i	−0.152438	−	0.116033i
$574$	34.3658	−	17.8799i	1.43440	−	0.746293i
$575$	−5.79088			−0.241496
$576$	−13.3412	−	19.9502i	−0.555884	−	0.831260i
$577$	12.7926	−	22.1575i	0.532564	−	0.922429i	−0.466713	−	0.884409i	$-0.654562\pi$
$577$	12.7926	−	22.1575i	0.532564	−	0.922429i	0.999277	−	0.0380196i	$-0.0121049\pi$
$578$	−16.0087	−	1.95016i	−0.665876	−	0.0811160i
$579$	2.15853	−	0.903914i	0.0897053	−	0.0375654i
$580$	0.00489909	−	0.00509252i	0.000203423	−	0.000211455i
$581$	6.72124	+	9.80413i	0.278844	+	0.406744i
$582$	−2.48206	+	9.79230i	−0.102885	+	0.405904i
$583$	6.27795	−	10.8737i	0.260006	−	0.450344i
$584$	−3.90990	+	3.18470i	−0.161793	+	0.131784i
$585$	−2.83615	+	2.88048i	−0.117260	+	0.119093i
$586$	−1.08945	+	0.463667i	−0.0450047	+	0.0191539i
$587$	14.1601	−	8.17531i	0.584448	−	0.337431i	−0.178451	−	0.983949i	$-0.557109\pi$
$587$	14.1601	−	8.17531i	0.584448	−	0.337431i	0.762899	+	0.646518i	$0.223775\pi$
$588$	23.1013	−	7.37101i	0.952680	−	0.303975i
$589$	32.3180	+	18.6588i	1.33164	+	0.768824i
$590$	4.29698	+	0.523452i	0.176904	+	0.0215502i
$591$	26.5698	+	3.39322i	1.09294	+	0.139578i
$592$	−19.8174	+	37.6159i	−0.814490	+	1.54600i
$593$	−15.7408	−	27.2639i	−0.646398	−	1.11959i	−0.983977	−	0.178297i	$-0.942941\pi$
$593$	−15.7408	−	27.2639i	−0.646398	−	1.11959i	0.337578	−	0.941297i	$-0.390392\pi$
$594$	−11.7458	+	7.11943i	−0.481936	+	0.292114i
$595$	−1.50195	+	3.13939i	−0.0615738	+	0.128703i
$596$	29.7155	−	8.58204i	1.21719	−	0.351534i
$597$	24.6778	+	18.7843i	1.00999	+	0.768791i
$598$	−8.32941	+	3.54499i	−0.340615	+	0.144965i
$599$	16.6671	+	28.8683i	0.681001	+	1.17953i	0.974676	+	0.223623i	$0.0717883\pi$
$599$	16.6671	+	28.8683i	0.681001	+	1.17953i	−0.293675	+	0.955905i	$0.594878\pi$
$600$	−11.4021	+	21.3415i	−0.465489	+	0.871264i
$601$	19.5850	+	33.9222i	0.798888	+	1.38371i	0.920341	+	0.391117i	$0.127911\pi$
$601$	19.5850	+	33.9222i	0.798888	+	1.38371i	−0.121454	+	0.992597i	$0.538756\pi$
$602$	−39.7323	−	1.74366i	−1.61937	−	0.0710664i
$603$	−5.69287	+	1.57282i	−0.231831	+	0.0640503i
$604$	−3.14104	−	10.8759i	−0.127807	−	0.442535i
$605$		−	1.85269i		−	0.0753225i
$606$	−19.9522	+	20.5007i	−0.810504	+	0.832783i
$607$	−20.7231			−0.841126			−0.420563	−	0.907263i	$-0.638167\pi$
$607$	−20.7231			−0.841126			−0.420563	+	0.907263i	$0.638167\pi$
$608$	−14.3231	−	30.3382i	−0.580879	−	1.23038i
$609$	0.0583709	−	0.0299404i	0.00236531	−	0.00121325i
$610$	−0.381186	−	0.895646i	−0.0154338	−	0.0362636i
$611$	43.5931	−	25.1685i	1.76359	−	1.01821i
$612$	28.1162	+	15.2319i	1.13653	+	0.615712i
$613$	−8.53195	−	4.92592i	−0.344602	−	0.198956i	0.317703	−	0.948190i	$-0.397088\pi$
$613$	−8.53195	−	4.92592i	−0.344602	−	0.198956i	−0.662305	+	0.749234i	$0.730422\pi$
$614$	−2.76211	−	2.07728i	−0.111470	−	0.0838323i
$615$	2.68072	−	3.52178i	0.108097	−	0.142012i
$616$	−13.4177	−	3.95000i	−0.540614	−	0.159150i
$617$	−15.8841	+	27.5121i	−0.639471	+	1.10760i	0.346078	+	0.938206i	$0.387513\pi$
$617$	−15.8841	+	27.5121i	−0.639471	+	1.10760i	−0.985549	+	0.169391i	$0.945820\pi$
$618$	−20.6352	−	20.0832i	−0.830070	−	0.807864i
$619$			39.3957i			1.58345i	0.610880	+	0.791724i	$0.290816\pi$
$619$			39.3957i			1.58345i	−0.610880	+	0.791724i	$0.709184\pi$
$620$	2.23837	+	2.15335i	0.0898952	+	0.0864807i
$621$	2.26578	−	5.65527i	0.0909224	−	0.226938i
$622$	12.2986	+	1.49820i	0.493129	+	0.0600723i
$623$	29.2996	−	20.0864i	1.17386	−	0.804744i
$624$	−3.33584	+	37.6770i	−0.133541	+	1.50829i
$625$	24.0900			0.963599
$626$	−4.78373	−	11.2400i	−0.191196	−	0.449241i
$627$	−17.7099	+	7.41625i	−0.707263	+	0.296177i
$628$	13.3201	+	12.8141i	0.531528	+	0.511339i
$629$		−	56.6484i		−	2.25872i
$630$	2.02844	−	1.88702i	0.0808149	−	0.0751808i
$631$	24.5273			0.976416			0.488208	−	0.872727i	$-0.337651\pi$
$631$	24.5273			0.976416			0.488208	+	0.872727i	$0.337651\pi$
$632$	−10.2023	+	8.31004i	−0.405827	+	0.330556i
$633$	3.96230	−	5.20544i	0.157487	−	0.206898i
$634$	18.4072	−	7.83408i	0.731043	−	0.311131i
$635$			1.54523i			0.0613206i
$636$	21.7003	+	8.40337i	0.860472	+	0.333215i
$637$	−35.6457	−	13.7794i	−1.41234	−	0.545959i
$638$	−0.0375624	−	0.00457580i	−0.00148711	−	0.000181158i
$639$	−25.5178	−	6.62579i	−1.00947	−	0.262112i
$640$	−0.551058	−	2.73744i	−0.0217825	−	0.108207i
$641$	−31.6572			−1.25038			−0.625192	−	0.780471i	$-0.714979\pi$
$641$	−31.6572			−1.25038			−0.625192	+	0.780471i	$0.714979\pi$
$642$	−4.87057	−	1.23455i	−0.192226	−	0.0487238i
$643$	−1.66533	−	0.961476i	−0.0656740	−	0.0379169i	0.466803	−	0.884361i	$-0.345406\pi$
$643$	−1.66533	−	0.961476i	−0.0656740	−	0.0379169i	−0.532477	+	0.846444i	$0.678739\pi$
$644$	5.80960	−	2.17694i	0.228930	−	0.0857835i
$645$	−4.19120	+	1.75512i	−0.165028	+	0.0691079i
$646$	35.7248	+	26.8673i	1.40557	+	1.05708i
$647$	−5.35164	+	9.26931i	−0.210395	+	0.364414i	−0.951838	−	0.306601i	$-0.900808\pi$
$647$	−5.35164	+	9.26931i	−0.210395	+	0.364414i	0.741443	+	0.671015i	$0.234142\pi$
$648$	−16.3805	−	19.4853i	−0.643488	−	0.765456i
$649$	−11.5900	−	20.0745i	−0.454947	−	0.787991i
$650$	35.0883	−	14.9336i	1.37628	−	0.585742i
$651$	13.1601	+	25.6564i	0.515783	+	1.00555i
$652$	−3.46352	−	3.33197i	−0.135642	−	0.130490i
$653$		−	28.3222i		−	1.10833i	−0.832406	−	0.554166i	$-0.813037\pi$
$653$		−	28.3222i		−	1.10833i	0.832406	−	0.554166i	$-0.186963\pi$
$654$	−6.66549	−	23.5919i	−0.260641	−	0.922517i
$655$	3.31924			0.129694
$656$	−1.60288	−	41.3825i	−0.0625821	−	1.61572i
$657$	−3.75264	+	3.81131i	−0.146404	+	0.148693i
$658$	−30.6041	+	15.9228i	−1.19307	+	0.620735i
$659$	−39.6810	+	22.9098i	−1.54575	+	0.892440i	−0.547292	+	0.836942i	$0.684341\pi$
$659$	−39.6810	+	22.9098i	−1.54575	+	0.892440i	−0.998459	+	0.0554980i	$0.982325\pi$
$660$	−1.57910	+	0.245340i	−0.0614662	+	0.00954983i
$661$	−31.4675	+	18.1677i	−1.22394	+	0.706643i	−0.965756	−	0.259452i	$-0.916458\pi$
$661$	−31.4675	+	18.1677i	−1.22394	+	0.706643i	−0.258186	+	0.966095i	$0.583125\pi$
$662$	−14.7774	+	6.28926i	−0.574342	+	0.244439i
$663$	−19.4662	−	46.4849i	−0.756005	−	1.80532i
$664$	12.5453	−	2.02373i	0.486854	−	0.0785358i
$665$	3.19424	−	2.18982i	0.123867	−	0.0849174i
$666$	−16.5285	+	41.9578i	−0.640467	+	1.62583i
$667$	0.0145356	−	0.00839216i	0.000562822	−	0.000324946i
$668$	−7.59620	−	1.87859i	−0.293906	−	0.0726850i
$669$	−6.42663	+	2.69124i	−0.248468	+	0.104049i
$670$	−0.682126	−	0.0830956i	−0.0263528	−	0.00321026i
$671$	−2.60619	+	4.51406i	−0.100611	+	0.174263i
$672$	3.41614	−	25.6969i	0.131780	−	0.991279i
$673$	−22.5166	−	38.9999i	−0.867952	−	1.50334i	−0.864086	−	0.503345i	$-0.832103\pi$
$673$	−22.5166	−	38.9999i	−0.867952	−	1.50334i	−0.00386641	−	0.999993i	$-0.501231\pi$
$674$	−7.76471	−	18.2442i	−0.299085	−	0.702740i
$675$	−9.54477	+	23.8233i	−0.367378	+	0.916960i
$676$	23.3026	−	24.2227i	0.896255	−	0.931643i
$677$	12.4287	+	7.17569i	0.477672	+	0.275784i	0.719446	−	0.694548i	$-0.244396\pi$
$677$	12.4287	+	7.17569i	0.477672	+	0.275784i	−0.241774	+	0.970333i	$0.577729\pi$
$678$	3.58003	−	1.01148i	0.137490	−	0.0388455i
$679$	−8.99961	+	6.16969i	−0.345373	+	0.236771i
$680$	2.34961	+	2.88465i	0.0901035	+	0.110621i
$681$	34.1877	+	4.36609i	1.31008	+	0.167309i
$682$	2.01125	−	16.5102i	0.0770148	−	0.632210i
$683$	−32.4429	−	18.7309i	−1.24139	−	0.716718i	−0.272014	−	0.962293i	$-0.587690\pi$
$683$	−32.4429	−	18.7309i	−1.24139	−	0.716718i	−0.969377	+	0.245576i	$0.921023\pi$
$684$	−18.6211	−	30.3234i	−0.711996	−	1.15944i
$685$		−	0.190295i		−	0.00727081i
$686$	23.9923	+	10.5057i	0.916030	+	0.401110i
$687$	24.2572	+	3.09786i	0.925468	+	0.118191i
$688$	−19.8172	+	37.6156i	−0.755524	+	1.43408i
$689$	−18.3374	−	31.7613i	−0.698599	−	1.21001i
$690$	0.494375	−	0.507964i	0.0188205	−	0.0193379i
$691$	−5.58089	−	3.22213i	−0.212307	−	0.122576i	0.390076	−	0.920783i	$-0.372449\pi$
$691$	−5.58089	−	3.22213i	−0.212307	−	0.122576i	−0.602383	+	0.798207i	$0.705782\pi$
$692$	−4.67661	+	18.9101i	−0.177778	+	0.718856i
$693$	−14.6045	−	2.60751i	−0.554781	−	0.0990511i
$694$	−1.08804	+	8.93168i	−0.0413016	+	0.339042i
$695$	−0.00385638	+	0.00667944i	−0.000146281	+	0.000253366i
$696$	−0.00230785	−	0.0700932i	−8.74787e−5	−	0.00265688i
$697$	27.5892	+	47.7859i	1.04501	+	1.81002i
$698$	−0.873495	+	7.17047i	−0.0330623	+	0.271406i
$699$	−3.43600	+	1.43887i	−0.129962	+	0.0544232i
$700$	−24.4734	+	9.17055i	−0.925008	+	0.346614i
$701$		−	9.34965i		−	0.353131i	−0.984289	−	0.176566i	$-0.943501\pi$
$701$		−	9.34965i		−	0.353131i	0.984289	−	0.176566i	$-0.0564988\pi$
$702$	0.854966	+	40.1097i	0.0322686	+	1.51384i
$703$	−31.5196	+	54.5935i	−1.18878	+	2.05903i
$704$	−9.94173	+	11.1690i	−0.374693	+	0.420949i
$705$	−2.38730	+	3.13629i	−0.0899108	+	0.118120i
$706$	−18.1630	+	24.1508i	−0.683572	+	0.908929i
$707$	−30.8068	+	2.38811i	−1.15861	+	0.0898141i
$708$	33.4663	−	26.9377i	1.25774	−	1.01238i
$709$	−34.4578	−	19.8942i	−1.29409	−	0.747142i	−0.314712	−	0.949187i	$-0.601908\pi$
$709$	−34.4578	−	19.8942i	−1.29409	−	0.747142i	−0.979376	+	0.202045i	$0.935241\pi$
$710$	−2.45149	−	1.84368i	−0.0920029	−	0.0691920i
$711$	−9.79199	+	9.94507i	−0.367228	+	0.372969i
$712$	−6.04790	−	37.4917i	−0.226655	−	1.40506i
$713$	3.68870	+	6.38902i	0.138143	+	0.239271i
$714$	11.9316	+	32.4128i	0.446529	+	1.21302i
$715$	2.18112	+	1.25927i	0.0815692	+	0.0470940i
$716$	−9.16663	+	37.0658i	−0.342573	+	1.38521i
$717$	28.8303	+	21.9451i	1.07669	+	0.819556i
$718$	−21.2644	−	2.59040i	−0.793580	−	0.0966727i
$719$	6.14870	+	10.6499i	0.229308	+	0.397173i	0.957603	−	0.288090i	$-0.0930204\pi$
$719$	6.14870	+	10.6499i	0.229308	+	0.397173i	−0.728295	+	0.685264i	$0.759687\pi$
$720$	−0.898622	−	2.82212i	−0.0334897	−	0.105174i
$721$	−2.40378	−	31.0090i	−0.0895215	−	1.15484i
$722$	−8.95723	−	21.0462i	−0.333354	−	0.783258i
$723$	−0.864975	+	6.77300i	−0.0321688	+	0.251891i
$724$	21.2060	−	6.12443i	0.788114	−	0.227613i
$725$	−0.0612326	+	0.0353527i	−0.00227412	+	0.00131296i
$726$	−13.1767	−	12.8242i	−0.489032	−	0.475949i
$727$	−9.42711	−	16.3282i	−0.349632	−	0.605581i	0.636552	−	0.771234i	$-0.280360\pi$
$727$	−9.42711	−	16.3282i	−0.349632	−	0.605581i	−0.986184	+	0.165653i	$0.947027\pi$
$728$	−29.5879	+	28.1725i	−1.09660	+	1.04414i
$729$	−19.5309	−	18.6425i	−0.723367	−	0.690464i
$730$	−0.572607	+	0.243701i	−0.0211931	+	0.00901976i
$731$		−	56.6479i		−	2.09520i
$732$	−9.00854	−	3.48853i	−0.332965	−	0.128940i
$733$			35.6402i			1.31640i	0.752842	+	0.658201i	$0.228682\pi$
$733$			35.6402i			1.31640i	−0.752842	+	0.658201i	$0.771318\pi$
$734$	20.7750	−	27.6240i	0.766819	−	1.01962i
$735$	2.99129	−	0.0828990i	0.110335	−	0.00305777i
$736$	0.546602	−	6.60987i	0.0201480	−	0.243643i
$737$	1.83986	+	3.18673i	0.0677720	+	0.117385i
$738$	−6.49181	−	43.4433i	−0.238967	−	1.59917i
$739$	23.5817	+	13.6149i	0.867465	+	0.500831i	0.866505	−	0.499168i	$-0.166361\pi$
$739$	23.5817	+	13.6149i	0.867465	+	0.500831i	0.000960259		1.00000i	$0.499694\pi$
$740$	−3.63756	+	3.78119i	−0.133720	+	0.138999i
$741$	−7.10444	+	55.6298i	−0.260988	+	2.04361i
$742$	11.6011	+	22.2977i	0.425890	+	0.818574i
$743$	4.04913	−	7.01330i	0.148548	−	0.257293i	−0.782143	−	0.623099i	$-0.785873\pi$
$743$	4.04913	−	7.01330i	0.148548	−	0.257293i	0.930691	+	0.365806i	$0.119207\pi$
$744$	30.8089	−	1.01440i	1.12951	−	0.0371895i
$745$	3.81694			0.139842
$746$	−34.9772	−	26.3051i	−1.28061	−	0.963098i
$747$	12.9917	−	3.58933i	0.475340	−	0.131327i
$748$	4.78293	−	19.3400i	0.174881	−	0.707142i
$749$	−3.06873	−	4.47630i	−0.112129	−	0.163560i
$750$	−4.19088	+	4.30607i	−0.153029	+	0.157236i
$751$	−2.06003			−0.0751716			−0.0375858	−	0.999293i	$-0.511967\pi$
$751$	−2.06003			−0.0751716			−0.0375858	+	0.999293i	$0.511967\pi$
$752$	1.42744	+	36.8528i	0.0520532	+	1.34388i
$753$	2.64498	+	0.337788i	0.0963883	+	0.0123097i
$754$	−0.0664333	+	0.0883348i	−0.00241936	+	0.00321696i
$755$		−	1.39700i		−	0.0508422i
$756$	0.619823	−	27.4885i	0.0225428	−	0.999746i
$757$		−	19.6209i		−	0.713134i	−0.934270	−	0.356567i	$-0.883947\pi$
$757$		−	19.6209i		−	0.713134i	0.934270	−	0.356567i	$-0.116053\pi$
$758$	−9.00758	−	6.77427i	−0.327170	−	0.246052i
$759$	−3.76510	−	0.480839i	−0.136665	−	0.0174533i
$760$	−0.659342	−	4.08735i	−0.0239168	−	0.148264i
$761$	−2.25946			−0.0819055			−0.0409527	−	0.999161i	$-0.513039\pi$
$761$	−2.25946			−0.0819055			−0.0409527	+	0.999161i	$0.513039\pi$
$762$	10.9900	+	10.6960i	0.398125	+	0.387474i
$763$	11.4279	−	23.8868i	0.413718	−	0.864760i
$764$	−5.14037	−	1.27125i	−0.185972	−	0.0459922i
$765$	2.81191	+	2.76862i	0.101665	+	0.100100i
$766$	5.87368	−	7.81009i	0.212225	−	0.282190i
$767$	−67.7069			−2.44475
$768$	−23.2836	−	15.0291i	−0.840174	−	0.542317i
$769$	5.98749	−	10.3706i	0.215914	−	0.373974i	−0.737641	−	0.675193i	$-0.764060\pi$
$769$	5.98749	−	10.3706i	0.215914	−	0.373974i	0.953555	+	0.301219i	$0.0973935\pi$
$770$	−1.45556	−	0.927749i	−0.0524546	−	0.0334338i
$771$	−0.573488	+	4.49057i	−0.0206537	+	0.161724i
$772$	1.87338	−	1.94735i	0.0674245	−	0.0700867i
$773$	−7.73185	−	4.46398i	−0.278095	−	0.160558i	0.354466	−	0.935069i	$-0.384663\pi$
$773$	−7.73185	−	4.46398i	−0.278095	−	0.160558i	−0.632561	+	0.774511i	$0.717996\pi$
$774$	−16.5284	+	41.9574i	−0.594100	+	1.50813i
$775$	−15.5390	−	26.9143i	−0.558176	−	0.966789i
$776$	1.85766	+	11.5159i	0.0666861	+	0.413396i
$777$	−43.3403	+	22.2307i	−1.55482	+	0.797522i
$778$	−42.5727	−	32.0173i	−1.52631	−	1.14788i
$779$		−	61.4032i		−	2.20000i
$780$	−1.68560	+	4.35277i	−0.0603541	+	0.155854i
$781$			16.4256i			0.587755i
$782$	3.46059	+	8.13111i	0.123750	+	0.290768i
$783$	−0.0105666	−	0.0736311i	−0.000377618	−	0.00263136i
$784$	21.1051	−	18.4004i	0.753754	−	0.657157i
$785$	1.14046	+	1.97534i	0.0407049	+	0.0705029i
$786$	22.9755	−	23.6071i	0.819510	−	0.842036i
$787$	3.07414	−	1.77486i	0.109581	−	0.0632668i	−0.444208	−	0.895924i	$-0.646515\pi$
$787$	3.07414	−	1.77486i	0.109581	−	0.0632668i	0.553789	+	0.832657i	$0.313181\pi$
$788$	29.7150	−	8.58188i	1.05855	−	0.305717i
$789$	−1.04961	+	8.21871i	−0.0373670	+	0.292594i
$790$	−1.49414	+	0.635903i	−0.0531590	+	0.0226244i
$791$	3.62478	+	1.73417i	0.128882	+	0.0616598i
$792$	−9.18548	+	12.9291i	−0.326392	+	0.459414i
$793$	7.61248	+	13.1852i	0.270327	+	0.468220i
$794$	0.411595	−	3.37876i	0.0146070	−	0.119908i
$795$	2.28505	+	1.73935i	0.0810425	+	0.0616883i
$796$	34.7641	+	8.59740i	1.23218	+	0.304727i
$797$	−14.0042	−	8.08535i	−0.496056	−	0.286398i	0.231028	−	0.972947i	$-0.425791\pi$
$797$	−14.0042	−	8.08535i	−0.496056	−	0.286398i	−0.727083	+	0.686549i	$0.759125\pi$
$798$	6.53591	−	37.8758i	0.231369	−	1.34079i
$799$	−24.5693	−	42.5553i	−0.869200	−	1.50550i
$800$	−2.30261	+	27.8446i	−0.0814095	+	0.984456i
$801$	−10.7267	−	38.8255i	−0.379009	−	1.37183i
$802$	30.0432	−	39.9477i	1.06086	−	1.41060i
$803$	2.88594	+	1.66620i	0.101843	+	0.0587989i
$804$	−5.31262	+	4.27623i	−0.187361	+	0.150811i
$805$	0.763329	−	0.0591723i	0.0269038	−	0.00208555i
$806$	−38.8268	−	29.2002i	−1.36762	−	1.02853i
$807$	−10.8123	+	14.2046i	−0.380612	+	0.500026i
$808$	−11.7498	+	30.8724i	−0.413355	+	1.08609i
$809$	−7.73189	+	13.3920i	−0.271839	+	0.470838i	−0.969333	−	0.245752i	$-0.920965\pi$
$809$	−7.73189	+	13.3920i	−0.271839	+	0.470838i	0.697494	+	0.716591i	$0.254298\pi$
$810$	−1.27488	−	2.87108i	−0.0447948	−	0.100879i
$811$		−	6.24515i		−	0.219297i	−0.993970	−	0.109648i	$-0.965028\pi$
$811$		−	6.24515i		−	0.219297i	0.993970	−	0.109648i	$-0.0349725\pi$
$812$	0.0481406	−	0.0584859i	0.00168940	−	0.00205245i
$813$	12.3269	−	5.16208i	0.432324	−	0.181042i
$814$	27.8901	+	3.39752i	0.977546	+	0.119083i
$815$	−0.296547	−	0.513634i	−0.0103876	−	0.0179918i
$816$	36.7800	+	3.25642i	1.28756	+	0.113998i
$817$	−31.5193	+	54.5930i	−1.10272	+	1.90997i
$818$	−34.3990	−	4.19043i	−1.20273	−	0.146515i
$819$	−27.9253	+	33.1353i	−0.975788	+	1.15784i
$820$	1.22694	−	4.96121i	0.0428467	−	0.173253i
$821$	14.9572	+	8.63556i	0.522011	+	0.301383i	0.737757	−	0.675066i	$-0.235885\pi$
$821$	14.9572	+	8.63556i	0.522011	+	0.301383i	−0.215746	+	0.976450i	$0.569218\pi$
$822$	−1.35342	−	1.31721i	−0.0472058	−	0.0459430i
$823$	−20.4285	−	35.3833i	−0.712094	−	1.23338i	−0.964070	−	0.265650i	$-0.914414\pi$
$823$	−20.4285	−	35.3833i	−0.712094	−	1.23338i	0.251975	−	0.967734i	$-0.418920\pi$
$824$	−31.0750	−	11.8269i	−1.08255	−	0.412008i
$825$	15.8608	+	2.02557i	0.552203	+	0.0705214i
$826$	46.3583	+	2.03445i	1.61301	+	0.0707875i
$827$			5.65493i			0.196641i	0.995155	+	0.0983206i	$0.0313471\pi$
$827$			5.65493i			0.196641i	−0.995155	+	0.0983206i	$0.968653\pi$
$828$	−0.190710	−	7.03217i	−0.00662763	−	0.244385i
$829$	−13.1244	−	7.57740i	−0.455830	−	0.263174i	0.254459	−	0.967084i	$-0.418103\pi$
$829$	−13.1244	−	7.57740i	−0.455830	−	0.263174i	−0.710289	+	0.703910i	$0.751436\pi$
$830$	1.55668	+	0.189632i	0.0540330	+	0.00658222i
$831$	37.2214	+	4.75352i	1.29120	+	0.164898i
$832$	13.7336	+	41.4604i	0.476126	+	1.43738i
$833$	−13.4513	+	34.7971i	−0.466061	+	1.20565i
$834$	0.0208119	+	0.0736618i	0.000720657	+	0.00255070i
$835$	−0.836284	−	0.482829i	−0.0289408	−	0.0167090i
$836$	−15.3704	+	15.9772i	−0.531595	+	0.552584i
$837$	32.3639	−	4.64444i	1.11866	−	0.160535i
$838$	−11.3722	+	4.83999i	−0.392846	+	0.167195i
$839$	−1.40726	−	2.43745i	−0.0485842	−	0.0841503i	0.840711	−	0.541485i	$-0.182138\pi$
$839$	−1.40726	−	2.43745i	−0.0485842	−	0.0841503i	−0.889295	+	0.457334i	$0.848804\pi$
$840$	1.28491	−	2.92966i	0.0443335	−	0.101083i
$841$	−14.4999	+	25.1146i	−0.499996	+	0.866019i
$842$	−0.192738	+	1.58217i	−0.00664218	+	0.0545252i
$843$	3.50798	−	1.46901i	0.120821	−	0.0505956i
$844$	1.81350	−	7.33301i	0.0624234	−	0.252413i
$845$	3.59218	−	2.07395i	0.123575	−	0.0713459i
$846$	5.78123	+	38.6881i	0.198763	+	1.33012i
$847$	−1.53494	−	19.8009i	−0.0527411	−	0.680366i
$848$	26.8504	−	1.04001i	0.922046	−	0.0357140i
$849$	14.0031	+	33.4392i	0.480587	+	1.14763i
$850$	−14.5780	−	34.2530i	−0.500022	−	1.17487i
$851$	−10.7927	+	6.23117i	−0.369969	+	0.213602i
$852$	−30.0816	+	4.67369i	−1.03058	+	0.160118i
$853$	28.8215	−	16.6401i	0.986830	−	0.569747i	0.0825050	−	0.996591i	$-0.473708\pi$
$853$	28.8215	−	16.6401i	0.986830	−	0.569747i	0.904325	+	0.426844i	$0.140375\pi$
$854$	−4.81602	−	9.25654i	−0.164801	−	0.316752i
$855$	−1.16942	−	4.23275i	−0.0399934	−	0.144757i
$856$	−5.72786	+	0.923978i	−0.195774	+	0.0315809i
$857$	22.9165			0.782812			0.391406	−	0.920218i	$-0.371989\pi$
$857$	22.9165			0.782812			0.391406	+	0.920218i	$0.371989\pi$
$858$	24.0537	−	6.79596i	0.821179	−	0.232010i
$859$		−	0.598606i		−	0.0204242i	−0.999948	−	0.0102121i	$-0.996749\pi$
$859$		−	0.598606i		−	0.0204242i	0.999948	−	0.0102121i	$-0.00325067\pi$
$860$	−3.63753	+	3.78115i	−0.124039	+	0.128936i
$861$	25.7329	−	39.8605i	0.876974	−	1.35844i
$862$	−14.5561	−	34.2015i	−0.495783	−	1.16491i
$863$	−12.0455	−	20.8635i	−0.410035	−	0.710201i	0.584858	−	0.811135i	$-0.301150\pi$
$863$	−12.0455	−	20.8635i	−0.410035	−	0.710201i	−0.994893	+	0.100935i	$0.967817\pi$
$864$	−26.2917	−	13.1434i	−0.894461	−	0.447146i
$865$	−1.20196	+	2.08186i	−0.0408680	+	0.0707854i
$866$	−15.1487	+	20.1429i	−0.514774	+	0.684482i
$867$	−18.2186	+	7.62931i	−0.618737	+	0.259105i
$868$	25.7070	+	21.1598i	0.872552	+	0.718210i
$869$	7.53046	+	4.34771i	0.255453	+	0.147486i
$870$	0.00212645	−	0.00838930i	7.20933e−5	−	0.000284424i
$871$	10.7481			0.364187
$872$	−17.8776	−	21.9485i	−0.605410	−	0.743270i
$873$	3.29479	+	11.9256i	0.111512	+	0.403619i
$874$	1.18915	−	9.76164i	0.0402235	−	0.330192i
$875$	−6.47083	+	0.501611i	−0.218754	+	0.0169576i
$876$	−2.23029	+	5.75936i	−0.0753547	+	0.194591i
$877$		−	49.4357i		−	1.66932i	−0.550763	−	0.834662i	$-0.685663\pi$
$877$		−	49.4357i		−	1.66932i	0.550763	−	0.834662i	$-0.314337\pi$
$878$	−5.02995	−	11.8185i	−0.169752	−	0.398856i
$879$	−0.878304	+	1.15387i	−0.0296245	+	0.0389189i
$880$	−1.56113	+	0.983790i	−0.0526258	+	0.0331635i
$881$	−18.6267			−0.627550			−0.313775	−	0.949497i	$-0.601594\pi$
$881$	−18.6267			−0.627550			−0.313775	+	0.949497i	$0.601594\pi$
$882$	20.1158	−	21.8484i	0.677336	−	0.735674i
$883$			7.79292i			0.262253i	0.991366	+	0.131126i	$0.0418594\pi$
$883$			7.79292i			0.262253i	−0.991366	+	0.131126i	$0.958141\pi$
$884$	−41.9371	−	40.3442i	−1.41050	−	1.35692i
$885$	4.89015	−	2.04782i	0.164381	−	0.0688367i
$886$	41.8475	−	17.8103i	1.40590	−	0.598347i
$887$	−27.9829			−0.939573			−0.469786	−	0.882780i	$-0.655669\pi$
$887$	−27.9829			−0.939573			−0.469786	+	0.882780i	$0.655669\pi$
$888$	1.71357	+	52.0441i	0.0575038	+	1.74649i
$889$	1.28021	+	16.5149i	0.0429370	+	0.553891i
$890$	0.566714	−	4.65212i	0.0189963	−	0.155939i
$891$	−8.18395	+	14.6969i	−0.274173	+	0.492364i
$892$	−5.57766	+	5.79788i	−0.186754	+	0.194128i
$893$			54.6821i			1.82987i
$894$	26.4205	−	27.1468i	0.883635	−	0.907924i
$895$	−2.35597	+	4.08066i	−0.0787514	+	0.136401i
$896$	−8.15747	−	28.8003i	−0.272522	−	0.962150i
$897$	−6.71511	+	8.82193i	−0.224211	+	0.294556i
$898$	26.8056	−	35.6428i	0.894516	−	1.18942i
$899$	0.0780085	+	0.0450382i	0.00260173	+	0.00150211i
$900$	0.803381	+	29.6236i	0.0267794	+	0.987454i
$901$	−31.0051	+	17.9008i	−1.03293	+	0.596362i
$902$	−25.1814	+	10.7172i	−0.838448	+	0.356842i
$903$	−43.3399	+	22.2305i	−1.44226	+	0.739785i
$904$	3.33065	−	2.71289i	0.110776	−	0.0902293i
$905$	2.72390			0.0905454
$906$	−9.93576	−	9.66996i	−0.330093	−	0.321263i
$907$			34.0348i			1.13011i	0.825054	+	0.565053i	$0.191144\pi$
$907$			34.0348i			1.13011i	−0.825054	+	0.565053i	$0.808856\pi$
$908$	38.2346	−	11.0424i	1.26886	−	0.366455i
$909$	−8.80535	+	33.9119i	−0.292055	+	1.12479i
$910$	−4.47260	+	2.32702i	−0.148265	+	0.0771399i
$911$	−16.3116	−	28.2525i	−0.540427	−	0.936047i	−0.998879	−	0.0473280i	$-0.984929\pi$
$911$	−16.3116	−	28.2525i	−0.540427	−	0.936047i	0.458452	−	0.888719i	$-0.348404\pi$
$912$	−33.6339	−	23.6029i	−1.11373	−	0.781571i
$913$	−4.19873	−	7.27241i	−0.138958	−	0.240682i
$914$	17.2285	+	40.4805i	0.569867	+	1.33898i
$915$	−0.948605	−	0.722063i	−0.0313599	−	0.0238707i
$916$	27.1285	−	7.83490i	0.896351	−	0.258872i
$917$	35.4749	−	2.74997i	1.17148	−	0.0908120i
$918$	39.1548	−	0.834611i	1.29230	−	0.0275463i
$919$	20.2462	+	35.0675i	0.667861	+	1.15677i	0.978501	+	0.206242i	$0.0661234\pi$
$919$	20.2462	+	35.0675i	0.667861	+	1.15677i	−0.310640	+	0.950528i	$0.600543\pi$
$920$	0.291134	−	0.764953i	0.00959841	−	0.0252197i
$921$	−4.19870	−	0.536212i	−0.138352	−	0.0176688i
$922$	3.79509	−	31.1536i	0.124985	−	1.02599i
$923$	41.5501	+	23.9890i	1.36764	+	0.789606i
$924$	−16.6736	+	3.93037i	−0.548520	+	0.129300i
$925$	45.4651	−	26.2493i	1.49488	−	0.863072i
$926$	20.7006	+	48.6389i	0.680265	+	1.59837i
$927$	−34.1345	−	8.86314i	−1.12112	−	0.291104i
$928$	−0.0345728	−	0.0732296i	−0.00113491	−	0.00240388i
$929$	5.60555	−	9.70909i	0.183912	−	0.318545i	−0.759297	−	0.650744i	$-0.774457\pi$
$929$	5.60555	−	9.70909i	0.183912	−	0.318545i	0.943209	+	0.332199i	$0.107790\pi$
$930$	3.68745	+	0.934661i	0.120916	+	0.0306487i
$931$	32.3247	−	26.0504i	1.05940	−	0.853767i
$932$	−2.98210	+	3.09984i	−0.0976820	+	0.101539i
$933$	13.9963	−	5.86116i	0.458219	−	0.191886i
$934$	3.65411	−	29.9963i	0.119566	−	0.981510i
$935$	1.22929	−	2.12919i	0.0402020	−	0.0696320i
$936$	19.2902	+	42.1179i	0.630519	+	1.37667i
$937$	−17.4506			−0.570085			−0.285042	−	0.958515i	$-0.592008\pi$
$937$	−17.4506			−0.570085			−0.285042	+	0.958515i	$0.592008\pi$
$938$	−7.35917	−	0.322959i	−0.240285	−	0.0105450i
$939$	−11.9046	−	9.06160i	−0.388492	−	0.295714i
$940$	−1.09264	+	4.41816i	−0.0356381	+	0.144105i
$941$	−45.8709	+	26.4836i	−1.49535	+	0.863341i	−0.999986	−	0.00534495i	$-0.998299\pi$
$941$	−45.8709	+	26.4836i	−1.49535	+	0.863341i	−0.495364	+	0.868686i	$0.664965\pi$
$942$	21.9432	+	5.56196i	0.714947	+	0.181218i
$943$	6.06946	−	10.5126i	0.197649	−	0.342338i
$944$	23.1221	−	43.8886i	0.752559	−	1.42845i
$945$	1.01472	−	3.23782i	0.0330088	−	0.105326i
$946$	27.8898	+	3.39749i	0.906776	+	0.110462i
$947$	14.1857	+	8.19013i	0.460974	+	0.266143i	0.712454	−	0.701719i	$-0.247584\pi$
$947$	14.1857	+	8.19013i	0.460974	+	0.266143i	−0.251480	+	0.967863i	$0.580917\pi$
$948$	−5.81964	+	15.0283i	−0.189013	+	0.488095i
$949$	8.42960	−	4.86683i	0.273636	−	0.157984i
$950$	−5.00939	+	41.1217i	−0.162526	+	1.33417i
$951$	14.8397	−	19.4956i	0.481212	−	0.632189i
$952$	27.5017	+	28.8835i	0.891337	+	0.936118i
$953$	13.8276			0.447919			0.223960	−	0.974598i	$-0.428102\pi$
$953$	13.8276			0.447919			0.223960	+	0.974598i	$0.428102\pi$
$954$	28.1875	−	4.21211i	0.912605	−	0.136372i
$955$	−0.565915	−	0.326731i	−0.0183126	−	0.0105728i
$956$	40.6138	+	10.0441i	1.31354	+	0.324849i
$957$	−0.0427476	+	0.0179012i	−0.00138183	+	0.000578663i
$958$	1.98636	−	2.64122i	0.0641765	−	0.0853340i
$959$	−0.157659	−	2.03381i	−0.00509106	−	0.0656752i
$960$	−2.24590	−	2.57911i	−0.0724860	−	0.0832405i
$961$	−4.29618	+	7.44120i	−0.138586	+	0.240039i
$962$	49.3266	−	65.5884i	1.59035	−	2.11466i
$963$	−5.93163	+	1.63879i	−0.191144	+	0.0528092i
$964$	2.18763	+	7.57473i	0.0704590	+	0.243966i
$965$	0.288788	−	0.166732i	0.00929642	−	0.00536729i
$966$	4.86286	−	5.83853i	0.156460	−	0.187851i
$967$	6.91834	−	11.9829i	0.222479	−	0.385345i	−0.733081	−	0.680141i	$-0.761919\pi$
$967$	6.91834	−	11.9829i	0.222479	−	0.385345i	0.955560	+	0.294796i	$0.0952518\pi$
$968$	−19.8430	−	7.55207i	−0.637778	−	0.242733i
$969$	54.3054	+	6.93530i	1.74454	+	0.222794i
$970$	−0.174071	+	1.42894i	−0.00558907	+	0.0458803i
$971$	−30.5544	+	17.6406i	−0.980538	+	0.566114i	−0.902433	−	0.430831i	$-0.858221\pi$
$971$	−30.5544	+	17.6406i	−0.980538	+	0.566114i	−0.0781058	+	0.996945i	$0.524887\pi$
$972$	−29.2443	−	10.8062i	−0.938010	−	0.346608i
$973$	−0.0356817	+	0.0745825i	−0.00114390	+	0.00239100i
$974$	−3.75550	−	8.82403i	−0.120334	−	0.282740i
$975$	28.2880	−	37.1631i	0.905940	−	1.19017i
$976$	−11.1465	+	0.431743i	−0.356792	+	0.0138198i
$977$	6.53232	+	11.3143i	0.208988	+	0.361977i	0.951396	−	0.307971i	$-0.0996498\pi$
$977$	6.53232	+	11.3143i	0.208988	+	0.361977i	−0.742408	+	0.669948i	$0.766317\pi$
$978$	−5.70573	−	1.44624i	−0.182449	−	0.0462456i
$979$	−21.7335	+	12.5479i	−0.694607	+	0.401032i
$980$	3.13228	−	1.45890i	0.100057	−	0.0466028i
$981$	−21.3950	−	21.0657i	−0.683091	−	0.672576i
$982$	−9.94150	+	4.23109i	−0.317246	+	0.135019i
$983$	−0.732479			−0.0233625			−0.0116812	−	0.999932i	$-0.503718\pi$
$983$	−0.732479			−0.0233625			−0.0116812	+	0.999932i	$0.503718\pi$
$984$	−26.7923	−	43.0673i	−0.854106	−	1.37294i
$985$	3.81687			0.121616
$986$	0.0862317	+	0.0648517i	0.00274618	+	0.00206530i
$987$	−22.9162	+	35.4975i	−0.729430	+	1.12990i
$988$	17.9680	+	62.2148i	0.571640	+	1.97932i
$989$	−10.7926	+	6.23111i	−0.343185	+	0.198138i
$990$	−1.53174	+	1.21835i	−0.0486818	+	0.0387218i
$991$	−9.51755	+	16.4849i	−0.302335	+	0.523659i	−0.976664	−	0.214771i	$-0.931099\pi$
$991$	−9.51755	+	16.4849i	−0.302335	+	0.523659i	0.674329	+	0.738431i	$0.264433\pi$
$992$	32.1874	−	15.1962i	1.02195	−	0.482479i
$993$	−11.9135	+	15.6512i	−0.378062	+	0.496677i
$994$	−27.7282	−	17.6735i	−0.879485	−	0.560570i
$995$	3.82726	+	2.20967i	0.121332	+	0.0700512i
$996$	12.1239	−	9.75875i	0.384160	−	0.309218i
$997$		−	19.7056i		−	0.624081i	−0.950069	−	0.312041i	$-0.898988\pi$
$997$		−	19.7056i		−	0.624081i	0.950069	−	0.312041i	$-0.101012\pi$
$998$	8.25668	+	6.20954i	0.261361	+	0.196560i
$999$	7.84565	+	54.6710i	0.248226	+	1.72971i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.w.a.445.65	yes	184
7.2	even	3		504.2.cq.a.373.3	yes	184
8.5	even	2	inner	504.2.w.a.445.58	yes	184
9.7	even	3		504.2.cq.a.277.3	yes	184
56.37	even	6		504.2.cq.a.373.4	yes	184
63.16	even	3	inner	504.2.w.a.205.58	✓	184
72.61	even	6		504.2.cq.a.277.4	yes	184
504.205	even	6	inner	504.2.w.a.205.65	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.w.a.205.58	✓	184	63.16	even	3	inner
504.2.w.a.205.65	yes	184	504.205	even	6	inner
504.2.w.a.445.58	yes	184	8.5	even	2	inner
504.2.w.a.445.65	yes	184	1.1	even	1	trivial
504.2.cq.a.277.3	yes	184	9.7	even	3
504.2.cq.a.277.4	yes	184	72.61	even	6
504.2.cq.a.373.3	yes	184	7.2	even	3
504.2.cq.a.373.4	yes	184	56.37	even	6

Overview	Random
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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

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	504.2.w.a.445.65

Level	$504$
Weight	$2$
Character	504.445
Analytic conductor	$4.024$
Analytic rank	$0$
Dimension	$184$
Inner twists	$4$