LMFDB - Embedded newform 560.2.cz.c.157.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(157,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 3, 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("560.157"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.cz (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [360,2,-24,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$90$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.14
Character	$\chi$	$=$	560.157
Dual form			560.2.cz.c.453.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.29449 - 0.569466i) q^{2} +(2.95419 + 1.70560i) q^{3} +(1.35142 + 1.47434i) q^{4} +(2.23531 - 0.0580249i) q^{5} +(-2.85289 - 3.89019i) q^{6} +(-1.25390 - 2.32975i) q^{7} +(-0.909815 - 2.67810i) q^{8} +(4.31815 + 7.47925i) q^{9} +(-2.92664 - 1.19782i) q^{10} +(0.547088 + 2.04176i) q^{11} +(1.47771 + 6.66045i) q^{12} -0.966590i q^{13} +(0.296452 + 3.72989i) q^{14} +(6.70251 + 3.64114i) q^{15} +(-0.347339 + 3.98489i) q^{16} +(-0.932306 - 3.47941i) q^{17} +(-1.33063 - 12.1409i) q^{18} +(-0.0327809 + 0.122340i) q^{19} +(3.10639 + 3.21719i) q^{20} +(0.269364 - 9.02117i) q^{21} +(0.454511 - 2.95459i) q^{22} +(0.676197 - 2.52360i) q^{23} +(1.88001 - 9.46340i) q^{24} +(4.99327 - 0.259408i) q^{25} +(-0.550440 + 1.25124i) q^{26} +19.2265i q^{27} +(1.74029 - 4.99714i) q^{28} +(-1.42218 + 1.42218i) q^{29} +(-6.60284 - 8.53027i) q^{30} +(-7.08438 - 4.09017i) q^{31} +(2.71889 - 4.96061i) q^{32} +(-1.86623 + 6.96485i) q^{33} +(-0.774543 + 5.03499i) q^{34} +(-2.93805 - 5.13497i) q^{35} +(-5.19132 + 16.4740i) q^{36} +(2.64442 + 4.58027i) q^{37} +(0.112103 - 0.139700i) q^{38} +(1.64862 - 2.85549i) q^{39} +(-2.18912 - 5.93361i) q^{40} -8.15686 q^{41} +(-5.48594 + 11.5244i) q^{42} +0.958523i q^{43} +(-2.27090 + 3.56586i) q^{44} +(10.0864 + 16.4679i) q^{45} +(-2.31244 + 2.88171i) q^{46} +(-4.47258 - 1.19843i) q^{47} +(-7.82274 + 11.1797i) q^{48} +(-3.85547 + 5.84255i) q^{49} +(-6.61147 - 2.50769i) q^{50} +(3.18028 - 11.8690i) q^{51} +(1.42508 - 1.30627i) q^{52} +(-2.10535 - 1.21552i) q^{53} +(10.9489 - 24.8886i) q^{54} +(1.34139 + 4.53223i) q^{55} +(-5.09849 + 5.47772i) q^{56} +(-0.305504 + 0.305504i) q^{57} +(2.65089 - 1.03112i) q^{58} +(-1.86096 - 6.94519i) q^{59} +(3.68962 + 14.8025i) q^{60} +(11.3063 + 3.02951i) q^{61} +(6.84146 + 9.32900i) q^{62} +(12.0103 - 19.4384i) q^{63} +(-6.34447 + 4.87316i) q^{64} +(-0.0560863 - 2.16063i) q^{65} +(6.38206 - 7.95319i) q^{66} +(4.87233 + 2.81304i) q^{67} +(3.86989 - 6.07667i) q^{68} +(6.30187 - 6.30187i) q^{69} +(0.879091 + 8.32029i) q^{70} -14.4961i q^{71} +(16.1015 - 18.3692i) q^{72} +(-1.00990 - 3.76901i) q^{73} +(-0.814874 - 7.43503i) q^{74} +(15.1935 + 7.75018i) q^{75} +(-0.224671 + 0.117002i) q^{76} +(4.07079 - 3.83474i) q^{77} +(-3.76022 + 2.75758i) q^{78} +(-11.6104 + 6.70327i) q^{79} +(-0.545190 + 8.92764i) q^{80} +(-19.8384 + 34.3611i) q^{81} +(10.5590 + 4.64505i) q^{82} +7.64983i q^{83} +(13.6643 - 11.7942i) q^{84} +(-2.28589 - 7.72348i) q^{85} +(0.545846 - 1.24080i) q^{86} +(-6.62707 + 1.77572i) q^{87} +(4.97029 - 3.32278i) q^{88} +(-3.01621 + 1.74141i) q^{89} +(-3.67885 - 27.0615i) q^{90} +(-2.25191 + 1.21201i) q^{91} +(4.63447 - 2.41350i) q^{92} +(-13.9524 - 24.1662i) q^{93} +(5.10726 + 4.09833i) q^{94} +(-0.0661768 + 0.275370i) q^{95} +(16.4929 - 10.0172i) q^{96} +(10.2159 - 10.2159i) q^{97} +(8.31800 - 5.36758i) q^{98} +(-12.9084 + 12.9084i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + 2 q^{2} - 24 q^{3} - 6 q^{5} - 8 q^{7} - 4 q^{8} + 164 q^{9} - 6 q^{10} - 2 q^{11} - 6 q^{12} - 4 q^{14} - 32 q^{15} - 20 q^{16} + 8 q^{18} - 30 q^{19} - 4 q^{21} - 8 q^{22} - 10 q^{23} - 12 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) $ 360 * q + 2 * q^2 - 24 * q^3 - 6 * q^5 - 8 * q^7 - 4 * q^8 + 164 * q^9 - 6 * q^10 - 2 * q^11 - 6 * q^12 - 4 * q^14 - 32 * q^15 - 20 * q^16 + 8 * q^18 - 30 * q^19 - 4 * q^21 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 12 * q^25 - 2 * q^28 + 8 * q^29 + 2 * q^30 - 24 * q^31 + 2 * q^32 - 24 * q^35 + 16 * q^36 + 4 * q^37 + 72 * q^38 + 28 * q^39 - 36 * q^40 - 50 * q^42 - 20 * q^44 - 72 * q^45 - 4 * q^46 - 6 * q^47 + 48 * q^50 + 16 * q^51 - 36 * q^52 + 24 * q^54 - 8 * q^56 - 80 * q^57 - 46 * q^58 - 84 * q^59 - 20 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 48 * q^68 - 16 * q^70 - 72 * q^72 + 52 * q^74 - 42 * q^75 + 152 * q^78 + 108 * q^80 - 124 * q^81 - 6 * q^82 - 28 * q^84 + 20 * q^85 + 8 * q^86 + 12 * q^88 - 48 * q^89 + 28 * q^91 + 4 * q^92 - 20 * q^93 + 72 * q^94 - 26 * q^95 - 60 * q^96 - 10 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.29449	−	0.569466i	−0.915344	−	0.402673i
$2$	−1.29449	−	0.569466i	−0.915344	−	0.402673i
$3$	2.95419	+	1.70560i	1.70560	+	0.984729i	0.939847	+	0.341595i	$0.110967\pi$
$3$	2.95419	+	1.70560i	1.70560	+	0.984729i	0.765754	+	0.643134i	$0.222366\pi$
$4$	1.35142	+	1.47434i	0.675709	+	0.737168i
$5$	2.23531	−	0.0580249i	0.999663	−	0.0259495i
$5$	2.23531	−	0.0580249i	0.999663	−	0.0259495i
$6$	−2.85289	−	3.89019i	−1.16469	−	1.58817i
$7$	−1.25390	−	2.32975i	−0.473930	−	0.880563i
$7$	−1.25390	−	2.32975i	−0.473930	−	0.880563i
$8$	−0.909815	−	2.67810i	−0.321668	−	0.946852i
$9$	4.31815	+	7.47925i	1.43938	+	2.49308i
$10$	−2.92664	−	1.19782i	−0.925485	−	0.378785i
$11$	0.547088	+	2.04176i	0.164953	+	0.615614i	0.998046	+	0.0624807i	$0.0199012\pi$
$11$	0.547088	+	2.04176i	0.164953	+	0.615614i	−0.833093	+	0.553133i	$0.813432\pi$
$12$	1.47771	+	6.66045i	0.426579	+	1.92271i
$13$		−	0.966590i		−	0.268084i	−0.990976	−	0.134042i	$-0.957204\pi$
$13$		−	0.966590i		−	0.268084i	0.990976	−	0.134042i	$-0.0427957\pi$
$14$	0.296452	+	3.72989i	0.0792302	+	0.996856i
$15$	6.70251	+	3.64114i	1.73058	+	0.940138i
$16$	−0.347339	+	3.98489i	−0.0868348	+	0.996223i
$17$	−0.932306	−	3.47941i	−0.226117	−	0.843881i	−0.981954	−	0.189121i	$-0.939436\pi$
$17$	−0.932306	−	3.47941i	−0.226117	−	0.843881i	0.755836	−	0.654760i	$-0.227230\pi$
$18$	−1.33063	−	12.1409i	−0.313633	−	2.86163i
$19$	−0.0327809	+	0.122340i	−0.00752045	+	0.0280667i	−0.969584	−	0.244758i	$-0.921291\pi$
$19$	−0.0327809	+	0.122340i	−0.00752045	+	0.0280667i	0.962064	+	0.272825i	$0.0879580\pi$
$20$	3.10639	+	3.21719i	0.694611	+	0.719386i
$21$	0.269364	−	9.02117i	0.0587802	−	1.96858i
$22$	0.454511	−	2.95459i	0.0969021	−	0.629920i
$23$	0.676197	−	2.52360i	0.140997	−	0.526207i	−0.858904	−	0.512136i	$-0.828854\pi$
$23$	0.676197	−	2.52360i	0.140997	−	0.526207i	0.999901	−	0.0140711i	$-0.00447911\pi$
$24$	1.88001	−	9.46340i	0.383755	−	1.93171i
$25$	4.99327	−	0.259408i	0.998653	−	0.0518815i
$26$	−0.550440	+	1.25124i	−0.107950	+	0.245389i
$27$			19.2265i			3.70015i
$28$	1.74029	−	4.99714i	0.328884	−	0.944370i
$29$	−1.42218	+	1.42218i	−0.264093	+	0.264093i	−0.826714	−	0.562622i	$-0.809793\pi$
$29$	−1.42218	+	1.42218i	−0.264093	+	0.264093i	0.562622	+	0.826714i	$0.309793\pi$
$30$	−6.60284	−	8.53027i	−1.20551	−	1.55741i
$31$	−7.08438	−	4.09017i	−1.27239	−	0.734616i	−0.296954	−	0.954892i	$-0.595971\pi$
$31$	−7.08438	−	4.09017i	−1.27239	−	0.734616i	−0.975438	+	0.220276i	$0.929304\pi$
$32$	2.71889	−	4.96061i	0.480636	−	0.876920i
$33$	−1.86623	+	6.96485i	−0.324868	+	1.21243i
$34$	−0.774543	+	5.03499i	−0.132833	+	0.863493i
$35$	−2.93805	−	5.13497i	−0.496621	−	0.867968i
$36$	−5.19132	+	16.4740i	−0.865219	+	2.74567i
$37$	2.64442	+	4.58027i	0.434740	+	0.752992i	0.997274	−	0.0737820i	$-0.0235069\pi$
$37$	2.64442	+	4.58027i	0.434740	+	0.752992i	−0.562534	+	0.826774i	$0.690174\pi$
$38$	0.112103	−	0.139700i	0.0181855	−	0.0226624i
$39$	1.64862	−	2.85549i	0.263990	−	0.457244i
$40$	−2.18912	−	5.93361i	−0.346130	−	0.938186i
$41$	−8.15686			−1.27389			−0.636944	−	0.770910i	$-0.719802\pi$
$41$	−8.15686			−1.27389			−0.636944	+	0.770910i	$0.719802\pi$
$42$	−5.48594	+	11.5244i	−0.846498	+	1.77826i
$43$			0.958523i			0.146173i	0.997326	+	0.0730867i	$0.0232850\pi$
$43$			0.958523i			0.146173i	−0.997326	+	0.0730867i	$0.976715\pi$
$44$	−2.27090	+	3.56586i	−0.342351	+	0.537574i
$45$	10.0864	+	16.4679i	1.50359	+	2.45489i
$46$	−2.31244	+	2.88171i	−0.340950	+	0.424885i
$47$	−4.47258	−	1.19843i	−0.652393	−	0.174808i	−0.0825826	−	0.996584i	$-0.526317\pi$
$47$	−4.47258	−	1.19843i	−0.652393	−	0.174808i	−0.569811	+	0.821776i	$0.692983\pi$
$48$	−7.82274	+	11.1797i	−1.12911	+	1.61365i
$49$	−3.85547	+	5.84255i	−0.550781	+	0.834650i
$50$	−6.61147	−	2.50769i	−0.935002	−	0.354641i
$51$	3.18028	−	11.8690i	0.445329	−	1.66199i
$52$	1.42508	−	1.30627i	0.197623	−	0.181147i
$53$	−2.10535	−	1.21552i	−0.289191	−	0.166965i	0.348386	−	0.937351i	$-0.386730\pi$
$53$	−2.10535	−	1.21552i	−0.289191	−	0.166965i	−0.637577	+	0.770386i	$0.720063\pi$
$54$	10.9489	−	24.8886i	1.48995	−	3.38691i
$55$	1.34139	+	4.53223i	0.180873	+	0.611126i
$56$	−5.09849	+	5.47772i	−0.681315	+	0.731991i
$57$	−0.305504	+	0.305504i	−0.0404650	+	0.0404650i
$58$	2.65089	−	1.03112i	0.348079	−	0.135393i
$59$	−1.86096	−	6.94519i	−0.242276	−	0.904186i	−0.974733	−	0.223373i	$-0.928293\pi$
$59$	−1.86096	−	6.94519i	−0.242276	−	0.904186i	0.732457	−	0.680813i	$-0.238373\pi$
$60$	3.68962	+	14.8025i	0.476328	+	1.91099i
$61$	11.3063	+	3.02951i	1.44762	+	0.387890i	0.895197	−	0.445672i	$-0.147035\pi$
$61$	11.3063	+	3.02951i	1.44762	+	0.387890i	0.552427	+	0.833561i	$0.313702\pi$
$62$	6.84146	+	9.32900i	0.868866	+	1.18478i
$63$	12.0103	−	19.4384i	1.51315	−	2.44901i
$64$	−6.34447	+	4.87316i	−0.793059	+	0.609145i
$65$	−0.0560863	−	2.16063i	−0.00695665	−	0.267994i
$66$	6.38206	−	7.95319i	0.785577	−	0.978971i
$67$	4.87233	+	2.81304i	0.595250	+	0.343667i	0.767170	−	0.641443i	$-0.221664\pi$
$67$	4.87233	+	2.81304i	0.595250	+	0.343667i	−0.171921	+	0.985111i	$0.554997\pi$
$68$	3.86989	−	6.07667i	0.469293	−	0.736905i
$69$	6.30187	−	6.30187i	0.758656	−	0.758656i
$70$	0.879091	+	8.32029i	0.105071	+	0.994465i
$71$		−	14.4961i		−	1.72038i	−0.509977	−	0.860188i	$-0.670346\pi$
$71$		−	14.4961i		−	1.72038i	0.509977	−	0.860188i	$-0.329654\pi$
$72$	16.1015	−	18.3692i	1.89758	−	2.16483i
$73$	−1.00990	−	3.76901i	−0.118200	−	0.441129i	0.881306	−	0.472546i	$-0.156665\pi$
$73$	−1.00990	−	3.76901i	−0.118200	−	0.441129i	−0.999506	+	0.0314165i	$0.989998\pi$
$74$	−0.814874	−	7.43503i	−0.0947272	−	0.864305i
$75$	15.1935	+	7.75018i	1.75439	+	0.894914i
$76$	−0.224671	+	0.117002i	−0.0257715	+	0.0134211i
$77$	4.07079	−	3.83474i	0.463910	−	0.437009i
$78$	−3.76022	+	2.75758i	−0.425761	+	0.312234i
$79$	−11.6104	+	6.70327i	−1.30627	+	0.754177i	−0.981472	−	0.191606i	$-0.938630\pi$
$79$	−11.6104	+	6.70327i	−1.30627	+	0.754177i	−0.324800	+	0.945783i	$0.605297\pi$
$80$	−0.545190	+	8.92764i	−0.0609540	+	0.998141i
$81$	−19.8384	+	34.3611i	−2.20426	+	3.81789i
$82$	10.5590	+	4.64505i	1.16605	+	0.512960i
$83$			7.64983i			0.839678i	0.907599	+	0.419839i	$0.137914\pi$
$83$			7.64983i			0.839678i	−0.907599	+	0.419839i	$0.862086\pi$
$84$	13.6643	−	11.7942i	1.49089	−	1.28686i
$85$	−2.28589	−	7.72348i	−0.247939	−	0.837730i
$86$	0.545846	−	1.24080i	0.0588601	−	0.133799i
$87$	−6.62707	+	1.77572i	−0.710497	+	0.190377i
$88$	4.97029	−	3.32278i	0.529835	−	0.354210i
$89$	−3.01621	+	1.74141i	−0.319718	+	0.184589i	−0.651267	−	0.758849i	$-0.725762\pi$
$89$	−3.01621	+	1.74141i	−0.319718	+	0.184589i	0.331549	+	0.943438i	$0.392429\pi$
$90$	−3.67885	−	27.0615i	−0.387785	−	2.85253i
$91$	−2.25191	+	1.21201i	−0.236065	+	0.127053i
$92$	4.63447	−	2.41350i	0.483176	−	0.251625i
$93$	−13.9524	−	24.1662i	−1.44679	−	2.50592i
$94$	5.10726	+	4.09833i	0.526774	+	0.422711i
$95$	−0.0661768	+	0.275370i	−0.00678960	+	0.0282524i
$96$	16.4929	−	10.0172i	1.68330	−	1.02238i
$97$	10.2159	−	10.2159i	1.03726	−	1.03726i	0.0379851	−	0.999278i	$-0.487906\pi$
$97$	10.2159	−	10.2159i	1.03726	−	1.03726i	0.999278	−	0.0379851i	$-0.0120939\pi$
$98$	8.31800	−	5.36758i	0.840245	−	0.542207i
$99$	−12.9084	+	12.9084i	−1.29735	+	1.29735i
$100$	7.13044	+	7.01119i	0.713044	+	0.701119i
$101$	7.70237	−	2.06384i	0.766415	−	0.205360i	0.145628	−	0.989339i	$-0.453480\pi$
$101$	7.70237	−	2.06384i	0.766415	−	0.205360i	0.620787	+	0.783979i	$0.286813\pi$
$102$	−10.8758	+	13.5532i	−1.07687	+	1.34197i
$103$	−1.67776	−	0.449553i	−0.165314	−	0.0442958i	0.175213	−	0.984531i	$-0.443939\pi$
$103$	−1.67776	−	0.449553i	−0.165314	−	0.0442958i	−0.340527	+	0.940235i	$0.610605\pi$
$104$	−2.58863	+	0.879418i	−0.253836	+	0.0862341i
$105$	0.0786622	−	20.1808i	0.00767665	−	1.96944i
$106$	2.03315	+	2.77241i	0.197477	+	0.269280i
$107$	−4.78920	−	8.29514i	−0.462990	−	0.801922i	0.536119	−	0.844143i	$-0.319890\pi$
$107$	−4.78920	−	8.29514i	−0.462990	−	0.801922i	−0.999108	+	0.0422209i	$0.986557\pi$
$108$	−28.3464	+	25.9831i	−2.72763	+	2.50022i
$109$	4.77041	+	17.8034i	0.456923	+	1.70526i	0.682373	+	0.731004i	$0.260948\pi$
$109$	4.77041	+	17.8034i	0.456923	+	1.70526i	−0.225451	+	0.974255i	$0.572385\pi$
$110$	0.844536	−	6.63081i	0.0805233	−	0.632223i
$111$			18.0413i			1.71240i
$112$	9.71933	−	4.18745i	0.918390	−	0.395676i
$113$	−3.82449	+	3.82449i	−0.359778	+	0.359778i	−0.863731	−	0.503953i	$-0.831878\pi$
$113$	−3.82449	+	3.82449i	−0.359778	+	0.359778i	0.503953	+	0.863731i	$0.331878\pi$
$114$	0.569446	−	0.221498i	0.0533335	−	0.0207452i
$115$	1.36508	−	5.68028i	0.127295	−	0.529689i
$116$	−4.01874	−	0.174813i	−0.373131	−	0.0162310i
$117$	7.22937	−	4.17388i	0.668356	−	0.385875i
$118$	−1.54605	+	10.0502i	−0.142326	+	0.925199i
$119$	−6.93714	+	6.53488i	−0.635926	+	0.599051i
$120$	3.65330	−	21.2628i	0.333499	−	1.94102i
$121$	5.65680	−	3.26596i	0.514255	−	0.296905i
$122$	−12.9107	−	10.3602i	−1.16888	−	0.937971i
$123$	−24.0969	−	13.9123i	−2.17274	−	1.25443i
$124$	−3.54367	−	15.9723i	−0.318231	−	1.43435i
$125$	11.1465	−	0.869592i	0.996971	−	0.0777786i
$126$	−26.6167	+	18.3235i	−2.37120	+	1.63239i
$127$	0.112343	+	0.112343i	0.00996879	+	0.00996879i	0.712074	−	0.702105i	$-0.247756\pi$
$127$	0.112343	+	0.112343i	0.00996879	+	0.00996879i	−0.702105	+	0.712074i	$0.747756\pi$
$128$	10.9880	−	2.69530i	0.971208	−	0.238234i
$129$	−1.63486	+	2.83166i	−0.143941	+	0.249313i
$130$	−1.15780	+	2.82886i	−0.101546	+	0.248108i
$131$	−7.07228	−	1.89501i	−0.617908	−	0.165568i	−0.0637316	−	0.997967i	$-0.520300\pi$
$131$	−7.07228	−	1.89501i	−0.617908	−	0.165568i	−0.554177	+	0.832399i	$0.686967\pi$
$132$	−12.7906	+	6.66098i	−1.11328	+	0.579764i
$133$	0.326125	−	0.0770309i	0.0282786	−	0.00667942i
$134$	−4.70526	−	6.41608i	−0.406472	−	0.554265i
$135$	1.11562	+	42.9774i	0.0960171	+	3.69890i
$136$	−8.47000	+	5.66243i	−0.726296	+	0.485550i
$137$	−4.21896	−	15.7454i	−0.360450	−	1.34522i	−0.873485	−	0.486851i	$-0.838146\pi$
$137$	−4.21896	−	15.7454i	−0.360450	−	1.34522i	0.513035	−	0.858368i	$-0.328521\pi$
$138$	−11.7464	+	4.56902i	−0.999922	+	0.388941i
$139$	−11.0132	+	11.0132i	−0.934128	+	0.934128i	−0.997961	−	0.0638330i	$-0.979667\pi$
$139$	−11.0132	+	11.0132i	−0.934128	+	0.934128i	0.0638330	+	0.997961i	$0.479667\pi$
$140$	3.60014	−	11.2712i	0.304268	−	0.952587i
$141$	−11.1688	−	11.1688i	−0.940584	−	0.940584i
$142$	−8.25506	+	18.7651i	−0.692749	+	1.57474i
$143$	1.97354	−	0.528810i	0.165036	−	0.0442213i
$144$	−31.3039	+	14.6095i	−2.60866	+	1.21746i
$145$	−3.09650	+	3.26155i	−0.257151	+	0.270857i
$146$	−0.839010	+	5.45406i	−0.0694370	+	0.451381i
$147$	−21.3548	+	10.6841i	−1.76132	+	0.881210i
$148$	−3.17915	+	10.0886i	−0.261324	+	0.829280i
$149$	1.28439	−	4.79340i	0.105221	−	0.392690i	−0.893149	−	0.449761i	$-0.851509\pi$
$149$	1.28439	−	4.79340i	0.105221	−	0.392690i	0.998370	+	0.0570704i	$0.0181759\pi$
$150$	−15.2544	−	18.6847i	−1.24552	−	1.52560i
$151$	1.43616	+	0.829167i	0.116873	+	0.0674767i	0.557297	−	0.830313i	$-0.311839\pi$
$151$	1.43616	+	0.829167i	0.116873	+	0.0674767i	−0.440424	+	0.897790i	$0.645172\pi$
$152$	0.357463	−	0.0235161i	0.0289941	−	0.00190741i
$153$	21.9976	−	21.9976i	1.77840	−	1.77840i
$154$	−7.45336	+	2.64586i	−0.600609	+	0.213210i
$155$	−16.0731	−	8.73174i	−1.29103	−	0.701350i
$156$	6.43792	−	1.42834i	0.515446	−	0.114359i
$157$	−2.66356	+	4.61343i	−0.212576	+	0.368192i	−0.952520	−	0.304477i	$-0.901518\pi$
$157$	−2.66356	+	4.61343i	−0.212576	+	0.368192i	0.739944	+	0.672668i	$0.234852\pi$
$158$	18.8468	−	2.06560i	1.49937	−	0.164330i
$159$	−4.14639	−	7.18176i	−0.328830	−	0.569551i
$160$	5.78973	−	11.2463i	0.457718	−	0.889097i
$161$	−6.72725	+	1.58898i	−0.530181	+	0.125229i
$162$	45.2480	−	33.1828i	3.55502	−	2.60709i
$163$	6.87832	+	11.9136i	0.538752	+	0.933146i	0.998972	+	0.0453407i	$0.0144373\pi$
$163$	6.87832	+	11.9136i	0.538752	+	0.933146i	−0.460220	+	0.887805i	$0.652229\pi$
$164$	−11.0233	−	12.0260i	−0.860777	−	0.939070i
$165$	−3.76747	+	15.6769i	−0.293297	+	1.22045i
$166$	4.35632	−	9.90265i	0.338116	−	0.768595i
$167$	−4.43116	−	4.43116i	−0.342893	−	0.342893i	0.514561	−	0.857454i	$-0.327955\pi$
$167$	−4.43116	−	4.43116i	−0.342893	−	0.342893i	−0.857454	+	0.514561i	$0.827955\pi$
$168$	−24.4047	+	7.48621i	−1.88286	+	0.577574i
$169$	12.0657			0.928131
$170$	−1.43919	+	11.2997i	−0.110381	+	0.866649i
$171$	−1.05656	+	0.283105i	−0.0807974	+	0.0216496i
$172$	−1.41319	+	1.29536i	−0.107754	+	0.0987707i
$173$	5.44575	−	3.14410i	0.414032	−	0.239042i	−0.278488	−	0.960440i	$-0.589833\pi$
$173$	5.44575	−	3.14410i	0.414032	−	0.239042i	0.692521	+	0.721398i	$0.256500\pi$
$174$	9.58990	+	1.47524i	0.727008	+	0.111837i
$175$	−6.86542	−	11.3078i	−0.518977	−	0.854788i
$176$	−8.32621	+	1.47090i	−0.627612	+	0.110873i
$177$	6.34810	−	23.6914i	0.477152	−	1.78076i
$178$	4.89613	−	0.536613i	0.366981	−	0.0402208i
$179$	−2.00882	−	7.49701i	−0.150146	−	0.560353i	−0.999472	−	0.0324844i	$-0.989658\pi$
$179$	−2.00882	−	7.49701i	−0.150146	−	0.560353i	0.849326	−	0.527868i	$-0.177009\pi$
$180$	−10.6483	+	37.1258i	−0.793679	+	2.76719i
$181$	−12.0645	−	12.0645i	−0.896746	−	0.896746i	0.0984009	−	0.995147i	$-0.468627\pi$
$181$	−12.0645	−	12.0645i	−0.896746	−	0.896746i	−0.995147	+	0.0984009i	$0.968627\pi$
$182$	3.60528	−	0.286548i	0.267241	−	0.0212403i
$183$	28.2338	+	28.2338i	2.08710	+	2.08710i
$184$	−7.37368	+	0.485086i	−0.543595	+	0.0357610i
$185$	6.17688	+	10.0849i	0.454133	+	0.741457i
$186$	4.29941	+	39.2284i	0.315248	+	2.87637i
$187$	6.59407	−	3.80709i	0.482206	−	0.278402i
$188$	−4.27745	−	8.21367i	−0.311965	−	0.599043i
$189$	44.7930	−	24.1082i	3.25821	−	1.75361i
$190$	0.242479	−	0.318779i	0.0175913	−	0.0231267i
$191$	−1.14777	−	1.98799i	−0.0830496	−	0.143846i	0.821509	−	0.570196i	$-0.193133\pi$
$191$	−1.14777	−	1.98799i	−0.0830496	−	0.143846i	−0.904558	+	0.426350i	$0.859799\pi$
$192$	−27.0544	+	3.57508i	−1.95248	+	0.258010i
$193$	−3.53224	−	13.1825i	−0.254256	−	0.948896i	−0.968503	−	0.249002i	$-0.919897\pi$
$193$	−3.53224	−	13.1825i	−0.254256	−	0.948896i	0.714247	−	0.699894i	$-0.246769\pi$
$194$	−19.0419	+	7.40677i	−1.36713	+	0.531775i
$195$	3.51949	−	6.47858i	0.252036	−	0.463940i
$196$	−13.8242	+	2.21147i	−0.987445	+	0.157962i
$197$	−7.88589			−0.561847			−0.280923	−	0.959730i	$-0.590641\pi$
$197$	−7.88589			−0.561847			−0.280923	+	0.959730i	$0.590641\pi$
$198$	24.0608	−	9.35895i	1.70992	−	0.665112i
$199$	7.02730	+	4.05722i	0.498152	+	0.287608i	0.727950	−	0.685630i	$-0.240473\pi$
$199$	7.02730	+	4.05722i	0.498152	+	0.287608i	−0.229798	+	0.973238i	$0.573807\pi$
$200$	−5.23767	−	13.1365i	−0.370359	−	0.928889i
$201$	9.59584	+	16.6205i	0.676839	+	1.17232i
$202$	−11.1459	−	1.71461i	−0.784226	−	0.120639i
$203$	5.09661	+	1.53005i	0.357712	+	0.107389i
$204$	21.7968	−	11.3511i	1.52608	−	0.794739i
$205$	−18.2332	+	0.473301i	−1.27346	+	0.0330568i
$206$	1.91584	+	1.53737i	0.133483	+	0.107113i
$207$	21.7946	−	5.83984i	1.51483	−	0.405897i
$208$	3.85176	+	0.335735i	0.267071	+	0.0232790i
$209$	−0.267723			−0.0185188
$210$	−11.5941	+	26.0791i	−0.800068	+	1.79963i
$211$	−4.51019	−	4.51019i	−0.310494	−	0.310494i	0.534607	−	0.845101i	$-0.320460\pi$
$211$	−4.51019	−	4.51019i	−0.310494	−	0.310494i	−0.845101	+	0.534607i	$0.820460\pi$
$212$	−1.05311	−	4.74667i	−0.0723281	−	0.326002i
$213$	24.7246	−	42.8243i	1.69410	−	2.93427i
$214$	1.47579	+	13.4653i	0.100883	+	0.920468i
$215$	0.0556182	+	2.14260i	0.00379313	+	0.146124i
$216$	51.4907	−	17.4926i	3.50350	−	1.19022i
$217$	−0.645958	+	21.6335i	−0.0438505	+	1.46858i
$218$	3.96318	−	25.7630i	0.268420	−	1.74489i
$219$	3.44498	−	12.8569i	0.232790	−	0.868785i
$220$	−4.86926	+	8.10259i	−0.328286	+	0.546277i
$221$	−3.36317	+	0.901157i	−0.226231	+	0.0606184i
$222$	10.2739	−	23.3543i	0.689539	−	1.56744i
$223$	−15.9719	−	15.9719i	−1.06956	−	1.06956i	−0.997393	−	0.0721669i	$-0.977009\pi$
$223$	−15.9719	−	15.9719i	−1.06956	−	1.06956i	−0.0721669	−	0.997393i	$-0.522991\pi$
$224$	−14.9662	−	0.114208i	−0.999971	−	0.00763085i
$225$	23.5018	+	36.2257i	1.56679	+	2.41505i
$226$	7.12869	−	2.77286i	0.474193	−	0.184448i
$227$	10.0015	−	17.3230i	0.663820	−	1.14977i	−0.315784	−	0.948831i	$-0.602268\pi$
$227$	10.0015	−	17.3230i	0.663820	−	1.14977i	0.979604	−	0.200938i	$-0.0643991\pi$
$228$	−0.863279	−	0.0375522i	−0.0571720	−	0.00248696i
$229$	4.99263	+	1.33777i	0.329922	+	0.0884024i	0.419978	−	0.907534i	$-0.362038\pi$
$229$	4.99263	+	1.33777i	0.329922	+	0.0884024i	−0.0900557	+	0.995937i	$0.528705\pi$
$230$	−5.00181	+	6.57571i	−0.329810	+	0.433590i
$231$	18.5664	−	4.38540i	1.22158	−	0.288538i
$232$	5.10268	+	2.51483i	0.335007	+	0.165107i
$233$	−5.26886	+	19.6637i	−0.345175	+	1.28821i	0.547233	+	0.836980i	$0.315681\pi$
$233$	−5.26886	+	19.6637i	−0.345175	+	1.28821i	−0.892408	+	0.451230i	$0.850986\pi$
$234$	−11.7352	+	1.28617i	−0.767157	+	0.0840799i
$235$	−10.0672	−	2.41934i	−0.656710	−	0.157820i
$236$	7.72461	−	12.1295i	0.502830	−	0.789565i
$237$	−45.7324			−2.97064
$238$	12.7015	−	4.50888i	0.823313	−	0.292267i
$239$			4.88879i			0.316230i	0.987421	+	0.158115i	$0.0505416\pi$
$239$			4.88879i			0.316230i	−0.987421	+	0.158115i	$0.949458\pi$
$240$	−16.8376	+	25.4440i	−1.08686	+	1.64241i
$241$	6.36005	+	3.67198i	0.409687	+	0.236533i	0.690655	−	0.723184i	$-0.257322\pi$
$241$	6.36005	+	3.67198i	0.409687	+	0.236533i	−0.280968	+	0.959717i	$0.590656\pi$
$242$	−9.18253	+	1.00640i	−0.590276	+	0.0646938i
$243$	−67.2605	+	38.8328i	−4.31476	+	2.49113i
$244$	10.8130	+	20.7634i	0.692232	+	1.32924i
$245$	−8.27917	+	13.2837i	−0.528936	+	0.848661i
$246$	23.2706	+	31.7318i	1.48368	+	2.02314i
$247$	0.118253	+	0.0316857i	0.00752423	+	0.00201611i
$248$	−4.50841	+	22.6940i	−0.286285	+	1.44107i
$249$	−13.0476	+	22.5990i	−0.826856	+	1.43216i
$250$	−14.9242	−	5.22185i	−0.943890	−	0.330259i
$251$	3.24859	+	3.24859i	0.205049	+	0.205049i	0.802159	−	0.597110i	$-0.203684\pi$
$251$	3.24859	+	3.24859i	0.205049	+	0.205049i	−0.597110	+	0.802159i	$0.703684\pi$
$252$	44.8897	−	8.56230i	2.82778	−	0.539374i
$253$	5.52253			0.347198
$254$	−0.0814513	−	0.209402i	−0.00511071	−	0.0131390i
$255$	6.42024	−	26.7154i	0.402051	−	1.67299i
$256$	−15.7587	−	2.76822i	−0.984919	−	0.173014i
$257$	18.5808	+	4.97870i	1.15904	+	0.310563i	0.786581	−	0.617488i	$-0.211849\pi$
$257$	18.5808	+	4.97870i	1.15904	+	0.310563i	0.372455	+	0.928050i	$0.378516\pi$
$258$	3.72884	−	2.73456i	0.232147	−	0.170246i
$259$	7.35504	−	11.9040i	0.457020	−	0.739681i
$260$	3.10971	−	3.00261i	0.192856	−	0.186214i
$261$	−16.7781	−	4.49567i	−1.03854	−	0.278275i
$262$	8.07587	+	6.48050i	0.498929	+	0.400367i
$263$	6.11137	−	1.63754i	0.376843	−	0.100975i	−0.0654254	−	0.997857i	$-0.520840\pi$
$263$	6.11137	−	1.63754i	0.376843	−	0.100975i	0.442269	+	0.896883i	$0.354174\pi$
$264$	20.3505	−	1.33878i	1.25249	−	0.0823964i
$265$	−4.77664	−	2.59491i	−0.293427	−	0.159404i
$266$	−0.466033	−	0.0860013i	−0.0285743	−	0.00527308i
$267$	−11.8806			−0.727081
$268$	2.43718	+	10.9850i	0.148875	+	0.671018i
$269$	−12.0773	+	3.23609i	−0.736364	+	0.197308i	−0.607461	−	0.794349i	$-0.707812\pi$
$269$	−12.0773	+	3.23609i	−0.736364	+	0.197308i	−0.128902	+	0.991657i	$0.541145\pi$
$270$	23.0300	−	56.2692i	1.40156	−	3.42443i
$271$	−9.35334	+	5.40016i	−0.568175	+	0.328036i	−0.756420	−	0.654086i	$-0.773053\pi$
$271$	−9.35334	+	5.40016i	−0.568175	+	0.328036i	0.188245	+	0.982122i	$0.439720\pi$
$272$	14.1889	−	2.50660i	0.860329	−	0.151985i
$273$	−8.71977	−	0.260365i	−0.527745	−	0.0157580i
$274$	−3.50504	+	22.7848i	−0.211747	+	1.37648i
$275$	3.26140	+	10.0531i	0.196670	+	0.606227i
$276$	17.8075	+	0.774620i	1.07189	+	0.0466266i
$277$	7.19044	−	12.4542i	0.432032	−	0.748301i	−0.565017	−	0.825080i	$-0.691130\pi$
$277$	7.19044	−	12.4542i	0.432032	−	0.748301i	0.997048	+	0.0767789i	$0.0244636\pi$
$278$	20.5281	−	7.98486i	1.23120	−	0.478900i
$279$		−	70.6478i		−	4.22957i
$280$	−11.0789	+	12.5403i	−0.662090	+	0.749424i
$281$		−	2.70972i		−	0.161649i	−0.996728	−	0.0808243i	$-0.974245\pi$
$281$		−	2.70972i		−	0.161649i	0.996728	−	0.0808243i	$-0.0257553\pi$
$282$	8.09768	+	20.8182i	0.482210	+	1.23971i
$283$	−7.72769	+	13.3847i	−0.459363	+	0.795641i	−0.998927	−	0.0463038i	$-0.985256\pi$
$283$	−7.72769	+	13.3847i	−0.459363	+	0.795641i	0.539564	+	0.841945i	$0.318589\pi$
$284$	21.3722	−	19.5904i	1.26821	−	1.16247i
$285$	−0.665170	+	0.700624i	−0.0394013	+	0.0415014i
$286$	−2.85588	−	0.439326i	−0.168872	−	0.0259779i
$287$	10.2279	+	19.0034i	0.603734	+	1.12174i
$288$	48.8422	−	1.08542i	2.87805	−	0.0639590i
$289$	3.48532	−	2.01225i	0.205019	−	0.118368i
$290$	5.86574	−	2.45870i	0.344448	−	0.144380i
$291$	47.6037	−	12.7554i	2.79058	−	0.747734i
$292$	4.19199	−	6.58244i	0.245318	−	0.385208i
$293$	8.90182			0.520050			0.260025	−	0.965602i	$-0.416269\pi$
$293$	8.90182			0.520050			0.260025	+	0.965602i	$0.416269\pi$
$294$	33.7279	−	1.66965i	1.96705	−	0.0973757i
$295$	−4.56282	−	15.4167i	−0.265658	−	0.897595i
$296$	9.86050	−	11.2492i	0.573130	−	0.653848i
$297$	−39.2560	+	10.5186i	−2.27786	+	0.610352i
$298$	−4.39230	+	5.47360i	−0.254439	+	0.317077i
$299$	−2.43929	−	0.653606i	−0.141068	−	0.0377990i
$300$	9.10638	+	32.8741i	0.525757	+	1.89798i
$301$	2.23312	−	1.20189i	0.128715	−	0.0692759i
$302$	−1.38691	−	1.89119i	−0.0798080	−	0.108826i
$303$	26.2744	+	7.04019i	1.50942	+	0.404448i
$304$	−0.476125	−	0.173122i	−0.0273076	−	0.00992920i
$305$	25.4489	+	6.11587i	1.45720	+	0.350194i
$306$	−41.0025	+	15.9488i	−2.34396	+	0.911733i
$307$	−25.6877			−1.46607			−0.733037	−	0.680189i	$-0.761898\pi$
$307$	−25.6877			−1.46607			−0.733037	+	0.680189i	$0.761898\pi$
$308$	11.1550	+	0.819384i	0.635618	+	0.0466887i
$309$	−4.18965	−	4.18965i	−0.238341	−	0.238341i
$310$	15.8341	+	20.4563i	0.899318	+	1.16184i
$311$	−9.40948	+	16.2977i	−0.533563	+	0.924158i	0.465669	+	0.884959i	$0.345814\pi$
$311$	−9.40948	+	16.2977i	−0.533563	+	0.924158i	−0.999231	+	0.0391987i	$0.987519\pi$
$312$	−9.14723	−	1.81720i	−0.517860	−	0.102879i
$313$	5.14286	+	1.37802i	0.290691	+	0.0778905i	0.401218	−	0.915983i	$-0.368587\pi$
$313$	5.14286	+	1.37802i	0.290691	+	0.0778905i	−0.110526	+	0.993873i	$0.535254\pi$
$314$	6.07515	−	4.45524i	0.342841	−	0.251424i
$315$	25.7188	−	44.1479i	1.44909	−	2.48745i
$316$	−25.5734	−	8.05873i	−1.43862	−	0.453339i
$317$	13.4260	−	7.75152i	0.754080	−	0.435369i	−0.0730859	−	0.997326i	$-0.523285\pi$
$317$	13.4260	−	7.75152i	0.754080	−	0.435369i	0.827166	+	0.561957i	$0.189951\pi$
$318$	1.27770	+	11.6580i	0.0716501	+	0.653746i
$319$	−3.68181	−	2.12570i	−0.206142	−	0.119016i
$320$	−13.8991	+	11.2612i	−0.776985	+	0.629519i
$321$		−	32.6739i		−	1.82368i
$322$	9.61323	+	1.77402i	0.535724	+	0.0988621i
$323$	0.456233			0.0253855
$324$	−77.4697	+	17.1877i	−4.30387	+	0.954873i
$325$	−0.250741	−	4.82644i	−0.0139086	−	0.267723i
$326$	−2.11955	−	19.3390i	−0.117391	−	1.07109i
$327$	−16.2728	+	60.7311i	−0.899890	+	3.35844i
$328$	7.42124	+	21.8449i	0.409769	+	1.20618i
$329$	2.81615	+	11.9227i	0.155259	+	0.657320i
$330$	13.8044	−	18.1482i	0.759909	−	0.999026i
$331$	34.7747	+	9.31786i	1.91139	+	0.512156i	0.993264	+	0.115870i	$0.0369654\pi$
$331$	34.7747	+	9.31786i	1.91139	+	0.512156i	0.918127	+	0.396286i	$0.129701\pi$
$332$	−11.2784	+	10.3381i	−0.618984	+	0.567378i
$333$	−22.8380	+	39.5566i	−1.25151	+	2.16769i
$334$	3.21271	+	8.25949i	0.175791	+	0.451939i
$335$	11.0544	+	6.00531i	0.603967	+	0.328105i
$336$	35.8548	+	4.20679i	1.95604	+	0.229499i
$337$	18.0541	+	18.0541i	0.983470	+	0.983470i	0.999866	−	0.0163955i	$-0.00521907\pi$
$337$	18.0541	+	18.0541i	0.983470	+	0.983470i	−0.0163955	+	0.999866i	$0.505219\pi$
$338$	−15.6190	−	6.87100i	−0.849559	−	0.373733i
$339$	−17.8213	+	4.77521i	−0.967921	+	0.259354i
$340$	8.29783	−	13.8078i	0.450013	−	0.748835i
$341$	4.47536	−	16.7023i	0.242354	−	0.904479i
$342$	1.52893	+	0.235199i	0.0826751	+	0.0127181i
$343$	18.4460	+	1.65629i	0.995993	+	0.0894312i
$344$	2.56702	−	0.872079i	0.138405	−	0.0470193i
$345$	13.7210	−	14.4523i	0.738714	−	0.778087i
$346$	−8.83993	+	0.968851i	−0.475238	+	0.0520857i
$347$	−3.86429	+	6.69314i	−0.207446	+	0.359306i	−0.950909	−	0.309470i	$-0.899848\pi$
$347$	−3.86429	+	6.69314i	−0.207446	+	0.359306i	0.743463	+	0.668777i	$0.233182\pi$
$348$	−11.5739	−	7.37080i	−0.620429	−	0.395116i
$349$	−6.91125	−	6.91125i	−0.369951	−	0.369951i	0.497508	−	0.867459i	$-0.334248\pi$
$349$	−6.91125	−	6.91125i	−0.369951	−	0.369951i	−0.867459	+	0.497508i	$0.834248\pi$
$350$	2.44783	+	18.5475i	0.130842	+	0.991403i
$351$	18.5842			0.991951
$352$	11.6158	+	2.83742i	0.619127	+	0.151235i
$353$	−6.27432	+	1.68120i	−0.333948	+	0.0894812i	−0.421897	−	0.906644i	$-0.638636\pi$
$353$	−6.27432	+	1.68120i	−0.333948	+	0.0894812i	0.0879484	+	0.996125i	$0.471969\pi$
$354$	−21.7090	+	27.0533i	−1.15382	+	1.43787i
$355$	−0.841137	−	32.4035i	−0.0446429	−	1.71980i
$356$	−6.64358	−	2.09354i	−0.352109	−	0.110957i
$357$	−31.6395	+	7.47326i	−1.67454	+	0.395527i
$358$	−1.66889	+	10.8488i	−0.0882036	+	0.573375i
$359$	−0.246788	−	0.427450i	−0.0130250	−	0.0225599i	0.859439	−	0.511238i	$-0.170813\pi$
$359$	−0.246788	−	0.427450i	−0.0130250	−	0.0225599i	−0.872464	+	0.488678i	$0.837479\pi$
$360$	34.9260	−	41.9952i	1.84076	−	2.21334i
$361$	16.4406	+	9.49198i	0.865294	+	0.499578i
$362$	8.74707	+	22.4877i	0.459736	+	1.18193i
$363$	22.2817			1.16948
$364$	−4.83018	−	1.68215i	−0.253170	−	0.0881685i
$365$	−2.47615	−	8.36632i	−0.129607	−	0.437913i
$366$	−20.4702	−	52.6266i	−1.07000	−	2.75084i
$367$	−4.20336	−	15.6872i	−0.219414	−	0.818863i	−0.984566	−	0.175014i	$-0.944003\pi$
$367$	−4.20336	−	15.6872i	−0.219414	−	0.818863i	0.765152	−	0.643849i	$-0.222664\pi$
$368$	9.82141	+	3.57112i	0.511976	+	0.186157i
$369$	−35.2225	−	61.0072i	−1.83361	−	3.17591i
$370$	−2.25292	−	16.5724i	−0.117124	−	0.861555i
$371$	−0.191967	+	6.42907i	−0.00996641	+	0.333781i
$372$	16.7737	−	53.2292i	0.869675	−	2.75981i
$373$	−17.1921	+	9.92587i	−0.890173	+	0.513942i	−0.873999	−	0.485927i	$-0.838482\pi$
$373$	−17.1921	+	9.92587i	−0.890173	+	0.513942i	−0.0161742	+	0.999869i	$0.505149\pi$
$374$	−10.7040	+	1.17315i	−0.553489	+	0.0606621i
$375$	34.4119	+	16.4425i	1.77702	+	0.849087i
$376$	0.859719	+	13.0684i	0.0443366	+	0.673951i
$377$	1.37467	+	1.37467i	0.0707990	+	0.0707990i
$378$	−71.7130	+	5.69975i	−3.68852	+	0.293164i
$379$	−12.0600	−	12.0600i	−0.619480	−	0.619480i	0.325918	−	0.945398i	$-0.394327\pi$
$379$	−12.0600	−	12.0600i	−0.619480	−	0.619480i	−0.945398	+	0.325918i	$0.894327\pi$
$380$	−0.495421	+	0.274573i	−0.0254146	+	0.0140853i
$381$	0.140269	+	0.523492i	0.00718622	+	0.0268193i
$382$	0.353683	+	3.22705i	0.0180960	+	0.165110i
$383$	0.486967	−	1.81739i	0.0248829	−	0.0928641i	−0.952368	−	0.304952i	$-0.901360\pi$
$383$	0.486967	−	1.81739i	0.0248829	−	0.0928641i	0.977251	+	0.212088i	$0.0680263\pi$
$384$	37.0576	+	10.7786i	1.89109	+	0.550045i
$385$	8.87700	−	8.80806i	0.452414	−	0.448901i
$386$	−2.93452	+	19.0761i	−0.149363	+	0.970948i
$387$	−7.16903	+	4.13904i	−0.364422	+	0.210399i
$388$	28.8675	+	1.25572i	1.46553	+	0.0637497i
$389$	−8.20289	+	2.19796i	−0.415903	+	0.111441i	−0.460702	−	0.887555i	$-0.652402\pi$
$389$	−8.20289	+	2.19796i	−0.415903	+	0.111441i	0.0447983	+	0.998996i	$0.485735\pi$
$390$	−8.24528	+	6.38224i	−0.417516	+	0.323177i
$391$	−9.41107			−0.475938
$392$	19.1547	+	5.00969i	0.967459	+	0.253028i
$393$	−17.6607	−	17.6607i	−0.890865	−	0.890865i
$394$	10.2082	+	4.49074i	0.514283	+	0.226240i
$395$	−25.5639	+	15.6576i	−1.28626	+	0.787820i
$396$	−36.4761	−	1.58669i	−1.83299	−	0.0797343i
$397$	7.42137	+	12.8542i	0.372468	+	0.645134i	0.989945	−	0.141456i	$-0.0451783\pi$
$397$	7.42137	+	12.8542i	0.372468	+	0.645134i	−0.617477	+	0.786589i	$0.711845\pi$
$398$	−6.78634	−	9.25384i	−0.340169	−	0.463853i
$399$	1.09482	+	0.328676i	0.0548095	+	0.0164544i
$400$	−0.700645	+	19.9877i	−0.0350323	+	0.999386i
$401$	5.30021	+	9.18023i	0.264680	+	0.458439i	0.967480	−	0.252949i	$-0.0814004\pi$
$401$	5.30021	+	9.18023i	0.264680	+	0.458439i	−0.702800	+	0.711388i	$0.748067\pi$
$402$	−2.95695	−	26.9796i	−0.147479	−	1.34562i
$403$	−3.95352	+	6.84769i	−0.196939	+	0.341108i
$404$	13.4519	+	8.56678i	0.669259	+	0.426213i
$405$	−42.3512	+	77.9589i	−2.10445	+	3.87381i
$406$	−5.72620	−	4.88298i	−0.284187	−	0.242338i
$407$	−7.90508	+	7.90508i	−0.391840	+	0.391840i
$408$	−34.6798	+	2.28145i	−1.71691	+	0.112949i
$409$	33.5667	+	19.3797i	1.65977	+	0.958267i	0.972821	+	0.231557i	$0.0743820\pi$
$409$	33.5667	+	19.3797i	1.65977	+	0.958267i	0.686945	+	0.726709i	$0.258951\pi$
$410$	23.8722	+	9.77047i	1.17896	+	0.482529i
$411$	14.3917	−	53.7106i	0.709891	−	2.64935i
$412$	−1.60456	−	3.08111i	−0.0790508	−	0.151796i
$413$	−13.8471	+	13.0441i	−0.681371	+	0.641860i
$414$	−31.5385	−	4.85164i	−1.55003	−	0.238445i
$415$	0.443881	+	17.0998i	0.0217892	+	0.839396i
$416$	−4.79488	−	2.62805i	−0.235088	−	0.128851i
$417$	−51.3192	+	13.7509i	−2.51311	+	0.673386i
$418$	0.346565	+	0.152459i	0.0169510	+	0.00745700i
$419$	9.45219	+	9.45219i	0.461770	+	0.461770i	0.899235	−	0.437466i	$-0.144124\pi$
$419$	9.45219	+	9.45219i	0.461770	+	0.461770i	−0.437466	+	0.899235i	$0.644124\pi$
$420$	29.8596	−	27.1567i	1.45700	−	1.32511i
$421$	−4.33136	+	4.33136i	−0.211098	+	0.211098i	−0.804734	−	0.593636i	$-0.797692\pi$
$421$	−4.33136	+	4.33136i	−0.211098	+	0.211098i	0.593636	+	0.804734i	$0.297692\pi$
$422$	3.27001	+	8.40680i	0.159181	+	0.409237i
$423$	−10.3500	−	38.6266i	−0.503232	−	1.87809i
$424$	−1.33982	+	6.74423i	−0.0650673	+	0.327529i
$425$	−5.55784	−	17.1318i	−0.269595	−	0.831014i
$426$	−56.3928	+	41.3559i	−2.73224	+	2.00370i
$427$	−7.11897	−	30.1396i	−0.344511	−	1.45856i
$428$	5.75762	−	18.2711i	0.278305	−	0.883167i
$429$	6.73216	+	1.80388i	0.325032	+	0.0870920i
$430$	1.14814	−	2.80525i	0.0553682	−	0.135281i
$431$	−6.01924	+	10.4256i	−0.289937	+	0.502185i	−0.973794	−	0.227430i	$-0.926968\pi$
$431$	−6.01924	+	10.4256i	−0.289937	+	0.502185i	0.683858	+	0.729615i	$0.260301\pi$
$432$	−76.6157	−	6.67813i	−3.68617	−	0.321302i
$433$	−20.6770	−	20.6770i	−0.993675	−	0.993675i	0.00630502	−	0.999980i	$-0.497993\pi$
$433$	−20.6770	−	20.6770i	−0.993675	−	0.993675i	−0.999980	+	0.00630502i	$0.997993\pi$
$434$	13.1557	−	27.6365i	0.631494	−	1.32660i
$435$	−14.7106	+	4.35382i	−0.705317	+	0.208750i
$436$	−19.8014	+	31.0931i	−0.948316	+	1.48909i
$437$	0.286571	+	0.165452i	0.0137085	+	0.00791463i
$438$	−11.7810	+	14.6813i	−0.562920	+	0.701499i
$439$	29.8679	−	17.2442i	1.42552	−	0.823022i	0.428753	−	0.903422i	$-0.358953\pi$
$439$	29.8679	−	17.2442i	1.42552	−	0.823022i	0.996763	+	0.0803998i	$0.0256197\pi$
$440$	10.9174	−	7.71587i	0.520465	−	0.367839i
$441$	−60.3464	−	3.60700i	−2.87364	−	0.171762i
$442$	4.86677	+	0.748666i	0.231489	+	0.0356104i
$443$	12.4914	−	7.21189i	0.593482	−	0.342647i	−0.172991	−	0.984923i	$-0.555343\pi$
$443$	12.4914	−	7.21189i	0.593482	−	0.342647i	0.766473	+	0.642276i	$0.222010\pi$
$444$	−26.5990	+	24.3813i	−1.26233	+	1.15709i
$445$	−6.64113	+	4.06761i	−0.314820	+	0.192823i
$446$	11.5801	+	29.7710i	0.548332	+	1.40970i
$447$	11.9699	−	11.9699i	0.566159	−	0.566159i
$448$	19.3086	+	8.67057i	0.912245	+	0.409646i
$449$			25.9853i			1.22632i	0.789958	+	0.613162i	$0.210103\pi$
$449$			25.9853i			1.22632i	−0.789958	+	0.613162i	$0.789897\pi$
$450$	−9.79363	−	60.2774i	−0.461676	−	2.84150i
$451$	−4.46252	−	16.6543i	−0.210132	−	0.784223i
$452$	−10.8071	−	0.470103i	−0.508322	−	0.0221118i
$453$	2.82846	+	4.89903i	0.132892	+	0.230176i
$454$	−22.8117	+	16.7290i	−1.07060	+	0.785132i
$455$	−4.96341	+	2.83989i	−0.232688	+	0.133136i
$456$	1.09612	+	0.540219i	0.0513306	+	0.0252981i
$457$	−3.55683	−	0.953049i	−0.166381	−	0.0445818i	0.174667	−	0.984628i	$-0.444115\pi$
$457$	−3.55683	−	0.953049i	−0.166381	−	0.0445818i	−0.341048	+	0.940046i	$0.610782\pi$
$458$	−5.70110	−	4.57486i	−0.266395	−	0.213769i
$459$	66.8971	−	17.9250i	3.12249	−	0.836668i
$460$	10.2194	−	5.66384i	0.476484	−	0.264078i
$461$	−3.81210	+	3.81210i	−0.177547	+	0.177547i	−0.790286	−	0.612739i	$-0.790068\pi$
$461$	−3.81210	+	3.81210i	−0.177547	+	0.177547i	0.612739	+	0.790286i	$0.290068\pi$
$462$	−26.5314	−	4.89608i	−1.23435	−	0.227786i
$463$	−18.1189	+	18.1189i	−0.842057	+	0.842057i	−0.989126	−	0.147069i	$-0.953016\pi$
$463$	−18.1189	+	18.1189i	−0.842057	+	0.842057i	0.147069	+	0.989126i	$0.453016\pi$
$464$	−5.17326	−	6.16122i	−0.240163	−	0.286028i
$465$	−32.5902	−	53.2096i	−1.51134	−	2.46753i
$466$	18.0183	−	22.4540i	0.834681	−	1.04016i
$467$	5.84297	+	10.1203i	0.270381	+	0.468313i	0.968959	−	0.247220i	$-0.0795171\pi$
$467$	5.84297	+	10.1203i	0.270381	+	0.468313i	−0.698579	+	0.715533i	$0.746184\pi$
$468$	15.9236	+	5.01787i	0.736069	+	0.231951i
$469$	0.444262	−	14.8786i	0.0205141	−	0.687029i
$470$	11.6541	+	8.86472i	0.537565	+	0.408899i
$471$	−15.7373	+	9.08595i	−0.725138	+	0.418659i
$472$	−16.9068	+	11.3027i	−0.778198	+	0.520248i
$473$	−1.95707	+	0.524396i	−0.0899863	+	0.0241118i
$474$	59.2002	+	26.0430i	2.71916	+	1.19620i
$475$	−0.131948	+	0.619379i	−0.00605418	+	0.0284191i
$476$	−19.0096	−	1.39633i	−0.871303	−	0.0640008i
$477$		−	20.9952i		−	0.961305i
$478$	2.78400	−	6.32850i	0.127337	−	0.289459i
$479$	−15.3272	+	26.5475i	−0.700318	+	1.21299i	0.268036	+	0.963409i	$0.413625\pi$
$479$	−15.3272	+	26.5475i	−0.700318	+	1.21299i	−0.968355	+	0.249578i	$0.919708\pi$
$480$	36.2856	−	23.3487i	1.65620	−	1.06572i
$481$	4.42724	−	2.55607i	0.201865	−	0.116547i
$482$	−6.14197	−	8.37517i	−0.279759	−	0.381479i
$483$	−22.5837	−	6.77986i	−1.02759	−	0.308494i
$484$	12.4598	+	3.92636i	0.566356	+	0.178471i
$485$	22.2429	−	23.4284i	1.01000	−	1.06383i
$486$	109.182	−	11.9663i	4.95260	−	0.542802i
$487$	3.24932	+	12.1266i	0.147241	+	0.549509i	0.999645	+	0.0266270i	$0.00847664\pi$
$487$	3.24932	+	12.1266i	0.147241	+	0.549509i	−0.852405	+	0.522882i	$0.824857\pi$
$488$	−2.17329	−	33.0357i	−0.0983804	−	1.49546i
$489$			46.9267i			2.12210i
$490$	18.2819	−	12.4809i	0.825892	−	0.563829i
$491$	5.93287	−	5.93287i	0.267747	−	0.267747i	−0.560445	−	0.828192i	$-0.689370\pi$
$491$	5.93287	−	5.93287i	0.267747	−	0.267747i	0.828192	+	0.560445i	$0.189370\pi$
$492$	−12.0535	−	54.3283i	−0.543413	−	2.44931i
$493$	6.27427	+	3.62245i	0.282579	+	0.163147i
$494$	−0.135033	−	0.108358i	−0.00607542	−	0.00487524i
$495$	−28.1054	+	29.6034i	−1.26324	+	1.33057i
$496$	18.7596	−	26.8098i	0.842329	−	1.20380i
$497$	−33.7724	+	18.1767i	−1.51490	+	0.815338i
$498$	29.7593	−	21.8241i	1.33355	−	0.977963i
$499$	29.9284	+	8.01930i	1.33978	+	0.358993i	0.856353	−	0.516391i	$-0.172725\pi$
$499$	29.9284	+	8.01930i	1.33978	+	0.358993i	0.483428	+	0.875384i	$0.339392\pi$
$500$	16.3456	+	15.2585i	0.730998	+	0.682380i
$501$	−5.53268	−	20.6483i	−0.247182	−	0.922496i
$502$	−2.35532	−	6.05524i	−0.105123	−	0.270259i
$503$	−14.2363	+	14.2363i	−0.634763	+	0.634763i	−0.949259	−	0.314496i	$-0.898165\pi$
$503$	−14.2363	+	14.2363i	−0.634763	+	0.634763i	0.314496	+	0.949259i	$0.398165\pi$
$504$	−62.9853	−	14.4793i	−2.80559	−	0.644959i
$505$	17.0975	−	5.06027i	0.760828	−	0.225179i
$506$	−7.14887	−	3.14489i	−0.317806	−	0.139807i
$507$	35.6443	+	20.5793i	1.58302	+	0.913958i
$508$	−0.0138090	+	0.317452i	−0.000612677	+	0.0140847i
$509$	−6.53285	+	24.3809i	−0.289563	+	1.08067i	0.655876	+	0.754868i	$0.272299\pi$
$509$	−6.53285	+	24.3809i	−0.289563	+	1.08067i	−0.945440	+	0.325797i	$0.894367\pi$
$510$	−23.5245	+	30.9268i	−1.04168	+	1.36946i
$511$	−7.51453	+	7.07879i	−0.332423	+	0.313147i
$512$	18.8231	+	12.5575i	0.831872	+	0.554967i
$513$	−2.35217	−	0.630263i	−0.103851	−	0.0278268i
$514$	−21.2174	−	17.0260i	−0.935861	−	0.750984i
$515$	−3.77640	−	0.907542i	−0.166408	−	0.0399911i
$516$	−6.38419	+	1.41642i	−0.281048	+	0.0623544i
$517$		−	9.78758i		−	0.430457i
$518$	−16.3000	+	11.2212i	−0.716180	+	0.493033i
$519$	21.4503			0.941565
$520$	−5.73537	+	2.11598i	−0.251513	+	0.0927920i
$521$	5.08994	−	8.81603i	0.222994	−	0.386237i	−0.732722	−	0.680529i	$-0.761750\pi$
$521$	5.08994	−	8.81603i	0.222994	−	0.386237i	0.955716	+	0.294291i	$0.0950835\pi$
$522$	19.1589	+	15.3741i	0.838564	+	0.672908i
$523$	−1.26777	−	2.19584i	−0.0554357	−	0.0960175i	0.836976	−	0.547240i	$-0.184321\pi$
$523$	−1.26777	−	2.19584i	−0.0554357	−	0.0960175i	−0.892412	+	0.451222i	$0.850988\pi$
$524$	−6.76372	−	12.9879i	−0.295475	−	0.567378i
$525$	−0.995153	−	45.1150i	−0.0434320	−	1.96898i
$526$	−8.84364	−	1.36044i	−0.385601	−	0.0593179i
$527$	−7.62657	+	28.4628i	−0.332219	+	1.23986i
$528$	−27.1060	−	9.85588i	−1.17964	−	0.428922i
$529$	14.0073	+	8.08709i	0.609011	+	0.351613i
$530$	4.70561	+	6.07923i	0.204399	+	0.264065i
$531$	43.9089	−	43.9089i	1.90548	−	1.90548i
$532$	0.554301	+	0.376718i	0.0240320	+	0.0163328i
$533$			7.88434i			0.341509i
$534$	15.3793	+	6.76559i	0.665529	+	0.292776i
$535$	−11.1867	−	18.2644i	−0.483643	−	0.789637i
$536$	3.10069	−	15.6079i	0.133929	−	0.674160i
$537$	6.85248	−	25.5738i	0.295706	−	1.10359i
$538$	17.4768	+	2.68849i	0.753477	+	0.115909i
$539$	−14.0384	−	4.67555i	−0.604675	−	0.201390i
$540$	−61.8555	+	59.7252i	−2.66184	+	2.57016i
$541$	−8.66197	+	32.3269i	−0.372407	+	1.38984i	0.484689	+	0.874686i	$0.338933\pi$
$541$	−8.66197	+	32.3269i	−0.372407	+	1.38984i	−0.857096	+	0.515156i	$0.827734\pi$
$542$	15.1830	−	1.66405i	0.652167	−	0.0714771i
$543$	−15.0635	−	56.2179i	−0.646439	−	2.41254i
$544$	−19.7948	−	4.83532i	−0.848697	−	0.207313i
$545$	11.6964	+	39.5194i	0.501019	+	1.69283i
$546$	11.1394	+	5.30265i	0.476723	+	0.226933i
$547$		−	6.43353i		−	0.275078i	−0.990496	−	0.137539i	$-0.956081\pi$
$547$		−	6.43353i		−	0.275078i	0.990496	−	0.137539i	$-0.0439192\pi$
$548$	17.5124	−	27.4988i	0.748093	−	1.17469i
$549$	26.1638	+	97.6446i	1.11664	+	4.16737i
$550$	1.50305	−	14.8710i	0.0640903	−	0.634100i
$551$	−0.127369	−	0.220610i	−0.00542611	−	0.00939830i
$552$	−22.6106	−	11.1435i	−0.962371	−	0.474300i
$553$	30.1752	+	18.6441i	1.28318	+	0.792827i
$554$	−16.4002	+	12.0272i	−0.696778	+	0.510985i
$555$	1.04684	+	40.3280i	0.0444361	+	1.71183i
$556$	−31.1206	−	1.35373i	−1.31981	−	0.0574110i
$557$	26.1682	+	15.1082i	1.10878	+	0.640155i	0.938513	−	0.345243i	$-0.112203\pi$
$557$	26.1682	+	15.1082i	1.10878	+	0.640155i	0.170268	+	0.985398i	$0.445537\pi$
$558$	−40.2315	+	91.4530i	−1.70313	+	3.87151i
$559$	0.926499			0.0391867
$560$	21.4828	−	9.92422i	0.907813	−	0.419375i
$561$	25.9735			1.09660
$562$	−1.54309	+	3.50772i	−0.0650915	+	0.147964i
$563$	28.5220	+	16.4672i	1.20206	+	0.694010i	0.961013	−	0.276503i	$-0.0891756\pi$
$563$	28.5220	+	16.4672i	1.20206	+	0.694010i	0.241048	+	0.970513i	$0.422509\pi$
$564$	1.37286	−	31.5603i	0.0578078	−	1.32893i
$565$	−8.32703	+	8.77086i	−0.350321	+	0.368993i
$566$	17.6256	−	12.9258i	0.740859	−	0.543312i
$567$	104.928	+	3.13306i	4.40656	+	0.131576i
$568$	−38.8222	+	13.1888i	−1.62894	+	0.553390i
$569$	−10.4739	−	18.1414i	−0.439091	−	0.760527i	0.558529	−	0.829485i	$-0.311366\pi$
$569$	−10.4739	−	18.1414i	−0.439091	−	0.760527i	−0.997620	+	0.0689576i	$0.978033\pi$
$570$	1.26004	−	0.528160i	0.0527772	−	0.0221222i
$571$	8.46635	+	31.5969i	0.354306	+	1.32229i	0.881356	+	0.472453i	$0.156631\pi$
$571$	8.46635	+	31.5969i	0.354306	+	1.32229i	−0.527050	+	0.849834i	$0.676702\pi$
$572$	3.44673	+	2.19503i	0.144115	+	0.0917787i
$573$		−	7.83054i		−	0.327125i
$574$	−2.41812	−	30.4242i	−0.100930	−	1.26988i
$575$	2.72179	−	12.7764i	0.113507	−	0.532814i
$576$	−63.8440	−	26.4089i	−2.66016	−	1.10037i
$577$	5.95245	+	22.2148i	0.247804	+	0.924816i	0.971953	+	0.235173i	$0.0755657\pi$
$577$	5.95245	+	22.2148i	0.247804	+	0.924816i	−0.724150	+	0.689643i	$0.757768\pi$
$578$	−5.65762	+	0.620072i	−0.235326	+	0.0257916i
$579$	12.0492	−	44.9681i	0.500747	−	1.86881i
$580$	−8.99329	−	0.157576i	−0.373426	−	0.00654299i
$581$	17.8222	−	9.59213i	0.739389	−	0.397949i
$582$	−68.8864	−	10.5970i	−2.85543	−	0.439258i
$583$	1.32999	−	4.96361i	0.0550828	−	0.205572i
$584$	−9.17497	+	6.13373i	−0.379663	+	0.253815i
$585$	15.9177	−	9.74942i	0.658117	−	0.403089i
$586$	−11.5233	−	5.06928i	−0.476024	−	0.209410i
$587$		−	22.8188i		−	0.941835i	−0.882177	−	0.470917i	$-0.843923\pi$
$587$		−	22.8188i		−	0.941835i	0.882177	−	0.470917i	$-0.156077\pi$
$588$	−44.6113	−	17.0455i	−1.83974	−	0.702945i
$589$	0.732623	−	0.732623i	0.0301872	−	0.0301872i
$590$	−2.87275	+	22.5552i	−0.118269	+	0.928581i
$591$	−23.2964	−	13.4502i	−0.958286	−	0.553267i
$592$	−19.1704	+	8.94682i	−0.787898	+	0.367712i
$593$	7.00146	−	26.1298i	0.287516	−	1.07302i	−0.659466	−	0.751735i	$-0.729217\pi$
$593$	7.00146	−	26.1298i	0.287516	−	1.07302i	0.946981	−	0.321288i	$-0.104116\pi$
$594$	56.8065	+	8.73868i	2.33080	+	0.358552i
$595$	−15.1275	+	15.0100i	−0.620167	+	0.615351i
$596$	8.80282	−	4.58426i	0.360578	−	0.187779i
$597$	13.8400	+	23.9715i	0.566433	+	0.981090i
$598$	2.78543	+	2.23518i	0.113905	+	0.0914032i
$599$	−5.56671	+	9.64182i	−0.227449	+	0.393954i	−0.957051	−	0.289918i	$-0.906372\pi$
$599$	−5.56671	+	9.64182i	−0.227449	+	0.393954i	0.729602	+	0.683872i	$0.239705\pi$
$600$	6.93251	−	47.7410i	0.283019	−	1.94902i
$601$	18.3334			0.747834			0.373917	−	0.927462i	$-0.378014\pi$
$601$	18.3334			0.747834			0.373917	+	0.927462i	$0.378014\pi$
$602$	−3.57519	+	0.284156i	−0.145714	+	0.0115813i
$603$			48.5885i			1.97868i
$604$	0.718380	+	3.23793i	0.0292305	+	0.131750i
$605$	12.4552	−	7.62868i	0.506377	−	0.310150i
$606$	−30.0028	−	24.0758i	−1.21878	−	0.978013i
$607$	24.5714	+	6.58388i	0.997322	+	0.267232i	0.720323	−	0.693639i	$-0.243994\pi$
$607$	24.5714	+	6.58388i	0.997322	+	0.267232i	0.276999	+	0.960870i	$0.410660\pi$
$608$	0.517753	+	0.495241i	0.0209977	+	0.0200847i
$609$	12.4467	+	13.2128i	0.504364	+	0.535411i
$610$	−29.4607	−	22.4092i	−1.19283	−	0.907324i
$611$	−1.15839	+	4.32316i	−0.0468633	+	0.174896i
$612$	62.1597	+	2.70392i	2.51266	+	0.109299i
$613$	−27.1176	−	15.6564i	−1.09527	−	0.632355i	−0.160296	−	0.987069i	$-0.551245\pi$
$613$	−27.1176	−	15.6564i	−1.09527	−	0.632355i	−0.934975	+	0.354714i	$0.884578\pi$
$614$	33.2525	+	14.6283i	1.34196	+	0.590348i
$615$	−54.6714	−	29.7003i	−2.20456	−	1.19763i
$616$	−13.9735	−	7.41310i	−0.563009	−	0.298682i
$617$	−13.8764	+	13.8764i	−0.558644	+	0.558644i	−0.928921	−	0.370277i	$-0.879263\pi$
$617$	−13.8764	+	13.8764i	−0.558644	+	0.558644i	0.370277	+	0.928921i	$0.379263\pi$
$618$	3.03760	+	7.80932i	0.122190	+	0.314137i
$619$	1.68690	+	6.29558i	0.0678020	+	0.253041i	0.991505	−	0.130069i	$-0.0415198\pi$
$619$	1.68690	+	6.29558i	0.0678020	+	0.253041i	−0.923703	+	0.383110i	$0.874853\pi$
$620$	−8.84801	−	35.4975i	−0.355345	−	1.42561i
$621$	48.5202	+	13.0009i	1.94705	+	0.521710i
$622$	21.4615	−	15.7389i	0.860527	−	0.631071i
$623$	7.83907	+	4.84346i	0.314066	+	0.194049i
$624$	10.8062	+	7.56138i	0.432593	+	0.302698i
$625$	24.8654	−	2.59058i	0.994617	−	0.103623i
$626$	−5.87265	−	4.71252i	−0.234718	−	0.188350i
$627$	−0.790903	−	0.456628i	−0.0315856	−	0.0182360i
$628$	−10.4013	+	2.30768i	−0.415058	+	0.0920864i
$629$	13.4712	−	13.4712i	0.537134	−	0.537134i
$630$	−58.4335	+	42.5032i	−2.32805	+	1.69337i
$631$		−	12.1815i		−	0.484936i	−0.970159	−	0.242468i	$-0.922043\pi$
$631$		−	12.1815i		−	0.484936i	0.970159	−	0.242468i	$-0.0779570\pi$
$632$	28.5154	+	24.9951i	1.13428	+	0.994252i
$633$	−5.63136	−	21.0165i	−0.223827	−	0.835332i
$634$	−21.7941	+	2.38862i	−0.865554	+	0.0948641i
$635$	0.257640	+	0.244602i	0.0102241	+	0.00970675i
$636$	4.98483	−	15.8187i	0.197661	−	0.627254i
$637$	5.64735	+	3.72665i	0.223756	+	0.147655i
$638$	3.55557	+	4.84836i	0.140766	+	0.191949i
$639$	108.420	−	62.5965i	4.28904	−	2.47628i
$640$	24.4052	−	6.66243i	0.964699	−	0.263356i
$641$	−7.68250	+	13.3065i	−0.303441	+	0.525575i	−0.976913	−	0.213638i	$-0.931469\pi$
$641$	−7.68250	+	13.3065i	−0.303441	+	0.525575i	0.673472	+	0.739213i	$0.264802\pi$
$642$	−18.6066	+	42.2961i	−0.734346	+	1.66929i
$643$		−	19.2835i		−	0.760468i	−0.924890	−	0.380234i	$-0.875844\pi$
$643$		−	19.2835i		−	0.760468i	0.924890	−	0.380234i	$-0.124156\pi$
$644$	−11.4340	−	7.77085i	−0.450563	−	0.306215i
$645$	−3.49011	+	6.42451i	−0.137423	+	0.252965i
$646$	−0.590589	−	0.259809i	−0.0232364	−	0.0102220i
$647$	29.0064	−	7.77224i	1.14036	−	0.305558i	0.361264	−	0.932464i	$-0.382345\pi$
$647$	29.0064	−	7.77224i	1.14036	−	0.305558i	0.779096	+	0.626905i	$0.215679\pi$
$648$	110.072	+	21.8670i	4.32402	+	0.859016i
$649$	13.1623	−	7.59925i	0.516665	−	0.298297i
$650$	−2.42391	+	6.39058i	−0.0950736	+	0.250659i
$651$	−38.8064	+	62.8076i	−1.52094	+	2.46163i
$652$	−8.26918	+	26.2412i	−0.323846	+	1.02769i
$653$	9.17958	+	15.8995i	0.359225	+	0.622196i	0.987832	−	0.155528i	$-0.0497078\pi$
$653$	9.17958	+	15.8995i	0.359225	+	0.622196i	−0.628607	+	0.777723i	$0.716374\pi$
$654$	55.6493	−	69.3490i	2.17606	−	2.71176i
$655$	−15.9187	−	3.82558i	−0.621997	−	0.149478i
$656$	2.83320	−	32.5042i	0.110618	−	1.26908i
$657$	23.8285	−	23.8285i	0.929637	−	0.929637i
$658$	3.14409	−	17.0375i	0.122569	−	0.664193i
$659$	−8.64946	+	8.64946i	−0.336935	+	0.336935i	−0.855213	−	0.518277i	$-0.826573\pi$
$659$	−8.64946	+	8.64946i	−0.336935	+	0.336935i	0.518277	+	0.855213i	$0.326573\pi$
$660$	−28.2045	+	15.6316i	−1.09786	+	0.608458i
$661$	8.53106	−	2.28589i	0.331820	−	0.0889108i	−0.0890628	−	0.996026i	$-0.528387\pi$
$661$	8.53106	−	2.28589i	0.331820	−	0.0889108i	0.420882	+	0.907115i	$0.361721\pi$
$662$	−39.7094	−	31.8649i	−1.54335	−	1.23846i
$663$	−11.4724	−	3.07403i	−0.445552	−	0.119385i
$664$	20.4870	−	6.95994i	0.795052	−	0.270098i
$665$	0.724523	−	0.191112i	0.0280958	−	0.00741099i
$666$	52.0897	−	38.2002i	2.01844	−	1.48023i
$667$	2.62735	+	4.55070i	0.101731	+	0.176204i
$668$	0.544674	−	12.5214i	0.0210741	−	0.484466i
$669$	−19.9423	−	74.4258i	−0.771015	−	2.87747i
$670$	−10.8900	−	14.0689i	−0.420718	−	0.543530i
$671$			24.7422i			0.955161i
$672$	−44.0181	−	25.8637i	−1.69804	−	0.997716i
$673$	−6.85366	+	6.85366i	−0.264189	+	0.264189i	−0.826753	−	0.562564i	$-0.809815\pi$
$673$	−6.85366	+	6.85366i	−0.264189	+	0.264189i	0.562564	+	0.826753i	$0.309815\pi$
$674$	−13.0897	−	33.6521i	−0.504197	−	1.29623i
$675$	4.98751	+	96.0033i	0.191969	+	3.69517i
$676$	16.3058	+	17.7889i	0.627146	+	0.684189i
$677$	−4.15869	+	2.40102i	−0.159832	+	0.0922788i	−0.577782	−	0.816191i	$-0.696082\pi$
$677$	−4.15869	+	2.40102i	−0.159832	+	0.0922788i	0.417951	+	0.908470i	$0.362748\pi$
$678$	25.7889	+	3.96716i	0.990416	+	0.152358i
$679$	−36.6101	−	10.9907i	−1.40497	−	0.421785i
$680$	−18.6046	+	13.1488i	−0.713452	+	0.504233i
$681$	59.0923	−	34.1170i	2.26442	−	1.30736i
$682$	−15.3047	+	19.0724i	−0.586047	+	0.730320i
$683$	15.1367	+	8.73917i	0.579189	+	0.334395i	0.760811	−	0.648973i	$-0.224801\pi$
$683$	15.1367	+	8.73917i	0.579189	+	0.334395i	−0.181622	+	0.983368i	$0.558135\pi$
$684$	−1.84525	−	1.17514i	−0.0705549	−	0.0449325i
$685$	−10.3443	−	34.9511i	−0.395236	−	1.33541i
$686$	−22.9351	−	12.6484i	−0.875665	−	0.482920i
$687$	12.4675	+	12.4675i	0.475663	+	0.475663i
$688$	−3.81961	−	0.332932i	−0.145621	−	0.0126929i
$689$	−1.17491	+	2.03501i	−0.0447606	+	0.0775276i
$690$	−25.9918	+	10.8948i	−0.989492	+	0.414757i
$691$	−14.2039	−	3.80594i	−0.540344	−	0.144785i	−0.0216830	−	0.999765i	$-0.506902\pi$
$691$	−14.2039	−	3.80594i	−0.540344	−	0.144785i	−0.518660	+	0.854980i	$0.673569\pi$
$692$	11.9949	+	3.77987i	0.455979	+	0.143689i
$693$	46.2593	+	13.8875i	1.75725	+	0.527543i
$694$	8.81380	−	6.46364i	0.334567	−	0.245356i
$695$	−23.9789	+	25.2570i	−0.909573	+	0.958053i
$696$	10.7850	+	16.1324i	0.408803	+	0.611497i
$697$	7.60469	+	28.3811i	0.288048	+	1.07501i
$698$	5.01084	+	12.8823i	0.189663	+	0.487601i
$699$	−49.1036	+	49.1036i	−1.85727	+	1.85727i
$700$	7.39344	−	25.4035i	0.279446	−	0.960161i
$701$	−17.8920	−	17.8920i	−0.675771	−	0.675771i	0.283270	−	0.959040i	$-0.408581\pi$
$701$	−17.8920	−	17.8920i	−0.675771	−	0.675771i	−0.959040	+	0.283270i	$0.908581\pi$
$702$	−24.0571	−	10.5831i	−0.907976	−	0.399432i
$703$	−0.647036	+	0.173373i	−0.0244034	+	0.00653888i
$704$	−13.4208	−	10.2878i	−0.505816	−	0.387738i
$705$	−25.6139	−	24.3177i	−0.964675	−	0.915859i
$706$	9.07944	+	1.39671i	0.341709	+	0.0525659i
$707$	−14.4663	−	15.3567i	−0.544060	−	0.577550i
$708$	43.5081	−	22.6578i	1.63513	−	0.851532i
$709$	0.624916	−	2.33222i	0.0234692	−	0.0875884i	−0.953198	−	0.302347i	$-0.902230\pi$
$709$	0.624916	−	2.33222i	0.0234692	−	0.0875884i	0.976667	+	0.214759i	$0.0688965\pi$
$710$	−17.3638	+	42.4250i	−0.651652	+	1.59218i
$711$	−100.271	−	57.8914i	−3.76045	−	2.17110i
$712$	7.40787	+	6.49336i	0.277622	+	0.243349i
$713$	−15.1124	+	15.1124i	−0.565964	+	0.565964i
$714$	45.2128	+	8.34353i	1.69205	+	0.312249i
$715$	4.38081	−	1.29657i	0.163833	−	0.0484890i
$716$	8.33837	−	13.0933i	0.311619	−	0.489318i
$717$	−8.33833	+	14.4424i	−0.311401	+	0.539362i
$718$	0.0760474	+	0.693867i	0.00283806	+	0.0258949i
$719$	16.5371	+	28.6431i	0.616730	+	1.06821i	0.990078	+	0.140516i	$0.0448762\pi$
$719$	16.5371	+	28.6431i	0.616730	+	1.06821i	−0.373348	+	0.927691i	$0.621790\pi$
$720$	−69.1263	+	34.4733i	−2.57618	+	1.28474i
$721$	1.05639	+	4.47245i	0.0393421	+	0.166563i
$722$	−15.8769	−	21.6496i	−0.590875	−	0.805716i
$723$	12.5258	+	21.6954i	0.465841	+	0.806861i
$724$	1.48295	−	34.0913i	0.0551136	−	1.26699i
$725$	−6.73241	+	7.47026i	−0.250036	+	0.277439i
$726$	−28.8434	−	12.6886i	−1.07048	−	0.470920i
$727$	−0.195237	−	0.195237i	−0.00724094	−	0.00724094i	0.703477	−	0.710718i	$-0.251630\pi$
$727$	−0.195237	−	0.195237i	−0.00724094	−	0.00724094i	−0.710718	+	0.703477i	$0.751630\pi$
$728$	5.29471	+	4.92815i	0.196235	+	0.182649i
$729$	−145.903			−5.40382
$730$	−1.55898	+	12.2402i	−0.0577005	+	0.453031i
$731$	3.33510	−	0.893636i	0.123353	−	0.0330523i
$732$	−3.47047	+	79.7818i	−0.128272	+	2.94882i
$733$	7.05038	−	4.07054i	0.260412	−	0.150349i	−0.364111	−	0.931356i	$-0.618627\pi$
$733$	7.05038	−	4.07054i	0.260412	−	0.150349i	0.624522	+	0.781007i	$0.285294\pi$
$734$	−3.49208	+	22.7006i	−0.128895	+	0.837893i
$735$	−47.1148	+	25.1214i	−1.73786	+	0.926618i
$736$	−10.6801	−	10.2157i	−0.393674	−	0.376557i
$737$	−3.07796	+	11.4871i	−0.113378	+	0.423133i
$738$	10.8538	+	99.0314i	0.399533	+	3.64539i
$739$	0.867037	+	3.23583i	0.0318945	+	0.119032i	0.980038	−	0.198811i	$-0.0637081\pi$
$739$	0.867037	+	3.23583i	0.0318945	+	0.119032i	−0.948143	+	0.317843i	$0.897041\pi$
$740$	−6.52100	+	22.7357i	−0.239717	+	0.835782i
$741$	0.295297	+	0.295297i	0.0108480	+	0.0108480i
$742$	3.90963	−	8.21306i	0.143527	−	0.301511i
$743$	−3.64048	−	3.64048i	−0.133556	−	0.133556i	0.637168	−	0.770725i	$-0.280106\pi$
$743$	−3.64048	−	3.64048i	−0.133556	−	0.133556i	−0.770725	+	0.637168i	$0.780106\pi$
$744$	−52.0256	+	59.3527i	−1.90735	+	2.17598i
$745$	2.59287	−	10.7893i	0.0949955	−	0.395289i
$746$	27.9075	−	3.05864i	1.02177	−	0.111985i
$747$	−57.2150	+	33.0331i	−2.09339	+	1.20862i
$748$	14.5243	+	4.57691i	0.531060	+	0.167349i
$749$	−13.3204	+	21.5589i	−0.486718	+	0.787746i
$750$	−35.1825	−	40.8811i	−1.28468	−	1.49277i
$751$	4.42696	+	7.66772i	0.161542	+	0.279799i	0.935422	−	0.353533i	$-0.115020\pi$
$751$	4.42696	+	7.66772i	0.161542	+	0.279799i	−0.773880	+	0.633332i	$0.781687\pi$
$752$	6.32910	−	17.4065i	0.230798	−	0.634750i
$753$	4.05615	+	15.1378i	0.147814	+	0.551650i
$754$	−0.996670	−	2.56232i	−0.0362966	−	0.0933143i
$755$	3.25838	+	1.77012i	0.118585	+	0.0644211i
$756$	96.0777	+	33.4598i	3.49431	+	1.21692i
$757$	−43.5428			−1.58259			−0.791295	−	0.611434i	$-0.790593\pi$
$757$	−43.5428			−1.58259			−0.791295	+	0.611434i	$0.790593\pi$
$758$	8.74381	+	22.4793i	0.317589	+	0.816485i
$759$	16.3146	+	9.41923i	0.592182	+	0.341896i
$760$	0.797679	−	0.0733077i	0.0289348	−	0.00265915i
$761$	−15.8494	−	27.4519i	−0.574540	−	0.995132i	−0.996091	−	0.0883278i	$-0.971848\pi$
$761$	−15.8494	−	27.4519i	−0.574540	−	0.995132i	0.421552	−	0.906804i	$-0.361486\pi$
$762$	0.116533	−	0.757535i	0.00422156	−	0.0274426i
$763$	35.4959	−	33.4376i	1.28504	−	1.21052i
$764$	1.37986	−	4.37881i	0.0499215	−	0.158420i
$765$	47.8951	−	50.4479i	1.73165	−	1.82395i
$766$	−1.66531	+	2.07528i	−0.0601702	+	0.0749829i
$767$	−6.71315	+	1.79878i	−0.242398	+	0.0649503i
$768$	−41.8327	−	35.0559i	−1.50951	−	1.26497i
$769$	−13.2028			−0.476104			−0.238052	−	0.971252i	$-0.576509\pi$
$769$	−13.2028			−0.476104			−0.238052	+	0.971252i	$0.576509\pi$
$770$	−16.5071	+	6.34682i	−0.594874	+	0.228724i
$771$	46.3994	+	46.3994i	1.67103	+	1.67103i
$772$	14.6619	−	23.0228i	0.527693	−	0.828607i
$773$	−0.755768	+	1.30903i	−0.0271831	+	0.0470825i	−0.879297	−	0.476274i	$-0.841987\pi$
$773$	−0.755768	+	1.30903i	−0.0271831	+	0.0470825i	0.852114	+	0.523356i	$0.175320\pi$
$774$	11.6373	−	1.27544i	0.418294	−	0.0458447i
$775$	−36.4352	−	18.5856i	−1.30879	−	0.667613i
$776$	−36.6537	−	18.0646i	−1.31579	−	0.648481i
$777$	42.0317	−	22.6220i	1.50788	−	0.811560i
$778$	11.8702	+	1.82603i	0.425569	+	0.0654662i
$779$	0.267389	−	0.997909i	0.00958020	−	0.0357538i
$780$	14.3079	−	3.56635i	0.512305	−	0.127696i
$781$	29.5976	−	7.93067i	1.05909	−	0.283782i
$782$	12.1826	+	5.35928i	0.435647	+	0.191648i
$783$	−27.3437	−	27.3437i	−0.977183	−	0.977183i
$784$	−21.9428	−	17.3930i	−0.783670	−	0.621177i
$785$	−5.68621	+	10.4670i	−0.202950	+	0.373584i
$786$	12.8045	+	32.9188i	0.456721	+	1.17418i
$787$	19.9295	−	34.5189i	0.710411	−	1.23047i	−0.254292	−	0.967127i	$-0.581842\pi$
$787$	19.9295	−	34.5189i	0.710411	−	1.23047i	0.964703	−	0.263340i	$-0.0848242\pi$
$788$	−10.6571	−	11.6265i	−0.379645	−	0.414176i
$789$	20.8471	+	5.58597i	0.742177	+	0.198866i
$790$	42.0088	−	5.71086i	1.49461	−	0.203183i
$791$	13.7056	+	4.11457i	0.487317	+	0.146297i
$792$	46.3144	+	22.8258i	1.64571	+	0.811080i
$793$	2.92830	−	10.9286i	0.103987	−	0.388085i
$794$	−2.28689	−	20.8659i	−0.0811585	−	0.740502i
$795$	−9.68521	−	15.8129i	−0.343499	−	0.560826i
$796$	3.51512	+	15.8436i	0.124590	+	0.561562i
$797$	−34.4574			−1.22054			−0.610272	−	0.792192i	$-0.708940\pi$
$797$	−34.4574			−1.22054			−0.610272	+	0.792192i	$0.708940\pi$
$798$	−1.23006	−	1.04893i	−0.0435438	−	0.0371317i
$799$			16.6793i			0.590070i
$800$	12.2893	−	25.4750i	0.434492	−	0.900676i
$801$	−26.0489	−	15.0393i	−0.920392	−	0.531388i
$802$	−1.63325	−	14.9020i	−0.0576721	−	0.526209i
$803$	7.14291	−	4.12396i	0.252068	−	0.145531i
$804$	−11.5362	+	36.6087i	−0.406851	+	1.29109i
$805$	−14.9453	+	3.94221i	−0.526753	+	0.138945i
$806$	9.01732	−	6.61289i	0.317621	−	0.232929i
$807$	−41.1980	−	11.0390i	−1.45024	−	0.388590i
$808$	−12.5349	−	18.7500i	−0.440977	−	0.659624i
$809$	−8.92541	+	15.4593i	−0.313801	+	0.543519i	−0.979182	−	0.202985i	$-0.934936\pi$
$809$	−8.92541	+	15.4593i	−0.313801	+	0.543519i	0.665381	+	0.746504i	$0.268269\pi$
$810$	99.2182	−	76.7996i	3.48617	−	2.69846i
$811$	27.8917	+	27.8917i	0.979409	+	0.979409i	0.999792	−	0.0203832i	$-0.00648862\pi$
$811$	27.8917	+	27.8917i	0.979409	+	0.979409i	−0.0203832	+	0.999792i	$0.506489\pi$
$812$	4.63183	+	9.58186i	0.162545	+	0.336257i
$813$	−36.8420			−1.29211
$814$	14.7347	−	5.73139i	0.516452	−	0.200885i
$815$	16.0665	+	26.2316i	0.562785	+	0.918851i
$816$	46.1919	+	16.7956i	1.61704	+	0.587965i
$817$	−0.117266	−	0.0314212i	−0.00410260	−	0.00109929i
$818$	−32.4157	−	44.2020i	−1.13339	−	1.54549i
$819$	−18.7890	−	11.6090i	−0.656541	−	0.405651i
$820$	−25.3384	−	26.2422i	−0.884856	−	0.916417i
$821$	−0.872174	−	0.233698i	−0.0304391	−	0.00815613i	0.243567	−	0.969884i	$-0.421682\pi$
$821$	−0.872174	−	0.233698i	−0.0304391	−	0.00815613i	−0.274006	+	0.961728i	$0.588349\pi$
$822$	−49.2163	+	61.3324i	−1.71662	+	2.13921i
$823$	−24.3517	+	6.52502i	−0.848847	+	0.227448i	−0.656919	−	0.753961i	$-0.728141\pi$
$823$	−24.3517	+	6.52502i	−0.848847	+	0.227448i	−0.191928	+	0.981409i	$0.561474\pi$
$824$	0.322498	+	4.90221i	0.0112347	+	0.170777i
$825$	−7.51183	+	35.2615i	−0.261528	+	1.22765i
$826$	25.3531	−	9.00009i	0.882148	−	0.313153i
$827$	−41.1644			−1.43143			−0.715713	−	0.698394i	$-0.753898\pi$
$827$	−41.1644			−1.43143			−0.715713	+	0.698394i	$0.753898\pi$
$828$	38.0635	+	24.2405i	1.32280	+	0.842415i
$829$	−20.5419	+	5.50419i	−0.713450	+	0.191168i	−0.597247	−	0.802057i	$-0.703739\pi$
$829$	−20.5419	+	5.50419i	−0.713450	+	0.191168i	−0.116203	+	0.993225i	$0.537072\pi$
$830$	9.16314	−	22.3883i	0.318057	−	0.777110i
$831$	42.4838	−	24.5280i	1.47375	−	0.850868i
$832$	4.71035	+	6.13250i	0.163302	+	0.212606i
$833$	23.9231	+	7.96771i	0.828887	+	0.276065i
$834$	74.2629	+	11.4240i	2.57152	+	0.395582i
$835$	−10.1622	−	9.64792i	−0.351676	−	0.333880i
$836$	−0.361805	−	0.394713i	−0.0125133	−	0.0136514i
$837$	78.6398	−	136.208i	2.71819	−	4.70804i
$838$	−6.85308	−	17.6185i	−0.236736	−	0.608620i
$839$			28.7420i			0.992283i	0.868242	+	0.496142i	$0.165250\pi$
$839$			28.7420i			0.992283i	−0.868242	+	0.496142i	$0.834750\pi$
$840$	−54.1178	+	18.1501i	−1.86724	+	0.626239i
$841$			24.9548i			0.860510i
$842$	8.07347	−	3.14035i	0.278230	−	0.108224i
$843$	4.62171	−	8.00503i	0.159180	−	0.275708i
$844$	0.554388	−	12.7447i	0.0190828	−	0.438690i
$845$	26.9706	−	0.700111i	0.927818	−	0.0240845i
$846$	−8.59856	+	55.8957i	−0.295625	+	1.92173i
$847$	−14.7019	−	9.08375i	−0.505164	−	0.312121i
$848$	5.57499	−	7.96738i	0.191446	−	0.273601i
$849$	−45.6581	+	26.3607i	−1.56698	+	0.904697i
$850$	−2.56139	+	25.3419i	−0.0878548	+	0.869222i
$851$	13.3469	−	3.57630i	0.457527	−	0.122594i
$852$	96.5508	−	21.4211i	3.30778	−	0.733875i
$853$	40.7729			1.39604			0.698018	−	0.716080i	$-0.254065\pi$
$853$	40.7729			1.39604			0.698018	+	0.716080i	$0.254065\pi$
$854$	−7.94799	+	43.0694i	−0.271975	+	1.47381i
$855$	−2.34532	+	0.694136i	−0.0802084	+	0.0237390i
$856$	−17.8580	+	20.3730i	−0.610372	+	0.696336i
$857$	1.55540	−	0.416769i	0.0531315	−	0.0142366i	−0.232155	−	0.972679i	$-0.574578\pi$
$857$	1.55540	−	0.416769i	0.0531315	−	0.0142366i	0.285287	+	0.958442i	$0.407911\pi$
$858$	−7.68748	−	6.16884i	−0.262446	−	0.210601i
$859$	−23.9876	−	6.42745i	−0.818446	−	0.219302i	−0.174779	−	0.984608i	$-0.555921\pi$
$859$	−23.9876	−	6.42745i	−0.818446	−	0.219302i	−0.643667	+	0.765306i	$0.722588\pi$
$860$	−3.08375	+	2.97755i	−0.105155	+	0.101534i
$861$	−2.19717	+	73.5844i	−0.0748793	+	2.50775i
$862$	13.7289	−	10.0681i	0.467608	−	0.342922i
$863$	−38.5305	−	10.3242i	−1.31159	−	0.351440i	−0.465771	−	0.884905i	$-0.654223\pi$
$863$	−38.5305	−	10.3242i	−1.31159	−	0.351440i	−0.845822	+	0.533465i	$0.820889\pi$
$864$	95.3754	+	52.2748i	3.24474	+	1.77842i
$865$	11.9905	−	7.34405i	0.407690	−	0.249705i
$866$	14.9914	+	38.5411i	0.509428	+	1.30968i
$867$	13.7284			0.466240
$868$	−32.7680	+	28.2835i	−1.11222	+	0.960005i
$869$	−20.0384	−	20.0384i	−0.679755	−	0.679755i
$870$	21.5220	+	2.74116i	0.729666	+	0.0929342i
$871$	2.71906	−	4.70954i	0.0921317	−	0.159577i
$872$	43.3392	−	28.9735i	1.46765	−	0.981166i
$873$	120.521	+	32.2934i	4.07900	+	1.09297i
$874$	−0.276745	−	0.377368i	−0.00936102	−	0.0127647i
$875$	−16.0025	−	24.8781i	−0.540983	−	0.841033i
$876$	23.6109	−	12.2959i	0.797740	−	0.415440i
$877$	−19.3795	+	11.1888i	−0.654401	+	0.377818i	−0.790140	−	0.612926i	$-0.789992\pi$
$877$	−19.3795	+	11.1888i	−0.654401	+	0.377818i	0.135740	+	0.990745i	$0.456659\pi$
$878$	−48.4837	+	5.31378i	−1.63625	+	0.179331i
$879$	26.2976	+	15.1829i	0.886997	+	0.512108i
$880$	−18.5264	+	3.77106i	−0.624524	+	0.127122i
$881$		−	27.0246i		−	0.910480i	−0.890369	−	0.455240i	$-0.849553\pi$
$881$		−	27.0246i		−	0.910480i	0.890369	−	0.455240i	$-0.150447\pi$
$882$	76.0638	+	39.0344i	2.56120	+	1.31436i
$883$	−31.5113			−1.06044			−0.530219	−	0.847861i	$-0.677890\pi$
$883$	−31.5113			−1.06044			−0.530219	+	0.847861i	$0.677890\pi$
$884$	−5.87365	−	3.74060i	−0.197552	−	0.125810i
$885$	12.8153	−	53.3262i	0.430782	−	1.79254i
$886$	−20.2769	+	2.22233i	−0.681215	+	0.0746607i
$887$	7.00311	−	26.1360i	0.235141	−	0.877560i	−0.742944	−	0.669354i	$-0.766571\pi$
$887$	7.00311	−	26.1360i	0.235141	−	0.877560i	0.978085	−	0.208206i	$-0.0667624\pi$
$888$	48.3165	−	16.4143i	1.62139	−	0.550826i
$889$	0.120864	−	0.402596i	0.00405363	−	0.0135026i
$890$	10.9133	−	1.48360i	0.365813	−	0.0497302i
$891$	−81.0103	−	21.7067i	−2.71395	−	0.727200i
$892$	1.96325	−	45.1328i	0.0657346	−	1.51116i
$893$	0.293230	−	0.507890i	0.00981258	−	0.0169959i
$894$	−22.3115	+	8.67852i	−0.746207	+	0.290253i
$895$	−4.92535	−	16.6416i	−0.164636	−	0.556268i
$896$	−20.0572	−	22.2196i	−0.670064	−	0.742303i
$897$	−6.09133	−	6.09133i	−0.203383	−	0.203383i
$898$	14.7977	−	33.6378i	0.493807	−	1.12251i
$899$	15.8922	−	4.25831i	0.530036	−	0.142023i
$900$	−21.6481	+	83.6057i	−0.721605	+	2.78686i
$901$	−2.26648	+	8.45860i	−0.0755073	+	0.281797i
$902$	−3.70738	+	24.1002i	−0.123442	+	0.802448i
$903$	8.64700	+	0.258192i	0.287754	+	0.00859209i
$904$	13.7220	+	6.76280i	0.456386	+	0.224927i
$905$	−27.6680	−	26.2679i	−0.919714	−	0.873174i
$906$	−0.871584	−	7.95246i	−0.0289565	−	0.264203i
$907$	11.4976	−	19.9144i	0.381772	−	0.661248i	−0.609544	−	0.792752i	$-0.708647\pi$
$907$	11.4976	−	19.9144i	0.381772	−	0.661248i	0.991316	+	0.131505i	$0.0419808\pi$
$908$	39.0561	−	8.66513i	1.29612	−	0.287563i
$909$	48.6960	+	48.6960i	1.61514	+	1.61514i
$910$	8.04231	−	0.849721i	0.266600	−	0.0281680i
$911$	22.6953			0.751929			0.375964	−	0.926634i	$-0.377311\pi$
$911$	22.6953			0.751929			0.375964	+	0.926634i	$0.377311\pi$
$912$	−1.11129	−	1.32351i	−0.0367984	−	0.0438259i
$913$	−15.6191	+	4.18513i	−0.516918	+	0.138508i
$914$	4.06156	+	3.25921i	0.134344	+	0.107805i
$915$	64.7497	+	61.4732i	2.14056	+	2.03224i
$916$	4.77480	+	9.16870i	0.157764	+	0.302942i
$917$	4.45304	+	18.8528i	0.147052	+	0.622575i
$918$	−96.8054	−	14.8918i	−3.19505	−	0.491502i
$919$	−19.7064	−	34.1325i	−0.650054	−	1.12593i	−0.983109	−	0.183020i	$-0.941413\pi$
$919$	−19.7064	−	34.1325i	−0.650054	−	1.12593i	0.333055	−	0.942907i	$-0.391920\pi$
$920$	−16.4544	+	1.51218i	−0.542484	+	0.0498550i
$921$	−75.8862	−	43.8129i	−2.50054	−	1.44369i
$922$	7.10559	−	2.76387i	0.234010	−	0.0910232i
$923$	−14.0118			−0.461205
$924$	31.5566	+	21.4467i	1.03813	+	0.705544i
$925$	14.3925	+	22.1845i	0.473221	+	0.729423i
$926$	33.7729	−	13.1367i	1.10984	−	0.431698i
$927$	−3.88248	−	14.4896i	−0.127517	−	0.475901i
$928$	3.18814	+	10.9216i	0.104656	+	0.358521i
$929$	−13.9954	−	24.2408i	−0.459175	−	0.795314i	0.539743	−	0.841830i	$-0.318521\pi$
$929$	−13.9954	−	24.2408i	−0.459175	−	0.795314i	−0.998918	+	0.0465162i	$0.985188\pi$
$930$	11.8867	+	87.4384i	0.389782	+	2.86722i
$931$	−0.588391	−	0.663201i	−0.0192837	−	0.0217355i
$932$	−36.1113	+	18.8058i	−1.18287	+	0.616003i
$933$	−55.5947	+	32.0976i	−1.82009	+	1.05083i
$934$	−1.80050	−	16.4281i	−0.0589143	−	0.537542i
$935$	14.5189	−	8.89266i	0.474819	−	0.290821i
$936$	−17.7555	−	15.5635i	−0.580356	−	0.508710i
$937$	−23.9413	−	23.9413i	−0.782127	−	0.782127i	0.198062	−	0.980189i	$-0.436535\pi$
$937$	−23.9413	−	23.9413i	−0.782127	−	0.782127i	−0.980189	+	0.198062i	$0.936535\pi$
$938$	−9.04793	+	19.0072i	−0.295425	+	0.620607i
$939$	12.8426	+	12.8426i	0.419103	+	0.419103i
$940$	−10.0380	−	18.1119i	−0.327405	−	0.590746i
$941$	−15.6547	−	58.4242i	−0.510329	−	1.90457i	−0.416910	−	0.908948i	$-0.636887\pi$
$941$	−15.6547	−	58.4242i	−0.510329	−	1.90457i	−0.0934192	−	0.995627i	$-0.529780\pi$
$942$	25.5460	−	2.79982i	0.832333	−	0.0912231i
$943$	−5.51565	+	20.5847i	−0.179614	+	0.670329i
$944$	28.3222	−	5.00338i	0.921809	−	0.162846i
$945$	98.7277	−	56.4885i	3.21161	−	1.83757i
$946$	2.83204	+	0.435659i	0.0920776	+	0.0141645i
$947$	41.5683	−	23.9994i	1.35079	−	0.779877i	0.362427	−	0.932012i	$-0.381948\pi$
$947$	41.5683	−	23.9994i	1.35079	−	0.779877i	0.988360	+	0.152135i	$0.0486148\pi$
$948$	−61.8036	−	67.4250i	−2.00729	−	2.18986i
$949$	−3.64309	+	0.976162i	−0.118260	+	0.0316876i
$950$	0.523520	−	0.726642i	0.0169852	−	0.0235754i
$951$	52.8840			1.71488
$952$	23.8126	+	12.6328i	0.771770	+	0.409433i
$953$	18.6569	+	18.6569i	0.604356	+	0.604356i	0.941465	−	0.337110i	$-0.109449\pi$
$953$	18.6569	+	18.6569i	0.604356	+	0.604356i	−0.337110	+	0.941465i	$0.609449\pi$
$954$	−11.9561	+	27.1781i	−0.387092	+	0.879925i
$955$	−2.68098	−	4.37719i	−0.0867543	−	0.141643i
$956$	−7.20773	+	6.60680i	−0.233115	+	0.213679i
$957$	−7.25118	−	12.5594i	−0.234397	−	0.405988i
$958$	34.9589	−	25.6372i	1.12947	−	0.828301i
$959$	−31.3926	+	29.5723i	−1.01372	+	0.954938i
$960$	−60.2677	+	9.56127i	−1.94513	+	0.308589i
$961$	17.9589	+	31.1058i	0.579320	+	1.00341i
$962$	−7.18663	+	0.787649i	−0.231706	+	0.0253948i
$963$	41.3610	−	71.6393i	1.33284	−	2.30854i
$964$	3.18135	+	14.3392i	0.102465	+	0.461835i
$965$	−8.66057	−	29.2621i	−0.278794	−	0.941979i
$966$	25.3735	+	21.6371i	0.816380	+	0.696163i
$967$	17.8541	−	17.8541i	0.574148	−	0.574148i	−0.359137	−	0.933285i	$-0.616929\pi$
$967$	17.8541	−	17.8541i	0.574148	−	0.574148i	0.933285	+	0.359137i	$0.116929\pi$
$968$	−13.8932	−	12.1781i	−0.446545	−	0.391418i
$969$	1.34780	+	0.778151i	0.0432975	+	0.0249978i
$970$	−42.1349	+	17.6614i	−1.35287	+	0.567072i
$971$	11.1328	−	41.5480i	0.357267	−	1.33334i	−0.520340	−	0.853959i	$-0.674195\pi$
$971$	11.1328	−	41.5480i	0.357267	−	1.33334i	0.877607	−	0.479380i	$-0.159139\pi$
$972$	−148.150	−	46.6852i	−4.75190	−	1.49743i
$973$	39.4675	+	11.8485i	1.26527	+	0.379847i
$974$	2.69948	−	17.5482i	0.0864968	−	0.562280i
$975$	7.49125	−	14.6859i	0.239912	−	0.470324i
$976$	−15.9994	+	44.0021i	−0.512128	+	1.40847i
$977$	−24.1696	+	6.47622i	−0.773254	+	0.207193i	−0.623809	−	0.781577i	$-0.714416\pi$
$977$	−24.1696	+	6.47622i	−0.773254	+	0.207193i	−0.149445	+	0.988770i	$0.547749\pi$
$978$	26.7231	−	60.7462i	0.854512	−	1.94245i
$979$	−5.20567	−	5.20567i	−0.166374	−	0.166374i
$980$	−30.7732	+	5.74549i	−0.983014	+	0.183533i
$981$	−112.557	+	112.557i	−3.59367	+	3.59367i
$982$	−11.0586	+	4.30149i	−0.352895	+	0.137266i
$983$	−4.52994	−	16.9060i	−0.144483	−	0.539217i	−0.999778	−	0.0210759i	$-0.993291\pi$
$983$	−4.52994	−	16.9060i	−0.144483	−	0.539217i	0.855295	−	0.518141i	$-0.173376\pi$
$984$	−15.3350	+	77.1916i	−0.488861	+	2.46078i
$985$	−17.6275	+	0.457578i	−0.561657	+	0.0145796i
$986$	−6.05913	−	8.26221i	−0.192962	−	0.263122i
$987$	−12.0160	+	40.0251i	−0.382472	+	1.27401i
$988$	0.113093	+	0.217165i	0.00359797	+	0.00690893i
$989$	2.41893	+	0.648150i	0.0769175	+	0.0206100i
$990$	53.2403	−	22.3163i	1.69209	−	0.709259i
$991$	−28.3871	+	49.1678i	−0.901745	+	1.56187i	−0.0765170	+	0.997068i	$0.524380\pi$
$991$	−28.3871	+	49.1678i	−0.901745	+	1.56187i	−0.825228	+	0.564800i	$0.808953\pi$
$992$	−39.5513	+	24.0221i	−1.25576	+	0.762704i
$993$	86.8385	+	86.8385i	2.75574	+	2.75574i
$994$	54.0691	−	4.29742i	1.71497	−	0.136306i
$995$	15.9437	+	8.66140i	0.505448	+	0.274585i
$996$	−50.9513	+	11.3042i	−1.61445	+	0.358189i
$997$	17.5088	+	10.1087i	0.554509	+	0.320146i	0.750939	−	0.660372i	$-0.229601\pi$
$997$	17.5088	+	10.1087i	0.554509	+	0.320146i	−0.196430	+	0.980518i	$0.562935\pi$
$998$	−34.1754	−	27.4241i	−1.08180	−	0.868096i
$999$	−88.0628	+	50.8431i	−2.78618	+	1.60860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cz.c.157.14	yes	360
5.3	odd	4		560.2.ch.c.493.33	yes	360
7.5	odd	6	inner	560.2.cz.c.397.48	yes	360
16.5	even	4		560.2.ch.c.437.88	yes	360
35.33	even	12		560.2.ch.c.173.88	yes	360
80.53	odd	4	inner	560.2.cz.c.213.48	yes	360
112.5	odd	12		560.2.ch.c.117.33	✓	360
560.453	even	12	inner	560.2.cz.c.453.14	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.ch.c.117.33	✓	360	112.5	odd	12
560.2.ch.c.173.88	yes	360	35.33	even	12
560.2.ch.c.437.88	yes	360	16.5	even	4
560.2.ch.c.493.33	yes	360	5.3	odd	4
560.2.cz.c.157.14	yes	360	1.1	even	1	trivial
560.2.cz.c.213.48	yes	360	80.53	odd	4	inner
560.2.cz.c.397.48	yes	360	7.5	odd	6	inner
560.2.cz.c.453.14	yes	360	560.453	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.cz (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29449 - 0.569466i) q^{2} +(2.95419 + 1.70560i) q^{3} +(1.35142 + 1.47434i) q^{4} +(2.23531 - 0.0580249i) q^{5} +(-2.85289 - 3.89019i) q^{6} +(-1.25390 - 2.32975i) q^{7} +(-0.909815 - 2.67810i) q^{8} +(4.31815 + 7.47925i) q^{9} +(-2.92664 - 1.19782i) q^{10} +(0.547088 + 2.04176i) q^{11} +(1.47771 + 6.66045i) q^{12} -0.966590i q^{13} +(0.296452 + 3.72989i) q^{14} +(6.70251 + 3.64114i) q^{15} +(-0.347339 + 3.98489i) q^{16} +(-0.932306 - 3.47941i) q^{17} +(-1.33063 - 12.1409i) q^{18} +(-0.0327809 + 0.122340i) q^{19} +(3.10639 + 3.21719i) q^{20} +(0.269364 - 9.02117i) q^{21} +(0.454511 - 2.95459i) q^{22} +(0.676197 - 2.52360i) q^{23} +(1.88001 - 9.46340i) q^{24} +(4.99327 - 0.259408i) q^{25} +(-0.550440 + 1.25124i) q^{26} +19.2265i q^{27} +(1.74029 - 4.99714i) q^{28} +(-1.42218 + 1.42218i) q^{29} +(-6.60284 - 8.53027i) q^{30} +(-7.08438 - 4.09017i) q^{31} +(2.71889 - 4.96061i) q^{32} +(-1.86623 + 6.96485i) q^{33} +(-0.774543 + 5.03499i) q^{34} +(-2.93805 - 5.13497i) q^{35} +(-5.19132 + 16.4740i) q^{36} +(2.64442 + 4.58027i) q^{37} +(0.112103 - 0.139700i) q^{38} +(1.64862 - 2.85549i) q^{39} +(-2.18912 - 5.93361i) q^{40} -8.15686 q^{41} +(-5.48594 + 11.5244i) q^{42} +0.958523i q^{43} +(-2.27090 + 3.56586i) q^{44} +(10.0864 + 16.4679i) q^{45} +(-2.31244 + 2.88171i) q^{46} +(-4.47258 - 1.19843i) q^{47} +(-7.82274 + 11.1797i) q^{48} +(-3.85547 + 5.84255i) q^{49} +(-6.61147 - 2.50769i) q^{50} +(3.18028 - 11.8690i) q^{51} +(1.42508 - 1.30627i) q^{52} +(-2.10535 - 1.21552i) q^{53} +(10.9489 - 24.8886i) q^{54} +(1.34139 + 4.53223i) q^{55} +(-5.09849 + 5.47772i) q^{56} +(-0.305504 + 0.305504i) q^{57} +(2.65089 - 1.03112i) q^{58} +(-1.86096 - 6.94519i) q^{59} +(3.68962 + 14.8025i) q^{60} +(11.3063 + 3.02951i) q^{61} +(6.84146 + 9.32900i) q^{62} +(12.0103 - 19.4384i) q^{63} +(-6.34447 + 4.87316i) q^{64} +(-0.0560863 - 2.16063i) q^{65} +(6.38206 - 7.95319i) q^{66} +(4.87233 + 2.81304i) q^{67} +(3.86989 - 6.07667i) q^{68} +(6.30187 - 6.30187i) q^{69} +(0.879091 + 8.32029i) q^{70} -14.4961i q^{71} +(16.1015 - 18.3692i) q^{72} +(-1.00990 - 3.76901i) q^{73} +(-0.814874 - 7.43503i) q^{74} +(15.1935 + 7.75018i) q^{75} +(-0.224671 + 0.117002i) q^{76} +(4.07079 - 3.83474i) q^{77} +(-3.76022 + 2.75758i) q^{78} +(-11.6104 + 6.70327i) q^{79} +(-0.545190 + 8.92764i) q^{80} +(-19.8384 + 34.3611i) q^{81} +(10.5590 + 4.64505i) q^{82} +7.64983i q^{83} +(13.6643 - 11.7942i) q^{84} +(-2.28589 - 7.72348i) q^{85} +(0.545846 - 1.24080i) q^{86} +(-6.62707 + 1.77572i) q^{87} +(4.97029 - 3.32278i) q^{88} +(-3.01621 + 1.74141i) q^{89} +(-3.67885 - 27.0615i) q^{90} +(-2.25191 + 1.21201i) q^{91} +(4.63447 - 2.41350i) q^{92} +(-13.9524 - 24.1662i) q^{93} +(5.10726 + 4.09833i) q^{94} +(-0.0661768 + 0.275370i) q^{95} +(16.4929 - 10.0172i) q^{96} +(10.2159 - 10.2159i) q^{97} +(8.31800 - 5.36758i) q^{98} +(-12.9084 + 12.9084i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + 2 q^{2} - 24 q^{3} - 6 q^{5} - 8 q^{7} - 4 q^{8} + 164 q^{9} - 6 q^{10} - 2 q^{11} - 6 q^{12} - 4 q^{14} - 32 q^{15} - 20 q^{16} + 8 q^{18} - 30 q^{19} - 4 q^{21} - 8 q^{22} - 10 q^{23} - 12 q^{24}+ \cdots + 4 q^{99}+O(q^{100}) \) 360 * q + 2 * q^2 - 24 * q^3 - 6 * q^5 - 8 * q^7 - 4 * q^8 + 164 * q^9 - 6 * q^10 - 2 * q^11 - 6 * q^12 - 4 * q^14 - 32 * q^15 - 20 * q^16 + 8 * q^18 - 30 * q^19 - 4 * q^21 - 8 * q^22 - 10 * q^23 - 12 * q^24 - 12 * q^25 - 2 * q^28 + 8 * q^29 + 2 * q^30 - 24 * q^31 + 2 * q^32 - 24 * q^35 + 16 * q^36 + 4 * q^37 + 72 * q^38 + 28 * q^39 - 36 * q^40 - 50 * q^42 - 20 * q^44 - 72 * q^45 - 4 * q^46 - 6 * q^47 + 48 * q^50 + 16 * q^51 - 36 * q^52 + 24 * q^54 - 8 * q^56 - 80 * q^57 - 46 * q^58 - 84 * q^59 - 20 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 48 * q^68 - 16 * q^70 - 72 * q^72 + 52 * q^74 - 42 * q^75 + 152 * q^78 + 108 * q^80 - 124 * q^81 - 6 * q^82 - 28 * q^84 + 20 * q^85 + 8 * q^86 + 12 * q^88 - 48 * q^89 + 28 * q^91 + 4 * q^92 - 20 * q^93 + 72 * q^94 - 26 * q^95 - 60 * q^96 - 10 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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