LMFDB - Embedded newform 560.2.ch.c.437.88

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [560,2,Mod(117,560)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("560.117"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(560, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 3, 3, 10])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [360,2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.47162251319$
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			437.88
Character	$\chi$	$=$	560.437
Dual form			560.2.ch.c.173.88

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40580 + 0.154074i) q^{2} +(1.70560 - 2.95419i) q^{3} +(1.95252 + 0.433194i) q^{4} +(0.0580249 + 2.23531i) q^{5} +(2.85289 - 3.89019i) q^{6} +(1.25390 + 2.32975i) q^{7} +(2.67810 + 0.909815i) q^{8} +(-4.31815 - 7.47925i) q^{9} +(-0.262833 + 3.15134i) q^{10} +(-2.04176 + 0.547088i) q^{11} +(4.60996 - 5.02926i) q^{12} -0.966590 q^{13} +(1.40377 + 3.46835i) q^{14} +(6.70251 + 3.64114i) q^{15} +(3.62469 + 1.69164i) q^{16} +(-0.932306 - 3.47941i) q^{17} +(-4.91807 - 11.1796i) q^{18} +(0.122340 + 0.0327809i) q^{19} +(-0.855030 + 4.38964i) q^{20} +(9.02117 + 0.269364i) q^{21} +(-2.95459 + 0.454511i) q^{22} +(-0.676197 + 2.52360i) q^{23} +(7.25554 - 6.35984i) q^{24} +(-4.99327 + 0.259408i) q^{25} +(-1.35883 - 0.148927i) q^{26} -19.2265 q^{27} +(1.43904 + 5.09207i) q^{28} +(1.42218 + 1.42218i) q^{29} +(8.86135 + 6.15138i) q^{30} +(-7.08438 - 4.09017i) q^{31} +(4.83493 + 2.93657i) q^{32} +(-1.86623 + 6.96485i) q^{33} +(-0.774543 - 5.03499i) q^{34} +(-5.13497 + 2.93805i) q^{35} +(-5.19132 - 16.4740i) q^{36} +(-4.58027 + 2.64442i) q^{37} +(0.166934 + 0.0649326i) q^{38} +(-1.64862 + 2.85549i) q^{39} +(-1.87833 + 6.03920i) q^{40} +8.15686 q^{41} +(12.6404 + 1.76860i) q^{42} -0.958523 q^{43} +(-4.22358 + 0.183724i) q^{44} +(16.4679 - 10.0864i) q^{45} +(-1.33942 + 3.44348i) q^{46} +(-4.47258 - 1.19843i) q^{47} +(11.1797 - 7.82274i) q^{48} +(-3.85547 + 5.84255i) q^{49} +(-7.05948 - 0.404660i) q^{50} +(-11.8690 - 3.18028i) q^{51} +(-1.88729 - 0.418721i) q^{52} +(1.21552 - 2.10535i) q^{53} +(-27.0286 - 2.96232i) q^{54} +(-1.34139 - 4.53223i) q^{55} +(1.23843 + 7.38013i) q^{56} +(0.305504 - 0.305504i) q^{57} +(1.78018 + 2.21842i) q^{58} +(6.94519 - 1.86096i) q^{59} +(11.5095 + 10.0129i) q^{60} +(3.02951 - 11.3063i) q^{61} +(-9.32900 - 6.84146i) q^{62} +(12.0103 - 19.4384i) q^{63} +(6.34447 + 4.87316i) q^{64} +(-0.0560863 - 2.16063i) q^{65} +(-3.69664 + 9.50362i) q^{66} +(2.81304 - 4.87233i) q^{67} +(-0.313088 - 7.19750i) q^{68} +(6.30187 + 6.30187i) q^{69} +(-7.67139 + 3.33913i) q^{70} +14.4961i q^{71} +(-4.75971 - 23.9589i) q^{72} +(1.00990 + 3.76901i) q^{73} +(-6.84636 + 3.01181i) q^{74} +(-7.75018 + 15.1935i) q^{75} +(0.224671 + 0.117002i) q^{76} +(-3.83474 - 4.07079i) q^{77} +(-2.75758 + 3.76022i) q^{78} +(-11.6104 + 6.70327i) q^{79} +(-3.57103 + 8.20047i) q^{80} +(-19.8384 + 34.3611i) q^{81} +(11.4669 + 1.25676i) q^{82} +7.64983 q^{83} +(17.4973 + 4.43386i) q^{84} +(7.72348 - 2.28589i) q^{85} +(-1.34749 - 0.147684i) q^{86} +(6.62707 - 1.77572i) q^{87} +(-5.96579 - 0.392466i) q^{88} +(3.01621 - 1.74141i) q^{89} +(24.7046 - 11.6421i) q^{90} +(-1.21201 - 2.25191i) q^{91} +(-2.41350 + 4.63447i) q^{92} +(-24.1662 + 13.9524i) q^{93} +(-6.10289 - 2.37385i) q^{94} +(-0.0661768 + 0.275370i) q^{95} +(16.9216 - 9.27467i) q^{96} +(10.2159 - 10.2159i) q^{97} +(-6.32018 + 7.61940i) q^{98} +(12.9084 + 12.9084i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + 2 q^{2} - 6 q^{5} + 8 q^{7} - 4 q^{8} - 164 q^{9} - 6 q^{10} - 2 q^{11} + 18 q^{12} + 4 q^{14} - 32 q^{15} - 20 q^{16} + 4 q^{18} + 30 q^{19} - 4 q^{21} - 16 q^{22} + 10 q^{23} + 12 q^{24} + 12 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) $ 360 * q + 2 * q^2 - 6 * q^5 + 8 * q^7 - 4 * q^8 - 164 * q^9 - 6 * q^10 - 2 * q^11 + 18 * q^12 + 4 * q^14 - 32 * q^15 - 20 * q^16 + 4 * q^18 + 30 * q^19 - 4 * q^21 - 16 * q^22 + 10 * q^23 + 12 * q^24 + 12 * q^25 + 10 * q^28 - 8 * q^29 + 58 * q^30 - 24 * q^31 - 38 * q^32 - 12 * q^35 + 16 * q^36 - 24 * q^38 - 28 * q^39 - 96 * q^40 - 6 * q^42 - 24 * q^43 + 20 * q^44 + 36 * q^45 - 4 * q^46 - 6 * q^47 - 64 * q^50 + 16 * q^51 - 108 * q^52 + 32 * q^53 - 24 * q^54 - 8 * q^56 + 80 * q^57 + 2 * q^58 + 84 * q^59 + 8 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 4 * q^67 + 84 * q^68 + 72 * q^70 + 36 * q^72 - 52 * q^74 - 54 * q^75 - 52 * q^77 + 96 * q^78 - 120 * q^80 - 124 * q^81 - 150 * q^82 + 28 * q^84 - 4 * q^85 + 8 * q^86 + 20 * q^88 + 48 * q^89 + 28 * q^91 + 84 * q^92 - 72 * q^94 - 26 * q^95 - 60 * q^96 + 26 * q^98 - 4 * q^99

Character values

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

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

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 $

$2$	1.40580	+	0.154074i	0.994048	+	0.108947i
$2$	1.40580	+	0.154074i	0.994048	+	0.108947i
$3$	1.70560	−	2.95419i	0.984729	−	1.70560i	0.341595	−	0.939847i	$-0.389033\pi$
$3$	1.70560	−	2.95419i	0.984729	−	1.70560i	0.643134	−	0.765754i	$-0.277634\pi$
$4$	1.95252	+	0.433194i	0.976261	+	0.216597i
$5$	0.0580249	+	2.23531i	0.0259495	+	0.999663i
$5$	0.0580249	+	2.23531i	0.0259495	+	0.999663i
$6$	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
$8$	2.67810	+	0.909815i	0.946852	+	0.321668i
$9$	−4.31815	−	7.47925i	−1.43938	−	2.49308i
$10$	−0.262833	+	3.15134i	−0.0831152	+	0.996540i
$11$	−2.04176	+	0.547088i	−0.615614	+	0.164953i	−0.553133	−	0.833093i	$-0.686568\pi$
$11$	−2.04176	+	0.547088i	−0.615614	+	0.164953i	−0.0624807	+	0.998046i	$0.519901\pi$
$12$	4.60996	−	5.02926i	1.33078	−	1.45182i
$13$	−0.966590			−0.268084			−0.134042	−	0.990976i	$-0.542796\pi$
$13$	−0.966590			−0.268084			−0.134042	+	0.990976i	$0.542796\pi$
$14$	1.40377	+	3.46835i	0.375174	+	0.926954i
$15$	6.70251	+	3.64114i	1.73058	+	0.940138i
$16$	3.62469	+	1.69164i	0.906172	+	0.422910i
$17$	−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	$-0.227230\pi$
$18$	−4.91807	−	11.1796i	−1.15920	−	2.63506i
$19$	0.122340	+	0.0327809i	0.0280667	+	0.00752045i	0.272825	−	0.962064i	$-0.412042\pi$
$19$	0.122340	+	0.0327809i	0.0280667	+	0.00752045i	−0.244758	+	0.969584i	$0.578709\pi$
$20$	−0.855030	+	4.38964i	−0.191190	+	0.981553i
$21$	9.02117	+	0.269364i	1.96858	+	0.0587802i
$22$	−2.95459	+	0.454511i	−0.629920	+	0.0969021i
$23$	−0.676197	+	2.52360i	−0.140997	+	0.526207i	0.858904	+	0.512136i	$0.171146\pi$
$23$	−0.676197	+	2.52360i	−0.140997	+	0.526207i	−0.999901	+	0.0140711i	$0.995521\pi$
$24$	7.25554	−	6.35984i	1.48103	−	1.29820i
$25$	−4.99327	+	0.259408i	−0.998653	+	0.0518815i
$26$	−1.35883	−	0.148927i	−0.266488	−	0.0292069i
$27$	−19.2265			−3.70015
$28$	1.43904	+	5.09207i	0.271952	+	0.962311i
$29$	1.42218	+	1.42218i	0.264093	+	0.264093i	0.826714	−	0.562622i	$-0.190207\pi$
$29$	1.42218	+	1.42218i	0.264093	+	0.264093i	−0.562622	+	0.826714i	$0.690207\pi$
$30$	8.86135	+	6.15138i	1.61785	+	1.12308i
$31$	−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	$0.929304\pi$
$32$	4.83493	+	2.93657i	0.854703	+	0.519118i
$33$	−1.86623	+	6.96485i	−0.324868	+	1.21243i
$34$	−0.774543	−	5.03499i	−0.132833	−	0.863493i
$35$	−5.13497	+	2.93805i	−0.867968	+	0.496621i
$36$	−5.19132	−	16.4740i	−0.865219	−	2.74567i
$37$	−4.58027	+	2.64442i	−0.752992	+	0.434740i	−0.826774	−	0.562534i	$-0.809826\pi$
$37$	−4.58027	+	2.64442i	−0.752992	+	0.434740i	0.0737820	+	0.997274i	$0.476493\pi$
$38$	0.166934	+	0.0649326i	0.0270803	+	0.0105335i
$39$	−1.64862	+	2.85549i	−0.263990	+	0.457244i
$40$	−1.87833	+	6.03920i	−0.296990	+	0.954881i
$41$	8.15686			1.27389			0.636944	−	0.770910i	$-0.280198\pi$
$41$	8.15686			1.27389			0.636944	+	0.770910i	$0.280198\pi$
$42$	12.6404	+	1.76860i	1.95046	+	0.272901i
$43$	−0.958523			−0.146173			−0.0730867	−	0.997326i	$-0.523285\pi$
$43$	−0.958523			−0.146173			−0.0730867	+	0.997326i	$0.523285\pi$
$44$	−4.22358	+	0.183724i	−0.636728	+	0.0276974i
$45$	16.4679	−	10.0864i	2.45489	−	1.50359i
$46$	−1.33942	+	3.44348i	−0.197486	+	0.507714i
$47$	−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	$0.692983\pi$
$48$	11.1797	−	7.82274i	1.61365	−	1.12911i
$49$	−3.85547	+	5.84255i	−0.550781	+	0.834650i
$50$	−7.05948	−	0.404660i	−0.998361	−	0.0572275i
$51$	−11.8690	−	3.18028i	−1.66199	−	0.445329i
$52$	−1.88729	−	0.418721i	−0.261720	−	0.0580661i
$53$	1.21552	−	2.10535i	0.166965	−	0.289191i	−0.770386	−	0.637577i	$-0.779937\pi$
$53$	1.21552	−	2.10535i	0.166965	−	0.289191i	0.937351	+	0.348386i	$0.113270\pi$
$54$	−27.0286	−	2.96232i	−3.67813	−	0.403120i
$55$	−1.34139	−	4.53223i	−0.180873	−	0.611126i
$56$	1.23843	+	7.38013i	0.165493	+	0.986211i
$57$	0.305504	−	0.305504i	0.0404650	−	0.0404650i
$58$	1.78018	+	2.21842i	0.233749	+	0.291293i
$59$	6.94519	−	1.86096i	0.904186	−	0.242276i	0.223373	−	0.974733i	$-0.428293\pi$
$59$	6.94519	−	1.86096i	0.904186	−	0.242276i	0.680813	+	0.732457i	$0.261627\pi$
$60$	11.5095	+	10.0129i	1.48587	+	1.29266i
$61$	3.02951	−	11.3063i	0.387890	−	1.44762i	−0.445672	−	0.895197i	$-0.647035\pi$
$61$	3.02951	−	11.3063i	0.387890	−	1.44762i	0.833561	−	0.552427i	$-0.186298\pi$
$62$	−9.32900	−	6.84146i	−1.18478	−	0.868866i
$63$	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
$66$	−3.69664	+	9.50362i	−0.455025	+	1.16982i
$67$	2.81304	−	4.87233i	0.343667	−	0.595250i	−0.641443	−	0.767170i	$-0.721664\pi$
$67$	2.81304	−	4.87233i	0.343667	−	0.595250i	0.985111	+	0.171921i	$0.0549974\pi$
$68$	−0.313088	−	7.19750i	−0.0379675	−	0.872825i
$69$	6.30187	+	6.30187i	0.758656	+	0.758656i
$70$	−7.67139	+	3.33913i	−0.916907	+	0.399102i
$71$			14.4961i			1.72038i	0.509977	+	0.860188i	$0.329654\pi$
$71$			14.4961i			1.72038i	−0.509977	+	0.860188i	$0.670346\pi$
$72$	−4.75971	−	23.9589i	−0.560937	−	2.82359i
$73$	1.00990	+	3.76901i	0.118200	+	0.441129i	0.999506	−	0.0314165i	$-0.0100018\pi$
$73$	1.00990	+	3.76901i	0.118200	+	0.441129i	−0.881306	+	0.472546i	$0.843335\pi$
$74$	−6.84636	+	3.01181i	−0.795873	+	0.350116i
$75$	−7.75018	+	15.1935i	−0.894914	+	1.75439i
$76$	0.224671	+	0.117002i	0.0257715	+	0.0134211i
$77$	−3.83474	−	4.07079i	−0.437009	−	0.463910i
$78$	−2.75758	+	3.76022i	−0.312234	+	0.425761i
$79$	−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	$0.605297\pi$
$80$	−3.57103	+	8.20047i	−0.399253	+	0.916841i
$81$	−19.8384	+	34.3611i	−2.20426	+	3.81789i
$82$	11.4669	+	1.25676i	1.26630	+	0.138786i
$83$	7.64983			0.839678			0.419839	−	0.907599i	$-0.362086\pi$
$83$	7.64983			0.839678			0.419839	+	0.907599i	$0.362086\pi$
$84$	17.4973	+	4.43386i	1.90912	+	0.483773i
$85$	7.72348	−	2.28589i	0.837730	−	0.247939i
$86$	−1.34749	−	0.147684i	−0.145303	−	0.0159251i
$87$	6.62707	−	1.77572i	0.710497	−	0.190377i
$88$	−5.96579	−	0.392466i	−0.635956	−	0.0418371i
$89$	3.01621	−	1.74141i	0.319718	−	0.184589i	−0.331549	−	0.943438i	$-0.607571\pi$
$89$	3.01621	−	1.74141i	0.319718	−	0.184589i	0.651267	+	0.758849i	$0.274238\pi$
$90$	24.7046	−	11.6421i	2.60409	−	1.22719i
$91$	−1.21201	−	2.25191i	−0.127053	−	0.236065i
$92$	−2.41350	+	4.63447i	−0.251625	+	0.483176i
$93$	−24.1662	+	13.9524i	−2.50592	+	1.44679i
$94$	−6.10289	−	2.37385i	−0.629465	−	0.244844i
$95$	−0.0661768	+	0.275370i	−0.00678960	+	0.0282524i
$96$	16.9216	−	9.27467i	1.72706	−	0.946592i
$97$	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	$-0.0120939\pi$
$98$	−6.32018	+	7.61940i	−0.638435	+	0.769676i
$99$	12.9084	+	12.9084i	1.29735	+	1.29735i
$100$	−9.86184	−	1.65655i	−0.986184	−	0.165655i
$101$	2.06384	+	7.70237i	0.205360	+	0.766415i	0.989339	+	0.145628i	$0.0465202\pi$
$101$	2.06384	+	7.70237i	0.205360	+	0.766415i	−0.783979	+	0.620787i	$0.786813\pi$
$102$	−16.1954	−	6.29953i	−1.60358	−	0.623746i
$103$	1.67776	+	0.449553i	0.165314	+	0.0442958i	0.340527	−	0.940235i	$-0.389395\pi$
$103$	1.67776	+	0.449553i	0.165314	+	0.0442958i	−0.175213	+	0.984531i	$0.556061\pi$
$104$	−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
$107$	8.29514	−	4.78920i	0.801922	−	0.462990i	−0.0422209	−	0.999108i	$-0.513443\pi$
$107$	8.29514	−	4.78920i	0.801922	−	0.462990i	0.844143	+	0.536119i	$0.180110\pi$
$108$	−37.5403	−	8.32882i	−3.61231	−	0.801441i
$109$	17.8034	−	4.77041i	1.70526	−	0.456923i	0.731004	−	0.682373i	$-0.239052\pi$
$109$	17.8034	−	4.77041i	1.70526	−	0.456923i	0.974255	+	0.225451i	$0.0723855\pi$
$110$	−1.18742	−	6.57806i	−0.113216	−	0.627194i
$111$			18.0413i			1.71240i
$112$	0.603898	+	10.5658i	0.0570630	+	0.998371i
$113$	−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	$0.331878\pi$
$114$	0.476546	−	0.382406i	0.0446326	−	0.0358156i
$115$	−5.68028	−	1.36508i	−0.529689	−	0.127295i
$116$	2.16076	+	3.39292i	0.200622	+	0.315025i
$117$	4.17388	+	7.22937i	0.385875	+	0.668356i
$118$	10.0502	−	1.54605i	0.925199	−	0.142326i
$119$	6.93714	−	6.53488i	0.635926	−	0.599051i
$120$	14.6372	+	15.8494i	1.33619	+	1.44684i
$121$	−5.65680	+	3.26596i	−0.514255	+	0.296905i
$122$	6.00089	−	15.4276i	0.543295	−	1.39675i
$123$	13.9123	−	24.0969i	1.25443	−	2.17274i
$124$	−12.0606	−	11.0551i	−1.08307	−	0.992773i
$125$	−0.869592	−	11.1465i	−0.0777786	−	0.996971i
$126$	19.8789	−	25.4760i	1.77096	−	2.26958i
$127$	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	$0.747756\pi$
$128$	8.16820	+	7.82818i	0.721974	+	0.691920i
$129$	−1.63486	+	2.83166i	−0.143941	+	0.249313i
$130$	0.254052	−	3.04605i	0.0222818	−	0.267156i
$131$	−1.89501	+	7.07228i	−0.165568	+	0.617908i	0.832399	+	0.554177i	$0.186967\pi$
$131$	−1.89501	+	7.07228i	−0.165568	+	0.617908i	−0.997967	+	0.0637316i	$0.979700\pi$
$132$	−6.66098	+	12.7906i	−0.579764	+	1.11328i
$133$	0.0770309	+	0.326125i	0.00667942	+	0.0282786i
$134$	4.70526	−	6.41608i	0.406472	−	0.554265i
$135$	−1.11562	−	42.9774i	−0.0960171	−	3.69890i
$136$	0.668812	−	10.1664i	0.0573501	−	0.871766i
$137$	4.21896	+	15.7454i	0.360450	+	1.34522i	0.873485	+	0.486851i	$0.161854\pi$
$137$	4.21896	+	15.7454i	0.360450	+	1.34522i	−0.513035	+	0.858368i	$0.671479\pi$
$138$	7.88819	+	9.83010i	0.671487	+	0.836794i
$139$	−11.0132	−	11.0132i	−0.934128	−	0.934128i	0.0638330	−	0.997961i	$-0.479667\pi$
$139$	−11.0132	−	11.0132i	−0.934128	−	0.934128i	−0.997961	+	0.0638330i	$0.979667\pi$
$140$	−11.2989	+	3.51217i	−0.954930	+	0.296832i
$141$	−11.1688	+	11.1688i	−0.940584	+	0.940584i
$142$	−2.23348	+	20.3786i	−0.187430	+	1.71014i
$143$	1.97354	−	0.528810i	0.165036	−	0.0442213i
$144$	−2.99972	−	34.4147i	−0.249977	−	2.86789i
$145$	−3.09650	+	3.26155i	−0.257151	+	0.270857i
$146$	0.839010	+	5.45406i	0.0694370	+	0.451381i
$147$	10.6841	+	21.3548i	0.881210	+	1.76132i
$148$	−10.0886	+	3.17915i	−0.829280	+	0.261324i
$149$	4.79340	+	1.28439i	0.392690	+	0.105221i	0.449761	−	0.893149i	$-0.351509\pi$
$149$	4.79340	+	1.28439i	0.392690	+	0.105221i	−0.0570704	+	0.998370i	$0.518176\pi$
$150$	−13.2361	+	20.1648i	−1.08072	+	1.64645i
$151$	−1.43616	−	0.829167i	−0.116873	−	0.0674767i	0.440424	−	0.897790i	$-0.354828\pi$
$151$	−1.43616	−	0.829167i	−0.116873	−	0.0674767i	−0.557297	+	0.830313i	$0.688161\pi$
$152$	0.297814	+	0.199097i	0.0241559	+	0.0161489i
$153$	−21.9976	+	21.9976i	−1.77840	+	1.77840i
$154$	−4.76366	−	6.31354i	−0.383867	−	0.508760i
$155$	8.73174	−	16.0731i	0.701350	−	1.29103i
$156$	−4.45594	+	4.86123i	−0.356761	+	0.389210i
$157$	4.61343	+	2.66356i	0.368192	+	0.212576i	0.672668	−	0.739944i	$-0.265148\pi$
$157$	4.61343	+	2.66356i	0.368192	+	0.212576i	−0.304477	+	0.952520i	$0.598482\pi$
$158$	−17.3547	+	7.63456i	−1.38066	+	0.607373i
$159$	−4.14639	−	7.18176i	−0.328830	−	0.569551i
$160$	−6.28362	+	10.9780i	−0.496764	+	0.867886i
$161$	−6.72725	+	1.58898i	−0.530181	+	0.125229i
$162$	−33.1828	+	45.2480i	−2.60709	+	3.55502i
$163$	11.9136	−	6.87832i	0.933146	−	0.538752i	0.0453407	−	0.998972i	$-0.485563\pi$
$163$	11.9136	−	6.87832i	0.933146	−	0.538752i	0.887805	+	0.460220i	$0.152229\pi$
$164$	15.9265	+	3.53350i	1.24365	+	0.275920i
$165$	−15.6769	−	3.76747i	−1.22045	−	0.293297i
$166$	10.7541	+	1.17864i	0.834680	+	0.0914804i
$167$	4.43116	+	4.43116i	0.342893	+	0.342893i	0.857454	−	0.514561i	$-0.172045\pi$
$167$	4.43116	+	4.43116i	0.342893	+	0.342893i	−0.514561	+	0.857454i	$0.672045\pi$
$168$	23.9146	+	8.92898i	1.84505	+	0.688886i
$169$	−12.0657			−0.928131
$170$	11.2098	−	2.02350i	0.859755	−	0.155196i
$171$	−0.283105	−	1.05656i	−0.0216496	−	0.0807974i
$172$	−1.87154	−	0.415226i	−0.142703	−	0.0316607i
$173$	−3.14410	−	5.44575i	−0.239042	−	0.414032i	0.721398	−	0.692521i	$-0.243500\pi$
$173$	−3.14410	−	5.44575i	−0.239042	−	0.414032i	−0.960440	+	0.278488i	$0.910167\pi$
$174$	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
$178$	4.50848	−	1.98335i	0.337925	−	0.148658i
$179$	−7.49701	+	2.00882i	−0.560353	+	0.150146i	−0.527868	−	0.849326i	$-0.677009\pi$
$179$	−7.49701	+	2.00882i	−0.560353	+	0.150146i	−0.0324844	+	0.999472i	$0.510342\pi$
$180$	36.5234	−	12.5601i	2.72229	−	0.936177i
$181$	12.0645	−	12.0645i	0.896746	−	0.896746i	−0.0984009	−	0.995147i	$-0.531373\pi$
$181$	12.0645	−	12.0645i	0.896746	−	0.896746i	0.995147	+	0.0984009i	$0.0313728\pi$
$182$	−1.35687	−	3.35247i	−0.100578	−	0.248501i
$183$	−28.2338	−	28.2338i	−2.08710	−	2.08710i
$184$	−4.10694	+	6.14325i	−0.302767	+	0.452887i
$185$	−6.17688	−	10.0849i	−0.454133	−	0.741457i
$186$	−36.1225	+	15.8908i	−2.64863	+	1.16517i
$187$	3.80709	+	6.59407i	0.278402	+	0.482206i
$188$	−8.21367	−	4.27745i	−0.599043	−	0.311965i
$189$	−24.1082	−	44.7930i	−1.75361	−	3.25821i
$190$	−0.135459	+	0.376918i	−0.00982719	+	0.0273445i
$191$	−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	$0.859799\pi$
$192$	25.2174	−	10.4311i	1.81991	−	0.752800i
$193$	−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	$-0.246769\pi$
$194$	15.9354	−	12.7874i	1.14410	−	0.918082i
$195$	−6.47858	−	3.51949i	−0.463940	−	0.252036i
$196$	−10.0588	+	9.73755i	−0.718488	+	0.695539i
$197$		−	7.88589i		−	0.561847i	−0.959730	−	0.280923i	$-0.909359\pi$
$197$		−	7.88589i		−	0.561847i	0.959730	−	0.280923i	$-0.0906406\pi$
$198$	16.1578	+	20.1355i	1.14828	+	1.43097i
$199$	−7.02730	−	4.05722i	−0.498152	−	0.287608i	0.229798	−	0.973238i	$-0.426193\pi$
$199$	−7.02730	−	4.05722i	−0.498152	−	0.287608i	−0.727950	+	0.685630i	$0.759527\pi$
$200$	−13.6085	−	3.84823i	−0.962266	−	0.272111i
$201$	−9.59584	−	16.6205i	−0.676839	−	1.17232i
$202$	1.71461	+	11.1459i	0.120639	+	0.784226i
$203$	−1.53005	+	5.09661i	−0.107389	+	0.357712i
$204$	−21.7968	−	11.3511i	−1.52608	−	0.794739i
$205$	0.473301	+	18.2332i	0.0330568	+	1.27346i
$206$	2.28932	+	0.890479i	0.159504	+	0.0620426i
$207$	21.7946	−	5.83984i	1.51483	−	0.405897i
$208$	−3.50359	−	1.63512i	−0.242930	−	0.113375i
$209$	−0.267723			−0.0185188
$210$	−3.21992	+	28.3579i	−0.222196	+	1.95688i
$211$	−4.51019	+	4.51019i	−0.310494	+	0.310494i	−0.845101	−	0.534607i	$-0.820460\pi$
$211$	−4.51019	+	4.51019i	−0.310494	+	0.310494i	0.534607	+	0.845101i	$0.320460\pi$
$212$	3.28536	−	3.58418i	0.225639	−	0.246162i
$213$	42.8243	+	24.7246i	2.93427	+	1.69410i
$214$	12.3992	−	5.45457i	0.847590	−	0.372867i
$215$	−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
$218$	25.7630	−	3.96318i	1.74489	−	0.268420i
$219$	12.8569	+	3.44498i	0.868785	+	0.232790i
$220$	−0.655753	−	9.43036i	−0.0442108	−	0.635795i
$221$	0.901157	+	3.36317i	0.0606184	+	0.226231i
$222$	−2.77970	+	25.3624i	−0.186561	+	1.70221i
$223$	−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	$-0.522991\pi$
$224$	−0.778955	+	14.9463i	−0.0520461	+	0.998645i
$225$	23.5018	+	36.2257i	1.56679	+	2.41505i
$226$	−5.96571	+	4.78720i	−0.396833	+	0.318440i
$227$	−17.3230	−	10.0015i	−1.14977	−	0.663820i	−0.200938	−	0.979604i	$-0.564399\pi$
$227$	−17.3230	−	10.0015i	−1.14977	−	0.663820i	−0.948831	+	0.315784i	$0.897732\pi$
$228$	0.728845	−	0.464161i	0.0482690	−	0.0307398i
$229$	−1.33777	+	4.99263i	−0.0884024	+	0.329922i	−0.995937	−	0.0900557i	$-0.971295\pi$
$229$	−1.33777	+	4.99263i	−0.0884024	+	0.329922i	0.907534	+	0.419978i	$0.137962\pi$
$230$	−7.77499	−	2.79421i	−0.512668	−	0.184245i
$231$	−18.5664	+	4.38540i	−1.22158	+	0.288538i
$232$	2.51483	+	5.10268i	0.165107	+	0.335007i
$233$	5.26886	−	19.6637i	0.345175	−	1.28821i	−0.547233	−	0.836980i	$-0.684319\pi$
$233$	5.26886	−	19.6637i	0.345175	−	1.28821i	0.892408	−	0.451230i	$-0.149014\pi$
$234$	4.75376	+	10.8061i	0.310763	+	0.706417i
$235$	2.41934	−	10.0672i	0.157820	−	0.656710i
$236$	14.3668	−	0.624949i	0.935198	−	0.0406807i
$237$			45.7324i			2.97064i
$238$	10.7591	−	8.11787i	0.697406	−	0.526203i
$239$			4.88879i			0.316230i	0.987421	+	0.158115i	$0.0505416\pi$
$239$			4.88879i			0.316230i	−0.987421	+	0.158115i	$0.949458\pi$
$240$	18.1350	+	24.5362i	1.17061	+	1.58381i
$241$	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	$0.590656\pi$
$242$	−8.45551	+	3.71970i	−0.543541	+	0.239111i
$243$	38.8328	+	67.2605i	2.49113	+	4.31476i
$244$	10.8130	−	20.7634i	0.692232	−	1.32924i
$245$	−13.2837	−	8.27917i	−0.848661	−	0.528936i
$246$	23.2706	−	31.7318i	1.48368	−	2.02314i
$247$	−0.118253	−	0.0316857i	−0.00752423	−	0.00201611i
$248$	−15.2514	−	17.3994i	−0.968465	−	1.10486i
$249$	13.0476	−	22.5990i	0.826856	−	1.43216i
$250$	0.494916	−	15.8036i	0.0313012	−	0.999510i
$251$	−3.24859	+	3.24859i	−0.205049	+	0.205049i	−0.802159	−	0.597110i	$-0.796316\pi$
$251$	−3.24859	+	3.24859i	−0.205049	+	0.205049i	0.597110	+	0.802159i	$0.296316\pi$
$252$	31.8709	−	32.7512i	2.00768	−	2.06313i
$253$		−	5.52253i		−	0.347198i
$254$	0.140622	+	0.175240i	0.00882338	+	0.0109955i
$255$	6.42024	−	26.7154i	0.402051	−	1.67299i
$256$	10.2767	+	12.2633i	0.642294	+	0.766458i
$257$	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	$0.378516\pi$
$258$	−2.73456	+	3.72884i	−0.170246	+	0.232147i
$259$	−11.9040	−	7.35504i	−0.739681	−	0.457020i
$260$	0.826463	−	4.24298i	0.0512551	−	0.263139i
$261$	4.49567	−	16.7781i	0.278275	−	1.03854i
$262$	−3.75366	+	9.65021i	−0.231902	+	0.596192i
$263$	−6.11137	+	1.63754i	−0.376843	+	0.100975i	−0.442269	−	0.896883i	$-0.645826\pi$
$263$	−6.11137	+	1.63754i	−0.376843	+	0.100975i	0.0654254	+	0.997857i	$0.479160\pi$
$264$	−11.3347	+	16.9547i	−0.697601	+	1.04349i
$265$	4.77664	+	2.59491i	0.293427	+	0.159404i
$266$	0.0580421	+	0.470334i	0.00355879	+	0.0288380i
$267$		−	11.8806i		−	0.727081i
$268$	7.60318	−	8.29474i	0.464438	−	0.506682i
$269$	3.23609	+	12.0773i	0.197308	+	0.736364i	0.991657	+	0.128902i	$0.0411454\pi$
$269$	3.23609	+	12.0773i	0.197308	+	0.736364i	−0.794349	+	0.607461i	$0.792188\pi$
$270$	5.05338	−	60.5893i	0.307539	−	3.68735i
$271$	−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	$0.439720\pi$
$272$	2.50660	−	14.1889i	0.151985	−	0.860329i
$273$	−8.71977	−	0.260365i	−0.527745	−	0.0157580i
$274$	3.50504	+	22.7848i	0.211747	+	1.37648i
$275$	10.0531	−	3.26140i	0.606227	−	0.196670i
$276$	9.57461	+	15.0345i	0.576324	+	0.904969i
$277$	12.4542	+	7.19044i	0.748301	+	0.432032i	0.825080	−	0.565017i	$-0.191130\pi$
$277$	12.4542	+	7.19044i	0.748301	+	0.432032i	−0.0767789	+	0.997048i	$0.524464\pi$
$278$	−13.7855	−	17.1792i	−0.826797	−	1.03034i
$279$			70.6478i			4.22957i
$280$	−16.4250	+	3.19652i	−0.981584	+	0.191029i
$281$			2.70972i			0.161649i	0.996728	+	0.0808243i	$0.0257553\pi$
$281$			2.70972i			0.161649i	−0.996728	+	0.0808243i	$0.974245\pi$
$282$	−17.4219	+	13.9802i	−1.03746	+	0.832511i
$283$	−13.3847	−	7.72769i	−0.795641	−	0.459363i	0.0463038	−	0.998927i	$-0.485256\pi$
$283$	−13.3847	−	7.72769i	−0.795641	−	0.459363i	−0.841945	+	0.539564i	$0.818589\pi$
$284$	−6.27964	+	28.3040i	−0.372628	+	1.67954i
$285$	0.700624	+	0.665170i	0.0415014	+	0.0394013i
$286$	2.85588	−	0.439326i	0.168872	−	0.0259779i
$287$	10.2279	+	19.0034i	0.603734	+	1.12174i
$288$	1.08542	−	48.8422i	0.0639590	−	2.87805i
$289$	3.48532	−	2.01225i	0.205019	−	0.118368i
$290$	−4.85557	+	4.10798i	−0.285129	+	0.241229i
$291$	−12.7554	−	47.6037i	−0.747734	−	2.79058i
$292$	0.339147	+	7.79656i	0.0198471	+	0.456259i
$293$			8.90182i			0.520050i	0.965602	+	0.260025i	$0.0837308\pi$
$293$			8.90182i			0.520050i	−0.965602	+	0.260025i	$0.916269\pi$
$294$	11.7294	+	31.6667i	0.684075	+	1.84684i
$295$	4.56282	+	15.4167i	0.265658	+	0.897595i
$296$	−14.6724	+	2.91483i	−0.852814	+	0.169421i
$297$	39.2560	−	10.5186i	2.27786	−	0.610352i
$298$	6.54064	+	2.54412i	0.378889	+	0.147377i
$299$	0.653606	−	2.43929i	0.0377990	−	0.141068i
$300$	−21.7141	+	26.3083i	−1.25367	+	1.51891i
$301$	−1.20189	−	2.23312i	−0.0692759	−	0.128715i
$302$	−1.89119	−	1.38691i	−0.108826	−	0.0798080i
$303$	26.2744	+	7.04019i	1.50942	+	0.404448i
$304$	0.387990	+	0.325775i	0.0222528	+	0.0186845i
$305$	25.4489	+	6.11587i	1.45720	+	0.350194i
$306$	−34.3133	+	27.5348i	−1.96156	+	1.57406i
$307$			25.6877i			1.46607i	0.680189	+	0.733037i	$0.261898\pi$
$307$			25.6877i			1.46607i	−0.680189	+	0.733037i	$0.738102\pi$
$308$	−5.72398	−	9.60950i	−0.326154	−	0.547552i
$309$	4.18965	−	4.18965i	0.238341	−	0.238341i
$310$	14.7515	−	21.2502i	0.837829	−	1.20693i
$311$	9.40948	−	16.2977i	0.533563	−	0.924158i	−0.465669	−	0.884959i	$-0.654186\pi$
$311$	9.40948	−	16.2977i	0.533563	−	0.924158i	0.999231	−	0.0391987i	$-0.0124805\pi$
$312$	−7.01313	+	6.14736i	−0.397040	+	0.348025i
$313$	−5.14286	−	1.37802i	−0.290691	−	0.0778905i	0.110526	−	0.993873i	$-0.464746\pi$
$313$	−5.14286	−	1.37802i	−0.290691	−	0.0778905i	−0.401218	+	0.915983i	$0.631413\pi$
$314$	6.07515	+	4.45524i	0.342841	+	0.251424i
$315$	44.1479	+	25.7188i	2.48745	+	1.44909i
$316$	−25.5734	+	8.05873i	−1.43862	+	0.453339i
$317$	−7.75152	−	13.4260i	−0.435369	−	0.754080i	0.561957	−	0.827166i	$-0.310049\pi$
$317$	−7.75152	−	13.4260i	−0.435369	−	0.754080i	−0.997326	+	0.0730859i	$0.976715\pi$
$318$	−4.72245	−	10.7349i	−0.264822	−	0.601985i
$319$	−3.68181	−	2.12570i	−0.206142	−	0.119016i
$320$	−10.5249	+	14.4647i	−0.588360	+	0.808599i
$321$		−	32.6739i		−	1.82368i
$322$	−9.70195	+	1.19728i	−0.540669	+	0.0667219i
$323$		−	0.456233i		−	0.0253855i
$324$	−53.6198	+	58.4969i	−2.97888	+	3.24983i
$325$	4.82644	−	0.250741i	0.267723	−	0.0139086i
$326$	17.8079	−	7.83394i	0.986287	−	0.433882i
$327$	16.2728	−	60.7311i	0.899890	−	3.35844i
$328$	21.8449	+	7.42124i	1.20618	+	0.409769i
$329$	−2.81615	−	11.9227i	−0.155259	−	0.657320i
$330$	−21.4581	−	7.71170i	−1.18123	−	0.424515i
$331$	−9.31786	+	34.7747i	−0.512156	+	1.91139i	−0.115870	+	0.993264i	$0.536965\pi$
$331$	−9.31786	+	34.7747i	−0.512156	+	1.91139i	−0.396286	+	0.918127i	$0.629701\pi$
$332$	14.9365	+	3.31386i	0.819745	+	0.181872i
$333$	39.5566	+	22.8380i	2.16769	+	1.25151i
$334$	5.54658	+	6.91203i	0.303495	+	0.378209i
$335$	11.0544	+	6.00531i	0.603967	+	0.328105i
$336$	32.2432	+	16.2369i	1.75901	+	0.885798i
$337$	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	$0.505219\pi$
$338$	−16.9619	−	1.85901i	−0.922606	−	0.101117i
$339$	4.77521	+	17.8213i	0.259354	+	0.967921i
$340$	16.0705	−	1.11748i	0.871546	−	0.0606041i
$341$	16.7023	+	4.47536i	0.904479	+	0.242354i
$342$	−0.235199	−	1.52893i	−0.0127181	−	0.0826751i
$343$	−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
$346$	−3.58092	−	8.14003i	−0.192511	−	0.437611i
$347$	−6.69314	−	3.86429i	−0.359306	−	0.207446i	0.309470	−	0.950909i	$-0.399848\pi$
$347$	−6.69314	−	3.86429i	−0.359306	−	0.207446i	−0.668777	+	0.743463i	$0.733182\pi$
$348$	13.7087	−	0.596324i	0.734865	−	0.0319663i
$349$	−6.91125	+	6.91125i	−0.369951	+	0.369951i	−0.867459	−	0.497508i	$-0.834248\pi$
$349$	−6.91125	+	6.91125i	−0.369951	+	0.369951i	0.497508	+	0.867459i	$0.334248\pi$
$350$	−7.90913	−	16.9542i	−0.422761	−	0.906241i
$351$	18.5842			0.991951
$352$	−11.4783	−	3.35064i	−0.611797	−	0.178590i
$353$	−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	$0.471969\pi$
$354$	12.5744	−	32.3272i	0.668320	−	1.71817i
$355$	−32.4035	+	0.841137i	−1.71980	+	0.0446429i
$356$	6.64358	−	2.09354i	0.352109	−	0.110957i
$357$	−7.47326	−	31.6395i	−0.395527	−	1.67454i
$358$	−10.8488	+	1.66889i	−0.573375	+	0.0882036i
$359$	0.246788	+	0.427450i	0.0130250	+	0.0225599i	0.872464	−	0.488678i	$-0.162521\pi$
$359$	0.246788	+	0.427450i	0.0130250	+	0.0225599i	−0.859439	+	0.511238i	$0.829187\pi$
$360$	53.2796	−	12.0297i	2.80808	−	0.634019i
$361$	−16.4406	−	9.49198i	−0.865294	−	0.499578i
$362$	18.8190	−	15.1014i	0.989106	−	0.793710i
$363$			22.2817i			1.16948i
$364$	−1.39096	−	4.92194i	−0.0729060	−	0.257980i
$365$	−8.36632	+	2.47615i	−0.437913	+	0.129607i
$366$	−35.3408	−	44.0410i	−1.84730	−	2.30206i
$367$	−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	$-0.222664\pi$
$368$	−6.72003	+	8.00338i	−0.350306	+	0.417205i
$369$	−35.2225	−	61.0072i	−1.83361	−	3.17591i
$370$	−7.12961	−	15.1290i	−0.370651	−	0.786520i
$371$	6.42907	+	0.191967i	0.333781	+	0.00996641i
$372$	−53.2292	+	16.7737i	−2.75981	+	0.869675i
$373$	−9.92587	−	17.1921i	−0.513942	−	0.890173i	−0.999869	−	0.0161742i	$-0.994851\pi$
$373$	−9.92587	−	17.1921i	−0.513942	−	0.890173i	0.485927	−	0.873999i	$-0.338482\pi$
$374$	4.33601	+	9.85649i	0.224210	+	0.509667i
$375$	−34.4119	−	16.4425i	−1.77702	−	0.849087i
$376$	−10.8877	−	7.27873i	−0.561490	−	0.375372i
$377$	−1.37467	−	1.37467i	−0.0707990	−	0.0707990i
$378$	−26.9897	−	66.6843i	−1.38820	−	3.42987i
$379$	12.0600	−	12.0600i	0.619480	−	0.619480i	−0.325918	−	0.945398i	$-0.605673\pi$
$379$	12.0600	−	12.0600i	0.619480	−	0.619480i	0.945398	+	0.325918i	$0.105673\pi$
$380$	−0.248500	+	0.508999i	−0.0127478	+	0.0261111i
$381$	0.523492	−	0.140269i	0.0268193	−	0.00718622i
$382$	−1.30723	−	2.97155i	−0.0668836	−	0.152038i
$383$	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
$387$	4.13904	+	7.16903i	0.210399	+	0.364422i
$388$	24.3721	−	15.5212i	1.23731	−	0.787972i
$389$	−2.19796	−	8.20289i	−0.111441	−	0.415903i	0.887555	−	0.460702i	$-0.152402\pi$
$389$	−2.19796	−	8.20289i	−0.111441	−	0.415903i	−0.998996	+	0.0447983i	$0.985735\pi$
$390$	−8.56529	−	5.94586i	−0.433720	−	0.301080i
$391$	9.41107			0.475938
$392$	−15.6410	+	12.1392i	−0.789988	+	0.613122i
$393$	17.6607	+	17.6607i	0.890865	+	0.890865i
$394$	1.21501	−	11.0860i	0.0612115	−	0.558502i
$395$	−15.6576	−	25.5639i	−0.787820	−	1.28626i
$396$	19.6121	+	30.7958i	0.985547	+	1.54755i
$397$	12.8542	−	7.42137i	0.645134	−	0.372468i	−0.141456	−	0.989945i	$-0.545178\pi$
$397$	12.8542	−	7.42137i	0.645134	−	0.372468i	0.786589	+	0.617477i	$0.211845\pi$
$398$	−9.25384	−	6.78634i	−0.463853	−	0.340169i
$399$	1.09482	+	0.328676i	0.0548095	+	0.0164544i
$400$	−18.5378	−	7.50654i	−0.926892	−	0.375327i
$401$	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	$0.748067\pi$
$402$	−10.9290	−	24.8435i	−0.545089	−	1.23908i
$403$	6.84769	+	3.95352i	0.341108	+	0.196939i
$404$	0.693083	+	15.9331i	0.0344821	+	0.792701i
$405$	−77.9589	−	42.3512i	−3.87381	−	2.10445i
$406$	−2.93620	+	6.92904i	−0.145721	+	0.343883i
$407$	7.90508	−	7.90508i	0.391840	−	0.391840i
$408$	−28.8929	−	19.3157i	−1.43041	−	0.956270i
$409$	−33.5667	−	19.3797i	−1.65977	−	0.958267i	−0.972821	−	0.231557i	$-0.925618\pi$
$409$	−33.5667	−	19.3797i	−1.65977	−	0.958267i	−0.686945	−	0.726709i	$-0.741049\pi$
$410$	−2.14390	+	25.7050i	−0.105879	+	1.26948i
$411$	53.7106	+	14.3917i	2.64935	+	0.709891i
$412$	3.08111	+	1.60456i	0.151796	+	0.0790508i
$413$	13.0441	+	13.8471i	0.641860	+	0.681371i
$414$	31.5385	−	4.85164i	1.55003	−	0.238445i
$415$	0.443881	+	17.0998i	0.0217892	+	0.839396i
$416$	−4.67340	−	2.83846i	−0.229132	−	0.139167i
$417$	−51.3192	+	13.7509i	−2.51311	+	0.673386i
$418$	−0.376363	−	0.0412492i	−0.0184085	−	0.00201756i
$419$	9.45219	−	9.45219i	0.461770	−	0.461770i	−0.437466	−	0.899235i	$-0.644124\pi$
$419$	9.45219	−	9.45219i	0.461770	−	0.461770i	0.899235	+	0.437466i	$0.144124\pi$
$420$	−8.89578	+	39.3694i	−0.434070	+	1.92103i
$421$	−4.33136	−	4.33136i	−0.211098	−	0.211098i	0.593636	−	0.804734i	$-0.297692\pi$
$421$	−4.33136	−	4.33136i	−0.211098	−	0.211098i	−0.804734	+	0.593636i	$0.797692\pi$
$422$	−7.03531	+	5.64550i	−0.342473	+	0.274819i
$423$	10.3500	+	38.6266i	0.503232	+	1.87809i
$424$	5.17077	−	4.53243i	0.251115	−	0.220114i
$425$	5.55784	+	17.1318i	0.269595	+	0.831014i
$426$	56.3928	+	41.3559i	2.73224	+	2.00370i
$427$	30.1396	−	7.11897i	1.45856	−	0.344511i
$428$	18.2711	−	5.75762i	0.883167	−	0.278305i
$429$	1.80388	−	6.73216i	0.0870920	−	0.325032i
$430$	0.251932	−	3.02063i	0.0121492	−	0.145668i
$431$	−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	$0.260301\pi$
$432$	−69.6902	−	32.5244i	−3.35297	−	1.56483i
$433$	−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	$0.997993\pi$
$434$	4.24125	−	30.3127i	0.203586	−	1.45506i
$435$	4.35382	+	14.7106i	0.208750	+	0.705317i
$436$	36.8281	−	1.60200i	1.76375	−	0.0767221i
$437$	−0.165452	+	0.286571i	−0.00791463	+	0.0137085i
$438$	17.5433	+	6.82385i	0.838252	+	0.326056i
$439$	−29.8679	+	17.2442i	−1.42552	+	0.823022i	−0.996763	−	0.0803998i	$-0.974380\pi$
$439$	−29.8679	+	17.2442i	−1.42552	+	0.823022i	−0.428753	+	0.903422i	$0.641047\pi$
$440$	0.531122	−	13.3582i	0.0253202	−	0.636827i
$441$	60.3464	+	3.60700i	2.87364	+	0.171762i
$442$	0.748666	+	4.86677i	0.0356104	+	0.231489i
$443$	7.21189	+	12.4914i	0.342647	+	0.593482i	0.984923	−	0.172991i	$-0.0553432\pi$
$443$	7.21189	+	12.4914i	0.342647	+	0.593482i	−0.642276	+	0.766473i	$0.722010\pi$
$444$	−7.81538	+	35.2260i	−0.370902	+	1.67175i
$445$	4.06761	+	6.64113i	0.192823	+	0.314820i
$446$	−19.9924	−	24.9141i	−0.946668	−	1.17972i
$447$	11.9699	−	11.9699i	0.566159	−	0.566159i
$448$	−3.39790	+	20.8915i	−0.160536	+	0.987030i
$449$			25.9853i			1.22632i	0.789958	+	0.613162i	$0.210103\pi$
$449$			25.9853i			1.22632i	−0.789958	+	0.613162i	$0.789897\pi$
$450$	27.4573	+	54.5470i	1.29435	+	2.57137i
$451$	−16.6543	+	4.46252i	−0.784223	+	0.210132i
$452$	−9.12415	+	5.81066i	−0.429164	+	0.273310i
$453$	−4.89903	+	2.82846i	−0.230176	+	0.132892i
$454$	−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	0.341048	−	0.940046i	$-0.389218\pi$
$457$	3.55683	+	0.953049i	0.166381	+	0.0445818i	−0.174667	+	0.984628i	$0.555885\pi$
$458$	−2.64987	+	6.81250i	−0.123820	+	0.318327i
$459$	17.9250	+	66.8971i	0.836668	+	3.12249i
$460$	−10.4995	−	5.12602i	−0.489543	−	0.239002i
$461$	3.81210	+	3.81210i	0.177547	+	0.177547i	0.790286	−	0.612739i	$-0.209932\pi$
$461$	3.81210	+	3.81210i	0.177547	+	0.177547i	−0.612739	+	0.790286i	$0.709932\pi$
$462$	−26.7763	+	3.30436i	−1.24575	+	0.153733i
$463$	−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	$0.453016\pi$
$464$	2.74914	+	7.56079i	0.127626	+	0.351001i
$465$	−32.5902	−	53.2096i	−1.51134	−	2.46753i
$466$	10.4366	−	26.8313i	0.483467	−	1.24294i
$467$	10.1203	−	5.84297i	0.468313	−	0.270381i	−0.247220	−	0.968959i	$-0.579517\pi$
$467$	10.1203	−	5.84297i	0.468313	−	0.270381i	0.715533	+	0.698579i	$0.246184\pi$
$468$	5.01787	+	15.9236i	0.231951	+	0.736069i
$469$	14.8786	+	0.444262i	0.687029	+	0.0205141i
$470$	4.95218	−	13.7796i	0.228427	−	0.635607i
$471$	15.7373	−	9.08595i	0.725138	−	0.418659i
$472$	20.2931	+	1.33500i	0.934063	+	0.0614484i
$473$	1.95707	−	0.524396i	0.0899863	−	0.0241118i
$474$	−7.04619	+	64.2904i	−0.323642	+	2.95296i
$475$	−0.619379	−	0.131948i	−0.0284191	−	0.00605418i
$476$	16.3758	−	9.75437i	0.750583	−	0.447091i
$477$	−20.9952			−0.961305
$478$	−0.753237	+	6.87264i	−0.0344523	+	0.314347i
$479$	−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	$0.919708\pi$
$480$	21.7137	+	37.2870i	0.991089	+	1.70191i
$481$	4.42724	−	2.55607i	0.201865	−	0.116547i
$482$	8.37517	+	6.14197i	0.381479	+	0.279759i
$483$	−6.77986	+	22.5837i	−0.308494	+	1.02759i
$484$	−12.4598	+	3.92636i	−0.566356	+	0.178471i
$485$	23.4284	+	22.2429i	1.06383	+	1.01000i
$486$	44.2279	+	100.538i	2.00622	+	4.56048i
$487$	−3.24932	−	12.1266i	−0.147241	−	0.549509i	−0.999645	−	0.0266270i	$-0.991523\pi$
$487$	−3.24932	−	12.1266i	−0.147241	−	0.549509i	0.852405	−	0.522882i	$-0.175143\pi$
$488$	18.4000	−	27.5231i	0.832929	−	1.24591i
$489$		−	46.9267i		−	2.12210i
$490$	−17.3985	−	13.6855i	−0.785984	−	0.618247i
$491$	5.93287	+	5.93287i	0.267747	+	0.267747i	0.828192	−	0.560445i	$-0.189370\pi$
$491$	5.93287	+	5.93287i	0.267747	+	0.267747i	−0.560445	+	0.828192i	$0.689370\pi$
$492$	37.6028	−	41.0230i	1.69526	−	1.84946i
$493$	3.62245	−	6.27427i	0.163147	−	0.282579i
$494$	−0.161357	−	0.0627632i	−0.00725979	−	0.00282385i
$495$	−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
$498$	21.8241	−	29.7593i	0.977963	−	1.33355i
$499$	8.01930	−	29.9284i	0.358993	−	1.33978i	−0.516391	−	0.856353i	$-0.672725\pi$
$499$	8.01930	−	29.9284i	0.358993	−	1.33978i	0.875384	−	0.483428i	$-0.160608\pi$
$500$	3.13068	−	22.1404i	0.140008	−	0.990150i
$501$	20.6483	−	5.53268i	0.922496	−	0.247182i
$502$	−5.06738	+	4.06633i	−0.226168	+	0.181489i
$503$	14.2363	−	14.2363i	0.634763	−	0.634763i	−0.314496	−	0.949259i	$-0.601835\pi$
$503$	14.2363	−	14.2363i	0.634763	−	0.634763i	0.949259	+	0.314496i	$0.101835\pi$
$504$	49.8501	−	41.1310i	2.22050	−	1.83212i
$505$	−17.0975	+	5.06027i	−0.760828	+	0.225179i
$506$	0.850880	−	7.76355i	0.0378262	−	0.345132i
$507$	−20.5793	+	35.6443i	−0.913958	+	1.58302i
$508$	0.170685	+	0.268017i	0.00757293	+	0.0118913i
$509$	24.3809	+	6.53285i	1.08067	+	0.289563i	0.754868	−	0.655876i	$-0.227701\pi$
$509$	24.3809	+	6.53285i	1.08067	+	0.289563i	0.325797	+	0.945440i	$0.394367\pi$
$510$	13.1417	−	36.5672i	0.581924	−	1.61922i
$511$	−7.51453	+	7.07879i	−0.332423	+	0.313147i
$512$	12.5575	+	18.8231i	0.554967	+	0.831872i
$513$	−2.35217	−	0.630263i	−0.103851	−	0.0278268i
$514$	25.3537	+	9.86185i	1.11830	+	0.434987i
$515$	−0.907542	+	3.77640i	−0.0399911	+	0.166408i
$516$	−4.41875	+	4.82066i	−0.194525	+	0.212218i
$517$	9.78758			0.430457
$518$	−15.6014	−	12.1738i	−0.685487	−	0.534886i
$519$	−21.4503			−0.941565
$520$	1.81557	−	5.83743i	0.0796181	−	0.255988i
$521$	−5.08994	+	8.81603i	−0.222994	+	0.386237i	−0.955716	−	0.294291i	$-0.904916\pi$
$521$	−5.08994	+	8.81603i	−0.222994	+	0.386237i	0.732722	+	0.680529i	$0.238250\pi$
$522$	8.90506	−	22.8939i	0.389764	−	1.00204i
$523$	2.19584	−	1.26777i	0.0960175	−	0.0554357i	−0.451222	−	0.892412i	$-0.649012\pi$
$523$	2.19584	−	1.26777i	0.0960175	−	0.0554357i	0.547240	+	0.836976i	$0.315679\pi$
$524$	−6.76372	+	12.9879i	−0.295475	+	0.567378i
$525$	−45.1150	+	0.995153i	−1.96898	+	0.0434320i
$526$	−8.84364	+	1.36044i	−0.385601	+	0.0593179i
$527$	−7.62657	+	28.4628i	−0.332219	+	1.23986i
$528$	−18.5465	+	22.0884i	−0.807134	+	0.961275i
$529$	14.0073	+	8.08709i	0.609011	+	0.351613i
$530$	6.31517	+	4.38387i	0.274314	+	0.190423i
$531$	−43.9089	−	43.9089i	−1.90548	−	1.90548i
$532$	0.00912906	+	0.670136i	0.000395795	+	0.0290541i
$533$	−7.88434			−0.341509
$534$	1.83049	−	16.7017i	0.0792132	−	0.722753i
$535$	11.1867	+	18.2644i	0.483643	+	0.789637i
$536$	11.9665	−	10.4892i	0.516875	−	0.453067i
$537$	−6.85248	+	25.5738i	−0.295706	+	1.10359i
$538$	2.68849	+	17.4768i	0.115909	+	0.753477i
$539$	4.67555	−	14.0384i	0.201390	−	0.604675i
$540$	16.4393	−	84.3976i	0.707433	−	3.63189i
$541$	32.3269	+	8.66197i	1.38984	+	0.372407i	0.874686	−	0.484689i	$-0.161067\pi$
$541$	32.3269	+	8.66197i	1.38984	+	0.372407i	0.515156	+	0.857096i	$0.327734\pi$
$542$	−13.9809	+	6.15041i	−0.600532	+	0.264183i
$543$	−15.0635	−	56.2179i	−0.646439	−	2.41254i
$544$	5.70991	−	19.5605i	0.244810	−	0.838649i
$545$	11.6964	+	39.5194i	0.501019	+	1.69283i
$546$	−12.2181	−	1.70951i	−0.522887	−	0.0731604i
$547$	−6.43353			−0.275078			−0.137539	−	0.990496i	$-0.543919\pi$
$547$	−6.43353			−0.275078			−0.137539	+	0.990496i	$0.543919\pi$
$548$	1.41682	+	32.5708i	0.0605234	+	1.39136i
$549$	−97.6446	+	26.1638i	−4.16737	+	1.11664i
$550$	14.6351	−	3.03594i	0.624045	−	0.129453i
$551$	0.127369	+	0.220610i	0.00542611	+	0.00939830i
$552$	11.1435	+	22.6106i	0.474300	+	0.962371i
$553$	−30.1752	−	18.6441i	−1.28318	−	0.792827i
$554$	16.4002	+	12.0272i	0.696778	+	0.510985i
$555$	−40.3280	+	1.04684i	−1.71183	+	0.0444361i
$556$	−16.7327	−	26.2744i	−0.709623	−	1.11428i
$557$	15.1082	−	26.1682i	0.640155	−	1.10878i	−0.345243	−	0.938513i	$-0.612203\pi$
$557$	15.1082	−	26.1682i	0.640155	−	1.10878i	0.985398	−	0.170268i	$-0.0544633\pi$
$558$	−10.8850	+	99.3163i	−0.460799	+	4.20440i
$559$	0.926499			0.0391867
$560$	−23.5828	+	1.96298i	−0.996554	+	0.0829510i
$561$	25.9735			1.09660
$562$	−0.417499	+	3.80932i	−0.0176111	+	0.160686i
$563$	16.4672	−	28.5220i	0.694010	−	1.20206i	−0.276503	−	0.961013i	$-0.589176\pi$
$563$	16.4672	−	28.5220i	0.694010	−	1.20206i	0.970513	−	0.241048i	$-0.0774911\pi$
$564$	−26.6456	+	16.9691i	−1.12198	+	0.714528i
$565$	−8.77086	−	8.32703i	−0.368993	−	0.350321i
$566$	−17.6256	−	12.9258i	−0.740859	−	0.543312i
$567$	−104.928	−	3.13306i	−4.40656	−	0.131576i
$568$	−13.1888	+	38.8222i	−0.553390	+	1.62894i
$569$	10.4739	+	18.1414i	0.439091	+	0.760527i	0.997620	−	0.0689576i	$-0.0219673\pi$
$569$	10.4739	+	18.1414i	0.439091	+	0.760527i	−0.558529	+	0.829485i	$0.688634\pi$
$570$	0.882449	+	1.04304i	0.0369617	+	0.0436882i
$571$	−31.5969	+	8.46635i	−1.32229	+	0.354306i	−0.849834	−	0.527050i	$-0.823298\pi$
$571$	−31.5969	+	8.46635i	−1.32229	+	0.354306i	−0.472453	+	0.881356i	$0.656631\pi$
$572$	4.08247	−	0.177585i	0.170697	−	0.00742522i
$573$	−7.83054			−0.327125
$574$	11.4504	+	28.2908i	0.477930	+	1.18084i
$575$	2.72179	−	12.7764i	0.113507	−	0.532814i
$576$	9.05121	−	68.4949i	0.377134	−	2.85396i
$577$	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	$0.757768\pi$
$578$	5.20968	−	2.29181i	0.216694	−	0.0953269i
$579$	−44.9681	−	12.0492i	−1.86881	−	0.500747i
$580$	−7.45888	+	5.02686i	−0.309713	+	0.208729i
$581$	9.59213	+	17.8222i	0.397949	+	0.739389i
$582$	−10.5970	−	68.8864i	−0.439258	−	2.85543i
$583$	−1.32999	+	4.96361i	−0.0550828	+	0.205572i
$584$	−0.724478	+	11.0126i	−0.0299791	+	0.455706i
$585$	−15.9177	+	9.74942i	−0.658117	+	0.403089i
$586$	−1.37154	+	12.5141i	−0.0566578	+	0.516954i
$587$	22.8188			0.941835			0.470917	−	0.882177i	$-0.343923\pi$
$587$	22.8188			0.941835			0.470917	+	0.882177i	$0.343923\pi$
$588$	11.6102	+	46.3241i	0.478795	+	1.91037i
$589$	−0.732623	−	0.732623i	−0.0301872	−	0.0301872i
$590$	4.03907	+	22.3757i	0.166286	+	0.921194i
$591$	−23.2964	−	13.4502i	−0.958286	−	0.553267i
$592$	−21.0755	+	1.83702i	−0.866196	+	0.0755011i
$593$	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
$595$	15.0100	+	15.1275i	0.615351	+	0.620167i
$596$	8.80282	+	4.58426i	0.360578	+	0.187779i
$597$	−23.9715	+	13.8400i	−0.981090	+	0.566433i
$598$	1.29467	−	3.32844i	0.0529429	−	0.136110i
$599$	5.56671	−	9.64182i	0.227449	−	0.393954i	−0.729602	−	0.683872i	$-0.760295\pi$
$599$	5.56671	−	9.64182i	0.227449	−	0.393954i	0.957051	+	0.289918i	$0.0936280\pi$
$600$	−34.5790	+	33.6385i	−1.41168	+	1.37329i
$601$	−18.3334			−0.747834			−0.373917	−	0.927462i	$-0.621986\pi$
$601$	−18.3334			−0.747834			−0.373917	+	0.927462i	$0.621986\pi$
$602$	−1.34555	−	3.32449i	−0.0548405	−	0.135496i
$603$	−48.5885			−1.97868
$604$	−2.44494	−	2.24110i	−0.0994833	−	0.0911892i
$605$	−7.62868	−	12.4552i	−0.310150	−	0.506377i
$606$	35.8517	+	13.9453i	1.45637	+	0.566488i
$607$	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	$0.410660\pi$
$608$	0.495241	+	0.517753i	0.0200847	+	0.0209977i
$609$	12.4467	+	13.2128i	0.504364	+	0.535411i
$610$	34.8337	+	12.5187i	1.41038	+	0.506867i
$611$	4.32316	+	1.15839i	0.174896	+	0.0468633i
$612$	−52.4799	+	33.4215i	−2.12138	+	1.35099i
$613$	15.6564	−	27.1176i	0.632355	−	1.09527i	−0.354714	−	0.934975i	$-0.615422\pi$
$613$	15.6564	−	27.1176i	0.632355	−	1.09527i	0.987069	−	0.160296i	$-0.0512448\pi$
$614$	−3.95781	+	36.1116i	−0.159724	+	1.45735i
$615$	54.6714	+	29.7003i	2.20456	+	1.19763i
$616$	−6.56616	−	14.3909i	−0.264558	−	0.579826i
$617$	13.8764	−	13.8764i	0.558644	−	0.558644i	−0.370277	−	0.928921i	$-0.620737\pi$
$617$	13.8764	−	13.8764i	0.558644	−	0.558644i	0.928921	+	0.370277i	$0.120737\pi$
$618$	6.53530	−	5.24427i	0.262889	−	0.210956i
$619$	−6.29558	+	1.68690i	−0.253041	+	0.0678020i	−0.383110	−	0.923703i	$-0.625147\pi$
$619$	−6.29558	+	1.68690i	−0.253041	+	0.0678020i	0.130069	+	0.991505i	$0.458480\pi$
$620$	24.0117	−	27.6006i	0.964333	−	1.10847i
$621$	13.0009	−	48.5202i	0.521710	−	1.94705i
$622$	15.7389	−	21.4615i	0.631071	−	0.860527i
$623$	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
$626$	−7.01749	−	2.72960i	−0.280475	−	0.109097i
$627$	−0.456628	+	0.790903i	−0.0182360	+	0.0315856i
$628$	7.85398	+	7.19918i	0.313408	+	0.287278i
$629$	13.4712	+	13.4712i	0.537134	+	0.537134i
$630$	58.1004	+	42.9574i	2.31477	+	1.71146i
$631$			12.1815i			0.484936i	0.970159	+	0.242468i	$0.0779570\pi$
$631$			12.1815i			0.484936i	−0.970159	+	0.242468i	$0.922043\pi$
$632$	−37.1926	+	7.38872i	−1.47944	+	0.293908i
$633$	5.63136	+	21.0165i	0.223827	+	0.835332i
$634$	−8.82844	−	20.0685i	−0.350622	−	0.797024i
$635$	−0.244602	+	0.257640i	−0.00970675	+	0.0102241i
$636$	−4.98483	−	15.8187i	−0.197661	−	0.627254i
$637$	3.72665	−	5.64735i	0.147655	−	0.223756i
$638$	−4.84836	−	3.55557i	−0.191949	−	0.140766i
$639$	108.420	−	62.5965i	4.28904	−	2.47628i
$640$	−17.0245	+	18.7127i	−0.672952	+	0.739686i
$641$	−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	$0.264802\pi$
$642$	5.03420	−	45.9328i	0.198684	−	1.81282i
$643$	−19.2835			−0.760468			−0.380234	−	0.924890i	$-0.624156\pi$
$643$	−19.2835			−0.760468			−0.380234	+	0.924890i	$0.624156\pi$
$644$	−13.8234	+	0.188312i	−0.544720	+	0.00742055i
$645$	−6.42451	−	3.49011i	−0.252965	−	0.137423i
$646$	0.0702937	−	0.641370i	0.00276567	−	0.0252344i
$647$	−29.0064	+	7.77224i	−1.14036	+	0.305558i	−0.779096	−	0.626905i	$-0.784321\pi$
$647$	−29.0064	+	7.77224i	−1.14036	+	0.305558i	−0.361264	+	0.932464i	$0.617655\pi$
$648$	−84.3914	+	73.9732i	−3.31521	+	2.90594i
$649$	−13.1623	+	7.59925i	−0.516665	+	0.298297i
$650$	6.82362	+	0.391140i	0.267645	+	0.0153418i
$651$	−62.8076	−	38.8064i	−2.46163	−	1.52094i
$652$	26.2412	−	8.26918i	1.02769	−	0.323846i
$653$	15.8995	−	9.17958i	0.622196	−	0.359225i	−0.155528	−	0.987832i	$-0.549708\pi$
$653$	15.8995	−	9.17958i	0.622196	−	0.359225i	0.777723	+	0.628607i	$0.216374\pi$
$654$	32.2334	−	82.8682i	1.26042	−	3.24040i
$655$	−15.9187	−	3.82558i	−0.621997	−	0.149478i
$656$	29.5661	+	13.7985i	1.15436	+	0.538740i
$657$	23.8285	−	23.8285i	0.929637	−	0.929637i
$658$	−2.12194	−	17.1948i	−0.0827220	−	0.670322i
$659$	8.64946	+	8.64946i	0.336935	+	0.336935i	0.855213	−	0.518277i	$-0.173427\pi$
$659$	8.64946	+	8.64946i	0.336935	+	0.336935i	−0.518277	+	0.855213i	$0.673427\pi$
$660$	−28.9775	−	14.1472i	−1.12795	−	0.550680i
$661$	2.28589	+	8.53106i	0.0889108	+	0.331820i	0.996026	−	0.0890628i	$-0.0283872\pi$
$661$	2.28589	+	8.53106i	0.0889108	+	0.331820i	−0.907115	+	0.420882i	$0.861721\pi$
$662$	−18.4569	+	47.4505i	−0.717347	+	1.84422i
$663$	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
$667$	−4.55070	+	2.62735i	−0.176204	+	0.101731i
$668$	6.73239	+	10.5715i	0.260484	+	0.409023i
$669$	−74.4258	+	19.9423i	−2.87747	+	0.771015i
$670$	14.6150	+	10.1454i	0.564626	+	0.391953i
$671$			24.7422i			0.955161i
$672$	42.8257	+	27.7937i	1.65204	+	1.07216i
$673$	−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	$0.309815\pi$
$674$	22.5987	+	28.1621i	0.870470	+	1.08476i
$675$	96.0033	−	4.98751i	3.69517	−	0.191969i
$676$	−23.5586	−	5.22679i	−0.906098	−	0.201030i
$677$	−2.40102	−	4.15869i	−0.0922788	−	0.159832i	0.816191	−	0.577782i	$-0.196082\pi$
$677$	−2.40102	−	4.15869i	−0.0922788	−	0.159832i	−0.908470	+	0.417951i	$0.862748\pi$
$678$	3.96716	+	25.7889i	0.152358	+	0.990416i
$679$	36.6101	+	10.9907i	1.40497	+	0.421785i
$680$	22.7640	+	0.905098i	0.872960	+	0.0347089i
$681$	−59.0923	+	34.1170i	−2.26442	+	1.30736i
$682$	22.7904	+	8.86483i	0.872691	+	0.339452i
$683$	−8.73917	+	15.1367i	−0.334395	+	0.579189i	−0.983368	−	0.181622i	$-0.941865\pi$
$683$	−8.73917	+	15.1367i	−0.334395	+	0.579189i	0.648973	+	0.760811i	$0.275199\pi$
$684$	−0.0950727	−	2.18560i	−0.00363520	−	0.0835686i
$685$	−34.9511	+	10.3443i	−1.33541	+	0.395236i
$686$	−25.6762	−	5.17046i	−0.980321	−	0.197409i
$687$	12.4675	+	12.4675i	0.475663	+	0.475663i
$688$	−3.47434	−	1.62148i	−0.132458	−	0.0618182i
$689$	−1.17491	+	2.03501i	−0.0447606	+	0.0775276i
$690$	−21.5157	+	18.2030i	−0.819087	+	0.692975i
$691$	−3.80594	+	14.2039i	−0.144785	+	0.540344i	0.854980	+	0.518660i	$0.173569\pi$
$691$	−3.80594	+	14.2039i	−0.144785	+	0.540344i	−0.999765	+	0.0216830i	$0.993098\pi$
$692$	−3.77987	−	11.9949i	−0.143689	−	0.455979i
$693$	−13.8875	+	46.2593i	−0.527543	+	1.75725i
$694$	−8.81380	−	6.46364i	−0.334567	−	0.245356i
$695$	23.9789	−	25.2570i	0.909573	−	0.958053i
$696$	19.3636	+	1.27385i	0.733974	+	0.0482853i
$697$	−7.60469	−	28.3811i	−0.288048	−	1.07501i
$698$	−10.7807	+	8.65096i	−0.408054	+	0.327444i
$699$	−49.1036	−	49.1036i	−1.85727	−	1.85727i
$700$	−8.50641	−	25.0528i	−0.321512	−	0.946905i
$701$	−17.8920	+	17.8920i	−0.675771	+	0.675771i	−0.959040	−	0.283270i	$-0.908581\pi$
$701$	−17.8920	+	17.8920i	−0.675771	+	0.675771i	0.283270	+	0.959040i	$0.408581\pi$
$702$	26.1256	+	2.86334i	0.986046	+	0.108070i
$703$	−0.647036	+	0.173373i	−0.0244034	+	0.00653888i
$704$	−15.6199	−	6.47883i	−0.588698	−	0.244180i
$705$	−25.6139	−	24.3177i	−0.964675	−	0.915859i
$706$	−9.07944	+	1.39671i	−0.341709	+	0.0525659i
$707$	−15.3567	+	14.4663i	−0.577550	+	0.544060i
$708$	22.6578	−	43.5081i	0.851532	−	1.63513i
$709$	2.33222	+	0.624916i	0.0875884	+	0.0234692i	0.302347	−	0.953198i	$-0.402230\pi$
$709$	2.33222	+	0.624916i	0.0875884	+	0.0234692i	−0.214759	+	0.976667i	$0.568897\pi$
$710$	−45.6822	−	3.81007i	−1.71442	−	0.142989i
$711$	100.271	+	57.8914i	3.76045	+	2.17110i
$712$	9.66208	−	1.91948i	0.362102	−	0.0719356i
$713$	15.1124	−	15.1124i	0.565964	−	0.565964i
$714$	−5.63104	−	45.6301i	−0.210736	−	1.70766i
$715$	1.29657	+	4.38081i	0.0484890	+	0.163833i
$716$	−15.5083	+	0.674603i	−0.579572	+	0.0252111i
$717$	14.4424	+	8.33833i	0.539362	+	0.311401i
$718$	0.281075	+	0.638930i	0.0104896	+	0.0238447i
$719$	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	$0.621790\pi$
$720$	76.7536	−	8.70224i	2.86044	−	0.324313i
$721$	1.05639	+	4.47245i	0.0393421	+	0.166563i
$722$	−21.6496	−	15.8769i	−0.805716	−	0.590875i
$723$	21.6954	−	12.5258i	0.806861	−	0.465841i
$724$	28.7824	−	18.3299i	1.06969	−	0.681226i
$725$	−7.47026	−	6.73241i	−0.277439	−	0.250036i
$726$	−3.43303	+	31.3235i	−0.127412	+	1.16252i
$727$	0.195237	+	0.195237i	0.00724094	+	0.00724094i	0.710718	−	0.703477i	$-0.248370\pi$
$727$	0.195237	+	0.195237i	0.00724094	+	0.00724094i	−0.703477	+	0.710718i	$0.748370\pi$
$728$	−1.19706	−	7.13356i	−0.0443659	−	0.264387i
$729$	145.903			5.40382
$730$	−12.1429	+	2.19192i	−0.449427	+	0.0811267i
$731$	0.893636	+	3.33510i	0.0330523	+	0.123353i
$732$	−42.8964	−	67.3578i	−1.58550	−	2.48962i
$733$	−4.07054	−	7.05038i	−0.150349	−	0.260412i	0.781007	−	0.624522i	$-0.214706\pi$
$733$	−4.07054	−	7.05038i	−0.150349	−	0.260412i	−0.931356	+	0.364111i	$0.881373\pi$
$734$	−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
$738$	−40.1160	−	91.1906i	−1.47669	−	3.35677i
$739$	3.23583	−	0.867037i	0.119032	−	0.0318945i	−0.198811	−	0.980038i	$-0.563708\pi$
$739$	3.23583	−	0.867037i	0.119032	−	0.0318945i	0.317843	+	0.948143i	$0.397041\pi$
$740$	−7.69178	−	22.3668i	−0.282756	−	0.822220i
$741$	−0.295297	+	0.295297i	−0.0108480	+	0.0108480i
$742$	9.00838	+	1.26042i	0.330708	+	0.0462715i
$743$	3.64048	+	3.64048i	0.133556	+	0.133556i	0.770725	−	0.637168i	$-0.219894\pi$
$743$	3.64048	+	3.64048i	0.133556	+	0.133556i	−0.637168	+	0.770725i	$0.719894\pi$
$744$	−77.4138	+	15.3791i	−2.83813	+	0.563826i
$745$	−2.59287	+	10.7893i	−0.0949955	+	0.395289i
$746$	−11.3049	−	25.6979i	−0.413901	−	0.940867i
$747$	−33.0331	−	57.2150i	−1.20862	−	2.09339i
$748$	4.57691	+	14.5243i	0.167349	+	0.531060i
$749$	21.5589	+	13.3204i	0.787746	+	0.486718i
$750$	−45.8428	−	28.4168i	−1.67394	−	1.03763i
$751$	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	$0.781687\pi$
$752$	−14.1844	−	11.9099i	−0.517252	−	0.434310i
$753$	4.05615	+	15.1378i	0.147814	+	0.551650i
$754$	−1.72070	−	2.14430i	−0.0626642	−	0.0780909i
$755$	1.77012	−	3.25838i	0.0644211	−	0.118585i
$756$	−27.6677	−	97.9029i	−1.00626	−	3.56069i
$757$		−	43.5428i		−	1.58259i	−0.611434	−	0.791295i	$-0.709407\pi$
$757$		−	43.5428i		−	1.58259i	0.611434	−	0.791295i	$-0.290593\pi$
$758$	18.8120	−	15.0957i	0.683283	−	0.548302i
$759$	−16.3146	−	9.41923i	−0.592182	−	0.341896i
$760$	−0.427764	+	0.677261i	−0.0155166	+	0.0245668i
$761$	15.8494	+	27.4519i	0.574540	+	0.995132i	0.996091	+	0.0883278i	$0.0281523\pi$
$761$	15.8494	+	27.4519i	0.574540	+	0.995132i	−0.421552	+	0.906804i	$0.638514\pi$
$762$	0.757535	−	0.116533i	0.0274426	−	0.00422156i
$763$	33.4376	+	35.4959i	1.21052	+	1.28504i
$764$	−1.37986	−	4.37881i	−0.0499215	−	0.158420i
$765$	−50.4479	−	47.8951i	−1.82395	−	1.73165i
$766$	0.964588	−	2.47984i	0.0348520	−	0.0896004i
$767$	−6.71315	+	1.79878i	−0.242398	+	0.0649503i
$768$	53.7561	−	9.44295i	1.93976	−	0.340743i
$769$	−13.2028			−0.476104			−0.238052	−	0.971252i	$-0.576509\pi$
$769$	−13.2028			−0.476104			−0.238052	+	0.971252i	$0.576509\pi$
$770$	13.8363	−	11.0146i	0.498627	−	0.396939i
$771$	46.3994	−	46.3994i	1.67103	−	1.67103i
$772$	−1.18620	−	27.2692i	−0.0426923	−	0.981442i
$773$	−1.30903	−	0.755768i	−0.0470825	−	0.0271831i	0.476274	−	0.879297i	$-0.341987\pi$
$773$	−1.30903	−	0.755768i	−0.0470825	−	0.0271831i	−0.523356	+	0.852114i	$0.675320\pi$
$774$	4.71409	+	10.7159i	0.169444	+	0.385176i
$775$	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
$778$	−1.82603	−	11.8702i	−0.0654662	−	0.425569i
$779$	0.997909	+	0.267389i	0.0357538	+	0.00958020i
$780$	−11.1249	−	9.67836i	−0.398337	−	0.346541i
$781$	−7.93067	−	29.5976i	−0.283782	−	1.05909i
$782$	13.2300	+	1.45000i	0.473106	+	0.0518520i
$783$	−27.3437	−	27.3437i	−0.977183	−	0.977183i
$784$	−23.8583	+	14.6553i	−0.852084	+	0.523405i
$785$	−5.68621	+	10.4670i	−0.202950	+	0.373584i
$786$	22.1063	+	27.5484i	0.788506	+	0.982620i
$787$	−34.5189	−	19.9295i	−1.23047	−	0.710411i	−0.263340	−	0.964703i	$-0.584824\pi$
$787$	−34.5189	−	19.9295i	−1.23047	−	0.710411i	−0.967127	+	0.254292i	$0.918158\pi$
$788$	3.41612	−	15.3974i	0.121694	−	0.548509i
$789$	−5.58597	+	20.8471i	−0.198866	+	0.742177i
$790$	−18.0727	−	38.3501i	−0.642996	−	1.36444i
$791$	−13.7056	−	4.11457i	−0.487317	−	0.146297i
$792$	22.8258	+	46.3144i	0.811080	+	1.64571i
$793$	−2.92830	+	10.9286i	−0.103987	+	0.388085i
$794$	19.2138	−	8.45243i	0.681873	−	0.299966i
$795$	15.8129	−	9.68521i	0.560826	−	0.343499i
$796$	−11.9634	−	10.9660i	−0.424032	−	0.388679i
$797$			34.4574i			1.22054i	0.792192	+	0.610272i	$0.208940\pi$
$797$			34.4574i			1.22054i	−0.792192	+	0.610272i	$0.791060\pi$
$798$	1.48845	+	0.630734i	0.0526906	+	0.0223278i
$799$			16.6793i			0.590070i
$800$	−24.9039	−	13.4089i	−0.880484	−	0.474075i
$801$	−26.0489	−	15.0393i	−0.920392	−	0.531388i
$802$	6.03658	+	13.7222i	0.213159	+	0.484546i
$803$	−4.12396	−	7.14291i	−0.145531	−	0.252068i
$804$	−11.5362	−	36.6087i	−0.406851	−	1.29109i
$805$	−3.94221	−	14.9453i	−0.138945	−	0.526753i
$806$	9.01732	+	6.61289i	0.317621	+	0.232929i
$807$	41.1980	+	11.0390i	1.45024	+	0.388590i
$808$	−1.48055	+	22.5055i	−0.0520855	+	0.791740i
$809$	8.92541	−	15.4593i	0.313801	−	0.543519i	−0.665381	−	0.746504i	$-0.731731\pi$
$809$	8.92541	−	15.4593i	0.313801	−	0.543519i	0.979182	+	0.202985i	$0.0650643\pi$
$810$	−103.069	−	71.5486i	−3.62148	−	2.51396i
$811$	−27.8917	+	27.8917i	−0.979409	+	0.979409i	−0.999792	−	0.0203832i	$-0.993511\pi$
$811$	−27.8917	+	27.8917i	−0.979409	+	0.979409i	0.0203832	+	0.999792i	$0.493511\pi$
$812$	−5.19528	+	9.28843i	−0.182319	+	0.325960i
$813$			36.8420i			1.29211i
$814$	12.3309	−	9.89496i	0.432198	−	0.346818i
$815$	16.0665	+	26.2316i	0.562785	+	0.918851i
$816$	−37.6414	−	31.6056i	−1.31771	−	1.10642i
$817$	−0.117266	−	0.0314212i	−0.00410260	−	0.00109929i
$818$	−44.2020	−	32.4157i	−1.54549	−	1.13339i
$819$	−11.6090	+	18.7890i	−0.405651	+	0.656541i
$820$	−6.97436	+	35.8057i	−0.243555	+	1.25039i
$821$	0.233698	−	0.872174i	0.00815613	−	0.0304391i	−0.961728	−	0.274006i	$-0.911651\pi$
$821$	0.233698	−	0.872174i	0.00815613	−	0.0304391i	0.969884	+	0.243567i	$0.0783177\pi$
$822$	73.2888	+	28.5073i	2.55624	+	0.994305i
$823$	24.3517	−	6.52502i	0.848847	−	0.227448i	0.191928	−	0.981409i	$-0.438526\pi$
$823$	24.3517	−	6.52502i	0.848847	−	0.227448i	0.656919	+	0.753961i	$0.271859\pi$
$824$	4.08419	+	2.73040i	0.142280	+	0.0951180i
$825$	7.51183	−	35.2615i	0.261528	−	1.22765i
$826$	16.2039	+	21.4759i	0.563806	+	0.747243i
$827$		−	41.1644i		−	1.43143i	−0.698394	−	0.715713i	$-0.746102\pi$
$827$		−	41.1644i		−	1.43143i	0.698394	−	0.715713i	$-0.253898\pi$
$828$	45.0842	−	1.96114i	1.56678	−	0.0681544i
$829$	5.50419	+	20.5419i	0.191168	+	0.713450i	0.993225	+	0.116203i	$0.0370723\pi$
$829$	5.50419	+	20.5419i	0.191168	+	0.713450i	−0.802057	+	0.597247i	$0.796261\pi$
$830$	−2.01063	+	24.1072i	−0.0697900	+	0.836773i
$831$	42.4838	−	24.5280i	1.47375	−	0.850868i
$832$	−6.13250	−	4.71035i	−0.212606	−	0.163302i
$833$	23.9231	+	7.96771i	0.828887	+	0.276065i
$834$	−74.2629	+	11.4240i	−2.57152	+	0.395582i
$835$	−9.64792	+	10.1622i	−0.333880	+	0.351676i
$836$	−0.522734	−	0.115976i	−0.0180791	−	0.00401111i
$837$	136.208	+	78.6398i	4.70804	+	2.71819i
$838$	14.7442	−	11.8315i	0.509329	−	0.408713i
$839$		−	28.7420i		−	0.992283i	−0.868242	−	0.496142i	$-0.834750\pi$
$839$		−	28.7420i		−	0.992283i	0.868242	−	0.496142i	$-0.165250\pi$
$840$	−18.5715	+	53.9747i	−0.640776	+	1.86230i
$841$		−	24.9548i		−	0.860510i
$842$	−5.42166	−	6.75636i	−0.186843	−	0.232840i
$843$	8.00503	+	4.62171i	0.275708	+	0.159180i
$844$	−10.7600	+	6.85246i	−0.370376	+	0.235871i
$845$	−0.700111	−	26.9706i	−0.0240845	−	0.927818i
$846$	8.59856	+	55.8957i	0.295625	+	1.92173i
$847$	−14.7019	−	9.08375i	−0.505164	−	0.312121i
$848$	7.96738	−	5.57499i	0.273601	−	0.191446i
$849$	−45.6581	+	26.3607i	−1.56698	+	0.904697i
$850$	5.17362	+	24.9401i	0.177454	+	0.855438i
$851$	−3.57630	−	13.3469i	−0.122594	−	0.457527i
$852$	72.9049	+	66.8266i	2.49768	+	2.28944i
$853$			40.7729i			1.39604i	0.716080	+	0.698018i	$0.245935\pi$
$853$			40.7729i			1.39604i	−0.716080	+	0.698018i	$0.754065\pi$
$854$	43.4669	−	5.36409i	1.48741	−	0.183555i
$855$	2.34532	−	0.694136i	0.0802084	−	0.0237390i
$856$	26.5725	−	5.27893i	0.908231	−	0.180430i
$857$	−1.55540	+	0.416769i	−0.0531315	+	0.0142366i	−0.285287	−	0.958442i	$-0.592089\pi$
$857$	−1.55540	+	0.416769i	−0.0531315	+	0.0142366i	0.232155	+	0.972679i	$0.425422\pi$
$858$	3.57313	−	9.18611i	0.121985	−	0.313609i
$859$	6.42745	−	23.9876i	0.219302	−	0.818446i	−0.765306	−	0.643667i	$-0.777412\pi$
$859$	6.42745	−	23.9876i	0.219302	−	0.818446i	0.984608	−	0.174779i	$-0.0559211\pi$
$860$	0.819565	−	4.20757i	0.0279470	−	0.143477i
$861$	73.5844	+	2.19717i	2.50775	+	0.0748793i
$862$	−10.0681	+	13.7289i	−0.342922	+	0.467608i
$863$	−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	$0.820889\pi$
$864$	−92.9590	−	56.4601i	−3.16253	−	1.92081i
$865$	11.9905	−	7.34405i	0.407690	−	0.249705i
$866$	−25.8819	−	32.2535i	−0.879502	−	1.09602i
$867$		−	13.7284i		−	0.466240i
$868$	10.6327	−	41.9600i	0.360899	−	1.42422i
$869$	20.0384	−	20.0384i	0.679755	−	0.679755i
$870$	3.85407	+	21.3508i	0.130665	+	0.723861i
$871$	−2.71906	+	4.70954i	−0.0921317	+	0.159577i
$872$	52.0196	+	3.42217i	1.76161	+	0.115889i
$873$	−120.521	−	32.2934i	−4.07900	−	1.09297i
$874$	−0.276745	+	0.377368i	−0.00936102	+	0.0127647i
$875$	24.8781	−	16.0025i	0.841033	−	0.540983i
$876$	23.6109	+	12.2959i	0.797740	+	0.415440i
$877$	11.1888	+	19.3795i	0.377818	+	0.654401i	0.990745	−	0.135740i	$-0.0433411\pi$
$877$	11.1888	+	19.3795i	0.377818	+	0.654401i	−0.612926	+	0.790140i	$0.710008\pi$
$878$	−44.6450	+	19.6400i	−1.50670	+	0.662817i
$879$	26.2976	+	15.1829i	0.886997	+	0.512108i
$880$	2.80480	−	18.6971i	0.0945499	−	0.630278i
$881$		−	27.0246i		−	0.910480i	−0.890369	−	0.455240i	$-0.849553\pi$
$881$		−	27.0246i		−	0.910480i	0.890369	−	0.455240i	$-0.150447\pi$
$882$	84.2789	+	14.3685i	2.83782	+	0.483813i
$883$			31.5113i			1.06044i	0.847861	+	0.530219i	$0.177890\pi$
$883$			31.5113i			1.06044i	−0.847861	+	0.530219i	$0.822110\pi$
$884$	0.302628	+	6.95703i	0.0101785	+	0.233990i
$885$	53.3262	+	12.8153i	1.79254	+	0.430782i
$886$	8.21384	+	18.6715i	0.275949	+	0.627280i
$887$	−7.00311	+	26.1360i	−0.235141	+	0.877560i	0.742944	+	0.669354i	$0.233429\pi$
$887$	−7.00311	+	26.1360i	−0.235141	+	0.877560i	−0.978085	+	0.208206i	$0.933238\pi$
$888$	−16.4143	+	48.3165i	−0.550826	+	1.62139i
$889$	−0.120864	+	0.402596i	−0.00405363	+	0.0135026i
$890$	4.69501	+	9.96279i	0.157377	+	0.333953i
$891$	21.7067	−	81.0103i	0.727200	−	2.71395i
$892$	−24.2666	−	38.1045i	−0.812506	−	1.27583i
$893$	−0.507890	−	0.293230i	−0.0169959	−	0.00981258i
$894$	18.6715	−	14.9830i	0.624470	−	0.501107i
$895$	−4.92535	−	16.6416i	−0.164636	−	0.556268i
$896$	−7.99559	+	28.8456i	−0.267114	+	0.963665i
$897$	−6.09133	−	6.09133i	−0.203383	−	0.203383i
$898$	−4.00367	+	36.5300i	−0.133604	+	1.21902i
$899$	−4.25831	−	15.8922i	−0.142023	−	0.530036i
$900$	30.1951	+	80.9124i	1.00650	+	2.69708i
$901$	−8.45860	−	2.26648i	−0.281797	−	0.0755073i
$902$	−24.1002	+	3.70738i	−0.802448	+	0.123442i
$903$	−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
$906$	−7.32283	+	3.22142i	−0.243285	+	0.107024i
$907$	19.9144	+	11.4976i	0.661248	+	0.381772i	0.792752	−	0.609544i	$-0.208647\pi$
$907$	19.9144	+	11.4976i	0.661248	+	0.381772i	−0.131505	+	0.991316i	$0.541981\pi$
$908$	−29.4910	−	27.0323i	−0.978694	−	0.897098i
$909$	48.6960	−	48.6960i	1.61514	−	1.61514i
$910$	7.41509	−	3.22757i	0.245808	−	0.106993i
$911$	22.6953			0.751929			0.375964	−	0.926634i	$-0.377311\pi$
$911$	22.6953			0.751929			0.375964	+	0.926634i	$0.377311\pi$
$912$	1.62416	−	0.590553i	0.0537813	−	0.0195552i
$913$	−15.6191	+	4.18513i	−0.516918	+	0.138508i
$914$	4.85333	+	1.88781i	0.160534	+	0.0624431i
$915$	61.4732	−	64.7497i	2.03224	−	2.14056i
$916$	−4.77480	+	9.16870i	−0.157764	+	0.302942i
$917$	−18.8528	+	4.45304i	−0.622575	+	0.147052i
$918$	14.8918	+	96.8054i	0.491502	+	3.19505i
$919$	19.7064	+	34.1325i	0.650054	+	1.12593i	0.983109	+	0.183020i	$0.0585872\pi$
$919$	19.7064	+	34.1325i	0.650054	+	1.12593i	−0.333055	+	0.942907i	$0.608080\pi$
$920$	−13.9704	−	8.82384i	−0.460591	−	0.290913i
$921$	75.8862	+	43.8129i	2.50054	+	1.44369i
$922$	4.77168	+	5.94638i	0.157147	+	0.195833i
$923$		−	14.0118i		−	0.461205i
$924$	−38.1511	+	0.519721i	−1.25508	+	0.0170976i
$925$	22.1845	−	14.3925i	0.729423	−	0.473221i
$926$	−28.2631	+	22.6798i	−0.928784	+	0.745305i
$927$	−3.88248	−	14.4896i	−0.127517	−	0.475901i
$928$	2.69981	+	11.0525i	0.0886257	+	0.362816i
$929$	−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	$0.985188\pi$
$930$	−37.6170	−	79.8231i	−1.23351	−	2.61750i
$931$	−0.663201	+	0.588391i	−0.0217355	+	0.0192837i
$932$	18.8058	−	36.1113i	0.616003	−	1.18287i
$933$	−32.0976	−	55.5947i	−1.05083	−	1.82009i
$934$	15.1274	−	6.65475i	0.494982	−	0.217750i
$935$	−14.5189	+	8.89266i	−0.474819	+	0.290821i
$936$	4.60069	+	23.1585i	0.150378	+	0.756958i
$937$	23.9413	+	23.9413i	0.782127	+	0.782127i	0.980189	−	0.198062i	$-0.0634648\pi$
$937$	23.9413	+	23.9413i	0.782127	+	0.782127i	−0.198062	+	0.980189i	$0.563465\pi$
$938$	20.8478	+	2.91695i	0.680704	+	0.0952417i
$939$	−12.8426	+	12.8426i	−0.419103	+	0.419103i
$940$	9.08484	−	18.6083i	0.296315	−	0.606937i
$941$	−58.4242	+	15.6547i	−1.90457	+	0.510329i	−0.908948	+	0.416910i	$0.863113\pi$
$941$	−58.4242	+	15.6547i	−1.90457	+	0.510329i	−0.995627	+	0.0934192i	$0.970220\pi$
$942$	23.5234	−	10.3483i	0.766433	−	0.337165i
$943$	−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
$947$	−23.9994	−	41.5683i	−0.779877	−	1.35079i	−0.932012	−	0.362427i	$-0.881948\pi$
$947$	−23.9994	−	41.5683i	−0.779877	−	1.35079i	0.152135	−	0.988360i	$-0.451385\pi$
$948$	−19.8110	+	89.2935i	−0.643431	+	2.90012i
$949$	−0.976162	−	3.64309i	−0.0316876	−	0.118260i
$950$	−0.850391	−	0.280922i	−0.0275903	−	0.00911431i
$951$	−52.8840			−1.71488
$952$	24.5239	−	11.1896i	0.794824	−	0.362656i
$953$	−18.6569	−	18.6569i	−0.604356	−	0.604356i	0.337110	−	0.941465i	$-0.390551\pi$
$953$	−18.6569	−	18.6569i	−0.604356	−	0.604356i	−0.941465	+	0.337110i	$0.890551\pi$
$954$	−29.5150	−	3.23482i	−0.955583	−	0.104731i
$955$	4.37719	−	2.68098i	0.141643	−	0.0867543i
$956$	−2.11779	+	9.54548i	−0.0684944	+	0.308723i
$957$	−12.5594	+	7.25118i	−0.405988	+	0.234397i
$958$	−25.6372	+	34.9589i	−0.828301	+	1.12947i
$959$	−31.3926	+	29.5723i	−1.01372	+	0.954938i
$960$	24.7800	+	55.7635i	0.799772	+	1.79976i
$961$	17.9589	+	31.1058i	0.579320	+	1.00341i
$962$	6.61763	−	2.91119i	0.213361	−	0.0938605i
$963$	−71.6393	−	41.3610i	−2.30854	−	1.33284i
$964$	10.8275	+	9.92475i	0.348729	+	0.319655i
$965$	29.2621	−	8.66057i	0.941979	−	0.278794i
$966$	−13.0107	+	30.7035i	−0.418611	+	0.987868i
$967$	−17.8541	+	17.8541i	−0.574148	+	0.574148i	−0.933285	−	0.359137i	$-0.883071\pi$
$967$	−17.8541	+	17.8541i	−0.574148	+	0.574148i	0.359137	+	0.933285i	$0.383071\pi$
$968$	−18.1209	+	3.59992i	−0.582428	+	0.115706i
$969$	−1.34780	−	0.778151i	−0.0432975	−	0.0249978i
$970$	29.5085	+	34.8787i	0.947462	+	1.11989i
$971$	41.5480	+	11.1328i	1.33334	+	0.357267i	0.853959	−	0.520340i	$-0.174195\pi$
$971$	41.5480	+	11.1328i	1.33334	+	0.357267i	0.479380	+	0.877607i	$0.340861\pi$
$972$	46.6852	+	148.150i	1.49743	+	4.75190i
$973$	11.8485	−	39.4675i	0.379847	−	1.26527i
$974$	−2.69948	−	17.5482i	−0.0864968	−	0.562280i
$975$	7.49125	−	14.6859i	0.239912	−	0.470324i
$976$	30.1072	−	35.8569i	0.963709	−	1.14775i
$977$	−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	$0.547749\pi$
$978$	7.23020	−	65.9694i	0.231196	−	2.10947i
$979$	−5.20567	+	5.20567i	−0.166374	+	0.166374i
$980$	−22.3501	−	21.9197i	−0.713949	−	0.700198i
$981$	−112.557	−	112.557i	−3.59367	−	3.59367i
$982$	7.42630	+	9.25451i	0.236983	+	0.295323i
$983$	4.52994	+	16.9060i	0.144483	+	0.539217i	0.999778	+	0.0210759i	$0.00670916\pi$
$983$	4.52994	+	16.9060i	0.144483	+	0.539217i	−0.855295	+	0.518141i	$0.826624\pi$
$984$	59.1824	−	51.8763i	1.88667	−	1.65376i
$985$	17.6275	−	0.457578i	0.561657	−	0.0145796i
$986$	6.05913	−	8.26221i	0.192962	−	0.263122i
$987$	−40.0251	−	12.0160i	−1.27401	−	0.382472i
$988$	−0.217165	−	0.113093i	−0.00690893	−	0.00359797i
$989$	0.648150	−	2.41893i	0.0206100	−	0.0769175i
$990$	−44.0716	+	37.2860i	−1.40069	+	1.18503i
$991$	−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	$0.808953\pi$
$992$	−22.2414	−	40.5795i	−0.706165	−	1.28840i
$993$	86.8385	+	86.8385i	2.75574	+	2.75574i
$994$	−50.2776	+	20.3493i	−1.59471	+	0.645441i
$995$	8.66140	−	15.9437i	0.274585	−	0.505448i
$996$	35.2654	−	38.4730i	1.11743	−	1.21906i
$997$	−10.1087	+	17.5088i	−0.320146	+	0.554509i	−0.980518	−	0.196430i	$-0.937065\pi$
$997$	−10.1087	+	17.5088i	−0.320146	+	0.554509i	0.660372	+	0.750939i	$0.270399\pi$
$998$	15.8847	−	40.8377i	0.502821	−	1.29269i
$999$	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.ch.c.437.88	yes	360
5.3	odd	4		560.2.cz.c.213.48	yes	360
7.5	odd	6	inner	560.2.ch.c.117.33	✓	360
16.13	even	4		560.2.cz.c.157.14	yes	360
35.33	even	12		560.2.cz.c.453.14	yes	360
80.13	odd	4	inner	560.2.ch.c.493.33	yes	360
112.61	odd	12		560.2.cz.c.397.48	yes	360
560.173	even	12	inner	560.2.ch.c.173.88	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.ch.c.117.33	✓	360	7.5	odd	6	inner
560.2.ch.c.173.88	yes	360	560.173	even	12	inner
560.2.ch.c.437.88	yes	360	1.1	even	1	trivial
560.2.ch.c.493.33	yes	360	80.13	odd	4	inner
560.2.cz.c.157.14	yes	360	16.13	even	4
560.2.cz.c.213.48	yes	360	5.3	odd	4
560.2.cz.c.397.48	yes	360	112.61	odd	12
560.2.cz.c.453.14	yes	360	35.33	even	12

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.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40580 + 0.154074i) q^{2} +(1.70560 - 2.95419i) q^{3} +(1.95252 + 0.433194i) q^{4} +(0.0580249 + 2.23531i) q^{5} +(2.85289 - 3.89019i) q^{6} +(1.25390 + 2.32975i) q^{7} +(2.67810 + 0.909815i) q^{8} +(-4.31815 - 7.47925i) q^{9} +(-0.262833 + 3.15134i) q^{10} +(-2.04176 + 0.547088i) q^{11} +(4.60996 - 5.02926i) q^{12} -0.966590 q^{13} +(1.40377 + 3.46835i) q^{14} +(6.70251 + 3.64114i) q^{15} +(3.62469 + 1.69164i) q^{16} +(-0.932306 - 3.47941i) q^{17} +(-4.91807 - 11.1796i) q^{18} +(0.122340 + 0.0327809i) q^{19} +(-0.855030 + 4.38964i) q^{20} +(9.02117 + 0.269364i) q^{21} +(-2.95459 + 0.454511i) q^{22} +(-0.676197 + 2.52360i) q^{23} +(7.25554 - 6.35984i) q^{24} +(-4.99327 + 0.259408i) q^{25} +(-1.35883 - 0.148927i) q^{26} -19.2265 q^{27} +(1.43904 + 5.09207i) q^{28} +(1.42218 + 1.42218i) q^{29} +(8.86135 + 6.15138i) q^{30} +(-7.08438 - 4.09017i) q^{31} +(4.83493 + 2.93657i) q^{32} +(-1.86623 + 6.96485i) q^{33} +(-0.774543 - 5.03499i) q^{34} +(-5.13497 + 2.93805i) q^{35} +(-5.19132 - 16.4740i) q^{36} +(-4.58027 + 2.64442i) q^{37} +(0.166934 + 0.0649326i) q^{38} +(-1.64862 + 2.85549i) q^{39} +(-1.87833 + 6.03920i) q^{40} +8.15686 q^{41} +(12.6404 + 1.76860i) q^{42} -0.958523 q^{43} +(-4.22358 + 0.183724i) q^{44} +(16.4679 - 10.0864i) q^{45} +(-1.33942 + 3.44348i) q^{46} +(-4.47258 - 1.19843i) q^{47} +(11.1797 - 7.82274i) q^{48} +(-3.85547 + 5.84255i) q^{49} +(-7.05948 - 0.404660i) q^{50} +(-11.8690 - 3.18028i) q^{51} +(-1.88729 - 0.418721i) q^{52} +(1.21552 - 2.10535i) q^{53} +(-27.0286 - 2.96232i) q^{54} +(-1.34139 - 4.53223i) q^{55} +(1.23843 + 7.38013i) q^{56} +(0.305504 - 0.305504i) q^{57} +(1.78018 + 2.21842i) q^{58} +(6.94519 - 1.86096i) q^{59} +(11.5095 + 10.0129i) q^{60} +(3.02951 - 11.3063i) q^{61} +(-9.32900 - 6.84146i) q^{62} +(12.0103 - 19.4384i) q^{63} +(6.34447 + 4.87316i) q^{64} +(-0.0560863 - 2.16063i) q^{65} +(-3.69664 + 9.50362i) q^{66} +(2.81304 - 4.87233i) q^{67} +(-0.313088 - 7.19750i) q^{68} +(6.30187 + 6.30187i) q^{69} +(-7.67139 + 3.33913i) q^{70} +14.4961i q^{71} +(-4.75971 - 23.9589i) q^{72} +(1.00990 + 3.76901i) q^{73} +(-6.84636 + 3.01181i) q^{74} +(-7.75018 + 15.1935i) q^{75} +(0.224671 + 0.117002i) q^{76} +(-3.83474 - 4.07079i) q^{77} +(-2.75758 + 3.76022i) q^{78} +(-11.6104 + 6.70327i) q^{79} +(-3.57103 + 8.20047i) q^{80} +(-19.8384 + 34.3611i) q^{81} +(11.4669 + 1.25676i) q^{82} +7.64983 q^{83} +(17.4973 + 4.43386i) q^{84} +(7.72348 - 2.28589i) q^{85} +(-1.34749 - 0.147684i) q^{86} +(6.62707 - 1.77572i) q^{87} +(-5.96579 - 0.392466i) q^{88} +(3.01621 - 1.74141i) q^{89} +(24.7046 - 11.6421i) q^{90} +(-1.21201 - 2.25191i) q^{91} +(-2.41350 + 4.63447i) q^{92} +(-24.1662 + 13.9524i) q^{93} +(-6.10289 - 2.37385i) q^{94} +(-0.0661768 + 0.275370i) q^{95} +(16.9216 - 9.27467i) q^{96} +(10.2159 - 10.2159i) q^{97} +(-6.32018 + 7.61940i) q^{98} +(12.9084 + 12.9084i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + 2 q^{2} - 6 q^{5} + 8 q^{7} - 4 q^{8} - 164 q^{9} - 6 q^{10} - 2 q^{11} + 18 q^{12} + 4 q^{14} - 32 q^{15} - 20 q^{16} + 4 q^{18} + 30 q^{19} - 4 q^{21} - 16 q^{22} + 10 q^{23} + 12 q^{24} + 12 q^{25}+ \cdots - 4 q^{99}+O(q^{100}) \) 360 * q + 2 * q^2 - 6 * q^5 + 8 * q^7 - 4 * q^8 - 164 * q^9 - 6 * q^10 - 2 * q^11 + 18 * q^12 + 4 * q^14 - 32 * q^15 - 20 * q^16 + 4 * q^18 + 30 * q^19 - 4 * q^21 - 16 * q^22 + 10 * q^23 + 12 * q^24 + 12 * q^25 + 10 * q^28 - 8 * q^29 + 58 * q^30 - 24 * q^31 - 38 * q^32 - 12 * q^35 + 16 * q^36 - 24 * q^38 - 28 * q^39 - 96 * q^40 - 6 * q^42 - 24 * q^43 + 20 * q^44 + 36 * q^45 - 4 * q^46 - 6 * q^47 - 64 * q^50 + 16 * q^51 - 108 * q^52 + 32 * q^53 - 24 * q^54 - 8 * q^56 + 80 * q^57 + 2 * q^58 + 84 * q^59 + 8 * q^60 - 48 * q^61 + 58 * q^63 - 36 * q^65 - 108 * q^66 - 4 * q^67 + 84 * q^68 + 72 * q^70 + 36 * q^72 - 52 * q^74 - 54 * q^75 - 52 * q^77 + 96 * q^78 - 120 * q^80 - 124 * q^81 - 150 * q^82 + 28 * q^84 - 4 * q^85 + 8 * q^86 + 20 * q^88 + 48 * q^89 + 28 * q^91 + 84 * q^92 - 72 * q^94 - 26 * q^95 - 60 * q^96 + 26 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

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