LMFDB - Embedded newform 560.2.cr.a.109.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(109,560)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 6, 8]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("560.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.47162251319$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$92$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			109.3
Character	$\chi$	$=$	560.109
Dual form			560.2.cr.a.149.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41398 - 0.0258393i) q^{2} +(-0.476445 - 1.77812i) q^{3} +(1.99866 + 0.0730723i) q^{4} +(-1.16968 - 1.90574i) q^{5} +(0.627737 + 2.52653i) q^{6} +(1.31827 - 2.29394i) q^{7} +(-2.82418 - 0.154967i) q^{8} +(-0.336625 + 0.194351i) q^{9} +(1.60466 + 2.72490i) q^{10} +(-0.198849 - 0.742114i) q^{11} +(-0.822323 - 3.58868i) q^{12} +(3.10762 - 3.10762i) q^{13} +(-1.92328 + 3.20951i) q^{14} +(-2.83134 + 2.98781i) q^{15} +(3.98932 + 0.292094i) q^{16} +(-0.714794 - 0.412687i) q^{17} +(0.481002 - 0.266109i) q^{18} +(0.968916 - 3.61604i) q^{19} +(-2.19854 - 3.89441i) q^{20} +(-4.70698 - 1.25111i) q^{21} +(0.261992 + 1.05447i) q^{22} +(1.01599 + 1.75974i) q^{23} +(1.07002 + 5.09555i) q^{24} +(-2.26370 + 4.45821i) q^{25} +(-4.47440 + 4.31381i) q^{26} +(-3.39906 - 3.39906i) q^{27} +(2.80241 - 4.48848i) q^{28} +(5.08244 + 5.08244i) q^{29} +(4.08066 - 4.15153i) q^{30} +(0.923821 - 1.60010i) q^{31} +(-5.63326 - 0.516095i) q^{32} +(-1.22482 + 0.707153i) q^{33} +(1.00004 + 0.601999i) q^{34} +(-5.91361 + 0.170881i) q^{35} +(-0.687002 + 0.363844i) q^{36} +(-0.0238820 + 0.0891288i) q^{37} +(-1.46346 + 5.08797i) q^{38} +(-7.00632 - 4.04510i) q^{39} +(3.00806 + 5.56342i) q^{40} +6.02642i q^{41} +(6.62323 + 1.89067i) q^{42} +(0.689366 + 0.689366i) q^{43} +(-0.343204 - 1.49777i) q^{44} +(0.764125 + 0.414192i) q^{45} +(-1.39111 - 2.51449i) q^{46} +(-7.84110 + 4.52706i) q^{47} +(-1.38132 - 7.23265i) q^{48} +(-3.52430 - 6.04808i) q^{49} +(3.31602 - 6.24532i) q^{50} +(-0.393245 + 1.46761i) q^{51} +(6.43817 - 5.98401i) q^{52} +(-4.60794 + 1.23470i) q^{53} +(4.71836 + 4.89402i) q^{54} +(-1.18169 + 1.24699i) q^{55} +(-4.07853 + 6.27420i) q^{56} -6.89138 q^{57} +(-7.05513 - 7.31778i) q^{58} +(-3.00914 - 11.2302i) q^{59} +(-5.87723 + 5.76473i) q^{60} +(-1.31826 + 4.91981i) q^{61} +(-1.34761 + 2.23864i) q^{62} +(0.00206383 + 1.02840i) q^{63} +(7.95197 + 0.875306i) q^{64} +(-9.55724 - 2.28740i) q^{65} +(1.75015 - 0.968250i) q^{66} +(0.118575 + 0.442530i) q^{67} +(-1.39848 - 0.877054i) q^{68} +(2.64497 - 2.64497i) q^{69} +(8.36613 - 0.0888179i) q^{70} +2.07493i q^{71} +(0.980807 - 0.496715i) q^{72} +(-7.58430 + 13.1364i) q^{73} +(0.0360716 - 0.125409i) q^{74} +(9.00575 + 1.90103i) q^{75} +(2.20077 - 7.15645i) q^{76} +(-1.96450 - 0.522163i) q^{77} +(9.80226 + 5.90072i) q^{78} +(-2.86503 - 4.96238i) q^{79} +(-4.10957 - 7.94427i) q^{80} +(-5.00751 + 8.67326i) q^{81} +(0.155718 - 8.52122i) q^{82} +(11.5823 - 11.5823i) q^{83} +(-9.31625 - 2.84450i) q^{84} +(0.0496059 + 1.84492i) q^{85} +(-0.956936 - 0.992561i) q^{86} +(6.61567 - 11.4587i) q^{87} +(0.446582 + 2.12668i) q^{88} +(11.6500 - 6.72615i) q^{89} +(-1.06975 - 0.605403i) q^{90} +(-3.03199 - 11.2254i) q^{91} +(1.90203 + 3.59137i) q^{92} +(-3.28532 - 0.880300i) q^{93} +(11.2041 - 6.19856i) q^{94} +(-8.02456 + 2.38311i) q^{95} +(1.76626 + 10.2625i) q^{96} -7.96570i q^{97} +(4.82701 + 8.64292i) q^{98} +(0.211168 + 0.211168i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q - 4 q^{4} - 2 q^{5} - 16 q^{6} - 8 q^{10} - 4 q^{11} + 16 q^{14} - 16 q^{15} - 4 q^{16} - 4 q^{19} - 8 q^{20} + 4 q^{21} - 4 q^{24} - 4 q^{26} - 16 q^{29} + 22 q^{30} - 56 q^{31} - 96 q^{34} + 18 q^{35}+ \cdots - 112 q^{99}+O(q^{100}) $ 368 * q - 4 * q^4 - 2 * q^5 - 16 * q^6 - 8 * q^10 - 4 * q^11 + 16 * q^14 - 16 * q^15 - 4 * q^16 - 4 * q^19 - 8 * q^20 + 4 * q^21 - 4 * q^24 - 4 * q^26 - 16 * q^29 + 22 * q^30 - 56 * q^31 - 96 * q^34 + 18 * q^35 + 32 * q^36 - 14 * q^40 - 12 * q^44 - 16 * q^45 + 12 * q^46 - 16 * q^49 - 12 * q^50 - 28 * q^51 - 8 * q^54 - 64 * q^56 + 12 * q^59 - 54 * q^60 - 4 * q^61 - 88 * q^64 - 4 * q^65 - 44 * q^66 + 8 * q^69 + 88 * q^70 - 72 * q^74 + 10 * q^75 + 104 * q^76 - 8 * q^79 + 48 * q^80 + 112 * q^81 + 68 * q^84 - 28 * q^85 + 44 * q^86 - 92 * q^90 - 80 * q^91 - 20 * q^94 + 20 * q^95 - 36 * q^96 - 112 * q^99

Character values

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

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.41398	−	0.0258393i	−0.999833	−	0.0182711i
$2$	−1.41398	−	0.0258393i	−0.999833	−	0.0182711i
$3$	−0.476445	−	1.77812i	−0.275076	−	1.02660i	−0.955791	−	0.294048i	$-0.904997\pi$
$3$	−0.476445	−	1.77812i	−0.275076	−	1.02660i	0.680715	−	0.732548i	$-0.261669\pi$
$4$	1.99866	+	0.0730723i	0.999332	+	0.0365361i
$5$	−1.16968	−	1.90574i	−0.523096	−	0.852274i
$5$	−1.16968	−	1.90574i	−0.523096	−	0.852274i
$6$	0.627737	+	2.52653i	0.256273	+	1.03145i
$7$	1.31827	−	2.29394i	0.498261	−	0.867027i
$7$	1.31827	−	2.29394i	0.498261	−	0.867027i
$8$	−2.82418	−	0.154967i	−0.998498	−	0.0547890i
$9$	−0.336625	+	0.194351i	−0.112208	+	0.0647835i
$10$	1.60466	+	2.72490i	0.507437	+	0.861689i
$11$	−0.198849	−	0.742114i	−0.0599552	−	0.223756i	0.929447	−	0.368955i	$-0.120284\pi$
$11$	−0.198849	−	0.742114i	−0.0599552	−	0.223756i	−0.989402	+	0.145199i	$0.953618\pi$
$12$	−0.822323	−	3.58868i	−0.237384	−	1.03596i
$13$	3.10762	−	3.10762i	0.861899	−	0.861899i	−0.129660	−	0.991559i	$-0.541389\pi$
$13$	3.10762	−	3.10762i	0.861899	−	0.861899i	0.991559	+	0.129660i	$0.0413885\pi$
$14$	−1.92328	+	3.20951i	−0.514019	+	0.857779i
$15$	−2.83134	+	2.98781i	−0.731050	+	0.771449i
$16$	3.98932	+	0.292094i	0.997330	+	0.0730235i
$17$	−0.714794	−	0.412687i	−0.173363	−	0.100091i	0.410808	−	0.911722i	$-0.365247\pi$
$17$	−0.714794	−	0.412687i	−0.173363	−	0.100091i	−0.584171	+	0.811631i	$0.698580\pi$
$18$	0.481002	−	0.266109i	0.113373	−	0.0627225i
$19$	0.968916	−	3.61604i	0.222284	−	0.829577i	−0.761190	−	0.648529i	$-0.775384\pi$
$19$	0.968916	−	3.61604i	0.222284	−	0.829577i	0.983474	−	0.181048i	$-0.0579489\pi$
$20$	−2.19854	−	3.89441i	−0.491608	−	0.870816i
$21$	−4.70698	−	1.25111i	−1.02715	−	0.273015i
$22$	0.261992	+	1.05447i	0.0558569	+	0.224814i
$23$	1.01599	+	1.75974i	0.211848	+	0.366932i	0.952293	−	0.305186i	$-0.0987185\pi$
$23$	1.01599	+	1.75974i	0.211848	+	0.366932i	−0.740445	+	0.672117i	$0.765385\pi$
$24$	1.07002	+	5.09555i	0.218416	+	1.04013i
$25$	−2.26370	+	4.45821i	−0.452740	+	0.891642i
$26$	−4.47440	+	4.31381i	−0.877503	+	0.846007i
$27$	−3.39906	−	3.39906i	−0.654148	−	0.654148i
$28$	2.80241	−	4.48848i	0.529606	−	0.848244i
$29$	5.08244	+	5.08244i	0.943785	+	0.943785i	0.998502	−	0.0547167i	$-0.0174256\pi$
$29$	5.08244	+	5.08244i	0.943785	+	0.943785i	−0.0547167	+	0.998502i	$0.517426\pi$
$30$	4.08066	−	4.15153i	0.745023	−	0.757963i
$31$	0.923821	−	1.60010i	0.165923	−	0.287387i	−0.771060	−	0.636763i	$-0.780273\pi$
$31$	0.923821	−	1.60010i	0.165923	−	0.287387i	0.936983	+	0.349376i	$0.113606\pi$
$32$	−5.63326	−	0.516095i	−0.995830	−	0.0912336i
$33$	−1.22482	+	0.707153i	−0.213215	+	0.123100i
$34$	1.00004	+	0.601999i	0.171505	+	0.103242i
$35$	−5.91361	+	0.170881i	−0.999583	+	0.0288841i
$36$	−0.687002	+	0.363844i	−0.114500	+	0.0606406i
$37$	−0.0238820	+	0.0891288i	−0.00392617	+	0.0146527i	−0.967861	−	0.251485i	$-0.919081\pi$
$37$	−0.0238820	+	0.0891288i	−0.00392617	+	0.0146527i	0.963935	+	0.266138i	$0.0857477\pi$
$38$	−1.46346	+	5.08797i	−0.237405	+	0.825377i
$39$	−7.00632	−	4.04510i	−1.12191	−	0.647735i
$40$	3.00806	+	5.56342i	0.475616	+	0.879653i
$41$			6.02642i			0.941168i	0.882355	+	0.470584i	$0.155957\pi$
$41$			6.02642i			0.941168i	−0.882355	+	0.470584i	$0.844043\pi$
$42$	6.62323	+	1.89067i	1.02199	+	0.291736i
$43$	0.689366	+	0.689366i	0.105127	+	0.105127i	0.757714	−	0.652587i	$-0.226316\pi$
$43$	0.689366	+	0.689366i	0.105127	+	0.105127i	−0.652587	+	0.757714i	$0.726316\pi$
$44$	−0.343204	−	1.49777i	−0.0517400	−	0.225797i
$45$	0.764125	+	0.414192i	0.113909	+	0.0617442i
$46$	−1.39111	−	2.51449i	−0.205108	−	0.370741i
$47$	−7.84110	+	4.52706i	−1.14374	+	0.660340i	−0.947355	−	0.320186i	$-0.896255\pi$
$47$	−7.84110	+	4.52706i	−1.14374	+	0.660340i	−0.196388	+	0.980526i	$0.562921\pi$
$48$	−1.38132	−	7.23265i	−0.199376	−	1.04394i
$49$	−3.52430	−	6.04808i	−0.503472	−	0.864012i
$50$	3.31602	−	6.24532i	0.468956	−	0.883222i
$51$	−0.393245	+	1.46761i	−0.0550653	+	0.205507i
$52$	6.43817	−	5.98401i	0.892814	−	0.829833i
$53$	−4.60794	+	1.23470i	−0.632950	+	0.169598i	−0.561008	−	0.827810i	$-0.689586\pi$
$53$	−4.60794	+	1.23470i	−0.632950	+	0.169598i	−0.0719419	+	0.997409i	$0.522920\pi$
$54$	4.71836	+	4.89402i	0.642087	+	0.665991i
$55$	−1.18169	+	1.24699i	−0.159339	+	0.168144i
$56$	−4.07853	+	6.27420i	−0.545016	+	0.838426i
$57$	−6.89138			−0.912786
$58$	−7.05513	−	7.31778i	−0.926384	−	0.960872i
$59$	−3.00914	−	11.2302i	−0.391756	−	1.46205i	−0.827236	−	0.561855i	$-0.810088\pi$
$59$	−3.00914	−	11.2302i	−0.391756	−	1.46205i	0.435480	−	0.900199i	$-0.356579\pi$
$60$	−5.87723	+	5.76473i	−0.758748	+	0.744224i
$61$	−1.31826	+	4.91981i	−0.168786	+	0.629917i	0.828741	+	0.559632i	$0.189057\pi$
$61$	−1.31826	+	4.91981i	−0.168786	+	0.629917i	−0.997527	+	0.0702848i	$0.977609\pi$
$62$	−1.34761	+	2.23864i	−0.171146	+	0.284308i
$63$	0.00206383	+	1.02840i	0.000260018	+	0.129567i
$64$	7.95197	+	0.875306i	0.993996	+	0.109413i
$65$	−9.55724	−	2.28740i	−1.18543	−	0.283717i
$66$	1.75015	−	0.968250i	0.215428	−	0.119183i
$67$	0.118575	+	0.442530i	0.0144863	+	0.0540636i	0.972791	−	0.231686i	$-0.0744242\pi$
$67$	0.118575	+	0.442530i	0.0144863	+	0.0540636i	−0.958304	+	0.285749i	$0.907757\pi$
$68$	−1.39848	−	0.877054i	−0.169590	−	0.106358i
$69$	2.64497	−	2.64497i	0.318416	−	0.318416i
$70$	8.36613	−	0.0888179i	0.999944	−	0.0106158i
$71$			2.07493i			0.246249i	0.992391	+	0.123124i	$0.0392914\pi$
$71$			2.07493i			0.246249i	−0.992391	+	0.123124i	$0.960709\pi$
$72$	0.980807	−	0.496715i	0.115589	−	0.0585384i
$73$	−7.58430	+	13.1364i	−0.887675	+	1.53750i	−0.0450580	+	0.998984i	$0.514347\pi$
$73$	−7.58430	+	13.1364i	−0.887675	+	1.53750i	−0.842617	+	0.538514i	$0.818986\pi$
$74$	0.0360716	−	0.125409i	0.00419324	−	0.0145785i
$75$	9.00575	+	1.90103i	1.03989	+	0.219512i
$76$	2.20077	−	7.15645i	0.252446	−	0.820902i
$77$	−1.96450	−	0.522163i	−0.223876	−	0.0595060i
$78$	9.80226	+	5.90072i	1.10989	+	0.668125i
$79$	−2.86503	−	4.96238i	−0.322342	−	0.558312i	0.658629	−	0.752468i	$-0.271137\pi$
$79$	−2.86503	−	4.96238i	−0.322342	−	0.558312i	−0.980971	+	0.194156i	$0.937803\pi$
$80$	−4.10957	−	7.94427i	−0.459464	−	0.888196i
$81$	−5.00751	+	8.67326i	−0.556390	+	0.963695i
$82$	0.155718	−	8.52122i	0.0171962	−	0.941011i
$83$	11.5823	−	11.5823i	1.27132	−	1.27132i	0.325927	−	0.945395i	$-0.394324\pi$
$83$	11.5823	−	11.5823i	1.27132	−	1.27132i	0.945395	−	0.325927i	$-0.105676\pi$
$84$	−9.31625	−	2.84450i	−1.01649	−	0.310361i
$85$	0.0496059	+	1.84492i	0.00538051	+	0.200110i
$86$	−0.956936	−	0.992561i	−0.103189	−	0.107031i
$87$	6.61567	−	11.4587i	0.709274	−	1.22850i
$88$	0.446582	+	2.12668i	0.0476058	+	0.226704i
$89$	11.6500	−	6.72615i	1.23490	−	0.712971i	0.266854	−	0.963737i	$-0.414016\pi$
$89$	11.6500	−	6.72615i	1.23490	−	0.712971i	0.968048	+	0.250766i	$0.0806826\pi$
$90$	−1.06975	−	0.605403i	−0.112762	−	0.0638151i
$91$	−3.03199	−	11.2254i	−0.317839	−	1.17674i
$92$	1.90203	+	3.59137i	0.198300	+	0.374427i
$93$	−3.28532	−	0.880300i	−0.340672	−	0.0912828i
$94$	11.2041	−	6.19856i	1.15562	−	0.639332i
$95$	−8.02456	+	2.38311i	−0.823303	+	0.244502i
$96$	1.76626	+	10.2625i	0.180268	+	1.04741i
$97$		−	7.96570i		−	0.808794i	−0.914584	−	0.404397i	$-0.867481\pi$
$97$		−	7.96570i		−	0.808794i	0.914584	−	0.404397i	$-0.132519\pi$
$98$	4.82701	+	8.64292i	0.487601	+	0.873066i
$99$	0.211168	+	0.211168i	0.0212231	+	0.0212231i
$100$	−4.85015	+	8.74506i	−0.485015	+	0.874506i
$101$	3.16869	+	11.8257i	0.315297	+	1.17670i	0.923713	+	0.383085i	$0.125139\pi$
$101$	3.16869	+	11.8257i	0.315297	+	1.17670i	−0.608416	+	0.793618i	$0.708195\pi$
$102$	0.593962	−	2.06501i	0.0588110	−	0.204466i
$103$	8.70645	+	15.0800i	0.857872	+	1.48588i	0.873955	+	0.486007i	$0.161547\pi$
$103$	8.70645	+	15.0800i	0.857872	+	1.48588i	−0.0160826	+	0.999871i	$0.505119\pi$
$104$	−9.25805	+	8.29490i	−0.907827	+	0.813382i
$105$	3.12136	+	10.4337i	0.304613	+	1.01822i
$106$	6.54743	−	1.62677i	0.635943	−	0.158005i
$107$	2.56428	−	9.57002i	0.247898	−	0.925169i	−0.724006	−	0.689793i	$-0.757701\pi$
$107$	2.56428	−	9.57002i	0.247898	−	0.925169i	0.971905	−	0.235375i	$-0.0756320\pi$
$108$	−6.54519	−	7.04195i	−0.629812	−	0.677612i
$109$	−5.67130	+	1.51962i	−0.543212	+	0.145553i	−0.519982	−	0.854177i	$-0.674061\pi$
$109$	−5.67130	+	1.51962i	−0.543212	+	0.145553i	−0.0232293	+	0.999730i	$0.507395\pi$
$110$	1.70310	−	1.73268i	0.162384	−	0.165205i
$111$	0.169860			0.0161224
$112$	5.92907	−	8.76619i	0.560244	−	0.828328i
$113$			17.2940i			1.62688i	0.581650	+	0.813439i	$0.302407\pi$
$113$			17.2940i			1.62688i	−0.581650	+	0.813439i	$0.697593\pi$
$114$	9.74426	+	0.178068i	0.912633	+	0.0166776i
$115$	2.16523	−	3.99454i	0.201909	−	0.372493i
$116$	9.78671	+	10.5295i	0.908673	+	0.977637i
$117$	−0.442135	+	1.65007i	−0.0408754	+	0.152549i
$118$	3.96467	+	15.9571i	0.364977	+	1.46897i
$119$	−1.88897	+	1.09566i	−0.173162	+	0.100439i
$120$	8.45923	−	7.99934i	0.772219	−	0.730236i
$121$	9.01509	−	5.20486i	0.819553	−	0.473169i
$122$	1.99111	−	6.92243i	0.180267	−	0.626728i
$123$	10.7157	−	2.87126i	0.966200	−	0.258893i
$124$	1.96333	−	3.13057i	0.176312	−	0.281133i
$125$	11.1440	−	0.900649i	0.996750	−	0.0805565i
$126$	0.0236550	−	1.45419i	0.00210735	−	0.129550i
$127$			8.43015i			0.748055i	0.927418	+	0.374027i	$0.122023\pi$
$127$			8.43015i			0.748055i	−0.927418	+	0.374027i	$0.877977\pi$
$128$	−11.2213	−	1.44314i	−0.991831	−	0.127556i
$129$	0.897329	−	1.55422i	0.0790054	−	0.136841i
$130$	13.4546	+	3.48129i	1.18005	+	0.305329i
$131$	1.89225	−	7.06197i	0.165327	−	0.617008i	−0.832672	−	0.553767i	$-0.813190\pi$
$131$	1.89225	−	7.06197i	0.165327	−	0.617008i	0.997998	−	0.0632405i	$-0.0201435\pi$
$132$	−2.49969	+	1.32386i	−0.217570	+	0.115227i
$133$	−7.01768	−	6.98957i	−0.608510	−	0.606073i
$134$	−0.156228	−	0.628791i	−0.0134961	−	0.0543192i
$135$	−2.50192	+	10.4535i	−0.215331	+	0.899696i
$136$	1.95475	+	1.27627i	0.167619	+	0.109439i
$137$	8.76985	−	15.1898i	0.749259	−	1.29775i	−0.198919	−	0.980016i	$-0.563743\pi$
$137$	8.76985	−	15.1898i	0.749259	−	1.29775i	0.948178	−	0.317739i	$-0.102923\pi$
$138$	−3.80827	+	3.67158i	−0.324181	+	0.312545i
$139$	8.85314	−	8.85314i	0.750913	−	0.750913i	−0.223737	−	0.974650i	$-0.571826\pi$
$139$	8.85314	−	8.85314i	0.750913	−	0.750913i	0.974650	+	0.223737i	$0.0718255\pi$
$140$	−11.8318	−	0.0905880i	−0.999971	−	0.00765609i
$141$	11.7855	+	11.7855i	0.992519	+	0.992519i
$142$	0.0536146	−	2.93390i	0.00449924	−	0.246208i
$143$	−2.92415	−	1.68826i	−0.244530	−	0.141179i
$144$	−1.39967	+	0.677001i	−0.116639	+	0.0564167i
$145$	3.74099	−	15.6306i	0.310672	−	1.29805i
$146$	11.0635	−	18.3786i	0.915618	−	1.52102i
$147$	−9.07506	+	9.14820i	−0.748498	+	0.754531i
$148$	−0.0542449	+	0.176393i	−0.00445891	+	0.0144995i
$149$	0.938801	+	0.251551i	0.0769096	+	0.0206079i	0.297069	−	0.954856i	$-0.403991\pi$
$149$	0.938801	+	0.251551i	0.0769096	+	0.0206079i	−0.220159	+	0.975464i	$0.570658\pi$
$150$	−12.6848	−	2.92072i	−1.03571	−	0.238476i
$151$	6.73879	+	3.89064i	0.548395	+	0.316616i	0.748474	−	0.663164i	$-0.230787\pi$
$151$	6.73879	+	3.89064i	0.548395	+	0.316616i	−0.200080	+	0.979780i	$0.564120\pi$
$152$	−3.29676	+	10.0622i	−0.267402	+	0.816152i
$153$	0.320823			0.0259370
$154$	2.76427	+	0.789088i	0.222751	+	0.0635865i
$155$	−4.12996	+	0.111045i	−0.331726	+	0.00891938i
$156$	−13.7077	−	8.59677i	−1.09749	−	0.688293i
$157$	2.72191	+	10.1583i	0.217232	+	0.810720i	0.985369	+	0.170435i	$0.0545173\pi$
$157$	2.72191	+	10.1583i	0.217232	+	0.810720i	−0.768137	+	0.640285i	$0.778816\pi$
$158$	3.92287	+	7.09073i	0.312087	+	0.564108i
$159$	4.39087	+	7.60520i	0.348218	+	0.603132i
$160$	5.60557	+	11.3392i	0.443159	+	0.896443i
$161$	5.37609	−	0.0107889i	0.423695	−	0.000850283i
$162$	7.30461	−	12.1344i	0.573905	−	0.953369i
$163$	9.79561	+	2.62472i	0.767251	+	0.205584i	0.621157	−	0.783686i	$-0.286663\pi$
$163$	9.79561	+	2.62472i	0.767251	+	0.205584i	0.146094	+	0.989271i	$0.453330\pi$
$164$	−0.440364	+	12.0448i	−0.0343867	+	0.940540i
$165$	2.78030	+	1.50706i	0.216446	+	0.117324i
$166$	−16.6764	+	16.0778i	−1.29434	+	1.24788i
$167$	17.9815			1.39145			0.695724	−	0.718309i	$-0.255084\pi$
$167$	17.9815			1.39145			0.695724	+	0.718309i	$0.255084\pi$
$168$	13.0995	+	4.26279i	1.01065	+	0.328881i
$169$		−	6.31461i		−	0.485739i
$170$	−0.0224701	−	2.60996i	−0.00172338	−	0.200175i
$171$	0.376619	+	1.40556i	0.0288007	+	0.107486i
$172$	1.32744	+	1.42819i	0.101216	+	0.108898i
$173$	3.07313	+	0.823442i	0.233646	+	0.0626051i	0.373742	−	0.927533i	$-0.378075\pi$
$173$	3.07313	+	0.823442i	0.233646	+	0.0626051i	−0.140096	+	0.990138i	$0.544741\pi$
$174$	−9.65049	+	16.0314i	−0.731602	+	1.21533i
$175$	7.24268	+	11.0699i	0.547495	+	0.836809i
$176$	−0.576505	−	3.01861i	−0.0434557	−	0.227536i
$177$	−18.5350	+	10.7012i	−1.39318	+	0.804351i
$178$	−16.6467	+	9.20960i	−1.24772	+	0.690289i
$179$	−24.0246	+	6.43737i	−1.79568	+	0.481152i	−0.993290	−	0.115646i	$-0.963106\pi$
$179$	−24.0246	+	6.43737i	−1.79568	+	0.481152i	−0.802392	+	0.596798i	$0.796439\pi$
$180$	1.49696	+	0.883668i	0.111577	+	0.0658647i
$181$	6.71013	−	6.71013i	0.498760	−	0.498760i	−0.412292	−	0.911052i	$-0.635272\pi$
$181$	6.71013	−	6.71013i	0.498760	−	0.498760i	0.911052	+	0.412292i	$0.135272\pi$
$182$	3.99711	+	15.9508i	0.296286	+	1.18235i
$183$	9.37607			0.693099
$184$	−2.59663	−	5.12727i	−0.191426	−	0.377987i
$185$	0.197791	−	0.0587392i	0.0145419	−	0.00431859i
$186$	4.62263	+	1.32961i	0.338947	+	0.0974921i
$187$	−0.164124	+	0.612521i	−0.0120020	+	0.0447919i
$188$	−16.0025	+	8.47511i	−1.16711	+	0.618111i
$189$	−12.2781	+	3.31633i	−0.893101	+	0.241228i
$190$	11.4081	−	3.16231i	0.827633	−	0.229418i
$191$	−8.27665	−	14.3356i	−0.598877	−	1.03729i	−0.992987	−	0.118222i	$-0.962280\pi$
$191$	−8.27665	−	14.3356i	−0.598877	−	1.03729i	0.394110	−	0.919063i	$-0.371053\pi$
$192$	−2.23228	−	14.5566i	−0.161101	−	1.05053i
$193$	12.9046	+	7.45046i	0.928892	+	0.536296i	0.886461	−	0.462803i	$-0.153156\pi$
$193$	12.9046	+	7.45046i	0.928892	+	0.536296i	0.0424309	+	0.999099i	$0.486490\pi$
$194$	−0.205828	+	11.2633i	−0.0147776	+	0.808659i
$195$	0.486230	+	18.0837i	0.0348197	+	1.29500i
$196$	−6.60195	−	12.3456i	−0.471568	−	0.881830i
$197$	−6.58567	−	6.58567i	−0.469210	−	0.469210i	0.432449	−	0.901658i	$-0.357650\pi$
$197$	−6.58567	−	6.58567i	−0.469210	−	0.469210i	−0.901658	+	0.432449i	$0.857650\pi$
$198$	−0.293130	−	0.304043i	−0.0208318	−	0.0216074i
$199$	−10.5053	−	6.06523i	−0.744700	−	0.429953i	0.0790755	−	0.996869i	$-0.474803\pi$
$199$	−10.5053	−	6.06523i	−0.744700	−	0.429953i	−0.823776	+	0.566916i	$0.808137\pi$
$200$	7.08397	−	12.2400i	0.500912	−	0.865498i
$201$	0.730375	−	0.421682i	0.0515167	−	0.0297432i
$202$	−4.17489	−	16.8032i	−0.293744	−	1.18227i
$203$	18.3589	−	4.95875i	1.28854	−	0.348036i
$204$	−0.893206	+	2.90453i	−0.0625370	+	0.203357i
$205$	11.4848	−	7.04898i	0.802133	−	0.492322i
$206$	−11.9211	−	21.5478i	−0.830580	−	1.50130i
$207$	−0.684014	−	0.394915i	−0.0475422	−	0.0274485i
$208$	13.3050	−	11.4896i	0.922537	−	0.796659i
$209$	−2.87618			−0.198950
$210$	−4.14393	−	14.8336i	−0.285958	−	1.02362i
$211$	0.931070	+	0.931070i	0.0640975	+	0.0640975i	0.738429	−	0.674331i	$-0.235568\pi$
$211$	0.931070	+	0.931070i	0.0640975	+	0.0640975i	−0.674331	+	0.738429i	$0.735568\pi$
$212$	−9.29996	+	2.13103i	−0.638724	+	0.146360i
$213$	3.68947	−	0.988590i	0.252798	−	0.0677371i
$214$	−3.87312	+	13.4655i	−0.264761	+	0.920485i
$215$	0.507417	−	2.12009i	0.0346055	−	0.144589i
$216$	9.07280	+	10.1263i	0.617326	+	0.689006i
$217$	−2.45269	−	4.22857i	−0.166500	−	0.287054i
$218$	8.05835	−	2.00217i	0.545780	−	0.135604i
$219$	26.9715	+	7.22700i	1.82257	+	0.488356i
$220$	−2.45292	+	2.40596i	−0.165376	+	0.162210i
$221$	−3.50378	+	0.938835i	−0.235690	+	0.0631529i
$222$	−0.240178	−	0.00438905i	−0.0161197	−	0.000294574i
$223$		−	10.7228i		−	0.718049i	−0.933328	−	0.359024i	$-0.883109\pi$
$223$		−	10.7228i		−	0.718049i	0.933328	−	0.359024i	$-0.116891\pi$
$224$	−8.61008	+	12.2420i	−0.575285	+	0.817953i
$225$	−0.104437	−	1.94070i	−0.00696250	−	0.129380i
$226$	0.446863	−	24.4533i	0.0297249	−	1.62661i
$227$	−4.22435	−	15.7655i	−0.280380	−	1.04639i	−0.952150	−	0.305633i	$-0.901132\pi$
$227$	−4.22435	−	15.7655i	−0.280380	−	1.04639i	0.671769	−	0.740760i	$-0.265535\pi$
$228$	−13.7736	−	0.503569i	−0.912176	−	0.0333497i
$229$	−11.4001	−	3.05465i	−0.753340	−	0.201857i	−0.138341	−	0.990385i	$-0.544177\pi$
$229$	−11.4001	−	3.05465i	−0.753340	−	0.201857i	−0.614999	+	0.788528i	$0.710844\pi$
$230$	−3.16481	+	5.59225i	−0.208681	+	0.368742i
$231$	0.00750934	+	3.74189i	0.000494078	+	0.246199i
$232$	−13.5661	−	15.1413i	−0.890659	−	0.994077i
$233$	−14.8384	−	25.7008i	−0.972095	−	1.68372i	−0.689205	−	0.724566i	$-0.742040\pi$
$233$	−14.8384	−	25.7008i	−0.972095	−	1.68372i	−0.282890	−	0.959152i	$-0.591293\pi$
$234$	0.667806	−	2.32174i	0.0436558	−	0.151777i
$235$	17.7990	+	9.64791i	1.16108	+	0.629360i
$236$	−5.19363	−	22.6654i	−0.338077	−	1.47539i
$237$	−7.45867	+	7.45867i	−0.484493	+	0.484493i
$238$	2.69928	−	1.50043i	0.174968	−	0.0972583i
$239$	−6.85260			−0.443258			−0.221629	−	0.975131i	$-0.571137\pi$
$239$	−6.85260			−0.443258			−0.221629	+	0.975131i	$0.571137\pi$
$240$	−12.1679	+	11.0923i	−0.785432	+	0.716005i
$241$	−12.4854	+	21.6253i	−0.804253	+	1.39301i	0.112542	+	0.993647i	$0.464101\pi$
$241$	−12.4854	+	21.6253i	−0.804253	+	1.39301i	−0.916794	+	0.399360i	$0.869232\pi$
$242$	−12.8816	+	7.12662i	−0.828062	+	0.458116i
$243$	3.87828	+	1.03918i	0.248792	+	0.0666636i
$244$	−2.99426	+	9.73671i	−0.191688	+	0.623329i
$245$	−7.40378	+	13.7907i	−0.473010	+	0.881057i
$246$	−15.2259	+	3.78301i	−0.970769	+	0.241196i
$247$	−8.22626	−	14.2483i	−0.523425	−	0.906598i
$248$	−2.85700	+	4.37582i	−0.181420	+	0.277865i
$249$	−26.1130	−	15.0763i	−1.65484	−	0.955425i
$250$	−15.7806	+	0.985544i	−0.998056	+	0.0623313i
$251$	0.321644	−	0.321644i	0.0203020	−	0.0203020i	−0.696883	−	0.717185i	$-0.745430\pi$
$251$	0.321644	−	0.321644i	0.0203020	−	0.0203020i	0.717185	+	0.696883i	$0.245430\pi$
$252$	−0.0710229	+	2.05559i	−0.00447402	+	0.129490i
$253$	1.10390	−	1.10390i	0.0694016	−	0.0694016i
$254$	0.217829	−	11.9200i	0.0136678	−	0.747930i
$255$	3.25686	−	0.967210i	0.203952	−	0.0605690i
$256$	15.8294	+	2.33051i	0.989335	+	0.145657i
$257$	7.36049	−	4.24958i	0.459135	−	0.265081i	−0.252546	−	0.967585i	$-0.581268\pi$
$257$	7.36049	−	4.24958i	0.459135	−	0.265081i	0.711680	+	0.702503i	$0.247934\pi$
$258$	−1.30896	+	2.17444i	−0.0814925	+	0.135375i
$259$	0.172973	+	0.172280i	0.0107480	+	0.0107050i
$260$	−18.9346	−	5.27012i	−1.17427	−	0.326839i
$261$	−2.69865	−	0.723101i	−0.167042	−	0.0447588i
$262$	−2.85808	+	9.93658i	−0.176573	+	0.613884i
$263$	−2.66836	+	4.62173i	−0.164538	+	0.284988i	−0.936491	−	0.350691i	$-0.885947\pi$
$263$	−2.66836	+	4.62173i	−0.164538	+	0.284988i	0.771953	+	0.635679i	$0.219280\pi$
$264$	3.56871	−	1.80732i	0.219639	−	0.111233i
$265$	7.74283	+	7.33735i	0.475638	+	0.450730i
$266$	9.74224	+	10.0644i	0.597335	+	0.617090i
$267$	−17.5105	−	17.5105i	−1.07162	−	1.07162i
$268$	0.204656	+	0.893133i	0.0125013	+	0.0545568i
$269$	16.0968	−	4.31311i	0.981436	−	0.262975i	0.267787	−	0.963478i	$-0.413708\pi$
$269$	16.0968	−	4.31311i	0.981436	−	0.262975i	0.713649	+	0.700503i	$0.247041\pi$
$270$	3.80776	−	14.7164i	0.231733	−	0.895612i
$271$	−5.83113	−	10.0998i	−0.354216	−	0.613520i	0.632767	−	0.774342i	$-0.281919\pi$
$271$	−5.83113	−	10.0998i	−0.354216	−	0.613520i	−0.986984	+	0.160822i	$0.948586\pi$
$272$	−2.73100	−	1.85513i	−0.165591	−	0.112484i
$273$	−18.5155	+	10.7395i	−1.12061	+	0.649985i
$274$	−12.7929	+	21.2515i	−0.772845	+	1.28385i
$275$	3.75863	+	0.793414i	0.226654	+	0.0478446i
$276$	5.47967	−	5.09313i	0.329838	−	0.306570i
$277$	18.1938	−	4.87501i	1.09316	−	0.292911i	0.333183	−	0.942862i	$-0.391877\pi$
$277$	18.1938	−	4.87501i	1.09316	−	0.292911i	0.759976	+	0.649951i	$0.225211\pi$
$278$	−12.7469	+	12.2894i	−0.764508	+	0.737068i
$279$			0.718180i			0.0429963i
$280$	16.7276	+	0.433815i	0.999664	+	0.0259254i
$281$		−	8.43759i		−	0.503344i	−0.967813	−	0.251672i	$-0.919020\pi$
$281$		−	8.43759i		−	0.503344i	0.967813	−	0.251672i	$-0.0809805\pi$
$282$	−16.3599	−	16.9690i	−0.974218	−	1.01049i
$283$	−21.3773	+	5.72803i	−1.27075	+	0.340496i	−0.830317	−	0.557291i	$-0.811841\pi$
$283$	−21.3773	+	5.72803i	−1.27075	+	0.340496i	−0.440431	+	0.897787i	$0.645174\pi$
$284$	−0.151620	+	4.14709i	−0.00899698	+	0.246084i
$285$	8.06071	+	13.1332i	0.477475	+	0.777943i
$286$	4.09106	+	2.46272i	0.241910	+	0.145624i
$287$	13.8242	+	7.94448i	0.816019	+	0.468948i
$288$	1.99660	−	0.921097i	0.117651	−	0.0542762i
$289$	−8.15938	−	14.1325i	−0.479964	−	0.831321i
$290$	−5.69356	+	22.0047i	−0.334337	+	1.29216i
$291$	−14.1639	+	3.79522i	−0.830305	+	0.222480i
$292$	−16.1184	+	25.7010i	−0.943256	+	1.50404i
$293$	−6.91903	−	6.91903i	−0.404214	−	0.404214i	0.475501	−	0.879715i	$-0.342267\pi$
$293$	−6.91903	−	6.91903i	−0.404214	−	0.404214i	−0.879715	+	0.475501i	$0.842267\pi$
$294$	13.0683	−	12.7009i	0.762160	−	0.740729i
$295$	−17.8822	+	18.8704i	−1.04114	+	1.09868i
$296$	0.0812590	−	0.248015i	0.00472308	−	0.0144156i
$297$	−1.84659	+	3.19838i	−0.107150	+	0.185589i
$298$	−1.32094	−	0.379945i	−0.0765202	−	0.0220096i
$299$	8.62591	+	2.31131i	0.498849	+	0.133666i
$300$	17.8606	+	4.45760i	1.03118	+	0.257360i
$301$	2.49014	−	0.672589i	0.143529	−	0.0387674i
$302$	−9.42796	−	5.67540i	−0.542518	−	0.326583i
$303$	19.5178	−	11.2686i	1.12127	−	0.647365i
$304$	4.92154	−	14.1425i	0.282270	−	0.811130i
$305$	10.9178	−	3.24234i	0.625152	−	0.185656i
$306$	−0.453637	−	0.00828984i	−0.0259327	−	0.000473899i
$307$	−9.72380	+	9.72380i	−0.554967	+	0.554967i	−0.927870	−	0.372903i	$-0.878362\pi$
$307$	−9.72380	+	9.72380i	−0.554967	+	0.554967i	0.372903	+	0.927870i	$0.378362\pi$
$308$	−3.88822	−	1.18718i	−0.221552	−	0.0676458i
$309$	22.6659	−	22.6659i	1.28942	−	1.28942i
$310$	5.84254	−	0.0503005i	0.331834	−	0.00285688i
$311$	22.0403	+	12.7250i	1.24979	+	0.721568i	0.971068	−	0.238803i	$-0.0767550\pi$
$311$	22.0403	+	12.7250i	1.24979	+	0.721568i	0.278725	+	0.960371i	$0.410088\pi$
$312$	19.1603	+	12.5098i	1.08474	+	0.708230i
$313$	−8.95689	−	15.5138i	−0.506273	−	0.876891i	−0.999974	−	0.00725877i	$-0.997689\pi$
$313$	−8.95689	−	15.5138i	−0.506273	−	0.876891i	0.493701	−	0.869632i	$-0.335644\pi$
$314$	−3.58623	−	14.4339i	−0.202383	−	0.814554i
$315$	1.95746	−	1.20684i	0.110290	−	0.0679975i
$316$	−5.36363	−	10.1275i	−0.301728	−	0.569716i
$317$	24.8247	+	6.65176i	1.39429	+	0.373600i	0.876292	−	0.481780i	$-0.160009\pi$
$317$	24.8247	+	6.65176i	1.39429	+	0.373600i	0.518002	+	0.855380i	$0.326676\pi$
$318$	−6.01207	−	10.8670i	−0.337140	−	0.609393i
$319$	2.76111	−	4.78238i	0.154593	−	0.267762i
$320$	−7.63315	−	16.1782i	−0.426706	−	0.904390i
$321$	−18.2384			−1.01797
$322$	−7.60195	−	0.123659i	−0.423640	−	0.00689124i
$323$	−2.18487	+	2.18487i	−0.121569	+	0.121569i
$324$	−10.6421	+	16.9690i	−0.591228	+	0.942723i
$325$	6.81971	+	20.8892i	0.378289	+	1.15872i
$326$	−13.7829	−	3.96441i	−0.763367	−	0.219569i
$327$	5.40412	+	9.36021i	0.298849	+	0.517621i
$328$	0.933893	−	17.0197i	0.0515656	−	0.939755i
$329$	0.0480734	+	23.9549i	0.00265037	+	1.32068i
$330$	−3.89234	−	2.20279i	−0.214266	−	0.121259i
$331$	27.0278	+	7.24206i	1.48558	+	0.398060i	0.908242	−	0.418445i	$-0.137425\pi$
$331$	27.0278	+	7.24206i	1.48558	+	0.398060i	0.577338	+	0.816505i	$0.304092\pi$
$332$	23.9955	−	22.3028i	1.31692	−	1.22402i
$333$	−0.00928295	−	0.0346445i	−0.000508703	−	0.00189850i
$334$	−25.4254	−	0.464628i	−1.39122	−	0.0254233i
$335$	0.704652	−	0.743592i	0.0384992	−	0.0406268i
$336$	−18.4122	−	6.36597i	−1.00447	−	0.347292i
$337$		−	24.1432i		−	1.31516i	−0.753384	−	0.657581i	$-0.771580\pi$
$337$		−	24.1432i		−	1.31516i	0.753384	−	0.657581i	$-0.228420\pi$
$338$	−0.163165	+	8.92871i	−0.00887499	+	0.485658i
$339$	30.7507	−	8.23962i	1.67015	−	0.447515i
$340$	−0.0356673	+	3.69101i	−0.00193433	+	0.200173i
$341$	−1.37116	−	0.367401i	−0.0742525	−	0.0198959i
$342$	−0.496212	−	1.99716i	−0.0268320	−	0.107994i
$343$	−18.5199	+	0.111500i	−0.999982	+	0.00602044i
$344$	−1.84006	−	2.05372i	−0.0992097	−	0.110729i
$345$	−8.13438	−	1.94686i	−0.437940	−	0.104815i
$346$	−4.32406	−	1.24374i	−0.232463	−	0.0668637i
$347$	−33.6756	+	9.02336i	−1.80780	+	0.484399i	−0.995152	−	0.0983519i	$-0.968643\pi$
$347$	−33.6756	+	9.02336i	−1.80780	+	0.484399i	−0.812651	+	0.582751i	$0.801976\pi$
$348$	14.0598	−	22.4186i	0.753685	−	1.20176i
$349$	−3.21795	−	3.21795i	−0.172253	−	0.172253i	0.615716	−	0.787969i	$-0.288867\pi$
$349$	−3.21795	−	3.21795i	−0.172253	−	0.172253i	−0.787969	+	0.615716i	$0.788867\pi$
$350$	−9.95495	−	15.8398i	−0.532114	−	0.846672i
$351$	−21.1259			−1.12762
$352$	0.737166	+	4.28315i	0.0392911	+	0.228292i
$353$	6.15248	+	3.55214i	0.327464	+	0.189061i	0.654714	−	0.755876i	$-0.272789\pi$
$353$	6.15248	+	3.55214i	0.327464	+	0.189061i	−0.327251	+	0.944937i	$0.606122\pi$
$354$	26.4846	−	14.6523i	1.40764	−	0.778762i
$355$	3.95428	−	2.42700i	0.209871	−	0.128812i
$356$	23.7760	−	12.5920i	1.26013	−	0.667376i
$357$	2.84820	+	2.83679i	0.150743	+	0.150139i
$358$	34.1366	−	8.48152i	1.80417	−	0.448262i
$359$	−22.5531	+	13.0211i	−1.19031	+	0.687225i	−0.958377	−	0.285507i	$-0.907838\pi$
$359$	−22.5531	+	13.0211i	−1.19031	+	0.687225i	−0.231932	+	0.972732i	$0.574505\pi$
$360$	−2.09384	−	1.28817i	−0.110355	−	0.0678924i
$361$	4.31752	+	2.49272i	0.227238	+	0.131196i
$362$	−9.66136	+	9.31459i	−0.507790	+	0.489564i
$363$	−13.5501	−	13.5501i	−0.711193	−	0.711193i
$364$	−5.23967	−	22.6573i	−0.274633	−	1.18757i
$365$	33.9058	−	0.911650i	1.77471	−	0.0477179i
$366$	−13.2576	−	0.242271i	−0.692983	−	0.0126637i
$367$	22.7562	+	13.1383i	1.18786	+	0.685813i	0.957820	−	0.287367i	$-0.0927801\pi$
$367$	22.7562	+	13.1383i	1.18786	+	0.685813i	0.230043	+	0.973181i	$0.426113\pi$
$368$	3.53909	+	7.31694i	0.184488	+	0.381422i
$369$	−1.17124	−	2.02864i	−0.0609722	−	0.105607i
$370$	−0.281189	+	0.0779451i	−0.0146183	+	0.00405217i
$371$	−3.24222	+	12.1980i	−0.168328	+	0.633289i
$372$	−6.50193	−	1.99949i	−0.337110	−	0.103669i
$373$	−4.71809	+	17.6082i	−0.244294	+	0.911716i	0.729443	+	0.684041i	$0.239779\pi$
$373$	−4.71809	+	17.6082i	−0.244294	+	0.911716i	−0.973737	+	0.227675i	$0.926888\pi$
$374$	0.247895	−	0.861850i	0.0128184	−	0.0445652i
$375$	−6.91096	−	19.3862i	−0.356881	−	1.00110i
$376$	22.8462	−	11.5701i	1.17820	−	0.596684i
$377$	31.5886			1.62689
$378$	17.4467	−	4.37196i	0.897360	−	0.224870i
$379$	−6.09775	+	6.09775i	−0.313220	+	0.313220i	−0.846156	−	0.532936i	$-0.821089\pi$
$379$	−6.09775	+	6.09775i	−0.313220	+	0.313220i	0.532936	+	0.846156i	$0.321089\pi$
$380$	−16.2125	+	4.17666i	−0.831686	+	0.214258i
$381$	14.9898	−	4.01650i	0.767951	−	0.205772i
$382$	11.3326	+	20.4840i	0.579825	+	1.04805i
$383$	−6.23196	+	3.59802i	−0.318438	+	0.183850i	−0.650696	−	0.759338i	$-0.725523\pi$
$383$	−6.23196	+	3.59802i	−0.318438	+	0.183850i	0.332258	+	0.943189i	$0.392189\pi$
$384$	2.78026	+	20.6403i	0.141880	+	1.05330i
$385$	1.30273	+	4.35459i	0.0663931	+	0.221931i
$386$	−18.0543	−	10.8682i	−0.918938	−	0.553178i
$387$	−0.366037	−	0.0980792i	−0.0186067	−	0.00498565i
$388$	0.582071	−	15.9208i	0.0295502	−	0.808254i
$389$	2.90453	+	10.8398i	0.147265	+	0.549602i	0.999644	+	0.0266770i	$0.00849256\pi$
$389$	2.90453	+	10.8398i	0.147265	+	0.549602i	−0.852379	+	0.522925i	$0.824841\pi$
$390$	−0.220249	−	25.5825i	−0.0111527	−	1.29542i
$391$		−	1.67714i		−	0.0848165i
$392$	9.01601	+	17.6270i	0.455377	+	0.890299i
$393$	−13.4586			−0.678895
$394$	9.14182	+	9.48216i	0.460558	+	0.477704i
$395$	−6.10585	+	11.2644i	−0.307219	+	0.566774i
$396$	0.406623	+	0.437484i	0.0204336	+	0.0219844i
$397$	29.9371	+	8.02161i	1.50250	+	0.402593i	0.913936	−	0.405859i	$-0.133027\pi$
$397$	29.9371	+	8.02161i	1.50250	+	0.402593i	0.588562	+	0.808452i	$0.299694\pi$
$398$	14.6975	+	8.84755i	0.736720	+	0.443488i
$399$	−9.08474	+	15.8084i	−0.454806	+	0.791410i
$400$	−10.3328	+	17.1240i	−0.516642	+	0.856201i
$401$	14.9111	+	25.8267i	0.744624	+	1.28973i	0.950370	+	0.311121i	$0.100704\pi$
$401$	14.9111	+	25.8267i	0.744624	+	1.28973i	−0.205747	+	0.978605i	$0.565962\pi$
$402$	−1.04363	+	0.577377i	−0.0520515	+	0.0287969i
$403$	−2.10163	−	7.84340i	−0.104690	−	0.390708i
$404$	5.46902	+	23.8672i	0.272094	+	1.18744i
$405$	22.3862	−	0.601914i	1.11238	−	0.0299093i
$406$	−26.0871	+	6.53718i	−1.29468	+	0.324435i
$407$	0.0708926			0.00351402
$408$	1.33802	−	4.08385i	0.0662421	−	0.202181i
$409$	−25.0386	−	14.4561i	−1.23808	−	0.714806i	−0.269379	−	0.963034i	$-0.586818\pi$
$409$	−25.0386	−	14.4561i	−1.23808	−	0.714806i	−0.968702	+	0.248228i	$0.920152\pi$
$410$	−16.4214	+	9.67033i	−0.810994	+	0.477584i
$411$	−31.1876	−	8.35670i	−1.53837	−	0.412206i
$412$	16.2993	+	30.7761i	0.803011	+	1.51623i
$413$	−29.7284	−	7.90178i	−1.46284	−	0.388821i
$414$	0.956976	+	0.576076i	0.0470328	+	0.0283126i
$415$	−35.6204	−	8.52529i	−1.74854	−	0.418490i
$416$	−19.1099	+	15.9022i	−0.936938	+	0.779670i
$417$	−19.9599	−	11.5239i	−0.977443	−	0.564327i
$418$	4.06686	+	0.0743184i	0.198916	+	0.00363503i
$419$	−8.55790	−	8.55790i	−0.418081	−	0.418081i	0.466461	−	0.884542i	$-0.345529\pi$
$419$	−8.55790	−	8.55790i	−0.418081	−	0.418081i	−0.884542	+	0.466461i	$0.845529\pi$
$420$	5.47613	+	21.0815i	0.267208	+	1.02867i
$421$	−15.6268	+	15.6268i	−0.761602	+	0.761602i	−0.976612	−	0.215010i	$-0.931022\pi$
$421$	−15.6268	+	15.6268i	−0.761602	+	0.761602i	0.215010	+	0.976612i	$0.431022\pi$
$422$	−1.29245	−	1.34057i	−0.0629157	−	0.0652579i
$423$	1.75967	−	3.04785i	0.0855583	−	0.148191i
$424$	13.2050	−	2.77292i	0.641291	−	0.134665i
$425$	3.45792	−	2.25250i	0.167734	−	0.109263i
$426$	−5.24237	+	1.30251i	−0.253994	+	0.0631069i
$427$	9.54790	+	9.50966i	0.462055	+	0.460205i
$428$	5.82444	−	18.9399i	0.281535	−	0.915494i
$429$	−1.60873	+	6.00385i	−0.0776701	+	0.289869i
$430$	−0.772257	+	2.98465i	−0.0372415	+	0.143933i
$431$	14.1339	−	24.4806i	0.680805	−	1.17919i	−0.293931	−	0.955827i	$-0.594963\pi$
$431$	14.1339	−	24.4806i	0.680805	−	1.17919i	0.974736	−	0.223362i	$-0.0717032\pi$
$432$	−12.5671	−	14.5528i	−0.604634	−	0.700170i
$433$			10.1558i			0.488058i	0.969768	+	0.244029i	$0.0784692\pi$
$433$			10.1558i			0.488058i	−0.969768	+	0.244029i	$0.921531\pi$
$434$	3.35879	+	6.04247i	0.161227	+	0.290048i
$435$	−29.5755	+	0.795218i	−1.41804	+	0.0381278i
$436$	−11.4461	+	2.62279i	−0.548167	+	0.125609i
$437$	7.34771	−	1.96881i	0.351489	−	0.0941811i
$438$	−37.9504	−	10.9157i	−1.81334	−	0.521574i
$439$	10.2949	−	5.94376i	0.491348	−	0.283680i	−0.233785	−	0.972288i	$-0.575111\pi$
$439$	10.2949	−	5.94376i	0.491348	−	0.283680i	0.725134	+	0.688608i	$0.241778\pi$
$440$	3.53054	−	3.33860i	0.168312	−	0.159161i
$441$	2.36182	+	1.35099i	0.112467	+	0.0643326i
$442$	4.97853	−	1.23696i	0.236804	−	0.0588360i
$443$	−0.838885	+	3.13076i	−0.0398566	+	0.148747i	−0.982987	−	0.183677i	$-0.941200\pi$
$443$	−0.838885	+	3.13076i	−0.0398566	+	0.148747i	0.943130	+	0.332424i	$0.107867\pi$
$444$	0.339493	+	0.0124120i	0.0161116	+	0.000589050i
$445$	−26.4451	−	14.3345i	−1.25362	−	0.679521i
$446$	−0.277068	+	15.1617i	−0.0131196	+	0.717929i
$447$		−	1.78915i		−	0.0846238i
$448$	12.4908	−	17.0874i	0.590134	−	0.807305i
$449$	32.2458			1.52177			0.760886	−	0.648886i	$-0.224765\pi$
$449$	32.2458			1.52177			0.760886	+	0.648886i	$0.224765\pi$
$450$	0.0975261	+	2.74680i	0.00459742	+	0.129485i
$451$	4.47229	−	1.19835i	0.210592	−	0.0564279i
$452$	−1.26371	+	34.5648i	−0.0594399	+	1.62579i
$453$	3.70735	−	13.8360i	0.174187	−	0.650073i
$454$	5.56577	+	22.4012i	0.261215	+	1.05134i
$455$	−17.8462	+	18.9083i	−0.836644	+	0.886434i
$456$	19.4625	+	1.06793i	0.911415	+	0.0500106i
$457$	−1.39657	−	2.41893i	−0.0653288	−	0.113153i	0.831511	−	0.555508i	$-0.187476\pi$
$457$	−1.39657	−	2.41893i	−0.0653288	−	0.113153i	−0.896840	+	0.442355i	$0.854143\pi$
$458$	16.0406	+	4.61378i	0.749526	+	0.215588i
$459$	1.02688	+	3.83237i	0.0479307	+	0.178880i
$460$	4.61947	−	7.82553i	0.215384	−	0.364867i
$461$	−17.3414	−	17.3414i	−0.807669	−	0.807669i	0.176612	−	0.984281i	$-0.443486\pi$
$461$	−17.3414	−	17.3414i	−0.807669	−	0.807669i	−0.984281	+	0.176612i	$0.943486\pi$
$462$	0.0860697	−	5.29115i	0.00400433	−	0.246166i
$463$			24.3556i			1.13190i	0.824439	+	0.565951i	$0.191491\pi$
$463$			24.3556i			1.13190i	−0.824439	+	0.565951i	$0.808509\pi$
$464$	18.7909	+	21.7600i	0.872347	+	1.01018i
$465$	2.16515	+	7.29065i	0.100406	+	0.338096i
$466$	20.3171	+	36.7238i	0.941170	+	1.70120i
$467$	2.47735	+	0.663804i	0.114638	+	0.0307172i	0.315682	−	0.948865i	$-0.397767\pi$
$467$	2.47735	+	0.663804i	0.114638	+	0.0307172i	−0.201044	+	0.979582i	$0.564433\pi$
$468$	−1.00425	+	3.26563i	−0.0464217	+	0.150954i
$469$	1.17145	+	0.311371i	0.0540925	+	0.0143778i
$470$	−24.9181	−	14.1018i	−1.14939	−	0.650469i
$471$	16.7658	−	9.67974i	0.772527	−	0.446019i
$472$	6.75802	+	32.1825i	0.311063	+	1.48132i
$473$	0.374509	−	0.648668i	0.0172199	−	0.0298258i
$474$	10.7391	−	10.3537i	0.493264	−	0.475560i
$475$	13.9277	+	12.5053i	0.639049	+	0.573781i
$476$	−3.85548	+	2.05182i	−0.176716	+	0.0940452i
$477$	1.31119	−	1.31119i	0.0600351	−	0.0600351i
$478$	9.68943	+	0.177066i	0.443184	+	0.00809882i
$479$	15.4042	−	26.6808i	0.703834	−	1.21908i	−0.263276	−	0.964721i	$-0.584803\pi$
$479$	15.4042	−	26.6808i	0.703834	−	1.21908i	0.967111	−	0.254357i	$-0.0818637\pi$
$480$	17.4917	−	15.3699i	0.798383	−	0.701535i
$481$	0.202762	+	0.351195i	0.00924516	+	0.0160131i
$482$	18.2128	−	30.2550i	0.829570	−	1.37808i
$483$	−2.58060	−	9.55418i	−0.117421	−	0.434730i
$484$	18.3985	−	9.74402i	0.836294	−	0.442910i
$485$	−15.1806	+	9.31731i	−0.689314	+	0.423077i
$486$	−5.45695	−	1.56959i	−0.247532	−	0.0711982i
$487$	−8.13697	+	14.0936i	−0.368721	+	0.638644i	−0.989366	−	0.145448i	$-0.953538\pi$
$487$	−8.13697	+	14.0936i	−0.368721	+	0.638644i	0.620645	+	0.784092i	$0.286871\pi$
$488$	4.48540	−	13.6901i	0.203045	−	0.619723i
$489$		−	18.6683i		−	0.844209i
$490$	10.8251	−	19.3085i	0.489029	−	0.872268i
$491$	−13.1859	+	13.1859i	−0.595072	+	0.595072i	−0.938997	−	0.343925i	$-0.888243\pi$
$491$	−13.1859	+	13.1859i	−0.595072	+	0.595072i	0.343925	+	0.938997i	$0.388243\pi$
$492$	21.6269	−	4.95566i	0.975014	−	0.223418i
$493$	−1.53544	−	5.73035i	−0.0691529	−	0.258082i
$494$	11.2636	+	20.3593i	0.506773	+	0.916010i
$495$	0.155433	−	0.649429i	0.00698617	−	0.0291897i
$496$	4.15280	−	6.11349i	0.186466	−	0.274504i
$497$	4.75976	+	2.73533i	0.213504	+	0.122696i
$498$	36.5336	+	21.9924i	1.63711	+	0.985501i
$499$	−2.39662	+	8.94432i	−0.107288	+	0.400403i	−0.998595	−	0.0529975i	$-0.983122\pi$
$499$	−2.39662	+	8.94432i	−0.107288	+	0.400403i	0.891307	+	0.453400i	$0.149789\pi$
$500$	22.3389	−	0.985777i	0.999028	−	0.0440853i
$501$	−8.56718	−	31.9732i	−0.382753	−	1.42846i
$502$	−0.463109	+	0.446487i	−0.0206696	+	0.0199277i
$503$	27.2997			1.21723			0.608617	−	0.793464i	$-0.291724\pi$
$503$	27.2997			1.21723			0.608617	+	0.793464i	$0.291724\pi$
$504$	0.153540	−	2.90472i	0.00683920	−	0.129386i
$505$	18.8304	−	19.8710i	0.837943	−	0.884249i
$506$	−1.58941	+	1.53237i	−0.0706581	+	0.0681220i
$507$	−11.2281	+	3.00856i	−0.498658	+	0.133615i
$508$	−0.616010	+	16.8490i	−0.0273310	+	0.747555i
$509$	−5.63079	+	21.0144i	−0.249580	+	0.931447i	0.721445	+	0.692471i	$0.243478\pi$
$509$	−5.63079	+	21.0144i	−0.249580	+	0.931447i	−0.971026	+	0.238975i	$0.923189\pi$
$510$	−4.63011	+	1.28346i	−0.205025	+	0.0568325i
$511$	20.1359	+	34.7153i	0.890759	+	1.53571i
$512$	−22.3221	−	3.70431i	−0.986509	−	0.163709i
$513$	−15.5845	+	8.99773i	−0.688074	+	0.397259i
$514$	−10.5174	+	5.81862i	−0.463901	+	0.256648i
$515$	18.5549	−	34.2310i	0.817625	−	1.50840i
$516$	1.90703	−	3.04079i	0.0839523	−	0.133863i
$517$	4.91879	+	4.91879i	0.216328	+	0.216328i
$518$	−0.240128	−	0.248070i	−0.0105506	−	0.0108996i
$519$		−	5.85671i		−	0.257081i
$520$	26.6369	+	7.94108i	1.16810	+	0.348240i
$521$	−10.5880	−	6.11300i	−0.463870	−	0.267816i	0.249800	−	0.968297i	$-0.419635\pi$
$521$	−10.5880	−	6.11300i	−0.463870	−	0.267816i	−0.713670	+	0.700482i	$0.752968\pi$
$522$	3.79715	+	1.09218i	0.166197	+	0.0478034i
$523$	−3.03849	+	11.3398i	−0.132864	+	0.495855i	−0.999998	−	0.00222085i	$-0.999293\pi$
$523$	−3.03849	+	11.3398i	−0.132864	+	0.495855i	0.867134	+	0.498075i	$0.165960\pi$
$524$	4.29801	−	13.9762i	0.187759	−	0.610555i
$525$	16.2329	−	18.1526i	0.708462	−	0.792243i
$526$	3.89242	−	6.46607i	0.169717	−	0.281934i
$527$	−1.32068	+	0.762497i	−0.0575299	+	0.0332149i
$528$	−5.09277	+	2.46330i	−0.221635	+	0.107201i
$529$	9.43554	−	16.3428i	0.410241	−	0.710558i
$530$	−10.7586	−	10.5749i	−0.467323	−	0.459345i
$531$	3.19556	+	3.19556i	0.138675	+	0.138675i
$532$	−13.5152	−	14.4826i	−0.585960	−	0.627900i
$533$	18.7278	+	18.7278i	0.811192	+	0.811192i
$534$	24.3070	+	25.2119i	1.05187	+	1.09103i
$535$	−21.2374	+	6.30700i	−0.918172	+	0.272675i
$536$	−0.266301	−	1.26816i	−0.0115024	−	0.0547761i
$537$	22.8928	+	39.6515i	0.987897	+	1.71109i
$538$	−22.8719	+	5.68271i	−0.986077	+	0.244999i
$539$	−3.78756	+	3.81809i	−0.163142	+	0.164457i
$540$	−5.76435	+	20.7103i	−0.248058	+	0.891228i
$541$	10.2808	−	38.3683i	0.442005	−	1.64958i	−0.281721	−	0.959496i	$-0.590905\pi$
$541$	10.2808	−	38.3683i	0.442005	−	1.64958i	0.723726	−	0.690088i	$-0.242428\pi$
$542$	7.98412	+	14.4316i	0.342947	+	0.619890i
$543$	−15.1284	−	8.73439i	−0.649222	−	0.374829i
$544$	3.81364	+	2.69367i	0.163508	+	0.115490i
$545$	9.52960	+	9.03056i	0.408203	+	0.386827i
$546$	26.4580	−	14.7070i	1.13230	−	0.629402i
$547$	−8.89816	+	8.89816i	−0.380458	+	0.380458i	−0.871267	−	0.490809i	$-0.836701\pi$
$547$	−8.89816	+	8.89816i	−0.380458	+	0.380458i	0.490809	+	0.871267i	$0.336701\pi$
$548$	18.6379	−	29.7185i	0.796174	−	1.26951i
$549$	−0.512408	−	1.91233i	−0.0218691	−	0.0816164i
$550$	−5.29412	−	1.21899i	−0.225742	−	0.0519779i
$551$	23.3028	−	13.4539i	0.992731	−	0.573154i
$552$	−7.87974	+	7.05997i	−0.335384	+	0.300492i
$553$	−15.1603	+	0.0304241i	−0.644682	+	0.00129377i
$554$	−25.8516	+	6.42304i	−1.09833	+	0.272889i
$555$	−0.198682	−	0.323709i	−0.00843356	−	0.0137407i
$556$	18.3414	−	17.0475i	0.777847	−	0.722976i
$557$	−6.69116	−	24.9717i	−0.283514	−	1.05809i	−0.949919	−	0.312497i	$-0.898835\pi$
$557$	−6.69116	−	24.9717i	−0.283514	−	1.05809i	0.666405	−	0.745590i	$-0.267832\pi$
$558$	0.0185572	−	1.01549i	0.000785591	−	0.0429892i
$559$	4.28458			0.181218
$560$	−23.6412	−	1.04563i	−0.999023	−	0.0441860i
$561$	1.16733			0.0492847
$562$	−0.218021	+	11.9306i	−0.00919666	+	0.503260i
$563$	4.85590	+	18.1225i	0.204652	+	0.763772i	0.989555	+	0.144153i	$0.0460459\pi$
$563$	4.85590	+	18.1225i	0.204652	+	0.763772i	−0.784903	+	0.619618i	$0.787287\pi$
$564$	22.6941	+	24.4165i	0.955593	+	1.02812i
$565$	32.9578	−	20.2284i	1.38655	−	0.851014i
$566$	30.3750	−	7.54693i	1.27676	−	0.317221i
$567$	13.2946	+	22.9206i	0.558323	+	0.962577i
$568$	0.321545	−	5.85997i	0.0134917	−	0.245879i
$569$	23.7632	−	13.7197i	0.996207	−	0.575160i	0.0890829	−	0.996024i	$-0.471606\pi$
$569$	23.7632	−	13.7197i	0.996207	−	0.575160i	0.907124	+	0.420864i	$0.138273\pi$
$570$	−11.0583	−	18.7783i	−0.463181	−	0.786537i
$571$	−9.02989	−	33.7000i	−0.377889	−	1.41030i	−0.849077	−	0.528269i	$-0.822841\pi$
$571$	−9.02989	−	33.7000i	−0.377889	−	1.41030i	0.471188	−	0.882033i	$-0.343825\pi$
$572$	−5.72104	−	3.58794i	−0.239209	−	0.150019i
$573$	−21.5470	+	21.5470i	−0.900137	+	0.900137i
$574$	−19.3419	−	11.5905i	−0.807314	−	0.483779i
$575$	−10.1452	+	0.545958i	−0.423084	+	0.0227680i
$576$	−2.84695	+	1.25082i	−0.118623	+	0.0521175i
$577$	16.9313	+	9.77526i	0.704857	+	0.406950i	0.809154	−	0.587597i	$-0.199926\pi$
$577$	16.9313	+	9.77526i	0.704857	+	0.406950i	−0.104297	+	0.994546i	$0.533259\pi$
$578$	11.1720	+	20.1938i	0.464694	+	0.839952i
$579$	7.09947	−	26.4956i	0.295044	−	1.10112i
$580$	8.61915	−	30.9670i	0.357891	−	1.28584i
$581$	−11.3004	−	41.8377i	−0.468820	−	1.73572i
$582$	20.1256	−	5.00037i	0.834231	−	0.207272i
$583$	1.83257	+	3.17410i	0.0758972	+	0.131458i
$584$	23.4551	−	35.9242i	0.970579	−	1.48655i
$585$	3.66176	−	1.08746i	0.151395	−	0.0449608i
$586$	9.60457	+	9.96214i	0.396761	+	0.411532i
$587$	−16.1691	−	16.1691i	−0.667372	−	0.667372i	0.289735	−	0.957107i	$-0.406433\pi$
$587$	−16.1691	−	16.1691i	−0.667372	−	0.667372i	−0.957107	+	0.289735i	$0.906433\pi$
$588$	−18.8065	+	17.6211i	−0.775566	+	0.726680i
$589$	−4.89094	−	4.89094i	−0.201528	−	0.201528i
$590$	25.7727	−	26.2203i	1.06104	−	1.07947i
$591$	−8.57238	+	14.8478i	−0.352621	+	0.610757i
$592$	−0.121307	+	0.348588i	−0.00498568	+	0.0143269i
$593$	−7.45031	+	4.30144i	−0.305948	+	0.176639i	−0.645112	−	0.764088i	$-0.723189\pi$
$593$	−7.45031	+	4.30144i	−0.305948	+	0.176639i	0.339164	+	0.940727i	$0.389856\pi$
$594$	2.69368	−	4.47473i	0.110523	−	0.183600i
$595$	4.29753	+	2.31832i	0.176182	+	0.0950420i
$596$	1.85797	+	0.571366i	0.0761053	+	0.0234041i
$597$	−5.77950	+	21.5694i	−0.236539	+	0.882776i
$598$	−12.1371	−	3.49102i	−0.496324	−	0.142759i
$599$	26.8583	+	15.5067i	1.09740	+	0.633585i	0.935537	−	0.353228i	$-0.114916\pi$
$599$	26.8583	+	15.5067i	1.09740	+	0.633585i	0.161864	+	0.986813i	$0.448249\pi$
$600$	−25.1393	−	6.76445i	−1.02631	−	0.276157i
$601$			2.87527i			0.117285i	0.998279	+	0.0586424i	$0.0186772\pi$
$601$			2.87527i			0.117285i	−0.998279	+	0.0586424i	$0.981323\pi$
$602$	−3.53838	+	0.886683i	−0.144214	+	0.0361385i
$603$	−0.125921	−	0.125921i	−0.00512791	−	0.00512791i
$604$	13.1843	+	8.26850i	0.536461	+	0.336441i
$605$	−20.4639	−	11.0924i	−0.831975	−	0.450970i
$606$	−27.8889	+	15.4292i	−1.13291	+	0.626770i
$607$	−9.65055	+	5.57175i	−0.391704	+	0.226150i	−0.682898	−	0.730514i	$-0.739281\pi$
$607$	−9.65055	+	5.57175i	−0.391704	+	0.226150i	0.291194	+	0.956664i	$0.405947\pi$
$608$	−7.32438	+	19.8701i	−0.297043	+	0.805837i
$609$	−17.5642	−	30.2816i	−0.711738	−	1.22707i
$610$	−15.5213	+	4.30248i	−0.628440	+	0.174202i
$611$	−10.2988	+	38.4356i	−0.416644	+	1.55494i
$612$	0.641218	+	0.0234433i	0.0259197	+	0.000947639i
$613$	10.8641	−	2.91102i	0.438795	−	0.117575i	−0.0326567	−	0.999467i	$-0.510397\pi$
$613$	10.8641	−	2.91102i	0.438795	−	0.117575i	0.471452	+	0.881892i	$0.343730\pi$
$614$	14.0005	−	13.4980i	0.565014	−	0.544734i
$615$	−18.0058	−	17.0629i	−0.726063	−	0.688041i
$616$	5.46718	+	1.77911i	0.220279	+	0.0716825i
$617$	−4.89542			−0.197082			−0.0985411	−	0.995133i	$-0.531418\pi$
$617$	−4.89542			−0.197082			−0.0985411	+	0.995133i	$0.531418\pi$
$618$	−32.6347	+	31.4634i	−1.31276	+	1.26564i
$619$	−10.8828	−	40.6152i	−0.437417	−	1.63246i	−0.735214	−	0.677835i	$-0.762918\pi$
$619$	−10.8828	−	40.6152i	−0.437417	−	1.63246i	0.297797	−	0.954629i	$-0.403748\pi$
$620$	−8.26252	−	0.0798431i	−0.331831	−	0.00320658i
$621$	2.52806	−	9.43486i	0.101448	−	0.378608i
$622$	−30.8357	−	18.5624i	−1.23640	−	0.744283i
$623$	−0.0714258	−	35.5914i	−0.00286161	−	1.42594i
$624$	−26.7689	−	18.1837i	−1.07161	−	0.727931i
$625$	−14.7513	−	20.1841i	−0.590053	−	0.807365i
$626$	12.2640	+	22.1676i	0.490167	+	0.885995i
$627$	1.37034	+	5.11419i	0.0547262	+	0.204241i
$628$	4.69789	+	20.5019i	0.187466	+	0.818116i
$629$	0.0538530	−	0.0538530i	0.00214726	−	0.00214726i
$630$	−2.79899	+	1.65586i	−0.111514	+	0.0659710i
$631$			9.66464i			0.384743i	0.981322	+	0.192372i	$0.0616179\pi$
$631$			9.66464i			0.384743i	−0.981322	+	0.192372i	$0.938382\pi$
$632$	7.32237	+	14.4586i	0.291268	+	0.575134i
$633$	1.21195	−	2.09916i	0.0481706	−	0.0834339i
$634$	−34.9297	−	10.0469i	−1.38724	−	0.399013i
$635$	16.0657	−	9.86057i	0.637547	−	0.391305i
$636$	8.22014	+	15.5211i	0.325950	+	0.615452i
$637$	−29.7473	−	7.84294i	−1.17863	−	0.310749i
$638$	−4.02772	+	6.69084i	−0.159459	+	0.264893i
$639$	−0.403264	−	0.698473i	−0.0159529	−	0.0276312i
$640$	10.3751	+	23.0729i	0.410110	+	0.912036i
$641$	−0.103732	+	0.179669i	−0.00409716	+	0.00709649i	−0.868067	−	0.496448i	$-0.834638\pi$
$641$	−0.103732	+	0.179669i	−0.00409716	+	0.00709649i	0.863970	+	0.503544i	$0.167971\pi$
$642$	25.7886	+	0.471266i	1.01780	+	0.0185994i
$643$	6.23677	−	6.23677i	0.245954	−	0.245954i	−0.573354	−	0.819308i	$-0.694358\pi$
$643$	6.23677	−	6.23677i	0.245954	−	0.245954i	0.819308	+	0.573354i	$0.194358\pi$
$644$	10.7458	+	0.371280i	0.423443	+	0.0146305i
$645$	−4.01153	+	0.107861i	−0.157954	+	0.00424702i
$646$	3.14581	−	3.03290i	0.123770	−	0.119328i
$647$	−6.57527	+	11.3887i	−0.258501	+	0.447736i	−0.965840	−	0.259138i	$-0.916562\pi$
$647$	−6.57527	+	11.3887i	−0.258501	+	0.447736i	0.707340	+	0.706874i	$0.249895\pi$
$648$	15.4862	−	23.7188i	0.608354	−	0.931764i
$649$	−7.73576	+	4.46624i	−0.303655	+	0.175315i
$650$	−9.10315	−	29.7130i	−0.357055	−	1.16544i
$651$	−6.35031	+	6.37585i	−0.248888	+	0.249889i
$652$	19.3863	+	5.96173i	0.759228	+	0.233479i
$653$	−5.15492	−	1.38126i	−0.201727	−	0.0540527i	0.156540	−	0.987672i	$-0.449966\pi$
$653$	−5.15492	−	1.38126i	−0.201727	−	0.0540527i	−0.358268	+	0.933619i	$0.616633\pi$
$654$	−7.39945	−	13.3748i	−0.289341	−	0.522995i
$655$	−15.6716	+	4.65410i	−0.612341	+	0.181851i
$656$	−1.76028	+	24.0413i	−0.0687274	+	0.938656i
$657$		−	5.89605i		−	0.230027i
$658$	0.551003	−	33.8730i	0.0214803	−	1.32051i
$659$	10.2755	+	10.2755i	0.400276	+	0.400276i	0.878330	−	0.478055i	$-0.158658\pi$
$659$	10.2755	+	10.2755i	0.400276	+	0.400276i	−0.478055	+	0.878330i	$0.658658\pi$
$660$	5.44677	+	3.21526i	0.212015	+	0.125154i
$661$	−6.30925	−	23.5464i	−0.245401	−	0.915850i	−0.973181	−	0.230040i	$-0.926114\pi$
$661$	−6.30925	−	23.5464i	−0.245401	−	0.915850i	0.727780	−	0.685811i	$-0.240552\pi$
$662$	−38.0295	−	10.9385i	−1.47806	−	0.425137i
$663$	3.33872	+	5.78283i	0.129665	+	0.224587i
$664$	−34.5053	+	30.9156i	−1.33907	+	1.19976i
$665$	−5.11188	+	21.5494i	−0.198230	+	0.835651i
$666$	0.0122307	+	0.0492263i	0.000473930	+	0.00190748i
$667$	−3.78009	+	14.1075i	−0.146366	+	0.546244i
$668$	35.9389	+	1.31395i	1.39052	+	0.0508381i
$669$	−19.0663	+	5.10880i	−0.737146	+	0.197518i
$670$	−1.01558	+	1.03321i	−0.0392351	+	0.0399165i
$671$	3.91319			0.151067
$672$	25.8699	+	9.47709i	0.997955	+	0.365587i
$673$		−	34.3638i		−	1.32463i	−0.749227	−	0.662313i	$-0.769575\pi$
$673$		−	34.3638i		−	1.32463i	0.749227	−	0.662313i	$-0.230425\pi$
$674$	−0.623842	+	34.1379i	−0.0240295	+	1.31494i
$675$	22.8482	−	7.45926i	0.879426	−	0.287107i
$676$	0.461423	−	12.6208i	0.0177470	−	0.485415i
$677$	−5.41758	+	20.2187i	−0.208215	+	0.777067i	0.780231	+	0.625491i	$0.215101\pi$
$677$	−5.41758	+	20.2187i	−0.208215	+	0.777067i	−0.988446	+	0.151576i	$0.951565\pi$
$678$	−43.6937	+	10.8561i	−1.67805	+	0.416925i
$679$	−18.2728	−	10.5010i	−0.701246	−	0.402990i
$680$	0.145806	−	5.21808i	0.00559139	−	0.200104i
$681$	−26.0202	+	15.0228i	−0.997098	+	0.575675i
$682$	1.92930	+	0.554927i	0.0738766	+	0.0212492i
$683$	31.0932	−	8.33140i	1.18975	−	0.318792i	0.390962	−	0.920407i	$-0.372142\pi$
$683$	31.0932	−	8.33140i	1.18975	−	0.318792i	0.798787	+	0.601615i	$0.205476\pi$
$684$	0.650027	+	2.83676i	0.0248544	+	0.108466i
$685$	−39.2058	+	1.05416i	−1.49798	+	0.0402772i
$686$	26.1896	+	0.320882i	0.999925	+	0.0122514i
$687$			21.7261i			0.828902i
$688$	2.54874	+	2.95146i	0.0971699	+	0.112523i
$689$	−10.4828	+	18.1567i	−0.399362	+	0.691715i
$690$	11.4515	+	2.96300i	0.435952	+	0.112800i
$691$	−9.50701	+	35.4806i	−0.361664	+	1.34975i	0.510224	+	0.860041i	$0.329562\pi$
$691$	−9.50701	+	35.4806i	−0.361664	+	1.34975i	−0.871888	+	0.489706i	$0.837104\pi$
$692$	6.08198	+	1.87034i	0.231202	+	0.0710998i
$693$	0.762782	−	0.206029i	0.0289757	−	0.00782638i
$694$	47.8497	−	11.8887i	1.81635	−	0.451288i
$695$	−27.2271	−	6.51646i	−1.03278	−	0.247183i
$696$	−20.4595	+	31.3361i	−0.775517	+	1.18779i
$697$	2.48702	−	4.30765i	0.0942027	−	0.163164i
$698$	4.46696	+	4.63326i	0.169077	+	0.175371i
$699$	−38.6294	+	38.6294i	−1.46110	+	1.46110i
$700$	13.6668	+	22.6543i	0.516556	+	0.856253i
$701$	13.1275	+	13.1275i	0.495819	+	0.495819i	0.910134	−	0.414315i	$-0.135979\pi$
$701$	13.1275	+	13.1275i	0.495819	+	0.495819i	−0.414315	+	0.910134i	$0.635979\pi$
$702$	29.8716	+	0.545879i	1.12743	+	0.0206029i
$703$	0.299154	+	0.172717i	0.0112828	+	0.00651413i
$704$	−0.931663	−	6.07532i	−0.0351134	−	0.228972i
$705$	8.67487	−	36.2454i	0.326714	−	1.36508i
$706$	−8.60769	−	5.18162i	−0.323955	−	0.195013i
$707$	31.3047	+	8.32077i	1.17733	+	0.312935i
$708$	−37.8272	+	20.0337i	−1.42163	+	0.752913i
$709$	−5.57679	−	1.49430i	−0.209441	−	0.0561195i	0.152573	−	0.988292i	$-0.451244\pi$
$709$	−5.57679	−	1.49430i	−0.209441	−	0.0561195i	−0.362014	+	0.932173i	$0.617911\pi$
$710$	−5.65397	+	3.32955i	−0.212190	+	0.124956i
$711$	1.92888	+	1.11364i	0.0723388	+	0.0417648i
$712$	−33.9441	+	17.1905i	−1.27211	+	0.644241i
$713$	3.75436			0.140602
$714$	−3.95399	−	4.08476i	−0.147974	−	0.152868i
$715$	0.202933	+	7.54740i	0.00758926	+	0.282257i
$716$	−48.4875	+	11.1106i	−1.81206	+	0.415223i
$717$	3.26489	+	12.1847i	0.121930	+	0.455047i
$718$	32.2261	−	17.8287i	1.20267	−	0.665362i
$719$	9.10814	+	15.7758i	0.339676	+	0.588336i	0.984372	−	0.176103i	$-0.0563492\pi$
$719$	9.10814	+	15.7758i	0.339676	+	0.588336i	−0.644696	+	0.764439i	$0.723016\pi$
$720$	2.92736	+	1.87554i	0.109096	+	0.0698974i
$721$	46.0701	−	0.0924548i	1.71574	−	0.00344320i
$722$	−6.04047	−	3.63621i	−0.224803	−	0.135326i
$723$	44.4009	+	11.8972i	1.65129	+	0.442461i
$724$	13.9016	−	12.9210i	0.516650	−	0.480204i
$725$	−34.1637	+	11.1535i	−1.26881	+	0.414229i
$726$	18.8093	+	19.5096i	0.698080	+	0.724069i
$727$	−20.9767			−0.777981			−0.388990	−	0.921242i	$-0.627176\pi$
$727$	−20.9767			−0.777981			−0.388990	+	0.921242i	$0.627176\pi$
$728$	6.82332	+	32.1724i	0.252889	+	1.19239i
$729$			22.6539i			0.839033i
$730$	−47.9655	+	0.412952i	−1.77528	+	0.0152841i
$731$	−0.208263	−	0.777247i	−0.00770288	−	0.0287475i
$732$	18.7396	+	0.685131i	0.692636	+	0.0253232i
$733$	−36.4133	−	9.75691i	−1.34496	−	0.360380i	−0.486685	−	0.873578i	$-0.661794\pi$
$733$	−36.4133	−	9.75691i	−1.34496	−	0.360380i	−0.858270	+	0.513198i	$0.828461\pi$
$734$	−31.8372	−	19.1652i	−1.17513	−	0.707402i
$735$	28.0490	+	6.59426i	1.03460	+	0.243233i
$736$	−4.81513	−	10.4374i	−0.177488	−	0.384729i
$737$	0.304829	−	0.175993i	0.0112285	−	0.00648278i
$738$	1.60369	+	2.89872i	0.0590325	+	0.106703i
$739$	11.8192	−	3.16693i	0.434775	−	0.116497i	−0.0347920	−	0.999395i	$-0.511077\pi$
$739$	11.8192	−	3.16693i	0.434775	−	0.116497i	0.469567	+	0.882897i	$0.344410\pi$
$740$	0.399609	−	0.102947i	0.0146899	−	0.00378440i
$741$	−21.4158	+	21.4158i	−0.786729	+	0.786729i
$742$	4.89962	−	17.1639i	0.179871	−	0.630108i
$743$	−0.566011			−0.0207649			−0.0103825	−	0.999946i	$-0.503305\pi$
$743$	−0.566011			−0.0207649			−0.0103825	+	0.999946i	$0.503305\pi$
$744$	9.14192	+	2.99524i	0.335159	+	0.109811i
$745$	−0.618705	−	2.08335i	−0.0226676	−	0.0763279i
$746$	7.12626	−	24.7756i	0.260911	−	0.907101i
$747$	−1.64786	+	6.14991i	−0.0602922	+	0.225014i
$748$	−0.372788	+	1.21223i	−0.0136305	+	0.0443235i
$749$	−18.5726	−	18.4982i	−0.678628	−	0.675910i
$750$	9.27102	+	27.5903i	0.338530	+	1.00745i
$751$	26.0560	+	45.1303i	0.950797	+	1.64683i	0.743705	+	0.668508i	$0.233067\pi$
$751$	26.0560	+	45.1303i	0.950797	+	1.64683i	0.207093	+	0.978321i	$0.433600\pi$
$752$	−32.6030	+	15.7696i	−1.18891	+	0.575057i
$753$	−0.725168	−	0.418676i	−0.0264266	−	0.0152574i
$754$	−44.6655	−	0.816226i	−1.62662	−	0.0297252i
$755$	−0.467664	−	17.3932i	−0.0170200	−	0.633003i
$756$	−24.7822	+	5.73105i	−0.901318	+	0.208436i
$757$	−24.8977	−	24.8977i	−0.904923	−	0.904923i	0.0909337	−	0.995857i	$-0.471015\pi$
$757$	−24.8977	−	24.8977i	−0.904923	−	0.904923i	−0.995857	+	0.0909337i	$0.971015\pi$
$758$	8.77964	−	8.46451i	0.318891	−	0.307445i
$759$	−2.48881	−	1.43692i	−0.0903382	−	0.0521568i
$760$	23.0321	−	5.48678i	0.835462	−	0.199026i
$761$	35.7098	−	20.6171i	1.29448	−	0.747368i	0.315035	−	0.949080i	$-0.397984\pi$
$761$	35.7098	−	20.6171i	1.29448	−	0.747368i	0.979445	+	0.201712i	$0.0646504\pi$
$762$	−21.2990	+	5.29192i	−0.771582	+	0.191706i
$763$	−3.99041	+	15.0129i	−0.144463	+	0.543503i
$764$	−15.4947	−	29.2568i	−0.560579	−	1.05847i
$765$	−0.375260	−	0.611407i	−0.0135676	−	0.0221055i
$766$	8.90481	−	4.92649i	0.321744	−	0.178001i
$767$	−44.2506	−	25.5481i	−1.59780	−	0.922488i
$768$	−3.39790	−	29.2568i	−0.122611	−	1.05571i
$769$	−46.3556			−1.67163			−0.835813	−	0.549015i	$-0.815003\pi$
$769$	−46.3556			−1.67163			−0.835813	+	0.549015i	$0.815003\pi$
$770$	−1.72951	−	6.19096i	−0.0623271	−	0.223107i
$771$	−11.0631	−	11.0631i	−0.398428	−	0.398428i
$772$	25.2475	+	15.8339i	0.908677	+	0.569876i
$773$	26.8783	−	7.20203i	0.966747	−	0.259039i	0.259293	−	0.965799i	$-0.416510\pi$
$773$	26.8783	−	7.20203i	0.966747	−	0.259039i	0.707454	+	0.706760i	$0.249844\pi$
$774$	0.515033	+	0.148140i	0.0185125	+	0.00532478i
$775$	5.04235	+	7.74075i	0.181127	+	0.278056i
$776$	−1.23442	+	22.4966i	−0.0443130	+	0.807579i
$777$	0.223922	−	0.389648i	0.00803316	−	0.0139785i
$778$	−3.82684	−	15.4023i	−0.137199	−	0.552201i
$779$	21.7918	+	5.83909i	0.780772	+	0.209207i
$780$	−0.349606	+	36.1788i	−0.0125179	+	1.29541i
$781$	1.53983	−	0.412597i	0.0550996	−	0.0147639i
$782$	−0.0433360	+	2.37143i	−0.00154969	+	0.0848023i
$783$		−	34.5510i		−	1.23475i
$784$	−12.2930	−	25.1572i	−0.439035	−	0.898470i
$785$	16.1753	−	17.0692i	0.577322	−	0.609226i
$786$	19.0301	+	0.347760i	0.678782	+	0.0124042i
$787$	−1.85431	−	6.92037i	−0.0660989	−	0.246684i	0.924969	−	0.380043i	$-0.124091\pi$
$787$	−1.85431	−	6.92037i	−0.0660989	−	0.246684i	−0.991068	+	0.133358i	$0.957424\pi$
$788$	−12.6813	−	13.6438i	−0.451753	−	0.486039i
$789$	9.48930	+	2.54265i	0.337828	+	0.0905208i
$790$	8.92460	−	15.7699i	0.317523	−	0.561066i
$791$	39.6713	+	22.7982i	1.41055	+	0.810610i
$792$	−0.563651	−	0.629099i	−0.0200285	−	0.0223541i
$793$	11.1922	+	19.3855i	0.397448	+	0.688401i
$794$	−42.1231	−	12.1159i	−1.49489	−	0.429978i
$795$	9.35765	−	17.2635i	0.331881	−	0.612273i
$796$	−20.5534	−	12.8900i	−0.728494	−	0.456874i
$797$	−36.9337	+	36.9337i	−1.30826	+	1.30826i	−0.385589	+	0.922671i	$0.626002\pi$
$797$	−36.9337	+	36.9337i	−1.30826	+	1.30826i	−0.922671	+	0.385589i	$0.873998\pi$
$798$	13.2541	−	22.1180i	0.469190	−	0.782968i
$799$	7.47303			0.264377
$800$	15.0529	−	23.9460i	0.532200	−	0.846619i
$801$	−2.61446	+	4.52838i	−0.0923775	+	0.160003i
$802$	−20.4166	−	36.9037i	−0.720935	−	1.30312i
$803$	11.2568	+	3.01626i	0.397245	+	0.106441i
$804$	1.49059	−	0.789431i	0.0525690	−	0.0278411i
$805$	−6.30886	−	10.2328i	−0.222358	−	0.360659i
$806$	2.76899	+	11.1447i	0.0975337	+	0.392555i
$807$	−15.3384	−	26.5670i	−0.539939	−	0.935201i
$808$	−7.11637	−	33.8890i	−0.250353	−	1.19221i
$809$	32.2555	+	18.6227i	1.13404	+	0.654739i	0.944948	−	0.327220i	$-0.106112\pi$
$809$	32.2555	+	18.6227i	1.13404	+	0.654739i	0.189093	+	0.981959i	$0.439445\pi$
$810$	−31.6691	+	0.272651i	−1.11274	+	0.00957996i
$811$	−30.5203	+	30.5203i	−1.07171	+	1.07171i	−0.0744906	+	0.997222i	$0.523733\pi$
$811$	−30.5203	+	30.5203i	−1.07171	+	1.07171i	−0.997222	+	0.0744906i	$0.976267\pi$
$812$	37.0555	−	8.56935i	1.30039	−	0.300725i
$813$	−15.1805	+	15.1805i	−0.532402	+	0.532402i
$814$	−0.100241	−	0.00183181i	−0.00351343	−	6.42050e-5i
$815$	−6.45567	−	21.7380i	−0.226132	−	0.761448i
$816$	−1.99746	+	5.73990i	−0.0699251	+	0.200937i
$817$	3.16072	−	1.82484i	0.110579	−	0.0638431i
$818$	35.0305	+	21.0875i	1.22481	+	0.737308i
$819$	3.20230	+	3.18948i	0.111898	+	0.111449i
$820$	23.4693	−	13.2493i	0.819585	−	0.462686i
$821$	−41.8288	−	11.2080i	−1.45983	−	0.391161i	−0.560401	−	0.828221i	$-0.689353\pi$
$821$	−41.8288	−	11.2080i	−1.45983	−	0.391161i	−0.899432	+	0.437060i	$0.856020\pi$
$822$	43.8827	+	12.6221i	1.53058	+	0.440245i
$823$	5.87787	−	10.1808i	0.204890	−	0.354879i	−0.745208	−	0.666832i	$-0.767650\pi$
$823$	5.87787	−	10.1808i	0.204890	−	0.354879i	0.950098	+	0.311953i	$0.100983\pi$
$824$	−22.2517	−	43.9379i	−0.775174	−	1.53065i
$825$	−0.380000	−	7.06131i	−0.0132299	−	0.245843i
$826$	41.8311	+	11.9411i	1.45549	+	0.415484i
$827$	31.6597	+	31.6597i	1.10092	+	1.10092i	0.994300	+	0.106617i	$0.0340017\pi$
$827$	31.6597	+	31.6597i	1.10092	+	1.10092i	0.106617	+	0.994300i	$0.465998\pi$
$828$	−1.33826	−	0.839286i	−0.0465076	−	0.0291672i
$829$	11.7638	−	3.15209i	0.408573	−	0.109477i	−0.0486782	−	0.998815i	$-0.515501\pi$
$829$	11.7638	−	3.15209i	0.408573	−	0.109477i	0.457251	+	0.889338i	$0.348834\pi$
$830$	50.1462	+	12.9750i	1.74060	+	0.450368i
$831$	−17.3367	−	30.0280i	−0.601403	−	1.04166i
$832$	27.4318	−	21.9916i	0.951027	−	0.762421i
$833$	0.0231893	+	5.77757i	0.000803460	+	0.200181i
$834$	27.9251	+	16.8103i	0.966969	+	0.582092i
$835$	−21.0325	−	34.2680i	−0.727861	−	1.18589i
$836$	−5.74852	−	0.210169i	−0.198817	−	0.00726885i
$837$	−8.57896	+	2.29873i	−0.296532	+	0.0794556i
$838$	11.8795	+	12.3218i	0.410372	+	0.425650i
$839$		−	10.1212i		−	0.349421i	−0.984620	−	0.174711i	$-0.944101\pi$
$839$		−	10.1212i		−	0.349421i	0.984620	−	0.174711i	$-0.0558990\pi$
$840$	−7.19840	−	29.9503i	−0.248368	−	1.03338i
$841$			22.6624i			0.781461i
$842$	22.4997	−	21.6921i	0.775390	−	0.747560i
$843$	−15.0030	+	4.02005i	−0.516732	+	0.138458i
$844$	1.79286	+	1.92893i	0.0617128	+	0.0663966i
$845$	−12.0340	+	7.38606i	−0.413982	+	0.254088i
$846$	−2.56689	+	4.26412i	−0.0882516	+	0.146603i
$847$	−0.0552710	−	27.5415i	−0.00189914	−	0.946337i
$848$	−18.7432	+	3.57964i	−0.643645	+	0.122925i
$849$	20.3702	+	35.2822i	0.699104	+	1.21088i
$850$	−4.94763	+	3.09564i	−0.169702	+	0.106180i
$851$	−0.181107	+	0.0485276i	−0.00620828	+	0.00166350i
$852$	7.44625	−	1.70626i	0.255104	−	0.0584556i
$853$	−5.42584	−	5.42584i	−0.185777	−	0.185777i	0.608090	−	0.793868i	$-0.291936\pi$
$853$	−5.42584	−	5.42584i	−0.185777	−	0.185777i	−0.793868	+	0.608090i	$0.791936\pi$
$854$	−13.2548	−	13.6932i	−0.453570	−	0.468570i
$855$	2.23811	−	2.36179i	0.0765418	−	0.0807716i
$856$	−8.72502	+	26.6301i	−0.298215	+	0.910197i
$857$	4.13602	−	7.16380i	0.141284	−	0.244711i	−0.786696	−	0.617340i	$-0.788210\pi$
$857$	4.13602	−	7.16380i	0.141284	−	0.244711i	0.927980	+	0.372629i	$0.121544\pi$
$858$	2.42984	−	8.44774i	0.0829533	−	0.288401i
$859$	−32.5231	−	8.71454i	−1.10967	−	0.297336i	−0.342976	−	0.939344i	$-0.611435\pi$
$859$	−32.5231	−	8.71454i	−1.10967	−	0.297336i	−0.766698	+	0.642008i	$0.778102\pi$
$860$	1.16908	−	4.20027i	0.0398651	−	0.143228i
$861$	7.53972	−	28.3662i	0.256953	−	0.966718i
$862$	−20.6175	+	34.2498i	−0.702236	+	1.16655i
$863$	22.8030	−	13.1653i	0.776224	−	0.448153i	−0.0588662	−	0.998266i	$-0.518749\pi$
$863$	22.8030	−	13.1653i	0.776224	−	0.448153i	0.835090	+	0.550113i	$0.185415\pi$
$864$	17.3935	+	20.9020i	0.591740	+	0.711101i
$865$	−2.02531	−	6.81975i	−0.0688625	−	0.231878i
$866$	0.262419	−	14.3601i	0.00891736	−	0.487976i
$867$	−21.2417	+	21.2417i	−0.721405	+	0.721405i
$868$	−4.59312	−	8.63071i	−0.155901	−	0.292945i
$869$	−3.11295	+	3.11295i	−0.105599	+	0.105599i
$870$	41.8396	−	0.360212i	1.41850	−	0.0122123i
$871$	1.74370	+	1.00673i	0.0590831	+	0.0341116i
$872$	16.2522	−	3.41281i	0.550370	−	0.115572i
$873$	1.54814	+	2.68145i	0.0523965	+	0.0907534i
$874$	−10.4404	+	2.59400i	−0.353151	+	0.0877433i
$875$	12.6248	−	26.7510i	0.426797	−	0.904347i
$876$	53.3790	+	16.4152i	1.80351	+	0.554619i
$877$	37.8760	+	10.1489i	1.27898	+	0.342703i	0.833466	−	0.552571i	$-0.186353\pi$
$877$	37.8760	+	10.1489i	1.27898	+	0.342703i	0.445517	+	0.895273i	$0.353020\pi$
$878$	−14.7103	+	8.13833i	−0.496449	+	0.274655i
$879$	−9.00631	+	15.5994i	−0.303775	+	0.526154i
$880$	−5.07837	+	4.62948i	−0.171192	+	0.156060i
$881$	−11.4218			−0.384811			−0.192406	−	0.981315i	$-0.561629\pi$
$881$	−11.4218			−0.384811			−0.192406	+	0.981315i	$0.561629\pi$
$882$	−3.30465	−	1.97129i	−0.111273	−	0.0663768i
$883$	−9.74194	+	9.74194i	−0.327842	+	0.327842i	−0.851766	−	0.523923i	$-0.824468\pi$
$883$	−9.74194	+	9.74194i	−0.327842	+	0.327842i	0.523923	+	0.851766i	$0.324468\pi$
$884$	−7.07149	+	1.62039i	−0.237840	+	0.0544995i
$885$	42.0737	+	22.8060i	1.41429	+	0.766614i
$886$	1.26706	−	4.40515i	0.0425677	−	0.147994i
$887$	−22.3547	−	38.7194i	−0.750597	−	1.30007i	−0.947534	−	0.319655i	$-0.896433\pi$
$887$	−22.3547	−	38.7194i	−0.750597	−	1.30007i	0.196937	−	0.980416i	$-0.436900\pi$
$888$	−0.479715	−	0.0263226i	−0.0160982	−	0.000883329i
$889$	19.3382	+	11.1133i	0.648584	+	0.372727i
$890$	37.0224	+	20.9520i	1.24099	+	0.702313i
$891$	7.43228	+	1.99147i	0.248991	+	0.0667169i
$892$	0.783536	−	21.4312i	0.0262347	−	0.717569i
$893$	8.77268	+	32.7401i	0.293567	+	1.09561i
$894$	−0.0462303	+	2.52982i	−0.00154617	+	0.0846097i
$895$	40.3690	+	38.2550i	1.34939	+	1.27872i
$896$	−18.1032	+	23.8385i	−0.604786	+	0.796388i
$897$		−	16.4391i		−	0.548885i
$898$	−45.5948	−	0.833207i	−1.52152	−	0.0278045i
$899$	12.8277	−	3.43717i	0.427828	−	0.114636i
$900$	−0.0669244	−	3.88643i	−0.00223081	−	0.129548i
$901$	3.80327	+	1.01908i	0.126705	+	0.0339506i
$902$	−6.35468	+	1.57887i	−0.211588	+	0.0525707i
$903$	−2.38236	−	4.10731i	−0.0792799	−	0.136683i
$904$	2.67998	−	48.8412i	0.0891350	−	1.62444i
$905$	−20.6365	−	4.93907i	−0.685980	−	0.164180i
$906$	−5.59963	+	19.4680i	−0.186035	+	0.646782i
$907$	34.9995	−	9.37810i	1.16214	−	0.311395i	0.374320	−	0.927300i	$-0.377876\pi$
$907$	34.9995	−	9.37810i	1.16214	−	0.311395i	0.787821	+	0.615905i	$0.211209\pi$
$908$	−7.29104	−	31.8186i	−0.241962	−	1.05594i
$909$	−3.36500	−	3.36500i	−0.111610	−	0.111610i
$910$	25.7227	−	26.2748i	0.852700	−	0.871000i
$911$	12.6076			0.417709			0.208854	−	0.977947i	$-0.433027\pi$
$911$	12.6076			0.417709			0.208854	+	0.977947i	$0.433027\pi$
$912$	−27.4919	−	2.01293i	−0.910349	−	0.0666548i
$913$	−10.8985	−	6.29225i	−0.360688	−	0.208243i
$914$	1.91222	+	3.45640i	0.0632505	+	0.114328i
$915$	−10.9670	−	17.8684i	−0.362558	−	0.590710i
$916$	−22.5618	−	6.93825i	−0.745462	−	0.229246i
$917$	−13.7052	−	13.6503i	−0.452586	−	0.450774i
$918$	−1.35296	−	5.44542i	−0.0446543	−	0.179726i
$919$	−33.0720	+	19.0941i	−1.09095	+	0.629858i	−0.933828	−	0.357722i	$-0.883554\pi$
$919$	−33.0720	+	19.0941i	−1.09095	+	0.629858i	−0.157118	+	0.987580i	$0.550220\pi$
$920$	−6.73403	+	10.9458i	−0.222014	+	0.360871i
$921$	21.9229	+	12.6572i	0.722385	+	0.417069i
$922$	24.0722	+	24.9684i	0.792777	+	0.822291i
$923$	6.44809	+	6.44809i	0.212242	+	0.212242i
$924$	−0.258420	+	7.47934i	−0.00850139	+	0.246052i
$925$	−0.343293	−	0.308232i	−0.0112874	−	0.0101346i
$926$	0.629331	−	34.4383i	0.0206811	−	1.13171i
$927$	−5.86162	−	3.38421i	−0.192521	−	0.111152i
$928$	−26.0077	−	31.2537i	−0.853744	−	1.02595i
$929$	22.6776	+	39.2788i	0.744030	+	1.28870i	0.950647	+	0.310275i	$0.100421\pi$
$929$	22.6776	+	39.2788i	0.744030	+	1.28870i	−0.206617	+	0.978422i	$0.566246\pi$
$930$	−2.87309	−	10.3648i	−0.0942123	−	0.339874i
$931$	−25.2849	+	6.88395i	−0.828678	+	0.225612i
$932$	−27.7789	−	52.4516i	−0.909930	−	1.71811i
$933$	12.1255	−	45.2531i	0.396972	−	1.48152i
$934$	−3.48577	−	1.00262i	−0.114058	−	0.0328066i
$935$	1.35928	−	0.403674i	0.0444532	−	0.0132015i
$936$	1.50437	−	4.59158i	0.0491720	−	0.150080i
$937$	−2.96862			−0.0969806			−0.0484903	−	0.998824i	$-0.515441\pi$
$937$	−2.96862			−0.0969806			−0.0484903	+	0.998824i	$0.515441\pi$
$938$	−1.64836	−	0.470541i	−0.0538208	−	0.0153637i
$939$	−23.3179	+	23.3179i	−0.760950	+	0.760950i
$940$	34.8692	+	20.5835i	1.13731	+	0.671361i
$941$	−0.363644	+	0.0974380i	−0.0118544	+	0.00317639i	−0.264741	−	0.964319i	$-0.585287\pi$
$941$	−0.363644	+	0.0974380i	−0.0118544	+	0.00317639i	0.252887	+	0.967496i	$0.418620\pi$
$942$	−23.9566	+	13.2537i	−0.780548	+	0.431830i
$943$	−10.6049	+	6.12277i	−0.345344	+	0.199385i
$944$	−8.72412	−	45.6800i	−0.283946	−	1.48676i
$945$	20.6815	+	19.5199i	0.672770	+	0.634981i
$946$	−0.546308	+	0.907525i	−0.0177620	+	0.0295062i
$947$	32.9676	+	8.83365i	1.07130	+	0.287055i	0.751029	−	0.660269i	$-0.229558\pi$
$947$	32.9676	+	8.83365i	1.07130	+	0.287055i	0.320275	+	0.947325i	$0.396225\pi$
$948$	−15.4524	+	14.3624i	−0.501871	+	0.466468i
$949$	17.2538	+	64.3920i	0.560082	+	2.09025i
$950$	−19.3704	−	18.0421i	−0.628459	−	0.585362i
$951$		−	47.3104i		−	1.53415i
$952$	5.50459	−	2.80161i	0.178405	−	0.0908007i
$953$	15.3388			0.496871			0.248436	−	0.968648i	$-0.420084\pi$
$953$	15.3388			0.496871			0.248436	+	0.968648i	$0.420084\pi$
$954$	−1.88787	+	1.82011i	−0.0611220	+	0.0589281i
$955$	−17.6389	+	32.5412i	−0.570781	+	1.05301i
$956$	−13.6961	−	0.500735i	−0.442962	−	0.0161949i
$957$	−9.81916	−	2.63104i	−0.317408	−	0.0850493i
$958$	−22.4706	+	37.3280i	−0.725991	+	1.20601i
$959$	−23.2834	−	40.1419i	−0.751862	−	1.29625i
$960$	−25.1300	+	21.2807i	−0.811068	+	0.686831i
$961$	13.7931	+	23.8904i	0.444939	+	0.770657i
$962$	−0.277627	−	0.501820i	−0.00895104	−	0.0161793i
$963$	0.996738	+	3.71988i	0.0321194	+	0.119871i
$964$	−26.5343	+	42.3093i	−0.854611	+	1.36269i
$965$	−0.895562	−	33.3074i	−0.0288292	−	1.07220i
$966$	3.40203	+	13.5761i	0.109459	+	0.436803i
$967$	−8.19730			−0.263607			−0.131804	−	0.991276i	$-0.542077\pi$
$967$	−8.19730			−0.263607			−0.131804	+	0.991276i	$0.542077\pi$
$968$	−26.2668	+	13.3024i	−0.844247	+	0.427556i
$969$	4.92592	+	2.84398i	0.158243	+	0.0913618i
$970$	21.7057	−	12.7822i	0.696929	−	0.410412i
$971$	−28.1801	−	7.55084i	−0.904343	−	0.242318i	−0.223462	−	0.974713i	$-0.571736\pi$
$971$	−28.1801	−	7.55084i	−0.904343	−	0.242318i	−0.680880	+	0.732395i	$0.738403\pi$
$972$	7.67545	+	2.36037i	0.246190	+	0.0757090i
$973$	−8.63768	−	31.9794i	−0.276911	−	1.02521i
$974$	11.8697	−	19.7178i	0.380329	−	0.631801i
$975$	33.8941	−	22.0788i	1.08548	−	0.707087i
$976$	−6.69600	+	19.2416i	−0.214334	+	0.615910i
$977$	41.8715	+	24.1745i	1.33959	+	0.773412i	0.986746	−	0.162271i	$-0.0518818\pi$
$977$	41.8715	+	24.1745i	1.33959	+	0.773412i	0.352843	+	0.935683i	$0.385215\pi$
$978$	−0.482374	+	26.3965i	−0.0154246	+	0.844068i
$979$	−7.30817	−	7.30817i	−0.233570	−	0.233570i
$980$	−15.8054	+	27.0220i	−0.504884	+	0.863187i
$981$	1.61376	−	1.61376i	0.0515234	−	0.0515234i
$982$	18.9853	−	18.3039i	0.605845	−	0.584100i
$983$	2.79368	−	4.83879i	0.0891045	−	0.154334i	−0.818028	−	0.575178i	$-0.804933\pi$
$983$	2.79368	−	4.83879i	0.0891045	−	0.154334i	0.907133	+	0.420844i	$0.138266\pi$
$984$	−30.7079	+	6.44837i	−0.978933	+	0.205567i
$985$	−4.84746	+	20.2537i	−0.154453	+	0.645337i
$986$	2.02301	+	8.14226i	0.0644259	+	0.259302i
$987$	42.5718	−	11.4987i	1.35507	−	0.366007i
$988$	−15.4004	−	29.0787i	−0.489952	−	0.925117i
$989$	−0.512719	+	1.91349i	−0.0163035	+	0.0608456i
$990$	−0.236559	+	0.914262i	−0.00751834	+	0.0290572i
$991$	−9.89456	+	17.1379i	−0.314311	+	0.544403i	−0.979291	−	0.202459i	$-0.935107\pi$
$991$	−9.89456	+	17.1379i	−0.314311	+	0.544403i	0.664980	+	0.746861i	$0.268440\pi$
$992$	−6.02993	+	8.53703i	−0.191451	+	0.271051i
$993$		−	51.5090i		−	1.63459i
$994$	−6.65951	−	3.99068i	−0.211227	−	0.126577i
$995$	0.729055	+	27.1147i	0.0231126	+	0.859595i
$996$	−51.0895	−	32.0407i	−1.61883	−	1.01525i
$997$	−12.9317	+	3.46503i	−0.409550	+	0.109739i	−0.457711	−	0.889101i	$-0.651331\pi$
$997$	−12.9317	+	3.46503i	−0.409550	+	0.109739i	0.0481608	+	0.998840i	$0.484664\pi$
$998$	3.61988	−	12.5851i	0.114585	−	0.398375i
$999$	0.384130	−	0.221777i	0.0121533	−	0.00701673i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.cr.a.109.3	✓	368
5.4	even	2	inner	560.2.cr.a.109.90	yes	368
7.2	even	3	inner	560.2.cr.a.429.61	yes	368
16.5	even	4	inner	560.2.cr.a.389.32	yes	368
35.9	even	6	inner	560.2.cr.a.429.32	yes	368
80.69	even	4	inner	560.2.cr.a.389.61	yes	368
112.37	even	12	inner	560.2.cr.a.149.90	yes	368
560.149	even	12	inner	560.2.cr.a.149.3	yes	368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.cr.a.109.3	✓	368	1.1	even	1	trivial
560.2.cr.a.109.90	yes	368	5.4	even	2	inner
560.2.cr.a.149.3	yes	368	560.149	even	12	inner
560.2.cr.a.149.90	yes	368	112.37	even	12	inner
560.2.cr.a.389.32	yes	368	16.5	even	4	inner
560.2.cr.a.389.61	yes	368	80.69	even	4	inner
560.2.cr.a.429.32	yes	368	35.9	even	6	inner
560.2.cr.a.429.61	yes	368	7.2	even	3	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.41398 - 0.0258393i) q^{2} +(-0.476445 - 1.77812i) q^{3} +(1.99866 + 0.0730723i) q^{4} +(-1.16968 - 1.90574i) q^{5} +(0.627737 + 2.52653i) q^{6} +(1.31827 - 2.29394i) q^{7} +(-2.82418 - 0.154967i) q^{8} +(-0.336625 + 0.194351i) q^{9} +(1.60466 + 2.72490i) q^{10} +(-0.198849 - 0.742114i) q^{11} +(-0.822323 - 3.58868i) q^{12} +(3.10762 - 3.10762i) q^{13} +(-1.92328 + 3.20951i) q^{14} +(-2.83134 + 2.98781i) q^{15} +(3.98932 + 0.292094i) q^{16} +(-0.714794 - 0.412687i) q^{17} +(0.481002 - 0.266109i) q^{18} +(0.968916 - 3.61604i) q^{19} +(-2.19854 - 3.89441i) q^{20} +(-4.70698 - 1.25111i) q^{21} +(0.261992 + 1.05447i) q^{22} +(1.01599 + 1.75974i) q^{23} +(1.07002 + 5.09555i) q^{24} +(-2.26370 + 4.45821i) q^{25} +(-4.47440 + 4.31381i) q^{26} +(-3.39906 - 3.39906i) q^{27} +(2.80241 - 4.48848i) q^{28} +(5.08244 + 5.08244i) q^{29} +(4.08066 - 4.15153i) q^{30} +(0.923821 - 1.60010i) q^{31} +(-5.63326 - 0.516095i) q^{32} +(-1.22482 + 0.707153i) q^{33} +(1.00004 + 0.601999i) q^{34} +(-5.91361 + 0.170881i) q^{35} +(-0.687002 + 0.363844i) q^{36} +(-0.0238820 + 0.0891288i) q^{37} +(-1.46346 + 5.08797i) q^{38} +(-7.00632 - 4.04510i) q^{39} +(3.00806 + 5.56342i) q^{40} +6.02642i q^{41} +(6.62323 + 1.89067i) q^{42} +(0.689366 + 0.689366i) q^{43} +(-0.343204 - 1.49777i) q^{44} +(0.764125 + 0.414192i) q^{45} +(-1.39111 - 2.51449i) q^{46} +(-7.84110 + 4.52706i) q^{47} +(-1.38132 - 7.23265i) q^{48} +(-3.52430 - 6.04808i) q^{49} +(3.31602 - 6.24532i) q^{50} +(-0.393245 + 1.46761i) q^{51} +(6.43817 - 5.98401i) q^{52} +(-4.60794 + 1.23470i) q^{53} +(4.71836 + 4.89402i) q^{54} +(-1.18169 + 1.24699i) q^{55} +(-4.07853 + 6.27420i) q^{56} -6.89138 q^{57} +(-7.05513 - 7.31778i) q^{58} +(-3.00914 - 11.2302i) q^{59} +(-5.87723 + 5.76473i) q^{60} +(-1.31826 + 4.91981i) q^{61} +(-1.34761 + 2.23864i) q^{62} +(0.00206383 + 1.02840i) q^{63} +(7.95197 + 0.875306i) q^{64} +(-9.55724 - 2.28740i) q^{65} +(1.75015 - 0.968250i) q^{66} +(0.118575 + 0.442530i) q^{67} +(-1.39848 - 0.877054i) q^{68} +(2.64497 - 2.64497i) q^{69} +(8.36613 - 0.0888179i) q^{70} +2.07493i q^{71} +(0.980807 - 0.496715i) q^{72} +(-7.58430 + 13.1364i) q^{73} +(0.0360716 - 0.125409i) q^{74} +(9.00575 + 1.90103i) q^{75} +(2.20077 - 7.15645i) q^{76} +(-1.96450 - 0.522163i) q^{77} +(9.80226 + 5.90072i) q^{78} +(-2.86503 - 4.96238i) q^{79} +(-4.10957 - 7.94427i) q^{80} +(-5.00751 + 8.67326i) q^{81} +(0.155718 - 8.52122i) q^{82} +(11.5823 - 11.5823i) q^{83} +(-9.31625 - 2.84450i) q^{84} +(0.0496059 + 1.84492i) q^{85} +(-0.956936 - 0.992561i) q^{86} +(6.61567 - 11.4587i) q^{87} +(0.446582 + 2.12668i) q^{88} +(11.6500 - 6.72615i) q^{89} +(-1.06975 - 0.605403i) q^{90} +(-3.03199 - 11.2254i) q^{91} +(1.90203 + 3.59137i) q^{92} +(-3.28532 - 0.880300i) q^{93} +(11.2041 - 6.19856i) q^{94} +(-8.02456 + 2.38311i) q^{95} +(1.76626 + 10.2625i) q^{96} -7.96570i q^{97} +(4.82701 + 8.64292i) q^{98} +(0.211168 + 0.211168i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q - 4 q^{4} - 2 q^{5} - 16 q^{6} - 8 q^{10} - 4 q^{11} + 16 q^{14} - 16 q^{15} - 4 q^{16} - 4 q^{19} - 8 q^{20} + 4 q^{21} - 4 q^{24} - 4 q^{26} - 16 q^{29} + 22 q^{30} - 56 q^{31} - 96 q^{34} + 18 q^{35}+ \cdots - 112 q^{99}+O(q^{100}) \) 368 * q - 4 * q^4 - 2 * q^5 - 16 * q^6 - 8 * q^10 - 4 * q^11 + 16 * q^14 - 16 * q^15 - 4 * q^16 - 4 * q^19 - 8 * q^20 + 4 * q^21 - 4 * q^24 - 4 * q^26 - 16 * q^29 + 22 * q^30 - 56 * q^31 - 96 * q^34 + 18 * q^35 + 32 * q^36 - 14 * q^40 - 12 * q^44 - 16 * q^45 + 12 * q^46 - 16 * q^49 - 12 * q^50 - 28 * q^51 - 8 * q^54 - 64 * q^56 + 12 * q^59 - 54 * q^60 - 4 * q^61 - 88 * q^64 - 4 * q^65 - 44 * q^66 + 8 * q^69 + 88 * q^70 - 72 * q^74 + 10 * q^75 + 104 * q^76 - 8 * q^79 + 48 * q^80 + 112 * q^81 + 68 * q^84 - 28 * q^85 + 44 * q^86 - 92 * q^90 - 80 * q^91 - 20 * q^94 + 20 * q^95 - 36 * q^96 - 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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