LMFDB - Embedded newform 360.2.bm.a.11.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(11,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1, 0]))

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

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

chi := DirichletCharacter("360.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bm (of order $6$, degree $2$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.3
Character	$\chi$	$=$	360.11
Dual form			360.2.bm.a.131.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29220 + 0.574647i) q^{2} +(-0.857820 + 1.50471i) q^{3} +(1.33956 - 1.48512i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.243800 - 2.43733i) q^{6} +(0.661806 + 0.382094i) q^{7} +(-0.877566 + 2.68884i) q^{8} +(-1.52829 - 2.58154i) q^{9} +O(q^{10})$	\(q+(-1.29220 + 0.574647i) q^{2} +(-0.857820 + 1.50471i) q^{3} +(1.33956 - 1.48512i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.243800 - 2.43733i) q^{6} +(0.661806 + 0.382094i) q^{7} +(-0.877566 + 2.68884i) q^{8} +(-1.52829 - 2.58154i) q^{9} +(1.14376 + 0.831755i) q^{10} +(-4.25821 - 2.45848i) q^{11} +(1.08556 + 3.28961i) q^{12} +(2.38455 - 1.37672i) q^{13} +(-1.07475 - 0.113437i) q^{14} +(1.73202 - 0.00945984i) q^{15} +(-0.411143 - 3.97881i) q^{16} -4.18737i q^{17} +(3.45833 + 2.45764i) q^{18} -5.61545 q^{19} +(-1.95593 - 0.417537i) q^{20} +(-1.14265 + 0.668056i) q^{21} +(6.91521 + 0.729880i) q^{22} +(0.420090 + 0.727618i) q^{23} +(-3.29313 - 3.62702i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.29019 + 3.14928i) q^{26} +(5.19545 - 0.0851352i) q^{27} +(1.45398 - 0.471020i) q^{28} +(2.03911 - 3.53184i) q^{29} +(-2.23269 + 1.00753i) q^{30} +(9.36257 - 5.40548i) q^{31} +(2.81769 + 4.90516i) q^{32} +(7.35206 - 4.29842i) q^{33} +(2.40626 + 5.41092i) q^{34} -0.764187i q^{35} +(-5.88112 - 1.18844i) q^{36} -4.95517i q^{37} +(7.25628 - 3.22690i) q^{38} +(0.0260471 + 4.76903i) q^{39} +(2.76739 - 0.584427i) q^{40} +(4.74052 - 2.73694i) q^{41} +(1.09264 - 1.51988i) q^{42} +(-0.563898 + 0.976700i) q^{43} +(-9.35526 + 3.03065i) q^{44} +(-1.47153 + 2.61431i) q^{45} +(-0.960964 - 0.698825i) q^{46} +(-2.53631 + 4.39302i) q^{47} +(6.33964 + 2.79446i) q^{48} +(-3.20801 - 5.55643i) q^{49} +(0.148442 - 1.40640i) q^{50} +(6.30076 + 3.59201i) q^{51} +(1.14966 - 5.38554i) q^{52} -12.8180 q^{53} +(-6.66465 + 3.09556i) q^{54} +4.91695i q^{55} +(-1.60817 + 1.44418i) q^{56} +(4.81704 - 8.44960i) q^{57} +(-0.605378 + 5.73562i) q^{58} +(-2.54261 + 1.46798i) q^{59} +(2.30611 - 2.58493i) q^{60} +(2.15631 + 1.24495i) q^{61} +(-8.99207 + 12.3651i) q^{62} +(-0.0250419 - 2.29243i) q^{63} +(-6.45976 - 4.71928i) q^{64} +(-2.38455 - 1.37672i) q^{65} +(-7.03026 + 9.77926i) q^{66} +(0.544092 + 0.942396i) q^{67} +(-6.21873 - 5.60924i) q^{68} +(-1.45521 + 0.00794798i) q^{69} +(0.439138 + 0.987483i) q^{70} +10.4086 q^{71} +(8.28252 - 1.84386i) q^{72} -6.10153 q^{73} +(2.84747 + 6.40308i) q^{74} +(-0.874205 - 1.49525i) q^{75} +(-7.52224 + 8.33959i) q^{76} +(-1.87874 - 3.25407i) q^{77} +(-2.77417 - 6.14758i) q^{78} +(-14.1154 - 8.14954i) q^{79} +(-3.24018 + 2.34547i) q^{80} +(-4.32866 + 7.89067i) q^{81} +(-4.55293 + 6.26080i) q^{82} +(-2.75284 - 1.58936i) q^{83} +(-0.538509 + 2.59187i) q^{84} +(-3.62637 + 2.09368i) q^{85} +(0.167412 - 1.58613i) q^{86} +(3.56520 + 6.09795i) q^{87} +(10.3473 - 9.29217i) q^{88} -7.54431i q^{89} +(0.399211 - 4.22382i) q^{90} +2.10415 q^{91} +(1.64333 + 0.350807i) q^{92} +(0.102270 + 18.7249i) q^{93} +(0.752989 - 7.13415i) q^{94} +(2.80772 + 4.86312i) q^{95} +(-9.79791 + 0.0320542i) q^{96} +(-9.53404 + 16.5134i) q^{97} +(7.33838 + 5.33655i) q^{98} +(0.161125 + 14.7500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) $ 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8	$ 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) $ 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8 - 15 * q^12 + 15 * q^14 + 12 * q^16 - 11 * q^18 - 4 * q^21 + 21 * q^22 - 24 * q^24 - 24 * q^25 + 12 * q^27 - 14 * q^30 - 8 * q^33 + 33 * q^34 - 23 * q^36 - 33 * q^38 + 16 * q^39 - 6 * q^40 + 12 * q^41 - 53 * q^42 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 45 * q^48 + 24 * q^49 - 20 * q^51 - 36 * q^52 - 36 * q^54 + 21 * q^56 + 4 * q^57 - 51 * q^58 - 36 * q^59 + 15 * q^60 + 12 * q^61 + 42 * q^62 + 56 * q^63 - 12 * q^64 + 24 * q^66 + 57 * q^68 - 40 * q^69 - 15 * q^70 + 46 * q^72 + 30 * q^74 + 57 * q^76 + 78 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 - 31 * q^84 + 27 * q^86 + 36 * q^87 + 57 * q^88 + 4 * q^90 - 51 * q^92 + 57 * q^94 - 119 * q^96 + 42 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.29220	+	0.574647i	−0.913724	+	0.406336i
$2$	−1.29220	+	0.574647i	−0.913724	+	0.406336i
$3$	−0.857820	+	1.50471i	−0.495263	+	0.868743i
$3$	−0.857820	+	1.50471i	−0.495263	+	0.868743i
$4$	1.33956	−	1.48512i	0.669781	−	0.742558i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	0.243800	−	2.43733i	0.0995310	−	0.995034i
$7$	0.661806	+	0.382094i	0.250139	+	0.144418i	0.619828	−	0.784738i	$-0.287202\pi$
$7$	0.661806	+	0.382094i	0.250139	+	0.144418i	−0.369689	+	0.929156i	$0.620536\pi$
$8$	−0.877566	+	2.68884i	−0.310266	+	0.950650i
$9$	−1.52829	−	2.58154i	−0.509430	−	0.860512i
$10$	1.14376	+	0.831755i	0.361688	+	0.263024i
$11$	−4.25821	−	2.45848i	−1.28390	−	0.741258i	−0.306339	−	0.951923i	$-0.599104\pi$
$11$	−4.25821	−	2.45848i	−1.28390	−	0.741258i	−0.977558	+	0.210664i	$0.932437\pi$
$12$	1.08556	+	3.28961i	0.313375	+	0.949629i
$13$	2.38455	−	1.37672i	0.661356	−	0.381834i	−0.131438	−	0.991324i	$-0.541959\pi$
$13$	2.38455	−	1.37672i	0.661356	−	0.381834i	0.792793	+	0.609490i	$0.208626\pi$
$14$	−1.07475	−	0.113437i	−0.287240	−	0.0303174i
$15$	1.73202	−	0.00945984i	0.447207	−	0.00244252i
$16$	−0.411143	−	3.97881i	−0.102786	−	0.994704i
$17$		−	4.18737i		−	1.01559i	−0.861479	−	0.507793i	$-0.830462\pi$
$17$		−	4.18737i		−	1.01559i	0.861479	−	0.507793i	$-0.169538\pi$
$18$	3.45833	+	2.45764i	0.815136	+	0.579270i
$19$	−5.61545			−1.28827			−0.644136	−	0.764911i	$-0.722783\pi$
$19$	−5.61545			−1.28827			−0.644136	+	0.764911i	$0.722783\pi$
$20$	−1.95593	−	0.417537i	−0.437359	−	0.0933641i
$21$	−1.14265	+	0.668056i	−0.249347	+	0.145782i
$22$	6.91521	+	0.729880i	1.47433	+	0.155611i
$23$	0.420090	+	0.727618i	0.0875949	+	0.151719i	0.906494	−	0.422219i	$-0.138749\pi$
$23$	0.420090	+	0.727618i	0.0875949	+	0.151719i	−0.818899	+	0.573937i	$0.805415\pi$
$24$	−3.29313	−	3.62702i	−0.672207	−	0.740363i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.29019	+	3.14928i	−0.449143	+	0.617624i
$27$	5.19545	−	0.0851352i	0.999866	−	0.0163843i
$28$	1.45398	−	0.471020i	0.274777	−	0.0890144i
$29$	2.03911	−	3.53184i	0.378653	−	0.655847i	−0.612213	−	0.790693i	$-0.709721\pi$
$29$	2.03911	−	3.53184i	0.378653	−	0.655847i	0.990867	+	0.134846i	$0.0430539\pi$
$30$	−2.23269	+	1.00753i	−0.407631	+	0.183948i
$31$	9.36257	−	5.40548i	1.68157	−	0.970853i	0.720945	−	0.692992i	$-0.243708\pi$
$31$	9.36257	−	5.40548i	1.68157	−	0.970853i	0.960621	−	0.277861i	$-0.0896254\pi$
$32$	2.81769	+	4.90516i	0.498102	+	0.867118i
$33$	7.35206	−	4.29842i	1.27983	−	0.748260i
$34$	2.40626	+	5.41092i	0.412669	+	0.927964i
$35$		−	0.764187i		−	0.129171i
$36$	−5.88112	−	1.18844i	−0.980187	−	0.198074i
$37$		−	4.95517i		−	0.814626i	−0.913289	−	0.407313i	$-0.866466\pi$
$37$		−	4.95517i		−	0.814626i	0.913289	−	0.407313i	$-0.133534\pi$
$38$	7.25628	−	3.22690i	1.17712	−	0.523472i
$39$	0.0260471	+	4.76903i	0.00417088	+	0.763657i
$40$	2.76739	−	0.584427i	0.437563	−	0.0924060i
$41$	4.74052	−	2.73694i	0.740345	−	0.427438i	−0.0818500	−	0.996645i	$-0.526083\pi$
$41$	4.74052	−	2.73694i	0.740345	−	0.427438i	0.822195	+	0.569207i	$0.192750\pi$
$42$	1.09264	−	1.51988i	0.168597	−	0.234523i
$43$	−0.563898	+	0.976700i	−0.0859936	+	0.148945i	−0.905814	−	0.423675i	$-0.860740\pi$
$43$	−0.563898	+	0.976700i	−0.0859936	+	0.148945i	0.819821	+	0.572620i	$0.194073\pi$
$44$	−9.35526	+	3.03065i	−1.41036	+	0.456887i
$45$	−1.47153	+	2.61431i	−0.219363	+	0.389718i
$46$	−0.960964	−	0.698825i	−0.141686	−	0.103036i
$47$	−2.53631	+	4.39302i	−0.369959	+	0.640789i	−0.989559	−	0.144130i	$-0.953962\pi$
$47$	−2.53631	+	4.39302i	−0.369959	+	0.640789i	0.619599	+	0.784918i	$0.287295\pi$
$48$	6.33964	+	2.79446i	0.915048	+	0.403345i
$49$	−3.20801	−	5.55643i	−0.458287	−	0.793776i
$50$	0.148442	−	1.40640i	0.0209928	−	0.198895i
$51$	6.30076	+	3.59201i	0.882283	+	0.502982i
$52$	1.14966	−	5.38554i	0.159430	−	0.746841i
$53$	−12.8180			−1.76069			−0.880343	−	0.474338i	$-0.842688\pi$
$53$	−12.8180			−1.76069			−0.880343	+	0.474338i	$0.842688\pi$
$54$	−6.66465	+	3.09556i	−0.906943	+	0.421253i
$55$			4.91695i			0.663002i
$56$	−1.60817	+	1.44418i	−0.214901	+	0.192987i
$57$	4.81704	−	8.44960i	0.638033	−	1.11918i
$58$	−0.605378	+	5.73562i	−0.0794900	+	0.753123i
$59$	−2.54261	+	1.46798i	−0.331020	+	0.191115i	−0.656294	−	0.754505i	$-0.727877\pi$
$59$	−2.54261	+	1.46798i	−0.331020	+	0.191115i	0.325274	+	0.945620i	$0.394544\pi$
$60$	2.30611	−	2.58493i	0.297717	−	0.333713i
$61$	2.15631	+	1.24495i	0.276087	+	0.159399i	0.631651	−	0.775253i	$-0.282378\pi$
$61$	2.15631	+	1.24495i	0.276087	+	0.159399i	−0.355564	+	0.934652i	$0.615711\pi$
$62$	−8.99207	+	12.3651i	−1.14199	+	1.57037i
$63$	−0.0250419	−	2.29243i	−0.00315499	−	0.288818i
$64$	−6.45976	−	4.71928i	−0.807469	−	0.589909i
$65$	−2.38455	−	1.37672i	−0.295767	−	0.170761i
$66$	−7.03026	+	9.77926i	−0.865365	+	1.20374i
$67$	0.544092	+	0.942396i	0.0664715	+	0.115132i	0.897346	−	0.441328i	$-0.145493\pi$
$67$	0.544092	+	0.942396i	0.0664715	+	0.115132i	−0.830874	+	0.556460i	$0.812159\pi$
$68$	−6.21873	−	5.60924i	−0.754132	−	0.680220i
$69$	−1.45521	+	0.00794798i	−0.175187	+	0.000956824i
$70$	0.439138	+	0.987483i	0.0524870	+	0.118027i
$71$	10.4086			1.23527			0.617635	−	0.786465i	$-0.288091\pi$
$71$	10.4086			1.23527			0.617635	+	0.786465i	$0.288091\pi$
$72$	8.28252	−	1.84386i	0.976105	−	0.217301i
$73$	−6.10153			−0.714130			−0.357065	−	0.934080i	$-0.616222\pi$
$73$	−6.10153			−0.714130			−0.357065	+	0.934080i	$0.616222\pi$
$74$	2.84747	+	6.40308i	0.331012	+	0.744343i
$75$	−0.874205	−	1.49525i	−0.100944	−	0.172656i
$76$	−7.52224	+	8.33959i	−0.862860	+	0.956617i
$77$	−1.87874	−	3.25407i	−0.214102	−	0.370835i
$78$	−2.77417	−	6.14758i	−0.314113	−	0.696076i
$79$	−14.1154	−	8.14954i	−1.58811	−	0.916895i	−0.993619	−	0.112792i	$-0.964021\pi$
$79$	−14.1154	−	8.14954i	−1.58811	−	0.916895i	−0.594490	−	0.804103i	$-0.702646\pi$
$80$	−3.24018	+	2.34547i	−0.362263	+	0.262231i
$81$	−4.32866	+	7.89067i	−0.480962	+	0.876741i
$82$	−4.55293	+	6.26080i	−0.502787	+	0.691389i
$83$	−2.75284	−	1.58936i	−0.302164	−	0.174454i	0.341251	−	0.939972i	$-0.389149\pi$
$83$	−2.75284	−	1.58936i	−0.302164	−	0.174454i	−0.643415	+	0.765518i	$0.722483\pi$
$84$	−0.538509	+	2.59187i	−0.0587561	+	0.282796i
$85$	−3.62637	+	2.09368i	−0.393335	+	0.227092i
$86$	0.167412	−	1.58613i	0.0180525	−	0.171037i
$87$	3.56520	+	6.09795i	0.382230	+	0.653769i
$88$	10.3473	−	9.29217i	1.10303	−	0.990549i
$89$		−	7.54431i		−	0.799695i	−0.916582	−	0.399848i	$-0.869063\pi$
$89$		−	7.54431i		−	0.799695i	0.916582	−	0.399848i	$-0.130937\pi$
$90$	0.399211	−	4.22382i	0.0420806	−	0.445229i
$91$	2.10415			0.220575
$92$	1.64333	+	0.350807i	0.171330	+	0.0365741i
$93$	0.102270	+	18.7249i	0.0106049	+	1.94168i
$94$	0.752989	−	7.13415i	0.0776649	−	0.735832i
$95$	2.80772	+	4.86312i	0.288066	+	0.498945i
$96$	−9.79791	+	0.0320542i	−0.999995	+	0.00327152i
$97$	−9.53404	+	16.5134i	−0.968035	+	1.67669i	−0.266806	+	0.963750i	$0.585968\pi$
$97$	−9.53404	+	16.5134i	−0.968035	+	1.67669i	−0.701229	+	0.712936i	$0.747365\pi$
$98$	7.33838	+	5.33655i	0.741288	+	0.539073i
$99$	0.161125	+	14.7500i	0.0161937	+	1.48243i
$100$	0.616367	+	1.90265i	0.0616367	+	0.190265i
$101$	3.32951	−	5.76687i	0.331298	−	0.573825i	−0.651468	−	0.758676i	$-0.725847\pi$
$101$	3.32951	−	5.76687i	0.331298	−	0.573825i	0.982767	+	0.184850i	$0.0591800\pi$
$102$	−10.2060	−	1.02088i	−1.01054	−	0.101082i
$103$	−8.44786	+	4.87737i	−0.832392	+	0.480582i	−0.854671	−	0.519170i	$-0.826241\pi$
$103$	−8.44786	+	4.87737i	−0.832392	+	0.480582i	0.0222789	+	0.999752i	$0.492908\pi$
$104$	1.60919	+	7.61985i	0.157794	+	0.747188i
$105$	1.14988	+	0.655535i	0.112217	+	0.0639737i
$106$	16.5634	−	7.36581i	1.60878	−	0.715431i
$107$			5.38330i			0.520424i	0.965552	+	0.260212i	$0.0837924\pi$
$107$			5.38330i			0.520424i	−0.965552	+	0.260212i	$0.916208\pi$
$108$	6.83320	−	7.82990i	0.657525	−	0.753433i
$109$			8.77193i			0.840199i	0.907478	+	0.420099i	$0.138005\pi$
$109$			8.77193i			0.840199i	−0.907478	+	0.420099i	$0.861995\pi$
$110$	−2.82551	−	6.35369i	−0.269402	−	0.605800i
$111$	7.45609	+	4.25065i	0.707701	+	0.403454i
$112$	1.24818	−	2.79030i	0.117942	−	0.263658i
$113$	12.3881	−	7.15229i	1.16538	−	0.672831i	0.212791	−	0.977098i	$-0.431745\pi$
$113$	12.3881	−	7.15229i	1.16538	−	0.672831i	0.952587	+	0.304267i	$0.0984114\pi$
$114$	−1.36905	+	13.6867i	−0.128223	+	1.28187i
$115$	0.420090	−	0.727618i	0.0391736	−	0.0678507i
$116$	−2.51368	−	7.75944i	−0.233390	−	0.720446i
$117$	−7.19834	−	4.05178i	−0.665487	−	0.374587i
$118$	2.44200	−	3.35803i	0.224804	−	0.309131i
$119$	1.59997	−	2.77122i	0.146669	−	0.254038i
$120$	−1.49453	+	4.66545i	−0.136431	+	0.425895i
$121$	6.58821	+	11.4111i	0.598928	+	1.03737i
$122$	−3.50179	−	0.369603i	−0.317037	−	0.0334623i
$123$	0.0517820	+	9.48090i	0.00466903	+	0.854864i
$124$	4.51398	−	21.1455i	0.405367	−	1.89892i
$125$	1.00000			0.0894427
$126$	1.34969	+	2.94788i	0.120240	+	0.262618i
$127$		−	11.7564i		−	1.04321i	−0.853187	−	0.521604i	$-0.825334\pi$
$127$		−	11.7564i		−	1.04321i	0.853187	−	0.521604i	$-0.174666\pi$
$128$	11.0592	+	2.38617i	0.977506	+	0.210910i
$129$	−0.985924	−	1.68633i	−0.0868058	−	0.148473i
$130$	3.87245	+	0.408726i	0.339636	+	0.0358476i
$131$	−2.65957	+	1.53550i	−0.232367	+	0.134157i	−0.611664	−	0.791118i	$-0.709499\pi$
$131$	−2.65957	+	1.53550i	−0.232367	+	0.134157i	0.379296	+	0.925275i	$0.376166\pi$
$132$	3.46489	−	16.6767i	0.301580	−	1.45152i
$133$	−3.71633	−	2.14563i	−0.322247	−	0.186049i
$134$	−1.24462	−	0.905103i	−0.107519	−	0.0781890i
$135$	−2.67146	−	4.45683i	−0.229922	−	0.383583i
$136$	11.2592	+	3.67469i	0.965466	+	0.315102i
$137$	−0.517724	−	0.298908i	−0.0442321	−	0.0255374i	0.477721	−	0.878512i	$-0.341463\pi$
$137$	−0.517724	−	0.298908i	−0.0442321	−	0.0255374i	−0.521953	+	0.852974i	$0.674796\pi$
$138$	1.87586	−	0.846504i	0.159684	−	0.0720592i
$139$	−6.83597	−	11.8402i	−0.579819	−	1.00428i	−0.995500	−	0.0947658i	$-0.969790\pi$
$139$	−6.83597	−	11.8402i	−0.579819	−	1.00428i	0.415680	−	0.909511i	$-0.363544\pi$
$140$	−1.13491	−	1.02368i	−0.0959172	−	0.0865165i
$141$	−4.43452	−	7.58484i	−0.373454	−	0.638758i
$142$	−13.4500	+	5.98125i	−1.12870	+	0.501935i
$143$	−13.5386			−1.13215
$144$	−9.64311	+	7.14216i	−0.803592	+	0.595180i
$145$	−4.07822			−0.338678
$146$	7.88439	−	3.50622i	0.652517	−	0.290177i
$147$	11.1127	−	0.0606945i	0.916560	−	0.00500600i
$148$	−7.35901	−	6.63777i	−0.604907	−	0.545621i
$149$	6.57797	+	11.3934i	0.538888	+	0.933381i	0.998964	+	0.0455020i	$0.0144887\pi$
$149$	6.57797	+	11.3934i	0.538888	+	0.933381i	−0.460076	+	0.887879i	$0.652178\pi$
$150$	1.98889	+	1.42980i	0.162392	+	0.116743i
$151$	−4.98907	−	2.88044i	−0.406004	−	0.234407i	0.283067	−	0.959100i	$-0.408648\pi$
$151$	−4.98907	−	2.88044i	−0.406004	−	0.234407i	−0.689072	+	0.724693i	$0.741981\pi$
$152$	4.92792	−	15.0991i	0.399707	−	1.22469i
$153$	−10.8098	+	6.39951i	−0.873924	+	0.517370i
$154$	4.29764	+	3.12530i	0.346314	+	0.251844i
$155$	−9.36257	−	5.40548i	−0.752019	−	0.434179i
$156$	7.11746	+	6.34974i	0.569853	+	0.508386i
$157$	10.5732	−	6.10445i	0.843835	−	0.487188i	−0.0147311	−	0.999891i	$-0.504689\pi$
$157$	10.5732	−	6.10445i	0.843835	−	0.487188i	0.858566	+	0.512703i	$0.171356\pi$
$158$	22.9231	+	2.41946i	1.82366	+	0.192482i
$159$	10.9955	−	19.2873i	0.872002	−	1.52958i
$160$	2.83915	−	4.89277i	0.224454	−	0.386808i
$161$			0.642056i			0.0506011i
$162$	1.05915	−	12.6838i	0.0832148	−	0.996532i
$163$	14.8146			1.16037			0.580186	−	0.814484i	$-0.302980\pi$
$163$	14.8146			1.16037			0.580186	+	0.814484i	$0.302980\pi$
$164$	2.28555	−	10.7065i	0.178471	−	0.836039i
$165$	−7.39857	−	4.21786i	−0.575978	−	0.328360i
$166$	4.47054	+	0.471853i	0.346981	+	0.0366229i
$167$	1.83489	+	3.17812i	0.141988	+	0.245930i	0.928245	−	0.371969i	$-0.121317\pi$
$167$	1.83489	+	3.17812i	0.141988	+	0.245930i	−0.786257	+	0.617899i	$0.787984\pi$
$168$	−0.793548	−	3.65867i	−0.0612236	−	0.282272i
$169$	−2.70927	+	4.69260i	−0.208406	+	0.360969i
$170$	3.48286	−	4.78934i	0.267123	−	0.367325i
$171$	8.58203	+	14.4965i	0.656284	+	1.10857i
$172$	0.695136	+	2.14580i	0.0530037	+	0.163616i
$173$	10.6649	−	18.4721i	0.810835	−	1.40441i	−0.101445	−	0.994841i	$-0.532347\pi$
$173$	10.6649	−	18.4721i	0.810835	−	1.40441i	0.912280	−	0.409566i	$-0.134320\pi$
$174$	−8.11112	−	5.83104i	−0.614902	−	0.442050i
$175$	−0.661806	+	0.382094i	−0.0500278	+	0.0288836i
$176$	−8.03109	+	17.9534i	−0.605366	+	1.35329i
$177$	−0.0277737	−	5.08515i	−0.00208760	−	0.382223i
$178$	4.33531	+	9.74876i	0.324945	+	0.730700i
$179$			10.5460i			0.788246i	0.919058	+	0.394123i	$0.128952\pi$
$179$			10.5460i			0.788246i	−0.919058	+	0.394123i	$0.871048\pi$
$180$	1.91134	+	5.68742i	0.142463	+	0.423915i
$181$			5.24370i			0.389761i	0.980827	+	0.194881i	$0.0624319\pi$
$181$			5.24370i			0.389761i	−0.980827	+	0.194881i	$0.937568\pi$
$182$	−2.71898	+	1.20914i	−0.201544	+	0.0896275i
$183$	−3.72300	+	2.17668i	−0.275212	+	0.160904i
$184$	−2.32511	+	0.491024i	−0.171409	+	0.0361988i
$185$	−4.29131	+	2.47759i	−0.315503	+	0.182156i
$186$	−10.8923	−	24.1375i	−0.798664	−	1.76985i
$187$	−10.2945	+	17.8307i	−0.752811	+	1.30391i
$188$	3.12660	+	9.65145i	0.228031	+	0.703905i
$189$	3.47091	+	1.92881i	0.252472	+	0.140300i
$190$	−6.42271	−	4.67067i	−0.465953	−	0.338846i
$191$	6.46180	−	11.1922i	0.467560	−	0.809837i	−0.531753	−	0.846899i	$-0.678467\pi$
$191$	6.46180	−	11.1922i	0.467560	−	0.809837i	0.999313	+	0.0370621i	$0.0117999\pi$
$192$	12.6424	−	5.67175i	0.912389	−	0.409324i
$193$	−0.869936	−	1.50677i	−0.0626193	−	0.108460i	0.833016	−	0.553249i	$-0.186612\pi$
$193$	−0.869936	−	1.50677i	−0.0626193	−	0.108460i	−0.895635	+	0.444789i	$0.853279\pi$
$194$	2.83050	−	26.8174i	0.203218	−	1.92538i
$195$	4.11708	−	2.40707i	0.294830	−	0.172374i
$196$	−12.5493	−	2.67893i	−0.896377	−	0.191352i
$197$	4.82922			0.344068			0.172034	−	0.985091i	$-0.444966\pi$
$197$	4.82922			0.344068			0.172034	+	0.985091i	$0.444966\pi$
$198$	−8.68423	−	18.9673i	−0.617161	−	1.34795i
$199$			19.3015i			1.36825i	0.729367	+	0.684123i	$0.239815\pi$
$199$			19.3015i			1.36825i	−0.729367	+	0.684123i	$0.760185\pi$
$200$	−1.88982	−	2.10442i	−0.133631	−	0.148805i
$201$	−1.88476	+	0.0102941i	−0.132941	+	0.000726087i
$202$	−0.988475	+	9.36525i	−0.0695488	+	0.658936i
$203$	2.69899	−	1.55826i	0.189432	−	0.109369i
$204$	13.7748	−	4.54565i	0.964430	−	0.318259i
$205$	−4.74052	−	2.73694i	−0.331092	−	0.191156i
$206$	8.11356	−	11.1571i	0.565298	−	0.777350i
$207$	1.23635	−	2.19649i	0.0859324	−	0.152667i
$208$	−6.45811	−	8.92166i	−0.447790	−	0.618606i
$209$	23.9117	+	13.8054i	1.65401	+	0.954942i
$210$	−1.86257	−	0.186309i	−0.128530	−	0.0128565i
$211$	−3.28205	−	5.68468i	−0.225946	−	0.391350i	0.730657	−	0.682745i	$-0.239214\pi$
$211$	−3.28205	−	5.68468i	−0.225946	−	0.391350i	−0.956603	+	0.291395i	$0.905881\pi$
$212$	−17.1705	+	19.0362i	−1.17927	+	1.30741i
$213$	−8.92868	+	15.6619i	−0.611783	+	1.07313i
$214$	−3.09350	−	6.95631i	−0.211467	−	0.475523i
$215$	1.12780			0.0769150
$216$	−4.33044	+	14.0445i	−0.294649	+	0.955606i
$217$	8.26160			0.560834
$218$	−5.04076	−	11.3351i	−0.341403	−	0.767710i
$219$	5.23401	−	9.18101i	0.353682	−	0.620395i
$220$	7.30225	+	6.58657i	0.492317	+	0.444066i
$221$	−5.76484	−	9.98499i	−0.387785	−	0.671663i
$222$	−12.0774	−	1.20807i	−0.810581	−	0.0810805i
$223$	4.94692	+	2.85610i	0.331270	+	0.191259i	0.656405	−	0.754409i	$-0.272076\pi$
$223$	4.94692	+	2.85610i	0.331270	+	0.191259i	−0.325135	+	0.945668i	$0.605410\pi$
$224$	−0.00946774	+	4.32289i	−0.000632590	+	0.288835i
$225$	2.99982	−	0.0327694i	0.199988	−	0.00218462i
$226$	−11.8979	+	16.3610i	−0.791437	+	1.08832i
$227$	−19.6884	−	11.3671i	−1.30677	−	0.754461i	−0.325211	−	0.945642i	$-0.605435\pi$
$227$	−19.6884	−	11.3671i	−1.30677	−	0.754461i	−0.981555	+	0.191180i	$0.938769\pi$
$228$	−6.09592	−	18.4726i	−0.403712	−	1.22338i
$229$	−0.117540	+	0.0678617i	−0.00776726	+	0.00448443i	−0.503879	−	0.863774i	$-0.668094\pi$
$229$	−0.117540	+	0.0678617i	−0.00776726	+	0.00448443i	0.496111	+	0.868259i	$0.334761\pi$
$230$	−0.124718	+	1.18163i	−0.00822365	+	0.0779145i
$231$	6.50804	−	0.0355451i	0.428197	−	0.00233870i
$232$	7.70712	+	8.58227i	0.505997	+	0.563454i
$233$		−	10.0275i		−	0.656922i	−0.944517	−	0.328461i	$-0.893470\pi$
$233$		−	10.0275i		−	0.656922i	0.944517	−	0.328461i	$-0.106530\pi$
$234$	11.6300	+	1.09921i	0.760280	+	0.0718574i
$235$	5.07263			0.330902
$236$	−1.22587	+	5.74253i	−0.0797974	+	0.373807i
$237$	24.3712	−	14.2487i	1.58308	−	0.925555i
$238$	−0.475003	+	4.50039i	−0.0307899	+	0.291717i
$239$	10.1038	+	17.5002i	0.653558	+	1.13200i	0.982253	+	0.187559i	$0.0600577\pi$
$239$	10.1038	+	17.5002i	0.653558	+	1.13200i	−0.328696	+	0.944436i	$0.606609\pi$
$240$	−0.749749	−	6.88752i	−0.0483961	−	0.444587i
$241$	−2.83041	+	4.90241i	−0.182323	+	0.315792i	−0.942671	−	0.333723i	$-0.891695\pi$
$241$	−2.83041	+	4.90241i	−0.182323	+	0.315792i	0.760348	+	0.649515i	$0.225028\pi$
$242$	−15.0706	−	10.9595i	−0.968777	−	0.704506i
$243$	−8.15994	−	13.2821i	−0.523460	−	0.852050i
$244$	4.73740	−	1.53469i	0.303281	−	0.0982483i
$245$	−3.20801	+	5.55643i	−0.204952	+	0.354988i
$246$	−5.51508	−	12.2215i	−0.351628	−	0.779212i
$247$	−13.3903	+	7.73091i	−0.852006	+	0.491906i
$248$	6.31822	+	29.9181i	0.401207	+	1.89980i
$249$	4.75296	−	2.77884i	0.301207	−	0.176102i
$250$	−1.29220	+	0.574647i	−0.0817259	+	0.0363438i
$251$		−	24.1060i		−	1.52155i	−0.649013	−	0.760777i	$-0.724818\pi$
$251$		−	24.1060i		−	1.52155i	0.649013	−	0.760777i	$-0.275182\pi$
$252$	−3.43806	−	3.03366i	−0.216578	−	0.191102i
$253$		−	4.13113i		−	0.259722i
$254$	6.75576	+	15.1916i	0.423894	+	0.953205i
$255$	−0.0396118	−	7.25262i	−0.00248059	−	0.454177i
$256$	−15.6619	+	3.27172i	−0.978870	+	0.204483i
$257$	−7.32769	+	4.23064i	−0.457089	+	0.263900i	−0.710819	−	0.703375i	$-0.751676\pi$
$257$	−7.32769	+	4.23064i	−0.457089	+	0.263900i	0.253731	+	0.967275i	$0.418342\pi$
$258$	2.24306	+	1.61252i	0.139647	+	0.100391i
$259$	1.89334	−	3.27936i	0.117646	−	0.203770i
$260$	−5.23885	+	1.69713i	−0.324900	+	0.105252i
$261$	−12.2339	+	0.133641i	−0.757261	+	0.00827215i
$262$	2.55432	−	3.51249i	0.157807	−	0.217002i
$263$	−14.7326	+	25.5177i	−0.908453	+	1.57349i	−0.0922402	+	0.995737i	$0.529403\pi$
$263$	−14.7326	+	25.5177i	−0.908453	+	1.57349i	−0.816213	+	0.577751i	$0.803931\pi$
$264$	5.10587	+	23.5407i	0.314244	+	1.44883i
$265$	6.40899	+	11.1007i	0.393701	+	0.681911i
$266$	6.03522	+	0.637000i	0.370043	+	0.0390570i
$267$	11.3520	+	6.47166i	0.694730	+	0.396059i
$268$	2.12841	+	0.454357i	0.130014	+	0.0277543i
$269$	21.5539			1.31416			0.657081	−	0.753820i	$-0.271791\pi$
$269$	21.5539			1.31416			0.657081	+	0.753820i	$0.271791\pi$
$270$	6.01316	+	4.22397i	0.365949	+	0.257063i
$271$		−	12.3147i		−	0.748063i	−0.927416	−	0.374032i	$-0.877975\pi$
$271$		−	12.3147i		−	0.748063i	0.927416	−	0.374032i	$-0.122025\pi$
$272$	−16.6608	+	1.72161i	−1.01021	+	0.104388i
$273$	−1.80498	+	3.16613i	−0.109242	+	0.191623i
$274$	0.840769	+	0.0887408i	0.0507927	+	0.00536103i
$275$	4.25821	−	2.45848i	0.256779	−	0.148252i
$276$	−1.93755	+	2.17181i	−0.116627	+	0.130728i
$277$	25.1744	+	14.5344i	1.51258	+	0.873290i	0.999892	+	0.0147172i	$0.00468479\pi$
$277$	25.1744	+	14.5344i	1.51258	+	0.873290i	0.512691	+	0.858573i	$0.328649\pi$
$278$	15.6374	+	11.3717i	0.937869	+	0.682029i
$279$	−28.2632	−	15.9087i	−1.69207	−	0.952427i
$280$	2.05478	+	0.670625i	0.122797	+	0.0400775i
$281$	22.0745	+	12.7447i	1.31686	+	0.760287i	0.983222	−	0.182415i	$-0.0583914\pi$
$281$	22.0745	+	12.7447i	1.31686	+	0.760287i	0.333635	+	0.942702i	$0.391725\pi$
$282$	10.0889	+	7.25285i	0.600784	+	0.431901i
$283$	−11.4768	−	19.8783i	−0.682222	−	1.18164i	−0.974301	−	0.225249i	$-0.927680\pi$
$283$	−11.4768	−	19.8783i	−0.682222	−	1.18164i	0.292079	−	0.956394i	$-0.405653\pi$
$284$	13.9429	−	15.4579i	0.827361	−	0.917261i
$285$	−9.72609	+	0.0531212i	−0.576124	+	0.00314663i
$286$	17.4945	−	7.77988i	1.03447	−	0.460034i
$287$	4.18307			0.246919
$288$	8.35661	−	14.7705i	0.492418	−	0.870359i
$289$	−0.534039			−0.0314141
$290$	5.26988	−	2.34354i	0.309458	−	0.137617i
$291$	−16.6694	−	28.5115i	−0.977178	−	1.67137i
$292$	−8.17338	+	9.06148i	−0.478311	+	0.530283i
$293$	11.3208	+	19.6082i	0.661367	+	1.14552i	0.980257	+	0.197729i	$0.0633567\pi$
$293$	11.3208	+	19.6082i	0.661367	+	1.14552i	−0.318890	+	0.947792i	$0.603310\pi$
$294$	−14.3250	+	6.46431i	−0.835449	+	0.377006i
$295$	2.54261	+	1.46798i	0.148037	+	0.0854690i
$296$	13.3237	+	4.34849i	0.774424	+	0.252751i
$297$	−22.3326	−	12.4104i	−1.29587	−	0.720123i
$298$	−15.0472	−	10.9425i	−0.871662	−	0.633883i
$299$	2.00346	+	1.15670i	0.115863	+	0.0668934i
$300$	−3.39167	−	0.704682i	−0.195818	−	0.0406848i
$301$	−0.746381	+	0.430924i	−0.0430207	+	0.0248380i
$302$	8.10211	+	0.855154i	0.466224	+	0.0492086i
$303$	5.82134	+	9.95687i	0.334427	+	0.572007i
$304$	2.30875	+	22.3428i	0.132416	+	1.28145i
$305$		−	2.48989i		−	0.142571i
$306$	10.2910	−	14.4813i	0.588299	−	0.827840i
$307$	20.8990			1.19277			0.596385	−	0.802699i	$-0.296603\pi$
$307$	20.8990			1.19277			0.596385	+	0.802699i	$0.296603\pi$
$308$	−7.34935	−	1.56888i	−0.418768	−	0.0893955i
$309$	−0.0922783	−	16.8955i	−0.00524953	−	0.961149i
$310$	15.2045	+	1.60480i	0.863560	+	0.0911463i
$311$	−0.580992	−	1.00631i	−0.0329450	−	0.0570625i	0.849083	−	0.528260i	$-0.177155\pi$
$311$	−0.580992	−	1.00631i	−0.0329450	−	0.0570625i	−0.882028	+	0.471197i	$0.843822\pi$
$312$	−12.8460	−	4.11511i	−0.727264	−	0.232972i
$313$	−14.1698	+	24.5428i	−0.800924	+	1.38724i	0.118085	+	0.993003i	$0.462324\pi$
$313$	−14.1698	+	24.5428i	−0.800924	+	1.38724i	−0.919009	+	0.394237i	$0.871009\pi$
$314$	−10.1548	+	13.9640i	−0.573069	+	0.788036i
$315$	−1.97278	+	1.16790i	−0.111153	+	0.0658037i
$316$	−31.0115	+	10.0462i	−1.74453	+	0.565144i
$317$	1.74126	−	3.01595i	0.0977989	−	0.169393i	−0.812974	−	0.582299i	$-0.802153\pi$
$317$	1.74126	−	3.01595i	0.0977989	−	0.169393i	0.910773	+	0.412907i	$0.135486\pi$
$318$	−3.12503	+	31.2416i	−0.175243	+	1.75194i
$319$	−17.3659	+	10.0262i	−0.972304	+	0.561360i
$320$	−0.857135	+	7.95395i	−0.0479153	+	0.444639i
$321$	−8.10030	−	4.61791i	−0.452115	−	0.257746i
$322$	−0.368955	−	0.829664i	−0.0205611	−	0.0462354i
$323$			23.5139i			1.30835i
$324$	5.92005	+	16.9986i	0.328892	+	0.944368i
$325$			2.75344i			0.152734i
$326$	−19.1435	+	8.51317i	−1.06026	+	0.471501i
$327$	−13.1992	−	7.52474i	−0.729917	−	0.416119i
$328$	3.19908	+	15.1484i	0.176640	+	0.836428i
$329$	−3.35709	+	1.93822i	−0.185083	+	0.106857i
$330$	11.9842	+	1.19875i	0.659709	+	0.0659892i
$331$	11.2013	−	19.4012i	0.615679	−	1.06639i	−0.374586	−	0.927192i	$-0.622215\pi$
$331$	11.2013	−	19.4012i	0.615679	−	1.06639i	0.990265	−	0.139195i	$-0.0444516\pi$
$332$	−6.04798	+	1.95925i	−0.331926	+	0.107528i
$333$	−12.7920	+	7.57294i	−0.700995	+	0.414995i
$334$	−4.19734	−	3.05236i	−0.229668	−	0.167017i
$335$	0.544092	−	0.942396i	0.0297269	−	0.0514886i
$336$	3.12786	+	4.27172i	0.170639	+	0.233042i
$337$	−3.92431	−	6.79710i	−0.213771	−	0.370262i	0.739121	−	0.673573i	$-0.235241\pi$
$337$	−3.92431	−	6.79710i	−0.213771	−	0.370262i	−0.952892	+	0.303311i	$0.901908\pi$
$338$	0.804338	−	7.62065i	0.0437502	−	0.414509i
$339$	0.135319	+	24.7759i	0.00734952	+	1.34564i
$340$	−1.74838	+	8.19020i	−0.0948193	+	0.444176i
$341$	−53.1570			−2.87861
$342$	−19.4200	−	13.8007i	−1.05012	−	0.746257i
$343$		−	10.2524i		−	0.553575i
$344$	−2.13133	−	2.37335i	−0.114914	−	0.127963i
$345$	0.734490	+	1.25628i	0.0395436	+	0.0676358i
$346$	−3.16622	+	29.9982i	−0.170217	+	1.61271i
$347$	−7.77620	+	4.48959i	−0.417449	+	0.241014i	−0.693985	−	0.719989i	$-0.744147\pi$
$347$	−7.77620	+	4.48959i	−0.417449	+	0.241014i	0.276537	+	0.961003i	$0.410813\pi$
$348$	13.8320	+	2.87385i	0.741472	+	0.154054i
$349$	−2.18402	−	1.26095i	−0.116908	−	0.0674970i	0.440406	−	0.897799i	$-0.354835\pi$
$349$	−2.18402	−	1.26095i	−0.116908	−	0.0674970i	−0.557314	+	0.830302i	$0.688168\pi$
$350$	0.635617	−	0.874046i	0.0339751	−	0.0467197i
$351$	12.2716	−	7.35571i	0.655011	−	0.392619i
$352$	0.0609176	−	27.8144i	0.00324692	−	1.48251i
$353$	−11.1624	−	6.44461i	−0.594114	−	0.343012i	0.172609	−	0.984991i	$-0.444780\pi$
$353$	−11.1624	−	6.44461i	−0.594114	−	0.343012i	−0.766723	+	0.641979i	$0.778114\pi$
$354$	2.95805	+	6.55507i	0.157219	+	0.348398i
$355$	−5.20429	−	9.01409i	−0.276215	−	0.478418i
$356$	−11.2042	−	10.1061i	−0.593820	−	0.535621i
$357$	2.79740	+	4.78469i	0.148054	+	0.253233i
$358$	−6.06023	−	13.6276i	−0.320293	−	0.720239i
$359$	7.35712			0.388294			0.194147	−	0.980972i	$-0.437806\pi$
$359$	7.35712			0.388294			0.194147	+	0.980972i	$0.437806\pi$
$360$	−5.73809	−	6.25094i	−0.302424	−	0.329454i
$361$	12.5332			0.659643
$362$	−3.01327	−	6.77591i	−0.158374	−	0.356134i
$363$	−22.8219	+	0.124647i	−1.19784	+	0.00654226i
$364$	2.81864	−	3.12490i	0.147737	−	0.163789i
$365$	3.05076	+	5.28408i	0.159684	+	0.276581i
$366$	3.56005	−	4.95211i	0.186087	−	0.258851i
$367$	−10.5509	−	6.09157i	−0.550753	−	0.317978i	0.198673	−	0.980066i	$-0.436337\pi$
$367$	−10.5509	−	6.09157i	−0.550753	−	0.317978i	−0.749426	+	0.662088i	$0.769670\pi$
$368$	2.72234	−	1.97062i	0.141912	−	0.102725i
$369$	−14.3104	−	8.05498i	−0.744969	−	0.419326i
$370$	4.12149	−	5.66752i	0.214266	−	0.294641i
$371$	−8.48302	−	4.89767i	−0.440416	−	0.254274i
$372$	27.9456	+	24.9312i	1.44891	+	1.29262i
$373$	10.5635	−	6.09884i	0.546957	−	0.315786i	−0.200937	−	0.979604i	$-0.564399\pi$
$373$	10.5635	−	6.09884i	0.546957	−	0.315786i	0.747894	+	0.663818i	$0.231065\pi$
$374$	3.05628	−	28.9565i	0.158036	−	1.49731i
$375$	−0.857820	+	1.50471i	−0.0442976	+	0.0777028i
$376$	−9.58637	−	10.6749i	−0.494379	−	0.550517i
$377$		−	11.2292i		−	0.578331i
$378$	−5.59349	−	0.497859i	−0.287698	−	0.0256071i
$379$	34.2532			1.75947			0.879735	−	0.475464i	$-0.157720\pi$
$379$	34.2532			1.75947			0.879735	+	0.475464i	$0.157720\pi$
$380$	10.9834	+	2.34466i	0.563437	+	0.120278i
$381$	17.6899	+	10.0848i	0.906281	+	0.516662i
$382$	−1.91840	+	18.1758i	−0.0981540	+	0.929954i
$383$	−15.7345	−	27.2529i	−0.803994	−	1.39256i	−0.916968	−	0.398960i	$-0.869371\pi$
$383$	−15.7345	−	27.2529i	−0.803994	−	1.39256i	0.112974	−	0.993598i	$-0.463962\pi$
$384$	−13.0773	+	14.5940i	−0.667349	+	0.744746i
$385$	−1.87874	+	3.25407i	−0.0957493	+	0.165843i
$386$	1.98999	+	1.44715i	0.101288	+	0.0736578i
$387$	3.38318	−	0.0369571i	0.171977	−	0.00187864i
$388$	11.7529	+	36.2800i	0.596665	+	1.84184i
$389$	9.79479	−	16.9651i	0.496616	−	0.860164i	−0.503377	−	0.864067i	$-0.667909\pi$
$389$	9.79479	−	16.9651i	0.496616	−	0.860164i	0.999992	+	0.00390344i	$0.00124251\pi$
$390$	−3.93688	+	5.47629i	−0.199351	+	0.277303i
$391$	3.04680	−	1.75907i	0.154083	−	0.0889601i
$392$	17.7556	−	3.74969i	0.896794	−	0.189388i
$393$	−0.0290512	−	5.31905i	−0.00146544	−	0.268311i
$394$	−6.24032	+	2.77510i	−0.314383	+	0.139807i
$395$			16.2991i			0.820096i
$396$	22.1213	+	19.5192i	1.11164	+	0.980878i
$397$			17.4311i			0.874840i	0.899257	+	0.437420i	$0.144108\pi$
$397$			17.4311i			0.874840i	−0.899257	+	0.437420i	$0.855892\pi$
$398$	−11.0915	−	24.9414i	−0.555968	−	1.25020i
$399$	6.41648	−	3.75143i	0.321226	−	0.187807i
$400$	3.65133	+	1.63335i	0.182566	+	0.0816673i
$401$	−28.3881	+	16.3899i	−1.41764	+	0.818472i	−0.996091	−	0.0883358i	$-0.971845\pi$
$401$	−28.3881	+	16.3899i	−1.41764	+	0.818472i	−0.421544	+	0.906808i	$0.638512\pi$
$402$	2.42958	−	1.09637i	0.121176	−	0.0546822i
$403$	14.8837	−	25.7793i	0.741409	−	1.28416i
$404$	−4.10440	−	12.6698i	−0.204201	−	0.630346i
$405$	8.99785	−	0.196604i	0.447107	−	0.00976935i
$406$	−2.59219	+	3.56455i	−0.128648	+	0.176906i
$407$	−12.1822	+	21.1002i	−0.603848	+	1.04590i
$408$	−15.1877	+	13.7895i	−0.751902	+	0.682684i
$409$	−10.7177	−	18.5636i	−0.529956	−	0.917911i	−0.999389	−	0.0349426i	$-0.988875\pi$
$409$	−10.7177	−	18.5636i	−0.529956	−	0.917911i	0.469433	−	0.882968i	$-0.344458\pi$
$410$	7.69847	+	0.812552i	0.380200	+	0.0401291i
$411$	0.893883	−	0.522614i	0.0440920	−	0.0257786i
$412$	−4.07297	+	19.0796i	−0.200661	+	0.939984i
$413$	−2.24362			−0.110401
$414$	−0.335410	+	3.54877i	−0.0164845	+	0.174413i
$415$			3.17871i			0.156037i
$416$	13.4720	+	7.81744i	0.660518	+	0.383282i
$417$	23.6801	−	0.129334i	1.15962	−	0.00633353i
$418$	−38.8320	−	4.09860i	−1.89933	−	0.200469i
$419$	20.7281	−	11.9673i	1.01263	−	0.584643i	0.100671	−	0.994920i	$-0.467901\pi$
$419$	20.7281	−	11.9673i	1.01263	−	0.584643i	0.911961	+	0.410277i	$0.134568\pi$
$420$	2.51388	−	0.829573i	0.122665	−	0.0404790i
$421$	17.2720	+	9.97202i	0.841788	+	0.486007i	0.857872	−	0.513864i	$-0.171786\pi$
$421$	17.2720	+	9.97202i	0.841788	+	0.486007i	−0.0160836	+	0.999871i	$0.505120\pi$
$422$	7.50776	+	5.45973i	0.365472	+	0.265775i
$423$	15.2170	−	0.166227i	0.739875	−	0.00808222i
$424$	11.2486	−	34.4656i	0.546282	−	1.67380i
$425$	3.62637	+	2.09368i	0.175905	+	0.101559i
$426$	2.53761	−	25.3691i	0.122948	−	1.22914i
$427$	0.951372	+	1.64782i	0.0460401	+	0.0797438i
$428$	7.99484	+	7.21127i	0.386445	+	0.348570i
$429$	11.6136	−	20.3716i	0.560712	−	0.983548i
$430$	−1.45734	+	0.648084i	−0.0702791	+	0.0312534i
$431$	32.8035			1.58009			0.790045	−	0.613049i	$-0.210057\pi$
$431$	32.8035			1.58009			0.790045	+	0.613049i	$0.210057\pi$
$432$	−2.47481	−	20.6367i	−0.119069	−	0.992886i
$433$	15.5016			0.744958			0.372479	−	0.928041i	$-0.378508\pi$
$433$	15.5016			0.744958			0.372479	+	0.928041i	$0.378508\pi$
$434$	−10.6756	+	4.74750i	−0.512447	+	0.227887i
$435$	3.49838	−	6.13653i	0.167734	−	0.294224i
$436$	13.0273	+	11.7506i	0.623897	+	0.562750i
$437$	−2.35899	−	4.08590i	−0.112846	−	0.195455i
$438$	−1.48755	+	14.8714i	−0.0710781	+	0.710584i
$439$	−12.3870	−	7.15166i	−0.591201	−	0.341330i	0.174371	−	0.984680i	$-0.444211\pi$
$439$	−12.3870	−	7.15166i	−0.591201	−	0.341330i	−0.765572	+	0.643350i	$0.777544\pi$
$440$	−13.2209	−	4.31495i	−0.630282	−	0.205707i
$441$	−9.44137	+	16.7734i	−0.449589	+	0.798735i
$442$	13.1872	+	9.58987i	0.627250	+	0.456143i
$443$	1.16788	+	0.674275i	0.0554876	+	0.0320358i	0.527487	−	0.849563i	$-0.323134\pi$
$443$	1.16788	+	0.674275i	0.0554876	+	0.0320358i	−0.472000	+	0.881599i	$0.656468\pi$
$444$	16.3006	−	5.37915i	0.773593	−	0.255283i
$445$	−6.53357	+	3.77216i	−0.309721	+	0.178817i
$446$	−8.03365	−	0.847929i	−0.380405	−	0.0401506i
$447$	−22.7864	+	0.124453i	−1.07776	+	0.00588643i
$448$	−2.47190	−	5.59147i	−0.116786	−	0.264172i
$449$			18.3615i			0.866533i	0.901266	+	0.433267i	$0.142639\pi$
$449$			18.3615i			0.866533i	−0.901266	+	0.433267i	$0.857361\pi$
$450$	−3.85754	+	1.76618i	−0.181846	+	0.0832586i
$451$	−26.9148			−1.26737
$452$	5.97269	−	27.9788i	0.280932	−	1.31601i
$453$	8.61394	−	5.03619i	0.404718	−	0.236621i
$454$	31.9734	+	3.37470i	1.50059	+	0.158383i
$455$	−1.05207	−	1.82224i	−0.0493220	−	0.0854282i
$456$	18.4924	+	20.3674i	0.865985	+	0.953789i
$457$	10.7123	−	18.5542i	0.501099	−	0.867930i	−0.498900	−	0.866660i	$-0.666262\pi$
$457$	10.7123	−	18.5542i	0.501099	−	0.867930i	0.999999	−	0.00127001i	$-0.000404257\pi$
$458$	0.112889	−	0.155235i	0.00527494	−	0.00725365i
$459$	−0.356492	−	21.7553i	−0.0166396	−	1.01545i
$460$	−0.517860	−	1.59857i	−0.0241453	−	0.0745339i
$461$	−12.1325	+	21.0141i	−0.565067	+	0.978724i	0.431977	+	0.901885i	$0.357816\pi$
$461$	−12.1325	+	21.0141i	−0.565067	+	0.978724i	−0.997043	+	0.0768396i	$0.975517\pi$
$462$	−8.38926	+	3.78575i	−0.390304	+	0.176129i
$463$	34.6941	−	20.0306i	1.61237	−	0.930903i	0.623552	−	0.781782i	$-0.285689\pi$
$463$	34.6941	−	20.0306i	1.61237	−	0.930903i	0.988819	−	0.149121i	$-0.0476444\pi$
$464$	−14.8909	−	6.66115i	−0.691293	−	0.309236i
$465$	16.1651	−	9.45099i	0.749637	−	0.438279i
$466$	5.76226	+	12.9575i	0.266931	+	0.600245i
$467$		−	0.768238i		−	0.0355498i	−0.999842	−	0.0177749i	$-0.994342\pi$
$467$		−	0.768238i		−	0.0355498i	0.999842	−	0.0177749i	$-0.00565823\pi$
$468$	−15.6600	+	5.26277i	−0.723884	+	0.243272i
$469$			0.831577i			0.0383987i
$470$	−6.55485	+	2.91497i	−0.302353	+	0.134457i
$471$	0.115494	+	21.1461i	0.00532169	+	0.974362i
$472$	−1.71585	−	8.12494i	−0.0789785	−	0.373981i
$473$	4.80238	−	2.77266i	0.220814	−	0.127487i
$474$	−23.3044	+	32.4170i	−1.07041	+	1.48896i
$475$	2.80772	−	4.86312i	0.128827	−	0.223135i
$476$	−1.97233	−	6.08836i	−0.0904018	−	0.279060i
$477$	19.5896	+	33.0901i	0.896946	+	1.51509i
$478$	−23.1125	−	16.8077i	−1.05714	−	0.768766i
$479$	10.2654	−	17.7802i	0.469037	−	0.812396i	−0.530336	−	0.847787i	$-0.677934\pi$
$479$	10.2654	−	17.7802i	0.469037	−	0.812396i	0.999374	+	0.0353911i	$0.0112677\pi$
$480$	4.92671	+	8.46921i	0.224873	+	0.386565i
$481$	−6.82190	−	11.8159i	−0.311052	−	0.538757i
$482$	0.840300	−	7.96138i	0.0382746	−	0.362631i
$483$	−0.966106	−	0.550768i	−0.0439593	−	0.0250608i
$484$	25.7721	+	5.50164i	1.17146	+	0.250075i
$485$	19.0681			0.865837
$486$	18.1768	+	12.4741i	0.824517	+	0.565837i
$487$			4.66770i			0.211514i	0.994392	+	0.105757i	$0.0337265\pi$
$487$			4.66770i			0.211514i	−0.994392	+	0.105757i	$0.966273\pi$
$488$	−5.23977	+	4.70545i	−0.237193	+	0.213006i
$489$	−12.7083	+	22.2917i	−0.574688	+	1.00806i
$490$	0.952404	−	9.02350i	0.0430252	−	0.407640i
$491$	20.2038	−	11.6647i	0.911784	−	0.526419i	0.0307794	−	0.999526i	$-0.490201\pi$
$491$	20.2038	−	11.6647i	0.911784	−	0.526419i	0.881005	+	0.473107i	$0.156868\pi$
$492$	14.1496	+	12.6234i	0.637913	+	0.569105i
$493$	−14.7891	−	8.53850i	−0.666069	−	0.384555i
$494$	12.8604	−	17.6846i	0.578619	−	0.795667i
$495$	12.6933	−	7.51453i	0.570521	−	0.337753i
$496$	−25.3568	−	35.0295i	−1.13855	−	1.57287i
$497$	6.88845	+	3.97705i	0.308989	+	0.178395i
$498$	−4.54492	+	6.32209i	−0.203663	+	0.283300i
$499$	−12.2705	−	21.2531i	−0.549303	−	0.951421i	−0.998322	−	0.0578987i	$-0.981560\pi$
$499$	−12.2705	−	21.2531i	−0.549303	−	0.951421i	0.449019	−	0.893522i	$-0.351773\pi$
$500$	1.33956	−	1.48512i	0.0599071	−	0.0664164i
$501$	−6.35615	+	0.0347155i	−0.283972	+	0.00155097i
$502$	13.8524	+	31.1497i	0.618263	+	1.39028i
$503$	−43.6562			−1.94653			−0.973266	−	0.229681i	$-0.926232\pi$
$503$	−43.6562			−1.94653			−0.973266	+	0.229681i	$0.926232\pi$
$504$	6.18595	+	1.94442i	0.275544	+	0.0866114i
$505$	−6.65901			−0.296322
$506$	2.37394	+	5.33824i	0.105534	+	0.237314i
$507$	−4.73692	−	8.10207i	−0.210374	−	0.359826i
$508$	−17.4596	−	15.7484i	−0.774644	−	0.698722i
$509$	−4.89817	−	8.48388i	−0.217108	−	0.376041i	0.736815	−	0.676095i	$-0.236329\pi$
$509$	−4.89817	−	8.48388i	−0.217108	−	0.376041i	−0.953922	+	0.300053i	$0.902996\pi$
$510$	4.21888	+	9.34908i	0.186815	+	0.413984i
$511$	−4.03803	−	2.33135i	−0.178632	−	0.103133i
$512$	18.3583	−	13.2278i	0.811328	−	0.584591i
$513$	−29.1748	+	0.478072i	−1.28810	+	0.0211074i
$514$	7.03772	−	9.67767i	0.310420	−	0.426864i
$515$	8.44786	+	4.87737i	0.372257	+	0.214923i
$516$	−3.82511	−	0.794737i	−0.168391	−	0.0349863i
$517$	21.6003	−	12.4709i	0.949980	−	0.548471i
$518$	−0.562101	+	5.32559i	−0.0246973	+	0.233993i
$519$	18.6466	+	31.8932i	0.818493	+	1.39996i
$520$	5.79439	−	5.20352i	0.254101	−	0.228190i
$521$			28.2300i			1.23678i	0.785871	+	0.618390i	$0.212215\pi$
$521$			28.2300i			1.23678i	−0.785871	+	0.618390i	$0.787785\pi$
$522$	15.7319	−	7.20288i	0.688566	−	0.315261i
$523$	−8.17301			−0.357381			−0.178690	−	0.983905i	$-0.557186\pi$
$523$	−8.17301			−0.357381			−0.178690	+	0.983905i	$0.557186\pi$
$524$	−1.28226	+	6.00667i	−0.0560157	+	0.262402i
$525$	−0.00722909	−	1.32359i	−0.000315503	−	0.0577663i
$526$	4.37387	−	41.4400i	0.190710	−	1.80687i
$527$	−22.6347	−	39.2045i	−0.985984	−	1.70777i
$528$	−20.1254	−	27.4852i	−0.875845	−	1.19614i
$529$	11.1470	−	19.3073i	0.484654	−	0.839446i
$530$	−14.6607	−	10.6614i	−0.636819	−	0.463103i
$531$	7.67549	+	4.32035i	0.333088	+	0.187487i
$532$	−8.16477	+	2.64499i	−0.353988	+	0.114675i
$533$	7.53601	−	13.0528i	0.326421	−	0.565377i
$534$	−18.3880	−	1.83931i	−0.795724	−	0.0795945i
$535$	4.66208	−	2.69165i	0.201559	−	0.116370i
$536$	−3.01143	+	0.635965i	−0.130074	+	0.0274695i
$537$	−15.8687	−	9.04658i	−0.684783	−	0.390389i
$538$	−27.8519	+	12.3858i	−1.20078	+	0.533992i
$539$			31.5473i			1.35884i
$540$	−10.1975	−	2.00278i	−0.438830	−	0.0861858i
$541$			5.34757i			0.229910i	0.993371	+	0.114955i	$0.0366724\pi$
$541$			5.34757i			0.229910i	−0.993371	+	0.114955i	$0.963328\pi$
$542$	7.07658	+	15.9130i	0.303965	+	0.683523i
$543$	−7.89024	−	4.49815i	−0.338603	−	0.193034i
$544$	20.5397	−	11.7987i	0.880633	−	0.505865i
$545$	7.59672	−	4.38597i	0.325408	−	0.187874i
$546$	0.512992	−	5.12849i	0.0219540	−	0.219479i
$547$	−7.11612	+	12.3255i	−0.304264	+	0.527000i	−0.977097	−	0.212794i	$-0.931744\pi$
$547$	−7.11612	+	12.3255i	−0.304264	+	0.527000i	0.672834	+	0.739794i	$0.265077\pi$
$548$	−1.13744	+	0.368474i	−0.0485889	+	0.0157404i
$549$	−0.0815921	−	7.46923i	−0.00348227	−	0.318779i
$550$	−4.08970	+	5.62381i	−0.174385	+	0.239800i
$551$	−11.4505	+	19.8329i	−0.487808	+	0.844909i
$552$	1.25568	−	3.91982i	0.0534451	−	0.166839i
$553$	−6.22778	−	10.7868i	−0.264832	−	0.458703i
$554$	−40.8825	−	4.31503i	−1.73693	−	0.183328i
$555$	−0.0468752	−	8.58249i	−0.00198974	−	0.364306i
$556$	−26.7414	−	5.70854i	−1.13409	−	0.242096i
$557$	6.09006			0.258044			0.129022	−	0.991642i	$-0.458816\pi$
$557$	6.09006			0.258044			0.129022	+	0.991642i	$0.458816\pi$
$558$	45.6635	+	4.31586i	1.93309	+	0.182705i
$559$			3.10532i			0.131341i
$560$	−3.04056	+	0.314190i	−0.128487	+	0.0132770i
$561$	−17.9991	−	30.7858i	−0.759922	−	1.29978i
$562$	−35.8484	−	3.78370i	−1.51218	−	0.159606i
$563$	−1.31608	+	0.759837i	−0.0554660	+	0.0320233i	−0.527477	−	0.849570i	$-0.676862\pi$
$563$	−1.31608	+	0.759837i	−0.0554660	+	0.0320233i	0.472011	+	0.881593i	$0.343528\pi$
$564$	−17.2047	−	3.57459i	−0.724448	−	0.150517i
$565$	−12.3881	−	7.15229i	−0.521173	−	0.300899i
$566$	26.2533	+	19.0917i	1.10351	+	0.802484i
$567$	−5.87971	+	3.56814i	−0.246925	+	0.149848i
$568$	−9.13421	+	27.9870i	−0.383263	+	1.17431i
$569$	−1.97592	−	1.14080i	−0.0828347	−	0.0478246i	0.458011	−	0.888947i	$-0.348562\pi$
$569$	−1.97592	−	1.14080i	−0.0828347	−	0.0478246i	−0.540845	+	0.841122i	$0.681896\pi$
$570$	12.5375	−	5.65771i	0.525139	−	0.236975i
$571$	10.4524	+	18.1041i	0.437419	+	0.757632i	0.997490	−	0.0708131i	$-0.0225594\pi$
$571$	10.4524	+	18.1041i	0.437419	+	0.757632i	−0.560071	+	0.828445i	$0.689226\pi$
$572$	−18.1357	+	20.1063i	−0.758293	+	0.840688i
$573$	11.2979	+	19.3240i	0.471976	+	0.807272i
$574$	−5.40536	+	2.40379i	−0.225615	+	0.100332i
$575$	−0.840181			−0.0350380
$576$	−2.31061	+	23.8885i	−0.0962752	+	0.995355i
$577$	38.2152			1.59092			0.795459	−	0.606007i	$-0.207230\pi$
$577$	38.2152			1.59092			0.795459	+	0.606007i	$0.207230\pi$
$578$	0.690086	−	0.306884i	0.0287038	−	0.0127647i
$579$	3.01350	−	0.0164589i	0.125237	−	0.000684009i
$580$	−5.46303	+	6.05663i	−0.226840	+	0.251488i
$581$	−1.21457	−	2.10369i	−0.0503886	−	0.0872757i
$582$	37.9243	+	27.2636i	1.57201	+	1.13011i
$583$	54.5816	+	31.5127i	2.26054	+	1.30512i
$584$	5.35449	−	16.4060i	0.221571	−	0.678887i
$585$	0.0902286	+	8.25984i	0.00373049	+	0.341502i
$586$	−25.8965	−	18.8322i	−1.06977	−	0.777952i
$587$	10.2941	+	5.94329i	0.424882	+	0.245306i	0.697164	−	0.716912i	$-0.254445\pi$
$587$	10.2941	+	5.94329i	0.424882	+	0.245306i	−0.272282	+	0.962218i	$0.587778\pi$
$588$	14.7960	−	16.5850i	0.610178	−	0.683952i
$589$	−52.5750	+	30.3542i	−2.16631	+	1.25072i
$590$	−4.12913	−	0.435818i	−0.169994	−	0.0179424i
$591$	−4.14261	+	7.26657i	−0.170404	+	0.298907i
$592$	−19.7157	+	2.03729i	−0.810311	+	0.0837319i
$593$		−	13.4833i		−	0.553691i	−0.960914	−	0.276846i	$-0.910711\pi$
$593$		−	13.4833i		−	0.553691i	0.960914	−	0.276846i	$-0.0892891\pi$
$594$	35.9898	+	3.20333i	1.47668	+	0.131434i
$595$	−3.19993			−0.131184
$596$	25.7321	+	5.49309i	1.05403	+	0.225006i
$597$	−29.0431	−	16.5572i	−1.18865	−	0.677641i
$598$	−3.25356	−	0.343403i	−0.133048	−	0.0140428i
$599$	8.79084	+	15.2262i	0.359184	+	0.622125i	0.987825	−	0.155571i	$-0.0497217\pi$
$599$	8.79084	+	15.2262i	0.359184	+	0.622125i	−0.628641	+	0.777696i	$0.716388\pi$
$600$	4.78766	−	1.03842i	0.195455	−	0.0423934i
$601$	3.65190	−	6.32528i	0.148964	−	0.258014i	−0.781881	−	0.623428i	$-0.785739\pi$
$601$	3.65190	−	6.32528i	0.148964	−	0.258014i	0.930845	+	0.365414i	$0.119073\pi$
$602$	0.716846	−	0.985745i	0.0292164	−	0.0401760i
$603$	1.60130	−	2.84485i	0.0652099	−	0.115851i
$604$	−10.9610	+	3.55082i	−0.445995	+	0.144481i
$605$	6.58821	−	11.4111i	0.267849	−	0.463928i
$606$	−13.2440	−	9.52106i	−0.538002	−	0.386767i
$607$	12.9495	−	7.47639i	0.525604	−	0.303457i	−0.213621	−	0.976917i	$-0.568526\pi$
$607$	12.9495	−	7.47639i	0.525604	−	0.303457i	0.739224	+	0.673459i	$0.235192\pi$
$608$	−15.8226	−	27.5447i	−0.641691	−	1.11708i
$609$	0.0294818	+	5.39790i	0.00119466	+	0.218734i
$610$	1.43081	+	3.21744i	0.0579317	+	0.130270i
$611$			13.9672i			0.565052i
$612$	−4.97644	+	24.6264i	−0.201161	+	0.995464i
$613$		−	37.8631i		−	1.52928i	−0.644459	−	0.764639i	$-0.722917\pi$
$613$		−	37.8631i		−	1.52928i	0.644459	−	0.764639i	$-0.277083\pi$
$614$	−27.0057	+	12.0095i	−1.08986	+	0.484666i
$615$	8.18481	−	4.78529i	0.330043	−	0.192962i
$616$	10.3984	−	2.19597i	0.418963	−	0.0884781i
$617$	−7.62315	+	4.40123i	−0.306897	+	0.177187i	−0.645537	−	0.763729i	$-0.723366\pi$
$617$	−7.62315	+	4.40123i	−0.306897	+	0.177187i	0.338640	+	0.940916i	$0.390033\pi$
$618$	9.82816	+	21.7793i	0.395347	+	0.876092i
$619$	−10.6025	+	18.3641i	−0.426152	+	0.738117i	−0.996527	−	0.0832675i	$-0.973464\pi$
$619$	−10.6025	+	18.3641i	−0.426152	+	0.738117i	0.570375	+	0.821384i	$0.306798\pi$
$620$	−20.5695	+	6.66352i	−0.826092	+	0.267614i
$621$	2.24451	+	3.74454i	0.0900689	+	0.150263i
$622$	1.32903	+	0.966486i	0.0532892	+	0.0387526i
$623$	2.88263	−	4.99287i	0.115490	−	0.200035i
$624$	18.9644	−	2.06439i	0.759183	−	0.0826418i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	4.20677	−	39.8568i	0.168136	−	1.59300i
$627$	−41.2851	+	24.1376i	−1.64877	+	0.963961i
$628$	5.09767	−	23.8798i	0.203419	−	0.952906i
$629$	−20.7491			−0.827322
$630$	1.87809	−	2.64281i	0.0748251	−	0.105292i
$631$		−	17.7179i		−	0.705340i	−0.935748	−	0.352670i	$-0.885274\pi$
$631$		−	17.7179i		−	0.705340i	0.935748	−	0.352670i	$-0.114726\pi$
$632$	34.3001	−	30.8024i	1.36438	−	1.22525i
$633$	11.3692	−	0.0620954i	0.451885	−	0.00246807i
$634$	−0.516951	+	4.89782i	−0.0205307	+	0.194517i
$635$	−10.1813	+	5.87818i	−0.404033	+	0.233269i
$636$	−13.9147	−	42.1662i	−0.551755	−	1.67200i
$637$	−15.2993	−	8.83307i	−0.606182	−	0.349979i
$638$	16.6787	−	22.9351i	0.660316	−	0.908010i
$639$	−15.9073	−	26.8701i	−0.629284	−	1.06297i
$640$	−3.46312	−	10.7706i	−0.136892	−	0.425747i
$641$	24.3423	+	14.0540i	0.961462	+	0.555100i	0.896623	−	0.442796i	$-0.146013\pi$
$641$	24.3423	+	14.0540i	0.961462	+	0.555100i	0.0648391	+	0.997896i	$0.479347\pi$
$642$	13.1209	+	1.31245i	0.517840	+	0.0517983i
$643$	23.2415	+	40.2554i	0.916554	+	1.58752i	0.804609	+	0.593804i	$0.202375\pi$
$643$	23.2415	+	40.2554i	0.916554	+	1.58752i	0.111945	+	0.993714i	$0.464292\pi$
$644$	0.953527	+	0.860074i	0.0375742	+	0.0338916i
$645$	−0.967446	+	1.69700i	−0.0380931	+	0.0668194i
$646$	−13.5122	−	30.3847i	−0.531630	−	1.19547i
$647$	19.8527			0.780490			0.390245	−	0.920711i	$-0.372390\pi$
$647$	19.8527			0.780490			0.390245	+	0.920711i	$0.372390\pi$
$648$	−17.4181	−	18.5637i	−0.684247	−	0.729250i
$649$	14.4360			0.566661
$650$	−1.58226	−	3.55800i	−0.0620612	−	0.139556i
$651$	−7.08696	+	12.4313i	−0.277760	+	0.487221i
$652$	19.8451	−	22.0014i	0.777195	−	0.861643i
$653$	−15.2215	−	26.3643i	−0.595662	−	1.03172i	−0.993453	−	0.114241i	$-0.963557\pi$
$653$	−15.2215	−	26.3643i	−0.595662	−	1.03172i	0.397791	−	0.917476i	$-0.369777\pi$
$654$	21.3801	+	2.13860i	0.836027	+	0.0836259i
$655$	2.65957	+	1.53550i	0.103918	+	0.0599970i
$656$	−12.8388	−	17.7364i	−0.501271	−	0.692489i
$657$	9.32490	+	15.7513i	0.363799	+	0.614517i
$658$	3.22425	−	4.43371i	0.125694	−	0.172844i
$659$	−7.25564	−	4.18905i	−0.282640	−	0.163182i	0.351978	−	0.936008i	$-0.385509\pi$
$659$	−7.25564	−	4.18905i	−0.282640	−	0.163182i	−0.634618	+	0.772826i	$0.718842\pi$
$660$	−16.1749	+	5.33766i	−0.629606	+	0.207768i
$661$	34.2470	−	19.7725i	1.33205	−	0.769062i	0.346440	−	0.938072i	$-0.387390\pi$
$661$	34.2470	−	19.7725i	1.33205	−	0.769062i	0.985614	+	0.169010i	$0.0540571\pi$
$662$	−3.32548	+	31.5071i	−0.129248	+	1.22456i
$663$	19.9697	−	0.109069i	0.775559	−	0.00423589i
$664$	6.68933	−	6.00720i	0.259596	−	0.233125i
$665$			4.29125i			0.166408i
$666$	12.1780	−	17.1366i	0.471888	−	0.664030i
$667$	3.42644			0.132672
$668$	7.17783	+	1.53227i	0.277719	+	0.0592852i
$669$	−8.54116	+	4.99364i	−0.330220	+	0.193065i
$670$	−0.161532	+	1.53042i	−0.00624052	+	0.0591255i
$671$	−6.12134	−	10.6025i	−0.236312	−	0.409304i
$672$	−6.49656	−	3.72250i	−0.250610	−	0.143599i
$673$	−4.60768	+	7.98074i	−0.177613	+	0.307635i	−0.941063	−	0.338233i	$-0.890171\pi$
$673$	−4.60768	+	7.98074i	−0.177613	+	0.307635i	0.763449	+	0.645868i	$0.223504\pi$
$674$	8.97692	+	6.52812i	0.345778	+	0.251454i
$675$	−2.52400	+	4.54196i	−0.0971487	+	0.174820i
$676$	3.33982	+	10.3096i	0.128454	+	0.396524i
$677$	−21.0969	+	36.5409i	−0.810821	+	1.40438i	0.101470	+	0.994839i	$0.467646\pi$
$677$	−21.0969	+	36.5409i	−0.810821	+	1.40438i	−0.912290	+	0.409544i	$0.865688\pi$
$678$	−14.4122	−	31.9377i	−0.553499	−	1.22656i
$679$	−12.6194	+	7.28579i	−0.484287	+	0.279603i
$680$	−2.44721	−	11.5881i	−0.0938462	−	0.444382i
$681$	33.9933	−	19.8744i	1.30263	−	0.761587i
$682$	68.6894	−	30.5465i	2.63025	−	1.16968i
$683$			13.1117i			0.501706i	0.968025	+	0.250853i	$0.0807111\pi$
$683$			13.1117i			0.501706i	−0.968025	+	0.250853i	$0.919289\pi$
$684$	33.0251	+	6.67363i	1.26275	+	0.255173i
$685$			0.597816i			0.0228414i
$686$	5.89148	+	13.2481i	0.224938	+	0.505814i
$687$	−0.00128392	−	0.235076i	−4.89847e−5	−	0.00896872i
$688$	4.11795	+	1.84208i	0.156995	+	0.0702287i
$689$	−30.5652	+	17.6468i	−1.16444	+	0.672290i
$690$	−1.67102	−	1.20129i	−0.0636148	−	0.0457324i
$691$	−15.4659	+	26.7877i	−0.588350	+	1.01905i	0.406099	+	0.913829i	$0.366889\pi$
$691$	−15.4659	+	26.7877i	−0.588350	+	1.01905i	−0.994449	+	0.105223i	$0.966444\pi$
$692$	−13.1470	−	40.5831i	−0.499772	−	1.54274i
$693$	−5.52924	+	9.82318i	−0.210038	+	0.373152i
$694$	7.46848	−	10.2700i	0.283500	−	0.389845i
$695$	−6.83597	+	11.8402i	−0.259303	+	0.449126i
$696$	−19.5251	+	4.23491i	−0.740098	+	0.160524i
$697$	−11.4606	−	19.8503i	−0.434100	−	0.751883i
$698$	3.54680	+	0.374354i	0.134248	+	0.0141695i
$699$	15.0884	+	8.60178i	0.570697	+	0.325349i
$700$	−0.319077	+	1.49470i	−0.0120600	+	0.0564942i
$701$	−22.2904			−0.841898			−0.420949	−	0.907084i	$-0.638303\pi$
$701$	−22.2904			−0.841898			−0.420949	+	0.907084i	$0.638303\pi$
$702$	−11.6305	+	16.5569i	−0.438964	+	0.624900i
$703$			27.8255i			1.04946i
$704$	15.9047	+	35.9768i	0.599432	+	1.35593i
$705$	−4.35140	+	7.63282i	−0.163883	+	0.287469i
$706$	18.1274	+	1.91330i	0.682234	+	0.0720079i
$707$	4.40697	−	2.54437i	0.165741	−	0.0956908i
$708$	−7.58925	−	6.77063i	−0.285221	−	0.254456i
$709$	29.9965	+	17.3185i	1.12654	+	0.650408i	0.943063	−	0.332615i	$-0.107931\pi$
$709$	29.9965	+	17.3185i	1.12654	+	0.650408i	0.183478	+	0.983024i	$0.441264\pi$
$710$	11.9049	+	8.65738i	0.446783	+	0.324906i
$711$	0.534111	+	48.8943i	0.0200307	+	1.83368i
$712$	20.2855	+	6.62063i	0.760230	+	0.248119i
$713$	7.86625	+	4.54158i	0.294593	+	0.170084i
$714$	−6.36430	−	4.57527i	−0.238178	−	0.171225i
$715$	6.76928	+	11.7247i	0.253157	+	0.438480i
$716$	15.6621	+	14.1270i	0.585319	+	0.527952i
$717$	−34.9999	+	0.191160i	−1.30710	+	0.00713900i
$718$	−9.50688	+	4.22775i	−0.354794	+	0.157778i
$719$	22.4585			0.837562			0.418781	−	0.908087i	$-0.362457\pi$
$719$	22.4585			0.837562			0.418781	+	0.908087i	$0.362457\pi$
$720$	11.0068	+	4.78010i	0.410201	+	0.178144i
$721$	−7.45445			−0.277618
$722$	−16.1954	+	7.20217i	−0.602732	+	0.268037i
$723$	−4.94871	−	8.46432i	−0.184045	−	0.314791i
$724$	7.78751	+	7.02427i	0.289420	+	0.261055i
$725$	2.03911	+	3.53184i	0.0757307	+	0.131169i
$726$	29.4188	−	13.2756i	1.09183	−	0.492703i
$727$	−15.5297	−	8.96609i	−0.575966	−	0.332534i	0.183563	−	0.983008i	$-0.441237\pi$
$727$	−15.5297	−	8.96609i	−0.575966	−	0.332534i	−0.759529	+	0.650474i	$0.774570\pi$
$728$	−1.84653	+	5.65772i	−0.0684369	+	0.209689i
$729$	26.9855	−	0.884632i	0.999463	−	0.0327641i
$730$	−6.97867	−	5.07498i	−0.258292	−	0.187833i
$731$	4.08980	+	2.36125i	0.151267	+	0.0873339i
$732$	−1.75458	+	8.44489i	−0.0648512	+	0.312132i
$733$	20.6548	−	11.9250i	0.762902	−	0.440462i	−0.0674348	−	0.997724i	$-0.521481\pi$
$733$	20.6548	−	11.9250i	0.762902	−	0.440462i	0.830337	+	0.557262i	$0.188148\pi$
$734$	17.1344	+	1.80849i	0.632442	+	0.0667524i
$735$	−5.60891	−	9.59354i	−0.206888	−	0.353863i
$736$	−2.38540	+	4.11081i	−0.0879270	+	0.151527i
$737$		−	5.35055i		−	0.197090i
$738$	23.1207	+	2.18524i	0.851083	+	0.0804396i
$739$	−21.9225			−0.806433			−0.403217	−	0.915105i	$-0.632108\pi$
$739$	−21.9225			−0.806433			−0.403217	+	0.915105i	$0.632108\pi$
$740$	−2.06897	+	9.69198i	−0.0760568	+	0.356284i
$741$	−0.146266	−	26.7802i	−0.00537323	−	0.983797i
$742$	13.7762	+	1.45404i	0.505740	+	0.0533794i
$743$	−5.92744	−	10.2666i	−0.217457	−	0.376646i	0.736573	−	0.676358i	$-0.236443\pi$
$743$	−5.92744	−	10.2666i	−0.217457	−	0.376646i	−0.954030	+	0.299712i	$0.903109\pi$
$744$	−50.4379	−	16.1573i	−1.84914	−	0.592356i
$745$	6.57797	−	11.3934i	0.240998	−	0.417421i
$746$	−10.1455	+	13.9512i	−0.371452	+	0.510790i
$747$	0.104164	+	9.53556i	0.00381117	+	0.348888i
$748$	12.6904	+	39.1739i	0.464008	+	1.43234i
$749$	−2.05693	+	3.56270i	−0.0751585	+	0.130178i
$750$	0.243800	−	2.43733i	0.00890233	−	0.0889986i
$751$	6.91375	−	3.99165i	0.252286	−	0.145658i	−0.368524	−	0.929618i	$-0.620137\pi$
$751$	6.91375	−	3.99165i	0.252286	−	0.145658i	0.620811	+	0.783961i	$0.286804\pi$
$752$	18.5218	+	8.28536i	0.675421	+	0.302136i
$753$	36.2724	+	20.6786i	1.32184	+	0.753569i
$754$	6.45279	+	14.5103i	0.234997	+	0.528434i
$755$			5.76088i			0.209660i
$756$	7.51401	−	2.57095i	0.273282	−	0.0935045i
$757$			7.84938i			0.285291i	0.989774	+	0.142645i	$0.0455608\pi$
$757$			7.84938i			0.285291i	−0.989774	+	0.142645i	$0.954439\pi$
$758$	−44.2620	+	19.6835i	−1.60767	+	0.714937i
$759$	6.21614	+	3.54376i	0.225632	+	0.128631i
$760$	−15.5401	+	3.28182i	−0.563700	+	0.119044i
$761$	−10.3058	+	5.95008i	−0.373586	+	0.215690i	−0.675024	−	0.737796i	$-0.735867\pi$
$761$	−10.3058	+	5.95008i	−0.373586	+	0.215690i	0.301438	+	0.953486i	$0.402533\pi$
$762$	−28.6541	−	2.86621i	−1.03803	−	0.103832i
$763$	−3.35170	+	5.80532i	−0.121340	+	0.210167i
$764$	−7.96569	−	24.5892i	−0.288189	−	0.889604i
$765$	10.9471	+	6.16184i	0.395792	+	0.222782i
$766$	35.9929	+	26.1745i	1.30048	+	0.945721i
$767$	−4.04200	+	7.00094i	−0.145948	+	0.252789i
$768$	8.51212	−	26.3732i	0.307155	−	0.951660i
$769$	6.45678	+	11.1835i	0.232837	+	0.403286i	0.958642	−	0.284615i	$-0.0918657\pi$
$769$	6.45678	+	11.1835i	0.232837	+	0.403286i	−0.725805	+	0.687901i	$0.758532\pi$
$770$	0.557765	−	5.28451i	0.0201005	−	0.190441i
$771$	−0.0800424	−	14.6552i	−0.00288266	−	0.527793i
$772$	−3.40307	−	0.726461i	−0.122479	−	0.0261459i
$773$	15.0694			0.542007			0.271004	−	0.962578i	$-0.412644\pi$
$773$	15.0694			0.542007			0.271004	+	0.962578i	$0.412644\pi$
$774$	−4.35051	+	1.99189i	−0.156376	+	0.0715971i
$775$			10.8110i			0.388341i
$776$	−36.0353	−	40.1272i	−1.29359	−	1.44048i
$777$	3.31034	+	5.66203i	0.118758	+	0.203124i
$778$	−2.90791	+	27.5508i	−0.104254	+	0.987745i
$779$	−26.6201	+	15.3691i	−0.953765	+	0.550656i
$780$	1.94030	−	9.33877i	0.0694739	−	0.334382i
$781$	−44.3218	−	25.5892i	−1.58596	−	0.915655i
$782$	−2.92623	+	4.02391i	−0.104642	+	0.143895i
$783$	10.2934	−	18.5231i	0.367857	−	0.661963i
$784$	−20.7891	+	15.0486i	−0.742467	+	0.537449i
$785$	−10.5732	−	6.10445i	−0.377374	−	0.217877i
$786$	3.09412	+	6.85659i	0.110363	+	0.244566i
$787$	−2.49676	−	4.32452i	−0.0889999	−	0.154152i	0.818089	−	0.575092i	$-0.195034\pi$
$787$	−2.49676	−	4.32452i	−0.0889999	−	0.154152i	−0.907089	+	0.420940i	$0.861700\pi$
$788$	6.46905	−	7.17196i	0.230450	−	0.255491i
$789$	−25.7587	−	44.0579i	−0.917034	−	1.56850i
$790$	−9.36621	−	21.0617i	−0.333235	−	0.749341i
$791$	10.9314			0.388675
$792$	−39.8018	−	12.5108i	−1.41429	−	0.444553i
$793$	6.85578			0.243456
$794$	−10.0167	−	22.5244i	−0.355479	−	0.799362i
$795$	−22.2011	+	0.121256i	−0.787391	+	0.00430051i
$796$	28.6650	+	25.8556i	1.01600	+	0.916426i
$797$	−3.71078	−	6.42726i	−0.131442	−	0.227665i	0.792790	−	0.609494i	$-0.208628\pi$
$797$	−3.71078	−	6.42726i	−0.131442	−	0.227665i	−0.924233	+	0.381829i	$0.875294\pi$
$798$	−6.13563	+	8.53481i	−0.217199	+	0.302129i
$799$	18.3952	+	10.6205i	0.650776	+	0.375725i
$800$	−5.65684	−	0.0123893i	−0.200000	−	0.000438028i
$801$	−19.4759	+	11.5299i	−0.688148	+	0.407389i
$802$	27.2647	−	37.4922i	0.962752	−	1.32389i
$803$	25.9816	+	15.0005i	0.916869	+	0.529355i
$804$	−2.50947	+	2.81288i	−0.0885022	+	0.0992027i
$805$	0.556036	−	0.321028i	0.0195977	−	0.0113147i
$806$	−4.41872	+	41.8649i	−0.155643	+	1.47463i
$807$	−18.4893	+	32.4322i	−0.650855	+	1.14167i
$808$	12.5844	+	14.0133i	0.442716	+	0.492987i
$809$		−	50.3212i		−	1.76920i	−0.466352	−	0.884599i	$-0.654432\pi$
$809$		−	50.3212i		−	1.76920i	0.466352	−	0.884599i	$-0.345568\pi$
$810$	−11.5140	+	5.42464i	−0.404562	+	0.190602i
$811$	−40.4222			−1.41942			−0.709708	−	0.704496i	$-0.751173\pi$
$811$	−40.4222			−1.41942			−0.709708	+	0.704496i	$0.751173\pi$
$812$	1.30126	−	6.09571i	0.0456654	−	0.213917i
$813$	18.5300	+	10.5638i	0.649875	+	0.370488i
$814$	3.61668	−	34.2661i	0.126765	−	1.20102i
$815$	−7.40731	−	12.8298i	−0.259467	−	0.449410i
$816$	11.7014	−	26.5464i	0.409631	−	0.929310i
$817$	3.16654	−	5.48460i	0.110783	−	0.191882i
$818$	24.5169	+	17.8290i	0.857214	+	0.623376i
$819$	−3.21575	−	5.43193i	−0.112367	−	0.189807i
$820$	−10.4149	+	3.37392i	−0.363704	+	0.117822i
$821$	−26.0952	+	45.1982i	−0.910729	+	1.57743i	−0.0976914	+	0.995217i	$0.531146\pi$
$821$	−26.0952	+	45.1982i	−0.910729	+	1.57743i	−0.813037	+	0.582212i	$0.802188\pi$
$822$	−0.854758	+	1.18899i	−0.0298131	+	0.0414707i
$823$	−5.60107	+	3.23378i	−0.195241	+	0.112723i	−0.594434	−	0.804145i	$-0.702624\pi$
$823$	−5.60107	+	3.23378i	−0.195241	+	0.112723i	0.399193	+	0.916867i	$0.369290\pi$
$824$	−5.70094	−	26.9952i	−0.198602	−	0.940422i
$825$	0.0465136	+	8.51628i	0.00161940	+	0.296499i
$826$	2.89921	−	1.28929i	0.100876	−	0.0448601i
$827$			2.24538i			0.0780796i	0.999238	+	0.0390398i	$0.0124299\pi$
$827$			2.24538i			0.0780796i	−0.999238	+	0.0390398i	$0.987570\pi$
$828$	−1.60587	−	4.77846i	−0.0558079	−	0.166063i
$829$		−	23.8040i		−	0.826746i	−0.910562	−	0.413373i	$-0.864351\pi$
$829$		−	23.8040i		−	0.826746i	0.910562	−	0.413373i	$-0.135649\pi$
$830$	−1.82663	−	4.10753i	−0.0634034	−	0.142574i
$831$	−43.4652	+	25.4122i	−1.50779	+	0.881538i
$832$	−21.9008	−	2.36007i	−0.759272	−	0.0818208i
$833$	−23.2668	+	13.4331i	−0.806148	+	0.465430i
$834$	−30.5252	+	13.7748i	−1.05700	+	0.476984i
$835$	1.83489	−	3.17812i	0.0634989	−	0.109983i
$836$	52.5339	−	17.0184i	1.81692	−	0.588595i
$837$	48.1826	−	28.8810i	1.66543	−	0.998274i
$838$	−19.9078	+	27.3755i	−0.687704	+	0.945671i
$839$	−12.6443	+	21.9007i	−0.436531	+	0.756094i	−0.997419	−	0.0717973i	$-0.977127\pi$
$839$	−12.6443	+	21.9007i	−0.436531	+	0.756094i	0.560888	+	0.827892i	$0.310460\pi$
$840$	−2.77173	+	2.51657i	−0.0956336	+	0.0868298i
$841$	6.18406	+	10.7111i	0.213243	+	0.369348i
$842$	−28.0493	−	2.96053i	−0.966644	−	0.102026i
$843$	−38.1131	+	22.2830i	−1.31268	+	0.767468i
$844$	−12.8389	−	2.74076i	−0.441934	−	0.0943408i
$845$	5.41855			0.186404
$846$	−19.5679	+	8.95918i	−0.672757	+	0.308023i
$847$			10.0692i			0.345984i
$848$	5.27003	+	51.0004i	0.180973	+	1.75136i
$849$	39.7560	−	0.217137i	1.36442	−	0.00745211i
$850$	−5.88912	−	0.621580i	−0.201995	−	0.0213200i
$851$	3.60547	−	2.08162i	0.123594	−	0.0713571i
$852$	11.2992	+	34.2402i	0.387103	+	1.17305i
$853$	−33.3452	−	19.2519i	−1.14172	−	0.659172i	−0.194863	−	0.980830i	$-0.562426\pi$
$853$	−33.3452	−	19.2519i	−1.14172	−	0.659172i	−0.946856	+	0.321659i	$0.895760\pi$
$854$	−2.17628	−	1.58262i	−0.0744707	−	0.0541560i
$855$	8.26330	−	14.6805i	0.282599	−	0.502062i
$856$	−14.4749	−	4.72421i	−0.494741	−	0.161470i
$857$	−15.1826	−	8.76570i	−0.518629	−	0.299431i	0.217745	−	0.976006i	$-0.430130\pi$
$857$	−15.1826	−	8.76570i	−0.518629	−	0.299431i	−0.736373	+	0.676575i	$0.763463\pi$
$858$	−3.30070	+	32.9979i	−0.112684	+	1.12653i
$859$	12.3718	+	21.4285i	0.422119	+	0.731131i	0.996147	−	0.0877046i	$-0.0279532\pi$
$859$	12.3718	+	21.4285i	0.422119	+	0.731131i	−0.574028	+	0.818836i	$0.694620\pi$
$860$	1.51075	−	1.67491i	0.0515162	−	0.0571139i
$861$	−3.58832	+	6.29430i	−0.122290	+	0.214509i
$862$	−42.3887	+	18.8504i	−1.44376	+	0.642048i
$863$	0.924028			0.0314543			0.0157271	−	0.999876i	$-0.494994\pi$
$863$	0.924028			0.0314543			0.0157271	+	0.999876i	$0.494994\pi$
$864$	15.0568	+	25.2447i	0.512242	+	0.858841i
$865$	−21.3297			−0.725233
$866$	−20.0311	+	8.90793i	−0.680686	+	0.302704i
$867$	0.458110	−	0.803573i	0.0155582	−	0.0272908i
$868$	11.0669	−	12.2694i	0.375636	−	0.416452i
$869$	40.0709	+	69.4048i	1.35931	+	2.35440i
$870$	−0.994271	+	9.93996i	−0.0337090	+	0.336996i
$871$	2.59483	+	1.49813i	0.0879226	+	0.0507621i
$872$	−23.5864	−	7.69795i	−0.798735	−	0.260686i
$873$	57.2008	−	0.624849i	1.93596	−	0.0211479i
$874$	5.39624	+	3.92421i	0.182531	+	0.132738i
$875$	0.661806	+	0.382094i	0.0223731	+	0.0129171i
$876$	−6.62359	−	20.0717i	−0.223790	−	0.678159i
$877$	−43.4791	+	25.1027i	−1.46818	+	0.847656i	−0.999365	−	0.0356377i	$-0.988654\pi$
$877$	−43.4791	+	25.1027i	−1.46818	+	0.847656i	−0.468819	+	0.883294i	$0.655320\pi$
$878$	20.1162	+	2.12321i	0.678890	+	0.0716548i
$879$	−39.2157	+	0.214186i	−1.32271	+	0.00722430i
$880$	19.5636	−	2.02157i	0.659490	−	0.0681471i
$881$		−	45.2518i		−	1.52457i	−0.647240	−	0.762286i	$-0.724077\pi$
$881$		−	45.2518i		−	1.52457i	0.647240	−	0.762286i	$-0.275923\pi$
$882$	2.56135	−	27.1001i	0.0862451	−	0.912507i
$883$	48.8839			1.64507			0.822537	−	0.568712i	$-0.192558\pi$
$883$	48.8839			1.64507			0.822537	+	0.568712i	$0.192558\pi$
$884$	−22.5512	−	4.81407i	−0.758481	−	0.161915i
$885$	−4.38998	+	2.56663i	−0.147568	+	0.0862763i
$886$	−1.89660	−	0.200181i	−0.0637177	−	0.00672522i
$887$	−11.8263	−	20.4838i	−0.397089	−	0.687779i	0.596276	−	0.802779i	$-0.296646\pi$
$887$	−11.8263	−	20.4838i	−0.397089	−	0.687779i	−0.993365	+	0.115001i	$0.963313\pi$
$888$	−17.9725	+	16.3180i	−0.603119	+	0.547597i
$889$	4.49203	−	7.78043i	0.150658	−	0.260947i
$890$	6.27502	−	8.62887i	0.210339	−	0.289240i
$891$	37.8314	−	22.9582i	1.26740	−	0.769128i
$892$	10.8683	−	3.52082i	0.363899	−	0.117886i
$893$	14.2425	−	24.6688i	0.476608	−	0.825510i
$894$	29.3731	−	13.2549i	0.982383	−	0.443312i
$895$	9.13311	−	5.27301i	0.305286	−	0.176257i
$896$	6.40731	+	5.80484i	0.214053	+	0.193926i
$897$	−3.45909	+	2.02238i	−0.115496	+	0.0675252i
$898$	−10.5514	−	23.7268i	−0.352104	−	0.791772i
$899$		−	44.0895i		−	1.47047i
$900$	3.96978	−	4.49898i	0.132326	−	0.149966i
$901$			53.6736i			1.78813i
$902$	34.7793	−	15.4665i	1.15802	−	0.514978i
$903$	−0.00815294	−	1.49274i	−0.000271313	−	0.0496753i
$904$	8.35999	+	39.5864i	0.278049	+	1.31662i
$905$	4.54118	−	2.62185i	0.150954	−	0.0871533i
$906$	−8.23691	+	11.4577i	−0.273653	+	0.380658i
$907$	−5.57832	+	9.66193i	−0.185225	+	0.320819i	−0.943652	−	0.330938i	$-0.892635\pi$
$907$	−5.57832	+	9.66193i	−0.185225	+	0.320819i	0.758427	+	0.651758i	$0.225968\pi$
$908$	−43.2553	+	14.0126i	−1.43548	+	0.465025i
$909$	−19.9758	+	0.218212i	−0.662557	+	0.00723762i
$910$	2.40664	+	1.75013i	0.0797792	+	0.0580164i
$911$	2.79600	−	4.84282i	0.0926357	−	0.160450i	−0.815984	−	0.578075i	$-0.803804\pi$
$911$	2.79600	−	4.84282i	0.0926357	−	0.160450i	0.908619	+	0.417625i	$0.137137\pi$
$912$	−35.5999	−	15.6921i	−1.17883	−	0.519618i
$913$	7.81478	+	13.5356i	0.258632	+	0.447963i
$914$	−3.18030	+	30.1315i	−0.105195	+	0.996663i
$915$	3.74656	+	2.13588i	0.123857	+	0.0706100i
$916$	−0.0566695	+	0.265465i	−0.00187241	+	0.00877123i
$917$	−2.34682			−0.0774989
$918$	12.9623	+	27.9073i	0.427818	+	0.921079i
$919$			10.6520i			0.351376i	0.984446	+	0.175688i	$0.0562150\pi$
$919$			10.6520i			0.351376i	−0.984446	+	0.175688i	$0.943785\pi$
$920$	1.58779	+	1.76809i	0.0523480	+	0.0582922i
$921$	−17.9276	+	31.4469i	−0.590734	+	1.03621i
$922$	3.60194	−	34.1263i	0.118623	−	1.12389i
$923$	24.8198	−	14.3297i	0.816953	−	0.471668i
$924$	8.66513	−	9.71281i	0.285062	−	0.319528i
$925$	4.29131	+	2.47759i	0.141097	+	0.0814626i
$926$	−33.3212	+	45.8204i	−1.09500	+	1.50575i
$927$	25.5019	+	14.3544i	0.837592	+	0.471461i
$928$	23.0698	+	0.0505263i	0.757305	+	0.00165861i
$929$	−12.1810	−	7.03270i	−0.399646	−	0.230735i	0.286685	−	0.958025i	$-0.407447\pi$
$929$	−12.1810	−	7.03270i	−0.399646	−	0.230735i	−0.686331	+	0.727289i	$0.740780\pi$
$930$	−15.4575	+	21.5018i	−0.506872	+	0.705071i
$931$	18.0144	+	31.2019i	0.590398	+	1.02260i
$932$	−14.8920	−	13.4324i	−0.487803	−	0.439994i
$933$	2.01259	−	0.0109922i	0.0658891	−	0.000359868i
$934$	0.441465	+	0.992718i	0.0144452	+	0.0324827i
$935$	20.5891			0.673335
$936$	17.2116	−	15.7995i	0.562579	−	0.516423i
$937$	−32.0671			−1.04759			−0.523794	−	0.851845i	$-0.675484\pi$
$937$	−32.0671			−1.04759			−0.523794	+	0.851845i	$0.675484\pi$
$938$	−0.477863	−	1.07456i	−0.0156028	−	0.0350858i
$939$	−24.7746	−	42.3747i	−0.808488	−	1.38285i
$940$	6.79510	−	7.53344i	0.221632	−	0.245714i
$941$	−2.02176	−	3.50180i	−0.0659076	−	0.114155i	0.831189	−	0.555991i	$-0.187661\pi$
$941$	−2.02176	−	3.50180i	−0.0659076	−	0.114155i	−0.897096	+	0.441835i	$0.854328\pi$
$942$	−12.3008	−	27.2587i	−0.400781	−	0.888135i
$943$	3.98289	+	2.29952i	0.129701	+	0.0748828i
$944$	6.88619	+	9.51304i	0.224126	+	0.309623i
$945$	−0.0650592	−	3.97030i	−0.00211638	−	0.129154i
$946$	−4.61234	+	6.34250i	−0.149960	+	0.206213i
$947$	−1.00129	−	0.578094i	−0.0325375	−	0.0187855i	0.483643	−	0.875265i	$-0.339313\pi$
$947$	−1.00129	−	0.578094i	−0.0325375	−	0.0187855i	−0.516181	+	0.856480i	$0.672647\pi$
$948$	11.4857	−	55.2811i	0.373037	−	1.79545i
$949$	−14.5494	+	8.40011i	−0.472294	+	0.272679i
$950$	−0.833566	+	7.89757i	−0.0270444	+	0.256231i
$951$	3.04444	+	5.20723i	0.0987226	+	0.168856i
$952$	6.04731	+	6.73399i	0.195994	+	0.218250i
$953$		−	52.3550i		−	1.69594i	−0.530042	−	0.847972i	$-0.677824\pi$
$953$		−	52.3550i		−	1.69594i	0.530042	−	0.847972i	$-0.322176\pi$
$954$	−44.3288	−	31.5019i	−1.43520	−	1.01991i
$955$	−12.9236			−0.418198
$956$	39.5245	+	8.43739i	1.27831	+	0.272885i
$957$	−0.189693	−	34.7313i	−0.00613189	−	1.12270i
$958$	−3.04762	+	28.8745i	−0.0984641	+	0.932892i
$959$	−0.228422	−	0.395638i	−0.00737612	−	0.0127758i
$960$	−11.2331	−	8.11279i	−0.362547	−	0.261839i
$961$	42.9384	−	74.3715i	1.38511	−	2.39908i
$962$	15.6052	+	11.3483i	0.503132	+	0.365884i
$963$	13.8972	−	8.22725i	0.447831	−	0.265119i
$964$	3.48914	+	10.7706i	0.112378	+	0.346897i
$965$	−0.869936	+	1.50677i	−0.0280042	+	0.0485047i
$966$	1.56490	+	0.156533i	0.0503498	+	0.00503638i
$967$	−13.4585	+	7.77028i	−0.432797	+	0.249875i	−0.700537	−	0.713616i	$-0.747056\pi$
$967$	−13.4585	+	7.77028i	−0.432797	+	0.249875i	0.267741	+	0.963491i	$0.413723\pi$
$968$	−36.4643	+	7.70065i	−1.17201	+	0.247508i
$969$	−35.3816	−	20.1707i	−1.13662	−	0.647977i
$970$	−24.6398	+	10.9574i	−0.791136	+	0.351821i
$971$		−	29.7172i		−	0.953670i	−0.878993	−	0.476835i	$-0.841784\pi$
$971$		−	29.7172i		−	0.953670i	0.878993	−	0.476835i	$-0.158216\pi$
$972$	−30.6563	−	5.67381i	−0.983301	−	0.181987i
$973$		−	10.4479i		−	0.334945i
$974$	−2.68228	−	6.03160i	−0.0859457	−	0.193265i
$975$	−4.14313	−	2.36196i	−0.132686	−	0.0756432i
$976$	4.06685	−	9.09140i	0.130177	−	0.291009i
$977$	16.3047	−	9.41355i	0.521635	−	0.301166i	−0.215968	−	0.976400i	$-0.569291\pi$
$977$	16.3047	−	9.41355i	0.521635	−	0.301166i	0.737603	+	0.675234i	$0.235958\pi$
$978$	3.61181	−	36.1081i	0.115493	−	1.15461i
$979$	−18.5475	+	32.1252i	−0.592781	+	1.02673i
$980$	3.95462	+	12.2075i	0.126326	+	0.389953i
$981$	22.6451	−	13.4061i	0.723001	−	0.428022i
$982$	−19.4043	+	26.6831i	−0.619216	+	0.851492i
$983$	24.5059	−	42.4454i	0.781615	−	1.35380i	−0.149385	−	0.988779i	$-0.547729\pi$
$983$	24.5059	−	42.4454i	0.781615	−	1.35380i	0.931000	−	0.365018i	$-0.118937\pi$
$984$	−25.5381	−	8.18088i	−0.814124	−	0.260797i
$985$	−2.41461	−	4.18223i	−0.0769359	−	0.133257i
$986$	24.0171	+	2.53494i	0.764861	+	0.0807289i
$987$	−0.0366705	−	6.71409i	−0.00116723	−	0.213712i
$988$	−6.45588	+	30.2422i	−0.205389	+	0.962133i
$989$	−0.947552			−0.0301304
$990$	−12.0841	+	17.0044i	−0.384057	+	0.540436i
$991$		−	20.7974i		−	0.660652i	−0.943867	−	0.330326i	$-0.892841\pi$
$991$		−	20.7974i		−	0.660652i	0.943867	−	0.330326i	$-0.107159\pi$
$992$	52.8956	+	30.6939i	1.67944	+	0.974533i
$993$	19.5845	+	33.4974i	0.621494	+	1.06301i
$994$	−11.1867	−	1.18072i	−0.354819	−	0.0374502i
$995$	16.7156	−	9.65074i	0.529919	−	0.305949i
$996$	2.23998	−	10.7811i	0.0709765	−	0.341613i
$997$	2.78066	+	1.60542i	0.0880644	+	0.0508440i	0.543386	−	0.839483i	$-0.317142\pi$
$997$	2.78066	+	1.60542i	0.0880644	+	0.0508440i	−0.455321	+	0.890327i	$0.650476\pi$
$998$	28.0690	+	20.4121i	0.888508	+	0.646134i
$999$	−0.421860	−	25.7444i	−0.0133470	−	0.814516i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bm.a.11.3	✓	48
3.2	odd	2		1080.2.bm.b.251.22		48
4.3	odd	2		1440.2.cc.a.911.16		48
8.3	odd	2		360.2.bm.b.11.11	yes	48
8.5	even	2		1440.2.cc.b.911.16		48
9.4	even	3		1080.2.bm.a.611.14		48
9.5	odd	6		360.2.bm.b.131.11	yes	48
12.11	even	2		4320.2.cc.b.1871.11		48
24.5	odd	2		4320.2.cc.a.1871.14		48
24.11	even	2		1080.2.bm.a.251.14		48
36.23	even	6		1440.2.cc.b.1391.16		48
36.31	odd	6		4320.2.cc.a.3311.14		48
72.5	odd	6		1440.2.cc.a.1391.16		48
72.13	even	6		4320.2.cc.b.3311.11		48
72.59	even	6	inner	360.2.bm.a.131.3	yes	48
72.67	odd	6		1080.2.bm.b.611.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bm.a.11.3	✓	48	1.1	even	1	trivial
360.2.bm.a.131.3	yes	48	72.59	even	6	inner
360.2.bm.b.11.11	yes	48	8.3	odd	2
360.2.bm.b.131.11	yes	48	9.5	odd	6
1080.2.bm.a.251.14		48	24.11	even	2
1080.2.bm.a.611.14		48	9.4	even	3
1080.2.bm.b.251.22		48	3.2	odd	2
1080.2.bm.b.611.22		48	72.67	odd	6
1440.2.cc.a.911.16		48	4.3	odd	2
1440.2.cc.a.1391.16		48	72.5	odd	6
1440.2.cc.b.911.16		48	8.5	even	2
1440.2.cc.b.1391.16		48	36.23	even	6
4320.2.cc.a.1871.14		48	24.5	odd	2
4320.2.cc.a.3311.14		48	36.31	odd	6
4320.2.cc.b.1871.11		48	12.11	even	2
4320.2.cc.b.3311.11		48	72.13	even	6

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.29220 + 0.574647i) q^{2} +(-0.857820 + 1.50471i) q^{3} +(1.33956 - 1.48512i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.243800 - 2.43733i) q^{6} +(0.661806 + 0.382094i) q^{7} +(-0.877566 + 2.68884i) q^{8} +(-1.52829 - 2.58154i) q^{9} +O(q^{10})\)	\(q+(-1.29220 + 0.574647i) q^{2} +(-0.857820 + 1.50471i) q^{3} +(1.33956 - 1.48512i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(0.243800 - 2.43733i) q^{6} +(0.661806 + 0.382094i) q^{7} +(-0.877566 + 2.68884i) q^{8} +(-1.52829 - 2.58154i) q^{9} +(1.14376 + 0.831755i) q^{10} +(-4.25821 - 2.45848i) q^{11} +(1.08556 + 3.28961i) q^{12} +(2.38455 - 1.37672i) q^{13} +(-1.07475 - 0.113437i) q^{14} +(1.73202 - 0.00945984i) q^{15} +(-0.411143 - 3.97881i) q^{16} -4.18737i q^{17} +(3.45833 + 2.45764i) q^{18} -5.61545 q^{19} +(-1.95593 - 0.417537i) q^{20} +(-1.14265 + 0.668056i) q^{21} +(6.91521 + 0.729880i) q^{22} +(0.420090 + 0.727618i) q^{23} +(-3.29313 - 3.62702i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.29019 + 3.14928i) q^{26} +(5.19545 - 0.0851352i) q^{27} +(1.45398 - 0.471020i) q^{28} +(2.03911 - 3.53184i) q^{29} +(-2.23269 + 1.00753i) q^{30} +(9.36257 - 5.40548i) q^{31} +(2.81769 + 4.90516i) q^{32} +(7.35206 - 4.29842i) q^{33} +(2.40626 + 5.41092i) q^{34} -0.764187i q^{35} +(-5.88112 - 1.18844i) q^{36} -4.95517i q^{37} +(7.25628 - 3.22690i) q^{38} +(0.0260471 + 4.76903i) q^{39} +(2.76739 - 0.584427i) q^{40} +(4.74052 - 2.73694i) q^{41} +(1.09264 - 1.51988i) q^{42} +(-0.563898 + 0.976700i) q^{43} +(-9.35526 + 3.03065i) q^{44} +(-1.47153 + 2.61431i) q^{45} +(-0.960964 - 0.698825i) q^{46} +(-2.53631 + 4.39302i) q^{47} +(6.33964 + 2.79446i) q^{48} +(-3.20801 - 5.55643i) q^{49} +(0.148442 - 1.40640i) q^{50} +(6.30076 + 3.59201i) q^{51} +(1.14966 - 5.38554i) q^{52} -12.8180 q^{53} +(-6.66465 + 3.09556i) q^{54} +4.91695i q^{55} +(-1.60817 + 1.44418i) q^{56} +(4.81704 - 8.44960i) q^{57} +(-0.605378 + 5.73562i) q^{58} +(-2.54261 + 1.46798i) q^{59} +(2.30611 - 2.58493i) q^{60} +(2.15631 + 1.24495i) q^{61} +(-8.99207 + 12.3651i) q^{62} +(-0.0250419 - 2.29243i) q^{63} +(-6.45976 - 4.71928i) q^{64} +(-2.38455 - 1.37672i) q^{65} +(-7.03026 + 9.77926i) q^{66} +(0.544092 + 0.942396i) q^{67} +(-6.21873 - 5.60924i) q^{68} +(-1.45521 + 0.00794798i) q^{69} +(0.439138 + 0.987483i) q^{70} +10.4086 q^{71} +(8.28252 - 1.84386i) q^{72} -6.10153 q^{73} +(2.84747 + 6.40308i) q^{74} +(-0.874205 - 1.49525i) q^{75} +(-7.52224 + 8.33959i) q^{76} +(-1.87874 - 3.25407i) q^{77} +(-2.77417 - 6.14758i) q^{78} +(-14.1154 - 8.14954i) q^{79} +(-3.24018 + 2.34547i) q^{80} +(-4.32866 + 7.89067i) q^{81} +(-4.55293 + 6.26080i) q^{82} +(-2.75284 - 1.58936i) q^{83} +(-0.538509 + 2.59187i) q^{84} +(-3.62637 + 2.09368i) q^{85} +(0.167412 - 1.58613i) q^{86} +(3.56520 + 6.09795i) q^{87} +(10.3473 - 9.29217i) q^{88} -7.54431i q^{89} +(0.399211 - 4.22382i) q^{90} +2.10415 q^{91} +(1.64333 + 0.350807i) q^{92} +(0.102270 + 18.7249i) q^{93} +(0.752989 - 7.13415i) q^{94} +(2.80772 + 4.86312i) q^{95} +(-9.79791 + 0.0320542i) q^{96} +(-9.53404 + 16.5134i) q^{97} +(7.33838 + 5.33655i) q^{98} +(0.161125 + 14.7500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8}+O(q^{10}) \) 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8	\( 48 q - 24 q^{5} + 7 q^{6} - 6 q^{8} - 15 q^{12} + 15 q^{14} + 12 q^{16} - 11 q^{18} - 4 q^{21} + 21 q^{22} - 24 q^{24} - 24 q^{25} + 12 q^{27} - 14 q^{30} - 8 q^{33} + 33 q^{34} - 23 q^{36} - 33 q^{38} + 16 q^{39} - 6 q^{40} + 12 q^{41} - 53 q^{42} - 24 q^{44} - 6 q^{46} + 12 q^{47} + 45 q^{48} + 24 q^{49} - 20 q^{51} - 36 q^{52} - 36 q^{54} + 21 q^{56} + 4 q^{57} - 51 q^{58} - 36 q^{59} + 15 q^{60} + 12 q^{61} + 42 q^{62} + 56 q^{63} - 12 q^{64} + 24 q^{66} + 57 q^{68} - 40 q^{69} - 15 q^{70} + 46 q^{72} + 30 q^{74} + 57 q^{76} + 78 q^{78} - 8 q^{81} - 18 q^{82} - 60 q^{83} - 31 q^{84} + 27 q^{86} + 36 q^{87} + 57 q^{88} + 4 q^{90} - 51 q^{92} + 57 q^{94} - 119 q^{96} + 42 q^{98} - 16 q^{99}+O(q^{100}) \) 48 * q - 24 * q^5 + 7 * q^6 - 6 * q^8 - 15 * q^12 + 15 * q^14 + 12 * q^16 - 11 * q^18 - 4 * q^21 + 21 * q^22 - 24 * q^24 - 24 * q^25 + 12 * q^27 - 14 * q^30 - 8 * q^33 + 33 * q^34 - 23 * q^36 - 33 * q^38 + 16 * q^39 - 6 * q^40 + 12 * q^41 - 53 * q^42 - 24 * q^44 - 6 * q^46 + 12 * q^47 + 45 * q^48 + 24 * q^49 - 20 * q^51 - 36 * q^52 - 36 * q^54 + 21 * q^56 + 4 * q^57 - 51 * q^58 - 36 * q^59 + 15 * q^60 + 12 * q^61 + 42 * q^62 + 56 * q^63 - 12 * q^64 + 24 * q^66 + 57 * q^68 - 40 * q^69 - 15 * q^70 + 46 * q^72 + 30 * q^74 + 57 * q^76 + 78 * q^78 - 8 * q^81 - 18 * q^82 - 60 * q^83 - 31 * q^84 + 27 * q^86 + 36 * q^87 + 57 * q^88 + 4 * q^90 - 51 * q^92 + 57 * q^94 - 119 * q^96 + 42 * q^98 - 16 * q^99

Introduction

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