LMFDB - Embedded newform 361.2.e.i.245.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [361,2,Mod(28,361)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("361.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(361, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,-18,0,0,0,3,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)

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

Self dual:	no
Analytic conductor:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.6053445140625.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} + 17x^{6} + 4x^{3} + 1 $ x^12 - 4x^9 + 17x^6 + 4*x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			245.1
Root			$-1.23949 - 1.04005i$ of defining polynomial
Character	$\chi$	$=$	361.245
Dual form			361.2.e.i.28.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.280969 + 1.59345i) q^{2} +(-0.292603 - 0.245523i) q^{3} +(-0.580762 - 0.211380i) q^{4} +(-3.04091 + 1.10680i) q^{5} +(0.473442 - 0.397265i) q^{6} +(-1.50000 - 2.59808i) q^{7} +(-1.11803 + 1.93649i) q^{8} +(-0.495610 - 2.81074i) q^{9} +(-0.909234 - 5.15652i) q^{10} +(0.809017 - 1.40126i) q^{11} +(0.118034 + 0.204441i) q^{12} +(0.766044 - 0.642788i) q^{13} +(4.56136 - 1.66020i) q^{14} +(1.16152 + 0.422760i) q^{15} +(-3.71846 - 3.12016i) q^{16} +(0.132655 - 0.752326i) q^{17} +4.61803 q^{18} +2.00000 q^{20} +(-0.198983 + 1.12849i) q^{21} +(2.00553 + 1.68284i) q^{22} +(-5.05739 - 1.84074i) q^{23} +(0.802593 - 0.292120i) q^{24} +(4.19190 - 3.51742i) q^{25} +(0.809017 + 1.40126i) q^{26} +(-1.11803 + 1.93649i) q^{27} +(0.321961 + 1.82593i) q^{28} +(0.628265 + 3.56307i) q^{29} +(-1.00000 + 1.73205i) q^{30} +(-4.42705 - 7.66788i) q^{31} +(2.59074 - 2.17389i) q^{32} +(-0.580762 + 0.211380i) q^{33} +(1.16152 + 0.422760i) q^{34} +(7.43692 + 6.24031i) q^{35} +(-0.306304 + 1.73713i) q^{36} -8.85410 q^{37} -0.381966 q^{39} +(1.25653 - 7.12614i) q^{40} +(2.29813 + 1.92836i) q^{41} +(-1.74229 - 0.634140i) q^{42} +(0.137099 - 0.0499001i) q^{43} +(-0.766044 + 0.642788i) q^{44} +(4.61803 + 7.99867i) q^{45} +(4.35410 - 7.54153i) q^{46} +(0.520945 + 2.95442i) q^{47} +(0.321961 + 1.82593i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(4.42705 + 7.66788i) q^{50} +(-0.223529 + 0.187563i) q^{51} +(-0.580762 + 0.211380i) q^{52} +(-5.94472 - 2.16370i) q^{53} +(-2.77157 - 2.32563i) q^{54} +(-0.909234 + 5.15652i) q^{55} +6.70820 q^{56} -5.85410 q^{58} +(-0.0566506 + 0.321282i) q^{59} +(-0.585206 - 0.491046i) q^{60} +(9.61876 + 3.50094i) q^{61} +(13.4623 - 4.89986i) q^{62} +(-6.55911 + 5.50374i) q^{63} +(-2.11803 - 3.66854i) q^{64} +(-1.61803 + 2.80252i) q^{65} +(-0.173648 - 0.984808i) q^{66} +(1.21554 + 6.89365i) q^{67} +(-0.236068 + 0.408882i) q^{68} +(1.02786 + 1.78031i) q^{69} +(-12.0332 + 10.0970i) q^{70} +(-7.02151 + 2.55562i) q^{71} +(5.99709 + 2.18276i) q^{72} +(-2.07460 - 1.74080i) q^{73} +(2.48773 - 14.1086i) q^{74} -2.09017 q^{75} -4.85410 q^{77} +(0.107320 - 0.608645i) q^{78} +(-10.2776 - 8.62390i) q^{79} +(14.7609 + 5.37252i) q^{80} +(-7.24334 + 2.63636i) q^{81} +(-3.71846 + 3.12016i) q^{82} +(-4.23607 - 7.33708i) q^{83} +(0.354102 - 0.613323i) q^{84} +(0.429282 + 2.43458i) q^{85} +(0.0409928 + 0.232482i) q^{86} +(0.690983 - 1.19682i) q^{87} +(1.80902 + 3.13331i) q^{88} +(5.94752 - 4.99056i) q^{89} +(-14.0430 + 5.11124i) q^{90} +(-2.81908 - 1.02606i) q^{91} +(2.54805 + 2.13806i) q^{92} +(-0.587272 + 3.33059i) q^{93} -4.85410 q^{94} -1.29180 q^{96} +(-2.40574 + 13.6436i) q^{97} +(-2.47897 - 2.08010i) q^{98} +(-4.33953 - 1.57946i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{7} + 3 q^{11} - 12 q^{12} + 42 q^{18} + 24 q^{20} + 3 q^{26} - 12 q^{30} - 33 q^{31} - 66 q^{37} - 18 q^{39} + 42 q^{45} + 12 q^{46} - 12 q^{49} + 33 q^{50} - 30 q^{58} - 12 q^{64} - 6 q^{65}+ \cdots - 96 q^{96}+O(q^{100}) $ 12 * q - 18 * q^7 + 3 * q^11 - 12 * q^12 + 42 * q^18 + 24 * q^20 + 3 * q^26 - 12 * q^30 - 33 * q^31 - 66 * q^37 - 18 * q^39 + 42 * q^45 + 12 * q^46 - 12 * q^49 + 33 * q^50 - 30 * q^58 - 12 * q^64 - 6 * q^65 + 24 * q^68 + 66 * q^69 + 42 * q^75 - 18 * q^77 - 24 * q^83 - 36 * q^84 + 15 * q^87 + 15 * q^88 - 18 * q^94 - 96 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

Coefficient data

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

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

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

$2$	−0.280969	+	1.59345i	−0.198675	+	1.12674i	0.708413	+	0.705799i	$0.249412\pi$
$2$	−0.280969	+	1.59345i	−0.198675	+	1.12674i	−0.907087	+	0.420942i	$0.861699\pi$
$3$	−0.292603	−	0.245523i	−0.168934	−	0.141753i	0.554401	−	0.832250i	$-0.312947\pi$
$3$	−0.292603	−	0.245523i	−0.168934	−	0.141753i	−0.723335	+	0.690497i	$0.757392\pi$
$4$	−0.580762	−	0.211380i	−0.290381	−	0.105690i
$5$	−3.04091	+	1.10680i	−1.35994	+	0.494976i	−0.916035	−	0.401099i	$-0.868628\pi$
$5$	−3.04091	+	1.10680i	−1.35994	+	0.494976i	−0.443901	+	0.896076i	$0.646406\pi$
$6$	0.473442	−	0.397265i	0.193282	−	0.162183i
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	0.429919	−	0.902867i	$-0.358542\pi$
$8$	−1.11803	+	1.93649i	−0.395285	+	0.684653i
$9$	−0.495610	−	2.81074i	−0.165203	−	0.936914i
$10$	−0.909234	−	5.15652i	−0.287525	−	1.63063i
$11$	0.809017	−	1.40126i	0.243928	−	0.422495i	−0.717902	−	0.696144i	$-0.754897\pi$
$11$	0.809017	−	1.40126i	0.243928	−	0.422495i	0.961830	+	0.273649i	$0.0882307\pi$
$12$	0.118034	+	0.204441i	0.0340735	+	0.0590170i
$13$	0.766044	−	0.642788i	0.212463	−	0.178277i	−0.530346	−	0.847781i	$-0.677938\pi$
$13$	0.766044	−	0.642788i	0.212463	−	0.178277i	0.742808	+	0.669504i	$0.233493\pi$
$14$	4.56136	−	1.66020i	1.21908	−	0.443707i
$15$	1.16152	+	0.422760i	0.299904	+	0.109156i
$16$	−3.71846	−	3.12016i	−0.929614	−	0.780039i
$17$	0.132655	−	0.752326i	0.0321737	−	0.182466i	−0.964486	−	0.264134i	$-0.914914\pi$
$17$	0.132655	−	0.752326i	0.0321737	−	0.182466i	0.996660	+	0.0816685i	$0.0260249\pi$
$18$	4.61803			1.08848
$19$		0			0
$19$		0			0
$20$	2.00000			0.447214
$21$	−0.198983	+	1.12849i	−0.0434217	+	0.246257i
$22$	2.00553	+	1.68284i	0.427581	+	0.358783i
$23$	−5.05739	−	1.84074i	−1.05454	−	0.383821i	−0.244165	−	0.969734i	$-0.578514\pi$
$23$	−5.05739	−	1.84074i	−1.05454	−	0.383821i	−0.810374	+	0.585913i	$0.800736\pi$
$24$	0.802593	−	0.292120i	0.163829	−	0.0596288i
$25$	4.19190	−	3.51742i	0.838380	−	0.703484i
$26$	0.809017	+	1.40126i	0.158661	+	0.274809i
$27$	−1.11803	+	1.93649i	−0.215166	+	0.372678i
$28$	0.321961	+	1.82593i	0.0608450	+	0.345069i
$29$	0.628265	+	3.56307i	0.116666	+	0.661645i	0.985912	+	0.167265i	$0.0534937\pi$
$29$	0.628265	+	3.56307i	0.116666	+	0.661645i	−0.869246	+	0.494380i	$0.835395\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$	−4.42705	−	7.66788i	−0.795122	−	1.37719i	−0.922762	−	0.385371i	$-0.874074\pi$
$31$	−4.42705	−	7.66788i	−0.795122	−	1.37719i	0.127640	−	0.991821i	$-0.459260\pi$
$32$	2.59074	−	2.17389i	0.457982	−	0.384292i
$33$	−0.580762	+	0.211380i	−0.101098	+	0.0367965i
$34$	1.16152	+	0.422760i	0.199200	+	0.0725028i
$35$	7.43692	+	6.24031i	1.25707	+	1.05481i
$36$	−0.306304	+	1.73713i	−0.0510506	+	0.289522i
$37$	−8.85410			−1.45561			−0.727803	−	0.685787i	$-0.759458\pi$
$37$	−8.85410			−1.45561			−0.727803	+	0.685787i	$0.759458\pi$
$38$		0			0
$39$	−0.381966			−0.0611635
$40$	1.25653	−	7.12614i	0.198675	−	1.12674i
$41$	2.29813	+	1.92836i	0.358908	+	0.301160i	0.804355	−	0.594149i	$-0.202511\pi$
$41$	2.29813	+	1.92836i	0.358908	+	0.301160i	−0.445447	+	0.895308i	$0.646955\pi$
$42$	−1.74229	−	0.634140i	−0.268841	−	0.0978500i
$43$	0.137099	−	0.0499001i	0.0209074	−	0.00760969i	−0.331545	−	0.943439i	$-0.607570\pi$
$43$	0.137099	−	0.0499001i	0.0209074	−	0.00760969i	0.352453	+	0.935830i	$0.385348\pi$
$44$	−0.766044	+	0.642788i	−0.115486	+	0.0969039i
$45$	4.61803	+	7.99867i	0.688416	+	1.19237i
$46$	4.35410	−	7.54153i	0.641977	−	1.11194i
$47$	0.520945	+	2.95442i	0.0759876	+	0.430947i	0.998940	+	0.0460327i	$0.0146579\pi$
$47$	0.520945	+	2.95442i	0.0759876	+	0.430947i	−0.922952	+	0.384914i	$0.874231\pi$
$48$	0.321961	+	1.82593i	0.0464711	+	0.263551i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	4.42705	+	7.66788i	0.626080	+	1.08440i
$51$	−0.223529	+	0.187563i	−0.0313003	+	0.0262641i
$52$	−0.580762	+	0.211380i	−0.0805372	+	0.0293131i
$53$	−5.94472	−	2.16370i	−0.816570	−	0.297207i	−0.100235	−	0.994964i	$-0.531959\pi$
$53$	−5.94472	−	2.16370i	−0.816570	−	0.297207i	−0.716335	+	0.697757i	$0.754182\pi$
$54$	−2.77157	−	2.32563i	−0.377164	−	0.316478i
$55$	−0.909234	+	5.15652i	−0.122601	+	0.695305i
$56$	6.70820			0.896421
$57$		0			0
$58$	−5.85410			−0.768681
$59$	−0.0566506	+	0.321282i	−0.00737528	+	0.0418273i	−0.988273	−	0.152695i	$-0.951205\pi$
$59$	−0.0566506	+	0.321282i	−0.00737528	+	0.0418273i	0.980898	+	0.194523i	$0.0623158\pi$
$60$	−0.585206	−	0.491046i	−0.0755498	−	0.0633938i
$61$	9.61876	+	3.50094i	1.23156	+	0.448250i	0.874130	−	0.485692i	$-0.161432\pi$
$61$	9.61876	+	3.50094i	1.23156	+	0.448250i	0.357426	+	0.933942i	$0.383655\pi$
$62$	13.4623	−	4.89986i	1.70971	−	0.622283i
$63$	−6.55911	+	5.50374i	−0.826370	+	0.693407i
$64$	−2.11803	−	3.66854i	−0.264754	−	0.458568i
$65$	−1.61803	+	2.80252i	−0.200692	+	0.347609i
$66$	−0.173648	−	0.984808i	−0.0213746	−	0.121221i
$67$	1.21554	+	6.89365i	0.148502	+	0.842194i	0.964489	+	0.264124i	$0.0850828\pi$
$67$	1.21554	+	6.89365i	0.148502	+	0.842194i	−0.815987	+	0.578070i	$0.803806\pi$
$68$	−0.236068	+	0.408882i	−0.0286274	+	0.0495842i
$69$	1.02786	+	1.78031i	0.123740	+	0.214324i
$70$	−12.0332	+	10.0970i	−1.43824	+	1.20683i
$71$	−7.02151	+	2.55562i	−0.833300	+	0.303296i	−0.723213	−	0.690625i	$-0.757335\pi$
$71$	−7.02151	+	2.55562i	−0.833300	+	0.303296i	−0.110087	+	0.993922i	$0.535113\pi$
$72$	5.99709	+	2.18276i	0.706763	+	0.257241i
$73$	−2.07460	−	1.74080i	−0.242814	−	0.203745i	0.513257	−	0.858235i	$-0.328439\pi$
$73$	−2.07460	−	1.74080i	−0.242814	−	0.203745i	−0.756071	+	0.654490i	$0.772883\pi$
$74$	2.48773	−	14.1086i	0.289192	−	1.64009i
$75$	−2.09017			−0.241352
$76$		0			0
$77$	−4.85410			−0.553176
$78$	0.107320	−	0.608645i	0.0121517	−	0.0689154i
$79$	−10.2776	−	8.62390i	−1.15632	−	0.970265i	−0.156468	−	0.987683i	$-0.550011\pi$
$79$	−10.2776	−	8.62390i	−1.15632	−	0.970265i	−0.999848	+	0.0174184i	$0.994455\pi$
$80$	14.7609	+	5.37252i	1.65032	+	0.600666i
$81$	−7.24334	+	2.63636i	−0.804816	+	0.292929i
$82$	−3.71846	+	3.12016i	−0.410635	+	0.344564i
$83$	−4.23607	−	7.33708i	−0.464969	−	0.805350i	0.534231	−	0.845338i	$-0.320601\pi$
$83$	−4.23607	−	7.33708i	−0.464969	−	0.805350i	−0.999200	+	0.0399887i	$0.987268\pi$
$84$	0.354102	−	0.613323i	0.0386357	−	0.0669190i
$85$	0.429282	+	2.43458i	0.0465622	+	0.264067i
$86$	0.0409928	+	0.232482i	0.00442036	+	0.0250691i
$87$	0.690983	−	1.19682i	0.0740812	−	0.128312i
$88$	1.80902	+	3.13331i	0.192842	+	0.334012i
$89$	5.94752	−	4.99056i	0.630436	−	0.528998i	−0.270629	−	0.962684i	$-0.587232\pi$
$89$	5.94752	−	4.99056i	0.630436	−	0.528998i	0.901064	+	0.433686i	$0.142787\pi$
$90$	−14.0430	+	5.11124i	−1.48026	+	0.538772i
$91$	−2.81908	−	1.02606i	−0.295520	−	0.107560i
$92$	2.54805	+	2.13806i	0.265652	+	0.222909i
$93$	−0.587272	+	3.33059i	−0.0608973	+	0.345366i
$94$	−4.85410			−0.500662
$95$		0			0
$96$	−1.29180			−0.131843
$97$	−2.40574	+	13.6436i	−0.244266	+	1.38530i	0.577926	+	0.816089i	$0.303862\pi$
$97$	−2.40574	+	13.6436i	−0.244266	+	1.38530i	−0.822191	+	0.569211i	$0.807249\pi$
$98$	−2.47897	−	2.08010i	−0.250414	−	0.210122i
$99$	−4.33953	−	1.57946i	−0.436139	−	0.158742i
$100$	−3.17801	+	1.15670i	−0.317801	+	0.115670i
$101$	−7.03255	+	5.90101i	−0.699765	+	0.587172i	−0.921707	−	0.387888i	$-0.873205\pi$
$101$	−7.03255	+	5.90101i	−0.699765	+	0.587172i	0.221942	+	0.975060i	$0.428760\pi$
$102$	−0.236068	−	0.408882i	−0.0233742	−	0.0404853i
$103$	7.16312	−	12.4069i	0.705803	−	1.22249i	−0.260598	−	0.965447i	$-0.583920\pi$
$103$	7.16312	−	12.4069i	0.705803	−	1.22249i	0.966401	−	0.257039i	$-0.0827470\pi$
$104$	0.388289	+	2.20210i	0.0380749	+	0.215933i
$105$	−0.643923	−	3.65187i	−0.0628404	−	0.356386i
$106$	5.11803	−	8.86469i	0.497107	−	0.861015i
$107$	8.20820	+	14.2170i	0.793517	+	1.37441i	0.923777	+	0.382932i	$0.125086\pi$
$107$	8.20820	+	14.2170i	0.793517	+	1.37441i	−0.130260	+	0.991480i	$0.541581\pi$
$108$	1.05865	−	0.888311i	0.101868	−	0.0854777i
$109$	−3.09328	+	1.12586i	−0.296282	+	0.107838i	−0.485884	−	0.874023i	$-0.661502\pi$
$109$	−3.09328	+	1.12586i	−0.296282	+	0.107838i	0.189602	+	0.981861i	$0.439280\pi$
$110$	−7.96120	−	2.89764i	−0.759071	−	0.276279i
$111$	2.59074	+	2.17389i	0.245902	+	0.206336i
$112$	−2.52872	+	14.3411i	−0.238941	+	1.35510i
$113$	−6.76393			−0.636297			−0.318149	−	0.948041i	$-0.603061\pi$
$113$	−6.76393			−0.636297			−0.318149	+	0.948041i	$0.603061\pi$
$114$		0			0
$115$	17.4164			1.62409
$116$	0.388289	−	2.20210i	0.0360517	−	0.204460i
$117$	−2.18637	−	1.83458i	−0.202130	−	0.169607i
$118$	−0.496030	−	0.180540i	−0.0456633	−	0.0166201i
$119$	−2.15358	+	0.783840i	−0.197419	+	0.0718545i
$120$	−2.11729	+	1.77662i	−0.193282	+	0.162183i
$121$	4.19098	+	7.25900i	0.380998	+	0.659909i
$122$	−8.28115	+	14.3434i	−0.749740	+	1.29859i
$123$	−0.198983	−	1.12849i	−0.0179417	−	0.101752i
$124$	0.950226	+	5.38900i	0.0853329	+	0.483947i
$125$	−0.763932	+	1.32317i	−0.0683282	+	0.118348i
$126$	−6.92705	−	11.9980i	−0.617111	−	1.06887i
$127$	−4.41543	+	3.70498i	−0.391806	+	0.328764i	−0.817316	−	0.576189i	$-0.804539\pi$
$127$	−4.41543	+	3.70498i	−0.391806	+	0.328764i	0.425510	+	0.904954i	$0.360095\pi$
$128$	12.7968	−	4.65764i	1.13109	−	0.411681i
$129$	−0.0523673	−	0.0190601i	−0.00461068	−	0.00167815i
$130$	−4.01106	−	3.36568i	−0.351793	−	0.295190i
$131$	2.62038	−	14.8609i	0.228944	−	1.29840i	−0.626057	−	0.779777i	$-0.715332\pi$
$131$	2.62038	−	14.8609i	0.228944	−	1.29840i	0.855001	−	0.518627i	$-0.173557\pi$
$132$	0.381966			0.0332459
$133$		0			0
$134$	−11.3262			−0.978438
$135$	1.25653	−	7.12614i	0.108145	−	0.613320i
$136$	1.30856	+	1.09801i	0.112208	+	0.0941538i
$137$	−7.02151	−	2.55562i	−0.599888	−	0.218341i	0.0241848	−	0.999708i	$-0.492301\pi$
$137$	−7.02151	−	2.55562i	−0.599888	−	0.218341i	−0.624073	+	0.781366i	$0.714523\pi$
$138$	−3.12564	+	1.13764i	−0.266072	+	0.0968424i
$139$	11.3362	−	9.51221i	0.961525	−	0.806815i	−0.0196755	−	0.999806i	$-0.506263\pi$
$139$	11.3362	−	9.51221i	0.961525	−	0.806815i	0.981200	+	0.192991i	$0.0618189\pi$
$140$	−3.00000	−	5.19615i	−0.253546	−	0.439155i
$141$	0.572949	−	0.992377i	0.0482510	−	0.0835732i
$142$	−2.09944	−	11.9065i	−0.176181	−	0.999171i
$143$	−0.280969	−	1.59345i	−0.0234958	−	0.133251i
$144$	−6.92705	+	11.9980i	−0.577254	+	0.999834i
$145$	−5.85410	−	10.1396i	−0.486157	−	0.842048i
$146$	3.35678	−	2.81667i	0.277809	−	0.233110i
$147$	0.717861	−	0.261280i	0.0592082	−	0.0215500i
$148$	5.14213	+	1.87158i	0.422680	+	0.153843i
$149$	−1.46301	−	1.22762i	−0.119855	−	0.100570i	0.580890	−	0.813982i	$-0.302705\pi$
$149$	−1.46301	−	1.22762i	−0.119855	−	0.100570i	−0.700745	+	0.713412i	$0.747149\pi$
$150$	0.587272	−	3.33059i	0.0479506	−	0.271941i
$151$	21.0902			1.71629			0.858147	−	0.513404i	$-0.171616\pi$
$151$	21.0902			1.71629			0.858147	+	0.513404i	$0.171616\pi$
$152$		0			0
$153$	−2.18034			−0.176270
$154$	1.36385	−	7.73478i	0.109902	−	0.623286i
$155$	21.9491	+	18.4175i	1.76299	+	1.47933i
$156$	0.221831	+	0.0807400i	0.0177607	+	0.00646437i
$157$	16.7774	−	6.10646i	1.33898	−	0.487349i	0.429489	−	0.903072i	$-0.358694\pi$
$157$	16.7774	−	6.10646i	1.33898	−	0.487349i	0.909491	+	0.415723i	$0.136472\pi$
$158$	16.6294	−	13.9538i	1.32297	−	1.11010i
$159$	1.20820	+	2.09267i	0.0958168	+	0.165960i
$160$	−5.47214	+	9.47802i	−0.432610	+	0.749303i
$161$	2.80371	+	15.9006i	0.220963	+	1.25314i
$162$	−2.16576	−	12.2827i	−0.170158	−	0.965017i
$163$	−0.881966	+	1.52761i	−0.0690809	+	0.119652i	−0.898497	−	0.438980i	$-0.855340\pi$
$163$	−0.881966	+	1.52761i	−0.0690809	+	0.119652i	0.829416	+	0.558631i	$0.188673\pi$
$164$	−0.927051	−	1.60570i	−0.0723905	−	0.125384i
$165$	1.53209	−	1.28558i	0.119273	−	0.100082i
$166$	12.8815	−	4.68848i	0.999798	−	0.363897i
$167$	19.0157	+	6.92114i	1.47148	+	0.535574i	0.948501	−	0.316773i	$-0.102599\pi$
$167$	19.0157	+	6.92114i	1.47148	+	0.535574i	0.522976	+	0.852347i	$0.324822\pi$
$168$	−1.96284	−	1.64702i	−0.151436	−	0.127070i
$169$	−2.08378	+	11.8177i	−0.160291	+	0.909053i
$170$	−4.00000			−0.306786
$171$		0			0
$172$	−0.0901699			−0.00687539
$173$	0.0819855	−	0.464963i	0.00623325	−	0.0353505i	−0.981533	−	0.191295i	$-0.938731\pi$
$173$	0.0819855	−	0.464963i	0.00623325	−	0.0353505i	0.987766	+	0.155945i	$0.0498422\pi$
$174$	1.71293	+	1.43732i	0.129857	+	0.108963i
$175$	−15.4264	−	5.61474i	−1.16612	−	0.424435i
$176$	−7.38044	+	2.68626i	−0.556322	+	0.202485i
$177$	0.0954582	−	0.0800989i	0.00717508	−	0.00602060i
$178$	6.28115	+	10.8793i	0.470792	+	0.815436i
$179$	6.11803	−	10.5967i	0.457283	−	0.792038i	−0.541533	−	0.840680i	$-0.682156\pi$
$179$	6.11803	−	10.5967i	0.457283	−	0.792038i	0.998816	+	0.0486416i	$0.0154892\pi$
$180$	−0.991219	−	5.62148i	−0.0738811	−	0.419001i
$181$	−2.08378	−	11.8177i	−0.154886	−	0.878402i	−0.958890	−	0.283778i	$-0.908412\pi$
$181$	−2.08378	−	11.8177i	−0.154886	−	0.878402i	0.804004	−	0.594624i	$-0.202699\pi$
$182$	2.42705	−	4.20378i	0.179905	−	0.311605i
$183$	−1.95492	−	3.38601i	−0.144511	−	0.250301i
$184$	9.21892	−	7.73559i	0.679628	−	0.570275i
$185$	26.9245	−	9.79972i	1.97953	−	0.720490i
$186$	−5.14213	−	1.87158i	−0.377039	−	0.137231i
$187$	−0.946883	−	0.794529i	−0.0692429	−	0.0581017i
$188$	0.321961	−	1.82593i	0.0234815	−	0.133170i
$189$	6.70820			0.487950
$190$		0			0
$191$	14.2361			1.03009			0.515043	−	0.857164i	$-0.327776\pi$
$191$	14.2361			1.03009			0.515043	+	0.857164i	$0.327776\pi$
$192$	−0.280969	+	1.59345i	−0.0202772	+	0.114998i
$193$	−3.87291	−	3.24976i	−0.278778	−	0.233923i	0.492668	−	0.870217i	$-0.336022\pi$
$193$	−3.87291	−	3.24976i	−0.278778	−	0.233923i	−0.771446	+	0.636295i	$0.780466\pi$
$194$	−21.0645	−	7.66686i	−1.51235	−	0.550449i
$195$	1.16152	−	0.422760i	0.0831785	−	0.0302745i
$196$	0.946883	−	0.794529i	0.0676345	−	0.0567521i
$197$	−1.50000	−	2.59808i	−0.106871	−	0.185105i	0.807630	−	0.589689i	$-0.200750\pi$
$197$	−1.50000	−	2.59808i	−0.106871	−	0.185105i	−0.914501	+	0.404584i	$0.867416\pi$
$198$	3.73607	−	6.47106i	0.265511	−	0.459878i
$199$	−2.32973	−	13.2126i	−0.165151	−	0.936615i	−0.948909	−	0.315550i	$-0.897811\pi$
$199$	−2.32973	−	13.2126i	−0.165151	−	0.936615i	0.783759	−	0.621066i	$-0.213300\pi$
$200$	2.12477	+	12.0502i	0.150244	+	0.852076i
$201$	1.33688	−	2.31555i	0.0942963	−	0.163326i
$202$	−7.42705	−	12.8640i	−0.522565	−	0.905110i
$203$	8.31472	−	6.97688i	0.583579	−	0.489681i
$204$	0.169464	−	0.0616799i	0.0118649	−	0.00431845i
$205$	−9.12273	−	3.32040i	−0.637159	−	0.231907i
$206$	17.7572	+	14.9000i	1.23720	+	1.03813i
$207$	−2.66735	+	15.1273i	−0.185394	+	1.05142i
$208$	−4.85410			−0.336571
$209$		0			0
$210$	6.00000			0.414039
$211$	0.669258	−	3.79555i	0.0460736	−	0.261296i	−0.953066	−	0.302762i	$-0.902091\pi$
$211$	0.669258	−	3.79555i	0.0460736	−	0.261296i	0.999140	+	0.0414651i	$0.0132025\pi$
$212$	2.99510	+	2.51319i	0.205705	+	0.172607i
$213$	2.68198	+	0.976160i	0.183766	+	0.0668854i
$214$	−24.9604	+	9.08484i	−1.70626	+	0.621027i
$215$	−0.361677	+	0.303483i	−0.0246662	+	0.0206974i
$216$	−2.50000	−	4.33013i	−0.170103	−	0.294628i
$217$	−13.2812	+	23.0036i	−0.901583	+	1.56159i
$218$	−0.924892	−	5.24532i	−0.0626416	−	0.355258i
$219$	0.179629	+	1.01873i	0.0121382	+	0.0688391i
$220$	1.61803	−	2.80252i	0.109088	−	0.188946i
$221$	−0.381966	−	0.661585i	−0.0256938	−	0.0445030i
$222$	−4.19190	+	3.51742i	−0.281342	+	0.236074i
$223$	−10.9497	+	3.98538i	−0.733249	+	0.266881i	−0.681540	−	0.731781i	$-0.738689\pi$
$223$	−10.9497	+	3.98538i	−0.733249	+	0.266881i	−0.0517096	+	0.998662i	$0.516467\pi$
$224$	−9.53403	−	3.47010i	−0.637019	−	0.231856i
$225$	−11.9641	−	10.0391i	−0.797607	−	0.669272i
$226$	1.90045	−	10.7780i	0.126416	−	0.716942i
$227$	−16.4164			−1.08960			−0.544798	−	0.838568i	$-0.683394\pi$
$227$	−16.4164			−1.08960			−0.544798	+	0.838568i	$0.683394\pi$
$228$		0			0
$229$	−13.6180			−0.899905			−0.449953	−	0.893052i	$-0.648559\pi$
$229$	−13.6180			−0.899905			−0.449953	+	0.893052i	$0.648559\pi$
$230$	−4.89346	+	27.7522i	−0.322666	+	1.82993i
$231$	1.42032	+	1.19179i	0.0934505	+	0.0784143i
$232$	−7.60227	−	2.76700i	−0.499114	−	0.181663i
$233$	−4.25480	+	1.54862i	−0.278741	+	0.101454i	−0.477608	−	0.878573i	$-0.658496\pi$
$233$	−4.25480	+	1.54862i	−0.278741	+	0.101454i	0.198867	+	0.980027i	$0.436274\pi$
$234$	3.53762	−	2.96842i	0.231261	−	0.194051i
$235$	−4.85410	−	8.40755i	−0.316647	−	0.548448i
$236$	0.100813	−	0.174613i	0.00656237	−	0.0113664i
$237$	0.889879	+	5.04676i	0.0578039	+	0.327822i
$238$	−0.643923	−	3.65187i	−0.0417393	−	0.236715i
$239$	0.163119	−	0.282530i	0.0105513	−	0.0182754i	−0.860702	−	0.509110i	$-0.829975\pi$
$239$	0.163119	−	0.282530i	0.0105513	−	0.0182754i	0.871253	+	0.490834i	$0.163308\pi$
$240$	−3.00000	−	5.19615i	−0.193649	−	0.335410i
$241$	−2.43628	+	2.04428i	−0.156935	+	0.131684i	−0.717874	−	0.696173i	$-0.754885\pi$
$241$	−2.43628	+	2.04428i	−0.156935	+	0.131684i	0.560939	+	0.827857i	$0.310440\pi$
$242$	−12.7444	+	4.63858i	−0.819241	+	0.298179i
$243$	9.07036	+	3.30134i	0.581864	+	0.211781i
$244$	−4.84618	−	4.06643i	−0.310245	−	0.260326i
$245$	1.12387	−	6.37381i	0.0718017	−	0.407208i
$246$	1.85410			0.118213
$247$		0			0
$248$	19.7984			1.25720
$249$	−0.561937	+	3.18690i	−0.0356113	+	0.201962i
$250$	−1.89377	−	1.58906i	−0.119772	−	0.100501i
$251$	23.8312	+	8.67386i	1.50421	+	0.547489i	0.957148	−	0.289600i	$-0.0935221\pi$
$251$	23.8312	+	8.67386i	1.50421	+	0.547489i	0.547067	+	0.837089i	$0.315744\pi$
$252$	4.97266	−	1.80990i	0.313248	−	0.114013i
$253$	−6.67087	+	5.59753i	−0.419394	+	0.351913i
$254$	−4.66312	−	8.07676i	−0.292590	−	0.506781i
$255$	0.472136	−	0.817763i	0.0295663	−	0.0512103i
$256$	2.35507	+	13.3563i	0.147192	+	0.834766i
$257$	−3.53559	−	20.0514i	−0.220544	−	1.25077i	−0.871022	−	0.491244i	$-0.836542\pi$
$257$	−3.53559	−	20.0514i	−0.220544	−	1.25077i	0.650478	−	0.759525i	$-0.274569\pi$
$258$	0.0450850	−	0.0780895i	0.00280687	−	0.00486164i
$259$	13.2812	+	23.0036i	0.825251	+	1.42938i
$260$	1.53209	−	1.28558i	0.0950161	−	0.0797280i
$261$	9.70349	−	3.53178i	0.600631	−	0.218612i
$262$	22.9439	+	8.35090i	1.41748	+	0.515921i
$263$	−11.4480	−	9.60599i	−0.705912	−	0.592331i	0.217536	−	0.976052i	$-0.430198\pi$
$263$	−11.4480	−	9.60599i	−0.705912	−	0.592331i	−0.923449	+	0.383721i	$0.874642\pi$
$264$	0.239976	−	1.36097i	0.0147695	−	0.0837620i
$265$	20.4721			1.25759
$266$		0			0
$267$	−2.96556			−0.181489
$268$	0.751243	−	4.26051i	0.0458895	−	0.260252i
$269$	−23.2312	−	19.4933i	−1.41643	−	1.18853i	−0.953218	−	0.302284i	$-0.902251\pi$
$269$	−23.2312	−	19.4933i	−1.41643	−	1.18853i	−0.463216	−	0.886245i	$-0.653305\pi$
$270$	11.0021	+	4.00444i	0.669567	+	0.243703i
$271$	−1.07679	+	0.391920i	−0.0654105	+	0.0238075i	−0.374518	−	0.927220i	$-0.622192\pi$
$271$	−1.07679	+	0.391920i	−0.0654105	+	0.0238075i	0.309108	+	0.951027i	$0.399970\pi$
$272$	−2.84065	+	2.38359i	−0.172240	+	0.144526i
$273$	0.572949	+	0.992377i	0.0346765	+	0.0600614i
$274$	6.04508	−	10.4704i	0.365197	−	0.632540i
$275$	−1.53750	−	8.71959i	−0.0927147	−	0.525811i
$276$	−0.220622	−	1.25121i	−0.0132799	−	0.0753139i
$277$	−5.70820	+	9.88690i	−0.342973	+	0.594046i	−0.984983	−	0.172650i	$-0.944767\pi$
$277$	−5.70820	+	9.88690i	−0.342973	+	0.594046i	0.642011	+	0.766696i	$0.278101\pi$
$278$	11.9721	+	20.7363i	0.718041	+	1.24368i
$279$	−19.3583	+	16.2436i	−1.15895	+	0.972477i
$280$	−20.3990	+	7.42464i	−1.21908	+	0.443707i
$281$	−27.7271	−	10.0918i	−1.65406	−	0.602029i	−0.664648	−	0.747157i	$-0.731418\pi$
$281$	−27.7271	−	10.0918i	−1.65406	−	0.602029i	−0.989413	+	0.145128i	$0.953641\pi$
$282$	1.42032	+	1.19179i	0.0845791	+	0.0709703i
$283$	4.52083	−	25.6389i	0.268736	−	1.52408i	−0.489447	−	0.872033i	$-0.662801\pi$
$283$	4.52083	−	25.6389i	0.268736	−	1.52408i	0.758182	−	0.652042i	$-0.226088\pi$
$284$	4.61803			0.274030
$285$		0			0
$286$	2.61803			0.154808
$287$	1.56283	−	8.86327i	0.0922512	−	0.523182i
$288$	−7.39423	−	6.20449i	−0.435709	−	0.365603i
$289$	15.4264	+	5.61474i	0.907434	+	0.330279i
$290$	17.8018	−	6.47932i	1.04536	−	0.380479i
$291$	4.05375	−	3.40150i	0.237635	−	0.199400i
$292$	0.836881	+	1.44952i	0.0489748	+	0.0848268i
$293$	−5.07295	+	8.78661i	−0.296365	+	0.513319i	−0.975301	−	0.220878i	$-0.929108\pi$
$293$	−5.07295	+	8.78661i	−0.296365	+	0.513319i	0.678937	+	0.734197i	$0.262441\pi$
$294$	0.214641	+	1.21729i	0.0125181	+	0.0709938i
$295$	−0.183325	−	1.03969i	−0.0106736	−	0.0605330i
$296$	9.89919	−	17.1459i	0.575379	−	0.996585i
$297$	1.80902	+	3.13331i	0.104970	+	0.181813i
$298$	2.36721	−	1.98632i	0.137129	−	0.115065i
$299$	−5.05739	+	1.84074i	−0.292477	+	0.106453i
$300$	1.21389	+	0.441820i	0.0700840	+	0.0255085i
$301$	−0.335293	−	0.281344i	−0.0193260	−	0.0162164i
$302$	−5.92568	+	33.6062i	−0.340984	+	1.93382i
$303$	3.50658			0.201448
$304$		0			0
$305$	−33.1246			−1.89671
$306$	0.612607	−	3.47427i	0.0350204	−	0.198611i
$307$	13.2727	+	11.1371i	0.757511	+	0.635627i	0.937478	−	0.348045i	$-0.113154\pi$
$307$	13.2727	+	11.1371i	0.757511	+	0.635627i	−0.179966	+	0.983673i	$0.557599\pi$
$308$	2.81908	+	1.02606i	0.160632	+	0.0584652i
$309$	−5.14213	+	1.87158i	−0.292525	+	0.106471i
$310$	−35.5143	+	29.8001i	−2.01708	+	1.69253i
$311$	−6.32624	−	10.9574i	−0.358728	−	0.621335i	0.629021	−	0.777389i	$-0.283456\pi$
$311$	−6.32624	−	10.9574i	−0.358728	−	0.621335i	−0.987749	+	0.156053i	$0.950123\pi$
$312$	0.427051	−	0.739674i	0.0241770	−	0.0418758i
$313$	−1.96678	−	11.1542i	−0.111169	−	0.630471i	−0.988576	−	0.150724i	$-0.951840\pi$
$313$	−1.96678	−	11.1542i	−0.111169	−	0.630471i	0.877407	−	0.479747i	$-0.159272\pi$
$314$	5.01644	+	28.4497i	0.283094	+	1.60551i
$315$	13.8541	−	23.9960i	0.780590	−	1.35202i
$316$	4.14590	+	7.18091i	0.233225	+	0.403958i
$317$	−13.7888	+	11.5702i	−0.774456	+	0.649846i	−0.941846	−	0.336045i	$-0.890911\pi$
$317$	−13.7888	+	11.5702i	−0.774456	+	0.649846i	0.167390	+	0.985891i	$0.446466\pi$
$318$	−3.67404	+	1.33724i	−0.206030	+	0.0749887i
$319$	5.50106	+	2.00222i	0.308000	+	0.112103i
$320$	10.5011	+	8.81146i	0.587029	+	0.492576i
$321$	1.08886	−	6.17525i	0.0607744	−	0.344669i
$322$	−26.1246			−1.45587
$323$		0			0
$324$	4.76393			0.264663
$325$	0.950226	−	5.38900i	0.0527091	−	0.298928i
$326$	−2.18637	−	1.83458i	−0.121092	−	0.101608i
$327$	1.18153	+	0.430040i	0.0653386	+	0.0237813i
$328$	−6.30365	+	2.29434i	−0.348061	+	0.126684i
$329$	6.89440	−	5.78509i	0.380101	−	0.318942i
$330$	1.61803	+	2.80252i	0.0890698	+	0.154273i
$331$	5.47214	−	9.47802i	0.300776	−	0.520959i	−0.675536	−	0.737327i	$-0.736088\pi$
$331$	5.47214	−	9.47802i	0.300776	−	0.520959i	0.976312	+	0.216368i	$0.0694211\pi$
$332$	0.909234	+	5.15652i	0.0499007	+	0.283001i
$333$	4.38818	+	24.8866i	0.240471	+	1.36378i
$334$	−16.3713	+	28.3560i	−0.895799	+	1.55157i
$335$	−11.3262	−	19.6176i	−0.618818	−	1.07183i
$336$	4.26097	−	3.57538i	0.232455	−	0.195053i
$337$	−16.0919	+	5.85696i	−0.876580	+	0.319049i	−0.740829	−	0.671694i	$-0.765567\pi$
$337$	−16.0919	+	5.85696i	−0.876580	+	0.319049i	−0.135751	+	0.990743i	$0.543345\pi$
$338$	−18.2455	−	6.64080i	−0.992422	−	0.361212i
$339$	1.97915	+	1.66070i	0.107492	+	0.0901969i
$340$	0.265311	−	1.50465i	0.0143885	−	0.0816012i
$341$	−14.3262			−0.775809
$342$		0			0
$343$	−15.0000			−0.809924
$344$	−0.0566506	+	0.321282i	−0.00305440	+	0.0173223i
$345$	−5.09609	−	4.27613i	−0.274364	−	0.230219i
$346$	0.717861	+	0.261280i	0.0385925	+	0.0140465i
$347$	23.8836	−	8.69292i	1.28214	−	0.466661i	0.391000	−	0.920391i	$-0.372129\pi$
$347$	23.8836	−	8.69292i	1.28214	−	0.466661i	0.891139	+	0.453730i	$0.149907\pi$
$348$	−0.654280	+	0.549006i	−0.0350731	+	0.0294298i
$349$	10.4894	+	18.1681i	0.561482	+	0.972516i	0.997367	+	0.0725137i	$0.0231021\pi$
$349$	10.4894	+	18.1681i	0.561482	+	0.972516i	−0.435885	+	0.900002i	$0.643565\pi$
$350$	13.2812	−	23.0036i	0.709907	−	1.22960i
$351$	0.388289	+	2.20210i	0.0207253	+	0.117539i
$352$	−0.950226	−	5.38900i	−0.0506472	−	0.287235i
$353$	−12.2254	+	21.1751i	−0.650694	+	1.12703i	0.332261	+	0.943187i	$0.392188\pi$
$353$	−12.2254	+	21.1751i	−0.650694	+	1.12703i	−0.982955	+	0.183847i	$0.941145\pi$
$354$	0.100813	+	0.174613i	0.00535815	+	0.00928059i
$355$	18.5232	−	15.5428i	0.983110	−	0.824927i
$356$	−4.50900	+	1.64114i	−0.238976	+	0.0869803i
$357$	0.822596	+	0.299400i	0.0435364	+	0.0158459i
$358$	15.1664	+	12.7261i	0.801571	+	0.672598i
$359$	1.22152	−	6.92757i	0.0644693	−	0.365623i	−0.935457	−	0.353442i	$-0.885011\pi$
$359$	1.22152	−	6.92757i	0.0644693	−	0.365623i	0.999926	−	0.0121816i	$-0.00387762\pi$
$360$	−20.6525			−1.08848
$361$		0			0
$362$	19.4164			1.02050
$363$	0.555957	−	3.15299i	0.0291802	−	0.165489i
$364$	1.42032	+	1.19179i	0.0744452	+	0.0624670i
$365$	8.23540	+	2.99744i	0.431061	+	0.156893i
$366$	5.94472	−	2.16370i	0.310735	−	0.113098i
$367$	−12.2140	+	10.2488i	−0.637567	+	0.534982i	−0.903270	−	0.429073i	$-0.858840\pi$
$367$	−12.2140	+	10.2488i	−0.637567	+	0.534982i	0.265703	+	0.964055i	$0.414396\pi$
$368$	13.0623	+	22.6246i	0.680920	+	1.17939i
$369$	4.28115	−	7.41517i	0.222868	−	0.386019i
$370$	8.05045	+	45.6564i	0.418523	+	2.37356i
$371$	3.29562	+	18.6904i	0.171100	+	0.970356i
$372$	1.04508	−	1.81014i	0.0541851	−	0.0938514i
$373$	−2.73607	−	4.73901i	−0.141668	−	0.245377i	0.786457	−	0.617645i	$-0.211913\pi$
$373$	−2.73607	−	4.73901i	−0.141668	−	0.245377i	−0.928125	+	0.372269i	$0.878580\pi$
$374$	1.53209	−	1.28558i	0.0792224	−	0.0664755i
$375$	0.548397	−	0.199600i	0.0283191	−	0.0103073i
$376$	−6.30365	−	2.29434i	−0.325086	−	0.118322i
$377$	2.77157	+	2.32563i	0.142743	+	0.119776i
$378$	−1.88480	+	10.6892i	−0.0969434	+	0.549793i
$379$	15.1246			0.776899			0.388450	−	0.921470i	$-0.373011\pi$
$379$	15.1246			0.776899			0.388450	+	0.921470i	$0.373011\pi$
$380$		0			0
$381$	2.20163			0.112793
$382$	−3.99989	+	22.6845i	−0.204652	+	1.16064i
$383$	−0.292603	−	0.245523i	−0.0149513	−	0.0125456i	0.635281	−	0.772281i	$-0.280884\pi$
$383$	−0.292603	−	0.245523i	−0.0149513	−	0.0125456i	−0.650233	+	0.759735i	$0.725329\pi$
$384$	−4.88793	−	1.77906i	−0.249436	−	0.0907873i
$385$	14.7609	−	5.37252i	0.752284	−	0.273809i
$386$	6.26650	−	5.25822i	0.318957	−	0.267636i
$387$	−0.208204	−	0.360620i	−0.0105836	−	0.0183313i
$388$	4.28115	−	7.41517i	0.217343	−	0.376448i
$389$	1.60981	+	9.12967i	0.0816205	+	0.462893i	0.998035	+	0.0626618i	$0.0199589\pi$
$389$	1.60981	+	9.12967i	0.0816205	+	0.462893i	−0.916414	+	0.400231i	$0.868930\pi$
$390$	0.347296	+	1.96962i	0.0175860	+	0.0997354i
$391$	−2.05573	+	3.56063i	−0.103963	+	0.180069i
$392$	−2.23607	−	3.87298i	−0.112938	−	0.195615i
$393$	−4.41543	+	3.70498i	−0.222729	+	0.186892i
$394$	4.56136	−	1.66020i	0.229798	−	0.0836397i
$395$	40.7981	+	14.8493i	2.05277	+	0.747149i
$396$	2.18637	+	1.83458i	0.109869	+	0.0921912i
$397$	−1.99212	+	11.2978i	−0.0999814	+	0.567023i	0.893125	+	0.449808i	$0.148508\pi$
$397$	−1.99212	+	11.2978i	−0.0999814	+	0.567023i	−0.993107	+	0.117215i	$0.962603\pi$
$398$	21.7082			1.08813
$399$		0			0
$400$	−26.5623			−1.32812
$401$	6.23198	−	35.3433i	0.311210	−	1.76496i	−0.281516	−	0.959557i	$-0.590837\pi$
$401$	6.23198	−	35.3433i	0.311210	−	1.76496i	0.592726	−	0.805404i	$-0.298052\pi$
$402$	3.31409	+	2.78085i	0.165292	+	0.138696i
$403$	−8.32013	−	3.02828i	−0.414455	−	0.150849i
$404$	5.33159	−	1.94054i	0.265257	−	0.0965455i
$405$	19.1084	−	16.0339i	0.949505	−	0.796729i
$406$	8.78115	+	15.2094i	0.435801	+	0.754830i
$407$	−7.16312	+	12.4069i	−0.355063	+	0.614987i
$408$	−0.113301	−	0.642563i	−0.00560925	−	0.0318116i
$409$	1.43986	+	8.16583i	0.0711963	+	0.403774i	0.999490	+	0.0319269i	$0.0101644\pi$
$409$	1.43986	+	8.16583i	0.0711963	+	0.403774i	−0.928294	+	0.371847i	$0.878725\pi$
$410$	7.85410	−	13.6037i	0.387886	−	0.671839i
$411$	1.42705	+	2.47172i	0.0703912	+	0.121921i
$412$	−6.78264	+	5.69131i	−0.334156	+	0.280391i
$413$	0.919690	−	0.334740i	0.0452550	−	0.0164715i
$414$	−23.3552	−	8.50060i	−1.14785	−	0.417782i
$415$	21.0022	+	17.6229i	1.03096	+	0.865075i
$416$	0.587272	−	3.33059i	0.0287934	−	0.163295i
$417$	−5.65248			−0.276803
$418$		0			0
$419$	−8.94427			−0.436956			−0.218478	−	0.975842i	$-0.570109\pi$
$419$	−8.94427			−0.436956			−0.218478	+	0.975842i	$0.570109\pi$
$420$	−0.397966	+	2.25698i	−0.0194188	+	0.110129i
$421$	21.0449	+	17.6587i	1.02566	+	0.860635i	0.990329	−	0.138741i	$-0.0443055\pi$
$421$	21.0449	+	17.6587i	1.02566	+	0.860635i	0.0353358	+	0.999375i	$0.488750\pi$
$422$	5.85999	+	2.13286i	0.285260	+	0.103826i
$423$	8.04594	−	2.92848i	0.391207	−	0.142388i
$424$	10.8364	−	9.09281i	0.526261	−	0.441586i
$425$	−2.09017	−	3.62028i	−0.101388	−	0.175609i
$426$	−2.30902	+	3.99933i	−0.111872	+	0.193768i
$427$	−5.33242	−	30.2417i	−0.258054	−	1.46350i
$428$	−1.76182	−	9.99176i	−0.0851606	−	0.482970i
$429$	−0.309017	+	0.535233i	−0.0149195	+	0.0258413i
$430$	−0.381966	−	0.661585i	−0.0184200	−	0.0319044i
$431$	−21.1830	+	17.7747i	−1.02035	+	0.856176i	−0.989672	−	0.143354i	$-0.954211\pi$
$431$	−21.1830	+	17.7747i	−1.02035	+	0.856176i	−0.0306789	+	0.999529i	$0.509767\pi$
$432$	10.1995	−	3.71232i	0.490725	−	0.178609i
$433$	−3.23038	−	1.17576i	−0.155242	−	0.0565034i	0.263230	−	0.964733i	$-0.415212\pi$
$433$	−3.23038	−	1.17576i	−0.155242	−	0.0565034i	−0.418472	+	0.908230i	$0.637434\pi$
$434$	−32.9236	−	27.6262i	−1.58038	−	1.32610i
$435$	−0.776578	+	4.40419i	−0.0372341	+	0.211165i
$436$	2.03444			0.0974321
$437$		0			0
$438$	−1.67376			−0.0799754
$439$	6.00766	−	34.0711i	0.286730	−	1.62613i	−0.412309	−	0.911044i	$-0.635278\pi$
$439$	6.00766	−	34.0711i	0.286730	−	1.62613i	0.699039	−	0.715083i	$-0.253611\pi$
$440$	−8.96900	−	7.52589i	−0.427581	−	0.358783i
$441$	5.36396	+	1.95232i	0.255427	+	0.0929677i
$442$	1.16152	−	0.422760i	0.0552481	−	0.0201086i
$443$	−5.80937	+	4.87464i	−0.276011	+	0.231601i	−0.770276	−	0.637710i	$-0.779882\pi$
$443$	−5.80937	+	4.87464i	−0.276011	+	0.231601i	0.494265	+	0.869311i	$0.335437\pi$
$444$	−1.04508	−	1.81014i	−0.0495975	−	0.0859055i
$445$	−12.5623	+	21.7586i	−0.595510	+	1.03145i
$446$	−3.27398	−	18.5677i	−0.155027	−	0.879204i
$447$	0.126675	+	0.718408i	0.00599150	+	0.0339795i
$448$	−6.35410	+	11.0056i	−0.300203	+	0.519967i
$449$	1.44427	+	2.50155i	0.0681594	+	0.118056i	0.898091	−	0.439809i	$-0.144954\pi$
$449$	1.44427	+	2.50155i	0.0681594	+	0.118056i	−0.829932	+	0.557865i	$0.811621\pi$
$450$	19.3583	−	16.2436i	0.912561	−	0.765729i
$451$	4.56136	−	1.66020i	0.214786	−	0.0781758i
$452$	3.92823	+	1.42976i	0.184769	+	0.0672503i
$453$	−6.17105	−	5.17812i	−0.289941	−	0.243289i
$454$	4.61250	−	26.1588i	0.216475	−	1.22769i
$455$	9.70820			0.455128
$456$		0			0
$457$	19.7082			0.921911			0.460955	−	0.887423i	$-0.347507\pi$
$457$	19.7082			0.921911			0.460955	+	0.887423i	$0.347507\pi$
$458$	3.82624	−	21.6997i	0.178788	−	1.01396i
$459$	1.30856	+	1.09801i	0.0610784	+	0.0512508i
$460$	−10.1148	−	3.68148i	−0.471604	−	0.171650i
$461$	−19.6812	+	7.16336i	−0.916644	+	0.333631i	−0.756902	−	0.653528i	$-0.773288\pi$
$461$	−19.6812	+	7.16336i	−0.916644	+	0.333631i	−0.159741	+	0.987159i	$0.551066\pi$
$462$	−2.29813	+	1.92836i	−0.106919	+	0.0897156i
$463$	−14.1353	−	24.4830i	−0.656921	−	1.13782i	−0.981409	−	0.191931i	$-0.938525\pi$
$463$	−14.1353	−	24.4830i	−0.656921	−	1.13782i	0.324487	−	0.945890i	$-0.394808\pi$
$464$	8.78115	−	15.2094i	0.407655	−	0.706079i
$465$	−1.90045	−	10.7780i	−0.0881314	−	0.499818i
$466$	−1.27219	−	7.21494i	−0.0589330	−	0.334225i
$467$	7.97214	−	13.8081i	0.368906	−	0.638965i	−0.620488	−	0.784216i	$-0.713066\pi$
$467$	7.97214	−	13.8081i	0.368906	−	0.638965i	0.989395	+	0.145251i	$0.0463989\pi$
$468$	0.881966	+	1.52761i	0.0407689	+	0.0706138i
$469$	16.0869	−	13.4985i	0.742826	−	0.623305i
$470$	14.7609	−	5.37252i	0.680869	−	0.247816i
$471$	−6.40838	−	2.33246i	−0.295283	−	0.107474i
$472$	−0.558822	−	0.468907i	−0.0257219	−	0.0215832i
$473$	0.0409928	−	0.232482i	0.00188485	−	0.0106895i
$474$	−8.29180			−0.380855
$475$		0			0
$476$	1.41641			0.0649209
$477$	−3.13534	+	17.7814i	−0.143558	+	0.814155i
$478$	0.404367	+	0.339304i	0.0184953	+	0.0155194i
$479$	−21.6977	−	7.89730i	−0.991391	−	0.360837i	−0.205133	−	0.978734i	$-0.565763\pi$
$479$	−21.6977	−	7.89730i	−0.991391	−	0.360837i	−0.786259	+	0.617897i	$0.787985\pi$
$480$	3.92823	−	1.42976i	0.179299	−	0.0652593i
$481$	−6.78264	+	5.69131i	−0.309262	+	0.259501i
$482$	−2.57295	−	4.45648i	−0.117195	−	0.202987i
$483$	3.08359	−	5.34094i	0.140308	−	0.243021i
$484$	−0.899557	−	5.10164i	−0.0408889	−	0.231893i
$485$	−7.78514	−	44.1517i	−0.353505	−	2.00483i
$486$	−7.80902	+	13.5256i	−0.354224	+	0.613534i
$487$	2.09017	+	3.62028i	0.0947146	+	0.164051i	0.909489	−	0.415727i	$-0.136473\pi$
$487$	2.09017	+	3.62028i	0.0947146	+	0.164051i	−0.814775	+	0.579778i	$0.803139\pi$
$488$	−17.5336	+	14.7125i	−0.793711	+	0.666002i
$489$	0.633129	−	0.230440i	0.0286311	−	0.0104209i
$490$	9.84059	+	3.58168i	0.444552	+	0.161804i
$491$	−16.2515	−	13.6366i	−0.733418	−	0.615411i	0.197643	−	0.980274i	$-0.436671\pi$
$491$	−16.2515	−	13.6366i	−0.733418	−	0.615411i	−0.931061	+	0.364863i	$0.881116\pi$
$492$	−0.122978	+	0.697445i	−0.00554429	+	0.0314432i
$493$	2.76393			0.124481
$494$		0			0
$495$	14.9443			0.671695
$496$	−7.46318	+	42.3258i	−0.335106	+	1.90048i
$497$	17.1720	+	14.4090i	0.770268	+	0.646331i
$498$	−4.92029	−	1.79084i	−0.220484	−	0.0802495i
$499$	−23.6094	+	8.59312i	−1.05690	+	0.384681i	−0.811264	−	0.584680i	$-0.801220\pi$
$499$	−23.6094	+	8.59312i	−1.05690	+	0.384681i	−0.245639	+	0.969361i	$0.578998\pi$
$500$	0.723354	−	0.606966i	0.0323494	−	0.0271444i
$501$	−3.86475	−	6.69393i	−0.172664	−	0.299063i
$502$	−20.5172	+	35.5369i	−0.915728	+	1.58609i
$503$	6.22230	+	35.2884i	0.277439	+	1.57343i	0.731107	+	0.682263i	$0.239004\pi$
$503$	6.22230	+	35.2884i	0.277439	+	1.57343i	−0.453668	+	0.891171i	$0.649885\pi$
$504$	−3.32465	−	18.8550i	−0.148092	−	0.839870i
$505$	14.8541	−	25.7281i	0.660999	−	1.14488i
$506$	−7.04508	−	12.2024i	−0.313192	−	0.542465i
$507$	3.51124	−	2.94628i	0.155939	−	0.130849i
$508$	3.34747	−	1.21838i	0.148520	−	0.0540569i
$509$	1.91175	+	0.695820i	0.0847368	+	0.0308417i	0.384041	−	0.923316i	$-0.374532\pi$
$509$	1.91175	+	0.695820i	0.0847368	+	0.0308417i	−0.299304	+	0.954158i	$0.596754\pi$
$510$	1.17041	+	0.982092i	0.0518267	+	0.0434878i
$511$	−1.41082	+	8.00118i	−0.0624112	+	0.353951i
$512$	5.29180			0.233867
$513$		0			0
$514$	32.9443			1.45311
$515$	−8.05045	+	45.6564i	−0.354745	+	2.01186i
$516$	0.0263840	+	0.0221388i	0.00116149	+	0.000974606i
$517$	4.56136	+	1.66020i	0.200609	+	0.0730155i
$518$	−40.3868	+	14.6996i	−1.77449	+	0.645863i
$519$	−0.138148	+	0.115920i	−0.00606404	+	0.00508833i
$520$	−3.61803	−	6.26662i	−0.158661	−	0.274809i
$521$	3.13525	−	5.43042i	0.137358	−	0.237911i	−0.789138	−	0.614216i	$-0.789472\pi$
$521$	3.13525	−	5.43042i	0.137358	−	0.237911i	0.926496	+	0.376305i	$0.122806\pi$
$522$	2.90135	+	16.4544i	0.126989	+	0.720188i
$523$	0.766901	+	4.34931i	0.0335342	+	0.190182i	0.996973	−	0.0777457i	$-0.0247722\pi$
$523$	0.766901	+	4.34931i	0.0335342	+	0.190182i	−0.963439	+	0.267928i	$0.913661\pi$
$524$	−4.66312	+	8.07676i	−0.203709	+	0.352835i
$525$	3.13525	+	5.43042i	0.136834	+	0.237003i
$526$	18.5232	−	15.5428i	0.807651	−	0.677699i
$527$	−6.35602	+	2.31340i	−0.276872	+	0.100773i
$528$	2.81908	+	1.02606i	0.122685	+	0.0446535i
$529$	4.56988	+	3.83459i	0.198691	+	0.166721i
$530$	−5.75203	+	32.6214i	−0.249852	+	1.41698i
$531$	0.931116			0.0404070
$532$		0			0
$533$	3.00000			0.129944
$534$	0.833229	−	4.72548i	0.0360573	−	0.204491i
$535$	−40.6958	−	34.1478i	−1.75943	−	1.47634i
$536$	−14.7085	−	5.35346i	−0.635311	−	0.231234i
$537$	−4.39190	+	1.59852i	−0.189524	+	0.0689813i
$538$	37.5889	−	31.5409i	1.62057	−	1.35982i
$539$	1.61803	+	2.80252i	0.0696937	+	0.120713i
$540$	−2.23607	+	3.87298i	−0.0962250	+	0.166667i
$541$	−5.18041	−	29.3796i	−0.222723	−	1.26313i	−0.866990	−	0.498326i	$-0.833948\pi$
$541$	−5.18041	−	29.3796i	−0.222723	−	1.26313i	0.644266	−	0.764801i	$-0.277163\pi$
$542$	−0.321961	−	1.82593i	−0.0138294	−	0.0784306i
$543$	−2.29180	+	3.96951i	−0.0983504	+	0.170348i
$544$	−1.29180	−	2.23746i	−0.0553853	−	0.0959302i
$545$	8.16027	−	6.84728i	0.349548	−	0.293305i
$546$	−1.74229	+	0.634140i	−0.0745630	+	0.0271387i
$547$	−25.2993	−	9.20820i	−1.08172	−	0.393714i	−0.261173	−	0.965292i	$-0.584109\pi$
$547$	−25.2993	−	9.20820i	−1.08172	−	0.393714i	−0.820548	+	0.571578i	$0.806332\pi$
$548$	3.53762	+	2.96842i	0.151120	+	0.126804i
$549$	5.07309	−	28.7709i	0.216514	−	1.22791i
$550$	14.3262			0.610873
$551$		0			0
$552$	−4.59675			−0.195651
$553$	−6.98920	+	39.6377i	−0.297211	+	1.68557i
$554$	−14.1505	−	11.8737i	−0.601196	−	0.504463i
$555$	−10.2843	−	3.74316i	−0.436542	−	0.158888i
$556$	−8.59433	+	3.12808i	−0.364481	+	0.132660i
$557$	−0.627896	+	0.526867i	−0.0266048	+	0.0223241i	−0.655993	−	0.754767i	$-0.727750\pi$
$557$	−0.627896	+	0.526867i	−0.0266048	+	0.0223241i	0.629388	+	0.777091i	$0.283306\pi$
$558$	−20.4443	−	35.4105i	−0.865475	−	1.49905i
$559$	0.0729490	−	0.126351i	0.00308541	−	0.00534409i
$560$	−8.18310	−	46.4087i	−0.345799	−	1.96112i
$561$	0.0819855	+	0.464963i	0.00346143	+	0.0196308i
$562$	23.8713	−	41.3463i	1.00695	−	1.74409i
$563$	−16.4164	−	28.4341i	−0.691869	−	1.19835i	−0.971225	−	0.238165i	$-0.923454\pi$
$563$	−16.4164	−	28.4341i	−0.691869	−	1.19835i	0.279356	−	0.960188i	$-0.409879\pi$
$564$	−0.542516	+	0.455225i	−0.0228440	+	0.0191684i
$565$	20.5685	−	7.48632i	0.865323	−	0.314952i
$566$	39.5842	+	14.4075i	1.66385	+	0.605591i
$567$	17.7145	+	14.8642i	0.743938	+	0.624238i
$568$	2.90135	−	16.4544i	0.121738	−	0.690410i
$569$	−16.9098			−0.708897			−0.354448	−	0.935076i	$-0.615331\pi$
$569$	−16.9098			−0.708897			−0.354448	+	0.935076i	$0.615331\pi$
$570$		0			0
$571$	6.67376			0.279288			0.139644	−	0.990202i	$-0.455404\pi$
$571$	6.67376			0.279288			0.139644	+	0.990202i	$0.455404\pi$
$572$	−0.173648	+	0.984808i	−0.00726060	+	0.0411769i
$573$	−4.16552	−	3.49528i	−0.174017	−	0.146018i
$574$	13.6841	+	4.98060i	0.571163	+	0.207886i
$575$	−27.6747	+	10.0728i	−1.15412	+	0.420064i
$576$	−9.26161	+	7.77141i	−0.385900	+	0.323809i
$577$	6.06231	+	10.5002i	0.252377	+	0.437130i	0.964180	−	0.265250i	$-0.0854543\pi$
$577$	6.06231	+	10.5002i	0.252377	+	0.437130i	−0.711803	+	0.702379i	$0.752121\pi$
$578$	−13.2812	+	23.0036i	−0.552423	+	0.956825i
$579$	0.335335	+	1.90178i	0.0139360	+	0.0790352i
$580$	1.25653	+	7.12614i	0.0521746	+	0.295897i
$581$	−12.7082	+	22.0113i	−0.527225	+	0.913181i
$582$	4.28115	+	7.41517i	0.177459	+	0.307369i
$583$	−7.84128	+	6.57962i	−0.324753	+	0.272500i
$584$	5.69052	−	2.07118i	0.235476	−	0.0857061i
$585$	8.67906	+	3.15892i	0.358835	+	0.130605i
$586$	−12.5757	−	10.5523i	−0.519497	−	0.435910i
$587$	−0.368935	+	2.09233i	−0.0152276	+	0.0863599i	−0.991474	−	0.130301i	$-0.958406\pi$
$587$	−0.368935	+	2.09233i	−0.0152276	+	0.0863599i	0.976247	+	0.216661i	$0.0695167\pi$
$588$	−0.472136			−0.0194706
$589$		0			0
$590$	1.70820			0.0703256
$591$	−0.198983	+	1.12849i	−0.00818507	+	0.0464198i
$592$	32.9236	+	27.6262i	1.35315	+	1.13543i
$593$	−0.665494	−	0.242220i	−0.0273286	−	0.00994678i	0.328320	−	0.944567i	$-0.393518\pi$
$593$	−0.665494	−	0.242220i	−0.0273286	−	0.00994678i	−0.355648	+	0.934620i	$0.615740\pi$
$594$	−5.50106	+	2.00222i	−0.225711	+	0.0821521i
$595$	5.68130	−	4.76718i	0.232911	−	0.195435i
$596$	0.590170	+	1.02220i	0.0241743	+	0.0418711i
$597$	−2.56231	+	4.43804i	−0.104868	+	0.181637i
$598$	−1.51216	−	8.57591i	−0.0618370	−	0.350695i
$599$	−4.93446	−	27.9847i	−0.201616	−	1.14342i	−0.902676	−	0.430321i	$-0.858400\pi$
$599$	−4.93446	−	27.9847i	−0.201616	−	1.14342i	0.701059	−	0.713103i	$-0.252711\pi$
$600$	2.33688	−	4.04760i	0.0954028	−	0.165242i
$601$	10.1459	+	17.5732i	0.413860	+	0.716826i	0.995308	−	0.0967572i	$-0.0308470\pi$
$601$	10.1459	+	17.5732i	0.413860	+	0.716826i	−0.581448	+	0.813583i	$0.697514\pi$
$602$	0.542516	−	0.455225i	0.0221113	−	0.0185536i
$603$	18.7738	−	6.83312i	0.764530	−	0.278266i
$604$	−12.2484	−	4.45804i	−0.498379	−	0.181395i
$605$	−20.7787	−	17.4354i	−0.844773	−	0.708848i
$606$	−0.985238	+	5.58756i	−0.0400226	+	0.226979i
$607$	6.27051			0.254512			0.127256	−	0.991870i	$-0.459383\pi$
$607$	6.27051			0.254512			0.127256	+	0.991870i	$0.459383\pi$
$608$		0			0
$609$	−4.14590			−0.168000
$610$	9.30698	−	52.7825i	0.376829	−	2.13710i
$611$	2.29813	+	1.92836i	0.0929725	+	0.0780132i
$612$	1.26626	+	0.460880i	0.0511855	+	0.0186300i
$613$	18.7415	−	6.82134i	0.756961	−	0.275511i	0.0654294	−	0.997857i	$-0.479158\pi$
$613$	18.7415	−	6.82134i	0.756961	−	0.275511i	0.691532	+	0.722346i	$0.256936\pi$
$614$	−21.4756	+	18.0202i	−0.866686	+	0.727236i
$615$	1.85410	+	3.21140i	0.0747646	+	0.129496i
$616$	5.42705	−	9.39993i	0.218662	−	0.378734i
$617$	1.33253	+	7.55718i	0.0536458	+	0.304241i	0.999811	−	0.0194437i	$-0.00618952\pi$
$617$	1.33253	+	7.55718i	0.0536458	+	0.304241i	−0.946165	+	0.323684i	$0.895078\pi$
$618$	−1.53750	−	8.71959i	−0.0618473	−	0.350753i
$619$	−5.06231	+	8.76817i	−0.203471	+	0.352423i	−0.949645	−	0.313329i	$-0.898556\pi$
$619$	−5.06231	+	8.76817i	−0.203471	+	0.352423i	0.746173	+	0.665752i	$0.231889\pi$
$620$	−8.85410	−	15.3358i	−0.355589	−	0.615899i
$621$	9.21892	−	7.73559i	0.369942	−	0.310419i
$622$	19.2375	−	7.00188i	0.771354	−	0.280750i
$623$	−21.8871	−	7.96626i	−0.876889	−	0.319162i
$624$	1.42032	+	1.19179i	0.0568585	+	0.0477099i
$625$	−3.89257	+	22.0759i	−0.155703	+	0.883034i
$626$	18.3262			0.732464
$627$		0			0
$628$	−11.0344			−0.440322
$629$	−1.17454	+	6.66117i	−0.0468322	+	0.265598i
$630$	34.3439	+	28.8180i	1.36829	+	1.14814i
$631$	−27.5900	−	10.0419i	−1.09834	−	0.399763i	−0.271637	−	0.962400i	$-0.587565\pi$
$631$	−27.5900	−	10.0419i	−1.09834	−	0.399763i	−0.826704	+	0.562636i	$0.809787\pi$
$632$	28.1908	−	10.2606i	1.12137	−	0.408145i
$633$	−1.12772	+	0.946271i	−0.0448229	+	0.0376109i
$634$	−14.5623	−	25.2227i	−0.578343	−	1.00172i
$635$	9.32624	−	16.1535i	0.370100	−	0.641033i
$636$	−0.259330	−	1.47073i	−0.0102831	−	0.0583184i
$637$	0.347296	+	1.96962i	0.0137604	+	0.0780390i
$638$	−4.73607	+	8.20311i	−0.187503	+	0.324764i
$639$	10.6631	+	18.4691i	0.421826	+	0.730625i
$640$	−33.7587	+	28.3269i	−1.33443	+	1.11972i
$641$	−37.1240	+	13.5120i	−1.46631	+	0.533694i	−0.947096	−	0.320950i	$-0.895998\pi$
$641$	−37.1240	+	13.5120i	−1.46631	+	0.533694i	−0.519215	+	0.854644i	$0.673776\pi$
$642$	9.53403	+	3.47010i	0.376278	+	0.136954i
$643$	−18.6086	−	15.6145i	−0.733851	−	0.615774i	0.197327	−	0.980338i	$-0.436774\pi$
$643$	−18.6086	−	15.6145i	−0.733851	−	0.615774i	−0.931179	+	0.364563i	$0.881218\pi$
$644$	1.73279	−	9.82711i	0.0682813	−	0.387243i
$645$	0.180340			0.00710088
$646$		0			0
$647$	7.47214			0.293760			0.146880	−	0.989154i	$-0.453077\pi$
$647$	7.47214			0.293760			0.146880	+	0.989154i	$0.453077\pi$
$648$	2.99301	−	16.9742i	0.117577	−	0.666810i
$649$	0.404367	+	0.339304i	0.0158728	+	0.0133189i
$650$	8.32013	+	3.02828i	0.326343	+	0.118779i
$651$	9.53403	−	3.47010i	0.373668	−	0.136004i
$652$	0.835119	−	0.700748i	0.0327058	−	0.0274434i
$653$	11.7812	+	20.4056i	0.461032	+	0.798531i	0.999013	−	0.0444262i	$-0.0141459\pi$
$653$	11.7812	+	20.4056i	0.461032	+	0.798531i	−0.537981	+	0.842957i	$0.680813\pi$
$654$	−1.01722	+	1.76188i	−0.0397765	+	0.0688949i
$655$	8.47973	+	48.0909i	0.331330	+	1.87907i
$656$	−2.52872	−	14.3411i	−0.0987298	−	0.559925i
$657$	−3.86475	+	6.69393i	−0.150778	+	0.261155i
$658$	7.28115	+	12.6113i	0.283849	+	0.491641i
$659$	19.7464	−	16.5692i	0.769210	−	0.645444i	−0.171296	−	0.985220i	$-0.554796\pi$
$659$	19.7464	−	16.5692i	0.769210	−	0.645444i	0.940507	+	0.339775i	$0.110351\pi$
$660$	−1.16152	+	0.422760i	−0.0452123	+	0.0164559i
$661$	5.08976	+	1.85252i	0.197969	+	0.0720547i	0.439102	−	0.898437i	$-0.355297\pi$
$661$	5.08976	+	1.85252i	0.197969	+	0.0720547i	−0.241133	+	0.970492i	$0.577519\pi$
$662$	13.5653	+	11.3826i	0.527229	+	0.442398i
$663$	−0.0506699	+	0.287363i	−0.00196785	+	0.0111603i
$664$	18.9443			0.735180
$665$		0			0
$666$	−40.8885			−1.58440
$667$	3.38130	−	19.1763i	0.130924	−	0.742510i
$668$	−9.58059	−	8.03907i	−0.370684	−	0.311041i
$669$	4.18243	+	1.52228i	0.161702	+	0.0588548i
$670$	34.4421	−	12.5359i	1.33061	−	0.484303i
$671$	12.6875	−	10.6460i	0.489794	−	0.410986i
$672$	1.93769	+	3.35618i	0.0747482	+	0.129468i
$673$	17.0623	−	29.5528i	0.657704	−	1.13918i	−0.323505	−	0.946226i	$-0.604861\pi$
$673$	17.0623	−	29.5528i	0.657704	−	1.13918i	0.981209	−	0.192950i	$-0.0618054\pi$
$674$	−4.81148	−	27.2873i	−0.185331	−	1.05107i
$675$	2.12477	+	12.0502i	0.0817825	+	0.463811i
$676$	3.70820	−	6.42280i	0.142623	−	0.247031i
$677$	−15.3713	−	26.6239i	−0.590768	−	1.02324i	−0.994129	−	0.108199i	$-0.965492\pi$
$677$	−15.3713	−	26.6239i	−0.590768	−	1.02324i	0.403361	−	0.915041i	$-0.367842\pi$
$678$	−3.20233	+	2.68707i	−0.122985	+	0.103196i
$679$	39.0558	−	14.2151i	1.49882	−	0.545527i
$680$	−5.19449	−	1.89064i	−0.199200	−	0.0725028i
$681$	4.80349	+	4.03061i	0.184070	+	0.154453i
$682$	4.02522	−	22.8282i	0.154134	−	0.874136i
$683$	−9.65248			−0.369342			−0.184671	−	0.982800i	$-0.559122\pi$
$683$	−9.65248			−0.369342			−0.184671	+	0.982800i	$0.559122\pi$
$684$		0			0
$685$	24.1803			0.923883
$686$	4.21453	−	23.9018i	0.160911	−	0.912574i
$687$	3.98468	+	3.34354i	0.152025	+	0.127564i
$688$	−0.665494	−	0.242220i	−0.0253717	−	0.00923455i
$689$	−5.94472	+	2.16370i	−0.226476	+	0.0824304i
$690$	8.24565	−	6.91892i	0.313907	−	0.263399i
$691$	19.5902	+	33.9312i	0.745245	+	1.29080i	0.950080	+	0.312006i	$0.101001\pi$
$691$	19.5902	+	33.9312i	0.745245	+	1.29080i	−0.204835	+	0.978797i	$0.565666\pi$
$692$	−0.145898	+	0.252703i	−0.00554621	+	0.00960632i
$693$	2.40574	+	13.6436i	0.0913865	+	0.518279i
$694$	7.14121	+	40.4998i	0.271077	+	1.53735i
$695$	−23.9443	+	41.4727i	−0.908258	+	1.57315i
$696$	1.54508	+	2.67617i	0.0585663	+	0.101440i
$697$	1.75562	−	1.47314i	0.0664988	−	0.0557991i
$698$	−31.8972	+	11.6096i	−1.20733	+	0.439431i
$699$	1.62519	+	0.591520i	0.0614703	+	0.0223734i
$700$	7.77221	+	6.52166i	0.293762	+	0.246495i
$701$	−6.88188	+	39.0291i	−0.259925	+	1.47411i	0.523181	+	0.852221i	$0.324745\pi$
$701$	−6.88188	+	39.0291i	−0.259925	+	1.47411i	−0.783107	+	0.621888i	$0.786366\pi$
$702$	−3.61803			−0.136554
$703$		0			0
$704$	−6.85410			−0.258324
$705$	−0.643923	+	3.65187i	−0.0242515	+	0.137537i
$706$	−30.3065	−	25.4302i	−1.14060	−	0.957077i
$707$	25.8801	+	9.41958i	0.973321	+	0.354260i
$708$	−0.0723698	+	0.0263405i	−0.00271982	+	0.000989935i
$709$	12.7038	−	10.6597i	0.477100	−	0.400334i	−0.372276	−	0.928122i	$-0.621423\pi$
$709$	12.7038	−	10.6597i	0.477100	−	0.400334i	0.849377	+	0.527787i	$0.176978\pi$
$710$	19.5623	+	33.8829i	0.734160	+	1.27160i
$711$	−19.1459	+	33.1617i	−0.718027	+	1.24366i
$712$	3.01465	+	17.0969i	0.112979	+	0.640735i
$713$	8.27477	+	46.9285i	0.309892	+	1.75749i
$714$	−0.708204	+	1.22665i	−0.0265039	+	0.0459060i
$715$	2.61803	+	4.53457i	0.0979089	+	0.169583i
$716$	−5.79306	+	4.86096i	−0.216497	+	0.181662i
$717$	−0.117097	+	0.0426197i	−0.00437306	+	0.00159166i
$718$	10.6955	+	3.89286i	0.399154	+	0.145280i
$719$	36.0305	+	30.2332i	1.34371	+	1.12751i	0.980656	+	0.195738i	$0.0627103\pi$
$719$	36.0305	+	30.2332i	1.34371	+	1.12751i	0.363054	+	0.931768i	$0.381734\pi$
$720$	7.78514	−	44.1517i	0.290135	−	1.64544i
$721$	−42.9787			−1.60061
$722$		0			0
$723$	1.21478			0.0451782
$724$	−1.28785	+	7.30374i	−0.0478624	+	0.271441i
$725$	15.1664	+	12.7261i	0.563267	+	0.472637i
$726$	4.86793	+	1.77178i	0.180666	+	0.0657569i
$727$	15.0998	−	5.49588i	0.560021	−	0.203831i	−0.0464723	−	0.998920i	$-0.514798\pi$
$727$	15.0998	−	5.49588i	0.560021	−	0.203831i	0.606493	+	0.795089i	$0.292576\pi$
$728$	5.13878	−	4.31195i	0.190456	−	0.159812i
$729$	9.71885	+	16.8335i	0.359957	+	0.623464i
$730$	−7.09017	+	12.2805i	−0.262419	+	0.454523i
$731$	−0.0193542	−	0.109763i	−0.000715840	−	0.00405973i
$732$	0.419605	+	2.37970i	0.0155090	+	0.0879561i
$733$	26.4787	−	45.8625i	0.978014	−	1.69397i	0.308405	−	0.951255i	$-0.400205\pi$
$733$	26.4787	−	45.8625i	0.978014	−	1.69397i	0.669609	−	0.742714i	$-0.266462\pi$
$734$	−12.8992	−	22.3420i	−0.476118	−	0.824660i
$735$	−1.89377	+	1.58906i	−0.0698526	+	0.0586133i
$736$	−17.1039	+	6.22532i	−0.630459	+	0.229468i
$737$	10.6432	+	3.87380i	0.392047	+	0.142693i
$738$	10.6129	+	8.90525i	0.390665	+	0.327807i
$739$	−4.34120	+	24.6202i	−0.159694	+	0.905668i	0.794674	+	0.607036i	$0.207642\pi$
$739$	−4.34120	+	24.6202i	−0.159694	+	0.905668i	−0.954368	+	0.298633i	$0.903470\pi$
$740$	−17.7082			−0.650967
$741$		0			0
$742$	−30.7082			−1.12733
$743$	0.583576	−	3.30962i	0.0214093	−	0.121418i	−0.972230	−	0.234027i	$-0.924810\pi$
$743$	0.583576	−	3.30962i	0.0214093	−	0.121418i	0.993639	+	0.112609i	$0.0359207\pi$
$744$	−5.79306	−	4.86096i	−0.212384	−	0.178211i
$745$	5.80762	+	2.11380i	0.212775	+	0.0774437i
$746$	8.32013	−	3.02828i	0.304622	−	0.110873i
$747$	−18.5232	+	15.5428i	−0.677729	+	0.568682i
$748$	0.381966	+	0.661585i	0.0139661	+	0.0241899i
$749$	24.6246	−	42.6511i	0.899764	−	1.55844i
$750$	0.163971	+	0.929926i	0.00598738	+	0.0339561i
$751$	2.97735	+	16.8854i	0.108645	+	0.616157i	0.989702	+	0.143146i	$0.0457219\pi$
$751$	2.97735	+	16.8854i	0.108645	+	0.616157i	−0.881056	+	0.473011i	$0.843167\pi$
$752$	7.28115	−	12.6113i	0.265516	−	0.459888i
$753$	−4.84346	−	8.38912i	−0.176505	−	0.305716i
$754$	−4.48450	+	3.76294i	−0.163316	+	0.137038i
$755$	−64.1333	+	23.3426i	−2.33405	+	0.849525i
$756$	−3.89587	−	1.41798i	−0.141691	−	0.0515715i
$757$	20.4861	+	17.1898i	0.744578	+	0.624775i	0.934063	−	0.357108i	$-0.116237\pi$
$757$	20.4861	+	17.1898i	0.744578	+	0.624775i	−0.189485	+	0.981884i	$0.560682\pi$
$758$	−4.24954	+	24.1003i	−0.154350	+	0.875364i
$759$	3.32624			0.120735
$760$		0			0
$761$	4.88854			0.177210			0.0886048	−	0.996067i	$-0.471759\pi$
$761$	4.88854			0.177210			0.0886048	+	0.996067i	$0.471759\pi$
$762$	−0.618588	+	3.50819i	−0.0224091	+	0.127088i
$763$	7.56499	+	6.34778i	0.273871	+	0.229805i
$764$	−8.26777	−	3.00922i	−0.299117	−	0.108870i
$765$	6.63022	−	2.41320i	0.239716	−	0.0872495i
$766$	0.473442	−	0.397265i	0.0171061	−	0.0143538i
$767$	0.163119	+	0.282530i	0.00588988	+	0.0102016i
$768$	2.59017	−	4.48631i	0.0934647	−	0.161886i
$769$	6.36094	+	36.0747i	0.229381	+	1.30089i	0.854130	+	0.520060i	$0.174090\pi$
$769$	6.36094	+	36.0747i	0.229381	+	1.30089i	−0.624748	+	0.780826i	$0.714798\pi$
$770$	4.41351	+	25.0303i	0.159052	+	0.902029i
$771$	−3.88854	+	6.73516i	−0.140042	+	0.242561i
$772$	1.56231	+	2.70599i	0.0562286	+	0.0973908i
$773$	27.5186	−	23.0909i	0.989775	−	0.830520i	0.00424018	−	0.999991i	$-0.498650\pi$
$773$	27.5186	−	23.0909i	0.989775	−	0.830520i	0.985535	+	0.169471i	$0.0542059\pi$
$774$	0.633129	−	0.230440i	0.0227574	−	0.00828300i
$775$	−45.5289	−	16.5712i	−1.63545	−	0.595254i
$776$	−23.7311	−	19.9127i	−0.851896	−	0.714825i
$777$	1.76182	−	9.99176i	0.0632048	−	0.358452i
$778$	−15.0000			−0.537776
$779$		0			0
$780$	−0.763932			−0.0273532
$781$	−2.09944	+	11.9065i	−0.0751237	+	0.426048i
$782$	−5.09609	−	4.27613i	−0.182236	−	0.152914i
$783$	−7.60227	−	2.76700i	−0.271683	−	0.0988846i
$784$	9.12273	−	3.32040i	0.325812	−	0.118586i
$785$	−44.2598	+	37.1384i	−1.57970	+	1.32553i
$786$	−4.66312	−	8.07676i	−0.166328	−	0.288088i
$787$	19.0000	−	32.9090i	0.677277	−	1.17308i	−0.298521	−	0.954403i	$-0.596493\pi$
$787$	19.0000	−	32.9090i	0.677277	−	1.17308i	0.975798	−	0.218675i	$-0.0701734\pi$
$788$	0.321961	+	1.82593i	0.0114694	+	0.0650462i
$789$	0.991219	+	5.62148i	0.0352883	+	0.200130i
$790$	−35.1246	+	60.8376i	−1.24968	+	2.16451i
$791$	10.1459	+	17.5732i	0.360747	+	0.624831i
$792$	7.91036	−	6.63758i	0.281082	−	0.235856i
$793$	9.61876	−	3.50094i	0.341572	−	0.124322i
$794$	−17.4429	−	6.34868i	−0.619024	−	0.225306i
$795$	−5.99021	−	5.02638i	−0.212451	−	0.178267i
$796$	−1.43986	+	8.16583i	−0.0510343	+	0.289430i
$797$	20.2918			0.718772			0.359386	−	0.933189i	$-0.382986\pi$
$797$	20.2918			0.718772			0.359386	+	0.933189i	$0.382986\pi$
$798$		0			0
$799$	2.29180			0.0810779
$800$	3.21363	−	18.2254i	0.113619	−	0.644366i
$801$	−16.9748	−	14.2436i	−0.599776	−	0.503272i
$802$	54.5669	+	19.8607i	1.92682	+	0.701307i
$803$	−4.11770	+	1.49872i	−0.145311	+	0.0528887i
$804$	−1.26587	+	1.06219i	−0.0446438	+	0.0374606i
$805$	−26.1246	−	45.2492i	−0.920772	−	1.59482i
$806$	7.16312	−	12.4069i	0.252310	−	0.437014i
$807$	2.01147	+	11.4076i	0.0708071	+	0.401567i
$808$	−3.56463	−	20.2160i	−0.125403	−	0.711196i
$809$	12.3992	−	21.4760i	0.435932	−	0.755057i	−0.561439	−	0.827518i	$-0.689752\pi$
$809$	12.3992	−	21.4760i	0.435932	−	0.755057i	0.997371	+	0.0724614i	$0.0230854\pi$
$810$	20.1803	+	34.9534i	0.709065	+	1.22814i
$811$	−17.6027	+	14.7704i	−0.618115	+	0.518660i	−0.897210	−	0.441603i	$-0.854410\pi$
$811$	−17.6027	+	14.7704i	−0.618115	+	0.518660i	0.279095	+	0.960263i	$0.409965\pi$
$812$	−6.30365	+	2.29434i	−0.221215	+	0.0805156i
$813$	0.411298	+	0.149700i	0.0144248	+	0.00525022i
$814$	−17.7572	−	14.9000i	−0.622389	−	0.522246i
$815$	0.991219	−	5.62148i	0.0347209	−	0.196912i
$816$	1.41641			0.0495842
$817$		0			0
$818$	−13.4164			−0.469094
$819$	−1.48683	+	8.43223i	−0.0519540	+	0.294646i
$820$	4.59627	+	3.85673i	0.160509	+	0.134683i
$821$	−48.9087	−	17.8013i	−1.70693	−	0.621271i	−0.710343	−	0.703856i	$-0.751460\pi$
$821$	−48.9087	−	17.8013i	−1.70693	−	0.621271i	−0.996584	+	0.0825852i	$0.973682\pi$
$822$	−4.33953	+	1.57946i	−0.151359	+	0.0550900i
$823$	−19.6082	+	16.4533i	−0.683501	+	0.573525i	−0.917027	−	0.398825i	$-0.869418\pi$
$823$	−19.6082	+	16.4533i	−0.683501	+	0.573525i	0.233526	+	0.972350i	$0.424973\pi$
$824$	16.0172	+	27.7426i	0.557986	+	0.966461i
$825$	−1.69098	+	2.92887i	−0.0588725	+	0.101970i
$826$	0.274988	+	1.55953i	0.00956805	+	0.0542631i
$827$	−5.66037	−	32.1015i	−0.196830	−	1.11628i	−0.909788	−	0.415073i	$-0.863756\pi$
$827$	−5.66037	−	32.1015i	−0.196830	−	1.11628i	0.712958	−	0.701207i	$-0.247355\pi$
$828$	4.74671	−	8.22154i	0.164960	−	0.285718i
$829$	2.33688	+	4.04760i	0.0811632	+	0.140579i	0.903750	−	0.428061i	$-0.140803\pi$
$829$	2.33688	+	4.04760i	0.0811632	+	0.140579i	−0.822587	+	0.568640i	$0.807470\pi$
$830$	−33.9823	+	28.5145i	−1.17954	+	0.989753i
$831$	4.09770	−	1.49144i	0.142148	−	0.0517375i
$832$	−3.98060	−	1.44882i	−0.138003	−	0.0502288i
$833$	1.17041	+	0.982092i	0.0405524	+	0.0340275i
$834$	1.58817	−	9.00695i	0.0549938	−	0.311885i
$835$	−65.4853			−2.26621
$836$		0			0
$837$	19.7984			0.684332
$838$	2.51306	−	14.2523i	0.0868122	−	0.492337i
$839$	−11.6451	−	9.77142i	−0.402034	−	0.337347i	0.419245	−	0.907873i	$-0.362295\pi$
$839$	−11.6451	−	9.77142i	−0.402034	−	0.337347i	−0.821279	+	0.570526i	$0.806739\pi$
$840$	7.79174	+	2.83596i	0.268841	+	0.0978500i
$841$	14.9503	−	5.44148i	0.515529	−	0.187637i
$842$	−34.0513	+	28.5725i	−1.17349	+	0.984672i
$843$	5.63525	+	9.76055i	0.194088	+	0.336171i
$844$	−1.19098	+	2.06284i	−0.0409953	+	0.0710060i
$845$	−6.74325	−	38.2429i	−0.231975	−	1.31559i
$846$	2.40574	+	13.6436i	0.0827110	+	0.469078i
$847$	12.5729	−	21.7770i	0.432012	−	0.748266i
$848$	15.3541	+	26.5941i	0.527262	+	0.913245i
$849$	−7.61775	+	6.39205i	−0.261441	+	0.219375i
$850$	6.35602	−	2.31340i	0.218010	−	0.0793490i
$851$	44.7787	+	16.2981i	1.53499	+	0.558692i
$852$	−1.35125	−	1.13383i	−0.0462931	−	0.0388445i
$853$	5.33242	−	30.2417i	0.182579	−	1.03546i	−0.746448	−	0.665443i	$-0.768242\pi$
$853$	5.33242	−	30.2417i	0.182579	−	1.03546i	0.929027	−	0.370012i	$-0.120646\pi$
$854$	49.6869			1.70025
$855$		0			0
$856$	−36.7082			−1.25466
$857$	1.84380	−	10.4567i	0.0629831	−	0.357195i	−0.936986	−	0.349366i	$-0.886397\pi$
$857$	1.84380	−	10.4567i	0.0629831	−	0.357195i	0.999969	−	0.00782864i	$-0.00249196\pi$
$858$	−0.766044	−	0.642788i	−0.0261523	−	0.0219444i
$859$	45.6136	+	16.6020i	1.55632	+	0.566453i	0.969889	−	0.243548i	$-0.0783113\pi$
$859$	45.6136	+	16.6020i	1.55632	+	0.566453i	0.586428	+	0.810001i	$0.300534\pi$
$860$	0.274199	−	0.0998001i	0.00935010	−	0.00340316i
$861$	−2.63343	+	2.20971i	−0.0897469	+	0.0753066i
$862$	−22.3713	−	38.7483i	−0.761970	−	1.31977i
$863$	−13.5279	+	23.4309i	−0.460494	+	0.797599i	−0.998986	−	0.0450321i	$-0.985661\pi$
$863$	−13.5279	+	23.4309i	−0.460494	+	0.797599i	0.538492	+	0.842631i	$0.318994\pi$
$864$	1.31318	+	7.44742i	0.0446753	+	0.253366i
$865$	0.265311	+	1.50465i	0.00902084	+	0.0511597i
$866$	2.78115	−	4.81710i	0.0945074	−	0.163692i
$867$	−3.13525	−	5.43042i	−0.106479	−	0.184427i
$868$	12.5757	−	10.5523i	0.426847	−	0.358167i
$869$	−20.3990	+	7.42464i	−0.691990	+	0.251864i
$870$	−6.79968	−	2.47488i	−0.230531	−	0.0839063i
$871$	5.36231	+	4.49951i	0.181695	+	0.152460i
$872$	1.27817	−	7.24885i	0.0432843	−	0.245477i
$873$	39.5410			1.33826
$874$		0			0
$875$	4.58359			0.154954
$876$	0.111017	−	0.629608i	0.00375091	−	0.0212725i
$877$	−9.05438	−	7.59753i	−0.305745	−	0.256550i	0.476986	−	0.878911i	$-0.341729\pi$
$877$	−9.05438	−	7.59753i	−0.305745	−	0.256550i	−0.782731	+	0.622361i	$0.786174\pi$
$878$	52.6028	+	19.1458i	1.77526	+	0.646141i
$879$	3.64167	−	1.32546i	0.122831	−	0.0447067i
$880$	19.4701	−	16.3374i	0.656337	−	0.550732i
$881$	−16.2254	−	28.1033i	−0.546648	−	0.946823i	−0.998501	−	0.0547303i	$-0.982570\pi$
$881$	−16.2254	−	28.1033i	−0.546648	−	0.946823i	0.451853	−	0.892093i	$-0.350763\pi$
$882$	−4.61803	+	7.99867i	−0.155497	+	0.269329i
$883$	−8.84268	−	50.1494i	−0.297580	−	1.68766i	−0.656527	−	0.754302i	$-0.727975\pi$
$883$	−8.84268	−	50.1494i	−0.297580	−	1.68766i	0.358947	−	0.933358i	$-0.383136\pi$
$884$	0.0819855	+	0.464963i	0.00275747	+	0.0156384i
$885$	−0.201626	+	0.349227i	−0.00677759	+	0.0117391i
$886$	−6.13525	−	10.6266i	−0.206118	−	0.357007i
$887$	−20.9494	+	17.5786i	−0.703413	+	0.590233i	−0.922742	−	0.385418i	$-0.874057\pi$
$887$	−20.9494	+	17.5786i	−0.703413	+	0.590233i	0.219330	+	0.975651i	$0.429613\pi$
$888$	−7.10624	+	2.58646i	−0.238470	+	0.0867959i
$889$	16.2490	+	5.91414i	0.544973	+	0.198354i
$890$	−31.1416	−	26.1309i	−1.04387	−	0.875910i
$891$	−2.16576	+	12.2827i	−0.0725558	+	0.411484i
$892$	7.20163			0.241128
$893$		0			0
$894$	−1.18034			−0.0394765
$895$	−6.87590	+	38.9952i	−0.229836	+	1.30347i
$896$	−31.2961	−	26.2605i	−1.04553	−	0.877302i
$897$	1.93175	+	0.703100i	0.0644993	+	0.0234758i
$898$	−4.39190	+	1.59852i	−0.146560	+	0.0533433i
$899$	24.5398	−	20.5913i	0.818448	−	0.686760i
$900$	4.82624	+	8.35929i	0.160875	+	0.278643i
$901$	−2.41641	+	4.18534i	−0.0805022	+	0.139434i
$902$	1.36385	+	7.73478i	0.0454113	+	0.257540i
$903$	0.0290312	+	0.164644i	0.000966099	+	0.00547902i
$904$	7.56231	−	13.0983i	0.251519	−	0.435643i
$905$	19.4164	+	33.6302i	0.645423	+	1.11791i
$906$	9.98496	−	8.37838i	0.331728	−	0.278353i
$907$	−24.8757	+	9.05400i	−0.825983	+	0.300633i	−0.720209	−	0.693757i	$-0.755954\pi$
$907$	−24.8757	+	9.05400i	−0.825983	+	0.300633i	−0.105774	+	0.994390i	$0.533732\pi$
$908$	9.53403	+	3.47010i	0.316398	+	0.115159i
$909$	20.0716	+	16.8421i	0.665733	+	0.558617i
$910$	−2.72770	+	15.4696i	−0.0904224	+	0.512811i
$911$	−3.38197			−0.112050			−0.0560248	−	0.998429i	$-0.517843\pi$
$911$	−3.38197			−0.112050			−0.0560248	+	0.998429i	$0.517843\pi$
$912$		0			0
$913$	−13.7082			−0.453675
$914$	−5.53739	+	31.4041i	−0.183160	+	1.03875i
$915$	9.69236	+	8.13285i	0.320419	+	0.268864i
$916$	7.90884	+	2.87858i	0.261315	+	0.0951110i
$917$	−42.5404	+	15.4834i	−1.40481	+	0.511308i
$918$	−2.11729	+	1.77662i	−0.0698811	+	0.0586372i
$919$	−11.6459	−	20.1713i	−0.384163	−	0.665389i	0.607490	−	0.794327i	$-0.292177\pi$
$919$	−11.6459	−	20.1713i	−0.384163	−	0.665389i	−0.991653	+	0.128938i	$0.958843\pi$
$920$	−19.4721	+	33.7267i	−0.641977	+	1.11194i
$921$	−1.14921	−	6.51749i	−0.0378677	−	0.214759i
$922$	−5.88468	−	33.3737i	−0.193802	−	1.09910i
$923$	−3.73607	+	6.47106i	−0.122974	+	0.212998i
$924$	−0.572949	−	0.992377i	−0.0188486	−	0.0326468i
$925$	−37.1155	+	31.1436i	−1.22035	+	1.02400i
$926$	42.9840	−	15.6449i	1.41254	−	0.514124i
$927$	−38.4227	−	13.9847i	−1.26197	−	0.459318i
$928$	9.37337	+	7.86519i	0.307696	+	0.258188i
$929$	2.84470	−	16.1331i	0.0933315	−	0.529309i	−0.901914	−	0.431915i	$-0.857838\pi$
$929$	2.84470	−	16.1331i	0.0933315	−	0.529309i	0.995246	−	0.0973944i	$-0.0310508\pi$
$930$	17.7082			0.580675
$931$		0			0
$932$	2.79837			0.0916638
$933$	−0.839210	+	4.75939i	−0.0274745	+	0.155816i
$934$	19.7627	+	16.5829i	0.646655	+	0.542608i
$935$	3.75877	+	1.36808i	0.122925	+	0.0447410i
$936$	5.99709	−	2.18276i	0.196021	−	0.0713458i
$937$	31.0725	−	26.0729i	1.01510	−	0.851766i	0.0260920	−	0.999660i	$-0.491694\pi$
$937$	31.0725	−	26.0729i	1.01510	−	0.851766i	0.989003	+	0.147893i	$0.0472493\pi$
$938$	16.9894	+	29.4264i	0.554722	+	0.960807i
$939$	−2.16312	+	3.74663i	−0.0705907	+	0.122267i
$940$	1.04189	+	5.90885i	0.0339827	+	0.192725i
$941$	1.85576	+	10.5246i	0.0604962	+	0.343091i	1.00000		0.000552015i	$0.000175712\pi$
$941$	1.85576	+	10.5246i	0.0604962	+	0.343091i	−0.939504	+	0.342539i	$0.888713\pi$
$942$	5.51722	−	9.55611i	0.179761	−	0.311355i
$943$	−8.07295	−	13.9828i	−0.262891	−	0.455341i
$944$	1.21310	−	1.01791i	0.0394831	−	0.0331303i
$945$	−20.3990	+	7.42464i	−0.663581	+	0.241524i
$946$	0.358931	+	0.130640i	0.0116698	+	0.00424748i
$947$	−25.0132	−	20.9886i	−0.812821	−	0.682038i	0.138458	−	0.990368i	$-0.455785\pi$
$947$	−25.0132	−	20.9886i	−0.812821	−	0.682038i	−0.951279	+	0.308330i	$0.900230\pi$
$948$	0.549976	−	3.11907i	0.0178624	−	0.101303i
$949$	−2.70820			−0.0879120
$950$		0			0
$951$	6.87539			0.222950
$952$	0.889879	−	5.04676i	0.0288412	−	0.163566i
$953$	−13.2463	−	11.1150i	−0.429089	−	0.360049i	0.402519	−	0.915412i	$-0.368135\pi$
$953$	−13.2463	−	11.1150i	−0.429089	−	0.360049i	−0.831608	+	0.555363i	$0.812579\pi$
$954$	−27.4529	−	9.99204i	−0.888821	−	0.323504i
$955$	−43.2906	+	15.7565i	−1.40085	+	0.509868i
$956$	−0.154455	+	0.129603i	−0.00499542	+	0.00419165i
$957$	−1.11803	−	1.93649i	−0.0361409	−	0.0625979i
$958$	18.6803	−	32.3553i	0.603534	−	1.04535i
$959$	3.89257	+	22.0759i	0.125698	+	0.712866i
$960$	−0.909234	−	5.15652i	−0.0293454	−	0.166426i
$961$	−23.6976	+	41.0454i	−0.764437	+	1.32404i
$962$	−7.16312	−	12.4069i	−0.230948	−	0.400014i
$963$	35.8923	−	30.1172i	1.15661	−	0.970514i
$964$	1.84702	−	0.672260i	0.0594885	−	0.0216521i
$965$	15.3740	+	5.59568i	0.494907	+	0.180131i
$966$	7.64414	+	6.41419i	0.245946	+	0.206373i
$967$	1.13584	−	6.44165i	0.0365260	−	0.207149i	−0.961083	−	0.276260i	$-0.910905\pi$
$967$	1.13584	−	6.44165i	0.0365260	−	0.207149i	0.997609	+	0.0691104i	$0.0220161\pi$
$968$	−18.7426			−0.602411
$969$		0			0
$970$	72.5410			2.32915
$971$	−4.08187	+	23.1495i	−0.130994	+	0.742902i	0.846573	+	0.532273i	$0.178662\pi$
$971$	−4.08187	+	23.1495i	−0.130994	+	0.742902i	−0.977566	+	0.210628i	$0.932449\pi$
$972$	−4.56988	−	3.83459i	−0.146579	−	0.122994i
$973$	−41.7178	−	15.1840i	−1.33741	−	0.486778i
$974$	−6.35602	+	2.31340i	−0.203660	+	0.0741261i
$975$	−1.60116	+	1.34354i	−0.0512783	+	0.0430276i
$976$	−24.8435	−	43.0301i	−0.795220	−	1.37736i
$977$	5.31966	−	9.21392i	0.170191	−	0.294779i	−0.768296	−	0.640095i	$-0.778895\pi$
$977$	5.31966	−	9.21392i	0.170191	−	0.294779i	0.938487	+	0.345316i	$0.112228\pi$
$978$	0.189306	+	1.07361i	0.00605334	+	0.0343302i
$979$	−2.18142	−	12.3715i	−0.0697185	−	0.395393i
$980$	−2.00000	+	3.46410i	−0.0638877	+	0.110657i
$981$	4.69756	+	8.13641i	0.149982	+	0.259776i
$982$	26.2954	−	22.0645i	0.839121	−	0.704106i
$983$	30.6509	−	11.1560i	0.977613	−	0.355822i	0.196701	−	0.980463i	$-0.436977\pi$
$983$	30.6509	−	11.1560i	0.977613	−	0.355822i	0.780912	+	0.624642i	$0.214755\pi$
$984$	2.40778	+	0.876360i	0.0767572	+	0.0279373i
$985$	7.43692	+	6.24031i	0.236960	+	0.198833i
$986$	−0.776578	+	4.40419i	−0.0247313	+	0.140258i
$987$	−3.43769			−0.109423
$988$		0			0
$989$	−0.785218			−0.0249685
$990$	−4.19887	+	23.8130i	−0.133449	+	0.756826i
$991$	−5.70768	−	4.78931i	−0.181310	−	0.152138i	0.547615	−	0.836730i	$-0.315536\pi$
$991$	−5.70768	−	4.78931i	−0.181310	−	0.152138i	−0.728926	+	0.684593i	$0.759980\pi$
$992$	−28.1384	−	10.2415i	−0.893395	−	0.325169i
$993$	−3.92823	+	1.42976i	−0.124659	+	0.0453721i
$994$	−27.7848	+	23.3142i	−0.881281	+	0.739483i
$995$	21.7082	+	37.5997i	0.688196	+	1.19199i
$996$	1.00000	−	1.73205i	0.0316862	−	0.0548821i
$997$	6.89526	+	39.1049i	0.218375	+	1.23847i	0.874953	+	0.484208i	$0.160892\pi$
$997$	6.89526	+	39.1049i	0.218375	+	1.23847i	−0.656578	+	0.754258i	$0.727997\pi$
$998$	−7.05923	−	40.0349i	−0.223456	−	1.26728i
$999$	9.89919	−	17.1459i	0.313196	−	0.542472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.i.245.1		12
19.2	odd	18		361.2.c.d.68.1		4
19.3	odd	18		361.2.a.f.1.2	yes	2
19.4	even	9	inner	361.2.e.i.234.1		12
19.5	even	9		361.2.c.g.292.2		4
19.6	even	9	inner	361.2.e.i.99.2		12
19.7	even	3	inner	361.2.e.i.54.1		12
19.8	odd	6		361.2.e.j.62.1		12
19.9	even	9	inner	361.2.e.i.28.1		12
19.10	odd	18		361.2.e.j.28.2		12
19.11	even	3	inner	361.2.e.i.62.2		12
19.12	odd	6		361.2.e.j.54.2		12
19.13	odd	18		361.2.e.j.99.1		12
19.14	odd	18		361.2.c.d.292.1		4
19.15	odd	18		361.2.e.j.234.2		12
19.16	even	9		361.2.a.c.1.1	✓	2
19.17	even	9		361.2.c.g.68.2		4
19.18	odd	2		361.2.e.j.245.2		12
57.35	odd	18		3249.2.a.o.1.2		2
57.41	even	18		3249.2.a.i.1.1		2
76.3	even	18		5776.2.a.s.1.2		2
76.35	odd	18		5776.2.a.bg.1.1		2
95.54	even	18		9025.2.a.s.1.2		2
95.79	odd	18		9025.2.a.n.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.a.c.1.1	✓	2	19.16	even	9
361.2.a.f.1.2	yes	2	19.3	odd	18
361.2.c.d.68.1		4	19.2	odd	18
361.2.c.d.292.1		4	19.14	odd	18
361.2.c.g.68.2		4	19.17	even	9
361.2.c.g.292.2		4	19.5	even	9
361.2.e.i.28.1		12	19.9	even	9	inner
361.2.e.i.54.1		12	19.7	even	3	inner
361.2.e.i.62.2		12	19.11	even	3	inner
361.2.e.i.99.2		12	19.6	even	9	inner
361.2.e.i.234.1		12	19.4	even	9	inner
361.2.e.i.245.1		12	1.1	even	1	trivial
361.2.e.j.28.2		12	19.10	odd	18
361.2.e.j.54.2		12	19.12	odd	6
361.2.e.j.62.1		12	19.8	odd	6
361.2.e.j.99.1		12	19.13	odd	18
361.2.e.j.234.2		12	19.15	odd	18
361.2.e.j.245.2		12	19.18	odd	2
3249.2.a.i.1.1		2	57.41	even	18
3249.2.a.o.1.2		2	57.35	odd	18
5776.2.a.s.1.2		2	76.3	even	18
5776.2.a.bg.1.1		2	76.35	odd	18
9025.2.a.n.1.1		2	95.79	odd	18
9025.2.a.s.1.2		2	95.54	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.280969 + 1.59345i) q^{2} +(-0.292603 - 0.245523i) q^{3} +(-0.580762 - 0.211380i) q^{4} +(-3.04091 + 1.10680i) q^{5} +(0.473442 - 0.397265i) q^{6} +(-1.50000 - 2.59808i) q^{7} +(-1.11803 + 1.93649i) q^{8} +(-0.495610 - 2.81074i) q^{9} +(-0.909234 - 5.15652i) q^{10} +(0.809017 - 1.40126i) q^{11} +(0.118034 + 0.204441i) q^{12} +(0.766044 - 0.642788i) q^{13} +(4.56136 - 1.66020i) q^{14} +(1.16152 + 0.422760i) q^{15} +(-3.71846 - 3.12016i) q^{16} +(0.132655 - 0.752326i) q^{17} +4.61803 q^{18} +2.00000 q^{20} +(-0.198983 + 1.12849i) q^{21} +(2.00553 + 1.68284i) q^{22} +(-5.05739 - 1.84074i) q^{23} +(0.802593 - 0.292120i) q^{24} +(4.19190 - 3.51742i) q^{25} +(0.809017 + 1.40126i) q^{26} +(-1.11803 + 1.93649i) q^{27} +(0.321961 + 1.82593i) q^{28} +(0.628265 + 3.56307i) q^{29} +(-1.00000 + 1.73205i) q^{30} +(-4.42705 - 7.66788i) q^{31} +(2.59074 - 2.17389i) q^{32} +(-0.580762 + 0.211380i) q^{33} +(1.16152 + 0.422760i) q^{34} +(7.43692 + 6.24031i) q^{35} +(-0.306304 + 1.73713i) q^{36} -8.85410 q^{37} -0.381966 q^{39} +(1.25653 - 7.12614i) q^{40} +(2.29813 + 1.92836i) q^{41} +(-1.74229 - 0.634140i) q^{42} +(0.137099 - 0.0499001i) q^{43} +(-0.766044 + 0.642788i) q^{44} +(4.61803 + 7.99867i) q^{45} +(4.35410 - 7.54153i) q^{46} +(0.520945 + 2.95442i) q^{47} +(0.321961 + 1.82593i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(4.42705 + 7.66788i) q^{50} +(-0.223529 + 0.187563i) q^{51} +(-0.580762 + 0.211380i) q^{52} +(-5.94472 - 2.16370i) q^{53} +(-2.77157 - 2.32563i) q^{54} +(-0.909234 + 5.15652i) q^{55} +6.70820 q^{56} -5.85410 q^{58} +(-0.0566506 + 0.321282i) q^{59} +(-0.585206 - 0.491046i) q^{60} +(9.61876 + 3.50094i) q^{61} +(13.4623 - 4.89986i) q^{62} +(-6.55911 + 5.50374i) q^{63} +(-2.11803 - 3.66854i) q^{64} +(-1.61803 + 2.80252i) q^{65} +(-0.173648 - 0.984808i) q^{66} +(1.21554 + 6.89365i) q^{67} +(-0.236068 + 0.408882i) q^{68} +(1.02786 + 1.78031i) q^{69} +(-12.0332 + 10.0970i) q^{70} +(-7.02151 + 2.55562i) q^{71} +(5.99709 + 2.18276i) q^{72} +(-2.07460 - 1.74080i) q^{73} +(2.48773 - 14.1086i) q^{74} -2.09017 q^{75} -4.85410 q^{77} +(0.107320 - 0.608645i) q^{78} +(-10.2776 - 8.62390i) q^{79} +(14.7609 + 5.37252i) q^{80} +(-7.24334 + 2.63636i) q^{81} +(-3.71846 + 3.12016i) q^{82} +(-4.23607 - 7.33708i) q^{83} +(0.354102 - 0.613323i) q^{84} +(0.429282 + 2.43458i) q^{85} +(0.0409928 + 0.232482i) q^{86} +(0.690983 - 1.19682i) q^{87} +(1.80902 + 3.13331i) q^{88} +(5.94752 - 4.99056i) q^{89} +(-14.0430 + 5.11124i) q^{90} +(-2.81908 - 1.02606i) q^{91} +(2.54805 + 2.13806i) q^{92} +(-0.587272 + 3.33059i) q^{93} -4.85410 q^{94} -1.29180 q^{96} +(-2.40574 + 13.6436i) q^{97} +(-2.47897 - 2.08010i) q^{98} +(-4.33953 - 1.57946i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{7} + 3 q^{11} - 12 q^{12} + 42 q^{18} + 24 q^{20} + 3 q^{26} - 12 q^{30} - 33 q^{31} - 66 q^{37} - 18 q^{39} + 42 q^{45} + 12 q^{46} - 12 q^{49} + 33 q^{50} - 30 q^{58} - 12 q^{64} - 6 q^{65}+ \cdots - 96 q^{96}+O(q^{100}) \) 12 * q - 18 * q^7 + 3 * q^11 - 12 * q^12 + 42 * q^18 + 24 * q^20 + 3 * q^26 - 12 * q^30 - 33 * q^31 - 66 * q^37 - 18 * q^39 + 42 * q^45 + 12 * q^46 - 12 * q^49 + 33 * q^50 - 30 * q^58 - 12 * q^64 - 6 * q^65 + 24 * q^68 + 66 * q^69 + 42 * q^75 - 18 * q^77 - 24 * q^83 - 36 * q^84 + 15 * q^87 + 15 * q^88 - 18 * q^94 - 96 * q^96

Introduction

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