LMFDB - Embedded newform 378.2.bf.a.101.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,2,Mod(5,378)] 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("378.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([5, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.bf (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.23
Character	$\chi$	$=$	378.101
Dual form			378.2.bf.a.131.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.642788 - 0.766044i) q^{2} +(1.51729 + 0.835363i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.65868 + 1.39179i) q^{5} +(1.61522 - 0.625351i) q^{6} +(1.78250 + 1.95517i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.60434 + 2.53498i) q^{9} +2.16525i q^{10} +(3.26445 - 3.89043i) q^{11} +(0.559197 - 1.63930i) q^{12} +(-1.92117 + 5.27837i) q^{13} +(2.64352 - 0.108713i) q^{14} +(-3.67934 + 0.726159i) q^{15} +(-0.939693 + 0.342020i) q^{16} +3.40603 q^{17} +(2.97315 + 0.400457i) q^{18} -5.51607i q^{19} +(1.65868 + 1.39179i) q^{20} +(1.07129 + 4.45560i) q^{21} +(-0.881888 - 5.00144i) q^{22} +(0.908716 - 2.49668i) q^{23} +(-0.896330 - 1.48209i) q^{24} +(-0.0541269 + 0.306969i) q^{25} +(2.80856 + 4.86457i) q^{26} +(0.316622 + 5.18650i) q^{27} +(1.61594 - 2.09493i) q^{28} +(-1.75522 - 4.82244i) q^{29} +(-1.80877 + 3.28531i) q^{30} +(-8.84310 + 1.55928i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(8.20304 - 3.17590i) q^{33} +(2.18935 - 2.60917i) q^{34} +(-5.67778 - 0.762124i) q^{35} +(2.21787 - 2.02016i) q^{36} +(2.24681 - 3.89159i) q^{37} +(-4.22555 - 3.54566i) q^{38} +(-7.32432 + 6.40394i) q^{39} +(2.13235 - 0.375991i) q^{40} +(-5.62761 - 2.04828i) q^{41} +(4.10180 + 2.04335i) q^{42} +(-0.146227 + 0.829295i) q^{43} +(-4.39819 - 2.53930i) q^{44} +(-6.18924 - 1.97179i) q^{45} +(-1.32845 - 2.30095i) q^{46} +(0.707350 - 4.01158i) q^{47} +(-1.71150 - 0.266041i) q^{48} +(-0.645395 + 6.97018i) q^{49} +(0.200360 + 0.238780i) q^{50} +(5.16793 + 2.84527i) q^{51} +(5.53178 + 0.975403i) q^{52} +(-4.18277 - 2.41492i) q^{53} +(4.17661 + 3.09127i) q^{54} +10.9964i q^{55} +(-0.566103 - 2.58448i) q^{56} +(4.60792 - 8.36947i) q^{57} +(-4.82244 - 1.75522i) q^{58} +(-1.18858 - 0.432607i) q^{59} +(1.35404 + 3.49735i) q^{60} +(-1.81769 - 0.320508i) q^{61} +(-4.48976 + 7.77649i) q^{62} +(-2.09658 + 7.65535i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-4.15980 - 11.4290i) q^{65} +(2.83993 - 8.32532i) q^{66} +(9.46485 - 7.94195i) q^{67} +(-0.591450 - 3.35428i) q^{68} +(3.46442 - 3.02907i) q^{69} +(-4.23343 + 3.85955i) q^{70} +(-0.143652 + 0.0829375i) q^{71} +(-0.121910 - 2.99752i) q^{72} +(-3.45044 + 1.99211i) q^{73} +(-1.53691 - 4.22263i) q^{74} +(-0.338557 + 0.420546i) q^{75} +(-5.43227 + 0.957855i) q^{76} +(13.4253 - 0.552110i) q^{77} +(0.197720 + 9.72713i) q^{78} +(-6.36875 - 5.34402i) q^{79} +(1.08262 - 1.87516i) q^{80} +(-3.85220 + 8.13391i) q^{81} +(-5.18644 + 2.99439i) q^{82} +(12.0275 - 4.37766i) q^{83} +(4.20188 - 1.82872i) q^{84} +(-5.64949 + 4.74049i) q^{85} +(0.541284 + 0.645077i) q^{86} +(1.36530 - 8.78329i) q^{87} +(-4.77231 + 1.73698i) q^{88} +6.94743 q^{89} +(-5.48885 + 3.47379i) q^{90} +(-13.7446 + 5.65247i) q^{91} +(-2.61654 - 0.461367i) q^{92} +(-14.7201 - 5.02132i) q^{93} +(-2.61837 - 3.12046i) q^{94} +(7.67723 + 9.14937i) q^{95} +(-1.30393 + 1.14008i) q^{96} +(14.0018 + 2.46890i) q^{97} +(4.92462 + 4.97475i) q^{98} +(15.0994 + 2.03375i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51}+ \cdots - 108 q^{99}+O(q^{100}) $ 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	1.51729	+	0.835363i	0.876008	+	0.482297i
$3$	1.51729	+	0.835363i	0.876008	+	0.482297i
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	−1.65868	+	1.39179i	−0.741782	+	0.622429i	−0.933316	−	0.359057i	$-0.883098\pi$
$5$	−1.65868	+	1.39179i	−0.741782	+	0.622429i	0.191533	+	0.981486i	$0.438654\pi$
$6$	1.61522	−	0.625351i	0.659411	−	0.255298i
$7$	1.78250	+	1.95517i	0.673721	+	0.738986i
$7$	1.78250	+	1.95517i	0.673721	+	0.738986i
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	1.60434	+	2.53498i	0.534779	+	0.844992i
$10$			2.16525i			0.684711i
$11$	3.26445	−	3.89043i	0.984270	−	1.17301i	−0.000650268	−	1.00000i	$-0.500207\pi$
$11$	3.26445	−	3.89043i	0.984270	−	1.17301i	0.984920	−	0.173008i	$-0.0553486\pi$
$12$	0.559197	−	1.63930i	0.161426	−	0.473225i
$13$	−1.92117	+	5.27837i	−0.532836	+	1.46396i	0.322845	+	0.946452i	$0.395361\pi$
$13$	−1.92117	+	5.27837i	−0.532836	+	1.46396i	−0.855681	+	0.517504i	$0.826861\pi$
$14$	2.64352	−	0.108713i	0.706510	−	0.0290548i
$15$	−3.67934	+	0.726159i	−0.950003	+	0.187494i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	3.40603			0.826083			0.413041	−	0.910712i	$-0.364467\pi$
$17$	3.40603			0.826083			0.413041	+	0.910712i	$0.364467\pi$
$18$	2.97315	+	0.400457i	0.700779	+	0.0943885i
$19$		−	5.51607i		−	1.26547i	−0.774367	−	0.632736i	$-0.781932\pi$
$19$		−	5.51607i		−	1.26547i	0.774367	−	0.632736i	$-0.218068\pi$
$20$	1.65868	+	1.39179i	0.370891	+	0.311215i
$21$	1.07129	+	4.45560i	0.233775	+	0.972291i
$22$	−0.881888	−	5.00144i	−0.188019	−	1.06631i
$23$	0.908716	−	2.49668i	0.189480	−	0.520593i	−0.808182	−	0.588933i	$-0.799548\pi$
$23$	0.908716	−	2.49668i	0.189480	−	0.520593i	0.997662	+	0.0683402i	$0.0217703\pi$
$24$	−0.896330	−	1.48209i	−0.182963	−	0.302530i
$25$	−0.0541269	+	0.306969i	−0.0108254	+	0.0613938i
$26$	2.80856	+	4.86457i	0.550804	+	0.954020i
$27$	0.316622	+	5.18650i	0.0609339	+	0.998142i
$28$	1.61594	−	2.09493i	0.305384	−	0.395905i
$29$	−1.75522	−	4.82244i	−0.325937	−	0.895504i	−0.989128	−	0.147055i	$-0.953021\pi$
$29$	−1.75522	−	4.82244i	−0.325937	−	0.895504i	0.663191	−	0.748450i	$-0.269202\pi$
$30$	−1.80877	+	3.28531i	−0.330234	+	0.599812i
$31$	−8.84310	+	1.55928i	−1.58827	+	0.280054i	−0.896828	−	0.442380i	$-0.854134\pi$
$31$	−8.84310	+	1.55928i	−1.58827	+	0.280054i	−0.691439	+	0.722434i	$0.743023\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	8.20304	−	3.17590i	1.42797	−	0.552853i
$34$	2.18935	−	2.60917i	0.375471	−	0.447468i
$35$	−5.67778	−	0.762124i	−0.959721	−	0.128823i
$36$	2.21787	−	2.02016i	0.369645	−	0.336693i
$37$	2.24681	−	3.89159i	0.369374	−	0.639774i	−0.620094	−	0.784528i	$-0.712906\pi$
$37$	2.24681	−	3.89159i	0.369374	−	0.639774i	0.989468	+	0.144753i	$0.0462389\pi$
$38$	−4.22555	−	3.54566i	−0.685475	−	0.575182i
$39$	−7.32432	+	6.40394i	−1.17283	+	1.02545i
$40$	2.13235	−	0.375991i	0.337154	−	0.0594494i
$41$	−5.62761	−	2.04828i	−0.878885	−	0.319888i	−0.137126	−	0.990554i	$-0.543786\pi$
$41$	−5.62761	−	2.04828i	−0.878885	−	0.319888i	−0.741760	+	0.670666i	$0.766009\pi$
$42$	4.10180	+	2.04335i	0.632921	+	0.315295i
$43$	−0.146227	+	0.829295i	−0.0222994	+	0.126466i	−0.993925	−	0.110057i	$-0.964897\pi$
$43$	−0.146227	+	0.829295i	−0.0222994	+	0.126466i	0.971626	+	0.236523i	$0.0760079\pi$
$44$	−4.39819	−	2.53930i	−0.663052	−	0.382813i
$45$	−6.18924	−	1.97179i	−0.922637	−	0.293938i
$46$	−1.32845	−	2.30095i	−0.195870	−	0.339256i
$47$	0.707350	−	4.01158i	0.103178	−	0.585149i	−0.888755	−	0.458383i	$-0.848429\pi$
$47$	0.707350	−	4.01158i	0.103178	−	0.585149i	0.991933	−	0.126767i	$-0.0404599\pi$
$48$	−1.71150	−	0.266041i	−0.247033	−	0.0383996i
$49$	−0.645395	+	6.97018i	−0.0921992	+	0.995741i
$50$	0.200360	+	0.238780i	0.0283352	+	0.0337685i
$51$	5.16793	+	2.84527i	0.723655	+	0.398417i
$52$	5.53178	+	0.975403i	0.767120	+	0.135264i
$53$	−4.18277	−	2.41492i	−0.574547	−	0.331715i	0.184416	−	0.982848i	$-0.440961\pi$
$53$	−4.18277	−	2.41492i	−0.574547	−	0.331715i	−0.758963	+	0.651133i	$0.774294\pi$
$54$	4.17661	+	3.09127i	0.568364	+	0.420668i
$55$			10.9964i			1.48275i
$56$	−0.566103	−	2.58448i	−0.0756488	−	0.345365i
$57$	4.60792	−	8.36947i	0.610334	−	1.10856i
$58$	−4.82244	−	1.75522i	−0.633217	−	0.230472i
$59$	−1.18858	−	0.432607i	−0.154740	−	0.0563207i	0.263489	−	0.964662i	$-0.415127\pi$
$59$	−1.18858	−	0.432607i	−0.154740	−	0.0563207i	−0.418229	+	0.908342i	$0.637349\pi$
$60$	1.35404	+	3.49735i	0.174806	+	0.451506i
$61$	−1.81769	−	0.320508i	−0.232732	−	0.0410369i	0.0560659	−	0.998427i	$-0.482144\pi$
$61$	−1.81769	−	0.320508i	−0.232732	−	0.0410369i	−0.288797	+	0.957390i	$0.593255\pi$
$62$	−4.48976	+	7.77649i	−0.570200	+	0.987615i
$63$	−2.09658	+	7.65535i	−0.264144	+	0.964483i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−4.15980	−	11.4290i	−0.515960	−	1.41759i
$66$	2.83993	−	8.32532i	0.349572	−	1.02478i
$67$	9.46485	−	7.94195i	1.15632	−	0.970264i	0.156467	−	0.987683i	$-0.449989\pi$
$67$	9.46485	−	7.94195i	1.15632	−	0.970264i	0.999848	+	0.0174194i	$0.00554505\pi$
$68$	−0.591450	−	3.35428i	−0.0717239	−	0.406766i
$69$	3.46442	−	3.02907i	0.417067	−	0.364658i
$70$	−4.23343	+	3.85955i	−0.505992	+	0.461305i
$71$	−0.143652	+	0.0829375i	−0.0170483	+	0.00984287i	−0.508500	−	0.861062i	$-0.669800\pi$
$71$	−0.143652	+	0.0829375i	−0.0170483	+	0.00984287i	0.491452	+	0.870905i	$0.336466\pi$
$72$	−0.121910	−	2.99752i	−0.0143672	−	0.353261i
$73$	−3.45044	+	1.99211i	−0.403843	+	0.233159i	−0.688141	−	0.725577i	$-0.741573\pi$
$73$	−3.45044	+	1.99211i	−0.403843	+	0.233159i	0.284298	+	0.958736i	$0.408240\pi$
$74$	−1.53691	−	4.22263i	−0.178662	−	0.490871i
$75$	−0.338557	+	0.420546i	−0.0390932	+	0.0485604i
$76$	−5.43227	+	0.957855i	−0.623124	+	0.109874i
$77$	13.4253	−	0.552110i	1.52996	−	0.0629187i
$78$	0.197720	+	9.72713i	0.0223874	+	1.10138i
$79$	−6.36875	−	5.34402i	−0.716540	−	0.601249i	0.209886	−	0.977726i	$-0.432691\pi$
$79$	−6.36875	−	5.34402i	−0.716540	−	0.601249i	−0.926426	+	0.376477i	$0.877135\pi$
$80$	1.08262	−	1.87516i	0.121041	−	0.209649i
$81$	−3.85220	+	8.13391i	−0.428022	+	0.903768i
$82$	−5.18644	+	2.99439i	−0.572746	+	0.330675i
$83$	12.0275	−	4.37766i	1.32019	−	0.480510i	0.416672	−	0.909057i	$-0.363196\pi$
$83$	12.0275	−	4.37766i	1.32019	−	0.480510i	0.903520	+	0.428546i	$0.140974\pi$
$84$	4.20188	−	1.82872i	0.458462	−	0.199530i
$85$	−5.64949	+	4.74049i	−0.612773	+	0.514178i
$86$	0.541284	+	0.645077i	0.0583681	+	0.0695604i
$87$	1.36530	−	8.78329i	0.146376	−	0.941667i
$88$	−4.77231	+	1.73698i	−0.508730	+	0.185163i
$89$	6.94743			0.736426			0.368213	−	0.929741i	$-0.379970\pi$
$89$	6.94743			0.736426			0.368213	+	0.929741i	$0.379970\pi$
$90$	−5.48885	+	3.47379i	−0.578575	+	0.366169i
$91$	−13.7446	+	5.65247i	−1.44082	+	0.592540i
$92$	−2.61654	−	0.461367i	−0.272793	−	0.0481008i
$93$	−14.7201	−	5.02132i	−1.52640	−	0.520687i
$94$	−2.61837	−	3.12046i	−0.270065	−	0.321850i
$95$	7.67723	+	9.14937i	0.787667	+	0.938705i
$96$	−1.30393	+	1.14008i	−0.133082	+	0.116358i
$97$	14.0018	+	2.46890i	1.42167	+	0.250679i	0.831018	−	0.556246i	$-0.187759\pi$
$97$	14.0018	+	2.46890i	1.42167	+	0.250679i	0.590654	+	0.806925i	$0.298870\pi$
$98$	4.92462	+	4.97475i	0.497462	+	0.502526i
$99$	15.0994	+	2.03375i	1.51755	+	0.204400i
$100$	0.311705			0.0311705
$101$	−12.0039	+	4.36907i	−1.19443	+	0.434738i	−0.861278	−	0.508133i	$-0.830336\pi$
$101$	−12.0039	+	4.36907i	−1.19443	+	0.434738i	−0.333156	+	0.942872i	$0.608114\pi$
$102$	5.50148	−	2.12996i	0.544728	−	0.210898i
$103$	−1.40776	−	1.67770i	−0.138711	−	0.165309i	0.692217	−	0.721689i	$-0.256634\pi$
$103$	−1.40776	−	1.67770i	−0.138711	−	0.165309i	−0.830928	+	0.556381i	$0.812190\pi$
$104$	4.30296	−	3.61062i	0.421940	−	0.354050i
$105$	−7.97819	−	5.89937i	−0.778592	−	0.575720i
$106$	−4.53857	+	1.65190i	−0.440825	+	0.160447i
$107$	−3.51277	+	2.02810i	−0.339592	+	0.196064i	−0.660092	−	0.751185i	$-0.729483\pi$
$107$	−3.51277	+	2.02810i	−0.339592	+	0.196064i	0.320499	+	0.947249i	$0.396149\pi$
$108$	5.05272	−	1.21244i	0.486198	−	0.116667i
$109$	−4.69202	+	8.12682i	−0.449414	+	0.778408i	−0.998348	−	0.0574575i	$-0.981701\pi$
$109$	−4.69202	+	8.12682i	−0.449414	+	0.778408i	0.548934	+	0.835866i	$0.315034\pi$
$110$	8.42373	+	7.06835i	0.803171	+	0.673941i
$111$	6.65996	−	4.02777i	0.632136	−	0.382299i
$112$	−2.34371	−	1.22761i	−0.221460	−	0.115998i
$113$	−16.2342	+	2.86253i	−1.52718	+	0.269284i	−0.873252	−	0.487269i	$-0.837993\pi$
$113$	−16.2342	+	2.86253i	−1.52718	+	0.269284i	−0.653933	+	0.756553i	$0.726882\pi$
$114$	−3.44948	−	8.90966i	−0.323073	−	0.834466i
$115$	1.96759	+	5.40592i	0.183479	+	0.504105i
$116$	−4.44438	+	2.56597i	−0.412651	+	0.238244i
$117$	−16.4627	+	3.59817i	−1.52198	+	0.332651i
$118$	−1.09540	+	0.632430i	−0.100840	+	0.0582199i
$119$	6.07124	+	6.65937i	0.556549	+	0.610463i
$120$	3.54949	+	1.21080i	0.324022	+	0.110530i
$121$	−2.56862	−	14.5674i	−0.233511	−	1.32430i
$122$	−1.41391	+	1.18641i	−0.128010	+	0.107413i
$123$	−6.82766	−	7.80894i	−0.615629	−	0.704108i
$124$	3.07118	+	8.43799i	0.275800	+	0.757753i
$125$	−5.75058	−	9.96029i	−0.514347	−	0.890876i
$126$	4.51668	+	6.52684i	0.402378	+	0.581457i
$127$	−5.40262	+	9.35761i	−0.479405	+	0.830354i	−0.999721	−	0.0236201i	$-0.992481\pi$
$127$	−5.40262	+	9.35761i	−0.479405	+	0.830354i	0.520316	+	0.853974i	$0.325814\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	−0.914631	+	1.13613i	−0.0805288	+	0.100031i
$130$	−11.4290	−	4.15980i	−1.00239	−	0.364839i
$131$	4.30565	+	1.56713i	0.376186	+	0.136921i	0.523192	−	0.852215i	$-0.324741\pi$
$131$	4.30565	+	1.56713i	0.376186	+	0.136921i	−0.147005	+	0.989136i	$0.546963\pi$
$132$	−4.55209	−	7.52693i	−0.396209	−	0.655135i
$133$	10.7849	−	9.83238i	0.935166	−	0.852576i
$134$		−	12.3555i		−	1.06735i
$135$	−7.74371	−	8.16204i	−0.666472	−	0.702477i
$136$	−2.94970	−	1.70301i	−0.252935	−	0.146032i
$137$	−18.8835	−	3.32967i	−1.61333	−	0.284473i	−0.707051	−	0.707163i	$-0.749975\pi$
$137$	−18.8835	−	3.32967i	−1.61333	−	0.284473i	−0.906274	+	0.422690i	$0.861086\pi$
$138$	−0.0935221	−	4.60095i	−0.00796113	−	0.391659i
$139$	−6.42679	−	7.65915i	−0.545113	−	0.649641i	0.421213	−	0.906962i	$-0.361605\pi$
$139$	−6.42679	−	7.65915i	−0.545113	−	0.649641i	−0.966326	+	0.257321i	$0.917160\pi$
$140$	0.235391	+	5.72387i	0.0198942	+	0.483755i
$141$	4.42438	−	5.49584i	0.372600	−	0.462833i
$142$	−0.0288039	+	0.163355i	−0.00241717	+	0.0137084i
$143$	14.2635	+	24.7052i	1.19278	+	2.06595i
$144$	−2.37460	−	1.83338i	−0.197883	−	0.152782i
$145$	9.62319	+	5.55595i	0.799162	+	0.461397i
$146$	−0.691853	+	3.92369i	−0.0572582	+	0.324727i
$147$	−6.80188	+	10.0367i	−0.561010	+	0.827809i
$148$	−4.22263	−	1.53691i	−0.347098	−	0.126333i
$149$	17.3109	−	3.05238i	1.41816	−	0.250061i	0.588578	−	0.808440i	$-0.299688\pi$
$149$	17.3109	−	3.05238i	1.41816	−	0.250061i	0.829586	+	0.558380i	$0.188577\pi$
$150$	0.104536	+	0.529671i	0.00853536	+	0.0432475i
$151$	16.2369	+	13.6244i	1.32134	+	1.10874i	0.986019	+	0.166633i	$0.0532895\pi$
$151$	16.2369	+	13.6244i	1.32134	+	1.10874i	0.335322	+	0.942104i	$0.391155\pi$
$152$	−2.75803	+	4.77705i	−0.223706	+	0.387470i
$153$	5.46442	+	8.63419i	0.441772	+	0.698033i
$154$	8.20670	−	10.6393i	0.661315	−	0.857339i
$155$	12.4976	−	14.8941i	1.00383	−	1.19632i
$156$	7.57850	+	6.10102i	0.606766	+	0.488472i
$157$	3.02853	−	8.32081i	0.241703	−	0.664073i	−0.758224	−	0.651994i	$-0.773933\pi$
$157$	3.02853	−	8.32081i	0.241703	−	0.664073i	0.999927	−	0.0120793i	$-0.00384504\pi$
$158$	−8.18751	+	1.44368i	−0.651363	+	0.114853i
$159$	−4.32914	−	7.15827i	−0.343323	−	0.567687i
$160$	−0.740558	−	2.03467i	−0.0585463	−	0.160855i
$161$	6.50122	−	2.67363i	0.512368	−	0.210711i
$162$	3.75479	+	8.17934i	0.295004	+	0.642629i
$163$	11.7958	+	20.4309i	0.923916	+	1.60027i	0.793296	+	0.608836i	$0.208363\pi$
$163$	11.7958	+	20.4309i	0.923916	+	1.60027i	0.130620	+	0.991433i	$0.458303\pi$
$164$	−1.03994	+	5.89780i	−0.0812057	+	0.460541i
$165$	−9.18599	+	16.6847i	−0.715128	+	1.29890i
$166$	4.37766	−	12.0275i	0.339772	−	0.933516i
$167$	1.56979	+	8.90272i	0.121474	+	0.688913i	0.983340	+	0.181777i	$0.0581848\pi$
$167$	1.56979	+	8.90272i	0.121474	+	0.688913i	−0.861866	+	0.507136i	$0.830704\pi$
$168$	1.30003	−	4.39430i	0.100300	−	0.339028i
$169$	−14.2117	−	11.9250i	−1.09321	−	0.917309i
$170$			7.37489i			0.565628i
$171$	13.9831	−	8.84964i	1.06931	−	0.676749i
$172$	0.842088			0.0642086
$173$	17.2210	−	6.26793i	1.30929	−	0.476542i	0.409277	−	0.912410i	$-0.365781\pi$
$173$	17.2210	−	6.26793i	1.30929	−	0.476542i	0.900010	+	0.435869i	$0.143559\pi$
$174$	−5.85079	−	6.69167i	−0.443547	−	0.507294i
$175$	−0.696659	+	0.441345i	−0.0526624	+	0.0333625i
$176$	−1.73698	+	4.77231i	−0.130930	+	0.359727i
$177$	−1.44204	−	1.64929i	−0.108390	−	0.123968i
$178$	4.46572	−	5.32204i	0.334720	−	0.398904i
$179$		−	9.73962i		−	0.727973i	−0.931404	−	0.363987i	$-0.881415\pi$
$179$		−	9.73962i		−	0.727973i	0.931404	−	0.363987i	$-0.118585\pi$
$180$	−0.867087	+	6.43761i	−0.0646289	+	0.479831i
$181$	20.4235	+	11.7915i	1.51807	+	0.876456i	0.999774	+	0.0212517i	$0.00676513\pi$
$181$	20.4235	+	11.7915i	1.51807	+	0.876456i	0.518292	+	0.855204i	$0.326568\pi$
$182$	−4.50481	+	14.1623i	−0.333919	+	1.04978i
$183$	−2.49023	−	2.00474i	−0.184083	−	0.148194i
$184$	−2.03531	+	1.70783i	−0.150045	+	0.125903i
$185$	1.68956	+	9.58199i	0.124219	+	0.704482i
$186$	−13.3085	+	8.04861i	−0.975823	+	0.590153i
$187$	11.1188	−	13.2509i	0.813088	−	0.969001i
$188$	−4.07347			−0.297088
$189$	−9.57612	+	9.86398i	−0.696560	+	0.717499i
$190$	11.9436			0.866483
$191$	3.14741	−	3.75094i	0.227739	−	0.271409i	−0.640059	−	0.768326i	$-0.721090\pi$
$191$	3.14741	−	3.75094i	0.227739	−	0.271409i	0.867798	+	0.496917i	$0.165535\pi$
$192$	0.0351996	+	1.73169i	0.00254031	+	0.124974i
$193$	−2.78463	−	15.7924i	−0.200442	−	1.13676i	−0.904453	−	0.426574i	$-0.859721\pi$
$193$	−2.78463	−	15.7924i	−0.200442	−	1.13676i	0.704011	−	0.710189i	$-0.251391\pi$
$194$	10.8915	−	9.13905i	0.781964	−	0.656146i
$195$	3.23571	−	20.8160i	0.231714	−	1.49067i
$196$	6.97636	−	0.574770i	0.498312	−	0.0410550i
$197$	7.27958	+	4.20287i	0.518649	+	0.299442i	0.736382	−	0.676566i	$-0.236533\pi$
$197$	7.27958	+	4.20287i	0.518649	+	0.299442i	−0.217733	+	0.976008i	$0.569866\pi$
$198$	11.2637	−	10.2596i	0.800474	−	0.729115i
$199$		−	22.3193i		−	1.58217i	−0.611706	−	0.791085i	$-0.709516\pi$
$199$		−	22.3193i		−	1.58217i	0.611706	−	0.791085i	$-0.290484\pi$
$200$	0.200360	−	0.238780i	0.0141676	−	0.0168843i
$201$	20.9953	−	4.14366i	1.48090	−	0.292271i
$202$	−4.36907	+	12.0039i	−0.307407	+	0.844593i
$203$	6.30001	−	12.0278i	0.442174	−	0.844183i
$204$	1.90464	−	5.58349i	0.133351	−	0.390923i
$205$	12.1852	−	4.43504i	0.851049	−	0.309757i
$206$	−2.19008			−0.152590
$207$	7.78690	−	1.70194i	0.541227	−	0.118293i
$208$		−	5.61712i		−	0.389477i
$209$	−21.4599	−	18.0070i	−1.48441	−	1.24557i
$210$	−9.64747	+	2.31961i	−0.665738	+	0.160068i
$211$	2.88308	+	16.3507i	0.198479	+	1.12563i	0.907376	+	0.420320i	$0.138082\pi$
$211$	2.88308	+	16.3507i	0.198479	+	1.12563i	−0.708897	+	0.705312i	$0.750807\pi$
$212$	−1.65190	+	4.53857i	−0.113453	+	0.311710i
$213$	−0.287244	+	0.00583873i	−0.0196817	+	0.000400063i
$214$	−0.704352	+	3.99458i	−0.0481485	+	0.273064i
$215$	−0.911665	−	1.57905i	−0.0621750	−	0.107690i
$216$	2.31905	−	4.64995i	0.157791	−	0.316389i
$217$	−18.8115	−	14.5104i	−1.27701	−	0.985028i
$218$	3.20953	+	8.81812i	0.217377	+	0.597238i
$219$	−6.89945	+	0.140243i	−0.466222	+	0.00947675i
$220$	10.8293	−	1.90951i	0.730114	−	0.128739i
$221$	−6.54355	+	17.9783i	−0.440167	+	1.20935i
$222$	1.19549	−	7.69083i	0.0802358	−	0.516175i
$223$	−8.11369	+	9.66952i	−0.543333	+	0.647519i	−0.965931	−	0.258798i	$-0.916674\pi$
$223$	−8.11369	+	9.66952i	−0.543333	+	0.647519i	0.422599	+	0.906317i	$0.361118\pi$
$224$	−2.44691	+	1.00629i	−0.163491	+	0.0672358i
$225$	−0.864997	+	0.355272i	−0.0576665	+	0.0236848i
$226$	−8.24232	+	14.2761i	−0.548271	+	0.949633i
$227$	−10.2663	−	8.61443i	−0.681397	−	0.571760i	0.235017	−	0.971991i	$-0.424485\pi$
$227$	−10.2663	−	8.61443i	−0.681397	−	0.571760i	−0.916414	+	0.400231i	$0.868930\pi$
$228$	−9.04248	−	3.08457i	−0.598853	−	0.204281i
$229$	10.1916	−	1.79706i	0.673482	−	0.118753i	0.173560	−	0.984823i	$-0.444473\pi$
$229$	10.1916	−	1.79706i	0.673482	−	0.118753i	0.499922	+	0.866070i	$0.333362\pi$
$230$	5.40592	+	1.96759i	0.356456	+	0.129739i
$231$	20.8313	+	10.3773i	1.37060	+	0.682777i
$232$	−0.891151	+	5.05397i	−0.0585069	+	0.331809i
$233$	−6.20733	−	3.58380i	−0.406656	−	0.234783i	0.282696	−	0.959210i	$-0.408771\pi$
$233$	−6.20733	−	3.58380i	−0.406656	−	0.234783i	−0.689352	+	0.724427i	$0.742105\pi$
$234$	−7.82568	+	14.9240i	−0.511581	+	0.975615i
$235$	4.41003	+	7.63840i	0.287679	+	0.498274i
$236$	−0.219641	+	1.24564i	−0.0142974	+	0.0810845i
$237$	−5.19905	−	13.4286i	−0.337714	−	0.872284i
$238$	9.00389	−	0.370280i	0.583635	−	0.0240017i
$239$	−0.439396	−	0.523652i	−0.0284222	−	0.0338722i	0.751646	−	0.659567i	$-0.229260\pi$
$239$	−0.439396	−	0.523652i	−0.0284222	−	0.0338722i	−0.780068	+	0.625694i	$0.784816\pi$
$240$	3.20909	−	1.94078i	0.207146	−	0.125277i
$241$	−3.36428	−	0.593213i	−0.216712	−	0.0382122i	0.0642378	−	0.997935i	$-0.479538\pi$
$241$	−3.36428	−	0.593213i	−0.216712	−	0.0382122i	−0.280950	+	0.959722i	$0.590649\pi$
$242$	−12.8103	−	7.39604i	−0.823478	−	0.475435i
$243$	−12.6397	+	9.12352i	−0.810835	+	0.585274i
$244$			1.84573i			0.118161i
$245$	−8.63056	−	12.4595i	−0.551386	−	0.796010i
$246$	−10.3707	+	0.210803i	−0.661214	+	0.0134403i
$247$	29.1158	+	10.5973i	1.85260	+	0.674290i
$248$	8.43799	+	3.07118i	0.535813	+	0.195020i
$249$	21.9062	+	3.40516i	1.38825	+	0.215793i
$250$	−11.3264	−	1.99715i	−0.716346	−	0.126311i
$251$	−10.7950	+	18.6976i	−0.681377	+	1.18018i	0.293184	+	0.956056i	$0.405285\pi$
$251$	−10.7950	+	18.6976i	−0.681377	+	1.18018i	−0.974561	+	0.224123i	$0.928048\pi$
$252$	7.90311	+	0.735393i	0.497849	+	0.0463254i
$253$	−6.74667	−	11.6856i	−0.424160	−	0.734666i
$254$	3.69561	+	10.1536i	0.231883	+	0.637094i
$255$	−12.5319	+	2.47332i	−0.784781	+	0.154885i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	1.21595	+	6.89600i	0.0758489	+	0.430161i	0.998959	+	0.0456240i	$0.0145276\pi$
$257$	1.21595	+	6.89600i	0.0758489	+	0.430161i	−0.923110	+	0.384537i	$0.874361\pi$
$258$	0.282411	+	1.43094i	0.0175822	+	0.0890863i
$259$	11.6137	−	2.54386i	0.721639	−	0.158068i
$260$	−10.5330	+	6.08123i	−0.653229	+	0.377142i
$261$	9.40879	−	12.1863i	0.582390	−	0.754311i
$262$	3.96811	−	2.29099i	0.245151	−	0.141538i
$263$	9.07559	+	24.9350i	0.559625	+	1.53756i	0.820184	+	0.572099i	$0.193871\pi$
$263$	9.07559	+	24.9350i	0.559625	+	1.53756i	−0.260559	+	0.965458i	$0.583907\pi$
$264$	−8.69199	−	1.35111i	−0.534955	−	0.0831551i
$265$	10.2989	−	1.81598i	0.632658	−	0.111555i
$266$	−0.599669	−	14.5818i	−0.0367681	−	0.894069i
$267$	10.5413	+	5.80363i	0.645115	+	0.355176i
$268$	−9.46485	−	7.94195i	−0.578158	−	0.485132i
$269$	−4.57551	+	7.92502i	−0.278974	+	0.483197i	−0.971130	−	0.238551i	$-0.923328\pi$
$269$	−4.57551	+	7.92502i	−0.278974	+	0.483197i	0.692156	+	0.721748i	$0.256661\pi$
$270$	−11.2300	+	0.685565i	−0.683439	+	0.0417221i
$271$	1.04350	−	0.602465i	0.0633881	−	0.0365971i	−0.467971	−	0.883744i	$-0.655015\pi$
$271$	1.04350	−	0.602465i	0.0633881	−	0.0365971i	0.531359	+	0.847147i	$0.321681\pi$
$272$	−3.20062	+	1.16493i	−0.194066	+	0.0706342i
$273$	−25.5764	−	2.90529i	−1.54795	−	0.175836i
$274$	−14.6887	+	12.3253i	−0.887380	+	0.744600i
$275$	1.01755	+	1.21266i	0.0613603	+	0.0731264i
$276$	−3.58465	−	2.88579i	−0.215770	−	0.173704i
$277$	7.71195	−	2.80692i	0.463366	−	0.168652i	−0.0997787	−	0.995010i	$-0.531813\pi$
$277$	7.71195	−	2.80692i	0.463366	−	0.168652i	0.563145	+	0.826358i	$0.309591\pi$
$278$	−9.99831			−0.599659
$279$	−18.1400	−	19.9154i	−1.08602	−	1.19231i
$280$	4.53604	+	3.49891i	0.271080	+	0.209100i
$281$	−15.5254	−	2.73755i	−0.926170	−	0.163309i	−0.309833	−	0.950791i	$-0.600273\pi$
$281$	−15.5254	−	2.73755i	−0.926170	−	0.163309i	−0.616337	+	0.787482i	$0.711384\pi$
$282$	−1.36612	−	6.92193i	−0.0813512	−	0.412195i
$283$	15.5803	+	18.5678i	0.926151	+	1.10374i	0.994358	+	0.106072i	$0.0338275\pi$
$283$	15.5803	+	18.5678i	0.926151	+	1.10374i	−0.0682078	+	0.997671i	$0.521728\pi$
$284$	0.106622	+	0.127068i	0.00632687	+	0.00754007i
$285$	4.00554	+	20.2955i	0.237268	+	1.20220i
$286$	28.0937	+	4.95367i	1.66121	+	0.292917i
$287$	−6.02647	−	14.6540i	−0.355731	−	0.864999i
$288$	−2.93081	+	0.640572i	−0.172700	+	0.0377461i
$289$	−5.39899			−0.317588
$290$	10.4418	−	3.80049i	0.613162	−	0.223173i
$291$	19.1824	+	15.4427i	1.12449	+	0.905265i
$292$	2.56101	+	3.05209i	0.149872	+	0.178610i
$293$	−19.1134	+	16.0380i	−1.11662	+	0.936952i	−0.998429	−	0.0560392i	$-0.982153\pi$
$293$	−19.1134	+	16.0380i	−1.11662	+	0.936952i	−0.118187	+	0.992991i	$0.537708\pi$
$294$	3.31636	+	11.6620i	0.193414	+	0.680141i
$295$	2.57357	−	0.936702i	0.149839	−	0.0545369i
$296$	−3.89159	+	2.24681i	−0.226194	+	0.130593i
$297$	21.2113	+	15.6993i	1.23080	+	0.910965i
$298$	8.78897	−	15.2229i	0.509132	−	0.881842i
$299$	11.4326	+	9.59307i	0.661163	+	0.554782i
$300$	0.472946	+	0.260386i	0.0273056	+	0.0150334i
$301$	−1.88206	+	1.19232i	−0.108480	+	0.0687241i
$302$	20.8738	−	3.68061i	1.20115	−	0.211795i
$303$	−21.8632	−	3.39848i	−1.25601	−	0.195238i
$304$	1.88661	+	5.18341i	0.108204	+	0.297289i
$305$	3.46104	−	1.99823i	0.198179	−	0.114419i
$306$	10.1266	+	1.36397i	0.578901	+	0.0779727i
$307$	−17.4801	+	10.0922i	−0.997643	+	0.575989i	−0.907550	−	0.419944i	$-0.862050\pi$
$307$	−17.4801	+	10.0922i	−0.997643	+	0.575989i	−0.0900929	+	0.995933i	$0.528716\pi$
$308$	−2.87501	−	13.1255i	−0.163819	−	0.747895i
$309$	−0.734489	−	3.72155i	−0.0417836	−	0.211711i
$310$	−3.37622	−	19.1475i	−0.191756	−	1.08750i
$311$	−4.25897	+	3.57370i	−0.241504	+	0.202646i	−0.755504	−	0.655145i	$-0.772608\pi$
$311$	−4.25897	+	3.57370i	−0.241504	+	0.202646i	0.514000	+	0.857790i	$0.328163\pi$
$312$	9.54502	−	1.88381i	0.540380	−	0.106650i
$313$	−6.57946	−	18.0769i	−0.371893	−	1.02177i	−0.974629	−	0.223827i	$-0.928145\pi$
$313$	−6.57946	−	18.0769i	−0.371893	−	1.02177i	0.602736	−	0.797941i	$-0.294077\pi$
$314$	−4.42741	−	7.66850i	−0.249853	−	0.432759i
$315$	−7.17712	−	15.6157i	−0.404385	−	0.879848i
$316$	−4.15691	+	7.19997i	−0.233844	+	0.405030i
$317$	0.291750	+	0.0514433i	0.0163863	+	0.00288935i	0.181835	−	0.983329i	$-0.441796\pi$
$317$	0.291750	+	0.0514433i	0.0163863	+	0.00288935i	−0.165449	+	0.986218i	$0.552907\pi$
$318$	−8.26626	−	1.28493i	−0.463549	−	0.0720555i
$319$	−24.4912	−	8.91406i	−1.37124	−	0.499092i
$320$	−2.03467	−	0.740558i	−0.113741	−	0.0413985i
$321$	−7.02409	+	0.142777i	−0.392047	+	0.00796901i
$322$	2.13078	−	6.69880i	0.118744	−	0.373309i
$323$		−	18.7879i		−	1.04538i
$324$	8.67927	+	2.38124i	0.482182	+	0.132291i
$325$	−1.51631	−	0.875441i	−0.0841097	−	0.0485607i
$326$	23.2331	+	4.09663i	1.28676	+	0.226891i
$327$	−13.9080	+	8.41120i	−0.769114	+	0.465141i
$328$	3.84951	+	4.58767i	0.212554	+	0.253312i
$329$	9.10418	−	5.76765i	0.501930	−	0.317981i
$330$	6.87661	+	17.7616i	0.378545	+	0.977745i
$331$	2.77870	−	15.7588i	0.152731	−	0.866180i	−0.808100	−	0.589045i	$-0.799504\pi$
$331$	2.77870	−	15.7588i	0.152731	−	0.866180i	0.960831	−	0.277135i	$-0.0893849\pi$
$332$	−6.39971	−	11.0846i	−0.351230	−	0.608348i
$333$	13.4697	−	0.547817i	0.738137	−	0.0300202i
$334$	7.82892	+	4.52003i	0.428379	+	0.247325i
$335$	−4.64555	+	26.3462i	−0.253814	+	1.43945i
$336$	−2.53059	−	3.82049i	−0.138055	−	0.208425i
$337$	−4.89494	−	1.78161i	−0.266644	−	0.0970506i	0.205238	−	0.978712i	$-0.434203\pi$
$337$	−4.89494	−	1.78161i	−0.266644	−	0.0970506i	−0.471882	+	0.881661i	$0.656425\pi$
$338$	−18.2702	+	3.22153i	−0.993767	+	0.175228i
$339$	−27.0232	−	9.21816i	−1.46770	−	0.500662i
$340$	5.64949	+	4.74049i	0.306387	+	0.257089i
$341$	−22.8016	+	39.4936i	−1.23478	+	2.13870i
$342$	2.20895	−	16.4001i	0.119446	−	0.886816i
$343$	−14.7783	+	11.1625i	−0.797954	+	0.602718i
$344$	0.541284	−	0.645077i	0.0291841	−	0.0347802i
$345$	−1.53049	+	9.84601i	−0.0823990	+	0.530091i
$346$	6.26793	−	17.2210i	0.336966	−	0.925806i
$347$	−6.19412	+	1.09219i	−0.332518	+	0.0586319i	−0.337415	−	0.941356i	$-0.609552\pi$
$347$	−6.19412	+	1.09219i	−0.332518	+	0.0586319i	0.00489674	+	0.999988i	$0.498441\pi$
$348$	−8.88693	+	0.180642i	−0.476390	+	0.00968342i
$349$	1.09019	+	2.99526i	0.0583564	+	0.160333i	0.965445	−	0.260607i	$-0.0839226\pi$
$349$	1.09019	+	2.99526i	0.0583564	+	0.160333i	−0.907089	+	0.420940i	$0.861700\pi$
$350$	−0.109714	+	0.817362i	−0.00586445	+	0.0436899i
$351$	−27.9845	−	8.29289i	−1.49370	−	0.442642i
$352$	2.53930	+	4.39819i	0.135345	+	0.234424i
$353$	−6.23315	+	35.3500i	−0.331757	+	1.88149i	0.125406	+	0.992105i	$0.459977\pi$
$353$	−6.23315	+	35.3500i	−0.331757	+	1.88149i	−0.457163	+	0.889383i	$0.651135\pi$
$354$	−2.19035	+	0.0445225i	−0.116416	+	0.00236635i
$355$	0.122840	−	0.337500i	0.00651967	−	0.0179126i
$356$	−1.20641	−	6.84189i	−0.0639395	−	0.362619i
$357$	3.64884	+	15.1759i	0.193117	+	0.803192i
$358$	−7.46098	−	6.26051i	−0.394325	−	0.330878i
$359$		−	2.75970i		−	0.145652i	−0.997345	−	0.0728258i	$-0.976798\pi$
$359$		−	2.75970i		−	0.145652i	0.997345	−	0.0728258i	$-0.0232017\pi$
$360$	4.37414	+	4.80224i	0.230538	+	0.253100i
$361$	−11.4270			−0.601421
$362$	22.1608	−	8.06586i	1.16474	−	0.423932i
$363$	8.27169	−	24.2486i	0.434151	−	1.27272i
$364$	7.95332	+	12.5542i	0.416867	+	0.658021i
$365$	2.95055	−	8.10657i	0.154439	−	0.424317i
$366$	−3.13640	+	0.619004i	−0.163942	+	0.0323558i
$367$	−5.55897	+	6.62492i	−0.290176	+	0.345818i	−0.891363	−	0.453290i	$-0.850250\pi$
$367$	−5.55897	+	6.62492i	−0.290176	+	0.345818i	0.601187	+	0.799108i	$0.294695\pi$
$368$			2.65691i			0.138501i
$369$	−3.83624	−	17.5520i	−0.199707	−	0.913720i
$370$	8.42626	+	4.86491i	0.438061	+	0.252914i
$371$	−2.73419	−	12.4826i	−0.141952	−	0.648066i
$372$	−2.38892	+	15.3684i	−0.123859	+	0.796815i
$373$	8.38023	−	7.03184i	0.433912	−	0.364095i	−0.399514	−	0.916727i	$-0.630821\pi$
$373$	8.38023	−	7.03184i	0.433912	−	0.364095i	0.833425	+	0.552632i	$0.186377\pi$
$374$	−3.00373	−	17.0350i	−0.155319	−	0.880860i
$375$	−0.404836	−	19.9165i	−0.0209056	−	1.02848i
$376$	−2.61837	+	3.12046i	−0.135032	+	0.160925i
$377$	28.8267			1.48465
$378$	1.40084	+	13.6762i	0.0720512	+	0.703426i
$379$	−0.0667035			−0.00342633			−0.00171316	−	0.999999i	$-0.500545\pi$
$379$	−0.0667035			−0.00342633			−0.00171316	+	0.999999i	$0.500545\pi$
$380$	7.67723	−	9.14937i	0.393834	−	0.469353i
$381$	−16.0143	+	9.68506i	−0.820439	+	0.496181i
$382$	−0.850269	−	4.82212i	−0.0435036	−	0.246721i
$383$	−9.37733	+	7.86852i	−0.479159	+	0.402062i	−0.850122	−	0.526585i	$-0.823472\pi$
$383$	−9.37733	+	7.86852i	−0.479159	+	0.402062i	0.370963	+	0.928648i	$0.379028\pi$
$384$	1.34918	+	1.08615i	0.0688500	+	0.0554272i
$385$	−21.4999	+	19.6011i	−1.09573	+	0.998963i
$386$	−13.8876	−	8.01802i	−0.706861	−	0.408106i
$387$	−2.33684	+	0.959788i	−0.118788	+	0.0487887i
$388$		−	14.2178i		−	0.721802i
$389$	8.28316	−	9.87148i	0.419973	−	0.500504i	−0.514029	−	0.857773i	$-0.671848\pi$
$389$	8.28316	−	9.87148i	0.419973	−	0.500504i	0.934002	+	0.357269i	$0.116292\pi$
$390$	−13.8661	−	15.8590i	−0.702138	−	0.803050i
$391$	3.09511	−	8.50374i	0.156526	−	0.430053i
$392$	4.04402	−	5.71366i	0.204254	−	0.288583i
$393$	5.22380	+	5.97457i	0.263506	+	0.301377i
$394$	7.89881	−	2.87493i	0.397936	−	0.144837i
$395$	18.0015			0.905752
$396$	−0.619130	−	15.2232i	−0.0311124	−	0.764994i
$397$		−	24.3579i		−	1.22249i	−0.791441	−	0.611245i	$-0.790669\pi$
$397$		−	24.3579i		−	1.22249i	0.791441	−	0.611245i	$-0.209331\pi$
$398$	−17.0976	−	14.3465i	−0.857023	−	0.719128i
$399$	24.5774	−	5.90931i	1.23041	−	0.295835i
$400$	−0.0541269	−	0.306969i	−0.00270635	−	0.0153485i
$401$	0.107679	−	0.295846i	0.00537724	−	0.0147738i	−0.936975	−	0.349396i	$-0.886387\pi$
$401$	0.107679	−	0.295846i	0.00537724	−	0.0147738i	0.942352	+	0.334623i	$0.108609\pi$
$402$	10.3213	−	18.7469i	0.514780	−	0.935008i
$403$	8.75864	−	49.6727i	0.436299	−	2.47438i
$404$	6.38715	+	11.0629i	0.317773	+	0.550398i
$405$	−4.93118	−	18.8530i	−0.245033	−	0.936813i
$406$	−5.16423	−	12.5574i	−0.256296	−	0.623212i
$407$	−7.80534	−	21.4450i	−0.386896	−	1.06299i
$408$	−3.05292	−	5.04804i	−0.151142	−	0.249915i
$409$	5.84386	−	1.03043i	0.288960	−	0.0509515i	−0.0272891	−	0.999628i	$-0.508687\pi$
$409$	5.84386	−	1.03043i	0.288960	−	0.0509515i	0.316249	+	0.948676i	$0.397576\pi$
$410$	4.43504	−	12.1852i	0.219031	−	0.601783i
$411$	−25.8702	−	20.8266i	−1.27609	−	1.02730i
$412$	−1.40776	+	1.67770i	−0.0693553	+	0.0826544i
$413$	−1.27282	−	3.09500i	−0.0626313	−	0.152295i
$414$	3.70156	−	7.05910i	0.181922	−	0.346936i
$415$	−13.8570	+	24.0009i	−0.680211	+	1.17816i
$416$	−4.30296	−	3.61062i	−0.210970	−	0.177025i
$417$	−3.35314	−	16.9899i	−0.164204	−	0.831997i
$418$	−27.5883	+	4.86455i	−1.34939	+	0.237933i
$419$	3.37802	+	1.22950i	0.165027	+	0.0600650i	0.423213	−	0.906030i	$-0.360902\pi$
$419$	3.37802	+	1.22950i	0.165027	+	0.0600650i	−0.258185	+	0.966095i	$0.583125\pi$
$420$	−4.42435	+	8.88140i	−0.215886	+	0.433368i
$421$	−3.57310	+	20.2640i	−0.174142	+	0.987609i	0.764987	+	0.644045i	$0.222745\pi$
$421$	−3.57310	+	20.2640i	−0.174142	+	0.987609i	−0.939129	+	0.343564i	$0.888366\pi$
$422$	14.3786	+	8.30149i	0.699939	+	0.404110i
$423$	11.3041	−	4.64282i	0.549623	−	0.225741i
$424$	2.41492	+	4.18277i	0.117279	+	0.203133i
$425$	−0.184358	+	1.04554i	−0.00894266	+	0.0507164i
$426$	−0.180164	+	0.223795i	−0.00872900	+	0.0108429i
$427$	−2.61339	−	4.12521i	−0.126471	−	0.199633i
$428$	2.60727	+	3.10723i	0.126027	+	0.150194i
$429$	1.00414	+	49.4001i	0.0484804	+	2.38506i
$430$	−1.79563	−	0.316618i	−0.0865929	−	0.0152687i
$431$	21.2645	+	12.2771i	1.02428	+	0.591366i	0.915339	−	0.402683i	$-0.131922\pi$
$431$	21.2645	+	12.2771i	1.02428	+	0.591366i	0.108936	+	0.994049i	$0.465256\pi$
$432$	−2.07141	−	4.76542i	−0.0996609	−	0.229276i
$433$		−	12.0477i		−	0.578978i	−0.957181	−	0.289489i	$-0.906515\pi$
$433$		−	12.0477i		−	0.578978i	0.957181	−	0.289489i	$-0.0934853\pi$
$434$	−23.2074	+	5.08334i	−1.11399	+	0.244008i
$435$	9.95993	+	16.4688i	0.477542	+	0.789621i
$436$	8.81812	+	3.20953i	0.422311	+	0.153709i
$437$	−13.7718	−	5.01254i	−0.658796	−	0.239782i
$438$	−4.32745	+	5.37543i	−0.206774	+	0.256848i
$439$	−12.5491	−	2.21274i	−0.598935	−	0.105608i	−0.134043	−	0.990976i	$-0.542796\pi$
$439$	−12.5491	−	2.21274i	−0.598935	−	0.105608i	−0.464893	+	0.885367i	$0.653907\pi$
$440$	5.49820	−	9.52316i	0.262116	−	0.453999i
$441$	−18.7047	+	9.54647i	−0.890699	+	0.454594i
$442$	9.56603	+	16.5688i	0.455010	+	0.788100i
$443$	4.23689	+	11.6407i	0.201301	+	0.553069i	0.998732	−	0.0503407i	$-0.0160307\pi$
$443$	4.23689	+	11.6407i	0.201301	+	0.553069i	−0.797432	+	0.603409i	$0.793809\pi$
$444$	−5.12307	−	5.85937i	−0.243130	−	0.278073i
$445$	−11.5235	+	9.66940i	−0.546268	+	0.458373i
$446$	2.19190	+	12.4309i	0.103790	+	0.588620i
$447$	28.8155	+	9.82954i	1.36293	+	0.464921i
$448$	−0.801979	+	2.52128i	−0.0378899	+	0.119119i
$449$	−0.144151	+	0.0832254i	−0.00680289	+	0.00392765i	−0.503398	−	0.864055i	$-0.667917\pi$
$449$	−0.144151	+	0.0832254i	−0.00680289	+	0.00392765i	0.496595	+	0.867983i	$0.334584\pi$
$450$	−0.283855	+	0.890990i	−0.0133811	+	0.0420017i
$451$	−26.3398	+	15.2073i	−1.24029	+	0.716083i
$452$	5.63808	+	15.4905i	0.265193	+	0.728611i
$453$	13.2548	+	34.2358i	0.622765	+	1.60854i
$454$	−13.1981	+	2.32718i	−0.619417	+	0.109220i
$455$	14.9308	−	28.5053i	0.699964	−	1.33635i
$456$	−8.17531	+	4.94422i	−0.382844	+	0.231534i
$457$	4.48861	+	3.76639i	0.209968	+	0.176184i	0.741707	−	0.670724i	$-0.234017\pi$
$457$	4.48861	+	3.76639i	0.209968	+	0.176184i	−0.531739	+	0.846909i	$0.678461\pi$
$458$	5.17443	−	8.96238i	0.241785	−	0.418784i
$459$	1.07842	+	17.6653i	0.0503364	+	0.824547i
$460$	4.98212	−	2.87643i	0.232293	−	0.134114i
$461$	−21.0665	+	7.66759i	−0.981166	+	0.357115i	−0.782294	−	0.622910i	$-0.785950\pi$
$461$	−21.0665	+	7.66759i	−0.981166	+	0.357115i	−0.198873	+	0.980025i	$0.563728\pi$
$462$	21.3396	−	9.28732i	0.992809	−	0.432085i
$463$	−19.7272	+	16.5531i	−0.916800	+	0.769287i	−0.973400	−	0.229110i	$-0.926418\pi$
$463$	−19.7272	+	16.5531i	−0.916800	+	0.769287i	0.0566005	+	0.998397i	$0.481974\pi$
$464$	3.29874	+	3.93129i	0.153140	+	0.182505i
$465$	31.4045	−	12.1586i	1.45635	−	0.563842i
$466$	−6.73535	+	2.45147i	−0.312009	+	0.113562i
$467$	−21.7907			−1.00835			−0.504176	−	0.863601i	$-0.668204\pi$
$467$	−21.7907			−1.00835			−0.504176	+	0.863601i	$0.668204\pi$
$468$	6.40223	+	15.5878i	0.295943	+	0.720547i
$469$	32.3990	+	4.34889i	1.49605	+	0.200813i
$470$	8.68606	+	1.53159i	0.400658	+	0.0706469i
$471$	11.5461	−	10.0952i	0.532014	−	0.465161i
$472$	0.813036	+	0.968939i	0.0374230	+	0.0445990i
$473$	2.74896	+	3.27608i	0.126397	+	0.150634i
$474$	−13.6288	−	4.64906i	−0.625992	−	0.213538i
$475$	1.69326	+	0.298568i	0.0776922	+	0.0136992i
$476$	5.50394	−	7.13539i	0.252272	−	0.327050i
$477$	−0.588805	−	14.4776i	−0.0269595	−	0.662882i
$478$	−0.683579			−0.0312662
$479$	−10.5969	+	3.85695i	−0.484184	+	0.176229i	−0.572567	−	0.819858i	$-0.694052\pi$
$479$	−10.5969	+	3.85695i	−0.484184	+	0.176229i	0.0883830	+	0.996087i	$0.471830\pi$
$480$	0.576043	−	3.70581i	0.0262927	−	0.169147i
$481$	16.2248	+	19.3359i	0.739785	+	0.881642i
$482$	−2.61694	+	2.19588i	−0.119199	+	0.100019i
$483$	12.0977	+	1.37421i	0.550463	+	0.0625286i
$484$	−13.9000	+	5.05919i	−0.631819	+	0.229963i
$485$	−26.6607	+	15.3926i	−1.21060	+	0.698941i
$486$	−1.13560	+	15.5470i	−0.0515119	+	0.705228i
$487$	5.48376	−	9.49815i	0.248493	−	0.430402i	−0.714615	−	0.699518i	$-0.753398\pi$
$487$	5.48376	−	9.49815i	0.248493	−	0.430402i	0.963108	+	0.269116i	$0.0867314\pi$
$488$	1.41391	+	1.18641i	0.0640049	+	0.0537065i
$489$	0.830412	+	40.8533i	0.0375525	+	1.84745i
$490$	−15.0922	−	1.39744i	−0.681795	−	0.0631299i
$491$	20.8102	−	3.66940i	0.939152	−	0.165598i	0.316939	−	0.948446i	$-0.397345\pi$
$491$	20.8102	−	3.66940i	0.939152	−	0.165598i	0.622213	+	0.782848i	$0.286234\pi$
$492$	−6.50469	+	8.07994i	−0.293254	+	0.364272i
$493$	−5.97834	−	16.4253i	−0.269251	−	0.739761i
$494$	26.8333	−	15.4922i	1.20729	−	0.697027i
$495$	−27.8756	+	17.6419i	−1.25292	+	0.792947i
$496$	7.77649	−	4.48976i	0.349175	−	0.201596i
$497$	−0.418216	−	0.133028i	−0.0187596	−	0.00596713i
$498$	16.6895	−	14.5923i	0.747875	−	0.653897i
$499$	5.64879	+	32.0359i	0.252875	+	1.43412i	0.801470	+	0.598035i	$0.204052\pi$
$499$	5.64879	+	32.0359i	0.252875	+	1.43412i	−0.548595	+	0.836088i	$0.684837\pi$
$500$	−8.81039	+	7.39280i	−0.394013	+	0.330616i
$501$	−5.05517	+	14.8193i	−0.225849	+	0.662080i
$502$	7.38424	+	20.2880i	0.329575	+	0.905500i
$503$	−7.43519	−	12.8781i	−0.331519	−	0.574207i	0.651291	−	0.758828i	$-0.274228\pi$
$503$	−7.43519	−	12.8781i	−0.331519	−	0.574207i	−0.982810	+	0.184621i	$0.940894\pi$
$504$	5.64337	−	5.58143i	0.251376	−	0.248617i
$505$	13.8298	−	23.9538i	0.615416	−	1.06593i
$506$	−13.2884	−	2.34309i	−0.590739	−	0.104163i
$507$	−11.6015	−	29.9656i	−0.515242	−	1.33082i
$508$	10.1536	+	3.69561i	0.450493	+	0.163966i
$509$	−10.5236	−	3.83026i	−0.466448	−	0.169773i	0.0980944	−	0.995177i	$-0.468725\pi$
$509$	−10.5236	−	3.83026i	−0.466448	−	0.169773i	−0.564543	+	0.825404i	$0.690948\pi$
$510$	−6.16071	+	11.1898i	−0.272801	+	0.495495i
$511$	−10.0453	−	3.19526i	−0.444379	−	0.141350i
$512$		−	1.00000i		−	0.0441942i
$513$	28.6091	−	1.74651i	1.26312	−	0.0771102i
$514$	6.06424	+	3.50119i	0.267482	+	0.154431i
$515$	4.67003	+	0.823452i	0.205786	+	0.0362856i
$516$	1.27769	+	0.703449i	0.0562473	+	0.0309676i
$517$	−13.2976	−	15.8475i	−0.584830	−	0.696973i
$518$	5.51642	−	10.5318i	0.242378	−	0.462739i
$519$	31.3652	+	4.87551i	1.37678	+	0.214011i
$520$	−2.11199	+	11.9777i	−0.0926168	+	0.525256i
$521$	−7.12689	−	12.3441i	−0.312235	−	0.540806i	0.666611	−	0.745406i	$-0.267744\pi$
$521$	−7.12689	−	12.3441i	−0.312235	−	0.540806i	−0.978846	+	0.204599i	$0.934411\pi$
$522$	−3.28737	−	15.0407i	−0.143884	−	0.658315i
$523$	−30.3319	−	17.5121i	−1.32632	−	0.765751i	−0.341591	−	0.939849i	$-0.610966\pi$
$523$	−30.3319	−	17.5121i	−1.32632	−	0.765751i	−0.984728	+	0.174098i	$0.944299\pi$
$524$	0.795652	−	4.51237i	0.0347582	−	0.197124i
$525$	−1.42572	+	0.0876852i	−0.0622233	+	0.00382689i
$526$	24.9350	+	9.07559i	1.08722	+	0.395715i
$527$	−30.1198	+	5.31094i	−1.31204	+	0.231348i
$528$	−6.62212	+	5.78998i	−0.288191	+	0.251976i
$529$	12.2114	+	10.2466i	0.530930	+	0.445503i
$530$	5.22890	−	9.05673i	0.227129	−	0.393399i
$531$	−0.810233	−	3.70707i	−0.0351611	−	0.160873i
$532$	−11.5558	−	8.91364i	−0.501007	−	0.386455i
$533$	21.6232	−	25.7695i	0.936604	−	1.11620i
$534$	11.2216	−	4.34458i	0.485608	−	0.188008i
$535$	3.00385	−	8.25301i	0.129868	−	0.356809i
$536$	−12.1678	+	2.14551i	−0.525568	+	0.0926718i
$537$	8.13611	−	14.7778i	0.351099	−	0.637710i
$538$	3.12984	+	8.59915i	0.134937	+	0.370736i
$539$	25.0101	+	25.2647i	1.07726	+	1.08823i
$540$	−6.69336	+	9.04339i	−0.288036	+	0.389165i
$541$	4.69380	+	8.12990i	0.201802	+	0.349532i	0.949109	−	0.314947i	$-0.101987\pi$
$541$	4.69380	+	8.12990i	0.201802	+	0.349532i	−0.747307	+	0.664479i	$0.768654\pi$
$542$	0.209234	−	1.18662i	0.00898737	−	0.0509699i
$543$	21.1382	+	34.9522i	0.907126	+	1.49994i
$544$	−1.16493	+	3.20062i	−0.0499459	+	0.137225i
$545$	−3.52832	−	20.0101i	−0.151137	−	0.857138i
$546$	−18.6658	+	17.7252i	−0.798821	+	0.758567i
$547$	−14.2268	−	11.9377i	−0.608293	−	0.510418i	0.285806	−	0.958287i	$-0.407739\pi$
$547$	−14.2268	−	11.9377i	−0.608293	−	0.510418i	−0.894099	+	0.447869i	$0.852183\pi$
$548$			19.1748i			0.819107i
$549$	−2.10371	−	5.12201i	−0.0897843	−	0.218602i
$550$	1.58302			0.0675002
$551$	−26.6009	+	9.68194i	−1.13324	+	0.412464i
$552$	−4.51481	+	0.891048i	−0.192163	+	0.0379255i
$553$	−0.903821	−	21.9777i	−0.0384344	−	0.934587i
$554$	2.80692	−	7.71195i	0.119255	−	0.327649i
$555$	−5.44088	+	15.9501i	−0.230953	+	0.677043i
$556$	−6.42679	+	7.65915i	−0.272557	+	0.324820i
$557$		−	45.5652i		−	1.93066i	−0.261034	−	0.965330i	$-0.584064\pi$
$557$		−	45.5652i		−	1.93066i	0.261034	−	0.965330i	$-0.415936\pi$
$558$	−26.9163	+	1.09469i	−1.13946	+	0.0463420i
$559$	−4.09640	−	2.36506i	−0.173259	−	0.100031i
$560$	5.59603	−	1.22575i	0.236476	−	0.0517976i
$561$	27.9398	−	10.8172i	1.17962	−	0.456702i
$562$	−12.0766	+	10.1335i	−0.509423	+	0.427456i
$563$	−1.47051	−	8.33967i	−0.0619746	−	0.351475i	−0.999988	−	0.00487660i	$-0.998448\pi$
$563$	−1.47051	−	8.33967i	−0.0619746	−	0.351475i	0.938014	−	0.346599i	$-0.112663\pi$
$564$	−6.18063	−	3.40282i	−0.260251	−	0.143285i
$565$	22.9432	−	27.3427i	0.965228	−	1.15031i
$566$	24.2386			1.01882
$567$	−22.7697	+	6.96698i	−0.956239	+	0.292586i
$568$	0.165875			0.00695996
$569$	18.5331	−	22.0869i	0.776949	−	0.925932i	−0.221842	−	0.975083i	$-0.571207\pi$
$569$	18.5331	−	22.0869i	0.776949	−	0.925932i	0.998791	+	0.0491509i	$0.0156515\pi$
$570$	18.1220	+	9.97728i	0.759046	+	0.417902i
$571$	−0.151629	−	0.859933i	−0.00634549	−	0.0359871i	0.981471	−	0.191613i	$-0.0613718\pi$
$571$	−0.151629	−	0.859933i	−0.00634549	−	0.0359871i	−0.987816	+	0.155626i	$0.950261\pi$
$572$	21.8530	−	18.3368i	0.913719	−	0.766702i
$573$	7.90893	−	3.06203i	0.330400	−	0.127918i
$574$	−15.0994	−	4.80288i	−0.630235	−	0.200468i
$575$	0.717216	+	0.414085i	0.0299100	+	0.0172685i
$576$	−1.39318	+	2.65689i	−0.0580493	+	0.110704i
$577$			1.95642i			0.0814468i	0.999170	+	0.0407234i	$0.0129662\pi$
$577$			1.95642i			0.0814468i	−0.999170	+	0.0407234i	$0.987034\pi$
$578$	−3.47040	+	4.13587i	−0.144350	+	0.172029i
$579$	8.96731	−	26.2878i	0.372668	−	1.09249i
$580$	3.80049	−	10.4418i	0.157807	−	0.433571i
$581$	29.9981	+	15.7127i	1.24453	+	0.651872i
$582$	24.1600	−	4.76824i	1.00146	−	0.197650i
$583$	−23.0495	+	8.38934i	−0.954614	+	0.347451i
$584$	3.98422			0.164868
$585$	22.2984	−	28.8809i	0.921926	−	1.19408i
$586$			24.9508i			1.03071i
$587$	20.6966	+	17.3665i	0.854242	+	0.716794i	0.960720	−	0.277521i	$-0.0895128\pi$
$587$	20.6966	+	17.3665i	0.854242	+	0.716794i	−0.106478	+	0.994315i	$0.533957\pi$
$588$	11.0653	+	4.95570i	0.456326	+	0.204370i
$589$	8.60107	+	48.7791i	0.354401	+	2.00991i
$590$	0.936702	−	2.57357i	0.0385634	−	0.105952i
$591$	7.53432	+	12.4581i	0.309920	+	0.512456i
$592$	−0.780310	+	4.42536i	−0.0320705	+	0.181881i
$593$	4.17229	+	7.22661i	0.171335	+	0.296761i	0.938887	−	0.344226i	$-0.111859\pi$
$593$	4.17229	+	7.22661i	0.171335	+	0.296761i	−0.767552	+	0.640987i	$0.778525\pi$
$594$	25.6607	−	6.15747i	1.05287	−	0.252644i
$595$	−19.3387	−	2.59582i	−0.792808	−	0.106418i
$596$	−6.01201	−	16.5179i	−0.246262	−	0.676598i
$597$	18.6447	−	33.8648i	0.763076	−	1.38599i
$598$	14.6974	−	2.59155i	0.601023	−	0.105977i
$599$	−2.42123	+	6.65229i	−0.0989290	+	0.271805i	−0.979278	−	0.202522i	$-0.935086\pi$
$599$	−2.42123	+	6.65229i	−0.0989290	+	0.271805i	0.880349	+	0.474327i	$0.157309\pi$
$600$	0.503472	−	0.194925i	0.0205541	−	0.00795777i
$601$	−29.4469	+	35.0935i	−1.20116	+	1.43149i	−0.327578	+	0.944824i	$0.606232\pi$
$601$	−29.4469	+	35.0935i	−1.20116	+	1.43149i	−0.873587	+	0.486669i	$0.838212\pi$
$602$	−0.296399	+	2.20815i	−0.0120803	+	0.0899976i
$603$	35.3175	+	11.2516i	1.43824	+	0.458200i
$604$	10.5979	−	18.3561i	0.431222	−	0.746898i
$605$	24.5353	+	20.5875i	0.997500	+	0.837002i
$606$	−16.6568	+	14.5637i	−0.676635	+	0.591608i
$607$	−0.101262	+	0.0178552i	−0.00411008	+	0.000724719i	−0.175703	−	0.984443i	$-0.556220\pi$
$607$	−0.101262	+	0.0178552i	−0.00411008	+	0.000724719i	0.171593	+	0.985168i	$0.445109\pi$
$608$	5.18341	+	1.88661i	0.210215	+	0.0765120i
$609$	19.6065	−	12.9868i	0.794495	−	0.526252i
$610$	0.693979	−	3.93575i	0.0280984	−	0.159354i
$611$	19.8157	+	11.4406i	0.801656	+	0.462836i
$612$	7.55413	−	6.88071i	0.305358	−	0.278136i
$613$	1.66911	+	2.89099i	0.0674149	+	0.116766i	0.897763	−	0.440479i	$-0.145192\pi$
$613$	1.66911	+	2.89099i	0.0674149	+	0.116766i	−0.830348	+	0.557246i	$0.811858\pi$
$614$	−3.50497	+	19.8777i	−0.141449	+	0.802197i
$615$	22.1933	+	3.44980i	0.894920	+	0.139109i
$616$	−11.9027	−	6.23453i	−0.479575	−	0.251196i
$617$	31.5624	+	37.6146i	1.27065	+	1.51430i	0.751706	+	0.659498i	$0.229231\pi$
$617$	31.5624	+	37.6146i	1.27065	+	1.51430i	0.518947	+	0.854807i	$0.326324\pi$
$618$	−3.32299	−	1.82951i	−0.133670	−	0.0735939i
$619$	11.5106	+	2.02963i	0.462650	+	0.0815777i	0.400115	−	0.916465i	$-0.368970\pi$
$619$	11.5106	+	2.02963i	0.462650	+	0.0815777i	0.0625353	+	0.998043i	$0.480081\pi$
$620$	−16.8380	−	9.72144i	−0.676231	−	0.390422i
$621$	13.2367	+	3.92255i	0.531171	+	0.157406i
$622$			5.55969i			0.222923i
$623$	12.3838	+	13.5834i	0.496146	+	0.544208i
$624$	4.69233	−	8.52280i	0.187844	−	0.341185i
$625$	21.9365	+	7.98423i	0.877459	+	0.319369i
$626$	−18.0769	−	6.57946i	−0.722499	−	0.262968i
$627$	−17.5185	−	45.2485i	−0.699621	−	1.80705i
$628$	−8.72030	−	1.53762i	−0.347978	−	0.0613579i
$629$	7.65270	−	13.2549i	0.305133	−	0.528506i
$630$	−16.5757	−	4.53962i	−0.660392	−	0.180863i
$631$	13.8204	+	23.9376i	0.550180	+	0.952939i	0.998261	+	0.0589465i	$0.0187741\pi$
$631$	13.8204	+	23.9376i	0.550180	+	0.952939i	−0.448081	+	0.893993i	$0.647893\pi$
$632$	2.84349	+	7.81243i	0.113108	+	0.310762i
$633$	−9.28434	+	27.2172i	−0.369019	+	1.08179i
$634$	0.226941	−	0.190426i	0.00901298	−	0.00756279i
$635$	−4.06267	−	23.0406i	−0.161222	−	0.914337i
$636$	−6.29777	+	5.50639i	−0.249723	+	0.218342i
$637$	−35.5513	−	16.7975i	−1.40859	−	0.665542i
$638$	−22.5712	+	13.0315i	−0.893603	+	0.515922i
$639$	−0.440711	−	0.231094i	−0.0174342	−	0.00914195i
$640$	−1.87516	+	1.08262i	−0.0741222	+	0.0427945i
$641$	7.95101	+	21.8452i	0.314046	+	0.862834i	0.991829	+	0.127572i	$0.0407185\pi$
$641$	7.95101	+	21.8452i	0.314046	+	0.862834i	−0.677783	+	0.735262i	$0.737059\pi$
$642$	−4.40563	+	5.47254i	−0.173876	+	0.215984i
$643$	16.3942	−	2.89074i	0.646525	−	0.114000i	0.159236	−	0.987241i	$-0.449097\pi$
$643$	16.3942	−	2.89074i	0.646525	−	0.114000i	0.487289	+	0.873241i	$0.337986\pi$
$644$	−3.76193	−	5.93818i	−0.148241	−	0.233997i
$645$	−0.0641805	−	3.15745i	−0.00252710	−	0.124324i
$646$	−14.3923	−	12.0766i	−0.566259	−	0.475148i
$647$	10.7427	−	18.6069i	0.422339	−	0.731512i	−0.573829	−	0.818975i	$-0.694543\pi$
$647$	10.7427	−	18.6069i	0.422339	−	0.731512i	0.996168	+	0.0874632i	$0.0278760\pi$
$648$	7.40306	−	5.11808i	0.290820	−	0.201057i
$649$	−5.56309	+	3.21185i	−0.218370	+	0.126076i
$650$	−1.64529	+	0.598837i	−0.0645336	+	0.0234883i
$651$	−16.4210	−	37.7308i	−0.643591	−	1.47879i
$652$	18.0722	−	15.1643i	0.707760	−	0.593881i
$653$	0.315312	+	0.375774i	0.0123391	+	0.0147052i	0.772179	−	0.635405i	$-0.219167\pi$
$653$	0.315312	+	0.375774i	0.0123391	+	0.0147052i	−0.759840	+	0.650111i	$0.774723\pi$
$654$	−2.49654	+	16.0608i	−0.0976223	+	0.628026i
$655$	−9.32280	+	3.39322i	−0.364272	+	0.132584i
$656$	5.98878			0.233823
$657$	−10.5856	−	5.55076i	−0.412984	−	0.216556i
$658$	1.43378	−	10.6816i	0.0558946	−	0.416411i
$659$	−37.5887	−	6.62790i	−1.46425	−	0.258186i	−0.615983	−	0.787759i	$-0.711241\pi$
$659$	−37.5887	−	6.62790i	−1.46425	−	0.258186i	−0.848264	+	0.529573i	$0.822352\pi$
$660$	18.0264	+	6.14916i	0.701676	+	0.239356i
$661$	3.30033	+	3.93318i	0.128368	+	0.152983i	0.826400	−	0.563084i	$-0.190385\pi$
$661$	3.30033	+	3.93318i	0.128368	+	0.152983i	−0.698032	+	0.716067i	$0.745941\pi$
$662$	−10.2858	−	12.2581i	−0.399769	−	0.476426i
$663$	−24.9468	+	21.8120i	−0.968854	+	0.847107i
$664$	−12.6050	−	2.22260i	−0.489168	−	0.0862534i
$665$	−4.20393	+	31.3190i	−0.163021	+	1.21450i
$666$	8.23853	−	10.6706i	0.319237	−	0.413476i
$667$	−13.6351			−0.527952
$668$	8.49488	−	3.09188i	0.328677	−	0.119628i
$669$	−20.3884	+	7.89359i	−0.788260	+	0.305184i
$670$	17.1963	+	20.4937i	0.664351	+	0.791742i
$671$	−7.18069	+	6.02531i	−0.277207	+	0.232605i
$672$	−4.55329	−	0.517220i	−0.175647	−	0.0199522i
$673$	−10.3021	+	3.74964i	−0.397115	+	0.144538i	−0.532855	−	0.846206i	$-0.678881\pi$
$673$	−10.3021	+	3.74964i	−0.397115	+	0.144538i	0.135740	+	0.990744i	$0.456659\pi$
$674$	−4.51120	+	2.60454i	−0.173765	+	0.100323i
$675$	−1.60923	−	0.183536i	−0.0619394	−	0.00706431i
$676$	−9.27602	+	16.0665i	−0.356770	+	0.617944i
$677$	−20.6146	−	17.2977i	−0.792284	−	0.664805i	0.154025	−	0.988067i	$-0.450776\pi$
$677$	−20.6146	−	17.2977i	−0.792284	−	0.664805i	−0.946310	+	0.323261i	$0.895221\pi$
$678$	−24.4317	+	14.7757i	−0.938295	+	0.567456i
$679$	20.1311	+	31.7768i	0.772562	+	1.21948i
$680$	7.26285	−	1.28064i	0.278517	−	0.0491101i
$681$	−8.38075	−	21.6467i	−0.321151	−	0.829502i
$682$	15.5972	+	42.8531i	0.597249	+	1.64093i
$683$	39.5825	−	22.8530i	1.51458	−	0.874445i	0.514730	−	0.857353i	$-0.327892\pi$
$683$	39.5825	−	22.8530i	1.51458	−	0.874445i	0.999854	−	0.0170927i	$-0.00544104\pi$
$684$	−11.1433	−	12.2339i	−0.426076	−	0.467776i
$685$	35.9558	−	20.7591i	1.37380	−	0.793164i
$686$	−0.948361	+	18.4960i	−0.0362086	+	0.706179i
$687$	16.9649	+	5.78705i	0.647250	+	0.220790i
$688$	−0.146227	−	0.829295i	−0.00557486	−	0.0316166i
$689$	20.7826	−	17.4387i	0.791756	−	0.664362i
$690$	6.55870	+	7.50132i	0.249685	+	0.285570i
$691$	−9.13898	−	25.1091i	−0.347663	−	0.955197i	−0.983104	−	0.183047i	$-0.941404\pi$
$691$	−9.13898	−	25.1091i	−0.347663	−	0.955197i	0.635441	−	0.772150i	$-0.280818\pi$
$692$	−9.16309	−	15.8709i	−0.348329	−	0.603323i
$693$	22.9384	+	33.1471i	0.871356	+	1.25916i
$694$	−3.14484	+	5.44702i	−0.119376	+	0.206766i
$695$	21.3199	+	3.75928i	0.808711	+	0.142598i
$696$	−5.57403	+	6.92390i	−0.211283	+	0.262450i
$697$	−19.1678	−	6.97651i	−0.726032	−	0.264254i
$698$	2.99526	+	1.09019i	0.113372	+	0.0412642i
$699$	−6.42455	−	10.6230i	−0.242999	−	0.401800i
$700$	0.555613	+	0.609436i	0.0210002	+	0.0230345i
$701$		−	38.9541i		−	1.47128i	−0.677375	−	0.735638i	$-0.736882\pi$
$701$		−	38.9541i		−	1.47128i	0.677375	−	0.735638i	$-0.263118\pi$
$702$	−24.3408	+	16.1068i	−0.918685	+	0.607913i
$703$	−21.4663	−	12.3936i	−0.809617	−	0.467432i
$704$	5.00144	+	0.881888i	0.188499	+	0.0332374i
$705$	0.310463	+	15.2736i	0.0116927	+	0.575238i
$706$	23.0730	+	27.4974i	0.868365	+	1.03488i
$707$	−29.9392	−	15.6819i	−1.12598	−	0.589777i
$708$	−1.37382	+	1.70652i	−0.0516314	+	0.0641351i
$709$	−5.69765	+	32.3130i	−0.213980	+	1.21354i	0.668688	+	0.743543i	$0.266856\pi$
$709$	−5.69765	+	32.3130i	−0.213980	+	1.21354i	−0.882668	+	0.469997i	$0.844255\pi$
$710$	−0.179580	−	0.311042i	−0.00673952	−	0.0116732i
$711$	3.32932	−	24.7182i	0.124859	−	0.927006i
$712$	−6.01665	−	3.47372i	−0.225484	−	0.130183i
$713$	−4.14285	+	23.4953i	−0.155151	+	0.879906i
$714$	13.9708	+	6.95969i	0.522845	+	0.260460i
$715$	−58.0430	−	21.1259i	−2.17069	−	0.790065i
$716$	−9.59165	+	1.69127i	−0.358457	+	0.0632056i
$717$	−0.229252	−	1.16159i	−0.00856158	−	0.0433803i
$718$	−2.11406	−	1.77390i	−0.0788958	−	0.0662015i
$719$	10.1337	−	17.5522i	0.377925	−	0.654585i	−0.612835	−	0.790211i	$-0.709971\pi$
$719$	10.1337	−	17.5522i	0.377925	−	0.654585i	0.990760	+	0.135626i	$0.0433044\pi$
$720$	6.49038	−	0.263965i	0.241882	−	0.00983739i
$721$	0.770866	−	5.74291i	0.0287086	−	0.213877i
$722$	−7.34513	+	8.75359i	−0.273358	+	0.325775i
$723$	−4.60904	−	3.71047i	−0.171412	−	0.137994i
$724$	8.06586	−	22.1608i	0.299765	−	0.823599i
$725$	1.57534	−	0.277776i	0.0585068	−	0.0103163i
$726$	−13.2586	−	21.9232i	−0.492072	−	0.813646i
$727$	−4.87942	−	13.4061i	−0.180968	−	0.497205i	0.815727	−	0.578436i	$-0.196337\pi$
$727$	−4.87942	−	13.4061i	−0.180968	−	0.497205i	−0.996695	+	0.0812315i	$0.974115\pi$
$728$	14.7294	+	1.97712i	0.545908	+	0.0732768i
$729$	−26.7995	+	3.28432i	−0.992574	+	0.121641i
$730$	−4.31341	−	7.47105i	−0.159647	−	0.276516i
$731$	−0.498053	+	2.82460i	−0.0184212	+	0.104472i
$732$	−1.54186	+	2.80051i	−0.0569887	+	0.103510i
$733$	13.3244	−	36.6085i	0.492148	−	1.35217i	−0.406562	−	0.913623i	$-0.633272\pi$
$733$	13.3244	−	36.6085i	0.492148	−	1.35217i	0.898710	−	0.438543i	$-0.144505\pi$
$734$	1.50175	+	8.51684i	0.0554305	+	0.314362i
$735$	−2.68683	−	26.1144i	−0.0991054	−	0.963243i
$736$	2.03531	+	1.70783i	0.0750225	+	0.0629513i
$737$		−	62.7484i		−	2.31137i
$738$	−15.9115	−	8.34347i	−0.585710	−	0.307127i
$739$	28.6074			1.05234			0.526170	−	0.850379i	$-0.323628\pi$
$739$	28.6074			1.05234			0.526170	+	0.850379i	$0.323628\pi$
$740$	9.14303	−	3.32779i	0.336105	−	0.122332i
$741$	35.3246	+	40.4014i	1.29768	+	1.48418i
$742$	−11.3197	−	5.92916i	−0.415561	−	0.217666i
$743$	−4.24164	+	11.6538i	−0.155611	+	0.427536i	−0.992860	−	0.119284i	$-0.961940\pi$
$743$	−4.24164	+	11.6538i	−0.155611	+	0.427536i	0.837250	+	0.546821i	$0.184162\pi$
$744$	10.2373	+	11.7086i	0.375319	+	0.429260i
$745$	−24.4649	+	29.1561i	−0.896324	+	1.06820i
$746$		−	10.9396i		−	0.400528i
$747$	30.3935	+	23.4662i	1.11204	+	0.858584i
$748$	−14.9803	−	8.64890i	−0.547736	−	0.316235i
$749$	−10.2268	−	3.25299i	−0.373679	−	0.118862i
$750$	−15.5171	−	12.4919i	−0.566605	−	0.456141i
$751$	−15.5394	+	13.0391i	−0.567039	+	0.475803i	−0.880662	−	0.473745i	$-0.842902\pi$
$751$	−15.5394	+	13.0391i	−0.567039	+	0.475803i	0.313623	+	0.949548i	$0.398457\pi$
$752$	0.707350	+	4.01158i	0.0257944	+	0.146287i
$753$	−31.9985	+	19.3518i	−1.16609	+	0.705220i
$754$	18.5294	−	22.0825i	0.674802	−	0.804198i
$755$	−45.8941			−1.67026
$756$	11.3770	+	7.71777i	0.413777	+	0.280693i
$757$	23.6303			0.858858			0.429429	−	0.903101i	$-0.358715\pi$
$757$	23.6303			0.858858			0.429429	+	0.903101i	$0.358715\pi$
$758$	−0.0428762	+	0.0510978i	−0.00155733	+	0.00185596i
$759$	−0.474960	−	23.3663i	−0.0172400	−	0.848144i
$760$	−2.07399	−	11.7622i	−0.0752316	−	0.426660i
$761$	−11.2836	+	9.46804i	−0.409029	+	0.343216i	−0.823971	−	0.566632i	$-0.808246\pi$
$761$	−11.2836	+	9.46804i	−0.409029	+	0.343216i	0.414942	+	0.909848i	$0.363802\pi$
$762$	−2.87463	+	18.4931i	−0.104137	+	0.669936i
$763$	−24.2529	+	5.31234i	−0.878013	+	0.192320i
$764$	−4.24050	−	2.44825i	−0.153416	−	0.0885747i
$765$	−21.0807	−	6.71598i	−0.762175	−	0.242817i
$766$			12.2412i			0.442294i
$767$	4.56692	−	5.44264i	0.164902	−	0.196522i
$768$	1.69927	−	0.335370i	0.0613172	−	0.0121016i
$769$	−0.546784	+	1.50228i	−0.0197175	+	0.0541735i	−0.949161	−	0.314791i	$-0.898065\pi$
$769$	−0.546784	+	1.50228i	−0.0197175	+	0.0541735i	0.929443	+	0.368965i	$0.120288\pi$
$770$	1.19545	+	29.0692i	0.0430812	+	1.04758i
$771$	−3.91571	+	11.4790i	−0.141021	+	0.413406i
$772$	−15.0689	+	5.48465i	−0.542343	+	0.197397i
$773$	39.4078			1.41740			0.708700	−	0.705510i	$-0.249282\pi$
$773$	39.4078			1.41740			0.708700	+	0.705510i	$0.249282\pi$
$774$	−0.766852	+	2.40706i	−0.0275639	+	0.0865201i
$775$		−	2.79896i		−	0.100541i
$776$	−10.8915	−	9.13905i	−0.390982	−	0.328073i
$777$	19.7464	+	5.84187i	0.708397	+	0.209576i
$778$	−2.23768	−	12.6905i	−0.0802248	−	0.454978i
$779$	−11.2985	+	31.0423i	−0.404810	+	1.11221i
$780$	−21.0616	+	0.428113i	−0.754128	+	0.0153289i
$781$	−0.146283	+	0.829613i	−0.00523442	+	0.0296859i
$782$	−4.52475	−	7.83709i	−0.161805	−	0.280254i
$783$	24.4558	−	10.6304i	0.873980	−	0.379898i
$784$	−1.77747	−	6.77057i	−0.0634811	−	0.241806i
$785$	6.55751	+	18.0166i	0.234048	+	0.643041i
$786$	7.93458	−	0.161284i	0.283017	−	0.00575280i
$787$	−0.416621	+	0.0734615i	−0.0148509	+	0.00261862i	−0.181069	−	0.983470i	$-0.557956\pi$
$787$	−0.416621	+	0.0734615i	−0.0148509	+	0.00261862i	0.166218	+	0.986089i	$0.446845\pi$
$788$	2.87493	−	7.89881i	0.102415	−	0.281383i
$789$	−7.05945	+	45.4150i	−0.251323	+	1.61682i
$790$	11.5711	−	13.7899i	0.411682	−	0.490623i
$791$	−34.5342	−	26.6382i	−1.22789	−	0.947145i
$792$	−12.0596	−	9.31099i	−0.428519	−	0.330852i
$793$	5.18385	−	8.97870i	0.184084	−	0.318843i
$794$	−18.6593	−	15.6570i	−0.662192	−	0.555645i
$795$	17.1435	+	5.84797i	0.608016	+	0.207406i
$796$	−21.9802	+	3.87570i	−0.779067	+	0.137371i
$797$	−41.7217	−	15.1855i	−1.47786	−	0.537897i	−0.527637	−	0.849470i	$-0.676922\pi$
$797$	−41.7217	−	15.1855i	−1.47786	−	0.537897i	−0.950222	+	0.311573i	$0.899144\pi$
$798$	11.2712	−	22.6258i	0.398997	−	0.800944i
$799$	2.40925	−	13.6635i	0.0852332	−	0.483381i
$800$	−0.269944	−	0.155852i	−0.00954396	−	0.00551021i
$801$	11.1460	+	17.6116i	0.393826	+	0.622274i
$802$	−0.157416	−	0.272653i	−0.00555856	−	0.00962771i
$803$	−3.51364	+	19.9268i	−0.123994	+	0.703203i
$804$	−7.72651	−	19.9568i	−0.272493	−	0.703823i
$805$	−7.06227	+	13.4830i	−0.248912	+	0.475215i
$806$	−32.4216	−	38.6385i	−1.14200	−	1.36098i
$807$	−13.5626	+	8.20234i	−0.477428	+	0.288736i
$808$	12.5802	+	2.21823i	0.442571	+	0.0780372i
$809$	−10.5796	−	6.10816i	−0.371960	−	0.214751i	0.302354	−	0.953196i	$-0.402227\pi$
$809$	−10.5796	−	6.10816i	−0.371960	−	0.214751i	−0.674315	+	0.738444i	$0.735561\pi$
$810$	−17.6119	−	8.34096i	−0.618820	−	0.293072i
$811$		−	51.6263i		−	1.81284i	−0.422373	−	0.906422i	$-0.638803\pi$
$811$		−	51.6263i		−	1.81284i	0.422373	−	0.906422i	$-0.361197\pi$
$812$	−12.9390	−	4.11570i	−0.454070	−	0.144433i
$813$	2.08657	−	0.0424131i	0.0731792	−	0.00148749i
$814$	−21.4450	−	7.80534i	−0.751647	−	0.273577i
$815$	−48.0009	−	17.4709i	−1.68140	−	0.611979i
$816$	−5.82940	−	0.906141i	−0.204070	−	0.0317213i
$817$	4.57445	+	0.806599i	0.160040	+	0.0282193i
$818$	2.96701	−	5.13901i	0.103739	−	0.179681i
$819$	−36.3798	−	25.7737i	−1.27121	−	0.900607i
$820$	−6.48359	−	11.2299i	−0.226417	−	0.392166i
$821$	−8.36081	−	22.9711i	−0.291794	−	0.801698i	−0.995804	−	0.0915083i	$-0.970831\pi$
$821$	−8.36081	−	22.9711i	−0.291794	−	0.801698i	0.704010	−	0.710190i	$-0.251391\pi$
$822$	−32.5832	+	6.43066i	−1.13647	+	0.224295i
$823$	−1.55777	+	1.30712i	−0.0543004	+	0.0455635i	−0.669534	−	0.742781i	$-0.733506\pi$
$823$	−1.55777	+	1.30712i	−0.0543004	+	0.0455635i	0.615234	+	0.788345i	$0.289062\pi$
$824$	0.380304	+	2.15681i	0.0132485	+	0.0751361i
$825$	0.530898	+	2.68998i	0.0184835	+	0.0936532i
$826$	−3.18906	−	1.01439i	−0.110962	−	0.0352952i
$827$	−31.7217	+	18.3145i	−1.10307	+	0.636859i	−0.937026	−	0.349259i	$-0.886433\pi$
$827$	−31.7217	+	18.3145i	−1.10307	+	0.636859i	−0.166046	+	0.986118i	$0.553100\pi$
$828$	−3.02827	−	7.37306i	−0.105239	−	0.256232i
$829$	0.887465	−	0.512378i	0.0308229	−	0.0177956i	−0.484509	−	0.874786i	$-0.661002\pi$
$829$	0.887465	−	0.512378i	0.0308229	−	0.0177956i	0.515332	+	0.856990i	$0.327669\pi$
$830$	9.47871	+	26.0426i	0.329011	+	0.903950i
$831$	14.0461	+	2.18336i	0.487253	+	0.0757401i
$832$	−5.53178	+	0.975403i	−0.191780	+	0.0338160i
$833$	−2.19823	+	23.7406i	−0.0761642	+	0.822564i
$834$	−15.1703	−	8.35222i	−0.525306	−	0.289214i
$835$	−14.9945	−	12.5819i	−0.518907	−	0.435415i
$836$	−14.0069	+	24.2607i	−0.484440	+	0.839074i
$837$	−10.8871	−	45.3710i	−0.376313	−	1.56825i
$838$	3.11320	−	1.79741i	0.107544	−	0.0620904i
$839$	40.7157	−	14.8193i	1.40566	−	0.511620i	0.475810	−	0.879548i	$-0.342155\pi$
$839$	40.7157	−	14.8193i	1.40566	−	0.511620i	0.929854	+	0.367928i	$0.119933\pi$
$840$	3.95963	+	9.09810i	0.136620	+	0.313914i
$841$	2.04018	−	1.71192i	0.0703512	−	0.0590316i
$842$	13.2264	+	15.7626i	0.455812	+	0.543216i
$843$	−21.2697	−	17.1230i	−0.732569	−	0.589749i
$844$	15.6017	−	5.67855i	0.537033	−	0.195464i
$845$	40.1698			1.38188
$846$	3.70952	−	11.6438i	0.127536	−	0.400321i
$847$	23.9031	−	30.9884i	0.821321	−	1.06477i
$848$	4.75647	+	0.838694i	0.163338	+	0.0288009i
$849$	8.12890	+	41.1880i	0.278983	+	1.41357i
$850$	0.682431	+	0.813289i	0.0234072	+	0.0278956i
$851$	−7.67434	−	9.14592i	−0.263073	−	0.313518i
$852$	0.0556295	+	0.281867i	0.00190584	+	0.00965659i
$853$	28.3349	+	4.99621i	0.970169	+	0.171067i	0.636206	−	0.771519i	$-0.280503\pi$
$853$	28.3349	+	4.99621i	0.970169	+	0.171067i	0.333963	+	0.942586i	$0.391614\pi$
$854$	−4.83994	−	0.649662i	−0.165619	−	0.0222310i
$855$	−10.8765	+	34.1403i	−0.371970	+	1.16757i
$856$	4.05620			0.138638
$857$	−16.3809	+	5.96214i	−0.559559	+	0.203663i	−0.606289	−	0.795245i	$-0.707342\pi$
$857$	−16.3809	+	5.96214i	−0.559559	+	0.203663i	0.0467293	+	0.998908i	$0.485120\pi$
$858$	38.4881	+	30.9846i	1.31396	+	1.05780i
$859$	26.4861	+	31.5649i	0.903694	+	1.07698i	0.996689	+	0.0813136i	$0.0259115\pi$
$859$	26.4861	+	31.5649i	0.903694	+	1.07698i	−0.0929949	+	0.995667i	$0.529644\pi$
$860$	−1.39675	+	1.17201i	−0.0476288	+	0.0399653i
$861$	3.09752	−	27.2687i	0.105563	−	0.929314i
$862$	23.0733	−	8.39801i	0.785881	−	0.286037i
$863$	29.0818	−	16.7904i	0.989955	−	0.571551i	0.0846943	−	0.996407i	$-0.473009\pi$
$863$	29.0818	−	16.7904i	0.989955	−	0.571551i	0.905261	+	0.424856i	$0.139675\pi$
$864$	−4.98200	−	1.47636i	−0.169491	−	0.0502268i
$865$	−19.8404	+	34.3645i	−0.674593	+	1.16843i
$866$	−9.22911	−	7.74414i	−0.313618	−	0.263157i
$867$	−8.19183	−	4.51012i	−0.278209	−	0.153172i
$868$	−11.0233	+	21.0454i	−0.374157	+	0.714327i
$869$	−41.5810	+	7.33185i	−1.41054	+	0.248716i
$870$	19.0180	+	2.95622i	0.644770	+	0.100225i
$871$	23.7370	+	65.2168i	0.804296	+	2.20979i
$872$	8.12682	−	4.69202i	0.275209	−	0.158892i
$873$	16.2051	+	39.4553i	0.548459	+	1.33536i
$874$	−12.6922	+	7.32784i	−0.429320	+	0.247868i
$875$	9.22368	−	28.9976i	0.311817	−	0.980297i
$876$	1.33619	+	6.77028i	0.0451457	+	0.228747i
$877$	−4.46625	−	25.3294i	−0.150815	−	0.855312i	−0.962513	−	0.271235i	$-0.912568\pi$
$877$	−4.46625	−	25.3294i	−0.150815	−	0.855312i	0.811699	−	0.584077i	$-0.198543\pi$
$878$	−9.76146	+	8.19084i	−0.329433	+	0.276427i
$879$	−42.3981	+	8.36774i	−1.43005	+	0.282237i
$880$	−3.76099	−	10.3332i	−0.126783	−	0.348333i
$881$	6.22630	+	10.7843i	0.209769	+	0.363331i	0.951642	−	0.307210i	$-0.0993953\pi$
$881$	6.22630	+	10.7843i	0.209769	+	0.363331i	−0.741872	+	0.670541i	$0.766062\pi$
$882$	−4.71011	+	20.4650i	−0.158598	+	0.689091i
$883$	23.4936	−	40.6921i	0.790622	−	1.36940i	−0.134960	−	0.990851i	$-0.543091\pi$
$883$	23.4936	−	40.6921i	0.790622	−	1.36940i	0.925582	−	0.378547i	$-0.123576\pi$
$884$	18.8414	+	3.32225i	0.633705	+	0.111739i
$885$	4.68733	+	0.728614i	0.157563	+	0.0244921i
$886$	11.6407	+	4.23689i	0.391079	+	0.142341i
$887$	0.837130	+	0.304690i	0.0281081	+	0.0102305i	0.356036	−	0.934472i	$-0.384128\pi$
$887$	0.837130	+	0.304690i	0.0281081	+	0.0102305i	−0.327928	+	0.944703i	$0.606350\pi$
$888$	−7.78158	+	0.158174i	−0.261133	+	0.00530797i
$889$	−27.9259	+	6.11688i	−0.936605	+	0.205154i
$890$			15.0429i			0.504239i
$891$	19.0691	+	41.5395i	0.638838	+	1.39163i
$892$	10.9315	+	6.31133i	0.366015	+	0.211319i
$893$	−22.1281	−	3.90179i	−0.740490	−	0.130568i
$894$	26.0521	−	15.7556i	0.871313	−	0.526948i
$895$	13.5555	+	16.1549i	0.453112	+	0.539998i
$896$	1.41591	+	2.23500i	0.0473021	+	0.0746660i
$897$	9.33284	+	24.1058i	0.311614	+	0.804870i
$898$	−0.0289039	+	0.163922i	−0.000964535	+	0.00547015i
$899$	23.0411	+	39.9084i	0.768465	+	1.33102i
$900$	0.500079	+	0.790163i	0.0166693	+	0.0263388i
$901$	−14.2466	−	8.22529i	−0.474623	−	0.274024i
$902$	−5.28143	+	29.9525i	−0.175852	+	0.997309i
$903$	−3.85166	+	0.236887i	−0.128175	+	0.00788309i
$904$	15.4905	+	5.63808i	0.515206	+	0.187520i
$905$	−50.2873	+	8.86700i	−1.67161	+	0.294749i
$906$	34.7462	+	11.8526i	1.15437	+	0.393777i
$907$	41.5537	+	34.8677i	1.37977	+	1.15776i	0.969298	+	0.245889i	$0.0790797\pi$
$907$	41.5537	+	34.8677i	1.37977	+	1.15776i	0.410470	+	0.911874i	$0.365365\pi$
$908$	−6.70084	+	11.6062i	−0.222375	+	0.385165i
$909$	−30.3338	−	23.4202i	−1.00611	−	0.776798i
$910$	−12.2390	−	29.7604i	−0.405719	−	0.986549i
$911$	27.7257	−	33.0422i	0.918593	−	1.09474i	−0.0766250	−	0.997060i	$-0.524414\pi$
$911$	27.7257	−	33.0422i	0.918593	−	1.09474i	0.995218	−	0.0976768i	$-0.0311411\pi$
$912$	−1.46750	+	9.44073i	−0.0485937	+	0.312614i
$913$	22.2323	−	61.0828i	0.735783	−	2.02155i
$914$	5.77044	−	1.01748i	0.190869	−	0.0336554i
$915$	6.92066	−	0.140674i	0.228790	−	0.00465054i
$916$	−3.53952	−	9.72475i	−0.116949	−	0.321315i
$917$	4.61081	+	11.2117i	0.152262	+	0.370243i
$918$	14.2256	+	10.5289i	0.469516	+	0.347507i
$919$	2.14704	+	3.71878i	0.0708242	+	0.122671i	0.899263	−	0.437409i	$-0.144104\pi$
$919$	2.14704	+	3.71878i	0.0708242	+	0.122671i	−0.828439	+	0.560080i	$0.810770\pi$
$920$	0.998974	−	5.66546i	0.0329352	−	0.186785i
$921$	−34.9530	+	0.710479i	−1.15174	+	0.0234111i
$922$	−7.66759	+	21.0665i	−0.252519	+	0.693789i
$923$	−0.161795	−	0.917584i	−0.00532554	−	0.0302026i
$924$	6.60234	−	22.3169i	0.217201	−	0.734171i
$925$	1.07299	+	0.900342i	0.0352796	+	0.0296031i
$926$			25.7520i			0.846264i
$927$	1.99441	−	6.26023i	0.0655050	−	0.205613i
$928$	5.13193			0.168464
$929$	−14.3148	+	5.21015i	−0.469653	+	0.170940i	−0.565995	−	0.824409i	$-0.691508\pi$
$929$	−14.3148	+	5.21015i	−0.469653	+	0.170940i	0.0963424	+	0.995348i	$0.469286\pi$
$930$	10.8724	−	31.8727i	0.356520	−	1.04515i
$931$	38.4480	+	3.56004i	1.26008	+	0.116676i
$932$	−2.45147	+	6.73535i	−0.0803005	+	0.220624i
$933$	−9.44742	+	1.86455i	−0.309295	+	0.0610427i
$934$	−14.0068	+	16.6926i	−0.458315	+	0.546199i
$935$			37.4540i			1.22488i
$936$	16.0562	+	5.11526i	0.524814	+	0.167197i
$937$	38.2653	+	22.0925i	1.25007	+	0.721730i	0.971124	−	0.238577i	$-0.0766808\pi$
$937$	38.2653	+	22.0925i	1.25007	+	0.721730i	0.278948	+	0.960306i	$0.410014\pi$
$938$	24.1571	−	22.0236i	0.788757	−	0.719097i
$939$	5.11783	−	32.9241i	0.167014	−	1.07444i
$940$	6.75656	−	5.66943i	0.220375	−	0.184916i
$941$	−7.61692	−	43.1977i	−0.248305	−	1.40821i	−0.812691	−	0.582695i	$-0.801998\pi$
$941$	−7.61692	−	43.1977i	−0.248305	−	1.40821i	0.564387	−	0.825511i	$-0.309113\pi$
$942$	−0.311686	−	15.3338i	−0.0101553	−	0.499603i
$943$	−10.2278	+	12.1890i	−0.333063	+	0.396929i
$944$	1.26486			0.0411677
$945$	2.15505	−	29.6891i	0.0701036	−	0.965787i
$946$	4.27662			0.139045
$947$	−2.67316	+	3.18574i	−0.0868659	+	0.103523i	−0.807727	−	0.589557i	$-0.799302\pi$
$947$	−2.67316	+	3.18574i	−0.0868659	+	0.103523i	0.720861	+	0.693080i	$0.243747\pi$
$948$	−12.3218	+	7.45192i	−0.400194	+	0.242027i
$949$	−3.88622	−	22.0399i	−0.126152	−	0.715444i
$950$	1.31712	−	1.10520i	0.0427332	−	0.0358574i
$951$	0.399695	+	0.321771i	0.0129610	+	0.0104341i
$952$	−1.92816	−	8.80280i	−0.0624921	−	0.285300i
$953$	48.1730	+	27.8127i	1.56048	+	0.900941i	0.997209	+	0.0746668i	$0.0237893\pi$
$953$	48.1730	+	27.8127i	1.56048	+	0.900941i	0.563268	+	0.826275i	$0.309544\pi$
$954$	−11.4689	−	8.85495i	−0.371320	−	0.286689i
$955$			10.6021i			0.343077i
$956$	−0.439396	+	0.523652i	−0.0142111	+	0.0169361i
$957$	−29.7138	−	33.9843i	−0.960510	−	1.09855i
$958$	−3.85695	+	10.5969i	−0.124612	+	0.342370i
$959$	−27.1497	−	42.8556i	−0.876710	−	1.38388i
$960$	−2.46854	−	2.82333i	−0.0796719	−	0.0911225i
$961$	46.6386	−	16.9750i	1.50447	−	0.547582i
$962$	25.2412			0.813810
$963$	−10.7769	−	5.65103i	−0.347279	−	0.182102i
$964$			3.41618i			0.110028i
$965$	26.5986	+	22.3189i	0.856239	+	0.718470i
$966$	8.82894	−	8.38404i	0.284067	−	0.269752i
$967$	−7.59589	−	43.0784i	−0.244267	−	1.38531i	−0.822188	−	0.569216i	$-0.807247\pi$
$967$	−7.59589	−	43.0784i	−0.244267	−	1.38531i	0.577921	−	0.816093i	$-0.303864\pi$
$968$	−5.05919	+	13.9000i	−0.162608	+	0.446763i
$969$	15.6947	−	28.5066i	0.504186	−	0.915765i
$970$	−5.34578	+	30.3174i	−0.171643	+	0.973435i
$971$	−2.98676	−	5.17322i	−0.0958497	−	0.166016i	0.814113	−	0.580706i	$-0.197223\pi$
$971$	−2.98676	−	5.17322i	−0.0958497	−	0.166016i	−0.909963	+	0.414690i	$0.863890\pi$
$972$	11.1798	+	10.8634i	0.358591	+	0.348443i
$973$	3.51921	−	26.2179i	0.112821	−	0.840507i
$974$	−3.75111	−	10.3061i	−0.120193	−	0.330229i
$975$	−1.56937	−	2.59497i	−0.0502600	−	0.0831054i
$976$	1.81769	−	0.320508i	0.0581829	−	0.0102592i
$977$	−14.7614	+	40.5567i	−0.472260	+	1.29752i	0.443672	+	0.896189i	$0.353675\pi$
$977$	−14.7614	+	40.5567i	−0.472260	+	1.29752i	−0.915932	+	0.401333i	$0.868547\pi$
$978$	31.8292	+	25.6239i	1.01779	+	0.819361i
$979$	22.6796	−	27.0285i	0.724843	−	0.863834i
$980$	−10.7716	+	10.6630i	−0.344085	+	0.340618i
$981$	−28.1289	+	1.14401i	−0.898086	+	0.0365253i
$982$	10.5656	−	18.3002i	0.337163	−	0.583983i
$983$	45.7949	+	38.4265i	1.46063	+	1.22562i	0.924333	+	0.381587i	$0.124622\pi$
$983$	45.7949	+	38.4265i	1.46063	+	1.22562i	0.536299	+	0.844028i	$0.319822\pi$
$984$	2.00846	+	10.1766i	0.0640273	+	0.324417i
$985$	−17.9240	+	3.16048i	−0.571106	+	0.100701i
$986$	−16.4253	−	5.97834i	−0.523090	−	0.190389i
$987$	18.6318	−	1.14590i	0.593055	−	0.0364744i
$988$	5.38039	−	30.5137i	0.171173	−	0.970770i
$989$	1.93760	+	1.11868i	0.0616122	+	0.0355718i
$990$	−4.40358	+	32.6940i	−0.139955	+	1.03908i
$991$	−24.9052	−	43.1371i	−0.791140	−	1.37030i	−0.925261	−	0.379330i	$-0.876154\pi$
$991$	−24.9052	−	43.1371i	−0.791140	−	1.37030i	0.134121	−	0.990965i	$-0.457179\pi$
$992$	1.55928	−	8.84310i	0.0495071	−	0.280769i
$993$	17.3804	−	21.5894i	0.551550	−	0.685119i
$994$	−0.370730	+	0.234863i	−0.0117588	+	0.00744942i
$995$	31.0638	+	37.0204i	0.984789	+	1.17363i
$996$	−0.450534	−	22.1647i	−0.0142757	−	0.702314i
$997$	4.33356	+	0.764124i	0.137245	+	0.0242000i	0.241849	−	0.970314i	$-0.422246\pi$
$997$	4.33356	+	0.764124i	0.137245	+	0.0242000i	−0.104603	+	0.994514i	$0.533357\pi$
$998$	28.1719	+	16.2651i	0.891766	+	0.514861i
$999$	20.8951	+	10.4209i	0.661093	+	0.329704i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.bf.a.101.23	yes	144
7.5	odd	6		378.2.ba.a.47.9	✓	144
27.23	odd	18		378.2.ba.a.185.9	yes	144
189.131	even	18	inner	378.2.bf.a.131.23	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.47.9	✓	144	7.5	odd	6
378.2.ba.a.185.9	yes	144	27.23	odd	18
378.2.bf.a.101.23	yes	144	1.1	even	1	trivial
378.2.bf.a.131.23	yes	144	189.131	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(1.51729 + 0.835363i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(-1.65868 + 1.39179i) q^{5} +(1.61522 - 0.625351i) q^{6} +(1.78250 + 1.95517i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(1.60434 + 2.53498i) q^{9} +2.16525i q^{10} +(3.26445 - 3.89043i) q^{11} +(0.559197 - 1.63930i) q^{12} +(-1.92117 + 5.27837i) q^{13} +(2.64352 - 0.108713i) q^{14} +(-3.67934 + 0.726159i) q^{15} +(-0.939693 + 0.342020i) q^{16} +3.40603 q^{17} +(2.97315 + 0.400457i) q^{18} -5.51607i q^{19} +(1.65868 + 1.39179i) q^{20} +(1.07129 + 4.45560i) q^{21} +(-0.881888 - 5.00144i) q^{22} +(0.908716 - 2.49668i) q^{23} +(-0.896330 - 1.48209i) q^{24} +(-0.0541269 + 0.306969i) q^{25} +(2.80856 + 4.86457i) q^{26} +(0.316622 + 5.18650i) q^{27} +(1.61594 - 2.09493i) q^{28} +(-1.75522 - 4.82244i) q^{29} +(-1.80877 + 3.28531i) q^{30} +(-8.84310 + 1.55928i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(8.20304 - 3.17590i) q^{33} +(2.18935 - 2.60917i) q^{34} +(-5.67778 - 0.762124i) q^{35} +(2.21787 - 2.02016i) q^{36} +(2.24681 - 3.89159i) q^{37} +(-4.22555 - 3.54566i) q^{38} +(-7.32432 + 6.40394i) q^{39} +(2.13235 - 0.375991i) q^{40} +(-5.62761 - 2.04828i) q^{41} +(4.10180 + 2.04335i) q^{42} +(-0.146227 + 0.829295i) q^{43} +(-4.39819 - 2.53930i) q^{44} +(-6.18924 - 1.97179i) q^{45} +(-1.32845 - 2.30095i) q^{46} +(0.707350 - 4.01158i) q^{47} +(-1.71150 - 0.266041i) q^{48} +(-0.645395 + 6.97018i) q^{49} +(0.200360 + 0.238780i) q^{50} +(5.16793 + 2.84527i) q^{51} +(5.53178 + 0.975403i) q^{52} +(-4.18277 - 2.41492i) q^{53} +(4.17661 + 3.09127i) q^{54} +10.9964i q^{55} +(-0.566103 - 2.58448i) q^{56} +(4.60792 - 8.36947i) q^{57} +(-4.82244 - 1.75522i) q^{58} +(-1.18858 - 0.432607i) q^{59} +(1.35404 + 3.49735i) q^{60} +(-1.81769 - 0.320508i) q^{61} +(-4.48976 + 7.77649i) q^{62} +(-2.09658 + 7.65535i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-4.15980 - 11.4290i) q^{65} +(2.83993 - 8.32532i) q^{66} +(9.46485 - 7.94195i) q^{67} +(-0.591450 - 3.35428i) q^{68} +(3.46442 - 3.02907i) q^{69} +(-4.23343 + 3.85955i) q^{70} +(-0.143652 + 0.0829375i) q^{71} +(-0.121910 - 2.99752i) q^{72} +(-3.45044 + 1.99211i) q^{73} +(-1.53691 - 4.22263i) q^{74} +(-0.338557 + 0.420546i) q^{75} +(-5.43227 + 0.957855i) q^{76} +(13.4253 - 0.552110i) q^{77} +(0.197720 + 9.72713i) q^{78} +(-6.36875 - 5.34402i) q^{79} +(1.08262 - 1.87516i) q^{80} +(-3.85220 + 8.13391i) q^{81} +(-5.18644 + 2.99439i) q^{82} +(12.0275 - 4.37766i) q^{83} +(4.20188 - 1.82872i) q^{84} +(-5.64949 + 4.74049i) q^{85} +(0.541284 + 0.645077i) q^{86} +(1.36530 - 8.78329i) q^{87} +(-4.77231 + 1.73698i) q^{88} +6.94743 q^{89} +(-5.48885 + 3.47379i) q^{90} +(-13.7446 + 5.65247i) q^{91} +(-2.61654 - 0.461367i) q^{92} +(-14.7201 - 5.02132i) q^{93} +(-2.61837 - 3.12046i) q^{94} +(7.67723 + 9.14937i) q^{95} +(-1.30393 + 1.14008i) q^{96} +(14.0018 + 2.46890i) q^{97} +(4.92462 + 4.97475i) q^{98} +(15.0994 + 2.03375i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51}+ \cdots - 108 q^{99}+O(q^{100}) \) 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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