LMFDB - Embedded newform 990.2.o.a.329.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(329,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.329"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.o (of order $6$, degree $2$, 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:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$72$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			329.4
Character	$\chi$	$=$	990.329
Dual form			990.2.o.a.659.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.62901 + 0.588492i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.65730 - 1.50112i) q^{5} +(1.11652 - 1.32415i) q^{6} +(-0.753042 - 1.30431i) q^{7} +1.00000i q^{8} +(2.30735 - 1.91732i) q^{9} +(-0.684705 + 2.12866i) q^{10} +(2.52618 + 2.14905i) q^{11} +(-0.304856 + 1.70501i) q^{12} +(0.181842 - 0.314960i) q^{13} +(1.30431 + 0.753042i) q^{14} +(-1.81636 + 3.42065i) q^{15} +(-0.500000 - 0.866025i) q^{16} -3.12994i q^{17} +(-1.03957 + 2.81413i) q^{18} +5.85203i q^{19} +(-0.471357 - 2.18582i) q^{20} +(1.99429 + 1.68157i) q^{21} +(-3.26226 - 0.598045i) q^{22} +(-0.170072 + 0.294573i) q^{23} +(-0.588492 - 1.62901i) q^{24} +(0.493286 - 4.97561i) q^{25} +0.363684i q^{26} +(-2.63038 + 4.48120i) q^{27} -1.50608 q^{28} +(-4.33590 - 7.51001i) q^{29} +(-0.137306 - 3.87055i) q^{30} +(4.09571 - 7.09397i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.37987 - 2.01419i) q^{33} +(1.56497 + 2.71061i) q^{34} +(-3.20594 - 1.03122i) q^{35} +(-0.506771 - 2.95689i) q^{36} +2.82562i q^{37} +(-2.92602 - 5.06801i) q^{38} +(-0.110871 + 0.620085i) q^{39} +(1.50112 + 1.65730i) q^{40} +(-0.736994 + 1.27651i) q^{41} +(-2.56789 - 0.459139i) q^{42} +(3.98317 + 6.89905i) q^{43} +(3.12422 - 1.11321i) q^{44} +(0.945852 - 6.64119i) q^{45} -0.340143i q^{46} +(-6.41122 - 11.1046i) q^{47} +(1.32415 + 1.11652i) q^{48} +(2.36586 - 4.09778i) q^{49} +(2.06061 + 4.55565i) q^{50} +(1.84195 + 5.09871i) q^{51} +(-0.181842 - 0.314960i) q^{52} +2.86456 q^{53} +(0.0373754 - 5.19602i) q^{54} +(7.41262 - 0.230468i) q^{55} +(1.30431 - 0.753042i) q^{56} +(-3.44388 - 9.53303i) q^{57} +(7.51001 + 4.33590i) q^{58} +(3.48092 + 2.00971i) q^{59} +(2.05419 + 3.28334i) q^{60} +(0.288024 - 0.166291i) q^{61} +8.19141i q^{62} +(-4.23831 - 1.56568i) q^{63} -1.00000 q^{64} +(-0.171425 - 0.794949i) q^{65} +(5.66620 - 0.945593i) q^{66} +(7.04145 + 4.06538i) q^{67} +(-2.71061 - 1.56497i) q^{68} +(0.103695 - 0.579948i) q^{69} +(3.29203 - 0.709903i) q^{70} -11.8375i q^{71} +(1.91732 + 2.30735i) q^{72} -2.32806 q^{73} +(-1.41281 - 2.44706i) q^{74} +(2.12454 + 8.39561i) q^{75} +(5.06801 + 2.92602i) q^{76} +(0.900706 - 4.91324i) q^{77} +(-0.214025 - 0.592445i) q^{78} +(4.28208 - 2.47226i) q^{79} +(-2.12866 - 0.684705i) q^{80} +(1.64776 - 8.84787i) q^{81} -1.47399i q^{82} +(4.81005 - 2.77708i) q^{83} +(2.45343 - 0.886319i) q^{84} +(-4.69841 - 5.18725i) q^{85} +(-6.89905 - 3.98317i) q^{86} +(11.4828 + 9.68224i) q^{87} +(-2.14905 + 2.52618i) q^{88} +6.43660i q^{89} +(2.50146 + 6.22436i) q^{90} -0.547739 q^{91} +(0.170072 + 0.294573i) q^{92} +(-2.49720 + 13.9664i) q^{93} +(11.1046 + 6.41122i) q^{94} +(8.78460 + 9.69857i) q^{95} +(-1.70501 - 0.304856i) q^{96} +(12.0066 - 6.93201i) q^{97} +4.73171i q^{98} +(9.94921 + 0.115132i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) $ 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.62901	+	0.588492i	−0.940510	+	0.339766i
$3$	−1.62901	+	0.588492i	−0.940510	+	0.339766i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.65730	−	1.50112i	0.741167	−	0.671321i
$5$	1.65730	−	1.50112i	0.741167	−	0.671321i
$6$	1.11652	−	1.32415i	0.455817	−	0.540584i
$7$	−0.753042	−	1.30431i	−0.284623	−	0.492982i	0.687895	−	0.725811i	$-0.258535\pi$
$7$	−0.753042	−	1.30431i	−0.284623	−	0.492982i	−0.972518	+	0.232829i	$0.925202\pi$
$8$			1.00000i			0.353553i
$9$	2.30735	−	1.91732i	0.769118	−	0.639107i
$10$	−0.684705	+	2.12866i	−0.216523	+	0.673140i
$11$	2.52618	+	2.14905i	0.761671	+	0.647964i
$11$	2.52618	+	2.14905i	0.761671	+	0.647964i
$12$	−0.304856	+	1.70501i	−0.0880045	+	0.492194i
$13$	0.181842	−	0.314960i	0.0504339	−	0.0873541i	−0.839706	−	0.543041i	$-0.817273\pi$
$13$	0.181842	−	0.314960i	0.0504339	−	0.0873541i	0.890140	+	0.455687i	$0.150606\pi$
$14$	1.30431	+	0.753042i	0.348591	+	0.201259i
$15$	−1.81636	+	3.42065i	−0.468983	+	0.883207i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		−	3.12994i		−	0.759122i	−0.925167	−	0.379561i	$-0.876075\pi$
$17$		−	3.12994i		−	0.759122i	0.925167	−	0.379561i	$-0.123925\pi$
$18$	−1.03957	+	2.81413i	−0.245028	+	0.663296i
$19$			5.85203i			1.34255i	0.741209	+	0.671274i	$0.234253\pi$
$19$			5.85203i			1.34255i	−0.741209	+	0.671274i	$0.765747\pi$
$20$	−0.471357	−	2.18582i	−0.105399	−	0.488765i
$21$	1.99429	+	1.68157i	0.435189	+	0.366949i
$22$	−3.26226	−	0.598045i	−0.695516	−	0.127504i
$23$	−0.170072	+	0.294573i	−0.0354624	+	0.0614226i	−0.883212	−	0.468974i	$-0.844624\pi$
$23$	−0.170072	+	0.294573i	−0.0354624	+	0.0614226i	0.847749	+	0.530397i	$0.177957\pi$
$24$	−0.588492	−	1.62901i	−0.120125	−	0.332520i
$25$	0.493286	−	4.97561i	0.0986572	−	0.995121i
$26$			0.363684i			0.0713243i
$27$	−2.63038	+	4.48120i	−0.506216	+	0.862407i
$28$	−1.50608			−0.284623
$29$	−4.33590	−	7.51001i	−0.805157	−	1.39457i	−0.916185	−	0.400756i	$-0.868748\pi$
$29$	−4.33590	−	7.51001i	−0.805157	−	1.39457i	0.111028	−	0.993817i	$-0.464586\pi$
$30$	−0.137306	−	3.87055i	−0.0250686	−	0.706662i
$31$	4.09571	−	7.09397i	0.735610	−	1.27411i	−0.218845	−	0.975760i	$-0.570229\pi$
$31$	4.09571	−	7.09397i	0.735610	−	1.27411i	0.954455	−	0.298355i	$-0.0964379\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−5.37987	−	2.01419i	−0.936516	−	0.350626i
$34$	1.56497	+	2.71061i	0.268390	+	0.464866i
$35$	−3.20594	−	1.03122i	−0.541902	−	0.174308i
$36$	−0.506771	−	2.95689i	−0.0844619	−	0.492815i
$37$			2.82562i			0.464529i	0.972653	+	0.232264i	$0.0746134\pi$
$37$			2.82562i			0.464529i	−0.972653	+	0.232264i	$0.925387\pi$
$38$	−2.92602	−	5.06801i	−0.474663	−	0.822140i
$39$	−0.110871	+	0.620085i	−0.0177536	+	0.0992931i
$40$	1.50112	+	1.65730i	0.237348	+	0.262042i
$41$	−0.736994	+	1.27651i	−0.115099	+	0.199358i	−0.917819	−	0.396998i	$-0.870052\pi$
$41$	−0.736994	+	1.27651i	−0.115099	+	0.199358i	0.802720	+	0.596356i	$0.203385\pi$
$42$	−2.56789	−	0.459139i	−0.396234	−	0.0708467i
$43$	3.98317	+	6.89905i	0.607427	+	1.05209i	0.991663	+	0.128860i	$0.0411317\pi$
$43$	3.98317	+	6.89905i	0.607427	+	1.05209i	−0.384236	+	0.923235i	$0.625535\pi$
$44$	3.12422	−	1.11321i	0.470994	−	0.167822i
$45$	0.945852	−	6.64119i	0.140999	−	0.990010i
$46$		−	0.340143i		−	0.0501514i
$47$	−6.41122	−	11.1046i	−0.935172	−	1.61977i	−0.774326	−	0.632787i	$-0.781911\pi$
$47$	−6.41122	−	11.1046i	−0.935172	−	1.61977i	−0.160846	−	0.986980i	$-0.551422\pi$
$48$	1.32415	+	1.11652i	0.191125	+	0.161156i
$49$	2.36586	−	4.09778i	0.337979	−	0.585397i
$50$	2.06061	+	4.55565i	0.291414	+	0.644266i
$51$	1.84195	+	5.09871i	0.257924	+	0.713962i
$52$	−0.181842	−	0.314960i	−0.0252170	−	0.0436770i
$53$	2.86456			0.393478			0.196739	−	0.980456i	$-0.436965\pi$
$53$	2.86456			0.393478			0.196739	+	0.980456i	$0.436965\pi$
$54$	0.0373754	−	5.19602i	0.00508614	−	0.707088i
$55$	7.41262	−	0.230468i	0.999517	−	0.0310763i
$56$	1.30431	−	0.753042i	0.174295	−	0.100629i
$57$	−3.44388	−	9.53303i	−0.456152	−	1.26268i
$58$	7.51001	+	4.33590i	0.986112	+	0.569332i
$59$	3.48092	+	2.00971i	0.453177	+	0.261642i	0.709171	−	0.705037i	$-0.249069\pi$
$59$	3.48092	+	2.00971i	0.453177	+	0.261642i	−0.255994	+	0.966678i	$0.582403\pi$
$60$	2.05419	+	3.28334i	0.265194	+	0.423877i
$61$	0.288024	−	0.166291i	0.0368777	−	0.0212914i	−0.481448	−	0.876475i	$-0.659889\pi$
$61$	0.288024	−	0.166291i	0.0368777	−	0.0212914i	0.518326	+	0.855183i	$0.326556\pi$
$62$			8.19141i			1.04031i
$63$	−4.23831	−	1.56568i	−0.533977	−	0.197257i
$64$	−1.00000			−0.125000
$65$	−0.171425	−	0.794949i	−0.0212626	−	0.0986013i
$66$	5.66620	−	0.945593i	0.697461	−	0.116394i
$67$	7.04145	+	4.06538i	0.860250	+	0.496666i	0.864096	−	0.503327i	$-0.167891\pi$
$67$	7.04145	+	4.06538i	0.860250	+	0.496666i	−0.00384595	+	0.999993i	$0.501224\pi$
$68$	−2.71061	−	1.56497i	−0.328710	−	0.189781i
$69$	0.103695	−	0.579948i	0.0124834	−	0.0698175i
$70$	3.29203	−	0.709903i	0.393473	−	0.0848496i
$71$		−	11.8375i		−	1.40485i	−0.711758	−	0.702425i	$-0.752101\pi$
$71$		−	11.8375i		−	1.40485i	0.711758	−	0.702425i	$-0.247899\pi$
$72$	1.91732	+	2.30735i	0.225958	+	0.271924i
$73$	−2.32806			−0.272479			−0.136239	−	0.990676i	$-0.543502\pi$
$73$	−2.32806			−0.272479			−0.136239	+	0.990676i	$0.543502\pi$
$74$	−1.41281	−	2.44706i	−0.164236	−	0.284465i
$75$	2.12454	+	8.39561i	0.245320	+	0.969442i
$76$	5.06801	+	2.92602i	0.581341	+	0.335637i
$77$	0.900706	−	4.91324i	0.102645	−	0.559916i
$78$	−0.214025	−	0.592445i	−0.0242336	−	0.0670812i
$79$	4.28208	−	2.47226i	0.481772	−	0.278151i	−0.239383	−	0.970925i	$-0.576945\pi$
$79$	4.28208	−	2.47226i	0.481772	−	0.278151i	0.721155	+	0.692774i	$0.243612\pi$
$80$	−2.12866	−	0.684705i	−0.237991	−	0.0765523i
$81$	1.64776	−	8.84787i	0.183085	−	0.983097i
$82$		−	1.47399i		−	0.162775i
$83$	4.81005	−	2.77708i	0.527971	−	0.304824i	−0.212219	−	0.977222i	$-0.568069\pi$
$83$	4.81005	−	2.77708i	0.527971	−	0.304824i	0.740190	+	0.672398i	$0.234736\pi$
$84$	2.45343	−	0.886319i	0.267691	−	0.0967053i
$85$	−4.69841	−	5.18725i	−0.509614	−	0.562636i
$86$	−6.89905	−	3.98317i	−0.743943	−	0.429516i
$87$	11.4828	+	9.68224i	1.23109	+	1.03804i
$88$	−2.14905	+	2.52618i	−0.229090	+	0.269291i
$89$			6.43660i			0.682278i	0.940013	+	0.341139i	$0.110813\pi$
$89$			6.43660i			0.682278i	−0.940013	+	0.341139i	$0.889187\pi$
$90$	2.50146	+	6.22436i	0.263677	+	0.656105i
$91$	−0.547739			−0.0574186
$92$	0.170072	+	0.294573i	0.0177312	+	0.0307113i
$93$	−2.49720	+	13.9664i	−0.258948	+	1.44825i
$94$	11.1046	+	6.41122i	1.14535	+	0.661267i
$95$	8.78460	+	9.69857i	0.901281	+	0.995053i
$96$	−1.70501	−	0.304856i	−0.174017	−	0.0311143i
$97$	12.0066	−	6.93201i	1.21908	−	0.703839i	0.254362	−	0.967109i	$-0.418135\pi$
$97$	12.0066	−	6.93201i	1.21908	−	0.703839i	0.964722	+	0.263271i	$0.0848012\pi$
$98$			4.73171i			0.477975i
$99$	9.94921	+	0.115132i	0.999933	+	0.0115712i
$100$	−4.06236	−	2.91500i	−0.406236	−	0.291500i
$101$	−1.26977	−	2.19930i	−0.126347	−	0.218839i	0.795912	−	0.605412i	$-0.206992\pi$
$101$	−1.26977	−	2.19930i	−0.126347	−	0.218839i	−0.922259	+	0.386574i	$0.873658\pi$
$102$	−4.14453	−	3.49464i	−0.410369	−	0.346021i
$103$	9.01251	+	5.20338i	0.888029	+	0.512704i	0.873297	−	0.487188i	$-0.161977\pi$
$103$	9.01251	+	5.20338i	0.888029	+	0.512704i	0.0147318	+	0.999891i	$0.495311\pi$
$104$	0.314960	+	0.181842i	0.0308843	+	0.0178311i
$105$	5.82937	−	0.206795i	0.568888	−	0.0201811i
$106$	−2.48078	+	1.43228i	−0.240955	+	0.139115i
$107$		−	20.0070i		−	1.93415i	−0.254484	−	0.967077i	$-0.581906\pi$
$107$		−	20.0070i		−	1.93415i	0.254484	−	0.967077i	$-0.418094\pi$
$108$	2.56564	+	4.51857i	0.246879	+	0.434800i
$109$		−	8.21498i		−	0.786853i	−0.919356	−	0.393426i	$-0.871290\pi$
$109$		−	8.21498i		−	0.786853i	0.919356	−	0.393426i	$-0.128710\pi$
$110$	−6.30428	+	3.90590i	−0.601090	+	0.372413i
$111$	−1.66285	−	4.60296i	−0.157831	−	0.436894i
$112$	−0.753042	+	1.30431i	−0.0711558	+	0.123245i
$113$	−3.11823	+	5.40093i	−0.293338	+	0.508076i	−0.974597	−	0.223966i	$-0.928099\pi$
$113$	−3.11823	+	5.40093i	−0.293338	+	0.508076i	0.681259	+	0.732043i	$0.261433\pi$
$114$	7.74900	+	6.53391i	0.725760	+	0.611956i
$115$	0.160329	+	0.743493i	0.0149507	+	0.0693311i
$116$	−8.67181			−0.805157
$117$	−0.184305	−	1.07537i	−0.0170390	−	0.0994182i
$118$	−4.01942			−0.370017
$119$	−4.08241	+	2.35698i	−0.374233	+	0.216064i
$120$	−3.42065	−	1.81636i	−0.312261	−	0.165811i
$121$	1.76315	+	10.8578i	0.160286	+	0.987071i
$122$	−0.166291	+	0.288024i	−0.0150553	+	0.0260765i
$123$	0.449355	−	2.51317i	0.0405170	−	0.226605i
$124$	−4.09571	−	7.09397i	−0.367805	−	0.637057i
$125$	−6.65145	−	8.98655i	−0.594924	−	0.803782i
$126$	4.45332	−	0.763240i	0.396733	−	0.0679948i
$127$	14.5254			1.28892			0.644458	−	0.764639i	$-0.277083\pi$
$127$	14.5254			1.28892			0.644458	+	0.764639i	$0.277083\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−10.5487	−	8.89456i	−0.928758	−	0.783122i
$130$	0.545933	+	0.602734i	0.0478815	+	0.0528632i
$131$	6.73265	−	11.6613i	0.588235	−	1.01885i	−0.406229	−	0.913771i	$-0.633157\pi$
$131$	6.73265	−	11.6613i	0.588235	−	1.01885i	0.994464	−	0.105081i	$-0.0335102\pi$
$132$	−4.43428	+	3.65201i	−0.385954	+	0.317867i
$133$	7.63285	−	4.40683i	0.661852	−	0.382120i
$134$	−8.13077			−0.702391
$135$	2.36748	+	11.3752i	0.203760	+	0.979021i
$136$	3.12994			0.268390
$137$	−2.36790	−	4.10133i	−0.202304	−	0.350400i	0.746967	−	0.664861i	$-0.231509\pi$
$137$	−2.36790	−	4.10133i	−0.202304	−	0.350400i	−0.949270	+	0.314461i	$0.898176\pi$
$138$	0.200172	+	0.554097i	0.0170397	+	0.0471679i
$139$	−13.3551	−	7.71058i	−1.13277	−	0.654003i	−0.188137	−	0.982143i	$-0.560245\pi$
$139$	−13.3551	−	7.71058i	−1.13277	−	0.654003i	−0.944629	+	0.328140i	$0.893578\pi$
$140$	−2.49603	+	2.26081i	−0.210953	+	0.191073i
$141$	16.9789	+	14.3165i	1.42988	+	1.20567i
$142$	5.91873	+	10.2515i	0.496689	+	0.860291i
$143$	1.13623	−	0.404856i	0.0950163	−	0.0338558i
$144$	−2.81413	−	1.03957i	−0.234510	−	0.0866306i
$145$	−18.4593	−	5.93763i	−1.53296	−	0.493093i
$146$	2.01616	−	1.16403i	0.166858	−	0.0963358i
$147$	−1.44249	+	8.06762i	−0.118975	+	0.665406i
$148$	2.44706	+	1.41281i	0.201147	+	0.116132i
$149$	7.15210	−	12.3878i	0.585923	−	1.01485i	−0.408837	−	0.912608i	$-0.634065\pi$
$149$	7.15210	−	12.3878i	0.585923	−	1.01485i	0.994760	−	0.102241i	$-0.0326012\pi$
$150$	−6.03771	−	6.20855i	−0.492977	−	0.506926i
$151$	−17.8768	+	10.3212i	−1.45479	+	0.839925i	−0.998748	−	0.0500312i	$-0.984068\pi$
$151$	−17.8768	+	10.3212i	−1.45479	+	0.839925i	−0.456046	+	0.889956i	$0.650735\pi$
$152$	−5.85203			−0.474663
$153$	−6.00110	−	7.22188i	−0.485160	−	0.583855i
$154$	1.67659	+	4.70534i	0.135103	+	0.379167i
$155$	−3.86108	−	17.9050i	−0.310129	−	1.43816i
$156$	0.481574	+	0.406060i	0.0385568	+	0.0325108i
$157$	−7.10527	−	4.10223i	−0.567062	−	0.327394i	0.188913	−	0.981994i	$-0.439504\pi$
$157$	−7.10527	−	4.10223i	−0.567062	−	0.327394i	−0.755975	+	0.654600i	$0.772837\pi$
$158$	−2.47226	+	4.28208i	−0.196683	+	0.340664i
$159$	−4.66640	+	1.68577i	−0.370070	+	0.133690i
$160$	2.18582	−	0.471357i	0.172804	−	0.0372640i
$161$	0.512284			0.0403737
$162$	2.99693	+	8.48637i	0.235461	+	0.666752i
$163$			15.7263i			1.23178i	0.787832	+	0.615891i	$0.211204\pi$
$163$			15.7263i			1.23178i	−0.787832	+	0.615891i	$0.788796\pi$
$164$	0.736994	+	1.27651i	0.0575496	+	0.0996788i
$165$	−11.9396	+	4.73770i	−0.929497	+	0.368830i
$166$	−2.77708	+	4.81005i	−0.215543	+	0.373332i
$167$	−4.76329	−	2.75009i	−0.368594	−	0.212808i	0.304250	−	0.952592i	$-0.401594\pi$
$167$	−4.76329	−	2.75009i	−0.368594	−	0.212808i	−0.672844	+	0.739784i	$0.734928\pi$
$168$	−1.68157	+	1.99429i	−0.129736	+	0.153863i
$169$	6.43387	+	11.1438i	0.494913	+	0.857214i
$170$	6.66257	+	2.14309i	0.510996	+	0.164367i
$171$	11.2202	+	13.5027i	0.858032	+	1.03258i
$172$	7.96633			0.607427
$173$	2.75941	−	1.59315i	0.209794	−	0.121125i	−0.391422	−	0.920211i	$-0.628017\pi$
$173$	2.75941	−	1.59315i	0.209794	−	0.121125i	0.601216	+	0.799087i	$0.294683\pi$
$174$	−14.7855	−	2.64366i	−1.12089	−	0.200415i
$175$	−6.86119	+	3.10345i	−0.518657	+	0.234598i
$176$	0.598045	−	3.26226i	0.0450793	−	0.245902i
$177$	−6.85315	−	1.22534i	−0.515114	−	0.0921026i
$178$	−3.21830	−	5.57426i	−0.241222	−	0.417808i
$179$			12.4641i			0.931613i	0.884887	+	0.465806i	$0.154236\pi$
$179$			12.4641i			0.931613i	−0.884887	+	0.465806i	$0.845764\pi$
$180$	−5.27851	−	4.13973i	−0.393437	−	0.308557i
$181$	−17.6187			−1.30959			−0.654793	−	0.755808i	$-0.727244\pi$
$181$	−17.6187			−1.30959			−0.654793	+	0.755808i	$0.727244\pi$
$182$	0.474356	−	0.273869i	0.0351616	−	0.0203005i
$183$	−0.371334	+	0.440389i	−0.0274498	+	0.0325545i
$184$	−0.294573	−	0.170072i	−0.0217162	−	0.0125378i
$185$	4.24159	+	4.68290i	0.311848	+	0.344293i
$186$	−4.82058	−	13.3439i	−0.353462	−	0.978422i
$187$	6.72641	−	7.90679i	0.491884	−	0.578202i
$188$	−12.8224			−0.935172
$189$	7.82564	+	0.0562905i	0.569232	+	0.00409453i
$190$	−12.4570	−	4.00691i	−0.903724	−	0.290692i
$191$	−21.1322	+	12.2007i	−1.52907	+	0.882809i	−0.529668	+	0.848205i	$0.677684\pi$
$191$	−21.1322	+	12.2007i	−1.52907	+	0.882809i	−0.999401	+	0.0346039i	$0.988983\pi$
$192$	1.62901	−	0.588492i	0.117564	−	0.0424708i
$193$	−0.0264713	+	0.0458496i	−0.00190545	+	0.00330033i	−0.866977	−	0.498349i	$-0.833940\pi$
$193$	−0.0264713	+	0.0458496i	−0.00190545	+	0.00330033i	0.865071	+	0.501649i	$0.167273\pi$
$194$	−6.93201	+	12.0066i	−0.497689	+	0.862023i
$195$	0.747074	+	1.19410i	0.0534991	+	0.0855112i
$196$	−2.36586	−	4.09778i	−0.168990	−	0.292699i
$197$		−	7.28037i		−	0.518705i	−0.965783	−	0.259352i	$-0.916491\pi$
$197$		−	7.28037i		−	0.518705i	0.965783	−	0.259352i	$-0.0835091\pi$
$198$	−8.67383	+	4.87490i	−0.616422	+	0.346444i
$199$	2.48315			0.176026			0.0880130	−	0.996119i	$-0.471948\pi$
$199$	2.48315			0.176026			0.0880130	+	0.996119i	$0.471948\pi$
$200$	4.97561	+	0.493286i	0.351829	+	0.0348806i
$201$	−13.8630	−	2.47872i	−0.977824	−	0.174835i
$202$	2.19930	+	1.26977i	0.154742	+	0.0893405i
$203$	−6.53024	+	11.3107i	−0.458333	+	0.793856i
$204$	5.33658	+	0.954183i	0.373636	+	0.0668061i
$205$	0.694774	+	3.22188i	0.0485252	+	0.225026i
$206$	−10.4068			−0.725073
$207$	0.172375	+	1.00577i	0.0119809	+	0.0699055i
$208$	−0.363684			−0.0252170
$209$	−12.5763	+	14.7833i	−0.869923	+	1.02258i
$210$	−4.94499	+	3.09378i	−0.341237	+	0.213491i
$211$	1.80220	+	1.04050i	0.124068	+	0.0716309i	0.560750	−	0.827985i	$-0.310513\pi$
$211$	1.80220	+	1.04050i	0.124068	+	0.0716309i	−0.436681	+	0.899616i	$0.643846\pi$
$212$	1.43228	−	2.48078i	0.0983694	−	0.170381i
$213$	6.96626	+	19.2834i	0.477320	+	1.32127i
$214$	10.0035	+	17.3266i	0.683827	+	1.18442i
$215$	16.9576	+	5.45459i	1.15650	+	0.372000i
$216$	−4.48120	−	2.63038i	−0.304907	−	0.178974i
$217$	−12.3370			−0.837487
$218$	4.10749	+	7.11438i	0.278194	+	0.481847i
$219$	3.79243	−	1.37004i	0.256269	−	0.0925790i
$220$	3.50672	−	6.53475i	0.236423	−	0.440573i
$221$	−0.985805	−	0.569155i	−0.0663124	−	0.0382855i
$222$	3.74155	+	3.15486i	0.251117	+	0.211740i
$223$	−7.47368	+	4.31493i	−0.500475	+	0.288949i	−0.728910	−	0.684610i	$-0.759973\pi$
$223$	−7.47368	+	4.31493i	−0.500475	+	0.288949i	0.228435	+	0.973559i	$0.426639\pi$
$224$		−	1.50608i		−	0.100629i
$225$	−8.40165	−	12.4263i	−0.560110	−	0.828418i
$226$		−	6.23645i		−	0.414843i
$227$	−20.6082	+	11.8981i	−1.36781	+	0.789706i	−0.990648	−	0.136441i	$-0.956434\pi$
$227$	−20.6082	+	11.8981i	−1.36781	+	0.789706i	−0.377163	+	0.926147i	$0.623100\pi$
$228$	−9.97778	−	1.78403i	−0.660795	−	0.118150i
$229$	10.3827	−	17.9834i	0.686109	−	1.18838i	−0.286978	−	0.957937i	$-0.592651\pi$
$229$	10.3827	−	17.9834i	0.686109	−	1.18838i	0.973087	−	0.230439i	$-0.0740161\pi$
$230$	−0.510595	−	0.563719i	−0.0336677	−	0.0371705i
$231$	1.42414	+	8.53378i	0.0937017	+	0.561481i
$232$	7.51001	−	4.33590i	0.493056	−	0.284666i
$233$		−	10.1115i		−	0.662423i	−0.943556	−	0.331212i	$-0.892543\pi$
$233$		−	10.1115i		−	0.662423i	0.943556	−	0.331212i	$-0.107457\pi$
$234$	0.697299	+	0.839148i	0.0455838	+	0.0548568i
$235$	−27.2946	−	8.77958i	−1.78050	−	0.572717i
$236$	3.48092	−	2.00971i	0.226588	−	0.130821i
$237$	−5.52065	+	6.54731i	−0.358605	+	0.425294i
$238$	2.35698	−	4.08241i	0.152780	−	0.264623i
$239$	8.54604	−	14.8022i	0.552798	−	0.957474i	−0.445274	−	0.895395i	$-0.646894\pi$
$239$	8.54604	−	14.8022i	0.552798	−	0.957474i	0.998071	−	0.0620790i	$-0.0197731\pi$
$240$	3.87055	−	0.137306i	0.249843	−	0.00886310i
$241$	3.16842	−	1.82929i	0.204096	−	0.117835i	−0.394469	−	0.918909i	$-0.629071\pi$
$241$	3.16842	−	1.82929i	0.204096	−	0.117835i	0.598564	+	0.801075i	$0.295738\pi$
$242$	−6.95582	−	8.52154i	−0.447137	−	0.547785i
$243$	2.52268	+	15.3830i	0.161830	+	0.986819i
$244$		−	0.332582i		−	0.0212914i
$245$	−2.23032	−	10.3427i	−0.142490	−	0.660770i
$246$	0.867431	+	2.40114i	0.0553054	+	0.153091i
$247$	1.84315	+	1.06415i	0.117277	+	0.0677100i
$248$	7.09397	+	4.09571i	0.450468	+	0.260078i
$249$	−6.20133	+	7.35457i	−0.392993	+	0.466077i
$250$	10.2536	+	4.45686i	0.648495	+	0.281876i
$251$			17.4379i			1.10067i	0.834945	+	0.550334i	$0.185499\pi$
$251$			17.4379i			1.10067i	−0.834945	+	0.550334i	$0.814501\pi$
$252$	−3.47507	+	2.88765i	−0.218909	+	0.181905i
$253$	−1.06268	+	0.378650i	−0.0668103	+	0.0238055i
$254$	−12.5793	+	7.26268i	−0.789297	+	0.455701i
$255$	10.7064	+	5.68511i	0.670462	+	0.356015i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	13.1384	−	22.7563i	0.819548	−	1.41950i	−0.0864672	−	0.996255i	$-0.527558\pi$
$257$	13.1384	−	22.7563i	0.819548	−	1.41950i	0.906015	−	0.423245i	$-0.139109\pi$
$258$	13.5827	+	2.42859i	0.845621	+	0.151197i
$259$	3.68547	−	2.12781i	0.229004	−	0.132216i
$260$	−0.774158	−	0.249016i	−0.0480113	−	0.0154433i
$261$	−24.4036	−	9.01493i	−1.51054	−	0.558010i
$262$			13.4653i			0.831889i
$263$	−13.7456	+	7.93601i	−0.847588	+	0.489355i	−0.859836	−	0.510570i	$-0.829435\pi$
$263$	−13.7456	+	7.93601i	−0.847588	+	0.489355i	0.0122481	+	0.999925i	$0.496101\pi$
$264$	2.01419	−	5.37987i	0.123965	−	0.331108i
$265$	4.74743	−	4.30004i	0.291633	−	0.264150i
$266$	−4.40683	+	7.63285i	−0.270200	+	0.468000i
$267$	−3.78789	−	10.4853i	−0.231815	−	0.641689i
$268$	7.04145	−	4.06538i	0.430125	−	0.248333i
$269$			14.6229i			0.891574i	0.895139	+	0.445787i	$0.147076\pi$
$269$			14.6229i			0.891574i	−0.895139	+	0.445787i	$0.852924\pi$
$270$	−7.73790	−	8.66747i	−0.470913	−	0.527485i
$271$		−	20.2780i		−	1.23180i	−0.787824	−	0.615901i	$-0.788792\pi$
$271$		−	20.2780i		−	1.23180i	0.787824	−	0.615901i	$-0.211208\pi$
$272$	−2.71061	+	1.56497i	−0.164355	+	0.0948903i
$273$	0.892273	−	0.322340i	0.0540028	−	0.0195089i
$274$	4.10133	+	2.36790i	0.247770	+	0.143050i
$275$	11.9390	−	11.5092i	0.719947	−	0.694029i
$276$	−0.450402	−	0.379776i	−0.0271110	−	0.0228598i
$277$	−3.22249	−	5.58151i	−0.193620	−	0.335360i	0.752827	−	0.658218i	$-0.228690\pi$
$277$	−3.22249	−	5.58151i	−0.193620	−	0.335360i	−0.946447	+	0.322858i	$0.895356\pi$
$278$	15.4212			0.924900
$279$	−4.15117	−	24.2211i	−0.248524	−	1.45008i
$280$	1.03122	−	3.20594i	0.0616273	−	0.191591i
$281$	13.0935	+	22.6787i	0.781095	+	1.35290i	0.931304	+	0.364242i	$0.118672\pi$
$281$	13.0935	+	22.6787i	0.781095	+	1.35290i	−0.150210	+	0.988654i	$0.547995\pi$
$282$	−21.8624	−	3.90900i	−1.30189	−	0.232778i
$283$	−12.4881	+	21.6300i	−0.742340	+	1.28577i	0.209087	+	0.977897i	$0.432951\pi$
$283$	−12.4881	+	21.6300i	−0.742340	+	1.28577i	−0.951427	+	0.307874i	$0.900382\pi$
$284$	−10.2515	−	5.91873i	−0.608318	−	0.351212i
$285$	−20.0177	−	10.6294i	−1.18575	−	0.629632i
$286$	−0.781576	+	0.918731i	−0.0462156	+	0.0543257i
$287$	2.21995			0.131040
$288$	2.95689	−	0.506771i	0.174236	−	0.0298618i
$289$	7.20347			0.423733
$290$	18.9550	−	4.08752i	1.11308	−	0.240027i
$291$	−15.4794	+	18.3581i	−0.907420	+	1.07617i
$292$	−1.16403	+	2.01616i	−0.0681197	+	0.117987i
$293$	19.3890	+	11.1942i	1.13272	+	0.653974i	0.944616	−	0.328176i	$-0.106434\pi$
$293$	19.3890	+	11.1942i	1.13272	+	0.653974i	0.188099	+	0.982150i	$0.439767\pi$
$294$	−2.78457	−	7.70801i	−0.162400	−	0.449540i
$295$	8.78573	−	1.89458i	0.511525	−	0.110307i
$296$	−2.82562			−0.164236
$297$	−16.2751	+	5.66748i	−0.944378	+	0.328861i
$298$			14.3042i			0.828620i
$299$	0.0618523	+	0.107131i	0.00357701	+	0.00619557i
$300$	8.33308	+	2.35790i	0.481111	+	0.136134i
$301$	5.99898	−	10.3905i	0.345776	−	0.598901i
$302$	10.3212	−	17.8768i	0.593917	−	1.02869i
$303$	3.36274	+	2.83544i	0.193184	+	0.162892i
$304$	5.06801	−	2.92602i	0.290670	−	0.167819i
$305$	0.227720	−	0.707952i	0.0130392	−	0.0405372i
$306$	8.80805	+	3.25378i	0.503523	+	0.186006i
$307$	21.9397			1.25216			0.626082	−	0.779758i	$-0.284658\pi$
$307$	21.9397			1.25216			0.626082	+	0.779758i	$0.284658\pi$
$308$	−3.80464	−	3.23665i	−0.216789	−	0.184425i
$309$	−17.7436	−	3.17256i	−1.00940	−	0.180481i
$310$	12.2963	+	13.5756i	0.698382	+	0.771044i
$311$	2.61183	+	1.50794i	0.148103	+	0.0855073i	0.572220	−	0.820100i	$-0.306082\pi$
$311$	2.61183	+	1.50794i	0.148103	+	0.0855073i	−0.424117	+	0.905607i	$0.639416\pi$
$312$	−0.620085	−	0.110871i	−0.0351054	−	0.00627686i
$313$	6.75928	−	3.90247i	0.382057	−	0.220581i	−0.296656	−	0.954984i	$-0.595871\pi$
$313$	6.75928	−	3.90247i	0.382057	−	0.220581i	0.678713	+	0.734404i	$0.262538\pi$
$314$	8.20446			0.463004
$315$	−9.37441	+	3.76741i	−0.528188	+	0.212270i
$316$		−	4.94452i		−	0.278151i
$317$	7.79149	+	13.4953i	0.437614	+	0.757970i	0.997505	−	0.0705967i	$-0.0224903\pi$
$317$	7.79149	+	13.4953i	0.437614	+	0.757970i	−0.559891	+	0.828566i	$0.689157\pi$
$318$	3.19833	−	3.79312i	0.179354	−	0.212708i
$319$	5.18613	−	28.2897i	0.290368	−	1.58392i
$320$	−1.65730	+	1.50112i	−0.0926459	+	0.0839151i
$321$	11.7740	+	32.5917i	0.657160	+	1.81909i
$322$	−0.443651	+	0.256142i	−0.0247237	+	0.0142742i
$323$	18.3165			1.01916
$324$	−6.83860	−	5.85094i	−0.379922	−	0.325052i
$325$	−1.47742	−	1.06014i	−0.0819522	−	0.0588060i
$326$	−7.86317	−	13.6194i	−0.435501	−	0.754309i
$327$	4.83445	+	13.3823i	0.267346	+	0.740043i
$328$	−1.27651	−	0.736994i	−0.0704835	−	0.0406937i
$329$	−9.65584	+	16.7244i	−0.532343	+	0.922046i
$330$	7.97115	−	10.0728i	0.438797	−	0.554488i
$331$	11.7578	+	20.3652i	0.646270	+	1.11937i	0.984007	+	0.178131i	$0.0570052\pi$
$331$	11.7578	+	20.3652i	0.646270	+	1.11937i	−0.337737	+	0.941240i	$0.609661\pi$
$332$		−	5.55417i		−	0.304824i
$333$	5.41761	+	6.51970i	0.296883	+	0.357277i
$334$	5.50017			0.300956
$335$	17.7724	−	3.83249i	0.971011	−	0.209391i
$336$	0.459139	−	2.56789i	0.0250481	−	0.140090i
$337$	3.98781	−	6.90710i	0.217230	−	0.376254i	−0.736730	−	0.676187i	$-0.763631\pi$
$337$	3.98781	−	6.90710i	0.217230	−	0.376254i	0.953960	+	0.299933i	$0.0969645\pi$
$338$	−11.1438	−	6.43387i	−0.606142	−	0.349956i
$339$	1.90122	−	10.6332i	0.103260	−	0.577517i
$340$	−6.84150	+	1.47532i	−0.371032	+	0.0800104i
$341$	25.5918	−	9.11875i	1.38587	−	0.493808i
$342$	−16.4684	−	6.08358i	−0.890507	−	0.328962i
$343$	−17.6689			−0.954033
$344$	−6.89905	+	3.98317i	−0.371972	+	0.214758i
$345$	−0.698717	−	1.11681i	−0.0376177	−	0.0601268i
$346$	−1.59315	+	2.75941i	−0.0856481	+	0.148347i
$347$	16.0767	+	9.28186i	0.863040	+	0.498277i	0.865029	−	0.501721i	$-0.167300\pi$
$347$	16.0767	+	9.28186i	0.863040	+	0.498277i	−0.00198889	+	0.999998i	$0.500633\pi$
$348$	14.1265	−	5.10329i	0.757258	−	0.273565i
$349$	−6.17070	+	3.56265i	−0.330310	+	0.190704i	−0.655979	−	0.754779i	$-0.727744\pi$
$349$	−6.17070	+	3.56265i	−0.330310	+	0.190704i	0.325669	+	0.945484i	$0.394411\pi$
$350$	4.39024	−	6.11826i	0.234668	−	0.327034i
$351$	0.933083	+	1.64333i	0.0498043	+	0.0877146i
$352$	1.11321	+	3.12422i	0.0593342	+	0.166522i
$353$	3.03775	+	5.26153i	0.161683	+	0.280043i	0.935472	−	0.353400i	$-0.114974\pi$
$353$	3.03775	+	5.26153i	0.161683	+	0.280043i	−0.773789	+	0.633443i	$0.781641\pi$
$354$	6.54767	−	2.36540i	0.348005	−	0.125719i
$355$	−17.7694	−	19.6182i	−0.943104	−	1.04123i
$356$	5.57426	+	3.21830i	0.295435	+	0.170569i
$357$	5.26322	−	6.24201i	0.278559	−	0.330362i
$358$	−6.23207	−	10.7943i	−0.329375	−	0.570494i
$359$	−25.5300			−1.34742			−0.673710	−	0.738996i	$-0.735300\pi$
$359$	−25.5300			−1.34742			−0.673710	+	0.738996i	$0.735300\pi$
$360$	6.64119	+	0.945852i	0.350021	+	0.0498508i
$361$	−15.2463			−0.802437
$362$	15.2582	−	8.80934i	0.801955	−	0.463009i
$363$	−9.26191	−	16.6498i	−0.486124	−	0.873890i
$364$	−0.273869	+	0.474356i	−0.0143547	+	0.0248630i
$365$	−3.85829	+	3.49469i	−0.201952	+	0.182921i
$366$	0.101390	−	0.567055i	0.00529972	−	0.0296404i
$367$	−20.5359	+	11.8564i	−1.07196	+	0.618899i	−0.928717	−	0.370788i	$-0.879088\pi$
$367$	−20.5359	+	11.8564i	−1.07196	+	0.618899i	−0.143247	+	0.989687i	$0.545754\pi$
$368$	0.340143			0.0177312
$369$	0.746975	+	4.35842i	0.0388860	+	0.226890i
$370$	−6.01477	−	1.93471i	−0.312693	−	0.100581i
$371$	−2.15713	−	3.73627i	−0.111993	−	0.193977i
$372$	10.8467	+	9.14587i	0.562375	+	0.474191i
$373$	−15.0638	+	26.0913i	−0.779975	+	1.35096i	0.151981	+	0.988383i	$0.451435\pi$
$373$	−15.0638	+	26.0913i	−0.779975	+	1.35096i	−0.931956	+	0.362572i	$0.881899\pi$
$374$	−1.87185	+	10.2107i	−0.0967908	+	0.527982i
$375$	16.1238	+	10.7249i	0.832630	+	0.553830i
$376$	11.1046	−	6.41122i	0.572674	−	0.330633i
$377$	−3.15380			−0.162429
$378$	−6.80535	+	3.86407i	−0.350029	+	0.198746i
$379$	11.9909			0.615931			0.307965	−	0.951398i	$-0.400352\pi$
$379$	11.9909			0.615931			0.307965	+	0.951398i	$0.400352\pi$
$380$	12.7915	−	2.75840i	0.656191	−	0.141503i
$381$	−23.6620	+	8.54806i	−1.21224	+	0.437930i
$382$	12.2007	−	21.1322i	0.624240	−	1.08122i
$383$	−1.06083	+	1.83740i	−0.0542057	+	0.0938870i	−0.891855	−	0.452321i	$-0.850596\pi$
$383$	−1.06083	+	1.83740i	−0.0542057	+	0.0938870i	0.837649	+	0.546208i	$0.183929\pi$
$384$	−1.11652	+	1.32415i	−0.0569771	+	0.0675730i
$385$	−5.88261	−	9.49478i	−0.299806	−	0.483899i
$386$		−	0.0529426i		−	0.00269471i
$387$	22.4183	+	8.28154i	1.13958	+	0.420974i
$388$		−	13.8640i		−	0.703839i
$389$	6.22087	−	3.59162i	0.315410	−	0.182102i	−0.333935	−	0.942596i	$-0.608376\pi$
$389$	6.22087	−	3.59162i	0.315410	−	0.182102i	0.649345	+	0.760494i	$0.275043\pi$
$390$	−1.24403	−	0.660582i	−0.0629941	−	0.0334499i
$391$	0.921995	+	0.532314i	0.0466273	+	0.0269203i
$392$	4.09778	+	2.36586i	0.206969	+	0.119494i
$393$	−4.10498	+	22.9585i	−0.207069	+	1.15810i
$394$	3.64018	+	6.30498i	0.183390	+	0.317640i
$395$	3.38554	−	10.5252i	0.170345	−	0.529580i
$396$	5.07431	−	8.55870i	0.254994	−	0.430091i
$397$		−	17.9036i		−	0.898558i	−0.893391	−	0.449279i	$-0.851681\pi$
$397$		−	17.9036i		−	0.898558i	0.893391	−	0.449279i	$-0.148319\pi$
$398$	−2.15047	+	1.24158i	−0.107794	+	0.0622346i
$399$	−9.84061	+	11.6706i	−0.492647	+	0.584263i
$400$	−4.55565	+	2.06061i	−0.227782	+	0.103030i
$401$	10.9120	+	6.30005i	0.544920	+	0.314610i	0.747071	−	0.664745i	$-0.231460\pi$
$401$	10.9120	+	6.30005i	0.544920	+	0.314610i	−0.202151	+	0.979354i	$0.564793\pi$
$402$	13.2451	−	4.78489i	0.660606	−	0.238649i
$403$	−1.48954	−	2.57996i	−0.0741994	−	0.128517i
$404$	−2.53954			−0.126347
$405$	−10.5509	−	17.1371i	−0.524277	−	0.851548i
$406$		−	13.0605i		−	0.648180i
$407$	−6.07240	+	7.13801i	−0.300998	+	0.353818i
$408$	−5.09871	+	1.84195i	−0.252424	+	0.0911899i
$409$	6.24514	+	3.60564i	0.308802	+	0.178287i	0.646390	−	0.763007i	$-0.276278\pi$
$409$	6.24514	+	3.60564i	0.308802	+	0.178287i	−0.337588	+	0.941294i	$0.609611\pi$
$410$	−2.21263	−	2.44284i	−0.109274	−	0.120643i
$411$	6.27094	+	5.28762i	0.309323	+	0.260819i
$412$	9.01251	−	5.20338i	0.444015	−	0.256352i
$413$		−	6.05358i		−	0.297877i
$414$	−0.652163	−	0.784831i	−0.0320521	−	0.0385723i
$415$	3.80296	−	11.8229i	0.186680	−	0.580364i
$416$	0.314960	−	0.181842i	0.0154422	−	0.00891554i
$417$	26.2933	+	4.70124i	1.28759	+	0.230221i
$418$	3.49978	−	19.0909i	0.171180	−	0.933764i
$419$	−3.37913	−	1.95094i	−0.165081	−	0.0953097i	0.415183	−	0.909738i	$-0.363717\pi$
$419$	−3.37913	−	1.95094i	−0.165081	−	0.0953097i	−0.580264	+	0.814428i	$0.697051\pi$
$420$	2.73560	−	5.15178i	0.133483	−	0.251381i
$421$	9.96379	+	17.2578i	0.485605	+	0.841093i	0.999863	−	0.0165423i	$-0.00526583\pi$
$421$	9.96379	+	17.2578i	0.485605	+	0.841093i	−0.514258	+	0.857636i	$0.671932\pi$
$422$	−2.08100			−0.101301
$423$	−36.0839	−	13.3298i	−1.75446	−	0.648116i
$424$			2.86456i			0.139115i
$425$	−15.5734	−	1.54396i	−0.755419	−	0.0748929i
$426$	−15.6746	−	13.2168i	−0.759439	−	0.640354i
$427$	−0.433788	−	0.250448i	−0.0209925	−	0.0121200i
$428$	−17.3266	−	10.0035i	−0.837513	−	0.483538i
$429$	−1.61268	+	1.32818i	−0.0778608	+	0.0641250i
$430$	−17.4130	+	3.75499i	−0.839729	+	0.181081i
$431$	12.3592			0.595322			0.297661	−	0.954672i	$-0.403794\pi$
$431$	12.3592			0.595322			0.297661	+	0.954672i	$0.403794\pi$
$432$	5.19602	+	0.0373754i	0.249994	+	0.00179822i
$433$			4.51989i			0.217212i	0.994085	+	0.108606i	$0.0346387\pi$
$433$			4.51989i			0.217212i	−0.994085	+	0.108606i	$0.965361\pi$
$434$	10.6841	−	6.16848i	0.512854	−	0.296096i
$435$	33.5647	−	1.19070i	1.60930	−	0.0570895i
$436$	−7.11438	−	4.10749i	−0.340717	−	0.196713i
$437$	−1.72385	−	0.995265i	−0.0824629	−	0.0476100i
$438$	−2.59932	+	3.08271i	−0.124200	+	0.147298i
$439$	−28.3774	+	16.3837i	−1.35438	+	0.781951i	−0.988859	−	0.148852i	$-0.952442\pi$
$439$	−28.3774	+	16.3837i	−1.35438	+	0.781951i	−0.365520	+	0.930804i	$0.619109\pi$
$440$	0.230468	+	7.41262i	0.0109871	+	0.353383i
$441$	−2.39789	−	13.9911i	−0.114185	−	0.666244i
$442$	1.13831			0.0541439
$443$	−2.37115	−	4.10695i	−0.112657	−	0.195127i	0.804184	−	0.594380i	$-0.202603\pi$
$443$	−2.37115	−	4.10695i	−0.112657	−	0.195127i	−0.916841	+	0.399254i	$0.869269\pi$
$444$	−4.81771	−	0.861407i	−0.228638	−	0.0408806i
$445$	9.66209	+	10.6674i	0.458027	+	0.505682i
$446$	4.31493	−	7.47368i	0.204318	−	0.353889i
$447$	−4.36073	+	24.3888i	−0.206255	+	1.15355i
$448$	0.753042	+	1.30431i	0.0355779	+	0.0616227i
$449$			22.6359i			1.06826i	0.845404	+	0.534128i	$0.179360\pi$
$449$			22.6359i			1.06826i	−0.845404	+	0.534128i	$0.820640\pi$
$450$	13.4892	+	6.56065i	0.635886	+	0.309272i
$451$	−4.60507	+	1.64086i	−0.216844	+	0.0772649i
$452$	3.11823	+	5.40093i	0.146669	+	0.254038i
$453$	23.0476	−	27.3337i	1.08287	−	1.28425i
$454$	11.8981	−	20.6082i	0.558407	−	0.967189i
$455$	−0.907767	+	0.822221i	−0.0425568	+	0.0385463i
$456$	9.53303	−	3.44388i	0.446425	−	0.161274i
$457$	−10.8349	−	18.7666i	−0.506835	−	0.877864i	−0.999969	−	0.00791072i	$-0.997482\pi$
$457$	−10.8349	−	18.7666i	−0.506835	−	0.877864i	0.493133	−	0.869954i	$-0.335851\pi$
$458$			20.7654i			0.970305i
$459$	14.0259	+	8.23293i	0.654672	+	0.384280i
$460$	0.724048	+	0.232898i	0.0337589	+	0.0108589i
$461$	12.4863	+	21.6268i	0.581543	+	1.00726i	0.995297	+	0.0968729i	$0.0308840\pi$
$461$	12.4863	+	21.6268i	0.581543	+	1.00726i	−0.413754	+	0.910389i	$0.635783\pi$
$462$	−5.50023	−	6.67840i	−0.255894	−	0.310707i
$463$	−11.8322	−	6.83134i	−0.549890	−	0.317479i	0.199188	−	0.979961i	$-0.436170\pi$
$463$	−11.8322	−	6.83134i	−0.549890	−	0.317479i	−0.749078	+	0.662482i	$0.769503\pi$
$464$	−4.33590	+	7.51001i	−0.201289	+	0.348643i
$465$	16.8267	+	26.8952i	0.780318	+	1.24723i
$466$	5.05573	+	8.75677i	0.234202	+	0.405650i
$467$	−30.3678			−1.40525			−0.702627	−	0.711559i	$-0.747990\pi$
$467$	−30.3678			−1.40525			−0.702627	+	0.711559i	$0.747990\pi$
$468$	−1.02345	−	0.378074i	−0.0473091	−	0.0174765i
$469$		−	12.2456i		−	0.565450i
$470$	28.0276	−	6.04394i	1.29282	−	0.278786i
$471$	13.9887	+	2.50118i	0.644565	+	0.115248i
$472$	−2.00971	+	3.48092i	−0.0925043	+	0.160222i
$473$	−4.76422	+	25.9883i	−0.219059	+	1.19494i
$474$	1.50737	−	8.43047i	0.0692358	−	0.387224i
$475$	29.1174	+	2.88673i	1.33600	+	0.132452i
$476$			4.71396i			0.216064i
$477$	6.60955	−	5.49228i	0.302631	−	0.251474i
$478$			17.0921i			0.781774i
$479$	−0.705741	−	1.22238i	−0.0322461	−	0.0558519i	0.849452	−	0.527666i	$-0.176933\pi$
$479$	−0.705741	−	1.22238i	−0.0322461	−	0.0558519i	−0.881698	+	0.471814i	$0.843599\pi$
$480$	−3.28334	+	2.05419i	−0.149863	+	0.0937603i
$481$	0.889955	+	0.513816i	0.0405785	+	0.0234280i
$482$	−1.82929	+	3.16842i	−0.0833217	+	0.144317i
$483$	−0.834517	+	0.301475i	−0.0379718	+	0.0137176i
$484$	10.2847	+	3.90196i	0.467486	+	0.177362i
$485$	9.49275	−	29.5117i	0.431044	−	1.34006i
$486$	−9.87619	−	12.0607i	−0.447993	−	0.547085i
$487$			19.8614i			0.900008i	0.893027	+	0.450004i	$0.148577\pi$
$487$			19.8614i			0.900008i	−0.893027	+	0.450004i	$0.851423\pi$
$488$	0.166291	+	0.288024i	0.00752763	+	0.0130382i
$489$	−9.25482	−	25.6184i	−0.418518	−	1.15850i
$490$	7.10286	+	7.84186i	0.320874	+	0.354259i
$491$	8.67395	−	15.0237i	0.391450	−	0.678011i	−0.601191	−	0.799105i	$-0.705307\pi$
$491$	8.67395	−	15.0237i	0.391450	−	0.678011i	0.992641	+	0.121094i	$0.0386402\pi$
$492$	−1.95179	−	1.64574i	−0.0879934	−	0.0741955i
$493$	−23.5059	+	13.5711i	−1.05865	+	0.611213i
$494$	−2.12829			−0.0957563
$495$	16.6616	−	14.7441i	0.748885	−	0.662700i
$496$	−8.19141			−0.367805
$497$	−15.4397	+	8.91411i	−0.692565	+	0.399853i
$498$	1.69322	−	9.46991i	0.0758751	−	0.424357i
$499$	5.80631	−	10.0568i	0.259926	−	0.450206i	−0.706296	−	0.707917i	$-0.749635\pi$
$499$	5.80631	−	10.0568i	0.259926	−	0.450206i	0.966222	+	0.257711i	$0.0829684\pi$
$500$	−11.1083	+	1.26705i	−0.496779	+	0.0566642i
$501$	9.37785	+	1.67676i	0.418971	+	0.0749122i
$502$	−8.71893	−	15.1016i	−0.389145	−	0.674018i
$503$			12.2467i			0.546054i	0.962006	+	0.273027i	$0.0880248\pi$
$503$			12.2467i			0.546054i	−0.962006	+	0.273027i	$0.911975\pi$
$504$	1.56568	−	4.23831i	0.0697407	−	0.188789i
$505$	−5.40580	−	1.73883i	−0.240555	−	0.0773770i
$506$	0.730985	−	0.859262i	0.0324963	−	0.0381989i
$507$	−17.0389	−	14.3671i	−0.756723	−	0.638064i
$508$	7.26268	−	12.5793i	0.322229	−	0.558117i
$509$	−20.4479	−	11.8056i	−0.906336	−	0.523273i	−0.0270855	−	0.999633i	$-0.508623\pi$
$509$	−20.4479	−	11.8056i	−0.906336	−	0.523273i	−0.879250	+	0.476360i	$0.841956\pi$
$510$	−12.1146	+	0.429761i	−0.536443	+	0.0190301i
$511$	1.75313	+	3.03650i	0.0775537	+	0.134327i
$512$		−	1.00000i		−	0.0441942i
$513$	−26.2241	−	15.3931i	−1.15782	−	0.679620i
$514$			26.2767i			1.15902i
$515$	22.7473	−	4.90529i	1.00237	−	0.216153i
$516$	−12.9772	+	4.68812i	−0.571291	+	0.206383i
$517$	7.66839	−	41.8301i	0.337256	−	1.83969i
$518$	−2.12781	+	3.68547i	−0.0934906	+	0.161930i
$519$	−3.55756	+	4.21914i	−0.156159	+	0.185200i
$520$	0.794949	−	0.171425i	0.0348608	−	0.00751748i
$521$		−	9.74880i		−	0.427102i	−0.976932	−	0.213551i	$-0.931497\pi$
$521$		−	9.74880i		−	0.427102i	0.976932	−	0.213551i	$-0.0685030\pi$
$522$	25.6416	−	4.39462i	1.12230	−	0.192347i
$523$	2.76402			0.120862			0.0604311	−	0.998172i	$-0.480752\pi$
$523$	2.76402			0.120862			0.0604311	+	0.998172i	$0.480752\pi$
$524$	−6.73265	−	11.6613i	−0.294117	−	0.509426i
$525$	9.35059	−	9.09330i	0.408093	−	0.396864i
$526$	7.93601	−	13.7456i	0.346026	−	0.599335i
$527$	−22.2037	−	12.8193i	−0.967209	−	0.558418i
$528$	0.945593	+	5.66620i	0.0411516	+	0.246590i
$529$	11.4422	+	19.8184i	0.497485	+	0.861669i
$530$	−1.96138	+	6.09766i	−0.0851968	+	0.264866i
$531$	11.8850	−	2.03692i	0.515763	−	0.0883950i
$532$		−	8.81366i		−	0.382120i
$533$	0.268033	+	0.464247i	0.0116098	+	0.0201088i
$534$	8.52305	+	7.18658i	0.368828	+	0.310994i
$535$	−30.0329	−	33.1577i	−1.29844	−	1.43353i
$536$	−4.06538	+	7.04145i	−0.175598	+	0.304144i
$537$	−7.33504	−	20.3042i	−0.316530	−	0.876191i
$538$	−7.31145	−	12.6638i	−0.315219	−	0.545975i
$539$	14.7829	−	5.26738i	0.636745	−	0.226882i
$540$	11.0349	+	3.63730i	0.474869	+	0.156524i
$541$		−	9.81289i		−	0.421889i	−0.977498	−	0.210945i	$-0.932346\pi$
$541$		−	9.81289i		−	0.421889i	0.977498	−	0.210945i	$-0.0676539\pi$
$542$	10.1390	+	17.5613i	0.435507	+	0.754321i
$543$	28.7010	−	10.3685i	1.23168	−	0.444953i
$544$	1.56497	−	2.71061i	0.0670976	−	0.116216i
$545$	−12.3317	−	13.6147i	−0.528230	−	0.583189i
$546$	−0.611561	+	0.725291i	−0.0261724	+	0.0310396i
$547$	19.7032	+	34.1270i	0.842450	+	1.45917i	0.887817	+	0.460196i	$0.152221\pi$
$547$	19.7032	+	34.1270i	0.842450	+	1.45917i	−0.0453673	+	0.998970i	$0.514446\pi$
$548$	−4.73581			−0.202304
$549$	0.345741	−	0.935926i	0.0147559	−	0.0399444i
$550$	−4.58486	+	15.9367i	−0.195499	+	0.679544i
$551$	43.9488	−	25.3739i	1.87228	−	1.08096i
$552$	0.579948	+	0.103695i	0.0246842	+	0.00441354i
$553$	−6.44918	−	3.72343i	−0.274247	−	0.158336i
$554$	5.58151	+	3.22249i	0.237136	+	0.136910i
$555$	−9.66544	−	5.13235i	−0.410275	−	0.217856i
$556$	−13.3551	+	7.71058i	−0.566383	+	0.327002i
$557$			12.1351i			0.514182i	0.966387	+	0.257091i	$0.0827640\pi$
$557$			12.1351i			0.514182i	−0.966387	+	0.257091i	$0.917236\pi$
$558$	15.7056	+	18.9005i	0.664869	+	0.800121i
$559$	2.89723			0.122540
$560$	0.709903	+	3.29203i	0.0299989	+	0.139114i
$561$	−6.30431	+	16.8387i	−0.266168	+	0.710930i
$562$	−22.6787	−	13.0935i	−0.956642	−	0.552317i
$563$	11.5798	+	6.68561i	0.488031	+	0.281765i	0.723757	−	0.690055i	$-0.242414\pi$
$563$	11.5798	+	6.68561i	0.488031	+	0.281765i	−0.235726	+	0.971819i	$0.575747\pi$
$564$	20.8879	−	7.54590i	0.879539	−	0.317740i
$565$	2.93959	+	13.6318i	0.123670	+	0.573493i
$566$		−	24.9762i		−	1.04983i
$567$	−12.7812	+	4.51363i	−0.536759	+	0.189555i
$568$	11.8375			0.496689
$569$	13.6393	+	23.6240i	0.571791	+	0.990371i	0.996382	+	0.0849857i	$0.0270845\pi$
$569$	13.6393	+	23.6240i	0.571791	+	0.990371i	−0.424591	+	0.905385i	$0.639582\pi$
$570$	22.6506	−	0.803522i	0.948728	−	0.0336558i
$571$	23.8350	+	13.7612i	0.997465	+	0.575887i	0.907497	−	0.420058i	$-0.137990\pi$
$571$	23.8350	+	13.7612i	0.997465	+	0.575887i	0.0899676	+	0.995945i	$0.471324\pi$
$572$	0.217499	−	1.18643i	0.00909411	−	0.0496072i
$573$	27.2445	−	32.3111i	1.13816	−	1.34982i
$574$	−1.92253	+	1.10998i	−0.0802450	+	0.0463295i
$575$	1.38178	+	0.991518i	0.0576244	+	0.0413492i
$576$	−2.30735	+	1.91732i	−0.0961397	+	0.0798884i
$577$			16.2329i			0.675783i	0.941185	+	0.337891i	$0.109714\pi$
$577$			16.2329i			0.675783i	−0.941185	+	0.337891i	$0.890286\pi$
$578$	−6.23838	+	3.60173i	−0.259483	+	0.149812i
$579$	0.0161399	−	0.0902677i	0.000670751	−	0.00375140i
$580$	−14.3718	+	13.0174i	−0.596756	+	0.540519i
$581$	−7.24434	−	4.18252i	−0.300546	−	0.173520i
$582$	4.22653	−	23.6383i	0.175195	−	0.979839i
$583$	7.23639	+	6.15609i	0.299701	+	0.254959i
$584$		−	2.32806i		−	0.0963358i
$585$	−1.91971	−	1.50555i	−0.0793702	−	0.0622469i
$586$	−22.3885			−0.924859
$587$	17.9107	+	31.0222i	0.739253	+	1.28042i	0.952832	+	0.303499i	$0.0981548\pi$
$587$	17.9107	+	31.0222i	0.739253	+	1.28042i	−0.213578	+	0.976926i	$0.568512\pi$
$588$	6.26552	+	5.28304i	0.258386	+	0.217869i
$589$	41.5142	+	23.9682i	1.71056	+	0.987593i
$590$	−6.66138	+	6.03362i	−0.274245	+	0.248400i
$591$	4.28444	+	11.8598i	0.176238	+	0.487847i
$592$	2.44706	−	1.41281i	0.100573	−	0.0580661i
$593$		−	43.9898i		−	1.80645i	−0.429172	−	0.903223i	$-0.641194\pi$
$593$		−	43.9898i		−	1.80645i	0.429172	−	0.903223i	$-0.358806\pi$
$594$	11.2609	−	13.0457i	0.462042	−	0.535273i
$595$	−3.22767	+	10.0344i	−0.132321	+	0.411370i
$596$	−7.15210	−	12.3878i	−0.292961	−	0.507424i
$597$	−4.04508	+	1.46132i	−0.165554	+	0.0598077i
$598$	−0.107131	−	0.0618523i	−0.00438093	−	0.00252933i
$599$	18.3747	+	10.6086i	0.750768	+	0.433456i	0.825971	−	0.563712i	$-0.190627\pi$
$599$	18.3747	+	10.6086i	0.750768	+	0.433456i	−0.0752032	+	0.997168i	$0.523961\pi$
$600$	−8.39561	+	2.12454i	−0.342750	+	0.0867339i
$601$	−20.5052	+	11.8387i	−0.836423	+	0.482909i	−0.856047	−	0.516898i	$-0.827087\pi$
$601$	−20.5052	+	11.8387i	−0.836423	+	0.482909i	0.0196237	+	0.999807i	$0.493753\pi$
$602$			11.9980i			0.489001i
$603$	24.0418	−	4.12044i	0.979056	−	0.167797i
$604$			20.6423i			0.839925i
$605$	19.2209	+	15.3479i	0.781440	+	0.623981i
$606$	−4.32994	−	0.774194i	−0.175892	−	0.0314495i
$607$	−7.94186	+	13.7557i	−0.322350	+	0.558327i	−0.980972	−	0.194147i	$-0.937806\pi$
$607$	−7.94186	+	13.7557i	−0.322350	+	0.558327i	0.658622	+	0.752474i	$0.271140\pi$
$608$	−2.92602	+	5.06801i	−0.118666	+	0.205535i
$609$	3.98157	−	22.2683i	0.161341	−	0.902355i
$610$	0.156765	+	0.726964i	0.00634721	+	0.0294339i
$611$	−4.66332			−0.188658
$612$	−9.25488	+	1.58616i	−0.374107	+	0.0641169i
$613$	−4.23480			−0.171042			−0.0855211	−	0.996336i	$-0.527255\pi$
$613$	−4.23480			−0.171042			−0.0855211	+	0.996336i	$0.527255\pi$
$614$	−19.0003	+	10.9698i	−0.766790	+	0.442706i
$615$	−3.02785	−	4.83961i	−0.122094	−	0.195152i
$616$	4.91324	+	0.900706i	0.197960	+	0.0362905i
$617$	3.39517	−	5.88060i	0.136684	−	0.236744i	−0.789555	−	0.613679i	$-0.789689\pi$
$617$	3.39517	−	5.88060i	0.136684	−	0.236744i	0.926240	+	0.376935i	$0.123022\pi$
$618$	16.9527	−	6.12429i	0.681938	−	0.246355i
$619$	8.99701	+	15.5833i	0.361620	+	0.626345i	0.988228	−	0.152990i	$-0.0488904\pi$
$619$	8.99701	+	15.5833i	0.361620	+	0.626345i	−0.626607	+	0.779335i	$0.715557\pi$
$620$	−17.4367	−	5.60870i	−0.700275	−	0.225251i
$621$	−0.872685	−	1.53696i	−0.0350197	−	0.0616761i
$622$	−3.01588			−0.120926
$623$	8.39530	−	4.84703i	0.336351	−	0.194192i
$624$	0.592445	−	0.214025i	0.0237168	−	0.00856786i
$625$	−24.5133	−	4.90880i	−0.980533	−	0.196352i
$626$	−3.90247	+	6.75928i	−0.155974	+	0.270155i
$627$	11.7871	−	31.4832i	0.470733	−	1.25732i
$628$	−7.10527	+	4.10223i	−0.283531	+	0.163697i
$629$	8.84402			0.352634
$630$	6.23478	−	7.94988i	0.248399	−	0.316731i
$631$	−24.1259			−0.960437			−0.480219	−	0.877149i	$-0.659443\pi$
$631$	−24.1259			−0.960437			−0.480219	+	0.877149i	$0.659443\pi$
$632$	2.47226	+	4.28208i	0.0983413	+	0.170332i
$633$	−3.54812	−	0.634405i	−0.141025	−	0.0252153i
$634$	−13.4953	−	7.79149i	−0.535965	−	0.309440i
$635$	24.0729	−	21.8043i	0.955303	−	0.865276i
$636$	−0.873279	+	4.88411i	−0.0346278	+	0.193667i
$637$	−0.860424	−	1.49030i	−0.0340912	−	0.0590477i
$638$	9.65353	+	27.0927i	0.382187	+	1.07261i
$639$	−22.6962	−	27.3132i	−0.897849	−	1.08049i
$640$	0.684705	−	2.12866i	0.0270653	−	0.0841425i
$641$	8.62677	−	4.98067i	0.340737	−	0.196725i	−0.319861	−	0.947465i	$-0.603636\pi$
$641$	8.62677	−	4.98067i	0.340737	−	0.196725i	0.660598	+	0.750740i	$0.270303\pi$
$642$	−26.4924	−	22.3382i	−1.04557	−	0.881620i
$643$	−32.7152	−	18.8881i	−1.29016	−	0.744876i	−0.311480	−	0.950253i	$-0.600825\pi$
$643$	−32.7152	−	18.8881i	−1.29016	−	0.744876i	−0.978683	+	0.205377i	$0.934158\pi$
$644$	0.256142	−	0.443651i	0.0100934	−	0.0174823i
$645$	−30.8341	+	1.09383i	−1.21409	+	0.0430695i
$646$	−15.8626	+	9.15826i	−0.624105	+	0.360327i
$647$	4.55021			0.178887			0.0894436	−	0.995992i	$-0.471491\pi$
$647$	4.55021			0.178887			0.0894436	+	0.995992i	$0.471491\pi$
$648$	8.84787	+	1.64776i	0.347577	+	0.0647303i
$649$	4.47445	+	12.5576i	0.175637	+	0.492927i
$650$	1.80955	+	0.179400i	0.0709763	+	0.00703666i
$651$	20.0970	−	7.26020i	0.787665	−	0.284550i
$652$	13.6194	+	7.86317i	0.533377	+	0.307945i
$653$	−9.97702	+	17.2807i	−0.390431	+	0.676246i	−0.992506	−	0.122193i	$-0.961007\pi$
$653$	−9.97702	+	17.2807i	−0.390431	+	0.676246i	0.602075	+	0.798439i	$0.294341\pi$
$654$	−10.8779	−	9.17218i	−0.425360	−	0.358661i
$655$	−6.34696	−	29.4328i	−0.247996	−	1.15003i
$656$	1.47399			0.0575496
$657$	−5.37166	+	4.46363i	−0.209568	+	0.174143i
$658$		−	19.3117i		−	0.752847i
$659$	−24.5552	−	42.5309i	−0.956535	−	1.65677i	−0.730816	−	0.682574i	$-0.760860\pi$
$659$	−24.5552	−	42.5309i	−0.956535	−	1.65677i	−0.225718	−	0.974193i	$-0.572473\pi$
$660$	−1.86683	+	12.7089i	−0.0726663	+	0.494691i
$661$	1.02601	−	1.77709i	0.0399070	−	0.0691209i	−0.845382	−	0.534162i	$-0.820627\pi$
$661$	1.02601	−	1.77709i	0.0399070	−	0.0691209i	0.885289	+	0.465041i	$0.153961\pi$
$662$	−20.3652	−	11.7578i	−0.791515	−	0.456982i
$663$	1.94083	+	0.347021i	0.0753756	+	0.0134772i
$664$	2.77708	+	4.81005i	0.107772	+	0.186666i
$665$	6.03475	−	18.7612i	0.234018	−	0.727530i
$666$	−7.95164	−	2.93742i	−0.308120	−	0.113823i
$667$	2.94966			0.114211
$668$	−4.76329	+	2.75009i	−0.184297	+	0.106404i
$669$	9.63540	−	11.4273i	0.372526	−	0.441804i
$670$	−13.4751	+	12.2052i	−0.520589	+	0.471530i
$671$	1.08497	+	0.198899i	0.0418847	+	0.00767840i
$672$	0.886319	+	2.45343i	0.0341905	+	0.0946430i
$673$	23.7337	+	41.1080i	0.914869	+	1.58460i	0.807094	+	0.590424i	$0.201039\pi$
$673$	23.7337	+	41.1080i	0.914869	+	1.58460i	0.107775	+	0.994175i	$0.465627\pi$
$674$			7.97563i			0.307210i
$675$	20.9991	+	15.2982i	0.808257	+	0.588829i
$676$	12.8677			0.494913
$677$	−3.49120	+	2.01564i	−0.134178	+	0.0774675i	−0.565586	−	0.824689i	$-0.691350\pi$
$677$	−3.49120	+	2.01564i	−0.134178	+	0.0774675i	0.431409	+	0.902157i	$0.358017\pi$
$678$	3.67010	+	10.1593i	0.140949	+	0.390164i
$679$	−18.0829	−	10.4402i	−0.693959	−	0.400658i
$680$	5.18725	−	4.69841i	0.198922	−	0.180176i
$681$	26.5690	−	31.5099i	1.01812	−	1.20746i
$682$	−17.6038	+	20.6930i	−0.674083	+	0.792374i
$683$	24.7477			0.946946			0.473473	−	0.880808i	$-0.343000\pi$
$683$	24.7477			0.946946			0.473473	+	0.880808i	$0.343000\pi$
$684$	17.3038	−	2.96564i	0.661627	−	0.113394i
$685$	−10.0809	−	3.24263i	−0.385172	−	0.123894i
$686$	15.3018	−	8.83447i	0.584224	−	0.337302i
$687$	−6.33047	+	35.4053i	−0.241523	+	1.35080i
$688$	3.98317	−	6.89905i	0.151857	−	0.263024i
$689$	0.520897	−	0.902221i	0.0198446	−	0.0343719i
$690$	1.16351	+	0.617824i	0.0442941	+	0.0235201i
$691$	−23.5702	−	40.8248i	−0.896653	−	1.55305i	−0.831745	−	0.555158i	$-0.812658\pi$
$691$	−23.5702	−	40.8248i	−0.896653	−	1.55305i	−0.0649084	−	0.997891i	$-0.520676\pi$
$692$		−	3.18629i		−	0.121125i
$693$	−7.34201	−	13.0635i	−0.278900	−	0.496242i
$694$	−18.5637			−0.704670
$695$	−33.7079	+	7.26887i	−1.27861	+	0.275724i
$696$	−9.68224	+	11.4828i	−0.367004	+	0.435255i
$697$	3.99541	+	2.30675i	0.151337	+	0.0873743i
$698$	3.56265	−	6.17070i	0.134848	−	0.233564i
$699$	5.95051	+	16.4717i	0.225069	+	0.623016i
$700$	−0.742931	+	7.49368i	−0.0280801	+	0.283235i
$701$	−44.8908			−1.69550			−0.847751	−	0.530395i	$-0.822044\pi$
$701$	−44.8908			−1.69550			−0.847751	+	0.530395i	$0.822044\pi$
$702$	−1.62974	−	0.956626i	−0.0615105	−	0.0361055i
$703$	−16.5356			−0.623652
$704$	−2.52618	−	2.14905i	−0.0952089	−	0.0809955i
$705$	49.6299	−	1.76060i	1.86917	−	0.0663082i
$706$	−5.26153	−	3.03775i	−0.198020	−	0.114327i
$707$	−1.91238	+	3.31233i	−0.0719223	+	0.124573i
$708$	−4.48775	+	5.32233i	−0.168660	+	0.200025i
$709$	21.7831	+	37.7294i	0.818081	+	1.41696i	0.907094	+	0.420927i	$0.138295\pi$
$709$	21.7831	+	37.7294i	0.818081	+	1.41696i	−0.0890137	+	0.996030i	$0.528371\pi$
$710$	25.1979	+	8.10517i	0.945661	+	0.304182i
$711$	5.14016	−	13.9145i	0.192771	−	0.521835i
$712$	−6.43660			−0.241222
$713$	1.39313	+	2.41297i	0.0521730	+	0.0903663i
$714$	−1.43708	+	8.03735i	−0.0537813	+	0.300790i
$715$	1.27534	−	2.37658i	0.0476949	−	0.0888792i
$716$	10.7943	+	6.23207i	0.403400	+	0.232903i
$717$	−5.21063	+	29.1422i	−0.194595	+	1.08834i
$718$	22.1096	−	12.7650i	0.825123	−	0.476385i
$719$			25.8427i			0.963772i	0.876234	+	0.481886i	$0.160048\pi$
$719$			25.8427i			0.963772i	−0.876234	+	0.481886i	$0.839952\pi$
$720$	−6.22436	+	2.50146i	−0.231968	+	0.0932240i
$721$		−	15.6734i		−	0.583710i
$722$	13.2037	−	7.62315i	0.491390	−	0.283704i
$723$	−4.08486	+	4.84451i	−0.151918	+	0.180169i
$724$	−8.80934	+	15.2582i	−0.327397	+	0.567068i
$725$	−39.5057	+	17.8692i	−1.46720	+	0.663644i
$726$	16.3460	+	9.78823i	0.606656	+	0.363275i
$727$	3.14315	−	1.81470i	0.116573	−	0.0673034i	−0.440580	−	0.897713i	$-0.645227\pi$
$727$	3.14315	−	1.81470i	0.116573	−	0.0673034i	0.557153	+	0.830410i	$0.311894\pi$
$728$		−	0.547739i		−	0.0203005i
$729$	−13.1622	−	23.5745i	−0.487490	−	0.873128i
$730$	1.59403	−	4.95564i	0.0589978	−	0.183416i
$731$	21.5936	−	12.4671i	0.798669	−	0.461112i
$732$	0.195722	+	0.541779i	0.00723408	+	0.0200247i
$733$	23.1061	−	40.0209i	0.853442	−	1.47821i	−0.0246406	−	0.999696i	$-0.507844\pi$
$733$	23.1061	−	40.0209i	0.853442	−	1.47821i	0.878083	−	0.478509i	$-0.158823\pi$
$734$	11.8564	−	20.5359i	0.437627	−	0.757993i
$735$	9.71981	+	15.5358i	0.358521	+	0.573047i
$736$	−0.294573	+	0.170072i	−0.0108581	+	0.00626892i
$737$	9.05124	+	25.4023i	0.333407	+	0.935707i
$738$	−2.82611	−	3.40101i	−0.104030	−	0.125193i
$739$			42.6408i			1.56857i	0.620402	+	0.784284i	$0.286969\pi$
$739$			42.6408i			1.56857i	−0.620402	+	0.784284i	$0.713031\pi$
$740$	6.17630	−	1.33187i	0.227045	−	0.0489607i
$741$	−3.62876	−	0.648823i	−0.133306	−	0.0238351i
$742$	3.73627	+	2.15713i	0.137163	+	0.0791909i
$743$	−5.50419	−	3.17785i	−0.201929	−	0.116584i	0.395626	−	0.918412i	$-0.370528\pi$
$743$	−5.50419	−	3.17785i	−0.201929	−	0.116584i	−0.597555	+	0.801828i	$0.703861\pi$
$744$	−13.9664	−	2.49720i	−0.512035	−	0.0915519i
$745$	−6.74238	−	31.2665i	−0.247022	−	1.14551i
$746$		−	30.1276i		−	1.10305i
$747$	5.77393	−	15.6301i	0.211257	−	0.571876i
$748$	−3.48428	−	9.77863i	−0.127398	−	0.357542i
$749$	−26.0953	+	15.0661i	−0.953503	+	0.550505i
$750$	−19.3261	−	1.22611i	−0.705688	−	0.0447710i
$751$	6.91244	−	11.9727i	0.252239	−	0.436890i	−0.711903	−	0.702278i	$-0.752167\pi$
$751$	6.91244	−	11.9727i	0.252239	−	0.436890i	0.964142	+	0.265387i	$0.0854999\pi$
$752$	−6.41122	+	11.1046i	−0.233793	+	0.404942i
$753$	−10.2620	−	28.4065i	−0.373969	−	1.03519i
$754$	2.73127	−	1.57690i	0.0994670	−	0.0574273i
$755$	−14.1339	+	43.9405i	−0.514386	+	1.59916i
$756$	3.96157	−	6.74906i	0.144081	−	0.245461i
$757$		−	15.6040i		−	0.567138i	−0.958952	−	0.283569i	$-0.908482\pi$
$757$		−	15.6040i		−	0.567138i	0.958952	−	0.283569i	$-0.0915185\pi$
$758$	−10.3844	+	5.99545i	−0.377179	+	0.217764i
$759$	1.50829	−	1.24221i	0.0547474	−	0.0450892i
$760$	−9.69857	+	8.78460i	−0.351804	+	0.318651i
$761$	−15.2214	+	26.3642i	−0.551774	+	0.955701i	0.446372	+	0.894847i	$0.352716\pi$
$761$	−15.2214	+	26.3642i	−0.551774	+	0.955701i	−0.998147	+	0.0608540i	$0.980618\pi$
$762$	16.2178	−	19.2338i	0.587510	−	0.696768i
$763$	−10.7149	+	6.18623i	−0.387904	+	0.223957i
$764$			24.4013i			0.882809i
$765$	−20.7865	−	2.96046i	−0.751538	−	0.107036i
$766$		−	2.12165i		−	0.0766584i
$767$	1.26595	−	0.730899i	0.0457109	−	0.0263912i
$768$	0.304856	−	1.70501i	0.0110006	−	0.0615243i
$769$	27.3115	+	15.7683i	0.984880	+	0.568621i	0.903740	−	0.428082i	$-0.140811\pi$
$769$	27.3115	+	15.7683i	0.984880	+	0.568621i	0.0811398	+	0.996703i	$0.474144\pi$
$770$	9.84188	+	5.28141i	0.354677	+	0.190329i
$771$	−8.01062	+	44.8021i	−0.288496	+	1.61351i
$772$	0.0264713	+	0.0458496i	0.000952723	+	0.00165016i
$773$	2.97363			0.106954			0.0534770	−	0.998569i	$-0.482970\pi$
$773$	2.97363			0.106954			0.0534770	+	0.998569i	$0.482970\pi$
$774$	−23.5556	+	4.03711i	−0.846687	+	0.145111i
$775$	−33.2765	−	23.8780i	−1.19533	−	0.857722i
$776$	6.93201	+	12.0066i	0.248845	+	0.431011i
$777$	−4.75148	+	5.63510i	−0.170458	+	0.202158i
$778$	−3.59162	+	6.22087i	−0.128766	+	0.223029i
$779$	−7.47019	−	4.31291i	−0.267647	−	0.154526i
$780$	1.40766	−	0.0499362i	0.0504022	−	0.00178800i
$781$	25.4393	−	29.9036i	0.910291	−	1.07003i
$782$	−1.06463			−0.0380710
$783$	45.0589	+	0.324112i	1.61027	+	0.0115828i
$784$	−4.73171			−0.168990
$785$	−17.9335	+	3.86723i	−0.640074	+	0.138027i
$786$	−7.92423	−	21.9351i	−0.282648	−	0.782400i
$787$	8.84713	−	15.3237i	0.315366	−	0.546230i	−0.664149	−	0.747600i	$-0.731206\pi$
$787$	8.84713	−	15.3237i	0.315366	−	0.546230i	0.979515	+	0.201370i	$0.0645394\pi$
$788$	−6.30498	−	3.64018i	−0.224606	−	0.129676i
$789$	17.7214	−	21.0170i	0.630899	−	0.748225i
$790$	2.33063	+	10.8079i	0.0829202	+	0.384526i
$791$	9.39262			0.333963
$792$	−0.115132	+	9.94921i	−0.00409102	+	0.353530i
$793$		−	0.120955i		−	0.00429522i
$794$	8.95182	+	15.5050i	0.317688	+	0.550252i
$795$	−5.20308	+	9.79865i	−0.184534	+	0.347522i
$796$	1.24158	−	2.15047i	0.0440065	−	0.0762215i
$797$	−9.61889	+	16.6604i	−0.340718	+	0.590142i	−0.984566	−	0.175012i	$-0.944004\pi$
$797$	−9.61889	+	16.6604i	−0.340718	+	0.590142i	0.643848	+	0.765154i	$0.277337\pi$
$798$	2.68690	−	15.0274i	0.0951152	−	0.531963i
$799$	−34.7566	+	20.0667i	−1.22960	+	0.709910i
$800$	2.91500	−	4.06236i	0.103061	−	0.143626i
$801$	12.3410	+	14.8515i	0.436048	+	0.524752i
$802$	−12.6001			−0.444925
$803$	−5.88109	−	5.00312i	−0.207539	−	0.176556i
$804$	−9.07815	+	10.7664i	−0.320162	+	0.379701i
$805$	0.849009	−	0.768999i	0.0299236	−	0.0271037i
$806$	2.57996	+	1.48954i	0.0908753	+	0.0524669i
$807$	−8.60546	−	23.8209i	−0.302927	−	0.838534i
$808$	2.19930	−	1.26977i	0.0773712	−	0.0446703i
$809$	−11.5554			−0.406267			−0.203133	−	0.979151i	$-0.565112\pi$
$809$	−11.5554			−0.406267			−0.203133	+	0.979151i	$0.565112\pi$
$810$	17.7059	+	9.56570i	0.622120	+	0.336105i
$811$			28.2510i			0.992028i	0.868315	+	0.496014i	$0.165204\pi$
$811$			28.2510i			0.992028i	−0.868315	+	0.496014i	$0.834796\pi$
$812$	6.53024	+	11.3107i	0.229166	+	0.396928i
$813$	11.9334	+	33.0331i	0.418524	+	1.15852i
$814$	1.68985	−	9.21790i	0.0592291	−	0.323087i
$815$	23.6071	+	26.0633i	0.826920	+	0.912956i
$816$	3.49464	−	4.14453i	0.122337	−	0.145087i
$817$	−40.3735	+	23.3096i	−1.41249	+	0.815501i
$818$	−7.21127			−0.252136
$819$	−1.26383	+	1.05019i	−0.0441617	+	0.0366966i
$820$	3.13762	+	1.00925i	0.109570	+	0.0352444i
$821$	−4.06864	−	7.04709i	−0.141996	−	0.245945i	0.786252	−	0.617906i	$-0.212019\pi$
$821$	−4.06864	−	7.04709i	−0.141996	−	0.245945i	−0.928248	+	0.371961i	$0.878685\pi$
$822$	−8.07460	−	1.44374i	−0.281634	−	0.0503562i
$823$	−27.1424	−	15.6707i	−0.946124	−	0.546245i	−0.0542491	−	0.998527i	$-0.517277\pi$
$823$	−27.1424	−	15.6707i	−0.946124	−	0.546245i	−0.891875	+	0.452283i	$0.850610\pi$
$824$	−5.20338	+	9.01251i	−0.181268	+	0.313966i
$825$	−12.6757	+	25.7746i	−0.441310	+	0.897355i
$826$	3.02679	+	5.24255i	0.105315	+	0.182412i
$827$		−	41.4786i		−	1.44235i	−0.692753	−	0.721175i	$-0.743602\pi$
$827$		−	41.4786i		−	1.44235i	0.692753	−	0.721175i	$-0.256398\pi$
$828$	0.957205	+	0.353602i	0.0332652	+	0.0122885i
$829$	46.8527			1.62726			0.813631	−	0.581382i	$-0.197488\pi$
$829$	46.8527			1.62726			0.813631	+	0.581382i	$0.197488\pi$
$830$	2.61799	+	12.1404i	0.0908719	+	0.421400i
$831$	8.53414	+	7.19593i	0.296046	+	0.249624i
$832$	−0.181842	+	0.314960i	−0.00630424	+	0.0109193i
$833$	−12.8258	−	7.40499i	−0.444388	−	0.256568i
$834$	−25.1212	+	9.07523i	−0.869878	+	0.314250i
$835$	−12.0224	+	2.59254i	−0.416052	+	0.0897186i
$836$	6.51453	+	18.2831i	0.225310	+	0.632333i
$837$	21.0162	+	37.0135i	0.726427	+	1.27937i
$838$	3.90188			0.134788
$839$	−36.3862	+	21.0076i	−1.25619	+	0.725263i	−0.972332	−	0.233603i	$-0.924948\pi$
$839$	−36.3862	+	21.0076i	−1.25619	+	0.725263i	−0.283860	+	0.958866i	$0.591615\pi$
$840$	0.206795	+	5.82937i	0.00713511	+	0.201132i
$841$	−23.1001	+	40.0106i	−0.796556	+	1.37968i
$842$	−17.2578	−	9.96379i	−0.594743	−	0.343375i
$843$	−34.6757	−	29.2384i	−1.19430	−	1.00702i
$844$	1.80220	−	1.04050i	0.0620341	−	0.0358154i
$845$	27.3910	+	8.81060i	0.942279	+	0.303094i
$846$	37.9145	−	6.49804i	1.30353	−	0.223407i
$847$	12.8342	−	10.4761i	0.440987	−	0.359961i
$848$	−1.43228	−	2.48078i	−0.0491847	−	0.0851904i
$849$	7.61415	−	42.5847i	0.261317	−	1.46150i
$850$	14.2589	−	6.44957i	0.489076	−	0.221219i
$851$	−0.832350	−	0.480557i	−0.0285326	−	0.0164733i
$852$	20.1830	+	3.60873i	0.691459	+	0.123633i
$853$	−11.1127	−	19.2477i	−0.380491	−	0.659029i	0.610642	−	0.791907i	$-0.290912\pi$
$853$	−11.1127	−	19.2477i	−0.380491	−	0.659029i	−0.991132	+	0.132878i	$0.957578\pi$
$854$	0.500896			0.0171403
$855$	38.8644	+	5.53516i	1.32914	+	0.189298i
$856$	20.0070			0.683827
$857$	−32.1607	+	18.5680i	−1.09859	+	0.634271i	−0.935850	−	0.352398i	$-0.885366\pi$
$857$	−32.1607	+	18.5680i	−1.09859	+	0.634271i	−0.162739	+	0.986669i	$0.552033\pi$
$858$	0.732530	−	1.95657i	0.0250082	−	0.0667963i
$859$	−8.10085	+	14.0311i	−0.276397	+	0.478734i	−0.970487	−	0.241155i	$-0.922474\pi$
$859$	−8.10085	+	14.0311i	−0.276397	+	0.478734i	0.694089	+	0.719889i	$0.255807\pi$
$860$	13.2026	−	11.9584i	0.450205	−	0.407778i
$861$	−3.61632	+	1.30642i	−0.123244	+	0.0445228i
$862$	−10.7034	+	6.17960i	−0.364559	+	0.210478i
$863$	32.0915			1.09241			0.546204	−	0.837652i	$-0.316072\pi$
$863$	32.0915			1.09241			0.546204	+	0.837652i	$0.316072\pi$
$864$	−4.51857	+	2.56564i	−0.153725	+	0.0872849i
$865$	2.18167	−	6.78252i	0.0741790	−	0.230613i
$866$	−2.25994	−	3.91434i	−0.0767960	−	0.133015i
$867$	−11.7345	+	4.23918i	−0.398525	+	0.143970i
$868$	−6.16848	+	10.6841i	−0.209372	+	0.362643i
$869$	16.1303	+	2.95705i	0.547184	+	0.100311i
$870$	−28.4725	+	17.8135i	−0.965308	+	0.603934i
$871$	2.56086	−	1.47851i	0.0867715	−	0.0500976i
$872$	8.21498			0.278194
$873$	14.4126	−	39.0151i	0.487792	−	1.32046i
$874$	1.99053			0.0673307
$875$	−6.71240	+	15.4428i	−0.226921	+	0.522062i
$876$	0.709724	−	3.96937i	0.0239793	−	0.134112i
$877$	7.57809	−	13.1256i	0.255894	−	0.443221i	−0.709244	−	0.704963i	$-0.750964\pi$
$877$	7.57809	−	13.1256i	0.255894	−	0.443221i	0.965138	+	0.261742i	$0.0842969\pi$
$878$	16.3837	−	28.3774i	0.552923	−	0.957691i
$879$	−38.1726	−	6.82526i	−1.28753	−	0.230210i
$880$	−3.90590	−	6.30428i	−0.131668	−	0.212517i
$881$		−	19.1623i		−	0.645596i	−0.946468	−	0.322798i	$-0.895377\pi$
$881$		−	19.1623i		−	0.645596i	0.946468	−	0.322798i	$-0.104623\pi$
$882$	9.07220	+	10.9177i	0.305477	+	0.367619i
$883$		−	20.4704i		−	0.688884i	−0.938808	−	0.344442i	$-0.888068\pi$
$883$		−	20.4704i		−	0.688884i	0.938808	−	0.344442i	$-0.111932\pi$
$884$	−0.985805	+	0.569155i	−0.0331562	+	0.0191428i
$885$	−13.1971	+	8.25663i	−0.443616	+	0.277543i
$886$	4.10695	+	2.37115i	0.137976	+	0.0796602i
$887$	22.9656	+	13.2592i	0.771111	+	0.445201i	0.833271	−	0.552865i	$-0.186466\pi$
$887$	22.9656	+	13.2592i	0.771111	+	0.445201i	−0.0621599	+	0.998066i	$0.519799\pi$
$888$	4.60296	−	1.66285i	0.154465	−	0.0558017i
$889$	−10.9382	−	18.9455i	−0.366856	−	0.635412i
$890$	−13.7013	−	4.40717i	−0.459269	−	0.147729i
$891$	23.1771	−	18.8102i	0.776462	−	0.630164i
$892$			8.62986i			0.288949i
$893$	64.9842	−	37.5187i	2.17461	−	1.25551i
$894$	−8.41791	−	23.3017i	−0.281537	−	0.779325i
$895$	18.7101	+	20.6568i	0.625411	+	0.690481i
$896$	−1.30431	−	0.753042i	−0.0435738	−	0.0251574i
$897$	−0.163804	−	0.138119i	−0.00546926	−	0.00461164i
$898$	−11.3180	−	19.6033i	−0.377685	−	0.654170i
$899$	−71.0344			−2.36913
$900$	−14.9623	+	1.06290i	−0.498743	+	0.0354301i
$901$		−	8.96590i		−	0.298698i
$902$	3.16768	−	3.72356i	0.105472	−	0.123981i
$903$	−3.65766	+	20.4567i	−0.121719	+	0.680755i
$904$	−5.40093	−	3.11823i	−0.179632	−	0.103711i
$905$	−29.1994	+	26.4477i	−0.970623	+	0.879153i
$906$	−6.29295	+	35.1954i	−0.209069	+	1.16929i
$907$	−6.45200	+	3.72506i	−0.214235	+	0.123689i	−0.603278	−	0.797531i	$-0.706139\pi$
$907$	−6.45200	+	3.72506i	−0.214235	+	0.123689i	0.389043	+	0.921220i	$0.372806\pi$
$908$			23.7962i			0.789706i
$909$	−7.14657	−	2.64002i	−0.237037	−	0.0875638i
$910$	0.375039	−	1.16595i	0.0124324	−	0.0386508i
$911$	−40.4973	+	23.3811i	−1.34173	+	0.774651i	−0.987062	−	0.160340i	$-0.948741\pi$
$911$	−40.4973	+	23.3811i	−1.34173	+	0.774651i	−0.354673	+	0.934991i	$0.615408\pi$
$912$	−6.53391	+	7.74900i	−0.216359	+	0.256595i
$913$	18.1191	+	3.32164i	0.599656	+	0.109930i
$914$	18.7666	+	10.8349i	0.620744	+	0.358387i
$915$	0.0456656	+	1.28727i	0.00150966	+	0.0425559i
$916$	−10.3827	−	17.9834i	−0.343055	−	0.594188i
$917$	−20.2799			−0.669701
$918$	−16.2632	−	0.116983i	−0.536767	−	0.00386101i
$919$		−	4.63494i		−	0.152892i	−0.997074	−	0.0764462i	$-0.975643\pi$
$919$		−	4.63494i		−	0.152892i	0.997074	−	0.0764462i	$-0.0243573\pi$
$920$	−0.743493	+	0.160329i	−0.0245122	+	0.00528588i
$921$	−35.7400	+	12.9113i	−1.17767	+	0.425443i
$922$	−21.6268	−	12.4863i	−0.712242	−	0.411213i
$923$	−3.72832	−	2.15255i	−0.122719	−	0.0708520i
$924$	8.10254	+	3.03355i	0.266554	+	0.0997963i
$925$	14.0592	+	1.39384i	0.462262	+	0.0458291i
$926$	13.6627			0.448983
$927$	30.7716	−	5.27384i	1.01067	−	0.173216i
$928$		−	8.67181i		−	0.284666i
$929$	11.2008	−	6.46676i	0.367485	−	0.212167i	−0.304874	−	0.952393i	$-0.598614\pi$
$929$	11.2008	−	6.46676i	0.367485	−	0.212167i	0.672359	+	0.740225i	$0.265281\pi$
$930$	−28.0199	−	14.8786i	−0.918810	−	0.487888i
$931$	23.9804	+	13.8451i	0.785924	+	0.453754i
$932$	−8.75677	−	5.05573i	−0.286838	−	0.165606i
$933$	−5.14210	−	0.919409i	−0.168345	−	0.0301001i
$934$	26.2993	−	15.1839i	0.860538	−	0.496832i
$935$	−0.721352	−	23.2011i	−0.0235907	−	0.758756i
$936$	1.07537	−	0.184305i	0.0351497	−	0.00602418i
$937$	−47.4230			−1.54924			−0.774620	−	0.632427i	$-0.782059\pi$
$937$	−47.4230			−1.54924			−0.774620	+	0.632427i	$0.782059\pi$
$938$	6.12281	+	10.6050i	0.199917	+	0.346266i
$939$	−8.71436	+	10.3349i	−0.284382	+	0.337268i
$940$	−21.2506	+	19.2480i	−0.693119	+	0.627800i
$941$	−7.78825	+	13.4896i	−0.253890	+	0.439750i	−0.964593	−	0.263742i	$-0.915043\pi$
$941$	−7.78825	+	13.4896i	−0.253890	+	0.439750i	0.710704	+	0.703492i	$0.248377\pi$
$942$	−13.3652	+	4.82826i	−0.435460	+	0.157313i
$943$	−0.250684	−	0.434197i	−0.00816338	−	0.0141394i
$944$		−	4.01942i		−	0.130821i
$945$	13.0539	−	11.6539i	0.424644	−	0.379102i
$946$	−8.86819	−	24.8886i	−0.288330	−	0.809198i
$947$	19.6484	+	34.0321i	0.638488	+	1.10589i	0.985765	+	0.168132i	$0.0537733\pi$
$947$	19.6484	+	34.0321i	0.638488	+	1.10589i	−0.347276	+	0.937763i	$0.612893\pi$
$948$	2.90981	+	8.05468i	0.0945063	+	0.261604i
$949$	−0.423339	+	0.733244i	−0.0137422	+	0.0238021i
$950$	−26.6598	+	12.0587i	−0.864958	+	0.391237i
$951$	−20.6343	−	17.3987i	−0.669113	−	0.564192i
$952$	−2.35698	−	4.08241i	−0.0763901	−	0.132312i
$953$			21.9842i			0.712137i	0.934460	+	0.356069i	$0.115883\pi$
$953$			21.9842i			0.712137i	−0.934460	+	0.356069i	$0.884117\pi$
$954$	−2.97790	+	8.06123i	−0.0964131	+	0.260992i
$955$	−16.7077	+	51.9420i	−0.540648	+	1.68080i
$956$	−8.54604	−	14.8022i	−0.276399	−	0.478737i
$957$	8.20000	+	49.1362i	0.265068	+	1.58835i
$958$	1.22238	+	0.705741i	0.0394933	+	0.0228015i
$959$	−3.56626	+	6.17695i	−0.115161	+	0.199464i
$960$	1.81636	−	3.42065i	0.0586229	−	0.110401i
$961$	−18.0496	−	31.2628i	−0.582245	−	1.00848i
$962$	−1.02763			−0.0331322
$963$	−38.3599	−	46.1633i	−1.23613	−	1.48759i
$964$		−	3.65857i		−	0.117835i
$965$	0.0249548	+	0.115723i	0.000803325	+	0.00372526i
$966$	0.571975	−	0.678344i	0.0184030	−	0.0218253i
$967$	−17.8952	+	30.9954i	−0.575470	+	0.996744i	0.420520	+	0.907283i	$0.361848\pi$
$967$	−17.8952	+	30.9954i	−0.575470	+	0.996744i	−0.995990	+	0.0894606i	$0.971486\pi$
$968$	−10.8578	+	1.76315i	−0.348982	+	0.0566698i
$969$	−29.8378	+	10.7791i	−0.958529	+	0.346276i
$970$	6.53490	+	30.3043i	0.209823	+	0.973012i
$971$		−	55.0798i		−	1.76760i	−0.467869	−	0.883798i	$-0.654978\pi$
$971$		−	55.0798i		−	1.76760i	0.467869	−	0.883798i	$-0.345022\pi$
$972$	14.5834	+	5.50679i	0.467762	+	0.176630i
$973$			23.2256i			0.744578i
$974$	−9.93072	−	17.2005i	−0.318201	−	0.551140i
$975$	3.03061	+	0.857532i	0.0970572	+	0.0274630i
$976$	−0.288024	−	0.166291i	−0.00921943	−	0.00532284i
$977$	6.44825	−	11.1687i	0.206298	−	0.357318i	−0.744248	−	0.667904i	$-0.767192\pi$
$977$	6.44825	−	11.1687i	0.206298	−	0.357318i	0.950545	+	0.310585i	$0.100525\pi$
$978$	20.8241	+	17.5587i	0.665881	+	0.561467i
$979$	−13.8326	+	16.2600i	−0.442091	+	0.519671i
$980$	−10.0722	−	3.23982i	−0.321744	−	0.103492i
$981$	−15.7508	−	18.9549i	−0.502883	−	0.605183i
$982$			17.3479i			0.553594i
$983$	−23.8595	−	41.3258i	−0.760998	−	1.31809i	−0.942336	−	0.334667i	$-0.891376\pi$
$983$	−23.8595	−	41.3258i	−0.760998	−	1.31809i	0.181338	−	0.983421i	$-0.441957\pi$
$984$	2.51317	+	0.449355i	0.0801168	+	0.0143249i
$985$	−10.9287	−	12.0658i	−0.348217	−	0.384447i
$986$	13.5711	−	23.5059i	0.432193	−	0.748580i
$987$	5.88729	−	32.9266i	0.187394	−	1.04807i
$988$	1.84315	−	1.06415i	0.0586385	−	0.0338550i
$989$	−2.70969			−0.0861633
$990$	−7.05734	+	21.0996i	−0.224297	+	0.670590i
$991$	−14.9261			−0.474144			−0.237072	−	0.971492i	$-0.576188\pi$
$991$	−14.9261			−0.474144			−0.237072	+	0.971492i	$0.576188\pi$
$992$	7.09397	−	4.09571i	0.225234	−	0.130039i
$993$	−31.1384	−	26.2557i	−0.988148	−	0.833200i
$994$	8.91411	−	15.4397i	0.282738	−	0.489717i
$995$	4.11533	−	3.72751i	0.130465	−	0.118170i
$996$	3.26858	+	9.04780i	0.103569	+	0.286690i
$997$	−5.05418	−	8.75410i	−0.160068	−	0.277245i	0.774825	−	0.632176i	$-0.217838\pi$
$997$	−5.05418	−	8.75410i	−0.160068	−	0.277245i	−0.934893	+	0.354930i	$0.884505\pi$
$998$			11.6126i			0.367591i
$999$	−12.6621	−	7.43244i	−0.400613	−	0.235152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.o.a.329.4	✓	144
5.4	even	2	inner	990.2.o.a.329.69	yes	144
9.2	odd	6	inner	990.2.o.a.659.33	yes	144
11.10	odd	2	inner	990.2.o.a.329.40	yes	144
45.29	odd	6	inner	990.2.o.a.659.40	yes	144
55.54	odd	2	inner	990.2.o.a.329.33	yes	144
99.65	even	6	inner	990.2.o.a.659.69	yes	144
495.164	even	6	inner	990.2.o.a.659.4	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.o.a.329.4	✓	144	1.1	even	1	trivial
990.2.o.a.329.33	yes	144	55.54	odd	2	inner
990.2.o.a.329.40	yes	144	11.10	odd	2	inner
990.2.o.a.329.69	yes	144	5.4	even	2	inner
990.2.o.a.659.4	yes	144	495.164	even	6	inner
990.2.o.a.659.33	yes	144	9.2	odd	6	inner
990.2.o.a.659.40	yes	144	45.29	odd	6	inner
990.2.o.a.659.69	yes	144	99.65	even	6	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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.62901 + 0.588492i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.65730 - 1.50112i) q^{5} +(1.11652 - 1.32415i) q^{6} +(-0.753042 - 1.30431i) q^{7} +1.00000i q^{8} +(2.30735 - 1.91732i) q^{9} +(-0.684705 + 2.12866i) q^{10} +(2.52618 + 2.14905i) q^{11} +(-0.304856 + 1.70501i) q^{12} +(0.181842 - 0.314960i) q^{13} +(1.30431 + 0.753042i) q^{14} +(-1.81636 + 3.42065i) q^{15} +(-0.500000 - 0.866025i) q^{16} -3.12994i q^{17} +(-1.03957 + 2.81413i) q^{18} +5.85203i q^{19} +(-0.471357 - 2.18582i) q^{20} +(1.99429 + 1.68157i) q^{21} +(-3.26226 - 0.598045i) q^{22} +(-0.170072 + 0.294573i) q^{23} +(-0.588492 - 1.62901i) q^{24} +(0.493286 - 4.97561i) q^{25} +0.363684i q^{26} +(-2.63038 + 4.48120i) q^{27} -1.50608 q^{28} +(-4.33590 - 7.51001i) q^{29} +(-0.137306 - 3.87055i) q^{30} +(4.09571 - 7.09397i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.37987 - 2.01419i) q^{33} +(1.56497 + 2.71061i) q^{34} +(-3.20594 - 1.03122i) q^{35} +(-0.506771 - 2.95689i) q^{36} +2.82562i q^{37} +(-2.92602 - 5.06801i) q^{38} +(-0.110871 + 0.620085i) q^{39} +(1.50112 + 1.65730i) q^{40} +(-0.736994 + 1.27651i) q^{41} +(-2.56789 - 0.459139i) q^{42} +(3.98317 + 6.89905i) q^{43} +(3.12422 - 1.11321i) q^{44} +(0.945852 - 6.64119i) q^{45} -0.340143i q^{46} +(-6.41122 - 11.1046i) q^{47} +(1.32415 + 1.11652i) q^{48} +(2.36586 - 4.09778i) q^{49} +(2.06061 + 4.55565i) q^{50} +(1.84195 + 5.09871i) q^{51} +(-0.181842 - 0.314960i) q^{52} +2.86456 q^{53} +(0.0373754 - 5.19602i) q^{54} +(7.41262 - 0.230468i) q^{55} +(1.30431 - 0.753042i) q^{56} +(-3.44388 - 9.53303i) q^{57} +(7.51001 + 4.33590i) q^{58} +(3.48092 + 2.00971i) q^{59} +(2.05419 + 3.28334i) q^{60} +(0.288024 - 0.166291i) q^{61} +8.19141i q^{62} +(-4.23831 - 1.56568i) q^{63} -1.00000 q^{64} +(-0.171425 - 0.794949i) q^{65} +(5.66620 - 0.945593i) q^{66} +(7.04145 + 4.06538i) q^{67} +(-2.71061 - 1.56497i) q^{68} +(0.103695 - 0.579948i) q^{69} +(3.29203 - 0.709903i) q^{70} -11.8375i q^{71} +(1.91732 + 2.30735i) q^{72} -2.32806 q^{73} +(-1.41281 - 2.44706i) q^{74} +(2.12454 + 8.39561i) q^{75} +(5.06801 + 2.92602i) q^{76} +(0.900706 - 4.91324i) q^{77} +(-0.214025 - 0.592445i) q^{78} +(4.28208 - 2.47226i) q^{79} +(-2.12866 - 0.684705i) q^{80} +(1.64776 - 8.84787i) q^{81} -1.47399i q^{82} +(4.81005 - 2.77708i) q^{83} +(2.45343 - 0.886319i) q^{84} +(-4.69841 - 5.18725i) q^{85} +(-6.89905 - 3.98317i) q^{86} +(11.4828 + 9.68224i) q^{87} +(-2.14905 + 2.52618i) q^{88} +6.43660i q^{89} +(2.50146 + 6.22436i) q^{90} -0.547739 q^{91} +(0.170072 + 0.294573i) q^{92} +(-2.49720 + 13.9664i) q^{93} +(11.1046 + 6.41122i) q^{94} +(8.78460 + 9.69857i) q^{95} +(-1.70501 - 0.304856i) q^{96} +(12.0066 - 6.93201i) q^{97} +4.73171i q^{98} +(9.94921 + 0.115132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 72 q^{4} - 6 q^{5} + 12 q^{9} + 12 q^{11} - 2 q^{15} - 72 q^{16} - 6 q^{20} + 6 q^{25} + 12 q^{31} + 12 q^{45} - 72 q^{49} + 12 q^{55} + 60 q^{59} - 4 q^{60} - 144 q^{64} - 36 q^{66} - 8 q^{69}+ \cdots - 40 q^{99}+O(q^{100}) \) 144 * q + 72 * q^4 - 6 * q^5 + 12 * q^9 + 12 * q^11 - 2 * q^15 - 72 * q^16 - 6 * q^20 + 6 * q^25 + 12 * q^31 + 12 * q^45 - 72 * q^49 + 12 * q^55 + 60 * q^59 - 4 * q^60 - 144 * q^64 - 36 * q^66 - 8 * q^69 + 12 * q^70 + 92 * q^75 - 100 * q^81 + 72 * q^86 - 48 * q^91 - 40 * q^99

Introduction

L-functions

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