LMFDB - Embedded newform 186.2.j.a.23.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [186,2,Mod(23,186)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(186, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 9]))

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

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

chi := DirichletCharacter("186.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 186 = 2 \cdot 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	186.j (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.48521747760$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			23.11
Character	$\chi$	$=$	186.23
Dual form			186.2.j.a.89.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(0.756502 + 1.55811i) q^{3} +(0.809017 + 0.587785i) q^{4} -3.78035i q^{5} +(0.237994 + 1.71562i) q^{6} +(2.28063 + 1.65697i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-1.85541 + 2.35743i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(0.756502 + 1.55811i) q^{3} +(0.809017 + 0.587785i) q^{4} -3.78035i q^{5} +(0.237994 + 1.71562i) q^{6} +(2.28063 + 1.65697i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-1.85541 + 2.35743i) q^{9} +(1.16819 - 3.59533i) q^{10} +(-2.54160 - 1.84658i) q^{11} +(-0.303810 + 1.70520i) q^{12} +(-1.84620 + 0.599867i) q^{13} +(1.65697 + 2.28063i) q^{14} +(5.89020 - 2.85985i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-5.42535 + 3.94174i) q^{17} +(-2.49308 + 1.66869i) q^{18} +(0.578279 - 1.77976i) q^{19} +(2.22204 - 3.05837i) q^{20} +(-0.856446 + 4.80698i) q^{21} +(-1.84658 - 2.54160i) q^{22} +(1.09255 - 0.793781i) q^{23} +(-0.815876 + 1.52786i) q^{24} -9.29108 q^{25} -1.94121 q^{26} +(-5.07675 - 1.10753i) q^{27} +(0.871123 + 2.68104i) q^{28} +(2.30221 - 7.08547i) q^{29} +(6.48566 - 0.899702i) q^{30} +(5.52082 + 0.721517i) q^{31} +1.00000i q^{32} +(0.954449 - 5.35704i) q^{33} +(-6.37788 + 2.07230i) q^{34} +(6.26395 - 8.62159i) q^{35} +(-2.88672 + 0.816616i) q^{36} -4.34136i q^{37} +(1.09995 - 1.51395i) q^{38} +(-2.33131 - 2.42278i) q^{39} +(3.05837 - 2.22204i) q^{40} +(10.5390 + 3.42433i) q^{41} +(-2.29997 + 4.30705i) q^{42} +(-4.75122 - 1.54376i) q^{43} +(-0.970805 - 2.98783i) q^{44} +(8.91191 + 7.01410i) q^{45} +(1.28436 - 0.417315i) q^{46} +(-4.88304 + 1.58660i) q^{47} +(-1.24808 + 1.20096i) q^{48} +(0.292590 + 0.900498i) q^{49} +(-8.83634 - 2.87110i) q^{50} +(-10.2460 - 5.47134i) q^{51} +(-1.84620 - 0.599867i) q^{52} +(-9.50156 + 6.90328i) q^{53} +(-4.48603 - 2.62213i) q^{54} +(-6.98073 + 9.60815i) q^{55} +2.81901i q^{56} +(3.21053 - 0.445370i) q^{57} +(4.37906 - 6.02726i) q^{58} +(2.20597 - 0.716762i) q^{59} +(6.44625 + 1.14851i) q^{60} +8.78602i q^{61} +(5.02765 + 2.39223i) q^{62} +(-8.13770 + 2.30205i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(2.26771 + 6.97929i) q^{65} +(2.56315 - 4.79990i) q^{66} +7.15912 q^{67} -6.70610 q^{68} +(2.06331 + 1.10181i) q^{69} +(8.62159 - 6.26395i) q^{70} +(5.73030 + 7.88708i) q^{71} +(-2.99778 - 0.115397i) q^{72} +(0.698039 - 0.960768i) q^{73} +(1.34156 - 4.12888i) q^{74} +(-7.02872 - 14.4765i) q^{75} +(1.51395 - 1.09995i) q^{76} +(-2.73671 - 8.42274i) q^{77} +(-1.46853 - 3.02462i) q^{78} +(-1.57212 - 2.16383i) q^{79} +(3.59533 - 1.16819i) q^{80} +(-2.11492 - 8.74798i) q^{81} +(8.96502 + 6.51347i) q^{82} +(0.646012 - 1.98822i) q^{83} +(-3.51835 + 3.38552i) q^{84} +(14.9012 + 20.5097i) q^{85} +(-4.04163 - 2.93641i) q^{86} +(12.7816 - 1.77308i) q^{87} -3.14159i q^{88} +(3.56798 + 2.59229i) q^{89} +(6.30825 + 9.42474i) q^{90} +(-5.20447 - 1.69103i) q^{91} +1.35046 q^{92} +(3.05231 + 9.14786i) q^{93} -5.13433 q^{94} +(-6.72812 - 2.18610i) q^{95} +(-1.55811 + 0.756502i) q^{96} +(-2.75033 - 1.99823i) q^{97} +0.946840i q^{98} +(9.06889 - 2.56547i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 12 q^{4} - 18 q^{7} - 4 q^{9}+O(q^{10}) $ 48 * q + 12 * q^4 - 18 * q^7 - 4 * q^9	$ 48 q + 12 q^{4} - 18 q^{7} - 4 q^{9} + 4 q^{10} + 10 q^{15} - 12 q^{16} + 8 q^{18} + 20 q^{19} - 10 q^{22} - 92 q^{25} - 22 q^{28} + 40 q^{31} - 12 q^{33} - 20 q^{34} + 4 q^{36} - 8 q^{39} + 6 q^{40} - 50 q^{43} + 6 q^{45} + 20 q^{46} - 10 q^{48} - 34 q^{49} - 10 q^{51} + 20 q^{55} - 20 q^{58} + 10 q^{60} - 148 q^{63} + 12 q^{64} - 36 q^{66} + 60 q^{67} + 54 q^{69} - 24 q^{70} - 8 q^{72} - 20 q^{73} + 30 q^{75} + 30 q^{76} + 10 q^{78} + 50 q^{79} - 56 q^{81} + 12 q^{82} + 20 q^{84} + 20 q^{85} + 104 q^{87} + 98 q^{90} + 70 q^{91} - 10 q^{93} + 24 q^{94} + 22 q^{97}+O(q^{100}) $ 48 * q + 12 * q^4 - 18 * q^7 - 4 * q^9 + 4 * q^10 + 10 * q^15 - 12 * q^16 + 8 * q^18 + 20 * q^19 - 10 * q^22 - 92 * q^25 - 22 * q^28 + 40 * q^31 - 12 * q^33 - 20 * q^34 + 4 * q^36 - 8 * q^39 + 6 * q^40 - 50 * q^43 + 6 * q^45 + 20 * q^46 - 10 * q^48 - 34 * q^49 - 10 * q^51 + 20 * q^55 - 20 * q^58 + 10 * q^60 - 148 * q^63 + 12 * q^64 - 36 * q^66 + 60 * q^67 + 54 * q^69 - 24 * q^70 - 8 * q^72 - 20 * q^73 + 30 * q^75 + 30 * q^76 + 10 * q^78 + 50 * q^79 - 56 * q^81 + 12 * q^82 + 20 * q^84 + 20 * q^85 + 104 * q^87 + 98 * q^90 + 70 * q^91 - 10 * q^93 + 24 * q^94 + 22 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/186\mathbb{Z}\right)^\times$.

$n$	$125$	$127$
$\chi(n)$	$-1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	0.756502	+	1.55811i	0.436767	+	0.899575i
$3$	0.756502	+	1.55811i	0.436767	+	0.899575i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$		−	3.78035i		−	1.69063i	−0.534272	−	0.845313i	$-0.679414\pi$
$5$		−	3.78035i		−	1.69063i	0.534272	−	0.845313i	$-0.320586\pi$
$6$	0.237994	+	1.71562i	0.0971607	+	0.700400i
$7$	2.28063	+	1.65697i	0.861997	+	0.626278i	0.928428	−	0.371513i	$-0.121161\pi$
$7$	2.28063	+	1.65697i	0.861997	+	0.626278i	−0.0664304	+	0.997791i	$0.521161\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	−1.85541	+	2.35743i	−0.618470	+	0.785809i
$10$	1.16819	−	3.59533i	0.369415	−	1.13694i
$11$	−2.54160	−	1.84658i	−0.766322	−	0.556765i	0.134521	−	0.990911i	$-0.457050\pi$
$11$	−2.54160	−	1.84658i	−0.766322	−	0.556765i	−0.900843	+	0.434145i	$0.857050\pi$
$12$	−0.303810	+	1.70520i	−0.0877025	+	0.492248i
$13$	−1.84620	+	0.599867i	−0.512044	+	0.166373i	−0.553632	−	0.832762i	$-0.686758\pi$
$13$	−1.84620	+	0.599867i	−0.512044	+	0.166373i	0.0415876	+	0.999135i	$0.486758\pi$
$14$	1.65697	+	2.28063i	0.442845	+	0.609524i
$15$	5.89020	−	2.85985i	1.52084	−	0.738409i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−5.42535	+	3.94174i	−1.31584	+	0.956013i	−0.315866	+	0.948804i	$0.602295\pi$
$17$	−5.42535	+	3.94174i	−1.31584	+	0.956013i	−0.999974	+	0.00720948i	$0.997705\pi$
$18$	−2.49308	+	1.66869i	−0.587625	+	0.393315i
$19$	0.578279	−	1.77976i	0.132666	−	0.408305i	−0.862553	−	0.505966i	$-0.831136\pi$
$19$	0.578279	−	1.77976i	0.132666	−	0.408305i	0.995220	+	0.0976612i	$0.0311362\pi$
$20$	2.22204	−	3.05837i	0.496862	−	0.683872i
$21$	−0.856446	+	4.80698i	−0.186892	+	1.04897i
$22$	−1.84658	−	2.54160i	−0.393693	−	0.541871i
$23$	1.09255	−	0.793781i	0.227811	−	0.165515i	−0.468024	−	0.883716i	$-0.655034\pi$
$23$	1.09255	−	0.793781i	0.227811	−	0.165515i	0.695836	+	0.718201i	$0.255034\pi$
$24$	−0.815876	+	1.52786i	−0.166540	+	0.311872i
$25$	−9.29108			−1.85822
$26$	−1.94121			−0.380703
$27$	−5.07675	−	1.10753i	−0.977021	−	0.213145i
$28$	0.871123	+	2.68104i	0.164627	+	0.506669i
$29$	2.30221	−	7.08547i	0.427509	−	1.31574i	−0.473061	−	0.881029i	$-0.656851\pi$
$29$	2.30221	−	7.08547i	0.427509	−	1.31574i	0.900571	−	0.434709i	$-0.143149\pi$
$30$	6.48566	−	0.899702i	1.18411	−	0.164262i
$31$	5.52082	+	0.721517i	0.991568	+	0.129588i
$31$	5.52082	+	0.721517i	0.991568	+	0.129588i
$32$			1.00000i			0.176777i
$33$	0.954449	−	5.35704i	0.166148	−	0.932540i
$34$	−6.37788	+	2.07230i	−1.09380	+	0.355396i
$35$	6.26395	−	8.62159i	1.05880	−	1.45731i
$36$	−2.88672	+	0.816616i	−0.481120	+	0.136103i
$37$		−	4.34136i		−	0.713716i	−0.934159	−	0.356858i	$-0.883848\pi$
$37$		−	4.34136i		−	0.713716i	0.934159	−	0.356858i	$-0.116152\pi$
$38$	1.09995	−	1.51395i	0.178436	−	0.245596i
$39$	−2.33131	−	2.42278i	−0.373309	−	0.387956i
$40$	3.05837	−	2.22204i	0.483571	−	0.351335i
$41$	10.5390	+	3.42433i	1.64592	+	0.534791i	0.977850	−	0.209308i	$-0.0671213\pi$
$41$	10.5390	+	3.42433i	1.64592	+	0.534791i	0.668069	+	0.744100i	$0.267121\pi$
$42$	−2.29997	+	4.30705i	−0.354892	+	0.664592i
$43$	−4.75122	−	1.54376i	−0.724554	−	0.235422i	−0.0765574	−	0.997065i	$-0.524393\pi$
$43$	−4.75122	−	1.54376i	−0.724554	−	0.235422i	−0.647996	+	0.761643i	$0.724393\pi$
$44$	−0.970805	−	2.98783i	−0.146354	−	0.450433i
$45$	8.91191	+	7.01410i	1.32851	+	1.04560i
$46$	1.28436	−	0.417315i	0.189369	−	0.0615298i
$47$	−4.88304	+	1.58660i	−0.712264	+	0.231429i	−0.642666	−	0.766146i	$-0.722172\pi$
$47$	−4.88304	+	1.58660i	−0.712264	+	0.231429i	−0.0695982	+	0.997575i	$0.522172\pi$
$48$	−1.24808	+	1.20096i	−0.180145	+	0.173343i
$49$	0.292590	+	0.900498i	0.0417985	+	0.128643i
$50$	−8.83634	−	2.87110i	−1.24965	−	0.406035i
$51$	−10.2460	−	5.47134i	−1.43472	−	0.766141i
$52$	−1.84620	−	0.599867i	−0.256022	−	0.0831866i
$53$	−9.50156	+	6.90328i	−1.30514	+	0.948239i	−0.999992	−	0.00406602i	$-0.998706\pi$
$53$	−9.50156	+	6.90328i	−1.30514	+	0.948239i	−0.305147	+	0.952305i	$0.598706\pi$
$54$	−4.48603	−	2.62213i	−0.610471	−	0.356826i
$55$	−6.98073	+	9.60815i	−0.941282	+	1.29556i
$56$			2.81901i			0.376707i
$57$	3.21053	−	0.445370i	0.425245	−	0.0589907i
$58$	4.37906	−	6.02726i	0.574999	−	0.791418i
$59$	2.20597	−	0.716762i	0.287192	−	0.0933144i	−0.161878	−	0.986811i	$-0.551755\pi$
$59$	2.20597	−	0.716762i	0.287192	−	0.0933144i	0.449071	+	0.893496i	$0.351755\pi$
$60$	6.44625	+	1.14851i	0.832207	+	0.148272i
$61$			8.78602i			1.12493i	0.826820	+	0.562467i	$0.190148\pi$
$61$			8.78602i			1.12493i	−0.826820	+	0.562467i	$0.809852\pi$
$62$	5.02765	+	2.39223i	0.638512	+	0.303813i
$63$	−8.13770	+	2.30205i	−1.02525	+	0.290031i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	2.26771	+	6.97929i	0.281275	+	0.865675i
$66$	2.56315	−	4.79990i	0.315502	−	0.590827i
$67$	7.15912			0.874626			0.437313	−	0.899309i	$-0.355930\pi$
$67$	7.15912			0.874626			0.437313	+	0.899309i	$0.355930\pi$
$68$	−6.70610			−0.813234
$69$	2.06331	+	1.10181i	0.248393	+	0.132642i
$70$	8.62159	−	6.26395i	1.03048	−	0.748685i
$71$	5.73030	+	7.88708i	0.680061	+	0.936024i	0.999935	−	0.0114361i	$-0.00364032\pi$
$71$	5.73030	+	7.88708i	0.680061	+	0.936024i	−0.319873	+	0.947460i	$0.603640\pi$
$72$	−2.99778	−	0.115397i	−0.353292	−	0.0135997i
$73$	0.698039	−	0.960768i	0.0816993	−	0.112449i	−0.766211	−	0.642589i	$-0.777860\pi$
$73$	0.698039	−	0.960768i	0.0816993	−	0.112449i	0.847911	+	0.530139i	$0.177860\pi$
$74$	1.34156	−	4.12888i	0.155953	−	0.479973i
$75$	−7.02872	−	14.4765i	−0.811607	−	1.67160i
$76$	1.51395	−	1.09995i	0.173662	−	0.126173i
$77$	−2.73671	−	8.42274i	−0.311877	−	0.959860i
$78$	−1.46853	−	3.02462i	−0.166278	−	0.342471i
$79$	−1.57212	−	2.16383i	−0.176877	−	0.243450i	0.711369	−	0.702819i	$-0.248076\pi$
$79$	−1.57212	−	2.16383i	−0.176877	−	0.243450i	−0.888246	+	0.459369i	$0.848076\pi$
$80$	3.59533	−	1.16819i	0.401970	−	0.130608i
$81$	−2.11492	−	8.74798i	−0.234991	−	0.971998i
$82$	8.96502	+	6.51347i	0.990021	+	0.719293i
$83$	0.646012	−	1.98822i	0.0709091	−	0.218236i	−0.909322	−	0.416094i	$-0.863399\pi$
$83$	0.646012	−	1.98822i	0.0709091	−	0.218236i	0.980231	+	0.197859i	$0.0633987\pi$
$84$	−3.51835	+	3.38552i	−0.383883	+	0.369390i
$85$	14.9012	+	20.5097i	1.61626	+	2.22459i
$86$	−4.04163	−	2.93641i	−0.435820	−	0.316642i
$87$	12.7816	−	1.77308i	1.37033	−	0.190094i
$88$		−	3.14159i		−	0.334895i
$89$	3.56798	+	2.59229i	0.378205	+	0.274782i	0.760605	−	0.649215i	$-0.224902\pi$
$89$	3.56798	+	2.59229i	0.378205	+	0.274782i	−0.382400	+	0.923997i	$0.624902\pi$
$90$	6.30825	+	9.42474i	0.664948	+	0.993455i
$91$	−5.20447	−	1.69103i	−0.545576	−	0.177268i
$92$	1.35046			0.140795
$93$	3.05231	+	9.14786i	0.316510	+	0.948589i
$94$	−5.13433			−0.529566
$95$	−6.72812	−	2.18610i	−0.690290	−	0.224289i
$96$	−1.55811	+	0.756502i	−0.159024	+	0.0772102i
$97$	−2.75033	−	1.99823i	−0.279254	−	0.202890i	0.439338	−	0.898322i	$-0.355213\pi$
$97$	−2.75033	−	1.99823i	−0.279254	−	0.202890i	−0.718592	+	0.695432i	$0.755213\pi$
$98$			0.946840i			0.0956452i
$99$	9.06889	−	2.56547i	0.911458	−	0.257840i
$100$	−7.51664	−	5.46116i	−0.751664	−	0.546116i
$101$	4.76941	+	6.56453i	0.474574	+	0.653195i	0.977451	−	0.211163i	$-0.0677250\pi$
$101$	4.76941	+	6.56453i	0.474574	+	0.653195i	−0.502877	+	0.864358i	$0.667725\pi$
$102$	−8.05374	−	8.36973i	−0.797439	−	0.828727i
$103$	−0.666660	+	2.05177i	−0.0656880	+	0.202167i	−0.978513	−	0.206183i	$-0.933896\pi$
$103$	−0.666660	+	2.05177i	−0.0656880	+	0.202167i	0.912825	+	0.408350i	$0.133896\pi$
$104$	−1.57047	−	1.14101i	−0.153997	−	0.111886i
$105$	18.1721	+	3.23767i	1.77341	+	0.315964i
$106$	−11.1697	+	3.62927i	−1.08490	+	0.352506i
$107$	5.77005	+	7.94180i	0.557812	+	0.767763i	0.991046	−	0.133519i	$-0.0426277\pi$
$107$	5.77005	+	7.94180i	0.557812	+	0.767763i	−0.433234	+	0.901281i	$0.642628\pi$
$108$	−3.45619	−	3.88005i	−0.332572	−	0.373358i
$109$	−4.22906	−	13.0157i	−0.405071	−	1.24668i	−0.920836	−	0.389950i	$-0.872492\pi$
$109$	−4.22906	−	13.0157i	−0.405071	−	1.24668i	0.515765	−	0.856730i	$-0.327508\pi$
$110$	−9.60815	+	6.98073i	−0.916101	+	0.665587i
$111$	6.76432	−	3.28425i	0.642041	−	0.311727i
$112$	−0.871123	+	2.68104i	−0.0823134	+	0.253335i
$113$	−3.80122	+	5.23193i	−0.357589	+	0.492178i	−0.949475	−	0.313843i	$-0.898383\pi$
$113$	−3.80122	+	5.23193i	−0.357589	+	0.492178i	0.591886	+	0.806021i	$0.298383\pi$
$114$	3.19102	+	0.568536i	0.298866	+	0.0532482i
$115$	−3.00077	−	4.13021i	−0.279823	−	0.385144i
$116$	6.02726	−	4.37906i	0.559617	−	0.406586i
$117$	2.01132	−	5.46528i	0.185946	−	0.505265i
$118$	2.31949			0.213526
$119$	−18.9046			−1.73298
$120$	5.77584	+	3.08430i	0.527260	+	0.281557i
$121$	−0.349312	−	1.07507i	−0.0317557	−	0.0977339i
$122$	−2.71503	+	8.35600i	−0.245807	+	0.756517i
$123$	2.63730	+	19.0115i	0.237798	+	1.71421i
$124$	4.04234	+	3.82877i	0.363013	+	0.343834i
$125$			16.2218i			1.45092i
$126$	−8.45078	−	0.325305i	−0.752856	−	0.0289805i
$127$	18.0198	−	5.85500i	1.59900	−	0.519547i	0.632141	−	0.774853i	$-0.282176\pi$
$127$	18.0198	−	5.85500i	1.59900	−	0.519547i	0.966860	+	0.255306i	$0.0821762\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	−1.18895	−	8.57078i	−0.104682	−	0.754615i
$130$			7.33846i			0.643626i
$131$	1.59639	−	2.19724i	0.139477	−	0.191974i	−0.733564	−	0.679620i	$-0.762145\pi$
$131$	1.59639	−	2.19724i	0.139477	−	0.191974i	0.873041	+	0.487647i	$0.162145\pi$
$132$	3.92095	−	3.77292i	0.341275	−	0.328391i
$133$	4.26786	−	3.10078i	0.370070	−	0.268872i
$134$	6.80873	+	2.21229i	0.588185	+	0.191113i
$135$	−4.18686	+	19.1919i	−0.360348	+	1.65178i
$136$	−6.37788	−	2.07230i	−0.546898	−	0.177698i
$137$	−0.403482	−	1.24179i	−0.0344718	−	0.106093i	0.932340	−	0.361583i	$-0.117763\pi$
$137$	−0.403482	−	1.24179i	−0.0344718	−	0.106093i	−0.966812	+	0.255489i	$0.917763\pi$
$138$	1.62185	+	1.68548i	0.138061	+	0.143478i
$139$	11.5826	−	3.76340i	0.982420	−	0.319208i	0.226601	−	0.973988i	$-0.427239\pi$
$139$	11.5826	−	3.76340i	0.982420	−	0.319208i	0.755819	+	0.654780i	$0.227239\pi$
$140$	10.1353	−	3.29315i	0.856588	−	0.278322i
$141$	−6.16612	−	6.40804i	−0.519281	−	0.539655i
$142$	3.01260	+	9.27182i	0.252811	+	0.778074i
$143$	5.80001	+	1.88454i	0.485021	+	0.157593i
$144$	−2.81540	−	1.03611i	−0.234617	−	0.0863428i
$145$	−26.7856	−	8.70316i	−2.22442	−	0.722758i
$146$	0.960768	−	0.698039i	0.0795138	−	0.0577701i
$147$	−1.18173	+	1.13712i	−0.0974674	+	0.0937877i
$148$	2.55179	−	3.51224i	0.209756	−	0.288704i
$149$		−	3.38490i		−	0.277302i	−0.990341	−	0.138651i	$-0.955723\pi$
$149$		−	3.38490i		−	0.277302i	0.990341	−	0.138651i	$-0.0442766\pi$
$150$	−2.21122	−	15.9400i	−0.180545	−	1.30149i
$151$	8.38437	−	11.5401i	0.682310	−	0.939119i	−0.317649	−	0.948208i	$-0.602893\pi$
$151$	8.38437	−	11.5401i	0.682310	−	0.939119i	0.999959	+	0.00908928i	$0.00289325\pi$
$152$	1.77976	−	0.578279i	0.144358	−	0.0469046i
$153$	0.773863	−	20.1034i	0.0625631	−	1.62526i
$154$		−	8.85619i		−	0.713652i
$155$	2.72759	−	20.8706i	0.219085	−	1.67637i
$156$	−0.461997	−	3.33038i	−0.0369893	−	0.266644i
$157$	−7.10518	+	21.8675i	−0.567055	+	1.74522i	0.0947108	+	0.995505i	$0.469807\pi$
$157$	−7.10518	+	21.8675i	−0.567055	+	1.74522i	−0.661766	+	0.749711i	$0.730193\pi$
$158$	−0.826511	−	2.54374i	−0.0657537	−	0.202369i
$159$	−17.9440	−	9.58211i	−1.42305	−	0.759911i
$160$	3.78035			0.298863
$161$	3.80697			0.300031
$162$	0.691869	−	8.97337i	0.0543584	−	0.705014i
$163$	4.44271	−	3.22782i	0.347980	−	0.252822i	−0.400041	−	0.916497i	$-0.631004\pi$
$163$	4.44271	−	3.22782i	0.347980	−	0.252822i	0.748021	+	0.663675i	$0.231004\pi$
$164$	6.51347	+	8.96502i	0.508617	+	0.700051i
$165$	−20.2515	−	3.60815i	−1.57658	−	0.280894i
$166$	1.22879	−	1.69128i	0.0953725	−	0.131269i
$167$	−6.08462	+	18.7265i	−0.470842	+	1.44910i	0.380642	+	0.924722i	$0.375703\pi$
$167$	−6.08462	+	18.7265i	−0.470842	+	1.44910i	−0.851484	+	0.524380i	$0.824297\pi$
$168$	−4.39233	+	2.13259i	−0.338876	+	0.164533i
$169$	−7.46860	+	5.42626i	−0.574508	+	0.417404i
$170$	7.83402	+	24.1106i	0.600842	+	1.84920i
$171$	3.12271	+	4.66543i	0.238799	+	0.356774i
$172$	−2.93641	−	4.04163i	−0.223899	−	0.308171i
$173$	8.22469	−	2.67236i	0.625312	−	0.203176i	0.0208145	−	0.999783i	$-0.493374\pi$
$173$	8.22469	−	2.67236i	0.625312	−	0.203176i	0.604497	+	0.796607i	$0.293374\pi$
$174$	12.7039	+	2.26342i	0.963080	+	0.171589i
$175$	−21.1895	−	15.3951i	−1.60178	−	1.16376i
$176$	0.970805	−	2.98783i	0.0731772	−	0.225216i
$177$	2.78561	+	2.89490i	0.209379	+	0.217594i
$178$	2.59229	+	3.56798i	0.194300	+	0.267431i
$179$	−9.34593	−	6.79021i	−0.698547	−	0.507524i	0.180911	−	0.983499i	$-0.442095\pi$
$179$	−9.34593	−	6.79021i	−0.698547	−	0.507524i	−0.879459	+	0.475975i	$0.842095\pi$
$180$	3.08710	+	10.9128i	0.230099	+	0.813393i
$181$			18.9695i			1.40999i	0.709211	+	0.704996i	$0.249051\pi$
$181$			18.9695i			1.40999i	−0.709211	+	0.704996i	$0.750949\pi$
$182$	−4.42718	−	3.21654i	−0.328165	−	0.238426i
$183$	−13.6896	+	6.64664i	−1.01196	+	0.491334i
$184$	1.28436	+	0.417315i	0.0946846	+	0.0307649i
$185$	−16.4119			−1.20663
$186$	0.0760712	+	9.64335i	0.00557781	+	0.707085i
$187$	21.0678			1.54063
$188$	−4.88304	−	1.58660i	−0.356132	−	0.115714i
$189$	−9.74303	−	10.9379i	−0.708701	−	0.795616i
$190$	−5.72328	−	4.15821i	−0.415210	−	0.301668i
$191$		−	19.2417i		−	1.39228i	−0.717906	−	0.696140i	$-0.754899\pi$
$191$		−	19.2417i		−	1.39228i	0.717906	−	0.696140i	$-0.245101\pi$
$192$	−1.71562	+	0.237994i	−0.123814	+	0.0171757i
$193$	−19.3570	−	14.0637i	−1.39335	−	1.01233i	−0.995489	−	0.0948793i	$-0.969753\pi$
$193$	−19.3570	−	14.0637i	−1.39335	−	1.01233i	−0.397859	−	0.917447i	$-0.630247\pi$
$194$	−1.99823	−	2.75033i	−0.143465	−	0.197462i
$195$	−9.15897	+	8.81319i	−0.655888	+	0.631126i
$196$	−0.292590	+	0.900498i	−0.0208993	+	0.0643213i
$197$	9.04168	+	6.56917i	0.644193	+	0.468034i	0.861288	−	0.508117i	$-0.169658\pi$
$197$	9.04168	+	6.56917i	0.644193	+	0.468034i	−0.217095	+	0.976150i	$0.569658\pi$
$198$	9.41780	+	0.362530i	0.669294	+	0.0257639i
$199$	−14.0168	+	4.55434i	−0.993626	+	0.322849i	−0.760316	−	0.649554i	$-0.774956\pi$
$199$	−14.0168	+	4.55434i	−0.993626	+	0.322849i	−0.233310	+	0.972402i	$0.574956\pi$
$200$	−5.46116	−	7.51664i	−0.386162	−	0.531507i
$201$	5.41589	+	11.1547i	0.382008	+	0.786792i
$202$	2.50743	+	7.71707i	0.176422	+	0.542971i
$203$	16.9909	−	12.3446i	1.19253	−	0.866424i
$204$	−5.07318	−	10.4488i	−0.355193	−	0.731564i
$205$	12.9452	−	39.8412i	0.904132	−	2.78263i
$206$	−1.26806	+	1.74534i	−0.0883502	+	0.121604i
$207$	−0.155839	+	4.04838i	−0.0108316	+	0.281382i
$208$	−1.14101	−	1.57047i	−0.0791152	−	0.108893i
$209$	−4.75622	+	3.45560i	−0.328995	+	0.239029i
$210$	16.2822	+	8.69468i	1.12358	+	0.599990i
$211$	6.84559			0.471270			0.235635	−	0.971842i	$-0.424283\pi$
$211$	6.84559			0.471270			0.235635	+	0.971842i	$0.424283\pi$
$212$	−11.7446			−0.806620
$213$	−7.95395	+	14.8950i	−0.544996	+	1.02059i
$214$	3.03350	+	9.33614i	0.207366	+	0.638206i
$215$	−5.83597	+	17.9613i	−0.398010	+	1.22495i
$216$	−2.08803	−	4.75817i	−0.142072	−	0.323752i
$217$	11.3954	+	10.7934i	0.773570	+	0.732702i
$218$		−	13.6855i		−	0.926902i
$219$	2.02505	+	0.360798i	0.136840	+	0.0243805i
$220$	−11.2951	+	3.66999i	−0.761513	+	0.247431i
$221$	7.65176	−	10.5317i	0.514713	−	0.708441i
$222$	7.44814	−	1.03322i	0.499886	−	0.0693451i
$223$		−	9.17709i		−	0.614543i	−0.951622	−	0.307272i	$-0.900584\pi$
$223$		−	9.17709i		−	0.614543i	0.951622	−	0.307272i	$-0.0994160\pi$
$224$	−1.65697	+	2.28063i	−0.110711	+	0.152381i
$225$	17.2387	−	21.9030i	1.14925	−	1.46020i
$226$	−5.23193	+	3.80122i	−0.348023	+	0.252853i
$227$	−21.0829	−	6.85025i	−1.39932	−	0.454667i	−0.490350	−	0.871526i	$-0.663131\pi$
$227$	−21.0829	−	6.85025i	−1.39932	−	0.454667i	−0.908971	+	0.416859i	$0.863131\pi$
$228$	2.85915	+	1.52679i	0.189352	+	0.101114i
$229$	−3.16269	−	1.02762i	−0.208996	−	0.0679070i	0.202648	−	0.979252i	$-0.435045\pi$
$229$	−3.16269	−	1.02762i	−0.208996	−	0.0679070i	−0.411644	+	0.911345i	$0.635045\pi$
$230$	−1.57760	−	4.85535i	−0.104024	−	0.320152i
$231$	11.0532	−	10.6359i	0.727248	−	0.699792i
$232$	7.08547	−	2.30221i	0.465184	−	0.151147i
$233$	−1.44224	+	0.468613i	−0.0944845	+	0.0306999i	−0.355878	−	0.934533i	$-0.615818\pi$
$233$	−1.44224	+	0.468613i	−0.0944845	+	0.0306999i	0.261393	+	0.965232i	$0.415818\pi$
$234$	3.60174	−	4.57626i	0.235453	−	0.299160i
$235$	5.99789	+	18.4596i	0.391259	+	1.20417i
$236$	2.20597	+	0.716762i	0.143596	+	0.0466572i
$237$	2.18218	−	4.08648i	0.141748	−	0.265445i
$238$	−17.9793	−	5.84184i	−1.16543	−	0.378670i
$239$	2.87982	−	2.09231i	0.186280	−	0.135340i	−0.490737	−	0.871308i	$-0.663272\pi$
$239$	2.87982	−	2.09231i	0.186280	−	0.135340i	0.677017	+	0.735967i	$0.263272\pi$
$240$	4.54005	+	4.71818i	0.293059	+	0.304557i
$241$	−1.94772	+	2.68080i	−0.125464	+	0.172686i	−0.867128	−	0.498085i	$-0.834037\pi$
$241$	−1.94772	+	2.68080i	−0.125464	+	0.172686i	0.741665	+	0.670771i	$0.234037\pi$
$242$		−	1.13040i		−	0.0726648i
$243$	12.0304	−	9.91314i	0.771748	−	0.635928i
$244$	−5.16429	+	7.10804i	−0.330610	+	0.455046i
$245$	3.40420	−	1.10609i	0.217486	−	0.0706656i
$246$	−3.36664	+	18.8959i	−0.214649	+	1.20476i
$247$			3.63268i			0.231142i
$248$	2.66133	+	4.89053i	0.168995	+	0.310549i
$249$	3.58658	−	0.497536i	0.227290	−	0.0315301i
$250$	−5.01281	+	15.4278i	−0.317038	+	0.975742i
$251$	−4.46154	−	13.7312i	−0.281610	−	0.866707i	−0.987394	−	0.158280i	$-0.949405\pi$
$251$	−4.46154	−	13.7312i	−0.281610	−	0.866707i	0.705784	−	0.708427i	$-0.250595\pi$
$252$	−7.93665	−	2.92082i	−0.499962	−	0.183994i
$253$	−4.24260			−0.266730
$254$	18.9472			1.18885
$255$	−20.6836	+	38.7333i	−1.29526	+	2.42558i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−14.2798	−	19.6544i	−0.890748	−	1.22601i	−0.973326	−	0.229425i	$-0.926316\pi$
$257$	−14.2798	−	19.6544i	−0.890748	−	1.22601i	0.0825786	−	0.996585i	$-0.473684\pi$
$258$	1.51775	−	8.51870i	0.0944912	−	0.530351i
$259$	7.19353	−	9.90105i	0.446984	−	0.615221i
$260$	−2.26771	+	6.97929i	−0.140637	+	0.432837i
$261$	12.4319	+	18.5737i	0.769517	+	1.14969i
$262$	2.19724	−	1.59639i	0.135746	−	0.0986253i
$263$	4.97192	+	15.3020i	0.306582	+	0.943561i	0.979082	+	0.203465i	$0.0652202\pi$
$263$	4.97192	+	15.3020i	0.306582	+	0.943561i	−0.672501	+	0.740096i	$0.734780\pi$
$264$	4.89494	−	2.37662i	0.301263	−	0.146271i
$265$	26.0969	+	35.9192i	1.60312	+	2.20650i
$266$	5.01717	−	1.63018i	0.307622	−	0.0999525i
$267$	−1.33988	+	7.52037i	−0.0819996	+	0.460239i
$268$	5.79185	+	4.20803i	0.353794	+	0.257046i
$269$	2.14002	−	6.58629i	0.130479	−	0.401573i	−0.864380	−	0.502838i	$-0.832289\pi$
$269$	2.14002	−	6.58629i	0.130479	−	0.401573i	0.994859	+	0.101265i	$0.0322891\pi$
$270$	−9.91257	+	16.9588i	−0.603260	+	1.03208i
$271$	9.69630	+	13.3458i	0.589008	+	0.810700i	0.994647	−	0.103333i	$-0.0329509\pi$
$271$	9.69630	+	13.3458i	0.589008	+	0.810700i	−0.405639	+	0.914034i	$0.632951\pi$
$272$	−5.42535	−	3.94174i	−0.328960	−	0.239003i
$273$	−1.30238	−	9.38840i	−0.0788233	−	0.568212i
$274$		−	1.30569i		−	0.0788799i
$275$	23.6142	+	17.1567i	1.42399	+	1.03459i
$276$	1.02163	+	2.10416i	0.0614947	+	0.126656i
$277$	0.136547	+	0.0443667i	0.00820428	+	0.00266573i	0.313116	−	0.949715i	$-0.398627\pi$
$277$	0.136547	+	0.0443667i	0.00820428	+	0.00266573i	−0.304912	+	0.952381i	$0.598627\pi$
$278$	12.1786			0.730425
$279$	−11.9443	+	11.6762i	−0.715086	+	0.699036i
$280$	10.6569			0.636870
$281$	−6.41400	−	2.08403i	−0.382627	−	0.124323i	0.111387	−	0.993777i	$-0.464471\pi$
$281$	−6.41400	−	2.08403i	−0.382627	−	0.124323i	−0.494014	+	0.869454i	$0.664471\pi$
$282$	−3.88413	−	7.99985i	−0.231297	−	0.476384i
$283$	−3.21987	−	2.33937i	−0.191401	−	0.139061i	0.487958	−	0.872867i	$-0.337742\pi$
$283$	−3.21987	−	2.33937i	−0.191401	−	0.139061i	−0.679359	+	0.733806i	$0.737742\pi$
$284$			9.74897i			0.578495i
$285$	−1.68366	−	12.1369i	−0.0997312	−	0.718930i
$286$	4.93378	+	3.58460i	0.291741	+	0.211962i
$287$	18.3616	+	25.2725i	1.08385	+	1.49179i
$288$	−2.35743	−	1.85541i	−0.138913	−	0.109331i
$289$	8.64374	−	26.6027i	0.508455	−	1.56486i
$290$	−22.7852	−	16.5544i	−1.33799	−	0.972108i
$291$	1.03283	−	5.79699i	0.0605458	−	0.339826i
$292$	1.12945	−	0.366981i	0.0660961	−	0.0214759i
$293$	−15.3900	−	21.1825i	−0.899091	−	1.23749i	−0.970757	−	0.240063i	$-0.922832\pi$
$293$	−15.3900	−	21.1825i	−0.899091	−	1.23749i	0.0716666	−	0.997429i	$-0.477168\pi$
$294$	−1.47528	+	0.716286i	−0.0860401	+	0.0417747i
$295$	−2.70961	−	8.33933i	−0.157760	−	0.485535i
$296$	3.51224	−	2.55179i	0.204145	−	0.148320i
$297$	10.8579	+	12.1895i	0.630041	+	0.707308i
$298$	1.04599	−	3.21923i	0.0605927	−	0.186485i
$299$	−1.54090	+	2.12086i	−0.0891123	+	0.122653i
$300$	2.82273	−	15.8431i	0.162970	−	0.914703i
$301$	−8.27779	−	11.3934i	−0.477124	−	0.656705i
$302$	11.5401	−	8.38437i	0.664058	−	0.482466i
$303$	−6.62019	+	12.3974i	−0.380320	+	0.712209i
$304$	1.87135			0.107329
$305$	33.2143			1.90184
$306$	6.94828	−	18.8803i	0.397207	−	1.07932i
$307$	9.63940	+	29.6670i	0.550150	+	1.69319i	0.708421	+	0.705791i	$0.249408\pi$
$307$	9.63940	+	29.6670i	0.550150	+	1.69319i	−0.158271	+	0.987396i	$0.550592\pi$
$308$	2.73671	−	8.42274i	0.155939	−	0.479930i
$309$	−3.70121	+	0.513439i	−0.210555	+	0.0292085i
$310$	9.04347	−	19.0063i	0.513635	−	1.07948i
$311$			0.433904i			0.0246045i	0.999924	+	0.0123022i	$0.00391602\pi$
$311$			0.433904i			0.0246045i	−0.999924	+	0.0123022i	$0.996084\pi$
$312$	0.589760	−	3.31015i	0.0333886	−	0.187400i
$313$	−6.32026	+	2.05358i	−0.357242	+	0.116075i	−0.482139	−	0.876095i	$-0.660140\pi$
$313$	−6.32026	+	2.05358i	−0.357242	+	0.116075i	0.124897	+	0.992170i	$0.460140\pi$
$314$	−13.5149	+	18.6016i	−0.762687	+	1.04975i
$315$	8.70257	+	30.7634i	0.490334	+	1.73332i
$316$		−	2.67465i		−	0.150461i
$317$	12.2562	−	16.8692i	0.688375	−	0.947467i	−0.311621	−	0.950206i	$-0.600872\pi$
$317$	12.2562	−	16.8692i	0.688375	−	0.947467i	0.999996	+	0.00273931i	$0.000871950\pi$
$318$	−14.1047	−	14.6581i	−0.790955	−	0.821988i
$319$	−18.9352	+	13.7572i	−1.06017	+	0.770257i
$320$	3.59533	+	1.16819i	0.200985	+	0.0653040i
$321$	−8.00913	+	14.9984i	−0.447026	+	0.837127i
$322$	3.62064	+	1.17642i	0.201770	+	0.0655592i
$323$	3.87799	+	11.9352i	0.215777	+	0.664094i
$324$	3.43093	−	8.32038i	0.190607	−	0.462243i
$325$	17.1532	−	5.57341i	0.951488	−	0.309157i
$326$	5.22272	−	1.69697i	0.289260	−	0.0939862i
$327$	17.0806	−	16.4358i	0.944560	−	0.908900i
$328$	3.42433	+	10.5390i	0.189077	+	0.581920i
$329$	−13.7654	−	4.47263i	−0.758908	−	0.246584i
$330$	−18.1453	−	9.68961i	−0.998868	−	0.533396i
$331$	2.00953	+	0.652936i	0.110454	+	0.0358886i	0.363722	−	0.931507i	$-0.381506\pi$
$331$	2.00953	+	0.652936i	0.110454	+	0.0358886i	−0.253269	+	0.967396i	$0.581506\pi$
$332$	1.69128	−	1.22879i	0.0928212	−	0.0674385i
$333$	10.2344	+	8.05500i	0.560844	+	0.441412i
$334$	−11.5736	+	15.9297i	−0.633281	+	0.871637i
$335$		−	27.0640i		−	1.47867i
$336$	−4.83636	+	0.670909i	−0.263845	+	0.0366011i
$337$	1.50915	−	2.07716i	0.0822084	−	0.113150i	−0.765932	−	0.642921i	$-0.777722\pi$
$337$	1.50915	−	2.07716i	0.0822084	−	0.113150i	0.848141	+	0.529771i	$0.177722\pi$
$338$	−8.77987	+	2.85275i	−0.477562	+	0.155169i
$339$	−11.0275	−	1.96475i	−0.598934	−	0.106710i
$340$			25.3514i			1.37487i
$341$	−12.6994	−	12.0284i	−0.687710	−	0.651377i
$342$	1.52817	+	5.40206i	0.0826342	+	0.292110i
$343$	5.27305	−	16.2288i	0.284718	−	0.876271i
$344$	−1.54376	−	4.75122i	−0.0832342	−	0.256168i
$345$	4.16522	−	7.80004i	0.224248	−	0.419940i
$346$	8.64795			0.464917
$347$	18.8871			1.01391			0.506956	−	0.861972i	$-0.330771\pi$
$347$	18.8871			1.01391			0.506956	+	0.861972i	$0.330771\pi$
$348$	11.3827	+	6.07836i	0.610176	+	0.325834i
$349$	0.971902	−	0.706128i	0.0520247	−	0.0377982i	−0.561469	−	0.827498i	$-0.689764\pi$
$349$	0.971902	−	0.706128i	0.0520247	−	0.0377982i	0.613494	+	0.789700i	$0.289764\pi$
$350$	−15.3951	−	21.1895i	−0.822902	−	1.13263i
$351$	10.0371	−	1.00065i	0.535739	−	0.0534107i
$352$	1.84658	−	2.54160i	0.0984231	−	0.135468i
$353$	−4.42036	+	13.6045i	−0.235272	+	0.724093i	0.761813	+	0.647797i	$0.224310\pi$
$353$	−4.42036	+	13.6045i	−0.235272	+	0.724093i	−0.997085	+	0.0762964i	$0.975690\pi$
$354$	1.75470	+	3.61402i	0.0932612	+	0.192083i
$355$	29.8160	−	21.6626i	1.58247	−	1.14973i
$356$	1.36285	+	4.19441i	0.0722307	+	0.222303i
$357$	−14.3014	−	29.4554i	−0.756908	−	1.55894i
$358$	−6.79021	−	9.34593i	−0.358874	−	0.493948i
$359$	−20.9402	+	6.80390i	−1.10518	+	0.359096i	−0.804095	−	0.594500i	$-0.797350\pi$
$359$	−20.9402	+	6.80390i	−1.10518	+	0.359096i	−0.301088	+	0.953596i	$0.597350\pi$
$360$	−0.436241	+	11.3327i	−0.0229919	+	0.597284i
$361$	12.5382	+	9.10953i	0.659905	+	0.479449i
$362$	−5.86190	+	18.0411i	−0.308095	+	0.948217i
$363$	1.41083	−	1.35756i	0.0740492	−	0.0712535i
$364$	−3.21654	−	4.42718i	−0.168592	−	0.232047i
$365$	−3.63204	−	2.63883i	−0.190110	−	0.138123i
$366$	−15.0735	+	2.09102i	−0.787904	+	0.109299i
$367$		−	18.7839i		−	0.980509i	−0.871579	−	0.490255i	$-0.836904\pi$
$367$		−	18.7839i		−	0.980509i	0.871579	−	0.490255i	$-0.163096\pi$
$368$	1.09255	+	0.793781i	0.0569529	+	0.0413787i
$369$	−27.6268	+	18.4914i	−1.43819	+	0.962625i
$370$	−15.6086	−	5.07155i	−0.811454	−	0.263658i
$371$	−33.1081			−1.71889
$372$	−2.90761	+	9.19488i	−0.150753	+	0.476732i
$373$	−24.9156			−1.29008			−0.645039	−	0.764149i	$-0.723159\pi$
$373$	−24.9156			−1.29008			−0.645039	+	0.764149i	$0.723159\pi$
$374$	20.0367	+	6.51031i	1.03607	+	0.336640i
$375$	−25.2753	+	12.2718i	−1.30521	+	0.633714i
$376$	−4.15376	−	3.01788i	−0.214214	−	0.155635i
$377$			14.4622i			0.744842i
$378$	−5.88617	−	13.4133i	−0.302752	−	0.689908i
$379$	−20.1733	−	14.6568i	−1.03623	−	0.752867i	−0.0666857	−	0.997774i	$-0.521242\pi$
$379$	−20.1733	−	14.6568i	−1.03623	−	0.752867i	−0.969547	+	0.244907i	$0.921242\pi$
$380$	−4.15821	−	5.72328i	−0.213311	−	0.293598i
$381$	22.7548	+	23.6475i	1.16576	+	1.21150i
$382$	5.94601	−	18.2999i	0.304224	−	0.936306i
$383$	10.7323	+	7.79746i	0.548394	+	0.398432i	0.827193	−	0.561918i	$-0.189936\pi$
$383$	10.7323	+	7.79746i	0.548394	+	0.398432i	−0.278799	+	0.960349i	$0.589936\pi$
$384$	−1.70520	−	0.303810i	−0.0870180	−	0.0155038i
$385$	−31.8409	+	10.3457i	−1.62276	+	0.527268i
$386$	−14.0637	−	19.3570i	−0.715823	−	0.985245i
$387$	12.4548	−	8.33633i	0.633111	−	0.423759i
$388$	−1.05053	−	3.23321i	−0.0533328	−	0.164141i
$389$	−5.43735	+	3.95047i	−0.275685	+	0.200297i	−0.717033	−	0.697039i	$-0.754500\pi$
$389$	−5.43735	+	3.95047i	−0.275685	+	0.200297i	0.441348	+	0.897336i	$0.354500\pi$
$390$	−11.4341	+	5.55156i	−0.578990	+	0.281114i
$391$	−2.79856	+	8.61307i	−0.141529	+	0.435582i
$392$	−0.556538	+	0.766009i	−0.0281094	+	0.0386893i
$393$	4.63121	+	0.825131i	0.233614	+	0.0416224i
$394$	6.56917	+	9.04168i	0.330950	+	0.455513i
$395$	−8.18006	+	5.94316i	−0.411584	+	0.299033i
$396$	8.84483	+	3.25505i	0.444470	+	0.163572i
$397$	−19.8774			−0.997619			−0.498809	−	0.866712i	$-0.666229\pi$
$397$	−19.8774			−0.997619			−0.498809	+	0.866712i	$0.666229\pi$
$398$	−14.7382			−0.738757
$399$	8.05999	+	4.30404i	0.403504	+	0.215471i
$400$	−2.87110	−	8.83634i	−0.143555	−	0.441817i
$401$	−3.08047	+	9.48071i	−0.153831	+	0.473444i	−0.998041	−	0.0625697i	$-0.980070\pi$
$401$	−3.08047	+	9.48071i	−0.153831	+	0.473444i	0.844209	+	0.536014i	$0.180070\pi$
$402$	1.70383	+	12.2823i	0.0849793	+	0.612588i
$403$	−10.6254	+	1.97969i	−0.529286	+	0.0986154i
$404$			8.11421i			0.403697i
$405$	−33.0705	+	7.99513i	−1.64328	+	0.397281i
$406$	19.9740	−	6.48996i	0.991295	−	0.322091i
$407$	−8.01668	+	11.0340i	−0.397372	+	0.546936i
$408$	−1.59601	−	11.5051i	−0.0790143	−	0.569589i
$409$		−	4.77676i		−	0.236195i	−0.993002	−	0.118098i	$-0.962320\pi$
$409$		−	4.77676i		−	0.236195i	0.993002	−	0.118098i	$-0.0376796\pi$
$410$	24.6232	−	33.8910i	1.21605	−	1.67376i
$411$	1.62961	−	1.56809i	0.0803827	−	0.0773479i
$412$	−1.74534	+	1.26806i	−0.0859867	+	0.0624730i
$413$	6.21865	+	2.02056i	0.306000	+	0.0994253i
$414$	−1.39923	+	3.80208i	−0.0687684	+	0.186862i
$415$	−7.51618	−	2.44216i	−0.368955	−	0.119881i
$416$	−0.599867	−	1.84620i	−0.0294109	−	0.0905175i
$417$	14.6260	+	15.1999i	0.716240	+	0.744341i
$418$	−5.59128	+	1.81672i	−0.273478	+	0.0888585i
$419$	−16.8524	+	5.47567i	−0.823292	+	0.267504i	−0.690217	−	0.723602i	$-0.742485\pi$
$419$	−16.8524	+	5.47567i	−0.823292	+	0.267504i	−0.133075	+	0.991106i	$0.542485\pi$
$420$	12.7985	+	13.3006i	0.624501	+	0.649003i
$421$	−6.00920	−	18.4944i	−0.292870	−	0.901363i	−0.983928	−	0.178563i	$-0.942855\pi$
$421$	−6.00920	−	18.4944i	−0.292870	−	0.901363i	0.691058	−	0.722799i	$-0.257145\pi$
$422$	6.51054	+	2.11540i	0.316928	+	0.102976i
$423$	5.31975	−	14.4552i	0.258655	−	0.702835i
$424$	−11.1697	−	3.62927i	−0.542451	−	0.176253i
$425$	50.4073	−	36.6230i	2.44511	−	1.77648i
$426$	−12.1675	+	11.7081i	−0.589516	+	0.567260i
$427$	−14.5582	+	20.0377i	−0.704521	+	0.969691i
$428$			9.81660i			0.474503i
$429$	1.45141	+	10.4627i	0.0700745	+	0.505144i
$430$	−11.1007	+	15.2788i	−0.535322	+	0.736808i
$431$	31.5774	−	10.2601i	1.52103	−	0.494212i	0.574961	−	0.818181i	$-0.305017\pi$
$431$	31.5774	−	10.2601i	1.52103	−	0.494212i	0.946068	+	0.323968i	$0.105017\pi$
$432$	−0.515477	−	5.17052i	−0.0248009	−	0.248767i
$433$			8.63608i			0.415023i	0.978233	+	0.207512i	$0.0665365\pi$
$433$			8.63608i			0.415023i	−0.978233	+	0.207512i	$0.933463\pi$
$434$	7.50234	+	13.7865i	0.360124	+	0.661772i
$435$	−6.70287	−	48.3188i	−0.321378	−	2.31671i
$436$	4.22906	−	13.0157i	0.202535	−	0.623340i
$437$	−0.780942	−	2.40349i	−0.0373575	−	0.114975i
$438$	1.81444	+	0.968914i	0.0866975	+	0.0462965i
$439$	−9.10196			−0.434413			−0.217206	−	0.976126i	$-0.569694\pi$
$439$	−9.10196			−0.434413			−0.217206	+	0.976126i	$0.569694\pi$
$440$	−11.8763			−0.566182
$441$	−2.66573	−	0.981034i	−0.126940	−	0.0467159i
$442$	10.5317	−	7.65176i	0.500944	−	0.363957i
$443$	10.8774	+	14.9715i	0.516803	+	0.711319i	0.985048	−	0.172280i	$-0.0551135\pi$
$443$	10.8774	+	14.9715i	0.516803	+	0.711319i	−0.468245	+	0.883599i	$0.655113\pi$
$444$	7.40288	+	1.31895i	0.351325	+	0.0625947i
$445$	9.79977	−	13.4882i	0.464554	−	0.639403i
$446$	2.83588	−	8.72793i	0.134283	−	0.413279i
$447$	5.27405	−	2.56069i	0.249454	−	0.121116i
$448$	−2.28063	+	1.65697i	−0.107750	+	0.0782847i
$449$	−11.2615	−	34.6594i	−0.531464	−	1.63568i	−0.751168	−	0.660111i	$-0.770509\pi$
$449$	−11.2615	−	34.6594i	−0.531464	−	1.63568i	0.219704	−	0.975567i	$-0.429491\pi$
$450$	23.1634	−	15.5040i	1.09193	−	0.730863i
$451$	−20.4627	−	28.1645i	−0.963550	−	1.32621i
$452$	−6.15050	+	1.99842i	−0.289295	+	0.0939977i
$453$	24.3235	+	4.33365i	1.14282	+	0.203613i
$454$	−17.9342	−	13.0299i	−0.841693	−	0.611526i
$455$	−6.39271	+	19.6747i	−0.299695	+	0.922365i
$456$	2.24741	+	2.33559i	0.105245	+	0.109374i
$457$	−13.2289	−	18.2081i	−0.618823	−	0.851737i	0.378443	−	0.925624i	$-0.376459\pi$
$457$	−13.2289	−	18.2081i	−0.618823	−	0.851737i	−0.997267	+	0.0738874i	$0.976459\pi$
$458$	−2.69034	−	1.95465i	−0.125712	−	0.0913348i
$459$	31.9087	−	14.0025i	1.48937	−	0.653581i
$460$		−	5.10522i		−	0.238032i
$461$	−16.3518	−	11.8803i	−0.761580	−	0.553320i	0.137815	−	0.990458i	$-0.455992\pi$
$461$	−16.3518	−	11.8803i	−0.761580	−	0.553320i	−0.899394	+	0.437138i	$0.855992\pi$
$462$	13.7989	−	6.69973i	0.641984	−	0.311700i
$463$	15.5608	+	5.05602i	0.723174	+	0.234973i	0.647399	−	0.762152i	$-0.275857\pi$
$463$	15.5608	+	5.05602i	0.723174	+	0.234973i	0.0757750	+	0.997125i	$0.475857\pi$
$464$	7.45010			0.345862
$465$	34.5822	−	11.5388i	1.60371	−	0.535099i
$466$	−1.51646			−0.0702489
$467$	40.8040	+	13.2580i	1.88818	+	0.613508i	0.981421	+	0.191867i	$0.0614542\pi$
$467$	40.8040	+	13.2580i	1.88818	+	0.613508i	0.906763	+	0.421641i	$0.138546\pi$
$468$	4.83960	−	3.23928i	0.223711	−	0.149736i
$469$	16.3273	+	11.8625i	0.753925	+	0.547759i
$470$			19.4096i			0.895297i
$471$	−39.4470	+	5.47216i	−1.81762	+	0.252144i
$472$	1.87651	+	1.36336i	0.0863732	+	0.0627538i
$473$	9.22501	+	12.6971i	0.424167	+	0.583815i
$474$	3.33817	−	3.21214i	0.153327	−	0.147538i
$475$	−5.37283	+	16.5359i	−0.246522	+	0.758718i
$476$	−15.2941	−	11.1118i	−0.701005	−	0.509310i
$477$	1.35529	−	35.2076i	0.0620543	−	1.61205i
$478$	3.38543	−	1.09999i	0.154846	−	0.0503125i
$479$	8.99937	+	12.3866i	0.411192	+	0.565957i	0.963509	−	0.267678i	$-0.0862562\pi$
$479$	8.99937	+	12.3866i	0.411192	+	0.565957i	−0.552317	+	0.833634i	$0.686256\pi$
$480$	2.85985	+	5.89020i	0.130534	+	0.268850i
$481$	2.60424	+	8.01503i	0.118743	+	0.365454i
$482$	−2.68080	+	1.94772i	−0.122107	+	0.0887161i
$483$	2.87998	+	5.93167i	0.131044	+	0.269900i
$484$	0.349312	−	1.07507i	0.0158778	−	0.0488670i
$485$	−7.55403	+	10.3972i	−0.343011	+	0.472114i
$486$	14.5049	−	5.71036i	0.657955	−	0.259027i
$487$	24.4397	+	33.6384i	1.10747	+	1.52430i	0.825091	+	0.564999i	$0.191124\pi$
$487$	24.4397	+	33.6384i	1.10747	+	1.52430i	0.282379	+	0.959303i	$0.408876\pi$
$488$	−7.10804	+	5.16429i	−0.321766	+	0.233777i
$489$	8.39022	+	4.48038i	0.379419	+	0.202610i
$490$	3.57939			0.161700
$491$	−8.11463			−0.366208			−0.183104	−	0.983094i	$-0.558614\pi$
$491$	−8.11463			−0.366208			−0.183104	+	0.983094i	$0.558614\pi$
$492$	−9.04103	+	16.9308i	−0.407601	+	0.763298i
$493$	15.4388	+	47.5158i	0.695330	+	2.14001i
$494$	−1.12256	+	3.45489i	−0.0505064	+	0.155443i
$495$	−9.69840	−	34.2836i	−0.435911	−	1.54093i
$496$	1.01982	+	5.47357i	0.0457914	+	0.245771i
$497$			27.4825i			1.23276i
$498$	3.56478	+	0.635128i	0.159742	+	0.0284608i
$499$	−5.46535	+	1.77580i	−0.244662	+	0.0794957i	−0.428781	−	0.903408i	$-0.641057\pi$
$499$	−5.46535	+	1.77580i	−0.244662	+	0.0794957i	0.184119	+	0.982904i	$0.441057\pi$
$500$	−9.53493	+	13.1237i	−0.426415	+	0.586910i
$501$	−33.7810	+	4.68616i	−1.50922	+	0.209362i
$502$		−	14.4379i		−	0.644393i
$503$	3.08578	−	4.24721i	0.137588	−	0.189374i	−0.734663	−	0.678433i	$-0.762660\pi$
$503$	3.08578	−	4.24721i	0.137588	−	0.189374i	0.872251	+	0.489059i	$0.162660\pi$
$504$	−6.64562	−	5.23042i	−0.296019	−	0.232982i
$505$	24.8163	−	18.0301i	1.10431	−	0.802328i
$506$	−4.03495	−	1.31103i	−0.179375	−	0.0582826i
$507$	−14.1047	−	7.53192i	−0.626412	−	0.334504i
$508$	18.0198	+	5.85500i	0.799501	+	0.259774i
$509$	3.71754	+	11.4414i	0.164777	+	0.507132i	0.999020	−	0.0442656i	$-0.0140948\pi$
$509$	3.71754	+	11.4414i	0.164777	+	0.507132i	−0.834243	+	0.551397i	$0.814095\pi$
$510$	−31.6405	+	30.4460i	−1.40107	+	1.34817i
$511$	3.18394	−	1.03452i	0.140849	−	0.0457647i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	−4.90691	+	8.39493i	−0.216646	+	0.370645i
$514$	−7.50732	−	23.1052i	−0.331134	−	1.01912i
$515$	7.75642	+	2.52021i	0.341789	+	0.111054i
$516$	4.07589	−	7.63275i	0.179431	−	0.336013i
$517$	15.3405	+	4.98443i	0.674675	+	0.219215i
$518$	9.90105	−	7.19353i	0.435027	−	0.316066i
$519$	10.3858	+	10.7933i	0.455887	+	0.473774i
$520$	−4.31344	+	5.93694i	−0.189157	+	0.260352i
$521$		−	1.84717i		−	0.0809260i	−0.999181	−	0.0404630i	$-0.987117\pi$
$521$		−	1.84717i		−	0.0809260i	0.999181	−	0.0404630i	$-0.0128833\pi$
$522$	6.08387	+	21.5063i	0.266284	+	0.941307i
$523$	7.14573	−	9.83525i	0.312461	−	0.430065i	−0.623686	−	0.781675i	$-0.714366\pi$
$523$	7.14573	−	9.83525i	0.312461	−	0.430065i	0.936147	+	0.351610i	$0.114366\pi$
$524$	2.58301	−	0.839272i	0.112839	−	0.0366637i
$525$	7.95730	−	44.6620i	0.347285	−	1.94921i
$526$			16.0895i			0.701534i
$527$	−32.7964	+	17.8472i	−1.42863	+	0.777435i
$528$	5.38978	−	0.747680i	0.234560	−	0.0325386i
$529$	−6.54382	+	20.1398i	−0.284514	+	0.875644i
$530$	13.7199	+	42.2256i	0.595956	+	1.83416i
$531$	−2.40326	+	6.53029i	−0.104292	+	0.283390i
$532$	5.27536			0.228716
$533$	−21.5113			−0.931758
$534$	−3.59823	+	6.73825i	−0.155711	+	0.291593i
$535$	30.0228	−	21.8128i	1.29800	−	0.943052i
$536$	4.20803	+	5.79185i	0.181759	+	0.250170i
$537$	3.50968	−	19.6988i	0.151454	−	0.850065i
$538$	4.07055	−	5.60263i	0.175494	−	0.241547i
$539$	0.919197	−	2.82900i	0.0395926	−	0.121854i
$540$	−14.6680	+	13.0656i	−0.631209	+	0.562254i
$541$	0.130596	−	0.0948836i	0.00561477	−	0.00407937i	−0.584974	−	0.811052i	$-0.698895\pi$
$541$	0.130596	−	0.0948836i	0.00561477	−	0.00407937i	0.590589	+	0.806972i	$0.298895\pi$
$542$	5.09764	+	15.6889i	0.218963	+	0.673898i
$543$	−29.5566	+	14.3505i	−1.26839	+	0.615838i
$544$	−3.94174	−	5.42535i	−0.169001	−	0.232610i
$545$	−49.2040	+	15.9874i	−2.10767	+	0.684823i
$546$	1.66254	−	9.33135i	0.0711502	−	0.399345i
$547$	−29.9568	−	21.7649i	−1.28086	−	0.930598i	−0.281280	−	0.959626i	$-0.590759\pi$
$547$	−29.9568	−	21.7649i	−1.28086	−	0.930598i	−0.999579	+	0.0290273i	$0.990759\pi$
$548$	0.403482	−	1.24179i	0.0172359	−	0.0530466i
$549$	−20.7124	−	16.3017i	−0.883983	−	0.695738i
$550$	17.1567	+	23.6142i	0.731565	+	1.00691i
$551$	−11.2791	−	8.19475i	−0.480506	−	0.349108i
$552$	0.321402	+	2.31688i	0.0136798	+	0.0986129i
$553$		−	7.53987i		−	0.320628i
$554$	0.116153	+	0.0843904i	0.00493489	+	0.00358540i
$555$	−12.4156	−	25.5715i	−0.527014	−	1.08545i
$556$	11.5826	+	3.76340i	0.491210	+	0.159604i
$557$	0.850259			0.0360267			0.0180133	−	0.999838i	$-0.494266\pi$
$557$	0.850259			0.0360267			0.0180133	+	0.999838i	$0.494266\pi$
$558$	−14.9678	+	7.41374i	−0.633639	+	0.313849i
$559$	9.69776			0.410171
$560$	10.1353	+	3.29315i	0.428294	+	0.139161i
$561$	15.9379	+	32.8260i	0.672897	+	1.38591i
$562$	−5.45607	−	3.96407i	−0.230151	−	0.167214i
$563$		−	22.5885i		−	0.951990i	−0.879448	−	0.475995i	$-0.842088\pi$
$563$		−	22.5885i		−	0.951990i	0.879448	−	0.475995i	$-0.157912\pi$
$564$	−1.22194	−	8.80857i	−0.0514530	−	0.370908i
$565$	19.7785	+	14.3700i	0.832089	+	0.604548i
$566$	−2.33937	−	3.21987i	−0.0983311	−	0.135341i
$567$	9.67184	−	23.4553i	0.406179	−	0.985029i
$568$	−3.01260	+	9.27182i	−0.126406	+	0.389037i
$569$	4.92793	+	3.58035i	0.206590	+	0.150096i	0.686269	−	0.727348i	$-0.259247\pi$
$569$	4.92793	+	3.58035i	0.206590	+	0.150096i	−0.479680	+	0.877444i	$0.659247\pi$
$570$	2.14927	−	12.0632i	0.0900228	−	0.505271i
$571$	−22.2955	+	7.24426i	−0.933040	+	0.303163i	−0.735805	−	0.677193i	$-0.763196\pi$
$571$	−22.2955	+	7.24426i	−0.933040	+	0.303163i	−0.197235	+	0.980356i	$0.563196\pi$
$572$	3.58460	+	4.93378i	0.149880	+	0.206292i
$573$	29.9807	−	14.5564i	1.25246	−	0.608102i
$574$	9.65325	+	29.7096i	0.402919	+	1.24006i
$575$	−10.1509	+	7.37508i	−0.423323	+	0.307562i
$576$	−1.66869	−	2.49308i	−0.0695289	−	0.103878i
$577$	−6.00330	+	18.4763i	−0.249921	+	0.769176i	0.744868	+	0.667212i	$0.232513\pi$
$577$	−6.00330	+	18.4763i	−0.249921	+	0.769176i	−0.994788	+	0.101964i	$0.967487\pi$
$578$	16.4414	−	22.6296i	0.683871	−	0.941267i
$579$	7.26914	−	40.7995i	0.302095	−	1.69557i
$580$	−16.5544	−	22.7852i	−0.687384	−	0.946103i
$581$	4.76775	−	3.46397i	0.197800	−	0.143710i
$582$	2.77365	−	5.19410i	0.114972	−	0.215302i
$583$	36.8966			1.52810
$584$	1.18757			0.0491422
$585$	−20.6607	−	7.60348i	−0.854215	−	0.314365i
$586$	−8.09098	−	24.9015i	−0.334235	−	1.02867i
$587$	3.67052	−	11.2967i	0.151499	−	0.466265i	−0.846291	−	0.532722i	$-0.821169\pi$
$587$	3.67052	−	11.2967i	0.151499	−	0.466265i	0.997789	+	0.0664563i	$0.0211693\pi$
$588$	−1.62442	+	0.225342i	−0.0669899	+	0.00929296i
$589$	4.47670	−	9.40848i	0.184459	−	0.387670i
$590$		−	8.76849i		−	0.360993i
$591$	−3.39543	+	19.0575i	−0.139669	+	0.783922i
$592$	4.12888	−	1.34156i	0.169696	−	0.0551376i
$593$	2.38810	−	3.28694i	0.0980676	−	0.134979i	−0.757163	−	0.653226i	$-0.773415\pi$
$593$	2.38810	−	3.28694i	0.0980676	−	0.134979i	0.855231	+	0.518247i	$0.173415\pi$
$594$	6.55973	+	14.9482i	0.269149	+	0.613333i
$595$			71.4660i			2.92982i
$596$	1.98960	−	2.73844i	0.0814970	−	0.112171i
$597$	−17.6999	−	18.3944i	−0.724409	−	0.752831i
$598$	−2.12086	+	1.54090i	−0.0867284	+	0.0630119i
$599$	4.66581	+	1.51601i	0.190640	+	0.0619427i	0.402781	−	0.915296i	$-0.368044\pi$
$599$	4.66581	+	1.51601i	0.190640	+	0.0619427i	−0.212141	+	0.977239i	$0.568044\pi$
$600$	7.58037	−	14.1954i	0.309467	−	0.579526i
$601$	−8.74025	−	2.83988i	−0.356522	−	0.115841i	0.125279	−	0.992122i	$-0.460017\pi$
$601$	−8.74025	−	2.83988i	−0.356522	−	0.115841i	−0.481801	+	0.876280i	$0.660017\pi$
$602$	−4.35189	−	13.3937i	−0.177370	−	0.545888i
$603$	−13.2831	+	16.8771i	−0.540930	+	0.687289i
$604$	13.5662	−	4.40792i	0.552000	−	0.179356i
$605$	−4.06416	+	1.32052i	−0.165232	+	0.0536870i
$606$	−10.1272	+	9.74483i	−0.411388	+	0.395857i
$607$	−0.978077	−	3.01021i	−0.0396989	−	0.122181i	0.929243	−	0.369469i	$-0.120460\pi$
$607$	−0.978077	−	3.01021i	−0.0396989	−	0.122181i	−0.968942	+	0.247288i	$0.920460\pi$
$608$	1.77976	+	0.578279i	0.0721788	+	0.0234523i
$609$	32.0880	+	17.1350i	1.30027	+	0.694345i
$610$	31.5886	+	10.2638i	1.27899	+	0.415568i
$611$	8.06332	−	5.85835i	0.326207	−	0.237003i
$612$	12.4425	−	15.8091i	0.502960	−	0.639046i
$613$	15.7543	−	21.6840i	0.636311	−	0.875806i	−0.362101	−	0.932139i	$-0.617941\pi$
$613$	15.7543	−	21.6840i	0.636311	−	0.875806i	0.998412	+	0.0563322i	$0.0179406\pi$
$614$			31.1938i			1.25888i
$615$	71.8700	−	9.96994i	2.89808	−	0.402027i
$616$	5.20554	−	7.16481i	0.209737	−	0.288678i
$617$	−20.5253	+	6.66907i	−0.826317	+	0.268487i	−0.691493	−	0.722383i	$-0.743047\pi$
$617$	−20.5253	+	6.66907i	−0.826317	+	0.268487i	−0.134824	+	0.990870i	$0.543047\pi$
$618$	−3.67872	−	0.655428i	−0.147980	−	0.0263652i
$619$			13.9151i			0.559296i	0.960103	+	0.279648i	$0.0902178\pi$
$619$			13.9151i			0.559296i	−0.960103	+	0.279648i	$0.909782\pi$
$620$	14.4741	−	15.2815i	0.581295	−	0.613718i
$621$	−6.42571	+	2.81980i	−0.257855	+	0.113155i
$622$	−0.134084	+	0.412667i	−0.00537627	+	0.0165465i
$623$	3.84188	+	11.8241i	0.153922	+	0.473723i
$624$	1.58379	−	2.96589i	0.0634022	−	0.118731i
$625$	14.8687			0.594749
$626$	−6.64551			−0.265608
$627$	−8.98229	−	4.79655i	−0.358718	−	0.191556i
$628$	−18.6016	+	13.5149i	−0.742285	+	0.539301i
$629$	17.1125	+	23.5534i	0.682322	+	0.939136i
$630$	−1.22977	+	31.9470i	−0.0489952	+	1.27280i
$631$	−25.6407	+	35.2914i	−1.02074	+	1.40493i	−0.109058	+	0.994035i	$0.534784\pi$
$631$	−25.6407	+	35.2914i	−1.02074	+	1.40493i	−0.911683	+	0.410895i	$0.865216\pi$
$632$	0.826511	−	2.54374i	0.0328769	−	0.101185i
$633$	5.17870	+	10.6662i	0.205835	+	0.423942i
$634$	16.8692	−	12.2562i	0.669960	−	0.486755i
$635$	−22.1340	−	68.1213i	−0.878360	−	2.70331i
$636$	−8.88479	−	18.2993i	−0.352305	−	0.725615i
$637$	−1.08036	−	1.48699i	−0.0428054	−	0.0589165i
$638$	−22.2597	+	7.23260i	−0.881268	+	0.286341i
$639$	−29.2253	−	1.12500i	−1.15613	−	0.0445043i
$640$	3.05837	+	2.22204i	0.120893	+	0.0878337i
$641$	−6.11295	+	18.8137i	−0.241447	+	0.743097i	0.754754	+	0.656008i	$0.227756\pi$
$641$	−6.11295	+	18.8137i	−0.241447	+	0.743097i	−0.996201	+	0.0870890i	$0.972244\pi$
$642$	−12.2519	+	11.7893i	−0.483543	+	0.465288i
$643$	−28.3939	−	39.0809i	−1.11975	−	1.54120i	−0.806215	−	0.591623i	$-0.798487\pi$
$643$	−28.3939	−	39.0809i	−1.11975	−	1.54120i	−0.313533	−	0.949577i	$-0.601513\pi$
$644$	3.07990	+	2.23768i	0.121365	+	0.0881769i
$645$	−32.4006	+	4.49466i	−1.27577	+	0.176977i
$646$			12.5494i			0.493751i
$647$	−14.1924	−	10.3113i	−0.557959	−	0.405381i	0.272752	−	0.962084i	$-0.412066\pi$
$647$	−14.1924	−	10.3113i	−0.557959	−	0.405381i	−0.830711	+	0.556703i	$0.812066\pi$
$648$	5.83415	−	6.85294i	0.229187	−	0.269209i
$649$	−6.93024	−	2.25177i	−0.272036	−	0.0883898i
$650$	18.0359			0.707428
$651$	−8.19660	+	25.9205i	−0.321250	+	1.01590i
$652$	5.49150			0.215064
$653$	20.2771	+	6.58843i	0.793504	+	0.257825i	0.677595	−	0.735435i	$-0.263022\pi$
$653$	20.2771	+	6.58843i	0.793504	+	0.257825i	0.115909	+	0.993260i	$0.463022\pi$
$654$	21.3236	−	10.3531i	0.833817	−	0.404840i
$655$	−8.30635	−	6.03492i	−0.324556	−	0.235804i
$656$			11.0814i			0.432655i
$657$	0.969793	+	3.42819i	0.0378352	+	0.133747i
$658$	−11.7095	−	8.50746i	−0.456484	−	0.331655i
$659$	7.28130	+	10.0218i	0.283639	+	0.390396i	0.926935	−	0.375222i	$-0.122433\pi$
$659$	7.28130	+	10.0218i	0.283639	+	0.390396i	−0.643296	+	0.765618i	$0.722433\pi$
$660$	−14.2630	−	14.8226i	−0.555186	−	0.576968i
$661$	−8.96464	+	27.5903i	−0.348684	+	1.07314i	0.610898	+	0.791709i	$0.290809\pi$
$661$	−8.96464	+	27.5903i	−0.348684	+	1.07314i	−0.959582	+	0.281430i	$0.909191\pi$
$662$	1.70941	+	1.24196i	0.0664381	+	0.0482701i
$663$	22.1982	+	3.95499i	0.862105	+	0.153599i
$664$	1.98822	−	0.646012i	0.0771580	−	0.0250701i
$665$	−11.7220	−	16.1340i	−0.454561	−	0.625650i
$666$	7.24440	+	10.8234i	0.280715	+	0.419398i
$667$	−3.10904	−	9.56865i	−0.120383	−	0.370499i
$668$	−15.9297	+	11.5736i	−0.616340	+	0.447797i
$669$	14.2989	−	6.94249i	0.552828	−	0.268412i
$670$	8.36324	−	25.7394i	0.323100	−	0.994400i
$671$	16.2241	−	22.3306i	0.626325	−	0.862062i
$672$	−4.80698	−	0.856446i	−0.185433	−	0.0330381i
$673$	−15.5326	−	21.3788i	−0.598738	−	0.824092i	0.396854	−	0.917882i	$-0.370102\pi$
$673$	−15.5326	−	21.3788i	−0.598738	−	0.824092i	−0.995592	+	0.0937900i	$0.970102\pi$
$674$	2.07716	−	1.50915i	0.0800092	−	0.0581301i
$675$	47.1685	+	10.2902i	1.81551	+	0.396068i
$676$	−9.23170			−0.355065
$677$	28.5127			1.09583			0.547915	−	0.836534i	$-0.315422\pi$
$677$	28.5127			1.09583			0.547915	+	0.836534i	$0.315422\pi$
$678$	−9.88068	−	5.27629i	−0.379465	−	0.202635i
$679$	−2.96147	−	9.11447i	−0.113651	−	0.349781i
$680$	−7.83402	+	24.1106i	−0.300421	+	0.924600i
$681$	−5.27582	−	38.0317i	−0.202170	−	1.45738i
$682$	−8.36083	−	15.3641i	−0.320153	−	0.588320i
$683$			28.7789i			1.10120i	0.834771	+	0.550598i	$0.185600\pi$
$683$			28.7789i			1.10120i	−0.834771	+	0.550598i	$0.814400\pi$
$684$	−0.215948	+	5.60989i	−0.00825697	+	0.214500i
$685$	−4.69440	+	1.52530i	−0.179364	+	0.0582789i
$686$	10.0299	−	13.8050i	0.382945	−	0.527078i
$687$	−0.791437	−	5.70521i	−0.0301952	−	0.217667i
$688$		−	4.99573i		−	0.190460i
$689$	13.4007	−	18.4445i	0.510527	−	0.702680i
$690$	6.37171	−	6.13115i	0.242567	−	0.233409i
$691$	−29.1179	+	21.1554i	−1.10770	+	0.804788i	−0.982299	−	0.187319i	$-0.940020\pi$
$691$	−29.1179	+	21.1554i	−1.10770	+	0.804788i	−0.125396	+	0.992107i	$0.540020\pi$
$692$	8.22469	+	2.67236i	0.312656	+	0.101588i
$693$	24.9337	+	9.17602i	0.947153	+	0.348568i
$694$	17.9627	+	5.83643i	0.681855	+	0.221548i
$695$	−14.2270	−	43.7862i	−0.539661	−	1.66090i
$696$	8.94727	+	9.29831i	0.339145	+	0.352452i
$697$	−70.6757	+	22.9639i	−2.67703	+	0.869820i
$698$	1.14254	−	0.371234i	0.0432458	−	0.0140514i
$699$	−1.82121	−	1.89267i	−0.0688845	−	0.0715872i
$700$	−8.09367	−	24.9098i	−0.305912	−	0.941500i
$701$	−13.8724	−	4.50741i	−0.523952	−	0.170242i	0.0350860	−	0.999384i	$-0.488829\pi$
$701$	−13.8724	−	4.50741i	−0.523952	−	0.170242i	−0.559038	+	0.829142i	$0.688829\pi$
$702$	9.85504	+	2.14995i	0.371954	+	0.0811447i
$703$	−7.72658	−	2.51052i	−0.291414	−	0.0946860i
$704$	2.54160	−	1.84658i	0.0957902	−	0.0695957i
$705$	−24.2247	+	23.3101i	−0.912354	+	0.877909i
$706$	−8.40803	+	11.5727i	−0.316440	+	0.435543i
$707$			22.8741i			0.860268i
$708$	0.552025	+	3.97937i	0.0207464	+	0.149554i
$709$	19.2570	−	26.5050i	0.723211	−	0.995415i	−0.276200	−	0.961100i	$-0.589075\pi$
$709$	19.2570	−	26.5050i	0.723211	−	0.995415i	0.999411	−	0.0343145i	$-0.0109248\pi$
$710$	35.0508	−	11.3887i	1.31543	−	0.427410i
$711$	8.01800	+	0.308646i	0.300699	+	0.0115751i
$712$			4.41026i			0.165282i
$713$	6.60447	−	3.59403i	0.247339	−	0.134597i
$714$	−4.49918	−	32.4331i	−0.168378	−	1.21378i
$715$	7.12422	−	21.9261i	0.266431	−	0.819989i
$716$	−3.56983	−	10.9868i	−0.133411	−	0.410596i
$717$	5.43864	+	2.90423i	0.203110	+	0.108461i
$718$	−22.0179			−0.821700
$719$	6.07698			0.226633			0.113317	−	0.993559i	$-0.463853\pi$
$719$	6.07698			0.226633			0.113317	+	0.993559i	$0.463853\pi$
$720$	−3.91688	+	10.6432i	−0.145973	+	0.396649i
$721$	−4.92014	+	3.57469i	−0.183235	+	0.133128i
$722$	9.10953	+	12.5382i	0.339021	+	0.466623i
$723$	−5.65044	−	1.00672i	−0.210142	−	0.0374404i
$724$	−11.1500	+	15.3466i	−0.414386	+	0.570354i
$725$	−21.3900	+	65.8316i	−0.794405	+	2.44493i
$726$	1.76129	−	0.855149i	0.0653674	−	0.0317376i
$727$	−0.924381	+	0.671602i	−0.0342834	+	0.0249083i	−0.604795	−	0.796381i	$-0.706745\pi$
$727$	−0.924381	+	0.671602i	−0.0342834	+	0.0249083i	0.570512	+	0.821290i	$0.306745\pi$
$728$	−1.69103	−	5.20447i	−0.0626739	−	0.192890i
$729$	24.5467	+	11.2453i	0.909139	+	0.416493i
$730$	−2.63883	−	3.63204i	−0.0976677	−	0.134428i
$731$	31.8621	−	10.3526i	1.17846	−	0.382906i
$732$	−14.9819	−	2.66929i	−0.553747	−	0.0986596i
$733$	27.9033	+	20.2729i	1.03063	+	0.748798i	0.968435	−	0.249266i	$-0.0801894\pi$
$733$	27.9033	+	20.2729i	1.03063	+	0.748798i	0.0621965	+	0.998064i	$0.480189\pi$
$734$	5.80453	−	17.8645i	0.214249	−	0.659391i
$735$	4.29870	+	4.46736i	0.158560	+	0.164781i
$736$	0.793781	+	1.09255i	0.0292591	+	0.0402718i
$737$	−18.1956	−	13.2199i	−0.670245	−	0.486961i
$738$	−31.9888	+	9.04923i	−1.17752	+	0.333107i
$739$			2.92459i			0.107583i	0.998552	+	0.0537914i	$0.0171306\pi$
$739$			2.92459i			0.107583i	−0.998552	+	0.0537914i	$0.982869\pi$
$740$	−13.2775	−	9.64667i	−0.488091	−	0.354619i
$741$	−5.66012	+	2.74813i	−0.207930	+	0.100955i
$742$	−31.4877	−	10.2310i	−1.15595	−	0.375591i
$743$	8.96000			0.328710			0.164355	−	0.986401i	$-0.447446\pi$
$743$	8.96000			0.328710			0.164355	+	0.986401i	$0.447446\pi$
$744$	−5.60668	+	7.84635i	−0.205551	+	0.287661i
$745$	−12.7961			−0.468814
$746$	−23.6961	−	7.69933i	−0.867576	−	0.281893i
$747$	3.48847	+	5.21189i	0.127636	+	0.190693i
$748$	17.0442	+	12.3834i	0.623199	+	0.452780i
$749$			27.6731i			1.01115i
$750$	−27.8305	+	3.86069i	−1.01622	+	0.140972i
$751$	24.1926	+	17.5770i	0.882801	+	0.641393i	0.933991	−	0.357296i	$-0.116301\pi$
$751$	24.1926	+	17.5770i	0.882801	+	0.641393i	−0.0511897	+	0.998689i	$0.516301\pi$
$752$	−3.01788	−	4.15376i	−0.110051	−	0.151472i
$753$	18.0196	−	17.3393i	0.656670	−	0.631878i
$754$	−4.46907	+	13.7544i	−0.162754	+	0.500905i
$755$	−43.6256	−	31.6959i	−1.58770	−	1.15353i
$756$	−1.45314	−	14.5758i	−0.0528500	−	0.530116i
$757$	13.7021	−	4.45209i	0.498012	−	0.161814i	−0.0492315	−	0.998787i	$-0.515677\pi$
$757$	13.7021	−	4.45209i	0.498012	−	0.161814i	0.547243	+	0.836974i	$0.315677\pi$
$758$	−14.6568	−	20.1733i	−0.532357	−	0.732727i
$759$	−3.20953	−	6.61043i	−0.116499	−	0.239943i
$760$	−2.18610	−	6.72812i	−0.0792981	−	0.244055i
$761$	26.6545	−	19.3657i	0.966226	−	0.702005i	0.0116380	−	0.999932i	$-0.496295\pi$
$761$	26.6545	−	19.3657i	0.966226	−	0.702005i	0.954588	+	0.297928i	$0.0962954\pi$
$762$	14.3336	+	29.5218i	0.519251	+	1.06946i
$763$	11.9218	−	36.6915i	0.431598	−	1.32832i
$764$	11.3100	−	15.5669i	0.409181	−	0.563189i
$765$	−75.9980	−	2.92547i	−2.74771	−	0.105771i
$766$	7.79746	+	10.7323i	0.281734	+	0.387773i
$767$	−3.64269	+	2.64657i	−0.131530	+	0.0955622i
$768$	−1.52786	−	0.815876i	−0.0551318	−	0.0294404i
$769$	12.7424			0.459504			0.229752	−	0.973249i	$-0.426209\pi$
$769$	12.7424			0.459504			0.229752	+	0.973249i	$0.426209\pi$
$770$	−33.4795			−1.20652
$771$	19.8211	−	37.1181i	0.713838	−	1.33677i
$772$	−7.39372	−	22.7555i	−0.266106	−	0.818989i
$773$	−2.68382	+	8.25996i	−0.0965304	+	0.297090i	−0.987650	−	0.156679i	$-0.949921\pi$
$773$	−2.68382	+	8.25996i	−0.0965304	+	0.297090i	0.891119	+	0.453770i	$0.149921\pi$
$774$	14.4212	−	4.07959i	0.518361	−	0.146638i
$775$	−51.2943	−	6.70367i	−1.84255	−	0.240803i
$776$		−	3.39960i		−	0.122039i
$777$	20.8688	+	3.71814i	0.748665	+	0.133388i
$778$	−6.39199	+	2.07688i	−0.229164	+	0.0744599i
$779$	12.1890	−	16.7767i	0.436716	−	0.601087i
$780$	−12.5900	+	1.74651i	−0.450795	+	0.0625351i
$781$		−	30.6273i		−	1.09593i
$782$	−5.32317	+	7.32671i	−0.190356	+	0.262003i
$783$	−19.5351	+	33.4214i	−0.698128	+	1.19438i
$784$	−0.766009	+	0.556538i	−0.0273575	+	0.0198764i
$785$	82.6668	+	26.8601i	2.95051	+	0.958678i
$786$	4.14957	+	2.21587i	0.148010	+	0.0790375i
$787$	−22.5425	−	7.32452i	−0.803555	−	0.261091i	−0.121689	−	0.992568i	$-0.538831\pi$
$787$	−22.5425	−	7.32452i	−0.803555	−	0.261091i	−0.681866	+	0.731477i	$0.738831\pi$
$788$	3.45362	+	10.6291i	0.123030	+	0.378647i
$789$	−20.0809	+	19.3228i	−0.714899	+	0.687909i
$790$	−9.61624	+	3.12451i	−0.342130	+	0.111165i
$791$	−17.3383	+	5.63357i	−0.616481	+	0.200307i
$792$	7.40607	+	5.82894i	0.263163	+	0.207122i
$793$	−5.27044	−	16.2208i	−0.187159	−	0.576016i
$794$	−18.9045	−	6.14246i	−0.670897	−	0.217988i
$795$	−36.2238	+	67.8347i	−1.28472	+	2.40585i
$796$	−14.0168	−	4.55434i	−0.496813	−	0.161424i
$797$	8.43070	−	6.12526i	0.298631	−	0.216968i	−0.428372	−	0.903602i	$-0.640913\pi$
$797$	8.43070	−	6.12526i	0.298631	−	0.216968i	0.727003	+	0.686634i	$0.240913\pi$
$798$	6.33549	+	6.58406i	0.224274	+	0.233073i
$799$	20.2382	−	27.8555i	0.715977	−	0.985457i
$800$		−	9.29108i		−	0.328489i
$801$	−12.7312	+	3.60149i	−0.449834	+	0.127252i
$802$	−5.85940	+	8.06477i	−0.206903	+	0.284777i
$803$	−3.54827	+	1.15290i	−0.125216	+	0.0406851i
$804$	−2.17502	+	12.2077i	−0.0767069	+	0.430533i
$805$		−	14.3917i		−	0.507240i
$806$	−10.7171	−	1.40062i	−0.377493	−	0.0493346i
$807$	11.8811	−	1.64817i	0.418234	−	0.0580182i
$808$	−2.50743	+	7.71707i	−0.0882110	+	0.271486i
$809$	−15.9055	−	48.9519i	−0.559206	−	1.72106i	−0.684569	−	0.728948i	$-0.740010\pi$
$809$	−15.9055	−	48.9519i	−0.559206	−	1.72106i	0.125363	−	0.992111i	$-0.459990\pi$
$810$	−33.9225	−	2.61551i	−1.19192	−	0.0918996i
$811$	50.8359			1.78509			0.892545	−	0.450959i	$-0.148918\pi$
$811$	50.8359			1.78509			0.892545	+	0.450959i	$0.148918\pi$
$812$	21.0019			0.737024
$813$	−13.4590	+	25.2040i	−0.472026	+	0.883944i
$814$	−11.0340	+	8.01668i	−0.386742	+	0.280985i
$815$	−12.2023	−	16.7950i	−0.427428	−	0.588304i
$816$	2.03738	−	11.4352i	0.0713226	−	0.400313i
$817$	−5.49506	+	7.56330i	−0.192248	+	0.264606i
$818$	1.47610	−	4.54297i	0.0516106	−	0.158841i
$819$	13.6429	−	9.13159i	0.476721	−	0.319083i
$820$	33.8910	−	24.6232i	1.18352	−	0.859880i
$821$	−4.36298	−	13.4279i	−0.152269	−	0.468636i	0.845605	−	0.533809i	$-0.179240\pi$
$821$	−4.36298	−	13.4279i	−0.152269	−	0.468636i	−0.997874	+	0.0651732i	$0.979240\pi$
$822$	2.03441	−	0.987761i	0.0709584	−	0.0344521i
$823$	13.0595	+	17.9748i	0.455225	+	0.626564i	0.973510	−	0.228644i	$-0.0734293\pi$
$823$	13.0595	+	17.9748i	0.455225	+	0.626564i	−0.518285	+	0.855208i	$0.673429\pi$
$824$	−2.05177	+	0.666660i	−0.0714768	+	0.0232242i
$825$	−8.86785	+	49.7726i	−0.308739	+	1.73286i
$826$	5.28990	+	3.84334i	0.184059	+	0.133727i
$827$	1.26451	−	3.89175i	0.0439712	−	0.135329i	−0.926661	−	0.375899i	$-0.877334\pi$
$827$	1.26451	−	3.89175i	0.0439712	−	0.135329i	0.970632	+	0.240569i	$0.0773341\pi$
$828$	−2.50566	+	3.18361i	−0.0870776	+	0.110638i
$829$	6.49968	+	8.94604i	0.225743	+	0.310709i	0.906832	−	0.421492i	$-0.138493\pi$
$829$	6.49968	+	8.94604i	0.225743	+	0.310709i	−0.681089	+	0.732201i	$0.738493\pi$
$830$	−6.39365	−	4.64526i	−0.221927	−	0.161239i
$831$	0.0341697	+	0.246318i	0.00118533	+	0.00854467i
$832$		−	1.94121i		−	0.0672994i
$833$	−5.13693	−	3.73220i	−0.177984	−	0.129313i
$834$	9.21316	+	18.9756i	0.319026	+	0.657072i
$835$	70.7929	+	23.0020i	2.44989	+	0.796018i
$836$	−5.87902			−0.203330
$837$	−27.2287	−	9.77744i	−0.941161	−	0.337958i
$838$	−17.7196			−0.612114
$839$	32.5251	+	10.5681i	1.12289	+	0.364850i	0.810871	−	0.585225i	$-0.198994\pi$
$839$	32.5251	+	10.5681i	1.12289	+	0.364850i	0.312022	+	0.950075i	$0.398994\pi$
$840$	8.06195	+	16.6046i	0.278164	+	0.572912i
$841$	−21.4422	−	15.5787i	−0.739387	−	0.537196i
$842$		−	19.4462i		−	0.670160i
$843$	−1.60505	−	11.5703i	−0.0552809	−	0.398502i
$844$	5.53819	+	4.02373i	0.190633	+	0.138503i
$845$	20.5132	+	28.2340i	0.705675	+	0.971278i
$846$	9.52628	−	12.1038i	0.327520	−	0.416137i
$847$	0.984717	−	3.03065i	0.0338353	−	0.104134i
$848$	−9.50156	−	6.90328i	−0.326285	−	0.237060i
$849$	1.20916	−	6.78664i	0.0414982	−	0.232917i
$850$	59.2573	−	19.2539i	2.03251	−	0.660402i
$851$	−3.44609	−	4.74314i	−0.118130	−	0.162593i
$852$	−15.1900	+	7.37512i	−0.520399	+	0.252667i
$853$	6.26376	+	19.2779i	0.214467	+	0.660062i	0.999191	+	0.0402165i	$0.0128048\pi$
$853$	6.26376	+	19.2779i	0.214467	+	0.660062i	−0.784724	+	0.619846i	$0.787195\pi$
$854$	−20.0377	+	14.5582i	−0.685675	+	0.498172i
$855$	17.6370	−	11.8049i	0.603172	−	0.403720i
$856$	−3.03350	+	9.33614i	−0.103683	+	0.319103i
$857$	−11.7215	+	16.1333i	−0.400400	+	0.551103i	−0.960844	−	0.277089i	$-0.910630\pi$
$857$	−11.7215	+	16.1333i	−0.400400	+	0.551103i	0.560444	+	0.828192i	$0.310630\pi$
$858$	−1.85279	+	10.3991i	−0.0632531	+	0.355021i
$859$	22.0690	+	30.3754i	0.752985	+	1.03639i	0.997765	+	0.0668164i	$0.0212842\pi$
$859$	22.0690	+	30.3754i	0.752985	+	1.03639i	−0.244780	+	0.969579i	$0.578716\pi$
$860$	−15.2788	+	11.1007i	−0.521002	+	0.378530i
$861$	−25.4868	+	47.7281i	−0.868588	+	1.62657i
$862$	33.2024			1.13088
$863$	−41.1472			−1.40067			−0.700333	−	0.713816i	$-0.746965\pi$
$863$	−41.1472			−1.40067			−0.700333	+	0.713816i	$0.746965\pi$
$864$	1.10753	−	5.07675i	0.0376790	−	0.172714i
$865$	−10.1025	−	31.0922i	−0.343495	−	1.05717i
$866$	−2.66869	+	8.21340i	−0.0906859	+	0.279103i
$867$	47.9889	−	6.65711i	1.62979	−	0.226087i
$868$	2.87489	+	15.4301i	0.0975803	+	0.523731i
$869$			8.40265i			0.285040i
$870$	8.55653	−	48.0252i	0.290093	−	1.62821i
$871$	−13.2172	+	4.29452i	−0.447847	+	0.145514i
$872$	8.04416	−	11.0718i	0.272410	−	0.374940i
$873$	9.81368	−	2.77617i	0.332143	−	0.0939590i
$874$		−	2.52718i		−	0.0854832i
$875$	−26.8791	+	36.9959i	−0.908679	+	1.25069i
$876$	1.42623	+	1.48219i	0.0481878	+	0.0500784i
$877$	−24.2414	+	17.6124i	−0.818575	+	0.594730i	−0.916304	−	0.400483i	$-0.868842\pi$
$877$	−24.2414	+	17.6124i	−0.818575	+	0.594730i	0.0977289	+	0.995213i	$0.468842\pi$
$878$	−8.65648	−	2.81266i	−0.292142	−	0.0949227i
$879$	21.3620	−	40.0038i	0.720524	−	1.34929i
$880$	−11.2951	−	3.66999i	−0.380756	−	0.123715i
$881$	0.0913908	+	0.281272i	0.00307903	+	0.00947629i	0.952584	−	0.304275i	$-0.0984142\pi$
$881$	0.0913908	+	0.281272i	0.00307903	+	0.00947629i	−0.949505	+	0.313751i	$0.898414\pi$
$882$	−2.23210	−	1.75677i	−0.0751589	−	0.0591537i
$883$	3.22359	−	1.04741i	0.108483	−	0.0352481i	−0.254273	−	0.967133i	$-0.581836\pi$
$883$	3.22359	−	1.04741i	0.108483	−	0.0352481i	0.362755	+	0.931884i	$0.381836\pi$
$884$	12.3808	−	4.02277i	0.416411	−	0.135300i
$885$	10.9438	−	10.5306i	0.367870	−	0.353982i
$886$	5.71861	+	17.6001i	0.192121	+	0.591286i
$887$	28.0248	+	9.10582i	0.940981	+	0.305743i	0.739046	−	0.673655i	$-0.235277\pi$
$887$	28.0248	+	9.10582i	0.940981	+	0.305743i	0.201936	+	0.979399i	$0.435277\pi$
$888$	6.63298	+	3.54201i	0.222588	+	0.118862i
$889$	50.7982	+	16.5053i	1.70372	+	0.553571i
$890$	13.4882	−	9.79977i	0.452126	−	0.328489i
$891$	−10.7786	+	26.1392i	−0.361096	+	0.875698i
$892$	5.39416	−	7.42442i	0.180610	−	0.248588i
$893$			9.60812i			0.321524i
$894$	5.80722	−	0.805587i	0.194222	−	0.0269429i
$895$	−25.6694	+	35.3309i	−0.858034	+	1.18098i
$896$	−2.68104	+	0.871123i	−0.0895673	+	0.0291022i
$897$	−4.47022	−	0.796448i	−0.149256	−	0.0265926i
$898$		−	36.4430i		−	1.21612i
$899$	17.8224	−	37.4565i	0.594409	−	1.24924i
$900$	26.8207	−	7.58724i	0.894024	−	0.252908i
$901$	24.3382	−	74.9054i	0.810824	−	2.49546i
$902$	−10.7579	−	33.1093i	−0.358198	−	1.10242i
$903$	11.4900	−	21.5168i	0.382363	−	0.716036i
$904$	−6.46702			−0.215090
$905$	71.7114			2.38377
$906$	21.7939	+	11.6379i	0.724053	+	0.386644i
$907$	−30.1979	+	21.9401i	−1.00271	+	0.728508i	−0.962667	−	0.270690i	$-0.912748\pi$
$907$	−30.1979	+	21.9401i	−1.00271	+	0.728508i	−0.0400386	+	0.999198i	$0.512748\pi$
$908$	−13.0299	−	17.9342i	−0.432414	−	0.595167i
$909$	−24.3246	−	0.936354i	−0.806797	−	0.0310569i
$910$	−12.1596	+	16.7363i	−0.403088	+	0.554804i
$911$	12.1081	−	37.2648i	0.401158	−	1.23464i	−0.522902	−	0.852393i	$-0.675151\pi$
$911$	12.1081	−	37.2648i	0.401158	−	1.23464i	0.924061	−	0.382246i	$-0.124849\pi$
$912$	1.41568	+	2.91577i	0.0468778	+	0.0965507i
$913$	−5.31332	+	3.86035i	−0.175845	+	0.127759i
$914$	−6.95486	−	21.4049i	−0.230046	−	0.708010i
$915$	25.1267	+	51.7515i	0.830662	+	1.71085i
$916$	−1.95465	−	2.69034i	−0.0645834	−	0.0888915i
$917$	7.28155	−	2.36592i	0.240458	−	0.0781295i
$918$	34.6740	−	3.45684i	1.14441	−	0.114093i
$919$	14.5208	+	10.5500i	0.478998	+	0.348013i	0.800938	−	0.598748i	$-0.204335\pi$
$919$	14.5208	+	10.5500i	0.478998	+	0.348013i	−0.321940	+	0.946760i	$0.604335\pi$
$920$	1.57760	−	4.85535i	0.0520119	−	0.160076i
$921$	−38.9322	+	37.4624i	−1.28286	+	1.23443i
$922$	−11.8803	−	16.3518i	−0.391256	−	0.538518i
$923$	−15.3105	−	11.1237i	−0.503951	−	0.366142i
$924$	15.1939	−	2.10772i	0.499842	−	0.0693390i
$925$			40.3359i			1.32624i
$926$	13.2368	+	9.61713i	0.434990	+	0.316038i
$927$	−3.59997	−	5.37847i	−0.118238	−	0.176652i
$928$	7.08547	+	2.30221i	0.232592	+	0.0755737i
$929$	−14.0462			−0.460841			−0.230420	−	0.973091i	$-0.574010\pi$
$929$	−14.0462			−0.460841			−0.230420	+	0.973091i	$0.574010\pi$
$930$	36.4553	−	0.287576i	1.19542	−	0.00942999i
$931$	1.77187			0.0580706
$932$	−1.44224	−	0.468613i	−0.0472422	−	0.0153499i
$933$	−0.676070	+	0.328250i	−0.0221335	+	0.0107464i
$934$	34.7100	+	25.2183i	1.13574	+	0.825167i
$935$		−	79.6438i		−	2.60463i
$936$	5.60373	−	1.58522i	0.183164	−	0.0518147i
$937$	−39.3000	−	28.5531i	−1.28388	−	0.932790i	−0.284213	−	0.958761i	$-0.591732\pi$
$937$	−39.3000	−	28.5531i	−1.28388	−	0.932790i	−0.999663	+	0.0259713i	$0.991732\pi$
$938$	11.8625	+	16.3273i	0.387324	+	0.533106i
$939$	−7.98098	−	8.29412i	−0.260450	−	0.270668i
$940$	−5.99789	+	18.4596i	−0.195630	+	0.602086i
$941$	43.0823	+	31.3011i	1.40444	+	1.02039i	0.994101	+	0.108457i	$0.0345910\pi$
$941$	43.0823	+	31.3011i	1.40444	+	1.02039i	0.410343	+	0.911931i	$0.365409\pi$
$942$	−39.2073	−	6.98547i	−1.27744	−	0.227599i
$943$	14.2325	−	4.62443i	0.463475	−	0.150592i
$944$	1.36336	+	1.87651i	0.0443736	+	0.0610751i
$945$	−41.3492	+	36.8321i	−1.34509	+	1.19815i
$946$	4.84988	+	14.9264i	0.157683	+	0.485299i
$947$	−24.8959	+	18.0879i	−0.809009	+	0.587779i	−0.913543	−	0.406742i	$-0.866665\pi$
$947$	−24.8959	+	18.0879i	−0.809009	+	0.587779i	0.104534	+	0.994521i	$0.466665\pi$
$948$	4.16739	−	2.02338i	0.135351	−	0.0657162i
$949$	−0.712387	+	2.19250i	−0.0231251	+	0.0711716i
$950$	−10.2197	+	14.0663i	−0.331572	+	0.456370i
$951$	35.5558	+	6.33489i	1.15298	+	0.205423i
$952$	−11.1118	−	15.2941i	−0.360137	−	0.495685i
$953$	31.4429	−	22.8446i	1.01853	−	0.740008i	0.0525521	−	0.998618i	$-0.483264\pi$
$953$	31.4429	−	22.8446i	1.01853	−	0.740008i	0.965982	+	0.258610i	$0.0832645\pi$
$954$	12.1687	−	33.0656i	0.393977	−	1.07054i
$955$	−72.7404			−2.35382
$956$	3.55965			0.115127
$957$	−35.7598	−	19.0957i	−1.15595	−	0.617277i
$958$	4.73125	+	14.5613i	0.152860	+	0.470454i
$959$	1.13742	−	3.50062i	0.0367292	−	0.113041i
$960$	0.899702	+	6.48566i	0.0290378	+	0.209324i
$961$	29.9588	+	7.96673i	0.966414	+	0.256991i
$962$			8.42750i			0.271714i
$963$	−29.4280	−	1.13281i	−0.948304	−	0.0365041i
$964$	−3.15147	+	1.02398i	−0.101502	+	0.0329800i
$965$	−53.1657	+	73.1763i	−1.71146	+	2.35563i
$966$	0.906036	+	6.53131i	0.0291512	+	0.210142i
$967$		−	12.3857i		−	0.398297i	−0.979969	−	0.199149i	$-0.936182\pi$
$967$		−	12.3857i		−	0.398297i	0.979969	−	0.199149i	$-0.0638176\pi$
$968$	0.664432	−	0.914512i	0.0213556	−	0.0293935i
$969$	−15.6627	+	15.0714i	−0.503158	+	0.484162i
$970$	−10.3972	+	7.55403i	−0.333835	+	0.242545i
$971$	−21.0799	−	6.84926i	−0.676485	−	0.219803i	−0.0494290	−	0.998778i	$-0.515740\pi$
$971$	−21.0799	−	6.84926i	−0.676485	−	0.219803i	−0.627056	+	0.778974i	$0.715740\pi$
$972$	15.5596	−	0.948623i	0.499073	−	0.0304271i
$973$	32.6514	+	10.6091i	1.04676	+	0.340112i
$974$	12.8487	+	39.5443i	0.411700	+	1.26708i
$975$	21.6604	+	22.5103i	0.693688	+	0.720905i
$976$	−8.35600	+	2.71503i	−0.267469	+	0.0869060i
$977$	−8.93256	+	2.90237i	−0.285778	+	0.0928549i	−0.448398	−	0.893834i	$-0.648005\pi$
$977$	−8.93256	+	2.90237i	−0.285778	+	0.0928549i	0.162620	+	0.986689i	$0.448005\pi$
$978$	6.59506	+	6.85382i	0.210887	+	0.219161i
$979$	−4.28151	−	13.1771i	−0.136838	−	0.421143i
$980$	3.40420	+	1.10609i	0.108743	+	0.0353328i
$981$	38.5302	+	14.1798i	1.23018	+	0.452725i
$982$	−7.71747	−	2.50756i	−0.246274	−	0.0800194i
$983$	6.05756	−	4.40107i	0.193206	−	0.140372i	−0.486977	−	0.873415i	$-0.661900\pi$
$983$	6.05756	−	4.40107i	0.193206	−	0.140372i	0.680183	+	0.733042i	$0.261900\pi$
$984$	−13.8304	+	13.3083i	−0.440898	+	0.424252i
$985$	24.8338	−	34.1808i	0.791270	−	1.08909i
$986$			49.9611i			1.59109i
$987$	−3.44467	−	24.8315i	−0.109645	−	0.790395i
$988$	−2.13524	+	2.93890i	−0.0679310	+	0.0934989i
$989$	−6.41633	+	2.08479i	−0.204027	+	0.0662925i
$990$	1.37049	−	35.6026i	0.0435571	−	1.13153i
$991$			4.46076i			0.141701i	0.997487	+	0.0708503i	$0.0225713\pi$
$991$			4.46076i			0.141701i	−0.997487	+	0.0708503i	$0.977429\pi$
$992$	−0.721517	+	5.52082i	−0.0229082	+	0.175286i
$993$	0.502869	+	3.62502i	0.0159581	+	0.115036i
$994$	−8.49255	+	26.1374i	−0.269367	+	0.829028i
$995$	17.2170	+	52.9885i	0.545816	+	1.67985i
$996$	3.19405	+	1.70562i	0.101207	+	0.0540447i
$997$	7.88478			0.249713			0.124857	−	0.992175i	$-0.460153\pi$
$997$	7.88478			0.249713			0.124857	+	0.992175i	$0.460153\pi$
$998$	−5.74660			−0.181906
$999$	−4.80820	+	22.0400i	−0.152125	+	0.697315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	186.2.j.a.23.11	yes	48
3.2	odd	2	inner	186.2.j.a.23.4	✓	48
31.27	odd	10	inner	186.2.j.a.89.4	yes	48
93.89	even	10	inner	186.2.j.a.89.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
186.2.j.a.23.4	✓	48	3.2	odd	2	inner
186.2.j.a.23.11	yes	48	1.1	even	1	trivial
186.2.j.a.89.4	yes	48	31.27	odd	10	inner
186.2.j.a.89.11	yes	48	93.89	even	10	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 186 = 2 \cdot 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	186.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.756502 + 1.55811i) q^{3} +(0.809017 + 0.587785i) q^{4} -3.78035i q^{5} +(0.237994 + 1.71562i) q^{6} +(2.28063 + 1.65697i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-1.85541 + 2.35743i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.756502 + 1.55811i) q^{3} +(0.809017 + 0.587785i) q^{4} -3.78035i q^{5} +(0.237994 + 1.71562i) q^{6} +(2.28063 + 1.65697i) q^{7} +(0.587785 + 0.809017i) q^{8} +(-1.85541 + 2.35743i) q^{9} +(1.16819 - 3.59533i) q^{10} +(-2.54160 - 1.84658i) q^{11} +(-0.303810 + 1.70520i) q^{12} +(-1.84620 + 0.599867i) q^{13} +(1.65697 + 2.28063i) q^{14} +(5.89020 - 2.85985i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-5.42535 + 3.94174i) q^{17} +(-2.49308 + 1.66869i) q^{18} +(0.578279 - 1.77976i) q^{19} +(2.22204 - 3.05837i) q^{20} +(-0.856446 + 4.80698i) q^{21} +(-1.84658 - 2.54160i) q^{22} +(1.09255 - 0.793781i) q^{23} +(-0.815876 + 1.52786i) q^{24} -9.29108 q^{25} -1.94121 q^{26} +(-5.07675 - 1.10753i) q^{27} +(0.871123 + 2.68104i) q^{28} +(2.30221 - 7.08547i) q^{29} +(6.48566 - 0.899702i) q^{30} +(5.52082 + 0.721517i) q^{31} +1.00000i q^{32} +(0.954449 - 5.35704i) q^{33} +(-6.37788 + 2.07230i) q^{34} +(6.26395 - 8.62159i) q^{35} +(-2.88672 + 0.816616i) q^{36} -4.34136i q^{37} +(1.09995 - 1.51395i) q^{38} +(-2.33131 - 2.42278i) q^{39} +(3.05837 - 2.22204i) q^{40} +(10.5390 + 3.42433i) q^{41} +(-2.29997 + 4.30705i) q^{42} +(-4.75122 - 1.54376i) q^{43} +(-0.970805 - 2.98783i) q^{44} +(8.91191 + 7.01410i) q^{45} +(1.28436 - 0.417315i) q^{46} +(-4.88304 + 1.58660i) q^{47} +(-1.24808 + 1.20096i) q^{48} +(0.292590 + 0.900498i) q^{49} +(-8.83634 - 2.87110i) q^{50} +(-10.2460 - 5.47134i) q^{51} +(-1.84620 - 0.599867i) q^{52} +(-9.50156 + 6.90328i) q^{53} +(-4.48603 - 2.62213i) q^{54} +(-6.98073 + 9.60815i) q^{55} +2.81901i q^{56} +(3.21053 - 0.445370i) q^{57} +(4.37906 - 6.02726i) q^{58} +(2.20597 - 0.716762i) q^{59} +(6.44625 + 1.14851i) q^{60} +8.78602i q^{61} +(5.02765 + 2.39223i) q^{62} +(-8.13770 + 2.30205i) q^{63} +(-0.309017 + 0.951057i) q^{64} +(2.26771 + 6.97929i) q^{65} +(2.56315 - 4.79990i) q^{66} +7.15912 q^{67} -6.70610 q^{68} +(2.06331 + 1.10181i) q^{69} +(8.62159 - 6.26395i) q^{70} +(5.73030 + 7.88708i) q^{71} +(-2.99778 - 0.115397i) q^{72} +(0.698039 - 0.960768i) q^{73} +(1.34156 - 4.12888i) q^{74} +(-7.02872 - 14.4765i) q^{75} +(1.51395 - 1.09995i) q^{76} +(-2.73671 - 8.42274i) q^{77} +(-1.46853 - 3.02462i) q^{78} +(-1.57212 - 2.16383i) q^{79} +(3.59533 - 1.16819i) q^{80} +(-2.11492 - 8.74798i) q^{81} +(8.96502 + 6.51347i) q^{82} +(0.646012 - 1.98822i) q^{83} +(-3.51835 + 3.38552i) q^{84} +(14.9012 + 20.5097i) q^{85} +(-4.04163 - 2.93641i) q^{86} +(12.7816 - 1.77308i) q^{87} -3.14159i q^{88} +(3.56798 + 2.59229i) q^{89} +(6.30825 + 9.42474i) q^{90} +(-5.20447 - 1.69103i) q^{91} +1.35046 q^{92} +(3.05231 + 9.14786i) q^{93} -5.13433 q^{94} +(-6.72812 - 2.18610i) q^{95} +(-1.55811 + 0.756502i) q^{96} +(-2.75033 - 1.99823i) q^{97} +0.946840i q^{98} +(9.06889 - 2.56547i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 12 q^{4} - 18 q^{7} - 4 q^{9}+O(q^{10}) \) 48 * q + 12 * q^4 - 18 * q^7 - 4 * q^9	\( 48 q + 12 q^{4} - 18 q^{7} - 4 q^{9} + 4 q^{10} + 10 q^{15} - 12 q^{16} + 8 q^{18} + 20 q^{19} - 10 q^{22} - 92 q^{25} - 22 q^{28} + 40 q^{31} - 12 q^{33} - 20 q^{34} + 4 q^{36} - 8 q^{39} + 6 q^{40} - 50 q^{43} + 6 q^{45} + 20 q^{46} - 10 q^{48} - 34 q^{49} - 10 q^{51} + 20 q^{55} - 20 q^{58} + 10 q^{60} - 148 q^{63} + 12 q^{64} - 36 q^{66} + 60 q^{67} + 54 q^{69} - 24 q^{70} - 8 q^{72} - 20 q^{73} + 30 q^{75} + 30 q^{76} + 10 q^{78} + 50 q^{79} - 56 q^{81} + 12 q^{82} + 20 q^{84} + 20 q^{85} + 104 q^{87} + 98 q^{90} + 70 q^{91} - 10 q^{93} + 24 q^{94} + 22 q^{97}+O(q^{100}) \) 48 * q + 12 * q^4 - 18 * q^7 - 4 * q^9 + 4 * q^10 + 10 * q^15 - 12 * q^16 + 8 * q^18 + 20 * q^19 - 10 * q^22 - 92 * q^25 - 22 * q^28 + 40 * q^31 - 12 * q^33 - 20 * q^34 + 4 * q^36 - 8 * q^39 + 6 * q^40 - 50 * q^43 + 6 * q^45 + 20 * q^46 - 10 * q^48 - 34 * q^49 - 10 * q^51 + 20 * q^55 - 20 * q^58 + 10 * q^60 - 148 * q^63 + 12 * q^64 - 36 * q^66 + 60 * q^67 + 54 * q^69 - 24 * q^70 - 8 * q^72 - 20 * q^73 + 30 * q^75 + 30 * q^76 + 10 * q^78 + 50 * q^79 - 56 * q^81 + 12 * q^82 + 20 * q^84 + 20 * q^85 + 104 * q^87 + 98 * q^90 + 70 * q^91 - 10 * q^93 + 24 * q^94 + 22 * q^97

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