LMFDB - Embedded newform 546.2.bn.e.173.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.9
Character	$\chi$	$=$	546.173
Dual form			546.2.bn.e.101.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.428009 + 1.67834i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.58996 + 0.917964i) q^{5} +(1.23948 - 1.20983i) q^{6} +(2.08732 + 1.62576i) q^{7} +1.00000 q^{8} +(-2.63362 + 1.43668i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.428009 + 1.67834i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.58996 + 0.917964i) q^{5} +(1.23948 - 1.20983i) q^{6} +(2.08732 + 1.62576i) q^{7} +1.00000 q^{8} +(-2.63362 + 1.43668i) q^{9} -1.83593i q^{10} +3.39249 q^{11} +(-1.66749 - 0.468501i) q^{12} +(-3.07128 + 1.88872i) q^{13} +(0.364289 - 2.62055i) q^{14} +(-0.860135 + 3.06138i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.59253 - 2.75834i) q^{17} +(2.56101 + 1.56244i) q^{18} -2.03164 q^{19} +(-1.58996 + 0.917964i) q^{20} +(-1.83518 + 4.19906i) q^{21} +(-1.69625 - 2.93798i) q^{22} +(-2.14393 + 1.23780i) q^{23} +(0.428009 + 1.67834i) q^{24} +(-0.814684 - 1.41107i) q^{25} +(3.17131 + 1.71545i) q^{26} +(-3.53845 - 3.80518i) q^{27} +(-2.45161 + 0.994793i) q^{28} +(1.81857 + 1.04995i) q^{29} +(3.08130 - 0.785793i) q^{30} +(3.14345 + 5.44461i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.45202 + 5.69374i) q^{33} -3.18506 q^{34} +(1.82637 + 4.50098i) q^{35} +(0.0726040 - 2.99912i) q^{36} +(-0.436402 + 0.251957i) q^{37} +(1.01582 + 1.75945i) q^{38} +(-4.48443 - 4.34625i) q^{39} +(1.58996 + 0.917964i) q^{40} +(-4.35184 - 2.51254i) q^{41} +(4.55408 - 0.510221i) q^{42} +(0.528972 + 0.916206i) q^{43} +(-1.69625 + 2.93798i) q^{44} +(-5.50617 - 0.133296i) q^{45} +(2.14393 + 1.23780i) q^{46} +(10.0977 + 5.82991i) q^{47} +(1.23948 - 1.20983i) q^{48} +(1.71381 + 6.78696i) q^{49} +(-0.814684 + 1.41107i) q^{50} +(5.31104 + 1.49220i) q^{51} +(-0.100036 - 3.60416i) q^{52} +(5.81668 - 3.35826i) q^{53} +(-1.52616 + 4.96698i) q^{54} +(5.39393 + 3.11418i) q^{55} +(2.08732 + 1.62576i) q^{56} +(-0.869560 - 3.40977i) q^{57} -2.09991i q^{58} +(-5.37709 - 3.10446i) q^{59} +(-2.22117 - 2.27559i) q^{60} +11.6806i q^{61} +(3.14345 - 5.44461i) q^{62} +(-7.83291 - 1.28281i) q^{63} +1.00000 q^{64} +(-6.61699 + 0.183658i) q^{65} +(4.20491 - 4.10435i) q^{66} -9.92794i q^{67} +(1.59253 + 2.75834i) q^{68} +(-2.99507 - 3.06845i) q^{69} +(2.98478 - 3.83217i) q^{70} +(-7.77030 - 13.4586i) q^{71} +(-2.63362 + 1.43668i) q^{72} +(4.47574 + 7.75221i) q^{73} +(0.436402 + 0.251957i) q^{74} +(2.01956 - 1.97126i) q^{75} +(1.01582 - 1.75945i) q^{76} +(7.08122 + 5.51537i) q^{77} +(-1.52175 + 6.05676i) q^{78} +(3.92399 - 6.79656i) q^{79} -1.83593i q^{80} +(4.87188 - 7.56735i) q^{81} +5.02507i q^{82} -13.0790i q^{83} +(-2.71891 - 3.68884i) q^{84} +(5.06412 - 2.92377i) q^{85} +(0.528972 - 0.916206i) q^{86} +(-0.983809 + 3.50156i) q^{87} +3.39249 q^{88} +(4.61906 - 2.66681i) q^{89} +(2.63765 + 4.83513i) q^{90} +(-9.48134 - 1.05081i) q^{91} -2.47560i q^{92} +(-7.79246 + 7.60610i) q^{93} -11.6598i q^{94} +(-3.23023 - 1.86497i) q^{95} +(-1.66749 - 0.468501i) q^{96} +(4.79907 + 8.31223i) q^{97} +(5.02077 - 4.87769i) q^{98} +(-8.93452 + 4.87394i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	$ 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) $ 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.428009	+	1.67834i	0.247111	+	0.968987i
$3$	0.428009	+	1.67834i	0.247111	+	0.968987i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.58996	+	0.917964i	0.711052	+	0.410526i	0.811450	−	0.584421i	$-0.198678\pi$
$5$	1.58996	+	0.917964i	0.711052	+	0.410526i	−0.100398	+	0.994947i	$0.532012\pi$
$6$	1.23948	−	1.20983i	0.506014	−	0.493913i
$7$	2.08732	+	1.62576i	0.788933	+	0.614479i
$7$	2.08732	+	1.62576i	0.788933	+	0.614479i
$8$	1.00000			0.353553
$9$	−2.63362	+	1.43668i	−0.877872	+	0.478895i
$10$		−	1.83593i		−	0.580572i
$11$	3.39249			1.02287			0.511437	−	0.859321i	$-0.329113\pi$
$11$	3.39249			1.02287			0.511437	+	0.859321i	$0.329113\pi$
$12$	−1.66749	−	0.468501i	−0.481361	−	0.135245i
$13$	−3.07128	+	1.88872i	−0.851820	+	0.523835i
$13$	−3.07128	+	1.88872i	−0.851820	+	0.523835i
$14$	0.364289	−	2.62055i	0.0973602	−	0.700372i
$15$	−0.860135	+	3.06138i	−0.222086	+	0.790446i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.59253	−	2.75834i	0.386245	−	0.668996i	−0.605696	−	0.795696i	$-0.707105\pi$
$17$	1.59253	−	2.75834i	0.386245	−	0.668996i	0.991941	+	0.126700i	$0.0404385\pi$
$18$	2.56101	+	1.56244i	0.603637	+	0.368270i
$19$	−2.03164			−0.466090			−0.233045	−	0.972466i	$-0.574869\pi$
$19$	−2.03164			−0.466090			−0.233045	+	0.972466i	$0.574869\pi$
$20$	−1.58996	+	0.917964i	−0.355526	+	0.205263i
$21$	−1.83518	+	4.19906i	−0.400469	+	0.916310i
$22$	−1.69625	−	2.93798i	−0.361641	−	0.626380i
$23$	−2.14393	+	1.23780i	−0.447041	+	0.258099i	−0.706580	−	0.707633i	$-0.749763\pi$
$23$	−2.14393	+	1.23780i	−0.447041	+	0.258099i	0.259539	+	0.965733i	$0.416430\pi$
$24$	0.428009	+	1.67834i	0.0873669	+	0.342589i
$25$	−0.814684	−	1.41107i	−0.162937	−	0.282215i
$26$	3.17131	+	1.71545i	0.621946	+	0.336427i
$27$	−3.53845	−	3.80518i	−0.680975	−	0.732307i
$28$	−2.45161	+	0.994793i	−0.463311	+	0.187998i
$29$	1.81857	+	1.04995i	0.337701	+	0.194971i	0.659255	−	0.751920i	$-0.270872\pi$
$29$	1.81857	+	1.04995i	0.337701	+	0.194971i	−0.321554	+	0.946891i	$0.604205\pi$
$30$	3.08130	−	0.785793i	0.562566	−	0.143466i
$31$	3.14345	+	5.44461i	0.564580	+	0.977881i	0.997089	+	0.0762515i	$0.0242952\pi$
$31$	3.14345	+	5.44461i	0.564580	+	0.977881i	−0.432509	+	0.901630i	$0.642371\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.45202	+	5.69374i	0.252763	+	0.991152i
$34$	−3.18506			−0.546233
$35$	1.82637	+	4.50098i	0.308713	+	0.760804i
$36$	0.0726040	−	2.99912i	0.0121007	−	0.499854i
$37$	−0.436402	+	0.251957i	−0.0717440	+	0.0414214i	−0.535443	−	0.844571i	$-0.679855\pi$
$37$	−0.436402	+	0.251957i	−0.0717440	+	0.0414214i	0.463699	+	0.885993i	$0.346522\pi$
$38$	1.01582	+	1.75945i	0.164788	+	0.285421i
$39$	−4.48443	−	4.34625i	−0.718084	−	0.695957i
$40$	1.58996	+	0.917964i	0.251395	+	0.145143i
$41$	−4.35184	−	2.51254i	−0.679643	−	0.392392i	0.120077	−	0.992765i	$-0.461686\pi$
$41$	−4.35184	−	2.51254i	−0.679643	−	0.392392i	−0.799721	+	0.600372i	$0.795019\pi$
$42$	4.55408	−	0.510221i	0.702710	−	0.0787287i
$43$	0.528972	+	0.916206i	0.0806674	+	0.139720i	0.903537	−	0.428511i	$-0.140962\pi$
$43$	0.528972	+	0.916206i	0.0806674	+	0.139720i	−0.822869	+	0.568231i	$0.807628\pi$
$44$	−1.69625	+	2.93798i	−0.255719	+	0.442918i
$45$	−5.50617	−	0.133296i	−0.820812	−	0.0198705i
$46$	2.14393	+	1.23780i	0.316106	+	0.182504i
$47$	10.0977	+	5.82991i	1.47290	+	0.850380i	0.999535	−	0.0304848i	$-0.00970512\pi$
$47$	10.0977	+	5.82991i	1.47290	+	0.850380i	0.473367	+	0.880865i	$0.343038\pi$
$48$	1.23948	−	1.20983i	0.178903	−	0.174624i
$49$	1.71381	+	6.78696i	0.244830	+	0.969566i
$50$	−0.814684	+	1.41107i	−0.115214	+	0.199556i
$51$	5.31104	+	1.49220i	0.743694	+	0.208950i
$52$	−0.100036	−	3.60416i	−0.0138724	−	0.499808i
$53$	5.81668	−	3.35826i	0.798983	−	0.461293i	−0.0441326	−	0.999026i	$-0.514052\pi$
$53$	5.81668	−	3.35826i	0.798983	−	0.461293i	0.843115	+	0.537733i	$0.180719\pi$
$54$	−1.52616	+	4.96698i	−0.207684	+	0.675920i
$55$	5.39393	+	3.11418i	0.727317	+	0.419917i
$56$	2.08732	+	1.62576i	0.278930	+	0.217251i
$57$	−0.869560	−	3.40977i	−0.115176	−	0.451636i
$58$		−	2.09991i		−	0.275731i
$59$	−5.37709	−	3.10446i	−0.700037	−	0.404167i	0.107324	−	0.994224i	$-0.465772\pi$
$59$	−5.37709	−	3.10446i	−0.700037	−	0.404167i	−0.807361	+	0.590057i	$0.799105\pi$
$60$	−2.22117	−	2.27559i	−0.286752	−	0.293777i
$61$			11.6806i			1.49554i	0.663957	+	0.747771i	$0.268876\pi$
$61$			11.6806i			1.49554i	−0.663957	+	0.747771i	$0.731124\pi$
$62$	3.14345	−	5.44461i	0.399218	−	0.691467i
$63$	−7.83291	−	1.28281i	−0.986853	−	0.161619i
$64$	1.00000			0.125000
$65$	−6.61699	+	0.183658i	−0.820736	+	0.0227800i
$66$	4.20491	−	4.10435i	0.517589	−	0.505211i
$67$		−	9.92794i		−	1.21289i	−0.795125	−	0.606445i	$-0.792595\pi$
$67$		−	9.92794i		−	1.21289i	0.795125	−	0.606445i	$-0.207405\pi$
$68$	1.59253	+	2.75834i	0.193123	+	0.334498i
$69$	−2.99507	−	3.06845i	−0.360564	−	0.369398i
$70$	2.98478	−	3.83217i	0.356749	−	0.458032i
$71$	−7.77030	−	13.4586i	−0.922165	−	1.59724i	−0.796058	−	0.605221i	$-0.793085\pi$
$71$	−7.77030	−	13.4586i	−0.922165	−	1.59724i	−0.126108	−	0.992017i	$-0.540248\pi$
$72$	−2.63362	+	1.43668i	−0.310375	+	0.169315i
$73$	4.47574	+	7.75221i	0.523846	+	0.907327i	0.999615	+	0.0277570i	$0.00883647\pi$
$73$	4.47574	+	7.75221i	0.523846	+	0.907327i	−0.475769	+	0.879570i	$0.657830\pi$
$74$	0.436402	+	0.251957i	0.0507307	+	0.0292894i
$75$	2.01956	−	1.97126i	0.233199	−	0.227622i
$76$	1.01582	−	1.75945i	0.116523	−	0.201823i
$77$	7.08122	+	5.51537i	0.806979	+	0.628535i
$78$	−1.52175	+	6.05676i	−0.172304	+	0.685793i
$79$	3.92399	−	6.79656i	0.441484	−	0.764672i	−0.556316	−	0.830971i	$-0.687786\pi$
$79$	3.92399	−	6.79656i	0.441484	−	0.764672i	0.997800	+	0.0662985i	$0.0211189\pi$
$80$		−	1.83593i		−	0.205263i
$81$	4.87188	−	7.56735i	0.541320	−	0.840817i
$82$			5.02507i			0.554926i
$83$		−	13.0790i		−	1.43561i	−0.696246	−	0.717803i	$-0.745148\pi$
$83$		−	13.0790i		−	1.43561i	0.696246	−	0.717803i	$-0.254852\pi$
$84$	−2.71891	−	3.68884i	−0.296657	−	0.402486i
$85$	5.06412	−	2.92377i	0.549281	−	0.317127i
$86$	0.528972	−	0.916206i	0.0570405	−	0.0987970i
$87$	−0.983809	+	3.50156i	−0.105475	+	0.375407i
$88$	3.39249			0.361641
$89$	4.61906	−	2.66681i	0.489619	−	0.282682i	−0.234797	−	0.972044i	$-0.575443\pi$
$89$	4.61906	−	2.66681i	0.489619	−	0.282682i	0.724416	+	0.689363i	$0.242109\pi$
$90$	2.63765	+	4.83513i	0.278033	+	0.509668i
$91$	−9.48134	−	1.05081i	−0.993914	−	0.110155i
$92$		−	2.47560i		−	0.258099i
$93$	−7.79246	+	7.60610i	−0.808041	+	0.788716i
$94$		−	11.6598i		−	1.20262i
$95$	−3.23023	−	1.86497i	−0.331414	−	0.191342i
$96$	−1.66749	−	0.468501i	−0.170187	−	0.0478162i
$97$	4.79907	+	8.31223i	0.487272	+	0.843979i	0.999893	−	0.0146357i	$-0.00465887\pi$
$97$	4.79907	+	8.31223i	0.487272	+	0.843979i	−0.512621	+	0.858615i	$0.671326\pi$
$98$	5.02077	−	4.87769i	0.507175	−	0.492721i
$99$	−8.93452	+	4.87394i	−0.897953	+	0.489849i
$100$	1.62937			0.162937
$101$	9.39069			0.934409			0.467204	−	0.884149i	$-0.345261\pi$
$101$	9.39069			0.934409			0.467204	+	0.884149i	$0.345261\pi$
$102$	−1.36323	−	5.34560i	−0.134980	−	0.529293i
$103$	−11.5646	−	6.67680i	−1.13949	−	0.657884i	−0.193185	−	0.981162i	$-0.561882\pi$
$103$	−11.5646	−	6.67680i	−1.13949	−	0.657884i	−0.946304	+	0.323278i	$0.895215\pi$
$104$	−3.07128	+	1.88872i	−0.301164	+	0.185204i
$105$	−6.77245	+	4.99172i	−0.660923	+	0.487142i
$106$	−5.81668	−	3.35826i	−0.564966	−	0.326183i
$107$	11.5796	−	6.68547i	1.11944	−	0.646309i	0.178182	−	0.983998i	$-0.442978\pi$
$107$	11.5796	−	6.68547i	1.11944	−	0.646309i	0.941258	+	0.337689i	$0.109645\pi$
$108$	5.06461	−	1.16180i	0.487342	−	0.111794i
$109$	−3.82963	+	2.21104i	−0.366812	+	0.211779i	−0.672065	−	0.740492i	$-0.734592\pi$
$109$	−3.82963	+	2.21104i	−0.366812	+	0.211779i	0.305253	+	0.952271i	$0.401259\pi$
$110$		−	6.22837i		−	0.593852i
$111$	−0.609651	−	0.624589i	−0.0578655	−	0.0592833i
$112$	0.364289	−	2.62055i	0.0344220	−	0.247619i
$113$	−13.8390	+	7.98994i	−1.30186	+	0.751631i	−0.980723	−	0.195402i	$-0.937399\pi$
$113$	−13.8390	+	7.98994i	−1.30186	+	0.751631i	−0.321139	+	0.947032i	$0.604066\pi$
$114$	−2.51817	+	2.45795i	−0.235848	+	0.230208i
$115$	−4.54503			−0.423826
$116$	−1.81857	+	1.04995i	−0.168850	+	0.0974857i
$117$	5.37509	−	9.38661i	0.496927	−	0.867792i
$118$			6.20893i			0.571578i
$119$	7.80852	−	3.16847i	0.715806	−	0.290454i
$120$	−0.860135	+	3.06138i	−0.0785192	+	0.279465i
$121$	0.508993			0.0462721
$122$	10.1157	−	5.84028i	0.915829	−	0.528754i
$123$	2.35425	−	8.37923i	0.212276	−	0.755530i
$124$	−6.28690			−0.564580
$125$		−	12.1710i		−	1.08861i
$126$	2.80551	+	7.42490i	0.249935	+	0.661463i
$127$	−0.475986	+	0.824432i	−0.0422370	+	0.0731566i	−0.886371	−	0.462976i	$-0.846782\pi$
$127$	−0.475986	+	0.824432i	−0.0422370	+	0.0731566i	0.844134	+	0.536132i	$0.180115\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−1.31130	+	1.27994i	−0.115453	+	0.112692i
$130$	3.46755	+	5.63865i	0.304124	+	0.494542i
$131$	4.95760	−	8.58681i	0.433147	−	0.750233i	−0.563995	−	0.825778i	$-0.690736\pi$
$131$	4.95760	−	8.58681i	0.433147	−	0.750233i	0.997142	+	0.0755449i	$0.0240696\pi$
$132$	−5.65693	−	1.58939i	−0.492372	−	0.138338i
$133$	−4.24069	−	3.30296i	−0.367714	−	0.286403i
$134$	−8.59785	+	4.96397i	−0.742741	+	0.428822i
$135$	−2.13297	−	9.29825i	−0.183577	−	0.800266i
$136$	1.59253	−	2.75834i	0.136558	−	0.236526i
$137$	−1.59153	+	2.75662i	−0.135974	+	0.235514i	−0.925969	−	0.377599i	$-0.876750\pi$
$137$	−1.59153	+	2.75662i	−0.135974	+	0.235514i	0.789995	+	0.613113i	$0.210083\pi$
$138$	−1.15982	+	4.12803i	−0.0987306	+	0.351401i
$139$	−0.0981681	+	0.0566774i	−0.00832651	+	0.00480731i	−0.504157	−	0.863612i	$-0.668197\pi$
$139$	−0.0981681	+	0.0566774i	−0.00832651	+	0.00480731i	0.495831	+	0.868419i	$0.334864\pi$
$140$	−4.81115	−	0.668808i	−0.406616	−	0.0565246i
$141$	−5.46264	+	19.4426i	−0.460038	+	1.63736i
$142$	−7.77030	+	13.4586i	−0.652069	+	1.12942i
$143$	−10.4193	+	6.40745i	−0.871304	+	0.535818i
$144$	2.56101	+	1.56244i	0.213418	+	0.130203i
$145$	1.92764	+	3.33877i	0.160082	+	0.277270i
$146$	4.47574	−	7.75221i	0.370415	−	0.641577i
$147$	−10.6573	+	5.78123i	−0.878997	+	0.476828i
$148$		−	0.503913i		−	0.0414214i
$149$	−21.7126			−1.77876			−0.889382	−	0.457165i	$-0.848865\pi$
$149$	−21.7126			−1.77876			−0.889382	+	0.457165i	$0.848865\pi$
$150$	−2.71695	−	0.763361i	−0.221838	−	0.0623281i
$151$	4.69698	−	2.71180i	0.382235	−	0.220684i	−0.296555	−	0.955016i	$-0.595838\pi$
$151$	4.69698	−	2.71180i	0.382235	−	0.220684i	0.678790	+	0.734332i	$0.262505\pi$
$152$	−2.03164			−0.164788
$153$	−0.231248	+	9.55238i	−0.0186953	+	0.772264i
$154$	1.23585	−	8.89020i	0.0995873	−	0.716393i
$155$			11.5423i			0.927099i
$156$	6.00618	−	1.71051i	0.480879	−	0.136950i
$157$	18.4221	−	10.6360i	1.47025	−	0.848848i	0.470805	−	0.882237i	$-0.343964\pi$
$157$	18.4221	−	10.6360i	1.47025	−	0.848848i	0.999442	+	0.0333895i	$0.0106302\pi$
$158$	−7.84799			−0.624352
$159$	8.12588	+	8.32498i	0.644424	+	0.660214i
$160$	−1.58996	+	0.917964i	−0.125697	+	0.0725714i
$161$	−6.48744	−	0.901834i	−0.511282	−	0.0710744i
$162$	−8.98946	−	0.435496i	−0.706278	−	0.0342158i
$163$		−	10.0187i		−	0.784728i	−0.919810	−	0.392364i	$-0.871657\pi$
$163$		−	10.0187i		−	0.784728i	0.919810	−	0.392364i	$-0.128343\pi$
$164$	4.35184	−	2.51254i	0.339822	−	0.196196i
$165$	−2.91800	+	10.3857i	−0.227166	+	0.808527i
$166$	−11.3267	+	6.53950i	−0.879126	+	0.507564i
$167$	−3.11618	−	1.79913i	−0.241137	−	0.139221i	0.374562	−	0.927202i	$-0.377793\pi$
$167$	−3.11618	−	1.79913i	−0.241137	−	0.139221i	−0.615699	+	0.787981i	$0.711126\pi$
$168$	−1.83518	+	4.19906i	−0.141587	+	0.323965i
$169$	5.86551	−	11.6015i	0.451193	−	0.892426i
$170$	−5.06412	−	2.92377i	−0.388400	−	0.224243i
$171$	5.35056	−	2.91883i	0.409168	−	0.223208i
$172$	−1.05794			−0.0806674
$173$	−0.953613			−0.0725019			−0.0362509	−	0.999343i	$-0.511542\pi$
$173$	−0.953613			−0.0725019			−0.0362509	+	0.999343i	$0.511542\pi$
$174$	3.52435	−	0.898778i	0.267180	−	0.0681362i
$175$	0.593560	−	4.26984i	0.0448689	−	0.322770i
$176$	−1.69625	−	2.93798i	−0.127859	−	0.221459i
$177$	2.90889	−	10.3533i	0.218645	−	0.778201i
$178$	−4.61906	−	2.66681i	−0.346213	−	0.199886i
$179$			17.7581i			1.32730i	0.748043	+	0.663650i	$0.230994\pi$
$179$			17.7581i			1.32730i	−0.748043	+	0.663650i	$0.769006\pi$
$180$	2.86852	−	4.70184i	0.213807	−	0.350454i
$181$		−	5.51564i		−	0.409975i	−0.978765	−	0.204987i	$-0.934285\pi$
$181$		−	5.51564i		−	0.409975i	0.978765	−	0.204987i	$-0.0657153\pi$
$182$	3.83064	+	8.73648i	0.283946	+	0.647591i
$183$	−19.6039	+	4.99938i	−1.44916	+	0.369565i
$184$	−2.14393	+	1.23780i	−0.158053	+	0.0912519i
$185$	−0.925149			−0.0680183
$186$	10.4833	+	2.94542i	0.768673	+	0.215969i
$187$	5.40264	−	9.35765i	0.395080	−	0.684299i
$188$	−10.0977	+	5.82991i	−0.736451	+	0.425190i
$189$	−1.19957	−	13.6953i	−0.0872558	−	0.996186i
$190$			3.72995i			0.270599i
$191$		−	20.1785i		−	1.46007i	−0.683411	−	0.730034i	$-0.739504\pi$
$191$		−	20.1785i		−	1.46007i	0.683411	−	0.730034i	$-0.260496\pi$
$192$	0.428009	+	1.67834i	0.0308889	+	0.121123i
$193$			4.54274i			0.326994i	0.986544	+	0.163497i	$0.0522774\pi$
$193$			4.54274i			0.326994i	−0.986544	+	0.163497i	$0.947723\pi$
$194$	4.79907	−	8.31223i	0.344553	−	0.596783i
$195$	−3.14037	−	11.0269i	−0.224886	−	0.789654i
$196$	−6.73459	−	1.90927i	−0.481042	−	0.136377i
$197$	5.74363	−	9.94826i	0.409217	−	0.708784i	−0.585585	−	0.810611i	$-0.699135\pi$
$197$	5.74363	−	9.94826i	0.409217	−	0.708784i	0.994802	+	0.101826i	$0.0324687\pi$
$198$	8.68821	+	5.30055i	0.617444	+	0.376694i
$199$	5.94498	+	3.43234i	0.421429	+	0.243312i	0.695688	−	0.718344i	$-0.255099\pi$
$199$	5.94498	+	3.43234i	0.421429	+	0.243312i	−0.274260	+	0.961656i	$0.588433\pi$
$200$	−0.814684	−	1.41107i	−0.0576068	−	0.0997780i
$201$	16.6624	−	4.24924i	1.17528	−	0.299718i
$202$	−4.69535	−	8.13258i	−0.330363	−	0.572206i
$203$	2.08897	+	5.14815i	0.146617	+	0.361329i
$204$	−3.94781	+	3.85339i	−0.276402	+	0.269791i
$205$	−4.61284	−	7.98966i	−0.322174	−	0.558022i
$206$			13.3536i			0.930389i
$207$	3.86797	−	6.34005i	0.268843	−	0.440664i
$208$	3.17131	+	1.71545i	0.219891	+	0.118945i
$209$	−6.89232			−0.476752
$210$	7.70918	+	3.36925i	0.531984	+	0.232501i
$211$	−2.63957	+	4.57187i	−0.181715	+	0.314740i	−0.942465	−	0.334305i	$-0.891498\pi$
$211$	−2.63957	+	4.57187i	−0.181715	+	0.314740i	0.760749	+	0.649046i	$0.224832\pi$
$212$			6.71653i			0.461293i
$213$	19.2622	−	18.8016i	1.31983	−	1.28826i
$214$	−11.5796	−	6.68547i	−0.791563	−	0.457009i
$215$			1.94231i			0.132464i
$216$	−3.53845	−	3.80518i	−0.240761	−	0.258910i
$217$	−2.29025	+	16.4751i	−0.155472	+	1.11841i
$218$	3.82963	+	2.21104i	0.259375	+	0.149750i
$219$	−11.0951	+	10.8298i	−0.749741	+	0.731810i
$220$	−5.39393	+	3.11418i	−0.363658	+	0.209958i
$221$	0.318619	+	11.4795i	0.0214327	+	0.772193i
$222$	−0.236084	+	0.840268i	−0.0158449	+	0.0563951i
$223$	14.2982	−	24.7653i	0.957481	−	1.65841i	0.228896	−	0.973451i	$-0.426488\pi$
$223$	14.2982	−	24.7653i	0.957481	−	1.65841i	0.728585	−	0.684955i	$-0.240178\pi$
$224$	−2.45161	+	0.994793i	−0.163805	+	0.0664674i
$225$	4.17283	+	2.54578i	0.278189	+	0.169719i
$226$	13.8390	+	7.98994i	0.920556	+	0.531483i
$227$	5.20466	+	3.00491i	0.345446	+	0.199443i	0.662677	−	0.748905i	$-0.269420\pi$
$227$	5.20466	+	3.00491i	0.345446	+	0.199443i	−0.317232	+	0.948348i	$0.602753\pi$
$228$	3.38773	+	0.951826i	0.224358	+	0.0630362i
$229$	7.02836	−	12.1735i	0.464447	−	0.804446i	−0.534729	−	0.845023i	$-0.679586\pi$
$229$	7.02836	−	12.1735i	0.464447	−	0.804446i	0.999176	+	0.0405773i	$0.0129197\pi$
$230$	2.27251	+	3.93611i	0.149845	+	0.259539i
$231$	−6.22582	+	14.2453i	−0.409629	+	0.937271i
$232$	1.81857	+	1.04995i	0.119395	+	0.0689328i
$233$	24.0450	+	13.8824i	1.57524	+	0.909465i	0.995510	+	0.0946555i	$0.0301750\pi$
$233$	24.0450	+	13.8824i	1.57524	+	0.909465i	0.579729	+	0.814809i	$0.303158\pi$
$234$	−10.8166	+	0.0383424i	−0.707102	+	0.00250652i
$235$	10.7033	+	18.5387i	0.698207	+	1.20933i
$236$	5.37709	−	3.10446i	0.350019	−	0.202083i
$237$	13.0864	+	3.67679i	0.850053	+	0.238833i
$238$	−6.64824	−	5.17814i	−0.430941	−	0.335649i
$239$	5.31347			0.343700			0.171850	−	0.985123i	$-0.445026\pi$
$239$	5.31347			0.343700			0.171850	+	0.985123i	$0.445026\pi$
$240$	3.08130	−	0.785793i	0.198897	−	0.0507227i
$241$	−9.62885	+	16.6777i	−0.620249	+	1.07430i	0.369190	+	0.929354i	$0.379635\pi$
$241$	−9.62885	+	16.6777i	−0.620249	+	1.07430i	−0.989439	+	0.144949i	$0.953698\pi$
$242$	−0.254496	−	0.440801i	−0.0163596	−	0.0283357i
$243$	14.7858	+	4.93775i	0.948507	+	0.316757i
$244$	−10.1157	−	5.84028i	−0.647589	−	0.373885i
$245$	−3.50529	+	12.3642i	−0.223945	+	0.789921i
$246$	−8.43375	+	2.15077i	−0.537716	+	0.137128i
$247$	6.23974	−	3.83719i	0.397025	−	0.244155i
$248$	3.14345	+	5.44461i	0.199609	+	0.345733i
$249$	21.9509	−	5.59792i	1.39108	−	0.354754i
$250$	−10.5404	+	6.08552i	−0.666635	+	0.384882i
$251$	4.75595	+	8.23755i	0.300193	+	0.519950i	0.976180	−	0.216964i	$-0.0696156\pi$
$251$	4.75595	+	8.23755i	0.300193	+	0.519950i	−0.675986	+	0.736914i	$0.736282\pi$
$252$	5.02740	−	6.14209i	0.316696	−	0.386915i
$253$	−7.27328	+	4.19923i	−0.457267	+	0.264003i
$254$	0.951973			0.0597321
$255$	7.07455	+	7.24789i	0.443026	+	0.453880i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−2.63187	−	4.55853i	−0.164171	−	0.284353i	0.772189	−	0.635392i	$-0.219162\pi$
$257$	−2.63187	−	4.55853i	−0.164171	−	0.284353i	−0.936361	+	0.351039i	$0.885828\pi$
$258$	1.76410	+	0.495648i	0.109828	+	0.0308577i
$259$	−1.32053	−	0.183570i	−0.0820538	−	0.0114065i
$260$	3.14944	−	5.82231i	0.195320	−	0.361084i
$261$	−6.29788	−	0.152462i	−0.389829	−	0.00943714i
$262$	−9.91520			−0.612563
$263$			10.8500i			0.669042i	0.942388	+	0.334521i	$0.108575\pi$
$263$			10.8500i			0.669042i	−0.942388	+	0.334521i	$0.891425\pi$
$264$	1.45202	+	5.69374i	0.0893654	+	0.350425i
$265$	12.3311			0.757491
$266$	−0.740104	+	5.32402i	−0.0453787	+	0.326437i
$267$	6.45280	+	6.61091i	0.394905	+	0.404581i
$268$	8.59785	+	4.96397i	0.525197	+	0.303223i
$269$	−9.05587	+	15.6852i	−0.552146	+	0.956346i	0.445973	+	0.895046i	$0.352858\pi$
$269$	−9.05587	+	15.6852i	−0.552146	+	0.956346i	−0.998119	+	0.0612993i	$0.980476\pi$
$270$	−6.98604	+	6.49634i	−0.425157	+	0.395354i
$271$	4.33664	+	7.51129i	0.263432	+	0.456278i	0.967152	−	0.254200i	$-0.0818121\pi$
$271$	4.33664	+	7.51129i	0.263432	+	0.456278i	−0.703719	+	0.710478i	$0.748479\pi$
$272$	−3.18506			−0.193123
$273$	−2.29449	−	16.3626i	−0.138869	−	0.990311i
$274$	3.18307			0.192296
$275$	−2.76381	−	4.78705i	−0.166664	−	0.288670i
$276$	4.15489	−	1.05958i	0.250095	−	0.0637792i
$277$	9.14175	−	15.8340i	0.549275	−	0.951372i	−0.449050	−	0.893507i	$-0.648237\pi$
$277$	9.14175	−	15.8340i	0.549275	−	0.951372i	0.998324	−	0.0578650i	$-0.0184293\pi$
$278$	0.0981681	+	0.0566774i	0.00588773	+	0.00339928i
$279$	−16.1008	−	9.82288i	−0.963931	−	0.588081i
$280$	1.82637	+	4.50098i	0.109146	+	0.268985i
$281$	−2.73779			−0.163323			−0.0816614	−	0.996660i	$-0.526023\pi$
$281$	−2.73779			−0.163323			−0.0816614	+	0.996660i	$0.526023\pi$
$282$	19.5691	−	4.99051i	1.16532	−	0.297180i
$283$		−	5.31213i		−	0.315773i	−0.987457	−	0.157887i	$-0.949532\pi$
$283$		−	5.31213i		−	0.315773i	0.987457	−	0.157887i	$-0.0504681\pi$
$284$	15.5406			0.922165
$285$	1.74748	−	6.21963i	0.103512	−	0.368419i
$286$	10.7587	+	5.81964i	0.636173	+	0.344123i
$287$	−4.99890	−	12.3195i	−0.295076	−	0.727198i
$288$	0.0726040	−	2.99912i	0.00427823	−	0.176725i
$289$	3.42770	+	5.93695i	0.201629	+	0.349232i
$290$	1.92764	−	3.33877i	0.113195	−	0.196059i
$291$	−11.8967	+	11.6122i	−0.697395	+	0.680716i
$292$	−8.95148			−0.523846
$293$	2.86877	−	1.65628i	0.167595	−	0.0967612i	−0.413856	−	0.910342i	$-0.635818\pi$
$293$	2.86877	−	1.65628i	0.167595	−	0.0967612i	0.581451	+	0.813581i	$0.302485\pi$
$294$	10.3353	+	6.33885i	0.602769	+	0.369689i
$295$	−5.69957	−	9.87195i	−0.331842	−	0.574767i
$296$	−0.436402	+	0.251957i	−0.0253653	+	0.0146447i
$297$	−12.0042	−	12.9090i	−0.696551	−	0.749058i
$298$	10.8563	+	18.8036i	0.628888	+	1.08927i
$299$	4.24677	−	7.85091i	0.245597	−	0.454030i
$300$	0.697383	+	2.73462i	0.0402634	+	0.157884i
$301$	−0.385397	+	2.77240i	−0.0222139	+	0.159798i
$302$	−4.69698	−	2.71180i	−0.270281	−	0.156047i
$303$	4.01930	+	15.7607i	0.230903	+	0.905430i
$304$	1.01582	+	1.75945i	0.0582613	+	0.100912i
$305$	−10.7223	+	18.5716i	−0.613959	+	1.06341i
$306$	8.38823	−	4.57592i	0.479523	−	0.261588i
$307$	−23.8813			−1.36298			−0.681490	−	0.731827i	$-0.738668\pi$
$307$	−23.8813			−1.36298			−0.681490	+	0.731827i	$0.738668\pi$
$308$	−8.31706	+	3.37483i	−0.473909	+	0.192299i
$309$	6.25617	−	22.2669i	0.355901	−	1.26672i
$310$	9.99592	−	5.77115i	0.567730	−	0.327779i
$311$	15.8352	+	27.4274i	0.897934	+	1.55527i	0.830131	+	0.557569i	$0.188266\pi$
$311$	15.8352	+	27.4274i	0.897934	+	1.55527i	0.0678034	+	0.997699i	$0.478401\pi$
$312$	−4.48443	−	4.34625i	−0.253881	−	0.246058i
$313$	12.5081	+	7.22158i	0.707002	+	0.408188i	0.809950	−	0.586499i	$-0.199494\pi$
$313$	12.5081	+	7.22158i	0.707002	+	0.408188i	−0.102948	+	0.994687i	$0.532828\pi$
$314$	−18.4221	−	10.6360i	−1.03962	−	0.600226i
$315$	−11.2764	−	9.22994i	−0.635355	−	0.520048i
$316$	3.92399	+	6.79656i	0.220742	+	0.382336i
$317$	12.7938	−	22.1596i	0.718573	−	1.24461i	−0.242992	−	0.970028i	$-0.578129\pi$
$317$	12.7938	−	22.1596i	0.718573	−	1.24461i	0.961565	−	0.274577i	$-0.0885379\pi$
$318$	3.14670	−	11.1997i	0.176458	−	0.628048i
$319$	6.16949	+	3.56196i	0.345425	+	0.199431i
$320$	1.58996	+	0.917964i	0.0888815	+	0.0513158i
$321$	16.1766	+	16.5730i	0.902891	+	0.925013i
$322$	2.46271	+	6.06921i	0.137242	+	0.338224i
$323$	−3.23545	+	5.60396i	−0.180025	+	0.311813i
$324$	4.11758	+	8.00285i	0.228754	+	0.444603i
$325$	5.16724	+	2.79510i	0.286627	+	0.155044i
$326$	−8.67648	+	5.00937i	−0.480546	+	0.277443i
$327$	−5.34998	−	5.48106i	−0.295854	−	0.303103i
$328$	−4.35184	−	2.51254i	−0.240290	−	0.138732i
$329$	11.5991	+	28.5853i	0.639480	+	1.57596i
$330$	10.4533	−	2.66580i	0.575435	−	0.146747i
$331$		−	8.37563i		−	0.460366i	−0.973147	−	0.230183i	$-0.926067\pi$
$331$		−	8.37563i		−	0.460366i	0.973147	−	0.230183i	$-0.0739325\pi$
$332$	11.3267	+	6.53950i	0.621636	+	0.358902i
$333$	0.787333	−	1.29053i	0.0431456	−	0.0707205i
$334$			3.59825i			0.196888i
$335$	9.11349	−	15.7850i	0.497923	−	0.862428i
$336$	4.55408	−	0.510221i	0.248446	−	0.0278348i
$337$	−9.14343			−0.498074			−0.249037	−	0.968494i	$-0.580114\pi$
$337$	−9.14343			−0.498074			−0.249037	+	0.968494i	$0.580114\pi$
$338$	−12.9800	+	0.721089i	−0.706018	+	0.0392221i
$339$	−19.3330	−	19.8067i	−1.05002	−	1.07575i
$340$			5.84754i			0.317127i
$341$	10.6641	+	18.4708i	0.577494	+	1.00025i
$342$	−5.20306	−	3.17431i	−0.281349	−	0.171647i
$343$	−7.45669	+	16.9528i	−0.402623	+	0.915366i
$344$	0.528972	+	0.916206i	0.0285202	+	0.0493985i
$345$	−1.94531	−	7.62808i	−0.104732	−	0.410682i
$346$	0.476807	+	0.825853i	0.0256333	+	0.0443982i
$347$	−26.9305	−	15.5484i	−1.44571	−	0.834679i	−0.447486	−	0.894291i	$-0.647680\pi$
$347$	−26.9305	−	15.5484i	−1.44571	−	0.834679i	−0.998222	+	0.0596117i	$0.981014\pi$
$348$	−2.54054	−	2.60279i	−0.136187	−	0.139524i
$349$	−14.0331	+	24.3060i	−0.751175	+	1.30107i	0.196079	+	0.980588i	$0.437179\pi$
$349$	−14.0331	+	24.3060i	−0.751175	+	1.30107i	−0.947254	+	0.320485i	$0.896154\pi$
$350$	−3.99457	+	1.62088i	−0.213519	+	0.0866398i
$351$	18.0545	+	5.00365i	0.963676	+	0.267075i
$352$	−1.69625	+	2.93798i	−0.0904102	+	0.156595i
$353$		−	28.3322i		−	1.50797i	−0.656893	−	0.753984i	$-0.728130\pi$
$353$		−	28.3322i		−	1.50797i	0.656893	−	0.753984i	$-0.271870\pi$
$354$	−10.4207	+	2.65747i	−0.553852	+	0.141243i
$355$		−	28.5314i		−	1.51429i
$356$			5.33363i			0.282682i
$357$	8.65988	+	11.7492i	0.458329	+	0.621833i
$358$	15.3789	−	8.87903i	0.812802	−	0.469271i
$359$	−10.8679	+	18.8238i	−0.573588	+	0.993483i	0.422606	+	0.906314i	$0.361116\pi$
$359$	−10.8679	+	18.8238i	−0.573588	+	0.993483i	−0.996193	+	0.0871698i	$0.972218\pi$
$360$	−5.50617	−	0.133296i	−0.290201	−	0.00702530i
$361$	−14.8724			−0.782760
$362$	−4.77669	+	2.75782i	−0.251057	+	0.144948i
$363$	0.217853	+	0.854260i	0.0114343	+	0.0448370i
$364$	5.65070	−	7.68568i	0.296177	−	0.402839i
$365$			16.4343i			0.860209i
$366$	14.1315	+	14.4778i	0.738667	+	0.756765i
$367$		−	15.7687i		−	0.823121i	−0.911382	−	0.411561i	$-0.864984\pi$
$367$		−	15.7687i		−	0.823121i	0.911382	−	0.411561i	$-0.135016\pi$
$368$	2.14393	+	1.23780i	0.111760	+	0.0645248i
$369$	15.0708	+	0.364840i	0.784554	+	0.0189928i
$370$	0.462574	+	0.801202i	0.0240481	+	0.0416525i
$371$	17.6010	+	2.44675i	0.913799	+	0.127029i
$372$	−2.69085	−	10.5515i	−0.139514	−	0.547071i
$373$	−7.24507			−0.375135			−0.187568	−	0.982252i	$-0.560060\pi$
$373$	−7.24507			−0.375135			−0.187568	+	0.982252i	$0.560060\pi$
$374$	−10.8053			−0.558728
$375$	20.4271	−	5.20931i	1.05485	−	0.269008i
$376$	10.0977	+	5.82991i	0.520750	+	0.300655i
$377$	−7.56841	+	0.210065i	−0.389793	+	0.0108189i
$378$	−11.2607	+	7.88650i	−0.579187	+	0.405638i
$379$	4.24213	+	2.44920i	0.217904	+	0.125807i	0.604979	−	0.796241i	$-0.293181\pi$
$379$	4.24213	+	2.44920i	0.217904	+	0.125807i	−0.387076	+	0.922048i	$0.626515\pi$
$380$	3.23023	−	1.86497i	0.165707	−	0.0956711i
$381$	−1.58740	−	0.446000i	−0.0813250	−	0.0228493i
$382$	−17.4751	+	10.0893i	−0.894106	+	0.516212i
$383$		−	7.91504i		−	0.404439i	−0.979340	−	0.202220i	$-0.935184\pi$
$383$		−	7.91504i		−	0.404439i	0.979340	−	0.202220i	$-0.0648155\pi$
$384$	1.23948	−	1.20983i	0.0632518	−	0.0617391i
$385$	6.19594	+	15.2695i	0.315774	+	0.778207i
$386$	3.93413	−	2.27137i	0.200242	−	0.115610i
$387$	−2.70941	−	1.65297i	−0.137727	−	0.0840252i
$388$	−9.59814			−0.487272
$389$	−2.27718	+	1.31473i	−0.115458	+	0.0666595i	−0.556617	−	0.830769i	$-0.687901\pi$
$389$	−2.27718	+	1.31473i	−0.115458	+	0.0666595i	0.441159	+	0.897429i	$0.354567\pi$
$390$	−7.97940	+	8.23309i	−0.404053	+	0.416899i
$391$			7.88494i			0.398758i
$392$	1.71381	+	6.78696i	0.0865606	+	0.342793i
$393$	16.5334	+	4.64528i	0.834002	+	0.234323i
$394$	−11.4873			−0.578720
$395$	12.4780	−	7.20417i	0.627836	−	0.362481i
$396$	0.246308	−	10.1745i	0.0123775	−	0.511287i
$397$	−33.1058			−1.66153			−0.830766	−	0.556622i	$-0.812097\pi$
$397$	−33.1058			−1.66153			−0.830766	+	0.556622i	$0.812097\pi$
$398$		−	6.86468i		−	0.344095i
$399$	3.72842	−	8.53099i	0.186655	−	0.427083i
$400$	−0.814684	+	1.41107i	−0.0407342	+	0.0705537i
$401$	−3.49869	−	6.05991i	−0.174716	−	0.302618i	0.765347	−	0.643618i	$-0.222567\pi$
$401$	−3.49869	−	6.05991i	−0.174716	−	0.302618i	−0.940063	+	0.341001i	$0.889234\pi$
$402$	−12.0112	−	12.3054i	−0.599062	−	0.613740i
$403$	−19.9377	−	10.7848i	−0.993169	−	0.537231i
$404$	−4.69535	+	8.13258i	−0.233602	+	0.404611i
$405$	14.6927	−	7.55958i	0.730084	−	0.375638i
$406$	3.41394	−	4.38318i	0.169431	−	0.217534i
$407$	−1.48049	+	0.854760i	−0.0733851	+	0.0423689i
$408$	5.31104	+	1.49220i	0.262936	+	0.0738751i
$409$	−15.9202	+	27.5747i	−0.787206	+	1.36348i	0.140467	+	0.990085i	$0.455140\pi$
$409$	−15.9202	+	27.5747i	−0.787206	+	1.36348i	−0.927673	+	0.373395i	$0.878194\pi$
$410$	−4.61284	+	7.98966i	−0.227812	+	0.394581i
$411$	−5.30772	−	1.49127i	−0.261811	−	0.0735590i
$412$	11.5646	−	6.67680i	0.569745	−	0.328942i
$413$	−6.17659	−	15.2219i	−0.303930	−	0.749019i
$414$	−7.42463	−	0.179738i	−0.364901	−	0.00883366i
$415$	12.0061	−	20.7951i	0.589354	−	1.02079i
$416$	−0.100036	−	3.60416i	−0.00490465	−	0.176709i
$417$	−0.137140	−	0.140501i	−0.00671580	−	0.00688034i
$418$	3.44616	+	5.96893i	0.168557	+	0.291950i
$419$	−5.19733	+	9.00204i	−0.253906	+	0.439778i	−0.964598	−	0.263725i	$-0.915049\pi$
$419$	−5.19733	+	9.00204i	−0.253906	+	0.439778i	0.710692	+	0.703504i	$0.248382\pi$
$420$	−0.936728	−	8.36097i	−0.0457077	−	0.407974i
$421$		−	0.111490i		−	0.00543368i	−0.999996	−	0.00271684i	$-0.999135\pi$
$421$		−	0.111490i		−	0.00543368i	0.999996	−	0.00271684i	$-0.000864798\pi$
$422$	5.27914			0.256984
$423$	−34.9692	−	0.846550i	−1.70026	−	0.0411607i
$424$	5.81668	−	3.35826i	0.282483	−	0.163092i
$425$	−5.18963			−0.251734
$426$	−25.9137	−	7.28079i	−1.25552	−	0.352756i
$427$	−18.9898	+	24.3811i	−0.918979	+	1.17988i
$428$			13.3709i			0.646309i
$429$	−15.2134	−	14.7446i	−0.734509	−	0.711876i
$430$	1.68209	−	0.971154i	0.0811175	−	0.0468332i
$431$	−38.6276			−1.86063			−0.930313	−	0.366767i	$-0.880465\pi$
$431$	−38.6276			−1.86063			−0.930313	+	0.366767i	$0.880465\pi$
$432$	−1.52616	+	4.96698i	−0.0734273	+	0.238974i
$433$	5.30602	−	3.06343i	0.254991	−	0.147219i	−0.367056	−	0.930199i	$-0.619634\pi$
$433$	5.30602	−	3.06343i	0.254991	−	0.147219i	0.622047	+	0.782980i	$0.286301\pi$
$434$	15.4130	−	6.25416i	0.739848	−	0.300209i
$435$	−4.77853	+	4.66425i	−0.229113	+	0.223634i
$436$		−	4.42208i		−	0.211779i
$437$	4.35570	−	2.51477i	0.208362	−	0.120298i
$438$	14.9265	+	4.19378i	0.713214	+	0.200386i
$439$	30.2778	−	17.4809i	1.44508	−	0.834318i	0.446899	−	0.894585i	$-0.352528\pi$
$439$	30.2778	−	17.4809i	1.44508	−	0.834318i	0.998182	+	0.0602668i	$0.0191951\pi$
$440$	5.39393	+	3.11418i	0.257145	+	0.148463i
$441$	−14.2642	−	15.4121i	−0.679250	−	0.733907i
$442$	9.78221	−	6.01567i	0.465292	−	0.286136i
$443$	−7.76750	−	4.48457i	−0.369045	−	0.213068i	0.303996	−	0.952673i	$-0.401679\pi$
$443$	−7.76750	−	4.48457i	−0.369045	−	0.213068i	−0.673041	+	0.739605i	$0.735012\pi$
$444$	0.845735	−	0.215679i	0.0401368	−	0.0102357i
$445$	9.79216			0.464193
$446$	−28.5965			−1.35408
$447$	−9.29317	−	36.4410i	−0.439552	−	1.72360i
$448$	2.08732	+	1.62576i	0.0986166	+	0.0768099i
$449$	−9.32220	−	16.1465i	−0.439942	−	0.762002i	0.557742	−	0.830014i	$-0.311668\pi$
$449$	−9.32220	−	16.1465i	−0.439942	−	0.762002i	−0.997684	+	0.0680121i	$0.978334\pi$
$450$	0.118299	−	4.88667i	0.00557665	−	0.230360i
$451$	−14.7636	−	8.52375i	−0.695190	−	0.401368i
$452$		−	15.9799i		−	0.751631i
$453$	6.56167	+	6.72244i	0.308294	+	0.315848i
$454$		−	6.00983i		−	0.282055i
$455$	−14.1104	−	10.3743i	−0.661504	−	0.486353i
$456$	−0.869560	−	3.40977i	−0.0407209	−	0.159677i
$457$	−24.6765	+	14.2470i	−1.15432	+	0.666445i	−0.949935	−	0.312446i	$-0.898852\pi$
$457$	−24.6765	+	14.2470i	−1.15432	+	0.666445i	−0.204382	+	0.978891i	$0.565518\pi$
$458$	−14.0567			−0.656828
$459$	−16.1311	+	3.70039i	−0.752934	+	0.172719i
$460$	2.27251	−	3.93611i	0.105956	−	0.183522i
$461$	−10.2455	+	5.91523i	−0.477180	+	0.275500i	−0.719240	−	0.694761i	$-0.755510\pi$
$461$	−10.2455	+	5.91523i	−0.477180	+	0.275500i	0.242061	+	0.970261i	$0.422177\pi$
$462$	15.4497	−	1.73092i	0.718784	−	0.0805296i
$463$			10.9649i			0.509582i	0.966996	+	0.254791i	$0.0820067\pi$
$463$			10.9649i			0.509582i	−0.966996	+	0.254791i	$0.917993\pi$
$464$		−	2.09991i		−	0.0974857i
$465$	−19.3718	+	4.94020i	−0.898347	+	0.229096i
$466$		−	27.7648i		−	1.28618i
$467$	10.0288	−	17.3705i	0.464080	−	0.803810i	−0.535080	−	0.844802i	$-0.679718\pi$
$467$	10.0288	−	17.3705i	0.464080	−	0.803810i	0.999159	+	0.0409918i	$0.0130517\pi$
$468$	5.44150	+	9.34827i	0.251533	+	0.432124i
$469$	16.1404	−	20.7228i	0.745296	−	0.956889i
$470$	10.7033	−	18.5387i	0.493707	−	0.855125i
$471$	25.7357	+	26.3662i	1.18584	+	1.21489i
$472$	−5.37709	−	3.10446i	−0.247501	−	0.142894i
$473$	1.79453	+	3.10822i	0.0825126	+	0.142916i
$474$	−3.35901	−	13.1716i	−0.154284	−	0.604989i
$475$	1.65514	+	2.86679i	0.0759432	+	0.131538i
$476$	−1.16028	+	8.34661i	−0.0531814	+	0.382566i
$477$	−10.4942	+	17.2011i	−0.480494	+	0.787585i
$478$	−2.65674	−	4.60160i	−0.121516	−	0.210472i
$479$			30.7699i			1.40591i	0.711232	+	0.702957i	$0.248138\pi$
$479$			30.7699i			1.40591i	−0.711232	+	0.702957i	$0.751862\pi$
$480$	−2.22117	−	2.27559i	−0.101382	−	0.103866i
$481$	0.864437	−	1.59807i	0.0394149	−	0.0728656i
$482$	19.2577			0.877164
$483$	−1.26310	−	11.2741i	−0.0574732	−	0.512989i
$484$	−0.254496	+	0.440801i	−0.0115680	+	0.0200364i
$485$			17.6215i			0.800151i
$486$	−3.11666	−	15.2737i	−0.141374	−	0.692830i
$487$	31.0757	+	17.9415i	1.40817	+	0.813009i	0.995212	−	0.0977403i	$-0.0311614\pi$
$487$	31.0757	+	17.9415i	1.40817	+	0.813009i	0.412960	+	0.910749i	$0.364495\pi$
$488$			11.6806i			0.528754i
$489$	16.8148	−	4.28811i	0.760391	−	0.193915i
$490$	12.4604	−	3.14644i	0.562902	−	0.142142i
$491$	−32.3384	−	18.6706i	−1.45941	−	0.842592i	−0.460430	−	0.887696i	$-0.652305\pi$
$491$	−32.3384	−	18.6706i	−1.45941	−	0.842592i	−0.998982	+	0.0451043i	$0.985638\pi$
$492$	6.07950	+	6.22846i	0.274085	+	0.280801i
$493$	5.79226	−	3.34416i	0.260870	−	0.150614i
$494$	−6.44297	−	3.48517i	−0.289883	−	0.156805i
$495$	−18.6796	−	0.452204i	−0.839587	−	0.0203251i
$496$	3.14345	−	5.44461i	0.141145	−	0.244470i
$497$	5.66127	−	40.7250i	0.253943	−	1.82676i
$498$	−15.8234	−	16.2111i	−0.709064	−	0.726437i
$499$	−19.1199	−	11.0389i	−0.855925	−	0.494169i	0.00672032	−	0.999977i	$-0.497861\pi$
$499$	−19.1199	−	11.0389i	−0.855925	−	0.494169i	−0.862646	+	0.505809i	$0.831194\pi$
$500$	10.5404	+	6.08552i	0.471382	+	0.272153i
$501$	1.68579	−	6.00003i	0.0753153	−	0.268062i
$502$	4.75595	−	8.23755i	0.212269	−	0.367660i
$503$	18.0289	+	31.2270i	0.803870	+	1.39234i	0.917051	+	0.398769i	$0.130563\pi$
$503$	18.0289	+	31.2270i	0.803870	+	1.39234i	−0.113181	+	0.993574i	$0.536104\pi$
$504$	−7.83291	−	1.28281i	−0.348905	−	0.0571408i
$505$	14.9308	+	8.62032i	0.664413	+	0.383599i
$506$	7.27328	+	4.19923i	0.323337	+	0.186678i
$507$	21.9818	+	4.87873i	0.976244	+	0.216672i
$508$	−0.475986	−	0.824432i	−0.0211185	−	0.0365783i
$509$	−23.5652	+	13.6054i	−1.04451	+	0.603047i	−0.921107	−	0.389310i	$-0.872714\pi$
$509$	−23.5652	+	13.6054i	−1.04451	+	0.603047i	−0.123402	+	0.992357i	$0.539380\pi$
$510$	2.73958	−	9.75069i	0.121311	−	0.431768i
$511$	−3.26092	+	23.4578i	−0.144255	+	1.03771i
$512$	1.00000			0.0441942
$513$	7.18885	+	7.73076i	0.317396	+	0.341321i
$514$	−2.63187	+	4.55853i	−0.116087	+	0.201068i
$515$	−12.2581	−	21.2317i	−0.540157	−	0.935580i
$516$	−0.452809	−	1.77558i	−0.0199338	−	0.0781657i
$517$	34.2564	+	19.7779i	1.50659	+	0.869832i
$518$	0.501289	+	1.23540i	0.0220254	+	0.0542803i
$519$	−0.408155	−	1.60048i	−0.0179160	−	0.0702534i
$520$	−6.61699	+	0.183658i	−0.290174	+	0.00805394i
$521$	7.90186	+	13.6864i	0.346187	+	0.599613i	0.985569	−	0.169276i	$-0.0541430\pi$
$521$	7.90186	+	13.6864i	0.346187	+	0.599613i	−0.639382	+	0.768889i	$0.720810\pi$
$522$	3.01690	+	5.53035i	0.132046	+	0.242057i
$523$	−1.52777	+	0.882061i	−0.0668049	+	0.0385698i	−0.533030	−	0.846096i	$-0.678947\pi$
$523$	−1.52777	+	0.882061i	−0.0668049	+	0.0385698i	0.466225	+	0.884666i	$0.345614\pi$
$524$	4.95760	+	8.58681i	0.216574	+	0.375117i
$525$	7.42027	−	0.831337i	0.323847	−	0.0362825i
$526$	9.39641	−	5.42502i	0.409703	−	0.236542i
$527$	20.0241			0.872265
$528$	4.20491	−	4.10435i	0.182995	−	0.178619i
$529$	−8.43570	+	14.6111i	−0.366769	+	0.635263i
$530$	−6.16553	−	10.6790i	−0.267813	−	0.463867i
$531$	18.6213	+	0.450793i	0.808097	+	0.0195627i
$532$	4.98079	−	2.02106i	0.215945	−	0.0876241i
$533$	18.1112	−	0.502686i	0.784482	−	0.0217737i
$534$	2.49881	−	8.89375i	0.108134	−	0.384870i
$535$	24.5481			1.06131
$536$		−	9.92794i		−	0.428822i
$537$	−29.8040	+	7.60060i	−1.28614	+	0.327990i
$538$	18.1117			0.780853
$539$	5.81410	+	23.0247i	0.250431	+	0.991744i
$540$	9.11901	+	2.80192i	0.392420	+	0.120575i
$541$	−18.1904	−	10.5022i	−0.782066	−	0.451526i	0.0550960	−	0.998481i	$-0.482454\pi$
$541$	−18.1904	−	10.5022i	−0.782066	−	0.451526i	−0.837162	+	0.546955i	$0.815787\pi$
$542$	4.33664	−	7.51129i	0.186275	−	0.322638i
$543$	9.25710	−	2.36074i	0.397260	−	0.101309i
$544$	1.59253	+	2.75834i	0.0682791	+	0.118263i
$545$	−8.11861			−0.347763
$546$	−13.0232	+	10.1684i	−0.557342	+	0.435167i
$547$	−37.9155			−1.62115			−0.810575	−	0.585635i	$-0.800845\pi$
$547$	−37.9155			−1.62115			−0.810575	+	0.585635i	$0.800845\pi$
$548$	−1.59153	−	2.75662i	−0.0679870	−	0.117757i
$549$	−16.7813	−	30.7621i	−0.716207	−	1.31289i
$550$	−2.76381	+	4.78705i	−0.117849	+	0.204121i
$551$	−3.69469	−	2.13313i	−0.157399	−	0.0908743i
$552$	−2.99507	−	3.06845i	−0.127479	−	0.130602i
$553$	19.2402	−	7.80712i	0.818176	−	0.331993i
$554$	−18.2835			−0.776792
$555$	−0.395972	−	1.55271i	−0.0168081	−	0.0659088i
$556$		−	0.113355i		−	0.00480731i
$557$	15.2846			0.647630			0.323815	−	0.946120i	$-0.395035\pi$
$557$	15.2846			0.647630			0.323815	+	0.946120i	$0.395035\pi$
$558$	−0.456454	+	18.8552i	−0.0193232	+	0.798203i
$559$	−3.35507	−	1.81485i	−0.141904	−	0.0767598i
$560$	2.98478	−	3.83217i	0.126130	−	0.161939i
$561$	18.0177	+	5.06229i	0.760706	+	0.213730i
$562$	1.36889	+	2.37099i	0.0577433	+	0.100014i
$563$	−9.39707	+	16.2762i	−0.396039	+	0.685960i	−0.993233	−	0.116137i	$-0.962949\pi$
$563$	−9.39707	+	16.2762i	−0.396039	+	0.685960i	0.597194	+	0.802097i	$0.296282\pi$
$564$	−14.1065	−	14.4521i	−0.593989	−	0.608543i
$565$	−29.3379			−1.23426
$566$	−4.60044	+	2.65607i	−0.193371	+	0.111643i
$567$	22.4719	−	7.87498i	0.943730	−	0.330718i
$568$	−7.77030	−	13.4586i	−0.326035	−	0.564709i
$569$	18.6401	−	10.7619i	0.781433	−	0.451160i	−0.0555050	−	0.998458i	$-0.517677\pi$
$569$	18.6401	−	10.7619i	0.781433	−	0.451160i	0.836938	+	0.547298i	$0.184344\pi$
$570$	−6.26010	+	1.59645i	−0.262207	+	0.0668679i
$571$	19.8438	+	34.3705i	0.830438	+	1.43836i	0.897691	+	0.440625i	$0.145243\pi$
$571$	19.8438	+	34.3705i	0.830438	+	1.43836i	−0.0672531	+	0.997736i	$0.521424\pi$
$572$	−0.339370	−	12.2271i	−0.0141898	−	0.511240i
$573$	33.8664	−	8.63659i	1.41479	−	0.360799i
$574$	−8.16956	+	10.4889i	−0.340991	+	0.437800i
$575$	3.49326	+	2.01683i	0.145679	+	0.0841077i
$576$	−2.63362	+	1.43668i	−0.109734	+	0.0598618i
$577$	20.4728	+	35.4599i	0.852293	+	1.47621i	0.879134	+	0.476575i	$0.158122\pi$
$577$	20.4728	+	35.4599i	0.852293	+	1.47621i	−0.0268412	+	0.999640i	$0.508545\pi$
$578$	3.42770	−	5.93695i	0.142573	−	0.246944i
$579$	−7.62425	+	1.94433i	−0.316853	+	0.0808038i
$580$	−3.85528			−0.160082
$581$	21.2633	−	27.3001i	0.882151	−	1.13260i
$582$	16.0047	+	4.49674i	0.663418	+	0.186396i
$583$	19.7330	−	11.3929i	0.817259	−	0.471845i
$584$	4.47574	+	7.75221i	0.185207	+	0.320789i
$585$	17.1627	−	9.99020i	0.709592	−	0.413044i
$586$	−2.86877	−	1.65628i	−0.118508	−	0.0684205i
$587$	−32.8994	−	18.9945i	−1.35790	−	0.783986i	−0.368563	−	0.929603i	$-0.620150\pi$
$587$	−32.8994	−	18.9945i	−1.35790	−	0.783986i	−0.989341	+	0.145616i	$0.953483\pi$
$588$	0.321941	−	12.1201i	0.0132766	−	0.499824i
$589$	−6.38636	−	11.0615i	−0.263145	−	0.455781i
$590$	−5.69957	+	9.87195i	−0.234648	+	0.406422i
$591$	19.1548	+	5.38180i	0.787925	+	0.221378i
$592$	0.436402	+	0.251957i	0.0179360	+	0.0103554i
$593$	−13.8054	−	7.97057i	−0.566921	−	0.327312i	0.188997	−	0.981978i	$-0.439476\pi$
$593$	−13.8054	−	7.97057i	−0.566921	−	0.327312i	−0.755919	+	0.654665i	$0.772810\pi$
$594$	−5.17748	+	16.8504i	−0.212434	+	0.691381i
$595$	15.3238	+	2.13019i	0.628214	+	0.0873294i
$596$	10.8563	−	18.8036i	0.444691	−	0.770227i
$597$	−3.21611	+	11.4467i	−0.131627	+	0.468484i
$598$	−8.92247	+	0.247648i	−0.364867	+	0.0101271i
$599$	−3.66862	+	2.11808i	−0.149896	+	0.0865423i	−0.573072	−	0.819505i	$-0.694248\pi$
$599$	−3.66862	+	2.11808i	−0.149896	+	0.0865423i	0.423176	+	0.906047i	$0.360915\pi$
$600$	2.01956	−	1.97126i	0.0824483	−	0.0804765i
$601$	2.17316	+	1.25468i	0.0886451	+	0.0511793i	0.543667	−	0.839301i	$-0.317035\pi$
$601$	2.17316	+	1.25468i	0.0886451	+	0.0511793i	−0.455022	+	0.890480i	$0.650369\pi$
$602$	2.59366	−	1.05243i	0.105710	−	0.0428940i
$603$	14.2633	+	26.1464i	0.580847	+	1.06476i
$604$			5.42361i			0.220684i
$605$	0.809278	+	0.467237i	0.0329018	+	0.0189959i
$606$	11.6395	−	11.3612i	0.472824	−	0.461516i
$607$		−	42.8486i		−	1.73917i	−0.493781	−	0.869586i	$-0.664386\pi$
$607$		−	42.8486i		−	1.73917i	0.493781	−	0.869586i	$-0.335614\pi$
$608$	1.01582	−	1.75945i	0.0411970	−	0.0713552i
$609$	−7.74623	+	5.70945i	−0.313893	+	0.231359i
$610$	21.4447			0.868269
$611$	−42.0239	+	1.16640i	−1.70011	+	0.0471874i
$612$	−8.15698	−	4.97646i	−0.329726	−	0.201161i
$613$		−	21.1506i		−	0.854266i	−0.904189	−	0.427133i	$-0.859524\pi$
$613$		−	21.1506i		−	0.854266i	0.904189	−	0.427133i	$-0.140476\pi$
$614$	11.9407	+	20.6819i	0.481886	+	0.834652i
$615$	11.4350	−	11.1615i	0.461104	−	0.450076i
$616$	7.08122	+	5.51537i	0.285310	+	0.222221i
$617$	−17.5132	−	30.3337i	−0.705053	−	1.22119i	−0.966672	−	0.256017i	$-0.917590\pi$
$617$	−17.5132	−	30.3337i	−0.705053	−	1.22119i	0.261619	−	0.965171i	$-0.415744\pi$
$618$	−22.4118	+	5.71545i	−0.901535	+	0.229909i
$619$	−15.4257	−	26.7180i	−0.620010	−	1.07389i	−0.989483	−	0.144648i	$-0.953795\pi$
$619$	−15.4257	−	26.7180i	−0.620010	−	1.07389i	0.369473	−	0.929241i	$-0.379538\pi$
$620$	−9.99592	−	5.77115i	−0.401446	−	0.231775i
$621$	12.2963	+	3.77816i	0.493432	+	0.151612i
$622$	15.8352	−	27.4274i	0.634935	−	1.09974i
$623$	13.9771	+	1.94298i	0.559979	+	0.0778439i
$624$	−1.52175	+	6.05676i	−0.0609186	+	0.242464i
$625$	7.09916	−	12.2961i	0.283967	−	0.491844i
$626$		−	14.4432i		−	0.577265i
$627$	−2.94997	−	11.5676i	−0.117811	−	0.461966i
$628$			21.2721i			0.848848i
$629$			1.60499i			0.0639953i
$630$	−2.35514	+	14.3807i	−0.0938312	+	0.572939i
$631$	−13.3366	+	7.69988i	−0.530921	+	0.306527i	−0.741391	−	0.671073i	$-0.765834\pi$
$631$	−13.3366	+	7.69988i	−0.530921	+	0.306527i	0.210470	+	0.977600i	$0.432500\pi$
$632$	3.92399	−	6.79656i	0.156088	−	0.270352i
$633$	−8.80289	−	2.47328i	−0.349883	−	0.0983042i
$634$	−25.5877			−1.01622
$635$	−1.51360	+	0.873877i	−0.0600653	+	0.0346787i
$636$	−11.2726	+	2.87473i	−0.446987	+	0.113990i
$637$	−18.0822	−	17.6077i	−0.716444	−	0.697644i
$638$		−	7.12392i		−	0.282039i
$639$	39.7997	+	24.2812i	1.57445	+	0.960551i
$640$		−	1.83593i		−	0.0725714i
$641$	−8.06018	−	4.65355i	−0.318358	−	0.183804i	0.332302	−	0.943173i	$-0.392175\pi$
$641$	−8.06018	−	4.65355i	−0.318358	−	0.183804i	−0.650660	+	0.759369i	$0.725508\pi$
$642$	6.26430	−	22.2958i	0.247232	−	0.879947i
$643$	3.03048	+	5.24895i	0.119511	+	0.206998i	0.919574	−	0.392917i	$-0.128534\pi$
$643$	3.03048	+	5.24895i	0.119511	+	0.206998i	−0.800063	+	0.599916i	$0.795201\pi$
$644$	4.02473	−	5.16737i	0.158597	−	0.203623i
$645$	−3.25984	+	0.831325i	−0.128356	+	0.0327334i
$646$	6.47090			0.254594
$647$	11.3010			0.444290			0.222145	−	0.975014i	$-0.428694\pi$
$647$	11.3010			0.444290			0.222145	+	0.975014i	$0.428694\pi$
$648$	4.87188	−	7.56735i	0.191385	−	0.297274i
$649$	−18.2417	−	10.5319i	−0.716050	−	0.413412i
$650$	−0.162995	−	5.87251i	−0.00639318	−	0.230339i
$651$	−28.6311	+	3.20770i	−1.12214	+	0.125720i
$652$	8.67648	+	5.00937i	0.339797	+	0.196182i
$653$	−31.1098	+	17.9612i	−1.21742	+	0.702878i	−0.964365	−	0.264574i	$-0.914769\pi$
$653$	−31.1098	+	17.9612i	−1.21742	+	0.702878i	−0.253055	+	0.967452i	$0.581435\pi$
$654$	−2.07175	+	7.37375i	−0.0810117	+	0.288336i
$655$	15.7648	−	9.10179i	0.615981	−	0.355637i
$656$			5.02507i			0.196196i
$657$	−22.9249	−	13.9861i	−0.894384	−	0.545651i
$658$	18.9561	−	24.3378i	0.738985	−	0.948786i
$659$	14.9107	−	8.60870i	0.580839	−	0.335348i	−0.180628	−	0.983552i	$-0.557813\pi$
$659$	14.9107	−	8.60870i	0.580839	−	0.335348i	0.761467	+	0.648204i	$0.224480\pi$
$660$	−7.53529	−	7.71992i	−0.293311	−	0.300497i
$661$	5.99169			0.233050			0.116525	−	0.993188i	$-0.462825\pi$
$661$	5.99169			0.233050			0.116525	+	0.993188i	$0.462825\pi$
$662$	−7.25351	+	4.18782i	−0.281916	+	0.162764i
$663$	−19.1300	+	5.44806i	−0.742949	+	0.211585i
$664$		−	13.0790i		−	0.507564i
$665$	−3.71052	−	9.14437i	−0.143888	−	0.354603i
$666$	−1.51130	−	0.0365861i	−0.0585616	−	0.00141768i
$667$	−5.19853			−0.201288
$668$	3.11618	−	1.79913i	0.120569	−	0.0696103i
$669$	47.6842	+	13.3975i	1.84358	+	0.517977i
$670$	−18.2270			−0.704170
$671$			39.6262i			1.52975i
$672$	−2.71891	−	3.68884i	−0.104884	−	0.142300i
$673$	−16.9593	+	29.3743i	−0.653732	+	1.13230i	0.328478	+	0.944512i	$0.393464\pi$
$673$	−16.9593	+	29.3743i	−0.653732	+	1.13230i	−0.982210	+	0.187786i	$0.939869\pi$
$674$	4.57171	+	7.91844i	0.176096	+	0.305007i
$675$	−2.48667	+	8.09303i	−0.0957120	+	0.311501i
$676$	7.11447	+	10.8805i	0.273634	+	0.418479i
$677$	6.91552	−	11.9780i	0.265785	−	0.460353i	−0.701984	−	0.712193i	$-0.747702\pi$
$677$	6.91552	−	11.9780i	0.265785	−	0.460353i	0.967769	+	0.251840i	$0.0810356\pi$
$678$	−7.48659	+	26.6462i	−0.287521	+	1.02334i
$679$	−3.49649	+	25.1524i	−0.134183	+	0.965261i
$680$	5.06412	−	2.92377i	0.194200	−	0.112121i
$681$	−2.81561	+	10.0213i	−0.107894	+	0.384017i
$682$	10.6641	−	18.4708i	0.408350	−	0.707283i
$683$	−2.34804	+	4.06692i	−0.0898451	+	0.155616i	−0.907446	−	0.420170i	$-0.861971\pi$
$683$	−2.34804	+	4.06692i	−0.0898451	+	0.155616i	0.817600	+	0.575786i	$0.195304\pi$
$684$	−0.147505	+	6.09314i	−0.00564000	+	0.232977i
$685$	−5.06095	+	2.92194i	−0.193369	+	0.111642i
$686$	18.4099	−	2.01872i	0.702894	−	0.0770752i
$687$	23.4394	+	6.58559i	0.894268	+	0.251256i
$688$	0.528972	−	0.916206i	0.0201669	−	0.0349300i
$689$	−11.5219	+	21.3002i	−0.438948	+	0.811474i
$690$	−5.63345	+	5.49873i	−0.214462	+	0.209333i
$691$	11.9009	+	20.6130i	0.452732	+	0.784156i	0.998555	−	0.0537454i	$-0.0171159\pi$
$691$	11.9009	+	20.6130i	0.452732	+	0.784156i	−0.545822	+	0.837901i	$0.683783\pi$
$692$	0.476807	−	0.825853i	0.0181255	−	0.0313942i
$693$	−26.5731	−	4.35192i	−1.00943	−	0.165316i
$694$			31.0967i			1.18042i
$695$	−0.208111			−0.00789411
$696$	−0.983809	+	3.50156i	−0.0372912	+	0.132726i
$697$	−13.8609	+	8.00258i	−0.525018	+	0.303119i
$698$	28.0662			1.06232
$699$	−13.0078	+	46.2973i	−0.492001	+	1.75113i
$700$	3.40101	+	2.64896i	0.128546	+	0.100121i
$701$		−	35.3397i		−	1.33476i	−0.744716	−	0.667382i	$-0.767415\pi$
$701$		−	35.3397i		−	1.33476i	0.744716	−	0.667382i	$-0.232585\pi$
$702$	−4.69394	−	18.1374i	−0.177161	−	0.684554i
$703$	0.886611	−	0.511885i	0.0334392	−	0.0193061i
$704$	3.39249			0.127859
$705$	−26.5330	+	25.8984i	−0.999290	+	0.975392i
$706$	−24.5364	+	14.1661i	−0.923438	+	0.533147i
$707$	19.6014	+	15.2670i	0.737186	+	0.574175i
$708$	7.51177	+	7.69582i	0.282310	+	0.289227i
$709$			12.3456i			0.463648i	0.972758	+	0.231824i	$0.0744694\pi$
$709$			12.3456i			0.463648i	−0.972758	+	0.231824i	$0.925531\pi$
$710$	−24.7090	+	14.2657i	−0.927310	+	0.535383i
$711$	−0.569795	+	23.5371i	−0.0213690	+	0.882709i
$712$	4.61906	−	2.66681i	0.173107	−	0.0999431i
$713$	−13.4787	−	7.78193i	−0.504781	−	0.291435i
$714$	5.84515	−	13.3743i	0.218749	−	0.500519i
$715$	−22.4481	+	0.623059i	−0.839510	+	0.0233011i
$716$	−15.3789	−	8.87903i	−0.574738	−	0.331825i
$717$	2.27421	+	8.91779i	0.0849320	+	0.333041i
$718$	21.7359			0.811176
$719$	3.75984			0.140218			0.0701091	−	0.997539i	$-0.477665\pi$
$719$	3.75984			0.140218			0.0701091	+	0.997539i	$0.477665\pi$
$720$	2.63765	+	4.83513i	0.0982994	+	0.180195i
$721$	−13.2841	−	32.7378i	−0.494724	−	1.21922i
$722$	7.43622	+	12.8799i	0.276747	+	0.479341i
$723$	−32.1119	−	9.02225i	−1.19426	−	0.335541i
$724$	4.77669	+	2.75782i	0.177524	+	0.102494i
$725$		−	3.42152i		−	0.127072i
$726$	0.630884	−	0.615796i	0.0234143	−	0.0228544i
$727$		−	10.4236i		−	0.386592i	−0.981141	−	0.193296i	$-0.938082\pi$
$727$		−	10.4236i		−	0.386592i	0.981141	−	0.193296i	$-0.0619177\pi$
$728$	−9.48134	−	1.05081i	−0.351402	−	0.0389455i
$729$	−1.95878	+	26.9289i	−0.0725473	+	0.997365i
$730$	14.2325	−	8.21714i	0.526768	−	0.304130i
$731$	3.36961			0.124630
$732$	5.47235	−	19.4772i	0.202264	−	0.719896i
$733$	−17.7435	+	30.7327i	−0.655373	+	1.13514i	0.326428	+	0.945222i	$0.394155\pi$
$733$	−17.7435	+	30.7327i	−0.655373	+	1.13514i	−0.981800	+	0.189917i	$0.939178\pi$
$734$	−13.6561	+	7.88437i	−0.504057	+	0.291017i
$735$	−22.2516	−	0.591061i	−0.820763	−	0.0218016i
$736$		−	2.47560i		−	0.0912519i
$737$		−	33.6804i		−	1.24063i
$738$	−7.21944	−	13.2341i	−0.265751	−	0.487154i
$739$			6.23954i			0.229525i	0.993393	+	0.114763i	$0.0366108\pi$
$739$			6.23954i			0.229525i	−0.993393	+	0.114763i	$0.963389\pi$
$740$	0.462574	−	0.801202i	0.0170046	−	0.0294528i
$741$	9.11075	+	8.83002i	0.334692	+	0.324379i
$742$	−6.68155	−	16.4663i	−0.245287	−	0.604497i
$743$	21.5450	−	37.3170i	0.790408	−	1.36903i	−0.135306	−	0.990804i	$-0.543202\pi$
$743$	21.5450	−	37.3170i	0.790408	−	1.36903i	0.925714	−	0.378223i	$-0.123465\pi$
$744$	−7.79246	+	7.60610i	−0.285685	+	0.278853i
$745$	−34.5221	−	19.9314i	−1.26479	−	0.730229i
$746$	3.62253	+	6.27441i	0.132630	+	0.229723i
$747$	18.7904	+	34.4451i	0.687504	+	1.26028i
$748$	5.40264	+	9.35765i	0.197540	+	0.342150i
$749$	35.0393	+	4.87088i	1.28031	+	0.177978i
$750$	−14.7249	−	15.0857i	−0.537679	−	0.550853i
$751$	15.6943	+	27.1834i	0.572695	+	0.991937i	0.996288	+	0.0860840i	$0.0274353\pi$
$751$	15.6943	+	27.1834i	0.572695	+	0.991937i	−0.423593	+	0.905853i	$0.639231\pi$
$752$		−	11.6598i		−	0.425190i
$753$	−11.7898	+	11.5078i	−0.429644	+	0.419368i
$754$	3.96613	+	6.44940i	0.144438	+	0.234873i
$755$	9.95736			0.362385
$756$	12.4603	+	5.80879i	0.453175	+	0.211264i
$757$	6.13845	−	10.6321i	0.223106	−	0.386430i	−0.732644	−	0.680612i	$-0.761714\pi$
$757$	6.13845	−	10.6321i	0.223106	−	0.386430i	0.955749	+	0.294182i	$0.0950472\pi$
$758$		−	4.89839i		−	0.177918i
$759$	−10.1607	−	10.4097i	−0.368811	−	0.377848i
$760$	−3.23023	−	1.86497i	−0.117173	−	0.0676497i
$761$			16.9601i			0.614801i	0.951580	+	0.307401i	$0.0994592\pi$
$761$			16.9601i			0.614801i	−0.951580	+	0.307401i	$0.900541\pi$
$762$	0.407452	+	1.59773i	0.0147604	+	0.0578796i
$763$	−11.5883	−	1.61091i	−0.419524	−	0.0583189i
$764$	17.4751	+	10.0893i	0.632228	+	0.365017i
$765$	−9.13642	+	14.9756i	−0.330328	+	0.541445i
$766$	−6.85462	+	3.95752i	−0.247668	+	0.142991i
$767$	22.3780	−	0.621114i	0.808022	−	0.0224271i
$768$	−1.66749	−	0.468501i	−0.0601702	−	0.0169056i
$769$	−18.2706	+	31.6457i	−0.658856	+	1.14117i	0.322056	+	0.946720i	$0.395626\pi$
$769$	−18.2706	+	31.6457i	−0.658856	+	1.14117i	−0.980912	+	0.194451i	$0.937707\pi$
$770$	10.1258	−	13.0006i	0.364910	−	0.468509i
$771$	6.52427	−	6.36824i	0.234966	−	0.229347i
$772$	−3.93413	−	2.27137i	−0.141593	−	0.0817485i
$773$	0.840536	+	0.485284i	0.0302320	+	0.0174545i	0.515040	−	0.857166i	$-0.327777\pi$
$773$	0.840536	+	0.485284i	0.0302320	+	0.0174545i	−0.484808	+	0.874621i	$0.661110\pi$
$774$	−0.0768109	+	3.17290i	−0.00276091	+	0.114048i
$775$	5.12183	−	8.87127i	0.183982	−	0.318666i
$776$	4.79907	+	8.31223i	0.172276	+	0.298392i
$777$	−0.257107	−	2.29486i	−0.00922366	−	0.0823277i
$778$	2.27718	+	1.31473i	0.0816408	+	0.0471354i
$779$	8.84137	+	5.10457i	0.316775	+	0.182890i
$780$	11.1198	+	2.79382i	0.398152	+	0.100035i
$781$	−26.3607	−	45.6580i	−0.943259	−	1.63377i
$782$	6.82856	−	3.94247i	0.244189	−	0.140982i
$783$	−2.43966	−	10.6352i	−0.0871865	−	0.380071i
$784$	5.02077	−	4.87769i	0.179313	−	0.174203i
$785$	39.0540			1.39390
$786$	−4.24379	−	16.6410i	−0.151371	−	0.593566i
$787$	11.7542	−	20.3588i	0.418990	−	0.725713i	−0.576848	−	0.816852i	$-0.695717\pi$
$787$	11.7542	−	20.3588i	0.418990	−	0.725713i	0.995838	+	0.0911389i	$0.0290507\pi$
$788$	5.74363	+	9.94826i	0.204608	+	0.354392i
$789$	−18.2100	+	4.64391i	−0.648293	+	0.165328i
$790$	−12.4780	−	7.20417i	−0.443947	−	0.256313i
$791$	−41.8761	−	5.82129i	−1.48894	−	0.206981i
$792$	−8.93452	+	4.87394i	−0.317474	+	0.173188i
$793$	−22.0612	−	35.8742i	−0.783418	−	1.27393i
$794$	16.5529	+	28.6705i	0.587440	+	1.01748i
$795$	5.27780	+	20.6956i	0.187184	+	0.733999i
$796$	−5.94498	+	3.43234i	−0.210714	+	0.121656i
$797$	21.5529	+	37.3307i	0.763443	+	1.32232i	0.941066	+	0.338224i	$0.109826\pi$
$797$	21.5529	+	37.3307i	0.763443	+	1.32232i	−0.177623	+	0.984099i	$0.556841\pi$
$798$	−9.25226	+	1.03658i	−0.327526	+	0.0366947i
$799$	32.1618	−	18.5686i	1.13780	−	0.656911i
$800$	1.62937			0.0576068
$801$	−8.33346	+	13.6595i	−0.294448	+	0.482634i
$802$	−3.49869	+	6.05991i	−0.123543	+	0.213983i
$803$	15.1839	+	26.2993i	0.535828	+	0.928082i
$804$	−4.65125	+	16.5547i	−0.164037	+	0.583839i
$805$	−9.48693	−	7.38912i	−0.334370	−	0.260432i
$806$	0.628914	+	22.6590i	0.0221525	+	0.798129i
$807$	−30.2011	−	8.48538i	−1.06313	−	0.298699i
$808$	9.39069			0.330363
$809$			23.2160i			0.816230i	0.912930	+	0.408115i	$0.133814\pi$
$809$			23.2160i			0.816230i	−0.912930	+	0.408115i	$0.866186\pi$
$810$	−13.8931	−	8.94442i	−0.488154	−	0.314275i
$811$	−14.3001			−0.502145			−0.251072	−	0.967968i	$-0.580783\pi$
$811$	−14.3001			−0.502145			−0.251072	+	0.967968i	$0.580783\pi$
$812$	−5.50292	−	0.764972i	−0.193115	−	0.0268453i
$813$	−10.7503	+	10.4932i	−0.377031	+	0.368014i
$814$	1.48049	+	0.854760i	0.0518911	+	0.0299593i
$815$	9.19684	−	15.9294i	0.322151	−	0.557982i
$816$	−1.36323	−	5.34560i	−0.0477227	−	0.187133i
$817$	−1.07468	−	1.86140i	−0.0375983	−	0.0651222i
$818$	31.8405			1.11328
$819$	26.4799	−	10.8543i	0.925283	−	0.379279i
$820$	9.22567			0.322174
$821$	6.02169	+	10.4299i	0.210158	+	0.364005i	0.951764	−	0.306831i	$-0.0992687\pi$
$821$	6.02169	+	10.4299i	0.210158	+	0.364005i	−0.741606	+	0.670836i	$0.765935\pi$
$822$	1.36238	+	5.34226i	0.0475185	+	0.186333i
$823$	18.7328	−	32.4461i	0.652983	−	1.13100i	−0.329412	−	0.944186i	$-0.606851\pi$
$823$	18.7328	−	32.4461i	0.652983	−	1.13100i	0.982395	−	0.186814i	$-0.0598162\pi$
$824$	−11.5646	−	6.67680i	−0.402870	−	0.232597i
$825$	6.85135	−	6.68749i	0.238533	−	0.232829i
$826$	−10.0942	+	12.9600i	−0.351223	+	0.450937i
$827$	12.7766			0.444287			0.222144	−	0.975014i	$-0.428695\pi$
$827$	12.7766			0.444287			0.222144	+	0.975014i	$0.428695\pi$
$828$	3.55666	+	6.51979i	0.123602	+	0.226578i
$829$			33.7625i			1.17262i	0.810086	+	0.586311i	$0.199420\pi$
$829$			33.7625i			1.17262i	−0.810086	+	0.586311i	$0.800580\pi$
$830$	−24.0121			−0.833472
$831$	30.4875	+	8.56585i	1.05760	+	0.297146i
$832$	−3.07128	+	1.88872i	−0.106477	+	0.0654794i
$833$	21.4501	+	6.08115i	0.743201	+	0.210699i
$834$	−0.0531068	+	0.189017i	−0.00183894	+	0.00654514i
$835$	−3.30307	−	5.72108i	−0.114307	−	0.197986i
$836$	3.44616	−	5.96893i	0.119188	−	0.206440i
$837$	9.59480	−	31.2269i	0.331645	−	1.07936i
$838$	10.3947			0.359078
$839$	30.8994	−	17.8398i	1.06677	−	0.615897i	0.139469	−	0.990226i	$-0.455460\pi$
$839$	30.8994	−	17.8398i	1.06677	−	0.615897i	0.927296	+	0.374329i	$0.122127\pi$
$840$	−6.77245	+	4.99172i	−0.233672	+	0.172231i
$841$	−12.2952	−	21.2959i	−0.423972	−	0.734341i
$842$	−0.0965530	+	0.0557449i	−0.00332744	+	0.00192110i
$843$	−1.17180	−	4.59493i	−0.0403588	−	0.158258i
$844$	−2.63957	−	4.57187i	−0.0908577	−	0.157370i
$845$	19.9757	−	13.0617i	0.687186	−	0.449335i
$846$	16.7515	+	30.7075i	0.575928	+	1.05575i
$847$	1.06243	+	0.827499i	0.0365055	+	0.0284332i
$848$	−5.81668	−	3.35826i	−0.199746	−	0.115323i
$849$	8.91554	−	2.27364i	0.305980	−	0.0780311i
$850$	2.59482	+	4.49435i	0.0890014	+	0.154155i
$851$	0.623744	−	1.08036i	0.0213817	−	0.0370341i
$852$	6.65151	+	26.0823i	0.227877	+	0.893566i
$853$	−50.6470			−1.73412			−0.867061	−	0.498202i	$-0.833994\pi$
$853$	−50.6470			−1.73412			−0.867061	+	0.498202i	$0.833994\pi$
$854$	30.6095	+	4.25509i	1.04744	+	0.145606i
$855$	11.1866	+	0.270809i	0.382572	+	0.00926147i
$856$	11.5796	−	6.68547i	0.395782	−	0.228505i
$857$	7.48332	+	12.9615i	0.255625	+	0.442756i	0.965065	−	0.262010i	$-0.0843854\pi$
$857$	7.48332	+	12.9615i	0.255625	+	0.442756i	−0.709440	+	0.704766i	$0.751052\pi$
$858$	−5.16251	+	20.5475i	−0.176245	+	0.701480i
$859$	42.5746	+	24.5804i	1.45263	+	0.838674i	0.998630	−	0.0523306i	$-0.0166650\pi$
$859$	42.5746	+	24.5804i	1.45263	+	0.838674i	0.453995	+	0.891004i	$0.349998\pi$
$860$	−1.68209	−	0.971154i	−0.0573587	−	0.0331161i
$861$	18.5367	−	13.6627i	0.631729	−	0.465623i
$862$	19.3138	+	33.4525i	0.657830	+	1.13940i
$863$	−25.6886	+	44.4940i	−0.874451	+	1.51459i	−0.0171055	+	0.999854i	$0.505445\pi$
$863$	−25.6886	+	44.4940i	−0.874451	+	1.51459i	−0.857346	+	0.514741i	$0.827888\pi$
$864$	5.06461	−	1.16180i	0.172301	−	0.0395251i
$865$	−1.51621	−	0.875383i	−0.0515526	−	0.0297639i
$866$	−5.30602	−	3.06343i	−0.180306	−	0.104100i
$867$	−8.49710	+	8.29389i	−0.288577	+	0.281675i
$868$	−13.1228	−	10.2210i	−0.445416	−	0.346923i
$869$	13.3121	−	23.0573i	0.451582	−	0.782164i
$870$	6.42862	+	1.80620i	0.217951	+	0.0612360i
$871$	18.7510	+	30.4915i	0.635355	+	1.03316i
$872$	−3.82963	+	2.21104i	−0.129688	+	0.0748752i
$873$	−24.5810	−	14.9965i	−0.831939	−	0.507554i
$874$	−4.35570	−	2.51477i	−0.147334	−	0.0850632i
$875$	19.7872	−	25.4049i	0.668929	−	0.858841i
$876$	−3.83131	−	15.0236i	−0.129448	−	0.507600i
$877$			47.4326i			1.60169i	0.598875	+	0.800843i	$0.295615\pi$
$877$			47.4326i			1.60169i	−0.598875	+	0.800843i	$0.704385\pi$
$878$	−30.2778	−	17.4809i	−1.02183	−	0.589952i
$879$	4.00766	+	4.10585i	0.135175	+	0.138487i
$880$		−	6.22837i		−	0.209958i
$881$	5.06534	−	8.77342i	0.170656	−	0.295584i	−0.767994	−	0.640457i	$-0.778745\pi$
$881$	5.06534	−	8.77342i	0.170656	−	0.295584i	0.938649	+	0.344873i	$0.112078\pi$
$882$	−6.21510	+	20.0592i	−0.209273	+	0.675429i
$883$	−12.1164			−0.407751			−0.203875	−	0.978997i	$-0.565354\pi$
$883$	−12.1164			−0.407751			−0.203875	+	0.978997i	$0.565354\pi$
$884$	−10.1008	−	5.46380i	−0.339728	−	0.183768i
$885$	14.1290	−	13.7911i	0.474940	−	0.463582i
$886$			8.96913i			0.301324i
$887$	−2.02991	−	3.51590i	−0.0681576	−	0.118052i	0.829933	−	0.557864i	$-0.188379\pi$
$887$	−2.02991	−	3.51590i	−0.0681576	−	0.118052i	−0.898090	+	0.439811i	$0.855045\pi$
$888$	−0.609651	−	0.624589i	−0.0204586	−	0.0209598i
$889$	−2.33386	+	0.947016i	−0.0782753	+	0.0317619i
$890$	−4.89608	−	8.48026i	−0.164117	−	0.284259i
$891$	16.5278	−	25.6722i	0.553702	−	0.860050i
$892$	14.2982	+	24.7653i	0.478741	+	0.829203i
$893$	−20.5149	−	11.8443i	−0.686505	−	0.396354i
$894$	−26.9122	+	26.2686i	−0.900079	+	0.878554i
$895$	−16.3013	+	28.2346i	−0.544891	+	0.943779i
$896$	0.364289	−	2.62055i	0.0121700	−	0.0875465i
$897$	14.9941	+	3.76724i	0.500639	+	0.125784i
$898$	−9.32220	+	16.1465i	−0.311086	+	0.538817i
$899$			13.2019i			0.440308i
$900$	−4.29113	+	2.34089i	−0.143038	+	0.0780295i
$901$		−	21.3925i		−	0.712689i
$902$			17.0475i			0.567620i
$903$	−4.81796	+	0.539784i	−0.160332	+	0.0179629i
$904$	−13.8390	+	7.98994i	−0.460278	+	0.265742i
$905$	5.06316	−	8.76966i	0.168305	−	0.291513i
$906$	2.54097	−	9.04379i	0.0844180	−	0.300460i
$907$	−13.3755			−0.444126			−0.222063	−	0.975032i	$-0.571279\pi$
$907$	−13.3755			−0.444126			−0.222063	+	0.975032i	$0.571279\pi$
$908$	−5.20466	+	3.00491i	−0.172723	+	0.0997215i
$909$	−24.7315	+	13.4915i	−0.820292	+	0.447483i
$910$	−1.92921	+	17.4071i	−0.0639526	+	0.577038i
$911$		−	21.8063i		−	0.722475i	−0.932474	−	0.361238i	$-0.882354\pi$
$911$		−	21.8063i		−	0.722475i	0.932474	−	0.361238i	$-0.117646\pi$
$912$	−2.51817	+	2.45795i	−0.0833850	+	0.0813908i
$913$		−	44.3704i		−	1.46845i
$914$	24.6765	+	14.2470i	0.816225	+	0.471248i
$915$	−35.7587	−	10.0468i	−1.18214	−	0.332139i
$916$	7.02836	+	12.1735i	0.232224	+	0.402223i
$917$	24.3082	−	9.86357i	0.802727	−	0.325724i
$918$	11.2702	+	12.1197i	0.371971	+	0.400010i
$919$	9.13726			0.301410			0.150705	−	0.988579i	$-0.451846\pi$
$919$	9.13726			0.301410			0.150705	+	0.988579i	$0.451846\pi$
$920$	−4.54503			−0.149845
$921$	−10.2214	−	40.0809i	−0.336807	−	1.32071i
$922$	10.2455	+	5.91523i	0.337417	+	0.194808i
$923$	49.2842	+	26.6591i	1.62221	+	0.877495i
$924$	−9.22386	−	12.5144i	−0.303443	−	0.411692i
$925$	0.711059	+	0.410530i	0.0233795	+	0.0134981i
$926$	9.49589	−	5.48245i	0.312054	−	0.180165i
$927$	40.0491	+	0.969524i	1.31538	+	0.0318433i
$928$	−1.81857	+	1.04995i	−0.0596976	+	0.0344664i
$929$		−	13.5735i		−	0.445331i	−0.974895	−	0.222665i	$-0.928524\pi$
$929$		−	13.5735i		−	0.445331i	0.974895	−	0.222665i	$-0.0714758\pi$
$930$	13.9643	+	14.3064i	0.457906	+	0.469125i
$931$	−3.48185	−	13.7887i	−0.114113	−	0.451905i
$932$	−24.0450	+	13.8824i	−0.787620	+	0.454732i
$933$	−39.2548	+	38.3160i	−1.28515	+	1.25441i
$934$	−20.0577			−0.656308
$935$	17.1800	−	9.91886i	0.561845	−	0.324382i
$936$	5.37509	−	9.38661i	0.175690	−	0.306811i
$937$		−	0.647634i		−	0.0211573i	−0.999944	−	0.0105786i	$-0.996633\pi$
$937$		−	0.647634i		−	0.0211573i	0.999944	−	0.0105786i	$-0.00336735\pi$
$938$	−26.0167	−	3.61664i	−0.849475	−	0.118087i
$939$	−6.76663	+	24.0837i	−0.220821	+	0.785943i
$940$	−21.4066			−0.698207
$941$	−43.1576	+	24.9171i	−1.40690	+	0.812273i	−0.995088	−	0.0989966i	$-0.968437\pi$
$941$	−43.1576	+	24.9171i	−1.40690	+	0.812273i	−0.411810	+	0.911270i	$0.635103\pi$
$942$	9.96599	−	35.4709i	0.324709	−	1.15570i
$943$	12.4401			0.405105
$944$			6.20893i			0.202083i
$945$	10.6645	−	22.8761i	0.346917	−	0.744161i
$946$	1.79453	−	3.10822i	0.0583452	−	0.101057i
$947$	−5.43523	−	9.41410i	−0.176621	−	0.305917i	0.764100	−	0.645098i	$-0.223183\pi$
$947$	−5.43523	−	9.41410i	−0.176621	−	0.305917i	−0.940721	+	0.339181i	$0.889850\pi$
$948$	−9.72740	+	9.49476i	−0.315931	+	0.308375i
$949$	−28.3880	−	15.3558i	−0.921512	−	0.498470i
$950$	1.65514	−	2.86679i	0.0537000	−	0.0930111i
$951$	42.6671	+	11.9879i	1.38357	+	0.388733i
$952$	7.80852	−	3.16847i	0.253076	−	0.102691i
$953$	26.6142	−	15.3657i	0.862119	−	0.497744i	−0.00260249	−	0.999997i	$-0.500828\pi$
$953$	26.6142	−	15.3657i	0.862119	−	0.497744i	0.864721	+	0.502252i	$0.167495\pi$
$954$	20.1437	+	0.487646i	0.652176	+	0.0157881i
$955$	18.5232	−	32.0831i	0.599396	−	1.03818i
$956$	−2.65674	+	4.60160i	−0.0859250	+	0.148826i
$957$	−3.33756	+	11.8790i	−0.107888	+	0.383994i
$958$	26.6476	−	15.3850i	0.860943	−	0.497066i
$959$	−7.80364	+	3.16649i	−0.251993	+	0.102251i
$960$	−0.860135	+	3.06138i	−0.0277607	+	0.0988057i
$961$	−4.26254	+	7.38293i	−0.137501	+	0.238159i
$962$	−1.81619	+	0.0504093i	−0.0585562	+	0.00162526i
$963$	−20.8913	+	34.2432i	−0.673212	+	1.10347i
$964$	−9.62885	−	16.6777i	−0.310124	−	0.537151i
$965$	−4.17008	+	7.22278i	−0.134240	+	0.232510i
$966$	−9.13210	+	6.73093i	−0.293821	+	0.216564i
$967$		−	25.4787i		−	0.819341i	−0.912234	−	0.409671i	$-0.865644\pi$
$967$		−	25.4787i		−	0.819341i	0.912234	−	0.409671i	$-0.134356\pi$
$968$	0.508993			0.0163596
$969$	−10.7901	−	3.03162i	−0.346629	−	0.0973897i
$970$	15.2607	−	8.81074i	0.489990	−	0.282896i
$971$	−19.1478			−0.614483			−0.307241	−	0.951632i	$-0.599406\pi$
$971$	−19.1478			−0.614483			−0.307241	+	0.951632i	$0.599406\pi$
$972$	−11.6691	+	10.3360i	−0.374287	+	0.331526i
$973$	−0.297052	−	0.0412939i	−0.00952305	−	0.00132382i
$974$		−	35.8831i		−	1.14977i
$975$	−2.47948	+	9.86868i	−0.0794071	+	0.316051i
$976$	10.1157	−	5.84028i	0.323794	−	0.186943i
$977$	−2.86774			−0.0917472			−0.0458736	−	0.998947i	$-0.514607\pi$
$977$	−2.86774			−0.0917472			−0.0458736	+	0.998947i	$0.514607\pi$
$978$	−12.1210	−	12.4180i	−0.387587	−	0.397083i
$979$	15.6701	−	9.04714i	0.500819	−	0.289148i
$980$	−8.95508	−	9.21778i	−0.286060	−	0.294451i
$981$	6.90922	−	11.3250i	0.220594	−	0.361579i
$982$			37.3412i			1.19160i
$983$	39.2792	−	22.6779i	1.25281	−	0.723312i	0.281146	−	0.959665i	$-0.409285\pi$
$983$	39.2792	−	22.6779i	1.25281	−	0.723312i	0.971667	+	0.236353i	$0.0759521\pi$
$984$	2.35425	−	8.37923i	0.0750508	−	0.267120i
$985$	18.2643	−	10.5449i	0.581949	−	0.335988i
$986$	−5.79226	−	3.34416i	−0.184463	−	0.106500i
$987$	−43.0113	+	31.7020i	−1.36906	+	1.00909i
$988$	0.203236	+	7.32236i	0.00646581	+	0.232955i
$989$	−2.26816	−	1.30952i	−0.0721233	−	0.0416404i
$990$	8.94820	+	16.4031i	0.284392	+	0.521326i
$991$	26.2568			0.834074			0.417037	−	0.908890i	$-0.363069\pi$
$991$	26.2568			0.834074			0.417037	+	0.908890i	$0.363069\pi$
$992$	−6.28690			−0.199609
$993$	14.0571	−	3.58484i	0.446089	−	0.113762i
$994$	−38.0995	+	15.4597i	−1.20844	+	0.490351i
$995$	6.30153	+	10.9146i	0.199772	+	0.346015i
$996$	−6.12753	+	21.8090i	−0.194158	+	0.691046i
$997$	21.8672	+	12.6250i	0.692542	+	0.399839i	0.804563	−	0.593867i	$-0.202399\pi$
$997$	21.8672	+	12.6250i	0.692542	+	0.399839i	−0.112022	+	0.993706i	$0.535733\pi$
$998$			22.0778i			0.698860i
$999$	2.50292	+	0.769051i	0.0791890	+	0.0243317i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.e.173.9	yes	34
3.2	odd	2		546.2.bn.f.173.9	yes	34
7.3	odd	6		546.2.bi.f.17.4	yes	34
13.10	even	6		546.2.bi.e.257.1	yes	34
21.17	even	6		546.2.bi.e.17.1	✓	34
39.23	odd	6		546.2.bi.f.257.4	yes	34
91.10	odd	6		546.2.bn.f.101.9	yes	34
273.101	even	6	inner	546.2.bn.e.101.9	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.1	✓	34	21.17	even	6
546.2.bi.e.257.1	yes	34	13.10	even	6
546.2.bi.f.17.4	yes	34	7.3	odd	6
546.2.bi.f.257.4	yes	34	39.23	odd	6
546.2.bn.e.101.9	yes	34	273.101	even	6	inner
546.2.bn.e.173.9	yes	34	1.1	even	1	trivial
546.2.bn.f.101.9	yes	34	91.10	odd	6
546.2.bn.f.173.9	yes	34	3.2	odd	2

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.428009 + 1.67834i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.58996 + 0.917964i) q^{5} +(1.23948 - 1.20983i) q^{6} +(2.08732 + 1.62576i) q^{7} +1.00000 q^{8} +(-2.63362 + 1.43668i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.428009 + 1.67834i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.58996 + 0.917964i) q^{5} +(1.23948 - 1.20983i) q^{6} +(2.08732 + 1.62576i) q^{7} +1.00000 q^{8} +(-2.63362 + 1.43668i) q^{9} -1.83593i q^{10} +3.39249 q^{11} +(-1.66749 - 0.468501i) q^{12} +(-3.07128 + 1.88872i) q^{13} +(0.364289 - 2.62055i) q^{14} +(-0.860135 + 3.06138i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.59253 - 2.75834i) q^{17} +(2.56101 + 1.56244i) q^{18} -2.03164 q^{19} +(-1.58996 + 0.917964i) q^{20} +(-1.83518 + 4.19906i) q^{21} +(-1.69625 - 2.93798i) q^{22} +(-2.14393 + 1.23780i) q^{23} +(0.428009 + 1.67834i) q^{24} +(-0.814684 - 1.41107i) q^{25} +(3.17131 + 1.71545i) q^{26} +(-3.53845 - 3.80518i) q^{27} +(-2.45161 + 0.994793i) q^{28} +(1.81857 + 1.04995i) q^{29} +(3.08130 - 0.785793i) q^{30} +(3.14345 + 5.44461i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.45202 + 5.69374i) q^{33} -3.18506 q^{34} +(1.82637 + 4.50098i) q^{35} +(0.0726040 - 2.99912i) q^{36} +(-0.436402 + 0.251957i) q^{37} +(1.01582 + 1.75945i) q^{38} +(-4.48443 - 4.34625i) q^{39} +(1.58996 + 0.917964i) q^{40} +(-4.35184 - 2.51254i) q^{41} +(4.55408 - 0.510221i) q^{42} +(0.528972 + 0.916206i) q^{43} +(-1.69625 + 2.93798i) q^{44} +(-5.50617 - 0.133296i) q^{45} +(2.14393 + 1.23780i) q^{46} +(10.0977 + 5.82991i) q^{47} +(1.23948 - 1.20983i) q^{48} +(1.71381 + 6.78696i) q^{49} +(-0.814684 + 1.41107i) q^{50} +(5.31104 + 1.49220i) q^{51} +(-0.100036 - 3.60416i) q^{52} +(5.81668 - 3.35826i) q^{53} +(-1.52616 + 4.96698i) q^{54} +(5.39393 + 3.11418i) q^{55} +(2.08732 + 1.62576i) q^{56} +(-0.869560 - 3.40977i) q^{57} -2.09991i q^{58} +(-5.37709 - 3.10446i) q^{59} +(-2.22117 - 2.27559i) q^{60} +11.6806i q^{61} +(3.14345 - 5.44461i) q^{62} +(-7.83291 - 1.28281i) q^{63} +1.00000 q^{64} +(-6.61699 + 0.183658i) q^{65} +(4.20491 - 4.10435i) q^{66} -9.92794i q^{67} +(1.59253 + 2.75834i) q^{68} +(-2.99507 - 3.06845i) q^{69} +(2.98478 - 3.83217i) q^{70} +(-7.77030 - 13.4586i) q^{71} +(-2.63362 + 1.43668i) q^{72} +(4.47574 + 7.75221i) q^{73} +(0.436402 + 0.251957i) q^{74} +(2.01956 - 1.97126i) q^{75} +(1.01582 - 1.75945i) q^{76} +(7.08122 + 5.51537i) q^{77} +(-1.52175 + 6.05676i) q^{78} +(3.92399 - 6.79656i) q^{79} -1.83593i q^{80} +(4.87188 - 7.56735i) q^{81} +5.02507i q^{82} -13.0790i q^{83} +(-2.71891 - 3.68884i) q^{84} +(5.06412 - 2.92377i) q^{85} +(0.528972 - 0.916206i) q^{86} +(-0.983809 + 3.50156i) q^{87} +3.39249 q^{88} +(4.61906 - 2.66681i) q^{89} +(2.63765 + 4.83513i) q^{90} +(-9.48134 - 1.05081i) q^{91} -2.47560i q^{92} +(-7.79246 + 7.60610i) q^{93} -11.6598i q^{94} +(-3.23023 - 1.86497i) q^{95} +(-1.66749 - 0.468501i) q^{96} +(4.79907 + 8.31223i) q^{97} +(5.02077 - 4.87769i) q^{98} +(-8.93452 + 4.87394i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9	\( 34 q - 17 q^{2} + 3 q^{3} - 17 q^{4} + 9 q^{5} - 6 q^{6} + 5 q^{7} + 34 q^{8} + 7 q^{9} - 18 q^{11} + 3 q^{12} - 8 q^{13} - 4 q^{14} - 17 q^{15} - 17 q^{16} + 6 q^{17} - 11 q^{18} - 10 q^{19} - 9 q^{20} - 4 q^{21} + 9 q^{22} + 6 q^{23} + 3 q^{24} + 16 q^{25} + 13 q^{26} + 18 q^{27} - q^{28} + 27 q^{29} + 13 q^{30} + q^{31} - 17 q^{32} + 21 q^{33} - 12 q^{34} - 3 q^{35} + 4 q^{36} + 6 q^{37} + 5 q^{38} + 20 q^{39} + 9 q^{40} + 3 q^{41} + 20 q^{42} - 3 q^{43} + 9 q^{44} - 6 q^{46} - 27 q^{47} - 6 q^{48} - 5 q^{49} + 16 q^{50} + 24 q^{51} - 5 q^{52} + 21 q^{53} - 18 q^{54} + 57 q^{55} + 5 q^{56} - 17 q^{57} - 6 q^{59} + 4 q^{60} + q^{62} - 21 q^{63} + 34 q^{64} + 33 q^{65} - 21 q^{66} + 6 q^{68} - 30 q^{69} + 3 q^{70} - 15 q^{71} + 7 q^{72} + 19 q^{73} - 6 q^{74} - 63 q^{75} + 5 q^{76} - 9 q^{77} - 10 q^{78} - 9 q^{79} - 5 q^{81} - 16 q^{84} - 42 q^{85} - 3 q^{86} - 75 q^{87} - 18 q^{88} - 18 q^{89} - 9 q^{90} - 27 q^{91} + 25 q^{93} - 3 q^{95} + 3 q^{96} - 19 q^{97} + 7 q^{98} - 27 q^{99}+O(q^{100}) \) 34 * q - 17 * q^2 + 3 * q^3 - 17 * q^4 + 9 * q^5 - 6 * q^6 + 5 * q^7 + 34 * q^8 + 7 * q^9 - 18 * q^11 + 3 * q^12 - 8 * q^13 - 4 * q^14 - 17 * q^15 - 17 * q^16 + 6 * q^17 - 11 * q^18 - 10 * q^19 - 9 * q^20 - 4 * q^21 + 9 * q^22 + 6 * q^23 + 3 * q^24 + 16 * q^25 + 13 * q^26 + 18 * q^27 - q^28 + 27 * q^29 + 13 * q^30 + q^31 - 17 * q^32 + 21 * q^33 - 12 * q^34 - 3 * q^35 + 4 * q^36 + 6 * q^37 + 5 * q^38 + 20 * q^39 + 9 * q^40 + 3 * q^41 + 20 * q^42 - 3 * q^43 + 9 * q^44 - 6 * q^46 - 27 * q^47 - 6 * q^48 - 5 * q^49 + 16 * q^50 + 24 * q^51 - 5 * q^52 + 21 * q^53 - 18 * q^54 + 57 * q^55 + 5 * q^56 - 17 * q^57 - 6 * q^59 + 4 * q^60 + q^62 - 21 * q^63 + 34 * q^64 + 33 * q^65 - 21 * q^66 + 6 * q^68 - 30 * q^69 + 3 * q^70 - 15 * q^71 + 7 * q^72 + 19 * q^73 - 6 * q^74 - 63 * q^75 + 5 * q^76 - 9 * q^77 - 10 * q^78 - 9 * q^79 - 5 * q^81 - 16 * q^84 - 42 * q^85 - 3 * q^86 - 75 * q^87 - 18 * q^88 - 18 * q^89 - 9 * q^90 - 27 * q^91 + 25 * q^93 - 3 * q^95 + 3 * q^96 - 19 * q^97 + 7 * q^98 - 27 * q^99

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