LMFDB - Embedded newform 546.2.bx.b.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(97,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("546.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bx (of order $12$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			97.1
Character	$\chi$	$=$	546.97
Dual form			546.2.bx.b.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.52974 - 2.52974i) q^{5} +(0.258819 - 0.965926i) q^{6} +(2.60750 + 0.448249i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.52974 - 2.52974i) q^{5} +(0.258819 - 0.965926i) q^{6} +(2.60750 + 0.448249i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.78880 + 3.09829i) q^{10} +(-0.141178 + 0.0378284i) q^{11} -1.00000 q^{12} +(3.09703 - 1.84618i) q^{13} +(-0.241896 - 2.63467i) q^{14} +(-0.925950 - 3.45569i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.55049 - 4.41758i) q^{17} +(0.707107 - 0.707107i) q^{18} +(1.37483 - 5.13093i) q^{19} +(3.45569 + 0.925950i) q^{20} +(2.03404 + 1.69195i) q^{21} +(0.0730789 + 0.126576i) q^{22} +(-4.87674 - 2.81559i) q^{23} +(0.258819 + 0.965926i) q^{24} +7.79920i q^{25} +(-2.58485 - 2.51368i) q^{26} +1.00000i q^{27} +(-2.48229 + 0.915557i) q^{28} +(-1.83299 + 3.17482i) q^{29} +(-3.09829 + 1.78880i) q^{30} +(-7.04095 - 7.04095i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-0.141178 - 0.0378284i) q^{33} +(-3.60694 + 3.60694i) q^{34} +(-5.46236 - 7.73027i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(3.66064 - 0.980866i) q^{37} -5.31193 q^{38} +(3.60520 - 0.0503243i) q^{39} -3.57760i q^{40} +(6.98851 - 1.87256i) q^{41} +(1.10785 - 2.40264i) q^{42} +(2.79434 - 1.61331i) q^{43} +(0.103349 - 0.103349i) q^{44} +(0.925950 - 3.45569i) q^{45} +(-1.45746 + 5.43930i) q^{46} +(-1.81311 + 1.81311i) q^{47} +(0.866025 - 0.500000i) q^{48} +(6.59815 + 2.33762i) q^{49} +(7.53345 - 2.01858i) q^{50} -5.10098i q^{51} +(-1.75902 + 3.14736i) q^{52} +7.13879 q^{53} +(0.965926 - 0.258819i) q^{54} +(0.452839 + 0.261447i) q^{55} +(1.52682 + 2.16074i) q^{56} +(3.75610 - 3.75610i) q^{57} +(3.54106 + 0.948823i) q^{58} +(4.08824 + 1.09544i) q^{59} +(2.52974 + 2.52974i) q^{60} +(-9.62468 + 5.55681i) q^{61} +(-4.97871 + 8.62337i) q^{62} +(0.915557 + 2.48229i) q^{63} +1.00000i q^{64} +(-12.5051 - 3.16433i) q^{65} +0.146158i q^{66} +(1.29264 + 4.82420i) q^{67} +(4.41758 + 2.55049i) q^{68} +(-2.81559 - 4.87674i) q^{69} +(-6.05310 + 7.27697i) q^{70} +(6.47842 + 1.73589i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(7.91676 - 7.91676i) q^{73} +(-1.89489 - 3.28204i) q^{74} +(-3.89960 + 6.75431i) q^{75} +(1.37483 + 5.13093i) q^{76} +(-0.385078 + 0.0353550i) q^{77} +(-0.981704 - 3.46933i) q^{78} -8.03063 q^{79} +(-3.45569 + 0.925950i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.61752 - 6.26572i) q^{82} +(5.59369 + 5.59369i) q^{83} +(-2.60750 - 0.448249i) q^{84} +(-4.72326 + 17.6274i) q^{85} +(-2.28157 - 2.28157i) q^{86} +(-3.17482 + 1.83299i) q^{87} +(-0.126576 - 0.0730789i) q^{88} +(3.28299 + 12.2523i) q^{89} -3.57760 q^{90} +(8.90307 - 3.42568i) q^{91} +5.63117 q^{92} +(-2.57717 - 9.61812i) q^{93} +(2.22059 + 1.28206i) q^{94} +(-16.4579 + 9.50198i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-1.80716 + 6.74442i) q^{97} +(0.550243 - 6.97834i) q^{98} +(-0.103349 - 0.103349i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 8 * q^7 + 20 * q^9	$ 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) $ 40 * q + 8 * q^7 + 20 * q^9 + 8 * q^11 - 40 * q^12 - 8 * q^14 + 20 * q^16 - 16 * q^17 - 16 * q^19 + 4 * q^21 + 8 * q^22 - 32 * q^26 - 8 * q^28 + 8 * q^33 - 16 * q^34 + 40 * q^35 + 40 * q^37 + 16 * q^38 - 16 * q^39 + 4 * q^41 - 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 - 16 * q^50 + 8 * q^52 + 32 * q^53 + 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 - 84 * q^59 + 48 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 - 20 * q^70 - 40 * q^71 + 48 * q^73 + 8 * q^74 - 36 * q^75 - 16 * q^76 + 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 - 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 - 12 * q^89 + 32 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 - 8 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	−2.52974	−	2.52974i	−1.13134	−	1.13134i	−0.989955	−	0.141380i	$-0.954846\pi$
$5$	−2.52974	−	2.52974i	−1.13134	−	1.13134i	−0.141380	−	0.989955i	$-0.545154\pi$
$6$	0.258819	−	0.965926i	0.105662	−	0.394338i
$7$	2.60750	+	0.448249i	0.985544	+	0.169422i
$7$	2.60750	+	0.448249i	0.985544	+	0.169422i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−1.78880	+	3.09829i	−0.565668	+	0.979765i
$11$	−0.141178	+	0.0378284i	−0.0425667	+	0.0114057i	−0.280040	−	0.959988i	$-0.590348\pi$
$11$	−0.141178	+	0.0378284i	−0.0425667	+	0.0114057i	0.237473	+	0.971394i	$0.423681\pi$
$12$	−1.00000			−0.288675
$13$	3.09703	−	1.84618i	0.858962	−	0.512039i
$13$	3.09703	−	1.84618i	0.858962	−	0.512039i
$14$	−0.241896	−	2.63467i	−0.0646495	−	0.704145i
$15$	−0.925950	−	3.45569i	−0.239079	−	0.892256i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.55049	−	4.41758i	−0.618585	−	1.07142i	−0.989744	−	0.142851i	$-0.954373\pi$
$17$	−2.55049	−	4.41758i	−0.618585	−	1.07142i	0.371159	−	0.928569i	$-0.378960\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	1.37483	−	5.13093i	0.315408	−	1.17712i	−0.608202	−	0.793782i	$-0.708109\pi$
$19$	1.37483	−	5.13093i	0.315408	−	1.17712i	0.923609	−	0.383335i	$-0.125224\pi$
$20$	3.45569	+	0.925950i	0.772717	+	0.207049i
$21$	2.03404	+	1.69195i	0.443864	+	0.369213i
$22$	0.0730789	+	0.126576i	0.0155805	+	0.0269862i
$23$	−4.87674	−	2.81559i	−1.01687	−	0.587090i	−0.103675	−	0.994611i	$-0.533060\pi$
$23$	−4.87674	−	2.81559i	−1.01687	−	0.587090i	−0.913196	+	0.407521i	$0.866393\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$			7.79920i			1.55984i
$26$	−2.58485	−	2.51368i	−0.506930	−	0.492973i
$27$			1.00000i			0.192450i
$28$	−2.48229	+	0.915557i	−0.469108	+	0.173024i
$29$	−1.83299	+	3.17482i	−0.340377	+	0.589550i	−0.984503	−	0.175370i	$-0.943888\pi$
$29$	−1.83299	+	3.17482i	−0.340377	+	0.589550i	0.644126	+	0.764920i	$0.277221\pi$
$30$	−3.09829	+	1.78880i	−0.565668	+	0.326588i
$31$	−7.04095	−	7.04095i	−1.26459	−	1.26459i	−0.948842	−	0.315750i	$-0.897744\pi$
$31$	−7.04095	−	7.04095i	−1.26459	−	1.26459i	−0.315750	−	0.948842i	$-0.602256\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−0.141178	−	0.0378284i	−0.0245759	−	0.00658508i
$34$	−3.60694	+	3.60694i	−0.618585	+	0.618585i
$35$	−5.46236	−	7.73027i	−0.923307	−	1.30665i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	3.66064	−	0.980866i	0.601806	−	0.161253i	0.0549627	−	0.998488i	$-0.482496\pi$
$37$	3.66064	−	0.980866i	0.601806	−	0.161253i	0.546843	+	0.837235i	$0.315829\pi$
$38$	−5.31193			−0.861710
$39$	3.60520	−	0.0503243i	0.577294	−	0.00805834i
$40$		−	3.57760i		−	0.565668i
$41$	6.98851	−	1.87256i	1.09142	−	0.292445i	0.332155	−	0.943225i	$-0.392224\pi$
$41$	6.98851	−	1.87256i	1.09142	−	0.292445i	0.759267	+	0.650780i	$0.225558\pi$
$42$	1.10785	−	2.40264i	0.170944	−	0.370735i
$43$	2.79434	−	1.61331i	0.426132	−	0.246028i	−0.271565	−	0.962420i	$-0.587541\pi$
$43$	2.79434	−	1.61331i	0.426132	−	0.246028i	0.697698	+	0.716392i	$0.254208\pi$
$44$	0.103349	−	0.103349i	0.0155805	−	0.0155805i
$45$	0.925950	−	3.45569i	0.138033	−	0.515144i
$46$	−1.45746	+	5.43930i	−0.214890	+	0.801981i
$47$	−1.81311	+	1.81311i	−0.264469	+	0.264469i	−0.826867	−	0.562398i	$-0.809879\pi$
$47$	−1.81311	+	1.81311i	−0.264469	+	0.264469i	0.562398	+	0.826867i	$0.309879\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	6.59815	+	2.33762i	0.942592	+	0.333946i
$50$	7.53345	−	2.01858i	1.06539	−	0.285471i
$51$		−	5.10098i		−	0.714281i
$52$	−1.75902	+	3.14736i	−0.243932	+	0.436460i
$53$	7.13879			0.980589			0.490294	−	0.871557i	$-0.336889\pi$
$53$	7.13879			0.980589			0.490294	+	0.871557i	$0.336889\pi$
$54$	0.965926	−	0.258819i	0.131446	−	0.0352208i
$55$	0.452839	+	0.261447i	0.0610608	+	0.0352535i
$56$	1.52682	+	2.16074i	0.204030	+	0.288741i
$57$	3.75610	−	3.75610i	0.497508	−	0.497508i
$58$	3.54106	+	0.948823i	0.464963	+	0.124587i
$59$	4.08824	+	1.09544i	0.532244	+	0.142614i	0.514924	−	0.857236i	$-0.327820\pi$
$59$	4.08824	+	1.09544i	0.532244	+	0.142614i	0.0173194	+	0.999850i	$0.494487\pi$
$60$	2.52974	+	2.52974i	0.326588	+	0.326588i
$61$	−9.62468	+	5.55681i	−1.23231	+	0.711477i	−0.967512	−	0.252825i	$-0.918640\pi$
$61$	−9.62468	+	5.55681i	−1.23231	+	0.711477i	−0.264803	+	0.964303i	$0.585307\pi$
$62$	−4.97871	+	8.62337i	−0.632296	+	1.09517i
$63$	0.915557	+	2.48229i	0.115349	+	0.312739i
$64$			1.00000i			0.125000i
$65$	−12.5051	−	3.16433i	−1.55106	−	0.392487i
$66$			0.146158i			0.0179908i
$67$	1.29264	+	4.82420i	0.157921	+	0.589370i	0.998837	+	0.0482049i	$0.0153500\pi$
$67$	1.29264	+	4.82420i	0.157921	+	0.589370i	−0.840916	+	0.541165i	$0.817983\pi$
$68$	4.41758	+	2.55049i	0.535710	+	0.309293i
$69$	−2.81559	−	4.87674i	−0.338957	−	0.587090i
$70$	−6.05310	+	7.27697i	−0.723484	+	0.869765i
$71$	6.47842	+	1.73589i	0.768847	+	0.206012i	0.621862	−	0.783127i	$-0.286376\pi$
$71$	6.47842	+	1.73589i	0.768847	+	0.206012i	0.146985	+	0.989139i	$0.453043\pi$
$72$	−0.258819	+	0.965926i	−0.0305021	+	0.113835i
$73$	7.91676	−	7.91676i	0.926587	−	0.926587i	−0.0708965	−	0.997484i	$-0.522586\pi$
$73$	7.91676	−	7.91676i	0.926587	−	0.926587i	0.997484	+	0.0708965i	$0.0225860\pi$
$74$	−1.89489	−	3.28204i	−0.220276	−	0.381530i
$75$	−3.89960	+	6.75431i	−0.450287	+	0.779920i
$76$	1.37483	+	5.13093i	0.157704	+	0.588559i
$77$	−0.385078	+	0.0353550i	−0.0438837	+	0.00402908i
$78$	−0.981704	−	3.46933i	−0.111156	−	0.392824i
$79$	−8.03063			−0.903517			−0.451758	−	0.892140i	$-0.649203\pi$
$79$	−8.03063			−0.903517			−0.451758	+	0.892140i	$0.649203\pi$
$80$	−3.45569	+	0.925950i	−0.386358	+	0.103524i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.61752	−	6.26572i	−0.399488	−	0.691933i
$83$	5.59369	+	5.59369i	0.613988	+	0.613988i	0.943983	−	0.329995i	$-0.107047\pi$
$83$	5.59369	+	5.59369i	0.613988	+	0.613988i	−0.329995	+	0.943983i	$0.607047\pi$
$84$	−2.60750	−	0.448249i	−0.284502	−	0.0489080i
$85$	−4.72326	+	17.6274i	−0.512309	+	1.91196i
$86$	−2.28157	−	2.28157i	−0.246028	−	0.246028i
$87$	−3.17482	+	1.83299i	−0.340377	+	0.196517i
$88$	−0.126576	−	0.0730789i	−0.0134931	−	0.00779024i
$89$	3.28299	+	12.2523i	0.347997	+	1.29874i	0.889072	+	0.457767i	$0.151351\pi$
$89$	3.28299	+	12.2523i	0.347997	+	1.29874i	−0.541075	+	0.840974i	$0.681983\pi$
$90$	−3.57760			−0.377112
$91$	8.90307	−	3.42568i	0.933296	−	0.359109i
$92$	5.63117			0.587090
$93$	−2.57717	−	9.61812i	−0.267240	−	0.997353i
$94$	2.22059	+	1.28206i	0.229037	+	0.132234i
$95$	−16.4579	+	9.50198i	−1.68855	+	0.974883i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−1.80716	+	6.74442i	−0.183489	+	0.684792i	0.811460	+	0.584409i	$0.198673\pi$
$97$	−1.80716	+	6.74442i	−0.183489	+	0.684792i	−0.994949	+	0.100383i	$0.967993\pi$
$98$	0.550243	−	6.97834i	0.0555830	−	0.704919i
$99$	−0.103349	−	0.103349i	−0.0103870	−	0.0103870i
$100$	−3.89960	−	6.75431i	−0.389960	−	0.675431i
$101$	5.05039	−	8.74753i	0.502532	−	0.870411i	−0.497463	−	0.867485i	$-0.665735\pi$
$101$	5.05039	−	8.74753i	0.502532	−	0.870411i	0.999996	−	0.00292646i	$-0.000931522\pi$
$102$	−4.92717	+	1.32023i	−0.487863	+	0.130722i
$103$	8.14972			0.803016			0.401508	−	0.915855i	$-0.368486\pi$
$103$	8.14972			0.803016			0.401508	+	0.915855i	$0.368486\pi$
$104$	3.49538	+	0.884485i	0.342750	+	0.0867309i
$105$	−0.865407	−	9.42579i	−0.0844551	−	0.919863i
$106$	−1.84766	−	6.89555i	−0.179460	−	0.669755i
$107$	0.0773176	−	0.133918i	0.00747457	−	0.0129463i	−0.862264	−	0.506459i	$-0.830954\pi$
$107$	0.0773176	−	0.133918i	0.00747457	−	0.0129463i	0.869738	+	0.493513i	$0.164287\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−5.77656	+	5.77656i	−0.553294	+	0.553294i	−0.927390	−	0.374096i	$-0.877953\pi$
$109$	−5.77656	+	5.77656i	−0.553294	+	0.553294i	0.374096	+	0.927390i	$0.377953\pi$
$110$	0.135335	−	0.505077i	0.0129037	−	0.0481572i
$111$	3.66064	+	0.980866i	0.347453	+	0.0930997i
$112$	1.69195	−	2.03404i	0.159874	−	0.192199i
$113$	−0.0357767	−	0.0619671i	−0.00336559	−	0.00582937i	0.864338	−	0.502912i	$-0.167738\pi$
$113$	−0.0357767	−	0.0619671i	−0.00336559	−	0.00582937i	−0.867703	+	0.497082i	$0.834405\pi$
$114$	−4.60027	−	2.65597i	−0.430855	−	0.248754i
$115$	5.21419	+	19.4596i	0.486225	+	1.81462i
$116$		−	3.66597i		−	0.340377i
$117$	3.14736	+	1.75902i	0.290973	+	0.162621i
$118$		−	4.23246i		−	0.389629i
$119$	−4.67024	−	12.6621i	−0.428120	−	1.16073i
$120$	1.78880	−	3.09829i	0.163294	−	0.282834i
$121$	−9.50778	+	5.48932i	−0.864344	+	0.499029i
$122$	7.85852	+	7.85852i	0.711477	+	0.711477i
$123$	6.98851	+	1.87256i	0.630132	+	0.168843i
$124$	9.61812	+	2.57717i	0.863733	+	0.231436i
$125$	7.08126	−	7.08126i	0.633367	−	0.633367i
$126$	2.16074	−	1.52682i	0.192494	−	0.136020i
$127$	−6.70337	−	3.87019i	−0.594828	−	0.343424i	0.172176	−	0.985066i	$-0.444920\pi$
$127$	−6.70337	−	3.87019i	−0.594828	−	0.343424i	−0.767004	+	0.641642i	$0.778254\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	3.22662			0.284088
$130$	0.180040	+	12.8980i	0.0157906	+	1.13123i
$131$			1.11889i			0.0977578i	0.998805	+	0.0488789i	$0.0155648\pi$
$131$			1.11889i			0.0977578i	−0.998805	+	0.0488789i	$0.984435\pi$
$132$	0.141178	−	0.0378284i	0.0122879	−	0.00329254i
$133$	5.88481	−	12.7627i	0.510278	−	1.10666i
$134$	4.32526	−	2.49719i	0.373646	−	0.215724i
$135$	2.52974	−	2.52974i	0.217726	−	0.217726i
$136$	1.32023	−	4.92717i	0.113209	−	0.422501i
$137$	3.69259	−	13.7809i	0.315479	−	1.17738i	−0.608064	−	0.793888i	$-0.708054\pi$
$137$	3.69259	−	13.7809i	0.315479	−	1.17738i	0.923543	−	0.383495i	$-0.125280\pi$
$138$	−3.98184	+	3.98184i	−0.338957	+	0.338957i
$139$	−13.4946	+	7.79111i	−1.14460	+	0.660834i	−0.947565	−	0.319563i	$-0.896464\pi$
$139$	−13.4946	+	7.79111i	−1.14460	+	0.660834i	−0.197032	+	0.980397i	$0.563130\pi$
$140$	8.59568	+	3.96343i	0.726467	+	0.334971i
$141$	−2.47675	+	0.663644i	−0.208580	+	0.0558889i
$142$		−	6.70695i		−	0.562835i
$143$	−0.367394	+	0.377795i	−0.0307230	+	0.0315928i
$144$	1.00000			0.0833333
$145$	12.6685	−	3.39451i	1.05206	−	0.281898i
$146$	−9.69602	−	5.59800i	−0.802448	−	0.463294i
$147$	4.54535	+	5.32351i	0.374894	+	0.439076i
$148$	−2.67978	+	2.67978i	−0.220276	+	0.220276i
$149$	17.7313	+	4.75108i	1.45260	+	0.389224i	0.896928	−	0.442176i	$-0.145793\pi$
$149$	17.7313	+	4.75108i	1.45260	+	0.389224i	0.555675	+	0.831400i	$0.312460\pi$
$150$	7.53345	+	2.01858i	0.615104	+	0.164817i
$151$	12.9899	+	12.9899i	1.05710	+	1.05710i	0.998268	+	0.0588357i	$0.0187388\pi$
$151$	12.9899	+	12.9899i	1.05710	+	1.05710i	0.0588357	+	0.998268i	$0.481261\pi$
$152$	4.60027	−	2.65597i	0.373131	−	0.215427i
$153$	2.55049	−	4.41758i	0.206195	−	0.357140i
$154$	0.133816	+	0.362806i	0.0107832	+	0.0292357i
$155$			35.6236i			2.86136i
$156$	−3.09703	+	1.84618i	−0.247961	+	0.147813i
$157$			14.7243i			1.17513i	0.809178	+	0.587564i	$0.199913\pi$
$157$			14.7243i			1.17513i	−0.809178	+	0.587564i	$0.800087\pi$
$158$	2.07848	+	7.75700i	0.165355	+	0.617114i
$159$	6.18238	+	3.56940i	0.490294	+	0.283072i
$160$	1.78880	+	3.09829i	0.141417	+	0.244941i
$161$	−11.4540	−	9.52765i	−0.902704	−	0.750884i
$162$	0.965926	+	0.258819i	0.0758903	+	0.0203347i
$163$	−3.21246	+	11.9891i	−0.251619	+	0.939055i	0.718321	+	0.695712i	$0.244911\pi$
$163$	−3.21246	+	11.9891i	−0.251619	+	0.939055i	−0.969940	+	0.243343i	$0.921756\pi$
$164$	−5.11594	+	5.11594i	−0.399488	+	0.399488i
$165$	0.261447	+	0.452839i	0.0203536	+	0.0352535i
$166$	3.95534	−	6.85085i	0.306994	−	0.531729i
$167$	−2.88019	−	10.7490i	−0.222876	−	0.831783i	−0.983244	−	0.182292i	$-0.941648\pi$
$167$	−2.88019	−	10.7490i	−0.222876	−	0.831783i	0.760369	−	0.649492i	$-0.225018\pi$
$168$	0.241896	+	2.63467i	0.0186627	+	0.203269i
$169$	6.18322	−	11.4354i	0.475633	−	0.879644i
$170$	18.2493			1.39965
$171$	5.13093	−	1.37483i	0.392372	−	0.105136i
$172$	−1.61331	+	2.79434i	−0.123014	+	0.213066i
$173$	6.62282	+	11.4711i	0.503523	+	0.872128i	0.999992	+	0.00407317i	$0.00129653\pi$
$173$	6.62282	+	11.4711i	0.503523	+	0.872128i	−0.496468	+	0.868055i	$0.665370\pi$
$174$	2.59223	+	2.59223i	0.196517	+	0.196517i
$175$	−3.49598	+	20.3364i	−0.264272	+	1.53729i
$176$	−0.0378284	+	0.141178i	−0.00285143	+	0.0106417i
$177$	2.99280	+	2.99280i	0.224953	+	0.224953i
$178$	10.9851	−	6.34226i	0.823369	−	0.475372i
$179$	13.1577	+	7.59659i	0.983451	+	0.567796i	0.903310	−	0.428988i	$-0.141130\pi$
$179$	13.1577	+	7.59659i	0.983451	+	0.567796i	0.0801407	+	0.996784i	$0.474463\pi$
$180$	0.925950	+	3.45569i	0.0690163	+	0.257572i
$181$	1.51565			0.112658			0.0563288	−	0.998412i	$-0.482060\pi$
$181$	1.51565			0.112658			0.0563288	+	0.998412i	$0.482060\pi$
$182$	−5.61324	−	7.71307i	−0.416081	−	0.571731i
$183$	−11.1136			−0.821543
$184$	−1.45746	−	5.43930i	−0.107445	−	0.400990i
$185$	−11.7418	−	6.77915i	−0.863276	−	0.498413i
$186$	−8.62337	+	4.97871i	−0.632296	+	0.365056i
$187$	0.527182	+	0.527182i	0.0385514	+	0.0385514i
$188$	0.663644	−	2.47675i	0.0484012	−	0.180636i
$189$	−0.448249	+	2.60750i	−0.0326053	+	0.189668i
$190$	13.4378	+	13.4378i	0.974883	+	0.974883i
$191$	−7.50536	−	12.9997i	−0.543069	−	0.940623i	−0.998726	−	0.0504674i	$-0.983929\pi$
$191$	−7.50536	−	12.9997i	−0.543069	−	0.940623i	0.455657	−	0.890156i	$-0.349404\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	19.8473	−	5.31807i	1.42864	−	0.382803i	0.540100	−	0.841601i	$-0.318386\pi$
$193$	19.8473	−	5.31807i	1.42864	−	0.382803i	0.888541	+	0.458797i	$0.151720\pi$
$194$	6.98233			0.501302
$195$	−9.24754	−	8.99292i	−0.662230	−	0.643997i
$196$	−6.88297	+	1.27463i	−0.491641	+	0.0910452i
$197$	−3.60071	−	13.4380i	−0.256540	−	0.957420i	−0.967227	−	0.253912i	$-0.918283\pi$
$197$	−3.60071	−	13.4380i	−0.256540	−	0.957420i	0.710687	−	0.703508i	$-0.248384\pi$
$198$	−0.0730789	+	0.126576i	−0.00519349	+	0.00899539i
$199$	−4.61379	−	7.99132i	−0.327063	−	0.566490i	0.654865	−	0.755746i	$-0.272726\pi$
$199$	−4.61379	−	7.99132i	−0.327063	−	0.566490i	−0.981928	+	0.189256i	$0.939392\pi$
$200$	−5.51487	+	5.51487i	−0.389960	+	0.389960i
$201$	−1.29264	+	4.82420i	−0.0911759	+	0.340273i
$202$	−9.75660	−	2.61427i	−0.686472	−	0.183940i
$203$	−6.20263	+	7.45673i	−0.435339	+	0.523360i
$204$	2.55049	+	4.41758i	0.178570	+	0.309293i
$205$	−22.4162	−	12.9420i	−1.56562	−	0.903910i
$206$	−2.10930	−	7.87203i	−0.146962	−	0.548470i
$207$		−	5.63117i		−	0.391394i
$208$	−0.0503243	−	3.60520i	−0.00348936	−	0.249976i
$209$			0.776381i			0.0537034i
$210$	−8.88063	+	3.27549i	−0.612822	+	0.226030i
$211$	7.84722	−	13.5918i	0.540225	−	0.935697i	−0.458666	−	0.888609i	$-0.651673\pi$
$211$	7.84722	−	13.5918i	0.540225	−	0.935697i	0.998891	−	0.0470880i	$-0.0149941\pi$
$212$	−6.18238	+	3.56940i	−0.424607	+	0.245147i
$213$	4.74253	+	4.74253i	0.324953	+	0.324953i
$214$	−0.149366	−	0.0400225i	−0.0102105	−	0.00273588i
$215$	−11.1502	−	2.98769i	−0.760439	−	0.203759i
$216$	−0.707107	+	0.707107i	−0.0481125	+	0.0481125i
$217$	−15.2032	−	21.5154i	−1.03206	−	1.46056i
$218$	7.07481	+	4.08464i	0.479167	+	0.276647i
$219$	10.8145	−	2.89774i	0.730776	−	0.195811i
$220$	−0.522894			−0.0352535
$221$	−16.0546	−	8.97272i	−1.07995	−	0.603571i
$222$		−	3.78978i		−	0.254353i
$223$	−3.98854	+	1.06873i	−0.267092	+	0.0715672i	−0.389880	−	0.920866i	$-0.627483\pi$
$223$	−3.98854	+	1.06873i	−0.267092	+	0.0715672i	0.122787	+	0.992433i	$0.460817\pi$
$224$	−2.40264	−	1.10785i	−0.160533	−	0.0740211i
$225$	−6.75431	+	3.89960i	−0.450287	+	0.259973i
$226$	−0.0505959	+	0.0505959i	−0.00336559	+	0.00336559i
$227$	−6.88324	+	25.6886i	−0.456857	+	1.70501i	0.225715	+	0.974193i	$0.427528\pi$
$227$	−6.88324	+	25.6886i	−0.456857	+	1.70501i	−0.682572	+	0.730819i	$0.739139\pi$
$228$	−1.37483	+	5.13093i	−0.0910503	+	0.339804i
$229$	14.2644	−	14.2644i	0.942616	−	0.942616i	−0.0558250	−	0.998441i	$-0.517779\pi$
$229$	14.2644	−	14.2644i	0.942616	−	0.942616i	0.998441	+	0.0558250i	$0.0177789\pi$
$230$	17.4470	−	10.0730i	1.15042	−	0.664196i
$231$	−0.351165	−	0.161920i	−0.0231049	−	0.0106536i
$232$	−3.54106	+	0.948823i	−0.232482	+	0.0622933i
$233$		−	13.2012i		−	0.864839i	−0.901673	−	0.432419i	$-0.857660\pi$
$233$		−	13.2012i		−	0.864839i	0.901673	−	0.432419i	$-0.142340\pi$
$234$	0.884485	−	3.49538i	0.0578206	−	0.228500i
$235$	9.17339			0.598406
$236$	−4.08824	+	1.09544i	−0.266122	+	0.0713071i
$237$	−6.95473	−	4.01532i	−0.451758	−	0.260823i
$238$	−11.0219	+	7.78830i	−0.714445	+	0.504840i
$239$	−16.1493	+	16.1493i	−1.04461	+	1.04461i	−0.0456558	+	0.998957i	$0.514538\pi$
$239$	−16.1493	+	16.1493i	−1.04461	+	1.04461i	−0.998957	+	0.0456558i	$0.985462\pi$
$240$	−3.45569	−	0.925950i	−0.223064	−	0.0597698i
$241$	−26.0443	−	6.97856i	−1.67766	−	0.449529i	−0.710503	−	0.703694i	$-0.751533\pi$
$241$	−26.0443	−	6.97856i	−1.67766	−	0.449529i	−0.967161	+	0.254165i	$0.918199\pi$
$242$	7.76307	+	7.76307i	0.499029	+	0.499029i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	5.55681	−	9.62468i	0.355739	−	0.616157i
$245$	−10.7780	−	22.6052i	−0.688583	−	1.44419i
$246$		−	7.23503i		−	0.461289i
$247$	−5.21475	−	18.4289i	−0.331806	−	1.17260i
$248$		−	9.95741i		−	0.632296i
$249$	2.04743	+	7.64113i	0.129751	+	0.484237i
$250$	−8.67274	−	5.00721i	−0.548512	−	0.316684i
$251$	14.9142	+	25.8321i	0.941374	+	1.63051i	0.762853	+	0.646572i	$0.223798\pi$
$251$	14.9142	+	25.8321i	0.941374	+	1.63051i	0.178522	+	0.983936i	$0.442869\pi$
$252$	−2.03404	−	1.69195i	−0.128132	−	0.106583i
$253$	0.794996	+	0.213018i	0.0499810	+	0.0133924i
$254$	−2.00336	+	7.47664i	−0.125702	+	0.469126i
$255$	−12.9042	+	12.9042i	−0.808091	+	0.808091i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−9.14454	+	15.8388i	−0.570421	+	0.987997i	0.426102	+	0.904675i	$0.359886\pi$
$257$	−9.14454	+	15.8388i	−0.570421	+	0.987997i	−0.996523	+	0.0833222i	$0.973447\pi$
$258$	−0.835111	−	3.11668i	−0.0519918	−	0.194036i
$259$	9.98481	−	0.916732i	0.620426	−	0.0569630i
$260$	12.4119	−	3.51214i	0.769751	−	0.217814i
$261$	−3.66597			−0.226918
$262$	1.08076	−	0.289590i	0.0667698	−	0.0178909i
$263$	−7.04212	+	12.1973i	−0.434236	+	0.752119i	−0.997233	−	0.0743403i	$-0.976315\pi$
$263$	−7.04212	+	12.1973i	−0.434236	+	0.752119i	0.562997	+	0.826459i	$0.309648\pi$
$264$	−0.0730789	−	0.126576i	−0.00449770	−	0.00779024i
$265$	−18.0593	−	18.0593i	−1.10938	−	1.10938i
$266$	−13.8509	−	2.38107i	−0.849252	−	0.145993i
$267$	−3.28299	+	12.2523i	−0.200916	+	0.749829i
$268$	−3.53156	−	3.53156i	−0.215724	−	0.215724i
$269$	18.5454	−	10.7072i	1.13074	−	0.652830i	0.186616	−	0.982433i	$-0.440248\pi$
$269$	18.5454	−	10.7072i	1.13074	−	0.652830i	0.944120	+	0.329603i	$0.106915\pi$
$270$	−3.09829	−	1.78880i	−0.188556	−	0.108863i
$271$	−8.10518	−	30.2489i	−0.492355	−	1.83749i	−0.544368	−	0.838846i	$-0.683231\pi$
$271$	−8.10518	−	30.2489i	−0.492355	−	1.83749i	0.0520136	−	0.998646i	$-0.483436\pi$
$272$	−5.10098			−0.309293
$273$	9.42313	+	1.48481i	0.570314	+	0.0898646i
$274$	−14.2671			−0.861905
$275$	−0.295032	−	1.10107i	−0.0177911	−	0.0663972i
$276$	4.87674	+	2.81559i	0.293545	+	0.169478i
$277$	1.43943	−	0.831056i	0.0864870	−	0.0499333i	−0.456133	−	0.889912i	$-0.650766\pi$
$277$	1.43943	−	0.831056i	0.0864870	−	0.0499333i	0.542620	+	0.839978i	$0.317432\pi$
$278$	11.0183	+	11.0183i	0.660834	+	0.660834i
$279$	2.57717	−	9.61812i	0.154291	−	0.575822i
$280$	1.60365	−	9.32860i	0.0958367	−	0.557490i
$281$	7.44786	+	7.44786i	0.444302	+	0.444302i	0.893455	−	0.449153i	$-0.148274\pi$
$281$	7.44786	+	7.44786i	0.444302	+	0.444302i	−0.449153	+	0.893455i	$0.648274\pi$
$282$	1.28206	+	2.22059i	0.0763456	+	0.132234i
$283$	5.72365	−	9.91366i	0.340236	−	0.589306i	−0.644240	−	0.764823i	$-0.722826\pi$
$283$	5.72365	−	9.91366i	0.340236	−	0.589306i	0.984476	+	0.175517i	$0.0561597\pi$
$284$	−6.47842	+	1.73589i	−0.384423	+	0.103006i
$285$	−19.0040			−1.12570
$286$	0.460011	+	0.257094i	0.0272010	+	0.0152023i
$287$	19.0619	−	1.75013i	1.12519	−	0.103307i
$288$	−0.258819	−	0.965926i	−0.0152511	−	0.0569177i
$289$	−4.51001	+	7.81157i	−0.265295	+	0.459504i
$290$	−6.55768	−	11.3582i	−0.385080	−	0.666979i
$291$	−4.93725	+	4.93725i	−0.289427	+	0.289427i
$292$	−2.89774	+	10.8145i	−0.169577	+	0.632871i
$293$	−26.4297	−	7.08181i	−1.54404	−	0.413724i	−0.616471	−	0.787378i	$-0.711438\pi$
$293$	−26.4297	−	7.08181i	−1.54404	−	0.413724i	−0.927568	+	0.373654i	$0.878105\pi$
$294$	3.96569	−	5.76830i	0.231284	−	0.336414i
$295$	−7.57101	−	13.1134i	−0.440801	−	0.763491i
$296$	3.28204	+	1.89489i	0.190765	+	0.110138i
$297$	−0.0378284	−	0.141178i	−0.00219503	−	0.00819196i
$298$		−	18.3568i		−	1.06338i
$299$	−20.3015	+	0.283385i	−1.17407	+	0.0163886i
$300$		−	7.79920i		−	0.450287i
$301$	8.00941	−	2.95416i	0.461655	−	0.170275i
$302$	9.18525	−	15.9093i	0.528552	−	0.915478i
$303$	8.74753	−	5.05039i	0.502532	−	0.290137i
$304$	−3.75610	−	3.75610i	−0.215427	−	0.215427i
$305$	38.4053	+	10.2907i	2.19908	+	0.589242i
$306$	−4.92717	−	1.32023i	−0.281668	−	0.0754726i
$307$	−17.1877	+	17.1877i	−0.980952	+	0.980952i	−0.999822	−	0.0188701i	$-0.993993\pi$
$307$	−17.1877	+	17.1877i	−0.980952	+	0.980952i	0.0188701	+	0.999822i	$0.493993\pi$
$308$	0.315810	−	0.223157i	0.0179949	−	0.0127156i
$309$	7.05787	+	4.07486i	0.401508	+	0.231811i
$310$	34.4098	−	9.22007i	1.95434	−	0.523665i
$311$	−12.9484			−0.734237			−0.367118	−	0.930174i	$-0.619656\pi$
$311$	−12.9484			−0.734237			−0.367118	+	0.930174i	$0.619656\pi$
$312$	2.58485	+	2.51368i	0.146338	+	0.142309i
$313$		−	14.9687i		−	0.846084i	−0.906110	−	0.423042i	$-0.860962\pi$
$313$		−	14.9687i		−	0.846084i	0.906110	−	0.423042i	$-0.139038\pi$
$314$	14.2226	−	3.81093i	0.802628	−	0.215063i
$315$	3.96343	−	8.59568i	0.223314	−	0.484311i
$316$	6.95473	−	4.01532i	0.391234	−	0.225879i
$317$	−6.93196	+	6.93196i	−0.389338	+	0.389338i	−0.874451	−	0.485113i	$-0.838778\pi$
$317$	−6.93196	+	6.93196i	−0.389338	+	0.389338i	0.485113	+	0.874451i	$0.338778\pi$
$318$	1.84766	−	6.89555i	0.103611	−	0.386683i
$319$	0.138678	−	0.517553i	0.00776447	−	0.0289774i
$320$	2.52974	−	2.52974i	0.141417	−	0.141417i
$321$	0.133918	−	0.0773176i	0.00747457	−	0.00431545i
$322$	−6.23848	+	13.5297i	−0.347657	+	0.753980i
$323$	−26.1728	+	7.01298i	−1.45629	+	0.390213i
$324$		−	1.00000i		−	0.0555556i
$325$	14.3987	+	24.1544i	0.798699	+	1.33984i
$326$	12.4120			0.687436
$327$	−7.89092	+	2.11437i	−0.436369	+	0.116925i
$328$	6.26572	+	3.61752i	0.345967	+	0.199744i
$329$	−5.54041	+	3.91496i	−0.305453	+	0.215839i
$330$	0.369742	−	0.369742i	0.0203536	−	0.0203536i
$331$	33.2990	+	8.92245i	1.83028	+	0.490422i	0.997958	−	0.0638711i	$-0.0203447\pi$
$331$	33.2990	+	8.92245i	1.83028	+	0.490422i	0.832322	+	0.554293i	$0.187011\pi$
$332$	−7.64113	−	2.04743i	−0.419361	−	0.112368i
$333$	2.67978	+	2.67978i	0.146851	+	0.146851i
$334$	−9.63730	+	5.56410i	−0.527330	+	0.304454i
$335$	8.93395	−	15.4740i	0.488114	−	0.845437i
$336$	2.48229	−	0.915557i	0.135420	−	0.0499477i
$337$			36.1304i			1.96815i	0.177751	+	0.984075i	$0.443118\pi$
$337$			36.1304i			1.96815i	−0.177751	+	0.984075i	$0.556882\pi$
$338$	−12.6461	−	3.01284i	−0.687855	−	0.163877i
$339$		−	0.0715534i		−	0.00388625i
$340$	−4.72326	−	17.6274i	−0.256155	−	0.955982i
$341$	1.26037	+	0.727677i	0.0682530	+	0.0394059i
$342$	−2.65597	−	4.60027i	−0.143618	−	0.248754i
$343$	16.1568	+	9.05297i	0.872388	+	0.488814i
$344$	3.11668	+	0.835111i	0.168040	+	0.0450262i
$345$	−5.21419	+	19.4596i	−0.280722	+	1.04767i
$346$	9.36608	−	9.36608i	0.503523	−	0.503523i
$347$	5.51197	+	9.54701i	0.295898	+	0.512510i	0.975193	−	0.221355i	$-0.0710478\pi$
$347$	5.51197	+	9.54701i	0.295898	+	0.512510i	−0.679295	+	0.733865i	$0.737715\pi$
$348$	1.83299	−	3.17482i	0.0982583	−	0.170188i
$349$	−1.93308	−	7.21435i	−0.103475	−	0.386175i	0.894692	−	0.446683i	$-0.147395\pi$
$349$	−1.93308	−	7.21435i	−0.103475	−	0.386175i	−0.998168	+	0.0605076i	$0.980728\pi$
$350$	20.5483	−	1.88660i	1.09835	−	0.100843i
$351$	1.84618	+	3.09703i	0.0985419	+	0.165307i
$352$	0.146158			0.00779024
$353$	11.9077	−	3.19067i	0.633785	−	0.169822i	0.0723982	−	0.997376i	$-0.476935\pi$
$353$	11.9077	−	3.19067i	0.633785	−	0.169822i	0.561387	+	0.827554i	$0.310268\pi$
$354$	2.11623	−	3.66542i	0.112476	−	0.194815i
$355$	−11.9974	−	20.7801i	−0.636755	−	1.10289i
$356$	−8.96931	−	8.96931i	−0.475372	−	0.475372i
$357$	2.28651	−	13.3008i	0.121015	−	0.703955i
$358$	3.93228	−	14.6755i	0.207828	−	0.775623i
$359$	−2.29322	−	2.29322i	−0.121031	−	0.121031i	0.643997	−	0.765028i	$-0.277275\pi$
$359$	−2.29322	−	2.29322i	−0.121031	−	0.121031i	−0.765028	+	0.643997i	$0.777275\pi$
$360$	3.09829	−	1.78880i	0.163294	−	0.0942780i
$361$	−7.98185	−	4.60832i	−0.420097	−	0.242543i
$362$	−0.392280	−	1.46401i	−0.0206178	−	0.0769466i
$363$	−10.9786			−0.576229
$364$	−5.99744	+	7.41827i	−0.314352	+	0.388823i
$365$	−40.0548			−2.09656
$366$	2.87642	+	10.7349i	0.150353	+	0.561124i
$367$	0.769489	+	0.444265i	0.0401670	+	0.0231904i	0.519949	−	0.854197i	$-0.325951\pi$
$367$	0.769489	+	0.444265i	0.0401670	+	0.0231904i	−0.479782	+	0.877388i	$0.659284\pi$
$368$	−4.87674	+	2.81559i	−0.254218	+	0.146773i
$369$	5.11594	+	5.11594i	0.266325	+	0.266325i
$370$	−3.50914	+	13.0963i	−0.182432	+	0.680845i
$371$	18.6144	+	3.19996i	0.966413	+	0.166134i
$372$	7.04095	+	7.04095i	0.365056	+	0.365056i
$373$	2.90414	+	5.03012i	0.150371	+	0.260450i	0.931364	−	0.364090i	$-0.118620\pi$
$373$	2.90414	+	5.03012i	0.150371	+	0.260450i	−0.780993	+	0.624540i	$0.785287\pi$
$374$	0.372774	−	0.645664i	0.0192757	−	0.0333865i
$375$	9.67318	−	2.59192i	0.499521	−	0.133846i
$376$	−2.56412			−0.132234
$377$	0.184487	+	13.2166i	0.00950158	+	0.680687i
$378$	2.63467	−	0.241896i	0.135513	−	0.0124418i
$379$	−5.36510	−	20.0228i	−0.275586	−	1.02850i	−0.955447	−	0.295162i	$-0.904627\pi$
$379$	−5.36510	−	20.0228i	−0.275586	−	1.02850i	0.679861	−	0.733341i	$-0.262040\pi$
$380$	9.50198	−	16.4579i	0.487441	−	0.844273i
$381$	−3.87019	−	6.70337i	−0.198276	−	0.343424i
$382$	−10.6142	+	10.6142i	−0.543069	+	0.543069i
$383$	1.97902	−	7.38580i	0.101123	−	0.377397i	−0.896753	−	0.442531i	$-0.854081\pi$
$383$	1.97902	−	7.38580i	0.101123	−	0.377397i	0.997877	+	0.0651339i	$0.0207474\pi$
$384$	0.965926	+	0.258819i	0.0492922	+	0.0132078i
$385$	1.06359	+	0.884708i	0.0542054	+	0.0450889i
$386$	−10.2737	−	17.7946i	−0.522919	−	0.905722i
$387$	2.79434	+	1.61331i	0.142044	+	0.0820092i
$388$	−1.80716	−	6.74442i	−0.0917447	−	0.342396i
$389$			14.5405i			0.737234i	0.929581	+	0.368617i	$0.120169\pi$
$389$			14.5405i			0.737234i	−0.929581	+	0.368617i	$0.879831\pi$
$390$	−6.29306	+	11.2600i	−0.318661	+	0.570171i
$391$			28.7245i			1.45266i
$392$	3.01265	+	6.31854i	0.152162	+	0.319135i
$393$	−0.559445	+	0.968986i	−0.0282202	+	0.0488789i
$394$	−12.0482	+	6.95604i	−0.606980	+	0.350440i
$395$	20.3154	+	20.3154i	1.02218	+	1.02218i
$396$	0.141178	+	0.0378284i	0.00709444	+	0.00190095i
$397$	−8.47081	−	2.26975i	−0.425138	−	0.113915i	0.0399051	−	0.999203i	$-0.487294\pi$
$397$	−8.47081	−	2.26975i	−0.425138	−	0.113915i	−0.465043	+	0.885288i	$0.653961\pi$
$398$	−6.52489	+	6.52489i	−0.327063	+	0.327063i
$399$	11.4777	−	8.11038i	0.574605	−	0.406027i
$400$	6.75431	+	3.89960i	0.337715	+	0.194980i
$401$	24.9872	−	6.69529i	1.24780	−	0.334347i	0.426313	−	0.904576i	$-0.359812\pi$
$401$	24.9872	−	6.69529i	1.24780	−	0.334347i	0.821486	+	0.570229i	$0.193145\pi$
$402$	4.99438			0.249097
$403$	−34.8049	−	8.80718i	−1.73376	−	0.438717i
$404$			10.1008i			0.502532i
$405$	3.45569	−	0.925950i	0.171715	−	0.0460108i
$406$	8.80800	+	4.06133i	0.437134	+	0.201561i
$407$	−0.479696	+	0.276953i	−0.0237777	+	0.0137280i
$408$	3.60694	−	3.60694i	0.178570	−	0.178570i
$409$	5.40561	−	20.1740i	0.267290	−	0.997541i	−0.693543	−	0.720415i	$-0.743951\pi$
$409$	5.40561	−	20.1740i	0.267290	−	0.997541i	0.960834	−	0.277126i	$-0.0893820\pi$
$410$	−6.69928	+	25.0021i	−0.330854	+	1.23476i
$411$	10.0883	−	10.0883i	0.497621	−	0.497621i
$412$	−7.05787	+	4.07486i	−0.347716	+	0.200754i
$413$	10.1691	+	4.68891i	0.500387	+	0.230726i
$414$	−5.43930	+	1.45746i	−0.267327	+	0.0716300i
$415$		−	28.3012i		−	1.38925i
$416$	−3.46933	+	0.981704i	−0.170098	+	0.0481320i
$417$	−15.5822			−0.763065
$418$	0.749926	−	0.200942i	0.0366801	−	0.00982840i
$419$	14.7014	+	8.48788i	0.718212	+	0.414660i	0.814094	−	0.580733i	$-0.197234\pi$
$419$	14.7014	+	8.48788i	0.718212	+	0.414660i	−0.0958821	+	0.995393i	$0.530567\pi$
$420$	5.46236	+	7.73027i	0.266536	+	0.377198i
$421$	16.0883	−	16.0883i	0.784096	−	0.784096i	−0.196423	−	0.980519i	$-0.562933\pi$
$421$	16.0883	−	16.0883i	0.784096	−	0.784096i	0.980519	+	0.196423i	$0.0629327\pi$
$422$	−15.1597	−	4.06202i	−0.737961	−	0.197736i
$423$	−2.47675	−	0.663644i	−0.120424	−	0.0322675i
$424$	5.04789	+	5.04789i	0.245147	+	0.245147i
$425$	34.4536	−	19.8918i	1.67125	−	0.964894i
$426$	3.35348	−	5.80839i	0.162476	−	0.281418i
$427$	−27.5872	+	10.1752i	−1.33504	+	0.492410i
$428$			0.154635i			0.00747457i
$429$	−0.507070	+	0.143484i	−0.0244816	+	0.00692746i
$430$			11.5436i			0.556680i
$431$	−0.746143	−	2.78464i	−0.0359404	−	0.134131i	0.945625	−	0.325260i	$-0.105452\pi$
$431$	−0.746143	−	2.78464i	−0.0359404	−	0.134131i	−0.981565	+	0.191129i	$0.938785\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	16.0890	+	27.8670i	0.773189	+	1.33920i	0.935807	+	0.352513i	$0.114673\pi$
$433$	16.0890	+	27.8670i	0.773189	+	1.33920i	−0.162618	+	0.986689i	$0.551994\pi$
$434$	−16.8474	+	20.2538i	−0.808701	+	0.972212i
$435$	12.6685	+	3.39451i	0.607407	+	0.162754i
$436$	2.11437	−	7.89092i	0.101260	−	0.377907i
$437$	−21.1513	+	21.1513i	−1.01180	+	1.01180i
$438$	−5.59800	−	9.69602i	−0.267483	−	0.463294i
$439$	9.52788	−	16.5028i	0.454741	−	0.787635i	−0.543932	−	0.839129i	$-0.683065\pi$
$439$	9.52788	−	16.5028i	0.454741	−	0.787635i	0.998673	+	0.0514945i	$0.0163985\pi$
$440$	0.135335	+	0.505077i	0.00645184	+	0.0240786i
$441$	1.27463	+	6.88297i	0.0606968	+	0.327761i
$442$	−4.51174	+	17.8299i	−0.214602	+	0.848081i
$443$	−15.5732			−0.739904			−0.369952	−	0.929051i	$-0.620626\pi$
$443$	−15.5732			−0.739904			−0.369952	+	0.929051i	$0.620626\pi$
$444$	−3.66064	+	0.980866i	−0.173726	+	0.0465499i
$445$	22.6900	−	39.3003i	1.07561	−	1.86301i
$446$	2.06462	+	3.57603i	0.0977626	+	0.169330i
$447$	12.9802	+	12.9802i	0.613942	+	0.613942i
$448$	−0.448249	+	2.60750i	−0.0211778	+	0.123193i
$449$	6.58392	−	24.5715i	0.310714	−	1.15960i	−0.617199	−	0.786807i	$-0.711733\pi$
$449$	6.58392	−	24.5715i	0.310714	−	1.15960i	0.927914	−	0.372795i	$-0.121600\pi$
$450$	5.51487	+	5.51487i	0.259973	+	0.259973i
$451$	−0.915784	+	0.528728i	−0.0431226	+	0.0248968i
$452$	0.0619671	+	0.0357767i	0.00291469	+	0.00168279i
$453$	4.75463	+	17.7445i	0.223392	+	0.833711i
$454$	26.5948			1.24816
$455$	−31.1886	−	13.8564i	−1.46214	−	0.649597i
$456$	5.31193			0.248754
$457$	7.14603	+	26.6694i	0.334277	+	1.24754i	0.904650	+	0.426154i	$0.140132\pi$
$457$	7.14603	+	26.6694i	0.334277	+	1.24754i	−0.570373	+	0.821386i	$0.693201\pi$
$458$	−17.4702	−	10.0864i	−0.816329	−	0.471308i
$459$	4.41758	−	2.55049i	0.206195	−	0.119047i
$460$	−14.2454	−	14.2454i	−0.664196	−	0.664196i
$461$	7.08637	−	26.4467i	0.330045	−	1.23174i	−0.579097	−	0.815259i	$-0.696595\pi$
$461$	7.08637	−	26.4467i	0.330045	−	1.23174i	0.909142	−	0.416486i	$-0.136739\pi$
$462$	−0.0655151	+	0.381107i	−0.00304804	+	0.0177307i
$463$	13.3036	+	13.3036i	0.618271	+	0.618271i	0.945088	−	0.326817i	$-0.105976\pi$
$463$	13.3036	+	13.3036i	0.618271	+	0.618271i	−0.326817	+	0.945088i	$0.605976\pi$
$464$	1.83299	+	3.17482i	0.0850942	+	0.147387i
$465$	−17.8118	+	30.8509i	−0.826003	+	1.43068i
$466$	−12.7514	+	3.41672i	−0.590696	+	0.158276i
$467$	−32.2700			−1.49328			−0.746640	−	0.665229i	$-0.768334\pi$
$467$	−32.2700			−1.49328			−0.746640	+	0.665229i	$0.768334\pi$
$468$	−3.60520	+	0.0503243i	−0.166650	+	0.00232624i
$469$	1.20812	+	13.1586i	0.0557859	+	0.607605i
$470$	−2.37425	−	8.86082i	−0.109516	−	0.408719i
$471$	−7.36216	+	12.7516i	−0.339230	+	0.587564i
$472$	2.11623	+	3.66542i	0.0974073	+	0.168714i
$473$	−0.333469	+	0.333469i	−0.0153329	+	0.0153329i
$474$	−2.07848	+	7.75700i	−0.0954678	+	0.356291i
$475$	40.0172	+	10.7226i	1.83611	+	0.491985i
$476$	10.3756	+	8.63059i	0.475565	+	0.395583i
$477$	3.56940	+	6.18238i	0.163431	+	0.283072i
$478$	19.7788	+	11.4193i	0.904661	+	0.522307i
$479$	−6.91383	−	25.8028i	−0.315901	−	1.17896i	−0.923148	−	0.384445i	$-0.874393\pi$
$479$	−6.91383	−	25.8028i	−0.315901	−	1.17896i	0.607247	−	0.794513i	$-0.292274\pi$
$480$			3.57760i			0.163294i
$481$	9.52627	−	9.79599i	0.434361	−	0.446659i
$482$			26.9631i			1.22814i
$483$	−5.15566	−	13.9782i	−0.234591	−	0.636030i
$484$	5.48932	−	9.50778i	0.249514	−	0.432172i
$485$	21.6333	−	12.4900i	0.982317	−	0.567141i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	7.81258	+	2.09337i	0.354022	+	0.0948598i	0.431447	−	0.902138i	$-0.358003\pi$
$487$	7.81258	+	2.09337i	0.354022	+	0.0948598i	−0.0774252	+	0.996998i	$0.524670\pi$
$488$	−10.7349	−	2.87642i	−0.485948	−	0.130209i
$489$	−8.77660	+	8.77660i	−0.396891	+	0.396891i
$490$	−19.0454	+	16.2614i	−0.860383	+	0.734617i
$491$	−24.2765	−	14.0161i	−1.09558	−	0.632536i	−0.160527	−	0.987031i	$-0.551319\pi$
$491$	−24.2765	−	14.0161i	−1.09558	−	0.632536i	−0.935058	+	0.354495i	$0.884653\pi$
$492$	−6.98851	+	1.87256i	−0.315066	+	0.0844217i
$493$	18.7001			0.842208
$494$	−16.4512	+	9.80680i	−0.740176	+	0.441229i
$495$			0.522894i			0.0235023i
$496$	−9.61812	+	2.57717i	−0.431866	+	0.115718i
$497$	16.1144	+	7.43028i	0.722829	+	0.333293i
$498$	6.85085	−	3.95534i	0.306994	−	0.177243i
$499$	16.4680	−	16.4680i	0.737210	−	0.737210i	−0.234827	−	0.972037i	$-0.575452\pi$
$499$	16.4680	−	16.4680i	0.737210	−	0.737210i	0.972037	+	0.234827i	$0.0754524\pi$
$500$	−2.59192	+	9.67318i	−0.115914	+	0.432598i
$501$	2.88019	−	10.7490i	0.128677	−	0.480230i
$502$	21.0918	−	21.0918i	0.941374	−	0.941374i
$503$	25.2775	−	14.5940i	1.12707	−	0.650713i	0.183872	−	0.982950i	$-0.441137\pi$
$503$	25.2775	−	14.5940i	1.12707	−	0.650713i	0.943196	+	0.332237i	$0.107803\pi$
$504$	−1.10785	+	2.40264i	−0.0493474	+	0.107022i
$505$	−34.9052	+	9.35281i	−1.55326	+	0.416195i
$506$		−	0.823040i		−	0.0365886i
$507$	11.0725	−	6.81171i	0.491748	−	0.302519i
$508$	7.74039			0.343424
$509$	−17.2162	+	4.61306i	−0.763093	+	0.204470i	−0.619318	−	0.785140i	$-0.712591\pi$
$509$	−17.2162	+	4.61306i	−0.763093	+	0.204470i	−0.143775	+	0.989610i	$0.545924\pi$
$510$	15.8043	+	9.12463i	0.699827	+	0.404045i
$511$	24.1917	−	17.0943i	1.07018	−	0.756208i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	5.13093	+	1.37483i	0.226536	+	0.0607002i
$514$	17.6659	+	4.73356i	0.779209	+	0.208788i
$515$	−20.6167	−	20.6167i	−0.908481	−	0.908481i
$516$	−2.79434	+	1.61331i	−0.123014	+	0.0710221i
$517$	0.187383	−	0.324557i	0.00824110	−	0.0142740i
$518$	−3.46975	−	9.40732i	−0.152452	−	0.413334i
$519$			13.2456i			0.581419i
$520$	−6.60490	−	11.0799i	−0.289644	−	0.485887i
$521$			23.2693i			1.01944i	0.860339	+	0.509722i	$0.170252\pi$
$521$			23.2693i			1.01944i	−0.860339	+	0.509722i	$0.829748\pi$
$522$	0.948823	+	3.54106i	0.0415289	+	0.154988i
$523$	22.0867	+	12.7518i	0.965785	+	0.557596i	0.897949	−	0.440101i	$-0.145057\pi$
$523$	22.0867	+	12.7518i	0.965785	+	0.557596i	0.0678360	+	0.997696i	$0.478391\pi$
$524$	−0.559445	−	0.968986i	−0.0244394	−	0.0423304i
$525$	−13.1958	+	15.8639i	−0.575913	+	0.692357i
$526$	13.6043	+	3.64527i	0.593177	+	0.158941i
$527$	−13.1461	+	49.0619i	−0.572653	+	2.13717i
$528$	−0.103349	+	0.103349i	−0.00449770	+	0.00449770i
$529$	4.35506	+	7.54319i	0.189350	+	0.327965i
$530$	−12.7699	+	22.1181i	−0.554688	+	0.960747i
$531$	1.09544	+	4.08824i	0.0475381	+	0.177415i
$532$	1.28494	+	13.9952i	0.0557091	+	0.606769i
$533$	18.1865	−	18.7014i	0.787746	−	0.810050i
$534$	12.6845			0.548913
$535$	−0.534372	+	0.143184i	−0.0231029	+	0.00619040i
$536$	−2.49719	+	4.32526i	−0.107862	+	0.186823i
$537$	7.59659	+	13.1577i	0.327817	+	0.567796i
$538$	−15.1423	−	15.1423i	−0.652830	−	0.652830i
$539$	−1.01994	−	0.0804224i	−0.0439319	−	0.00346404i
$540$	−0.925950	+	3.45569i	−0.0398466	+	0.148709i
$541$	−8.39604	−	8.39604i	−0.360974	−	0.360974i	0.503197	−	0.864171i	$-0.332157\pi$
$541$	−8.39604	−	8.39604i	−0.360974	−	0.360974i	−0.864171	+	0.503197i	$0.832157\pi$
$542$	−27.1205	+	15.6580i	−1.16492	+	0.672569i
$543$	1.31259	+	0.757827i	0.0563288	+	0.0325215i
$544$	1.32023	+	4.92717i	0.0566045	+	0.211251i
$545$	29.2264			1.25192
$546$	−1.00467	−	9.48634i	−0.0429960	−	0.405978i
$547$	−16.6366			−0.711330			−0.355665	−	0.934613i	$-0.615746\pi$
$547$	−16.6366			−0.711330			−0.355665	+	0.934613i	$0.615746\pi$
$548$	3.69259	+	13.7809i	0.157739	+	0.588692i
$549$	−9.62468	−	5.55681i	−0.410772	−	0.237159i
$550$	−0.987195	+	0.569957i	−0.0420941	+	0.0243031i
$551$	13.7698	+	13.7698i	0.586612	+	0.586612i
$552$	1.45746	−	5.43930i	0.0620334	−	0.231512i
$553$	−20.9399	−	3.59972i	−0.890455	−	0.153076i
$554$	−1.17529	−	1.17529i	−0.0499333	−	0.0499333i
$555$	−6.77915	−	11.7418i	−0.287759	−	0.498413i
$556$	7.79111	−	13.4946i	0.330417	−	0.572299i
$557$	40.4995	−	10.8518i	1.71602	−	0.459806i	0.739132	−	0.673561i	$-0.235236\pi$
$557$	40.4995	−	10.8518i	1.71602	−	0.459806i	0.976887	+	0.213755i	$0.0685694\pi$
$558$	−9.95741			−0.421531
$559$	5.67569	−	10.1553i	0.240056	−	0.429525i
$560$	−9.42579	+	0.865407i	−0.398312	+	0.0365701i
$561$	0.192962	+	0.720145i	0.00814687	+	0.0304045i
$562$	5.26643	−	9.12173i	0.222151	−	0.384777i
$563$	−4.65785	−	8.06763i	−0.196305	−	0.340010i	0.751023	−	0.660276i	$-0.229561\pi$
$563$	−4.65785	−	8.06763i	−0.196305	−	0.340010i	−0.947327	+	0.320266i	$0.896228\pi$
$564$	1.81311	−	1.81311i	0.0763456	−	0.0763456i
$565$	−0.0662549	+	0.247267i	−0.00278737	+	0.0104026i
$566$	−11.0573	−	2.96278i	−0.464771	−	0.124535i
$567$	−1.69195	+	2.03404i	−0.0710551	+	0.0854216i
$568$	3.35348	+	5.80839i	0.140709	+	0.243715i
$569$	1.41738	+	0.818326i	0.0594198	+	0.0343060i	0.529416	−	0.848363i	$-0.322411\pi$
$569$	1.41738	+	0.818326i	0.0594198	+	0.0343060i	−0.469996	+	0.882669i	$0.655745\pi$
$570$	4.91859	+	18.3564i	0.206017	+	0.768866i
$571$			12.7108i			0.531931i	0.963983	+	0.265966i	$0.0856908\pi$
$571$			12.7108i			0.531931i	−0.963983	+	0.265966i	$0.914309\pi$
$572$	0.129274	−	0.510877i	0.00540523	−	0.0213608i
$573$		−	15.0107i		−	0.627082i
$574$	−6.62408	−	17.9594i	−0.276484	−	0.749613i
$575$	21.9593	−	38.0347i	0.915767	−	1.58616i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$	−31.8482	−	31.8482i	−1.32586	−	1.32586i	−0.908948	−	0.416910i	$-0.863113\pi$
$577$	−31.8482	−	31.8482i	−1.32586	−	1.32586i	−0.416910	−	0.908948i	$-0.636887\pi$
$578$	8.71268	+	2.33456i	0.362400	+	0.0971047i
$579$	19.8473	+	5.31807i	0.824826	+	0.221012i
$580$	−9.27396	+	9.27396i	−0.385080	+	0.385080i
$581$	12.0782	+	17.0929i	0.501088	+	0.709135i
$582$	6.04688	+	3.49117i	0.250651	+	0.144713i
$583$	−1.00784	+	0.270049i	−0.0417404	+	0.0111843i
$584$	11.1960			0.463294
$585$	−3.51214	−	12.4119i	−0.145209	−	0.513168i
$586$			27.3620i			1.13031i
$587$	−25.6092	+	6.86196i	−1.05700	+	0.283224i	−0.745144	−	0.666904i	$-0.767619\pi$
$587$	−25.6092	+	6.86196i	−1.05700	+	0.283224i	−0.311861	+	0.950128i	$0.600952\pi$
$588$	−6.59815	−	2.33762i	−0.272103	−	0.0964019i
$589$	−45.8068	+	26.4466i	−1.88744	+	1.08971i
$590$	−10.7070	+	10.7070i	−0.440801	+	0.440801i
$591$	3.60071	−	13.4380i	0.148113	−	0.552767i
$592$	0.980866	−	3.66064i	0.0403134	−	0.150452i
$593$	5.45292	−	5.45292i	0.223925	−	0.223925i	−0.586224	−	0.810149i	$-0.699386\pi$
$593$	5.45292	−	5.45292i	0.223925	−	0.223925i	0.810149	+	0.586224i	$0.199386\pi$
$594$	−0.126576	+	0.0730789i	−0.00519349	+	0.00299846i
$595$	−20.2174	+	43.8464i	−0.828832	+	1.79753i
$596$	−17.7313	+	4.75108i	−0.726302	+	0.194612i
$597$		−	9.22759i		−	0.377660i
$598$	5.52815	+	19.5364i	0.226063	+	0.798903i
$599$	−1.76811			−0.0722431			−0.0361216	−	0.999347i	$-0.511500\pi$
$599$	−1.76811			−0.0722431			−0.0361216	+	0.999347i	$0.511500\pi$
$600$	−7.53345	+	2.01858i	−0.307552	+	0.0824083i
$601$	−6.83600	−	3.94677i	−0.278846	−	0.160992i	0.354055	−	0.935225i	$-0.384803\pi$
$601$	−6.83600	−	3.94677i	−0.278846	−	0.160992i	−0.632901	+	0.774233i	$0.718136\pi$
$602$	−4.92648	−	6.97190i	−0.200788	−	0.284154i
$603$	−3.53156	+	3.53156i	−0.143816	+	0.143816i
$604$	−17.7445	−	4.75463i	−0.722015	−	0.193463i
$605$	37.9388	+	10.1657i	1.54243	+	0.413293i
$606$	−7.14233	−	7.14233i	−0.290137	−	0.290137i
$607$	−29.6635	+	17.1262i	−1.20401	+	0.695133i	−0.961443	−	0.275003i	$-0.911321\pi$
$607$	−29.6635	+	17.1262i	−1.20401	+	0.695133i	−0.242562	+	0.970136i	$0.577988\pi$
$608$	−2.65597	+	4.60027i	−0.107714	+	0.186566i
$609$	−9.10000	+	3.35640i	−0.368750	+	0.136008i
$610$		−	39.7601i		−	1.60984i
$611$	−2.26793	+	8.96258i	−0.0917505	+	0.362587i
$612$			5.10098i			0.206195i
$613$	−3.59944	−	13.4333i	−0.145380	−	0.542565i	−0.999738	−	0.0228806i	$-0.992716\pi$
$613$	−3.59944	−	13.4333i	−0.145380	−	0.542565i	0.854358	−	0.519684i	$-0.173950\pi$
$614$	21.0505	+	12.1535i	0.849529	+	0.490476i
$615$	−12.9420	−	22.4162i	−0.521873	−	0.903910i
$616$	−0.297291	−	0.247291i	−0.0119782	−	0.00996365i
$617$	−10.0295	−	2.68739i	−0.403772	−	0.108190i	0.0512170	−	0.998688i	$-0.483690\pi$
$617$	−10.0295	−	2.68739i	−0.403772	−	0.108190i	−0.454989	+	0.890497i	$0.650357\pi$
$618$	2.10930	−	7.87203i	0.0848486	−	0.316659i
$619$	−0.0354371	+	0.0354371i	−0.00142434	+	0.00142434i	−0.707819	−	0.706394i	$-0.750321\pi$
$619$	−0.0354371	+	0.0354371i	−0.00142434	+	0.00142434i	0.706394	+	0.707819i	$0.250321\pi$
$620$	−17.8118	−	30.8509i	−0.715339	−	1.23900i
$621$	2.81559	−	4.87674i	0.112986	−	0.195697i
$622$	3.35129	+	12.5072i	0.134375	+	0.501493i
$623$	3.06834	+	33.4195i	0.122930	+	1.33892i
$624$	1.75902	−	3.14736i	0.0704171	−	0.125995i
$625$	3.16846			0.126738
$626$	−14.4587	+	3.87420i	−0.577886	+	0.154844i
$627$	−0.388190	+	0.672365i	−0.0155028	+	0.0268517i
$628$	−7.36216	−	12.7516i	−0.293782	−	0.508845i
$629$	−13.6695	−	13.6695i	−0.545039	−	0.545039i
$630$	−9.32860	−	1.60365i	−0.371660	−	0.0638911i
$631$	−5.82232	+	21.7292i	−0.231783	+	0.865026i	0.747790	+	0.663936i	$0.231115\pi$
$631$	−5.82232	+	21.7292i	−0.231783	+	0.865026i	−0.979573	+	0.201090i	$0.935552\pi$
$632$	−5.67852	−	5.67852i	−0.225879	−	0.225879i
$633$	13.5918	−	7.84722i	0.540225	−	0.311899i
$634$	8.48989	+	4.90164i	0.337177	+	0.194669i
$635$	7.16722	+	26.7484i	0.284422	+	1.06148i
$636$	−7.13879			−0.283072
$637$	24.7503	−	4.94169i	0.980644	−	0.195797i
$638$	−0.535810			−0.0212129
$639$	1.73589	+	6.47842i	0.0686706	+	0.256282i
$640$	−3.09829	−	1.78880i	−0.122471	−	0.0707085i
$641$	12.8186	−	7.40080i	0.506303	−	0.292314i	−0.225010	−	0.974356i	$-0.572241\pi$
$641$	12.8186	−	7.40080i	0.506303	−	0.292314i	0.731312	+	0.682043i	$0.238908\pi$
$642$	−0.109344	−	0.109344i	−0.00431545	−	0.00431545i
$643$	−1.02867	+	3.83904i	−0.0405667	+	0.151397i	−0.983238	−	0.182325i	$-0.941638\pi$
$643$	−1.02867	+	3.83904i	−0.0405667	+	0.151397i	0.942672	+	0.333721i	$0.108305\pi$
$644$	14.6833	+	2.52417i	0.578603	+	0.0994662i
$645$	−8.16253	−	8.16253i	−0.321399	−	0.321399i
$646$	13.5480	+	23.4659i	0.533041	+	0.923254i
$647$	18.0664	−	31.2919i	0.710263	−	1.23021i	−0.254496	−	0.967074i	$-0.581909\pi$
$647$	18.0664	−	31.2919i	0.710263	−	1.23021i	0.964758	−	0.263137i	$-0.0847572\pi$
$648$	−0.965926	+	0.258819i	−0.0379452	+	0.0101674i
$649$	−0.618607			−0.0242824
$650$	19.6047	−	20.1597i	0.768959	−	0.790730i
$651$	−2.40866	−	26.2345i	−0.0944028	−	1.02821i
$652$	−3.21246	−	11.9891i	−0.125810	−	0.469528i
$653$	−13.0737	+	22.6443i	−0.511612	+	0.886139i	0.488297	+	0.872678i	$0.337618\pi$
$653$	−13.0737	+	22.6443i	−0.511612	+	0.886139i	−0.999909	+	0.0134612i	$0.995715\pi$
$654$	4.08464	+	7.07481i	0.159722	+	0.276647i
$655$	2.83050	−	2.83050i	0.110597	−	0.110597i
$656$	1.87256	−	6.98851i	0.0731114	−	0.272855i
$657$	10.8145	+	2.89774i	0.421914	+	0.113051i
$658$	5.21552	+	4.33836i	0.203322	+	0.169127i
$659$	3.33965	+	5.78444i	0.130094	+	0.225330i	0.923713	−	0.383086i	$-0.125139\pi$
$659$	3.33965	+	5.78444i	0.130094	+	0.225330i	−0.793618	+	0.608416i	$0.791805\pi$
$660$	−0.452839	−	0.261447i	−0.0176267	−	0.0101768i
$661$	5.95568	+	22.2269i	0.231649	+	0.864527i	0.979631	+	0.200807i	$0.0643564\pi$
$661$	5.95568	+	22.2269i	0.231649	+	0.864527i	−0.747982	+	0.663719i	$0.768977\pi$
$662$		−	34.4737i		−	1.33986i
$663$	−9.41734	−	15.7979i	−0.365739	−	0.613540i
$664$			7.91068i			0.306994i
$665$	−47.1733	+	17.3992i	−1.82930	+	0.674712i
$666$	1.89489	−	3.28204i	0.0734254	−	0.127177i
$667$	17.8780	−	10.3219i	0.692238	−	0.399664i
$668$	7.86882	+	7.86882i	0.304454	+	0.304454i
$669$	−3.98854	−	1.06873i	−0.154206	−	0.0413193i
$670$	−17.2591	−	4.62455i	−0.666776	−	0.178662i
$671$	1.14858	−	1.14858i	0.0443406	−	0.0443406i
$672$	−1.52682	−	2.16074i	−0.0588985	−	0.0833525i
$673$	21.7119	+	12.5354i	0.836932	+	0.483203i	0.856220	−	0.516611i	$-0.172807\pi$
$673$	21.7119	+	12.5354i	0.836932	+	0.483203i	−0.0192884	+	0.999814i	$0.506140\pi$
$674$	34.8993	−	9.35125i	1.34427	−	0.360197i
$675$	−7.79920			−0.300191
$676$	0.362858	+	12.9949i	0.0139561	+	0.499805i
$677$			11.0346i			0.424096i	0.977259	+	0.212048i	$0.0680133\pi$
$677$			11.0346i			0.424096i	−0.977259	+	0.212048i	$0.931987\pi$
$678$	−0.0691153	+	0.0185194i	−0.00265436	+	0.000711233i
$679$	−7.73535	+	16.7760i	−0.296856	+	0.643805i
$680$	−15.8043	+	9.12463i	−0.606068	+	0.349914i
$681$	−18.8054	+	18.8054i	−0.720623	+	0.720623i
$682$	0.376673	−	1.40576i	0.0144236	−	0.0538295i
$683$	−3.55612	+	13.2716i	−0.136071	+	0.507825i	0.863920	+	0.503629i	$0.168002\pi$
$683$	−3.55612	+	13.2716i	−0.136071	+	0.507825i	−0.999991	+	0.00419577i	$0.998664\pi$
$684$	−3.75610	+	3.75610i	−0.143618	+	0.143618i
$685$	−44.2035	+	25.5209i	−1.68893	+	0.975103i
$686$	4.56280	−	17.9494i	0.174208	−	0.685311i
$687$	19.4855	−	5.22112i	0.743417	−	0.199198i
$688$		−	3.22662i		−	0.123014i
$689$	22.1091	−	13.1795i	0.842289	−	0.502100i
$690$	20.1461			0.766948
$691$	33.1008	−	8.86934i	1.25922	−	0.337406i	0.433326	−	0.901237i	$-0.357340\pi$
$691$	33.1008	−	8.86934i	1.25922	−	0.337406i	0.825890	+	0.563832i	$0.190673\pi$
$692$	−11.4711	−	6.62282i	−0.436064	−	0.251762i
$693$	−0.223157	−	0.315810i	−0.00847704	−	0.0119966i
$694$	7.79510	−	7.79510i	0.295898	−	0.295898i
$695$	53.8474	+	14.4284i	2.04255	+	0.547299i
$696$	−3.54106	−	0.948823i	−0.134223	−	0.0359650i
$697$	−26.0963	−	26.0963i	−0.988469	−	0.988469i
$698$	−6.46821	+	3.73442i	−0.244825	+	0.141350i
$699$	6.60060	−	11.4326i	0.249657	−	0.432419i
$700$	−7.14061	−	19.3599i	−0.269890	−	0.731734i
$701$		−	23.3747i		−	0.882848i	−0.897299	−	0.441424i	$-0.854473\pi$
$701$		−	23.3747i		−	0.882848i	0.897299	−	0.441424i	$-0.145527\pi$
$702$	2.51368	−	2.58485i	0.0948726	−	0.0975587i
$703$		−	20.1310i		−	0.759257i
$704$	−0.0378284	−	0.141178i	−0.00142571	−	0.00532083i
$705$	7.94439	+	4.58670i	0.299203	+	0.172745i
$706$	−6.16390	−	10.6762i	−0.231981	−	0.401803i
$707$	17.0900	−	20.5454i	0.642734	−	0.772688i
$708$	−4.08824	−	1.09544i	−0.153645	−	0.0411692i
$709$	−7.88323	+	29.4206i	−0.296061	+	1.10491i	0.644310	+	0.764764i	$0.277145\pi$
$709$	−7.88323	+	29.4206i	−0.296061	+	1.10491i	−0.940371	+	0.340150i	$0.889522\pi$
$710$	−16.9669	+	16.9669i	−0.636755	+	0.636755i
$711$	−4.01532	−	6.95473i	−0.150586	−	0.260823i
$712$	−6.34226	+	10.9851i	−0.237686	+	0.411685i
$713$	14.5125	+	54.1613i	0.543497	+	2.02836i
$714$	−13.4394	+	1.23391i	−0.502957	+	0.0461779i
$715$	1.88514	−	0.0263143i	0.0705001	−	0.000984098i
$716$	−15.1932			−0.567796
$717$	−22.0604	+	5.91106i	−0.823860	+	0.220753i
$718$	−1.62155	+	2.80860i	−0.0605156	+	0.104816i
$719$	−4.79230	−	8.30051i	−0.178723	−	0.309557i	0.762721	−	0.646728i	$-0.223863\pi$
$719$	−4.79230	−	8.30051i	−0.178723	−	0.309557i	−0.941443	+	0.337171i	$0.890530\pi$
$720$	−2.52974	−	2.52974i	−0.0942780	−	0.0942780i
$721$	21.2504	+	3.65311i	0.791407	+	0.136049i
$722$	−2.38544	+	8.90260i	−0.0887770	+	0.331320i
$723$	−19.0658	−	19.0658i	−0.709064	−	0.709064i
$724$	−1.31259	+	0.757827i	−0.0487822	+	0.0281644i
$725$	−24.7611	−	14.2958i	−0.919604	−	0.530933i
$726$	2.84148	+	10.6045i	0.105457	+	0.393572i
$727$	−28.0599			−1.04068			−0.520341	−	0.853958i	$-0.674195\pi$
$727$	−28.0599			−1.04068			−0.520341	+	0.853958i	$0.674195\pi$
$728$	8.71775	+	3.87310i	0.323101	+	0.143547i
$729$	−1.00000			−0.0370370
$730$	10.3669	+	38.6899i	0.383697	+	1.43198i
$731$	−14.2539	−	8.22947i	−0.527198	−	0.304378i
$732$	9.62468	−	5.55681i	0.355739	−	0.205386i
$733$	24.8749	+	24.8749i	0.918776	+	0.918776i	0.996940	−	0.0781647i	$-0.0249060\pi$
$733$	24.8749	+	24.8749i	0.918776	+	0.918776i	−0.0781647	+	0.996940i	$0.524906\pi$
$734$	0.229968	−	0.858254i	0.00848829	−	0.0316787i
$735$	1.96855	−	24.9657i	0.0726110	−	0.920873i
$736$	3.98184	+	3.98184i	0.146773	+	0.146773i
$737$	−0.364984	−	0.632171i	−0.0134444	−	0.0232863i
$738$	3.61752	−	6.26572i	0.133163	−	0.230644i
$739$	−28.0890	+	7.52644i	−1.03327	+	0.276864i	−0.735323	−	0.677717i	$-0.762969\pi$
$739$	−28.0890	+	7.52644i	−1.03327	+	0.276864i	−0.297949	+	0.954582i	$0.596303\pi$
$740$	13.5583			0.498413
$741$	4.69833	−	18.5672i	0.172597	−	0.682084i
$742$	−1.72685	−	18.8084i	−0.0633945	−	0.690477i
$743$	5.86267	+	21.8798i	0.215080	+	0.802691i	0.986138	+	0.165926i	$0.0530613\pi$
$743$	5.86267	+	21.8798i	0.215080	+	0.802691i	−0.771058	+	0.636765i	$0.780272\pi$
$744$	4.97871	−	8.62337i	0.182528	−	0.316148i
$745$	−32.8366	−	56.8746i	−1.20304	−	2.08372i
$746$	4.10708	−	4.10708i	0.150371	−	0.150371i
$747$	−2.04743	+	7.64113i	−0.0749117	+	0.279574i
$748$	−0.720145	−	0.192962i	−0.0263311	−	0.00705540i
$749$	0.261634	−	0.314534i	0.00955991	−	0.0114928i
$750$	−5.00721	−	8.67274i	−0.182837	−	0.316684i
$751$	11.5957	+	6.69480i	0.423135	+	0.244297i	0.696418	−	0.717637i	$-0.254776\pi$
$751$	11.5957	+	6.69480i	0.423135	+	0.244297i	−0.273283	+	0.961934i	$0.588110\pi$
$752$	0.663644	+	2.47675i	0.0242006	+	0.0903178i
$753$			29.8283i			1.08701i
$754$	12.7185	−	3.59890i	0.463179	−	0.131064i
$755$		−	65.7222i		−	2.39188i
$756$	−0.915557	−	2.48229i	−0.0332985	−	0.0902800i
$757$	−3.11864	+	5.40165i	−0.113349	+	0.196326i	−0.917119	−	0.398615i	$-0.869491\pi$
$757$	−3.11864	+	5.40165i	−0.113349	+	0.196326i	0.803770	+	0.594941i	$0.202824\pi$
$758$	−17.9520	+	10.3646i	−0.652045	+	0.376458i
$759$	0.581977	+	0.581977i	0.0211244	+	0.0211244i
$760$	−18.3564	−	4.91859i	−0.665857	−	0.178416i
$761$	1.21124	+	0.324552i	0.0439075	+	0.0117650i	0.280706	−	0.959794i	$-0.409431\pi$
$761$	1.21124	+	0.324552i	0.0439075	+	0.0117650i	−0.236798	+	0.971559i	$0.576098\pi$
$762$	−5.47328	+	5.47328i	−0.198276	+	0.198276i
$763$	−17.6517	+	12.4731i	−0.639035	+	0.451555i
$764$	12.9997	+	7.50536i	0.470311	+	0.271534i
$765$	−17.6274	+	4.72326i	−0.637321	+	0.170770i
$766$	−7.64634			−0.276274
$767$	14.6838	−	4.15502i	0.530201	−	0.150029i
$768$		−	1.00000i		−	0.0360844i
$769$	14.0382	−	3.76152i	0.506230	−	0.135644i	0.00334025	−	0.999994i	$-0.498937\pi$
$769$	14.0382	−	3.76152i	0.506230	−	0.135644i	0.502890	+	0.864350i	$0.332270\pi$
$770$	0.579286	−	1.25633i	0.0208760	−	0.0452748i
$771$	−15.8388	+	9.14454i	−0.570421	+	0.329332i
$772$	−14.5292	+	14.5292i	−0.522919	+	0.522919i
$773$	0.719646	−	2.68575i	0.0258839	−	0.0965999i	−0.951776	−	0.306795i	$-0.900743\pi$
$773$	0.719646	−	2.68575i	0.0258839	−	0.0965999i	0.977659	+	0.210195i	$0.0674100\pi$
$774$	0.835111	−	3.11668i	0.0300175	−	0.112027i
$775$	54.9138	−	54.9138i	1.97256	−	1.97256i
$776$	−6.04688	+	3.49117i	−0.217070	+	0.125326i
$777$	9.10547	+	4.19849i	0.326657	+	0.150620i
$778$	14.0451	−	3.76337i	0.503540	−	0.134923i
$779$		−	38.4320i		−	1.37697i
$780$	12.5051	+	3.16433i	0.447753	+	0.113301i
$781$	−0.980274			−0.0350770
$782$	27.7458	−	7.43445i	0.992186	−	0.265856i
$783$	−3.17482	−	1.83299i	−0.113459	−	0.0655055i
$784$	5.32351	−	4.54535i	0.190125	−	0.162334i
$785$	37.2487	−	37.2487i	1.32946	−	1.32946i
$786$	1.08076	+	0.289590i	0.0385496	+	0.0103293i
$787$	15.6974	+	4.20610i	0.559551	+	0.149931i	0.527500	−	0.849555i	$-0.323130\pi$
$787$	15.6974	+	4.20610i	0.559551	+	0.149931i	0.0320508	+	0.999486i	$0.489796\pi$
$788$	9.83732	+	9.83732i	0.350440	+	0.350440i
$789$	−12.1973	+	7.04212i	−0.434236	+	0.250706i
$790$	14.3652	−	24.8812i	0.511090	−	0.885235i
$791$	−0.0655112	−	0.177616i	−0.00232931	−	0.00631531i
$792$		−	0.146158i		−	0.00519349i
$793$	−19.5491	+	34.9786i	−0.694208	+	1.24212i
$794$			8.76963i			0.311222i
$795$	−6.61017	−	24.6695i	−0.234439	−	0.874937i
$796$	7.99132	+	4.61379i	0.283245	+	0.163532i
$797$	23.1421	+	40.0833i	0.819735	+	1.41982i	0.905878	+	0.423539i	$0.139212\pi$
$797$	23.1421	+	40.0833i	0.819735	+	1.41982i	−0.0861432	+	0.996283i	$0.527454\pi$
$798$	−10.8047	−	8.98751i	−0.382482	−	0.318154i
$799$	12.6339	+	3.38523i	0.446954	+	0.119761i
$800$	2.01858	−	7.53345i	0.0713676	−	0.266348i
$801$	−8.96931	+	8.96931i	−0.316915	+	0.316915i
$802$	−12.9343	−	22.4029i	−0.456726	−	0.791073i
$803$	−0.818191	+	1.41715i	−0.0288733	+	0.0500101i
$804$	−1.29264	−	4.82420i	−0.0455879	−	0.170137i
$805$	4.87326	+	53.0783i	0.171760	+	1.87076i
$806$	0.501100	+	35.8985i	0.0176505	+	1.26447i
$807$	21.4144			0.753824
$808$	9.75660	−	2.61427i	0.343236	−	0.0919698i
$809$	27.3471	−	47.3666i	0.961474	−	1.66532i	0.242670	−	0.970109i	$-0.421977\pi$
$809$	27.3471	−	47.3666i	0.961474	−	1.66532i	0.718804	−	0.695213i	$-0.244690\pi$
$810$	−1.78880	−	3.09829i	−0.0628520	−	0.108863i
$811$	1.16693	+	1.16693i	0.0409764	+	0.0409764i	0.727298	−	0.686322i	$-0.240776\pi$
$811$	1.16693	+	1.16693i	0.0409764	+	0.0409764i	−0.686322	+	0.727298i	$0.740776\pi$
$812$	1.64327	−	9.55903i	0.0576674	−	0.335456i
$813$	8.10518	−	30.2489i	0.284261	−	1.06088i
$814$	0.391670	+	0.391670i	0.0137280	+	0.0137280i
$815$	38.4559	−	22.2025i	1.34705	−	0.777721i
$816$	−4.41758	−	2.55049i	−0.154646	−	0.0892851i
$817$	−4.43606	−	16.5556i	−0.155198	−	0.579207i
$818$	−20.8857			−0.730251
$819$	7.41827	+	5.99744i	0.259215	+	0.209568i
$820$	25.8840			0.903910
$821$	−0.998281	−	3.72564i	−0.0348402	−	0.130026i	0.946315	−	0.323245i	$-0.104774\pi$
$821$	−0.998281	−	3.72564i	−0.0348402	−	0.130026i	−0.981156	+	0.193219i	$0.938107\pi$
$822$	−12.3556	−	7.13353i	−0.430952	−	0.248810i
$823$	−15.2505	+	8.80488i	−0.531599	+	0.306919i	−0.741667	−	0.670768i	$-0.765965\pi$
$823$	−15.2505	+	8.80488i	−0.531599	+	0.306919i	0.210068	+	0.977687i	$0.432631\pi$
$824$	5.76273	+	5.76273i	0.200754	+	0.200754i
$825$	0.295032	−	1.10107i	0.0102717	−	0.0383344i
$826$	1.89720	−	11.0361i	0.0660119	−	0.383997i
$827$	19.8789	+	19.8789i	0.691256	+	0.691256i	0.962508	−	0.271252i	$-0.0874377\pi$
$827$	19.8789	+	19.8789i	0.691256	+	0.691256i	−0.271252	+	0.962508i	$0.587438\pi$
$828$	2.81559	+	4.87674i	0.0978484	+	0.169478i
$829$	14.3732	−	24.8952i	0.499203	−	0.864645i	−0.500797	−	0.865565i	$-0.666960\pi$
$829$	14.3732	−	24.8952i	0.499203	−	0.864645i	1.00000		0.000920314i	$0.000292945\pi$
$830$	−27.3369	+	7.32489i	−0.948877	+	0.254251i
$831$	1.66211			0.0576580
$832$	1.84618	+	3.09703i	0.0640049	+	0.107370i
$833$	−6.50188	−	35.1099i	−0.225277	−	1.21649i
$834$	4.03298	+	15.0513i	0.139651	+	0.521183i
$835$	−19.9061	+	34.4784i	−0.688879	+	1.19317i
$836$	−0.388190	−	0.672365i	−0.0134258	−	0.0232542i
$837$	7.04095	−	7.04095i	0.243371	−	0.243371i
$838$	4.39365	−	16.3973i	0.151776	−	0.566436i
$839$	−51.8462	−	13.8921i	−1.78993	−	0.479610i	−0.797594	−	0.603195i	$-0.793894\pi$
$839$	−51.8462	−	13.8921i	−1.78993	−	0.479610i	−0.992334	+	0.123585i	$0.960561\pi$
$840$	6.05310	−	7.27697i	0.208852	−	0.251079i
$841$	7.78033	+	13.4759i	0.268287	+	0.464687i
$842$	−19.7041	−	11.3761i	−0.679047	−	0.392048i
$843$	2.72611	+	10.1740i	0.0938921	+	0.350410i
$844$			15.6944i			0.540225i
$845$	−44.5705	+	13.2866i	−1.53327	+	0.457073i
$846$			2.56412i			0.0881563i
$847$	−27.2521	+	10.0516i	−0.936395	+	0.345376i
$848$	3.56940	−	6.18238i	0.122574	−	0.212304i
$849$	9.91366	−	5.72365i	0.340236	−	0.196435i
$850$	−28.1313	−	28.1313i	−0.964894	−	0.964894i
$851$	−20.6137	−	5.52343i	−0.706629	−	0.189341i
$852$	−6.47842	−	1.73589i	−0.221947	−	0.0594705i
$853$	−7.44167	+	7.44167i	−0.254798	+	0.254798i	−0.822934	−	0.568136i	$-0.807665\pi$
$853$	−7.44167	+	7.44167i	−0.254798	+	0.254798i	0.568136	+	0.822934i	$0.307665\pi$
$854$	16.9685	+	24.0137i	0.580652	+	0.821732i
$855$	−16.4579	−	9.50198i	−0.562849	−	0.324961i
$856$	0.149366	−	0.0400225i	0.00510523	−	0.00136794i
$857$	−34.4161			−1.17563			−0.587816	−	0.808995i	$-0.700012\pi$
$857$	−34.4161			−1.17563			−0.587816	+	0.808995i	$0.700012\pi$
$858$	0.269834	+	0.452656i	0.00921198	+	0.0154534i
$859$			5.57158i			0.190100i	0.995473	+	0.0950500i	$0.0303011\pi$
$859$			5.57158i			0.190100i	−0.995473	+	0.0950500i	$0.969699\pi$
$860$	11.1502	−	2.98769i	0.380219	−	0.101879i
$861$	17.3832	+	8.01531i	0.592417	+	0.273161i
$862$	−2.49664	+	1.44144i	−0.0850360	+	0.0490955i
$863$	12.8891	−	12.8891i	0.438750	−	0.438750i	−0.452841	−	0.891591i	$-0.649590\pi$
$863$	12.8891	−	12.8891i	0.438750	−	0.438750i	0.891591	+	0.452841i	$0.149590\pi$
$864$	0.258819	−	0.965926i	0.00880520	−	0.0328615i
$865$	12.2648	−	45.7728i	0.417016	−	1.55632i
$866$	22.7533	−	22.7533i	0.773189	−	0.773189i
$867$	−7.81157	+	4.51001i	−0.265295	+	0.153168i
$868$	23.9241	+	11.0313i	0.812036	+	0.374426i
$869$	1.13375	−	0.303786i	0.0384597	−	0.0103052i
$870$		−	13.1154i		−	0.444653i
$871$	12.9097	+	12.5543i	0.437429	+	0.425385i
$872$	−8.16929			−0.276647
$873$	−6.74442	+	1.80716i	−0.228264	+	0.0611631i
$874$	25.9049	+	14.9562i	0.876247	+	0.505901i
$875$	21.6386	−	15.2902i	0.731518	−	0.516905i
$876$	−7.91676	+	7.91676i	−0.267483	+	0.267483i
$877$	−7.31466	−	1.95996i	−0.246999	−	0.0661831i	0.133196	−	0.991090i	$-0.457476\pi$
$877$	−7.31466	−	1.95996i	−0.246999	−	0.0661831i	−0.380194	+	0.924907i	$0.624143\pi$
$878$	−18.4065	−	4.93200i	−0.621188	−	0.166447i
$879$	−19.3479	−	19.3479i	−0.652588	−	0.652588i
$880$	0.452839	−	0.261447i	0.0152652	−	0.00881337i
$881$	−26.2441	+	45.4561i	−0.884186	+	1.53145i	−0.0375419	+	0.999295i	$0.511953\pi$
$881$	−26.2441	+	45.4561i	−0.884186	+	1.53145i	−0.846644	+	0.532160i	$0.821381\pi$
$882$	6.31854	−	3.01265i	0.212756	−	0.101441i
$883$		−	42.0177i		−	1.41401i	−0.707209	−	0.707004i	$-0.750046\pi$
$883$		−	42.0177i		−	1.41401i	0.707209	−	0.707004i	$-0.249954\pi$
$884$	18.3901	−	0.256703i	0.618525	−	0.00863387i
$885$		−	15.1420i		−	0.508994i
$886$	4.03064	+	15.0425i	0.135412	+	0.505364i
$887$	17.3437	+	10.0134i	0.582345	+	0.336217i	0.762065	−	0.647501i	$-0.224186\pi$
$887$	17.3437	+	10.0134i	0.582345	+	0.336217i	−0.179720	+	0.983718i	$0.557519\pi$
$888$	1.89489	+	3.28204i	0.0635883	+	0.110138i
$889$	−15.7443	−	13.0963i	−0.528045	−	0.439237i
$890$	−43.8338	−	11.7452i	−1.46931	−	0.393701i
$891$	0.0378284	−	0.141178i	0.00126730	−	0.00472963i
$892$	2.91981	−	2.91981i	0.0977626	−	0.0977626i
$893$	6.81022	+	11.7957i	0.227895	+	0.394726i
$894$	9.17839	−	15.8974i	0.306971	−	0.531690i
$895$	−14.0681	−	52.5030i	−0.470246	−	1.75498i
$896$	2.63467	−	0.241896i	0.0880181	−	0.00808118i
$897$	−17.7233	−	9.90534i	−0.591764	−	0.330730i
$898$	−25.4383			−0.848887
$899$	35.2597	−	9.44782i	1.17598	−	0.315102i
$900$	3.89960	−	6.75431i	0.129987	−	0.225144i
$901$	−18.2074	−	31.5362i	−0.606578	−	1.05062i
$902$	0.747735	+	0.747735i	0.0248968	+	0.0248968i
$903$	8.41343	+	1.44633i	0.279981	+	0.0481309i
$904$	0.0185194	−	0.0691153i	0.000615946	−	0.00229874i
$905$	−3.83421	−	3.83421i	−0.127454	−	0.127454i
$906$	15.9093	−	9.18525i	0.528552	−	0.305159i
$907$	17.8984	+	10.3337i	0.594307	+	0.343124i	0.766799	−	0.641888i	$-0.221848\pi$
$907$	17.8984	+	10.3337i	0.594307	+	0.343124i	−0.172491	+	0.985011i	$0.555182\pi$
$908$	−6.88324	−	25.6886i	−0.228428	−	0.852506i
$909$	10.1008			0.335021
$910$	−5.31204	+	33.7122i	−0.176092	+	1.11755i
$911$	−16.4643			−0.545486			−0.272743	−	0.962087i	$-0.587931\pi$
$911$	−16.4643			−0.545486			−0.272743	+	0.962087i	$0.587931\pi$
$912$	−1.37483	−	5.13093i	−0.0455252	−	0.169902i
$913$	−1.00131	−	0.578104i	−0.0331384	−	0.0191324i
$914$	23.9111	−	13.8051i	0.790909	−	0.456631i
$915$	28.1146	+	28.1146i	0.929441	+	0.929441i
$916$	−5.22112	+	19.4855i	−0.172511	+	0.643818i
$917$	−0.501541	+	2.91751i	−0.0165623	+	0.0963446i
$918$	−3.60694	−	3.60694i	−0.119047	−	0.119047i
$919$	−3.06087	−	5.30158i	−0.100969	−	0.174883i	0.811115	−	0.584886i	$-0.198861\pi$
$919$	−3.06087	−	5.30158i	−0.100969	−	0.174883i	−0.912084	+	0.410003i	$0.865528\pi$
$920$	−10.0730	+	17.4470i	−0.332098	+	0.575211i
$921$	−23.4788	+	6.29112i	−0.773652	+	0.207300i
$922$	−27.3796			−0.901700
$923$	23.2686	−	6.58424i	0.765897	−	0.216723i
$924$	0.385078	−	0.0353550i	0.0126681	−	0.00116309i
$925$	7.64998	+	28.5501i	0.251530	+	0.938721i
$926$	9.40707	−	16.2935i	0.309136	−	0.535439i
$927$	4.07486	+	7.05787i	0.133836	+	0.231811i
$928$	2.59223	−	2.59223i	0.0850942	−	0.0850942i
$929$	1.05842	−	3.95009i	0.0347257	−	0.129598i	−0.946387	−	0.323035i	$-0.895297\pi$
$929$	1.05842	−	3.95009i	0.0347257	−	0.129598i	0.981113	+	0.193437i	$0.0619635\pi$
$930$	34.4098	+	9.22007i	1.12834	+	0.302338i
$931$	21.0655	−	30.6408i	0.690394	−	1.00421i
$932$	6.60060	+	11.4326i	0.216210	+	0.374486i
$933$	−11.2136	−	6.47420i	−0.367118	−	0.211956i
$934$	8.35210	+	31.1705i	0.273289	+	1.01993i
$935$		−	2.66727i		−	0.0872291i
$936$	0.981704	+	3.46933i	0.0320880	+	0.113399i
$937$			25.5831i			0.835763i	0.908502	+	0.417882i	$0.137227\pi$
$937$			25.5831i			0.835763i	−0.908502	+	0.417882i	$0.862773\pi$
$938$	12.3975	−	4.57264i	0.404793	−	0.149302i
$939$	7.48437	−	12.9633i	0.244243	−	0.423042i
$940$	−7.94439	+	4.58670i	−0.259118	+	0.149602i
$941$	4.87350	+	4.87350i	0.158871	+	0.158871i	0.782066	−	0.623195i	$-0.214166\pi$
$941$	4.87350	+	4.87350i	0.158871	+	0.158871i	−0.623195	+	0.782066i	$0.714166\pi$
$942$	14.2226	+	3.81093i	0.463397	+	0.124167i
$943$	−39.3535	−	10.5447i	−1.28153	−	0.343384i
$944$	2.99280	−	2.99280i	0.0974073	−	0.0974073i
$945$	7.73027	−	5.46236i	0.251466	−	0.177691i
$946$	0.408414	+	0.235798i	0.0132787	+	0.00766646i
$947$	−40.2565	+	10.7867i	−1.30816	+	0.350520i	−0.844530	−	0.535509i	$-0.820120\pi$
$947$	−40.2565	+	10.7867i	−1.30816	+	0.350520i	−0.463630	+	0.886029i	$0.653453\pi$
$948$	8.03063			0.260823
$949$	9.90269	−	39.1343i	0.321455	−	1.27035i
$950$		−	41.4288i		−	1.34413i
$951$	−9.46924	+	2.53728i	−0.307061	+	0.0822768i
$952$	5.65111	−	12.2558i	0.183153	−	0.397213i
$953$	4.66440	−	2.69299i	0.151095	−	0.0872347i	−0.422546	−	0.906341i	$-0.638864\pi$
$953$	4.66440	−	2.69299i	0.151095	−	0.0872347i	0.573641	+	0.819107i	$0.305530\pi$
$954$	5.04789	−	5.04789i	0.163431	−	0.163431i
$955$	−13.8992	+	51.8725i	−0.449767	+	1.67855i
$956$	5.91106	−	22.0604i	0.191177	−	0.713484i
$957$	0.378875	−	0.378875i	0.0122473	−	0.0122473i
$958$	−23.1341	+	13.3565i	−0.747429	+	0.431529i
$959$	15.8057	−	34.2786i	0.510393	−	1.10691i
$960$	3.45569	−	0.925950i	0.111532	−	0.0298849i
$961$			68.1500i			2.19839i
$962$	−11.9278	−	6.66629i	−0.384567	−	0.214930i
$963$	0.154635			0.00498305
$964$	26.0443	−	6.97856i	0.838832	−	0.224764i
$965$	−63.6620	−	36.7553i	−2.04935	−	1.18319i
$966$	−12.1675	+	8.59781i	−0.391484	+	0.276630i
$967$	−25.0814	+	25.0814i	−0.806565	+	0.806565i	−0.984112	−	0.177548i	$-0.943184\pi$
$967$	−25.0814	+	25.0814i	−0.806565	+	0.806565i	0.177548	+	0.984112i	$0.443184\pi$
$968$	−10.6045	−	2.84148i	−0.340843	−	0.0913286i
$969$	−26.1728	−	7.01298i	−0.840792	−	0.225289i
$970$	−17.6635	−	17.6635i	−0.567141	−	0.567141i
$971$	−18.2197	+	10.5191i	−0.584697	+	0.337575i	−0.762998	−	0.646401i	$-0.776273\pi$
$971$	−18.2197	+	10.5191i	−0.584697	+	0.337575i	0.178301	+	0.983976i	$0.442940\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−38.6796	+	14.2664i	−1.24001	+	0.457360i
$974$		−	8.08818i		−	0.259162i
$975$	0.392489	+	28.1177i	0.0125697	+	0.900487i
$976$			11.1136i			0.355739i
$977$	−8.19242	−	30.5745i	−0.262099	−	0.978165i	−0.964002	−	0.265894i	$-0.914333\pi$
$977$	−8.19242	−	30.5745i	−0.262099	−	0.978165i	0.701904	−	0.712272i	$-0.252334\pi$
$978$	10.7491	+	6.20599i	0.343718	+	0.198446i
$979$	−0.926971	−	1.60556i	−0.0296261	−	0.0513139i
$980$	20.6366	+	14.1877i	0.659214	+	0.453208i
$981$	−7.89092	−	2.11437i	−0.251938	−	0.0675065i
$982$	−7.25525	+	27.0770i	−0.231524	+	0.864060i
$983$	−27.5835	+	27.5835i	−0.879777	+	0.879777i	−0.993511	−	0.113734i	$-0.963719\pi$
$983$	−27.5835	+	27.5835i	−0.879777	+	0.879777i	0.113734	+	0.993511i	$0.463719\pi$
$984$	3.61752	+	6.26572i	0.115322	+	0.199744i
$985$	−24.8859	+	43.1036i	−0.792931	+	1.37340i
$986$	−4.83993	−	18.0629i	−0.154135	−	0.575239i
$987$	−6.75561	+	0.620251i	−0.215034	+	0.0197428i
$988$	13.7305	+	13.3525i	0.436826	+	0.424799i
$989$	−18.1697			−0.577762
$990$	0.505077	−	0.135335i	0.0160524	−	0.00430122i
$991$	−18.1434	+	31.4254i	−0.576345	+	0.998259i	0.419549	+	0.907733i	$0.362188\pi$
$991$	−18.1434	+	31.4254i	−0.576345	+	0.998259i	−0.995894	+	0.0905266i	$0.971145\pi$
$992$	4.97871	+	8.62337i	0.158074	+	0.273792i
$993$	24.3766	+	24.3766i	0.773567	+	0.773567i
$994$	3.00639	−	17.4884i	0.0953568	−	0.554698i
$995$	−8.54429	+	31.8877i	−0.270872	+	1.01091i
$996$	−5.59369	−	5.59369i	−0.177243	−	0.177243i
$997$	4.09769	−	2.36580i	0.129775	−	0.0749257i	−0.433707	−	0.901054i	$-0.642795\pi$
$997$	4.09769	−	2.36580i	0.129775	−	0.0749257i	0.563482	+	0.826128i	$0.309461\pi$
$998$	−20.1691	−	11.6447i	−0.638443	−	0.368605i
$999$	0.980866	+	3.66064i	0.0310332	+	0.115818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bx.b.97.1	yes	40
7.6	odd	2		546.2.bx.a.97.5	✓	40
13.11	odd	12		546.2.bx.a.349.5	yes	40
91.76	even	12	inner	546.2.bx.b.349.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bx.a.97.5	✓	40	7.6	odd	2
546.2.bx.a.349.5	yes	40	13.11	odd	12
546.2.bx.b.97.1	yes	40	1.1	even	1	trivial
546.2.bx.b.349.1	yes	40	91.76	even	12	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bx (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.52974 - 2.52974i) q^{5} +(0.258819 - 0.965926i) q^{6} +(2.60750 + 0.448249i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-2.52974 - 2.52974i) q^{5} +(0.258819 - 0.965926i) q^{6} +(2.60750 + 0.448249i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-1.78880 + 3.09829i) q^{10} +(-0.141178 + 0.0378284i) q^{11} -1.00000 q^{12} +(3.09703 - 1.84618i) q^{13} +(-0.241896 - 2.63467i) q^{14} +(-0.925950 - 3.45569i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.55049 - 4.41758i) q^{17} +(0.707107 - 0.707107i) q^{18} +(1.37483 - 5.13093i) q^{19} +(3.45569 + 0.925950i) q^{20} +(2.03404 + 1.69195i) q^{21} +(0.0730789 + 0.126576i) q^{22} +(-4.87674 - 2.81559i) q^{23} +(0.258819 + 0.965926i) q^{24} +7.79920i q^{25} +(-2.58485 - 2.51368i) q^{26} +1.00000i q^{27} +(-2.48229 + 0.915557i) q^{28} +(-1.83299 + 3.17482i) q^{29} +(-3.09829 + 1.78880i) q^{30} +(-7.04095 - 7.04095i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-0.141178 - 0.0378284i) q^{33} +(-3.60694 + 3.60694i) q^{34} +(-5.46236 - 7.73027i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(3.66064 - 0.980866i) q^{37} -5.31193 q^{38} +(3.60520 - 0.0503243i) q^{39} -3.57760i q^{40} +(6.98851 - 1.87256i) q^{41} +(1.10785 - 2.40264i) q^{42} +(2.79434 - 1.61331i) q^{43} +(0.103349 - 0.103349i) q^{44} +(0.925950 - 3.45569i) q^{45} +(-1.45746 + 5.43930i) q^{46} +(-1.81311 + 1.81311i) q^{47} +(0.866025 - 0.500000i) q^{48} +(6.59815 + 2.33762i) q^{49} +(7.53345 - 2.01858i) q^{50} -5.10098i q^{51} +(-1.75902 + 3.14736i) q^{52} +7.13879 q^{53} +(0.965926 - 0.258819i) q^{54} +(0.452839 + 0.261447i) q^{55} +(1.52682 + 2.16074i) q^{56} +(3.75610 - 3.75610i) q^{57} +(3.54106 + 0.948823i) q^{58} +(4.08824 + 1.09544i) q^{59} +(2.52974 + 2.52974i) q^{60} +(-9.62468 + 5.55681i) q^{61} +(-4.97871 + 8.62337i) q^{62} +(0.915557 + 2.48229i) q^{63} +1.00000i q^{64} +(-12.5051 - 3.16433i) q^{65} +0.146158i q^{66} +(1.29264 + 4.82420i) q^{67} +(4.41758 + 2.55049i) q^{68} +(-2.81559 - 4.87674i) q^{69} +(-6.05310 + 7.27697i) q^{70} +(6.47842 + 1.73589i) q^{71} +(-0.258819 + 0.965926i) q^{72} +(7.91676 - 7.91676i) q^{73} +(-1.89489 - 3.28204i) q^{74} +(-3.89960 + 6.75431i) q^{75} +(1.37483 + 5.13093i) q^{76} +(-0.385078 + 0.0353550i) q^{77} +(-0.981704 - 3.46933i) q^{78} -8.03063 q^{79} +(-3.45569 + 0.925950i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.61752 - 6.26572i) q^{82} +(5.59369 + 5.59369i) q^{83} +(-2.60750 - 0.448249i) q^{84} +(-4.72326 + 17.6274i) q^{85} +(-2.28157 - 2.28157i) q^{86} +(-3.17482 + 1.83299i) q^{87} +(-0.126576 - 0.0730789i) q^{88} +(3.28299 + 12.2523i) q^{89} -3.57760 q^{90} +(8.90307 - 3.42568i) q^{91} +5.63117 q^{92} +(-2.57717 - 9.61812i) q^{93} +(2.22059 + 1.28206i) q^{94} +(-16.4579 + 9.50198i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-1.80716 + 6.74442i) q^{97} +(0.550243 - 6.97834i) q^{98} +(-0.103349 - 0.103349i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 8 * q^7 + 20 * q^9	\( 40 q + 8 q^{7} + 20 q^{9} + 8 q^{11} - 40 q^{12} - 8 q^{14} + 20 q^{16} - 16 q^{17} - 16 q^{19} + 4 q^{21} + 8 q^{22} - 32 q^{26} - 8 q^{28} + 8 q^{33} - 16 q^{34} + 40 q^{35} + 40 q^{37} + 16 q^{38} - 16 q^{39} + 4 q^{41} - 12 q^{42} + 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} - 20 q^{49} - 16 q^{50} + 8 q^{52} + 32 q^{53} + 72 q^{55} + 12 q^{56} + 8 q^{57} - 36 q^{58} - 84 q^{59} + 48 q^{61} + 4 q^{62} + 4 q^{63} - 16 q^{65} - 12 q^{68} + 8 q^{69} - 20 q^{70} - 40 q^{71} + 48 q^{73} + 8 q^{74} - 36 q^{75} - 16 q^{76} + 24 q^{77} - 8 q^{78} - 48 q^{79} - 20 q^{81} - 36 q^{83} - 8 q^{84} + 8 q^{85} - 8 q^{86} - 12 q^{89} + 32 q^{91} - 16 q^{92} - 24 q^{93} - 96 q^{95} - 8 q^{98} - 8 q^{99}+O(q^{100}) \) 40 * q + 8 * q^7 + 20 * q^9 + 8 * q^11 - 40 * q^12 - 8 * q^14 + 20 * q^16 - 16 * q^17 - 16 * q^19 + 4 * q^21 + 8 * q^22 - 32 * q^26 - 8 * q^28 + 8 * q^33 - 16 * q^34 + 40 * q^35 + 40 * q^37 + 16 * q^38 - 16 * q^39 + 4 * q^41 - 12 * q^42 + 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 - 20 * q^49 - 16 * q^50 + 8 * q^52 + 32 * q^53 + 72 * q^55 + 12 * q^56 + 8 * q^57 - 36 * q^58 - 84 * q^59 + 48 * q^61 + 4 * q^62 + 4 * q^63 - 16 * q^65 - 12 * q^68 + 8 * q^69 - 20 * q^70 - 40 * q^71 + 48 * q^73 + 8 * q^74 - 36 * q^75 - 16 * q^76 + 24 * q^77 - 8 * q^78 - 48 * q^79 - 20 * q^81 - 36 * q^83 - 8 * q^84 + 8 * q^85 - 8 * q^86 - 12 * q^89 + 32 * q^91 - 16 * q^92 - 24 * q^93 - 96 * q^95 - 8 * q^98 - 8 * q^99

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