LMFDB - Embedded newform 546.2.u.a.185.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(185,546)]

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, 2]))

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

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

chi := DirichletCharacter("546.185");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.u (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:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.8
Character	$\chi$	$=$	546.185
Dual form			546.2.u.a.425.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.266485 + 1.71143i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.279399 + 0.483934i) q^{5} +(1.08650 - 1.34890i) q^{6} +(0.253211 - 2.63361i) q^{7} -1.00000i q^{8} +(-2.85797 - 0.912140i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.266485 + 1.71143i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.279399 + 0.483934i) q^{5} +(1.08650 - 1.34890i) q^{6} +(0.253211 - 2.63361i) q^{7} -1.00000i q^{8} +(-2.85797 - 0.912140i) q^{9} -0.558798i q^{10} -6.43977i q^{11} +(-1.61538 + 0.624931i) q^{12} +(-1.74302 + 3.15624i) q^{13} +(-1.53609 + 2.15416i) q^{14} +(-0.902673 + 0.349210i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.19575 - 5.53520i) q^{17} +(2.01901 + 2.21892i) q^{18} +1.04432i q^{19} +(-0.279399 + 0.483934i) q^{20} +(4.43975 + 1.13517i) q^{21} +(-3.21989 + 5.57701i) q^{22} +(0.412061 + 0.237904i) q^{23} +(1.71143 + 0.266485i) q^{24} +(2.34387 - 4.05971i) q^{25} +(3.08762 - 1.86188i) q^{26} +(2.32267 - 4.64814i) q^{27} +(2.40738 - 1.09752i) q^{28} +(-3.00015 + 1.73214i) q^{29} +(0.956343 + 0.148911i) q^{30} +(0.995309 + 0.574642i) q^{31} +(0.866025 - 0.500000i) q^{32} +(11.0212 + 1.71610i) q^{33} +6.39150i q^{34} +(1.34524 - 0.613290i) q^{35} +(-0.639049 - 2.93115i) q^{36} +(5.01086 - 8.67906i) q^{37} +(0.522160 - 0.904408i) q^{38} +(-4.93719 - 3.82415i) q^{39} +(0.483934 - 0.279399i) q^{40} +(3.45773 + 5.98897i) q^{41} +(-3.27735 - 3.20296i) q^{42} +(1.50624 - 2.60888i) q^{43} +(5.57701 - 3.21989i) q^{44} +(-0.357100 - 1.63792i) q^{45} +(-0.237904 - 0.412061i) q^{46} +(-0.145367 - 0.251784i) q^{47} +(-1.34890 - 1.08650i) q^{48} +(-6.87177 - 1.33372i) q^{49} +(-4.05971 + 2.34387i) q^{50} +(10.3247 - 3.99425i) q^{51} +(-3.60490 + 0.0686197i) q^{52} +(-8.18418 - 4.72514i) q^{53} +(-4.33556 + 2.86407i) q^{54} +(3.11642 - 1.79927i) q^{55} +(-2.63361 - 0.253211i) q^{56} +(-1.78728 - 0.278296i) q^{57} +3.46428 q^{58} +(4.85874 + 8.41558i) q^{59} +(-0.753762 - 0.607133i) q^{60} -6.08860i q^{61} +(-0.574642 - 0.995309i) q^{62} +(-3.12589 + 7.29581i) q^{63} -1.00000 q^{64} +(-2.01441 + 0.0383446i) q^{65} +(-8.68659 - 6.99679i) q^{66} +11.3956 q^{67} +(3.19575 - 5.53520i) q^{68} +(-0.516963 + 0.641815i) q^{69} +(-1.47166 - 0.141494i) q^{70} +(-7.85983 - 4.53787i) q^{71} +(-0.912140 + 2.85797i) q^{72} +(-9.17149 - 5.29516i) q^{73} +(-8.67906 + 5.01086i) q^{74} +(6.32329 + 5.09322i) q^{75} +(-0.904408 + 0.522160i) q^{76} +(-16.9598 - 1.63062i) q^{77} +(2.36366 + 5.78041i) q^{78} +(5.66566 + 9.81321i) q^{79} -0.558798 q^{80} +(7.33600 + 5.21374i) q^{81} -6.91546i q^{82} -2.89483 q^{83} +(1.23679 + 4.41252i) q^{84} +(1.78578 - 3.09306i) q^{85} +(-2.60888 + 1.50624i) q^{86} +(-2.16494 - 5.59614i) q^{87} -6.43977 q^{88} +(1.61861 - 2.80351i) q^{89} +(-0.509702 + 1.59703i) q^{90} +(7.87095 + 5.38963i) q^{91} +0.475807i q^{92} +(-1.24869 + 1.55027i) q^{93} +0.290735i q^{94} +(-0.505382 + 0.291782i) q^{95} +(0.624931 + 1.61538i) q^{96} +(-3.63348 - 2.09779i) q^{97} +(5.28427 + 4.59092i) q^{98} +(-5.87397 + 18.4047i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	$ 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) $ 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.266485	+	1.71143i	−0.153855	+	0.988093i
$3$	−0.266485	+	1.71143i	−0.153855	+	0.988093i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.279399	+	0.483934i	0.124951	+	0.216422i	0.921714	−	0.387871i	$-0.126789\pi$
$5$	0.279399	+	0.483934i	0.124951	+	0.216422i	−0.796763	+	0.604292i	$0.793456\pi$
$6$	1.08650	−	1.34890i	0.443560	−	0.550685i
$7$	0.253211	−	2.63361i	0.0957048	−	0.995410i
$7$	0.253211	−	2.63361i	0.0957048	−	0.995410i
$8$		−	1.00000i		−	0.353553i
$9$	−2.85797	−	0.912140i	−0.952657	−	0.304047i
$10$		−	0.558798i		−	0.176708i
$11$		−	6.43977i		−	1.94166i	−0.239760	−	0.970832i	$-0.577069\pi$
$11$		−	6.43977i		−	1.94166i	0.239760	−	0.970832i	$-0.422931\pi$
$12$	−1.61538	+	0.624931i	−0.466321	+	0.180402i
$13$	−1.74302	+	3.15624i	−0.483428	+	0.875384i
$13$	−1.74302	+	3.15624i	−0.483428	+	0.875384i
$14$	−1.53609	+	2.15416i	−0.410537	+	0.575725i
$15$	−0.902673	+	0.349210i	−0.233069	+	0.0901658i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.19575	−	5.53520i	−0.775083	−	1.34248i	−0.934748	−	0.355312i	$-0.884374\pi$
$17$	−3.19575	−	5.53520i	−0.775083	−	1.34248i	0.159664	−	0.987171i	$-0.448959\pi$
$18$	2.01901	+	2.21892i	0.475884	+	0.523005i
$19$			1.04432i			0.239583i	0.992799	+	0.119792i	$0.0382227\pi$
$19$			1.04432i			0.239583i	−0.992799	+	0.119792i	$0.961777\pi$
$20$	−0.279399	+	0.483934i	−0.0624756	+	0.108211i
$21$	4.43975	+	1.13517i	0.968833	+	0.247714i
$22$	−3.21989	+	5.57701i	−0.686482	+	1.18902i
$23$	0.412061	+	0.237904i	0.0859207	+	0.0496063i	0.542345	−	0.840156i	$-0.317537\pi$
$23$	0.412061	+	0.237904i	0.0859207	+	0.0496063i	−0.456424	+	0.889762i	$0.650870\pi$
$24$	1.71143	+	0.266485i	0.349344	+	0.0543960i
$25$	2.34387	−	4.05971i	0.468774	−	0.811941i
$26$	3.08762	−	1.86188i	0.605533	−	0.365144i
$27$	2.32267	−	4.64814i	0.446998	−	0.894535i
$28$	2.40738	−	1.09752i	0.454951	−	0.207411i
$29$	−3.00015	+	1.73214i	−0.557114	+	0.321650i	−0.751987	−	0.659178i	$-0.770904\pi$
$29$	−3.00015	+	1.73214i	−0.557114	+	0.321650i	0.194872	+	0.980829i	$0.437571\pi$
$30$	0.956343	+	0.148911i	0.174604	+	0.0271874i
$31$	0.995309	+	0.574642i	0.178763	+	0.103209i	0.586711	−	0.809796i	$-0.300422\pi$
$31$	0.995309	+	0.574642i	0.178763	+	0.103209i	−0.407949	+	0.913005i	$0.633756\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	11.0212	+	1.71610i	1.91855	+	0.298735i
$34$			6.39150i			1.09613i
$35$	1.34524	−	0.613290i	0.227387	−	0.103665i
$36$	−0.639049	−	2.93115i	−0.106508	−	0.488524i
$37$	5.01086	−	8.67906i	0.823780	−	1.42683i	−0.0790679	−	0.996869i	$-0.525194\pi$
$37$	5.01086	−	8.67906i	0.823780	−	1.42683i	0.902848	−	0.429960i	$-0.141472\pi$
$38$	0.522160	−	0.904408i	0.0847055	−	0.146714i
$39$	−4.93719	−	3.82415i	−0.790584	−	0.612354i
$40$	0.483934	−	0.279399i	0.0765166	−	0.0441769i
$41$	3.45773	+	5.98897i	0.540007	+	0.935319i	0.998903	+	0.0468294i	$0.0149117\pi$
$41$	3.45773	+	5.98897i	0.540007	+	0.935319i	−0.458896	+	0.888490i	$0.651755\pi$
$42$	−3.27735	−	3.20296i	−0.505706	−	0.494228i
$43$	1.50624	−	2.60888i	0.229699	−	0.397851i	−0.728020	−	0.685556i	$-0.759559\pi$
$43$	1.50624	−	2.60888i	0.229699	−	0.397851i	0.957719	+	0.287706i	$0.0928925\pi$
$44$	5.57701	−	3.21989i	0.840765	−	0.485416i
$45$	−0.357100	−	1.63792i	−0.0532333	−	0.244167i
$46$	−0.237904	−	0.412061i	−0.0350770	−	0.0607551i
$47$	−0.145367	−	0.251784i	−0.0212040	−	0.0367264i	0.855229	−	0.518251i	$-0.173417\pi$
$47$	−0.145367	−	0.251784i	−0.0212040	−	0.0367264i	−0.876433	+	0.481524i	$0.840083\pi$
$48$	−1.34890	−	1.08650i	−0.194697	−	0.156822i
$49$	−6.87177	−	1.33372i	−0.981681	−	0.190531i
$50$	−4.05971	+	2.34387i	−0.574129	+	0.331474i
$51$	10.3247	−	3.99425i	1.44575	−	0.559307i
$52$	−3.60490	+	0.0686197i	−0.499909	+	0.00951584i
$53$	−8.18418	−	4.72514i	−1.12418	−	0.649048i	−0.181718	−	0.983351i	$-0.558166\pi$
$53$	−8.18418	−	4.72514i	−1.12418	−	0.649048i	−0.942466	+	0.334303i	$0.891499\pi$
$54$	−4.33556	+	2.86407i	−0.589995	+	0.389751i
$55$	3.11642	−	1.79927i	0.420218	−	0.242613i
$56$	−2.63361	−	0.253211i	−0.351930	−	0.0338368i
$57$	−1.78728	−	0.278296i	−0.236731	−	0.0368612i
$58$	3.46428			0.454882
$59$	4.85874	+	8.41558i	0.632554	+	1.09562i	0.987028	+	0.160549i	$0.0513266\pi$
$59$	4.85874	+	8.41558i	0.632554	+	1.09562i	−0.354474	+	0.935066i	$0.615340\pi$
$60$	−0.753762	−	0.607133i	−0.0973102	−	0.0783805i
$61$		−	6.08860i		−	0.779565i	−0.920907	−	0.389783i	$-0.872550\pi$
$61$		−	6.08860i		−	0.779565i	0.920907	−	0.389783i	$-0.127450\pi$
$62$	−0.574642	−	0.995309i	−0.0729796	−	0.126404i
$63$	−3.12589	+	7.29581i	−0.393825	+	0.919185i
$64$	−1.00000			−0.125000
$65$	−2.01441	+	0.0383446i	−0.249857	+	0.00475606i
$66$	−8.68659	−	6.99679i	−1.06925	−	0.861246i
$67$	11.3956			1.39219			0.696097	−	0.717948i	$-0.254918\pi$
$67$	11.3956			1.39219			0.696097	+	0.717948i	$0.254918\pi$
$68$	3.19575	−	5.53520i	0.387542	−	0.671242i
$69$	−0.516963	+	0.641815i	−0.0622350	+	0.0772655i
$70$	−1.47166	−	0.141494i	−0.175896	−	0.0169118i
$71$	−7.85983	−	4.53787i	−0.932790	−	0.538546i	−0.0450969	−	0.998983i	$-0.514360\pi$
$71$	−7.85983	−	4.53787i	−0.932790	−	0.538546i	−0.887693	+	0.460436i	$0.847693\pi$
$72$	−0.912140	+	2.85797i	−0.107497	+	0.336815i
$73$	−9.17149	−	5.29516i	−1.07344	−	0.619752i	−0.144322	−	0.989531i	$-0.546100\pi$
$73$	−9.17149	−	5.29516i	−1.07344	−	0.619752i	−0.929120	+	0.369779i	$0.879433\pi$
$74$	−8.67906	+	5.01086i	−1.00892	+	0.582501i
$75$	6.32329	+	5.09322i	0.730150	+	0.588114i
$76$	−0.904408	+	0.522160i	−0.103743	+	0.0598959i
$77$	−16.9598	−	1.63062i	−1.93275	−	0.185827i
$78$	2.36366	+	5.78041i	0.267632	+	0.654502i
$79$	5.66566	+	9.81321i	0.637437	+	1.10407i	0.985993	+	0.166785i	$0.0533385\pi$
$79$	5.66566	+	9.81321i	0.637437	+	1.10407i	−0.348557	+	0.937288i	$0.613328\pi$
$80$	−0.558798			−0.0624756
$81$	7.33600	+	5.21374i	0.815111	+	0.579304i
$82$		−	6.91546i		−	0.763685i
$83$	−2.89483			−0.317749			−0.158875	−	0.987299i	$-0.550787\pi$
$83$	−2.89483			−0.317749			−0.158875	+	0.987299i	$0.550787\pi$
$84$	1.23679	+	4.41252i	0.134945	+	0.481446i
$85$	1.78578	−	3.09306i	0.193695	−	0.335490i
$86$	−2.60888	+	1.50624i	−0.281323	+	0.162422i
$87$	−2.16494	−	5.59614i	−0.232105	−	0.599969i
$88$	−6.43977			−0.686482
$89$	1.61861	−	2.80351i	0.171572	−	0.297171i	−0.767398	−	0.641171i	$-0.778449\pi$
$89$	1.61861	−	2.80351i	0.171572	−	0.297171i	0.938970	+	0.344000i	$0.111782\pi$
$90$	−0.509702	+	1.59703i	−0.0537273	+	0.168342i
$91$	7.87095	+	5.38963i	0.825100	+	0.564987i
$92$			0.475807i			0.0496063i
$93$	−1.24869	+	1.55027i	−0.129483	+	0.160755i
$94$			0.290735i			0.0299870i
$95$	−0.505382	+	0.291782i	−0.0518511	+	0.0299362i
$96$	0.624931	+	1.61538i	0.0637818	+	0.164869i
$97$	−3.63348	−	2.09779i	−0.368924	−	0.212998i	0.304064	−	0.952651i	$-0.401656\pi$
$97$	−3.63348	−	2.09779i	−0.368924	−	0.212998i	−0.672988	+	0.739653i	$0.734990\pi$
$98$	5.28427	+	4.59092i	0.533792	+	0.463753i
$99$	−5.87397	+	18.4047i	−0.590357	+	1.84974i
$100$	4.68774			0.468774
$101$	10.2322			1.01814			0.509069	−	0.860726i	$-0.329990\pi$
$101$	10.2322			1.01814			0.509069	+	0.860726i	$0.329990\pi$
$102$	−10.9386	−	1.70324i	−1.08308	−	0.168646i
$103$	−10.5459	+	6.08867i	−1.03912	+	0.599935i	−0.919583	−	0.392895i	$-0.871474\pi$
$103$	−10.5459	+	6.08867i	−1.03912	+	0.599935i	−0.119534	+	0.992830i	$0.538140\pi$
$104$	3.15624	+	1.74302i	0.309495	+	0.170917i
$105$	0.691116	+	2.46571i	0.0674460	+	0.240629i
$106$	4.72514	+	8.18418i	0.458946	+	0.794918i
$107$	6.17914	+	3.56753i	0.597360	+	0.344886i	0.768002	−	0.640447i	$-0.221251\pi$
$107$	6.17914	+	3.56753i	0.597360	+	0.344886i	−0.170643	+	0.985333i	$0.554584\pi$
$108$	5.18674	−	0.312580i	0.499094	−	0.0300780i
$109$	2.30907	−	3.99943i	0.221169	−	0.383076i	−0.733994	−	0.679156i	$-0.762346\pi$
$109$	2.30907	−	3.99943i	0.221169	−	0.383076i	0.955163	+	0.296080i	$0.0956794\pi$
$110$	−3.59853			−0.343107
$111$	13.5183	+	10.8886i	1.28310	+	1.03350i
$112$	2.15416	+	1.53609i	0.203549	+	0.145147i
$113$	−5.54013	−	3.19860i	−0.521172	−	0.300899i	0.216242	−	0.976340i	$-0.430620\pi$
$113$	−5.54013	−	3.19860i	−0.521172	−	0.300899i	−0.737414	+	0.675441i	$0.763953\pi$
$114$	1.40868	+	1.13465i	0.131935	+	0.106270i
$115$			0.265880i			0.0247935i
$116$	−3.00015	−	1.73214i	−0.278557	−	0.160825i
$117$	7.86045	−	7.43057i	0.726698	−	0.686957i
$118$		−	9.71748i		−	0.894566i
$119$	−15.3867	+	7.01478i	−1.41050	+	0.643043i
$120$	0.349210	+	0.902673i	0.0318784	+	0.0824024i
$121$	−30.4707			−2.77006
$122$	−3.04430	+	5.27288i	−0.275618	+	0.477384i
$123$	−11.1711	+	4.32169i	−1.00727	+	0.389673i
$124$			1.14928i			0.103209i
$125$	5.41350			0.484198
$126$	6.35500	−	4.75541i	0.566149	−	0.423646i
$127$	3.35100	+	5.80411i	0.297354	+	0.515031i	0.975530	−	0.219868i	$-0.0705627\pi$
$127$	3.35100	+	5.80411i	0.297354	+	0.515031i	−0.678176	+	0.734899i	$0.737229\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	4.06352	+	3.27305i	0.357773	+	0.288176i
$130$	1.76370	+	0.973998i	0.154687	+	0.0854253i
$131$	−7.69518	−	13.3284i	−0.672331	−	1.16451i	−0.977241	−	0.212130i	$-0.931960\pi$
$131$	−7.69518	−	13.3284i	−0.672331	−	1.16451i	0.304910	−	0.952381i	$-0.401373\pi$
$132$	4.02441	+	10.4027i	0.350280	+	0.905439i
$133$	2.75033	+	0.264433i	0.238484	+	0.0229293i
$134$	−9.86888	−	5.69780i	−0.852541	−	0.492215i
$135$	2.89834	−	0.174669i	0.249450	−	0.0150331i
$136$	−5.53520	+	3.19575i	−0.474640	+	0.274033i
$137$	4.68256	−	2.70348i	0.400058	−	0.230974i	−0.286451	−	0.958095i	$-0.592475\pi$
$137$	4.68256	−	2.70348i	0.400058	−	0.230974i	0.686509	+	0.727121i	$0.259142\pi$
$138$	0.768611	−	0.297347i	0.0654285	−	0.0253118i
$139$	13.8462	+	7.99412i	1.17442	+	0.678053i	0.954717	−	0.297514i	$-0.0961574\pi$
$139$	13.8462	+	7.99412i	1.17442	+	0.678053i	0.219704	+	0.975567i	$0.429491\pi$
$140$	1.20374	+	0.858365i	0.101735	+	0.0725451i
$141$	0.469648	−	0.181689i	0.0395515	−	0.0153010i
$142$	4.53787	+	7.85983i	0.380810	+	0.659582i
$143$	20.3255	+	11.2247i	1.69970	+	0.938654i
$144$	2.21892	−	2.01901i	0.184910	−	0.168250i
$145$	−1.67648	−	0.967917i	−0.139224	−	0.0803811i
$146$	5.29516	+	9.17149i	0.438231	+	0.759038i
$147$	4.11378	−	11.4051i	0.339299	−	0.940679i
$148$	10.0217			0.823780
$149$			11.0299i			0.903608i	0.892117	+	0.451804i	$0.149219\pi$
$149$			11.0299i			0.903608i	−0.892117	+	0.451804i	$0.850781\pi$
$150$	−2.92952	−	7.57250i	−0.239194	−	0.618292i
$151$	0.722893	−	1.25209i	0.0588282	−	0.101893i	−0.835111	−	0.550081i	$-0.814597\pi$
$151$	0.722893	−	1.25209i	0.0588282	−	0.101893i	0.893940	+	0.448187i	$0.147930\pi$
$152$	1.04432			0.0847055
$153$	4.08448	+	18.7344i	0.330211	+	1.51459i
$154$	13.8723	+	9.89207i	1.11786	+	0.797126i
$155$			0.642218i			0.0515842i
$156$	0.843214	−	6.18781i	0.0675111	−	0.495421i
$157$	4.98415	+	2.87760i	0.397778	+	0.229657i	0.685525	−	0.728049i	$-0.259573\pi$
$157$	4.98415	+	2.87760i	0.397778	+	0.229657i	−0.287747	+	0.957707i	$0.592906\pi$
$158$		−	11.3313i		−	0.901471i
$159$	10.2677	−	12.7475i	0.814281	−	1.01094i
$160$	0.483934	+	0.279399i	0.0382583	+	0.0220884i
$161$	0.730883	−	1.02497i	0.0576016	−	0.0807787i
$162$	−3.74629	−	8.18323i	−0.294337	−	0.642935i
$163$	−1.85495			−0.145291			−0.0726453	−	0.997358i	$-0.523144\pi$
$163$	−1.85495			−0.145291			−0.0726453	+	0.997358i	$0.523144\pi$
$164$	−3.45773	+	5.98897i	−0.270003	+	0.467660i
$165$	2.24884	+	5.81301i	0.175072	+	0.452542i
$166$	2.50700	+	1.44742i	0.194581	+	0.112341i
$167$	7.81988	+	13.5444i	0.605121	+	1.04810i	0.992032	+	0.125983i	$0.0402084\pi$
$167$	7.81988	+	13.5444i	0.605121	+	1.04810i	−0.386912	+	0.922117i	$0.626458\pi$
$168$	1.13517	−	4.43975i	0.0875802	−	0.342534i
$169$	−6.92374	−	11.0028i	−0.532596	−	0.846370i
$170$	−3.09306	+	1.78578i	−0.237227	+	0.136963i
$171$	0.952566	−	2.98464i	0.0728446	−	0.228241i
$172$	3.01248			0.229699
$173$	−11.0579			−0.840717			−0.420359	−	0.907358i	$-0.638096\pi$
$173$	−11.0579			−0.840717			−0.420359	+	0.907358i	$0.638096\pi$
$174$	−0.923179	+	5.92886i	−0.0699860	+	0.449466i
$175$	−10.0982	−	7.20080i	−0.763350	−	0.544329i
$176$	5.57701	+	3.21989i	0.420383	+	0.242708i
$177$	−15.6974	+	6.07275i	−1.17989	+	0.456456i
$178$	−2.80351	+	1.61861i	−0.210132	+	0.121320i
$179$			0.0284194i			0.00212416i	0.999999	+	0.00106208i	$0.000338071\pi$
$179$			0.0284194i			0.00212416i	−0.999999	+	0.00106208i	$0.999662\pi$
$180$	1.23993	−	1.12822i	0.0924189	−	0.0840923i
$181$			2.04392i			0.151924i	0.997111	+	0.0759618i	$0.0242027\pi$
$181$			2.04392i			0.151924i	−0.997111	+	0.0759618i	$0.975797\pi$
$182$	−4.12163	−	8.60303i	−0.305515	−	0.637699i
$183$	10.4202	+	1.62252i	0.770283	+	0.119940i
$184$	0.237904	−	0.412061i	0.0175385	−	0.0303775i
$185$	5.60012			0.411729
$186$	1.85653	−	0.718223i	0.136128	−	0.0526627i
$187$	−35.6454	+	20.5799i	−2.60665	+	1.50495i
$188$	0.145367	−	0.251784i	0.0106020	−	0.0183632i
$189$	−11.6532	−	7.29396i	−0.847649	−	0.530557i
$190$	0.583564			0.0423362
$191$		−	8.31147i		−	0.601397i	−0.953719	−	0.300699i	$-0.902780\pi$
$191$		−	8.31147i		−	0.601397i	0.953719	−	0.300699i	$-0.0972198\pi$
$192$	0.266485	−	1.71143i	0.0192319	−	0.123512i
$193$	−17.9361			−1.29107			−0.645535	−	0.763731i	$-0.723366\pi$
$193$	−17.9361			−1.29107			−0.645535	+	0.763731i	$0.723366\pi$
$194$	2.09779	+	3.63348i	0.150612	+	0.260868i
$195$	0.471187	−	3.45774i	0.0337424	−	0.247614i
$196$	−2.28085	−	6.61798i	−0.162918	−	0.472713i
$197$	−19.6371	+	11.3375i	−1.39908	+	0.807762i	−0.994297	−	0.106649i	$-0.965988\pi$
$197$	−19.6371	+	11.3375i	−1.39908	+	0.807762i	−0.404788	+	0.914411i	$0.632655\pi$
$198$	14.2894	−	13.0019i	1.01550	−	0.924008i
$199$	0.445421	−	0.257164i	0.0315751	−	0.0182299i	−0.484129	−	0.874996i	$-0.660864\pi$
$199$	0.445421	−	0.257164i	0.0315751	−	0.0182299i	0.515704	+	0.856767i	$0.327530\pi$
$200$	−4.05971	−	2.34387i	−0.287065	−	0.165737i
$201$	−3.03676	+	19.5028i	−0.214196	+	1.37562i
$202$	−8.86132	−	5.11608i	−0.623480	−	0.359966i
$203$	3.80210	+	8.33982i	0.266855	+	0.585341i
$204$	8.62148	+	6.94435i	0.603624	+	0.486201i
$205$	−1.93217	+	3.34662i	−0.134949	+	0.233738i
$206$	12.1773			0.848436
$207$	−0.960658	−	1.05578i	−0.0667703	−	0.0733817i
$208$	−1.86188	−	3.08762i	−0.129098	−	0.214088i
$209$	6.72518			0.465191
$210$	0.634331	−	2.48093i	0.0437730	−	0.171200i
$211$	−4.07178	−	7.05253i	−0.280313	−	0.485516i	0.691149	−	0.722712i	$-0.257105\pi$
$211$	−4.07178	−	7.05253i	−0.280313	−	0.485516i	−0.971462	+	0.237196i	$0.923772\pi$
$212$		−	9.45028i		−	0.649048i
$213$	9.86077	−	12.2422i	0.675649	−	0.838825i
$214$	−3.56753	−	6.17914i	−0.243871	−	0.422397i
$215$	1.68337			0.114805
$216$	−4.64814	−	2.32267i	−0.316266	−	0.158038i
$217$	1.76540	−	2.47575i	0.119843	−	0.168065i
$218$	−3.99943	+	2.30907i	−0.270876	+	0.156390i
$219$	11.5064	−	14.2853i	0.777528	−	0.965309i
$220$	3.11642	+	1.79927i	0.210109	+	0.121307i
$221$	23.0407	−	0.438583i	1.54989	−	0.0295023i
$222$	−6.26288	−	16.1889i	−0.420337	−	1.08653i
$223$	14.6126	−	8.43659i	0.978532	−	0.564956i	0.0767054	−	0.997054i	$-0.475560\pi$
$223$	14.6126	−	8.43659i	0.978532	−	0.564956i	0.901827	+	0.432098i	$0.142227\pi$
$224$	−1.09752	−	2.40738i	−0.0733309	−	0.160850i
$225$	−10.4017	+	9.46458i	−0.693449	+	0.630972i
$226$	3.19860	+	5.54013i	0.212767	+	0.368524i
$227$	−14.9919	−	25.9667i	−0.995046	−	1.72347i	−0.583620	−	0.812027i	$-0.698364\pi$
$227$	−14.9919	−	25.9667i	−0.995046	−	1.72347i	−0.411426	−	0.911443i	$-0.634969\pi$
$228$	−0.652628	−	1.68698i	−0.0432214	−	0.111723i
$229$	18.9964	−	10.9676i	1.25532	−	0.724758i	0.283157	−	0.959074i	$-0.408618\pi$
$229$	18.9964	−	10.9676i	1.25532	−	0.724758i	0.972161	+	0.234315i	$0.0752849\pi$
$230$	0.132940	−	0.230259i	0.00876581	−	0.0151828i
$231$	7.31023	−	28.5910i	0.480978	−	1.88115i
$232$	1.73214	+	3.00015i	0.113721	+	0.196970i
$233$	−10.9565	+	6.32576i	−0.717786	+	0.414414i	−0.813937	−	0.580953i	$-0.802680\pi$
$233$	−10.9565	+	6.32576i	−0.717786	+	0.414414i	0.0961511	+	0.995367i	$0.469347\pi$
$234$	−10.5226	+	2.50484i	−0.687886	+	0.163747i
$235$	0.0812311	−	0.140696i	0.00529893	−	0.00917802i
$236$	−4.85874	+	8.41558i	−0.316277	+	0.547808i
$237$	−18.3044	+	7.08129i	−1.18900	+	0.459979i
$238$	16.8327	+	1.61840i	1.09110	+	0.104905i
$239$			16.0816i			1.04023i	0.854095	+	0.520117i	$0.174112\pi$
$239$			16.0816i			1.04023i	−0.854095	+	0.520117i	$0.825888\pi$
$240$	0.148911	−	0.956343i	0.00961219	−	0.0617317i
$241$	2.95573	−	1.70649i	0.190395	−	0.109925i	−0.401772	−	0.915740i	$-0.631606\pi$
$241$	2.95573	−	1.70649i	0.190395	−	0.109925i	0.592167	+	0.805815i	$0.298272\pi$
$242$	26.3884	+	15.2353i	1.69631	+	0.979365i
$243$	−10.8779	+	11.1657i	−0.697816	+	0.716277i
$244$	5.27288	−	3.04430i	0.337562	−	0.194891i
$245$	−1.27454	−	3.69812i	−0.0814271	−	0.236264i
$246$	11.8353	+	1.84287i	0.754592	+	0.117497i
$247$	−3.29613	−	1.82027i	−0.209728	−	0.115821i
$248$	0.574642	−	0.995309i	0.0364898	−	0.0632022i
$249$	0.771430	−	4.95430i	0.0488874	−	0.313966i
$250$	−4.68822	−	2.70675i	−0.296509	−	0.171190i
$251$	6.77003	−	11.7260i	0.427321	−	0.740141i	−0.569313	−	0.822121i	$-0.692791\pi$
$251$	6.77003	−	11.7260i	0.427321	−	0.740141i	0.996634	+	0.0819797i	$0.0261243\pi$
$252$	−7.88130	+	0.940806i	−0.496475	+	0.0592652i
$253$	1.53205	−	2.65358i	0.0963189	−	0.166829i
$254$		−	6.70201i		−	0.420521i
$255$	4.81767	+	3.88049i	0.301694	+	0.243006i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.8702	−	18.8277i	0.678064	−	1.17444i	−0.297499	−	0.954722i	$-0.596153\pi$
$257$	10.8702	−	18.8277i	0.678064	−	1.17444i	0.975563	−	0.219719i	$-0.0705142\pi$
$258$	−1.88259	−	4.86630i	−0.117205	−	0.302963i
$259$	−21.5884	−	15.3943i	−1.34144	−	0.956553i
$260$	−1.04041	−	1.72536i	−0.0645237	−	0.107002i
$261$	10.1543	−	2.21384i	0.628536	−	0.137034i
$262$			15.3904i			0.950820i
$263$		−	16.8349i		−	1.03808i	−0.854749	−	0.519042i	$-0.826289\pi$
$263$		−	16.8349i		−	1.03808i	0.854749	−	0.519042i	$-0.173711\pi$
$264$	1.71610	−	11.0212i	0.105619	−	0.678308i
$265$		−	5.28080i		−	0.324397i
$266$	−2.24964	−	1.60417i	−0.137934	−	0.0983580i
$267$	4.36667	+	3.51722i	0.267236	+	0.215250i
$268$	5.69780	+	9.86888i	0.348049	+	0.602838i
$269$	8.00614	+	13.8670i	0.488143	+	0.845488i	0.999907	−	0.0136377i	$-0.00434113\pi$
$269$	8.00614	+	13.8670i	0.488143	+	0.845488i	−0.511764	+	0.859126i	$0.671008\pi$
$270$	−2.59737	−	1.29790i	−0.158071	−	0.0789879i
$271$	10.8364	+	6.25638i	0.658263	+	0.380048i	0.791615	−	0.611021i	$-0.209241\pi$
$271$	10.8364	+	6.25638i	0.658263	+	0.380048i	−0.133352	+	0.991069i	$0.542574\pi$
$272$	6.39150			0.387542
$273$	−11.3215	+	12.0343i	−0.685206	+	0.728349i
$274$	−5.40696			−0.326646
$275$	−26.1436	−	15.0940i	−1.57652	−	0.910203i
$276$	−0.814310	−	0.126796i	−0.0490157	−	0.00763219i
$277$	−0.307936	−	0.533360i	−0.0185021	−	0.0320465i	0.856626	−	0.515938i	$-0.172556\pi$
$277$	−0.307936	−	0.533360i	−0.0185021	−	0.0320465i	−0.875128	+	0.483891i	$0.839223\pi$
$278$	−7.99412	−	13.8462i	−0.479456	−	0.830442i
$279$	−2.32041	−	2.55017i	−0.138919	−	0.152675i
$280$	−0.613290	−	1.34524i	−0.0366511	−	0.0803933i
$281$			24.8711i			1.48368i	0.670575	+	0.741842i	$0.266047\pi$
$281$			24.8711i			1.48368i	−0.670575	+	0.741842i	$0.733953\pi$
$282$	−0.497572	−	0.0774765i	−0.0296300	−	0.00461366i
$283$		−	26.8615i		−	1.59675i	−0.602161	−	0.798375i	$-0.705693\pi$
$283$		−	26.8615i		−	1.59675i	0.602161	−	0.798375i	$-0.294307\pi$
$284$		−	9.07574i		−	0.538546i
$285$	−0.364688	−	0.942680i	−0.0216022	−	0.0558395i
$286$	−11.9901	−	19.8836i	−0.708987	−	1.17574i
$287$	16.6481	−	7.58983i	0.982707	−	0.448014i
$288$	−2.93115	+	0.639049i	−0.172719	+	0.0376563i
$289$	−11.9256	+	20.6558i	−0.701508	+	1.21505i
$290$	0.967917	+	1.67648i	0.0568380	+	0.0984463i
$291$	4.55848	−	5.65940i	0.267223	−	0.331760i
$292$		−	10.5903i		−	0.619752i
$293$	5.43236	−	9.40912i	0.317362	−	0.549687i	−0.662575	−	0.748996i	$-0.730536\pi$
$293$	5.43236	−	9.40912i	0.317362	−	0.549687i	0.979937	+	0.199309i	$0.0638697\pi$
$294$	−9.26520	+	7.82023i	−0.540358	+	0.456085i
$295$	−2.71505	+	4.70261i	−0.158077	+	0.273797i
$296$	−8.67906	−	5.01086i	−0.504460	−	0.291250i
$297$	−29.9330	−	14.9575i	−1.73689	−	0.867920i
$298$	5.51497	−	9.55221i	0.319474	−	0.553345i
$299$	−1.46911	+	0.885894i	−0.0849610	+	0.0512326i
$300$	−1.24921	+	8.02274i	−0.0721234	+	0.463193i
$301$	−6.48937	−	4.62744i	−0.374041	−	0.266721i
$302$	−1.25209	+	0.722893i	−0.0720496	+	0.0415978i
$303$	−2.72672	+	17.5116i	−0.156646	+	1.00602i
$304$	−0.904408	−	0.522160i	−0.0518713	−	0.0299479i
$305$	2.94648	−	1.70115i	0.168715	−	0.0974076i
$306$	5.82994	−	18.2667i	0.333276	−	1.04424i
$307$			9.52511i			0.543627i	0.962350	+	0.271813i	$0.0876234\pi$
$307$			9.52511i			0.543627i	−0.962350	+	0.271813i	$0.912377\pi$
$308$	−7.06775	−	15.5030i	−0.402723	−	0.883363i
$309$	−7.61000	−	19.6711i	−0.432918	−	1.11905i
$310$	0.321109	−	0.556177i	0.0182378	−	0.0315887i
$311$	−12.0559	+	20.8814i	−0.683627	+	1.18408i	0.290240	+	0.956954i	$0.406265\pi$
$311$	−12.0559	+	20.8814i	−0.683627	+	1.18408i	−0.973866	+	0.227122i	$0.927068\pi$
$312$	−3.82415	+	4.93719i	−0.216500	+	0.279514i
$313$	1.32306	−	0.763869i	0.0747838	−	0.0431764i	−0.462142	−	0.886806i	$-0.652919\pi$
$313$	1.32306	−	0.763869i	0.0747838	−	0.0431764i	0.536926	+	0.843630i	$0.319586\pi$
$314$	−2.87760	−	4.98415i	−0.162392	−	0.281272i
$315$	−4.40406	+	0.525721i	−0.248141	+	0.0296210i
$316$	−5.66566	+	9.81321i	−0.318718	+	0.552036i
$317$	25.7779	−	14.8829i	1.44783	−	0.835907i	0.449482	−	0.893290i	$-0.351609\pi$
$317$	25.7779	−	14.8829i	1.44783	−	0.835907i	0.998352	+	0.0573823i	$0.0182754\pi$
$318$	−15.2658	+	5.90577i	−0.856065	+	0.331179i
$319$	11.1546	+	19.3203i	0.624537	+	1.08173i
$320$	−0.279399	−	0.483934i	−0.0156189	−	0.0270527i
$321$	−7.75221	+	9.62445i	−0.432686	+	0.537185i
$322$	−1.14545	+	0.522206i	−0.0638333	+	0.0291014i
$323$	5.78052	−	3.33739i	0.321637	−	0.185697i
$324$	−0.847231	+	8.96003i	−0.0470684	+	0.497780i
$325$	8.72800	+	14.4740i	0.484142	+	0.802873i
$326$	1.60643	+	0.927473i	0.0889720	+	0.0513680i
$327$	6.22941	+	5.01760i	0.344487	+	0.277474i
$328$	5.98897	−	3.45773i	0.330685	−	0.190921i
$329$	−0.699908	+	0.319086i	−0.0385872	+	0.0175918i
$330$	0.958956	−	6.15863i	0.0527888	−	0.339022i
$331$	25.8006			1.41813			0.709065	−	0.705143i	$-0.249117\pi$
$331$	25.8006			1.41813			0.709065	+	0.705143i	$0.249117\pi$
$332$	−1.44742	−	2.50700i	−0.0794373	−	0.137589i
$333$	−22.2374	+	20.2339i	−1.21860	+	1.10881i
$334$		−	15.6398i		−	0.855770i
$335$	3.18392	+	5.51471i	0.173956	+	0.301301i
$336$	−3.20296	+	3.27735i	−0.174736	+	0.178794i
$337$	−22.2563			−1.21238			−0.606189	−	0.795320i	$-0.707303\pi$
$337$	−22.2563			−1.21238			−0.606189	+	0.795320i	$0.707303\pi$
$338$	0.494734	+	12.9906i	0.0269100	+	0.706595i
$339$	6.95053	−	8.62916i	0.377501	−	0.468672i
$340$	3.57156			0.193695
$341$	3.70056	−	6.40956i	0.200397	−	0.347097i
$342$	−2.31727	+	2.10849i	−0.125303	+	0.114014i
$343$	−5.25249	+	17.7598i	−0.283608	+	0.958940i
$344$	−2.60888	−	1.50624i	−0.140661	−	0.0812109i
$345$	−0.455035	−	0.0708531i	−0.0244983	−	0.00381460i
$346$	9.57643	+	5.52895i	0.514832	+	0.297238i
$347$	17.7328	−	10.2380i	0.951947	−	0.549607i	0.0582617	−	0.998301i	$-0.481444\pi$
$347$	17.7328	−	10.2380i	0.951947	−	0.549607i	0.893685	+	0.448695i	$0.148111\pi$
$348$	3.76393	−	4.67296i	0.201768	−	0.250497i
$349$	−4.41920	+	2.55143i	−0.236555	+	0.136575i	−0.613592	−	0.789623i	$-0.710276\pi$
$349$	−4.41920	+	2.55143i	−0.236555	+	0.136575i	0.377038	+	0.926198i	$0.376943\pi$
$350$	5.14487	+	11.2852i	0.275005	+	0.603217i
$351$	10.6222	+	15.4327i	0.566971	+	0.823738i
$352$	−3.21989	−	5.57701i	−0.171621	−	0.297255i
$353$	9.91190			0.527557			0.263779	−	0.964583i	$-0.415031\pi$
$353$	9.91190			0.527557			0.263779	+	0.964583i	$0.415031\pi$
$354$	16.6308	+	2.58956i	0.883915	+	0.137634i
$355$		−	5.07151i		−	0.269168i
$356$	3.23721			0.171572
$357$	−7.90494	−	28.2026i	−0.418374	−	1.49264i
$358$	0.0142097	−	0.0246119i	0.000751005	−	0.00130078i
$359$	7.41640	−	4.28186i	0.391423	−	0.225988i	−0.291354	−	0.956615i	$-0.594106\pi$
$359$	7.41640	−	4.28186i	0.391423	−	0.225988i	0.682776	+	0.730627i	$0.260772\pi$
$360$	−1.63792	+	0.357100i	−0.0863259	+	0.0188208i
$361$	17.9094			0.942600
$362$	1.02196	−	1.77009i	0.0537131	−	0.0930338i
$363$	8.11998	−	52.1484i	0.426188	−	2.73708i
$364$	−0.732083	+	9.51126i	−0.0383716	+	0.498525i
$365$		−	5.91786i		−	0.309755i
$366$	−8.21290	−	6.61524i	−0.429295	−	0.345784i
$367$			7.20024i			0.375850i	0.982183	+	0.187925i	$0.0601761\pi$
$367$			7.20024i			0.375850i	−0.982183	+	0.187925i	$0.939824\pi$
$368$	−0.412061	+	0.237904i	−0.0214802	+	0.0124016i
$369$	−4.41932	−	20.2702i	−0.230061	−	1.05523i
$370$	−4.84985	−	2.80006i	−0.252131	−	0.145568i
$371$	−14.5165	+	20.3575i	−0.753658	+	1.05691i
$372$	−1.96692	−	0.306267i	−0.101980	−	0.0158792i
$373$	−21.3561			−1.10578			−0.552889	−	0.833255i	$-0.686475\pi$
$373$	−21.3561			−1.10578			−0.552889	+	0.833255i	$0.686475\pi$
$374$	41.1598			2.12832
$375$	−1.44262	+	9.26481i	−0.0744964	+	0.478433i
$376$	−0.251784	+	0.145367i	−0.0129848	+	0.00749675i
$377$	−0.237718	−	12.4884i	−0.0122431	−	0.643184i
$378$	6.44503	+	12.1434i	0.331497	+	0.624588i
$379$	10.0507	+	17.4083i	0.516270	+	0.894206i	0.999822	+	0.0188903i	$0.00601332\pi$
$379$	10.0507	+	17.4083i	0.516270	+	0.894206i	−0.483551	+	0.875316i	$0.660653\pi$
$380$	−0.505382	−	0.291782i	−0.0259255	−	0.0149681i
$381$	−10.8263	+	4.18829i	−0.554649	+	0.214573i
$382$	−4.15574	+	7.19795i	−0.212626	+	0.368279i
$383$	32.5913			1.66534			0.832669	−	0.553772i	$-0.186812\pi$
$383$	32.5913			1.66534			0.832669	+	0.553772i	$0.186812\pi$
$384$	−1.08650	+	1.34890i	−0.0554451	+	0.0688356i
$385$	−3.94945	−	8.66302i	−0.201283	−	0.441509i
$386$	15.5331	+	8.96806i	0.790616	+	0.456462i
$387$	−6.68445	+	6.08221i	−0.339790	+	0.309176i
$388$		−	4.19558i		−	0.212998i
$389$	27.0880	+	15.6393i	1.37342	+	0.792942i	0.991356	−	0.131196i	$-0.0418816\pi$
$389$	27.0880	+	15.6393i	1.37342	+	0.792942i	0.382059	+	0.924138i	$0.375215\pi$
$390$	−2.13693	+	2.75890i	−0.108208	+	0.139702i
$391$		−	3.04112i		−	0.153796i
$392$	−1.33372	+	6.87177i	−0.0673629	+	0.347077i
$393$	24.8613	−	9.61791i	1.25409	−	0.485160i
$394$	22.6750			1.14235
$395$	−3.16596	+	5.48361i	−0.159297	+	0.275910i
$396$	−18.8759	+	4.11533i	−0.948550	+	0.206803i
$397$			4.58033i			0.229880i	0.993372	+	0.114940i	$0.0366676\pi$
$397$			4.58033i			0.229880i	−0.993372	+	0.114940i	$0.963332\pi$
$398$	−0.514328			−0.0257809
$399$	−1.18548	+	4.63652i	−0.0593482	+	0.232116i
$400$	2.34387	+	4.05971i	0.117194	+	0.202985i
$401$	19.4982	+	11.2573i	0.973694	+	0.562162i	0.900360	−	0.435145i	$-0.143303\pi$
$401$	19.4982	+	11.2573i	0.973694	+	0.562162i	0.0733333	+	0.997307i	$0.476636\pi$
$402$	12.3813	−	15.3715i	0.617522	−	0.766661i
$403$	−3.54855	+	2.13982i	−0.176766	+	0.106592i
$404$	5.11608	+	8.86132i	0.254535	+	0.440867i
$405$	−0.473431	+	5.00685i	−0.0235250	+	0.248792i
$406$	0.877194	−	9.12355i	0.0435344	−	0.452794i
$407$	−55.8912	−	32.2688i	−2.77042	−	1.59950i
$408$	−3.99425	−	10.3247i	−0.197745	−	0.511150i
$409$	5.35808	−	3.09349i	0.264940	−	0.152963i	−0.361646	−	0.932316i	$-0.617785\pi$
$409$	5.35808	−	3.09349i	0.264940	−	0.152963i	0.626586	+	0.779352i	$0.284452\pi$
$410$	3.34662	−	1.93217i	0.165278	−	0.0954233i
$411$	3.37898	+	8.73431i	0.166673	+	0.430832i
$412$	−10.5459	−	6.08867i	−0.519559	−	0.299967i
$413$	23.3936	−	10.6651i	1.15112	−	0.524795i
$414$	0.304064	+	1.39466i	0.0149439	+	0.0685438i
$415$	−0.808814	−	1.40091i	−0.0397031	−	0.0687678i
$416$	0.0686197	+	3.60490i	0.00336436	+	0.176745i
$417$	−17.3712	+	21.5665i	−0.850670	+	1.05612i
$418$	−5.82418	−	3.36259i	−0.284870	−	0.164470i
$419$	10.1893	+	17.6485i	0.497782	+	0.862184i	0.999997	−	0.00255900i	$-0.000814557\pi$
$419$	10.1893	+	17.6485i	0.497782	+	0.862184i	−0.502215	+	0.864743i	$0.667481\pi$
$420$	−1.78981	+	1.83138i	−0.0873338	+	0.0893622i
$421$	34.5026			1.68155			0.840777	−	0.541382i	$-0.182099\pi$
$421$	34.5026			1.68155			0.840777	+	0.541382i	$0.182099\pi$
$422$			8.14356i			0.396422i
$423$	0.185794	+	0.852186i	0.00903361	+	0.0414347i
$424$	−4.72514	+	8.18418i	−0.229473	+	0.397459i
$425$	−29.9617			−1.45336
$426$	−14.6608	+	5.67172i	−0.710318	+	0.274795i
$427$	−16.0350	−	1.54170i	−0.775987	−	0.0746082i
$428$			7.13505i			0.344886i
$429$	−24.6267	+	31.7944i	−1.18899	+	1.53505i
$430$	−1.45784	−	0.841683i	−0.0703032	−	0.0405896i
$431$			1.42774i			0.0687719i	0.999409	+	0.0343859i	$0.0109475\pi$
$431$			1.42774i			0.0687719i	−0.999409	+	0.0343859i	$0.989052\pi$
$432$	2.86407	+	4.33556i	0.137798	+	0.208595i
$433$	7.62829	+	4.40419i	0.366592	+	0.211652i	0.671969	−	0.740580i	$-0.265449\pi$
$433$	7.62829	+	4.40419i	0.366592	+	0.211652i	−0.305376	+	0.952232i	$0.598782\pi$
$434$	−2.76676	+	1.26136i	−0.132809	+	0.0605471i
$435$	2.10328	−	2.61124i	0.100844	−	0.125199i
$436$	4.61815			0.221169
$437$	−0.248448	+	0.430324i	−0.0118849	+	0.0205852i
$438$	−17.1074	+	6.61823i	−0.817425	+	0.316231i
$439$	−6.28070	−	3.62617i	−0.299762	−	0.173067i	0.342574	−	0.939491i	$-0.388701\pi$
$439$	−6.28070	−	3.62617i	−0.299762	−	0.173067i	−0.642336	+	0.766423i	$0.722035\pi$
$440$	−1.79927	−	3.11642i	−0.0857767	−	0.148570i
$441$	18.4228	+	10.0797i	0.877275	+	0.479988i
$442$	−20.1731	−	11.1405i	−0.959538	−	0.529901i
$443$	−9.44613	+	5.45373i	−0.448799	+	0.259114i	−0.707323	−	0.706890i	$-0.750097\pi$
$443$	−9.44613	+	5.45373i	−0.448799	+	0.259114i	0.258524	+	0.966005i	$0.416764\pi$
$444$	−2.67064	+	17.1514i	−0.126743	+	0.813972i
$445$	1.80895			0.0857524
$446$	−16.8732			−0.798968
$447$	−18.8770	−	2.93931i	−0.892849	−	0.139025i
$448$	−0.253211	+	2.63361i	−0.0119631	+	0.124426i
$449$	3.81282	+	2.20133i	0.179938	+	0.103887i	0.587264	−	0.809396i	$-0.300205\pi$
$449$	3.81282	+	2.20133i	0.179938	+	0.103887i	−0.407326	+	0.913283i	$0.633539\pi$
$450$	13.7405	−	2.99570i	0.647732	−	0.141219i
$451$	38.5676	−	22.2670i	1.81608	−	1.04851i
$452$		−	6.39719i		−	0.300899i
$453$	1.95022	+	1.57084i	0.0916293	+	0.0738046i
$454$			29.9838i			1.40721i
$455$	−0.409087	+	5.31488i	−0.0191783	+	0.249165i
$456$	−0.278296	+	1.78728i	−0.0130324	+	0.0836970i
$457$	0.0923367	−	0.159932i	0.00431933	−	0.00748130i	−0.863858	−	0.503736i	$-0.831958\pi$
$457$	0.0923367	−	0.159932i	0.00431933	−	0.00748130i	0.868177	+	0.496255i	$0.165292\pi$
$458$	−21.9352			−1.02496
$459$	−33.1511	+	1.99786i	−1.54736	+	0.0932519i
$460$	−0.230259	+	0.132940i	−0.0107359	+	0.00619837i
$461$	−1.67764	+	2.90576i	−0.0781356	+	0.135335i	−0.902446	−	0.430804i	$-0.858230\pi$
$461$	−1.67764	+	2.90576i	−0.0781356	+	0.135335i	0.824310	+	0.566139i	$0.191563\pi$
$462$	−20.6263	+	21.1054i	−0.959624	+	0.981912i
$463$	27.7151			1.28803			0.644014	−	0.765014i	$-0.277268\pi$
$463$	27.7151			1.28803			0.644014	+	0.765014i	$0.277268\pi$
$464$		−	3.46428i		−	0.160825i
$465$	−1.09911	−	0.171141i	−0.0509700	−	0.00793649i
$466$	12.6515			0.586070
$467$	15.5226	+	26.8860i	0.718302	+	1.24414i	0.961672	+	0.274202i	$0.0884138\pi$
$467$	15.5226	+	26.8860i	0.718302	+	1.24414i	−0.243370	+	0.969934i	$0.578253\pi$
$468$	10.3653	+	3.09206i	0.479136	+	0.142930i
$469$	2.88549	−	30.0115i	0.133240	−	1.38580i
$470$	−0.140696	+	0.0812311i	−0.00648984	+	0.00374691i
$471$	−6.25300	+	7.76317i	−0.288123	+	0.357708i
$472$	8.41558	−	4.85874i	0.387359	−	0.223642i
$473$	−16.8006	−	9.69983i	−0.772492	−	0.445999i
$474$	19.3927	+	3.01963i	0.890738	+	0.138696i
$475$	4.23963	+	2.44775i	0.194528	+	0.112311i
$476$	−13.7683	−	9.81792i	−0.631071	−	0.450004i
$477$	19.0802	+	20.9694i	0.873621	+	0.960124i
$478$	8.04081	−	13.9271i	0.367778	−	0.637010i
$479$	17.2835			0.789705			0.394852	−	0.918745i	$-0.370796\pi$
$479$	17.2835			0.789705			0.394852	+	0.918745i	$0.370796\pi$
$480$	−0.607133	+	0.753762i	−0.0277117	+	0.0344044i
$481$	18.6592	+	30.9433i	0.850786	+	1.41089i
$482$	−3.41298			−0.155457
$483$	1.55939	+	1.52399i	0.0709546	+	0.0693440i
$484$	−15.2353	−	26.3884i	−0.692515	−	1.19947i
$485$		−	2.34448i		−	0.106457i
$486$	15.0033	−	4.23080i	0.680565	−	0.191913i
$487$	−2.86232	−	4.95769i	−0.129704	−	0.224654i	0.793858	−	0.608104i	$-0.208069\pi$
$487$	−2.86232	−	4.95769i	−0.129704	−	0.224654i	−0.923562	+	0.383449i	$0.874736\pi$
$488$	−6.08860			−0.275618
$489$	0.494316	−	3.17461i	0.0223537	−	0.143561i
$490$	−0.745279	+	3.83993i	−0.0336683	+	0.173470i
$491$	33.9357	−	19.5928i	1.53150	−	0.884211i	0.532206	−	0.846615i	$-0.321363\pi$
$491$	33.9357	−	19.5928i	1.53150	−	0.884211i	0.999293	−	0.0375963i	$-0.0119701\pi$
$492$	−9.32825	−	7.51363i	−0.420550	−	0.338741i
$493$	19.1755	+	11.0710i	0.863620	+	0.498611i
$494$	1.94439	+	3.22447i	0.0874824	+	0.145076i
$495$	−10.5478	+	2.29964i	−0.474090	+	0.103361i
$496$	−0.995309	+	0.574642i	−0.0446907	+	0.0258022i
$497$	−13.9412	+	19.5506i	−0.625347	+	0.876966i
$498$	−3.14523	+	3.90483i	−0.140941	+	0.174980i
$499$	−13.0911	−	22.6744i	−0.586037	−	1.01505i	−0.994745	−	0.102381i	$-0.967354\pi$
$499$	−13.0911	−	22.6744i	−0.586037	−	1.01505i	0.408709	−	0.912665i	$-0.365979\pi$
$500$	2.70675	+	4.68822i	0.121049	+	0.209664i
$501$	−25.2642	+	9.77377i	−1.12872	+	0.436660i
$502$	−11.7260	+	6.77003i	−0.523359	+	0.302161i
$503$	−1.72780	+	2.99265i	−0.0770390	+	0.133435i	−0.901971	−	0.431796i	$-0.857880\pi$
$503$	−1.72780	+	2.99265i	−0.0770390	+	0.133435i	0.824932	+	0.565232i	$0.191213\pi$
$504$	7.29581	+	3.12589i	0.324981	+	0.139238i
$505$	2.85886	+	4.95169i	0.127218	+	0.220347i
$506$	−2.65358	+	1.53205i	−0.117966	+	0.0681077i
$507$	20.6756	−	8.91740i	0.918235	−	0.396036i
$508$	−3.35100	+	5.80411i	−0.148677	+	0.257516i
$509$	−12.5186	+	21.6829i	−0.554879	+	0.961078i	0.443034	+	0.896505i	$0.353902\pi$
$509$	−12.5186	+	21.6829i	−0.554879	+	0.961078i	−0.997913	+	0.0645734i	$0.979431\pi$
$510$	−2.23198	−	5.76944i	−0.0988337	−	0.255475i
$511$	−16.2677	+	22.8133i	−0.719641	+	1.00920i
$512$			1.00000i			0.0441942i
$513$	4.85415	+	2.42561i	0.214316	+	0.107093i
$514$	−18.8277	+	10.8702i	−0.830456	+	0.479464i
$515$	−5.89303	−	3.40234i	−0.259678	−	0.149925i
$516$	−0.802780	+	5.15564i	−0.0353404	+	0.226964i
$517$	−1.62143	+	0.936133i	−0.0713104	+	0.0411711i
$518$	10.9990	+	24.1260i	0.483268	+	1.06004i
$519$	2.94677	−	18.9248i	0.129349	−	0.830707i
$520$	0.0383446	+	2.01441i	0.00168152	+	0.0883378i
$521$	−17.0217	+	29.4824i	−0.745732	+	1.29165i	0.204119	+	0.978946i	$0.434567\pi$
$521$	−17.0217	+	29.4824i	−0.745732	+	1.29165i	−0.949852	+	0.312701i	$0.898766\pi$
$522$	−9.90081	−	3.15991i	−0.433347	−	0.138305i
$523$	−10.5809	−	6.10886i	−0.462669	−	0.267122i	0.250497	−	0.968117i	$-0.419406\pi$
$523$	−10.5809	−	6.10886i	−0.462669	−	0.267122i	−0.713166	+	0.700995i	$0.752739\pi$
$524$	7.69518	−	13.3284i	0.336165	−	0.582256i
$525$	15.0147	−	15.3634i	0.655294	−	0.670513i
$526$	−8.41744	+	14.5794i	−0.367018	+	0.635693i
$527$		−	7.34565i		−	0.319981i
$528$	−6.99679	+	8.68659i	−0.304496	+	0.378035i
$529$	−11.3868	−	19.7225i	−0.495078	−	0.857501i
$530$	−2.64040	+	4.57331i	−0.114692	+	0.198652i
$531$	−6.20995	−	28.4833i	−0.269489	−	1.23607i
$532$	1.14616	+	2.51407i	0.0496923	+	0.108999i
$533$	−24.9295	+	0.474537i	−1.07982	+	0.0205545i
$534$	−2.02303	−	5.22933i	−0.0875452	−	0.226295i
$535$			3.98705i			0.172375i
$536$		−	11.3956i		−	0.492215i
$537$	−0.0486377	−	0.00757333i	−0.00209887	−	0.000326813i
$538$		−	16.0123i		−	0.690338i
$539$	−8.58883	+	44.2526i	−0.369947	+	1.90610i
$540$	1.60044	+	2.42270i	0.0688719	+	0.104257i
$541$	−18.7767	−	32.5222i	−0.807273	−	1.39824i	−0.914746	−	0.404030i	$-0.867609\pi$
$541$	−18.7767	−	32.5222i	−0.807273	−	1.39824i	0.107472	−	0.994208i	$-0.465724\pi$
$542$	−6.25638	−	10.8364i	−0.268735	−	0.465462i
$543$	−3.49803	−	0.544675i	−0.150115	−	0.0233742i
$544$	−5.53520	−	3.19575i	−0.237320	−	0.137017i
$545$	2.58061			0.110541
$546$	15.8218	−	4.76129i	0.677112	−	0.203764i
$547$	35.7930			1.53040			0.765199	−	0.643794i	$-0.222640\pi$
$547$	35.7930			1.53040			0.765199	+	0.643794i	$0.222640\pi$
$548$	4.68256	+	2.70348i	0.200029	+	0.115487i
$549$	−5.55366	+	17.4010i	−0.237024	+	0.742658i
$550$	15.0940	+	26.1436i	0.643611	+	1.11477i
$551$	−1.80891	−	3.13312i	−0.0770621	−	0.133475i
$552$	0.641815	+	0.516963i	0.0273175	+	0.0220034i
$553$	27.2787	−	12.4363i	1.16001	−	0.528845i
$554$			0.615872i			0.0261659i
$555$	−1.49235	+	9.58420i	−0.0633467	+	0.406827i
$556$			15.9882i			0.678053i
$557$		−	0.484593i		−	0.0205329i	−0.999947	−	0.0102664i	$-0.996732\pi$
$557$		−	0.484593i		−	0.0205329i	0.999947	−	0.0102664i	$-0.00326796\pi$
$558$	0.734449	+	3.36872i	0.0310917	+	0.142609i
$559$	5.60885	+	9.30139i	0.237229	+	0.393407i
$560$	−0.141494	+	1.47166i	−0.00597921	+	0.0621888i
$561$	−25.7220	−	66.4889i	−1.08599	−	2.80716i
$562$	12.4355	−	21.5390i	0.524561	−	0.908567i
$563$	−7.46317	−	12.9266i	−0.314535	−	0.544791i	0.664803	−	0.747018i	$-0.268515\pi$
$563$	−7.46317	−	12.9266i	−0.314535	−	0.544791i	−0.979339	+	0.202227i	$0.935182\pi$
$564$	0.392172	+	0.315883i	0.0165134	+	0.0133011i
$565$		−	3.57474i		−	0.150390i
$566$	−13.4307	+	23.2627i	−0.564536	+	0.977805i
$567$	15.5885	−	18.0000i	0.654655	−	0.755927i
$568$	−4.53787	+	7.85983i	−0.190405	+	0.329791i
$569$	−2.82588	−	1.63152i	−0.118467	−	0.0683971i	0.439595	−	0.898196i	$-0.355122\pi$
$569$	−2.82588	−	1.63152i	−0.118467	−	0.0683971i	−0.558063	+	0.829799i	$0.688455\pi$
$570$	−0.155511	+	0.998728i	−0.00651365	+	0.0418321i
$571$	−13.9187	+	24.1078i	−0.582478	+	1.00888i	0.412706	+	0.910864i	$0.364584\pi$
$571$	−13.9187	+	24.1078i	−0.582478	+	1.00888i	−0.995185	+	0.0980177i	$0.968750\pi$
$572$	0.441895	+	23.2147i	0.0184766	+	0.970656i
$573$	14.2245	+	2.21488i	0.594237	+	0.0925281i
$574$	−18.2126	−	1.75107i	−0.760180	−	0.0730883i
$575$	1.93164	−	1.11523i	0.0805548	−	0.0465084i
$576$	2.85797	+	0.912140i	0.119082	+	0.0380058i
$577$	−15.4524	−	8.92144i	−0.643291	−	0.371404i	0.142590	−	0.989782i	$-0.454457\pi$
$577$	−15.4524	−	8.92144i	−0.643291	−	0.371404i	−0.785881	+	0.618378i	$0.787790\pi$
$578$	20.6558	−	11.9256i	0.859169	−	0.496041i
$579$	4.77971	−	30.6964i	0.198638	−	1.27570i
$580$		−	1.93583i		−	0.0803811i
$581$	−0.733004	+	7.62385i	−0.0304101	+	0.316291i
$582$	−6.77746	+	2.62195i	−0.280935	+	0.108683i
$583$	−30.4288	+	52.7043i	−1.26023	+	2.18279i
$584$	−5.29516	+	9.17149i	−0.219115	+	0.379519i
$585$	5.79211	+	1.72784i	0.239474	+	0.0714373i
$586$	−9.40912	+	5.43236i	−0.388687	+	0.224409i
$587$	−10.1829	−	17.6373i	−0.420293	−	0.727969i	0.575675	−	0.817679i	$-0.304739\pi$
$587$	−10.1829	−	17.6373i	−0.420293	−	0.727969i	−0.995968	+	0.0897099i	$0.971406\pi$
$588$	11.9340	−	2.13992i	0.492151	−	0.0882488i
$589$	−0.600110	+	1.03942i	−0.0247271	+	0.0428286i
$590$	4.70261	−	2.71505i	0.193604	−	0.111777i
$591$	−14.1703	−	36.6287i	−0.582888	−	1.50670i
$592$	5.01086	+	8.67906i	0.205945	+	0.356707i
$593$	16.1774	+	28.0200i	0.664325	+	1.15064i	0.979468	+	0.201600i	$0.0646140\pi$
$593$	16.1774	+	28.0200i	0.664325	+	1.15064i	−0.315143	+	0.949044i	$0.602053\pi$
$594$	18.4440	+	27.9200i	0.756766	+	1.14557i
$595$	−7.69373	−	5.48624i	−0.315412	−	0.224914i
$596$	−9.55221	+	5.51497i	−0.391274	+	0.225902i
$597$	0.321420	+	0.830837i	0.0131548	+	0.0340039i
$598$	1.71524	−	0.0326498i	0.0701412	−	0.00133515i
$599$	22.7092	+	13.1112i	0.927875	+	0.535709i	0.886139	−	0.463420i	$-0.153378\pi$
$599$	22.7092	+	13.1112i	0.927875	+	0.535709i	0.0417359	+	0.999129i	$0.486711\pi$
$600$	5.09322	−	6.32329i	0.207930	−	0.258147i
$601$	−11.2795	+	6.51220i	−0.460099	+	0.265638i	−0.712086	−	0.702092i	$-0.752249\pi$
$601$	−11.2795	+	6.51220i	−0.460099	+	0.265638i	0.251987	+	0.967731i	$0.418916\pi$
$602$	3.30624	+	7.25216i	0.134752	+	0.295576i
$603$	−32.5683	−	10.3944i	−1.32628	−	0.423292i
$604$	1.44579			0.0588282
$605$	−8.51348	−	14.7458i	−0.346122	−	0.599501i
$606$	11.1172	−	13.8021i	0.451606	−	0.560674i
$607$			16.5542i			0.671914i	0.941877	+	0.335957i	$0.109060\pi$
$607$			16.5542i			0.671914i	−0.941877	+	0.335957i	$0.890940\pi$
$608$	0.522160	+	0.904408i	0.0211764	+	0.0366786i
$609$	−15.2862	+	4.28459i	−0.619428	+	0.173620i
$610$	−3.40230			−0.137755
$611$	1.04807	−	0.0199501i	0.0424004	−	0.000807097i
$612$	−14.1822	+	12.9045i	−0.573283	+	0.521633i
$613$	6.40588			0.258731			0.129366	−	0.991597i	$-0.458706\pi$
$613$	6.40588			0.258731			0.129366	+	0.991597i	$0.458706\pi$
$614$	4.76256	−	8.24899i	0.192201	−	0.332902i
$615$	−5.21261	−	4.19860i	−0.210193	−	0.169304i
$616$	−1.63062	+	16.9598i	−0.0656996	+	0.683331i
$617$	−1.20187	−	0.693899i	−0.0483854	−	0.0279353i	0.475612	−	0.879655i	$-0.342227\pi$
$617$	−1.20187	−	0.693899i	−0.0483854	−	0.0279353i	−0.523998	+	0.851720i	$0.675560\pi$
$618$	−3.24508	+	20.8407i	−0.130536	+	0.838334i
$619$	−33.9833	−	19.6203i	−1.36591	−	0.788606i	−0.375503	−	0.926821i	$-0.622530\pi$
$619$	−33.9833	−	19.6203i	−1.36591	−	0.788606i	−0.990402	+	0.138215i	$0.955863\pi$
$620$	−0.556177	+	0.321109i	−0.0223366	+	0.0128960i
$621$	2.06289	−	1.36275i	0.0827810	−	0.0546851i
$622$	20.8814	−	12.0559i	0.837268	−	0.483397i
$623$	−6.97349	−	4.97265i	−0.279387	−	0.199225i
$624$	5.78041	−	2.36366i	0.231401	−	0.0946221i
$625$	−10.2068	−	17.6788i	−0.408273	−	0.707150i
$626$	−1.52774			−0.0610607
$627$	−1.79216	+	11.5097i	−0.0715720	+	0.459652i
$628$			5.75520i			0.229657i
$629$	−64.0538			−2.55399
$630$	4.07689	+	1.74674i	0.162427	+	0.0695918i
$631$	14.6605	−	25.3928i	0.583627	−	1.01087i	−0.411418	−	0.911447i	$-0.634966\pi$
$631$	14.6605	−	25.3928i	0.583627	−	1.01087i	0.995045	−	0.0994248i	$-0.0317003\pi$
$632$	9.81321	−	5.66566i	0.390349	−	0.225368i
$633$	13.1550	−	5.08916i	0.522863	−	0.202276i
$634$	−29.7658			−1.18215
$635$	−1.87254	+	3.24333i	−0.0743093	+	0.128707i
$636$	16.1735	+	2.51836i	0.641320	+	0.0998594i
$637$	16.1872	−	19.3643i	0.641360	−	0.767240i
$638$		−	22.3092i		−	0.883228i
$639$	18.3240	+	20.1384i	0.724885	+	0.796662i
$640$			0.558798i			0.0220884i
$641$	−18.8464	+	10.8810i	−0.744389	+	0.429773i	−0.823663	−	0.567080i	$-0.808073\pi$
$641$	−18.8464	+	10.8810i	−0.744389	+	0.429773i	0.0792742	+	0.996853i	$0.474740\pi$
$642$	11.5258	−	4.45892i	0.454889	−	0.175979i
$643$	−7.70064	−	4.44597i	−0.303684	−	0.175332i	0.340413	−	0.940276i	$-0.389433\pi$
$643$	−7.70064	−	4.44597i	−0.303684	−	0.175332i	−0.644097	+	0.764944i	$0.722767\pi$
$644$	1.25309	+	0.120480i	0.0493786	+	0.00474756i
$645$	−0.448592	+	2.88096i	−0.0176633	+	0.113438i
$646$	−6.67477			−0.262615
$647$	27.6612			1.08747			0.543736	−	0.839256i	$-0.317009\pi$
$647$	27.6612			1.08747			0.543736	+	0.839256i	$0.317009\pi$
$648$	5.21374	−	7.33600i	0.204815	−	0.288185i
$649$	54.1944	−	31.2892i	2.12732	−	1.22821i
$650$	−0.321672	−	16.8988i	−0.0126170	−	0.662827i
$651$	3.76661	+	3.68111i	0.147625	+	0.144274i
$652$	−0.927473	−	1.60643i	−0.0363227	−	0.0629127i
$653$	0.677621	+	0.391225i	0.0265174	+	0.0153098i	0.513200	−	0.858269i	$-0.328460\pi$
$653$	0.677621	+	0.391225i	0.0265174	+	0.0153098i	−0.486683	+	0.873579i	$0.661793\pi$
$654$	−2.88602	−	7.46008i	−0.112852	−	0.291712i
$655$	4.30005	−	7.44791i	0.168017	−	0.291014i
$656$	−6.91546			−0.270003
$657$	21.3819	+	23.4991i	0.834189	+	0.916788i
$658$	0.765681	+	0.0736173i	0.0298494	+	0.00286990i
$659$	4.04939	+	2.33792i	0.157742	+	0.0910723i	0.576793	−	0.816890i	$-0.304304\pi$
$659$	4.04939	+	2.33792i	0.157742	+	0.0910723i	−0.419051	+	0.907963i	$0.637637\pi$
$660$	−3.90980	+	4.85405i	−0.152189	+	0.188944i
$661$		−	12.1466i		−	0.472449i	−0.971699	−	0.236224i	$-0.924090\pi$
$661$		−	12.1466i		−	0.472449i	0.971699	−	0.236224i	$-0.0759101\pi$
$662$	−22.3440	−	12.9003i	−0.868424	−	0.501385i
$663$	−5.38940	+	39.5494i	−0.209307	+	1.53597i
$664$			2.89483i			0.112341i
$665$	0.640471	+	1.40486i	0.0248364	+	0.0544781i
$666$	29.3751	−	6.40437i	1.13826	−	0.248164i
$667$	−1.64833			−0.0638235
$668$	−7.81988	+	13.5444i	−0.302560	+	0.524050i
$669$	10.5446	+	27.2566i	0.407677	+	1.05380i
$670$		−	6.36784i		−	0.246011i
$671$	−39.2092			−1.51365
$672$	4.41252	−	1.23679i	0.170217	−	0.0477102i
$673$	12.6791	+	21.9608i	0.488743	+	0.846527i	0.999916	−	0.0129505i	$-0.00412238\pi$
$673$	12.6791	+	21.9608i	0.488743	+	0.846527i	−0.511173	+	0.859478i	$0.670789\pi$
$674$	19.2745	+	11.1282i	0.742427	+	0.428641i
$675$	−13.4260	−	20.3240i	−0.516769	−	0.782271i
$676$	6.06684	−	11.4975i	0.233340	−	0.442213i
$677$	−20.8673	−	36.1433i	−0.801997	−	1.38910i	−0.918300	−	0.395886i	$-0.870438\pi$
$677$	−20.8673	−	36.1433i	−0.801997	−	1.38910i	0.116303	−	0.993214i	$-0.462896\pi$
$678$	−10.3339	+	3.99781i	−0.396872	+	0.153535i
$679$	−6.44479	+	9.03797i	−0.247328	+	0.346845i
$680$	−3.09306	−	1.78578i	−0.118614	−	0.0684815i
$681$	48.4352	−	18.7378i	1.85604	−	0.718033i
$682$	−6.40956	+	3.70056i	−0.245435	+	0.141702i
$683$	12.4836	−	7.20742i	0.477672	−	0.275784i	−0.241774	−	0.970333i	$-0.577729\pi$
$683$	12.4836	−	7.20742i	0.477672	−	0.275784i	0.719446	+	0.694548i	$0.244396\pi$
$684$	3.06105	−	0.667372i	0.117042	−	0.0255176i
$685$	2.61661	+	1.51070i	0.0999755	+	0.0577209i
$686$	13.4287	−	12.7542i	0.512710	−	0.486958i
$687$	13.7080	+	35.4337i	0.522991	+	1.35188i
$688$	1.50624	+	2.60888i	0.0574248	+	0.0994626i
$689$	29.1789	−	17.5952i	1.11163	−	0.670325i
$690$	0.358645	+	0.288878i	0.0136534	+	0.0109974i
$691$	−0.200407	−	0.115705i	−0.00762385	−	0.00440163i	0.496183	−	0.868218i	$-0.334734\pi$
$691$	−0.200407	−	0.115705i	−0.00762385	−	0.00440163i	−0.503807	+	0.863816i	$0.668068\pi$
$692$	−5.52895	−	9.57643i	−0.210179	−	0.364041i
$693$	46.9833	+	20.1300i	1.78475	+	0.764676i
$694$	−20.4761			−0.777261
$695$			8.93421i			0.338894i
$696$	−5.59614	+	2.16494i	−0.212121	+	0.0820617i
$697$	22.1001	−	38.2785i	0.837101	−	1.44990i
$698$	5.10286			0.193146
$699$	−7.90632	−	20.4370i	−0.299045	−	0.773000i
$700$	1.18699	−	12.3457i	0.0448640	−	0.466623i
$701$		−	5.73534i		−	0.216621i	−0.994117	−	0.108310i	$-0.965456\pi$
$701$		−	5.73534i		−	0.216621i	0.994117	−	0.108310i	$-0.0345441\pi$
$702$	−1.48273	−	18.6762i	−0.0559621	−	0.704889i
$703$	9.06372	+	5.23294i	0.341845	+	0.197364i
$704$			6.43977i			0.242708i
$705$	0.219145	+	0.176515i	0.00825347	+	0.00664793i
$706$	−8.58396	−	4.95595i	−0.323062	−	0.186520i
$707$	2.59090	−	26.9475i	0.0974408	−	1.01347i
$708$	−13.1079	−	10.5580i	−0.492624	−	0.396794i
$709$	26.1866			0.983458			0.491729	−	0.870748i	$-0.336365\pi$
$709$	26.1866			0.983458			0.491729	+	0.870748i	$0.336365\pi$
$710$	−2.53576	+	4.39206i	−0.0951652	+	0.164831i
$711$	−7.24127	−	33.2137i	−0.271569	−	1.24561i
$712$	−2.80351	−	1.61861i	−0.105066	−	0.0606598i
$713$	0.273419	+	0.473575i	0.0102396	+	0.0177355i
$714$	−7.25544	+	28.3767i	−0.271528	+	1.06197i
$715$	0.246930	+	12.9724i	0.00923467	+	0.485138i
$716$	−0.0246119	+	0.0142097i	−0.000919789	+	0.000531041i
$717$	−27.5225	−	4.28551i	−1.02785	−	0.160045i
$718$	−8.56372			−0.319595
$719$	20.5524			0.766477			0.383238	−	0.923649i	$-0.374809\pi$
$719$	20.5524			0.766477			0.383238	+	0.923649i	$0.374809\pi$
$720$	1.59703	+	0.509702i	0.0595178	+	0.0189955i
$721$	13.3648	+	29.3155i	0.497733	+	1.09176i
$722$	−15.5100	−	8.95470i	−0.577222	−	0.333259i
$723$	2.13288	+	5.51327i	0.0793225	+	0.205041i
$724$	−1.77009	+	1.02196i	−0.0657849	+	0.0379809i
$725$			16.2397i			0.603126i
$726$	−33.1063	+	41.1018i	−1.22869	+	1.52543i
$727$			32.5075i			1.20564i	0.797879	+	0.602818i	$0.205956\pi$
$727$			32.5075i			1.20564i	−0.797879	+	0.602818i	$0.794044\pi$
$728$	5.38963	−	7.87095i	0.199753	−	0.291717i
$729$	−16.2104	−	21.5922i	−0.600386	−	0.799710i
$730$	−2.95893	+	5.12501i	−0.109515	+	0.189685i
$731$	−19.2542			−0.712144
$732$	3.80496	+	9.83542i	0.140635	+	0.363528i
$733$	26.9299	−	15.5480i	0.994677	−	0.574277i	0.0880082	−	0.996120i	$-0.471950\pi$
$733$	26.9299	−	15.5480i	0.994677	−	0.574277i	0.906669	+	0.421843i	$0.138616\pi$
$734$	3.60012	−	6.23559i	0.132883	−	0.230160i
$735$	6.66871	−	1.19578i	0.245979	−	0.0441071i
$736$	0.475807			0.0175385
$737$		−	73.3851i		−	2.70317i
$738$	−6.30787	+	19.7642i	−0.232196	+	0.727530i
$739$	16.2385			0.597345			0.298672	−	0.954356i	$-0.403456\pi$
$739$	16.2385			0.597345			0.298672	+	0.954356i	$0.403456\pi$
$740$	2.80006	+	4.84985i	0.102932	+	0.178284i
$741$	3.99364	−	5.15601i	0.146710	−	0.189411i
$742$	22.7504	−	10.3718i	0.835193	−	0.380762i
$743$	41.5039	−	23.9623i	1.52263	−	0.879091i	0.522989	−	0.852340i	$-0.324817\pi$
$743$	41.5039	−	23.9623i	1.52263	−	0.879091i	0.999642	−	0.0267517i	$-0.00851636\pi$
$744$	1.55027	+	1.24869i	0.0568355	+	0.0457793i
$745$	−5.33776	+	3.08176i	−0.195560	+	0.112907i
$746$	18.4949	+	10.6781i	0.677148	+	0.390951i
$747$	8.27335	+	2.64049i	0.302706	+	0.0966106i
$748$	−35.6454	−	20.5799i	−1.30333	−	0.752476i
$749$	10.9601	−	15.3701i	0.400473	−	0.561610i
$750$	5.88175	−	7.30225i	0.214771	−	0.266641i
$751$	−4.85920	+	8.41637i	−0.177315	+	0.307118i	−0.940960	−	0.338518i	$-0.890074\pi$
$751$	−4.85920	+	8.41637i	−0.177315	+	0.307118i	0.763645	+	0.645636i	$0.223408\pi$
$752$	0.290735			0.0106020
$753$	18.2642	+	14.7112i	0.665583	+	0.536107i
$754$	−6.03832	+	10.9341i	−0.219903	+	0.398197i
$755$	0.807903			0.0294026
$756$	0.490128	−	13.7390i	0.0178258	−	0.499682i
$757$	−12.8376	−	22.2353i	−0.466589	−	0.808156i	0.532682	−	0.846315i	$-0.321184\pi$
$757$	−12.8376	−	22.2353i	−0.466589	−	0.808156i	−0.999272	+	0.0381589i	$0.987851\pi$
$758$		−	20.1014i		−	0.730116i
$759$	4.13314	+	3.32912i	0.150024	+	0.120840i
$760$	0.291782	+	0.505382i	0.0105841	+	0.0183321i
$761$	16.2660			0.589642			0.294821	−	0.955553i	$-0.404740\pi$
$761$	16.2660			0.589642			0.294821	+	0.955553i	$0.404740\pi$
$762$	11.4700	+	1.78599i	0.415514	+	0.0646994i
$763$	−9.94825	−	7.09389i	−0.360151	−	0.256816i
$764$	7.19795	−	4.15574i	0.260413	−	0.150349i
$765$	−7.92501	+	7.21100i	−0.286530	+	0.260714i
$766$	−28.2249	−	16.2956i	−1.01981	−	0.588786i
$767$	−35.0305	+	0.666810i	−1.26488	+	0.0240771i
$768$	1.61538	−	0.624931i	0.0582901	−	0.0225503i
$769$	−11.5748	+	6.68271i	−0.417398	+	0.240985i	−0.693963	−	0.720010i	$-0.744137\pi$
$769$	−11.5748	+	6.68271i	−0.417398	+	0.240985i	0.276566	+	0.960995i	$0.410804\pi$
$770$	−0.911189	+	9.47712i	−0.0328370	+	0.341532i
$771$	29.3256	+	23.6209i	1.05613	+	0.850685i
$772$	−8.96806	−	15.5331i	−0.322767	−	0.559050i
$773$	12.4704	+	21.5993i	0.448527	+	0.776872i	0.998290	−	0.0584484i	$-0.0186153\pi$
$773$	12.4704	+	21.5993i	0.448527	+	0.776872i	−0.549763	+	0.835321i	$0.685282\pi$
$774$	8.83001	−	1.92512i	0.317388	−	0.0691970i
$775$	4.66575	−	2.69377i	0.167599	−	0.0967632i
$776$	−2.09779	+	3.63348i	−0.0753062	+	0.130434i
$777$	32.0992	−	32.8447i	1.15155	−	1.17830i
$778$	−15.6393	−	27.0880i	−0.560695	−	0.971152i
$779$	−6.25440	+	3.61098i	−0.224087	+	0.129377i
$780$	3.23008	−	1.32081i	0.115655	−	0.0472926i
$781$	−29.2229	+	50.6155i	−1.04568	+	1.81116i
$782$	−1.52056	+	2.63369i	−0.0543752	+	0.0941805i
$783$	1.08286	+	17.9683i	0.0386984	+	0.642135i
$784$	4.59092	−	5.28427i	0.163961	−	0.188724i
$785$			3.21599i			0.114784i
$786$	−26.3395	−	4.10130i	−0.939499	−	0.146289i
$787$	−33.5261	+	19.3563i	−1.19508	+	0.689978i	−0.959454	−	0.281866i	$-0.909047\pi$
$787$	−33.5261	+	19.3563i	−1.19508	+	0.689978i	−0.235624	+	0.971844i	$0.575713\pi$
$788$	−19.6371	−	11.3375i	−0.699542	−	0.403881i
$789$	28.8117	+	4.48624i	1.02572	+	0.159715i
$790$	5.48361	−	3.16596i	0.195098	−	0.112640i
$791$	−9.82667	+	13.7806i	−0.349396	+	0.489982i
$792$	18.4047	+	5.87397i	0.653982	+	0.208723i
$793$	19.2171	+	10.6126i	0.682419	+	0.376863i
$794$	2.29017	−	3.96668i	0.0812749	−	0.140772i
$795$	9.03771	+	1.40725i	0.320535	+	0.0499102i
$796$	0.445421	+	0.257164i	0.0157875	+	0.00911494i
$797$	16.4095	−	28.4221i	0.581255	−	1.00676i	−0.414076	−	0.910242i	$-0.635895\pi$
$797$	16.4095	−	28.4221i	0.581255	−	1.00676i	0.995331	−	0.0965204i	$-0.0307713\pi$
$798$	3.34492	−	3.42261i	0.118409	−	0.121159i
$799$	−0.929116	+	1.60928i	−0.0328698	+	0.0569321i
$800$		−	4.68774i		−	0.165737i
$801$	−7.18312	+	6.53595i	−0.253803	+	0.230936i
$802$	−11.2573	−	19.4982i	−0.397509	−	0.688505i
$803$	−34.0997	+	59.0623i	−1.20335	+	2.08426i
$804$	−18.4083	+	7.12147i	−0.649209	+	0.251155i
$805$	0.700224	+	0.0673238i	0.0246797	+	0.00237285i
$806$	4.14305	−	0.0788635i	0.145933	−	0.00277785i
$807$	−25.8660	+	10.0066i	−0.910525	+	0.352248i
$808$		−	10.2322i		−	0.359966i
$809$		−	42.4295i		−	1.49174i	−0.666090	−	0.745872i	$-0.732033\pi$
$809$		−	42.4295i		−	1.49174i	0.666090	−	0.745872i	$-0.267967\pi$
$810$	2.91343	−	4.09935i	0.102367	−	0.144036i
$811$		−	19.0509i		−	0.668969i	−0.942401	−	0.334485i	$-0.891438\pi$
$811$		−	19.0509i		−	0.668969i	0.942401	−	0.334485i	$-0.108562\pi$
$812$	−5.32145	+	7.46263i	−0.186746	+	0.261887i
$813$	−13.5951	+	16.8784i	−0.476800	+	0.591952i
$814$	32.2688	+	55.8912i	1.13102	+	1.95899i
$815$	−0.518271	−	0.897671i	−0.0181542	−	0.0314440i
$816$	−1.70324	+	10.9386i	−0.0596253	+	0.382927i
$817$	2.72451	+	1.57299i	0.0953184	+	0.0550321i
$818$	−6.18698			−0.216323
$819$	−17.5789	−	22.5828i	−0.614255	−	0.789108i
$820$	−3.86435			−0.134949
$821$	−38.1823	−	22.0445i	−1.33257	−	0.769360i	−0.346877	−	0.937911i	$-0.612758\pi$
$821$	−38.1823	−	22.0445i	−1.33257	−	0.769360i	−0.985693	+	0.168551i	$0.946091\pi$
$822$	1.44087	−	9.25362i	0.0502563	−	0.322757i
$823$	−12.7954	−	22.1623i	−0.446019	−	0.772528i	0.552103	−	0.833776i	$-0.313825\pi$
$823$	−12.7954	−	22.1623i	−0.446019	−	0.772528i	−0.998123	+	0.0612476i	$0.980492\pi$
$824$	6.08867	+	10.5459i	0.212109	+	0.367384i
$825$	32.7992	−	40.7205i	1.14192	−	1.41771i
$826$	−25.5920	−	2.46057i	−0.890460	−	0.0856143i
$827$		−	7.82132i		−	0.271974i	−0.990711	−	0.135987i	$-0.956579\pi$
$827$		−	7.82132i		−	0.271974i	0.990711	−	0.135987i	$-0.0434205\pi$
$828$	0.434003	−	1.35984i	0.0150826	−	0.0472578i
$829$		−	4.44686i		−	0.154446i	−0.997014	−	0.0772229i	$-0.975395\pi$
$829$		−	4.44686i		−	0.154446i	0.997014	−	0.0772229i	$-0.0246053\pi$
$830$			1.61763i			0.0561487i
$831$	0.994868	−	0.384877i	0.0345116	−	0.0133512i
$832$	1.74302	−	3.15624i	0.0604284	−	0.109423i
$833$	14.5781	+	42.2989i	0.505100	+	1.46557i
$834$	25.8271	−	9.99155i	0.894321	−	0.345979i
$835$	−4.36974	+	7.56861i	−0.151221	+	0.261922i
$836$	3.36259	+	5.82418i	0.116298	+	0.201433i
$837$	4.98279	−	3.29163i	0.172230	−	0.113775i
$838$		−	20.3787i		−	0.703970i
$839$	10.1248	−	17.5366i	0.349546	−	0.605432i	−0.636623	−	0.771175i	$-0.719669\pi$
$839$	10.1248	−	17.5366i	0.349546	−	0.605432i	0.986169	+	0.165744i	$0.0530025\pi$
$840$	2.46571	−	0.691116i	0.0850751	−	0.0238458i
$841$	−8.49939	+	14.7214i	−0.293082	+	0.507633i
$842$	−29.8801	−	17.2513i	−1.02974	−	0.594519i
$843$	−42.5650	−	6.62777i	−1.46602	−	0.228272i
$844$	4.07178	−	7.05253i	0.140156	−	0.242758i
$845$	3.39014	−	6.42481i	0.116624	−	0.221020i
$846$	0.265191	−	0.830912i	0.00911745	−	0.0285673i
$847$	−7.71551	+	80.2478i	−0.265108	+	2.75735i
$848$	8.18418	−	4.72514i	0.281046	−	0.162262i
$849$	45.9715	+	7.15818i	1.57774	+	0.245668i
$850$	25.9476	+	14.9809i	0.889996	+	0.513839i
$851$	4.12956	−	2.38420i	0.141560	−	0.0817294i
$852$	15.5325	+	2.41855i	0.532134	+	0.0828582i
$853$			20.8437i			0.713674i	0.934167	+	0.356837i	$0.116145\pi$
$853$			20.8437i			0.713674i	−0.934167	+	0.356837i	$0.883855\pi$
$854$	13.1158	+	9.35264i	0.448815	+	0.320041i
$855$	1.71051	−	0.372926i	0.0584983	−	0.0127538i
$856$	3.56753	−	6.17914i	0.121936	−	0.211199i
$857$	−1.48162	+	2.56624i	−0.0506111	+	0.0876610i	−0.890221	−	0.455529i	$-0.849450\pi$
$857$	−1.48162	+	2.56624i	−0.0506111	+	0.0876610i	0.839610	+	0.543190i	$0.182784\pi$
$858$	37.2245	−	15.2214i	1.27082	−	0.519651i
$859$	−10.0619	+	5.80927i	−0.343309	+	0.198210i	−0.661734	−	0.749738i	$-0.730179\pi$
$859$	−10.0619	+	5.80927i	−0.343309	+	0.198210i	0.318425	+	0.947948i	$0.396846\pi$
$860$	0.841683	+	1.45784i	0.0287012	+	0.0497119i
$861$	8.55297	+	30.5146i	0.291485	+	1.03994i
$862$	0.713871	−	1.23646i	0.0243145	−	0.0421140i
$863$	4.68796	−	2.70660i	0.159580	−	0.0921336i	−0.418083	−	0.908409i	$-0.637298\pi$
$863$	4.68796	−	2.70660i	0.159580	−	0.0921336i	0.577663	+	0.816275i	$0.303965\pi$
$864$	−0.312580	−	5.18674i	−0.0106342	−	0.176457i
$865$	−3.08957	−	5.35129i	−0.105049	−	0.181949i
$866$	−4.40419	−	7.62829i	−0.149661	−	0.259220i
$867$	−32.1729	−	25.9143i	−1.09265	−	0.880097i
$868$	3.02676	+	0.291011i	0.102735	+	0.00987757i
$869$	63.1948	−	36.4856i	2.14374	−	1.23769i
$870$	−3.12711	+	1.20976i	−0.106019	+	0.0410148i
$871$	−19.8628	+	35.9673i	−0.673025	+	1.21871i
$872$	−3.99943	−	2.30907i	−0.135438	−	0.0781951i
$873$	8.47090	+	9.30966i	0.286696	+	0.315084i
$874$	0.430324	−	0.248448i	0.0145559	−	0.00840386i
$875$	1.37076	−	14.2570i	0.0463401	−	0.481975i
$876$	18.1246	+	2.82216i	0.612373	+	0.0953521i
$877$	−14.8655			−0.501972			−0.250986	−	0.967991i	$-0.580755\pi$
$877$	−14.8655			−0.501972			−0.250986	+	0.967991i	$0.580755\pi$
$878$	3.62617	+	6.28070i	0.122377	+	0.211963i
$879$	14.6554	+	11.8045i	0.494314	+	0.398155i
$880$			3.59853i			0.121307i
$881$	−23.3804	−	40.4960i	−0.787704	−	1.36434i	−0.927370	−	0.374145i	$-0.877936\pi$
$881$	−23.3804	−	40.4960i	−0.787704	−	1.36434i	0.139666	−	0.990199i	$-0.455397\pi$
$882$	−10.9147	−	17.9407i	−0.367518	−	0.604095i
$883$	−14.3174			−0.481818			−0.240909	−	0.970548i	$-0.577446\pi$
$883$	−14.3174			−0.481818			−0.240909	+	0.970548i	$0.577446\pi$
$884$	11.9002	+	19.7345i	0.400246	+	0.663745i
$885$	−7.32466	−	5.89980i	−0.246216	−	0.198320i
$886$	10.9075			0.366443
$887$	−9.04691	+	15.6697i	−0.303766	+	0.526137i	−0.976986	−	0.213305i	$-0.931577\pi$
$887$	−9.04691	+	15.6697i	−0.303766	+	0.526137i	0.673220	+	0.739442i	$0.264911\pi$
$888$	10.8886	−	13.5183i	0.365396	−	0.453643i
$889$	16.1343	−	7.35556i	0.541125	−	0.246698i
$890$	−1.56659	−	0.904474i	−0.0525124	−	0.0303180i
$891$	33.5753	−	47.2422i	1.12481	−	1.58267i
$892$	14.6126	+	8.43659i	0.489266	+	0.282478i
$893$	0.262943	−	0.151810i	0.00879905	−	0.00508013i
$894$	14.8783	+	11.9840i	0.497603	+	0.400805i
$895$	−0.0137531	+	0.00794034i	−0.000459715	+	0.000265416i
$896$	1.53609	−	2.15416i	0.0513172	−	0.0719656i
$897$	−1.12465	−	2.75036i	−0.0375509	−	0.0918318i
$898$	−2.20133	−	3.81282i	−0.0734594	−	0.127235i
$899$	−3.98144			−0.132788
$900$	−13.3974	−	4.27588i	−0.446581	−	0.142529i
$901$			60.4015i			2.01226i
$902$	−44.5340			−1.48282
$903$	9.64884	−	9.87294i	0.321093	−	0.328551i
$904$	−3.19860	+	5.54013i	−0.106384	+	0.184262i
$905$	−0.989123	+	0.571071i	−0.0328796	+	0.0189830i
$906$	−0.903517	−	2.33550i	−0.0300174	−	0.0775918i
$907$	0.843621			0.0280120			0.0140060	−	0.999902i	$-0.495542\pi$
$907$	0.843621			0.0280120			0.0140060	+	0.999902i	$0.495542\pi$
$908$	14.9919	−	25.9667i	0.497523	−	0.861735i
$909$	−29.2432	−	9.33317i	−0.969937	−	0.309562i
$910$	3.01172	−	4.39827i	0.0998375	−	0.145801i
$911$			0.306963i			0.0101701i	0.999987	+	0.00508507i	$0.00161863\pi$
$911$			0.306963i			0.0101701i	−0.999987	+	0.00508507i	$0.998381\pi$
$912$	1.13465	−	1.40868i	0.0375720	−	0.0466461i
$913$			18.6421i			0.616962i
$914$	−0.159932	+	0.0923367i	−0.00529008	+	0.00305423i
$915$	2.12620	+	5.49602i	0.0702901	+	0.181693i
$916$	18.9964	+	10.9676i	0.627659	+	0.362379i
$917$	−37.0504	+	16.8912i	−1.22351	+	0.557795i
$918$	29.7086	+	14.8453i	0.980530	+	0.489969i
$919$	−0.276314			−0.00911477			−0.00455738	−	0.999990i	$-0.501451\pi$
$919$	−0.276314			−0.00911477			−0.00455738	+	0.999990i	$0.501451\pi$
$920$	0.265880			0.00876581
$921$	−16.3015	−	2.53830i	−0.537154	−	0.0836398i
$922$	2.90576	−	1.67764i	0.0956962	−	0.0552502i
$923$	28.0225	−	16.8979i	0.922371	−	0.556201i
$924$	28.4156	−	7.96465i	0.934806	−	0.262018i
$925$	−23.4896	−	40.6852i	−0.772334	−	1.33772i
$926$	−24.0019	−	13.8575i	−0.788753	−	0.455387i
$927$	35.6936	−	7.78193i	1.17233	−	0.255592i
$928$	−1.73214	+	3.00015i	−0.0568603	+	0.0984849i
$929$	−20.4366			−0.670502			−0.335251	−	0.942129i	$-0.608821\pi$
$929$	−20.4366			−0.670502			−0.335251	+	0.942129i	$0.608821\pi$
$930$	0.866286	+	0.697767i	0.0284066	+	0.0228807i
$931$	1.39283	−	7.17633i	0.0456481	−	0.235195i
$932$	−10.9565	−	6.32576i	−0.358893	−	0.207207i
$933$	−32.5243	−	26.1974i	−1.06480	−	0.857663i
$934$		−	31.0453i		−	1.01583i
$935$	−19.9186	−	11.5000i	−0.651408	−	0.376091i
$936$	−7.43057	−	7.86045i	−0.242876	−	0.256927i
$937$			44.5899i			1.45669i	0.685211	+	0.728345i	$0.259710\pi$
$937$			44.5899i			1.45669i	−0.685211	+	0.728345i	$0.740290\pi$
$938$	−17.5047	+	24.5480i	−0.571548	+	0.801521i
$939$	0.954731	+	2.46788i	0.0311565	+	0.0805363i
$940$	0.162462			0.00529893
$941$	−20.2833	+	35.1318i	−0.661218	+	1.14526i	0.319078	+	0.947728i	$0.396627\pi$
$941$	−20.2833	+	35.1318i	−0.661218	+	1.14526i	−0.980296	+	0.197535i	$0.936707\pi$
$942$	9.29684	−	3.59660i	0.302908	−	0.117184i
$943$			3.29043i			0.107151i
$944$	−9.71748			−0.316277
$945$	0.273883	−	7.67732i	0.00890940	−	0.249743i
$946$	9.69983	+	16.8006i	0.315369	+	0.546235i
$947$	8.86351	+	5.11735i	0.288025	+	0.166292i	0.637051	−	0.770822i	$-0.280154\pi$
$947$	8.86351	+	5.11735i	0.288025	+	0.166292i	−0.349026	+	0.937113i	$0.613487\pi$
$948$	−15.2848	−	12.3114i	−0.496427	−	0.399857i
$949$	32.6989	−	19.7179i	1.06145	−	0.640069i
$950$	−2.44775	−	4.23963i	−0.0794156	−	0.137552i
$951$	18.6016	+	48.0832i	0.603198	+	1.55920i
$952$	7.01478	+	15.3867i	0.227350	+	0.498687i
$953$	−16.1418	−	9.31945i	−0.522883	−	0.301887i	0.215230	−	0.976563i	$-0.430950\pi$
$953$	−16.1418	−	9.31945i	−0.522883	−	0.301887i	−0.738113	+	0.674677i	$0.764283\pi$
$954$	−6.03919	−	27.7001i	−0.195526	−	0.896825i
$955$	4.02220	−	2.32222i	0.130155	−	0.0751452i
$956$	−13.9271	+	8.04081i	−0.450434	+	0.260058i
$957$	−36.0378	+	13.9417i	−1.16494	+	0.450671i
$958$	−14.9680	−	8.64177i	−0.483594	−	0.279203i
$959$	−5.93423	−	13.0166i	−0.191626	−	0.420327i
$960$	0.902673	−	0.349210i	0.0291337	−	0.0112707i
$961$	−14.8396	−	25.7029i	−0.478696	−	0.829126i
$962$	−0.687687	−	36.1273i	−0.0221719	−	1.16479i
$963$	−14.4057	−	15.8321i	−0.464218	−	0.510183i
$964$	2.95573	+	1.70649i	0.0951975	+	0.0549623i
$965$	−5.01134	−	8.67989i	−0.161321	−	0.279415i
$966$	−0.588474	−	2.09951i	−0.0189338	−	0.0675506i
$967$	−2.55327			−0.0821076			−0.0410538	−	0.999157i	$-0.513071\pi$
$967$	−2.55327			−0.0821076			−0.0410538	+	0.999157i	$0.513071\pi$
$968$			30.4707i			0.979365i
$969$	4.17127	+	10.7823i	0.134001	+	0.346378i
$970$	−1.17224	+	2.03038i	−0.0376384	+	0.0651916i
$971$	−53.0048			−1.70101			−0.850503	−	0.525970i	$-0.823702\pi$
$971$	−53.0048			−1.70101			−0.850503	+	0.525970i	$0.823702\pi$
$972$	−15.1087	−	3.83769i	−0.484611	−	0.123094i
$973$	24.5594	−	34.4413i	0.787338	−	1.10414i
$974$			5.72465i			0.183430i
$975$	−27.0971	+	11.0802i	−0.867801	+	0.354852i
$976$	5.27288	+	3.04430i	0.168781	+	0.0974457i
$977$		−	9.78242i		−	0.312967i	−0.987681	−	0.156484i	$-0.949984\pi$
$977$		−	9.78242i		−	0.312967i	0.987681	−	0.156484i	$-0.0500159\pi$
$978$	−2.01539	+	2.50213i	−0.0644452	+	0.0800094i
$979$	−18.0539	−	10.4235i	−0.577007	−	0.333135i
$980$	2.56540	−	2.95284i	0.0819486	−	0.0943250i
$981$	−10.2473	+	9.32407i	−0.327172	+	0.297695i
$982$	−39.1856			−1.25046
$983$	−8.72238	+	15.1076i	−0.278201	+	0.481858i	−0.970938	−	0.239332i	$-0.923071\pi$
$983$	−8.72238	+	15.1076i	−0.278201	+	0.481858i	0.692737	+	0.721190i	$0.256405\pi$
$984$	4.32169	+	11.1711i	0.137770	+	0.356122i
$985$	−10.9732	−	6.33536i	−0.349634	−	0.201861i
$986$	−11.0710	−	19.1755i	−0.352572	−	0.610672i
$987$	−0.359578	−	1.28287i	−0.0114455	−	0.0408343i
$988$	−0.0716610	−	3.76467i	−0.00227984	−	0.119770i
$989$	1.24132	−	0.716679i	0.0394718	−	0.0227891i
$990$	10.2845	+	3.28237i	0.326863	+	0.104320i
$991$	−22.1496			−0.703607			−0.351803	−	0.936074i	$-0.614431\pi$
$991$	−22.1496			−0.703607			−0.351803	+	0.936074i	$0.614431\pi$
$992$	1.14928			0.0364898
$993$	−6.87548	+	44.1559i	−0.218187	+	1.40124i
$994$	21.8487	−	9.96078i	0.693000	−	0.315937i
$995$	0.248901	+	0.143703i	0.00789068	+	0.00455569i
$996$	4.67626	−	1.80907i	0.148173	−	0.0573226i
$997$	16.6914	−	9.63676i	0.528621	−	0.305199i	−0.211834	−	0.977306i	$-0.567944\pi$
$997$	16.6914	−	9.63676i	0.528621	−	0.305199i	0.740455	+	0.672106i	$0.234610\pi$
$998$			26.1821i			0.828781i
$999$	−28.7029	−	43.4498i	−0.908121	−	1.37469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.u.a.185.8	✓	76
3.2	odd	2	inner	546.2.u.a.185.31	yes	76
7.5	odd	6		546.2.bb.a.341.35	yes	76
13.9	even	3		546.2.bb.a.269.37	yes	76
21.5	even	6		546.2.bb.a.341.18	yes	76
39.35	odd	6		546.2.bb.a.269.16	yes	76
91.61	odd	6	inner	546.2.u.a.425.31	yes	76
273.152	even	6	inner	546.2.u.a.425.8	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.8	✓	76	1.1	even	1	trivial
546.2.u.a.185.31	yes	76	3.2	odd	2	inner
546.2.u.a.425.8	yes	76	273.152	even	6	inner
546.2.u.a.425.31	yes	76	91.61	odd	6	inner
546.2.bb.a.269.16	yes	76	39.35	odd	6
546.2.bb.a.269.37	yes	76	13.9	even	3
546.2.bb.a.341.18	yes	76	21.5	even	6
546.2.bb.a.341.35	yes	76	7.5	odd	6

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.u (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.266485 + 1.71143i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.279399 + 0.483934i) q^{5} +(1.08650 - 1.34890i) q^{6} +(0.253211 - 2.63361i) q^{7} -1.00000i q^{8} +(-2.85797 - 0.912140i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.266485 + 1.71143i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.279399 + 0.483934i) q^{5} +(1.08650 - 1.34890i) q^{6} +(0.253211 - 2.63361i) q^{7} -1.00000i q^{8} +(-2.85797 - 0.912140i) q^{9} -0.558798i q^{10} -6.43977i q^{11} +(-1.61538 + 0.624931i) q^{12} +(-1.74302 + 3.15624i) q^{13} +(-1.53609 + 2.15416i) q^{14} +(-0.902673 + 0.349210i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.19575 - 5.53520i) q^{17} +(2.01901 + 2.21892i) q^{18} +1.04432i q^{19} +(-0.279399 + 0.483934i) q^{20} +(4.43975 + 1.13517i) q^{21} +(-3.21989 + 5.57701i) q^{22} +(0.412061 + 0.237904i) q^{23} +(1.71143 + 0.266485i) q^{24} +(2.34387 - 4.05971i) q^{25} +(3.08762 - 1.86188i) q^{26} +(2.32267 - 4.64814i) q^{27} +(2.40738 - 1.09752i) q^{28} +(-3.00015 + 1.73214i) q^{29} +(0.956343 + 0.148911i) q^{30} +(0.995309 + 0.574642i) q^{31} +(0.866025 - 0.500000i) q^{32} +(11.0212 + 1.71610i) q^{33} +6.39150i q^{34} +(1.34524 - 0.613290i) q^{35} +(-0.639049 - 2.93115i) q^{36} +(5.01086 - 8.67906i) q^{37} +(0.522160 - 0.904408i) q^{38} +(-4.93719 - 3.82415i) q^{39} +(0.483934 - 0.279399i) q^{40} +(3.45773 + 5.98897i) q^{41} +(-3.27735 - 3.20296i) q^{42} +(1.50624 - 2.60888i) q^{43} +(5.57701 - 3.21989i) q^{44} +(-0.357100 - 1.63792i) q^{45} +(-0.237904 - 0.412061i) q^{46} +(-0.145367 - 0.251784i) q^{47} +(-1.34890 - 1.08650i) q^{48} +(-6.87177 - 1.33372i) q^{49} +(-4.05971 + 2.34387i) q^{50} +(10.3247 - 3.99425i) q^{51} +(-3.60490 + 0.0686197i) q^{52} +(-8.18418 - 4.72514i) q^{53} +(-4.33556 + 2.86407i) q^{54} +(3.11642 - 1.79927i) q^{55} +(-2.63361 - 0.253211i) q^{56} +(-1.78728 - 0.278296i) q^{57} +3.46428 q^{58} +(4.85874 + 8.41558i) q^{59} +(-0.753762 - 0.607133i) q^{60} -6.08860i q^{61} +(-0.574642 - 0.995309i) q^{62} +(-3.12589 + 7.29581i) q^{63} -1.00000 q^{64} +(-2.01441 + 0.0383446i) q^{65} +(-8.68659 - 6.99679i) q^{66} +11.3956 q^{67} +(3.19575 - 5.53520i) q^{68} +(-0.516963 + 0.641815i) q^{69} +(-1.47166 - 0.141494i) q^{70} +(-7.85983 - 4.53787i) q^{71} +(-0.912140 + 2.85797i) q^{72} +(-9.17149 - 5.29516i) q^{73} +(-8.67906 + 5.01086i) q^{74} +(6.32329 + 5.09322i) q^{75} +(-0.904408 + 0.522160i) q^{76} +(-16.9598 - 1.63062i) q^{77} +(2.36366 + 5.78041i) q^{78} +(5.66566 + 9.81321i) q^{79} -0.558798 q^{80} +(7.33600 + 5.21374i) q^{81} -6.91546i q^{82} -2.89483 q^{83} +(1.23679 + 4.41252i) q^{84} +(1.78578 - 3.09306i) q^{85} +(-2.60888 + 1.50624i) q^{86} +(-2.16494 - 5.59614i) q^{87} -6.43977 q^{88} +(1.61861 - 2.80351i) q^{89} +(-0.509702 + 1.59703i) q^{90} +(7.87095 + 5.38963i) q^{91} +0.475807i q^{92} +(-1.24869 + 1.55027i) q^{93} +0.290735i q^{94} +(-0.505382 + 0.291782i) q^{95} +(0.624931 + 1.61538i) q^{96} +(-3.63348 - 2.09779i) q^{97} +(5.28427 + 4.59092i) q^{98} +(-5.87397 + 18.4047i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9}+O(q^{10}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9	\( 76 q + 38 q^{4} + 10 q^{7} - 8 q^{9} + 2 q^{13} + 12 q^{15} - 38 q^{16} - 8 q^{21} - 42 q^{25} + 20 q^{28} + 20 q^{30} + 12 q^{31} - 4 q^{36} - 6 q^{37} + 12 q^{39} + 8 q^{42} - 2 q^{43} - 4 q^{46} + 2 q^{49} + 10 q^{51} - 14 q^{52} + 18 q^{54} + 24 q^{55} + 8 q^{57} + 16 q^{58} - 12 q^{60} + 32 q^{63} - 76 q^{64} - 24 q^{66} + 96 q^{67} - 30 q^{69} - 54 q^{73} - 12 q^{75} + 18 q^{76} - 12 q^{78} - 60 q^{79} + 8 q^{81} + 8 q^{84} + 8 q^{85} - 24 q^{87} + 48 q^{91} + 16 q^{93} - 66 q^{97}+O(q^{100}) \) 76 * q + 38 * q^4 + 10 * q^7 - 8 * q^9 + 2 * q^13 + 12 * q^15 - 38 * q^16 - 8 * q^21 - 42 * q^25 + 20 * q^28 + 20 * q^30 + 12 * q^31 - 4 * q^36 - 6 * q^37 + 12 * q^39 + 8 * q^42 - 2 * q^43 - 4 * q^46 + 2 * q^49 + 10 * q^51 - 14 * q^52 + 18 * q^54 + 24 * q^55 + 8 * q^57 + 16 * q^58 - 12 * q^60 + 32 * q^63 - 76 * q^64 - 24 * q^66 + 96 * q^67 - 30 * q^69 - 54 * q^73 - 12 * q^75 + 18 * q^76 - 12 * q^78 - 60 * q^79 + 8 * q^81 + 8 * q^84 + 8 * q^85 - 24 * q^87 + 48 * q^91 + 16 * q^93 - 66 * q^97

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