LMFDB - Embedded newform 546.2.bg.b.311.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(311,546)]

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, 3]))

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

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

chi := DirichletCharacter("546.311");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bg (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:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			311.15
Character	$\chi$	$=$	546.311
Dual form			546.2.bg.b.467.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.40752 + 1.00940i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.19770 + 1.26884i) q^{5} +(-0.170404 + 1.72365i) q^{6} +(2.61925 + 0.373536i) q^{7} -1.00000 q^{8} +(0.962231 + 2.84150i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.40752 + 1.00940i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.19770 + 1.26884i) q^{5} +(-0.170404 + 1.72365i) q^{6} +(2.61925 + 0.373536i) q^{7} -1.00000 q^{8} +(0.962231 + 2.84150i) q^{9} +(-2.19770 - 1.26884i) q^{10} +(-1.32440 + 2.29393i) q^{11} +(-1.57792 + 0.714250i) q^{12} +(-3.59958 - 0.207354i) q^{13} +(0.986133 + 2.45511i) q^{14} +(-4.37407 - 0.432430i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.84623 - 3.19777i) q^{17} +(-1.97969 + 2.25407i) q^{18} +(0.241819 + 0.418842i) q^{19} -2.53768i q^{20} +(3.30960 + 3.16963i) q^{21} -2.64880 q^{22} +(4.09436 - 2.36388i) q^{23} +(-1.40752 - 1.00940i) q^{24} +(0.719909 - 1.24692i) q^{25} +(-1.62022 - 3.22101i) q^{26} +(-1.51384 + 4.97074i) q^{27} +(-1.63312 + 2.08157i) q^{28} +6.93400i q^{29} +(-1.81254 - 4.00427i) q^{30} +(2.71148 - 4.69643i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-4.17960 + 1.89190i) q^{33} +3.69246 q^{34} +(-6.23027 + 2.50249i) q^{35} +(-2.94193 - 0.587433i) q^{36} +(-5.90071 + 3.40678i) q^{37} +(-0.241819 + 0.418842i) q^{38} +(-4.85719 - 3.92527i) q^{39} +(2.19770 - 1.26884i) q^{40} +3.03693i q^{41} +(-1.09018 + 4.45101i) q^{42} +5.11062 q^{43} +(-1.32440 - 2.29393i) q^{44} +(-5.72010 - 5.02383i) q^{45} +(4.09436 + 2.36388i) q^{46} +(6.66192 - 3.84626i) q^{47} +(0.170404 - 1.72365i) q^{48} +(6.72094 + 1.95677i) q^{49} +1.43982 q^{50} +(5.82643 - 2.63734i) q^{51} +(1.97937 - 3.01365i) q^{52} +(-8.13530 - 4.69692i) q^{53} +(-5.06171 + 1.17435i) q^{54} -6.72180i q^{55} +(-2.61925 - 0.373536i) q^{56} +(-0.0824136 + 0.833620i) q^{57} +(-6.00502 + 3.46700i) q^{58} +(4.98510 + 2.87815i) q^{59} +(2.56153 - 3.57184i) q^{60} +(4.25236 - 2.45510i) q^{61} +5.42297 q^{62} +(1.45892 + 7.80202i) q^{63} +1.00000 q^{64} +(8.17389 - 4.11159i) q^{65} +(-3.72824 - 2.67369i) q^{66} +(1.38217 + 0.797996i) q^{67} +(1.84623 + 3.19777i) q^{68} +(8.14900 + 0.805629i) q^{69} +(-5.28236 - 4.14433i) q^{70} +12.9028 q^{71} +(-0.962231 - 2.84150i) q^{72} +(6.57447 - 11.3873i) q^{73} +(-5.90071 - 3.40678i) q^{74} +(2.27193 - 1.02839i) q^{75} -0.483637 q^{76} +(-4.32580 + 5.51365i) q^{77} +(0.970788 - 6.16908i) q^{78} +(-3.75864 - 6.51016i) q^{79} +(2.19770 + 1.26884i) q^{80} +(-7.14822 + 5.46836i) q^{81} +(-2.63006 + 1.51847i) q^{82} +3.10022i q^{83} +(-4.39978 + 1.28139i) q^{84} +9.37029i q^{85} +(2.55531 + 4.42592i) q^{86} +(-6.99916 + 9.75974i) q^{87} +(1.32440 - 2.29393i) q^{88} +(2.37997 - 1.37408i) q^{89} +(1.49072 - 7.46566i) q^{90} +(-9.35076 - 1.88769i) q^{91} +4.72776i q^{92} +(8.55703 - 3.87335i) q^{93} +(6.66192 + 3.84626i) q^{94} +(-1.06289 - 0.613658i) q^{95} +(1.57792 - 0.714250i) q^{96} -5.91584 q^{97} +(1.66586 + 6.79889i) q^{98} +(-7.79256 - 1.55599i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9}+O(q^{10}) $ 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9	$ 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9} + 14 q^{15} - 18 q^{16} - 4 q^{18} - 23 q^{21} + 14 q^{25} + 6 q^{26} + 7 q^{30} + 18 q^{32} - 24 q^{33} - 8 q^{36} + 10 q^{39} - 16 q^{42} - 16 q^{43} + 9 q^{45} - 72 q^{47} + 12 q^{49} + 28 q^{50} - 3 q^{51} + 6 q^{52} - 9 q^{54} + 8 q^{57} - 24 q^{59} - 7 q^{60} - 36 q^{61} + 39 q^{63} + 36 q^{64} - 18 q^{65} - 24 q^{66} + 72 q^{71} - 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} + 7 q^{84} - 8 q^{86} - 24 q^{87} + 72 q^{89} - 2 q^{91} + 14 q^{93} - 72 q^{94} + 12 q^{98} - 72 q^{99}+O(q^{100}) $ 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9 + 14 * q^15 - 18 * q^16 - 4 * q^18 - 23 * q^21 + 14 * q^25 + 6 * q^26 + 7 * q^30 + 18 * q^32 - 24 * q^33 - 8 * q^36 + 10 * q^39 - 16 * q^42 - 16 * q^43 + 9 * q^45 - 72 * q^47 + 12 * q^49 + 28 * q^50 - 3 * q^51 + 6 * q^52 - 9 * q^54 + 8 * q^57 - 24 * q^59 - 7 * q^60 - 36 * q^61 + 39 * q^63 + 36 * q^64 - 18 * q^65 - 24 * q^66 + 72 * q^71 - 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 + 7 * q^84 - 8 * q^86 - 24 * q^87 + 72 * q^89 - 2 * q^91 + 14 * q^93 - 72 * q^94 + 12 * q^98 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.40752	+	1.00940i	0.812633	+	0.582776i
$3$	1.40752	+	1.00940i	0.812633	+	0.582776i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.19770	+	1.26884i	−0.982839	+	0.567442i	−0.903126	−	0.429375i	$-0.858734\pi$
$5$	−2.19770	+	1.26884i	−0.982839	+	0.567442i	−0.0797131	+	0.996818i	$0.525400\pi$
$6$	−0.170404	+	1.72365i	−0.0695671	+	0.703676i
$7$	2.61925	+	0.373536i	0.989983	+	0.141183i
$7$	2.61925	+	0.373536i	0.989983	+	0.141183i
$8$	−1.00000			−0.353553
$9$	0.962231	+	2.84150i	0.320744	+	0.947166i
$10$	−2.19770	−	1.26884i	−0.694972	−	0.401242i
$11$	−1.32440	+	2.29393i	−0.399321	+	0.691645i	−0.993642	−	0.112583i	$-0.964087\pi$
$11$	−1.32440	+	2.29393i	−0.399321	+	0.691645i	0.594321	+	0.804228i	$0.297421\pi$
$12$	−1.57792	+	0.714250i	−0.455508	+	0.206186i
$13$	−3.59958	−	0.207354i	−0.998345	−	0.0575096i
$13$	−3.59958	−	0.207354i	−0.998345	−	0.0575096i
$14$	0.986133	+	2.45511i	0.263555	+	0.656154i
$15$	−4.37407	−	0.432430i	−1.12938	−	0.111653i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.84623	−	3.19777i	0.447777	−	0.775572i	−0.550464	−	0.834859i	$-0.685549\pi$
$17$	1.84623	−	3.19777i	0.447777	−	0.775572i	0.998241	+	0.0592866i	$0.0188826\pi$
$18$	−1.97969	+	2.25407i	−0.466618	+	0.531288i
$19$	0.241819	+	0.418842i	0.0554770	+	0.0960890i	0.892430	−	0.451185i	$-0.148999\pi$
$19$	0.241819	+	0.418842i	0.0554770	+	0.0960890i	−0.836953	+	0.547274i	$0.815665\pi$
$20$		−	2.53768i		−	0.567442i
$21$	3.30960	+	3.16963i	0.722214	+	0.691669i
$22$	−2.64880			−0.564725
$23$	4.09436	−	2.36388i	0.853734	−	0.492903i	−0.00817520	−	0.999967i	$-0.502602\pi$
$23$	4.09436	−	2.36388i	0.853734	−	0.492903i	0.861909	+	0.507063i	$0.169269\pi$
$24$	−1.40752	−	1.00940i	−0.287309	−	0.206043i
$25$	0.719909	−	1.24692i	0.143982	−	0.249384i
$26$	−1.62022	−	3.22101i	−0.317751	−	0.631692i
$27$	−1.51384	+	4.97074i	−0.291339	+	0.956620i
$28$	−1.63312	+	2.08157i	−0.308630	+	0.393380i
$29$			6.93400i			1.28761i	0.765189	+	0.643805i	$0.222645\pi$
$29$			6.93400i			1.28761i	−0.765189	+	0.643805i	$0.777355\pi$
$30$	−1.81254	−	4.00427i	−0.330923	−	0.731076i
$31$	2.71148	−	4.69643i	0.486997	−	0.843503i	−0.512891	−	0.858453i	$-0.671426\pi$
$31$	2.71148	−	4.69643i	0.486997	−	0.843503i	0.999888	+	0.0149503i	$0.00475901\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−4.17960	+	1.89190i	−0.727575	+	0.329338i
$34$	3.69246			0.633252
$35$	−6.23027	+	2.50249i	−1.05311	+	0.422998i
$36$	−2.94193	−	0.587433i	−0.490321	−	0.0979054i
$37$	−5.90071	+	3.40678i	−0.970071	+	0.560071i	−0.899258	−	0.437419i	$-0.855893\pi$
$37$	−5.90071	+	3.40678i	−0.970071	+	0.560071i	−0.0708132	+	0.997490i	$0.522559\pi$
$38$	−0.241819	+	0.418842i	−0.0392282	+	0.0679452i
$39$	−4.85719	−	3.92527i	−0.777772	−	0.628546i
$40$	2.19770	−	1.26884i	0.347486	−	0.200621i
$41$			3.03693i			0.474289i	0.971474	+	0.237145i	$0.0762115\pi$
$41$			3.03693i			0.474289i	−0.971474	+	0.237145i	$0.923788\pi$
$42$	−1.09018	+	4.45101i	−0.168218	+	0.686806i
$43$	5.11062			0.779362			0.389681	−	0.920950i	$-0.372585\pi$
$43$	5.11062			0.779362			0.389681	+	0.920950i	$0.372585\pi$
$44$	−1.32440	−	2.29393i	−0.199661	−	0.345822i
$45$	−5.72010	−	5.02383i	−0.852702	−	0.748908i
$46$	4.09436	+	2.36388i	0.603681	+	0.348535i
$47$	6.66192	−	3.84626i	0.971741	−	0.561035i	0.0719745	−	0.997406i	$-0.477070\pi$
$47$	6.66192	−	3.84626i	0.971741	−	0.561035i	0.899767	+	0.436371i	$0.143737\pi$
$48$	0.170404	−	1.72365i	0.0245957	−	0.248787i
$49$	6.72094	+	1.95677i	0.960134	+	0.279539i
$50$	1.43982			0.203621
$51$	5.82643	−	2.63734i	0.815863	−	0.369302i
$52$	1.97937	−	3.01365i	0.274489	−	0.417919i
$53$	−8.13530	−	4.69692i	−1.11747	−	0.645171i	−0.176716	−	0.984262i	$-0.556547\pi$
$53$	−8.13530	−	4.69692i	−1.11747	−	0.645171i	−0.940754	+	0.339091i	$0.889881\pi$
$54$	−5.06171	+	1.17435i	−0.688812	+	0.159808i
$55$		−	6.72180i		−	0.906367i
$56$	−2.61925	−	0.373536i	−0.350012	−	0.0499159i
$57$	−0.0824136	+	0.833620i	−0.0109160	+	0.110416i
$58$	−6.00502	+	3.46700i	−0.788497	+	0.455239i
$59$	4.98510	+	2.87815i	0.649005	+	0.374703i	0.788075	−	0.615579i	$-0.211078\pi$
$59$	4.98510	+	2.87815i	0.649005	+	0.374703i	−0.139070	+	0.990283i	$0.544411\pi$
$60$	2.56153	−	3.57184i	0.330692	−	0.461122i
$61$	4.25236	−	2.45510i	0.544459	−	0.314343i	−0.202425	−	0.979298i	$-0.564882\pi$
$61$	4.25236	−	2.45510i	0.544459	−	0.314343i	0.746884	+	0.664954i	$0.231549\pi$
$62$	5.42297			0.688717
$63$	1.45892	+	7.80202i	0.183807	+	0.982962i
$64$	1.00000			0.125000
$65$	8.17389	−	4.11159i	1.01385	−	0.509981i
$66$	−3.72824	−	2.67369i	−0.458914	−	0.329109i
$67$	1.38217	+	0.797996i	0.168859	+	0.0974908i	0.582048	−	0.813155i	$-0.302252\pi$
$67$	1.38217	+	0.797996i	0.168859	+	0.0974908i	−0.413189	+	0.910645i	$0.635585\pi$
$68$	1.84623	+	3.19777i	0.223888	+	0.387786i
$69$	8.14900	+	0.805629i	0.981024	+	0.0969863i
$70$	−5.28236	−	4.14433i	−0.631362	−	0.495342i
$71$	12.9028			1.53128			0.765638	−	0.643272i	$-0.222423\pi$
$71$	12.9028			1.53128			0.765638	+	0.643272i	$0.222423\pi$
$72$	−0.962231	−	2.84150i	−0.113400	−	0.334874i
$73$	6.57447	−	11.3873i	0.769484	−	1.33279i	−0.168359	−	0.985726i	$-0.553847\pi$
$73$	6.57447	−	11.3873i	0.769484	−	1.33279i	0.937843	−	0.347060i	$-0.112820\pi$
$74$	−5.90071	−	3.40678i	−0.685944	−	0.396030i
$75$	2.27193	−	1.02839i	0.262339	−	0.118748i
$76$	−0.483637			−0.0554770
$77$	−4.32580	+	5.51365i	−0.492970	+	0.628339i
$78$	0.970788	−	6.16908i	0.109920	−	0.698511i
$79$	−3.75864	−	6.51016i	−0.422880	−	0.732450i	0.573339	−	0.819318i	$-0.305648\pi$
$79$	−3.75864	−	6.51016i	−0.422880	−	0.732450i	−0.996220	+	0.0868676i	$0.972314\pi$
$80$	2.19770	+	1.26884i	0.245710	+	0.141861i
$81$	−7.14822	+	5.46836i	−0.794247	+	0.607595i
$82$	−2.63006	+	1.51847i	−0.290442	+	0.167687i
$83$			3.10022i			0.340293i	0.985419	+	0.170146i	$0.0544241\pi$
$83$			3.10022i			0.340293i	−0.985419	+	0.170146i	$0.945576\pi$
$84$	−4.39978	+	1.28139i	−0.480055	+	0.139811i
$85$			9.37029i			1.01635i
$86$	2.55531	+	4.42592i	0.275546	+	0.477260i
$87$	−6.99916	+	9.75974i	−0.750389	+	1.04635i
$88$	1.32440	−	2.29393i	0.141181	−	0.244533i
$89$	2.37997	−	1.37408i	0.252276	−	0.145652i	−0.368530	−	0.929616i	$-0.620139\pi$
$89$	2.37997	−	1.37408i	0.252276	−	0.145652i	0.620806	+	0.783964i	$0.286805\pi$
$90$	1.49072	−	7.46566i	0.157135	−	0.786950i
$91$	−9.35076	−	1.88769i	−0.980226	−	0.197883i
$92$			4.72776i			0.492903i
$93$	8.55703	−	3.87335i	0.887323	−	0.401648i
$94$	6.66192	+	3.84626i	0.687125	+	0.396712i
$95$	−1.06289	−	0.613658i	−0.109050	−	0.0629600i
$96$	1.57792	−	0.714250i	0.161046	−	0.0728978i
$97$	−5.91584			−0.600663			−0.300331	−	0.953835i	$-0.597097\pi$
$97$	−5.91584			−0.600663			−0.300331	+	0.953835i	$0.597097\pi$
$98$	1.66586	+	6.79889i	0.168277	+	0.686792i
$99$	−7.79256	−	1.55599i	−0.783182	−	0.156383i
$100$	0.719909	+	1.24692i	0.0719909	+	0.124692i
$101$	6.93191	−	12.0064i	0.689751	−	1.19468i	−0.282167	−	0.959365i	$-0.591053\pi$
$101$	6.93191	−	12.0064i	0.689751	−	1.19468i	0.971918	−	0.235318i	$-0.0756133\pi$
$102$	5.19722	+	3.72716i	0.514601	+	0.369044i
$103$	−7.90784	+	4.56559i	−0.779183	+	0.449861i	−0.836141	−	0.548515i	$-0.815193\pi$
$103$	−7.90784	+	4.56559i	−0.779183	+	0.449861i	0.0569579	+	0.998377i	$0.481860\pi$
$104$	3.59958	+	0.207354i	0.352968	+	0.0203327i
$105$	−11.2952	−	2.76652i	−1.10230	−	0.269984i
$106$		−	9.39383i		−	0.912410i
$107$	6.73065	−	3.88594i	0.650677	−	0.375668i	−0.138039	−	0.990427i	$-0.544080\pi$
$107$	6.73065	−	3.88594i	0.650677	−	0.375668i	0.788716	+	0.614758i	$0.210746\pi$
$108$	−3.54787	−	3.79640i	−0.341394	−	0.365308i
$109$	11.8250	+	6.82718i	1.13263	+	0.653925i	0.944596	−	0.328237i	$-0.106454\pi$
$109$	11.8250	+	6.82718i	1.13263	+	0.653925i	0.188037	+	0.982162i	$0.439788\pi$
$110$	5.82125	−	3.36090i	0.555034	−	0.320449i
$111$	−11.7442	−	1.16106i	−1.11471	−	0.110203i
$112$	−0.986133	−	2.45511i	−0.0931808	−	0.231986i
$113$			20.5235i			1.93068i	0.260987	+	0.965342i	$0.415952\pi$
$113$			20.5235i			1.93068i	−0.260987	+	0.965342i	$0.584048\pi$
$114$	−0.763143	+	0.345438i	−0.0714749	+	0.0323532i
$115$	−5.99877	+	10.3902i	−0.559389	+	0.968889i
$116$	−6.00502	−	3.46700i	−0.557552	−	0.321903i
$117$	−2.87444	−	10.4277i	−0.265742	−	0.964044i
$118$			5.75630i			0.529910i
$119$	6.03022	−	7.68611i	0.552790	−	0.704585i
$120$	4.37407	+	0.432430i	0.399296	+	0.0394753i
$121$	1.99194	+	3.45014i	0.181085	+	0.313649i
$122$	4.25236	+	2.45510i	0.384990	+	0.222274i
$123$	−3.06547	+	4.27455i	−0.276405	+	0.385423i
$124$	2.71148	+	4.69643i	0.243498	+	0.421752i
$125$		−	9.03460i		−	0.808079i
$126$	−6.02729	+	5.16447i	−0.536954	+	0.460088i
$127$	−10.7047			−0.949889			−0.474945	−	0.880016i	$-0.657532\pi$
$127$	−10.7047			−0.949889			−0.474945	+	0.880016i	$0.657532\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	7.19330	+	5.15865i	0.633335	+	0.454193i
$130$	7.64769	+	5.02300i	0.670747	+	0.440546i
$131$	−3.16842	−	5.48787i	−0.276826	−	0.479478i	0.693768	−	0.720199i	$-0.255949\pi$
$131$	−3.16842	−	5.48787i	−0.276826	−	0.479478i	−0.970594	+	0.240721i	$0.922616\pi$
$132$	0.451365	−	4.56559i	0.0392863	−	0.397384i
$133$	0.476931	+	1.18738i	0.0413551	+	0.102959i
$134$			1.59599i			0.137873i
$135$	−2.98011	−	12.8450i	−0.256487	−	1.10552i
$136$	−1.84623	+	3.19777i	−0.158313	+	0.274206i
$137$	8.84134	−	15.3136i	0.755367	−	1.30833i	−0.189825	−	0.981818i	$-0.560792\pi$
$137$	8.84134	−	15.3136i	0.755367	−	1.30833i	0.945192	−	0.326515i	$-0.105874\pi$
$138$	3.37680	+	7.46005i	0.287453	+	0.635042i
$139$			16.0938i			1.36506i	0.730858	+	0.682530i	$0.239120\pi$
$139$			16.0938i			1.36506i	−0.730858	+	0.682530i	$0.760880\pi$
$140$	0.947916	−	6.64682i	0.0801135	−	0.561759i
$141$	13.2592	+	1.31084i	1.11663	+	0.110392i
$142$	6.45138	+	11.1741i	0.541388	+	0.937711i
$143$	5.24294	−	7.98256i	0.438437	−	0.667535i
$144$	1.97969	−	2.25407i	0.164975	−	0.187839i
$145$	−8.79813	−	15.2388i	−0.730645	−	1.26551i
$146$	13.1489			1.08821
$147$	7.48471	+	9.53830i	0.617328	+	0.786706i
$148$		−	6.81356i		−	0.560071i
$149$	1.28692	+	2.22901i	0.105429	+	0.182608i	0.913913	−	0.405910i	$-0.133045\pi$
$149$	1.28692	+	2.22901i	0.105429	+	0.182608i	−0.808485	+	0.588517i	$0.799712\pi$
$150$	2.02658	+	1.45335i	0.165469	+	0.118666i
$151$	−3.68114	−	2.12531i	−0.299567	−	0.172955i	0.342681	−	0.939452i	$-0.388665\pi$
$151$	−3.68114	−	2.12531i	−0.299567	−	0.172955i	−0.642248	+	0.766497i	$0.721998\pi$
$152$	−0.241819	−	0.418842i	−0.0196141	−	0.0339726i
$153$	10.8629	+	2.16907i	0.878217	+	0.175359i
$154$	−6.93786	−	0.989422i	−0.559069	−	0.0797299i
$155$			13.7618i			1.10537i
$156$	5.82798	−	2.24381i	0.466611	−	0.179649i
$157$	−0.823957	−	0.475712i	−0.0657589	−	0.0379659i	0.466760	−	0.884384i	$-0.345421\pi$
$157$	−0.823957	−	0.475712i	−0.0657589	−	0.0379659i	−0.532519	+	0.846418i	$0.678755\pi$
$158$	3.75864	−	6.51016i	0.299022	−	0.517921i
$159$	−6.70955	−	14.8228i	−0.532102	−	1.17552i
$160$			2.53768i			0.200621i
$161$	11.6072	−	4.66220i	0.914772	−	0.367433i
$162$	−8.30985	−	3.45636i	−0.652883	−	0.271558i
$163$	4.74897	−	2.74182i	0.371968	−	0.214756i	−0.302350	−	0.953197i	$-0.597771\pi$
$163$	4.74897	−	2.74182i	0.371968	−	0.214756i	0.674318	+	0.738441i	$0.264438\pi$
$164$	−2.63006	−	1.51847i	−0.205373	−	0.118572i
$165$	6.78497	−	9.46107i	0.528209	−	0.736544i
$166$	−2.68487	+	1.55011i	−0.208386	+	0.120312i
$167$		−	6.15740i		−	0.476474i	−0.971207	−	0.238237i	$-0.923431\pi$
$167$		−	6.15740i		−	0.476474i	0.971207	−	0.238237i	$-0.0765694\pi$
$168$	−3.30960	−	3.16963i	−0.255341	−	0.244542i
$169$	12.9140	+	1.49278i	0.993385	+	0.114829i
$170$	−8.11491	+	4.68514i	−0.622385	+	0.359334i
$171$	−0.957454	+	1.09015i	−0.0732183	+	0.0833658i
$172$	−2.55531	+	4.42592i	−0.194840	+	0.337473i
$173$	−3.45361	−	5.98183i	−0.262573	−	0.454790i	0.704352	−	0.709851i	$-0.251238\pi$
$173$	−3.45361	−	5.98183i	−0.262573	−	0.454790i	−0.966925	+	0.255061i	$0.917905\pi$
$174$	−11.9518	−	1.18158i	−0.906061	−	0.0895753i
$175$	2.35139	−	2.99708i	0.177749	−	0.226558i
$176$	2.64880			0.199661
$177$	4.11144	+	9.08301i	0.309035	+	0.682721i
$178$	2.37997	+	1.37408i	0.178386	+	0.102991i
$179$	−1.49413	−	0.862637i	−0.111677	−	0.0644765i	0.443121	−	0.896462i	$-0.353871\pi$
$179$	−1.49413	−	0.862637i	−0.111677	−	0.0644765i	−0.554798	+	0.831985i	$0.687204\pi$
$180$	7.21081	−	2.44183i	0.537462	−	0.182004i
$181$		−	22.0637i		−	1.63998i	−0.572376	−	0.819991i	$-0.693978\pi$
$181$		−	22.0637i		−	1.63998i	0.572376	−	0.819991i	$-0.306022\pi$
$182$	−3.04059	−	9.04184i	−0.225384	−	0.670225i
$183$	8.46346	+	0.836717i	0.625637	+	0.0618519i
$184$	−4.09436	+	2.36388i	−0.301840	+	0.174268i
$185$	8.64531	−	14.9741i	0.635616	−	1.10092i
$186$	7.63294	+	5.47393i	0.559674	+	0.401368i
$187$	4.89029	+	8.47023i	0.357614	+	0.619405i
$188$			7.69252i			0.561035i
$189$	−5.82188	+	12.4541i	−0.423480	+	0.905906i
$190$		−	1.22732i		−	0.0890389i
$191$	−22.6677	+	13.0872i	−1.64018	+	0.946957i	−0.659409	+	0.751785i	$0.729193\pi$
$191$	−22.6677	+	13.0872i	−1.64018	+	0.946957i	−0.980769	+	0.195172i	$0.937473\pi$
$192$	1.40752	+	1.00940i	0.101579	+	0.0728470i
$193$	1.84511	+	1.06527i	0.132814	+	0.0766801i	0.564935	−	0.825136i	$-0.308901\pi$
$193$	1.84511	+	1.06527i	0.132814	+	0.0766801i	−0.432121	+	0.901816i	$0.642235\pi$
$194$	−2.95792	−	5.12327i	−0.212366	−	0.367829i
$195$	15.6552	+	2.46355i	1.12109	+	0.176418i
$196$	−5.05508	+	4.84212i	−0.361077	+	0.345866i
$197$	4.36762			0.311180			0.155590	−	0.987822i	$-0.450272\pi$
$197$	4.36762			0.311180			0.155590	+	0.987822i	$0.450272\pi$
$198$	−2.54875	−	7.52655i	−0.181132	−	0.534889i
$199$	−23.1724	−	13.3786i	−1.64265	−	0.948383i	−0.979887	−	0.199551i	$-0.936052\pi$
$199$	−23.1724	−	13.3786i	−1.64265	−	0.948383i	−0.662760	−	0.748832i	$-0.730615\pi$
$200$	−0.719909	+	1.24692i	−0.0509053	+	0.0881705i
$201$	1.13994	+	2.51836i	0.0804050	+	0.177631i
$202$	13.8638			0.975455
$203$	−2.59010	+	18.1619i	−0.181789	+	1.27471i
$204$	−0.629210	+	6.36451i	−0.0440535	+	0.445604i
$205$	−3.85338	−	6.67425i	−0.269132	−	0.466150i
$206$	−7.90784	−	4.56559i	−0.550965	−	0.318100i
$207$	10.6567	+	9.35952i	0.740691	+	0.650532i
$208$	1.62022	+	3.22101i	0.112342	+	0.223337i
$209$	−1.28106			−0.0886125
$210$	−3.25175	−	11.1652i	−0.224392	−	0.770474i
$211$	−17.3315			−1.19315			−0.596575	−	0.802557i	$-0.703472\pi$
$211$	−17.3315			−1.19315			−0.596575	+	0.802557i	$0.703472\pi$
$212$	8.13530	−	4.69692i	0.558735	−	0.322586i
$213$	18.1609	+	13.0240i	1.24437	+	0.892391i
$214$	6.73065	+	3.88594i	0.460098	+	0.265638i
$215$	−11.2316	+	6.48455i	−0.765987	+	0.442243i
$216$	1.51384	−	4.97074i	0.103004	−	0.338216i
$217$	8.85634	−	11.2883i	0.601207	−	0.766298i
$218$			13.6544i			0.924790i
$219$	20.7481	−	9.39164i	1.40202	−	0.634628i
$220$	5.82125	+	3.36090i	0.392468	+	0.226592i
$221$	−7.30873	+	11.1278i	−0.491639	+	0.748537i
$222$	−4.86658	−	10.7513i	−0.326624	−	0.721579i
$223$	−4.35497			−0.291630			−0.145815	−	0.989312i	$-0.546580\pi$
$223$	−4.35497			−0.291630			−0.145815	+	0.989312i	$0.546580\pi$
$224$	1.63312	−	2.08157i	0.109117	−	0.139081i
$225$	4.23584	+	0.845796i	0.282389	+	0.0563864i
$226$	−17.7738	+	10.2617i	−1.18230	+	0.682600i
$227$	−17.3580	−	10.0217i	−1.15209	−	0.665160i	−0.202696	−	0.979242i	$-0.564970\pi$
$227$	−17.3580	−	10.0217i	−1.15209	−	0.665160i	−0.949396	+	0.314081i	$0.898304\pi$
$228$	−0.680730	−	0.488182i	−0.0450824	−	0.0323307i
$229$	−13.3120	−	23.0571i	−0.879683	−	1.52365i	−0.851689	−	0.524047i	$-0.824422\pi$
$229$	−13.3120	−	23.0571i	−0.879683	−	1.52365i	−0.0279931	−	0.999608i	$-0.508912\pi$
$230$	−11.9975			−0.791095
$231$	−11.6541	+	3.39413i	−0.766785	+	0.223318i
$232$		−	6.93400i		−	0.455239i
$233$	−20.2573	+	11.6956i	−1.32710	+	0.766203i	−0.984850	−	0.173406i	$-0.944523\pi$
$233$	−20.2573	+	11.6956i	−1.32710	+	0.766203i	−0.342252	+	0.939608i	$0.611190\pi$
$234$	7.59346	−	7.70320i	0.496400	−	0.503574i
$235$	−9.76058	+	16.9058i	−0.636710	+	1.10281i
$236$	−4.98510	+	2.87815i	−0.324503	+	0.187352i
$237$	1.28097	−	12.9572i	0.0832082	−	0.841658i
$238$	9.67148	+	1.37927i	0.626909	+	0.0894047i
$239$	−10.6771			−0.690642			−0.345321	−	0.938485i	$-0.612230\pi$
$239$	−10.6771			−0.690642			−0.345321	+	0.938485i	$0.612230\pi$
$240$	1.81254	+	4.00427i	0.116999	+	0.258474i
$241$	−6.08041	+	10.5316i	−0.391673	+	0.678398i	−0.992670	−	0.120853i	$-0.961437\pi$
$241$	−6.08041	+	10.5316i	−0.391673	+	0.678398i	0.600997	+	0.799251i	$0.294770\pi$
$242$	−1.99194	+	3.45014i	−0.128047	+	0.221783i
$243$	−15.5810	+	0.481423i	−0.999523	+	0.0308833i
$244$			4.91020i			0.314343i
$245$	−17.2534	+	4.22741i	−1.10228	+	0.270080i
$246$	−5.23460	−	0.517505i	−0.333746	−	0.0329949i
$247$	−0.783598	−	1.55780i	−0.0498591	−	0.0991204i
$248$	−2.71148	+	4.69643i	−0.172179	+	0.298223i
$249$	−3.12935	+	4.36362i	−0.198315	+	0.276533i
$250$	7.82419	−	4.51730i	0.494845	−	0.285699i
$251$	25.7551			1.62565			0.812825	−	0.582508i	$-0.197928\pi$
$251$	25.7551			1.62565			0.812825	+	0.582508i	$0.197928\pi$
$252$	−7.48621	−	2.63755i	−0.471587	−	0.166150i
$253$			12.5229i			0.787307i
$254$	−5.35236	−	9.27055i	−0.335837	−	0.581686i
$255$	−9.45835	+	13.1889i	−0.592305	+	0.825919i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.74076	−	15.1394i	−0.545233	−	0.944372i	−0.998592	−	0.0530439i	$-0.983108\pi$
$257$	−8.74076	−	15.1394i	−0.545233	−	0.944372i	0.453359	−	0.891328i	$-0.350226\pi$
$258$	−0.870869	+	8.80890i	−0.0542179	+	0.548418i
$259$	−16.7280	+	6.71907i	−1.03943	+	0.417503i
$260$	−0.526198	+	9.13459i	−0.0326334	+	0.566503i
$261$	−19.7029	+	6.67211i	−1.21958	+	0.412993i
$262$	3.16842	−	5.48787i	0.195746	−	0.339042i
$263$	17.8986	+	10.3338i	1.10368	+	0.637208i	0.937184	−	0.348834i	$-0.113422\pi$
$263$	17.8986	+	10.3338i	1.10368	+	0.637208i	0.166493	+	0.986043i	$0.446756\pi$
$264$	4.17960	−	1.89190i	0.257237	−	0.116439i
$265$	23.8385			1.46439
$266$	−0.789836	+	1.00672i	−0.0484280	+	0.0617262i
$267$	4.73684	+	0.468295i	0.289890	+	0.0286592i
$268$	−1.38217	+	0.797996i	−0.0844295	+	0.0487454i
$269$	0.237662	−	0.411643i	0.0144905	−	0.0250983i	−0.858689	−	0.512497i	$-0.828721\pi$
$269$	0.237662	−	0.411643i	0.0144905	−	0.0250983i	0.873180	+	0.487398i	$0.162054\pi$
$270$	9.63404	−	9.00335i	0.586309	−	0.547927i
$271$	0.772450	+	1.33792i	0.0469230	+	0.0812730i	0.888533	−	0.458813i	$-0.151725\pi$
$271$	0.772450	+	1.33792i	0.0469230	+	0.0812730i	−0.841610	+	0.540086i	$0.818392\pi$
$272$	−3.69246			−0.223888
$273$	−11.2560	−	12.0956i	−0.681242	−	0.732059i
$274$	17.6827			1.06825
$275$	1.90689	+	3.30284i	0.114990	+	0.199169i
$276$	−4.77219	+	6.65443i	−0.287252	+	0.400549i
$277$	14.0171	−	24.2784i	0.842209	−	1.45875i	−0.0458149	−	0.998950i	$-0.514588\pi$
$277$	14.0171	−	24.2784i	0.842209	−	1.45875i	0.888023	−	0.459798i	$-0.152078\pi$
$278$	−13.9377	+	8.04691i	−0.835925	+	0.482622i
$279$	15.9540	+	3.18563i	0.955139	+	0.190718i
$280$	6.23027	−	2.50249i	0.372330	−	0.149552i
$281$	−30.3889			−1.81285			−0.906426	−	0.422365i	$-0.861200\pi$
$281$	−30.3889			−1.81285			−0.906426	+	0.422365i	$0.861200\pi$
$282$	5.49439	+	12.1382i	0.327186	+	0.722821i
$283$	6.07652	+	3.50828i	0.361212	+	0.208546i	0.669612	−	0.742711i	$-0.266460\pi$
$283$	6.07652	+	3.50828i	0.361212	+	0.208546i	−0.308400	+	0.951257i	$0.599794\pi$
$284$	−6.45138	+	11.1741i	−0.382819	+	0.663062i
$285$	−0.876611	−	1.93661i	−0.0519259	−	0.114715i
$286$	9.53457	+	0.549239i	0.563791	+	0.0324772i
$287$	−1.13441	+	7.95449i	−0.0669618	+	0.469539i
$288$	2.94193	+	0.587433i	0.173355	+	0.0346148i
$289$	1.68286	+	2.91480i	0.0989918	+	0.171459i
$290$	8.79813	−	15.2388i	0.516644	−	0.894854i
$291$	−8.32667	−	5.97144i	−0.488118	−	0.350052i
$292$	6.57447	+	11.3873i	0.384742	+	0.666393i
$293$			32.4228i			1.89416i	0.321000	+	0.947079i	$0.395981\pi$
$293$			32.4228i			1.89416i	−0.321000	+	0.947079i	$0.604019\pi$
$294$	−4.51806	+	11.2511i	−0.263498	+	0.656177i
$295$	−14.6076			−0.850490
$296$	5.90071	−	3.40678i	0.342972	−	0.198015i
$297$	−9.39758	−	10.0559i	−0.545303	−	0.583502i
$298$	−1.28692	+	2.22901i	−0.0745493	+	0.129123i
$299$	−15.2282	+	7.66001i	−0.880667	+	0.442990i
$300$	−0.245351	+	2.48174i	−0.0141653	+	0.143283i
$301$	13.3860	+	1.90900i	0.771555	+	0.110033i
$302$		−	4.25062i		−	0.244595i
$303$	21.8761	−	9.90223i	1.25675	−	0.568868i
$304$	0.241819	−	0.418842i	0.0138692	−	0.0240222i
$305$	−6.23026	+	10.7911i	−0.356743	+	0.617898i
$306$	3.55300	+	10.4921i	0.203112	+	0.599795i
$307$	−30.0357			−1.71423			−0.857113	−	0.515128i	$-0.827744\pi$
$307$	−30.0357			−1.71423			−0.857113	+	0.515128i	$0.827744\pi$
$308$	−2.61207	−	6.50308i	−0.148836	−	0.370547i
$309$	−15.7390	−	1.55599i	−0.895358	−	0.0885172i
$310$	−11.9180	+	6.88088i	−0.676898	+	0.390808i
$311$	3.19493	−	5.53379i	0.181168	−	0.313792i	−0.761111	−	0.648622i	$-0.775346\pi$
$311$	3.19493	−	5.53379i	0.181168	−	0.313792i	0.942279	+	0.334830i	$0.108679\pi$
$312$	4.85719	+	3.92527i	0.274984	+	0.222225i
$313$	8.58761	−	4.95806i	0.485400	−	0.280246i	−0.237264	−	0.971445i	$-0.576251\pi$
$313$	8.58761	−	4.95806i	0.485400	−	0.280246i	0.722664	+	0.691199i	$0.242917\pi$
$314$		−	0.951424i		−	0.0536920i
$315$	−13.1058	−	15.2953i	−0.738427	−	0.861794i
$316$	7.51729			0.422880
$317$	−15.9691	−	27.6594i	−0.896916	−	1.55350i	−0.831415	−	0.555652i	$-0.812469\pi$
$317$	−15.9691	−	27.6594i	−0.896916	−	1.55350i	−0.0655007	−	0.997853i	$-0.520864\pi$
$318$	9.48212	−	13.2220i	0.531731	−	0.741454i
$319$	−15.9061	−	9.18337i	−0.890569	−	0.514170i
$320$	−2.19770	+	1.26884i	−0.122855	+	0.0709303i
$321$	13.3960	+	1.32436i	0.747692	+	0.0739186i
$322$	9.84116	+	7.72099i	0.548427	+	0.430274i
$323$	1.78581			0.0993652
$324$	−1.16162	−	8.92472i	−0.0645346	−	0.495818i
$325$	−2.84993	+	4.33912i	−0.158086	+	0.240691i
$326$	4.74897	+	2.74182i	0.263021	+	0.151855i
$327$	9.75263	+	21.5456i	0.539322	+	1.19147i
$328$		−	3.03693i		−	0.167687i
$329$	18.8860	−	7.58585i	1.04122	−	0.418222i
$330$	11.5860	+	1.14542i	0.637789	+	0.0630533i
$331$	13.1995	−	7.62074i	0.725511	−	0.418874i	−0.0912670	−	0.995826i	$-0.529092\pi$
$331$	13.1995	−	7.62074i	0.725511	−	0.418874i	0.816778	+	0.576953i	$0.195758\pi$
$332$	−2.68487	−	1.55011i	−0.147351	−	0.0850732i
$333$	−15.3582	−	13.4888i	−0.841624	−	0.739179i
$334$	5.33246	−	3.07870i	0.291779	−	0.168459i
$335$	−4.05012			−0.221282
$336$	1.09018	−	4.45101i	0.0594740	−	0.242823i
$337$	23.2445			1.26621			0.633103	−	0.774067i	$-0.281781\pi$
$337$	23.2445			1.26621			0.633103	+	0.774067i	$0.281781\pi$
$338$	5.16422	+	11.9302i	0.280897	+	0.648920i
$339$	−20.7163	+	28.8872i	−1.12516	+	1.56894i
$340$	−8.11491	−	4.68514i	−0.440093	−	0.254088i
$341$	7.18217	+	12.4399i	0.388936	+	0.673657i
$342$	−1.42282	−	0.284104i	−0.0769375	−	0.0153626i
$343$	16.8729	+	7.63579i	0.911051	+	0.412294i
$344$	−5.11062			−0.275546
$345$	−18.9312	+	8.56925i	−1.01922	+	0.461353i
$346$	3.45361	−	5.98183i	0.185667	−	0.321585i
$347$	−21.2374	−	12.2614i	−1.14008	−	0.658226i	−0.193631	−	0.981074i	$-0.562026\pi$
$347$	−21.2374	−	12.2614i	−1.14008	−	0.658226i	−0.946451	+	0.322848i	$0.895360\pi$
$348$	−4.95261	−	10.9413i	−0.265488	−	0.586517i
$349$	1.10347			0.0590671			0.0295336	−	0.999564i	$-0.490598\pi$
$349$	1.10347			0.0590671			0.0295336	+	0.999564i	$0.490598\pi$
$350$	3.77125	+	0.537825i	0.201582	+	0.0287479i
$351$	6.47991	−	17.5787i	0.345872	−	0.938282i
$352$	1.32440	+	2.29393i	0.0705907	+	0.122267i
$353$	−5.34237	−	3.08442i	−0.284346	−	0.164167i	0.351043	−	0.936359i	$-0.385827\pi$
$353$	−5.34237	−	3.08442i	−0.284346	−	0.164167i	−0.635389	+	0.772192i	$0.719160\pi$
$354$	−5.81040	+	8.10211i	−0.308819	+	0.430622i
$355$	−28.3563	+	16.3715i	−1.50500	+	0.868911i
$356$			2.74815i			0.145652i
$357$	16.2460	−	4.73147i	0.859830	−	0.250416i
$358$		−	1.72527i		−	0.0911836i
$359$	6.24235	+	10.8121i	0.329459	+	0.570639i	0.982405	−	0.186765i	$-0.0598004\pi$
$359$	6.24235	+	10.8121i	0.329459	+	0.570639i	−0.652946	+	0.757405i	$0.726467\pi$
$360$	5.72010	+	5.02383i	0.301476	+	0.264779i
$361$	9.38305	−	16.2519i	0.493845	−	0.855364i
$362$	19.1077	−	11.0319i	1.00428	−	0.579821i
$363$	−0.678868	+	6.86680i	−0.0356313	+	0.360413i
$364$	6.31016	−	7.15415i	0.330742	−	0.374979i
$365$			33.3678i			1.74655i
$366$	3.50711	+	7.74793i	0.183320	+	0.404991i
$367$	20.5085	+	11.8406i	1.07053	+	0.618073i	0.928327	−	0.371764i	$-0.121247\pi$
$367$	20.5085	+	11.8406i	1.07053	+	0.618073i	0.142207	+	0.989837i	$0.454580\pi$
$368$	−4.09436	−	2.36388i	−0.213433	−	0.123226i
$369$	−8.62944	+	2.92223i	−0.449231	+	0.152125i
$370$	17.2906			0.898897
$371$	−19.5539	−	15.3412i	−1.01519	−	0.796477i
$372$	−0.924094	+	9.34729i	−0.0479121	+	0.484634i
$373$	1.11557	+	1.93222i	0.0577619	+	0.100046i	0.893460	−	0.449142i	$-0.148270\pi$
$373$	1.11557	+	1.93222i	0.0577619	+	0.100046i	−0.835699	+	0.549188i	$0.814937\pi$
$374$	−4.89029	+	8.47023i	−0.252871	+	0.437985i
$375$	9.11951	−	12.7164i	0.470929	−	0.656672i
$376$	−6.66192	+	3.84626i	−0.343562	+	0.198356i
$377$	1.43779	−	24.9595i	0.0740500	−	1.28548i
$378$	−13.6965	+	1.18517i	−0.704474	+	0.0609586i
$379$			7.75732i			0.398467i	0.979952	+	0.199233i	$0.0638452\pi$
$379$			7.75732i			0.398467i	−0.979952	+	0.199233i	$0.936155\pi$
$380$	1.06289	−	0.613658i	0.0545250	−	0.0314800i
$381$	−15.0671	−	10.8053i	−0.771911	−	0.553573i
$382$	−22.6677	−	13.0872i	−1.15978	−	0.669600i
$383$	7.94443	−	4.58672i	0.405941	−	0.234370i	−0.283103	−	0.959090i	$-0.591364\pi$
$383$	7.94443	−	4.58672i	0.405941	−	0.234370i	0.689044	+	0.724719i	$0.258030\pi$
$384$	−0.170404	+	1.72365i	−0.00869589	+	0.0879595i
$385$	2.51084	−	17.6061i	0.127964	−	0.897288i
$386$			2.13055i			0.108442i
$387$	4.91759	+	14.5218i	0.249975	+	0.738185i
$388$	2.95792	−	5.12327i	0.150166	−	0.260095i
$389$	−29.7827	−	17.1950i	−1.51004	−	0.871823i	−0.999931	−	0.0117132i	$-0.996271\pi$
$389$	−29.7827	−	17.1950i	−1.51004	−	0.871823i	−0.510110	−	0.860109i	$-0.670395\pi$
$390$	5.69408	+	14.7895i	0.288331	+	0.748897i
$391$		−	17.4571i		−	0.882843i
$392$	−6.72094	−	1.95677i	−0.339459	−	0.0988318i
$393$	1.07982	−	10.9225i	0.0544699	−	0.550967i
$394$	2.18381	+	3.78247i	0.110019	+	0.190558i
$395$	16.5207	+	9.53823i	0.831247	+	0.479921i
$396$	5.24381	−	5.97056i	0.263511	−	0.300032i
$397$	−6.32491	−	10.9551i	−0.317438	−	0.549819i	0.662515	−	0.749049i	$-0.269489\pi$
$397$	−6.32491	−	10.9551i	−0.317438	−	0.549819i	−0.979953	+	0.199230i	$0.936156\pi$
$398$		−	26.7572i		−	1.34122i
$399$	−0.527249	+	2.15268i	−0.0263955	+	0.107769i
$400$	−1.43982			−0.0719909
$401$	11.1563	+	19.3233i	0.557121	+	0.964962i	0.997735	+	0.0672652i	$0.0214274\pi$
$401$	11.1563	+	19.3233i	0.557121	+	0.964962i	−0.440614	+	0.897697i	$0.645239\pi$
$402$	−1.61099	+	2.24639i	−0.0803490	+	0.112040i
$403$	−10.7340	+	16.3429i	−0.534700	+	0.814100i
$404$	6.93191	+	12.0064i	0.344875	+	0.597342i
$405$	8.77115	−	21.0877i	0.435842	−	1.04786i
$406$	−17.0237	+	6.83784i	−0.844872	+	0.339356i
$407$		−	18.0477i		−	0.894593i
$408$	−5.82643	+	2.63734i	−0.288451	+	0.130568i
$409$	−15.2106	+	26.3456i	−0.752118	+	1.30271i	0.194677	+	0.980867i	$0.437634\pi$
$409$	−15.2106	+	26.3456i	−0.752118	+	1.30271i	−0.946794	+	0.321839i	$0.895699\pi$
$410$	3.85338	−	6.67425i	0.190305	−	0.329618i
$411$	27.9019	−	12.6299i	1.37630	−	0.622985i
$412$		−	9.13119i		−	0.449861i
$413$	11.9821	+	9.40071i	0.589602	+	0.462579i
$414$	−2.77724	+	13.9087i	−0.136494	+	0.683577i
$415$	−3.93368	−	6.81333i	−0.193097	−	0.334453i
$416$	−1.97937	+	3.01365i	−0.0970464	+	0.147757i
$417$	−16.2451	+	22.6524i	−0.795525	+	1.10929i
$418$	−0.640528	−	1.10943i	−0.0313293	−	0.0542639i
$419$	22.9563			1.12149			0.560744	−	0.827989i	$-0.310515\pi$
$419$	22.9563			1.12149			0.560744	+	0.827989i	$0.310515\pi$
$420$	8.04350	−	8.39871i	0.392482	−	0.409815i
$421$			11.7102i			0.570721i	0.958420	+	0.285360i	$0.0921133\pi$
$421$			11.7102i			0.570721i	−0.958420	+	0.285360i	$0.907887\pi$
$422$	−8.66575	−	15.0095i	−0.421842	−	0.730652i
$423$	17.3395	+	15.2288i	0.843073	+	0.740452i
$424$	8.13530	+	4.69692i	0.395085	+	0.228102i
$425$	−2.65824	−	4.60420i	−0.128944	−	0.223337i
$426$	−2.19868	+	22.2398i	−0.106526	+	1.07752i
$427$	12.0551	−	4.84211i	0.583385	−	0.234326i
$428$			7.77189i			0.375668i
$429$	15.4371	−	5.94341i	0.745311	−	0.286950i
$430$	−11.2316	−	6.48455i	−0.541635	−	0.312713i
$431$	−9.15519	+	15.8573i	−0.440990	+	0.763817i	−0.997763	−	0.0668476i	$-0.978706\pi$
$431$	−9.15519	+	15.8573i	−0.440990	+	0.763817i	0.556773	+	0.830664i	$0.312039\pi$
$432$	5.06171	−	1.17435i	0.243532	−	0.0565007i
$433$			21.1787i			1.01778i	0.860831	+	0.508891i	$0.169944\pi$
$433$			21.1787i			1.01778i	−0.860831	+	0.508891i	$0.830056\pi$
$434$	14.2041	+	2.02568i	0.681819	+	0.0972355i
$435$	2.99847	−	30.3298i	0.143766	−	1.45420i
$436$	−11.8250	+	6.82718i	−0.566316	+	0.326963i
$437$	1.98019	+	1.14326i	0.0947251	+	0.0546896i
$438$	18.5074	+	13.2725i	0.884319	+	0.634186i
$439$	−7.13298	+	4.11823i	−0.340439	+	0.196552i	−0.660466	−	0.750856i	$-0.729641\pi$
$439$	−7.13298	+	4.11823i	−0.340439	+	0.196552i	0.320027	+	0.947408i	$0.396308\pi$
$440$			6.72180i			0.320449i
$441$	0.906938	+	20.9804i	0.0431875	+	0.999067i
$442$	−13.2913	−	0.765647i	−0.632204	−	0.0364181i
$443$	−7.54716	+	4.35736i	−0.358577	+	0.207024i	−0.668456	−	0.743752i	$-0.733045\pi$
$443$	−7.54716	+	4.35736i	−0.358577	+	0.207024i	0.309880	+	0.950776i	$0.399711\pi$
$444$	6.87759	−	9.59022i	0.326396	−	0.455132i
$445$	−3.48696	+	6.03960i	−0.165298	+	0.286304i
$446$	−2.17749	−	3.77151i	−0.103107	−	0.178586i
$447$	−0.438593	+	4.43640i	−0.0207447	+	0.209834i
$448$	2.61925	+	0.373536i	0.123748	+	0.0176479i
$449$	22.6845			1.07055			0.535274	−	0.844679i	$-0.320208\pi$
$449$	22.6845			1.07055			0.535274	+	0.844679i	$0.320208\pi$
$450$	1.38544	+	4.09124i	0.0653102	+	0.192863i
$451$	−6.96650	−	4.02211i	−0.328040	−	0.189394i
$452$	−17.7738	−	10.2617i	−0.836011	−	0.482671i
$453$	−3.03600	−	6.70715i	−0.142644	−	0.315130i
$454$		−	20.0433i		−	0.940679i
$455$	22.9453	−	7.71605i	1.07569	−	0.361734i
$456$	0.0824136	−	0.833620i	0.00385937	−	0.0390378i
$457$	11.5835	−	6.68771i	0.541851	−	0.312838i	−0.203978	−	0.978976i	$-0.565387\pi$
$457$	11.5835	−	6.68771i	0.541851	−	0.312838i	0.745829	+	0.666138i	$0.232054\pi$
$458$	13.3120	−	23.0571i	0.622029	−	1.07739i
$459$	13.1004	+	14.0181i	0.611473	+	0.654307i
$460$	−5.99877	−	10.3902i	−0.279694	−	0.484445i
$461$		−	0.777510i		−	0.0362123i	−0.999836	−	0.0181061i	$-0.994236\pi$
$461$		−	0.777510i		−	0.0362123i	0.999836	−	0.0181061i	$-0.00576367\pi$
$462$	−8.76647	−	8.39570i	−0.407853	−	0.390603i
$463$			3.19686i			0.148571i	0.997237	+	0.0742854i	$0.0236676\pi$
$463$			3.19686i			0.148571i	−0.997237	+	0.0742854i	$0.976332\pi$
$464$	6.00502	−	3.46700i	0.278776	−	0.160951i
$465$	−13.8911	+	19.3700i	−0.644184	+	0.898260i
$466$	−20.2573	−	11.6956i	−0.938403	−	0.541787i
$467$	−0.719079	−	1.24548i	−0.0332750	−	0.0576340i	0.848908	−	0.528540i	$-0.177260\pi$
$467$	−0.719079	−	1.24548i	−0.0332750	−	0.0576340i	−0.882183	+	0.470906i	$0.843927\pi$
$468$	10.4679	+	2.72453i	0.483879	+	0.125942i
$469$	3.32217	+	2.60644i	0.153404	+	0.120354i
$470$	−19.5212			−0.900444
$471$	−0.679554	−	1.50128i	−0.0313122	−	0.0691751i
$472$	−4.98510	−	2.87815i	−0.229458	−	0.132478i
$473$	−6.76849	+	11.7234i	−0.311216	+	0.539041i
$474$	11.8617	−	5.36922i	0.544826	−	0.246616i
$475$	0.696350			0.0319507
$476$	3.64126	+	9.06538i	0.166897	+	0.415511i
$477$	5.51824	−	27.6360i	0.252663	−	1.26536i
$478$	−5.33853	−	9.24661i	−0.244179	−	0.422930i
$479$	−9.04541	−	5.22237i	−0.413295	−	0.238616i	0.278909	−	0.960317i	$-0.410027\pi$
$479$	−9.04541	−	5.22237i	−0.413295	−	0.238616i	−0.692205	+	0.721701i	$0.743360\pi$
$480$	−2.56153	+	3.57184i	−0.116917	+	0.163031i
$481$	21.9465	−	11.0394i	1.00068	−	0.503355i
$482$	−12.1608			−0.553910
$483$	21.0433	+	5.15409i	0.957505	+	0.234519i
$484$	−3.98387			−0.181085
$485$	13.0012	−	7.50626i	0.590355	−	0.340842i
$486$	−8.20744	−	13.2528i	−0.372297	−	0.601161i
$487$	−2.08097	−	1.20145i	−0.0942979	−	0.0544429i	0.452109	−	0.891962i	$-0.350672\pi$
$487$	−2.08097	−	1.20145i	−0.0942979	−	0.0544429i	−0.546407	+	0.837520i	$0.684005\pi$
$488$	−4.25236	+	2.45510i	−0.192495	+	0.111137i
$489$	9.45187	+	0.934434i	0.427428	+	0.0422565i
$490$	−12.2878	−	12.8282i	−0.555104	−	0.579518i
$491$			12.3575i			0.557686i	0.960337	+	0.278843i	$0.0899509\pi$
$491$			12.3575i			0.557686i	−0.960337	+	0.278843i	$0.910049\pi$
$492$	−2.16913	−	4.79205i	−0.0977919	−	0.216042i
$493$	22.1733	+	12.8018i	0.998635	+	0.576562i
$494$	0.957295	−	1.45752i	0.0430707	−	0.0655767i
$495$	19.1000	−	6.46792i	0.858480	−	0.290712i
$496$	−5.42297			−0.243498
$497$	33.7956	+	4.81965i	1.51594	+	0.216191i
$498$	−5.34368	−	0.528289i	−0.239456	−	0.0236732i
$499$	14.9074	−	8.60680i	0.667348	−	0.385293i	−0.127723	−	0.991810i	$-0.540767\pi$
$499$	14.9074	−	8.60680i	0.667348	−	0.385293i	0.795071	+	0.606516i	$0.207434\pi$
$500$	7.82419	+	4.51730i	0.349909	+	0.202020i
$501$	6.21526	−	8.66666i	0.277678	−	0.387198i
$502$	12.8776	+	22.3046i	0.574754	+	0.995503i
$503$	−31.1852			−1.39048			−0.695240	−	0.718778i	$-0.744702\pi$
$503$	−31.1852			−1.39048			−0.695240	+	0.718778i	$0.744702\pi$
$504$	−1.45892	−	7.80202i	−0.0649855	−	0.347530i
$505$			35.1819i			1.56558i
$506$	−10.8451	+	6.26144i	−0.482125	+	0.278355i
$507$	16.6699	+	15.1365i	0.740338	+	0.672235i
$508$	5.35236	−	9.27055i	0.237472	−	0.411314i
$509$	−4.87130	+	2.81245i	−0.215917	+	0.124660i	−0.604058	−	0.796940i	$-0.706451\pi$
$509$	−4.87130	+	2.81245i	−0.215917	+	0.124660i	0.388141	+	0.921600i	$0.373117\pi$
$510$	−16.1511	−	1.59673i	−0.715182	−	0.0707045i
$511$	21.4738	−	27.3704i	0.949944	−	1.21080i
$512$	−1.00000			−0.0441942
$513$	−2.44803	+	0.567957i	−0.108083	+	0.0250759i
$514$	8.74076	−	15.1394i	0.385538	−	0.667772i
$515$	11.5860	−	20.0676i	0.510541	−	0.884283i
$516$	−8.06417	+	3.65026i	−0.355005	+	0.160694i
$517$			20.3759i			0.896133i
$518$	−14.1829	−	11.1273i	−0.623160	−	0.488907i
$519$	1.17702	−	11.9056i	0.0516654	−	0.522599i
$520$	−8.17389	+	4.11159i	−0.358449	+	0.180305i
$521$	1.86664	−	3.23312i	0.0817791	−	0.141646i	−0.822235	−	0.569148i	$-0.807273\pi$
$521$	1.86664	−	3.23312i	0.0817791	−	0.141646i	0.904014	+	0.427502i	$0.140606\pi$
$522$	−15.6297	−	13.7272i	−0.684093	−	0.600823i
$523$	20.8918	−	12.0619i	0.913533	−	0.527428i	0.0319666	−	0.999489i	$-0.489823\pi$
$523$	20.8918	−	12.0619i	0.913533	−	0.527428i	0.881566	+	0.472061i	$0.156490\pi$
$524$	6.33685			0.276826
$525$	6.33488	−	1.84496i	0.276477	−	0.0805209i
$526$			20.6676i			0.901149i
$527$	−10.0120	−	17.3414i	−0.436132	−	0.755402i
$528$	3.72824	+	2.67369i	0.162251	+	0.116357i
$529$	−0.324129	+	0.561408i	−0.0140926	+	0.0244090i
$530$	11.9193	+	20.6448i	0.517740	+	0.896752i
$531$	−3.38144	+	16.9346i	−0.146742	+	0.734899i
$532$	−1.26677	−	0.180656i	−0.0549213	−	0.00783244i
$533$	0.629720	−	10.9317i	0.0272762	−	0.473504i
$534$	1.96287	+	4.33638i	0.0849415	+	0.187653i
$535$	−9.86128	+	17.0802i	−0.426340	+	0.738443i
$536$	−1.38217	−	0.797996i	−0.0597007	−	0.0344682i
$537$	−1.23228	−	2.72235i	−0.0531767	−	0.117478i
$538$	0.475324			0.0204927
$539$	−13.3899	+	12.8258i	−0.576743	+	0.552446i
$540$	12.6142	+	3.84165i	0.542827	+	0.165318i
$541$	29.5203	−	17.0435i	1.26917	−	0.732759i	0.294343	−	0.955700i	$-0.404899\pi$
$541$	29.5203	−	17.0435i	1.26917	−	0.732759i	0.974832	+	0.222941i	$0.0715658\pi$
$542$	−0.772450	+	1.33792i	−0.0331796	+	0.0574687i
$543$	22.2711	−	31.0551i	0.955743	−	1.33270i
$544$	−1.84623	−	3.19777i	−0.0791565	−	0.137103i
$545$	−34.6504			−1.48426
$546$	4.84711	−	15.7957i	0.207437	−	0.675995i
$547$	16.3522			0.699170			0.349585	−	0.936905i	$-0.386323\pi$
$547$	16.3522			0.699170			0.349585	+	0.936905i	$0.386323\pi$
$548$	8.84134	+	15.3136i	0.377683	+	0.654167i
$549$	11.0679	+	9.72069i	0.472367	+	0.414869i
$550$	−1.90689	+	3.30284i	−0.0813102	+	0.140833i
$551$	−2.90425	+	1.67677i	−0.123725	+	0.0714328i
$552$	−8.14900	−	0.805629i	−0.346844	−	0.0342898i
$553$	−7.41304	−	18.4557i	−0.315235	−	0.784817i
$554$	28.0343			1.19106
$555$	27.2833	−	12.3498i	1.15811	−	0.524221i
$556$	−13.9377	−	8.04691i	−0.591088	−	0.341265i
$557$	9.83768	−	17.0394i	0.416836	−	0.721981i	−0.578784	−	0.815481i	$-0.696472\pi$
$557$	9.83768	−	17.0394i	0.416836	−	0.721981i	0.995619	+	0.0935006i	$0.0298057\pi$
$558$	5.21815	+	15.4093i	0.220902	+	0.652330i
$559$	−18.3961	−	1.05971i	−0.778072	−	0.0448208i
$560$	5.28236	+	4.14433i	0.223220	+	0.175130i
$561$	−1.66665	+	16.8583i	−0.0703660	+	0.711757i
$562$	−15.1945	−	26.3176i	−0.640940	−	1.11014i
$563$	7.14030	−	12.3674i	0.300928	−	0.521222i	−0.675419	−	0.737435i	$-0.736037\pi$
$563$	7.14030	−	12.3674i	0.300928	−	0.521222i	0.976346	+	0.216212i	$0.0693704\pi$
$564$	−7.76482	+	10.8274i	−0.326958	+	0.455915i
$565$	−26.0410	−	45.1043i	−1.09555	−	1.89755i
$566$			7.01656i			0.294928i
$567$	−20.7656	+	11.6529i	−0.872074	+	0.489374i
$568$	−12.9028			−0.541388
$569$	−14.4405	+	8.33720i	−0.605376	+	0.349514i	−0.771153	−	0.636649i	$-0.780320\pi$
$569$	−14.4405	+	8.33720i	−0.605376	+	0.349514i	0.165778	+	0.986163i	$0.446987\pi$
$570$	1.23885	−	1.72747i	0.0518897	−	0.0723559i
$571$	−0.208287	+	0.360764i	−0.00871655	+	0.0150975i	−0.870351	−	0.492432i	$-0.836108\pi$
$571$	−0.208287	+	0.360764i	−0.00871655	+	0.0150975i	0.861634	+	0.507530i	$0.169441\pi$
$572$	4.29163	+	8.53180i	0.179442	+	0.356732i
$573$	−45.1155	−	4.46022i	−1.88473	−	0.186328i
$574$	−7.45599	+	2.99482i	−0.311207	+	0.125001i
$575$		−	6.80712i		−	0.283877i
$576$	0.962231	+	2.84150i	0.0400930	+	0.118396i
$577$	1.18972	−	2.06066i	0.0495287	−	0.0857863i	−0.840198	−	0.542279i	$-0.817561\pi$
$577$	1.18972	−	2.06066i	0.0495287	−	0.0857863i	0.889727	+	0.456493i	$0.150895\pi$
$578$	−1.68286	+	2.91480i	−0.0699978	+	0.121240i
$579$	1.52174	+	3.36184i	0.0632415	+	0.139713i
$580$	17.5963			0.730645
$581$	−1.15804	+	8.12024i	−0.0480437	+	0.336884i
$582$	1.00808	−	10.1968i	0.0417864	−	0.422672i
$583$	21.5488	−	12.4412i	0.892458	−	0.515261i
$584$	−6.57447	+	11.3873i	−0.272054	+	0.471211i
$585$	19.5483	+	19.2698i	0.808221	+	0.796707i
$586$	−28.0789	+	16.2114i	−1.15993	+	0.669686i
$587$		−	28.1076i		−	1.16013i	−0.814572	−	0.580063i	$-0.803028\pi$
$587$		−	28.1076i		−	1.16013i	0.814572	−	0.580063i	$-0.196972\pi$
$588$	−12.0028	+	1.71279i	−0.494986	+	0.0706345i
$589$	2.62275			0.108068
$590$	−7.30382	−	12.6506i	−0.300694	−	0.520817i
$591$	6.14751	+	4.40866i	0.252875	+	0.181348i
$592$	5.90071	+	3.40678i	0.242518	+	0.140018i
$593$	16.2280	−	9.36924i	0.666404	−	0.384749i	−0.128309	−	0.991734i	$-0.540955\pi$
$593$	16.2280	−	9.36924i	0.666404	−	0.384749i	0.794713	+	0.606986i	$0.207621\pi$
$594$	4.00986	−	13.1665i	0.164527	−	0.540228i
$595$	−3.50014	+	24.5431i	−0.143492	+	1.00617i
$596$	−2.57384			−0.105429
$597$	−19.1113	−	42.2208i	−0.782174	−	1.72798i
$598$	−14.2478	−	9.35797i	−0.582638	−	0.382676i
$599$	−0.243067	−	0.140335i	−0.00993147	−	0.00573394i	0.495026	−	0.868878i	$-0.335159\pi$
$599$	−0.243067	−	0.140335i	−0.00993147	−	0.00573394i	−0.504958	+	0.863144i	$0.668492\pi$
$600$	−2.27193	+	1.02839i	−0.0927510	+	0.0419839i
$601$		−	7.38730i		−	0.301334i	−0.988585	−	0.150667i	$-0.951858\pi$
$601$		−	7.38730i		−	0.301334i	0.988585	−	0.150667i	$-0.0481421\pi$
$602$	5.03975	+	12.5471i	0.205405	+	0.511382i
$603$	−0.937538	+	4.69529i	−0.0381795	+	0.191207i
$604$	3.68114	−	2.12531i	0.149784	−	0.0864776i
$605$	−8.75534	−	5.05490i	−0.355955	−	0.205511i
$606$	19.5136	+	13.9941i	0.792687	+	0.568472i
$607$	22.6313	−	13.0662i	0.918577	−	0.530341i	0.0353963	−	0.999373i	$-0.488731\pi$
$607$	22.6313	−	13.0662i	0.918577	−	0.530341i	0.883181	+	0.469033i	$0.155397\pi$
$608$	0.483637			0.0196141
$609$	−21.9782	+	22.9488i	−0.890601	+	0.929931i
$610$	−12.4605			−0.504511
$611$	−24.7777	+	12.4636i	−1.00240	+	0.504222i
$612$	−7.30995	+	8.32305i	−0.295487	+	0.336439i
$613$	15.4716	+	8.93253i	0.624892	+	0.360781i	0.778771	−	0.627308i	$-0.215843\pi$
$613$	15.4716	+	8.93253i	0.624892	+	0.360781i	−0.153879	+	0.988090i	$0.549177\pi$
$614$	−15.0178	−	26.0117i	−0.606071	−	1.04974i
$615$	1.31326	−	13.2837i	0.0529558	−	0.535652i
$616$	4.32580	−	5.51365i	0.174291	−	0.222151i
$617$	29.5144			1.18821			0.594103	−	0.804389i	$-0.297507\pi$
$617$	29.5144			1.18821			0.594103	+	0.804389i	$0.297507\pi$
$618$	−6.52195	−	14.4083i	−0.262351	−	0.579588i
$619$	−16.8277	+	29.1465i	−0.676363	+	1.17149i	0.299706	+	0.954032i	$0.403112\pi$
$619$	−16.8277	+	29.1465i	−0.676363	+	1.17149i	−0.976069	+	0.217463i	$0.930222\pi$
$620$	−11.9180	−	6.88088i	−0.478640	−	0.276343i
$621$	5.55203	+	23.9306i	0.222795	+	0.960301i
$622$	6.38987			0.256210
$623$	6.74700	−	2.71004i	0.270313	−	0.108576i
$624$	−0.970788	+	6.16908i	−0.0388626	+	0.246961i
$625$	15.0630	+	26.0899i	0.602520	+	1.04360i
$626$	8.58761	+	4.95806i	0.343230	+	0.198164i
$627$	−1.80311	−	1.29310i	−0.0720094	−	0.0516413i
$628$	0.823957	−	0.475712i	0.0328795	−	0.0189830i
$629$			25.1588i			1.00315i
$630$	6.69325	−	18.9976i	0.266666	−	0.756883i
$631$		−	41.0344i		−	1.63356i	−0.576953	−	0.816778i	$-0.695758\pi$
$631$		−	41.0344i		−	1.63356i	0.576953	−	0.816778i	$-0.304242\pi$
$632$	3.75864	+	6.51016i	0.149511	+	0.258960i
$633$	−24.3945	−	17.4944i	−0.969593	−	0.695340i
$634$	15.9691	−	27.6594i	0.634215	−	1.09849i
$635$	23.5257	−	13.5826i	0.933589	−	0.539008i
$636$	16.1917	+	1.60075i	0.642041	+	0.0634737i
$637$	−23.7868	−	8.43717i	−0.942469	−	0.334293i
$638$		−	18.3667i		−	0.727146i
$639$	12.4154	+	36.6632i	0.491147	+	1.45037i
$640$	−2.19770	−	1.26884i	−0.0868715	−	0.0501553i
$641$	−10.8867	−	6.28542i	−0.429998	−	0.248259i	0.269348	−	0.963043i	$-0.413192\pi$
$641$	−10.8867	−	6.28542i	−0.429998	−	0.248259i	−0.699346	+	0.714784i	$0.746525\pi$
$642$	5.55107	+	12.2635i	0.219083	+	0.484000i
$643$	−44.1388			−1.74067			−0.870333	−	0.492464i	$-0.836096\pi$
$643$	−44.1388			−1.74067			−0.870333	+	0.492464i	$0.836096\pi$
$644$	−1.76599	+	12.3832i	−0.0695898	+	0.487966i
$645$	−22.3542	−	2.20999i	−0.880195	−	0.0870181i
$646$	0.892906	+	1.54656i	0.0351309	+	0.0608485i
$647$	6.42771	−	11.1331i	0.252699	−	0.437688i	−0.711569	−	0.702616i	$-0.752015\pi$
$647$	6.42771	−	11.1331i	0.252699	−	0.437688i	0.964268	+	0.264928i	$0.0853483\pi$
$648$	7.14822	−	5.46836i	0.280809	−	0.214817i
$649$	−13.2045	+	7.62364i	−0.518323	+	0.299254i
$650$	−5.18275	−	0.298552i	−0.203284	−	0.0117102i
$651$	23.8598	−	6.94892i	0.935141	−	0.272350i
$652$			5.48364i			0.214756i
$653$	38.8978	−	22.4576i	1.52219	−	0.878835i	0.522531	−	0.852620i	$-0.324988\pi$
$653$	38.8978	−	22.4576i	1.52219	−	0.878835i	0.999656	−	0.0262147i	$-0.00834536\pi$
$654$	−13.7827	+	19.2188i	−0.538946	+	0.751515i
$655$	13.9265	+	8.04045i	0.544152	+	0.314166i
$656$	2.63006	−	1.51847i	0.102687	−	0.0592862i
$657$	38.6832	+	7.72412i	1.50918	+	0.301347i
$658$	16.0125	+	12.5628i	0.624233	+	0.489749i
$659$		−	4.26760i		−	0.166242i	−0.996539	−	0.0831210i	$-0.973511\pi$
$659$		−	4.26760i		−	0.166242i	0.996539	−	0.0831210i	$-0.0264888\pi$
$660$	4.80104	+	10.6065i	0.186880	+	0.412857i
$661$	−6.63233	+	11.4875i	−0.257968	+	0.446814i	−0.965697	−	0.259670i	$-0.916386\pi$
$661$	−6.63233	+	11.4875i	−0.257968	+	0.446814i	0.707729	+	0.706484i	$0.249720\pi$
$662$	13.1995	+	7.62074i	0.513013	+	0.296188i
$663$	−21.5196	+	8.28520i	−0.835751	+	0.321770i
$664$		−	3.10022i		−	0.120312i
$665$	−2.55474	−	2.00435i	−0.0990687	−	0.0777254i
$666$	4.00250	−	20.0450i	0.155094	−	0.776727i
$667$	16.3911	+	28.3903i	0.634668	+	1.09928i
$668$	5.33246	+	3.07870i	0.206319	+	0.119118i
$669$	−6.12971	−	4.39590i	−0.236988	−	0.169955i
$670$	−2.02506	−	3.50751i	−0.0782349	−	0.135507i
$671$			13.0061i			0.502096i
$672$	4.39978	−	1.28139i	0.169725	−	0.0494306i
$673$	5.86953			0.226254			0.113127	−	0.993581i	$-0.463913\pi$
$673$	5.86953			0.226254			0.113127	+	0.993581i	$0.463913\pi$
$674$	11.6222	+	20.1303i	0.447672	+	0.775390i
$675$	5.10829	+	5.46612i	0.196618	+	0.210391i
$676$	−7.74979	+	10.4375i	−0.298069	+	0.401441i
$677$	18.4065	+	31.8810i	0.707419	+	1.22529i	0.965811	+	0.259245i	$0.0834739\pi$
$677$	18.4065	+	31.8810i	0.707419	+	1.22529i	−0.258393	+	0.966040i	$0.583193\pi$
$678$	−35.3752	−	3.49728i	−1.35858	−	0.134312i
$679$	−15.4951	−	2.20978i	−0.594646	−	0.0848037i
$680$		−	9.37029i		−	0.359334i
$681$	−14.3159	−	31.6268i	−0.548588	−	1.21194i
$682$	−7.18217	+	12.4399i	−0.275019	+	0.476348i
$683$	5.49782	−	9.52250i	0.210368	−	0.364368i	−0.741462	−	0.670995i	$-0.765867\pi$
$683$	5.49782	−	9.52250i	0.210368	−	0.364368i	0.951830	+	0.306627i	$0.0992004\pi$
$684$	−0.465371	−	1.37425i	−0.0177939	−	0.0525459i
$685$			44.8730i			1.71451i
$686$	1.82366	+	18.4303i	0.0696278	+	0.703670i
$687$	4.53684	−	45.8904i	0.173091	−	1.75083i
$688$	−2.55531	−	4.42592i	−0.0974202	−	0.168737i
$689$	28.3098	+	18.5938i	1.07852	+	0.708369i
$690$	−16.8868	−	12.1103i	−0.642870	−	0.461031i
$691$	17.4124	+	30.1592i	0.662400	+	1.14731i	0.979983	+	0.199081i	$0.0637956\pi$
$691$	17.4124	+	30.1592i	0.662400	+	1.14731i	−0.317583	+	0.948231i	$0.602871\pi$
$692$	6.90723			0.262573
$693$	−19.8294	−	6.98633i	−0.753259	−	0.265389i
$694$		−	24.5228i		−	0.930873i
$695$	−20.4205	−	35.3693i	−0.774593	−	1.34163i
$696$	6.99916	−	9.75974i	0.265303	−	0.369942i
$697$	9.71140	+	5.60688i	0.367846	+	0.212376i
$698$	0.551733	+	0.955629i	0.0208834	+	0.0361711i
$699$	−40.3181	−	3.98594i	−1.52497	−	0.150762i
$700$	1.41985	+	3.53491i	0.0536654	+	0.133607i
$701$		−	32.7821i		−	1.23816i	−0.785327	−	0.619081i	$-0.787505\pi$
$701$		−	32.7821i		−	1.23816i	0.785327	−	0.619081i	$-0.212495\pi$
$702$	18.4636	−	3.17759i	0.696862	−	0.119930i
$703$	−2.85380	−	1.64764i	−0.107633	−	0.0621421i
$704$	−1.32440	+	2.29393i	−0.0499151	+	0.0864556i
$705$	−30.8029	+	13.9430i	−1.16011	+	0.525123i
$706$		−	6.16884i		−	0.232167i
$707$	22.6412	−	28.8585i	0.851512	−	1.08534i
$708$	−9.92184	−	0.980896i	−0.372885	−	0.0368643i
$709$	30.7026	−	17.7261i	1.15306	−	0.665719i	0.203428	−	0.979090i	$-0.434792\pi$
$709$	30.7026	−	17.7261i	1.15306	−	0.665719i	0.949631	+	0.313371i	$0.101458\pi$
$710$	−28.3563	−	16.3715i	−1.06419	−	0.614413i
$711$	14.8819	−	16.9445i	0.558116	−	0.635467i
$712$	−2.37997	+	1.37408i	−0.0891931	+	0.0514956i
$713$		−	25.6385i		−	0.960169i
$714$	12.2206	+	11.7037i	0.457344	+	0.438001i
$715$	−1.39379	+	24.1957i	−0.0521249	+	0.904867i
$716$	1.49413	−	0.862637i	0.0558383	−	0.0322383i
$717$	−15.0282	−	10.7774i	−0.561238	−	0.402490i
$718$	−6.24235	+	10.8121i	−0.232962	+	0.403503i
$719$	22.2486	+	38.5357i	0.829733	+	1.43714i	0.898248	+	0.439489i	$0.144841\pi$
$719$	22.2486	+	38.5357i	0.829733	+	1.43714i	−0.0685151	+	0.997650i	$0.521826\pi$
$720$	−1.49072	+	7.46566i	−0.0555557	+	0.278229i
$721$	−22.4180	+	9.00456i	−0.834891	+	0.335348i
$722$	18.7661			0.698402
$723$	−19.1888	+	8.68586i	−0.713641	+	0.323031i
$724$	19.1077	+	11.0319i	0.710133	+	0.409996i
$725$	8.64614	+	4.99185i	0.321109	+	0.185393i
$726$	−6.28625	+	2.84548i	−0.233305	+	0.105606i
$727$			4.60691i			0.170861i	0.996344	+	0.0854305i	$0.0272265\pi$
$727$			4.60691i			0.170861i	−0.996344	+	0.0854305i	$0.972773\pi$
$728$	9.35076	+	1.88769i	0.346562	+	0.0699624i
$729$	−22.4166	−	15.0498i	−0.830243	−	0.557402i
$730$	−28.8974	+	16.6839i	−1.06954	+	0.617499i
$731$	9.43538	−	16.3426i	0.348980	−	0.604451i
$732$	−4.95635	+	6.91121i	−0.183192	+	0.255446i
$733$	−0.675297	−	1.16965i	−0.0249427	−	0.0432020i	0.853285	−	0.521445i	$-0.174607\pi$
$733$	−0.675297	−	1.16965i	−0.0249427	−	0.0432020i	−0.878227	+	0.478243i	$0.841274\pi$
$734$			23.6812i			0.874088i
$735$	−28.5517	−	11.4654i	−1.05314	−	0.422907i
$736$		−	4.72776i		−	0.174268i
$737$	−3.66109	+	2.11373i	−0.134858	+	0.0778603i
$738$	−6.84545	−	6.01220i	−0.251984	−	0.221312i
$739$	21.6402	+	12.4940i	0.796049	+	0.459599i	0.842088	−	0.539340i	$-0.181326\pi$
$739$	21.6402	+	12.4940i	0.796049	+	0.459599i	−0.0460384	+	0.998940i	$0.514660\pi$
$740$	8.64531	+	14.9741i	0.317808	+	0.550460i
$741$	0.469509	−	2.98360i	0.0172479	−	0.109605i
$742$	3.50894	−	24.6048i	0.128817	−	0.903271i
$743$	−45.1839			−1.65764			−0.828818	−	0.559519i	$-0.810986\pi$
$743$	−45.1839			−1.65764			−0.828818	+	0.559519i	$0.810986\pi$
$744$	−8.55703	+	3.87335i	−0.313716	+	0.142004i
$745$	−5.65652	−	3.26579i	−0.207239	−	0.119649i
$746$	−1.11557	+	1.93222i	−0.0408438	+	0.0707435i
$747$	−8.80926	+	2.98312i	−0.322314	+	0.109147i
$748$	−9.78058			−0.357614
$749$	19.0808	−	7.66412i	0.697198	−	0.280041i
$750$	15.5725	+	1.53953i	0.568626	+	0.0562157i
$751$	−13.1428	−	22.7639i	−0.479586	−	0.830667i	0.520140	−	0.854081i	$-0.325880\pi$
$751$	−13.1428	−	22.7639i	−0.479586	−	0.830667i	−0.999726	+	0.0234139i	$0.992546\pi$
$752$	−6.66192	−	3.84626i	−0.242935	−	0.140259i
$753$	36.2509	+	25.9972i	1.32106	+	0.947390i
$754$	22.3345	−	11.2346i	0.813373	−	0.409139i
$755$	10.7867			0.392568
$756$	−7.87466	−	11.2690i	−0.286399	−	0.409849i
$757$	−15.5743			−0.566056			−0.283028	−	0.959112i	$-0.591339\pi$
$757$	−15.5743			−0.566056			−0.283028	+	0.959112i	$0.591339\pi$
$758$	−6.71804	+	3.87866i	−0.244010	+	0.140879i
$759$	−12.6406	+	17.6262i	−0.458824	+	0.639791i
$760$	1.06289	+	0.613658i	0.0385550	+	0.0222597i
$761$	−12.9920	+	7.50093i	−0.470959	+	0.271909i	−0.716641	−	0.697442i	$-0.754321\pi$
$761$	−12.9920	+	7.50093i	−0.470959	+	0.271909i	0.245682	+	0.969351i	$0.420988\pi$
$762$	1.82412	−	18.4512i	0.0660810	−	0.668415i
$763$	28.4225	+	22.2992i	1.02896	+	0.807284i
$764$		−	26.1744i		−	0.946957i
$765$	−26.6257	+	9.01638i	−0.962652	+	0.325988i
$766$	7.94443	+	4.58672i	0.287044	+	0.165725i
$767$	−17.3475	−	11.3938i	−0.626382	−	0.411407i
$768$	−1.57792	+	0.714250i	−0.0569385	+	0.0257733i
$769$	34.6475			1.24942			0.624710	−	0.780857i	$-0.285217\pi$
$769$	34.6475			1.24942			0.624710	+	0.780857i	$0.285217\pi$
$770$	16.5027	−	6.62859i	0.594717	−	0.238878i
$771$	2.97892	−	30.1320i	0.107283	−	1.08518i
$772$	−1.84511	+	1.06527i	−0.0664069	+	0.0383400i
$773$	−0.0831890	−	0.0480292i	−0.00299210	−	0.00172749i	0.498503	−	0.866888i	$-0.333883\pi$
$773$	−0.0831890	−	0.0480292i	−0.00299210	−	0.00172749i	−0.501495	+	0.865160i	$0.667217\pi$
$774$	−10.1175	+	11.5197i	−0.363664	+	0.414066i
$775$	−3.90404	−	6.76200i	−0.140237	−	0.242898i
$776$	5.91584			0.212366
$777$	−30.3272	−	7.42797i	−1.08798	−	0.266477i
$778$		−	34.3901i		−	1.23294i
$779$	−1.27200	+	0.734387i	−0.0455740	+	0.0263121i
$780$	−9.96107	+	12.3260i	−0.356664	+	0.441341i
$781$	−17.0884	+	29.5980i	−0.611471	+	1.05910i
$782$	15.1183	−	8.72854i	0.540629	−	0.312132i
$783$	−34.4671	−	10.4970i	−1.23175	−	0.375131i
$784$	−1.66586	−	6.79889i	−0.0594949	−	0.242818i
$785$	2.41441			0.0861740
$786$	9.99907	−	4.52609i	0.356655	−	0.161440i
$787$	22.1104	−	38.2963i	0.788150	−	1.36512i	−0.138949	−	0.990300i	$-0.544372\pi$
$787$	22.1104	−	38.2963i	0.788150	−	1.36512i	0.927099	−	0.374817i	$-0.122294\pi$
$788$	−2.18381	+	3.78247i	−0.0777949	+	0.134745i
$789$	14.7618	+	32.6119i	0.525534	+	1.16101i
$790$			19.0765i			0.678710i
$791$	−7.66626	+	53.7561i	−0.272581	+	1.91135i
$792$	7.79256	+	1.55599i	0.276897	+	0.0552897i
$793$	−15.8158	+	7.95559i	−0.561635	+	0.282511i
$794$	6.32491	−	10.9551i	0.224462	−	0.388780i
$795$	33.5533	+	24.0626i	1.19001	+	0.853412i
$796$	23.1724	−	13.3786i	0.821324	−	0.474191i
$797$	−50.7960			−1.79929			−0.899644	−	0.436624i	$-0.856174\pi$
$797$	−50.7960			−1.79929			−0.899644	+	0.436624i	$0.856174\pi$
$798$	−2.12790	+	0.619726i	−0.0753267	+	0.0219381i
$799$		−	28.4044i		−	1.00487i
$800$	−0.719909	−	1.24692i	−0.0254526	−	0.0440853i
$801$	6.19451	+	5.44050i	0.218872	+	0.192231i
$802$	−11.1563	+	19.3233i	−0.393944	+	0.682331i
$803$	17.4144	+	30.1627i	0.614543	+	1.06442i
$804$	−2.75093	−	0.271963i	−0.0970178	−	0.00959141i
$805$	−19.5934	+	24.9737i	−0.690577	+	0.880208i
$806$	−19.5204	−	1.12447i	−0.687578	−	0.0396079i
$807$	0.750026	−	0.339500i	0.0264022	−	0.0119510i
$808$	−6.93191	+	12.0064i	−0.243864	+	0.422384i
$809$	−17.7051	−	10.2220i	−0.622477	−	0.359387i	0.155356	−	0.987859i	$-0.450348\pi$
$809$	−17.7051	−	10.2220i	−0.622477	−	0.359387i	−0.777833	+	0.628471i	$0.783681\pi$
$810$	22.6481	−	2.94783i	0.795773	−	0.103576i
$811$	−41.1944			−1.44653			−0.723266	−	0.690570i	$-0.757360\pi$
$811$	−41.1944			−1.44653			−0.723266	+	0.690570i	$0.757360\pi$
$812$	−14.4336	−	11.3240i	−0.506520	−	0.397395i
$813$	−0.263257	+	2.66286i	−0.00923282	+	0.0933907i
$814$	15.6298	−	9.02386i	0.547824	−	0.316286i
$815$	−6.95786	+	12.0514i	−0.243723	+	0.422141i
$816$	−5.19722	−	3.72716i	−0.181939	−	0.130477i
$817$	1.23584	+	2.14054i	0.0432366	+	0.0748881i
$818$	−30.4213			−1.06366
$819$	−3.63373	−	28.3865i	−0.126973	−	0.991906i
$820$	7.70676			0.269132
$821$	17.3162	+	29.9925i	0.604338	+	1.04674i	0.992156	+	0.125008i	$0.0398956\pi$
$821$	17.3162	+	29.9925i	0.604338	+	1.04674i	−0.387818	+	0.921736i	$0.626771\pi$
$822$	24.8887	+	17.8489i	0.868094	+	0.622550i
$823$	5.62828	−	9.74847i	0.196190	−	0.339810i	−0.751100	−	0.660188i	$-0.770477\pi$
$823$	5.62828	−	9.74847i	0.196190	−	0.339810i	0.947290	+	0.320378i	$0.103810\pi$
$824$	7.90784	−	4.56559i	0.275483	−	0.159050i
$825$	−0.649884	+	6.57363i	−0.0226261	+	0.228864i
$826$	−2.15019	+	15.0772i	−0.0748146	+	0.524602i
$827$	−35.0834			−1.21997			−0.609985	−	0.792413i	$-0.708824\pi$
$827$	−35.0834			−1.21997			−0.609985	+	0.792413i	$0.708824\pi$
$828$	−13.4339	+	4.54920i	−0.466861	+	0.158096i
$829$	39.8985	+	23.0354i	1.38573	+	0.800054i	0.992831	−	0.119526i	$-0.0381376\pi$
$829$	39.8985	+	23.0354i	1.38573	+	0.800054i	0.392903	+	0.919580i	$0.371471\pi$
$830$	3.93368	−	6.81333i	0.136540	−	0.236494i
$831$	44.2360	−	20.0235i	1.53453	−	0.694607i
$832$	−3.59958	−	0.207354i	−0.124793	−	0.00718871i
$833$	18.6657	−	17.8793i	0.646728	−	0.619483i
$834$	−27.7401	−	2.74245i	−0.960560	−	0.0949632i
$835$	7.81275	+	13.5321i	0.270371	+	0.468297i
$836$	0.640528	−	1.10943i	0.0221531	−	0.0383704i
$837$	19.2400	+	20.5877i	0.665031	+	0.711616i
$838$	11.4781	+	19.8807i	0.396506	+	0.686768i
$839$			53.0141i			1.83025i	0.403171	+	0.915125i	$0.367908\pi$
$839$			53.0141i			1.83025i	−0.403171	+	0.915125i	$0.632092\pi$
$840$	11.2952	+	2.76652i	0.389723	+	0.0954539i
$841$	−19.0803			−0.657941
$842$	−10.1413	+	5.85510i	−0.349494	+	0.201780i
$843$	−42.7731	−	30.6745i	−1.47318	−	1.05649i
$844$	8.66575	−	15.0095i	0.298288	−	0.516649i
$845$	−30.2751	+	13.1051i	−1.04150	+	0.450831i
$846$	−4.51884	+	22.6308i	−0.155361	+	0.778064i
$847$	3.92863	+	9.78083i	0.134989	+	0.336073i
$848$			9.39383i			0.322586i
$849$	5.01158	+	11.0716i	0.171997	+	0.379977i
$850$	2.65824	−	4.60420i	0.0911768	−	0.157923i
$851$	−16.1064	+	27.8972i	−0.552122	+	0.956303i
$852$	−20.3596	+	9.21580i	−0.697508	+	0.315728i
$853$	22.2010			0.760147			0.380074	−	0.924956i	$-0.375899\pi$
$853$	22.2010			0.760147			0.380074	+	0.924956i	$0.375899\pi$
$854$	10.2209	+	8.01893i	0.349753	+	0.274402i
$855$	0.720966	−	3.61067i	0.0246565	−	0.123482i
$856$	−6.73065	+	3.88594i	−0.230049	+	0.132819i
$857$	−18.4059	+	31.8799i	−0.628732	+	1.08900i	0.359074	+	0.933309i	$0.383093\pi$
$857$	−18.4059	+	31.8799i	−0.628732	+	1.08900i	−0.987806	+	0.155687i	$0.950241\pi$
$858$	12.8657	+	10.3972i	0.439228	+	0.354956i
$859$	−6.38470	+	3.68621i	−0.217843	+	0.125772i	−0.604951	−	0.796263i	$-0.706807\pi$
$859$	−6.38470	+	3.68621i	−0.217843	+	0.125772i	0.387108	+	0.922034i	$0.373474\pi$
$860$		−	12.9691i		−	0.442243i
$861$	−9.62594	+	10.0510i	−0.328051	+	0.342539i
$862$	−18.3104			−0.623654
$863$	17.7758	+	30.7886i	0.605096	+	1.04806i	0.992036	+	0.125952i	$0.0401986\pi$
$863$	17.7758	+	30.7886i	0.605096	+	1.04806i	−0.386940	+	0.922105i	$0.626468\pi$
$864$	3.54787	+	3.79640i	0.120701	+	0.129156i
$865$	15.1800	+	8.76417i	0.516135	+	0.297991i
$866$	−18.3413	+	10.5893i	−0.623261	+	0.359840i
$867$	−0.573532	+	5.80132i	−0.0194782	+	0.197023i
$868$	5.34777	+	13.3140i	0.181515	+	0.451905i
$869$	19.9118			0.675460
$870$	27.7656	−	12.5681i	0.941341	−	0.426099i
$871$	−4.80977	−	3.15905i	−0.162973	−	0.107040i
$872$	−11.8250	−	6.82718i	−0.400446	−	0.231198i
$873$	−5.69241	−	16.8099i	−0.192659	−	0.568928i
$874$			2.28652i			0.0773428i
$875$	3.37475	−	23.6639i	0.114087	−	0.799985i
$876$	−2.24063	+	22.6642i	−0.0757039	+	0.765751i
$877$	−33.3702	+	19.2663i	−1.12683	+	0.650576i	−0.943136	−	0.332407i	$-0.892139\pi$
$877$	−33.3702	+	19.2663i	−1.12683	+	0.650576i	−0.183695	+	0.982983i	$0.558806\pi$
$878$	−7.13298	−	4.11823i	−0.240727	−	0.138984i
$879$	−32.7275	+	45.6357i	−1.10387	+	1.53925i
$880$	−5.82125	+	3.36090i	−0.196234	+	0.113296i
$881$	19.2791			0.649530			0.324765	−	0.945795i	$-0.394715\pi$
$881$	19.2791			0.649530			0.324765	+	0.945795i	$0.394715\pi$
$882$	−17.7161	+	11.2756i	−0.596532	+	0.379670i
$883$	5.53806			0.186371			0.0931853	−	0.995649i	$-0.470295\pi$
$883$	5.53806			0.186371			0.0931853	+	0.995649i	$0.470295\pi$
$884$	−5.98259	−	11.8935i	−0.201216	−	0.400020i
$885$	−20.5606	−	14.7449i	−0.691136	−	0.495645i
$886$	−7.54716	−	4.35736i	−0.253552	−	0.146388i
$887$	25.0298	+	43.3529i	0.840418	+	1.45565i	0.889541	+	0.456855i	$0.151024\pi$
$887$	25.0298	+	43.3529i	0.840418	+	1.45565i	−0.0491228	+	0.998793i	$0.515643\pi$
$888$	11.7442	+	1.16106i	0.394109	+	0.0389625i
$889$	−28.0383	−	3.99860i	−0.940375	−	0.134109i
$890$	−6.97393			−0.233767
$891$	−3.07690	−	23.6398i	−0.103080	−	0.791962i
$892$	2.17749	−	3.77151i	0.0729076	−	0.126280i
$893$	3.22195	+	1.86020i	0.107819	+	0.0622491i
$894$	−4.06133	+	1.83837i	−0.135831	+	0.0614842i
$895$	4.37819			0.146347
$896$	0.986133	+	2.45511i	0.0329444	+	0.0820193i
$897$	−29.1660	−	4.58966i	−0.973823	−	0.153244i
$898$	11.3423	+	19.6454i	0.378496	+	0.655574i
$899$	32.5650	+	18.8014i	1.08610	+	0.627062i
$900$	−2.85040	+	3.24545i	−0.0950134	+	0.108182i
$901$	−30.0393	+	17.3432i	−1.00075	+	0.577785i
$902$		−	8.04422i		−	0.267843i
$903$	16.9141	+	16.1987i	0.562866	+	0.539060i
$904$		−	20.5235i		−	0.682600i
$905$	27.9953	+	48.4893i	0.930596	+	1.61184i
$906$	4.29056	−	5.98283i	0.142544	−	0.198766i
$907$	2.26274	−	3.91918i	0.0751330	−	0.130134i	−0.826011	−	0.563654i	$-0.809395\pi$
$907$	2.26274	−	3.91918i	0.0751330	−	0.130134i	0.901144	+	0.433520i	$0.142729\pi$
$908$	17.3580	−	10.0217i	0.576046	−	0.332580i
$909$	40.7863	+	8.14406i	1.35280	+	0.270121i
$910$	18.1549	+	16.0132i	0.601830	+	0.530832i
$911$		−	35.0796i		−	1.16224i	−0.813818	−	0.581120i	$-0.802615\pi$
$911$		−	35.0796i		−	1.16224i	0.813818	−	0.581120i	$-0.197385\pi$
$912$	0.763143	−	0.345438i	0.0252702	−	0.0114386i
$913$	−7.11166	−	4.10592i	−0.235362	−	0.135886i
$914$	11.5835	+	6.68771i	0.383147	+	0.221210i
$915$	−19.6618	+	8.89992i	−0.649998	+	0.294222i
$916$	26.6240			0.879683
$917$	−6.24897	−	15.5576i	−0.206359	−	0.513758i
$918$	−5.58981	+	18.3543i	−0.184491	+	0.605781i
$919$	−20.4670	−	35.4499i	−0.675144	−	1.16938i	−0.976427	−	0.215848i	$-0.930748\pi$
$919$	−20.4670	−	35.4499i	−0.675144	−	1.16938i	0.301283	−	0.953535i	$-0.402585\pi$
$920$	5.99877	−	10.3902i	0.197774	−	0.342554i
$921$	−42.2758	−	30.3179i	−1.39304	−	0.999010i
$922$	0.673343	−	0.388755i	0.0221754	−	0.0128030i
$923$	−46.4446	−	2.67544i	−1.52874	−	0.0880632i
$924$	2.88765	−	11.7898i	0.0949968	−	0.387857i
$925$			9.81029i			0.322560i
$926$	−2.76857	+	1.59843i	−0.0909807	+	0.0525277i
$927$	−20.5823	−	18.0770i	−0.676011	−	0.593725i
$928$	6.00502	+	3.46700i	0.197124	+	0.113810i
$929$	−15.4303	+	8.90866i	−0.506250	+	0.292284i	−0.731291	−	0.682066i	$-0.761082\pi$
$929$	−15.4303	+	8.90866i	−0.506250	+	0.292284i	0.225041	+	0.974349i	$0.427749\pi$
$930$	−23.7204	−	2.34506i	−0.777823	−	0.0768974i
$931$	0.805671	+	3.28820i	0.0264048	+	0.107766i
$932$		−	23.3912i		−	0.766203i
$933$	10.0827	−	4.56396i	0.330094	−	0.149417i
$934$	0.719079	−	1.24548i	0.0235290	−	0.0407534i
$935$	−21.4947	−	12.4100i	−0.702953	−	0.405850i
$936$	2.87444	+	10.4277i	0.0939539	+	0.340841i
$937$		−	30.8788i		−	1.00877i	−0.863480	−	0.504383i	$-0.831720\pi$
$937$		−	30.8788i		−	1.00877i	0.863480	−	0.504383i	$-0.168280\pi$
$938$	−0.596161	+	4.18030i	−0.0194654	+	0.136492i
$939$	17.0919	+	1.68974i	0.557773	+	0.0551427i
$940$	−9.76058	−	16.9058i	−0.318355	−	0.551407i
$941$	−12.9864	−	7.49770i	−0.423344	−	0.244418i	0.273163	−	0.961968i	$-0.411930\pi$
$941$	−12.9864	−	7.49770i	−0.423344	−	0.244418i	−0.696507	+	0.717550i	$0.745264\pi$
$942$	0.960365	−	1.33915i	0.0312904	−	0.0436318i
$943$	7.17895	+	12.4343i	0.233779	+	0.404917i
$944$		−	5.75630i		−	0.187352i
$945$	−3.00758	−	34.7574i	−0.0978367	−	1.13066i
$946$	−13.5370			−0.440125
$947$	−8.13729	−	14.0942i	−0.264426	−	0.458000i	0.702987	−	0.711203i	$-0.251849\pi$
$947$	−8.13729	−	14.0942i	−0.264426	−	0.458000i	−0.967413	+	0.253203i	$0.918516\pi$
$948$	10.5807	+	7.58793i	0.343646	+	0.246445i
$949$	−26.0266	+	39.6264i	−0.844859	+	1.28633i
$950$	0.348175	+	0.603057i	0.0112963	+	0.0195657i
$951$	5.44240	−	55.0503i	0.176482	−	1.78513i
$952$	−6.03022	+	7.68611i	−0.195441	+	0.249108i
$953$			35.3790i			1.14604i	0.819542	+	0.573019i	$0.194228\pi$
$953$			35.3790i			1.14604i	−0.819542	+	0.573019i	$0.805772\pi$
$954$	26.6926	−	9.03904i	0.864204	−	0.292650i
$955$	33.2111	−	57.5234i	1.07469	−	1.86141i
$956$	5.33853	−	9.24661i	0.172660	−	0.299057i
$957$	−13.1184	−	28.9813i	−0.424059	−	0.936834i
$958$		−	10.4447i		−	0.337454i
$959$	28.8779	−	36.8077i	0.932515	−	1.18858i
$960$	−4.37407	−	0.432430i	−0.141172	−	0.0139566i
$961$	0.795717	+	1.37822i	0.0256683	+	0.0444588i
$962$	20.5337	+	13.4865i	0.662033	+	0.434823i
$963$	17.5183	+	15.3860i	0.564521	+	0.495806i
$964$	−6.08041	−	10.5316i	−0.195837	−	0.339199i
$965$	−5.40665			−0.174046
$966$	6.05809	+	20.8011i	0.194916	+	0.669265i
$967$			8.97650i			0.288665i	0.989529	+	0.144332i	$0.0461035\pi$
$967$			8.97650i			0.288665i	−0.989529	+	0.144332i	$0.953897\pi$
$968$	−1.99194	−	3.45014i	−0.0640233	−	0.110892i
$969$	2.51357	+	1.80260i	0.0807474	+	0.0579077i
$970$	13.0012	+	7.50626i	0.417444	+	0.241011i
$971$	−1.17336	−	2.03232i	−0.0376550	−	0.0652203i	0.846584	−	0.532256i	$-0.178655\pi$
$971$	−1.17336	−	2.03232i	−0.0376550	−	0.0652203i	−0.884239	+	0.467035i	$0.845322\pi$
$972$	7.37359	−	13.7343i	0.236508	−	0.440527i
$973$	−6.01163	+	42.1537i	−0.192724	+	1.35139i
$974$		−	2.40290i		−	0.0769939i
$975$	−8.39123	+	3.23069i	−0.268734	+	0.103465i
$976$	−4.25236	−	2.45510i	−0.136115	−	0.0785858i
$977$	17.3396	−	30.0330i	0.554742	−	0.960841i	−0.443182	−	0.896432i	$-0.646150\pi$
$977$	17.3396	−	30.0330i	0.554742	−	0.960841i	0.997924	−	0.0644089i	$-0.0205162\pi$
$978$	3.91669	+	8.65277i	0.125242	+	0.276685i
$979$			7.27929i			0.232647i
$980$	4.96566	−	17.0556i	0.158622	−	0.544821i
$981$	−8.02102	+	40.1701i	−0.256091	+	1.28253i
$982$	−10.7019	+	6.17874i	−0.341511	+	0.197172i
$983$	−22.3427	−	12.8996i	−0.712621	−	0.411432i	0.0994096	−	0.995047i	$-0.468305\pi$
$983$	−22.3427	−	12.8996i	−0.712621	−	0.411432i	−0.812031	+	0.583615i	$0.801638\pi$
$984$	3.06547	−	4.27455i	0.0977238	−	0.136268i
$985$	−9.59869	+	5.54180i	−0.305840	+	0.176577i
$986$			25.6035i			0.815382i
$987$	34.2395	+	8.38620i	1.08986	+	0.266936i
$988$	1.74089	+	0.100284i	0.0553852	+	0.00319046i
$989$	20.9247	−	12.0809i	0.665367	−	0.384150i
$990$	15.1514	+	13.3071i	0.481542	+	0.422928i
$991$	25.4169	−	44.0233i	0.807394	−	1.39845i	−0.107270	−	0.994230i	$-0.534211\pi$
$991$	25.4169	−	44.0233i	0.807394	−	1.39845i	0.914663	−	0.404217i	$-0.132456\pi$
$992$	−2.71148	−	4.69643i	−0.0860897	−	0.149112i
$993$	26.2709	+	2.59721i	0.833683	+	0.0824199i
$994$	12.7238	+	31.6776i	0.403576	+	1.00475i
$995$	67.9011			2.15261
$996$	−2.21433	−	4.89191i	−0.0701637	−	0.155006i
$997$	−31.3253	−	18.0857i	−0.992082	−	0.572779i	−0.0861859	−	0.996279i	$-0.527468\pi$
$997$	−31.3253	−	18.0857i	−0.992082	−	0.572779i	−0.905896	+	0.423500i	$0.860801\pi$
$998$	14.9074	+	8.60680i	0.471886	+	0.272444i
$999$	−8.00147	−	34.4882i	−0.253155	−	1.09116i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bg.b.311.15	yes	36
3.2	odd	2		546.2.bg.a.311.16	yes	36
7.5	odd	6	inner	546.2.bg.b.467.16	yes	36
13.12	even	2		546.2.bg.a.311.15	✓	36
21.5	even	6		546.2.bg.a.467.15	yes	36
39.38	odd	2	inner	546.2.bg.b.311.16	yes	36
91.12	odd	6		546.2.bg.a.467.16	yes	36
273.194	even	6	inner	546.2.bg.b.467.15	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bg.a.311.15	✓	36	13.12	even	2
546.2.bg.a.311.16	yes	36	3.2	odd	2
546.2.bg.a.467.15	yes	36	21.5	even	6
546.2.bg.a.467.16	yes	36	91.12	odd	6
546.2.bg.b.311.15	yes	36	1.1	even	1	trivial
546.2.bg.b.311.16	yes	36	39.38	odd	2	inner
546.2.bg.b.467.15	yes	36	273.194	even	6	inner
546.2.bg.b.467.16	yes	36	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.40752 + 1.00940i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.19770 + 1.26884i) q^{5} +(-0.170404 + 1.72365i) q^{6} +(2.61925 + 0.373536i) q^{7} -1.00000 q^{8} +(0.962231 + 2.84150i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.40752 + 1.00940i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.19770 + 1.26884i) q^{5} +(-0.170404 + 1.72365i) q^{6} +(2.61925 + 0.373536i) q^{7} -1.00000 q^{8} +(0.962231 + 2.84150i) q^{9} +(-2.19770 - 1.26884i) q^{10} +(-1.32440 + 2.29393i) q^{11} +(-1.57792 + 0.714250i) q^{12} +(-3.59958 - 0.207354i) q^{13} +(0.986133 + 2.45511i) q^{14} +(-4.37407 - 0.432430i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.84623 - 3.19777i) q^{17} +(-1.97969 + 2.25407i) q^{18} +(0.241819 + 0.418842i) q^{19} -2.53768i q^{20} +(3.30960 + 3.16963i) q^{21} -2.64880 q^{22} +(4.09436 - 2.36388i) q^{23} +(-1.40752 - 1.00940i) q^{24} +(0.719909 - 1.24692i) q^{25} +(-1.62022 - 3.22101i) q^{26} +(-1.51384 + 4.97074i) q^{27} +(-1.63312 + 2.08157i) q^{28} +6.93400i q^{29} +(-1.81254 - 4.00427i) q^{30} +(2.71148 - 4.69643i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-4.17960 + 1.89190i) q^{33} +3.69246 q^{34} +(-6.23027 + 2.50249i) q^{35} +(-2.94193 - 0.587433i) q^{36} +(-5.90071 + 3.40678i) q^{37} +(-0.241819 + 0.418842i) q^{38} +(-4.85719 - 3.92527i) q^{39} +(2.19770 - 1.26884i) q^{40} +3.03693i q^{41} +(-1.09018 + 4.45101i) q^{42} +5.11062 q^{43} +(-1.32440 - 2.29393i) q^{44} +(-5.72010 - 5.02383i) q^{45} +(4.09436 + 2.36388i) q^{46} +(6.66192 - 3.84626i) q^{47} +(0.170404 - 1.72365i) q^{48} +(6.72094 + 1.95677i) q^{49} +1.43982 q^{50} +(5.82643 - 2.63734i) q^{51} +(1.97937 - 3.01365i) q^{52} +(-8.13530 - 4.69692i) q^{53} +(-5.06171 + 1.17435i) q^{54} -6.72180i q^{55} +(-2.61925 - 0.373536i) q^{56} +(-0.0824136 + 0.833620i) q^{57} +(-6.00502 + 3.46700i) q^{58} +(4.98510 + 2.87815i) q^{59} +(2.56153 - 3.57184i) q^{60} +(4.25236 - 2.45510i) q^{61} +5.42297 q^{62} +(1.45892 + 7.80202i) q^{63} +1.00000 q^{64} +(8.17389 - 4.11159i) q^{65} +(-3.72824 - 2.67369i) q^{66} +(1.38217 + 0.797996i) q^{67} +(1.84623 + 3.19777i) q^{68} +(8.14900 + 0.805629i) q^{69} +(-5.28236 - 4.14433i) q^{70} +12.9028 q^{71} +(-0.962231 - 2.84150i) q^{72} +(6.57447 - 11.3873i) q^{73} +(-5.90071 - 3.40678i) q^{74} +(2.27193 - 1.02839i) q^{75} -0.483637 q^{76} +(-4.32580 + 5.51365i) q^{77} +(0.970788 - 6.16908i) q^{78} +(-3.75864 - 6.51016i) q^{79} +(2.19770 + 1.26884i) q^{80} +(-7.14822 + 5.46836i) q^{81} +(-2.63006 + 1.51847i) q^{82} +3.10022i q^{83} +(-4.39978 + 1.28139i) q^{84} +9.37029i q^{85} +(2.55531 + 4.42592i) q^{86} +(-6.99916 + 9.75974i) q^{87} +(1.32440 - 2.29393i) q^{88} +(2.37997 - 1.37408i) q^{89} +(1.49072 - 7.46566i) q^{90} +(-9.35076 - 1.88769i) q^{91} +4.72776i q^{92} +(8.55703 - 3.87335i) q^{93} +(6.66192 + 3.84626i) q^{94} +(-1.06289 - 0.613658i) q^{95} +(1.57792 - 0.714250i) q^{96} -5.91584 q^{97} +(1.66586 + 6.79889i) q^{98} +(-7.79256 - 1.55599i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9}+O(q^{10}) \) 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9	\( 36 q + 18 q^{2} - 18 q^{4} - 36 q^{8} + 4 q^{9} + 14 q^{15} - 18 q^{16} - 4 q^{18} - 23 q^{21} + 14 q^{25} + 6 q^{26} + 7 q^{30} + 18 q^{32} - 24 q^{33} - 8 q^{36} + 10 q^{39} - 16 q^{42} - 16 q^{43} + 9 q^{45} - 72 q^{47} + 12 q^{49} + 28 q^{50} - 3 q^{51} + 6 q^{52} - 9 q^{54} + 8 q^{57} - 24 q^{59} - 7 q^{60} - 36 q^{61} + 39 q^{63} + 36 q^{64} - 18 q^{65} - 24 q^{66} + 72 q^{71} - 4 q^{72} + 54 q^{75} + 20 q^{78} + 20 q^{79} - 20 q^{81} - 24 q^{82} + 7 q^{84} - 8 q^{86} - 24 q^{87} + 72 q^{89} - 2 q^{91} + 14 q^{93} - 72 q^{94} + 12 q^{98} - 72 q^{99}+O(q^{100}) \) 36 * q + 18 * q^2 - 18 * q^4 - 36 * q^8 + 4 * q^9 + 14 * q^15 - 18 * q^16 - 4 * q^18 - 23 * q^21 + 14 * q^25 + 6 * q^26 + 7 * q^30 + 18 * q^32 - 24 * q^33 - 8 * q^36 + 10 * q^39 - 16 * q^42 - 16 * q^43 + 9 * q^45 - 72 * q^47 + 12 * q^49 + 28 * q^50 - 3 * q^51 + 6 * q^52 - 9 * q^54 + 8 * q^57 - 24 * q^59 - 7 * q^60 - 36 * q^61 + 39 * q^63 + 36 * q^64 - 18 * q^65 - 24 * q^66 + 72 * q^71 - 4 * q^72 + 54 * q^75 + 20 * q^78 + 20 * q^79 - 20 * q^81 - 24 * q^82 + 7 * q^84 - 8 * q^86 - 24 * q^87 + 72 * q^89 - 2 * q^91 + 14 * q^93 - 72 * q^94 + 12 * q^98 - 72 * q^99

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