LMFDB - Embedded newform 462.2.bc.a.95.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(95,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 20, 21]))

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

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

chi := DirichletCharacter("462.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.bc (of order $30$, degree $8$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			95.9
Character	$\chi$	$=$	462.95
Dual form			462.2.bc.a.107.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 - 0.994522i) q^{2} +(0.333518 + 1.69964i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.0756668 - 0.169950i) q^{5} +(1.72519 - 0.154030i) q^{6} +(1.63703 + 2.07849i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.77753 + 1.13372i) q^{9} +O(q^{10})$	\(q+(0.104528 - 0.994522i) q^{2} +(0.333518 + 1.69964i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.0756668 - 0.169950i) q^{5} +(1.72519 - 0.154030i) q^{6} +(1.63703 + 2.07849i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.77753 + 1.13372i) q^{9} +(-0.161110 - 0.0930169i) q^{10} +(1.90510 - 2.71488i) q^{11} +(0.0271446 - 1.73184i) q^{12} +(0.557091 - 0.766770i) q^{13} +(2.23822 - 1.41080i) q^{14} +(0.314090 + 0.0719245i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.846849 + 8.05723i) q^{17} +(0.837177 + 2.88082i) q^{18} +(1.02248 + 4.81041i) q^{19} +(-0.109348 + 0.150504i) q^{20} +(-2.98670 + 3.47557i) q^{21} +(-2.50087 - 2.17845i) q^{22} +(0.938796 - 0.542014i) q^{23} +(-1.71951 - 0.208022i) q^{24} +(3.32250 + 3.69000i) q^{25} +(-0.704338 - 0.634189i) q^{26} +(-2.85327 - 4.34268i) q^{27} +(-1.16912 - 2.37343i) q^{28} +(-0.413615 - 1.27298i) q^{29} +(0.104362 - 0.304851i) q^{30} +(-4.24813 + 1.89139i) q^{31} +(0.500000 - 0.866025i) q^{32} +(5.24970 + 2.33252i) q^{33} +8.10161 q^{34} +(0.477109 - 0.120941i) q^{35} +(2.95255 - 0.531463i) q^{36} +(2.32721 - 2.58463i) q^{37} +(4.89094 - 0.514059i) q^{38} +(1.48903 + 0.691121i) q^{39} +(0.138250 + 0.124481i) q^{40} +(1.18944 - 3.66071i) q^{41} +(3.14434 + 3.33364i) q^{42} -11.0307i q^{43} +(-2.42792 + 2.25946i) q^{44} +(-0.0174909 + 0.557827i) q^{45} +(-0.440914 - 0.990309i) q^{46} +(0.589942 + 2.77546i) q^{47} +(-0.386621 + 1.68835i) q^{48} +(-1.64025 + 6.80511i) q^{49} +(4.01709 - 2.91858i) q^{50} +(-13.4119 + 4.12657i) q^{51} +(-0.704338 + 0.634189i) q^{52} +(2.35586 + 5.29135i) q^{53} +(-4.61714 + 2.38370i) q^{54} +(-0.317243 - 0.529199i) q^{55} +(-2.48263 + 0.914621i) q^{56} +(-7.83494 + 3.34221i) q^{57} +(-1.30924 + 0.278287i) q^{58} +(-0.705877 + 3.32089i) q^{59} +(-0.292272 - 0.135656i) q^{60} +(5.92942 - 13.3177i) q^{61} +(1.43698 + 4.42256i) q^{62} +(-6.90333 - 3.91714i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.0881596 - 0.152697i) q^{65} +(2.86848 - 4.97713i) q^{66} +(0.0659471 - 0.114224i) q^{67} +(0.846849 - 8.05723i) q^{68} +(1.23433 + 1.41484i) q^{69} +(-0.0704074 - 0.487137i) q^{70} +(-5.19792 - 7.15433i) q^{71} +(-0.219926 - 2.99193i) q^{72} +(2.96575 - 13.9527i) q^{73} +(-2.32721 - 2.58463i) q^{74} +(-5.16356 + 6.87772i) q^{75} -4.91788i q^{76} +(8.76157 - 0.484618i) q^{77} +(0.842981 - 1.40863i) q^{78} +(-12.4597 - 1.30956i) q^{79} +(0.138250 - 0.124481i) q^{80} +(6.42936 - 6.29788i) q^{81} +(-3.51633 - 1.56557i) q^{82} +(5.65811 - 4.11086i) q^{83} +(3.64405 - 2.77865i) q^{84} +(1.43341 + 0.465742i) q^{85} +(-10.9703 - 1.15303i) q^{86} +(2.02565 - 1.12756i) q^{87} +(1.99330 + 2.65080i) q^{88} +(-1.52736 + 0.881821i) q^{89} +(0.552943 + 0.0757039i) q^{90} +(2.50570 - 0.0973181i) q^{91} +(-1.03097 + 0.334983i) q^{92} +(-4.63150 - 6.58946i) q^{93} +(2.82192 - 0.296596i) q^{94} +(0.894899 + 0.190217i) q^{95} +(1.63869 + 0.560983i) q^{96} +(7.39198 + 5.37059i) q^{97} +(6.59638 + 2.34260i) q^{98} +(-2.21356 + 9.70052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	$ 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9} + 6 q^{11} - 12 q^{15} + 16 q^{16} + 2 q^{17} + 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} - 38 q^{29} - 6 q^{30} - 3 q^{31} + 64 q^{32} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) $ 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9 + 6 * q^11 - 12 * q^15 + 16 * q^16 + 2 * q^17 + 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 - 38 * q^29 - 6 * q^30 - 3 * q^31 + 64 * q^32 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	0.104528	−	0.994522i	0.0739128	−	0.703233i
$2$	0.104528	−	0.994522i	0.0739128	−	0.703233i
$3$	0.333518	+	1.69964i	0.192557	+	0.981286i
$3$	0.333518	+	1.69964i	0.192557	+	0.981286i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	0.0756668	−	0.169950i	0.0338392	−	0.0760041i	−0.895835	−	0.444387i	$-0.853422\pi$
$5$	0.0756668	−	0.169950i	0.0338392	−	0.0760041i	0.929674	+	0.368383i	$0.120088\pi$
$6$	1.72519	−	0.154030i	0.704305	−	0.0628827i
$7$	1.63703	+	2.07849i	0.618740	+	0.785596i
$7$	1.63703	+	2.07849i	0.618740	+	0.785596i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−2.77753	+	1.13372i	−0.925844	+	0.377906i
$10$	−0.161110	−	0.0930169i	−0.0509475	−	0.0294145i
$11$	1.90510	−	2.71488i	0.574409	−	0.818568i
$11$	1.90510	−	2.71488i	0.574409	−	0.818568i
$12$	0.0271446	−	1.73184i	0.00783596	−	0.499939i
$13$	0.557091	−	0.766770i	0.154509	−	0.212664i	−0.724744	−	0.689018i	$-0.758042\pi$
$13$	0.557091	−	0.766770i	0.154509	−	0.212664i	0.879253	+	0.476354i	$0.158042\pi$
$14$	2.23822	−	1.41080i	0.598190	−	0.377053i
$15$	0.314090	+	0.0719245i	0.0810977	+	0.0185708i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	0.846849	+	8.05723i	0.205391	+	1.95417i	0.288121	+	0.957594i	$0.406969\pi$
$17$	0.846849	+	8.05723i	0.205391	+	1.95417i	−0.0827301	+	0.996572i	$0.526364\pi$
$18$	0.837177	+	2.88082i	0.197325	+	0.679016i
$19$	1.02248	+	4.81041i	0.234574	+	1.10358i	0.924937	+	0.380121i	$0.124118\pi$
$19$	1.02248	+	4.81041i	0.234574	+	1.10358i	−0.690363	+	0.723464i	$0.742549\pi$
$20$	−0.109348	+	0.150504i	−0.0244509	+	0.0336538i
$21$	−2.98670	+	3.47557i	−0.651752	+	0.758432i
$22$	−2.50087	−	2.17845i	−0.533188	−	0.464446i
$23$	0.938796	−	0.542014i	0.195753	−	0.113018i	−0.398920	−	0.916986i	$-0.630615\pi$
$23$	0.938796	−	0.542014i	0.195753	−	0.113018i	0.594673	+	0.803968i	$0.297282\pi$
$24$	−1.71951	−	0.208022i	−0.350994	−	0.0424624i
$25$	3.32250	+	3.69000i	0.664499	+	0.738001i
$26$	−0.704338	−	0.634189i	−0.138132	−	0.124375i
$27$	−2.85327	−	4.34268i	−0.549112	−	0.835749i
$28$	−1.16912	−	2.37343i	−0.220942	−	0.448536i
$29$	−0.413615	−	1.27298i	−0.0768063	−	0.236386i	0.905281	−	0.424814i	$-0.139661\pi$
$29$	−0.413615	−	1.27298i	−0.0768063	−	0.236386i	−0.982087	+	0.188429i	$0.939661\pi$
$30$	0.104362	−	0.304851i	0.0190538	−	0.0556580i
$31$	−4.24813	+	1.89139i	−0.762986	+	0.339703i	−0.751067	−	0.660226i	$-0.770461\pi$
$31$	−4.24813	+	1.89139i	−0.762986	+	0.339703i	−0.0119190	+	0.999929i	$0.503794\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	5.24970	+	2.33252i	0.913856	+	0.406039i
$34$	8.10161			1.38942
$35$	0.477109	−	0.120941i	0.0806462	−	0.0204428i
$36$	2.95255	−	0.531463i	0.492092	−	0.0885772i
$37$	2.32721	−	2.58463i	0.382592	−	0.424911i	−0.520833	−	0.853659i	$-0.674378\pi$
$37$	2.32721	−	2.58463i	0.382592	−	0.424911i	0.903424	+	0.428748i	$0.141045\pi$
$38$	4.89094	−	0.514059i	0.793415	−	0.0833913i
$39$	1.48903	+	0.691121i	0.238436	+	0.110668i
$40$	0.138250	+	0.124481i	0.0218593	+	0.0196822i
$41$	1.18944	−	3.66071i	0.185759	−	0.571707i	−0.814202	−	0.580582i	$-0.802825\pi$
$41$	1.18944	−	3.66071i	0.185759	−	0.571707i	0.999961	+	0.00887490i	$0.00282500\pi$
$42$	3.14434	+	3.33364i	0.485182	+	0.514391i
$43$		−	11.0307i		−	1.68217i	−0.540902	−	0.841085i	$-0.681917\pi$
$43$		−	11.0307i		−	1.68217i	0.540902	−	0.841085i	$-0.318083\pi$
$44$	−2.42792	+	2.25946i	−0.366023	+	0.340627i
$45$	−0.0174909	+	0.557827i	−0.00260739	+	0.0831560i
$46$	−0.440914	−	0.990309i	−0.0650092	−	0.146013i
$47$	0.589942	+	2.77546i	0.0860519	+	0.404842i	1.00000		0.000989776i	$-0.000315056\pi$
$47$	0.589942	+	2.77546i	0.0860519	+	0.404842i	−0.913948	+	0.405832i	$0.866982\pi$
$48$	−0.386621	+	1.68835i	−0.0558039	+	0.243692i
$49$	−1.64025	+	6.80511i	−0.234322	+	0.972159i
$50$	4.01709	−	2.91858i	0.568102	−	0.412750i
$51$	−13.4119	+	4.12657i	−1.87805	+	0.577835i
$52$	−0.704338	+	0.634189i	−0.0976741	+	0.0879461i
$53$	2.35586	+	5.29135i	0.323602	+	0.726822i	0.999952	−	0.00975796i	$-0.00310610\pi$
$53$	2.35586	+	5.29135i	0.323602	+	0.726822i	−0.676350	+	0.736580i	$0.736439\pi$
$54$	−4.61714	+	2.38370i	−0.628313	+	0.324381i
$55$	−0.317243	−	0.529199i	−0.0427770	−	0.0713572i
$56$	−2.48263	+	0.914621i	−0.331756	+	0.122221i
$57$	−7.83494	+	3.34221i	−1.03776	+	0.442687i
$58$	−1.30924	+	0.278287i	−0.171911	+	0.0365409i
$59$	−0.705877	+	3.32089i	−0.0918974	+	0.432343i	0.908013	+	0.418942i	$0.137599\pi$
$59$	−0.705877	+	3.32089i	−0.0918974	+	0.432343i	−0.999910	+	0.0134009i	$0.995734\pi$
$60$	−0.292272	−	0.135656i	−0.0377322	−	0.0175131i
$61$	5.92942	−	13.3177i	0.759185	−	1.70516i	0.0514538	−	0.998675i	$-0.483615\pi$
$61$	5.92942	−	13.3177i	0.759185	−	1.70516i	0.707731	−	0.706482i	$-0.249719\pi$
$62$	1.43698	+	4.42256i	0.182496	+	0.561666i
$63$	−6.90333	−	3.91714i	−0.869738	−	0.493513i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	−0.0881596	−	0.152697i	−0.0109348	−	0.0189397i
$66$	2.86848	−	4.97713i	0.353086	−	0.612642i
$67$	0.0659471	−	0.114224i	0.00805672	−	0.0139547i	−0.861969	−	0.506961i	$-0.830769\pi$
$67$	0.0659471	−	0.114224i	0.00805672	−	0.0139547i	0.870026	+	0.493006i	$0.164102\pi$
$68$	0.846849	−	8.05723i	0.102696	−	0.977083i
$69$	1.23433	+	1.41484i	0.148596	+	0.170327i
$70$	−0.0704074	−	0.487137i	−0.00841529	−	0.0582240i
$71$	−5.19792	−	7.15433i	−0.616880	−	0.849063i	0.380241	−	0.924887i	$-0.375841\pi$
$71$	−5.19792	−	7.15433i	−0.616880	−	0.849063i	−0.997121	+	0.0758247i	$0.975841\pi$
$72$	−0.219926	−	2.99193i	−0.0259186	−	0.352602i
$73$	2.96575	−	13.9527i	0.347115	−	1.63305i	−0.365018	−	0.931000i	$-0.618937\pi$
$73$	2.96575	−	13.9527i	0.347115	−	1.63305i	0.712133	−	0.702045i	$-0.247729\pi$
$74$	−2.32721	−	2.58463i	−0.270533	−	0.300457i
$75$	−5.16356	+	6.87772i	−0.596236	+	0.794171i
$76$		−	4.91788i		−	0.564120i
$77$	8.76157	−	0.484618i	0.998474	−	0.0552273i
$78$	0.842981	−	1.40863i	0.0954488	−	0.159496i
$79$	−12.4597	−	1.30956i	−1.40182	−	0.147337i	−0.626755	−	0.779217i	$-0.715617\pi$
$79$	−12.4597	−	1.30956i	−1.40182	−	0.147337i	−0.775067	+	0.631879i	$0.782284\pi$
$80$	0.138250	−	0.124481i	0.0154568	−	0.0139174i
$81$	6.42936	−	6.29788i	0.714374	−	0.699764i
$82$	−3.51633	−	1.56557i	−0.388314	−	0.172888i
$83$	5.65811	−	4.11086i	0.621058	−	0.451225i	−0.232233	−	0.972660i	$-0.574603\pi$
$83$	5.65811	−	4.11086i	0.621058	−	0.451225i	0.853291	+	0.521435i	$0.174603\pi$
$84$	3.64405	−	2.77865i	0.397598	−	0.303176i
$85$	1.43341	+	0.465742i	0.155475	+	0.0505169i
$86$	−10.9703	−	1.15303i	−1.18296	−	0.124334i
$87$	2.02565	−	1.12756i	0.217172	−	0.120887i
$88$	1.99330	+	2.65080i	0.212486	+	0.282577i
$89$	−1.52736	+	0.881821i	−0.161900	+	0.0934729i	−0.578761	−	0.815497i	$-0.696464\pi$
$89$	−1.52736	+	0.881821i	−0.161900	+	0.0934729i	0.416861	+	0.908970i	$0.363130\pi$
$90$	0.552943	+	0.0757039i	0.0582853	+	0.00797989i
$91$	2.50570	−	0.0973181i	0.262669	−	0.0102017i
$92$	−1.03097	+	0.334983i	−0.107486	+	0.0349244i
$93$	−4.63150	−	6.58946i	−0.480264	−	0.683296i
$94$	2.82192	−	0.296596i	0.291059	−	0.0305915i
$95$	0.894899	+	0.190217i	0.0918147	+	0.0195158i
$96$	1.63869	+	0.560983i	0.167248	+	0.0572551i
$97$	7.39198	+	5.37059i	0.750542	+	0.545301i	0.895995	−	0.444064i	$-0.146464\pi$
$97$	7.39198	+	5.37059i	0.750542	+	0.545301i	−0.145453	+	0.989365i	$0.546464\pi$
$98$	6.59638	+	2.34260i	0.666335	+	0.236638i
$99$	−2.21356	+	9.70052i	−0.222471	+	0.974939i
$100$	−2.48270	−	4.30016i	−0.248270	−	0.430016i
$101$	−8.42077	+	3.74917i	−0.837898	+	0.373056i	−0.780393	−	0.625289i	$-0.784981\pi$
$101$	−8.42077	+	3.74917i	−0.837898	+	0.373056i	−0.0575045	+	0.998345i	$0.518314\pi$
$102$	2.70203	+	13.7698i	0.267541	+	1.36341i
$103$	7.37362	−	8.18923i	0.726544	−	0.806909i	−0.260818	−	0.965388i	$-0.583992\pi$
$103$	7.37362	−	8.18923i	0.726544	−	0.806909i	0.987362	+	0.158479i	$0.0506590\pi$
$104$	0.557091	+	0.766770i	0.0546273	+	0.0751880i
$105$	0.364681	+	0.770576i	0.0355892	+	0.0752005i
$106$	5.50861	−	1.78986i	0.535044	−	0.173846i
$107$	−16.7964	+	3.57019i	−1.62377	+	0.345143i	−0.927844	−	0.372970i	$-0.878340\pi$
$107$	−16.7964	+	3.57019i	−1.62377	+	0.345143i	−0.695927	+	0.718113i	$0.745006\pi$
$108$	1.88802	+	4.84101i	0.181675	+	0.465826i
$109$	−12.9826	−	7.49549i	−1.24351	−	0.717938i	−0.273699	−	0.961815i	$-0.588247\pi$
$109$	−12.9826	−	7.49549i	−1.24351	−	0.717938i	−0.969806	+	0.243877i	$0.921581\pi$
$110$	−0.559461	+	0.260188i	−0.0533425	+	0.0248080i
$111$	5.16910	+	3.09340i	0.490630	+	0.293612i
$112$	0.650104	+	2.56464i	0.0614291	+	0.242335i
$113$	−6.78724	−	2.20531i	−0.638490	−	0.207458i	−0.0281578	−	0.999603i	$-0.508964\pi$
$113$	−6.78724	−	2.20531i	−0.638490	−	0.207458i	−0.610332	+	0.792145i	$0.708964\pi$
$114$	2.50493	+	8.14138i	0.234608	+	0.762510i
$115$	−0.0210798	−	0.200561i	−0.00196570	−	0.0187024i
$116$	0.139910	+	1.33115i	0.0129903	+	0.123594i
$117$	−0.678036	+	2.76131i	−0.0626845	+	0.255283i
$118$	3.22892	+	1.04914i	0.297246	+	0.0965810i
$119$	−15.3606	+	14.9501i	−1.40810	+	1.37047i
$120$	−0.165463	+	0.276492i	−0.0151047	+	0.0252401i
$121$	−3.74119	−	10.3442i	−0.340108	−	0.940386i
$122$	−12.6250	−	7.28902i	−1.14301	−	0.659917i
$123$	6.61858	+	0.800699i	0.596777	+	0.0721966i
$124$	4.54854	−	0.966822i	0.408471	−	0.0868231i
$125$	1.76316	−	0.572886i	0.157702	−	0.0512405i
$126$	−4.61728	+	6.45606i	−0.411340	+	0.575152i
$127$	1.03011	+	1.41783i	0.0914077	+	0.125812i	0.852271	−	0.523100i	$-0.175224\pi$
$127$	1.03011	+	1.41783i	0.0914077	+	0.125812i	−0.760864	+	0.648912i	$0.775224\pi$
$128$	−0.669131	+	0.743145i	−0.0591433	+	0.0656853i
$129$	18.7482	−	3.67895i	1.65069	−	0.323913i
$130$	−0.161076	+	0.0717154i	−0.0141273	+	0.00628986i
$131$	3.60622	+	6.24616i	0.315077	+	0.545729i	0.979454	−	0.201668i	$-0.0646364\pi$
$131$	3.60622	+	6.24616i	0.315077	+	0.545729i	−0.664377	+	0.747398i	$0.731303\pi$
$132$	−4.65003	−	3.37302i	−0.404733	−	0.293584i
$133$	−8.32456	+	10.0000i	−0.721831	+	0.867112i
$134$	−0.106705	−	0.0775255i	−0.00921788	−	0.00669718i
$135$	−0.953937	+	0.156317i	−0.0821018	+	0.0134536i
$136$	−7.92457	−	1.68442i	−0.679527	−	0.144438i
$137$	9.49700	−	0.998175i	0.811383	−	0.0852798i	0.310256	−	0.950653i	$-0.399585\pi$
$137$	9.49700	−	0.998175i	0.811383	−	0.0852798i	0.501128	+	0.865373i	$0.332919\pi$
$138$	1.53611	−	1.07968i	0.130763	−	0.0919085i
$139$	5.10004	−	1.65710i	0.432580	−	0.140554i	−0.0846300	−	0.996412i	$-0.526971\pi$
$139$	5.10004	−	1.65710i	0.432580	−	0.140554i	0.517209	+	0.855859i	$0.326971\pi$
$140$	−0.491828	+	0.0191020i	−0.0415671	+	0.00161441i
$141$	−4.52052	+	1.92835i	−0.380696	+	0.162397i
$142$	−7.65847	+	4.42162i	−0.642684	+	0.371054i
$143$	−1.02038	−	2.97321i	−0.0853283	−	0.248632i
$144$	−2.99853	−	0.0940200i	−0.249877	−	0.00783500i
$145$	−0.247639	−	0.0260280i	−0.0205653	−	0.00216150i
$146$	−13.5663	−	4.40796i	−1.12276	−	0.364805i
$147$	−12.1133	−	0.518207i	−0.999086	−	0.0427410i
$148$	−2.81373	+	2.04430i	−0.231287	+	0.168040i
$149$	12.2038	+	5.43347i	0.999772	+	0.445127i	0.840327	−	0.542080i	$-0.182363\pi$
$149$	12.2038	+	5.43347i	0.999772	+	0.445127i	0.159445	+	0.987207i	$0.449030\pi$
$150$	6.30030	+	5.85419i	0.514418	+	0.477992i
$151$	−0.517635	+	0.466080i	−0.0421245	+	0.0379291i	−0.689924	−	0.723882i	$-0.742356\pi$
$151$	−0.517635	+	0.466080i	−0.0421245	+	0.0379291i	0.647800	+	0.761811i	$0.275689\pi$
$152$	−4.89094	−	0.514059i	−0.396708	−	0.0416957i
$153$	−11.4868	−	21.4191i	−0.928652	−	1.73163i
$154$	0.433871	−	8.76423i	0.0349623	−	0.706242i
$155$			0.865086i			0.0694854i
$156$	−1.31280	−	0.985605i	−0.105108	−	0.0789116i
$157$	−1.78002	−	1.97691i	−0.142061	−	0.157774i	0.667916	−	0.744237i	$-0.267187\pi$
$157$	−1.78002	−	1.97691i	−0.142061	−	0.157774i	−0.809976	+	0.586463i	$0.800520\pi$
$158$	−2.60478	+	12.2545i	−0.207225	+	0.974917i
$159$	−8.20764	+	5.76886i	−0.650909	+	0.457501i
$160$	−0.109348	−	0.150504i	−0.00864471	−	0.0118984i
$161$	2.66341	+	1.06399i	0.209906	+	0.0838538i
$162$	−5.59133	−	7.05245i	−0.439296	−	0.554093i
$163$	−0.557582	+	5.30503i	−0.0436732	+	0.415522i	0.950742	+	0.309983i	$0.100323\pi$
$163$	−0.557582	+	5.30503i	−0.0436732	+	0.415522i	−0.994415	+	0.105539i	$0.966343\pi$
$164$	−1.92455	+	3.33342i	−0.150282	+	0.260296i
$165$	0.793640	−	0.715695i	0.0617848	−	0.0557168i
$166$	−3.49690	−	6.05681i	−0.271412	−	0.470100i
$167$	−12.9631	−	9.41822i	−1.00311	−	0.728804i	−0.0403593	−	0.999185i	$-0.512850\pi$
$167$	−12.9631	−	9.41822i	−1.00311	−	0.728804i	−0.962753	+	0.270381i	$0.912850\pi$
$168$	−2.38253	−	3.91453i	−0.183816	−	0.302013i
$169$	3.73963	+	11.5094i	0.287664	+	0.885339i
$170$	0.613023	−	1.37687i	0.0470167	−	0.105601i
$171$	−8.29364	−	12.2019i	−0.634231	−	0.933100i
$172$	−2.29342	+	10.7897i	−0.174871	+	0.822706i
$173$	18.9964	−	4.03780i	1.44427	−	0.306988i	0.581895	−	0.813264i	$-0.302311\pi$
$173$	18.9964	−	4.03780i	1.44427	−	0.306988i	0.862372	+	0.506276i	$0.168978\pi$
$174$	−0.909641	−	2.13241i	−0.0689597	−	0.161658i
$175$	−2.23061	+	12.9464i	−0.168618	+	0.978658i
$176$	2.84464	−	1.70530i	0.214423	−	0.128542i
$177$	−5.87973	−	0.0921581i	−0.441948	−	0.00692703i
$178$	0.717338	+	1.61117i	0.0537668	+	0.120762i
$179$	8.79765	−	7.92144i	0.657567	−	0.592076i	−0.271298	−	0.962496i	$-0.587453\pi$
$179$	8.79765	−	7.92144i	0.657567	−	0.592076i	0.928865	+	0.370420i	$0.120786\pi$
$180$	0.133087	−	0.542001i	0.00991976	−	0.0403984i
$181$	5.65813	−	4.11087i	0.420565	−	0.305559i	−0.357300	−	0.933990i	$-0.616303\pi$
$181$	5.65813	−	4.11087i	0.420565	−	0.305559i	0.777865	+	0.628431i	$0.216303\pi$
$182$	0.165132	−	2.50215i	0.0122404	−	0.185471i
$183$	24.6128	+	5.63617i	1.81943	+	0.416638i
$184$	0.225382	+	1.06034i	0.0166154	+	0.0781693i
$185$	−0.263166	−	0.591081i	−0.0193484	−	0.0434572i
$186$	−7.03749	+	3.91734i	−0.516014	+	0.287234i
$187$	23.4878	+	13.0507i	1.71760	+	0.954364i
$188$		−	2.83747i		−	0.206943i
$189$	4.35533	−	13.0396i	0.316804	−	0.948491i
$190$	0.282717	−	0.870114i	0.0205105	−	0.0631247i
$191$	8.11838	+	7.30982i	0.587425	+	0.528920i	0.908364	−	0.418180i	$-0.137332\pi$
$191$	8.11838	+	7.30982i	0.587425	+	0.528920i	−0.320939	+	0.947100i	$0.603998\pi$
$192$	0.729200	−	1.57107i	0.0526255	−	0.113382i
$193$	−18.1295	+	1.90548i	−1.30499	+	0.137160i	−0.731379	−	0.681971i	$-0.761123\pi$
$193$	−18.1295	+	1.90548i	−1.30499	+	0.137160i	−0.573607	+	0.819130i	$0.694456\pi$
$194$	6.11384	−	6.79011i	0.438948	−	0.487501i
$195$	0.230126	−	0.200766i	0.0164797	−	0.0143772i
$196$	3.01927	−	6.31538i	0.215662	−	0.451098i
$197$	24.1037			1.71731			0.858657	−	0.512550i	$-0.171299\pi$
$197$	24.1037			1.71731			0.858657	+	0.512550i	$0.171299\pi$
$198$	9.41600	+	3.21541i	0.669166	+	0.228510i
$199$	2.84621	−	4.92977i	0.201762	−	0.349462i	−0.747334	−	0.664448i	$-0.768667\pi$
$199$	2.84621	−	4.92977i	0.201762	−	0.349462i	0.949096	+	0.314986i	$0.102000\pi$
$200$	−4.53611	+	2.01961i	−0.320751	+	0.142808i
$201$	0.216134	+	0.0739905i	0.0152449	+	0.00521889i
$202$	2.84842	+	8.76653i	0.200414	+	0.616811i
$203$	1.96877	−	2.94360i	0.138180	−	0.206600i
$204$	13.9768	−	1.24790i	0.978572	−	0.0873702i
$205$	−0.532138	−	0.479140i	−0.0371662	−	0.0334646i
$206$	−7.37362	−	8.18923i	−0.513744	−	0.570571i
$207$	−1.99304	+	2.56979i	−0.138526	+	0.178613i
$208$	0.820802	−	0.473890i	0.0569124	−	0.0328584i
$209$	15.0077	+	6.38839i	1.03810	+	0.441894i
$210$	0.804474	−	0.282136i	0.0555140	−	0.0194692i
$211$	1.37246	−	1.88903i	0.0944839	−	0.130046i	−0.759158	−	0.650907i	$-0.774389\pi$
$211$	1.37246	−	1.88903i	0.0944839	−	0.130046i	0.853642	+	0.520861i	$0.174389\pi$
$212$	−1.20424	−	5.66553i	−0.0827079	−	0.389110i
$213$	10.4262	−	11.2207i	0.714389	−	0.768829i
$214$	1.79493	+	17.0776i	0.122699	+	1.16740i
$215$	−1.87468	−	0.834660i	−0.127852	−	0.0569233i
$216$	5.01184	−	1.37166i	0.341013	−	0.0933294i
$217$	−10.8856	−	5.73343i	−0.738960	−	0.389211i
$218$	−8.81148	+	12.1280i	−0.596789	+	0.821409i
$219$	24.7037	+	0.387203i	1.66932	+	0.0261647i
$220$	0.200284	+	0.583593i	0.0135031	+	0.0393458i
$221$	6.64982	+	3.83927i	0.447315	+	0.258258i
$222$	3.61677	−	4.81744i	0.242742	−	0.323325i
$223$	−2.68030	+	8.24911i	−0.179486	+	0.552401i	−0.999810	−	0.0194982i	$-0.993793\pi$
$223$	−2.68030	+	8.24911i	−0.179486	+	0.552401i	0.820324	+	0.571899i	$0.193793\pi$
$224$	2.61854	−	0.378465i	0.174959	−	0.0252873i
$225$	−13.4118	−	6.48233i	−0.894118	−	0.432155i
$226$	−2.90269	+	6.51954i	−0.193084	+	0.433674i
$227$	−21.8962	−	4.65419i	−1.45330	−	0.308909i	−0.587472	−	0.809244i	$-0.699877\pi$
$227$	−21.8962	−	4.65419i	−1.45330	−	0.308909i	−0.865832	+	0.500335i	$0.833210\pi$
$228$	8.35861	−	1.64020i	0.553563	−	0.108625i
$229$	−1.79470	+	17.0755i	−0.118597	+	1.12838i	0.759703	+	0.650270i	$0.225344\pi$
$229$	−1.79470	+	17.0755i	−0.118597	+	1.12838i	−0.878301	+	0.478109i	$0.841322\pi$
$230$	−0.201666			−0.0132975
$231$	3.74582	+	14.7299i	0.246457	+	0.969154i
$232$	1.33849			0.0878759
$233$	1.39522	−	13.2746i	0.0914036	−	0.869647i	−0.848727	−	0.528832i	$-0.822630\pi$
$233$	1.39522	−	13.2746i	0.0914036	−	0.869647i	0.940130	−	0.340815i	$-0.110703\pi$
$234$	2.67531	+	0.962958i	0.174891	+	0.0629505i
$235$	0.516329	+	0.109749i	0.0336816	+	0.00715925i
$236$	1.38090	−	3.10156i	0.0898892	−	0.201895i
$237$	−1.92974	−	21.6137i	−0.125350	−	1.40396i
$238$	13.2626	+	16.8391i	0.859687	+	1.09152i
$239$	6.91610	−	21.2856i	0.447365	−	1.37685i	−0.432504	−	0.901632i	$-0.642370\pi$
$239$	6.91610	−	21.2856i	0.447365	−	1.37685i	0.879869	−	0.475217i	$-0.157630\pi$
$240$	0.257681	+	0.193458i	0.0166333	+	0.0124877i
$241$	15.7983	+	9.12117i	1.01766	+	0.587546i	0.913425	−	0.407007i	$-0.133427\pi$
$241$	15.7983	+	9.12117i	1.01766	+	0.587546i	0.104234	+	0.994553i	$0.466761\pi$
$242$	−10.6786	+	2.63943i	−0.686449	+	0.169669i
$243$	12.8484	+	8.82713i	0.824226	+	0.566260i
$244$	−8.56876	+	11.7939i	−0.548559	+	0.755026i
$245$	1.03242	+	0.793682i	0.0659588	+	0.0507065i
$246$	1.48814	−	6.49863i	0.0948805	−	0.414337i
$247$	4.25810	+	1.89583i	0.270936	+	0.120629i
$248$	−0.486074	−	4.62468i	−0.0308657	−	0.293668i
$249$	8.87404	+	8.24569i	0.562370	+	0.522549i
$250$	−0.385447	−	1.81339i	−0.0243778	−	0.114689i
$251$	−6.49573	+	8.94061i	−0.410007	+	0.564326i	−0.963220	−	0.268713i	$-0.913402\pi$
$251$	−6.49573	+	8.94061i	−0.410007	+	0.564326i	0.553213	+	0.833040i	$0.313402\pi$
$252$	5.93806	+	5.26683i	0.374063	+	0.331779i
$253$	0.316995	−	3.58131i	0.0199293	−	0.225155i
$254$	1.51774	−	0.876266i	0.0952313	−	0.0549818i
$255$	−0.313526	+	2.59161i	−0.0196337	+	0.162293i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	−9.59065	−	8.63546i	−0.598248	−	0.538665i	0.313408	−	0.949619i	$-0.398529\pi$
$257$	−9.59065	−	8.63546i	−0.598248	−	0.538665i	−0.911656	+	0.410953i	$0.865196\pi$
$258$	−1.69907	−	19.0301i	−0.105779	−	1.18476i
$259$	9.18186	+	0.605968i	0.570533	+	0.0376530i
$260$	0.0544856	+	0.167689i	0.00337905	+	0.0103997i
$261$	2.59202	+	3.06681i	0.160442	+	0.189831i
$262$	6.58889	−	2.93356i	0.407063	−	0.181236i
$263$	11.5982	−	20.0886i	0.715174	−	1.23872i	−0.247718	−	0.968832i	$-0.579681\pi$
$263$	11.5982	−	20.0886i	0.715174	−	1.23872i	0.962892	−	0.269886i	$-0.0869860\pi$
$264$	−3.84060	+	4.27198i	−0.236373	+	0.262922i
$265$	1.07753			0.0661919
$266$	9.07509	+	9.32425i	0.556430	+	0.571706i
$267$	−2.00818	−	2.30185i	−0.122898	−	0.140871i
$268$	−0.0882545	+	0.0980165i	−0.00539100	+	0.00598731i
$269$	12.2454	−	1.28705i	0.746617	−	0.0784726i	0.276423	−	0.961036i	$-0.410851\pi$
$269$	12.2454	−	1.28705i	0.746617	−	0.0784726i	0.470194	+	0.882563i	$0.344184\pi$
$270$	0.0557473	+	0.965051i	0.00339267	+	0.0587311i
$271$	−17.2056	−	15.4920i	−1.04516	−	0.941070i	−0.0468380	−	0.998903i	$-0.514914\pi$
$271$	−17.2056	−	15.4920i	−1.04516	−	0.941070i	−0.998326	+	0.0578324i	$0.981581\pi$
$272$	−2.50354	+	7.70509i	−0.151799	+	0.467190i
$273$	1.00110	+	4.22633i	0.0605894	+	0.255789i
$274$		−	9.54931i		−	0.576895i
$275$	16.3476	−	1.99036i	0.985799	−	0.120023i
$276$	−0.913198	−	1.64056i	−0.0549680	−	0.0987499i
$277$	−5.39464	−	12.1166i	−0.324133	−	0.728014i	0.675826	−	0.737061i	$-0.263787\pi$
$277$	−5.39464	−	12.1166i	−0.324133	−	0.728014i	−0.999959	+	0.00904683i	$0.997120\pi$
$278$	−1.11493	−	5.24531i	−0.0668688	−	0.314593i
$279$	9.65501	−	10.0696i	0.578030	−	0.602850i
$280$	−0.0324128	+	0.491131i	−0.00193703	+	0.0293507i
$281$	−9.80903	+	7.12668i	−0.585158	+	0.425142i	−0.840580	−	0.541688i	$-0.817786\pi$
$281$	−9.80903	+	7.12668i	−0.585158	+	0.425142i	0.255422	+	0.966830i	$0.417786\pi$
$282$	1.44527	+	4.69732i	0.0860644	+	0.279721i
$283$	−14.5634	+	13.1129i	−0.865704	+	0.779484i	−0.976761	−	0.214330i	$-0.931243\pi$
$283$	−14.5634	+	13.1129i	−0.865704	+	0.779484i	0.111057	+	0.993814i	$0.464576\pi$
$284$	3.59687	+	8.07870i	0.213435	+	0.479383i
$285$	−0.0248344	+	1.58444i	−0.00147106	+	0.0938544i
$286$	−3.06358	+	0.704003i	−0.181153	+	0.0416286i
$287$	9.55591	−	3.52047i	0.564067	−	0.207807i
$288$	−0.406936	+	2.97227i	−0.0239790	+	0.175143i
$289$	−47.5733	+	10.1120i	−2.79843	+	0.594825i
$290$	−0.0517708	+	0.243562i	−0.00304008	+	0.0143025i
$291$	−6.66269	+	14.3549i	−0.390574	+	0.841498i
$292$	−5.80188	+	13.0312i	−0.339529	+	0.762595i
$293$	5.72859	+	17.6308i	0.334668	+	1.03000i	0.966885	+	0.255211i	$0.0821449\pi$
$293$	5.72859	+	17.6308i	0.334668	+	1.03000i	−0.632217	+	0.774791i	$0.717855\pi$
$294$	−1.78155	+	11.9928i	−0.103902	+	0.699431i
$295$	0.510975	+	0.371245i	0.0297501	+	0.0216147i
$296$	1.73898	+	3.01201i	0.101076	+	0.175069i
$297$	−17.2256	−	0.526949i	−0.999532	−	0.0305767i
$298$	6.67935	−	11.5690i	0.386924	−	0.670172i
$299$	0.107395	−	1.02179i	0.00621080	−	0.0590918i
$300$	6.48068	−	5.65386i	0.374162	−	0.326426i
$301$	22.9273	−	18.0577i	1.32151	−	1.04083i
$302$	0.409420	+	0.563518i	0.0235594	+	0.0324268i
$303$	−9.18070	−	13.0618i	−0.527417	−	0.750383i
$304$	−1.02248	+	4.81041i	−0.0586435	+	0.275896i
$305$	−1.81469	−	2.01541i	−0.103909	−	0.115402i
$306$	−22.5025	+	9.18495i	−1.28638	+	0.525069i
$307$			13.5211i			0.771687i	0.922564	+	0.385844i	$0.126090\pi$
$307$			13.5211i			0.771687i	−0.922564	+	0.385844i	$0.873910\pi$
$308$	−8.67087	−	1.34761i	−0.494069	−	0.0767870i
$309$	16.3780	+	9.80122i	0.931709	+	0.557572i
$310$	0.860347	+	0.0904261i	0.0488644	+	0.00513586i
$311$	−5.26865	+	4.74391i	−0.298758	+	0.269003i	−0.804852	−	0.593476i	$-0.797755\pi$
$311$	−5.26865	+	4.74391i	−0.298758	+	0.269003i	0.506094	+	0.862478i	$0.331089\pi$
$312$	−1.11743	+	1.20258i	−0.0632621	+	0.0680829i
$313$	17.8652	+	7.95408i	1.00980	+	0.449591i	0.843871	−	0.536547i	$-0.180271\pi$
$313$	17.8652	+	7.95408i	1.00980	+	0.449591i	0.165928	+	0.986138i	$0.446938\pi$
$314$	−2.15214	+	1.56362i	−0.121452	+	0.0882403i
$315$	−1.18807	+	0.876826i	−0.0669403	+	0.0494036i
$316$	11.9151	+	3.87145i	0.670277	+	0.217786i
$317$	18.0462	+	1.89673i	1.01358	+	0.106531i	0.596727	−	0.802444i	$-0.296467\pi$
$317$	18.0462	+	1.89673i	1.01358	+	0.106531i	0.416850	+	0.908975i	$0.363134\pi$
$318$	4.87933	+	8.76569i	0.273619	+	0.491556i
$319$	−4.24396	−	1.30223i	−0.237616	−	0.0729108i
$320$	−0.161110	+	0.0930169i	−0.00900632	+	0.00519980i
$321$	−11.6699	−	27.3571i	−0.651352	−	1.52692i
$322$	1.33656	−	2.53760i	0.0744835	−	0.141415i
$323$	−37.8927	+	12.3121i	−2.10841	+	0.685063i
$324$	−7.59827	+	4.82352i	−0.422126	+	0.267973i
$325$	4.68032	−	0.491921i	0.259617	−	0.0272869i
$326$	5.21769	+	1.10905i	0.288981	+	0.0614248i
$327$	8.40969	−	24.5655i	0.465057	−	1.35848i
$328$	3.11399	+	2.26244i	0.171941	+	0.124923i
$329$	−4.80302	+	5.76971i	−0.264799	+	0.318094i
$330$	−0.628816	−	0.864103i	−0.0346152	−	0.0475673i
$331$	6.63676	+	11.4952i	0.364789	+	0.631834i	0.988742	−	0.149628i	$-0.0478077\pi$
$331$	6.63676	+	11.4952i	0.364789	+	0.631834i	−0.623953	+	0.781462i	$0.714474\pi$
$332$	−6.38916	+	2.84464i	−0.350651	+	0.156120i
$333$	−3.53366	+	9.81730i	−0.193643	+	0.537985i
$334$	−10.7216	+	11.9076i	−0.586662	+	0.651554i
$335$	−0.0144224	−	0.0198507i	−0.000787978	−	0.00108456i
$336$	−4.14213	+	1.96029i	−0.225972	+	0.106943i
$337$	7.44549	−	2.41919i	0.405582	−	0.131781i	−0.0991196	−	0.995076i	$-0.531603\pi$
$337$	7.44549	−	2.41919i	0.405582	−	0.131781i	0.504701	+	0.863294i	$0.331603\pi$
$338$	11.8373	−	2.51609i	0.643862	−	0.136857i
$339$	1.48456	−	12.2714i	0.0806301	−	0.666489i
$340$	−1.30525	−	0.753587i	−0.0707872	−	0.0408690i
$341$	−2.95821	+	15.1365i	−0.160196	+	0.819685i
$342$	−13.0019	+	6.97277i	−0.703065	+	0.377044i
$343$	−16.8295	+	7.73094i	−0.908708	+	0.417431i
$344$	10.4908	+	3.40868i	0.565629	+	0.183784i
$345$	0.333851	−	0.102719i	0.0179739	−	0.00553020i
$346$	−2.03002	−	19.3144i	−0.109135	−	1.03835i
$347$	1.48856	+	14.1627i	0.0799101	+	0.760294i	0.958956	+	0.283556i	$0.0915142\pi$
$347$	1.48856	+	14.1627i	0.0799101	+	0.760294i	−0.879046	+	0.476738i	$0.841819\pi$
$348$	−2.21581	+	0.681760i	−0.118780	+	0.0365461i
$349$	6.82596	+	2.21789i	0.365385	+	0.118721i	0.485955	−	0.873984i	$-0.338472\pi$
$349$	6.82596	+	2.21789i	0.365385	+	0.118721i	−0.120569	+	0.992705i	$0.538472\pi$
$350$	12.6423	+	3.57166i	0.675762	+	0.190913i
$351$	−4.91937	−	0.231468i	−0.262576	−	0.0123548i
$352$	−1.39861	−	3.00731i	−0.0745461	−	0.160290i
$353$	4.73455	+	2.73349i	0.251995	+	0.145489i	0.620677	−	0.784066i	$-0.286858\pi$
$353$	4.73455	+	2.73349i	0.251995	+	0.145489i	−0.368683	+	0.929555i	$0.620191\pi$
$354$	−0.706253	+	5.83789i	−0.0375369	+	0.310280i
$355$	−1.60919	+	0.342044i	−0.0854070	+	0.0181538i
$356$	1.67732	−	0.544995i	0.0888980	−	0.0288847i
$357$	−30.5328	−	21.1213i	−1.61597	−	1.11786i
$358$	−6.95844	−	9.57747i	−0.367765	−	0.506185i
$359$	−12.8504	+	14.2718i	−0.678219	+	0.753239i	−0.979752	−	0.200217i	$-0.935835\pi$
$359$	−12.8504	+	14.2718i	−0.678219	+	0.753239i	0.301532	+	0.953456i	$0.402502\pi$
$360$	−0.525120	−	0.189013i	−0.0276763	−	0.00996186i
$361$	−4.73724	+	2.10916i	−0.249328	+	0.111008i
$362$	−3.49691	−	6.05683i	−0.183794	−	0.318340i
$363$	16.3337	−	9.80866i	0.857298	−	0.514821i
$364$	−2.47118	−	0.425773i	−0.129525	−	0.0223166i
$365$	−2.14687	−	1.55979i	−0.112372	−	0.0816431i
$366$	8.17804	−	23.8889i	0.427473	−	1.24869i
$367$	−16.2502	−	3.45408i	−0.848252	−	0.180302i	−0.236776	−	0.971564i	$-0.576091\pi$
$367$	−16.2502	−	3.45408i	−0.848252	−	0.180302i	−0.611476	+	0.791263i	$0.709424\pi$
$368$	1.07809	−	0.113312i	0.0561993	−	0.00590679i
$369$	0.846519	+	11.5162i	0.0440680	+	0.599511i
$370$	−0.615352	+	0.199940i	−0.0319906	+	0.0103944i
$371$	−7.14140	+	13.5587i	−0.370763	+	0.703934i
$372$	3.16027	+	7.40841i	0.163852	+	0.384108i
$373$	8.68414	−	5.01379i	0.449648	−	0.259604i	−0.258034	−	0.966136i	$-0.583075\pi$
$373$	8.68414	−	5.01379i	0.449648	−	0.259604i	0.707681	+	0.706532i	$0.249741\pi$
$374$	15.4344	−	21.9949i	0.798093	−	1.13733i
$375$	1.56175	+	2.80567i	0.0806482	+	0.144884i
$376$	−2.82192	−	0.296596i	−0.145529	−	0.0152958i
$377$	−1.20650	−	0.392016i	−0.0621380	−	0.0201898i
$378$	−12.5129	−	5.69448i	−0.643595	−	0.292893i
$379$	−27.2351	+	19.7875i	−1.39897	+	1.01641i	−0.404160	+	0.914688i	$0.632436\pi$
$379$	−27.2351	+	19.7875i	−1.39897	+	1.01641i	−0.994813	+	0.101725i	$0.967564\pi$
$380$	−0.835795	−	0.372120i	−0.0428754	−	0.0190894i
$381$	−2.06623	+	2.22369i	−0.105856	+	0.113923i
$382$	8.11838	−	7.30982i	0.415373	−	0.374003i
$383$	−19.5058	−	2.05014i	−0.996699	−	0.104757i	−0.407891	−	0.913031i	$-0.633736\pi$
$383$	−19.5058	−	2.05014i	−0.996699	−	0.104757i	−0.588807	+	0.808273i	$0.700402\pi$
$384$	−1.48624	−	0.889427i	−0.0758445	−	0.0453884i
$385$	0.580599	−	1.52570i	0.0295901	−	0.0777569i
$386$			18.2293i			0.927848i
$387$	12.5057	+	30.6382i	0.635703	+	1.55743i
$388$	−6.11384	−	6.79011i	−0.310383	−	0.344716i
$389$	7.27976	−	34.2486i	0.369099	−	1.73647i	−0.265938	−	0.963990i	$-0.585682\pi$
$389$	7.27976	−	34.2486i	0.369099	−	1.73647i	0.635037	−	0.772482i	$-0.280985\pi$
$390$	−0.175612	−	0.249852i	−0.00889245	−	0.0126517i
$391$	5.16215	+	7.10510i	0.261061	+	0.359320i
$392$	−5.96518	−	3.66287i	−0.301287	−	0.185003i
$393$	−9.41346	+	8.21247i	−0.474846	+	0.414264i
$394$	2.51952	−	23.9716i	0.126931	−	1.20767i
$395$	−1.16534	+	2.01843i	−0.0586348	+	0.101558i
$396$	4.18204	−	9.02832i	0.210155	−	0.453690i
$397$	−18.5110	−	32.0620i	−0.929040	−	1.60915i	−0.784931	−	0.619584i	$-0.787302\pi$
$397$	−18.5110	−	32.0620i	−0.929040	−	1.60915i	−0.144110	−	0.989562i	$-0.546032\pi$
$398$	−4.60526	−	3.34592i	−0.230841	−	0.167716i
$399$	−19.7728	−	10.8135i	−0.989878	−	0.541354i
$400$	1.53439	+	4.72237i	0.0767195	+	0.236118i
$401$	1.65249	−	3.71156i	0.0825215	−	0.185346i	−0.867572	−	0.497312i	$-0.834321\pi$
$401$	1.65249	−	3.71156i	0.0825215	−	0.185346i	0.950094	+	0.311965i	$0.100987\pi$
$402$	0.0961773	−	0.207215i	0.00479689	−	0.0103350i
$403$	−0.916334	+	4.31101i	−0.0456459	+	0.214747i
$404$	9.01625	−	1.91646i	0.448575	−	0.0953476i
$405$	−0.583838	−	1.56921i	−0.0290111	−	0.0779748i
$406$	−2.72168	−	2.26567i	−0.135075	−	0.112443i
$407$	−2.58340	−	11.2421i	−0.128055	−	0.557250i
$408$	0.219915	−	14.0307i	0.0108874	−	0.694622i
$409$	8.28475	+	18.6079i	0.409655	+	0.920099i	0.994080	+	0.108652i	$0.0346533\pi$
$409$	8.28475	+	18.6079i	0.409655	+	0.920099i	−0.584425	+	0.811448i	$0.698680\pi$
$410$	−0.532138	+	0.479140i	−0.0262804	+	0.0236630i
$411$	4.86395	+	15.8085i	0.239921	+	0.779778i
$412$	−8.91512	+	6.47722i	−0.439217	+	0.319110i
$413$	−8.05799	+	3.96925i	−0.396508	+	0.195314i
$414$	2.34739	+	2.25074i	0.115368	+	0.110618i
$415$	−0.270511	−	1.27265i	−0.0132788	−	0.0624721i
$416$	−0.385497	−	0.865840i	−0.0189005	−	0.0424513i
$417$	4.51743	+	8.11554i	0.221219	+	0.397420i
$418$	7.92212	−	14.2577i	0.387484	−	0.697365i
$419$		−	9.94577i		−	0.485883i	−0.970041	−	0.242941i	$-0.921888\pi$
$419$		−	9.94577i		−	0.485883i	0.970041	−	0.242941i	$-0.0781123\pi$
$420$	−0.196500	−	0.829559i	−0.00958822	−	0.0404783i
$421$	−2.87160	+	8.83787i	−0.139953	+	0.430731i	−0.996328	−	0.0856240i	$-0.972712\pi$
$421$	−2.87160	+	8.83787i	−0.139953	+	0.430731i	0.856374	+	0.516355i	$0.172712\pi$
$422$	−1.73522	−	1.56240i	−0.0844691	−	0.0760563i
$423$	−4.78517	−	7.04010i	−0.232663	−	0.342301i
$424$	−5.76037	+	0.605439i	−0.279748	+	0.0294027i
$425$	−26.9176	+	29.8950i	−1.30569	+	1.45012i
$426$	−10.0694	−	11.5419i	−0.487863	−	0.559208i
$427$	37.3874	−	9.47725i	1.80930	−	0.458636i
$428$	17.1717			0.830023
$429$	4.71307	−	2.72589i	0.227549	−	0.131607i
$430$	−1.02604	+	1.77716i	−0.0494802	+	0.0857023i
$431$	−15.7282	+	7.00265i	−0.757601	+	0.337306i	−0.748923	−	0.662657i	$-0.769429\pi$
$431$	−15.7282	+	7.00265i	−0.757601	+	0.337306i	−0.00867770	+	0.999962i	$0.502762\pi$
$432$	−0.840263	−	5.12776i	−0.0404272	−	0.246710i
$433$	3.77437	+	11.6163i	0.181384	+	0.558244i	0.999867	−	0.0162869i	$-0.00518452\pi$
$433$	3.77437	+	11.6163i	0.181384	+	0.558244i	−0.818483	+	0.574531i	$0.805185\pi$
$434$	−6.83988	+	10.2266i	−0.328325	+	0.490893i
$435$	−0.0383541	−	0.429578i	−0.00183894	−	0.0205967i
$436$	11.1405	+	10.0309i	0.533532	+	0.480394i
$437$	3.56722	+	3.96180i	0.170643	+	0.189518i
$438$	2.96732	−	24.5279i	0.141784	−	1.17199i
$439$	14.1328	−	8.15957i	0.674522	−	0.389435i	−0.123266	−	0.992374i	$-0.539337\pi$
$439$	14.1328	−	8.15957i	0.674522	−	0.389435i	0.797788	+	0.602938i	$0.206004\pi$
$440$	0.601331	−	0.138184i	0.0286673	−	0.00658768i
$441$	−3.15923	−	20.7610i	−0.150440	−	0.988619i
$442$	4.51334	−	6.21208i	0.214678	−	0.295478i
$443$	−2.69115	−	12.6609i	−0.127860	−	0.601536i	−0.994689	−	0.102929i	$-0.967178\pi$
$443$	−2.69115	−	12.6609i	−0.127860	−	0.601536i	0.866828	−	0.498607i	$-0.166155\pi$
$444$	−4.41299	−	4.10052i	−0.209431	−	0.194602i
$445$	0.0342955	+	0.326300i	0.00162576	+	0.0154681i
$446$	7.92375	+	3.52788i	0.375200	+	0.167050i
$447$	−5.16475	+	22.5541i	−0.244284	+	1.06677i
$448$	−0.102680	−	2.64376i	−0.00485117	−	0.124906i
$449$	−5.60450	+	7.71394i	−0.264493	+	0.364043i	−0.920521	−	0.390693i	$-0.872235\pi$
$449$	−5.60450	+	7.71394i	−0.264493	+	0.364043i	0.656028	+	0.754737i	$0.272235\pi$
$450$	−7.84873	+	12.6607i	−0.369993	+	0.596831i
$451$	−7.67241	−	10.2032i	−0.361280	−	0.480450i
$452$	6.18042	+	3.56826i	0.290702	+	0.167837i
$453$	−0.964808	−	0.724345i	−0.0453306	−	0.0340327i
$454$	−6.91747	+	21.2898i	−0.324653	+	0.999179i
$455$	0.173059	−	0.433208i	0.00811313	−	0.0203091i
$456$	−0.757504	−	8.48427i	−0.0354734	−	0.397312i
$457$	−1.70037	+	3.81910i	−0.0795401	+	0.178650i	−0.948938	−	0.315463i	$-0.897840\pi$
$457$	−1.70037	+	3.81910i	−0.0795401	+	0.178650i	0.869398	+	0.494113i	$0.164507\pi$
$458$	16.7943	+	3.56974i	0.784747	+	0.166803i
$459$	32.5737	−	26.6670i	1.52041	−	1.24471i
$460$	−0.0210798	+	0.200561i	−0.000982852	+	0.00935121i
$461$	33.7485			1.57183			0.785913	−	0.618337i	$-0.212193\pi$
$461$	33.7485			1.57183			0.785913	+	0.618337i	$0.212193\pi$
$462$	15.0407	−	2.18561i	0.699757	−	0.101684i
$463$	17.5992			0.817905			0.408952	−	0.912556i	$-0.365894\pi$
$463$	17.5992			0.817905			0.408952	+	0.912556i	$0.365894\pi$
$464$	0.139910	−	1.33115i	0.00649515	−	0.0617972i
$465$	−1.47033	+	0.288522i	−0.0681850	+	0.0133799i
$466$	−13.0560	−	2.77514i	−0.604809	−	0.128556i
$467$	3.63202	−	8.15766i	0.168070	−	0.377491i	−0.809800	−	0.586707i	$-0.800424\pi$
$467$	3.63202	−	8.15766i	0.168070	−	0.377491i	0.977870	+	0.209215i	$0.0670909\pi$
$468$	1.23733	−	2.56000i	0.0571955	−	0.118336i
$469$	0.345371	−	0.0499174i	0.0159477	−	0.00230497i
$470$	0.163119	−	0.502029i	0.00752412	−	0.0231569i
$471$	2.76636	−	3.68471i	0.127467	−	0.169783i
$472$	−2.94023	−	1.69754i	−0.135335	−	0.0781357i
$473$	−29.9472	−	21.0146i	−1.37697	−	0.966254i
$474$	−21.6970	−	0.340075i	−0.996575	−	0.0156202i
$475$	−14.3532	+	19.7556i	−0.658572	+	0.906447i
$476$	18.1332	−	11.4298i	0.831134	−	0.523883i
$477$	−12.5424	−	12.0260i	−0.574276	−	0.550633i
$478$	−20.4460	−	9.10316i	−0.935180	−	0.416369i
$479$	−1.11850	−	10.6418i	−0.0511053	−	0.486235i	−0.989901	−	0.141760i	$-0.954724\pi$
$479$	−1.11850	−	10.6418i	−0.0511053	−	0.486235i	0.938796	−	0.344475i	$-0.111943\pi$
$480$	0.219334	−	0.236048i	0.0100112	−	0.0107741i
$481$	−0.685349	−	3.22431i	−0.0312492	−	0.147016i
$482$	10.7226	−	14.7584i	0.488400	−	0.672225i
$483$	−0.920093	+	4.88169i	−0.0418657	+	0.222125i
$484$	1.50874	+	10.8960i	0.0685793	+	0.495275i
$485$	1.47206	−	0.849895i	0.0668428	−	0.0385917i
$486$	10.1218	−	11.8553i	0.459134	−	0.537769i
$487$	−18.2777	−	20.2994i	−0.828241	−	0.919854i	0.169602	−	0.985513i	$-0.445752\pi$
$487$	−18.2777	−	20.2994i	−0.828241	−	0.919854i	−0.997842	+	0.0656584i	$0.979085\pi$
$488$	10.8336	+	9.75461i	0.490414	+	0.441571i
$489$	−9.20260	+	0.821638i	−0.416156	+	0.0371558i
$490$	0.897252	−	0.943800i	0.0405337	−	0.0426366i
$491$	−2.66387	−	8.19855i	−0.120219	−	0.369995i	0.872781	−	0.488112i	$-0.162314\pi$
$491$	−2.66387	−	8.19855i	−0.120219	−	0.369995i	−0.993000	+	0.118117i	$0.962314\pi$
$492$	−6.30747	−	2.15928i	−0.284363	−	0.0973479i
$493$	9.90639	−	4.41061i	0.446161	−	0.198644i
$494$	2.33053	−	4.03660i	0.104856	−	0.181615i
$495$	1.48111	+	1.11020i	0.0665711	+	0.0498999i
$496$	−4.65016			−0.208798
$497$	6.36104	−	22.5157i	0.285332	−	1.00997i
$498$	9.12810	−	7.96352i	0.409040	−	0.356854i
$499$	8.40530	−	9.33503i	0.376273	−	0.417893i	−0.525029	−	0.851084i	$-0.675946\pi$
$499$	8.40530	−	9.33503i	0.376273	−	0.417893i	0.901302	+	0.433191i	$0.142612\pi$
$500$	−1.84374	+	0.193785i	−0.0824547	+	0.00866634i
$501$	11.6841	−	25.1737i	0.522009	−	1.12468i
$502$	8.21265	+	7.39470i	0.366548	+	0.330042i
$503$	3.33866	−	10.2753i	0.148864	−	0.458155i	−0.848624	−	0.528996i	$-0.822568\pi$
$503$	3.33866	−	10.2753i	0.148864	−	0.458155i	0.997488	+	0.0708415i	$0.0225685\pi$
$504$	5.85867	−	5.35500i	0.260966	−	0.238530i
$505$			1.71480i			0.0763076i
$506$	−3.52856	−	0.689608i	−0.156864	−	0.0306568i
$507$	−18.3146	+	10.1946i	−0.813379	+	0.452759i
$508$	−0.712819	−	1.60102i	−0.0316262	−	0.0710336i
$509$	6.67417	+	31.3995i	0.295827	+	1.39176i	0.835318	+	0.549767i	$0.185284\pi$
$509$	6.67417	+	31.3995i	0.295827	+	1.39176i	−0.539491	+	0.841992i	$0.681383\pi$
$510$	2.54464	+	0.582705i	0.112678	+	0.0258026i
$511$	33.8557	−	16.6768i	1.49769	−	0.737739i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	17.9727	−	18.1657i	0.793512	−	0.802036i
$514$	−9.59065	+	8.63546i	−0.423025	+	0.380894i
$515$	−0.833825	−	1.87280i	−0.0367427	−	0.0825255i
$516$	−19.1034	−	0.299425i	−0.840982	−	0.0131814i
$517$	8.65895	+	3.68590i	0.380820	+	0.162106i
$518$	1.56241	−	9.06822i	0.0686485	−	0.398435i
$519$	13.1984	+	30.9402i	0.579347	+	1.35813i
$520$	0.172466	−	0.0366588i	0.00756314	−	0.00160759i
$521$	−5.68170	+	26.7303i	−0.248920	+	1.17108i	0.659069	+	0.752082i	$0.270950\pi$
$521$	−5.68170	+	26.7303i	−0.248920	+	1.17108i	−0.907989	+	0.418994i	$0.862383\pi$
$522$	3.32095	−	2.25726i	0.145354	−	0.0987974i
$523$	2.09602	−	4.70774i	0.0916526	−	0.205855i	−0.861902	−	0.507074i	$-0.830727\pi$
$523$	2.09602	−	4.70774i	0.0916526	−	0.205855i	0.953555	+	0.301219i	$0.0973936\pi$
$524$	−2.22877	−	6.85944i	−0.0973641	−	0.299656i
$525$	−22.7482	+	0.526637i	−0.992812	+	0.0229843i
$526$	−18.7662	−	13.6345i	−0.818247	−	0.594491i
$527$	−18.8369	−	32.6264i	−0.820547	−	1.42123i
$528$	3.84712	+	4.26611i	0.167424	+	0.185658i
$529$	−10.9124	+	18.9009i	−0.474454	+	0.821778i
$530$	0.112632	−	1.07162i	0.00489243	−	0.0465483i
$531$	−1.80436	−	10.0241i	−0.0783026	−	0.435011i
$532$	10.2218	−	8.05073i	0.443170	−	0.349043i
$533$	−2.14430	−	2.95138i	−0.0928799	−	0.127838i
$534$	−2.49915	+	1.75657i	−0.108149	+	0.0760141i
$535$	−0.664176	+	3.12470i	−0.0287148	+	0.135093i
$536$	0.0882545	+	0.0980165i	0.00381201	+	0.00423367i
$537$	16.3977	+	12.3109i	0.707615	+	0.531253i
$538$		−	12.3129i		−	0.530846i
$539$	15.3502	+	17.4175i	0.661182	+	0.750226i
$540$	0.965592	+	0.0454334i	0.0415524	+	0.00195514i
$541$	11.1340	+	1.17023i	0.478689	+	0.0503122i	0.340801	−	0.940136i	$-0.389302\pi$
$541$	11.1340	+	1.17023i	0.478689	+	0.0503122i	0.137888	+	0.990448i	$0.455969\pi$
$542$	−17.2056	+	15.4920i	−0.739043	+	0.665437i
$543$	8.87407	+	8.24571i	0.380823	+	0.353857i
$544$	7.40119	+	3.29522i	0.317324	+	0.141282i
$545$	−2.25621	+	1.63923i	−0.0966455	+	0.0702170i
$546$	4.30782	−	0.553846i	0.184358	−	0.0237024i
$547$	−25.1284	−	8.16471i	−1.07441	−	0.349098i	−0.282208	−	0.959353i	$-0.591067\pi$
$547$	−25.1284	−	8.16471i	−1.07441	−	0.349098i	−0.792205	+	0.610256i	$0.791067\pi$
$548$	−9.49700	−	0.998175i	−0.405692	−	0.0426399i
$549$	−1.37063	+	43.7126i	−0.0584970	+	1.86561i
$550$	−0.270666	−	16.4661i	−0.0115412	−	0.702118i
$551$	5.70062	−	3.29126i	0.242855	−	0.140212i
$552$	−1.72702	+	0.736710i	−0.0735070	+	0.0313565i
$553$	−17.6749	−	28.0411i	−0.751615	−	1.19243i
$554$	−12.6141	+	4.09857i	−0.535921	+	0.174131i
$555$	0.916853	−	0.644424i	0.0389182	−	0.0273543i
$556$	−5.33312	+	0.560534i	−0.226175	+	0.0237719i
$557$	−26.6377	−	5.66202i	−1.12868	−	0.239907i	−0.394519	−	0.918888i	$-0.629089\pi$
$557$	−26.6377	−	5.66202i	−1.12868	−	0.239907i	−0.734156	+	0.678980i	$0.762422\pi$
$558$	−9.00519	−	10.6547i	−0.381220	−	0.451048i
$559$	−8.45804	−	6.14512i	−0.357737	−	0.259911i
$560$	0.485052	+	0.0835723i	0.0204972	+	0.00353158i
$561$	−14.3479	+	44.2734i	−0.605769	+	1.86922i
$562$	6.06232	+	10.5002i	0.255723	+	0.442926i
$563$	−24.5232	+	10.9184i	−1.03353	+	0.460156i	−0.852172	−	0.523261i	$-0.824715\pi$
$563$	−24.5232	+	10.9184i	−1.03353	+	0.460156i	−0.181355	+	0.983418i	$0.558048\pi$
$564$	4.82266	−	0.946346i	0.203071	−	0.0398483i
$565$	−0.888362	+	0.986626i	−0.0373737	+	0.0415076i
$566$	11.5188	+	15.8543i	0.484172	+	0.666406i
$567$	23.6152	+	3.05354i	0.991744	+	0.128237i
$568$	8.41042	−	2.73271i	0.352893	−	0.114662i
$569$	−23.6037	+	5.01713i	−0.989520	+	0.210329i	−0.674114	−	0.738628i	$-0.735474\pi$
$569$	−23.6037	+	5.01713i	−0.989520	+	0.210329i	−0.315406	+	0.948957i	$0.602141\pi$
$570$	1.57317	+	0.190318i	0.0658928	+	0.00797154i
$571$	−7.26544	−	4.19470i	−0.304049	−	0.175543i	0.340211	−	0.940349i	$-0.389501\pi$
$571$	−7.26544	−	4.19470i	−0.304049	−	0.175543i	−0.644260	+	0.764806i	$0.722835\pi$
$572$	0.379915	+	3.12039i	0.0158850	+	0.130470i
$573$	−9.71642	+	16.2363i	−0.405909	+	0.678279i
$574$	−2.50232	−	9.87155i	−0.104445	−	0.412030i
$575$	5.11918	+	1.66332i	0.213485	+	0.0693654i
$576$	2.91345	+	0.715394i	0.121394	+	0.0298081i
$577$	−1.36982	−	13.0329i	−0.0570263	−	0.542569i	−0.985320	−	0.170720i	$-0.945391\pi$
$577$	−1.36982	−	13.0329i	−0.0570263	−	0.542569i	0.928293	−	0.371849i	$-0.121276\pi$
$578$	5.08386	+	48.3697i	0.211461	+	2.01191i
$579$	−9.28513	−	30.1780i	−0.385877	−	1.25415i
$580$	0.236816	+	0.0769463i	0.00983327	+	0.00319502i
$581$	17.8069	+	5.03073i	0.738754	+	0.208710i
$582$	13.5798	+	8.12669i	0.562901	+	0.336862i
$583$	18.8535	+	3.68466i	0.780834	+	0.152603i
$584$	12.3534	+	7.13223i	0.511187	+	0.295134i
$585$	0.417981	+	0.324172i	0.0172814	+	0.0134029i
$586$	18.1330	−	3.85429i	0.749068	−	0.159219i
$587$	−14.1420	+	4.59502i	−0.583704	+	0.189657i	−0.585959	−	0.810341i	$-0.699282\pi$
$587$	−14.1420	+	4.59502i	−0.583704	+	0.189657i	0.00225547	+	0.999997i	$0.499282\pi$
$588$	11.7408	+	3.02537i	0.484184	+	0.124764i
$589$	−13.4420	−	18.5013i	−0.553868	−	0.762334i
$590$	0.422623	−	0.469370i	0.0173991	−	0.0193237i
$591$	8.03900	+	40.9675i	0.330680	+	1.68518i
$592$	3.17728	−	1.41462i	0.130585	−	0.0581404i
$593$	−20.0364	−	34.7041i	−0.822797	−	1.42513i	−0.903592	−	0.428395i	$-0.859079\pi$
$593$	−20.0364	−	34.7041i	−0.822797	−	1.42513i	0.0807952	−	0.996731i	$-0.474254\pi$
$594$	−2.32463	+	17.0762i	−0.0953807	+	0.700644i
$595$	1.37849	+	3.74176i	0.0565127	+	0.153397i
$596$	−10.8074	−	7.85204i	−0.442689	−	0.321632i
$597$	9.32808	+	3.19335i	0.381773	+	0.130695i
$598$	−1.00497	−	0.213613i	−0.0410962	−	0.00873528i
$599$	27.4654	−	2.88673i	1.12221	−	0.117949i	0.474800	−	0.880094i	$-0.342520\pi$
$599$	27.4654	−	2.88673i	1.12221	−	0.117949i	0.647406	+	0.762145i	$0.275854\pi$
$600$	−4.94547	−	7.03617i	−0.201898	−	0.287250i
$601$	−14.6565	+	4.76219i	−0.597851	+	0.194254i	−0.592282	−	0.805731i	$-0.701773\pi$
$601$	−14.6565	+	4.76219i	−0.597851	+	0.194254i	−0.00556952	+	0.999984i	$0.501773\pi$
$602$	−15.5622	−	24.6892i	−0.634267	−	1.00626i
$603$	−0.0536726	+	0.392026i	−0.00218572	+	0.0159645i
$604$	0.603227	−	0.348273i	0.0245449	−	0.0141710i
$605$	−2.04109	−	0.146900i	−0.0829822	−	0.00597232i
$606$	−13.9499	+	7.76507i	−0.566677	+	0.315435i
$607$	15.2545	+	1.60332i	0.619163	+	0.0650766i	0.408916	−	0.912572i	$-0.365907\pi$
$607$	15.2545	+	1.60332i	0.619163	+	0.0650766i	0.210246	+	0.977648i	$0.432573\pi$
$608$	4.67718	+	1.51971i	0.189685	+	0.0616323i
$609$	5.65966	+	2.36445i	0.229341	+	0.0958123i
$610$	−2.19406	+	1.59408i	−0.0888349	+	0.0645424i
$611$	2.45679	+	1.09383i	0.0993912	+	0.0442518i
$612$	6.78249	+	23.3393i	0.274166	+	0.943436i
$613$	1.87029	−	1.68402i	0.0755405	−	0.0680170i	−0.630496	−	0.776193i	$-0.717148\pi$
$613$	1.87029	−	1.68402i	0.0755405	−	0.0680170i	0.706036	+	0.708176i	$0.250482\pi$
$614$	13.4470	+	1.41333i	0.542676	+	0.0570375i
$615$	0.636886	−	1.06424i	0.0256817	−	0.0429144i
$616$	−2.24658	+	8.48251i	−0.0905171	+	0.341770i
$617$			16.0248i			0.645136i	0.946546	+	0.322568i	$0.104546\pi$
$617$			16.0248i			0.645136i	−0.946546	+	0.322568i	$0.895454\pi$
$618$	11.4595	−	15.2637i	0.460968	−	0.613997i
$619$	−7.01196	−	7.78757i	−0.281834	−	0.313009i	0.585561	−	0.810628i	$-0.300874\pi$
$619$	−7.01196	−	7.78757i	−0.281834	−	0.313009i	−0.867395	+	0.497620i	$0.834208\pi$
$620$	0.179861	−	0.846182i	0.00722341	−	0.0339835i
$621$	−5.03243	−	2.53038i	−0.201944	−	0.101541i
$622$	4.16720	+	5.73566i	0.167090	+	0.229979i
$623$	−4.33319	−	1.73103i	−0.173606	−	0.0693524i
$624$	1.07919	+	1.23701i	0.0432023	+	0.0495202i
$625$	−2.55907	+	24.3480i	−0.102363	+	0.973918i
$626$	9.77793	−	16.9359i	0.390805	−	0.676893i
$627$	−5.85262	+	27.6382i	−0.233731	+	1.10376i
$628$	1.33010	+	2.30379i	0.0530766	+	0.0919314i
$629$	22.7958	+	16.5621i	0.908927	+	0.660374i
$630$	0.747836	+	1.27322i	0.0297945	+	0.0507262i
$631$	−6.60112	−	20.3162i	−0.262786	−	0.808773i	−0.992195	−	0.124695i	$-0.960205\pi$
$631$	−6.60112	−	20.3162i	−0.262786	−	0.808773i	0.729409	−	0.684078i	$-0.239795\pi$
$632$	5.09572	−	11.4452i	0.202697	−	0.455264i
$633$	3.66840	+	1.70266i	0.145806	+	0.0676745i
$634$	3.77269	−	17.7491i	0.149833	−	0.704907i
$635$	0.318905	−	0.0677854i	0.0126554	−	0.00268998i
$636$	9.22770	−	3.93633i	0.365902	−	0.156086i
$637$	4.30419	+	5.04877i	0.170538	+	0.200039i
$638$	−1.73871	+	4.08459i	−0.0688362	+	0.161710i
$639$	22.5484	+	13.9784i	0.892001	+	0.552977i
$640$	0.0756668	+	0.169950i	0.00299099	+	0.00671788i
$641$	−25.9746	+	23.3876i	−1.02593	+	0.923756i	−0.997121	−	0.0758291i	$-0.975840\pi$
$641$	−25.9746	+	23.3876i	−1.02593	+	0.923756i	−0.0288138	+	0.999585i	$0.509173\pi$
$642$	−28.4271	+	8.74641i	−1.12193	+	0.345193i
$643$	−4.94811	+	3.59501i	−0.195134	+	0.141773i	−0.681062	−	0.732226i	$-0.738482\pi$
$643$	−4.94811	+	3.59501i	−0.195134	+	0.141773i	0.485928	+	0.873999i	$0.338482\pi$
$644$	−2.38399	−	1.59449i	−0.0939425	−	0.0628317i
$645$	0.793380	−	3.46464i	0.0312393	−	0.136420i
$646$	8.28378	+	38.9721i	0.325921	+	1.53334i
$647$	1.10988	+	2.49282i	0.0436337	+	0.0980029i	0.934047	−	0.357150i	$-0.116251\pi$
$647$	1.10988	+	2.49282i	0.0436337	+	0.0980029i	−0.890413	+	0.455153i	$0.849585\pi$
$648$	4.00286	+	8.06084i	0.157247	+	0.316660i
$649$	7.67107	+	8.24301i	0.301116	+	0.323566i
$650$		−	4.70610i		−	0.184588i
$651$	6.11423	−	20.4137i	0.239636	−	0.800076i
$652$	1.64838	−	5.07318i	0.0645554	−	0.198681i
$653$	7.27024	+	6.54616i	0.284507	+	0.256171i	0.799010	−	0.601317i	$-0.205357\pi$
$653$	7.27024	+	6.54616i	0.284507	+	0.256171i	−0.514504	+	0.857488i	$0.672024\pi$
$654$	−23.5519	−	10.9314i	−0.920953	−	0.427453i
$655$	1.33441	−	0.140252i	0.0521396	−	0.00548009i
$656$	2.57555	−	2.86044i	0.100558	−	0.111681i
$657$	7.58103	+	42.1165i	0.295764	+	1.64312i
$658$	5.23605	+	5.37980i	0.204122	+	0.209727i
$659$	19.7562			0.769592			0.384796	−	0.923002i	$-0.374272\pi$
$659$	19.7562			0.769592			0.384796	+	0.923002i	$0.374272\pi$
$660$	−0.925098	+	0.535048i	−0.0360094	+	0.0208267i
$661$	−21.5420	+	37.3118i	−0.837885	+	1.45126i	0.0537747	+	0.998553i	$0.482875\pi$
$661$	−21.5420	+	37.3118i	−0.837885	+	1.45126i	−0.891660	+	0.452706i	$0.850459\pi$
$662$	12.1260	−	5.39883i	0.471289	−	0.209831i
$663$	−4.30754	+	12.5827i	−0.167291	+	0.488673i
$664$	2.16121	+	6.65151i	0.0838710	+	0.258128i
$665$	1.06962	+	2.17143i	0.0414779	+	0.0842045i
$666$	9.39415	+	4.54049i	0.364016	+	0.175940i
$667$	−1.07827	−	0.970880i	−0.0417508	−	0.0375926i
$668$	10.7216	+	11.9076i	0.414833	+	0.460718i
$669$	−14.9144	−	1.80431i	−0.576624	−	0.0697585i
$670$	−0.0212495	+	0.0122684i	−0.000820939	+	0.000473969i
$671$	−24.8599	−	41.4693i	−0.959705	−	1.60090i
$672$	1.51658	+	4.32435i	0.0585035	+	0.166815i
$673$	11.4623	−	15.7765i	0.441839	−	0.608139i	−0.528781	−	0.848759i	$-0.677351\pi$
$673$	11.4623	−	15.7765i	0.441839	−	0.608139i	0.970620	+	0.240619i	$0.0773505\pi$
$674$	−1.62767	−	7.65758i	−0.0626954	−	0.294959i
$675$	6.54454	−	24.9571i	0.251900	−	0.960599i
$676$	−1.26497	−	12.0354i	−0.0486528	−	0.462901i
$677$	−33.2939	−	14.8234i	−1.27959	−	0.569710i	−0.349464	−	0.936950i	$-0.613636\pi$
$677$	−33.2939	−	14.8234i	−1.27959	−	0.569710i	−0.930126	+	0.367240i	$0.880303\pi$
$678$	−12.0490	−	2.75913i	−0.462737	−	0.105964i
$679$	0.938187	+	24.1560i	0.0360043	+	0.927022i
$680$	−0.885895	+	1.21933i	−0.0339725	+	0.0467591i
$681$	0.607642	−	38.7679i	0.0232849	−	1.48559i
$682$	14.7443	+	4.52419i	0.564589	+	0.173240i
$683$	−7.36169	−	4.25027i	−0.281687	−	0.162632i	0.352500	−	0.935812i	$-0.385332\pi$
$683$	−7.36169	−	4.25027i	−0.281687	−	0.162632i	−0.634187	+	0.773180i	$0.718665\pi$
$684$	5.57550	+	13.6596i	0.213184	+	0.522287i
$685$	0.548967	−	1.68955i	0.0209749	−	0.0645543i
$686$	5.92942	+	17.5454i	0.226386	+	0.669887i
$687$	−29.6207	+	2.64463i	−1.13010	+	0.100899i
$688$	4.48660	−	10.0771i	0.171050	−	0.384185i
$689$	5.36967	+	1.14136i	0.204568	+	0.0434823i
$690$	−0.0672592	−	0.342759i	−0.00256051	−	0.0130486i
$691$	−0.285338	+	2.71481i	−0.0108548	+	0.103276i	−0.998608	−	0.0527494i	$-0.983202\pi$
$691$	−0.285338	+	2.71481i	−0.0108548	+	0.103276i	0.987753	+	0.156026i	$0.0498682\pi$
$692$	−19.4208			−0.738266
$693$	−23.7861	+	11.2792i	−0.903560	+	0.428461i
$694$	14.2407			0.540570
$695$	0.104278	−	0.992141i	0.00395550	−	0.0376340i
$696$	0.446409	+	2.27494i	0.0169211	+	0.0862314i
$697$	30.5025	+	6.48350i	1.15536	+	0.245580i
$698$	2.91925	−	6.55674i	0.110495	−	0.248176i
$699$	23.0273	−	2.05595i	0.870973	−	0.0777633i
$700$	4.87358	−	12.1998i	0.184204	−	0.461107i
$701$	13.1558	−	40.4895i	0.496889	−	1.52927i	−0.317102	−	0.948392i	$-0.602710\pi$
$701$	13.1558	−	40.4895i	0.496889	−	1.52927i	0.813991	−	0.580877i	$-0.197290\pi$
$702$	−0.744414	+	4.86822i	−0.0280961	+	0.183739i
$703$	14.8127	+	8.55211i	0.558671	+	0.322549i
$704$	−3.13703	+	1.07660i	−0.118231	+	0.0405758i
$705$	−0.0143287	+	0.914176i	−0.000539648	+	0.0344299i
$706$	3.21341	−	4.42288i	0.120938	−	0.166457i
$707$	−21.5777	−	11.3650i	−0.811512	−	0.427424i
$708$	5.73209	+	1.31261i	0.215425	+	0.0493309i
$709$	35.8899	+	15.9792i	1.34787	+	0.600112i	0.948529	−	0.316690i	$-0.102571\pi$
$709$	35.8899	+	15.9792i	1.34787	+	0.600112i	0.399343	+	0.916801i	$0.369238\pi$
$710$	0.171964	+	1.63613i	0.00645370	+	0.0614028i
$711$	36.0918	−	10.4884i	1.35355	−	0.393346i
$712$	−0.366682	−	1.72510i	−0.0137420	−	0.0646510i
$713$	−2.96297	+	4.07817i	−0.110964	+	0.152729i
$714$	−24.1971	+	28.1578i	−0.905554	+	1.05378i
$715$	−0.582507	−	0.0515598i	−0.0217845	−	0.00192823i
$716$	−10.2524	+	5.91920i	−0.383149	+	0.221211i
$717$	38.4844	+	4.65574i	1.43723	+	0.173872i
$718$	12.8504	+	14.2718i	0.479573	+	0.532620i
$719$	19.8283	+	17.8535i	0.739471	+	0.665823i	0.950171	−	0.311728i	$-0.100908\pi$
$719$	19.8283	+	17.8535i	0.739471	+	0.665823i	−0.210700	+	0.977551i	$0.567574\pi$
$720$	−0.242867	+	0.502486i	−0.00905114	+	0.0187266i
$721$	29.0921	+	1.91997i	1.08345	+	0.0715033i
$722$	1.60242	+	4.93176i	0.0596361	+	0.183541i
$723$	−10.2336	+	29.8935i	−0.380593	+	1.11175i
$724$	−6.38918	+	2.84465i	−0.237452	+	0.105720i
$725$	3.32305	−	5.75570i	0.123415	−	0.213761i
$726$	−8.04759	−	17.2695i	−0.298674	−	0.640932i
$727$	−8.99304			−0.333533			−0.166767	−	0.985996i	$-0.553333\pi$
$727$	−8.99304			−0.333533			−0.166767	+	0.985996i	$0.553333\pi$
$728$	−0.681749	+	2.41314i	−0.0252673	+	0.0894368i
$729$	−10.7177	+	24.7817i	−0.396953	+	0.917839i
$730$	−1.77565	+	1.97206i	−0.0657199	+	0.0729893i
$731$	88.8772	−	9.34137i	3.28724	−	0.345503i
$732$	−22.9032	−	10.6303i	−0.846525	−	0.392907i
$733$	1.57753	+	1.42041i	0.0582673	+	0.0524641i	0.697750	−	0.716342i	$-0.254185\pi$
$733$	1.57753	+	1.42041i	0.0582673	+	0.0524641i	−0.639483	+	0.768806i	$0.720851\pi$
$734$	−5.13377	+	15.8001i	−0.189491	+	0.583193i
$735$	−1.00464	+	2.01944i	−0.0370568	+	0.0744883i
$736$		−	1.08403i		−	0.0399578i
$737$	−0.184468	−	0.396647i	−0.00679498	−	0.0146107i
$738$	11.5416	+	0.361893i	0.424853	+	0.0133214i
$739$	−18.3565	−	41.2293i	−0.675253	−	1.51664i	−0.847051	−	0.531511i	$-0.821624\pi$
$739$	−18.3565	−	41.2293i	−0.675253	−	1.51664i	0.171798	−	0.985132i	$-0.445042\pi$
$740$	0.134523	+	0.632880i	0.00494516	+	0.0232651i
$741$	−1.80207	+	7.86952i	−0.0662006	+	0.289094i
$742$	12.7380	+	8.51955i	0.467626	+	0.312763i
$743$	3.16638	−	2.30051i	0.116163	−	0.0843976i	−0.528187	−	0.849128i	$-0.677128\pi$
$743$	3.16638	−	2.30051i	0.116163	−	0.0843976i	0.644350	+	0.764731i	$0.277128\pi$
$744$	7.69816	−	2.36856i	0.282228	−	0.0868357i
$745$	1.84684	−	1.66290i	0.0676630	−	0.0609240i
$746$	−4.07859	−	9.16065i	−0.149328	−	0.335395i
$747$	−11.0550	+	17.8327i	−0.404482	+	0.652466i
$748$	−20.2611	−	17.6489i	−0.740820	−	0.645309i
$749$	−34.9169	−	29.0667i	−1.27583	−	1.06207i
$750$	2.95355	−	1.25992i	0.107848	−	0.0460057i
$751$	48.7762	−	10.3677i	1.77987	−	0.378323i	0.803648	−	0.595105i	$-0.202890\pi$
$751$	48.7762	−	10.3677i	1.77987	−	0.378323i	0.976220	+	0.216783i	$0.0695564\pi$
$752$	−0.589942	+	2.77546i	−0.0215130	+	0.101211i
$753$	−17.3622	−	8.05854i	−0.632715	−	0.293669i
$754$	−0.515982	+	1.15891i	−0.0187910	+	0.0422052i
$755$	0.0400428	+	0.123239i	0.00145731	+	0.00448512i
$756$	−6.97124	+	11.8491i	−0.253542	+	0.430949i
$757$	7.53714	+	5.47606i	0.273942	+	0.199031i	0.716271	−	0.697822i	$-0.245848\pi$
$757$	7.53714	+	5.47606i	0.273942	+	0.199031i	−0.442329	+	0.896853i	$0.645848\pi$
$758$	16.8322	+	29.1543i	0.611374	+	1.05893i
$759$	6.19266	−	0.655657i	0.224779	−	0.0237988i
$760$	−0.457446	+	0.792320i	−0.0165933	+	0.0287405i
$761$	−1.03654	+	9.86204i	−0.0375746	+	0.357499i	0.959539	+	0.281576i	$0.0908570\pi$
$761$	−1.03654	+	9.86204i	−0.0375746	+	0.357499i	−0.997114	+	0.0759231i	$0.975810\pi$
$762$	1.99553	+	2.28735i	0.0722903	+	0.0828620i
$763$	−5.67357	−	39.2545i	−0.205397	−	1.42111i
$764$	−6.42118	−	8.83799i	−0.232310	−	0.319747i
$765$	−4.50936	+	0.331467i	−0.163036	+	0.0119842i
$766$	−4.07782	+	19.1846i	−0.147338	+	0.693169i
$767$	2.15312	+	2.39129i	0.0777448	+	0.0863443i
$768$	−1.03991	+	1.38513i	−0.0375245	+	0.0499816i
$769$			40.7034i			1.46780i	0.679256	+	0.733902i	$0.262303\pi$
$769$			40.7034i			1.46780i	−0.679256	+	0.733902i	$0.737697\pi$
$770$	−1.45665	−	0.736897i	−0.0524942	−	0.0265559i
$771$	11.4785	−	19.1807i	0.413388	−	0.690776i
$772$	18.1295	+	1.90548i	0.652493	+	0.0685798i
$773$	12.9898	−	11.6961i	0.467210	−	0.420678i	−0.401606	−	0.915813i	$-0.631548\pi$
$773$	12.9898	−	11.6961i	0.467210	−	0.420678i	0.868816	+	0.495134i	$0.164881\pi$
$774$	31.7776	−	9.23468i	1.14222	−	0.331934i
$775$	−21.0936	−	9.39148i	−0.757705	−	0.337352i
$776$	−7.39198	+	5.37059i	−0.265357	+	0.192793i
$777$	2.03239	+	15.8079i	0.0729116	+	0.567106i
$778$	−33.3000	−	10.8198i	−1.19386	−	0.387910i
$779$	18.8257	+	1.97866i	0.674502	+	0.0708930i
$780$	−0.266839	+	0.148533i	−0.00955438	+	0.00531834i
$781$	−29.3257	+	0.482050i	−1.04936	+	0.0172491i
$782$	7.60576	−	4.39119i	0.271982	−	0.157029i
$783$	−4.34797	+	5.42834i	−0.155384	+	0.193993i
$784$	−4.26633	+	5.54963i	−0.152369	+	0.198201i
$785$	−0.470664	+	0.152928i	−0.0167987	+	0.00545824i
$786$	7.18351	+	10.2203i	0.256227	+	0.364547i
$787$	14.3754	−	1.51092i	0.512428	−	0.0538583i	0.155214	−	0.987881i	$-0.450393\pi$
$787$	14.3754	−	1.51092i	0.512428	−	0.0538583i	0.357214	+	0.934023i	$0.383727\pi$
$788$	−23.5769	−	5.01143i	−0.839893	−	0.178525i
$789$	38.0116	+	13.0128i	1.35325	+	0.463267i
$790$	1.88556	+	1.36994i	0.0670854	+	0.0487404i
$791$	−6.52722	−	17.7174i	−0.232081	−	0.629958i
$792$	−8.54172	−	5.10285i	−0.303517	−	0.181322i
$793$	−6.90839	−	11.9657i	−0.245324	−	0.424914i
$794$	−33.8213	+	15.0582i	−1.20027	+	0.534396i
$795$	0.359374	+	1.83140i	0.0127457	+	0.0649532i
$796$	−3.80897	+	4.23029i	−0.135005	+	0.149938i
$797$	25.6237	+	35.2680i	0.907638	+	1.24926i	0.967967	+	0.251078i	$0.0807849\pi$
$797$	25.6237	+	35.2680i	0.907638	+	1.24926i	−0.0603293	+	0.998179i	$0.519215\pi$
$798$	−12.8211	+	18.5342i	−0.453863	+	0.656102i
$799$	−21.8629	+	7.10370i	−0.773455	+	0.251311i
$800$	4.85689	−	1.03236i	0.171717	−	0.0364995i
$801$	3.24255	−	4.18088i	0.114570	−	0.147724i
$802$	−3.51849	−	2.03140i	−0.124242	−	0.0717313i
$803$	−32.2300	−	34.6330i	−1.13737	−	1.22217i
$804$	−0.196027	−	0.117310i	−0.00691334	−	0.00413722i
$805$	0.382356	−	0.372139i	0.0134763	−	0.0131162i
$806$	4.19161	+	1.36194i	0.147643	+	0.0479722i
$807$	6.27158	+	20.3835i	0.220770	+	0.717534i
$808$	−0.963510	−	9.16718i	−0.0338961	−	0.322500i
$809$	−0.104928	−	0.998320i	−0.00368906	−	0.0350991i	0.992523	−	0.122062i	$-0.0389506\pi$
$809$	−0.104928	−	0.998320i	−0.00368906	−	0.0350991i	−0.996212	+	0.0869627i	$0.972284\pi$
$810$	−1.62164	+	0.416612i	−0.0569788	+	0.0146383i
$811$	19.3691	+	6.29341i	0.680142	+	0.220991i	0.628657	−	0.777682i	$-0.283605\pi$
$811$	19.3691	+	6.29341i	0.680142	+	0.220991i	0.0514842	+	0.998674i	$0.483605\pi$
$812$	−2.53775	+	2.46994i	−0.0890577	+	0.0866780i
$813$	20.5924	−	34.4101i	0.722205	−	1.20681i
$814$	−11.4505	+	1.39413i	−0.401342	+	0.0488643i
$815$	0.859402	+	0.496176i	0.0301035	+	0.0173803i
$816$	−13.9308	−	1.68532i	−0.487677	−	0.0589979i
$817$	53.0624	−	11.2788i	1.85642	−	0.394594i
$818$	19.3719	−	6.29432i	0.677323	−	0.220076i
$819$	−6.84933	+	3.11106i	−0.239335	+	0.108709i
$820$	0.420891	+	0.579307i	0.0146982	+	0.0202303i
$821$	20.0680	−	22.2878i	0.700378	−	0.777848i	−0.283058	−	0.959103i	$-0.591349\pi$
$821$	20.0680	−	22.2878i	0.700378	−	0.777848i	0.983436	+	0.181254i	$0.0580157\pi$
$822$	16.2304	−	3.18487i	0.566099	−	0.111085i
$823$	−8.49701	+	3.78311i	−0.296187	+	0.131871i	−0.549450	−	0.835526i	$-0.685163\pi$
$823$	−8.49701	+	3.78311i	−0.296187	+	0.131871i	0.253263	+	0.967397i	$0.418496\pi$
$824$	5.50985	+	9.54334i	0.191945	+	0.332458i
$825$	8.83512	+	27.1212i	0.307599	+	0.944239i
$826$	3.10521	+	8.42875i	0.108044	+	0.293274i
$827$	31.6484	+	22.9939i	1.10052	+	0.799577i	0.981145	−	0.193272i	$-0.0619099\pi$
$827$	31.6484	+	22.9939i	1.10052	+	0.799577i	0.119378	+	0.992849i	$0.461910\pi$
$828$	2.48378	−	2.09926i	0.0863174	−	0.0729543i
$829$	−15.7167	−	3.34069i	−0.545865	−	0.116027i	−0.0732784	−	0.997312i	$-0.523346\pi$
$829$	−15.7167	−	3.34069i	−0.545865	−	0.116027i	−0.472586	+	0.881284i	$0.656680\pi$
$830$	−1.29396	+	0.136000i	−0.0449139	+	0.00472064i
$831$	18.7946	−	13.2100i	0.651976	−	0.458251i
$832$	−0.901392	+	0.292880i	−0.0312502	+	0.0101538i
$833$	−56.2194	−	7.45300i	−1.94789	−	0.258231i
$834$	8.54328	−	3.64438i	0.295830	−	0.126194i
$835$	−2.58150	+	1.49043i	−0.0893366	+	0.0515785i
$836$	−13.3515	−	9.36905i	−0.461770	−	0.324036i
$837$	20.3347	+	13.0516i	0.702871	+	0.451130i
$838$	−9.89129	−	1.03962i	−0.341689	−	0.0359130i
$839$	−16.7564	−	5.44447i	−0.578494	−	0.187964i	0.00513186	−	0.999987i	$-0.498366\pi$
$839$	−16.7564	−	5.44447i	−0.578494	−	0.187964i	−0.583626	+	0.812023i	$0.698366\pi$
$840$	−0.845554	+	0.108711i	−0.0291744	+	0.00375089i
$841$	22.0121	−	15.9927i	0.759038	−	0.551473i
$842$	8.48929	+	3.77968i	0.292560	+	0.130256i
$843$	−15.3843	−	14.2949i	−0.529862	−	0.492343i
$844$	−1.73522	+	1.56240i	−0.0597287	+	0.0537799i
$845$	2.23899	+	0.235328i	0.0770238	+	0.00809552i
$846$	−7.50172	+	4.02307i	−0.257914	+	0.138316i
$847$	15.3760	−	24.7099i	0.528325	−	0.849042i
$848$			5.79210i			0.198901i
$849$	−27.1444	−	20.3791i	−0.931594	−	0.699409i
$850$	26.9176	+	29.8950i	0.923265	+	1.02539i
$851$	0.783872	−	3.68783i	0.0268708	−	0.126417i
$852$	−12.5312	+	8.80776i	−0.429313	+	0.301749i
$853$	−18.7136	−	25.7571i	−0.640742	−	0.881905i	0.357913	−	0.933755i	$-0.383488\pi$
$853$	−18.7136	−	25.7571i	−0.640742	−	0.881905i	−0.998655	+	0.0518497i	$0.983488\pi$
$854$	−5.51729	−	38.1732i	−0.188798	−	1.30626i
$855$	−2.70126	+	0.486231i	−0.0923813	+	0.0166288i
$856$	1.79493	−	17.0776i	0.0613493	−	0.583700i
$857$	6.44371	−	11.1608i	0.220113	−	0.381247i	−0.734729	−	0.678361i	$-0.762691\pi$
$857$	6.44371	−	11.1608i	0.220113	−	0.381247i	0.954842	+	0.297114i	$0.0960241\pi$
$858$	−2.21831	−	4.97218i	−0.0757318	−	0.169747i
$859$	−24.4529	−	42.3537i	−0.834322	−	1.44509i	−0.894581	−	0.446906i	$-0.852526\pi$
$859$	−24.4529	−	42.3537i	−0.834322	−	1.44509i	0.0602586	−	0.998183i	$-0.480807\pi$
$860$	1.66017	+	1.20619i	0.0566115	+	0.0411306i
$861$	9.17058	+	15.0674i	0.312533	+	0.513497i
$862$	5.32024	+	16.3740i	0.181208	+	0.557701i
$863$	−19.3664	+	43.4975i	−0.659238	+	1.48067i	0.205607	+	0.978635i	$0.434083\pi$
$863$	−19.3664	+	43.4975i	−0.659238	+	1.48067i	−0.864845	+	0.502039i	$0.832583\pi$
$864$	−5.18750	+	0.299662i	−0.176482	+	0.0101947i
$865$	0.751168	−	3.53397i	0.0255405	−	0.120158i
$866$	11.9472	−	2.53946i	0.405982	−	0.0862942i
$867$	−33.0533	−	77.4849i	−1.12255	−	2.63152i
$868$	9.45563	+	7.87138i	0.320945	+	0.267172i
$869$	−27.2922	+	31.3317i	−0.925825	+	1.06285i
$870$	−0.431234	−	0.00675910i	−0.0146202	−	0.000229155i
$871$	−0.0508448	−	0.114199i	−0.00172281	−	0.00386950i
$872$	11.1405	−	10.0309i	0.377264	−	0.339690i
$873$	−26.6202	−	6.53655i	−0.900957	−	0.221229i
$874$	4.31297	−	3.13356i	0.145888	−	0.105994i
$875$	4.07709	+	2.72689i	0.137831	+	0.0921856i
$876$	−24.0834	−	5.51494i	−0.813702	−	0.186332i
$877$	3.86014	+	18.1605i	0.130348	+	0.613237i	0.994021	+	0.109186i	$0.0348244\pi$
$877$	3.86014	+	18.1605i	0.130348	+	0.613237i	−0.863674	+	0.504051i	$0.831842\pi$
$878$	−6.63760	−	14.9083i	−0.224008	−	0.503130i
$879$	−28.0554	+	15.6167i	−0.946284	+	0.526739i
$880$	−0.0745710	−	0.612481i	−0.00251379	−	0.0206467i
$881$			40.5540i			1.36630i	0.730279	+	0.683149i	$0.239390\pi$
$881$			40.5540i			1.36630i	−0.730279	+	0.683149i	$0.760610\pi$
$882$	−20.9775	+	0.971809i	−0.706349	+	0.0327225i
$883$	9.41817	−	28.9861i	0.316946	−	0.975461i	−0.657999	−	0.753019i	$-0.728597\pi$
$883$	9.41817	−	28.9861i	0.316946	−	0.975461i	0.974946	−	0.222442i	$-0.0714030\pi$
$884$	−5.70627	−	5.13795i	−0.191923	−	0.172808i
$885$	−0.460563	+	0.992289i	−0.0154816	+	0.0333554i
$886$	−12.8728	+	1.35299i	−0.432471	+	0.0454545i
$887$	28.2516	−	31.3766i	0.948595	−	1.05352i	−0.0499039	−	0.998754i	$-0.515892\pi$
$887$	28.2516	−	31.3766i	0.948595	−	1.05352i	0.998499	−	0.0547677i	$-0.0174418\pi$
$888$	−4.53934	+	3.96020i	−0.152330	+	0.132896i
$889$	−1.26062	+	4.46211i	−0.0422797	+	0.149654i
$890$	0.328097			0.0109978
$891$	−4.84944	−	29.4531i	−0.162462	−	0.986715i
$892$	4.33681	−	7.51158i	0.145207	−	0.251506i
$893$	−12.7479	+	5.67573i	−0.426592	+	0.189931i
$894$	21.8907	+	7.49401i	0.732136	+	0.250637i
$895$	−0.680561	−	2.09455i	−0.0227487	−	0.0700132i
$896$	−2.64001	−	0.174230i	−0.0881965	−	0.00582063i
$897$	1.77249	−	0.158254i	0.0591819	−	0.00528395i
$898$	7.08585	+	6.38013i	0.236458	+	0.212908i
$899$	4.16478	+	4.62546i	0.138903	+	0.154268i
$900$	11.7709	+	9.12914i	0.392364	+	0.304305i
$901$	−40.6385	+	23.4627i	−1.35387	+	0.781655i
$902$	−10.9493	+	6.56386i	−0.364572	+	0.218553i
$903$	38.3381	+	32.9455i	1.27581	+	1.09636i
$904$	4.19475	−	5.77357i	0.139515	−	0.192026i
$905$	−0.270512	−	1.27266i	−0.00899211	−	0.0423045i
$906$	−0.821227	+	0.883808i	−0.0272834	+	0.0293625i
$907$	−2.20044	−	20.9358i	−0.0730644	−	0.695161i	−0.968338	−	0.249644i	$-0.919686\pi$
$907$	−2.20044	−	20.9358i	−0.0730644	−	0.695161i	0.895273	−	0.445517i	$-0.146980\pi$
$908$	20.4501	+	9.10496i	0.678660	+	0.302159i
$909$	19.1384	−	19.9602i	0.634782	−	0.662038i
$910$	−0.412746	−	0.217394i	−0.0136824	−	0.00720653i
$911$	31.7075	−	43.6417i	1.05052	−	1.44591i	0.162158	−	0.986765i	$-0.448155\pi$
$911$	31.7075	−	43.6417i	1.05052	−	1.44591i	0.888360	−	0.459148i	$-0.151845\pi$
$912$	−8.51697	−	0.133494i	−0.282025	−	0.00442042i
$913$	−0.381236	−	23.1927i	−0.0126171	−	0.767566i
$914$	3.62044	+	2.09026i	0.119754	+	0.0691398i
$915$	2.82024	−	3.75649i	0.0932343	−	0.124186i
$916$	5.30567	−	16.3292i	0.175304	−	0.539532i
$917$	−7.07908	+	17.7207i	−0.233772	+	0.585188i
$918$	−23.1161	−	35.1827i	−0.762944	−	1.16120i
$919$	−11.3305	+	25.4488i	−0.373760	+	0.839478i	0.624529	+	0.781002i	$0.285291\pi$
$919$	−11.3305	+	25.4488i	−0.373760	+	0.839478i	−0.998289	+	0.0584766i	$0.981376\pi$
$920$	0.197259	+	0.0419287i	0.00650344	+	0.00138235i
$921$	−22.9809	+	4.50951i	−0.757246	+	0.148594i
$922$	3.52768	−	33.5637i	0.116178	−	1.10536i
$923$	−8.38144			−0.275879
$924$	−0.601450	−	15.1868i	−0.0197863	−	0.499608i
$925$	17.2695			0.567816
$926$	1.83962	−	17.5028i	0.0604536	−	0.575178i
$927$	−11.1962	+	31.1055i	−0.367730	+	1.02164i
$928$	−1.30924	−	0.278287i	−0.0429778	−	0.00913521i
$929$	−8.31813	+	18.6828i	−0.272909	+	0.612963i	−0.997056	−	0.0766826i	$-0.975567\pi$
$929$	−8.31813	+	18.6828i	−0.272909	+	0.612963i	0.724147	+	0.689646i	$0.242234\pi$
$930$	0.133250	+	1.49244i	0.00436943	+	0.0489389i
$931$	−34.4125	−	0.932170i	−1.12783	−	0.0305506i
$932$	−4.12467	+	12.6944i	−0.135108	+	0.415820i
$933$	−9.82012	−	7.37261i	−0.321496	−	0.241368i
$934$	−7.73332	−	4.46483i	−0.253042	−	0.146094i
$935$	3.99522	−	3.00425i	0.130658	−	0.0982495i
$936$	−2.41664	−	1.49814i	−0.0789904	−	0.0489684i
$937$	8.78002	−	12.0847i	0.286831	−	0.394788i	−0.641151	−	0.767415i	$-0.721543\pi$
$937$	8.78002	−	12.0847i	0.286831	−	0.394788i	0.927981	+	0.372626i	$0.121543\pi$
$938$	−0.0135429	−	0.348697i	−0.000442192	−	0.0113853i
$939$	−7.56070	+	33.0171i	−0.246734	+	1.07747i
$940$	−0.482228	−	0.214702i	−0.0157285	−	0.00700280i
$941$	5.34404	+	50.8452i	0.174211	+	1.65751i	0.636872	+	0.770970i	$0.280228\pi$
$941$	5.34404	+	50.8452i	0.174211	+	1.65751i	−0.462661	+	0.886535i	$0.653105\pi$
$942$	−3.37537	−	3.13636i	−0.109975	−	0.102188i
$943$	−0.867519	−	4.08136i	−0.0282503	−	0.132907i
$944$	−1.99558	+	2.74668i	−0.0649506	+	0.0893968i
$945$	−1.88653	−	1.72685i	−0.0613688	−	0.0561746i
$946$	−24.0299	+	27.5865i	−0.781278	+	0.896914i
$947$	30.7303	−	17.7422i	0.998601	−	0.576543i	0.0907670	−	0.995872i	$-0.471068\pi$
$947$	30.7303	−	17.7422i	0.998601	−	0.576543i	0.907834	+	0.419330i	$0.137735\pi$
$948$	−2.60616	+	21.5426i	−0.0846443	+	0.699670i
$949$	−9.04636	−	10.0470i	−0.293657	−	0.326139i
$950$	18.1470	+	16.3396i	0.588767	+	0.530128i
$951$	2.79498	+	31.3046i	0.0906334	+	1.01512i
$952$	−9.47173	−	19.2286i	−0.306980	−	0.623203i
$953$	−14.4939	−	44.6076i	−0.469503	−	1.44498i	−0.853229	−	0.521536i	$-0.825359\pi$
$953$	−14.4939	−	44.6076i	−0.469503	−	1.44498i	0.383726	−	0.923447i	$-0.374641\pi$
$954$	−13.2712	+	11.2166i	−0.429669	+	0.363151i
$955$	1.85660	−	0.826611i	0.0600781	−	0.0267485i
$956$	−11.1905	+	19.3825i	−0.361926	+	0.626874i
$957$	0.797881	−	7.64751i	0.0257918	−	0.247209i
$958$	−10.7004			−0.345714
$959$	17.6216	+	18.1054i	0.569031	+	0.584653i
$960$	−0.211828	−	0.242806i	−0.00683672	−	0.00783652i
$961$	−6.27381	+	6.96777i	−0.202381	+	0.224767i
$962$	−3.27829	+	0.344562i	−0.105696	+	0.0111091i
$963$	42.6050	−	28.9587i	1.37293	−	0.933182i
$964$	−13.5567	−	12.2065i	−0.436632	−	0.393145i
$965$	−1.04796	+	3.22529i	−0.0337350	+	0.103826i
$966$	4.75877	+	1.42533i	0.153111	+	0.0458592i
$967$			3.79528i			0.122048i	0.998136	+	0.0610240i	$0.0194366\pi$
$967$			3.79528i			0.122048i	−0.998136	+	0.0610240i	$0.980563\pi$
$968$	10.9941	−	0.361533i	0.353362	−	0.0116201i
$969$	−33.5640	−	60.2976i	−1.07823	−	1.93704i
$970$	−0.691367	−	1.55283i	−0.0221984	−	0.0498585i
$971$	4.55446	+	21.4270i	0.146160	+	0.687627i	0.988812	+	0.149169i	$0.0476597\pi$
$971$	4.55446	+	21.4270i	0.146160	+	0.687627i	−0.842652	+	0.538458i	$0.819007\pi$
$972$	−10.7324	−	11.3056i	−0.344241	−	0.362626i
$973$	11.7932	+	7.88765i	0.378073	+	0.252867i
$974$	−22.0988	+	16.0557i	−0.708090	+	0.514457i
$975$	2.39706	+	7.79078i	0.0767673	+	0.249505i
$976$	10.8336	−	9.75461i	0.346775	−	0.312238i
$977$	−0.369081	−	0.828970i	−0.0118080	−	0.0265211i	0.907545	−	0.419954i	$-0.137954\pi$
$977$	−0.369081	−	0.828970i	−0.0118080	−	0.0265211i	−0.919353	+	0.393433i	$0.871287\pi$
$978$	−0.144796	+	9.23807i	−0.00463007	+	0.295401i
$979$	−0.515730	+	5.82656i	−0.0164828	+	0.186218i
$980$	−0.844842	−	0.990990i	−0.0269875	−	0.0316560i
$981$	44.5573	+	6.10038i	1.42260	+	0.194770i
$982$	−8.43209	+	1.79230i	−0.269079	+	0.0571944i
$983$	2.67834	−	12.6006i	0.0854259	−	0.401897i	−0.914571	−	0.404426i	$-0.867471\pi$
$983$	2.67834	−	12.6006i	0.0854259	−	0.401897i	0.999997	+	0.00252843i	$0.000804826\pi$
$984$	−2.80676	+	6.04722i	−0.0894764	+	0.192778i
$985$	1.82385	−	4.09642i	0.0581125	−	0.130523i
$986$	−3.35095	−	10.3132i	−0.106716	−	0.328438i
$987$	−11.4083	−	6.23908i	−0.363130	−	0.198592i
$988$	−3.77088	−	2.73971i	−0.119968	−	0.0871617i
$989$	−5.97881	−	10.3556i	−0.190115	−	0.329289i
$990$	1.25894	−	1.35695i	0.0400117	−	0.0431268i
$991$	3.01029	−	5.21398i	0.0956252	−	0.165628i	−0.814244	−	0.580523i	$-0.802848\pi$
$991$	3.01029	−	5.21398i	0.0956252	−	0.165628i	0.909869	+	0.414895i	$0.136182\pi$
$992$	−0.486074	+	4.62468i	−0.0154329	+	0.146834i
$993$	−17.3242	+	15.1139i	−0.549767	+	0.479626i
$994$	−21.7275	−	8.67973i	−0.689153	−	0.275304i
$995$	−0.622453	−	0.856733i	−0.0197331	−	0.0271603i
$996$	−6.96575	−	9.91051i	−0.220718	−	0.314027i
$997$	8.09070	−	38.0637i	0.256235	−	1.20549i	−0.642253	−	0.766493i	$-0.722000\pi$
$997$	8.09070	−	38.0637i	0.256235	−	1.20549i	0.898488	−	0.438998i	$-0.144667\pi$
$998$	−8.40530	−	9.33503i	−0.266065	−	0.295495i
$999$	−17.8644	−	2.73169i	−0.565204	−	0.0864270i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.bc.a.95.9	✓	128
3.2	odd	2		462.2.bc.b.95.14	yes	128
7.2	even	3	inner	462.2.bc.a.359.2	yes	128
11.8	odd	10		462.2.bc.b.305.5	yes	128
21.2	odd	6		462.2.bc.b.359.5	yes	128
33.8	even	10	inner	462.2.bc.a.305.2	yes	128
77.30	odd	30		462.2.bc.b.107.14	yes	128
231.107	even	30	inner	462.2.bc.a.107.9	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.9	✓	128	1.1	even	1	trivial
462.2.bc.a.107.9	yes	128	231.107	even	30	inner
462.2.bc.a.305.2	yes	128	33.8	even	10	inner
462.2.bc.a.359.2	yes	128	7.2	even	3	inner
462.2.bc.b.95.14	yes	128	3.2	odd	2
462.2.bc.b.107.14	yes	128	77.30	odd	30
462.2.bc.b.305.5	yes	128	11.8	odd	10
462.2.bc.b.359.5	yes	128	21.2	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104528 - 0.994522i) q^{2} +(0.333518 + 1.69964i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.0756668 - 0.169950i) q^{5} +(1.72519 - 0.154030i) q^{6} +(1.63703 + 2.07849i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.77753 + 1.13372i) q^{9} +O(q^{10})\)	\(q+(0.104528 - 0.994522i) q^{2} +(0.333518 + 1.69964i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(0.0756668 - 0.169950i) q^{5} +(1.72519 - 0.154030i) q^{6} +(1.63703 + 2.07849i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.77753 + 1.13372i) q^{9} +(-0.161110 - 0.0930169i) q^{10} +(1.90510 - 2.71488i) q^{11} +(0.0271446 - 1.73184i) q^{12} +(0.557091 - 0.766770i) q^{13} +(2.23822 - 1.41080i) q^{14} +(0.314090 + 0.0719245i) q^{15} +(0.913545 + 0.406737i) q^{16} +(0.846849 + 8.05723i) q^{17} +(0.837177 + 2.88082i) q^{18} +(1.02248 + 4.81041i) q^{19} +(-0.109348 + 0.150504i) q^{20} +(-2.98670 + 3.47557i) q^{21} +(-2.50087 - 2.17845i) q^{22} +(0.938796 - 0.542014i) q^{23} +(-1.71951 - 0.208022i) q^{24} +(3.32250 + 3.69000i) q^{25} +(-0.704338 - 0.634189i) q^{26} +(-2.85327 - 4.34268i) q^{27} +(-1.16912 - 2.37343i) q^{28} +(-0.413615 - 1.27298i) q^{29} +(0.104362 - 0.304851i) q^{30} +(-4.24813 + 1.89139i) q^{31} +(0.500000 - 0.866025i) q^{32} +(5.24970 + 2.33252i) q^{33} +8.10161 q^{34} +(0.477109 - 0.120941i) q^{35} +(2.95255 - 0.531463i) q^{36} +(2.32721 - 2.58463i) q^{37} +(4.89094 - 0.514059i) q^{38} +(1.48903 + 0.691121i) q^{39} +(0.138250 + 0.124481i) q^{40} +(1.18944 - 3.66071i) q^{41} +(3.14434 + 3.33364i) q^{42} -11.0307i q^{43} +(-2.42792 + 2.25946i) q^{44} +(-0.0174909 + 0.557827i) q^{45} +(-0.440914 - 0.990309i) q^{46} +(0.589942 + 2.77546i) q^{47} +(-0.386621 + 1.68835i) q^{48} +(-1.64025 + 6.80511i) q^{49} +(4.01709 - 2.91858i) q^{50} +(-13.4119 + 4.12657i) q^{51} +(-0.704338 + 0.634189i) q^{52} +(2.35586 + 5.29135i) q^{53} +(-4.61714 + 2.38370i) q^{54} +(-0.317243 - 0.529199i) q^{55} +(-2.48263 + 0.914621i) q^{56} +(-7.83494 + 3.34221i) q^{57} +(-1.30924 + 0.278287i) q^{58} +(-0.705877 + 3.32089i) q^{59} +(-0.292272 - 0.135656i) q^{60} +(5.92942 - 13.3177i) q^{61} +(1.43698 + 4.42256i) q^{62} +(-6.90333 - 3.91714i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(-0.0881596 - 0.152697i) q^{65} +(2.86848 - 4.97713i) q^{66} +(0.0659471 - 0.114224i) q^{67} +(0.846849 - 8.05723i) q^{68} +(1.23433 + 1.41484i) q^{69} +(-0.0704074 - 0.487137i) q^{70} +(-5.19792 - 7.15433i) q^{71} +(-0.219926 - 2.99193i) q^{72} +(2.96575 - 13.9527i) q^{73} +(-2.32721 - 2.58463i) q^{74} +(-5.16356 + 6.87772i) q^{75} -4.91788i q^{76} +(8.76157 - 0.484618i) q^{77} +(0.842981 - 1.40863i) q^{78} +(-12.4597 - 1.30956i) q^{79} +(0.138250 - 0.124481i) q^{80} +(6.42936 - 6.29788i) q^{81} +(-3.51633 - 1.56557i) q^{82} +(5.65811 - 4.11086i) q^{83} +(3.64405 - 2.77865i) q^{84} +(1.43341 + 0.465742i) q^{85} +(-10.9703 - 1.15303i) q^{86} +(2.02565 - 1.12756i) q^{87} +(1.99330 + 2.65080i) q^{88} +(-1.52736 + 0.881821i) q^{89} +(0.552943 + 0.0757039i) q^{90} +(2.50570 - 0.0973181i) q^{91} +(-1.03097 + 0.334983i) q^{92} +(-4.63150 - 6.58946i) q^{93} +(2.82192 - 0.296596i) q^{94} +(0.894899 + 0.190217i) q^{95} +(1.63869 + 0.560983i) q^{96} +(7.39198 + 5.37059i) q^{97} +(6.59638 + 2.34260i) q^{98} +(-2.21356 + 9.70052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9}+O(q^{10}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9	\( 128 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 4 q^{9} + 6 q^{11} - 12 q^{15} + 16 q^{16} + 2 q^{17} + 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} - 38 q^{29} - 6 q^{30} - 3 q^{31} + 64 q^{32} - 4 q^{33} - 16 q^{34} + 31 q^{35} + 8 q^{36} + 2 q^{37} + 22 q^{39} + 5 q^{40} - 16 q^{41} + 17 q^{42} + q^{44} + 28 q^{45} + 38 q^{49} - 34 q^{50} + 16 q^{51} - 25 q^{53} + 6 q^{54} - 42 q^{55} + 20 q^{57} - 19 q^{58} - 40 q^{59} - 4 q^{60} + 40 q^{61} + 4 q^{62} + 6 q^{63} - 32 q^{64} - 20 q^{65} - 41 q^{66} + 16 q^{67} + 2 q^{68} - 68 q^{69} - 21 q^{70} - 80 q^{71} - 16 q^{72} + 10 q^{73} - 2 q^{74} - 14 q^{75} - q^{77} - 16 q^{78} + 5 q^{80} - 88 q^{81} - 8 q^{82} + 92 q^{83} - 48 q^{84} - 100 q^{85} + 40 q^{86} + 38 q^{87} - q^{88} - 164 q^{90} + 12 q^{91} + 20 q^{92} + 47 q^{93} + 40 q^{94} - 38 q^{95} - 16 q^{97} - 18 q^{98} - 138 q^{99}+O(q^{100}) \) 128 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 4 * q^9 + 6 * q^11 - 12 * q^15 + 16 * q^16 + 2 * q^17 + 4 * q^18 + 2 * q^22 - 12 * q^25 - 18 * q^27 - 5 * q^28 - 38 * q^29 - 6 * q^30 - 3 * q^31 + 64 * q^32 - 4 * q^33 - 16 * q^34 + 31 * q^35 + 8 * q^36 + 2 * q^37 + 22 * q^39 + 5 * q^40 - 16 * q^41 + 17 * q^42 + q^44 + 28 * q^45 + 38 * q^49 - 34 * q^50 + 16 * q^51 - 25 * q^53 + 6 * q^54 - 42 * q^55 + 20 * q^57 - 19 * q^58 - 40 * q^59 - 4 * q^60 + 40 * q^61 + 4 * q^62 + 6 * q^63 - 32 * q^64 - 20 * q^65 - 41 * q^66 + 16 * q^67 + 2 * q^68 - 68 * q^69 - 21 * q^70 - 80 * q^71 - 16 * q^72 + 10 * q^73 - 2 * q^74 - 14 * q^75 - q^77 - 16 * q^78 + 5 * q^80 - 88 * q^81 - 8 * q^82 + 92 * q^83 - 48 * q^84 - 100 * q^85 + 40 * q^86 + 38 * q^87 - q^88 - 164 * q^90 + 12 * q^91 + 20 * q^92 + 47 * q^93 + 40 * q^94 - 38 * q^95 - 16 * q^97 - 18 * q^98 - 138 * q^99

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