LMFDB - Embedded newform 462.2.bc.b.95.14

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			95.14
Character	$\chi$	$=$	462.95
Dual form			462.2.bc.b.107.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 + 0.994522i) q^{2} +(1.65546 + 0.509351i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.0756668 + 0.169950i) q^{5} +(-0.679604 + 1.59315i) q^{6} +(1.63703 + 2.07849i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.48112 + 1.68643i) q^{9} +O(q^{10})$	\(q+(-0.104528 + 0.994522i) q^{2} +(1.65546 + 0.509351i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.0756668 + 0.169950i) q^{5} +(-0.679604 + 1.59315i) q^{6} +(1.63703 + 2.07849i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.48112 + 1.68643i) q^{9} +(-0.161110 - 0.0930169i) q^{10} +(-1.90510 + 2.71488i) q^{11} +(-1.51339 - 0.842411i) q^{12} +(0.557091 - 0.766770i) q^{13} +(-2.23822 + 1.41080i) q^{14} +(-0.211828 + 0.242806i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.846849 - 8.05723i) q^{17} +(-1.93654 + 2.29125i) q^{18} +(1.02248 + 4.81041i) q^{19} +(0.109348 - 0.150504i) q^{20} +(1.65136 + 4.27469i) q^{21} +(-2.50087 - 2.17845i) q^{22} +(-0.938796 + 0.542014i) q^{23} +(0.995988 - 1.41704i) q^{24} +(3.32250 + 3.69000i) q^{25} +(0.704338 + 0.634189i) q^{26} +(3.24843 + 4.05558i) q^{27} +(-1.16912 - 2.37343i) q^{28} +(0.413615 + 1.27298i) q^{29} +(-0.219334 - 0.236048i) q^{30} +(-4.24813 + 1.89139i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-4.53665 + 3.52403i) q^{33} +8.10161 q^{34} +(-0.477109 + 0.120941i) q^{35} +(-2.07628 - 2.16543i) q^{36} +(2.32721 - 2.58463i) q^{37} +(-4.89094 + 0.514059i) q^{38} +(1.31280 - 0.985605i) q^{39} +(0.138250 + 0.124481i) q^{40} +(-1.18944 + 3.66071i) q^{41} +(-4.42389 + 1.19549i) q^{42} -11.0307i q^{43} +(2.42792 - 2.25946i) q^{44} +(-0.474347 + 0.294061i) q^{45} +(-0.440914 - 0.990309i) q^{46} +(-0.589942 - 2.77546i) q^{47} +(1.30517 + 1.13865i) q^{48} +(-1.64025 + 6.80511i) q^{49} +(-4.01709 + 2.91858i) q^{50} +(2.70203 - 13.7698i) q^{51} +(-0.704338 + 0.634189i) q^{52} +(-2.35586 - 5.29135i) q^{53} +(-4.37292 + 2.80671i) q^{54} +(-0.317243 - 0.529199i) q^{55} +(2.48263 - 0.914621i) q^{56} +(-0.757504 + 8.48427i) q^{57} +(-1.30924 + 0.278287i) q^{58} +(0.705877 - 3.32089i) q^{59} +(0.257681 - 0.193458i) q^{60} +(5.92942 - 13.3177i) q^{61} +(-1.43698 - 4.42256i) q^{62} +(0.556455 + 7.91772i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.0881596 + 0.152697i) q^{65} +(-3.03051 - 4.88016i) q^{66} +(0.0659471 - 0.114224i) q^{67} +(-0.846849 + 8.05723i) q^{68} +(-1.83022 + 0.419108i) q^{69} +(-0.0704074 - 0.487137i) q^{70} +(5.19792 + 7.15433i) q^{71} +(2.37060 - 1.83855i) q^{72} +(2.96575 - 13.9527i) q^{73} +(2.32721 + 2.58463i) q^{74} +(3.62076 + 7.80099i) 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} +(3.31194 + 8.36846i) q^{81} +(-3.51633 - 1.56557i) q^{82} +(-5.65811 + 4.11086i) q^{83} +(-0.726520 - 4.52462i) q^{84} +(1.43341 + 0.465742i) q^{85} +(10.9703 + 1.15303i) q^{86} +(0.0363326 + 2.31804i) q^{87} +(1.99330 + 2.65080i) q^{88} +(1.52736 - 0.881821i) q^{89} +(-0.242867 - 0.502486i) q^{90} +(2.50570 - 0.0973181i) q^{91} +(1.03097 - 0.334983i) q^{92} +(-7.99600 + 0.967336i) q^{93} +(2.82192 - 0.296596i) q^{94} +(-0.894899 - 0.190217i) q^{95} +(-1.26884 + 1.17900i) q^{96} +(7.39198 + 5.37059i) q^{97} +(-6.59638 - 2.34260i) q^{98} +(-9.30524 + 3.52315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	$ 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 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} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) $ 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * 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 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * 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
$3$	1.65546	+	0.509351i	0.955783	+	0.294074i
$3$	1.65546	+	0.509351i	0.955783	+	0.294074i
$4$	−0.978148	−	0.207912i	−0.489074	−	0.103956i
$5$	−0.0756668	+	0.169950i	−0.0338392	+	0.0760041i	−0.929674	−	0.368383i	$-0.879912\pi$
$5$	−0.0756668	+	0.169950i	−0.0338392	+	0.0760041i	0.895835	+	0.444387i	$0.146578\pi$
$6$	−0.679604	+	1.59315i	−0.277447	+	0.650402i
$7$	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
$9$	2.48112	+	1.68643i	0.827041	+	0.562142i
$10$	−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
$12$	−1.51339	−	0.842411i	−0.436878	−	0.243183i
$13$	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
$15$	−0.211828	+	0.242806i	−0.0546938	+	0.0626922i
$16$	0.913545	+	0.406737i	0.228386	+	0.101684i
$17$	−0.846849	−	8.05723i	−0.205391	−	1.95417i	−0.288121	−	0.957594i	$-0.593031\pi$
$17$	−0.846849	−	8.05723i	−0.205391	−	1.95417i	0.0827301	−	0.996572i	$-0.473636\pi$
$18$	−1.93654	+	2.29125i	−0.456446	+	0.540053i
$19$	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
$21$	1.65136	+	4.27469i	0.360357	+	0.932814i
$22$	−2.50087	−	2.17845i	−0.533188	−	0.464446i
$23$	−0.938796	+	0.542014i	−0.195753	+	0.113018i	−0.594673	−	0.803968i	$-0.702718\pi$
$23$	−0.938796	+	0.542014i	−0.195753	+	0.113018i	0.398920	+	0.916986i	$0.369385\pi$
$24$	0.995988	−	1.41704i	0.203305	−	0.289252i
$25$	3.32250	+	3.69000i	0.664499	+	0.738001i
$26$	0.704338	+	0.634189i	0.138132	+	0.124375i
$27$	3.24843	+	4.05558i	0.625160	+	0.780497i
$28$	−1.16912	−	2.37343i	−0.220942	−	0.448536i
$29$	0.413615	+	1.27298i	0.0768063	+	0.236386i	0.982087	−	0.188429i	$-0.0603394\pi$
$29$	0.413615	+	1.27298i	0.0768063	+	0.236386i	−0.905281	+	0.424814i	$0.860339\pi$
$30$	−0.219334	−	0.236048i	−0.0400446	−	0.0430962i
$31$	−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
$33$	−4.53665	+	3.52403i	−0.789730	+	0.613454i
$34$	8.10161			1.38942
$35$	−0.477109	+	0.120941i	−0.0806462	+	0.0204428i
$36$	−2.07628	−	2.16543i	−0.346046	−	0.360905i
$37$	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
$39$	1.31280	−	0.985605i	0.210216	−	0.157823i
$40$	0.138250	+	0.124481i	0.0218593	+	0.0196822i
$41$	−1.18944	+	3.66071i	−0.185759	+	0.571707i	−0.999961	−	0.00887490i	$-0.997175\pi$
$41$	−1.18944	+	3.66071i	−0.185759	+	0.571707i	0.814202	+	0.580582i	$0.197175\pi$
$42$	−4.42389	+	1.19549i	−0.682621	+	0.184468i
$43$		−	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
$45$	−0.474347	+	0.294061i	−0.0707115	+	0.0438361i
$46$	−0.440914	−	0.990309i	−0.0650092	−	0.146013i
$47$	−0.589942	−	2.77546i	−0.0860519	−	0.404842i	0.913948	−	0.405832i	$-0.133018\pi$
$47$	−0.589942	−	2.77546i	−0.0860519	−	0.404842i	−1.00000		0.000989776i	$0.999685\pi$
$48$	1.30517	+	1.13865i	0.188385	+	0.164350i
$49$	−1.64025	+	6.80511i	−0.234322	+	0.972159i
$50$	−4.01709	+	2.91858i	−0.568102	+	0.412750i
$51$	2.70203	−	13.7698i	0.378360	−	1.92816i
$52$	−0.704338	+	0.634189i	−0.0976741	+	0.0879461i
$53$	−2.35586	−	5.29135i	−0.323602	−	0.726822i	0.676350	−	0.736580i	$-0.263561\pi$
$53$	−2.35586	−	5.29135i	−0.323602	−	0.726822i	−0.999952	+	0.00975796i	$0.996894\pi$
$54$	−4.37292	+	2.80671i	−0.595079	+	0.381944i
$55$	−0.317243	−	0.529199i	−0.0427770	−	0.0713572i
$56$	2.48263	−	0.914621i	0.331756	−	0.122221i
$57$	−0.757504	+	8.48427i	−0.100334	+	1.12377i
$58$	−1.30924	+	0.278287i	−0.171911	+	0.0365409i
$59$	0.705877	−	3.32089i	0.0918974	−	0.432343i	−0.908013	−	0.418942i	$-0.862401\pi$
$59$	0.705877	−	3.32089i	0.0918974	−	0.432343i	0.999910	−	0.0134009i	$-0.00426577\pi$
$60$	0.257681	−	0.193458i	0.0332665	−	0.0249754i
$61$	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
$63$	0.556455	+	7.91772i	0.0701067	+	0.997539i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	0.0881596	+	0.152697i	0.0109348	+	0.0189397i
$66$	−3.03051	−	4.88016i	−0.373030	−	0.600707i
$67$	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
$69$	−1.83022	+	0.419108i	−0.220332	+	0.0504547i
$70$	−0.0704074	−	0.487137i	−0.00841529	−	0.0582240i
$71$	5.19792	+	7.15433i	0.616880	+	0.849063i	0.997121	−	0.0758247i	$-0.0241589\pi$
$71$	5.19792	+	7.15433i	0.616880	+	0.849063i	−0.380241	+	0.924887i	$0.624159\pi$
$72$	2.37060	−	1.83855i	0.279377	−	0.216676i
$73$	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
$75$	3.62076	+	7.80099i	0.418090	+	0.900781i
$76$		−	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
$81$	3.31194	+	8.36846i	0.367993	+	0.929829i
$82$	−3.51633	−	1.56557i	−0.388314	−	0.172888i
$83$	−5.65811	+	4.11086i	−0.621058	+	0.451225i	−0.853291	−	0.521435i	$-0.825397\pi$
$83$	−5.65811	+	4.11086i	−0.621058	+	0.451225i	0.232233	+	0.972660i	$0.425397\pi$
$84$	−0.726520	−	4.52462i	−0.0792698	−	0.493676i
$85$	1.43341	+	0.465742i	0.155475	+	0.0505169i
$86$	10.9703	+	1.15303i	1.18296	+	0.124334i
$87$	0.0363326	+	2.31804i	0.00389527	+	0.248520i
$88$	1.99330	+	2.65080i	0.212486	+	0.282577i
$89$	1.52736	−	0.881821i	0.161900	−	0.0934729i	−0.416861	−	0.908970i	$-0.636870\pi$
$89$	1.52736	−	0.881821i	0.161900	−	0.0934729i	0.578761	+	0.815497i	$0.303536\pi$
$90$	−0.242867	−	0.502486i	−0.0256005	−	0.0529667i
$91$	2.50570	−	0.0973181i	0.262669	−	0.0102017i
$92$	1.03097	−	0.334983i	0.107486	−	0.0349244i
$93$	−7.99600	+	0.967336i	−0.829147	+	0.100308i
$94$	2.82192	−	0.296596i	0.291059	−	0.0305915i
$95$	−0.894899	−	0.190217i	−0.0918147	−	0.0195158i
$96$	−1.26884	+	1.17900i	−0.129501	+	0.120331i
$97$	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
$99$	−9.30524	+	3.52315i	−0.935211	+	0.354090i
$100$	−2.48270	−	4.30016i	−0.248270	−	0.430016i
$101$	8.42077	−	3.74917i	0.837898	−	0.373056i	0.0575045	−	0.998345i	$-0.481686\pi$
$101$	8.42077	−	3.74917i	0.837898	−	0.373056i	0.780393	+	0.625289i	$0.215019\pi$
$102$	13.4119	+	4.12657i	1.32798	+	0.408591i
$103$	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
$105$	−0.851439	−	0.0428021i	−0.0830919	−	0.00417706i
$106$	5.50861	−	1.78986i	0.535044	−	0.173846i
$107$	16.7964	−	3.57019i	1.62377	−	0.345143i	0.695927	−	0.718113i	$-0.254994\pi$
$107$	16.7964	−	3.57019i	1.62377	−	0.345143i	0.927844	+	0.372970i	$0.121660\pi$
$108$	−2.33424	−	4.64234i	−0.224612	−	0.446710i
$109$	−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	0.610332	−	0.792145i	$-0.291036\pi$
$113$	6.78724	+	2.20531i	0.638490	+	0.207458i	0.0281578	+	0.999603i	$0.491036\pi$
$114$	−8.35861	−	1.64020i	−0.782856	−	0.153619i
$115$	−0.0210798	−	0.200561i	−0.00196570	−	0.0187024i
$116$	−0.139910	−	1.33115i	−0.0129903	−	0.123594i
$117$	2.67531	−	0.962958i	0.247333	−	0.0890255i
$118$	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
$123$	−3.83366	+	5.45434i	−0.345670	+	0.491801i
$124$	4.54854	−	0.966822i	0.408471	−	0.0868231i
$125$	−1.76316	+	0.572886i	−0.157702	+	0.0512405i
$126$	−7.93252	−	0.274221i	−0.706685	−	0.0244295i
$127$	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
$129$	5.61852	−	18.2610i	0.494683	−	1.60779i
$130$	−0.161076	+	0.0717154i	−0.0141273	+	0.00628986i
$131$	−3.60622	−	6.24616i	−0.315077	−	0.545729i	0.664377	−	0.747398i	$-0.268697\pi$
$131$	−3.60622	−	6.24616i	−0.315077	−	0.545729i	−0.979454	+	0.201668i	$0.935364\pi$
$132$	5.17020	−	2.50380i	0.450008	−	0.217927i
$133$	−8.32456	+	10.0000i	−0.721831	+	0.867112i
$134$	0.106705	+	0.0775255i	0.00921788	+	0.00669718i
$135$	−0.935045	+	0.245198i	−0.0804759	+	0.0211033i
$136$	−7.92457	−	1.68442i	−0.679527	−	0.144438i
$137$	−9.49700	+	0.998175i	−0.811383	+	0.0852798i	−0.501128	−	0.865373i	$-0.667081\pi$
$137$	−9.49700	+	0.998175i	−0.811383	+	0.0852798i	−0.310256	+	0.950653i	$0.600415\pi$
$138$	−0.225502	−	1.86400i	−0.0191960	−	0.158674i
$139$	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
$141$	0.437056	−	4.89516i	0.0368068	−	0.412247i
$142$	−7.65847	+	4.42162i	−0.642684	+	0.371054i
$143$	1.02038	+	2.97321i	0.0853283	+	0.248632i
$144$	1.58069	+	2.54979i	0.131724	+	0.212482i
$145$	−0.247639	−	0.0260280i	−0.0205653	−	0.00216150i
$146$	13.5663	+	4.40796i	1.12276	+	0.364805i
$147$	−6.18157	+	10.4302i	−0.509848	+	0.860265i
$148$	−2.81373	+	2.04430i	−0.231287	+	0.168040i
$149$	−12.2038	−	5.43347i	−0.999772	−	0.445127i	−0.159445	−	0.987207i	$-0.550970\pi$
$149$	−12.2038	−	5.43347i	−0.999772	−	0.445127i	−0.840327	+	0.542080i	$0.817637\pi$
$150$	−8.13673	+	2.78550i	−0.664361	+	0.227435i
$151$	−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
$156$	−1.48903	+	0.691121i	−0.119218	+	0.0553340i
$157$	−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
$159$	−1.20489	−	9.95959i	−0.0955536	−	0.789847i
$160$	−0.109348	−	0.150504i	−0.00864471	−	0.0118984i
$161$	−2.66341	−	1.06399i	−0.209906	−	0.0838538i
$162$	−8.66881	+	2.41905i	−0.681086	+	0.190059i
$163$	−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
$165$	−0.255636	−	1.03766i	−0.0199012	−	0.0807815i
$166$	−3.49690	−	6.05681i	−0.271412	−	0.470100i
$167$	12.9631	+	9.41822i	1.00311	+	0.728804i	0.962753	−	0.270381i	$-0.0871498\pi$
$167$	12.9631	+	9.41822i	1.00311	+	0.728804i	0.0403593	+	0.999185i	$0.487150\pi$
$168$	4.57577	−	0.249589i	0.353029	−	0.0192562i
$169$	3.73963	+	11.5094i	0.287664	+	0.885339i
$170$	−0.613023	+	1.37687i	−0.0470167	+	0.105601i
$171$	−5.57550	+	13.6596i	−0.426369	+	1.04457i
$172$	−2.29342	+	10.7897i	−0.174871	+	0.822706i
$173$	−18.9964	+	4.03780i	−1.44427	+	0.306988i	−0.862372	−	0.506276i	$-0.831022\pi$
$173$	−18.9964	+	4.03780i	−1.44427	+	0.306988i	−0.581895	+	0.813264i	$0.697689\pi$
$174$	−2.30914	−	0.206168i	−0.175055	−	0.0156295i
$175$	−2.23061	+	12.9464i	−0.168618	+	0.978658i
$176$	−2.84464	+	1.70530i	−0.214423	+	0.128542i
$177$	2.86006	−	5.13808i	0.214975	−	0.386202i
$178$	0.717338	+	1.61117i	0.0537668	+	0.120762i
$179$	−8.79765	+	7.92144i	−0.657567	+	0.592076i	−0.928865	−	0.370420i	$-0.879214\pi$
$179$	−8.79765	+	7.92144i	−0.657567	+	0.592076i	0.271298	+	0.962496i	$0.412547\pi$
$180$	0.525120	−	0.189013i	0.0391401	−	0.0140882i
$181$	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
$183$	16.5993	−	19.0268i	1.22706	−	1.40650i
$184$	0.225382	+	1.06034i	0.0166154	+	0.0781693i
$185$	0.263166	+	0.591081i	0.0193484	+	0.0434572i
$186$	−0.126227	−	8.05332i	−0.00925538	−	0.590498i
$187$	23.4878	+	13.0507i	1.71760	+	0.954364i
$188$			2.83747i			0.206943i
$189$	−3.11171	+	13.3909i	−0.226344	+	0.974047i
$190$	0.282717	−	0.870114i	0.0205105	−	0.0631247i
$191$	−8.11838	−	7.30982i	−0.587425	−	0.528920i	0.320939	−	0.947100i	$-0.396002\pi$
$191$	−8.11838	−	7.30982i	−0.587425	−	0.528920i	−0.908364	+	0.418180i	$0.862668\pi$
$192$	−1.03991	−	1.38513i	−0.0750490	−	0.0999632i
$193$	−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
$195$	0.0681686	+	0.297688i	0.00488166	+	0.0213179i
$196$	3.01927	−	6.31538i	0.215662	−	0.451098i
$197$	−24.1037			−1.71731			−0.858657	−	0.512550i	$-0.828701\pi$
$197$	−24.1037			−1.71731			−0.858657	+	0.512550i	$0.828701\pi$
$198$	−2.53119	−	9.62253i	−0.179884	−	0.683843i
$199$	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
$201$	0.167353	−	0.155503i	0.0118042	−	0.0109683i
$202$	2.84842	+	8.76653i	0.200414	+	0.616811i
$203$	−1.96877	+	2.94360i	−0.138180	+	0.206600i
$204$	−5.50589	+	12.9071i	−0.385489	+	0.903679i
$205$	−0.532138	−	0.479140i	−0.0371662	−	0.0334646i
$206$	7.37362	+	8.18923i	0.513744	+	0.570571i
$207$	−3.24334	−	0.238406i	−0.225427	−	0.0165704i
$208$	0.820802	−	0.473890i	0.0569124	−	0.0328584i
$209$	−15.0077	−	6.38839i	−1.03810	−	0.441894i
$210$	0.131567	−	0.842300i	0.00907900	−	0.0581243i
$211$	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
$213$	4.96091	+	14.4913i	0.339916	+	0.992928i
$214$	1.79493	+	17.0776i	0.122699	+	1.16740i
$215$	1.87468	+	0.834660i	0.127852	+	0.0569233i
$216$	4.86090	−	1.83619i	0.330743	−	0.124937i
$217$	−10.8856	−	5.73343i	−0.738960	−	0.389211i
$218$	8.81148	−	12.1280i	0.596789	−	0.821409i
$219$	12.0165	−	21.5877i	0.812002	−	1.45876i
$220$	0.200284	+	0.583593i	0.0135031	+	0.0393458i
$221$	−6.64982	−	3.83927i	−0.447315	−	0.258258i
$222$	2.53613	+	5.46413i	0.170214	+	0.366729i
$223$	−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
$225$	2.02060	+	14.7585i	0.134707	+	0.983900i
$226$	−2.90269	+	6.51954i	−0.193084	+	0.433674i
$227$	21.8962	+	4.65419i	1.45330	+	0.308909i	0.865832	−	0.500335i	$-0.166790\pi$
$227$	21.8962	+	4.65419i	1.45330	+	0.308909i	0.587472	+	0.809244i	$0.300123\pi$
$228$	2.50493	−	8.14138i	0.165893	−	0.539176i
$229$	−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
$231$	−14.7513	−	3.66045i	−0.970565	−	0.240840i
$232$	1.33849			0.0878759
$233$	−1.39522	+	13.2746i	−0.0914036	+	0.869647i	0.848727	+	0.528832i	$0.177370\pi$
$233$	−1.39522	+	13.2746i	−0.0914036	+	0.869647i	−0.940130	+	0.340815i	$0.889297\pi$
$234$	0.678036	+	2.76131i	0.0443246	+	0.180513i
$235$	0.516329	+	0.109749i	0.0336816	+	0.00715925i
$236$	−1.38090	+	3.10156i	−0.0898892	+	0.201895i
$237$	−19.9595	−	8.51428i	−1.29651	−	0.553062i
$238$	13.2626	+	16.8391i	0.859687	+	1.09152i
$239$	−6.91610	+	21.2856i	−0.447365	+	1.37685i	0.432504	+	0.901632i	$0.357630\pi$
$239$	−6.91610	+	21.2856i	−0.447365	+	1.37685i	−0.879869	+	0.475217i	$0.842370\pi$
$240$	−0.292272	+	0.135656i	−0.0188661	+	0.00875654i
$241$	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
$243$	1.22031	+	15.5406i	0.0782827	+	0.996931i
$244$	−8.56876	+	11.7939i	−0.548559	+	0.755026i
$245$	−1.03242	−	0.793682i	−0.0659588	−	0.0507065i
$246$	−5.02373	−	4.38279i	−0.320301	−	0.279437i
$247$	4.25810	+	1.89583i	0.270936	+	0.120629i
$248$	0.486074	+	4.62468i	0.0308657	+	0.293668i
$249$	−11.4607	+	3.92341i	−0.726290	+	0.248636i
$250$	−0.385447	−	1.81339i	−0.0243778	−	0.114689i
$251$	6.49573	−	8.94061i	0.410007	−	0.564326i	−0.553213	−	0.833040i	$-0.686598\pi$
$251$	6.49573	−	8.94061i	0.410007	−	0.564326i	0.963220	+	0.268713i	$0.0865985\pi$
$252$	1.10189	−	7.86040i	0.0694127	−	0.495158i
$253$	0.316995	−	3.58131i	0.0199293	−	0.225155i
$254$	−1.51774	+	0.876266i	−0.0952313	+	0.0549818i
$255$	2.13573	+	1.50113i	0.133744	+	0.0940043i
$256$	0.669131	+	0.743145i	0.0418207	+	0.0464466i
$257$	9.59065	+	8.63546i	0.598248	+	0.538665i	0.911656	−	0.410953i	$-0.134804\pi$
$257$	9.59065	+	8.63546i	0.598248	+	0.538665i	−0.313408	+	0.949619i	$0.601471\pi$
$258$	17.5736	+	7.49653i	1.09409	+	0.466714i
$259$	9.18186	+	0.605968i	0.570533	+	0.0376530i
$260$	−0.0544856	−	0.167689i	−0.00337905	−	0.0103997i
$261$	−1.12055	+	3.85594i	−0.0693603	+	0.238677i
$262$	6.58889	−	2.93356i	0.407063	−	0.181236i
$263$	−11.5982	+	20.0886i	−0.715174	+	1.23872i	0.247718	+	0.968832i	$0.420319\pi$
$263$	−11.5982	+	20.0886i	−0.715174	+	1.23872i	−0.962892	+	0.269886i	$0.913014\pi$
$264$	1.94965	+	5.40360i	0.119992	+	0.332569i
$265$	1.07753			0.0661919
$266$	−9.07509	−	9.32425i	−0.556430	−	0.571706i
$267$	2.97764	−	0.681861i	0.182229	−	0.0417292i
$268$	−0.0882545	+	0.0980165i	−0.00539100	+	0.00598731i
$269$	−12.2454	+	1.28705i	−0.746617	+	0.0784726i	−0.470194	−	0.882563i	$-0.655816\pi$
$269$	−12.2454	+	1.28705i	−0.746617	+	0.0784726i	−0.276423	+	0.961036i	$0.589149\pi$
$270$	−0.146116	−	0.955553i	−0.00889236	−	0.0581531i
$271$	−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
$273$	4.19767	+	1.11518i	0.254054	+	0.0674935i
$274$		−	9.54931i		−	0.576895i
$275$	−16.3476	+	1.99036i	−0.985799	+	0.120023i
$276$	1.87736	−	0.0294255i	0.113004	−	0.00177121i
$277$	−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
$279$	−13.7298	−	2.47139i	−0.821982	−	0.147958i
$280$	−0.0324128	+	0.491131i	−0.00193703	+	0.0293507i
$281$	9.80903	−	7.12668i	0.585158	−	0.425142i	−0.255422	−	0.966830i	$-0.582214\pi$
$281$	9.80903	−	7.12668i	0.585158	−	0.425142i	0.840580	+	0.541688i	$0.182214\pi$
$282$	4.82266	+	0.946346i	0.287185	+	0.0563541i
$283$	−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
$285$	−1.38459	−	0.770715i	−0.0820158	−	0.0456532i
$286$	−3.06358	+	0.704003i	−0.181153	+	0.0416286i
$287$	−9.55591	+	3.52047i	−0.564067	+	0.207807i
$288$	−2.70105	+	1.30550i	−0.159161	+	0.0769274i
$289$	−47.5733	+	10.1120i	−2.79843	+	0.594825i
$290$	0.0517708	−	0.243562i	0.00304008	−	0.0143025i
$291$	9.50164	+	12.6559i	0.556996	+	0.741904i
$292$	−5.80188	+	13.0312i	−0.339529	+	0.762595i
$293$	−5.72859	−	17.6308i	−0.334668	−	1.03000i	−0.966885	−	0.255211i	$-0.917855\pi$
$293$	−5.72859	−	17.6308i	−0.334668	−	1.03000i	0.632217	−	0.774791i	$-0.282145\pi$
$294$	−9.72687	−	7.23796i	−0.567282	−	0.422126i
$295$	0.510975	+	0.371245i	0.0297501	+	0.0216147i
$296$	−1.73898	−	3.01201i	−0.101076	−	0.175069i
$297$	−17.1990	+	1.09281i	−0.997987	+	0.0634114i
$298$	6.67935	−	11.5690i	0.386924	−	0.670172i
$299$	−0.107395	+	1.02179i	−0.00621080	+	0.0590918i
$300$	−1.91972	−	8.38332i	−0.110835	−	0.484011i
$301$	22.9273	−	18.0577i	1.32151	−	1.04083i
$302$	−0.409420	−	0.563518i	−0.0235594	−	0.0324268i
$303$	15.8499	−	1.91748i	0.910554	−	0.110156i
$304$	−1.02248	+	4.81041i	−0.0586435	+	0.275896i
$305$	1.81469	+	2.01541i	0.103909	+	0.115402i
$306$	20.1011	+	13.6628i	1.14910	+	0.781049i
$307$			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	−0.506094	−	0.862478i	$-0.668911\pi$
$311$	5.26865	−	4.74391i	0.298758	−	0.269003i	0.804852	+	0.593476i	$0.202245\pi$
$312$	−0.531689	−	1.55312i	−0.0301010	−	0.0879279i
$313$	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
$315$	−1.38772	−	0.504539i	−0.0781894	−	0.0284275i
$316$	11.9151	+	3.87145i	0.670277	+	0.217786i
$317$	−18.0462	−	1.89673i	−1.01358	−	0.106531i	−0.416850	−	0.908975i	$-0.636866\pi$
$317$	−18.0462	−	1.89673i	−1.01358	−	0.106531i	−0.596727	+	0.802444i	$0.703533\pi$
$318$	10.0310	−	0.157224i	0.562509	−	0.00881669i
$319$	−4.24396	−	1.30223i	−0.237616	−	0.0729108i
$320$	0.161110	−	0.0930169i	0.00900632	−	0.00519980i
$321$	29.6243	+	2.64496i	1.65347	+	0.147627i
$322$	1.33656	−	2.53760i	0.0744835	−	0.141415i
$323$	37.8927	−	12.3121i	2.10841	−	0.685063i
$324$	−1.49966	−	8.87418i	−0.0833146	−	0.493010i
$325$	4.68032	−	0.491921i	0.259617	−	0.0272869i
$326$	−5.21769	−	1.10905i	−0.288981	−	0.0614248i
$327$	−17.6743	−	19.0212i	−0.977394	−	1.05188i
$328$	3.11399	+	2.26244i	0.171941	+	0.124923i
$329$	4.80302	−	5.76971i	0.264799	−	0.318094i
$330$	1.05869	−	0.145771i	0.0582792	−	0.00802440i
$331$	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
$333$	10.1329	−	2.48812i	0.555279	−	0.136348i
$334$	−10.7216	+	11.9076i	−0.586662	+	0.651554i
$335$	0.0144224	+	0.0198507i	0.000787978	+	0.00108456i
$336$	−0.230077	+	4.57680i	−0.0125517	+	0.249685i
$337$	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
$339$	10.1128	+	7.10790i	0.549250	+	0.386048i
$340$	−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
$345$	0.0672592	−	0.342759i	0.00362111	−	0.0184535i
$346$	−2.03002	−	19.3144i	−0.109135	−	1.03835i
$347$	−1.48856	−	14.1627i	−0.0799101	−	0.760294i	−0.958956	−	0.283556i	$-0.908486\pi$
$347$	−1.48856	−	14.1627i	−0.0799101	−	0.760294i	0.879046	−	0.476738i	$-0.158181\pi$
$348$	0.446409	−	2.27494i	0.0239300	−	0.121950i
$349$	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	0.368683	−	0.929555i	$-0.379809\pi$
$353$	−4.73455	−	2.73349i	−0.251995	−	0.145489i	−0.620677	+	0.784066i	$0.713142\pi$
$354$	4.81097	+	3.38146i	0.255700	+	0.179723i
$355$	−1.60919	+	0.342044i	−0.0854070	+	0.0181538i
$356$	−1.67732	+	0.544995i	−0.0888980	+	0.0288847i
$357$	33.0437	−	16.9255i	1.74886	−	0.895790i
$358$	−6.95844	−	9.57747i	−0.367765	−	0.506185i
$359$	12.8504	−	14.2718i	0.678219	−	0.753239i	−0.301532	−	0.953456i	$-0.597498\pi$
$359$	12.8504	−	14.2718i	0.678219	−	0.753239i	0.979752	+	0.200217i	$0.0641648\pi$
$360$	0.133087	+	0.542001i	0.00701433	+	0.0285659i
$361$	−4.73724	+	2.10916i	−0.249328	+	0.111008i
$362$	3.49691	+	6.05683i	0.183794	+	0.318340i
$363$	−0.924546	−	19.0301i	−0.0485261	−	0.998822i
$364$	−2.47118	−	0.425773i	−0.129525	−	0.0223166i
$365$	2.14687	+	1.55979i	0.112372	+	0.0816431i
$366$	17.1875	+	18.4972i	0.898404	+	0.966867i
$367$	−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
$369$	−9.12466	+	7.07678i	−0.475011	+	0.368402i
$370$	−0.615352	+	0.199940i	−0.0319906	+	0.0103944i
$371$	7.14140	−	13.5587i	0.370763	−	0.703934i
$372$	8.02239	+	0.716266i	0.415942	+	0.0371366i
$373$	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
$375$	−3.21065	+	0.0503233i	−0.165797	+	0.00259868i
$376$	−2.82192	−	0.296596i	−0.145529	−	0.0152958i
$377$	1.20650	+	0.392016i	0.0621380	+	0.0201898i
$378$	−12.9923	−	4.49440i	−0.668253	−	0.231167i
$379$	−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
$381$	0.983141	+	2.87185i	0.0503678	+	0.147129i
$382$	8.11838	−	7.30982i	0.415373	−	0.374003i
$383$	19.5058	+	2.05014i	0.996699	+	0.104757i	0.588807	−	0.808273i	$-0.299598\pi$
$383$	19.5058	+	2.05014i	0.996699	+	0.104757i	0.407891	+	0.913031i	$0.366264\pi$
$384$	1.48624	−	0.889427i	0.0758445	−	0.0453884i
$385$	0.580599	−	1.52570i	0.0295901	−	0.0777569i
$386$		−	18.2293i		−	0.927848i
$387$	18.6025	−	27.3686i	0.945619	−	1.39122i
$388$	−6.11384	−	6.79011i	−0.310383	−	0.344716i
$389$	−7.27976	+	34.2486i	−0.369099	+	1.73647i	0.265938	+	0.963990i	$0.414318\pi$
$389$	−7.27976	+	34.2486i	−0.369099	+	1.73647i	−0.635037	+	0.772482i	$0.719015\pi$
$390$	−0.303183	+	0.0366783i	−0.0153523	+	0.00185728i
$391$	5.16215	+	7.10510i	0.261061	+	0.359320i
$392$	5.96518	+	3.66287i	0.301287	+	0.185003i
$393$	−2.78848	−	12.1771i	−0.140660	−	0.614254i
$394$	2.51952	−	23.9716i	0.126931	−	1.20767i
$395$	1.16534	−	2.01843i	0.0586348	−	0.101558i
$396$	9.83440	−	1.51149i	0.494197	−	0.0759554i
$397$	−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
$399$	−18.8745	+	12.3146i	−0.944909	+	0.616499i
$400$	1.53439	+	4.72237i	0.0767195	+	0.236118i
$401$	−1.65249	+	3.71156i	−0.0825215	+	0.185346i	−0.950094	−	0.311965i	$-0.899013\pi$
$401$	−1.65249	+	3.71156i	−0.0825215	+	0.185346i	0.867572	+	0.497312i	$0.165679\pi$
$402$	0.137158	+	0.182691i	0.00684082	+	0.00911179i
$403$	−0.916334	+	4.31101i	−0.0456459	+	0.214747i
$404$	−9.01625	+	1.91646i	−0.448575	+	0.0953476i
$405$	−1.67283	−	0.0703494i	−0.0831234	−	0.00349569i
$406$	−2.72168	−	2.26567i	−0.135075	−	0.112443i
$407$	2.58340	+	11.2421i	0.128055	+	0.557250i
$408$	−12.2609	−	6.82489i	−0.607004	−	0.337882i
$409$	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
$411$	−16.2304	−	3.18487i	−0.800585	−	0.157098i
$412$	−8.91512	+	6.47722i	−0.439217	+	0.319110i
$413$	8.05799	−	3.96925i	0.396508	−	0.195314i
$414$	0.576121	−	3.20065i	0.0283148	−	0.157303i
$415$	−0.270511	−	1.27265i	−0.0132788	−	0.0624721i
$416$	0.385497	+	0.865840i	0.0189005	+	0.0424513i
$417$	9.28698	−	0.145563i	0.454785	−	0.00712824i
$418$	7.92212	−	14.2577i	0.387484	−	0.697365i
$419$			9.94577i			0.485883i	0.970041	+	0.242941i	$0.0781123\pi$
$419$			9.94577i			0.485883i	−0.970041	+	0.242941i	$0.921888\pi$
$420$	0.823934	+	0.218891i	0.0402038	+	0.0106808i
$421$	−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
$423$	3.21689	−	7.88115i	0.156410	−	0.383195i
$424$	−5.76037	+	0.605439i	−0.279748	+	0.0294027i
$425$	26.9176	−	29.8950i	1.30569	−	1.45012i
$426$	−14.9305	+	3.41898i	−0.723384	+	0.165650i
$427$	37.3874	−	9.47725i	1.80930	−	0.458636i
$428$	−17.1717			−0.830023
$429$	0.174789	+	5.44178i	0.00843890	+	0.262731i
$430$	−1.02604	+	1.77716i	−0.0494802	+	0.0857023i
$431$	15.7282	−	7.00265i	0.757601	−	0.337306i	0.00867770	−	0.999962i	$-0.497238\pi$
$431$	15.7282	−	7.00265i	0.757601	−	0.337306i	0.748923	+	0.662657i	$0.230571\pi$
$432$	1.31803	+	5.02621i	0.0634138	+	0.241824i
$433$	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
$435$	−0.396701	−	0.169224i	−0.0190204	−	0.00811366i
$436$	11.1405	+	10.0309i	0.533532	+	0.480394i
$437$	−3.56722	−	3.96180i	−0.170643	−	0.189518i
$438$	20.2133	+	14.2072i	0.965830	+	0.678848i
$439$	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
$441$	−15.5460	+	14.1182i	−0.740285	+	0.672293i
$442$	4.51334	−	6.21208i	0.214678	−	0.295478i
$443$	2.69115	+	12.6609i	0.127860	+	0.601536i	0.994689	+	0.102929i	$0.0328215\pi$
$443$	2.69115	+	12.6609i	0.127860	+	0.601536i	−0.866828	+	0.498607i	$0.833845\pi$
$444$	−5.69930	+	1.95108i	−0.270477	+	0.0925942i
$445$	0.0342955	+	0.326300i	0.00162576	+	0.0154681i
$446$	−7.92375	−	3.52788i	−0.375200	−	0.167050i
$447$	−17.4354	−	15.2109i	−0.824664	−	0.719452i
$448$	−0.102680	−	2.64376i	−0.00485117	−	0.124906i
$449$	5.60450	−	7.71394i	0.264493	−	0.364043i	−0.656028	−	0.754737i	$-0.727765\pi$
$449$	5.60450	−	7.71394i	0.264493	−	0.364043i	0.920521	+	0.390693i	$0.127765\pi$
$450$	−14.8889	+	0.466846i	−0.701867	+	0.0220073i
$451$	−7.67241	−	10.2032i	−0.361280	−	0.480450i
$452$	−6.18042	−	3.56826i	−0.290702	−	0.167837i
$453$	−1.09432	+	0.507921i	−0.0514158	+	0.0238642i
$454$	−6.91747	+	21.2898i	−0.324653	+	0.999179i
$455$	−0.173059	+	0.433208i	−0.00811313	+	0.0203091i
$456$	7.83494	+	3.34221i	0.366905	+	0.156513i
$457$	−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
$459$	29.9258	−	29.6078i	1.39682	−	1.38197i
$460$	−0.0210798	+	0.200561i	−0.000982852	+	0.00935121i
$461$	−33.7485			−1.57183			−0.785913	−	0.618337i	$-0.787807\pi$
$461$	−33.7485			−1.57183			−0.785913	+	0.618337i	$0.787807\pi$
$462$	5.18233	−	14.2879i	0.241104	−	0.664732i
$463$	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
$465$	0.440633	−	1.43212i	0.0204339	−	0.0664129i
$466$	−13.0560	−	2.77514i	−0.604809	−	0.128556i
$467$	−3.63202	+	8.15766i	−0.168070	+	0.377491i	−0.977870	−	0.209215i	$-0.932909\pi$
$467$	−3.63202	+	8.15766i	−0.168070	+	0.377491i	0.809800	+	0.586707i	$0.199576\pi$
$468$	−2.81706	+	0.385686i	−0.130219	+	0.0178283i
$469$	0.345371	−	0.0499174i	0.0159477	−	0.00230497i
$470$	−0.163119	+	0.502029i	−0.00752412	+	0.0231569i
$471$	−1.93981	−	4.17935i	−0.0893818	−	0.192574i
$472$	−2.94023	−	1.69754i	−0.135335	−	0.0781357i
$473$	29.9472	+	21.0146i	1.37697	+	0.966254i
$474$	10.5540	−	18.9602i	0.484760	−	0.870869i
$475$	−14.3532	+	19.7556i	−0.658572	+	0.906447i
$476$	−18.1332	+	11.4298i	−0.831134	+	0.523883i
$477$	3.07829	−	17.1015i	0.140945	−	0.783022i
$478$	−20.4460	−	9.10316i	−0.935180	−	0.416369i
$479$	1.11850	+	10.6418i	0.0511053	+	0.486235i	0.989901	+	0.141760i	$0.0452762\pi$
$479$	1.11850	+	10.6418i	0.0511053	+	0.486235i	−0.938796	+	0.344475i	$0.888057\pi$
$480$	−0.104362	−	0.304851i	−0.00476345	−	0.0139145i
$481$	−0.685349	−	3.22431i	−0.0312492	−	0.147016i
$482$	−10.7226	+	14.7584i	−0.488400	+	0.672225i
$483$	−3.86724	−	3.11800i	−0.175965	−	0.141874i
$484$	1.50874	+	10.8960i	0.0685793	+	0.495275i
$485$	−1.47206	+	0.849895i	−0.0668428	+	0.0385917i
$486$	−15.5830	−	0.410816i	−0.706861	−	0.0186350i
$487$	−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
$489$	−3.62518	+	8.49829i	−0.163936	+	0.384306i
$490$	0.897252	−	0.943800i	0.0405337	−	0.0426366i
$491$	2.66387	+	8.19855i	0.120219	+	0.369995i	0.993000	−	0.118117i	$-0.0376857\pi$
$491$	2.66387	+	8.19855i	0.120219	+	0.369995i	−0.872781	+	0.488112i	$0.837686\pi$
$492$	4.88391	−	4.53808i	0.220183	−	0.204593i
$493$	9.90639	−	4.41061i	0.446161	−	0.198644i
$494$	−2.33053	+	4.03660i	−0.104856	+	0.181615i
$495$	0.105337	−	1.84801i	0.00473453	−	0.0830620i
$496$	−4.65016			−0.208798
$497$	−6.36104	+	22.5157i	−0.285332	+	1.00997i
$498$	−2.70395	−	11.8080i	−0.121167	−	0.529129i
$499$	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
$501$	16.6627	+	22.1943i	0.744435	+	0.991568i
$502$	8.21265	+	7.39470i	0.366548	+	0.330042i
$503$	−3.33866	+	10.2753i	−0.148864	+	0.458155i	−0.997488	−	0.0708415i	$-0.977432\pi$
$503$	−3.33866	+	10.2753i	−0.148864	+	0.458155i	0.848624	+	0.528996i	$0.177432\pi$
$504$	7.70216	+	1.91749i	0.343081	+	0.0854119i
$505$			1.71480i			0.0763076i
$506$	3.52856	+	0.689608i	0.156864	+	0.0306568i
$507$	0.328496	+	20.9582i	0.0145890	+	0.930787i
$508$	−0.712819	−	1.60102i	−0.0316262	−	0.0710336i
$509$	−6.67417	−	31.3995i	−0.295827	−	1.39176i	−0.835318	−	0.549767i	$-0.814716\pi$
$509$	−6.67417	−	31.3995i	−0.295827	−	1.39176i	0.539491	−	0.841992i	$-0.318617\pi$
$510$	−1.71615	+	1.96712i	−0.0759924	+	0.0871054i
$511$	33.8557	−	16.6768i	1.49769	−	0.737739i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−16.1876	+	19.7730i	−0.714698	+	0.873001i
$514$	−9.59065	+	8.63546i	−0.423025	+	0.380894i
$515$	0.833825	+	1.87280i	0.0367427	+	0.0825255i
$516$	−9.29241	+	16.6938i	−0.409076	+	0.734903i
$517$	8.65895	+	3.68590i	0.380820	+	0.162106i
$518$	−1.56241	+	9.06822i	−0.0686485	+	0.398435i
$519$	−33.5045	−	2.99139i	−1.47068	−	0.131307i
$520$	0.172466	−	0.0366588i	0.00756314	−	0.00160759i
$521$	5.68170	−	26.7303i	0.248920	−	1.17108i	−0.659069	−	0.752082i	$-0.729050\pi$
$521$	5.68170	−	26.7303i	0.248920	−	1.17108i	0.907989	−	0.418994i	$-0.137617\pi$
$522$	−3.71769	−	1.51747i	−0.162719	−	0.0664177i
$523$	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
$525$	−10.2870	+	20.2962i	−0.448961	+	0.885798i
$526$	−18.7662	−	13.6345i	−0.818247	−	0.594491i
$527$	18.8369	+	32.6264i	0.820547	+	1.42123i
$528$	−5.57779	+	1.37414i	−0.242742	+	0.0598016i
$529$	−10.9124	+	18.9009i	−0.474454	+	0.821778i
$530$	−0.112632	+	1.07162i	−0.00489243	+	0.0465483i
$531$	7.35181	−	7.04913i	0.319041	−	0.305906i
$532$	10.2218	−	8.05073i	0.443170	−	0.349043i
$533$	2.14430	+	2.95138i	0.0928799	+	0.127838i
$534$	0.366877	+	3.03261i	0.0158763	+	0.131234i
$535$	−0.664176	+	3.12470i	−0.0287148	+	0.135093i
$536$	−0.0882545	−	0.0980165i	−0.00381201	−	0.00423367i
$537$	−18.5990	+	8.63256i	−0.802605	+	0.372522i
$538$		−	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
$543$	11.4607	−	3.92342i	0.491826	−	0.168370i
$544$	7.40119	+	3.29522i	0.317324	+	0.141282i
$545$	2.25621	−	1.63923i	0.0966455	−	0.0702170i
$546$	−1.54784	+	4.05810i	−0.0662415	+	0.173671i
$547$	−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
$549$	37.1709	−	23.0433i	1.58642	−	0.983465i
$550$	−0.270666	−	16.4661i	−0.0115412	−	0.702118i
$551$	−5.70062	+	3.29126i	−0.242855	+	0.140212i
$552$	−0.166973	+	1.87015i	−0.00710686	+	0.0795990i
$553$	−17.6749	−	28.0411i	−0.751615	−	1.19243i
$554$	12.6141	−	4.09857i	0.535921	−	0.174131i
$555$	0.134594	+	1.11256i	0.00571321	+	0.0472255i
$556$	−5.33312	+	0.560534i	−0.226175	+	0.0237719i
$557$	26.6377	+	5.66202i	1.12868	+	0.239907i	0.734156	−	0.678980i	$-0.237578\pi$
$557$	26.6377	+	5.66202i	1.12868	+	0.239907i	0.394519	+	0.918888i	$0.370911\pi$
$558$	3.89300	−	13.3963i	0.164804	−	0.567109i
$559$	−8.45804	−	6.14512i	−0.357737	−	0.259911i
$560$	−0.485052	−	0.0835723i	−0.0204972	−	0.00353158i
$561$	32.2358	+	33.5686i	1.36100	+	1.41727i
$562$	6.06232	+	10.5002i	0.255723	+	0.442926i
$563$	24.5232	−	10.9184i	1.03353	−	0.460156i	0.181355	−	0.983418i	$-0.441952\pi$
$563$	24.5232	−	10.9184i	1.03353	−	0.460156i	0.852172	+	0.523261i	$0.175285\pi$
$564$	−1.44527	+	4.69732i	−0.0608567	+	0.197793i
$565$	−0.888362	+	0.986626i	−0.0373737	+	0.0415076i
$566$	−11.5188	−	15.8543i	−0.484172	−	0.666406i
$567$	−11.9720	+	20.5833i	−0.502778	+	0.864416i
$568$	8.41042	−	2.73271i	0.352893	−	0.114662i
$569$	23.6037	−	5.01713i	0.989520	−	0.210329i	0.315406	−	0.948957i	$-0.397859\pi$
$569$	23.6037	−	5.01713i	0.989520	−	0.210329i	0.674114	+	0.738628i	$0.264526\pi$
$570$	0.911222	−	1.29644i	0.0381669	−	0.0543019i
$571$	−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
$576$	−1.01601	−	2.82271i	−0.0423339	−	0.117613i
$577$	−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
$579$	−30.9832	−	6.07980i	−1.28762	−	0.252668i
$580$	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
$585$	−0.0387772	+	0.527534i	−0.00160324	+	0.0218108i
$586$	18.1330	−	3.85429i	0.749068	−	0.159219i
$587$	14.1420	−	4.59502i	0.583704	−	0.189657i	−0.00225547	−	0.999997i	$-0.500718\pi$
$587$	14.1420	−	4.59502i	0.583704	−	0.189657i	0.585959	+	0.810341i	$0.300718\pi$
$588$	8.21504	−	8.91701i	0.338783	−	0.367731i
$589$	−13.4420	−	18.5013i	−0.553868	−	0.762334i
$590$	−0.422623	+	0.469370i	−0.0173991	+	0.0193237i
$591$	−39.9027	−	12.2772i	−1.64138	−	0.505018i
$592$	3.17728	−	1.41462i	0.130585	−	0.0581404i
$593$	20.0364	+	34.7041i	0.822797	+	1.42513i	0.903592	+	0.428395i	$0.140921\pi$
$593$	20.0364	+	34.7041i	0.822797	+	1.42513i	−0.0807952	+	0.996731i	$0.525746\pi$
$594$	0.710959	−	17.2190i	0.0291710	−	0.706505i
$595$	1.37849	+	3.74176i	0.0565127	+	0.153397i
$596$	10.8074	+	7.85204i	0.442689	+	0.321632i
$597$	7.22278	−	6.71134i	0.295609	−	0.274677i
$598$	−1.00497	−	0.213613i	−0.0410962	−	0.00873528i
$599$	−27.4654	+	2.88673i	−1.12221	+	0.117949i	−0.647406	−	0.762145i	$-0.724146\pi$
$599$	−27.4654	+	2.88673i	−1.12221	+	0.117949i	−0.474800	+	0.880094i	$0.657480\pi$
$600$	8.53806	−	1.03291i	0.348565	−	0.0421685i
$601$	−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
$603$	0.356253	−	0.172188i	0.0145077	−	0.00701205i
$604$	0.603227	−	0.348273i	0.0245449	−	0.0141710i
$605$	2.04109	+	0.146900i	0.0829822	+	0.00597232i
$606$	0.250210	+	15.9635i	0.0101641	+	0.648474i
$607$	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
$609$	−4.75855	+	3.87022i	−0.192826	+	0.156829i
$610$	−2.19406	+	1.59408i	−0.0888349	+	0.0645424i
$611$	−2.45679	−	1.09383i	−0.0993912	−	0.0442518i
$612$	−15.6891	+	18.5628i	−0.634193	+	0.750358i
$613$	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	$-0.895454\pi$
$617$		−	16.0248i		−	0.645136i	0.946546	−	0.322568i	$-0.104546\pi$
$618$	8.03556	+	17.3127i	0.323238	+	0.696421i
$619$	−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
$621$	−5.24779	−	2.04667i	−0.210587	−	0.0821301i
$622$	4.16720	+	5.73566i	0.167090	+	0.229979i
$623$	4.33319	+	1.73103i	0.173606	+	0.0693524i
$624$	1.60018	−	0.366431i	0.0640586	−	0.0146690i
$625$	−2.55907	+	24.3480i	−0.102363	+	0.973918i
$626$	−9.77793	+	16.9359i	−0.390805	+	0.676893i
$627$	−21.5907	−	18.2199i	−0.862249	−	0.727633i
$628$	1.33010	+	2.30379i	0.0530766	+	0.0919314i
$629$	−22.7958	−	16.5621i	−0.908927	−	0.660374i
$630$	0.646832	−	1.32738i	0.0257704	−	0.0528843i
$631$	−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
$633$	3.23423	−	2.42815i	0.128549	−	0.0965104i
$634$	3.77269	−	17.7491i	0.149833	−	0.704907i
$635$	−0.318905	+	0.0677854i	−0.0126554	+	0.00268998i
$636$	−0.892160	+	9.99246i	−0.0353764	+	0.396227i
$637$	4.30419	+	5.04877i	0.170538	+	0.200039i
$638$	1.73871	−	4.08459i	0.0688362	−	0.161710i
$639$	0.831441	+	26.5167i	0.0328913	+	1.04898i
$640$	0.0756668	+	0.169950i	0.00299099	+	0.00671788i
$641$	25.9746	−	23.3876i	1.02593	−	0.923756i	0.0288138	−	0.999585i	$-0.490827\pi$
$641$	25.9746	−	23.3876i	1.02593	−	0.923756i	0.997121	+	0.0758291i	$0.0241603\pi$
$642$	−5.72706	+	29.1856i	−0.226029	+	1.15186i
$643$	−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
$645$	2.67832	+	2.33662i	0.105459	+	0.0920042i
$646$	8.28378	+	38.9721i	0.325921	+	1.53334i
$647$	−1.10988	−	2.49282i	−0.0436337	−	0.0980029i	0.890413	−	0.455153i	$-0.150415\pi$
$647$	−1.10988	−	2.49282i	−0.0436337	−	0.0980029i	−0.934047	+	0.357150i	$0.883749\pi$
$648$	8.98232	−	0.563843i	0.352859	−	0.0221498i
$649$	7.67107	+	8.24301i	0.301116	+	0.323566i
$650$			4.70610i			0.184588i
$651$	−15.1003	−	15.0361i	−0.591828	−	0.589310i
$652$	1.64838	−	5.07318i	0.0645554	−	0.198681i
$653$	−7.27024	−	6.54616i	−0.284507	−	0.256171i	0.514504	−	0.857488i	$-0.327976\pi$
$653$	−7.27024	−	6.54616i	−0.284507	−	0.256171i	−0.799010	+	0.601317i	$0.794643\pi$
$654$	20.7645	−	15.5893i	0.811956	−	0.609589i
$655$	1.33441	−	0.140252i	0.0521396	−	0.00548009i
$656$	−2.57555	+	2.86044i	−0.100558	+	0.111681i
$657$	30.8887	−	29.6170i	1.20508	−	1.15547i
$658$	5.23605	+	5.37980i	0.204122	+	0.209727i
$659$	−19.7562			−0.769592			−0.384796	−	0.923002i	$-0.625728\pi$
$659$	−19.7562			−0.769592			−0.384796	+	0.923002i	$0.625728\pi$
$660$	0.0343083	+	1.06813i	0.00133545	+	0.0415770i
$661$	−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
$663$	−9.05299	−	9.74287i	−0.351589	−	0.378382i
$664$	2.16121	+	6.65151i	0.0838710	+	0.258128i
$665$	−1.06962	−	2.17143i	−0.0414779	−	0.0842045i
$666$	1.41531	+	10.3375i	0.0548422	+	0.400568i
$667$	−1.07827	−	0.970880i	−0.0417508	−	0.0375926i
$668$	−10.7216	−	11.9076i	−0.414833	−	0.460718i
$669$	−8.63883	+	12.2909i	−0.333996	+	0.475193i
$670$	−0.0212495	+	0.0122684i	−0.000820939	+	0.000473969i
$671$	24.8599	+	41.4693i	0.959705	+	1.60090i
$672$	−4.52767	−	0.707222i	−0.174659	−	0.0272817i
$673$	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
$675$	−4.17223	+	25.4614i	−0.160589	+	0.980008i
$676$	−1.26497	−	12.0354i	−0.0486528	−	0.462901i
$677$	33.2939	+	14.8234i	1.27959	+	0.569710i	0.930126	−	0.367240i	$-0.119697\pi$
$677$	33.2939	+	14.8234i	1.27959	+	0.569710i	0.349464	+	0.936950i	$0.386364\pi$
$678$	−8.12603	+	9.31438i	−0.312078	+	0.357717i
$679$	0.938187	+	24.1560i	0.0360043	+	0.927022i
$680$	0.885895	−	1.21933i	0.0339725	−	0.0467591i
$681$	33.8778	+	18.8577i	1.29820	+	0.722629i
$682$	14.7443	+	4.52419i	0.564589	+	0.173240i
$683$	7.36169	+	4.25027i	0.281687	+	0.162632i	0.634187	−	0.773180i	$-0.281335\pi$
$683$	7.36169	+	4.25027i	0.281687	+	0.162632i	−0.352500	+	0.935812i	$0.614668\pi$
$684$	8.29364	−	12.2019i	0.317115	−	0.466550i
$685$	0.548967	−	1.68955i	0.0209749	−	0.0645543i
$686$	−5.92942	−	17.5454i	−0.226386	−	0.669887i
$687$	−11.6685	+	27.3537i	−0.445180	+	1.04361i
$688$	4.48660	−	10.0771i	0.171050	−	0.384185i
$689$	−5.36967	−	1.14136i	−0.204568	−	0.0434823i
$690$	0.333851	+	0.102719i	0.0127095	+	0.00391044i
$691$	−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
$693$	−22.5558	−	13.5733i	−0.856824	−	0.515609i
$694$	14.2407			0.540570
$695$	−0.104278	+	0.992141i	−0.00395550	+	0.0376340i
$696$	2.21581	+	0.681760i	0.0839902	+	0.0258420i
$697$	30.5025	+	6.48350i	1.15536	+	0.245580i
$698$	−2.91925	+	6.55674i	−0.110495	+	0.248176i
$699$	−9.07116	+	21.2649i	−0.343103	+	0.804314i
$700$	4.87358	−	12.1998i	0.184204	−	0.461107i
$701$	−13.1558	+	40.4895i	−0.496889	+	1.52927i	0.317102	+	0.948392i	$0.397290\pi$
$701$	−13.1558	+	40.4895i	−0.496889	+	1.52927i	−0.813991	+	0.580877i	$0.802710\pi$
$702$	−0.284014	+	4.91661i	−0.0107194	+	0.185566i
$703$	14.8127	+	8.55211i	0.558671	+	0.322549i
$704$	3.13703	−	1.07660i	0.118231	−	0.0405758i
$705$	0.798864	+	0.444679i	0.0300869	+	0.0167476i
$706$	3.21341	−	4.42288i	0.120938	−	0.166457i
$707$	21.5777	+	11.3650i	0.811512	+	0.427424i
$708$	−3.86582	+	4.43116i	−0.145287	+	0.166533i
$709$	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
$711$	−28.7055	−	24.2615i	−1.07654	−	0.909877i
$712$	−0.366682	−	1.72510i	−0.0137420	−	0.0646510i
$713$	2.96297	−	4.07817i	0.110964	−	0.152729i
$714$	13.3787	+	34.6319i	0.500686	+	1.29607i
$715$	−0.582507	−	0.0515598i	−0.0217845	−	0.00192823i
$716$	10.2524	−	5.91920i	0.383149	−	0.221211i
$717$	−22.2912	+	31.7148i	−0.832480	+	1.18441i
$718$	12.8504	+	14.2718i	0.479573	+	0.532620i
$719$	−19.8283	−	17.8535i	−0.739471	−	0.665823i	0.210700	−	0.977551i	$-0.432426\pi$
$719$	−19.8283	−	17.8535i	−0.739471	−	0.665823i	−0.950171	+	0.311728i	$0.899092\pi$
$720$	−0.552943	+	0.0757039i	−0.0206070	+	0.00282132i
$721$	29.0921	+	1.91997i	1.08345	+	0.0715033i
$722$	−1.60242	−	4.93176i	−0.0596361	−	0.183541i
$723$	21.5077	+	23.1467i	0.799879	+	0.860834i
$724$	−6.38918	+	2.84465i	−0.237452	+	0.105720i
$725$	−3.32305	+	5.75570i	−0.123415	+	0.213761i
$726$	19.0225	+	1.06971i	0.705991	+	0.0397006i
$727$	−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
$729$	−5.89546	+	26.3485i	−0.218350	+	0.975870i
$730$	−1.77565	+	1.97206i	−0.0657199	+	0.0729893i
$731$	−88.8772	+	9.34137i	−3.28724	+	0.345503i
$732$	−20.1925	+	15.1598i	−0.746336	+	0.560324i
$733$	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
$735$	−1.30487	−	1.83978i	−0.0481308	−	0.0678612i
$736$		−	1.08403i		−	0.0399578i
$737$	0.184468	+	0.396647i	0.00679498	+	0.0146107i
$738$	−6.08422	−	9.81440i	−0.223963	−	0.361273i
$739$	−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
$741$	6.08349	+	5.30734i	0.223482	+	0.194970i
$742$	12.7380	+	8.51955i	0.467626	+	0.312763i
$743$	−3.16638	+	2.30051i	−0.116163	+	0.0843976i	−0.644350	−	0.764731i	$-0.722872\pi$
$743$	−3.16638	+	2.30051i	−0.116163	+	0.0843976i	0.528187	+	0.849128i	$0.322872\pi$
$744$	−1.55091	+	7.90358i	−0.0568591	+	0.289759i
$745$	1.84684	−	1.66290i	0.0676630	−	0.0609240i
$746$	4.07859	+	9.16065i	0.149328	+	0.335395i
$747$	−20.9711	+	0.657558i	−0.767293	+	0.0240588i
$748$	−20.2611	−	17.6489i	−0.740820	−	0.645309i
$749$	34.9169	+	29.0667i	1.27583	+	1.06207i
$750$	0.285557	−	3.19833i	0.0104271	−	0.116786i
$751$	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
$753$	15.3074	−	11.4922i	0.557832	−	0.418801i
$754$	−0.515982	+	1.15891i	−0.0187910	+	0.0422052i
$755$	−0.0400428	−	0.123239i	−0.00145731	−	0.00448512i
$756$	5.82785	−	12.4514i	0.211957	−	0.452851i
$757$	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
$759$	2.34892	−	5.76727i	0.0852604	−	0.209339i
$760$	−0.457446	+	0.792320i	−0.0165933	+	0.0287405i
$761$	1.03654	−	9.86204i	0.0375746	−	0.357499i	−0.959539	−	0.281576i	$-0.909143\pi$
$761$	1.03654	−	9.86204i	0.0375746	−	0.357499i	0.997114	−	0.0759231i	$-0.0241904\pi$
$762$	−2.95889	+	0.677565i	−0.107189	+	0.0245456i
$763$	−5.67357	−	39.2545i	−0.205397	−	1.42111i
$764$	6.42118	+	8.83799i	0.232310	+	0.319747i
$765$	2.77102	+	3.57290i	0.100186	+	0.129178i
$766$	−4.07782	+	19.1846i	−0.147338	+	0.693169i
$767$	−2.15312	−	2.39129i	−0.0777448	−	0.0863443i
$768$	0.729200	+	1.57107i	0.0263127	+	0.0566912i
$769$			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	−0.868816	−	0.495134i	$-0.835119\pi$
$773$	−12.9898	+	11.6961i	−0.467210	+	0.420678i	0.401606	+	0.915813i	$0.368452\pi$
$774$	25.2742	+	21.3614i	0.908461	+	0.767820i
$775$	−21.0936	−	9.39148i	−0.757705	−	0.337352i
$776$	7.39198	−	5.37059i	0.265357	−	0.192793i
$777$	14.8916	+	5.67995i	0.534233	+	0.203767i
$778$	−33.3000	−	10.8198i	−1.19386	−	0.387910i
$779$	−18.8257	−	1.97866i	−0.674502	−	0.0708930i
$780$	−0.00478611	−	0.305356i	−0.000171370	−	0.0109335i
$781$	−29.3257	+	0.482050i	−1.04936	+	0.0172491i
$782$	−7.60576	+	4.39119i	−0.271982	+	0.157029i
$783$	−3.81906	+	5.81261i	−0.136482	+	0.207726i
$784$	−4.26633	+	5.54963i	−0.152369	+	0.198201i
$785$	0.470664	−	0.152928i	0.0167987	−	0.00545824i
$786$	12.4019	−	1.50035i	0.442361	−	0.0535156i
$787$	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
$789$	−29.4325	+	27.3485i	−1.04783	+	0.973631i
$790$	1.88556	+	1.36994i	0.0670854	+	0.0487404i
$791$	6.52722	+	17.7174i	0.232081	+	0.629958i
$792$	0.475238	+	9.93852i	0.0168869	+	0.353150i
$793$	−6.90839	−	11.9657i	−0.245324	−	0.424914i
$794$	33.8213	−	15.0582i	1.20027	−	0.534396i
$795$	1.78381	+	0.548839i	0.0632651	+	0.0194653i
$796$	−3.80897	+	4.23029i	−0.135005	+	0.149938i
$797$	−25.6237	−	35.2680i	−0.907638	−	1.24926i	−0.967967	−	0.251078i	$-0.919215\pi$
$797$	−25.6237	−	35.2680i	−0.907638	−	1.24926i	0.0603293	−	0.998179i	$-0.480785\pi$
$798$	−10.2742	−	20.0584i	−0.363702	−	0.710058i
$799$	−21.8629	+	7.10370i	−0.773455	+	0.251311i
$800$	−4.85689	+	1.03236i	−0.171717	+	0.0364995i
$801$	5.27669	+	0.387871i	0.186443	+	0.0137048i
$802$	−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
$807$	−20.9274	−	4.10657i	−0.736680	−	0.144558i
$808$	−0.963510	−	9.16718i	−0.0338961	−	0.322500i
$809$	0.104928	+	0.998320i	0.00368906	+	0.0350991i	0.996212	−	0.0869627i	$-0.0277161\pi$
$809$	0.104928	+	0.998320i	0.00368906	+	0.0350991i	−0.992523	+	0.122062i	$0.961049\pi$
$810$	0.244822	−	1.65631i	0.00860216	−	0.0581967i
$811$	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
$816$	8.06911	−	11.4803i	0.282475	−	0.401892i
$817$	53.0624	−	11.2788i	1.85642	−	0.394594i
$818$	−19.3719	+	6.29432i	−0.677323	+	0.220076i
$819$	6.38107	+	3.98422i	0.222973	+	0.139220i
$820$	0.420891	+	0.579307i	0.0146982	+	0.0202303i
$821$	−20.0680	+	22.2878i	−0.700378	+	0.777848i	−0.983436	−	0.181254i	$-0.941984\pi$
$821$	−20.0680	+	22.2878i	−0.700378	+	0.777848i	0.283058	+	0.959103i	$0.408651\pi$
$822$	4.86395	−	15.8085i	0.169650	−	0.551386i
$823$	−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
$825$	−28.0767	−	5.03171i	−0.977505	−	0.175182i
$826$	3.10521	+	8.42875i	0.108044	+	0.293274i
$827$	−31.6484	−	22.9939i	−1.10052	−	0.799577i	−0.119378	−	0.992849i	$-0.538090\pi$
$827$	−31.6484	−	22.9939i	−1.10052	−	0.799577i	−0.981145	+	0.193272i	$0.938090\pi$
$828$	3.12289	+	0.907524i	0.108528	+	0.0315386i
$829$	−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
$831$	−2.75905	−	22.8063i	−0.0957103	−	0.791142i
$832$	−0.901392	+	0.292880i	−0.0312502	+	0.0101538i
$833$	56.2194	+	7.45300i	1.94789	+	0.258231i
$834$	−0.825988	+	9.25132i	−0.0286016	+	0.320347i
$835$	−2.58150	+	1.49043i	−0.0893366	+	0.0515785i
$836$	13.3515	+	9.36905i	0.461770	+	0.324036i
$837$	−21.4704	−	11.0846i	−0.742126	−	0.383139i
$838$	−9.89129	−	1.03962i	−0.341689	−	0.0359130i
$839$	16.7564	+	5.44447i	0.578494	+	0.187964i	0.583626	−	0.812023i	$-0.301634\pi$
$839$	16.7564	+	5.44447i	0.578494	+	0.187964i	−0.00513186	+	0.999987i	$0.501634\pi$
$840$	−0.303816	+	0.796540i	−0.0104827	+	0.0274832i
$841$	22.0121	−	15.9927i	0.759038	−	0.551473i
$842$	−8.48929	−	3.77968i	−0.292560	−	0.130256i
$843$	19.8685	−	6.80172i	0.684307	−	0.234264i
$844$	−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
$849$	−30.7883	+	14.2901i	−1.05665	+	0.490436i
$850$	26.9176	+	29.8950i	0.923265	+	1.02539i
$851$	−0.783872	+	3.68783i	−0.0268708	+	0.126417i
$852$	−1.83959	−	15.2061i	−0.0630233	−	0.520951i
$853$	−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
$855$	−1.89957	−	1.98113i	−0.0649639	−	0.0677533i
$856$	1.79493	−	17.0776i	0.0613493	−	0.583700i
$857$	−6.44371	+	11.1608i	−0.220113	+	0.381247i	−0.954842	−	0.297114i	$-0.903976\pi$
$857$	−6.44371	+	11.1608i	−0.220113	+	0.381247i	0.734729	+	0.678361i	$0.237309\pi$
$858$	−5.43024	−	0.394989i	−0.185385	−	0.0134847i
$859$	−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
$861$	−17.6126	+	0.960693i	−0.600236	+	0.0327403i
$862$	5.32024	+	16.3740i	0.181208	+	0.557701i
$863$	19.3664	−	43.4975i	0.659238	−	1.48067i	−0.205607	−	0.978635i	$-0.565917\pi$
$863$	19.3664	−	43.4975i	0.659238	−	1.48067i	0.864845	−	0.502039i	$-0.167417\pi$
$864$	−5.13645	+	0.785429i	−0.174746	+	0.0267208i
$865$	0.751168	−	3.53397i	0.0255405	−	0.120158i
$866$	−11.9472	+	2.53946i	−0.405982	+	0.0862942i
$867$	−83.9065	−	7.49145i	−2.84961	−	0.254423i
$868$	9.45563	+	7.87138i	0.320945	+	0.267172i
$869$	27.2922	−	31.3317i	0.925825	−	1.06285i
$870$	0.209763	−	0.376839i	0.00711164	−	0.0127760i
$871$	−0.0508448	−	0.114199i	−0.00172281	−	0.00386950i
$872$	−11.1405	+	10.0309i	−0.377264	+	0.339690i
$873$	9.28331	+	25.7911i	0.314193	+	0.872897i
$874$	4.31297	−	3.13356i	0.145888	−	0.105994i
$875$	−4.07709	−	2.72689i	−0.137831	−	0.0921856i
$876$	−16.2423	+	18.6175i	−0.548776	+	0.629028i
$877$	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
$879$	−0.503209	−	32.1050i	−0.0169728	−	1.08288i
$880$	−0.0745710	−	0.612481i	−0.00251379	−	0.0206467i
$881$		−	40.5540i		−	1.36630i	−0.730279	−	0.683149i	$-0.760610\pi$
$881$		−	40.5540i		−	1.36630i	0.730279	−	0.683149i	$-0.239390\pi$
$882$	−12.4158	−	16.9366i	−0.418062	−	0.570284i
$883$	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
$885$	0.656807	+	0.874849i	0.0220783	+	0.0294077i
$886$	−12.8728	+	1.35299i	−0.432471	+	0.0454545i
$887$	−28.2516	+	31.3766i	−0.948595	+	1.05352i	0.0499039	+	0.998754i	$0.484108\pi$
$887$	−28.2516	+	31.3766i	−0.948595	+	1.05352i	−0.998499	+	0.0547677i	$0.982558\pi$
$888$	−1.34465	−	5.87202i	−0.0451236	−	0.197052i
$889$	−1.26062	+	4.46211i	−0.0422797	+	0.149654i
$890$	−0.328097			−0.0109978
$891$	−29.0290	−	6.95122i	−0.972507	−	0.232875i
$892$	4.33681	−	7.51158i	0.145207	−	0.251506i
$893$	12.7479	−	5.67573i	0.426592	−	0.189931i
$894$	16.9501	−	15.7499i	0.566896	−	0.526755i
$895$	−0.680561	−	2.09455i	−0.0227487	−	0.0700132i
$896$	2.64001	+	0.174230i	0.0881965	+	0.00582063i
$897$	−0.698239	+	1.63684i	−0.0233135	+	0.0546525i
$898$	7.08585	+	6.38013i	0.236458	+	0.212908i
$899$	−4.16478	−	4.62546i	−0.138903	−	0.154268i
$900$	1.09202	−	14.8561i	0.0364007	−	0.495203i
$901$	−40.6385	+	23.4627i	−1.35387	+	0.781655i
$902$	10.9493	−	6.56386i	0.364572	−	0.218553i
$903$	47.1530	−	18.2158i	1.56915	−	0.606183i
$904$	4.19475	−	5.77357i	0.139515	−	0.192026i
$905$	0.270512	+	1.27266i	0.00899211	+	0.0423045i
$906$	−0.390751	−	1.14142i	−0.0129818	−	0.0379212i
$907$	−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
$909$	27.2156	+	4.89886i	0.902686	+	0.162485i
$910$	−0.412746	−	0.217394i	−0.0136824	−	0.00720653i
$911$	−31.7075	+	43.6417i	−1.05052	+	1.44591i	−0.162158	+	0.986765i	$0.551845\pi$
$911$	−31.7075	+	43.6417i	−1.05052	+	1.44591i	−0.888360	+	0.459148i	$0.848155\pi$
$912$	−4.14288	+	7.44266i	−0.137184	+	0.246451i
$913$	−0.381236	−	23.1927i	−0.0126171	−	0.767566i
$914$	−3.62044	−	2.09026i	−0.119754	−	0.0691398i
$915$	1.97760	+	4.26076i	0.0653773	+	0.140856i
$916$	5.30567	−	16.3292i	0.175304	−	0.539532i
$917$	7.07908	−	17.7207i	0.233772	−	0.585188i
$918$	26.3175	+	32.8567i	0.868607	+	1.08443i
$919$	−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
$921$	−6.88697	+	22.3836i	−0.226933	+	0.737565i
$922$	3.52768	−	33.5637i	0.116178	−	1.10536i
$923$	8.38144			0.275879
$924$	13.6679	+	6.64743i	0.449641	+	0.218684i
$925$	17.2695			0.567816
$926$	−1.83962	+	17.5028i	−0.0604536	+	0.575178i
$927$	32.1054	−	7.88343i	1.05448	−	0.258926i
$928$	−1.30924	−	0.278287i	−0.0429778	−	0.00913521i
$929$	8.31813	−	18.6828i	0.272909	−	0.612963i	−0.724147	−	0.689646i	$-0.757766\pi$
$929$	8.31813	−	18.6828i	0.272909	−	0.612963i	0.997056	+	0.0766826i	$0.0244328\pi$
$930$	1.37821	+	0.587916i	0.0451934	+	0.0192785i
$931$	−34.4125	−	0.932170i	−1.12783	−	0.0305506i
$932$	4.12467	−	12.6944i	0.135108	−	0.415820i
$933$	11.1384	−	5.16978i	0.364654	−	0.169251i
$934$	−7.73332	−	4.46483i	−0.253042	−	0.146094i
$935$	−3.99522	+	3.00425i	−0.130658	+	0.0982495i
$936$	−0.0891103	−	2.84194i	−0.00291266	−	0.0928918i
$937$	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
$939$	25.5237	+	22.2673i	0.832935	+	0.726667i
$940$	−0.482228	−	0.214702i	−0.0157285	−	0.00700280i
$941$	−5.34404	−	50.8452i	−0.174211	−	1.65751i	−0.636872	−	0.770970i	$-0.719772\pi$
$941$	−5.34404	−	50.8452i	−0.174211	−	1.65751i	0.462661	−	0.886535i	$-0.346895\pi$
$942$	4.35922	−	1.49232i	0.142031	−	0.0486225i
$943$	−0.867519	−	4.08136i	−0.0282503	−	0.132907i
$944$	1.99558	−	2.74668i	0.0649506	−	0.0893968i
$945$	−2.04034	−	1.54209i	−0.0663723	−	0.0501640i
$946$	−24.0299	+	27.5865i	−0.781278	+	0.896914i
$947$	−30.7303	+	17.7422i	−0.998601	+	0.576543i	−0.907834	−	0.419330i	$-0.862265\pi$
$947$	−30.7303	+	17.7422i	−0.998601	+	0.576543i	−0.0907670	+	0.995872i	$0.528932\pi$
$948$	17.7531	+	12.4780i	0.576594	+	0.405268i
$949$	−9.04636	−	10.0470i	−0.293657	−	0.326139i
$950$	−18.1470	−	16.3396i	−0.588767	−	0.530128i
$951$	−28.9088	−	12.3318i	−0.937431	−	0.399887i
$952$	−9.47173	−	19.2286i	−0.306980	−	0.623203i
$953$	14.4939	+	44.6076i	0.469503	+	1.44498i	0.853229	+	0.521536i	$0.174641\pi$
$953$	14.4939	+	44.6076i	0.469503	+	1.44498i	−0.383726	+	0.923447i	$0.625359\pi$
$954$	16.6860	+	4.84901i	0.540229	+	0.156993i
$955$	1.85660	−	0.826611i	0.0600781	−	0.0267485i
$956$	11.1905	−	19.3825i	0.361926	−	0.626874i
$957$	−6.36243	−	4.31746i	−0.205668	−	0.139564i
$958$	−10.7004			−0.345714
$959$	−17.6216	−	18.1054i	−0.569031	−	0.584653i
$960$	0.314090	−	0.0719245i	0.0101372	−	0.00232135i
$961$	−6.27381	+	6.96777i	−0.202381	+	0.224767i
$962$	3.27829	−	0.344562i	0.105696	−	0.0111091i
$963$	47.6948	+	19.4678i	1.53694	+	0.627342i
$964$	−13.5567	−	12.2065i	−0.436632	−	0.393145i
$965$	1.04796	−	3.22529i	0.0337350	−	0.103826i
$966$	3.50516	−	3.52013i	0.112777	−	0.113258i
$967$			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
$969$	69.0012	−	1.08152i	2.21664	−	0.0347433i
$970$	−0.691367	−	1.55283i	−0.0221984	−	0.0498585i
$971$	−4.55446	−	21.4270i	−0.146160	−	0.687627i	−0.988812	−	0.149169i	$-0.952340\pi$
$971$	−4.55446	−	21.4270i	−0.146160	−	0.687627i	0.842652	−	0.538458i	$-0.180993\pi$
$972$	2.03744	−	15.4547i	0.0653508	−	0.495711i
$973$	11.7932	+	7.88765i	0.378073	+	0.252867i
$974$	22.0988	−	16.0557i	0.708090	−	0.514457i
$975$	7.99866	+	1.56957i	0.256162	+	0.0502664i
$976$	10.8336	−	9.75461i	0.346775	−	0.312238i
$977$	0.369081	+	0.828970i	0.0118080	+	0.0265211i	0.919353	−	0.393433i	$-0.128713\pi$
$977$	0.369081	+	0.828970i	0.0118080	+	0.0265211i	−0.907545	+	0.419954i	$0.862046\pi$
$978$	−8.07280	−	4.49364i	−0.258140	−	0.143691i
$979$	−0.515730	+	5.82656i	−0.0164828	+	0.186218i
$980$	0.844842	+	0.990990i	0.0269875	+	0.0316560i
$981$	−19.5708	−	40.4914i	−0.624846	−	1.29279i
$982$	−8.43209	+	1.79230i	−0.269079	+	0.0571944i
$983$	−2.67834	+	12.6006i	−0.0854259	+	0.401897i	−0.999997	−	0.00252843i	$-0.999195\pi$
$983$	−2.67834	+	12.6006i	−0.0854259	+	0.401897i	0.914571	+	0.404426i	$0.132529\pi$
$984$	4.00272	+	5.33151i	0.127602	+	0.169962i
$985$	1.82385	−	4.09642i	0.0581125	−	0.130523i
$986$	3.35095	+	10.3132i	0.106716	+	0.328438i
$987$	10.8900	−	7.10512i	0.346633	−	0.226158i
$988$	−3.77088	−	2.73971i	−0.119968	−	0.0871617i
$989$	5.97881	+	10.3556i	0.190115	+	0.329289i
$990$	1.82688	+	0.297930i	0.0580620	+	0.00946882i
$991$	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
$993$	5.13182	+	22.4103i	0.162853	+	0.711171i
$994$	−21.7275	−	8.67973i	−0.689153	−	0.275304i
$995$	0.622453	+	0.856733i	0.0197331	+	0.0271603i
$996$	12.0259	−	1.45487i	0.381057	−	0.0460992i
$997$	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
$999$	18.0420	+	1.04222i	0.570822	+	0.0329742i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.bc.a.95.9	✓	128	3.2	odd	2
462.2.bc.a.107.9	yes	128	77.30	odd	30
462.2.bc.a.305.2	yes	128	11.8	odd	10
462.2.bc.a.359.2	yes	128	21.2	odd	6
462.2.bc.b.95.14	yes	128	1.1	even	1	trivial
462.2.bc.b.107.14	yes	128	231.107	even	30	inner
462.2.bc.b.305.5	yes	128	33.8	even	10	inner
462.2.bc.b.359.5	yes	128	7.2	even	3	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.bc (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 + 0.994522i) q^{2} +(1.65546 + 0.509351i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.0756668 + 0.169950i) q^{5} +(-0.679604 + 1.59315i) q^{6} +(1.63703 + 2.07849i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.48112 + 1.68643i) q^{9} +O(q^{10})\)	\(q+(-0.104528 + 0.994522i) q^{2} +(1.65546 + 0.509351i) q^{3} +(-0.978148 - 0.207912i) q^{4} +(-0.0756668 + 0.169950i) q^{5} +(-0.679604 + 1.59315i) q^{6} +(1.63703 + 2.07849i) q^{7} +(0.309017 - 0.951057i) q^{8} +(2.48112 + 1.68643i) q^{9} +(-0.161110 - 0.0930169i) q^{10} +(-1.90510 + 2.71488i) q^{11} +(-1.51339 - 0.842411i) q^{12} +(0.557091 - 0.766770i) q^{13} +(-2.23822 + 1.41080i) q^{14} +(-0.211828 + 0.242806i) q^{15} +(0.913545 + 0.406737i) q^{16} +(-0.846849 - 8.05723i) q^{17} +(-1.93654 + 2.29125i) q^{18} +(1.02248 + 4.81041i) q^{19} +(0.109348 - 0.150504i) q^{20} +(1.65136 + 4.27469i) q^{21} +(-2.50087 - 2.17845i) q^{22} +(-0.938796 + 0.542014i) q^{23} +(0.995988 - 1.41704i) q^{24} +(3.32250 + 3.69000i) q^{25} +(0.704338 + 0.634189i) q^{26} +(3.24843 + 4.05558i) q^{27} +(-1.16912 - 2.37343i) q^{28} +(0.413615 + 1.27298i) q^{29} +(-0.219334 - 0.236048i) q^{30} +(-4.24813 + 1.89139i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-4.53665 + 3.52403i) q^{33} +8.10161 q^{34} +(-0.477109 + 0.120941i) q^{35} +(-2.07628 - 2.16543i) q^{36} +(2.32721 - 2.58463i) q^{37} +(-4.89094 + 0.514059i) q^{38} +(1.31280 - 0.985605i) q^{39} +(0.138250 + 0.124481i) q^{40} +(-1.18944 + 3.66071i) q^{41} +(-4.42389 + 1.19549i) q^{42} -11.0307i q^{43} +(2.42792 - 2.25946i) q^{44} +(-0.474347 + 0.294061i) q^{45} +(-0.440914 - 0.990309i) q^{46} +(-0.589942 - 2.77546i) q^{47} +(1.30517 + 1.13865i) q^{48} +(-1.64025 + 6.80511i) q^{49} +(-4.01709 + 2.91858i) q^{50} +(2.70203 - 13.7698i) q^{51} +(-0.704338 + 0.634189i) q^{52} +(-2.35586 - 5.29135i) q^{53} +(-4.37292 + 2.80671i) q^{54} +(-0.317243 - 0.529199i) q^{55} +(2.48263 - 0.914621i) q^{56} +(-0.757504 + 8.48427i) q^{57} +(-1.30924 + 0.278287i) q^{58} +(0.705877 - 3.32089i) q^{59} +(0.257681 - 0.193458i) q^{60} +(5.92942 - 13.3177i) q^{61} +(-1.43698 - 4.42256i) q^{62} +(0.556455 + 7.91772i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(0.0881596 + 0.152697i) q^{65} +(-3.03051 - 4.88016i) q^{66} +(0.0659471 - 0.114224i) q^{67} +(-0.846849 + 8.05723i) q^{68} +(-1.83022 + 0.419108i) q^{69} +(-0.0704074 - 0.487137i) q^{70} +(5.19792 + 7.15433i) q^{71} +(2.37060 - 1.83855i) q^{72} +(2.96575 - 13.9527i) q^{73} +(2.32721 + 2.58463i) q^{74} +(3.62076 + 7.80099i) 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} +(3.31194 + 8.36846i) q^{81} +(-3.51633 - 1.56557i) q^{82} +(-5.65811 + 4.11086i) q^{83} +(-0.726520 - 4.52462i) q^{84} +(1.43341 + 0.465742i) q^{85} +(10.9703 + 1.15303i) q^{86} +(0.0363326 + 2.31804i) q^{87} +(1.99330 + 2.65080i) q^{88} +(1.52736 - 0.881821i) q^{89} +(-0.242867 - 0.502486i) q^{90} +(2.50570 - 0.0973181i) q^{91} +(1.03097 - 0.334983i) q^{92} +(-7.99600 + 0.967336i) q^{93} +(2.82192 - 0.296596i) q^{94} +(-0.894899 - 0.190217i) q^{95} +(-1.26884 + 1.17900i) q^{96} +(7.39198 + 5.37059i) q^{97} +(-6.59638 - 2.34260i) q^{98} +(-9.30524 + 3.52315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * q^9	\( 128 q + 16 q^{2} + 16 q^{4} - 32 q^{8} + 16 q^{9} - 6 q^{11} - 12 q^{15} + 16 q^{16} - 2 q^{17} - 4 q^{18} + 2 q^{22} - 12 q^{25} - 18 q^{27} - 5 q^{28} + 38 q^{29} + 6 q^{30} - 3 q^{31} - 64 q^{32} + 28 q^{33} - 16 q^{34} - 31 q^{35} + 8 q^{36} + 2 q^{37} - 2 q^{39} + 5 q^{40} + 16 q^{41} - 13 q^{42} - q^{44} + 28 q^{45} + 38 q^{49} + 34 q^{50} + 4 q^{51} + 25 q^{53} - 6 q^{54} - 42 q^{55} - 100 q^{57} - 19 q^{58} + 40 q^{59} - 4 q^{60} + 40 q^{61} - 4 q^{62} - 106 q^{63} - 32 q^{64} + 20 q^{65} - 7 q^{66} + 16 q^{67} - 2 q^{68} - 68 q^{69} - 21 q^{70} + 80 q^{71} - 4 q^{72} + 10 q^{73} + 2 q^{74} - 14 q^{75} + q^{77} - 16 q^{78} - 5 q^{80} + 32 q^{81} - 8 q^{82} - 92 q^{83} + 8 q^{84} - 100 q^{85} - 40 q^{86} - 38 q^{87} - q^{88} + 4 q^{90} + 12 q^{91} - 20 q^{92} - 33 q^{93} + 40 q^{94} + 38 q^{95} - 16 q^{97} + 18 q^{98} + 2 q^{99}+O(q^{100}) \) 128 * q + 16 * q^2 + 16 * q^4 - 32 * q^8 + 16 * 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 + 28 * q^33 - 16 * q^34 - 31 * q^35 + 8 * q^36 + 2 * q^37 - 2 * q^39 + 5 * q^40 + 16 * q^41 - 13 * q^42 - q^44 + 28 * q^45 + 38 * q^49 + 34 * q^50 + 4 * q^51 + 25 * q^53 - 6 * q^54 - 42 * q^55 - 100 * q^57 - 19 * q^58 + 40 * q^59 - 4 * q^60 + 40 * q^61 - 4 * q^62 - 106 * q^63 - 32 * q^64 + 20 * q^65 - 7 * q^66 + 16 * q^67 - 2 * q^68 - 68 * q^69 - 21 * q^70 + 80 * q^71 - 4 * q^72 + 10 * q^73 + 2 * q^74 - 14 * q^75 + q^77 - 16 * q^78 - 5 * q^80 + 32 * q^81 - 8 * q^82 - 92 * q^83 + 8 * q^84 - 100 * q^85 - 40 * q^86 - 38 * q^87 - q^88 + 4 * q^90 + 12 * q^91 - 20 * q^92 - 33 * q^93 + 40 * q^94 + 38 * q^95 - 16 * q^97 + 18 * q^98 + 2 * q^99

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