LMFDB - Embedded newform 200.2.o.a.29.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [200,2,Mod(29,200)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(200, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("200.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 200 = 2^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	200.o (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.59700804043$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.15
Character	$\chi$	$=$	200.29
Dual form			200.2.o.a.69.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0299570 + 1.41390i) q^{2} +(1.06117 + 0.770982i) q^{3} +(-1.99821 - 0.0847122i) q^{4} +(-1.15605 + 1.91404i) q^{5} +(-1.12188 + 1.47728i) q^{6} +2.31589i q^{7} +(0.179635 - 2.82272i) q^{8} +(-0.395392 - 1.21689i) q^{9} +O(q^{10})$	\(q+(-0.0299570 + 1.41390i) q^{2} +(1.06117 + 0.770982i) q^{3} +(-1.99821 - 0.0847122i) q^{4} +(-1.15605 + 1.91404i) q^{5} +(-1.12188 + 1.47728i) q^{6} +2.31589i q^{7} +(0.179635 - 2.82272i) q^{8} +(-0.395392 - 1.21689i) q^{9} +(-2.67162 - 1.69188i) q^{10} +(-0.219837 - 0.0714294i) q^{11} +(-2.05511 - 1.63047i) q^{12} +(0.659008 + 2.02822i) q^{13} +(-3.27443 - 0.0693772i) q^{14} +(-2.70245 + 1.13982i) q^{15} +(3.98565 + 0.338545i) q^{16} +(1.33923 + 1.84329i) q^{17} +(1.73240 - 0.522589i) q^{18} +(-0.307368 - 0.423055i) q^{19} +(2.47217 - 3.72671i) q^{20} +(-1.78551 + 2.45754i) q^{21} +(0.107579 - 0.308687i) q^{22} +(6.59576 + 2.14309i) q^{23} +(2.36689 - 2.85688i) q^{24} +(-2.32708 - 4.42546i) q^{25} +(-2.88743 + 0.871009i) q^{26} +(1.73461 - 5.33859i) q^{27} +(0.196184 - 4.62763i) q^{28} +(-5.13469 + 7.06729i) q^{29} +(-1.53062 - 3.85513i) q^{30} +(6.95750 - 5.05492i) q^{31} +(-0.598065 + 5.62515i) q^{32} +(-0.178213 - 0.245289i) q^{33} +(-2.64634 + 1.83831i) q^{34} +(-4.43271 - 2.67729i) q^{35} +(0.686988 + 2.46509i) q^{36} +(-2.46601 - 7.58959i) q^{37} +(0.607364 - 0.421912i) q^{38} +(-0.864403 + 2.66036i) q^{39} +(5.19512 + 3.60704i) q^{40} +(1.84490 + 5.67801i) q^{41} +(-3.42122 - 2.59815i) q^{42} +9.74670 q^{43} +(0.433228 + 0.161353i) q^{44} +(2.78627 + 0.649995i) q^{45} +(-3.22770 + 9.26151i) q^{46} +(-0.657286 + 0.904676i) q^{47} +(3.96842 + 3.43211i) q^{48} +1.63664 q^{49} +(6.32685 - 3.15768i) q^{50} +2.98855i q^{51} +(-1.14502 - 4.10862i) q^{52} +(-3.51671 - 2.55504i) q^{53} +(7.49624 + 2.61249i) q^{54} +(0.390862 - 0.338200i) q^{55} +(6.53711 + 0.416014i) q^{56} -0.685906i q^{57} +(-9.83860 - 7.47163i) q^{58} +(4.66275 - 1.51502i) q^{59} +(5.49661 - 2.04865i) q^{60} +(-2.16726 - 0.704186i) q^{61} +(6.93871 + 9.98861i) q^{62} +(2.81819 - 0.915685i) q^{63} +(-7.93546 - 1.01411i) q^{64} +(-4.64393 - 1.08336i) q^{65} +(0.352152 - 0.244626i) q^{66} +(2.55761 - 1.85821i) q^{67} +(-2.51990 - 3.79672i) q^{68} +(5.34690 + 7.35938i) q^{69} +(3.91821 - 6.18718i) q^{70} +(-5.30236 - 3.85239i) q^{71} +(-3.50596 + 0.897484i) q^{72} +(-5.24971 - 1.70573i) q^{73} +(10.8048 - 3.25932i) q^{74} +(0.942529 - 6.49028i) q^{75} +(0.578346 + 0.871389i) q^{76} +(0.165423 - 0.509119i) q^{77} +(-3.73557 - 1.30187i) q^{78} +(-10.1775 - 7.39438i) q^{79} +(-5.25561 + 7.23731i) q^{80} +(2.85122 - 2.07153i) q^{81} +(-8.08339 + 2.43840i) q^{82} +(4.44876 - 3.23222i) q^{83} +(3.77600 - 4.75942i) q^{84} +(-5.07634 + 0.432393i) q^{85} +(-0.291982 + 13.7808i) q^{86} +(-10.8975 + 3.54081i) q^{87} +(-0.241115 + 0.607706i) q^{88} +(-4.88895 + 15.0466i) q^{89} +(-1.00249 + 3.92002i) q^{90} +(-4.69713 + 1.52619i) q^{91} +(-12.9981 - 4.84108i) q^{92} +11.2803 q^{93} +(-1.25943 - 0.956435i) q^{94} +(1.16508 - 0.0992390i) q^{95} +(-4.97154 + 5.50812i) q^{96} +(7.50193 - 10.3255i) q^{97} +(-0.0490290 + 2.31405i) q^{98} +0.295760i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9}+O(q^{10}) $ 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9	$ 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28} - 33 q^{30} - 18 q^{31} - 10 q^{33} + 9 q^{34} + 41 q^{36} + 45 q^{38} - 10 q^{39} - 14 q^{40} - 10 q^{41} + 75 q^{42} - 32 q^{44} + 13 q^{46} - 10 q^{47} - 70 q^{48} - 80 q^{49} - 19 q^{50} - 100 q^{52} + 43 q^{54} - 34 q^{55} + 36 q^{56} - 30 q^{58} - 28 q^{60} + 20 q^{62} + 60 q^{63} - 36 q^{64} + 40 q^{65} + 40 q^{66} + 42 q^{70} + 22 q^{71} - 65 q^{72} - 10 q^{73} + 4 q^{74} - 36 q^{76} - 55 q^{78} + 14 q^{79} - 76 q^{80} - 6 q^{81} + 78 q^{84} - 59 q^{86} - 10 q^{87} + 110 q^{88} + 24 q^{89} + 49 q^{90} + 90 q^{92} + 45 q^{94} - 86 q^{95} + 46 q^{96} - 50 q^{97} + 90 q^{98}+O(q^{100}) $ 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/200\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$177$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.0299570	+	1.41390i	−0.0211828	+	0.999776i
$2$	−0.0299570	+	1.41390i	−0.0211828	+	0.999776i
$3$	1.06117	+	0.770982i	0.612664	+	0.445127i	0.850351	−	0.526215i	$-0.176389\pi$
$3$	1.06117	+	0.770982i	0.612664	+	0.445127i	−0.237687	+	0.971342i	$0.576389\pi$
$4$	−1.99821	−	0.0847122i	−0.999103	−	0.0423561i
$5$	−1.15605	+	1.91404i	−0.517003	+	0.855984i
$5$	−1.15605	+	1.91404i	−0.517003	+	0.855984i
$6$	−1.12188	+	1.47728i	−0.458005	+	0.603098i
$7$			2.31589i			0.875325i	0.899139	+	0.437662i	$0.144194\pi$
$7$			2.31589i			0.875325i	−0.899139	+	0.437662i	$0.855806\pi$
$8$	0.179635	−	2.82272i	0.0635104	−	0.997981i
$9$	−0.395392	−	1.21689i	−0.131797	−	0.405630i
$10$	−2.67162	−	1.69188i	−0.844840	−	0.535019i
$11$	−0.219837	−	0.0714294i	−0.0662834	−	0.0215368i	0.275688	−	0.961247i	$-0.411094\pi$
$11$	−0.219837	−	0.0714294i	−0.0662834	−	0.0215368i	−0.341971	+	0.939711i	$0.611094\pi$
$12$	−2.05511	−	1.63047i	−0.593261	−	0.470677i
$13$	0.659008	+	2.02822i	0.182776	+	0.562526i	0.999903	−	0.0139312i	$-0.00443460\pi$
$13$	0.659008	+	2.02822i	0.182776	+	0.562526i	−0.817127	+	0.576458i	$0.804435\pi$
$14$	−3.27443	−	0.0693772i	−0.875128	−	0.0185418i
$15$	−2.70245	+	1.13982i	−0.697770	+	0.294299i
$16$	3.98565	+	0.338545i	0.996412	+	0.0846362i
$17$	1.33923	+	1.84329i	0.324810	+	0.447063i	0.939928	−	0.341372i	$-0.110892\pi$
$17$	1.33923	+	1.84329i	0.324810	+	0.447063i	−0.615118	+	0.788435i	$0.710892\pi$
$18$	1.73240	−	0.522589i	0.408331	−	0.123175i
$19$	−0.307368	−	0.423055i	−0.0705150	−	0.0970555i	0.772303	−	0.635255i	$-0.219105\pi$
$19$	−0.307368	−	0.423055i	−0.0705150	−	0.0970555i	−0.842818	+	0.538199i	$0.819105\pi$
$20$	2.47217	−	3.72671i	0.552795	−	0.833317i
$21$	−1.78551	+	2.45754i	−0.389630	+	0.536280i
$22$	0.107579	−	0.308687i	0.0229360	−	0.0658123i
$23$	6.59576	+	2.14309i	1.37531	+	0.446865i	0.901125	−	0.433560i	$-0.142743\pi$
$23$	6.59576	+	2.14309i	1.37531	+	0.446865i	0.474185	+	0.880425i	$0.342743\pi$
$24$	2.36689	−	2.85688i	0.483139	−	0.583157i
$25$	−2.32708	−	4.42546i	−0.465417	−	0.885092i
$26$	−2.88743	+	0.871009i	−0.566272	+	0.170819i
$27$	1.73461	−	5.33859i	0.333826	−	1.02741i
$28$	0.196184	−	4.62763i	0.0370754	−	0.874539i
$29$	−5.13469	+	7.06729i	−0.953487	+	1.31236i	−0.00352661	+	0.999994i	$0.501123\pi$
$29$	−5.13469	+	7.06729i	−0.953487	+	1.31236i	−0.949961	+	0.312369i	$0.898877\pi$
$30$	−1.53062	−	3.85513i	−0.279452	−	0.703848i
$31$	6.95750	−	5.05492i	1.24960	−	0.907890i	0.251405	−	0.967882i	$-0.419107\pi$
$31$	6.95750	−	5.05492i	1.24960	−	0.907890i	0.998199	+	0.0599915i	$0.0191074\pi$
$32$	−0.598065	+	5.62515i	−0.105724	+	0.994396i
$33$	−0.178213	−	0.245289i	−0.0310228	−	0.0426993i
$34$	−2.64634	+	1.83831i	−0.453843	+	0.315267i
$35$	−4.43271	−	2.67729i	−0.749264	−	0.452545i
$36$	0.686988	+	2.46509i	0.114498	+	0.410849i
$37$	−2.46601	−	7.58959i	−0.405409	−	1.24772i	−0.920553	−	0.390617i	$-0.872262\pi$
$37$	−2.46601	−	7.58959i	−0.405409	−	1.24772i	0.515144	−	0.857104i	$-0.327738\pi$
$38$	0.607364	−	0.421912i	0.0985275	−	0.0684432i
$39$	−0.864403	+	2.66036i	−0.138415	+	0.425998i
$40$	5.19512	+	3.60704i	0.821421	+	0.570323i
$41$	1.84490	+	5.67801i	0.288125	+	0.886756i	0.985445	+	0.169996i	$0.0543756\pi$
$41$	1.84490	+	5.67801i	0.288125	+	0.886756i	−0.697320	+	0.716760i	$0.745624\pi$
$42$	−3.42122	−	2.59815i	−0.527906	−	0.400903i
$43$	9.74670			1.48636			0.743179	−	0.669093i	$-0.233317\pi$
$43$	9.74670			1.48636			0.743179	+	0.669093i	$0.233317\pi$
$44$	0.433228	+	0.161353i	0.0653117	+	0.0243249i
$45$	2.78627	+	0.649995i	0.415352	+	0.0968956i
$46$	−3.22770	+	9.26151i	−0.475898	+	1.36554i
$47$	−0.657286	+	0.904676i	−0.0958750	+	0.131961i	−0.854259	−	0.519847i	$-0.825989\pi$
$47$	−0.657286	+	0.904676i	−0.0958750	+	0.131961i	0.758384	+	0.651807i	$0.225989\pi$
$48$	3.96842	+	3.43211i	0.572792	+	0.495383i
$49$	1.63664			0.233806
$50$	6.32685	−	3.15768i	0.894752	−	0.446563i
$51$			2.98855i			0.418481i
$52$	−1.14502	−	4.10862i	−0.158785	−	0.569763i
$53$	−3.51671	−	2.55504i	−0.483057	−	0.350962i	0.319451	−	0.947603i	$-0.396502\pi$
$53$	−3.51671	−	2.55504i	−0.483057	−	0.350962i	−0.802508	+	0.596641i	$0.796502\pi$
$54$	7.49624	+	2.61249i	1.02011	+	0.355515i
$55$	0.390862	−	0.338200i	0.0527038	−	0.0456029i
$56$	6.53711	+	0.416014i	0.873558	+	0.0555922i
$57$		−	0.685906i		−	0.0908505i
$58$	−9.83860	−	7.47163i	−1.29187	−	0.981073i
$59$	4.66275	−	1.51502i	0.607038	−	0.197239i	0.0106611	−	0.999943i	$-0.496606\pi$
$59$	4.66275	−	1.51502i	0.607038	−	0.197239i	0.596377	+	0.802705i	$0.296606\pi$
$60$	5.49661	−	2.04865i	0.709609	−	0.264480i
$61$	−2.16726	−	0.704186i	−0.277490	−	0.0901618i	0.166966	−	0.985963i	$-0.446603\pi$
$61$	−2.16726	−	0.704186i	−0.277490	−	0.0901618i	−0.444456	+	0.895801i	$0.646603\pi$
$62$	6.93871	+	9.98861i	0.881217	+	1.26856i
$63$	2.81819	−	0.915685i	0.355058	−	0.115365i
$64$	−7.93546	−	1.01411i	−0.991933	−	0.126764i
$65$	−4.64393	−	1.08336i	−0.576009	−	0.134374i
$66$	0.352152	−	0.244626i	0.0433469	−	0.0301114i
$67$	2.55761	−	1.85821i	0.312462	−	0.227017i	−0.420490	−	0.907297i	$-0.638142\pi$
$67$	2.55761	−	1.85821i	0.312462	−	0.227017i	0.732952	+	0.680280i	$0.238142\pi$
$68$	−2.51990	−	3.79672i	−0.305583	−	0.460419i
$69$	5.34690	+	7.35938i	0.643692	+	0.885966i
$70$	3.91821	−	6.18718i	0.468315	−	0.739510i
$71$	−5.30236	−	3.85239i	−0.629274	−	0.457194i	0.226875	−	0.973924i	$-0.427149\pi$
$71$	−5.30236	−	3.85239i	−0.629274	−	0.457194i	−0.856149	+	0.516730i	$0.827149\pi$
$72$	−3.50596	+	0.897484i	−0.413182	+	0.105769i
$73$	−5.24971	−	1.70573i	−0.614432	−	0.199641i	−0.0147656	−	0.999891i	$-0.504700\pi$
$73$	−5.24971	−	1.70573i	−0.614432	−	0.199641i	−0.599667	+	0.800250i	$0.704700\pi$
$74$	10.8048	−	3.25932i	1.25603	−	0.378888i
$75$	0.942529	−	6.49028i	0.108834	−	0.749433i
$76$	0.578346	+	0.871389i	0.0663408	+	0.0999552i
$77$	0.165423	−	0.509119i	0.0188517	−	0.0580195i
$78$	−3.73557	−	1.30187i	−0.422971	−	0.147408i
$79$	−10.1775	−	7.39438i	−1.14506	−	0.831933i	−0.157241	−	0.987560i	$-0.550260\pi$
$79$	−10.1775	−	7.39438i	−1.14506	−	0.831933i	−0.987816	+	0.155628i	$0.950260\pi$
$80$	−5.25561	+	7.23731i	−0.587595	+	0.809155i
$81$	2.85122	−	2.07153i	0.316802	−	0.230170i
$82$	−8.08339	+	2.43840i	−0.892661	+	0.269276i
$83$	4.44876	−	3.23222i	0.488315	−	0.354782i	−0.316221	−	0.948686i	$-0.602414\pi$
$83$	4.44876	−	3.23222i	0.488315	−	0.354782i	0.804536	+	0.593904i	$0.202414\pi$
$84$	3.77600	−	4.75942i	0.411995	−	0.519296i
$85$	−5.07634	+	0.432393i	−0.550606	+	0.0468996i
$86$	−0.291982	+	13.7808i	−0.0314852	+	1.48602i
$87$	−10.8975	+	3.54081i	−1.16834	+	0.379615i
$88$	−0.241115	+	0.607706i	−0.0257030	+	0.0647817i
$89$	−4.88895	+	15.0466i	−0.518227	+	1.59494i	0.259105	+	0.965849i	$0.416573\pi$
$89$	−4.88895	+	15.0466i	−0.518227	+	1.59494i	−0.777332	+	0.629091i	$0.783427\pi$
$90$	−1.00249	+	3.92002i	−0.105672	+	0.413207i
$91$	−4.69713	+	1.52619i	−0.492393	+	0.159988i
$92$	−12.9981	−	4.84108i	−1.35515	−	0.504717i
$93$	11.2803			1.16971
$94$	−1.25943	−	0.956435i	−0.129900	−	0.0986487i
$95$	1.16508	−	0.0992390i	0.119534	−	0.0101817i
$96$	−4.97154	+	5.50812i	−0.507405	+	0.562170i
$97$	7.50193	−	10.3255i	0.761706	−	1.04840i	−0.235364	−	0.971907i	$-0.575628\pi$
$97$	7.50193	−	10.3255i	0.761706	−	1.04840i	0.997070	−	0.0764911i	$-0.0243717\pi$
$98$	−0.0490290	+	2.31405i	−0.00495267	+	0.233754i
$99$			0.295760i			0.0297250i
$100$	4.27510	+	9.04011i	0.427510	+	0.904011i
$101$		−	11.5894i		−	1.15318i	−0.817032	−	0.576592i	$-0.804382\pi$
$101$		−	11.5894i		−	1.15318i	0.817032	−	0.576592i	$-0.195618\pi$
$102$	−4.22550	−	0.0895281i	−0.418387	−	0.00886461i
$103$	−3.94133	+	5.42478i	−0.388351	+	0.534519i	−0.957773	−	0.287526i	$-0.907167\pi$
$103$	−3.94133	+	5.42478i	−0.388351	+	0.534519i	0.569422	+	0.822045i	$0.307167\pi$
$104$	5.84346	−	1.49585i	0.572999	−	0.146681i
$105$	−2.63969	−	6.25859i	−0.257607	−	0.610776i
$106$	3.71791	−	4.89572i	0.361116	−	0.475515i
$107$	−7.65011			−0.739564			−0.369782	−	0.929119i	$-0.620568\pi$
$107$	−7.65011			−0.739564			−0.369782	+	0.929119i	$0.620568\pi$
$108$	−3.91835	+	10.5206i	−0.377044	+	1.01235i
$109$	−6.41848	+	2.08549i	−0.614779	+	0.199754i	−0.599821	−	0.800134i	$-0.704761\pi$
$109$	−6.41848	+	2.08549i	−0.614779	+	0.199754i	−0.0149580	+	0.999888i	$0.504761\pi$
$110$	0.466471	+	0.562769i	0.0444763	+	0.0536580i
$111$	3.23459	−	9.95506i	0.307014	−	0.944892i
$112$	−0.784033	+	9.23033i	−0.0740842	+	0.872184i
$113$	−14.4512	+	4.69549i	−1.35946	+	0.441714i	−0.895862	−	0.444333i	$-0.853441\pi$
$113$	−14.4512	+	4.69549i	−1.35946	+	0.441714i	−0.463595	+	0.886047i	$0.653441\pi$
$114$	0.969801	+	0.0205477i	0.0908301	+	0.00192447i
$115$	−11.7270	+	10.1470i	−1.09355	+	0.946213i
$116$	10.8588	−	13.6869i	1.00822	−	1.27080i
$117$	2.20755	−	1.60388i	0.204088	−	0.148279i
$118$	2.00240	+	6.63803i	0.184336	+	0.611080i
$119$	−4.26886	+	3.10151i	−0.391325	+	0.284315i
$120$	2.73192	+	7.83301i	0.249389	+	0.715053i
$121$	−8.85596	−	6.43423i	−0.805087	−	0.584930i
$122$	1.06057	−	3.04319i	0.0960196	−	0.275517i
$123$	−2.41990	+	7.44769i	−0.218195	+	0.671536i
$124$	−14.3307	+	9.51138i	−1.28694	+	0.854147i
$125$	11.1607	+	0.661940i	0.998246	+	0.0592057i
$126$	1.21026	+	4.01206i	0.107818	+	0.357422i
$127$	−4.34009	−	1.41018i	−0.385121	−	0.125133i	0.110056	−	0.993925i	$-0.464897\pi$
$127$	−4.34009	−	1.41018i	−0.385121	−	0.125133i	−0.495177	+	0.868792i	$0.664897\pi$
$128$	1.67158	−	11.1895i	0.147748	−	0.989025i
$129$	10.3429	+	7.51453i	0.910638	+	0.661618i
$130$	1.67088	−	6.53359i	0.146546	−	0.573033i
$131$	−9.12255	−	12.5561i	−0.797041	−	1.09703i	−0.993195	−	0.116460i	$-0.962845\pi$
$131$	−9.12255	−	12.5561i	−0.797041	−	1.09703i	0.196154	−	0.980573i	$-0.437155\pi$
$132$	0.335327	+	0.505234i	0.0291864	+	0.0439750i
$133$	0.979750	−	0.711830i	0.0849551	−	0.0617235i
$134$	2.55070	+	3.67186i	0.220347	+	0.317201i
$135$	8.21295	+	9.49180i	0.706859	+	0.816924i
$136$	5.44365	−	3.44914i	0.466789	−	0.295761i
$137$	13.9802	−	4.54244i	1.19441	−	0.388087i	0.356708	−	0.934216i	$-0.383899\pi$
$137$	13.9802	−	4.54244i	1.19441	−	0.388087i	0.837701	+	0.546129i	$0.183899\pi$
$138$	−10.5656	+	7.33950i	−0.899402	+	0.624780i
$139$	5.61357	+	1.82396i	0.476137	+	0.154706i	0.537247	−	0.843425i	$-0.319464\pi$
$139$	5.61357	+	1.82396i	0.476137	+	0.154706i	−0.0611104	+	0.998131i	$0.519464\pi$
$140$	8.63065	+	5.72529i	0.729423	+	0.483875i
$141$	−1.39498	+	0.453256i	−0.117478	+	0.0381710i
$142$	5.60572	−	7.38158i	0.470421	−	0.619448i
$143$		−	0.492950i		−	0.0412225i
$144$	−1.16392	−	4.98396i	−0.0969934	−	0.415330i
$145$	−7.59109	−	17.9981i	−0.630406	−	1.49466i
$146$	2.56900	−	7.37145i	0.212612	−	0.610066i
$147$	1.73675	+	1.26182i	0.143245	+	0.104073i
$148$	4.28466	+	15.3745i	0.352197	+	1.26377i
$149$		−	9.14052i		−	0.748820i	−0.927263	−	0.374410i	$-0.877845\pi$
$149$		−	9.14052i		−	0.748820i	0.927263	−	0.374410i	$-0.122155\pi$
$150$	9.14835	+	1.52707i	0.746960	+	0.124685i
$151$	8.59512			0.699461			0.349730	−	0.936850i	$-0.386273\pi$
$151$	8.59512			0.699461			0.349730	+	0.936850i	$0.386273\pi$
$152$	−1.24938	+	0.791616i	−0.101338	+	0.0642086i
$153$	1.71356	−	2.35851i	0.138533	−	0.190675i
$154$	0.714886	+	0.249142i	0.0576071	+	0.0200765i
$155$	1.63207	+	19.1607i	0.131091	+	1.53902i
$156$	1.95262	−	5.24271i	0.156335	−	0.419753i
$157$	4.64663			0.370842			0.185421	−	0.982659i	$-0.440635\pi$
$157$	4.64663			0.370842			0.185421	+	0.982659i	$0.440635\pi$
$158$	10.7598	−	14.1684i	0.856002	−	1.12718i
$159$	−1.76192	−	5.42264i	−0.139730	−	0.430043i
$160$	−10.0754	−	7.64769i	−0.796527	−	0.604603i
$161$	−4.96317	+	15.2751i	−0.391152	+	1.20384i
$162$	2.84352	+	4.09338i	0.223408	+	0.321606i
$163$	4.05889	+	12.4920i	0.317917	+	0.978448i	0.974537	+	0.224226i	$0.0719855\pi$
$163$	4.05889	+	12.4920i	0.317917	+	0.978448i	−0.656620	+	0.754221i	$0.728015\pi$
$164$	−3.20549	−	11.5021i	−0.250306	−	0.898164i
$165$	0.675515	−	0.0575391i	0.0525888	−	0.00447941i
$166$	4.43675	+	6.38692i	0.344358	+	0.495721i
$167$	12.2739	+	16.8935i	0.949780	+	1.30726i	0.951625	+	0.307261i	$0.0994126\pi$
$167$	12.2739	+	16.8935i	0.949780	+	1.30726i	−0.00184537	+	0.999998i	$0.500587\pi$
$168$	6.61621	+	5.48145i	0.510452	+	0.422903i
$169$	6.83785	−	4.96799i	0.525988	−	0.382153i
$170$	−0.459287	−	7.19037i	−0.0352257	−	0.551476i
$171$	−0.393281	+	0.541305i	−0.0300750	+	0.0413947i
$172$	−19.4759	−	0.825665i	−1.48502	−	0.0629563i
$173$	2.43455	−	7.49277i	0.185095	−	0.569664i	−0.814855	−	0.579665i	$-0.803183\pi$
$173$	2.43455	−	7.49277i	0.185095	−	0.569664i	0.999950	+	0.0100007i	$0.00318338\pi$
$174$	−4.67989	−	15.5140i	−0.354781	−	1.17611i
$175$	10.2489	−	5.38927i	0.774743	−	0.407391i
$176$	−0.852011	−	0.359117i	−0.0642227	−	0.0270695i
$177$	6.11600	+	1.98721i	0.459706	+	0.149368i
$178$	−21.1279	−	7.36322i	−1.58360	−	0.551896i
$179$	−9.43646	+	12.9882i	−0.705314	+	0.970782i	0.294571	+	0.955630i	$0.404823\pi$
$179$	−9.43646	+	12.9882i	−0.705314	+	0.970782i	−0.999885	+	0.0151522i	$0.995177\pi$
$180$	−5.51247	−	1.53486i	−0.410876	−	0.114401i
$181$	−10.0809	−	13.8751i	−0.749305	−	1.03133i	−0.998029	−	0.0627560i	$-0.980011\pi$
$181$	−10.0809	−	13.8751i	−0.749305	−	1.03133i	0.248723	−	0.968575i	$-0.419989\pi$
$182$	−2.01716	−	6.68698i	−0.149522	−	0.495672i
$183$	−1.75691	−	2.41818i	−0.129874	−	0.178757i
$184$	7.23416	−	18.2330i	0.533310	−	1.34415i
$185$	17.3776	+	4.05394i	1.27763	+	0.298051i
$186$	−0.337924	+	15.9492i	−0.0247778	+	1.16945i
$187$	−0.162747	−	0.500883i	−0.0119012	−	0.0366282i
$188$	1.39003	−	1.75205i	0.101378	−	0.127781i
$189$	12.3636	+	4.01717i	0.899319	+	0.292206i
$190$	0.105411	+	1.65027i	0.00764735	+	0.119723i
$191$	−0.923572	−	2.84246i	−0.0668273	−	0.205673i	0.912067	−	0.410042i	$-0.134486\pi$
$191$	−0.923572	−	2.84246i	−0.0668273	−	0.205673i	−0.978894	+	0.204369i	$0.934486\pi$
$192$	−7.63898	−	7.19424i	−0.551296	−	0.519200i
$193$			14.9349i			1.07504i	0.843252	+	0.537518i	$0.180638\pi$
$193$			14.9349i			1.07504i	−0.843252	+	0.537518i	$0.819362\pi$
$194$	14.3745	+	10.9163i	1.03203	+	0.783743i
$195$	−4.09273	−	4.73001i	−0.293087	−	0.338723i
$196$	−3.27035	−	0.138644i	−0.233597	−	0.00990313i
$197$	22.2749	+	16.1837i	1.58702	+	1.15304i	0.908039	+	0.418887i	$0.137580\pi$
$197$	22.2749	+	16.1837i	1.58702	+	1.15304i	0.678984	+	0.734153i	$0.262420\pi$
$198$	−0.418174	−	0.00886009i	−0.0297184	−	0.000629659i
$199$	−11.3822			−0.806862			−0.403431	−	0.915010i	$-0.632182\pi$
$199$	−11.3822			−0.806862			−0.403431	+	0.915010i	$0.632182\pi$
$200$	−12.9098	+	5.77373i	−0.912864	+	0.408264i
$201$	4.14670			0.292485
$202$	16.3862	+	0.347183i	1.15293	+	0.0244277i
$203$	−16.3671	−	11.8914i	−1.14874	−	0.834611i
$204$	0.253167	−	5.97174i	0.0177252	−	0.418106i
$205$	−13.0007	−	3.03288i	−0.908010	−	0.211825i
$206$	−7.55200	−	5.73514i	−0.526173	−	0.399586i
$207$		−	8.87368i		−	0.616763i
$208$	1.93993	+	8.30686i	0.134510	+	0.575977i
$209$	0.0373522	+	0.114958i	0.00258371	+	0.00795183i
$210$	8.92807	−	3.54476i	0.616095	−	0.244611i
$211$	15.0746	+	4.89802i	1.03778	+	0.337194i	0.777860	−	0.628438i	$-0.216305\pi$
$211$	15.0746	+	4.89802i	1.03778	+	0.337194i	0.259916	+	0.965631i	$0.416305\pi$
$212$	6.81067	+	5.40340i	0.467759	+	0.371107i
$213$	−2.65656	−	8.17604i	−0.182024	−	0.560213i
$214$	0.229174	−	10.8165i	0.0156660	−	0.739398i
$215$	−11.2677	+	18.6556i	−0.768451	+	1.27230i
$216$	−14.7577	−	5.85531i	−1.00414	−	0.398404i
$217$	11.7066	+	16.1128i	0.794699	+	1.09381i
$218$	−2.75639	−	9.13754i	−0.186686	−	0.618872i
$219$	−4.25572	−	5.85750i	−0.287575	−	0.395813i
$220$	−0.809672	+	0.642683i	−0.0545881	+	0.0433297i
$221$	−2.85603	+	3.93099i	−0.192117	+	0.264427i
$222$	13.9785	+	4.87160i	0.938177	+	0.326961i
$223$	22.1415	+	7.19420i	1.48270	+	0.481759i	0.934919	−	0.354861i	$-0.115472\pi$
$223$	22.1415	+	7.19420i	1.48270	+	0.481759i	0.547783	+	0.836620i	$0.315472\pi$
$224$	−13.0272	−	1.38505i	−0.870419	−	0.0925428i
$225$	−4.46519	+	4.58160i	−0.297679	+	0.305440i
$226$	−6.20602	−	20.5732i	−0.412818	−	1.36851i
$227$	1.38398	−	4.25947i	0.0918583	−	0.282711i	−0.894564	−	0.446940i	$-0.852514\pi$
$227$	1.38398	−	4.25947i	0.0918583	−	0.282711i	0.986422	+	0.164229i	$0.0525137\pi$
$228$	−0.0581047	+	1.37058i	−0.00384807	+	0.0907690i
$229$	2.99987	−	4.12897i	0.198237	−	0.272850i	−0.698313	−	0.715793i	$-0.746066\pi$
$229$	2.99987	−	4.12897i	0.198237	−	0.272850i	0.896550	+	0.442943i	$0.146066\pi$
$230$	−13.9955	−	16.8847i	−0.922836	−	1.11335i
$231$	0.568062	−	0.412721i	0.0373757	−	0.0271551i
$232$	19.0266	+	15.7633i	1.24916	+	1.03491i
$233$	−2.05646	−	2.83047i	−0.134723	−	0.185430i	0.736325	−	0.676628i	$-0.236559\pi$
$233$	−2.05646	−	2.83047i	−0.134723	−	0.185430i	−0.871048	+	0.491197i	$0.836559\pi$
$234$	2.20159	+	3.16930i	0.143922	+	0.207184i
$235$	−0.971727	−	2.30392i	−0.0633885	−	0.150291i
$236$	−9.44546	+	2.63233i	−0.614847	+	0.171350i
$237$	−5.09907	−	15.6933i	−0.331220	−	1.01939i
$238$	−4.25732	−	6.12863i	−0.275961	−	0.397260i
$239$	6.27635	−	19.3166i	0.405983	−	1.24949i	−0.514088	−	0.857738i	$-0.671869\pi$
$239$	6.27635	−	19.3166i	0.405983	−	1.24949i	0.920071	−	0.391751i	$-0.128131\pi$
$240$	−11.1569	+	3.62800i	−0.720175	+	0.234186i
$241$	5.98561	+	18.4218i	0.385567	+	1.18665i	0.936068	+	0.351819i	$0.114437\pi$
$241$	5.98561	+	18.4218i	0.385567	+	1.18665i	−0.550501	+	0.834835i	$0.685563\pi$
$242$	9.36263	−	12.3287i	0.601853	−	0.792516i
$243$	−12.2172			−0.783736
$244$	4.27098	+	1.59070i	0.273422	+	0.101834i
$245$	−1.89205	+	3.13260i	−0.120879	+	0.200134i
$246$	−10.4578	−	3.64460i	−0.666763	−	0.232371i
$247$	0.655490	−	0.902205i	0.0417079	−	0.0574059i
$248$	−13.0188	−	20.5471i	−0.826695	−	1.30474i
$249$	7.21286			0.457096
$250$	−1.27026	+	15.7603i	−0.0803381	+	0.996768i
$251$			4.56980i			0.288443i	0.989545	+	0.144222i	$0.0460679\pi$
$251$			4.56980i			0.288443i	−0.989545	+	0.144222i	$0.953932\pi$
$252$	−5.70889	+	1.59099i	−0.359626	+	0.100223i
$253$	−1.29691	−	0.942261i	−0.0815361	−	0.0592395i
$254$	2.12387	−	6.09419i	0.133263	−	0.382384i
$255$	−5.72020	−	3.45493i	−0.358213	−	0.216356i
$256$	15.7708	+	2.69864i	0.985673	+	0.168665i
$257$		−	27.4389i		−	1.71159i	−0.517312	−	0.855797i	$-0.673067\pi$
$257$		−	27.4389i		−	1.71159i	0.517312	−	0.855797i	$-0.326933\pi$
$258$	−10.9346	+	14.3986i	−0.680759	+	0.896419i
$259$	17.5767	−	5.71101i	1.09216	−	0.354865i
$260$	9.18776	+	2.55818i	0.569801	+	0.158651i
$261$	10.6303	+	3.45400i	0.658001	+	0.213798i
$262$	18.0263	−	12.5222i	1.11367	−	0.773624i
$263$	12.2444	−	3.97845i	0.755022	−	0.245322i	0.0938814	−	0.995583i	$-0.470073\pi$
$263$	12.2444	−	3.97845i	0.755022	−	0.245322i	0.661141	+	0.750262i	$0.270073\pi$
$264$	−0.724394	+	0.458982i	−0.0445834	+	0.0282484i
$265$	8.95595	−	3.77736i	0.550160	−	0.232041i
$266$	0.977104	+	1.40659i	0.0599101	+	0.0862435i
$267$	−16.7887	+	12.1977i	−1.02745	+	0.746486i
$268$	−5.26805	+	3.49643i	−0.321797	+	0.213578i
$269$	0.897279	+	1.23500i	0.0547081	+	0.0752992i	0.835495	−	0.549499i	$-0.185181\pi$
$269$	0.897279	+	1.23500i	0.0547081	+	0.0752992i	−0.780786	+	0.624798i	$0.785181\pi$
$270$	−13.6665	+	11.3279i	−0.831714	+	0.689395i
$271$	−19.8030	−	14.3877i	−1.20294	−	0.873990i	−0.208373	−	0.978049i	$-0.566817\pi$
$271$	−19.8030	−	14.3877i	−1.20294	−	0.873990i	−0.994571	+	0.104059i	$0.966817\pi$
$272$	4.71365	+	7.80008i	0.285807	+	0.472950i
$273$	−6.16110	−	2.00186i	−0.372887	−	0.121158i
$274$	6.00374	+	19.9026i	0.362699	+	1.20236i
$275$	0.195471	+	1.13910i	0.0117874	+	0.0686904i
$276$	−10.0608	−	15.1585i	−0.605588	−	0.912435i
$277$	−8.46626	+	26.0565i	−0.508689	+	1.56558i	0.285791	+	0.958292i	$0.407744\pi$
$277$	−8.46626	+	26.0565i	−0.508689	+	1.56558i	−0.794480	+	0.607290i	$0.792256\pi$
$278$	−2.74706	+	7.88237i	−0.164757	+	0.472753i
$279$	−8.90222	−	6.46784i	−0.532962	−	0.387220i
$280$	−8.35351	+	12.0313i	−0.499218	+	0.719010i
$281$	−23.5098	+	17.0809i	−1.40248	+	1.01896i	−0.408116	+	0.912930i	$0.633814\pi$
$281$	−23.5098	+	17.0809i	−1.40248	+	1.01896i	−0.994363	+	0.106031i	$0.966186\pi$
$282$	−0.599067	−	1.98593i	−0.0356739	−	0.118261i
$283$	−8.02169	+	5.82810i	−0.476840	+	0.346444i	−0.800101	−	0.599865i	$-0.795221\pi$
$283$	−8.02169	+	5.82810i	−0.476840	+	0.346444i	0.323261	+	0.946310i	$0.395221\pi$
$284$	10.2689	+	8.14704i	0.609344	+	0.483438i
$285$	1.31285	+	0.792944i	0.0777666	+	0.0469700i
$286$	0.696980	+	0.0147673i	0.0412133	+	0.000873209i
$287$	−13.1497	+	4.27258i	−0.776200	+	0.252203i
$288$	7.08166	−	1.49636i	0.417291	−	0.0881738i
$289$	3.64911	−	11.2308i	0.214653	−	0.660635i
$290$	25.6749	−	10.1938i	1.50768	−	0.598603i
$291$	15.9216	−	5.17324i	0.933340	−	0.303261i
$292$	10.3455	+	3.85312i	0.605425	+	0.225487i
$293$	−6.22226			−0.363508			−0.181754	−	0.983344i	$-0.558177\pi$
$293$	−6.22226			−0.363508			−0.181754	+	0.983344i	$0.558177\pi$
$294$	−1.83612	+	2.41778i	−0.107084	+	0.141008i
$295$	−2.49058	+	10.6761i	−0.145007	+	0.621587i
$296$	−21.8662	+	5.59749i	−1.27095	+	0.325347i
$297$	−0.762664	+	1.04972i	−0.0442542	+	0.0609107i
$298$	12.9237	+	0.273823i	0.748652	+	0.0158621i
$299$			14.7899i			0.855324i
$300$	−2.43317	+	12.8891i	−0.140479	+	0.744151i
$301$			22.5723i			1.30105i
$302$	−0.257484	+	12.1526i	−0.0148165	+	0.699304i
$303$	8.93519	−	12.2982i	0.513313	−	0.706515i
$304$	−1.08184	−	1.79021i	−0.0620475	−	0.102675i
$305$	3.85331	−	3.33415i	0.220640	−	0.190913i
$306$	3.28336	+	2.49345i	0.187697	+	0.142541i
$307$	29.6136			1.69014			0.845070	−	0.534656i	$-0.179559\pi$
$307$	29.6136			1.69014			0.845070	+	0.534656i	$0.179559\pi$
$308$	−0.373677	+	1.00331i	−0.0212922	+	0.0571689i
$309$	−8.36481	+	2.71789i	−0.475857	+	0.154615i
$310$	−27.1401	+	1.73358i	−1.54145	+	0.0984607i
$311$	−1.32670	+	4.08315i	−0.0752301	+	0.231534i	−0.981599	−	0.190952i	$-0.938843\pi$
$311$	−1.32670	+	4.08315i	−0.0752301	+	0.231534i	0.906369	+	0.422486i	$0.138843\pi$
$312$	7.35416	+	2.91786i	0.416347	+	0.165191i
$313$	−13.0617	+	4.24400i	−0.738290	+	0.239885i	−0.653935	−	0.756551i	$-0.726883\pi$
$313$	−13.0617	+	4.24400i	−0.738290	+	0.239885i	−0.0843552	+	0.996436i	$0.526883\pi$
$314$	−0.139199	+	6.56986i	−0.00785547	+	0.370759i
$315$	−1.50532	+	6.45270i	−0.0848151	+	0.363568i
$316$	19.7103	+	15.6376i	1.10879	+	0.879686i
$317$	−10.3334	+	7.50769i	−0.580384	+	0.421674i	−0.838863	−	0.544343i	$-0.816779\pi$
$317$	−10.3334	+	7.50769i	−0.580384	+	0.421674i	0.258478	+	0.966017i	$0.416779\pi$
$318$	7.71983	−	2.32873i	0.432907	−	0.130589i
$319$	1.63361	−	1.18688i	0.0914644	−	0.0664528i
$320$	11.1149	−	14.0164i	0.621340	−	0.783541i
$321$	−8.11803	−	5.89809i	−0.453104	−	0.329200i
$322$	−21.4487	−	7.47500i	−1.19529	−	0.416565i
$323$	0.368178	−	1.13313i	0.0204859	−	0.0630493i
$324$	−5.87280	+	3.89781i	−0.326267	+	0.216545i
$325$	7.44223	−	7.63624i	0.412821	−	0.423583i
$326$	−17.7840	+	5.36463i	−0.984963	+	0.297119i
$327$	−8.41894	−	2.73548i	−0.465569	−	0.151272i
$328$	16.3588	−	4.18766i	0.903265	−	0.231225i
$329$	−2.09513	−	1.52220i	−0.115508	−	0.0839217i
$330$	0.0611179	+	0.956832i	0.00336443	+	0.0526719i
$331$	2.79298	+	3.84421i	0.153516	+	0.211297i	0.878847	−	0.477103i	$-0.158313\pi$
$331$	2.79298	+	3.84421i	0.153516	+	0.211297i	−0.725331	+	0.688400i	$0.758313\pi$
$332$	−9.16335	+	6.08177i	−0.502904	+	0.333780i
$333$	−8.26066	+	6.00172i	−0.452682	+	0.328892i
$334$	−24.2534	+	16.8479i	−1.32709	+	0.921875i
$335$	0.599957	+	7.04356i	0.0327791	+	0.384831i
$336$	−7.94841	+	9.19043i	−0.433621	+	0.501379i
$337$	−28.1678	+	9.15228i	−1.53440	+	0.498556i	−0.949824	−	0.312784i	$-0.898739\pi$
$337$	−28.1678	+	9.15228i	−1.53440	+	0.498556i	−0.584574	+	0.811340i	$0.698739\pi$
$338$	6.81937	+	9.81683i	0.370925	+	0.533965i
$339$	−18.9553	−	6.15894i	−1.02951	−	0.334508i
$340$	10.1802	−	0.433982i	0.552099	−	0.0235360i
$341$	−1.89059	+	0.614289i	−0.102381	+	0.0332656i
$342$	−0.753568	−	0.572275i	−0.0407483	−	0.0309451i
$343$			20.0015i			1.07998i
$344$	1.75084	−	27.5122i	0.0943992	−	1.48336i
$345$	−20.2674	+	1.72634i	−1.09116	+	0.0929431i
$346$	10.5211	+	3.66666i	0.565616	+	0.197121i
$347$	−15.6090	−	11.3406i	−0.837937	−	0.608797i	0.0838564	−	0.996478i	$-0.473276\pi$
$347$	−15.6090	−	11.3406i	−0.837937	−	0.608797i	−0.921794	+	0.387681i	$0.873276\pi$
$348$	22.0754	−	6.15212i	1.18337	−	0.329788i
$349$		−	33.1221i		−	1.77299i	−0.462742	−	0.886493i	$-0.653134\pi$
$349$		−	33.1221i		−	1.77299i	0.462742	−	0.886493i	$-0.346866\pi$
$350$	7.31285	+	14.6523i	0.390888	+	0.783199i
$351$	11.9709			0.638961
$352$	0.533278	−	1.19390i	0.0284238	−	0.0636349i
$353$	7.81083	−	10.7507i	0.415729	−	0.572202i	−0.548875	−	0.835904i	$-0.684944\pi$
$353$	7.81083	−	10.7507i	0.415729	−	0.572202i	0.964604	+	0.263703i	$0.0849438\pi$
$354$	−2.99292	+	8.58785i	−0.159072	+	0.456439i
$355$	13.5034	−	5.69535i	0.716687	−	0.302278i
$356$	11.0438	−	29.6521i	0.585318	−	1.57156i
$357$	−6.92117			−0.366307
$358$	−18.0812	−	13.7313i	−0.955623	−	0.725720i
$359$	5.23366	+	16.1076i	0.276222	+	0.850124i	0.988893	+	0.148626i	$0.0474851\pi$
$359$	5.23366	+	16.1076i	0.276222	+	0.850124i	−0.712671	+	0.701498i	$0.752515\pi$
$360$	2.33526	−	7.74809i	0.123079	−	0.408360i
$361$	5.78682	−	17.8100i	0.304570	−	0.937369i
$362$	19.9200	−	13.8377i	1.04697	−	0.727291i
$363$	−4.43696	−	13.6556i	−0.232880	−	0.716732i
$364$	9.51512	−	2.65174i	0.498728	−	0.138989i
$365$	9.33379	−	8.07623i	0.488553	−	0.422729i
$366$	3.47169	−	2.41165i	0.181468	−	0.126059i
$367$	−5.13516	−	7.06794i	−0.268053	−	0.368944i	0.653678	−	0.756773i	$-0.273225\pi$
$367$	−5.13516	−	7.06794i	−0.268053	−	0.368944i	−0.921731	+	0.387829i	$0.873225\pi$
$368$	25.5628	+	10.7746i	1.33255	+	0.561663i
$369$	6.18006	−	4.49008i	0.321721	−	0.233744i
$370$	−6.25243	+	24.4487i	−0.325048	+	1.27103i
$371$	5.91720	−	8.14432i	0.307206	−	0.422832i
$372$	−22.5404	−	0.955580i	−1.16866	−	0.0495445i
$373$	0.310042	−	0.954212i	0.0160534	−	0.0494072i	−0.942709	−	0.333616i	$-0.891731\pi$
$373$	0.310042	−	0.954212i	0.0160534	−	0.0494072i	0.958762	+	0.284209i	$0.0917310\pi$
$374$	0.713072	−	0.215102i	0.0368721	−	0.0111227i
$375$	11.3330	+	9.30715i	0.585235	+	0.480619i
$376$	2.43557	+	2.01784i	0.125605	+	0.104062i
$377$	−17.7178	−	5.75686i	−0.912513	−	0.296494i
$378$	−6.05024	+	17.3605i	−0.311191	+	0.892927i
$379$	21.2264	−	29.2157i	1.09033	−	1.50071i	0.242712	−	0.970098i	$-0.421963\pi$
$379$	21.2264	−	29.2157i	1.09033	−	1.50071i	0.847616	−	0.530610i	$-0.178037\pi$
$380$	−2.33647	+	0.0996037i	−0.119858	+	0.00510956i
$381$	−3.51833	−	4.84257i	−0.180250	−	0.248092i
$382$	4.04661	−	1.22068i	0.207043	−	0.0624556i
$383$	−18.1528	−	24.9852i	−0.927565	−	1.27668i	−0.960802	−	0.277236i	$-0.910582\pi$
$383$	−18.1528	−	24.9852i	−0.927565	−	1.27668i	0.0332373	−	0.999447i	$-0.489418\pi$
$384$	10.4008	−	10.5852i	0.530761	−	0.540174i
$385$	0.783235	+	0.905194i	0.0399174	+	0.0461329i
$386$	−21.1164	−	0.447404i	−1.07480	−	0.0227723i
$387$	−3.85377	−	11.8607i	−0.195898	−	0.602912i
$388$	−15.8651	+	19.9970i	−0.805428	+	1.01519i
$389$	−1.26254	−	0.410223i	−0.0640132	−	0.0207991i	0.276835	−	0.960917i	$-0.410714\pi$
$389$	−1.26254	−	0.410223i	−0.0640132	−	0.0207991i	−0.340849	+	0.940118i	$0.610714\pi$
$390$	6.81035	−	5.64500i	0.344856	−	0.285846i
$391$	4.88288	+	15.0280i	0.246938	+	0.759997i
$392$	0.293998	−	4.61978i	0.0148491	−	0.233334i
$393$		−	20.3574i		−	1.02690i
$394$	−23.5493	+	31.0096i	−1.18640	+	1.56224i
$395$	25.9188	−	10.9318i	1.30412	−	0.550039i
$396$	0.0250545	−	0.590990i	0.00125904	−	0.0296983i
$397$	7.80606	+	5.67144i	0.391775	+	0.284641i	0.766182	−	0.642623i	$-0.222154\pi$
$397$	7.80606	+	5.67144i	0.391775	+	0.284641i	−0.374407	+	0.927264i	$0.622154\pi$
$398$	0.340976	−	16.0932i	0.0170916	−	0.806681i
$399$	1.58849			0.0795237
$400$	−7.77672	−	18.4261i	−0.388836	−	0.921307i
$401$	11.7737			0.587953			0.293976	−	0.955813i	$-0.405021\pi$
$401$	11.7737			0.587953			0.293976	+	0.955813i	$0.405021\pi$
$402$	−0.124223	+	5.86300i	−0.00619566	+	0.292420i
$403$	14.8375	+	10.7801i	0.739110	+	0.536995i
$404$	−0.981760	+	23.1579i	−0.0488444	+	1.15215i
$405$	0.668830	+	7.85214i	0.0332344	+	0.390176i
$406$	17.3035	−	22.7851i	0.858758	−	1.13081i
$407$			1.84462i			0.0914343i
$408$	8.43584	+	0.536847i	0.417636	+	0.0265779i
$409$	−0.0454622	−	0.139918i	−0.00224796	−	0.00691851i	0.949926	−	0.312474i	$-0.101158\pi$
$409$	−0.0454622	−	0.139918i	−0.00224796	−	0.00691851i	−0.952174	+	0.305556i	$0.901158\pi$
$410$	4.67764	−	18.2908i	0.231012	−	0.903319i
$411$	18.3375	+	5.95820i	0.904520	+	0.293896i
$412$	8.33513	−	10.5059i	0.410642	−	0.517590i
$413$	3.50862	+	10.7984i	0.172648	+	0.531355i
$414$	12.5465	+	0.265829i	0.616625	+	0.0130648i
$415$	1.04358	+	12.2517i	0.0512272	+	0.601413i
$416$	−11.8032	+	2.49401i	−0.578697	+	0.122279i
$417$	4.55069	+	6.26349i	0.222848	+	0.306724i
$418$	−0.163658	+	0.0493683i	−0.00800478	+	0.00241468i
$419$	−20.0431	−	27.5869i	−0.979168	−	1.34771i	−0.937277	−	0.348587i	$-0.886662\pi$
$419$	−20.0431	−	27.5869i	−0.979168	−	1.34771i	−0.0418913	−	0.999122i	$-0.513338\pi$
$420$	4.74446	+	12.7296i	0.231506	+	0.621139i
$421$	−3.43224	+	4.72407i	−0.167277	+	0.230237i	−0.884423	−	0.466686i	$-0.845448\pi$
$421$	−3.43224	+	4.72407i	−0.167277	+	0.230237i	0.717146	+	0.696923i	$0.245448\pi$
$422$	−7.37688	+	21.1671i	−0.359101	+	1.03040i
$423$	1.36078	+	0.442143i	0.0661633	+	0.0214977i
$424$	−7.84388	+	9.46771i	−0.380932	+	0.459793i
$425$	5.04090	−	10.2162i	0.244520	−	0.495557i
$426$	11.6397	−	3.51117i	0.563943	−	0.170117i
$427$	1.63082	−	5.01915i	0.0789209	−	0.242894i
$428$	15.2865	+	0.648057i	0.738900	+	0.0313250i
$429$	0.380055	−	0.523101i	0.0183492	−	0.0252556i
$430$	−26.0395	−	16.4902i	−1.25574	−	0.795230i
$431$	−3.30954	+	2.40452i	−0.159415	+	0.115822i	−0.664633	−	0.747170i	$-0.731412\pi$
$431$	−3.30954	+	2.40452i	−0.159415	+	0.115822i	0.505218	+	0.862992i	$0.331412\pi$
$432$	8.72090	−	20.6905i	0.419585	−	0.995471i
$433$	2.79701	+	3.84976i	0.134416	+	0.185008i	0.870919	−	0.491427i	$-0.163524\pi$
$433$	2.79701	+	3.84976i	0.134416	+	0.185008i	−0.736503	+	0.676434i	$0.763524\pi$
$434$	−23.1326	+	16.0693i	−1.11040	+	0.771351i
$435$	5.82084	−	24.9516i	0.279088	−	1.19634i
$436$	13.0021	−	3.62351i	0.622688	−	0.173535i
$437$	−1.12068	−	3.44909i	−0.0536092	−	0.164992i
$438$	8.40939	−	5.84168i	0.401816	−	0.279126i
$439$	0.541600	−	1.66687i	0.0258492	−	0.0795556i	−0.937300	−	0.348524i	$-0.886683\pi$
$439$	0.541600	−	1.66687i	0.0258492	−	0.0795556i	0.963149	+	0.268969i	$0.0866829\pi$
$440$	−0.884431	−	1.16404i	−0.0421636	−	0.0554936i
$441$	−0.647116	−	1.99162i	−0.0308150	−	0.0948389i
$442$	−5.47245	−	4.15589i	−0.260298	−	0.197675i
$443$	−3.43488			−0.163196			−0.0815981	−	0.996665i	$-0.526002\pi$
$443$	−3.43488			−0.163196			−0.0815981	+	0.996665i	$0.526002\pi$
$444$	−7.30670	+	19.6182i	−0.346761	+	0.931040i
$445$	−23.1479	−	26.7523i	−1.09732	−	1.26818i
$446$	−10.8351	+	31.0902i	−0.513059	+	1.47216i
$447$	7.04717	−	9.69960i	0.333320	−	0.458775i
$448$	2.34858	−	18.3777i	0.110960	−	0.868264i
$449$	5.54236			0.261560			0.130780	−	0.991411i	$-0.458252\pi$
$449$	5.54236			0.261560			0.130780	+	0.991411i	$0.458252\pi$
$450$	−6.34414	−	6.45057i	−0.299065	−	0.304083i
$451$		−	1.38002i		−	0.0649825i
$452$	29.2743	−	8.15835i	1.37695	−	0.383737i
$453$	9.12084	+	6.62668i	0.428534	+	0.311348i
$454$	5.98098	+	2.08441i	0.280701	+	0.0978263i
$455$	2.50895	−	10.7548i	0.117621	−	0.504195i
$456$	−1.93612	−	0.123212i	−0.0906671	−	0.00576995i
$457$		−	3.02813i		−	0.141650i	−0.997489	−	0.0708250i	$-0.977437\pi$
$457$		−	3.02813i		−	0.141650i	0.997489	−	0.0708250i	$-0.0225632\pi$
$458$	5.74806	+	4.36520i	0.268589	+	0.203972i
$459$	12.1636	−	3.95219i	0.567748	−	0.184472i
$460$	24.2925	−	19.2824i	1.13264	−	0.899045i
$461$	11.9787	+	3.89211i	0.557903	+	0.181274i	0.574377	−	0.818591i	$-0.305244\pi$
$461$	11.9787	+	3.89211i	0.557903	+	0.181274i	−0.0164747	+	0.999864i	$0.505244\pi$
$462$	0.566528	+	0.815545i	0.0263573	+	0.0379426i
$463$	−4.16641	+	1.35375i	−0.193629	+	0.0629140i	−0.404226	−	0.914659i	$-0.632459\pi$
$463$	−4.16641	+	1.35375i	−0.193629	+	0.0629140i	0.210597	+	0.977573i	$0.432459\pi$
$464$	−22.8576	+	26.4294i	−1.06114	+	1.22695i
$465$	−13.0406	+	21.5909i	−0.604745	+	1.00126i
$466$	4.06360	−	2.82283i	0.188243	−	0.130765i
$467$	−18.3661	+	13.3438i	−0.849883	+	0.617476i	−0.925114	−	0.379690i	$-0.876031\pi$
$467$	−18.3661	+	13.3438i	−0.849883	+	0.617476i	0.0752308	+	0.997166i	$0.476031\pi$
$468$	−4.54701	+	3.01788i	−0.210186	+	0.139501i
$469$	4.30342	+	5.92315i	0.198714	+	0.273506i
$470$	3.28662	−	1.30490i	0.151600	−	0.0601907i
$471$	4.93085	+	3.58247i	0.227201	+	0.165072i
$472$	−3.43888	−	13.4338i	−0.158287	−	0.618339i
$473$	−2.14269	−	0.696201i	−0.0985208	−	0.0320113i
$474$	22.3415	−	6.73943i	1.02618	−	0.309552i
$475$	−1.15694	+	2.34473i	−0.0530842	+	0.107583i
$476$	8.79278	−	5.83582i	0.403017	−	0.267484i
$477$	−1.71873	+	5.28970i	−0.0786951	+	0.242199i
$478$	27.1237	+	9.45278i	1.24061	+	0.432360i
$479$	5.58405	+	4.05705i	0.255142	+	0.185371i	0.708002	−	0.706210i	$-0.249597\pi$
$479$	5.58405	+	4.05705i	0.255142	+	0.185371i	−0.452861	+	0.891581i	$0.649597\pi$
$480$	−4.79539	−	15.8834i	−0.218879	−	0.724974i
$481$	13.7682	−	10.0032i	0.627777	−	0.456107i
$482$	−26.2258	+	7.91117i	−1.19455	+	0.360344i
$483$	−17.0435	+	12.3829i	−0.775508	+	0.563439i
$484$	17.1510	+	13.6071i	0.779589	+	0.618506i
$485$	11.0908	+	26.2958i	0.503608	+	1.19403i
$486$	0.365992	−	17.2739i	0.0166017	−	0.783561i
$487$	−34.1041	+	11.0811i	−1.54540	+	0.502132i	−0.952861	−	0.303407i	$-0.901876\pi$
$487$	−34.1041	+	11.0811i	−1.54540	+	0.502132i	−0.592543	+	0.805539i	$0.701876\pi$
$488$	−2.37703	+	5.99107i	−0.107603	+	0.271203i
$489$	−5.32394	+	16.3854i	−0.240757	+	0.740973i
$490$	−4.37249	−	2.76900i	−0.197529	−	0.125091i
$491$	−7.36748	+	2.39384i	−0.332490	+	0.108032i	−0.470504	−	0.882398i	$-0.655928\pi$
$491$	−7.36748	+	2.39384i	−0.332490	+	0.108032i	0.138014	+	0.990430i	$0.455928\pi$
$492$	5.46637	−	14.6770i	0.246443	−	0.661691i
$493$	−19.9036			−0.896411
$494$	1.25599	+	0.953823i	0.0565096	+	0.0429145i
$495$	−0.566096	−	0.341914i	−0.0254441	−	0.0153679i
$496$	29.4415	−	17.7917i	1.32196	−	0.798871i
$497$	8.92171	−	12.2797i	0.400194	−	0.550819i
$498$	−0.216076	+	10.1982i	−0.00968258	+	0.456994i
$499$			36.4452i			1.63151i	0.578396	+	0.815756i	$0.303679\pi$
$499$			36.4452i			1.63151i	−0.578396	+	0.815756i	$0.696321\pi$
$500$	−22.2453	−	2.26814i	−0.994842	−	0.101434i
$501$			27.3897i			1.22368i
$502$	−6.46123	−	0.136898i	−0.288379	−	0.00611004i
$503$	−7.52915	+	10.3630i	−0.335708	+	0.462063i	−0.943182	−	0.332277i	$-0.892183\pi$
$503$	−7.52915	+	10.3630i	−0.335708	+	0.462063i	0.607473	+	0.794340i	$0.292183\pi$
$504$	−2.07847	−	8.11943i	−0.0925826	−	0.361668i
$505$	22.1825	+	13.3979i	0.987107	+	0.596199i
$506$	1.37111	−	1.80547i	0.0609533	−	0.0802630i
$507$	11.0863			0.492360
$508$	8.55293	+	3.18549i	0.379475	+	0.141333i
$509$	−40.6350	+	13.2031i	−1.80111	+	0.585217i	−0.999913	−	0.0131803i	$-0.995804\pi$
$509$	−40.6350	+	13.2031i	−1.80111	+	0.585217i	−0.801200	+	0.598397i	$0.795804\pi$
$510$	5.05627	−	7.98428i	0.223895	−	0.353550i
$511$	3.95030	−	12.1578i	0.174751	−	0.537828i
$512$	−4.28804	+	22.2174i	−0.189506	+	0.981879i
$513$	−2.79168	+	0.907072i	−0.123256	+	0.0400482i
$514$	38.7958	+	0.821989i	1.71121	+	0.0362564i
$515$	−5.82684	−	13.8152i	−0.256761	−	0.608770i
$516$	−20.0306	−	15.8917i	−0.881798	−	0.699595i
$517$	0.209116	−	0.151932i	0.00919692	−	0.00668195i
$518$	7.54823	+	25.0227i	0.331650	+	1.09943i
$519$	8.36024	−	6.07407i	0.366974	−	0.266622i
$520$	−3.89223	+	12.9139i	−0.170686	+	0.566312i
$521$	−1.68871	−	1.22692i	−0.0739836	−	0.0537522i	0.550179	−	0.835047i	$-0.314560\pi$
$521$	−1.68871	−	1.22692i	−0.0739836	−	0.0537522i	−0.624162	+	0.781295i	$0.714560\pi$
$522$	−5.20206	+	14.9267i	−0.227688	+	0.653325i
$523$	10.0536	−	30.9419i	0.439615	−	1.35300i	−0.448668	−	0.893699i	$-0.648101\pi$
$523$	10.0536	−	30.9419i	0.439615	−	1.35300i	0.888283	−	0.459297i	$-0.151899\pi$
$524$	17.1651	+	25.8625i	0.749860	+	1.12981i
$525$	15.0308	+	2.18279i	0.655998	+	0.0952650i
$526$	5.25831	+	17.4315i	0.229273	+	0.760049i
$527$	18.6353	+	6.05499i	0.811768	+	0.263760i
$528$	−0.627252	−	1.03797i	−0.0272976	−	0.0451717i
$529$	20.3038	+	14.7515i	0.882772	+	0.641372i
$530$	5.07250	+	12.7759i	0.220335	+	0.554951i
$531$	−3.68722	−	5.07503i	−0.160012	−	0.220237i
$532$	−2.01804	+	1.33939i	−0.0874932	+	0.0580697i
$533$	−10.3004	+	7.48371i	−0.446162	+	0.324155i
$534$	−16.7433	−	24.1028i	−0.724554	−	1.04303i
$535$	8.84393	−	14.6426i	0.382356	−	0.633055i
$536$	−4.78577	−	7.55321i	−0.206714	−	0.326249i
$537$	−20.0273	+	6.50726i	−0.864242	+	0.280809i
$538$	−1.77304	+	1.23166i	−0.0764412	+	0.0531008i
$539$	−0.359795	−	0.116904i	−0.0154975	−	0.00503543i
$540$	−15.6071	−	19.6623i	−0.671623	−	0.846131i
$541$	−5.01695	+	1.63011i	−0.215696	+	0.0700838i	−0.414872	−	0.909880i	$-0.636174\pi$
$541$	−5.01695	+	1.63011i	−0.215696	+	0.0700838i	0.199176	+	0.979964i	$0.436174\pi$
$542$	20.9360	−	27.5683i	0.899276	−	1.18416i
$543$		−	22.4960i		−	0.965395i
$544$	−11.1697	+	6.43095i	−0.478898	+	0.275725i
$545$	3.42839	−	14.6962i	0.146856	−	0.629514i
$546$	3.01499	−	8.65119i	0.129030	−	0.370237i
$547$	12.2753	+	8.91852i	0.524854	+	0.381329i	0.818429	−	0.574607i	$-0.194845\pi$
$547$	12.2753	+	8.91852i	0.524854	+	0.381329i	−0.293575	+	0.955936i	$0.594845\pi$
$548$	−28.3201	+	7.89244i	−1.20978	+	0.337148i
$549$			2.91575i			0.124441i
$550$	−1.61643	+	0.242252i	−0.0689247	+	0.0103297i
$551$	4.56809			0.194607
$552$	21.7339	−	13.7708i	0.925058	−	0.586124i
$553$	17.1246	−	23.5700i	0.728211	−	1.00230i
$554$	−36.5875	−	12.7510i	−1.55446	−	0.541738i
$555$	15.3150	+	17.6997i	0.650085	+	0.751311i
$556$	−11.0626	−	4.12018i	−0.469157	−	0.174735i
$557$	−21.0806			−0.893213			−0.446606	−	0.894731i	$-0.647368\pi$
$557$	−21.0806			−0.893213			−0.446606	+	0.894731i	$0.647368\pi$
$558$	9.41154	−	12.3931i	0.398422	−	0.524640i
$559$	6.42315	+	19.7684i	0.271670	+	0.836116i
$560$	−16.7608	−	12.1714i	−0.708274	−	0.514336i
$561$	0.213470	−	0.656995i	0.00901273	−	0.0277383i
$562$	−23.4463	−	33.7522i	−0.989024	−	1.42375i
$563$	5.40722	+	16.6417i	0.227887	+	0.701365i	0.997986	+	0.0634396i	$0.0202070\pi$
$563$	5.40722	+	16.6417i	0.227887	+	0.701365i	−0.770099	+	0.637925i	$0.779793\pi$
$564$	2.82585	−	0.787526i	0.118990	−	0.0331608i
$565$	7.71904	−	33.0884i	0.324743	−	1.39204i
$566$	−8.00002	−	11.5164i	−0.336266	−	0.484071i
$567$	4.79744	+	6.60311i	0.201474	+	0.277305i
$568$	−11.8267	+	14.2750i	−0.496237	+	0.598967i
$569$	−26.4646	+	19.2277i	−1.10945	+	0.806065i	−0.982578	−	0.185853i	$-0.940495\pi$
$569$	−26.4646	+	19.2277i	−1.10945	+	0.806065i	−0.126876	+	0.991919i	$0.540495\pi$
$570$	−1.16047	+	1.83248i	−0.0486067	+	0.0767542i
$571$	−17.4500	+	24.0179i	−0.730261	+	1.00512i	0.268860	+	0.963179i	$0.413353\pi$
$571$	−17.4500	+	24.0179i	−0.730261	+	1.00512i	−0.999120	+	0.0419380i	$0.986647\pi$
$572$	−0.0417589	+	0.985015i	−0.00174603	+	0.0411855i
$573$	1.21142	−	3.72838i	0.0506080	−	0.155755i
$574$	−5.64707	−	18.7202i	−0.235704	−	0.781368i
$575$	−5.86471	−	34.1764i	−0.244575	−	1.42525i
$576$	1.90355	+	10.0576i	0.0793146	+	0.419065i
$577$	−7.08229	−	2.30117i	−0.294839	−	0.0957992i	0.157862	−	0.987461i	$-0.449540\pi$
$577$	−7.08229	−	2.30117i	−0.294839	−	0.0957992i	−0.452702	+	0.891662i	$0.649540\pi$
$578$	15.7699	+	5.49590i	0.655940	+	0.228599i
$579$	−11.5145	+	15.8484i	−0.478527	+	0.658636i
$580$	13.6439	+	36.6071i	0.566532	+	1.52003i
$581$	7.48546	+	10.3029i	0.310549	+	0.427435i
$582$	6.83746	+	22.6664i	0.283422	+	0.939554i
$583$	0.590598	+	0.812889i	0.0244601	+	0.0336664i
$584$	−5.75784	+	14.5120i	−0.238261	+	0.600513i
$585$	0.517841	+	6.07951i	0.0214101	+	0.251357i
$586$	0.186400	−	8.79762i	0.00770012	−	0.363427i
$587$	4.32742	+	13.3184i	0.178612	+	0.549710i	0.999780	−	0.0209758i	$-0.00667728\pi$
$587$	4.32742	+	13.3184i	0.178612	+	0.549710i	−0.821168	+	0.570686i	$0.806677\pi$
$588$	−3.36349	−	2.66851i	−0.138708	−	0.110047i
$589$	−4.27702	−	1.38969i	−0.176232	−	0.0572611i
$590$	−15.0203	−	3.84125i	−0.618376	−	0.158142i
$591$	11.1601	+	34.3471i	0.459063	+	1.41285i
$592$	−7.25922	−	31.0843i	−0.298352	−	1.27756i
$593$			10.4531i			0.429258i	0.976696	+	0.214629i	$0.0688542\pi$
$593$			10.4531i			0.429258i	−0.976696	+	0.214629i	$0.931146\pi$
$594$	−1.46134	−	1.10977i	−0.0599596	−	0.0455346i
$595$	−1.00138	−	11.7563i	−0.0410524	−	0.481960i
$596$	−0.774313	+	18.2646i	−0.0317171	+	0.748148i
$597$	−12.0784	−	8.77546i	−0.494335	−	0.359156i
$598$	−20.9114	−	0.443062i	−0.855132	−	0.0181182i
$599$	25.1691			1.02838			0.514191	−	0.857676i	$-0.328092\pi$
$599$	25.1691			1.02838			0.514191	+	0.857676i	$0.328092\pi$
$600$	−18.1509	−	3.82637i	−0.741008	−	0.156211i
$601$	−9.80217			−0.399839			−0.199919	−	0.979812i	$-0.564068\pi$
$601$	−9.80217			−0.399839			−0.199919	+	0.979812i	$0.564068\pi$
$602$	−31.9149	−	0.676199i	−1.30075	−	0.0275598i
$603$	−3.27250	−	2.37761i	−0.133267	−	0.0968238i
$604$	−17.1748	−	0.728111i	−0.698833	−	0.0296264i
$605$	22.5533	−	9.51233i	0.916923	−	0.386731i
$606$	17.1207	+	13.0018i	0.695483	+	0.528164i
$607$		−	2.47771i		−	0.100567i	−0.998735	−	0.0502836i	$-0.983987\pi$
$607$		−	2.47771i		−	0.100567i	0.998735	−	0.0502836i	$-0.0160125\pi$
$608$	2.56358	−	1.47597i	0.103967	−	0.0598587i
$609$	−8.20014	−	25.2374i	−0.332287	−	1.02267i
$610$	4.59870	+	5.54806i	0.186196	+	0.224634i
$611$	−2.26804	−	0.736930i	−0.0917549	−	0.0298130i
$612$	−3.62384	+	4.56764i	−0.146485	+	0.184636i
$613$	0.797806	+	2.45539i	0.0322231	+	0.0991725i	0.965875	−	0.259010i	$-0.0833964\pi$
$613$	0.797806	+	2.45539i	0.0322231	+	0.0991725i	−0.933651	+	0.358183i	$0.883396\pi$
$614$	−0.887136	+	41.8706i	−0.0358019	+	1.68976i
$615$	−11.4576	−	13.2417i	−0.462016	−	0.533957i
$616$	−1.40738	−	0.558397i	−0.0567051	−	0.0224984i
$617$	10.4128	+	14.3320i	0.419205	+	0.576986i	0.965433	−	0.260650i	$-0.0839369\pi$
$617$	10.4128	+	14.3320i	0.419205	+	0.576986i	−0.546228	+	0.837636i	$0.683937\pi$
$618$	−3.59223	−	11.9084i	−0.144501	−	0.479026i
$619$	−12.1197	−	16.6813i	−0.487130	−	0.670477i	0.492726	−	0.870185i	$-0.336001\pi$
$619$	−12.1197	−	16.6813i	−0.487130	−	0.670477i	−0.979855	+	0.199708i	$0.936001\pi$
$620$	−1.63807	−	38.4252i	−0.0657863	−	1.54319i
$621$	22.8822	−	31.4946i	0.918229	−	1.26383i
$622$	−5.73341	−	1.99813i	−0.229889	−	0.0801178i
$623$	−34.8464	−	11.3223i	−1.39609	−	0.453617i
$624$	−4.34585	+	10.3106i	−0.173973	+	0.412755i
$625$	−14.1694	+	20.5968i	−0.566775	+	0.823873i
$626$	−5.60929	−	18.5950i	−0.224192	−	0.743206i
$627$	−0.0489939	+	0.150788i	−0.00195663	+	0.00602188i
$628$	−9.28493	−	0.393627i	−0.370509	−	0.0157074i
$629$	10.6873	−	14.7097i	0.426129	−	0.586516i
$630$	−9.07835	−	2.32167i	−0.361690	−	0.0924975i
$631$	−26.5548	+	19.2932i	−1.05713	+	0.768050i	−0.973555	−	0.228452i	$-0.926634\pi$
$631$	−26.5548	+	19.2932i	−1.05713	+	0.768050i	−0.0835747	+	0.996502i	$0.526634\pi$
$632$	−22.7005	+	27.3999i	−0.902976	+	1.08991i
$633$	12.2203	+	16.8198i	0.485714	+	0.668528i
$634$	−10.3055	−	14.8353i	−0.409285	−	0.589186i
$635$	7.71651	−	6.67685i	0.306221	−	0.264963i
$636$	3.06132	+	10.9848i	0.121389	+	0.435576i
$637$	1.07856	+	3.31947i	0.0427342	+	0.131522i
$638$	1.62919	+	2.34531i	0.0645004	+	0.0928515i
$639$	−2.59143	+	7.97559i	−0.102515	+	0.315510i
$640$	19.4848	+	16.1352i	0.770203	+	0.637798i
$641$	6.10344	+	18.7845i	0.241072	+	0.741942i	0.996258	+	0.0864316i	$0.0275464\pi$
$641$	6.10344	+	18.7845i	0.241072	+	0.741942i	−0.755186	+	0.655510i	$0.772454\pi$
$642$	8.58249	−	11.3014i	0.338724	−	0.446029i
$643$	21.0042			0.828324			0.414162	−	0.910203i	$-0.364075\pi$
$643$	21.0042			0.828324			0.414162	+	0.910203i	$0.364075\pi$
$644$	11.2114	−	30.1023i	0.441791	−	1.18620i
$645$	−26.3400	+	11.1094i	−1.03714	+	0.437434i
$646$	1.59110	+	0.554510i	0.0626012	+	0.0218169i
$647$	19.4638	−	26.7896i	0.765202	−	1.05321i	−0.231562	−	0.972820i	$-0.574384\pi$
$647$	19.4638	−	26.7896i	0.765202	−	1.05321i	0.996764	−	0.0803896i	$-0.0256164\pi$
$648$	−5.33517	−	8.42030i	−0.209585	−	0.330781i
$649$	−1.13326			−0.0444844
$650$	10.5739	+	10.7513i	0.414743	+	0.421701i
$651$			26.1240i			1.02388i
$652$	−7.05227	−	25.3054i	−0.276188	−	0.991035i
$653$	0.267998	+	0.194712i	0.0104876	+	0.00761966i	0.593017	−	0.805190i	$-0.297937\pi$
$653$	0.267998	+	0.194712i	0.0104876	+	0.00761966i	−0.582529	+	0.812810i	$0.697937\pi$
$654$	4.11989	−	11.8216i	0.161101	−	0.462260i
$655$	34.5790	−	2.94538i	1.35111	−	0.115085i
$656$	5.43085	+	23.2551i	0.212039	+	0.907960i
$657$			7.06276i			0.275545i
$658$	2.21500	−	2.91670i	0.0863497	−	0.113705i
$659$	−2.06861	+	0.672132i	−0.0805816	+	0.0261826i	−0.349030	−	0.937111i	$-0.613489\pi$
$659$	−2.06861	+	0.672132i	−0.0805816	+	0.0261826i	0.268449	+	0.963294i	$0.413489\pi$
$660$	−1.35469	+	0.0577505i	−0.0527313	+	0.00224794i
$661$	14.4168	+	4.68430i	0.560748	+	0.182198i	0.575658	−	0.817691i	$-0.304746\pi$
$661$	14.4168	+	4.68430i	0.560748	+	0.182198i	−0.0149097	+	0.999889i	$0.504746\pi$
$662$	−5.51899	+	3.83383i	−0.214501	+	0.149006i
$663$	−6.06144	+	1.96948i	−0.235407	+	0.0764883i
$664$	−8.32448	−	13.1382i	−0.323052	−	0.509862i
$665$	0.229827	+	2.69819i	0.00891230	+	0.104631i
$666$	−8.23835	−	11.8595i	−0.319230	−	0.459547i
$667$	−49.0130	+	35.6100i	−1.89779	+	1.37883i
$668$	−23.0946	−	34.7965i	−0.893557	−	1.34632i
$669$	17.9492	+	24.7049i	0.693955	+	0.955147i
$670$	−9.97683	+	0.637272i	−0.385439	+	0.0246200i
$671$	0.426145	+	0.309612i	0.0164511	+	0.0119525i
$672$	−12.7562	−	11.5135i	−0.492081	−	0.444144i
$673$	3.94041	+	1.28032i	0.151892	+	0.0493526i	0.383976	−	0.923343i	$-0.374555\pi$
$673$	3.94041	+	1.28032i	0.151892	+	0.0493526i	−0.232084	+	0.972696i	$0.574555\pi$
$674$	−12.0965	−	40.1005i	−0.465942	−	1.54462i
$675$	−27.6623	+	4.74688i	−1.06472	+	0.182707i
$676$	−14.0843	+	9.34781i	−0.541703	+	0.359531i
$677$	6.92852	−	21.3238i	0.266285	−	0.819540i	−0.725110	−	0.688633i	$-0.758211\pi$
$677$	6.92852	−	21.3238i	0.266285	−	0.819540i	0.991395	−	0.130907i	$-0.0417890\pi$
$678$	9.27595	−	26.6163i	0.356241	−	1.02219i
$679$	23.9128	+	17.3737i	0.917689	+	0.666740i
$680$	0.308637	+	14.4067i	0.0118357	+	0.552473i
$681$	4.75261	−	3.45297i	0.182120	−	0.132318i
$682$	−0.811904	−	2.69149i	−0.0310894	−	0.103063i
$683$	26.5359	−	19.2795i	1.01537	−	0.737709i	0.0500406	−	0.998747i	$-0.484065\pi$
$683$	26.5359	−	19.2795i	1.01537	−	0.737709i	0.965328	+	0.261038i	$0.0840649\pi$
$684$	0.831712	−	1.04832i	0.0318013	−	0.0400836i
$685$	−7.46745	+	32.0100i	−0.285317	+	1.22304i
$686$	−28.2801	−	0.599186i	−1.07974	−	0.0228770i
$687$	6.36672	−	2.06867i	0.242905	−	0.0789247i
$688$	38.8469	+	3.29969i	1.48103	+	0.125800i
$689$	2.86464	−	8.81645i	0.109134	−	0.335880i
$690$	−1.83372	−	28.7078i	−0.0698084	−	1.09289i
$691$	−35.7160	+	11.6048i	−1.35870	+	0.441468i	−0.895609	−	0.444843i	$-0.853259\pi$
$691$	−35.7160	+	11.6048i	−1.35870	+	0.441468i	−0.463090	+	0.886311i	$0.653259\pi$
$692$	−5.49945	+	14.7658i	−0.209058	+	0.561313i
$693$	−0.684949			−0.0260190
$694$	16.5021	−	21.7298i	0.626410	−	0.824853i
$695$	−9.98072	+	8.63600i	−0.378590	+	0.327582i
$696$	8.03715	+	31.3966i	0.304647	+	1.19009i
$697$	−7.99547	+	11.0048i	−0.302850	+	0.416837i
$698$	46.8312	+	0.992240i	1.77259	+	0.0375568i
$699$		−	4.58909i		−	0.173575i
$700$	−20.9359	+	9.90067i	−0.791303	+	0.374210i
$701$		−	23.3655i		−	0.882503i	−0.897383	−	0.441252i	$-0.854535\pi$
$701$		−	23.3655i		−	0.882503i	0.897383	−	0.441252i	$-0.145465\pi$
$702$	−0.358614	+	16.9257i	−0.0135350	+	0.638818i
$703$	−2.45284	+	3.37605i	−0.0925108	+	0.127330i
$704$	1.67207	+	0.789765i	0.0630185	+	0.0297654i
$705$	0.745120	−	3.19403i	0.0280628	−	0.120294i
$706$	14.9664	+	11.3658i	0.563267	+	0.427756i
$707$	26.8397			1.00941
$708$	−12.0527	−	4.48895i	−0.452967	−	0.168705i
$709$	−12.3034	+	3.99762i	−0.462064	+	0.150134i	−0.530793	−	0.847502i	$-0.678106\pi$
$709$	−12.3034	+	3.99762i	−0.462064	+	0.150134i	0.0687289	+	0.997635i	$0.478106\pi$
$710$	7.64811	+	19.2631i	0.287028	+	0.722929i
$711$	−4.97406	+	15.3086i	−0.186542	+	0.574116i
$712$	41.5942	+	16.5030i	1.55881	+	0.618476i
$713$	56.7231	−	18.4305i	2.12430	−	0.690226i
$714$	0.207337	−	9.78581i	0.00775941	−	0.366225i
$715$	0.943525	+	0.569876i	0.0352858	+	0.0213122i
$716$	19.9562	−	25.1537i	0.745800	−	0.940036i
$717$	21.5530	−	15.6592i	0.804912	−	0.584803i
$718$	−22.9312	+	6.91732i	−0.855785	+	0.258152i
$719$	−1.77973	+	1.29305i	−0.0663726	+	0.0482225i	−0.620477	−	0.784225i	$-0.713061\pi$
$719$	−1.77973	+	1.29305i	−0.0663726	+	0.0482225i	0.554104	+	0.832447i	$0.313061\pi$
$720$	10.8850	+	3.53393i	0.405661	+	0.131702i
$721$	−12.5632	−	9.12770i	−0.467878	−	0.339933i
$722$	25.0081	+	8.71550i	0.930707	+	0.324357i
$723$	−7.85116	+	24.1634i	−0.291988	+	0.898646i
$724$	18.9683	+	28.5793i	0.704950	+	1.06214i
$725$	43.2248	+	6.27718i	1.60533	+	0.233128i
$726$	19.4405	−	5.86433i	0.721504	−	0.217646i
$727$	4.25417	+	1.38226i	0.157778	+	0.0512653i	0.386841	−	0.922146i	$-0.373566\pi$
$727$	4.25417	+	1.38226i	0.157778	+	0.0512653i	−0.229063	+	0.973412i	$0.573566\pi$
$728$	3.46424	+	13.5328i	0.128393	+	0.501560i
$729$	−21.5182	−	15.6339i	−0.796969	−	0.579032i
$730$	11.1393	+	13.4389i	0.412285	+	0.497398i
$731$	13.0530	+	17.9660i	0.482784	+	0.664496i
$732$	3.30582	+	4.98085i	0.122186	+	0.184097i
$733$	10.5599	−	7.67219i	0.390037	−	0.283379i	−0.375433	−	0.926849i	$-0.622506\pi$
$733$	10.5599	−	7.67219i	0.390037	−	0.283379i	0.765471	+	0.643471i	$0.222506\pi$
$734$	10.1472	−	7.04885i	0.374539	−	0.260178i
$735$	−4.42295	+	1.86547i	−0.163143	+	0.0688090i
$736$	−15.9999	+	35.8204i	−0.589764	+	1.32036i
$737$	−0.694989	+	0.225815i	−0.0256002	+	0.00831802i
$738$	6.16337	+	8.87248i	0.226877	+	0.326600i
$739$	−29.8146	−	9.68735i	−1.09675	−	0.356355i	−0.295898	−	0.955220i	$-0.595619\pi$
$739$	−29.8146	−	9.68735i	−1.09675	−	0.356355i	−0.800850	+	0.598865i	$0.795619\pi$
$740$	−34.3806	−	9.57269i	−1.26386	−	0.351899i
$741$	1.39117	−	0.452018i	0.0511058	−	0.0166053i
$742$	11.3380	+	8.61028i	0.416230	+	0.316093i
$743$		−	28.1541i		−	1.03287i	−0.856325	−	0.516437i	$-0.827258\pi$
$743$		−	28.1541i		−	1.03287i	0.856325	−	0.516437i	$-0.172742\pi$
$744$	2.02633	−	31.8411i	0.0742890	−	1.16735i
$745$	17.4953	+	10.5669i	0.640978	+	0.387142i
$746$	1.33987	+	0.466953i	0.0490561	+	0.0170964i
$747$	−5.69226	−	4.13567i	−0.208269	−	0.151316i
$748$	0.282771	+	1.01465i	0.0103391	+	0.0370994i
$749$		−	17.7168i		−	0.647359i
$750$	−13.4988	+	15.7449i	−0.492908	+	0.574923i
$751$	−12.9756			−0.473487			−0.236743	−	0.971572i	$-0.576080\pi$
$751$	−12.9756			−0.473487			−0.236743	+	0.971572i	$0.576080\pi$
$752$	−2.92598	+	3.38320i	−0.106700	+	0.123373i
$753$	−3.52324	+	4.84932i	−0.128394	+	0.176719i
$754$	8.67038	−	24.8787i	0.315757	−	0.906028i
$755$	−9.93641	+	16.4514i	−0.361623	+	0.598727i
$756$	−24.3647	−	9.07449i	−0.886135	−	0.330036i
$757$	−16.0395			−0.582965			−0.291482	−	0.956576i	$-0.594149\pi$
$757$	−16.0395			−0.582965			−0.291482	+	0.956576i	$0.594149\pi$
$758$	40.6720	+	30.8872i	1.47728	+	1.12187i
$759$	−0.649771	−	1.99979i	−0.0235852	−	0.0725878i
$760$	−0.0708356	−	3.30651i	−0.00256948	−	0.119940i
$761$	3.49479	−	10.7559i	0.126686	−	0.389900i	−0.867518	−	0.497405i	$-0.834286\pi$
$761$	3.49479	−	10.7559i	0.126686	−	0.389900i	0.994205	+	0.107505i	$0.0342863\pi$
$762$	6.95228	−	4.82948i	0.251855	−	0.174954i
$763$	−4.82977	−	14.8645i	−0.174849	−	0.538131i
$764$	1.60470	+	5.75806i	0.0580558	+	0.208319i
$765$	2.53332	+	6.00639i	0.0915923	+	0.217161i
$766$	35.8703	−	24.9177i	1.29605	−	0.900313i
$767$	6.14557	+	8.45866i	0.221904	+	0.305424i
$768$	14.6548	+	15.0227i	0.528810	+	0.542084i
$769$	3.25219	−	2.36285i	0.117277	−	0.0852066i	−0.527601	−	0.849492i	$-0.676908\pi$
$769$	3.25219	−	2.36285i	0.117277	−	0.0852066i	0.644878	+	0.764286i	$0.276908\pi$
$770$	−1.30331	+	1.08030i	−0.0469681	+	0.0389312i
$771$	21.1549	−	29.1173i	0.761876	−	1.04863i
$772$	1.26517	−	29.8430i	0.0455343	−	1.07407i
$773$	0.759693	−	2.33810i	0.0273243	−	0.0840955i	−0.936464	−	0.350763i	$-0.885922\pi$
$773$	0.759693	−	2.33810i	0.0273243	−	0.0840955i	0.963789	+	0.266667i	$0.0859224\pi$
$774$	16.8852	−	5.09352i	0.606926	−	0.183083i
$775$	−38.5610	−	19.0269i	−1.38515	−	0.683467i
$776$	−27.7984	−	23.0307i	−0.997906	−	0.826752i
$777$	23.0548	+	7.49097i	0.827088	+	0.268737i
$778$	0.617835	−	1.77281i	0.0221505	−	0.0635582i
$779$	1.83505	−	2.52573i	0.0657475	−	0.0904937i
$780$	7.77742	+	9.79824i	0.278476	+	0.350833i
$781$	0.890481	+	1.22564i	0.0318639	+	0.0438569i
$782$	−21.3943	+	6.45369i	−0.765057	+	0.230784i
$783$	28.8227	+	39.6710i	1.03004	+	1.41773i
$784$	6.52309	+	0.554077i	0.232967	+	0.0197885i
$785$	−5.37175	+	8.89383i	−0.191726	+	0.317435i
$786$	28.7833	+	0.609848i	1.02667	+	0.0217526i
$787$	9.27720	+	28.5523i	0.330697	+	1.01778i	0.968803	+	0.247831i	$0.0797179\pi$
$787$	9.27720	+	28.5523i	0.330697	+	1.01778i	−0.638107	+	0.769948i	$0.720282\pi$
$788$	−43.1389	−	34.2253i	−1.53676	−	1.21922i
$789$	16.0606	+	5.21842i	0.571774	+	0.185781i
$790$	14.6800	+	36.9740i	0.522291	+	1.31548i
$791$	−10.8742	−	33.4675i	−0.386644	−	1.18997i
$792$	0.834847	+	0.0531287i	0.0296650	+	0.00188785i
$793$		−	4.85974i		−	0.172575i
$794$	−8.25267	+	10.8671i	−0.292876	+	0.385658i
$795$	12.4160	+	2.89647i	0.440351	+	0.102727i
$796$	22.7439	+	0.964210i	0.806138	+	0.0341755i
$797$	17.9888	+	13.0696i	0.637196	+	0.462950i	0.858886	−	0.512167i	$-0.171157\pi$
$797$	17.9888	+	13.0696i	0.637196	+	0.462950i	−0.221690	+	0.975117i	$0.571157\pi$
$798$	−0.0475863	+	2.24595i	−0.00168454	+	0.0795059i
$799$	−2.54783			−0.0901359
$800$	26.2856	−	10.4435i	0.929337	−	0.369233i
$801$	20.2432			0.715257
$802$	−0.352706	+	16.6469i	−0.0124545	+	0.587821i
$803$	1.03224	+	0.749967i	0.0364270	+	0.0264658i
$804$	−8.28595	−	0.351276i	−0.292223	−	0.0123885i
$805$	−23.4994	−	27.1585i	−0.828243	−	0.957210i
$806$	−15.6864	+	20.6558i	−0.552531	+	0.727569i
$807$			2.00232i			0.0704852i
$808$	−32.7135	−	2.08185i	−1.15086	−	0.0732392i
$809$	−10.2871	−	31.6605i	−0.361676	−	1.11313i	−0.952036	−	0.305985i	$-0.901014\pi$
$809$	−10.2871	−	31.6605i	−0.361676	−	1.11313i	0.590360	−	0.807140i	$-0.298986\pi$
$810$	−11.1221	+	0.710429i	−0.390792	+	0.0249619i
$811$	−41.7447	−	13.5637i	−1.46585	−	0.476285i	−0.536002	−	0.844217i	$-0.680066\pi$
$811$	−41.7447	−	13.5637i	−1.46585	−	0.476285i	−0.929853	+	0.367932i	$0.880066\pi$
$812$	31.6974	+	25.1479i	1.11236	+	0.882519i
$813$	−9.92157	−	30.5355i	−0.347965	−	1.07093i
$814$	−2.60810	−	0.0552592i	−0.0914138	−	0.00193684i
$815$	−28.6024	−	6.67252i	−1.00190	−	0.233728i
$816$	−1.01176	+	11.9113i	−0.0354187	+	0.416980i
$817$	−2.99582	−	4.12339i	−0.104810	−	0.144259i
$818$	0.199192	−	0.0600873i	0.00696458	−	0.00210090i
$819$	3.71442	+	5.11245i	0.129792	+	0.178644i
$820$	25.7212	+	7.16163i	0.898223	+	0.250095i
$821$	17.1793	−	23.6453i	0.599561	−	0.825225i	−0.396107	−	0.918205i	$-0.629639\pi$
$821$	17.1793	−	23.6453i	0.599561	−	0.825225i	0.995668	+	0.0929790i	$0.0296390\pi$
$822$	−8.97361	+	25.7488i	−0.312991	+	0.898092i
$823$	−12.8489	−	4.17485i	−0.447883	−	0.145526i	0.0763866	−	0.997078i	$-0.475662\pi$
$823$	−12.8489	−	4.17485i	−0.447883	−	0.145526i	−0.524270	+	0.851552i	$0.675662\pi$
$824$	14.6046	+	12.0997i	0.508776	+	0.421514i
$825$	−0.670799	+	1.35948i	−0.0233542	+	0.0473310i
$826$	−15.3729	+	4.63733i	−0.534893	+	0.161353i
$827$	8.92624	−	27.4721i	0.310396	−	0.955300i	−0.667213	−	0.744867i	$-0.732513\pi$
$827$	8.92624	−	27.4721i	0.310396	−	0.955300i	0.977608	−	0.210433i	$-0.0674872\pi$
$828$	−0.751709	+	17.7314i	−0.0261237	+	0.616210i
$829$	21.9589	−	30.2238i	0.762663	−	1.04972i	−0.234325	−	0.972158i	$-0.575288\pi$
$829$	21.9589	−	30.2238i	0.762663	−	1.04972i	0.996988	−	0.0775572i	$-0.0247120\pi$
$830$	−17.3539	+	1.10849i	−0.602363	+	0.0384761i
$831$	−29.0732	+	21.1229i	−1.00854	+	0.732745i
$832$	−3.17269	−	16.7632i	−0.109993	−	0.581158i
$833$	2.19184	+	3.01681i	0.0759427	+	0.104526i
$834$	−8.99224	+	6.24657i	−0.311376	+	0.216301i
$835$	−46.5241	+	3.96283i	−1.61003	+	0.137139i
$836$	−0.0648990	−	0.232874i	−0.00224458	−	0.00805413i
$837$	−14.9176	−	45.9115i	−0.515627	−	1.58694i
$838$	39.6055	−	27.5124i	1.36815	−	0.950400i
$839$	2.47513	−	7.61767i	0.0854510	−	0.262991i	−0.899197	−	0.437545i	$-0.855848\pi$
$839$	2.47513	−	7.61767i	0.0854510	−	0.262991i	0.984648	+	0.174553i	$0.0558482\pi$
$840$	−18.1404	+	6.32684i	−0.625903	+	0.218297i
$841$	−14.6201	−	44.9960i	−0.504141	−	1.55159i
$842$	−6.57653	−	4.99435i	−0.226642	−	0.172117i
$843$	−38.1169			−1.31282
$844$	−29.7071	−	11.0643i	−1.02256	−	0.380847i
$845$	1.60400	+	18.8312i	0.0551793	+	0.647811i
$846$	−0.665910	+	1.91075i	−0.0228944	+	0.0656930i
$847$	14.9010	−	20.5094i	0.512004	−	0.704713i
$848$	−13.1514	−	11.3741i	−0.451620	−	0.390587i
$849$	−13.0057			−0.446354
$850$	14.2936	+	7.43336i	0.490267	+	0.254962i
$851$		−	55.3440i		−	1.89717i
$852$	4.61574	+	16.5625i	0.158132	+	0.567420i
$853$	13.5745	+	9.86242i	0.464780	+	0.337683i	0.795404	−	0.606080i	$-0.207259\pi$
$853$	13.5745	+	9.86242i	0.464780	+	0.337683i	−0.330623	+	0.943763i	$0.607259\pi$
$854$	7.04770	+	2.45617i	0.241167	+	0.0840483i
$855$	−0.581425	−	1.37853i	−0.0198843	−	0.0471448i
$856$	−1.37422	+	21.5941i	−0.0469700	+	0.738071i
$857$			12.0516i			0.411675i	0.978586	+	0.205837i	$0.0659918\pi$
$857$			12.0516i			0.411675i	−0.978586	+	0.205837i	$0.934008\pi$
$858$	0.728226	+	0.553029i	0.0248612	+	0.0188801i
$859$	53.1530	−	17.2704i	1.81356	−	0.589260i	0.813587	−	0.581443i	$-0.197512\pi$
$859$	53.1530	−	17.2704i	1.81356	−	0.589260i	0.999969	−	0.00781665i	$-0.00248814\pi$
$860$	24.0955	−	36.3231i	0.821651	−	1.23861i
$861$	−17.2481	−	5.60423i	−0.587812	−	0.190992i
$862$	−3.30060	−	4.75137i	−0.112419	−	0.161832i
$863$	−27.1681	+	8.82744i	−0.924812	+	0.300490i	−0.732439	−	0.680832i	$-0.761618\pi$
$863$	−27.1681	+	8.82744i	−0.924812	+	0.300490i	−0.192373	+	0.981322i	$0.561618\pi$
$864$	28.9929	+	12.9503i	0.986360	+	0.440577i
$865$	11.5270	+	13.3218i	0.391929	+	0.452956i
$866$	−5.52695	+	3.83936i	−0.187813	+	0.130467i
$867$	12.5310	−	9.10434i	0.425577	−	0.309200i
$868$	−22.0273	−	33.1884i	−0.747656	−	1.12649i
$869$	1.70921	+	2.35253i	0.0579811	+	0.0798041i
$870$	35.1046	+	8.97754i	1.19016	+	0.304367i
$871$	5.45435	+	3.96281i	0.184813	+	0.134275i
$872$	4.73377	+	18.4922i	0.160306	+	0.626224i
$873$	−15.5312	−	5.04641i	−0.525653	−	0.170795i
$874$	4.91022	−	1.48120i	0.166091	−	0.0501022i
$875$	−1.53298	+	25.8470i	−0.0518243	+	0.873789i
$876$	8.00761	+	12.0650i	0.270552	+	0.407639i
$877$	1.52668	−	4.69863i	0.0515522	−	0.158661i	−0.921966	−	0.387271i	$-0.873418\pi$
$877$	1.52668	−	4.69863i	0.0515522	−	0.158661i	0.973518	+	0.228609i	$0.0734178\pi$
$878$	2.34056	+	0.815701i	0.0789902	+	0.0275286i
$879$	−6.60284	−	4.79725i	−0.222708	−	0.161807i
$880$	1.67233	−	1.21562i	0.0563743	−	0.0409786i
$881$	−0.550583	+	0.400022i	−0.0185496	+	0.0134771i	−0.597021	−	0.802225i	$-0.703649\pi$
$881$	−0.550583	+	0.400022i	−0.0185496	+	0.0134771i	0.578472	+	0.815702i	$0.303649\pi$
$882$	2.83533	−	0.855292i	0.0954704	−	0.0287992i
$883$	−1.43973	+	1.04603i	−0.0484509	+	0.0352017i	−0.611747	−	0.791053i	$-0.709533\pi$
$883$	−1.43973	+	1.04603i	−0.0484509	+	0.0352017i	0.563296	+	0.826255i	$0.309533\pi$
$884$	6.03993	−	7.61297i	0.203145	−	0.256052i
$885$	−10.8740	+	9.40893i	−0.365526	+	0.316278i
$886$	0.102899	−	4.85657i	0.00345695	−	0.163159i
$887$	42.8681	−	13.9287i	1.43937	−	0.467680i	0.517669	−	0.855581i	$-0.326800\pi$
$887$	42.8681	−	13.9287i	1.43937	−	0.467680i	0.921701	+	0.387901i	$0.126800\pi$
$888$	−27.5193	−	10.9186i	−0.923486	−	0.366405i
$889$	3.26583	−	10.0512i	0.109532	−	0.337106i
$890$	38.5185	−	31.9274i	1.29114	−	1.07021i
$891$	−0.774771	+	0.251738i	−0.0259558	+	0.00843355i
$892$	−43.6338	−	16.2511i	−1.46097	−	0.544128i
$893$	0.584756			0.0195681
$894$	13.5031	+	10.2545i	0.451612	+	0.342963i
$895$	−13.9508	−	33.0768i	−0.466324	−	1.10563i
$896$	25.9138	+	3.87119i	0.865718	+	0.129327i
$897$	−11.4028	+	15.6946i	−0.380728	+	0.524027i
$898$	−0.166033	+	7.83632i	−0.00554058	+	0.261501i
$899$			75.1261i			2.50560i
$900$	9.31048	−	8.77671i	0.310349	−	0.292557i
$901$		−	9.90409i		−	0.329953i
$902$	1.95120	+	0.0413412i	0.0649679	+	0.00137651i
$903$	−17.4028	+	23.9530i	−0.579130	+	0.797104i
$904$	10.6581	+	41.6352i	0.354483	+	1.38477i
$905$	38.2116	−	3.25479i	1.27020	−	0.108193i
$906$	−9.64267	+	12.6974i	−0.320356	+	0.421843i
$907$	22.9525			0.762127			0.381063	−	0.924549i	$-0.375558\pi$
$907$	22.9525			0.762127			0.381063	+	0.924549i	$0.375558\pi$
$908$	−3.12631	+	8.39405i	−0.103750	+	0.278566i
$909$	−14.1030	+	4.58234i	−0.467766	+	0.151987i
$910$	15.1311	+	3.86957i	0.501590	+	0.128275i
$911$	1.55833	−	4.79606i	0.0516299	−	0.158900i	−0.921917	−	0.387387i	$-0.873378\pi$
$911$	1.55833	−	4.79606i	0.0516299	−	0.158900i	0.973547	+	0.228487i	$0.0733777\pi$
$912$	0.232210	−	2.73378i	0.00768924	−	0.0905246i
$913$	−1.20888	+	0.392788i	−0.0400080	+	0.0129994i
$914$	4.28146	+	0.0907138i	0.141618	+	0.00300054i
$915$	6.65957	−	0.567249i	0.220158	−	0.0187527i
$916$	−6.34413	+	7.99640i	−0.209616	+	0.264208i
$917$	29.0786	−	21.1268i	0.960260	−	0.697670i
$918$	5.22360	+	17.3165i	0.172405	+	0.571528i
$919$	−0.772993	+	0.561613i	−0.0254987	+	0.0185259i	−0.600462	−	0.799654i	$-0.705016\pi$
$919$	−0.772993	+	0.561613i	−0.0254987	+	0.0185259i	0.574963	+	0.818179i	$0.305016\pi$
$920$	26.5355	+	34.9248i	0.874851	+	1.15144i
$921$	31.4250	+	22.8316i	1.03549	+	0.752326i
$922$	−5.86188	+	16.8200i	−0.193051	+	0.553937i
$923$	4.31919	−	13.2931i	0.142168	−	0.437547i
$924$	−1.17007	+	0.776580i	−0.0384924	+	0.0255476i
$925$	−27.8488	+	28.5748i	−0.915663	+	0.939534i
$926$	−1.78925	−	5.93142i	−0.0587983	−	0.194919i
$927$	8.15973	+	2.65126i	0.268001	+	0.0870787i
$928$	−36.6837	−	33.1101i	−1.20420	−	1.08689i
$929$	−46.5656	−	33.8319i	−1.52777	−	1.10999i	−0.957463	−	0.288555i	$-0.906825\pi$
$929$	−46.5656	−	33.8319i	−1.52777	−	1.10999i	−0.570304	−	0.821433i	$-0.693175\pi$
$930$	−30.1367	−	19.0849i	−0.988221	−	0.625819i
$931$	−0.503052	−	0.692391i	−0.0164868	−	0.0226922i
$932$	3.86945	+	5.83007i	0.126748	+	0.190970i
$933$	−4.55588	+	3.31004i	−0.149153	+	0.108366i
$934$	−18.3165	−	26.3675i	−0.599335	−	0.862772i
$935$	1.14685	+	0.267544i	0.0375061	+	0.00874962i
$936$	−4.13075	−	6.51941i	−0.135018	−	0.213094i
$937$	−33.6886	+	10.9461i	−1.10056	+	0.357593i	−0.802317	−	0.596898i	$-0.796400\pi$
$937$	−33.6886	+	10.9461i	−1.10056	+	0.357593i	−0.298240	+	0.954491i	$0.596400\pi$
$938$	−8.50364	+	5.90715i	−0.277654	+	0.192875i
$939$	−17.1327	−	5.56674i	−0.559103	−	0.181664i
$940$	1.74654	+	4.68603i	0.0569659	+	0.152841i
$941$	−0.202380	+	0.0657573i	−0.00659741	+	0.00214363i	−0.312314	−	0.949979i	$-0.601104\pi$
$941$	−0.202380	+	0.0657573i	−0.00659741	+	0.00214363i	0.305716	+	0.952123i	$0.401104\pi$
$942$	−5.21295	+	6.86439i	−0.169847	+	0.223654i
$943$			41.4046i			1.34832i
$944$	19.0970	−	4.45978i	0.621553	−	0.145153i
$945$	−21.9820	+	19.0203i	−0.715074	+	0.618731i
$946$	1.04854	−	3.00868i	0.0340911	−	0.0978206i
$947$	4.78799	+	3.47868i	0.155589	+	0.113042i	0.662856	−	0.748747i	$-0.269344\pi$
$947$	4.78799	+	3.47868i	0.155589	+	0.113042i	−0.507267	+	0.861789i	$0.669344\pi$
$948$	8.85957	+	31.7904i	0.287745	+	1.03251i
$949$		−	11.7717i		−	0.382124i
$950$	−3.28054	−	1.70604i	−0.106435	−	0.0553512i
$951$	−16.7538			−0.543279
$952$	7.98784	+	12.6069i	0.258887	+	0.408592i
$953$	−30.3932	+	41.8326i	−0.984531	+	1.35509i	−0.0501787	+	0.998740i	$0.515979\pi$
$953$	−30.3932	+	41.8326i	−0.984531	+	1.35509i	−0.934352	+	0.356351i	$0.884021\pi$
$954$	−7.42759	−	2.58856i	−0.240477	−	0.0838079i
$955$	6.50828	+	1.51829i	0.210603	+	0.0491306i
$956$	−14.1778	+	38.0669i	−0.458543	+	1.23117i
$957$	2.64859			0.0856169
$958$	−5.90353	+	7.77373i	−0.190734	+	0.251158i
$959$	10.5198	+	32.3766i	0.339702	+	1.04550i
$960$	22.6011	−	6.30436i	0.729448	−	0.203472i
$961$	13.2751	−	40.8565i	0.428228	−	1.31795i
$962$	13.7310	+	19.7665i	0.442706	+	0.637298i
$963$	3.02479	+	9.30935i	0.0974725	+	0.299989i
$964$	−10.3999	−	37.3176i	−0.334959	−	1.20192i
$965$	−28.5859	−	17.2655i	−0.920214	−	0.555797i
$966$	−16.9975	−	24.4687i	−0.546885	−	0.787269i
$967$	−11.6201	−	15.9937i	−0.373677	−	0.514323i	0.580218	−	0.814461i	$-0.302967\pi$
$967$	−11.6201	−	15.9937i	−0.373677	−	0.514323i	−0.953896	+	0.300138i	$0.902967\pi$
$968$	−19.7529	+	23.8421i	−0.634881	+	0.766313i
$969$	1.26432	−	0.918585i	0.0406159	−	0.0295092i
$970$	−37.5118	+	14.8935i	−1.20443	+	0.478202i
$971$	−11.7741	+	16.2057i	−0.377850	+	0.520065i	−0.955013	−	0.296563i	$-0.904159\pi$
$971$	−11.7741	+	16.2057i	−0.377850	+	0.520065i	0.577164	+	0.816628i	$0.304159\pi$
$972$	24.4126	+	1.03495i	0.783033	+	0.0331960i
$973$	−4.22409	+	13.0004i	−0.135418	+	0.416775i
$974$	−14.6459	−	48.5516i	−0.469283	−	1.55569i
$975$	13.7848	−	2.36549i	0.441468	−	0.0757564i
$976$	−8.39955	−	3.54035i	−0.268863	−	0.113324i
$977$	−44.2455	−	14.3762i	−1.41554	−	0.459937i	−0.501357	−	0.865240i	$-0.667166\pi$
$977$	−44.2455	−	14.3762i	−1.41554	−	0.459937i	−0.914182	+	0.405304i	$0.867166\pi$
$978$	−23.0078	−	8.01835i	−0.735707	−	0.256399i
$979$	2.14954	−	2.95859i	0.0686997	−	0.0945570i
$980$	4.04607	−	6.09930i	0.129247	−	0.194835i
$981$	5.07563	+	6.98600i	0.162052	+	0.223046i
$982$	−3.16393	−	10.4886i	−0.100965	−	0.334704i
$983$	−18.2599	−	25.1326i	−0.582401	−	0.801606i	0.411555	−	0.911385i	$-0.364986\pi$
$983$	−18.2599	−	25.1326i	−0.582401	−	0.801606i	−0.993956	+	0.109779i	$0.964986\pi$
$984$	20.5880	+	8.16856i	0.656322	+	0.260404i
$985$	−56.7272	+	23.9259i	−1.80748	+	0.762341i
$986$	0.596251	−	28.1416i	0.0189885	−	0.896210i
$987$	−1.04969	−	3.23062i	−0.0334120	−	0.102832i
$988$	−1.38623	+	1.74726i	−0.0441019	+	0.0555878i
$989$	64.2869	+	20.8881i	2.04420	+	0.664202i
$990$	0.500390	−	0.790159i	0.0159034	−	0.0251129i
$991$	4.56887	+	14.0615i	0.145135	+	0.446679i	0.997028	−	0.0770360i	$-0.0245457\pi$
$991$	4.56887	+	14.0615i	0.145135	+	0.446679i	−0.851893	+	0.523715i	$0.824546\pi$
$992$	24.2736	+	42.1602i	0.770689	+	1.33859i
$993$			6.23268i			0.197788i
$994$	17.0949	+	12.9822i	0.542218	+	0.411772i
$995$	13.1584	−	21.7859i	0.417150	−	0.690661i
$996$	−14.4128	−	0.611017i	−0.456686	−	0.0193608i
$997$	21.0204	+	15.2722i	0.665723	+	0.483676i	0.868591	−	0.495530i	$-0.165026\pi$
$997$	21.0204	+	15.2722i	0.665723	+	0.483676i	−0.202868	+	0.979206i	$0.565026\pi$
$998$	−51.5298	−	1.09179i	−1.63115	−	0.0345600i
$999$	−44.7952			−1.41726

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	200.2.o.a.29.15	✓	112
4.3	odd	2		800.2.be.a.529.10		112
5.2	odd	4		1000.2.t.b.101.1		224
5.3	odd	4		1000.2.t.b.101.56		224
5.4	even	2		1000.2.o.a.149.14		112
8.3	odd	2		800.2.be.a.529.19		112
8.5	even	2	inner	200.2.o.a.29.20	yes	112
25.6	even	5		1000.2.o.a.349.9		112
25.8	odd	20		1000.2.t.b.901.11		224
25.17	odd	20		1000.2.t.b.901.46		224
25.19	even	10	inner	200.2.o.a.69.20	yes	112
40.13	odd	4		1000.2.t.b.101.11		224
40.29	even	2		1000.2.o.a.149.9		112
40.37	odd	4		1000.2.t.b.101.46		224
100.19	odd	10		800.2.be.a.369.19		112
200.19	odd	10		800.2.be.a.369.10		112
200.69	even	10	inner	200.2.o.a.69.15	yes	112
200.117	odd	20		1000.2.t.b.901.1		224
200.133	odd	20		1000.2.t.b.901.56		224
200.181	even	10		1000.2.o.a.349.14		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.29.15	✓	112	1.1	even	1	trivial
200.2.o.a.29.20	yes	112	8.5	even	2	inner
200.2.o.a.69.15	yes	112	200.69	even	10	inner
200.2.o.a.69.20	yes	112	25.19	even	10	inner
800.2.be.a.369.10		112	200.19	odd	10
800.2.be.a.369.19		112	100.19	odd	10
800.2.be.a.529.10		112	4.3	odd	2
800.2.be.a.529.19		112	8.3	odd	2
1000.2.o.a.149.9		112	40.29	even	2
1000.2.o.a.149.14		112	5.4	even	2
1000.2.o.a.349.9		112	25.6	even	5
1000.2.o.a.349.14		112	200.181	even	10
1000.2.t.b.101.1		224	5.2	odd	4
1000.2.t.b.101.11		224	40.13	odd	4
1000.2.t.b.101.46		224	40.37	odd	4
1000.2.t.b.101.56		224	5.3	odd	4
1000.2.t.b.901.1		224	200.117	odd	20
1000.2.t.b.901.11		224	25.8	odd	20
1000.2.t.b.901.46		224	25.17	odd	20
1000.2.t.b.901.56		224	200.133	odd	20

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:	\( N \)	\(=\)	\( 200 = 2^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	200.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0299570 + 1.41390i) q^{2} +(1.06117 + 0.770982i) q^{3} +(-1.99821 - 0.0847122i) q^{4} +(-1.15605 + 1.91404i) q^{5} +(-1.12188 + 1.47728i) q^{6} +2.31589i q^{7} +(0.179635 - 2.82272i) q^{8} +(-0.395392 - 1.21689i) q^{9} +O(q^{10})\)	\(q+(-0.0299570 + 1.41390i) q^{2} +(1.06117 + 0.770982i) q^{3} +(-1.99821 - 0.0847122i) q^{4} +(-1.15605 + 1.91404i) q^{5} +(-1.12188 + 1.47728i) q^{6} +2.31589i q^{7} +(0.179635 - 2.82272i) q^{8} +(-0.395392 - 1.21689i) q^{9} +(-2.67162 - 1.69188i) q^{10} +(-0.219837 - 0.0714294i) q^{11} +(-2.05511 - 1.63047i) q^{12} +(0.659008 + 2.02822i) q^{13} +(-3.27443 - 0.0693772i) q^{14} +(-2.70245 + 1.13982i) q^{15} +(3.98565 + 0.338545i) q^{16} +(1.33923 + 1.84329i) q^{17} +(1.73240 - 0.522589i) q^{18} +(-0.307368 - 0.423055i) q^{19} +(2.47217 - 3.72671i) q^{20} +(-1.78551 + 2.45754i) q^{21} +(0.107579 - 0.308687i) q^{22} +(6.59576 + 2.14309i) q^{23} +(2.36689 - 2.85688i) q^{24} +(-2.32708 - 4.42546i) q^{25} +(-2.88743 + 0.871009i) q^{26} +(1.73461 - 5.33859i) q^{27} +(0.196184 - 4.62763i) q^{28} +(-5.13469 + 7.06729i) q^{29} +(-1.53062 - 3.85513i) q^{30} +(6.95750 - 5.05492i) q^{31} +(-0.598065 + 5.62515i) q^{32} +(-0.178213 - 0.245289i) q^{33} +(-2.64634 + 1.83831i) q^{34} +(-4.43271 - 2.67729i) q^{35} +(0.686988 + 2.46509i) q^{36} +(-2.46601 - 7.58959i) q^{37} +(0.607364 - 0.421912i) q^{38} +(-0.864403 + 2.66036i) q^{39} +(5.19512 + 3.60704i) q^{40} +(1.84490 + 5.67801i) q^{41} +(-3.42122 - 2.59815i) q^{42} +9.74670 q^{43} +(0.433228 + 0.161353i) q^{44} +(2.78627 + 0.649995i) q^{45} +(-3.22770 + 9.26151i) q^{46} +(-0.657286 + 0.904676i) q^{47} +(3.96842 + 3.43211i) q^{48} +1.63664 q^{49} +(6.32685 - 3.15768i) q^{50} +2.98855i q^{51} +(-1.14502 - 4.10862i) q^{52} +(-3.51671 - 2.55504i) q^{53} +(7.49624 + 2.61249i) q^{54} +(0.390862 - 0.338200i) q^{55} +(6.53711 + 0.416014i) q^{56} -0.685906i q^{57} +(-9.83860 - 7.47163i) q^{58} +(4.66275 - 1.51502i) q^{59} +(5.49661 - 2.04865i) q^{60} +(-2.16726 - 0.704186i) q^{61} +(6.93871 + 9.98861i) q^{62} +(2.81819 - 0.915685i) q^{63} +(-7.93546 - 1.01411i) q^{64} +(-4.64393 - 1.08336i) q^{65} +(0.352152 - 0.244626i) q^{66} +(2.55761 - 1.85821i) q^{67} +(-2.51990 - 3.79672i) q^{68} +(5.34690 + 7.35938i) q^{69} +(3.91821 - 6.18718i) q^{70} +(-5.30236 - 3.85239i) q^{71} +(-3.50596 + 0.897484i) q^{72} +(-5.24971 - 1.70573i) q^{73} +(10.8048 - 3.25932i) q^{74} +(0.942529 - 6.49028i) q^{75} +(0.578346 + 0.871389i) q^{76} +(0.165423 - 0.509119i) q^{77} +(-3.73557 - 1.30187i) q^{78} +(-10.1775 - 7.39438i) q^{79} +(-5.25561 + 7.23731i) q^{80} +(2.85122 - 2.07153i) q^{81} +(-8.08339 + 2.43840i) q^{82} +(4.44876 - 3.23222i) q^{83} +(3.77600 - 4.75942i) q^{84} +(-5.07634 + 0.432393i) q^{85} +(-0.291982 + 13.7808i) q^{86} +(-10.8975 + 3.54081i) q^{87} +(-0.241115 + 0.607706i) q^{88} +(-4.88895 + 15.0466i) q^{89} +(-1.00249 + 3.92002i) q^{90} +(-4.69713 + 1.52619i) q^{91} +(-12.9981 - 4.84108i) q^{92} +11.2803 q^{93} +(-1.25943 - 0.956435i) q^{94} +(1.16508 - 0.0992390i) q^{95} +(-4.97154 + 5.50812i) q^{96} +(7.50193 - 10.3255i) q^{97} +(-0.0490290 + 2.31405i) q^{98} +0.295760i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9}+O(q^{10}) \) 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9	\( 112 q - 5 q^{2} - 3 q^{4} + q^{6} + 10 q^{8} - 30 q^{9} - 9 q^{10} - 5 q^{12} - 3 q^{14} - 2 q^{15} - 15 q^{16} - 10 q^{17} - 17 q^{20} - 30 q^{22} - 10 q^{23} - 16 q^{24} - 6 q^{25} - 14 q^{26} + 15 q^{28} - 33 q^{30} - 18 q^{31} - 10 q^{33} + 9 q^{34} + 41 q^{36} + 45 q^{38} - 10 q^{39} - 14 q^{40} - 10 q^{41} + 75 q^{42} - 32 q^{44} + 13 q^{46} - 10 q^{47} - 70 q^{48} - 80 q^{49} - 19 q^{50} - 100 q^{52} + 43 q^{54} - 34 q^{55} + 36 q^{56} - 30 q^{58} - 28 q^{60} + 20 q^{62} + 60 q^{63} - 36 q^{64} + 40 q^{65} + 40 q^{66} + 42 q^{70} + 22 q^{71} - 65 q^{72} - 10 q^{73} + 4 q^{74} - 36 q^{76} - 55 q^{78} + 14 q^{79} - 76 q^{80} - 6 q^{81} + 78 q^{84} - 59 q^{86} - 10 q^{87} + 110 q^{88} + 24 q^{89} + 49 q^{90} + 90 q^{92} + 45 q^{94} - 86 q^{95} + 46 q^{96} - 50 q^{97} + 90 q^{98}+O(q^{100}) \) 112 * q - 5 * q^2 - 3 * q^4 + q^6 + 10 * q^8 - 30 * q^9 - 9 * q^10 - 5 * q^12 - 3 * q^14 - 2 * q^15 - 15 * q^16 - 10 * q^17 - 17 * q^20 - 30 * q^22 - 10 * q^23 - 16 * q^24 - 6 * q^25 - 14 * q^26 + 15 * q^28 - 33 * q^30 - 18 * q^31 - 10 * q^33 + 9 * q^34 + 41 * q^36 + 45 * q^38 - 10 * q^39 - 14 * q^40 - 10 * q^41 + 75 * q^42 - 32 * q^44 + 13 * q^46 - 10 * q^47 - 70 * q^48 - 80 * q^49 - 19 * q^50 - 100 * q^52 + 43 * q^54 - 34 * q^55 + 36 * q^56 - 30 * q^58 - 28 * q^60 + 20 * q^62 + 60 * q^63 - 36 * q^64 + 40 * q^65 + 40 * q^66 + 42 * q^70 + 22 * q^71 - 65 * q^72 - 10 * q^73 + 4 * q^74 - 36 * q^76 - 55 * q^78 + 14 * q^79 - 76 * q^80 - 6 * q^81 + 78 * q^84 - 59 * q^86 - 10 * q^87 + 110 * q^88 + 24 * q^89 + 49 * q^90 + 90 * q^92 + 45 * q^94 - 86 * q^95 + 46 * q^96 - 50 * q^97 + 90 * q^98

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