LMFDB - Embedded newform 572.2.bs.a.15.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(15,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 12, 5]))

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

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

chi := DirichletCharacter("572.15");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bs (of order $60$, degree $16$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$1280$
Relative dimension:	$80$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			15.18
Character	$\chi$	$=$	572.15
Dual form			572.2.bs.a.267.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12541 - 0.856423i) q^{2} +(-0.683893 - 3.21746i) q^{3} +(0.533078 + 1.92765i) q^{4} +(-0.317452 + 2.00431i) q^{5} +(-1.98585 + 4.20665i) q^{6} +(-0.619612 + 0.402380i) q^{7} +(1.05095 - 2.62593i) q^{8} +(-7.14372 + 3.18059i) q^{9} +O(q^{10})$	\(q+(-1.12541 - 0.856423i) q^{2} +(-0.683893 - 3.21746i) q^{3} +(0.533078 + 1.92765i) q^{4} +(-0.317452 + 2.00431i) q^{5} +(-1.98585 + 4.20665i) q^{6} +(-0.619612 + 0.402380i) q^{7} +(1.05095 - 2.62593i) q^{8} +(-7.14372 + 3.18059i) q^{9} +(2.07380 - 1.98379i) q^{10} +(-1.86459 - 2.74287i) q^{11} +(5.83757 - 3.03346i) q^{12} +(0.285400 + 3.59424i) q^{13} +(1.04192 + 0.0778085i) q^{14} +(6.66590 - 0.349345i) q^{15} +(-3.43166 + 2.05517i) q^{16} +(1.27303 - 0.133801i) q^{17} +(10.7635 + 2.53859i) q^{18} +(-0.266740 + 5.08970i) q^{19} +(-4.03284 + 0.456519i) q^{20} +(1.71839 + 1.71839i) q^{21} +(-0.250636 + 4.68371i) q^{22} +(3.13416 + 5.42853i) q^{23} +(-9.16756 - 1.58555i) q^{24} +(0.838792 + 0.272540i) q^{25} +(2.75700 - 4.28940i) q^{26} +(9.31868 + 12.8261i) q^{27} +(-1.10595 - 0.979893i) q^{28} +(1.57608 - 1.75042i) q^{29} +(-7.80103 - 5.31568i) q^{30} +(-0.286767 - 1.81057i) q^{31} +(5.62211 + 0.626047i) q^{32} +(-7.54989 + 7.87507i) q^{33} +(-1.54727 - 0.939675i) q^{34} +(-0.609799 - 1.36963i) q^{35} +(-9.93921 - 12.0751i) q^{36} +(-3.21450 + 0.168465i) q^{37} +(4.65913 - 5.49954i) q^{38} +(11.3691 - 3.37634i) q^{39} +(4.92955 + 2.94005i) q^{40} +(-1.77639 + 2.73540i) q^{41} +(-0.462218 - 3.40556i) q^{42} +(0.568949 - 0.985448i) q^{43} +(4.29331 - 5.05643i) q^{44} +(-4.10710 - 15.3279i) q^{45} +(1.12191 - 8.79347i) q^{46} +(-3.08581 - 6.05624i) q^{47} +(8.95933 + 9.63571i) q^{48} +(-2.62515 + 5.89618i) q^{49} +(-0.710572 - 1.02508i) q^{50} +(-1.30112 - 4.00443i) q^{51} +(-6.77629 + 2.46616i) q^{52} +(6.81671 + 4.95263i) q^{53} +(0.497241 - 22.4153i) q^{54} +(6.08947 - 2.86649i) q^{55} +(0.405438 + 2.04994i) q^{56} +(16.5583 - 2.62258i) q^{57} +(-3.27283 + 0.620136i) q^{58} +(4.27505 - 2.77625i) q^{59} +(4.22686 + 12.6633i) q^{60} +(-1.43435 - 13.6469i) q^{61} +(-1.22789 + 2.28323i) q^{62} +(3.14652 - 4.84522i) q^{63} +(-5.79099 - 5.51946i) q^{64} +(-7.29457 - 0.568966i) q^{65} +(15.2411 - 2.39675i) q^{66} +(-2.62361 + 9.79143i) q^{67} +(0.936547 + 2.38263i) q^{68} +(15.3227 - 13.7966i) q^{69} +(-0.486713 + 2.06364i) q^{70} +(-3.27413 + 4.04321i) q^{71} +(0.844273 + 22.1015i) q^{72} +(-5.66560 + 11.1194i) q^{73} +(3.76190 + 2.56339i) q^{74} +(0.303244 - 2.88517i) q^{75} +(-9.95335 + 2.19903i) q^{76} +(2.25900 + 0.949237i) q^{77} +(-15.6865 - 5.93705i) q^{78} +(-5.55811 + 7.65009i) q^{79} +(-3.02982 - 7.53053i) q^{80} +(19.1970 - 21.3205i) q^{81} +(4.34182 - 1.55709i) q^{82} +(-7.70085 - 1.21970i) q^{83} +(-2.39642 + 4.22849i) q^{84} +(-0.135947 + 2.59403i) q^{85} +(-1.48426 + 0.621768i) q^{86} +(-6.70977 - 3.87389i) q^{87} +(-9.16216 + 2.01365i) q^{88} +(-3.63168 + 13.5536i) q^{89} +(-8.50503 + 20.7676i) q^{90} +(-1.62309 - 2.11219i) q^{91} +(-8.79354 + 8.93539i) q^{92} +(-5.62934 + 2.16090i) q^{93} +(-1.71392 + 9.45848i) q^{94} +(-10.1167 - 2.15036i) q^{95} +(-1.83063 - 18.5171i) q^{96} +(-3.07407 + 8.00823i) q^{97} +(8.00398 - 4.38736i) q^{98} +(22.0440 + 13.6638i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9}+O(q^{10}) $ 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9	$ 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9} - 48 q^{10} - 24 q^{13} - 40 q^{14} + 18 q^{16} - 36 q^{17} - 8 q^{18} + 18 q^{20} - 40 q^{21} - 10 q^{22} - 100 q^{24} - 44 q^{26} - 4 q^{28} - 12 q^{29} - 114 q^{30} - 92 q^{32} - 20 q^{33} + 36 q^{34} - 72 q^{36} - 24 q^{37} + 8 q^{40} + 26 q^{42} - 20 q^{44} - 80 q^{45} + 32 q^{46} + 30 q^{48} - 36 q^{49} - 78 q^{50} + 34 q^{52} - 80 q^{53} - 188 q^{54} - 48 q^{56} - 92 q^{58} + 20 q^{60} - 28 q^{61} + 42 q^{62} - 48 q^{65} + 204 q^{66} + 26 q^{68} - 36 q^{69} + 38 q^{70} - 136 q^{72} - 24 q^{73} - 6 q^{74} - 276 q^{76} - 156 q^{78} - 80 q^{80} + 60 q^{81} + 162 q^{82} - 108 q^{84} + 16 q^{85} - 88 q^{86} + 6 q^{88} - 64 q^{89} - 16 q^{92} + 64 q^{93} + 34 q^{94} + 114 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) $ 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9 - 48 * q^10 - 24 * q^13 - 40 * q^14 + 18 * q^16 - 36 * q^17 - 8 * q^18 + 18 * q^20 - 40 * q^21 - 10 * q^22 - 100 * q^24 - 44 * q^26 - 4 * q^28 - 12 * q^29 - 114 * q^30 - 92 * q^32 - 20 * q^33 + 36 * q^34 - 72 * q^36 - 24 * q^37 + 8 * q^40 + 26 * q^42 - 20 * q^44 - 80 * q^45 + 32 * q^46 + 30 * q^48 - 36 * q^49 - 78 * q^50 + 34 * q^52 - 80 * q^53 - 188 * q^54 - 48 * q^56 - 92 * q^58 + 20 * q^60 - 28 * q^61 + 42 * q^62 - 48 * q^65 + 204 * q^66 + 26 * q^68 - 36 * q^69 + 38 * q^70 - 136 * q^72 - 24 * q^73 - 6 * q^74 - 276 * q^76 - 156 * q^78 - 80 * q^80 + 60 * q^81 + 162 * q^82 - 108 * q^84 + 16 * q^85 - 88 * q^86 + 6 * q^88 - 64 * q^89 - 16 * q^92 + 64 * q^93 + 34 * q^94 + 114 * q^96 - 8 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.12541	−	0.856423i	−0.795782	−	0.605583i
$2$	−1.12541	−	0.856423i	−0.795782	−	0.605583i
$3$	−0.683893	−	3.21746i	−0.394846	−	1.85760i	−0.504181	−	0.863598i	$-0.668206\pi$
$3$	−0.683893	−	3.21746i	−0.394846	−	1.85760i	0.109336	−	0.994005i	$-0.465128\pi$
$4$	0.533078	+	1.92765i	0.266539	+	0.963824i
$5$	−0.317452	+	2.00431i	−0.141969	+	0.896356i	0.809166	+	0.587580i	$0.199919\pi$
$5$	−0.317452	+	2.00431i	−0.141969	+	0.896356i	−0.951135	+	0.308776i	$0.900081\pi$
$6$	−1.98585	+	4.20665i	−0.810721	+	1.71736i
$7$	−0.619612	+	0.402380i	−0.234191	+	0.152086i	−0.656400	−	0.754413i	$-0.727922\pi$
$7$	−0.619612	+	0.402380i	−0.234191	+	0.152086i	0.422209	+	0.906499i	$0.361255\pi$
$8$	1.05095	−	2.62593i	0.371568	−	0.928406i
$9$	−7.14372	+	3.18059i	−2.38124	+	1.06020i
$10$	2.07380	−	1.98379i	0.655794	−	0.627330i
$11$	−1.86459	−	2.74287i	−0.562194	−	0.827005i
$11$	−1.86459	−	2.74287i	−0.562194	−	0.827005i
$12$	5.83757	−	3.03346i	1.68516	−	0.875685i
$13$	0.285400	+	3.59424i	0.0791558	+	0.996862i
$13$	0.285400	+	3.59424i	0.0791558	+	0.996862i
$14$	1.04192	+	0.0778085i	0.278466	+	0.0207952i
$15$	6.66590	−	0.349345i	1.72113	−	0.0902005i
$16$	−3.43166	+	2.05517i	−0.857914	+	0.513793i
$17$	1.27303	−	0.133801i	0.308756	−	0.0324516i	0.0511165	−	0.998693i	$-0.483722\pi$
$17$	1.27303	−	0.133801i	0.308756	−	0.0324516i	0.257639	+	0.966241i	$0.417055\pi$
$18$	10.7635	+	2.53859i	2.53698	+	0.598352i
$19$	−0.266740	+	5.08970i	−0.0611943	+	1.16766i	0.779591	+	0.626289i	$0.215427\pi$
$19$	−0.266740	+	5.08970i	−0.0611943	+	1.16766i	−0.840785	+	0.541369i	$0.817906\pi$
$20$	−4.03284	+	0.456519i	−0.901769	+	0.102081i
$21$	1.71839	+	1.71839i	0.374984	+	0.374984i
$22$	−0.250636	+	4.68371i	−0.0534357	+	0.998571i
$23$	3.13416	+	5.42853i	0.653518	+	1.13193i	0.982263	+	0.187508i	$0.0600410\pi$
$23$	3.13416	+	5.42853i	0.653518	+	1.13193i	−0.328745	+	0.944419i	$0.606626\pi$
$24$	−9.16756	−	1.58555i	−1.87132	−	0.323650i
$25$	0.838792	+	0.272540i	0.167758	+	0.0545080i
$26$	2.75700	−	4.28940i	0.540692	−	0.841221i
$27$	9.31868	+	12.8261i	1.79338	+	2.46838i
$28$	−1.10595	−	0.979893i	−0.209005	−	0.185182i
$29$	1.57608	−	1.75042i	0.292671	−	0.325044i	−0.578820	−	0.815455i	$-0.696487\pi$
$29$	1.57608	−	1.75042i	0.292671	−	0.325044i	0.871491	+	0.490411i	$0.163153\pi$
$30$	−7.80103	−	5.31568i	−1.42427	−	0.970506i
$31$	−0.286767	−	1.81057i	−0.0515048	−	0.325189i	−0.999966	−	0.00829416i	$-0.997360\pi$
$31$	−0.286767	−	1.81057i	−0.0515048	−	0.325189i	0.948461	−	0.316895i	$-0.102640\pi$
$32$	5.62211	+	0.626047i	0.993857	+	0.110670i
$33$	−7.54989	+	7.87507i	−1.31427	+	1.37087i
$34$	−1.54727	−	0.939675i	−0.265355	−	0.161153i
$35$	−0.609799	−	1.36963i	−0.103075	−	0.231510i
$36$	−9.93921	−	12.0751i	−1.65654	−	2.01251i
$37$	−3.21450	+	0.168465i	−0.528461	+	0.0276955i	−0.314701	−	0.949191i	$-0.601904\pi$
$37$	−3.21450	+	0.168465i	−0.528461	+	0.0276955i	−0.213760	+	0.976886i	$0.568571\pi$
$38$	4.65913	−	5.49954i	0.755811	−	0.892143i
$39$	11.3691	−	3.37634i	1.82052	−	0.540647i
$40$	4.92955	+	2.94005i	0.779430	+	0.464862i
$41$	−1.77639	+	2.73540i	−0.277425	+	0.427197i	−0.949727	−	0.313080i	$-0.898639\pi$
$41$	−1.77639	+	2.73540i	−0.277425	+	0.427197i	0.672302	+	0.740277i	$0.265306\pi$
$42$	−0.462218	−	3.40556i	−0.0713217	−	0.525489i
$43$	0.568949	−	0.985448i	0.0867639	−	0.150279i	−0.819378	−	0.573254i	$-0.805681\pi$
$43$	0.568949	−	0.985448i	0.0867639	−	0.150279i	0.906141	+	0.422975i	$0.139014\pi$
$44$	4.29331	−	5.05643i	0.647241	−	0.762286i
$45$	−4.10710	−	15.3279i	−0.612251	−	2.28495i
$46$	1.12191	−	8.79347i	0.165417	−	1.29653i
$47$	−3.08581	−	6.05624i	−0.450111	−	0.883393i	−0.998875	−	0.0474157i	$-0.984901\pi$
$47$	−3.08581	−	6.05624i	−0.450111	−	0.883393i	0.548764	−	0.835977i	$-0.315099\pi$
$48$	8.95933	+	9.63571i	1.29317	+	1.39079i
$49$	−2.62515	+	5.89618i	−0.375021	+	0.842311i
$50$	−0.710572	−	1.02508i	−0.100490	−	0.144968i
$51$	−1.30112	−	4.00443i	−0.182193	−	0.560732i
$52$	−6.77629	+	2.46616i	−0.939702	+	0.341995i
$53$	6.81671	+	4.95263i	0.936347	+	0.680296i	0.947539	−	0.319641i	$-0.103562\pi$
$53$	6.81671	+	4.95263i	0.936347	+	0.680296i	−0.0111916	+	0.999937i	$0.503562\pi$
$54$	0.497241	−	22.4153i	0.0676660	−	3.05033i
$55$	6.08947	−	2.86649i	0.821105	−	0.386517i
$56$	0.405438	+	2.04994i	0.0541790	+	0.273935i
$57$	16.5583	−	2.62258i	2.19321	−	0.347370i
$58$	−3.27283	+	0.620136i	−0.429744	+	0.0814278i
$59$	4.27505	−	2.77625i	0.556564	−	0.361437i	−0.235500	−	0.971874i	$-0.575673\pi$
$59$	4.27505	−	2.77625i	0.556564	−	0.361437i	0.792065	+	0.610437i	$0.209006\pi$
$60$	4.22686	+	12.6633i	0.545685	+	1.63482i
$61$	−1.43435	−	13.6469i	−0.183650	−	1.74731i	−0.567011	−	0.823710i	$-0.691900\pi$
$61$	−1.43435	−	13.6469i	−0.183650	−	1.74731i	0.383361	−	0.923598i	$-0.374766\pi$
$62$	−1.22789	+	2.28323i	−0.155942	+	0.289970i
$63$	3.14652	−	4.84522i	0.396425	−	0.610441i
$64$	−5.79099	−	5.51946i	−0.723874	−	0.689932i
$65$	−7.29457	−	0.568966i	−0.904781	−	0.0705716i
$66$	15.2411	−	2.39675i	1.87605	−	0.295019i
$67$	−2.62361	+	9.79143i	−0.320524	+	1.19621i	0.598211	+	0.801339i	$0.295879\pi$
$67$	−2.62361	+	9.79143i	−0.320524	+	1.19621i	−0.918735	+	0.394874i	$0.870788\pi$
$68$	0.936547	+	2.38263i	0.113573	+	0.288937i
$69$	15.3227	−	13.7966i	1.84463	−	1.66091i
$70$	−0.486713	+	2.06364i	−0.0581733	+	0.246652i
$71$	−3.27413	+	4.04321i	−0.388567	+	0.479841i	−0.933468	−	0.358660i	$-0.883234\pi$
$71$	−3.27413	+	4.04321i	−0.388567	+	0.479841i	0.544901	+	0.838500i	$0.316567\pi$
$72$	0.844273	+	22.1015i	0.0994985	+	2.60469i
$73$	−5.66560	+	11.1194i	−0.663108	+	1.30142i	0.277106	+	0.960839i	$0.410625\pi$
$73$	−5.66560	+	11.1194i	−0.663108	+	1.30142i	−0.940214	+	0.340583i	$0.889375\pi$
$74$	3.76190	+	2.56339i	0.437312	+	0.297988i
$75$	0.303244	−	2.88517i	0.0350156	−	0.333151i
$76$	−9.95335	+	2.19903i	−1.14173	+	0.252246i
$77$	2.25900	+	0.949237i	0.257436	+	0.108176i
$78$	−15.6865	−	5.93705i	−1.77614	−	0.672238i
$79$	−5.55811	+	7.65009i	−0.625337	+	0.860702i	−0.997728	−	0.0673738i	$-0.978538\pi$
$79$	−5.55811	+	7.65009i	−0.625337	+	0.860702i	0.372391	+	0.928076i	$0.378538\pi$
$80$	−3.02982	−	7.53053i	−0.338744	−	0.841939i
$81$	19.1970	−	21.3205i	2.13300	−	2.36894i
$82$	4.34182	−	1.55709i	0.479473	−	0.171952i
$83$	−7.70085	−	1.21970i	−0.845279	−	0.133879i	−0.281250	−	0.959634i	$-0.590749\pi$
$83$	−7.70085	−	1.21970i	−0.845279	−	0.133879i	−0.564028	+	0.825755i	$0.690749\pi$
$84$	−2.39642	+	4.22849i	−0.261471	+	0.461366i
$85$	−0.135947	+	2.59403i	−0.0147456	+	0.281362i
$86$	−1.48426	+	0.621768i	−0.160052	+	0.0670470i
$87$	−6.70977	−	3.87389i	−0.719363	−	0.415324i
$88$	−9.16216	+	2.01365i	−0.976690	+	0.214655i
$89$	−3.63168	+	13.5536i	−0.384958	+	1.43668i	0.453276	+	0.891370i	$0.350255\pi$
$89$	−3.63168	+	13.5536i	−0.384958	+	1.43668i	−0.838233	+	0.545312i	$0.816411\pi$
$90$	−8.50503	+	20.7676i	−0.896509	+	2.18909i
$91$	−1.62309	−	2.11219i	−0.170146	−	0.221418i
$92$	−8.79354	+	8.93539i	−0.916790	+	0.931579i
$93$	−5.62934	+	2.16090i	−0.583735	+	0.224075i
$94$	−1.71392	+	9.45848i	−0.176777	+	0.975568i
$95$	−10.1167	−	2.15036i	−1.03795	−	0.220623i
$96$	−1.83063	−	18.5171i	−0.186838	−	1.88989i
$97$	−3.07407	+	8.00823i	−0.312125	+	0.813113i	0.684345	+	0.729158i	$0.260088\pi$
$97$	−3.07407	+	8.00823i	−0.312125	+	0.813113i	−0.996470	+	0.0839542i	$0.973245\pi$
$98$	8.00398	−	4.38736i	0.808524	−	0.443190i
$99$	22.0440	+	13.6638i	2.21551	+	1.37326i
$100$	−0.0782200	+	1.76218i	−0.00782200	+	0.176218i
$101$	13.4930	+	1.41817i	1.34261	+	0.141114i	0.748426	−	0.663219i	$-0.230810\pi$
$101$	13.4930	+	1.41817i	1.34261	+	0.141114i	0.594180	+	0.804332i	$0.297477\pi$
$102$	−1.96520	+	5.62092i	−0.194584	+	0.556554i
$103$	4.62452	+	14.2328i	0.455667	+	1.40240i	0.870350	+	0.492433i	$0.163892\pi$
$103$	4.62452	+	14.2328i	0.455667	+	1.40240i	−0.414683	+	0.909966i	$0.636108\pi$
$104$	9.73815	+	3.02794i	0.954904	+	0.296914i
$105$	−3.98970	+	2.89869i	−0.389355	+	0.282883i
$106$	−3.43002	−	11.4117i	−0.333153	−	1.10840i
$107$	−2.79555	−	13.1520i	−0.270256	−	1.27145i	−0.878515	−	0.477715i	$-0.841465\pi$
$107$	−2.79555	−	13.1520i	−0.270256	−	1.27145i	0.608259	−	0.793739i	$-0.291868\pi$
$108$	−19.7566	+	24.8004i	−1.90108	+	2.38642i
$109$	6.56113	−	6.56113i	0.628443	−	0.628443i	−0.319234	−	0.947676i	$-0.603425\pi$
$109$	6.56113	−	6.56113i	0.628443	−	0.628443i	0.947676	+	0.319234i	$0.103425\pi$
$110$	−9.30806	−	1.98921i	−0.887489	−	0.189663i
$111$	2.74041	+	10.2273i	0.260108	+	0.970736i
$112$	1.29933	−	2.65424i	0.122775	−	0.250802i
$113$	6.64377	+	7.37866i	0.624994	+	0.694126i	0.969621	−	0.244614i	$-0.0786612\pi$
$113$	6.64377	+	7.37866i	0.624994	+	0.694126i	−0.344627	+	0.938740i	$0.611995\pi$
$114$	−20.8809	−	11.2295i	−1.95568	−	1.05174i
$115$	−11.8754	+	4.55854i	−1.10739	+	0.425086i
$116$	4.21436	+	2.10502i	0.391294	+	0.195447i
$117$	−13.4706	−	24.7685i	−1.24536	−	2.28985i
$118$	−7.18881	−	0.536845i	−0.661784	−	0.0494205i
$119$	−0.734947	+	0.595148i	−0.0673725	+	0.0545572i
$120$	6.08820	−	17.8713i	0.555774	−	1.63142i
$121$	−4.04662	+	10.2286i	−0.367875	+	0.929875i
$122$	−10.0733	+	16.5867i	−0.911995	+	1.50169i
$123$	10.0159	+	3.84474i	0.903103	+	0.346669i
$124$	3.33728	−	1.51796i	0.299697	−	0.136317i
$125$	−5.41894	+	10.6353i	−0.484684	+	0.951247i
$126$	−7.69068	+	2.75809i	−0.685140	+	0.245710i
$127$	4.42963	+	1.97220i	0.393066	+	0.175004i	0.593746	−	0.804653i	$-0.297648\pi$
$127$	4.42963	+	1.97220i	0.393066	+	0.175004i	−0.200680	+	0.979657i	$0.564315\pi$
$128$	1.79022	+	11.1712i	0.158235	+	0.987402i
$129$	−3.55974	−	1.15663i	−0.313418	−	0.101836i
$130$	7.72208	+	6.88756i	0.677271	+	0.604079i
$131$		−	0.152665i		−	0.0133384i	−0.999978	−	0.00666919i	$-0.997877\pi$
$131$		−	0.152665i		−	0.0133384i	0.999978	−	0.00666919i	$-0.00212288\pi$
$132$	−19.2050	−	10.3555i	−1.67158	−	0.901331i
$133$	−1.88272	−	3.26097i	−0.163253	−	0.282762i
$134$	11.3382	−	8.77242i	0.979474	−	0.757821i
$135$	−28.6657	+	14.6059i	−2.46715	+	1.25707i
$136$	0.986548	−	3.48351i	0.0845958	−	0.298709i
$137$	11.5667	−	14.2837i	0.988212	−	1.22034i	0.0128080	−	0.999918i	$-0.495923\pi$
$137$	11.5667	−	14.2837i	0.988212	−	1.22034i	0.975404	−	0.220423i	$-0.0707437\pi$
$138$	−29.0599	+	2.40407i	−2.47374	+	0.204648i
$139$	1.46885	−	6.91039i	0.124586	−	0.586131i	−0.870919	−	0.491426i	$-0.836476\pi$
$139$	1.46885	−	6.91039i	0.124586	−	0.586131i	0.995505	−	0.0947053i	$-0.0301909\pi$
$140$	2.31510	−	1.90560i	0.195661	−	0.161052i
$141$	−17.3754	+	14.0703i	−1.46327	+	1.18493i
$142$	7.14742	−	1.74621i	0.599799	−	0.146539i
$143$	9.32636	−	7.48459i	0.779909	−	0.625893i
$144$	17.9781	−	25.5963i	1.49818	−	2.13302i
$145$	3.00805	+	3.71463i	0.249805	+	0.308484i
$146$	15.8990	−	7.66165i	1.31581	−	0.634082i
$147$	20.7661	+	4.41396i	1.71276	+	0.364057i
$148$	−2.03832	−	6.10663i	−0.167549	−	0.501962i
$149$	−4.63523	−	3.75353i	−0.379733	−	0.307502i	0.420383	−	0.907347i	$-0.361896\pi$
$149$	−4.63523	−	3.75353i	−0.379733	−	0.307502i	−0.800116	+	0.599845i	$0.795229\pi$
$150$	−2.81220	+	2.98728i	−0.229615	+	0.243911i
$151$	−1.01324	−	1.98860i	−0.0824564	−	0.161830i	0.846097	−	0.533030i	$-0.178947\pi$
$151$	−1.01324	−	1.98860i	−0.0824564	−	0.161830i	−0.928553	+	0.371200i	$0.878947\pi$
$152$	13.0849	+	6.04948i	1.06132	+	0.490678i
$153$	−8.66862	+	5.00483i	−0.700817	+	0.404617i
$154$	−1.72934	−	3.00293i	−0.139354	−	0.241983i
$155$	3.71999			0.298797
$156$	12.5690	+	20.1159i	1.00633	+	1.61056i
$157$	−2.17624	+	6.69776i	−0.173683	+	0.534540i	−0.999571	−	0.0292939i	$-0.990674\pi$
$157$	−2.17624	+	6.69776i	−0.173683	+	0.534540i	0.825888	+	0.563834i	$0.190674\pi$
$158$	12.8069	−	3.84936i	1.01886	−	0.306238i
$159$	11.2730	−	25.3196i	0.894007	−	2.00797i
$160$	−3.03954	+	11.0697i	−0.240297	+	0.875138i
$161$	−4.12630	−	2.10245i	−0.325198	−	0.165697i
$162$	−39.8638	+	7.55340i	−3.13200	+	0.593451i
$163$	−7.17589	+	18.6938i	−0.562059	+	1.46421i	0.298274	+	0.954480i	$0.403589\pi$
$163$	−7.17589	+	18.6938i	−0.562059	+	1.46421i	−0.860333	+	0.509733i	$0.829744\pi$
$164$	−6.21984	−	1.96607i	−0.485688	−	0.153524i
$165$	−13.3874	−	17.6323i	−1.04221	−	1.37267i
$166$	7.62201	+	7.96784i	0.591583	+	0.618425i
$167$	−14.9642	−	18.4793i	−1.15797	−	1.42997i	−0.883537	−	0.468361i	$-0.844845\pi$
$167$	−14.9642	−	18.4793i	−1.15797	−	1.42997i	−0.274428	−	0.961608i	$-0.588489\pi$
$168$	6.31832	−	2.70642i	0.487469	−	0.208805i
$169$	−12.8371	+	2.05159i	−0.987469	+	0.157815i
$170$	2.37459	−	2.80291i	0.182122	−	0.214973i
$171$	−14.2827	−	37.2078i	−1.09223	−	2.84535i
$172$	2.20289	+	0.571413i	0.167969	+	0.0435698i
$173$	−0.606747	+	0.546317i	−0.0461301	+	0.0415357i	−0.691873	−	0.722019i	$-0.743214\pi$
$173$	−0.606747	+	0.546317i	−0.0461301	+	0.0415357i	0.645743	+	0.763555i	$0.276548\pi$
$174$	4.23353	+	10.1061i	0.320943	+	0.766142i
$175$	−0.629390	+	0.168645i	−0.0475774	+	0.0127483i
$176$	12.0357	+	5.58052i	0.907224	+	0.420648i
$177$	−11.8562	−	11.8562i	−0.891163	−	0.891163i
$178$	15.6948	−	12.1431i	1.17637	−	0.910162i
$179$	−16.3791	+	3.48149i	−1.22423	+	0.260219i	−0.774285	−	0.632837i	$-0.781890\pi$
$179$	−16.3791	+	3.48149i	−1.22423	+	0.260219i	−0.449947	+	0.893055i	$0.648557\pi$
$180$	27.3574	−	16.0880i	2.03910	−	1.19913i
$181$	−4.24560	−	5.84356i	−0.315573	−	0.434349i	0.621536	−	0.783385i	$-0.286509\pi$
$181$	−4.24560	−	5.84356i	−0.315573	−	0.434349i	−0.937109	+	0.349037i	$0.886509\pi$
$182$	0.0177030	+	3.76712i	0.00131223	+	0.279238i
$183$	−42.9275	+	13.9480i	−3.17329	+	1.03107i
$184$	17.5488	−	2.52495i	1.29371	−	0.186142i
$185$	0.682794	−	6.49635i	0.0502000	−	0.477621i
$186$	8.18594	+	2.38921i	0.600222	+	0.175185i
$187$	−2.74068	−	3.24228i	−0.200418	−	0.237099i
$188$	10.0293	−	9.17680i	0.731463	−	0.669287i
$189$	−10.9349	−	4.19752i	−0.795398	−	0.305325i
$190$	9.54374	+	11.0842i	0.692376	+	0.804132i
$191$	0.651634	−	3.06570i	0.0471506	−	0.221826i	−0.948264	−	0.317484i	$-0.897162\pi$
$191$	0.651634	−	3.06570i	0.0471506	−	0.221826i	0.995414	+	0.0956578i	$0.0304954\pi$
$192$	−13.7982	+	22.4070i	−0.995802	+	1.61709i
$193$	2.86844	+	7.47254i	0.206475	+	0.537885i	0.997241	−	0.0742331i	$-0.0236509\pi$
$193$	2.86844	+	7.47254i	0.206475	+	0.537885i	−0.790766	+	0.612119i	$0.790318\pi$
$194$	10.3180	−	6.37980i	0.740790	−	0.458043i
$195$	3.15808	+	23.8591i	0.226155	+	1.70859i
$196$	−12.7652	−	1.91724i	−0.911798	−	0.136946i
$197$	11.7349	+	3.14435i	0.836076	+	0.224026i	0.651363	−	0.758766i	$-0.274198\pi$
$197$	11.7349	+	3.14435i	0.836076	+	0.224026i	0.184714	+	0.982792i	$0.440864\pi$
$198$	−13.1065	−	34.2563i	−0.931438	−	2.43449i
$199$	−4.84303	+	8.38837i	−0.343313	+	0.594636i	−0.985046	−	0.172293i	$-0.944883\pi$
$199$	−4.84303	+	8.38837i	−0.343313	+	0.594636i	0.641733	+	0.766928i	$0.278216\pi$
$200$	1.59720	−	1.91618i	0.112939	−	0.135494i
$201$	33.2978	+	1.74506i	2.34865	+	0.123087i
$202$	−13.9706	−	13.1518i	−0.982966	−	0.925355i
$203$	−0.272225	+	1.71876i	−0.0191065	+	0.120634i
$204$	7.02554	−	4.64277i	0.491886	−	0.325059i
$205$	−4.91867	−	4.42879i	−0.343535	−	0.309320i
$206$	6.98484	−	19.9782i	0.486657	−	1.39195i
$207$	−39.6555	−	28.8114i	−2.75625	−	2.00253i
$208$	−8.36618	−	11.7476i	−0.580090	−	0.814552i
$209$	14.4577	−	8.75856i	1.00006	−	0.605843i
$210$	6.97254	+	0.154673i	0.481151	+	0.0106734i
$211$	4.76245	+	0.500553i	0.327860	+	0.0344595i	0.267029	−	0.963689i	$-0.413958\pi$
$211$	4.76245	+	0.500553i	0.327860	+	0.0344595i	0.0608315	+	0.998148i	$0.480625\pi$
$212$	−5.91309	+	15.7804i	−0.406113	+	1.08380i
$213$	15.2480	+	7.76926i	1.04478	+	0.532341i
$214$	−8.11757	+	17.1955i	−0.554906	+	1.17546i
$215$	1.79453	+	1.45318i	0.122386	+	0.0991063i
$216$	43.4738	−	10.9906i	2.95802	−	0.747814i
$217$	0.906224	+	1.00646i	0.0615185	+	0.0683232i
$218$	−13.0030	+	1.76483i	−0.880677	+	0.119529i
$219$	39.6508	+	10.6244i	2.67935	+	0.717930i
$220$	8.77175	+	10.2103i	0.591391	+	0.688379i
$221$	0.844237	+	4.53740i	0.0567896	+	0.305218i
$222$	5.67486	−	13.8569i	0.380872	−	0.930011i
$223$	10.3622	+	6.72932i	0.693907	+	0.450629i	0.842802	−	0.538224i	$-0.180905\pi$
$223$	10.3622	+	6.72932i	0.693907	+	0.450629i	−0.148894	+	0.988853i	$0.547571\pi$
$224$	−3.73543	+	1.87432i	−0.249584	+	0.125233i
$225$	−6.85893	+	0.720903i	−0.457262	+	0.0480602i
$226$	−1.15769	−	13.9939i	−0.0770082	−	0.930858i
$227$	0.643007	+	0.990144i	0.0426779	+	0.0657182i	0.859366	−	0.511362i	$-0.170859\pi$
$227$	0.643007	+	0.990144i	0.0426779	+	0.0657182i	−0.816688	+	0.577080i	$0.804192\pi$
$228$	13.8823	+	30.5206i	0.919378	+	2.02128i
$229$	2.91387	+	18.3974i	0.192554	+	1.21574i	0.874753	+	0.484570i	$0.161024\pi$
$229$	2.91387	+	18.3974i	0.192554	+	1.21574i	−0.682199	+	0.731167i	$0.738976\pi$
$230$	17.2687	+	5.04017i	1.13866	+	0.332339i
$231$	1.50922	−	7.91741i	0.0992997	−	0.520927i
$232$	−2.94008	−	5.97829i	−0.193026	−	0.392494i
$233$	−8.18651	+	11.2678i	−0.536316	+	0.738176i	−0.988077	−	0.153963i	$-0.950796\pi$
$233$	−8.18651	+	11.2678i	−0.536316	+	0.738176i	0.451760	+	0.892139i	$0.350796\pi$
$234$	−6.05240	+	39.4111i	−0.395658	+	2.57639i
$235$	13.1182	−	4.26236i	0.855736	−	0.278045i
$236$	7.63057	+	6.76084i	0.496708	+	0.440093i
$237$	28.4150	+	12.6512i	1.84575	+	0.821783i
$238$	1.33681	−	0.0403577i	0.0866527	−	0.00261600i
$239$	6.54806	−	3.33640i	0.423559	−	0.215814i	−0.229201	−	0.973379i	$-0.573611\pi$
$239$	6.54806	−	3.33640i	0.423559	−	0.215814i	0.652760	+	0.757565i	$0.273611\pi$
$240$	−22.1571	+	14.8984i	−1.43024	+	0.961688i
$241$	−13.6609	+	3.66043i	−0.879978	+	0.235789i	−0.670397	−	0.742002i	$-0.733876\pi$
$241$	−13.6609	+	3.66043i	−0.879978	+	0.235789i	−0.209580	+	0.977791i	$0.567210\pi$
$242$	13.3141	−	8.04574i	0.855865	−	0.517200i
$243$	−40.5369	−	23.4040i	−2.60045	−	1.50137i
$244$	25.5418	−	10.0398i	1.63515	−	0.642732i
$245$	−10.9844	−	7.13337i	−0.701769	−	0.455734i
$246$	−7.97922	−	12.9047i	−0.508737	−	0.822776i
$247$	−18.3697	+	0.493876i	−1.16884	+	0.0314246i
$248$	−5.05582	−	1.14980i	−0.321045	−	0.0730125i
$249$	1.34223	+	25.6113i	0.0850606	+	1.62305i
$250$	15.2068	−	7.32808i	0.961762	−	0.463469i
$251$	18.0733	−	8.04674i	1.14078	−	0.507906i	0.252673	−	0.967552i	$-0.418690\pi$
$251$	18.0733	−	8.04674i	1.14078	−	0.507906i	0.888102	+	0.459646i	$0.152024\pi$
$252$	11.0172	+	3.48251i	0.694020	+	0.219378i
$253$	9.04580	−	18.7186i	0.568705	−	1.17683i
$254$	−3.29610	−	6.01317i	−0.206816	−	0.377300i
$255$	8.43917	−	1.33663i	0.528481	−	0.0837032i
$256$	7.55253	−	14.1053i	0.472033	−	0.881581i
$257$	4.45934	+	4.01521i	0.278166	+	0.250462i	0.796390	−	0.604783i	$-0.206740\pi$
$257$	4.45934	+	4.01521i	0.278166	+	0.250462i	−0.518224	+	0.855245i	$0.673407\pi$
$258$	3.01559	+	4.35033i	0.187742	+	0.270839i
$259$	1.92396	−	1.39784i	0.119549	−	0.0868573i
$260$	−2.79181	−	14.3647i	−0.173141	−	0.890860i
$261$	−5.69173	+	17.5174i	−0.352309	+	1.08430i
$262$	−0.130746	+	0.171810i	−0.00807749	+	0.0106144i
$263$	−21.4115	+	12.3619i	−1.32029	+	0.762270i	−0.983775	−	0.179409i	$-0.942582\pi$
$263$	−21.4115	+	12.3619i	−1.32029	+	0.762270i	−0.336515	+	0.941678i	$0.609248\pi$
$264$	12.7448	+	28.1018i	0.784386	+	1.72955i
$265$	−12.0906	+	12.0906i	−0.742719	+	0.742719i
$266$	−0.673944	+	5.28232i	−0.0413222	+	0.323880i
$267$	46.0920	+	2.41558i	2.82078	+	0.147831i
$268$	−20.2730	+	0.162204i	−1.23837	+	0.00990820i
$269$	−0.888703	−	8.45544i	−0.0541852	−	0.515538i	−0.987628	−	0.156812i	$-0.949878\pi$
$269$	−0.888703	−	8.45544i	−0.0541852	−	0.515538i	0.933443	−	0.358725i	$-0.116788\pi$
$270$	44.7693	+	8.11239i	2.72457	+	0.493704i
$271$	−0.386079	−	7.36683i	−0.0234526	−	0.447503i	−0.984966	−	0.172746i	$-0.944736\pi$
$271$	−0.386079	−	7.36683i	−0.0234526	−	0.447503i	0.961514	−	0.274757i	$-0.0885974\pi$
$272$	−4.09363	+	3.07546i	−0.248213	+	0.186477i
$273$	−5.68588	+	6.66674i	−0.344125	+	0.403489i
$274$	−25.2502	+	6.16897i	−1.52542	+	0.372681i
$275$	−0.816461	−	2.80887i	−0.0492344	−	0.169381i
$276$	34.7631	+	22.1820i	2.09249	+	1.33520i
$277$	−11.2352	−	25.2348i	−0.675060	−	1.51621i	−0.847277	−	0.531151i	$-0.821760\pi$
$277$	−11.2352	−	25.2348i	−0.675060	−	1.51621i	0.172218	−	0.985059i	$-0.444907\pi$
$278$	−7.57127	+	6.51904i	−0.454095	+	0.390986i
$279$	7.80727	+	12.0221i	0.467409	+	0.719747i
$280$	−4.23742	+	0.161868i	−0.253234	+	0.00967349i
$281$	−31.8653	−	5.04697i	−1.90093	−	0.301077i	−0.907920	−	0.419143i	$-0.862330\pi$
$281$	−31.8653	−	5.04697i	−1.90093	−	0.301077i	−0.993006	+	0.118066i	$0.962330\pi$
$282$	31.6045	−	0.954123i	1.88202	−	0.0568172i
$283$	−1.97638	+	0.420092i	−0.117483	+	0.0249719i	−0.266278	−	0.963896i	$-0.585794\pi$
$283$	−1.97638	+	0.420092i	−0.117483	+	0.0249719i	0.148795	+	0.988868i	$0.452461\pi$
$284$	−9.53925	−	4.15602i	−0.566051	−	0.246614i
$285$			34.0206i			2.01521i
$286$	−16.9059	+	0.435890i	−0.999668	+	0.0257747i
$287$		−	2.40967i		−	0.142238i
$288$	−42.1539	+	13.4093i	−2.48394	+	0.790151i
$289$	−15.0258	+	3.19383i	−0.883870	+	0.187872i
$290$	−0.203980	−	6.75664i	−0.0119781	−	0.396763i
$291$	27.8685	+	4.41394i	1.63368	+	0.258750i
$292$	−24.4544	−	4.99380i	−1.43109	−	0.292240i
$293$	7.12630	+	10.9735i	0.416323	+	0.641081i	0.983160	−	0.182749i	$-0.0584996\pi$
$293$	7.12630	+	10.9735i	0.416323	+	0.641081i	−0.566837	+	0.823830i	$0.691833\pi$
$294$	−19.5900	−	22.7520i	−1.14251	−	1.32693i
$295$	4.20735	+	9.44986i	0.244961	+	0.550192i
$296$	−2.93592	+	8.61811i	−0.170647	+	0.500917i
$297$	17.8047	−	49.4752i	1.03313	−	2.87084i
$298$	2.00190	+	8.19397i	0.115967	+	0.474664i
$299$	−18.6169	+	12.8142i	−1.07664	+	0.741066i
$300$	5.72325	−	0.953473i	0.330432	−	0.0550488i
$301$	0.0439979	+	0.839529i	0.00253599	+	0.0483896i
$302$	−0.562774	+	3.10574i	−0.0323840	+	0.178716i
$303$	−4.66486	−	44.3832i	−0.267989	−	2.54975i
$304$	−9.54486	−	18.0143i	−0.547435	−	1.03319i
$305$	27.8080	+	1.45736i	1.59228	+	0.0834480i
$306$	14.0420	+	1.79154i	0.802726	+	0.102416i
$307$	−0.285624	+	0.285624i	−0.0163014	+	0.0163014i	−0.715211	−	0.698909i	$-0.753669\pi$
$307$	−0.285624	+	0.285624i	−0.0163014	+	0.0163014i	0.698909	+	0.715211i	$0.253669\pi$
$308$	−0.625575	+	4.86057i	−0.0356455	+	0.276957i
$309$	42.6308	−	24.6129i	2.42518	−	1.40018i
$310$	−4.18650	−	3.18589i	−0.237777	−	0.180946i
$311$	4.53298	−	13.9511i	0.257042	−	0.791093i	−0.736379	−	0.676569i	$-0.763466\pi$
$311$	4.53298	−	13.9511i	0.257042	−	0.791093i	0.993421	−	0.114524i	$-0.0365341\pi$
$312$	3.08243	−	33.4029i	0.174508	−	1.89107i
$313$	12.0990	−	8.79042i	0.683874	−	0.496864i	−0.190766	−	0.981635i	$-0.561097\pi$
$313$	12.0990	−	8.79042i	0.683874	−	0.496864i	0.874641	+	0.484772i	$0.161097\pi$
$314$	8.18527	−	5.67393i	0.461922	−	0.320198i
$315$	8.71247	+	7.84474i	0.490892	+	0.442001i
$316$	−17.7096	−	6.63600i	−0.996242	−	0.373304i
$317$	−9.87769	+	1.56447i	−0.554786	+	0.0878695i	−0.427531	−	0.904001i	$-0.640617\pi$
$317$	−9.87769	+	1.56447i	−0.554786	+	0.0878695i	−0.127255	+	0.991870i	$0.540617\pi$
$318$	−34.3710	+	18.8403i	−1.92743	+	1.05651i
$319$	−7.73990	−	1.05918i	−0.433351	−	0.0593025i
$320$	12.9011	−	9.85479i	0.721192	−	0.550899i
$321$	−40.4043	+	17.9891i	−2.25515	+	1.00406i
$322$	2.84317	+	5.89997i	0.158444	+	0.328793i
$323$	0.341439	+	6.51505i	0.0189982	+	0.362507i
$324$	51.3319	+	25.6397i	2.85177	+	1.42443i
$325$	−0.740182	+	3.09260i	−0.0410579	+	0.171547i
$326$	24.0856	−	14.8925i	1.33398	−	0.824822i
$327$	−25.5973	−	16.6231i	−1.41553	−	0.919259i
$328$	5.31605	+	7.53944i	0.293530	+	0.416296i
$329$	4.34891	+	2.51085i	0.239763	+	0.138427i
$330$	−0.0344793	+	31.3087i	−0.00189802	+	1.72349i
$331$	−0.988846	+	0.264960i	−0.0543519	+	0.0145635i	−0.285893	−	0.958262i	$-0.592290\pi$
$331$	−0.988846	+	0.264960i	−0.0543519	+	0.0145635i	0.231541	+	0.972825i	$0.425623\pi$
$332$	−1.75401	−	15.4947i	−0.0962638	−	0.850384i
$333$	22.4277	−	11.4275i	1.22903	−	0.626222i
$334$	1.01474	+	33.6124i	0.0555242	+	1.83919i
$335$	−18.7922	−	8.36683i	−1.02673	−	0.457129i
$336$	−9.42852	−	2.36534i	−0.514368	−	0.129040i
$337$	23.3493	−	7.58664i	1.27192	−	0.413271i	0.406190	−	0.913789i	$-0.366857\pi$
$337$	23.3493	−	7.58664i	1.27192	−	0.413271i	0.865726	+	0.500518i	$0.166857\pi$
$338$	16.2040	+	8.68511i	0.881380	+	0.472408i
$339$	19.1969	−	26.4223i	1.04263	−	1.43506i
$340$	−5.07285	+	1.12076i	−0.275114	+	0.0607818i
$341$	−4.43146	+	4.16254i	−0.239977	+	0.225414i
$342$	−15.7917	+	54.1059i	−0.853920	+	2.92571i
$343$	−1.55495	−	9.81759i	−0.0839596	−	0.530100i
$344$	−1.98978	−	2.52968i	−0.107282	−	0.136391i
$345$	22.7884	+	35.0911i	1.22689	+	1.88924i
$346$	1.15072	−	0.0951966i	0.0618628	−	0.00511780i
$347$	−12.0650	+	1.26808i	−0.647681	+	0.0680740i	−0.422672	−	0.906283i	$-0.638908\pi$
$347$	−12.0650	+	1.26808i	−0.647681	+	0.0680740i	−0.225009	+	0.974357i	$0.572241\pi$
$348$	3.89067	−	14.9992i	0.208562	−	0.804040i
$349$	15.8906	+	10.3195i	0.850604	+	0.552389i	0.894715	−	0.446638i	$-0.147379\pi$
$349$	15.8906	+	10.3195i	0.850604	+	0.552389i	−0.0441108	+	0.999027i	$0.514045\pi$
$350$	0.852751	+	0.349231i	0.0455814	+	0.0186672i
$351$	−43.4404	+	37.1541i	−2.31867	+	1.98314i
$352$	−8.76575	−	16.5880i	−0.467216	−	0.884143i
$353$	−19.9444	−	5.34407i	−1.06153	−	0.284436i	−0.314522	−	0.949250i	$-0.601844\pi$
$353$	−19.9444	−	5.34407i	−1.06153	−	0.284436i	−0.747009	+	0.664814i	$0.768511\pi$
$354$	3.18910	+	23.4969i	0.169499	+	1.24885i
$355$	−7.06448	−	7.84590i	−0.374944	−	0.416417i
$356$	−28.0626	+	0.224529i	−1.48731	+	0.0119000i
$357$	2.41749	+	1.95765i	0.127947	+	0.103610i
$358$	21.4148	+	10.1094i	1.13181	+	0.534297i
$359$	13.8984	+	7.08159i	0.733530	+	0.373752i	0.780510	−	0.625144i	$-0.214960\pi$
$359$	13.8984	+	7.08159i	0.733530	+	0.373752i	−0.0469798	+	0.998896i	$0.514960\pi$
$360$	−44.5664	−	5.32399i	−2.34886	−	0.280599i
$361$	−6.93799	−	0.729212i	−0.365157	−	0.0383796i
$362$	−0.226544	+	10.2124i	−0.0119069	+	0.536752i
$363$	35.6777	+	6.02457i	1.87259	+	0.316208i
$364$	3.20633	−	4.25471i	0.168057	−	0.223007i
$365$	−20.4881	−	14.8855i	−1.07240	−	0.779142i
$366$	60.2563	+	21.0670i	3.14965	+	1.10119i
$367$	8.69387	+	7.82799i	0.453816	+	0.408618i	0.864084	−	0.503347i	$-0.167898\pi$
$367$	8.69387	+	7.82799i	0.453816	+	0.408618i	−0.410268	+	0.911965i	$0.634565\pi$
$368$	−21.9119	−	12.1876i	−1.14224	−	0.635322i
$369$	3.98984	−	25.1909i	0.207703	−	1.31138i
$370$	−6.33205	+	6.72627i	−0.329187	+	0.349682i
$371$	−6.21655	−	0.325796i	−0.322747	−	0.0169145i
$372$	−7.16633	−	9.69945i	−0.371557	−	0.502893i
$373$	16.1652	−	27.9989i	0.837000	−	1.44973i	−0.0553911	−	0.998465i	$-0.517641\pi$
$373$	16.1652	−	27.9989i	0.837000	−	1.44973i	0.892391	−	0.451262i	$-0.149026\pi$
$374$	0.307619	+	5.99606i	0.0159066	+	0.310049i
$375$	37.9245	+	10.1618i	1.95841	+	0.524755i
$376$	−19.1463	+	1.73828i	−0.987394	+	0.0896448i
$377$	6.74123	+	5.16525i	0.347191	+	0.266024i
$378$	8.71137	+	14.0888i	0.448064	+	0.724651i
$379$	−12.2287	−	31.8568i	−0.628145	−	1.63637i	−0.763676	−	0.645600i	$-0.776607\pi$
$379$	−12.2287	−	31.8568i	−0.628145	−	1.63637i	0.135531	−	0.990773i	$-0.456726\pi$
$380$	−1.24783	−	20.6477i	−0.0640121	−	1.05920i
$381$	3.31608	−	15.6009i	0.169888	−	0.799261i
$382$	−3.35889	+	2.89208i	−0.171856	+	0.147972i
$383$	21.7523	+	8.34994i	1.11149	+	0.426662i	0.843700	−	0.536815i	$-0.180373\pi$
$383$	21.7523	+	8.34994i	1.11149	+	0.426662i	0.267792	+	0.963477i	$0.413706\pi$
$384$	34.7185	−	13.3999i	1.77172	−	0.683808i
$385$	−2.61969	+	4.22640i	−0.133512	+	0.215397i
$386$	3.17150	−	10.8662i	0.161425	−	0.553077i
$387$	−0.930105	+	8.84936i	−0.0472799	+	0.449838i
$388$	−17.0758	−	1.65672i	−0.866891	−	0.0841072i
$389$	32.0572	−	10.4160i	1.62536	−	0.528113i	0.652164	−	0.758078i	$-0.273861\pi$
$389$	32.0572	−	10.4160i	1.62536	−	0.528113i	0.973199	+	0.229965i	$0.0738612\pi$
$390$	16.8794	−	29.5559i	0.854721	−	1.49662i
$391$	4.71624	+	6.49134i	0.238510	+	0.328281i
$392$	12.7240	+	13.0901i	0.642660	+	0.661148i
$393$	−0.491193	+	0.104406i	−0.0247774	+	0.00526660i
$394$	−10.5136	−	13.5887i	−0.529668	−	0.684589i
$395$	−13.5687	−	13.5687i	−0.682717	−	0.682717i
$396$	−14.5878	+	49.7770i	−0.733063	+	2.50139i
$397$	16.3031	−	4.36840i	0.818229	−	0.219244i	0.174657	−	0.984629i	$-0.444118\pi$
$397$	16.3031	−	4.36840i	0.818229	−	0.219244i	0.643572	+	0.765386i	$0.277452\pi$
$398$	12.6344	−	5.29264i	0.633304	−	0.265296i
$399$	−9.20446	+	8.28774i	−0.460800	+	0.414906i
$400$	−3.43856	+	0.788599i	−0.171928	+	0.0394299i
$401$	−5.81351	−	15.1447i	−0.290313	−	0.756290i	−0.998725	−	0.0504910i	$-0.983921\pi$
$401$	−5.81351	−	15.1447i	−0.290313	−	0.756290i	0.708412	−	0.705799i	$-0.249412\pi$
$402$	−35.9790	−	30.4809i	−1.79447	−	1.52025i
$403$	6.42579	−	1.54745i	0.320091	−	0.0770838i
$404$	4.45909	+	26.7658i	0.221848	+	1.33165i
$405$	36.6387	+	45.2451i	1.82059	+	2.24825i
$406$	1.77835	−	1.70117i	0.0882582	−	0.0844275i
$407$	6.45580	+	8.50284i	0.320002	+	0.421470i
$408$	−11.8828	−	0.791831i	−0.588284	−	0.0392015i
$409$	1.62226	−	4.22612i	0.0802154	−	0.208968i	−0.887607	−	0.460601i	$-0.847634\pi$
$409$	1.62226	−	4.22612i	0.0802154	−	0.208968i	0.967823	+	0.251632i	$0.0809674\pi$
$410$	1.74258	+	9.19665i	0.0860600	+	0.454190i
$411$	−53.8677	−	27.4470i	−2.65710	−	1.35386i
$412$	−24.9706	+	16.5016i	−1.23021	+	0.812977i
$413$	−1.53176	+	3.44039i	−0.0753731	+	0.169291i
$414$	19.9538	+	66.3864i	0.980674	+	3.26271i
$415$	4.88930	−	15.0477i	0.240006	−	0.738663i
$416$	−0.645610	+	20.3859i	−0.0316536	+	0.999499i
$417$	−23.2384			−1.13799
$418$	−23.7719	−	2.52499i	−1.16272	−	0.123501i
$419$	−9.29924	+	5.36892i	−0.454298	+	0.262289i	−0.709644	−	0.704561i	$-0.751144\pi$
$419$	−9.29924	+	5.36892i	−0.454298	+	0.262289i	0.255346	+	0.966850i	$0.417811\pi$
$420$	−7.71447	−	6.14551i	−0.376428	−	0.299870i
$421$	4.75283	+	9.32796i	0.231639	+	0.454617i	0.977343	−	0.211660i	$-0.0678869\pi$
$421$	4.75283	+	9.32796i	0.231639	+	0.454617i	−0.745704	+	0.666277i	$0.767887\pi$
$422$	−4.93100	−	4.64200i	−0.240037	−	0.225969i
$423$	41.3065	+	33.4494i	2.00839	+	1.62636i
$424$	20.1693	−	12.6952i	0.979507	−	0.616533i
$425$	1.10428	+	0.234721i	0.0535653	+	0.0113857i
$426$	−10.5065	−	21.8023i	−0.509039	−	1.05633i
$427$	6.37999	+	7.87863i	0.308749	+	0.381274i
$428$	23.8622	−	12.3999i	1.15342	−	0.599371i
$429$	−30.4596	−	24.8885i	−1.47060	−	1.20163i
$430$	−0.775037	−	3.17230i	−0.0373756	−	0.152982i
$431$	−6.18452	+	5.00812i	−0.297898	+	0.241233i	−0.766602	−	0.642122i	$-0.778054\pi$
$431$	−6.18452	+	5.00812i	−0.297898	+	0.241233i	0.468705	+	0.883355i	$0.344721\pi$
$432$	−58.3383	−	24.8631i	−2.80680	−	1.19623i
$433$	5.33643	−	25.1059i	0.256452	−	1.20651i	−0.641744	−	0.766919i	$-0.721789\pi$
$433$	5.33643	−	25.1059i	0.256452	−	1.20651i	0.898196	−	0.439594i	$-0.144878\pi$
$434$	−0.157911	−	1.90879i	−0.00757996	−	0.0916249i
$435$	9.89451	−	12.2187i	0.474406	−	0.585842i
$436$	16.1452	+	9.14996i	0.773212	+	0.438204i
$437$	−28.4656	+	14.5039i	−1.36169	+	0.693818i
$438$	−35.5243	−	45.9146i	−1.69741	−	2.19389i
$439$	−6.57456	−	11.3875i	−0.313787	−	0.543495i	0.665392	−	0.746494i	$-0.268264\pi$
$439$	−6.57456	−	11.3875i	−0.313787	−	0.543495i	−0.979179	+	0.202999i	$0.934931\pi$
$440$	−1.12743	−	19.0031i	−0.0537482	−	0.905936i
$441$		−	50.4702i		−	2.40334i
$442$	2.93582	−	5.82944i	0.139643	−	0.277278i
$443$	27.3153	+	8.87529i	1.29779	+	0.421678i	0.874812	−	0.484462i	$-0.160985\pi$
$443$	27.3153	+	8.87529i	1.29779	+	0.421678i	0.422978	+	0.906140i	$0.360985\pi$
$444$	−18.2539	+	10.7345i	−0.866290	+	0.509437i
$445$	−26.0128	−	11.5817i	−1.23313	−	0.549023i
$446$	−5.89859	−	16.4477i	−0.279306	−	0.778821i
$447$	−8.90686	+	17.4807i	−0.421280	+	0.826808i
$448$	5.80909	+	1.08974i	0.274454	+	0.0514854i
$449$	−12.4716	−	4.78739i	−0.588570	−	0.225931i	0.0458125	−	0.998950i	$-0.485412\pi$
$449$	−12.4716	−	4.78739i	−0.588570	−	0.225931i	−0.634383	+	0.773019i	$0.718746\pi$
$450$	8.33648	+	5.06284i	0.392985	+	0.238665i
$451$	10.8151	−	0.227996i	0.509261	−	0.0107359i
$452$	−10.6818	+	16.7403i	−0.502430	+	0.787396i
$453$	−5.70529	+	4.62005i	−0.268058	+	0.217069i
$454$	0.124338	−	1.66500i	0.00583549	−	0.0781423i
$455$	4.74874	−	2.58266i	0.222625	−	0.121077i
$456$	10.5153	−	46.2372i	0.492426	−	2.16526i
$457$	36.4089	−	13.9761i	1.70314	−	0.653774i	0.704693	−	0.709512i	$-0.251085\pi$
$457$	36.4089	−	13.9761i	1.70314	−	0.653774i	0.998445	+	0.0557385i	$0.0177513\pi$
$458$	12.4767	−	23.2001i	0.582998	−	1.08407i
$459$	13.5791	+	15.0812i	0.633820	+	0.703928i
$460$	−15.1178	−	20.4616i	−0.704870	−	0.954025i
$461$	−3.35885	−	12.5354i	−0.156437	−	0.583833i	−0.998978	−	0.0451996i	$-0.985608\pi$
$461$	−3.35885	−	12.5354i	−0.156437	−	0.583833i	0.842541	−	0.538633i	$-0.181059\pi$
$462$	−8.47915	+	7.61777i	−0.394486	+	0.354411i
$463$	13.0457	−	13.0457i	0.606283	−	0.606283i	−0.335689	−	0.941973i	$-0.608969\pi$
$463$	13.0457	−	13.0457i	0.606283	−	0.606283i	0.941973	+	0.335689i	$0.108969\pi$
$464$	−1.81116	+	9.24595i	−0.0840812	+	0.429233i
$465$	−2.54407	−	11.9689i	−0.117979	−	0.555046i
$466$	18.8631	−	5.66969i	0.873818	−	0.262643i
$467$	−30.5632	+	22.2054i	−1.41429	+	1.02755i	−0.421614	+	0.906775i	$0.638536\pi$
$467$	−30.5632	+	22.2054i	−1.41429	+	1.02755i	−0.992680	+	0.120770i	$0.961464\pi$
$468$	40.5640	−	39.1701i	1.87507	−	1.81064i
$469$	−2.31426	−	7.12257i	−0.106863	−	0.328890i
$470$	−18.4137	−	6.43784i	−0.849359	−	0.296955i
$471$	23.0381	+	2.42140i	1.06154	+	0.111572i
$472$	−2.79735	−	14.1437i	−0.128758	−	0.651016i
$473$	−3.76381	+	0.276905i	−0.173060	+	0.0127321i
$474$	−21.1437	−	38.5730i	−0.971161	−	1.77172i
$475$	−1.61089	+	4.19650i	−0.0739126	+	0.192549i
$476$	−1.53902	−	1.09946i	−0.0705409	−	0.0503936i
$477$	−64.4489	−	13.6990i	−2.95091	−	0.627236i
$478$	−10.2266	−	1.85310i	−0.467754	−	0.0847590i
$479$	−21.5475	+	8.27130i	−0.984529	+	0.377925i	−0.796765	−	0.604289i	$-0.793457\pi$
$479$	−21.5475	+	8.27130i	−0.984529	+	0.377925i	−0.187764	+	0.982214i	$0.560124\pi$
$480$	37.6951	+	2.20911i	1.72054	+	0.100832i
$481$	−1.52292	−	11.5056i	−0.0694394	−	0.524611i
$482$	18.5090	+	7.58006i	0.843060	+	0.345262i
$483$	−3.94262	+	14.7141i	−0.179395	+	0.669513i
$484$	−21.8744	−	2.34781i	−0.994289	−	0.106719i
$485$	−15.0751	−	8.70363i	−0.684526	−	0.395211i
$486$	25.5768	+	61.0558i	1.16019	+	2.76955i
$487$	0.121685	−	2.32188i	0.00551406	−	0.105215i	−0.994486	−	0.104871i	$-0.966557\pi$
$487$	0.121685	−	2.32188i	0.00551406	−	0.105215i	1.00000		0.000343983i	$-0.000109493\pi$
$488$	−37.3432	−	10.5758i	−1.69045	−	0.478744i
$489$	65.0542	+	10.3036i	2.94185	+	0.465944i
$490$	6.25275	+	17.4353i	0.282471	+	0.787644i
$491$	20.3125	−	22.5594i	0.916692	−	1.01809i	−0.0830755	−	0.996543i	$-0.526474\pi$
$491$	20.3125	−	22.5594i	0.916692	−	1.01809i	0.999768	−	0.0215468i	$-0.00685908\pi$
$492$	−2.07206	+	21.3567i	−0.0934157	+	0.962833i
$493$	1.77220	−	2.43922i	0.0798158	−	0.109857i
$494$	21.0964	+	15.1765i	0.949170	+	0.682821i
$495$	−34.3844	+	39.8455i	−1.54546	+	1.79092i
$496$	4.70513	+	5.62391i	0.211266	+	0.252521i
$497$	0.401778	−	3.82267i	0.0180222	−	0.171470i
$498$	20.4236	−	29.9727i	0.915203	−	1.34311i
$499$	11.8354	−	23.2283i	0.529825	−	1.03984i	−0.458673	−	0.888605i	$-0.651675\pi$
$499$	11.8354	−	23.2283i	0.529825	−	1.03984i	0.988498	−	0.151235i	$-0.0483250\pi$
$500$	−23.3898	−	4.77638i	−1.04602	−	0.213606i
$501$	−49.2224	+	60.7846i	−2.19910	+	2.71566i
$502$	−27.2312	−	6.42253i	−1.21539	−	0.286651i
$503$	−17.0483	+	15.3503i	−0.760145	+	0.684438i	−0.955070	−	0.296380i	$-0.904220\pi$
$503$	−17.0483	+	15.3503i	−0.760145	+	0.684438i	0.194925	+	0.980818i	$0.437554\pi$
$504$	−9.41635	−	13.3546i	−0.419437	−	0.594863i
$505$	−7.12585	+	26.5940i	−0.317096	+	1.18342i
$506$	−26.2112	+	13.3189i	−1.16523	+	0.592099i
$507$	15.3801	+	39.8998i	0.683055	+	1.77201i
$508$	−1.44037	+	9.59011i	−0.0639060	+	0.425492i
$509$	−6.02077	+	9.27117i	−0.266866	+	0.410937i	−0.946545	−	0.322572i	$-0.895452\pi$
$509$	−6.02077	+	9.27117i	−0.266866	+	0.410937i	0.679679	+	0.733510i	$0.262119\pi$
$510$	−10.6422	−	5.72325i	−0.471245	−	0.253430i
$511$	−0.963744	−	9.16941i	−0.0426335	−	0.405631i
$512$	−20.5798	+	9.40602i	−0.909506	+	0.415691i
$513$	−67.7665	+	44.0081i	−2.99196	+	1.94300i
$514$	−1.57985	−	8.33782i	−0.0696842	−	0.367765i
$515$	−29.9950	+	4.75074i	−1.32174	+	0.209343i
$516$	0.331957	−	7.47851i	0.0146136	−	0.329223i
$517$	−10.8577	+	19.7563i	−0.477520	+	0.868883i
$518$	−3.36237	−	0.0745881i	−0.147734	−	0.00327721i
$519$	2.17270	+	1.57856i	0.0953711	+	0.0692912i
$520$	−9.16033	+	18.5571i	−0.401707	+	0.813781i
$521$	−10.0963	−	31.0732i	−0.442326	−	1.36134i	−0.885390	−	0.464850i	$-0.846108\pi$
$521$	−10.0963	−	31.0732i	−0.442326	−	1.36134i	0.443063	−	0.896490i	$-0.353892\pi$
$522$	21.4078	−	14.8396i	0.936993	−	0.649512i
$523$	−7.91582	+	17.7792i	−0.346135	+	0.777431i	0.653652	+	0.756795i	$0.273236\pi$
$523$	−7.91582	+	17.7792i	−0.346135	+	0.777431i	−0.999787	+	0.0206364i	$0.993431\pi$
$524$	0.294284	−	0.0813822i	0.0128559	−	0.00355520i
$525$	0.973043	+	1.90970i	0.0424671	+	0.0833463i
$526$	34.6837	+	4.42511i	1.51228	+	0.192944i
$527$	−0.607321	−	2.26655i	−0.0264553	−	0.0987325i
$528$	9.72400	−	42.5409i	0.423183	−	1.85135i
$529$	−8.14595	+	14.1092i	−0.354172	+	0.613443i
$530$	23.9615	−	3.25216i	1.04082	−	0.141265i
$531$	−21.7096	+	33.4299i	−0.942118	+	1.45074i
$532$	5.28236	−	5.36757i	0.229020	−	0.232714i
$533$	−10.3386	−	5.60408i	−0.447817	−	0.242739i
$534$	−49.8034	−	42.1928i	−2.15521	−	1.82586i
$535$	27.2482	−	1.42802i	1.17804	−	0.0617386i
$536$	22.9543	+	17.1797i	0.991474	+	0.742052i
$537$	22.4031	+	50.3182i	0.966765	+	2.17139i
$538$	−6.24129	+	10.2769i	−0.269081	+	0.443069i
$539$	21.0672	−	3.79352i	0.907431	−	0.163398i
$540$	−43.4360	−	47.4712i	−1.86919	−	2.04284i
$541$	−1.22082	−	7.70794i	−0.0524871	−	0.331390i	−0.999934	−	0.0114777i	$-0.996346\pi$
$541$	−1.22082	−	7.70794i	−0.0524871	−	0.331390i	0.947447	−	0.319913i	$-0.103654\pi$
$542$	−5.87463	+	8.62132i	−0.252337	+	0.370318i
$543$	−15.8979	+	17.6564i	−0.682245	+	0.757710i
$544$	7.24089	+	0.0447340i	0.310451	+	0.00191795i
$545$	11.0677	+	15.2334i	0.474089	+	0.652527i
$546$	12.1085	−	2.63327i	0.518195	−	0.112693i
$547$	24.4162	+	7.93330i	1.04396	+	0.339203i	0.780295	−	0.625411i	$-0.215069\pi$
$547$	24.4162	+	7.93330i	1.04396	+	0.339203i	0.263665	+	0.964614i	$0.415069\pi$
$548$	33.7000	+	14.6823i	1.43959	+	0.627195i
$549$	53.6518	+	92.9277i	2.28980	+	3.96606i
$550$	−1.48673	+	3.86035i	−0.0633944	+	0.164606i
$551$	8.48870	+	8.48870i	0.361631	+	0.361631i
$552$	−20.1254	−	54.7358i	−0.856594	−	2.32971i
$553$	0.365626	−	6.97656i	0.0155480	−	0.296673i
$554$	−8.96743	+	38.0215i	−0.380990	+	1.61538i
$555$	−21.3687	+	2.24594i	−0.907052	+	0.0953350i
$556$	14.1038	−	0.852351i	0.598135	−	0.0361477i
$557$	−1.89850	+	0.0994963i	−0.0804421	+	0.00421579i	−0.0925146	−	0.995711i	$-0.529490\pi$
$557$	−1.89850	+	0.0994963i	−0.0804421	+	0.00421579i	0.0120724	+	0.999927i	$0.496157\pi$
$558$	1.50970	−	20.2161i	0.0639105	−	0.855817i
$559$	3.70431	+	1.76369i	0.156676	+	0.0745961i
$560$	4.90745	+	3.44686i	0.207378	+	0.145656i
$561$	−8.55757	+	11.0354i	−0.361301	+	0.465915i
$562$	31.5391	+	32.9701i	1.33040	+	1.39076i
$563$	1.05755	−	0.470850i	0.0445702	−	0.0198439i	−0.384330	−	0.923196i	$-0.625568\pi$
$563$	1.05755	−	0.470850i	0.0445702	−	0.0198439i	0.428901	+	0.903352i	$0.358901\pi$
$564$	−36.3850	−	25.9930i	−1.53208	−	1.09450i
$565$	−16.8982	+	10.9738i	−0.710913	+	0.461672i
$566$	2.58400	+	1.21984i	0.108614	+	0.0512738i
$567$	−3.31577	+	20.9349i	−0.139249	+	0.879184i
$568$	7.17622	+	12.8469i	0.301108	+	0.539042i
$569$	−4.45248	−	20.9473i	−0.186658	−	0.878156i	−0.967390	−	0.253290i	$-0.918487\pi$
$569$	−4.45248	−	20.9473i	−0.186658	−	0.878156i	0.780733	−	0.624865i	$-0.214846\pi$
$570$	29.1361	−	38.2870i	1.22038	−	1.60367i
$571$	−10.4015			−0.435289			−0.217644	−	0.976028i	$-0.569837\pi$
$571$	−10.4015			−0.435289			−0.217644	+	0.976028i	$0.569837\pi$
$572$	19.3993	+	13.9881i	0.811127	+	0.584871i
$573$	−10.3094			−0.430682
$574$	−2.06370	+	2.71185i	−0.0861370	+	0.113191i
$575$	1.14942	+	5.40759i	0.0479341	+	0.225512i
$576$	58.9243	+	21.0107i	2.45518	+	0.875446i
$577$	−1.07807	+	6.80665i	−0.0448805	+	0.283364i	−0.999914	−	0.0131343i	$-0.995819\pi$
$577$	−1.07807	+	6.80665i	−0.0448805	+	0.283364i	0.955033	+	0.296499i	$0.0958191\pi$
$578$	19.6454	+	9.27409i	0.817141	+	0.385751i
$579$	22.0809	−	14.3395i	0.917652	−	0.595930i
$580$	−5.55698	+	7.77865i	−0.230741	+	0.322991i
$581$	5.26232	−	2.34294i	0.218318	−	0.0972014i
$582$	−27.5832	−	28.8347i	−1.14336	−	1.19524i
$583$	0.874041	−	27.9319i	0.0361991	−	1.15682i
$584$	23.2444	+	26.5634i	0.961858	+	1.09920i
$585$	53.9200	−	19.1365i	2.22932	−	0.791197i
$586$	1.37802	−	18.4528i	0.0569253	−	0.762279i
$587$	−6.04354	+	0.316728i	−0.249444	+	0.0130728i	−0.176648	−	0.984274i	$-0.556525\pi$
$587$	−6.04354	+	0.316728i	−0.249444	+	0.0130728i	−0.0727956	+	0.997347i	$0.523192\pi$
$588$	2.56136	+	42.3826i	0.105629	+	1.74783i
$589$	9.29177	−	0.976605i	0.382861	−	0.0402403i
$590$	3.35811	−	14.2382i	0.138251	−	0.586178i
$591$	2.09144	−	39.9070i	0.0860302	−	1.64155i
$592$	10.6849	−	7.18448i	0.439145	−	0.295280i
$593$	22.2428	+	22.2428i	0.913402	+	0.913402i	0.996538	−	0.0831360i	$-0.0264936\pi$
$593$	22.2428	+	22.2428i	0.913402	+	0.913402i	−0.0831360	+	0.996538i	$0.526494\pi$
$594$	−62.4092	+	40.4314i	−2.56068	+	1.65892i
$595$	−0.959553	−	1.66199i	−0.0393378	−	0.0681351i
$596$	4.76456	−	10.9360i	0.195164	−	0.447957i
$597$	30.3014	+	9.84552i	1.24015	+	0.402950i
$598$	31.9260	+	1.52277i	1.30555	+	0.0622705i
$599$	−7.41285	−	10.2029i	−0.302881	−	0.416880i	0.630264	−	0.776381i	$-0.282947\pi$
$599$	−7.41285	−	10.2029i	−0.302881	−	0.416880i	−0.933145	+	0.359501i	$0.882947\pi$
$600$	−7.25755	−	3.82848i	−0.296288	−	0.156297i
$601$	−6.72418	+	7.46796i	−0.274285	+	0.304624i	−0.864511	−	0.502614i	$-0.832372\pi$
$601$	−6.72418	+	7.46796i	−0.274285	+	0.304624i	0.590226	+	0.807238i	$0.299039\pi$
$602$	0.669477	−	0.982492i	0.0272858	−	0.0400434i
$603$	−12.4002	−	78.2918i	−0.504975	−	3.18829i
$604$	3.29318	−	3.01325i	0.133998	−	0.122607i
$605$	−19.2168	−	11.3578i	−0.781272	−	0.461760i
$606$	−32.7609	+	53.9442i	−1.33082	+	2.19133i
$607$	14.8319	+	33.3130i	0.602009	+	1.35213i	0.915413	+	0.402515i	$0.131864\pi$
$607$	14.8319	+	33.3130i	0.602009	+	1.35213i	−0.313404	+	0.949620i	$0.601469\pi$
$608$	−4.68603	+	28.4478i	−0.190044	+	1.15371i
$609$	5.71623	−	0.299575i	0.231633	−	0.0121394i
$610$	−30.0472	−	25.4556i	−1.21658	−	1.03067i
$611$	20.8869	−	12.8196i	0.844992	−	0.518625i
$612$	−14.2686	−	14.0421i	−0.576774	−	0.567618i
$613$	11.0078	−	16.9506i	0.444603	−	0.684628i	−0.543329	−	0.839520i	$-0.682836\pi$
$613$	11.0078	−	16.9506i	0.444603	−	0.684628i	0.987931	+	0.154892i	$0.0495029\pi$
$614$	0.566058	−	0.0768279i	0.0228442	−	0.00310052i
$615$	−10.8856	+	18.8545i	−0.438951	+	0.760285i
$616$	4.86673	−	4.93435i	0.196086	−	0.198811i
$617$	2.36550	+	8.82815i	0.0952313	+	0.355408i	0.997054	−	0.0766973i	$-0.0244375\pi$
$617$	2.36550	+	8.82815i	0.0952313	+	0.355408i	−0.901823	+	0.432105i	$0.857771\pi$
$618$	−69.0560	−	8.81051i	−2.77784	−	0.354411i
$619$	−8.36125	−	16.4099i	−0.336067	−	0.659568i	0.659695	−	0.751533i	$-0.270685\pi$
$619$	−8.36125	−	16.4099i	−0.336067	−	0.659568i	−0.995762	+	0.0919648i	$0.970685\pi$
$620$	1.98304	+	7.17083i	0.0796410	+	0.287988i
$621$	−40.4204	+	90.7857i	−1.62201	+	3.64310i
$622$	−17.0495	+	11.8185i	−0.683622	+	0.473878i
$623$	−3.20348	−	9.85930i	−0.128345	−	0.395005i
$624$	−32.0760	+	34.9520i	−1.28407	+	1.39920i
$625$	−16.0285	−	11.6454i	−0.641141	−	0.465816i
$626$	−21.1446	−	0.469054i	−0.845107	−	0.0187472i
$627$	−38.0679	−	40.5273i	−1.52028	−	1.61850i
$628$	−14.0710	−	0.624588i	−0.561495	−	0.0249238i
$629$	−4.06963	+	0.644566i	−0.162267	+	0.0257005i
$630$	−3.08664	−	16.2901i	−0.122975	−	0.649012i
$631$	−17.3764	+	11.2844i	−0.691744	+	0.449224i	−0.842038	−	0.539418i	$-0.818644\pi$
$631$	−17.3764	+	11.2844i	−0.691744	+	0.449224i	0.150295	+	0.988641i	$0.451978\pi$
$632$	14.2473	+	22.6351i	0.566725	+	0.900376i
$633$	−1.64649	−	15.6653i	−0.0654422	−	0.622641i
$634$	12.4563	+	6.69882i	0.494701	+	0.266044i
$635$	−5.35910	+	8.25229i	−0.212669	+	0.327482i
$636$	54.8166	+	8.23308i	2.17362	+	0.326463i
$637$	−21.9415	−	7.75264i	−0.869353	−	0.307171i
$638$	7.80343	+	7.82064i	0.308941	+	0.309622i
$639$	10.5297	−	39.2972i	0.416547	−	1.55457i
$640$	−22.9588	+	0.0418524i	−0.907527	+	0.00165436i
$641$	−8.58176	+	7.72705i	−0.338959	+	0.305200i	−0.820977	−	0.570961i	$-0.806571\pi$
$641$	−8.58176	+	7.72705i	−0.338959	+	0.305200i	0.482018	+	0.876161i	$0.339904\pi$
$642$	60.8776	+	14.3581i	2.40265	+	0.566668i
$643$	−4.52829	+	5.59197i	−0.178578	+	0.220526i	−0.858573	−	0.512691i	$-0.828649\pi$
$643$	−4.52829	+	5.59197i	−0.178578	+	0.220526i	0.679995	+	0.733217i	$0.261982\pi$
$644$	1.85315	−	9.07482i	0.0730245	−	0.357598i
$645$	3.44829	−	6.76766i	0.135776	−	0.266476i
$646$	5.19538	−	7.62449i	0.204410	−	0.299982i
$647$	−4.87861	+	46.4169i	−0.191798	+	1.82484i	0.299788	+	0.954006i	$0.403084\pi$
$647$	−4.87861	+	46.4169i	−0.191798	+	1.82484i	−0.491585	+	0.870829i	$0.663582\pi$
$648$	−35.8108	−	72.8169i	−1.40678	−	2.86052i
$649$	−15.5861	−	6.54933i	−0.611808	−	0.257084i
$650$	3.48158	−	2.84652i	0.136559	−	0.111650i
$651$	2.61850	−	3.60405i	0.102627	−	0.141254i
$652$	−39.8604	−	3.86732i	−1.56105	−	0.151456i
$653$	19.1611	−	21.2805i	0.749830	−	0.832771i	−0.240623	−	0.970619i	$-0.577352\pi$
$653$	19.1611	−	21.2805i	0.749830	−	0.832771i	0.990453	+	0.137848i	$0.0440185\pi$
$654$	14.5710	+	40.6299i	0.569770	+	1.58875i
$655$	0.305988	+	0.0484637i	0.0119559	+	0.00189363i
$656$	0.474238	−	13.0377i	0.0185159	−	0.509038i
$657$	5.10732	−	97.4535i	0.199256	−	3.80202i
$658$	−2.74395	−	6.55023i	−0.106970	−	0.255355i
$659$	−0.146285	−	0.0844577i	−0.00569845	−	0.00329000i	0.497148	−	0.867666i	$-0.334381\pi$
$659$	−0.146285	−	0.0844577i	−0.00569845	−	0.00329000i	−0.502847	+	0.864376i	$0.667714\pi$
$660$	26.8523	−	35.2055i	1.04523	−	1.37037i
$661$	1.23428	−	4.60640i	0.0480080	−	0.179168i	−0.937759	−	0.347288i	$-0.887103\pi$
$661$	1.23428	−	4.60640i	0.0480080	−	0.179168i	0.985767	+	0.168119i	$0.0537694\pi$
$662$	1.33977	+	0.548683i	0.0520717	+	0.0213252i
$663$	14.0215	−	5.81940i	0.544551	−	0.226007i
$664$	−11.2961	+	18.9400i	−0.438373	+	0.735016i
$665$	7.13367	−	2.73836i	0.276632	−	0.106189i
$666$	−35.0270	−	6.34705i	−1.35727	−	0.245943i
$667$	14.4419	+	3.06972i	0.559192	+	0.118860i
$668$	27.6444	−	38.6966i	1.06960	−	1.49722i
$669$	14.5647	−	37.9423i	0.563103	−	1.46693i
$670$	13.9833	+	25.5102i	0.540223	+	0.985544i
$671$	−34.7572	+	29.3801i	−1.34179	+	1.13421i
$672$	8.58519	+	10.7368i	0.331181	+	0.414180i
$673$	39.0453	+	4.10383i	1.50509	+	0.158191i	0.820881	−	0.571099i	$-0.193483\pi$
$673$	39.0453	+	4.10383i	1.50509	+	0.158191i	0.684204	+	0.729290i	$0.260150\pi$
$674$	−32.7748	−	11.4588i	−1.26244	−	0.441377i
$675$	4.32082	+	13.2981i	0.166308	+	0.511845i
$676$	−10.7979	−	23.6517i	−0.415305	−	0.909682i
$677$	25.1243	−	18.2539i	0.965606	−	0.701554i	0.0111599	−	0.999938i	$-0.496448\pi$
$677$	25.1243	−	18.2539i	0.965606	−	0.701554i	0.954446	+	0.298384i	$0.0964476\pi$
$678$	−44.2330	+	13.2951i	−1.69876	+	0.510596i
$679$	−1.31763	−	6.19894i	−0.0505658	−	0.237893i
$680$	6.66886	+	3.08320i	0.255739	+	0.118235i
$681$	2.74600	−	2.74600i	0.105227	−	0.105227i
$682$	8.55209	−	0.889339i	0.327476	−	0.0340546i
$683$	−10.1511	−	37.8844i	−0.388421	−	1.44961i	−0.832703	−	0.553720i	$-0.813208\pi$
$683$	−10.1511	−	37.8844i	−0.388421	−	1.44961i	0.444282	−	0.895887i	$-0.353459\pi$
$684$	64.1097	−	47.3667i	2.45130	−	1.81111i
$685$	24.9572	+	27.7177i	0.953564	+	1.05904i
$686$	−6.65806	+	12.3805i	−0.254206	+	0.472689i
$687$	57.2003	−	21.9571i	2.18233	−	0.837717i
$688$	0.0728298	+	4.55101i	0.00277661	+	0.173506i
$689$	−15.8554	+	25.9144i	−0.604044	+	0.987258i
$690$	4.40661	−	59.0083i	0.167757	−	2.24641i
$691$	−1.76173	+	1.42662i	−0.0670193	+	0.0542711i	−0.662245	−	0.749288i	$-0.730396\pi$
$691$	−1.76173	+	1.42662i	−0.0670193	+	0.0542711i	0.595225	+	0.803559i	$0.297063\pi$
$692$	−1.37655	−	0.878365i	−0.0523286	−	0.0333904i
$693$	−19.1568	+	0.403851i	−0.727705	+	0.0153410i
$694$	14.6640	+	8.90561i	0.556637	+	0.338052i
$695$	13.3843	+	5.13775i	0.507695	+	0.194886i
$696$	−17.2242	+	13.5481i	−0.652882	+	0.513539i
$697$	−1.89540	+	3.71993i	−0.0717934	+	0.140903i
$698$	−9.04553	−	25.2227i	−0.342378	−	0.954692i
$699$	41.8523	+	18.6338i	1.58300	+	0.704797i
$700$	−0.660601	−	1.12334i	−0.0249684	−	0.0424583i
$701$	−23.5231	−	7.64311i	−0.888454	−	0.288676i	−0.170991	−	0.985273i	$-0.554697\pi$
$701$	−23.5231	−	7.64311i	−0.888454	−	0.288676i	−0.717463	+	0.696596i	$0.754697\pi$
$702$	80.7077	−	4.61012i	3.04612	−	0.173998i
$703$		−	16.4058i		−	0.618757i
$704$	−4.34132	+	26.1754i	−0.163620	+	0.986523i
$705$	−22.6854	−	39.2923i	−0.854382	−	1.47983i
$706$	17.8687	+	23.0951i	0.672498	+	0.869194i
$707$	−8.93108	+	4.55061i	−0.335888	+	0.171143i
$708$	16.5342	−	29.1748i	0.621395	−	1.09645i
$709$	−4.56797	+	5.64097i	−0.171554	+	0.211851i	−0.855670	−	0.517522i	$-0.826855\pi$
$709$	−4.56797	+	5.64097i	−0.171554	+	0.211851i	0.684116	+	0.729373i	$0.260188\pi$
$710$	1.23100	+	14.8800i	0.0461985	+	0.558437i
$711$	15.3738	−	72.3281i	0.576563	−	2.71252i
$712$	31.7741	+	23.7808i	1.19079	+	0.891223i
$713$	8.92998	−	7.23136i	0.334430	−	0.270816i
$714$	−1.04409	−	4.27355i	−0.0390739	−	0.159933i
$715$	12.0408	+	21.0689i	0.450300	+	0.787933i
$716$	−15.4424	−	29.7173i	−0.577110	−	1.11059i
$717$	−15.2129	−	18.7864i	−0.568137	−	0.701591i
$718$	−9.57651	−	19.8726i	−0.357392	−	0.741638i
$719$	24.3004	+	5.16520i	0.906251	+	0.192630i	0.637383	−	0.770547i	$-0.280017\pi$
$719$	24.3004	+	5.16520i	0.906251	+	0.192630i	0.268868	+	0.963177i	$0.413350\pi$
$720$	45.5957	+	44.1593i	1.69925	+	1.64572i
$721$	−8.59240	−	6.95799i	−0.319998	−	0.259129i
$722$	7.18354	+	6.76252i	0.267344	+	0.251675i
$723$	21.1199	+	41.4502i	0.785458	+	1.54155i
$724$	9.00110	−	11.2991i	0.334523	−	0.419928i
$725$	1.79906	−	1.03869i	0.0668156	−	0.0385760i
$726$	−34.9923	−	37.3353i	−1.29869	−	1.38564i
$727$	19.5505			0.725089			0.362544	−	0.931966i	$-0.381908\pi$
$727$	19.5505			0.725089			0.362544	+	0.931966i	$0.381908\pi$
$728$	−7.25225	+	2.04230i	−0.268786	+	0.0756925i
$729$	−20.9820	+	64.5758i	−0.777110	+	2.39170i
$730$	10.3092	+	34.2987i	0.381559	+	1.26945i
$731$	0.592437	−	1.33063i	0.0219121	−	0.0492153i
$732$	−49.7705	−	75.3138i	−1.83957	−	2.78368i
$733$	−26.6709	−	13.5895i	−0.985114	−	0.501940i	−0.114243	−	0.993453i	$-0.536444\pi$
$733$	−26.6709	−	13.5895i	−0.985114	−	0.501940i	−0.870871	+	0.491512i	$0.836444\pi$
$734$	−3.08005	−	16.2553i	−0.113687	−	0.599994i
$735$	−15.4392	+	40.2204i	−0.569483	+	1.48355i
$736$	14.2221	+	32.4819i	0.524233	+	1.19730i
$737$	31.7485	−	11.0608i	1.16947	−	0.407429i
$738$	−26.0642	+	24.9330i	−0.959438	+	0.917795i
$739$	6.63206	+	8.18991i	0.243964	+	0.301271i	0.884389	−	0.466750i	$-0.154575\pi$
$739$	6.63206	+	8.18991i	0.243964	+	0.301271i	−0.640425	+	0.768021i	$0.721242\pi$
$740$	12.8867	−	2.14687i	0.473723	−	0.0789206i
$741$	14.1519	+	58.7661i	0.519885	+	2.15883i
$742$	6.71713	+	5.69065i	0.246593	+	0.208910i
$743$	2.02271	+	5.26934i	0.0742061	+	0.193314i	0.965666	−	0.259785i	$-0.0836518\pi$
$743$	2.02271	+	5.26934i	0.0742061	+	0.193314i	−0.891460	+	0.453099i	$0.850318\pi$
$744$	−0.241809	+	17.0532i	−0.00886515	+	0.625202i
$745$	8.99472	−	8.09888i	0.329541	−	0.296720i
$746$	−42.1713	+	17.6659i	−1.54400	+	0.646794i
$747$	58.8921	−	15.7801i	2.15475	−	0.577363i
$748$	4.78897	−	7.01145i	0.175102	−	0.256364i
$749$	7.02427	+	7.02427i	0.256661	+	0.256661i
$750$	−33.9776	−	43.9157i	−1.24069	−	1.60357i
$751$	28.6178	−	6.08289i	1.04428	−	0.221968i	0.346327	−	0.938114i	$-0.387429\pi$
$751$	28.6178	−	6.08289i	1.04428	−	0.221968i	0.697950	+	0.716146i	$0.254096\pi$
$752$	23.0360	+	14.4411i	0.840038	+	0.526611i
$753$	−38.2503	−	52.6470i	−1.39392	−	1.91856i
$754$	−3.16298	−	11.5863i	−0.115189	−	0.421950i
$755$	4.30743	−	1.39957i	0.156763	−	0.0509355i
$756$	2.26218	−	23.3163i	0.0822748	−	0.848005i
$757$	−3.73211	+	35.5086i	−0.135646	+	1.29058i	0.688929	+	0.724829i	$0.258081\pi$
$757$	−3.73211	+	35.5086i	−0.135646	+	1.29058i	−0.824574	+	0.565754i	$0.808585\pi$
$758$	−13.5207	+	46.3247i	−0.491093	+	1.68259i
$759$	−66.4126	−	16.3030i	−2.41062	−	0.591763i
$760$	−16.2789	+	24.3057i	−0.590496	+	0.881661i
$761$	47.6404	+	18.2874i	1.72696	+	0.662919i	0.999725	−	0.0234655i	$-0.00746999\pi$
$761$	47.6404	+	18.2874i	1.72696	+	0.662919i	0.727239	+	0.686385i	$0.240803\pi$
$762$	−17.0930	+	14.7174i	−0.619213	+	0.533156i
$763$	−1.42528	+	6.70543i	−0.0515987	+	0.242753i
$764$	6.25695	−	0.378134i	0.226369	−	0.0136804i
$765$	−7.27937	−	18.9634i	−0.263186	−	0.685624i
$766$	−17.3291	−	28.0263i	−0.626127	−	1.01263i
$767$	11.1986	+	14.5732i	0.404358	+	0.526208i
$768$	−50.5484	−	14.6535i	−1.82401	−	0.528762i
$769$	−22.0276	−	5.90228i	−0.794336	−	0.212842i	−0.161240	−	0.986915i	$-0.551549\pi$
$769$	−22.0276	−	5.90228i	−0.794336	−	0.212842i	−0.633096	+	0.774073i	$0.718216\pi$
$770$	6.56780	−	2.51285i	0.236687	−	0.0905567i
$771$	9.86907	−	17.0937i	0.355426	−	0.615615i
$772$	−12.8753	+	9.51279i	−0.463393	+	0.342373i
$773$	5.26448	+	0.275900i	0.189350	+	0.00992342i	0.146775	−	0.989170i	$-0.453111\pi$
$773$	5.26448	+	0.275900i	0.189350	+	0.00992342i	0.0425748	+	0.999093i	$0.486444\pi$
$774$	8.62554	−	9.16256i	0.310039	−	0.329341i
$775$	0.252916	−	1.59685i	0.00908502	−	0.0573606i
$776$	17.7983	+	16.4886i	0.638923	+	0.591905i
$777$	−5.81327	−	5.23429i	−0.208550	−	0.187779i
$778$	−44.9979	−	15.7323i	−1.61325	−	0.564029i
$779$	−13.4485	−	9.77092i	−0.481843	−	0.350080i
$780$	−44.3085	+	18.8064i	−1.58650	+	0.673379i
$781$	17.1949	+	1.44157i	0.615281	+	0.0515834i
$782$	0.251657	−	11.3445i	0.00899923	−	0.405678i
$783$	37.1380	+	3.90336i	1.32720	+	0.139495i
$784$	−3.10906	−	25.6288i	−0.111038	−	0.915314i
$785$	−12.7336	−	6.48807i	−0.454480	−	0.231569i
$786$	0.642208	+	0.303170i	0.0229068	+	0.0108137i
$787$	25.7420	+	20.8455i	0.917604	+	0.743061i	0.966748	−	0.255730i	$-0.0823159\pi$
$787$	25.7420	+	20.8455i	0.917604	+	0.743061i	−0.0491437	+	0.998792i	$0.515649\pi$
$788$	0.194399	+	24.2969i	0.00692520	+	0.865542i
$789$	54.4172	+	60.4365i	1.93730	+	2.15159i
$790$	3.64975	+	26.8909i	0.129852	+	0.956736i
$791$	−7.08559	−	1.89858i	−0.251934	−	0.0675056i
$792$	59.0473	−	43.5260i	2.09816	−	1.54663i
$793$	48.6409	−	9.05023i	1.72729	−	0.321383i
$794$	−22.0888	−	9.04613i	−0.783902	−	0.321035i
$795$	47.1697	+	30.6323i	1.67294	+	1.08642i
$796$	−18.7515	−	4.86400i	−0.664631	−	0.172400i
$797$	9.18515	−	0.965398i	0.325355	−	0.0341962i	0.0595568	−	0.998225i	$-0.481031\pi$
$797$	9.18515	−	0.965398i	0.325355	−	0.0341962i	0.265798	+	0.964029i	$0.414365\pi$
$798$	17.4566	−	1.44415i	0.617956	−	0.0511224i
$799$	−4.73867	−	7.29691i	−0.167642	−	0.258146i
$800$	4.54515	+	2.05737i	0.160695	+	0.0727391i
$801$	−17.1648	−	108.374i	−0.606488	−	3.82921i
$802$	−6.42772	+	22.0228i	−0.226971	+	0.777651i
$803$	41.0629	−	5.19306i	1.44908	−	0.183259i
$804$	14.3865	+	65.1167i	0.507371	+	2.29649i
$805$	5.52387	−	7.60296i	0.194691	−	0.267969i
$806$	−8.55689	−	3.76169i	−0.301404	−	0.132500i
$807$	−26.5973	+	8.64198i	−0.936269	+	0.304212i
$808$	17.9046	−	33.9413i	0.629880	−	1.19405i
$809$	−32.7157	−	14.5660i	−1.15022	−	0.512112i	−0.259089	−	0.965853i	$-0.583422\pi$
$809$	−32.7157	−	14.5660i	−1.15022	−	0.512112i	−0.891133	+	0.453742i	$0.850089\pi$
$810$	−2.48452	−	82.2974i	−0.0872971	−	2.89163i
$811$	−40.7067	+	20.7411i	−1.42940	+	0.728318i	−0.985803	−	0.167906i	$-0.946299\pi$
$811$	−40.7067	+	20.7411i	−1.42940	+	0.728318i	−0.443601	+	0.896224i	$0.646299\pi$
$812$	−3.45829	+	0.391480i	−0.121362	+	0.0137382i
$813$	−23.4385	+	6.28032i	−0.822023	+	0.220260i
$814$	0.0166270	−	15.0980i	0.000582776	−	0.529186i
$815$	−35.1903	−	20.3171i	−1.23266	−	0.711677i
$816$	12.6948	+	11.0678i	0.444407	+	0.387451i
$817$	4.86388	+	3.15864i	0.170165	+	0.110507i
$818$	−5.44505	+	3.36676i	−0.190382	+	0.117716i
$819$	18.3129	+	9.92653i	0.639904	+	0.346861i
$820$	5.91512	−	11.8424i	0.206565	−	0.413553i
$821$	−1.03060	−	19.6650i	−0.0359681	−	0.686312i	−0.955803	−	0.294007i	$-0.905011\pi$
$821$	−1.03060	−	19.6650i	−0.0359681	−	0.686312i	0.919835	−	0.392305i	$-0.128322\pi$
$822$	37.1168	+	77.0226i	1.29460	+	2.68647i
$823$	−28.6507	+	12.7561i	−0.998701	+	0.444650i	−0.839947	−	0.542668i	$-0.817414\pi$
$823$	−28.6507	+	12.7561i	−0.998701	+	0.444650i	−0.158753	+	0.987318i	$0.550747\pi$
$824$	42.2344	+	2.81437i	1.47131	+	0.0980434i
$825$	−8.47906	+	4.54790i	−0.295203	+	0.158337i
$826$	4.67029	−	2.56000i	0.162500	−	0.0890739i
$827$	1.65543	−	0.262194i	0.0575649	−	0.00911739i	−0.127586	−	0.991828i	$-0.540723\pi$
$827$	1.65543	−	0.262194i	0.0575649	−	0.00911739i	0.185150	+	0.982710i	$0.440723\pi$
$828$	34.3988	−	91.8005i	1.19544	−	3.19029i
$829$	−6.83477	−	6.15405i	−0.237381	−	0.213739i	0.541851	−	0.840475i	$-0.317724\pi$
$829$	−6.83477	−	6.15405i	−0.237381	−	0.213739i	−0.779232	+	0.626736i	$0.784391\pi$
$830$	−18.3897	+	12.7475i	−0.638315	+	0.442472i
$831$	−73.5082	+	53.4068i	−2.54997	+	1.85266i
$832$	18.1855	−	22.3895i	0.630469	−	0.776215i
$833$	−2.55299	+	7.85728i	−0.0884557	+	0.272239i
$834$	26.1527	+	19.9020i	0.905594	+	0.689148i
$835$	41.7886	−	24.1267i	1.44615	−	0.834938i
$836$	24.5905	+	23.2004i	0.850481	+	0.802403i
$837$	20.5502	−	20.5502i	0.710320	−	0.710320i
$838$	15.0635	+	1.92187i	0.520360	+	0.0663900i
$839$	11.6214	+	0.609054i	0.401217	+	0.0210269i	0.251877	−	0.967759i	$-0.418952\pi$
$839$	11.6214	+	0.609054i	0.401217	+	0.0210269i	0.149339	+	0.988786i	$0.452285\pi$
$840$	3.41875	+	13.5230i	0.117958	+	0.466590i
$841$	2.45140	+	23.3235i	0.0845311	+	0.804260i
$842$	2.63982	−	14.5682i	0.0909741	−	0.502053i
$843$	5.55402	+	105.977i	0.191291	+	3.65004i
$844$	1.57386	+	9.44716i	0.0541746	+	0.325185i
$845$	−0.0368747	−	26.3808i	−0.00126853	−	0.907528i
$846$	−17.8398	−	73.0200i	−0.613345	−	2.51048i
$847$	−1.60847	−	7.96606i	−0.0552675	−	0.273717i
$848$	−33.5711	−	2.98620i	−1.15284	−	0.102547i
$849$	2.70326	+	6.07162i	0.0927757	+	0.208378i
$850$	−1.04174	−	1.20988i	−0.0357313	−	0.0414987i
$851$	−10.9893	−	16.9220i	−0.376708	−	0.580080i
$852$	−6.84802	+	33.5345i	−0.234609	+	1.14887i
$853$	−2.83586	−	0.449156i	−0.0970981	−	0.0153788i	0.107696	−	0.994184i	$-0.465653\pi$
$853$	−2.83586	−	0.449156i	−0.0970981	−	0.0153788i	−0.204794	+	0.978805i	$0.565653\pi$
$854$	−0.432635	−	14.3306i	−0.0148045	−	0.490384i
$855$	79.1101	−	16.8154i	2.70551	−	0.575073i
$856$	−37.4743	−	6.48127i	−1.28084	−	0.221525i
$857$			31.0297i			1.05996i	0.848012	+	0.529978i	$0.177800\pi$
$857$			31.0297i			1.05996i	−0.848012	+	0.529978i	$0.822200\pi$
$858$	12.9643	+	54.0960i	0.442594	+	1.84681i
$859$			53.8802i			1.83837i	0.393826	+	0.919185i	$0.371151\pi$
$859$			53.8802i			1.83837i	−0.393826	+	0.919185i	$0.628849\pi$
$860$	−1.84460	+	4.23389i	−0.0629004	+	0.144374i
$861$	−7.75301	+	1.64795i	−0.264222	+	0.0561621i
$862$	11.2492	−	0.339607i	0.383148	−	0.0115671i
$863$	−24.3949	−	3.86377i	−0.830412	−	0.131524i	−0.273265	−	0.961939i	$-0.588104\pi$
$863$	−24.3949	−	3.86377i	−0.830412	−	0.131524i	−0.557146	+	0.830414i	$0.688104\pi$
$864$	44.3609	+	77.9434i	1.50919	+	2.65169i
$865$	−0.902377	−	1.38954i	−0.0306817	−	0.0472457i
$866$	−27.5069	+	23.6841i	−0.934724	+	0.804819i
$867$	20.5521	+	46.1607i	0.697985	+	1.56770i
$868$	−1.45702	+	2.28340i	−0.0494545	+	0.0775038i
$869$	31.3468	+	0.980897i	1.06337	+	0.0332747i
$870$	−21.5997	+	5.27711i	−0.732299	+	0.178911i
$871$	−35.9415	−	6.63538i	−1.21783	−	0.224831i
$872$	−10.3336	−	24.1245i	−0.349940	−	0.816959i
$873$	−3.51058	−	66.9859i	−0.118815	−	2.26713i
$874$	44.4569	+	8.05577i	1.50378	+	0.272491i
$875$	−0.921786	−	8.77021i	−0.0311620	−	0.296487i
$876$	0.656853	+	82.0964i	0.0221930	+	2.77378i
$877$	30.5278	+	1.59990i	1.03085	+	0.0540247i	0.560252	−	0.828322i	$-0.310704\pi$
$877$	30.5278	+	1.59990i	1.03085	+	0.0540247i	0.470600	+	0.882347i	$0.344038\pi$
$878$	−2.35345	+	18.4461i	−0.0794250	+	0.622527i
$879$	30.4333	−	30.4333i	1.02649	−	1.02649i
$880$	−15.0059	+	22.3517i	−0.505847	+	0.753477i
$881$	1.08239	−	0.624918i	0.0364667	−	0.0210540i	−0.481656	−	0.876360i	$-0.659964\pi$
$881$	1.08239	−	0.624918i	0.0364667	−	0.0210540i	0.518123	+	0.855306i	$0.326631\pi$
$882$	−43.2238	+	56.7994i	−1.45542	+	1.91254i
$883$	−4.10494	+	12.6337i	−0.138142	+	0.425159i	−0.996066	−	0.0886195i	$-0.971754\pi$
$883$	−4.10494	+	12.6337i	−0.138142	+	0.425159i	0.857923	+	0.513778i	$0.171754\pi$
$884$	−8.29646	+	4.04618i	−0.279040	+	0.136088i
$885$	27.5272	−	19.9997i	0.925316	−	0.672282i
$886$	−23.1398	−	33.3818i	−0.777398	−	1.12148i
$887$	−16.1366	−	14.5294i	−0.541812	−	0.487850i	0.352180	−	0.935932i	$-0.385441\pi$
$887$	−16.1366	−	14.5294i	−0.541812	−	0.487850i	−0.893992	+	0.448082i	$0.852107\pi$
$888$	29.7363	+	3.55235i	0.997884	+	0.119209i
$889$	−3.53823	+	0.560400i	−0.118668	+	0.0187952i
$890$	19.3562	+	35.3120i	0.648821	+	1.18366i
$891$	−94.2738	−	12.9010i	−3.15829	−	0.432200i
$892$	−7.44788	+	23.5620i	−0.249374	+	0.788915i
$893$	31.6475	−	14.0904i	1.05904	−	0.471517i
$894$	24.9947	−	12.0448i	0.835948	−	0.402839i
$895$	−1.77841	−	33.9340i	−0.0594456	−	1.13429i
$896$	−5.60430	−	6.20144i	−0.187227	−	0.207176i
$897$	53.9613	+	51.1357i	1.80171	+	1.70737i
$898$	9.93556	+	16.0687i	0.331554	+	0.536220i
$899$	−3.62123	−	2.35165i	−0.120775	−	0.0784320i
$900$	−5.04599	−	12.8373i	−0.168200	−	0.427910i
$901$	9.34056	+	5.39278i	0.311179	+	0.179659i
$902$	−12.3666	−	9.00568i	−0.411763	−	0.299856i
$903$	2.67106	−	0.715709i	0.0888874	−	0.0238173i
$904$	26.3581	−	9.69144i	0.876658	−	0.322332i
$905$	13.0601	−	6.65445i	0.434132	−	0.221201i
$906$	10.3775	−	0.313291i	0.344769	−	0.0104084i
$907$	1.55102	+	0.690557i	0.0515007	+	0.0229296i	0.432325	−	0.901718i	$-0.357693\pi$
$907$	1.55102	+	0.690557i	0.0515007	+	0.0229296i	−0.380825	+	0.924647i	$0.624360\pi$
$908$	−1.56588	+	1.76731i	−0.0519654	+	0.0586504i
$909$	−100.901	+	32.7847i	−3.34667	+	1.08740i
$910$	−7.55611	−	1.16040i	−0.250483	−	0.0384668i
$911$	−14.1893	+	19.5299i	−0.470113	+	0.647054i	−0.976567	−	0.215212i	$-0.930956\pi$
$911$	−14.1893	+	19.5299i	−0.470113	+	0.647054i	0.506455	+	0.862267i	$0.330956\pi$
$912$	−51.4327	+	43.0301i	−1.70311	+	1.42487i
$913$	11.0135	+	23.3966i	0.364492	+	0.774316i
$914$	−52.9443	−	15.4527i	−1.75124	−	0.511130i
$915$	−14.3287	−	90.4679i	−0.473693	−	2.99078i
$916$	−33.9105	+	15.4242i	−1.12043	+	0.509629i
$917$	0.0614293	+	0.0945928i	0.00202857	+	0.00312373i
$918$	−2.36618	−	28.6019i	−0.0780957	−	0.944004i
$919$	38.2054	−	4.01555i	1.26028	−	0.132461i	0.549272	−	0.835644i	$-0.314905\pi$
$919$	38.2054	−	4.01555i	1.26028	−	0.132461i	0.711009	+	0.703183i	$0.248238\pi$
$920$	−0.510110	+	35.9748i	−0.0168178	+	1.18605i
$921$	1.11432	+	0.723648i	0.0367181	+	0.0238450i
$922$	−6.95555	+	16.9840i	−0.229069	+	0.559339i
$923$	−15.4667	−	10.6141i	−0.509093	−	0.349366i
$924$	16.0665	−	1.31134i	0.528550	−	0.0431399i
$925$	−2.74221	−	0.734774i	−0.0901635	−	0.0241592i
$926$	−25.8543	+	3.50906i	−0.849625	+	0.115315i
$927$	−78.3049	−	86.9664i	−2.57187	−	2.85635i
$928$	9.95675	−	8.85433i	0.326846	−	0.290658i
$929$	25.7426	+	20.8459i	0.844587	+	0.683933i	0.950595	−	0.310433i	$-0.100474\pi$
$929$	25.7426	+	20.8459i	0.844587	+	0.683933i	−0.106009	+	0.994365i	$0.533807\pi$
$930$	−7.38735	+	15.6487i	−0.242241	+	0.513141i
$931$	−29.3096	−	14.9340i	−0.960582	−	0.489441i
$932$	−26.0843	−	9.77412i	−0.854421	−	0.320162i
$933$	−47.9871	−	5.04365i	−1.57103	−	0.165122i
$934$	53.4132	+	1.18487i	1.74773	+	0.0387703i
$935$	7.36856	−	4.46391i	0.240978	−	0.145986i
$936$	−79.1972	+	9.34230i	−2.58864	+	0.305363i
$937$	−12.1134	−	8.80090i	−0.395727	−	0.287513i	0.372071	−	0.928204i	$-0.378648\pi$
$937$	−12.1134	−	8.80090i	−0.395727	−	0.287513i	−0.767798	+	0.640691i	$0.778648\pi$
$938$	−3.49545	+	9.99777i	−0.114130	+	0.326439i
$939$	−36.5572	−	32.9163i	−1.19300	−	1.07418i
$940$	15.2093	+	23.0151i	0.496074	+	0.750669i
$941$	2.66822	−	16.8465i	0.0869814	−	0.549179i	−0.905261	−	0.424857i	$-0.860324\pi$
$941$	2.66822	−	16.8465i	0.0869814	−	0.549179i	0.992242	−	0.124322i	$-0.0396756\pi$
$942$	−23.8535	−	22.4554i	−0.777189	−	0.731638i
$943$	−20.4167	−	1.06999i	−0.664858	−	0.0348437i
$944$	−8.96483	+	18.3131i	−0.291780	+	0.596041i
$945$	11.8845	−	20.5845i	0.386601	−	0.669613i
$946$	4.47296	+	2.91178i	0.145428	+	0.0946702i
$947$	−10.4392	−	2.79718i	−0.339229	−	0.0908963i	0.0851828	−	0.996365i	$-0.472853\pi$
$947$	−10.4392	−	2.79718i	−0.339229	−	0.0908963i	−0.424412	+	0.905469i	$0.639519\pi$
$948$	−9.23962	+	61.5182i	−0.300089	+	1.99802i
$949$	−41.5826	−	17.1900i	−1.34983	−	0.558012i
$950$	5.40689	−	3.34317i	0.175423	−	0.108467i
$951$	11.7889	+	30.7112i	0.382282	+	0.995878i
$952$	0.790421	+	2.55539i	0.0256177	+	0.0828207i
$953$	−0.400921	+	1.88618i	−0.0129871	+	0.0610995i	−0.984164	−	0.177261i	$-0.943276\pi$
$953$	−0.400921	+	1.88618i	−0.0129871	+	0.0610995i	0.971177	+	0.238360i	$0.0766098\pi$
$954$	60.7990	+	70.6125i	1.96844	+	2.28617i
$955$	5.93775	+	2.27929i	0.192141	+	0.0737560i
$956$	9.92204	+	10.8438i	0.320902	+	0.350713i
$957$	1.88541	+	25.6272i	0.0609465	+	0.828410i
$958$	31.3334	+	9.14519i	1.01234	+	0.295468i
$959$	−1.41939	+	13.5046i	−0.0458345	+	0.436086i
$960$	−40.5304	−	34.7691i	−1.30811	−	1.12217i
$961$	26.2868	−	8.54110i	0.847962	−	0.275519i
$962$	−8.13977	+	14.2528i	−0.262437	+	0.459527i
$963$	61.8018	+	85.0629i	1.99153	+	2.74111i
$964$	−14.3384	−	24.3822i	−0.461808	−	0.785297i
$965$	−15.8879	+	3.37708i	−0.511450	+	0.108712i
$966$	17.0385	−	13.1827i	0.548205	−	0.424148i
$967$	4.45236	+	4.45236i	0.143178	+	0.143178i	0.775063	−	0.631884i	$-0.217718\pi$
$967$	4.45236	+	4.45236i	0.143178	+	0.143178i	−0.631884	+	0.775063i	$0.717718\pi$
$968$	22.6068	+	21.3760i	0.726611	+	0.687049i
$969$	20.7284	−	5.55416i	0.665893	−	0.178425i
$970$	9.51164	+	22.7058i	0.305401	+	0.729039i
$971$	−16.8790	+	15.1979i	−0.541673	+	0.487725i	−0.893947	−	0.448172i	$-0.852075\pi$
$971$	−16.8790	+	15.1979i	−0.541673	+	0.487725i	0.352274	+	0.935897i	$0.385408\pi$
$972$	23.5054	−	90.6171i	0.753935	−	2.90655i
$973$	1.87049	+	4.87279i	0.0599651	+	0.156215i
$974$	−2.12546	+	2.50885i	−0.0681041	+	0.0803886i
$975$	10.4565	+	0.266501i	0.334877	+	0.00853487i
$976$	32.9690	+	43.8837i	1.05531	+	1.40468i
$977$	−20.8489	−	25.7463i	−0.667016	−	0.823696i	0.325535	−	0.945530i	$-0.394456\pi$
$977$	−20.8489	−	25.7463i	−0.667016	−	0.823696i	−0.992550	+	0.121834i	$0.961122\pi$
$978$	−64.3882	−	67.3097i	−2.05891	−	2.15233i
$979$	43.9474	−	15.3107i	1.40456	−	0.489333i
$980$	7.89507	−	24.9767i	0.252199	−	0.797853i
$981$	−26.0026	+	67.7391i	−0.830200	+	2.16274i
$982$	−42.1802	+	7.99231i	−1.34603	+	0.255045i
$983$	−7.30700	−	3.72310i	−0.233057	−	0.118749i	0.333563	−	0.942728i	$-0.391749\pi$
$983$	−7.30700	−	3.72310i	−0.233057	−	0.118749i	−0.566620	+	0.823979i	$0.691749\pi$
$984$	20.6223	−	22.2604i	0.657414	−	0.709635i
$985$	−10.0275	+	22.5222i	−0.319504	+	0.717617i
$986$	−4.08345	+	1.22736i	−0.130043	+	0.0390872i
$987$	5.10436	−	15.7096i	0.162474	−	0.500043i
$988$	−10.7445	−	35.1471i	−0.341828	−	1.11818i
$989$	7.13271			0.226807
$990$	72.8210	−	15.3948i	2.31440	−	0.489278i
$991$	52.4178	−	30.2634i	1.66510	−	0.961349i	0.694885	−	0.719120i	$-0.255455\pi$
$991$	52.4178	−	30.2634i	1.66510	−	0.961349i	0.970219	−	0.242228i	$-0.0778783\pi$
$992$	−0.478729	−	10.3588i	−0.0151997	−	0.328891i
$993$	1.52876	+	3.00037i	0.0485139	+	0.0952138i
$994$	−3.72598	+	3.95796i	−0.118181	+	0.125539i
$995$	−15.2755	−	12.3698i	−0.484265	−	0.392150i
$996$	−48.6542	+	16.2402i	−1.54167	+	0.514590i
$997$	57.5851	+	12.2401i	1.82374	+	0.387648i	0.987100	−	0.160106i	$-0.0511836\pi$
$997$	57.5851	+	12.2401i	1.82374	+	0.387648i	0.836640	+	0.547754i	$0.184517\pi$
$998$	−33.2129	+	16.0051i	−1.05133	+	0.506634i
$999$	−32.1157	−	39.6596i	−1.01610	−	1.25477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bs.a.15.18	✓	1280
4.3	odd	2	inner	572.2.bs.a.15.30	yes	1280
11.3	even	5	inner	572.2.bs.a.223.14	yes	1280
13.7	odd	12	inner	572.2.bs.a.59.4	yes	1280
44.3	odd	10	inner	572.2.bs.a.223.4	yes	1280
52.7	even	12	inner	572.2.bs.a.59.14	yes	1280
143.124	odd	60	inner	572.2.bs.a.267.30	yes	1280
572.267	even	60	inner	572.2.bs.a.267.18	yes	1280

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bs.a.15.18	✓	1280	1.1	even	1	trivial
572.2.bs.a.15.30	yes	1280	4.3	odd	2	inner
572.2.bs.a.59.4	yes	1280	13.7	odd	12	inner
572.2.bs.a.59.14	yes	1280	52.7	even	12	inner
572.2.bs.a.223.4	yes	1280	44.3	odd	10	inner
572.2.bs.a.223.14	yes	1280	11.3	even	5	inner
572.2.bs.a.267.18	yes	1280	572.267	even	60	inner
572.2.bs.a.267.30	yes	1280	143.124	odd	60	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12541 - 0.856423i) q^{2} +(-0.683893 - 3.21746i) q^{3} +(0.533078 + 1.92765i) q^{4} +(-0.317452 + 2.00431i) q^{5} +(-1.98585 + 4.20665i) q^{6} +(-0.619612 + 0.402380i) q^{7} +(1.05095 - 2.62593i) q^{8} +(-7.14372 + 3.18059i) q^{9} +O(q^{10})\)	\(q+(-1.12541 - 0.856423i) q^{2} +(-0.683893 - 3.21746i) q^{3} +(0.533078 + 1.92765i) q^{4} +(-0.317452 + 2.00431i) q^{5} +(-1.98585 + 4.20665i) q^{6} +(-0.619612 + 0.402380i) q^{7} +(1.05095 - 2.62593i) q^{8} +(-7.14372 + 3.18059i) q^{9} +(2.07380 - 1.98379i) q^{10} +(-1.86459 - 2.74287i) q^{11} +(5.83757 - 3.03346i) q^{12} +(0.285400 + 3.59424i) q^{13} +(1.04192 + 0.0778085i) q^{14} +(6.66590 - 0.349345i) q^{15} +(-3.43166 + 2.05517i) q^{16} +(1.27303 - 0.133801i) q^{17} +(10.7635 + 2.53859i) q^{18} +(-0.266740 + 5.08970i) q^{19} +(-4.03284 + 0.456519i) q^{20} +(1.71839 + 1.71839i) q^{21} +(-0.250636 + 4.68371i) q^{22} +(3.13416 + 5.42853i) q^{23} +(-9.16756 - 1.58555i) q^{24} +(0.838792 + 0.272540i) q^{25} +(2.75700 - 4.28940i) q^{26} +(9.31868 + 12.8261i) q^{27} +(-1.10595 - 0.979893i) q^{28} +(1.57608 - 1.75042i) q^{29} +(-7.80103 - 5.31568i) q^{30} +(-0.286767 - 1.81057i) q^{31} +(5.62211 + 0.626047i) q^{32} +(-7.54989 + 7.87507i) q^{33} +(-1.54727 - 0.939675i) q^{34} +(-0.609799 - 1.36963i) q^{35} +(-9.93921 - 12.0751i) q^{36} +(-3.21450 + 0.168465i) q^{37} +(4.65913 - 5.49954i) q^{38} +(11.3691 - 3.37634i) q^{39} +(4.92955 + 2.94005i) q^{40} +(-1.77639 + 2.73540i) q^{41} +(-0.462218 - 3.40556i) q^{42} +(0.568949 - 0.985448i) q^{43} +(4.29331 - 5.05643i) q^{44} +(-4.10710 - 15.3279i) q^{45} +(1.12191 - 8.79347i) q^{46} +(-3.08581 - 6.05624i) q^{47} +(8.95933 + 9.63571i) q^{48} +(-2.62515 + 5.89618i) q^{49} +(-0.710572 - 1.02508i) q^{50} +(-1.30112 - 4.00443i) q^{51} +(-6.77629 + 2.46616i) q^{52} +(6.81671 + 4.95263i) q^{53} +(0.497241 - 22.4153i) q^{54} +(6.08947 - 2.86649i) q^{55} +(0.405438 + 2.04994i) q^{56} +(16.5583 - 2.62258i) q^{57} +(-3.27283 + 0.620136i) q^{58} +(4.27505 - 2.77625i) q^{59} +(4.22686 + 12.6633i) q^{60} +(-1.43435 - 13.6469i) q^{61} +(-1.22789 + 2.28323i) q^{62} +(3.14652 - 4.84522i) q^{63} +(-5.79099 - 5.51946i) q^{64} +(-7.29457 - 0.568966i) q^{65} +(15.2411 - 2.39675i) q^{66} +(-2.62361 + 9.79143i) q^{67} +(0.936547 + 2.38263i) q^{68} +(15.3227 - 13.7966i) q^{69} +(-0.486713 + 2.06364i) q^{70} +(-3.27413 + 4.04321i) q^{71} +(0.844273 + 22.1015i) q^{72} +(-5.66560 + 11.1194i) q^{73} +(3.76190 + 2.56339i) q^{74} +(0.303244 - 2.88517i) q^{75} +(-9.95335 + 2.19903i) q^{76} +(2.25900 + 0.949237i) q^{77} +(-15.6865 - 5.93705i) q^{78} +(-5.55811 + 7.65009i) q^{79} +(-3.02982 - 7.53053i) q^{80} +(19.1970 - 21.3205i) q^{81} +(4.34182 - 1.55709i) q^{82} +(-7.70085 - 1.21970i) q^{83} +(-2.39642 + 4.22849i) q^{84} +(-0.135947 + 2.59403i) q^{85} +(-1.48426 + 0.621768i) q^{86} +(-6.70977 - 3.87389i) q^{87} +(-9.16216 + 2.01365i) q^{88} +(-3.63168 + 13.5536i) q^{89} +(-8.50503 + 20.7676i) q^{90} +(-1.62309 - 2.11219i) q^{91} +(-8.79354 + 8.93539i) q^{92} +(-5.62934 + 2.16090i) q^{93} +(-1.71392 + 9.45848i) q^{94} +(-10.1167 - 2.15036i) q^{95} +(-1.83063 - 18.5171i) q^{96} +(-3.07407 + 8.00823i) q^{97} +(8.00398 - 4.38736i) q^{98} +(22.0440 + 13.6638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9}+O(q^{10}) \) 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9	\( 1280 q - 12 q^{2} - 18 q^{4} - 24 q^{5} - 4 q^{6} - 12 q^{8} - 156 q^{9} - 48 q^{10} - 24 q^{13} - 40 q^{14} + 18 q^{16} - 36 q^{17} - 8 q^{18} + 18 q^{20} - 40 q^{21} - 10 q^{22} - 100 q^{24} - 44 q^{26} - 4 q^{28} - 12 q^{29} - 114 q^{30} - 92 q^{32} - 20 q^{33} + 36 q^{34} - 72 q^{36} - 24 q^{37} + 8 q^{40} + 26 q^{42} - 20 q^{44} - 80 q^{45} + 32 q^{46} + 30 q^{48} - 36 q^{49} - 78 q^{50} + 34 q^{52} - 80 q^{53} - 188 q^{54} - 48 q^{56} - 92 q^{58} + 20 q^{60} - 28 q^{61} + 42 q^{62} - 48 q^{65} + 204 q^{66} + 26 q^{68} - 36 q^{69} + 38 q^{70} - 136 q^{72} - 24 q^{73} - 6 q^{74} - 276 q^{76} - 156 q^{78} - 80 q^{80} + 60 q^{81} + 162 q^{82} - 108 q^{84} + 16 q^{85} - 88 q^{86} + 6 q^{88} - 64 q^{89} - 16 q^{92} + 64 q^{93} + 34 q^{94} + 114 q^{96} - 8 q^{97} - 24 q^{98}+O(q^{100}) \) 1280 * q - 12 * q^2 - 18 * q^4 - 24 * q^5 - 4 * q^6 - 12 * q^8 - 156 * q^9 - 48 * q^10 - 24 * q^13 - 40 * q^14 + 18 * q^16 - 36 * q^17 - 8 * q^18 + 18 * q^20 - 40 * q^21 - 10 * q^22 - 100 * q^24 - 44 * q^26 - 4 * q^28 - 12 * q^29 - 114 * q^30 - 92 * q^32 - 20 * q^33 + 36 * q^34 - 72 * q^36 - 24 * q^37 + 8 * q^40 + 26 * q^42 - 20 * q^44 - 80 * q^45 + 32 * q^46 + 30 * q^48 - 36 * q^49 - 78 * q^50 + 34 * q^52 - 80 * q^53 - 188 * q^54 - 48 * q^56 - 92 * q^58 + 20 * q^60 - 28 * q^61 + 42 * q^62 - 48 * q^65 + 204 * q^66 + 26 * q^68 - 36 * q^69 + 38 * q^70 - 136 * q^72 - 24 * q^73 - 6 * q^74 - 276 * q^76 - 156 * q^78 - 80 * q^80 + 60 * q^81 + 162 * q^82 - 108 * q^84 + 16 * q^85 - 88 * q^86 + 6 * q^88 - 64 * q^89 - 16 * q^92 + 64 * q^93 + 34 * q^94 + 114 * q^96 - 8 * q^97 - 24 * q^98

Introduction

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