LMFDB - Embedded newform 189.2.bd.a.59.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(47,189)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("189.47"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 15])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			59.3
Character	$\chi$	$=$	189.59
Dual form			189.2.bd.a.173.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.679845 + 1.86786i) q^{2} +(-1.58663 - 0.694689i) q^{3} +(-1.49462 - 1.25413i) q^{4} +(2.86600 + 2.40486i) q^{5} +(2.37625 - 2.49133i) q^{6} +(-2.62036 + 0.365676i) q^{7} +(-0.0842052 + 0.0486159i) q^{8} +(2.03481 + 2.20443i) q^{9} +(-6.44036 + 3.71835i) q^{10} +(-0.343883 - 0.409824i) q^{11} +(1.50018 + 3.02814i) q^{12} +(-3.22666 + 3.84539i) q^{13} +(1.09841 - 5.14306i) q^{14} +(-2.87666 - 5.80660i) q^{15} +(-0.711166 - 4.03322i) q^{16} +(-2.26888 - 3.92982i) q^{17} +(-5.50093 + 2.30207i) q^{18} +(-1.04580 - 0.603796i) q^{19} +(-1.26756 - 7.18868i) q^{20} +(4.41158 + 1.24014i) q^{21} +(0.999281 - 0.363709i) q^{22} +(2.84690 + 7.82179i) q^{23} +(0.167376 - 0.0186392i) q^{24} +(1.56236 + 8.86058i) q^{25} +(-4.98901 - 8.64122i) q^{26} +(-1.69711 - 4.91119i) q^{27} +(4.37504 + 2.73973i) q^{28} +(2.30869 + 2.75138i) q^{29} +(12.8016 - 1.42560i) q^{30} +(0.0629483 - 0.0750188i) q^{31} +(7.82546 + 1.37984i) q^{32} +(0.260916 + 0.889133i) q^{33} +(8.88283 - 1.56628i) q^{34} +(-8.38934 - 5.25356i) q^{35} +(-0.276613 - 5.84671i) q^{36} +0.535477 q^{37} +(1.83879 - 1.54293i) q^{38} +(7.79089 - 3.85970i) q^{39} +(-0.358246 - 0.0631685i) q^{40} +(5.79016 + 4.85852i) q^{41} +(-5.31560 + 7.39710i) q^{42} +(-0.0316146 - 0.0115068i) q^{43} +1.04381i q^{44} +(0.530418 + 11.2113i) q^{45} -16.5455 q^{46} +(4.23256 - 3.55154i) q^{47} +(-1.67348 + 6.89328i) q^{48} +(6.73256 - 1.91640i) q^{49} +(-17.6125 - 3.10555i) q^{50} +(0.869881 + 7.81135i) q^{51} +(9.64526 - 1.70072i) q^{52} +(8.57774 + 4.95236i) q^{53} +(10.3272 + 0.168895i) q^{54} -2.00154i q^{55} +(0.202870 - 0.158183i) q^{56} +(1.23986 + 1.68451i) q^{57} +(-6.70874 + 2.44178i) q^{58} +(-0.132324 + 0.750447i) q^{59} +(-2.98275 + 12.2864i) q^{60} +(-4.16506 - 4.96372i) q^{61} +(0.0973295 + 0.168580i) q^{62} +(-6.13805 - 5.03233i) q^{63} +(-3.80200 + 6.58526i) q^{64} +(-18.4952 + 3.26121i) q^{65} +(-1.83816 - 0.117118i) q^{66} +(6.19033 - 2.25310i) q^{67} +(-1.53740 + 8.71905i) q^{68} +(0.916728 - 14.3880i) q^{69} +(15.5164 - 12.0985i) q^{70} +(3.13261 + 1.80861i) q^{71} +(-0.278513 - 0.0867006i) q^{72} -6.65395i q^{73} +(-0.364041 + 1.00019i) q^{74} +(3.67646 - 15.1438i) q^{75} +(0.805838 + 2.21402i) q^{76} +(1.05096 + 0.948137i) q^{77} +(1.91277 + 17.1763i) q^{78} +(4.92306 + 1.79185i) q^{79} +(7.66112 - 13.2694i) q^{80} +(-0.719067 + 8.97123i) q^{81} +(-13.0114 + 7.51215i) q^{82} +(1.39005 - 1.16639i) q^{83} +(-5.03832 - 7.38625i) q^{84} +(2.94804 - 16.7192i) q^{85} +(0.0429861 - 0.0512288i) q^{86} +(-1.75168 - 5.96926i) q^{87} +(0.0488808 + 0.0177911i) q^{88} +(-4.60651 + 7.97870i) q^{89} +(-21.3018 - 6.63122i) q^{90} +(7.04886 - 11.2562i) q^{91} +(5.55454 - 15.2610i) q^{92} +(-0.151991 + 0.0752979i) q^{93} +(3.75629 + 10.3203i) q^{94} +(-1.54523 - 4.24549i) q^{95} +(-11.4576 - 7.62556i) q^{96} +(4.37434 - 12.0184i) q^{97} +(-0.997529 + 13.8783i) q^{98} +(0.203692 - 1.59198i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20}+ \cdots + 96 q^{99}+O(q^{100}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.679845	+	1.86786i	−0.480723	+	1.32078i	0.428152	+	0.903707i	$0.359165\pi$
$2$	−0.679845	+	1.86786i	−0.480723	+	1.32078i	−0.908875	+	0.417069i	$0.863057\pi$
$3$	−1.58663	−	0.694689i	−0.916043	−	0.401079i
$3$	−1.58663	−	0.694689i	−0.916043	−	0.401079i
$4$	−1.49462	−	1.25413i	−0.747309	−	0.627066i
$5$	2.86600	+	2.40486i	1.28171	+	1.07548i	0.993006	+	0.118067i	$0.0376697\pi$
$5$	2.86600	+	2.40486i	1.28171	+	1.07548i	0.288707	+	0.957418i	$0.406775\pi$
$6$	2.37625	−	2.49133i	0.970098	−	1.01708i
$7$	−2.62036	+	0.365676i	−0.990403	+	0.138212i
$7$	−2.62036	+	0.365676i	−0.990403	+	0.138212i
$8$	−0.0842052	+	0.0486159i	−0.0297710	+	0.0171883i
$9$	2.03481	+	2.20443i	0.678271	+	0.734812i
$10$	−6.44036	+	3.71835i	−2.03662	+	1.17584i
$11$	−0.343883	−	0.409824i	−0.103685	−	0.123567i	0.711707	−	0.702477i	$-0.247923\pi$
$11$	−0.343883	−	0.409824i	−0.103685	−	0.123567i	−0.815391	+	0.578910i	$0.803478\pi$
$12$	1.50018	+	3.02814i	0.433064	+	0.874150i
$13$	−3.22666	+	3.84539i	−0.894916	+	1.06652i	0.102504	+	0.994733i	$0.467314\pi$
$13$	−3.22666	+	3.84539i	−0.894916	+	1.06652i	−0.997420	+	0.0717866i	$0.977130\pi$
$14$	1.09841	−	5.14306i	0.293562	−	1.37454i
$15$	−2.87666	−	5.80660i	−0.742750	−	1.49926i
$16$	−0.711166	−	4.03322i	−0.177791	−	1.00831i
$17$	−2.26888	−	3.92982i	−0.550284	−	0.953120i	−0.998254	−	0.0590716i	$-0.981186\pi$
$17$	−2.26888	−	3.92982i	−0.550284	−	0.953120i	0.447969	−	0.894049i	$-0.352147\pi$
$18$	−5.50093	+	2.30207i	−1.29658	+	0.542603i
$19$	−1.04580	−	0.603796i	−0.239924	−	0.138520i	0.375218	−	0.926937i	$-0.377568\pi$
$19$	−1.04580	−	0.603796i	−0.239924	−	0.138520i	−0.615142	+	0.788416i	$0.710901\pi$
$20$	−1.26756	−	7.18868i	−0.283435	−	1.60744i
$21$	4.41158	+	1.24014i	0.962686	+	0.270621i
$22$	0.999281	−	0.363709i	0.213047	−	0.0775429i
$23$	2.84690	+	7.82179i	0.593620	+	1.63096i	0.763733	+	0.645532i	$0.223364\pi$
$23$	2.84690	+	7.82179i	0.593620	+	1.63096i	−0.170114	+	0.985424i	$0.554413\pi$
$24$	0.167376	−	0.0186392i	0.0341654	−	0.00380471i
$25$	1.56236	+	8.86058i	0.312472	+	1.77212i
$26$	−4.98901	−	8.64122i	−0.978426	−	1.69468i
$27$	−1.69711	−	4.91119i	−0.326608	−	0.945160i
$28$	4.37504	+	2.73973i	0.826805	+	0.517761i
$29$	2.30869	+	2.75138i	0.428712	+	0.510919i	0.936550	−	0.350533i	$-0.114000\pi$
$29$	2.30869	+	2.75138i	0.428712	+	0.510919i	−0.507838	+	0.861452i	$0.669555\pi$
$30$	12.8016	−	1.42560i	2.33724	−	0.260278i
$31$	0.0629483	−	0.0750188i	0.0113058	−	0.0134738i	−0.760362	−	0.649500i	$-0.774978\pi$
$31$	0.0629483	−	0.0750188i	0.0113058	−	0.0134738i	0.771668	+	0.636026i	$0.219423\pi$
$32$	7.82546	+	1.37984i	1.38336	+	0.243923i
$33$	0.260916	+	0.889133i	0.0454197	+	0.154778i
$34$	8.88283	−	1.56628i	1.52339	−	0.268615i
$35$	−8.38934	−	5.25356i	−1.41806	−	0.888014i
$36$	−0.276613	−	5.84671i	−0.0461022	−	0.974452i
$37$	0.535477			0.0880319			0.0440159	−	0.999031i	$-0.485985\pi$
$37$	0.535477			0.0880319			0.0440159	+	0.999031i	$0.485985\pi$
$38$	1.83879	−	1.54293i	0.298291	−	0.250296i
$39$	7.79089	−	3.85970i	1.24754	−	0.618046i
$40$	−0.358246	−	0.0631685i	−0.0566437	−	0.00998781i
$41$	5.79016	+	4.85852i	0.904271	+	0.758773i	0.971020	−	0.238997i	$-0.0768185\pi$
$41$	5.79016	+	4.85852i	0.904271	+	0.758773i	−0.0667499	+	0.997770i	$0.521263\pi$
$42$	−5.31560	+	7.39710i	−0.820215	+	1.14140i
$43$	−0.0316146	−	0.0115068i	−0.00482118	−	0.00175477i	0.339608	−	0.940567i	$-0.389705\pi$
$43$	−0.0316146	−	0.0115068i	−0.00482118	−	0.00175477i	−0.344430	+	0.938812i	$0.611928\pi$
$44$			1.04381i			0.157360i
$45$	0.530418	+	11.2113i	0.0790701	+	1.67129i
$46$	−16.5455			−2.43949
$47$	4.23256	−	3.55154i	0.617382	−	0.518045i	−0.279597	−	0.960117i	$-0.590201\pi$
$47$	4.23256	−	3.55154i	0.617382	−	0.518045i	0.896979	+	0.442072i	$0.145756\pi$
$48$	−1.67348	+	6.89328i	−0.241545	+	0.994960i
$49$	6.73256	−	1.91640i	0.961795	−	0.273772i
$50$	−17.6125	−	3.10555i	−2.49078	−	0.439191i
$51$	0.869881	+	7.81135i	0.121808	+	1.09381i
$52$	9.64526	−	1.70072i	1.33756	−	0.235847i
$53$	8.57774	+	4.95236i	1.17824	+	0.680259i	0.955608	−	0.294642i	$-0.0952005\pi$
$53$	8.57774	+	4.95236i	1.17824	+	0.680259i	0.222636	+	0.974902i	$0.428534\pi$
$54$	10.3272	+	0.168895i	1.40535	+	0.0229837i
$55$		−	2.00154i		−	0.269888i
$56$	0.202870	−	0.158183i	0.0271097	−	0.0211381i
$57$	1.23986	+	1.68451i	0.164223	+	0.223119i
$58$	−6.70874	+	2.44178i	−0.880901	+	0.320622i
$59$	−0.132324	+	0.750447i	−0.0172271	+	0.0976999i	−0.992209	−	0.124584i	$-0.960240\pi$
$59$	−0.132324	+	0.750447i	−0.0172271	+	0.0976999i	0.974982	+	0.222284i	$0.0713513\pi$
$60$	−2.98275	+	12.2864i	−0.385071	+	1.58616i
$61$	−4.16506	−	4.96372i	−0.533281	−	0.635539i	0.430387	−	0.902645i	$-0.358377\pi$
$61$	−4.16506	−	4.96372i	−0.533281	−	0.635539i	−0.963667	+	0.267105i	$0.913933\pi$
$62$	0.0973295	+	0.168580i	0.0123609	+	0.0214096i
$63$	−6.13805	−	5.03233i	−0.773322	−	0.634014i
$64$	−3.80200	+	6.58526i	−0.475250	+	0.823158i
$65$	−18.4952	+	3.26121i	−2.29405	+	0.404503i
$66$	−1.83816	−	0.117118i	−0.226262	−	0.0144162i
$67$	6.19033	−	2.25310i	0.756270	−	0.275260i	0.0650282	−	0.997883i	$-0.479286\pi$
$67$	6.19033	−	2.25310i	0.756270	−	0.275260i	0.691242	+	0.722624i	$0.257064\pi$
$68$	−1.53740	+	8.71905i	−0.186438	+	1.05734i
$69$	0.916728	−	14.3880i	0.110361	−	1.73212i
$70$	15.5164	−	12.0985i	1.85456	−	1.44605i
$71$	3.13261	+	1.80861i	0.371772	+	0.214643i	0.674232	−	0.738519i	$-0.264475\pi$
$71$	3.13261	+	1.80861i	0.371772	+	0.214643i	−0.302460	+	0.953162i	$0.597808\pi$
$72$	−0.278513	−	0.0867006i	−0.0328230	−	0.0102178i
$73$		−	6.65395i		−	0.778786i	−0.921072	−	0.389393i	$-0.872685\pi$
$73$		−	6.65395i		−	0.778786i	0.921072	−	0.389393i	$-0.127315\pi$
$74$	−0.364041	+	1.00019i	−0.0423189	+	0.116270i
$75$	3.67646	−	15.1438i	0.424521	−	1.74866i
$76$	0.805838	+	2.21402i	0.0924360	+	0.253966i
$77$	1.05096	+	0.948137i	0.119768	+	0.108050i
$78$	1.91277	+	17.1763i	0.216579	+	1.94483i
$79$	4.92306	+	1.79185i	0.553887	+	0.201598i	0.603773	−	0.797157i	$-0.293663\pi$
$79$	4.92306	+	1.79185i	0.553887	+	0.201598i	−0.0498856	+	0.998755i	$0.515886\pi$
$80$	7.66112	−	13.2694i	0.856539	−	1.48357i
$81$	−0.719067	+	8.97123i	−0.0798964	+	0.996803i
$82$	−13.0114	+	7.51215i	−1.43687	+	0.829579i
$83$	1.39005	−	1.16639i	0.152578	−	0.128028i	−0.563303	−	0.826250i	$-0.690470\pi$
$83$	1.39005	−	1.16639i	0.152578	−	0.128028i	0.715881	+	0.698222i	$0.246025\pi$
$84$	−5.03832	−	7.38625i	−0.549726	−	0.805905i
$85$	2.94804	−	16.7192i	0.319760	−	1.81345i
$86$	0.0429861	−	0.0512288i	0.00463531	−	0.00552414i
$87$	−1.75168	−	5.96926i	−0.187800	−	0.639972i
$88$	0.0488808	+	0.0177911i	0.00521071	+	0.00189654i
$89$	−4.60651	+	7.97870i	−0.488289	+	0.845741i	−0.999909	−	0.0134707i	$-0.995712\pi$
$89$	−4.60651	+	7.97870i	−0.488289	+	0.845741i	0.511621	+	0.859211i	$0.329045\pi$
$90$	−21.3018	−	6.63122i	−2.24541	−	0.698992i
$91$	7.04886	−	11.2562i	0.738921	−	1.17997i
$92$	5.55454	−	15.2610i	0.579101	−	1.59107i
$93$	−0.151991	+	0.0752979i	−0.0157607	+	0.00780803i
$94$	3.75629	+	10.3203i	0.387432	+	1.06446i
$95$	−1.54523	−	4.24549i	−0.158537	−	0.435578i
$96$	−11.4576	−	7.62556i	−1.16938	−	0.778281i
$97$	4.37434	−	12.0184i	0.444147	−	1.22028i	−0.492593	−	0.870260i	$-0.663951\pi$
$97$	4.37434	−	12.0184i	0.444147	−	1.22028i	0.936741	−	0.350025i	$-0.113827\pi$
$98$	−0.997529	+	13.8783i	−0.100766	+	1.40192i
$99$	0.203692	−	1.59198i	0.0204719	−	0.160000i
$100$	8.77721	−	15.2026i	0.877721	−	1.52026i
$101$	−2.00251	−	0.728853i	−0.199257	−	0.0725235i	0.240464	−	0.970658i	$-0.422700\pi$
$101$	−2.00251	−	0.728853i	−0.199257	−	0.0725235i	−0.439721	+	0.898135i	$0.644923\pi$
$102$	−15.1819	−	3.68569i	−1.50323	−	0.364938i
$103$	−7.67148	+	9.14251i	−0.755893	+	0.900839i	−0.997581	−	0.0695155i	$-0.977855\pi$
$103$	−7.67148	+	9.14251i	−0.755893	+	0.900839i	0.241687	+	0.970354i	$0.422299\pi$
$104$	0.0847549	−	0.480669i	0.00831091	−	0.0471335i
$105$	9.66121	+	14.1635i	0.942838	+	1.38221i
$106$	−15.0818	+	12.6552i	−1.46488	+	1.22918i
$107$	−13.4523	+	7.76670i	−1.30048	+	0.750835i	−0.980487	−	0.196583i	$-0.937015\pi$
$107$	−13.4523	+	7.76670i	−1.30048	+	0.750835i	−0.319998	+	0.947418i	$0.603682\pi$
$108$	−3.62276	+	9.46875i	−0.348601	+	0.911131i
$109$	−1.01428	+	1.75678i	−0.0971503	+	0.168269i	−0.910504	−	0.413500i	$-0.864306\pi$
$109$	−1.01428	+	1.75678i	−0.0971503	+	0.168269i	0.813354	+	0.581770i	$0.197639\pi$
$110$	3.73860	+	1.36074i	0.356462	+	0.129741i
$111$	−0.849606	−	0.371990i	−0.0806410	−	0.0353077i
$112$	3.33836	+	10.3084i	0.315445	+	0.974055i
$113$	−2.57486	−	7.07437i	−0.242222	−	0.665501i	−0.999917	−	0.0128913i	$-0.995896\pi$
$113$	−2.57486	−	7.07437i	−0.242222	−	0.665501i	0.757694	−	0.652610i	$-0.226326\pi$
$114$	−3.98934	+	1.17067i	−0.373636	+	0.109644i
$115$	−10.6511	+	29.2636i	−0.993219	+	2.72885i
$116$		−	7.00766i		−	0.650645i
$117$	−15.0426	+	0.711678i	−1.39069	+	0.0657946i
$118$	−1.31177	−	0.757350i	−0.120758	−	0.0697197i
$119$	7.38232	+	9.46786i	0.676736	+	0.867917i
$120$	0.524523	+	0.349095i	0.0478822	+	0.0318679i
$121$	1.86043	−	10.5510i	0.169130	−	0.959184i
$122$	12.1031	−	4.40518i	1.09576	−	0.398826i
$123$	−5.81170	−	11.7310i	−0.524023	−	1.05775i
$124$	−0.188167	+	0.0331789i	−0.0168979	+	0.00297956i
$125$	−7.47747	+	12.9514i	−0.668805	+	1.15840i
$126$	13.5726	−	8.04381i	1.20914	−	0.716599i
$127$	9.23798	+	16.0006i	0.819738	+	1.41983i	0.905875	+	0.423545i	$0.139214\pi$
$127$	9.23798	+	16.0006i	0.819738	+	1.41983i	−0.0861371	+	0.996283i	$0.527452\pi$
$128$	0.499846	+	0.595693i	0.0441805	+	0.0526523i
$129$	0.0421672	+	0.0402194i	0.00371261	+	0.00354112i
$130$	6.48241	−	36.7636i	0.568545	−	3.22438i
$131$	0.539709	−	0.196438i	0.0471546	−	0.0171629i	−0.318335	−	0.947978i	$-0.603124\pi$
$131$	0.539709	−	0.196438i	0.0471546	−	0.0171629i	0.365490	+	0.930815i	$0.380902\pi$
$132$	0.725121	−	1.65614i	0.0631137	−	0.144148i
$133$	2.96118	+	1.19974i	0.256767	+	0.104030i
$134$			13.0944i			1.13119i
$135$	6.94681	−	18.1568i	0.597887	−	1.56269i
$136$	0.382103	+	0.220607i	0.0327651	+	0.0189169i
$137$	2.30208	−	0.405919i	0.196680	−	0.0346800i	−0.0744402	−	0.997225i	$-0.523717\pi$
$137$	2.30208	−	0.405919i	0.196680	−	0.0346800i	0.271120	+	0.962545i	$0.412606\pi$
$138$	26.2516	+	11.4939i	2.23468	+	0.978430i
$139$	−0.461702	−	0.0814105i	−0.0391610	−	0.00690515i	0.154033	−	0.988066i	$-0.450774\pi$
$139$	−0.461702	−	0.0814105i	−0.0391610	−	0.00690515i	−0.193194	+	0.981161i	$0.561885\pi$
$140$	5.95018	+	18.3734i	0.502882	+	1.55284i
$141$	−9.18274	+	2.69468i	−0.773326	+	0.226933i
$142$	−5.50791	+	4.62169i	−0.462214	+	0.387844i
$143$	2.68553			0.224575
$144$	7.44388	−	9.77457i	0.620324	−	0.814547i
$145$			13.4375i			1.11592i
$146$	12.4286	+	4.52365i	1.02860	+	0.374380i
$147$	−12.0134	−	1.63641i	−0.990850	−	0.134969i
$148$	−0.800333	−	0.671559i	−0.0657870	−	0.0552018i
$149$	10.1157	+	1.78368i	0.828712	+	0.146124i	0.571886	−	0.820333i	$-0.306212\pi$
$149$	10.1157	+	1.78368i	0.828712	+	0.146124i	0.256827	+	0.966458i	$0.417323\pi$
$150$	25.7871	+	17.1626i	2.10551	+	1.40132i
$151$	0.437964	−	0.367495i	0.0356410	−	0.0299063i	−0.624793	−	0.780790i	$-0.714817\pi$
$151$	0.437964	−	0.367495i	0.0356410	−	0.0299063i	0.660434	+	0.750884i	$0.270372\pi$
$152$	0.117416			0.00952372
$153$	4.04628	−	12.9980i	0.327122	−	1.05083i
$154$	−2.48548	+	1.31846i	−0.200285	+	0.106245i
$155$	0.360819	−	0.0636221i	0.0289817	−	0.00511025i
$156$	−16.4850	−	4.00204i	−1.31985	−	0.320420i
$157$	−7.80658	−	1.37651i	−0.623033	−	0.109858i	−0.146785	−	0.989168i	$-0.546893\pi$
$157$	−7.80658	−	1.37651i	−0.623033	−	0.109858i	−0.476248	+	0.879311i	$0.658004\pi$
$158$	−6.69383	+	7.97739i	−0.532532	+	0.634647i
$159$	−10.1694	−	13.8165i	−0.806485	−	1.09572i
$160$	19.1094	+	22.7737i	1.51073	+	1.80042i
$161$	−10.3201	−	19.4549i	−0.813341	−	1.53326i
$162$	−16.2681	−	7.44216i	−1.27815	−	0.584711i
$163$	−2.96576	−	5.13684i	−0.232296	−	0.402349i	0.726187	−	0.687497i	$-0.241290\pi$
$163$	−2.96576	−	5.13684i	−0.232296	−	0.402349i	−0.958483	+	0.285148i	$0.907957\pi$
$164$	−2.56084	−	14.5232i	−0.199968	−	1.13408i
$165$	−1.39045	+	3.17572i	−0.108247	+	0.247229i
$166$	1.23363	+	3.38938i	0.0957485	+	0.263067i
$167$	−10.6282	+	3.86836i	−0.822438	+	0.299343i	−0.718752	−	0.695267i	$-0.755286\pi$
$167$	−10.6282	+	3.86836i	−0.822438	+	0.299343i	−0.103687	+	0.994610i	$0.533064\pi$
$168$	−0.431769	+	0.110047i	−0.0333117	+	0.00849028i
$169$	−2.11823	−	12.0131i	−0.162941	−	0.924082i
$170$	29.2248	+	16.8730i	2.24144	+	1.29410i
$171$	−0.796990	−	3.53402i	−0.0609473	−	0.270253i
$172$	0.0328207	+	0.0568472i	0.00250256	+	0.00433455i
$173$	1.79123	+	10.1586i	0.136185	+	0.772342i	0.974027	+	0.226430i	$0.0727055\pi$
$173$	1.79123	+	10.1586i	0.136185	+	0.772342i	−0.837843	+	0.545912i	$0.816183\pi$
$174$	12.3406	+	0.786277i	0.935538	+	0.0596075i
$175$	−7.33404	−	22.6466i	−0.554401	−	1.71192i
$176$	−1.40835	+	1.67841i	−0.106159	+	0.126515i
$177$	0.731277	−	1.09876i	0.0549662	−	0.0825879i
$178$	−11.7714	−	14.0286i	−0.882302	−	1.05149i
$179$	−6.49945	+	3.75246i	−0.485792	+	0.280472i	−0.722827	−	0.691029i	$-0.757158\pi$
$179$	−6.49945	+	3.75246i	−0.485792	+	0.280472i	0.237035	+	0.971501i	$0.423824\pi$
$180$	13.2677	−	17.4219i	0.988918	−	1.29855i
$181$	−15.7096	+	9.06992i	−1.16768	+	0.674162i	−0.953133	−	0.302552i	$-0.902162\pi$
$181$	−15.7096	+	9.06992i	−1.16768	+	0.674162i	−0.214549	+	0.976713i	$0.568828\pi$
$182$	16.2329	+	20.8187i	1.20326	+	1.54319i
$183$	3.16018	+	10.7690i	0.233607	+	0.796069i
$184$	−0.619987	−	0.520231i	−0.0457061	−	0.0383520i
$185$	1.53467	+	1.28774i	0.112832	+	0.0946769i
$186$	−0.0373158	−	0.335088i	−0.00273613	−	0.0245698i
$187$	−0.830304	+	2.28124i	−0.0607178	+	0.166821i
$188$	−10.7802			−0.786224
$189$	6.24293	+	12.2485i	0.454107	+	0.890947i
$190$	8.98049			0.651513
$191$	4.07115	−	11.1854i	0.294578	−	0.809346i	−0.700804	−	0.713354i	$-0.747175\pi$
$191$	4.07115	−	11.1854i	0.294578	−	0.809346i	0.995382	−	0.0959923i	$-0.0306024\pi$
$192$	10.6071	−	7.80719i	0.765501	−	0.563435i
$193$	−5.64453	−	4.73632i	−0.406302	−	0.340928i	0.416622	−	0.909080i	$-0.363214\pi$
$193$	−5.64453	−	4.73632i	−0.406302	−	0.340928i	−0.822923	+	0.568152i	$0.807658\pi$
$194$	19.4748	+	16.3413i	1.39821	+	1.17324i
$195$	31.6107	+	7.67409i	2.26369	+	0.549553i
$196$	−12.4660	−	5.57924i	−0.890430	−	0.398517i
$197$	7.81959	−	4.51464i	0.557123	−	0.321655i	−0.194867	−	0.980830i	$-0.562428\pi$
$197$	7.81959	−	4.51464i	0.557123	−	0.321655i	0.751990	+	0.659175i	$0.229094\pi$
$198$	2.83512	+	1.46277i	0.201483	+	0.103955i
$199$	23.4627	−	13.5462i	1.66323	−	0.960264i	0.692067	−	0.721833i	$-0.256700\pi$
$199$	23.4627	−	13.5462i	1.66323	−	0.960264i	0.971159	−	0.238431i	$-0.0766330\pi$
$200$	−0.562324	−	0.670151i	−0.0397623	−	0.0473869i
$201$	−11.3870	−	0.725518i	−0.803177	−	0.0511741i
$202$	2.72279	−	3.24489i	0.191575	−	0.228310i
$203$	−7.05570	−	6.36538i	−0.495213	−	0.446762i
$204$	8.49633	−	12.7659i	0.594862	−	0.893793i
$205$	4.91053	+	27.8490i	0.342966	+	1.94506i
$206$	−11.8615	−	20.5447i	−0.826430	−	1.43142i
$207$	−11.4497	+	22.1917i	−0.795811	+	1.54243i
$208$	17.8040	+	10.2791i	1.23448	+	0.712730i
$209$	0.112185	+	0.636232i	0.00775998	+	0.0440091i
$210$	−33.0235	+	8.41682i	−2.27884	+	0.580816i
$211$	4.05592	−	1.47623i	0.279221	−	0.101628i	−0.198614	−	0.980078i	$-0.563644\pi$
$211$	4.05592	−	1.47623i	0.279221	−	0.101628i	0.477835	+	0.878450i	$0.341422\pi$
$212$	−6.60952	−	18.1595i	−0.453944	−	1.24720i
$213$	−3.71388	−	5.04579i	−0.254471	−	0.345732i
$214$	−5.36161	−	30.4072i	−0.366512	−	2.07859i
$215$	−0.0629352	−	0.109007i	−0.00429215	−	0.00743421i
$216$	0.381667	+	0.331042i	0.0259692	+	0.0225245i
$217$	−0.137515	+	0.219595i	−0.00933509	+	0.0149071i
$218$	−2.59187	−	3.08887i	−0.175544	−	0.209205i
$219$	−4.62243	+	10.5574i	−0.312355	+	0.713402i
$220$	−2.51020	+	2.99154i	−0.169238	+	0.201690i
$221$	22.4326	+	3.95547i	1.50898	+	0.266074i
$222$	1.27242	−	1.33405i	0.0853996	−	0.0895354i
$223$	−1.40482	+	0.247708i	−0.0940737	+	0.0165877i	−0.220487	−	0.975390i	$-0.570765\pi$
$223$	−1.40482	+	0.247708i	−0.0940737	+	0.0165877i	0.126413	+	0.991978i	$0.459653\pi$
$224$	−21.0101	−	0.754095i	−1.40380	−	0.0503851i
$225$	−16.3535	+	21.4737i	−1.09023	+	1.43158i
$226$	14.9644			0.995419
$227$	14.8550	−	12.4649i	0.985963	−	0.827321i	0.000984837	−	1.00000i	$-0.499687\pi$
$227$	14.8550	−	12.4649i	0.985963	−	0.827321i	0.984978	+	0.172678i	$0.0552421\pi$
$228$	0.259487	−	4.07265i	0.0171850	−	0.269718i
$229$	2.54233	+	0.448282i	0.168002	+	0.0296233i	0.257016	−	0.966407i	$-0.417261\pi$
$229$	2.54233	+	0.448282i	0.168002	+	0.0296233i	−0.0890143	+	0.996030i	$0.528372\pi$
$230$	−47.4192	−	39.7894i	−3.12673	−	2.62364i
$231$	−1.00883	−	2.23444i	−0.0663761	−	0.147015i
$232$	−0.328164	−	0.119442i	−0.0215450	−	0.00784176i
$233$		−	24.4282i		−	1.60035i	−0.599770	−	0.800173i	$-0.704741\pi$
$233$		−	24.4282i		−	1.60035i	0.599770	−	0.800173i	$-0.295259\pi$
$234$	8.89730	−	28.5812i	0.581635	−	1.86841i
$235$	20.6714			1.34846
$236$	1.13893	−	0.955679i	0.0741383	−	0.0622094i
$237$	−6.56631	−	6.26300i	−0.426528	−	0.406825i
$238$	−22.7034	+	7.35245i	−1.47165	+	0.476589i
$239$	−23.2178	−	4.09392i	−1.50183	−	0.264813i	−0.638568	−	0.769566i	$-0.720473\pi$
$239$	−23.2178	−	4.09392i	−1.50183	−	0.264813i	−0.863264	+	0.504752i	$0.831584\pi$
$240$	−21.3735	+	15.7317i	−1.37966	+	1.01547i
$241$	−9.44310	+	1.66507i	−0.608284	+	0.107257i	−0.469301	−	0.883038i	$-0.655494\pi$
$241$	−9.44310	+	1.66507i	−0.608284	+	0.107257i	−0.138982	+	0.990295i	$0.544383\pi$
$242$	18.4430	+	10.6481i	1.18556	+	0.684484i
$243$	7.37311	−	13.7345i	0.472985	−	0.881070i
$244$			12.6424i			0.809346i
$245$	23.9042	+	10.6984i	1.52718	+	0.683498i
$246$	25.8630	−	2.88013i	1.64896	−	0.183631i
$247$	5.69629	−	2.07328i	0.362446	−	0.131920i
$248$	−0.00165346	+	0.00937727i	−0.000104995	+	0.000595457i
$249$	−3.01578	+	0.884982i	−0.191117	+	0.0560834i
$250$	−19.1078	−	22.7718i	−1.20848	−	1.44021i
$251$	6.84105	+	11.8491i	0.431803	+	0.747906i	0.997029	−	0.0770311i	$-0.0245441\pi$
$251$	6.84105	+	11.8491i	0.431803	+	0.747906i	−0.565225	+	0.824937i	$0.691211\pi$
$252$	2.86283	+	15.2193i	0.180341	+	0.958728i
$253$	2.22656	−	3.85651i	0.139983	−	0.242457i
$254$	−36.1673	+	6.37728i	−2.26934	+	0.400146i
$255$	−16.2921	+	24.4792i	−1.02025	+	1.53295i
$256$	−15.7433	+	5.73011i	−0.983959	+	0.358132i
$257$	5.31836	−	30.1619i	0.331750	−	1.88145i	−0.125471	−	0.992097i	$-0.540044\pi$
$257$	5.31836	−	30.1619i	0.331750	−	1.88145i	0.457222	−	0.889353i	$-0.348845\pi$
$258$	−0.103791	+	0.0514194i	−0.00646176	+	0.00320123i
$259$	−1.40314	+	0.195811i	−0.0871870	+	0.0121671i
$260$	31.7333	+	18.3212i	1.96801	+	1.13623i
$261$	−1.36750	+	10.6879i	−0.0846463	+	0.661564i
$262$			1.14165i			0.0705312i
$263$	1.24570	−	3.42255i	0.0768135	−	0.211043i	−0.895342	−	0.445379i	$-0.853069\pi$
$263$	1.24570	−	3.42255i	0.0768135	−	0.211043i	0.972156	+	0.234335i	$0.0752913\pi$
$264$	−0.0651966	−	0.0621850i	−0.00401257	−	0.00382722i
$265$	12.6741	+	34.8217i	0.778561	+	2.13908i
$266$	−4.25408	+	4.71543i	−0.260834	+	0.289121i
$267$	12.8516	−	9.45919i	0.786503	−	0.578893i
$268$	−12.0779	−	4.39598i	−0.737773	−	0.268527i
$269$	−16.1461	+	27.9659i	−0.984446	+	1.70511i	−0.340071	+	0.940400i	$0.610451\pi$
$269$	−16.1461	+	27.9659i	−0.984446	+	1.70511i	−0.644374	+	0.764710i	$0.722882\pi$
$270$	29.1915	+	25.3194i	1.77654	+	1.54089i
$271$	21.4767	−	12.3996i	1.30462	−	0.753220i	0.323424	−	0.946254i	$-0.395166\pi$
$271$	21.4767	−	12.3996i	1.30462	−	0.753220i	0.981192	+	0.193034i	$0.0618328\pi$
$272$	−14.2363	+	11.9456i	−0.863200	+	0.724311i
$273$	−19.0035	+	12.9627i	−1.15015	+	0.784540i
$274$	−0.806859	+	4.57593i	−0.0487441	+	0.276442i
$275$	3.09401	−	3.68730i	0.186576	−	0.222352i
$276$	−19.4147	+	20.3549i	−1.16862	+	1.22522i
$277$	14.7443	+	5.36648i	0.885898	+	0.322441i	0.744588	−	0.667525i	$-0.232646\pi$
$277$	14.7443	+	5.36648i	0.885898	+	0.322441i	0.141311	+	0.989965i	$0.454868\pi$
$278$	0.465949	−	0.807047i	0.0279457	−	0.0484035i
$279$	0.293462	−	0.0138840i	0.0175691	−	0.000831211i
$280$	0.961833	+	0.0345222i	0.0574805	+	0.00206309i
$281$	4.41595	−	12.1327i	0.263433	−	0.723777i	−0.735497	−	0.677528i	$-0.763051\pi$
$281$	4.41595	−	12.1327i	0.263433	−	0.723777i	0.998930	−	0.0462486i	$-0.0147266\pi$
$282$	1.20956	−	18.9840i	0.0720282	−	1.13048i
$283$	7.78805	+	21.3975i	0.462952	+	1.27195i	0.923255	+	0.384188i	$0.125518\pi$
$283$	7.78805	+	21.3975i	0.462952	+	1.27195i	−0.460303	+	0.887762i	$0.652259\pi$
$284$	−2.41381	−	6.63188i	−0.143233	−	0.393530i
$285$	−0.497579	+	7.80949i	−0.0294740	+	0.462594i
$286$	−1.82574	+	5.01619i	−0.107959	+	0.296614i
$287$	−16.9489	−	10.6137i	−1.00046	−	0.626509i
$288$	12.8816	+	20.0584i	0.759054	+	1.18195i
$289$	−1.79564	+	3.11014i	−0.105626	+	0.182949i
$290$	−25.0994	−	9.13542i	−1.47389	−	0.536450i
$291$	−15.2895	+	16.0300i	−0.896288	+	0.939695i
$292$	−8.34494	+	9.94511i	−0.488351	+	0.581993i
$293$	−0.0377838	+	0.214282i	−0.00220735	+	0.0125185i	−0.985892	−	0.167385i	$-0.946468\pi$
$293$	−0.0377838	+	0.214282i	−0.00220735	+	0.0125185i	0.983684	+	0.179904i	$0.0575787\pi$
$294$	11.2238	−	21.3269i	0.654588	−	1.24381i
$295$	−2.18396	+	1.83256i	−0.127155	+	0.106696i
$296$	−0.0450900	+	0.0260327i	−0.00262080	+	0.00151312i
$297$	−1.42912	+	2.38439i	−0.0829259	+	0.138357i
$298$	−10.2088	+	17.6821i	−0.591379	+	1.02430i
$299$	−39.2638	−	14.2909i	−2.27069	−	0.826462i
$300$	−24.4873	+	18.0235i	−1.41377	+	1.04059i
$301$	0.0870494	+	0.0185912i	0.00501744	+	0.00107158i
$302$	0.388682	+	1.06789i	0.0223661	+	0.0614504i
$303$	2.67092	+	2.54754i	0.153440	+	0.146352i
$304$	−1.69150	+	4.64736i	−0.0970142	+	0.266544i
$305$		−	24.2424i		−	1.38811i
$306$	21.5277	+	16.3945i	1.23065	+	0.937213i
$307$	−17.3825	−	10.0358i	−0.992072	−	0.572773i	−0.0861792	−	0.996280i	$-0.527466\pi$
$307$	−17.3825	−	10.0358i	−0.992072	−	0.572773i	−0.905893	+	0.423506i	$0.860799\pi$
$308$	−0.381694	−	2.73515i	−0.0217491	−	0.155849i
$309$	18.5230	−	9.17653i	1.05374	−	0.522034i
$310$	−0.126464	+	0.717212i	−0.00718266	+	0.0407349i
$311$	−0.186479	+	0.0678730i	−0.0105743	+	0.00384872i	−0.347302	−	0.937753i	$-0.612902\pi$
$311$	−0.186479	+	0.0678730i	−0.0105743	+	0.00384872i	0.336728	+	0.941602i	$0.390680\pi$
$312$	−0.468391	+	0.703768i	−0.0265174	+	0.0398430i
$313$	16.1381	−	2.84559i	0.912182	−	0.160842i	0.302188	−	0.953248i	$-0.402283\pi$
$313$	16.1381	−	2.84559i	0.912182	−	0.160842i	0.609994	+	0.792406i	$0.291172\pi$
$314$	7.87839	−	13.6458i	0.444604	−	0.770076i
$315$	−5.48960	−	29.1838i	−0.309304	−	1.64432i
$316$	−5.11087	−	8.85229i	−0.287509	−	0.497980i
$317$	−9.00259	−	10.7289i	−0.505636	−	0.602593i	0.451486	−	0.892278i	$-0.350894\pi$
$317$	−9.00259	−	10.7289i	−0.505636	−	0.602593i	−0.957122	+	0.289685i	$0.906449\pi$
$318$	32.7208	−	9.60193i	1.83489	−	0.538449i
$319$	0.333665	−	1.89231i	0.0186817	−	0.105949i
$320$	−26.7331	+	9.73006i	−1.49443	+	0.543927i
$321$	26.7394	−	2.97773i	1.49245	−	0.166201i
$322$	43.3550	−	6.05027i	2.41608	−	0.337168i
$323$			5.47976i			0.304902i
$324$	12.3258	−	12.5067i	0.684769	−	0.694819i
$325$	−39.1136	−	22.5822i	−2.16963	−	1.25264i
$326$	11.6111	−	2.04736i	0.643082	−	0.113393i
$327$	2.82971	−	2.08276i	0.156483	−	0.115177i
$328$	−0.723763	−	0.127619i	−0.0399631	−	0.00704658i
$329$	−9.79211	+	10.8541i	−0.539857	+	0.598403i
$330$	−4.98650	−	4.75616i	−0.274498	−	0.261818i
$331$	−11.2116	+	9.40767i	−0.616247	+	0.517092i	−0.896621	−	0.442798i	$-0.853986\pi$
$331$	−11.2116	+	9.40767i	−0.616247	+	0.517092i	0.280374	+	0.959891i	$0.409541\pi$
$332$	−3.54040			−0.194305
$333$	1.08960	+	1.18042i	0.0597095	+	0.0646868i
$334$		−	22.4819i		−	1.23016i
$335$	23.1598	+	8.42950i	1.26536	+	0.460553i
$336$	1.86440	−	18.6748i	0.101711	−	1.01880i
$337$	15.3298	+	12.8633i	0.835070	+	0.700707i	0.956449	−	0.291899i	$-0.0942873\pi$
$337$	15.3298	+	12.8633i	0.835070	+	0.700707i	−0.121379	+	0.992606i	$0.538732\pi$
$338$	23.8788	+	4.21047i	1.29883	+	0.229019i
$339$	−0.829129	+	13.0132i	−0.0450321	+	0.706778i
$340$	−25.3742	+	21.2915i	−1.37611	+	1.15469i
$341$	−0.0523914			−0.00283715
$342$	7.14288	+	0.913922i	0.386243	+	0.0494193i
$343$	−16.9409	+	7.48360i	−0.914725	+	0.404076i
$344$	0.00322153		0.000568042i	0.000173693		3.06268e-5i
$345$	37.2285	−	39.0314i	2.00431	−	2.10138i
$346$	−20.1925	−	3.56049i	−1.08556	−	0.191413i
$347$	−6.94916	+	8.28168i	−0.373050	+	0.444584i	−0.919608	−	0.392838i	$-0.871493\pi$
$347$	−6.94916	+	8.28168i	−0.373050	+	0.444584i	0.546558	+	0.837421i	$0.315938\pi$
$348$	−4.86815	+	11.1186i	−0.260960	+	0.596019i
$349$	−18.8455	−	22.4591i	−1.00877	−	1.20221i	−0.979252	−	0.202646i	$-0.935046\pi$
$349$	−18.8455	−	22.4591i	−1.00877	−	1.20221i	−0.0295221	−	0.999564i	$-0.509399\pi$
$350$	47.2866	+	1.69721i	2.52758	+	0.0907199i
$351$	24.3614	+	9.32074i	1.30032	+	0.497504i
$352$	−2.12555	−	3.68157i	−0.113292	−	0.196228i
$353$	3.50173	+	19.8593i	0.186378	+	1.05700i	0.924172	+	0.381977i	$0.124757\pi$
$353$	3.50173	+	19.8593i	0.186378	+	1.05700i	−0.737793	+	0.675026i	$0.764132\pi$
$354$	1.55517	+	2.11291i	0.0826566	+	0.112300i
$355$	4.62859	+	12.7169i	0.245660	+	0.674945i
$356$	16.8913	−	6.14794i	0.895238	−	0.325840i
$357$	−5.13582	−	20.1504i	−0.271816	−	1.06647i
$358$	−2.59045	−	14.6911i	−0.136909	−	0.776451i
$359$	−14.4933	−	8.36769i	−0.764925	−	0.441630i	0.0661360	−	0.997811i	$-0.478933\pi$
$359$	−14.4933	−	8.36769i	−0.764925	−	0.441630i	−0.831061	+	0.556181i	$0.812266\pi$
$360$	−0.589713	−	0.918266i	−0.0310806	−	0.0483969i
$361$	−8.77086	−	15.1916i	−0.461624	−	0.799557i
$362$	−6.26126	−	35.5094i	−0.329084	−	1.86633i
$363$	−10.2815	+	15.4482i	−0.539639	+	0.810820i
$364$	−24.6521	+	7.98353i	−1.29212	+	0.418451i
$365$	16.0018	−	19.0702i	0.837572	−	0.998180i
$366$	−22.2634	−	1.41851i	−1.16373	−	0.0741466i
$367$	−5.29020	−	6.30462i	−0.276146	−	0.329098i	0.610090	−	0.792332i	$-0.291133\pi$
$367$	−5.29020	−	6.30462i	−0.276146	−	0.329098i	−0.886236	+	0.463234i	$0.846689\pi$
$368$	29.5224	−	17.0448i	1.53896	−	0.888520i
$369$	1.07160	+	22.6502i	0.0557854	+	1.17912i
$370$	−3.44867	+	1.99109i	−0.179288	+	0.103512i
$371$	−24.2877	−	9.84030i	−1.26096	−	0.510883i
$372$	0.321601	+	0.0780749i	0.0166743	+	0.00404799i
$373$	11.5003	+	9.64991i	0.595464	+	0.499653i	0.889984	−	0.455992i	$-0.150715\pi$
$373$	11.5003	+	9.64991i	0.595464	+	0.499653i	−0.294520	+	0.955645i	$0.595160\pi$
$374$	−3.69656	−	3.10178i	−0.191144	−	0.160389i
$375$	20.8612	−	15.3545i	1.07727	−	0.792905i
$376$	−0.183742	+	0.504828i	−0.00947579	+	0.0260345i
$377$	−18.0295			−0.928566
$378$	−27.1227	+	3.33383i	−1.39504	+	0.171474i
$379$	−23.6638			−1.21553			−0.607763	−	0.794118i	$-0.707933\pi$
$379$	−23.6638			−1.21553			−0.607763	+	0.794118i	$0.707933\pi$
$380$	−3.01488	+	8.28330i	−0.154660	+	0.424924i
$381$	−3.54181	−	31.8047i	−0.181452	−	1.62940i
$382$	18.1250	+	15.2087i	0.927354	+	0.778142i
$383$	−1.47519	−	1.23783i	−0.0753789	−	0.0632504i	0.604320	−	0.796742i	$-0.293445\pi$
$383$	−1.47519	−	1.23783i	−0.0753789	−	0.0632504i	−0.679699	+	0.733492i	$0.737889\pi$
$384$	−0.379251	−	1.29238i	−0.0193536	−	0.0659517i
$385$	0.731916	+	5.24477i	0.0373019	+	0.267298i
$386$	12.6842	−	7.32321i	0.645608	−	0.372742i
$387$	−0.0389639	−	0.0931065i	−0.00198065	−	0.00473287i
$388$	−21.6106	+	12.4769i	−1.09711	+	0.633419i
$389$	18.3028	+	21.8124i	0.927986	+	1.10593i	0.994138	+	0.108122i	$0.0344836\pi$
$389$	18.3028	+	21.8124i	0.927986	+	1.10593i	−0.0661512	+	0.997810i	$0.521072\pi$
$390$	−35.8245	+	53.8270i	−1.81404	+	2.72564i
$391$	24.2789	−	28.9345i	1.22784	−	1.46328i
$392$	−0.473749	+	0.488681i	−0.0239280	+	0.0246821i
$393$	−0.992784	−	0.0632549i	−0.0500793	−	0.00319079i
$394$	3.11661	+	17.6751i	0.157012	+	0.890461i
$395$	9.80033	+	16.9747i	0.493108	+	0.854088i
$396$	−2.30100	+	2.12395i	−0.115630	+	0.106733i
$397$	15.3758	+	8.87725i	0.771692	+	0.445536i	0.833478	−	0.552553i	$-0.186346\pi$
$397$	15.3758	+	8.87725i	0.771692	+	0.445536i	−0.0617862	+	0.998089i	$0.519680\pi$
$398$	9.35138	+	53.0343i	0.468742	+	2.65837i
$399$	−3.86486	−	3.96064i	−0.193485	−	0.198280i
$400$	34.6256	−	12.6027i	1.73128	−	0.630134i
$401$	8.25703	+	22.6860i	0.412336	+	1.13288i	0.955945	+	0.293546i	$0.0948353\pi$
$401$	8.25703	+	22.6860i	0.412336	+	1.13288i	−0.543609	+	0.839339i	$0.682942\pi$
$402$	9.09656	−	20.7761i	0.453695	−	1.03622i
$403$	0.0853636	+	0.484121i	0.00425227	+	0.0241158i
$404$	2.07890	+	3.60076i	0.103429	+	0.179145i
$405$	−23.6354	+	23.9823i	−1.17445	+	1.19169i
$406$	16.6864	−	8.85157i	0.828133	−	0.439296i
$407$	−0.184142	−	0.219451i	−0.00912756	−	0.0108778i
$408$	−0.453004	−	0.615466i	−0.0224271	−	0.0304701i
$409$	12.2257	−	14.5700i	0.604520	−	0.720439i	−0.373806	−	0.927507i	$-0.621948\pi$
$409$	12.2257	−	14.5700i	0.604520	−	0.720439i	0.978327	+	0.207067i	$0.0663919\pi$
$410$	−55.3564	−	9.76082i	−2.73386	−	0.482053i
$411$	−3.93455	−	0.955187i	−0.194077	−	0.0471159i
$412$	22.9319	−	4.04350i	1.12977	−	0.199209i
$413$	0.0723164	−	2.01483i	0.00355846	−	0.0991432i
$414$	−33.6669	−	36.4734i	−1.65464	−	1.79257i
$415$	6.78888			0.333253
$416$	−30.5561	+	25.6397i	−1.49814	+	1.25709i
$417$	0.675997	+	0.449908i	0.0331037	+	0.0220321i
$418$	−1.26466	−	0.222993i	−0.0618565	−	0.0109070i
$419$	24.5217	+	20.5762i	1.19796	+	1.00521i	0.999686	+	0.0250662i	$0.00797965\pi$
$419$	24.5217	+	20.5762i	1.19796	+	1.00521i	0.198279	+	0.980146i	$0.436465\pi$
$420$	3.32305	−	33.2854i	0.162148	−	1.62416i
$421$	−11.0428	−	4.01925i	−0.538193	−	0.195886i	0.0585997	−	0.998282i	$-0.481336\pi$
$421$	−11.0428	−	4.01925i	−0.538193	−	0.195886i	−0.596793	+	0.802395i	$0.703559\pi$
$422$			8.57949i			0.417643i
$423$	16.4416	+	2.10368i	0.799418	+	0.102285i
$424$	−0.963054			−0.0467701
$425$	31.2756	−	26.2434i	1.51709	−	1.27299i
$426$	11.9497	−	3.50664i	0.578964	−	0.169897i
$427$	12.7291	+	11.4837i	0.616002	+	0.555734i
$428$	29.8465	+	5.26275i	1.44269	+	0.254385i
$429$	−4.26095	−	1.86561i	−0.205721	−	0.0900725i
$430$	0.246396	−	0.0434462i	0.0118823	−	0.00209516i
$431$	8.85449	+	5.11214i	0.426506	+	0.246243i	0.697857	−	0.716237i	$-0.254137\pi$
$431$	8.85449	+	5.11214i	0.426506	+	0.246243i	−0.271351	+	0.962480i	$0.587470\pi$
$432$	−18.6010	+	10.3375i	−0.894941	+	0.497362i
$433$		−	2.62462i		−	0.126131i	−0.998009	−	0.0630656i	$-0.979912\pi$
$433$		−	2.62462i		−	0.126131i	0.998009	−	0.0630656i	$-0.0200877\pi$
$434$	−0.316684	−	0.406148i	−0.0152013	−	0.0194957i
$435$	9.33489	−	21.3204i	0.447574	−	1.02224i
$436$	3.71920	−	1.35368i	0.178117	−	0.0648294i
$437$	1.74546	−	9.89901i	0.0834968	−	0.473534i
$438$	−16.5772	−	15.8114i	−0.792088	−	0.755499i
$439$	0.583853	+	0.695809i	0.0278658	+	0.0332092i	0.779797	−	0.626032i	$-0.215322\pi$
$439$	0.583853	+	0.695809i	0.0278658	+	0.0332092i	−0.751932	+	0.659241i	$0.770878\pi$
$440$	0.0973069	+	0.168541i	0.00463893	+	0.00803486i
$441$	17.9241	+	10.9420i	0.853528	+	0.521046i
$442$	−22.6389	+	39.2118i	−1.07682	+	1.86512i
$443$	11.5051	−	2.02865i	0.546622	−	0.0963842i	0.106484	−	0.994314i	$-0.466041\pi$
$443$	11.5051	−	2.02865i	0.546622	−	0.0963842i	0.440138	+	0.897930i	$0.354930\pi$
$444$	0.803310	+	1.62150i	0.0381234	+	0.0769530i
$445$	−32.3899	+	11.7889i	−1.53543	+	0.558850i
$446$	0.492377	−	2.79241i	0.0233147	−	0.132224i
$447$	−14.8109	−	9.85732i	−0.700529	−	0.466235i
$448$	7.55454	−	18.6460i	0.356919	−	0.880943i
$449$	8.77509	+	5.06630i	0.414122	+	0.239094i	0.692559	−	0.721361i	$-0.256483\pi$
$449$	8.77509	+	5.06630i	0.414122	+	0.239094i	−0.278437	+	0.960454i	$0.589816\pi$
$450$	−28.9921	−	45.1448i	−1.36670	−	2.12814i
$451$		−	4.04371i		−	0.190411i
$452$	−5.02377	+	13.8027i	−0.236298	+	0.649224i
$453$	−0.950183	+	0.278832i	−0.0446435	+	0.0131007i
$454$	13.1835	+	36.2213i	0.618731	+	1.69995i
$455$	47.2716	−	15.3088i	2.21613	−	0.717687i
$456$	−0.186297	−	0.0815679i	−0.00872414	−	0.00381977i
$457$	−25.9278	−	9.43695i	−1.21285	−	0.441442i	−0.345159	−	0.938544i	$-0.612175\pi$
$457$	−25.9278	−	9.43695i	−1.21285	−	0.441442i	−0.867692	+	0.497102i	$0.834397\pi$
$458$	−2.56572	+	4.44395i	−0.119888	+	0.207652i
$459$	−15.4496	+	17.8122i	−0.721124	+	0.831404i
$460$	52.6197	−	30.3800i	2.45341	−	1.41648i
$461$	−14.3944	+	12.0783i	−0.670413	+	0.562543i	−0.913188	−	0.407540i	$-0.866387\pi$
$461$	−14.3944	+	12.0783i	−0.670413	+	0.562543i	0.242775	+	0.970083i	$0.421942\pi$
$462$	4.85946	−	0.365279i	0.226083	−	0.0169943i
$463$	0.164111	−	0.930721i	0.00762690	−	0.0432543i	−0.980757	−	0.195233i	$-0.937454\pi$
$463$	0.164111	−	0.930721i	0.00762690	−	0.0432543i	0.988384	+	0.151979i	$0.0485647\pi$
$464$	9.45508	−	11.2681i	0.438941	−	0.523110i
$465$	−0.616685	−	0.149712i	−0.0285981	−	0.00694273i
$466$	45.6284	+	16.6074i	2.11370	+	0.769323i
$467$	−5.26428	+	9.11801i	−0.243602	+	0.421931i	−0.961738	−	0.273972i	$-0.911662\pi$
$467$	−5.26428	+	9.11801i	−0.243602	+	0.421931i	0.718136	+	0.695903i	$0.244996\pi$
$468$	23.3754	+	17.8017i	1.08053	+	0.822884i
$469$	−15.3970	+	8.16758i	−0.710967	+	0.377144i
$470$	−14.0534	+	38.6113i	−0.648234	+	1.78101i
$471$	11.4299	+	7.60717i	0.526664	+	0.350520i
$472$	−0.0253413	−	0.0696246i	−0.00116643	−	0.00320473i
$473$	0.00615598	+	0.0169134i	0.000283052	+	0.000777680i
$474$	16.1625	−	8.00707i	0.742367	−	0.367777i
$475$	3.71606	−	10.2098i	0.170504	−	0.468457i
$476$	0.840206	−	23.4092i	0.0385108	−	1.07296i
$477$	6.53695	+	28.9862i	0.299306	+	1.32719i
$478$	23.4313	−	40.5843i	1.07172	−	1.85628i
$479$	−4.15179	−	1.51113i	−0.189700	−	0.0690452i	0.245423	−	0.969416i	$-0.421073\pi$
$479$	−4.15179	−	1.51113i	−0.189700	−	0.0690452i	−0.435123	+	0.900371i	$0.643295\pi$
$480$	−14.4990	−	49.4086i	−0.661785	−	2.25519i
$481$	−1.72780	+	2.05912i	−0.0787811	+	0.0938877i
$482$	3.30972	−	18.7704i	0.150754	−	0.854967i
$483$	2.85919	+	38.0370i	0.130098	+	1.73074i
$484$	−16.0130	+	13.4365i	−0.727864	+	0.610751i
$485$	41.4394	−	23.9250i	1.88167	−	1.08638i
$486$	20.6416	+	23.1093i	0.936321	+	1.04826i
$487$	17.8504	−	30.9178i	0.808879	−	1.40102i	−0.104761	−	0.994497i	$-0.533408\pi$
$487$	17.8504	−	30.9178i	0.808879	−	1.40102i	0.913641	−	0.406523i	$-0.133259\pi$
$488$	0.592035	+	0.215483i	0.0268002	+	0.00975447i
$489$	1.13706	+	10.2106i	0.0514197	+	0.461738i
$490$	−36.2343	+	37.3763i	−1.63690	+	1.68849i
$491$	7.59387	+	20.8640i	0.342707	+	0.941579i	0.984606	+	0.174790i	$0.0559246\pi$
$491$	7.59387	+	20.8640i	0.342707	+	0.941579i	−0.641899	+	0.766789i	$0.721853\pi$
$492$	−6.02603	+	24.8221i	−0.271674	+	1.11907i
$493$	5.57430	−	15.3153i	0.251054	−	0.689765i
$494$			12.0494i			0.542127i
$495$	4.41227	−	4.07277i	0.198317	−	0.183057i
$496$	−0.347334	−	0.200533i	−0.0155958	−	0.00900422i
$497$	−8.86992	−	3.59369i	−0.397870	−	0.161199i
$498$	0.397242	−	6.23470i	0.0178008	−	0.279383i
$499$	−6.29637	+	35.7085i	−0.281864	+	1.59853i	0.434412	+	0.900714i	$0.356956\pi$
$499$	−6.29637	+	35.7085i	−0.281864	+	1.59853i	−0.716276	+	0.697817i	$0.754155\pi$
$500$	27.4187	−	9.97958i	1.22620	−	0.446300i
$501$	19.5504	+	1.24565i	0.873449	+	0.0556515i
$502$	−26.7832	+	4.72260i	−1.19539	+	0.210780i
$503$	1.90297	−	3.29604i	0.0848491	−	0.146963i	−0.820478	−	0.571678i	$-0.806292\pi$
$503$	1.90297	−	3.29604i	0.0848491	−	0.146963i	0.905327	+	0.424715i	$0.139626\pi$
$504$	0.761507	+	0.125342i	0.0339202	+	0.00558316i
$505$	−3.98639	−	6.90463i	−0.177392	−	0.307252i
$506$	5.68971	+	6.78073i	0.252938	+	0.301440i
$507$	−4.98450	+	20.5318i	−0.221369	+	0.911851i
$508$	6.25970	−	35.5005i	0.277729	−	1.57508i
$509$	−10.0573	+	3.66056i	−0.445782	+	0.162251i	−0.555151	−	0.831750i	$-0.687339\pi$
$509$	−10.0573	+	3.66056i	−0.445782	+	0.162251i	0.109368	+	0.994001i	$0.465117\pi$
$510$	−34.6476	−	47.0734i	−1.53422	−	2.08444i
$511$	2.43319	+	17.4357i	0.107638	+	0.771312i
$512$		−	31.7467i		−	1.40302i
$513$	−1.19052	+	6.16086i	−0.0525626	+	0.272008i
$514$	52.7226	+	30.4394i	2.32549	+	1.34262i
$515$	−43.9729	+	7.75360i	−1.93768	+	0.341665i
$516$	−0.0125834	−	0.112996i	−0.000553951	−	0.00497436i
$517$	−2.91101	−	0.513290i	−0.128026	−	0.0225745i
$518$	0.588172	−	2.75399i	0.0258428	−	0.121003i
$519$	4.21503	−	17.3623i	0.185019	−	0.762120i
$520$	1.39885	−	1.17377i	0.0613435	−	0.0514733i
$521$	41.0842			1.79993			0.899965	−	0.435963i	$-0.143592\pi$
$521$	41.0842			1.79993			0.899965	+	0.435963i	$0.143592\pi$
$522$	−19.0338	−	9.82041i	−0.833086	−	0.429828i
$523$			36.6483i			1.60252i	0.598319	+	0.801258i	$0.295836\pi$
$523$			36.6483i			1.60252i	−0.598319	+	0.801258i	$0.704164\pi$
$524$	−1.05302	−	0.383267i	−0.0460013	−	0.0167431i
$525$	−4.09590	+	41.0267i	−0.178760	+	1.79055i
$526$	5.54595	+	4.65360i	0.241815	+	0.202907i
$527$	−0.437632	−	0.0771664i	−0.0190636	−	0.00336142i
$528$	3.40051	−	1.68465i	0.147988	−	0.0733152i
$529$	−35.4566	+	29.7516i	−1.54159	+	1.29355i
$530$	−73.6584			−3.19952
$531$	−1.92357	+	1.23532i	−0.0834757	+	0.0536083i
$532$	−2.92120	−	5.50686i	−0.126650	−	0.238753i
$533$	−37.3658	+	6.58860i	−1.61849	+	0.285384i
$534$	8.93136	+	30.4357i	0.386498	+	1.31708i
$535$	−57.2321	−	10.0916i	−2.47436	−	0.436296i
$536$	−0.411722	+	0.490671i	−0.0177837	+	0.0211938i
$537$	12.9190	−	1.43868i	0.557498	−	0.0620836i
$538$	−41.2595	−	49.1711i	−1.77882	−	2.11992i
$539$	−3.10060	−	2.10015i	−0.133553	−	0.0904598i
$540$	−33.1538	+	18.4252i	−1.42671	+	0.792893i
$541$	−17.5845	−	30.4573i	−0.756018	−	1.30946i	−0.944867	−	0.327455i	$-0.893809\pi$
$541$	−17.5845	−	30.4573i	−0.756018	−	1.30946i	0.188849	−	0.982006i	$-0.439524\pi$
$542$	8.55983	+	48.5452i	0.367676	+	2.08519i
$543$	31.2261	−	3.47738i	1.34004	−	0.149228i
$544$	−12.3325	−	33.8833i	−0.528752	−	1.45273i
$545$	−7.13173	+	2.59574i	−0.305490	+	0.111189i
$546$	−11.2931	−	44.3085i	−0.483300	−	1.89623i
$547$	−5.94589	−	33.7208i	−0.254228	−	1.44180i	−0.798046	−	0.602596i	$-0.794133\pi$
$547$	−5.94589	−	33.7208i	−0.254228	−	1.44180i	0.543818	−	0.839203i	$-0.316978\pi$
$548$	−3.94981	−	2.28042i	−0.168727	−	0.0974148i
$549$	2.46709	−	19.2818i	0.105293	−	0.822929i
$550$	4.78390	+	8.28596i	0.203986	+	0.353315i
$551$	−0.753160	−	4.27139i	−0.0320857	−	0.181967i
$552$	0.622294	+	1.25612i	0.0264866	+	0.0534638i
$553$	−13.5554	−	2.89504i	−0.576435	−	0.123110i
$554$	−20.0477	+	23.8919i	−0.851743	+	1.01507i
$555$	−1.54038	−	3.10930i	−0.0653857	−	0.131982i
$556$	0.587968	+	0.700713i	0.0249354	+	0.0297168i
$557$	29.7140	−	17.1554i	1.25902	−	0.726897i	0.286139	−	0.958188i	$-0.407628\pi$
$557$	29.7140	−	17.1554i	1.25902	−	0.726897i	0.972885	+	0.231291i	$0.0742949\pi$
$558$	−0.173575	+	0.557585i	−0.00734803	+	0.0236044i
$559$	0.146258	−	0.0844420i	0.00618605	−	0.00357152i
$560$	−15.2226	+	37.5722i	−0.643271	+	1.58771i
$561$	2.90214	−	3.04269i	0.122529	−	0.128462i
$562$	19.6600	+	16.4967i	0.829308	+	0.695872i
$563$	−9.85545	−	8.26971i	−0.415358	−	0.348527i	0.411036	−	0.911619i	$-0.365167\pi$
$563$	−9.85545	−	8.26971i	−0.415358	−	0.348527i	−0.826394	+	0.563093i	$0.809611\pi$
$564$	17.1042	+	7.48886i	0.720215	+	0.315338i
$565$	9.63330	−	26.4673i	0.405276	−	1.11349i
$566$	−45.2622			−1.90251
$567$	−1.39635	−	23.7708i	−0.0586410	−	0.998279i
$568$	−0.351709			−0.0147574
$569$	0.941385	−	2.58643i	0.0394649	−	0.108429i	−0.918395	−	0.395665i	$-0.870514\pi$
$569$	0.941385	−	2.58643i	0.0394649	−	0.108429i	0.957860	+	0.287236i	$0.0927364\pi$
$570$	−14.2487	−	6.23865i	−0.596814	−	0.261308i
$571$	21.1404	+	17.7389i	0.884697	+	0.742349i	0.967139	−	0.254247i	$-0.0818275\pi$
$571$	21.1404	+	17.7389i	0.884697	+	0.742349i	−0.0824421	+	0.996596i	$0.526272\pi$
$572$	−4.01384	−	3.36801i	−0.167827	−	0.140824i
$573$	−14.2298	+	14.9189i	−0.594458	+	0.623247i
$574$	31.3476	−	24.4425i	1.30842	−	1.02021i
$575$	−64.8577	+	37.4456i	−2.70475	+	1.56159i
$576$	−22.2531	+	5.01851i	−0.927214	+	0.209105i
$577$	−7.06990	+	4.08181i	−0.294324	+	0.169928i	−0.639890	−	0.768466i	$-0.721020\pi$
$577$	−7.06990	+	4.08181i	−0.294324	+	0.169928i	0.345566	+	0.938394i	$0.387687\pi$
$578$	−4.58854	−	5.46841i	−0.190858	−	0.227456i
$579$	5.66553	+	11.4360i	0.235451	+	0.475264i
$580$	16.8524	−	20.0839i	0.699759	−	0.833940i
$581$	−3.21591	+	3.56467i	−0.133418	+	0.147887i
$582$	−19.5473	−	39.4566i	−0.810260	−	1.63553i
$583$	−0.920145	−	5.21840i	−0.0381085	−	0.216124i
$584$	0.323488	+	0.560298i	0.0133860	+	0.0231853i
$585$	−44.8234	−	34.1356i	−1.85322	−	1.41133i
$586$	−0.374562	−	0.216253i	−0.0154730	−	0.00893335i
$587$	−4.51916	−	25.6294i	−0.186526	−	1.05784i	−0.923979	−	0.382442i	$-0.875083\pi$
$587$	−4.51916	−	25.6294i	−0.186526	−	1.05784i	0.737454	−	0.675398i	$-0.236028\pi$
$588$	15.9032	+	17.5122i	0.655836	+	0.722192i
$589$	−0.111128	+	0.0404472i	−0.00457894	+	0.00166660i
$590$	−1.93821	−	5.32518i	−0.0797947	−	0.219234i
$591$	−15.5431	+	1.73090i	−0.639358	+	0.0711997i
$592$	−0.380813	−	2.15970i	−0.0156513	−	0.0887630i
$593$	11.0942	+	19.2157i	0.455584	+	0.789095i	0.998722	−	0.0505489i	$-0.0160971\pi$
$593$	11.0942	+	19.2157i	0.455584	+	0.789095i	−0.543137	+	0.839644i	$0.682764\pi$
$594$	−3.48213	−	4.29041i	−0.142874	−	0.176038i
$595$	−1.61113	+	44.8883i	−0.0660500	+	1.84024i
$596$	−12.8822	−	15.3524i	−0.527674	−	0.628858i
$597$	−46.6371	+	5.19357i	−1.90873	+	0.212558i
$598$	53.3866	−	63.6237i	2.18314	−	2.60177i
$599$	−16.1800	−	2.85297i	−0.661097	−	0.116569i	−0.166974	−	0.985961i	$-0.553400\pi$
$599$	−16.1800	−	2.85297i	−0.661097	−	0.116569i	−0.494123	+	0.869392i	$0.664511\pi$
$600$	0.426655	+	1.45393i	0.0174181	+	0.0593562i
$601$	23.4204	−	4.12965i	0.955338	−	0.168452i	0.325815	−	0.945434i	$-0.394361\pi$
$601$	23.4204	−	4.12965i	0.955338	−	0.168452i	0.629523	+	0.776982i	$0.283250\pi$
$602$	−0.0939058	+	0.149957i	−0.00382732	+	0.00611178i
$603$	17.5630	+	9.06156i	0.715220	+	0.369015i
$604$	−1.11548			−0.0453881
$605$	30.7057	−	25.7651i	1.24836	−	1.04750i
$606$	−6.57426	+	3.25696i	−0.267061	+	0.132305i
$607$	20.2257	+	3.56633i	0.820935	+	0.144753i	0.568313	−	0.822812i	$-0.307596\pi$
$607$	20.2257	+	3.56633i	0.820935	+	0.144753i	0.252622	+	0.967565i	$0.418707\pi$
$608$	−7.35076	−	6.16802i	−0.298113	−	0.250146i
$609$	6.77284	+	15.0010i	0.274450	+	0.607873i
$610$	45.2813	+	16.4810i	1.83339	+	0.667298i
$611$			27.7355i			1.12206i
$612$	−22.3489	+	14.3525i	−0.903401	+	0.580167i
$613$	−7.57151			−0.305811			−0.152905	−	0.988241i	$-0.548863\pi$
$613$	−7.57151			−0.305811			−0.152905	+	0.988241i	$0.548863\pi$
$614$	30.5629	−	25.6453i	1.23342	−	1.03496i
$615$	11.5552	−	47.5974i	0.465950	−	1.91931i
$616$	−0.134591	−	0.0287447i	−0.00542282	−	0.00115816i
$617$	−20.9804	−	3.69941i	−0.844639	−	0.148933i	−0.265448	−	0.964125i	$-0.585520\pi$
$617$	−20.9804	−	3.69941i	−0.844639	−	0.148933i	−0.579190	+	0.815192i	$0.696631\pi$
$618$	4.54766	+	40.8370i	0.182934	+	1.64271i
$619$	41.2677	−	7.27661i	1.65869	−	0.292472i	0.735703	−	0.677305i	$-0.236852\pi$
$619$	41.2677	−	7.27661i	1.65869	−	0.292472i	0.922986	+	0.384833i	$0.125741\pi$
$620$	−0.619077	−	0.357424i	−0.0248627	−	0.0143545i
$621$	33.5828	−	27.2561i	1.34763	−	1.09375i
$622$		−	0.394460i		−	0.0158164i
$623$	9.15308	−	22.5916i	0.366711	−	0.905111i
$624$	−21.1076	−	28.6775i	−0.844981	−	1.14802i
$625$	−10.3032	+	3.75006i	−0.412129	+	0.150003i
$626$	−5.65628	+	32.0783i	−0.226070	+	1.28211i
$627$	0.263987	−	1.08740i	0.0105426	−	0.0434266i
$628$	9.94153	+	11.8478i	0.396710	+	0.472781i
$629$	−1.21493	−	2.10433i	−0.0484426	−	0.0839050i
$630$	58.2432	+	9.58664i	2.32047	+	0.381941i
$631$	15.3609	−	26.6058i	0.611507	−	1.05916i	−0.379479	−	0.925200i	$-0.623897\pi$
$631$	15.3609	−	26.6058i	0.611507	−	1.05916i	0.990987	−	0.133961i	$-0.0427698\pi$
$632$	−0.501659	+	0.0884561i	−0.0199549	+	0.00351859i
$633$	−7.46078	−	0.475361i	−0.296539	−	0.0188939i
$634$	26.1604	−	9.52159i	1.03896	−	0.378151i
$635$	−12.0032	+	68.0738i	−0.476334	+	2.70143i
$636$	−2.12833	+	33.4041i	−0.0843937	+	1.32456i
$637$	−14.3544	+	32.0729i	−0.568742	+	1.27078i
$638$	3.30773	+	1.90972i	0.130954	+	0.0756064i
$639$	2.38730	+	10.5858i	0.0944403	+	0.418768i
$640$			2.90931i			0.115001i
$641$	−3.21594	+	8.83573i	−0.127022	+	0.348990i	−0.986860	−	0.161576i	$-0.948342\pi$
$641$	−3.21594	+	8.83573i	−0.127022	+	0.348990i	0.859838	+	0.510567i	$0.170564\pi$
$642$	−12.6166	+	51.9697i	−0.497939	+	2.05108i
$643$	−11.5765	−	31.8061i	−0.456531	−	1.25431i	−0.928051	−	0.372454i	$-0.878516\pi$
$643$	−11.5765	−	31.8061i	−0.456531	−	1.25431i	0.471519	−	0.881856i	$-0.343706\pi$
$644$	−8.97432	+	42.0204i	−0.353638	+	1.65584i
$645$	0.0241292	+	0.216675i	0.000950084	+	0.00853155i
$646$	−10.2354	−	3.72539i	−0.402707	−	0.146573i
$647$	13.4560	−	23.3065i	0.529011	−	0.916274i	−0.470417	−	0.882444i	$-0.655896\pi$
$647$	13.4560	−	23.3065i	0.529011	−	0.916274i	0.999428	−	0.0338292i	$-0.0107702\pi$
$648$	−0.375595	−	0.790383i	−0.0147548	−	0.0310492i
$649$	0.353055	−	0.203837i	0.0138586	−	0.00800129i
$650$	68.7716	−	57.7062i	2.69744	−	2.26342i
$651$	0.370735	−	0.252887i	0.0145303	−	0.00991142i
$652$	−2.00961	+	11.3971i	−0.0787024	+	0.446344i
$653$	24.8064	−	29.5631i	0.970749	−	1.15689i	−0.0168437	−	0.999858i	$-0.505362\pi$
$653$	24.8064	−	29.5631i	0.970749	−	1.15689i	0.987593	−	0.157036i	$-0.0501938\pi$
$654$	1.96654	+	6.70145i	0.0768979	+	0.262047i
$655$	2.01921	+	0.734932i	0.0788970	+	0.0287162i
$656$	15.4777	−	26.8082i	0.604303	−	1.04668i
$657$	14.6682	−	13.5396i	0.572261	−	0.528228i
$658$	−13.6167	−	25.6694i	−0.530835	−	1.00070i
$659$	−4.48755	+	12.3294i	−0.174810	+	0.480287i	−0.995895	−	0.0905197i	$-0.971147\pi$
$659$	−4.48755	+	12.3294i	−0.174810	+	0.480287i	0.821085	+	0.570807i	$0.193369\pi$
$660$	6.06096	−	3.00267i	0.235923	−	0.116879i
$661$	−15.4800	−	42.5309i	−0.602101	−	1.65426i	−0.747010	−	0.664813i	$-0.768511\pi$
$661$	−15.4800	−	42.5309i	−0.602101	−	1.65426i	0.144909	−	0.989445i	$-0.453711\pi$
$662$	−9.95003	−	27.3375i	−0.386719	−	1.06250i
$663$	−32.8445	−	21.8596i	−1.27557	−	0.848955i
$664$	−0.0603443	+	0.165795i	−0.00234181	+	0.00643408i
$665$	5.60153	+	10.5596i	0.217218	+	0.409486i
$666$	−2.94562	+	1.23271i	−0.114140	+	0.0477664i
$667$	−14.9482	+	25.8910i	−0.578795	+	1.00250i
$668$	20.7366	+	7.54750i	0.802323	+	0.292022i
$669$	2.40101	+	0.582892i	0.0928286	+	0.0225359i
$670$	−31.4902	+	37.5286i	−1.21657	+	1.44986i
$671$	−0.601960	+	3.41388i	−0.0232384	+	0.131791i
$672$	32.8114	+	15.7920i	1.26573	+	0.609188i
$673$	13.0981	−	10.9906i	0.504895	−	0.423657i	−0.354434	−	0.935081i	$-0.615326\pi$
$673$	13.0981	−	10.9906i	0.504895	−	0.423657i	0.859328	+	0.511424i	$0.170882\pi$
$674$	−34.4487	+	19.8890i	−1.32691	+	0.766094i
$675$	40.8645	−	22.7104i	1.57288	−	0.874123i
$676$	−11.9000	+	20.6115i	−0.457694	+	0.792749i
$677$	15.2799	+	5.56144i	0.587256	+	0.213744i	0.618522	−	0.785767i	$-0.287732\pi$
$677$	15.2799	+	5.56144i	0.587256	+	0.213744i	−0.0312663	+	0.999511i	$0.509954\pi$
$678$	−23.7431	−	10.3956i	−0.911847	−	0.399242i
$679$	−7.06751	+	33.0921i	−0.271226	+	1.26996i
$680$	0.564577	+	1.55116i	0.0216505	+	0.0594844i
$681$	−32.2287	+	9.45752i	−1.23501	+	0.362413i
$682$	0.0356180	−	0.0978597i	0.00136388	−	0.00374724i
$683$		−	17.5513i		−	0.671583i	−0.941936	−	0.335791i	$-0.890996\pi$
$683$		−	17.5513i		−	0.671583i	0.941936	−	0.335791i	$-0.109004\pi$
$684$	−3.24094	+	6.28154i	−0.123920	+	0.240181i
$685$	7.57394	+	4.37281i	0.289385	+	0.167077i
$686$	−2.46108	−	36.7310i	−0.0939646	−	1.40240i
$687$	−3.72233	−	2.47739i	−0.142016	−	0.0945183i
$688$	−0.0239261	+	0.135692i	−0.000912176	+	0.00517321i
$689$	−46.7213	+	17.0051i	−1.77994	+	0.647845i
$690$	47.5956	+	96.0729i	1.81193	+	3.65743i
$691$	−14.8096	+	2.61133i	−0.563384	+	0.0993397i	−0.448085	−	0.893991i	$-0.647894\pi$
$691$	−14.8096	+	2.61133i	−0.563384	+	0.0993397i	−0.115299	+	0.993331i	$0.536783\pi$
$692$	10.0630	−	17.4296i	0.382538	−	0.662575i
$693$	0.0484029	+	4.24606i	0.00183867	+	0.161294i
$694$	−10.7447	−	18.6103i	−0.407862	−	0.706437i
$695$	−1.12745	−	1.34365i	−0.0427668	−	0.0509675i
$696$	0.437702	+	0.417483i	0.0165910	+	0.0158247i
$697$	5.95591	−	33.7776i	0.225596	−	1.27942i
$698$	54.7625	−	19.9319i	2.07279	−	0.754434i
$699$	−16.9700	+	38.7586i	−0.641865	+	1.46599i
$700$	−17.4402	+	43.0458i	−0.659179	+	1.62698i
$701$		−	29.7179i		−	1.12243i	−0.827670	−	0.561215i	$-0.810334\pi$
$701$		−	29.7179i		−	1.12243i	0.827670	−	0.561215i	$-0.189666\pi$
$702$	−33.9718	+	39.1671i	−1.28218	+	1.47827i
$703$	−0.560004	−	0.323319i	−0.0211210	−	0.0121942i
$704$	4.00624	−	0.706409i	0.150991	−	0.0266238i
$705$	−32.7980	−	14.3602i	−1.23524	−	0.540837i
$706$	−39.4750	−	6.96051i	−1.48566	−	0.261962i
$707$	5.51381	+	1.17759i	0.207368	+	0.0442878i
$708$	−2.47097	+	0.725108i	−0.0928648	+	0.0272512i
$709$	−10.3817	+	8.71129i	−0.389894	+	0.327160i	−0.816572	−	0.577244i	$-0.804128\pi$
$709$	−10.3817	+	8.71129i	−0.389894	+	0.327160i	0.426678	+	0.904404i	$0.359684\pi$
$710$	−26.9002			−1.00954
$711$	6.06749	+	14.4986i	0.227549	+	0.543741i
$712$		−	0.895798i		−	0.0335715i
$713$	0.765989	+	0.278797i	0.0286865	+	0.0104410i
$714$	41.1297	+	4.10619i	1.53924	+	0.153670i
$715$	7.69672	+	6.45831i	0.287841	+	0.241527i
$716$	14.4203	+	2.54268i	0.538911	+	0.0950245i
$717$	33.9941	+	22.6247i	1.26953	+	0.844934i
$718$	25.4828	−	21.3826i	0.951011	−	0.797993i
$719$	−12.0974			−0.451158			−0.225579	−	0.974225i	$-0.572427\pi$
$719$	−12.0974			−0.451158			−0.225579	+	0.974225i	$0.572427\pi$
$720$	44.8406	−	10.1124i	1.67111	−	0.376867i
$721$	16.7588	−	26.7619i	0.624132	−	0.996667i
$722$	34.3385	−	6.05481i	1.27795	−	0.225337i
$723$	16.1395	+	3.91816i	0.600233	+	0.145718i
$724$	34.8547	+	6.14582i	1.29536	+	0.228407i
$725$	−20.7719	+	24.7549i	−0.771447	+	0.919375i
$726$	−21.8652	−	29.7068i	−0.811494	−	1.10252i
$727$	12.2167	+	14.5592i	0.453091	+	0.539973i	0.943436	−	0.331556i	$-0.107574\pi$
$727$	12.2167	+	14.5592i	0.453091	+	0.539973i	−0.490345	+	0.871529i	$0.663129\pi$
$728$	−0.0463194	+	1.29052i	−0.00171671	+	0.0478298i
$729$	−21.2397	+	16.6696i	−0.786654	+	0.617394i
$730$	24.7417	+	42.8539i	0.915731	+	1.58609i
$731$	0.0265103	+	0.150347i	0.000980517	+	0.00556079i
$732$	8.78254	−	20.0589i	0.324612	−	0.741396i
$733$	0.149681	+	0.411244i	0.00552858	+	0.0151897i	0.942426	−	0.334414i	$-0.108538\pi$
$733$	0.149681	+	0.411244i	0.00552858	+	0.0151897i	−0.936898	+	0.349604i	$0.886316\pi$
$734$	15.3726	−	5.59518i	0.567415	−	0.206522i
$735$	−30.4951	−	33.5805i	−1.12483	−	1.23863i
$736$	11.4855	+	65.1374i	0.423360	+	2.40100i
$737$	−3.05213	−	1.76215i	−0.112427	−	0.0649095i
$738$	−43.0359	−	13.3970i	−1.58417	−	0.493151i
$739$	11.7661	+	20.3794i	0.432822	+	0.749670i	0.997115	−	0.0759047i	$-0.0241845\pi$
$739$	11.7661	+	20.3794i	0.432822	+	0.749670i	−0.564293	+	0.825575i	$0.690851\pi$
$740$	−0.678748	−	3.84937i	−0.0249513	−	0.141506i
$741$	−10.4782	−	0.667616i	−0.384927	−	0.0245255i
$742$	34.8922	−	38.6762i	1.28093	−	1.41985i
$743$	24.1698	−	28.8045i	0.886705	−	1.05673i	−0.111312	−	0.993786i	$-0.535505\pi$
$743$	24.1698	−	28.8045i	0.886705	−	1.05673i	0.998017	−	0.0629481i	$-0.0200503\pi$
$744$	0.00913773	−	0.0137296i	0.000335005	−	0.000503353i
$745$	24.7021	+	29.4389i	0.905016	+	1.07856i
$746$	−25.8431	+	14.9205i	−0.946183	+	0.546279i
$747$	5.39972	+	0.690888i	0.197566	+	0.0252783i
$748$	4.10196	−	2.36827i	0.149983	−	0.0865925i
$749$	32.4098	−	25.2707i	1.18423	−	0.923372i
$750$	14.4977	+	49.4044i	0.529383	+	1.80399i
$751$	32.1150	+	26.9477i	1.17189	+	0.983336i	0.999998	−	0.00177927i	$-0.000566360\pi$
$751$	32.1150	+	26.9477i	1.17189	+	0.983336i	0.171896	+	0.985115i	$0.445011\pi$
$752$	−17.3342	−	14.5451i	−0.632113	−	0.530406i
$753$	−2.62284	−	23.5525i	−0.0955815	−	0.858301i
$754$	12.2573	−	33.6765i	0.446383	−	1.22643i
$755$	2.13898			0.0778453
$756$	6.03045	−	26.1363i	0.219325	−	0.950568i
$757$	−48.7358			−1.77133			−0.885667	−	0.464321i	$-0.846298\pi$
$757$	−48.7358			−1.77133			−0.885667	+	0.464321i	$0.846298\pi$
$758$	16.0877	−	44.2006i	0.584331	−	1.60544i
$759$	−6.21181	+	4.57211i	−0.225474	+	0.165957i
$760$	0.336515	+	0.282369i	0.0122067	+	0.0102426i
$761$	17.5546	+	14.7300i	0.636353	+	0.533964i	0.902896	−	0.429859i	$-0.141437\pi$
$761$	17.5546	+	14.7300i	0.636353	+	0.533964i	−0.266543	+	0.963823i	$0.585881\pi$
$762$	61.8146	+	15.0067i	2.23930	+	0.543634i
$763$	2.01536	−	4.97430i	0.0729610	−	0.180082i
$764$	−20.1128	+	11.6121i	−0.727654	+	0.420111i
$765$	42.8550	−	27.5216i	1.54943	−	0.995047i
$766$	3.31500	−	1.91392i	0.119776	−	0.0691526i
$767$	−2.45880	−	2.93028i	−0.0887820	−	0.105806i
$768$	28.9596	+	1.84515i	1.04499	+	0.0665810i
$769$	−6.82411	+	8.13266i	−0.246084	+	0.293271i	−0.874921	−	0.484266i	$-0.839087\pi$
$769$	−6.82411	+	8.13266i	−0.246084	+	0.293271i	0.628837	+	0.777537i	$0.283531\pi$
$770$	−10.2941	−	2.19851i	−0.370972	−	0.0792288i
$771$	−29.3915	+	44.1613i	−1.05851	+	1.59043i
$772$	2.49643	+	14.1580i	0.0898486	+	0.509557i
$773$	18.2500	+	31.6099i	0.656406	+	1.13693i	0.981539	+	0.191260i	$0.0612575\pi$
$773$	18.2500	+	31.6099i	0.656406	+	1.13693i	−0.325133	+	0.945668i	$0.605409\pi$
$774$	0.200399	−	0.00948107i	0.00720320	−	0.000340790i
$775$	0.763058	+	0.440552i	0.0274098	+	0.0158251i
$776$	0.215943	+	1.22468i	0.00775191	+	0.0439633i
$777$	2.36230	+	0.664067i	0.0847470	+	0.0238233i
$778$	−53.1855	+	19.3579i	−1.90679	+	0.694015i
$779$	−3.12182	−	8.57713i	−0.111851	−	0.307308i
$780$	−37.6215	−	51.1138i	−1.34707	−	1.83017i
$781$	−0.336038	−	1.90577i	−0.0120244	−	0.0681938i
$782$	37.5397	+	65.0206i	1.34242	+	2.32513i
$783$	9.59450	−	16.0078i	0.342879	−	0.572072i
$784$	−12.5172	−	25.7910i	−0.447044	−	0.921108i
$785$	−19.0633	−	22.7188i	−0.680399	−	0.810868i
$786$	0.793090	−	1.81138i	0.0282886	−	0.0646097i
$787$	−14.7250	+	17.5485i	−0.524889	+	0.625538i	−0.961729	−	0.274001i	$-0.911653\pi$
$787$	−14.7250	+	17.5485i	−0.524889	+	0.625538i	0.436841	+	0.899539i	$0.356097\pi$
$788$	−17.3493	−	3.05914i	−0.618042	−	0.108977i
$789$	−4.35408	+	4.56495i	−0.155009	+	0.162517i
$790$	−38.3690	+	6.76549i	−1.36511	+	0.240705i
$791$	9.33398	+	17.5958i	0.331878	+	0.625636i
$792$	0.0602438	+	0.143956i	0.00214067	+	0.00511526i
$793$	32.5267			1.15506
$794$	−27.0346	+	22.6847i	−0.959423	+	0.805052i
$795$	4.08116	−	64.0538i	0.144744	−	2.27175i
$796$	−52.0565	−	9.17896i	−1.84509	−	0.325340i
$797$	9.18486	+	7.70701i	0.325344	+	0.272996i	0.790800	−	0.612075i	$-0.209665\pi$
$797$	9.18486	+	7.70701i	0.325344	+	0.272996i	−0.465455	+	0.885071i	$0.654109\pi$
$798$	10.0254	−	4.52639i	0.354896	−	0.160233i
$799$	−23.5601	−	8.57516i	−0.833495	−	0.303367i
$800$			71.4939i			2.52769i
$801$	−26.9619	+	6.08043i	−0.952652	+	0.214841i
$802$	−47.9877			−1.69451
$803$	−2.72695	+	2.28818i	−0.0962320	+	0.0807482i
$804$	16.1093	+	15.3652i	0.568131	+	0.541888i
$805$	17.2087	−	80.5760i	0.606526	−	2.83993i
$806$	−0.962304	−	0.169680i	−0.0338957	−	0.00597673i
$807$	45.0456	−	33.1551i	1.58568	−	1.16711i
$808$	0.204055	−	0.0359805i	0.00717864	−	0.00126579i
$809$	−40.1666	−	23.1902i	−1.41218	−	0.815324i	−0.416588	−	0.909095i	$-0.636774\pi$
$809$	−40.1666	−	23.1902i	−1.41218	−	0.815324i	−0.995594	+	0.0937717i	$0.970108\pi$
$810$	−28.7271	−	60.4517i	−1.00937	−	2.12406i
$811$			11.1740i			0.392373i	0.980567	+	0.196187i	$0.0628558\pi$
$811$			11.1740i			0.392373i	−0.980567	+	0.196187i	$0.937144\pi$
$812$	2.56253	+	18.3626i	0.0899272	+	0.644401i
$813$	−42.6895	+	4.75395i	−1.49719	+	0.166728i
$814$	0.535092	−	0.194758i	0.0187550	−	0.00682625i
$815$	3.85352	−	21.8544i	0.134983	−	0.765526i
$816$	30.8863	−	9.06358i	1.08124	−	0.317289i
$817$	0.0261150	+	0.0311226i	0.000913647	+	0.00108884i
$818$	18.9031	+	32.7411i	0.660932	+	1.14477i
$819$	39.1567	−	7.36555i	1.36825	−	0.257373i
$820$	27.5870	−	47.7820i	0.963379	−	1.66862i
$821$	−16.2787	+	2.87037i	−0.568129	+	0.100177i	−0.450332	−	0.892861i	$-0.648694\pi$
$821$	−16.2787	+	2.87037i	−0.568129	+	0.100177i	−0.117797	+	0.993038i	$0.537583\pi$
$822$	4.45904	−	6.69980i	0.155527	−	0.233682i
$823$	−42.8340	+	15.5903i	−1.49310	+	0.543444i	−0.954264	−	0.298966i	$-0.903358\pi$
$823$	−42.8340	+	15.5903i	−1.49310	+	0.543444i	−0.538837	+	0.842410i	$0.681136\pi$
$824$	0.201507	−	1.14280i	0.00701983	−	0.0398114i
$825$	−7.47059	+	3.70102i	−0.260092	+	0.128853i
$826$	3.71425	+	1.50485i	0.129235	+	0.0523603i
$827$	39.6502	+	22.8921i	1.37877	+	0.796035i	0.992012	−	0.126145i	$-0.0402604\pi$
$827$	39.6502	+	22.8921i	1.37877	+	0.796035i	0.386761	+	0.922180i	$0.373594\pi$
$828$	44.9443	−	18.8086i	1.56192	−	0.653645i
$829$			17.4049i			0.604496i	0.953229	+	0.302248i	$0.0977370\pi$
$829$			17.4049i			0.604496i	−0.953229	+	0.302248i	$0.902263\pi$
$830$	−4.61538	+	12.6807i	−0.160202	+	0.440152i
$831$	−19.6657	−	18.7573i	−0.682197	−	0.650685i
$832$	−13.0551	−	35.8686i	−0.452604	−	1.24352i
$833$	−22.8065	−	22.1096i	−0.790198	−	0.766054i
$834$	−1.29994	+	0.956798i	−0.0450131	+	0.0331312i
$835$	−39.7634	−	14.4727i	−1.37607	−	0.500848i
$836$	0.630245	−	1.09162i	0.0217975	−	0.0377544i
$837$	−0.475262	−	0.181836i	−0.0164275	−	0.00628518i
$838$	−55.1043	+	31.8145i	−1.90355	+	1.09901i
$839$	3.94033	−	3.30633i	0.136035	−	0.114147i	−0.572231	−	0.820092i	$-0.693922\pi$
$839$	3.94033	−	3.30633i	0.136035	−	0.114147i	0.708266	+	0.705945i	$0.249478\pi$
$840$	−1.50209	−	0.722949i	−0.0518272	−	0.0249441i
$841$	2.79571	−	15.8553i	0.0964038	−	0.546733i
$842$	15.0148	−	17.8939i	0.517444	−	0.616666i
$843$	−15.4350	+	16.1825i	−0.531608	+	0.557354i
$844$	−7.91344	−	2.88026i	−0.272392	−	0.0991425i
$845$	22.8189	−	39.5234i	0.784993	−	1.35965i
$846$	−15.1071	+	29.2804i	−0.519394	+	1.00668i
$847$	−1.01674	+	28.3278i	−0.0349357	+	0.973354i
$848$	13.8738	−	38.1179i	0.476427	−	1.30897i
$849$	2.50783	−	39.3603i	0.0860683	−	1.35084i
$850$	27.7563	+	76.2599i	0.952034	+	2.61569i
$851$	1.52445	+	4.18839i	0.0522574	+	0.143576i
$852$	−0.777269	+	12.1992i	−0.0266288	+	0.417938i
$853$	−1.43875	+	3.95294i	−0.0492620	+	0.135346i	−0.961884	−	0.273459i	$-0.911832\pi$
$853$	−1.43875	+	3.95294i	−0.0492620	+	0.135346i	0.912622	+	0.408805i	$0.134054\pi$
$854$	−30.1037	+	15.9690i	−1.03013	+	0.546446i
$855$	6.21464	−	12.0451i	0.212536	−	0.411935i
$856$	0.755171	−	1.30799i	0.0258112	−	0.0447063i
$857$	18.2004	+	6.62440i	0.621714	+	0.226285i	0.633621	−	0.773644i	$-0.281568\pi$
$857$	18.2004	+	6.62440i	0.621714	+	0.226285i	−0.0119070	+	0.999929i	$0.503790\pi$
$858$	6.38148	−	6.69053i	0.217860	−	0.228411i
$859$	1.32959	−	1.58454i	0.0453650	−	0.0540638i	−0.742885	−	0.669419i	$-0.766543\pi$
$859$	1.32959	−	1.58454i	0.0453650	−	0.0540638i	0.788250	+	0.615355i	$0.210987\pi$
$860$	−0.0426452	+	0.241853i	−0.00145419	+	0.00824711i
$861$	19.5185	+	28.6144i	0.665188	+	0.975175i
$862$	−15.5684	+	13.0635i	−0.530263	+	0.444944i
$863$	5.67206	−	3.27476i	0.193079	−	0.111474i	−0.400344	−	0.916365i	$-0.631109\pi$
$863$	5.67206	−	3.27476i	0.193079	−	0.111474i	0.593423	+	0.804891i	$0.297776\pi$
$864$	−6.50398	−	40.7741i	−0.221270	−	1.38716i
$865$	−19.2962	+	33.4221i	−0.656092	+	1.13638i
$866$	4.90242	+	1.78433i	0.166591	+	0.0606341i
$867$	5.00960	−	3.68724i	0.170135	−	0.125225i
$868$	0.480933	−	0.155749i	0.0163239	−	0.00528646i
$869$	−0.958615	−	2.63377i	−0.0325188	−	0.0893447i
$870$	33.4772	+	31.9308i	1.13498	+	1.08256i
$871$	−11.3101	+	31.0742i	−0.383228	+	1.05291i
$872$		−	0.197240i		−	0.00667940i
$873$	35.3948	−	14.8123i	1.19793	−	0.501319i
$874$	17.3033	+	9.99007i	0.585293	+	0.337919i
$875$	14.8577	−	36.6715i	0.502280	−	1.23972i
$876$	20.1491	−	9.98211i	0.680776	−	0.337264i
$877$	5.14456	−	29.1762i	0.173719	−	0.985211i	−0.765892	−	0.642969i	$-0.777702\pi$
$877$	5.14456	−	29.1762i	0.173719	−	0.985211i	0.939612	−	0.342243i	$-0.111186\pi$
$878$	−1.69660	+	0.617513i	−0.0572576	+	0.0208400i
$879$	0.208809	−	0.313740i	0.00704294	−	0.0105822i
$880$	−8.07267	+	1.42343i	−0.272130	+	0.0479838i
$881$	15.7274	−	27.2407i	0.529870	−	0.917762i	−0.469522	−	0.882921i	$-0.655574\pi$
$881$	15.7274	−	27.2407i	0.529870	−	0.917762i	0.999393	−	0.0348419i	$-0.0110928\pi$
$882$	−32.6237	+	26.0408i	−1.09850	+	0.876840i
$883$	−5.78793	−	10.0250i	−0.194779	−	0.337368i	0.752049	−	0.659107i	$-0.229066\pi$
$883$	−5.78793	−	10.0250i	−0.194779	−	0.337368i	−0.946828	+	0.321740i	$0.895732\pi$
$884$	−28.5674	−	34.0454i	−0.960827	−	1.14507i
$885$	4.73820	−	1.39043i	0.159273	−	0.0467387i
$886$	−4.03242	+	22.8690i	−0.135472	+	0.768299i
$887$	1.25548	−	0.456957i	0.0421549	−	0.0153431i	−0.320857	−	0.947128i	$-0.603971\pi$
$887$	1.25548	−	0.456957i	0.0421549	−	0.0153431i	0.363012	+	0.931785i	$0.381749\pi$
$888$	0.0896259	−	0.00998085i	0.00300765	−	0.000334935i
$889$	−30.0579	−	38.5493i	−1.00811	−	1.29290i
$890$		−	68.5143i		−	2.29661i
$891$	3.92390	−	2.79037i	0.131456	−	0.0934808i
$892$	2.41033	+	1.39160i	0.0807037	+	0.0465943i
$893$	−6.57084	+	1.15862i	−0.219885	+	0.0387716i
$894$	28.4812	−	20.9631i	0.952553	−	0.701112i
$895$	−27.6515	−	4.87571i	−0.924289	−	0.162977i
$896$	−1.52761	−	1.37815i	−0.0510337	−	0.0460407i
$897$	52.3696	+	49.9505i	1.74857	+	1.66780i
$898$	−15.4288	+	12.9463i	−0.514867	+	0.432025i
$899$	0.351733			0.0117310
$900$	51.3731	−	11.5856i	1.71244	−	0.386187i
$901$		−	44.9453i		−	1.49734i
$902$	7.55308	+	2.74910i	0.251490	+	0.0915349i
$903$	−0.125200	−	0.0899697i	−0.00416641	−	0.00299400i
$904$	0.560744	+	0.470520i	0.0186501	+	0.0156493i
$905$	−66.8354	−	11.7849i	−2.22168	−	0.391743i
$906$	0.125159	−	1.96437i	0.00415813	−	0.0652618i
$907$	35.3947	−	29.6996i	1.17526	−	0.986161i	0.175262	−	0.984522i	$-0.443923\pi$
$907$	35.3947	−	29.6996i	1.17526	−	0.986161i	0.999999	−	0.00163866i	$-0.000521603\pi$
$908$	−37.8352			−1.25560
$909$	−2.46802	−	5.89747i	−0.0818590	−	0.195607i
$910$	−3.54270	+	98.7042i	−0.117439	+	3.27201i
$911$	−4.92566	+	0.868526i	−0.163194	+	0.0287756i	−0.254648	−	0.967034i	$-0.581960\pi$
$911$	−4.92566	+	0.868526i	−0.163194	+	0.0287756i	0.0914540	+	0.995809i	$0.470849\pi$
$912$	5.91226	−	6.19859i	0.195775	−	0.205256i
$913$	−0.956030	−	0.168574i	−0.0316400	−	0.00557898i
$914$	35.2538	−	42.0138i	1.16609	−	1.38969i
$915$	−16.8409	+	38.4638i	−0.556743	+	1.27157i
$916$	−3.23761	−	3.85843i	−0.106974	−	0.127486i
$917$	−1.34240	+	0.712097i	−0.0443299	+	0.0235155i
$918$	−22.7674	−	40.9671i	−0.751437	−	1.35212i
$919$	−20.9077	−	36.2133i	−0.689683	−	1.19457i	−0.971940	−	0.235227i	$-0.924417\pi$
$919$	−20.9077	−	36.2133i	−0.689683	−	1.19457i	0.282258	−	0.959339i	$-0.408917\pi$
$920$	−0.525800	−	2.98196i	−0.0173351	−	0.0983123i
$921$	20.6079	+	27.9986i	0.679054	+	0.922585i
$922$	−12.7746	−	35.0980i	−0.420710	−	1.15589i
$923$	−17.0627	+	6.21031i	−0.561625	+	0.204415i
$924$	−1.29447	+	4.60483i	−0.0425848	+	0.151488i
$925$	0.836607	+	4.74463i	0.0275075	+	0.156003i
$926$	1.62689	+	0.939283i	0.0534628	+	0.0308667i
$927$	−35.7641	+	1.69203i	−1.17465	+	0.0555736i
$928$	14.2700	+	24.7164i	0.468437	+	0.811357i
$929$	8.60738	+	48.8149i	0.282399	+	1.60156i	0.714431	+	0.699706i	$0.246686\pi$
$929$	8.60738	+	48.8149i	0.282399	+	1.60156i	−0.432031	+	0.901859i	$0.642203\pi$
$930$	0.698891	−	1.05010i	0.0229175	−	0.0344341i
$931$	−8.19806	−	2.06091i	−0.268681	−	0.0675436i
$932$	−30.6362	+	36.5108i	−1.00352	+	1.19595i
$933$	0.343025	+	0.0218557i	0.0112301	+	0.000715525i
$934$	−13.4522	−	16.0318i	−0.440171	−	0.524575i
$935$	−7.86570	+	4.54127i	−0.257236	+	0.148515i
$936$	1.23206	−	0.791235i	0.0402713	−	0.0258623i
$937$	−22.5053	+	12.9934i	−0.735215	+	0.424477i	−0.820327	−	0.571895i	$-0.806209\pi$
$937$	−22.5053	+	12.9934i	−0.735215	+	0.424477i	0.0851120	+	0.996371i	$0.472875\pi$
$938$	−4.78831	−	34.3121i	−0.156344	−	1.12033i
$939$	−27.5821	−	6.69609i	−0.900109	−	0.218519i
$940$	−30.8959	−	25.9247i	−1.00771	−	0.845571i
$941$	6.89635	+	5.78672i	0.224814	+	0.188642i	0.748237	−	0.663432i	$-0.230901\pi$
$941$	6.89635	+	5.78672i	0.224814	+	0.188642i	−0.523423	+	0.852073i	$0.675345\pi$
$942$	−21.9797	+	16.1778i	−0.716137	+	0.527102i
$943$	−21.5183	+	59.1211i	−0.700733	+	1.92525i
$944$	3.12082			0.101574
$945$	−11.5637	+	50.1175i	−0.376166	+	1.63032i
$946$	−0.0357770			−0.00116321
$947$	−10.5955	+	29.1109i	−0.344307	+	0.945976i	0.639822	+	0.768523i	$0.279008\pi$
$947$	−10.5955	+	29.1109i	−0.344307	+	0.945976i	−0.984129	+	0.177453i	$0.943214\pi$
$948$	1.95949	+	17.5958i	0.0636413	+	0.571485i
$949$	25.5870	+	21.4701i	0.830590	+	0.696948i
$950$	16.5441	+	13.8821i	0.536761	+	0.450396i
$951$	6.83058	+	23.2768i	0.221497	+	0.754801i
$952$	−1.08192	−	0.438345i	−0.0350652	−	0.0142068i
$953$	26.4646	−	15.2793i	0.857272	−	0.494946i	−0.00582605	−	0.999983i	$-0.501854\pi$
$953$	26.4646	−	15.2793i	0.857272	−	0.494946i	0.863098	+	0.505037i	$0.168521\pi$
$954$	−58.5862	−	7.49603i	−1.89680	−	0.242693i
$955$	38.5671	−	22.2667i	1.24800	−	0.720535i
$956$	29.5673	+	35.2370i	0.956276	+	1.13965i
$957$	−1.84397	+	2.77061i	−0.0596072	+	0.0895611i
$958$	5.64515	−	6.72762i	0.182386	−	0.217360i
$959$	−5.88385	+	1.90547i	−0.189999	+	0.0615308i
$960$	49.1751	+	3.13317i	1.58712	+	0.101123i
$961$	5.38143	+	30.5196i	0.173594	+	0.984503i
$962$	−2.67150	−	4.62717i	−0.0861326	−	0.149186i
$963$	−44.4942	−	13.8510i	−1.43380	−	0.446342i
$964$	16.2020	+	9.35425i	0.521833	+	0.301280i
$965$	−4.78702	−	27.1486i	−0.154100	−	0.873943i
$966$	−72.9916	−	20.5187i	−2.34847	−	0.660179i
$967$	36.5940	−	13.3191i	1.17678	−	0.428314i	0.321719	−	0.946835i	$-0.395739\pi$
$967$	36.5940	−	13.3191i	1.17678	−	0.428314i	0.855065	+	0.518521i	$0.173517\pi$
$968$	0.356290	+	0.978898i	0.0114516	+	0.0314630i
$969$	3.80673	−	8.69438i	0.122290	−	0.279304i
$970$	16.5162	+	93.6682i	0.530304	+	3.00750i
$971$	−1.63236	−	2.82733i	−0.0523849	−	0.0907333i	0.838644	−	0.544680i	$-0.183349\pi$
$971$	−1.63236	−	2.82733i	−0.0523849	−	0.0907333i	−0.891029	+	0.453947i	$0.850016\pi$
$972$	−28.2449	+	11.2810i	−0.905956	+	0.361838i
$973$	1.23959	+	0.0444916i	0.0397396	+	0.00142634i
$974$	45.6146	+	54.3614i	1.46159	+	1.74185i
$975$	46.3713	+	63.0015i	1.48507	+	2.01766i
$976$	−17.0577	+	20.3286i	−0.546005	+	0.650703i
$977$	−37.8806	−	6.67938i	−1.21191	−	0.213692i	−0.469069	−	0.883161i	$-0.655411\pi$
$977$	−37.8806	−	6.67938i	−1.21191	−	0.213692i	−0.742840	+	0.669469i	$0.766522\pi$
$978$	−19.8449	−	4.81773i	−0.634571	−	0.154054i
$979$	4.85397	−	0.855885i	0.155133	−	0.0273542i
$980$	−22.3103	−	45.9691i	−0.712677	−	1.46843i
$981$	−5.93658	+	1.33881i	−0.189541	+	0.0427450i
$982$	−44.1336			−1.40836
$983$	9.55295	−	8.01588i	0.304692	−	0.255667i	−0.477602	−	0.878576i	$-0.658494\pi$
$983$	9.55295	−	8.01588i	0.304692	−	0.255667i	0.782294	+	0.622909i	$0.214049\pi$
$984$	1.05969	+	0.705275i	0.0337817	+	0.0224833i
$985$	33.2680	+	5.86604i	1.06001	+	0.186908i
$986$	24.8171	+	20.8240i	0.790337	+	0.663172i
$987$	23.0767	−	10.4189i	0.734539	−	0.331638i
$988$	−11.1139	−	4.04515i	−0.353582	−	0.128693i
$989$		−	0.280042i		−	0.00890481i
$990$	4.60770	+	11.0104i	0.146442	+	0.349932i
$991$	28.6551			0.910258			0.455129	−	0.890426i	$-0.349593\pi$
$991$	28.6551			0.910258			0.455129	+	0.890426i	$0.349593\pi$
$992$	0.596113	−	0.500198i	0.0189266	−	0.0158813i
$993$	24.3242	−	7.13793i	0.771904	−	0.226515i
$994$	12.7427	−	14.1246i	0.404173	−	0.448005i
$995$	99.8206	+	17.6011i	3.16453	+	0.557991i
$996$	5.61732	+	2.45948i	0.177992	+	0.0779315i
$997$	5.66816	−	0.999450i	0.179512	−	0.0316529i	−0.0831692	−	0.996535i	$-0.526504\pi$
$997$	5.66816	−	0.999450i	0.179512	−	0.0316529i	0.262682	+	0.964883i	$0.415393\pi$
$998$	−62.4178	−	36.0370i	−1.97580	−	1.14073i
$999$	−0.908761	−	2.62983i	−0.0287519	−	0.0832042i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.59.3	yes	132
3.2	odd	2		567.2.bd.a.206.20		132
7.5	odd	6		189.2.ba.a.5.20	✓	132
21.5	even	6		567.2.ba.a.530.3		132
27.11	odd	18		189.2.ba.a.38.20	yes	132
27.16	even	9		567.2.ba.a.521.3		132
189.124	odd	18		567.2.bd.a.278.20		132
189.173	even	18	inner	189.2.bd.a.173.3	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.20	✓	132	7.5	odd	6
189.2.ba.a.38.20	yes	132	27.11	odd	18
189.2.bd.a.59.3	yes	132	1.1	even	1	trivial
189.2.bd.a.173.3	yes	132	189.173	even	18	inner
567.2.ba.a.521.3		132	27.16	even	9
567.2.ba.a.530.3		132	21.5	even	6
567.2.bd.a.206.20		132	3.2	odd	2
567.2.bd.a.278.20		132	189.124	odd	18

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.679845 + 1.86786i) q^{2} +(-1.58663 - 0.694689i) q^{3} +(-1.49462 - 1.25413i) q^{4} +(2.86600 + 2.40486i) q^{5} +(2.37625 - 2.49133i) q^{6} +(-2.62036 + 0.365676i) q^{7} +(-0.0842052 + 0.0486159i) q^{8} +(2.03481 + 2.20443i) q^{9} +(-6.44036 + 3.71835i) q^{10} +(-0.343883 - 0.409824i) q^{11} +(1.50018 + 3.02814i) q^{12} +(-3.22666 + 3.84539i) q^{13} +(1.09841 - 5.14306i) q^{14} +(-2.87666 - 5.80660i) q^{15} +(-0.711166 - 4.03322i) q^{16} +(-2.26888 - 3.92982i) q^{17} +(-5.50093 + 2.30207i) q^{18} +(-1.04580 - 0.603796i) q^{19} +(-1.26756 - 7.18868i) q^{20} +(4.41158 + 1.24014i) q^{21} +(0.999281 - 0.363709i) q^{22} +(2.84690 + 7.82179i) q^{23} +(0.167376 - 0.0186392i) q^{24} +(1.56236 + 8.86058i) q^{25} +(-4.98901 - 8.64122i) q^{26} +(-1.69711 - 4.91119i) q^{27} +(4.37504 + 2.73973i) q^{28} +(2.30869 + 2.75138i) q^{29} +(12.8016 - 1.42560i) q^{30} +(0.0629483 - 0.0750188i) q^{31} +(7.82546 + 1.37984i) q^{32} +(0.260916 + 0.889133i) q^{33} +(8.88283 - 1.56628i) q^{34} +(-8.38934 - 5.25356i) q^{35} +(-0.276613 - 5.84671i) q^{36} +0.535477 q^{37} +(1.83879 - 1.54293i) q^{38} +(7.79089 - 3.85970i) q^{39} +(-0.358246 - 0.0631685i) q^{40} +(5.79016 + 4.85852i) q^{41} +(-5.31560 + 7.39710i) q^{42} +(-0.0316146 - 0.0115068i) q^{43} +1.04381i q^{44} +(0.530418 + 11.2113i) q^{45} -16.5455 q^{46} +(4.23256 - 3.55154i) q^{47} +(-1.67348 + 6.89328i) q^{48} +(6.73256 - 1.91640i) q^{49} +(-17.6125 - 3.10555i) q^{50} +(0.869881 + 7.81135i) q^{51} +(9.64526 - 1.70072i) q^{52} +(8.57774 + 4.95236i) q^{53} +(10.3272 + 0.168895i) q^{54} -2.00154i q^{55} +(0.202870 - 0.158183i) q^{56} +(1.23986 + 1.68451i) q^{57} +(-6.70874 + 2.44178i) q^{58} +(-0.132324 + 0.750447i) q^{59} +(-2.98275 + 12.2864i) q^{60} +(-4.16506 - 4.96372i) q^{61} +(0.0973295 + 0.168580i) q^{62} +(-6.13805 - 5.03233i) q^{63} +(-3.80200 + 6.58526i) q^{64} +(-18.4952 + 3.26121i) q^{65} +(-1.83816 - 0.117118i) q^{66} +(6.19033 - 2.25310i) q^{67} +(-1.53740 + 8.71905i) q^{68} +(0.916728 - 14.3880i) q^{69} +(15.5164 - 12.0985i) q^{70} +(3.13261 + 1.80861i) q^{71} +(-0.278513 - 0.0867006i) q^{72} -6.65395i q^{73} +(-0.364041 + 1.00019i) q^{74} +(3.67646 - 15.1438i) q^{75} +(0.805838 + 2.21402i) q^{76} +(1.05096 + 0.948137i) q^{77} +(1.91277 + 17.1763i) q^{78} +(4.92306 + 1.79185i) q^{79} +(7.66112 - 13.2694i) q^{80} +(-0.719067 + 8.97123i) q^{81} +(-13.0114 + 7.51215i) q^{82} +(1.39005 - 1.16639i) q^{83} +(-5.03832 - 7.38625i) q^{84} +(2.94804 - 16.7192i) q^{85} +(0.0429861 - 0.0512288i) q^{86} +(-1.75168 - 5.96926i) q^{87} +(0.0488808 + 0.0177911i) q^{88} +(-4.60651 + 7.97870i) q^{89} +(-21.3018 - 6.63122i) q^{90} +(7.04886 - 11.2562i) q^{91} +(5.55454 - 15.2610i) q^{92} +(-0.151991 + 0.0752979i) q^{93} +(3.75629 + 10.3203i) q^{94} +(-1.54523 - 4.24549i) q^{95} +(-11.4576 - 7.62556i) q^{96} +(4.37434 - 12.0184i) q^{97} +(-0.997529 + 13.8783i) q^{98} +(0.203692 - 1.59198i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20}+ \cdots + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

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