LMFDB - Embedded newform 189.2.u.a.4.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(4,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 12]))

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

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

chi := DirichletCharacter("189.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.u (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			4.12
Character	$\chi$	$=$	189.4
Dual form			189.2.u.a.142.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0290601 + 0.164808i) q^{2} +(0.733837 - 1.56891i) q^{3} +(1.85307 - 0.674462i) q^{4} +(-0.999212 + 0.363683i) q^{5} +(0.279894 + 0.0753494i) q^{6} +(1.97858 + 1.75648i) q^{7} +(0.332357 + 0.575660i) q^{8} +(-1.92297 - 2.30265i) q^{9} +O(q^{10})$	\(q+(0.0290601 + 0.164808i) q^{2} +(0.733837 - 1.56891i) q^{3} +(1.85307 - 0.674462i) q^{4} +(-0.999212 + 0.363683i) q^{5} +(0.279894 + 0.0753494i) q^{6} +(1.97858 + 1.75648i) q^{7} +(0.332357 + 0.575660i) q^{8} +(-1.92297 - 2.30265i) q^{9} +(-0.0889751 - 0.154109i) q^{10} +(-1.03647 - 0.377243i) q^{11} +(0.301679 - 3.40224i) q^{12} +(-1.14619 + 0.417180i) q^{13} +(-0.231985 + 0.377129i) q^{14} +(-0.162671 + 1.83456i) q^{15} +(2.93605 - 2.46364i) q^{16} +(-1.95396 - 3.38436i) q^{17} +(0.323613 - 0.383835i) q^{18} +(-0.705034 + 1.22115i) q^{19} +(-1.60632 + 1.34786i) q^{20} +(4.20772 - 1.81524i) q^{21} +(0.0320529 - 0.181781i) q^{22} +(-0.811107 + 4.60002i) q^{23} +(1.14706 - 0.0989989i) q^{24} +(-2.96406 + 2.48714i) q^{25} +(-0.102063 - 0.176778i) q^{26} +(-5.02380 + 1.32720i) q^{27} +(4.85112 + 1.92041i) q^{28} +(8.20907 + 2.98786i) q^{29} +(-0.307077 + 0.0265029i) q^{30} +(-2.90602 + 1.05771i) q^{31} +(1.50975 + 1.26683i) q^{32} +(-1.35246 + 1.34929i) q^{33} +(0.500988 - 0.420379i) q^{34} +(-2.61582 - 1.03552i) q^{35} +(-5.11644 - 2.97000i) q^{36} +4.37450 q^{37} +(-0.221744 - 0.0807084i) q^{38} +(-0.186600 + 2.10442i) q^{39} +(-0.541453 - 0.454333i) q^{40} +(-8.04440 + 2.92792i) q^{41} +(0.421443 + 0.640715i) q^{42} +(-1.05735 - 5.99651i) q^{43} -2.17508 q^{44} +(2.75889 + 1.60148i) q^{45} -0.781690 q^{46} +(-1.73596 - 0.631839i) q^{47} +(-1.71065 - 6.41432i) q^{48} +(0.829534 + 6.95067i) q^{49} +(-0.496037 - 0.416225i) q^{50} +(-6.74366 + 0.582025i) q^{51} +(-1.84260 + 1.54613i) q^{52} +(-4.55546 + 7.89029i) q^{53} +(-0.364724 - 0.789393i) q^{54} +1.17285 q^{55} +(-0.353542 + 1.72277i) q^{56} +(1.39850 + 2.00226i) q^{57} +(-0.253866 + 1.43975i) q^{58} +(0.0125627 + 0.0105414i) q^{59} +(0.935899 + 3.50928i) q^{60} +(-7.36629 - 2.68111i) q^{61} +(-0.258768 - 0.448199i) q^{62} +(0.239827 - 7.93363i) q^{63} +(3.66784 - 6.35288i) q^{64} +(0.993568 - 0.833703i) q^{65} +(-0.261676 - 0.183686i) q^{66} +(-1.27108 + 7.20865i) q^{67} +(-5.90345 - 4.95358i) q^{68} +(6.62180 + 4.64822i) q^{69} +(0.0946464 - 0.461201i) q^{70} +(8.19310 - 14.1909i) q^{71} +(0.686431 - 1.87228i) q^{72} +9.16921 q^{73} +(0.127123 + 0.720953i) q^{74} +(1.72697 + 6.47551i) q^{75} +(-0.482854 + 2.73840i) q^{76} +(-1.38811 - 2.56694i) q^{77} +(-0.352247 + 0.0304014i) q^{78} +(-1.89813 - 10.7649i) q^{79} +(-2.03776 + 3.52950i) q^{80} +(-1.60440 + 8.85584i) q^{81} +(-0.716316 - 1.24070i) q^{82} +(11.3691 + 4.13802i) q^{83} +(6.57288 - 6.20171i) q^{84} +(3.18326 + 2.67107i) q^{85} +(0.957545 - 0.348518i) q^{86} +(10.7118 - 10.6867i) q^{87} +(-0.127314 - 0.722032i) q^{88} +(8.07668 - 13.9892i) q^{89} +(-0.183764 + 0.501226i) q^{90} +(-3.00060 - 1.18785i) q^{91} +(1.59950 + 9.07121i) q^{92} +(-0.473100 + 5.33548i) q^{93} +(0.0536849 - 0.304462i) q^{94} +(0.260365 - 1.47660i) q^{95} +(3.09546 - 1.43902i) q^{96} +(-0.0674999 - 0.382811i) q^{97} +(-1.12142 + 0.338701i) q^{98} +(1.12443 + 3.11205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.0290601	+	0.164808i	0.0205486	+	0.116537i	0.993357	−	0.115076i	$-0.0367110\pi$
$2$	0.0290601	+	0.164808i	0.0205486	+	0.116537i	−0.972808	+	0.231612i	$0.925600\pi$
$3$	0.733837	−	1.56891i	0.423681	−	0.905812i
$3$	0.733837	−	1.56891i	0.423681	−	0.905812i
$4$	1.85307	−	0.674462i	0.926534	−	0.337231i
$5$	−0.999212	+	0.363683i	−0.446861	+	0.162644i	−0.555642	−	0.831422i	$-0.687528\pi$
$5$	−0.999212	+	0.363683i	−0.446861	+	0.162644i	0.108781	+	0.994066i	$0.465305\pi$
$6$	0.279894	+	0.0753494i	0.114266	+	0.0307613i
$7$	1.97858	+	1.75648i	0.747832	+	0.663888i
$7$	1.97858	+	1.75648i	0.747832	+	0.663888i
$8$	0.332357	+	0.575660i	0.117506	+	0.203526i
$9$	−1.92297	−	2.30265i	−0.640989	−	0.767550i
$10$	−0.0889751	−	0.154109i	−0.0281364	−	0.0487337i
$11$	−1.03647	−	0.377243i	−0.312507	−	0.113743i	0.181005	−	0.983482i	$-0.442065\pi$
$11$	−1.03647	−	0.377243i	−0.312507	−	0.113743i	−0.493512	+	0.869739i	$0.664287\pi$
$12$	0.301679	−	3.40224i	0.0870872	−	0.982143i
$13$	−1.14619	+	0.417180i	−0.317897	+	0.115705i	−0.496040	−	0.868300i	$-0.665213\pi$
$13$	−1.14619	+	0.417180i	−0.317897	+	0.115705i	0.178143	+	0.984005i	$0.442991\pi$
$14$	−0.231985	+	0.377129i	−0.0620005	+	0.100792i
$15$	−0.162671	+	1.83456i	−0.0420016	+	0.473681i
$16$	2.93605	−	2.46364i	0.734014	−	0.615911i
$17$	−1.95396	−	3.38436i	−0.473906	−	0.820829i	0.525648	−	0.850702i	$-0.323823\pi$
$17$	−1.95396	−	3.38436i	−0.473906	−	0.820829i	−0.999554	+	0.0298734i	$0.990490\pi$
$18$	0.323613	−	0.383835i	0.0762764	−	0.0904709i
$19$	−0.705034	+	1.22115i	−0.161746	+	0.280152i	−0.935495	−	0.353340i	$-0.885046\pi$
$19$	−0.705034	+	1.22115i	−0.161746	+	0.280152i	0.773749	+	0.633492i	$0.218379\pi$
$20$	−1.60632	+	1.34786i	−0.359183	+	0.301391i
$21$	4.20772	−	1.81524i	0.918200	−	0.396118i
$22$	0.0320529	−	0.181781i	0.00683369	−	0.0387558i
$23$	−0.811107	+	4.60002i	−0.169128	+	0.959170i	0.775578	+	0.631251i	$0.217458\pi$
$23$	−0.811107	+	4.60002i	−0.169128	+	0.959170i	−0.944706	+	0.327919i	$0.893653\pi$
$24$	1.14706	−	0.0989989i	0.234142	−	0.0202081i
$25$	−2.96406	+	2.48714i	−0.592813	+	0.497429i
$26$	−0.102063	−	0.176778i	−0.0200162	−	0.0346691i
$27$	−5.02380	+	1.32720i	−0.966830	+	0.255419i
$28$	4.85112	+	1.92041i	0.916775	+	0.362923i
$29$	8.20907	+	2.98786i	1.52439	+	0.554831i	0.962239	−	0.272207i	$-0.0877535\pi$
$29$	8.20907	+	2.98786i	1.52439	+	0.554831i	0.562147	+	0.827038i	$0.309976\pi$
$30$	−0.307077	+	0.0265029i	−0.0560644	+	0.00483875i
$31$	−2.90602	+	1.05771i	−0.521937	+	0.189970i	−0.589535	−	0.807743i	$-0.700689\pi$
$31$	−2.90602	+	1.05771i	−0.521937	+	0.189970i	0.0675976	+	0.997713i	$0.478467\pi$
$32$	1.50975	+	1.26683i	0.266889	+	0.223946i
$33$	−1.35246	+	1.34929i	−0.235433	+	0.234881i
$34$	0.500988	−	0.420379i	0.0859187	−	0.0720943i
$35$	−2.61582	−	1.03552i	−0.442155	−	0.175035i
$36$	−5.11644	−	2.97000i	−0.852740	−	0.495000i
$37$	4.37450			0.719164			0.359582	−	0.933113i	$-0.382919\pi$
$37$	4.37450			0.719164			0.359582	+	0.933113i	$0.382919\pi$
$38$	−0.221744	−	0.0807084i	−0.0359717	−	0.0130926i
$39$	−0.186600	+	2.10442i	−0.0298799	+	0.336977i
$40$	−0.541453	−	0.454333i	−0.0856113	−	0.0718364i
$41$	−8.04440	+	2.92792i	−1.25632	+	0.457265i	−0.882534	−	0.470248i	$-0.844164\pi$
$41$	−8.04440	+	2.92792i	−1.25632	+	0.457265i	−0.373790	+	0.927513i	$0.621942\pi$
$42$	0.421443	+	0.640715i	0.0650300	+	0.0988644i
$43$	−1.05735	−	5.99651i	−0.161244	−	0.914459i	−0.952853	−	0.303431i	$-0.901868\pi$
$43$	−1.05735	−	5.99651i	−0.161244	−	0.914459i	0.791610	−	0.611027i	$-0.209243\pi$
$44$	−2.17508			−0.327906
$45$	2.75889	+	1.60148i	0.411271	+	0.238735i
$46$	−0.781690			−0.115254
$47$	−1.73596	−	0.631839i	−0.253216	−	0.0921632i	0.212293	−	0.977206i	$-0.431907\pi$
$47$	−1.73596	−	0.631839i	−0.253216	−	0.0921632i	−0.465510	+	0.885043i	$0.654129\pi$
$48$	−1.71065	−	6.41432i	−0.246911	−	0.925828i
$49$	0.829534	+	6.95067i	0.118505	+	0.992953i
$50$	−0.496037	−	0.416225i	−0.0701502	−	0.0588630i
$51$	−6.74366	+	0.582025i	−0.944301	+	0.0814998i
$52$	−1.84260	+	1.54613i	−0.255523	+	0.214409i
$53$	−4.55546	+	7.89029i	−0.625741	+	1.08382i	0.362656	+	0.931923i	$0.381870\pi$
$53$	−4.55546	+	7.89029i	−0.625741	+	1.08382i	−0.988397	+	0.151892i	$0.951463\pi$
$54$	−0.364724	−	0.789393i	−0.0496327	−	0.107423i
$55$	1.17285			0.158147
$56$	−0.353542	+	1.72277i	−0.0472440	+	0.230214i
$57$	1.39850	+	2.00226i	0.185236	+	0.265206i
$58$	−0.253866	+	1.43975i	−0.0333343	+	0.189048i
$59$	0.0125627	+	0.0105414i	0.00163553	+	0.00137237i	0.643605	−	0.765358i	$-0.277438\pi$
$59$	0.0125627	+	0.0105414i	0.00163553	+	0.00137237i	−0.641969	+	0.766730i	$0.721882\pi$
$60$	0.935899	+	3.50928i	0.120824	+	0.453046i
$61$	−7.36629	−	2.68111i	−0.943157	−	0.343281i	−0.175745	−	0.984436i	$-0.556233\pi$
$61$	−7.36629	−	2.68111i	−0.943157	−	0.343281i	−0.767412	+	0.641155i	$0.778456\pi$
$62$	−0.258768	−	0.448199i	−0.0328635	−	0.0569213i
$63$	0.239827	−	7.93363i	0.0302154	−	0.999543i
$64$	3.66784	−	6.35288i	0.458480	−	0.794110i
$65$	0.993568	−	0.833703i	0.123237	−	0.103408i
$66$	−0.261676	−	0.183686i	−0.0322101	−	0.0226101i
$67$	−1.27108	+	7.20865i	−0.155287	+	0.880677i	0.803236	+	0.595661i	$0.203110\pi$
$67$	−1.27108	+	7.20865i	−0.155287	+	0.880677i	−0.958523	+	0.285016i	$0.908001\pi$
$68$	−5.90345	−	4.95358i	−0.715899	−	0.600710i
$69$	6.62180	+	4.64822i	0.797171	+	0.559580i
$70$	0.0946464	−	0.461201i	0.0113124	−	0.0551240i
$71$	8.19310	−	14.1909i	0.972342	−	1.68415i	0.283902	−	0.958853i	$-0.408371\pi$
$71$	8.19310	−	14.1909i	0.972342	−	1.68415i	0.688440	−	0.725293i	$-0.258296\pi$
$72$	0.686431	−	1.87228i	0.0808967	−	0.220650i
$73$	9.16921			1.07317			0.536587	−	0.843845i	$-0.319713\pi$
$73$	9.16921			1.07317			0.536587	+	0.843845i	$0.319713\pi$
$74$	0.127123	+	0.720953i	0.0147778	+	0.0838091i
$75$	1.72697	+	6.47551i	0.199413	+	0.747728i
$76$	−0.482854	+	2.73840i	−0.0553872	+	0.314116i
$77$	−1.38811	−	2.56694i	−0.158190	−	0.292530i
$78$	−0.352247	+	0.0304014i	−0.0398842	+	0.00344228i
$79$	−1.89813	−	10.7649i	−0.213557	−	1.21114i	−0.883393	−	0.468632i	$-0.844747\pi$
$79$	−1.89813	−	10.7649i	−0.213557	−	1.21114i	0.669836	−	0.742509i	$-0.266364\pi$
$80$	−2.03776	+	3.52950i	−0.227828	+	0.394610i
$81$	−1.60440	+	8.85584i	−0.178266	+	0.983982i
$82$	−0.716316	−	1.24070i	−0.0791039	−	0.137012i
$83$	11.3691	+	4.13802i	1.24792	+	0.454207i	0.879700	−	0.475530i	$-0.157744\pi$
$83$	11.3691	+	4.13802i	1.24792	+	0.454207i	0.368224	+	0.929737i	$0.379966\pi$
$84$	6.57288	−	6.20171i	0.717160	−	0.676662i
$85$	3.18326	+	2.67107i	0.345273	+	0.289719i
$86$	0.957545	−	0.348518i	0.103255	−	0.0375817i
$87$	10.7118	−	10.6867i	1.14843	−	1.14573i
$88$	−0.127314	−	0.722032i	−0.0135717	−	0.0769689i
$89$	8.07668	−	13.9892i	0.856127	−	1.48286i	−0.0194689	−	0.999810i	$-0.506198\pi$
$89$	8.07668	−	13.9892i	0.856127	−	1.48286i	0.875596	−	0.483045i	$-0.160469\pi$
$90$	−0.183764	+	0.501226i	−0.0193704	+	0.0528338i
$91$	−3.00060	−	1.18785i	−0.314548	−	0.124520i
$92$	1.59950	+	9.07121i	0.166759	+	0.945739i
$93$	−0.473100	+	5.33548i	−0.0490581	+	0.553263i
$94$	0.0536849	−	0.304462i	0.00553717	−	0.0314029i
$95$	0.260365	−	1.47660i	0.0267129	−	0.151496i
$96$	3.09546	−	1.43902i	0.315929	−	0.146869i
$97$	−0.0674999	−	0.382811i	−0.00685357	−	0.0388685i	0.981189	−	0.193049i	$-0.0618375\pi$
$97$	−0.0674999	−	0.382811i	−0.00685357	−	0.0388685i	−0.988043	+	0.154180i	$0.950726\pi$
$98$	−1.12142	+	0.338701i	−0.113281	+	0.0342140i
$99$	1.12443	+	3.11205i	0.113010	+	0.312773i
$100$	−3.81513	+	6.60799i	−0.381513	+	0.660799i
$101$	−0.0271522	−	0.153988i	−0.00270174	−	0.0153223i	0.983427	−	0.181304i	$-0.0580318\pi$
$101$	−0.0271522	−	0.153988i	−0.00270174	−	0.0153223i	−0.986129	+	0.165982i	$0.946921\pi$
$102$	−0.291894	−	1.09449i	−0.0289018	−	0.108371i
$103$	−12.1426	+	4.41953i	−1.19644	+	0.435469i	−0.861981	−	0.506940i	$-0.830777\pi$
$103$	−12.1426	+	4.41953i	−1.19644	+	0.435469i	−0.334461	+	0.942410i	$0.608554\pi$
$104$	−0.621100	−	0.521164i	−0.0609038	−	0.0511044i
$105$	−3.54423	+	3.34409i	−0.345881	+	0.326350i
$106$	−1.43277	−	0.521484i	−0.139162	−	0.0506510i
$107$	−0.102633	−	0.177765i	−0.00992187	−	0.0171852i	0.861022	−	0.508568i	$-0.169825\pi$
$107$	−0.102633	−	0.177765i	−0.00992187	−	0.0171852i	−0.870944	+	0.491383i	$0.836492\pi$
$108$	−8.41430	+	5.84774i	−0.809666	+	0.562699i
$109$	3.12301	−	5.40921i	0.299130	−	0.518109i	−0.676807	−	0.736160i	$-0.736637\pi$
$109$	3.12301	−	5.40921i	0.299130	−	0.518109i	0.975937	+	0.218052i	$0.0699702\pi$
$110$	0.0340831	+	0.193295i	0.00324969	+	0.0184299i
$111$	3.21017	−	6.86321i	0.304696	−	0.651427i
$112$	10.1366	+	0.282624i	0.957815	+	0.0267055i
$113$	−2.15911	+	12.2449i	−0.203112	+	1.15191i	0.697270	+	0.716808i	$0.254398\pi$
$113$	−2.15911	+	12.2449i	−0.203112	+	1.15191i	−0.900383	+	0.435099i	$0.856713\pi$
$114$	−0.289348	+	0.288671i	−0.0271000	+	0.0270365i
$115$	−0.862482	−	4.89138i	−0.0804269	−	0.456123i
$116$	17.2272			1.59950
$117$	3.16471	+	1.83706i	0.292578	+	0.169836i
$118$	−0.00137223	+	0.00237677i	−0.000126324	+	0.000218800i
$119$	2.07851	−	10.1283i	0.190537	−	0.928462i
$120$	−1.11015	+	0.516086i	−0.101342	+	0.0471120i
$121$	−7.49454	−	6.28866i	−0.681322	−	0.571697i
$122$	0.227803	−	1.29194i	0.0206243	−	0.116966i
$123$	−1.30963	+	14.7696i	−0.118085	+	1.33173i
$124$	−4.67168	+	3.92000i	−0.419529	+	0.352026i
$125$	4.71554	−	8.16756i	0.421771	−	0.730529i
$126$	1.31449	−	0.191027i	0.117104	−	0.0170180i
$127$	−5.53843	−	9.59284i	−0.491456	−	0.851227i	0.508496	−	0.861065i	$-0.330202\pi$
$127$	−5.53843	−	9.59284i	−0.491456	−	0.851227i	−0.999952	+	0.00983786i	$0.996868\pi$
$128$	4.85756	+	1.76801i	0.429352	+	0.156271i
$129$	−10.1839	−	2.74157i	−0.896643	−	0.241382i
$130$	0.166274	+	0.139520i	0.0145832	+	0.0122368i
$131$	3.76740	−	21.3660i	0.329159	−	1.86675i	−0.149512	−	0.988760i	$-0.547770\pi$
$131$	3.76740	−	21.3660i	0.329159	−	1.86675i	0.478671	−	0.877994i	$-0.341119\pi$
$132$	−1.59615	+	3.41251i	−0.138927	+	0.297021i
$133$	−3.53990	+	1.17777i	−0.306948	+	0.102125i
$134$	−1.22498			−0.105822
$135$	4.53716	−	3.15322i	0.390497	−	0.271386i
$136$	1.29883	−	2.24964i	0.111374	−	0.192905i
$137$	2.74303	−	2.30168i	0.234353	−	0.196646i	−0.518047	−	0.855352i	$-0.673341\pi$
$137$	2.74303	−	2.30168i	0.234353	−	0.196646i	0.752400	+	0.658707i	$0.228896\pi$
$138$	−0.573633	+	1.22640i	−0.0488309	+	0.104398i
$139$	−8.63704	−	7.24733i	−0.732584	−	0.614711i	0.198251	−	0.980151i	$-0.436474\pi$
$139$	−8.63704	−	7.24733i	−0.732584	−	0.614711i	−0.930835	+	0.365440i	$0.880918\pi$
$140$	−5.54572	−	0.154624i	−0.468699	−	0.0130681i
$141$	−2.26521	+	2.25991i	−0.190765	+	0.190319i
$142$	2.57686	+	0.937900i	0.216245	+	0.0787068i
$143$	1.34537			0.112506
$144$	−11.3188	−	2.02320i	−0.943237	−	0.168600i
$145$	−9.28923			−0.771429
$146$	0.266458	+	1.51116i	0.0220522	+	0.125064i
$147$	11.5137	+	3.79919i	0.949637	+	0.313352i
$148$	8.10625	−	2.95044i	0.666330	−	0.242524i
$149$	8.24863	+	6.92142i	0.675754	+	0.567025i	0.914762	−	0.403993i	$-0.132378\pi$
$149$	8.24863	+	6.92142i	0.675754	+	0.567025i	−0.239008	+	0.971018i	$0.576822\pi$
$150$	−1.01703	+	0.472797i	−0.0830401	+	0.0386038i
$151$	−9.05289	−	3.29498i	−0.736714	−	0.268142i	−0.0537099	−	0.998557i	$-0.517105\pi$
$151$	−9.05289	−	3.29498i	−0.736714	−	0.268142i	−0.683004	+	0.730415i	$0.739327\pi$
$152$	−0.937293			−0.0760245
$153$	−4.03560	+	11.0073i	−0.326259	+	0.889889i
$154$	0.382714	−	0.303367i	0.0308400	−	0.0244460i
$155$	2.51906	−	2.11374i	0.202336	−	0.169780i
$156$	1.07357	+	4.02548i	0.0859541	+	0.322297i
$157$	4.52487	+	3.79682i	0.361124	+	0.303019i	0.805239	−	0.592951i	$-0.202037\pi$
$157$	4.52487	+	3.79682i	0.361124	+	0.303019i	−0.444114	+	0.895970i	$0.646482\pi$
$158$	1.71897	−	0.625655i	0.136754	−	0.0497745i
$159$	9.03621	+	12.9373i	0.716618	+	1.02600i
$160$	−1.96929	−	0.716762i	−0.155686	−	0.0566650i
$161$	−9.68469	+	7.67679i	−0.763261	+	0.605016i
$162$	−1.50614	−	0.00706558i	−0.118333	−	0.000555124i
$163$	6.14002	+	10.6348i	0.480924	+	0.832984i	0.999760	−	0.0218892i	$-0.00696809\pi$
$163$	6.14002	+	10.6348i	0.480924	+	0.832984i	−0.518837	+	0.854873i	$0.673635\pi$
$164$	−12.9321	+	10.8513i	−1.00982	+	0.847343i
$165$	0.860679	−	1.84009i	0.0670038	−	0.143251i
$166$	−0.351591	+	1.99397i	−0.0272888	+	0.154762i
$167$	1.00808	−	5.71710i	0.0780075	−	0.442403i	−0.920640	−	0.390412i	$-0.872332\pi$
$167$	1.00808	−	5.71710i	0.0780075	−	0.442403i	0.998648	−	0.0519902i	$-0.0165564\pi$
$168$	2.44343	+	1.81891i	0.188515	+	0.140332i
$169$	−8.81886	+	7.39990i	−0.678374	+	0.569223i
$170$	−0.347708	+	0.602248i	−0.0266680	+	0.0461903i
$171$	4.16765	−	0.724794i	0.318708	−	0.0554264i
$172$	−6.00375	−	10.3988i	−0.457781	−	0.792901i
$173$	−1.99539	+	1.67433i	−0.151707	+	0.127297i	−0.715482	−	0.698631i	$-0.753793\pi$
$173$	−1.99539	+	1.67433i	−0.151707	+	0.127297i	0.563775	+	0.825928i	$0.309348\pi$
$174$	2.07254	+	1.45483i	0.157119	+	0.110291i
$175$	−10.2333	−	0.285320i	−0.773561	−	0.0215682i
$176$	−3.97252	+	1.44588i	−0.299440	+	0.108987i
$177$	0.0257575	−	0.0119742i	0.00193605	−	0.000900034i
$178$	2.54024	+	0.924574i	0.190399	+	0.0692997i
$179$	−6.48035	−	11.2243i	−0.484364	−	0.838944i	0.515474	−	0.856905i	$-0.327616\pi$
$179$	−6.48035	−	11.2243i	−0.484364	−	0.838944i	−0.999839	+	0.0179614i	$0.994282\pi$
$180$	6.19255	+	1.10690i	0.461565	+	0.0825031i
$181$	3.49102	+	6.04662i	0.259485	+	0.449442i	0.966104	−	0.258153i	$-0.0831137\pi$
$181$	3.49102	+	6.04662i	0.259485	+	0.449442i	−0.706619	+	0.707594i	$0.749780\pi$
$182$	0.108569	−	0.529042i	0.00804765	−	0.0392152i
$183$	−9.61208	+	9.58956i	−0.710545	+	0.708881i
$184$	−2.91762	+	1.06193i	−0.215090	+	0.0782864i
$185$	−4.37106	+	1.59093i	−0.321366	+	0.116968i
$186$	−0.893077	+	0.0770788i	−0.0654836	+	0.00565169i
$187$	0.748491	+	4.24490i	0.0547351	+	0.310418i
$188$	−3.64301			−0.265694
$189$	−12.2712	−	6.19826i	−0.892596	−	0.450857i
$190$	0.250922			0.0182038
$191$	−3.58675	−	20.3415i	−0.259528	−	1.47186i	−0.784176	−	0.620538i	$-0.786914\pi$
$191$	−3.58675	−	20.3415i	−0.259528	−	1.47186i	0.524648	−	0.851319i	$-0.324197\pi$
$192$	−7.27551	−	10.4165i	−0.525065	−	0.751745i
$193$	−4.24624	+	1.54551i	−0.305651	+	0.111248i	−0.490292	−	0.871558i	$-0.663110\pi$
$193$	−4.24624	+	1.54551i	−0.305651	+	0.111248i	0.184641	+	0.982806i	$0.440888\pi$
$194$	0.0611287	−	0.0222490i	0.00438879	−	0.00159739i
$195$	−0.578889	−	2.17062i	−0.0414551	−	0.155442i
$196$	6.22515	+	12.3206i	0.444653	+	0.880042i
$197$	2.46875	+	4.27599i	0.175891	+	0.304652i	0.940469	−	0.339879i	$-0.110386\pi$
$197$	2.46875	+	4.27599i	0.175891	+	0.304652i	−0.764578	+	0.644531i	$0.777053\pi$
$198$	−0.480214	+	0.275752i	−0.0341273	+	0.0195968i
$199$	12.7724	+	22.1225i	0.905413	+	1.56822i	0.820362	+	0.571844i	$0.193772\pi$
$199$	12.7724	+	22.1225i	0.905413	+	1.56822i	0.0850503	+	0.996377i	$0.472895\pi$
$200$	−2.41688	−	0.879671i	−0.170899	−	0.0622022i
$201$	10.3770	+	7.28419i	0.731935	+	0.513787i
$202$	0.0245893	−	0.00894979i	0.00173010	−	0.000629705i
$203$	10.9942	+	20.3308i	0.771638	+	1.42694i
$204$	−12.1039	+	5.62687i	−0.847443	+	0.393960i
$205$	6.97323	−	5.85123i	0.487031	−	0.408668i
$206$	−1.08124	−	1.87276i	−0.0753334	−	0.130481i
$207$	12.1520	−	6.97799i	0.844620	−	0.485004i
$208$	−2.33750	+	4.04867i	−0.162077	+	0.280725i
$209$	1.19142	−	0.999718i	0.0824121	−	0.0691519i
$210$	−0.654128	−	0.486938i	−0.0451391	−	0.0336019i
$211$	2.17639	−	12.3429i	0.149829	−	0.849723i	−0.813533	−	0.581519i	$-0.802459\pi$
$211$	2.17639	−	12.3429i	0.149829	−	0.849723i	0.963362	−	0.268204i	$-0.0864302\pi$
$212$	−3.11988	+	17.6937i	−0.214274	+	1.21521i
$213$	−16.2518	−	23.2680i	−1.11356	−	1.59430i
$214$	0.0263145	−	0.0220805i	0.00179883	−	0.00150939i
$215$	3.23734	+	5.60724i	0.220785	+	0.382411i
$216$	−2.43371	−	2.45090i	−0.165593	−	0.166762i
$217$	−7.60763	−	3.01163i	−0.516440	−	0.204443i
$218$	0.982236	+	0.357505i	0.0665254	+	0.0242133i
$219$	6.72870	−	14.3857i	0.454684	−	0.972094i
$220$	2.17337	−	0.791041i	0.146528	−	0.0533320i
$221$	3.65151	+	3.06398i	0.245627	+	0.206106i
$222$	1.22440	+	0.329616i	0.0821763	+	0.0221224i
$223$	15.4961	−	13.0027i	1.03769	−	0.870729i	0.0459475	−	0.998944i	$-0.485369\pi$
$223$	15.4961	−	13.0027i	1.03769	−	0.870729i	0.991746	+	0.128215i	$0.0409249\pi$
$224$	0.761991	+	5.15838i	0.0509127	+	0.344659i
$225$	11.4268	+	2.04250i	0.761788	+	0.136167i
$226$	−2.08081			−0.138413
$227$	−0.00667054	−	0.00242788i	−0.000442739	−	0.000161144i	0.341799	−	0.939773i	$-0.388964\pi$
$227$	−0.00667054	−	0.00242788i	−0.000442739	−	0.000161144i	−0.342242	+	0.939612i	$0.611186\pi$
$228$	3.94197	+	2.76710i	0.261064	+	0.183255i
$229$	9.76722	+	8.19567i	0.645436	+	0.541585i	0.905682	−	0.423957i	$-0.139359\pi$
$229$	9.76722	+	8.19567i	0.645436	+	0.541585i	−0.260246	+	0.965542i	$0.583804\pi$
$230$	0.781074	−	0.284288i	0.0515025	−	0.0187454i
$231$	−5.04595	+	0.294104i	−0.331999	+	0.0193506i
$232$	1.00835	+	5.71867i	0.0662017	+	0.375449i
$233$	−25.7318			−1.68575			−0.842874	−	0.538110i	$-0.819138\pi$
$233$	−25.7318			−1.68575			−0.842874	+	0.538110i	$0.819138\pi$
$234$	−0.210795	+	0.574955i	−0.0137801	+	0.0375860i
$235$	1.96439			0.128142
$236$	0.0303894	+	0.0110608i	0.00197818	+	0.000719999i
$237$	−18.2820	−	4.92164i	−1.18755	−	0.319695i
$238$	1.72963	+	0.0482250i	0.112115	+	0.00312596i
$239$	−5.87757	−	4.93187i	−0.380188	−	0.319016i	0.432588	−	0.901592i	$-0.357600\pi$
$239$	−5.87757	−	4.93187i	−0.380188	−	0.319016i	−0.812776	+	0.582576i	$0.802045\pi$
$240$	4.04209	+	5.78713i	0.260916	+	0.373558i
$241$	14.3640	−	12.0528i	0.925266	−	0.776391i	−0.0496951	−	0.998764i	$-0.515825\pi$
$241$	14.3640	−	12.0528i	0.925266	−	0.776391i	0.974961	+	0.222374i	$0.0713805\pi$
$242$	0.818630	−	1.41791i	0.0526235	−	0.0911466i
$243$	12.7167	+	9.01590i	0.815775	+	0.578370i
$244$	−15.4585			−0.989632
$245$	−3.35673	−	6.64351i	−0.214453	−	0.424438i
$246$	−2.47220	+	0.213368i	−0.157622	+	0.0136039i
$247$	0.298664	−	1.69381i	0.0190035	−	0.107774i
$248$	−1.57472	−	1.32134i	−0.0999946	−	0.0839054i
$249$	14.8353	−	14.8005i	0.940148	−	0.937945i
$250$	1.48311	+	0.539809i	0.0938003	+	0.0341405i
$251$	12.2199	+	21.1655i	0.771315	+	1.33596i	0.936842	+	0.349752i	$0.113734\pi$
$251$	12.2199	+	21.1655i	0.771315	+	1.33596i	−0.165527	+	0.986205i	$0.552933\pi$
$252$	−4.90651	−	14.8633i	−0.309081	−	0.936301i
$253$	2.57601	−	4.46178i	0.161953	−	0.280510i
$254$	1.42003	−	1.19155i	0.0891005	−	0.0747642i
$255$	6.52667	−	3.03412i	0.408716	−	0.190004i
$256$	2.39743	−	13.5965i	0.149840	−	0.849782i
$257$	4.03394	+	3.38488i	0.251630	+	0.211143i	0.759874	−	0.650070i	$-0.225261\pi$
$257$	4.03394	+	3.38488i	0.251630	+	0.211143i	−0.508244	+	0.861213i	$0.669705\pi$
$258$	0.155888	−	1.75806i	0.00970517	−	0.109452i
$259$	8.65529	+	7.68374i	0.537814	+	0.477445i
$260$	1.27885	−	2.21503i	0.0793109	−	0.137370i
$261$	−8.90578	−	24.6482i	−0.551254	−	1.52568i
$262$	3.63076			0.224309
$263$	−2.22418	−	12.6140i	−0.137149	−	0.777811i	−0.973339	−	0.229371i	$-0.926333\pi$
$263$	−2.22418	−	12.6140i	−0.137149	−	0.777811i	0.836190	−	0.548440i	$-0.184778\pi$
$264$	−1.22623	−	0.330110i	−0.0754694	−	0.0203169i
$265$	1.68230	−	9.54082i	0.103343	−	0.586088i
$266$	−0.296976	−	0.549178i	−0.0182087	−	0.0336723i
$267$	−16.0209	−	22.9374i	−0.980463	−	1.40375i
$268$	2.50656	+	14.2154i	0.153113	+	0.868345i
$269$	−13.9193	+	24.1090i	−0.848676	+	1.46995i	0.0337142	+	0.999432i	$0.489266\pi$
$269$	−13.9193	+	24.1090i	−0.848676	+	1.46995i	−0.882390	+	0.470518i	$0.844067\pi$
$270$	0.651526	+	0.656127i	0.0396506	+	0.0399306i
$271$	3.06182	+	5.30324i	0.185993	+	0.322149i	0.943911	−	0.330201i	$-0.107117\pi$
$271$	3.06182	+	5.30324i	0.185993	+	0.322149i	−0.757918	+	0.652350i	$0.773783\pi$
$272$	−14.0748	−	5.12281i	−0.853411	−	0.310616i
$273$	−4.06558	+	3.83599i	−0.246060	+	0.232165i
$274$	0.459048	+	0.385187i	0.0277321	+	0.0232700i
$275$	4.01041	−	1.45967i	0.241837	−	0.0880215i
$276$	15.4057	+	4.14731i	0.927314	+	0.249639i
$277$	−1.20896	−	6.85633i	−0.0726391	−	0.411957i	−0.999346	−	0.0361710i	$-0.988484\pi$
$277$	−1.20896	−	6.85633i	−0.0726391	−	0.411957i	0.926706	−	0.375786i	$-0.122627\pi$
$278$	0.943425	−	1.63406i	0.0565829	−	0.0980044i
$279$	8.02371	+	4.65762i	0.480367	+	0.278844i
$280$	−0.273278	−	1.84999i	−0.0163315	−	0.110558i
$281$	4.40712	+	24.9940i	0.262907	+	1.49102i	0.774930	+	0.632047i	$0.217785\pi$
$281$	4.40712	+	24.9940i	0.262907	+	1.49102i	−0.512023	+	0.858971i	$0.671104\pi$
$282$	−0.438278	−	0.307652i	−0.0260991	−	0.0183204i
$283$	−3.26995	+	18.5448i	−0.194378	+	1.10237i	0.718923	+	0.695090i	$0.244635\pi$
$283$	−3.26995	+	18.5448i	−0.194378	+	1.10237i	−0.913301	+	0.407285i	$0.866476\pi$
$284$	5.61118	−	31.8226i	0.332962	−	1.88832i
$285$	−2.12559	−	1.49207i	−0.125909	−	0.0883828i
$286$	0.0390966	+	0.221728i	0.00231183	+	0.0131110i
$287$	−21.0593	−	8.33673i	−1.24309	−	0.492102i
$288$	0.0138683	−	5.91251i	0.000817196	−	0.348398i
$289$	0.864054	−	1.49658i	0.0508267	−	0.0880344i
$290$	−0.269946	−	1.53094i	−0.0158518	−	0.0898998i
$291$	−0.650130	−	0.175019i	−0.0381113	−	0.0102598i
$292$	16.9912	−	6.18428i	0.994333	−	0.361908i
$293$	22.7437	+	19.0842i	1.32870	+	1.11491i	0.984379	+	0.176061i	$0.0563356\pi$
$293$	22.7437	+	19.0842i	1.32870	+	1.11491i	0.344322	+	0.938852i	$0.388109\pi$
$294$	−0.291547	+	2.00796i	−0.0170034	+	0.117107i
$295$	−0.0163866	−	0.00596423i	−0.000954063	−	0.000347251i
$296$	1.45390	+	2.51823i	0.0845061	+	0.146369i
$297$	5.70768	+	0.519599i	0.331193	+	0.0301502i
$298$	−0.900999	+	1.56058i	−0.0521935	+	0.0904018i
$299$	−0.989351	−	5.61089i	−0.0572156	−	0.324486i
$300$	7.56768	+	10.8348i	0.436920	+	0.625547i
$301$	8.44072	−	13.7218i	0.486515	−	0.790909i
$302$	0.279962	−	1.58774i	0.0161100	−	0.0913642i
$303$	−0.261518	−	0.0704024i	−0.0150238	−	0.00404451i
$304$	0.938470	+	5.32233i	0.0538250	+	0.305257i
$305$	8.33556			0.477293
$306$	−1.93137	−	0.345225i	−0.110409	−	0.0197352i
$307$	−0.592505	+	1.02625i	−0.0338161	+	0.0585711i	−0.882438	−	0.470428i	$-0.844099\pi$
$307$	−0.592505	+	1.02625i	−0.0338161	+	0.0585711i	0.848622	+	0.529000i	$0.177433\pi$
$308$	−4.30357	−	3.82049i	−0.245218	−	0.217693i
$309$	−1.97681	+	22.2938i	−0.112457	+	1.26825i
$310$	0.421566	+	0.353736i	0.0239433	+	0.0200908i
$311$	2.74241	−	15.5530i	0.155508	−	0.881929i	−0.802812	−	0.596232i	$-0.796664\pi$
$311$	2.74241	−	15.5530i	0.155508	−	0.881929i	0.958320	−	0.285697i	$-0.0922251\pi$
$312$	−1.27345	+	0.592001i	−0.0720947	+	0.0335154i
$313$	−13.4998	+	11.3276i	−0.763051	+	0.640276i	−0.938919	−	0.344138i	$-0.888171\pi$
$313$	−13.4998	+	11.3276i	−0.763051	+	0.640276i	0.175868	+	0.984414i	$0.443727\pi$
$314$	−0.494253	+	0.856071i	−0.0278923	+	0.0483109i
$315$	2.64569	+	8.01460i	0.149068	+	0.451571i
$316$	−10.7779	−	18.6678i	−0.606302	−	1.05015i
$317$	11.5041	+	4.18714i	0.646132	+	0.235173i	0.644238	−	0.764825i	$-0.277175\pi$
$317$	11.5041	+	4.18714i	0.646132	+	0.235173i	0.00189457	+	0.999998i	$0.499397\pi$
$318$	−1.86958	+	1.86520i	−0.104841	+	0.104595i
$319$	−7.38128	−	6.19363i	−0.413272	−	0.346777i
$320$	−1.35451	+	7.68180i	−0.0757194	+	0.429426i
$321$	−0.354213	+	0.0305711i	−0.0197702	+	0.00170631i
$322$	−1.54663	−	1.37303i	−0.0861906	−	0.0765157i
$323$	5.51044			0.306609
$324$	2.99987	+	17.4926i	0.166660	+	0.971810i
$325$	2.35980	−	4.08730i	0.130898	−	0.226722i
$326$	−1.57427	+	1.32097i	−0.0871910	+	0.0731620i
$327$	−6.19480	−	8.86921i	−0.342573	−	0.490468i
$328$	−4.35910	−	3.65772i	−0.240691	−	0.201964i
$329$	−2.32492	−	4.29934i	−0.128177	−	0.237030i
$330$	0.328274	+	0.0883734i	0.0180709	+	0.00486480i
$331$	12.8509	+	4.67734i	0.706349	+	0.257090i	0.670119	−	0.742254i	$-0.266243\pi$
$331$	12.8509	+	4.67734i	0.706349	+	0.257090i	0.0362296	+	0.999343i	$0.488465\pi$
$332$	23.8587			1.30942
$333$	−8.41203	−	10.0730i	−0.460976	−	0.551994i
$334$	0.971518			0.0531591
$335$	−1.35159	−	7.66524i	−0.0738452	−	0.418797i
$336$	7.88199	−	15.6960i	0.429998	−	0.856285i
$337$	23.9720	−	8.72509i	1.30584	−	0.475286i	0.406944	−	0.913453i	$-0.366595\pi$
$337$	23.9720	−	8.72509i	1.30584	−	0.475286i	0.898893	+	0.438168i	$0.144372\pi$
$338$	−1.47584	−	1.23838i	−0.0802751	−	0.0673588i
$339$	17.6268	+	12.3732i	0.957356	+	0.672023i
$340$	7.70033	+	2.80269i	0.417609	+	0.151997i
$341$	3.41101			0.184717
$342$	0.240564	+	0.665799i	0.0130082	+	0.0360023i
$343$	−10.5674	+	15.2095i	−0.570588	+	0.821236i
$344$	3.10053	−	2.60165i	0.167169	−	0.140272i
$345$	−8.30706	−	2.23632i	−0.447237	−	0.120399i
$346$	−0.333929	−	0.280200i	−0.0179521	−	0.0150636i
$347$	−8.59346	+	3.12776i	−0.461321	+	0.167907i	−0.562217	−	0.826990i	$-0.690051\pi$
$347$	−8.59346	+	3.12776i	−0.461321	+	0.167907i	0.100896	+	0.994897i	$0.467829\pi$
$348$	12.6419	−	27.0279i	0.677678	−	1.44885i
$349$	18.1898	+	6.62055i	0.973678	+	0.354390i	0.779379	−	0.626553i	$-0.215535\pi$
$349$	18.1898	+	6.62055i	0.973678	+	0.354390i	0.194299	+	0.980942i	$0.437757\pi$
$350$	−0.250356	−	1.69481i	−0.0133821	−	0.0905916i
$351$	5.20456	−	3.61705i	0.277799	−	0.193064i
$352$	−1.08690	−	1.88257i	−0.0579322	−	0.100342i
$353$	−26.7293	+	22.4285i	−1.42266	+	1.19375i	−0.472757	+	0.881193i	$0.656741\pi$
$353$	−26.7293	+	22.4285i	−1.42266	+	1.19375i	−0.949899	+	0.312557i	$0.898814\pi$
$354$	0.00272195	+	0.00389707i	0.000144670	+	0.000207127i
$355$	−3.02566	+	17.1594i	−0.160585	+	0.910725i
$356$	5.53145	−	31.3704i	0.293166	−	1.66263i
$357$	−14.3652	−	10.6935i	−0.760285	−	0.565962i
$358$	1.66153	−	1.39419i	0.0878148	−	0.0736854i
$359$	−8.51495	+	14.7483i	−0.449402	+	0.778387i	−0.998347	−	0.0574713i	$-0.981696\pi$
$359$	−8.51495	+	14.7483i	−0.449402	+	0.778387i	0.548945	+	0.835858i	$0.315030\pi$
$360$	−0.00497368	+	2.12045i	−0.000262136	+	0.111757i
$361$	8.50585	+	14.7326i	0.447677	+	0.775398i
$362$	−0.895082	+	0.751063i	−0.0470445	+	0.0394750i
$363$	−15.3661	+	7.14341i	−0.806512	+	0.374932i
$364$	−6.36148	−	0.177368i	−0.333432	−	0.00929664i
$365$	−9.16198	+	3.33469i	−0.479560	+	0.174546i
$366$	−1.85976	−	1.30547i	−0.0972114	−	0.0682382i
$367$	−10.4089	−	3.78853i	−0.543340	−	0.197760i	0.0557451	−	0.998445i	$-0.482247\pi$
$367$	−10.4089	−	3.78853i	−0.543340	−	0.197760i	−0.599085	+	0.800685i	$0.704469\pi$
$368$	8.95135	+	15.5042i	0.466621	+	0.808211i
$369$	22.2111	+	12.8931i	1.15626	+	0.671190i
$370$	−0.389222	−	0.674152i	−0.0202347	−	0.0350475i
$371$	−22.8725	+	7.60996i	−1.18748	+	0.395089i
$372$	2.72189	+	10.2061i	0.141123	+	0.529161i
$373$	22.1971	−	8.07909i	1.14932	−	0.418319i	0.304051	−	0.952656i	$-0.401661\pi$
$373$	22.1971	−	8.07909i	1.14932	−	0.418319i	0.845272	+	0.534336i	$0.179438\pi$
$374$	−0.677842	+	0.246714i	−0.0350504	+	0.0127573i
$375$	−9.35374	−	13.3919i	−0.483025	−	0.691556i
$376$	−0.213236	−	1.20932i	−0.0109968	−	0.0623660i
$377$	−10.6557			−0.548794
$378$	0.664921	−	2.20251i	0.0341998	−	0.113285i
$379$	−34.6919			−1.78200			−0.891002	−	0.454000i	$-0.849997\pi$
$379$	−34.6919			−1.78200			−0.891002	+	0.454000i	$0.849997\pi$
$380$	−0.513438	−	2.91185i	−0.0263388	−	0.149375i
$381$	−19.1146	+	1.64973i	−0.979271	+	0.0845180i
$382$	3.24820	−	1.18225i	0.166193	−	0.0604892i
$383$	−11.8246	+	4.30380i	−0.604209	+	0.219914i	−0.625968	−	0.779849i	$-0.715296\pi$
$383$	−11.8246	+	4.30380i	−0.604209	+	0.219914i	0.0217584	+	0.999763i	$0.493074\pi$
$384$	6.33851	−	6.32366i	0.323461	−	0.322703i
$385$	2.32057	+	2.06009i	0.118267	+	0.104992i
$386$	−0.378108	−	0.654902i	−0.0192452	−	0.0333337i
$387$	−11.7746	+	13.9658i	−0.598537	+	0.709921i
$388$	−0.383273	−	0.663848i	−0.0194577	−	0.0337018i
$389$	−11.0087	−	4.00685i	−0.558164	−	0.203155i	0.0475058	−	0.998871i	$-0.484873\pi$
$389$	−11.0087	−	4.00685i	−0.558164	−	0.203155i	−0.605670	+	0.795716i	$0.707095\pi$
$390$	0.340913	−	0.158484i	0.0172628	−	0.00802515i
$391$	17.1530	−	6.24319i	0.867465	−	0.315731i
$392$	−3.72552	+	2.78764i	−0.188167	+	0.140797i
$393$	−30.7567	−	21.5899i	−1.55147	−	1.08906i
$394$	−0.632976	+	0.531130i	−0.0318889	+	0.0267579i
$395$	5.81164	+	10.0661i	0.292415	+	0.506478i
$396$	4.18261	+	5.00845i	0.210184	+	0.251684i
$397$	13.3007	−	23.0375i	0.667545	−	1.15622i	−0.311044	−	0.950396i	$-0.600679\pi$
$397$	13.3007	−	23.0375i	0.667545	−	1.15622i	0.978589	−	0.205826i	$-0.0659881\pi$
$398$	−3.27479	+	2.74788i	−0.164150	+	0.137739i
$399$	−0.749896	+	6.41808i	−0.0375417	+	0.321306i
$400$	−2.57522	+	14.6048i	−0.128761	+	0.730239i
$401$	0.404650	−	2.29488i	0.0202072	−	0.114601i	−0.973036	−	0.230654i	$-0.925913\pi$
$401$	0.404650	−	2.29488i	0.0202072	−	0.114601i	0.993243	+	0.116054i	$0.0370244\pi$
$402$	−0.898936	+	1.92189i	−0.0448349	+	0.0958550i
$403$	2.88961	−	2.42467i	0.143942	−	0.120781i
$404$	−0.154174	−	0.267036i	−0.00767042	−	0.0132856i
$405$	−1.61759	−	9.43235i	−0.0803788	−	0.468697i
$406$	−3.03118	+	2.40274i	−0.150435	+	0.119246i
$407$	−4.53403	−	1.65025i	−0.224744	−	0.0818000i
$408$	−2.57635	−	3.68861i	−0.127548	−	0.182614i
$409$	−28.6571	+	10.4303i	−1.41700	+	0.515747i	−0.933177	−	0.359416i	$-0.882976\pi$
$409$	−28.6571	+	10.4303i	−1.41700	+	0.515747i	−0.483827	+	0.875164i	$0.660754\pi$
$410$	1.16697	+	0.979206i	0.0576326	+	0.0483595i
$411$	−1.59819	−	5.99264i	−0.0788330	−	0.295595i
$412$	−19.5202	+	16.3794i	−0.961691	+	0.806955i
$413$	0.00634058	+	0.0429232i	0.000311999	+	0.00211211i
$414$	1.50316	+	1.79996i	0.0738765	+	0.0884632i
$415$	−12.8651			−0.631523
$416$	−2.25896	−	0.822196i	−0.110755	−	0.0403115i
$417$	−17.7086	+	8.23239i	−0.867194	+	0.403142i
$418$	0.199384	+	0.167303i	0.00975220	+	0.00818307i
$419$	7.62224	−	2.77427i	0.372371	−	0.135532i	−0.149054	−	0.988829i	$-0.547623\pi$
$419$	7.62224	−	2.77427i	0.372371	−	0.135532i	0.521425	+	0.853297i	$0.325401\pi$
$420$	−4.31224	+	8.58727i	−0.210416	+	0.419016i
$421$	5.46441	+	30.9902i	0.266319	+	1.51037i	0.765253	+	0.643730i	$0.222614\pi$
$421$	5.46441	+	30.9902i	0.266319	+	1.51037i	−0.498934	+	0.866640i	$0.666275\pi$
$422$	2.09746			0.102103
$423$	1.88330	+	5.21232i	0.0915691	+	0.253432i
$424$	−6.05617			−0.294113
$425$	14.2091	+	5.17168i	0.689241	+	0.250863i
$426$	3.36248	−	3.35460i	0.162913	−	0.162531i
$427$	−9.86545	−	18.2435i	−0.477422	−	0.882867i
$428$	−0.310081	−	0.260189i	−0.0149883	−	0.0125767i
$429$	0.987282	−	2.11077i	0.0476664	−	0.101909i
$430$	−0.830040	+	0.696487i	−0.0400281	+	0.0335876i
$431$	−5.08992	+	8.81601i	−0.245173	+	0.424652i	−0.962180	−	0.272414i	$-0.912178\pi$
$431$	−5.08992	+	8.81601i	−0.245173	+	0.424652i	0.717007	+	0.697066i	$0.245511\pi$
$432$	−11.4804	+	16.2736i	−0.552352	+	0.782962i
$433$	20.3762			0.979219			0.489610	−	0.871942i	$-0.337139\pi$
$433$	20.3762			0.979219			0.489610	+	0.871942i	$0.337139\pi$
$434$	0.275262	−	1.34132i	0.0132130	−	0.0643852i
$435$	−6.81678	+	14.5740i	−0.326840	+	0.698769i
$436$	2.13884	−	12.1300i	0.102432	−	0.580921i
$437$	−5.04548	−	4.23366i	−0.241358	−	0.202523i
$438$	2.56641	+	0.690895i	0.122628	+	0.0330122i
$439$	−20.4921	−	7.45852i	−0.978035	−	0.355976i	−0.196959	−	0.980412i	$-0.563107\pi$
$439$	−20.4921	−	7.45852i	−0.978035	−	0.355976i	−0.781076	+	0.624436i	$0.785329\pi$
$440$	0.389805	+	0.675161i	0.0185832	+	0.0321871i
$441$	14.4098	−	15.2760i	0.686181	−	0.727431i
$442$	−0.398855	+	0.690837i	−0.0189716	+	0.0328598i
$443$	−6.33793	+	5.31816i	−0.301124	+	0.252673i	−0.780812	−	0.624766i	$-0.785194\pi$
$443$	−6.33793	+	5.31816i	−0.301124	+	0.252673i	0.479688	+	0.877439i	$0.340750\pi$
$444$	1.31970	−	14.8831i	0.0626300	−	0.706322i
$445$	−2.98267	+	16.9156i	−0.141392	+	0.801874i
$446$	2.59327	+	2.17601i	0.122795	+	0.103037i
$447$	16.9122	−	7.86218i	0.799922	−	0.371868i
$448$	18.4158	−	6.12717i	0.870066	−	0.289482i
$449$	6.47670	−	11.2180i	0.305654	−	0.529409i	−0.671753	−	0.740776i	$-0.734458\pi$
$449$	6.47670	−	11.2180i	0.305654	−	0.529409i	0.977407	+	0.211367i	$0.0677915\pi$
$450$	−0.00455650	+	1.94259i	−0.000214795	+	0.0915744i
$451$	9.44230			0.444621
$452$	4.25776	+	24.1470i	0.200268	+	1.13578i
$453$	−11.8129	+	11.7852i	−0.555018	+	0.553717i
$454$	0.000206287	−	0.00116991i	9.68153e−6	−	5.49067e-5i
$455$	3.43024	+	0.0956407i	0.160812	+	0.00448370i
$456$	−0.687820	+	1.47053i	−0.0322101	+	0.0688639i
$457$	3.45753	+	19.6086i	0.161736	+	0.917252i	0.952366	+	0.304958i	$0.0986423\pi$
$457$	3.45753	+	19.6086i	0.161736	+	0.917252i	−0.790630	+	0.612295i	$0.790247\pi$
$458$	−1.06688	+	1.84788i	−0.0498518	+	0.0863458i
$459$	14.3080	+	14.4091i	0.667842	+	0.672558i
$460$	−4.89729	−	8.48235i	−0.228337	−	0.395492i
$461$	−1.38048	−	0.502454i	−0.0642954	−	0.0234016i	0.309672	−	0.950843i	$-0.399781\pi$
$461$	−1.38048	−	0.502454i	−0.0642954	−	0.0234016i	−0.373968	+	0.927442i	$0.622003\pi$
$462$	−0.195106	−	0.823066i	−0.00907717	−	0.0382925i
$463$	4.74179	+	3.97883i	0.220369	+	0.184912i	0.746288	−	0.665623i	$-0.231834\pi$
$463$	4.74179	+	3.97883i	0.220369	+	0.184912i	−0.525919	+	0.850535i	$0.676278\pi$
$464$	31.4633	−	11.4517i	1.46065	−	0.531632i
$465$	−1.46770	−	5.50333i	−0.0680628	−	0.255211i
$466$	−0.747769	−	4.24081i	−0.0346397	−	0.196452i
$467$	−0.466732	+	0.808403i	−0.0215978	+	0.0374084i	−0.876622	−	0.481179i	$-0.840209\pi$
$467$	−0.466732	+	0.808403i	−0.0215978	+	0.0374084i	0.855025	+	0.518588i	$0.173542\pi$
$468$	7.10345	+	1.26972i	0.328357	+	0.0586927i
$469$	−15.1768	+	12.0302i	−0.700800	+	0.555505i
$470$	0.0570852	+	0.323746i	0.00263314	+	0.0149333i
$471$	9.27739	−	4.31288i	0.427480	−	0.198727i
$472$	−0.00189294	+	0.0107354i	−8.71295e−5	+	0.000494136i
$473$	−1.16624	+	6.61406i	−0.0536236	+	0.304115i
$474$	0.279848	−	3.15605i	0.0128539	−	0.144962i
$475$	−0.947423	−	5.37310i	−0.0434707	−	0.246535i
$476$	−2.97955	−	20.1704i	−0.136567	−	0.924507i
$477$	26.9286	−	4.68314i	1.23298	−	0.214426i
$478$	0.642008	−	1.11199i	0.0293648	−	0.0508613i
$479$	−6.13650	−	34.8018i	−0.280384	−	1.59014i	−0.721322	−	0.692600i	$-0.756465\pi$
$479$	−6.13650	−	34.8018i	−0.280384	−	1.59014i	0.440938	−	0.897537i	$-0.354646\pi$
$480$	−2.56967	+	2.56365i	−0.117289	+	0.117014i
$481$	−5.01403	+	1.82496i	−0.228620	+	0.0832109i
$482$	2.40382	+	2.01704i	0.109491	+	0.0918739i
$483$	4.93723	+	20.8279i	0.224652	+	0.947704i
$484$	−18.1293	−	6.59854i	−0.824061	−	0.299934i
$485$	0.206669	+	0.357961i	0.00938434	+	0.0162541i
$486$	−1.11634	+	2.35781i	−0.0506384	+	0.106952i
$487$	1.31737	−	2.28176i	0.0596958	−	0.103396i	−0.834633	−	0.550806i	$-0.814320\pi$
$487$	1.31737	−	2.28176i	0.0596958	−	0.103396i	0.894329	+	0.447410i	$0.147654\pi$
$488$	−0.904833	−	5.13156i	−0.0409599	−	0.232295i
$489$	21.1909	−	1.82892i	0.958285	−	0.0827067i
$490$	0.997356	−	0.746276i	0.0450560	−	0.0337133i
$491$	−1.44686	+	8.20554i	−0.0652958	+	0.370311i	0.934598	+	0.355707i	$0.115760\pi$
$491$	−1.44686	+	8.20554i	−0.0652958	+	0.370311i	−0.999893	+	0.0146040i	$0.995351\pi$
$492$	7.53468	+	28.2523i	0.339690	+	1.27371i
$493$	−5.92822	−	33.6206i	−0.266994	−	1.51420i
$494$	0.287832			0.0129502
$495$	−2.25535	−	2.70066i	−0.101370	−	0.121386i
$496$	−5.92643	+	10.2649i	−0.266105	+	0.460907i
$497$	41.1367	−	13.6867i	1.84523	−	0.613932i
$498$	2.87036	+	2.01487i	0.128624	+	0.0902884i
$499$	−14.8063	−	12.4239i	−0.662820	−	0.556172i	0.248111	−	0.968732i	$-0.420190\pi$
$499$	−14.8063	−	12.4239i	−0.662820	−	0.556172i	−0.910931	+	0.412560i	$0.864635\pi$
$500$	3.22952	−	18.3155i	0.144428	−	0.819094i
$501$	−8.22986	−	5.77701i	−0.367683	−	0.258098i
$502$	−3.13314	+	2.62901i	−0.139839	+	0.117339i
$503$	−15.6608	+	27.1253i	−0.698279	+	1.20946i	0.270783	+	0.962640i	$0.412717\pi$
$503$	−15.6608	+	27.1253i	−0.698279	+	1.20946i	−0.969063	+	0.246815i	$0.920616\pi$
$504$	4.64678	−	2.49874i	0.206984	−	0.111303i
$505$	0.0831335	+	0.143991i	0.00369939	+	0.00640754i
$506$	0.810197	+	0.294887i	0.0360176	+	0.0131093i
$507$	5.13819	+	19.2663i	0.228195	+	0.855648i
$508$	−16.7331	−	14.0407i	−0.742411	−	0.622956i
$509$	3.91248	−	22.1888i	0.173418	−	0.983500i	−0.766537	−	0.642200i	$-0.778022\pi$
$509$	3.91248	−	22.1888i	0.173418	−	0.983500i	0.939954	−	0.341300i	$-0.110867\pi$
$510$	0.689713	+	0.987475i	0.0305410	+	0.0437261i
$511$	18.1420	+	16.1056i	0.802554	+	0.712468i
$512$	12.6491			0.559017
$513$	1.92124	−	7.07055i	0.0848247	−	0.312173i
$514$	−0.440628	+	0.763191i	−0.0194353	+	0.0336629i
$515$	10.5257	−	8.83210i	0.463817	−	0.389189i
$516$	−20.7206	+	1.78833i	−0.912172	+	0.0787268i
$517$	1.56091	+	1.30976i	0.0686489	+	0.0576033i
$518$	−1.01482	+	1.64975i	−0.0445886	+	0.0724859i
$519$	1.16259	+	4.35927i	0.0510319	+	0.191351i
$520$	0.810149	+	0.294870i	0.0355274	+	0.0129309i
$521$	27.1773			1.19066			0.595329	−	0.803482i	$-0.297022\pi$
$521$	27.1773			1.19066			0.595329	+	0.803482i	$0.297022\pi$
$522$	3.80341	−	2.18402i	0.166471	−	0.0955920i
$523$	10.9931			0.480693			0.240346	−	0.970687i	$-0.422739\pi$
$523$	10.9931			0.480693			0.240346	+	0.970687i	$0.422739\pi$
$524$	−7.42929	−	42.1336i	−0.324550	−	1.84061i
$525$	−7.95718	+	15.8457i	−0.347280	+	0.691563i
$526$	2.01425	−	0.733127i	0.0878254	−	0.0319658i
$527$	9.25792	+	7.76832i	0.403281	+	0.338393i
$528$	−0.646725	+	7.29357i	−0.0281451	+	0.317412i
$529$	1.11066	+	0.404246i	0.0482894	+	0.0175759i
$530$	1.62129			0.0704244
$531$	0.000115399	−	0.0491984i	5.00788e−6	−	0.00213503i
$532$	−5.76532	+	4.57001i	−0.249958	+	0.198135i
$533$	7.99897	−	6.71193i	0.346474	−	0.290726i
$534$	3.31470	−	3.30693i	0.143441	−	0.143105i
$535$	0.167202	+	0.140299i	0.00722876	+	0.00606565i
$536$	−4.57219	+	1.66414i	−0.197488	+	0.0718799i
$537$	−22.3655	+	1.93030i	−0.965141	+	0.0832984i
$538$	−4.37785	−	1.59341i	−0.188742	−	0.0686966i
$539$	1.76231	−	7.51708i	0.0759081	−	0.323784i
$540$	6.28094	−	8.90328i	0.270289	−	0.383136i
$541$	−12.6595	−	21.9269i	−0.544274	−	0.942710i	−0.998652	−	0.0519013i	$-0.983472\pi$
$541$	−12.6595	−	21.9269i	−0.544274	−	0.942710i	0.454378	−	0.890809i	$-0.349861\pi$
$542$	−0.785038	+	0.658725i	−0.0337203	+	0.0282947i
$543$	12.0485	−	1.03987i	0.517049	−	0.0446249i
$544$	1.33742	−	7.58489i	0.0573415	−	0.325200i
$545$	−1.15331	+	6.54074i	−0.0494023	+	0.280174i
$546$	−0.750348	−	0.558565i	−0.0321119	−	0.0239044i
$547$	−18.5056	+	15.5280i	−0.791242	+	0.663931i	−0.946053	−	0.324013i	$-0.894968\pi$
$547$	−18.5056	+	15.5280i	−0.791242	+	0.663931i	0.154811	+	0.987944i	$0.450523\pi$
$548$	3.53064	−	6.11524i	0.150821	−	0.261230i
$549$	7.99147	+	22.1177i	0.341068	+	0.943959i
$550$	0.357108	+	0.618530i	0.0152272	+	0.0263742i
$551$	−9.43631	+	7.91800i	−0.402000	+	0.337318i
$552$	−0.474988	+	5.35677i	−0.0202168	+	0.227999i
$553$	15.1527	−	24.6331i	0.644358	−	1.04751i
$554$	1.09485	−	0.398491i	0.0465155	−	0.0169303i
$555$	−0.711607	+	8.02529i	−0.0302060	+	0.340655i
$556$	−20.8931	−	7.60445i	−0.886063	−	0.322501i
$557$	−5.57957	−	9.66411i	−0.236414	−	0.409481i	0.723269	−	0.690567i	$-0.242639\pi$
$557$	−5.57957	−	9.66411i	−0.236414	−	0.409481i	−0.959683	+	0.281086i	$0.909306\pi$
$558$	−0.534443	+	1.45772i	−0.0226248	+	0.0617103i
$559$	3.71355	+	6.43205i	0.157066	+	0.272047i
$560$	−10.2314	+	3.40410i	−0.432354	+	0.143849i
$561$	7.20915	+	1.94075i	0.304370	+	0.0819385i
$562$	−3.99114	+	1.45266i	−0.168356	+	0.0612766i
$563$	34.6151	−	12.5989i	1.45885	−	0.530979i	0.513803	−	0.857908i	$-0.328236\pi$
$563$	34.6151	−	12.5989i	1.45885	−	0.530979i	0.945049	+	0.326930i	$0.106014\pi$
$564$	−2.67338	+	5.71556i	−0.112569	+	0.240669i
$565$	−2.29587	−	13.0205i	−0.0965880	−	0.547778i
$566$	−3.15136			−0.132461
$567$	−18.7296	+	14.7039i	−0.786567	+	0.617505i
$568$	10.8921			0.457024
$569$	−4.02818	−	22.8449i	−0.168870	−	0.957709i	−0.944984	−	0.327117i	$-0.893923\pi$
$569$	−4.02818	−	22.8449i	−0.168870	−	0.957709i	0.776114	−	0.630593i	$-0.217188\pi$
$570$	0.184136	−	0.393674i	0.00771260	−	0.0164892i
$571$	−7.61983	+	2.77339i	−0.318880	+	0.116063i	−0.496501	−	0.868036i	$-0.665382\pi$
$571$	−7.61983	+	2.77339i	−0.318880	+	0.116063i	0.177621	+	0.984099i	$0.443160\pi$
$572$	2.49306	−	0.907401i	0.104240	−	0.0379403i
$573$	−34.5461	−	9.30003i	−1.44318	−	0.388514i
$574$	0.761975	−	3.71301i	0.0318042	−	0.154978i
$575$	−9.03674	−	15.6521i	−0.376858	−	0.652737i
$576$	−21.6816	+	3.77063i	−0.903400	+	0.157110i
$577$	−11.9048	−	20.6198i	−0.495605	−	0.858414i	0.504382	−	0.863481i	$-0.331720\pi$
$577$	−11.9048	−	20.6198i	−0.495605	−	0.858414i	−0.999987	+	0.00506711i	$0.998387\pi$
$578$	0.271759	+	0.0989120i	0.0113037	+	0.00411420i
$579$	−0.691287	+	7.79613i	−0.0287289	+	0.323996i
$580$	−17.2136	+	6.26523i	−0.714755	+	0.260149i
$581$	15.2263	+	28.1571i	0.631695	+	1.16815i
$582$	0.00995173	−	0.112233i	0.000412513	−	0.00465219i
$583$	7.69815	−	6.45952i	0.318825	−	0.267526i
$584$	3.04745	+	5.27835i	0.126105	+	0.218419i
$585$	−3.83033	−	0.684657i	−0.158364	−	0.0283071i
$586$	−2.48430	+	4.30293i	−0.102625	+	0.177752i
$587$	−29.0802	+	24.4012i	−1.20027	+	1.00715i	−0.200647	+	0.979664i	$0.564304\pi$
$587$	−29.0802	+	24.4012i	−1.20027	+	1.00715i	−0.999622	+	0.0274816i	$0.991251\pi$
$588$	23.8981	−	0.725407i	0.985543	−	0.0299153i
$589$	0.757222	−	4.29442i	0.0312008	−	0.176949i
$590$	0.000506756	−	0.00287396i	2.08628e−5	−	0.000118319i
$591$	8.52031	−	0.735363i	0.350479	−	0.0302488i
$592$	12.8438	−	10.7772i	0.527876	−	0.442941i
$593$	−5.68593	−	9.84832i	−0.233493	−	0.404422i	0.725341	−	0.688390i	$-0.241682\pi$
$593$	−5.68593	−	9.84832i	−0.233493	−	0.404422i	−0.958834	+	0.283968i	$0.908349\pi$
$594$	0.0802316	+	0.955771i	0.00329194	+	0.0392157i
$595$	1.60663	+	10.8763i	0.0658655	+	0.445883i
$596$	19.9535	+	7.26248i	0.817327	+	0.297483i
$597$	44.0811	−	3.80451i	1.80412	−	0.155708i
$598$	0.895968	−	0.326106i	0.0366389	−	0.0133355i
$599$	15.1611	+	12.7216i	0.619464	+	0.519792i	0.897635	−	0.440740i	$-0.145284\pi$
$599$	15.1611	+	12.7216i	0.619464	+	0.519792i	−0.278171	+	0.960532i	$0.589728\pi$
$600$	−3.15372	+	3.14633i	−0.128750	+	0.128448i
$601$	12.8458	−	10.7789i	0.523990	−	0.439679i	−0.342030	−	0.939689i	$-0.611115\pi$
$601$	12.8458	−	10.7789i	0.523990	−	0.439679i	0.866020	+	0.500009i	$0.166670\pi$
$602$	2.50674	+	0.992342i	0.102167	+	0.0404449i
$603$	19.0433	−	10.9352i	0.775501	−	0.445314i
$604$	−18.9980			−0.773016
$605$	9.77571	+	3.55807i	0.397439	+	0.144656i
$606$	0.00400314	−	0.0451462i	0.000162616	−	0.00183394i
$607$	−14.8286	−	12.4427i	−0.601876	−	0.505034i	0.290172	−	0.956974i	$-0.406287\pi$
$607$	−14.8286	−	12.4427i	−0.601876	−	0.505034i	−0.892048	+	0.451941i	$0.850732\pi$
$608$	−2.61143	+	0.950481i	−0.105907	+	0.0385471i
$609$	39.9651	−	2.32937i	1.61947	−	0.0943909i
$610$	0.242232	+	1.37377i	0.00980769	+	0.0556222i
$611$	2.25334			0.0911604
$612$	−0.0542279	+	23.1192i	−0.00219203	+	0.934537i
$613$	27.9450			1.12869			0.564344	−	0.825540i	$-0.309129\pi$
$613$	27.9450			1.12869			0.564344	+	0.825540i	$0.309129\pi$
$614$	−0.186352	−	0.0678267i	−0.00752057	−	0.00273726i
$615$	−4.06285	−	15.2342i	−0.163830	−	0.614303i
$616$	1.01634	−	1.65222i	0.0409494	−	0.0665699i
$617$	−26.9774	−	22.6367i	−1.08607	−	0.911319i	−0.0896574	−	0.995973i	$-0.528577\pi$
$617$	−26.9774	−	22.6367i	−1.08607	−	0.911319i	−0.996410	+	0.0846535i	$0.973022\pi$
$618$	−3.73165	+	0.322067i	−0.150109	+	0.0129554i
$619$	−0.182175	+	0.152863i	−0.00732225	+	0.00614409i	−0.646441	−	0.762964i	$-0.723744\pi$
$619$	−0.182175	+	0.152863i	−0.00732225	+	0.00614409i	0.639119	+	0.769108i	$0.279299\pi$
$620$	3.24235	−	5.61592i	0.130216	−	0.225541i
$621$	−2.03029	−	24.1861i	−0.0814726	−	0.970553i
$622$	2.64295			0.105973
$623$	40.5522	−	13.4922i	1.62469	−	0.540554i
$624$	4.63667	+	6.63840i	0.185615	+	0.265749i
$625$	1.61807	−	9.17655i	0.0647229	−	0.367062i
$626$	−2.25919	−	1.89568i	−0.0902953	−	0.0757668i
$627$	−0.694163	−	2.60286i	−0.0277222	−	0.103948i
$628$	10.9457	+	3.98391i	0.436781	+	0.158975i
$629$	−8.54762	−	14.8049i	−0.340816	−	0.590311i
$630$	−1.24399	+	0.668936i	−0.0495616	+	0.0266510i
$631$	16.1764	−	28.0184i	0.643974	−	1.11540i	−0.340563	−	0.940222i	$-0.610618\pi$
$631$	16.1764	−	28.0184i	0.643974	−	1.11540i	0.984537	−	0.175175i	$-0.0560490\pi$
$632$	5.56604	−	4.67046i	0.221405	−	0.185781i
$633$	−17.7679	−	12.4723i	−0.706209	−	0.495728i
$634$	−0.355764	+	2.01764i	−0.0141292	+	0.0801307i
$635$	9.02282	+	7.57104i	0.358060	+	0.300448i
$636$	25.4704	+	17.8791i	1.00997	+	0.708954i
$637$	−3.85049	−	7.62075i	−0.152562	−	0.301945i
$638$	0.806259	−	1.39648i	0.0319201	−	0.0552872i
$639$	−48.4317	+	8.42273i	−1.91593	+	0.333198i
$640$	−5.49673			−0.217277
$641$	4.00357	+	22.7053i	0.158131	+	0.896807i	0.955867	+	0.293800i	$0.0949199\pi$
$641$	4.00357	+	22.7053i	0.158131	+	0.896807i	−0.797736	+	0.603007i	$0.793969\pi$
$642$	−0.0153318	−	0.0574887i	−0.000605098	−	0.00226890i
$643$	−4.82429	+	27.3599i	−0.190251	+	1.07897i	0.728769	+	0.684760i	$0.240093\pi$
$643$	−4.82429	+	27.3599i	−0.190251	+	1.07897i	−0.919020	+	0.394210i	$0.871018\pi$
$644$	−12.7687	+	20.7576i	−0.503157	+	0.817963i
$645$	11.1729	−	0.964304i	0.439934	−	0.0379694i
$646$	0.160134	+	0.908165i	0.00630039	+	0.0357313i
$647$	11.0845	−	19.1989i	0.435776	−	0.754787i	−0.561582	−	0.827421i	$-0.689807\pi$
$647$	11.0845	−	19.1989i	0.435776	−	0.754787i	0.997359	+	0.0726341i	$0.0231405\pi$
$648$	−5.63118	+	2.01972i	−0.221214	+	0.0793420i
$649$	−0.00904421	−	0.0156650i	−0.000355016	−	0.000614906i
$650$	0.742195	+	0.270137i	0.0291113	+	0.0105956i
$651$	−10.3077	+	9.72566i	−0.403992	+	0.381179i
$652$	18.5507	+	15.5659i	0.726500	+	0.609606i
$653$	−19.8853	+	7.23766i	−0.778172	+	0.283232i	−0.700410	−	0.713740i	$-0.747000\pi$
$653$	−19.8853	+	7.23766i	−0.778172	+	0.283232i	−0.0777620	+	0.996972i	$0.524777\pi$
$654$	1.28169	−	1.27869i	0.0501182	−	0.0500008i
$655$	4.00602	+	22.7193i	0.156528	+	0.887716i
$656$	−16.4054	+	28.4151i	−0.640525	+	1.10942i
$657$	−17.6321	−	21.1135i	−0.687893	−	0.823715i
$658$	0.641002	−	0.508105i	0.0249889	−	0.0198080i
$659$	−0.954608	−	5.41385i	−0.0371863	−	0.210894i	0.960553	−	0.278097i	$-0.0897036\pi$
$659$	−0.954608	−	5.41385i	−0.0371863	−	0.210894i	−0.997739	+	0.0672030i	$0.978592\pi$
$660$	0.353823	−	3.99032i	0.0137726	−	0.155323i
$661$	−2.21984	+	12.5893i	−0.0863418	+	0.489669i	0.910717	+	0.413031i	$0.135530\pi$
$661$	−2.21984	+	12.5893i	−0.0863418	+	0.489669i	−0.997059	+	0.0766382i	$0.975581\pi$
$662$	−0.397415	+	2.25385i	−0.0154460	+	0.0875985i
$663$	7.48673	−	3.48043i	0.290760	−	0.135169i
$664$	1.39652	+	7.92005i	0.0541955	+	0.307358i
$665$	3.10878	−	2.46424i	0.120553	−	0.0955593i
$666$	1.41565	−	1.67909i	0.0548553	−	0.0650634i
$667$	−20.4026	+	35.3384i	−0.789993	+	1.36831i
$668$	−1.98793	−	11.2741i	−0.0769152	−	0.436208i
$669$	−9.02858	−	33.8539i	−0.349065	−	1.30887i
$670$	1.22402	−	0.445505i	0.0472879	−	0.0172114i
$671$	6.62349	+	5.55777i	0.255697	+	0.214555i
$672$	8.65222	+	2.58991i	0.333767	+	0.0999080i
$673$	13.5940	+	4.94780i	0.524008	+	0.190723i	0.590461	−	0.807066i	$-0.298946\pi$
$673$	13.5940	+	4.94780i	0.524008	+	0.190723i	−0.0664526	+	0.997790i	$0.521168\pi$
$674$	2.13459	+	3.69722i	0.0822214	+	0.142412i
$675$	11.5899	−	16.4288i	0.446097	−	0.632345i
$676$	−11.3510	+	19.6605i	−0.436577	+	0.756173i
$677$	6.23545	+	35.3630i	0.239648	+	1.35911i	0.832601	+	0.553874i	$0.186851\pi$
$677$	6.23545	+	35.3630i	0.239648	+	1.35911i	−0.592953	+	0.805237i	$0.702038\pi$
$678$	−1.52697	+	3.26460i	−0.0586431	+	0.125376i
$679$	0.538847	−	0.875983i	0.0206790	−	0.0336171i
$680$	−0.479649	+	2.72023i	−0.0183937	+	0.104316i
$681$	−0.00870421	+	0.00868382i	−0.000333546	+	0.000332765i
$682$	0.0991242	+	0.562162i	0.00379566	+	0.0215263i
$683$	−35.2464			−1.34867			−0.674333	−	0.738427i	$-0.735569\pi$
$683$	−35.2464			−1.34867			−0.674333	+	0.738427i	$0.735569\pi$
$684$	7.23409	−	4.15401i	0.276602	−	0.158833i
$685$	−1.90379	+	3.29746i	−0.0727401	+	0.125990i
$686$	−2.81374	−	1.29961i	−0.107429	−	0.0496193i
$687$	20.0258	−	9.30962i	0.764033	−	0.355184i
$688$	−17.8777	−	15.0011i	−0.681580	−	0.571913i
$689$	1.92977	−	10.9443i	0.0735183	−	0.416943i
$690$	0.127159	−	1.43406i	0.00484085	−	0.0545936i
$691$	31.3746	−	26.3264i	1.19355	−	1.00150i	0.193754	−	0.981050i	$-0.437934\pi$
$691$	31.3746	−	26.3264i	1.19355	−	1.00150i	0.999791	−	0.0204532i	$-0.00651092\pi$
$692$	−2.56832	+	4.44846i	−0.0976329	+	0.169105i
$693$	−3.24148	+	8.13248i	−0.123134	+	0.308927i
$694$	−0.765207	−	1.32538i	−0.0290469	−	0.0503106i
$695$	11.2660	+	4.10048i	0.427342	+	0.155540i
$696$	9.71205	+	2.61455i	0.368134	+	0.0991042i
$697$	25.6276	+	21.5041i	0.970715	+	0.814527i
$698$	−0.562521	+	3.19022i	−0.0212917	+	0.120751i
$699$	−18.8830	+	40.3710i	−0.714219	+	1.52697i
$700$	−19.1554	+	6.37322i	−0.724004	+	0.240885i
$701$	−6.46856			−0.244314			−0.122157	−	0.992511i	$-0.538981\pi$
$701$	−6.46856			−0.244314			−0.122157	+	0.992511i	$0.538981\pi$
$702$	0.747364	+	0.752642i	0.0282074	+	0.0284066i
$703$	−3.08417	+	5.34195i	−0.116322	+	0.201475i
$704$	−6.19818	+	5.20089i	−0.233603	+	0.196016i
$705$	1.44154	−	3.08195i	0.0542915	−	0.116073i
$706$	−4.47315	−	3.75342i	−0.168349	−	0.141262i
$707$	0.216754	−	0.352369i	0.00815187	−	0.0132522i
$708$	0.0396543	−	0.0395614i	0.00149030	−	0.00148681i
$709$	12.6373	+	4.59961i	0.474605	+	0.172742i	0.568237	−	0.822865i	$-0.307626\pi$
$709$	12.6373	+	4.59961i	0.474605	+	0.172742i	−0.0936324	+	0.995607i	$0.529848\pi$
$710$	−2.91593			−0.109433
$711$	−21.1376	+	25.0712i	−0.792724	+	0.940244i
$712$	10.7374			0.402400
$713$	−2.50837	−	14.2257i	−0.0939392	−	0.532755i
$714$	1.34493	−	2.67825i	0.0503326	−	0.100231i
$715$	−1.34431	+	0.489289i	−0.0502743	+	0.0182984i
$716$	−19.5789	−	16.4286i	−0.731698	−	0.613967i
$717$	−12.0508	+	5.60220i	−0.450047	+	0.209218i
$718$	−2.67809	−	0.974744i	−0.0999453	−	0.0363771i
$719$	19.4441			0.725144			0.362572	−	0.931956i	$-0.381899\pi$
$719$	19.4441			0.725144			0.362572	+	0.931956i	$0.381899\pi$
$720$	12.0457	−	2.09487i	0.448918	−	0.0780711i
$721$	−31.7878	−	12.5838i	−1.18384	−	0.468646i
$722$	−2.18086	+	1.82996i	−0.0811633	+	0.0681041i
$723$	−8.36899	−	31.3806i	−0.311246	−	1.16706i
$724$	10.5473	+	8.85024i	0.391988	+	0.328917i
$725$	−31.7634	+	11.5609i	−1.17966	+	0.429363i
$726$	−1.62383	−	2.32487i	−0.0602661	−	0.0862841i
$727$	−42.7100	−	15.5452i	−1.58402	−	0.576538i	−0.607950	−	0.793975i	$-0.708008\pi$
$727$	−42.7100	−	15.5452i	−1.58402	−	0.576538i	−0.976074	+	0.217437i	$0.930230\pi$
$728$	−0.313477	−	2.12211i	−0.0116182	−	0.0786508i
$729$	23.4771	−	13.3351i	0.869522	−	0.493894i
$730$	−0.815831	−	1.41306i	−0.0301953	−	0.0522997i
$731$	−18.2283	+	15.2954i	−0.674200	+	0.565721i
$732$	−11.3440	+	24.2531i	−0.419288	+	0.896420i
$733$	1.17356	−	6.65559i	0.0433464	−	0.245830i	−0.955434	−	0.295205i	$-0.904612\pi$
$733$	1.17356	−	6.65559i	0.0433464	−	0.245830i	0.998780	+	0.0493755i	$0.0157231\pi$
$734$	0.321896	−	1.82556i	0.0118814	−	0.0673828i
$735$	−12.8864	+	0.391154i	−0.475321	+	0.0144279i
$736$	−7.05202	+	5.91735i	−0.259941	+	0.218116i
$737$	4.03685	−	6.99203i	0.148699	−	0.257555i
$738$	−1.47944	+	4.03524i	−0.0544588	+	0.148539i
$739$	8.02470	+	13.8992i	0.295193	+	0.511290i	0.975030	−	0.222074i	$-0.0712826\pi$
$739$	8.02470	+	13.8992i	0.295193	+	0.511290i	−0.679837	+	0.733364i	$0.737949\pi$
$740$	−7.02684	+	5.89622i	−0.258312	+	0.216749i
$741$	−2.43826	−	1.71155i	−0.0895718	−	0.0628755i
$742$	−1.91886	−	3.54842i	−0.0704435	−	0.130267i
$743$	−15.4896	+	5.63775i	−0.568258	+	0.206829i	−0.610140	−	0.792294i	$-0.708887\pi$
$743$	−15.4896	+	5.63775i	−0.568258	+	0.206829i	0.0418821	+	0.999123i	$0.486665\pi$
$744$	−3.22866	+	1.50094i	−0.118368	+	0.0550271i
$745$	−10.7593	−	3.91608i	−0.394192	−	0.143474i
$746$	1.97655	+	3.42348i	0.0723666	+	0.125343i
$747$	−12.3340	−	34.1364i	−0.451279	−	1.24899i
$748$	4.25003	+	7.36127i	0.155396	+	0.269155i
$749$	0.109174	−	0.531994i	0.00398915	−	0.0194386i
$750$	1.93527	−	1.93074i	0.0706662	−	0.0705007i
$751$	−4.26983	+	1.55409i	−0.155808	+	0.0567096i	−0.418747	−	0.908103i	$-0.637531\pi$
$751$	−4.26983	+	1.55409i	−0.155808	+	0.0567096i	0.262939	+	0.964813i	$0.415308\pi$
$752$	−6.65351	+	2.42168i	−0.242629	+	0.0883096i
$753$	42.1743	−	3.63994i	1.53692	−	0.132647i
$754$	−0.309654	−	1.75614i	−0.0112769	−	0.0639547i
$755$	10.2441			0.372820
$756$	−26.9198	−	3.20936i	−0.979064	−	0.116723i
$757$	9.45226			0.343548			0.171774	−	0.985136i	$-0.445050\pi$
$757$	9.45226			0.343548			0.171774	+	0.985136i	$0.445050\pi$
$758$	−1.00815	−	5.71750i	−0.0366177	−	0.207669i
$759$	−5.10977	−	7.31576i	−0.185473	−	0.265545i
$760$	0.936554	−	0.340878i	0.0339724	−	0.0123649i
$761$	−40.8639	+	14.8732i	−1.48131	+	0.539154i	−0.951147	−	0.308738i	$-0.900093\pi$
$761$	−40.8639	+	14.8732i	−1.48131	+	0.539154i	−0.530168	+	0.847893i	$0.677871\pi$
$762$	−0.827360	−	3.10230i	−0.0299721	−	0.112384i
$763$	15.6803	−	5.21703i	0.567665	−	0.188869i
$764$	−20.3660	−	35.2750i	−0.736817	−	1.27620i
$765$	0.0292408	−	12.4663i	0.00105720	−	0.450721i
$766$	−1.05293	−	1.82372i	−0.0380437	−	0.0658937i
$767$	−0.0187970	−	0.00684155i	−0.000678720	−	0.000247034i
$768$	−19.5724	−	13.7390i	−0.706258	−	0.495763i
$769$	−25.9649	+	9.45045i	−0.936318	+	0.340792i	−0.764711	−	0.644374i	$-0.777118\pi$
$769$	−25.9649	+	9.45045i	−0.936318	+	0.340792i	−0.171607	+	0.985165i	$0.554896\pi$
$770$	−0.272083	+	0.442315i	−0.00980518	+	0.0159399i
$771$	8.27083	−	3.84495i	0.297867	−	0.138473i
$772$	−6.82620	+	5.72786i	−0.245680	+	0.206150i
$773$	23.2039	+	40.1903i	0.834585	+	1.44554i	0.894368	+	0.447332i	$0.147626\pi$
$773$	23.2039	+	40.1903i	0.834585	+	1.44554i	−0.0597835	+	0.998211i	$0.519041\pi$
$774$	−2.64384	−	1.53470i	−0.0950310	−	0.0551638i
$775$	5.98297	−	10.3628i	0.214915	−	0.372243i
$776$	0.197935	−	0.166087i	0.00710544	−	0.00596217i
$777$	18.4067	−	7.94078i	0.660336	−	0.284874i
$778$	0.340446	−	1.93076i	0.0122056	−	0.0692213i
$779$	2.09613	−	11.8877i	0.0751017	−	0.425923i
$780$	−2.53672	−	3.63187i	−0.0908292	−	0.130042i
$781$	−13.8453	+	11.6176i	−0.495424	+	0.415710i
$782$	1.52739	+	2.64552i	0.0546195	+	0.0946038i
$783$	−45.2062	−	4.11535i	−1.61554	−	0.147070i
$784$	19.5595	+	18.3639i	0.698555	+	0.655853i
$785$	−5.90215	−	2.14821i	−0.210657	−	0.0766728i
$786$	2.66439	−	5.69635i	0.0950356	−	0.203182i
$787$	3.03430	−	1.10439i	0.108161	−	0.0393674i	−0.287373	−	0.957819i	$-0.592782\pi$
$787$	3.03430	−	1.10439i	0.108161	−	0.0393674i	0.395534	+	0.918451i	$0.370560\pi$
$788$	7.45875	+	6.25863i	0.265707	+	0.222955i
$789$	−21.4224	−	5.76705i	−0.762658	−	0.205312i
$790$	−1.49008	+	1.25032i	−0.0530146	+	0.0444846i
$791$	−25.7800	+	20.4351i	−0.916632	+	0.726589i
$792$	−1.41777	+	1.68160i	−0.0503782	+	0.0597532i
$793$	9.56170			0.339546
$794$	4.18329	+	1.52259i	0.148459	+	0.0540348i
$795$	−13.7342	−	9.64079i	−0.487101	−	0.341924i
$796$	38.5889	+	32.3799i	1.36775	+	1.14768i
$797$	−12.1596	+	4.42574i	−0.430716	+	0.156768i	−0.548275	−	0.836298i	$-0.684715\pi$
$797$	−12.1596	+	4.42574i	−0.430716	+	0.156768i	0.117559	+	0.993066i	$0.462493\pi$
$798$	−1.07954	+	0.0629213i	−0.0382154	+	0.00222739i
$799$	1.25364	+	7.10973i	0.0443505	+	0.251524i
$800$	−7.62579			−0.269613
$801$	−47.7435	+	8.30305i	−1.68693	+	0.293374i
$802$	0.389974			0.0137705
$803$	−9.50359	−	3.45902i	−0.335374	−	0.122066i
$804$	24.1421	+	6.49923i	0.851428	+	0.229210i
$805$	6.88514	−	11.1929i	0.242669	−	0.394498i
$806$	0.483577	+	0.405769i	0.0170333	+	0.0142926i
$807$	27.6103	+	39.5302i	0.971930	+	1.39153i
$808$	0.0796203	−	0.0668093i	0.00280103	−	0.00235034i
$809$	5.94609	−	10.2989i	0.209053	−	0.362091i	−0.742363	−	0.669998i	$-0.766295\pi$
$809$	5.94609	−	10.2989i	0.209053	−	0.362091i	0.951417	+	0.307906i	$0.0996284\pi$
$810$	1.50752	−	0.540697i	0.0529688	−	0.0189982i
$811$	34.2251			1.20180			0.600902	−	0.799323i	$-0.294808\pi$
$811$	34.2251			1.20180			0.600902	+	0.799323i	$0.294808\pi$
$812$	34.0853	+	30.2592i	1.19616	+	1.06189i
$813$	10.5672	−	0.912022i	0.370607	−	0.0319860i
$814$	0.140215	−	0.795201i	0.00491455	−	0.0278718i
$815$	−10.0029	−	8.39342i	−0.350386	−	0.294009i
$816$	−18.3658	+	18.3228i	−0.642933	+	0.641427i
$817$	8.06813	+	2.93656i	0.282268	+	0.102737i
$818$	−2.55178	−	4.41982i	−0.0892210	−	0.154535i
$819$	3.03486	+	9.19352i	0.106047	+	0.321248i
$820$	8.97543	−	15.5459i	0.313436	−	0.542886i
$821$	−37.2276	+	31.2377i	−1.29925	+	1.09020i	−0.308980	+	0.951069i	$0.599988\pi$
$821$	−37.2276	+	31.2377i	−1.29925	+	1.09020i	−0.990273	+	0.139134i	$0.955568\pi$
$822$	0.941190	−	0.437541i	0.0328278	−	0.0152610i
$823$	−2.20852	+	12.5251i	−0.0769842	+	0.436599i	0.921816	+	0.387628i	$0.126705\pi$
$823$	−2.20852	+	12.5251i	−0.0769842	+	0.436599i	−0.998800	+	0.0489712i	$0.984406\pi$
$824$	−6.57982	−	5.52112i	−0.229219	−	0.192337i
$825$	0.652894	−	7.36315i	0.0227309	−	0.256352i
$826$	−0.00688983	+	0.00229233i	−0.000239728	+	7.97603e-5i
$827$	9.76448	−	16.9126i	0.339544	−	0.588108i	−0.644803	−	0.764349i	$-0.723061\pi$
$827$	9.76448	−	16.9126i	0.339544	−	0.588108i	0.984347	+	0.176241i	$0.0563939\pi$
$828$	17.8120	−	21.1267i	0.619011	−	0.734204i
$829$	28.5269			0.990781			0.495390	−	0.868670i	$-0.335025\pi$
$829$	28.5269			0.990781			0.495390	+	0.868670i	$0.335025\pi$
$830$	−0.373861	−	2.12027i	−0.0129769	−	0.0735957i
$831$	−11.6442	−	3.13468i	−0.403931	−	0.108741i
$832$	−1.55375	+	8.81178i	−0.0538667	+	0.305493i
$833$	21.9027	−	16.3888i	0.758885	−	0.567839i
$834$	−1.87138	−	2.67928i	−0.0648005	−	0.0927760i
$835$	1.07193	+	6.07922i	0.0370957	+	0.210380i
$836$	1.53351	−	2.65611i	0.0530374	−	0.0918635i
$837$	13.1955	−	9.17056i	0.456103	−	0.316981i
$838$	0.678724	+	1.17558i	0.0234461	+	0.0406099i
$839$	36.9809	+	13.4600i	1.27672	+	0.464689i	0.889347	−	0.457232i	$-0.151159\pi$
$839$	36.9809	+	13.4600i	1.27672	+	0.464689i	0.387376	+	0.921922i	$0.373381\pi$
$840$	−3.10301	−	0.928839i	−0.107064	−	0.0320480i
$841$	36.2462	+	30.4142i	1.24987	+	1.04876i
$842$	−4.94863	+	1.80116i	−0.170541	+	0.0620719i
$843$	42.4475	+	11.4272i	1.46197	+	0.393572i
$844$	−4.29184	−	24.3402i	−0.147731	−	0.837825i
$845$	6.12069	−	10.6013i	0.210558	−	0.364697i
$846$	−0.804304	+	0.461853i	−0.0276525	+	0.0158788i
$847$	−3.78259	−	25.6066i	−0.129971	−	0.879854i
$848$	6.06377	+	34.3894i	0.208231	+	1.18094i
$849$	26.6956	+	18.7391i	0.916189	+	0.643125i
$850$	−0.439417	+	2.49206i	−0.0150719	+	0.0854769i
$851$	−3.54819	+	20.1228i	−0.121630	+	0.689801i
$852$	−45.8091	−	32.1560i	−1.56939	−	1.10165i
$853$	−8.73661	−	49.5478i	−0.299136	−	1.69648i	−0.649900	−	0.760020i	$-0.725189\pi$
$853$	−8.73661	−	49.5478i	−0.299136	−	1.69648i	0.350764	−	0.936464i	$-0.385922\pi$
$854$	2.71999	−	2.15606i	0.0930762	−	0.0737790i
$855$	−3.90077	+	2.23993i	−0.133404	+	0.0766039i
$856$	0.0682214	−	0.118163i	0.00233176	−	0.00403872i
$857$	−5.12429	−	29.0613i	−0.175042	−	0.992715i	−0.938095	−	0.346378i	$-0.887411\pi$
$857$	−5.12429	−	29.0613i	−0.175042	−	0.992715i	0.763052	−	0.646337i	$-0.223700\pi$
$858$	0.376562	+	0.101373i	0.0128556	+	0.00346081i
$859$	−17.6215	+	6.41369i	−0.601237	+	0.218832i	−0.624664	−	0.780893i	$-0.714764\pi$
$859$	−17.6215	+	6.41369i	−0.601237	+	0.218832i	0.0234277	+	0.999726i	$0.492542\pi$
$860$	9.78088	+	8.20714i	0.333525	+	0.279861i
$861$	−28.5337	+	26.9224i	−0.972426	+	0.917513i
$862$	−1.60086	−	0.582666i	−0.0545256	−	0.0198457i
$863$	−2.77440	−	4.80539i	−0.0944415	−	0.163578i	0.814934	−	0.579554i	$-0.196773\pi$
$863$	−2.77440	−	4.80539i	−0.0944415	−	0.163578i	−0.909375	+	0.415976i	$0.863440\pi$
$864$	−9.26602	−	4.36057i	−0.315237	−	0.148350i
$865$	1.38489	−	2.39870i	0.0470877	−	0.0815583i
$866$	0.592135	+	3.35817i	0.0201216	+	0.114115i
$867$	−1.71394	−	2.45387i	−0.0582083	−	0.0833379i
$868$	−16.1287	−	0.449695i	−0.547443	−	0.0152636i
$869$	−2.09362	+	11.8735i	−0.0710210	+	0.402780i
$870$	−2.60000	−	0.699938i	−0.0881484	−	0.0237301i
$871$	−1.55040	−	8.79278i	−0.0525334	−	0.297932i
$872$	4.15182			0.140598
$873$	−0.751679	+	0.891561i	−0.0254405	+	0.0301748i
$874$	0.551118	−	0.954565i	0.0186419	−	0.0322886i
$875$	23.6762	−	7.87737i	0.800403	−	0.266304i
$876$	2.76616	−	31.1959i	0.0934598	−	1.05401i
$877$	17.8728	+	14.9971i	0.603523	+	0.506416i	0.892576	−	0.450897i	$-0.148896\pi$
$877$	17.8728	+	14.9971i	0.603523	+	0.506416i	−0.289053	+	0.957313i	$0.593340\pi$
$878$	0.633721	−	3.59401i	0.0213870	−	0.121292i
$879$	46.6316	−	21.6781i	1.57285	−	0.731186i
$880$	3.44355	−	2.88948i	0.116082	−	0.0974043i
$881$	2.91901	−	5.05587i	0.0983438	−	0.170337i	−0.812655	−	0.582745i	$-0.801979\pi$
$881$	2.91901	−	5.05587i	0.0983438	−	0.170337i	0.910999	+	0.412408i	$0.135312\pi$
$882$	2.93636	+	1.93093i	0.0988725	+	0.0650177i
$883$	−4.41916	−	7.65422i	−0.148717	−	0.257585i	0.782037	−	0.623232i	$-0.214181\pi$
$883$	−4.41916	−	7.65422i	−0.148717	−	0.257585i	−0.930753	+	0.365647i	$0.880848\pi$
$884$	8.83303	+	3.21496i	0.297087	+	0.108131i
$885$	−0.0213824	+	0.0213323i	−0.000718762	+	0.000717078i
$886$	−1.06066	−	0.889995i	−0.0356334	−	0.0299000i
$887$	−0.0146997	+	0.0833663i	−0.000493569	+	0.00279917i	−0.985054	−	0.172248i	$-0.944897\pi$
$887$	−0.0146997	+	0.0833663i	−0.000493569	+	0.00279917i	0.984560	+	0.175048i	$0.0560079\pi$
$888$	5.01780	−	0.433071i	0.168386	−	0.0145329i
$889$	5.89145	−	28.7083i	0.197593	−	0.962846i
$890$	−2.87450			−0.0963533
$891$	5.00371	−	8.57354i	0.167631	−	0.287225i
$892$	19.9454	−	34.5465i	0.667822	−	1.15670i
$893$	1.99549	−	1.67441i	0.0667765	−	0.0560321i
$894$	1.78722	+	2.55880i	0.0597736	+	0.0855790i
$895$	10.5573	+	8.85866i	0.352893	+	0.296112i
$896$	6.50558	+	12.0304i	0.217336	+	0.401906i
$897$	−9.52901	−	2.56527i	−0.318164	−	0.0856519i
$898$	2.03702	+	0.741416i	0.0679764	+	0.0247414i
$899$	−27.0160			−0.901034
$900$	22.5523	−	3.92205i	0.751742	−	0.130735i
$901$	35.6048			1.18617
$902$	0.274394	+	1.55617i	0.00913632	+	0.0518147i
$903$	−15.3341	−	23.3123i	−0.510287	−	0.775784i
$904$	−7.76652	+	2.82678i	−0.258311	+	0.0940174i
$905$	−5.68732	−	4.77223i	−0.189053	−	0.158634i
$906$	−2.28558	−	1.60438i	−0.0759333	−	0.0533019i
$907$	6.10331	+	2.22142i	0.202657	+	0.0737611i	0.441354	−	0.897333i	$-0.354498\pi$
$907$	6.10331	+	2.22142i	0.202657	+	0.0737611i	−0.238697	+	0.971094i	$0.576720\pi$
$908$	−0.0139985			−0.000464556
$909$	−0.302367	+	0.358635i	−0.0100289	+	0.0118952i
$910$	0.0839206	+	0.568110i	0.00278194	+	0.0188326i
$911$	13.7194	−	11.5120i	0.454545	−	0.381409i	−0.386574	−	0.922258i	$-0.626342\pi$
$911$	13.7194	−	11.5120i	0.454545	−	0.381409i	0.841119	+	0.540850i	$0.181897\pi$
$912$	9.03895	+	2.43334i	0.299310	+	0.0805761i
$913$	−10.2227	−	8.57786i	−0.338322	−	0.283886i
$914$	−3.13118	+	1.13966i	−0.103570	+	0.0376965i
$915$	6.11694	−	13.0778i	0.202220	−	0.432337i
$916$	23.6270	+	8.59952i	0.780657	+	0.284136i
$917$	44.9831	−	35.6569i	1.48547	−	1.17749i
$918$	−1.95894	+	2.77681i	−0.0646545	+	0.0916483i
$919$	20.9221	+	36.2381i	0.690156	+	1.19539i	0.971786	+	0.235862i	$0.0757914\pi$
$919$	20.9221	+	36.2381i	0.690156	+	1.19539i	−0.281630	+	0.959523i	$0.590875\pi$
$920$	2.52912	−	2.12218i	0.0833826	−	0.0699663i
$921$	1.17529	+	1.68269i	0.0387272	+	0.0554464i
$922$	0.0426915	−	0.242115i	0.00140597	−	0.00797365i
$923$	−3.47073	+	19.6835i	−0.114240	+	0.647889i
$924$	−9.15213	+	3.94830i	−0.301083	+	0.129889i
$925$	−12.9663	+	10.8800i	−0.426330	+	0.357733i
$926$	−0.517946	+	0.897109i	−0.0170208	+	0.0294808i
$927$	33.5264	+	19.4615i	1.10115	+	0.639198i
$928$	8.60854	+	14.9104i	0.282589	+	0.489459i
$929$	−25.4264	+	21.3353i	−0.834214	+	0.699989i	−0.956254	−	0.292536i	$-0.905501\pi$
$929$	−25.4264	+	21.3353i	−0.834214	+	0.699989i	0.122040	+	0.992525i	$0.461056\pi$
$930$	0.864341	−	0.401815i	0.0283429	−	0.0131760i
$931$	−9.07270	−	3.88747i	−0.297346	−	0.127407i
$932$	−47.6828	+	17.3551i	−1.56190	+	0.568486i
$933$	−22.3888	−	15.7160i	−0.732976	−	0.514518i
$934$	−0.146795	−	0.0534288i	−0.00480326	−	0.00174825i
$935$	−2.29170	−	3.96934i	−0.0749467	−	0.129811i
$936$	−0.00570529	+	2.43236i	−0.000186483	+	0.0795041i
$937$	−3.94382	−	6.83089i	−0.128839	−	0.223155i	0.794388	−	0.607410i	$-0.207792\pi$
$937$	−3.94382	−	6.83089i	−0.128839	−	0.223155i	−0.923227	+	0.384255i	$0.874458\pi$
$938$	−2.42372	−	2.15166i	−0.0791373	−	0.0702541i
$939$	7.86545	+	29.4926i	0.256679	+	0.962453i
$940$	3.64014	−	1.32490i	0.118728	−	0.0432136i
$941$	8.17747	−	2.97636i	0.266578	−	0.0970264i	−0.205273	−	0.978705i	$-0.565808\pi$
$941$	8.17747	−	2.97636i	0.266578	−	0.0970264i	0.471851	+	0.881678i	$0.343586\pi$
$942$	0.980399	+	1.40366i	0.0319431	+	0.0457336i
$943$	−6.94362	−	39.3793i	−0.226116	−	1.28236i
$944$	0.0628551			0.00204576
$945$	14.5157	+	1.73055i	0.472196	+	0.0562949i
$946$	−1.12394			−0.0365425
$947$	−1.77259	−	10.0528i	−0.0576013	−	0.326673i	0.942367	−	0.334580i	$-0.108594\pi$
$947$	−1.77259	−	10.0528i	−0.0576013	−	0.326673i	−0.999969	+	0.00790657i	$0.997483\pi$
$948$	−37.1973	+	3.21039i	−1.20811	+	0.104269i
$949$	−10.5097	+	3.82521i	−0.341159	+	0.124172i
$950$	0.857998	−	0.312286i	0.0278371	−	0.0101319i
$951$	15.0113	−	14.9762i	0.486776	−	0.485636i
$952$	6.52128	−	2.16971i	0.211356	−	0.0703207i
$953$	−10.9981	−	19.0493i	−0.356264	−	0.617068i	0.631069	−	0.775727i	$-0.282616\pi$
$953$	−10.9981	−	19.0493i	−0.356264	−	0.617068i	−0.987334	+	0.158659i	$0.949283\pi$
$954$	1.55437	+	4.30195i	0.0503244	+	0.139281i
$955$	10.9818	+	19.0210i	0.355362	+	0.615505i
$956$	−14.2179	−	5.17489i	−0.459840	−	0.167368i
$957$	−15.1339	+	7.03546i	−0.489210	+	0.227424i
$958$	5.55729	−	2.02269i	0.179548	−	0.0653501i
$959$	9.47017	+	0.264044i	0.305808	+	0.00852642i
$960$	11.0581	+	7.76230i	0.356898	+	0.250527i
$961$	−16.4212	+	13.7790i	−0.529715	+	0.444483i
$962$	−0.446475	−	0.773318i	−0.0143949	−	0.0249328i
$963$	−0.211971	+	0.578163i	−0.00683068	+	0.0186310i
$964$	18.4883	−	32.0227i	0.595468	−	1.03138i
$965$	3.68082	−	3.08858i	0.118490	−	0.0994248i
$966$	−3.28913	+	1.41896i	−0.105826	+	0.0456542i
$967$	−8.52160	+	48.3284i	−0.274036	+	1.55414i	0.467971	+	0.883744i	$0.344985\pi$
$967$	−8.52160	+	48.3284i	−0.274036	+	1.55414i	−0.742007	+	0.670392i	$0.766126\pi$
$968$	1.12927	−	6.40439i	0.0362960	−	0.205845i
$969$	4.04377	−	8.64540i	0.129904	−	0.277730i
$970$	−0.0529889	+	0.0444630i	−0.00170137	+	0.00142762i
$971$	11.4776	+	19.8797i	0.368333	+	0.637971i	0.989305	−	0.145861i	$-0.0465953\pi$
$971$	11.4776	+	19.8797i	0.368333	+	0.637971i	−0.620972	+	0.783833i	$0.713262\pi$
$972$	29.6457	+	8.13017i	0.950887	+	0.260775i
$973$	−4.35922	−	29.5102i	−0.139750	−	0.946054i
$974$	0.414334	+	0.150805i	0.0132761	+	0.00483212i
$975$	−4.68090	−	6.70173i	−0.149909	−	0.214627i
$976$	−28.2331	+	10.2760i	−0.903720	+	0.328927i
$977$	−26.6398	−	22.3534i	−0.852282	−	0.715150i	0.108009	−	0.994150i	$-0.465553\pi$
$977$	−26.6398	−	22.3534i	−0.852282	−	0.715150i	−0.960291	+	0.279000i	$0.909997\pi$
$978$	0.917230	+	3.43928i	0.0293298	+	0.109976i
$979$	−13.6486	+	11.4525i	−0.436210	+	0.366024i
$980$	−10.7010	−	10.0469i	−0.341832	−	0.320936i
$981$	−18.4610	+	3.21054i	−0.589414	+	0.102505i
$982$	−1.39438			−0.0444966
$983$	11.5958	+	4.22053i	0.369849	+	0.134614i	0.520256	−	0.854010i	$-0.325836\pi$
$983$	11.5958	+	4.22053i	0.369849	+	0.134614i	−0.150408	+	0.988624i	$0.548059\pi$
$984$	−8.93751	+	4.15488i	−0.284917	+	0.132453i
$985$	−4.02191	−	3.37478i	−0.128149	−	0.107530i
$986$	5.36867	−	1.95404i	0.170973	−	0.0622292i
$987$	−8.45139	+	0.492590i	−0.269011	+	0.0156793i
$988$	−0.588963	−	3.34017i	−0.0187374	−	0.106265i
$989$	28.4417			0.904392
$990$	0.379549	−	0.450181i	0.0120629	−	0.0143077i
$991$	6.70738			0.213067			0.106533	−	0.994309i	$-0.466025\pi$
$991$	6.70738			0.213067			0.106533	+	0.994309i	$0.466025\pi$
$992$	−5.72731	−	2.08457i	−0.181842	−	0.0661851i
$993$	16.7688	−	16.7295i	0.532141	−	0.530895i
$994$	3.45111	+	6.38192i	0.109463	+	0.202422i
$995$	−20.8079	−	17.4599i	−0.659656	−	0.553517i
$996$	17.5084	−	37.4322i	0.554775	−	1.18608i
$997$	−25.6108	+	21.4900i	−0.811103	+	0.680596i	−0.950871	−	0.309588i	$-0.899809\pi$
$997$	−25.6108	+	21.4900i	−0.811103	+	0.680596i	0.139768	+	0.990184i	$0.455364\pi$
$998$	1.61729	−	2.80123i	0.0511945	−	0.0886715i
$999$	−21.9766	+	5.80582i	−0.695310	+	0.183688i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.4.12	✓	132
3.2	odd	2		567.2.u.a.550.11		132
7.2	even	3		189.2.w.a.58.12	yes	132
21.2	odd	6		567.2.w.a.226.11		132
27.7	even	9		189.2.w.a.88.12	yes	132
27.20	odd	18		567.2.w.a.424.11		132
189.128	odd	18		567.2.u.a.100.11		132
189.142	even	9	inner	189.2.u.a.142.12	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.12	✓	132	1.1	even	1	trivial
189.2.u.a.142.12	yes	132	189.142	even	9	inner
189.2.w.a.58.12	yes	132	7.2	even	3
189.2.w.a.88.12	yes	132	27.7	even	9
567.2.u.a.100.11		132	189.128	odd	18
567.2.u.a.550.11		132	3.2	odd	2
567.2.w.a.226.11		132	21.2	odd	6
567.2.w.a.424.11		132	27.20	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0290601 + 0.164808i) q^{2} +(0.733837 - 1.56891i) q^{3} +(1.85307 - 0.674462i) q^{4} +(-0.999212 + 0.363683i) q^{5} +(0.279894 + 0.0753494i) q^{6} +(1.97858 + 1.75648i) q^{7} +(0.332357 + 0.575660i) q^{8} +(-1.92297 - 2.30265i) q^{9} +O(q^{10})\)	\(q+(0.0290601 + 0.164808i) q^{2} +(0.733837 - 1.56891i) q^{3} +(1.85307 - 0.674462i) q^{4} +(-0.999212 + 0.363683i) q^{5} +(0.279894 + 0.0753494i) q^{6} +(1.97858 + 1.75648i) q^{7} +(0.332357 + 0.575660i) q^{8} +(-1.92297 - 2.30265i) q^{9} +(-0.0889751 - 0.154109i) q^{10} +(-1.03647 - 0.377243i) q^{11} +(0.301679 - 3.40224i) q^{12} +(-1.14619 + 0.417180i) q^{13} +(-0.231985 + 0.377129i) q^{14} +(-0.162671 + 1.83456i) q^{15} +(2.93605 - 2.46364i) q^{16} +(-1.95396 - 3.38436i) q^{17} +(0.323613 - 0.383835i) q^{18} +(-0.705034 + 1.22115i) q^{19} +(-1.60632 + 1.34786i) q^{20} +(4.20772 - 1.81524i) q^{21} +(0.0320529 - 0.181781i) q^{22} +(-0.811107 + 4.60002i) q^{23} +(1.14706 - 0.0989989i) q^{24} +(-2.96406 + 2.48714i) q^{25} +(-0.102063 - 0.176778i) q^{26} +(-5.02380 + 1.32720i) q^{27} +(4.85112 + 1.92041i) q^{28} +(8.20907 + 2.98786i) q^{29} +(-0.307077 + 0.0265029i) q^{30} +(-2.90602 + 1.05771i) q^{31} +(1.50975 + 1.26683i) q^{32} +(-1.35246 + 1.34929i) q^{33} +(0.500988 - 0.420379i) q^{34} +(-2.61582 - 1.03552i) q^{35} +(-5.11644 - 2.97000i) q^{36} +4.37450 q^{37} +(-0.221744 - 0.0807084i) q^{38} +(-0.186600 + 2.10442i) q^{39} +(-0.541453 - 0.454333i) q^{40} +(-8.04440 + 2.92792i) q^{41} +(0.421443 + 0.640715i) q^{42} +(-1.05735 - 5.99651i) q^{43} -2.17508 q^{44} +(2.75889 + 1.60148i) q^{45} -0.781690 q^{46} +(-1.73596 - 0.631839i) q^{47} +(-1.71065 - 6.41432i) q^{48} +(0.829534 + 6.95067i) q^{49} +(-0.496037 - 0.416225i) q^{50} +(-6.74366 + 0.582025i) q^{51} +(-1.84260 + 1.54613i) q^{52} +(-4.55546 + 7.89029i) q^{53} +(-0.364724 - 0.789393i) q^{54} +1.17285 q^{55} +(-0.353542 + 1.72277i) q^{56} +(1.39850 + 2.00226i) q^{57} +(-0.253866 + 1.43975i) q^{58} +(0.0125627 + 0.0105414i) q^{59} +(0.935899 + 3.50928i) q^{60} +(-7.36629 - 2.68111i) q^{61} +(-0.258768 - 0.448199i) q^{62} +(0.239827 - 7.93363i) q^{63} +(3.66784 - 6.35288i) q^{64} +(0.993568 - 0.833703i) q^{65} +(-0.261676 - 0.183686i) q^{66} +(-1.27108 + 7.20865i) q^{67} +(-5.90345 - 4.95358i) q^{68} +(6.62180 + 4.64822i) q^{69} +(0.0946464 - 0.461201i) q^{70} +(8.19310 - 14.1909i) q^{71} +(0.686431 - 1.87228i) q^{72} +9.16921 q^{73} +(0.127123 + 0.720953i) q^{74} +(1.72697 + 6.47551i) q^{75} +(-0.482854 + 2.73840i) q^{76} +(-1.38811 - 2.56694i) q^{77} +(-0.352247 + 0.0304014i) q^{78} +(-1.89813 - 10.7649i) q^{79} +(-2.03776 + 3.52950i) q^{80} +(-1.60440 + 8.85584i) q^{81} +(-0.716316 - 1.24070i) q^{82} +(11.3691 + 4.13802i) q^{83} +(6.57288 - 6.20171i) q^{84} +(3.18326 + 2.67107i) q^{85} +(0.957545 - 0.348518i) q^{86} +(10.7118 - 10.6867i) q^{87} +(-0.127314 - 0.722032i) q^{88} +(8.07668 - 13.9892i) q^{89} +(-0.183764 + 0.501226i) q^{90} +(-3.00060 - 1.18785i) q^{91} +(1.59950 + 9.07121i) q^{92} +(-0.473100 + 5.33548i) q^{93} +(0.0536849 - 0.304462i) q^{94} +(0.260365 - 1.47660i) q^{95} +(3.09546 - 1.43902i) q^{96} +(-0.0674999 - 0.382811i) q^{97} +(-1.12142 + 0.338701i) q^{98} +(1.12443 + 3.11205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Introduction

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