LMFDB - Embedded newform 189.2.u.a.79.20

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			79.20
Character	$\chi$	$=$	189.79
Dual form			189.2.u.a.67.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72703 + 1.44915i) q^{2} +(-1.10323 + 1.33525i) q^{3} +(0.535296 + 3.03582i) q^{4} +(0.280502 + 1.59081i) q^{5} +(-3.84028 + 0.707271i) q^{6} +(0.455150 - 2.60631i) q^{7} +(-1.22040 + 2.11380i) q^{8} +(-0.565779 - 2.94617i) q^{9} +O(q^{10})$	\(q+(1.72703 + 1.44915i) q^{2} +(-1.10323 + 1.33525i) q^{3} +(0.535296 + 3.03582i) q^{4} +(0.280502 + 1.59081i) q^{5} +(-3.84028 + 0.707271i) q^{6} +(0.455150 - 2.60631i) q^{7} +(-1.22040 + 2.11380i) q^{8} +(-0.565779 - 2.94617i) q^{9} +(-1.82088 + 3.15386i) q^{10} +(-0.167538 + 0.950156i) q^{11} +(-4.64412 - 2.63444i) q^{12} +(-0.0325017 - 0.184326i) q^{13} +(4.56298 - 3.84158i) q^{14} +(-2.43358 - 1.38048i) q^{15} +(0.622616 - 0.226614i) q^{16} +(-2.35408 + 4.07738i) q^{17} +(3.29231 - 5.90800i) q^{18} +(-0.252171 - 0.436773i) q^{19} +(-4.67925 + 1.70311i) q^{20} +(2.97794 + 3.48309i) q^{21} +(-1.66626 + 1.39816i) q^{22} +(6.01177 - 5.04448i) q^{23} +(-1.47607 - 3.96154i) q^{24} +(2.24647 - 0.817650i) q^{25} +(0.210985 - 0.365436i) q^{26} +(4.55805 + 2.49484i) q^{27} +(8.15591 - 0.0133961i) q^{28} +(-1.02634 + 5.82066i) q^{29} +(-2.20234 - 5.91075i) q^{30} +(-0.648287 - 3.67662i) q^{31} +(5.99088 + 2.18050i) q^{32} +(-1.08386 - 1.27194i) q^{33} +(-9.97427 + 3.63034i) q^{34} +(4.27381 - 0.00701971i) q^{35} +(8.64116 - 3.29467i) q^{36} -9.68721 q^{37} +(0.197443 - 1.11975i) q^{38} +(0.281978 + 0.159956i) q^{39} +(-3.70497 - 1.34850i) q^{40} +(-1.93086 - 10.9505i) q^{41} +(0.0954665 + 10.3309i) q^{42} +(-6.60401 - 5.54143i) q^{43} -2.97418 q^{44} +(4.52808 - 1.72645i) q^{45} +17.6927 q^{46} +(-0.262617 + 1.48937i) q^{47} +(-0.384301 + 1.08135i) q^{48} +(-6.58568 - 2.37252i) q^{49} +(5.06461 + 1.84337i) q^{50} +(-2.84723 - 7.64155i) q^{51} +(0.542182 - 0.197338i) q^{52} +(1.38569 + 2.40009i) q^{53} +(4.25649 + 10.9139i) q^{54} -1.55851 q^{55} +(4.95374 + 4.14284i) q^{56} +(0.861403 + 0.145149i) q^{57} +(-10.2075 + 8.56512i) q^{58} +(0.653703 + 0.237928i) q^{59} +(2.88820 - 8.12688i) q^{60} +(-1.54362 + 8.75430i) q^{61} +(4.20835 - 7.28908i) q^{62} +(-7.93613 + 0.133647i) q^{63} +(6.52397 + 11.2998i) q^{64} +(0.284111 - 0.103408i) q^{65} +(-0.0286255 - 3.76735i) q^{66} +(-2.44274 + 2.04970i) q^{67} +(-13.6383 - 4.96394i) q^{68} +(0.103279 + 13.5924i) q^{69} +(7.39115 + 6.18125i) q^{70} +(-1.43937 - 2.49307i) q^{71} +(6.91807 + 2.39956i) q^{72} -0.0348339 q^{73} +(-16.7301 - 14.0382i) q^{74} +(-1.38661 + 3.90165i) q^{75} +(1.19098 - 0.999349i) q^{76} +(2.40014 + 0.869119i) q^{77} +(0.255184 + 0.684876i) q^{78} +(6.40479 + 5.37426i) q^{79} +(0.535144 + 0.926896i) q^{80} +(-8.35979 + 3.33376i) q^{81} +(12.5342 - 21.7098i) q^{82} +(2.38942 - 13.5510i) q^{83} +(-8.97994 + 10.9049i) q^{84} +(-7.14665 - 2.60117i) q^{85} +(-3.37497 - 19.1404i) q^{86} +(-6.63975 - 7.79193i) q^{87} +(-1.80397 - 1.51371i) q^{88} +(5.70612 + 9.88329i) q^{89} +(10.3220 + 3.58023i) q^{90} +(-0.495204 + 0.000813371i) q^{91} +(18.5322 + 15.5503i) q^{92} +(5.62441 + 3.19052i) q^{93} +(-2.61187 + 2.19162i) q^{94} +(0.624088 - 0.523672i) q^{95} +(-9.52081 + 5.59373i) q^{96} +(-7.73226 - 6.48814i) q^{97} +(-7.93551 - 13.6410i) q^{98} +(2.89411 - 0.0439831i) 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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.72703	+	1.44915i	1.22119	+	1.02470i	0.998762	+	0.0497534i	$0.0158435\pi$
$2$	1.72703	+	1.44915i	1.22119	+	1.02470i	0.222431	+	0.974949i	$0.428601\pi$
$3$	−1.10323	+	1.33525i	−0.636949	+	0.770906i
$3$	−1.10323	+	1.33525i	−0.636949	+	0.770906i
$4$	0.535296	+	3.03582i	0.267648	+	1.51791i
$5$	0.280502	+	1.59081i	0.125444	+	0.711431i	0.981043	+	0.193791i	$0.0620783\pi$
$5$	0.280502	+	1.59081i	0.125444	+	0.711431i	−0.855598	+	0.517640i	$0.826811\pi$
$6$	−3.84028	+	0.707271i	−1.56779	+	0.288742i
$7$	0.455150	−	2.60631i	0.172030	−	0.985092i
$7$	0.455150	−	2.60631i	0.172030	−	0.985092i
$8$	−1.22040	+	2.11380i	−0.431477	+	0.747340i
$9$	−0.565779	−	2.94617i	−0.188593	−	0.982055i
$10$	−1.82088	+	3.15386i	−0.575813	+	0.997337i
$11$	−0.167538	+	0.950156i	−0.0505146	+	0.286483i	−0.999592	−	0.0285602i	$-0.990908\pi$
$11$	−0.167538	+	0.950156i	−0.0505146	+	0.286483i	0.949077	+	0.315043i	$0.102019\pi$
$12$	−4.64412	−	2.63444i	−1.34064	−	0.760498i
$13$	−0.0325017	−	0.184326i	−0.00901434	−	0.0511229i	0.979969	−	0.199151i	$-0.0638185\pi$
$13$	−0.0325017	−	0.184326i	−0.00901434	−	0.0511229i	−0.988983	+	0.148028i	$0.952707\pi$
$14$	4.56298	−	3.84158i	1.21951	−	1.02671i
$15$	−2.43358	−	1.38048i	−0.628348	−	0.356439i
$16$	0.622616	−	0.226614i	0.155654	−	0.0566534i
$17$	−2.35408	+	4.07738i	−0.570947	+	0.988910i	0.425522	+	0.904948i	$0.360091\pi$
$17$	−2.35408	+	4.07738i	−0.570947	+	0.988910i	−0.996469	+	0.0839614i	$0.973243\pi$
$18$	3.29231	−	5.90800i	0.776006	−	1.39253i
$19$	−0.252171	−	0.436773i	−0.0578520	−	0.100203i	0.835649	−	0.549264i	$-0.185092\pi$
$19$	−0.252171	−	0.436773i	−0.0578520	−	0.100203i	−0.893501	+	0.449061i	$0.851758\pi$
$20$	−4.67925	+	1.70311i	−1.04631	+	0.380826i
$21$	2.97794	+	3.48309i	0.649839	+	0.760072i
$22$	−1.66626	+	1.39816i	−0.355247	+	0.298088i
$23$	6.01177	−	5.04448i	1.25354	−	1.05185i	0.257202	−	0.966358i	$-0.417199\pi$
$23$	6.01177	−	5.04448i	1.25354	−	1.05185i	0.996339	−	0.0854883i	$-0.0272450\pi$
$24$	−1.47607	−	3.96154i	−0.301301	−	0.808646i
$25$	2.24647	−	0.817650i	0.449295	−	0.163530i
$26$	0.210985	−	0.365436i	0.0413775	−	0.0716679i
$27$	4.55805	+	2.49484i	0.877197	+	0.480131i
$28$	8.15591	−	0.0133961i	1.54132	−	0.00253162i
$29$	−1.02634	+	5.82066i	−0.190587	+	1.08087i	0.727978	+	0.685600i	$0.240460\pi$
$29$	−1.02634	+	5.82066i	−0.190587	+	1.08087i	−0.918565	+	0.395270i	$0.870651\pi$
$30$	−2.20234	−	5.91075i	−0.402090	−	1.07915i
$31$	−0.648287	−	3.67662i	−0.116436	−	0.660340i	−0.986029	−	0.166572i	$-0.946730\pi$
$31$	−0.648287	−	3.67662i	−0.116436	−	0.660340i	0.869594	−	0.493768i	$-0.164381\pi$
$32$	5.99088	+	2.18050i	1.05905	+	0.385462i
$33$	−1.08386	−	1.27194i	−0.188676	−	0.221417i
$34$	−9.97427	+	3.63034i	−1.71057	+	0.622598i
$35$	4.27381	−	0.00701971i	0.722405	−	0.00118655i
$36$	8.64116	−	3.29467i	1.44019	−	0.549112i
$37$	−9.68721			−1.59257			−0.796284	−	0.604923i	$-0.793204\pi$
$37$	−9.68721			−1.59257			−0.796284	+	0.604923i	$0.793204\pi$
$38$	0.197443	−	1.11975i	0.0320294	−	0.181648i
$39$	0.281978	+	0.159956i	0.0451526	+	0.0256134i
$40$	−3.70497	−	1.34850i	−0.585807	−	0.213216i
$41$	−1.93086	−	10.9505i	−0.301550	−	1.71017i	−0.639316	−	0.768944i	$-0.720783\pi$
$41$	−1.93086	−	10.9505i	−0.301550	−	1.71017i	0.337767	−	0.941230i	$-0.390329\pi$
$42$	0.0954665	+	10.3309i	0.0147308	+	1.59409i
$43$	−6.60401	−	5.54143i	−1.00710	−	0.845060i	−0.0191503	−	0.999817i	$-0.506096\pi$
$43$	−6.60401	−	5.54143i	−1.00710	−	0.845060i	−0.987953	+	0.154757i	$0.950541\pi$
$44$	−2.97418			−0.448375
$45$	4.52808	−	1.72645i	0.675007	−	0.257364i
$46$	17.6927			2.60864
$47$	−0.262617	+	1.48937i	−0.0383066	+	0.217248i	−0.997952	−	0.0639648i	$-0.979625\pi$
$47$	−0.262617	+	1.48937i	−0.0383066	+	0.217248i	0.959646	+	0.281212i	$0.0907366\pi$
$48$	−0.384301	+	1.08135i	−0.0554691	+	0.156080i
$49$	−6.58568	−	2.37252i	−0.940811	−	0.338931i
$50$	5.06461	+	1.84337i	0.716245	+	0.260692i
$51$	−2.84723	−	7.64155i	−0.398693	−	1.07003i
$52$	0.542182	−	0.197338i	0.0751872	−	0.0273659i
$53$	1.38569	+	2.40009i	0.190340	+	0.329678i	0.945363	−	0.326020i	$-0.105708\pi$
$53$	1.38569	+	2.40009i	0.190340	+	0.329678i	−0.755023	+	0.655698i	$0.772374\pi$
$54$	4.25649	+	10.9139i	0.579234	+	1.48520i
$55$	−1.55851			−0.210149
$56$	4.95374	+	4.14284i	0.661971	+	0.553610i
$57$	0.861403	+	0.145149i	0.114096	+	0.0192255i
$58$	−10.2075	+	8.56512i	−1.34031	+	1.12466i
$59$	0.653703	+	0.237928i	0.0851049	+	0.0309756i	0.384222	−	0.923241i	$-0.374470\pi$
$59$	0.653703	+	0.237928i	0.0851049	+	0.0309756i	−0.299117	+	0.954216i	$0.596692\pi$
$60$	2.88820	−	8.12688i	0.372866	−	1.04918i
$61$	−1.54362	+	8.75430i	−0.197640	+	1.12087i	0.710968	+	0.703224i	$0.248257\pi$
$61$	−1.54362	+	8.75430i	−0.197640	+	1.12087i	−0.908608	+	0.417649i	$0.862854\pi$
$62$	4.20835	−	7.28908i	0.534461	−	0.925714i
$63$	−7.93613	+	0.133647i	−0.999858	+	0.0168380i
$64$	6.52397	+	11.2998i	0.815496	+	1.41248i
$65$	0.284111	−	0.103408i	0.0352396	−	0.0128262i
$66$	−0.0286255	−	3.76735i	−0.00352355	−	0.463729i
$67$	−2.44274	+	2.04970i	−0.298428	+	0.250411i	−0.779690	−	0.626166i	$-0.784623\pi$
$67$	−2.44274	+	2.04970i	−0.298428	+	0.250411i	0.481262	+	0.876577i	$0.340179\pi$
$68$	−13.6383	−	4.96394i	−1.65389	−	0.601966i
$69$	0.103279	+	13.5924i	0.0124334	+	1.63633i
$70$	7.39115	+	6.18125i	0.883411	+	0.738801i
$71$	−1.43937	−	2.49307i	−0.170822	−	0.295873i	0.767885	−	0.640587i	$-0.221309\pi$
$71$	−1.43937	−	2.49307i	−0.170822	−	0.295873i	−0.938708	+	0.344714i	$0.887976\pi$
$72$	6.91807	+	2.39956i	0.815303	+	0.282791i
$73$	−0.0348339			−0.00407700			−0.00203850	−	0.999998i	$-0.500649\pi$
$73$	−0.0348339			−0.00407700			−0.00203850	+	0.999998i	$0.500649\pi$
$74$	−16.7301	−	14.0382i	−1.94483	−	1.63191i
$75$	−1.38661	+	3.90165i	−0.160111	+	0.450524i
$76$	1.19098	−	0.999349i	0.136614	−	0.114633i
$77$	2.40014	+	0.869119i	0.273522	+	0.0990453i
$78$	0.255184	+	0.684876i	0.0288939	+	0.0775469i
$79$	6.40479	+	5.37426i	0.720595	+	0.604651i	0.927550	−	0.373699i	$-0.121911\pi$
$79$	6.40479	+	5.37426i	0.720595	+	0.604651i	−0.206955	+	0.978351i	$0.566355\pi$
$80$	0.535144	+	0.926896i	0.0598309	+	0.103630i
$81$	−8.35979	+	3.33376i	−0.928865	+	0.370417i
$82$	12.5342	−	21.7098i	1.38417	−	2.39745i
$83$	2.38942	−	13.5510i	0.262272	−	1.48742i	−0.514419	−	0.857539i	$-0.671992\pi$
$83$	2.38942	−	13.5510i	0.262272	−	1.48742i	0.776691	−	0.629882i	$-0.216897\pi$
$84$	−8.97994	+	10.9049i	−0.979791	+	1.18983i
$85$	−7.14665	−	2.60117i	−0.775163	−	0.282136i
$86$	−3.37497	−	19.1404i	−0.363932	−	2.06396i
$87$	−6.63975	−	7.79193i	−0.711856	−	0.835383i
$88$	−1.80397	−	1.51371i	−0.192304	−	0.161362i
$89$	5.70612	+	9.88329i	0.604848	+	1.04763i	0.992076	+	0.125643i	$0.0400994\pi$
$89$	5.70612	+	9.88329i	0.604848	+	1.04763i	−0.387228	+	0.921984i	$0.626567\pi$
$90$	10.3220	+	3.58023i	1.08803	+	0.377389i
$91$	−0.495204		0.000813371i	−0.0519115		8.52644e-5i
$92$	18.5322	+	15.5503i	1.93211	+	1.62124i
$93$	5.62441	+	3.19052i	0.583224	+	0.330842i
$94$	−2.61187	+	2.19162i	−0.269394	+	0.226048i
$95$	0.624088	−	0.523672i	0.0640301	−	0.0537276i
$96$	−9.52081	+	5.59373i	−0.971714	+	0.570907i
$97$	−7.73226	−	6.48814i	−0.785092	−	0.658770i	0.159433	−	0.987209i	$-0.449033\pi$
$97$	−7.73226	−	6.48814i	−0.785092	−	0.658770i	−0.944525	+	0.328438i	$0.893478\pi$
$98$	−7.93551	−	13.6410i	−0.801607	−	1.37795i
$99$	2.89411	−	0.0439831i	0.290869	−	0.00442047i
$100$	3.68476	+	6.38220i	0.368476	+	0.638220i
$101$	−1.58110	−	1.32670i	−0.157326	−	0.132012i	0.560727	−	0.828001i	$-0.310522\pi$
$101$	−1.58110	−	1.32670i	−0.157326	−	0.132012i	−0.718052	+	0.695989i	$0.754966\pi$
$102$	6.15649	−	17.3232i	0.609583	−	1.71525i
$103$	−3.07787	−	17.4554i	−0.303271	−	1.71994i	−0.631532	−	0.775350i	$-0.717574\pi$
$103$	−3.07787	−	17.4554i	−0.303271	−	1.71994i	0.328261	−	0.944587i	$-0.393537\pi$
$104$	0.429293	+	0.156250i	0.0420957	+	0.0153216i
$105$	−4.70561	+	5.71434i	−0.459220	+	0.557662i
$106$	−1.08496	+	6.15310i	−0.105380	+	0.597642i
$107$	−8.44399	+	14.6254i	−0.816311	+	1.41389i	0.0920719	+	0.995752i	$0.470651\pi$
$107$	−8.44399	+	14.6254i	−0.816311	+	1.41389i	−0.908383	+	0.418140i	$0.862682\pi$
$108$	−5.13396	+	15.1729i	−0.494015	+	1.46001i
$109$	−6.03251	−	10.4486i	−0.577810	−	1.00080i	−0.995730	−	0.0923121i	$-0.970574\pi$
$109$	−6.03251	−	10.4486i	−0.577810	−	1.00080i	0.417920	−	0.908484i	$-0.362759\pi$
$110$	−2.69159	−	2.25851i	−0.256633	−	0.215341i
$111$	10.6872	−	12.9348i	1.01438	−	1.22772i
$112$	−0.307241	−	1.72587i	−0.0290316	−	0.163079i
$113$	−12.9494	+	10.8658i	−1.21818	+	1.02217i	−0.219258	+	0.975667i	$0.570364\pi$
$113$	−12.9494	+	10.8658i	−1.21818	+	1.02217i	−0.998918	+	0.0465043i	$0.985192\pi$
$114$	1.27732	+	1.49898i	0.119632	+	0.140392i
$115$	9.71111	+	8.14859i	0.905566	+	0.759860i
$116$	−18.2199			−1.69167
$117$	−0.524667	+	0.200043i	−0.0485055	+	0.0184940i
$118$	0.784169	+	1.35822i	0.0721886	+	0.125034i
$119$	9.55545	+	7.99126i	0.875946	+	0.732558i
$120$	5.88801	−	3.45936i	0.537499	−	0.315795i
$121$	9.46189	+	3.44385i	0.860172	+	0.313077i
$122$	−15.3521	+	12.8820i	−1.38992	+	1.16628i
$123$	16.7518	+	9.50266i	1.51046	+	0.856826i
$124$	10.8145	−	3.93616i	0.971172	−	0.353478i
$125$	5.96924	+	10.3390i	0.533905	+	0.924750i
$126$	−13.8996	−	11.2698i	−1.23827	−	1.00399i
$127$	−3.25167	+	5.63206i	−0.288539	+	0.499765i	−0.973461	−	0.228852i	$-0.926503\pi$
$127$	−3.25167	+	5.63206i	−0.288539	+	0.499765i	0.684922	+	0.728616i	$0.259836\pi$
$128$	−2.89393	+	16.4123i	−0.255790	+	1.45066i
$129$	14.6849	−	2.70455i	1.29293	−	0.238122i
$130$	0.640520	+	0.233130i	0.0561773	+	0.0204469i
$131$	1.72965	−	1.45135i	0.151120	−	0.126805i	−0.564093	−	0.825711i	$-0.690774\pi$
$131$	1.72965	−	1.45135i	0.151120	−	0.126805i	0.715213	+	0.698906i	$0.246330\pi$
$132$	3.28120	−	3.97127i	0.285592	−	0.345655i
$133$	−1.25314	+	0.458438i	−0.108661	+	0.0397517i
$134$	−7.18899			−0.621034
$135$	−2.69026	+	7.95079i	−0.231541	+	0.684295i
$136$	−5.74583	−	9.95208i	−0.492701	−	0.853383i
$137$	−10.0511	+	3.65829i	−0.858720	+	0.312548i	−0.733590	−	0.679592i	$-0.762157\pi$
$137$	−10.0511	+	3.65829i	−0.858720	+	0.312548i	−0.125130	+	0.992140i	$0.539935\pi$
$138$	−19.5190	+	23.6241i	−1.66157	+	2.01102i
$139$	5.14608	+	1.87302i	0.436485	+	0.158868i	0.550911	−	0.834564i	$-0.314281\pi$
$139$	5.14608	+	1.87302i	0.436485	+	0.158868i	−0.114426	+	0.993432i	$0.536503\pi$
$140$	2.30906	+	12.9707i	0.195151	+	1.09623i
$141$	−1.69896	−	1.99378i	−0.143078	−	0.167906i
$142$	1.12699	−	6.39146i	0.0945747	−	0.536360i
$143$	0.180584			0.0151012
$144$	−1.01990	−	1.70612i	−0.0849920	−	0.142176i
$145$	−9.54745			−0.792873
$146$	−0.0601590	−	0.0504794i	−0.00497880	−	0.00417771i
$147$	10.4334	−	6.17609i	0.860533	−	0.509395i
$148$	−5.18553	−	29.4086i	−0.426248	−	2.41737i
$149$	11.0310	+	4.01497i	0.903698	+	0.328919i	0.751734	−	0.659467i	$-0.229218\pi$
$149$	11.0310	+	4.01497i	0.903698	+	0.328919i	0.151964	+	0.988386i	$0.451440\pi$
$150$	−8.04878	+	4.72887i	−0.657180	+	0.386110i
$151$	0.0379586	−	0.215274i	0.00308902	−	0.0175187i	−0.983224	−	0.182401i	$-0.941613\pi$
$151$	0.0379586	−	0.215274i	0.00308902	−	0.0175187i	0.986313	+	0.164882i	$0.0527243\pi$
$152$	1.23100			0.0998473
$153$	13.3445	+	4.62860i	1.07884	+	0.374200i
$154$	2.88563	+	4.97915i	0.232531	+	0.401231i
$155$	5.66695	−	2.06260i	0.455180	−	0.165672i
$156$	−0.334655	+	0.941658i	−0.0267938	+	0.0753929i
$157$	20.3772	+	7.41669i	1.62628	+	0.591916i	0.984563	−	0.175029i	$-0.0560020\pi$
$157$	20.3772	+	7.41669i	1.62628	+	0.591916i	0.641713	+	0.766945i	$0.278224\pi$
$158$	3.27315	+	18.5630i	0.260398	+	1.47679i
$159$	−4.73346	−	0.797602i	−0.375388	−	0.0632539i
$160$	−1.78830	+	10.1420i	−0.141378	+	0.801794i
$161$	−10.4112	−	17.9645i	−0.820517	−	1.41580i
$162$	−19.2687	−	6.35708i	−1.51389	−	0.499459i
$163$	4.59071	−	7.95135i	0.359572	−	0.622798i	−0.628317	−	0.777957i	$-0.716256\pi$
$163$	4.59071	−	7.95135i	0.359572	−	0.622798i	0.987889	+	0.155160i	$0.0495892\pi$
$164$	32.2100	−	11.7235i	2.51518	−	0.915450i
$165$	1.71939	−	2.08100i	0.133854	−	0.162006i
$166$	23.7641	−	19.9404i	1.84445	−	1.54768i
$167$	6.56510	−	5.50878i	0.508023	−	0.426282i	−0.352410	−	0.935846i	$-0.614638\pi$
$167$	6.56510	−	5.50878i	0.508023	−	0.426282i	0.860433	+	0.509564i	$0.170193\pi$
$168$	−10.9968	+	2.04399i	−0.848423	+	0.157697i
$169$	12.1831	−	4.43428i	0.937160	−	0.341098i
$170$	−8.57298	−	14.8488i	−0.657518	−	1.13885i
$171$	−1.14413	+	0.990055i	−0.0874941	+	0.0757114i
$172$	13.2876	−	23.0149i	1.01317	−	1.75487i
$173$	−18.3856	+	6.69181i	−1.39783	+	0.508769i	−0.927534	−	0.373740i	$-0.878075\pi$
$173$	−18.3856	+	6.69181i	−1.39783	+	0.508769i	−0.470297	+	0.882508i	$0.655853\pi$
$174$	−0.175360	−	23.0788i	−0.0132940	−	1.74960i
$175$	−1.10856	−	6.22715i	−0.0837996	−	0.470729i
$176$	0.111006	+	0.629548i	0.00836742	+	0.0474540i
$177$	−1.03888	+	0.610367i	−0.0780867	+	0.0458780i
$178$	−4.46772	+	25.3377i	−0.334870	+	1.89914i
$179$	−2.92618	+	5.06828i	−0.218713	+	0.378821i	−0.954415	−	0.298484i	$-0.903519\pi$
$179$	−2.92618	+	5.06828i	−0.218713	+	0.378821i	0.735702	+	0.677305i	$0.236852\pi$
$180$	7.66506	+	12.8223i	0.571320	+	0.955715i
$181$	−0.331408	+	0.574015i	−0.0246334	+	0.0426662i	−0.878079	−	0.478515i	$-0.841175\pi$
$181$	−0.331408	+	0.574015i	−0.0246334	+	0.0426662i	0.853446	+	0.521181i	$0.174509\pi$
$182$	−0.856409	−	0.716219i	−0.0634813	−	0.0530897i
$183$	−9.98620	−	11.7191i	−0.738201	−	0.866300i
$184$	3.32622	+	18.8640i	0.245212	+	1.39067i
$185$	−2.71729	−	15.4105i	−0.199779	−	1.13300i
$186$	5.08997	+	13.6607i	0.373214	+	1.00165i
$187$	−3.47975	−	2.91985i	−0.254464	−	0.213521i
$188$	−4.66205			−0.340015
$189$	8.57690	−	10.7442i	0.623878	−	0.781522i
$190$	1.83669			0.133248
$191$	6.75954	+	5.67192i	0.489103	+	0.410406i	0.853705	−	0.520757i	$-0.174350\pi$
$191$	6.75954	+	5.67192i	0.489103	+	0.410406i	−0.364602	+	0.931164i	$0.618795\pi$
$192$	−22.2855	−	3.75517i	−1.60832	−	0.271006i
$193$	1.49498	+	8.47848i	0.107611	+	0.610294i	0.990145	+	0.140045i	$0.0447248\pi$
$193$	1.49498	+	8.47848i	0.107611	+	0.610294i	−0.882534	+	0.470249i	$0.844164\pi$
$194$	−3.95155	−	22.4104i	−0.283705	−	1.60897i
$195$	−0.175364	+	0.493441i	−0.0125580	+	0.0353360i
$196$	3.67725	−	21.2629i	0.262660	−	1.51878i
$197$	−8.50014	+	14.7227i	−0.605610	+	1.04895i	0.386345	+	0.922354i	$0.373737\pi$
$197$	−8.50014	+	14.7227i	−0.605610	+	1.04895i	−0.991955	+	0.126593i	$0.959596\pi$
$198$	5.06193	+	4.11803i	0.359736	+	0.292655i
$199$	−11.4590	+	19.8476i	−0.812309	+	1.40696i	0.0989355	+	0.995094i	$0.468456\pi$
$199$	−11.4590	+	19.8476i	−0.812309	+	1.40696i	−0.911244	+	0.411866i	$0.864877\pi$
$200$	−1.01325	+	5.74645i	−0.0716479	+	0.406335i
$201$	−0.0419650	−	5.52295i	−0.00295998	−	0.389559i
$202$	−0.808019	−	4.58250i	−0.0568520	−	0.322424i
$203$	14.7033	+	5.32423i	1.03197	+	0.373688i
$204$	21.6742	−	12.7342i	1.51750	−	0.891571i
$205$	16.8785	−	6.14326i	1.17884	−	0.429064i
$206$	19.9800	−	34.6063i	1.39207	−	2.41114i
$207$	−18.2632	−	14.8576i	−1.26938	−	1.03268i
$208$	−0.0620069	−	0.107399i	−0.00429940	−	0.00744678i
$209$	0.457251	−	0.166426i	0.0316287	−	0.0115119i
$210$	−16.4076	+	3.04970i	−1.13223	+	0.210449i
$211$	12.0864	−	10.1417i	0.832064	−	0.698184i	−0.123700	−	0.992320i	$-0.539476\pi$
$211$	12.0864	−	10.1417i	0.832064	−	0.698184i	0.955764	+	0.294135i	$0.0950316\pi$
$212$	−6.54449	+	5.49148i	−0.449477	+	0.377156i
$213$	4.91683	+	0.828499i	0.336895	+	0.0567678i
$214$	−35.7774	+	13.0219i	−2.44569	+	0.890158i
$215$	6.96290	−	12.0601i	0.474866	−	0.822492i
$216$	−10.8362	+	6.59009i	−0.737312	+	0.448399i
$217$	−9.87747	+	0.0162237i	−0.670526	+	0.00110134i
$218$	4.72328	−	26.7870i	0.319901	−	1.81425i
$219$	0.0384297	−	0.0465119i	0.00259684	−	0.00314298i
$220$	−0.834265	−	4.73135i	−0.0562461	−	0.318988i
$221$	0.828079	+	0.301396i	0.0557026	+	0.0202741i
$222$	37.2016	−	6.85149i	2.49681	−	0.459842i
$223$	−9.82253	+	3.57511i	−0.657765	+	0.239407i	−0.649271	−	0.760557i	$-0.724926\pi$
$223$	−9.82253	+	3.57511i	−0.657765	+	0.239407i	−0.00849389	+	0.999964i	$0.502704\pi$
$224$	8.40980	−	14.6216i	0.561904	−	0.976948i
$225$	−3.67994	−	6.15588i	−0.245329	−	0.410392i
$226$	−38.1101			−2.53505
$227$	−0.602393	+	3.41634i	−0.0399822	+	0.226751i	−0.998251	−	0.0591183i	$-0.981171\pi$
$227$	−0.602393	+	3.41634i	−0.0399822	+	0.226751i	0.958269	+	0.285869i	$0.0922822\pi$
$228$	0.0204604	+	2.69276i	0.00135502	+	0.178332i
$229$	18.3627	+	6.68348i	1.21344	+	0.441657i	0.867896	−	0.496746i	$-0.165472\pi$
$229$	18.3627	+	6.68348i	1.21344	+	0.441657i	0.345545	+	0.938402i	$0.387694\pi$
$230$	4.96284	+	28.1457i	0.327240	+	1.85587i
$231$	−3.80839	+	2.24595i	−0.250574	+	0.147773i
$232$	−11.0512	−	9.27302i	−0.725544	−	0.608804i
$233$	0.0152370			0.000998206			0.000499103	−	1.00000i	$-0.499841\pi$
$233$	0.0152370			0.000998206			0.000499103		1.00000i	$0.499841\pi$
$234$	−1.19601	−	0.414840i	−0.0781853	−	0.0271189i
$235$	−2.44297			−0.159362
$236$	−0.372382	+	2.11188i	−0.0242400	+	0.137472i
$237$	−14.2419	+	2.62296i	−0.925112	+	0.170380i
$238$	4.92199	+	27.6484i	0.319045	+	1.79218i
$239$	−10.5505	−	3.84008i	−0.682458	−	0.248394i	−0.0225552	−	0.999746i	$-0.507180\pi$
$239$	−10.5505	−	3.84008i	−0.682458	−	0.248394i	−0.659902	+	0.751351i	$0.729402\pi$
$240$	−1.82802	−	0.308027i	−0.117998	−	0.0198831i
$241$	28.3775	−	10.3286i	1.82796	−	0.665322i	0.834515	−	0.550986i	$-0.185748\pi$
$241$	28.3775	−	10.3286i	1.82796	−	0.665322i	0.993442	−	0.114336i	$-0.0364741\pi$
$242$	11.3503	+	19.6593i	0.729625	+	1.26375i
$243$	4.77135	−	14.8403i	0.306082	−	0.952005i
$244$	−27.4027			−1.75428
$245$	1.92693	−	11.1420i	0.123107	−	0.711839i
$246$	15.1600	+	40.6871i	0.966565	+	2.59412i
$247$	−0.0723128	+	0.0606776i	−0.00460115	+	0.00386082i
$248$	8.56280	+	3.11660i	0.543738	+	0.197904i
$249$	15.4580	+	18.1404i	0.979608	+	1.14960i
$250$	−4.67374	+	26.5061i	−0.295593	+	1.67639i
$251$	3.95625	−	6.85242i	0.249716	−	0.432521i	−0.713731	−	0.700420i	$-0.752996\pi$
$251$	3.95625	−	6.85242i	0.249716	−	0.432521i	0.963447	+	0.267899i	$0.0863294\pi$
$252$	−4.65391	−	24.0211i	−0.293169	−	1.51319i
$253$	3.78584	+	6.55726i	0.238013	+	0.412251i
$254$	−13.7774	+	5.01457i	−0.864472	+	0.314642i
$255$	11.3576	−	6.67288i	0.711240	−	0.417872i
$256$	−8.79115	+	7.37665i	−0.549447	+	0.461041i
$257$	−0.565571	−	0.205851i	−0.0352793	−	0.0128406i	0.324320	−	0.945947i	$-0.394864\pi$
$257$	−0.565571	−	0.205851i	−0.0352793	−	0.0128406i	−0.359600	+	0.933107i	$0.617087\pi$
$258$	29.2805	+	16.6098i	1.82293	+	1.03408i
$259$	−4.40913	+	25.2479i	−0.273970	+	1.56883i
$260$	0.466011	+	0.807154i	0.0289008	+	0.0500576i
$261$	17.7293	−	0.269441i	1.09742	−	0.0166780i
$262$	5.09037			0.314484
$263$	−0.398449	−	0.334338i	−0.0245694	−	0.0206162i	0.630420	−	0.776254i	$-0.282883\pi$
$263$	−0.398449	−	0.334338i	−0.0245694	−	0.0206162i	−0.654990	+	0.755638i	$0.727327\pi$
$264$	4.01137	−	0.738783i	0.246883	−	0.0454689i
$265$	−3.42940	+	2.87761i	−0.210666	+	0.176770i
$266$	−2.82855	−	1.02425i	−0.173430	−	0.0628009i
$267$	−19.4918	−	3.28443i	−1.19288	−	0.201004i
$268$	−7.53011	−	6.31851i	−0.459974	−	0.385964i
$269$	−0.0763972	−	0.132324i	−0.00465802	−	0.00806793i	0.863687	−	0.504029i	$-0.168149\pi$
$269$	−0.0763972	−	0.132324i	−0.00465802	−	0.00806793i	−0.868345	+	0.495961i	$0.834816\pi$
$270$	−16.1680	+	9.83264i	−0.983954	+	0.598395i
$271$	−9.93447	+	17.2070i	−0.603476	+	1.04525i	0.388814	+	0.921316i	$0.372885\pi$
$271$	−9.93447	+	17.2070i	−0.603476	+	1.04525i	−0.992290	+	0.123935i	$0.960449\pi$
$272$	−0.541695	+	3.07211i	−0.0328451	+	0.186274i
$273$	0.545236	−	0.662118i	0.0329992	−	0.0400732i
$274$	−22.6598	−	8.24751i	−1.36893	−	0.498250i
$275$	0.400524	+	2.27149i	0.0241525	+	0.136976i
$276$	−41.2088	+	7.58951i	−2.48048	+	0.456835i
$277$	−4.19915	−	3.52350i	−0.252302	−	0.211707i	0.507861	−	0.861439i	$-0.330436\pi$
$277$	−4.19915	−	3.52350i	−0.252302	−	0.211707i	−0.760163	+	0.649733i	$0.774881\pi$
$278$	6.17314	+	10.6922i	0.370240	+	0.641275i
$279$	−10.4651	+	3.99011i	−0.626532	+	0.238882i
$280$	−5.20092	+	9.04253i	−0.310814	+	0.540394i
$281$	14.9522	+	12.5464i	0.891972	+	0.748454i	0.968605	−	0.248606i	$-0.0799724\pi$
$281$	14.9522	+	12.5464i	0.891972	+	0.748454i	−0.0766325	+	0.997059i	$0.524417\pi$
$282$	−0.0448706	−	5.90535i	−0.00267200	−	0.351658i
$283$	−17.3173	+	14.5309i	−1.02941	+	0.863773i	−0.990780	−	0.135480i	$-0.956742\pi$
$283$	−17.3173	+	14.5309i	−1.02941	+	0.863773i	−0.0386251	+	0.999254i	$0.512298\pi$
$284$	6.79801	−	5.70421i	0.403388	−	0.338482i
$285$	0.0107215	+	1.41104i	0.000635088	+	0.0835829i
$286$	0.311873	+	0.261693i	0.0184414	+	0.0154742i
$287$	−29.4191	+	0.0483207i	−1.73655	+	0.00285228i
$288$	3.03461	−	18.8838i	0.178816	−	1.11274i
$289$	−2.58334	−	4.47448i	−0.151961	−	0.263205i
$290$	−16.4887	−	13.8357i	−0.968250	−	0.812458i
$291$	17.1937	−	3.16660i	1.00791	−	0.185629i
$292$	−0.0186464	−	0.105749i	−0.00109120	−	0.00618851i
$293$	−10.9601	−	3.98916i	−0.640298	−	0.233049i	0.00140924	−	0.999999i	$-0.499551\pi$
$293$	−10.9601	−	3.98916i	−0.640298	−	0.233049i	−0.641707	+	0.766950i	$0.721774\pi$
$294$	26.9688	+	4.45327i	1.57285	+	0.259720i
$295$	−0.195133	+	1.10666i	−0.0113611	+	0.0644320i
$296$	11.8223	−	20.4768i	0.687157	−	1.19019i
$297$	−3.13413	+	3.91287i	−0.181861	+	0.227048i
$298$	13.2326	+	22.9196i	0.766545	+	1.32769i
$299$	−1.12522	−	0.944173i	−0.0650733	−	0.0546029i
$300$	−12.5870	−	2.12094i	−0.726708	−	0.122452i
$301$	−17.4485	+	14.6899i	−1.00571	+	0.846713i
$302$	0.377519	−	0.316776i	0.0217238	−	0.0182284i
$303$	3.51580	−	0.647511i	0.201977	−	0.0371985i
$304$	−0.255985	−	0.214797i	−0.0146817	−	0.0123194i
$305$	−14.3594			−0.822217
$306$	16.3388	+	27.3319i	0.934028	+	1.56246i
$307$	−4.58756	−	7.94588i	−0.261826	−	0.453495i	0.704901	−	0.709305i	$-0.250991\pi$
$307$	−4.58756	−	7.94588i	−0.261826	−	0.453495i	−0.966727	+	0.255810i	$0.917658\pi$
$308$	−1.35370	+	7.75163i	−0.0771341	+	0.441690i
$309$	26.7030	+	15.1476i	1.51908	+	0.861717i
$310$	12.7760	+	4.65008i	0.725627	+	0.264107i
$311$	−5.53638	+	4.64557i	−0.313939	+	0.263426i	−0.786118	−	0.618077i	$-0.787912\pi$
$311$	−5.53638	+	4.64557i	−0.313939	+	0.263426i	0.472179	+	0.881503i	$0.343468\pi$
$312$	−0.682241	+	0.400834i	−0.0386243	+	0.0226928i
$313$	4.33576	−	1.57809i	0.245072	−	0.0891988i	−0.216564	−	0.976268i	$-0.569485\pi$
$313$	4.33576	−	1.57809i	0.245072	−	0.0891988i	0.461636	+	0.887070i	$0.347263\pi$
$314$	24.4441	+	42.3383i	1.37946	+	2.38929i
$315$	−2.43871	−	12.5874i	−0.137406	−	0.709218i
$316$	−12.8868	+	22.3206i	−0.724939	+	1.25563i
$317$	1.83100	−	10.3841i	0.102839	−	0.583229i	−0.889222	−	0.457475i	$-0.848754\pi$
$317$	1.83100	−	10.3841i	0.102839	−	0.583229i	0.992061	−	0.125754i	$-0.0401350\pi$
$318$	−7.01897	−	8.23696i	−0.393604	−	0.461906i
$319$	−5.35858	−	1.95036i	−0.300023	−	0.109199i
$320$	−16.1459	+	13.5480i	−0.902583	+	0.757357i
$321$	−10.2129	−	27.4100i	−0.570030	−	1.52988i
$322$	8.05282	−	46.1126i	0.448766	−	2.56975i
$323$	2.37452			0.132122
$324$	−14.5956	−	23.5942i	−0.810869	−	1.31079i
$325$	−0.223728	−	0.387509i	−0.0124102	−	0.0214951i
$326$	19.4510	−	7.07957i	1.07729	−	0.392101i
$327$	20.6067	+	3.47229i	1.13955	+	0.192018i
$328$	25.5035	+	9.28250i	1.40819	+	0.512540i
$329$	3.76224	+	1.36235i	0.207419	+	0.0751087i
$330$	5.98511	−	1.10229i	0.329469	−	0.0606790i
$331$	4.36025	−	24.7282i	0.239661	−	1.35919i	−0.592910	−	0.805269i	$-0.702021\pi$
$331$	4.36025	−	24.7282i	0.239661	−	1.35919i	0.832571	−	0.553918i	$-0.186868\pi$
$332$	42.4175			2.32797
$333$	5.48082	+	28.5401i	0.300347	+	1.56399i
$334$	19.3211			1.05721
$335$	−3.94588	−	3.31098i	−0.215586	−	0.180898i
$336$	2.64342	+	1.49378i	0.144211	+	0.0814926i
$337$	1.88012	+	10.6627i	0.102417	+	0.580834i	0.992221	+	0.124491i	$0.0397298\pi$
$337$	1.88012	+	10.6627i	0.102417	+	0.580834i	−0.889804	+	0.456343i	$0.849159\pi$
$338$	27.4664	+	9.99696i	1.49398	+	0.543763i
$339$	−0.222464	−	29.2781i	−0.0120826	−	1.59017i
$340$	4.07109	−	23.0883i	0.220786	−	1.25214i
$341$	3.60197			0.195058
$342$	−3.41069	+	0.0518338i	−0.184429	+	0.00280285i
$343$	−9.18099	+	16.0844i	−0.495727	+	0.868479i
$344$	19.7730	−	7.19678i	1.06609	−	0.388025i
$345$	−21.5940	+	3.97700i	−1.16258	+	0.214115i
$346$	−41.4498	−	15.0865i	−2.22836	−	0.811055i
$347$	−0.291060	−	1.65068i	−0.0156249	−	0.0886133i	0.975998	−	0.217779i	$-0.0698812\pi$
$347$	−0.291060	−	1.65068i	−0.0156249	−	0.0886133i	−0.991623	+	0.129166i	$0.958770\pi$
$348$	20.1006	−	24.3280i	1.07751	−	1.30412i
$349$	1.60438	−	9.09890i	0.0858806	−	0.487053i	−0.911283	−	0.411782i	$-0.864907\pi$
$349$	1.60438	−	9.09890i	0.0858806	−	0.487053i	0.997163	−	0.0752713i	$-0.0239823\pi$
$350$	7.10954	−	12.3609i	0.380021	−	0.660720i
$351$	0.311719	−	0.921254i	0.0166383	−	0.0491729i
$352$	−3.07552	+	5.32695i	−0.163926	+	0.283927i
$353$	−15.6794	+	5.70683i	−0.834530	+	0.303744i	−0.723717	−	0.690097i	$-0.757568\pi$
$353$	−15.6794	+	5.70683i	−0.834530	+	0.303744i	−0.110813	+	0.993841i	$0.535346\pi$
$354$	−2.67868	−	0.451365i	−0.142370	−	0.0239898i
$355$	3.56225	−	2.98908i	0.189064	−	0.158644i
$356$	−26.9494	+	22.6132i	−1.42832	+	1.19850i
$357$	−21.2122	+	3.94272i	−1.12267	+	0.208671i
$358$	−12.3983	+	4.51260i	−0.655269	+	0.238498i
$359$	3.42639	+	5.93468i	0.180838	+	0.313220i	0.942166	−	0.335146i	$-0.108786\pi$
$359$	3.42639	+	5.93468i	0.180838	+	0.313220i	−0.761328	+	0.648367i	$0.775452\pi$
$360$	−1.87671	+	11.6784i	−0.0989112	+	0.615506i
$361$	9.37282	−	16.2342i	0.493306	−	0.854432i
$362$	−1.40418	+	0.511081i	−0.0738022	+	0.0268618i
$363$	−15.0370	+	8.83463i	−0.789238	+	0.463698i
$364$	−0.267550	−	1.50291i	−0.0140234	−	0.0787740i
$365$	−0.00977099	−	0.0554140i	−0.000511437	−	0.00290050i
$366$	−0.263742	−	34.7107i	−0.0137860	−	1.81436i
$367$	−1.24776	+	7.07641i	−0.0651327	+	0.369386i	0.934768	+	0.355260i	$0.115608\pi$
$367$	−1.24776	+	7.07641i	−0.0651327	+	0.369386i	−0.999900	+	0.0141259i	$0.995503\pi$
$368$	2.59988	−	4.50312i	0.135528	−	0.234741i
$369$	−31.1694	+	11.8842i	−1.62262	+	0.618665i
$370$	17.6393	−	30.5521i	0.917021	−	1.58833i
$371$	6.88608	−	2.51914i	0.357507	−	0.130787i
$372$	−6.67511	+	18.7825i	−0.346088	+	0.973830i
$373$	−5.08813	−	28.8562i	−0.263453	−	1.49412i	−0.773403	−	0.633914i	$-0.781447\pi$
$373$	−5.08813	−	28.8562i	−0.263453	−	1.49412i	0.509950	−	0.860204i	$-0.329664\pi$
$374$	−1.77832	−	10.0853i	−0.0919545	−	0.521500i
$375$	−20.3906	−	3.43587i	−1.05297	−	0.177428i
$376$	−2.82774	−	2.37275i	−0.145829	−	0.122365i
$377$	1.10626			0.0569752
$378$	30.3824	−	6.12624i	1.56270	−	0.315100i
$379$	0.333430			0.0171272			0.00856359	−	0.999963i	$-0.497274\pi$
$379$	0.333430			0.0171272			0.00856359	+	0.999963i	$0.497274\pi$
$380$	1.92384	+	1.61430i	0.0986911	+	0.0828117i
$381$	−3.93287	−	10.5552i	−0.201487	−	0.540761i
$382$	3.45444	+	19.5911i	0.176745	+	1.00237i
$383$	−2.50141	−	14.1862i	−0.127816	−	0.724880i	−0.979595	−	0.200980i	$-0.935588\pi$
$383$	−2.50141	−	14.1862i	−0.127816	−	0.724880i	0.851780	−	0.523900i	$-0.175524\pi$
$384$	−18.7218	−	21.9706i	−0.955395	−	1.12118i
$385$	−0.709355	+	4.06196i	−0.0361521	+	0.207016i
$386$	−9.70468	+	16.8090i	−0.493955	+	0.855556i
$387$	−12.5895	+	22.5917i	−0.639963	+	1.14840i
$388$	15.5577	−	26.9468i	0.789825	−	1.36802i
$389$	3.96743	−	22.5004i	0.201157	−	1.14082i	−0.702217	−	0.711963i	$-0.747806\pi$
$389$	3.96743	−	22.5004i	0.201157	−	1.14082i	0.903374	−	0.428854i	$-0.141083\pi$
$390$	−1.01793	+	0.598058i	−0.0515447	+	0.0302839i
$391$	6.41607	+	36.3873i	0.324475	+	1.84019i
$392$	13.0522	−	11.0254i	0.659235	−	0.556865i
$393$	0.0297145	+	3.91068i	0.00149890	+	0.197268i
$394$	−36.0153	+	13.1085i	−1.81442	+	0.660396i
$395$	−6.75286	+	11.6963i	−0.339773	+	0.588504i
$396$	1.68273	+	8.76243i	0.0845603	+	0.440329i
$397$	−11.3010	−	19.5739i	−0.567181	−	0.982387i	−0.996843	−	0.0793969i	$-0.974701\pi$
$397$	−11.3010	−	19.5739i	−0.567181	−	0.982387i	0.429662	−	0.902990i	$-0.358633\pi$
$398$	−48.5522	+	17.6715i	−2.43370	+	0.885794i
$399$	0.770370	−	2.17902i	0.0385668	−	0.109087i
$400$	1.21340	−	1.01816i	0.0606700	−	0.0509081i
$401$	−10.1124	+	8.48533i	−0.504991	+	0.423737i	−0.859362	−	0.511367i	$-0.829139\pi$
$401$	−10.1124	+	8.48533i	−0.504991	+	0.423737i	0.354372	+	0.935105i	$0.384695\pi$
$402$	7.93109	−	9.59910i	0.395567	−	0.478759i
$403$	−0.656627	+	0.238993i	−0.0327089	+	0.0119051i
$404$	3.18127	−	5.51012i	0.158274	−	0.274139i
$405$	−7.64831	−	12.3637i	−0.380048	−	0.614357i
$406$	17.6774	+	30.5023i	0.877314	+	1.51381i
$407$	1.62298	−	9.20436i	0.0804480	−	0.456243i
$408$	19.6275	+	3.30728i	0.971704	+	0.163735i
$409$	0.464911	+	2.63664i	0.0229884	+	0.130374i	0.994142	−	0.108081i	$-0.0344704\pi$
$409$	0.464911	+	2.63664i	0.0229884	+	0.130374i	−0.971154	+	0.238454i	$0.923359\pi$
$410$	38.0520	+	13.8498i	1.87926	+	0.683993i
$411$	6.20388	−	17.4566i	0.306015	−	0.861070i
$412$	51.3440	−	18.6877i	2.52954	−	0.920676i
$413$	0.917647	−	1.59546i	0.0451545	−	0.0785073i
$414$	−10.0101	−	52.1256i	−0.491972	−	2.56183i
$415$	22.2274			1.09110
$416$	0.207210	−	1.17515i	0.0101593	−	0.0576163i
$417$	−8.17825	+	4.80493i	−0.400490	+	0.235299i
$418$	1.03086	+	0.375202i	0.0504210	+	0.0183517i
$419$	−4.94281	−	28.0321i	−0.241472	−	1.36946i	−0.828545	−	0.559922i	$-0.810831\pi$
$419$	−4.94281	−	28.0321i	−0.241472	−	1.36946i	0.587073	−	0.809534i	$-0.300280\pi$
$420$	−19.8666	−	11.2265i	−0.969390	−	0.547797i
$421$	−18.7196	−	15.7076i	−0.912339	−	0.765543i	0.0602237	−	0.998185i	$-0.480819\pi$
$421$	−18.7196	−	15.7076i	−0.912339	−	0.765543i	−0.972562	+	0.232642i	$0.925263\pi$
$422$	35.5704			1.73154
$423$	4.53653	−	0.0689437i	0.220574	−	0.00335216i
$424$	−6.76441			−0.328509
$425$	−1.95450	+	11.0845i	−0.0948073	+	0.537679i
$426$	7.29087	+	8.55604i	0.353244	+	0.414542i
$427$	22.1138	+	8.00766i	1.07016	+	0.387518i
$428$	−48.9201	−	17.8055i	−2.36464	−	0.860659i
$429$	−0.199225	+	0.241124i	−0.00961867	+	0.0116416i
$430$	29.5020	−	10.7378i	1.42271	−	0.517825i
$431$	11.9105	+	20.6296i	0.573709	+	0.993692i	0.996181	+	0.0873164i	$0.0278291\pi$
$431$	11.9105	+	20.6296i	0.573709	+	0.993692i	−0.422472	+	0.906376i	$0.638838\pi$
$432$	3.40328	+	0.520408i	0.163740	+	0.0250381i
$433$	32.7062			1.57176			0.785880	−	0.618379i	$-0.212210\pi$
$433$	32.7062			1.57176			0.785880	+	0.618379i	$0.212210\pi$
$434$	−17.0822	−	14.2859i	−0.819970	−	0.685744i
$435$	10.5330	−	12.7482i	0.505019	−	0.611230i
$436$	28.4909	−	23.9067i	1.36447	−	1.14492i
$437$	−3.71929	−	1.35371i	−0.177918	−	0.0647567i
$438$	0.133772	−	0.0246370i	0.00639186	−	0.00117720i
$439$	−4.25105	+	24.1089i	−0.202891	+	1.15065i	0.697832	+	0.716261i	$0.254148\pi$
$439$	−4.25105	+	24.1089i	−0.202891	+	1.15065i	−0.900724	+	0.434393i	$0.856963\pi$
$440$	1.90201	−	3.29437i	0.0906747	−	0.157053i
$441$	−3.26380	+	20.7448i	−0.155419	+	0.987849i
$442$	0.993347	+	1.72053i	0.0472487	+	0.0818372i
$443$	3.48136	−	1.26711i	0.165405	−	0.0602023i	−0.257991	−	0.966147i	$-0.583060\pi$
$443$	3.48136	−	1.26711i	0.165405	−	0.0602023i	0.423395	+	0.905945i	$0.360838\pi$
$444$	44.9886	+	25.5204i	2.13507	+	1.21114i
$445$	−14.1218	+	11.8496i	−0.669440	+	0.561727i
$446$	−22.1446	−	8.05998i	−1.04858	−	0.381651i
$447$	−17.5307	+	10.2998i	−0.829175	+	0.487162i
$448$	32.4202	−	11.8603i	1.53171	−	0.560348i
$449$	−4.45575	−	7.71759i	−0.210280	−	0.364215i	0.741522	−	0.670928i	$-0.234104\pi$
$449$	−4.45575	−	7.71759i	−0.210280	−	0.364215i	−0.951802	+	0.306713i	$0.900771\pi$
$450$	2.56542	−	15.9641i	0.120935	−	0.752557i
$451$	10.7281			0.505168
$452$	−39.9184	−	33.4955i	−1.87760	−	1.57550i
$453$	0.245567	+	0.288180i	0.0115377	+	0.0135399i
$454$	−5.99113	+	5.02716i	−0.281178	+	0.235936i
$455$	−0.140200	−	0.787546i	−0.00657267	−	0.0369207i
$456$	−1.35807	+	1.64369i	−0.0635976	+	0.0769729i
$457$	5.55040	+	4.65734i	0.259637	+	0.217861i	0.763309	−	0.646034i	$-0.223574\pi$
$457$	5.55040	+	4.65734i	0.259637	+	0.217861i	−0.503672	+	0.863895i	$0.668018\pi$
$458$	22.0275	+	38.1528i	1.02928	+	1.78276i
$459$	−20.9024	+	12.7119i	−0.975639	+	0.593339i
$460$	−19.5393	+	33.8431i	−0.911025	+	1.57794i
$461$	−0.937013	+	5.31406i	−0.0436410	+	0.247501i	−0.998822	−	0.0485214i	$-0.984549\pi$
$461$	−0.937013	+	5.31406i	−0.0436410	+	0.247501i	0.955181	+	0.296022i	$0.0956602\pi$
$462$	−9.83191	−	1.64010i	−0.457422	−	0.0763045i
$463$	−4.18639	−	1.52372i	−0.194558	−	0.0708133i	0.242904	−	0.970050i	$-0.421900\pi$
$463$	−4.18639	−	1.52372i	−0.194558	−	0.0708133i	−0.437461	+	0.899237i	$0.644122\pi$
$464$	0.680026	+	3.85662i	0.0315694	+	0.179039i
$465$	−3.49785	+	9.84230i	−0.162209	+	0.456426i
$466$	0.0263146	+	0.0220806i	0.00121900	+	0.00102286i
$467$	14.3395	+	24.8368i	0.663554	+	1.14931i	0.979675	+	0.200591i	$0.0642862\pi$
$467$	14.3395	+	24.8368i	0.663554	+	1.14931i	−0.316121	+	0.948719i	$0.602381\pi$
$468$	−0.888147	−	1.48571i	−0.0410546	−	0.0686770i
$469$	4.23034	+	7.29945i	0.195339	+	0.337057i
$470$	−4.21908	−	3.54023i	−0.194612	−	0.163299i
$471$	−32.3838	+	19.0263i	−1.49217	+	0.876686i
$472$	−1.30071	+	1.09143i	−0.0598701	+	0.0502370i
$473$	6.37164	−	5.34644i	0.292968	−	0.245830i
$474$	−28.3972	−	16.1087i	−1.30433	−	0.739897i
$475$	−0.923624	−	0.775012i	−0.0423788	−	0.0355600i
$476$	−19.1450	+	33.2863i	−0.877510	+	1.52567i
$477$	6.28708	−	5.44041i	0.287866	−	0.249099i
$478$	−12.6562	−	21.9212i	−0.578882	−	1.00265i
$479$	−8.59520	−	7.21223i	−0.392725	−	0.329535i	0.424949	−	0.905217i	$-0.360292\pi$
$479$	−8.59520	−	7.21223i	−0.392725	−	0.329535i	−0.817674	+	0.575682i	$0.804737\pi$
$480$	−11.5692	−	13.5767i	−0.528057	−	0.619690i
$481$	0.314851	+	1.78561i	0.0143560	+	0.0814167i
$482$	63.9764	+	23.2855i	2.91404	+	1.06062i
$483$	35.4730	+	5.91741i	1.61408	+	0.269251i
$484$	−5.38997	+	30.5680i	−0.244999	+	1.38946i
$485$	8.15246	−	14.1205i	0.370184	−	0.641178i
$486$	29.7460	−	18.7152i	1.34931	−	0.848938i
$487$	−13.8374	−	23.9671i	−0.627033	−	1.08605i	−0.988144	−	0.153530i	$-0.950936\pi$
$487$	−13.8374	−	23.9671i	−0.627033	−	1.08605i	0.361111	−	0.932523i	$-0.382398\pi$
$488$	−16.6210	−	13.9467i	−0.752396	−	0.631335i
$489$	5.55243	+	14.9019i	0.251089	+	0.673887i
$490$	19.4743	−	16.4502i	0.879760	−	0.743145i
$491$	23.0453	−	19.3373i	1.04002	−	0.872682i	0.0480122	−	0.998847i	$-0.484711\pi$
$491$	23.0453	−	19.3373i	1.04002	−	0.872682i	0.992009	+	0.126165i	$0.0402669\pi$
$492$	−19.8812	+	55.9420i	−0.896313	+	2.52206i
$493$	−21.3170	−	17.8871i	−0.960068	−	0.805592i
$494$	−0.212817			−0.00957509
$495$	0.881772	+	4.59163i	0.0396327	+	0.206378i
$496$	−1.23681	−	2.14221i	−0.0555342	−	0.0961880i
$497$	−7.15284	+	2.61673i	−0.320849	+	0.117376i
$498$	0.408254	+	53.7297i	0.0182943	+	2.40769i
$499$	11.9400	+	4.34579i	0.534507	+	0.194544i	0.595149	−	0.803615i	$-0.297093\pi$
$499$	11.9400	+	4.34579i	0.534507	+	0.194544i	−0.0606429	+	0.998160i	$0.519315\pi$
$500$	−28.1921	+	23.6560i	−1.26079	+	1.05793i
$501$	0.112785	+	14.8435i	0.00503887	+	0.663158i
$502$	16.7627	−	6.10113i	0.748156	−	0.272307i
$503$	5.27617	+	9.13860i	0.235253	+	0.407470i	0.959346	−	0.282232i	$-0.0910748\pi$
$503$	5.27617	+	9.13860i	0.235253	+	0.407470i	−0.724093	+	0.689702i	$0.757741\pi$
$504$	9.40276	−	16.9385i	0.418832	−	0.754499i
$505$	1.66703	−	2.88738i	0.0741817	−	0.128487i
$506$	−2.96420	+	16.8108i	−0.131775	+	0.747331i
$507$	−7.51984	+	21.1595i	−0.333968	+	0.939725i
$508$	−18.8385	−	6.85666i	−0.835824	−	0.304215i
$509$	3.36943	−	2.82729i	0.149348	−	0.125317i	−0.565053	−	0.825055i	$-0.691144\pi$
$509$	3.36943	−	2.82729i	0.149348	−	0.125317i	0.714400	+	0.699737i	$0.246700\pi$
$510$	29.2848	+	4.93458i	1.29675	+	0.218507i
$511$	−0.0158546	+	0.0907878i	−0.000701367	+	0.00401622i
$512$	7.45857			0.329625
$513$	−0.0597309	−	2.61996i	−0.00263718	−	0.115674i
$514$	−0.678447	−	1.17511i	−0.0299250	−	0.0518317i
$515$	26.9049	−	9.79259i	1.18557	−	0.431513i
$516$	16.0713	+	43.1330i	0.707499	+	1.89882i
$517$	−1.37114	−	0.499054i	−0.0603026	−	0.0219484i
$518$	−44.2026	+	37.2142i	−1.94215	+	1.63510i
$519$	11.3483	−	31.9319i	0.498133	−	1.40166i
$520$	−0.128146	+	0.726752i	−0.00561957	+	0.0318702i
$521$	−22.3191			−0.977819			−0.488909	−	0.872335i	$-0.662605\pi$
$521$	−22.3191			−0.977819			−0.488909	+	0.872335i	$0.662605\pi$
$522$	31.0095	+	25.2271i	1.35725	+	1.10416i
$523$	18.1646			0.794283			0.397142	−	0.917757i	$-0.370002\pi$
$523$	18.1646			0.794283			0.397142	+	0.917757i	$0.370002\pi$
$524$	5.33190	+	4.47400i	0.232925	+	0.195447i
$525$	9.53780	+	5.38976i	0.416264	+	0.235228i
$526$	−0.203626	−	1.15482i	−0.00887853	−	0.0503527i
$527$	16.5171	+	6.01173i	0.719495	+	0.261875i
$528$	−0.963069	−	0.546314i	−0.0419122	−	0.0237752i
$529$	6.70076	−	38.0019i	0.291337	−	1.65226i
$530$	−10.0927			−0.438401
$531$	0.331125	−	2.06053i	0.0143696	−	0.0894195i
$532$	−2.06254	−	3.55891i	−0.0894223	−	0.154298i
$533$	−1.95570	+	0.711816i	−0.0847107	+	0.0308322i
$534$	−28.9033	−	33.9188i	−1.25077	−	1.46781i
$535$	−25.6348	−	9.33030i	−1.10829	−	0.403384i
$536$	−1.35153	−	7.66491i	−0.0583772	−	0.331074i
$537$	−3.53918	−	9.49864i	−0.152727	−	0.409897i
$538$	0.0598168	−	0.339238i	0.00257888	−	0.0146256i
$539$	3.35761	−	5.85993i	0.144623	−	0.252405i
$540$	−25.5772	−	3.91111i	−1.10067	−	0.168307i
$541$	−14.1984	+	24.5924i	−0.610438	+	1.05731i	0.380729	+	0.924687i	$0.375673\pi$
$541$	−14.1984	+	24.5924i	−0.610438	+	1.05731i	−0.991167	+	0.132623i	$0.957660\pi$
$542$	−42.0926	+	15.3204i	−1.80803	+	0.658069i
$543$	−0.400835	−	1.07578i	−0.0172015	−	0.0461662i
$544$	−22.9937	+	19.2940i	−0.985847	+	0.827224i
$545$	14.9296	−	12.5274i	0.639514	−	0.536616i
$546$	1.90114	−	0.353367i	0.0813614	−	0.0151227i
$547$	12.9097	−	4.69873i	0.551977	−	0.200903i	−0.0509474	−	0.998701i	$-0.516224\pi$
$547$	12.9097	−	4.69873i	0.551977	−	0.200903i	0.602925	+	0.797798i	$0.294002\pi$
$548$	−16.4862	−	28.5549i	−0.704255	−	1.21981i
$549$	26.6650	−	0.405240i	1.13803	−	0.0172952i
$550$	−2.60000	+	4.50334i	−0.110864	+	0.192023i
$551$	2.80112	−	1.01953i	0.119332	−	0.0434333i
$552$	−28.8577	−	16.3699i	−1.22826	−	0.696749i
$553$	16.9221	−	14.2468i	0.719601	−	0.605834i
$554$	−2.14596	−	12.1704i	−0.0911732	−	0.517069i
$555$	23.5746	+	13.3730i	1.00069	+	0.567653i
$556$	−2.93147	+	16.6252i	−0.124322	+	0.705065i
$557$	−5.29404	+	9.16954i	−0.224316	+	0.388526i	−0.956114	−	0.292995i	$-0.905348\pi$
$557$	−5.29404	+	9.16954i	−0.224316	+	0.388526i	0.731798	+	0.681521i	$0.238681\pi$
$558$	−23.8558	−	8.27450i	−1.00990	−	0.350287i
$559$	−0.806788	+	1.39740i	−0.0341235	+	0.0591037i
$560$	2.65935	−	0.972873i	0.112378	−	0.0411114i
$561$	7.73768	−	1.42506i	0.326685	−	0.0601663i
$562$	7.64127	+	43.3358i	0.322328	+	1.82801i
$563$	2.62933	+	14.9116i	0.110813	+	0.628451i	0.988738	+	0.149654i	$0.0478159\pi$
$563$	2.62933	+	14.9116i	0.110813	+	0.628451i	−0.877926	+	0.478797i	$0.841073\pi$
$564$	5.14330	−	6.22499i	0.216572	−	0.262119i
$565$	−20.9178	−	17.5521i	−0.880018	−	0.738423i
$566$	−50.9648			−2.14221
$567$	4.88384	+	23.3055i	0.205102	+	0.978741i
$568$	7.02646			0.294824
$569$	−17.2162	−	14.4461i	−0.721742	−	0.605613i	0.206125	−	0.978526i	$-0.433915\pi$
$569$	−17.2162	−	14.4461i	−0.721742	−	0.605613i	−0.927867	+	0.372912i	$0.878359\pi$
$570$	−2.02629	+	2.45244i	−0.0848720	+	0.102722i
$571$	−1.65271	−	9.37297i	−0.0691636	−	0.392247i	−0.999663	−	0.0259534i	$-0.991738\pi$
$571$	−1.65271	−	9.37297i	−0.0691636	−	0.392247i	0.930500	−	0.366293i	$-0.119373\pi$
$572$	0.0966659	+	0.548219i	0.00404180	+	0.0229222i
$573$	−15.0307	+	2.76824i	−0.627918	+	0.115645i
$574$	−50.8776	−	42.5491i	−2.12359	−	1.77597i
$575$	9.38068	−	16.2478i	0.391201	−	0.677580i
$576$	29.6001	−	25.6139i	1.23334	−	1.06725i
$577$	21.1508	−	36.6343i	0.880521	−	1.52511i	0.0297588	−	0.999557i	$-0.490526\pi$
$577$	21.1508	−	36.6343i	0.880521	−	1.52511i	0.850762	−	0.525550i	$-0.176141\pi$
$578$	2.02268	−	11.4712i	0.0841324	−	0.477139i
$579$	−12.9702	−	7.35751i	−0.539022	−	0.305768i
$580$	−5.11071	−	28.9843i	−0.212211	−	1.20351i
$581$	−34.2307	−	12.3953i	−1.42013	−	0.514244i
$582$	34.2829	+	19.4474i	1.42107	+	0.806122i
$583$	−2.51262	+	0.914518i	−0.104062	+	0.0378755i
$584$	0.0425113	−	0.0736318i	0.00175913	−	0.00304690i
$585$	−0.465401	−	0.778532i	−0.0192420	−	0.0321883i
$586$	−13.1476	−	22.7723i	−0.543121	−	0.940713i
$587$	12.4550	−	4.53327i	0.514075	−	0.187108i	−0.0719389	−	0.997409i	$-0.522919\pi$
$587$	12.4550	−	4.53327i	0.514075	−	0.187108i	0.586014	+	0.810301i	$0.300696\pi$
$588$	24.3344	+	28.3679i	1.00354	+	1.16987i
$589$	−1.44237	+	1.21029i	−0.0594318	+	0.0498692i
$590$	−1.94071	+	1.62845i	−0.0798976	+	0.0670421i
$591$	−10.2808	−	27.5923i	−0.422898	−	1.13499i
$592$	−6.03141	+	2.19525i	−0.247889	+	0.0902244i
$593$	22.2156	−	38.4786i	0.912287	−	1.58013i	0.101460	−	0.994840i	$-0.467649\pi$
$593$	22.2156	−	38.4786i	0.912287	−	1.58013i	0.810826	−	0.585287i	$-0.199018\pi$
$594$	−11.0831	+	2.21582i	−0.454743	+	0.0909164i
$595$	−10.0322	+	17.4424i	−0.411282	+	0.715071i
$596$	−6.28384	+	35.6374i	−0.257396	+	1.45977i
$597$	−13.8596	−	37.1971i	−0.567235	−	1.52238i
$598$	−0.575042	−	3.26122i	−0.0235152	−	0.133361i
$599$	−36.6885	−	13.3535i	−1.49905	−	0.545609i	−0.543235	−	0.839581i	$-0.682801\pi$
$599$	−36.6885	−	13.3535i	−1.49905	−	0.545609i	−0.955814	+	0.293971i	$0.905023\pi$
$600$	−6.55509	−	7.69259i	−0.267610	−	0.314049i
$601$	28.8690	−	10.5074i	1.17759	−	0.428608i	0.322240	−	0.946658i	$-0.395564\pi$
$601$	28.8690	−	10.5074i	1.17759	−	0.428608i	0.855350	+	0.518050i	$0.173342\pi$
$602$	−51.4218	+	0.0844602i	−2.09580	+	0.00344234i
$603$	7.42081	+	6.03704i	0.302199	+	0.245847i
$604$	0.673851			0.0274186
$605$	−2.82442	+	16.0181i	−0.114829	+	0.651227i
$606$	7.01021	+	3.97664i	0.284770	+	0.161540i
$607$	6.95959	+	2.53308i	0.282481	+	0.102815i	0.479375	−	0.877610i	$-0.340863\pi$
$607$	6.95959	+	2.53308i	0.282481	+	0.102815i	−0.196894	+	0.980425i	$0.563086\pi$
$608$	−0.558342	−	3.16652i	−0.0226438	−	0.128419i
$609$	−23.3303	+	13.7587i	−0.945390	+	0.557532i
$610$	−24.7991	−	20.8089i	−1.00408	−	0.842527i
$611$	0.283066			0.0114516
$612$	−6.90831	+	42.9892i	−0.279252	+	1.73773i
$613$	−23.8910			−0.964949			−0.482475	−	0.875910i	$-0.660262\pi$
$613$	−23.8910			−0.964949			−0.482475	+	0.875910i	$0.660262\pi$
$614$	3.59192	−	20.3708i	0.144958	−	0.822099i
$615$	−10.4180	+	29.3144i	−0.420094	+	1.18207i
$616$	−4.76628	+	4.01274i	−0.192039	+	0.161678i
$617$	12.6845	+	4.61680i	0.510661	+	0.185865i	0.584483	−	0.811406i	$-0.301297\pi$
$617$	12.6845	+	4.61680i	0.510661	+	0.185865i	−0.0738220	+	0.997271i	$0.523520\pi$
$618$	24.1656	+	64.8568i	0.972083	+	2.60892i
$619$	−25.7365	+	9.36731i	−1.03444	+	0.376504i	−0.802768	−	0.596291i	$-0.796640\pi$
$619$	−25.7365	+	9.36731i	−1.03444	+	0.376504i	−0.231668	+	0.972795i	$0.574418\pi$
$620$	9.29517	+	16.0997i	0.373303	+	0.646580i
$621$	39.9871	−	7.99458i	1.60463	−	0.320811i
$622$	−16.2936			−0.653314
$623$	28.3560	−	10.3735i	1.13606	−	0.415607i
$624$	0.211812	+	0.0356910i	0.00847927	+	0.00142878i
$625$	−5.61631	+	4.71264i	−0.224652	+	0.188506i
$626$	9.77485	+	3.55776i	0.390682	+	0.142197i
$627$	−0.282232	+	0.794149i	−0.0112713	+	0.0317153i
$628$	−11.6079	+	65.8315i	−0.463204	+	2.62696i
$629$	22.8044	−	39.4984i	0.909272	−	1.57491i
$630$	14.0292	−	25.2728i	0.558938	−	1.00689i
$631$	14.5897	+	25.2701i	0.580808	+	1.00599i	0.995384	+	0.0959739i	$0.0305965\pi$
$631$	14.5897	+	25.2701i	0.580808	+	1.00599i	−0.414576	+	0.910015i	$0.636070\pi$
$632$	−19.1765	+	6.97968i	−0.762801	+	0.277637i
$633$	0.207639	+	27.3270i	0.00825289	+	1.08615i
$634$	18.2103	−	15.2802i	0.723222	−	0.606855i
$635$	−9.87163	−	3.59298i	−0.391744	−	0.142583i
$636$	−0.112431	−	14.7969i	−0.00445818	−	0.586734i
$637$	−0.223272	+	1.29102i	−0.00884636	+	0.0511522i
$638$	−6.42805	−	11.1337i	−0.254489	−	0.440788i
$639$	−6.53063	+	5.65116i	−0.258348	+	0.223557i
$640$	−26.9206			−1.06413
$641$	35.0076	+	29.3748i	1.38272	+	1.16024i	0.968195	+	0.250197i	$0.0804952\pi$
$641$	35.0076	+	29.3748i	1.38272	+	1.16024i	0.414521	+	0.910040i	$0.363949\pi$
$642$	22.0831	−	62.1378i	0.871550	−	2.45238i
$643$	−1.84788	+	1.55055i	−0.0728732	+	0.0611479i	−0.678497	−	0.734603i	$-0.737368\pi$
$643$	−1.84788	+	1.55055i	−0.0728732	+	0.0611479i	0.605623	+	0.795751i	$0.292924\pi$
$644$	48.9639	−	41.2228i	1.92945	−	1.62441i
$645$	8.42157	+	22.6022i	0.331599	+	0.889963i
$646$	4.10086	+	3.44103i	0.161346	+	0.135386i
$647$	−10.6983	−	18.5300i	−0.420594	−	0.728491i	0.575403	−	0.817870i	$-0.304845\pi$
$647$	−10.6983	−	18.5300i	−0.420594	−	0.728491i	−0.995998	+	0.0893790i	$0.971512\pi$
$648$	3.15541	−	21.7394i	0.123956	−	0.854005i
$649$	−0.335589	+	0.581257i	−0.0131730	+	0.0228163i
$650$	0.175173	−	0.993454i	0.00687084	−	0.0389665i
$651$	10.8754	−	13.2068i	0.426242	−	0.517614i
$652$	26.5962	+	9.68023i	1.04159	+	0.379107i
$653$	7.30141	+	41.4084i	0.285726	+	1.62043i	0.702680	+	0.711506i	$0.251987\pi$
$653$	7.30141	+	41.4084i	0.285726	+	1.62043i	−0.416953	+	0.908928i	$0.636902\pi$
$654$	30.5565	+	35.8589i	1.19485	+	1.40220i
$655$	2.79399	+	2.34443i	0.109170	+	0.0916046i
$656$	−3.68371	−	6.38037i	−0.143825	−	0.249111i
$657$	0.0197083	+	0.102626i	0.000768893	+	0.00400384i
$658$	4.52324	+	7.80485i	0.176334	+	0.304265i
$659$	18.8582	+	15.8239i	0.734612	+	0.616413i	0.931385	−	0.364036i	$-0.118602\pi$
$659$	18.8582	+	15.8239i	0.734612	+	0.616413i	−0.196772	+	0.980449i	$0.563046\pi$
$660$	7.23791	+	4.10580i	0.281735	+	0.159818i
$661$	14.9627	−	12.5552i	0.581982	−	0.488341i	−0.303615	−	0.952795i	$-0.598194\pi$
$661$	14.9627	−	12.5552i	0.581982	−	0.488341i	0.885597	+	0.464454i	$0.153749\pi$
$662$	43.3651	−	36.3877i	1.68543	−	1.41425i
$663$	−1.31600	+	0.773183i	−0.0511091	+	0.0300279i
$664$	25.7281	+	21.5885i	0.998445	+	0.837795i
$665$	−1.08080	−	1.86491i	−0.0419115	−	0.0723183i
$666$	−31.8933	+	57.2321i	−1.23584	+	2.21770i
$667$	23.1921	+	40.1698i	0.898001	+	1.55538i
$668$	20.2379	+	16.9816i	0.783028	+	0.657039i
$669$	6.06282	−	17.0597i	0.234402	−	0.659565i
$670$	−2.01653	−	11.4363i	−0.0779054	−	0.441823i
$671$	−8.05933	−	2.93336i	−0.311127	−	0.113241i
$672$	10.2456	+	27.3601i	0.395232	+	1.05544i
$673$	−3.20923	+	18.2004i	−0.123707	+	0.701575i	0.858361	+	0.513046i	$0.171483\pi$
$673$	−3.20923	+	18.2004i	−0.123707	+	0.701575i	−0.982068	+	0.188529i	$0.939628\pi$
$674$	−12.2048	+	21.1393i	−0.470111	+	0.814256i
$675$	12.2794	+	1.87770i	0.472636	+	0.0722726i
$676$	19.9832	+	34.6120i	0.768585	+	1.33123i
$677$	5.23642	+	4.39387i	0.201252	+	0.168870i	0.737844	−	0.674972i	$-0.235844\pi$
$677$	5.23642	+	4.39387i	0.201252	+	0.168870i	−0.536592	+	0.843842i	$0.680289\pi$
$678$	42.0441	−	50.8865i	1.61470	−	1.95428i
$679$	−20.4294	+	17.1996i	−0.784009	+	0.660059i
$680$	14.2201	−	11.9321i	0.545317	−	0.457575i
$681$	−3.89709	−	4.57335i	−0.149337	−	0.175251i
$682$	6.22070	+	5.21979i	0.238203	+	0.199876i
$683$	−16.3455			−0.625442			−0.312721	−	0.949845i	$-0.601241\pi$
$683$	−16.3455			−0.625442			−0.312721	+	0.949845i	$0.601241\pi$
$684$	−3.61808	−	2.94341i	−0.138341	−	0.112544i
$685$	−8.63898	−	14.9631i	−0.330078	−	0.571713i
$686$	−39.1645	+	14.4737i	−1.49531	+	0.552607i
$687$	−29.1823	+	17.1454i	−1.11338	+	0.654137i
$688$	−5.36753	−	1.95362i	−0.204635	−	0.0744810i
$689$	0.397363	−	0.333427i	0.0151383	−	0.0127026i
$690$	−43.0566	−	24.4244i	−1.63914	−	0.929822i
$691$	25.3958	−	9.24331i	0.966101	−	0.351632i	0.189680	−	0.981846i	$-0.439255\pi$
$691$	25.3958	−	9.24331i	0.966101	−	0.351632i	0.776422	+	0.630214i	$0.217033\pi$
$692$	−30.1568	−	52.2332i	−1.14639	−	1.98561i
$693$	1.20262	−	7.56295i	0.0456837	−	0.287293i
$694$	1.88941	−	3.27256i	0.0717212	−	0.124225i
$695$	−1.53613	+	8.71181i	−0.0582687	+	0.330458i
$696$	24.5737	−	4.52579i	0.931465	−	0.171550i
$697$	49.1945	+	17.9053i	1.86338	+	0.678213i
$698$	15.9565	−	13.3891i	0.603961	−	0.506783i
$699$	−0.0168098	+	0.0203451i	−0.000635806	+	0.000769523i
$700$	18.3111	−	6.69877i	0.692094	−	0.253190i
$701$	−10.3899			−0.392422			−0.196211	−	0.980562i	$-0.562864\pi$
$701$	−10.3899			−0.392422			−0.196211	+	0.980562i	$0.562864\pi$
$702$	1.87338	−	1.13930i	0.0707062	−	0.0430002i
$703$	2.44284	+	4.23112i	0.0921333	+	0.159580i
$704$	−11.8296	+	4.30563i	−0.445845	+	0.162274i
$705$	2.69516	−	3.26198i	0.101505	−	0.122853i
$706$	−35.3488	−	12.8659i	−1.33037	−	0.484215i
$707$	−4.17743	+	3.51699i	−0.157109	+	0.132270i
$708$	−2.40907	−	2.82711i	−0.0905383	−	0.106249i
$709$	0.451203	−	2.55890i	0.0169453	−	0.0961014i	−0.975162	−	0.221492i	$-0.928907\pi$
$709$	0.451203	−	2.55890i	0.0169453	−	0.0961014i	0.992107	+	0.125391i	$0.0400184\pi$
$710$	10.4837			0.393447
$711$	12.2098	−	21.9102i	0.457902	−	0.821698i
$712$	−27.8550			−1.04391
$713$	−22.4440	−	18.8327i	−0.840533	−	0.705291i
$714$	−42.3475	−	23.9304i	−1.58482	−	0.895571i
$715$	0.0506542	+	0.287274i	0.00189436	+	0.0107434i
$716$	−16.9528	−	6.17030i	−0.633554	−	0.230595i
$717$	16.7671	−	9.85111i	0.626179	−	0.367896i
$718$	−2.68276	+	15.2147i	−0.100120	+	0.567807i
$719$	−5.64974			−0.210700			−0.105350	−	0.994435i	$-0.533596\pi$
$719$	−5.64974			−0.210700			−0.105350	+	0.994435i	$0.533596\pi$
$720$	2.42802	−	2.10104i	0.0904869	−	0.0783012i
$721$	−46.8952	+	0.0770251i	−1.74647	+	0.00286857i
$722$	39.7129	−	14.4543i	1.47796	−	0.537933i
$723$	−17.5156	+	49.2858i	−0.651414	+	1.83296i
$724$	−1.92001	−	0.698825i	−0.0713565	−	0.0259716i
$725$	2.45362	+	13.9152i	0.0911250	+	0.516796i
$726$	−38.7720	−	6.53320i	−1.43896	−	0.242470i
$727$	0.0852680	−	0.483579i	0.00316241	−	0.0179349i	−0.983186	−	0.182608i	$-0.941546\pi$
$727$	0.0852680	−	0.483579i	0.00316241	−	0.0179349i	0.986348	+	0.164674i	$0.0526570\pi$
$728$	0.602628	−	1.04775i	0.0223349	−	0.0388323i
$729$	14.5516	+	22.7432i	0.538948	+	0.842339i
$730$	0.0634283	−	0.109861i	0.00234759	−	0.00406614i
$731$	38.1408	−	13.8821i	1.41069	−	0.513449i
$732$	30.2314	−	36.5895i	1.11739	−	1.35239i
$733$	−19.1922	+	16.1041i	−0.708878	+	0.594819i	−0.924284	−	0.381705i	$-0.875337\pi$
$733$	−19.1922	+	16.1041i	−0.708878	+	0.594819i	0.215406	+	0.976525i	$0.430893\pi$
$734$	−12.4097	+	10.4130i	−0.458050	+	0.384350i
$735$	12.7516	+	14.8651i	0.470349	+	0.548309i
$736$	47.0153	−	17.1122i	1.73301	−	0.630763i
$737$	−1.53828	−	2.66438i	−0.0566634	−	0.0981439i
$738$	−71.0523	−	24.6448i	−2.61547	−	0.907187i
$739$	4.91874	−	8.51950i	0.180939	−	0.313395i	−0.761262	−	0.648445i	$-0.775420\pi$
$739$	4.91874	−	8.51950i	0.180939	−	0.313395i	0.942200	+	0.335050i	$0.108753\pi$
$740$	45.3289	−	16.4984i	1.66632	−	0.606492i
$741$	−0.00124230	−	0.163497i	−4.56369e−5	−	0.00600620i
$742$	15.5431	+	5.62832i	0.570604	+	0.206622i
$743$	−1.59945	−	9.07091i	−0.0586780	−	0.332779i	0.941311	−	0.337541i	$-0.109595\pi$
$743$	−1.59945	−	9.07091i	−0.0586780	−	0.332779i	−0.999989	+	0.00476202i	$0.998484\pi$
$744$	−13.6081	+	7.99514i	−0.498899	+	0.293116i
$745$	−3.29282	+	18.6745i	−0.120639	+	0.684180i
$746$	33.0296	−	57.2089i	1.20930	−	2.09457i
$747$	−41.2755	+	0.627283i	−1.51019	+	0.0229511i
$748$	7.00144	−	12.1269i	0.255998	−	0.443402i
$749$	34.2750	+	28.6644i	1.25238	+	1.04737i
$750$	−30.2360	−	35.4828i	−1.10406	−	1.29565i
$751$	−6.94306	−	39.3761i	−0.253356	−	1.43685i	−0.800258	−	0.599656i	$-0.795304\pi$
$751$	−6.94306	−	39.3761i	−0.253356	−	1.43685i	0.546902	−	0.837197i	$-0.315807\pi$
$752$	0.174003	+	0.986820i	0.00634524	+	0.0359856i
$753$	4.78505	+	12.8424i	0.174377	+	0.468001i
$754$	1.91054	+	1.60313i	0.0695777	+	0.0583826i
$755$	0.353107			0.0128509
$756$	37.2085	+	20.2866i	1.35326	+	0.737816i
$757$	28.8482			1.04850			0.524252	−	0.851563i	$-0.324345\pi$
$757$	28.8482			1.04850			0.524252	+	0.851563i	$0.324345\pi$
$758$	0.575843	+	0.483190i	0.0209156	+	0.0175502i
$759$	−12.9322	−	2.17912i	−0.469410	−	0.0790969i
$760$	0.345299	+	1.95829i	0.0125253	+	0.0710345i
$761$	3.22695	+	18.3010i	0.116977	+	0.663410i	0.985752	+	0.168203i	$0.0537965\pi$
$761$	3.22695	+	18.3010i	0.116977	+	0.663410i	−0.868775	+	0.495206i	$0.835092\pi$
$762$	8.50392	−	23.9285i	0.308065	−	0.866838i
$763$	−29.9780	+	10.9669i	−1.08528	+	0.397028i
$764$	−13.6006	+	23.5569i	−0.492051	+	0.852258i
$765$	−3.62005	+	22.5269i	−0.130883	+	0.814462i
$766$	16.2379	−	28.1248i	0.586698	−	1.01619i
$767$	0.0226100	−	0.128228i	0.000816399	−	0.00463003i
$768$	−0.151027	−	19.8765i	−0.00544974	−	0.717231i
$769$	3.72729	+	21.1385i	0.134409	+	0.762274i	0.975269	+	0.221021i	$0.0709389\pi$
$769$	3.72729	+	21.1385i	0.134409	+	0.762274i	−0.840860	+	0.541253i	$0.817950\pi$
$770$	−7.11145	+	5.98715i	−0.256279	+	0.215762i
$771$	0.898815	−	0.528077i	0.0323700	−	0.0190182i
$772$	−24.9388	+	9.07700i	−0.897569	+	0.326688i
$773$	9.34650	−	16.1886i	0.336170	−	0.582264i	−0.647539	−	0.762033i	$-0.724202\pi$
$773$	9.34650	−	16.1886i	0.336170	−	0.582264i	0.983709	+	0.179769i	$0.0575349\pi$
$774$	−54.4813	+	20.7724i	−1.95829	+	0.746650i
$775$	−4.46255	−	7.72935i	−0.160299	−	0.277647i
$776$	23.1511	−	8.42630i	0.831075	−	0.302486i
$777$	−28.8479	−	33.7414i	−1.03491	−	1.21047i
$778$	39.4583	−	33.1094i	1.41465	−	1.18703i
$779$	−4.29596	+	3.60474i	−0.153919	+	0.129153i
$780$	−1.59187	−	0.268234i	−0.0569980	−	0.00960433i
$781$	2.60995	−	0.949945i	0.0933915	−	0.0339917i
$782$	−41.6499	+	72.1398i	−1.48940	+	2.57971i
$783$	−19.1997	+	23.9703i	−0.686141	+	0.856629i
$784$	−4.63799	+	0.0152358i	−0.165643	+	0.000544136i
$785$	−6.08268	+	34.4966i	−0.217100	+	1.23124i
$786$	−5.61583	+	6.79691i	−0.200310	+	0.242438i
$787$	1.37090	+	7.77474i	0.0488672	+	0.277140i	0.999444	−	0.0333508i	$-0.0106179\pi$
$787$	1.37090	+	7.77474i	0.0488672	+	0.277140i	−0.950577	+	0.310490i	$0.899507\pi$
$788$	−49.2454	−	17.9239i	−1.75430	−	0.638511i
$789$	0.886005	−	0.163177i	0.0315426	−	0.00580927i
$790$	−28.6120	+	10.4139i	−1.01797	+	0.370511i
$791$	22.4258	+	38.6957i	0.797369	+	1.37586i
$792$	−3.43900	+	6.17123i	−0.122200	+	0.219285i
$793$	1.66382			0.0590839
$794$	8.84835	−	50.1815i	0.314016	−	1.78087i
$795$	−0.0589153	−	7.75375i	−0.00208951	−	0.274997i
$796$	−66.3877	−	24.1631i	−2.35305	−	0.856440i
$797$	−0.0774178	−	0.439058i	−0.00274228	−	0.0155522i	0.983406	−	0.181419i	$-0.0580690\pi$
$797$	−0.0774178	−	0.439058i	−0.00274228	−	0.0155522i	−0.986148	+	0.165867i	$0.946958\pi$
$798$	4.48817	−	2.64684i	0.158879	−	0.0936971i
$799$	−5.45452	−	4.57689i	−0.192967	−	0.161919i
$800$	15.2412			0.538859
$801$	25.8894	−	22.4029i	0.914758	−	0.791569i
$802$	−29.7609			−1.05090
$803$	0.00583600	−	0.0330976i	0.000205948	−	0.00116799i
$804$	16.7442	−	3.08381i	0.590522	−	0.108758i
$805$	25.6577	−	21.6013i	0.904316	−	0.761346i
$806$	−1.48035	−	0.538802i	−0.0521430	−	0.0189785i
$807$	0.260969	+	0.0439740i	0.00918654	+	0.00154796i
$808$	4.73396	−	1.72302i	0.166540	−	0.0606157i
$809$	−23.7254	−	41.0936i	−0.834140	−	1.44477i	−0.894729	−	0.446610i	$-0.852631\pi$
$809$	−23.7254	−	41.0936i	−0.834140	−	1.44477i	0.0605883	−	0.998163i	$-0.480702\pi$
$810$	4.70798	−	32.4360i	0.165422	−	1.13968i
$811$	−16.8993			−0.593416			−0.296708	−	0.954968i	$-0.595889\pi$
$811$	−16.8993			−0.593416			−0.296708	+	0.954968i	$0.595889\pi$
$812$	−8.29276	+	47.4866i	−0.291019	+	1.66645i
$813$	−12.0157	−	32.2482i	−0.421407	−	1.13099i
$814$	16.1414	−	13.5442i	0.565756	−	0.474725i
$815$	13.9368	+	5.07257i	0.488184	+	0.177684i
$816$	−3.50441	−	4.11253i	−0.122679	−	0.143967i
$817$	−0.755005	+	4.28185i	−0.0264143	+	0.149803i
$818$	−3.01797	+	5.22728i	−0.105521	+	0.182767i
$819$	0.282572	+	1.45849i	0.00987387	+	0.0509639i
$820$	27.6848	+	47.9515i	0.966795	+	1.67454i
$821$	−15.1923	+	5.52955i	−0.530215	+	0.192983i	−0.593234	−	0.805030i	$-0.702149\pi$
$821$	−15.1923	+	5.52955i	−0.530215	+	0.192983i	0.0630192	+	0.998012i	$0.479927\pi$
$822$	36.0114	−	21.1577i	1.25604	−	0.737958i
$823$	17.7996	−	14.9356i	0.620454	−	0.520622i	−0.277492	−	0.960728i	$-0.589503\pi$
$823$	17.7996	−	14.9356i	0.620454	−	0.520622i	0.897946	+	0.440105i	$0.145059\pi$
$824$	40.6535	+	14.7967i	1.41623	+	0.515466i
$825$	−3.47487	−	1.97117i	−0.120979	−	0.0686272i
$826$	3.89685	−	1.42559i	0.135589	−	0.0496027i
$827$	−1.36430	−	2.36304i	−0.0474415	−	0.0821710i	0.841330	−	0.540523i	$-0.181773\pi$
$827$	−1.36430	−	2.36304i	−0.0474415	−	0.0821710i	−0.888771	+	0.458352i	$0.848440\pi$
$828$	35.3288	−	63.3969i	1.22776	−	2.20320i
$829$	12.0255			0.417663			0.208831	−	0.977952i	$-0.433034\pi$
$829$	12.0255			0.417663			0.208831	+	0.977952i	$0.433034\pi$
$830$	38.3872	+	32.2107i	1.33244	+	1.11805i
$831$	9.33736	−	1.71968i	0.323910	−	0.0596551i
$832$	1.87082	−	1.56980i	0.0648589	−	0.0544231i
$833$	25.1768	−	21.2672i	0.872326	−	0.736865i
$834$	−21.0871	−	3.55324i	−0.730187	−	0.123039i
$835$	10.6049	+	8.89860i	0.366999	+	0.307949i
$836$	0.750003	+	1.29904i	0.0259394	+	0.0449283i
$837$	6.21763	−	18.3756i	0.214913	−	0.635153i
$838$	32.0862	−	55.5750i	1.10840	−	1.91981i
$839$	−7.27989	+	41.2863i	−0.251330	+	1.42536i	0.553991	+	0.832522i	$0.313104\pi$
$839$	−7.27989	+	41.2863i	−0.251330	+	1.42536i	−0.805321	+	0.592839i	$0.798007\pi$
$840$	−6.33622	−	16.9205i	−0.218621	−	0.583812i
$841$	−5.57566	−	2.02937i	−0.192264	−	0.0699784i
$842$	−9.56662	−	54.2550i	−0.329687	−	1.86975i
$843$	−33.2482	+	6.12338i	−1.14513	+	0.210901i
$844$	37.2582	+	31.2633i	1.28248	+	1.07613i
$845$	10.4715	+	18.1371i	0.360230	+	0.623936i
$846$	7.93461	+	6.45503i	0.272798	+	0.221928i
$847$	13.2823	−	23.0931i	0.456385	−	0.793490i
$848$	1.40665	+	1.18032i	0.0483045	+	0.0405323i
$849$	−0.297502	−	39.1538i	−0.0102102	−	1.34375i
$850$	−19.4386	+	16.3109i	−0.666738	+	0.559460i
$851$	−58.2373	+	48.8669i	−1.99635	+	1.67514i
$852$	0.116786	+	15.3701i	0.00400103	+	0.526570i
$853$	14.2353	+	11.9448i	0.487406	+	0.408982i	0.853096	−	0.521754i	$-0.174722\pi$
$853$	14.2353	+	11.9448i	0.487406	+	0.408982i	−0.365689	+	0.930737i	$0.619167\pi$
$854$	26.5869	+	45.8756i	0.909784	+	1.56983i
$855$	−1.89592	−	1.54238i	−0.0648391	−	0.0527484i
$856$	−20.6101	−	35.6977i	−0.704439	−	1.22012i
$857$	−44.7328	−	37.5353i	−1.52804	−	1.28218i	−0.810700	−	0.585462i	$-0.800913\pi$
$857$	−44.7328	−	37.5353i	−1.52804	−	1.28218i	−0.717344	−	0.696719i	$-0.754642\pi$
$858$	−0.693492	+	0.127722i	−0.0236754	+	0.00436035i
$859$	5.05090	+	28.6451i	0.172335	+	0.977358i	0.941176	+	0.337918i	$0.109723\pi$
$859$	5.05090	+	28.6451i	0.172335	+	0.977358i	−0.768841	+	0.639440i	$0.779166\pi$
$860$	40.3395	+	14.6824i	1.37556	+	0.500665i
$861$	32.3914	−	39.3351i	1.10390	−	1.34054i
$862$	−9.32557	+	52.8879i	−0.317630	+	1.80137i
$863$	1.95160	−	3.38027i	0.0664332	−	0.115066i	−0.830896	−	0.556428i	$-0.812171\pi$
$863$	1.95160	−	3.38027i	0.0664332	−	0.115066i	0.897329	+	0.441363i	$0.145505\pi$
$864$	21.8667	+	24.8851i	0.743921	+	0.846608i
$865$	−15.8026	−	27.3709i	−0.537304	−	0.930638i
$866$	56.4845	+	47.3961i	1.91942	+	1.61059i
$867$	8.82456	+	1.48696i	0.299698	+	0.0505000i
$868$	−5.33662	−	29.9775i	−0.181137	−	1.01750i
$869$	−6.17943	+	5.18516i	−0.209623	+	0.175894i
$870$	36.6648	−	6.75264i	1.24305	−	0.228936i
$871$	0.457207	+	0.383642i	0.0154919	+	0.0129992i
$872$	29.4483			0.997246
$873$	−14.7404	+	26.4514i	−0.498886	+	0.895243i
$874$	−4.46158	−	7.72769i	−0.150915	−	0.261393i
$875$	29.6636	−	10.8519i	1.00281	−	0.366860i
$876$	0.161773	+	0.0917678i	0.00546580	+	0.00310055i
$877$	−37.9686	−	13.8194i	−1.28211	−	0.466649i	−0.390978	−	0.920400i	$-0.627863\pi$
$877$	−37.9686	−	13.8194i	−1.28211	−	0.466649i	−0.891128	+	0.453751i	$0.850086\pi$
$878$	−42.2790	+	35.4763i	−1.42685	+	1.19727i
$879$	17.4181	−	10.2336i	0.587496	−	0.345169i
$880$	−0.970353	+	0.353180i	−0.0327106	+	0.0119057i
$881$	−2.36050	−	4.08851i	−0.0795274	−	0.137745i	0.823519	−	0.567289i	$-0.192008\pi$
$881$	−2.36050	−	4.08851i	−0.0795274	−	0.137745i	−0.903046	+	0.429544i	$0.858674\pi$
$882$	−35.6990	+	31.0971i	−1.20205	+	1.04709i
$883$	27.0064	−	46.7765i	0.908838	−	1.57415i	0.0931577	−	0.995651i	$-0.470304\pi$
$883$	27.0064	−	46.7765i	0.908838	−	1.57415i	0.815681	−	0.578503i	$-0.196363\pi$
$884$	−0.471716	+	2.67523i	−0.0158655	+	0.0899778i
$885$	−1.26238	−	1.48144i	−0.0424346	−	0.0497982i
$886$	7.84864	+	2.85667i	0.263680	+	0.0959718i
$887$	−27.7324	+	23.2703i	−0.931163	+	0.781339i	−0.976026	−	0.217654i	$-0.930159\pi$
$887$	−27.7324	+	23.2703i	−0.931163	+	0.781339i	0.0448626	+	0.998993i	$0.485715\pi$
$888$	14.2990	+	38.3763i	0.479842	+	1.28782i
$889$	13.1989	+	11.0383i	0.442677	+	0.370212i
$890$	−41.5607			−1.39312
$891$	−1.76701	−	8.50163i	−0.0591969	−	0.284815i
$892$	−16.1113	−	27.9056i	−0.539447	−	0.934350i
$893$	0.716744	−	0.260873i	0.0239849	−	0.00872979i
$894$	−45.2019	−	7.61666i	−1.51178	−	0.254739i
$895$	−8.88347	−	3.23332i	−0.296942	−	0.108078i
$896$	41.4583	+	15.0125i	1.38503	+	0.501533i
$897$	2.50208	−	0.460813i	0.0835421	−	0.0153861i
$898$	3.48872	−	19.7855i	0.116420	−	0.660251i
$899$	22.0657			0.735933
$900$	16.7183	−	14.4668i	0.557275	−	0.482228i
$901$	−13.0481			−0.434696
$902$	18.5278	+	15.5466i	0.616907	+	0.517646i
$903$	−0.365056	−	39.5044i	−0.0121483	−	1.31462i
$904$	−7.16470	−	40.6331i	−0.238295	−	1.35144i
$905$	−1.00611	−	0.366194i	−0.0334442	−	0.0121727i
$906$	0.00648558	+	0.853558i	0.000215469	+	0.0283575i
$907$	−8.72914	+	49.5054i	−0.289846	+	1.64380i	0.397595	+	0.917561i	$0.369845\pi$
$907$	−8.72914	+	49.5054i	−0.289846	+	1.64380i	−0.687442	+	0.726240i	$0.741266\pi$
$908$	−10.6938			−0.354888
$909$	−3.01413	+	5.40881i	−0.0999725	+	0.179399i
$910$	0.899142	−	1.56328i	0.0298063	−	0.0518223i
$911$	−10.2931	+	3.74638i	−0.341026	+	0.124123i	−0.506855	−	0.862031i	$-0.669192\pi$
$911$	−10.2931	+	3.74638i	−0.341026	+	0.124123i	0.165829	+	0.986154i	$0.446970\pi$
$912$	0.569216	−	0.104834i	0.0188486	−	0.00347139i
$913$	12.4753	+	4.54063i	0.412872	+	0.150273i
$914$	2.83652	+	16.0867i	0.0938237	+	0.532101i
$915$	15.8417	−	19.1734i	0.523710	−	0.633852i
$916$	−10.4603	+	59.3234i	−0.345619	+	1.96010i
$917$	−2.99541	−	5.16858i	−0.0989171	−	0.170681i
$918$	−54.5203	−	8.33691i	−1.79944	−	0.275159i
$919$	6.42767	−	11.1330i	0.212029	−	0.367245i	−0.740320	−	0.672254i	$-0.765326\pi$
$919$	6.42767	−	11.1330i	0.212029	−	0.367245i	0.952349	+	0.305009i	$0.0986595\pi$
$920$	−29.0759	+	10.5828i	−0.958605	+	0.348904i
$921$	15.6709	+	2.64058i	0.516372	+	0.0870102i
$922$	−9.31911	+	7.81966i	−0.306908	+	0.257527i
$923$	−0.412756	+	0.346343i	−0.0135860	+	0.0114000i
$924$	−8.85692	−	10.3593i	−0.291371	−	0.340797i
$925$	−21.7621	+	7.92075i	−0.715532	+	0.260433i
$926$	−5.02191	−	8.69820i	−0.165030	−	0.285841i
$927$	−49.6853	+	18.9438i	−1.63188	+	0.622197i
$928$	−18.8406	+	32.6329i	−0.618474	+	1.07123i
$929$	24.9085	−	9.06596i	0.817222	−	0.297445i	0.100618	−	0.994925i	$-0.467918\pi$
$929$	24.9085	−	9.06596i	0.817222	−	0.297445i	0.716604	+	0.697481i	$0.245696\pi$
$930$	−20.3038	+	11.9290i	−0.665789	+	0.391168i
$931$	0.624465	+	3.47473i	0.0204660	+	0.113880i
$932$	0.00815629	+	0.0462566i	0.000267168	+	0.00151519i
$933$	−0.0951122	−	12.5176i	−0.00311383	−	0.409807i
$934$	−11.2274	+	63.6739i	−0.367373	+	2.08347i
$935$	3.66885	−	6.35464i	0.119984	−	0.207819i
$936$	0.217453	−	1.35317i	0.00710768	−	0.0442298i
$937$	−15.7304	+	27.2459i	−0.513890	+	0.890083i	0.485980	+	0.873970i	$0.338463\pi$
$937$	−15.7304	+	27.2459i	−0.513890	+	0.890083i	−0.999870	+	0.0161137i	$0.994871\pi$
$938$	−3.27207	+	18.7367i	−0.106837	+	0.611776i
$939$	−2.67619	+	7.53031i	−0.0873341	+	0.245742i
$940$	−1.30772	−	7.41642i	−0.0426530	−	0.241897i
$941$	4.45804	+	25.2828i	0.145328	+	0.824196i	0.967103	+	0.254384i	$0.0818728\pi$
$941$	4.45804	+	25.2828i	0.145328	+	0.824196i	−0.821775	+	0.569812i	$0.807016\pi$
$942$	−83.4996	−	14.0699i	−2.72056	−	0.458423i
$943$	−66.8472	−	56.0915i	−2.17684	−	1.82659i
$944$	0.460923			0.0150018
$945$	19.4977	+	10.6304i	0.634261	+	0.345808i
$946$	18.7518			0.609673
$947$	−19.7672	−	16.5866i	−0.642347	−	0.538993i	0.262391	−	0.964962i	$-0.415489\pi$
$947$	−19.7672	−	16.5866i	−0.642347	−	0.538993i	−0.904738	+	0.425968i	$0.859933\pi$
$948$	−15.5865	−	41.8318i	−0.506225	−	1.35863i
$949$	0.00113216	+	0.00642080i	3.67515e−5	+	0.000208428i
$950$	−0.472016	−	2.67693i	−0.0153142	−	0.0868512i
$951$	11.8453	+	13.9009i	0.384112	+	0.450766i
$952$	−28.5534	+	10.4457i	−0.925421	+	0.338548i
$953$	−11.0856	+	19.2009i	−0.359098	+	0.621977i	−0.987810	−	0.155661i	$-0.950249\pi$
$953$	−11.0856	+	19.2009i	−0.359098	+	0.621977i	0.628712	+	0.777638i	$0.283582\pi$
$954$	18.7419	−	0.284829i	0.606792	−	0.00922170i
$955$	−7.12688	+	12.3441i	−0.230620	+	0.399446i
$956$	6.01012	−	34.0851i	0.194381	−	1.10239i
$957$	8.51596	−	5.00335i	0.275282	−	0.161735i
$958$	−4.39256	−	24.9114i	−0.141917	−	0.804852i
$959$	4.95988	+	27.8612i	0.160163	+	0.899686i
$960$	−0.277378	−	36.5053i	−0.00895234	−	1.17820i
$961$	16.0332	−	5.83562i	0.517201	−	0.188246i
$962$	−2.04385	+	3.54006i	−0.0658964	+	0.114136i
$963$	47.8663	+	16.6026i	1.54247	+	0.535012i
$964$	46.5460	+	80.6201i	1.49915	+	2.59660i
$965$	−13.0683	+	4.75647i	−0.420683	+	0.153116i
$966$	52.6877	+	61.6252i	1.69520	+	1.98276i
$967$	−26.4029	+	22.1546i	−0.849059	+	0.712445i	−0.959582	−	0.281428i	$-0.909192\pi$
$967$	−26.4029	+	22.1546i	−0.849059	+	0.712445i	0.110523	+	0.993874i	$0.464747\pi$
$968$	−18.8269	+	15.7976i	−0.605120	+	0.507756i
$969$	−2.61964	+	3.17058i	−0.0841548	+	0.101854i
$970$	34.5422	−	12.5723i	1.10908	−	0.403673i
$971$	−0.797770	+	1.38178i	−0.0256017	+	0.0443434i	−0.878542	−	0.477664i	$-0.841483\pi$
$971$	−0.797770	+	1.38178i	−0.0256017	+	0.0443434i	0.852941	+	0.522008i	$0.174817\pi$
$972$	47.6065	+	6.54099i	1.52698	+	0.209802i
$973$	7.22390	−	12.5598i	0.231588	−	0.402648i
$974$	10.8343	−	61.4443i	0.347153	−	1.96880i
$975$	0.764244	+	0.128777i	0.0244754	+	0.00412418i
$976$	1.02276	+	5.80037i	0.0327378	+	0.185665i
$977$	−15.9895	−	5.81970i	−0.511550	−	0.186189i	0.0733319	−	0.997308i	$-0.476637\pi$
$977$	−15.9895	−	5.81970i	−0.511550	−	0.186189i	−0.584881	+	0.811119i	$0.698859\pi$
$978$	−12.0058	+	33.7822i	−0.383904	+	1.08024i
$979$	−10.3467	+	3.76588i	−0.330681	+	0.120358i
$980$	34.8567	−	0.114504i	1.11346	−	0.00365771i
$981$	−27.3703	+	23.6844i	−0.873866	+	0.756184i
$982$	67.8226			2.16430
$983$	1.51266	−	8.57874i	0.0482465	−	0.273619i	−0.951135	−	0.308774i	$-0.900081\pi$
$983$	1.51266	−	8.57874i	0.0482465	−	0.273619i	0.999382	+	0.0351548i	$0.0111924\pi$
$984$	−40.5306	+	23.8128i	−1.29207	+	0.759123i
$985$	−25.8053	−	9.39235i	−0.822224	−	0.299265i
$986$	−10.8940	−	61.7828i	−0.346935	−	1.96757i
$987$	−5.96968	+	3.52054i	−0.190017	+	0.112060i
$988$	−0.222915	−	0.187048i	−0.00709187	−	0.00595078i
$989$	−67.6554			−2.15132
$990$	−5.13110	+	9.20768i	−0.163077	+	0.292639i
$991$	39.1080			1.24231			0.621154	−	0.783689i	$-0.286664\pi$
$991$	39.1080			1.24231			0.621154	+	0.783689i	$0.286664\pi$
$992$	4.13306	−	23.4398i	0.131225	−	0.744213i
$993$	28.2080	+	33.1029i	0.895153	+	1.05049i
$994$	−16.1452	−	5.84635i	−0.512094	−	0.185435i
$995$	−34.7880	−	12.6618i	−1.10285	−	0.401406i
$996$	−46.7962	+	56.6380i	−1.48279	+	1.79464i
$997$	19.1300	−	6.96275i	0.605853	−	0.220512i	−0.0208347	−	0.999783i	$-0.506632\pi$
$997$	19.1300	−	6.96275i	0.605853	−	0.220512i	0.626688	+	0.779270i	$0.284410\pi$
$998$	14.3230	+	24.8081i	0.453385	+	0.785286i
$999$	−44.1548	−	24.1680i	−1.39700	−	0.764642i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.79.20	yes	132
3.2	odd	2		567.2.u.a.478.3		132
7.4	even	3		189.2.w.a.25.3	yes	132
21.11	odd	6		567.2.w.a.235.20		132
27.13	even	9		189.2.w.a.121.3	yes	132
27.14	odd	18		567.2.w.a.415.20		132
189.67	even	9	inner	189.2.u.a.67.20	✓	132
189.95	odd	18		567.2.u.a.172.3		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.20	✓	132	189.67	even	9	inner
189.2.u.a.79.20	yes	132	1.1	even	1	trivial
189.2.w.a.25.3	yes	132	7.4	even	3
189.2.w.a.121.3	yes	132	27.13	even	9
567.2.u.a.172.3		132	189.95	odd	18
567.2.u.a.478.3		132	3.2	odd	2
567.2.w.a.235.20		132	21.11	odd	6
567.2.w.a.415.20		132	27.14	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)

\(f(q)\)	\(=\)	\(q+(1.72703 + 1.44915i) q^{2} +(-1.10323 + 1.33525i) q^{3} +(0.535296 + 3.03582i) q^{4} +(0.280502 + 1.59081i) q^{5} +(-3.84028 + 0.707271i) q^{6} +(0.455150 - 2.60631i) q^{7} +(-1.22040 + 2.11380i) q^{8} +(-0.565779 - 2.94617i) q^{9} +O(q^{10})\)	\(q+(1.72703 + 1.44915i) q^{2} +(-1.10323 + 1.33525i) q^{3} +(0.535296 + 3.03582i) q^{4} +(0.280502 + 1.59081i) q^{5} +(-3.84028 + 0.707271i) q^{6} +(0.455150 - 2.60631i) q^{7} +(-1.22040 + 2.11380i) q^{8} +(-0.565779 - 2.94617i) q^{9} +(-1.82088 + 3.15386i) q^{10} +(-0.167538 + 0.950156i) q^{11} +(-4.64412 - 2.63444i) q^{12} +(-0.0325017 - 0.184326i) q^{13} +(4.56298 - 3.84158i) q^{14} +(-2.43358 - 1.38048i) q^{15} +(0.622616 - 0.226614i) q^{16} +(-2.35408 + 4.07738i) q^{17} +(3.29231 - 5.90800i) q^{18} +(-0.252171 - 0.436773i) q^{19} +(-4.67925 + 1.70311i) q^{20} +(2.97794 + 3.48309i) q^{21} +(-1.66626 + 1.39816i) q^{22} +(6.01177 - 5.04448i) q^{23} +(-1.47607 - 3.96154i) q^{24} +(2.24647 - 0.817650i) q^{25} +(0.210985 - 0.365436i) q^{26} +(4.55805 + 2.49484i) q^{27} +(8.15591 - 0.0133961i) q^{28} +(-1.02634 + 5.82066i) q^{29} +(-2.20234 - 5.91075i) q^{30} +(-0.648287 - 3.67662i) q^{31} +(5.99088 + 2.18050i) q^{32} +(-1.08386 - 1.27194i) q^{33} +(-9.97427 + 3.63034i) q^{34} +(4.27381 - 0.00701971i) q^{35} +(8.64116 - 3.29467i) q^{36} -9.68721 q^{37} +(0.197443 - 1.11975i) q^{38} +(0.281978 + 0.159956i) q^{39} +(-3.70497 - 1.34850i) q^{40} +(-1.93086 - 10.9505i) q^{41} +(0.0954665 + 10.3309i) q^{42} +(-6.60401 - 5.54143i) q^{43} -2.97418 q^{44} +(4.52808 - 1.72645i) q^{45} +17.6927 q^{46} +(-0.262617 + 1.48937i) q^{47} +(-0.384301 + 1.08135i) q^{48} +(-6.58568 - 2.37252i) q^{49} +(5.06461 + 1.84337i) q^{50} +(-2.84723 - 7.64155i) q^{51} +(0.542182 - 0.197338i) q^{52} +(1.38569 + 2.40009i) q^{53} +(4.25649 + 10.9139i) q^{54} -1.55851 q^{55} +(4.95374 + 4.14284i) q^{56} +(0.861403 + 0.145149i) q^{57} +(-10.2075 + 8.56512i) q^{58} +(0.653703 + 0.237928i) q^{59} +(2.88820 - 8.12688i) q^{60} +(-1.54362 + 8.75430i) q^{61} +(4.20835 - 7.28908i) q^{62} +(-7.93613 + 0.133647i) q^{63} +(6.52397 + 11.2998i) q^{64} +(0.284111 - 0.103408i) q^{65} +(-0.0286255 - 3.76735i) q^{66} +(-2.44274 + 2.04970i) q^{67} +(-13.6383 - 4.96394i) q^{68} +(0.103279 + 13.5924i) q^{69} +(7.39115 + 6.18125i) q^{70} +(-1.43937 - 2.49307i) q^{71} +(6.91807 + 2.39956i) q^{72} -0.0348339 q^{73} +(-16.7301 - 14.0382i) q^{74} +(-1.38661 + 3.90165i) q^{75} +(1.19098 - 0.999349i) q^{76} +(2.40014 + 0.869119i) q^{77} +(0.255184 + 0.684876i) q^{78} +(6.40479 + 5.37426i) q^{79} +(0.535144 + 0.926896i) q^{80} +(-8.35979 + 3.33376i) q^{81} +(12.5342 - 21.7098i) q^{82} +(2.38942 - 13.5510i) q^{83} +(-8.97994 + 10.9049i) q^{84} +(-7.14665 - 2.60117i) q^{85} +(-3.37497 - 19.1404i) q^{86} +(-6.63975 - 7.79193i) q^{87} +(-1.80397 - 1.51371i) q^{88} +(5.70612 + 9.88329i) q^{89} +(10.3220 + 3.58023i) q^{90} +(-0.495204 + 0.000813371i) q^{91} +(18.5322 + 15.5503i) q^{92} +(5.62441 + 3.19052i) q^{93} +(-2.61187 + 2.19162i) q^{94} +(0.624088 - 0.523672i) q^{95} +(-9.52081 + 5.59373i) q^{96} +(-7.73226 - 6.48814i) q^{97} +(-7.93551 - 13.6410i) q^{98} +(2.89411 - 0.0439831i) 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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