LMFDB - Embedded newform 189.2.w.a.184.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(25,189)]

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([10, 12]))

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

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

chi := DirichletCharacter("189.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.w (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			184.5
Character	$\chi$	$=$	189.184
Dual form			189.2.w.a.151.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.303930 - 1.72367i) q^{2} +(-1.25318 + 1.19564i) q^{3} +(-0.999292 + 0.363713i) q^{4} +(0.0231991 - 0.131569i) q^{5} +(2.44176 + 1.79668i) q^{6} +(1.74352 - 1.99001i) q^{7} +(-0.819627 - 1.41964i) q^{8} +(0.140909 - 2.99669i) q^{9} +O(q^{10})$	\(q+(-0.303930 - 1.72367i) q^{2} +(-1.25318 + 1.19564i) q^{3} +(-0.999292 + 0.363713i) q^{4} +(0.0231991 - 0.131569i) q^{5} +(2.44176 + 1.79668i) q^{6} +(1.74352 - 1.99001i) q^{7} +(-0.819627 - 1.41964i) q^{8} +(0.140909 - 2.99669i) q^{9} -0.233833 q^{10} +(-0.550020 - 3.11932i) q^{11} +(0.817423 - 1.65059i) q^{12} +(-1.13051 - 0.948610i) q^{13} +(-3.96004 - 2.40043i) q^{14} +(0.128236 + 0.192617i) q^{15} +(-3.82714 + 3.21135i) q^{16} -0.883439 q^{17} +(-5.20814 + 0.667903i) q^{18} +6.03584 q^{19} +(0.0246705 + 0.139914i) q^{20} +(0.194394 + 4.57845i) q^{21} +(-5.20952 + 1.89611i) q^{22} +(-3.25114 - 2.72803i) q^{23} +(2.72451 + 0.799080i) q^{24} +(4.68169 + 1.70400i) q^{25} +(-1.29150 + 2.23694i) q^{26} +(3.40637 + 3.92386i) q^{27} +(-1.01849 + 2.62274i) q^{28} +(2.60068 - 2.18223i) q^{29} +(0.293034 - 0.279579i) q^{30} +(-5.70378 + 2.07601i) q^{31} +(4.18702 + 3.51333i) q^{32} +(4.41885 + 3.25144i) q^{33} +(0.268504 + 1.52276i) q^{34} +(-0.221376 - 0.275559i) q^{35} +(0.949124 + 3.04582i) q^{36} +(1.87653 + 3.25025i) q^{37} +(-1.83447 - 10.4038i) q^{38} +(2.55092 - 0.162901i) q^{39} +(-0.205795 + 0.0749031i) q^{40} +(6.09240 + 5.11213i) q^{41} +(7.83267 - 1.72660i) q^{42} +(-6.38712 - 2.32472i) q^{43} +(1.68417 + 2.91706i) q^{44} +(-0.391002 - 0.0880599i) q^{45} +(-3.71411 + 6.43303i) q^{46} +(-3.12343 - 1.13684i) q^{47} +(0.956479 - 8.60026i) q^{48} +(-0.920298 - 6.93924i) q^{49} +(1.51423 - 8.58760i) q^{50} +(1.10711 - 1.05627i) q^{51} +(1.47473 + 0.536758i) q^{52} +(6.45006 + 11.1718i) q^{53} +(5.72816 - 7.06404i) q^{54} -0.423166 q^{55} +(-4.25413 - 0.844091i) q^{56} +(-7.56397 + 7.21666i) q^{57} +(-4.55187 - 3.81947i) q^{58} +(5.32937 + 4.47187i) q^{59} +(-0.198202 - 0.145840i) q^{60} +(12.1063 + 4.40633i) q^{61} +(5.31191 + 9.20049i) q^{62} +(-5.71777 - 5.50519i) q^{63} +(-0.212705 + 0.368416i) q^{64} +(-0.151034 + 0.126733i) q^{65} +(4.26140 - 8.60486i) q^{66} +(0.662043 - 3.75463i) q^{67} +(0.882814 - 0.321318i) q^{68} +(7.33598 - 0.468472i) q^{69} +(-0.407691 + 0.465330i) q^{70} +(-2.23138 + 3.86486i) q^{71} +(-4.36970 + 2.25613i) q^{72} +(0.0471967 - 0.0817471i) q^{73} +(5.03204 - 4.22238i) q^{74} +(-7.90435 + 3.46219i) q^{75} +(-6.03156 + 2.19531i) q^{76} +(-7.16646 - 4.34404i) q^{77} +(-1.05609 - 4.34744i) q^{78} +(-0.562555 - 3.19041i) q^{79} +(0.333728 + 0.578033i) q^{80} +(-8.96029 - 0.844521i) q^{81} +(6.95998 - 12.0550i) q^{82} +(-8.18383 + 6.86705i) q^{83} +(-1.85950 - 4.50451i) q^{84} +(-0.0204950 + 0.116233i) q^{85} +(-2.06582 + 11.7159i) q^{86} +(-0.649961 + 5.84418i) q^{87} +(-3.97749 + 3.33751i) q^{88} -3.76455 q^{89} +(-0.0329492 + 0.700724i) q^{90} +(-3.85881 + 0.595810i) q^{91} +(4.24105 + 1.54362i) q^{92} +(4.66570 - 9.42125i) q^{93} +(-1.01023 + 5.72929i) q^{94} +(0.140026 - 0.794128i) q^{95} +(-9.44775 + 0.603329i) q^{96} +(-14.4400 - 5.25573i) q^{97} +(-11.6813 + 3.69534i) q^{98} +(-9.42514 + 1.20870i) 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} + 3 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 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.303930	−	1.72367i	−0.214911	−	1.21882i	−0.881061	−	0.473003i	$-0.843170\pi$
$2$	−0.303930	−	1.72367i	−0.214911	−	1.21882i	0.666150	−	0.745818i	$-0.267941\pi$
$3$	−1.25318	+	1.19564i	−0.723523	+	0.690301i
$3$	−1.25318	+	1.19564i	−0.723523	+	0.690301i
$4$	−0.999292	+	0.363713i	−0.499646	+	0.181856i
$5$	0.0231991	−	0.131569i	0.0103750	−	0.0588394i	−0.979181	−	0.202990i	$-0.934934\pi$
$5$	0.0231991	−	0.131569i	0.0103750	−	0.0588394i	0.989556	+	0.144151i	$0.0460451\pi$
$6$	2.44176	+	1.79668i	0.996846	+	0.733491i
$7$	1.74352	−	1.99001i	0.658987	−	0.752154i
$7$	1.74352	−	1.99001i	0.658987	−	0.752154i
$8$	−0.819627	−	1.41964i	−0.289782	−	0.501917i
$9$	0.140909	−	2.99669i	0.0469697	−	0.998896i
$10$	−0.233833			−0.0739444
$11$	−0.550020	−	3.11932i	−0.165837	−	0.940511i	−0.948197	−	0.317683i	$-0.897095\pi$
$11$	−0.550020	−	3.11932i	−0.165837	−	0.940511i	0.782359	−	0.622827i	$-0.214016\pi$
$12$	0.817423	−	1.65059i	0.235970	−	0.476483i
$13$	−1.13051	−	0.948610i	−0.313547	−	0.263097i	0.472409	−	0.881379i	$-0.343384\pi$
$13$	−1.13051	−	0.948610i	−0.313547	−	0.263097i	−0.785956	+	0.618282i	$0.787829\pi$
$14$	−3.96004	−	2.40043i	−1.05837	−	0.641542i
$15$	0.128236	+	0.192617i	0.0331104	+	0.0497335i
$16$	−3.82714	+	3.21135i	−0.956785	+	0.802838i
$17$	−0.883439			−0.214266			−0.107133	−	0.994245i	$-0.534167\pi$
$17$	−0.883439			−0.214266			−0.107133	+	0.994245i	$0.534167\pi$
$18$	−5.20814	+	0.667903i	−1.22757	+	0.157426i
$19$	6.03584			1.38472			0.692358	−	0.721554i	$-0.256572\pi$
$19$	6.03584			1.38472			0.692358	+	0.721554i	$0.256572\pi$
$20$	0.0246705	+	0.139914i	0.00551650	+	0.0312856i
$21$	0.194394	+	4.57845i	0.0424202	+	0.999100i
$22$	−5.20952	+	1.89611i	−1.11067	+	0.404252i
$23$	−3.25114	−	2.72803i	−0.677909	−	0.568833i	0.237486	−	0.971391i	$-0.423677\pi$
$23$	−3.25114	−	2.72803i	−0.677909	−	0.568833i	−0.915394	+	0.402558i	$0.868121\pi$
$24$	2.72451	+	0.799080i	0.556137	+	0.163112i
$25$	4.68169	+	1.70400i	0.936338	+	0.340799i
$26$	−1.29150	+	2.23694i	−0.253284	+	0.438700i
$27$	3.40637	+	3.92386i	0.655555	+	0.755147i
$28$	−1.01849	+	2.62274i	−0.192477	+	0.495652i
$29$	2.60068	−	2.18223i	0.482933	−	0.405229i	−0.368552	−	0.929607i	$-0.620146\pi$
$29$	2.60068	−	2.18223i	0.482933	−	0.405229i	0.851486	+	0.524378i	$0.175702\pi$
$30$	0.293034	−	0.279579i	0.0535005	−	0.0510439i
$31$	−5.70378	+	2.07601i	−1.02443	+	0.372862i	−0.798957	−	0.601388i	$-0.794615\pi$
$31$	−5.70378	+	2.07601i	−1.02443	+	0.372862i	−0.225472	+	0.974250i	$0.572392\pi$
$32$	4.18702	+	3.51333i	0.740168	+	0.621075i
$33$	4.41885	+	3.25144i	0.769222	+	0.566003i
$34$	0.268504	+	1.52276i	0.0460480	+	0.261151i
$35$	−0.221376	−	0.275559i	−0.0374193	−	0.0465780i
$36$	0.949124	+	3.04582i	0.158187	+	0.507636i
$37$	1.87653	+	3.25025i	0.308500	+	0.534338i	0.978035	−	0.208443i	$-0.0668396\pi$
$37$	1.87653	+	3.25025i	0.308500	+	0.534338i	−0.669534	+	0.742781i	$0.733506\pi$
$38$	−1.83447	−	10.4038i	−0.297591	−	1.68772i
$39$	2.55092	−	0.162901i	0.408474	−	0.0260850i
$40$	−0.205795	+	0.0749031i	−0.0325390	+	0.0118432i
$41$	6.09240	+	5.11213i	0.951473	+	0.798381i	0.979545	−	0.201225i	$-0.0644922\pi$
$41$	6.09240	+	5.11213i	0.951473	+	0.798381i	−0.0280717	+	0.999606i	$0.508937\pi$
$42$	7.83267	−	1.72660i	1.20861	−	0.266420i
$43$	−6.38712	−	2.32472i	−0.974027	−	0.354517i	−0.194512	−	0.980900i	$-0.562312\pi$
$43$	−6.38712	−	2.32472i	−0.974027	−	0.354517i	−0.779515	+	0.626383i	$0.784535\pi$
$44$	1.68417	+	2.91706i	0.253898	+	0.439764i
$45$	−0.391002	−	0.0880599i	−0.0582872	−	0.0131272i
$46$	−3.71411	+	6.43303i	−0.547616	+	0.948498i
$47$	−3.12343	−	1.13684i	−0.455599	−	0.165825i	0.104019	−	0.994575i	$-0.466830\pi$
$47$	−3.12343	−	1.13684i	−0.455599	−	0.165825i	−0.559618	+	0.828751i	$0.689052\pi$
$48$	0.956479	−	8.60026i	0.138056	−	1.24134i
$49$	−0.920298	−	6.93924i	−0.131471	−	0.991320i
$50$	1.51423	−	8.58760i	0.214144	−	1.21447i
$51$	1.10711	−	1.05627i	0.155026	−	0.147908i
$52$	1.47473	+	0.536758i	0.204508	+	0.0744349i
$53$	6.45006	+	11.1718i	0.885984	+	1.53457i	0.844582	+	0.535427i	$0.179849\pi$
$53$	6.45006	+	11.1718i	0.885984	+	1.53457i	0.0414022	+	0.999143i	$0.486817\pi$
$54$	5.72816	−	7.06404i	0.779503	−	0.961294i
$55$	−0.423166			−0.0570597
$56$	−4.25413	−	0.844091i	−0.568482	−	0.112796i
$57$	−7.56397	+	7.21666i	−1.00187	+	0.955870i
$58$	−4.55187	−	3.81947i	−0.597690	−	0.501521i
$59$	5.32937	+	4.47187i	0.693824	+	0.582188i	0.920009	−	0.391897i	$-0.128181\pi$
$59$	5.32937	+	4.47187i	0.693824	+	0.582188i	−0.226185	+	0.974084i	$0.572625\pi$
$60$	−0.198202	−	0.145840i	−0.0255878	−	0.0188278i
$61$	12.1063	+	4.40633i	1.55005	+	0.564172i	0.968430	−	0.249287i	$-0.0801964\pi$
$61$	12.1063	+	4.40633i	1.55005	+	0.564172i	0.581621	+	0.813460i	$0.302419\pi$
$62$	5.31191	+	9.20049i	0.674613	+	1.16846i
$63$	−5.71777	−	5.50519i	−0.720371	−	0.693589i
$64$	−0.212705	+	0.368416i	−0.0265882	+	0.0460520i
$65$	−0.151034	+	0.126733i	−0.0187335	+	0.0157193i
$66$	4.26140	−	8.60486i	0.524542	−	1.05919i
$67$	0.662043	−	3.75463i	0.0808814	−	0.458701i	−0.917288	−	0.398224i	$-0.869627\pi$
$67$	0.662043	−	3.75463i	0.0808814	−	0.458701i	0.998170	−	0.0604772i	$-0.0192623\pi$
$68$	0.882814	−	0.321318i	0.107057	−	0.0389655i
$69$	7.33598	−	0.468472i	0.883148	−	0.0563974i
$70$	−0.407691	+	0.465330i	−0.0487284	+	0.0556176i
$71$	−2.23138	+	3.86486i	−0.264816	+	0.458675i	−0.967515	−	0.252812i	$-0.918645\pi$
$71$	−2.23138	+	3.86486i	−0.264816	+	0.458675i	0.702699	+	0.711487i	$0.251978\pi$
$72$	−4.36970	+	2.25613i	−0.514974	+	0.265887i
$73$	0.0471967	−	0.0817471i	0.00552395	−	0.00956777i	−0.863250	−	0.504776i	$-0.831575\pi$
$73$	0.0471967	−	0.0817471i	0.00552395	−	0.00956777i	0.868774	+	0.495208i	$0.164908\pi$
$74$	5.03204	−	4.22238i	0.584963	−	0.490842i
$75$	−7.90435	+	3.46219i	−0.912716	+	0.399779i
$76$	−6.03156	+	2.19531i	−0.691868	+	0.251819i
$77$	−7.16646	−	4.34404i	−0.816694	−	0.495049i
$78$	−1.05609	−	4.34744i	−0.119579	−	0.492251i
$79$	−0.562555	−	3.19041i	−0.0632924	−	0.358949i	−0.999962	−	0.00873437i	$-0.997220\pi$
$79$	−0.562555	−	3.19041i	−0.0632924	−	0.358949i	0.936669	−	0.350215i	$-0.113891\pi$
$80$	0.333728	+	0.578033i	0.0373119	+	0.0646261i
$81$	−8.96029	−	0.844521i	−0.995588	−	0.0938357i
$82$	6.95998	−	12.0550i	0.768602	−	1.33126i
$83$	−8.18383	+	6.86705i	−0.898292	+	0.753756i	−0.969856	−	0.243680i	$-0.921645\pi$
$83$	−8.18383	+	6.86705i	−0.898292	+	0.753756i	0.0715639	+	0.997436i	$0.477201\pi$
$84$	−1.85950	−	4.50451i	−0.202888	−	0.491482i
$85$	−0.0204950	+	0.116233i	−0.00222300	+	0.0126073i
$86$	−2.06582	+	11.7159i	−0.222764	+	1.26335i
$87$	−0.649961	+	5.84418i	−0.0696831	+	0.626562i
$88$	−3.97749	+	3.33751i	−0.424002	+	0.355780i
$89$	−3.76455			−0.399042			−0.199521	−	0.979894i	$-0.563939\pi$
$89$	−3.76455			−0.399042			−0.199521	+	0.979894i	$0.563939\pi$
$90$	−0.0329492	+	0.700724i	−0.00347315	+	0.0738628i
$91$	−3.85881	+	0.595810i	−0.404513	+	0.0624578i
$92$	4.24105	+	1.54362i	0.442160	+	0.160933i
$93$	4.66570	−	9.42125i	0.483811	−	0.976938i
$94$	−1.01023	+	5.72929i	−0.104197	+	0.590932i
$95$	0.140026	−	0.794128i	0.0143664	−	0.0814758i
$96$	−9.44775	+	0.603329i	−0.964257	+	0.0615770i
$97$	−14.4400	−	5.25573i	−1.46616	−	0.533638i	−0.519104	−	0.854711i	$-0.673734\pi$
$97$	−14.4400	−	5.25573i	−1.46616	−	0.533638i	−0.947055	+	0.321073i	$0.895957\pi$
$98$	−11.6813	+	3.69534i	−1.17999	+	0.373286i
$99$	−9.42514	+	1.20870i	−0.947262	+	0.121479i
$100$	−5.29814			−0.529814
$101$	−3.43450	+	2.88189i	−0.341745	+	0.286758i	−0.797465	−	0.603365i	$-0.793826\pi$
$101$	−3.43450	+	2.88189i	−0.341745	+	0.286758i	0.455720	+	0.890123i	$0.349382\pi$
$102$	−2.15715	−	1.58726i	−0.213590	−	0.157162i
$103$	2.25007	−	12.7608i	0.221706	−	1.25736i	−0.647176	−	0.762340i	$-0.724050\pi$
$103$	2.25007	−	12.7608i	0.221706	−	1.25736i	0.868883	−	0.495018i	$-0.164839\pi$
$104$	−0.420084	+	2.38242i	−0.0411927	+	0.233615i
$105$	0.606892	+	0.0806400i	0.0592265	+	0.00786966i
$106$	17.2962	−	14.5133i	1.67996	−	1.40965i
$107$	9.57634	−	16.5867i	0.925779	−	1.60350i	0.135477	−	0.990781i	$-0.456743\pi$
$107$	9.57634	−	16.5867i	0.925779	−	1.60350i	0.790303	−	0.612717i	$-0.209923\pi$
$108$	−4.83111	−	2.68214i	−0.464874	−	0.258090i
$109$	9.15485	+	15.8567i	0.876875	+	1.51879i	0.854752	+	0.519037i	$0.173709\pi$
$109$	9.15485	+	15.8567i	0.876875	+	1.51879i	0.0221235	+	0.999755i	$0.492957\pi$
$110$	0.128613	+	0.729400i	0.0122628	+	0.0695455i
$111$	−6.23775	−	1.82949i	−0.592061	−	0.173648i
$112$	−0.282054	+	13.2151i	−0.0266516	+	1.24871i
$113$	5.34773	−	1.94641i	0.503072	−	0.183103i	−0.0780031	−	0.996953i	$-0.524854\pi$
$113$	5.34773	−	1.94641i	0.503072	−	0.183103i	0.581075	+	0.813850i	$0.302632\pi$
$114$	14.7381	+	10.8445i	1.38035	+	1.01568i
$115$	−0.434347	+	0.364460i	−0.0405031	+	0.0339861i
$116$	−1.80513	+	3.12658i	−0.167602	+	0.290296i
$117$	−3.00199	+	3.25412i	−0.277534	+	0.300843i
$118$	6.08829	−	10.5452i	0.560472	−	0.970767i
$119$	−1.54029	+	1.75806i	−0.141198	+	0.161161i
$120$	0.168340	−	0.339922i	0.0153673	−	0.0310305i
$121$	0.908976	−	0.330840i	0.0826342	−	0.0300764i
$122$	3.91560	−	22.2065i	0.354502	−	2.01048i
$123$	−13.7471	+	0.877885i	−1.23954	+	0.0791562i
$124$	4.94467	−	4.14907i	0.444045	−	0.372598i
$125$	0.666801	−	1.15493i	0.0596405	−	0.103300i
$126$	−7.75135	+	11.5288i	−0.690545	+	1.02706i
$127$	−1.39192	−	2.41087i	−0.123513	−	0.213930i	0.797638	−	0.603137i	$-0.206083\pi$
$127$	−1.39192	−	2.41087i	−0.123513	−	0.213930i	−0.921151	+	0.389206i	$0.872749\pi$
$128$	10.9720	+	3.99347i	0.969794	+	0.352976i
$129$	10.7837	−	4.72338i	0.949454	−	0.415871i
$130$	0.264350	+	0.221816i	0.0231850	+	0.0194546i
$131$	8.36287	+	7.01728i	0.730667	+	0.613102i	0.930313	−	0.366766i	$-0.119535\pi$
$131$	8.36287	+	7.01728i	0.730667	+	0.613102i	−0.199646	+	0.979868i	$0.563979\pi$
$132$	−5.59831	−	1.64195i	−0.487270	−	0.142913i
$133$	10.5236	−	12.0114i	0.912510	−	1.04152i
$134$	−6.67298			−0.576457
$135$	0.595283	−	0.357142i	0.0512338	−	0.0307378i
$136$	0.724091	+	1.25416i	0.0620903	+	0.107544i
$137$	−5.79620	−	2.10964i	−0.495203	−	0.180239i	0.0823323	−	0.996605i	$-0.473763\pi$
$137$	−5.79620	−	2.10964i	−0.495203	−	0.180239i	−0.577535	+	0.816366i	$0.695985\pi$
$138$	−3.03712	−	12.5024i	−0.258537	−	1.06428i
$139$	2.47765	−	14.0515i	0.210152	−	1.19183i	−0.678972	−	0.734164i	$-0.737574\pi$
$139$	2.47765	−	14.0515i	0.210152	−	1.19183i	0.889124	−	0.457667i	$-0.151315\pi$
$140$	0.321443	+	0.194847i	0.0271669	+	0.0164676i
$141$	5.27346	−	2.30983i	0.444105	−	0.194523i
$142$	7.33994	+	2.67152i	0.615954	+	0.224189i
$143$	−2.33722	+	4.04818i	−0.195448	+	0.338525i
$144$	9.08415	+	11.9213i	0.757012	+	0.993438i
$145$	−0.226780	−	0.392794i	−0.0188330	−	0.0326198i
$146$	−0.155250	−	0.0565063i	−0.0128486	−	0.00467649i
$147$	9.45010	+	7.59576i	0.779431	+	0.626488i
$148$	−3.05736	−	2.56543i	−0.251314	−	0.210877i
$149$	15.1359	−	5.50902i	1.23998	−	0.451317i	0.362977	−	0.931798i	$-0.381760\pi$
$149$	15.1359	−	5.50902i	1.23998	−	0.451317i	0.877005	+	0.480482i	$0.159538\pi$
$150$	8.37005	+	12.5723i	0.683412	+	1.02652i
$151$	−1.29391	−	7.33811i	−0.105297	−	0.597167i	−0.991101	−	0.133109i	$-0.957504\pi$
$151$	−1.29391	−	7.33811i	−0.105297	−	0.597167i	0.885805	−	0.464058i	$-0.153607\pi$
$152$	−4.94713	−	8.56869i	−0.401266	−	0.695012i
$153$	−0.124485	+	2.64739i	−0.0100640	+	0.214029i
$154$	−5.30961	+	13.6729i	−0.427860	+	1.10180i
$155$	0.140815	+	0.798601i	0.0113105	+	0.0641452i
$156$	−2.48987	+	1.09059i	−0.199349	+	0.0873169i
$157$	11.3878	+	9.55548i	0.908843	+	0.762610i	0.971899	−	0.235400i	$-0.0756400\pi$
$157$	11.3878	+	9.55548i	0.908843	+	0.762610i	−0.0630552	+	0.998010i	$0.520084\pi$
$158$	−5.32825	+	1.93932i	−0.423893	+	0.154284i
$159$	−21.4405	−	6.28837i	−1.70034	−	0.498700i
$160$	0.559380	−	0.469376i	0.0442229	−	0.0371074i
$161$	−11.0972	+	1.71344i	−0.874583	+	0.135038i
$162$	1.26762	+	15.7013i	0.0995939	+	1.23361i
$163$	−2.60404	+	4.51033i	−0.203964	+	0.353276i	−0.949802	−	0.312851i	$-0.898716\pi$
$163$	−2.60404	+	4.51033i	−0.203964	+	0.353276i	0.745838	+	0.666127i	$0.232049\pi$
$164$	−7.94744	−	2.89263i	−0.620591	−	0.225877i
$165$	0.530302	−	0.505952i	0.0412839	−	0.0393883i
$166$	14.3239	+	12.0191i	1.11175	+	0.932867i
$167$	−3.20224	+	1.16552i	−0.247797	+	0.0901906i	−0.462933	−	0.886393i	$-0.653203\pi$
$167$	−3.20224	+	1.16552i	−0.247797	+	0.0901906i	0.215136	+	0.976584i	$0.430981\pi$
$168$	6.34040	−	4.02859i	0.489173	−	0.310813i
$169$	−1.87924	−	10.6577i	−0.144557	−	0.819821i
$170$	0.206577			0.0158437
$171$	0.850504	−	18.0875i	0.0650396	−	1.38319i
$172$	7.22813			0.551140
$173$	−16.9118	+	14.1907i	−1.28578	+	1.07890i	−0.293362	+	0.956001i	$0.594774\pi$
$173$	−16.9118	+	14.1907i	−1.28578	+	1.07890i	−0.992419	+	0.122898i	$0.960781\pi$
$174$	10.2710	−	0.655902i	0.778643	−	0.0497238i
$175$	11.5536	−	6.34568i	0.873369	−	0.479688i
$176$	12.1222	+	10.1718i	0.913749	+	0.766726i
$177$	−12.0254	+	0.767935i	−0.903882	+	0.0577215i
$178$	1.14416	+	6.48886i	0.0857585	+	0.486361i
$179$	21.2705			1.58984			0.794918	−	0.606717i	$-0.207514\pi$
$179$	21.2705			1.58984			0.794918	+	0.606717i	$0.207514\pi$
$180$	0.422754	−	0.0542149i	0.0315102	−	0.00404094i
$181$	−2.07880	−	3.60058i	−0.154516	−	0.267629i	0.778367	−	0.627810i	$-0.216048\pi$
$181$	−2.07880	−	3.60058i	−0.154516	−	0.267629i	−0.932883	+	0.360181i	$0.882715\pi$
$182$	2.19979	+	6.47024i	0.163059	+	0.479606i
$183$	−20.4397	+	8.95280i	−1.51095	+	0.661810i
$184$	−1.20809	+	6.85139i	−0.0890612	+	0.505091i
$185$	0.471166	−	0.171490i	0.0346408	−	0.0126082i
$186$	−17.6572	−	5.17874i	−1.29469	−	0.379724i
$187$	0.485910	+	2.75573i	0.0355332	+	0.201519i
$188$	3.53470			0.257795
$189$	13.7476	+	0.0626071i	0.999990	+	0.00455400i
$190$	−1.41138			−0.102392
$191$	3.94296	+	22.3616i	0.285302	+	1.61803i	0.704203	+	0.709998i	$0.251304\pi$
$191$	3.94296	+	22.3616i	0.285302	+	1.61803i	−0.418901	+	0.908032i	$0.637585\pi$
$192$	−0.173934	−	0.716009i	−0.0125526	−	0.0516735i
$193$	13.2986	−	4.84031i	0.957258	−	0.348413i	0.184299	−	0.982870i	$-0.440998\pi$
$193$	13.2986	−	4.84031i	0.957258	−	0.348413i	0.772958	+	0.634457i	$0.218776\pi$
$194$	−4.67041	+	26.4872i	−0.335316	+	1.90167i
$195$	0.0377465	−	0.339401i	0.00270308	−	0.0243050i
$196$	3.44354	+	6.59961i	0.245967	+	0.471400i
$197$	−2.34920	−	4.06894i	−0.167374	−	0.289900i	0.770122	−	0.637897i	$-0.220195\pi$
$197$	−2.34920	−	4.06894i	−0.167374	−	0.289900i	−0.937496	+	0.347997i	$0.886862\pi$
$198$	4.94799	+	15.8785i	0.351638	+	1.12844i
$199$	−10.3443			−0.733287			−0.366643	−	0.930362i	$-0.619493\pi$
$199$	−10.3443			−0.733287			−0.366643	+	0.930362i	$0.619493\pi$
$200$	−1.41819	−	8.04294i	−0.100281	−	0.568722i
$201$	3.65952	+	5.49678i	0.258122	+	0.387713i
$202$	6.01128	+	5.04406i	0.422952	+	0.354899i
$203$	0.191665	−	8.98013i	0.0134523	−	0.630281i
$204$	−0.722144	+	1.45819i	−0.0505602	+	0.102094i
$205$	0.813936	−	0.682974i	0.0568478	−	0.0477009i
$206$	−22.6793			−1.58014
$207$	−8.63316	+	9.35824i	−0.600046	+	0.650442i
$208$	7.37294			0.511221
$209$	−3.31983	−	18.8277i	−0.229638	−	1.30234i
$210$	−0.0454557	−	1.07059i	−0.00313674	−	0.0738779i
$211$	−11.3402	+	4.12750i	−0.780693	+	0.284149i	−0.701461	−	0.712707i	$-0.747469\pi$
$211$	−11.3402	+	4.12750i	−0.780693	+	0.284149i	−0.0792311	+	0.996856i	$0.525247\pi$
$212$	−10.5088	−	8.81796i	−0.721750	−	0.605620i
$213$	−1.82465	−	7.51128i	−0.125023	−	0.514664i
$214$	−31.5006	−	11.4653i	−2.15334	−	0.783751i
$215$	−0.454037	+	0.786415i	−0.0309651	+	0.0536331i
$216$	2.77850	−	8.05190i	0.189053	−	0.547862i
$217$	−5.81336	+	14.9701i	−0.394636	+	1.01624i
$218$	24.5493	−	20.5993i	1.66269	−	1.39516i
$219$	0.0385939	+	0.158874i	0.00260793	+	0.0107357i
$220$	0.422866	−	0.153911i	0.0285096	−	0.0103767i
$221$	0.998736	+	0.838039i	0.0671823	+	0.0563726i
$222$	−1.25761	+	11.3079i	−0.0844051	+	0.758935i
$223$	2.37838	+	13.4885i	0.159268	+	0.903256i	0.954779	+	0.297316i	$0.0960916\pi$
$223$	2.37838	+	13.4885i	0.159268	+	0.903256i	−0.795511	+	0.605940i	$0.792797\pi$
$224$	14.2917	−	2.20668i	0.954906	−	0.147440i
$225$	5.76604	−	13.7895i	0.384403	−	0.919298i
$226$	−4.98032	−	8.62617i	−0.331286	−	0.573804i
$227$	2.68530	+	15.2291i	0.178229	+	1.01079i	0.934350	+	0.356357i	$0.115981\pi$
$227$	2.68530	+	15.2291i	0.178229	+	1.01079i	−0.756121	+	0.654432i	$0.772908\pi$
$228$	4.93383	−	9.96267i	0.326751	−	0.659794i
$229$	−22.0080	+	8.01025i	−1.45433	+	0.529332i	−0.943796	−	0.330527i	$-0.892773\pi$
$229$	−22.0080	+	8.01025i	−1.45433	+	0.529332i	−0.510531	+	0.859859i	$0.670551\pi$
$230$	0.760222	+	0.637902i	0.0501276	+	0.0420620i
$231$	14.1747	−	3.12462i	0.932629	−	0.205585i
$232$	−5.22955	−	1.90340i	−0.343337	−	0.124964i
$233$	−5.79081	−	10.0300i	−0.379369	−	0.657086i	0.611602	−	0.791166i	$-0.290525\pi$
$233$	−5.79081	−	10.0300i	−0.379369	−	0.657086i	−0.990971	+	0.134080i	$0.957192\pi$
$234$	6.52143	+	4.18542i	0.426319	+	0.273610i
$235$	−0.222033	+	0.384573i	−0.0144838	+	0.0250868i
$236$	−6.95207	−	2.53035i	−0.452541	−	0.164712i
$237$	4.51955	+	3.32554i	0.293576	+	0.216017i
$238$	3.49846	+	2.12063i	0.226771	+	0.137460i
$239$	−1.43847	+	8.15797i	−0.0930469	+	0.527695i	0.902281	+	0.431147i	$0.141891\pi$
$239$	−1.43847	+	8.15797i	−0.0930469	+	0.527695i	−0.995328	+	0.0965476i	$0.969220\pi$
$240$	−1.10934	−	0.325362i	−0.0716074	−	0.0210020i
$241$	−9.23157	−	3.36002i	−0.594658	−	0.216438i	0.0271190	−	0.999632i	$-0.491367\pi$
$241$	−9.23157	−	3.36002i	−0.594658	−	0.216438i	−0.621777	+	0.783194i	$0.713589\pi$
$242$	−0.846526	−	1.46623i	−0.0544168	−	0.0942526i
$243$	12.2386	−	9.65491i	0.785105	−	0.619363i
$244$	−13.7004			−0.877075
$245$	−0.934338	−	0.0399018i	−0.0596927	−	0.00254924i
$246$	5.69135	+	23.4287i	0.362867	+	1.49376i
$247$	−6.82357	−	5.72565i	−0.434173	−	0.364314i
$248$	7.62214	+	6.39574i	0.484007	+	0.406130i
$249$	2.04530	−	18.3905i	0.129616	−	1.16545i
$250$	−2.19339	−	0.798328i	−0.138722	−	0.0504907i
$251$	−1.26511	−	2.19123i	−0.0798530	−	0.138309i	0.823333	−	0.567558i	$-0.192112\pi$
$251$	−1.26511	−	2.19123i	−0.0798530	−	0.138309i	−0.903186	+	0.429249i	$0.858778\pi$
$252$	7.71603	+	3.42167i	0.486064	+	0.215545i
$253$	−6.72140	+	11.6418i	−0.422571	+	0.731914i
$254$	−3.73251	+	3.13195i	−0.234199	+	0.196516i
$255$	−0.113289	−	0.170165i	−0.00709441	−	0.0106562i
$256$	3.40098	−	19.2879i	0.212561	−	1.20550i
$257$	21.6724	−	7.88812i	1.35189	−	0.492048i	0.438353	−	0.898803i	$-0.355562\pi$
$257$	21.6724	−	7.88812i	1.35189	−	0.492048i	0.913537	+	0.406756i	$0.133340\pi$
$258$	−11.4191	−	17.1520i	−0.710920	−	1.06784i
$259$	9.73981	+	1.93254i	0.605202	+	0.120082i
$260$	0.104833	−	0.181576i	0.00650148	−	0.0112609i
$261$	−6.17300	−	8.10091i	−0.382099	−	0.501434i
$262$	9.55377	−	16.5476i	0.590234	−	1.02232i
$263$	−4.14425	+	3.47744i	−0.255545	+	0.214428i	−0.761556	−	0.648099i	$-0.775564\pi$
$263$	−4.14425	+	3.47744i	−0.255545	+	0.214428i	0.506011	+	0.862527i	$0.331120\pi$
$264$	0.994054	−	8.93812i	0.0611798	−	0.550103i
$265$	1.61950	−	0.589450i	0.0994852	−	0.0362097i
$266$	−23.9021	−	14.4886i	−1.46553	−	0.888353i
$267$	4.71765	−	4.50103i	0.288716	−	0.275459i
$268$	0.704033	+	3.99277i	0.0430056	+	0.243897i
$269$	0.224334	+	0.388558i	0.0136779	+	0.0236908i	0.872783	−	0.488108i	$-0.162313\pi$
$269$	0.224334	+	0.388558i	0.0136779	+	0.0236908i	−0.859105	+	0.511799i	$0.828979\pi$
$270$	−0.796520	−	0.917527i	−0.0484747	−	0.0558389i
$271$	4.59452	−	7.95793i	0.279097	−	0.483410i	−0.692064	−	0.721837i	$-0.743298\pi$
$271$	4.59452	−	7.95793i	0.279097	−	0.483410i	0.971161	+	0.238426i	$0.0766316\pi$
$272$	3.38105	−	2.83704i	0.205006	−	0.172021i
$273$	4.12340	−	5.36038i	0.249559	−	0.324425i
$274$	−1.87470	+	10.6319i	−0.113255	+	0.642299i
$275$	2.74029	−	15.5409i	0.165245	−	0.937153i
$276$	−7.16040	+	3.13633i	−0.431005	+	0.188785i
$277$	−1.20623	+	1.01215i	−0.0724755	+	0.0608142i	−0.678306	−	0.734780i	$-0.737286\pi$
$277$	−1.20623	+	1.01215i	−0.0724755	+	0.0608142i	0.605830	+	0.795594i	$0.292841\pi$
$278$	−24.9732			−1.49779
$279$	5.41743	+	17.3850i	0.324333	+	1.04081i
$280$	−0.209748	+	0.540129i	−0.0125349	+	0.0322789i
$281$	28.2751	+	10.2913i	1.68675	+	0.613926i	0.994210	−	0.107455i	$-0.0342700\pi$
$281$	28.2751	+	10.2913i	1.68675	+	0.613926i	0.692539	+	0.721381i	$0.256492\pi$
$282$	−5.58415	−	8.38769i	−0.332531	−	0.499480i
$283$	−1.15080	+	6.52652i	−0.0684080	+	0.387961i	0.931310	+	0.364227i	$0.118667\pi$
$283$	−1.15080	+	6.52652i	−0.0684080	+	0.387961i	−0.999718	+	0.0237344i	$0.992444\pi$
$284$	0.824101	−	4.67371i	0.0489014	−	0.277333i
$285$	0.774011	+	1.16260i	0.0458484	+	0.0688667i
$286$	7.68808	+	2.79823i	0.454606	+	0.165463i
$287$	20.7954	−	3.21087i	1.22751	−	0.189531i
$288$	11.1183	−	12.0521i	0.655155	−	0.710180i
$289$	−16.2195			−0.954090
$290$	−0.608123	+	0.510276i	−0.0357102	+	0.0299644i
$291$	24.3798	−	10.6786i	1.42917	−	0.625991i
$292$	−0.0174308	+	0.0988552i	−0.00102006	+	0.00578507i
$293$	1.50256	−	8.52144i	0.0877805	−	0.497828i	−0.908941	−	0.416924i	$-0.863108\pi$
$293$	1.50256	−	8.52144i	0.0877805	−	0.497828i	0.996722	−	0.0809039i	$-0.0257807\pi$
$294$	10.2204	−	18.5975i	0.596068	−	1.08463i
$295$	0.711996	−	0.597435i	0.0414540	−	0.0347840i
$296$	3.07612	−	5.32799i	0.178796	−	0.309683i
$297$	10.3662	−	12.7838i	0.601508	−	0.741788i
$298$	−14.0960	−	24.4150i	−0.816560	−	1.41432i
$299$	1.08761	+	6.16812i	0.0628978	+	0.356711i
$300$	6.63951	−	6.33465i	0.383333	−	0.365731i
$301$	−15.7623	+	8.65726i	−0.908523	+	0.498996i
$302$	−12.2552	+	4.46054i	−0.705210	+	0.256675i
$303$	0.858350	−	7.71793i	0.0493109	−	0.443383i
$304$	−23.1000	+	19.3832i	−1.32488	+	1.11170i
$305$	0.860591	−	1.49059i	0.0492773	−	0.0853508i
$306$	4.60108	−	0.590052i	0.263026	−	0.0337310i
$307$	−9.43951	+	16.3497i	−0.538741	+	0.933128i	0.460231	+	0.887799i	$0.347767\pi$
$307$	−9.43951	+	16.3497i	−0.538741	+	0.933128i	−0.998972	+	0.0453282i	$0.985567\pi$
$308$	8.74137	+	1.73444i	0.498086	+	0.0988287i
$309$	12.4375	+	18.6818i	0.707546	+	1.06277i
$310$	1.33373	−	0.485438i	0.0757508	−	0.0275710i
$311$	0.491278	−	2.78618i	0.0278578	−	0.157990i	−0.967705	−	0.252083i	$-0.918884\pi$
$311$	0.491278	−	2.78618i	0.0278578	−	0.157990i	0.995563	+	0.0940938i	$0.0299954\pi$
$312$	−2.32206	−	3.48786i	−0.131461	−	0.197461i
$313$	−12.7278	+	10.6799i	−0.719417	+	0.603662i	−0.927224	−	0.374507i	$-0.877812\pi$
$313$	−12.7278	+	10.6799i	−0.719417	+	0.603662i	0.207807	+	0.978170i	$0.433367\pi$
$314$	13.0094	−	22.5330i	0.734165	−	1.27161i
$315$	−0.856959	+	0.624565i	−0.0482842	+	0.0351903i
$316$	1.72255	+	2.98354i	0.0969010	+	0.167837i
$317$	−30.9079	−	11.2495i	−1.73596	−	0.631838i	−0.736934	−	0.675965i	$-0.763727\pi$
$317$	−30.9079	−	11.2495i	−1.73596	−	0.631838i	−0.999026	+	0.0441275i	$0.985949\pi$
$318$	−4.32267	+	38.8677i	−0.242403	+	2.17959i
$319$	−8.23749	−	6.91208i	−0.461211	−	0.387002i
$320$	0.0435375	+	0.0365323i	0.00243382	+	0.00204222i
$321$	7.83081	+	32.2359i	0.437073	+	1.79923i
$322$	6.32619	+	18.6072i	0.352545	+	1.03694i
$323$	−5.33230			−0.296697
$324$	9.26111	−	2.41505i	0.514506	−	0.134169i
$325$	−3.67627	−	6.36748i	−0.203923	−	0.353204i
$326$	8.56578	+	3.11769i	0.474415	+	0.172673i
$327$	−30.4314	−	8.92535i	−1.68286	−	0.493573i
$328$	2.26387	−	12.8390i	0.125001	−	0.708917i
$329$	−7.70807	+	4.23357i	−0.424960	+	0.233404i
$330$	−1.03327	−	0.760293i	−0.0568797	−	0.0418528i
$331$	7.10073	+	2.58445i	0.390291	+	0.142054i	0.529709	−	0.848179i	$-0.322301\pi$
$331$	7.10073	+	2.58445i	0.390291	+	0.142054i	−0.139418	+	0.990234i	$0.544523\pi$
$332$	5.68041	−	9.83875i	0.311753	−	0.539972i
$333$	10.0044	−	5.16540i	0.548239	−	0.283062i
$334$	2.98223	+	5.16538i	0.163181	+	0.282637i
$335$	−0.478634	−	0.174209i	−0.0261506	−	0.00951803i
$336$	−15.4470	−	16.8981i	−0.842702	−	0.921867i
$337$	16.8247	+	14.1176i	0.916502	+	0.769036i	0.973345	−	0.229347i	$-0.0736590\pi$
$337$	16.8247	+	14.1176i	0.916502	+	0.769036i	−0.0568430	+	0.998383i	$0.518103\pi$
$338$	−17.7992	+	6.47838i	−0.968149	+	0.352377i
$339$	−4.37445	+	8.83314i	−0.237588	+	0.479750i
$340$	−0.0217949	−	0.123605i	−0.00118200	−	0.00670343i
$341$	9.61292	+	16.6501i	0.520569	+	0.901652i
$342$	−31.4355	+	4.03135i	−1.69984	+	0.217991i
$343$	−15.4137	−	10.2673i	−0.832263	−	0.554381i
$344$	1.93480	+	10.9728i	0.104317	+	0.591613i
$345$	0.108552	−	0.976055i	0.00584424	−	0.0525490i
$346$	29.6002	+	24.8375i	1.59131	+	1.33527i
$347$	−32.4734	+	11.8193i	−1.74326	+	0.634495i	−0.999426	−	0.0338684i	$-0.989217\pi$
$347$	−32.4734	+	11.8193i	−1.74326	+	0.634495i	−0.743835	+	0.668364i	$0.766995\pi$
$348$	−1.47610	−	6.07644i	−0.0791273	−	0.325732i
$349$	−22.8048	+	19.1355i	−1.22072	+	1.02430i	−0.221928	+	0.975063i	$0.571235\pi$
$349$	−22.8048	+	19.1355i	−1.22072	+	1.02430i	−0.998787	+	0.0492390i	$0.984320\pi$
$350$	−14.4494	−	17.9860i	−0.772351	−	0.961390i
$351$	−0.128715	−	7.66727i	−0.00687030	−	0.409249i
$352$	8.65626	−	14.9931i	0.461380	−	0.799134i
$353$	−8.44879	−	3.07511i	−0.449684	−	0.163671i	0.107244	−	0.994233i	$-0.465798\pi$
$353$	−8.44879	−	3.07511i	−0.449684	−	0.163671i	−0.556927	+	0.830561i	$0.688020\pi$
$354$	4.97854	+	20.4944i	0.264607	+	1.08927i
$355$	0.456730	+	0.383242i	0.0242407	+	0.0203403i
$356$	3.76189	−	1.36922i	0.199380	−	0.0725683i
$357$	−0.171735	−	4.04478i	−0.00908919	−	0.214073i
$358$	−6.46476	−	36.6635i	−0.341673	−	1.93773i
$359$	0.901675			0.0475886			0.0237943	−	0.999717i	$-0.492425\pi$
$359$	0.901675			0.0475886			0.0237943	+	0.999717i	$0.492425\pi$
$360$	0.195463	+	0.627257i	0.0103018	+	0.0330593i
$361$	17.4313			0.917437
$362$	−5.57442	+	4.67749i	−0.292985	+	0.245844i
$363$	−0.743544	+	1.50141i	−0.0390260	+	0.0788034i
$364$	3.63937	−	1.99888i	0.190755	−	0.104770i
$365$	−0.00966045	−	0.00810608i	−0.000505651	−	0.000424292i
$366$	21.6439	+	32.5103i	1.13135	+	1.69934i
$367$	−0.486342	−	2.75818i	−0.0253868	−	0.143976i	0.969480	−	0.245172i	$-0.0788443\pi$
$367$	−0.486342	−	2.75818i	−0.0253868	−	0.143976i	−0.994867	+	0.101196i	$0.967733\pi$
$368$	21.2032			1.10529
$369$	16.1779	−	17.5367i	0.842190	−	0.912924i
$370$	−0.438795	−	0.760016i	−0.0228119	−	0.0395113i
$371$	33.4779	+	6.64258i	1.73808	+	0.344865i
$372$	−1.23577	+	11.1116i	−0.0640718	+	0.576107i
$373$	−0.126283	+	0.716185i	−0.00653867	+	0.0370827i	−0.987903	−	0.155076i	$-0.950438\pi$
$373$	−0.126283	+	0.716185i	−0.00653867	+	0.0370827i	0.981364	+	0.192159i	$0.0615488\pi$
$374$	4.60230	−	1.67510i	0.237979	−	0.0866174i
$375$	0.545259	+	2.24459i	0.0281571	+	0.115910i
$376$	0.946156	+	5.36591i	0.0487942	+	0.276726i
$377$	−5.01017			−0.258037
$378$	−4.07039	−	23.7154i	−0.209358	−	1.21979i
$379$	−8.73484			−0.448679			−0.224339	−	0.974511i	$-0.572022\pi$
$379$	−8.73484			−0.448679			−0.224339	+	0.974511i	$0.572022\pi$
$380$	0.148907	+	0.844496i	0.00763879	+	0.0433217i
$381$	4.62685	+	1.35702i	0.237040	+	0.0695225i
$382$	37.3458	−	13.5927i	1.91078	−	0.695465i
$383$	−2.84250	+	16.1206i	−0.145245	+	0.823724i	0.821925	+	0.569595i	$0.192900\pi$
$383$	−2.84250	+	16.1206i	−0.145245	+	0.823724i	−0.967170	+	0.254129i	$0.918211\pi$
$384$	−18.5246	+	8.11395i	−0.945328	+	0.414063i
$385$	−0.737797	+	0.842105i	−0.0376016	+	0.0429176i
$386$	−12.3850	−	21.4514i	−0.630379	−	1.09185i
$387$	−7.86647	+	18.8126i	−0.399875	+	0.956301i
$388$	16.3413			0.829606
$389$	−6.00443	−	34.0528i	−0.304437	−	1.72655i	−0.626144	−	0.779708i	$-0.715368\pi$
$389$	−6.00443	−	34.0528i	−0.304437	−	1.72655i	0.321707	−	0.946839i	$-0.395744\pi$
$390$	−0.596489	+	0.0380915i	−0.0302044	+	0.00192884i
$391$	2.87218	+	2.41005i	0.145252	+	0.121881i
$392$	−9.09689	+	6.99408i	−0.459462	+	0.353254i
$393$	−18.8703	+	1.20505i	−0.951879	+	0.0607866i
$394$	−6.29953	+	5.28593i	−0.317366	+	0.266301i
$395$	−0.432809			−0.0217770
$396$	8.97885	−	4.63589i	0.451204	−	0.232962i
$397$	27.1920			1.36473			0.682364	−	0.731013i	$-0.260952\pi$
$397$	27.1920			1.36473			0.682364	+	0.731013i	$0.260952\pi$
$398$	3.14394	+	17.8302i	0.157591	+	0.893745i
$399$	1.17333	+	27.6348i	0.0587399	+	1.38347i
$400$	−23.3896	+	8.51313i	−1.16948	+	0.425656i
$401$	−18.1001	−	15.1878i	−0.903875	−	0.758441i	0.0670687	−	0.997748i	$-0.478635\pi$
$401$	−18.1001	−	15.1878i	−0.903875	−	0.758441i	−0.970944	+	0.239307i	$0.923080\pi$
$402$	8.36242	−	7.97845i	0.417080	−	0.397929i
$403$	8.41749	+	3.06372i	0.419305	+	0.152615i
$404$	2.38389	−	4.12902i	0.118603	−	0.205426i
$405$	−0.318984	+	1.15930i	−0.0158504	+	0.0576062i
$406$	−15.5371	+	2.39896i	−0.771091	+	0.119059i
$407$	9.10645	−	7.64122i	0.451390	−	0.378761i
$408$	−2.40694	−	0.705939i	−0.119161	−	0.0349492i
$409$	−26.1198	+	9.50682i	−1.29154	+	0.470082i	−0.894232	−	0.447604i	$-0.852278\pi$
$409$	−26.1198	+	9.50682i	−1.29154	+	0.470082i	−0.397307	+	0.917686i	$0.630055\pi$
$410$	−1.42460	−	1.19538i	−0.0703561	−	0.0590358i
$411$	9.78603	−	4.28639i	0.482710	−	0.211432i
$412$	2.39278	+	13.5701i	0.117884	+	0.668553i
$413$	18.1909	−	2.80873i	0.895116	−	0.138208i
$414$	18.7544	+	12.0365i	0.921730	+	0.591562i
$415$	0.713632	+	1.23605i	0.0350308	+	0.0606752i
$416$	−1.40069	−	7.94370i	−0.0686744	−	0.389472i
$417$	13.6955	+	20.5714i	0.670672	+	1.00738i
$418$	−31.4438	+	11.4446i	−1.53797	+	0.559775i
$419$	−23.0519	−	19.3429i	−1.12616	−	0.944961i	−0.127262	−	0.991869i	$-0.540619\pi$
$419$	−23.0519	−	19.3429i	−1.12616	−	0.944961i	−0.998899	+	0.0469079i	$0.985063\pi$
$420$	−0.635792	+	0.140151i	−0.0310235	+	0.00683868i
$421$	26.3588	+	9.59383i	1.28465	+	0.467574i	0.891968	−	0.452100i	$-0.149325\pi$
$421$	26.3588	+	9.59383i	1.28465	+	0.467574i	0.392683	+	0.919674i	$0.371547\pi$
$422$	10.5611	+	18.2924i	0.514106	+	0.890458i
$423$	−3.84686	+	9.19976i	−0.187041	+	0.447308i
$424$	10.5733	−	18.3135i	0.513484	−	0.889381i
$425$	−4.13599	−	1.50538i	−0.200625	−	0.0730215i
$426$	−12.3924	+	5.42801i	−0.600415	+	0.262988i
$427$	29.8762	−	16.4091i	1.44581	−	0.794094i
$428$	−3.53677	+	20.0580i	−0.170956	+	0.969540i
$429$	−1.91120	−	7.86754i	−0.0922735	−	0.379849i
$430$	1.49352	+	0.543596i	0.0720239	+	0.0262145i
$431$	−0.807372	−	1.39841i	−0.0388897	−	0.0673590i	0.845925	−	0.533301i	$-0.179049\pi$
$431$	−0.807372	−	1.39841i	−0.0388897	−	0.0673590i	−0.884815	+	0.465942i	$0.845715\pi$
$432$	−25.6375	−	4.07813i	−1.23349	−	0.196209i
$433$	31.1822			1.49852			0.749260	−	0.662276i	$-0.230409\pi$
$433$	31.1822			1.49852			0.749260	+	0.662276i	$0.230409\pi$
$434$	27.5705	+	5.47045i	1.32343	+	0.262590i
$435$	0.753834	+	0.221095i	0.0361436	+	0.0106007i
$436$	−14.9156	−	12.5157i	−0.714329	−	0.599393i
$437$	−19.6233	−	16.4659i	−0.938711	−	0.787672i
$438$	0.262117	−	0.114810i	0.0125244	−	0.00548582i
$439$	−8.96222	−	3.26198i	−0.427743	−	0.155686i	0.119172	−	0.992874i	$-0.461976\pi$
$439$	−8.96222	−	3.26198i	−0.427743	−	0.155686i	−0.546916	+	0.837188i	$0.684198\pi$
$440$	0.346838	+	0.600741i	0.0165349	+	0.0286392i
$441$	−20.9244	+	1.78005i	−0.996401	+	0.0847641i
$442$	1.14096	−	1.97620i	0.0542699	−	0.0939983i
$443$	4.04078	−	3.39061i	0.191983	−	0.161093i	−0.541730	−	0.840553i	$-0.682230\pi$
$443$	4.04078	−	3.39061i	0.191983	−	0.161093i	0.733713	+	0.679460i	$0.237786\pi$
$444$	6.89874	−	0.440551i	0.327400	−	0.0209076i
$445$	−0.0873344	+	0.495298i	−0.00414005	+	0.0234794i
$446$	22.5269	−	8.19912i	1.06668	−	0.388239i
$447$	−12.3812	+	25.0008i	−0.585611	+	1.18250i
$448$	0.362298	+	1.06563i	0.0171170	+	0.0503461i
$449$	−10.3983	+	18.0105i	−0.490728	+	0.849966i	−0.999943	−	0.0106736i	$-0.996602\pi$
$449$	−10.3983	+	18.0105i	−0.490728	+	0.849966i	0.509215	+	0.860639i	$0.329936\pi$
$450$	−25.5210	−	5.74774i	−1.20307	−	0.270951i
$451$	12.5954	−	21.8159i	0.593096	−	1.02727i
$452$	−4.63601	+	3.89007i	−0.218060	+	0.182974i
$453$	10.3952	+	7.64891i	0.488409	+	0.359377i
$454$	25.4338	−	9.25715i	1.19367	−	0.434460i
$455$	−0.0111310	+	0.521521i	−0.000521828	+	0.0244493i
$456$	16.4447	+	4.82312i	0.770092	+	0.225863i
$457$	6.22843	+	35.3232i	0.291354	+	1.65235i	0.681664	+	0.731665i	$0.261256\pi$
$457$	6.22843	+	35.3232i	0.291354	+	1.65235i	−0.390311	+	0.920683i	$0.627632\pi$
$458$	20.4959	+	35.5000i	0.957712	+	1.65881i
$459$	−3.00932	−	3.46649i	−0.140463	−	0.161802i
$460$	0.301481	−	0.522180i	0.0140566	−	0.0243468i
$461$	−6.06547	+	5.08953i	−0.282497	+	0.237043i	−0.773015	−	0.634388i	$-0.781252\pi$
$461$	−6.06547	+	5.08953i	−0.282497	+	0.237043i	0.490518	+	0.871431i	$0.336808\pi$
$462$	−9.69395	−	23.4830i	−0.451004	−	1.09253i
$463$	6.37043	−	36.1285i	0.296059	−	1.67903i	−0.366808	−	0.930297i	$-0.619549\pi$
$463$	6.37043	−	36.1285i	0.296059	−	1.67903i	0.662867	−	0.748737i	$-0.269339\pi$
$464$	−2.94526	+	16.7034i	−0.136730	+	0.775435i
$465$	−1.13130	−	0.832426i	−0.0524629	−	0.0386028i
$466$	−15.5284	+	13.0299i	−0.719340	+	0.603598i
$467$	37.3212			1.72702			0.863511	−	0.504331i	$-0.168261\pi$
$467$	37.3212			1.72702			0.863511	+	0.504331i	$0.168261\pi$
$468$	1.81630	−	4.34367i	0.0839585	−	0.200786i
$469$	−6.31748	−	7.86374i	−0.291714	−	0.363114i
$470$	0.730360	+	0.265829i	0.0336890	+	0.0122618i
$471$	−25.6958	+	1.64092i	−1.18400	+	0.0756097i
$472$	1.98033	−	11.2310i	0.0911522	−	0.516950i
$473$	−3.73851	+	21.2021i	−0.171897	+	0.974875i
$474$	4.35852	−	8.80096i	0.200193	−	0.404242i
$475$	28.2579	+	10.2850i	1.29656	+	0.471910i
$476$	0.899775	−	2.31703i	0.0412411	−	0.106201i
$477$	34.3874	−	17.7546i	1.57449	−	0.812928i
$478$	14.4989			0.663163
$479$	−16.8558	+	14.1437i	−0.770161	+	0.646242i	−0.940750	−	0.339100i	$-0.889877\pi$
$479$	−16.8558	+	14.1437i	−0.770161	+	0.646242i	0.170589	+	0.985342i	$0.445433\pi$
$480$	−0.139800	+	1.25703i	−0.00638098	+	0.0573752i
$481$	0.961782	−	5.45454i	0.0438535	−	0.248706i
$482$	−2.98582	+	16.9334i	−0.136000	+	0.771297i
$483$	11.8581	−	15.4155i	0.539564	−	0.701428i
$484$	−0.788002	+	0.661212i	−0.0358183	+	0.0300551i
$485$	−1.02649	+	1.77793i	−0.0466103	+	0.0807314i
$486$	−20.3616	−	18.1609i	−0.923620	−	0.823795i
$487$	7.53232	+	13.0464i	0.341322	+	0.591187i	0.984678	−	0.174380i	$-0.0557920\pi$
$487$	7.53232	+	13.0464i	0.341322	+	0.591187i	−0.643356	+	0.765567i	$0.722459\pi$
$488$	−3.66726	−	20.7981i	−0.166009	−	0.941484i
$489$	−2.12939	−	8.76573i	−0.0962942	−	0.396400i
$490$	0.215196	+	1.62262i	0.00972156	+	0.0733026i
$491$	2.53386	−	0.922251i	0.114352	−	0.0416206i	−0.284211	−	0.958762i	$-0.591732\pi$
$491$	2.53386	−	0.922251i	0.114352	−	0.0416206i	0.398562	+	0.917141i	$0.369509\pi$
$492$	13.4181	−	5.87726i	0.604934	−	0.264967i
$493$	−2.29754	+	1.92787i	−0.103476	+	0.0868267i
$494$	−7.79527	+	13.5018i	−0.350726	+	0.607475i
$495$	−0.0596279	+	1.26810i	−0.00268007	+	0.0569967i
$496$	15.1624	−	26.2620i	0.680811	−	1.17920i
$497$	3.80068	+	11.1789i	0.170484	+	0.501443i
$498$	−32.3209	+	2.06400i	−1.44833	+	0.0924899i
$499$	18.3605	−	6.68266i	0.821927	−	0.299157i	0.103386	−	0.994641i	$-0.467032\pi$
$499$	18.3605	−	6.68266i	0.821927	−	0.299157i	0.718541	+	0.695484i	$0.244810\pi$
$500$	−0.246265	+	1.39664i	−0.0110133	+	0.0624596i
$501$	2.61944	−	5.28932i	0.117028	−	0.236309i
$502$	−3.39247	+	2.84662i	−0.151413	+	0.127051i
$503$	−0.458205	+	0.793635i	−0.0204304	+	0.0353864i	−0.876060	−	0.482202i	$-0.839837\pi$
$503$	−0.458205	+	0.793635i	−0.0204304	+	0.0353864i	0.855629	+	0.517589i	$0.173170\pi$
$504$	−3.12892	+	12.6294i	−0.139373	+	0.562556i
$505$	0.299489	+	0.518731i	0.0133271	+	0.0230832i
$506$	22.1095	+	8.04720i	0.982888	+	0.357742i
$507$	15.0977	+	11.1091i	0.670513	+	0.493372i
$508$	2.26780	+	1.90291i	0.100617	+	0.0844279i
$509$	−13.1193	−	11.0084i	−0.581505	−	0.487940i	0.303936	−	0.952692i	$-0.401699\pi$
$509$	−13.1193	−	11.0084i	−0.581505	−	0.487940i	−0.885441	+	0.464752i	$0.846143\pi$
$510$	−0.258878	+	0.246991i	−0.0114633	+	0.0109369i
$511$	−0.0803894	−	0.236449i	−0.00355622	−	0.0104599i
$512$	−10.9275			−0.482933
$513$	20.5603	+	23.6838i	0.907758	+	1.04566i
$514$	−20.1835	−	34.9588i	−0.890254	−	1.54197i
$515$	−1.62672	−	0.592079i	−0.0716820	−	0.0260901i
$516$	−9.05814	+	8.64222i	−0.398762	+	0.380452i
$517$	−1.82820	+	10.3683i	−0.0804044	+	0.455996i
$518$	0.370852	−	17.3756i	0.0162943	−	0.763441i
$519$	4.22660	−	38.0039i	0.185527	−	1.66818i
$520$	0.303706	+	0.110540i	0.0133184	+	0.00484750i
$521$	7.96109	−	13.7890i	0.348782	−	0.604108i	−0.637251	−	0.770656i	$-0.719929\pi$
$521$	7.96109	−	13.7890i	0.348782	−	0.604108i	0.986033	+	0.166548i	$0.0532621\pi$
$522$	−12.0872	+	13.1023i	−0.529041	+	0.573474i
$523$	−4.95484	−	8.58203i	−0.216660	−	0.375266i	0.737125	−	0.675757i	$-0.236183\pi$
$523$	−4.95484	−	8.58203i	−0.216660	−	0.375266i	−0.953785	+	0.300491i	$0.902850\pi$
$524$	−10.9092	−	3.97063i	−0.476572	−	0.173458i
$525$	−6.89157	+	21.7661i	−0.300773	+	0.949952i
$526$	7.25353	+	6.08643i	0.316269	+	0.265381i
$527$	5.03894	−	1.83403i	0.219500	−	0.0798914i
$528$	−27.3531	+	1.74676i	−1.19039	+	0.0760178i
$529$	−0.866156	−	4.91221i	−0.0376590	−	0.213575i
$530$	−1.50824	−	2.61234i	−0.0655136	−	0.113473i
$531$	14.1518	−	15.3403i	0.614134	−	0.665714i
$532$	−6.14744	+	15.8304i	−0.266525	+	0.686337i
$533$	−2.03810	−	11.5586i	−0.0882798	−	0.500660i
$534$	−9.19215	−	6.76369i	−0.397783	−	0.292694i
$535$	−1.96013	−	1.64475i	−0.0847439	−	0.0711086i
$536$	−5.87284	+	2.13754i	−0.253668	+	0.0923276i
$537$	−26.6558	+	25.4318i	−1.15028	+	1.09746i
$538$	0.601565	−	0.504773i	0.0259353	−	0.0217623i
$539$	−21.1395	+	6.68743i	−0.910544	+	0.288048i
$540$	−0.464965	+	0.573401i	−0.0200089	+	0.0246752i
$541$	−12.6959	+	21.9899i	−0.545837	+	0.945418i	0.452716	+	0.891655i	$0.350455\pi$
$541$	−12.6959	+	21.9899i	−0.545837	+	0.945418i	−0.998554	+	0.0537633i	$0.982878\pi$
$542$	−15.1133	−	5.50079i	−0.649172	−	0.236279i
$543$	6.91009	+	2.02669i	0.296540	+	0.0869734i
$544$	−3.69898	−	3.10381i	−0.158593	−	0.133075i
$545$	2.29863	−	0.836632i	0.0984624	−	0.0358374i
$546$	−10.4928	−	5.47821i	−0.449049	−	0.234446i
$547$	0.375540	+	2.12979i	0.0160569	+	0.0910633i	0.991783	−	0.127931i	$-0.0408336\pi$
$547$	0.375540	+	2.12979i	0.0160569	+	0.0910633i	−0.975726	+	0.218994i	$0.929722\pi$
$548$	6.55940			0.280204
$549$	14.9103	−	35.6579i	0.636355	−	1.52184i
$550$	−27.6203			−1.17774
$551$	15.6973	−	13.1716i	0.668726	−	0.561127i
$552$	−6.67783	−	10.0304i	−0.284227	−	0.426924i
$553$	−7.32978	−	4.44304i	−0.311694	−	0.188937i
$554$	2.11123	+	1.77153i	0.0896974	+	0.0752651i
$555$	−0.385415	+	0.778251i	−0.0163599	+	0.0330349i
$556$	2.63480	+	14.9427i	0.111740	+	0.633711i
$557$	−25.7724			−1.09201			−0.546006	−	0.837781i	$-0.683852\pi$
$557$	−25.7724			−1.09201			−0.546006	+	0.837781i	$0.683852\pi$
$558$	28.3195	−	14.6217i	1.19886	−	0.618986i
$559$	5.01545	+	8.68701i	0.212131	+	0.367421i
$560$	1.73215	+	0.343689i	0.0731968	+	0.0145235i
$561$	−3.90378	−	2.87245i	−0.164818	−	0.121275i
$562$	9.14516	−	51.8648i	0.385765	−	2.18778i
$563$	25.8272	−	9.40034i	1.08849	−	0.396177i	0.265427	−	0.964131i	$-0.414487\pi$
$563$	25.8272	−	9.40034i	1.08849	−	0.396177i	0.823060	+	0.567954i	$0.192265\pi$
$564$	−4.42961	+	4.22622i	−0.186520	+	0.177956i
$565$	−0.132025	−	0.748750i	−0.00555433	−	0.0315002i
$566$	11.5993			0.487557
$567$	−17.3030	+	16.3586i	−0.726659	+	0.686999i
$568$	7.31559			0.306956
$569$	−1.03329	−	5.86006i	−0.0433176	−	0.245667i	0.955459	−	0.295125i	$-0.0953614\pi$
$569$	−1.03329	−	5.86006i	−0.0433176	−	0.245667i	−0.998776	+	0.0494589i	$0.984250\pi$
$570$	1.76871	−	1.68749i	0.0740829	−	0.0706813i
$571$	−10.7965	+	3.92960i	−0.451819	+	0.164449i	−0.557899	−	0.829909i	$-0.688392\pi$
$571$	−10.7965	+	3.92960i	−0.451819	+	0.164449i	0.106080	+	0.994358i	$0.466170\pi$
$572$	0.863189	−	4.89539i	0.0360917	−	0.204686i
$573$	−31.6776	−	23.3087i	−1.32335	−	0.973737i
$574$	−11.8548	−	34.8686i	−0.494811	−	1.45539i
$575$	−10.5723	−	18.3117i	−0.440894	−	0.763651i
$576$	1.07406	+	0.689325i	0.0447524	+	0.0287219i
$577$	−15.1161			−0.629291			−0.314645	−	0.949209i	$-0.601886\pi$
$577$	−15.1161			−0.629291			−0.314645	+	0.949209i	$0.601886\pi$
$578$	4.92961	+	27.9572i	0.205045	+	1.16287i
$579$	−10.8783	+	21.9661i	−0.452088	+	0.912881i
$580$	0.369483	+	0.310033i	0.0153420	+	0.0128734i
$581$	−0.603134	+	28.2587i	−0.0250222	+	1.17237i
$582$	−25.8162	−	38.7773i	−1.07012	−	1.60737i
$583$	31.3009	−	26.2645i	1.29635	−	1.08777i
$584$	−0.154735			−0.00640297
$585$	0.358497	+	0.470461i	0.0148220	+	0.0194512i
$586$	−15.1449			−0.625628
$587$	−4.68324	−	26.5600i	−0.193298	−	1.09625i	−0.914822	−	0.403858i	$-0.867669\pi$
$587$	−4.68324	−	26.5600i	−0.193298	−	1.09625i	0.721524	−	0.692390i	$-0.243442\pi$
$588$	−12.2061	−	4.15326i	−0.503371	−	0.171278i
$589$	−34.4271	+	12.5304i	−1.41854	+	0.516307i
$590$	−1.24618	−	1.04567i	−0.0513044	−	0.0430495i
$591$	7.80893	+	2.29031i	0.321217	+	0.0942108i
$592$	−17.6195	−	6.41296i	−0.724156	−	0.263571i
$593$	5.20371	−	9.01309i	0.213691	−	0.370123i	−0.739176	−	0.673512i	$-0.764785\pi$
$593$	5.20371	−	9.01309i	0.213691	−	0.370123i	0.952867	+	0.303389i	$0.0981182\pi$
$594$	−25.1856	−	13.9826i	−1.03338	−	0.573713i
$595$	0.195572	+	0.243440i	0.00801767	+	0.00998006i
$596$	−13.1215	+	11.0102i	−0.537477	+	0.450997i
$597$	12.9632	−	12.3680i	0.530549	−	0.506188i
$598$	10.3013	−	3.74935i	0.421250	−	0.153322i
$599$	−5.33293	−	4.47486i	−0.217897	−	0.182838i	0.527305	−	0.849676i	$-0.323203\pi$
$599$	−5.33293	−	4.47486i	−0.217897	−	0.182838i	−0.745202	+	0.666839i	$0.767647\pi$
$600$	11.3937	+	8.38360i	0.465144	+	0.342259i
$601$	−6.23190	−	35.3429i	−0.254205	−	1.44167i	−0.798106	−	0.602517i	$-0.794165\pi$
$601$	−6.23190	−	35.3429i	−0.254205	−	1.44167i	0.543902	−	0.839149i	$-0.316946\pi$
$602$	19.7129	+	24.5378i	0.803439	+	1.00009i
$603$	−11.1582	−	2.51300i	−0.454396	−	0.102337i
$604$	3.96195	+	6.86230i	0.161210	+	0.279223i
$605$	−0.0224408	−	0.127268i	−0.000912349	−	0.00517419i
$606$	−13.5641	+	0.866195i	−0.551002	+	0.0351868i
$607$	−29.5961	+	10.7721i	−1.20127	+	0.437227i	−0.863668	−	0.504062i	$-0.831838\pi$
$607$	−29.5961	+	10.7721i	−1.20127	+	0.437227i	−0.337603	+	0.941289i	$0.609616\pi$
$608$	25.2722	+	21.2059i	1.02492	+	0.860012i
$609$	10.4968	+	11.4829i	0.425351	+	0.465309i
$610$	−2.83085	−	1.03034i	−0.114618	−	0.0417174i
$611$	2.45265	+	4.24812i	0.0992237	+	0.171861i
$612$	−0.838494	−	2.69080i	−0.0338941	−	0.108769i
$613$	0.891210	−	1.54362i	0.0359957	−	0.0623463i	−0.847466	−	0.530849i	$-0.821873\pi$
$613$	0.891210	−	1.54362i	0.0359957	−	0.0623463i	0.883462	+	0.468503i	$0.155206\pi$
$614$	31.0505	+	11.3015i	1.25310	+	0.456090i
$615$	−0.203419	+	1.82906i	−0.00820264	+	0.0737548i
$616$	−0.293134	+	13.7343i	−0.0118107	+	0.553369i
$617$	−5.63979	+	31.9848i	−0.227049	+	1.28766i	0.631679	+	0.775230i	$0.282366\pi$
$617$	−5.63979	+	31.9848i	−0.227049	+	1.28766i	−0.858729	+	0.512431i	$0.828745\pi$
$618$	28.4212	−	27.1162i	1.14327	−	1.09077i
$619$	−31.7594	−	11.5595i	−1.27652	−	0.464615i	−0.387240	−	0.921979i	$-0.626571\pi$
$619$	−31.7594	−	11.5595i	−1.27652	−	0.464615i	−0.889280	+	0.457364i	$0.848794\pi$
$620$	−0.431177	−	0.746820i	−0.0173165	−	0.0299930i
$621$	−0.370161	−	22.0497i	−0.0148540	−	0.884822i
$622$	−4.95178			−0.198548
$623$	−6.56356	+	7.49151i	−0.262963	+	0.300141i
$624$	−9.23960	+	8.81535i	−0.369880	+	0.352896i
$625$	18.9463	+	15.8978i	0.757851	+	0.635912i
$626$	22.2770	+	18.6926i	0.890367	+	0.747107i
$627$	26.6714	+	19.6252i	1.06515	+	0.783753i
$628$	−14.8552	−	5.40684i	−0.592786	−	0.215756i
$629$	−1.65780	−	2.87140i	−0.0661010	−	0.114490i
$630$	1.33700	+	1.28729i	0.0532674	+	0.0512870i
$631$	−4.20986	+	7.29169i	−0.167592	+	0.290278i	−0.937573	−	0.347789i	$-0.886932\pi$
$631$	−4.20986	+	7.29169i	−0.167592	+	0.290278i	0.769981	+	0.638067i	$0.220266\pi$
$632$	−4.06813	+	3.41357i	−0.161822	+	0.135785i
$633$	9.27632	−	18.7313i	0.368700	−	0.744501i
$634$	−9.99671	+	56.6942i	−0.397020	+	2.25161i
$635$	−0.349487	+	0.127203i	−0.0138690	+	0.00504789i
$636$	23.7125	−	1.51427i	0.940262	−	0.0600447i
$637$	−5.54222	+	8.71788i	−0.219591	+	0.345415i
$638$	−9.41054	+	16.2995i	−0.372567	+	0.645305i
$639$	11.2674	+	7.23134i	0.445730	+	0.286067i
$640$	0.779957	−	1.35092i	0.0308305	−	0.0534000i
$641$	−13.7190	+	11.5116i	−0.541866	+	0.454680i	−0.872176	−	0.489193i	$-0.837291\pi$
$641$	−13.7190	+	11.5116i	−0.541866	+	0.454680i	0.330309	+	0.943873i	$0.392847\pi$
$642$	53.1842	−	23.2952i	2.09901	−	0.919389i
$643$	−6.42598	+	2.33887i	−0.253416	+	0.0922359i	−0.465605	−	0.884993i	$-0.654163\pi$
$643$	−6.42598	+	2.33887i	−0.253416	+	0.0922359i	0.212189	+	0.977229i	$0.431941\pi$
$644$	10.4662	−	5.74842i	0.412425	−	0.226520i
$645$	−0.371277	−	1.52838i	−0.0146190	−	0.0601800i
$646$	1.62065	+	9.19114i	0.0637634	+	0.361620i
$647$	20.1014	+	34.8167i	0.790269	+	1.36879i	0.925800	+	0.378013i	$0.123393\pi$
$647$	20.1014	+	34.8167i	0.790269	+	1.36879i	−0.135531	+	0.990773i	$0.543274\pi$
$648$	6.14518	+	13.4125i	0.241406	+	0.526894i
$649$	11.0179	−	19.0836i	0.432492	−	0.749098i
$650$	−9.85813	+	8.27195i	−0.386668	+	0.324453i
$651$	−10.6137	−	25.7109i	−0.415982	−	1.00769i
$652$	0.961733	−	5.45426i	0.0376644	−	0.213605i
$653$	0.111827	−	0.634200i	0.00437611	−	0.0248182i	−0.982542	−	0.186043i	$-0.940433\pi$
$653$	0.111827	−	0.634200i	0.00437611	−	0.0248182i	0.986918	+	0.161225i	$0.0515446\pi$
$654$	−6.13535	+	55.1666i	−0.239911	+	2.15718i
$655$	1.11727	−	0.937498i	0.0436552	−	0.0366311i
$656$	−39.7333			−1.55133
$657$	−0.238320	−	0.152953i	−0.00929775	−	0.00596725i
$658$	9.64001	+	11.9995i	0.375807	+	0.467789i
$659$	20.0522	+	7.29841i	0.781123	+	0.284306i	0.701641	−	0.712531i	$-0.252451\pi$
$659$	20.0522	+	7.29841i	0.781123	+	0.284306i	0.0794822	+	0.996836i	$0.474673\pi$
$660$	−0.345905	+	0.698472i	−0.0134643	+	0.0271880i
$661$	4.74455	−	26.9077i	0.184542	−	1.04659i	−0.742002	−	0.670398i	$-0.766123\pi$
$661$	4.74455	−	26.9077i	0.184542	−	1.04659i	0.926543	−	0.376189i	$-0.122766\pi$
$662$	2.29663	−	13.0248i	0.0892610	−	0.506224i
$663$	−2.25358	+	0.143913i	−0.0875219	+	0.00558911i
$664$	16.4564	+	5.98964i	0.638632	+	0.232443i
$665$	−1.33619	−	1.66323i	−0.0518151	−	0.0644973i
$666$	−11.9441	−	15.6744i	−0.462825	−	0.607372i
$667$	−14.4083			−0.557892
$668$	2.77606	−	2.32939i	0.107409	−	0.0901268i
$669$	−19.1079	−	14.0598i	−0.738753	−	0.543583i
$670$	−0.154807	+	0.877956i	−0.00598073	+	0.0339184i
$671$	7.08605	−	40.1870i	0.273554	−	1.55140i
$672$	−15.2717	+	19.8531i	−0.589118	+	0.765848i
$673$	11.9391	−	10.0181i	0.460220	−	0.386171i	−0.382992	−	0.923752i	$-0.625106\pi$
$673$	11.9391	−	10.0181i	0.460220	−	0.386171i	0.843212	+	0.537581i	$0.180662\pi$
$674$	19.2206	−	33.2911i	0.740352	−	1.28233i
$675$	9.26131	+	24.1747i	0.356468	+	0.930486i
$676$	5.75424	+	9.96663i	0.221317	+	0.383332i
$677$	0.197954	+	1.12265i	0.00760797	+	0.0431470i	0.988375	−	0.152033i	$-0.0485820\pi$
$677$	0.197954	+	1.12265i	0.00760797	+	0.0431470i	−0.980767	+	0.195180i	$0.937471\pi$
$678$	16.5550	+	4.85547i	0.635790	+	0.186473i
$679$	−35.6353	+	19.5723i	−1.36756	+	0.751116i
$680$	0.181807	−	0.0661724i	0.00697198	−	0.00253759i
$681$	−21.5736	−	15.8741i	−0.826702	−	0.608297i
$682$	25.7776	−	21.6300i	0.987076	−	0.828256i
$683$	−15.4945	+	26.8373i	−0.592881	+	1.02690i	0.400961	+	0.916095i	$0.368676\pi$
$683$	−15.4945	+	26.8373i	−0.592881	+	1.02690i	−0.993842	+	0.110805i	$0.964657\pi$
$684$	5.72876	+	18.3841i	0.219045	+	0.702932i
$685$	−0.412030	+	0.713658i	−0.0157429	+	0.0272675i
$686$	−13.0127	+	29.6888i	−0.496829	+	1.13352i
$687$	18.0026	−	36.3518i	0.686841	−	1.38691i
$688$	31.9099	−	11.6143i	1.21655	−	0.442790i
$689$	3.30586	−	18.7484i	0.125943	−	0.714259i
$690$	−1.71539	+	0.109544i	−0.0653039	+	0.00417028i
$691$	24.0267	−	20.1608i	0.914020	−	0.766954i	−0.0588598	−	0.998266i	$-0.518747\pi$
$691$	24.0267	−	20.1608i	0.914020	−	0.766954i	0.972879	+	0.231313i	$0.0743021\pi$
$692$	11.7385	−	20.3317i	0.446231	−	0.772895i
$693$	−14.0276	+	20.8635i	−0.532863	+	0.792540i
$694$	30.2423	+	52.3812i	1.14798	+	1.98836i
$695$	−1.79126	−	0.651965i	−0.0679463	−	0.0247304i
$696$	8.82933	−	3.86734i	0.334675	−	0.146591i
$697$	−5.38227	−	4.51626i	−0.203868	−	0.171066i
$698$	39.9145	+	33.4922i	1.51079	+	1.26770i
$699$	19.2491	+	5.64564i	0.728069	+	0.213538i
$700$	−9.23740	+	10.5434i	−0.349141	+	0.398502i
$701$	−17.8979			−0.675996			−0.337998	−	0.941147i	$-0.609750\pi$
$701$	−17.8979			−0.675996			−0.337998	+	0.941147i	$0.609750\pi$
$702$	−13.1768	+	2.55218i	−0.497324	+	0.0963257i
$703$	11.3265	+	19.6180i	0.427185	+	0.739906i
$704$	1.26620	+	0.460859i	0.0477217	+	0.0173693i
$705$	−0.181562	−	0.747409i	−0.00683802	−	0.0281490i
$706$	−2.73264	+	15.4976i	−0.102844	+	0.583259i
$707$	−0.253116	+	11.8593i	−0.00951943	+	0.446015i
$708$	11.7376	−	5.14117i	0.441124	−	0.193217i
$709$	−2.47833	−	0.902038i	−0.0930756	−	0.0338768i	0.295063	−	0.955478i	$-0.404659\pi$
$709$	−2.47833	−	0.902038i	−0.0930756	−	0.0338768i	−0.388138	+	0.921601i	$0.626882\pi$
$710$	0.521770	−	0.903731i	0.0195817	−	0.0339164i
$711$	−9.63993	+	1.23625i	−0.361526	+	0.0463628i
$712$	3.08553	+	5.34429i	0.115635	+	0.200286i
$713$	24.2071	+	8.81068i	0.906565	+	0.329963i
$714$	−6.91969	+	1.52535i	−0.258963	+	0.0570847i
$715$	0.478393	+	0.401419i	0.0178909	+	0.0150122i
$716$	−21.2555	+	7.73637i	−0.794355	+	0.289122i
$717$	−7.95130	−	11.9433i	−0.296947	−	0.446030i
$718$	−0.274046	−	1.55419i	−0.0102273	−	0.0580020i
$719$	−11.3325	−	19.6285i	−0.422631	−	0.732018i	0.573565	−	0.819160i	$-0.305560\pi$
$719$	−11.3325	−	19.6285i	−0.422631	−	0.732018i	−0.996196	+	0.0871418i	$0.972227\pi$
$720$	1.77921	−	0.918628i	0.0663073	−	0.0342352i
$721$	−21.4711	−	26.7263i	−0.799626	−	0.995341i
$722$	−5.29790	−	30.0459i	−0.197167	−	1.11819i
$723$	15.5862	−	6.82690i	0.579656	−	0.253895i
$724$	3.38690	+	2.84195i	0.125873	+	0.105620i
$725$	15.8941	−	5.78497i	0.590291	−	0.214848i
$726$	2.81392	+	0.825305i	0.104434	+	0.0306299i
$727$	−5.87837	+	4.93253i	−0.218017	+	0.182938i	−0.745255	−	0.666780i	$-0.767672\pi$
$727$	−5.87837	+	4.93253i	−0.218017	+	0.182938i	0.527238	+	0.849718i	$0.323228\pi$
$728$	4.00862	+	4.98976i	0.148569	+	0.184933i
$729$	−3.79335	+	26.7322i	−0.140495	+	0.990081i
$730$	−0.0110361	+	0.0191151i	−0.000408466	+	0.000707483i
$731$	5.64264	+	2.05375i	0.208700	+	0.0759608i
$732$	17.1690	−	16.3806i	0.634584	−	0.605446i
$733$	37.7160	+	31.6475i	1.39307	+	1.16893i	0.964078	+	0.265619i	$0.0855764\pi$
$733$	37.7160	+	31.6475i	1.39307	+	1.16893i	0.428994	+	0.903307i	$0.358868\pi$
$734$	−4.60639	+	1.67659i	−0.170025	+	0.0618840i
$735$	1.21860	−	1.06712i	0.0449487	−	0.0393615i
$736$	−4.02812	−	22.8446i	−0.148479	−	0.842064i
$737$	−12.0760			−0.444827
$738$	−35.1445	−	22.5556i	−1.29369	−	0.830282i
$739$	4.41390			0.162368			0.0811840	−	0.996699i	$-0.474130\pi$
$739$	4.41390			0.162368			0.0811840	+	0.996699i	$0.474130\pi$
$740$	−0.408459	+	0.342738i	−0.0150153	+	0.0125993i
$741$	15.3969	−	0.983242i	0.565621	−	0.0361203i
$742$	1.27470	−	59.7238i	0.0467958	−	2.19253i
$743$	−17.5719	−	14.7446i	−0.644650	−	0.540925i	0.260792	−	0.965395i	$-0.416016\pi$
$743$	−17.5719	−	14.7446i	−0.644650	−	0.540925i	−0.905442	+	0.424469i	$0.860461\pi$
$744$	−17.1989	+	1.09831i	−0.630541	+	0.0402661i
$745$	−0.373676	−	2.11922i	−0.0136904	−	0.0776422i
$746$	1.27285			0.0466024
$747$	19.4252	+	25.4920i	0.710732	+	0.932704i
$748$	−1.48786	−	2.57705i	−0.0544016	−	0.0942263i
$749$	−16.3112	−	47.9762i	−0.596000	−	1.75301i
$750$	3.70321	−	1.62205i	0.135222	−	0.0592288i
$751$	−5.62655	+	31.9097i	−0.205316	+	1.16440i	0.691627	+	0.722255i	$0.256894\pi$
$751$	−5.62655	+	31.9097i	−0.205316	+	1.16440i	−0.896942	+	0.442147i	$0.854217\pi$
$752$	15.6046	−	5.67961i	0.569041	−	0.207114i
$753$	4.20533	+	1.23340i	0.153251	+	0.0449474i
$754$	1.52274	+	8.63590i	0.0554550	+	0.314501i
$755$	−0.995484			−0.0362294
$756$	−13.7606	+	4.93761i	−0.500469	+	0.179579i
$757$	35.6150			1.29445			0.647224	−	0.762300i	$-0.275930\pi$
$757$	35.6150			1.29445			0.647224	+	0.762300i	$0.275930\pi$
$758$	2.65478	+	15.0560i	0.0964261	+	0.546859i
$759$	−5.49625	−	22.6256i	−0.199501	−	0.821257i
$760$	−1.24214	+	0.452103i	−0.0450572	+	0.0163995i
$761$	6.51564	−	36.9520i	0.236192	−	1.33951i	−0.603898	−	0.797062i	$-0.706387\pi$
$761$	6.51564	−	36.9520i	0.236192	−	1.33951i	0.840090	−	0.542448i	$-0.182502\pi$
$762$	0.932829	−	8.38761i	0.0337928	−	0.303851i
$763$	47.5166	+	9.42809i	1.72022	+	0.341320i
$764$	−12.0734	−	20.9117i	−0.436799	−	0.756558i
$765$	0.345427	+	0.0777956i	0.0124889	+	0.00281270i
$766$	28.6506			1.03519
$767$	−1.78284	−	10.1110i	−0.0643746	−	0.365086i
$768$	18.7993	+	28.2375i	0.678362	+	1.01893i
$769$	−14.8702	−	12.4776i	−0.536233	−	0.449953i	0.334014	−	0.942568i	$-0.391597\pi$
$769$	−14.8702	−	12.4776i	−0.536233	−	0.449953i	−0.870247	+	0.492615i	$0.836041\pi$
$770$	1.67575	+	1.01578i	0.0603899	+	0.0366061i
$771$	−17.7281	+	35.7976i	−0.638462	+	1.28922i
$772$	−11.5288	+	9.67377i	−0.414929	+	0.348167i
$773$	−47.6507			−1.71388			−0.856938	−	0.515420i	$-0.827636\pi$
$773$	−47.6507			−1.71388			−0.856938	+	0.515420i	$0.827636\pi$
$774$	34.8177	+	7.84150i	1.25150	+	0.281857i
$775$	−30.2408			−1.08628
$776$	4.37419	+	24.8073i	0.157024	+	0.890529i
$777$	−14.5163	+	9.22345i	−0.520771	+	0.330889i
$778$	−56.8710	+	20.6994i	−2.03893	+	0.742108i
$779$	36.7727	+	30.8560i	1.31752	+	1.10553i
$780$	0.0857246	+	0.352890i	0.00306943	+	0.0126355i
$781$	13.2830	+	4.83463i	0.475305	+	0.172997i
$782$	3.28119	−	5.68319i	0.117335	−	0.203230i
$783$	17.4216	+	2.77123i	0.622597	+	0.0990356i
$784$	25.8065	+	23.6020i	0.921659	+	0.842930i
$785$	1.52139	−	1.27660i	0.0543008	−	0.0455637i
$786$	7.81235	+	32.1599i	0.278657	+	1.14711i
$787$	35.1534	−	12.7948i	1.25308	−	0.456085i	0.371640	−	0.928377i	$-0.378795\pi$
$787$	35.1534	−	12.7948i	1.25308	−	0.456085i	0.881442	+	0.472292i	$0.156573\pi$
$788$	3.82746	+	3.21162i	0.136348	+	0.114409i
$789$	1.03573	−	9.31285i	0.0368730	−	0.331546i
$790$	0.131544	+	0.746022i	0.00468012	+	0.0265423i
$791$	5.45047	−	14.0357i	0.193796	−	0.499050i
$792$	9.44101	+	12.3896i	0.335472	+	0.440245i
$793$	−9.50638	−	16.4655i	−0.337581	−	0.584708i
$794$	−8.26447	−	46.8702i	−0.293295	−	1.66336i
$795$	−1.32476	+	2.67502i	−0.0469842	+	0.0948732i
$796$	10.3370	−	3.76235i	0.366384	−	0.133353i
$797$	−22.8982	−	19.2139i	−0.811096	−	0.680590i	0.139773	−	0.990184i	$-0.455363\pi$
$797$	−22.8982	−	19.2139i	−0.811096	−	0.680590i	−0.950869	+	0.309593i	$0.899807\pi$
$798$	47.2767	−	10.4215i	1.67358	−	0.368916i
$799$	2.75936	+	1.00433i	0.0976192	+	0.0355305i
$800$	13.6157	+	23.5830i	0.481386	+	0.833785i
$801$	−0.530459	+	11.2812i	−0.0187429	+	0.398601i
$802$	−20.6776	+	35.8147i	−0.730152	+	1.26466i
$803$	−0.280955	−	0.102259i	−0.00991467	−	0.00360864i
$804$	−5.65618	−	4.16188i	−0.199478	−	0.146778i
$805$	−0.0320106	+	1.49980i	−0.00112823	+	0.0528610i
$806$	2.72252	−	15.4402i	0.0958966	−	0.543857i
$807$	−0.745704	−	0.218710i	−0.0262500	−	0.00769897i
$808$	6.90624	+	2.51366i	0.242961	+	0.0884304i
$809$	−4.28914	−	7.42901i	−0.150798	−	0.261190i	0.780723	−	0.624877i	$-0.214851\pi$
$809$	−4.28914	−	7.42901i	−0.150798	−	0.261190i	−0.931521	+	0.363687i	$0.881518\pi$
$810$	2.09521	+	0.197477i	0.0736182	+	0.00693862i
$811$	−28.4524			−0.999098			−0.499549	−	0.866286i	$-0.666501\pi$
$811$	−28.4524			−0.999098			−0.499549	+	0.866286i	$0.666501\pi$
$812$	3.07466	+	9.04348i	0.107899	+	0.317364i
$813$	3.75705	+	15.4661i	0.131765	+	0.542419i
$814$	−15.9387	−	13.3742i	−0.558651	−	0.468764i
$815$	0.533008	+	0.447247i	0.0186704	+	0.0156664i
$816$	−0.844991	+	7.59781i	−0.0295806	+	0.265977i
$817$	−38.5516	−	14.0316i	−1.34875	−	0.490905i
$818$	24.3252	+	42.1326i	0.850512	+	1.47313i
$819$	1.24172	+	11.6476i	0.0433891	+	0.407000i
$820$	−0.564954	+	0.978529i	−0.0197291	+	0.0341717i
$821$	−35.0751	+	29.4315i	−1.22413	+	1.02717i	−0.225531	+	0.974236i	$0.572412\pi$
$821$	−35.0751	+	29.4315i	−1.22413	+	1.02717i	−0.998598	+	0.0529300i	$0.983144\pi$
$822$	−10.3626	−	15.5652i	−0.361437	−	0.542898i
$823$	−7.19638	+	40.8127i	−0.250850	+	1.42264i	0.555654	+	0.831413i	$0.312468\pi$
$823$	−7.19638	+	40.8127i	−0.250850	+	1.42264i	−0.806504	+	0.591228i	$0.798643\pi$
$824$	−19.9599	+	7.26481i	−0.695336	+	0.253082i
$825$	15.1472	+	22.7519i	0.527359	+	0.792121i
$826$	−10.3701	−	30.5015i	−0.360822	−	1.06128i
$827$	3.73938	−	6.47679i	0.130031	−	0.225220i	−0.793657	−	0.608365i	$-0.791826\pi$
$827$	3.73938	−	6.47679i	0.130031	−	0.225220i	0.923688	+	0.383145i	$0.125159\pi$
$828$	5.22334	−	12.4916i	0.181524	−	0.434113i
$829$	−4.77827	+	8.27620i	−0.165956	+	0.287444i	−0.936994	−	0.349344i	$-0.886404\pi$
$829$	−4.77827	+	8.27620i	−0.165956	+	0.287444i	0.771038	+	0.636789i	$0.219738\pi$
$830$	1.91365	−	1.60574i	0.0664237	−	0.0557361i
$831$	0.301462	−	2.71062i	0.0104576	−	0.0940304i
$832$	0.589948	−	0.214724i	0.0204528	−	0.00744420i
$833$	0.813028	+	6.13040i	0.0281697	+	0.212406i
$834$	31.2959	−	29.8589i	1.08369	−	1.03393i
$835$	0.0790570	+	0.448354i	0.00273588	+	0.0155159i
$836$	10.1654	+	17.6069i	0.351576	+	0.608948i
$837$	−27.5751	−	15.3092i	−0.953135	−	0.529163i
$838$	−26.3346	+	45.6129i	−0.909715	+	1.57567i
$839$	−23.6307	+	19.8285i	−0.815822	+	0.684556i	−0.951990	−	0.306130i	$-0.900966\pi$
$839$	−23.6307	+	19.8285i	−0.815822	+	0.684556i	0.136168	+	0.990686i	$0.456521\pi$
$840$	−0.382945	−	0.927660i	−0.0132129	−	0.0320073i
$841$	−3.03439	+	17.2089i	−0.104634	+	0.593410i
$842$	8.52538	−	48.3499i	0.293804	−	1.66625i
$843$	−47.7383	+	20.9099i	−1.64419	+	0.720174i
$844$	9.83096	−	8.24916i	0.338396	−	0.283948i
$845$	−1.44582			−0.0497376
$846$	17.0266	+	3.83465i	0.585385	+	0.131838i
$847$	0.926439	−	2.38570i	0.0318328	−	0.0819736i
$848$	−60.5620	−	22.0428i	−2.07971	−	0.756951i
$849$	−6.36118	−	9.55483i	−0.218315	−	0.327921i
$850$	−1.33773	+	7.58663i	−0.0458837	+	0.260219i
$851$	2.76591	−	15.6862i	0.0948141	−	0.537718i
$852$	4.55531	+	6.84231i	0.156062	+	0.234414i
$853$	−25.0473	−	9.11647i	−0.857603	−	0.312142i	−0.124467	−	0.992224i	$-0.539722\pi$
$853$	−25.0473	−	9.11647i	−0.857603	−	0.312142i	−0.733136	+	0.680082i	$0.761944\pi$
$854$	−37.3643	−	46.5095i	−1.27858	−	1.59152i
$855$	−2.36002	−	0.531515i	−0.0807111	−	0.0181774i
$856$	−31.3961			−1.07310
$857$	12.3350	−	10.3503i	0.421357	−	0.353560i	−0.407322	−	0.913285i	$-0.633537\pi$
$857$	12.3350	−	10.3503i	0.421357	−	0.353560i	0.828679	+	0.559724i	$0.189093\pi$
$858$	−12.9802	+	5.68547i	−0.443137	+	0.194099i
$859$	3.38068	−	19.1728i	0.115347	−	0.654167i	−0.871230	−	0.490875i	$-0.836677\pi$
$859$	3.38068	−	19.1728i	0.115347	−	0.654167i	0.986578	−	0.163293i	$-0.0522116\pi$
$860$	0.167687	−	0.950998i	0.00571806	−	0.0324288i
$861$	−22.2213	+	28.8875i	−0.757301	+	0.984484i
$862$	−2.16502	+	1.81666i	−0.0737407	+	0.0618758i
$863$	13.6639	−	23.6665i	0.465124	−	0.805619i	−0.534083	−	0.845432i	$-0.679343\pi$
$863$	13.6639	−	23.6665i	0.465124	−	0.805619i	0.999207	+	0.0398134i	$0.0126764\pi$
$864$	0.476717	+	28.3970i	0.0162182	+	0.966085i
$865$	1.47472	+	2.55428i	0.0501418	+	0.0868482i
$866$	−9.47720	−	53.7479i	−0.322048	−	1.82643i
$867$	20.3260	−	19.3927i	0.690306	−	0.658609i
$868$	0.364414	−	17.0739i	0.0123690	−	0.579527i
$869$	−9.64249	+	3.50958i	−0.327099	+	0.119054i
$870$	0.151982	−	1.36656i	0.00515268	−	0.0463308i
$871$	−4.31013	+	3.61662i	−0.146043	+	0.122545i
$872$	15.0071	−	25.9931i	0.508205	−	0.880237i
$873$	−17.7845	+	42.5316i	−0.601914	+	1.43948i
$874$	−22.4178	+	38.8287i	−0.758292	+	1.31340i
$875$	−1.13575	−	3.34059i	−0.0383954	−	0.112932i
$876$	−0.0963509	−	0.144724i	−0.00325540	−	0.00488978i
$877$	11.7221	−	4.26650i	0.395828	−	0.144070i	−0.136434	−	0.990649i	$-0.543564\pi$
$877$	11.7221	−	4.26650i	0.395828	−	0.144070i	0.532262	+	0.846580i	$0.321342\pi$
$878$	−2.89870	+	16.4394i	−0.0978264	+	0.554801i
$879$	8.30556	+	12.4754i	0.280140	+	0.420784i
$880$	1.61951	−	1.35893i	0.0545938	−	0.0458097i
$881$	−5.29900	+	9.17814i	−0.178528	+	0.309219i	−0.941377	−	0.337358i	$-0.890467\pi$
$881$	−5.29900	+	9.17814i	−0.178528	+	0.309219i	0.762849	+	0.646577i	$0.223800\pi$
$882$	9.42778	+	35.5259i	0.317450	+	1.19622i
$883$	4.21221	+	7.29577i	0.141752	+	0.245522i	0.928157	−	0.372190i	$-0.121393\pi$
$883$	4.21221	+	7.29577i	0.141752	+	0.245522i	−0.786404	+	0.617712i	$0.788060\pi$
$884$	−1.30283	−	0.474193i	−0.0438191	−	0.0159488i
$885$	−0.177942	+	1.59998i	−0.00598146	+	0.0537828i
$886$	−7.07242	−	5.93447i	−0.237603	−	0.199372i
$887$	−16.0010	−	13.4265i	−0.537262	−	0.450816i	0.333338	−	0.942807i	$-0.391825\pi$
$887$	−16.0010	−	13.4265i	−0.537262	−	0.450816i	−0.870600	+	0.491991i	$0.836269\pi$
$888$	2.51542	+	10.3548i	0.0844118	+	0.347485i
$889$	−7.22450	−	1.43346i	−0.242302	−	0.0480768i
$890$	0.880276			0.0295069
$891$	2.29401	+	28.4145i	0.0768522	+	0.951922i
$892$	−7.28264	−	12.6139i	−0.243841	−	0.422344i
$893$	−18.8525	−	6.86175i	−0.630875	−	0.229620i
$894$	46.8563	+	13.7426i	1.56711	+	0.459623i
$895$	0.493459	−	2.79854i	0.0164945	−	0.0935450i
$896$	27.0769	−	14.8717i	0.904575	−	0.496828i
$897$	−8.73778	−	6.42937i	−0.291746	−	0.214670i
$898$	34.2045	+	12.4494i	1.14142	+	0.415443i
$899$	−10.3034	+	17.8460i	−0.343636	+	0.595196i
$900$	−0.746556	+	15.8769i	−0.0248852	+	0.529230i
$901$	−5.69824	−	9.86964i	−0.189836	−	0.328805i
$902$	−41.4317	−	15.0799i	−1.37952	−	0.502106i
$903$	9.40201	−	29.6950i	0.312879	−	0.988189i
$904$	−7.14634	−	5.99650i	−0.237684	−	0.199440i
$905$	−0.521951	+	0.189975i	−0.0173502	+	0.00631497i
$906$	10.0248	−	20.2427i	0.333052	−	0.672518i
$907$	5.65612	+	32.0775i	0.187808	+	1.06511i	0.922294	+	0.386490i	$0.126313\pi$
$907$	5.65612	+	32.0775i	0.187808	+	1.06511i	−0.734485	+	0.678625i	$0.762576\pi$
$908$	−8.22240	−	14.2416i	−0.272870	−	0.472625i
$909$	8.15217	+	10.6982i	0.270390	+	0.354837i
$910$	0.902315	−	0.139320i	0.0299115	−	0.00461841i
$911$	2.94200	+	16.6849i	0.0974727	+	0.552795i	0.993962	+	0.109729i	$0.0349983\pi$
$911$	2.94200	+	16.6849i	0.0974727	+	0.552795i	−0.896489	+	0.443066i	$0.853891\pi$
$912$	5.77315	−	51.9098i	0.191168	−	1.71890i
$913$	25.9218	+	21.7510i	0.857886	+	0.719852i
$914$	58.9926	−	21.4716i	1.95130	−	0.710216i
$915$	0.703726	+	2.89692i	0.0232645	+	0.0957694i
$916$	19.0790	−	16.0092i	0.630387	−	0.528957i
$917$	28.5453	−	4.40746i	0.942648	−	0.145547i
$918$	−5.06048	+	6.24065i	−0.167021	+	0.205972i
$919$	−17.8114	+	30.8502i	−0.587544	+	1.01766i	0.407009	+	0.913424i	$0.366572\pi$
$919$	−17.8114	+	30.8502i	−0.587544	+	1.01766i	−0.994553	+	0.104231i	$0.966762\pi$
$920$	0.873404	+	0.317893i	0.0287953	+	0.0104806i
$921$	−7.71892	−	31.7753i	−0.254347	−	1.04703i
$922$	10.6162	+	8.90802i	0.349625	+	0.293370i
$923$	6.18884	−	2.25255i	0.203708	−	0.0741437i
$924$	−13.0282	+	8.27794i	−0.428598	+	0.272324i
$925$	3.24694	+	18.4143i	0.106759	+	0.605458i
$926$	−64.2099			−2.11007
$927$	−37.9231	−	8.54088i	−1.24556	−	0.280519i
$928$	18.5560			0.609130
$929$	30.9442	−	25.9653i	1.01525	−	0.851892i	0.0262232	−	0.999656i	$-0.491652\pi$
$929$	30.9442	−	25.9653i	1.01525	−	0.851892i	0.989023	+	0.147764i	$0.0472075\pi$
$930$	−1.09099	+	2.20300i	−0.0357751	+	0.0722391i
$931$	−5.55477	−	41.8841i	−0.182050	−	1.37270i
$932$	9.43474	+	7.91669i	0.309045	+	0.259320i
$933$	2.71560	+	4.07897i	0.0889046	+	0.133539i
$934$	−11.3431	−	64.3296i	−0.371156	−	2.10493i
$935$	0.373841			0.0122259
$936$	7.08017	+	1.59457i	0.231423	+	0.0521200i
$937$	−0.0121839	−	0.0211031i	−0.000398029	−	0.000689407i	0.865826	−	0.500345i	$-0.166793\pi$
$937$	−0.0121839	−	0.0211031i	−0.000398029	−	0.000689407i	−0.866224	+	0.499655i	$0.833460\pi$
$938$	−11.6344	+	13.2793i	−0.379878	+	0.433585i
$939$	3.18093	−	28.6016i	0.103806	−	0.933377i
$940$	0.0820021	−	0.465057i	0.00267461	−	0.0151685i
$941$	21.5793	−	7.85424i	0.703467	−	0.256041i	0.0345763	−	0.999402i	$-0.488992\pi$
$941$	21.5793	−	7.85424i	0.703467	−	0.256041i	0.668890	+	0.743361i	$0.266770\pi$
$942$	10.6381	+	43.7924i	0.346609	+	1.42683i
$943$	−5.86119	−	33.2405i	−0.190867	−	1.08246i
$944$	−34.7570			−1.13124
$945$	0.327169	−	1.80730i	0.0106428	−	0.0587915i
$946$	37.6818			1.22514
$947$	2.31074	+	13.1049i	0.0750890	+	0.425851i	0.999058	+	0.0433845i	$0.0138141\pi$
$947$	2.31074	+	13.1049i	0.0750890	+	0.425851i	−0.923969	+	0.382466i	$0.875075\pi$
$948$	−5.72589	−	1.67937i	−0.185968	−	0.0545433i
$949$	−0.130902	+	0.0476446i	−0.00424927	+	0.00154661i
$950$	9.13962	−	51.8334i	0.296528	−	1.68170i
$951$	52.1834	−	22.8569i	1.69216	−	0.741185i
$952$	3.75826	+	0.745703i	0.121806	+	0.0241684i
$953$	−0.430414	−	0.745498i	−0.0139425	−	0.0241491i	0.858970	−	0.512026i	$-0.171105\pi$
$953$	−0.430414	−	0.745498i	−0.0139425	−	0.0241491i	−0.872912	+	0.487877i	$0.837772\pi$
$954$	−41.0545	−	53.8765i	−1.32919	−	1.74431i
$955$	3.03357			0.0981639
$956$	−1.52970	−	8.67538i	−0.0494742	−	0.280582i
$957$	18.5874	−	1.18698i	0.600844	−	0.0383697i
$958$	29.5021	+	24.7552i	0.953169	+	0.799804i
$959$	−14.3040	+	7.85631i	−0.461900	+	0.253693i
$960$	−0.0982397	+	0.00627354i	−0.00317067	+	0.000202478i
$961$	4.47591	−	3.75573i	0.144384	−	0.121153i
$962$	−9.69416			−0.312552
$963$	−48.3558	−	31.0345i	−1.55824	−	1.00007i
$964$	10.4471			0.336479
$965$	−0.328317	−	1.86198i	−0.0105689	−	0.0599393i
$966$	−30.1753	−	15.7543i	−0.970874	−	0.506887i
$967$	17.5971	−	6.40483i	0.565886	−	0.205966i	−0.0432048	−	0.999066i	$-0.513757\pi$
$967$	17.5971	−	6.40483i	0.565886	−	0.205966i	0.609091	+	0.793101i	$0.291535\pi$
$968$	−1.21469	−	1.01925i	−0.0390418	−	0.0327599i
$969$	6.68231	−	6.37548i	0.214667	−	0.204810i
$970$	3.37654	+	1.22896i	0.108414	+	0.0394596i
$971$	−4.20871	+	7.28970i	−0.135064	+	0.233938i	−0.925622	−	0.378450i	$-0.876457\pi$
$971$	−4.20871	+	7.28970i	−0.135064	+	0.233938i	0.790558	+	0.612387i	$0.209791\pi$
$972$	−8.71830	+	14.0994i	−0.279640	+	0.452239i
$973$	−23.6428	−	29.4296i	−0.757953	−	0.943468i
$974$	20.1984	−	16.9484i	0.647198	−	0.543063i
$975$	12.2202	+	3.58411i	0.391360	+	0.114783i
$976$	−60.4827	+	22.0139i	−1.93600	+	0.704648i
$977$	24.8148	+	20.8221i	0.793896	+	0.666158i	0.946706	−	0.322098i	$-0.104388\pi$
$977$	24.8148	+	20.8221i	0.793896	+	0.666158i	−0.152811	+	0.988256i	$0.548832\pi$
$978$	−14.4621	+	6.33454i	−0.462446	+	0.202556i
$979$	2.07058	+	11.7428i	0.0661761	+	0.375303i
$980$	0.948190	−	0.299957i	0.0302888	−	0.00958178i
$981$	48.8075	−	25.1999i	1.55830	−	0.804570i
$982$	−2.35978	−	4.08725i	−0.0753035	−	0.130429i
$983$	3.22600	+	18.2955i	0.102893	+	0.583537i	0.992041	+	0.125916i	$0.0401871\pi$
$983$	3.22600	+	18.2955i	0.102893	+	0.583537i	−0.889148	+	0.457621i	$0.848702\pi$
$984$	12.5138	+	18.7964i	0.398925	+	0.599206i
$985$	−0.589845	+	0.214686i	−0.0187940	+	0.00684047i
$986$	4.02130	+	3.37427i	0.128064	+	0.107459i
$987$	4.59777	−	14.5215i	0.146349	−	0.462223i
$988$	8.90123	+	3.23978i	0.283186	+	0.103071i
$989$	14.4235	+	24.9822i	0.458641	+	0.794389i
$990$	2.20391	−	0.282634i	0.0700447	−	0.00898269i
$991$	11.5180	−	19.9498i	0.365882	−	0.633725i	−0.623036	−	0.782193i	$-0.714101\pi$
$991$	11.5180	−	19.9498i	0.365882	−	0.633725i	0.988917	+	0.148468i	$0.0474342\pi$
$992$	−31.1755	−	11.3470i	−0.989825	−	0.360267i
$993$	−11.9885	+	5.25110i	−0.380445	+	0.166639i
$994$	18.1137	−	9.94874i	0.574531	−	0.315555i
$995$	−0.239978	+	1.36099i	−0.00760783	+	0.0431461i
$996$	4.64501	+	19.1214i	0.147183	+	0.605885i
$997$	18.4190	+	6.70396i	0.583335	+	0.212316i	0.616795	−	0.787124i	$-0.288431\pi$
$997$	18.4190	+	6.70396i	0.583335	+	0.212316i	−0.0334607	+	0.999440i	$0.510653\pi$
$998$	−17.0990	−	29.6164i	−0.541260	−	0.937490i
$999$	−6.36137	+	18.4348i	−0.201265	+	0.583251i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.184.5	yes	132
3.2	odd	2		567.2.w.a.37.18		132
7.4	even	3		189.2.u.a.130.18	yes	132
21.11	odd	6		567.2.u.a.361.5		132
27.11	odd	18		567.2.u.a.289.5		132
27.16	even	9		189.2.u.a.16.18	✓	132
189.11	odd	18		567.2.w.a.46.18		132
189.151	even	9	inner	189.2.w.a.151.5	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.16.18	✓	132	27.16	even	9
189.2.u.a.130.18	yes	132	7.4	even	3
189.2.w.a.151.5	yes	132	189.151	even	9	inner
189.2.w.a.184.5	yes	132	1.1	even	1	trivial
567.2.u.a.289.5		132	27.11	odd	18
567.2.u.a.361.5		132	21.11	odd	6
567.2.w.a.37.18		132	3.2	odd	2
567.2.w.a.46.18		132	189.11	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.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.303930 - 1.72367i) q^{2} +(-1.25318 + 1.19564i) q^{3} +(-0.999292 + 0.363713i) q^{4} +(0.0231991 - 0.131569i) q^{5} +(2.44176 + 1.79668i) q^{6} +(1.74352 - 1.99001i) q^{7} +(-0.819627 - 1.41964i) q^{8} +(0.140909 - 2.99669i) q^{9} +O(q^{10})\)	\(q+(-0.303930 - 1.72367i) q^{2} +(-1.25318 + 1.19564i) q^{3} +(-0.999292 + 0.363713i) q^{4} +(0.0231991 - 0.131569i) q^{5} +(2.44176 + 1.79668i) q^{6} +(1.74352 - 1.99001i) q^{7} +(-0.819627 - 1.41964i) q^{8} +(0.140909 - 2.99669i) q^{9} -0.233833 q^{10} +(-0.550020 - 3.11932i) q^{11} +(0.817423 - 1.65059i) q^{12} +(-1.13051 - 0.948610i) q^{13} +(-3.96004 - 2.40043i) q^{14} +(0.128236 + 0.192617i) q^{15} +(-3.82714 + 3.21135i) q^{16} -0.883439 q^{17} +(-5.20814 + 0.667903i) q^{18} +6.03584 q^{19} +(0.0246705 + 0.139914i) q^{20} +(0.194394 + 4.57845i) q^{21} +(-5.20952 + 1.89611i) q^{22} +(-3.25114 - 2.72803i) q^{23} +(2.72451 + 0.799080i) q^{24} +(4.68169 + 1.70400i) q^{25} +(-1.29150 + 2.23694i) q^{26} +(3.40637 + 3.92386i) q^{27} +(-1.01849 + 2.62274i) q^{28} +(2.60068 - 2.18223i) q^{29} +(0.293034 - 0.279579i) q^{30} +(-5.70378 + 2.07601i) q^{31} +(4.18702 + 3.51333i) q^{32} +(4.41885 + 3.25144i) q^{33} +(0.268504 + 1.52276i) q^{34} +(-0.221376 - 0.275559i) q^{35} +(0.949124 + 3.04582i) q^{36} +(1.87653 + 3.25025i) q^{37} +(-1.83447 - 10.4038i) q^{38} +(2.55092 - 0.162901i) q^{39} +(-0.205795 + 0.0749031i) q^{40} +(6.09240 + 5.11213i) q^{41} +(7.83267 - 1.72660i) q^{42} +(-6.38712 - 2.32472i) q^{43} +(1.68417 + 2.91706i) q^{44} +(-0.391002 - 0.0880599i) q^{45} +(-3.71411 + 6.43303i) q^{46} +(-3.12343 - 1.13684i) q^{47} +(0.956479 - 8.60026i) q^{48} +(-0.920298 - 6.93924i) q^{49} +(1.51423 - 8.58760i) q^{50} +(1.10711 - 1.05627i) q^{51} +(1.47473 + 0.536758i) q^{52} +(6.45006 + 11.1718i) q^{53} +(5.72816 - 7.06404i) q^{54} -0.423166 q^{55} +(-4.25413 - 0.844091i) q^{56} +(-7.56397 + 7.21666i) q^{57} +(-4.55187 - 3.81947i) q^{58} +(5.32937 + 4.47187i) q^{59} +(-0.198202 - 0.145840i) q^{60} +(12.1063 + 4.40633i) q^{61} +(5.31191 + 9.20049i) q^{62} +(-5.71777 - 5.50519i) q^{63} +(-0.212705 + 0.368416i) q^{64} +(-0.151034 + 0.126733i) q^{65} +(4.26140 - 8.60486i) q^{66} +(0.662043 - 3.75463i) q^{67} +(0.882814 - 0.321318i) q^{68} +(7.33598 - 0.468472i) q^{69} +(-0.407691 + 0.465330i) q^{70} +(-2.23138 + 3.86486i) q^{71} +(-4.36970 + 2.25613i) q^{72} +(0.0471967 - 0.0817471i) q^{73} +(5.03204 - 4.22238i) q^{74} +(-7.90435 + 3.46219i) q^{75} +(-6.03156 + 2.19531i) q^{76} +(-7.16646 - 4.34404i) q^{77} +(-1.05609 - 4.34744i) q^{78} +(-0.562555 - 3.19041i) q^{79} +(0.333728 + 0.578033i) q^{80} +(-8.96029 - 0.844521i) q^{81} +(6.95998 - 12.0550i) q^{82} +(-8.18383 + 6.86705i) q^{83} +(-1.85950 - 4.50451i) q^{84} +(-0.0204950 + 0.116233i) q^{85} +(-2.06582 + 11.7159i) q^{86} +(-0.649961 + 5.84418i) q^{87} +(-3.97749 + 3.33751i) q^{88} -3.76455 q^{89} +(-0.0329492 + 0.700724i) q^{90} +(-3.85881 + 0.595810i) q^{91} +(4.24105 + 1.54362i) q^{92} +(4.66570 - 9.42125i) q^{93} +(-1.01023 + 5.72929i) q^{94} +(0.140026 - 0.794128i) q^{95} +(-9.44775 + 0.603329i) q^{96} +(-14.4400 - 5.25573i) q^{97} +(-11.6813 + 3.69534i) q^{98} +(-9.42514 + 1.20870i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Introduction

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