LMFDB - Embedded newform 162.2.e.a.145.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(19,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, degree $6$, not 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			145.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	162.145
Dual form			162.2.e.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.939693 - 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(-0.439693 + 2.49362i) q^{5} +(-1.79813 + 1.50881i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.26604 - 2.19285i) q^{10} +(0.745100 + 4.22567i) q^{11} +(-0.713011 + 0.259515i) q^{13} +(2.20574 - 0.802823i) q^{14} +(0.173648 + 0.984808i) q^{16} +(2.46064 - 4.26195i) q^{17} +(3.62449 + 6.27779i) q^{19} +(-1.93969 + 1.62760i) q^{20} +(0.745100 - 4.22567i) q^{22} +(0.233956 + 0.196312i) q^{23} +(-1.32635 - 0.482753i) q^{25} +0.758770 q^{26} -2.34730 q^{28} +(-2.91875 - 1.06234i) q^{29} +(-6.58512 - 5.52557i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-3.76991 + 3.16333i) q^{34} +(-2.97178 - 5.14728i) q^{35} +(3.78699 - 6.55926i) q^{37} +(-1.25877 - 7.13884i) q^{38} +(2.37939 - 0.866025i) q^{40} +(4.60607 - 1.67647i) q^{41} +(-0.283119 - 1.60565i) q^{43} +(-2.14543 + 3.71599i) q^{44} +(-0.152704 - 0.264490i) q^{46} +(1.39053 - 1.16679i) q^{47} +(-0.258770 + 1.46756i) q^{49} +(1.08125 + 0.907278i) q^{50} +(-0.713011 - 0.259515i) q^{52} -0.573978 q^{53} -10.8648 q^{55} +(2.20574 + 0.802823i) q^{56} +(2.37939 + 1.99654i) q^{58} +(-0.950837 + 5.39246i) q^{59} +(8.46451 - 7.10257i) q^{61} +(4.29813 + 7.44459i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-0.333626 - 1.89209i) q^{65} +(-0.0393628 + 0.0143269i) q^{67} +(4.62449 - 1.68317i) q^{68} +(1.03209 + 5.85327i) q^{70} +(-2.10220 + 3.64111i) q^{71} +(5.54576 + 9.60554i) q^{73} +(-5.80200 + 4.86846i) q^{74} +(-1.25877 + 7.13884i) q^{76} +(-7.71554 - 6.47410i) q^{77} +(6.92989 + 2.52227i) q^{79} -2.53209 q^{80} -4.90167 q^{82} +(6.41147 + 2.33359i) q^{83} +(9.54576 + 8.00984i) q^{85} +(-0.283119 + 1.60565i) q^{86} +(3.28699 - 2.75811i) q^{88} +(3.96064 + 6.86002i) q^{89} +(0.890530 - 1.54244i) q^{91} +(0.0530334 + 0.300767i) q^{92} +(-1.70574 + 0.620838i) q^{94} +(-17.2481 + 6.27779i) q^{95} +(-0.570108 - 3.23324i) q^{97} +(0.745100 - 1.29055i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{10} + 3 q^{11} - 12 q^{13} + 3 q^{14} + 6 q^{17} + 9 q^{19} - 6 q^{20} + 3 q^{22} + 6 q^{23} - 9 q^{25} - 18 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} + 6 q^{34}+ \cdots + 3 q^{98}+O(q^{100}) $ 6 * q + 3 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^10 + 3 * q^11 - 12 * q^13 + 3 * q^14 + 6 * q^17 + 9 * q^19 - 6 * q^20 + 3 * q^22 + 6 * q^23 - 9 * q^25 - 18 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 + 6 * q^34 - 3 * q^35 + 15 * q^37 + 15 * q^38 + 3 * q^40 + 3 * q^41 - 18 * q^43 + 3 * q^44 - 3 * q^46 - 9 * q^47 + 21 * q^49 + 9 * q^50 - 12 * q^52 + 12 * q^53 - 18 * q^55 + 3 * q^56 + 3 * q^58 + 6 * q^59 + 18 * q^61 + 12 * q^62 - 3 * q^64 - 21 * q^65 - 9 * q^67 + 15 * q^68 - 3 * q^70 - 12 * q^71 + 3 * q^73 + 3 * q^74 + 15 * q^76 - 39 * q^77 + 33 * q^79 - 6 * q^80 - 6 * q^82 + 18 * q^83 + 27 * q^85 - 18 * q^86 + 12 * q^88 + 15 * q^89 - 12 * q^91 - 12 * q^92 - 21 * q^95 - 12 * q^97 + 3 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$2$	−0.939693	−	0.342020i	−0.664463	−	0.241845i
$3$		0			0
$3$		0			0
$4$	0.766044	+	0.642788i	0.383022	+	0.321394i
$5$	−0.439693	+	2.49362i	−0.196637	+	1.11518i	0.713432	+	0.700724i	$0.247140\pi$
$5$	−0.439693	+	2.49362i	−0.196637	+	1.11518i	−0.910069	+	0.414457i	$0.863972\pi$
$6$		0			0
$7$	−1.79813	+	1.50881i	−0.679631	+	0.570278i	−0.915898	−	0.401410i	$-0.868520\pi$
$7$	−1.79813	+	1.50881i	−0.679631	+	0.570278i	0.236268	+	0.971688i	$0.424076\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$		0			0
$10$	1.26604	−	2.19285i	0.400358	−	0.693441i
$11$	0.745100	+	4.22567i	0.224656	+	1.27409i	0.863342	+	0.504620i	$0.168367\pi$
$11$	0.745100	+	4.22567i	0.224656	+	1.27409i	−0.638685	+	0.769468i	$0.720521\pi$
$12$		0			0
$13$	−0.713011	+	0.259515i	−0.197754	+	0.0719765i	−0.438998	−	0.898488i	$-0.644667\pi$
$13$	−0.713011	+	0.259515i	−0.197754	+	0.0719765i	0.241245	+	0.970464i	$0.422444\pi$
$14$	2.20574	−	0.802823i	0.589508	−	0.214563i
$15$		0			0
$16$	0.173648	+	0.984808i	0.0434120	+	0.246202i
$17$	2.46064	−	4.26195i	0.596792	−	1.03367i	−0.396499	−	0.918035i	$-0.629775\pi$
$17$	2.46064	−	4.26195i	0.596792	−	1.03367i	0.993291	−	0.115639i	$-0.0368917\pi$
$18$		0			0
$19$	3.62449	+	6.27779i	0.831514	+	1.44022i	0.896837	+	0.442360i	$0.145859\pi$
$19$	3.62449	+	6.27779i	0.831514	+	1.44022i	−0.0653235	+	0.997864i	$0.520808\pi$
$20$	−1.93969	+	1.62760i	−0.433728	+	0.363941i
$21$		0			0
$22$	0.745100	−	4.22567i	0.158856	−	0.900916i
$23$	0.233956	+	0.196312i	0.0487831	+	0.0409339i	0.666853	−	0.745189i	$-0.267641\pi$
$23$	0.233956	+	0.196312i	0.0487831	+	0.0409339i	−0.618070	+	0.786123i	$0.712085\pi$
$24$		0			0
$25$	−1.32635	−	0.482753i	−0.265270	−	0.0965505i
$26$	0.758770			0.148807
$27$		0			0
$28$	−2.34730			−0.443597
$29$	−2.91875	−	1.06234i	−0.541998	−	0.197271i	0.0564897	−	0.998403i	$-0.482009\pi$
$29$	−2.91875	−	1.06234i	−0.541998	−	0.197271i	−0.598488	+	0.801132i	$0.704231\pi$
$30$		0			0
$31$	−6.58512	−	5.52557i	−1.18272	−	0.992422i	−0.999957	−	0.00926586i	$-0.997051\pi$
$31$	−6.58512	−	5.52557i	−1.18272	−	0.992422i	−0.182766	−	0.983156i	$-0.558505\pi$
$32$	0.173648	−	0.984808i	0.0306970	−	0.174091i
$33$		0			0
$34$	−3.76991	+	3.16333i	−0.646535	+	0.542507i
$35$	−2.97178	−	5.14728i	−0.502323	−	0.870049i
$36$		0			0
$37$	3.78699	−	6.55926i	0.622577	−	1.07834i	−0.366427	−	0.930447i	$-0.619419\pi$
$37$	3.78699	−	6.55926i	0.622577	−	1.07834i	0.989004	−	0.147888i	$-0.0472477\pi$
$38$	−1.25877	−	7.13884i	−0.204200	−	1.15807i
$39$		0			0
$40$	2.37939	−	0.866025i	0.376214	−	0.136931i
$41$	4.60607	−	1.67647i	0.719347	−	0.261821i	0.0436983	−	0.999045i	$-0.486086\pi$
$41$	4.60607	−	1.67647i	0.719347	−	0.261821i	0.675648	+	0.737224i	$0.263864\pi$
$42$		0			0
$43$	−0.283119	−	1.60565i	−0.0431752	−	0.244859i	0.955580	−	0.294730i	$-0.0952298\pi$
$43$	−0.283119	−	1.60565i	−0.0431752	−	0.244859i	−0.998756	+	0.0498718i	$0.984119\pi$
$44$	−2.14543	+	3.71599i	−0.323436	+	0.560207i
$45$		0			0
$46$	−0.152704	−	0.264490i	−0.0225149	−	0.0389970i
$47$	1.39053	−	1.16679i	0.202830	−	0.170194i	−0.535715	−	0.844399i	$-0.679958\pi$
$47$	1.39053	−	1.16679i	0.202830	−	0.170194i	0.738545	+	0.674205i	$0.235513\pi$
$48$		0			0
$49$	−0.258770	+	1.46756i	−0.0369672	+	0.209651i
$50$	1.08125	+	0.907278i	0.152912	+	0.128308i
$51$		0			0
$52$	−0.713011	−	0.259515i	−0.0988768	−	0.0359882i
$53$	−0.573978			−0.0788419			−0.0394210	−	0.999223i	$-0.512551\pi$
$53$	−0.573978			−0.0788419			−0.0394210	+	0.999223i	$0.512551\pi$
$54$		0			0
$55$	−10.8648			−1.46501
$56$	2.20574	+	0.802823i	0.294754	+	0.107282i
$57$		0			0
$58$	2.37939	+	1.99654i	0.312429	+	0.262159i
$59$	−0.950837	+	5.39246i	−0.123788	+	0.702039i	0.858232	+	0.513263i	$0.171563\pi$
$59$	−0.950837	+	5.39246i	−0.123788	+	0.702039i	−0.982020	+	0.188777i	$0.939548\pi$
$60$		0			0
$61$	8.46451	−	7.10257i	1.08377	−	0.909390i	0.0875408	−	0.996161i	$-0.472099\pi$
$61$	8.46451	−	7.10257i	1.08377	−	0.909390i	0.996228	+	0.0867707i	$0.0276547\pi$
$62$	4.29813	+	7.44459i	0.545863	+	0.945463i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.333626	−	1.89209i	−0.0413812	−	0.234684i
$66$		0			0
$67$	−0.0393628	+	0.0143269i	−0.00480894	+	0.00175031i	−0.344423	−	0.938814i	$-0.611926\pi$
$67$	−0.0393628	+	0.0143269i	−0.00480894	+	0.00175031i	0.339615	+	0.940565i	$0.389703\pi$
$68$	4.62449	−	1.68317i	0.560801	−	0.204115i
$69$		0			0
$70$	1.03209	+	5.85327i	0.123358	+	0.699599i
$71$	−2.10220	+	3.64111i	−0.249485	+	0.432120i	−0.963383	−	0.268129i	$-0.913595\pi$
$71$	−2.10220	+	3.64111i	−0.249485	+	0.432120i	0.713898	+	0.700250i	$0.246928\pi$
$72$		0			0
$73$	5.54576	+	9.60554i	0.649082	+	1.12424i	0.983342	+	0.181762i	$0.0581802\pi$
$73$	5.54576	+	9.60554i	0.649082	+	1.12424i	−0.334260	+	0.942481i	$0.608487\pi$
$74$	−5.80200	+	4.86846i	−0.674469	+	0.565947i
$75$		0			0
$76$	−1.25877	+	7.13884i	−0.144391	+	0.818881i
$77$	−7.71554	−	6.47410i	−0.879267	−	0.737793i
$78$		0			0
$79$	6.92989	+	2.52227i	0.779674	+	0.283778i	0.701037	−	0.713125i	$-0.252721\pi$
$79$	6.92989	+	2.52227i	0.779674	+	0.283778i	0.0786372	+	0.996903i	$0.474943\pi$
$80$	−2.53209			−0.283096
$81$		0			0
$82$	−4.90167			−0.541299
$83$	6.41147	+	2.33359i	0.703751	+	0.256144i	0.669011	−	0.743252i	$-0.266718\pi$
$83$	6.41147	+	2.33359i	0.703751	+	0.256144i	0.0347393	+	0.999396i	$0.488940\pi$
$84$		0			0
$85$	9.54576	+	8.00984i	1.03538	+	0.868789i
$86$	−0.283119	+	1.60565i	−0.0305295	+	0.173141i
$87$		0			0
$88$	3.28699	−	2.75811i	0.350394	−	0.294016i
$89$	3.96064	+	6.86002i	0.419827	+	0.727161i	0.995922	−	0.0902216i	$-0.0287575\pi$
$89$	3.96064	+	6.86002i	0.419827	+	0.727161i	−0.576095	+	0.817383i	$0.695424\pi$
$90$		0			0
$91$	0.890530	−	1.54244i	0.0933529	−	0.161692i
$92$	0.0530334	+	0.300767i	0.00552912	+	0.0313572i
$93$		0			0
$94$	−1.70574	+	0.620838i	−0.175933	+	0.0640345i
$95$	−17.2481	+	6.27779i	−1.76962	+	0.644088i
$96$		0			0
$97$	−0.570108	−	3.23324i	−0.0578857	−	0.328286i	0.942089	−	0.335362i	$-0.108859\pi$
$97$	−0.570108	−	3.23324i	−0.0578857	−	0.328286i	−0.999975	+	0.00707624i	$0.997748\pi$
$98$	0.745100	−	1.29055i	0.0752665	−	0.130365i
$99$		0			0
$100$	−0.705737	−	1.22237i	−0.0705737	−	0.122237i
$101$	9.18732	−	7.70908i	0.914172	−	0.767082i	−0.0587358	−	0.998274i	$-0.518707\pi$
$101$	9.18732	−	7.70908i	0.914172	−	0.767082i	0.972908	+	0.231192i	$0.0742625\pi$
$102$		0			0
$103$	0.418748	−	2.37484i	0.0412605	−	0.234000i	−0.957203	−	0.289418i	$-0.906538\pi$
$103$	0.418748	−	2.37484i	0.0412605	−	0.234000i	0.998463	+	0.0554184i	$0.0176493\pi$
$104$	0.581252	+	0.487728i	0.0569964	+	0.0478257i
$105$		0			0
$106$	0.539363	+	0.196312i	0.0523876	+	0.0190675i
$107$	2.42602			0.234532			0.117266	−	0.993101i	$-0.462587\pi$
$107$	2.42602			0.234532			0.117266	+	0.993101i	$0.462587\pi$
$108$		0			0
$109$	−2.32770			−0.222953			−0.111476	−	0.993767i	$-0.535558\pi$
$109$	−2.32770			−0.222953			−0.111476	+	0.993767i	$0.535558\pi$
$110$	10.2096	+	3.71599i	0.973448	+	0.354306i
$111$		0			0
$112$	−1.79813	−	1.50881i	−0.169908	−	0.142569i
$113$	2.96198	−	16.7982i	0.278640	−	1.58024i	−0.448518	−	0.893774i	$-0.648048\pi$
$113$	2.96198	−	16.7982i	0.278640	−	1.58024i	0.727157	−	0.686471i	$-0.240841\pi$
$114$		0			0
$115$	−0.592396	+	0.497079i	−0.0552412	+	0.0463529i
$116$	−1.55303	−	2.68993i	−0.144196	−	0.249754i
$117$		0			0
$118$	2.73783	−	4.74205i	0.252037	−	0.436541i
$119$	2.00593	+	11.3762i	0.183883	+	1.04285i
$120$		0			0
$121$	−6.96451	+	2.53487i	−0.633137	+	0.230443i
$122$	−10.3833	+	3.77920i	−0.940056	+	0.342152i
$123$		0			0
$124$	−1.49273	−	8.46567i	−0.134051	−	0.760240i
$125$	−4.54323	+	7.86911i	−0.406359	+	0.703835i
$126$		0			0
$127$	−6.32295	−	10.9517i	−0.561071	−	0.971803i	−0.997403	−	0.0720178i	$-0.977056\pi$
$127$	−6.32295	−	10.9517i	−0.561071	−	0.971803i	0.436332	−	0.899786i	$-0.356277\pi$
$128$	0.766044	−	0.642788i	0.0677094	−	0.0568149i
$129$		0			0
$130$	−0.333626	+	1.89209i	−0.0292609	+	0.165947i
$131$	3.97565	+	3.33597i	0.347354	+	0.291465i	0.799727	−	0.600364i	$-0.204978\pi$
$131$	3.97565	+	3.33597i	0.347354	+	0.291465i	−0.452372	+	0.891829i	$0.649422\pi$
$132$		0			0
$133$	−15.9893	−	5.81964i	−1.38645	−	0.504627i
$134$	0.0418891			0.00361866
$135$		0			0
$136$	−4.92127			−0.421996
$137$	−16.0817	−	5.85327i	−1.37395	−	0.500078i	−0.453614	−	0.891198i	$-0.649866\pi$
$137$	−16.0817	−	5.85327i	−1.37395	−	0.500078i	−0.920340	+	0.391120i	$0.872088\pi$
$138$		0			0
$139$	9.34389	+	7.84046i	0.792539	+	0.665019i	0.946372	−	0.323078i	$-0.104718\pi$
$139$	9.34389	+	7.84046i	0.792539	+	0.665019i	−0.153834	+	0.988097i	$0.549162\pi$
$140$	1.03209	−	5.85327i	0.0872274	−	0.494691i
$141$		0			0
$142$	3.22075	−	2.70253i	0.270279	−	0.226791i
$143$	−1.62789	−	2.81959i	−0.136131	−	0.235786i
$144$		0			0
$145$	3.93242	−	6.81115i	0.326570	−	0.565635i
$146$	−1.92602	−	10.9230i	−0.159399	−	0.903995i
$147$		0			0
$148$	7.11721	−	2.59045i	0.585031	−	0.212934i
$149$	7.23783	−	2.63435i	0.592946	−	0.215815i	−0.0280788	−	0.999606i	$-0.508939\pi$
$149$	7.23783	−	2.63435i	0.592946	−	0.215815i	0.621025	+	0.783791i	$0.286717\pi$
$150$		0			0
$151$	−0.135630	−	0.769193i	−0.0110374	−	0.0625961i	0.978792	−	0.204858i	$-0.0656734\pi$
$151$	−0.135630	−	0.769193i	−0.0110374	−	0.0625961i	−0.989829	+	0.142262i	$0.954562\pi$
$152$	3.62449	−	6.27779i	0.293985	−	0.509196i
$153$		0			0
$154$	5.03596	+	8.72254i	0.405809	+	0.702882i
$155$	16.6741	−	13.9912i	1.33930	−	1.12380i
$156$		0			0
$157$	−1.80793	+	10.2533i	−0.144289	+	0.818302i	0.823647	+	0.567103i	$0.191936\pi$
$157$	−1.80793	+	10.2533i	−0.144289	+	0.818302i	−0.967935	+	0.251199i	$0.919175\pi$
$158$	−5.64930	−	4.74033i	−0.449434	−	0.377120i
$159$		0			0
$160$	2.37939	+	0.866025i	0.188107	+	0.0684653i
$161$	−0.716881			−0.0564982
$162$		0			0
$163$	−10.5740			−0.828218			−0.414109	−	0.910227i	$-0.635907\pi$
$163$	−10.5740			−0.828218			−0.414109	+	0.910227i	$0.635907\pi$
$164$	4.60607	+	1.67647i	0.359673	+	0.130910i
$165$		0			0
$166$	−5.22668	−	4.38571i	−0.405669	−	0.340397i
$167$	−0.260992	+	1.48016i	−0.0201962	+	0.114538i	−0.993239	−	0.116085i	$-0.962965\pi$
$167$	−0.260992	+	1.48016i	−0.0201962	+	0.114538i	0.973043	+	0.230623i	$0.0740765\pi$
$168$		0			0
$169$	−9.51754	+	7.98617i	−0.732119	+	0.614320i
$170$	−6.23055	−	10.7916i	−0.477862	−	0.827680i
$171$		0			0
$172$	0.815207	−	1.41198i	0.0621590	−	0.107663i
$173$	1.93629	+	10.9812i	0.147213	+	0.834888i	0.965563	+	0.260168i	$0.0837780\pi$
$173$	1.93629	+	10.9812i	0.147213	+	0.834888i	−0.818350	+	0.574720i	$0.805111\pi$
$174$		0			0
$175$	3.11334	−	1.13316i	0.235346	−	0.0856591i
$176$	−4.03209	+	1.46756i	−0.303930	+	0.110622i
$177$		0			0
$178$	−1.37551	−	7.80093i	−0.103099	−	0.584705i
$179$	3.90420	−	6.76227i	0.291814	−	0.505436i	−0.682425	−	0.730956i	$-0.739075\pi$
$179$	3.90420	−	6.76227i	0.291814	−	0.505436i	0.974239	+	0.225520i	$0.0724080\pi$
$180$		0			0
$181$	−5.23783	−	9.07218i	−0.389325	−	0.674330i	0.603034	−	0.797715i	$-0.293958\pi$
$181$	−5.23783	−	9.07218i	−0.389325	−	0.674330i	−0.992359	+	0.123385i	$0.960625\pi$
$182$	−1.36437	+	1.14484i	−0.101134	+	0.0848614i
$183$		0			0
$184$	0.0530334	−	0.300767i	0.00390968	−	0.0221729i
$185$	14.6912	+	12.3274i	1.08012	+	0.906326i
$186$		0			0
$187$	19.8430	+	7.22227i	1.45107	+	0.528144i
$188$	1.81521			0.132388
$189$		0			0
$190$	18.3550			1.33161
$191$	−11.4918	−	4.18269i	−0.831521	−	0.302649i	−0.109038	−	0.994038i	$-0.534777\pi$
$191$	−11.4918	−	4.18269i	−0.831521	−	0.302649i	−0.722483	+	0.691389i	$0.756999\pi$
$192$		0			0
$193$	−12.5385	−	10.5210i	−0.902540	−	0.757321i	0.0681452	−	0.997675i	$-0.478292\pi$
$193$	−12.5385	−	10.5210i	−0.902540	−	0.757321i	−0.970685	+	0.240354i	$0.922736\pi$
$194$	−0.570108	+	3.23324i	−0.0409313	+	0.232133i
$195$		0			0
$196$	−1.14156	+	0.957882i	−0.0815399	+	0.0684201i
$197$	9.49794	+	16.4509i	0.676700	+	1.17208i	0.975969	+	0.217910i	$0.0699240\pi$
$197$	9.49794	+	16.4509i	0.676700	+	1.17208i	−0.299269	+	0.954169i	$0.596743\pi$
$198$		0			0
$199$	−11.5214	+	19.9557i	−0.816731	+	1.41462i	0.0913469	+	0.995819i	$0.470883\pi$
$199$	−11.5214	+	19.9557i	−0.816731	+	1.41462i	−0.908078	+	0.418801i	$0.862451\pi$
$200$	0.245100	+	1.39003i	0.0173312	+	0.0982900i
$201$		0			0
$202$	−11.2699	+	4.10191i	−0.792948	+	0.288610i
$203$	6.85117	−	2.49362i	0.480858	−	0.175018i
$204$		0			0
$205$	2.15523	+	12.2229i	0.150528	+	0.853685i
$206$	−1.20574	+	2.08840i	−0.0840077	+	0.145506i
$207$		0			0
$208$	−0.379385	−	0.657115i	−0.0263056	−	0.0455627i
$209$	−23.8273	+	19.9935i	−1.64817	+	1.38298i
$210$		0			0
$211$	3.03849	−	17.2321i	0.209178	−	1.18631i	−0.681550	−	0.731771i	$-0.738694\pi$
$211$	3.03849	−	17.2321i	0.209178	−	1.18631i	0.890728	−	0.454536i	$-0.150195\pi$
$212$	−0.439693	−	0.368946i	−0.0301982	−	0.0253393i
$213$		0			0
$214$	−2.27972	−	0.829748i	−0.155838	−	0.0567204i
$215$	4.12836			0.281552
$216$		0			0
$217$	20.1780			1.36977
$218$	2.18732	+	0.796119i	0.148144	+	0.0539200i
$219$		0			0
$220$	−8.32295	−	6.98378i	−0.561133	−	0.470847i
$221$	−0.648423	+	3.67739i	−0.0436176	+	0.247368i
$222$		0			0
$223$	−3.23190	+	2.71188i	−0.216424	+	0.181601i	−0.744554	−	0.667562i	$-0.767338\pi$
$223$	−3.23190	+	2.71188i	−0.216424	+	0.181601i	0.528130	+	0.849163i	$0.322893\pi$
$224$	1.17365	+	2.03282i	0.0784177	+	0.135823i
$225$		0			0
$226$	−8.52869	+	14.7721i	−0.567320	+	0.982627i
$227$	−2.77244	−	15.7233i	−0.184013	−	1.04359i	−0.927216	−	0.374526i	$-0.877806\pi$
$227$	−2.77244	−	15.7233i	−0.184013	−	1.04359i	0.743203	−	0.669066i	$-0.233306\pi$
$228$		0			0
$229$	16.7713	−	6.10424i	1.10828	−	0.403379i	0.277915	−	0.960606i	$-0.410357\pi$
$229$	16.7713	−	6.10424i	1.10828	−	0.403379i	0.830361	+	0.557226i	$0.188134\pi$
$230$	0.726682	−	0.264490i	0.0479160	−	0.0174400i
$231$		0			0
$232$	0.539363	+	3.05888i	0.0354109	+	0.200825i
$233$	−0.368241	+	0.637812i	−0.0241243	+	0.0417844i	−0.877835	−	0.478962i	$-0.841013\pi$
$233$	−0.368241	+	0.637812i	−0.0241243	+	0.0417844i	0.853711	+	0.520747i	$0.174346\pi$
$234$		0			0
$235$	2.29813	+	3.98048i	0.149914	+	0.259658i
$236$	−4.19459	+	3.51968i	−0.273045	+	0.229112i
$237$		0			0
$238$	2.00593	−	11.3762i	0.130025	−	0.737409i
$239$	2.20187	+	1.84759i	0.142427	+	0.119510i	0.711218	−	0.702972i	$-0.248144\pi$
$239$	2.20187	+	1.84759i	0.142427	+	0.119510i	−0.568791	+	0.822482i	$0.692589\pi$
$240$		0			0
$241$	−2.05051	−	0.746324i	−0.132085	−	0.0480749i	0.275132	−	0.961406i	$-0.411278\pi$
$241$	−2.05051	−	0.746324i	−0.132085	−	0.0480749i	−0.407217	+	0.913332i	$0.633501\pi$
$242$	7.41147			0.476428
$243$		0			0
$244$	11.0496			0.707380
$245$	−3.54576	−	1.29055i	−0.226530	−	0.0824503i
$246$		0			0
$247$	−4.21348	−	3.53553i	−0.268097	−	0.224960i
$248$	−1.49273	+	8.46567i	−0.0947882	+	0.537571i
$249$		0			0
$250$	6.96064	−	5.84067i	0.440229	−	0.369396i
$251$	−13.0189	−	22.5494i	−0.821745	−	1.42330i	−0.904382	−	0.426724i	$-0.859668\pi$
$251$	−13.0189	−	22.5494i	−0.821745	−	1.42330i	0.0826372	−	0.996580i	$-0.473666\pi$
$252$		0			0
$253$	−0.655230	+	1.13489i	−0.0411939	+	0.0713500i
$254$	2.19594	+	12.4538i	0.137785	+	0.781419i
$255$		0			0
$256$	−0.939693	+	0.342020i	−0.0587308	+	0.0213763i
$257$	9.38965	−	3.41755i	0.585710	−	0.213181i	−0.0321313	−	0.999484i	$-0.510229\pi$
$257$	9.38965	−	3.41755i	0.585710	−	0.213181i	0.617842	+	0.786302i	$0.288007\pi$
$258$		0			0
$259$	3.08718	+	17.5083i	0.191828	+	1.08791i
$260$	0.960637	−	1.66387i	0.0595762	−	0.103189i
$261$		0			0
$262$	−2.59492	−	4.49454i	−0.160315	−	0.277673i
$263$	−11.6612	+	9.78487i	−0.719058	+	0.603361i	−0.927125	−	0.374753i	$-0.877727\pi$
$263$	−11.6612	+	9.78487i	−0.719058	+	0.603361i	0.208067	+	0.978115i	$0.433283\pi$
$264$		0			0
$265$	0.252374	−	1.43128i	0.0155032	−	0.0879230i
$266$	13.0346	+	10.9373i	0.799204	+	0.670611i
$267$		0			0
$268$	−0.0393628	−	0.0143269i	−0.00240447	−	0.000875155i
$269$	−30.5476			−1.86252			−0.931259	−	0.364358i	$-0.881289\pi$
$269$	−30.5476			−1.86252			−0.931259	+	0.364358i	$0.881289\pi$
$270$		0			0
$271$	25.8307			1.56910			0.784551	−	0.620064i	$-0.212893\pi$
$271$	25.8307			1.56910			0.784551	+	0.620064i	$0.212893\pi$
$272$	4.62449	+	1.68317i	0.280401	+	0.102057i
$273$		0			0
$274$	13.1099	+	11.0005i	0.792000	+	0.664567i
$275$	1.05169	−	5.96443i	0.0634192	−	0.359668i
$276$		0			0
$277$	−17.1860	+	14.4207i	−1.03261	+	0.866459i	−0.991159	−	0.132682i	$-0.957641\pi$
$277$	−17.1860	+	14.4207i	−1.03261	+	0.866459i	−0.0414465	+	0.999141i	$0.513197\pi$
$278$	−6.09879	−	10.5634i	−0.365781	−	0.633552i
$279$		0			0
$280$	−2.97178	+	5.14728i	−0.177598	+	0.307609i
$281$	−1.01485	−	5.75552i	−0.0605410	−	0.343345i	−1.00000		0.000683195i	$-0.999783\pi$
$281$	−1.01485	−	5.75552i	−0.0605410	−	0.343345i	0.939459	−	0.342662i	$-0.111329\pi$
$282$		0			0
$283$	6.96451	−	2.53487i	0.413997	−	0.150683i	−0.126620	−	0.991951i	$-0.540413\pi$
$283$	6.96451	−	2.53487i	0.413997	−	0.150683i	0.540617	+	0.841269i	$0.318191\pi$
$284$	−3.95084	+	1.43799i	−0.234439	+	0.0853288i
$285$		0			0
$286$	0.565360	+	3.20631i	0.0334304	+	0.189593i
$287$	−5.75284	+	9.96421i	−0.339579	+	0.588169i
$288$		0			0
$289$	−3.60947	−	6.25179i	−0.212322	−	0.367752i
$290$	−6.02481	+	5.05542i	−0.353789	+	0.296864i
$291$		0			0
$292$	−1.92602	+	10.9230i	−0.112712	+	0.639221i
$293$	6.79994	+	5.70583i	0.397257	+	0.333338i	0.819432	−	0.573176i	$-0.194289\pi$
$293$	6.79994	+	5.70583i	0.397257	+	0.333338i	−0.422175	+	0.906514i	$0.638733\pi$
$294$		0			0
$295$	−13.0287	−	4.74205i	−0.758559	−	0.276093i
$296$	−7.57398			−0.440229
$297$		0			0
$298$	−7.70233			−0.446184
$299$	−0.217759	−	0.0792577i	−0.0125933	−	0.00458359i
$300$		0			0
$301$	2.93170	+	2.45999i	0.168981	+	0.141792i
$302$	−0.135630	+	0.769193i	−0.00780460	+	0.0442621i
$303$		0			0
$304$	−5.55303	+	4.65955i	−0.318488	+	0.267243i
$305$	13.9893	+	24.2302i	0.801026	+	1.38742i
$306$		0			0
$307$	8.04963	−	13.9424i	0.459417	−	0.795733i	−0.539514	−	0.841977i	$-0.681392\pi$
$307$	8.04963	−	13.9424i	0.459417	−	0.795733i	0.998930	+	0.0462440i	$0.0147252\pi$
$308$	−1.74897	−	9.91890i	−0.0996568	−	0.565182i
$309$		0			0
$310$	−20.4538	+	7.44459i	−1.16170	+	0.422824i
$311$	12.7699	−	4.64787i	0.724115	−	0.263556i	0.0464436	−	0.998921i	$-0.485211\pi$
$311$	12.7699	−	4.64787i	0.724115	−	0.263556i	0.677672	+	0.735364i	$0.262989\pi$
$312$		0			0
$313$	−3.73442	−	21.1790i	−0.211082	−	1.19711i	−0.887577	−	0.460659i	$-0.847613\pi$
$313$	−3.73442	−	21.1790i	−0.211082	−	1.19711i	0.676495	−	0.736447i	$-0.263498\pi$
$314$	5.20574	−	9.01660i	0.293777	−	0.508836i
$315$		0			0
$316$	3.68732	+	6.38662i	0.207428	+	0.359276i
$317$	16.1578	−	13.5580i	0.907510	−	0.761491i	−0.0641337	−	0.997941i	$-0.520428\pi$
$317$	16.1578	−	13.5580i	0.907510	−	0.761491i	0.971644	+	0.236450i	$0.0759840\pi$
$318$		0			0
$319$	2.31433	−	13.1252i	0.129578	−	0.734871i
$320$	−1.93969	−	1.62760i	−0.108432	−	0.0909853i
$321$		0			0
$322$	0.673648	+	0.245188i	0.0375409	+	0.0136638i
$323$	35.6742			1.98496
$324$		0			0
$325$	1.07098			0.0594076
$326$	9.93629	+	3.61651i	0.550320	+	0.200300i
$327$		0			0
$328$	−3.75490	−	3.15074i	−0.207330	−	0.173970i
$329$	−0.739885	+	4.19610i	−0.0407912	+	0.231338i
$330$		0			0
$331$	12.5929	−	10.5667i	0.692166	−	0.580797i	−0.227367	−	0.973809i	$-0.573012\pi$
$331$	12.5929	−	10.5667i	0.692166	−	0.580797i	0.919533	+	0.393013i	$0.128567\pi$
$332$	3.41147	+	5.90885i	0.187229	+	0.324290i
$333$		0			0
$334$	0.751497	−	1.30163i	0.0411201	−	0.0712220i
$335$	−0.0184183	−	0.104455i	−0.00100630	−	0.00570701i
$336$		0			0
$337$	−9.91534	+	3.60889i	−0.540123	+	0.196589i	−0.597653	−	0.801755i	$-0.703900\pi$
$337$	−9.91534	+	3.60889i	−0.540123	+	0.196589i	0.0575296	+	0.998344i	$0.481678\pi$
$338$	11.6750	−	4.24935i	0.635036	−	0.231134i
$339$		0			0
$340$	2.16385	+	12.2718i	0.117351	+	0.665531i
$341$	18.4427	−	31.9437i	0.998727	−	1.72985i
$342$		0			0
$343$	−9.96451	−	17.2590i	−0.538033	−	0.931900i
$344$	−1.24897	+	1.04801i	−0.0673400	+	0.0565049i
$345$		0			0
$346$	1.93629	−	10.9812i	0.104096	−	0.590355i
$347$	−21.7251	−	18.2295i	−1.16626	−	0.978612i	−0.166292	−	0.986077i	$-0.553179\pi$
$347$	−21.7251	−	18.2295i	−1.16626	−	0.978612i	−0.999972	+	0.00746500i	$0.997624\pi$
$348$		0			0
$349$	−14.7554	−	5.37051i	−0.789837	−	0.287477i	−0.0845685	−	0.996418i	$-0.526951\pi$
$349$	−14.7554	−	5.37051i	−0.789837	−	0.287477i	−0.705268	+	0.708941i	$0.749173\pi$
$350$	−3.31315			−0.177095
$351$		0			0
$352$	4.29086			0.228704
$353$	−1.93969	−	0.705990i	−0.103239	−	0.0375761i	0.289884	−	0.957062i	$-0.406383\pi$
$353$	−1.93969	−	0.705990i	−0.103239	−	0.0375761i	−0.393123	+	0.919486i	$0.628605\pi$
$354$		0			0
$355$	−8.15523	−	6.84305i	−0.432835	−	0.363191i
$356$	−1.37551	+	7.80093i	−0.0729021	+	0.413449i
$357$		0			0
$358$	−5.98158	+	5.01914i	−0.316136	+	0.265270i
$359$	−17.4820	−	30.2798i	−0.922667	−	1.59811i	−0.795271	−	0.606255i	$-0.792671\pi$
$359$	−17.4820	−	30.2798i	−0.922667	−	1.59811i	−0.127397	−	0.991852i	$-0.540662\pi$
$360$		0			0
$361$	−16.7738	+	29.0530i	−0.882831	+	1.52911i
$362$	1.81908	+	10.3165i	0.0956086	+	0.542223i
$363$		0			0
$364$	1.67365	−	0.609158i	0.0877230	−	0.0319286i
$365$	−26.3910	+	9.60554i	−1.38137	+	0.502777i
$366$		0			0
$367$	−0.0773815	−	0.438852i	−0.00403928	−	0.0229079i	0.982722	−	0.185090i	$-0.0592578\pi$
$367$	−0.0773815	−	0.438852i	−0.00403928	−	0.0229079i	−0.986761	+	0.162182i	$0.948147\pi$
$368$	−0.152704	+	0.264490i	−0.00796023	+	0.0137875i
$369$		0			0
$370$	−9.58899	−	16.6086i	−0.498508	−	0.863441i
$371$	1.03209	−	0.866025i	0.0535834	−	0.0449618i
$372$		0			0
$373$	−3.83110	+	21.7272i	−0.198367	+	1.12499i	0.709175	+	0.705032i	$0.249068\pi$
$373$	−3.83110	+	21.7272i	−0.198367	+	1.12499i	−0.907542	+	0.419962i	$0.862044\pi$
$374$	−16.1762	−	13.5734i	−0.836450	−	0.701865i
$375$		0			0
$376$	−1.70574	−	0.620838i	−0.0879667	−	0.0320173i
$377$	2.35679			0.121381
$378$		0			0
$379$	13.1138			0.673611			0.336806	−	0.941574i	$-0.390654\pi$
$379$	13.1138			0.673611			0.336806	+	0.941574i	$0.390654\pi$
$380$	−17.2481	−	6.27779i	−0.884808	−	0.322044i
$381$		0			0
$382$	9.36824	+	7.86089i	0.479321	+	0.402198i
$383$	−2.79767	+	15.8664i	−0.142954	+	0.810733i	0.826033	+	0.563622i	$0.190592\pi$
$383$	−2.79767	+	15.8664i	−0.142954	+	0.810733i	−0.968987	+	0.247111i	$0.920519\pi$
$384$		0			0
$385$	19.5364	−	16.3930i	0.995668	−	0.835465i
$386$	8.18392	+	14.1750i	0.416550	+	0.721486i
$387$		0			0
$388$	1.64156	−	2.84326i	0.0833375	−	0.144345i
$389$	−0.0984882	−	0.558554i	−0.00499355	−	0.0283198i	0.982209	−	0.187790i	$-0.0601325\pi$
$389$	−0.0984882	−	0.558554i	−0.00499355	−	0.0283198i	−0.987203	+	0.159470i	$0.949021\pi$
$390$		0			0
$391$	1.41235	−	0.514054i	0.0714257	−	0.0259968i
$392$	1.40033	−	0.509678i	0.0707273	−	0.0257426i
$393$		0			0
$394$	−3.29860	−	18.7073i	−0.166181	−	0.942460i
$395$	−9.33662	+	16.1715i	−0.469776	+	0.813676i
$396$		0			0
$397$	−18.0107	−	31.1955i	−0.903933	−	1.56566i	−0.822343	−	0.568992i	$-0.807334\pi$
$397$	−18.0107	−	31.1955i	−0.903933	−	1.56566i	−0.0815894	−	0.996666i	$-0.526000\pi$
$398$	17.6518	−	14.8116i	0.884806	−	0.742440i
$399$		0			0
$400$	0.245100	−	1.39003i	0.0122550	−	0.0695015i
$401$	−27.5724	−	23.1360i	−1.37690	−	1.15536i	−0.970344	−	0.241730i	$-0.922285\pi$
$401$	−27.5724	−	23.1360i	−1.37690	−	1.15536i	−0.406556	−	0.913626i	$-0.633270\pi$
$402$		0			0
$403$	6.12923	+	2.23086i	0.305319	+	0.111127i
$404$	11.9932			0.596684
$405$		0			0
$406$	−7.29086			−0.361839
$407$	30.5390	+	11.1153i	1.51376	+	0.550963i
$408$		0			0
$409$	9.71032	+	8.14793i	0.480145	+	0.402889i	0.850479	−	0.526009i	$-0.176312\pi$
$409$	9.71032	+	8.14793i	0.480145	+	0.402889i	−0.370334	+	0.928899i	$0.620757\pi$
$410$	2.15523	−	12.2229i	0.106439	−	0.603647i
$411$		0			0
$412$	1.84730	−	1.55007i	0.0910098	−	0.0763663i
$413$	−6.42649	−	11.1310i	−0.316227	−	0.547721i
$414$		0			0
$415$	−8.63816	+	14.9617i	−0.424030	+	0.734442i
$416$	0.131759	+	0.747243i	0.00646002	+	0.0366366i
$417$		0			0
$418$	29.2285	−	10.6383i	1.42961	−	0.520336i
$419$	13.3991	−	4.87689i	0.654591	−	0.238252i	0.00669178	−	0.999978i	$-0.497870\pi$
$419$	13.3991	−	4.87689i	0.654591	−	0.238252i	0.647899	+	0.761726i	$0.275648\pi$
$420$		0			0
$421$	0.546637	+	3.10013i	0.0266414	+	0.151091i	0.995227	−	0.0975909i	$-0.0311137\pi$
$421$	0.546637	+	3.10013i	0.0266414	+	0.151091i	−0.968585	+	0.248682i	$0.920003\pi$
$422$	−8.74897	+	15.1537i	−0.425893	+	0.737669i
$423$		0			0
$424$	0.286989	+	0.497079i	0.0139374	+	0.0241403i
$425$	−5.32114	+	4.46496i	−0.258113	+	0.216583i
$426$		0			0
$427$	−4.50387	+	25.5427i	−0.217958	+	1.23610i
$428$	1.85844	+	1.55942i	0.0898311	+	0.0753773i
$429$		0			0
$430$	−3.87939	−	1.41198i	−0.187081	−	0.0680918i
$431$	−15.4911			−0.746182			−0.373091	−	0.927795i	$-0.621702\pi$
$431$	−15.4911			−0.746182			−0.373091	+	0.927795i	$0.621702\pi$
$432$		0			0
$433$	−2.22844			−0.107092			−0.0535459	−	0.998565i	$-0.517052\pi$
$433$	−2.22844			−0.107092			−0.0535459	+	0.998565i	$0.517052\pi$
$434$	−18.9611	−	6.90128i	−0.910162	−	0.331272i
$435$		0			0
$436$	−1.78312	−	1.49621i	−0.0853959	−	0.0716557i
$437$	−0.384438	+	2.18025i	−0.0183901	+	0.104296i
$438$		0			0
$439$	13.1570	−	11.0401i	0.627951	−	0.526914i	−0.272340	−	0.962201i	$-0.587798\pi$
$439$	13.1570	−	11.0401i	0.627951	−	0.526914i	0.900292	+	0.435287i	$0.143353\pi$
$440$	5.43242	+	9.40923i	0.258980	+	0.448567i
$441$		0			0
$442$	1.86706	−	3.23384i	0.0888069	−	0.153818i
$443$	4.10173	+	23.2621i	0.194879	+	1.10521i	0.912591	+	0.408874i	$0.134078\pi$
$443$	4.10173	+	23.2621i	0.194879	+	1.10521i	−0.717712	+	0.696340i	$0.754810\pi$
$444$		0			0
$445$	−18.8478	+	6.86002i	−0.893470	+	0.325196i
$446$	3.96451	−	1.44296i	0.187725	−	0.0683263i
$447$		0			0
$448$	−0.407604	−	2.31164i	−0.0192575	−	0.109215i
$449$	−10.1295	+	17.5449i	−0.478042	+	0.827994i	−0.999683	−	0.0251715i	$-0.991987\pi$
$449$	−10.1295	+	17.5449i	−0.478042	+	0.827994i	0.521641	+	0.853165i	$0.325320\pi$
$450$		0			0
$451$	10.5162	+	18.2146i	0.495188	+	0.857691i
$452$	13.0667	−	10.9643i	0.614606	−	0.515716i
$453$		0			0
$454$	−2.77244	+	15.7233i	−0.130117	+	0.737931i
$455$	3.45471	+	2.89884i	0.161959	+	0.135900i
$456$		0			0
$457$	38.1143	+	13.8725i	1.78291	+	0.648926i	0.999628	+	0.0272600i	$0.00867822\pi$
$457$	38.1143	+	13.8725i	1.78291	+	0.648926i	0.783282	+	0.621666i	$0.213544\pi$
$458$	−17.8476			−0.833964
$459$		0			0
$460$	−0.773318			−0.0360562
$461$	12.8824	+	4.68880i	0.599992	+	0.218379i	0.624119	−	0.781330i	$-0.285458\pi$
$461$	12.8824	+	4.68880i	0.599992	+	0.218379i	−0.0241264	+	0.999709i	$0.507680\pi$
$462$		0			0
$463$	4.14022	+	3.47405i	0.192412	+	0.161453i	0.733904	−	0.679253i	$-0.237696\pi$
$463$	4.14022	+	3.47405i	0.192412	+	0.161453i	−0.541492	+	0.840706i	$0.682140\pi$
$464$	0.539363	−	3.05888i	0.0250393	−	0.142005i
$465$		0			0
$466$	0.564178	−	0.473401i	0.0261350	−	0.0219299i
$467$	15.7451	+	27.2713i	0.728596	+	1.26197i	0.957477	+	0.288511i	$0.0931603\pi$
$467$	15.7451	+	27.2713i	0.728596	+	1.26197i	−0.228880	+	0.973455i	$0.573506\pi$
$468$		0			0
$469$	0.0491630	−	0.0851529i	0.00227014	−	0.00393199i
$470$	−0.798133	−	4.52644i	−0.0368151	−	0.208789i
$471$		0			0
$472$	5.14543	−	1.87278i	0.236838	−	0.0862018i
$473$	6.57398	−	2.39273i	0.302272	−	0.110018i
$474$		0			0
$475$	−1.77672	−	10.0763i	−0.0815216	−	0.462332i
$476$	−5.77584	+	10.0041i	−0.264735	+	0.458535i
$477$		0			0
$478$	−1.43717	−	2.48925i	−0.0657345	−	0.113855i
$479$	16.0667	−	13.4816i	0.734106	−	0.615988i	−0.197141	−	0.980375i	$-0.563166\pi$
$479$	16.0667	−	13.4816i	0.734106	−	0.615988i	0.931248	+	0.364387i	$0.118721\pi$
$480$		0			0
$481$	−0.997941	+	5.65960i	−0.0455022	+	0.258056i
$482$	1.67159	+	1.40263i	0.0761388	+	0.0638880i
$483$		0			0
$484$	−6.96451	−	2.53487i	−0.316569	−	0.115222i
$485$	8.31315			0.377481
$486$		0			0
$487$	−15.4492			−0.700072			−0.350036	−	0.936736i	$-0.613831\pi$
$487$	−15.4492			−0.700072			−0.350036	+	0.936736i	$0.613831\pi$
$488$	−10.3833	−	3.77920i	−0.470028	−	0.171076i
$489$		0			0
$490$	2.89053	+	2.42544i	0.130581	+	0.109570i
$491$	−2.75443	+	15.6212i	−0.124306	+	0.704973i	0.857412	+	0.514631i	$0.172071\pi$
$491$	−2.75443	+	15.6212i	−0.124306	+	0.704973i	−0.981718	+	0.190343i	$0.939040\pi$
$492$		0			0
$493$	−11.7096	+	9.82553i	−0.527374	+	0.442519i
$494$	2.75015	+	4.76340i	0.123735	+	0.214316i
$495$		0			0
$496$	4.29813	−	7.44459i	0.192992	−	0.334272i
$497$	−1.71373	−	9.71902i	−0.0768711	−	0.435958i
$498$		0			0
$499$	7.03596	−	2.56088i	0.314973	−	0.114641i	−0.179696	−	0.983722i	$-0.557511\pi$
$499$	7.03596	−	2.56088i	0.314973	−	0.114641i	0.494669	+	0.869081i	$0.335289\pi$
$500$	−8.53849	+	3.10775i	−0.381853	+	0.138983i
$501$		0			0
$502$	4.52141	+	25.6422i	0.201800	+	1.14447i
$503$	−10.0667	+	17.4360i	−0.448852	+	0.777435i	−0.998312	−	0.0580857i	$-0.981500\pi$
$503$	−10.0667	+	17.4360i	−0.448852	+	0.777435i	0.549459	+	0.835520i	$0.314834\pi$
$504$		0			0
$505$	15.1839	+	26.2993i	0.675675	+	1.17030i
$506$	1.00387	−	0.842347i	0.0446275	−	0.0374469i
$507$		0			0
$508$	2.19594	−	12.4538i	0.0974289	−	0.552547i
$509$	28.7900	+	24.1577i	1.27609	+	1.07077i	0.993770	+	0.111450i	$0.0355496\pi$
$509$	28.7900	+	24.1577i	1.27609	+	1.07077i	0.282324	+	0.959319i	$0.408895\pi$
$510$		0			0
$511$	−24.4650	−	8.90452i	−1.08227	−	0.393913i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−9.99226			−0.440740
$515$	5.73783	+	2.08840i	0.252839	+	0.0920258i
$516$		0			0
$517$	5.96657	+	5.00654i	0.262409	+	0.220188i
$518$	3.08718	−	17.5083i	0.135643	−	0.769270i
$519$		0			0
$520$	−1.47178	+	1.23497i	−0.0645419	+	0.0541571i
$521$	13.9645	+	24.1872i	0.611796	+	1.05966i	0.990938	+	0.134323i	$0.0428861\pi$
$521$	13.9645	+	24.1872i	0.611796	+	1.05966i	−0.379141	+	0.925339i	$0.623781\pi$
$522$		0			0
$523$	−3.64677	+	6.31640i	−0.159462	+	0.276197i	−0.934675	−	0.355504i	$-0.884309\pi$
$523$	−3.64677	+	6.31640i	−0.159462	+	0.276197i	0.775213	+	0.631700i	$0.217643\pi$
$524$	0.901207	+	5.11100i	0.0393694	+	0.223275i
$525$		0			0
$526$	14.3045	−	5.20642i	0.623707	−	0.227011i
$527$	−39.7533	+	14.4690i	−1.73168	+	0.630280i
$528$		0			0
$529$	−3.97771	−	22.5587i	−0.172944	−	0.980814i
$530$	−0.726682	+	1.25865i	−0.0315650	+	0.0546722i
$531$		0			0
$532$	−8.50774	−	14.7358i	−0.368857	−	0.638880i
$533$	−2.84911	+	2.39068i	−0.123409	+	0.103552i
$534$		0			0
$535$	−1.06670	+	6.04958i	−0.0461176	+	0.261546i
$536$	0.0320889	+	0.0269258i	0.00138603	+	0.00116302i
$537$		0			0
$538$	28.7053	+	10.4479i	1.23757	+	0.450440i
$539$	−6.39424			−0.275419
$540$		0			0
$541$	−2.88444			−0.124012			−0.0620058	−	0.998076i	$-0.519750\pi$
$541$	−2.88444			−0.124012			−0.0620058	+	0.998076i	$0.519750\pi$
$542$	−24.2729	−	8.83462i	−1.04261	−	0.379479i
$543$		0			0
$544$	−3.76991	−	3.16333i	−0.161634	−	0.135627i
$545$	1.02347	−	5.80439i	0.0438407	−	0.248633i
$546$		0			0
$547$	−8.57263	+	7.19329i	−0.366539	+	0.307563i	−0.807391	−	0.590017i	$-0.799121\pi$
$547$	−8.57263	+	7.19329i	−0.366539	+	0.307563i	0.440851	+	0.897580i	$0.354677\pi$
$548$	−8.55690	−	14.8210i	−0.365533	−	0.633121i
$549$		0			0
$550$	−3.02822	+	5.24503i	−0.129124	+	0.223649i
$551$	−3.90983	−	22.1737i	−0.166564	−	0.944632i
$552$		0			0
$553$	−16.2665	+	5.92053i	−0.691722	+	0.251766i
$554$	21.0817	−	7.67312i	0.895676	−	0.326000i
$555$		0			0
$556$	2.11809	+	12.0123i	0.0898270	+	0.509434i
$557$	16.6741	−	28.8804i	0.706505	−	1.22370i	−0.259641	−	0.965705i	$-0.583604\pi$
$557$	16.6741	−	28.8804i	0.706505	−	1.22370i	0.966146	−	0.257997i	$-0.0830625\pi$
$558$		0			0
$559$	0.618555	+	1.07137i	0.0261621	+	0.0453141i
$560$	4.55303	−	3.82045i	0.192401	−	0.161443i
$561$		0			0
$562$	−1.01485	+	5.75552i	−0.0428090	+	0.242782i
$563$	−14.1668	−	11.8874i	−0.597061	−	0.500994i	0.293438	−	0.955978i	$-0.405200\pi$
$563$	−14.1668	−	11.8874i	−0.597061	−	0.500994i	−0.890500	+	0.454984i	$0.849645\pi$
$564$		0			0
$565$	40.5861	+	14.7721i	1.70747	+	0.621468i
$566$	−7.41147			−0.311527
$567$		0			0
$568$	4.20439			0.176412
$569$	27.5638	+	10.0324i	1.15553	+	0.420580i	0.847500	−	0.530796i	$-0.178107\pi$
$569$	27.5638	+	10.0324i	1.15553	+	0.420580i	0.308033	+	0.951376i	$0.400329\pi$
$570$		0			0
$571$	1.50387	+	1.26190i	0.0629350	+	0.0528087i	0.673713	−	0.738993i	$-0.264699\pi$
$571$	1.50387	+	1.26190i	0.0629350	+	0.0528087i	−0.610778	+	0.791802i	$0.709143\pi$
$572$	0.565360	−	3.20631i	0.0236389	−	0.134063i
$573$		0			0
$574$	8.81386	−	7.39571i	0.367884	−	0.308691i
$575$	−0.215537	−	0.373321i	−0.00898852	−	0.0155686i
$576$		0			0
$577$	5.52956	−	9.57748i	0.230199	−	0.398716i	−0.727668	−	0.685930i	$-0.759396\pi$
$577$	5.52956	−	9.57748i	0.230199	−	0.398716i	0.957866	+	0.287214i	$0.0927291\pi$
$578$	1.25356	+	7.10927i	0.0521411	+	0.295707i
$579$		0			0
$580$	7.39053	−	2.68993i	0.306875	−	0.111693i
$581$	−15.0496	+	5.47762i	−0.624364	+	0.227250i
$582$		0			0
$583$	−0.427671	−	2.42544i	−0.0177123	−	0.100452i
$584$	5.54576	−	9.60554i	0.229485	−	0.397480i
$585$		0			0
$586$	−4.43835	−	7.68745i	−0.183346	−	0.317565i
$587$	−25.3917	+	21.3062i	−1.04803	+	0.879400i	−0.992885	−	0.119078i	$-0.962006\pi$
$587$	−25.3917	+	21.3062i	−1.04803	+	0.879400i	−0.0551433	+	0.998478i	$0.517562\pi$
$588$		0			0
$589$	10.8207	−	61.3674i	0.445860	−	2.52860i
$590$	10.6211	+	8.91215i	0.437263	+	0.366907i
$591$		0			0
$592$	7.11721	+	2.59045i	0.292516	+	0.106467i
$593$	−14.8283			−0.608926			−0.304463	−	0.952524i	$-0.598477\pi$
$593$	−14.8283			−0.608926			−0.304463	+	0.952524i	$0.598477\pi$
$594$		0			0
$595$	−29.2499			−1.19913
$596$	7.23783	+	2.63435i	0.296473	+	0.107907i
$597$		0			0
$598$	0.177519	+	0.148956i	0.00725927	+	0.00609125i
$599$	8.20930	−	46.5573i	0.335423	−	1.90228i	−0.0875932	−	0.996156i	$-0.527918\pi$
$599$	8.20930	−	46.5573i	0.335423	−	1.90228i	0.423016	−	0.906122i	$-0.360971\pi$
$600$		0			0
$601$	28.1996	−	23.6623i	1.15029	−	0.965206i	0.150561	−	0.988601i	$-0.451892\pi$
$601$	28.1996	−	23.6623i	1.15029	−	0.965206i	0.999726	+	0.0233949i	$0.00744749\pi$
$602$	−1.91353	−	3.31434i	−0.0779898	−	0.135082i
$603$		0			0
$604$	0.390530	−	0.676417i	0.0158904	−	0.0275230i
$605$	−3.25877	−	18.4814i	−0.132488	−	0.751376i
$606$		0			0
$607$	−38.8764	+	14.1499i	−1.57795	+	0.574326i	−0.974756	−	0.223272i	$-0.928326\pi$
$607$	−38.8764	+	14.1499i	−1.57795	+	0.574326i	−0.603190	+	0.797597i	$0.706104\pi$
$608$	6.81180	−	2.47929i	0.276255	−	0.100549i
$609$		0			0
$610$	−4.85844	−	27.5536i	−0.196713	−	1.11561i
$611$	−0.688663	+	1.19280i	−0.0278603	+	0.0482555i
$612$		0			0
$613$	20.6755	+	35.8109i	0.835074	+	1.44639i	0.893970	+	0.448126i	$0.147909\pi$
$613$	20.6755	+	35.8109i	0.835074	+	1.44639i	−0.0588963	+	0.998264i	$0.518758\pi$
$614$	−12.3327	+	10.3484i	−0.497709	+	0.417628i
$615$		0			0
$616$	−1.74897	+	9.91890i	−0.0704680	+	0.399644i
$617$	−18.7867	−	15.7639i	−0.756326	−	0.634633i	0.180842	−	0.983512i	$-0.442118\pi$
$617$	−18.7867	−	15.7639i	−0.756326	−	0.634633i	−0.937168	+	0.348880i	$0.886562\pi$
$618$		0			0
$619$	−37.2768	−	13.5676i	−1.49828	−	0.545329i	−0.542666	−	0.839949i	$-0.682585\pi$
$619$	−37.2768	−	13.5676i	−1.49828	−	0.545329i	−0.955615	+	0.294619i	$0.904807\pi$
$620$	21.7665			0.874164
$621$		0			0
$622$	−13.5895			−0.544888
$623$	−17.4722	−	6.35938i	−0.700011	−	0.254783i
$624$		0			0
$625$	−23.0312	−	19.3255i	−0.921248	−	0.773019i
$626$	−3.73442	+	21.1790i	−0.149258	+	0.846482i
$627$		0			0
$628$	−7.97565	+	6.69237i	−0.318263	+	0.267054i
$629$	−18.6368	−	32.2799i	−0.743098	−	1.28708i
$630$		0			0
$631$	16.6596	−	28.8552i	0.663207	−	1.14871i	−0.316561	−	0.948572i	$-0.602528\pi$
$631$	16.6596	−	28.8552i	0.663207	−	1.14871i	0.979768	−	0.200136i	$-0.0641384\pi$
$632$	−1.28059	−	7.26260i	−0.0509392	−	0.288891i
$633$		0			0
$634$	−19.8204	+	7.21404i	−0.787170	+	0.286506i
$635$	30.0895	−	10.9517i	1.19406	−	0.434604i
$636$		0			0
$637$	−0.196347	−	1.11354i	−0.00777957	−	0.0441201i
$638$	−6.66385	+	11.5421i	−0.263824	+	0.456957i
$639$		0			0
$640$	1.26604	+	2.19285i	0.0500448	+	0.0866801i
$641$	−5.55690	+	4.66280i	−0.219485	+	0.184169i	−0.745900	−	0.666058i	$-0.767980\pi$
$641$	−5.55690	+	4.66280i	−0.219485	+	0.184169i	0.526415	+	0.850228i	$0.323536\pi$
$642$		0			0
$643$	−1.34120	+	7.60635i	−0.0528919	+	0.299965i	−0.999766	−	0.0216400i	$-0.993111\pi$
$643$	−1.34120	+	7.60635i	−0.0528919	+	0.299965i	0.946874	+	0.321605i	$0.104222\pi$
$644$	−0.549163	−	0.460802i	−0.0216401	−	0.0181582i
$645$		0			0
$646$	−33.5228	−	12.2013i	−1.31894	−	0.480053i
$647$	40.9469			1.60979			0.804894	−	0.593419i	$-0.202222\pi$
$647$	40.9469			1.60979			0.804894	+	0.593419i	$0.202222\pi$
$648$		0			0
$649$	−23.4953			−0.922269
$650$	−1.00640	−	0.366298i	−0.0394741	−	0.0143674i
$651$		0			0
$652$	−8.10014	−	6.79682i	−0.317226	−	0.266184i
$653$	−3.45171	+	19.5756i	−0.135076	+	0.766054i	0.839731	+	0.543003i	$0.182713\pi$
$653$	−3.45171	+	19.5756i	−0.135076	+	0.766054i	−0.974807	+	0.223051i	$0.928398\pi$
$654$		0			0
$655$	−10.0667	+	8.44697i	−0.393339	+	0.330050i
$656$	2.45084	+	4.24497i	0.0956891	+	0.165738i
$657$		0			0
$658$	2.13041	−	3.68999i	0.0830522	−	0.143851i
$659$	−2.98499	−	16.9287i	−0.116279	−	0.659448i	−0.986109	−	0.166098i	$-0.946883\pi$
$659$	−2.98499	−	16.9287i	−0.116279	−	0.659448i	0.869831	−	0.493350i	$-0.164228\pi$
$660$		0			0
$661$	32.3276	−	11.7663i	1.25740	−	0.457655i	0.374503	−	0.927226i	$-0.377813\pi$
$661$	32.3276	−	11.7663i	1.25740	−	0.457655i	0.882895	+	0.469571i	$0.155591\pi$
$662$	−15.4474	+	5.62241i	−0.600382	+	0.218521i
$663$		0			0
$664$	−1.18479	−	6.71929i	−0.0459789	−	0.260759i
$665$	21.5424	−	37.3125i	0.835377	−	1.44691i
$666$		0			0
$667$	−0.474308	−	0.821525i	−0.0183653	−	0.0318096i
$668$	−1.15136	+	0.966105i	−0.0445474	+	0.0373797i
$669$		0			0
$670$	−0.0184183	+	0.104455i	−0.000711562	+	0.00403547i
$671$	36.3200	+	30.4761i	1.40212	+	1.17652i
$672$		0			0
$673$	−22.4513	−	8.17161i	−0.865434	−	0.314992i	−0.129117	−	0.991629i	$-0.541214\pi$
$673$	−22.4513	−	8.17161i	−0.865434	−	0.314992i	−0.736317	+	0.676637i	$0.763437\pi$
$674$	10.5517			0.406436
$675$		0			0
$676$	−12.4243			−0.477856
$677$	32.6238	+	11.8741i	1.25383	+	0.456358i	0.881695	−	0.471819i	$-0.156403\pi$
$677$	32.6238	+	11.8741i	1.25383	+	0.456358i	0.372138	+	0.928177i	$0.378625\pi$
$678$		0			0
$679$	5.90348	+	4.95361i	0.226555	+	0.190102i
$680$	2.16385	−	12.2718i	0.0829798	−	0.470602i
$681$		0			0
$682$	−28.2558	+	23.7095i	−1.08197	+	0.907882i
$683$	−19.5030	−	33.7802i	−0.746261	−	1.29256i	−0.949603	−	0.313455i	$-0.898514\pi$
$683$	−19.5030	−	33.7802i	−0.746261	−	1.29256i	0.203342	−	0.979108i	$-0.434820\pi$
$684$		0			0
$685$	21.6668	−	37.5281i	0.827847	−	1.43387i
$686$	3.46064	+	19.6262i	0.132128	+	0.749334i
$687$		0			0
$688$	1.53209	−	0.557635i	0.0584103	−	0.0212596i
$689$	0.409253	−	0.148956i	0.0155913	−	0.00567476i
$690$		0			0
$691$	4.39780	+	24.9412i	0.167300	+	0.948807i	0.946661	+	0.322232i	$0.104433\pi$
$691$	4.39780	+	24.9412i	0.167300	+	0.948807i	−0.779361	+	0.626576i	$0.784456\pi$
$692$	−5.57532	+	9.65674i	−0.211942	+	0.367094i
$693$		0			0
$694$	14.1800	+	24.5606i	0.538267	+	0.932306i
$695$	−23.6596	+	19.8527i	−0.897459	+	0.753057i
$696$		0			0
$697$	4.18883	−	23.7560i	0.158663	−	0.899823i
$698$	12.0287	+	10.0933i	0.455292	+	0.382036i
$699$		0			0
$700$	3.11334	+	1.13316i	0.117673	+	0.0428295i
$701$	−42.3054			−1.59785			−0.798927	−	0.601429i	$-0.794598\pi$
$701$	−42.3054			−1.59785			−0.798927	+	0.601429i	$0.794598\pi$
$702$		0			0
$703$	54.9035			2.07073
$704$	−4.03209	−	1.46756i	−0.151965	−	0.0553108i
$705$		0			0
$706$	1.58125	+	1.32683i	0.0595112	+	0.0499358i
$707$	−4.88847	+	27.7239i	−0.183850	+	1.04266i
$708$		0			0
$709$	−36.7098	+	30.8032i	−1.37867	+	1.15684i	−0.408964	+	0.912551i	$0.634110\pi$
$709$	−36.7098	+	30.8032i	−1.37867	+	1.15684i	−0.969703	+	0.244288i	$0.921446\pi$
$710$	5.32295	+	9.21962i	0.199767	+	0.346006i
$711$		0			0
$712$	3.96064	−	6.86002i	0.148431	−	0.257090i
$713$	−0.455889	−	2.58548i	−0.0170732	−	0.0968269i
$714$		0			0
$715$	7.74675	−	2.81959i	0.289712	−	0.105447i
$716$	7.33750	−	2.67063i	0.274215	−	0.0998061i
$717$		0			0
$718$	6.07145	+	34.4329i	0.226585	+	1.28502i
$719$	6.15451	−	10.6599i	0.229525	−	0.397548i	−0.728143	−	0.685426i	$-0.759616\pi$
$719$	6.15451	−	10.6599i	0.229525	−	0.397548i	0.957667	+	0.287877i	$0.0929495\pi$
$720$		0			0
$721$	2.83022	+	4.90209i	0.105403	+	0.182563i
$722$	25.6989	−	21.5640i	0.956415	−	0.802528i
$723$		0			0
$724$	1.81908	−	10.3165i	0.0676055	−	0.383410i
$725$	3.35844	+	2.81807i	0.124729	+	0.104660i
$726$		0			0
$727$	16.3542	+	5.95243i	0.606542	+	0.220763i	0.626990	−	0.779028i	$-0.284287\pi$
$727$	16.3542	+	5.95243i	0.606542	+	0.220763i	−0.0204474	+	0.999791i	$0.506509\pi$
$728$	−1.78106			−0.0660104
$729$		0			0
$730$	28.0847			1.03946
$731$	−7.53983	−	2.74427i	−0.278871	−	0.101501i
$732$		0			0
$733$	11.0266	+	9.25244i	0.407278	+	0.341747i	0.823299	−	0.567608i	$-0.192131\pi$
$733$	11.0266	+	9.25244i	0.407278	+	0.341747i	−0.416021	+	0.909355i	$0.636576\pi$
$734$	−0.0773815	+	0.438852i	−0.00285620	+	0.0161983i
$735$		0			0
$736$	0.233956	−	0.196312i	0.00862372	−	0.00723616i
$737$	−0.0898700	−	0.155659i	−0.00331041	−	0.00573379i
$738$		0			0
$739$	6.82383	−	11.8192i	0.251018	−	0.434777i	−0.712788	−	0.701380i	$-0.752568\pi$
$739$	6.82383	−	11.8192i	0.251018	−	0.434777i	0.963806	+	0.266603i	$0.0859012\pi$
$740$	3.33022	+	18.8866i	0.122421	+	0.694286i
$741$		0			0
$742$	−1.26604	+	0.460802i	−0.0464780	+	0.0169166i
$743$	−17.2459	+	6.27698i	−0.632690	+	0.230280i	−0.638402	−	0.769703i	$-0.720404\pi$
$743$	−17.2459	+	6.27698i	−0.632690	+	0.230280i	0.00571190	+	0.999984i	$0.498182\pi$
$744$		0			0
$745$	3.38666	+	19.2067i	0.124078	+	0.703679i
$746$	11.0312	−	19.1066i	0.403881	−	0.699543i
$747$		0			0
$748$	10.5582	+	18.2874i	0.386048	+	0.668654i
$749$	−4.36231	+	3.66041i	−0.159395	+	0.133749i
$750$		0			0
$751$	−7.01460	+	39.7818i	−0.255967	+	1.45166i	0.537613	+	0.843192i	$0.319326\pi$
$751$	−7.01460	+	39.7818i	−0.255967	+	1.45166i	−0.793579	+	0.608467i	$0.791785\pi$
$752$	1.39053	+	1.16679i	0.0507074	+	0.0425486i
$753$		0			0
$754$	−2.21466	−	0.806070i	−0.0806532	−	0.0293553i
$755$	1.97771			0.0719763
$756$		0			0
$757$	3.71595			0.135058			0.0675292	−	0.997717i	$-0.478488\pi$
$757$	3.71595			0.135058			0.0675292	+	0.997717i	$0.478488\pi$
$758$	−12.3229	−	4.48519i	−0.447590	−	0.162909i
$759$		0			0
$760$	14.0608	+	11.7984i	0.510038	+	0.427973i
$761$	6.41147	−	36.3613i	0.232416	−	1.31810i	−0.615573	−	0.788080i	$-0.711075\pi$
$761$	6.41147	−	36.3613i	0.232416	−	1.31810i	0.847988	−	0.530015i	$-0.177814\pi$
$762$		0			0
$763$	4.18551	−	3.51206i	0.151526	−	0.127145i
$764$	−6.11468	−	10.5909i	−0.221222	−	0.383167i
$765$		0			0
$766$	8.05556	−	13.9526i	0.291059	−	0.504129i
$767$	−0.721467	−	4.09164i	−0.0260507	−	0.147741i
$768$		0			0
$769$	25.5501	−	9.29947i	0.921360	−	0.335348i	0.162581	−	0.986695i	$-0.448018\pi$
$769$	25.5501	−	9.29947i	0.921360	−	0.335348i	0.758779	+	0.651348i	$0.225796\pi$
$770$	−23.9650	+	8.72254i	−0.863638	+	0.314338i
$771$		0			0
$772$	−2.84224	−	16.1192i	−0.102295	−	0.580141i
$773$	−0.869585	+	1.50617i	−0.0312768	+	0.0541730i	−0.881240	−	0.472669i	$-0.843291\pi$
$773$	−0.869585	+	1.50617i	−0.0312768	+	0.0541730i	0.849963	+	0.526842i	$0.176624\pi$
$774$		0			0
$775$	6.06670	+	10.5078i	0.217922	+	0.377453i
$776$	−2.51501	+	2.11035i	−0.0902838	+	0.0757571i
$777$		0			0
$778$	−0.0984882	+	0.558554i	−0.00353097	+	0.0200251i
$779$	27.2192	+	22.8396i	0.975228	+	0.818313i
$780$		0			0
$781$	−16.9525	−	6.17020i	−0.606608	−	0.220787i

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.939693 - 0.342020i) q^{2} +(0.766044 + 0.642788i) q^{4} +(-0.439693 + 2.49362i) q^{5} +(-1.79813 + 1.50881i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(1.26604 - 2.19285i) q^{10} +(0.745100 + 4.22567i) q^{11} +(-0.713011 + 0.259515i) q^{13} +(2.20574 - 0.802823i) q^{14} +(0.173648 + 0.984808i) q^{16} +(2.46064 - 4.26195i) q^{17} +(3.62449 + 6.27779i) q^{19} +(-1.93969 + 1.62760i) q^{20} +(0.745100 - 4.22567i) q^{22} +(0.233956 + 0.196312i) q^{23} +(-1.32635 - 0.482753i) q^{25} +0.758770 q^{26} -2.34730 q^{28} +(-2.91875 - 1.06234i) q^{29} +(-6.58512 - 5.52557i) q^{31} +(0.173648 - 0.984808i) q^{32} +(-3.76991 + 3.16333i) q^{34} +(-2.97178 - 5.14728i) q^{35} +(3.78699 - 6.55926i) q^{37} +(-1.25877 - 7.13884i) q^{38} +(2.37939 - 0.866025i) q^{40} +(4.60607 - 1.67647i) q^{41} +(-0.283119 - 1.60565i) q^{43} +(-2.14543 + 3.71599i) q^{44} +(-0.152704 - 0.264490i) q^{46} +(1.39053 - 1.16679i) q^{47} +(-0.258770 + 1.46756i) q^{49} +(1.08125 + 0.907278i) q^{50} +(-0.713011 - 0.259515i) q^{52} -0.573978 q^{53} -10.8648 q^{55} +(2.20574 + 0.802823i) q^{56} +(2.37939 + 1.99654i) q^{58} +(-0.950837 + 5.39246i) q^{59} +(8.46451 - 7.10257i) q^{61} +(4.29813 + 7.44459i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(-0.333626 - 1.89209i) q^{65} +(-0.0393628 + 0.0143269i) q^{67} +(4.62449 - 1.68317i) q^{68} +(1.03209 + 5.85327i) q^{70} +(-2.10220 + 3.64111i) q^{71} +(5.54576 + 9.60554i) q^{73} +(-5.80200 + 4.86846i) q^{74} +(-1.25877 + 7.13884i) q^{76} +(-7.71554 - 6.47410i) q^{77} +(6.92989 + 2.52227i) q^{79} -2.53209 q^{80} -4.90167 q^{82} +(6.41147 + 2.33359i) q^{83} +(9.54576 + 8.00984i) q^{85} +(-0.283119 + 1.60565i) q^{86} +(3.28699 - 2.75811i) q^{88} +(3.96064 + 6.86002i) q^{89} +(0.890530 - 1.54244i) q^{91} +(0.0530334 + 0.300767i) q^{92} +(-1.70574 + 0.620838i) q^{94} +(-17.2481 + 6.27779i) q^{95} +(-0.570108 - 3.23324i) q^{97} +(0.745100 - 1.29055i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{5} + 3 q^{7} - 3 q^{8} + 3 q^{10} + 3 q^{11} - 12 q^{13} + 3 q^{14} + 6 q^{17} + 9 q^{19} - 6 q^{20} + 3 q^{22} + 6 q^{23} - 9 q^{25} - 18 q^{26} - 12 q^{28} - 15 q^{29} - 18 q^{31} + 6 q^{34}+ \cdots + 3 q^{98}+O(q^{100}) \) 6 * q + 3 * q^5 + 3 * q^7 - 3 * q^8 + 3 * q^10 + 3 * q^11 - 12 * q^13 + 3 * q^14 + 6 * q^17 + 9 * q^19 - 6 * q^20 + 3 * q^22 + 6 * q^23 - 9 * q^25 - 18 * q^26 - 12 * q^28 - 15 * q^29 - 18 * q^31 + 6 * q^34 - 3 * q^35 + 15 * q^37 + 15 * q^38 + 3 * q^40 + 3 * q^41 - 18 * q^43 + 3 * q^44 - 3 * q^46 - 9 * q^47 + 21 * q^49 + 9 * q^50 - 12 * q^52 + 12 * q^53 - 18 * q^55 + 3 * q^56 + 3 * q^58 + 6 * q^59 + 18 * q^61 + 12 * q^62 - 3 * q^64 - 21 * q^65 - 9 * q^67 + 15 * q^68 - 3 * q^70 - 12 * q^71 + 3 * q^73 + 3 * q^74 + 15 * q^76 - 39 * q^77 + 33 * q^79 - 6 * q^80 - 6 * q^82 + 18 * q^83 + 27 * q^85 - 18 * q^86 + 12 * q^88 + 15 * q^89 - 12 * q^91 - 12 * q^92 - 21 * q^95 - 12 * q^97 + 3 * q^98

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