LMFDB - Embedded newform 162.2.g.b.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

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("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			31.5
Character	$\chi$	$=$	162.31
Dual form			162.2.g.b.115.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.396080 + 0.918216i) q^{2} +(1.72468 + 0.159609i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(0.0350699 - 0.602127i) q^{5} +(0.536555 + 1.64685i) q^{6} +(0.510080 - 0.120891i) q^{7} +(-0.939693 - 0.342020i) q^{8} +(2.94905 + 0.550550i) q^{9} +O(q^{10})$	\(q+(0.396080 + 0.918216i) q^{2} +(1.72468 + 0.159609i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(0.0350699 - 0.602127i) q^{5} +(0.536555 + 1.64685i) q^{6} +(0.510080 - 0.120891i) q^{7} +(-0.939693 - 0.342020i) q^{8} +(2.94905 + 0.550550i) q^{9} +(0.566774 - 0.206289i) q^{10} +(-2.01981 + 1.32845i) q^{11} +(-1.29964 + 1.14496i) q^{12} +(-1.15841 + 0.135399i) q^{13} +(0.313036 + 0.420481i) q^{14} +(0.156590 - 1.03288i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(-4.35000 - 3.65009i) q^{17} +(0.662535 + 2.92593i) q^{18} +(1.35309 - 1.13538i) q^{19} +(0.413905 + 0.438714i) q^{20} +(0.899020 - 0.127085i) q^{21} +(-2.01981 - 1.32845i) q^{22} +(-4.95439 - 1.17421i) q^{23} +(-1.56608 - 0.739859i) q^{24} +(4.60486 + 0.538231i) q^{25} +(-0.583149 - 1.01004i) q^{26} +(4.99830 + 1.42022i) q^{27} +(-0.262105 + 0.453979i) q^{28} +(-3.44579 + 4.62851i) q^{29} +(1.01043 - 0.265320i) q^{30} +(-0.468359 - 1.56443i) q^{31} +(0.893633 - 0.448799i) q^{32} +(-3.69556 + 1.96877i) q^{33} +(1.62862 - 5.43997i) q^{34} +(-0.0549034 - 0.311373i) q^{35} +(-2.42422 + 1.76725i) q^{36} +(1.24273 - 7.04785i) q^{37} +(1.57846 + 0.792732i) q^{38} +(-2.01950 + 0.0486267i) q^{39} +(-0.238895 + 0.553820i) q^{40} +(3.14622 - 7.29375i) q^{41} +(0.472775 + 0.775159i) q^{42} +(2.30628 + 1.15826i) q^{43} +(0.419798 - 2.38079i) q^{44} +(0.434924 - 1.75640i) q^{45} +(-0.884154 - 5.01428i) q^{46} +(-1.76161 + 5.88420i) q^{47} +(0.0590580 - 1.73104i) q^{48} +(-6.00986 + 3.01827i) q^{49} +(1.32968 + 4.44144i) q^{50} +(-6.91978 - 6.98954i) q^{51} +(0.696465 - 0.935515i) q^{52} +(1.11214 - 1.92629i) q^{53} +(0.675656 + 5.15204i) q^{54} +(0.729061 + 1.26277i) q^{55} +(-0.520665 - 0.0608570i) q^{56} +(2.51487 - 1.74220i) q^{57} +(-5.61478 - 1.33073i) q^{58} +(4.64678 + 3.05623i) q^{59} +(0.643832 + 0.822704i) q^{60} +(-2.51525 - 2.66601i) q^{61} +(1.25098 - 1.04969i) q^{62} +(1.57081 - 0.0756894i) q^{63} +(0.766044 + 0.642788i) q^{64} +(0.0409020 + 0.702260i) q^{65} +(-3.27149 - 2.61353i) q^{66} +(9.01315 + 12.1068i) q^{67} +(5.64013 - 0.659237i) q^{68} +(-8.35733 - 2.81591i) q^{69} +(0.264161 - 0.173742i) q^{70} +(-5.71305 + 2.07938i) q^{71} +(-2.58290 - 1.52598i) q^{72} +(-10.8918 - 3.96429i) q^{73} +(6.96367 - 1.65042i) q^{74} +(7.85602 + 1.66326i) q^{75} +(-0.102703 + 1.76335i) q^{76} +(-0.869665 + 0.921792i) q^{77} +(-0.844534 - 1.83508i) q^{78} +(6.47803 + 15.0178i) q^{79} -0.603148 q^{80} +(8.39379 + 3.24720i) q^{81} +7.94339 q^{82} +(5.81950 + 13.4911i) q^{83} +(-0.524507 + 0.741135i) q^{84} +(-2.35037 + 2.49125i) q^{85} +(-0.150060 + 2.57643i) q^{86} +(-6.68165 + 7.43272i) q^{87} +(2.35235 - 0.557518i) q^{88} +(12.1445 + 4.42023i) q^{89} +(1.78502 - 0.296318i) q^{90} +(-0.574514 + 0.209106i) q^{91} +(4.25400 - 2.79790i) q^{92} +(-0.558073 - 2.77289i) q^{93} +(-6.10071 + 0.713071i) q^{94} +(-0.636191 - 0.854553i) q^{95} +(1.61286 - 0.631403i) q^{96} +(0.237977 + 4.08591i) q^{97} +(-5.15181 - 4.32288i) q^{98} +(-6.68789 + 2.80566i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

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 $

$2$	0.396080	+	0.918216i	0.280071	+	0.649277i
$2$	0.396080	+	0.918216i	0.280071	+	0.649277i
$3$	1.72468	+	0.159609i	0.995745	+	0.0921505i
$3$	1.72468	+	0.159609i	0.995745	+	0.0921505i
$4$	−0.686242	+	0.727374i	−0.343121	+	0.363687i
$5$	0.0350699	−	0.602127i	0.0156837	−	0.269280i	−0.981345	−	0.192253i	$-0.938420\pi$
$5$	0.0350699	−	0.602127i	0.0156837	−	0.269280i	0.997029	−	0.0770262i	$-0.0245425\pi$
$6$	0.536555	+	1.64685i	0.219048	+	0.672323i
$7$	0.510080	−	0.120891i	0.192792	−	0.0456925i	−0.133085	−	0.991105i	$-0.542488\pi$
$7$	0.510080	−	0.120891i	0.192792	−	0.0456925i	0.325877	+	0.945412i	$0.394340\pi$
$8$	−0.939693	−	0.342020i	−0.332232	−	0.120922i
$9$	2.94905	+	0.550550i	0.983017	+	0.183517i
$10$	0.566774	−	0.206289i	0.179230	−	0.0652342i
$11$	−2.01981	+	1.32845i	−0.608995	+	0.400542i	−0.816212	−	0.577753i	$-0.803930\pi$
$11$	−2.01981	+	1.32845i	−0.608995	+	0.400542i	0.207217	+	0.978295i	$0.433559\pi$
$12$	−1.29964	+	1.14496i	−0.375175	+	0.330521i
$13$	−1.15841	+	0.135399i	−0.321286	+	0.0375529i	−0.275207	−	0.961385i	$-0.588746\pi$
$13$	−1.15841	+	0.135399i	−0.321286	+	0.0375529i	−0.0460785	+	0.998938i	$0.514672\pi$
$14$	0.313036	+	0.420481i	0.0836625	+	0.112378i
$15$	0.156590	−	1.03288i	0.0404312	−	0.266689i
$16$	−0.0581448	−	0.998308i	−0.0145362	−	0.249577i
$17$	−4.35000	−	3.65009i	−1.05503	−	0.885276i	−0.0614173	−	0.998112i	$-0.519562\pi$
$17$	−4.35000	−	3.65009i	−1.05503	−	0.885276i	−0.993614	+	0.112836i	$0.964006\pi$
$18$	0.662535	+	2.92593i	0.156161	+	0.689648i
$19$	1.35309	−	1.13538i	0.310421	−	0.260474i	−0.474245	−	0.880393i	$-0.657279\pi$
$19$	1.35309	−	1.13538i	0.310421	−	0.260474i	0.784666	+	0.619919i	$0.212834\pi$
$20$	0.413905	+	0.438714i	0.0925520	+	0.0980994i
$21$	0.899020	−	0.127085i	0.196182	−	0.0277323i
$22$	−2.01981	−	1.32845i	−0.430625	−	0.283226i
$23$	−4.95439	−	1.17421i	−1.03306	−	0.244840i	−0.321091	−	0.947048i	$-0.604049\pi$
$23$	−4.95439	−	1.17421i	−1.03306	−	0.244840i	−0.711972	+	0.702208i	$0.752198\pi$
$24$	−1.56608	−	0.739859i	−0.319675	−	0.151023i
$25$	4.60486	+	0.538231i	0.920973	+	0.107646i
$26$	−0.583149	−	1.01004i	−0.114365	−	0.198086i
$27$	4.99830	+	1.42022i	0.961923	+	0.273321i
$28$	−0.262105	+	0.453979i	−0.0495332	+	0.0857940i
$29$	−3.44579	+	4.62851i	−0.639868	+	0.859492i	−0.997223	−	0.0744768i	$-0.976271\pi$
$29$	−3.44579	+	4.62851i	−0.639868	+	0.859492i	0.357355	+	0.933969i	$0.383679\pi$
$30$	1.01043	−	0.265320i	0.184478	−	0.0484406i
$31$	−0.468359	−	1.56443i	−0.0841197	−	0.280979i	0.905572	−	0.424192i	$-0.139442\pi$
$31$	−0.468359	−	1.56443i	−0.0841197	−	0.280979i	−0.989692	+	0.143213i	$0.954257\pi$
$32$	0.893633	−	0.448799i	0.157973	−	0.0793372i
$33$	−3.69556	+	1.96877i	−0.643314	+	0.342719i
$34$	1.62862	−	5.43997i	0.279306	−	0.932947i
$35$	−0.0549034	−	0.311373i	−0.00928037	−	0.0526316i
$36$	−2.42422	+	1.76725i	−0.404036	+	0.294542i
$37$	1.24273	−	7.04785i	0.204303	−	1.15866i	−0.694230	−	0.719753i	$-0.744255\pi$
$37$	1.24273	−	7.04785i	0.204303	−	1.15866i	0.898533	−	0.438906i	$-0.144634\pi$
$38$	1.57846	+	0.792732i	0.256060	+	0.128598i
$39$	−2.01950	+	0.0486267i	−0.323379	+	0.00778650i
$40$	−0.238895	+	0.553820i	−0.0377726	+	0.0875666i
$41$	3.14622	−	7.29375i	0.491357	−	1.13909i	−0.474556	−	0.880225i	$-0.657391\pi$
$41$	3.14622	−	7.29375i	0.491357	−	1.13909i	0.965913	−	0.258868i	$-0.0833493\pi$
$42$	0.472775	+	0.775159i	0.0729508	+	0.119610i
$43$	2.30628	+	1.15826i	0.351705	+	0.176633i	0.615876	−	0.787843i	$-0.288802\pi$
$43$	2.30628	+	1.15826i	0.351705	+	0.176633i	−0.264171	+	0.964476i	$0.585098\pi$
$44$	0.419798	−	2.38079i	0.0632869	−	0.358918i
$45$	0.434924	−	1.75640i	0.0648347	−	0.261828i
$46$	−0.884154	−	5.01428i	−0.130361	−	0.739316i
$47$	−1.76161	+	5.88420i	−0.256958	+	0.858299i	0.728011	+	0.685566i	$0.240445\pi$
$47$	−1.76161	+	5.88420i	−0.256958	+	0.858299i	−0.984969	+	0.172733i	$0.944740\pi$
$48$	0.0590580	−	1.73104i	0.00852428	−	0.249855i
$49$	−6.00986	+	3.01827i	−0.858552	+	0.431181i
$50$	1.32968	+	4.44144i	0.188045	+	0.628115i
$51$	−6.91978	−	6.98954i	−0.968963	−	0.978731i
$52$	0.696465	−	0.935515i	0.0965823	−	0.129733i
$53$	1.11214	−	1.92629i	0.152764	−	0.264596i	−0.779478	−	0.626429i	$-0.784516\pi$
$53$	1.11214	−	1.92629i	0.152764	−	0.264596i	0.932243	+	0.361833i	$0.117849\pi$
$54$	0.675656	+	5.15204i	0.0919452	+	0.701103i
$55$	0.729061	+	1.26277i	0.0983065	+	0.170272i
$56$	−0.520665	−	0.0608570i	−0.0695768	−	0.00813236i
$57$	2.51487	−	1.74220i	0.333103	−	0.230760i
$58$	−5.61478	−	1.33073i	−0.737256	−	0.174733i
$59$	4.64678	+	3.05623i	0.604959	+	0.397888i	0.814711	−	0.579867i	$-0.196895\pi$
$59$	4.64678	+	3.05623i	0.604959	+	0.397888i	−0.209752	+	0.977755i	$0.567266\pi$
$60$	0.643832	+	0.822704i	0.0831183	+	0.106211i
$61$	−2.51525	−	2.66601i	−0.322044	−	0.341347i	0.546044	−	0.837756i	$-0.316133\pi$
$61$	−2.51525	−	2.66601i	−0.322044	−	0.341347i	−0.868089	+	0.496409i	$0.834652\pi$
$62$	1.25098	−	1.04969i	0.158874	−	0.133311i
$63$	1.57081	−	0.0756894i	0.197903	−	0.00953597i
$64$	0.766044	+	0.642788i	0.0957556	+	0.0803485i
$65$	0.0409020	+	0.702260i	0.00507327	+	0.0871047i
$66$	−3.27149	−	2.61353i	−0.402693	−	0.321703i
$67$	9.01315	+	12.1068i	1.10113	+	1.47908i	0.861186	+	0.508289i	$0.169722\pi$
$67$	9.01315	+	12.1068i	1.10113	+	1.47908i	0.239945	+	0.970787i	$0.422871\pi$
$68$	5.64013	−	0.659237i	0.683966	−	0.0799442i
$69$	−8.35733	−	2.81591i	−1.00610	−	0.338996i
$70$	0.264161	−	0.173742i	0.0315733	−	0.0207661i
$71$	−5.71305	+	2.07938i	−0.678014	+	0.246777i	−0.657995	−	0.753023i	$-0.728595\pi$
$71$	−5.71305	+	2.07938i	−0.678014	+	0.246777i	−0.0200196	+	0.999800i	$0.506373\pi$
$72$	−2.58290	−	1.52598i	−0.304398	−	0.179839i
$73$	−10.8918	−	3.96429i	−1.27479	−	0.463986i	−0.386084	−	0.922464i	$-0.626173\pi$
$73$	−10.8918	−	3.96429i	−1.27479	−	0.463986i	−0.888706	+	0.458478i	$0.848395\pi$
$74$	6.96367	−	1.65042i	0.809510	−	0.191857i
$75$	7.85602	+	1.66326i	0.907135	+	0.192056i
$76$	−0.102703	+	1.76335i	−0.0117809	+	0.202270i
$77$	−0.869665	+	0.921792i	−0.0991076	+	0.105048i
$78$	−0.844534	−	1.83508i	−0.0956246	−	0.207782i
$79$	6.47803	+	15.0178i	0.728836	+	1.68963i	0.724150	+	0.689642i	$0.242232\pi$
$79$	6.47803	+	15.0178i	0.728836	+	1.68963i	0.00468577	+	0.999989i	$0.498508\pi$
$80$	−0.603148			−0.0674340
$81$	8.39379	+	3.24720i	0.932643	+	0.360800i
$82$	7.94339			0.877201
$83$	5.81950	+	13.4911i	0.638773	+	1.48084i	0.862431	+	0.506175i	$0.168941\pi$
$83$	5.81950	+	13.4911i	0.638773	+	1.48084i	−0.223658	+	0.974668i	$0.571800\pi$
$84$	−0.524507	+	0.741135i	−0.0572284	+	0.0808644i
$85$	−2.35037	+	2.49125i	−0.254934	+	0.270214i
$86$	−0.150060	+	2.57643i	−0.0161814	+	0.277823i
$87$	−6.68165	+	7.43272i	−0.716348	+	0.796871i
$88$	2.35235	−	0.557518i	0.250762	−	0.0594317i
$89$	12.1445	+	4.42023i	1.28731	+	0.468544i	0.892844	−	0.450366i	$-0.148706\pi$
$89$	12.1445	+	4.42023i	1.28731	+	0.468544i	0.394469	+	0.918909i	$0.370929\pi$
$90$	1.78502	−	0.296318i	0.188157	−	0.0312347i
$91$	−0.574514	+	0.209106i	−0.0602254	+	0.0219203i
$92$	4.25400	−	2.79790i	0.443510	−	0.291701i
$93$	−0.558073	−	2.77289i	−0.0578694	−	0.287536i
$94$	−6.10071	+	0.713071i	−0.629240	+	0.0735476i
$95$	−0.636191	−	0.854553i	−0.0652718	−	0.0876753i
$96$	1.61286	−	0.631403i	0.164612	−	0.0644423i
$97$	0.237977	+	4.08591i	0.0241629	+	0.414861i	0.988602	+	0.150555i	$0.0481060\pi$
$97$	0.237977	+	4.08591i	0.0241629	+	0.414861i	−0.964439	+	0.264306i	$0.914857\pi$
$98$	−5.15181	−	4.32288i	−0.520411	−	0.436677i
$99$	−6.68789	+	2.80566i	−0.672158	+	0.281979i
$100$	−3.55155	+	2.98010i	−0.355155	+	0.298010i
$101$	−10.5659	−	11.1992i	−1.05135	−	1.11437i	−0.993243	−	0.116055i	$-0.962975\pi$
$101$	−10.5659	−	11.1992i	−1.05135	−	1.11437i	−0.0581064	−	0.998310i	$-0.518506\pi$
$102$	3.67712	−	9.12227i	0.364089	−	0.903239i
$103$	0.345880	+	0.227489i	0.0340805	+	0.0224151i	0.566435	−	0.824106i	$-0.308322\pi$
$103$	0.345880	+	0.227489i	0.0340805	+	0.0224151i	−0.532354	+	0.846522i	$0.678693\pi$
$104$	1.13486	+	0.268967i	0.111282	+	0.0263744i
$105$	−0.0449929	−	0.545781i	−0.00439086	−	0.0532628i
$106$	2.20924	+	0.258224i	0.214581	+	0.0250809i
$107$	0.571449	+	0.989778i	0.0552440	+	0.0956855i	0.892325	−	0.451394i	$-0.149073\pi$
$107$	0.571449	+	0.989778i	0.0552440	+	0.0956855i	−0.837081	+	0.547079i	$0.815740\pi$
$108$	−4.46307	+	2.66102i	−0.429459	+	0.256056i
$109$	−4.46427	+	7.73235i	−0.427600	+	0.740625i	−0.996659	−	0.0816717i	$-0.973974\pi$
$109$	−4.46427	+	7.73235i	−0.427600	+	0.740625i	0.569059	+	0.822296i	$0.307307\pi$
$110$	−0.870730	+	1.16959i	−0.0830208	+	0.111516i
$111$	3.26821	−	11.9569i	0.310205	−	1.13490i
$112$	−0.150345	−	0.502188i	−0.0142063	−	0.0474523i
$113$	15.0553	−	7.56104i	1.41628	−	0.711282i	0.434388	−	0.900726i	$-0.356965\pi$
$113$	15.0553	−	7.56104i	1.41628	−	0.711282i	0.981892	+	0.189443i	$0.0606683\pi$
$114$	2.59581	+	1.61915i	0.243120	+	0.151647i
$115$	−0.880776	+	2.94200i	−0.0821328	+	0.274342i
$116$	−1.00201	−	5.68265i	−0.0930338	−	0.527621i
$117$	−3.49076	−	0.238466i	−0.322721	−	0.0220462i
$118$	−0.965788	+	5.47726i	−0.0889080	+	0.504222i
$119$	−2.66011	−	1.33596i	−0.243852	−	0.122467i
$120$	−0.500412	+	0.917033i	−0.0456811	+	0.0837133i
$121$	−2.04203	+	4.73395i	−0.185639	+	0.430359i
$122$	1.45173	−	3.36549i	0.131434	−	0.304697i
$123$	6.59037	−	12.0772i	0.594234	−	1.08897i
$124$	1.45933	+	0.732903i	0.131052	+	0.0658167i
$125$	1.00925	−	5.72376i	0.0902704	−	0.511949i
$126$	0.691664	+	1.41236i	0.0616183	+	0.125823i
$127$	−3.02978	−	17.1827i	−0.268850	−	1.52472i	−0.757845	−	0.652435i	$-0.773747\pi$
$127$	−3.02978	−	17.1827i	−0.268850	−	1.52472i	0.488995	−	0.872287i	$-0.337364\pi$
$128$	−0.286803	+	0.957990i	−0.0253501	+	0.0846751i
$129$	3.79273	+	2.36573i	0.333931	+	0.208291i
$130$	−0.628626	+	0.315708i	−0.0551342	+	0.0276894i
$131$	−2.12283	−	7.09074i	−0.185472	−	0.619521i	−0.999264	−	0.0383641i	$-0.987785\pi$
$131$	−2.12283	−	7.09074i	−0.185472	−	0.619521i	0.813791	−	0.581157i	$-0.197400\pi$
$132$	1.10401	−	4.03910i	0.0960921	−	0.351559i
$133$	0.552928	−	0.742712i	0.0479450	−	0.0644013i
$134$	−7.54669	+	13.0713i	−0.651935	+	1.12918i
$135$	1.03044	−	2.95980i	0.0886864	−	0.254739i
$136$	2.83926	+	4.91775i	0.243465	+	0.421693i
$137$	−1.14322	−	0.133623i	−0.0976715	−	0.0114162i	0.0671168	−	0.997745i	$-0.478620\pi$
$137$	−1.14322	−	0.133623i	−0.0976715	−	0.0114162i	−0.164788	+	0.986329i	$0.552694\pi$
$138$	−0.724557	−	8.78916i	−0.0616784	−	0.748183i
$139$	5.42884	+	1.28666i	0.460469	+	0.109133i	0.454302	−	0.890848i	$-0.349889\pi$
$139$	5.42884	+	1.28666i	0.460469	+	0.109133i	0.00616691	+	0.999981i	$0.498037\pi$
$140$	0.264161	+	0.173742i	0.0223257	+	0.0146838i
$141$	−3.97740	+	9.86720i	−0.334957	+	0.830968i
$142$	−4.17214	−	4.42221i	−0.350119	−	0.371104i
$143$	2.15990	−	1.81237i	0.180620	−	0.151558i
$144$	0.378147	−	2.97607i	0.0315122	−	0.248006i
$145$	2.66611	+	2.23713i	0.221408	+	0.185783i
$146$	−0.673946	−	11.5712i	−0.0557762	−	0.957640i
$147$	−10.8468	+	4.24632i	−0.894632	+	0.350230i
$148$	4.27361	+	5.74045i	0.351289	+	0.471862i
$149$	10.0534	−	1.17508i	0.823608	−	0.0962660i	0.306159	−	0.951980i	$-0.400956\pi$
$149$	10.0534	−	1.17508i	0.823608	−	0.0962660i	0.517449	+	0.855714i	$0.326882\pi$
$150$	1.58438	+	7.87230i	0.129364	+	0.642771i
$151$	−8.50922	+	5.59660i	−0.692470	+	0.455445i	−0.846338	−	0.532647i	$-0.821197\pi$
$151$	−8.50922	+	5.59660i	−0.692470	+	0.455445i	0.153868	+	0.988091i	$0.450827\pi$
$152$	−1.65982	+	0.604124i	−0.134629	+	0.0490009i
$153$	−10.8188	−	13.1592i	−0.874650	−	1.06386i
$154$	−1.19086	−	0.433438i	−0.0959623	−	0.0349274i
$155$	−0.958410	+	0.227147i	−0.0769813	+	0.0182449i
$156$	1.35050	−	1.50230i	0.108126	−	0.120280i
$157$	1.41088	−	24.2238i	0.112600	−	1.93327i	−0.193172	−	0.981165i	$-0.561878\pi$
$157$	1.41088	−	24.2238i	0.112600	−	1.93327i	0.305772	−	0.952105i	$-0.401085\pi$
$158$	−11.2237	+	11.8965i	−0.892913	+	0.946432i
$159$	2.22554	−	3.14472i	0.176497	−	0.249393i
$160$	−0.238895	−	0.553820i	−0.0188863	−	0.0437833i
$161$	−2.66909			−0.210354
$162$	0.342978	+	8.99346i	0.0269469	+	0.706593i
$163$	−6.49707			−0.508890			−0.254445	−	0.967087i	$-0.581893\pi$
$163$	−6.49707			−0.508890			−0.254445	+	0.967087i	$0.581893\pi$
$164$	3.14622	+	7.29375i	0.245678	+	0.569546i
$165$	1.05585	+	2.29424i	0.0821976	+	0.178606i
$166$	−10.0828	+	10.6871i	−0.782575	+	0.829481i
$167$	−0.148594	+	2.55126i	−0.0114985	+	0.197422i	0.987667	+	0.156571i	$0.0500440\pi$
$167$	−0.148594	+	2.55126i	−0.0114985	+	0.197422i	−0.999165	+	0.0408513i	$0.986993\pi$
$168$	−0.888268	−	0.188062i	−0.0685314	−	0.0145093i
$169$	−11.3260	+	2.68431i	−0.871231	+	0.206485i
$170$	−3.21844	−	1.17142i	−0.246843	−	0.0898435i
$171$	4.61543	−	2.60335i	0.352950	−	0.199083i
$172$	−2.42515	+	0.882683i	−0.184916	+	0.0673040i
$173$	11.6523	−	7.66386i	0.885910	−	0.582672i	−0.0229671	−	0.999736i	$-0.507311\pi$
$173$	11.6523	−	7.66386i	0.885910	−	0.582672i	0.908877	+	0.417064i	$0.136941\pi$
$174$	−9.47131	−	3.19125i	−0.718018	−	0.241928i
$175$	2.41392	−	0.282146i	0.182475	−	0.0213282i
$176$	1.44364	+	1.93915i	0.108819	+	0.146169i
$177$	7.52641	+	6.01270i	0.565719	+	0.451942i
$178$	0.751457	+	12.9020i	0.0563241	+	0.967048i
$179$	−5.53837	−	4.64725i	−0.413957	−	0.347351i	0.411901	−	0.911228i	$-0.364865\pi$
$179$	−5.53837	−	4.64725i	−0.413957	−	0.347351i	−0.825859	+	0.563877i	$0.809309\pi$
$180$	0.979093	+	1.52166i	0.0729773	+	0.113418i
$181$	−4.52209	+	3.79449i	−0.336124	+	0.282042i	−0.795190	−	0.606361i	$-0.792629\pi$
$181$	−4.52209	+	3.79449i	−0.336124	+	0.282042i	0.459065	+	0.888403i	$0.348184\pi$
$182$	−0.419558	−	0.444705i	−0.0310997	−	0.0329638i
$183$	−3.91248	−	4.99947i	−0.289219	−	0.369571i
$184$	4.25400	+	2.79790i	0.313609	+	0.206264i
$185$	−4.20012	−	0.995447i	−0.308799	−	0.0731867i
$186$	2.32507	−	1.61072i	0.170483	−	0.118104i
$187$	13.6351	+	1.59372i	0.997099	+	0.116544i
$188$	−3.07112	−	5.31934i	−0.223985	−	0.387953i
$189$	2.72122	+	0.120175i	0.197940	+	0.00874147i
$190$	0.532682	−	0.922632i	0.0386448	−	0.0669347i
$191$	0.821643	−	1.10366i	0.0594520	−	0.0798579i	−0.771403	−	0.636347i	$-0.780445\pi$
$191$	0.821643	−	1.10366i	0.0594520	−	0.0798579i	0.830855	+	0.556489i	$0.187852\pi$
$192$	1.21859	+	1.23087i	0.0879440	+	0.0888305i
$193$	−6.35654	−	21.2323i	−0.457554	−	1.52834i	−0.806524	−	0.591202i	$-0.798654\pi$
$193$	−6.35654	−	21.2323i	−0.457554	−	1.52834i	0.348970	−	0.937134i	$-0.386531\pi$
$194$	−3.65749	+	1.83686i	−0.262592	+	0.131879i
$195$	−0.0415443	+	1.21770i	−0.00297505	+	0.0872015i
$196$	1.92881	−	6.44267i	0.137772	−	0.460191i
$197$	2.83378	+	16.0712i	0.201898	+	1.14502i	0.902246	+	0.431221i	$0.141917\pi$
$197$	2.83378	+	16.0712i	0.201898	+	1.14502i	−0.700348	+	0.713802i	$0.746972\pi$
$198$	−5.22514	−	5.02967i	−0.371334	−	0.357443i
$199$	3.25591	−	18.4652i	0.230805	−	1.30896i	−0.620466	−	0.784234i	$-0.713056\pi$
$199$	3.25591	−	18.4652i	0.230805	−	1.30896i	0.851271	−	0.524727i	$-0.175833\pi$
$200$	−4.14307	−	2.08073i	−0.292959	−	0.147130i
$201$	13.6125	+	22.3189i	0.960148	+	1.57425i
$202$	6.09836	−	14.1376i	0.429079	−	0.994718i
$203$	−1.19808	+	2.77747i	−0.0840891	+	0.194940i
$204$	9.83265	−	0.236756i	0.688423	−	0.0165762i
$205$	−4.28143	−	2.15022i	−0.299028	−	0.150178i
$206$	−0.0718878	+	0.407696i	−0.00500866	+	0.0284055i
$207$	−13.9643	−	6.19045i	−0.970585	−	0.430266i
$208$	0.202526	+	1.14858i	0.0140426	+	0.0796397i
$209$	−1.22470	+	4.09077i	−0.0847140	+	0.282964i
$210$	0.483325	−	0.257486i	0.0333526	−	0.0177682i
$211$	14.5024	−	7.28336i	0.998383	−	0.501407i	0.126944	−	0.991910i	$-0.459483\pi$
$211$	14.5024	−	7.28336i	0.998383	−	0.501407i	0.871440	+	0.490503i	$0.163187\pi$
$212$	0.637932	+	2.13084i	0.0438133	+	0.146347i
$213$	−10.1851	+	2.67441i	−0.697870	+	0.183248i
$214$	−0.682491	+	0.916744i	−0.0466541	+	0.0626674i
$215$	0.778300	−	1.34805i	0.0530796	−	0.0919366i
$216$	−4.21112	−	3.04409i	−0.286530	−	0.207124i
$217$	−0.428026	−	0.741362i	−0.0290563	−	0.0503270i
$218$	−8.86818	−	1.03654i	−0.600629	−	0.0702034i
$219$	−18.1522	−	8.57558i	−1.22661	−	0.579484i
$220$	−1.41882	−	0.336266i	−0.0956567	−	0.0226710i
$221$	5.53332	+	3.63932i	0.372211	+	0.244807i
$222$	12.2735	−	1.73498i	0.823745	−	0.116444i
$223$	−7.90196	−	8.37559i	−0.529154	−	0.560871i	0.406562	−	0.913623i	$-0.366727\pi$
$223$	−7.90196	−	8.37559i	−0.529154	−	0.560871i	−0.935717	+	0.352752i	$0.885246\pi$
$224$	0.401568	−	0.336956i	0.0268309	−	0.0225138i
$225$	13.2837	+	4.12248i	0.885577	+	0.274832i
$226$	12.9057	+	10.8292i	0.858478	+	0.720348i
$227$	0.209678	+	3.60003i	0.0139168	+	0.238942i	0.998092	+	0.0617442i	$0.0196663\pi$
$227$	0.209678	+	3.60003i	0.0139168	+	0.238942i	−0.984175	+	0.177198i	$0.943297\pi$
$228$	−0.458578	+	3.02483i	−0.0303701	+	0.200324i
$229$	17.2562	+	23.1792i	1.14032	+	1.53172i	0.808613	+	0.588340i	$0.200218\pi$
$229$	17.2562	+	23.1792i	1.14032	+	1.53172i	0.331711	+	0.943381i	$0.392374\pi$
$230$	−3.05025	+	0.356523i	−0.201127	+	0.0235084i
$231$	−1.64702	+	1.45099i	−0.108366	+	0.0954681i
$232$	4.82103	−	3.17084i	0.316516	−	0.208176i
$233$	−5.21578	+	1.89839i	−0.341697	+	0.124367i	−0.507168	−	0.861847i	$-0.669308\pi$
$233$	−5.21578	+	1.89839i	−0.341697	+	0.124367i	0.165471	+	0.986215i	$0.447085\pi$
$234$	−1.16366	−	3.29972i	−0.0760706	−	0.215710i
$235$	3.48126	+	1.26707i	0.227092	+	0.0826549i
$236$	−5.41184	+	1.28263i	−0.352281	+	0.0834920i
$237$	8.77557	+	26.9348i	0.570034	+	1.74960i
$238$	0.173082	−	2.97170i	0.0112192	−	0.192627i
$239$	−6.87332	+	7.28529i	−0.444598	+	0.471246i	−0.910452	−	0.413615i	$-0.864266\pi$
$239$	−6.87332	+	7.28529i	−0.444598	+	0.471246i	0.465854	+	0.884862i	$0.345747\pi$
$240$	−1.04024	−	0.0962680i	−0.0671470	−	0.00621407i
$241$	−4.59180	−	10.6450i	−0.295784	−	0.685704i	0.703914	−	0.710285i	$-0.251434\pi$
$241$	−4.59180	−	10.6450i	−0.295784	−	0.685704i	−0.999698	+	0.0245811i	$0.992175\pi$
$242$	−5.15560			−0.331414
$243$	13.9583	+	6.94011i	0.895427	+	0.445208i
$244$	3.66525			0.234644
$245$	1.60662	+	3.72455i	0.102643	+	0.237953i
$246$	13.6998	+	1.26784i	0.873469	+	0.0808345i
$247$	−1.41371	+	1.49845i	−0.0899523	+	0.0953439i
$248$	−0.0949524	+	1.63027i	−0.00602948	+	0.103522i
$249$	7.88347	+	24.1967i	0.499595	+	1.53340i
$250$	5.65540	−	1.34035i	0.357679	−	0.0847714i
$251$	26.1345	+	9.51218i	1.64960	+	0.600404i	0.988678	−	0.150055i	$-0.0479451\pi$
$251$	26.1345	+	9.51218i	1.64960	+	0.600404i	0.660917	+	0.750459i	$0.270167\pi$
$252$	−1.02290	+	1.19450i	−0.0644366	+	0.0752467i
$253$	11.5668	−	4.20997i	0.727199	−	0.264679i
$254$	14.5774	−	9.58773i	0.914670	−	0.601588i
$255$	−4.45127	+	3.92147i	−0.278749	+	0.245572i
$256$	−0.993238	+	0.116093i	−0.0620774	+	0.00725581i
$257$	−7.49849	−	10.0722i	−0.467743	−	0.628288i	0.504177	−	0.863601i	$-0.331796\pi$
$257$	−7.49849	−	10.0722i	−0.467743	−	0.628288i	−0.971920	+	0.235313i	$0.924389\pi$
$258$	−0.670027	+	4.41956i	−0.0417141	+	0.275150i
$259$	−0.218133	−	3.74520i	−0.0135541	−	0.232715i
$260$	−0.538874	−	0.452169i	−0.0334196	−	0.0280423i
$261$	−12.7100	+	11.7526i	−0.786732	+	0.727468i
$262$	5.67003	−	4.75772i	0.350295	−	0.293933i
$263$	−16.5821	−	17.5760i	−1.02250	−	1.08378i	−0.996456	−	0.0841208i	$-0.973192\pi$
$263$	−16.5821	−	17.5760i	−1.02250	−	1.08378i	−0.0260397	−	0.999661i	$-0.508290\pi$
$264$	4.14605	−	0.586084i	0.255172	−	0.0360710i
$265$	−1.12087	−	0.737206i	−0.0688543	−	0.0452862i
$266$	0.900974	+	0.213535i	0.0552422	+	0.0130927i
$267$	20.2399	+	9.56186i	1.23866	+	0.585176i
$268$	−14.9913	−	1.75224i	−0.915741	−	0.107035i
$269$	12.0050	+	20.7933i	0.731958	+	1.26779i	0.956045	+	0.293219i	$0.0947266\pi$
$269$	12.0050	+	20.7933i	0.731958	+	1.26779i	−0.224087	+	0.974569i	$0.571940\pi$
$270$	3.12588	−	0.226150i	0.190235	−	0.0137630i
$271$	−6.40272	+	11.0898i	−0.388938	+	0.673660i	−0.992307	−	0.123802i	$-0.960491\pi$
$271$	−6.40272	+	11.0898i	−0.388938	+	0.673660i	0.603369	+	0.797462i	$0.293825\pi$
$272$	−3.39098	+	4.55488i	−0.205608	+	0.276180i
$273$	−1.02423	+	0.268943i	−0.0619891	+	0.0162772i
$274$	−0.330110	−	1.10264i	−0.0199427	−	0.0666132i
$275$	−10.0160	+	5.03020i	−0.603985	+	0.303333i
$276$	7.78337	−	4.14651i	0.468504	−	0.249590i
$277$	4.54939	−	15.1960i	0.273346	−	0.913040i	−0.705546	−	0.708664i	$-0.749298\pi$
$277$	4.54939	−	15.1960i	0.273346	−	0.913040i	0.978892	−	0.204376i	$-0.0655166\pi$
$278$	0.968824	+	5.49447i	0.0581062	+	0.329536i
$279$	−0.519918	−	4.87143i	−0.0311267	−	0.291645i
$280$	−0.0549034	+	0.311373i	−0.00328110	+	0.0186081i
$281$	−3.42138	−	1.71828i	−0.204103	−	0.102504i	0.343812	−	0.939039i	$-0.388282\pi$
$281$	−3.42138	−	1.71828i	−0.204103	−	0.102504i	−0.547914	+	0.836534i	$0.684578\pi$
$282$	−10.6356	+	0.256090i	−0.633340	+	0.0152499i
$283$	11.2108	−	25.9894i	0.666410	−	1.54491i	−0.163215	−	0.986591i	$-0.552186\pi$
$283$	11.2108	−	25.9894i	0.666410	−	1.54491i	0.829625	−	0.558321i	$-0.188554\pi$
$284$	2.40805	−	5.58248i	0.142891	−	0.331259i
$285$	−0.960832	−	1.57537i	−0.0569148	−	0.0933170i
$286$	2.51964	+	1.26541i	0.148990	+	0.0748253i
$287$	0.723072	−	4.10074i	0.0426816	−	0.242059i
$288$	2.88245	−	0.831541i	0.169850	−	0.0489990i
$289$	2.64738	+	15.0141i	0.155728	+	0.883179i
$290$	−0.998177	+	3.33414i	−0.0586150	+	0.195788i
$291$	−0.241714	+	7.08487i	−0.0141695	+	0.415323i
$292$	10.3579	−	5.20195i	0.606152	−	0.304421i
$293$	−0.429579	−	1.43489i	−0.0250963	−	0.0838274i	0.944524	−	0.328442i	$-0.106524\pi$
$293$	−0.429579	−	1.43489i	−0.0250963	−	0.0838274i	−0.969620	+	0.244615i	$0.921338\pi$
$294$	−8.19525	−	8.27786i	−0.477957	−	0.482775i
$295$	2.00320	−	2.69077i	0.116631	−	0.156663i
$296$	−3.57829	+	6.19777i	−0.207984	+	0.360238i
$297$	−11.9823	+	3.77141i	−0.695283	+	0.218839i
$298$	5.06093	+	8.76579i	0.293172	+	0.507788i
$299$	5.89822	+	0.689403i	0.341103	+	0.0398692i
$300$	−6.60093	+	4.57286i	−0.381105	+	0.264014i
$301$	1.31641	+	0.311995i	0.0758766	+	0.0179831i
$302$	−8.50922	−	5.59660i	−0.489650	−	0.322048i
$303$	−16.4354	−	21.0015i	−0.944187	−	1.20651i
$304$	−1.21214	−	1.28479i	−0.0695207	−	0.0736877i
$305$	−1.69348	+	1.42100i	−0.0969686	+	0.0813664i
$306$	7.79786	−	15.1461i	0.445774	−	0.865845i
$307$	1.22369	+	1.02679i	0.0698394	+	0.0586022i	0.677039	−	0.735947i	$-0.263263\pi$
$307$	1.22369	+	1.02679i	0.0698394	+	0.0586022i	−0.607200	+	0.794549i	$0.707707\pi$
$308$	−0.0736862	−	1.26514i	−0.00419866	−	0.0720882i
$309$	0.560223	+	0.447551i	0.0318700	+	0.0254603i
$310$	−0.588177	−	0.790059i	−0.0334062	−	0.0448723i
$311$	−27.4410	+	3.20739i	−1.55603	+	0.181874i	−0.850183	−	0.526487i	$-0.823509\pi$
$311$	−27.4410	+	3.20739i	−1.55603	+	0.181874i	−0.705850	+	0.708361i	$0.749435\pi$
$312$	1.91434	+	0.645016i	0.108378	+	0.0365169i
$313$	−12.3621	+	8.13065i	−0.698745	+	0.459572i	−0.848530	−	0.529147i	$-0.822512\pi$
$313$	−12.3621	+	8.13065i	−0.698745	+	0.459572i	0.149785	+	0.988719i	$0.452142\pi$
$314$	22.8015	−	8.29907i	1.28676	−	0.468343i
$315$	0.00951343	−	0.948480i	0.000536021	−	0.0534408i
$316$	−15.3690	−	5.59387i	−0.864575	−	0.314680i
$317$	−9.39219	+	2.22599i	−0.527518	+	0.125024i	−0.485741	−	0.874103i	$-0.661450\pi$
$317$	−9.39219	+	2.22599i	−0.527518	+	0.125024i	−0.0417770	+	0.999127i	$0.513302\pi$
$318$	3.76903	+	0.797969i	0.211357	+	0.0447479i
$319$	0.811112	−	13.9263i	0.0454136	−	0.779721i
$320$	0.413905	−	0.438714i	0.0231380	−	0.0245248i
$321$	0.827589	+	1.79826i	0.0461915	+	0.100369i
$322$	−1.05717	−	2.45080i	−0.0589139	−	0.136578i
$323$	−10.0302			−0.558095
$324$	−8.12210	+	3.87706i	−0.451228	+	0.215392i
$325$	−5.40721			−0.299938
$326$	−2.57336	−	5.96572i	−0.142525	−	0.330410i
$327$	−8.93360	+	12.6233i	−0.494029	+	0.698070i
$328$	−5.45109	+	5.77782i	−0.300986	+	0.319026i
$329$	−0.187216	+	3.21438i	−0.0103216	+	0.177214i
$330$	−1.68841	+	1.87820i	−0.0929439	+	0.103391i
$331$	−12.8231	+	3.03914i	−0.704823	+	0.167046i	−0.567371	−	0.823462i	$-0.692039\pi$
$331$	−12.8231	+	3.03914i	−0.704823	+	0.167046i	−0.137452	+	0.990508i	$0.543891\pi$
$332$	−13.8067	−	5.02522i	−0.757739	−	0.275795i
$333$	7.54506	−	20.1003i	0.413467	−	1.10149i
$334$	−2.40146	+	0.874060i	−0.131402	+	0.0478265i
$335$	7.60590	−	5.00248i	0.415555	−	0.273315i
$336$	−0.179144	−	0.890110i	−0.00977308	−	0.0485595i
$337$	−22.4706	+	2.62644i	−1.22405	+	0.143071i	−0.703461	−	0.710734i	$-0.748363\pi$
$337$	−22.4706	+	2.62644i	−1.22405	+	0.143071i	−0.520593	+	0.853805i	$0.674289\pi$
$338$	−6.95078	−	9.33651i	−0.378072	−	0.507839i
$339$	27.1723	−	10.6374i	1.47580	−	0.577745i
$340$	−0.199146	−	3.41920i	−0.0108002	−	0.185432i
$341$	3.02426	+	2.53765i	0.163773	+	0.137422i
$342$	4.21851	+	3.20683i	0.228111	+	0.173405i
$343$	−5.51160	+	4.62478i	−0.297599	+	0.249715i
$344$	−1.77105	−	1.87720i	−0.0954885	−	0.101212i
$345$	−1.98863	+	4.93342i	−0.107064	+	0.265607i
$346$	11.6523	+	7.66386i	0.626433	+	0.412011i
$347$	−28.8673	−	6.84166i	−1.54968	−	0.367280i	−0.635338	−	0.772234i	$-0.719139\pi$
$347$	−28.8673	−	6.84166i	−1.54968	−	0.367280i	−0.914337	+	0.404954i	$0.867287\pi$
$348$	−0.821135	−	9.96069i	−0.0440175	−	0.533949i
$349$	10.7165	+	1.25258i	0.573643	+	0.0670493i	0.397969	−	0.917399i	$-0.369715\pi$
$349$	10.7165	+	1.25258i	0.573643	+	0.0670493i	0.175674	+	0.984448i	$0.443789\pi$
$350$	1.21517	+	2.10474i	0.0649538	+	0.112503i
$351$	−5.98239	−	0.968435i	−0.319316	−	0.0516912i
$352$	−1.20876	+	2.09363i	−0.0644271	+	0.111591i
$353$	20.3884	−	27.3863i	1.08516	−	1.45763i	0.207569	−	0.978220i	$-0.433445\pi$
$353$	20.3884	−	27.3863i	1.08516	−	1.45763i	0.877593	−	0.479406i	$-0.159148\pi$
$354$	−2.53990	+	9.29237i	−0.134994	+	0.493884i
$355$	1.05170	+	3.51291i	0.0558182	+	0.186446i
$356$	−11.5492	+	5.80023i	−0.612107	+	0.307412i
$357$	−4.37461	−	2.72868i	−0.231529	−	0.144417i
$358$	2.07354	−	6.92610i	0.109590	−	0.366056i
$359$	−2.51732	−	14.2765i	−0.132859	−	0.753482i	−0.976327	−	0.216302i	$-0.930600\pi$
$359$	−2.51732	−	14.2765i	−0.132859	−	0.753482i	0.843467	−	0.537181i	$-0.180511\pi$
$360$	−1.00942	+	1.50172i	−0.0532010	+	0.0791476i
$361$	−2.75754	+	15.6388i	−0.145134	+	0.823094i
$362$	−5.27527	−	2.64934i	−0.277262	−	0.139246i
$363$	−4.27743	+	7.83863i	−0.224507	+	0.411422i
$364$	0.242157	−	0.561384i	0.0126925	−	0.0294245i
$365$	−2.76898	+	6.41923i	−0.144935	+	0.335998i
$366$	3.04094	−	5.57269i	0.158952	−	0.291289i
$367$	−22.0962	−	11.0971i	−1.15341	−	0.579265i	−0.233873	−	0.972267i	$-0.575140\pi$
$367$	−22.0962	−	11.0971i	−1.15341	−	0.579265i	−0.919537	+	0.393002i	$0.871436\pi$
$368$	−0.884154	+	5.01428i	−0.0460897	+	0.261388i
$369$	13.2939	−	19.7775i	0.692054	−	1.02957i
$370$	−0.749547	−	4.25089i	−0.0389671	−	0.220993i
$371$	0.334410	−	1.11701i	0.0173617	−	0.0579922i
$372$	2.39990	+	1.49695i	0.124429	+	0.0776131i
$373$	−15.9685	+	8.01969i	−0.826819	+	0.415244i	−0.811296	−	0.584636i	$-0.801237\pi$
$373$	−15.9685	+	8.01969i	−0.826819	+	0.415244i	−0.0155225	+	0.999880i	$0.504941\pi$
$374$	3.93722	+	13.1512i	0.203589	+	0.680034i
$375$	2.65421	−	9.71058i	0.137063	−	0.501452i
$376$	3.66789	−	4.92683i	0.189157	−	0.254082i
$377$	3.36496	−	5.82828i	0.173304	−	0.300171i
$378$	0.967474	+	2.54627i	0.0497615	+	0.130966i
$379$	5.46182	+	9.46016i	0.280555	+	0.485936i	0.971522	−	0.236951i	$-0.0761481\pi$
$379$	5.46182	+	9.46016i	0.280555	+	0.485936i	−0.690967	+	0.722887i	$0.742815\pi$
$380$	1.05816	+	0.123681i	0.0542825	+	0.00634471i
$381$	−2.48288	−	30.1183i	−0.127202	−	1.54301i
$382$	1.33883	+	0.317309i	0.0685007	+	0.0162350i
$383$	19.1036	+	12.5646i	0.976148	+	0.642022i	0.934069	−	0.357092i	$-0.116232\pi$
$383$	19.1036	+	12.5646i	0.976148	+	0.642022i	0.0420785	+	0.999114i	$0.486602\pi$
$384$	−0.647548	+	1.60645i	−0.0330451	+	0.0819788i
$385$	0.524537	+	0.555977i	0.0267329	+	0.0283352i
$386$	16.9782	−	14.2464i	0.864165	−	0.725121i
$387$	6.16366	+	4.68548i	0.313316	+	0.238177i
$388$	−3.13529	−	2.63082i	−0.159170	−	0.133560i
$389$	0.570051	+	9.78739i	0.0289027	+	0.496240i	0.981434	+	0.191800i	$0.0614324\pi$
$389$	0.570051	+	9.78739i	0.0289027	+	0.496240i	−0.952531	+	0.304441i	$0.901531\pi$
$390$	−1.13457	+	0.444161i	−0.0574512	+	0.0224910i
$391$	17.2656	+	23.1918i	0.873161	+	1.17286i
$392$	6.67973	−	0.780749i	0.337377	−	0.0394338i
$393$	−2.52946	−	12.5681i	−0.127594	−	0.633977i
$394$	−13.6344	+	8.96748i	−0.686891	+	0.451775i
$395$	9.26980	−	3.37393i	0.466414	−	0.169761i
$396$	2.54875	−	6.78995i	0.128080	−	0.341208i
$397$	28.9904	+	10.5516i	1.45499	+	0.529571i	0.943979	−	0.330006i	$-0.107051\pi$
$397$	28.9904	+	10.5516i	1.45499	+	0.529571i	0.511006	+	0.859577i	$0.329273\pi$
$398$	18.2446	−	4.32405i	0.914519	−	0.216745i
$399$	1.07217	−	1.19269i	0.0536756	−	0.0597091i
$400$	0.269572	−	4.62837i	0.0134786	−	0.231418i
$401$	5.19386	−	5.50517i	0.259369	−	0.274915i	−0.584583	−	0.811334i	$-0.698742\pi$
$401$	5.19386	−	5.50517i	0.259369	−	0.274915i	0.843952	+	0.536419i	$0.180223\pi$
$402$	−15.1019	+	21.3392i	−0.753216	+	1.06430i
$403$	0.754375	+	1.74884i	0.0375781	+	0.0871158i
$404$	15.3968			0.766020
$405$	2.24960	−	4.94025i	0.111783	−	0.245483i
$406$	−3.02486			−0.150121
$407$	6.85264	+	15.8862i	0.339673	+	0.787450i
$408$	4.11191	+	8.93472i	0.203570	+	0.442335i
$409$	−11.7536	+	12.4581i	−0.581177	+	0.616012i	−0.949531	−	0.313674i	$-0.898440\pi$
$409$	−11.7536	+	12.4581i	−0.581177	+	0.616012i	0.368354	+	0.929686i	$0.379922\pi$
$410$	0.278574	−	4.78293i	0.0137578	−	0.236212i
$411$	−1.95035	−	0.412924i	−0.0962039	−	0.0203681i
$412$	−0.402826	+	0.0954716i	−0.0198458	+	0.00470355i
$413$	2.73970	+	0.997169i	0.134812	+	0.0490675i
$414$	0.153202	−	15.2741i	0.00752949	−	0.750683i
$415$	8.32746	−	3.03095i	0.408779	−	0.148783i
$416$	−0.974428	+	0.640891i	−0.0477753	+	0.0314223i
$417$	9.15766	+	3.08557i	0.448453	+	0.151101i
$418$	−4.24129	+	0.495735i	−0.207448	+	0.0242472i
$419$	−3.93496	−	5.28557i	−0.192235	−	0.258217i	0.695547	−	0.718481i	$-0.255162\pi$
$419$	−3.93496	−	5.28557i	−0.192235	−	0.258217i	−0.887782	+	0.460264i	$0.847755\pi$
$420$	0.427863	+	0.341811i	0.0208776	+	0.0166787i
$421$	−0.936365	−	16.0768i	−0.0456356	−	0.783533i	−0.941043	−	0.338286i	$-0.890153\pi$
$421$	−0.936365	−	16.0768i	−0.0456356	−	0.783533i	0.895408	−	0.445247i	$-0.146884\pi$
$422$	12.4318	+	10.4315i	0.605170	+	0.507798i
$423$	−8.43464	+	16.3830i	−0.410106	+	0.796566i
$424$	−1.70390	+	1.42974i	−0.0827487	+	0.0694344i
$425$	−18.0666	−	19.1495i	−0.876358	−	0.928885i
$426$	−6.48979	−	8.29282i	−0.314431	−	0.401789i
$427$	−1.60527	−	1.05580i	−0.0776846	−	0.0510940i
$428$	−1.11209	−	0.263570i	−0.0537549	−	0.0127401i
$429$	4.01441	−	2.78102i	0.193818	−	0.134269i
$430$	1.54607	+	0.180710i	0.0745583	+	0.00871462i
$431$	−0.473396	−	0.819946i	−0.0228027	−	0.0394954i	0.854399	−	0.519618i	$-0.173926\pi$
$431$	−0.473396	−	0.819946i	−0.0228027	−	0.0394954i	−0.877202	+	0.480122i	$0.840592\pi$
$432$	1.12719	−	5.07242i	0.0542320	−	0.244047i
$433$	−6.44048	+	11.1552i	−0.309510	+	0.536087i	−0.978255	−	0.207405i	$-0.933498\pi$
$433$	−6.44048	+	11.1552i	−0.309510	+	0.536087i	0.668745	+	0.743492i	$0.266832\pi$
$434$	0.511198	−	0.686659i	0.0245383	−	0.0329607i
$435$	4.24112	+	4.28387i	0.203346	+	0.205396i
$436$	−2.56074	−	8.55346i	−0.122637	−	0.409636i
$437$	−8.03694	+	4.03630i	−0.384459	+	0.193083i
$438$	0.684530	−	20.0642i	0.0327081	−	0.958705i
$439$	−9.83414	+	32.8483i	−0.469358	+	1.56776i	0.316023	+	0.948751i	$0.397652\pi$
$439$	−9.83414	+	32.8483i	−0.469358	+	1.56776i	−0.785381	+	0.619013i	$0.787533\pi$
$440$	−0.253200	−	1.43597i	−0.0120708	−	0.0684572i
$441$	−19.3851	+	5.59229i	−0.923099	+	0.266299i
$442$	−1.15005	+	6.52224i	−0.0547022	+	0.310231i
$443$	16.6157	+	8.34471i	0.789435	+	0.396469i	0.797363	−	0.603499i	$-0.206227\pi$
$443$	16.6157	+	8.34471i	0.789435	+	0.396469i	−0.00792842	+	0.999969i	$0.502524\pi$
$444$	6.45438	+	10.5826i	0.306311	+	0.502226i
$445$	3.08745	−	7.15751i	0.146359	−	0.339298i
$446$	4.56079	−	10.5731i	0.215960	−	0.500651i
$447$	17.5265	−	0.422012i	0.828975	−	0.0199605i
$448$	0.468451	+	0.235265i	0.0221322	+	0.0111152i
$449$	1.42811	−	8.09924i	0.0673969	−	0.382227i	−0.932387	−	0.361460i	$-0.882278\pi$
$449$	1.42811	−	8.09924i	0.0673969	−	0.382227i	0.999784	−	0.0207663i	$-0.00661059\pi$
$450$	1.47606	+	13.8301i	0.0695820	+	0.651957i
$451$	3.33462	+	18.9116i	0.157021	+	0.890511i
$452$	−4.83185	+	16.1395i	−0.227271	+	0.759138i
$453$	−15.5690	+	8.29420i	−0.731493	+	0.389695i
$454$	−3.22256	+	1.61843i	−0.151242	+	0.0759566i
$455$	0.105760	+	0.353264i	0.00495812	+	0.0165613i
$456$	−2.95908	+	0.776998i	−0.138571	+	0.0363863i
$457$	7.94177	−	10.6676i	0.371500	−	0.499011i	−0.576581	−	0.817040i	$-0.695613\pi$
$457$	7.94177	−	10.6676i	0.371500	−	0.499011i	0.948081	+	0.318029i	$0.103021\pi$
$458$	−14.4486	+	25.0257i	−0.675140	+	1.16938i
$459$	−16.5587	−	24.4222i	−0.772893	−	1.13993i
$460$	−1.53551	−	2.65957i	−0.0715933	−	0.124003i
$461$	−1.03017	−	0.120409i	−0.0479798	−	0.00560803i	0.0920692	−	0.995753i	$-0.470652\pi$
$461$	−1.03017	−	0.120409i	−0.0479798	−	0.00560803i	−0.140049	+	0.990145i	$0.544726\pi$
$462$	−1.98467	−	0.937615i	−0.0923354	−	0.0436218i
$463$	26.9384	+	6.38452i	1.25193	+	0.296714i	0.802528	−	0.596614i	$-0.203488\pi$
$463$	26.9384	+	6.38452i	1.25193	+	0.296714i	0.449405	+	0.893328i	$0.351636\pi$
$464$	4.82103	+	3.17084i	0.223811	+	0.147203i
$465$	−1.68921	+	0.238786i	−0.0783351	+	0.0110734i
$466$	−3.80899	−	4.03730i	−0.176448	−	0.187024i
$467$	7.21055	−	6.05037i	0.333664	−	0.279978i	−0.460527	−	0.887646i	$-0.652339\pi$
$467$	7.21055	−	6.05037i	0.333664	−	0.279978i	0.794191	+	0.607668i	$0.207895\pi$
$468$	2.56896	−	2.37544i	0.118750	−	0.109805i
$469$	6.06102	+	5.08580i	0.279872	+	0.234841i
$470$	0.215408	+	3.69841i	0.00993603	+	0.170595i
$471$	6.29965	−	41.5531i	0.290273	−	1.91467i
$472$	−3.32125	−	4.46121i	−0.152873	−	0.205344i
$473$	−6.19693	+	0.724317i	−0.284935	+	0.0333042i
$474$	−21.2562	+	18.7262i	−0.976328	+	0.860123i
$475$	6.84191	−	4.50000i	0.313929	−	0.206474i
$476$	2.79722	−	1.01810i	0.128210	−	0.0466648i
$477$	4.34028	−	5.06843i	0.198728	−	0.232067i
$478$	−9.41185	−	3.42563i	−0.430488	−	0.156685i
$479$	22.1517	−	5.25005i	1.01214	−	0.239881i	0.309097	−	0.951031i	$-0.399973\pi$
$479$	22.1517	−	5.25005i	1.01214	−	0.239881i	0.703041	+	0.711150i	$0.251825\pi$
$480$	−0.323622	−	0.993293i	−0.0147713	−	0.0453374i
$481$	−0.485317	+	8.33258i	−0.0221286	+	0.379933i
$482$	7.95568	−	8.43253i	0.362371	−	0.384091i
$483$	−4.60332	−	0.426011i	−0.209458	−	0.0193842i
$484$	−2.04203	−	4.73395i	−0.0928195	−	0.215180i
$485$	2.46858			0.112093
$486$	−0.843912	+	15.5656i	−0.0382806	+	0.706070i
$487$	−3.37255			−0.152825			−0.0764124	−	0.997076i	$-0.524347\pi$
$487$	−3.37255			−0.152825			−0.0764124	+	0.997076i	$0.524347\pi$
$488$	1.45173	+	3.36549i	0.0657168	+	0.152349i
$489$	−11.2054	−	1.03699i	−0.506725	−	0.0468944i
$490$	−2.78360	+	2.95044i	−0.125750	+	0.133287i
$491$	−0.886715	+	15.2243i	−0.0400169	+	0.687063i	0.917331	+	0.398125i	$0.130339\pi$
$491$	−0.886715	+	15.2243i	−0.0400169	+	0.687063i	−0.957348	+	0.288938i	$0.906698\pi$
$492$	4.26207	+	13.0816i	0.192149	+	0.589762i
$493$	31.8837	−	7.55657i	1.43597	−	0.340331i
$494$	−1.93584	−	0.704588i	−0.0870976	−	0.0317009i
$495$	1.45482	+	4.12536i	0.0653892	+	0.185421i
$496$	−1.53455	+	0.558530i	−0.0689032	+	0.0250787i
$497$	−2.66273	+	1.75131i	−0.119440	+	0.0785568i
$498$	−19.0953	+	16.8226i	−0.855682	+	0.753837i
$499$	−39.9026	+	4.66395i	−1.78629	+	0.208787i	−0.943933	−	0.330137i	$-0.892905\pi$
$499$	−39.9026	+	4.66395i	−1.78629	+	0.208787i	−0.842354	+	0.538924i	$0.818831\pi$
$500$	3.47072	+	4.66199i	0.155215	+	0.208490i
$501$	−0.663482	+	4.37639i	−0.0296422	+	0.195523i
$502$	1.61711	+	27.7647i	0.0721751	+	1.23920i
$503$	1.15131	+	0.966068i	0.0513346	+	0.0430748i	0.668094	−	0.744077i	$-0.267110\pi$
$503$	1.15131	+	0.966068i	0.0513346	+	0.0430748i	−0.616759	+	0.787152i	$0.711555\pi$
$504$	−1.50196	−	0.466123i	−0.0669028	−	0.0207628i
$505$	−7.11391	+	5.96928i	−0.316565	+	0.265629i
$506$	8.44704	+	8.95334i	0.375517	+	0.398025i
$507$	−19.9622	+	2.82185i	−0.886551	+	0.125323i
$508$	14.5774	+	9.58773i	0.646769	+	0.425387i
$509$	32.2705	+	7.64826i	1.43037	+	0.339003i	0.871557	−	0.490294i	$-0.163110\pi$
$509$	32.2705	+	7.64826i	1.43037	+	0.339003i	0.558809	+	0.829297i	$0.311259\pi$
$510$	−5.36381	−	2.53401i	−0.237514	−	0.112208i
$511$	−6.03494	−	0.705383i	−0.266970	−	0.0312043i
$512$	−0.500000	−	0.866025i	−0.0220971	−	0.0382733i
$513$	8.37566	−	3.75328i	0.369794	−	0.165711i
$514$	6.27848	−	10.8746i	0.276932	−	0.479660i
$515$	0.149107	−	0.200286i	0.00657044	−	0.00882564i
$516$	−4.32350	+	1.13527i	−0.190331	+	0.0499775i
$517$	−4.25874	−	14.2252i	−0.187299	−	0.625623i
$518$	3.35250	−	1.68369i	0.147301	−	0.0739771i
$519$	21.3198	−	11.3579i	0.935834	−	0.498556i
$520$	0.201752	−	0.673898i	0.00884740	−	0.0295524i
$521$	0.751612	+	4.26260i	0.0329287	+	0.186748i	0.996836	−	0.0794919i	$-0.0253298\pi$
$521$	0.751612	+	4.26260i	0.0329287	+	0.186748i	−0.963907	+	0.266240i	$0.914219\pi$
$522$	−15.8256	−	7.01560i	−0.692669	−	0.307064i
$523$	2.48169	−	14.0744i	0.108517	−	0.615429i	−0.881240	−	0.472668i	$-0.843291\pi$
$523$	2.48169	−	14.0744i	0.108517	−	0.615429i	0.989757	−	0.142761i	$-0.0455980\pi$
$524$	6.61439	+	3.32187i	0.288951	+	0.145117i
$525$	4.20827	−	0.101329i	0.183664	−	0.00442236i
$526$	9.57072	−	22.1874i	0.417303	−	0.967418i
$527$	−3.67293	+	8.51482i	−0.159995	+	0.370911i
$528$	2.18032	+	3.57483i	0.0948861	+	0.155575i
$529$	2.61368	+	1.31264i	0.113638	+	0.0570712i
$530$	0.232962	−	1.32119i	0.0101192	−	0.0573889i
$531$	12.0210	+	11.5713i	0.521666	+	0.502150i
$532$	0.160786	+	0.911865i	0.00697098	+	0.0395344i
$533$	−2.65705	+	8.87517i	−0.115090	+	0.384426i
$534$	−0.763259	+	22.3718i	−0.0330294	+	0.968123i
$535$	0.616013	−	0.309373i	0.0266326	−	0.0133754i
$536$	−4.32883	−	14.4593i	−0.186977	−	0.624547i
$537$	−8.81018	−	8.89899i	−0.380187	−	0.384020i
$538$	−14.3378	+	19.2590i	−0.618146	+	0.830314i
$539$	8.12916	−	14.0801i	0.350148	−	0.606473i
$540$	1.44575	+	2.78066i	0.0622152	+	0.119660i
$541$	−2.72610	−	4.72175i	−0.117204	−	0.203004i	0.801454	−	0.598056i	$-0.204060\pi$
$541$	−2.72610	−	4.72175i	−0.117204	−	0.203004i	−0.918659	+	0.395052i	$0.870727\pi$
$542$	−12.7189	−	1.48662i	−0.546322	−	0.0638559i
$543$	−8.40480	+	5.82251i	−0.360685	+	0.249868i
$544$	−5.52546	−	1.30956i	−0.236902	−	0.0561469i
$545$	4.49930	+	2.95923i	0.192729	+	0.126760i
$546$	−0.652624	−	0.833940i	−0.0279297	−	0.0356894i
$547$	7.38735	+	7.83014i	0.315860	+	0.334792i	0.865780	−	0.500425i	$-0.166823\pi$
$547$	7.38735	+	7.83014i	0.315860	+	0.334792i	−0.549919	+	0.835218i	$0.685342\pi$
$548$	0.881716	−	0.739847i	0.0376650	−	0.0316047i
$549$	−5.94982	−	9.24695i	−0.253932	−	0.394650i
$550$	−8.58593	−	7.20445i	−0.366105	−	0.307199i
$551$	0.592632	+	10.1751i	0.0252470	+	0.433474i
$552$	6.89023	+	5.50446i	0.293267	+	0.234286i
$553$	5.11983	+	6.87712i	0.217717	+	0.292445i
$554$	15.7552	−	1.84151i	0.669372	−	0.0782384i
$555$	−7.08499	−	2.38721i	−0.300741	−	0.101331i
$556$	−4.66138	+	3.06584i	−0.197687	+	0.130021i
$557$	−41.4633	+	15.0914i	−1.75686	+	0.639443i	−0.999902	−	0.0140247i	$-0.995536\pi$
$557$	−41.4633	+	15.0914i	−1.75686	+	0.639443i	−0.756954	+	0.653468i	$0.773313\pi$
$558$	4.26710	−	2.40687i	0.180641	−	0.101891i
$559$	−2.82845	−	1.02947i	−0.119631	−	0.0435420i
$560$	−0.307653	+	0.0729152i	−0.0130007	+	0.00308123i
$561$	23.2619	+	4.92495i	0.982117	+	0.207931i
$562$	0.222615	−	3.82215i	0.00939043	−	0.161228i
$563$	17.4517	−	18.4977i	0.735501	−	0.779586i	−0.246362	−	0.969178i	$-0.579235\pi$
$563$	17.4517	−	18.4977i	0.735501	−	0.779586i	0.981863	+	0.189592i	$0.0607166\pi$
$564$	−4.44769	−	9.66434i	−0.187281	−	0.406942i
$565$	−4.02472	−	9.33035i	−0.169321	−	0.392531i
$566$	28.3043			1.18972
$567$	4.67406	+	0.641596i	0.196292	+	0.0269445i
$568$	6.07970			0.255099
$569$	−13.5651	−	31.4473i	−0.568677	−	1.31834i	−0.923568	−	0.383434i	$-0.874741\pi$
$569$	−13.5651	−	31.4473i	−0.568677	−	1.31834i	0.354891	−	0.934908i	$-0.384518\pi$
$570$	1.06597	−	1.50622i	0.0446484	−	0.0630888i
$571$	−14.1247	+	14.9713i	−0.591099	+	0.626528i	−0.952008	−	0.306073i	$-0.900985\pi$
$571$	−14.1247	+	14.9713i	−0.591099	+	0.626528i	0.360909	+	0.932601i	$0.382466\pi$
$572$	−0.163942	+	2.81478i	−0.00685477	+	0.117692i
$573$	1.59323	−	1.77232i	0.0665580	−	0.0740396i
$574$	4.05176	−	0.960286i	0.169117	−	0.0400816i
$575$	−22.1823	−	8.07370i	−0.925066	−	0.336697i
$576$	1.90522	+	2.31736i	0.0793840	+	0.0965566i
$577$	29.1695	−	10.6168i	1.21434	−	0.441984i	0.346133	−	0.938185i	$-0.387495\pi$
$577$	29.1695	−	10.6168i	1.21434	−	0.441984i	0.868207	+	0.496202i	$0.165272\pi$
$578$	−12.7376	+	8.37763i	−0.529813	+	0.348463i
$579$	−7.57413	−	37.6335i	−0.314770	−	1.56400i
$580$	−3.45682	+	0.404044i	−0.143537	+	0.0167770i
$581$	4.59936	+	6.17802i	0.190814	+	0.256307i
$582$	−6.60118	+	2.58423i	−0.273628	+	0.107120i
$583$	0.312659	+	5.36815i	0.0129490	+	0.222326i
$584$	8.87908	+	7.45044i	0.367419	+	0.308301i
$585$	−0.266007	+	2.09352i	−0.0109981	+	0.0865563i
$586$	1.14740	−	0.962779i	0.0473985	−	0.0397720i
$587$	14.4106	+	15.2744i	0.594790	+	0.630441i	0.952917	−	0.303232i	$-0.0980657\pi$
$587$	14.4106	+	15.2744i	0.594790	+	0.630441i	−0.358126	+	0.933673i	$0.616584\pi$
$588$	4.35489	−	10.8037i	0.179593	−	0.445537i
$589$	−2.40995	−	1.58505i	−0.0993005	−	0.0653109i
$590$	3.26414	+	0.773615i	0.134382	+	0.0318492i
$591$	2.32226	+	28.1699i	0.0955249	+	1.15876i
$592$	−7.10818	−	0.830827i	−0.292145	−	0.0341468i
$593$	−0.0907517	−	0.157187i	−0.00372672	−	0.00645488i	0.864156	−	0.503224i	$-0.167853\pi$
$593$	−0.0907517	−	0.157187i	−0.00372672	−	0.00645488i	−0.867883	+	0.496769i	$0.834520\pi$
$594$	−8.20891	−	9.50855i	−0.336816	−	0.390141i
$595$	−0.897707	+	1.55487i	−0.0368024	+	0.0637436i
$596$	−6.04435	+	8.11898i	−0.247586	+	0.332566i
$597$	8.56261	−	31.3268i	0.350444	−	1.28212i
$598$	1.70314	+	5.68890i	0.0696467	+	0.232636i
$599$	15.8917	−	7.98110i	0.649316	−	0.326099i	−0.0934754	−	0.995622i	$-0.529798\pi$
$599$	15.8917	−	7.98110i	0.649316	−	0.326099i	0.742792	+	0.669523i	$0.233501\pi$
$600$	−6.81337	−	4.24987i	−0.278155	−	0.173500i
$601$	0.917694	−	3.06531i	0.0374335	−	0.125037i	−0.937231	−	0.348710i	$-0.886620\pi$
$601$	0.917694	−	3.06531i	0.0374335	−	0.125037i	0.974664	+	0.223674i	$0.0718049\pi$
$602$	0.234925	+	1.33232i	0.00957481	+	0.0543015i
$603$	19.9148	+	40.6656i	0.810995	+	1.65603i
$604$	1.76856	−	10.0300i	0.0719617	−	0.408115i
$605$	2.77883	+	1.39558i	0.112975	+	0.0567384i
$606$	12.7742	−	23.4095i	0.518917	−	0.950945i
$607$	11.8721	−	27.5225i	0.481872	−	1.11710i	−0.487858	−	0.872923i	$-0.662222\pi$
$607$	11.8721	−	27.5225i	0.481872	−	1.11710i	0.969730	−	0.244181i	$-0.0785191\pi$
$608$	0.699611	−	1.62188i	0.0283730	−	0.0657760i
$609$	−2.50962	+	4.59903i	−0.101695	+	0.186362i
$610$	−1.97554	−	0.992155i	−0.0799874	−	0.0401712i
$611$	1.24396	−	7.05485i	0.0503253	−	0.285409i
$612$	16.9960	+	1.16105i	0.687021	+	0.0469328i
$613$	3.35934	+	19.0517i	0.135682	+	0.769493i	0.974382	+	0.224899i	$0.0722052\pi$
$613$	3.35934	+	19.0517i	0.135682	+	0.769493i	−0.838700	+	0.544594i	$0.816684\pi$
$614$	−0.458142	+	1.53030i	−0.0184891	+	0.0617579i
$615$	−7.04091	−	4.39179i	−0.283917	−	0.177094i
$616$	1.13249	−	0.568758i	0.0456293	−	0.0229159i
$617$	−3.59062	−	11.9935i	−0.144553	−	0.482841i	0.854794	−	0.518967i	$-0.173683\pi$
$617$	−3.59062	−	11.9935i	−0.144553	−	0.482841i	−0.999347	+	0.0361265i	$0.988498\pi$
$618$	−0.189056	+	0.691671i	−0.00760493	+	0.0278231i
$619$	1.63583	−	2.19730i	0.0657495	−	0.0883169i	−0.768032	−	0.640411i	$-0.778764\pi$
$619$	1.63583	−	2.19730i	0.0657495	−	0.0883169i	0.833782	+	0.552095i	$0.186171\pi$
$620$	0.492480	−	0.853000i	0.0197785	−	0.0342573i
$621$	−23.0959	−	12.9054i	−0.926806	−	0.517875i
$622$	−13.8139	−	23.9263i	−0.553886	−	0.959359i
$623$	6.72902	+	0.786510i	0.269593	+	0.0315109i
$624$	0.165968	+	2.01326i	0.00664404	+	0.0805948i
$625$	19.1452	+	4.53749i	0.765807	+	0.181500i
$626$	−12.3621	−	8.13065i	−0.494087	−	0.324966i
$627$	−2.76513	+	6.85980i	−0.110429	+	0.273954i
$628$	16.6516	+	17.6496i	0.664469	+	0.704296i
$629$	−31.1311	+	26.1221i	−1.24128	+	1.04156i
$630$	0.874678	−	0.366938i	0.0348480	−	0.0146192i
$631$	−31.6227	−	26.5346i	−1.25888	−	1.05633i	−0.995800	−	0.0915516i	$-0.970817\pi$
$631$	−31.6227	−	26.5346i	−1.25888	−	1.05633i	−0.263080	−	0.964774i	$-0.584738\pi$
$632$	−0.950981	−	16.3277i	−0.0378280	−	0.649481i
$633$	26.1744	−	10.2468i	1.04034	−	0.407272i
$634$	−5.76399	−	7.74239i	−0.228917	−	0.307489i
$635$	−10.4525	+	1.22172i	−0.414793	+	0.0484823i
$636$	0.760127	+	3.77684i	0.0301410	+	0.149762i
$637$	6.55323	−	4.31013i	0.259648	−	0.170773i
$638$	13.1086	−	4.77113i	0.518974	−	0.188891i
$639$	−17.9929	+	2.98687i	−0.711787	+	0.118159i
$640$	0.566774	+	0.206289i	0.0224037	+	0.00815428i
$641$	−11.3383	+	2.68724i	−0.447838	+	0.106139i	−0.448345	−	0.893860i	$-0.647987\pi$
$641$	−11.3383	+	2.68724i	−0.447838	+	0.106139i	0.000507802		1.00000i	$0.499838\pi$
$642$	−1.32340	+	1.47216i	−0.0522304	+	0.0581015i
$643$	−0.425303	+	7.30216i	−0.0167723	+	0.287969i	0.979484	+	0.201522i	$0.0645886\pi$
$643$	−0.425303	+	7.30216i	−0.0167723	+	0.287969i	−0.996256	+	0.0864477i	$0.972448\pi$
$644$	1.83164	−	1.94142i	0.0721767	−	0.0765028i
$645$	1.55748	−	2.20074i	0.0613258	−	0.0866541i
$646$	−3.97276	−	9.20989i	−0.156306	−	0.362358i
$647$	−49.7900			−1.95745			−0.978723	−	0.205185i	$-0.934220\pi$
$647$	−49.7900			−1.95745			−0.978723	+	0.205185i	$0.934220\pi$
$648$	−6.77697	−	5.92221i	−0.266225	−	0.232647i
$649$	−13.4456			−0.527788
$650$	−2.14169	−	4.96499i	−0.0840038	−	0.194743i
$651$	−0.619880	−	1.34693i	−0.0242950	−	0.0527904i
$652$	4.45856	−	4.72580i	0.174611	−	0.185077i
$653$	−0.128004	+	2.19775i	−0.00500920	+	0.0860046i	−0.999886	−	0.0150886i	$-0.995197\pi$
$653$	−0.128004	+	2.19775i	−0.00500920	+	0.0860046i	0.994877	+	0.101093i	$0.0322340\pi$
$654$	−15.1293	−	3.20315i	−0.591604	−	0.125253i
$655$	−4.34398	+	1.02954i	−0.169733	+	0.0402275i
$656$	−7.46435	−	2.71680i	−0.291434	−	0.106073i
$657$	−29.9379	−	17.6874i	−1.16799	−	0.690051i
$658$	−3.02564	+	1.10124i	−0.117952	+	0.0429310i
$659$	−28.8035	+	18.9443i	−1.12202	+	0.737966i	−0.968211	−	0.250134i	$-0.919525\pi$
$659$	−28.8035	+	18.9443i	−1.12202	+	0.737966i	−0.153812	+	0.988100i	$0.549155\pi$
$660$	−2.39334	−	0.806408i	−0.0931605	−	0.0313894i
$661$	−35.4857	+	4.14768i	−1.38023	+	0.161326i	−0.773609	−	0.633663i	$-0.781551\pi$
$661$	−35.4857	+	4.14768i	−1.38023	+	0.161326i	−0.606624	+	0.794989i	$0.707477\pi$
$662$	−7.86956	−	10.5707i	−0.305859	−	0.410840i
$663$	8.96234	+	7.15983i	0.348068	+	0.278065i
$664$	−0.854307	−	14.6679i	−0.0331536	−	0.569225i
$665$	−0.427816	−	0.358980i	−0.0165900	−	0.0139207i
$666$	21.4448	−	1.03332i	0.830971	−	0.0400404i
$667$	22.5067	−	18.8853i	0.871462	−	0.731243i
$668$	−1.75375	−	1.85886i	−0.0678545	−	0.0719216i
$669$	−12.2915	−	15.7064i	−0.475218	−	0.607246i
$670$	7.60590	+	5.00248i	0.293842	+	0.193263i
$671$	8.62197	+	2.04344i	0.332847	+	0.0788863i
$672$	0.746358	−	0.517047i	0.0287914	−	0.0199455i
$673$	2.35360	+	0.275097i	0.0907247	+	0.0106042i	0.161334	−	0.986900i	$-0.448420\pi$
$673$	2.35360	+	0.275097i	0.0907247	+	0.0106042i	−0.0706094	+	0.997504i	$0.522494\pi$
$674$	−11.3118	−	19.5926i	−0.435715	−	0.754680i
$675$	22.2521	+	9.23016i	0.856483	+	0.355269i
$676$	5.81987	−	10.0803i	0.223841	−	0.387705i
$677$	2.08069	−	2.79485i	0.0799675	−	0.107415i	−0.760339	−	0.649526i	$-0.774967\pi$
$677$	2.08069	−	2.79485i	0.0799675	−	0.107415i	0.840307	+	0.542111i	$0.182375\pi$
$678$	20.5299	+	20.7368i	0.788444	+	0.796392i
$679$	0.615337	+	2.05537i	0.0236145	+	0.0788778i
$680$	3.06068	−	1.53713i	0.117372	−	0.0589464i
$681$	−0.212971	+	6.24237i	−0.00816106	+	0.239208i
$682$	−1.13227	+	3.78203i	−0.0433567	+	0.144822i
$683$	−5.63583	−	31.9624i	−0.215649	−	1.22301i	−0.879777	−	0.475387i	$-0.842308\pi$
$683$	−5.63583	−	31.9624i	−0.215649	−	1.22301i	0.664127	−	0.747619i	$-0.268803\pi$
$684$	−1.27369	+	5.14367i	−0.0487008	+	0.196673i
$685$	−0.120550	+	0.683675i	−0.00460599	+	0.0261219i
$686$	−6.42959	−	3.22906i	−0.245483	−	0.123286i
$687$	26.0619	+	42.7309i	0.994324	+	1.63029i
$688$	1.02220	−	2.36973i	0.0389710	−	0.0903450i
$689$	−1.02750	+	2.38202i	−0.0391447	+	0.0907476i
$690$	−5.31760	+	0.128040i	−0.202438	+	0.00487441i
$691$	4.97481	+	2.49844i	0.189251	+	0.0950453i	0.540901	−	0.841086i	$-0.318083\pi$
$691$	4.97481	+	2.49844i	0.189251	+	0.0950453i	−0.351651	+	0.936131i	$0.614380\pi$
$692$	−2.42182	+	13.7349i	−0.0920640	+	0.522121i
$693$	−3.07218	+	2.23961i	−0.116702	+	0.0850759i
$694$	−5.15161	−	29.2162i	−0.195552	−	1.10903i
$695$	0.965122	−	3.22373i	0.0366092	−	0.122283i
$696$	8.82084	−	4.69921i	0.334353	−	0.178123i
$697$	−40.3089	+	20.2439i	−1.52681	+	0.766792i
$698$	3.09446	+	10.3362i	0.117127	+	0.391232i
$699$	−9.29855	+	2.44163i	−0.351703	+	0.0923508i
$700$	−1.45130	+	1.94944i	−0.0548541	+	0.0736819i
$701$	15.5570	−	26.9455i	0.587580	−	1.01772i	−0.406969	−	0.913442i	$-0.633414\pi$
$701$	15.5570	−	26.9455i	0.587580	−	1.01772i	0.994548	−	0.104276i	$-0.0332524\pi$
$702$	−1.48027	−	5.87670i	−0.0558692	−	0.221802i
$703$	−6.32047	−	10.9474i	−0.238381	−	0.412888i
$704$	−2.40117	−	0.280657i	−0.0904976	−	0.0105777i
$705$	5.80183	+	2.74094i	0.218509	+	0.103230i
$706$	33.2220	+	7.87375i	1.25032	+	0.296332i
$707$	−6.74335	−	4.43517i	−0.253610	−	0.166802i
$708$	−9.53841	+	1.34835i	−0.358475	+	0.0506739i
$709$	21.7672	+	23.0719i	0.817485	+	0.866483i	0.993015	−	0.117991i	$-0.0376453\pi$
$709$	21.7672	+	23.0719i	0.817485	+	0.866483i	−0.175530	+	0.984474i	$0.556164\pi$
$710$	−2.80905	+	2.35708i	−0.105422	+	0.0884594i
$711$	10.8360	+	47.8546i	0.406382	+	1.79469i
$712$	−9.90028	−	8.30732i	−0.371029	−	0.311330i
$713$	0.483463	+	8.30074i	0.0181058	+	0.310865i
$714$	0.772823	−	5.09762i	0.0289222	−	0.190773i
$715$	−1.01553	−	1.36409i	−0.0379787	−	0.0510142i
$716$	7.18095	−	0.839332i	0.268365	−	0.0313673i
$717$	−13.0171	+	11.4678i	−0.486132	+	0.428271i
$718$	12.1118	−	7.96606i	0.452009	−	0.297291i
$719$	−9.36299	+	3.40785i	−0.349180	+	0.127091i	−0.510655	−	0.859786i	$-0.670597\pi$
$719$	−9.36299	+	3.40785i	−0.349180	+	0.127091i	0.161475	+	0.986877i	$0.448375\pi$
$720$	−1.77871	−	0.332063i	−0.0662887	−	0.0123753i
$721$	0.203928	+	0.0742235i	0.00759466	+	0.00276423i
$722$	−15.4520	+	3.66219i	−0.575064	+	0.136293i
$723$	−6.22035	−	19.0921i	−0.231337	−	0.710043i
$724$	0.343239	−	5.89318i	0.0127564	−	0.219018i
$725$	−18.3586	+	19.4590i	−0.681822	+	0.722689i
$726$	−8.89176	−	0.822882i	−0.330004	−	0.0305400i
$727$	8.21648	+	19.0479i	0.304732	+	0.706449i	0.999923	−	0.0123759i	$-0.00393949\pi$
$727$	8.21648	+	19.0479i	0.304732	+	0.706449i	−0.695191	+	0.718825i	$0.744680\pi$
$728$	0.611385			0.0226594
$729$	22.9660	+	14.1974i	0.850591	+	0.525828i
$730$	−6.99098			−0.258748
$731$	−5.80459	−	13.4566i	−0.214691	−	0.497709i
$732$	6.32139	+	0.585008i	0.233645	+	0.0216225i
$733$	16.5845	−	17.5786i	0.612563	−	0.649279i	−0.344627	−	0.938740i	$-0.611994\pi$
$733$	16.5845	−	17.5786i	0.612563	−	0.649279i	0.957190	+	0.289461i	$0.0934760\pi$
$734$	1.43770	−	24.6844i	0.0530666	−	0.911118i
$735$	2.17643	+	6.68010i	0.0802787	+	0.246399i
$736$	−4.95439	+	1.17421i	−0.182621	+	0.0432820i
$737$	−34.2880	−	12.4798i	−1.26302	−	0.459700i
$738$	23.4255	+	4.37324i	0.862303	+	0.160981i
$739$	−33.0042	+	12.0126i	−1.21408	+	0.441889i	−0.868117	−	0.496359i	$-0.834670\pi$
$739$	−33.0042	+	12.0126i	−1.21408	+	0.441889i	−0.345963	+	0.938248i	$0.612448\pi$
$740$	3.60636	−	2.37194i	0.132572	−	0.0871942i
$741$	−2.67737	+	2.35870i	−0.0983556	+	0.0866491i
$742$	1.15811	−	0.135363i	0.0425155	−	0.00496935i
$743$	23.7154	+	31.8553i	0.870034	+	1.16866i	0.984527	+	0.175234i	$0.0560682\pi$
$743$	23.7154	+	31.8553i	0.870034	+	1.16866i	−0.114493	+	0.993424i	$0.536524\pi$
$744$	−0.423969	+	2.79654i	−0.0155434	+	0.102526i
$745$	−0.354973	−	6.09465i	−0.0130052	−	0.223291i
$746$	−13.6886	−	11.4861i	−0.501176	−	0.420536i
$747$	9.73446	+	42.9899i	0.356165	+	1.57292i
$748$	−10.5162	+	8.82416i	−0.384511	+	0.322643i
$749$	0.411140	+	0.435783i	0.0150227	+	0.0159231i
$750$	9.96769	−	1.40903i	0.363968	−	0.0514504i
$751$	29.7283	+	19.5526i	1.08480	+	0.713484i	0.960365	−	0.278744i	$-0.0899181\pi$
$751$	29.7283	+	19.5526i	1.08480	+	0.713484i	0.124434	+	0.992228i	$0.460288\pi$
$752$	5.97668	+	1.41650i	0.217947	+	0.0516544i
$753$	43.5554	+	20.5768i	1.58725	+	0.749860i
$754$	6.68441	+	0.781295i	0.243432	+	0.0284531i
$755$	3.07145	+	5.31990i	0.111781	+	0.193611i
$756$	−1.95483	+	1.89688i	−0.0710964	+	0.0689887i
$757$	26.5049	−	45.9078i	0.963336	−	1.66855i	0.249314	−	0.968423i	$-0.419795\pi$
$757$	26.5049	−	45.9078i	0.963336	−	1.66855i	0.714022	−	0.700123i	$-0.246872\pi$
$758$	−6.52315	+	8.76211i	−0.236931	+	0.318254i
$759$	20.6210	−	5.41469i	0.748495	−	0.196541i
$760$	0.305550	+	1.02061i	0.0110835	+	0.0370213i
$761$	1.09219	−	0.548520i	0.0395920	−	0.0198838i	−0.428893	−	0.903355i	$-0.641096\pi$
$761$	1.09219	−	0.548520i	0.0395920	−	0.0198838i	0.468485	+	0.883471i	$0.344800\pi$
$762$	26.6717	−	14.2091i	0.966214	−	0.514741i
$763$	−1.34236	+	4.48381i	−0.0485968	+	0.162325i
$764$	0.238926	+	1.35502i	0.00864405	+	0.0490228i
$765$	−8.30292	+	6.05282i	−0.300193	+	0.218840i
$766$	−3.97050	+	22.5178i	−0.143460	+	0.813602i
$767$	−5.79669	−

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.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(0.396080 + 0.918216i) q^{2} +(1.72468 + 0.159609i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(0.0350699 - 0.602127i) q^{5} +(0.536555 + 1.64685i) q^{6} +(0.510080 - 0.120891i) q^{7} +(-0.939693 - 0.342020i) q^{8} +(2.94905 + 0.550550i) q^{9} +O(q^{10})\)	\(q+(0.396080 + 0.918216i) q^{2} +(1.72468 + 0.159609i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(0.0350699 - 0.602127i) q^{5} +(0.536555 + 1.64685i) q^{6} +(0.510080 - 0.120891i) q^{7} +(-0.939693 - 0.342020i) q^{8} +(2.94905 + 0.550550i) q^{9} +(0.566774 - 0.206289i) q^{10} +(-2.01981 + 1.32845i) q^{11} +(-1.29964 + 1.14496i) q^{12} +(-1.15841 + 0.135399i) q^{13} +(0.313036 + 0.420481i) q^{14} +(0.156590 - 1.03288i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(-4.35000 - 3.65009i) q^{17} +(0.662535 + 2.92593i) q^{18} +(1.35309 - 1.13538i) q^{19} +(0.413905 + 0.438714i) q^{20} +(0.899020 - 0.127085i) q^{21} +(-2.01981 - 1.32845i) q^{22} +(-4.95439 - 1.17421i) q^{23} +(-1.56608 - 0.739859i) q^{24} +(4.60486 + 0.538231i) q^{25} +(-0.583149 - 1.01004i) q^{26} +(4.99830 + 1.42022i) q^{27} +(-0.262105 + 0.453979i) q^{28} +(-3.44579 + 4.62851i) q^{29} +(1.01043 - 0.265320i) q^{30} +(-0.468359 - 1.56443i) q^{31} +(0.893633 - 0.448799i) q^{32} +(-3.69556 + 1.96877i) q^{33} +(1.62862 - 5.43997i) q^{34} +(-0.0549034 - 0.311373i) q^{35} +(-2.42422 + 1.76725i) q^{36} +(1.24273 - 7.04785i) q^{37} +(1.57846 + 0.792732i) q^{38} +(-2.01950 + 0.0486267i) q^{39} +(-0.238895 + 0.553820i) q^{40} +(3.14622 - 7.29375i) q^{41} +(0.472775 + 0.775159i) q^{42} +(2.30628 + 1.15826i) q^{43} +(0.419798 - 2.38079i) q^{44} +(0.434924 - 1.75640i) q^{45} +(-0.884154 - 5.01428i) q^{46} +(-1.76161 + 5.88420i) q^{47} +(0.0590580 - 1.73104i) q^{48} +(-6.00986 + 3.01827i) q^{49} +(1.32968 + 4.44144i) q^{50} +(-6.91978 - 6.98954i) q^{51} +(0.696465 - 0.935515i) q^{52} +(1.11214 - 1.92629i) q^{53} +(0.675656 + 5.15204i) q^{54} +(0.729061 + 1.26277i) q^{55} +(-0.520665 - 0.0608570i) q^{56} +(2.51487 - 1.74220i) q^{57} +(-5.61478 - 1.33073i) q^{58} +(4.64678 + 3.05623i) q^{59} +(0.643832 + 0.822704i) q^{60} +(-2.51525 - 2.66601i) q^{61} +(1.25098 - 1.04969i) q^{62} +(1.57081 - 0.0756894i) q^{63} +(0.766044 + 0.642788i) q^{64} +(0.0409020 + 0.702260i) q^{65} +(-3.27149 - 2.61353i) q^{66} +(9.01315 + 12.1068i) q^{67} +(5.64013 - 0.659237i) q^{68} +(-8.35733 - 2.81591i) q^{69} +(0.264161 - 0.173742i) q^{70} +(-5.71305 + 2.07938i) q^{71} +(-2.58290 - 1.52598i) q^{72} +(-10.8918 - 3.96429i) q^{73} +(6.96367 - 1.65042i) q^{74} +(7.85602 + 1.66326i) q^{75} +(-0.102703 + 1.76335i) q^{76} +(-0.869665 + 0.921792i) q^{77} +(-0.844534 - 1.83508i) q^{78} +(6.47803 + 15.0178i) q^{79} -0.603148 q^{80} +(8.39379 + 3.24720i) q^{81} +7.94339 q^{82} +(5.81950 + 13.4911i) q^{83} +(-0.524507 + 0.741135i) q^{84} +(-2.35037 + 2.49125i) q^{85} +(-0.150060 + 2.57643i) q^{86} +(-6.68165 + 7.43272i) q^{87} +(2.35235 - 0.557518i) q^{88} +(12.1445 + 4.42023i) q^{89} +(1.78502 - 0.296318i) q^{90} +(-0.574514 + 0.209106i) q^{91} +(4.25400 - 2.79790i) q^{92} +(-0.558073 - 2.77289i) q^{93} +(-6.10071 + 0.713071i) q^{94} +(-0.636191 - 0.854553i) q^{95} +(1.61286 - 0.631403i) q^{96} +(0.237977 + 4.08591i) q^{97} +(-5.15181 - 4.32288i) q^{98} +(-6.68789 + 2.80566i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

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